Properties

Label 74.5.d.a.43.4
Level $74$
Weight $5$
Character 74.43
Analytic conductor $7.649$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.64937726820\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.4
Root \(3.21245i\) of defining polynomial
Character \(\chi\) \(=\) 74.43
Dual form 74.5.d.a.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +O(q^{10})\) \(q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +76.7077 q^{10} +199.490i q^{11} +33.6996 q^{12} +(-144.421 - 144.421i) q^{13} +(-139.296 + 139.296i) q^{14} +(80.7817 - 80.7817i) q^{15} -64.0000 q^{16} +(182.724 + 182.724i) q^{17} +(-126.511 + 126.511i) q^{18} +(286.750 + 286.750i) q^{19} +(-153.415 + 153.415i) q^{20} +293.388i q^{21} +(-398.981 - 398.981i) q^{22} +(522.190 + 522.190i) q^{23} +(-67.3991 + 67.3991i) q^{24} +110.508i q^{25} +577.683 q^{26} +607.668i q^{27} -557.184i q^{28} +(807.381 - 807.381i) q^{29} +323.127i q^{30} +(-14.9070 + 14.9070i) q^{31} +(128.000 - 128.000i) q^{32} -840.342 q^{33} -730.895 q^{34} +(-1335.63 - 1335.63i) q^{35} -506.042i q^{36} +(563.418 - 1247.69i) q^{37} -1147.00 q^{38} +(608.365 - 608.365i) q^{39} -613.661i q^{40} +1999.86i q^{41} +(-586.777 - 586.777i) q^{42} +(-695.357 - 695.357i) q^{43} +1595.92 q^{44} +(-1213.04 - 1213.04i) q^{45} -2088.76 q^{46} +3634.49 q^{47} -269.597i q^{48} +2449.84 q^{49} +(-221.017 - 221.017i) q^{50} +(-769.715 + 769.715i) q^{51} +(-1155.37 + 1155.37i) q^{52} -5476.01 q^{53} +(-1215.34 - 1215.34i) q^{54} +(3825.61 - 3825.61i) q^{55} +(1114.37 + 1114.37i) q^{56} +(-1207.92 + 1207.92i) q^{57} +3229.52i q^{58} +(-2654.85 - 2654.85i) q^{59} +(-646.254 - 646.254i) q^{60} +(2147.75 - 2147.75i) q^{61} -59.6280i q^{62} +4405.60 q^{63} +512.000i q^{64} +5539.09i q^{65} +(1680.68 - 1680.68i) q^{66} +3139.82i q^{67} +(1461.79 - 1461.79i) q^{68} +(-2199.70 + 2199.70i) q^{69} +5342.53 q^{70} -8727.42 q^{71} +(1012.08 + 1012.08i) q^{72} +2589.63i q^{73} +(1368.54 + 3622.21i) q^{74} -465.511 q^{75} +(2294.00 - 2294.00i) q^{76} +13894.1i q^{77} +2433.46i q^{78} +(-5000.77 - 5000.77i) q^{79} +(1227.32 + 1227.32i) q^{80} +2563.91 q^{81} +(-3999.72 - 3999.72i) q^{82} +7655.48 q^{83} +2347.11 q^{84} -7008.16i q^{85} +2781.43 q^{86} +(3401.05 + 3401.05i) q^{87} +(-3191.85 + 3191.85i) q^{88} +(1510.94 - 1510.94i) q^{89} +4852.17 q^{90} +(-10058.6 - 10058.6i) q^{91} +(4177.52 - 4177.52i) q^{92} +(-62.7950 - 62.7950i) q^{93} +(-7268.97 + 7268.97i) q^{94} -10998.0i q^{95} +(539.193 + 539.193i) q^{96} +(6903.19 + 6903.19i) q^{97} +(-4899.68 + 4899.68i) q^{98} +12618.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + O(q^{10}) \) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 + 2.00000i −0.500000 + 0.500000i
\(3\) 4.21245i 0.468050i 0.972231 + 0.234025i \(0.0751897\pi\)
−0.972231 + 0.234025i \(0.924810\pi\)
\(4\) 8.00000i 0.500000i
\(5\) −19.1769 19.1769i −0.767077 0.767077i 0.210514 0.977591i \(-0.432486\pi\)
−0.977591 + 0.210514i \(0.932486\pi\)
\(6\) −8.42489 8.42489i −0.234025 0.234025i
\(7\) 69.6480 1.42139 0.710694 0.703502i \(-0.248381\pi\)
0.710694 + 0.703502i \(0.248381\pi\)
\(8\) 16.0000 + 16.0000i 0.250000 + 0.250000i
\(9\) 63.2553 0.780930
\(10\) 76.7077 0.767077
\(11\) 199.490i 1.64868i 0.566095 + 0.824340i \(0.308454\pi\)
−0.566095 + 0.824340i \(0.691546\pi\)
\(12\) 33.6996 0.234025
\(13\) −144.421 144.421i −0.854561 0.854561i 0.136130 0.990691i \(-0.456534\pi\)
−0.990691 + 0.136130i \(0.956534\pi\)
\(14\) −139.296 + 139.296i −0.710694 + 0.710694i
\(15\) 80.7817 80.7817i 0.359030 0.359030i
\(16\) −64.0000 −0.250000
\(17\) 182.724 + 182.724i 0.632262 + 0.632262i 0.948635 0.316373i \(-0.102465\pi\)
−0.316373 + 0.948635i \(0.602465\pi\)
\(18\) −126.511 + 126.511i −0.390465 + 0.390465i
\(19\) 286.750 + 286.750i 0.794321 + 0.794321i 0.982193 0.187873i \(-0.0601592\pi\)
−0.187873 + 0.982193i \(0.560159\pi\)
\(20\) −153.415 + 153.415i −0.383538 + 0.383538i
\(21\) 293.388i 0.665280i
\(22\) −398.981 398.981i −0.824340 0.824340i
\(23\) 522.190 + 522.190i 0.987126 + 0.987126i 0.999918 0.0127919i \(-0.00407190\pi\)
−0.0127919 + 0.999918i \(0.504072\pi\)
\(24\) −67.3991 + 67.3991i −0.117012 + 0.117012i
\(25\) 110.508i 0.176813i
\(26\) 577.683 0.854561
\(27\) 607.668i 0.833563i
\(28\) 557.184i 0.710694i
\(29\) 807.381 807.381i 0.960025 0.960025i −0.0392061 0.999231i \(-0.512483\pi\)
0.999231 + 0.0392061i \(0.0124829\pi\)
\(30\) 323.127i 0.359030i
\(31\) −14.9070 + 14.9070i −0.0155120 + 0.0155120i −0.714820 0.699308i \(-0.753491\pi\)
0.699308 + 0.714820i \(0.253491\pi\)
\(32\) 128.000 128.000i 0.125000 0.125000i
\(33\) −840.342 −0.771664
\(34\) −730.895 −0.632262
\(35\) −1335.63 1335.63i −1.09031 1.09031i
\(36\) 506.042i 0.390465i
\(37\) 563.418 1247.69i 0.411554 0.911385i
\(38\) −1147.00 −0.794321
\(39\) 608.365 608.365i 0.399977 0.399977i
\(40\) 613.661i 0.383538i
\(41\) 1999.86i 1.18969i 0.803842 + 0.594843i \(0.202786\pi\)
−0.803842 + 0.594843i \(0.797214\pi\)
\(42\) −586.777 586.777i −0.332640 0.332640i
\(43\) −695.357 695.357i −0.376072 0.376072i 0.493611 0.869683i \(-0.335677\pi\)
−0.869683 + 0.493611i \(0.835677\pi\)
\(44\) 1595.92 0.824340
\(45\) −1213.04 1213.04i −0.599033 0.599033i
\(46\) −2088.76 −0.987126
\(47\) 3634.49 1.64531 0.822654 0.568542i \(-0.192492\pi\)
0.822654 + 0.568542i \(0.192492\pi\)
\(48\) 269.597i 0.117012i
\(49\) 2449.84 1.02034
\(50\) −221.017 221.017i −0.0884067 0.0884067i
\(51\) −769.715 + 769.715i −0.295930 + 0.295930i
\(52\) −1155.37 + 1155.37i −0.427281 + 0.427281i
\(53\) −5476.01 −1.94945 −0.974726 0.223404i \(-0.928283\pi\)
−0.974726 + 0.223404i \(0.928283\pi\)
\(54\) −1215.34 1215.34i −0.416782 0.416782i
\(55\) 3825.61 3825.61i 1.26466 1.26466i
\(56\) 1114.37 + 1114.37i 0.355347 + 0.355347i
\(57\) −1207.92 + 1207.92i −0.371782 + 0.371782i
\(58\) 3229.52i 0.960025i
\(59\) −2654.85 2654.85i −0.762668 0.762668i 0.214136 0.976804i \(-0.431306\pi\)
−0.976804 + 0.214136i \(0.931306\pi\)
\(60\) −646.254 646.254i −0.179515 0.179515i
\(61\) 2147.75 2147.75i 0.577198 0.577198i −0.356933 0.934130i \(-0.616177\pi\)
0.934130 + 0.356933i \(0.116177\pi\)
\(62\) 59.6280i 0.0155120i
\(63\) 4405.60 1.11000
\(64\) 512.000i 0.125000i
\(65\) 5539.09i 1.31103i
\(66\) 1680.68 1680.68i 0.385832 0.385832i
\(67\) 3139.82i 0.699447i 0.936853 + 0.349723i \(0.113724\pi\)
−0.936853 + 0.349723i \(0.886276\pi\)
\(68\) 1461.79 1461.79i 0.316131 0.316131i
\(69\) −2199.70 + 2199.70i −0.462024 + 0.462024i
\(70\) 5342.53 1.09031
\(71\) −8727.42 −1.73129 −0.865644 0.500660i \(-0.833091\pi\)
−0.865644 + 0.500660i \(0.833091\pi\)
\(72\) 1012.08 + 1012.08i 0.195232 + 0.195232i
\(73\) 2589.63i 0.485951i 0.970032 + 0.242975i \(0.0781234\pi\)
−0.970032 + 0.242975i \(0.921877\pi\)
\(74\) 1368.54 + 3622.21i 0.249916 + 0.661470i
\(75\) −465.511 −0.0827574
\(76\) 2294.00 2294.00i 0.397160 0.397160i
\(77\) 13894.1i 2.34341i
\(78\) 2433.46i 0.399977i
\(79\) −5000.77 5000.77i −0.801277 0.801277i 0.182018 0.983295i \(-0.441737\pi\)
−0.983295 + 0.182018i \(0.941737\pi\)
\(80\) 1227.32 + 1227.32i 0.191769 + 0.191769i
\(81\) 2563.91 0.390780
\(82\) −3999.72 3999.72i −0.594843 0.594843i
\(83\) 7655.48 1.11126 0.555630 0.831429i \(-0.312477\pi\)
0.555630 + 0.831429i \(0.312477\pi\)
\(84\) 2347.11 0.332640
\(85\) 7008.16i 0.969988i
\(86\) 2781.43 0.376072
\(87\) 3401.05 + 3401.05i 0.449339 + 0.449339i
\(88\) −3191.85 + 3191.85i −0.412170 + 0.412170i
\(89\) 1510.94 1510.94i 0.190751 0.190751i −0.605269 0.796021i \(-0.706935\pi\)
0.796021 + 0.605269i \(0.206935\pi\)
\(90\) 4852.17 0.599033
\(91\) −10058.6 10058.6i −1.21466 1.21466i
\(92\) 4177.52 4177.52i 0.493563 0.493563i
\(93\) −62.7950 62.7950i −0.00726037 0.00726037i
\(94\) −7268.97 + 7268.97i −0.822654 + 0.822654i
\(95\) 10998.0i 1.21861i
\(96\) 539.193 + 539.193i 0.0585062 + 0.0585062i
\(97\) 6903.19 + 6903.19i 0.733679 + 0.733679i 0.971347 0.237668i \(-0.0763829\pi\)
−0.237668 + 0.971347i \(0.576383\pi\)
\(98\) −4899.68 + 4899.68i −0.510171 + 0.510171i
\(99\) 12618.8i 1.28750i
\(100\) 884.067 0.0884067
\(101\) 4067.47i 0.398733i 0.979925 + 0.199366i \(0.0638884\pi\)
−0.979925 + 0.199366i \(0.936112\pi\)
\(102\) 3078.86i 0.295930i
\(103\) −3530.32 + 3530.32i −0.332766 + 0.332766i −0.853636 0.520870i \(-0.825608\pi\)
0.520870 + 0.853636i \(0.325608\pi\)
\(104\) 4621.47i 0.427281i
\(105\) 5626.28 5626.28i 0.510321 0.510321i
\(106\) 10952.0 10952.0i 0.974726 0.974726i
\(107\) −3980.95 −0.347711 −0.173856 0.984771i \(-0.555623\pi\)
−0.173856 + 0.984771i \(0.555623\pi\)
\(108\) 4861.34 0.416782
\(109\) −10492.1 10492.1i −0.883100 0.883100i 0.110749 0.993848i \(-0.464675\pi\)
−0.993848 + 0.110749i \(0.964675\pi\)
\(110\) 15302.4i 1.26466i
\(111\) 5255.81 + 2373.37i 0.426574 + 0.192628i
\(112\) −4457.47 −0.355347
\(113\) 3833.10 3833.10i 0.300188 0.300188i −0.540899 0.841087i \(-0.681916\pi\)
0.841087 + 0.540899i \(0.181916\pi\)
\(114\) 4831.67i 0.371782i
\(115\) 20028.0i 1.51440i
\(116\) −6459.05 6459.05i −0.480013 0.480013i
\(117\) −9135.38 9135.38i −0.667352 0.667352i
\(118\) 10619.4 0.762668
\(119\) 12726.3 + 12726.3i 0.898690 + 0.898690i
\(120\) 2585.02 0.179515
\(121\) −25155.4 −1.71815
\(122\) 8591.01i 0.577198i
\(123\) −8424.31 −0.556832
\(124\) 119.256 + 119.256i 0.00775599 + 0.00775599i
\(125\) −9866.36 + 9866.36i −0.631447 + 0.631447i
\(126\) −8811.21 + 8811.21i −0.555002 + 0.555002i
\(127\) −11767.5 −0.729584 −0.364792 0.931089i \(-0.618860\pi\)
−0.364792 + 0.931089i \(0.618860\pi\)
\(128\) −1024.00 1024.00i −0.0625000 0.0625000i
\(129\) 2929.15 2929.15i 0.176020 0.176020i
\(130\) −11078.2 11078.2i −0.655514 0.655514i
\(131\) 3889.24 3889.24i 0.226633 0.226633i −0.584652 0.811284i \(-0.698769\pi\)
0.811284 + 0.584652i \(0.198769\pi\)
\(132\) 6722.74i 0.385832i
\(133\) 19971.5 + 19971.5i 1.12904 + 1.12904i
\(134\) −6279.63 6279.63i −0.349723 0.349723i
\(135\) 11653.2 11653.2i 0.639407 0.639407i
\(136\) 5847.16i 0.316131i
\(137\) −4011.56 −0.213733 −0.106867 0.994273i \(-0.534082\pi\)
−0.106867 + 0.994273i \(0.534082\pi\)
\(138\) 8798.79i 0.462024i
\(139\) 12804.1i 0.662703i −0.943507 0.331352i \(-0.892495\pi\)
0.943507 0.331352i \(-0.107505\pi\)
\(140\) −10685.1 + 10685.1i −0.545156 + 0.545156i
\(141\) 15310.1i 0.770086i
\(142\) 17454.8 17454.8i 0.865644 0.865644i
\(143\) 28810.6 28810.6i 1.40890 1.40890i
\(144\) −4048.34 −0.195232
\(145\) −30966.2 −1.47283
\(146\) −5179.26 5179.26i −0.242975 0.242975i
\(147\) 10319.8i 0.477570i
\(148\) −9981.49 4507.34i −0.455693 0.205777i
\(149\) −10327.6 −0.465188 −0.232594 0.972574i \(-0.574721\pi\)
−0.232594 + 0.972574i \(0.574721\pi\)
\(150\) 931.021 931.021i 0.0413787 0.0413787i
\(151\) 3098.02i 0.135872i −0.997690 0.0679361i \(-0.978359\pi\)
0.997690 0.0679361i \(-0.0216414\pi\)
\(152\) 9175.99i 0.397160i
\(153\) 11558.3 + 11558.3i 0.493752 + 0.493752i
\(154\) −27788.2 27788.2i −1.17171 1.17171i
\(155\) 571.741 0.0237977
\(156\) −4866.92 4866.92i −0.199989 0.199989i
\(157\) 25876.9 1.04982 0.524908 0.851159i \(-0.324100\pi\)
0.524908 + 0.851159i \(0.324100\pi\)
\(158\) 20003.1 0.801277
\(159\) 23067.4i 0.912440i
\(160\) −4909.29 −0.191769
\(161\) 36369.5 + 36369.5i 1.40309 + 1.40309i
\(162\) −5127.82 + 5127.82i −0.195390 + 0.195390i
\(163\) 25137.3 25137.3i 0.946113 0.946113i −0.0525075 0.998621i \(-0.516721\pi\)
0.998621 + 0.0525075i \(0.0167214\pi\)
\(164\) 15998.9 0.594843
\(165\) 16115.2 + 16115.2i 0.591926 + 0.591926i
\(166\) −15311.0 + 15311.0i −0.555630 + 0.555630i
\(167\) −14868.5 14868.5i −0.533133 0.533133i 0.388370 0.921503i \(-0.373038\pi\)
−0.921503 + 0.388370i \(0.873038\pi\)
\(168\) −4694.21 + 4694.21i −0.166320 + 0.166320i
\(169\) 13153.8i 0.460550i
\(170\) 14016.3 + 14016.3i 0.484994 + 0.484994i
\(171\) 18138.4 + 18138.4i 0.620308 + 0.620308i
\(172\) −5562.86 + 5562.86i −0.188036 + 0.188036i
\(173\) 16482.6i 0.550722i −0.961341 0.275361i \(-0.911203\pi\)
0.961341 0.275361i \(-0.0887974\pi\)
\(174\) −13604.2 −0.449339
\(175\) 7696.68i 0.251320i
\(176\) 12767.4i 0.412170i
\(177\) 11183.4 11183.4i 0.356966 0.356966i
\(178\) 6043.77i 0.190751i
\(179\) −26077.6 + 26077.6i −0.813883 + 0.813883i −0.985214 0.171331i \(-0.945193\pi\)
0.171331 + 0.985214i \(0.445193\pi\)
\(180\) −9704.33 + 9704.33i −0.299516 + 0.299516i
\(181\) 22685.0 0.692440 0.346220 0.938153i \(-0.387465\pi\)
0.346220 + 0.938153i \(0.387465\pi\)
\(182\) 40234.5 1.21466
\(183\) 9047.29 + 9047.29i 0.270157 + 0.270157i
\(184\) 16710.1i 0.493563i
\(185\) −34731.4 + 13122.2i −1.01480 + 0.383409i
\(186\) 251.180 0.00726037
\(187\) −36451.6 + 36451.6i −1.04240 + 1.04240i
\(188\) 29075.9i 0.822654i
\(189\) 42322.8i 1.18482i
\(190\) 21995.9 + 21995.9i 0.609305 + 0.609305i
\(191\) 12997.0 + 12997.0i 0.356267 + 0.356267i 0.862435 0.506168i \(-0.168938\pi\)
−0.506168 + 0.862435i \(0.668938\pi\)
\(192\) −2156.77 −0.0585062
\(193\) 658.999 + 658.999i 0.0176917 + 0.0176917i 0.715897 0.698206i \(-0.246018\pi\)
−0.698206 + 0.715897i \(0.746018\pi\)
\(194\) −27612.7 −0.733679
\(195\) −23333.1 −0.613626
\(196\) 19598.7i 0.510171i
\(197\) −18678.2 −0.481286 −0.240643 0.970614i \(-0.577358\pi\)
−0.240643 + 0.970614i \(0.577358\pi\)
\(198\) −25237.6 25237.6i −0.643752 0.643752i
\(199\) −220.974 + 220.974i −0.00558002 + 0.00558002i −0.709891 0.704311i \(-0.751256\pi\)
0.704311 + 0.709891i \(0.251256\pi\)
\(200\) −1768.13 + 1768.13i −0.0442033 + 0.0442033i
\(201\) −13226.3 −0.327376
\(202\) −8134.95 8134.95i −0.199366 0.199366i
\(203\) 56232.5 56232.5i 1.36457 1.36457i
\(204\) 6157.72 + 6157.72i 0.147965 + 0.147965i
\(205\) 38351.2 38351.2i 0.912580 0.912580i
\(206\) 14121.3i 0.332766i
\(207\) 33031.3 + 33031.3i 0.770876 + 0.770876i
\(208\) 9242.93 + 9242.93i 0.213640 + 0.213640i
\(209\) −57203.8 + 57203.8i −1.30958 + 1.30958i
\(210\) 22505.1i 0.510321i
\(211\) −11470.3 −0.257639 −0.128819 0.991668i \(-0.541119\pi\)
−0.128819 + 0.991668i \(0.541119\pi\)
\(212\) 43808.1i 0.974726i
\(213\) 36763.8i 0.810329i
\(214\) 7961.89 7961.89i 0.173856 0.173856i
\(215\) 26669.6i 0.576952i
\(216\) −9722.68 + 9722.68i −0.208391 + 0.208391i
\(217\) −1038.24 + 1038.24i −0.0220485 + 0.0220485i
\(218\) 41968.4 0.883100
\(219\) −10908.7 −0.227449
\(220\) −30604.9 30604.9i −0.632332 0.632332i
\(221\) 52778.3i 1.08061i
\(222\) −15258.4 + 5764.89i −0.309601 + 0.116973i
\(223\) 62440.7 1.25562 0.627809 0.778367i \(-0.283952\pi\)
0.627809 + 0.778367i \(0.283952\pi\)
\(224\) 8914.94 8914.94i 0.177673 0.177673i
\(225\) 6990.24i 0.138079i
\(226\) 15332.4i 0.300188i
\(227\) 3157.08 + 3157.08i 0.0612680 + 0.0612680i 0.737077 0.675809i \(-0.236206\pi\)
−0.675809 + 0.737077i \(0.736206\pi\)
\(228\) 9663.35 + 9663.35i 0.185891 + 0.185891i
\(229\) 23594.7 0.449929 0.224965 0.974367i \(-0.427773\pi\)
0.224965 + 0.974367i \(0.427773\pi\)
\(230\) 40056.0 + 40056.0i 0.757202 + 0.757202i
\(231\) −58528.1 −1.09683
\(232\) 25836.2 0.480013
\(233\) 66323.8i 1.22168i −0.791754 0.610840i \(-0.790832\pi\)
0.791754 0.610840i \(-0.209168\pi\)
\(234\) 36541.5 0.667352
\(235\) −69698.2 69698.2i −1.26208 1.26208i
\(236\) −21238.8 + 21238.8i −0.381334 + 0.381334i
\(237\) 21065.5 21065.5i 0.375038 0.375038i
\(238\) −50905.4 −0.898690
\(239\) −60579.6 60579.6i −1.06055 1.06055i −0.998045 0.0625039i \(-0.980091\pi\)
−0.0625039 0.998045i \(-0.519909\pi\)
\(240\) −5170.03 + 5170.03i −0.0897575 + 0.0897575i
\(241\) −35030.0 35030.0i −0.603124 0.603124i 0.338016 0.941140i \(-0.390244\pi\)
−0.941140 + 0.338016i \(0.890244\pi\)
\(242\) 50310.8 50310.8i 0.859074 0.859074i
\(243\) 60021.4i 1.01647i
\(244\) −17182.0 17182.0i −0.288599 0.288599i
\(245\) −46980.4 46980.4i −0.782680 0.782680i
\(246\) 16848.6 16848.6i 0.278416 0.278416i
\(247\) 82825.3i 1.35759i
\(248\) −477.024 −0.00775599
\(249\) 32248.3i 0.520125i
\(250\) 39465.5i 0.631447i
\(251\) −626.235 + 626.235i −0.00994008 + 0.00994008i −0.712059 0.702119i \(-0.752237\pi\)
0.702119 + 0.712059i \(0.252237\pi\)
\(252\) 35244.8i 0.555002i
\(253\) −104172. + 104172.i −1.62746 + 1.62746i
\(254\) 23534.9 23534.9i 0.364792 0.364792i
\(255\) 29521.5 0.454002
\(256\) 4096.00 0.0625000
\(257\) −81648.3 81648.3i −1.23618 1.23618i −0.961551 0.274627i \(-0.911446\pi\)
−0.274627 0.961551i \(-0.588554\pi\)
\(258\) 11716.6i 0.176020i
\(259\) 39240.9 86898.8i 0.584978 1.29543i
\(260\) 44312.7 0.655514
\(261\) 51071.1 51071.1i 0.749712 0.749712i
\(262\) 15557.0i 0.226633i
\(263\) 101344.i 1.46516i 0.680682 + 0.732579i \(0.261684\pi\)
−0.680682 + 0.732579i \(0.738316\pi\)
\(264\) −13445.5 13445.5i −0.192916 0.192916i
\(265\) 105013. + 105013.i 1.49538 + 1.49538i
\(266\) −79886.2 −1.12904
\(267\) 6364.76 + 6364.76i 0.0892811 + 0.0892811i
\(268\) 25118.5 0.349723
\(269\) −57952.5 −0.800880 −0.400440 0.916323i \(-0.631143\pi\)
−0.400440 + 0.916323i \(0.631143\pi\)
\(270\) 46612.8i 0.639407i
\(271\) −20499.4 −0.279127 −0.139563 0.990213i \(-0.544570\pi\)
−0.139563 + 0.990213i \(0.544570\pi\)
\(272\) −11694.3 11694.3i −0.158066 0.158066i
\(273\) 42371.4 42371.4i 0.568522 0.568522i
\(274\) 8023.12 8023.12i 0.106867 0.106867i
\(275\) −22045.3 −0.291509
\(276\) 17597.6 + 17597.6i 0.231012 + 0.231012i
\(277\) −28228.9 + 28228.9i −0.367904 + 0.367904i −0.866712 0.498808i \(-0.833771\pi\)
0.498808 + 0.866712i \(0.333771\pi\)
\(278\) 25608.2 + 25608.2i 0.331352 + 0.331352i
\(279\) −942.947 + 942.947i −0.0121138 + 0.0121138i
\(280\) 42740.3i 0.545156i
\(281\) 19823.4 + 19823.4i 0.251053 + 0.251053i 0.821402 0.570349i \(-0.193192\pi\)
−0.570349 + 0.821402i \(0.693192\pi\)
\(282\) −30620.2 30620.2i −0.385043 0.385043i
\(283\) 2415.84 2415.84i 0.0301645 0.0301645i −0.691864 0.722028i \(-0.743210\pi\)
0.722028 + 0.691864i \(0.243210\pi\)
\(284\) 69819.4i 0.865644i
\(285\) 46328.3 0.570370
\(286\) 115242.i 1.40890i
\(287\) 139286.i 1.69100i
\(288\) 8096.68 8096.68i 0.0976162 0.0976162i
\(289\) 16745.0i 0.200488i
\(290\) 61932.3 61932.3i 0.736413 0.736413i
\(291\) −29079.3 + 29079.3i −0.343398 + 0.343398i
\(292\) 20717.0 0.242975
\(293\) 155148. 1.80722 0.903610 0.428357i \(-0.140907\pi\)
0.903610 + 0.428357i \(0.140907\pi\)
\(294\) −20639.6 20639.6i −0.238785 0.238785i
\(295\) 101824.i 1.17005i
\(296\) 28977.7 10948.3i 0.330735 0.124958i
\(297\) −121224. −1.37428
\(298\) 20655.3 20655.3i 0.232594 0.232594i
\(299\) 150830.i 1.68712i
\(300\) 3724.08i 0.0413787i
\(301\) −48430.2 48430.2i −0.534544 0.534544i
\(302\) 6196.05 + 6196.05i 0.0679361 + 0.0679361i
\(303\) −17134.0 −0.186627
\(304\) −18352.0 18352.0i −0.198580 0.198580i
\(305\) −82374.5 −0.885510
\(306\) −46233.0 −0.493752
\(307\) 80298.9i 0.851987i 0.904726 + 0.425994i \(0.140075\pi\)
−0.904726 + 0.425994i \(0.859925\pi\)
\(308\) 111153. 1.17171
\(309\) −14871.3 14871.3i −0.155751 0.155751i
\(310\) −1143.48 + 1143.48i −0.0118989 + 0.0118989i
\(311\) −78560.0 + 78560.0i −0.812233 + 0.812233i −0.984968 0.172735i \(-0.944739\pi\)
0.172735 + 0.984968i \(0.444739\pi\)
\(312\) 19467.7 0.199989
\(313\) 43754.1 + 43754.1i 0.446611 + 0.446611i 0.894226 0.447615i \(-0.147726\pi\)
−0.447615 + 0.894226i \(0.647726\pi\)
\(314\) −51753.9 + 51753.9i −0.524908 + 0.524908i
\(315\) −84485.9 84485.9i −0.851458 0.851458i
\(316\) −40006.2 + 40006.2i −0.400639 + 0.400639i
\(317\) 49960.2i 0.497171i 0.968610 + 0.248585i \(0.0799656\pi\)
−0.968610 + 0.248585i \(0.920034\pi\)
\(318\) 46134.8 + 46134.8i 0.456220 + 0.456220i
\(319\) 161065. + 161065.i 1.58277 + 1.58277i
\(320\) 9818.58 9818.58i 0.0958846 0.0958846i
\(321\) 16769.5i 0.162746i
\(322\) −145478. −1.40309
\(323\) 104792.i 1.00444i
\(324\) 20511.3i 0.195390i
\(325\) 15959.7 15959.7i 0.151098 0.151098i
\(326\) 100549.i 0.946113i
\(327\) 44197.5 44197.5i 0.413335 0.413335i
\(328\) −31997.8 + 31997.8i −0.297421 + 0.297421i
\(329\) 253135. 2.33862
\(330\) −64460.7 −0.591926
\(331\) 64683.8 + 64683.8i 0.590390 + 0.590390i 0.937737 0.347347i \(-0.112917\pi\)
−0.347347 + 0.937737i \(0.612917\pi\)
\(332\) 61243.8i 0.555630i
\(333\) 35639.1 78922.8i 0.321395 0.711728i
\(334\) 59474.2 0.533133
\(335\) 60212.0 60212.0i 0.536529 0.536529i
\(336\) 18776.9i 0.166320i
\(337\) 170793.i 1.50387i −0.659235 0.751937i \(-0.729120\pi\)
0.659235 0.751937i \(-0.270880\pi\)
\(338\) −26307.5 26307.5i −0.230275 0.230275i
\(339\) 16146.7 + 16146.7i 0.140503 + 0.140503i
\(340\) −56065.3 −0.484994
\(341\) −2973.80 2973.80i −0.0255743 0.0255743i
\(342\) −72553.8 −0.620308
\(343\) 3401.58 0.0289130
\(344\) 22251.4i 0.188036i
\(345\) 84366.8 0.708816
\(346\) 32965.1 + 32965.1i 0.275361 + 0.275361i
\(347\) −50001.2 + 50001.2i −0.415261 + 0.415261i −0.883567 0.468305i \(-0.844865\pi\)
0.468305 + 0.883567i \(0.344865\pi\)
\(348\) 27208.4 27208.4i 0.224670 0.224670i
\(349\) −24999.4 −0.205248 −0.102624 0.994720i \(-0.532724\pi\)
−0.102624 + 0.994720i \(0.532724\pi\)
\(350\) −15393.4 15393.4i −0.125660 0.125660i
\(351\) 87759.9 87759.9i 0.712331 0.712331i
\(352\) 25534.8 + 25534.8i 0.206085 + 0.206085i
\(353\) 116533. 116533.i 0.935187 0.935187i −0.0628372 0.998024i \(-0.520015\pi\)
0.998024 + 0.0628372i \(0.0200149\pi\)
\(354\) 44733.6i 0.356966i
\(355\) 167365. + 167365.i 1.32803 + 1.32803i
\(356\) −12087.5 12087.5i −0.0953757 0.0953757i
\(357\) −53609.1 + 53609.1i −0.420631 + 0.420631i
\(358\) 104310.i 0.813883i
\(359\) −60037.0 −0.465833 −0.232917 0.972497i \(-0.574827\pi\)
−0.232917 + 0.972497i \(0.574827\pi\)
\(360\) 38817.3i 0.299516i
\(361\) 34129.9i 0.261891i
\(362\) −45370.1 + 45370.1i −0.346220 + 0.346220i
\(363\) 105966.i 0.804178i
\(364\) −80468.9 + 80468.9i −0.607331 + 0.607331i
\(365\) 49661.1 49661.1i 0.372761 0.372761i
\(366\) −36189.2 −0.270157
\(367\) 21.3647 0.000158622 7.93112e−5 1.00000i \(-0.499975\pi\)
7.93112e−5 1.00000i \(0.499975\pi\)
\(368\) −33420.1 33420.1i −0.246782 0.246782i
\(369\) 126502.i 0.929061i
\(370\) 43218.4 95707.1i 0.315694 0.699102i
\(371\) −381393. −2.77093
\(372\) −502.360 + 502.360i −0.00363019 + 0.00363019i
\(373\) 98144.9i 0.705424i 0.935732 + 0.352712i \(0.114740\pi\)
−0.935732 + 0.352712i \(0.885260\pi\)
\(374\) 145807.i 1.04240i
\(375\) −41561.5 41561.5i −0.295549 0.295549i
\(376\) 58151.8 + 58151.8i 0.411327 + 0.411327i
\(377\) −233205. −1.64080
\(378\) −84645.6 84645.6i −0.592408 0.592408i
\(379\) −74487.3 −0.518565 −0.259283 0.965801i \(-0.583486\pi\)
−0.259283 + 0.965801i \(0.583486\pi\)
\(380\) −87983.6 −0.609305
\(381\) 49569.8i 0.341482i
\(382\) −51987.9 −0.356267
\(383\) −55770.1 55770.1i −0.380192 0.380192i 0.490979 0.871171i \(-0.336639\pi\)
−0.871171 + 0.490979i \(0.836639\pi\)
\(384\) 4313.55 4313.55i 0.0292531 0.0292531i
\(385\) 266446. 266446.i 1.79758 1.79758i
\(386\) −2636.00 −0.0176917
\(387\) −43985.0 43985.0i −0.293686 0.293686i
\(388\) 55225.5 55225.5i 0.366839 0.366839i
\(389\) −7558.69 7558.69i −0.0499514 0.0499514i 0.681690 0.731641i \(-0.261245\pi\)
−0.731641 + 0.681690i \(0.761245\pi\)
\(390\) 46666.3 46666.3i 0.306813 0.306813i
\(391\) 190833.i 1.24825i
\(392\) 39197.4 + 39197.4i 0.255085 + 0.255085i
\(393\) 16383.2 + 16383.2i 0.106075 + 0.106075i
\(394\) 37356.5 37356.5i 0.240643 0.240643i
\(395\) 191799.i 1.22928i
\(396\) 100951. 0.643752
\(397\) 161347.i 1.02371i −0.859070 0.511857i \(-0.828958\pi\)
0.859070 0.511857i \(-0.171042\pi\)
\(398\) 883.898i 0.00558002i
\(399\) −84129.0 + 84129.0i −0.528445 + 0.528445i
\(400\) 7072.53i 0.0442033i
\(401\) 45498.0 45498.0i 0.282946 0.282946i −0.551337 0.834283i \(-0.685882\pi\)
0.834283 + 0.551337i \(0.185882\pi\)
\(402\) 26452.6 26452.6i 0.163688 0.163688i
\(403\) 4305.77 0.0265119
\(404\) 32539.8 0.199366
\(405\) −49167.9 49167.9i −0.299759 0.299759i
\(406\) 224930.i 1.36457i
\(407\) 248901. + 112396.i 1.50258 + 0.678521i
\(408\) −24630.9 −0.147965
\(409\) −66276.5 + 66276.5i −0.396199 + 0.396199i −0.876890 0.480691i \(-0.840386\pi\)
0.480691 + 0.876890i \(0.340386\pi\)
\(410\) 153405.i 0.912580i
\(411\) 16898.5i 0.100038i
\(412\) 28242.6 + 28242.6i 0.166383 + 0.166383i
\(413\) −184905. 184905.i −1.08405 1.08405i
\(414\) −132125. −0.770876
\(415\) −146808. 146808.i −0.852422 0.852422i
\(416\) −36971.7 −0.213640
\(417\) 53936.5 0.310178
\(418\) 228815.i 1.30958i
\(419\) −214467. −1.22161 −0.610804 0.791782i \(-0.709154\pi\)
−0.610804 + 0.791782i \(0.709154\pi\)
\(420\) −45010.3 45010.3i −0.255160 0.255160i
\(421\) −198155. + 198155.i −1.11800 + 1.11800i −0.125962 + 0.992035i \(0.540202\pi\)
−0.992035 + 0.125962i \(0.959798\pi\)
\(422\) 22940.7 22940.7i 0.128819 0.128819i
\(423\) 229900. 1.28487
\(424\) −87616.2 87616.2i −0.487363 0.487363i
\(425\) −20192.5 + 20192.5i −0.111792 + 0.111792i
\(426\) 73527.6 + 73527.6i 0.405164 + 0.405164i
\(427\) 149587. 149587.i 0.820421 0.820421i
\(428\) 31847.6i 0.173856i
\(429\) 121363. + 121363.i 0.659434 + 0.659434i
\(430\) −53339.2 53339.2i −0.288476 0.288476i
\(431\) 175370. 175370.i 0.944061 0.944061i −0.0544557 0.998516i \(-0.517342\pi\)
0.998516 + 0.0544557i \(0.0173424\pi\)
\(432\) 38890.7i 0.208391i
\(433\) 249227. 1.32929 0.664645 0.747159i \(-0.268583\pi\)
0.664645 + 0.747159i \(0.268583\pi\)
\(434\) 4152.97i 0.0220485i
\(435\) 130443.i 0.689356i
\(436\) −83936.9 + 83936.9i −0.441550 + 0.441550i
\(437\) 299476.i 1.56819i
\(438\) 21817.4 21817.4i 0.113725 0.113725i
\(439\) 198606. 198606.i 1.03054 1.03054i 0.0310166 0.999519i \(-0.490126\pi\)
0.999519 0.0310166i \(-0.00987446\pi\)
\(440\) 122420. 0.632332
\(441\) 154965. 0.796815
\(442\) 105557. + 105557.i 0.540307 + 0.540307i
\(443\) 167529.i 0.853657i −0.904333 0.426828i \(-0.859631\pi\)
0.904333 0.426828i \(-0.140369\pi\)
\(444\) 18986.9 42046.5i 0.0963139 0.213287i
\(445\) −57950.4 −0.292642
\(446\) −124881. + 124881.i −0.627809 + 0.627809i
\(447\) 43504.6i 0.217731i
\(448\) 35659.8i 0.177673i
\(449\) −229629. 229629.i −1.13903 1.13903i −0.988625 0.150403i \(-0.951943\pi\)
−0.150403 0.988625i \(-0.548057\pi\)
\(450\) −13980.5 13980.5i −0.0690394 0.0690394i
\(451\) −398953. −1.96141
\(452\) −30664.8 30664.8i −0.150094 0.150094i
\(453\) 13050.3 0.0635950
\(454\) −12628.3 −0.0612680
\(455\) 385787.i 1.86348i
\(456\) −38653.4 −0.185891
\(457\) 82109.9 + 82109.9i 0.393154 + 0.393154i 0.875810 0.482656i \(-0.160328\pi\)
−0.482656 + 0.875810i \(0.660328\pi\)
\(458\) −47189.5 + 47189.5i −0.224965 + 0.224965i
\(459\) −111035. + 111035.i −0.527031 + 0.527031i
\(460\) −160224. −0.757202
\(461\) −16255.6 16255.6i −0.0764893 0.0764893i 0.667827 0.744316i \(-0.267225\pi\)
−0.744316 + 0.667827i \(0.767225\pi\)
\(462\) 117056. 117056.i 0.548417 0.548417i
\(463\) −20732.0 20732.0i −0.0967119 0.0967119i 0.657095 0.753807i \(-0.271785\pi\)
−0.753807 + 0.657095i \(0.771785\pi\)
\(464\) −51672.4 + 51672.4i −0.240006 + 0.240006i
\(465\) 2408.43i 0.0111385i
\(466\) 132648. + 132648.i 0.610840 + 0.610840i
\(467\) −5055.37 5055.37i −0.0231803 0.0231803i 0.695422 0.718602i \(-0.255218\pi\)
−0.718602 + 0.695422i \(0.755218\pi\)
\(468\) −73083.1 + 73083.1i −0.333676 + 0.333676i
\(469\) 218682.i 0.994184i
\(470\) 278793. 1.26208
\(471\) 109005.i 0.491366i
\(472\) 84955.1i 0.381334i
\(473\) 138717. 138717.i 0.620022 0.620022i
\(474\) 84261.9i 0.375038i
\(475\) −31688.2 + 31688.2i −0.140447 + 0.140447i
\(476\) 101811. 101811.i 0.449345 0.449345i
\(477\) −346387. −1.52238
\(478\) 242318. 1.06055
\(479\) −206623. 206623.i −0.900552 0.900552i 0.0949321 0.995484i \(-0.469737\pi\)
−0.995484 + 0.0949321i \(0.969737\pi\)
\(480\) 20680.1i 0.0897575i
\(481\) −261561. + 98822.7i −1.13053 + 0.427136i
\(482\) 140120. 0.603124
\(483\) −153204. + 153204.i −0.656715 + 0.656715i
\(484\) 201243.i 0.859074i
\(485\) 264764.i 1.12558i
\(486\) −120043. 120043.i −0.508234 0.508234i
\(487\) 237079. + 237079.i 0.999621 + 0.999621i 1.00000 0.000378852i \(-0.000120592\pi\)
−0.000378852 1.00000i \(0.500121\pi\)
\(488\) 68728.1 0.288599
\(489\) 105889. + 105889.i 0.442828 + 0.442828i
\(490\) 187921. 0.782680
\(491\) 194287. 0.805901 0.402950 0.915222i \(-0.367985\pi\)
0.402950 + 0.915222i \(0.367985\pi\)
\(492\) 67394.5i 0.278416i
\(493\) 295056. 1.21398
\(494\) 165651. + 165651.i 0.678796 + 0.678796i
\(495\) 241990. 241990.i 0.987614 0.987614i
\(496\) 954.049 954.049i 0.00387799 0.00387799i
\(497\) −607847. −2.46083
\(498\) −64496.6 64496.6i −0.260063 0.260063i
\(499\) 120495. 120495.i 0.483913 0.483913i −0.422466 0.906379i \(-0.638835\pi\)
0.906379 + 0.422466i \(0.138835\pi\)
\(500\) 78930.9 + 78930.9i 0.315724 + 0.315724i
\(501\) 62632.9 62632.9i 0.249533 0.249533i
\(502\) 2504.94i 0.00994008i
\(503\) 50836.2 + 50836.2i 0.200926 + 0.200926i 0.800397 0.599471i \(-0.204622\pi\)
−0.599471 + 0.800397i \(0.704622\pi\)
\(504\) 70489.6 + 70489.6i 0.277501 + 0.277501i
\(505\) 78001.6 78001.6i 0.305859 0.305859i
\(506\) 416687.i 1.62746i
\(507\) −55409.5 −0.215560
\(508\) 94139.7i 0.364792i
\(509\) 398680.i 1.53882i −0.638754 0.769411i \(-0.720550\pi\)
0.638754 0.769411i \(-0.279450\pi\)
\(510\) −59043.0 + 59043.0i −0.227001 + 0.227001i
\(511\) 180363.i 0.690724i
\(512\) −8192.00 + 8192.00i −0.0312500 + 0.0312500i
\(513\) −174249. + 174249.i −0.662117 + 0.662117i
\(514\) 326593. 1.23618
\(515\) 135401. 0.510515
\(516\) −23433.2 23433.2i −0.0880102 0.0880102i
\(517\) 725045.i 2.71259i
\(518\) 95315.9 + 252279.i 0.355227 + 0.940205i
\(519\) 69431.9 0.257765
\(520\) −88625.5 + 88625.5i −0.327757 + 0.327757i
\(521\) 231023.i 0.851099i −0.904935 0.425549i \(-0.860081\pi\)
0.904935 0.425549i \(-0.139919\pi\)
\(522\) 204284.i 0.749712i
\(523\) 110607. + 110607.i 0.404370 + 0.404370i 0.879770 0.475400i \(-0.157697\pi\)
−0.475400 + 0.879770i \(0.657697\pi\)
\(524\) −31113.9 31113.9i −0.113316 0.113316i
\(525\) −32421.9 −0.117630
\(526\) −202687. 202687.i −0.732579 0.732579i
\(527\) −5447.73 −0.0196153
\(528\) 53781.9 0.192916
\(529\) 265523.i 0.948837i
\(530\) −420052. −1.49538
\(531\) −167933. 167933.i −0.595590 0.595590i
\(532\) 159772. 159772.i 0.564519 0.564519i
\(533\) 288822. 288822.i 1.01666 1.01666i
\(534\) −25459.0 −0.0892811
\(535\) 76342.3 + 76342.3i 0.266721 + 0.266721i
\(536\) −50237.1 + 50237.1i −0.174862 + 0.174862i
\(537\) −109851. 109851.i −0.380937 0.380937i
\(538\) 115905. 115905.i 0.400440 0.400440i
\(539\) 488719.i 1.68222i
\(540\) −93225.6 93225.6i −0.319704 0.319704i
\(541\) −66024.0 66024.0i −0.225583 0.225583i 0.585261 0.810845i \(-0.300992\pi\)
−0.810845 + 0.585261i \(0.800992\pi\)
\(542\) 40998.7 40998.7i 0.139563 0.139563i
\(543\) 95559.5i 0.324097i
\(544\) 46777.3 0.158066
\(545\) 402413.i 1.35481i
\(546\) 169486.i 0.568522i
\(547\) −272800. + 272800.i −0.911737 + 0.911737i −0.996409 0.0846714i \(-0.973016\pi\)
0.0846714 + 0.996409i \(0.473016\pi\)
\(548\) 32092.5i 0.106867i
\(549\) 135857. 135857.i 0.450751 0.450751i
\(550\) 44090.7 44090.7i 0.145754 0.145754i
\(551\) 463033. 1.52514
\(552\) −70390.3 −0.231012
\(553\) −348294. 348294.i −1.13893 1.13893i
\(554\) 112916.i 0.367904i
\(555\) −55276.4 146304.i −0.179454 0.474975i
\(556\) −102433. −0.331352
\(557\) 391170. 391170.i 1.26082 1.26082i 0.310131 0.950694i \(-0.399627\pi\)
0.950694 0.310131i \(-0.100373\pi\)
\(558\) 3771.79i 0.0121138i
\(559\) 200848.i 0.642753i
\(560\) 85480.5 + 85480.5i 0.272578 + 0.272578i
\(561\) −153551. 153551.i −0.487894 0.487894i
\(562\) −79293.5 −0.251053
\(563\) −208350. 208350.i −0.657319 0.657319i 0.297426 0.954745i \(-0.403872\pi\)
−0.954745 + 0.297426i \(0.903872\pi\)
\(564\) 122481. 0.385043
\(565\) −147014. −0.460534
\(566\) 9663.38i 0.0301645i
\(567\) 178571. 0.555450
\(568\) −139639. 139639.i −0.432822 0.432822i
\(569\) −245827. + 245827.i −0.759287 + 0.759287i −0.976193 0.216906i \(-0.930404\pi\)
0.216906 + 0.976193i \(0.430404\pi\)
\(570\) −92656.6 + 92656.6i −0.285185 + 0.285185i
\(571\) −579445. −1.77722 −0.888608 0.458668i \(-0.848327\pi\)
−0.888608 + 0.458668i \(0.848327\pi\)
\(572\) −230484. 230484.i −0.704449 0.704449i
\(573\) −54749.1 + 54749.1i −0.166751 + 0.166751i
\(574\) −278573. 278573.i −0.845502 0.845502i
\(575\) −57706.3 + 57706.3i −0.174537 + 0.174537i
\(576\) 32386.7i 0.0976162i
\(577\) −221758. 221758.i −0.666082 0.666082i 0.290725 0.956807i \(-0.406104\pi\)
−0.956807 + 0.290725i \(0.906104\pi\)
\(578\) 33490.0 + 33490.0i 0.100244 + 0.100244i
\(579\) −2776.00 + 2776.00i −0.00828060 + 0.00828060i
\(580\) 247729.i 0.736413i
\(581\) 533188. 1.57953
\(582\) 116317.i 0.343398i
\(583\) 1.09241e6i 3.21402i
\(584\) −41434.1 + 41434.1i −0.121488 + 0.121488i
\(585\) 350377.i 1.02382i
\(586\) −310296. + 310296.i −0.903610 + 0.903610i
\(587\) −34541.0 + 34541.0i −0.100244 + 0.100244i −0.755450 0.655206i \(-0.772582\pi\)
0.655206 + 0.755450i \(0.272582\pi\)
\(588\) 82558.6 0.238785
\(589\) −8549.16 −0.0246430
\(590\) −203647. 203647.i −0.585025 0.585025i
\(591\) 78681.1i 0.225266i
\(592\) −36058.7 + 79851.9i −0.102889 + 0.227846i
\(593\) −162820. −0.463019 −0.231509 0.972833i \(-0.574366\pi\)
−0.231509 + 0.972833i \(0.574366\pi\)
\(594\) 242448. 242448.i 0.687140 0.687140i
\(595\) 488104.i 1.37873i
\(596\) 82621.1i 0.232594i
\(597\) −930.843 930.843i −0.00261173 0.00261173i
\(598\) 301660. + 301660.i 0.843560 + 0.843560i
\(599\) 236840. 0.660086 0.330043 0.943966i \(-0.392937\pi\)
0.330043 + 0.943966i \(0.392937\pi\)
\(600\) −7448.17 7448.17i −0.0206894 0.0206894i
\(601\) 232467. 0.643595 0.321797 0.946809i \(-0.395713\pi\)
0.321797 + 0.946809i \(0.395713\pi\)
\(602\) 193721. 0.534544
\(603\) 198610.i 0.546219i
\(604\) −24784.2 −0.0679361
\(605\) 482403. + 482403.i 1.31795 + 1.31795i
\(606\) 34268.0 34268.0i 0.0933134 0.0933134i
\(607\) 28031.0 28031.0i 0.0760785 0.0760785i −0.668044 0.744122i \(-0.732868\pi\)
0.744122 + 0.668044i \(0.232868\pi\)
\(608\) 73407.9 0.198580
\(609\) 236876. + 236876.i 0.638685 + 0.638685i
\(610\) 164749. 164749.i 0.442755 0.442755i
\(611\) −524895. 524895.i −1.40602 1.40602i
\(612\) 92466.0 92466.0i 0.246876 0.246876i
\(613\) 52773.8i 0.140442i 0.997531 + 0.0702211i \(0.0223705\pi\)
−0.997531 + 0.0702211i \(0.977630\pi\)
\(614\) −160598. 160598.i −0.425994 0.425994i
\(615\) 161552. + 161552.i 0.427133 + 0.427133i
\(616\) −222306. + 222306.i −0.585853 + 0.585853i
\(617\) 514111.i 1.35048i 0.737600 + 0.675238i \(0.235959\pi\)
−0.737600 + 0.675238i \(0.764041\pi\)
\(618\) 59485.1 0.155751
\(619\) 625597.i 1.63273i −0.577539 0.816363i \(-0.695987\pi\)
0.577539 0.816363i \(-0.304013\pi\)
\(620\) 4573.93i 0.0118989i
\(621\) −317318. + 317318.i −0.822832 + 0.822832i
\(622\) 314240.i 0.812233i
\(623\) 105234. 105234.i 0.271132 0.271132i
\(624\) −38935.4 + 38935.4i −0.0999943 + 0.0999943i
\(625\) 447481. 1.14555
\(626\) −175016. −0.446611
\(627\) −240968. 240968.i −0.612949 0.612949i
\(628\) 207015.i 0.524908i
\(629\) 330932. 125032.i 0.836445 0.316025i
\(630\) 337944. 0.851458
\(631\) 218729. 218729.i 0.549349 0.549349i −0.376904 0.926253i \(-0.623011\pi\)
0.926253 + 0.376904i \(0.123011\pi\)
\(632\) 160025.i 0.400639i
\(633\) 48318.2i 0.120588i
\(634\) −99920.3 99920.3i −0.248585 0.248585i
\(635\) 225664. + 225664.i 0.559647 + 0.559647i
\(636\) −184539. −0.456220
\(637\) −353808. 353808.i −0.871944 0.871944i
\(638\) −644259. −1.58277
\(639\) −552056. −1.35201
\(640\) 39274.3i 0.0958846i
\(641\) 38109.6 0.0927511 0.0463755 0.998924i \(-0.485233\pi\)
0.0463755 + 0.998924i \(0.485233\pi\)
\(642\) 33539.1 + 33539.1i 0.0813731 + 0.0813731i
\(643\) −62224.6 + 62224.6i −0.150501 + 0.150501i −0.778342 0.627841i \(-0.783939\pi\)
0.627841 + 0.778342i \(0.283939\pi\)
\(644\) 290956. 290956.i 0.701544 0.701544i
\(645\) −112344. −0.270042
\(646\) −209584. 209584.i −0.502219 0.502219i
\(647\) 272326. 272326.i 0.650551 0.650551i −0.302575 0.953126i \(-0.597846\pi\)
0.953126 + 0.302575i \(0.0978463\pi\)
\(648\) 41022.6 + 41022.6i 0.0976951 + 0.0976951i
\(649\) 529616. 529616.i 1.25740 1.25740i
\(650\) 63838.8i 0.151098i
\(651\) −4373.54 4373.54i −0.0103198 0.0103198i
\(652\) −201098. 201098.i −0.473056 0.473056i
\(653\) −424148. + 424148.i −0.994698 + 0.994698i −0.999986 0.00528820i \(-0.998317\pi\)
0.00528820 + 0.999986i \(0.498317\pi\)
\(654\) 176790.i 0.413335i
\(655\) −149167. −0.347689
\(656\) 127991.i 0.297421i
\(657\) 163808.i 0.379493i
\(658\) −506269. + 506269.i −1.16931 + 1.16931i
\(659\) 266367.i 0.613352i −0.951814 0.306676i \(-0.900783\pi\)
0.951814 0.306676i \(-0.0992169\pi\)
\(660\) 128921. 128921.i 0.295963 0.295963i
\(661\) −569447. + 569447.i −1.30332 + 1.30332i −0.377175 + 0.926142i \(0.623105\pi\)
−0.926142 + 0.377175i \(0.876895\pi\)
\(662\) −258735. −0.590390
\(663\) 222326. 0.505781
\(664\) 122488. + 122488.i 0.277815 + 0.277815i
\(665\) 765985.i 1.73212i
\(666\) 86567.3 + 229124.i 0.195167 + 0.516561i
\(667\) 843212. 1.89533
\(668\) −118948. + 118948.i −0.266566 + 0.266566i
\(669\) 263028.i 0.587692i
\(670\) 240848.i 0.536529i
\(671\) 428456. + 428456.i 0.951614 + 0.951614i
\(672\) 37553.7 + 37553.7i 0.0831600 + 0.0831600i
\(673\) 32355.9 0.0714369 0.0357185 0.999362i \(-0.488628\pi\)
0.0357185 + 0.999362i \(0.488628\pi\)
\(674\) 341587. + 341587.i 0.751937 + 0.751937i
\(675\) −67152.4 −0.147385
\(676\) 105230. 0.230275
\(677\) 812423.i 1.77258i 0.463134 + 0.886288i \(0.346725\pi\)
−0.463134 + 0.886288i \(0.653275\pi\)
\(678\) −64586.9 −0.140503
\(679\) 480793. + 480793.i 1.04284 + 1.04284i
\(680\) 112131. 112131.i 0.242497 0.242497i
\(681\) −13299.0 + 13299.0i −0.0286765 + 0.0286765i
\(682\) 11895.2 0.0255743
\(683\) 33054.4 + 33054.4i 0.0708579 + 0.0708579i 0.741648 0.670790i \(-0.234045\pi\)
−0.670790 + 0.741648i \(0.734045\pi\)
\(684\) 145108. 145108.i 0.310154 0.310154i
\(685\) 76929.3 + 76929.3i 0.163950 + 0.163950i
\(686\) −6803.16 + 6803.16i −0.0144565 + 0.0144565i
\(687\) 99391.6i 0.210589i
\(688\) 44502.8 + 44502.8i 0.0940180 + 0.0940180i
\(689\) 790850. + 790850.i 1.66593 + 1.66593i
\(690\) −168734. + 168734.i −0.354408 + 0.354408i
\(691\) 523499.i 1.09638i −0.836355 0.548188i \(-0.815318\pi\)
0.836355 0.548188i \(-0.184682\pi\)
\(692\) −131860. −0.275361
\(693\) 878875.i 1.83004i
\(694\) 200005.i 0.415261i
\(695\) −245543. + 245543.i −0.508344 + 0.508344i
\(696\) 108834.i 0.224670i
\(697\) −365423. + 365423.i −0.752194 + 0.752194i
\(698\) 49998.7 49998.7i 0.102624 0.102624i
\(699\) 279386. 0.571807
\(700\) 61573.5 0.125660
\(701\) 107321. + 107321.i 0.218398 + 0.218398i 0.807823 0.589425i \(-0.200646\pi\)
−0.589425 + 0.807823i \(0.700646\pi\)
\(702\) 351040.i 0.712331i
\(703\) 519334. 196214.i 1.05084 0.397026i
\(704\) −102139. −0.206085
\(705\) 293600. 293600.i 0.590715 0.590715i
\(706\) 466131.i 0.935187i
\(707\) 283291.i 0.566754i
\(708\) −89467.2 89467.2i −0.178483 0.178483i
\(709\) −539094. 539094.i −1.07244 1.07244i −0.997163 0.0752745i \(-0.976017\pi\)
−0.0752745 0.997163i \(-0.523983\pi\)
\(710\) −669460. −1.32803
\(711\) −316325. 316325.i −0.625741 0.625741i
\(712\) 48350.1 0.0953757
\(713\) −15568.6 −0.0306246
\(714\) 214436.i 0.420631i
\(715\) −1.10500e6 −2.16147
\(716\) 208621. + 208621.i 0.406941 + 0.406941i
\(717\) 255188. 255188.i 0.496389 0.496389i
\(718\) 120074. 120074.i 0.232917 0.232917i
\(719\) −14756.3 −0.0285444 −0.0142722 0.999898i \(-0.504543\pi\)
−0.0142722 + 0.999898i \(0.504543\pi\)
\(720\) 77634.7 + 77634.7i 0.149758 + 0.149758i
\(721\) −245880. + 245880.i −0.472990 + 0.472990i
\(722\) −68259.7 68259.7i −0.130945 0.130945i
\(723\) 147562. 147562.i 0.282292 0.282292i
\(724\) 181480.i 0.346220i
\(725\) 89222.4 + 89222.4i 0.169745 + 0.169745i
\(726\) 211932. + 211932.i 0.402089 + 0.402089i
\(727\) −543736. + 543736.i −1.02877 + 1.02877i −0.0291996 + 0.999574i \(0.509296\pi\)
−0.999574 + 0.0291996i \(0.990704\pi\)
\(728\) 321876.i 0.607331i
\(729\) −45160.3 −0.0849771
\(730\) 198645.i 0.372761i
\(731\) 254117.i 0.475552i
\(732\) 72378.3 72378.3i 0.135079 0.135079i
\(733\) 199595.i 0.371486i 0.982598 + 0.185743i \(0.0594692\pi\)
−0.982598 + 0.185743i \(0.940531\pi\)
\(734\) −42.7294 + 42.7294i −7.93112e−5 + 7.93112e-5i
\(735\) 197902. 197902.i 0.366333 0.366333i
\(736\) 133681. 0.246782
\(737\) −626363. −1.15316
\(738\) −253004. 253004.i −0.464530 0.464530i
\(739\) 743712.i 1.36181i 0.732373 + 0.680904i \(0.238413\pi\)
−0.732373 + 0.680904i \(0.761587\pi\)
\(740\) 104977. + 277851.i 0.191704 + 0.507398i
\(741\) 348897. 0.635420
\(742\) 762786. 762786.i 1.38546 1.38546i
\(743\) 323198.i 0.585451i −0.956196 0.292726i \(-0.905438\pi\)
0.956196 0.292726i \(-0.0945623\pi\)
\(744\) 2009.44i 0.00363019i
\(745\) 198052. + 198052.i 0.356835 + 0.356835i
\(746\) −196290. 196290.i −0.352712 0.352712i
\(747\) 484249. 0.867816
\(748\) 291613. + 291613.i 0.521199 + 0.521199i
\(749\) −277265. −0.494232
\(750\) 166246. 0.295549
\(751\) 117607.i 0.208522i −0.994550 0.104261i \(-0.966752\pi\)
0.994550 0.104261i \(-0.0332477\pi\)
\(752\) −232607. −0.411327
\(753\) −2637.98 2637.98i −0.00465245 0.00465245i
\(754\) 466411. 466411.i 0.820400 0.820400i
\(755\) −59410.5 + 59410.5i −0.104224 + 0.104224i
\(756\) 338583. 0.592408
\(757\) 65440.6 + 65440.6i 0.114197 + 0.114197i 0.761896 0.647699i \(-0.224269\pi\)
−0.647699 + 0.761896i \(0.724269\pi\)
\(758\) 148975. 148975.i 0.259283 0.259283i
\(759\) −438818. 438818.i −0.761730 0.761730i
\(760\) 175967. 175967.i 0.304652 0.304652i
\(761\) 333975.i 0.576693i −0.957526 0.288347i \(-0.906894\pi\)
0.957526 0.288347i \(-0.0931055\pi\)
\(762\) 99139.6 + 99139.6i 0.170741 + 0.170741i
\(763\) −730754. 730754.i −1.25523 1.25523i
\(764\) 103976. 103976.i 0.178134 0.178134i
\(765\) 443303.i 0.757492i
\(766\) 223080. 0.380192
\(767\) 766831.i 1.30349i
\(768\) 17254.2i 0.0292531i
\(769\) −45343.9 + 45343.9i −0.0766772 + 0.0766772i −0.744405 0.667728i \(-0.767267\pi\)
0.667728 + 0.744405i \(0.267267\pi\)
\(770\) 1.06578e6i 1.79758i
\(771\) 343939. 343939.i 0.578593 0.578593i
\(772\) 5271.99 5271.99i 0.00884586 0.00884586i
\(773\) −16725.0 −0.0279903 −0.0139951 0.999902i \(-0.504455\pi\)
−0.0139951 + 0.999902i \(0.504455\pi\)
\(774\) 175940. 0.293686
\(775\) −1647.35