Properties

Label 43.6.c.a.6.6
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 6.6
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.6

$q$-expansion

\(f(q)\) \(=\) \(q-4.45148 q^{2} +(9.81167 - 16.9943i) q^{3} -12.1844 q^{4} +(-39.8809 + 69.0757i) q^{5} +(-43.6764 + 75.6497i) q^{6} +(8.78791 + 15.2211i) q^{7} +196.686 q^{8} +(-71.0376 - 123.041i) q^{9} +O(q^{10})\) \(q-4.45148 q^{2} +(9.81167 - 16.9943i) q^{3} -12.1844 q^{4} +(-39.8809 + 69.0757i) q^{5} +(-43.6764 + 75.6497i) q^{6} +(8.78791 + 15.2211i) q^{7} +196.686 q^{8} +(-71.0376 - 123.041i) q^{9} +(177.529 - 307.489i) q^{10} +296.199 q^{11} +(-119.549 + 207.065i) q^{12} +(198.091 + 343.104i) q^{13} +(-39.1192 - 67.7564i) q^{14} +(782.595 + 1355.50i) q^{15} -485.641 q^{16} +(676.236 + 1171.28i) q^{17} +(316.222 + 547.713i) q^{18} +(-680.888 + 1179.33i) q^{19} +(485.923 - 841.644i) q^{20} +344.896 q^{21} -1318.52 q^{22} +(-570.380 + 987.927i) q^{23} +(1929.81 - 3342.54i) q^{24} +(-1618.47 - 2803.27i) q^{25} +(-881.799 - 1527.32i) q^{26} +1980.48 q^{27} +(-107.075 - 185.460i) q^{28} +(-1198.69 - 2076.18i) q^{29} +(-3483.70 - 6033.95i) q^{30} +(-2838.29 + 4916.07i) q^{31} -4132.12 q^{32} +(2906.21 - 5033.70i) q^{33} +(-3010.25 - 5213.90i) q^{34} -1401.88 q^{35} +(865.548 + 1499.17i) q^{36} +(-3038.57 + 5262.96i) q^{37} +(3030.95 - 5249.77i) q^{38} +7774.43 q^{39} +(-7843.99 + 13586.2i) q^{40} +10487.5 q^{41} -1535.30 q^{42} +(865.356 + 12093.8i) q^{43} -3609.00 q^{44} +11332.2 q^{45} +(2539.03 - 4397.73i) q^{46} -26809.0 q^{47} +(-4764.95 + 8253.14i) q^{48} +(8249.05 - 14287.8i) q^{49} +(7204.56 + 12478.7i) q^{50} +26540.0 q^{51} +(-2413.62 - 4180.51i) q^{52} +(15179.4 - 26291.4i) q^{53} -8816.06 q^{54} +(-11812.7 + 20460.1i) q^{55} +(1728.46 + 2993.77i) q^{56} +(13361.3 + 23142.4i) q^{57} +(5335.92 + 9242.08i) q^{58} -3000.82 q^{59} +(-9535.43 - 16515.9i) q^{60} +(-6411.35 - 11104.8i) q^{61} +(12634.6 - 21883.7i) q^{62} +(1248.54 - 2162.54i) q^{63} +33934.6 q^{64} -31600.2 q^{65} +(-12936.9 + 22407.4i) q^{66} +(-19495.3 + 33766.8i) q^{67} +(-8239.51 - 14271.2i) q^{68} +(11192.8 + 19386.4i) q^{69} +6240.42 q^{70} +(23187.6 + 40162.2i) q^{71} +(-13972.1 - 24200.3i) q^{72} +(14894.3 + 25797.6i) q^{73} +(13526.1 - 23427.9i) q^{74} -63519.4 q^{75} +(8296.19 - 14369.4i) q^{76} +(2602.97 + 4508.48i) q^{77} -34607.7 q^{78} +(34046.1 + 58969.5i) q^{79} +(19367.8 - 33546.0i) q^{80} +(36694.0 - 63555.8i) q^{81} -46684.9 q^{82} +(38356.7 - 66435.8i) q^{83} -4202.34 q^{84} -107876. q^{85} +(-3852.11 - 53835.2i) q^{86} -47044.4 q^{87} +58258.1 q^{88} +(64520.1 - 111752. i) q^{89} -50444.8 q^{90} +(-3481.62 + 6030.34i) q^{91} +(6949.72 - 12037.3i) q^{92} +(55696.8 + 96469.6i) q^{93} +119340. q^{94} +(-54308.8 - 94065.5i) q^{95} +(-40543.0 + 70222.5i) q^{96} -57031.7 q^{97} +(-36720.4 + 63601.6i) q^{98} +(-21041.3 - 36444.5i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45148 −0.786917 −0.393459 0.919342i \(-0.628722\pi\)
−0.393459 + 0.919342i \(0.628722\pi\)
\(3\) 9.81167 16.9943i 0.629419 1.09019i −0.358250 0.933626i \(-0.616626\pi\)
0.987669 0.156559i \(-0.0500403\pi\)
\(4\) −12.1844 −0.380762
\(5\) −39.8809 + 69.0757i −0.713411 + 1.23566i 0.250159 + 0.968205i \(0.419517\pi\)
−0.963569 + 0.267458i \(0.913816\pi\)
\(6\) −43.6764 + 75.6497i −0.495300 + 0.857885i
\(7\) 8.78791 + 15.2211i 0.0677861 + 0.117409i 0.897926 0.440145i \(-0.145073\pi\)
−0.830140 + 0.557554i \(0.811740\pi\)
\(8\) 196.686 1.08654
\(9\) −71.0376 123.041i −0.292336 0.506341i
\(10\) 177.529 307.489i 0.561395 0.972365i
\(11\) 296.199 0.738077 0.369039 0.929414i \(-0.379687\pi\)
0.369039 + 0.929414i \(0.379687\pi\)
\(12\) −119.549 + 207.065i −0.239658 + 0.415101i
\(13\) 198.091 + 343.104i 0.325093 + 0.563077i 0.981531 0.191303i \(-0.0612712\pi\)
−0.656438 + 0.754380i \(0.727938\pi\)
\(14\) −39.1192 67.7564i −0.0533420 0.0923911i
\(15\) 782.595 + 1355.50i 0.898068 + 1.55550i
\(16\) −485.641 −0.474259
\(17\) 676.236 + 1171.28i 0.567513 + 0.982962i 0.996811 + 0.0797988i \(0.0254278\pi\)
−0.429298 + 0.903163i \(0.641239\pi\)
\(18\) 316.222 + 547.713i 0.230044 + 0.398448i
\(19\) −680.888 + 1179.33i −0.432704 + 0.749466i −0.997105 0.0760348i \(-0.975774\pi\)
0.564401 + 0.825501i \(0.309107\pi\)
\(20\) 485.923 841.644i 0.271639 0.470493i
\(21\) 344.896 0.170663
\(22\) −1318.52 −0.580806
\(23\) −570.380 + 987.927i −0.224825 + 0.389408i −0.956267 0.292495i \(-0.905514\pi\)
0.731442 + 0.681904i \(0.238848\pi\)
\(24\) 1929.81 3342.54i 0.683892 1.18454i
\(25\) −1618.47 2803.27i −0.517909 0.897045i
\(26\) −881.799 1527.32i −0.255821 0.443095i
\(27\) 1980.48 0.522831
\(28\) −107.075 185.460i −0.0258103 0.0447048i
\(29\) −1198.69 2076.18i −0.264673 0.458428i 0.702805 0.711383i \(-0.251931\pi\)
−0.967478 + 0.252955i \(0.918597\pi\)
\(30\) −3483.70 6033.95i −0.706705 1.22405i
\(31\) −2838.29 + 4916.07i −0.530460 + 0.918784i 0.468908 + 0.883247i \(0.344648\pi\)
−0.999368 + 0.0355371i \(0.988686\pi\)
\(32\) −4132.12 −0.713342
\(33\) 2906.21 5033.70i 0.464560 0.804641i
\(34\) −3010.25 5213.90i −0.446586 0.773509i
\(35\) −1401.88 −0.193437
\(36\) 865.548 + 1499.17i 0.111310 + 0.192795i
\(37\) −3038.57 + 5262.96i −0.364893 + 0.632013i −0.988759 0.149518i \(-0.952228\pi\)
0.623866 + 0.781531i \(0.285561\pi\)
\(38\) 3030.95 5249.77i 0.340503 0.589768i
\(39\) 7774.43 0.818478
\(40\) −7843.99 + 13586.2i −0.775153 + 1.34260i
\(41\) 10487.5 0.974345 0.487172 0.873306i \(-0.338028\pi\)
0.487172 + 0.873306i \(0.338028\pi\)
\(42\) −1535.30 −0.134298
\(43\) 865.356 + 12093.8i 0.0713713 + 0.997450i
\(44\) −3609.00 −0.281031
\(45\) 11332.2 0.834222
\(46\) 2539.03 4397.73i 0.176919 0.306432i
\(47\) −26809.0 −1.77026 −0.885129 0.465346i \(-0.845930\pi\)
−0.885129 + 0.465346i \(0.845930\pi\)
\(48\) −4764.95 + 8253.14i −0.298508 + 0.517030i
\(49\) 8249.05 14287.8i 0.490810 0.850108i
\(50\) 7204.56 + 12478.7i 0.407552 + 0.705900i
\(51\) 26540.0 1.42881
\(52\) −2413.62 4180.51i −0.123783 0.214398i
\(53\) 15179.4 26291.4i 0.742273 1.28565i −0.209185 0.977876i \(-0.567081\pi\)
0.951458 0.307778i \(-0.0995855\pi\)
\(54\) −8816.06 −0.411424
\(55\) −11812.7 + 20460.1i −0.526552 + 0.912015i
\(56\) 1728.46 + 2993.77i 0.0736526 + 0.127570i
\(57\) 13361.3 + 23142.4i 0.544705 + 0.943456i
\(58\) 5335.92 + 9242.08i 0.208276 + 0.360745i
\(59\) −3000.82 −0.112230 −0.0561152 0.998424i \(-0.517871\pi\)
−0.0561152 + 0.998424i \(0.517871\pi\)
\(60\) −9535.43 16515.9i −0.341950 0.592274i
\(61\) −6411.35 11104.8i −0.220610 0.382108i 0.734383 0.678735i \(-0.237471\pi\)
−0.954993 + 0.296627i \(0.904138\pi\)
\(62\) 12634.6 21883.7i 0.417428 0.723007i
\(63\) 1248.54 2162.54i 0.0396326 0.0686457i
\(64\) 33934.6 1.03560
\(65\) −31600.2 −0.927698
\(66\) −12936.9 + 22407.4i −0.365570 + 0.633186i
\(67\) −19495.3 + 33766.8i −0.530570 + 0.918974i 0.468794 + 0.883307i \(0.344689\pi\)
−0.999364 + 0.0356661i \(0.988645\pi\)
\(68\) −8239.51 14271.2i −0.216087 0.374274i
\(69\) 11192.8 + 19386.4i 0.283018 + 0.490202i
\(70\) 6240.42 0.152219
\(71\) 23187.6 + 40162.2i 0.545897 + 0.945521i 0.998550 + 0.0538344i \(0.0171443\pi\)
−0.452653 + 0.891687i \(0.649522\pi\)
\(72\) −13972.1 24200.3i −0.317636 0.550162i
\(73\) 14894.3 + 25797.6i 0.327124 + 0.566595i 0.981940 0.189193i \(-0.0605872\pi\)
−0.654816 + 0.755788i \(0.727254\pi\)
\(74\) 13526.1 23427.9i 0.287140 0.497342i
\(75\) −63519.4 −1.30393
\(76\) 8296.19 14369.4i 0.164757 0.285368i
\(77\) 2602.97 + 4508.48i 0.0500314 + 0.0866568i
\(78\) −34607.7 −0.644074
\(79\) 34046.1 + 58969.5i 0.613761 + 1.06306i 0.990601 + 0.136786i \(0.0436774\pi\)
−0.376840 + 0.926278i \(0.622989\pi\)
\(80\) 19367.8 33546.0i 0.338341 0.586025i
\(81\) 36694.0 63555.8i 0.621415 1.07632i
\(82\) −46684.9 −0.766729
\(83\) 38356.7 66435.8i 0.611148 1.05854i −0.379899 0.925028i \(-0.624041\pi\)
0.991047 0.133512i \(-0.0426254\pi\)
\(84\) −4202.34 −0.0649820
\(85\) −107876. −1.61948
\(86\) −3852.11 53835.2i −0.0561633 0.784910i
\(87\) −47044.4 −0.666361
\(88\) 58258.1 0.801954
\(89\) 64520.1 111752.i 0.863416 1.49548i −0.00519552 0.999987i \(-0.501654\pi\)
0.868611 0.495494i \(-0.165013\pi\)
\(90\) −50444.8 −0.656463
\(91\) −3481.62 + 6030.34i −0.0440735 + 0.0763376i
\(92\) 6949.72 12037.3i 0.0856047 0.148272i
\(93\) 55696.8 + 96469.6i 0.667763 + 1.15660i
\(94\) 119340. 1.39305
\(95\) −54308.8 94065.5i −0.617392 1.06935i
\(96\) −40543.0 + 70222.5i −0.448991 + 0.777675i
\(97\) −57031.7 −0.615442 −0.307721 0.951477i \(-0.599566\pi\)
−0.307721 + 0.951477i \(0.599566\pi\)
\(98\) −36720.4 + 63601.6i −0.386227 + 0.668965i
\(99\) −21041.3 36444.5i −0.215766 0.373718i
\(100\) 19720.0 + 34156.0i 0.197200 + 0.341560i
\(101\) 8496.24 + 14715.9i 0.0828749 + 0.143544i 0.904484 0.426508i \(-0.140256\pi\)
−0.821609 + 0.570052i \(0.806923\pi\)
\(102\) −118142. −1.12436
\(103\) −94549.7 163765.i −0.878147 1.52099i −0.853373 0.521302i \(-0.825447\pi\)
−0.0247742 0.999693i \(-0.507887\pi\)
\(104\) 38961.7 + 67483.7i 0.353228 + 0.611809i
\(105\) −13754.8 + 23823.9i −0.121753 + 0.210882i
\(106\) −67570.5 + 117036.i −0.584107 + 1.01170i
\(107\) 160449. 1.35481 0.677404 0.735612i \(-0.263105\pi\)
0.677404 + 0.735612i \(0.263105\pi\)
\(108\) −24130.9 −0.199074
\(109\) −100638. + 174310.i −0.811326 + 1.40526i 0.100611 + 0.994926i \(0.467920\pi\)
−0.911936 + 0.410331i \(0.865413\pi\)
\(110\) 52583.8 91077.8i 0.414353 0.717680i
\(111\) 59626.9 + 103277.i 0.459341 + 0.795601i
\(112\) −4267.77 7392.00i −0.0321482 0.0556823i
\(113\) 213998. 1.57657 0.788287 0.615308i \(-0.210968\pi\)
0.788287 + 0.615308i \(0.210968\pi\)
\(114\) −59477.4 103018.i −0.428637 0.742422i
\(115\) −45494.5 78798.8i −0.320785 0.555616i
\(116\) 14605.2 + 25297.0i 0.100777 + 0.174552i
\(117\) 28143.9 48746.6i 0.190073 0.329215i
\(118\) 13358.1 0.0883160
\(119\) −11885.4 + 20586.1i −0.0769390 + 0.133262i
\(120\) 153925. + 266606.i 0.975791 + 1.69012i
\(121\) −73317.2 −0.455242
\(122\) 28540.0 + 49432.7i 0.173602 + 0.300687i
\(123\) 102900. 178228.i 0.613271 1.06222i
\(124\) 34582.8 59899.2i 0.201979 0.349838i
\(125\) 8927.90 0.0511063
\(126\) −5557.86 + 9626.50i −0.0311876 + 0.0540185i
\(127\) 252575. 1.38957 0.694786 0.719217i \(-0.255499\pi\)
0.694786 + 0.719217i \(0.255499\pi\)
\(128\) −18831.0 −0.101589
\(129\) 214016. + 103954.i 1.13233 + 0.550006i
\(130\) 140668. 0.730022
\(131\) −300526. −1.53004 −0.765022 0.644004i \(-0.777272\pi\)
−0.765022 + 0.644004i \(0.777272\pi\)
\(132\) −35410.3 + 61332.4i −0.176886 + 0.306376i
\(133\) −23934.3 −0.117325
\(134\) 86782.7 150312.i 0.417514 0.723156i
\(135\) −78983.3 + 136803.i −0.372993 + 0.646043i
\(136\) 133006. + 230373.i 0.616629 + 1.06803i
\(137\) −329912. −1.50174 −0.750872 0.660447i \(-0.770367\pi\)
−0.750872 + 0.660447i \(0.770367\pi\)
\(138\) −49824.3 86298.2i −0.222712 0.385748i
\(139\) −14130.2 + 24474.2i −0.0620312 + 0.107441i −0.895373 0.445317i \(-0.853091\pi\)
0.833342 + 0.552758i \(0.186424\pi\)
\(140\) 17081.0 0.0736534
\(141\) −263041. + 455601.i −1.11423 + 1.92991i
\(142\) −103219. 178781.i −0.429576 0.744047i
\(143\) 58674.5 + 101627.i 0.239944 + 0.415594i
\(144\) 34498.8 + 59753.7i 0.138643 + 0.240137i
\(145\) 191218. 0.755283
\(146\) −66301.5 114838.i −0.257419 0.445864i
\(147\) −161874. 280374.i −0.617850 1.07015i
\(148\) 37023.1 64125.9i 0.138937 0.240646i
\(149\) 70895.8 122795.i 0.261610 0.453122i −0.705060 0.709148i \(-0.749080\pi\)
0.966670 + 0.256026i \(0.0824132\pi\)
\(150\) 282755. 1.02608
\(151\) −111899. −0.399379 −0.199690 0.979859i \(-0.563993\pi\)
−0.199690 + 0.979859i \(0.563993\pi\)
\(152\) −133921. + 231958.i −0.470153 + 0.814329i
\(153\) 96076.4 166409.i 0.331809 0.574710i
\(154\) −11587.1 20069.4i −0.0393705 0.0681918i
\(155\) −226387. 392114.i −0.756872 1.31094i
\(156\) −94726.5 −0.311645
\(157\) −95117.5 164748.i −0.307972 0.533423i 0.669947 0.742409i \(-0.266317\pi\)
−0.977919 + 0.208986i \(0.932984\pi\)
\(158\) −151555. 262501.i −0.482979 0.836544i
\(159\) −297869. 515925.i −0.934401 1.61843i
\(160\) 164792. 285429.i 0.508906 0.881451i
\(161\) −20049.8 −0.0609600
\(162\) −163342. + 282917.i −0.489002 + 0.846977i
\(163\) −214841. 372115.i −0.633356 1.09700i −0.986861 0.161572i \(-0.948344\pi\)
0.353505 0.935433i \(-0.384990\pi\)
\(164\) −127784. −0.370993
\(165\) 231804. + 401496.i 0.662843 + 1.14808i
\(166\) −170744. + 295737.i −0.480923 + 0.832983i
\(167\) −89065.7 + 154266.i −0.247126 + 0.428036i −0.962727 0.270474i \(-0.912820\pi\)
0.715601 + 0.698509i \(0.246153\pi\)
\(168\) 67836.1 0.185433
\(169\) 107166. 185617.i 0.288629 0.499921i
\(170\) 480205. 1.27440
\(171\) 193475. 0.505980
\(172\) −10543.8 147355.i −0.0271754 0.379791i
\(173\) 210147. 0.533836 0.266918 0.963719i \(-0.413995\pi\)
0.266918 + 0.963719i \(0.413995\pi\)
\(174\) 209417. 0.524371
\(175\) 28445.9 49269.7i 0.0702141 0.121614i
\(176\) −143846. −0.350040
\(177\) −29443.1 + 50996.9i −0.0706399 + 0.122352i
\(178\) −287210. + 497462.i −0.679437 + 1.17682i
\(179\) 206524. + 357710.i 0.481767 + 0.834446i 0.999781 0.0209267i \(-0.00666166\pi\)
−0.518014 + 0.855372i \(0.673328\pi\)
\(180\) −138075. −0.317640
\(181\) −43809.7 75880.6i −0.0993971 0.172161i 0.812038 0.583604i \(-0.198358\pi\)
−0.911435 + 0.411444i \(0.865025\pi\)
\(182\) 15498.3 26843.9i 0.0346822 0.0600713i
\(183\) −251624. −0.555424
\(184\) −112186. + 194311.i −0.244283 + 0.423110i
\(185\) −242362. 419783.i −0.520637 0.901769i
\(186\) −247933. 429432.i −0.525474 0.910148i
\(187\) 200300. + 346930.i 0.418869 + 0.725502i
\(188\) 326651. 0.674046
\(189\) 17404.3 + 30145.1i 0.0354406 + 0.0613850i
\(190\) 241754. + 418730.i 0.485836 + 0.841493i
\(191\) 188778. 326974.i 0.374428 0.648529i −0.615813 0.787892i \(-0.711172\pi\)
0.990241 + 0.139364i \(0.0445057\pi\)
\(192\) 332955. 576694.i 0.651826 1.12900i
\(193\) 315911. 0.610480 0.305240 0.952275i \(-0.401263\pi\)
0.305240 + 0.952275i \(0.401263\pi\)
\(194\) 253875. 0.484302
\(195\) −310051. + 537024.i −0.583911 + 1.01136i
\(196\) −100509. + 174087.i −0.186882 + 0.323688i
\(197\) 390412. + 676213.i 0.716733 + 1.24142i 0.962287 + 0.272035i \(0.0876968\pi\)
−0.245554 + 0.969383i \(0.578970\pi\)
\(198\) 93664.7 + 162232.i 0.169790 + 0.294085i
\(199\) −100876. −0.180574 −0.0902870 0.995916i \(-0.528778\pi\)
−0.0902870 + 0.995916i \(0.528778\pi\)
\(200\) −318329. 551362.i −0.562731 0.974680i
\(201\) 382562. + 662617.i 0.667901 + 1.15684i
\(202\) −37820.8 65507.5i −0.0652157 0.112957i
\(203\) 21067.9 36490.6i 0.0358823 0.0621500i
\(204\) −323373. −0.544037
\(205\) −418251. + 724432.i −0.695108 + 1.20396i
\(206\) 420886. + 728995.i 0.691029 + 1.19690i
\(207\) 162074. 0.262898
\(208\) −96201.4 166626.i −0.154178 0.267044i
\(209\) −201678. + 349317.i −0.319369 + 0.553164i
\(210\) 61229.0 106052.i 0.0958095 0.165947i
\(211\) 332166. 0.513628 0.256814 0.966461i \(-0.417327\pi\)
0.256814 + 0.966461i \(0.417327\pi\)
\(212\) −184951. + 320344.i −0.282629 + 0.489528i
\(213\) 910037. 1.37439
\(214\) −714235. −1.06612
\(215\) −869897. 422535.i −1.28343 0.623400i
\(216\) 389532. 0.568079
\(217\) −99770.6 −0.143831
\(218\) 447987. 775936.i 0.638446 1.10582i
\(219\) 584551. 0.823592
\(220\) 143930. 249294.i 0.200491 0.347260i
\(221\) −267913. + 464039.i −0.368989 + 0.639107i
\(222\) −265428. 459734.i −0.361463 0.626072i
\(223\) 185608. 0.249939 0.124970 0.992161i \(-0.460117\pi\)
0.124970 + 0.992161i \(0.460117\pi\)
\(224\) −36312.7 62895.4i −0.0483547 0.0837527i
\(225\) −229944. + 398275.i −0.302807 + 0.524477i
\(226\) −952608. −1.24063
\(227\) 498203. 862912.i 0.641714 1.11148i −0.343336 0.939213i \(-0.611557\pi\)
0.985050 0.172268i \(-0.0551096\pi\)
\(228\) −162799. 281976.i −0.207403 0.359232i
\(229\) −77766.5 134696.i −0.0979950 0.169732i 0.812860 0.582460i \(-0.197910\pi\)
−0.910855 + 0.412727i \(0.864576\pi\)
\(230\) 202518. + 350771.i 0.252431 + 0.437224i
\(231\) 102158. 0.125963
\(232\) −235764. 408356.i −0.287579 0.498102i
\(233\) −712861. 1.23471e6i −0.860231 1.48996i −0.871705 0.490030i \(-0.836986\pi\)
0.0114740 0.999934i \(-0.496348\pi\)
\(234\) −125282. + 216994.i −0.149571 + 0.259065i
\(235\) 1.06917e6 1.85185e6i 1.26292 2.18744i
\(236\) 36563.1 0.0427330
\(237\) 1.33619e6 1.54525
\(238\) 52907.6 91638.6i 0.0605446 0.104866i
\(239\) −499112. + 864488.i −0.565202 + 0.978958i 0.431829 + 0.901955i \(0.357868\pi\)
−0.997031 + 0.0770026i \(0.975465\pi\)
\(240\) −380061. 658284.i −0.425917 0.737710i
\(241\) 368394. + 638077.i 0.408573 + 0.707670i 0.994730 0.102528i \(-0.0326931\pi\)
−0.586157 + 0.810198i \(0.699360\pi\)
\(242\) 326370. 0.358238
\(243\) −479429. 830396.i −0.520846 0.902131i
\(244\) 78118.3 + 135305.i 0.0839998 + 0.145492i
\(245\) 657958. + 1.13962e6i 0.700298 + 1.21295i
\(246\) −458057. + 793377.i −0.482593 + 0.835876i
\(247\) −539512. −0.562676
\(248\) −558251. + 966919.i −0.576369 + 0.998300i
\(249\) −752687. 1.30369e6i −0.769336 1.33253i
\(250\) −39742.3 −0.0402164
\(251\) 582987. + 1.00976e6i 0.584083 + 1.01166i 0.994989 + 0.0999839i \(0.0318791\pi\)
−0.410906 + 0.911678i \(0.634788\pi\)
\(252\) −15212.7 + 26349.2i −0.0150906 + 0.0261376i
\(253\) −168946. + 292623.i −0.165938 + 0.287414i
\(254\) −1.12433e6 −1.09348
\(255\) −1.05844e6 + 1.83327e6i −1.01933 + 1.76553i
\(256\) −1.00208e6 −0.955658
\(257\) 809150. 0.764181 0.382090 0.924125i \(-0.375204\pi\)
0.382090 + 0.924125i \(0.375204\pi\)
\(258\) −952687. 462749.i −0.891048 0.432809i
\(259\) −106811. −0.0989386
\(260\) 385029. 0.353232
\(261\) −170303. + 294974.i −0.154747 + 0.268030i
\(262\) 1.33778e6 1.20402
\(263\) −484033. + 838370.i −0.431505 + 0.747388i −0.997003 0.0773612i \(-0.975351\pi\)
0.565498 + 0.824749i \(0.308684\pi\)
\(264\) 571609. 990056.i 0.504765 0.874278i
\(265\) 1.21073e6 + 2.09705e6i 1.05909 + 1.83440i
\(266\) 106543. 0.0923253
\(267\) −1.26610e6 2.19295e6i −1.08690 1.88257i
\(268\) 237538. 411427.i 0.202020 0.349910i
\(269\) 55719.5 0.0469490 0.0234745 0.999724i \(-0.492527\pi\)
0.0234745 + 0.999724i \(0.492527\pi\)
\(270\) 351592. 608975.i 0.293515 0.508382i
\(271\) −176169. 305134.i −0.145716 0.252388i 0.783924 0.620857i \(-0.213215\pi\)
−0.929640 + 0.368469i \(0.879882\pi\)
\(272\) −328408. 568820.i −0.269148 0.466179i
\(273\) 68321.0 + 118335.i 0.0554814 + 0.0960966i
\(274\) 1.46859e6 1.18175
\(275\) −479388. 830324.i −0.382257 0.662088i
\(276\) −136377. 236211.i −0.107762 0.186650i
\(277\) 636770. 1.10292e6i 0.498636 0.863662i −0.501363 0.865237i \(-0.667168\pi\)
0.999999 + 0.00157482i \(0.000501282\pi\)
\(278\) 62900.1 108946.i 0.0488134 0.0845473i
\(279\) 806502. 0.620290
\(280\) −275729. −0.210178
\(281\) 182712. 316467.i 0.138039 0.239091i −0.788715 0.614759i \(-0.789253\pi\)
0.926754 + 0.375668i \(0.122587\pi\)
\(282\) 1.17092e6 2.02810e6i 0.876809 1.51868i
\(283\) −79267.0 137295.i −0.0588337 0.101903i 0.835108 0.550085i \(-0.185405\pi\)
−0.893942 + 0.448182i \(0.852072\pi\)
\(284\) −282527. 489351.i −0.207857 0.360018i
\(285\) −2.13144e6 −1.55439
\(286\) −261188. 452391.i −0.188816 0.327038i
\(287\) 92163.3 + 159631.i 0.0660470 + 0.114397i
\(288\) 293536. + 508419.i 0.208535 + 0.361194i
\(289\) −204662. + 354485.i −0.144143 + 0.249662i
\(290\) −851204. −0.594345
\(291\) −559576. + 969215.i −0.387371 + 0.670946i
\(292\) −181477. 314328.i −0.124556 0.215738i
\(293\) 808240. 0.550011 0.275006 0.961443i \(-0.411320\pi\)
0.275006 + 0.961443i \(0.411320\pi\)
\(294\) 720577. + 1.24808e6i 0.486197 + 0.842118i
\(295\) 119675. 207284.i 0.0800663 0.138679i
\(296\) −597643. + 1.03515e6i −0.396472 + 0.686710i
\(297\) 586616. 0.385890
\(298\) −315591. + 546619.i −0.205866 + 0.356570i
\(299\) −451950. −0.292356
\(300\) 773944. 0.496485
\(301\) −176476. + 119451.i −0.112272 + 0.0759928i
\(302\) 498118. 0.314278
\(303\) 333449. 0.208652
\(304\) 330667. 572732.i 0.205214 0.355441i
\(305\) 1.02276e6 0.629542
\(306\) −427682. + 740766.i −0.261106 + 0.452249i
\(307\) 208378. 360922.i 0.126185 0.218558i −0.796011 0.605282i \(-0.793060\pi\)
0.922195 + 0.386724i \(0.126393\pi\)
\(308\) −31715.5 54932.9i −0.0190500 0.0329956i
\(309\) −3.71076e6 −2.21089
\(310\) 1.00776e6 + 1.74549e6i 0.595595 + 1.03160i
\(311\) −791941. + 1.37168e6i −0.464293 + 0.804179i −0.999169 0.0407516i \(-0.987025\pi\)
0.534877 + 0.844930i \(0.320358\pi\)
\(312\) 1.52912e6 0.889313
\(313\) −834811. + 1.44594e6i −0.481645 + 0.834234i −0.999778 0.0210658i \(-0.993294\pi\)
0.518133 + 0.855300i \(0.326627\pi\)
\(314\) 423413. + 733373.i 0.242348 + 0.419760i
\(315\) 99586.0 + 172488.i 0.0565486 + 0.0979451i
\(316\) −414830. 718506.i −0.233697 0.404774i
\(317\) 2.42601e6 1.35595 0.677977 0.735083i \(-0.262857\pi\)
0.677977 + 0.735083i \(0.262857\pi\)
\(318\) 1.32596e6 + 2.29663e6i 0.735296 + 1.27357i
\(319\) −355049. 614963.i −0.195349 0.338355i
\(320\) −1.35334e6 + 2.34405e6i −0.738808 + 1.27965i
\(321\) 1.57427e6 2.72672e6i 0.852741 1.47699i
\(322\) 89251.2 0.0479705
\(323\) −1.84176e6 −0.982262
\(324\) −447093. + 774387.i −0.236611 + 0.409822i
\(325\) 641208. 1.11061e6i 0.336737 0.583246i
\(326\) 956358. + 1.65646e6i 0.498398 + 0.863251i
\(327\) 1.97485e6 + 3.42054e6i 1.02133 + 1.76899i
\(328\) 2.06274e6 1.05867
\(329\) −235595. 408063.i −0.119999 0.207844i
\(330\) −1.03187e6 1.78725e6i −0.521603 0.903443i
\(331\) 1.08077e6 + 1.87196e6i 0.542207 + 0.939130i 0.998777 + 0.0494426i \(0.0157445\pi\)
−0.456570 + 0.889688i \(0.650922\pi\)
\(332\) −467353. + 809479.i −0.232702 + 0.403051i
\(333\) 863412. 0.426685
\(334\) 396474. 686713.i 0.194468 0.336829i
\(335\) −1.55498e6 2.69330e6i −0.757028 1.31121i
\(336\) −167496. −0.0809386
\(337\) −1.62857e6 2.82077e6i −0.781145 1.35298i −0.931275 0.364317i \(-0.881303\pi\)
0.150130 0.988666i \(-0.452031\pi\)
\(338\) −477047. + 826270.i −0.227127 + 0.393396i
\(339\) 2.09968e6 3.63675e6i 0.992325 1.71876i
\(340\) 1.31439e6 0.616636
\(341\) −840699. + 1.45613e6i −0.391521 + 0.678134i
\(342\) −861247. −0.398164
\(343\) 585364. 0.268652
\(344\) 170203. + 2.37867e6i 0.0775481 + 1.08377i
\(345\) −1.78551e6 −0.807633
\(346\) −935465. −0.420085
\(347\) 1.40807e6 2.43886e6i 0.627772 1.08733i −0.360226 0.932865i \(-0.617300\pi\)
0.987998 0.154468i \(-0.0493664\pi\)
\(348\) 573206. 0.253725
\(349\) 1.32927e6 2.30236e6i 0.584184 1.01184i −0.410792 0.911729i \(-0.634748\pi\)
0.994977 0.100108i \(-0.0319188\pi\)
\(350\) −126626. + 219323.i −0.0552526 + 0.0957004i
\(351\) 392316. + 679512.i 0.169968 + 0.294394i
\(352\) −1.22393e6 −0.526502
\(353\) −114987. 199164.i −0.0491149 0.0850695i 0.840423 0.541931i \(-0.182307\pi\)
−0.889538 + 0.456862i \(0.848973\pi\)
\(354\) 131065. 227011.i 0.0555877 0.0962807i
\(355\) −3.69897e6 −1.55779
\(356\) −786137. + 1.36163e6i −0.328756 + 0.569421i
\(357\) 233231. + 403968.i 0.0968537 + 0.167756i
\(358\) −919335. 1.59234e6i −0.379111 0.656640i
\(359\) −183276. 317444.i −0.0750533 0.129996i 0.826056 0.563588i \(-0.190579\pi\)
−0.901109 + 0.433592i \(0.857246\pi\)
\(360\) 2.22887e6 0.906419
\(361\) 310834. + 538380.i 0.125534 + 0.217431i
\(362\) 195018. + 337781.i 0.0782173 + 0.135476i
\(363\) −719364. + 1.24597e6i −0.286538 + 0.496298i
\(364\) 42421.3 73475.9i 0.0167815 0.0290664i
\(365\) −2.37599e6 −0.933495
\(366\) 1.12010e6 0.437073
\(367\) 492872. 853679.i 0.191015 0.330849i −0.754572 0.656218i \(-0.772155\pi\)
0.945587 + 0.325369i \(0.105489\pi\)
\(368\) 277000. 479778.i 0.106625 0.184681i
\(369\) −745008. 1.29039e6i −0.284836 0.493350i
\(370\) 1.07887e6 + 1.86865e6i 0.409698 + 0.709618i
\(371\) 533579. 0.201263
\(372\) −678630. 1.17542e6i −0.254259 0.440389i
\(373\) −2.43355e6 4.21503e6i −0.905665 1.56866i −0.820022 0.572332i \(-0.806039\pi\)
−0.0856428 0.996326i \(-0.527294\pi\)
\(374\) −891632. 1.54435e6i −0.329615 0.570910i
\(375\) 87597.6 151724.i 0.0321673 0.0557153i
\(376\) −5.27295e6 −1.92346
\(377\) 474899. 822548.i 0.172087 0.298063i
\(378\) −77474.7 134190.i −0.0278888 0.0483049i
\(379\) 1.75391e6 0.627203 0.313602 0.949555i \(-0.398464\pi\)
0.313602 + 0.949555i \(0.398464\pi\)
\(380\) 661718. + 1.14613e6i 0.235079 + 0.407169i
\(381\) 2.47818e6 4.29234e6i 0.874622 1.51489i
\(382\) −840342. + 1.45551e6i −0.294644 + 0.510338i
\(383\) −2.01371e6 −0.701456 −0.350728 0.936477i \(-0.614066\pi\)
−0.350728 + 0.936477i \(0.614066\pi\)
\(384\) −184763. + 320020.i −0.0639422 + 0.110751i
\(385\) −415235. −0.142772
\(386\) −1.40627e6 −0.480397
\(387\) 1.42656e6 965588.i 0.484185 0.327729i
\(388\) 694896. 0.234337
\(389\) 4.27059e6 1.43092 0.715458 0.698656i \(-0.246218\pi\)
0.715458 + 0.698656i \(0.246218\pi\)
\(390\) 1.38018e6 2.39055e6i 0.459489 0.795859i
\(391\) −1.54285e6 −0.510365
\(392\) 1.62247e6 2.81020e6i 0.533287 0.923680i
\(393\) −2.94866e6 + 5.10723e6i −0.963038 + 1.66803i
\(394\) −1.73791e6 3.01015e6i −0.564010 0.976893i
\(395\) −5.43115e6 −1.75145
\(396\) 256375. + 444054.i 0.0821556 + 0.142298i
\(397\) −1.70889e6 + 2.95989e6i −0.544174 + 0.942537i 0.454484 + 0.890755i \(0.349824\pi\)
−0.998658 + 0.0517826i \(0.983510\pi\)
\(398\) 449047. 0.142097
\(399\) −234836. + 406747.i −0.0738468 + 0.127906i
\(400\) 785994. + 1.36138e6i 0.245623 + 0.425432i
\(401\) 1.54136e6 + 2.66972e6i 0.478679 + 0.829097i 0.999701 0.0244467i \(-0.00778239\pi\)
−0.521022 + 0.853543i \(0.674449\pi\)
\(402\) −1.70297e6 2.94962e6i −0.525583 0.910336i
\(403\) −2.24896e6 −0.689795
\(404\) −103521. 179304.i −0.0315556 0.0546559i
\(405\) 2.92677e6 + 5.06932e6i 0.886649 + 1.53572i
\(406\) −93783.1 + 162437.i −0.0282364 + 0.0489069i
\(407\) −900022. + 1.55888e6i −0.269319 + 0.466474i
\(408\) 5.22004e6 1.55247
\(409\) −337991. −0.0999071 −0.0499535 0.998752i \(-0.515907\pi\)
−0.0499535 + 0.998752i \(0.515907\pi\)
\(410\) 1.86183e6 3.22479e6i 0.546992 0.947418i
\(411\) −3.23698e6 + 5.60662e6i −0.945226 + 1.63718i
\(412\) 1.15203e6 + 1.99537e6i 0.334364 + 0.579136i
\(413\) −26370.9 45675.8i −0.00760765 0.0131768i
\(414\) −721467. −0.206879
\(415\) 3.05940e6 + 5.29904e6i 0.871999 + 1.51035i
\(416\) −818537. 1.41775e6i −0.231902 0.401667i
\(417\) 277281. + 480265.i 0.0780872 + 0.135251i
\(418\) 897765. 1.55498e6i 0.251317 0.435294i
\(419\) 3.63873e6 1.01255 0.506273 0.862373i \(-0.331023\pi\)
0.506273 + 0.862373i \(0.331023\pi\)
\(420\) 167593. 290280.i 0.0463589 0.0802959i
\(421\) −2.31773e6 4.01443e6i −0.637321 1.10387i −0.986018 0.166637i \(-0.946709\pi\)
0.348697 0.937236i \(-0.386624\pi\)
\(422\) −1.47863e6 −0.404183
\(423\) 1.90445e6 + 3.29860e6i 0.517510 + 0.896353i
\(424\) 2.98556e6 5.17114e6i 0.806513 1.39692i
\(425\) 2.18893e6 3.79134e6i 0.587841 1.01817i
\(426\) −4.05101e6 −1.08153
\(427\) 112685. 195176.i 0.0299086 0.0518031i
\(428\) −1.95497e6 −0.515858
\(429\) 2.30278e6 0.604100
\(430\) 3.87233e6 + 1.88091e6i 1.00995 + 0.490564i
\(431\) 4.38405e6 1.13680 0.568398 0.822754i \(-0.307563\pi\)
0.568398 + 0.822754i \(0.307563\pi\)
\(432\) −961803. −0.247957
\(433\) −495379. + 858022.i −0.126975 + 0.219927i −0.922503 0.385989i \(-0.873860\pi\)
0.795528 + 0.605917i \(0.207193\pi\)
\(434\) 444126. 0.113183
\(435\) 1.87617e6 3.24962e6i 0.475389 0.823398i
\(436\) 1.22621e6 2.12386e6i 0.308922 0.535068i
\(437\) −776729. 1.34533e6i −0.194566 0.336998i
\(438\) −2.60211e6 −0.648098
\(439\) 1.80657e6 + 3.12907e6i 0.447397 + 0.774914i 0.998216 0.0597107i \(-0.0190178\pi\)
−0.550819 + 0.834625i \(0.685684\pi\)
\(440\) −2.32338e6 + 4.02422e6i −0.572122 + 0.990945i
\(441\) −2.34397e6 −0.573926
\(442\) 1.19261e6 2.06566e6i 0.290364 0.502925i
\(443\) 2.54236e6 + 4.40350e6i 0.615500 + 1.06608i 0.990297 + 0.138970i \(0.0443790\pi\)
−0.374797 + 0.927107i \(0.622288\pi\)
\(444\) −726516. 1.25836e6i −0.174899 0.302934i
\(445\) 5.14623e6 + 8.91354e6i 1.23194 + 2.13378i
\(446\) −826229. −0.196681
\(447\) −1.39121e6 2.40965e6i −0.329325 0.570407i
\(448\) 298214. + 516521.i 0.0701993 + 0.121589i
\(449\) −54511.0 + 94415.9i −0.0127605 + 0.0221019i −0.872335 0.488908i \(-0.837395\pi\)
0.859575 + 0.511010i \(0.170729\pi\)
\(450\) 1.02359e6 1.77291e6i 0.238284 0.412720i
\(451\) 3.10639e6 0.719142
\(452\) −2.60743e6 −0.600298
\(453\) −1.09792e6 + 1.90165e6i −0.251377 + 0.435397i
\(454\) −2.21774e6 + 3.84123e6i −0.504975 + 0.874643i
\(455\) −277700. 480990.i −0.0628850 0.108920i
\(456\) 2.62797e6 + 4.55178e6i 0.591846 + 1.02511i
\(457\) −3.66704e6 −0.821343 −0.410671 0.911783i \(-0.634706\pi\)
−0.410671 + 0.911783i \(0.634706\pi\)
\(458\) 346176. + 599594.i 0.0771139 + 0.133565i
\(459\) 1.33927e6 + 2.31969e6i 0.296713 + 0.513923i
\(460\) 554322. + 960113.i 0.122143 + 0.211557i
\(461\) 3.35227e6 5.80630e6i 0.734660 1.27247i −0.220213 0.975452i \(-0.570675\pi\)
0.954872 0.297016i \(-0.0959915\pi\)
\(462\) −454753. −0.0991222
\(463\) 3.94174e6 6.82729e6i 0.854546 1.48012i −0.0225195 0.999746i \(-0.507169\pi\)
0.877066 0.480371i \(-0.159498\pi\)
\(464\) 582131. + 1.00828e6i 0.125524 + 0.217414i
\(465\) −8.88494e6 −1.90556
\(466\) 3.17328e6 + 5.49629e6i 0.676931 + 1.17248i
\(467\) 3.10939e6 5.38562e6i 0.659756 1.14273i −0.320923 0.947105i \(-0.603993\pi\)
0.980679 0.195625i \(-0.0626735\pi\)
\(468\) −342915. + 593947.i −0.0723723 + 0.125352i
\(469\) −685291. −0.143861
\(470\) −4.75937e6 + 8.24347e6i −0.993813 + 1.72134i
\(471\) −3.73304e6 −0.775373
\(472\) −590219. −0.121943
\(473\) 256317. + 3.58217e6i 0.0526775 + 0.736195i
\(474\) −5.94804e6 −1.21598
\(475\) 4.40797e6 0.896406
\(476\) 144816. 250829.i 0.0292954 0.0507411i
\(477\) −4.31322e6 −0.867972
\(478\) 2.22179e6 3.84825e6i 0.444767 0.770359i
\(479\) 1.17090e6 2.02806e6i 0.233174 0.403869i −0.725566 0.688152i \(-0.758422\pi\)
0.958740 + 0.284283i \(0.0917554\pi\)
\(480\) −3.23378e6 5.60107e6i −0.640630 1.10960i
\(481\) −2.40766e6 −0.474496
\(482\) −1.63990e6 2.84038e6i −0.321513 0.556877i
\(483\) −196722. + 340732.i −0.0383694 + 0.0664577i
\(484\) 893324. 0.173339
\(485\) 2.27448e6 3.93951e6i 0.439063 0.760479i
\(486\) 2.13417e6 + 3.69649e6i 0.409862 + 0.709902i
\(487\) −542302. 939295.i −0.103614 0.179465i 0.809557 0.587041i \(-0.199707\pi\)
−0.913171 + 0.407576i \(0.866374\pi\)
\(488\) −1.26102e6 2.18415e6i −0.239703 0.415177i
\(489\) −8.43178e6 −1.59458
\(490\) −2.92888e6 5.07298e6i −0.551077 0.954493i
\(491\) −1.44190e6 2.49744e6i −0.269918 0.467511i 0.698923 0.715197i \(-0.253663\pi\)
−0.968840 + 0.247686i \(0.920330\pi\)
\(492\) −1.25377e6 + 2.17159e6i −0.233510 + 0.404451i
\(493\) 1.62119e6 2.80798e6i 0.300411 0.520328i
\(494\) 2.40162e6 0.442780
\(495\) 3.35658e6 0.615720
\(496\) 1.37839e6 2.38744e6i 0.251576 0.435742i
\(497\) −407542. + 705883.i −0.0740084 + 0.128186i
\(498\) 3.35057e6 + 5.80335e6i 0.605404 + 1.04859i
\(499\) 3.43988e6 + 5.95805e6i 0.618433 + 1.07116i 0.989772 + 0.142659i \(0.0455653\pi\)
−0.371339 + 0.928497i \(0.621101\pi\)
\(500\) −108781. −0.0194593
\(501\) 1.74777e6 + 3.02722e6i 0.311092 + 0.538827i
\(502\) −2.59515e6 4.49494e6i −0.459625 0.796094i
\(503\) −4.67564e6 8.09845e6i −0.823989 1.42719i −0.902690 0.430292i \(-0.858411\pi\)
0.0787012 0.996898i \(-0.474923\pi\)
\(504\) 245571. 425341.i 0.0430626 0.0745866i
\(505\) −1.35535e6 −0.236495
\(506\) 752059. 1.30260e6i 0.130580 0.226171i
\(507\) −2.10296e6 3.64243e6i −0.363338 0.629319i
\(508\) −3.07747e6 −0.529095
\(509\) 36537.0 + 63283.9i 0.00625084 + 0.0108268i 0.869134 0.494577i \(-0.164677\pi\)
−0.862883 + 0.505404i \(0.831344\pi\)
\(510\) 4.71161e6 8.16075e6i 0.802129 1.38933i
\(511\) −261779. + 453415.i −0.0443489 + 0.0768145i
\(512\) 5.06333e6 0.853613
\(513\) −1.34848e6 + 2.33564e6i −0.226231 + 0.391844i
\(514\) −3.60191e6 −0.601347
\(515\) 1.50829e7 2.50592
\(516\) −2.60765e6 1.26661e6i −0.431147 0.209421i
\(517\) −7.94080e6 −1.30659
\(518\) 475466. 0.0778565
\(519\) 2.06189e6 3.57130e6i 0.336007 0.581981i
\(520\) −6.21531e6 −1.00799
\(521\) 2.77754e6 4.81083e6i 0.448297 0.776472i −0.549979 0.835179i \(-0.685364\pi\)
0.998275 + 0.0587062i \(0.0186975\pi\)
\(522\) 758102. 1.31307e6i 0.121773 0.210917i
\(523\) 1.65658e6 + 2.86928e6i 0.264824 + 0.458689i 0.967518 0.252804i \(-0.0813527\pi\)
−0.702693 + 0.711493i \(0.748019\pi\)
\(524\) 3.66172e6 0.582582
\(525\) −558203. 966835.i −0.0883881 0.153093i
\(526\) 2.15466e6 3.73198e6i 0.339558 0.588133i
\(527\) −7.67742e6 −1.20417
\(528\) −1.41137e6 + 2.44457e6i −0.220322 + 0.381608i
\(529\) 2.56750e6 + 4.44705e6i 0.398907 + 0.690928i
\(530\) −5.38954e6 9.33496e6i −0.833416 1.44352i
\(531\) 213171. + 369223.i 0.0328089 + 0.0568268i
\(532\) 291624. 0.0446730
\(533\) 2.07749e6 + 3.59831e6i 0.316752 + 0.548631i
\(534\) 5.63601e6 + 9.76186e6i 0.855300 + 1.48142i
\(535\) −6.39884e6 + 1.10831e7i −0.966534 + 1.67409i
\(536\) −3.83444e6 + 6.64145e6i −0.576488 + 0.998506i
\(537\) 8.10537e6 1.21293
\(538\) −248034. −0.0369450
\(539\) 2.44336e6 4.23202e6i 0.362256 0.627445i
\(540\) 962361. 1.66686e6i 0.142021 0.245988i
\(541\) 2.99744e6 + 5.19171e6i 0.440308 + 0.762636i 0.997712 0.0676052i \(-0.0215358\pi\)
−0.557404 + 0.830241i \(0.688203\pi\)
\(542\) 784214. + 1.35830e6i 0.114666 + 0.198608i
\(543\) −1.71938e6 −0.250250
\(544\) −2.79429e6 4.83985e6i −0.404831 0.701188i
\(545\) −8.02705e6 1.39033e7i −1.15762 2.00505i
\(546\) −304129. 526767.i −0.0436593 0.0756200i
\(547\) −5.28219e6 + 9.14901e6i −0.754823 + 1.30739i 0.190639 + 0.981660i \(0.438944\pi\)
−0.945462 + 0.325732i \(0.894389\pi\)
\(548\) 4.01976e6 0.571807
\(549\) −910894. + 1.57772e6i −0.128984 + 0.223407i
\(550\) 2.13398e6 + 3.69617e6i 0.300805 + 0.521009i
\(551\) 3.26468e6 0.458101
\(552\) 2.20145e6 + 3.81303e6i 0.307512 + 0.532626i
\(553\) −598387. + 1.03644e6i −0.0832089 + 0.144122i
\(554\) −2.83457e6 + 4.90961e6i −0.392385 + 0.679630i
\(555\) −9.51189e6 −1.31079
\(556\) 172167. 298202.i 0.0236191 0.0409095i
\(557\) 6.71609e6 0.917231 0.458615 0.888635i \(-0.348346\pi\)
0.458615 + 0.888635i \(0.348346\pi\)
\(558\) −3.59012e6 −0.488117
\(559\) −3.97801e6 + 2.69258e6i −0.538439 + 0.364451i
\(560\) 680810. 0.0917394
\(561\) 7.86112e6 1.05458
\(562\) −813339. + 1.40874e6i −0.108625 + 0.188144i
\(563\) −9.15631e6 −1.21745 −0.608723 0.793383i \(-0.708318\pi\)
−0.608723 + 0.793383i \(0.708318\pi\)
\(564\) 3.20499e6 5.55121e6i 0.424257 0.734835i
\(565\) −8.53444e6 + 1.47821e7i −1.12474 + 1.94811i
\(566\) 352855. + 611163.i 0.0462973 + 0.0801892i
\(567\) 1.28985e6 0.168493
\(568\) 4.56067e6 + 7.89932e6i 0.593141 + 1.02735i
\(569\) 6.56898e6 1.13778e7i 0.850584 1.47325i −0.0300980 0.999547i \(-0.509582\pi\)
0.880682 0.473708i \(-0.157085\pi\)
\(570\) 9.48804e6 1.22318
\(571\) −1.18937e6 + 2.06005e6i −0.152661 + 0.264416i −0.932205 0.361931i \(-0.882118\pi\)
0.779544 + 0.626347i \(0.215451\pi\)
\(572\) −714911. 1.23826e6i −0.0913613 0.158242i
\(573\) −3.70446e6 6.41631e6i −0.471344 0.816392i
\(574\) −410263. 710596.i −0.0519735 0.0900208i
\(575\) 3.69256e6 0.465756
\(576\) −2.41063e6 4.17533e6i −0.302743 0.524366i
\(577\) −688919. 1.19324e6i −0.0861447 0.149207i 0.819734 0.572745i \(-0.194121\pi\)
−0.905878 + 0.423538i \(0.860788\pi\)
\(578\) 911048. 1.57798e6i 0.113428 0.196464i
\(579\) 3.09961e6 5.36869e6i 0.384248 0.665537i
\(580\) −2.32988e6 −0.287583
\(581\) 1.34830e6 0.165709
\(582\) 2.49094e6 4.31444e6i 0.304829 0.527979i
\(583\) 4.49611e6 7.78749e6i 0.547855 0.948912i
\(584\) 2.92949e6 + 5.07403e6i 0.355435 + 0.615631i
\(585\) 2.24480e6 + 3.88812e6i 0.271199 + 0.469731i
\(586\) −3.59786e6 −0.432813
\(587\) 7.30371e6 + 1.26504e7i 0.874879 + 1.51534i 0.856891 + 0.515497i \(0.172393\pi\)
0.0179882 + 0.999838i \(0.494274\pi\)
\(588\) 1.97233e6 + 3.41618e6i 0.235254 + 0.407471i
\(589\) −3.86512e6 6.69458e6i −0.459065 0.795124i
\(590\) −532732. + 922719.i −0.0630055 + 0.109129i
\(591\) 1.53224e7 1.80450
\(592\) 1.47566e6 2.55591e6i 0.173054 0.299738i
\(593\) −6.35547e6 1.10080e7i −0.742183 1.28550i −0.951499 0.307651i \(-0.900457\pi\)
0.209316 0.977848i \(-0.432876\pi\)
\(594\) −2.61131e6 −0.303663
\(595\) −948000. 1.64198e6i −0.109778 0.190141i
\(596\) −863820. + 1.49618e6i −0.0996111 + 0.172532i
\(597\) −989761. + 1.71432e6i −0.113657 + 0.196859i
\(598\) 2.01184e6 0.230060
\(599\) −5.86128e6 + 1.01520e7i −0.667461 + 1.15608i 0.311151 + 0.950360i \(0.399285\pi\)
−0.978612 + 0.205715i \(0.934048\pi\)
\(600\) −1.24934e7 −1.41677
\(601\) −5.06231e6 −0.571693 −0.285847 0.958275i \(-0.592275\pi\)
−0.285847 + 0.958275i \(0.592275\pi\)
\(602\) 785579. 531732.i 0.0883484 0.0598001i
\(603\) 5.53959e6 0.620418
\(604\) 1.36342e6 0.152068
\(605\) 2.92395e6 5.06443e6i 0.324774 0.562526i
\(606\) −1.48434e6 −0.164192
\(607\) −3.05915e6 + 5.29861e6i −0.337000 + 0.583700i −0.983867 0.178902i \(-0.942745\pi\)
0.646867 + 0.762603i \(0.276079\pi\)
\(608\) 2.81351e6 4.87314e6i 0.308666 0.534626i
\(609\) −413422. 716068.i −0.0451700 0.0782368i
\(610\) −4.55279e6 −0.495397
\(611\) −5.31064e6 9.19829e6i −0.575498 0.996791i
\(612\) −1.17063e6 + 2.02759e6i −0.126340 + 0.218827i
\(613\) 4.53703e6 0.487663 0.243832 0.969818i \(-0.421596\pi\)
0.243832 + 0.969818i \(0.421596\pi\)
\(614\) −927590. + 1.60663e6i −0.0992968 + 0.171987i
\(615\) 8.20748e6 + 1.42158e7i 0.875028 + 1.51559i
\(616\) 511967. + 886752.i 0.0543613 + 0.0941565i
\(617\) −1.90739e6 3.30370e6i −0.201710 0.349371i 0.747370 0.664408i \(-0.231316\pi\)
−0.949079 + 0.315037i \(0.897983\pi\)
\(618\) 1.65184e7 1.73979
\(619\) 7.15409e6 + 1.23912e7i 0.750460 + 1.29983i 0.947600 + 0.319459i \(0.103501\pi\)
−0.197140 + 0.980375i \(0.563165\pi\)
\(620\) 2.75838e6 + 4.77766e6i 0.288188 + 0.499156i
\(621\) −1.12963e6 + 1.95657e6i −0.117545 + 0.203595i
\(622\) 3.52531e6 6.10601e6i 0.365360 0.632822i
\(623\) 2.26799e6 0.234110
\(624\) −3.77558e6 −0.388171
\(625\) 4.70165e6 8.14350e6i 0.481449 0.833895i
\(626\) 3.71614e6 6.43655e6i 0.379015 0.656473i
\(627\) 3.95760e6 + 6.85476e6i 0.402034 + 0.696343i
\(628\) 1.15895e6 + 2.00735e6i 0.117264 + 0.203107i
\(629\) −8.21917e6 −0.828326
\(630\) −443305. 767826.i −0.0444991 0.0770747i
\(631\) −5.00017e6 8.66055e6i −0.499932 0.865908i 0.500068 0.865986i \(-0.333309\pi\)
−1.00000 7.79706e-5i \(0.999975\pi\)
\(632\) 6.69637e6 + 1.15985e7i 0.666879 + 1.15507i
\(633\) 3.25910e6 5.64493e6i 0.323287 0.559950i
\(634\) −1.07993e7 −1.06702
\(635\) −1.00729e7 + 1.74468e7i −0.991335 + 1.71704i
\(636\) 3.62935e6 + 6.28622e6i 0.355784 + 0.616236i
\(637\) 6.53626e6 0.638235
\(638\) 1.58049e6 + 2.73749e6i 0.153724 + 0.266257i
\(639\) 3.29439e6 5.70605e6i 0.319170 0.552819i
\(640\) 750996. 1.30076e6i 0.0724749 0.125530i
\(641\) −1.66557e7 −1.60110 −0.800548 0.599268i \(-0.795458\pi\)
−0.800548 + 0.599268i \(0.795458\pi\)
\(642\) −7.00783e6 + 1.21379e7i −0.671036 + 1.16227i
\(643\) −1.53313e7 −1.46235 −0.731175 0.682190i \(-0.761027\pi\)
−0.731175 + 0.682190i \(0.761027\pi\)
\(644\) 244294. 0.0232112
\(645\) −1.57158e7 + 1.06375e7i −1.48744 + 1.00680i
\(646\) 8.19856e6 0.772959
\(647\) −7.10962e6 −0.667706 −0.333853 0.942625i \(-0.608349\pi\)
−0.333853 + 0.942625i \(0.608349\pi\)
\(648\) 7.21717e6 1.25005e7i 0.675196 1.16947i
\(649\) −888840. −0.0828346
\(650\) −2.85432e6 + 4.94383e6i −0.264984 + 0.458966i
\(651\) −978916. + 1.69553e6i −0.0905301 + 0.156803i
\(652\) 2.61770e6 + 4.53399e6i 0.241157 + 0.417697i
\(653\) −1.42306e6 −0.130599 −0.0652995 0.997866i \(-0.520800\pi\)
−0.0652995 + 0.997866i \(0.520800\pi\)
\(654\) −8.79100e6 1.52265e7i −0.803700 1.39205i
\(655\) 1.19852e7 2.07590e7i 1.09155 1.89062i
\(656\) −5.09317e6 −0.462092
\(657\) 2.11611e6 3.66521e6i 0.191260 0.331272i
\(658\) 1.04875e6 + 1.81648e6i 0.0944291 + 0.163556i
\(659\) 341284. + 591120.i 0.0306127 + 0.0530228i 0.880926 0.473254i \(-0.156921\pi\)
−0.850313 + 0.526277i \(0.823587\pi\)
\(660\) −2.82438e6 4.89198e6i −0.252385 0.437144i
\(661\) 1.15905e7 1.03180 0.515902 0.856648i \(-0.327457\pi\)
0.515902 + 0.856648i \(0.327457\pi\)
\(662\) −4.81104e6 8.33297e6i −0.426672 0.739018i
\(663\) 5.25735e6 + 9.10599e6i 0.464497 + 0.804532i
\(664\) 7.54422e6 1.30670e7i 0.664040 1.15015i
\(665\) 954521. 1.65328e6i 0.0837011 0.144975i
\(666\) −3.84346e6 −0.335766
\(667\) 2.73483e6 0.238021
\(668\) 1.08521e6 1.87964e6i 0.0940962 0.162979i
\(669\) 1.82112e6 3.15428e6i 0.157316 0.272480i
\(670\) 6.92194e6 + 1.19892e7i 0.595718 + 1.03181i
\(671\) −1.89904e6 3.28923e6i −0.162827 0.282025i
\(672\) −1.42515e6 −0.121741
\(673\) −9.68947e6 1.67827e7i −0.824636 1.42831i −0.902197 0.431324i \(-0.858047\pi\)
0.0775613 0.996988i \(-0.475287\pi\)
\(674\) 7.24954e6 + 1.25566e7i 0.614696 + 1.06469i
\(675\) −3.20534e6 5.55181e6i −0.270779 0.469003i
\(676\) −1.30575e6 + 2.26163e6i −0.109899 + 0.190351i
\(677\) 1.75397e7 1.47079 0.735395 0.677638i \(-0.236997\pi\)
0.735395 + 0.677638i \(0.236997\pi\)
\(678\) −9.34667e6 + 1.61889e7i −0.780877 + 1.35252i
\(679\) −501190. 868086.i −0.0417184 0.0722584i
\(680\) −2.12176e7 −1.75964
\(681\) −9.77640e6 1.69332e7i −0.807813 1.39917i
\(682\) 3.74235e6 6.48194e6i 0.308094 0.533635i
\(683\) 76409.6 132345.i 0.00626753 0.0108557i −0.862875 0.505418i \(-0.831338\pi\)
0.869142 + 0.494562i \(0.164672\pi\)
\(684\) −2.35736e6 −0.192658
\(685\) 1.31572e7 2.27889e7i 1.07136 1.85565i
\(686\) −2.60573e6 −0.211407
\(687\) −3.05208e6 −0.246720
\(688\) −420252. 5.87324e6i −0.0338485 0.473050i
\(689\) 1.20276e7 0.965230
\(690\) 7.94814e6 0.635540
\(691\) −8.17735e6 + 1.41636e7i −0.651505 + 1.12844i 0.331253 + 0.943542i \(0.392529\pi\)
−0.982758 + 0.184897i \(0.940805\pi\)
\(692\) −2.56051e6 −0.203264
\(693\) 369817. 640543.i 0.0292519 0.0506658i
\(694\) −6.26801e6 + 1.08565e7i −0.494005 + 0.855641i
\(695\) −1.12705e6 1.95210e6i −0.0885074 0.153299i
\(696\) −9.25296e6 −0.724032
\(697\) 7.09203e6 + 1.22838e7i 0.552954 + 0.957744i
\(698\) −5.91721e6 + 1.02489e7i −0.459705 + 0.796232i
\(699\) −2.79774e7 −2.16578
\(700\) −346595. + 600320.i −0.0267348 + 0.0463060i
\(701\) 5.61313e6 + 9.72223e6i 0.431430 + 0.747259i 0.996997 0.0774439i \(-0.0246759\pi\)
−0.565567 + 0.824703i \(0.691343\pi\)
\(702\) −1.74639e6 3.02483e6i −0.133751 0.231664i
\(703\) −4.13785e6 7.16697e6i −0.315781 0.546950i
\(704\) 1.00514e7 0.764353
\(705\) −2.09806e7 3.63395e7i −1.58981 2.75363i
\(706\) 511864. + 886574.i 0.0386494 + 0.0669427i
\(707\) −149328. + 258644.i −0.0112355 + 0.0194605i
\(708\) 358745. 621365.i 0.0268969 0.0465869i
\(709\) 1.11943e7 0.836334 0.418167 0.908370i \(-0.362673\pi\)
0.418167 + 0.908370i \(0.362673\pi\)
\(710\) 1.64659e7 1.22585
\(711\) 4.83710e6 8.37811e6i 0.358849 0.621544i
\(712\) 1.26902e7 2.19800e7i 0.938140 1.62491i
\(713\) −3.23781e6 5.60805e6i −0.238522 0.413131i
\(714\) −1.03822e6 1.79825e6i −0.0762158 0.132010i
\(715\) −9.35995e6 −0.684713
\(716\) −2.51636e6 4.35847e6i −0.183439 0.317725i
\(717\) 9.79424e6 + 1.69641e7i 0.711497 + 1.23235i
\(718\) 815849. + 1.41309e6i 0.0590607 + 0.102296i
\(719\) −5.86717e6 + 1.01622e7i −0.423259 + 0.733107i −0.996256 0.0864509i \(-0.972447\pi\)
0.572997 + 0.819558i \(0.305781\pi\)
\(720\) −5.50337e6 −0.395637
\(721\) 1.66179e6 2.87830e6i 0.119052 0.206205i
\(722\) −1.38367e6 2.39658e6i −0.0987846 0.171100i
\(723\) 1.44582e7 1.02865
\(724\) 533793. + 924557.i 0.0378466 + 0.0655522i
\(725\) −3.88006e6 + 6.72047e6i −0.274153 + 0.474848i
\(726\) 3.20223e6 5.54643e6i 0.225482 0.390545i
\(727\) −1.61910e7 −1.13616 −0.568079 0.822974i \(-0.692313\pi\)
−0.568079 + 0.822974i \(0.692313\pi\)
\(728\) −684784. + 1.18608e6i −0.0478879 + 0.0829442i
\(729\) −982741. −0.0684889
\(730\) 1.05766e7 0.734583
\(731\) −1.35800e7 + 9.19182e6i −0.939951 + 0.636221i
\(732\) 3.06588e6 0.211484
\(733\) −8.05149e6 −0.553499 −0.276749 0.960942i \(-0.589257\pi\)
−0.276749 + 0.960942i \(0.589257\pi\)
\(734\) −2.19401e6 + 3.80013e6i −0.150313 + 0.260350i
\(735\) 2.58227e7 1.76312
\(736\) 2.35688e6 4.08223e6i 0.160377 0.277782i
\(737\) −5.77448e6 + 1.00017e7i −0.391601 + 0.678273i
\(738\) 3.31638e6 + 5.74414e6i 0.224142 + 0.388226i
\(739\) −3.25656e6 −0.219356 −0.109678 0.993967i \(-0.534982\pi\)
−0.109678 + 0.993967i \(0.534982\pi\)
\(740\) 2.95302e6 + 5.11479e6i 0.198238 + 0.343359i
\(741\) −5.29351e6 + 9.16863e6i −0.354159 + 0.613421i
\(742\) −2.37521e6 −0.158377
\(743\) 3.71609e6 6.43646e6i 0.246953 0.427735i −0.715726 0.698381i \(-0.753904\pi\)
0.962679 + 0.270646i \(0.0872374\pi\)
\(744\) 1.09548e7 + 1.89742e7i 0.725555 + 1.25670i
\(745\) 5.65477e6 + 9.79435e6i 0.373271 + 0.646524i
\(746\) 1.08329e7 + 1.87631e7i 0.712683 + 1.23440i
\(747\) −1.08991e7 −0.714642
\(748\) −2.44053e6 4.22713e6i −0.159489 0.276243i
\(749\) 1.41001e6 + 2.44221e6i 0.0918370 + 0.159066i
\(750\) −389939. + 675393.i −0.0253130 + 0.0438433i
\(751\) 7.80320e6 1.35155e7i 0.504862 0.874447i −0.495122 0.868824i \(-0.664877\pi\)
0.999984 0.00562381i \(-0.00179012\pi\)
\(752\) 1.30196e7 0.839561
\(753\) 2.28803e7 1.47053
\(754\) −2.11400e6 + 3.66155e6i −0.135418 + 0.234551i
\(755\) 4.46265e6 7.72953e6i 0.284921 0.493498i
\(756\) −212060. 367299.i −0.0134944 0.0233730i
\(757\) 1.37363e7 + 2.37920e7i 0.871226 + 1.50901i 0.860730 + 0.509062i \(0.170008\pi\)
0.0104957 + 0.999945i \(0.496659\pi\)
\(758\) −7.80747e6 −0.493557
\(759\) 3.31528e6 + 5.74224e6i 0.208889 + 0.361807i
\(760\) −1.06818e7 1.85013e7i −0.670824 1.16190i
\(761\) 4.67913e6 + 8.10448e6i 0.292889 + 0.507299i 0.974492 0.224424i \(-0.0720500\pi\)
−0.681603 + 0.731723i \(0.738717\pi\)
\(762\) −1.10316e7 + 1.91072e7i −0.688255 + 1.19209i
\(763\) −3.53759e6 −0.219986
\(764\) −2.30014e6 + 3.98397e6i −0.142568 + 0.246935i
\(765\) 7.66322e6 + 1.32731e7i 0.473432 + 0.820008i
\(766\) 8.96399e6 0.551988
\(767\) −594437. 1.02960e6i −0.0364853 0.0631943i
\(768\) −9.83207e6 + 1.70297e7i −0.601509 + 1.04184i
\(769\) −4.85000e6 + 8.40045e6i −0.295751 + 0.512256i −0.975159 0.221505i \(-0.928903\pi\)
0.679408 + 0.733760i \(0.262236\pi\)
\(770\) 1.84841e6 0.112349
\(771\) 7.93911e6 1.37509e7i 0.480990 0.833099i
\(772\) −3.84918e6 −0.232447
\(773\)