Properties

Label 43.6.c.a.6.15
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 6.15
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.15

$q$-expansion

\(f(q)\) \(=\) \(q+7.09985 q^{2} +(1.12246 - 1.94417i) q^{3} +18.4079 q^{4} +(51.2710 - 88.8039i) q^{5} +(7.96933 - 13.8033i) q^{6} +(-36.3371 - 62.9377i) q^{7} -96.5019 q^{8} +(118.980 + 206.080i) q^{9} +O(q^{10})\) \(q+7.09985 q^{2} +(1.12246 - 1.94417i) q^{3} +18.4079 q^{4} +(51.2710 - 88.8039i) q^{5} +(7.96933 - 13.8033i) q^{6} +(-36.3371 - 62.9377i) q^{7} -96.5019 q^{8} +(118.980 + 206.080i) q^{9} +(364.016 - 630.495i) q^{10} +469.005 q^{11} +(20.6622 - 35.7880i) q^{12} +(235.694 + 408.234i) q^{13} +(-257.988 - 446.849i) q^{14} +(-115.100 - 199.359i) q^{15} -1274.20 q^{16} +(-406.800 - 704.599i) q^{17} +(844.741 + 1463.13i) q^{18} +(-548.500 + 950.029i) q^{19} +(943.790 - 1634.69i) q^{20} -163.149 q^{21} +3329.86 q^{22} +(-1429.37 + 2475.75i) q^{23} +(-108.320 + 187.616i) q^{24} +(-3694.92 - 6399.79i) q^{25} +(1673.39 + 2898.40i) q^{26} +1079.72 q^{27} +(-668.890 - 1158.55i) q^{28} +(3905.30 + 6764.18i) q^{29} +(-817.191 - 1415.42i) q^{30} +(1206.95 - 2090.49i) q^{31} -5958.58 q^{32} +(526.441 - 911.823i) q^{33} +(-2888.22 - 5002.55i) q^{34} -7452.16 q^{35} +(2190.17 + 3793.49i) q^{36} +(-3725.79 + 6453.25i) q^{37} +(-3894.27 + 6745.07i) q^{38} +1058.23 q^{39} +(-4947.75 + 8569.75i) q^{40} +15259.8 q^{41} -1158.33 q^{42} +(-12106.0 - 673.174i) q^{43} +8633.39 q^{44} +24400.9 q^{45} +(-10148.3 + 17577.5i) q^{46} -15397.4 q^{47} +(-1430.25 + 2477.26i) q^{48} +(5762.73 - 9981.34i) q^{49} +(-26233.4 - 45437.6i) q^{50} -1826.48 q^{51} +(4338.63 + 7514.72i) q^{52} +(4749.35 - 8226.11i) q^{53} +7665.87 q^{54} +(24046.3 - 41649.5i) q^{55} +(3506.60 + 6073.62i) q^{56} +(1231.34 + 2132.75i) q^{57} +(27727.1 + 48024.7i) q^{58} +34820.0 q^{59} +(-2118.74 - 3669.77i) q^{60} +(-21484.1 - 37211.5i) q^{61} +(8569.13 - 14842.2i) q^{62} +(8646.79 - 14976.7i) q^{63} -1530.59 q^{64} +48337.0 q^{65} +(3737.66 - 6473.81i) q^{66} +(-19497.4 + 33770.5i) q^{67} +(-7488.34 - 12970.2i) q^{68} +(3208.85 + 5557.88i) q^{69} -52909.2 q^{70} +(-3446.29 - 5969.16i) q^{71} +(-11481.8 - 19887.1i) q^{72} +(10178.8 + 17630.2i) q^{73} +(-26452.5 + 45817.1i) q^{74} -16589.7 q^{75} +(-10096.7 + 17488.0i) q^{76} +(-17042.3 - 29518.1i) q^{77} +7513.29 q^{78} +(-10925.8 - 18924.0i) q^{79} +(-65329.6 + 113154. i) q^{80} +(-27700.2 + 47978.2i) q^{81} +108342. q^{82} +(6525.66 - 11302.8i) q^{83} -3003.22 q^{84} -83428.2 q^{85} +(-85950.8 - 4779.44i) q^{86} +17534.3 q^{87} -45259.9 q^{88} +(-16761.5 + 29031.8i) q^{89} +173243. q^{90} +(17128.9 - 29668.1i) q^{91} +(-26311.8 + 45573.3i) q^{92} +(-2709.51 - 4693.00i) q^{93} -109319. q^{94} +(56244.2 + 97417.8i) q^{95} +(-6688.30 + 11584.5i) q^{96} +66439.7 q^{97} +(40914.5 - 70866.0i) q^{98} +(55802.3 + 96652.3i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.09985 1.25509 0.627544 0.778581i \(-0.284060\pi\)
0.627544 + 0.778581i \(0.284060\pi\)
\(3\) 1.12246 1.94417i 0.0720062 0.124718i −0.827774 0.561061i \(-0.810393\pi\)
0.899780 + 0.436343i \(0.143727\pi\)
\(4\) 18.4079 0.575247
\(5\) 51.2710 88.8039i 0.917163 1.58857i 0.113459 0.993543i \(-0.463807\pi\)
0.803703 0.595030i \(-0.202860\pi\)
\(6\) 7.96933 13.8033i 0.0903741 0.156533i
\(7\) −36.3371 62.9377i −0.280289 0.485474i 0.691167 0.722695i \(-0.257097\pi\)
−0.971456 + 0.237221i \(0.923764\pi\)
\(8\) −96.5019 −0.533103
\(9\) 118.980 + 206.080i 0.489630 + 0.848064i
\(10\) 364.016 630.495i 1.15112 1.99380i
\(11\) 469.005 1.16868 0.584340 0.811509i \(-0.301354\pi\)
0.584340 + 0.811509i \(0.301354\pi\)
\(12\) 20.6622 35.7880i 0.0414213 0.0717438i
\(13\) 235.694 + 408.234i 0.386803 + 0.669963i 0.992018 0.126100i \(-0.0402460\pi\)
−0.605214 + 0.796062i \(0.706913\pi\)
\(14\) −257.988 446.849i −0.351787 0.609313i
\(15\) −115.100 199.359i −0.132083 0.228774i
\(16\) −1274.20 −1.24434
\(17\) −406.800 704.599i −0.341396 0.591316i 0.643296 0.765618i \(-0.277567\pi\)
−0.984692 + 0.174302i \(0.944233\pi\)
\(18\) 844.741 + 1463.13i 0.614529 + 1.06440i
\(19\) −548.500 + 950.029i −0.348572 + 0.603744i −0.985996 0.166769i \(-0.946667\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(20\) 943.790 1634.69i 0.527595 0.913821i
\(21\) −163.149 −0.0807300
\(22\) 3329.86 1.46680
\(23\) −1429.37 + 2475.75i −0.563412 + 0.975859i 0.433783 + 0.901017i \(0.357178\pi\)
−0.997195 + 0.0748415i \(0.976155\pi\)
\(24\) −108.320 + 187.616i −0.0383867 + 0.0664877i
\(25\) −3694.92 6399.79i −1.18238 2.04793i
\(26\) 1673.39 + 2898.40i 0.485472 + 0.840862i
\(27\) 1079.72 0.285038
\(28\) −668.890 1158.55i −0.161235 0.279267i
\(29\) 3905.30 + 6764.18i 0.862303 + 1.49355i 0.869701 + 0.493579i \(0.164312\pi\)
−0.00739834 + 0.999973i \(0.502355\pi\)
\(30\) −817.191 1415.42i −0.165776 0.287132i
\(31\) 1206.95 2090.49i 0.225571 0.390701i −0.730920 0.682464i \(-0.760909\pi\)
0.956491 + 0.291763i \(0.0942419\pi\)
\(32\) −5958.58 −1.02865
\(33\) 526.441 911.823i 0.0841521 0.145756i
\(34\) −2888.22 5002.55i −0.428483 0.742154i
\(35\) −7452.16 −1.02828
\(36\) 2190.17 + 3793.49i 0.281658 + 0.487846i
\(37\) −3725.79 + 6453.25i −0.447418 + 0.774951i −0.998217 0.0596871i \(-0.980990\pi\)
0.550799 + 0.834638i \(0.314323\pi\)
\(38\) −3894.27 + 6745.07i −0.437488 + 0.757752i
\(39\) 1058.23 0.111409
\(40\) −4947.75 + 8569.75i −0.488942 + 0.846873i
\(41\) 15259.8 1.41771 0.708856 0.705353i \(-0.249212\pi\)
0.708856 + 0.705353i \(0.249212\pi\)
\(42\) −1158.33 −0.101323
\(43\) −12106.0 673.174i −0.998458 0.0555209i
\(44\) 8633.39 0.672279
\(45\) 24400.9 1.79628
\(46\) −10148.3 + 17577.5i −0.707132 + 1.22479i
\(47\) −15397.4 −1.01672 −0.508361 0.861144i \(-0.669749\pi\)
−0.508361 + 0.861144i \(0.669749\pi\)
\(48\) −1430.25 + 2477.26i −0.0896000 + 0.155192i
\(49\) 5762.73 9981.34i 0.342877 0.593880i
\(50\) −26233.4 45437.6i −1.48399 2.57034i
\(51\) −1826.48 −0.0983306
\(52\) 4338.63 + 7514.72i 0.222507 + 0.385394i
\(53\) 4749.35 8226.11i 0.232244 0.402258i −0.726224 0.687458i \(-0.758727\pi\)
0.958468 + 0.285200i \(0.0920599\pi\)
\(54\) 7665.87 0.357748
\(55\) 24046.3 41649.5i 1.07187 1.85653i
\(56\) 3506.60 + 6073.62i 0.149423 + 0.258808i
\(57\) 1231.34 + 2132.75i 0.0501986 + 0.0869466i
\(58\) 27727.1 + 48024.7i 1.08227 + 1.87454i
\(59\) 34820.0 1.30226 0.651131 0.758965i \(-0.274295\pi\)
0.651131 + 0.758965i \(0.274295\pi\)
\(60\) −2118.74 3669.77i −0.0759802 0.131601i
\(61\) −21484.1 37211.5i −0.739252 1.28042i −0.952833 0.303496i \(-0.901846\pi\)
0.213581 0.976925i \(-0.431487\pi\)
\(62\) 8569.13 14842.2i 0.283112 0.490364i
\(63\) 8646.79 14976.7i 0.274476 0.475406i
\(64\) −1530.59 −0.0467099
\(65\) 48337.0 1.41905
\(66\) 3737.66 6473.81i 0.105618 0.182936i
\(67\) −19497.4 + 33770.5i −0.530628 + 0.919075i 0.468733 + 0.883340i \(0.344711\pi\)
−0.999361 + 0.0357350i \(0.988623\pi\)
\(68\) −7488.34 12970.2i −0.196387 0.340152i
\(69\) 3208.85 + 5557.88i 0.0811383 + 0.140536i
\(70\) −52909.2 −1.29058
\(71\) −3446.29 5969.16i −0.0811347 0.140529i 0.822603 0.568616i \(-0.192521\pi\)
−0.903738 + 0.428087i \(0.859188\pi\)
\(72\) −11481.8 19887.1i −0.261023 0.452106i
\(73\) 10178.8 + 17630.2i 0.223557 + 0.387212i 0.955886 0.293739i \(-0.0948998\pi\)
−0.732329 + 0.680952i \(0.761566\pi\)
\(74\) −26452.5 + 45817.1i −0.561549 + 0.972632i
\(75\) −16589.7 −0.340553
\(76\) −10096.7 + 17488.0i −0.200515 + 0.347302i
\(77\) −17042.3 29518.1i −0.327568 0.567364i
\(78\) 7513.29 0.139828
\(79\) −10925.8 18924.0i −0.196963 0.341150i 0.750579 0.660781i \(-0.229775\pi\)
−0.947542 + 0.319630i \(0.896441\pi\)
\(80\) −65329.6 + 113154.i −1.14126 + 1.97672i
\(81\) −27700.2 + 47978.2i −0.469106 + 0.812515i
\(82\) 108342. 1.77935
\(83\) 6525.66 11302.8i 0.103975 0.180090i −0.809344 0.587335i \(-0.800177\pi\)
0.913319 + 0.407245i \(0.133510\pi\)
\(84\) −3003.22 −0.0464397
\(85\) −83428.2 −1.25246
\(86\) −85950.8 4779.44i −1.25315 0.0696836i
\(87\) 17534.3 0.248364
\(88\) −45259.9 −0.623027
\(89\) −16761.5 + 29031.8i −0.224304 + 0.388507i −0.956111 0.293006i \(-0.905344\pi\)
0.731806 + 0.681513i \(0.238678\pi\)
\(90\) 173243. 2.25449
\(91\) 17128.9 29668.1i 0.216833 0.375566i
\(92\) −26311.8 + 45573.3i −0.324101 + 0.561360i
\(93\) −2709.51 4693.00i −0.0324850 0.0562657i
\(94\) −109319. −1.27608
\(95\) 56244.2 + 97417.8i 0.639394 + 1.10746i
\(96\) −6688.30 + 11584.5i −0.0740692 + 0.128292i
\(97\) 66439.7 0.716966 0.358483 0.933536i \(-0.383294\pi\)
0.358483 + 0.933536i \(0.383294\pi\)
\(98\) 40914.5 70866.0i 0.430340 0.745371i
\(99\) 55802.3 + 96652.3i 0.572221 + 0.991116i
\(100\) −68015.8 117807.i −0.680158 1.17807i
\(101\) −52560.3 91037.2i −0.512690 0.888005i −0.999892 0.0147155i \(-0.995316\pi\)
0.487202 0.873289i \(-0.338018\pi\)
\(102\) −12967.7 −0.123414
\(103\) −6641.19 11502.9i −0.0616812 0.106835i 0.833536 0.552465i \(-0.186313\pi\)
−0.895217 + 0.445630i \(0.852980\pi\)
\(104\) −22744.9 39395.4i −0.206206 0.357159i
\(105\) −8364.79 + 14488.2i −0.0740426 + 0.128246i
\(106\) 33719.7 58404.2i 0.291487 0.504870i
\(107\) −109313. −0.923021 −0.461511 0.887135i \(-0.652692\pi\)
−0.461511 + 0.887135i \(0.652692\pi\)
\(108\) 19875.4 0.163967
\(109\) 98417.2 170464.i 0.793423 1.37425i −0.130413 0.991460i \(-0.541630\pi\)
0.923836 0.382789i \(-0.125036\pi\)
\(110\) 170725. 295705.i 1.34529 2.33011i
\(111\) 8364.13 + 14487.1i 0.0644337 + 0.111602i
\(112\) 46300.8 + 80195.4i 0.348774 + 0.604094i
\(113\) −31713.2 −0.233638 −0.116819 0.993153i \(-0.537270\pi\)
−0.116819 + 0.993153i \(0.537270\pi\)
\(114\) 8742.35 + 15142.2i 0.0630037 + 0.109126i
\(115\) 146571. + 253868.i 1.03348 + 1.79004i
\(116\) 71888.4 + 124514.i 0.496037 + 0.859161i
\(117\) −56085.8 + 97143.4i −0.378781 + 0.656068i
\(118\) 247217. 1.63445
\(119\) −29563.9 + 51206.2i −0.191379 + 0.331478i
\(120\) 11107.3 + 19238.5i 0.0704137 + 0.121960i
\(121\) 58914.4 0.365812
\(122\) −152534. 264196.i −0.927826 1.60704i
\(123\) 17128.5 29667.5i 0.102084 0.176815i
\(124\) 22217.3 38481.5i 0.129759 0.224749i
\(125\) −437326. −2.50340
\(126\) 61390.9 106332.i 0.344491 0.596676i
\(127\) −256824. −1.41295 −0.706475 0.707738i \(-0.749716\pi\)
−0.706475 + 0.707738i \(0.749716\pi\)
\(128\) 179808. 0.970026
\(129\) −14897.3 + 22780.5i −0.0788196 + 0.120528i
\(130\) 343186. 1.78103
\(131\) −362959. −1.84790 −0.923952 0.382508i \(-0.875060\pi\)
−0.923952 + 0.382508i \(0.875060\pi\)
\(132\) 9690.68 16784.7i 0.0484082 0.0838455i
\(133\) 79723.6 0.390803
\(134\) −138429. + 239766.i −0.665985 + 1.15352i
\(135\) 55358.4 95883.5i 0.261426 0.452803i
\(136\) 39257.0 + 67995.2i 0.181999 + 0.315232i
\(137\) −211981. −0.964930 −0.482465 0.875915i \(-0.660259\pi\)
−0.482465 + 0.875915i \(0.660259\pi\)
\(138\) 22782.3 + 39460.1i 0.101836 + 0.176385i
\(139\) −66055.8 + 114412.i −0.289984 + 0.502267i −0.973806 0.227382i \(-0.926983\pi\)
0.683822 + 0.729649i \(0.260317\pi\)
\(140\) −137179. −0.591515
\(141\) −17283.0 + 29935.1i −0.0732103 + 0.126804i
\(142\) −24468.2 42380.1i −0.101831 0.176377i
\(143\) 110542. + 191464.i 0.452049 + 0.782972i
\(144\) −151605. 262587.i −0.609265 1.05528i
\(145\) 800914. 3.16349
\(146\) 72267.8 + 125171.i 0.280584 + 0.485985i
\(147\) −12936.9 22407.4i −0.0493784 0.0855260i
\(148\) −68583.9 + 118791.i −0.257376 + 0.445788i
\(149\) 99030.8 171526.i 0.365430 0.632944i −0.623415 0.781891i \(-0.714255\pi\)
0.988845 + 0.148948i \(0.0475886\pi\)
\(150\) −117784. −0.427424
\(151\) −62947.5 −0.224666 −0.112333 0.993671i \(-0.535832\pi\)
−0.112333 + 0.993671i \(0.535832\pi\)
\(152\) 52931.3 91679.7i 0.185825 0.321858i
\(153\) 96802.3 167667.i 0.334316 0.579052i
\(154\) −120998. 209574.i −0.411126 0.712092i
\(155\) −123762. 214363.i −0.413771 0.716672i
\(156\) 19479.8 0.0640875
\(157\) 78891.4 + 136644.i 0.255435 + 0.442427i 0.965014 0.262200i \(-0.0844479\pi\)
−0.709578 + 0.704626i \(0.751115\pi\)
\(158\) −77571.5 134358.i −0.247206 0.428174i
\(159\) −10662.0 18467.0i −0.0334460 0.0579302i
\(160\) −305502. + 529145.i −0.943441 + 1.63409i
\(161\) 207757. 0.631672
\(162\) −196667. + 340638.i −0.588769 + 1.01978i
\(163\) 235774. + 408372.i 0.695067 + 1.20389i 0.970158 + 0.242473i \(0.0779586\pi\)
−0.275091 + 0.961418i \(0.588708\pi\)
\(164\) 280900. 0.815534
\(165\) −53982.3 93500.1i −0.154362 0.267364i
\(166\) 46331.2 80248.0i 0.130498 0.226029i
\(167\) 44307.0 76742.0i 0.122937 0.212933i −0.797988 0.602674i \(-0.794102\pi\)
0.920925 + 0.389741i \(0.127435\pi\)
\(168\) 15744.2 0.0430374
\(169\) 74543.3 129113.i 0.200767 0.347738i
\(170\) −592328. −1.57195
\(171\) −261042. −0.682685
\(172\) −222846. 12391.7i −0.574359 0.0319382i
\(173\) −165529. −0.420494 −0.210247 0.977648i \(-0.567427\pi\)
−0.210247 + 0.977648i \(0.567427\pi\)
\(174\) 124491. 0.311719
\(175\) −268526. + 465100.i −0.662813 + 1.14803i
\(176\) −597607. −1.45423
\(177\) 39084.2 67695.8i 0.0937709 0.162416i
\(178\) −119004. + 206121.i −0.281522 + 0.487610i
\(179\) −135306. 234357.i −0.315635 0.546696i 0.663937 0.747788i \(-0.268884\pi\)
−0.979572 + 0.201093i \(0.935551\pi\)
\(180\) 449169. 1.03331
\(181\) −50328.3 87171.1i −0.114187 0.197777i 0.803268 0.595618i \(-0.203093\pi\)
−0.917454 + 0.397841i \(0.869760\pi\)
\(182\) 121612. 210639.i 0.272145 0.471368i
\(183\) −96460.5 −0.212923
\(184\) 137937. 238915.i 0.300357 0.520233i
\(185\) 382049. + 661729.i 0.820710 + 1.42151i
\(186\) −19237.1 33319.6i −0.0407716 0.0706184i
\(187\) −190791. 330460.i −0.398983 0.691059i
\(188\) −283434. −0.584866
\(189\) −39234.0 67955.3i −0.0798929 0.138379i
\(190\) 399325. + 691652.i 0.802496 + 1.38996i
\(191\) 343847. 595561.i 0.681997 1.18125i −0.292374 0.956304i \(-0.594445\pi\)
0.974371 0.224949i \(-0.0722216\pi\)
\(192\) −1718.03 + 2975.72i −0.00336340 + 0.00582558i
\(193\) 808019. 1.56145 0.780726 0.624874i \(-0.214850\pi\)
0.780726 + 0.624874i \(0.214850\pi\)
\(194\) 471712. 0.899856
\(195\) 54256.6 93975.2i 0.102180 0.176981i
\(196\) 106080. 183735.i 0.197239 0.341627i
\(197\) 98710.8 + 170972.i 0.181217 + 0.313877i 0.942295 0.334783i \(-0.108663\pi\)
−0.761078 + 0.648660i \(0.775330\pi\)
\(198\) 396188. + 686217.i 0.718188 + 1.24394i
\(199\) −1.03882e6 −1.85956 −0.929779 0.368118i \(-0.880002\pi\)
−0.929779 + 0.368118i \(0.880002\pi\)
\(200\) 356567. + 617593.i 0.630328 + 1.09176i
\(201\) 43770.3 + 75812.5i 0.0764170 + 0.132358i
\(202\) −373171. 646350.i −0.643471 1.11452i
\(203\) 283815. 491582.i 0.483387 0.837251i
\(204\) −33621.6 −0.0565643
\(205\) 782383. 1.35513e6i 1.30027 2.25214i
\(206\) −47151.4 81668.7i −0.0774153 0.134087i
\(207\) −680269. −1.10345
\(208\) −300322. 520172.i −0.481314 0.833660i
\(209\) −257249. + 445568.i −0.407369 + 0.705584i
\(210\) −59388.7 + 102864.i −0.0929300 + 0.160959i
\(211\) 263842. 0.407979 0.203989 0.978973i \(-0.434609\pi\)
0.203989 + 0.978973i \(0.434609\pi\)
\(212\) 87425.5 151425.i 0.133598 0.231398i
\(213\) −15473.4 −0.0233688
\(214\) −776105. −1.15847
\(215\) −680467. + 1.04055e6i −1.00395 + 1.53520i
\(216\) −104195. −0.151955
\(217\) −175428. −0.252900
\(218\) 698747. 1.21027e6i 0.995816 1.72480i
\(219\) 45701.3 0.0643899
\(220\) 442642. 766679.i 0.616589 1.06796i
\(221\) 191761. 332139.i 0.264106 0.457446i
\(222\) 59384.1 + 102856.i 0.0808700 + 0.140071i
\(223\) 1.42378e6 1.91726 0.958632 0.284647i \(-0.0918765\pi\)
0.958632 + 0.284647i \(0.0918765\pi\)
\(224\) 216518. + 375020.i 0.288319 + 0.499383i
\(225\) 879245. 1.52290e6i 1.15785 2.00546i
\(226\) −225159. −0.293236
\(227\) 4771.88 8265.15i 0.00614646 0.0106460i −0.862936 0.505314i \(-0.831377\pi\)
0.869082 + 0.494668i \(0.164710\pi\)
\(228\) 22666.4 + 39259.4i 0.0288766 + 0.0500157i
\(229\) −93985.2 162787.i −0.118432 0.205131i 0.800714 0.599047i \(-0.204454\pi\)
−0.919147 + 0.393916i \(0.871120\pi\)
\(230\) 1.04063e6 + 1.80243e6i 1.29711 + 2.24666i
\(231\) −76517.5 −0.0943476
\(232\) −376869. 652757.i −0.459696 0.796217i
\(233\) −90013.3 155908.i −0.108622 0.188138i 0.806590 0.591111i \(-0.201310\pi\)
−0.915212 + 0.402972i \(0.867977\pi\)
\(234\) −398201. + 689704.i −0.475404 + 0.823423i
\(235\) −789439. + 1.36735e6i −0.932500 + 1.61514i
\(236\) 640962. 0.749122
\(237\) −49055.2 −0.0567302
\(238\) −209899. + 363556.i −0.240198 + 0.416034i
\(239\) −216029. + 374174.i −0.244635 + 0.423720i −0.962029 0.272948i \(-0.912001\pi\)
0.717394 + 0.696667i \(0.245335\pi\)
\(240\) 146660. + 254023.i 0.164356 + 0.284672i
\(241\) −178192. 308638.i −0.197627 0.342299i 0.750132 0.661288i \(-0.229990\pi\)
−0.947758 + 0.318989i \(0.896657\pi\)
\(242\) 418284. 0.459127
\(243\) 193371. + 334929.i 0.210076 + 0.363862i
\(244\) −395477. 684986.i −0.425252 0.736558i
\(245\) −590921. 1.02351e6i −0.628947 1.08937i
\(246\) 121610. 210635.i 0.128124 0.221918i
\(247\) −517112. −0.539315
\(248\) −116473. + 201736.i −0.120253 + 0.208284i
\(249\) −14649.6 25373.9i −0.0149737 0.0259352i
\(250\) −3.10495e6 −3.14199
\(251\) 931723. + 1.61379e6i 0.933475 + 1.61683i 0.777331 + 0.629092i \(0.216573\pi\)
0.156144 + 0.987734i \(0.450094\pi\)
\(252\) 159169. 275689.i 0.157891 0.273475i
\(253\) −670383. + 1.16114e6i −0.658449 + 1.14047i
\(254\) −1.82341e6 −1.77338
\(255\) −93645.2 + 162198.i −0.0901852 + 0.156205i
\(256\) 1.32559e6 1.26418
\(257\) −57458.9 −0.0542656 −0.0271328 0.999632i \(-0.508638\pi\)
−0.0271328 + 0.999632i \(0.508638\pi\)
\(258\) −105769. + 161738.i −0.0989255 + 0.151273i
\(259\) 541537. 0.501625
\(260\) 889782. 0.816301
\(261\) −929307. + 1.60961e6i −0.844419 + 1.46258i
\(262\) −2.57696e6 −2.31928
\(263\) 48494.0 83994.0i 0.0432313 0.0748788i −0.843600 0.536972i \(-0.819568\pi\)
0.886831 + 0.462093i \(0.152901\pi\)
\(264\) −50802.6 + 87992.7i −0.0448618 + 0.0777028i
\(265\) −487007. 843522.i −0.426011 0.737873i
\(266\) 566026. 0.490492
\(267\) 37628.4 + 65174.3i 0.0323026 + 0.0559497i
\(268\) −358906. + 621644.i −0.305242 + 0.528695i
\(269\) 1.60163e6 1.34953 0.674763 0.738034i \(-0.264246\pi\)
0.674763 + 0.738034i \(0.264246\pi\)
\(270\) 393036. 680759.i 0.328113 0.568308i
\(271\) 1.16906e6 + 2.02488e6i 0.966974 + 1.67485i 0.704216 + 0.709986i \(0.251299\pi\)
0.262758 + 0.964862i \(0.415368\pi\)
\(272\) 518346. + 897801.i 0.424812 + 0.735797i
\(273\) −38453.1 66602.8i −0.0312266 0.0540861i
\(274\) −1.50504e6 −1.21107
\(275\) −1.73294e6 3.00153e6i −1.38182 2.39338i
\(276\) 59068.1 + 102309.i 0.0466745 + 0.0808427i
\(277\) −354921. + 614742.i −0.277928 + 0.481386i −0.970870 0.239608i \(-0.922981\pi\)
0.692942 + 0.720994i \(0.256314\pi\)
\(278\) −468987. + 812309.i −0.363956 + 0.630390i
\(279\) 574410. 0.441786
\(280\) 719148. 0.548180
\(281\) 873468. 1.51289e6i 0.659905 1.14299i −0.320735 0.947169i \(-0.603930\pi\)
0.980640 0.195820i \(-0.0627367\pi\)
\(282\) −122707. + 212535.i −0.0918854 + 0.159150i
\(283\) 281492. + 487559.i 0.208930 + 0.361877i 0.951378 0.308027i \(-0.0996687\pi\)
−0.742448 + 0.669904i \(0.766335\pi\)
\(284\) −63439.0 109880.i −0.0466724 0.0808390i
\(285\) 252529. 0.184161
\(286\) 784829. + 1.35936e6i 0.567361 + 0.982699i
\(287\) −554496. 960415.i −0.397369 0.688263i
\(288\) −708953. 1.22794e6i −0.503659 0.872362i
\(289\) 378956. 656370.i 0.266897 0.462279i
\(290\) 5.68637e6 3.97046
\(291\) 74576.3 129170.i 0.0516260 0.0894188i
\(292\) 187370. + 324534.i 0.128600 + 0.222742i
\(293\) −233768. −0.159080 −0.0795401 0.996832i \(-0.525345\pi\)
−0.0795401 + 0.996832i \(0.525345\pi\)
\(294\) −91850.2 159089.i −0.0619743 0.107343i
\(295\) 1.78525e6 3.09215e6i 1.19439 2.06874i
\(296\) 359546. 622751.i 0.238520 0.413129i
\(297\) 506395. 0.333118
\(298\) 703104. 1.21781e6i 0.458647 0.794400i
\(299\) −1.34758e6 −0.871719
\(300\) −305381. −0.195902
\(301\) 397529. + 786386.i 0.252902 + 0.500287i
\(302\) −446918. −0.281975
\(303\) −235989. −0.147667
\(304\) 698899. 1.21053e6i 0.433741 0.751262i
\(305\) −4.40604e6 −2.71206
\(306\) 687282. 1.19041e6i 0.419596 0.726762i
\(307\) −916125. + 1.58678e6i −0.554765 + 0.960881i 0.443157 + 0.896444i \(0.353858\pi\)
−0.997922 + 0.0644368i \(0.979475\pi\)
\(308\) −313713. 543366.i −0.188432 0.326374i
\(309\) −29818.0 −0.0177657
\(310\) −878695. 1.52195e6i −0.519319 0.899487i
\(311\) 573155. 992734.i 0.336025 0.582012i −0.647656 0.761933i \(-0.724251\pi\)
0.983681 + 0.179920i \(0.0575840\pi\)
\(312\) −102121. −0.0593924
\(313\) −1.06140e6 + 1.83840e6i −0.612378 + 1.06067i 0.378461 + 0.925617i \(0.376453\pi\)
−0.990839 + 0.135052i \(0.956880\pi\)
\(314\) 560117. + 970152.i 0.320594 + 0.555284i
\(315\) −886659. 1.53574e6i −0.503478 0.872049i
\(316\) −201121. 348351.i −0.113302 0.196245i
\(317\) 1.91895e6 1.07255 0.536273 0.844045i \(-0.319832\pi\)
0.536273 + 0.844045i \(0.319832\pi\)
\(318\) −75698.3 131113.i −0.0419777 0.0727075i
\(319\) 1.83161e6 + 3.17243e6i 1.00776 + 1.74548i
\(320\) −78474.8 + 135922.i −0.0428406 + 0.0742021i
\(321\) −122700. + 212522.i −0.0664632 + 0.115118i
\(322\) 1.47505e6 0.792805
\(323\) 892519. 0.476005
\(324\) −509903. + 883177.i −0.269851 + 0.467397i
\(325\) 1.74174e6 3.01678e6i 0.914693 1.58429i
\(326\) 1.67396e6 + 2.89938e6i 0.872370 + 1.51099i
\(327\) −220940. 382679.i −0.114263 0.197909i
\(328\) −1.47260e6 −0.755787
\(329\) 559497. + 969077.i 0.284976 + 0.493593i
\(330\) −383266. 663837.i −0.193738 0.335565i
\(331\) 148596. + 257376.i 0.0745482 + 0.129121i 0.900890 0.434048i \(-0.142915\pi\)
−0.826342 + 0.563169i \(0.809582\pi\)
\(332\) 120124. 208060.i 0.0598113 0.103596i
\(333\) −1.77318e6 −0.876278
\(334\) 314573. 544857.i 0.154296 0.267249i
\(335\) 1.99930e6 + 3.46290e6i 0.973345 + 1.68588i
\(336\) 207884. 0.100455
\(337\) −1.00193e6 1.73539e6i −0.480575 0.832380i 0.519177 0.854667i \(-0.326239\pi\)
−0.999752 + 0.0222869i \(0.992905\pi\)
\(338\) 529246. 916682.i 0.251980 0.436442i
\(339\) −35596.9 + 61655.7i −0.0168234 + 0.0291389i
\(340\) −1.53574e6 −0.720476
\(341\) 566063. 980450.i 0.263620 0.456604i
\(342\) −1.85336e6 −0.856830
\(343\) −2.05904e6 −0.944995
\(344\) 1.16825e6 + 64962.6i 0.532281 + 0.0295984i
\(345\) 658082. 0.297668
\(346\) −1.17523e6 −0.527757
\(347\) −1.17777e6 + 2.03996e6i −0.525095 + 0.909491i 0.474478 + 0.880267i \(0.342637\pi\)
−0.999573 + 0.0292238i \(0.990696\pi\)
\(348\) 322769. 0.142871
\(349\) 780096. 1.35117e6i 0.342835 0.593807i −0.642123 0.766601i \(-0.721946\pi\)
0.984958 + 0.172794i \(0.0552796\pi\)
\(350\) −1.90649e6 + 3.30214e6i −0.831889 + 1.44087i
\(351\) 254484. + 440779.i 0.110254 + 0.190965i
\(352\) −2.79460e6 −1.20216
\(353\) 925396. + 1.60283e6i 0.395267 + 0.684623i 0.993135 0.116972i \(-0.0373187\pi\)
−0.597868 + 0.801595i \(0.703985\pi\)
\(354\) 277492. 480630.i 0.117691 0.203846i
\(355\) −706779. −0.297655
\(356\) −308544. + 534414.i −0.129030 + 0.223487i
\(357\) 66368.9 + 114954.i 0.0275609 + 0.0477370i
\(358\) −960653. 1.66390e6i −0.396150 0.686151i
\(359\) −2.07679e6 3.59711e6i −0.850467 1.47305i −0.880788 0.473511i \(-0.842986\pi\)
0.0303214 0.999540i \(-0.490347\pi\)
\(360\) −2.35473e6 −0.957604
\(361\) 636346. + 1.10218e6i 0.256995 + 0.445129i
\(362\) −357323. 618902.i −0.143314 0.248228i
\(363\) 66129.4 114539.i 0.0263407 0.0456235i
\(364\) 315306. 546127.i 0.124732 0.216043i
\(365\) 2.08750e6 0.820153
\(366\) −684855. −0.267237
\(367\) −27048.3 + 46849.1i −0.0104828 + 0.0181567i −0.871219 0.490894i \(-0.836670\pi\)
0.860736 + 0.509051i \(0.170003\pi\)
\(368\) 1.82131e6 3.15460e6i 0.701075 1.21430i
\(369\) 1.81561e6 + 3.14473e6i 0.694155 + 1.20231i
\(370\) 2.71249e6 + 4.69817e6i 1.03006 + 1.78412i
\(371\) −690311. −0.260381
\(372\) −49876.3 86388.3i −0.0186869 0.0323666i
\(373\) 322797. + 559102.i 0.120132 + 0.208074i 0.919820 0.392342i \(-0.128335\pi\)
−0.799688 + 0.600416i \(0.795002\pi\)
\(374\) −1.35459e6 2.34622e6i −0.500759 0.867340i
\(375\) −490883. + 850234.i −0.180260 + 0.312220i
\(376\) 1.48588e6 0.542018
\(377\) −1.84091e6 + 3.18855e6i −0.667083 + 1.15542i
\(378\) −278556. 482472.i −0.100273 0.173677i
\(379\) 660396. 0.236160 0.118080 0.993004i \(-0.462326\pi\)
0.118080 + 0.993004i \(0.462326\pi\)
\(380\) 1.03534e6 + 1.79326e6i 0.367809 + 0.637065i
\(381\) −288276. + 499309.i −0.101741 + 0.176221i
\(382\) 2.44127e6 4.22840e6i 0.855966 1.48258i
\(383\) −5.53899e6 −1.92945 −0.964726 0.263258i \(-0.915203\pi\)
−0.964726 + 0.263258i \(0.915203\pi\)
\(384\) 201828. 349576.i 0.0698478 0.120980i
\(385\) −3.49510e6 −1.20173
\(386\) 5.73682e6 1.95976
\(387\) −1.30165e6 2.57490e6i −0.441790 0.873941i
\(388\) 1.22302e6 0.412432
\(389\) 728262. 0.244014 0.122007 0.992529i \(-0.461067\pi\)
0.122007 + 0.992529i \(0.461067\pi\)
\(390\) 385214. 667210.i 0.128245 0.222127i
\(391\) 2.32588e6 0.769388
\(392\) −556114. + 963218.i −0.182789 + 0.316599i
\(393\) −407409. + 705653.i −0.133060 + 0.230467i
\(394\) 700832. + 1.21388e6i 0.227443 + 0.393943i
\(395\) −2.24070e6 −0.722589
\(396\) 1.02720e6 + 1.77917e6i 0.329168 + 0.570136i
\(397\) 2.91495e6 5.04884e6i 0.928228 1.60774i 0.141942 0.989875i \(-0.454666\pi\)
0.786286 0.617862i \(-0.212001\pi\)
\(398\) −7.37550e6 −2.33391
\(399\) 89486.9 154996.i 0.0281402 0.0487403i
\(400\) 4.70808e6 + 8.15463e6i 1.47127 + 2.54832i
\(401\) −633165. 1.09667e6i −0.196633 0.340578i 0.750802 0.660528i \(-0.229667\pi\)
−0.947435 + 0.319950i \(0.896334\pi\)
\(402\) 310763. + 538257.i 0.0959101 + 0.166121i
\(403\) 1.13788e6 0.349006
\(404\) −967525. 1.67580e6i −0.294923 0.510822i
\(405\) 2.84043e6 + 4.91978e6i 0.860493 + 1.49042i
\(406\) 2.01504e6 3.49016e6i 0.606694 1.05082i
\(407\) −1.74741e6 + 3.02660e6i −0.522888 + 0.905669i
\(408\) 176259. 0.0524203
\(409\) −4.39882e6 −1.30025 −0.650127 0.759825i \(-0.725284\pi\)
−0.650127 + 0.759825i \(0.725284\pi\)
\(410\) 5.55480e6 9.62120e6i 1.63196 2.82663i
\(411\) −237942. + 412127.i −0.0694809 + 0.120345i
\(412\) −122250. 211744.i −0.0354819 0.0614564i
\(413\) −1.26526e6 2.19149e6i −0.365009 0.632215i
\(414\) −4.82981e6 −1.38493
\(415\) −669154. 1.15901e6i −0.190724 0.330344i
\(416\) −1.40440e6 2.43249e6i −0.397885 0.689158i
\(417\) 148291. + 256847.i 0.0417613 + 0.0723327i
\(418\) −1.82643e6 + 3.16347e6i −0.511284 + 0.885570i
\(419\) 2.64432e6 0.735832 0.367916 0.929859i \(-0.380071\pi\)
0.367916 + 0.929859i \(0.380071\pi\)
\(420\) −153978. + 266698.i −0.0425927 + 0.0737728i
\(421\) −98604.7 170788.i −0.0271139 0.0469627i 0.852150 0.523298i \(-0.175298\pi\)
−0.879264 + 0.476335i \(0.841965\pi\)
\(422\) 1.87324e6 0.512049
\(423\) −1.83198e6 3.17309e6i −0.497818 0.862246i
\(424\) −458321. + 793836.i −0.123810 + 0.214445i
\(425\) −3.00619e6 + 5.20688e6i −0.807317 + 1.39831i
\(426\) −109859. −0.0293299
\(427\) −1.56134e6 + 2.70432e6i −0.414408 + 0.717775i
\(428\) −2.01222e6 −0.530965
\(429\) 496316. 0.130201
\(430\) −4.83121e6 + 7.38772e6i −1.26004 + 1.92681i
\(431\) 6.39918e6 1.65932 0.829662 0.558266i \(-0.188533\pi\)
0.829662 + 0.558266i \(0.188533\pi\)
\(432\) −1.37578e6 −0.354683
\(433\) 2.79489e6 4.84089e6i 0.716382 1.24081i −0.246042 0.969259i \(-0.579130\pi\)
0.962424 0.271551i \(-0.0875365\pi\)
\(434\) −1.24551e6 −0.317412
\(435\) 898998. 1.55711e6i 0.227791 0.394545i
\(436\) 1.81165e6 3.13787e6i 0.456414 0.790532i
\(437\) −1.56802e6 2.71589e6i −0.392779 0.680314i
\(438\) 324472. 0.0808151
\(439\) −425440. 736884.i −0.105360 0.182489i 0.808525 0.588462i \(-0.200266\pi\)
−0.913885 + 0.405972i \(0.866933\pi\)
\(440\) −2.32052e6 + 4.01925e6i −0.571417 + 0.989723i
\(441\) 2.74260e6 0.671531
\(442\) 1.36147e6 2.35814e6i 0.331477 0.574135i
\(443\) −586661. 1.01613e6i −0.142029 0.246002i 0.786231 0.617932i \(-0.212029\pi\)
−0.928261 + 0.371930i \(0.878696\pi\)
\(444\) 153966. + 266677.i 0.0370653 + 0.0641989i
\(445\) 1.71876e6 + 2.97697e6i 0.411447 + 0.712648i
\(446\) 1.01087e7 2.40634
\(447\) −222317. 385065.i −0.0526264 0.0911517i
\(448\) 55617.2 + 96331.9i 0.0130923 + 0.0226765i
\(449\) −2.65705e6 + 4.60215e6i −0.621991 + 1.07732i 0.367124 + 0.930172i \(0.380343\pi\)
−0.989115 + 0.147148i \(0.952991\pi\)
\(450\) 6.24251e6 1.08123e7i 1.45321 2.51703i
\(451\) 7.15690e6 1.65685
\(452\) −583773. −0.134400
\(453\) −70656.4 + 122381.i −0.0161773 + 0.0280199i
\(454\) 33879.7 58681.3i 0.00771435 0.0133617i
\(455\) −1.75643e6 3.04222e6i −0.397742 0.688910i
\(456\) −118827. 205814.i −0.0267610 0.0463515i
\(457\) 854616. 0.191417 0.0957085 0.995409i \(-0.469488\pi\)
0.0957085 + 0.995409i \(0.469488\pi\)
\(458\) −667281. 1.15576e6i −0.148643 0.257457i
\(459\) −439231. 760771.i −0.0973109 0.168547i
\(460\) 2.69806e6 + 4.67318e6i 0.594507 + 1.02972i
\(461\) −3.47571e6 + 6.02011e6i −0.761713 + 1.31933i 0.180253 + 0.983620i \(0.442308\pi\)
−0.941967 + 0.335706i \(0.891025\pi\)
\(462\) −543263. −0.118415
\(463\) 104993. 181854.i 0.0227619 0.0394248i −0.854420 0.519583i \(-0.826087\pi\)
0.877182 + 0.480158i \(0.159421\pi\)
\(464\) −4.97614e6 8.61893e6i −1.07300 1.85848i
\(465\) −555676. −0.119176
\(466\) −639081. 1.10692e6i −0.136330 0.236130i
\(467\) 3.11367e6 5.39303e6i 0.660664 1.14430i −0.319778 0.947493i \(-0.603608\pi\)
0.980442 0.196810i \(-0.0630584\pi\)
\(468\) −1.03242e6 + 1.78821e6i −0.217892 + 0.377401i
\(469\) 2.83392e6 0.594916
\(470\) −5.60490e6 + 9.70797e6i −1.17037 + 2.02714i
\(471\) 354211. 0.0735716
\(472\) −3.36020e6 −0.694240
\(473\) −5.67777e6 315722.i −1.16688 0.0648861i
\(474\) −348285. −0.0712015
\(475\) 8.10666e6 1.64857
\(476\) −544209. + 942598.i −0.110090 + 0.190682i
\(477\) 2.26031e6 0.454855
\(478\) −1.53378e6 + 2.65658e6i −0.307038 + 0.531805i
\(479\) 2.98723e6 5.17404e6i 0.594881 1.03036i −0.398683 0.917089i \(-0.630532\pi\)
0.993564 0.113275i \(-0.0361342\pi\)
\(480\) 685831. + 1.18789e6i 0.135867 + 0.235329i
\(481\) −3.51258e6 −0.692251
\(482\) −1.26514e6 2.19128e6i −0.248039 0.429616i
\(483\) 233200. 403915.i 0.0454843 0.0787811i
\(484\) 1.08449e6 0.210432
\(485\) 3.40643e6 5.90011e6i 0.657575 1.13895i
\(486\) 1.37291e6 + 2.37795e6i 0.263664 + 0.456679i
\(487\) −2.50193e6 4.33347e6i −0.478028 0.827968i 0.521655 0.853156i \(-0.325315\pi\)
−0.999683 + 0.0251883i \(0.991981\pi\)
\(488\) 2.07326e6 + 3.59098e6i 0.394097 + 0.682596i
\(489\) 1.05859e6 0.200196
\(490\) −4.19545e6 7.26674e6i −0.789384 1.36725i
\(491\) −3.48873e6 6.04266e6i −0.653077 1.13116i −0.982372 0.186935i \(-0.940145\pi\)
0.329296 0.944227i \(-0.393189\pi\)
\(492\) 315300. 546116.i 0.0587235 0.101712i
\(493\) 3.17736e6 5.50334e6i 0.588774 1.01979i
\(494\) −3.67142e6 −0.676887
\(495\) 1.14441e7 2.09928
\(496\) −1.53789e6 + 2.66371e6i −0.280687 + 0.486163i
\(497\) −250457. + 433804.i −0.0454822 + 0.0787776i
\(498\) −104010. 180151.i −0.0187933 0.0325509i
\(499\) 4.31579e6 + 7.47517e6i 0.775905 + 1.34391i 0.934284 + 0.356529i \(0.116040\pi\)
−0.158379 + 0.987378i \(0.550627\pi\)
\(500\) −8.05024e6 −1.44007
\(501\) −99466.2 172280.i −0.0177044 0.0306649i
\(502\) 6.61510e6 + 1.14577e7i 1.17159 + 2.02926i
\(503\) 2.69830e6 + 4.67358e6i 0.475521 + 0.823626i 0.999607 0.0280392i \(-0.00892632\pi\)
−0.524086 + 0.851665i \(0.675593\pi\)
\(504\) −834432. + 1.44528e6i −0.146324 + 0.253440i
\(505\) −1.07793e7 −1.88088
\(506\) −4.75962e6 + 8.24391e6i −0.826411 + 1.43139i
\(507\) −167344. 289849.i −0.0289129 0.0500786i
\(508\) −4.72759e6 −0.812795
\(509\) 2.43181e6 + 4.21201e6i 0.416039 + 0.720601i 0.995537 0.0943727i \(-0.0300845\pi\)
−0.579498 + 0.814974i \(0.696751\pi\)
\(510\) −664867. + 1.15158e6i −0.113190 + 0.196051i
\(511\) 739735. 1.28126e6i 0.125321 0.217062i
\(512\) 3.65762e6 0.616629
\(513\) −592227. + 1.02577e6i −0.0993562 + 0.172090i
\(514\) −407949. −0.0681081
\(515\) −1.36200e6 −0.226287
\(516\) −274228. + 419340.i −0.0453407 + 0.0693334i
\(517\) −7.22145e6 −1.18822
\(518\) 3.84483e6 0.629583
\(519\) −185801. + 321817.i −0.0302782 + 0.0524433i
\(520\) −4.66462e6 −0.756497
\(521\) 441789. 765201.i 0.0713051 0.123504i −0.828168 0.560479i \(-0.810617\pi\)
0.899474 + 0.436975i \(0.143950\pi\)
\(522\) −6.59794e6 + 1.14280e7i −1.05982 + 1.83566i
\(523\) −3.15804e6 5.46989e6i −0.504852 0.874429i −0.999984 0.00561121i \(-0.998214\pi\)
0.495133 0.868817i \(-0.335119\pi\)
\(524\) −6.68131e6 −1.06300
\(525\) 602822. + 1.04412e6i 0.0954532 + 0.165330i
\(526\) 344300. 596345.i 0.0542591 0.0939795i
\(527\) −1.96394e6 −0.308037
\(528\) −670793. + 1.16185e6i −0.104714 + 0.181369i
\(529\) −868051. 1.50351e6i −0.134867 0.233597i
\(530\) −3.45768e6 5.98888e6i −0.534681 0.926096i
\(531\) 4.14289e6 + 7.17569e6i 0.637627 + 1.10440i
\(532\) 1.46754e6 0.224808
\(533\) 3.59663e6 + 6.22955e6i 0.548375 + 0.949814i
\(534\) 267156. + 462728.i 0.0405426 + 0.0702219i
\(535\) −5.60457e6 + 9.70740e6i −0.846561 + 1.46629i
\(536\) 1.88154e6 3.25892e6i 0.282879 0.489962i
\(537\) −607506. −0.0909106
\(538\) 1.13713e7 1.69378
\(539\) 2.70275e6 4.68129e6i 0.400713 0.694055i
\(540\) 1.01903e6 1.76501e6i 0.150385 0.260474i
\(541\) 899421. + 1.55784e6i 0.132120 + 0.228839i 0.924494 0.381197i \(-0.124488\pi\)
−0.792373 + 0.610036i \(0.791155\pi\)
\(542\) 8.30017e6 + 1.43763e7i 1.21364 + 2.10208i
\(543\) −225967. −0.0328886
\(544\) 2.42395e6 + 4.19841e6i 0.351178 + 0.608258i
\(545\) −1.00919e7 1.74797e7i −1.45540 2.52082i
\(546\) −273011. 472870.i −0.0391922 0.0678828i
\(547\) −3.55444e6 + 6.15647e6i −0.507929 + 0.879759i 0.492029 + 0.870579i \(0.336255\pi\)
−0.999958 + 0.00918000i \(0.997078\pi\)
\(548\) −3.90213e6 −0.555073
\(549\) 5.11236e6 8.85486e6i 0.723920 1.25387i
\(550\) −1.23036e7 2.13104e7i −1.73430 3.00390i
\(551\) −8.56823e6 −1.20230
\(552\) −309660. 536347.i −0.0432551 0.0749200i
\(553\) −794023. + 1.37529e6i −0.110413 + 0.191241i
\(554\) −2.51989e6 + 4.36457e6i −0.348824 + 0.604182i
\(555\) 1.71535e6 0.236385
\(556\) −1.21595e6 + 2.10608e6i −0.166812 + 0.288927i
\(557\) −5.20103e6 −0.710316 −0.355158 0.934806i \(-0.615573\pi\)
−0.355158 + 0.934806i \(0.615573\pi\)
\(558\) 4.07823e6 0.554480
\(559\) −2.57850e6 5.10074e6i −0.349009 0.690405i
\(560\) 9.49555e6 1.27953
\(561\) −856626. −0.114917
\(562\) 6.20149e6 1.07413e7i 0.828239 1.43455i
\(563\) 8.05054e6 1.07042 0.535210 0.844719i \(-0.320233\pi\)
0.535210 + 0.844719i \(0.320233\pi\)
\(564\) −318144. + 551042.i −0.0421140 + 0.0729436i
\(565\) −1.62597e6 + 2.81625e6i −0.214284 + 0.371151i
\(566\) 1.99855e6 + 3.46159e6i 0.262225 + 0.454187i
\(567\) 4.02619e6 0.525940
\(568\) 332574. + 576035.i 0.0432531 + 0.0749166i
\(569\) −5.07759e6 + 8.79465e6i −0.657472 + 1.13877i 0.323796 + 0.946127i \(0.395041\pi\)
−0.981268 + 0.192648i \(0.938292\pi\)
\(570\) 1.79292e6 0.231139
\(571\) 1.81629e6 3.14591e6i 0.233128 0.403790i −0.725599 0.688118i \(-0.758437\pi\)
0.958727 + 0.284328i \(0.0917705\pi\)
\(572\) 2.03484e6 + 3.52444e6i 0.260040 + 0.450402i
\(573\) −771913. 1.33699e6i −0.0982159 0.170115i
\(574\) −3.93684e6 6.81880e6i −0.498733 0.863831i
\(575\) 2.11257e7 2.66466
\(576\) −182110. 315423.i −0.0228706 0.0396130i
\(577\) 222608. + 385568.i 0.0278356 + 0.0482127i 0.879608 0.475700i \(-0.157805\pi\)
−0.851772 + 0.523913i \(0.824472\pi\)
\(578\) 2.69053e6 4.66013e6i 0.334979 0.580201i
\(579\) 906973. 1.57092e6i 0.112434 0.194742i
\(580\) 1.47431e7 1.81979
\(581\) −948495. −0.116572
\(582\) 529480. 917087.i 0.0647952 0.112228i
\(583\) 2.22747e6 3.85809e6i 0.271419 0.470111i
\(584\) −982272. 1.70134e6i −0.119179 0.206424i
\(585\) 5.75114e6 + 9.96127e6i 0.694808 + 1.20344i
\(586\) −1.65972e6 −0.199660
\(587\) −6.90848e6 1.19658e7i −0.827536 1.43334i −0.899965 0.435962i \(-0.856408\pi\)
0.0724289 0.997374i \(-0.476925\pi\)
\(588\) −238141. 412473.i −0.0284048 0.0491985i
\(589\) 1.32402e6 + 2.29327e6i 0.157255 + 0.272374i
\(590\) 1.26750e7 2.19538e7i 1.49906 2.59645i
\(591\) 443198. 0.0521950
\(592\) 4.74740e6 8.22274e6i 0.556739 0.964301i
\(593\) 6.22169e6 + 1.07763e7i 0.726560 + 1.25844i 0.958329 + 0.285668i \(0.0922153\pi\)
−0.231769 + 0.972771i \(0.574451\pi\)
\(594\) 3.59533e6 0.418093
\(595\) 3.03154e6 + 5.25078e6i 0.351052 + 0.608039i
\(596\) 1.82295e6 3.15744e6i 0.210212 0.364099i
\(597\) −1.16604e6 + 2.01965e6i −0.133900 + 0.231921i
\(598\) −9.56761e6 −1.09408
\(599\) −3.80462e6 + 6.58979e6i −0.433256 + 0.750421i −0.997151 0.0754253i \(-0.975969\pi\)
0.563896 + 0.825846i \(0.309302\pi\)
\(600\) 1.60094e6 0.181550
\(601\) 3.77890e6 0.426756 0.213378 0.976970i \(-0.431553\pi\)
0.213378 + 0.976970i \(0.431553\pi\)
\(602\) 2.82240e6 + 5.58322e6i 0.317415 + 0.627905i
\(603\) −9.27923e6 −1.03925
\(604\) −1.15873e6 −0.129238
\(605\) 3.02060e6 5.23183e6i 0.335509 0.581119i
\(606\) −1.67548e6 −0.185336
\(607\) 5.35895e6 9.28197e6i 0.590348 1.02251i −0.403838 0.914831i \(-0.632324\pi\)
0.994185 0.107681i \(-0.0343426\pi\)
\(608\) 3.26828e6 5.66083e6i 0.358559 0.621042i
\(609\) −637145. 1.10357e6i −0.0696137 0.120574i
\(610\) −3.12822e7 −3.40387
\(611\) −3.62907e6 6.28574e6i −0.393271 0.681166i
\(612\) 1.78193e6 3.08639e6i 0.192314 0.333098i
\(613\) −5.49329e6 −0.590448 −0.295224 0.955428i \(-0.595394\pi\)
−0.295224 + 0.955428i \(0.595394\pi\)
\(614\) −6.50435e6 + 1.12659e7i −0.696279 + 1.20599i
\(615\) −1.75639e6 3.04216e6i −0.187255 0.324336i
\(616\) 1.64461e6 + 2.84855e6i 0.174627 + 0.302463i
\(617\) 1.11045e6 + 1.92336e6i 0.117432 + 0.203398i 0.918749 0.394841i \(-0.129200\pi\)
−0.801317 + 0.598240i \(0.795867\pi\)
\(618\) −211703. −0.0222975
\(619\) −1.16731e6 2.02184e6i −0.122450 0.212090i 0.798283 0.602283i \(-0.205742\pi\)
−0.920733 + 0.390192i \(0.872409\pi\)
\(620\) −2.27821e6 3.94597e6i −0.238020 0.412263i
\(621\) −1.54333e6 + 2.67312e6i −0.160594 + 0.278157i
\(622\) 4.06932e6 7.04827e6i 0.421741 0.730477i
\(623\) 2.43626e6 0.251480
\(624\) −1.34840e6 −0.138630
\(625\) −1.08755e7 + 1.88369e7i −1.11365 + 1.92889i
\(626\) −7.53580e6 + 1.30524e7i −0.768588 + 1.33123i
\(627\) 577506. + 1.00027e6i 0.0586661 + 0.101613i
\(628\) 1.45222e6 + 2.51533e6i 0.146938 + 0.254504i
\(629\) 6.06260e6 0.610988
\(630\) −6.29515e6 1.09035e7i −0.631909 1.09450i
\(631\) −6.54495e6 1.13362e7i −0.654384 1.13343i −0.982048 0.188632i \(-0.939595\pi\)
0.327663 0.944795i \(-0.393739\pi\)
\(632\) 1.05436e6 + 1.82620e6i 0.105002 + 0.181868i
\(633\) 296153. 512953.i 0.0293770 0.0508824i
\(634\) 1.36243e7 1.34614
\(635\) −1.31676e7 + 2.28070e7i −1.29591 + 2.24457i
\(636\) −196264. 339939.i −0.0192397 0.0333241i
\(637\) 5.43296e6 0.530503
\(638\) 1.30041e7 + 2.25238e7i 1.26482 + 2.19074i
\(639\) 820081. 1.42042e6i 0.0794520 0.137615i
\(640\) 9.21891e6 1.59676e7i 0.889672 1.54096i
\(641\) −8.80594e6 −0.846507 −0.423253 0.906011i \(-0.639112\pi\)
−0.423253 + 0.906011i \(0.639112\pi\)
\(642\) −871150. + 1.50888e6i −0.0834172 + 0.144483i
\(643\) 1.22225e7 1.16582 0.582911 0.812536i \(-0.301914\pi\)
0.582911 + 0.812536i \(0.301914\pi\)
\(644\) 3.82438e6 0.363367
\(645\) 1.25919e6 + 2.49092e6i 0.119177 + 0.235755i
\(646\) 6.33675e6 0.597428
\(647\) −7.85754e6 −0.737948 −0.368974 0.929440i \(-0.620291\pi\)
−0.368974 + 0.929440i \(0.620291\pi\)
\(648\) 2.67313e6 4.62999e6i 0.250082 0.433154i
\(649\) 1.63307e7 1.52193
\(650\) 1.23661e7 2.14187e7i 1.14802 1.98843i
\(651\) −196911. + 341061.i −0.0182104 + 0.0315413i
\(652\) 4.34010e6 + 7.51727e6i 0.399835 + 0.692534i
\(653\) −1.64362e7 −1.50840 −0.754201 0.656643i \(-0.771976\pi\)
−0.754201 + 0.656643i \(0.771976\pi\)
\(654\) −1.56864e6 2.71696e6i −0.143410 0.248393i
\(655\) −1.86093e7 + 3.22322e7i −1.69483 + 2.93553i
\(656\) −1.94440e7 −1.76411
\(657\) −2.42214e6 + 4.19528e6i −0.218921 + 0.379182i
\(658\) 3.97235e6 + 6.88031e6i 0.357670 + 0.619502i
\(659\) 4.41034e6 + 7.63893e6i 0.395602 + 0.685203i 0.993178 0.116610i \(-0.0372026\pi\)
−0.597576 + 0.801812i \(0.703869\pi\)
\(660\) −993701. 1.72114e6i −0.0887965 0.153800i
\(661\) −1.02490e7 −0.912386 −0.456193 0.889881i \(-0.650787\pi\)
−0.456193 + 0.889881i \(0.650787\pi\)
\(662\) 1.05501e6 + 1.82733e6i 0.0935646 + 0.162059i
\(663\) −430489. 745629.i −0.0380346 0.0658778i
\(664\) −629739. + 1.09074e6i −0.0554294 + 0.0960065i
\(665\) 4.08751e6 7.07977e6i 0.358430 0.620819i
\(666\) −1.25893e7 −1.09981
\(667\) −2.23286e7 −1.94333
\(668\) 815599. 1.41266e6i 0.0707189 0.122489i
\(669\) 1.59815e6 2.76807e6i 0.138055 0.239118i
\(670\) 1.41948e7 + 2.45860e7i 1.22163 + 2.11593i
\(671\) −1.00761e7 1.74524e7i −0.863948 1.49640i
\(672\) 972135. 0.0830430
\(673\) 1.03583e7 + 1.79412e7i 0.881561 + 1.52691i 0.849606 + 0.527418i \(0.176840\pi\)
0.0319548 + 0.999489i \(0.489827\pi\)
\(674\) −7.11353e6 1.23210e7i −0.603164 1.04471i
\(675\) −3.98949e6 6.91000e6i −0.337022 0.583739i
\(676\) 1.37219e6 2.37669e6i 0.115490 0.200035i
\(677\) −2.97495e6 −0.249464 −0.124732 0.992190i \(-0.539807\pi\)
−0.124732 + 0.992190i \(0.539807\pi\)
\(678\) −252733. + 437746.i −0.0211148 + 0.0365720i
\(679\) −2.41423e6 4.18157e6i −0.200957 0.348068i
\(680\) 8.05098e6 0.667693
\(681\) −10712.5 18554.7i −0.000885166 0.00153315i
\(682\) 4.01896e6 6.96105e6i 0.330867 0.573078i
\(683\) 6.32339e6 1.09524e7i 0.518678 0.898377i −0.481086 0.876673i \(-0.659758\pi\)
0.999764 0.0217036i \(-0.00690902\pi\)
\(684\) −4.80524e6 −0.392712
\(685\) −1.08685e7 + 1.88248e7i −0.884998 + 1.53286i
\(686\) −1.46189e7 −1.18605
\(687\) −421980. −0.0341115
\(688\) 1.54255e7 + 857760.i 1.24242 + 0.0690868i
\(689\) 4.47757e6 0.359331
\(690\) 4.67229e6 0.373600
\(691\) 3.83813e6 6.64784e6i 0.305791 0.529646i −0.671646 0.740872i \(-0.734412\pi\)
0.977437 + 0.211226i \(0.0677457\pi\)
\(692\) −3.04705e6 −0.241888
\(693\) 4.05539e6 7.02414e6i 0.320774 0.555597i
\(694\) −8.36201e6 + 1.44834e7i −0.659041 + 1.14149i
\(695\) 6.77349e6 + 1.17320e7i 0.531925 + 0.921322i
\(696\) −1.69209e6 −0.132404
\(697\) −6.20768e6 1.07520e7i −0.484002 0.838316i
\(698\) 5.53857e6 9.59308e6i 0.430288 0.745280i
\(699\) −404147. −0.0312858
\(700\) −4.94299e6 + 8.56152e6i −0.381281 + 0.660398i
\(701\) −8.11120e6 1.40490e7i −0.623434 1.07982i −0.988842 0.148971i \(-0.952404\pi\)
0.365408 0.930847i \(-0.380929\pi\)
\(702\) 1.80680e6 + 3.12947e6i 0.138378 + 0.239678i
\(703\) −4.08718e6 7.07921e6i −0.311915 0.540252i
\(704\) −717854. −0.0545889
\(705\) 1.77224e6 + 3.06960e6i 0.134292 + 0.232600i
\(706\) 6.57017e6 + 1.13799e7i 0.496095 + 0.859262i
\(707\) −3.81978e6 + 6.61606e6i −0.287402 + 0.497795i
\(708\) 719458. 1.24614e6i 0.0539414 0.0934292i
\(709\) 1.91218e7 1.42861 0.714303 0.699837i \(-0.246744\pi\)
0.714303 + 0.699837i \(0.246744\pi\)
\(710\) −5.01803e6 −0.373583
\(711\) 2.59990e6 4.50316e6i 0.192878 0.334075i
\(712\) 1.61752e6 2.80162e6i 0.119577 0.207114i
\(713\) 3.45035e6 + 5.97619e6i 0.254179 + 0.440251i
\(714\) 471209. + 816158.i 0.0345914 + 0.0599141i
\(715\) 2.26703e7 1.65841
\(716\) −2.49070e6 4.31402e6i −0.181568 0.314485i
\(717\) 484971. + 839994.i 0.0352304 + 0.0610208i
\(718\) −1.47449e7 2.55390e7i −1.06741 1.84881i
\(719\) 484440. 839074.i 0.0349476 0.0605310i −0.848023 0.529960i \(-0.822207\pi\)
0.882970 + 0.469429i \(0.155540\pi\)
\(720\) −3.10917e7 −2.23518
\(721\) −482643. + 835963.i −0.0345771 + 0.0598892i
\(722\) 4.51796e6 + 7.82534e6i 0.322552 + 0.558676i
\(723\) −800057. −0.0569213
\(724\) −926437. 1.60464e6i −0.0656855 0.113771i
\(725\) 2.88596e7 4.99863e7i 2.03913 3.53188i
\(726\) 469509. 813213.i 0.0330600 0.0572615i
\(727\) 1.36847e7 0.960281 0.480140 0.877192i \(-0.340586\pi\)
0.480140 + 0.877192i \(0.340586\pi\)
\(728\) −1.65297e6 + 2.86303e6i −0.115594 + 0.200215i
\(729\) −1.25941e7 −0.877704
\(730\) 1.48210e7 1.02936
\(731\) 4.45041e6 + 8.80372e6i 0.308039 + 0.609358i
\(732\) −1.77563e6 −0.122483
\(733\) 1.17482e7 0.807629 0.403815 0.914841i \(-0.367684\pi\)
0.403815 + 0.914841i \(0.367684\pi\)
\(734\) −192039. + 332622.i −0.0131568 + 0.0227882i
\(735\) −2.65315e6 −0.181152
\(736\) 8.51705e6 1.47520e7i 0.579555 1.00382i
\(737\) −9.14438e6 + 1.58385e7i −0.620134 + 1.07410i
\(738\) 1.28906e7 + 2.23271e7i 0.871226 + 1.50901i
\(739\) 6.94058e6 0.467503 0.233751 0.972296i \(-0.424900\pi\)
0.233751 + 0.972296i \(0.424900\pi\)
\(740\) 7.03272e6 + 1.21810e7i 0.472111 + 0.817720i
\(741\) −580440. + 1.00535e6i −0.0388340 + 0.0672624i
\(742\) −4.90110e6 −0.326802
\(743\) −3.30653e6 + 5.72709e6i −0.219736 + 0.380594i −0.954727 0.297483i \(-0.903853\pi\)
0.734991 + 0.678077i \(0.237186\pi\)
\(744\) 261473. + 452884.i 0.0173179 + 0.0299954i
\(745\) −1.01548e7 1.75886e7i −0.670318 1.16102i
\(746\) 2.29181e6 + 3.96954e6i 0.150776 + 0.261152i
\(747\) 3.10570e6 0.203637
\(748\) −3.51206e6 6.08307e6i −0.229514 0.397529i
\(749\) 3.97211e6 + 6.87990e6i 0.258712 + 0.448103i
\(750\) −3.48519e6 + 6.03653e6i −0.226242 + 0.391863i
\(751\) 9.57156e6 1.65784e7i 0.619274 1.07261i −0.370345 0.928894i \(-0.620760\pi\)
0.989618 0.143719i \(-0.0459063\pi\)
\(752\) 1.96194e7 1.26515
\(753\) 4.18331e6 0.268864
\(754\) −1.30702e7 + 2.26382e7i −0.837247 + 1.45016i
\(755\) −3.22738e6 + 5.58999e6i −0.206055 + 0.356898i
\(756\) −722215. 1.25091e6i −0.0459581 0.0796018i
\(757\) −1.95749e6 3.39047e6i −0.124154 0.215040i 0.797248 0.603652i \(-0.206288\pi\)
−0.921402 + 0.388611i \(0.872955\pi\)
\(758\) 4.68872e6 0.296402
\(759\) 1.50496e6 + 2.60667e6i 0.0948247 + 0.164241i
\(760\) −5.42768e6 9.40101e6i −0.340863 0.590392i
\(761\) 7.99500e6 + 1.38477e7i 0.500446 + 0.866797i 1.00000 0.000514627i \(0.000163811\pi\)
−0.499554 + 0.866283i \(0.666503\pi\)
\(762\) −2.04672e6 + 3.54502e6i −0.127694 + 0.221173i
\(763\) −1.43048e7 −0.889549
\(764\) 6.32951e6 1.09630e7i 0.392316 0.679512i
\(765\) −9.92630e6 1.71928e7i −0.613244 1.06217i
\(766\) −3.93260e7 −2.42163
\(767\) 8.20686e6 + 1.42147e7i 0.503719 + 0.872467i
\(768\) 1.48792e6 2.57716e6i 0.0910286 0.157666i
\(769\) 7.22983e6 1.25224e7i 0.440872 0.763612i −0.556883 0.830591i \(-0.688003\pi\)
0.997754 + 0.0669789i \(0.0213360\pi\)
\(770\) −2.48147e7 −1.50828
\(771\) −64495.6 + 111710.i −0.00390745 + 0.00676791i
\(772\) 1.48739e7 0.898220