Properties

Label 668.2.e.a.21.3
Level $668$
Weight $2$
Character 668.21
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 21.3
Character \(\chi\) \(=\) 668.21
Dual form 668.2.e.a.509.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.90829 - 0.291147i) q^{3} +(1.01478 + 1.20422i) q^{5} +(2.44900 - 3.39773i) q^{7} +(0.693279 + 0.216588i) q^{9} +O(q^{10})\) \(q+(-1.90829 - 0.291147i) q^{3} +(1.01478 + 1.20422i) q^{5} +(2.44900 - 3.39773i) q^{7} +(0.693279 + 0.216588i) q^{9} +(0.410057 - 0.387413i) q^{11} +(-0.251414 + 1.88668i) q^{13} +(-1.58589 - 2.59345i) q^{15} +(-2.11599 + 3.18308i) q^{17} +(0.744309 + 0.172002i) q^{19} +(-5.66262 + 5.77082i) q^{21} +(-1.46291 - 6.92542i) q^{23} +(0.427164 - 2.48360i) q^{25} +(3.94403 + 1.92568i) q^{27} +(2.16132 - 10.2317i) q^{29} +(4.67062 - 0.894634i) q^{31} +(-0.895301 + 0.619908i) q^{33} +(6.57681 - 0.498825i) q^{35} +(6.06457 - 1.89464i) q^{37} +(1.02907 - 3.52713i) q^{39} +(-3.75057 + 1.49153i) q^{41} +(7.49058 + 2.65521i) q^{43} +(0.442708 + 1.05465i) q^{45} +(0.564216 - 2.24684i) q^{47} +(-3.33350 - 10.0012i) q^{49} +(4.96466 - 5.45816i) q^{51} +(-6.20880 - 4.65619i) q^{53} +(0.882650 + 0.100659i) q^{55} +(-1.37028 - 0.544933i) q^{57} +(-1.69167 - 2.54477i) q^{59} +(5.65813 + 7.25464i) q^{61} +(2.43375 - 1.82515i) q^{63} +(-2.52711 + 1.61181i) q^{65} +(6.95757 - 8.25639i) q^{67} +(0.775347 + 13.6416i) q^{69} +(-0.707032 - 7.44952i) q^{71} +(2.02670 - 3.61492i) q^{73} +(-1.53824 + 4.61505i) q^{75} +(-0.312093 - 2.34204i) q^{77} +(-10.3455 - 0.391771i) q^{79} +(-8.75713 - 6.06345i) q^{81} +(3.43858 - 0.933000i) q^{83} +(-5.98040 + 0.682018i) q^{85} +(-7.10334 + 18.8957i) q^{87} +(-4.06478 + 6.64722i) q^{89} +(5.79471 + 5.47471i) q^{91} +(-9.17336 + 0.347382i) q^{93} +(0.548184 + 1.07086i) q^{95} +(7.06846 + 1.35393i) q^{97} +(0.368193 - 0.179772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{23}{83}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.90829 0.291147i −1.10175 0.168094i −0.425639 0.904893i \(-0.639951\pi\)
−0.676111 + 0.736800i \(0.736336\pi\)
\(4\) 0 0
\(5\) 1.01478 + 1.20422i 0.453825 + 0.538544i 0.942626 0.333852i \(-0.108349\pi\)
−0.488800 + 0.872396i \(0.662565\pi\)
\(6\) 0 0
\(7\) 2.44900 3.39773i 0.925634 1.28422i −0.0329643 0.999457i \(-0.510495\pi\)
0.958598 0.284763i \(-0.0919149\pi\)
\(8\) 0 0
\(9\) 0.693279 + 0.216588i 0.231093 + 0.0721961i
\(10\) 0 0
\(11\) 0.410057 0.387413i 0.123637 0.116809i −0.622445 0.782664i \(-0.713860\pi\)
0.746082 + 0.665854i \(0.231933\pi\)
\(12\) 0 0
\(13\) −0.251414 + 1.88668i −0.0697297 + 0.523271i 0.921221 + 0.389041i \(0.127193\pi\)
−0.990950 + 0.134230i \(0.957144\pi\)
\(14\) 0 0
\(15\) −1.58589 2.59345i −0.409476 0.669625i
\(16\) 0 0
\(17\) −2.11599 + 3.18308i −0.513203 + 0.772010i −0.994521 0.104536i \(-0.966664\pi\)
0.481318 + 0.876546i \(0.340158\pi\)
\(18\) 0 0
\(19\) 0.744309 + 0.172002i 0.170756 + 0.0394600i 0.309668 0.950845i \(-0.399782\pi\)
−0.138912 + 0.990305i \(0.544360\pi\)
\(20\) 0 0
\(21\) −5.66262 + 5.77082i −1.23569 + 1.25930i
\(22\) 0 0
\(23\) −1.46291 6.92542i −0.305039 1.44405i −0.812795 0.582550i \(-0.802055\pi\)
0.507756 0.861501i \(-0.330475\pi\)
\(24\) 0 0
\(25\) 0.427164 2.48360i 0.0854328 0.496720i
\(26\) 0 0
\(27\) 3.94403 + 1.92568i 0.759029 + 0.370598i
\(28\) 0 0
\(29\) 2.16132 10.2317i 0.401348 1.89998i −0.0334349 0.999441i \(-0.510645\pi\)
0.434783 0.900535i \(-0.356825\pi\)
\(30\) 0 0
\(31\) 4.67062 0.894634i 0.838869 0.160681i 0.249327 0.968419i \(-0.419790\pi\)
0.589541 + 0.807738i \(0.299309\pi\)
\(32\) 0 0
\(33\) −0.895301 + 0.619908i −0.155852 + 0.107912i
\(34\) 0 0
\(35\) 6.57681 0.498825i 1.11168 0.0843168i
\(36\) 0 0
\(37\) 6.06457 1.89464i 0.997009 0.311477i 0.244206 0.969723i \(-0.421473\pi\)
0.752803 + 0.658246i \(0.228701\pi\)
\(38\) 0 0
\(39\) 1.02907 3.52713i 0.164783 0.564792i
\(40\) 0 0
\(41\) −3.75057 + 1.49153i −0.585741 + 0.232938i −0.643568 0.765389i \(-0.722547\pi\)
0.0578271 + 0.998327i \(0.481583\pi\)
\(42\) 0 0
\(43\) 7.49058 + 2.65521i 1.14230 + 0.404916i 0.836926 0.547316i \(-0.184350\pi\)
0.305376 + 0.952232i \(0.401218\pi\)
\(44\) 0 0
\(45\) 0.442708 + 1.05465i 0.0659950 + 0.157218i
\(46\) 0 0
\(47\) 0.564216 2.24684i 0.0822994 0.327735i −0.914794 0.403920i \(-0.867647\pi\)
0.997094 + 0.0761848i \(0.0242739\pi\)
\(48\) 0 0
\(49\) −3.33350 10.0012i −0.476214 1.42874i
\(50\) 0 0
\(51\) 4.96466 5.45816i 0.695191 0.764296i
\(52\) 0 0
\(53\) −6.20880 4.65619i −0.852844 0.639577i 0.0812141 0.996697i \(-0.474120\pi\)
−0.934059 + 0.357120i \(0.883759\pi\)
\(54\) 0 0
\(55\) 0.882650 + 0.100659i 0.119017 + 0.0135729i
\(56\) 0 0
\(57\) −1.37028 0.544933i −0.181498 0.0721781i
\(58\) 0 0
\(59\) −1.69167 2.54477i −0.220237 0.331301i 0.706022 0.708190i \(-0.250488\pi\)
−0.926259 + 0.376889i \(0.876994\pi\)
\(60\) 0 0
\(61\) 5.65813 + 7.25464i 0.724449 + 0.928861i 0.999469 0.0325769i \(-0.0103714\pi\)
−0.275020 + 0.961438i \(0.588685\pi\)
\(62\) 0 0
\(63\) 2.43375 1.82515i 0.306623 0.229947i
\(64\) 0 0
\(65\) −2.52711 + 1.61181i −0.313449 + 0.199921i
\(66\) 0 0
\(67\) 6.95757 8.25639i 0.850003 1.00868i −0.149798 0.988717i \(-0.547862\pi\)
0.999801 0.0199620i \(-0.00635453\pi\)
\(68\) 0 0
\(69\) 0.775347 + 13.6416i 0.0933408 + 1.64226i
\(70\) 0 0
\(71\) −0.707032 7.44952i −0.0839092 0.884095i −0.933956 0.357388i \(-0.883667\pi\)
0.850047 0.526707i \(-0.176574\pi\)
\(72\) 0 0
\(73\) 2.02670 3.61492i 0.237207 0.423095i −0.727619 0.685981i \(-0.759373\pi\)
0.964827 + 0.262886i \(0.0846745\pi\)
\(74\) 0 0
\(75\) −1.53824 + 4.61505i −0.177621 + 0.532900i
\(76\) 0 0
\(77\) −0.312093 2.34204i −0.0355663 0.266900i
\(78\) 0 0
\(79\) −10.3455 0.391771i −1.16396 0.0440777i −0.551221 0.834359i \(-0.685838\pi\)
−0.612744 + 0.790282i \(0.709934\pi\)
\(80\) 0 0
\(81\) −8.75713 6.06345i −0.973015 0.673717i
\(82\) 0 0
\(83\) 3.43858 0.933000i 0.377434 0.102410i −0.0680926 0.997679i \(-0.521691\pi\)
0.445526 + 0.895269i \(0.353017\pi\)
\(84\) 0 0
\(85\) −5.98040 + 0.682018i −0.648666 + 0.0739752i
\(86\) 0 0
\(87\) −7.10334 + 18.8957i −0.761558 + 2.02583i
\(88\) 0 0
\(89\) −4.06478 + 6.64722i −0.430865 + 0.704604i −0.992428 0.122830i \(-0.960803\pi\)
0.561562 + 0.827434i \(0.310200\pi\)
\(90\) 0 0
\(91\) 5.79471 + 5.47471i 0.607451 + 0.573905i
\(92\) 0 0
\(93\) −9.17336 + 0.347382i −0.951233 + 0.0360218i
\(94\) 0 0
\(95\) 0.548184 + 1.07086i 0.0562425 + 0.109868i
\(96\) 0 0
\(97\) 7.06846 + 1.35393i 0.717693 + 0.137470i 0.533965 0.845507i \(-0.320701\pi\)
0.183728 + 0.982977i \(0.441183\pi\)
\(98\) 0 0
\(99\) 0.368193 0.179772i 0.0370048 0.0180677i
\(100\) 0 0
\(101\) −5.90222 + 2.09218i −0.587293 + 0.208180i −0.611122 0.791536i \(-0.709282\pi\)
0.0238296 + 0.999716i \(0.492414\pi\)
\(102\) 0 0
\(103\) 0.238422 12.5966i 0.0234924 1.24118i −0.772162 0.635425i \(-0.780825\pi\)
0.795655 0.605750i \(-0.207127\pi\)
\(104\) 0 0
\(105\) −12.6957 0.962916i −1.23897 0.0939709i
\(106\) 0 0
\(107\) 0.220685 + 11.6595i 0.0213345 + 1.12717i 0.836510 + 0.547952i \(0.184592\pi\)
−0.815175 + 0.579215i \(0.803359\pi\)
\(108\) 0 0
\(109\) −7.17969 + 14.0253i −0.687690 + 1.34338i 0.240274 + 0.970705i \(0.422763\pi\)
−0.927964 + 0.372671i \(0.878442\pi\)
\(110\) 0 0
\(111\) −12.1246 + 1.84984i −1.15081 + 0.175579i
\(112\) 0 0
\(113\) 5.58984 + 4.89436i 0.525848 + 0.460423i 0.880142 0.474711i \(-0.157447\pi\)
−0.354294 + 0.935134i \(0.615279\pi\)
\(114\) 0 0
\(115\) 6.85520 8.78948i 0.639250 0.819623i
\(116\) 0 0
\(117\) −0.582933 + 1.25354i −0.0538921 + 0.115890i
\(118\) 0 0
\(119\) 5.63318 + 14.9849i 0.516392 + 1.37366i
\(120\) 0 0
\(121\) −0.606140 + 10.6646i −0.0551036 + 0.969505i
\(122\) 0 0
\(123\) 7.59142 1.75430i 0.684495 0.158180i
\(124\) 0 0
\(125\) 10.2183 5.98581i 0.913953 0.535387i
\(126\) 0 0
\(127\) −1.17928 + 12.4253i −0.104645 + 1.10257i 0.776628 + 0.629960i \(0.216929\pi\)
−0.881272 + 0.472609i \(0.843312\pi\)
\(128\) 0 0
\(129\) −13.5211 7.24776i −1.19047 0.638130i
\(130\) 0 0
\(131\) 3.46403 + 3.80837i 0.302654 + 0.332739i 0.872135 0.489266i \(-0.162735\pi\)
−0.569481 + 0.822005i \(0.692856\pi\)
\(132\) 0 0
\(133\) 2.40723 2.10773i 0.208733 0.182763i
\(134\) 0 0
\(135\) 1.68339 + 6.70363i 0.144883 + 0.576957i
\(136\) 0 0
\(137\) 6.44608 + 22.0939i 0.550725 + 1.88761i 0.450834 + 0.892608i \(0.351127\pi\)
0.0998916 + 0.994998i \(0.468150\pi\)
\(138\) 0 0
\(139\) −5.24107 + 2.31764i −0.444541 + 0.196580i −0.614575 0.788858i \(-0.710673\pi\)
0.170034 + 0.985438i \(0.445612\pi\)
\(140\) 0 0
\(141\) −1.73085 + 4.12334i −0.145764 + 0.347248i
\(142\) 0 0
\(143\) 0.627830 + 0.871048i 0.0525018 + 0.0728407i
\(144\) 0 0
\(145\) 14.5145 7.78024i 1.20536 0.646114i
\(146\) 0 0
\(147\) 3.44946 + 20.0557i 0.284506 + 1.65417i
\(148\) 0 0
\(149\) −6.97952 4.45161i −0.571785 0.364690i 0.219991 0.975502i \(-0.429397\pi\)
−0.791776 + 0.610812i \(0.790843\pi\)
\(150\) 0 0
\(151\) −3.88296 6.92584i −0.315991 0.563617i 0.667492 0.744617i \(-0.267368\pi\)
−0.983483 + 0.181000i \(0.942067\pi\)
\(152\) 0 0
\(153\) −2.15639 + 1.74846i −0.174334 + 0.141355i
\(154\) 0 0
\(155\) 5.81701 + 4.71660i 0.467233 + 0.378846i
\(156\) 0 0
\(157\) −4.94755 10.6392i −0.394857 0.849104i −0.998649 0.0519621i \(-0.983453\pi\)
0.603792 0.797142i \(-0.293656\pi\)
\(158\) 0 0
\(159\) 10.4925 + 10.6930i 0.832112 + 0.848011i
\(160\) 0 0
\(161\) −27.1134 11.9898i −2.13683 0.944925i
\(162\) 0 0
\(163\) −7.89579 4.62529i −0.618446 0.362281i 0.162657 0.986683i \(-0.447993\pi\)
−0.781103 + 0.624402i \(0.785343\pi\)
\(164\) 0 0
\(165\) −1.65504 0.449067i −0.128845 0.0349598i
\(166\) 0 0
\(167\) −12.5320 + 3.15409i −0.969757 + 0.244071i
\(168\) 0 0
\(169\) 9.05001 + 2.45556i 0.696154 + 0.188889i
\(170\) 0 0
\(171\) 0.478760 + 0.280454i 0.0366117 + 0.0214469i
\(172\) 0 0
\(173\) 13.0565 + 5.77367i 0.992664 + 0.438964i 0.836025 0.548692i \(-0.184874\pi\)
0.156639 + 0.987656i \(0.449934\pi\)
\(174\) 0 0
\(175\) −7.39247 7.53371i −0.558818 0.569495i
\(176\) 0 0
\(177\) 2.48729 + 5.34868i 0.186956 + 0.402031i
\(178\) 0 0
\(179\) −8.03152 6.51219i −0.600304 0.486744i 0.280736 0.959785i \(-0.409421\pi\)
−0.881041 + 0.473041i \(0.843156\pi\)
\(180\) 0 0
\(181\) 6.85299 5.55660i 0.509379 0.413019i −0.340302 0.940316i \(-0.610529\pi\)
0.849681 + 0.527297i \(0.176794\pi\)
\(182\) 0 0
\(183\) −8.68516 15.4913i −0.642026 1.14515i
\(184\) 0 0
\(185\) 8.43579 + 5.38043i 0.620212 + 0.395577i
\(186\) 0 0
\(187\) 0.365488 + 2.12501i 0.0267271 + 0.155396i
\(188\) 0 0
\(189\) 16.2019 8.68473i 1.17851 0.631721i
\(190\) 0 0
\(191\) −2.72683 3.78319i −0.197306 0.273742i 0.700953 0.713207i \(-0.252758\pi\)
−0.898260 + 0.439465i \(0.855168\pi\)
\(192\) 0 0
\(193\) −1.90046 + 4.52741i −0.136798 + 0.325890i −0.975946 0.218014i \(-0.930042\pi\)
0.839148 + 0.543904i \(0.183054\pi\)
\(194\) 0 0
\(195\) 5.29172 2.34004i 0.378948 0.167574i
\(196\) 0 0
\(197\) 3.42029 + 11.7230i 0.243686 + 0.835230i 0.986222 + 0.165425i \(0.0528995\pi\)
−0.742537 + 0.669805i \(0.766378\pi\)
\(198\) 0 0
\(199\) −3.16532 12.6050i −0.224384 0.893547i −0.973049 0.230599i \(-0.925931\pi\)
0.748665 0.662948i \(-0.230695\pi\)
\(200\) 0 0
\(201\) −15.6809 + 13.7299i −1.10604 + 0.968431i
\(202\) 0 0
\(203\) −29.4714 32.4009i −2.06849 2.27410i
\(204\) 0 0
\(205\) −5.60215 3.00294i −0.391271 0.209734i
\(206\) 0 0
\(207\) 0.485758 5.11810i 0.0337625 0.355733i
\(208\) 0 0
\(209\) 0.371846 0.217824i 0.0257211 0.0150672i
\(210\) 0 0
\(211\) 12.6037 2.91260i 0.867678 0.200511i 0.232235 0.972660i \(-0.425396\pi\)
0.635442 + 0.772148i \(0.280818\pi\)
\(212\) 0 0
\(213\) −0.819682 + 14.4217i −0.0561637 + 0.988156i
\(214\) 0 0
\(215\) 4.40386 + 11.7148i 0.300340 + 0.798941i
\(216\) 0 0
\(217\) 8.39862 18.0604i 0.570135 1.22602i
\(218\) 0 0
\(219\) −4.92000 + 6.30824i −0.332463 + 0.426271i
\(220\) 0 0
\(221\) −5.47346 4.79247i −0.368185 0.322376i
\(222\) 0 0
\(223\) −12.6757 + 1.93392i −0.848827 + 0.129505i −0.560630 0.828066i \(-0.689441\pi\)
−0.288196 + 0.957571i \(0.593056\pi\)
\(224\) 0 0
\(225\) 0.834062 1.62931i 0.0556042 0.108621i
\(226\) 0 0
\(227\) 0.337455 + 17.8288i 0.0223977 + 1.18334i 0.817157 + 0.576415i \(0.195549\pi\)
−0.794760 + 0.606924i \(0.792403\pi\)
\(228\) 0 0
\(229\) 8.51009 + 0.645456i 0.562363 + 0.0426529i 0.353741 0.935343i \(-0.384909\pi\)
0.208622 + 0.977996i \(0.433102\pi\)
\(230\) 0 0
\(231\) −0.0863121 + 4.56014i −0.00567892 + 0.300035i
\(232\) 0 0
\(233\) 16.8200 5.96225i 1.10191 0.390600i 0.279879 0.960035i \(-0.409706\pi\)
0.822036 + 0.569436i \(0.192838\pi\)
\(234\) 0 0
\(235\) 3.27825 1.60062i 0.213849 0.104413i
\(236\) 0 0
\(237\) 19.6282 + 3.75968i 1.27499 + 0.244218i
\(238\) 0 0
\(239\) −6.92720 13.5320i −0.448084 0.875314i −0.999165 0.0408627i \(-0.986989\pi\)
0.551081 0.834452i \(-0.314215\pi\)
\(240\) 0 0
\(241\) −30.2885 + 1.14698i −1.95105 + 0.0738836i −0.983728 0.179662i \(-0.942500\pi\)
−0.967323 + 0.253546i \(0.918403\pi\)
\(242\) 0 0
\(243\) 5.37470 + 5.07789i 0.344787 + 0.325747i
\(244\) 0 0
\(245\) 8.66087 14.1633i 0.553323 0.904862i
\(246\) 0 0
\(247\) −0.511643 + 1.36103i −0.0325551 + 0.0866003i
\(248\) 0 0
\(249\) −6.83344 + 0.779300i −0.433052 + 0.0493861i
\(250\) 0 0
\(251\) 6.84278 1.85667i 0.431912 0.117192i −0.0392682 0.999229i \(-0.512503\pi\)
0.471181 + 0.882037i \(0.343828\pi\)
\(252\) 0 0
\(253\) −3.28288 2.27307i −0.206393 0.142907i
\(254\) 0 0
\(255\) 11.6109 + 0.439688i 0.727102 + 0.0275343i
\(256\) 0 0
\(257\) −1.30378 9.78393i −0.0813276 0.610305i −0.983762 0.179478i \(-0.942559\pi\)
0.902434 0.430827i \(-0.141778\pi\)
\(258\) 0 0
\(259\) 8.41464 25.2457i 0.522860 1.56869i
\(260\) 0 0
\(261\) 3.71446 6.62530i 0.229919 0.410095i
\(262\) 0 0
\(263\) 1.89454 + 19.9615i 0.116822 + 1.23088i 0.840912 + 0.541172i \(0.182019\pi\)
−0.724090 + 0.689706i \(0.757740\pi\)
\(264\) 0 0
\(265\) −0.693511 12.2018i −0.0426021 0.749550i
\(266\) 0 0
\(267\) 9.69207 11.5014i 0.593145 0.703872i
\(268\) 0 0
\(269\) −18.8524 + 12.0243i −1.14945 + 0.733132i −0.968169 0.250298i \(-0.919471\pi\)
−0.181284 + 0.983431i \(0.558025\pi\)
\(270\) 0 0
\(271\) 10.4286 7.82080i 0.633495 0.475080i −0.234192 0.972190i \(-0.575244\pi\)
0.867687 + 0.497111i \(0.165606\pi\)
\(272\) 0 0
\(273\) −9.46402 12.1344i −0.572789 0.734409i
\(274\) 0 0
\(275\) −0.787017 1.18391i −0.0474589 0.0713923i
\(276\) 0 0
\(277\) 25.1156 + 9.98800i 1.50905 + 0.600121i 0.970206 0.242283i \(-0.0778963\pi\)
0.538847 + 0.842404i \(0.318860\pi\)
\(278\) 0 0
\(279\) 3.43181 + 0.391371i 0.205457 + 0.0234308i
\(280\) 0 0
\(281\) 9.17793 + 6.88284i 0.547509 + 0.410596i 0.837503 0.546433i \(-0.184015\pi\)
−0.289994 + 0.957029i \(0.593653\pi\)
\(282\) 0 0
\(283\) −11.7235 + 12.8888i −0.696888 + 0.766161i −0.981288 0.192545i \(-0.938326\pi\)
0.284400 + 0.958706i \(0.408205\pi\)
\(284\) 0 0
\(285\) −0.734317 2.20311i −0.0434972 0.130501i
\(286\) 0 0
\(287\) −4.11733 + 16.3962i −0.243038 + 0.967835i
\(288\) 0 0
\(289\) 0.925277 + 2.20426i 0.0544281 + 0.129662i
\(290\) 0 0
\(291\) −13.0945 4.64164i −0.767610 0.272098i
\(292\) 0 0
\(293\) 7.05648 2.80622i 0.412244 0.163941i −0.154204 0.988039i \(-0.549281\pi\)
0.566448 + 0.824098i \(0.308317\pi\)
\(294\) 0 0
\(295\) 1.34779 4.61954i 0.0784713 0.268960i
\(296\) 0 0
\(297\) 2.36331 0.738326i 0.137133 0.0428420i
\(298\) 0 0
\(299\) 13.4339 1.01890i 0.776900 0.0589247i
\(300\) 0 0
\(301\) 27.3661 18.9483i 1.57735 1.09216i
\(302\) 0 0
\(303\) 11.8723 2.27407i 0.682043 0.130642i
\(304\) 0 0
\(305\) −2.99441 + 14.1755i −0.171460 + 0.811688i
\(306\) 0 0
\(307\) 25.7144 + 12.5551i 1.46760 + 0.716560i 0.987051 0.160408i \(-0.0512810\pi\)
0.480548 + 0.876968i \(0.340438\pi\)
\(308\) 0 0
\(309\) −4.12242 + 23.9684i −0.234516 + 1.36352i
\(310\) 0 0
\(311\) 4.62163 + 21.8788i 0.262069 + 1.24063i 0.887667 + 0.460486i \(0.152325\pi\)
−0.625598 + 0.780146i \(0.715145\pi\)
\(312\) 0 0
\(313\) −11.4909 + 11.7104i −0.649502 + 0.661912i −0.957151 0.289588i \(-0.906482\pi\)
0.307649 + 0.951500i \(0.400458\pi\)
\(314\) 0 0
\(315\) 4.66760 + 1.07864i 0.262990 + 0.0607742i
\(316\) 0 0
\(317\) −10.7372 + 16.1520i −0.603062 + 0.907184i −0.999943 0.0106857i \(-0.996599\pi\)
0.396881 + 0.917870i \(0.370093\pi\)
\(318\) 0 0
\(319\) −3.07762 5.03290i −0.172314 0.281789i
\(320\) 0 0
\(321\) 2.97349 22.3139i 0.165964 1.24544i
\(322\) 0 0
\(323\) −2.12245 + 2.00524i −0.118096 + 0.111575i
\(324\) 0 0
\(325\) 4.57836 + 1.43033i 0.253962 + 0.0793406i
\(326\) 0 0
\(327\) 17.7843 24.6739i 0.983475 1.36447i
\(328\) 0 0
\(329\) −6.25238 7.41956i −0.344705 0.409053i
\(330\) 0 0
\(331\) −25.2865 3.85795i −1.38987 0.212052i −0.587667 0.809103i \(-0.699953\pi\)
−0.802203 + 0.597051i \(0.796339\pi\)
\(332\) 0 0
\(333\) 4.61479 0.252889
\(334\) 0 0
\(335\) 17.0029 0.928970
\(336\) 0 0
\(337\) −18.3825 2.80460i −1.00136 0.152777i −0.370629 0.928781i \(-0.620858\pi\)
−0.630727 + 0.776005i \(0.717243\pi\)
\(338\) 0 0
\(339\) −9.24203 10.9673i −0.501958 0.595662i
\(340\) 0 0
\(341\) 1.56863 2.17631i 0.0849461 0.117854i
\(342\) 0 0
\(343\) −14.1606 4.42394i −0.764602 0.238870i
\(344\) 0 0
\(345\) −15.6407 + 14.7770i −0.842067 + 0.795566i
\(346\) 0 0
\(347\) −0.0857410 + 0.643425i −0.00460282 + 0.0345408i −0.993389 0.114799i \(-0.963378\pi\)
0.988786 + 0.149340i \(0.0477149\pi\)
\(348\) 0 0
\(349\) 8.50292 + 13.9050i 0.455151 + 0.744319i 0.995257 0.0972777i \(-0.0310135\pi\)
−0.540106 + 0.841597i \(0.681616\pi\)
\(350\) 0 0
\(351\) −4.62473 + 6.95697i −0.246850 + 0.371336i
\(352\) 0 0
\(353\) −4.15508 0.960196i −0.221153 0.0511061i 0.113125 0.993581i \(-0.463914\pi\)
−0.334278 + 0.942475i \(0.608492\pi\)
\(354\) 0 0
\(355\) 8.25338 8.41107i 0.438044 0.446413i
\(356\) 0 0
\(357\) −6.38691 30.2356i −0.338031 1.60024i
\(358\) 0 0
\(359\) 2.90482 16.8891i 0.153310 0.891371i −0.802340 0.596867i \(-0.796412\pi\)
0.955650 0.294504i \(-0.0951544\pi\)
\(360\) 0 0
\(361\) −16.5492 8.08019i −0.871009 0.425273i
\(362\) 0 0
\(363\) 4.26164 20.1745i 0.223678 1.05889i
\(364\) 0 0
\(365\) 6.40983 1.22777i 0.335506 0.0642644i
\(366\) 0 0
\(367\) 7.24387 5.01566i 0.378127 0.261816i −0.364943 0.931030i \(-0.618911\pi\)
0.743069 + 0.669214i \(0.233369\pi\)
\(368\) 0 0
\(369\) −2.92324 + 0.221716i −0.152178 + 0.0115421i
\(370\) 0 0
\(371\) −31.0258 + 9.69281i −1.61078 + 0.503226i
\(372\) 0 0
\(373\) −5.18296 + 17.7645i −0.268363 + 0.919813i 0.708457 + 0.705754i \(0.249391\pi\)
−0.976821 + 0.214059i \(0.931331\pi\)
\(374\) 0 0
\(375\) −21.2422 + 8.44761i −1.09694 + 0.436233i
\(376\) 0 0
\(377\) 18.7605 + 6.65011i 0.966216 + 0.342498i
\(378\) 0 0
\(379\) 2.09480 + 4.99038i 0.107603 + 0.256339i 0.966909 0.255123i \(-0.0821161\pi\)
−0.859306 + 0.511462i \(0.829104\pi\)
\(380\) 0 0
\(381\) 5.86800 23.3677i 0.300627 1.19716i
\(382\) 0 0
\(383\) 4.99573 + 14.9883i 0.255270 + 0.765864i 0.995607 + 0.0936286i \(0.0298466\pi\)
−0.740337 + 0.672236i \(0.765334\pi\)
\(384\) 0 0
\(385\) 2.50362 2.75249i 0.127596 0.140280i
\(386\) 0 0
\(387\) 4.61797 + 3.46317i 0.234745 + 0.176043i
\(388\) 0 0
\(389\) −12.4991 1.42542i −0.633727 0.0722716i −0.209473 0.977815i \(-0.567175\pi\)
−0.424255 + 0.905543i \(0.639464\pi\)
\(390\) 0 0
\(391\) 25.1397 + 9.99756i 1.27137 + 0.505599i
\(392\) 0 0
\(393\) −5.50157 8.27599i −0.277517 0.417469i
\(394\) 0 0
\(395\) −10.0267 12.8559i −0.504499 0.646850i
\(396\) 0 0
\(397\) 30.1017 22.5743i 1.51076 1.13297i 0.557758 0.830004i \(-0.311662\pi\)
0.953002 0.302965i \(-0.0979767\pi\)
\(398\) 0 0
\(399\) −5.20734 + 3.32129i −0.260693 + 0.166272i
\(400\) 0 0
\(401\) −2.79696 + 3.31908i −0.139673 + 0.165747i −0.830024 0.557728i \(-0.811673\pi\)
0.690350 + 0.723475i \(0.257456\pi\)
\(402\) 0 0
\(403\) 0.513629 + 9.03689i 0.0255857 + 0.450160i
\(404\) 0 0
\(405\) −1.58486 16.6986i −0.0787524 0.829761i
\(406\) 0 0
\(407\) 1.75281 3.12640i 0.0868838 0.154970i
\(408\) 0 0
\(409\) −2.39010 + 7.17081i −0.118183 + 0.354574i −0.991069 0.133350i \(-0.957426\pi\)
0.872886 + 0.487924i \(0.162246\pi\)
\(410\) 0 0
\(411\) −5.86841 44.0382i −0.289467 2.17224i
\(412\) 0 0
\(413\) −12.7893 0.484314i −0.629322 0.0238315i
\(414\) 0 0
\(415\) 4.61296 + 3.19402i 0.226441 + 0.156788i
\(416\) 0 0
\(417\) 10.6762 2.89681i 0.522817 0.141857i
\(418\) 0 0
\(419\) −7.34723 + 0.837894i −0.358936 + 0.0409338i −0.290912 0.956750i \(-0.593959\pi\)
−0.0680240 + 0.997684i \(0.521669\pi\)
\(420\) 0 0
\(421\) −0.842178 + 2.24029i −0.0410452 + 0.109185i −0.954974 0.296689i \(-0.904117\pi\)
0.913929 + 0.405875i \(0.133033\pi\)
\(422\) 0 0
\(423\) 0.877798 1.43548i 0.0426800 0.0697956i
\(424\) 0 0
\(425\) 7.00162 + 6.61497i 0.339629 + 0.320873i
\(426\) 0 0
\(427\) 38.5060 1.45817i 1.86344 0.0705657i
\(428\) 0 0
\(429\) −0.944477 1.84500i −0.0455998 0.0890774i
\(430\) 0 0
\(431\) −30.3581 5.81495i −1.46230 0.280096i −0.605542 0.795814i \(-0.707043\pi\)
−0.856759 + 0.515718i \(0.827525\pi\)
\(432\) 0 0
\(433\) 11.9300 5.82488i 0.573321 0.279926i −0.129165 0.991623i \(-0.541230\pi\)
0.702486 + 0.711697i \(0.252073\pi\)
\(434\) 0 0
\(435\) −29.9630 + 10.6211i −1.43661 + 0.509242i
\(436\) 0 0
\(437\) 0.102328 5.40628i 0.00489499 0.258618i
\(438\) 0 0
\(439\) 22.2484 + 1.68745i 1.06186 + 0.0805375i 0.594945 0.803767i \(-0.297174\pi\)
0.466911 + 0.884304i \(0.345367\pi\)
\(440\) 0 0
\(441\) −0.144902 7.65562i −0.00690009 0.364553i
\(442\) 0 0
\(443\) 5.00270 9.77258i 0.237685 0.464309i −0.740496 0.672060i \(-0.765410\pi\)
0.978182 + 0.207751i \(0.0666144\pi\)
\(444\) 0 0
\(445\) −12.1296 + 1.85061i −0.574998 + 0.0877272i
\(446\) 0 0
\(447\) 12.0229 + 10.5270i 0.568662 + 0.497910i
\(448\) 0 0
\(449\) −0.600226 + 0.769588i −0.0283264 + 0.0363191i −0.802482 0.596676i \(-0.796488\pi\)
0.774156 + 0.632995i \(0.218175\pi\)
\(450\) 0 0
\(451\) −0.960113 + 2.06463i −0.0452099 + 0.0972198i
\(452\) 0 0
\(453\) 5.39337 + 14.3470i 0.253403 + 0.674081i
\(454\) 0 0
\(455\) −0.712379 + 12.5338i −0.0333968 + 0.587591i
\(456\) 0 0
\(457\) 19.8696 4.59167i 0.929463 0.214789i 0.266839 0.963741i \(-0.414021\pi\)
0.662624 + 0.748952i \(0.269443\pi\)
\(458\) 0 0
\(459\) −14.4751 + 8.47942i −0.675641 + 0.395786i
\(460\) 0 0
\(461\) 2.60878 27.4870i 0.121503 1.28020i −0.701709 0.712463i \(-0.747580\pi\)
0.823213 0.567733i \(-0.192180\pi\)
\(462\) 0 0
\(463\) 6.72587 + 3.60529i 0.312578 + 0.167552i 0.621241 0.783619i \(-0.286629\pi\)
−0.308663 + 0.951171i \(0.599882\pi\)
\(464\) 0 0
\(465\) −9.72730 10.6942i −0.451093 0.495933i
\(466\) 0 0
\(467\) −15.7101 + 13.7554i −0.726975 + 0.636526i −0.940257 0.340464i \(-0.889416\pi\)
0.213283 + 0.976991i \(0.431584\pi\)
\(468\) 0 0
\(469\) −11.0139 43.8598i −0.508574 2.02526i
\(470\) 0 0
\(471\) 6.34376 + 21.7432i 0.292305 + 1.00187i
\(472\) 0 0
\(473\) 4.10023 1.81316i 0.188529 0.0833690i
\(474\) 0 0
\(475\) 0.745127 1.77509i 0.0341888 0.0814469i
\(476\) 0 0
\(477\) −3.29596 4.57279i −0.150911 0.209374i
\(478\) 0 0
\(479\) 23.5133 12.6039i 1.07435 0.575888i 0.162626 0.986688i \(-0.448004\pi\)
0.911725 + 0.410800i \(0.134751\pi\)
\(480\) 0 0
\(481\) 2.04986 + 11.9182i 0.0934657 + 0.543425i
\(482\) 0 0
\(483\) 48.2493 + 30.7739i 2.19542 + 1.40026i
\(484\) 0 0
\(485\) 5.54253 + 9.88592i 0.251673 + 0.448897i
\(486\) 0 0
\(487\) 29.1360 23.6243i 1.32028 1.07052i 0.328238 0.944595i \(-0.393545\pi\)
0.992040 0.125925i \(-0.0401899\pi\)
\(488\) 0 0
\(489\) 13.7208 + 11.1252i 0.620476 + 0.503100i
\(490\) 0 0
\(491\) −7.26115 15.6144i −0.327691 0.704670i 0.671653 0.740866i \(-0.265584\pi\)
−0.999345 + 0.0361958i \(0.988476\pi\)
\(492\) 0 0
\(493\) 27.9949 + 28.5298i 1.26083 + 1.28492i
\(494\) 0 0
\(495\) 0.590121 + 0.260957i 0.0265240 + 0.0117291i
\(496\) 0 0
\(497\) −27.0429 15.8415i −1.21304 0.710590i
\(498\) 0 0
\(499\) 29.7943 + 8.08417i 1.33378 + 0.361897i 0.856178 0.516681i \(-0.172833\pi\)
0.477598 + 0.878578i \(0.341508\pi\)
\(500\) 0 0
\(501\) 24.8330 2.37026i 1.10946 0.105895i
\(502\) 0 0
\(503\) −19.6169 5.32270i −0.874672 0.237327i −0.203901 0.978991i \(-0.565362\pi\)
−0.670771 + 0.741664i \(0.734037\pi\)
\(504\) 0 0
\(505\) −8.50892 4.98446i −0.378642 0.221806i
\(506\) 0 0
\(507\) −16.5551 7.32080i −0.735237 0.325128i
\(508\) 0 0
\(509\) 16.6988 + 17.0179i 0.740163 + 0.754305i 0.976067 0.217472i \(-0.0697810\pi\)
−0.235904 + 0.971776i \(0.575805\pi\)
\(510\) 0 0
\(511\) −7.31913 15.7391i −0.323779 0.696257i
\(512\) 0 0
\(513\) 2.60436 + 2.11169i 0.114985 + 0.0932333i
\(514\) 0 0
\(515\) 15.4110 12.4957i 0.679089 0.550625i
\(516\) 0 0
\(517\) −0.639094 1.13992i −0.0281073 0.0501335i
\(518\) 0 0
\(519\) −23.2345 14.8192i −1.01988 0.650489i
\(520\) 0 0
\(521\) 1.44572 + 8.40568i 0.0633383 + 0.368259i 0.999845 + 0.0176094i \(0.00560554\pi\)
−0.936507 + 0.350650i \(0.885961\pi\)
\(522\) 0 0
\(523\) −11.0384 + 5.91695i −0.482676 + 0.258730i −0.695721 0.718312i \(-0.744915\pi\)
0.213045 + 0.977042i \(0.431662\pi\)
\(524\) 0 0
\(525\) 11.9135 + 16.5288i 0.519949 + 0.721375i
\(526\) 0 0
\(527\) −7.03530 + 16.7600i −0.306463 + 0.730077i
\(528\) 0 0
\(529\) −24.7863 + 10.9607i −1.07767 + 0.476553i
\(530\) 0 0
\(531\) −0.621631 2.13063i −0.0269765 0.0924616i
\(532\) 0 0
\(533\) −1.87109 7.45112i −0.0810460 0.322744i
\(534\) 0 0
\(535\) −13.8167 + 12.0976i −0.597347 + 0.523026i
\(536\) 0 0
\(537\) 13.4304 + 14.7655i 0.579567 + 0.637178i
\(538\) 0 0
\(539\) −5.24152 2.80963i −0.225768 0.121019i
\(540\) 0 0
\(541\) 2.92832 30.8537i 0.125898 1.32650i −0.679458 0.733714i \(-0.737785\pi\)
0.805357 0.592791i \(-0.201974\pi\)
\(542\) 0 0
\(543\) −14.6953 + 8.60837i −0.630634 + 0.369420i
\(544\) 0 0
\(545\) −24.1753 + 5.58667i −1.03556 + 0.239307i
\(546\) 0 0
\(547\) −1.61929 + 28.4901i −0.0692358 + 1.21815i 0.756462 + 0.654037i \(0.226926\pi\)
−0.825698 + 0.564112i \(0.809218\pi\)
\(548\) 0 0
\(549\) 2.35139 + 6.25497i 0.100355 + 0.266956i
\(550\) 0 0
\(551\) 3.36857 7.24379i 0.143506 0.308596i
\(552\) 0 0
\(553\) −26.6673 + 34.1919i −1.13401 + 1.45399i
\(554\) 0 0
\(555\) −14.5314 12.7234i −0.616824 0.540080i
\(556\) 0 0
\(557\) 10.6225 1.62067i 0.450089 0.0686699i 0.0781805 0.996939i \(-0.475089\pi\)
0.371909 + 0.928269i \(0.378703\pi\)
\(558\) 0 0
\(559\) −6.89277 + 13.4648i −0.291533 + 0.569499i
\(560\) 0 0
\(561\) −0.0787675 4.16153i −0.00332557 0.175700i
\(562\) 0 0
\(563\) −34.5114 2.61755i −1.45448 0.110317i −0.675500 0.737360i \(-0.736072\pi\)
−0.778984 + 0.627044i \(0.784265\pi\)
\(564\) 0 0
\(565\) −0.221416 + 11.6981i −0.00931505 + 0.492143i
\(566\) 0 0
\(567\) −42.0481 + 14.9050i −1.76586 + 0.625949i
\(568\) 0 0
\(569\) 6.11784 2.98706i 0.256473 0.125224i −0.306022 0.952024i \(-0.598998\pi\)
0.562495 + 0.826801i \(0.309841\pi\)
\(570\) 0 0
\(571\) −43.1947 8.27371i −1.80764 0.346244i −0.830201 0.557464i \(-0.811775\pi\)
−0.977439 + 0.211219i \(0.932257\pi\)
\(572\) 0 0
\(573\) 4.10211 + 8.01332i 0.171368 + 0.334761i
\(574\) 0 0
\(575\) −17.8249 + 0.675004i −0.743349 + 0.0281496i
\(576\) 0 0
\(577\) −22.1067 20.8859i −0.920312 0.869490i 0.0714681 0.997443i \(-0.477232\pi\)
−0.991780 + 0.127953i \(0.959159\pi\)
\(578\) 0 0
\(579\) 4.94476 8.08628i 0.205497 0.336054i
\(580\) 0 0
\(581\) 5.25100 13.9683i 0.217848 0.579502i
\(582\) 0 0
\(583\) −4.34983 + 0.496064i −0.180152 + 0.0205449i
\(584\) 0 0
\(585\) −2.10109 + 0.570095i −0.0868694 + 0.0235705i
\(586\) 0 0
\(587\) 2.41319 + 1.67089i 0.0996029 + 0.0689652i 0.618018 0.786164i \(-0.287936\pi\)
−0.518415 + 0.855129i \(0.673478\pi\)
\(588\) 0 0
\(589\) 3.63027 + 0.137473i 0.149583 + 0.00566448i
\(590\) 0 0
\(591\) −3.11378 23.3667i −0.128084 0.961176i
\(592\) 0 0
\(593\) 0.175527 0.526619i 0.00720804 0.0216257i −0.945024 0.327000i \(-0.893962\pi\)
0.952232 + 0.305374i \(0.0987816\pi\)
\(594\) 0 0
\(595\) −12.3287 + 21.9900i −0.505426 + 0.901503i
\(596\) 0 0
\(597\) 2.37043 + 24.9756i 0.0970151 + 1.02218i
\(598\) 0 0
\(599\) −2.23606 39.3417i −0.0913628 1.60746i −0.637965 0.770065i \(-0.720224\pi\)
0.546602 0.837392i \(-0.315921\pi\)
\(600\) 0 0
\(601\) −14.5037 + 17.2112i −0.591619 + 0.702061i −0.975170 0.221459i \(-0.928918\pi\)
0.383550 + 0.923520i \(0.374701\pi\)
\(602\) 0 0
\(603\) 6.61178 4.21705i 0.269252 0.171732i
\(604\) 0 0
\(605\) −13.4576 + 10.0923i −0.547128 + 0.410310i
\(606\) 0 0
\(607\) 24.4204 + 31.3110i 0.991194 + 1.27087i 0.962499 + 0.271285i \(0.0874484\pi\)
0.0286951 + 0.999588i \(0.490865\pi\)
\(608\) 0 0
\(609\) 46.8064 + 70.4108i 1.89669 + 2.85319i
\(610\) 0 0
\(611\) 4.09722 + 1.62938i 0.165756 + 0.0659178i
\(612\) 0 0
\(613\) 28.4595 + 3.24558i 1.14947 + 0.131088i 0.667160 0.744915i \(-0.267510\pi\)
0.482307 + 0.876002i \(0.339799\pi\)
\(614\) 0 0
\(615\) 9.81621 + 7.36151i 0.395828 + 0.296845i
\(616\) 0 0
\(617\) 4.64585 5.10766i 0.187035 0.205627i −0.639062 0.769156i \(-0.720677\pi\)
0.826096 + 0.563529i \(0.190557\pi\)
\(618\) 0 0
\(619\) 1.97269 + 5.91848i 0.0792890 + 0.237884i 0.980849 0.194771i \(-0.0623963\pi\)
−0.901560 + 0.432655i \(0.857577\pi\)
\(620\) 0 0
\(621\) 7.56641 30.1312i 0.303630 1.20912i
\(622\) 0 0
\(623\) 12.6308 + 30.0900i 0.506043 + 1.20553i
\(624\) 0 0
\(625\) 5.70133 + 2.02097i 0.228053 + 0.0808388i
\(626\) 0 0
\(627\) −0.773007 + 0.307410i −0.0308709 + 0.0122768i
\(628\) 0 0
\(629\) −6.80178 + 23.3130i −0.271205 + 0.929552i
\(630\) 0 0
\(631\) −0.222181 + 0.0694119i −0.00884489 + 0.00276324i −0.302617 0.953112i \(-0.597860\pi\)
0.293772 + 0.955875i \(0.405089\pi\)
\(632\) 0 0
\(633\) −24.8996 + 1.88853i −0.989668 + 0.0750624i
\(634\) 0 0
\(635\) −16.1595 + 11.1889i −0.641272 + 0.444018i
\(636\) 0 0
\(637\) 19.7072 3.77481i 0.780826 0.149563i
\(638\) 0 0
\(639\) 1.12331 5.31773i 0.0444374 0.210366i
\(640\) 0 0
\(641\) −2.02441 0.988425i −0.0799594 0.0390405i 0.398335 0.917240i \(-0.369588\pi\)
−0.478294 + 0.878200i \(0.658745\pi\)
\(642\) 0 0
\(643\) 0.551951 3.20914i 0.0217668 0.126556i −0.972612 0.232433i \(-0.925331\pi\)
0.994379 + 0.105877i \(0.0337650\pi\)
\(644\) 0 0
\(645\) −4.99310 23.6373i −0.196603 0.930718i
\(646\) 0 0
\(647\) −30.7614 + 31.3492i −1.20936 + 1.23246i −0.244511 + 0.969647i \(0.578627\pi\)
−0.964846 + 0.262817i \(0.915348\pi\)
\(648\) 0 0
\(649\) −1.67956 0.388129i −0.0659285 0.0152354i
\(650\) 0 0
\(651\) −21.2852 + 32.0193i −0.834233 + 1.25493i
\(652\) 0 0
\(653\) 12.3835 + 20.2510i 0.484602 + 0.792481i 0.997835 0.0657681i \(-0.0209498\pi\)
−0.513233 + 0.858250i \(0.671552\pi\)
\(654\) 0 0
\(655\) −1.07087 + 8.03612i −0.0418424 + 0.313997i
\(656\) 0 0
\(657\) 2.18802 2.06719i 0.0853627 0.0806488i
\(658\) 0 0
\(659\) 13.3448 + 4.16907i 0.519840 + 0.162404i 0.546849 0.837231i \(-0.315827\pi\)
−0.0270089 + 0.999635i \(0.508598\pi\)
\(660\) 0 0
\(661\) −7.00629 + 9.72049i −0.272513 + 0.378083i −0.925159 0.379580i \(-0.876069\pi\)
0.652646 + 0.757663i \(0.273659\pi\)
\(662\) 0 0
\(663\) 9.04963 + 10.7390i 0.351458 + 0.417068i
\(664\) 0 0
\(665\) 4.98098 + 0.759947i 0.193154 + 0.0294695i
\(666\) 0 0
\(667\) −74.0206 −2.86609
\(668\) 0 0
\(669\) 24.7519 0.956963
\(670\) 0 0
\(671\) 5.13070 + 0.782789i 0.198068 + 0.0302192i
\(672\) 0 0
\(673\) −25.5979 30.3764i −0.986725 1.17092i −0.985284 0.170925i \(-0.945324\pi\)
−0.00144148 0.999999i \(-0.500459\pi\)
\(674\) 0 0
\(675\) 6.46738 8.97281i 0.248929 0.345363i
\(676\) 0 0
\(677\) 26.0426 + 8.13600i 1.00090 + 0.312692i 0.754374 0.656445i \(-0.227941\pi\)
0.246524 + 0.969137i \(0.420712\pi\)
\(678\) 0 0
\(679\) 21.9109 20.7009i 0.840863 0.794428i
\(680\) 0 0
\(681\) 4.54683 34.1207i 0.174235 1.30751i
\(682\) 0 0
\(683\) 8.59312 + 14.0525i 0.328806 + 0.537705i 0.974068 0.226257i \(-0.0726490\pi\)
−0.645261 + 0.763962i \(0.723251\pi\)
\(684\) 0 0
\(685\) −20.0645 + 30.1830i −0.766626 + 1.15323i
\(686\) 0 0
\(687\) −16.0518 3.70940i −0.612413 0.141522i
\(688\) 0 0
\(689\) 10.3457 10.5434i 0.394141 0.401671i
\(690\) 0 0
\(691\) 2.78739 + 13.1955i 0.106037 + 0.501980i 0.998687 + 0.0512289i \(0.0163138\pi\)
−0.892649 + 0.450751i \(0.851156\pi\)
\(692\) 0 0
\(693\) 0.290890 1.69128i 0.0110500 0.0642464i
\(694\) 0 0
\(695\) −8.10950 3.95949i −0.307611 0.150192i
\(696\) 0 0
\(697\) 3.18852 15.0944i 0.120774 0.571742i
\(698\) 0 0
\(699\) −33.8333 + 6.48059i −1.27969 + 0.245118i
\(700\) 0 0
\(701\) 19.3153 13.3739i 0.729528 0.505126i −0.145404 0.989372i \(-0.546448\pi\)
0.874932 + 0.484246i \(0.160906\pi\)
\(702\) 0 0
\(703\) 4.83980 0.367079i 0.182536 0.0138447i
\(704\) 0 0
\(705\) −6.72185 + 2.09998i −0.253160 + 0.0790899i
\(706\) 0 0
\(707\) −7.34586 + 25.1779i −0.276269 + 0.946911i
\(708\) 0 0
\(709\) −33.3436 + 13.2601i −1.25224 + 0.497993i −0.899169 0.437602i \(-0.855828\pi\)
−0.353075 + 0.935595i \(0.614864\pi\)
\(710\) 0 0
\(711\) −7.08750 2.51233i −0.265802 0.0942197i
\(712\) 0 0
\(713\) −13.0284 31.0373i −0.487919 1.16236i
\(714\) 0 0
\(715\) −0.411822 + 1.63997i −0.0154013 + 0.0613315i
\(716\) 0 0
\(717\) 9.27929 + 27.8398i 0.346541 + 1.03970i
\(718\) 0 0
\(719\) −12.9380 + 14.2241i −0.482506 + 0.530469i −0.931828 0.362901i \(-0.881786\pi\)
0.449322 + 0.893370i \(0.351666\pi\)
\(720\) 0 0
\(721\) −42.2157 31.6590i −1.57220 1.17904i
\(722\) 0 0
\(723\) 58.1330 + 6.62961i 2.16199 + 0.246558i
\(724\) 0 0
\(725\) −24.4882 9.73847i −0.909468 0.361678i
\(726\) 0 0
\(727\) −10.0099 15.0579i −0.371247 0.558466i 0.598949 0.800787i \(-0.295585\pi\)
−0.970196 + 0.242321i \(0.922091\pi\)
\(728\) 0 0
\(729\) 10.8738 + 13.9420i 0.402732 + 0.516369i
\(730\) 0 0
\(731\) −24.3017 + 18.2247i −0.898833 + 0.674065i
\(732\) 0 0
\(733\) 37.3406 23.8162i 1.37921 0.879671i 0.380230 0.924892i \(-0.375845\pi\)
0.998977 + 0.0452206i \(0.0143991\pi\)
\(734\) 0 0
\(735\) −20.6510 + 24.5061i −0.761725 + 0.903921i
\(736\) 0 0
\(737\) −0.345628 6.08105i −0.0127314 0.223998i
\(738\) 0 0
\(739\) 1.49529 + 15.7548i 0.0550050 + 0.579550i 0.979922 + 0.199381i \(0.0638932\pi\)
−0.924917 + 0.380169i \(0.875866\pi\)
\(740\) 0 0
\(741\) 1.37262 2.44827i 0.0504245 0.0899395i
\(742\) 0 0
\(743\) 14.6665 44.0027i 0.538063 1.61430i −0.229486 0.973312i \(-0.573704\pi\)
0.767549 0.640991i \(-0.221476\pi\)
\(744\) 0 0
\(745\) −1.72199 12.9223i −0.0630889 0.473437i
\(746\) 0 0
\(747\) 2.58597 + 0.0979272i 0.0946159 + 0.00358297i
\(748\) 0 0
\(749\) 40.1563 + 27.8043i 1.46728 + 1.01595i
\(750\) 0 0
\(751\) 20.1781 5.47499i 0.736310 0.199785i 0.126092 0.992019i \(-0.459757\pi\)
0.610218 + 0.792233i \(0.291082\pi\)
\(752\) 0 0
\(753\) −13.5985 + 1.55081i −0.495559 + 0.0565146i
\(754\) 0 0
\(755\) 4.39987 11.7042i 0.160128 0.425958i
\(756\) 0 0
\(757\) −15.4440 + 25.2560i −0.561323 + 0.917944i 0.438493 + 0.898735i \(0.355512\pi\)
−0.999815 + 0.0192092i \(0.993885\pi\)
\(758\) 0 0
\(759\) 5.60288 + 5.29347i 0.203371 + 0.192141i
\(760\) 0 0
\(761\) 47.7811 1.80940i 1.73206 0.0655909i 0.847153 0.531350i \(-0.178315\pi\)
0.884912 + 0.465759i \(0.154219\pi\)
\(762\) 0 0
\(763\) 30.0709 + 58.7424i 1.08864 + 2.12662i
\(764\) 0 0
\(765\) −4.29380 0.822456i −0.155243 0.0297360i
\(766\) 0 0
\(767\) 5.22648 2.55185i 0.188717 0.0921418i
\(768\) 0 0
\(769\) −7.37397 + 2.61388i −0.265912 + 0.0942588i −0.463719 0.885982i \(-0.653485\pi\)
0.197807 + 0.980241i \(0.436618\pi\)
\(770\) 0 0
\(771\) −0.360572 + 19.0501i −0.0129857 + 0.686074i
\(772\) 0 0
\(773\) −7.23974 0.549105i −0.260395 0.0197499i −0.0552163 0.998474i \(-0.517585\pi\)
−0.205179 + 0.978724i \(0.565778\pi\)
\(774\) 0 0
\(775\) −0.226792 11.9821i −0.00814660 0.430410i
\(776\) 0 0
\(777\) −23.4077 + 45.7261i −0.839748 + 1.64042i
\(778\) 0 0
\(779\) −3.04813 + 0.465052i −0.109211 + 0.0166622i
\(780\) 0 0
\(781\) −3.17596 2.78082i −0.113645 0.0995055i
\(782\) 0 0
\(783\) 28.2273 36.1920i 1.00876 1.29340i
\(784\) 0 0
\(785\) 7.79130 16.7545i 0.278084 0.597993i
\(786\) 0 0
\(787\) −4.92098 13.0904i −0.175414 0.466622i 0.818795 0.574086i \(-0.194643\pi\)
−0.994209 + 0.107464i \(0.965727\pi\)
\(788\) 0 0
\(789\) 2.19639 38.6438i 0.0781936 1.37576i
\(790\) 0 0
\(791\) 30.3192 7.00645i 1.07803 0.249121i
\(792\) 0 0
\(793\) −15.1097 + 8.85116i −0.536562 + 0.314314i
\(794\) 0 0
\(795\) −2.22909 + 23.4864i −0.0790577 + 0.832978i
\(796\) 0 0