Properties

Label 460.2.m.a.261.1
Level $460$
Weight $2$
Character 460.261
Analytic conductor $3.673$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 261.1
Character \(\chi\) \(=\) 460.261
Dual form 460.2.m.a.141.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +O(q^{10})\) \(q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +(-0.824724 - 5.73608i) q^{11} +(-3.15165 + 2.02545i) q^{13} +(-1.08673 + 2.37960i) q^{15} +(-1.70862 + 0.501697i) q^{17} +(3.27048 + 0.960300i) q^{19} +(0.0241006 - 0.167623i) q^{21} +(-4.09742 + 2.49222i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(2.11716 + 0.621655i) q^{27} +(-1.26492 + 0.371413i) q^{29} +(-1.01893 + 2.23114i) q^{31} +(-12.7533 + 8.19607i) q^{33} +(-0.00921274 - 0.0640760i) q^{35} +(-1.23564 + 1.42600i) q^{37} +(8.24474 + 5.29857i) q^{39} +(-0.0704270 - 0.0812771i) q^{41} +(-0.298488 - 0.653598i) q^{43} +3.84348 q^{45} +0.878185 q^{47} +(-2.90616 - 6.36361i) q^{49} +(3.05065 + 3.52064i) q^{51} +(-7.32895 - 4.71003i) q^{53} +(-3.79496 + 4.37962i) q^{55} +(-1.26899 - 8.82603i) q^{57} +(12.8806 - 8.27784i) q^{59} +(0.555050 - 1.21539i) q^{61} +(-0.238729 + 0.0700971i) q^{63} +(3.59462 + 1.05548i) q^{65} +(1.53543 - 10.6792i) q^{67} +(10.3833 + 7.04185i) q^{69} +(1.57890 - 10.9815i) q^{71} +(-4.82197 - 1.41586i) q^{73} +(2.51004 - 0.737014i) q^{75} +(0.155840 - 0.341242i) q^{77} +(-6.43071 + 4.13277i) q^{79} +(0.819465 + 5.69950i) q^{81} +(8.70437 - 10.0454i) q^{83} +(1.49807 + 0.962750i) q^{85} +(2.25843 + 2.60637i) q^{87} +(0.981628 + 2.14946i) q^{89} -0.242522 q^{91} +6.41651 q^{93} +(-1.41596 - 3.10053i) q^{95} +(4.21722 + 4.86694i) q^{97} +(18.7374 + 12.0418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 3q^{5} + q^{7} + 21q^{9} + O(q^{10}) \) \( 30q - 3q^{5} + q^{7} + 21q^{9} + 2q^{13} + 10q^{17} + 3q^{19} + 39q^{21} + 10q^{23} - 3q^{25} + 21q^{27} + 14q^{29} - 2q^{31} - 50q^{33} - 10q^{35} + 9q^{37} + 38q^{39} - 3q^{41} - 50q^{43} + 10q^{45} - 6q^{47} - 36q^{49} - 36q^{51} - 5q^{53} - 11q^{55} + 23q^{57} + 14q^{59} - 16q^{61} - 52q^{63} + 2q^{65} + 27q^{67} + 42q^{69} + 19q^{71} + 24q^{73} - 10q^{77} - 22q^{79} + 35q^{81} + 36q^{83} + 10q^{85} - 3q^{87} - 28q^{89} - 98q^{91} - 60q^{93} - 19q^{95} - 2q^{97} - 14q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.08673 2.37960i −0.627422 1.37386i −0.909996 0.414618i \(-0.863915\pi\)
0.282573 0.959246i \(-0.408812\pi\)
\(4\) 0 0
\(5\) −0.654861 0.755750i −0.292863 0.337981i
\(6\) 0 0
\(7\) 0.0544585 + 0.0349983i 0.0205834 + 0.0132281i 0.550892 0.834577i \(-0.314288\pi\)
−0.530309 + 0.847805i \(0.677924\pi\)
\(8\) 0 0
\(9\) −2.51694 + 2.90471i −0.838981 + 0.968236i
\(10\) 0 0
\(11\) −0.824724 5.73608i −0.248664 1.72949i −0.605953 0.795500i \(-0.707208\pi\)
0.357289 0.933994i \(-0.383701\pi\)
\(12\) 0 0
\(13\) −3.15165 + 2.02545i −0.874112 + 0.561758i −0.899008 0.437933i \(-0.855711\pi\)
0.0248961 + 0.999690i \(0.492075\pi\)
\(14\) 0 0
\(15\) −1.08673 + 2.37960i −0.280592 + 0.614410i
\(16\) 0 0
\(17\) −1.70862 + 0.501697i −0.414402 + 0.121679i −0.482286 0.876014i \(-0.660193\pi\)
0.0678839 + 0.997693i \(0.478375\pi\)
\(18\) 0 0
\(19\) 3.27048 + 0.960300i 0.750300 + 0.220308i 0.634456 0.772959i \(-0.281224\pi\)
0.115845 + 0.993267i \(0.463043\pi\)
\(20\) 0 0
\(21\) 0.0241006 0.167623i 0.00525918 0.0365784i
\(22\) 0 0
\(23\) −4.09742 + 2.49222i −0.854371 + 0.519664i
\(24\) 0 0
\(25\) −0.142315 + 0.989821i −0.0284630 + 0.197964i
\(26\) 0 0
\(27\) 2.11716 + 0.621655i 0.407448 + 0.119637i
\(28\) 0 0
\(29\) −1.26492 + 0.371413i −0.234889 + 0.0689696i −0.397059 0.917793i \(-0.629969\pi\)
0.162170 + 0.986763i \(0.448151\pi\)
\(30\) 0 0
\(31\) −1.01893 + 2.23114i −0.183004 + 0.400724i −0.978793 0.204850i \(-0.934329\pi\)
0.795789 + 0.605574i \(0.207057\pi\)
\(32\) 0 0
\(33\) −12.7533 + 8.19607i −2.22007 + 1.42675i
\(34\) 0 0
\(35\) −0.00921274 0.0640760i −0.00155724 0.0108308i
\(36\) 0 0
\(37\) −1.23564 + 1.42600i −0.203138 + 0.234433i −0.848173 0.529719i \(-0.822297\pi\)
0.645035 + 0.764153i \(0.276843\pi\)
\(38\) 0 0
\(39\) 8.24474 + 5.29857i 1.32022 + 0.848451i
\(40\) 0 0
\(41\) −0.0704270 0.0812771i −0.0109988 0.0126933i 0.750223 0.661184i \(-0.229946\pi\)
−0.761222 + 0.648491i \(0.775400\pi\)
\(42\) 0 0
\(43\) −0.298488 0.653598i −0.0455190 0.0996728i 0.885506 0.464627i \(-0.153812\pi\)
−0.931025 + 0.364955i \(0.881084\pi\)
\(44\) 0 0
\(45\) 3.84348 0.572952
\(46\) 0 0
\(47\) 0.878185 0.128096 0.0640482 0.997947i \(-0.479599\pi\)
0.0640482 + 0.997947i \(0.479599\pi\)
\(48\) 0 0
\(49\) −2.90616 6.36361i −0.415166 0.909087i
\(50\) 0 0
\(51\) 3.05065 + 3.52064i 0.427176 + 0.492988i
\(52\) 0 0
\(53\) −7.32895 4.71003i −1.00671 0.646972i −0.0701691 0.997535i \(-0.522354\pi\)
−0.936539 + 0.350563i \(0.885990\pi\)
\(54\) 0 0
\(55\) −3.79496 + 4.37962i −0.511713 + 0.590548i
\(56\) 0 0
\(57\) −1.26899 8.82603i −0.168082 1.16904i
\(58\) 0 0
\(59\) 12.8806 8.27784i 1.67691 1.07768i 0.794386 0.607414i \(-0.207793\pi\)
0.882523 0.470270i \(-0.155843\pi\)
\(60\) 0 0
\(61\) 0.555050 1.21539i 0.0710668 0.155615i −0.870765 0.491700i \(-0.836376\pi\)
0.941832 + 0.336085i \(0.109103\pi\)
\(62\) 0 0
\(63\) −0.238729 + 0.0700971i −0.0300770 + 0.00883141i
\(64\) 0 0
\(65\) 3.59462 + 1.05548i 0.445858 + 0.130916i
\(66\) 0 0
\(67\) 1.53543 10.6792i 0.187583 1.30467i −0.650660 0.759369i \(-0.725508\pi\)
0.838243 0.545297i \(-0.183583\pi\)
\(68\) 0 0
\(69\) 10.3833 + 7.04185i 1.25000 + 0.847739i
\(70\) 0 0
\(71\) 1.57890 10.9815i 0.187381 1.30326i −0.651374 0.758757i \(-0.725807\pi\)
0.838756 0.544508i \(-0.183284\pi\)
\(72\) 0 0
\(73\) −4.82197 1.41586i −0.564369 0.165714i −0.0129114 0.999917i \(-0.504110\pi\)
−0.551458 + 0.834203i \(0.685928\pi\)
\(74\) 0 0
\(75\) 2.51004 0.737014i 0.289834 0.0851030i
\(76\) 0 0
\(77\) 0.155840 0.341242i 0.0177596 0.0388882i
\(78\) 0 0
\(79\) −6.43071 + 4.13277i −0.723512 + 0.464973i −0.849857 0.527014i \(-0.823312\pi\)
0.126345 + 0.991986i \(0.459675\pi\)
\(80\) 0 0
\(81\) 0.819465 + 5.69950i 0.0910516 + 0.633278i
\(82\) 0 0
\(83\) 8.70437 10.0454i 0.955428 1.10262i −0.0392122 0.999231i \(-0.512485\pi\)
0.994641 0.103392i \(-0.0329697\pi\)
\(84\) 0 0
\(85\) 1.49807 + 0.962750i 0.162488 + 0.104425i
\(86\) 0 0
\(87\) 2.25843 + 2.60637i 0.242129 + 0.279432i
\(88\) 0 0
\(89\) 0.981628 + 2.14946i 0.104052 + 0.227843i 0.954496 0.298223i \(-0.0963939\pi\)
−0.850444 + 0.526066i \(0.823667\pi\)
\(90\) 0 0
\(91\) −0.242522 −0.0254232
\(92\) 0 0
\(93\) 6.41651 0.665361
\(94\) 0 0
\(95\) −1.41596 3.10053i −0.145275 0.318108i
\(96\) 0 0
\(97\) 4.21722 + 4.86694i 0.428194 + 0.494163i 0.928316 0.371793i \(-0.121257\pi\)
−0.500122 + 0.865955i \(0.666711\pi\)
\(98\) 0 0
\(99\) 18.7374 + 12.0418i 1.88318 + 1.21025i
\(100\) 0 0
\(101\) 7.44091 8.58727i 0.740399 0.854466i −0.253202 0.967413i \(-0.581484\pi\)
0.993601 + 0.112948i \(0.0360293\pi\)
\(102\) 0 0
\(103\) −2.49247 17.3355i −0.245591 1.70812i −0.623123 0.782123i \(-0.714137\pi\)
0.377533 0.925996i \(-0.376773\pi\)
\(104\) 0 0
\(105\) −0.142464 + 0.0915558i −0.0139030 + 0.00893493i
\(106\) 0 0
\(107\) −5.10088 + 11.1694i −0.493121 + 1.07978i 0.485523 + 0.874224i \(0.338629\pi\)
−0.978644 + 0.205561i \(0.934098\pi\)
\(108\) 0 0
\(109\) −10.4148 + 3.05807i −0.997558 + 0.292910i −0.739454 0.673207i \(-0.764916\pi\)
−0.258105 + 0.966117i \(0.583098\pi\)
\(110\) 0 0
\(111\) 4.73612 + 1.39065i 0.449533 + 0.131995i
\(112\) 0 0
\(113\) 2.22817 15.4973i 0.209609 1.45786i −0.564828 0.825209i \(-0.691057\pi\)
0.774437 0.632652i \(-0.218033\pi\)
\(114\) 0 0
\(115\) 4.56673 + 1.46456i 0.425850 + 0.136571i
\(116\) 0 0
\(117\) 2.04921 14.2526i 0.189449 1.31765i
\(118\) 0 0
\(119\) −0.110608 0.0324773i −0.0101394 0.00297719i
\(120\) 0 0
\(121\) −21.6681 + 6.36232i −1.96982 + 0.578392i
\(122\) 0 0
\(123\) −0.116872 + 0.255914i −0.0105380 + 0.0230750i
\(124\) 0 0
\(125\) 0.841254 0.540641i 0.0752440 0.0483564i
\(126\) 0 0
\(127\) 1.96308 + 13.6535i 0.174195 + 1.21155i 0.869901 + 0.493226i \(0.164183\pi\)
−0.695706 + 0.718327i \(0.744908\pi\)
\(128\) 0 0
\(129\) −1.23093 + 1.42057i −0.108377 + 0.125074i
\(130\) 0 0
\(131\) −15.9747 10.2663i −1.39571 0.896971i −0.395941 0.918276i \(-0.629582\pi\)
−0.999773 + 0.0213045i \(0.993218\pi\)
\(132\) 0 0
\(133\) 0.144497 + 0.166758i 0.0125294 + 0.0144598i
\(134\) 0 0
\(135\) −0.916631 2.00714i −0.0788910 0.172747i
\(136\) 0 0
\(137\) 16.1235 1.37752 0.688760 0.724990i \(-0.258156\pi\)
0.688760 + 0.724990i \(0.258156\pi\)
\(138\) 0 0
\(139\) 19.0178 1.61307 0.806536 0.591184i \(-0.201339\pi\)
0.806536 + 0.591184i \(0.201339\pi\)
\(140\) 0 0
\(141\) −0.954348 2.08973i −0.0803706 0.175987i
\(142\) 0 0
\(143\) 14.2174 + 16.4077i 1.18892 + 1.37208i
\(144\) 0 0
\(145\) 1.10904 + 0.712736i 0.0921007 + 0.0591895i
\(146\) 0 0
\(147\) −11.9846 + 13.8310i −0.988477 + 1.14076i
\(148\) 0 0
\(149\) 1.05958 + 7.36956i 0.0868045 + 0.603738i 0.986069 + 0.166334i \(0.0531930\pi\)
−0.899265 + 0.437404i \(0.855898\pi\)
\(150\) 0 0
\(151\) 1.44428 0.928183i 0.117534 0.0755345i −0.480553 0.876966i \(-0.659564\pi\)
0.598087 + 0.801431i \(0.295928\pi\)
\(152\) 0 0
\(153\) 2.84323 6.22580i 0.229861 0.503326i
\(154\) 0 0
\(155\) 2.35343 0.691031i 0.189032 0.0555049i
\(156\) 0 0
\(157\) 11.8120 + 3.46830i 0.942697 + 0.276801i 0.716743 0.697337i \(-0.245632\pi\)
0.225954 + 0.974138i \(0.427450\pi\)
\(158\) 0 0
\(159\) −3.24342 + 22.5585i −0.257220 + 1.78900i
\(160\) 0 0
\(161\) −0.310363 0.00768017i −0.0244600 0.000605283i
\(162\) 0 0
\(163\) −1.67265 + 11.6336i −0.131012 + 0.911211i 0.813226 + 0.581948i \(0.197709\pi\)
−0.944238 + 0.329263i \(0.893200\pi\)
\(164\) 0 0
\(165\) 14.5458 + 4.27104i 1.13239 + 0.332500i
\(166\) 0 0
\(167\) −21.1058 + 6.19723i −1.63322 + 0.479556i −0.964527 0.263984i \(-0.914963\pi\)
−0.668691 + 0.743541i \(0.733145\pi\)
\(168\) 0 0
\(169\) 0.430103 0.941795i 0.0330849 0.0724458i
\(170\) 0 0
\(171\) −11.0210 + 7.08277i −0.842798 + 0.541633i
\(172\) 0 0
\(173\) −1.06525 7.40900i −0.0809897 0.563296i −0.989400 0.145216i \(-0.953612\pi\)
0.908410 0.418080i \(-0.137297\pi\)
\(174\) 0 0
\(175\) −0.0423924 + 0.0489234i −0.00320456 + 0.00369826i
\(176\) 0 0
\(177\) −33.6956 21.6549i −2.53272 1.62768i
\(178\) 0 0
\(179\) −9.56587 11.0396i −0.714987 0.825139i 0.275708 0.961242i \(-0.411088\pi\)
−0.990695 + 0.136102i \(0.956542\pi\)
\(180\) 0 0
\(181\) 4.39220 + 9.61758i 0.326470 + 0.714869i 0.999698 0.0245653i \(-0.00782017\pi\)
−0.673228 + 0.739435i \(0.735093\pi\)
\(182\) 0 0
\(183\) −3.49533 −0.258382
\(184\) 0 0
\(185\) 1.88687 0.138726
\(186\) 0 0
\(187\) 4.28692 + 9.38705i 0.313491 + 0.686449i
\(188\) 0 0
\(189\) 0.0935405 + 0.107952i 0.00680407 + 0.00785232i
\(190\) 0 0
\(191\) 14.7857 + 9.50217i 1.06985 + 0.687553i 0.952192 0.305501i \(-0.0988239\pi\)
0.117661 + 0.993054i \(0.462460\pi\)
\(192\) 0 0
\(193\) 8.41940 9.71650i 0.606042 0.699409i −0.366952 0.930240i \(-0.619599\pi\)
0.972994 + 0.230831i \(0.0741443\pi\)
\(194\) 0 0
\(195\) −1.39476 9.70079i −0.0998810 0.694688i
\(196\) 0 0
\(197\) −2.75418 + 1.77001i −0.196228 + 0.126108i −0.635065 0.772459i \(-0.719027\pi\)
0.438838 + 0.898566i \(0.355390\pi\)
\(198\) 0 0
\(199\) 9.71532 21.2736i 0.688701 1.50804i −0.164453 0.986385i \(-0.552586\pi\)
0.853154 0.521660i \(-0.174687\pi\)
\(200\) 0 0
\(201\) −27.0807 + 7.95162i −1.91013 + 0.560864i
\(202\) 0 0
\(203\) −0.0818843 0.0240434i −0.00574715 0.00168752i
\(204\) 0 0
\(205\) −0.0153053 + 0.106450i −0.00106897 + 0.00743482i
\(206\) 0 0
\(207\) 3.07379 18.1746i 0.213643 1.26322i
\(208\) 0 0
\(209\) 2.81112 19.5517i 0.194449 1.35242i
\(210\) 0 0
\(211\) −25.9891 7.63108i −1.78916 0.525345i −0.792716 0.609591i \(-0.791334\pi\)
−0.996445 + 0.0842454i \(0.973152\pi\)
\(212\) 0 0
\(213\) −27.8474 + 8.17674i −1.90807 + 0.560261i
\(214\) 0 0
\(215\) −0.298488 + 0.653598i −0.0203567 + 0.0445750i
\(216\) 0 0
\(217\) −0.133575 + 0.0858436i −0.00906768 + 0.00582744i
\(218\) 0 0
\(219\) 1.87099 + 13.0130i 0.126430 + 0.879338i
\(220\) 0 0
\(221\) 4.36883 5.04190i 0.293880 0.339155i
\(222\) 0 0
\(223\) −4.10368 2.63728i −0.274803 0.176605i 0.395979 0.918259i \(-0.370405\pi\)
−0.670782 + 0.741654i \(0.734042\pi\)
\(224\) 0 0
\(225\) −2.51694 2.90471i −0.167796 0.193647i
\(226\) 0 0
\(227\) −6.10354 13.3649i −0.405106 0.887058i −0.996727 0.0808422i \(-0.974239\pi\)
0.591621 0.806216i \(-0.298488\pi\)
\(228\) 0 0
\(229\) 11.1857 0.739171 0.369585 0.929197i \(-0.379500\pi\)
0.369585 + 0.929197i \(0.379500\pi\)
\(230\) 0 0
\(231\) −0.981377 −0.0645698
\(232\) 0 0
\(233\) −8.86878 19.4199i −0.581013 1.27224i −0.940722 0.339177i \(-0.889851\pi\)
0.359709 0.933065i \(-0.382876\pi\)
\(234\) 0 0
\(235\) −0.575089 0.663688i −0.0375147 0.0432942i
\(236\) 0 0
\(237\) 16.8228 + 10.8113i 1.09276 + 0.702272i
\(238\) 0 0
\(239\) −6.83331 + 7.88606i −0.442010 + 0.510107i −0.932416 0.361387i \(-0.882303\pi\)
0.490406 + 0.871494i \(0.336849\pi\)
\(240\) 0 0
\(241\) 3.82894 + 26.6308i 0.246644 + 1.71544i 0.617346 + 0.786692i \(0.288208\pi\)
−0.370702 + 0.928752i \(0.620883\pi\)
\(242\) 0 0
\(243\) 18.2408 11.7226i 1.17015 0.752008i
\(244\) 0 0
\(245\) −2.90616 + 6.36361i −0.185668 + 0.406556i
\(246\) 0 0
\(247\) −12.2525 + 3.59765i −0.779606 + 0.228913i
\(248\) 0 0
\(249\) −33.3633 9.79634i −2.11431 0.620818i
\(250\) 0 0
\(251\) 0.352955 2.45486i 0.0222783 0.154949i −0.975646 0.219353i \(-0.929605\pi\)
0.997924 + 0.0644037i \(0.0205145\pi\)
\(252\) 0 0
\(253\) 17.6748 + 21.4477i 1.11121 + 1.34841i
\(254\) 0 0
\(255\) 0.662969 4.61105i 0.0415167 0.288755i
\(256\) 0 0
\(257\) 14.8676 + 4.36554i 0.927418 + 0.272315i 0.710356 0.703843i \(-0.248534\pi\)
0.217063 + 0.976158i \(0.430352\pi\)
\(258\) 0 0
\(259\) −0.117199 + 0.0344127i −0.00728238 + 0.00213830i
\(260\) 0 0
\(261\) 2.10488 4.60904i 0.130289 0.285292i
\(262\) 0 0
\(263\) −9.43624 + 6.06431i −0.581864 + 0.373941i −0.798213 0.602375i \(-0.794221\pi\)
0.216350 + 0.976316i \(0.430585\pi\)
\(264\) 0 0
\(265\) 1.23984 + 8.62326i 0.0761626 + 0.529723i
\(266\) 0 0
\(267\) 4.04811 4.67177i 0.247740 0.285907i
\(268\) 0 0
\(269\) 10.2596 + 6.59344i 0.625539 + 0.402009i 0.814655 0.579945i \(-0.196926\pi\)
−0.189117 + 0.981955i \(0.560562\pi\)
\(270\) 0 0
\(271\) −8.93878 10.3159i −0.542992 0.626646i 0.416244 0.909253i \(-0.363346\pi\)
−0.959236 + 0.282607i \(0.908801\pi\)
\(272\) 0 0
\(273\) 0.263555 + 0.577105i 0.0159511 + 0.0349280i
\(274\) 0 0
\(275\) 5.79507 0.349456
\(276\) 0 0
\(277\) −17.5457 −1.05422 −0.527109 0.849797i \(-0.676724\pi\)
−0.527109 + 0.849797i \(0.676724\pi\)
\(278\) 0 0
\(279\) −3.91622 8.57532i −0.234458 0.513391i
\(280\) 0 0
\(281\) 15.3782 + 17.7474i 0.917388 + 1.05872i 0.998077 + 0.0619825i \(0.0197423\pi\)
−0.0806896 + 0.996739i \(0.525712\pi\)
\(282\) 0 0
\(283\) −3.55779 2.28646i −0.211489 0.135916i 0.430608 0.902539i \(-0.358299\pi\)
−0.642097 + 0.766623i \(0.721935\pi\)
\(284\) 0 0
\(285\) −5.83925 + 6.73886i −0.345888 + 0.399176i
\(286\) 0 0
\(287\) −0.000990784 0.00689106i −5.84842e−5 0.000406766i
\(288\) 0 0
\(289\) −11.6336 + 7.47647i −0.684330 + 0.439792i
\(290\) 0 0
\(291\) 6.99839 15.3243i 0.410253 0.898329i
\(292\) 0 0
\(293\) 24.8945 7.30969i 1.45435 0.427036i 0.543374 0.839491i \(-0.317147\pi\)
0.910978 + 0.412454i \(0.135328\pi\)
\(294\) 0 0
\(295\) −14.6910 4.31366i −0.855341 0.251151i
\(296\) 0 0
\(297\) 1.81979 12.6569i 0.105595 0.734428i
\(298\) 0 0
\(299\) 7.86578 16.1537i 0.454890 0.934194i
\(300\) 0 0
\(301\) 0.00661963 0.0460406i 0.000381549 0.00265373i
\(302\) 0 0
\(303\) −28.5205 8.37438i −1.63846 0.481096i
\(304\) 0 0
\(305\) −1.28201 + 0.376432i −0.0734077 + 0.0215544i
\(306\) 0 0
\(307\) −0.602560 + 1.31942i −0.0343899 + 0.0753034i −0.926047 0.377407i \(-0.876816\pi\)
0.891657 + 0.452711i \(0.149543\pi\)
\(308\) 0 0
\(309\) −38.5430 + 24.7701i −2.19263 + 1.40912i
\(310\) 0 0
\(311\) 0.354101 + 2.46282i 0.0200792 + 0.139654i 0.997395 0.0721333i \(-0.0229807\pi\)
−0.977316 + 0.211787i \(0.932072\pi\)
\(312\) 0 0
\(313\) −12.6641 + 14.6151i −0.715816 + 0.826095i −0.990797 0.135354i \(-0.956783\pi\)
0.274982 + 0.961450i \(0.411328\pi\)
\(314\) 0 0
\(315\) 0.209310 + 0.134515i 0.0117933 + 0.00757908i
\(316\) 0 0
\(317\) −5.88940 6.79673i −0.330782 0.381743i 0.565858 0.824502i \(-0.308545\pi\)
−0.896640 + 0.442760i \(0.853999\pi\)
\(318\) 0 0
\(319\) 3.17366 + 6.94935i 0.177691 + 0.389089i
\(320\) 0 0
\(321\) 32.1219 1.79287
\(322\) 0 0
\(323\) −6.06981 −0.337733
\(324\) 0 0
\(325\) −1.55630 3.40783i −0.0863281 0.189032i
\(326\) 0 0
\(327\) 18.5950 + 21.4598i 1.02831 + 1.18673i
\(328\) 0 0
\(329\) 0.0478246 + 0.0307350i 0.00263666 + 0.00169448i
\(330\) 0 0
\(331\) 3.01753 3.48241i 0.165858 0.191411i −0.666736 0.745294i \(-0.732309\pi\)
0.832594 + 0.553883i \(0.186855\pi\)
\(332\) 0 0
\(333\) −1.03209 7.17834i −0.0565581 0.393370i
\(334\) 0 0
\(335\) −9.07626 + 5.83296i −0.495889 + 0.318689i
\(336\) 0 0
\(337\) −6.92004 + 15.1528i −0.376958 + 0.825424i 0.622137 + 0.782908i \(0.286265\pi\)
−0.999096 + 0.0425157i \(0.986463\pi\)
\(338\) 0 0
\(339\) −39.2987 + 11.5391i −2.13441 + 0.626720i
\(340\) 0 0
\(341\) 13.6383 + 4.00457i 0.738556 + 0.216860i
\(342\) 0 0
\(343\) 0.128940 0.896796i 0.00696209 0.0484224i
\(344\) 0 0
\(345\) −1.47772 12.4586i −0.0795577 0.670748i
\(346\) 0 0
\(347\) −1.53348 + 10.6656i −0.0823216 + 0.572559i 0.906357 + 0.422512i \(0.138852\pi\)
−0.988679 + 0.150047i \(0.952057\pi\)
\(348\) 0 0
\(349\) 31.9663 + 9.38615i 1.71112 + 0.502429i 0.983090 0.183121i \(-0.0586202\pi\)
0.728025 + 0.685550i \(0.240438\pi\)
\(350\) 0 0
\(351\) −7.93169 + 2.32895i −0.423362 + 0.124310i
\(352\) 0 0
\(353\) −2.22376 + 4.86936i −0.118359 + 0.259170i −0.959534 0.281593i \(-0.909137\pi\)
0.841175 + 0.540763i \(0.181864\pi\)
\(354\) 0 0
\(355\) −9.33323 + 5.99810i −0.495356 + 0.318346i
\(356\) 0 0
\(357\) 0.0429173 + 0.298496i 0.00227142 + 0.0157981i
\(358\) 0 0
\(359\) 17.4800 20.1730i 0.922561 1.06469i −0.0751571 0.997172i \(-0.523946\pi\)
0.997718 0.0675202i \(-0.0215087\pi\)
\(360\) 0 0
\(361\) −6.20994 3.99088i −0.326839 0.210047i
\(362\) 0 0
\(363\) 38.6871 + 44.6472i 2.03054 + 2.34337i
\(364\) 0 0
\(365\) 2.08768 + 4.57139i 0.109274 + 0.239278i
\(366\) 0 0
\(367\) 36.8508 1.92360 0.961799 0.273758i \(-0.0882666\pi\)
0.961799 + 0.273758i \(0.0882666\pi\)
\(368\) 0 0
\(369\) 0.413347 0.0215180
\(370\) 0 0
\(371\) −0.234280 0.513002i −0.0121632 0.0266337i
\(372\) 0 0
\(373\) 7.19723 + 8.30605i 0.372659 + 0.430071i 0.910841 0.412757i \(-0.135434\pi\)
−0.538182 + 0.842828i \(0.680889\pi\)
\(374\) 0 0
\(375\) −2.20072 1.41432i −0.113645 0.0730351i
\(376\) 0 0
\(377\) 3.23430 3.73258i 0.166575 0.192238i
\(378\) 0 0
\(379\) −1.98479 13.8045i −0.101952 0.709092i −0.975121 0.221674i \(-0.928848\pi\)
0.873169 0.487418i \(-0.162061\pi\)
\(380\) 0 0
\(381\) 30.3566 19.5090i 1.55521 0.999476i
\(382\) 0 0
\(383\) −4.53694 + 9.93451i −0.231827 + 0.507630i −0.989417 0.145101i \(-0.953649\pi\)
0.757590 + 0.652731i \(0.226377\pi\)
\(384\) 0 0
\(385\) −0.359947 + 0.105690i −0.0183446 + 0.00538647i
\(386\) 0 0
\(387\) 2.64979 + 0.778048i 0.134696 + 0.0395504i
\(388\) 0 0
\(389\) −1.87506 + 13.0414i −0.0950695 + 0.661223i 0.885440 + 0.464753i \(0.153857\pi\)
−0.980510 + 0.196470i \(0.937052\pi\)
\(390\) 0 0
\(391\) 5.75061 6.31393i 0.290821 0.319309i
\(392\) 0 0
\(393\) −7.06959 + 49.1700i −0.356613 + 2.48030i
\(394\) 0 0
\(395\) 7.33456 + 2.15362i 0.369042 + 0.108360i
\(396\) 0 0
\(397\) 8.24921 2.42219i 0.414016 0.121566i −0.0680895 0.997679i \(-0.521690\pi\)
0.482106 + 0.876113i \(0.339872\pi\)
\(398\) 0 0
\(399\) 0.239789 0.525065i 0.0120045 0.0262861i
\(400\) 0 0
\(401\) 17.5090 11.2523i 0.874357 0.561915i −0.0247259 0.999694i \(-0.507871\pi\)
0.899082 + 0.437779i \(0.144235\pi\)
\(402\) 0 0
\(403\) −1.30774 9.09555i −0.0651433 0.453082i
\(404\) 0 0
\(405\) 3.77076 4.35169i 0.187371 0.216237i
\(406\) 0 0
\(407\) 9.19873 + 5.91167i 0.455964 + 0.293031i
\(408\) 0 0
\(409\) −8.81821 10.1768i −0.436033 0.503208i 0.494622 0.869108i \(-0.335307\pi\)
−0.930654 + 0.365900i \(0.880761\pi\)
\(410\) 0 0
\(411\) −17.5218 38.3674i −0.864286 1.89252i
\(412\) 0 0
\(413\) 0.991168 0.0487722
\(414\) 0 0
\(415\) −13.2919 −0.652476
\(416\) 0 0
\(417\) −20.6672 45.2549i −1.01208 2.21614i
\(418\) 0 0
\(419\) −14.8040 17.0848i −0.723224 0.834645i 0.268467 0.963289i \(-0.413483\pi\)
−0.991691 + 0.128644i \(0.958938\pi\)
\(420\) 0 0
\(421\) −3.89603 2.50383i −0.189881 0.122029i 0.442246 0.896894i \(-0.354182\pi\)
−0.632127 + 0.774864i \(0.717818\pi\)
\(422\) 0 0
\(423\) −2.21034 + 2.55087i −0.107470 + 0.124028i
\(424\) 0 0
\(425\) −0.253428 1.76263i −0.0122931 0.0855002i
\(426\) 0 0
\(427\) 0.0727638 0.0467624i 0.00352129 0.00226299i
\(428\) 0 0
\(429\) 23.5934 51.6624i 1.13910 2.49428i
\(430\) 0 0
\(431\) 27.8595 8.18029i 1.34195 0.394031i 0.469582 0.882889i \(-0.344405\pi\)
0.872363 + 0.488858i \(0.162586\pi\)
\(432\) 0 0
\(433\) 27.4854 + 8.07045i 1.32087 + 0.387841i 0.864805 0.502107i \(-0.167442\pi\)
0.456061 + 0.889949i \(0.349260\pi\)
\(434\) 0 0
\(435\) 0.490805 3.41362i 0.0235323 0.163671i
\(436\) 0 0
\(437\) −15.7938 + 4.21602i −0.755521 + 0.201679i
\(438\) 0 0
\(439\) 0.178976 1.24480i 0.00854204 0.0594112i −0.985105 0.171956i \(-0.944991\pi\)
0.993647 + 0.112545i \(0.0359003\pi\)
\(440\) 0 0
\(441\) 25.7991 + 7.57529i 1.22853 + 0.360728i
\(442\) 0 0
\(443\) −12.8094 + 3.76119i −0.608594 + 0.178699i −0.571486 0.820612i \(-0.693633\pi\)
−0.0371082 + 0.999311i \(0.511815\pi\)
\(444\) 0 0
\(445\) 0.981628 2.14946i 0.0465336 0.101894i
\(446\) 0 0
\(447\) 16.3851 10.5301i 0.774991 0.498056i
\(448\) 0 0
\(449\) −2.36172 16.4261i −0.111456 0.775196i −0.966505 0.256648i \(-0.917382\pi\)
0.855049 0.518548i \(-0.173527\pi\)
\(450\) 0 0
\(451\) −0.408129 + 0.471006i −0.0192181 + 0.0221788i
\(452\) 0 0
\(453\) −3.77825 2.42813i −0.177517 0.114084i
\(454\) 0 0
\(455\) 0.158818 + 0.183286i 0.00744550 + 0.00859256i
\(456\) 0 0
\(457\) −0.977533 2.14050i −0.0457271 0.100128i 0.885390 0.464849i \(-0.153892\pi\)
−0.931117 + 0.364721i \(0.881164\pi\)
\(458\) 0 0
\(459\) −3.92932 −0.183405
\(460\) 0 0
\(461\) 1.30382 0.0607249 0.0303625 0.999539i \(-0.490334\pi\)
0.0303625 + 0.999539i \(0.490334\pi\)
\(462\) 0 0
\(463\) −11.1553 24.4268i −0.518433 1.13521i −0.970030 0.242987i \(-0.921873\pi\)
0.451597 0.892222i \(-0.350855\pi\)
\(464\) 0 0
\(465\) −4.20192 4.84927i −0.194859 0.224880i
\(466\) 0 0
\(467\) 11.9402 + 7.67353i 0.552528 + 0.355088i 0.786921 0.617054i \(-0.211674\pi\)
−0.234393 + 0.972142i \(0.575310\pi\)
\(468\) 0 0
\(469\) 0.457370 0.527833i 0.0211194 0.0243731i
\(470\) 0 0
\(471\) −4.58320 31.8768i −0.211183 1.46881i
\(472\) 0 0
\(473\) −3.50292 + 2.25119i −0.161065 + 0.103510i
\(474\) 0 0
\(475\) −1.41596 + 3.10053i −0.0649689 + 0.142262i
\(476\) 0 0
\(477\) 32.1278 9.43357i 1.47103 0.431934i
\(478\) 0 0
\(479\) −9.00073 2.64285i −0.411254 0.120755i 0.0695599 0.997578i \(-0.477840\pi\)
−0.480814 + 0.876823i \(0.659659\pi\)
\(480\) 0 0
\(481\) 1.00602 6.99699i 0.0458703 0.319035i
\(482\) 0 0
\(483\) 0.319004 + 0.746886i 0.0145152 + 0.0339845i
\(484\) 0 0
\(485\) 0.916490 6.37433i 0.0416157 0.289443i
\(486\) 0 0
\(487\) 20.7429 + 6.09067i 0.939952 + 0.275995i 0.715597 0.698513i \(-0.246155\pi\)
0.224354 + 0.974508i \(0.427973\pi\)
\(488\) 0 0
\(489\) 29.5010 8.66227i 1.33408 0.391721i
\(490\) 0 0
\(491\) −17.4103 + 38.1231i −0.785714 + 1.72047i −0.0971830 + 0.995267i \(0.530983\pi\)
−0.688531 + 0.725207i \(0.741744\pi\)
\(492\) 0 0
\(493\) 1.97493 1.26921i 0.0889464 0.0571624i
\(494\) 0 0
\(495\) −3.16981 22.0465i −0.142472 0.990917i
\(496\) 0 0
\(497\) 0.470319 0.542777i 0.0210967 0.0243469i
\(498\) 0 0
\(499\) 9.75265 + 6.26765i 0.436588 + 0.280578i 0.740416 0.672149i \(-0.234628\pi\)
−0.303828 + 0.952727i \(0.598265\pi\)
\(500\) 0 0
\(501\) 37.6832 + 43.4887i 1.68356 + 1.94293i
\(502\) 0 0
\(503\) 2.03334 + 4.45239i 0.0906621 + 0.198522i 0.949531 0.313673i \(-0.101560\pi\)
−0.858869 + 0.512195i \(0.828832\pi\)
\(504\) 0 0
\(505\) −11.3626 −0.505629
\(506\) 0 0
\(507\) −2.70850 −0.120289
\(508\) 0 0
\(509\) −13.3829 29.3044i −0.593185 1.29889i −0.933498 0.358581i \(-0.883261\pi\)
0.340314 0.940312i \(-0.389467\pi\)
\(510\) 0 0
\(511\) −0.213045 0.245866i −0.00942453 0.0108765i
\(512\) 0 0
\(513\) 6.32716 + 4.06622i 0.279351 + 0.179528i
\(514\) 0 0
\(515\) −11.4691 + 13.2360i −0.505389 + 0.583249i
\(516\) 0 0
\(517\) −0.724261 5.03734i −0.0318529 0.221542i
\(518\) 0 0
\(519\) −16.4728 + 10.5864i −0.723076 + 0.464693i
\(520\) 0 0
\(521\) −2.12966 + 4.66330i −0.0933020 + 0.204303i −0.950529 0.310636i \(-0.899458\pi\)
0.857227 + 0.514939i \(0.172185\pi\)
\(522\) 0 0
\(523\) 16.6666 4.89376i 0.728781 0.213989i 0.103765 0.994602i \(-0.466911\pi\)
0.625015 + 0.780612i \(0.285093\pi\)
\(524\) 0 0
\(525\) 0.162487 + 0.0477105i 0.00709152 + 0.00208226i
\(526\) 0 0
\(527\) 0.621606 4.32337i 0.0270776 0.188329i
\(528\) 0 0
\(529\) 10.5777 20.4233i 0.459898 0.887972i
\(530\) 0 0
\(531\) −8.37496 + 58.2492i −0.363443 + 2.52780i
\(532\) 0 0
\(533\) 0.386584 + 0.113511i 0.0167448 + 0.00491672i
\(534\) 0 0
\(535\) 11.7816 3.45940i 0.509364 0.149563i
\(536\) 0 0
\(537\) −15.8744 + 34.7600i −0.685029 + 1.50001i
\(538\) 0 0
\(539\) −34.1054 + 21.9182i −1.46902 + 0.944085i
\(540\) 0 0
\(541\) 4.71171 + 32.7706i 0.202572 + 1.40892i 0.796615 + 0.604487i \(0.206622\pi\)
−0.594043 + 0.804433i \(0.702469\pi\)
\(542\) 0 0
\(543\) 18.1129 20.9034i 0.777298 0.897050i
\(544\) 0 0
\(545\) 9.13138 + 5.86838i 0.391146 + 0.251374i
\(546\) 0 0
\(547\) 5.81210 + 6.70752i 0.248508 + 0.286793i 0.866275 0.499568i \(-0.166508\pi\)
−0.617767 + 0.786361i \(0.711963\pi\)
\(548\) 0 0
\(549\) 2.13332 + 4.67132i 0.0910479 + 0.199367i
\(550\) 0 0
\(551\) −4.49355 −0.191432
\(552\) 0 0
\(553\) −0.494847 −0.0210430
\(554\) 0 0
\(555\) −2.05052 4.49000i −0.0870396 0.190590i
\(556\) 0 0
\(557\) −3.76373 4.34358i −0.159474 0.184043i 0.670389 0.742010i \(-0.266127\pi\)
−0.829864 + 0.557966i \(0.811582\pi\)
\(558\) 0 0
\(559\) 2.26456 + 1.45534i 0.0957806 + 0.0615545i
\(560\) 0 0
\(561\) 17.6787 20.4023i 0.746396 0.861387i
\(562\) 0 0
\(563\) 0.819990 + 5.70316i 0.0345585 + 0.240359i 0.999778 0.0210823i \(-0.00671119\pi\)
−0.965219 + 0.261442i \(0.915802\pi\)
\(564\) 0 0
\(565\) −13.1712 + 8.46461i −0.554116 + 0.356109i
\(566\) 0 0
\(567\) −0.154846 + 0.339066i −0.00650294 + 0.0142394i
\(568\) 0 0
\(569\) −22.0700 + 6.48033i −0.925222 + 0.271670i −0.709435 0.704771i \(-0.751050\pi\)
−0.215787 + 0.976440i \(0.569232\pi\)
\(570\) 0 0
\(571\) −8.06585 2.36835i −0.337545 0.0991122i 0.108567 0.994089i \(-0.465374\pi\)
−0.446113 + 0.894977i \(0.647192\pi\)
\(572\) 0 0
\(573\) 6.54339 45.5102i 0.273354 1.90122i
\(574\) 0 0
\(575\) −1.88373 4.41039i −0.0785570 0.183926i
\(576\) 0 0
\(577\) −2.26843 + 15.7773i −0.0944360 + 0.656817i 0.886535 + 0.462662i \(0.153106\pi\)
−0.980971 + 0.194155i \(0.937803\pi\)
\(578\) 0 0
\(579\) −32.2710 9.47562i −1.34114 0.393793i
\(580\) 0 0
\(581\) 0.825598 0.242418i 0.0342516 0.0100572i
\(582\) 0 0
\(583\) −20.9728 + 45.9239i −0.868603 + 1.90197i
\(584\) 0 0
\(585\) −12.1133 + 7.78476i −0.500824 + 0.321860i
\(586\) 0 0
\(587\) −4.47077 31.0949i −0.184528 1.28342i −0.845891 0.533356i \(-0.820930\pi\)
0.661362 0.750067i \(-0.269979\pi\)
\(588\) 0 0
\(589\) −5.47494 + 6.31842i −0.225591 + 0.260346i
\(590\) 0 0
\(591\) 7.20496 + 4.63035i 0.296372 + 0.190467i
\(592\) 0 0
\(593\) 12.5227 + 14.4520i 0.514245 + 0.593471i 0.952181 0.305536i \(-0.0988356\pi\)
−0.437935 + 0.899006i \(0.644290\pi\)
\(594\) 0 0
\(595\) 0.0478879 + 0.104860i 0.00196321 + 0.00429883i
\(596\) 0 0
\(597\) −61.1806 −2.50395
\(598\) 0 0
\(599\) −39.8003 −1.62620 −0.813098 0.582126i \(-0.802221\pi\)
−0.813098 + 0.582126i \(0.802221\pi\)
\(600\) 0 0
\(601\) −11.4277 25.0232i −0.466145 1.02072i −0.986044 0.166488i \(-0.946757\pi\)
0.519898 0.854228i \(-0.325970\pi\)
\(602\) 0 0
\(603\) 27.1552 + 31.3388i 1.10585 + 1.27621i
\(604\) 0 0
\(605\) 18.9979 + 12.2092i 0.772374 + 0.496374i
\(606\) 0 0
\(607\) 20.2039 23.3165i 0.820051 0.946389i −0.179249 0.983804i \(-0.557367\pi\)
0.999300 + 0.0374144i \(0.0119121\pi\)
\(608\) 0 0
\(609\) 0.0317722 + 0.220980i 0.00128747 + 0.00895458i
\(610\) 0 0
\(611\) −2.76774 + 1.77872i −0.111971 + 0.0719592i
\(612\) 0 0
\(613\) 18.1595 39.7637i 0.733455 1.60604i −0.0605756 0.998164i \(-0.519294\pi\)
0.794030 0.607878i \(-0.207979\pi\)
\(614\) 0 0
\(615\) 0.269942 0.0792621i 0.0108851 0.00319616i
\(616\) 0 0
\(617\) −13.3389 3.91666i −0.537005 0.157679i 0.00197396 0.999998i \(-0.499372\pi\)
−0.538979 + 0.842319i \(0.681190\pi\)
\(618\) 0 0
\(619\) −4.82263 + 33.5421i −0.193838 + 1.34817i 0.627895 + 0.778298i \(0.283917\pi\)
−0.821733 + 0.569873i \(0.806992\pi\)
\(620\) 0 0
\(621\) −10.2242 + 2.72926i −0.410283 + 0.109521i
\(622\) 0 0
\(623\) −0.0217698 + 0.151412i −0.000872187 + 0.00606619i
\(624\) 0 0
\(625\) −0.959493 0.281733i −0.0383797 0.0112693i
\(626\) 0 0
\(627\) −49.5803 + 14.5581i −1.98005 + 0.581394i
\(628\) 0 0
\(629\) 1.39582 3.05642i 0.0556550 0.121867i
\(630\) 0 0
\(631\) −7.17855 + 4.61338i −0.285774 + 0.183656i −0.675672 0.737202i \(-0.736146\pi\)
0.389898 + 0.920858i \(0.372510\pi\)
\(632\) 0 0
\(633\) 10.0841 + 70.1365i 0.400807 + 2.78768i
\(634\) 0 0
\(635\) 9.03309 10.4247i 0.358467 0.413693i
\(636\) 0 0
\(637\) 22.0484 + 14.1696i 0.873588 + 0.561421i
\(638\) 0 0
\(639\) 27.9240 + 32.2261i 1.10466 + 1.27484i
\(640\) 0 0
\(641\) −3.62416 7.93581i −0.143146 0.313445i 0.824456 0.565926i \(-0.191481\pi\)
−0.967602 + 0.252480i \(0.918754\pi\)
\(642\) 0 0
\(643\) −0.118338 −0.00466680 −0.00233340 0.999997i \(-0.500743\pi\)
−0.00233340 + 0.999997i \(0.500743\pi\)
\(644\) 0 0
\(645\) 1.87968 0.0740122
\(646\) 0 0
\(647\) 14.6796 + 32.1439i 0.577115 + 1.26371i 0.942922 + 0.333015i \(0.108066\pi\)
−0.365807 + 0.930691i \(0.619207\pi\)
\(648\) 0 0
\(649\) −58.1053 67.0571i −2.28083 2.63222i
\(650\) 0 0
\(651\) 0.349433 + 0.224567i 0.0136954 + 0.00880148i
\(652\) 0 0
\(653\) 28.0706 32.3952i 1.09849 1.26772i 0.137690 0.990475i \(-0.456032\pi\)
0.960798 0.277248i \(-0.0894224\pi\)
\(654\) 0 0
\(655\) 2.70244 + 18.7959i 0.105593 + 0.734415i
\(656\) 0 0
\(657\) 16.2493 10.4428i 0.633945 0.407411i
\(658\) 0 0
\(659\) −13.4612 + 29.4758i −0.524373 + 1.14822i 0.443385 + 0.896331i \(0.353778\pi\)
−0.967757 + 0.251885i \(0.918950\pi\)
\(660\) 0 0
\(661\) −31.0309 + 9.11149i −1.20696 + 0.354396i −0.822511 0.568749i \(-0.807427\pi\)
−0.384451 + 0.923145i \(0.625609\pi\)
\(662\) 0 0
\(663\) −16.7454 4.91691i −0.650339 0.190957i
\(664\) 0 0
\(665\) 0.0314021 0.218407i 0.00121772 0.00846944i
\(666\) 0 0
\(667\) 4.25725 4.67429i 0.164841 0.180989i
\(668\) 0 0
\(669\) −1.81608 + 12.6311i −0.0702138 + 0.488348i
\(670\) 0 0
\(671\) −7.42934 2.18145i −0.286806 0.0842140i
\(672\) 0 0
\(673\) 36.1768 10.6225i 1.39451 0.409466i 0.503717 0.863869i \(-0.331965\pi\)
0.890796 + 0.454403i \(0.150147\pi\)
\(674\) 0 0
\(675\) −0.916631 + 2.00714i −0.0352811 + 0.0772549i
\(676\) 0 0
\(677\) −28.2760 + 18.1719i −1.08674 + 0.698403i −0.956104 0.293028i \(-0.905337\pi\)
−0.130632 + 0.991431i \(0.541701\pi\)
\(678\) 0 0
\(679\) 0.0593290 + 0.412642i 0.00227684 + 0.0158357i
\(680\) 0 0
\(681\) −25.1702 + 29.0480i −0.964525 + 1.11312i
\(682\) 0 0
\(683\) 0.546455 + 0.351185i 0.0209095 + 0.0134377i 0.551054 0.834470i \(-0.314226\pi\)
−0.530144 + 0.847907i \(0.677862\pi\)
\(684\) 0 0
\(685\) −10.5586 12.1853i −0.403424 0.465576i
\(686\) 0 0
\(687\) −12.1558 26.6175i −0.463772 1.01552i
\(688\) 0 0
\(689\) 32.6382 1.24342
\(690\) 0 0
\(691\) −44.9140 −1.70861 −0.854305 0.519773i \(-0.826017\pi\)
−0.854305 + 0.519773i \(0.826017\pi\)
\(692\) 0 0
\(693\) 0.598968 + 1.31156i 0.0227529 + 0.0498220i
\(694\) 0 0
\(695\) −12.4540 14.3727i −0.472409 0.545189i
\(696\) 0 0
\(697\) 0.161110 + 0.103539i 0.00610247 + 0.00392182i
\(698\) 0 0
\(699\) −36.5737 + 42.2083i −1.38335 + 1.59647i
\(700\) 0 0
\(701\) 1.94415 + 13.5218i 0.0734294 + 0.510713i 0.993030 + 0.117859i \(0.0376031\pi\)
−0.919601 + 0.392854i \(0.871488\pi\)
\(702\) 0 0
\(703\) −5.41053 + 3.47713i −0.204062 + 0.131143i
\(704\) 0 0
\(705\) −0.954348 + 2.08973i −0.0359428 + 0.0787038i
\(706\) 0 0
\(707\) 0.705761 0.207230i 0.0265429 0.00779370i
\(708\) 0 0
\(709\) 18.8162 + 5.52494i 0.706658 + 0.207493i 0.615264 0.788321i \(-0.289050\pi\)
0.0913940 + 0.995815i \(0.470868\pi\)
\(710\) 0 0
\(711\) 4.18126 29.0813i 0.156809 1.09063i
\(712\) 0 0
\(713\) −1.38552 11.6813i −0.0518882 0.437468i
\(714\) 0 0
\(715\) 3.08973 21.4895i 0.115549 0.803663i
\(716\) 0 0
\(717\) 26.1916 + 7.69055i 0.978144 + 0.287209i
\(718\) 0 0
\(719\) 31.5351 9.25955i 1.17606 0.345323i 0.365408 0.930848i \(-0.380930\pi\)
0.810655 + 0.585524i \(0.199111\pi\)
\(720\) 0 0
\(721\) 0.470978 1.03130i 0.0175402 0.0384076i
\(722\) 0 0
\(723\) 59.2098 38.0518i 2.20204 1.41516i
\(724\) 0 0
\(725\) −0.187616 1.30490i −0.00696789 0.0484627i
\(726\) 0 0
\(727\) 22.7009 26.1983i 0.841931 0.971641i −0.157944 0.987448i \(-0.550486\pi\)
0.999875 + 0.0158076i \(0.00503193\pi\)
\(728\) 0 0
\(729\) −33.1859 21.3273i −1.22911 0.789899i
\(730\) 0 0
\(731\) 0.837913 + 0.967003i 0.0309913 + 0.0357659i
\(732\) 0 0
\(733\) −15.4169 33.7583i −0.569437 1.24689i −0.947097 0.320949i \(-0.895998\pi\)
0.377660 0.925944i \(-0.376729\pi\)
\(734\) 0 0
\(735\) 18.3011 0.675045
\(736\) 0 0
\(737\) −62.5228 −2.30306
\(738\) 0 0
\(739\) −9.83154 21.5281i −0.361659 0.791923i −0.999759 0.0219691i \(-0.993006\pi\)
0.638100 0.769954i \(-0.279721\pi\)
\(740\) 0 0
\(741\) 21.8761 + 25.2463i 0.803637 + 0.927447i
\(742\) 0 0
\(743\) −35.4486 22.7814i −1.30048 0.835769i −0.307218 0.951639i \(-0.599398\pi\)
−0.993264 + 0.115870i \(0.963034\pi\)
\(744\) 0 0
\(745\) 4.87567 5.62682i 0.178631 0.206151i
\(746\) 0 0
\(747\) 7.27048 + 50.5673i 0.266013 + 1.85016i
\(748\) 0 0
\(749\) −0.668696 + 0.429745i −0.0244336 + 0.0157025i
\(750\) 0 0
\(751\) 11.9646 26.1989i 0.436595 0.956010i −0.555616 0.831439i \(-0.687517\pi\)
0.992211 0.124571i \(-0.0397554\pi\)
\(752\) 0 0
\(753\) −6.22514 + 1.82787i −0.226857 + 0.0666112i
\(754\) 0 0
\(755\) −1.64728 0.483684i −0.0599506 0.0176031i
\(756\) 0 0
\(757\) 0.514907 3.58125i 0.0187146 0.130163i −0.978322 0.207088i \(-0.933601\pi\)
0.997037 + 0.0769254i \(0.0245103\pi\)
\(758\) 0 0
\(759\) 31.8293 65.3669i 1.15533 2.37267i
\(760\) 0 0
\(761\) 1.04364 7.25865i 0.0378318 0.263126i −0.962123 0.272615i \(-0.912111\pi\)
0.999955 + 0.00948916i \(0.00302054\pi\)
\(762\) 0 0
\(763\) −0.674202 0.197964i −0.0244078 0.00716677i
\(764\) 0 0
\(765\) −6.56706 + 1.92826i −0.237433 + 0.0697165i
\(766\) 0 0
\(767\) −23.8288 + 52.1778i −0.860408 + 1.88403i
\(768\) 0 0
\(769\) −3.51169 + 2.25683i −0.126635 + 0.0813833i −0.602425 0.798176i \(-0.705799\pi\)
0.475790 + 0.879559i \(0.342162\pi\)
\(770\) 0 0
\(771\) −5.76885 40.1232i −0.207760 1.44500i
\(772\) 0 0
\(773\) −8.17733 + 9.43714i −0.294118 + 0.339430i −0.883506 0.468420i \(-0.844823\pi\)
0.589388 + 0.807850i \(0.299369\pi\)
\(774\) 0 0
\(775\) −2.06342 1.32608i −0.0741202 0.0476341i
\(776\) 0 0
\(777\) 0.209252 + 0.241489i 0.00750686 + 0.00866338i
\(778\) 0 0
\(779\) −0.152280 0.333446i −0.00545599 0.0119470i
\(780\) 0 0
\(781\) −64.2930 −2.30058
\(782\) 0 0
\(783\) −2.90892 −0.103956
\(784\) 0 0
\(785\) −5.11402 11.1981i −0.182527 0.399679i
\(786\) 0 0
\(787\) −0.202945 0.234211i −0.00723422 0.00834873i 0.752121 0.659025i \(-0.229031\pi\)
−0.759355 + 0.650676i \(0.774485\pi\)
\(788\) 0 0
\(789\) 24.6853 + 15.8642i 0.878818 + 0.564782i
\(790\) 0 0
\(791\) 0.663722 0.765976i 0.0235992 0.0272350i
\(792\) 0 0
\(793\) 0.712380 + 4.95471i 0.0252974 + 0.175947i
\(794\) 0 0
\(795\) 19.1726 12.3215i 0.679980 0.436997i
\(796\)