Properties

Label 105.4.d.b.64.9
Level $105$
Weight $4$
Character 105.64
Analytic conductor $6.195$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.9
Root \(1.37042i\) of defining polynomial
Character \(\chi\) \(=\) 105.64
Dual form 105.4.d.b.64.2

$q$-expansion

\(f(q)\) \(=\) \(q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +(27.7702 - 47.0855i) q^{10} +54.9009 q^{11} +47.7176i q^{12} -49.7580i q^{13} +34.2255 q^{14} +(-17.0392 + 28.8906i) q^{15} +61.7496 q^{16} -133.661i q^{17} -44.0043i q^{18} -138.986 q^{19} +(153.177 + 90.3409i) q^{20} -21.0000 q^{21} +268.430i q^{22} +7.32751i q^{23} -115.964 q^{24} +(60.4815 + 109.394i) q^{25} +243.285 q^{26} +27.0000i q^{27} +111.341i q^{28} -87.2408 q^{29} +(-141.257 - 83.3106i) q^{30} -209.479 q^{31} -7.32107i q^{32} -164.703i q^{33} +653.519 q^{34} +(-39.7580 + 67.4114i) q^{35} +143.153 q^{36} +67.9041i q^{37} -679.555i q^{38} -149.274 q^{39} +(-219.547 + 372.252i) q^{40} +77.6804 q^{41} -102.677i q^{42} -197.692i q^{43} -873.246 q^{44} +(86.6718 + 51.1175i) q^{45} -35.8269 q^{46} -4.97613i q^{47} -185.249i q^{48} -49.0000 q^{49} +(-534.865 + 295.716i) q^{50} -400.984 q^{51} +791.444i q^{52} -53.0843i q^{53} -132.013 q^{54} +(-528.706 - 311.822i) q^{55} -270.582 q^{56} +416.959i q^{57} -426.552i q^{58} +683.950 q^{59} +(271.023 - 459.530i) q^{60} -26.8658 q^{61} -1024.22i q^{62} +63.0000i q^{63} +529.792 q^{64} +(-282.612 + 479.180i) q^{65} +805.291 q^{66} -149.300i q^{67} +2126.00i q^{68} +21.9825 q^{69} +(-329.599 - 194.391i) q^{70} +6.15571 q^{71} +347.892i q^{72} +294.545i q^{73} -332.008 q^{74} +(328.181 - 181.445i) q^{75} +2210.70 q^{76} -384.306i q^{77} -729.855i q^{78} +938.669 q^{79} +(-594.661 - 350.720i) q^{80} +81.0000 q^{81} +379.807i q^{82} +784.907i q^{83} +334.023 q^{84} +(-759.160 + 1287.19i) q^{85} +966.590 q^{86} +261.722i q^{87} -2122.17i q^{88} -275.928 q^{89} +(-249.932 + 423.770i) q^{90} -348.306 q^{91} -116.550i q^{92} +628.437i q^{93} +24.3301 q^{94} +(1338.47 + 789.404i) q^{95} -21.9632 q^{96} -1165.27i q^{97} -239.579i q^{98} -494.108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10}) \) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.88936i 1.72865i 0.502933 + 0.864325i \(0.332254\pi\)
−0.502933 + 0.864325i \(0.667746\pi\)
\(3\) 3.00000i 0.577350i
\(4\) −15.9059 −1.98823
\(5\) −9.63020 5.67972i −0.861351 0.508010i
\(6\) 14.6681 0.998037
\(7\) 7.00000i 0.377964i
\(8\) 38.6546i 1.70831i
\(9\) −9.00000 −0.333333
\(10\) 27.7702 47.0855i 0.878171 1.48898i
\(11\) 54.9009 1.50484 0.752420 0.658684i \(-0.228887\pi\)
0.752420 + 0.658684i \(0.228887\pi\)
\(12\) 47.7176i 1.14791i
\(13\) 49.7580i 1.06157i −0.847507 0.530784i \(-0.821897\pi\)
0.847507 0.530784i \(-0.178103\pi\)
\(14\) 34.2255 0.653368
\(15\) −17.0392 + 28.8906i −0.293300 + 0.497301i
\(16\) 61.7496 0.964837
\(17\) 133.661i 1.90692i −0.301517 0.953461i \(-0.597493\pi\)
0.301517 0.953461i \(-0.402507\pi\)
\(18\) 44.0043i 0.576217i
\(19\) −138.986 −1.67819 −0.839097 0.543983i \(-0.816916\pi\)
−0.839097 + 0.543983i \(0.816916\pi\)
\(20\) 153.177 + 90.3409i 1.71257 + 1.01004i
\(21\) −21.0000 −0.218218
\(22\) 268.430i 2.60134i
\(23\) 7.32751i 0.0664301i 0.999448 + 0.0332150i \(0.0105746\pi\)
−0.999448 + 0.0332150i \(0.989425\pi\)
\(24\) −115.964 −0.986293
\(25\) 60.4815 + 109.394i 0.483852 + 0.875150i
\(26\) 243.285 1.83508
\(27\) 27.0000i 0.192450i
\(28\) 111.341i 0.751481i
\(29\) −87.2408 −0.558628 −0.279314 0.960200i \(-0.590107\pi\)
−0.279314 + 0.960200i \(0.590107\pi\)
\(30\) −141.257 83.3106i −0.859660 0.507012i
\(31\) −209.479 −1.21366 −0.606831 0.794831i \(-0.707560\pi\)
−0.606831 + 0.794831i \(0.707560\pi\)
\(32\) 7.32107i 0.0404436i
\(33\) 164.703i 0.868820i
\(34\) 653.519 3.29640
\(35\) −39.7580 + 67.4114i −0.192010 + 0.325560i
\(36\) 143.153 0.662744
\(37\) 67.9041i 0.301713i 0.988556 + 0.150856i \(0.0482031\pi\)
−0.988556 + 0.150856i \(0.951797\pi\)
\(38\) 679.555i 2.90101i
\(39\) −149.274 −0.612897
\(40\) −219.547 + 372.252i −0.867838 + 1.47145i
\(41\) 77.6804 0.295894 0.147947 0.988995i \(-0.452734\pi\)
0.147947 + 0.988995i \(0.452734\pi\)
\(42\) 102.677i 0.377222i
\(43\) 197.692i 0.701112i −0.936542 0.350556i \(-0.885993\pi\)
0.936542 0.350556i \(-0.114007\pi\)
\(44\) −873.246 −2.99197
\(45\) 86.6718 + 51.1175i 0.287117 + 0.169337i
\(46\) −35.8269 −0.114834
\(47\) 4.97613i 0.0154435i −0.999970 0.00772173i \(-0.997542\pi\)
0.999970 0.00772173i \(-0.00245793\pi\)
\(48\) 185.249i 0.557049i
\(49\) −49.0000 −0.142857
\(50\) −534.865 + 295.716i −1.51283 + 0.836412i
\(51\) −400.984 −1.10096
\(52\) 791.444i 2.11065i
\(53\) 53.0843i 0.137579i −0.997631 0.0687895i \(-0.978086\pi\)
0.997631 0.0687895i \(-0.0219137\pi\)
\(54\) −132.013 −0.332679
\(55\) −528.706 311.822i −1.29620 0.764473i
\(56\) −270.582 −0.645680
\(57\) 416.959i 0.968905i
\(58\) 426.552i 0.965673i
\(59\) 683.950 1.50920 0.754599 0.656186i \(-0.227831\pi\)
0.754599 + 0.656186i \(0.227831\pi\)
\(60\) 271.023 459.530i 0.583148 0.988751i
\(61\) −26.8658 −0.0563904 −0.0281952 0.999602i \(-0.508976\pi\)
−0.0281952 + 0.999602i \(0.508976\pi\)
\(62\) 1024.22i 2.09800i
\(63\) 63.0000i 0.125988i
\(64\) 529.792 1.03475
\(65\) −282.612 + 479.180i −0.539287 + 0.914383i
\(66\) 805.291 1.50189
\(67\) 149.300i 0.272237i −0.990693 0.136119i \(-0.956537\pi\)
0.990693 0.136119i \(-0.0434628\pi\)
\(68\) 2126.00i 3.79140i
\(69\) 21.9825 0.0383534
\(70\) −329.599 194.391i −0.562780 0.331918i
\(71\) 6.15571 0.0102894 0.00514470 0.999987i \(-0.498362\pi\)
0.00514470 + 0.999987i \(0.498362\pi\)
\(72\) 347.892i 0.569436i
\(73\) 294.545i 0.472245i 0.971723 + 0.236123i \(0.0758767\pi\)
−0.971723 + 0.236123i \(0.924123\pi\)
\(74\) −332.008 −0.521556
\(75\) 328.181 181.445i 0.505268 0.279352i
\(76\) 2210.70 3.33664
\(77\) 384.306i 0.568776i
\(78\) 729.855i 1.05948i
\(79\) 938.669 1.33682 0.668409 0.743794i \(-0.266976\pi\)
0.668409 + 0.743794i \(0.266976\pi\)
\(80\) −594.661 350.720i −0.831063 0.490146i
\(81\) 81.0000 0.111111
\(82\) 379.807i 0.511496i
\(83\) 784.907i 1.03801i 0.854772 + 0.519004i \(0.173697\pi\)
−0.854772 + 0.519004i \(0.826303\pi\)
\(84\) 334.023 0.433868
\(85\) −759.160 + 1287.19i −0.968735 + 1.64253i
\(86\) 966.590 1.21198
\(87\) 261.722i 0.322524i
\(88\) 2122.17i 2.57073i
\(89\) −275.928 −0.328633 −0.164316 0.986408i \(-0.552542\pi\)
−0.164316 + 0.986408i \(0.552542\pi\)
\(90\) −249.932 + 423.770i −0.292724 + 0.496325i
\(91\) −348.306 −0.401235
\(92\) 116.550i 0.132078i
\(93\) 628.437i 0.700708i
\(94\) 24.3301 0.0266963
\(95\) 1338.47 + 789.404i 1.44551 + 0.852538i
\(96\) −21.9632 −0.0233501
\(97\) 1165.27i 1.21975i −0.792499 0.609873i \(-0.791220\pi\)
0.792499 0.609873i \(-0.208780\pi\)
\(98\) 239.579i 0.246950i
\(99\) −494.108 −0.501613
\(100\) −962.011 1740.00i −0.962011 1.74000i
\(101\) −0.162999 −0.000160584 −8.02919e−5 1.00000i \(-0.500026\pi\)
−8.02919e−5 1.00000i \(0.500026\pi\)
\(102\) 1960.56i 1.90318i
\(103\) 1300.78i 1.24437i 0.782871 + 0.622184i \(0.213755\pi\)
−0.782871 + 0.622184i \(0.786245\pi\)
\(104\) −1923.38 −1.81349
\(105\) 202.234 + 119.274i 0.187962 + 0.110857i
\(106\) 259.548 0.237826
\(107\) 1531.63i 1.38382i −0.721985 0.691908i \(-0.756770\pi\)
0.721985 0.691908i \(-0.243230\pi\)
\(108\) 429.458i 0.382636i
\(109\) −1971.39 −1.73234 −0.866171 0.499748i \(-0.833426\pi\)
−0.866171 + 0.499748i \(0.833426\pi\)
\(110\) 1524.61 2585.04i 1.32151 2.24067i
\(111\) 203.712 0.174194
\(112\) 432.247i 0.364674i
\(113\) 262.817i 0.218794i −0.993998 0.109397i \(-0.965108\pi\)
0.993998 0.109397i \(-0.0348920\pi\)
\(114\) −2038.66 −1.67490
\(115\) 41.6182 70.5654i 0.0337471 0.0572196i
\(116\) 1387.64 1.11068
\(117\) 447.822i 0.353856i
\(118\) 3344.08i 2.60888i
\(119\) −935.630 −0.720749
\(120\) 1116.76 + 658.642i 0.849545 + 0.501046i
\(121\) 1683.11 1.26454
\(122\) 131.357i 0.0974793i
\(123\) 233.041i 0.170834i
\(124\) 3331.94 2.41304
\(125\) 38.8765 1397.00i 0.0278177 0.999613i
\(126\) −308.030 −0.217789
\(127\) 569.649i 0.398017i −0.979998 0.199009i \(-0.936228\pi\)
0.979998 0.199009i \(-0.0637722\pi\)
\(128\) 2531.78i 1.74828i
\(129\) −593.077 −0.404787
\(130\) −2342.88 1381.79i −1.58065 0.932239i
\(131\) 984.808 0.656817 0.328409 0.944536i \(-0.393488\pi\)
0.328409 + 0.944536i \(0.393488\pi\)
\(132\) 2619.74i 1.72742i
\(133\) 972.905i 0.634297i
\(134\) 729.982 0.470603
\(135\) 153.352 260.015i 0.0977665 0.165767i
\(136\) −5166.63 −3.25761
\(137\) 1377.35i 0.858942i 0.903081 + 0.429471i \(0.141300\pi\)
−0.903081 + 0.429471i \(0.858700\pi\)
\(138\) 107.481i 0.0662997i
\(139\) −839.673 −0.512375 −0.256188 0.966627i \(-0.582466\pi\)
−0.256188 + 0.966627i \(0.582466\pi\)
\(140\) 632.386 1072.24i 0.381760 0.647289i
\(141\) −14.9284 −0.00891629
\(142\) 30.0975i 0.0177868i
\(143\) 2731.76i 1.59749i
\(144\) −555.746 −0.321612
\(145\) 840.147 + 495.504i 0.481175 + 0.283788i
\(146\) −1440.14 −0.816347
\(147\) 147.000i 0.0824786i
\(148\) 1080.07i 0.599875i
\(149\) 1470.33 0.808416 0.404208 0.914667i \(-0.367547\pi\)
0.404208 + 0.914667i \(0.367547\pi\)
\(150\) 887.148 + 1604.60i 0.482902 + 0.873432i
\(151\) −1695.79 −0.913916 −0.456958 0.889488i \(-0.651061\pi\)
−0.456958 + 0.889488i \(0.651061\pi\)
\(152\) 5372.47i 2.86687i
\(153\) 1202.95i 0.635641i
\(154\) 1879.01 0.983215
\(155\) 2017.32 + 1189.78i 1.04539 + 0.616552i
\(156\) 2374.33 1.21858
\(157\) 959.433i 0.487714i −0.969811 0.243857i \(-0.921587\pi\)
0.969811 0.243857i \(-0.0784127\pi\)
\(158\) 4589.49i 2.31089i
\(159\) −159.253 −0.0794312
\(160\) −41.5816 + 70.5033i −0.0205457 + 0.0348361i
\(161\) 51.2926 0.0251082
\(162\) 396.038i 0.192072i
\(163\) 3865.27i 1.85737i −0.370869 0.928685i \(-0.620940\pi\)
0.370869 0.928685i \(-0.379060\pi\)
\(164\) −1235.57 −0.588305
\(165\) −935.465 + 1586.12i −0.441369 + 0.748359i
\(166\) −3837.69 −1.79435
\(167\) 465.084i 0.215505i 0.994178 + 0.107752i \(0.0343653\pi\)
−0.994178 + 0.107752i \(0.965635\pi\)
\(168\) 811.747i 0.372784i
\(169\) −278.860 −0.126927
\(170\) −6293.52 3711.81i −2.83936 1.67460i
\(171\) 1250.88 0.559398
\(172\) 3144.47i 1.39397i
\(173\) 2048.04i 0.900057i 0.893014 + 0.450028i \(0.148586\pi\)
−0.893014 + 0.450028i \(0.851414\pi\)
\(174\) −1279.66 −0.557531
\(175\) 765.756 423.371i 0.330775 0.182879i
\(176\) 3390.10 1.45192
\(177\) 2051.85i 0.871336i
\(178\) 1349.11i 0.568091i
\(179\) 911.856 0.380756 0.190378 0.981711i \(-0.439029\pi\)
0.190378 + 0.981711i \(0.439029\pi\)
\(180\) −1378.59 813.068i −0.570856 0.336681i
\(181\) −2029.81 −0.833562 −0.416781 0.909007i \(-0.636842\pi\)
−0.416781 + 0.909007i \(0.636842\pi\)
\(182\) 1702.99i 0.693595i
\(183\) 80.5975i 0.0325570i
\(184\) 283.242 0.113483
\(185\) 385.677 653.930i 0.153273 0.259881i
\(186\) −3072.66 −1.21128
\(187\) 7338.13i 2.86961i
\(188\) 79.1496i 0.0307052i
\(189\) 189.000 0.0727393
\(190\) −3859.68 + 6544.25i −1.47374 + 2.49879i
\(191\) 4984.11 1.88815 0.944077 0.329725i \(-0.106956\pi\)
0.944077 + 0.329725i \(0.106956\pi\)
\(192\) 1589.38i 0.597413i
\(193\) 3393.44i 1.26562i −0.774306 0.632811i \(-0.781901\pi\)
0.774306 0.632811i \(-0.218099\pi\)
\(194\) 5697.43 2.10852
\(195\) 1437.54 + 847.835i 0.527919 + 0.311358i
\(196\) 779.387 0.284033
\(197\) 762.475i 0.275757i −0.990449 0.137878i \(-0.955972\pi\)
0.990449 0.137878i \(-0.0440283\pi\)
\(198\) 2415.87i 0.867114i
\(199\) 1272.32 0.453227 0.226613 0.973985i \(-0.427235\pi\)
0.226613 + 0.973985i \(0.427235\pi\)
\(200\) 4228.57 2337.89i 1.49503 0.826569i
\(201\) −447.900 −0.157176
\(202\) 0.796959i 0.000277593i
\(203\) 610.686i 0.211142i
\(204\) 6378.00 2.18897
\(205\) −748.077 441.203i −0.254868 0.150317i
\(206\) −6360.00 −2.15108
\(207\) 65.9476i 0.0221434i
\(208\) 3072.53i 1.02424i
\(209\) −7630.47 −2.52541
\(210\) −583.174 + 988.796i −0.191633 + 0.324921i
\(211\) 2010.72 0.656035 0.328017 0.944672i \(-0.393620\pi\)
0.328017 + 0.944672i \(0.393620\pi\)
\(212\) 844.351i 0.273539i
\(213\) 18.4671i 0.00594059i
\(214\) 7488.70 2.39214
\(215\) −1122.84 + 1903.82i −0.356172 + 0.603904i
\(216\) 1043.67 0.328764
\(217\) 1466.35i 0.458721i
\(218\) 9638.85i 2.99461i
\(219\) 883.635 0.272651
\(220\) 8409.53 + 4959.79i 2.57714 + 1.51995i
\(221\) −6650.73 −2.02433
\(222\) 996.024i 0.301120i
\(223\) 1516.44i 0.455374i 0.973734 + 0.227687i \(0.0731163\pi\)
−0.973734 + 0.227687i \(0.926884\pi\)
\(224\) −51.2475 −0.0152862
\(225\) −544.334 984.543i −0.161284 0.291717i
\(226\) 1285.01 0.378219
\(227\) 4101.17i 1.19914i −0.800323 0.599568i \(-0.795339\pi\)
0.800323 0.599568i \(-0.204661\pi\)
\(228\) 6632.10i 1.92641i
\(229\) 1029.24 0.297004 0.148502 0.988912i \(-0.452555\pi\)
0.148502 + 0.988912i \(0.452555\pi\)
\(230\) 345.020 + 203.487i 0.0989128 + 0.0583370i
\(231\) −1152.92 −0.328383
\(232\) 3372.26i 0.954309i
\(233\) 5578.41i 1.56847i 0.620463 + 0.784236i \(0.286945\pi\)
−0.620463 + 0.784236i \(0.713055\pi\)
\(234\) −2189.56 −0.611694
\(235\) −28.2630 + 47.9211i −0.00784543 + 0.0133022i
\(236\) −10878.8 −3.00064
\(237\) 2816.01i 0.771812i
\(238\) 4574.64i 1.24592i
\(239\) −5389.67 −1.45870 −0.729348 0.684142i \(-0.760177\pi\)
−0.729348 + 0.684142i \(0.760177\pi\)
\(240\) −1052.16 + 1783.98i −0.282986 + 0.479815i
\(241\) 3976.27 1.06280 0.531399 0.847122i \(-0.321667\pi\)
0.531399 + 0.847122i \(0.321667\pi\)
\(242\) 8229.31i 2.18595i
\(243\) 243.000i 0.0641500i
\(244\) 427.324 0.112117
\(245\) 471.880 + 278.306i 0.123050 + 0.0725728i
\(246\) 1139.42 0.295313
\(247\) 6915.69i 1.78152i
\(248\) 8097.33i 2.07331i
\(249\) 2354.72 0.599294
\(250\) 6830.45 + 190.081i 1.72798 + 0.0480871i
\(251\) 7095.76 1.78438 0.892192 0.451655i \(-0.149166\pi\)
0.892192 + 0.451655i \(0.149166\pi\)
\(252\) 1002.07i 0.250494i
\(253\) 402.287i 0.0999666i
\(254\) 2785.22 0.688033
\(255\) 3861.56 + 2277.48i 0.948315 + 0.559299i
\(256\) −8140.43 −1.98741
\(257\) 2526.56i 0.613239i 0.951832 + 0.306619i \(0.0991979\pi\)
−0.951832 + 0.306619i \(0.900802\pi\)
\(258\) 2899.77i 0.699735i
\(259\) 475.329 0.114037
\(260\) 4495.18 7621.77i 1.07223 1.81801i
\(261\) 785.167 0.186209
\(262\) 4815.08i 1.13541i
\(263\) 3842.34i 0.900871i −0.892809 0.450435i \(-0.851269\pi\)
0.892809 0.450435i \(-0.148731\pi\)
\(264\) −6366.52 −1.48421
\(265\) −301.504 + 511.212i −0.0698914 + 0.118504i
\(266\) −4756.88 −1.09648
\(267\) 827.784i 0.189736i
\(268\) 2374.75i 0.541271i
\(269\) 8411.04 1.90643 0.953216 0.302291i \(-0.0977514\pi\)
0.953216 + 0.302291i \(0.0977514\pi\)
\(270\) 1271.31 + 749.796i 0.286553 + 0.169004i
\(271\) 5659.73 1.26865 0.634325 0.773067i \(-0.281278\pi\)
0.634325 + 0.773067i \(0.281278\pi\)
\(272\) 8253.54i 1.83987i
\(273\) 1044.92i 0.231653i
\(274\) −6734.37 −1.48481
\(275\) 3320.49 + 6005.81i 0.728120 + 1.31696i
\(276\) −349.651 −0.0762555
\(277\) 881.409i 0.191187i 0.995420 + 0.0955934i \(0.0304749\pi\)
−0.995420 + 0.0955934i \(0.969525\pi\)
\(278\) 4105.47i 0.885718i
\(279\) 1885.31 0.404554
\(280\) 2605.76 + 1536.83i 0.556157 + 0.328012i
\(281\) −3853.71 −0.818124 −0.409062 0.912506i \(-0.634144\pi\)
−0.409062 + 0.912506i \(0.634144\pi\)
\(282\) 72.9902i 0.0154131i
\(283\) 1891.60i 0.397328i −0.980068 0.198664i \(-0.936340\pi\)
0.980068 0.198664i \(-0.0636603\pi\)
\(284\) −97.9118 −0.0204577
\(285\) 2368.21 4015.40i 0.492213 0.834568i
\(286\) 13356.6 2.76150
\(287\) 543.763i 0.111837i
\(288\) 65.8896i 0.0134812i
\(289\) −12952.4 −2.63635
\(290\) −2422.70 + 4107.78i −0.490571 + 0.831784i
\(291\) −3495.81 −0.704221
\(292\) 4684.99i 0.938933i
\(293\) 4076.18i 0.812742i −0.913708 0.406371i \(-0.866794\pi\)
0.913708 0.406371i \(-0.133206\pi\)
\(294\) −718.736 −0.142577
\(295\) −6586.58 3884.65i −1.29995 0.766687i
\(296\) 2624.81 0.515419
\(297\) 1482.32i 0.289607i
\(298\) 7188.97i 1.39747i
\(299\) 364.602 0.0705201
\(300\) −5220.00 + 2886.03i −1.00459 + 0.555417i
\(301\) −1383.85 −0.264995
\(302\) 8291.33i 1.57984i
\(303\) 0.488996i 9.27131e-5i
\(304\) −8582.35 −1.61918
\(305\) 258.723 + 152.590i 0.0485720 + 0.0286469i
\(306\) −5881.67 −1.09880
\(307\) 6201.87i 1.15296i −0.817110 0.576481i \(-0.804425\pi\)
0.817110 0.576481i \(-0.195575\pi\)
\(308\) 6112.72i 1.13086i
\(309\) 3902.35 0.718437
\(310\) −5817.28 + 9863.43i −1.06580 + 1.80711i
\(311\) −6601.95 −1.20374 −0.601868 0.798595i \(-0.705577\pi\)
−0.601868 + 0.798595i \(0.705577\pi\)
\(312\) 5770.13i 1.04702i
\(313\) 2291.01i 0.413724i 0.978370 + 0.206862i \(0.0663251\pi\)
−0.978370 + 0.206862i \(0.933675\pi\)
\(314\) 4691.02 0.843087
\(315\) 357.822 606.703i 0.0640032 0.108520i
\(316\) −14930.3 −2.65790
\(317\) 3124.07i 0.553517i −0.960939 0.276759i \(-0.910740\pi\)
0.960939 0.276759i \(-0.0892603\pi\)
\(318\) 778.644i 0.137309i
\(319\) −4789.60 −0.840646
\(320\) −5102.00 3009.07i −0.891283 0.525663i
\(321\) −4594.89 −0.798947
\(322\) 250.788i 0.0434033i
\(323\) 18577.1i 3.20018i
\(324\) −1288.37 −0.220915
\(325\) 5443.21 3009.44i 0.929031 0.513642i
\(326\) 18898.7 3.21074
\(327\) 5914.18i 1.00017i
\(328\) 3002.70i 0.505478i
\(329\) −34.8329 −0.00583708
\(330\) −7755.11 4573.83i −1.29365 0.762972i
\(331\) 9825.49 1.63159 0.815797 0.578338i \(-0.196298\pi\)
0.815797 + 0.578338i \(0.196298\pi\)
\(332\) 12484.6i 2.06380i
\(333\) 611.137i 0.100571i
\(334\) −2273.96 −0.372532
\(335\) −847.983 + 1437.79i −0.138299 + 0.234492i
\(336\) −1296.74 −0.210545
\(337\) 8526.35i 1.37822i 0.724657 + 0.689110i \(0.241998\pi\)
−0.724657 + 0.689110i \(0.758002\pi\)
\(338\) 1363.45i 0.219413i
\(339\) −788.451 −0.126321
\(340\) 12075.1 20473.8i 1.92607 3.26573i
\(341\) −11500.6 −1.82637
\(342\) 6115.99i 0.967003i
\(343\) 343.000i 0.0539949i
\(344\) −7641.73 −1.19772
\(345\) −211.696 124.855i −0.0330358 0.0194839i
\(346\) −10013.6 −1.55588
\(347\) 4164.54i 0.644277i −0.946693 0.322138i \(-0.895598\pi\)
0.946693 0.322138i \(-0.104402\pi\)
\(348\) 4162.92i 0.641253i
\(349\) −2584.60 −0.396420 −0.198210 0.980160i \(-0.563513\pi\)
−0.198210 + 0.980160i \(0.563513\pi\)
\(350\) 2070.01 + 3744.06i 0.316134 + 0.571795i
\(351\) 1343.47 0.204299
\(352\) 401.933i 0.0608611i
\(353\) 4199.25i 0.633154i 0.948567 + 0.316577i \(0.102534\pi\)
−0.948567 + 0.316577i \(0.897466\pi\)
\(354\) 10032.2 1.50624
\(355\) −59.2807 34.9627i −0.00886280 0.00522712i
\(356\) 4388.87 0.653398
\(357\) 2806.89i 0.416124i
\(358\) 4458.39i 0.658194i
\(359\) 990.277 0.145584 0.0727922 0.997347i \(-0.476809\pi\)
0.0727922 + 0.997347i \(0.476809\pi\)
\(360\) 1975.93 3350.27i 0.289279 0.490485i
\(361\) 12458.2 1.81633
\(362\) 9924.48i 1.44094i
\(363\) 5049.32i 0.730084i
\(364\) 5540.11 0.797749
\(365\) 1672.93 2836.53i 0.239905 0.406769i
\(366\) −394.070 −0.0562797
\(367\) 4179.24i 0.594427i −0.954811 0.297213i \(-0.903943\pi\)
0.954811 0.297213i \(-0.0960573\pi\)
\(368\) 452.471i 0.0640942i
\(369\) −699.123 −0.0986312
\(370\) 3197.30 + 1885.71i 0.449243 + 0.264955i
\(371\) −371.590 −0.0519999
\(372\) 9995.83i 1.39317i
\(373\) 7365.36i 1.02242i −0.859455 0.511212i \(-0.829197\pi\)
0.859455 0.511212i \(-0.170803\pi\)
\(374\) 35878.8 4.96056
\(375\) −4191.00 116.629i −0.577127 0.0160606i
\(376\) −192.350 −0.0263822
\(377\) 4340.93i 0.593022i
\(378\) 924.089i 0.125741i
\(379\) 6214.13 0.842213 0.421106 0.907011i \(-0.361642\pi\)
0.421106 + 0.907011i \(0.361642\pi\)
\(380\) −21289.5 12556.2i −2.87402 1.69504i
\(381\) −1708.95 −0.229795
\(382\) 24369.1i 3.26396i
\(383\) 1755.04i 0.234148i −0.993123 0.117074i \(-0.962649\pi\)
0.993123 0.117074i \(-0.0373514\pi\)
\(384\) 7595.33 1.00937
\(385\) −2182.75 + 3700.94i −0.288944 + 0.489916i
\(386\) 16591.7 2.18782
\(387\) 1779.23i 0.233704i
\(388\) 18534.6i 2.42514i
\(389\) −8805.69 −1.14773 −0.573864 0.818950i \(-0.694556\pi\)
−0.573864 + 0.818950i \(0.694556\pi\)
\(390\) −4145.37 + 7028.65i −0.538228 + 0.912588i
\(391\) 979.406 0.126677
\(392\) 1894.08i 0.244044i
\(393\) 2954.42i 0.379214i
\(394\) 3728.01 0.476687
\(395\) −9039.57 5331.38i −1.15147 0.679116i
\(396\) 7859.21 0.997324
\(397\) 13717.2i 1.73413i 0.498199 + 0.867063i \(0.333995\pi\)
−0.498199 + 0.867063i \(0.666005\pi\)
\(398\) 6220.82i 0.783471i
\(399\) 2918.71 0.366212
\(400\) 3734.71 + 6755.01i 0.466838 + 0.844377i
\(401\) 307.220 0.0382590 0.0191295 0.999817i \(-0.493911\pi\)
0.0191295 + 0.999817i \(0.493911\pi\)
\(402\) 2189.95i 0.271703i
\(403\) 10423.3i 1.28839i
\(404\) 2.59263 0.000319278
\(405\) −780.046 460.057i −0.0957057 0.0564455i
\(406\) −2985.86 −0.364990
\(407\) 3728.00i 0.454029i
\(408\) 15499.9i 1.88078i
\(409\) −12390.7 −1.49799 −0.748997 0.662573i \(-0.769464\pi\)
−0.748997 + 0.662573i \(0.769464\pi\)
\(410\) 2157.20 3657.62i 0.259845 0.440578i
\(411\) 4132.05 0.495910
\(412\) 20690.1i 2.47409i
\(413\) 4787.65i 0.570423i
\(414\) 322.442 0.0382781
\(415\) 4458.05 7558.81i 0.527318 0.894090i
\(416\) −364.282 −0.0429336
\(417\) 2519.02i 0.295820i
\(418\) 37308.2i 4.36555i
\(419\) −2664.10 −0.310620 −0.155310 0.987866i \(-0.549638\pi\)
−0.155310 + 0.987866i \(0.549638\pi\)
\(420\) −3216.71 1897.16i −0.373713 0.220409i
\(421\) −6851.11 −0.793118 −0.396559 0.918009i \(-0.629796\pi\)
−0.396559 + 0.918009i \(0.629796\pi\)
\(422\) 9831.12i 1.13406i
\(423\) 44.7851i 0.00514782i
\(424\) −2051.95 −0.235027
\(425\) 14621.7 8084.05i 1.66884 0.922668i
\(426\) 90.2924 0.0102692
\(427\) 188.061i 0.0213136i
\(428\) 24361.9i 2.75135i
\(429\) −8195.27 −0.922311
\(430\) −9308.45 5489.96i −1.04394 0.615696i
\(431\) −7651.38 −0.855114 −0.427557 0.903988i \(-0.640626\pi\)
−0.427557 + 0.903988i \(0.640626\pi\)
\(432\) 1667.24i 0.185683i
\(433\) 691.572i 0.0767548i 0.999263 + 0.0383774i \(0.0122189\pi\)
−0.999263 + 0.0383774i \(0.987781\pi\)
\(434\) −7169.53 −0.792969
\(435\) 1486.51 2520.44i 0.163845 0.277807i
\(436\) 31356.7 3.44430
\(437\) 1018.42i 0.111483i
\(438\) 4320.41i 0.471318i
\(439\) −10621.7 −1.15478 −0.577389 0.816469i \(-0.695928\pi\)
−0.577389 + 0.816469i \(0.695928\pi\)
\(440\) −12053.3 + 20436.9i −1.30596 + 2.21430i
\(441\) 441.000 0.0476190
\(442\) 32517.8i 3.49936i
\(443\) 3133.67i 0.336084i −0.985780 0.168042i \(-0.946256\pi\)
0.985780 0.168042i \(-0.0537444\pi\)
\(444\) −3240.22 −0.346338
\(445\) 2657.24 + 1567.19i 0.283068 + 0.166949i
\(446\) −7414.43 −0.787182
\(447\) 4410.99i 0.466739i
\(448\) 3708.54i 0.391099i
\(449\) 9144.92 0.961192 0.480596 0.876942i \(-0.340420\pi\)
0.480596 + 0.876942i \(0.340420\pi\)
\(450\) 4813.79 2661.45i 0.504276 0.278804i
\(451\) 4264.72 0.445272
\(452\) 4180.33i 0.435014i
\(453\) 5087.37i 0.527650i
\(454\) 20052.1 2.07289
\(455\) 3354.26 + 1978.28i 0.345604 + 0.203831i
\(456\) 16117.4 1.65519
\(457\) 8142.60i 0.833468i 0.909029 + 0.416734i \(0.136825\pi\)
−0.909029 + 0.416734i \(0.863175\pi\)
\(458\) 5032.32i 0.513417i
\(459\) 3608.86 0.366987
\(460\) −661.974 + 1122.40i −0.0670971 + 0.113766i
\(461\) −9287.29 −0.938291 −0.469145 0.883121i \(-0.655438\pi\)
−0.469145 + 0.883121i \(0.655438\pi\)
\(462\) 5637.04i 0.567659i
\(463\) 2440.53i 0.244970i −0.992470 0.122485i \(-0.960914\pi\)
0.992470 0.122485i \(-0.0390864\pi\)
\(464\) −5387.08 −0.538985
\(465\) 3569.35 6051.97i 0.355967 0.603556i
\(466\) −27274.9 −2.71134
\(467\) 12066.3i 1.19564i −0.801632 0.597818i \(-0.796034\pi\)
0.801632 0.597818i \(-0.203966\pi\)
\(468\) 7123.00i 0.703548i
\(469\) −1045.10 −0.102896
\(470\) −234.304 138.188i −0.0229949 0.0135620i
\(471\) −2878.30 −0.281582
\(472\) 26437.8i 2.57818i
\(473\) 10853.5i 1.05506i
\(474\) 13768.5 1.33419
\(475\) −8406.11 15204.2i −0.811998 1.46867i
\(476\) 14882.0 1.43302
\(477\) 477.758i 0.0458596i
\(478\) 26352.0i 2.52158i
\(479\) −395.211 −0.0376987 −0.0188493 0.999822i \(-0.506000\pi\)
−0.0188493 + 0.999822i \(0.506000\pi\)
\(480\) 211.510 + 124.745i 0.0201126 + 0.0118621i
\(481\) 3378.77 0.320289
\(482\) 19441.4i 1.83721i
\(483\) 153.878i 0.0144962i
\(484\) −26771.2 −2.51420
\(485\) −6618.42 + 11221.8i −0.619643 + 1.05063i
\(486\) 1188.11 0.110893
\(487\) 9609.06i 0.894102i −0.894508 0.447051i \(-0.852474\pi\)
0.894508 0.447051i \(-0.147526\pi\)
\(488\) 1038.49i 0.0963323i
\(489\) −11595.8 −1.07235
\(490\) −1360.74 + 2307.19i −0.125453 + 0.212711i
\(491\) 10941.0 1.00562 0.502810 0.864397i \(-0.332299\pi\)
0.502810 + 0.864397i \(0.332299\pi\)
\(492\) 3706.72i 0.339658i
\(493\) 11660.7i 1.06526i
\(494\) −33813.3 −3.07962
\(495\) 4758.36 + 2806.39i 0.432065 + 0.254824i
\(496\) −12935.2 −1.17099
\(497\) 43.0899i 0.00388903i
\(498\) 11513.1i 1.03597i
\(499\) −9269.90 −0.831618 −0.415809 0.909452i \(-0.636502\pi\)
−0.415809 + 0.909452i \(0.636502\pi\)
\(500\) −618.363 + 22220.5i −0.0553081 + 1.98746i
\(501\) 1395.25 0.124422
\(502\) 34693.8i 3.08458i
\(503\) 15085.4i 1.33723i −0.743609 0.668615i \(-0.766888\pi\)
0.743609 0.668615i \(-0.233112\pi\)
\(504\) 2435.24 0.215227
\(505\) 1.56971 + 0.925787i 0.000138319 + 8.15781e-5i
\(506\) −1966.93 −0.172807
\(507\) 836.579i 0.0732816i
\(508\) 9060.76i 0.791351i
\(509\) −8650.44 −0.753289 −0.376645 0.926358i \(-0.622922\pi\)
−0.376645 + 0.926358i \(0.622922\pi\)
\(510\) −11135.4 + 18880.6i −0.966833 + 1.63931i
\(511\) 2061.82 0.178492
\(512\) 19547.3i 1.68726i
\(513\) 3752.63i 0.322968i
\(514\) −12353.3 −1.06008
\(515\) 7388.09 12526.8i 0.632151 1.07184i
\(516\) 9433.40 0.804811
\(517\) 273.194i 0.0232399i
\(518\) 2324.06i 0.197130i
\(519\) 6144.13 0.519648
\(520\) 18522.5 + 10924.2i 1.56205 + 0.921269i
\(521\) 10661.6 0.896535 0.448268 0.893899i \(-0.352041\pi\)
0.448268 + 0.893899i \(0.352041\pi\)
\(522\) 3838.97i 0.321891i
\(523\) 3449.22i 0.288382i −0.989550 0.144191i \(-0.953942\pi\)
0.989550 0.144191i \(-0.0460580\pi\)
\(524\) −15664.2 −1.30591
\(525\) −1270.11 2297.27i −0.105585 0.190973i
\(526\) 18786.6 1.55729
\(527\) 27999.3i 2.31436i
\(528\) 10170.3i 0.838269i
\(529\) 12113.3 0.995587
\(530\) −2499.50 1474.16i −0.204852 0.120818i
\(531\) −6155.55 −0.503066
\(532\) 15474.9i 1.26113i
\(533\) 3865.22i 0.314111i
\(534\) −4047.34 −0.327988
\(535\) −8699.24 + 14749.9i −0.702992 + 1.19195i
\(536\) −5771.14 −0.465066
\(537\) 2735.57i 0.219829i
\(538\) 41124.6i 3.29555i
\(539\) −2690.14 −0.214977
\(540\) −2439.20 + 4135.77i −0.194383 + 0.329584i
\(541\) 13403.2 1.06516 0.532578 0.846381i \(-0.321223\pi\)
0.532578 + 0.846381i \(0.321223\pi\)
\(542\) 27672.5i 2.19305i
\(543\) 6089.43i 0.481257i
\(544\) −978.544 −0.0771227
\(545\) 18984.9 + 11197.0i 1.49215 + 0.880046i
\(546\) −5108.98 −0.400447
\(547\) 3670.29i 0.286893i 0.989658 + 0.143446i \(0.0458184\pi\)
−0.989658 + 0.143446i \(0.954182\pi\)
\(548\) 21907.9i 1.70778i
\(549\) 241.792 0.0187968
\(550\) −29364.6 + 16235.1i −2.27656 + 1.25867i
\(551\) 12125.3 0.937486
\(552\) 849.727i 0.0655195i
\(553\) 6570.69i 0.505269i
\(554\) −4309.53 −0.330495
\(555\) −1961.79 1157.03i −0.150042 0.0884922i
\(556\) 13355.7 1.01872
\(557\) 521.169i 0.0396456i −0.999804 0.0198228i \(-0.993690\pi\)
0.999804 0.0198228i \(-0.00631021\pi\)
\(558\) 9217.97i 0.699333i
\(559\) −9836.78 −0.744278
\(560\) −2455.04 + 4162.62i −0.185258 + 0.314112i
\(561\) −22014.4 −1.65677
\(562\) 18842.2i 1.41425i
\(563\) 17970.2i 1.34521i −0.740000 0.672606i \(-0.765175\pi\)
0.740000 0.672606i \(-0.234825\pi\)
\(564\) 237.449 0.0177277
\(565\) −1492.73 + 2530.98i −0.111150 + 0.188459i
\(566\) 9248.71 0.686842
\(567\) 567.000i 0.0419961i
\(568\) 237.947i 0.0175775i
\(569\) 21808.6 1.60679 0.803396 0.595445i \(-0.203024\pi\)
0.803396 + 0.595445i \(0.203024\pi\)
\(570\) 19632.7 + 11579.0i 1.44268 + 0.850865i
\(571\) 6604.75 0.484064 0.242032 0.970268i \(-0.422186\pi\)
0.242032 + 0.970268i \(0.422186\pi\)
\(572\) 43451.0i 3.17618i
\(573\) 14952.3i 1.09013i
\(574\) 2658.65 0.193327
\(575\) −801.584 + 443.179i −0.0581363 + 0.0321423i
\(576\) −4768.13 −0.344916
\(577\) 25886.9i 1.86774i 0.357618 + 0.933868i \(0.383589\pi\)
−0.357618 + 0.933868i \(0.616411\pi\)
\(578\) 63328.9i 4.55733i
\(579\) −10180.3 −0.730707
\(580\) −13363.3 7881.41i −0.956688 0.564238i
\(581\) 5494.35 0.392330
\(582\) 17092.3i 1.21735i
\(583\) 2914.37i 0.207034i
\(584\) 11385.5 0.806741
\(585\) 2543.50 4312.62i 0.179762 0.304794i
\(586\) 19929.9 1.40495
\(587\) 4949.88i 0.348046i 0.984742 + 0.174023i \(0.0556768\pi\)
−0.984742 + 0.174023i \(0.944323\pi\)
\(588\) 2338.16i 0.163987i
\(589\) 29114.7 2.03676
\(590\) 18993.4 32204.2i 1.32533 2.24716i
\(591\) −2287.42 −0.159208
\(592\) 4193.05i 0.291104i
\(593\) 31.3988i 0.00217436i 0.999999 + 0.00108718i \(0.000346059\pi\)
−0.999999 + 0.00108718i \(0.999654\pi\)
\(594\) −7247.62 −0.500628
\(595\) 9010.31 + 5314.12i 0.620818 + 0.366147i
\(596\) −23386.8 −1.60732
\(597\) 3816.95i 0.261671i
\(598\) 1782.67i 0.121905i
\(599\) 11870.4 0.809704 0.404852 0.914382i \(-0.367323\pi\)
0.404852 + 0.914382i \(0.367323\pi\)
\(600\) −7013.67 12685.7i −0.477220 0.863154i
\(601\) −967.320 −0.0656536 −0.0328268 0.999461i \(-0.510451\pi\)
−0.0328268 + 0.999461i \(0.510451\pi\)
\(602\) 6766.13i 0.458084i
\(603\) 1343.70i 0.0907458i
\(604\) 26973.0 1.81708
\(605\) −16208.6 9559.57i −1.08922 0.642400i
\(606\) −2.39088 −0.000160269
\(607\) 9518.28i 0.636466i 0.948013 + 0.318233i \(0.103089\pi\)
−0.948013 + 0.318233i \(0.896911\pi\)
\(608\) 1017.53i 0.0678721i
\(609\) 1832.06 0.121903
\(610\) −746.070 + 1264.99i −0.0495205 + 0.0839640i
\(611\) −247.602 −0.0163943
\(612\) 19134.0i 1.26380i
\(613\) 3607.19i 0.237672i −0.992914 0.118836i \(-0.962084\pi\)
0.992914 0.118836i \(-0.0379163\pi\)
\(614\) 30323.2 1.99307
\(615\) −1323.61 + 2244.23i −0.0867854 + 0.147148i
\(616\) −14855.2 −0.971645
\(617\) 22473.2i 1.46635i −0.680042 0.733173i \(-0.738038\pi\)
0.680042 0.733173i \(-0.261962\pi\)
\(618\) 19080.0i 1.24193i
\(619\) −19200.1 −1.24672 −0.623358 0.781936i \(-0.714232\pi\)
−0.623358 + 0.781936i \(0.714232\pi\)
\(620\) −32087.3 18924.5i −2.07848 1.22585i
\(621\) −197.843 −0.0127845
\(622\) 32279.3i 2.08084i
\(623\) 1931.50i 0.124211i
\(624\) −9217.60 −0.591345
\(625\) −8308.97 + 13232.6i −0.531774 + 0.846886i
\(626\) −11201.6 −0.715184
\(627\) 22891.4i 1.45805i
\(628\) 15260.6i 0.969689i
\(629\) 9076.17 0.575343
\(630\) 2966.39 + 1749.52i 0.187593 + 0.110639i
\(631\) −6980.64 −0.440404 −0.220202 0.975454i \(-0.570672\pi\)
−0.220202 + 0.975454i \(0.570672\pi\)
\(632\) 36283.9i 2.28370i
\(633\) 6032.15i 0.378762i
\(634\) 15274.7 0.956838
\(635\) −3235.45 + 5485.83i −0.202197 + 0.342833i
\(636\) 2533.05 0.157928
\(637\) 2438.14i 0.151653i
\(638\) 23418.1i 1.45318i
\(639\) −55.4014 −0.00342980
\(640\) 14379.8 24381.5i 0.888142 1.50588i
\(641\) −1083.82 −0.0667837 −0.0333919 0.999442i \(-0.510631\pi\)
−0.0333919 + 0.999442i \(0.510631\pi\)
\(642\) 22466.1i 1.38110i
\(643\) 4151.42i 0.254613i 0.991863 + 0.127307i \(0.0406332\pi\)
−0.991863 + 0.127307i \(0.959367\pi\)
\(644\) −815.853 −0.0499210
\(645\) 5711.45 + 3368.51i 0.348664 + 0.205636i
\(646\) −90830.3 −5.53200
\(647\) 3014.99i 0.183202i −0.995796 0.0916008i \(-0.970802\pi\)
0.995796 0.0916008i \(-0.0291984\pi\)
\(648\) 3131.02i 0.189812i
\(649\) 37549.4 2.27110
\(650\) 14714.2 + 26613.8i 0.887908 + 1.60597i
\(651\) 4399.06 0.264843
\(652\) 61480.5i 3.69288i
\(653\) 21130.7i 1.26632i 0.774019 + 0.633162i \(0.218243\pi\)
−0.774019 + 0.633162i \(0.781757\pi\)
\(654\) −28916.6 −1.72894
\(655\) −9483.90 5593.44i −0.565751 0.333670i
\(656\) 4796.73 0.285489
\(657\) 2650.91i 0.157415i
\(658\) 170.311i 0.0100903i
\(659\) 9961.24 0.588824 0.294412 0.955679i \(-0.404876\pi\)
0.294412 + 0.955679i \(0.404876\pi\)
\(660\) 14879.4 25228.6i 0.877544 1.48791i
\(661\) 1581.43 0.0930569 0.0465285 0.998917i \(-0.485184\pi\)
0.0465285 + 0.998917i \(0.485184\pi\)
\(662\) 48040.4i 2.82046i
\(663\) 19952.2i 1.16875i
\(664\) 30340.3 1.77324
\(665\) 5525.83 9369.27i 0.322229 0.546353i
\(666\) 2988.07 0.173852
\(667\) 639.258i 0.0371097i
\(668\) 7397.56i 0.428473i
\(669\) 4549.32 0.262910
\(670\) −7029.87 4146.09i −0.405355 0.239071i
\(671\) −1474.96 −0.0848586
\(672\) 153.742i 0.00882551i
\(673\) 11101.6i 0.635865i −0.948113 0.317932i \(-0.897012\pi\)
0.948113 0.317932i \(-0.102988\pi\)
\(674\) −41688.4 −2.38246
\(675\) −2953.63 + 1633.00i −0.168423 + 0.0931174i
\(676\) 4435.50 0.252361
\(677\) 18249.8i 1.03603i −0.855370 0.518017i \(-0.826670\pi\)
0.855370 0.518017i \(-0.173330\pi\)
\(678\) 3855.02i 0.218365i
\(679\) −8156.90 −0.461021
\(680\) 49755.7 + 29345.0i 2.80595 + 1.65490i
\(681\) −12303.5 −0.692322
\(682\) 56230.5i 3.15715i
\(683\) 14144.2i 0.792403i 0.918164 + 0.396202i \(0.129672\pi\)
−0.918164 + 0.396202i \(0.870328\pi\)
\(684\) −19896.3 −1.11221
\(685\) 7822.97 13264.2i 0.436351 0.739851i
\(686\) −1677.05 −0.0933384
\(687\) 3087.71i 0.171475i
\(688\) 12207.4i 0.676458i
\(689\) −2641.37 −0.146049
\(690\) 610.460 1035.06i 0.0336809 0.0571073i
\(691\) 19621.7 1.08024 0.540120 0.841588i \(-0.318379\pi\)
0.540120 + 0.841588i \(0.318379\pi\)
\(692\) 32575.9i 1.78952i
\(693\) 3458.75i 0.189592i
\(694\) 20361.9 1.11373
\(695\) 8086.22 + 4769.11i 0.441335 + 0.260292i
\(696\) 10116.8 0.550971
\(697\) 10382.9i 0.564246i
\(698\) 12637.1i 0.685272i
\(699\) 16735.2 0.905557
\(700\) −12180.0 + 6734.08i −0.657659 + 0.363606i
\(701\) 21609.1 1.16428 0.582142 0.813087i \(-0.302215\pi\)
0.582142 + 0.813087i \(0.302215\pi\)
\(702\) 6568.69i 0.353161i
\(703\) 9437.75i 0.506332i
\(704\) 29086.0 1.55713
\(705\) 143.763 + 84.7890i 0.00768005 + 0.00452956i
\(706\) −20531.6 −1.09450
\(707\) 1.14099i 6.06950e-5i
\(708\) 32636.4i 1.73242i
\(709\) 12557.2 0.665158 0.332579 0.943075i \(-0.392081\pi\)
0.332579 + 0.943075i \(0.392081\pi\)
\(710\) 170.945 289.845i 0.00903586 0.0153207i
\(711\) −8448.02 −0.445606
\(712\) 10665.9i 0.561406i
\(713\) 1534.96i 0.0806237i
\(714\) −13723.9 −0.719334
\(715\) −15515.6 + 26307.4i −0.811540 + 1.37600i
\(716\) −14503.9 −0.757031
\(717\) 16169.0i 0.842179i
\(718\) 4841.82i 0.251665i
\(719\) −36151.9 −1.87516 −0.937580 0.347771i \(-0.886939\pi\)
−0.937580 + 0.347771i \(0.886939\pi\)
\(720\) 5351.95 + 3156.48i 0.277021 + 0.163382i
\(721\) 9105.48 0.470327
\(722\) 60912.8i 3.13980i
\(723\) 11928.8i 0.613606i
\(724\) 32285.9 1.65731
\(725\) −5276.46 9543.60i −0.270293 0.488883i
\(726\) 24687.9 1.26206
\(727\) 12007.2i 0.612550i 0.951943 + 0.306275i \(0.0990828\pi\)
−0.951943 + 0.306275i \(0.900917\pi\)
\(728\) 13463.6i 0.685434i
\(729\) −729.000 −0.0370370
\(730\) 13868.8 + 8179.58i 0.703162 + 0.414712i
\(731\) −26423.9 −1.33697
\(732\) 1281.97i 0.0647310i
\(733\) 15920.2i 0.802220i 0.916030 + 0.401110i \(0.131375\pi\)
−0.916030 + 0.401110i \(0.868625\pi\)
\(734\) 20433.8 1.02756
\(735\) 834.919 1415.64i 0.0418999 0.0710431i
\(736\) 53.6452 0.00268667
\(737\) 8196.70i 0.409674i
\(738\) 3418.27i 0.170499i
\(739\) 26581.1 1.32314 0.661571 0.749882i \(-0.269890\pi\)
0.661571 + 0.749882i \(0.269890\pi\)
\(740\) −6134.52 + 10401.3i −0.304742 + 0.516703i
\(741\) 20747.1 1.02856
\(742\) 1816.84i 0.0898897i
\(743\) 6601.38i 0.325950i 0.986630 + 0.162975i \(0.0521090\pi\)
−0.986630 + 0.162975i \(0.947891\pi\)
\(744\) 24292.0 1.19703
\(745\) −14159.6 8351.06i −0.696330 0.410683i
\(746\) 36011.9 1.76741
\(747\) 7064.16i 0.346003i
\(748\) 116719.i 5.70546i
\(749\) −10721.4 −0.523034
\(750\) 570.243 20491.3i 0.0277631 0.997651i
\(751\) −29809.6 −1.44842 −0.724212 0.689578i \(-0.757796\pi\)
−0.724212 + 0.689578i \(0.757796\pi\)
\(752\) 307.274i 0.0149004i
\(753\) 21287.3i 1.03022i
\(754\) −21224.4 −1.02513
\(755\) 16330.8 + 9631.61i 0.787203 + 0.464278i
\(756\) −3006.21 −0.144623
\(757\) 8179.09i 0.392700i −0.980534 0.196350i \(-0.937091\pi\)
0.980534 0.196350i \(-0.0629089\pi\)
\(758\) 30383.2i 1.45589i
\(759\) 1206.86 0.0577158
\(760\) 30514.1 51737.9i 1.45640 2.46938i
\(761\) −31616.8 −1.50605 −0.753027 0.657990i \(-0.771407\pi\)
−0.753027 + 0.657990i \(0.771407\pi\)
\(762\) 8355.66i 0.397236i
\(763\) 13799.8i 0.654763i
\(764\) −79276.5 −3.75409
\(765\) 6832.44 11584.7i 0.322912 0.547510i
\(766\) 8581.05 0.404760
\(767\) 34032.0i 1.60212i
\(768\) 24421.3i 1.14743i
\(769\) −24651.3 −1.15598 −0.577991 0.816043i \(-0.696163\pi\)
−0.577991 + 0.816043i \(0.696163\pi\)
\(770\) −18095.3 10672.3i −0.846893 0.499483i
\(771\) 7579.67 0.354054
\(772\) 53975.6i 2.51635i
\(773\) 7888.63i 0.367056i 0.983015 + 0.183528i \(0.0587518\pi\)
−0.983015 + 0.183528i \(0.941248\pi\)
\(774\) −8699.31 −0.403992
\(775\) −12669.6 22915.7i −0.587233 1.06214i
\(776\) −45043.1 −2.08370
\(777\) 1425.99i 0.0658391i
\(778\) 43054.2i 1.98402i
\(779\) −10796.5 −0.496566
\(780\) −22865.3 13485.5i −1.04963 0.619051i
\(781\) 337.954 0.0154839
\(782\) 4788.67i 0.218980i
\(783\) 2355.50i 0.107508i
\(784\) −3025.73