Properties

Label 177.4.d.c.176.7
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.7
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.8

$q$-expansion

\(f(q)\) \(=\) \(q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +O(q^{10})\) \(q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +27.2857i q^{10} +53.2996 q^{11} +(57.0921 - 39.9951i) q^{12} -28.7582i q^{13} -46.7120 q^{14} +(-17.5786 - 25.0930i) q^{15} +8.64556 q^{16} +131.636i q^{17} +(-42.6825 + 117.430i) q^{18} +46.0847 q^{19} -79.0989i q^{20} +(42.9583 - 30.0938i) q^{21} -246.652 q^{22} -74.5942 q^{23} +(-106.648 + 74.7108i) q^{24} +90.2346 q^{25} +133.083i q^{26} +(-36.4010 - 135.492i) q^{27} +135.414 q^{28} -76.0280i q^{29} +(81.3476 + 116.122i) q^{30} -6.76067i q^{31} +160.468 q^{32} +(226.832 - 158.904i) q^{33} -609.164i q^{34} -59.5171i q^{35} +(123.733 - 340.420i) q^{36} -329.691i q^{37} -213.264 q^{38} +(-85.7378 - 122.389i) q^{39} +147.757i q^{40} -319.534i q^{41} +(-198.796 + 139.264i) q^{42} +116.364i q^{43} +715.024 q^{44} +(-149.621 - 54.3829i) q^{45} +345.196 q^{46} +301.449 q^{47} +(36.7936 - 25.7753i) q^{48} -241.109 q^{49} -417.574 q^{50} +(392.449 + 560.212i) q^{51} -385.797i q^{52} -314.489i q^{53} +(168.451 + 627.008i) q^{54} -314.266i q^{55} -252.954 q^{56} +(196.126 - 137.394i) q^{57} +351.831i q^{58} +(-118.720 + 437.361i) q^{59} +(-235.820 - 336.627i) q^{60} -559.302i q^{61} +31.2860i q^{62} +(93.1014 - 256.146i) q^{63} -811.754 q^{64} -169.565 q^{65} +(-1049.70 + 735.351i) q^{66} +221.837i q^{67} +1765.91i q^{68} +(-317.456 + 222.390i) q^{69} +275.424i q^{70} -250.765i q^{71} +(-231.133 + 635.906i) q^{72} +450.880i q^{73} +1525.70i q^{74} +(384.019 - 269.019i) q^{75} +618.234 q^{76} +538.012 q^{77} +(396.765 + 566.373i) q^{78} -403.620 q^{79} -50.9761i q^{80} +(-558.860 - 468.099i) q^{81} +1478.69i q^{82} +341.648 q^{83} +(576.293 - 403.714i) q^{84} +776.152 q^{85} -538.491i q^{86} +(-226.665 - 323.559i) q^{87} -1335.67 q^{88} -1523.84 q^{89} +(692.395 + 251.665i) q^{90} -290.289i q^{91} -1000.69 q^{92} +(-20.1558 - 28.7719i) q^{93} -1395.00 q^{94} -271.726i q^{95} +(682.916 - 478.408i) q^{96} +1030.41i q^{97} +1115.77 q^{98} +(491.601 - 1352.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.62765 −1.63612 −0.818061 0.575131i \(-0.804951\pi\)
−0.818061 + 0.575131i \(0.804951\pi\)
\(3\) 4.25578 2.98133i 0.819025 0.573757i
\(4\) 13.4152 1.67690
\(5\) 5.89622i 0.527374i −0.964608 0.263687i \(-0.915061\pi\)
0.964608 0.263687i \(-0.0849386\pi\)
\(6\) −19.6943 + 13.7966i −1.34003 + 0.938737i
\(7\) 10.0941 0.545030 0.272515 0.962152i \(-0.412145\pi\)
0.272515 + 0.962152i \(0.412145\pi\)
\(8\) −25.0596 −1.10749
\(9\) 9.22335 25.3758i 0.341605 0.939843i
\(10\) 27.2857i 0.862849i
\(11\) 53.2996 1.46095 0.730475 0.682940i \(-0.239299\pi\)
0.730475 + 0.682940i \(0.239299\pi\)
\(12\) 57.0921 39.9951i 1.37342 0.962132i
\(13\) 28.7582i 0.613546i −0.951783 0.306773i \(-0.900751\pi\)
0.951783 0.306773i \(-0.0992493\pi\)
\(14\) −46.7120 −0.891736
\(15\) −17.5786 25.0930i −0.302585 0.431933i
\(16\) 8.64556 0.135087
\(17\) 131.636i 1.87802i 0.343892 + 0.939009i \(0.388254\pi\)
−0.343892 + 0.939009i \(0.611746\pi\)
\(18\) −42.6825 + 117.430i −0.558908 + 1.53770i
\(19\) 46.0847 0.556450 0.278225 0.960516i \(-0.410254\pi\)
0.278225 + 0.960516i \(0.410254\pi\)
\(20\) 79.0989i 0.884352i
\(21\) 42.9583 30.0938i 0.446394 0.312715i
\(22\) −246.652 −2.39029
\(23\) −74.5942 −0.676259 −0.338130 0.941100i \(-0.609794\pi\)
−0.338130 + 0.941100i \(0.609794\pi\)
\(24\) −106.648 + 74.7108i −0.907060 + 0.635428i
\(25\) 90.2346 0.721877
\(26\) 133.083i 1.00384i
\(27\) −36.4010 135.492i −0.259458 0.965754i
\(28\) 135.414 0.913960
\(29\) 76.0280i 0.486829i −0.969922 0.243415i \(-0.921732\pi\)
0.969922 0.243415i \(-0.0782676\pi\)
\(30\) 81.3476 + 116.122i 0.495066 + 0.706695i
\(31\) 6.76067i 0.0391694i −0.999808 0.0195847i \(-0.993766\pi\)
0.999808 0.0195847i \(-0.00623440\pi\)
\(32\) 160.468 0.886468
\(33\) 226.832 158.904i 1.19655 0.838230i
\(34\) 609.164i 3.07267i
\(35\) 59.5171i 0.287435i
\(36\) 123.733 340.420i 0.572837 1.57602i
\(37\) 329.691i 1.46489i −0.680826 0.732445i \(-0.738379\pi\)
0.680826 0.732445i \(-0.261621\pi\)
\(38\) −213.264 −0.910421
\(39\) −85.7378 122.389i −0.352027 0.502510i
\(40\) 147.757i 0.584060i
\(41\) 319.534i 1.21714i −0.793500 0.608571i \(-0.791743\pi\)
0.793500 0.608571i \(-0.208257\pi\)
\(42\) −198.796 + 139.264i −0.730355 + 0.511640i
\(43\) 116.364i 0.412681i 0.978480 + 0.206341i \(0.0661555\pi\)
−0.978480 + 0.206341i \(0.933845\pi\)
\(44\) 715.024 2.44986
\(45\) −149.621 54.3829i −0.495649 0.180154i
\(46\) 345.196 1.10644
\(47\) 301.449 0.935550 0.467775 0.883848i \(-0.345056\pi\)
0.467775 + 0.883848i \(0.345056\pi\)
\(48\) 36.7936 25.7753i 0.110640 0.0775071i
\(49\) −241.109 −0.702942
\(50\) −417.574 −1.18108
\(51\) 392.449 + 560.212i 1.07753 + 1.53814i
\(52\) 385.797i 1.02885i
\(53\) 314.489i 0.815064i −0.913191 0.407532i \(-0.866389\pi\)
0.913191 0.407532i \(-0.133611\pi\)
\(54\) 168.451 + 627.008i 0.424506 + 1.58009i
\(55\) 314.266i 0.770467i
\(56\) −252.954 −0.603614
\(57\) 196.126 137.394i 0.455747 0.319267i
\(58\) 351.831i 0.796513i
\(59\) −118.720 + 437.361i −0.261966 + 0.965077i
\(60\) −235.820 336.627i −0.507403 0.724307i
\(61\) 559.302i 1.17396i −0.809603 0.586978i \(-0.800318\pi\)
0.809603 0.586978i \(-0.199682\pi\)
\(62\) 31.2860i 0.0640860i
\(63\) 93.1014 256.146i 0.186185 0.512243i
\(64\) −811.754 −1.58546
\(65\) −169.565 −0.323568
\(66\) −1049.70 + 735.351i −1.95771 + 1.37145i
\(67\) 221.837i 0.404502i 0.979334 + 0.202251i \(0.0648257\pi\)
−0.979334 + 0.202251i \(0.935174\pi\)
\(68\) 1765.91i 3.14924i
\(69\) −317.456 + 222.390i −0.553873 + 0.388008i
\(70\) 275.424i 0.470279i
\(71\) 250.765i 0.419159i −0.977792 0.209580i \(-0.932790\pi\)
0.977792 0.209580i \(-0.0672096\pi\)
\(72\) −231.133 + 635.906i −0.378324 + 1.04086i
\(73\) 450.880i 0.722897i 0.932392 + 0.361448i \(0.117718\pi\)
−0.932392 + 0.361448i \(0.882282\pi\)
\(74\) 1525.70i 2.39674i
\(75\) 384.019 269.019i 0.591235 0.414182i
\(76\) 618.234 0.933110
\(77\) 538.012 0.796261
\(78\) 396.765 + 566.373i 0.575959 + 0.822168i
\(79\) −403.620 −0.574820 −0.287410 0.957808i \(-0.592794\pi\)
−0.287410 + 0.957808i \(0.592794\pi\)
\(80\) 50.9761i 0.0712413i
\(81\) −558.860 468.099i −0.766611 0.642111i
\(82\) 1478.69i 1.99139i
\(83\) 341.648 0.451816 0.225908 0.974149i \(-0.427465\pi\)
0.225908 + 0.974149i \(0.427465\pi\)
\(84\) 576.293 403.714i 0.748556 0.524391i
\(85\) 776.152 0.990418
\(86\) 538.491i 0.675197i
\(87\) −226.665 323.559i −0.279322 0.398726i
\(88\) −1335.67 −1.61798
\(89\) −1523.84 −1.81491 −0.907454 0.420151i \(-0.861977\pi\)
−0.907454 + 0.420151i \(0.861977\pi\)
\(90\) 692.395 + 251.665i 0.810943 + 0.294754i
\(91\) 290.289i 0.334401i
\(92\) −1000.69 −1.13402
\(93\) −20.1558 28.7719i −0.0224737 0.0320807i
\(94\) −1395.00 −1.53067
\(95\) 271.726i 0.293457i
\(96\) 682.916 478.408i 0.726040 0.508617i
\(97\) 1030.41i 1.07858i 0.842119 + 0.539291i \(0.181308\pi\)
−0.842119 + 0.539291i \(0.818692\pi\)
\(98\) 1115.77 1.15010
\(99\) 491.601 1352.52i 0.499068 1.37306i
\(100\) 1210.51 1.21051
\(101\) 1800.46 1.77378 0.886891 0.461979i \(-0.152860\pi\)
0.886891 + 0.461979i \(0.152860\pi\)
\(102\) −1816.12 2592.47i −1.76297 2.51659i
\(103\) 1115.61i 1.06723i 0.845727 + 0.533616i \(0.179167\pi\)
−0.845727 + 0.533616i \(0.820833\pi\)
\(104\) 720.669i 0.679494i
\(105\) −177.440 253.292i −0.164918 0.235416i
\(106\) 1455.35i 1.33354i
\(107\) 294.975i 0.266507i 0.991082 + 0.133254i \(0.0425425\pi\)
−0.991082 + 0.133254i \(0.957457\pi\)
\(108\) −488.326 1817.64i −0.435085 1.61947i
\(109\) 408.894i 0.359311i −0.983730 0.179655i \(-0.942502\pi\)
0.983730 0.179655i \(-0.0574983\pi\)
\(110\) 1454.32i 1.26058i
\(111\) −982.919 1403.09i −0.840491 1.19978i
\(112\) 87.2691 0.0736264
\(113\) −33.0548 −0.0275180 −0.0137590 0.999905i \(-0.504380\pi\)
−0.0137590 + 0.999905i \(0.504380\pi\)
\(114\) −907.605 + 635.810i −0.745658 + 0.522360i
\(115\) 439.824i 0.356642i
\(116\) 1019.93i 0.816363i
\(117\) −729.763 265.247i −0.576637 0.209591i
\(118\) 549.393 2023.96i 0.428608 1.57898i
\(119\) 1328.74i 1.02358i
\(120\) 440.512 + 628.820i 0.335109 + 0.478360i
\(121\) 1509.85 1.13437
\(122\) 2588.26i 1.92074i
\(123\) −952.636 1359.87i −0.698344 0.996870i
\(124\) 90.6956i 0.0656831i
\(125\) 1269.07i 0.908073i
\(126\) −430.841 + 1185.35i −0.304622 + 0.838092i
\(127\) −605.304 −0.422929 −0.211465 0.977386i \(-0.567823\pi\)
−0.211465 + 0.977386i \(0.567823\pi\)
\(128\) 2472.77 1.70753
\(129\) 346.918 + 495.218i 0.236779 + 0.337996i
\(130\) 784.688 0.529398
\(131\) 279.269 0.186258 0.0931292 0.995654i \(-0.470313\pi\)
0.0931292 + 0.995654i \(0.470313\pi\)
\(132\) 3042.99 2131.72i 2.00650 1.40563i
\(133\) 465.183 0.303282
\(134\) 1026.58i 0.661815i
\(135\) −798.888 + 214.628i −0.509314 + 0.136832i
\(136\) 3298.73i 2.07988i
\(137\) 1534.48i 0.956930i 0.878107 + 0.478465i \(0.158807\pi\)
−0.878107 + 0.478465i \(0.841193\pi\)
\(138\) 1469.08 1029.14i 0.906205 0.634829i
\(139\) 1166.12 0.711577 0.355789 0.934566i \(-0.384212\pi\)
0.355789 + 0.934566i \(0.384212\pi\)
\(140\) 798.432i 0.481999i
\(141\) 1282.90 898.719i 0.766239 0.536779i
\(142\) 1160.45i 0.685796i
\(143\) 1532.80i 0.896360i
\(144\) 79.7410 219.388i 0.0461464 0.126960i
\(145\) −448.278 −0.256741
\(146\) 2086.51i 1.18275i
\(147\) −1026.11 + 718.826i −0.575728 + 0.403318i
\(148\) 4422.87i 2.45647i
\(149\) −1325.90 −0.729009 −0.364505 0.931202i \(-0.618762\pi\)
−0.364505 + 0.931202i \(0.618762\pi\)
\(150\) −1777.10 + 1244.93i −0.967333 + 0.677652i
\(151\) 3043.52i 1.64025i 0.572184 + 0.820125i \(0.306096\pi\)
−0.572184 + 0.820125i \(0.693904\pi\)
\(152\) −1154.86 −0.616261
\(153\) 3340.35 + 1214.12i 1.76504 + 0.641541i
\(154\) −2489.73 −1.30278
\(155\) −39.8624 −0.0206569
\(156\) −1150.19 1641.87i −0.590312 0.842658i
\(157\) 2731.12i 1.38832i 0.719819 + 0.694162i \(0.244225\pi\)
−0.719819 + 0.694162i \(0.755775\pi\)
\(158\) 1867.81 0.940475
\(159\) −937.596 1338.40i −0.467649 0.667558i
\(160\) 946.154i 0.467500i
\(161\) −752.961 −0.368582
\(162\) 2586.21 + 2166.20i 1.25427 + 1.05057i
\(163\) −513.998 −0.246991 −0.123495 0.992345i \(-0.539410\pi\)
−0.123495 + 0.992345i \(0.539410\pi\)
\(164\) 4286.60i 2.04102i
\(165\) −936.932 1337.45i −0.442061 0.631032i
\(166\) −1581.03 −0.739227
\(167\) 1602.55i 0.742571i −0.928519 0.371286i \(-0.878917\pi\)
0.928519 0.371286i \(-0.121083\pi\)
\(168\) −1076.52 + 754.138i −0.494375 + 0.346328i
\(169\) 1369.96 0.623561
\(170\) −3591.76 −1.62045
\(171\) 425.055 1169.43i 0.190086 0.522976i
\(172\) 1561.04i 0.692024i
\(173\) −2474.48 −1.08746 −0.543731 0.839260i \(-0.682989\pi\)
−0.543731 + 0.839260i \(0.682989\pi\)
\(174\) 1048.93 + 1497.32i 0.457005 + 0.652364i
\(175\) 910.837 0.393444
\(176\) 460.805 0.197355
\(177\) 798.672 + 2215.26i 0.339163 + 0.940728i
\(178\) 7051.81 2.96941
\(179\) −1696.42 −0.708360 −0.354180 0.935177i \(-0.615240\pi\)
−0.354180 + 0.935177i \(0.615240\pi\)
\(180\) −2007.19 729.556i −0.831153 0.302100i
\(181\) 2390.68 0.981756 0.490878 0.871228i \(-0.336676\pi\)
0.490878 + 0.871228i \(0.336676\pi\)
\(182\) 1343.35i 0.547121i
\(183\) −1667.46 2380.27i −0.673566 0.961500i
\(184\) 1869.30 0.748948
\(185\) −1943.93 −0.772545
\(186\) 93.2740 + 133.146i 0.0367698 + 0.0524880i
\(187\) 7016.12i 2.74369i
\(188\) 4043.99 1.56882
\(189\) −367.435 1367.67i −0.141413 0.526365i
\(190\) 1257.45i 0.480132i
\(191\) −2544.85 −0.964076 −0.482038 0.876150i \(-0.660103\pi\)
−0.482038 + 0.876150i \(0.660103\pi\)
\(192\) −3454.65 + 2420.11i −1.29853 + 0.909667i
\(193\) −3082.48 −1.14965 −0.574824 0.818277i \(-0.694929\pi\)
−0.574824 + 0.818277i \(0.694929\pi\)
\(194\) 4768.39i 1.76469i
\(195\) −721.631 + 505.529i −0.265011 + 0.185650i
\(196\) −3234.52 −1.17876
\(197\) 4018.40i 1.45330i 0.687010 + 0.726648i \(0.258923\pi\)
−0.687010 + 0.726648i \(0.741077\pi\)
\(198\) −2274.96 + 6258.99i −0.816537 + 2.24650i
\(199\) 4500.71 1.60325 0.801626 0.597826i \(-0.203969\pi\)
0.801626 + 0.597826i \(0.203969\pi\)
\(200\) −2261.24 −0.799469
\(201\) 661.368 + 944.088i 0.232086 + 0.331298i
\(202\) −8331.88 −2.90213
\(203\) 767.435i 0.265337i
\(204\) 5264.77 + 7515.34i 1.80690 + 2.57931i
\(205\) −1884.04 −0.641889
\(206\) 5162.68i 1.74612i
\(207\) −688.008 + 1892.88i −0.231014 + 0.635578i
\(208\) 248.631i 0.0828820i
\(209\) 2456.30 0.812945
\(210\) 821.131 + 1172.15i 0.269826 + 0.385170i
\(211\) 4567.43i 1.49021i −0.666946 0.745106i \(-0.732399\pi\)
0.666946 0.745106i \(-0.267601\pi\)
\(212\) 4218.93i 1.36678i
\(213\) −747.613 1067.20i −0.240496 0.343302i
\(214\) 1365.04i 0.436039i
\(215\) 686.106 0.217637
\(216\) 912.193 + 3395.36i 0.287347 + 1.06956i
\(217\) 68.2429i 0.0213485i
\(218\) 1892.22i 0.587877i
\(219\) 1344.22 + 1918.84i 0.414767 + 0.592071i
\(220\) 4215.94i 1.29199i
\(221\) 3785.61 1.15225
\(222\) 4548.61 + 6493.04i 1.37515 + 1.96299i
\(223\) 247.649 0.0743669 0.0371835 0.999308i \(-0.488161\pi\)
0.0371835 + 0.999308i \(0.488161\pi\)
\(224\) 1619.78 0.483152
\(225\) 832.265 2289.77i 0.246597 0.678451i
\(226\) 152.966 0.0450228
\(227\) 1175.81 0.343795 0.171897 0.985115i \(-0.445010\pi\)
0.171897 + 0.985115i \(0.445010\pi\)
\(228\) 2631.07 1843.16i 0.764241 0.535378i
\(229\) 3872.27i 1.11741i −0.829367 0.558704i \(-0.811299\pi\)
0.829367 0.558704i \(-0.188701\pi\)
\(230\) 2035.35i 0.583509i
\(231\) 2289.66 1603.99i 0.652158 0.456861i
\(232\) 1905.23i 0.539157i
\(233\) 2609.60 0.733736 0.366868 0.930273i \(-0.380430\pi\)
0.366868 + 0.930273i \(0.380430\pi\)
\(234\) 3377.09 + 1227.47i 0.943449 + 0.342916i
\(235\) 1777.41i 0.493385i
\(236\) −1592.64 + 5867.28i −0.439290 + 1.61834i
\(237\) −1717.72 + 1203.32i −0.470792 + 0.329807i
\(238\) 6148.96i 1.67470i
\(239\) 5126.17i 1.38738i 0.720273 + 0.693691i \(0.244017\pi\)
−0.720273 + 0.693691i \(0.755983\pi\)
\(240\) −151.977 216.943i −0.0408752 0.0583485i
\(241\) −3001.15 −0.802161 −0.401081 0.916043i \(-0.631365\pi\)
−0.401081 + 0.916043i \(0.631365\pi\)
\(242\) −6987.06 −1.85597
\(243\) −3773.94 325.983i −0.996290 0.0860568i
\(244\) 7503.14i 1.96860i
\(245\) 1421.63i 0.370713i
\(246\) 4408.47 + 6292.99i 1.14258 + 1.63100i
\(247\) 1325.31i 0.341408i
\(248\) 169.419i 0.0433796i
\(249\) 1453.98 1018.57i 0.370049 0.259233i
\(250\) 5872.82i 1.48572i
\(251\) 5448.19i 1.37007i −0.728512 0.685034i \(-0.759788\pi\)
0.728512 0.685034i \(-0.240212\pi\)
\(252\) 1248.97 3436.24i 0.312214 0.858979i
\(253\) −3975.84 −0.987980
\(254\) 2801.14 0.691964
\(255\) 3303.13 2313.97i 0.811178 0.568260i
\(256\) −4949.11 −1.20828
\(257\) 1304.07i 0.316519i 0.987398 + 0.158260i \(0.0505883\pi\)
−0.987398 + 0.158260i \(0.949412\pi\)
\(258\) −1605.42 2291.70i −0.387399 0.553003i
\(259\) 3327.94i 0.798409i
\(260\) −2274.74 −0.542591
\(261\) −1929.27 701.233i −0.457543 0.166304i
\(262\) −1292.36 −0.304742
\(263\) 41.3337i 0.00969105i 0.999988 + 0.00484552i \(0.00154238\pi\)
−0.999988 + 0.00484552i \(0.998458\pi\)
\(264\) −5684.30 + 3982.06i −1.32517 + 0.928329i
\(265\) −1854.30 −0.429844
\(266\) −2152.71 −0.496207
\(267\) −6485.13 + 4543.07i −1.48646 + 1.04132i
\(268\) 2975.98i 0.678309i
\(269\) 6337.69 1.43649 0.718245 0.695791i \(-0.244946\pi\)
0.718245 + 0.695791i \(0.244946\pi\)
\(270\) 3696.98 993.226i 0.833300 0.223873i
\(271\) 4545.70 1.01893 0.509467 0.860490i \(-0.329842\pi\)
0.509467 + 0.860490i \(0.329842\pi\)
\(272\) 1138.06i 0.253696i
\(273\) −865.446 1235.40i −0.191865 0.273883i
\(274\) 7101.04i 1.56565i
\(275\) 4809.47 1.05462
\(276\) −4258.73 + 2983.40i −0.928789 + 0.650650i
\(277\) 6321.46 1.37119 0.685595 0.727983i \(-0.259542\pi\)
0.685595 + 0.727983i \(0.259542\pi\)
\(278\) −5396.41 −1.16423
\(279\) −171.557 62.3560i −0.0368131 0.0133805i
\(280\) 1491.47i 0.318330i
\(281\) 2091.33i 0.443979i 0.975049 + 0.221989i \(0.0712551\pi\)
−0.975049 + 0.221989i \(0.928745\pi\)
\(282\) −5936.82 + 4158.96i −1.25366 + 0.878236i
\(283\) 7506.42i 1.57672i −0.615217 0.788358i \(-0.710932\pi\)
0.615217 0.788358i \(-0.289068\pi\)
\(284\) 3364.05i 0.702887i
\(285\) −810.104 1156.40i −0.168373 0.240349i
\(286\) 7093.28i 1.46655i
\(287\) 3225.41i 0.663379i
\(288\) 1480.05 4072.00i 0.302822 0.833141i
\(289\) −12414.9 −2.52695
\(290\) 2074.48 0.420060
\(291\) 3072.00 + 4385.21i 0.618845 + 0.883387i
\(292\) 6048.63i 1.21222i
\(293\) 7349.25i 1.46535i 0.680578 + 0.732675i \(0.261729\pi\)
−0.680578 + 0.732675i \(0.738271\pi\)
\(294\) 4748.47 3326.48i 0.941961 0.659878i
\(295\) 2578.78 + 699.997i 0.508957 + 0.138154i
\(296\) 8261.92i 1.62235i
\(297\) −1940.16 7221.65i −0.379055 1.41092i
\(298\) 6135.83 1.19275
\(299\) 2145.20i 0.414916i
\(300\) 5151.68 3608.94i 0.991441 0.694540i
\(301\) 1174.59i 0.224924i
\(302\) 14084.3i 2.68365i
\(303\) 7662.34 5367.75i 1.45277 1.01772i
\(304\) 398.428 0.0751691
\(305\) −3297.77 −0.619114
\(306\) −15458.0 5618.53i −2.88783 1.04964i
\(307\) 4822.74 0.896574 0.448287 0.893890i \(-0.352034\pi\)
0.448287 + 0.893890i \(0.352034\pi\)
\(308\) 7217.52 1.33525
\(309\) 3326.02 + 4747.81i 0.612332 + 0.874090i
\(310\) 184.469 0.0337973
\(311\) 5273.14i 0.961454i 0.876870 + 0.480727i \(0.159627\pi\)
−0.876870 + 0.480727i \(0.840373\pi\)
\(312\) 2148.55 + 3067.01i 0.389865 + 0.556523i
\(313\) 8851.82i 1.59851i 0.600990 + 0.799256i \(0.294773\pi\)
−0.600990 + 0.799256i \(0.705227\pi\)
\(314\) 12638.7i 2.27147i
\(315\) −1510.29 548.946i −0.270144 0.0981893i
\(316\) −5414.63 −0.963913
\(317\) 8125.27i 1.43962i 0.694169 + 0.719812i \(0.255772\pi\)
−0.694169 + 0.719812i \(0.744228\pi\)
\(318\) 4338.87 + 6193.64i 0.765131 + 1.09221i
\(319\) 4052.27i 0.711233i
\(320\) 4786.28i 0.836129i
\(321\) 879.417 + 1255.35i 0.152911 + 0.218276i
\(322\) 3484.44 0.603045
\(323\) 6066.38i 1.04502i
\(324\) −7497.20 6279.63i −1.28553 1.07675i
\(325\) 2594.99i 0.442905i
\(326\) 2378.61 0.404107
\(327\) −1219.05 1740.16i −0.206157 0.294285i
\(328\) 8007.38i 1.34797i
\(329\) 3042.86 0.509903
\(330\) 4335.80 + 6189.25i 0.723266 + 1.03245i
\(331\) −11740.5 −1.94959 −0.974795 0.223104i \(-0.928381\pi\)
−0.974795 + 0.223104i \(0.928381\pi\)
\(332\) 4583.27 0.757650
\(333\) −8366.18 3040.86i −1.37677 0.500415i
\(334\) 7416.07i 1.21494i
\(335\) 1308.00 0.213324
\(336\) 371.398 260.178i 0.0603019 0.0422437i
\(337\) 7342.61i 1.18688i 0.804880 + 0.593438i \(0.202230\pi\)
−0.804880 + 0.593438i \(0.797770\pi\)
\(338\) −6339.72 −1.02022
\(339\) −140.674 + 98.5472i −0.0225379 + 0.0157886i
\(340\) 10412.2 1.66083
\(341\) 360.341i 0.0572245i
\(342\) −1967.01 + 5411.74i −0.311005 + 0.855653i
\(343\) −5896.06 −0.928155
\(344\) 2916.02i 0.457039i
\(345\) 1311.26 + 1871.79i 0.204626 + 0.292099i
\(346\) 11451.0 1.77922
\(347\) −11274.9 −1.74429 −0.872144 0.489250i \(-0.837271\pi\)
−0.872144 + 0.489250i \(0.837271\pi\)
\(348\) −3040.75 4340.60i −0.468394 0.668622i
\(349\) 2405.99i 0.369025i 0.982830 + 0.184513i \(0.0590706\pi\)
−0.982830 + 0.184513i \(0.940929\pi\)
\(350\) −4215.04 −0.643723
\(351\) −3896.50 + 1046.83i −0.592535 + 0.159190i
\(352\) 8552.88 1.29508
\(353\) 2454.37 0.370065 0.185033 0.982732i \(-0.440761\pi\)
0.185033 + 0.982732i \(0.440761\pi\)
\(354\) −3695.98 10251.4i −0.554913 1.53915i
\(355\) −1478.57 −0.221054
\(356\) −20442.6 −3.04341
\(357\) 3961.42 + 5654.84i 0.587284 + 0.838335i
\(358\) 7850.45 1.15896
\(359\) 3927.04i 0.577330i −0.957430 0.288665i \(-0.906789\pi\)
0.957430 0.288665i \(-0.0932113\pi\)
\(360\) 3749.44 + 1362.81i 0.548925 + 0.199518i
\(361\) −4735.20 −0.690363
\(362\) −11063.2 −1.60627
\(363\) 6425.59 4501.36i 0.929080 0.650854i
\(364\) 3894.27i 0.560756i
\(365\) 2658.49 0.381237
\(366\) 7716.45 + 11015.1i 1.10204 + 1.57313i
\(367\) 11433.0i 1.62615i 0.582160 + 0.813074i \(0.302208\pi\)
−0.582160 + 0.813074i \(0.697792\pi\)
\(368\) −644.908 −0.0913537
\(369\) −8108.42 2947.17i −1.14392 0.415782i
\(370\) 8995.85 1.26398
\(371\) 3174.48i 0.444234i
\(372\) −270.393 385.980i −0.0376861 0.0537961i
\(373\) 3095.15 0.429653 0.214827 0.976652i \(-0.431081\pi\)
0.214827 + 0.976652i \(0.431081\pi\)
\(374\) 32468.2i 4.48901i
\(375\) −3783.52 5400.89i −0.521013 0.743735i
\(376\) −7554.18 −1.03611
\(377\) −2186.43 −0.298692
\(378\) 1700.36 + 6329.08i 0.231368 + 0.861198i
\(379\) 3022.14 0.409597 0.204798 0.978804i \(-0.434346\pi\)
0.204798 + 0.978804i \(0.434346\pi\)
\(380\) 3645.25i 0.492098i
\(381\) −2576.04 + 1804.61i −0.346390 + 0.242659i
\(382\) 11776.7 1.57735
\(383\) 6729.51i 0.897812i −0.893579 0.448906i \(-0.851814\pi\)
0.893579 0.448906i \(-0.148186\pi\)
\(384\) 10523.6 7372.15i 1.39851 0.979710i
\(385\) 3172.24i 0.419928i
\(386\) 14264.7 1.88096
\(387\) 2952.82 + 1073.26i 0.387856 + 0.140974i
\(388\) 13823.2i 1.80867i
\(389\) 4796.16i 0.625129i 0.949897 + 0.312564i \(0.101188\pi\)
−0.949897 + 0.312564i \(0.898812\pi\)
\(390\) 3339.46 2339.41i 0.433590 0.303746i
\(391\) 9819.24i 1.27003i
\(392\) 6042.09 0.778499
\(393\) 1188.51 832.593i 0.152550 0.106867i
\(394\) 18595.8i 2.37777i
\(395\) 2379.83i 0.303145i
\(396\) 6594.91 18144.3i 0.836886 2.30249i
\(397\) 6475.19i 0.818590i −0.912402 0.409295i \(-0.865775\pi\)
0.912402 0.409295i \(-0.134225\pi\)
\(398\) −20827.7 −2.62312
\(399\) 1979.72 1386.87i 0.248396 0.174010i
\(400\) 780.128 0.0975160
\(401\) 5689.94 0.708584 0.354292 0.935135i \(-0.384722\pi\)
0.354292 + 0.935135i \(0.384722\pi\)
\(402\) −3060.58 4368.91i −0.379721 0.542044i
\(403\) −194.425 −0.0240322
\(404\) 24153.4 2.97445
\(405\) −2760.02 + 3295.16i −0.338633 + 0.404291i
\(406\) 3551.42i 0.434123i
\(407\) 17572.4i 2.14013i
\(408\) −9834.60 14038.7i −1.19335 1.70347i
\(409\) 6415.64i 0.775631i −0.921737 0.387815i \(-0.873230\pi\)
0.921737 0.387815i \(-0.126770\pi\)
\(410\) 8718.70 1.05021
\(411\) 4574.79 + 6530.41i 0.549045 + 0.783750i
\(412\) 14966.2i 1.78964i
\(413\) −1198.37 + 4414.77i −0.142779 + 0.525996i
\(414\) 3183.86 8759.61i 0.377967 1.03988i
\(415\) 2014.43i 0.238276i
\(416\) 4614.77i 0.543889i
\(417\) 4962.76 3476.60i 0.582800 0.408273i
\(418\) −11366.9 −1.33008
\(419\) −56.4393 −0.00658052 −0.00329026 0.999995i \(-0.501047\pi\)
−0.00329026 + 0.999995i \(0.501047\pi\)
\(420\) −2380.39 3397.95i −0.276550 0.394769i
\(421\) 6070.96i 0.702804i 0.936225 + 0.351402i \(0.114295\pi\)
−0.936225 + 0.351402i \(0.885705\pi\)
\(422\) 21136.5i 2.43817i
\(423\) 2780.37 7649.50i 0.319589 0.879271i
\(424\) 7880.96i 0.902673i
\(425\) 11878.1i 1.35570i
\(426\) 3459.69 + 4938.63i 0.393480 + 0.561684i
\(427\) 5645.65i 0.639841i
\(428\) 3957.14i 0.446906i
\(429\) −4569.79 6523.28i −0.514293 0.734142i
\(430\) −3175.06 −0.356081
\(431\) 1006.47 0.112482 0.0562412 0.998417i \(-0.482088\pi\)
0.0562412 + 0.998417i \(0.482088\pi\)
\(432\) −314.707 1171.40i −0.0350494 0.130461i
\(433\) −12899.6 −1.43167 −0.715836 0.698268i \(-0.753954\pi\)
−0.715836 + 0.698268i \(0.753954\pi\)
\(434\) 315.804i 0.0349288i
\(435\) −1907.77 + 1336.47i −0.210278 + 0.147307i
\(436\) 5485.38i 0.602528i
\(437\) −3437.65 −0.376305
\(438\) −6220.59 8879.75i −0.678610 0.968700i
\(439\) 13595.9 1.47813 0.739064 0.673635i \(-0.235268\pi\)
0.739064 + 0.673635i \(0.235268\pi\)
\(440\) 7875.38i 0.853282i
\(441\) −2223.83 + 6118.33i −0.240129 + 0.660656i
\(442\) −17518.5 −1.88522
\(443\) 16463.4 1.76569 0.882843 0.469668i \(-0.155626\pi\)
0.882843 + 0.469668i \(0.155626\pi\)
\(444\) −13186.0 18822.8i −1.40942 2.01191i
\(445\) 8984.90i 0.957136i
\(446\) −1146.04 −0.121673
\(447\) −5642.76 + 3952.96i −0.597077 + 0.418274i
\(448\) −8193.93 −0.864122
\(449\) 14660.1i 1.54088i 0.637513 + 0.770440i \(0.279963\pi\)
−0.637513 + 0.770440i \(0.720037\pi\)
\(450\) −3851.43 + 10596.3i −0.403463 + 1.11003i
\(451\) 17031.0i 1.77818i
\(452\) −443.436 −0.0461448
\(453\) 9073.72 + 12952.5i 0.941105 + 1.34341i
\(454\) −5441.25 −0.562490
\(455\) −1711.61 −0.176355
\(456\) −4914.84 + 3443.03i −0.504734 + 0.353584i
\(457\) 1970.40i 0.201688i 0.994902 + 0.100844i \(0.0321543\pi\)
−0.994902 + 0.100844i \(0.967846\pi\)
\(458\) 17919.5i 1.82822i
\(459\) 17835.5 4791.66i 1.81370 0.487267i
\(460\) 5900.31i 0.598051i
\(461\) 10954.7i 1.10674i −0.832934 0.553372i \(-0.813341\pi\)
0.832934 0.553372i \(-0.186659\pi\)
\(462\) −10595.8 + 7422.71i −1.06701 + 0.747480i
\(463\) 16309.2i 1.63704i 0.574475 + 0.818522i \(0.305206\pi\)
−0.574475 + 0.818522i \(0.694794\pi\)
\(464\) 657.305i 0.0657643i
\(465\) −169.646 + 118.843i −0.0169186 + 0.0118521i
\(466\) −12076.3 −1.20048
\(467\) −10124.7 −1.00324 −0.501622 0.865087i \(-0.667263\pi\)
−0.501622 + 0.865087i \(0.667263\pi\)
\(468\) −9789.89 3558.34i −0.966962 0.351462i
\(469\) 2239.24i 0.220466i
\(470\) 8225.24i 0.807238i
\(471\) 8142.36 + 11623.0i 0.796561 + 1.13707i
\(472\) 2975.06 10960.1i 0.290124 1.06881i
\(473\) 6202.14i 0.602906i
\(474\) 7949.00 5568.56i 0.770273 0.539604i
\(475\) 4158.43 0.401688
\(476\) 17825.3i 1.71643i
\(477\) −7980.40 2900.64i −0.766033 0.278430i
\(478\) 23722.1i 2.26993i
\(479\) 1871.94i 0.178562i −0.996006 0.0892808i \(-0.971543\pi\)
0.996006 0.0892808i \(-0.0284568\pi\)
\(480\) −2820.80 4026.62i −0.268232 0.382895i
\(481\) −9481.35 −0.898778
\(482\) 13888.3 1.31243
\(483\) −3204.44 + 2244.82i −0.301878 + 0.211476i
\(484\) 20254.9 1.90223
\(485\) 6075.54 0.568817
\(486\) 17464.5 + 1508.53i 1.63005 + 0.140799i
\(487\) −5575.34 −0.518773 −0.259387 0.965774i \(-0.583520\pi\)
−0.259387 + 0.965774i \(0.583520\pi\)
\(488\) 14015.9i 1.30014i
\(489\) −2187.47 + 1532.40i −0.202292 + 0.141713i
\(490\) 6578.83i 0.606533i
\(491\) 386.189i 0.0354959i 0.999842 + 0.0177479i \(0.00564964\pi\)
−0.999842 + 0.0177479i \(0.994350\pi\)
\(492\) −12779.8 18242.8i −1.17105 1.67165i
\(493\) 10008.0 0.914274
\(494\) 6133.10i 0.558585i
\(495\) −7974.75 2898.59i −0.724118 0.263196i
\(496\) 58.4498i 0.00529127i
\(497\) 2531.25i 0.228454i
\(498\) −6728.51 + 4713.57i −0.605446 + 0.424137i
\(499\) 7220.37 0.647752 0.323876 0.946100i \(-0.395014\pi\)
0.323876 + 0.946100i \(0.395014\pi\)
\(500\) 17024.8i 1.52275i
\(501\) −4777.74 6820.12i −0.426055 0.608185i
\(502\) 25212.3i 2.24160i
\(503\) −5269.99 −0.467152 −0.233576 0.972339i \(-0.575043\pi\)
−0.233576 + 0.972339i \(0.575043\pi\)
\(504\) −2333.08 + 6418.90i −0.206198 + 0.567302i
\(505\) 10615.9i 0.935447i
\(506\) 18398.8 1.61646
\(507\) 5830.27 4084.31i 0.510712 0.357773i
\(508\) −8120.26 −0.709209
\(509\) −21337.4 −1.85808 −0.929039 0.369982i \(-0.879364\pi\)
−0.929039 + 0.369982i \(0.879364\pi\)
\(510\) −15285.8 + 10708.2i −1.32719 + 0.929742i
\(511\) 4551.22i 0.394001i
\(512\) 3120.57 0.269357
\(513\) −1677.53 6244.09i −0.144376 0.537394i
\(514\) 6034.77i 0.517864i
\(515\) 6577.91 0.562830
\(516\) 4653.97 + 6643.44i 0.397054 + 0.566785i
\(517\) 16067.1 1.36679
\(518\) 15400.5i 1.30630i
\(519\) −10530.8 + 7377.23i −0.890659 + 0.623939i
\(520\) 4249.22 0.358348
\(521\) 2794.35i 0.234976i 0.993074 + 0.117488i \(0.0374842\pi\)
−0.993074 + 0.117488i \(0.962516\pi\)
\(522\) 8927.99 + 3245.06i 0.748597 + 0.272093i
\(523\) 16502.9 1.37977 0.689886 0.723918i \(-0.257661\pi\)
0.689886 + 0.723918i \(0.257661\pi\)
\(524\) 3746.44 0.312336
\(525\) 3876.32 2715.50i 0.322241 0.225742i
\(526\) 191.278i 0.0158557i
\(527\) 889.944 0.0735609
\(528\) 1961.09 1373.81i 0.161639 0.113234i
\(529\) −6602.71 −0.542674
\(530\) 8581.05 0.703277
\(531\) 10003.4 + 7046.54i 0.817533 + 0.575882i
\(532\) 6240.52 0.508573
\(533\) −9189.23 −0.746773
\(534\) 30011.0 21023.8i 2.43202 1.70372i
\(535\) 1739.24 0.140549
\(536\) 5559.13i 0.447981i
\(537\) −7219.60 + 5057.59i −0.580165 + 0.406427i
\(538\) −29328.6 −2.35027
\(539\) −12851.0 −1.02696
\(540\) −10717.2 + 2879.28i −0.854067 + 0.229453i
\(541\) 13410.8i 1.06576i −0.846192 0.532878i \(-0.821111\pi\)
0.846192 0.532878i \(-0.178889\pi\)
\(542\) −21035.9 −1.66710
\(543\) 10174.2 7127.41i 0.804083 0.563290i
\(544\) 21123.3i 1.66480i
\(545\) −2410.93 −0.189491
\(546\) 4004.98 + 5717.02i 0.313915 + 0.448106i
\(547\) 6557.46 0.512572 0.256286 0.966601i \(-0.417501\pi\)
0.256286 + 0.966601i \(0.417501\pi\)
\(548\) 20585.3i 1.60467i
\(549\) −14192.7 5158.64i −1.10333 0.401030i
\(550\) −22256.6 −1.72550
\(551\) 3503.73i 0.270896i
\(552\) 7955.32 5572.99i 0.613407 0.429714i
\(553\) −4074.18 −0.313294
\(554\) −29253.5 −2.24344
\(555\) −8272.96 + 5795.51i −0.632734 + 0.443253i
\(556\) 15643.7 1.19324
\(557\) 17276.0i 1.31420i 0.753805 + 0.657099i \(0.228217\pi\)
−0.753805 + 0.657099i \(0.771783\pi\)
\(558\) 793.907 + 288.562i 0.0602308 + 0.0218921i
\(559\) 3346.41 0.253199
\(560\) 514.558i 0.0388287i
\(561\) 20917.4 + 29859.1i 1.57421 + 2.24715i
\(562\) 9677.93i 0.726404i
\(563\) 15957.9 1.19457 0.597285 0.802029i \(-0.296246\pi\)
0.597285 + 0.802029i \(0.296246\pi\)
\(564\) 17210.3 12056.5i 1.28490 0.900122i
\(565\) 194.898i 0.0145123i
\(566\) 34737.1i 2.57970i
\(567\) −5641.19 4725.04i −0.417826 0.349970i
\(568\) 6284.06i 0.464213i
\(569\) 16378.5 1.20672 0.603358 0.797471i \(-0.293829\pi\)
0.603358 + 0.797471i \(0.293829\pi\)
\(570\) 3748.88 + 5351.44i 0.275479 + 0.393241i
\(571\) 5837.15i 0.427806i 0.976855 + 0.213903i \(0.0686177\pi\)
−0.976855 + 0.213903i \(0.931382\pi\)
\(572\) 20562.8i 1.50310i
\(573\) −10830.3 + 7587.02i −0.789603 + 0.553146i
\(574\) 14926.1i 1.08537i
\(575\) −6730.97 −0.488176
\(576\) −7487.09 + 20598.9i −0.541601 + 1.49008i
\(577\) −24908.4 −1.79714 −0.898572 0.438826i \(-0.855394\pi\)
−0.898572 + 0.438826i \(0.855394\pi\)
\(578\) 57451.9 4.13440
\(579\) −13118.4 + 9189.89i −0.941590 + 0.659618i
\(580\) −6013.73 −0.430529
\(581\) 3448.63 0.246254
\(582\) −14216.1 20293.2i −1.01251 1.44533i
\(583\) 16762.1i 1.19077i
\(584\) 11298.8i 0.800598i
\(585\) −1563.96 + 4302.84i −0.110533 + 0.304104i
\(586\) 34009.8i 2.39749i
\(587\) −24884.5 −1.74973 −0.874866 0.484365i \(-0.839051\pi\)
−0.874866 + 0.484365i \(0.839051\pi\)
\(588\) −13765.4 + 9643.18i −0.965436 + 0.676323i
\(589\) 311.563i 0.0217958i
\(590\) −11933.7 3239.35i −0.832716 0.226037i
\(591\) 11980.2 + 17101.4i 0.833839 + 1.19029i
\(592\) 2850.37i 0.197887i
\(593\) 4214.97i 0.291885i 0.989293 + 0.145943i \(0.0466215\pi\)
−0.989293 + 0.145943i \(0.953378\pi\)
\(594\) 8978.38 + 33419.3i 0.620181 + 2.30843i
\(595\) 7834.56 0.539808
\(596\) −17787.2 −1.22247
\(597\) 19154.0 13418.1i 1.31310 0.919877i
\(598\) 9927.23i 0.678854i
\(599\) 26573.3i 1.81261i −0.422620 0.906307i \(-0.638890\pi\)
0.422620 0.906307i \(-0.361110\pi\)
\(600\) −9623.34 + 6741.50i −0.654785 + 0.458701i
\(601\) 20051.3i 1.36092i −0.732787 0.680458i \(-0.761781\pi\)
0.732787 0.680458i \(-0.238219\pi\)
\(602\) 5435.58i 0.368003i
\(603\) 5629.28 + 2046.08i 0.380169 + 0.138180i
\(604\) 40829.3i 2.75053i
\(605\) 8902.41i 0.598239i
\(606\) −35458.7 + 24840.1i −2.37691 + 1.66511i
\(607\) −12265.2 −0.820145 −0.410072 0.912053i \(-0.634497\pi\)
−0.410072 + 0.912053i \(0.634497\pi\)
\(608\) 7395.11 0.493275
\(609\) −2287.98 3266.03i −0.152239 0.217318i
\(610\) 15260.9 1.01295
\(611\) 8669.14i 0.574003i
\(612\) 44811.4 + 16287.6i 2.95980 + 1.07580i
\(613\) 12455.2i 0.820657i −0.911938 0.410328i \(-0.865414\pi\)
0.911938 0.410328i \(-0.134586\pi\)
\(614\) −22318.0 −1.46691
\(615\) −8018.07 + 5616.95i −0.525723 + 0.368288i
\(616\) −13482.3 −0.881849
\(617\) 13837.4i 0.902872i 0.892304 + 0.451436i \(0.149088\pi\)
−0.892304 + 0.451436i \(0.850912\pi\)
\(618\) −15391.6 21971.2i −1.00185 1.43012i
\(619\) −751.124 −0.0487726 −0.0243863 0.999703i \(-0.507763\pi\)
−0.0243863 + 0.999703i \(0.507763\pi\)
\(620\) −534.761 −0.0346396
\(621\) 2715.30 + 10106.9i 0.175461 + 0.653100i
\(622\) 24402.2i 1.57306i
\(623\) −15381.8 −0.989180
\(624\) −741.251 1058.12i −0.0475542 0.0678825i
\(625\) 3796.60 0.242982
\(626\) 40963.2i 2.61536i
\(627\) 10453.5 7323.03i 0.665823 0.466433i
\(628\) 36638.4i 2.32808i
\(629\) 43399.1 2.75109
\(630\) 6989.10 + 2540.33i 0.441988 + 0.160650i
\(631\) 8416.49 0.530991 0.265495 0.964112i \(-0.414465\pi\)
0.265495 + 0.964112i \(0.414465\pi\)
\(632\) 10114.5 0.636605
\(633\) −13617.0 19438.0i −0.855020 1.22052i
\(634\) 37600.9i 2.35540i
\(635\) 3569.00i 0.223042i
\(636\) −12578.0 17954.8i −0.784199 1.11943i
\(637\) 6933.88i 0.431287i
\(638\) 18752.5i 1.16366i
\(639\) −6363.35 2312.89i −0.393944 0.143187i
\(640\) 14580.0i 0.900509i
\(641\) 3885.41i 0.239414i 0.992809 + 0.119707i \(0.0381955\pi\)
−0.992809 + 0.119707i \(0.961804\pi\)
\(642\) −4069.64 5809.32i −0.250180 0.357127i
\(643\) −1897.58 −0.116382 −0.0581908 0.998305i \(-0.518533\pi\)
−0.0581908 + 0.998305i \(0.518533\pi\)
\(644\) −10101.1 −0.618073
\(645\) 2919.92 2045.51i 0.178251 0.124871i
\(646\) 28073.1i 1.70979i
\(647\) 17928.3i 1.08939i −0.838635 0.544694i \(-0.816646\pi\)
0.838635 0.544694i \(-0.183354\pi\)
\(648\) 14004.8 + 11730.4i 0.849012 + 0.711130i
\(649\) −6327.71 + 23311.2i −0.382719 + 1.40993i
\(650\) 12008.7i 0.724646i
\(651\) −203.454 290.427i −0.0122489 0.0174850i
\(652\) −6895.38 −0.414178
\(653\) 1789.92i 0.107266i 0.998561 + 0.0536331i \(0.0170801\pi\)
−0.998561 + 0.0536331i \(0.982920\pi\)
\(654\) 5641.32 + 8052.86i 0.337299 + 0.481486i
\(655\) 1646.63i 0.0982279i
\(656\) 2762.55i 0.164420i
\(657\) 11441.4 + 4158.62i 0.679410 + 0.246945i
\(658\) −14081.3 −0.834264
\(659\) −15179.7 −0.897298 −0.448649 0.893708i \(-0.648095\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(660\) −12569.1 17942.1i −0.741291 1.05818i
\(661\) −23153.2 −1.36241 −0.681207 0.732091i \(-0.738545\pi\)
−0.681207 + 0.732091i \(0.738545\pi\)
\(662\) 54330.8 3.18977
\(663\) 16110.7 11286.1i 0.943723 0.661112i
\(664\) −8561.55 −0.500381
\(665\) 2742.83i 0.159943i
\(666\) 38715.8 + 14072.0i 2.25256 + 0.818740i
\(667\) 5671.25i 0.329223i
\(668\) 21498.5i 1.24522i
\(669\) 1053.94 738.324i 0.0609084 0.0426686i
\(670\) −6052.96 −0.349024
\(671\) 29810.6i 1.71509i
\(672\) 6893.42 4829.09i 0.395714 0.277212i
\(673\) 20396.6i 1.16825i −0.811664 0.584125i \(-0.801438\pi\)
0.811664 0.584125i \(-0.198562\pi\)
\(674\) 33979.0i 1.94188i
\(675\) −3284.63 12226.0i −0.187297 0.697155i
\(676\) 18378.3 1.04565
\(677\) 19292.1i 1.09521i −0.836738 0.547603i \(-0.815540\pi\)
0.836738 0.547603i \(-0.184460\pi\)
\(678\) 650.990 456.042i 0.0368748 0.0258321i
\(679\) 10401.1i 0.587860i
\(680\) −19450.0 −1.09687
\(681\) 5004.00 3505.48i 0.281577 0.197255i
\(682\) 1667.53i 0.0936263i
\(683\) 29395.9 1.64685 0.823427 0.567422i \(-0.192059\pi\)
0.823427 + 0.567422i \(0.192059\pi\)
\(684\) 5702.19 15688.2i 0.318755 0.876977i
\(685\) 9047.63 0.504660
\(686\) 27284.9 1.51858
\(687\) −11544.5 16479.5i −0.641121 0.915186i
\(688\) 1006.03i 0.0557478i
\(689\) −9044.15 −0.500079
\(690\) −6068.06 8662.01i −0.334793 0.477909i
\(691\) 19024.6i 1.04736i 0.851914 + 0.523682i \(0.175442\pi\)
−0.851914 + 0.523682i \(0.824558\pi\)
\(692\) −33195.5 −1.82356
\(693\) 4962.27 13652.5i 0.272007 0.748361i
\(694\) 52176.3 2.85387
\(695\) 6875.72i 0.375268i
\(696\) 5680.12 + 8108.24i 0.309345 + 0.441583i
\(697\) 42062.0 2.28581
\(698\) 11134.1i 0.603770i
\(699\) 11105.9 7780.08i 0.600949 0.420987i
\(700\) 12219.0 0.659766
\(701\) −29699.6 −1.60020 −0.800099 0.599868i \(-0.795220\pi\)
−0.800099 + 0.599868i \(0.795220\pi\)
\(702\) 18031.6 4844.36i 0.969460 0.260454i
\(703\) 15193.7i 0.815139i
\(704\) −43266.2 −2.31627
\(705\) −5299.05 7564.27i −0.283083 0.404095i
\(706\) −11358.0 −0.605472
\(707\) 18174.0 0.966765
\(708\) 10714.3 + 29718.0i 0.568742 + 1.57750i
\(709\) 10911.1 0.577961 0.288981 0.957335i \(-0.406684\pi\)
0.288981 + 0.957335i \(0.406684\pi\)
\(710\) 6842.29 0.361671
\(711\) −3722.72 + 10242.2i −0.196362 + 0.540240i
\(712\) 38186.8 2.00999
\(713\) 504.306i 0.0264887i
\(714\) −18332.1 26168.6i −0.960869 1.37162i
\(715\) −9037.75 −0.472717
\(716\) −22757.8 −1.18785
\(717\) 15282.8 + 21815.9i 0.796020 + 1.13630i
\(718\) 18173.0i 0.944582i
\(719\) −1121.25 −0.0581579 −0.0290790 0.999577i \(-0.509257\pi\)
−0.0290790 + 0.999577i \(0.509257\pi\)
\(720\) −1293.56 470.171i −0.0669557 0.0243364i
\(721\) 11261.1i 0.581673i
\(722\) 21912.9 1.12952
\(723\) −12772.2 + 8947.41i −0.656991 + 0.460246i
\(724\) 32071.4 1.64630
\(725\) 6860.36i 0.351431i
\(726\) −29735.4 + 20830.7i −1.52009 + 1.06488i
\(727\) −8366.74 −0.426830 −0.213415 0.976962i \(-0.568459\pi\)
−0.213415 + 0.976962i \(0.568459\pi\)
\(728\) 7274.50i 0.370345i
\(729\) −17032.9 + 9864.06i −0.865363 + 0.501146i
\(730\) −12302.6 −0.623751
\(731\) −15317.6 −0.775023
\(732\) −22369.3 31931.7i −1.12950 1.61234i
\(733\) −13068.8 −0.658535 −0.329267 0.944237i \(-0.606802\pi\)
−0.329267 + 0.944237i \(0.606802\pi\)
\(734\) 52907.9i 2.66058i
\(735\) 4238.36 + 6050.16i 0.212700 + 0.303624i
\(736\) −11970.0 −0.599482
\(737\) 11823.8i 0.590957i
\(738\) 37523.0 + 13638.5i 1.87160 + 0.680271i
\(739\) 27498.4i 1.36880i −0.729105 0.684402i \(-0.760063\pi\)
0.729105 0.684402i \(-0.239937\pi\)
\(740\) −26078.2 −1.29548
\(741\) −3951.20 5640.25i −0.195885 0.279622i
\(742\) 14690.4i 0.726822i
\(743\) 15660.2i 0.773241i −0.922239 0.386621i \(-0.873642\pi\)
0.922239 0.386621i \(-0.126358\pi\)
\(744\) 505.095 + 721.012i 0.0248894 + 0.0355290i
\(745\) 7817.83i 0.384461i
\(746\) −14323.3 −0.702965
\(747\) 3151.14 8669.59i 0.154343 0.424637i
\(748\) 94122.6i 4.60088i
\(749\) 2977.51i 0.145255i
\(750\) 17508.8 + 24993.4i 0.852442 + 1.21684i
\(751\) 8067.62i 0.392000i −0.980604 0.196000i \(-0.937205\pi\)
0.980604 0.196000i \(-0.0627952\pi\)
\(752\) 2606.20 0.126381
\(753\) −16242.9 23186.3i −0.786086 1.12212i
\(754\) 10118.1 0.488697
\(755\) 17945.2 0.865026
\(756\) −4929.21 18347.5i −0.237134 0.882660i
\(757\) 11714.4 0.562438 0.281219 0.959644i \(-0.409261\pi\)
0.281219 + 0.959644i \(0.409261\pi\)
\(758\) −13985.4 −0.670150
\(759\) −16920.3 + 11853.3i −0.809181 + 0.566861i
\(760\) 6809.32i 0.325000i
\(761\) 27554.7i 1.31256i 0.754517 + 0.656280i \(0.227871\pi\)
−0.754517 + 0.656280i \(0.772129\pi\)
\(762\) 11921.0 8351.11i 0.566736 0.397019i
\(763\) 4127.41i 0.195835i
\(764\) −34139.6 −1.61666
\(765\) 7158.72 19695.5i 0.338332 0.930838i
\(766\) 31141.9i 1.46893i
\(767\) 12577.7 + 3414.17i 0.592119 + 0.160728i
\(768\) −21062.3 + 14754.9i −0.989611 + 0.693258i
\(769\) 10523.3i 0.493471i 0.969083 + 0.246735i \(0.0793579\pi\)
−0.969083 + 0.246735i \(0.920642\pi\)
\(770\) 14680.0i 0.687053i
\(771\) 3887.85 + 5549.82i 0.181605 + 0.259237i
\(772\) −41352.0 −1.92784
\(773\) 9615.25 0.447395 0.223698 0.974659i \(-0.428187\pi\)
0.223698 + 0.974659i \(0.428187\pi\)
\(774\) −13664.6 4966.69i −0.634579 0.230651i
\(775\) 610.046i 0.0282755i
\(776\) 25821.7i 1.19452i
\(777\) −9921.68 14163.0i −0.458093 0.653918i
\(778\) 22195.0i 1.02279i
\(779\) 14725.6i 0.677279i
\(780\) −9680.81 + 6781.76i −0.444396 + 0.311315i
\(781\) 13365.7i 0.612370i
\(782\) 45440.1i 2.07792i
\(783\) −10301.2 + 2767.50i −0.470158 + 0.126312i
\(784\) −2084.52