Properties

Label 1805.2.b.i.1084.4
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.4
Root \(-1.85244i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.i.1084.13

$q$-expansion

\(f(q)\) \(=\) \(q-1.85244i q^{2} -1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} -1.05306i q^{8} +0.884731 q^{9} +O(q^{10})\) \(q-1.85244i q^{2} -1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} -1.05306i q^{8} +0.884731 q^{9} +(4.09862 + 0.599118i) q^{10} +1.95728 q^{11} +2.08200i q^{12} +3.06043i q^{13} +0.884731 q^{14} +(3.21793 + 0.470383i) q^{15} -4.81379 q^{16} +0.973502i q^{17} -1.63891i q^{18} +(0.462986 - 3.16733i) q^{20} +0.694625 q^{21} -3.62574i q^{22} +5.59328i q^{23} -1.53157 q^{24} +(-4.79080 - 1.43117i) q^{25} +5.66926 q^{26} -5.64994i q^{27} -0.683702i q^{28} +10.1756 q^{29} +(0.871355 - 5.96102i) q^{30} +5.60367 q^{31} +6.81111i q^{32} -2.84666i q^{33} +1.80335 q^{34} +(-1.05672 - 0.154467i) q^{35} -1.26651 q^{36} +5.65754i q^{37} +4.45108 q^{39} +(2.32996 + 0.340584i) q^{40} +10.4679 q^{41} -1.28675i q^{42} -6.20983i q^{43} -2.80189 q^{44} +(-0.286141 + 1.95752i) q^{45} +10.3612 q^{46} +2.47845i q^{47} +7.00115i q^{48} +6.77189 q^{49} +(-2.65116 + 8.87465i) q^{50} +1.41586 q^{51} -4.38109i q^{52} -10.7711i q^{53} -10.4662 q^{54} +(-0.633026 + 4.33059i) q^{55} +0.502948 q^{56} -18.8496i q^{58} -7.32031 q^{59} +(-4.60655 - 0.673365i) q^{60} +8.76766 q^{61} -10.3805i q^{62} +0.422551i q^{63} +2.98958 q^{64} +(-6.77138 - 0.989809i) q^{65} -5.27326 q^{66} -8.82042i q^{67} -1.39359i q^{68} +8.13485 q^{69} +(-0.286141 + 1.95752i) q^{70} -13.1846 q^{71} -0.931679i q^{72} -4.97121i q^{73} +10.4802 q^{74} +(-2.08150 + 6.96772i) q^{75} +0.934804i q^{77} -8.24535i q^{78} +0.707984 q^{79} +(1.55688 - 10.6508i) q^{80} -5.56306 q^{81} -19.3911i q^{82} +11.8783i q^{83} -0.994373 q^{84} +(-2.15393 - 0.314851i) q^{85} -11.5033 q^{86} -14.7993i q^{87} -2.06114i q^{88} -2.14855 q^{89} +(3.62618 + 0.530058i) q^{90} -1.46167 q^{91} -8.00692i q^{92} -8.14996i q^{93} +4.59117 q^{94} +9.90605 q^{96} -5.89541i q^{97} -12.5445i q^{98} +1.73167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85244i 1.30987i −0.755685 0.654936i \(-0.772696\pi\)
0.755685 0.654936i \(-0.227304\pi\)
\(3\) 1.45440i 0.839696i −0.907594 0.419848i \(-0.862083\pi\)
0.907594 0.419848i \(-0.137917\pi\)
\(4\) −1.43152 −0.715762
\(5\) −0.323421 + 2.21255i −0.144638 + 0.989485i
\(6\) −2.69418 −1.09989
\(7\) 0.477604i 0.180517i 0.995918 + 0.0902586i \(0.0287694\pi\)
−0.995918 + 0.0902586i \(0.971231\pi\)
\(8\) 1.05306i 0.372315i
\(9\) 0.884731 0.294910
\(10\) 4.09862 + 0.599118i 1.29610 + 0.189458i
\(11\) 1.95728 0.590142 0.295071 0.955475i \(-0.404657\pi\)
0.295071 + 0.955475i \(0.404657\pi\)
\(12\) 2.08200i 0.601023i
\(13\) 3.06043i 0.848812i 0.905472 + 0.424406i \(0.139517\pi\)
−0.905472 + 0.424406i \(0.860483\pi\)
\(14\) 0.884731 0.236454
\(15\) 3.21793 + 0.470383i 0.830866 + 0.121452i
\(16\) −4.81379 −1.20345
\(17\) 0.973502i 0.236109i 0.993007 + 0.118054i \(0.0376657\pi\)
−0.993007 + 0.118054i \(0.962334\pi\)
\(18\) 1.63891i 0.386295i
\(19\) 0 0
\(20\) 0.462986 3.16733i 0.103527 0.708236i
\(21\) 0.694625 0.151580
\(22\) 3.62574i 0.773010i
\(23\) 5.59328i 1.16628i 0.812372 + 0.583140i \(0.198176\pi\)
−0.812372 + 0.583140i \(0.801824\pi\)
\(24\) −1.53157 −0.312631
\(25\) −4.79080 1.43117i −0.958159 0.286235i
\(26\) 5.66926 1.11183
\(27\) 5.64994i 1.08733i
\(28\) 0.683702i 0.129207i
\(29\) 10.1756 1.88955 0.944777 0.327714i \(-0.106278\pi\)
0.944777 + 0.327714i \(0.106278\pi\)
\(30\) 0.871355 5.96102i 0.159087 1.08833i
\(31\) 5.60367 1.00645 0.503225 0.864156i \(-0.332147\pi\)
0.503225 + 0.864156i \(0.332147\pi\)
\(32\) 6.81111i 1.20405i
\(33\) 2.84666i 0.495540i
\(34\) 1.80335 0.309272
\(35\) −1.05672 0.154467i −0.178619 0.0261097i
\(36\) −1.26651 −0.211086
\(37\) 5.65754i 0.930094i 0.885286 + 0.465047i \(0.153963\pi\)
−0.885286 + 0.465047i \(0.846037\pi\)
\(38\) 0 0
\(39\) 4.45108 0.712744
\(40\) 2.32996 + 0.340584i 0.368400 + 0.0538510i
\(41\) 10.4679 1.63481 0.817404 0.576065i \(-0.195413\pi\)
0.817404 + 0.576065i \(0.195413\pi\)
\(42\) 1.28675i 0.198550i
\(43\) 6.20983i 0.946990i −0.880796 0.473495i \(-0.842992\pi\)
0.880796 0.473495i \(-0.157008\pi\)
\(44\) −2.80189 −0.422401
\(45\) −0.286141 + 1.95752i −0.0426554 + 0.291809i
\(46\) 10.3612 1.52768
\(47\) 2.47845i 0.361519i 0.983527 + 0.180759i \(0.0578555\pi\)
−0.983527 + 0.180759i \(0.942144\pi\)
\(48\) 7.00115i 1.01053i
\(49\) 6.77189 0.967414
\(50\) −2.65116 + 8.87465i −0.374931 + 1.25507i
\(51\) 1.41586 0.198260
\(52\) 4.38109i 0.607547i
\(53\) 10.7711i 1.47953i −0.672866 0.739764i \(-0.734937\pi\)
0.672866 0.739764i \(-0.265063\pi\)
\(54\) −10.4662 −1.42426
\(55\) −0.633026 + 4.33059i −0.0853572 + 0.583936i
\(56\) 0.502948 0.0672092
\(57\) 0 0
\(58\) 18.8496i 2.47507i
\(59\) −7.32031 −0.953024 −0.476512 0.879168i \(-0.658099\pi\)
−0.476512 + 0.879168i \(0.658099\pi\)
\(60\) −4.60655 0.673365i −0.594703 0.0869310i
\(61\) 8.76766 1.12258 0.561292 0.827618i \(-0.310305\pi\)
0.561292 + 0.827618i \(0.310305\pi\)
\(62\) 10.3805i 1.31832i
\(63\) 0.422551i 0.0532364i
\(64\) 2.98958 0.373698
\(65\) −6.77138 0.989809i −0.839886 0.122771i
\(66\) −5.27326 −0.649093
\(67\) 8.82042i 1.07759i −0.842438 0.538793i \(-0.818880\pi\)
0.842438 0.538793i \(-0.181120\pi\)
\(68\) 1.39359i 0.168998i
\(69\) 8.13485 0.979321
\(70\) −0.286141 + 1.95752i −0.0342004 + 0.233968i
\(71\) −13.1846 −1.56472 −0.782362 0.622825i \(-0.785985\pi\)
−0.782362 + 0.622825i \(0.785985\pi\)
\(72\) 0.931679i 0.109799i
\(73\) 4.97121i 0.581836i −0.956748 0.290918i \(-0.906039\pi\)
0.956748 0.290918i \(-0.0939606\pi\)
\(74\) 10.4802 1.21830
\(75\) −2.08150 + 6.96772i −0.240350 + 0.804563i
\(76\) 0 0
\(77\) 0.934804i 0.106531i
\(78\) 8.24535i 0.933603i
\(79\) 0.707984 0.0796544 0.0398272 0.999207i \(-0.487319\pi\)
0.0398272 + 0.999207i \(0.487319\pi\)
\(80\) 1.55688 10.6508i 0.174065 1.19079i
\(81\) −5.56306 −0.618118
\(82\) 19.3911i 2.14139i
\(83\) 11.8783i 1.30382i 0.758297 + 0.651909i \(0.226032\pi\)
−0.758297 + 0.651909i \(0.773968\pi\)
\(84\) −0.994373 −0.108495
\(85\) −2.15393 0.314851i −0.233626 0.0341504i
\(86\) −11.5033 −1.24043
\(87\) 14.7993i 1.58665i
\(88\) 2.06114i 0.219718i
\(89\) −2.14855 −0.227746 −0.113873 0.993495i \(-0.536326\pi\)
−0.113873 + 0.993495i \(0.536326\pi\)
\(90\) 3.62618 + 0.530058i 0.382232 + 0.0558730i
\(91\) −1.46167 −0.153225
\(92\) 8.00692i 0.834779i
\(93\) 8.14996i 0.845112i
\(94\) 4.59117 0.473543
\(95\) 0 0
\(96\) 9.90605 1.01103
\(97\) 5.89541i 0.598588i −0.954161 0.299294i \(-0.903249\pi\)
0.954161 0.299294i \(-0.0967512\pi\)
\(98\) 12.5445i 1.26719i
\(99\) 1.73167 0.174039
\(100\) 6.85815 + 2.04876i 0.685815 + 0.204876i
\(101\) 0.258211 0.0256930 0.0128465 0.999917i \(-0.495911\pi\)
0.0128465 + 0.999917i \(0.495911\pi\)
\(102\) 2.62279i 0.259695i
\(103\) 14.3714i 1.41605i 0.706186 + 0.708026i \(0.250414\pi\)
−0.706186 + 0.708026i \(0.749586\pi\)
\(104\) 3.22283 0.316025
\(105\) −0.224657 + 1.53690i −0.0219242 + 0.149986i
\(106\) −19.9529 −1.93799
\(107\) 5.73115i 0.554051i 0.960863 + 0.277026i \(0.0893487\pi\)
−0.960863 + 0.277026i \(0.910651\pi\)
\(108\) 8.08803i 0.778271i
\(109\) 5.77812 0.553444 0.276722 0.960950i \(-0.410752\pi\)
0.276722 + 0.960950i \(0.410752\pi\)
\(110\) 8.02214 + 1.17264i 0.764881 + 0.111807i
\(111\) 8.22830 0.780996
\(112\) 2.29908i 0.217243i
\(113\) 13.9762i 1.31477i −0.753554 0.657386i \(-0.771662\pi\)
0.753554 0.657386i \(-0.228338\pi\)
\(114\) 0 0
\(115\) −12.3754 1.80899i −1.15402 0.168689i
\(116\) −14.5666 −1.35247
\(117\) 2.70766i 0.250323i
\(118\) 13.5604i 1.24834i
\(119\) −0.464948 −0.0426217
\(120\) 0.495344 3.38869i 0.0452185 0.309344i
\(121\) −7.16906 −0.651733
\(122\) 16.2415i 1.47044i
\(123\) 15.2244i 1.37274i
\(124\) −8.02180 −0.720379
\(125\) 4.71600 10.1370i 0.421812 0.906683i
\(126\) 0.782749 0.0697328
\(127\) 9.23319i 0.819313i 0.912240 + 0.409657i \(0.134351\pi\)
−0.912240 + 0.409657i \(0.865649\pi\)
\(128\) 8.08421i 0.714550i
\(129\) −9.03155 −0.795184
\(130\) −1.83356 + 12.5436i −0.160814 + 1.10014i
\(131\) −13.9316 −1.21721 −0.608603 0.793475i \(-0.708270\pi\)
−0.608603 + 0.793475i \(0.708270\pi\)
\(132\) 4.07506i 0.354689i
\(133\) 0 0
\(134\) −16.3393 −1.41150
\(135\) 12.5008 + 1.82731i 1.07590 + 0.157270i
\(136\) 1.02516 0.0879068
\(137\) 3.84336i 0.328360i 0.986430 + 0.164180i \(0.0524978\pi\)
−0.986430 + 0.164180i \(0.947502\pi\)
\(138\) 15.0693i 1.28278i
\(139\) 18.8730 1.60079 0.800395 0.599473i \(-0.204623\pi\)
0.800395 + 0.599473i \(0.204623\pi\)
\(140\) 1.51273 + 0.221124i 0.127849 + 0.0186884i
\(141\) 3.60464 0.303566
\(142\) 24.4236i 2.04959i
\(143\) 5.99012i 0.500919i
\(144\) −4.25891 −0.354909
\(145\) −3.29099 + 22.5140i −0.273302 + 1.86968i
\(146\) −9.20885 −0.762130
\(147\) 9.84902i 0.812333i
\(148\) 8.09891i 0.665726i
\(149\) 23.9268 1.96016 0.980082 0.198594i \(-0.0636375\pi\)
0.980082 + 0.198594i \(0.0636375\pi\)
\(150\) 12.9073 + 3.85584i 1.05387 + 0.314828i
\(151\) −5.90301 −0.480380 −0.240190 0.970726i \(-0.577210\pi\)
−0.240190 + 0.970726i \(0.577210\pi\)
\(152\) 0 0
\(153\) 0.861288i 0.0696310i
\(154\) 1.73167 0.139542
\(155\) −1.81235 + 12.3984i −0.145571 + 0.995866i
\(156\) −6.37184 −0.510155
\(157\) 10.5707i 0.843631i 0.906682 + 0.421815i \(0.138607\pi\)
−0.906682 + 0.421815i \(0.861393\pi\)
\(158\) 1.31150i 0.104337i
\(159\) −15.6655 −1.24235
\(160\) −15.0700 2.20286i −1.19138 0.174151i
\(161\) −2.67137 −0.210534
\(162\) 10.3052i 0.809654i
\(163\) 18.6090i 1.45757i 0.684743 + 0.728785i \(0.259915\pi\)
−0.684743 + 0.728785i \(0.740085\pi\)
\(164\) −14.9850 −1.17013
\(165\) 6.29839 + 0.920670i 0.490329 + 0.0716741i
\(166\) 22.0039 1.70783
\(167\) 2.77731i 0.214914i −0.994210 0.107457i \(-0.965729\pi\)
0.994210 0.107457i \(-0.0342708\pi\)
\(168\) 0.731485i 0.0564353i
\(169\) 3.63375 0.279519
\(170\) −0.583242 + 3.99001i −0.0447327 + 0.306020i
\(171\) 0 0
\(172\) 8.88952i 0.677820i
\(173\) 8.92075i 0.678232i −0.940745 0.339116i \(-0.889872\pi\)
0.940745 0.339116i \(-0.110128\pi\)
\(174\) −27.4148 −2.07831
\(175\) 0.683534 2.28810i 0.0516703 0.172964i
\(176\) −9.42192 −0.710204
\(177\) 10.6466i 0.800250i
\(178\) 3.98006i 0.298318i
\(179\) −15.2646 −1.14093 −0.570467 0.821321i \(-0.693238\pi\)
−0.570467 + 0.821321i \(0.693238\pi\)
\(180\) 0.409618 2.80223i 0.0305311 0.208866i
\(181\) −8.54101 −0.634848 −0.317424 0.948284i \(-0.602818\pi\)
−0.317424 + 0.948284i \(0.602818\pi\)
\(182\) 2.70766i 0.200705i
\(183\) 12.7516i 0.942629i
\(184\) 5.89009 0.434223
\(185\) −12.5176 1.82977i −0.920313 0.134527i
\(186\) −15.0973 −1.10699
\(187\) 1.90542i 0.139338i
\(188\) 3.54796i 0.258761i
\(189\) 2.69843 0.196282
\(190\) 0 0
\(191\) −16.2967 −1.17919 −0.589594 0.807700i \(-0.700712\pi\)
−0.589594 + 0.807700i \(0.700712\pi\)
\(192\) 4.34804i 0.313792i
\(193\) 16.4692i 1.18548i −0.805394 0.592739i \(-0.798046\pi\)
0.805394 0.592739i \(-0.201954\pi\)
\(194\) −10.9209 −0.784074
\(195\) −1.43958 + 9.84827i −0.103090 + 0.705249i
\(196\) −9.69414 −0.692438
\(197\) 10.0229i 0.714102i −0.934085 0.357051i \(-0.883782\pi\)
0.934085 0.357051i \(-0.116218\pi\)
\(198\) 3.20780i 0.227969i
\(199\) 12.6643 0.897748 0.448874 0.893595i \(-0.351825\pi\)
0.448874 + 0.893595i \(0.351825\pi\)
\(200\) −1.50712 + 5.04502i −0.106569 + 0.356737i
\(201\) −12.8284 −0.904845
\(202\) 0.478321i 0.0336545i
\(203\) 4.85988i 0.341097i
\(204\) −2.02684 −0.141907
\(205\) −3.38553 + 23.1607i −0.236456 + 1.61762i
\(206\) 26.6221 1.85485
\(207\) 4.94855i 0.343948i
\(208\) 14.7323i 1.02150i
\(209\) 0 0
\(210\) 2.84700 + 0.416162i 0.196462 + 0.0287179i
\(211\) 5.73609 0.394888 0.197444 0.980314i \(-0.436736\pi\)
0.197444 + 0.980314i \(0.436736\pi\)
\(212\) 15.4191i 1.05899i
\(213\) 19.1756i 1.31389i
\(214\) 10.6166 0.725736
\(215\) 13.7396 + 2.00839i 0.937032 + 0.136971i
\(216\) −5.94975 −0.404829
\(217\) 2.67634i 0.181682i
\(218\) 10.7036i 0.724940i
\(219\) −7.23010 −0.488565
\(220\) 0.906192 6.19934i 0.0610955 0.417960i
\(221\) −2.97934 −0.200412
\(222\) 15.2424i 1.02300i
\(223\) 12.8478i 0.860353i −0.902745 0.430176i \(-0.858451\pi\)
0.902745 0.430176i \(-0.141549\pi\)
\(224\) −3.25301 −0.217351
\(225\) −4.23857 1.26620i −0.282571 0.0844136i
\(226\) −25.8901 −1.72218
\(227\) 15.5808i 1.03413i 0.855945 + 0.517067i \(0.172976\pi\)
−0.855945 + 0.517067i \(0.827024\pi\)
\(228\) 0 0
\(229\) 3.77930 0.249743 0.124871 0.992173i \(-0.460148\pi\)
0.124871 + 0.992173i \(0.460148\pi\)
\(230\) −3.35103 + 22.9247i −0.220961 + 1.51161i
\(231\) 1.35958 0.0894535
\(232\) 10.7155i 0.703508i
\(233\) 11.0745i 0.725512i 0.931884 + 0.362756i \(0.118164\pi\)
−0.931884 + 0.362756i \(0.881836\pi\)
\(234\) 5.01577 0.327891
\(235\) −5.48370 0.801583i −0.357717 0.0522895i
\(236\) 10.4792 0.682139
\(237\) 1.02969i 0.0668855i
\(238\) 0.861288i 0.0558290i
\(239\) 10.6496 0.688865 0.344433 0.938811i \(-0.388071\pi\)
0.344433 + 0.938811i \(0.388071\pi\)
\(240\) −15.4904 2.26432i −0.999903 0.146161i
\(241\) 5.01271 0.322897 0.161448 0.986881i \(-0.448383\pi\)
0.161448 + 0.986881i \(0.448383\pi\)
\(242\) 13.2802i 0.853686i
\(243\) 8.85892i 0.568300i
\(244\) −12.5511 −0.803503
\(245\) −2.19018 + 14.9832i −0.139925 + 0.957241i
\(246\) −28.2023 −1.79811
\(247\) 0 0
\(248\) 5.90103i 0.374716i
\(249\) 17.2758 1.09481
\(250\) −18.7782 8.73609i −1.18764 0.552519i
\(251\) −26.1721 −1.65197 −0.825986 0.563691i \(-0.809381\pi\)
−0.825986 + 0.563691i \(0.809381\pi\)
\(252\) 0.604892i 0.0381046i
\(253\) 10.9476i 0.688271i
\(254\) 17.1039 1.07319
\(255\) −0.457919 + 3.13266i −0.0286760 + 0.196175i
\(256\) 20.9546 1.30967
\(257\) 22.4024i 1.39742i −0.715403 0.698712i \(-0.753757\pi\)
0.715403 0.698712i \(-0.246243\pi\)
\(258\) 16.7304i 1.04159i
\(259\) −2.70206 −0.167898
\(260\) 9.69339 + 1.41694i 0.601159 + 0.0878747i
\(261\) 9.00263 0.557249
\(262\) 25.8074i 1.59438i
\(263\) 25.9338i 1.59915i −0.600569 0.799573i \(-0.705059\pi\)
0.600569 0.799573i \(-0.294941\pi\)
\(264\) −2.99772 −0.184497
\(265\) 23.8317 + 3.48361i 1.46397 + 0.213997i
\(266\) 0 0
\(267\) 3.12485i 0.191238i
\(268\) 12.6267i 0.771296i
\(269\) 9.24978 0.563969 0.281985 0.959419i \(-0.409007\pi\)
0.281985 + 0.959419i \(0.409007\pi\)
\(270\) 3.38498 23.1569i 0.206003 1.40929i
\(271\) −22.4688 −1.36488 −0.682441 0.730941i \(-0.739082\pi\)
−0.682441 + 0.730941i \(0.739082\pi\)
\(272\) 4.68623i 0.284145i
\(273\) 2.12585i 0.128663i
\(274\) 7.11958 0.430110
\(275\) −9.37693 2.80121i −0.565450 0.168919i
\(276\) −11.6452 −0.700961
\(277\) 9.16598i 0.550730i 0.961340 + 0.275365i \(0.0887987\pi\)
−0.961340 + 0.275365i \(0.911201\pi\)
\(278\) 34.9611i 2.09683i
\(279\) 4.95774 0.296812
\(280\) −0.162664 + 1.11280i −0.00972103 + 0.0665025i
\(281\) −19.3577 −1.15479 −0.577393 0.816467i \(-0.695930\pi\)
−0.577393 + 0.816467i \(0.695930\pi\)
\(282\) 6.67738i 0.397632i
\(283\) 8.72514i 0.518656i −0.965789 0.259328i \(-0.916499\pi\)
0.965789 0.259328i \(-0.0835010\pi\)
\(284\) 18.8741 1.11997
\(285\) 0 0
\(286\) 11.0963 0.656140
\(287\) 4.99950i 0.295111i
\(288\) 6.02600i 0.355085i
\(289\) 16.0523 0.944253
\(290\) 41.7057 + 6.09636i 2.44905 + 0.357990i
\(291\) −8.57427 −0.502632
\(292\) 7.11641i 0.416456i
\(293\) 16.7749i 0.980002i 0.871722 + 0.490001i \(0.163004\pi\)
−0.871722 + 0.490001i \(0.836996\pi\)
\(294\) −18.2447 −1.06405
\(295\) 2.36755 16.1966i 0.137844 0.943002i
\(296\) 5.95776 0.346287
\(297\) 11.0585i 0.641680i
\(298\) 44.3230i 2.56756i
\(299\) −17.1179 −0.989952
\(300\) 2.97971 9.97446i 0.172034 0.575876i
\(301\) 2.96584 0.170948
\(302\) 10.9350i 0.629236i
\(303\) 0.375542i 0.0215743i
\(304\) 0 0
\(305\) −2.83565 + 19.3989i −0.162369 + 1.11078i
\(306\) 1.59548 0.0912076
\(307\) 6.40893i 0.365777i −0.983134 0.182889i \(-0.941455\pi\)
0.983134 0.182889i \(-0.0585448\pi\)
\(308\) 1.33819i 0.0762507i
\(309\) 20.9017 1.18905
\(310\) 22.9673 + 3.35726i 1.30446 + 0.190680i
\(311\) 10.6248 0.602477 0.301238 0.953549i \(-0.402600\pi\)
0.301238 + 0.953549i \(0.402600\pi\)
\(312\) 4.68728i 0.265365i
\(313\) 4.75656i 0.268857i 0.990923 + 0.134428i \(0.0429198\pi\)
−0.990923 + 0.134428i \(0.957080\pi\)
\(314\) 19.5815 1.10505
\(315\) −0.934917 0.136662i −0.0526766 0.00770003i
\(316\) −1.01350 −0.0570136
\(317\) 0.0612218i 0.00343856i −0.999999 0.00171928i \(-0.999453\pi\)
0.999999 0.00171928i \(-0.000547264\pi\)
\(318\) 29.0194i 1.62732i
\(319\) 19.9164 1.11510
\(320\) −0.966894 + 6.61461i −0.0540510 + 0.369768i
\(321\) 8.33536 0.465235
\(322\) 4.94855i 0.275772i
\(323\) 0 0
\(324\) 7.96366 0.442425
\(325\) 4.38002 14.6619i 0.242960 0.813297i
\(326\) 34.4720 1.90923
\(327\) 8.40368i 0.464724i
\(328\) 11.0234i 0.608663i
\(329\) −1.18372 −0.0652603
\(330\) 1.70548 11.6674i 0.0938838 0.642268i
\(331\) 17.6067 0.967752 0.483876 0.875137i \(-0.339229\pi\)
0.483876 + 0.875137i \(0.339229\pi\)
\(332\) 17.0041i 0.933224i
\(333\) 5.00540i 0.274294i
\(334\) −5.14478 −0.281510
\(335\) 19.5157 + 2.85271i 1.06625 + 0.155860i
\(336\) −3.34378 −0.182418
\(337\) 6.90874i 0.376343i −0.982136 0.188171i \(-0.939744\pi\)
0.982136 0.188171i \(-0.0602560\pi\)
\(338\) 6.73129i 0.366134i
\(339\) −20.3270 −1.10401
\(340\) 3.08340 + 0.450718i 0.167221 + 0.0244436i
\(341\) 10.9680 0.593948
\(342\) 0 0
\(343\) 6.57751i 0.355152i
\(344\) −6.53935 −0.352578
\(345\) −2.63098 + 17.9988i −0.141647 + 0.969023i
\(346\) −16.5251 −0.888396
\(347\) 7.32576i 0.393267i 0.980477 + 0.196634i \(0.0630010\pi\)
−0.980477 + 0.196634i \(0.936999\pi\)
\(348\) 21.1856i 1.13567i
\(349\) 2.16127 0.115690 0.0578452 0.998326i \(-0.481577\pi\)
0.0578452 + 0.998326i \(0.481577\pi\)
\(350\) −4.23857 1.26620i −0.226561 0.0676815i
\(351\) 17.2913 0.922939
\(352\) 13.3312i 0.710557i
\(353\) 16.6022i 0.883644i 0.897103 + 0.441822i \(0.145668\pi\)
−0.897103 + 0.441822i \(0.854332\pi\)
\(354\) 19.7222 1.04822
\(355\) 4.26418 29.1716i 0.226319 1.54827i
\(356\) 3.07571 0.163012
\(357\) 0.676219i 0.0357893i
\(358\) 28.2768i 1.49448i
\(359\) −17.0830 −0.901608 −0.450804 0.892623i \(-0.648863\pi\)
−0.450804 + 0.892623i \(0.648863\pi\)
\(360\) 2.06139 + 0.301325i 0.108645 + 0.0158812i
\(361\) 0 0
\(362\) 15.8217i 0.831569i
\(363\) 10.4267i 0.547257i
\(364\) 2.09242 0.109673
\(365\) 10.9991 + 1.60779i 0.575717 + 0.0841558i
\(366\) −23.6216 −1.23472
\(367\) 19.5631i 1.02119i 0.859822 + 0.510594i \(0.170574\pi\)
−0.859822 + 0.510594i \(0.829426\pi\)
\(368\) 26.9249i 1.40356i
\(369\) 9.26125 0.482122
\(370\) −3.38953 + 23.1881i −0.176213 + 1.20549i
\(371\) 5.14433 0.267080
\(372\) 11.6669i 0.604899i
\(373\) 6.59700i 0.341580i 0.985307 + 0.170790i \(0.0546320\pi\)
−0.985307 + 0.170790i \(0.945368\pi\)
\(374\) 3.52966 0.182515
\(375\) −14.7433 6.85893i −0.761339 0.354194i
\(376\) 2.60997 0.134599
\(377\) 31.1416i 1.60387i
\(378\) 4.99868i 0.257104i
\(379\) −21.6574 −1.11246 −0.556232 0.831027i \(-0.687753\pi\)
−0.556232 + 0.831027i \(0.687753\pi\)
\(380\) 0 0
\(381\) 13.4287 0.687974
\(382\) 30.1886i 1.54458i
\(383\) 24.3214i 1.24277i 0.783507 + 0.621383i \(0.213429\pi\)
−0.783507 + 0.621383i \(0.786571\pi\)
\(384\) 11.7576 0.600005
\(385\) −2.06830 0.302335i −0.105411 0.0154084i
\(386\) −30.5082 −1.55282
\(387\) 5.49403i 0.279277i
\(388\) 8.43943i 0.428447i
\(389\) −15.8227 −0.802241 −0.401120 0.916025i \(-0.631379\pi\)
−0.401120 + 0.916025i \(0.631379\pi\)
\(390\) 18.2433 + 2.66672i 0.923785 + 0.135035i
\(391\) −5.44507 −0.275369
\(392\) 7.13124i 0.360182i
\(393\) 20.2620i 1.02208i
\(394\) −18.5668 −0.935381
\(395\) −0.228977 + 1.56645i −0.0115211 + 0.0788168i
\(396\) −2.47892 −0.124571
\(397\) 35.4753i 1.78046i −0.455515 0.890228i \(-0.650545\pi\)
0.455515 0.890228i \(-0.349455\pi\)
\(398\) 23.4598i 1.17593i
\(399\) 0 0
\(400\) 23.0619 + 6.88937i 1.15309 + 0.344468i
\(401\) −11.2107 −0.559837 −0.279919 0.960024i \(-0.590307\pi\)
−0.279919 + 0.960024i \(0.590307\pi\)
\(402\) 23.7638i 1.18523i
\(403\) 17.1497i 0.854286i
\(404\) −0.369636 −0.0183901
\(405\) 1.79921 12.3086i 0.0894035 0.611618i
\(406\) 9.00263 0.446793
\(407\) 11.0734i 0.548887i
\(408\) 1.49099i 0.0738150i
\(409\) −1.91450 −0.0946660 −0.0473330 0.998879i \(-0.515072\pi\)
−0.0473330 + 0.998879i \(0.515072\pi\)
\(410\) 42.9038 + 6.27149i 2.11887 + 0.309727i
\(411\) 5.58977 0.275723
\(412\) 20.5730i 1.01356i
\(413\) 3.49621i 0.172037i
\(414\) 9.16688 0.450528
\(415\) −26.2815 3.84171i −1.29011 0.188582i
\(416\) −20.8449 −1.02201
\(417\) 27.4489i 1.34418i
\(418\) 0 0
\(419\) 22.1856 1.08384 0.541918 0.840431i \(-0.317698\pi\)
0.541918 + 0.840431i \(0.317698\pi\)
\(420\) 0.321601 2.20010i 0.0156925 0.107354i
\(421\) 13.3793 0.652069 0.326034 0.945358i \(-0.394287\pi\)
0.326034 + 0.945358i \(0.394287\pi\)
\(422\) 10.6257i 0.517253i
\(423\) 2.19276i 0.106616i
\(424\) −11.3427 −0.550850
\(425\) 1.39325 4.66385i 0.0675826 0.226230i
\(426\) 35.5216 1.72103
\(427\) 4.18747i 0.202646i
\(428\) 8.20428i 0.396569i
\(429\) 8.71201 0.420620
\(430\) 3.72042 25.4517i 0.179415 1.22739i
\(431\) −37.1687 −1.79035 −0.895177 0.445711i \(-0.852951\pi\)
−0.895177 + 0.445711i \(0.852951\pi\)
\(432\) 27.1976i 1.30855i
\(433\) 8.32630i 0.400137i 0.979782 + 0.200068i \(0.0641164\pi\)
−0.979782 + 0.200068i \(0.935884\pi\)
\(434\) 4.95774 0.237979
\(435\) 32.7443 + 4.78641i 1.56997 + 0.229491i
\(436\) −8.27152 −0.396134
\(437\) 0 0
\(438\) 13.3933i 0.639957i
\(439\) 17.0746 0.814928 0.407464 0.913221i \(-0.366413\pi\)
0.407464 + 0.913221i \(0.366413\pi\)
\(440\) 4.56039 + 0.666617i 0.217408 + 0.0317797i
\(441\) 5.99131 0.285300
\(442\) 5.51904i 0.262514i
\(443\) 7.18135i 0.341196i 0.985341 + 0.170598i \(0.0545700\pi\)
−0.985341 + 0.170598i \(0.945430\pi\)
\(444\) −11.7790 −0.559008
\(445\) 0.694888 4.75379i 0.0329409 0.225351i
\(446\) −23.7998 −1.12695
\(447\) 34.7991i 1.64594i
\(448\) 1.42784i 0.0674589i
\(449\) −23.1024 −1.09027 −0.545134 0.838349i \(-0.683521\pi\)
−0.545134 + 0.838349i \(0.683521\pi\)
\(450\) −2.34557 + 7.85168i −0.110571 + 0.370132i
\(451\) 20.4886 0.964768
\(452\) 20.0073i 0.941065i
\(453\) 8.58532i 0.403373i
\(454\) 28.8625 1.35458
\(455\) 0.472737 3.23403i 0.0221622 0.151614i
\(456\) 0 0
\(457\) 13.7430i 0.642872i 0.946931 + 0.321436i \(0.104166\pi\)
−0.946931 + 0.321436i \(0.895834\pi\)
\(458\) 7.00091i 0.327131i
\(459\) 5.50023 0.256729
\(460\) 17.7158 + 2.58961i 0.826001 + 0.120741i
\(461\) −26.0522 −1.21337 −0.606686 0.794942i \(-0.707501\pi\)
−0.606686 + 0.794942i \(0.707501\pi\)
\(462\) 2.51853i 0.117173i
\(463\) 4.24698i 0.197374i 0.995119 + 0.0986869i \(0.0314642\pi\)
−0.995119 + 0.0986869i \(0.968536\pi\)
\(464\) −48.9830 −2.27398
\(465\) 18.0322 + 2.63587i 0.836225 + 0.122236i
\(466\) 20.5147 0.950327
\(467\) 27.7571i 1.28444i −0.766519 0.642222i \(-0.778013\pi\)
0.766519 0.642222i \(-0.221987\pi\)
\(468\) 3.87608i 0.179172i
\(469\) 4.21267 0.194523
\(470\) −1.48488 + 10.1582i −0.0684925 + 0.468563i
\(471\) 15.3739 0.708394
\(472\) 7.70877i 0.354825i
\(473\) 12.1544i 0.558858i
\(474\) −1.90744 −0.0876114
\(475\) 0 0
\(476\) 0.665585 0.0305070
\(477\) 9.52956i 0.436328i
\(478\) 19.7277i 0.902325i
\(479\) 7.11883 0.325268 0.162634 0.986686i \(-0.448001\pi\)
0.162634 + 0.986686i \(0.448001\pi\)
\(480\) −3.20383 + 21.9177i −0.146234 + 1.00040i
\(481\) −17.3145 −0.789474
\(482\) 9.28573i 0.422953i
\(483\) 3.88523i 0.176784i
\(484\) 10.2627 0.466486
\(485\) 13.0439 + 1.90670i 0.592294 + 0.0865789i
\(486\) −16.4106 −0.744400
\(487\) 3.54621i 0.160694i 0.996767 + 0.0803470i \(0.0256028\pi\)
−0.996767 + 0.0803470i \(0.974397\pi\)
\(488\) 9.23291i 0.417954i
\(489\) 27.0649 1.22392
\(490\) 27.7554 + 4.05716i 1.25386 + 0.183284i
\(491\) −32.1308 −1.45004 −0.725020 0.688727i \(-0.758170\pi\)
−0.725020 + 0.688727i \(0.758170\pi\)
\(492\) 21.7942i 0.982557i
\(493\) 9.90593i 0.446141i
\(494\) 0 0
\(495\) −0.560057 + 3.83140i −0.0251727 + 0.172209i
\(496\) −26.9749 −1.21121
\(497\) 6.29701i 0.282459i
\(498\) 32.0024i 1.43406i
\(499\) 11.9147 0.533376 0.266688 0.963783i \(-0.414071\pi\)
0.266688 + 0.963783i \(0.414071\pi\)
\(500\) −6.75107 + 14.5114i −0.301917 + 0.648970i
\(501\) −4.03930 −0.180463
\(502\) 48.4823i 2.16387i
\(503\) 0.239744i 0.0106896i −0.999986 0.00534482i \(-0.998299\pi\)
0.999986 0.00534482i \(-0.00170132\pi\)
\(504\) 0.444973 0.0198207
\(505\) −0.0835111 + 0.571307i −0.00371620 + 0.0254228i
\(506\) 20.2798 0.901546
\(507\) 5.28491i 0.234711i
\(508\) 13.2175i 0.586434i
\(509\) 29.3663 1.30164 0.650819 0.759233i \(-0.274426\pi\)
0.650819 + 0.759233i \(0.274426\pi\)
\(510\) 5.80306 + 0.848266i 0.256964 + 0.0375618i
\(511\) 2.37427 0.105031
\(512\) 22.6488i 1.00094i
\(513\) 0 0
\(514\) −41.4991 −1.83045
\(515\) −31.7974 4.64801i −1.40116 0.204816i
\(516\) 12.9289 0.569163
\(517\) 4.85101i 0.213347i
\(518\) 5.00540i 0.219925i
\(519\) −12.9743 −0.569509
\(520\) −1.04233 + 7.13070i −0.0457093 + 0.312702i
\(521\) 12.1069 0.530414 0.265207 0.964191i \(-0.414560\pi\)
0.265207 + 0.964191i \(0.414560\pi\)
\(522\) 16.6768i 0.729924i
\(523\) 6.43779i 0.281505i −0.990045 0.140752i \(-0.955048\pi\)
0.990045 0.140752i \(-0.0449522\pi\)
\(524\) 19.9434 0.871231
\(525\) −3.32781 0.994130i −0.145237 0.0433874i
\(526\) −48.0407 −2.09467
\(527\) 5.45519i 0.237632i
\(528\) 13.7032i 0.596356i
\(529\) −8.28480 −0.360209
\(530\) 6.45318 44.1468i 0.280308 1.91761i
\(531\) −6.47651 −0.281057
\(532\) 0 0
\(533\) 32.0362i 1.38764i
\(534\) 5.78859 0.250497
\(535\) −12.6805 1.85358i −0.548225 0.0801371i
\(536\) −9.28848 −0.401201
\(537\) 22.2008i 0.958037i
\(538\) 17.1346i 0.738727i
\(539\) 13.2545 0.570911
\(540\) −17.8952 2.61584i −0.770087 0.112568i
\(541\) −15.1179 −0.649969 −0.324985 0.945719i \(-0.605359\pi\)
−0.324985 + 0.945719i \(0.605359\pi\)
\(542\) 41.6220i 1.78782i
\(543\) 12.4220i 0.533079i
\(544\) −6.63063 −0.284286
\(545\) −1.86877 + 12.7844i −0.0800492 + 0.547624i
\(546\) 3.93801 0.168531
\(547\) 36.1694i 1.54649i −0.634106 0.773246i \(-0.718632\pi\)
0.634106 0.773246i \(-0.281368\pi\)
\(548\) 5.50186i 0.235028i
\(549\) 7.75702 0.331061
\(550\) −5.18906 + 17.3702i −0.221262 + 0.740667i
\(551\) 0 0
\(552\) 8.56652i 0.364615i
\(553\) 0.338136i 0.0143790i
\(554\) 16.9794 0.721386
\(555\) −2.66121 + 18.2056i −0.112962 + 0.772784i
\(556\) −27.0172 −1.14579
\(557\) 37.0585i 1.57022i 0.619358 + 0.785109i \(0.287393\pi\)
−0.619358 + 0.785109i \(0.712607\pi\)
\(558\) 9.18391i 0.388786i
\(559\) 19.0048 0.803816
\(560\) 5.08685 + 0.743572i 0.214958 + 0.0314217i
\(561\) 2.77123 0.117001
\(562\) 35.8590i 1.51262i
\(563\) 12.9283i 0.544863i −0.962175 0.272432i \(-0.912172\pi\)
0.962175 0.272432i \(-0.0878279\pi\)
\(564\) −5.16014 −0.217281
\(565\) 30.9232 + 4.52021i 1.30095 + 0.190167i
\(566\) −16.1628 −0.679372
\(567\) 2.65694i 0.111581i
\(568\) 13.8842i 0.582569i
\(569\) −18.5114 −0.776038 −0.388019 0.921651i \(-0.626841\pi\)
−0.388019 + 0.921651i \(0.626841\pi\)
\(570\) 0 0
\(571\) 16.2207 0.678816 0.339408 0.940639i \(-0.389773\pi\)
0.339408 + 0.940639i \(0.389773\pi\)
\(572\) 8.57501i 0.358539i
\(573\) 23.7019i 0.990160i
\(574\) 9.26125 0.386557
\(575\) 8.00496 26.7963i 0.333830 1.11748i
\(576\) 2.64498 0.110207
\(577\) 17.7980i 0.740939i 0.928845 + 0.370470i \(0.120803\pi\)
−0.928845 + 0.370470i \(0.879197\pi\)
\(578\) 29.7359i 1.23685i
\(579\) −23.9527 −0.995442
\(580\) 4.71114 32.2293i 0.195619 1.33825i
\(581\) −5.67314 −0.235362
\(582\) 15.8833i 0.658384i
\(583\) 21.0821i 0.873132i
\(584\) −5.23500 −0.216626
\(585\) −5.99085 0.875715i −0.247691 0.0362064i
\(586\) 31.0745 1.28368
\(587\) 35.8593i 1.48007i 0.672567 + 0.740036i \(0.265191\pi\)
−0.672567 + 0.740036i \(0.734809\pi\)
\(588\) 14.0991i 0.581438i
\(589\) 0 0
\(590\) −30.0032 4.38573i −1.23521 0.180558i
\(591\) −14.5773 −0.599628
\(592\) 27.2342i 1.11932i
\(593\) 18.2848i 0.750868i −0.926849 0.375434i \(-0.877494\pi\)
0.926849 0.375434i \(-0.122506\pi\)
\(594\) −20.4852 −0.840518
\(595\) 0.150374 1.02872i 0.00616474 0.0421735i
\(596\) −34.2519 −1.40301
\(597\) 18.4189i 0.753836i
\(598\) 31.7098i 1.29671i
\(599\) 7.85141 0.320800 0.160400 0.987052i \(-0.448722\pi\)
0.160400 + 0.987052i \(0.448722\pi\)
\(600\) 7.33746 + 2.19195i 0.299551 + 0.0894860i
\(601\) 17.3527 0.707833 0.353917 0.935277i \(-0.384850\pi\)
0.353917 + 0.935277i \(0.384850\pi\)
\(602\) 5.49403i 0.223920i
\(603\) 7.80370i 0.317791i
\(604\) 8.45030 0.343838
\(605\) 2.31863 15.8619i 0.0942656 0.644879i
\(606\) −0.695668 −0.0282596
\(607\) 40.7364i 1.65344i 0.562614 + 0.826720i \(0.309796\pi\)
−0.562614 + 0.826720i \(0.690204\pi\)
\(608\) 0 0
\(609\) 7.06820 0.286418
\(610\) 35.9353 + 5.25286i 1.45498 + 0.212682i
\(611\) −7.58512 −0.306861
\(612\) 1.23295i 0.0498392i
\(613\) 27.0535i 1.09268i 0.837564 + 0.546340i \(0.183979\pi\)
−0.837564 + 0.546340i \(0.816021\pi\)
\(614\) −11.8721 −0.479121
\(615\) 33.6849 + 4.92391i 1.35831 + 0.198551i
\(616\) 0.984409 0.0396630
\(617\) 19.8932i 0.800871i −0.916325 0.400436i \(-0.868859\pi\)
0.916325 0.400436i \(-0.131141\pi\)
\(618\) 38.7190i 1.55751i
\(619\) −16.8447 −0.677044 −0.338522 0.940958i \(-0.609927\pi\)
−0.338522 + 0.940958i \(0.609927\pi\)
\(620\) 2.59442 17.7487i 0.104194 0.712804i
\(621\) 31.6017 1.26813
\(622\) 19.6818i 0.789167i
\(623\) 1.02616i 0.0411121i
\(624\) −21.4266 −0.857749
\(625\) 20.9035 + 13.7129i 0.836139 + 0.548517i
\(626\) 8.81123 0.352168
\(627\) 0 0
\(628\) 15.1322i 0.603839i
\(629\) −5.50763 −0.219603
\(630\) −0.253158 + 1.73187i −0.0100860 + 0.0689995i
\(631\) 27.2013 1.08287 0.541433 0.840744i \(-0.317882\pi\)
0.541433 + 0.840744i \(0.317882\pi\)
\(632\) 0.745553i 0.0296565i
\(633\) 8.34254i 0.331586i
\(634\) −0.113410 −0.00450407
\(635\) −20.4289 2.98621i −0.810698 0.118504i
\(636\) 22.4255 0.889231
\(637\) 20.7249i 0.821152i
\(638\) 36.8939i 1.46064i
\(639\) −11.6648 −0.461453
\(640\) −17.8867 2.61460i −0.707036 0.103351i
\(641\) −17.6090 −0.695514 −0.347757 0.937585i \(-0.613057\pi\)
−0.347757 + 0.937585i \(0.613057\pi\)
\(642\) 15.4407i 0.609398i
\(643\) 8.95765i 0.353255i −0.984278 0.176628i \(-0.943481\pi\)
0.984278 0.176628i \(-0.0565188\pi\)
\(644\) 3.82414 0.150692
\(645\) 2.92100 19.9828i 0.115014 0.786822i
\(646\) 0 0
\(647\) 49.1850i 1.93366i −0.255416 0.966831i \(-0.582212\pi\)
0.255416 0.966831i \(-0.417788\pi\)
\(648\) 5.85826i 0.230134i
\(649\) −14.3279 −0.562419
\(650\) −27.1603 8.11371i −1.06531 0.318246i
\(651\) 3.89245 0.152557
\(652\) 26.6393i 1.04327i
\(653\) 11.7035i 0.457993i 0.973427 + 0.228997i \(0.0735445\pi\)
−0.973427 + 0.228997i \(0.926456\pi\)
\(654\) −15.5673 −0.608729
\(655\) 4.50576 30.8243i 0.176055 1.20441i
\(656\) −50.3901 −1.96740
\(657\) 4.39818i 0.171589i
\(658\) 2.19276i 0.0854826i
\(659\) −34.7573 −1.35395 −0.676976 0.736005i \(-0.736710\pi\)
−0.676976 + 0.736005i \(0.736710\pi\)
\(660\) −9.01630 1.31796i −0.350959 0.0513016i
\(661\) −17.9064 −0.696477 −0.348239 0.937406i \(-0.613220\pi\)
−0.348239 + 0.937406i \(0.613220\pi\)
\(662\) 32.6153i 1.26763i
\(663\) 4.33314i 0.168285i
\(664\) 12.5087 0.485431
\(665\) 0 0
\(666\) 9.27219 0.359290
\(667\) 56.9148i 2.20375i
\(668\) 3.97578i 0.153828i
\(669\) −18.6858 −0.722435
\(670\) 5.28447 36.1516i 0.204157 1.39666i
\(671\) 17.1607 0.662483
\(672\) 4.73117i 0.182509i
\(673\) 10.9828i 0.423355i −0.977340 0.211677i \(-0.932107\pi\)
0.977340 0.211677i \(-0.0678926\pi\)
\(674\) −12.7980 −0.492961
\(675\) −8.08605 + 27.0677i −0.311232 + 1.04184i
\(676\) −5.20180 −0.200069
\(677\) 4.77520i 0.183526i 0.995781 + 0.0917630i \(0.0292502\pi\)
−0.995781 + 0.0917630i \(0.970750\pi\)
\(678\) 37.6544i 1.44611i
\(679\) 2.81567 0.108056
\(680\) −0.331559 + 2.26822i −0.0127147 + 0.0869824i
\(681\) 22.6607 0.868359
\(682\) 20.3175i 0.777995i
\(683\) 46.0853i 1.76341i 0.471805 + 0.881703i \(0.343603\pi\)
−0.471805 + 0.881703i \(0.656397\pi\)
\(684\) 0 0
\(685\) −8.50364 1.24302i −0.324907 0.0474935i
\(686\) 12.1844 0.465203
\(687\) 5.49660i 0.209708i
\(688\) 29.8928i 1.13965i
\(689\) 32.9643 1.25584
\(690\) 33.3417 + 4.87373i 1.26930 + 0.185540i
\(691\) 15.2699 0.580893 0.290447 0.956891i \(-0.406196\pi\)
0.290447 + 0.956891i \(0.406196\pi\)
\(692\) 12.7703i 0.485453i
\(693\) 0.827050i 0.0314170i
\(694\) 13.5705 0.515130
\(695\) −6.10394 + 41.7576i −0.231536 + 1.58396i
\(696\) −15.5846 −0.590733
\(697\) 10.1905i 0.385993i
\(698\) 4.00362i 0.151539i
\(699\) 16.1067 0.609210
\(700\) −0.978496 + 3.27548i −0.0369837 + 0.123801i
\(701\) −16.6852 −0.630191 −0.315096 0.949060i \(-0.602037\pi\)
−0.315096 + 0.949060i \(0.602037\pi\)
\(702\) 32.0310i 1.20893i
\(703\) 0 0
\(704\) 5.85144 0.220535
\(705\) −1.16582 + 7.97547i −0.0439073 + 0.300374i
\(706\) 30.7545 1.15746
\(707\) 0.123323i 0.00463803i
\(708\) 15.2409i 0.572789i
\(709\) −1.95870 −0.0735604 −0.0367802 0.999323i \(-0.511710\pi\)
−0.0367802 + 0.999323i \(0.511710\pi\)
\(710\) −54.0386 7.89912i −2.02803 0.296449i
\(711\) 0.626375 0.0234909
\(712\) 2.26257i 0.0847933i
\(713\) 31.3429i 1.17380i
\(714\) 1.25265 0.0468794
\(715\) −13.2535 1.93733i −0.495652 0.0724522i
\(716\) 21.8517 0.816637
\(717\) 15.4887i 0.578438i
\(718\) 31.6452i 1.18099i
\(719\) 23.0165 0.858370 0.429185 0.903217i \(-0.358801\pi\)
0.429185 + 0.903217i \(0.358801\pi\)
\(720\) 1.37742 9.42306i 0.0513334 0.351177i
\(721\) −6.86382 −0.255622
\(722\) 0 0
\(723\) 7.29046i 0.271135i
\(724\) 12.2267 0.454400
\(725\) −48.7490 14.5630i −1.81049 0.540856i
\(726\) 19.3147 0.716837
\(727\) 10.3883i 0.385279i −0.981270 0.192640i \(-0.938295\pi\)
0.981270 0.192640i \(-0.0617048\pi\)
\(728\) 1.53924i 0.0570479i
\(729\) −29.5736 −1.09532
\(730\) 2.97834 20.3751i 0.110233 0.754116i
\(731\) 6.04528 0.223593
\(732\) 18.2543i 0.674698i
\(733\) 40.7900i 1.50661i −0.657670 0.753306i \(-0.728458\pi\)
0.657670 0.753306i \(-0.271542\pi\)
\(734\) 36.2395 1.33762
\(735\) 21.7915 + 3.18538i 0.803791 + 0.117495i
\(736\) −38.0965 −1.40425
\(737\) 17.2640i 0.635929i
\(738\) 17.1559i 0.631517i
\(739\) 7.92965 0.291697 0.145848 0.989307i \(-0.453409\pi\)
0.145848 + 0.989307i \(0.453409\pi\)
\(740\) 17.9193 + 2.61936i 0.658726 + 0.0962896i
\(741\) 0 0
\(742\) 9.52956i 0.349841i
\(743\) 7.27911i 0.267045i 0.991046 + 0.133522i \(0.0426288\pi\)
−0.991046 + 0.133522i \(0.957371\pi\)
\(744\) −8.58244 −0.314648
\(745\) −7.73845 + 52.9395i −0.283515 + 1.93955i
\(746\) 12.2205 0.447426
\(747\) 10.5091i 0.384509i
\(748\) 2.72765i 0.0997327i
\(749\) −2.73722 −0.100016
\(750\) −12.7057 + 27.3110i −0.463948 + 0.997255i
\(751\) −37.8815 −1.38232 −0.691158 0.722704i \(-0.742899\pi\)
−0.691158 + 0.722704i \(0.742899\pi\)
\(752\) 11.9307i 0.435068i
\(753\) 38.0647i 1.38715i
\(754\) 57.6879 2.10087
\(755\) 1.90916 13.0607i 0.0694814 0.475329i
\(756\) −3.86287 −0.140491
\(757\) 51.1527i 1.85917i 0.368602 + 0.929587i \(0.379837\pi\)
−0.368602 + 0.929587i \(0.620163\pi\)
\(758\) 40.1189i 1.45718i
\(759\) 15.9222 0.577938
\(760\) 0 0
\(761\) −10.8749 −0.394213 −0.197107 0.980382i \(-0.563155\pi\)
−0.197107 + 0.980382i \(0.563155\pi\)
\(762\) 24.8759i 0.901158i
\(763\) 2.75965i 0.0999061i
\(764\) 23.3291 0.844019
\(765\) −1.90565 0.278559i −0.0688988 0.0100713i
\(766\) 45.0539 1.62786
\(767\) 22.4033i 0.808938i
\(768\) 30.4764i 1.09972i
\(769\) 18.8020 0.678016 0.339008 0.940783i \(-0.389909\pi\)
0.339008 + 0.940783i \(0.389909\pi\)
\(770\) −0.560057 + 3.83140i −0.0201831 + 0.138074i
\(771\) −32.5820 −1.17341
\(772\) 23.5761i 0.848521i
\(773\) 24.3856i 0.877090i 0.898709 + 0.438545i \(0.144506\pi\)
−0.898709 + 0.438545i \(0.855494\pi\)
\(774\) −10.1773 −0.365817
\(775\) −26.8461 8.01984i −0.964339 0.288081i
\(776\) −6.20825 −0.222863
\(777\) 3.92987i 0.140983i
\(778\) 29.3105i 1.05083i
\(779\) 0 0
\(780\) 2.06079 14.0980i 0.0737880 0.504791i
\(781\) −25.8059 −0.923408
\(782\) 10.0867i 0.360698i
\(783\) 57.4913i 2.05457i
\(784\) −32.5985 −1.16423
\(785\) −23.3882 3.41878i −0.834760 0.122021i
\(786\) 37.5341 1.33880
\(787\) 9.17617i 0.327095i 0.986535 + 0.163547i \(0.0522937\pi\)
−0.986535