Properties

Label 105.4.d.b.64.4
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 64.4
Root \(1.35311i\) of defining polynomial
Character \(\chi\) \(=\) 105.64
Dual form 105.4.d.b.64.7

$q$-expansion

\(f(q)\) \(=\) \(q-2.20666i q^{2} +3.00000i q^{3} +3.13065 q^{4} +(-1.50045 - 11.0792i) q^{5} +6.61998 q^{6} +7.00000i q^{7} -24.5616i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-2.20666i q^{2} +3.00000i q^{3} +3.13065 q^{4} +(-1.50045 - 11.0792i) q^{5} +6.61998 q^{6} +7.00000i q^{7} -24.5616i q^{8} -9.00000 q^{9} +(-24.4480 + 3.31098i) q^{10} +56.2010 q^{11} +9.39196i q^{12} -38.9026i q^{13} +15.4466 q^{14} +(33.2376 - 4.50134i) q^{15} -29.1538 q^{16} -119.322i q^{17} +19.8599i q^{18} +13.0045 q^{19} +(-4.69738 - 34.6851i) q^{20} -21.0000 q^{21} -124.016i q^{22} +130.565i q^{23} +73.6847 q^{24} +(-120.497 + 33.2475i) q^{25} -85.8448 q^{26} -27.0000i q^{27} +21.9146i q^{28} -77.9925 q^{29} +(-9.93293 - 73.3441i) q^{30} +61.0660 q^{31} -132.160i q^{32} +168.603i q^{33} -263.303 q^{34} +(77.5544 - 10.5031i) q^{35} -28.1759 q^{36} +167.391i q^{37} -28.6964i q^{38} +116.708 q^{39} +(-272.122 + 36.8533i) q^{40} +436.142 q^{41} +46.3398i q^{42} +393.030i q^{43} +175.946 q^{44} +(13.5040 + 99.7128i) q^{45} +288.112 q^{46} +365.271i q^{47} -87.4613i q^{48} -49.0000 q^{49} +(73.3659 + 265.897i) q^{50} +357.966 q^{51} -121.791i q^{52} +282.048i q^{53} -59.5798 q^{54} +(-84.3266 - 622.662i) q^{55} +171.931 q^{56} +39.0134i q^{57} +172.103i q^{58} -414.842 q^{59} +(104.055 - 14.0921i) q^{60} -563.802 q^{61} -134.752i q^{62} -63.0000i q^{63} -524.862 q^{64} +(-431.009 + 58.3713i) q^{65} +372.049 q^{66} +395.230i q^{67} -373.556i q^{68} -391.694 q^{69} +(-23.1768 - 171.136i) q^{70} +103.990 q^{71} +221.054i q^{72} +128.026i q^{73} +369.376 q^{74} +(-99.7426 - 361.492i) q^{75} +40.7125 q^{76} +393.407i q^{77} -257.534i q^{78} +641.999 q^{79} +(43.7437 + 323.000i) q^{80} +81.0000 q^{81} -962.417i q^{82} -512.010i q^{83} -65.7437 q^{84} +(-1321.99 + 179.037i) q^{85} +867.283 q^{86} -233.977i q^{87} -1380.38i q^{88} -1225.10 q^{89} +(220.032 - 29.7988i) q^{90} +272.318 q^{91} +408.753i q^{92} +183.198i q^{93} +806.028 q^{94} +(-19.5125 - 144.079i) q^{95} +396.480 q^{96} +186.760i q^{97} +108.126i q^{98} -505.809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10}) \) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.20666i 0.780172i −0.920778 0.390086i \(-0.872445\pi\)
0.920778 0.390086i \(-0.127555\pi\)
\(3\) 3.00000i 0.577350i
\(4\) 3.13065 0.391332
\(5\) −1.50045 11.0792i −0.134204 0.990954i
\(6\) 6.61998 0.450432
\(7\) 7.00000i 0.377964i
\(8\) 24.5616i 1.08548i
\(9\) −9.00000 −0.333333
\(10\) −24.4480 + 3.31098i −0.773114 + 0.104702i
\(11\) 56.2010 1.54048 0.770238 0.637757i \(-0.220138\pi\)
0.770238 + 0.637757i \(0.220138\pi\)
\(12\) 9.39196i 0.225936i
\(13\) 38.9026i 0.829972i −0.909828 0.414986i \(-0.863786\pi\)
0.909828 0.414986i \(-0.136214\pi\)
\(14\) 15.4466 0.294877
\(15\) 33.2376 4.50134i 0.572127 0.0774828i
\(16\) −29.1538 −0.455528
\(17\) 119.322i 1.70235i −0.524886 0.851173i \(-0.675892\pi\)
0.524886 0.851173i \(-0.324108\pi\)
\(18\) 19.8599i 0.260057i
\(19\) 13.0045 0.157023 0.0785113 0.996913i \(-0.474983\pi\)
0.0785113 + 0.996913i \(0.474983\pi\)
\(20\) −4.69738 34.6851i −0.0525183 0.387792i
\(21\) −21.0000 −0.218218
\(22\) 124.016i 1.20184i
\(23\) 130.565i 1.18368i 0.806055 + 0.591840i \(0.201598\pi\)
−0.806055 + 0.591840i \(0.798402\pi\)
\(24\) 73.6847 0.626701
\(25\) −120.497 + 33.2475i −0.963979 + 0.265980i
\(26\) −85.8448 −0.647521
\(27\) 27.0000i 0.192450i
\(28\) 21.9146i 0.147910i
\(29\) −77.9925 −0.499408 −0.249704 0.968322i \(-0.580333\pi\)
−0.249704 + 0.968322i \(0.580333\pi\)
\(30\) −9.93293 73.3441i −0.0604499 0.446358i
\(31\) 61.0660 0.353799 0.176900 0.984229i \(-0.443393\pi\)
0.176900 + 0.984229i \(0.443393\pi\)
\(32\) 132.160i 0.730088i
\(33\) 168.603i 0.889394i
\(34\) −263.303 −1.32812
\(35\) 77.5544 10.5031i 0.374545 0.0507244i
\(36\) −28.1759 −0.130444
\(37\) 167.391i 0.743757i 0.928282 + 0.371878i \(0.121286\pi\)
−0.928282 + 0.371878i \(0.878714\pi\)
\(38\) 28.6964i 0.122505i
\(39\) 116.708 0.479185
\(40\) −272.122 + 36.8533i −1.07566 + 0.145676i
\(41\) 436.142 1.66132 0.830658 0.556783i \(-0.187964\pi\)
0.830658 + 0.556783i \(0.187964\pi\)
\(42\) 46.3398i 0.170247i
\(43\) 393.030i 1.39387i 0.717134 + 0.696936i \(0.245454\pi\)
−0.717134 + 0.696936i \(0.754546\pi\)
\(44\) 175.946 0.602837
\(45\) 13.5040 + 99.7128i 0.0447347 + 0.330318i
\(46\) 288.112 0.923474
\(47\) 365.271i 1.13362i 0.823848 + 0.566811i \(0.191823\pi\)
−0.823848 + 0.566811i \(0.808177\pi\)
\(48\) 87.4613i 0.262999i
\(49\) −49.0000 −0.142857
\(50\) 73.3659 + 265.897i 0.207510 + 0.752069i
\(51\) 357.966 0.982849
\(52\) 121.791i 0.324794i
\(53\) 282.048i 0.730987i 0.930814 + 0.365494i \(0.119100\pi\)
−0.930814 + 0.365494i \(0.880900\pi\)
\(54\) −59.5798 −0.150144
\(55\) −84.3266 622.662i −0.206738 1.52654i
\(56\) 171.931 0.410272
\(57\) 39.0134i 0.0906570i
\(58\) 172.103i 0.389624i
\(59\) −414.842 −0.915388 −0.457694 0.889110i \(-0.651324\pi\)
−0.457694 + 0.889110i \(0.651324\pi\)
\(60\) 104.055 14.0921i 0.223892 0.0303215i
\(61\) −563.802 −1.18340 −0.591701 0.806158i \(-0.701543\pi\)
−0.591701 + 0.806158i \(0.701543\pi\)
\(62\) 134.752i 0.276024i
\(63\) 63.0000i 0.125988i
\(64\) −524.862 −1.02512
\(65\) −431.009 + 58.3713i −0.822464 + 0.111386i
\(66\) 372.049 0.693880
\(67\) 395.230i 0.720673i 0.932822 + 0.360336i \(0.117338\pi\)
−0.932822 + 0.360336i \(0.882662\pi\)
\(68\) 373.556i 0.666182i
\(69\) −391.694 −0.683398
\(70\) −23.1768 171.136i −0.0395737 0.292210i
\(71\) 103.990 0.173821 0.0869107 0.996216i \(-0.472301\pi\)
0.0869107 + 0.996216i \(0.472301\pi\)
\(72\) 221.054i 0.361826i
\(73\) 128.026i 0.205264i 0.994719 + 0.102632i \(0.0327264\pi\)
−0.994719 + 0.102632i \(0.967274\pi\)
\(74\) 369.376 0.580258
\(75\) −99.7426 361.492i −0.153564 0.556553i
\(76\) 40.7125 0.0614479
\(77\) 393.407i 0.582245i
\(78\) 257.534i 0.373846i
\(79\) 641.999 0.914310 0.457155 0.889387i \(-0.348868\pi\)
0.457155 + 0.889387i \(0.348868\pi\)
\(80\) 43.7437 + 323.000i 0.0611337 + 0.451407i
\(81\) 81.0000 0.111111
\(82\) 962.417i 1.29611i
\(83\) 512.010i 0.677113i −0.940946 0.338557i \(-0.890061\pi\)
0.940946 0.338557i \(-0.109939\pi\)
\(84\) −65.7437 −0.0853956
\(85\) −1321.99 + 179.037i −1.68695 + 0.228462i
\(86\) 867.283 1.08746
\(87\) 233.977i 0.288333i
\(88\) 1380.38i 1.67215i
\(89\) −1225.10 −1.45911 −0.729554 0.683923i \(-0.760272\pi\)
−0.729554 + 0.683923i \(0.760272\pi\)
\(90\) 220.032 29.7988i 0.257705 0.0349008i
\(91\) 272.318 0.313700
\(92\) 408.753i 0.463212i
\(93\) 183.198i 0.204266i
\(94\) 806.028 0.884420
\(95\) −19.5125 144.079i −0.0210731 0.155602i
\(96\) 396.480 0.421517
\(97\) 186.760i 0.195491i 0.995211 + 0.0977454i \(0.0311631\pi\)
−0.995211 + 0.0977454i \(0.968837\pi\)
\(98\) 108.126i 0.111453i
\(99\) −505.809 −0.513492
\(100\) −377.235 + 104.086i −0.377235 + 0.104086i
\(101\) 1650.68 1.62623 0.813114 0.582104i \(-0.197770\pi\)
0.813114 + 0.582104i \(0.197770\pi\)
\(102\) 789.910i 0.766792i
\(103\) 72.1876i 0.0690568i 0.999404 + 0.0345284i \(0.0109929\pi\)
−0.999404 + 0.0345284i \(0.989007\pi\)
\(104\) −955.508 −0.900916
\(105\) 31.5094 + 232.663i 0.0292857 + 0.216244i
\(106\) 622.385 0.570296
\(107\) 1202.55i 1.08649i −0.839574 0.543246i \(-0.817195\pi\)
0.839574 0.543246i \(-0.182805\pi\)
\(108\) 84.5277i 0.0753118i
\(109\) 1551.36 1.36324 0.681622 0.731704i \(-0.261275\pi\)
0.681622 + 0.731704i \(0.261275\pi\)
\(110\) −1374.00 + 186.080i −1.19096 + 0.161291i
\(111\) −502.174 −0.429408
\(112\) 204.076i 0.172173i
\(113\) 2080.90i 1.73234i −0.499749 0.866170i \(-0.666574\pi\)
0.499749 0.866170i \(-0.333426\pi\)
\(114\) 86.0893 0.0707281
\(115\) 1446.55 195.906i 1.17297 0.158855i
\(116\) −244.167 −0.195434
\(117\) 350.123i 0.276657i
\(118\) 915.416i 0.714160i
\(119\) 835.255 0.643426
\(120\) −110.560 816.367i −0.0841059 0.621032i
\(121\) 1827.55 1.37306
\(122\) 1244.12i 0.923257i
\(123\) 1308.43i 0.959161i
\(124\) 191.177 0.138453
\(125\) 549.156 + 1285.13i 0.392944 + 0.919562i
\(126\) −139.020 −0.0982924
\(127\) 1414.70i 0.988461i 0.869331 + 0.494231i \(0.164550\pi\)
−0.869331 + 0.494231i \(0.835450\pi\)
\(128\) 100.912i 0.0696832i
\(129\) −1179.09 −0.804752
\(130\) 128.806 + 951.091i 0.0869000 + 0.641663i
\(131\) −2472.51 −1.64904 −0.824520 0.565833i \(-0.808555\pi\)
−0.824520 + 0.565833i \(0.808555\pi\)
\(132\) 527.837i 0.348048i
\(133\) 91.0313i 0.0593490i
\(134\) 872.139 0.562249
\(135\) −299.138 + 40.5121i −0.190709 + 0.0258276i
\(136\) −2930.74 −1.84786
\(137\) 214.391i 0.133698i −0.997763 0.0668491i \(-0.978705\pi\)
0.997763 0.0668491i \(-0.0212946\pi\)
\(138\) 864.336i 0.533168i
\(139\) −942.774 −0.575288 −0.287644 0.957737i \(-0.592872\pi\)
−0.287644 + 0.957737i \(0.592872\pi\)
\(140\) 242.796 32.8817i 0.146571 0.0198501i
\(141\) −1095.81 −0.654497
\(142\) 229.470i 0.135611i
\(143\) 2186.36i 1.27855i
\(144\) 262.384 0.151843
\(145\) 117.024 + 864.094i 0.0670226 + 0.494890i
\(146\) 282.509 0.160141
\(147\) 147.000i 0.0824786i
\(148\) 524.045i 0.291056i
\(149\) −1693.07 −0.930882 −0.465441 0.885079i \(-0.654104\pi\)
−0.465441 + 0.885079i \(0.654104\pi\)
\(150\) −797.690 + 220.098i −0.434207 + 0.119806i
\(151\) 2519.69 1.35795 0.678973 0.734163i \(-0.262425\pi\)
0.678973 + 0.734163i \(0.262425\pi\)
\(152\) 319.410i 0.170445i
\(153\) 1073.90i 0.567448i
\(154\) 868.115 0.454251
\(155\) −91.6263 676.562i −0.0474813 0.350599i
\(156\) 365.372 0.187520
\(157\) 1621.48i 0.824258i 0.911125 + 0.412129i \(0.135215\pi\)
−0.911125 + 0.412129i \(0.864785\pi\)
\(158\) 1416.67i 0.713319i
\(159\) −846.145 −0.422036
\(160\) −1464.23 + 198.299i −0.723484 + 0.0979808i
\(161\) −913.954 −0.447389
\(162\) 178.739i 0.0866858i
\(163\) 925.194i 0.444582i −0.974980 0.222291i \(-0.928647\pi\)
0.974980 0.222291i \(-0.0713534\pi\)
\(164\) 1365.41 0.650126
\(165\) 1867.98 252.980i 0.881348 0.119360i
\(166\) −1129.83 −0.528265
\(167\) 2681.55i 1.24254i 0.783596 + 0.621271i \(0.213383\pi\)
−0.783596 + 0.621271i \(0.786617\pi\)
\(168\) 515.793i 0.236871i
\(169\) 683.589 0.311147
\(170\) 395.073 + 2917.19i 0.178239 + 1.31611i
\(171\) −117.040 −0.0523409
\(172\) 1230.44i 0.545466i
\(173\) 287.591i 0.126388i −0.998001 0.0631940i \(-0.979871\pi\)
0.998001 0.0631940i \(-0.0201287\pi\)
\(174\) −516.308 −0.224950
\(175\) −232.733 843.481i −0.100531 0.364350i
\(176\) −1638.47 −0.701729
\(177\) 1244.53i 0.528499i
\(178\) 2703.38i 1.13835i
\(179\) −3683.47 −1.53808 −0.769038 0.639203i \(-0.779265\pi\)
−0.769038 + 0.639203i \(0.779265\pi\)
\(180\) 42.2764 + 312.166i 0.0175061 + 0.129264i
\(181\) 3132.65 1.28645 0.643227 0.765676i \(-0.277595\pi\)
0.643227 + 0.765676i \(0.277595\pi\)
\(182\) 600.913i 0.244740i
\(183\) 1691.41i 0.683237i
\(184\) 3206.88 1.28486
\(185\) 1854.56 251.162i 0.737028 0.0998152i
\(186\) 404.256 0.159363
\(187\) 6706.02i 2.62242i
\(188\) 1143.54i 0.443622i
\(189\) 189.000 0.0727393
\(190\) −317.933 + 43.0575i −0.121396 + 0.0164406i
\(191\) 1586.93 0.601184 0.300592 0.953753i \(-0.402816\pi\)
0.300592 + 0.953753i \(0.402816\pi\)
\(192\) 1574.59i 0.591854i
\(193\) 5179.00i 1.93157i 0.259352 + 0.965783i \(0.416491\pi\)
−0.259352 + 0.965783i \(0.583509\pi\)
\(194\) 412.116 0.152516
\(195\) −175.114 1293.03i −0.0643085 0.474850i
\(196\) −153.402 −0.0559045
\(197\) 903.798i 0.326868i 0.986554 + 0.163434i \(0.0522570\pi\)
−0.986554 + 0.163434i \(0.947743\pi\)
\(198\) 1116.15i 0.400612i
\(199\) 1171.51 0.417317 0.208659 0.977989i \(-0.433090\pi\)
0.208659 + 0.977989i \(0.433090\pi\)
\(200\) 816.611 + 2959.60i 0.288716 + 1.04638i
\(201\) −1185.69 −0.416081
\(202\) 3642.50i 1.26874i
\(203\) 545.947i 0.188759i
\(204\) 1120.67 0.384620
\(205\) −654.409 4832.11i −0.222955 1.64629i
\(206\) 159.293 0.0538762
\(207\) 1175.08i 0.394560i
\(208\) 1134.16i 0.378075i
\(209\) 730.864 0.241889
\(210\) 513.408 69.5305i 0.168707 0.0228479i
\(211\) −1103.16 −0.359928 −0.179964 0.983673i \(-0.557598\pi\)
−0.179964 + 0.983673i \(0.557598\pi\)
\(212\) 882.996i 0.286059i
\(213\) 311.969i 0.100356i
\(214\) −2653.61 −0.847651
\(215\) 4354.45 589.721i 1.38126 0.187063i
\(216\) −663.162 −0.208900
\(217\) 427.462i 0.133724i
\(218\) 3423.33i 1.06357i
\(219\) −384.077 −0.118509
\(220\) −263.997 1949.34i −0.0809032 0.597383i
\(221\) −4641.94 −1.41290
\(222\) 1108.13i 0.335012i
\(223\) 4079.95i 1.22517i −0.790404 0.612586i \(-0.790129\pi\)
0.790404 0.612586i \(-0.209871\pi\)
\(224\) 925.120 0.275947
\(225\) 1084.48 299.228i 0.321326 0.0886600i
\(226\) −4591.83 −1.35152
\(227\) 931.964i 0.272496i 0.990675 + 0.136248i \(0.0435044\pi\)
−0.990675 + 0.136248i \(0.956496\pi\)
\(228\) 122.137i 0.0354770i
\(229\) 1471.55 0.424641 0.212321 0.977200i \(-0.431898\pi\)
0.212321 + 0.977200i \(0.431898\pi\)
\(230\) −432.297 3192.05i −0.123934 0.915120i
\(231\) −1180.22 −0.336159
\(232\) 1915.62i 0.542097i
\(233\) 2479.06i 0.697034i −0.937303 0.348517i \(-0.886685\pi\)
0.937303 0.348517i \(-0.113315\pi\)
\(234\) 772.603 0.215840
\(235\) 4046.91 548.070i 1.12337 0.152137i
\(236\) −1298.73 −0.358220
\(237\) 1926.00i 0.527877i
\(238\) 1843.12i 0.501983i
\(239\) 954.068 0.258216 0.129108 0.991631i \(-0.458789\pi\)
0.129108 + 0.991631i \(0.458789\pi\)
\(240\) −969.001 + 131.231i −0.260620 + 0.0352956i
\(241\) −5297.02 −1.41581 −0.707906 0.706306i \(-0.750360\pi\)
−0.707906 + 0.706306i \(0.750360\pi\)
\(242\) 4032.77i 1.07123i
\(243\) 243.000i 0.0641500i
\(244\) −1765.07 −0.463103
\(245\) 73.5219 + 542.881i 0.0191720 + 0.141565i
\(246\) 2887.25 0.748311
\(247\) 505.907i 0.130324i
\(248\) 1499.88i 0.384041i
\(249\) 1536.03 0.390931
\(250\) 2835.84 1211.80i 0.717417 0.306564i
\(251\) 1855.17 0.466524 0.233262 0.972414i \(-0.425060\pi\)
0.233262 + 0.972414i \(0.425060\pi\)
\(252\) 197.231i 0.0493032i
\(253\) 7337.87i 1.82343i
\(254\) 3121.77 0.771170
\(255\) −537.110 3965.98i −0.131902 0.973958i
\(256\) −3976.22 −0.970757
\(257\) 6233.09i 1.51288i 0.654065 + 0.756438i \(0.273062\pi\)
−0.654065 + 0.756438i \(0.726938\pi\)
\(258\) 2601.85i 0.627845i
\(259\) −1171.74 −0.281114
\(260\) −1349.34 + 182.740i −0.321856 + 0.0435887i
\(261\) 701.932 0.166469
\(262\) 5455.99i 1.28653i
\(263\) 1184.50i 0.277716i −0.990312 0.138858i \(-0.955657\pi\)
0.990312 0.138858i \(-0.0443432\pi\)
\(264\) 4141.15 0.965417
\(265\) 3124.87 423.199i 0.724375 0.0981015i
\(266\) 200.875 0.0463024
\(267\) 3675.31i 0.842416i
\(268\) 1237.33i 0.282022i
\(269\) 1916.03 0.434283 0.217141 0.976140i \(-0.430327\pi\)
0.217141 + 0.976140i \(0.430327\pi\)
\(270\) 89.3964 + 660.097i 0.0201500 + 0.148786i
\(271\) −1168.95 −0.262025 −0.131013 0.991381i \(-0.541823\pi\)
−0.131013 + 0.991381i \(0.541823\pi\)
\(272\) 3478.69i 0.775465i
\(273\) 816.954i 0.181115i
\(274\) −473.088 −0.104308
\(275\) −6772.06 + 1868.54i −1.48498 + 0.409736i
\(276\) −1226.26 −0.267435
\(277\) 7269.54i 1.57684i −0.615138 0.788419i \(-0.710900\pi\)
0.615138 0.788419i \(-0.289100\pi\)
\(278\) 2080.38i 0.448824i
\(279\) −549.594 −0.117933
\(280\) −257.973 1904.86i −0.0550602 0.406561i
\(281\) 298.126 0.0632908 0.0316454 0.999499i \(-0.489925\pi\)
0.0316454 + 0.999499i \(0.489925\pi\)
\(282\) 2418.09i 0.510620i
\(283\) 4496.30i 0.944444i −0.881480 0.472222i \(-0.843452\pi\)
0.881480 0.472222i \(-0.156548\pi\)
\(284\) 325.556 0.0680218
\(285\) 432.237 58.5376i 0.0898369 0.0121665i
\(286\) −4824.56 −0.997490
\(287\) 3053.00i 0.627919i
\(288\) 1189.44i 0.243363i
\(289\) −9324.77 −1.89798
\(290\) 1906.76 258.231i 0.386100 0.0522892i
\(291\) −560.280 −0.112867
\(292\) 400.804i 0.0803264i
\(293\) 1644.33i 0.327859i −0.986472 0.163929i \(-0.947583\pi\)
0.986472 0.163929i \(-0.0524169\pi\)
\(294\) −324.379 −0.0643475
\(295\) 622.449 + 4596.12i 0.122849 + 0.907107i
\(296\) 4111.40 0.807331
\(297\) 1517.43i 0.296465i
\(298\) 3736.02i 0.726248i
\(299\) 5079.31 0.982421
\(300\) −312.259 1131.71i −0.0600944 0.217797i
\(301\) −2751.21 −0.526834
\(302\) 5560.11i 1.05943i
\(303\) 4952.05i 0.938904i
\(304\) −379.129 −0.0715281
\(305\) 845.956 + 6246.48i 0.158817 + 1.17270i
\(306\) 2369.73 0.442707
\(307\) 4726.18i 0.878623i 0.898335 + 0.439312i \(0.144778\pi\)
−0.898335 + 0.439312i \(0.855222\pi\)
\(308\) 1231.62i 0.227851i
\(309\) −216.563 −0.0398700
\(310\) −1492.94 + 202.188i −0.273527 + 0.0370436i
\(311\) −4853.99 −0.885031 −0.442515 0.896761i \(-0.645914\pi\)
−0.442515 + 0.896761i \(0.645914\pi\)
\(312\) 2866.52i 0.520144i
\(313\) 1690.87i 0.305348i 0.988277 + 0.152674i \(0.0487884\pi\)
−0.988277 + 0.152674i \(0.951212\pi\)
\(314\) 3578.06 0.643063
\(315\) −697.990 + 94.5282i −0.124848 + 0.0169081i
\(316\) 2009.88 0.357799
\(317\) 3878.38i 0.687166i 0.939122 + 0.343583i \(0.111641\pi\)
−0.939122 + 0.343583i \(0.888359\pi\)
\(318\) 1867.15i 0.329260i
\(319\) −4383.25 −0.769326
\(320\) 787.529 + 5815.06i 0.137576 + 1.01585i
\(321\) 3607.64 0.627286
\(322\) 2016.78i 0.349040i
\(323\) 1551.72i 0.267307i
\(324\) 253.583 0.0434813
\(325\) 1293.41 + 4687.66i 0.220756 + 0.800075i
\(326\) −2041.59 −0.346850
\(327\) 4654.09i 0.787070i
\(328\) 10712.3i 1.80332i
\(329\) −2556.90 −0.428469
\(330\) −558.240 4122.01i −0.0931215 0.687603i
\(331\) 9927.71 1.64857 0.824284 0.566176i \(-0.191578\pi\)
0.824284 + 0.566176i \(0.191578\pi\)
\(332\) 1602.93i 0.264976i
\(333\) 1506.52i 0.247919i
\(334\) 5917.26 0.969396
\(335\) 4378.84 593.023i 0.714153 0.0967173i
\(336\) 612.229 0.0994043
\(337\) 5283.88i 0.854099i 0.904228 + 0.427050i \(0.140447\pi\)
−0.904228 + 0.427050i \(0.859553\pi\)
\(338\) 1508.45i 0.242748i
\(339\) 6242.70 1.00017
\(340\) −4138.71 + 560.502i −0.660155 + 0.0894043i
\(341\) 3431.97 0.545019
\(342\) 258.268i 0.0408349i
\(343\) 343.000i 0.0539949i
\(344\) 9653.42 1.51302
\(345\) 587.717 + 4339.66i 0.0917148 + 0.677216i
\(346\) −634.615 −0.0986044
\(347\) 10548.3i 1.63188i −0.578137 0.815940i \(-0.696220\pi\)
0.578137 0.815940i \(-0.303780\pi\)
\(348\) 732.502i 0.112834i
\(349\) −628.411 −0.0963841 −0.0481921 0.998838i \(-0.515346\pi\)
−0.0481921 + 0.998838i \(0.515346\pi\)
\(350\) −1861.28 + 513.562i −0.284255 + 0.0784315i
\(351\) −1050.37 −0.159728
\(352\) 7427.52i 1.12468i
\(353\) 2548.17i 0.384209i −0.981375 0.192104i \(-0.938469\pi\)
0.981375 0.192104i \(-0.0615312\pi\)
\(354\) −2746.25 −0.412320
\(355\) −156.031 1152.12i −0.0233275 0.172249i
\(356\) −3835.37 −0.570995
\(357\) 2505.76i 0.371482i
\(358\) 8128.17i 1.19996i
\(359\) −13046.3 −1.91799 −0.958996 0.283420i \(-0.908531\pi\)
−0.958996 + 0.283420i \(0.908531\pi\)
\(360\) 2449.10 331.680i 0.358553 0.0485585i
\(361\) −6689.88 −0.975344
\(362\) 6912.69i 1.00366i
\(363\) 5482.64i 0.792738i
\(364\) 852.534 0.122761
\(365\) 1418.42 192.096i 0.203407 0.0275473i
\(366\) −3732.36 −0.533043
\(367\) 8068.23i 1.14757i 0.819006 + 0.573785i \(0.194525\pi\)
−0.819006 + 0.573785i \(0.805475\pi\)
\(368\) 3806.46i 0.539199i
\(369\) −3925.28 −0.553772
\(370\) −554.229 4092.39i −0.0778730 0.575009i
\(371\) −1974.34 −0.276287
\(372\) 573.530i 0.0799358i
\(373\) 3623.32i 0.502972i 0.967861 + 0.251486i \(0.0809193\pi\)
−0.967861 + 0.251486i \(0.919081\pi\)
\(374\) −14797.9 −2.04594
\(375\) −3855.38 + 1647.47i −0.530910 + 0.226866i
\(376\) 8971.62 1.23052
\(377\) 3034.11i 0.414495i
\(378\) 417.059i 0.0567492i
\(379\) −7486.58 −1.01467 −0.507335 0.861749i \(-0.669369\pi\)
−0.507335 + 0.861749i \(0.669369\pi\)
\(380\) −61.0870 451.062i −0.00824657 0.0608921i
\(381\) −4244.11 −0.570688
\(382\) 3501.81i 0.469027i
\(383\) 8926.58i 1.19093i −0.803381 0.595466i \(-0.796967\pi\)
0.803381 0.595466i \(-0.203033\pi\)
\(384\) −302.736 −0.0402316
\(385\) 4358.63 590.286i 0.576978 0.0781397i
\(386\) 11428.3 1.50695
\(387\) 3537.27i 0.464624i
\(388\) 584.681i 0.0765018i
\(389\) 12600.1 1.64228 0.821141 0.570725i \(-0.193338\pi\)
0.821141 + 0.570725i \(0.193338\pi\)
\(390\) −2853.27 + 386.417i −0.370464 + 0.0501717i
\(391\) 15579.3 2.01503
\(392\) 1203.52i 0.155068i
\(393\) 7417.53i 0.952074i
\(394\) 1994.37 0.255013
\(395\) −963.286 7112.83i −0.122704 0.906039i
\(396\) −1583.51 −0.200946
\(397\) 12713.4i 1.60722i −0.595154 0.803612i \(-0.702909\pi\)
0.595154 0.803612i \(-0.297091\pi\)
\(398\) 2585.12i 0.325579i
\(399\) −273.094 −0.0342651
\(400\) 3512.95 969.290i 0.439119 0.121161i
\(401\) −6133.51 −0.763822 −0.381911 0.924199i \(-0.624734\pi\)
−0.381911 + 0.924199i \(0.624734\pi\)
\(402\) 2616.42i 0.324614i
\(403\) 2375.62i 0.293643i
\(404\) 5167.72 0.636395
\(405\) −121.536 897.415i −0.0149116 0.110106i
\(406\) −1204.72 −0.147264
\(407\) 9407.56i 1.14574i
\(408\) 8792.21i 1.06686i
\(409\) −10600.3 −1.28154 −0.640769 0.767733i \(-0.721385\pi\)
−0.640769 + 0.767733i \(0.721385\pi\)
\(410\) −10662.8 + 1444.06i −1.28439 + 0.173944i
\(411\) 643.173 0.0771907
\(412\) 225.994i 0.0270241i
\(413\) 2903.90i 0.345984i
\(414\) −2593.01 −0.307825
\(415\) −5672.66 + 768.244i −0.670988 + 0.0908714i
\(416\) −5141.37 −0.605953
\(417\) 2828.32i 0.332143i
\(418\) 1612.77i 0.188715i
\(419\) −4296.43 −0.500941 −0.250470 0.968124i \(-0.580585\pi\)
−0.250470 + 0.968124i \(0.580585\pi\)
\(420\) 98.6450 + 728.388i 0.0114604 + 0.0846231i
\(421\) 3916.78 0.453425 0.226713 0.973962i \(-0.427202\pi\)
0.226713 + 0.973962i \(0.427202\pi\)
\(422\) 2434.30i 0.280806i
\(423\) 3287.44i 0.377874i
\(424\) 6927.55 0.793471
\(425\) 3967.16 + 14378.0i 0.452790 + 1.64102i
\(426\) 688.410 0.0782948
\(427\) 3946.62i 0.447284i
\(428\) 3764.76i 0.425179i
\(429\) 6559.09 0.738172
\(430\) −1301.31 9608.80i −0.145942 1.07762i
\(431\) 13408.9 1.49857 0.749287 0.662246i \(-0.230396\pi\)
0.749287 + 0.662246i \(0.230396\pi\)
\(432\) 787.152i 0.0876663i
\(433\) 7792.31i 0.864837i −0.901673 0.432419i \(-0.857660\pi\)
0.901673 0.432419i \(-0.142340\pi\)
\(434\) 943.263 0.104327
\(435\) −2592.28 + 351.071i −0.285725 + 0.0386955i
\(436\) 4856.78 0.533481
\(437\) 1697.93i 0.185865i
\(438\) 847.528i 0.0924576i
\(439\) −1039.29 −0.112990 −0.0564948 0.998403i \(-0.517992\pi\)
−0.0564948 + 0.998403i \(0.517992\pi\)
\(440\) −15293.5 + 2071.19i −1.65702 + 0.224410i
\(441\) 441.000 0.0476190
\(442\) 10243.2i 1.10230i
\(443\) 2846.33i 0.305267i 0.988283 + 0.152633i \(0.0487754\pi\)
−0.988283 + 0.152633i \(0.951225\pi\)
\(444\) −1572.13 −0.168041
\(445\) 1838.20 + 13573.2i 0.195818 + 1.44591i
\(446\) −9003.05 −0.955845
\(447\) 5079.20i 0.537445i
\(448\) 3674.04i 0.387460i
\(449\) −7472.64 −0.785425 −0.392713 0.919661i \(-0.628463\pi\)
−0.392713 + 0.919661i \(0.628463\pi\)
\(450\) −660.294 2393.07i −0.0691701 0.250690i
\(451\) 24511.6 2.55922
\(452\) 6514.57i 0.677920i
\(453\) 7559.08i 0.784010i
\(454\) 2056.53 0.212594
\(455\) −408.599 3017.07i −0.0420998 0.310862i
\(456\) 958.230 0.0984062
\(457\) 11014.3i 1.12742i −0.825974 0.563708i \(-0.809374\pi\)
0.825974 0.563708i \(-0.190626\pi\)
\(458\) 3247.21i 0.331293i
\(459\) −3221.70 −0.327616
\(460\) 4528.66 613.313i 0.459021 0.0621649i
\(461\) 7944.67 0.802647 0.401323 0.915936i \(-0.368550\pi\)
0.401323 + 0.915936i \(0.368550\pi\)
\(462\) 2604.34i 0.262262i
\(463\) 7627.25i 0.765591i 0.923833 + 0.382795i \(0.125039\pi\)
−0.923833 + 0.382795i \(0.874961\pi\)
\(464\) 2273.77 0.227494
\(465\) 2029.69 274.879i 0.202418 0.0274133i
\(466\) −5470.45 −0.543806
\(467\) 3284.28i 0.325436i −0.986673 0.162718i \(-0.947974\pi\)
0.986673 0.162718i \(-0.0520260\pi\)
\(468\) 1096.11i 0.108265i
\(469\) −2766.61 −0.272389
\(470\) −1209.40 8930.15i −0.118693 0.876419i
\(471\) −4864.45 −0.475886
\(472\) 10189.2i 0.993633i
\(473\) 22088.6i 2.14722i
\(474\) 4250.02 0.411835
\(475\) −1567.00 + 432.366i −0.151366 + 0.0417649i
\(476\) 2614.89 0.251793
\(477\) 2538.44i 0.243662i
\(478\) 2105.30i 0.201453i
\(479\) 2909.45 0.277528 0.138764 0.990325i \(-0.455687\pi\)
0.138764 + 0.990325i \(0.455687\pi\)
\(480\) −594.898 4392.68i −0.0565693 0.417703i
\(481\) 6511.96 0.617297
\(482\) 11688.7i 1.10458i
\(483\) 2741.86i 0.258300i
\(484\) 5721.42 0.537323
\(485\) 2069.15 280.224i 0.193722 0.0262357i
\(486\) 536.218 0.0500481
\(487\) 2201.84i 0.204876i −0.994739 0.102438i \(-0.967336\pi\)
0.994739 0.102438i \(-0.0326644\pi\)
\(488\) 13847.9i 1.28456i
\(489\) 2775.58 0.256679
\(490\) 1197.95 162.238i 0.110445 0.0149575i
\(491\) −11827.6 −1.08711 −0.543556 0.839373i \(-0.682922\pi\)
−0.543556 + 0.839373i \(0.682922\pi\)
\(492\) 4096.23i 0.375350i
\(493\) 9306.23i 0.850165i
\(494\) −1116.37 −0.101675
\(495\) 758.939 + 5603.95i 0.0689127 + 0.508846i
\(496\) −1780.30 −0.161165
\(497\) 727.928i 0.0656983i
\(498\) 3389.49i 0.304994i
\(499\) −1408.66 −0.126374 −0.0631868 0.998002i \(-0.520126\pi\)
−0.0631868 + 0.998002i \(0.520126\pi\)
\(500\) 1719.22 + 4023.29i 0.153771 + 0.359854i
\(501\) −8044.65 −0.717382
\(502\) 4093.74i 0.363969i
\(503\) 11018.9i 0.976758i 0.872632 + 0.488379i \(0.162412\pi\)
−0.872632 + 0.488379i \(0.837588\pi\)
\(504\) −1547.38 −0.136757
\(505\) −2476.76 18288.2i −0.218247 1.61152i
\(506\) 16192.2 1.42259
\(507\) 2050.77i 0.179641i
\(508\) 4428.95i 0.386816i
\(509\) −7032.93 −0.612434 −0.306217 0.951962i \(-0.599063\pi\)
−0.306217 + 0.951962i \(0.599063\pi\)
\(510\) −8751.57 + 1185.22i −0.759855 + 0.102907i
\(511\) −896.180 −0.0775825
\(512\) 9581.46i 0.827041i
\(513\) 351.121i 0.0302190i
\(514\) 13754.3 1.18030
\(515\) 799.781 108.314i 0.0684321 0.00926771i
\(516\) −3691.32 −0.314925
\(517\) 20528.6i 1.74632i
\(518\) 2585.63i 0.219317i
\(519\) 862.773 0.0729702
\(520\) 1433.69 + 10586.3i 0.120907 + 0.892766i
\(521\) 3049.04 0.256394 0.128197 0.991749i \(-0.459081\pi\)
0.128197 + 0.991749i \(0.459081\pi\)
\(522\) 1548.93i 0.129875i
\(523\) 8714.06i 0.728564i −0.931289 0.364282i \(-0.881314\pi\)
0.931289 0.364282i \(-0.118686\pi\)
\(524\) −7740.58 −0.645322
\(525\) 2530.44 698.198i 0.210357 0.0580416i
\(526\) −2613.79 −0.216666
\(527\) 7286.52i 0.602288i
\(528\) 4915.41i 0.405143i
\(529\) −4880.17 −0.401099
\(530\) −933.856 6895.53i −0.0765361 0.565137i
\(531\) 3733.58 0.305129
\(532\) 284.987i 0.0232251i
\(533\) 16967.1i 1.37885i
\(534\) −8110.15 −0.657230
\(535\) −13323.3 + 1804.36i −1.07666 + 0.145812i
\(536\) 9707.48 0.782275
\(537\) 11050.4i 0.888009i
\(538\) 4228.02i 0.338815i
\(539\) −2753.85 −0.220068
\(540\) −936.499 + 126.829i −0.0746305 + 0.0101072i
\(541\) −5999.45 −0.476778 −0.238389 0.971170i \(-0.576619\pi\)
−0.238389 + 0.971170i \(0.576619\pi\)
\(542\) 2579.48i 0.204425i
\(543\) 9397.95i 0.742734i
\(544\) −15769.6 −1.24286
\(545\) −2327.74 17187.9i −0.182953 1.35091i
\(546\) 1802.74 0.141301
\(547\) 7759.95i 0.606566i 0.952901 + 0.303283i \(0.0980828\pi\)
−0.952901 + 0.303283i \(0.901917\pi\)
\(548\) 671.184i 0.0523203i
\(549\) 5074.22 0.394467
\(550\) 4123.24 + 14943.6i 0.319664 + 1.15854i
\(551\) −1014.25 −0.0784184
\(552\) 9620.63i 0.741814i
\(553\) 4493.99i 0.345577i
\(554\) −16041.4 −1.23021
\(555\) 753.487 + 5563.69i 0.0576283 + 0.425523i
\(556\) −2951.50 −0.225128
\(557\) 6392.82i 0.486306i −0.969988 0.243153i \(-0.921818\pi\)
0.969988 0.243153i \(-0.0781817\pi\)
\(558\) 1212.77i 0.0920081i
\(559\) 15289.9 1.15687
\(560\) −2261.00 + 306.206i −0.170616 + 0.0231064i
\(561\) 20118.1 1.51406
\(562\) 657.863i 0.0493777i
\(563\) 7682.70i 0.575111i 0.957764 + 0.287555i \(0.0928425\pi\)
−0.957764 + 0.287555i \(0.907157\pi\)
\(564\) −3430.61 −0.256125
\(565\) −23054.7 + 3122.28i −1.71667 + 0.232487i
\(566\) −9921.81 −0.736828
\(567\) 567.000i 0.0419961i
\(568\) 2554.15i 0.188679i
\(569\) −143.175 −0.0105487 −0.00527434 0.999986i \(-0.501679\pi\)
−0.00527434 + 0.999986i \(0.501679\pi\)
\(570\) −129.172 953.800i −0.00949200 0.0700883i
\(571\) 1077.72 0.0789863 0.0394932 0.999220i \(-0.487426\pi\)
0.0394932 + 0.999220i \(0.487426\pi\)
\(572\) 6844.74i 0.500338i
\(573\) 4760.78i 0.347094i
\(574\) 6736.92 0.489884
\(575\) −4340.96 15732.7i −0.314835 1.14104i
\(576\) 4723.76 0.341707
\(577\) 12651.7i 0.912818i −0.889770 0.456409i \(-0.849135\pi\)
0.889770 0.456409i \(-0.150865\pi\)
\(578\) 20576.6i 1.48075i
\(579\) −15537.0 −1.11519
\(580\) 366.361 + 2705.18i 0.0262281 + 0.193666i
\(581\) 3584.07 0.255925
\(582\) 1236.35i 0.0880554i
\(583\) 15851.4i 1.12607i
\(584\) 3144.51 0.222810
\(585\) 3879.09 525.342i 0.274155 0.0371286i
\(586\) −3628.47 −0.255786
\(587\) 2920.89i 0.205380i −0.994713 0.102690i \(-0.967255\pi\)
0.994713 0.102690i \(-0.0327450\pi\)
\(588\) 460.206i 0.0322765i
\(589\) 794.131 0.0555545
\(590\) 10142.1 1373.53i 0.707699 0.0958432i
\(591\) −2711.39 −0.188717
\(592\) 4880.09i 0.338802i
\(593\) 9801.70i 0.678765i 0.940648 + 0.339382i \(0.110218\pi\)
−0.940648 + 0.339382i \(0.889782\pi\)
\(594\) −3348.44 −0.231293
\(595\) −1253.26 9253.96i −0.0863504 0.637605i
\(596\) −5300.41 −0.364284
\(597\) 3514.53i 0.240938i
\(598\) 11208.3i 0.766458i
\(599\) 6992.54 0.476974 0.238487 0.971146i \(-0.423349\pi\)
0.238487 + 0.971146i \(0.423349\pi\)
\(600\) −8878.81 + 2449.83i −0.604126 + 0.166690i
\(601\) −26159.1 −1.77546 −0.887730 0.460364i \(-0.847719\pi\)
−0.887730 + 0.460364i \(0.847719\pi\)
\(602\) 6070.98i 0.411021i
\(603\) 3557.07i 0.240224i
\(604\) 7888.29 0.531407
\(605\) −2742.14 20247.8i −0.184271 1.36064i
\(606\) 10927.5 0.732506
\(607\) 264.526i 0.0176883i 0.999961 + 0.00884415i \(0.00281522\pi\)
−0.999961 + 0.00884415i \(0.997185\pi\)
\(608\) 1718.67i 0.114640i
\(609\) 1637.84 0.108980
\(610\) 13783.9 1866.74i 0.914905 0.123905i
\(611\) 14210.0 0.940875
\(612\) 3362.01i 0.222061i
\(613\) 29371.1i 1.93521i −0.252461 0.967607i \(-0.581240\pi\)
0.252461 0.967607i \(-0.418760\pi\)
\(614\) 10429.1 0.685477
\(615\) 14496.3 1963.23i 0.950485 0.128723i
\(616\) 9662.68 0.632014
\(617\) 26226.1i 1.71122i −0.517622 0.855609i \(-0.673183\pi\)
0.517622 0.855609i \(-0.326817\pi\)
\(618\) 477.880i 0.0311054i
\(619\) 8903.12 0.578105 0.289052 0.957313i \(-0.406660\pi\)
0.289052 + 0.957313i \(0.406660\pi\)
\(620\) −286.850 2118.08i −0.0185809 0.137200i
\(621\) 3525.25 0.227799
\(622\) 10711.1i 0.690476i
\(623\) 8575.72i 0.551491i
\(624\) −3402.47 −0.218282
\(625\) 13414.2 8012.47i 0.858509 0.512798i
\(626\) 3731.18 0.238224
\(627\) 2192.59i 0.139655i
\(628\) 5076.31i 0.322558i
\(629\) 19973.5 1.26613
\(630\) 208.592 + 1540.23i 0.0131912 + 0.0974032i
\(631\) −14136.0 −0.891832 −0.445916 0.895075i \(-0.647122\pi\)
−0.445916 + 0.895075i \(0.647122\pi\)
\(632\) 15768.5i 0.992464i
\(633\) 3309.49i 0.207805i
\(634\) 8558.27 0.536108
\(635\) 15673.8 2122.69i 0.979519 0.132656i
\(636\) −2648.99 −0.165156
\(637\) 1906.23i 0.118567i
\(638\) 9672.34i 0.600206i
\(639\) −935.908 −0.0579404
\(640\) 1118.02 151.413i 0.0690528 0.00935177i
\(641\) 17665.7 1.08854 0.544270 0.838910i \(-0.316807\pi\)
0.544270 + 0.838910i \(0.316807\pi\)
\(642\) 7960.84i 0.489391i
\(643\) 10890.0i 0.667901i −0.942591 0.333951i \(-0.891618\pi\)
0.942591 0.333951i \(-0.108382\pi\)
\(644\) −2861.27 −0.175078
\(645\) 1769.16 + 13063.4i 0.108001 + 0.797472i
\(646\) −3424.12 −0.208545
\(647\) 24281.0i 1.47540i 0.675128 + 0.737701i \(0.264089\pi\)
−0.675128 + 0.737701i \(0.735911\pi\)
\(648\) 1989.49i 0.120609i
\(649\) −23314.5 −1.41013
\(650\) 10344.1 2854.12i 0.624196 0.172228i
\(651\) −1282.39 −0.0772053
\(652\) 2896.46i 0.173979i
\(653\) 1865.16i 0.111776i −0.998437 0.0558878i \(-0.982201\pi\)
0.998437 0.0558878i \(-0.0177989\pi\)
\(654\) 10270.0 0.614050
\(655\) 3709.87 + 27393.4i 0.221308 + 1.63412i
\(656\) −12715.2 −0.756775
\(657\) 1152.23i 0.0684214i
\(658\) 5642.20i 0.334279i
\(659\) 8327.14 0.492230 0.246115 0.969241i \(-0.420846\pi\)
0.246115 + 0.969241i \(0.420846\pi\)
\(660\) 5848.01 791.992i 0.344899 0.0467095i
\(661\) −20665.7 −1.21604 −0.608021 0.793921i \(-0.708036\pi\)
−0.608021 + 0.793921i \(0.708036\pi\)
\(662\) 21907.1i 1.28617i
\(663\) 13925.8i 0.815737i
\(664\) −12575.8 −0.734991
\(665\) 1008.55 136.588i 0.0588121 0.00796488i
\(666\) −3324.38 −0.193419
\(667\) 10183.1i 0.591140i
\(668\) 8395.00i 0.486246i
\(669\) 12239.8 0.707353
\(670\) −1308.60 9662.60i −0.0754561 0.557163i
\(671\) −31686.2 −1.82300
\(672\) 2775.36i 0.159318i
\(673\) 1283.48i 0.0735136i 0.999324 + 0.0367568i \(0.0117027\pi\)
−0.999324 + 0.0367568i \(0.988297\pi\)
\(674\) 11659.7 0.666344
\(675\) 897.683 + 3253.43i 0.0511879 + 0.185518i
\(676\) 2140.08 0.121762
\(677\) 13783.2i 0.782467i −0.920291 0.391234i \(-0.872048\pi\)
0.920291 0.391234i \(-0.127952\pi\)
\(678\) 13775.5i 0.780302i
\(679\) −1307.32 −0.0738886
\(680\) 4397.42 + 32470.2i 0.247990 + 1.83114i
\(681\) −2795.89 −0.157326
\(682\) 7573.18i 0.425208i
\(683\) 10796.5i 0.604856i −0.953172 0.302428i \(-0.902203\pi\)
0.953172 0.302428i \(-0.0977972\pi\)
\(684\) −366.412 −0.0204826
\(685\) −2375.28 + 321.682i −0.132489 + 0.0179428i
\(686\) −756.884 −0.0421253
\(687\) 4414.66i 0.245167i
\(688\) 11458.3i 0.634947i
\(689\) 10972.4 0.606699
\(690\) 9576.15 1296.89i 0.528345 0.0715533i
\(691\) −12082.4 −0.665173 −0.332587 0.943073i \(-0.607921\pi\)
−0.332587 + 0.943073i \(0.607921\pi\)
\(692\) 900.348i 0.0494597i
\(693\) 3540.66i 0.194082i
\(694\) −23276.5 −1.27315
\(695\) 1414.58 + 10445.2i 0.0772060 + 0.570084i
\(696\) −5746.85 −0.312980
\(697\) 52041.4i 2.82813i
\(698\) 1386.69i 0.0751962i
\(699\) 7437.19 0.402433
\(700\) −728.605 2640.65i −0.0393410 0.142582i
\(701\) −28753.5 −1.54922 −0.774610 0.632439i \(-0.782054\pi\)
−0.774610 + 0.632439i \(0.782054\pi\)
\(702\) 2317.81i 0.124615i
\(703\) 2176.84i 0.116787i
\(704\) −29497.8 −1.57917
\(705\) 1644.21 + 12140.7i 0.0878362 + 0.648576i
\(706\) −5622.95 −0.299749
\(707\) 11554.8i 0.614657i
\(708\) 3896.18i 0.206819i
\(709\) −4577.21 −0.242455 −0.121228 0.992625i \(-0.538683\pi\)
−0.121228 + 0.992625i \(0.538683\pi\)
\(710\) −2542.34 + 344.308i −0.134384 + 0.0181995i
\(711\) −5777.99 −0.304770
\(712\) 30090.4i 1.58383i
\(713\) 7973.07i 0.418785i
\(714\) 5529.37 0.289820
\(715\) −24223.1 + 3280.52i −1.26698 + 0.171587i
\(716\) −11531.7 −0.601898
\(717\) 2862.20i 0.149081i
\(718\) 28788.8i 1.49636i
\(719\) −30875.9 −1.60150 −0.800749 0.599000i \(-0.795565\pi\)
−0.800749 + 0.599000i \(0.795565\pi\)
\(720\) −393.693 2907.00i −0.0203779 0.150469i
\(721\) −505.313 −0.0261010
\(722\) 14762.3i 0.760936i
\(723\) 15891.1i 0.817420i
\(724\) 9807.25 0.503430
\(725\) 9397.88 2593.06i 0.481419 0.132833i
\(726\) 12098.3 0.618472
\(727\) 520.090i 0.0265324i −0.999912 0.0132662i \(-0.995777\pi\)
0.999912 0.0132662i \(-0.00422289\pi\)
\(728\) 6688.56i 0.340514i
\(729\) −729.000 −0.0370370
\(730\) −423.890 3129.98i −0.0214916 0.158693i
\(731\) 46897.1 2.37285
\(732\) 5295.21i 0.267372i
\(733\) 393.396i 0.0198232i −0.999951 0.00991160i \(-0.996845\pi\)
0.999951 0.00991160i \(-0.00315501\pi\)
\(734\) 17803.8 0.895301
\(735\) −1628.64 + 220.566i −0.0817325 + 0.0110690i
\(736\) 17255.5 0.864191
\(737\) 22212.3i 1.11018i
\(738\) 8661.76i 0.432037i
\(739\) 9348.92 0.465366 0.232683 0.972553i \(-0.425250\pi\)
0.232683 + 0.972553i \(0.425250\pi\)
\(740\) 5806.00 786.302i 0.288423 0.0390609i
\(741\) 1517.72 0.0752428
\(742\) 4356.69i 0.215552i
\(743\) 33710.8i 1.66451i 0.554394 + 0.832254i \(0.312950\pi\)
−0.554394 + 0.832254i \(0.687050\pi\)
\(744\) 4499.63 0.221726
\(745\) 2540.36 + 18757.8i 0.124928 + 0.922461i
\(746\) 7995.44 0.392405
\(747\) 4608.09i 0.225704i
\(748\) 20994.2i 1.02624i
\(749\) 8417.83 0.410655
\(750\) 3635.40 + 8507.52i 0.176995 + 0.414201i
\(751\) −21116.6 −1.02604 −0.513019 0.858377i \(-0.671473\pi\)
−0.513019 + 0.858377i \(0.671473\pi\)
\(752\) 10649.0i 0.516396i
\(753\) 5565.52i 0.269348i
\(754\) 6695.24 0.323377
\(755\) −3780.67 27916.2i −0.182242 1.34566i
\(756\) 591.694 0.0284652
\(757\) 7385.25i 0.354586i 0.984158 + 0.177293i \(0.0567340\pi\)
−0.984158 + 0.177293i \(0.943266\pi\)
\(758\) 16520.3i 0.791616i
\(759\) −22013.6 −1.05276
\(760\) −3538.81 + 479.258i −0.168903 + 0.0228744i
\(761\) −27682.0 −1.31862 −0.659311 0.751871i \(-0.729152\pi\)
−0.659311 + 0.751871i \(0.729152\pi\)
\(762\) 9365.30i 0.445235i
\(763\) 10859.5i 0.515258i
\(764\) 4968.12 0.235262
\(765\) 11897.9 1611.33i 0.562315 0.0761539i
\(766\) −19697.9 −0.929132
\(767\) 16138.4i 0.759746i
\(768\) 11928.7i 0.560467i
\(769\) 22248.6 1.04331 0.521654 0.853157i \(-0.325315\pi\)
0.521654 + 0.853157i \(0.325315\pi\)
\(770\) −1302.56 9618.01i −0.0609624 0.450142i
\(771\) −18699.3 −0.873460
\(772\) 16213.6i 0.755883i
\(773\) 11372.3i 0.529152i −0.964365 0.264576i \(-0.914768\pi\)
0.964365 0.264576i \(-0.0852321\pi\)
\(774\) −7805.54 −0.362486
\(775\) −7358.29 + 2030.29i −0.341055 + 0.0941036i
\(776\) 4587.12 0.212201
\(777\) 3515.22i 0.162301i
\(778\) 27804.0i 1.28126i
\(779\) 5671.80 0.260864
\(780\) −548.221 4048.02i −0.0251660 0.185824i
\(781\) 5844.32 0.267767
\(782\) 34378.1i 1.57207i
\(783\) 2105.80i 0.0961112i
\(784\) 1428.53 0.0650754