Properties

Label 432.2.be.b.335.6
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.6
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.b.383.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48063 - 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(-0.862991 - 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +O(q^{10})\) \(q+(1.48063 - 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(-0.862991 - 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +(0.855132 - 0.311243i) q^{11} +(0.662306 - 0.555741i) q^{13} +(-0.353454 - 1.77571i) q^{15} +(4.52256 - 2.61110i) q^{17} +(-3.63632 - 2.09943i) q^{19} +(-1.41453 + 0.550297i) q^{21} +(0.356585 + 2.02229i) q^{23} +(2.99317 + 2.51157i) q^{25} +(-0.341901 - 5.18489i) q^{27} +(0.526265 - 0.627178i) q^{29} +(-8.52362 + 1.50294i) q^{31} +(0.986410 - 1.22937i) q^{33} +(-0.458008 + 0.793293i) q^{35} +(1.44045 + 2.49493i) q^{37} +(0.481166 - 1.41809i) q^{39} +(5.04026 + 6.00675i) q^{41} +(0.0722797 + 0.198587i) q^{43} +(-2.11923 - 2.31151i) q^{45} +(-1.30305 + 7.38995i) q^{47} +(-5.85625 - 2.13150i) q^{49} +(4.34955 - 7.93067i) q^{51} -8.58900i q^{53} -0.951252i q^{55} +(-7.27088 + 0.159613i) q^{57} +(11.8016 + 4.29544i) q^{59} +(-1.82666 + 10.3595i) q^{61} +(-1.59983 + 2.08608i) q^{63} +(-0.309104 - 0.849256i) q^{65} +(-1.37313 - 1.63643i) q^{67} +(2.34548 + 2.67380i) q^{69} +(1.76808 + 3.06241i) q^{71} +(-0.656039 + 1.13629i) q^{73} +(6.68903 + 1.02863i) q^{75} +(-0.785333 + 0.138475i) q^{77} +(-0.814135 + 0.970249i) q^{79} +(-5.16609 - 7.36964i) q^{81} +(9.32579 + 7.82526i) q^{83} +(-0.947921 - 5.37593i) q^{85} +(0.215536 - 1.40159i) q^{87} +(4.27725 + 2.46947i) q^{89} +(-0.656130 + 0.378817i) q^{91} +(-11.2696 + 9.88581i) q^{93} +(-3.36228 + 2.82128i) q^{95} +(-13.6037 + 4.95134i) q^{97} +(0.355626 - 2.70678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

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
\(3\) 1.48063 0.898737i 0.854843 0.518886i
\(4\) 0 0
\(5\) 0.357520 0.982277i 0.159888 0.439288i −0.833718 0.552190i \(-0.813792\pi\)
0.993606 + 0.112902i \(0.0360146\pi\)
\(6\) 0 0
\(7\) −0.862991 0.152169i −0.326180 0.0575143i 0.00816043 0.999967i \(-0.497402\pi\)
−0.334340 + 0.942452i \(0.608514\pi\)
\(8\) 0 0
\(9\) 1.38454 2.66140i 0.461514 0.887133i
\(10\) 0 0
\(11\) 0.855132 0.311243i 0.257832 0.0938432i −0.209870 0.977729i \(-0.567304\pi\)
0.467702 + 0.883886i \(0.345082\pi\)
\(12\) 0 0
\(13\) 0.662306 0.555741i 0.183691 0.154135i −0.546306 0.837586i \(-0.683966\pi\)
0.729996 + 0.683451i \(0.239522\pi\)
\(14\) 0 0
\(15\) −0.353454 1.77571i −0.0912615 0.458486i
\(16\) 0 0
\(17\) 4.52256 2.61110i 1.09688 0.633285i 0.161481 0.986876i \(-0.448373\pi\)
0.935400 + 0.353591i \(0.115040\pi\)
\(18\) 0 0
\(19\) −3.63632 2.09943i −0.834228 0.481642i 0.0210701 0.999778i \(-0.493293\pi\)
−0.855298 + 0.518136i \(0.826626\pi\)
\(20\) 0 0
\(21\) −1.41453 + 0.550297i −0.308676 + 0.120085i
\(22\) 0 0
\(23\) 0.356585 + 2.02229i 0.0743531 + 0.421678i 0.999150 + 0.0412169i \(0.0131235\pi\)
−0.924797 + 0.380461i \(0.875765\pi\)
\(24\) 0 0
\(25\) 2.99317 + 2.51157i 0.598635 + 0.502314i
\(26\) 0 0
\(27\) −0.341901 5.18489i −0.0657990 0.997833i
\(28\) 0 0
\(29\) 0.526265 0.627178i 0.0977250 0.116464i −0.714965 0.699160i \(-0.753558\pi\)
0.812690 + 0.582696i \(0.198002\pi\)
\(30\) 0 0
\(31\) −8.52362 + 1.50294i −1.53089 + 0.269937i −0.874702 0.484662i \(-0.838943\pi\)
−0.656187 + 0.754599i \(0.727832\pi\)
\(32\) 0 0
\(33\) 0.986410 1.22937i 0.171712 0.214007i
\(34\) 0 0
\(35\) −0.458008 + 0.793293i −0.0774175 + 0.134091i
\(36\) 0 0
\(37\) 1.44045 + 2.49493i 0.236808 + 0.410163i 0.959797 0.280697i \(-0.0905655\pi\)
−0.722989 + 0.690860i \(0.757232\pi\)
\(38\) 0 0
\(39\) 0.481166 1.41809i 0.0770483 0.227076i
\(40\) 0 0
\(41\) 5.04026 + 6.00675i 0.787157 + 0.938097i 0.999233 0.0391564i \(-0.0124671\pi\)
−0.212077 + 0.977253i \(0.568023\pi\)
\(42\) 0 0
\(43\) 0.0722797 + 0.198587i 0.0110226 + 0.0302842i 0.945082 0.326834i \(-0.105982\pi\)
−0.934059 + 0.357118i \(0.883759\pi\)
\(44\) 0 0
\(45\) −2.11923 2.31151i −0.315916 0.344579i
\(46\) 0 0
\(47\) −1.30305 + 7.38995i −0.190069 + 1.07794i 0.729198 + 0.684302i \(0.239893\pi\)
−0.919268 + 0.393633i \(0.871218\pi\)
\(48\) 0 0
\(49\) −5.85625 2.13150i −0.836607 0.304500i
\(50\) 0 0
\(51\) 4.34955 7.93067i 0.609059 1.11052i
\(52\) 0 0
\(53\) 8.58900i 1.17979i −0.807480 0.589895i \(-0.799169\pi\)
0.807480 0.589895i \(-0.200831\pi\)
\(54\) 0 0
\(55\) 0.951252i 0.128267i
\(56\) 0 0
\(57\) −7.27088 + 0.159613i −0.963052 + 0.0211413i
\(58\) 0 0
\(59\) 11.8016 + 4.29544i 1.53644 + 0.559218i 0.965188 0.261556i \(-0.0842358\pi\)
0.571252 + 0.820775i \(0.306458\pi\)
\(60\) 0 0
\(61\) −1.82666 + 10.3595i −0.233880 + 1.32640i 0.611079 + 0.791570i \(0.290736\pi\)
−0.844959 + 0.534831i \(0.820375\pi\)
\(62\) 0 0
\(63\) −1.59983 + 2.08608i −0.201560 + 0.262821i
\(64\) 0 0
\(65\) −0.309104 0.849256i −0.0383396 0.105337i
\(66\) 0 0
\(67\) −1.37313 1.63643i −0.167755 0.199922i 0.675617 0.737253i \(-0.263877\pi\)
−0.843372 + 0.537331i \(0.819433\pi\)
\(68\) 0 0
\(69\) 2.34548 + 2.67380i 0.282363 + 0.321887i
\(70\) 0 0
\(71\) 1.76808 + 3.06241i 0.209833 + 0.363441i 0.951662 0.307148i \(-0.0993747\pi\)
−0.741829 + 0.670589i \(0.766041\pi\)
\(72\) 0 0
\(73\) −0.656039 + 1.13629i −0.0767835 + 0.132993i −0.901860 0.432027i \(-0.857798\pi\)
0.825077 + 0.565020i \(0.191132\pi\)
\(74\) 0 0
\(75\) 6.68903 + 1.02863i 0.772383 + 0.118777i
\(76\) 0 0
\(77\) −0.785333 + 0.138475i −0.0894970 + 0.0157807i
\(78\) 0 0
\(79\) −0.814135 + 0.970249i −0.0915974 + 0.109161i −0.809896 0.586573i \(-0.800477\pi\)
0.718299 + 0.695735i \(0.244921\pi\)
\(80\) 0 0
\(81\) −5.16609 7.36964i −0.574010 0.818849i
\(82\) 0 0
\(83\) 9.32579 + 7.82526i 1.02364 + 0.858934i 0.990080 0.140503i \(-0.0448718\pi\)
0.0335576 + 0.999437i \(0.489316\pi\)
\(84\) 0 0
\(85\) −0.947921 5.37593i −0.102816 0.583101i
\(86\) 0 0
\(87\) 0.215536 1.40159i 0.0231079 0.150267i
\(88\) 0 0
\(89\) 4.27725 + 2.46947i 0.453388 + 0.261764i 0.709260 0.704947i \(-0.249029\pi\)
−0.255872 + 0.966711i \(0.582363\pi\)
\(90\) 0 0
\(91\) −0.656130 + 0.378817i −0.0687812 + 0.0397108i
\(92\) 0 0
\(93\) −11.2696 + 9.88581i −1.16860 + 1.02511i
\(94\) 0 0
\(95\) −3.36228 + 2.82128i −0.344962 + 0.289458i
\(96\) 0 0
\(97\) −13.6037 + 4.95134i −1.38125 + 0.502733i −0.922556 0.385863i \(-0.873904\pi\)
−0.458691 + 0.888596i \(0.651681\pi\)
\(98\) 0 0
\(99\) 0.355626 2.70678i 0.0357417 0.272041i
\(100\) 0 0
\(101\) −17.0598 3.00811i −1.69752 0.299318i −0.760691 0.649114i \(-0.775140\pi\)
−0.936826 + 0.349797i \(0.886251\pi\)
\(102\) 0 0
\(103\) −4.35114 + 11.9547i −0.428730 + 1.17793i 0.517853 + 0.855469i \(0.326731\pi\)
−0.946584 + 0.322458i \(0.895491\pi\)
\(104\) 0 0
\(105\) 0.0348210 + 1.58620i 0.00339818 + 0.154798i
\(106\) 0 0
\(107\) −5.72690 −0.553641 −0.276820 0.960922i \(-0.589281\pi\)
−0.276820 + 0.960922i \(0.589281\pi\)
\(108\) 0 0
\(109\) 18.7360 1.79459 0.897294 0.441434i \(-0.145530\pi\)
0.897294 + 0.441434i \(0.145530\pi\)
\(110\) 0 0
\(111\) 4.37505 + 2.39948i 0.415262 + 0.227749i
\(112\) 0 0
\(113\) −2.64000 + 7.25335i −0.248351 + 0.682337i 0.751397 + 0.659851i \(0.229381\pi\)
−0.999747 + 0.0224866i \(0.992842\pi\)
\(114\) 0 0
\(115\) 2.11394 + 0.372745i 0.197126 + 0.0347586i
\(116\) 0 0
\(117\) −0.562057 2.53211i −0.0519622 0.234093i
\(118\) 0 0
\(119\) −4.30026 + 1.56516i −0.394204 + 0.143478i
\(120\) 0 0
\(121\) −7.79211 + 6.53836i −0.708374 + 0.594396i
\(122\) 0 0
\(123\) 12.8613 + 4.36391i 1.15966 + 0.393481i
\(124\) 0 0
\(125\) 8.06354 4.65549i 0.721225 0.416399i
\(126\) 0 0
\(127\) −11.3108 6.53030i −1.00367 0.579470i −0.0943395 0.995540i \(-0.530074\pi\)
−0.909333 + 0.416070i \(0.863407\pi\)
\(128\) 0 0
\(129\) 0.285497 + 0.229074i 0.0251366 + 0.0201688i
\(130\) 0 0
\(131\) −2.97506 16.8724i −0.259933 1.47415i −0.783087 0.621913i \(-0.786356\pi\)
0.523154 0.852238i \(-0.324755\pi\)
\(132\) 0 0
\(133\) 2.81864 + 2.36512i 0.244407 + 0.205082i
\(134\) 0 0
\(135\) −5.21524 1.51786i −0.448856 0.130637i
\(136\) 0 0
\(137\) −4.25955 + 5.07633i −0.363917 + 0.433700i −0.916670 0.399646i \(-0.869133\pi\)
0.552752 + 0.833346i \(0.313578\pi\)
\(138\) 0 0
\(139\) 5.35032 0.943406i 0.453808 0.0800187i 0.0579280 0.998321i \(-0.481551\pi\)
0.395880 + 0.918302i \(0.370439\pi\)
\(140\) 0 0
\(141\) 4.71229 + 12.1129i 0.396847 + 1.02009i
\(142\) 0 0
\(143\) 0.393389 0.681369i 0.0328968 0.0569790i
\(144\) 0 0
\(145\) −0.427913 0.741167i −0.0355362 0.0615506i
\(146\) 0 0
\(147\) −10.5866 + 2.10726i −0.873169 + 0.173804i
\(148\) 0 0
\(149\) 9.57370 + 11.4095i 0.784308 + 0.934702i 0.999120 0.0419534i \(-0.0133581\pi\)
−0.214811 + 0.976656i \(0.568914\pi\)
\(150\) 0 0
\(151\) 2.94957 + 8.10389i 0.240033 + 0.659485i 0.999955 + 0.00947108i \(0.00301478\pi\)
−0.759922 + 0.650014i \(0.774763\pi\)
\(152\) 0 0
\(153\) −0.687507 15.6515i −0.0555816 1.26535i
\(154\) 0 0
\(155\) −1.57106 + 8.90990i −0.126190 + 0.715660i
\(156\) 0 0
\(157\) −6.78417 2.46924i −0.541436 0.197066i 0.0568016 0.998385i \(-0.481910\pi\)
−0.598237 + 0.801319i \(0.704132\pi\)
\(158\) 0 0
\(159\) −7.71926 12.7172i −0.612177 1.00854i
\(160\) 0 0
\(161\) 1.79948i 0.141819i
\(162\) 0 0
\(163\) 2.30077i 0.180210i −0.995932 0.0901051i \(-0.971280\pi\)
0.995932 0.0901051i \(-0.0287203\pi\)
\(164\) 0 0
\(165\) −0.854926 1.40845i −0.0665559 0.109648i
\(166\) 0 0
\(167\) 16.6973 + 6.07731i 1.29207 + 0.470277i 0.894407 0.447253i \(-0.147598\pi\)
0.397667 + 0.917530i \(0.369820\pi\)
\(168\) 0 0
\(169\) −2.12762 + 12.0664i −0.163663 + 0.928182i
\(170\) 0 0
\(171\) −10.6220 + 6.77094i −0.812288 + 0.517787i
\(172\) 0 0
\(173\) −3.83276 10.5304i −0.291399 0.800613i −0.995863 0.0908727i \(-0.971034\pi\)
0.704463 0.709741i \(-0.251188\pi\)
\(174\) 0 0
\(175\) −2.20090 2.62293i −0.166372 0.198275i
\(176\) 0 0
\(177\) 21.3343 4.24659i 1.60359 0.319194i
\(178\) 0 0
\(179\) −10.9900 19.0352i −0.821431 1.42276i −0.904616 0.426227i \(-0.859843\pi\)
0.0831849 0.996534i \(-0.473491\pi\)
\(180\) 0 0
\(181\) 9.50948 16.4709i 0.706834 1.22427i −0.259191 0.965826i \(-0.583456\pi\)
0.966025 0.258447i \(-0.0832107\pi\)
\(182\) 0 0
\(183\) 6.60588 + 16.9803i 0.488320 + 1.25522i
\(184\) 0 0
\(185\) 2.96570 0.522932i 0.218042 0.0384468i
\(186\) 0 0
\(187\) 3.05470 3.64045i 0.223382 0.266216i
\(188\) 0 0
\(189\) −0.493920 + 4.52654i −0.0359274 + 0.329258i
\(190\) 0 0
\(191\) −11.7943 9.89655i −0.853402 0.716089i 0.107134 0.994245i \(-0.465833\pi\)
−0.960536 + 0.278155i \(0.910277\pi\)
\(192\) 0 0
\(193\) −3.48037 19.7381i −0.250522 1.42078i −0.807310 0.590127i \(-0.799078\pi\)
0.556788 0.830655i \(-0.312034\pi\)
\(194\) 0 0
\(195\) −1.22093 0.979633i −0.0874324 0.0701529i
\(196\) 0 0
\(197\) −6.20995 3.58532i −0.442441 0.255443i 0.262192 0.965016i \(-0.415555\pi\)
−0.704632 + 0.709572i \(0.748888\pi\)
\(198\) 0 0
\(199\) 15.1085 8.72292i 1.07102 0.618352i 0.142558 0.989787i \(-0.454467\pi\)
0.928459 + 0.371435i \(0.121134\pi\)
\(200\) 0 0
\(201\) −3.50382 1.18887i −0.247141 0.0838565i
\(202\) 0 0
\(203\) −0.549599 + 0.461168i −0.0385743 + 0.0323677i
\(204\) 0 0
\(205\) 7.70229 2.80340i 0.537951 0.195798i
\(206\) 0 0
\(207\) 5.87584 + 1.85094i 0.408399 + 0.128649i
\(208\) 0 0
\(209\) −3.76296 0.663512i −0.260289 0.0458961i
\(210\) 0 0
\(211\) 0.945207 2.59694i 0.0650708 0.178780i −0.902896 0.429859i \(-0.858563\pi\)
0.967967 + 0.251079i \(0.0807854\pi\)
\(212\) 0 0
\(213\) 5.37018 + 2.94526i 0.367959 + 0.201806i
\(214\) 0 0
\(215\) 0.220909 0.0150659
\(216\) 0 0
\(217\) 7.58451 0.514870
\(218\) 0 0
\(219\) 0.0498766 + 2.27204i 0.00337035 + 0.153530i
\(220\) 0 0
\(221\) 1.54422 4.24272i 0.103876 0.285396i
\(222\) 0 0
\(223\) 24.2380 + 4.27381i 1.62309 + 0.286195i 0.909918 0.414789i \(-0.136145\pi\)
0.713177 + 0.700984i \(0.247256\pi\)
\(224\) 0 0
\(225\) 10.8285 4.48865i 0.721898 0.299244i
\(226\) 0 0
\(227\) −4.15263 + 1.51143i −0.275620 + 0.100317i −0.476132 0.879374i \(-0.657962\pi\)
0.200512 + 0.979691i \(0.435739\pi\)
\(228\) 0 0
\(229\) 13.7629 11.5484i 0.909477 0.763142i −0.0625423 0.998042i \(-0.519921\pi\)
0.972019 + 0.234900i \(0.0754764\pi\)
\(230\) 0 0
\(231\) −1.03834 + 0.910839i −0.0683175 + 0.0599288i
\(232\) 0 0
\(233\) 8.65324 4.99595i 0.566893 0.327296i −0.189015 0.981974i \(-0.560529\pi\)
0.755907 + 0.654679i \(0.227196\pi\)
\(234\) 0 0
\(235\) 6.79312 + 3.92201i 0.443134 + 0.255844i
\(236\) 0 0
\(237\) −0.333436 + 2.16827i −0.0216590 + 0.140845i
\(238\) 0 0
\(239\) −4.63317 26.2760i −0.299695 1.69965i −0.647482 0.762080i \(-0.724178\pi\)
0.347787 0.937573i \(-0.386933\pi\)
\(240\) 0 0
\(241\) −5.01164 4.20527i −0.322828 0.270885i 0.466942 0.884288i \(-0.345356\pi\)
−0.789770 + 0.613403i \(0.789800\pi\)
\(242\) 0 0
\(243\) −14.2724 6.26876i −0.915578 0.402141i
\(244\) 0 0
\(245\) −4.18745 + 4.99041i −0.267526 + 0.318825i
\(246\) 0 0
\(247\) −3.57509 + 0.630385i −0.227478 + 0.0401104i
\(248\) 0 0
\(249\) 20.8409 + 3.20490i 1.32074 + 0.203102i
\(250\) 0 0
\(251\) −0.963757 + 1.66928i −0.0608318 + 0.105364i −0.894837 0.446392i \(-0.852709\pi\)
0.834006 + 0.551756i \(0.186042\pi\)
\(252\) 0 0
\(253\) 0.934352 + 1.61834i 0.0587422 + 0.101744i
\(254\) 0 0
\(255\) −6.23507 7.10784i −0.390455 0.445110i
\(256\) 0 0
\(257\) 19.6622 + 23.4325i 1.22649 + 1.46168i 0.842807 + 0.538215i \(0.180901\pi\)
0.383687 + 0.923463i \(0.374654\pi\)
\(258\) 0 0
\(259\) −0.863443 2.37229i −0.0536517 0.147407i
\(260\) 0 0
\(261\) −0.940535 2.26896i −0.0582177 0.140445i
\(262\) 0 0
\(263\) 2.25823 12.8071i 0.139249 0.789718i −0.832558 0.553938i \(-0.813124\pi\)
0.971807 0.235780i \(-0.0757644\pi\)
\(264\) 0 0
\(265\) −8.43678 3.07074i −0.518267 0.188634i
\(266\) 0 0
\(267\) 8.55245 0.187747i 0.523401 0.0114899i
\(268\) 0 0
\(269\) 12.5617i 0.765899i −0.923769 0.382950i \(-0.874908\pi\)
0.923769 0.382950i \(-0.125092\pi\)
\(270\) 0 0
\(271\) 22.0527i 1.33961i −0.742539 0.669803i \(-0.766379\pi\)
0.742539 0.669803i \(-0.233621\pi\)
\(272\) 0 0
\(273\) −0.631031 + 1.15058i −0.0381917 + 0.0696361i
\(274\) 0 0
\(275\) 3.34127 + 1.21612i 0.201486 + 0.0733349i
\(276\) 0 0
\(277\) 0.542604 3.07726i 0.0326019 0.184895i −0.964158 0.265329i \(-0.914520\pi\)
0.996760 + 0.0804340i \(0.0256306\pi\)
\(278\) 0 0
\(279\) −7.80138 + 24.7657i −0.467056 + 1.48268i
\(280\) 0 0
\(281\) −2.09238 5.74876i −0.124821 0.342942i 0.861505 0.507749i \(-0.169522\pi\)
−0.986326 + 0.164807i \(0.947300\pi\)
\(282\) 0 0
\(283\) 9.26570 + 11.0424i 0.550789 + 0.656404i 0.967570 0.252602i \(-0.0812864\pi\)
−0.416781 + 0.909007i \(0.636842\pi\)
\(284\) 0 0
\(285\) −2.44270 + 7.19909i −0.144693 + 0.426437i
\(286\) 0 0
\(287\) −3.43566 5.95074i −0.202801 0.351261i
\(288\) 0 0
\(289\) 5.13568 8.89527i 0.302099 0.523251i
\(290\) 0 0
\(291\) −15.6921 + 19.5573i −0.919888 + 1.14647i
\(292\) 0 0
\(293\) −28.7692 + 5.07278i −1.68071 + 0.296355i −0.930895 0.365288i \(-0.880971\pi\)
−0.749819 + 0.661643i \(0.769860\pi\)
\(294\) 0 0
\(295\) 8.43862 10.0568i 0.491316 0.585527i
\(296\) 0 0
\(297\) −1.90613 4.32735i −0.110605 0.251098i
\(298\) 0 0
\(299\) 1.36004 + 1.14121i 0.0786531 + 0.0659978i
\(300\) 0 0
\(301\) −0.0321581 0.182378i −0.00185356 0.0105121i
\(302\) 0 0
\(303\) −27.9628 + 10.8784i −1.60642 + 0.624948i
\(304\) 0 0
\(305\) 9.52286 + 5.49802i 0.545277 + 0.314816i
\(306\) 0 0
\(307\) −5.30538 + 3.06306i −0.302794 + 0.174818i −0.643697 0.765280i \(-0.722600\pi\)
0.340903 + 0.940098i \(0.389267\pi\)
\(308\) 0 0
\(309\) 4.30166 + 21.6110i 0.244713 + 1.22941i
\(310\) 0 0
\(311\) −20.5489 + 17.2426i −1.16522 + 0.977739i −0.999964 0.00851113i \(-0.997291\pi\)
−0.165260 + 0.986250i \(0.552846\pi\)
\(312\) 0 0
\(313\) −8.31736 + 3.02727i −0.470125 + 0.171111i −0.566209 0.824262i \(-0.691590\pi\)
0.0960841 + 0.995373i \(0.469368\pi\)
\(314\) 0 0
\(315\) 1.47714 + 2.31729i 0.0832273 + 0.130565i
\(316\) 0 0
\(317\) −16.2536 2.86595i −0.912894 0.160968i −0.302577 0.953125i \(-0.597847\pi\)
−0.610317 + 0.792157i \(0.708958\pi\)
\(318\) 0 0
\(319\) 0.254821 0.700116i 0.0142673 0.0391990i
\(320\) 0 0
\(321\) −8.47944 + 5.14698i −0.473276 + 0.287277i
\(322\) 0 0
\(323\) −21.9273 −1.22007
\(324\) 0 0
\(325\) 3.37818 0.187388
\(326\) 0 0
\(327\) 27.7412 16.8388i 1.53409 0.931187i
\(328\) 0 0
\(329\) 2.24904 6.17918i 0.123994 0.340669i
\(330\) 0 0
\(331\) −1.90388 0.335705i −0.104646 0.0184520i 0.121080 0.992643i \(-0.461364\pi\)
−0.225726 + 0.974191i \(0.572475\pi\)
\(332\) 0 0
\(333\) 8.63435 0.379272i 0.473160 0.0207840i
\(334\) 0 0
\(335\) −2.09835 + 0.763738i −0.114645 + 0.0417274i
\(336\) 0 0
\(337\) −5.93398 + 4.97920i −0.323244 + 0.271234i −0.789941 0.613183i \(-0.789889\pi\)
0.466696 + 0.884418i \(0.345444\pi\)
\(338\) 0 0
\(339\) 2.60998 + 13.1122i 0.141755 + 0.712157i
\(340\) 0 0
\(341\) −6.82104 + 3.93813i −0.369380 + 0.213262i
\(342\) 0 0
\(343\) 10.0419 + 5.79767i 0.542209 + 0.313045i
\(344\) 0 0
\(345\) 3.46497 1.34798i 0.186548 0.0725728i
\(346\) 0 0
\(347\) −3.62921 20.5823i −0.194826 1.10491i −0.912666 0.408706i \(-0.865980\pi\)
0.717840 0.696208i \(-0.245131\pi\)
\(348\) 0 0
\(349\) 3.68709 + 3.09384i 0.197365 + 0.165609i 0.736115 0.676857i \(-0.236658\pi\)
−0.538749 + 0.842466i \(0.681103\pi\)
\(350\) 0 0
\(351\) −3.10790 3.24398i −0.165887 0.173151i
\(352\) 0 0
\(353\) −18.0088 + 21.4620i −0.958510 + 1.14231i 0.0312417 + 0.999512i \(0.490054\pi\)
−0.989752 + 0.142796i \(0.954391\pi\)
\(354\) 0 0
\(355\) 3.64026 0.641876i 0.193205 0.0340672i
\(356\) 0 0
\(357\) −4.96042 + 6.18223i −0.262533 + 0.327198i
\(358\) 0 0
\(359\) 14.8329 25.6913i 0.782849 1.35593i −0.147427 0.989073i \(-0.547099\pi\)
0.930276 0.366861i \(-0.119568\pi\)
\(360\) 0 0
\(361\) −0.684806 1.18612i −0.0360424 0.0624273i
\(362\) 0 0
\(363\) −5.66098 + 16.6840i −0.297124 + 0.875681i
\(364\) 0 0
\(365\) 0.881607 + 1.05066i 0.0461454 + 0.0549940i
\(366\) 0 0
\(367\) 5.16356 + 14.1868i 0.269536 + 0.740543i 0.998435 + 0.0559224i \(0.0178099\pi\)
−0.728899 + 0.684621i \(0.759968\pi\)
\(368\) 0 0
\(369\) 22.9648 5.09755i 1.19550 0.265368i
\(370\) 0 0
\(371\) −1.30698 + 7.41223i −0.0678549 + 0.384824i
\(372\) 0 0
\(373\) −11.0141 4.00882i −0.570291 0.207569i 0.0407481 0.999169i \(-0.487026\pi\)
−0.611039 + 0.791601i \(0.709248\pi\)
\(374\) 0 0
\(375\) 7.75507 14.1401i 0.400470 0.730190i
\(376\) 0 0
\(377\) 0.707851i 0.0364562i
\(378\) 0 0
\(379\) 21.9951i 1.12981i 0.825155 + 0.564906i \(0.191087\pi\)
−0.825155 + 0.564906i \(0.808913\pi\)
\(380\) 0 0
\(381\) −22.6162 + 0.496479i −1.15866 + 0.0254354i
\(382\) 0 0
\(383\) 17.1381 + 6.23776i 0.875716 + 0.318735i 0.740480 0.672079i \(-0.234598\pi\)
0.135236 + 0.990813i \(0.456821\pi\)
\(384\) 0 0
\(385\) −0.144751 + 0.820922i −0.00737718 + 0.0418381i
\(386\) 0 0
\(387\) 0.628593 + 0.0825868i 0.0319532 + 0.00419812i
\(388\) 0 0
\(389\) 4.30124 + 11.8176i 0.218082 + 0.599174i 0.999698 0.0245854i \(-0.00782655\pi\)
−0.781616 + 0.623760i \(0.785604\pi\)
\(390\) 0 0
\(391\) 6.89309 + 8.21487i 0.348599 + 0.415444i
\(392\) 0 0
\(393\) −19.5689 22.3081i −0.987118 1.12529i
\(394\) 0 0
\(395\) 0.661984 + 1.14659i 0.0333080 + 0.0576912i
\(396\) 0 0
\(397\) −4.83557 + 8.37546i −0.242690 + 0.420352i −0.961480 0.274876i \(-0.911363\pi\)
0.718789 + 0.695228i \(0.244697\pi\)
\(398\) 0 0
\(399\) 6.29899 + 0.968655i 0.315344 + 0.0484934i
\(400\) 0 0
\(401\) −23.9107 + 4.21610i −1.19404 + 0.210542i −0.735122 0.677935i \(-0.762875\pi\)
−0.458921 + 0.888477i \(0.651764\pi\)
\(402\) 0 0
\(403\) −4.81000 + 5.73233i −0.239603 + 0.285548i
\(404\) 0 0
\(405\) −9.08601 + 2.43974i −0.451487 + 0.121232i
\(406\) 0 0
\(407\) 2.00830 + 1.68516i 0.0995477 + 0.0835304i
\(408\) 0 0
\(409\) 0.524727 + 2.97587i 0.0259461 + 0.147148i 0.995029 0.0995891i \(-0.0317528\pi\)
−0.969083 + 0.246737i \(0.920642\pi\)
\(410\) 0 0
\(411\) −1.74453 + 11.3444i −0.0860514 + 0.559577i
\(412\) 0 0
\(413\) −9.53106 5.50276i −0.468993 0.270773i
\(414\) 0 0
\(415\) 11.0207 6.36282i 0.540986 0.312339i
\(416\) 0 0
\(417\) 7.07398 6.20537i 0.346414 0.303878i
\(418\) 0 0
\(419\) −4.03376 + 3.38472i −0.197062 + 0.165355i −0.735979 0.677004i \(-0.763278\pi\)
0.538917 + 0.842359i \(0.318834\pi\)
\(420\) 0 0
\(421\) −2.10173 + 0.764966i −0.102432 + 0.0372822i −0.392728 0.919655i \(-0.628469\pi\)
0.290296 + 0.956937i \(0.406246\pi\)
\(422\) 0 0
\(423\) 17.8635 + 13.6996i 0.868553 + 0.666099i
\(424\) 0 0
\(425\) 20.0948 + 3.54325i 0.974739 + 0.171873i
\(426\) 0 0
\(427\) 3.15279 8.66222i 0.152574 0.419194i
\(428\) 0 0
\(429\) −0.0299081 1.36241i −0.00144398 0.0657778i
\(430\) 0 0
\(431\) 16.1724 0.778995 0.389498 0.921028i \(-0.372649\pi\)
0.389498 + 0.921028i \(0.372649\pi\)
\(432\) 0 0
\(433\) −24.5777 −1.18113 −0.590564 0.806991i \(-0.701094\pi\)
−0.590564 + 0.806991i \(0.701094\pi\)
\(434\) 0 0
\(435\) −1.29970 0.712814i −0.0623156 0.0341768i
\(436\) 0 0
\(437\) 2.94901 8.10233i 0.141070 0.387587i
\(438\) 0 0
\(439\) 11.9050 + 2.09917i 0.568195 + 0.100188i 0.450363 0.892845i \(-0.351295\pi\)
0.117832 + 0.993034i \(0.462406\pi\)
\(440\) 0 0
\(441\) −13.7810 + 12.6347i −0.656238 + 0.601651i
\(442\) 0 0
\(443\) 1.19218 0.433918i 0.0566422 0.0206161i −0.313544 0.949574i \(-0.601516\pi\)
0.370186 + 0.928958i \(0.379294\pi\)
\(444\) 0 0
\(445\) 3.95491 3.31856i 0.187481 0.157315i
\(446\) 0 0
\(447\) 24.4293 + 8.28902i 1.15546 + 0.392057i
\(448\) 0 0
\(449\) −12.4201 + 7.17076i −0.586142 + 0.338409i −0.763570 0.645724i \(-0.776555\pi\)
0.177429 + 0.984134i \(0.443222\pi\)
\(450\) 0 0
\(451\) 6.17964 + 3.56782i 0.290988 + 0.168002i
\(452\) 0 0
\(453\) 11.6505 + 9.34798i 0.547388 + 0.439207i
\(454\) 0 0
\(455\) 0.137524 + 0.779937i 0.00644722 + 0.0365640i
\(456\) 0 0
\(457\) 2.18801 + 1.83596i 0.102351 + 0.0858825i 0.692527 0.721392i \(-0.256497\pi\)
−0.590176 + 0.807274i \(0.700942\pi\)
\(458\) 0 0
\(459\) −15.0845 22.5562i −0.704086 1.05283i
\(460\) 0 0
\(461\) 16.1365 19.2307i 0.751551 0.895664i −0.245731 0.969338i \(-0.579028\pi\)
0.997282 + 0.0736740i \(0.0234724\pi\)
\(462\) 0 0
\(463\) −21.9130 + 3.86385i −1.01838 + 0.179568i −0.657827 0.753169i \(-0.728524\pi\)
−0.360556 + 0.932738i \(0.617413\pi\)
\(464\) 0 0
\(465\) 5.68150 + 14.6042i 0.263473 + 0.677256i
\(466\) 0 0
\(467\) −16.0152 + 27.7392i −0.741097 + 1.28362i 0.210899 + 0.977508i \(0.432361\pi\)
−0.951996 + 0.306110i \(0.900972\pi\)
\(468\) 0 0
\(469\) 0.935986 + 1.62117i 0.0432198 + 0.0748589i
\(470\) 0 0
\(471\) −12.2641 + 2.44116i −0.565098 + 0.112483i
\(472\) 0 0
\(473\) 0.123617 + 0.147322i 0.00568394 + 0.00677385i
\(474\) 0 0
\(475\) −5.61126 15.4168i −0.257462 0.707372i
\(476\) 0 0
\(477\) −22.8588 11.8918i −1.04663 0.544490i
\(478\) 0 0
\(479\) 4.52904 25.6855i 0.206937 1.17360i −0.687425 0.726256i \(-0.741259\pi\)
0.894362 0.447344i \(-0.147630\pi\)
\(480\) 0 0
\(481\) 2.34055 + 0.851890i 0.106720 + 0.0388428i
\(482\) 0 0
\(483\) −1.61726 2.66437i −0.0735880 0.121233i
\(484\) 0 0
\(485\) 15.1328i 0.687145i
\(486\) 0 0
\(487\) 12.8151i 0.580706i −0.956920 0.290353i \(-0.906227\pi\)
0.956920 0.290353i \(-0.0937727\pi\)
\(488\) 0 0
\(489\) −2.06779 3.40659i −0.0935086 0.154051i
\(490\) 0 0
\(491\) 32.9705 + 12.0003i 1.48794 + 0.541566i 0.952906 0.303266i \(-0.0980769\pi\)
0.535033 + 0.844831i \(0.320299\pi\)
\(492\) 0 0
\(493\) 0.742439 4.21058i 0.0334378 0.189635i
\(494\) 0 0
\(495\) −2.53166 1.31705i −0.113790 0.0591969i
\(496\) 0 0
\(497\) −1.05984 2.91188i −0.0475402 0.130616i
\(498\) 0 0
\(499\) −3.47692 4.14363i −0.155648 0.185494i 0.682585 0.730806i \(-0.260856\pi\)
−0.838233 + 0.545312i \(0.816411\pi\)
\(500\) 0 0
\(501\) 30.1844 6.00821i 1.34854 0.268427i
\(502\) 0 0
\(503\) 8.89978 + 15.4149i 0.396822 + 0.687315i 0.993332 0.115290i \(-0.0367798\pi\)
−0.596510 + 0.802606i \(0.703446\pi\)
\(504\) 0 0
\(505\) −9.05402 + 15.6820i −0.402899 + 0.697841i
\(506\) 0 0
\(507\) 7.69426 + 19.7780i 0.341714 + 0.878372i
\(508\) 0 0
\(509\) 4.55607 0.803358i 0.201944 0.0356082i −0.0717610 0.997422i \(-0.522862\pi\)
0.273705 + 0.961814i \(0.411751\pi\)
\(510\) 0 0
\(511\) 0.739064 0.880782i 0.0326942 0.0389635i
\(512\) 0 0
\(513\) −9.64204 + 19.5717i −0.425707 + 0.864112i
\(514\) 0 0
\(515\) 10.1872 + 8.54805i 0.448900 + 0.376672i
\(516\) 0 0
\(517\) 1.18579 + 6.72495i 0.0521510 + 0.295763i
\(518\) 0 0
\(519\) −15.1390 12.1470i −0.664528 0.533196i
\(520\) 0 0
\(521\) −6.04248 3.48863i −0.264726 0.152839i 0.361763 0.932270i \(-0.382175\pi\)
−0.626488 + 0.779431i \(0.715508\pi\)
\(522\) 0 0
\(523\) −29.9008 + 17.2632i −1.30747 + 0.754869i −0.981673 0.190571i \(-0.938966\pi\)
−0.325798 + 0.945440i \(0.605633\pi\)
\(524\) 0 0
\(525\) −5.61605 1.90556i −0.245104 0.0831656i
\(526\) 0 0
\(527\) −34.6242 + 29.0532i −1.50826 + 1.26558i
\(528\) 0 0
\(529\) 17.6504 6.42422i 0.767409 0.279314i
\(530\) 0 0
\(531\) 27.7717 25.4616i 1.20519 1.10494i
\(532\) 0 0
\(533\) 6.67639 + 1.17723i 0.289186 + 0.0509914i
\(534\) 0 0
\(535\) −2.04748 + 5.62541i −0.0885203 + 0.243208i
\(536\) 0 0
\(537\) −33.3798 18.3071i −1.44045 0.790008i
\(538\) 0 0
\(539\) −5.67128 −0.244279
\(540\) 0 0
\(541\) −7.84296 −0.337195 −0.168598 0.985685i \(-0.553924\pi\)
−0.168598 + 0.985685i \(0.553924\pi\)
\(542\) 0 0
\(543\) −0.722977 32.9339i −0.0310259 1.41333i
\(544\) 0 0
\(545\) 6.69851 18.4040i 0.286932 0.788340i
\(546\) 0 0
\(547\) −44.9004 7.91716i −1.91980 0.338513i −0.921097 0.389334i \(-0.872705\pi\)
−0.998708 + 0.0508207i \(0.983816\pi\)
\(548\) 0 0
\(549\) 25.0417 + 19.2047i 1.06875 + 0.819636i
\(550\) 0 0
\(551\) −3.23038 + 1.17576i −0.137619 + 0.0500892i
\(552\) 0 0
\(553\) 0.850233 0.713430i 0.0361556 0.0303381i
\(554\) 0 0
\(555\) 3.92113 3.43965i 0.166443 0.146005i
\(556\) 0 0
\(557\) 15.3982 8.89017i 0.652444 0.376689i −0.136948 0.990578i \(-0.543729\pi\)
0.789392 + 0.613890i \(0.210396\pi\)
\(558\) 0 0
\(559\) 0.158234 + 0.0913565i 0.00669259 + 0.00386397i
\(560\) 0 0
\(561\) 1.25108 8.13553i 0.0528205 0.343483i
\(562\) 0 0
\(563\) −5.94955 33.7416i −0.250744 1.42204i −0.806766 0.590871i \(-0.798784\pi\)
0.556022 0.831167i \(-0.312327\pi\)
\(564\) 0 0
\(565\) 6.18095 + 5.18643i 0.260034 + 0.218195i
\(566\) 0 0
\(567\) 3.33686 + 7.14605i 0.140135 + 0.300106i
\(568\) 0 0
\(569\) 7.97000 9.49828i 0.334120 0.398189i −0.572660 0.819793i \(-0.694088\pi\)
0.906780 + 0.421604i \(0.138533\pi\)
\(570\) 0 0
\(571\) 31.1551 5.49348i 1.30380 0.229895i 0.521743 0.853103i \(-0.325282\pi\)
0.782056 + 0.623208i \(0.214171\pi\)
\(572\) 0 0
\(573\) −26.3573 4.05322i −1.10109 0.169326i
\(574\) 0 0
\(575\) −4.01182 + 6.94867i −0.167304 + 0.289780i
\(576\) 0 0
\(577\) 1.81116 + 3.13703i 0.0753997 + 0.130596i 0.901260 0.433279i \(-0.142643\pi\)
−0.825860 + 0.563875i \(0.809310\pi\)
\(578\) 0 0
\(579\) −22.8925 26.0970i −0.951381 1.08455i
\(580\) 0 0
\(581\) −6.85731 8.17223i −0.284489 0.339041i
\(582\) 0 0
\(583\) −2.67326 7.34473i −0.110715 0.304188i
\(584\) 0 0
\(585\) −2.68818 0.353182i −0.111142 0.0146023i
\(586\) 0 0
\(587\) −4.78428 + 27.1330i −0.197468 + 1.11990i 0.711391 + 0.702797i \(0.248066\pi\)
−0.908859 + 0.417103i \(0.863046\pi\)
\(588\) 0 0
\(589\) 34.1499 + 12.4296i 1.40712 + 0.512151i
\(590\) 0 0
\(591\) −12.4169 + 0.272581i −0.510764 + 0.0112125i
\(592\) 0 0
\(593\) 10.7012i 0.439445i 0.975562 + 0.219723i \(0.0705152\pi\)
−0.975562 + 0.219723i \(0.929485\pi\)
\(594\) 0 0
\(595\) 4.78362i 0.196109i
\(596\) 0 0
\(597\) 14.5306 26.4941i 0.594697 1.08433i
\(598\) 0 0
\(599\) 11.5378 + 4.19943i 0.471423 + 0.171584i 0.566797 0.823858i \(-0.308182\pi\)
−0.0953740 + 0.995442i \(0.530405\pi\)
\(600\) 0 0
\(601\) 1.12791 6.39667i 0.0460082 0.260926i −0.953124 0.302581i \(-0.902152\pi\)
0.999132 + 0.0416548i \(0.0132630\pi\)
\(602\) 0 0
\(603\) −6.25636 + 1.38874i −0.254779 + 0.0565537i
\(604\) 0 0
\(605\) 3.63665 + 9.99161i 0.147851 + 0.406217i
\(606\) 0 0
\(607\) −25.3826 30.2499i −1.03025 1.22780i −0.973326 0.229425i \(-0.926315\pi\)
−0.0569233 0.998379i \(-0.518129\pi\)
\(608\) 0 0
\(609\) −0.399285 + 1.17677i −0.0161798 + 0.0476850i
\(610\) 0 0
\(611\) 3.24388 + 5.61857i 0.131233 + 0.227303i
\(612\) 0 0
\(613\) 0.172794 0.299289i 0.00697910 0.0120882i −0.862515 0.506032i \(-0.831112\pi\)
0.869494 + 0.493944i \(0.164445\pi\)
\(614\) 0 0
\(615\) 8.88473 11.0731i 0.358267 0.446512i
\(616\) 0 0
\(617\) 11.0241 1.94385i 0.443814 0.0782564i 0.0527246 0.998609i \(-0.483209\pi\)
0.391089 + 0.920353i \(0.372098\pi\)
\(618\) 0 0
\(619\) −6.45918 + 7.69775i −0.259616 + 0.309399i −0.880070 0.474845i \(-0.842504\pi\)
0.620453 + 0.784243i \(0.286949\pi\)
\(620\) 0 0
\(621\) 10.3635 2.54028i 0.415871 0.101938i
\(622\) 0 0
\(623\) −3.31546 2.78200i −0.132831 0.111458i
\(624\) 0 0
\(625\) 1.70238 + 9.65469i 0.0680953 + 0.386188i
\(626\) 0 0
\(627\) −6.16788 + 2.39950i −0.246322 + 0.0958267i
\(628\) 0 0
\(629\) 13.0290 + 7.52230i 0.519500 + 0.299934i
\(630\) 0 0
\(631\) −30.2407 + 17.4595i −1.20386 + 0.695050i −0.961412 0.275113i \(-0.911285\pi\)
−0.242451 + 0.970164i \(0.577951\pi\)
\(632\) 0 0
\(633\) −0.934459 4.69460i −0.0371414 0.186594i
\(634\) 0 0
\(635\) −10.4584 + 8.77564i −0.415029 + 0.348251i
\(636\) 0 0
\(637\) −5.06319 + 1.84285i −0.200611 + 0.0730164i
\(638\) 0 0
\(639\) 10.5983 0.465539i 0.419261 0.0184164i
\(640\) 0 0
\(641\) 36.8418 + 6.49620i 1.45516 + 0.256585i 0.844606 0.535388i \(-0.179834\pi\)
0.610557 + 0.791972i \(0.290946\pi\)
\(642\) 0 0
\(643\) 2.88367 7.92281i 0.113721 0.312445i −0.869755 0.493483i \(-0.835723\pi\)
0.983476 + 0.181038i \(0.0579457\pi\)
\(644\) 0 0
\(645\) 0.327085 0.198539i 0.0128790 0.00781747i
\(646\) 0 0
\(647\) 34.7421 1.36585 0.682927 0.730487i \(-0.260707\pi\)
0.682927 + 0.730487i \(0.260707\pi\)
\(648\) 0 0
\(649\) 11.4289 0.448622
\(650\) 0 0
\(651\) 11.2299 6.81649i 0.440133 0.267159i
\(652\) 0 0
\(653\) 12.1343 33.3388i 0.474853 1.30465i −0.438958 0.898508i \(-0.644652\pi\)
0.913811 0.406140i \(-0.133126\pi\)
\(654\) 0 0
\(655\) −17.6370 3.10989i −0.689136 0.121513i
\(656\) 0 0
\(657\) 2.11581 + 3.31922i 0.0825458 + 0.129495i
\(658\) 0 0
\(659\) 23.3441 8.49655i 0.909356 0.330978i 0.155360 0.987858i \(-0.450346\pi\)
0.753996 + 0.656879i \(0.228124\pi\)
\(660\) 0 0
\(661\) −20.4085 + 17.1248i −0.793800 + 0.666078i −0.946683 0.322167i \(-0.895589\pi\)
0.152883 + 0.988244i \(0.451144\pi\)
\(662\) 0 0
\(663\) −1.52666 7.66975i −0.0592907 0.297868i
\(664\) 0 0
\(665\) 3.33092 1.92311i 0.129168 0.0745750i
\(666\) 0 0
\(667\) 1.45600 + 0.840621i 0.0563765 + 0.0325490i
\(668\) 0 0
\(669\) 39.7285 15.4556i 1.53599 0.597549i
\(670\) 0 0
\(671\) 1.66229 + 9.42729i 0.0641719 + 0.363937i
\(672\) 0 0
\(673\) −20.2278 16.9732i −0.779726 0.654267i 0.163454 0.986551i \(-0.447736\pi\)
−0.943180 + 0.332284i \(0.892181\pi\)
\(674\) 0 0
\(675\) 11.9989 16.3780i 0.461836 0.630389i
\(676\) 0 0
\(677\) 19.7326 23.5164i 0.758385 0.903808i −0.239360 0.970931i \(-0.576938\pi\)
0.997745 + 0.0671230i \(0.0213820\pi\)
\(678\) 0 0
\(679\) 12.4933 2.20291i 0.479449 0.0845399i
\(680\) 0 0
\(681\) −4.79013 + 5.97000i −0.183558 + 0.228771i
\(682\) 0 0
\(683\) 3.64903 6.32031i 0.139626 0.241840i −0.787729 0.616022i \(-0.788743\pi\)
0.927355 + 0.374182i \(0.122077\pi\)
\(684\) 0 0
\(685\) 3.46349 + 5.99894i 0.132333 + 0.229208i
\(686\) 0 0
\(687\) 9.99876 29.4682i 0.381477 1.12428i
\(688\) 0 0
\(689\) −4.77326 5.68855i −0.181847 0.216716i
\(690\) 0 0
\(691\) −7.71959 21.2094i −0.293667 0.806843i −0.995523 0.0945240i \(-0.969867\pi\)
0.701856 0.712319i \(-0.252355\pi\)
\(692\) 0 0
\(693\) −0.718788 + 2.28181i −0.0273045 + 0.0866787i
\(694\) 0 0
\(695\) 0.986159 5.59279i 0.0374072 0.212147i
\(696\) 0 0
\(697\) 38.4791 + 14.0052i 1.45750 + 0.530486i
\(698\) 0 0
\(699\) 8.32222 15.1742i 0.314775 0.573940i
\(700\) 0 0
\(701\) 17.4254i 0.658149i 0.944304 + 0.329075i \(0.106737\pi\)
−0.944304 + 0.329075i \(0.893263\pi\)
\(702\) 0 0
\(703\) 12.0965i 0.456226i
\(704\) 0 0
\(705\) 13.5830 0.298178i 0.511564 0.0112300i
\(706\) 0 0
\(707\) 14.2647 + 5.19194i 0.536481 + 0.195263i
\(708\) 0 0
\(709\) 7.38273 41.8695i 0.277264 1.57244i −0.454413 0.890791i \(-0.650151\pi\)
0.731677 0.681652i \(-0.238738\pi\)
\(710\) 0 0
\(711\) 1.45501 + 3.51009i 0.0545673 + 0.131639i
\(712\) 0 0
\(713\) −6.07880 16.7014i −0.227653 0.625471i
\(714\) 0 0
\(715\) −0.528649 0.630020i −0.0197704 0.0235614i
\(716\) 0 0
\(717\) −30.4753 34.7411i −1.13812 1.29743i
\(718\) 0 0
\(719\) 15.9720 + 27.6643i 0.595655 + 1.03170i 0.993454 + 0.114232i \(0.0364407\pi\)
−0.397799 + 0.917472i \(0.630226\pi\)
\(720\) 0 0
\(721\) 5.57412 9.65466i 0.207591 0.359558i
\(722\) 0 0
\(723\) −11.1998 1.72230i −0.416526 0.0640531i
\(724\) 0 0
\(725\) 3.15041 0.555501i 0.117003 0.0206308i
\(726\) 0 0
\(727\) −21.2524 + 25.3276i −0.788207 + 0.939348i −0.999273 0.0381237i \(-0.987862\pi\)
0.211066 + 0.977472i \(0.432306\pi\)
\(728\) 0 0
\(729\) −26.7662 + 3.54544i −0.991341 + 0.131313i
\(730\) 0 0
\(731\) 0.845420 + 0.709391i 0.0312690 + 0.0262378i
\(732\) 0 0
\(733\) 7.27308 + 41.2477i 0.268637 + 1.52352i 0.758473 + 0.651704i \(0.225946\pi\)
−0.489836 + 0.871815i \(0.662943\pi\)
\(734\) 0 0
\(735\) −1.71501 + 11.1524i −0.0632589 + 0.411362i
\(736\) 0 0
\(737\) −1.68353 0.971989i −0.0620138 0.0358037i
\(738\) 0 0
\(739\) 18.0221 10.4051i 0.662953 0.382756i −0.130448 0.991455i \(-0.541642\pi\)
0.793401 + 0.608699i \(0.208308\pi\)
\(740\) 0 0
\(741\) −4.72684 + 4.14644i −0.173645 + 0.152323i
\(742\) 0 0
\(743\) −34.8189 + 29.2165i −1.27738 + 1.07185i −0.283783 + 0.958888i \(0.591590\pi\)
−0.993599 + 0.112963i \(0.963966\pi\)
\(744\) 0 0
\(745\) 14.6301 5.32491i 0.536004 0.195090i
\(746\) 0 0
\(747\) 33.7381 13.9852i 1.23441 0.511693i
\(748\) 0 0
\(749\) 4.94227 + 0.871455i 0.180587 + 0.0318423i
\(750\) 0 0
\(751\) −8.29032 + 22.7775i −0.302518 + 0.831162i 0.691543 + 0.722336i \(0.256931\pi\)
−0.994061 + 0.108826i \(0.965291\pi\)
\(752\) 0 0
\(753\) 0.0732715 + 3.33775i 0.00267016 + 0.121634i
\(754\) 0 0
\(755\) 9.01480 0.328082
\(756\) 0 0
\(757\) −52.0732 −1.89263 −0.946317 0.323240i \(-0.895228\pi\)
−0.946317 + 0.323240i \(0.895228\pi\)
\(758\) 0 0
\(759\) 2.83790 + 1.55644i 0.103009 + 0.0564950i
\(760\) 0 0
\(761\) 15.6086 42.8843i 0.565811 1.55455i −0.245170 0.969480i \(-0.578844\pi\)
0.810981 0.585073i \(-0.198934\pi\)
\(762\) 0 0
\(763\) −16.1690 2.85104i −0.585359 0.103215i
\(764\) 0 0
\(765\) −15.6199 4.92040i −0.564739 0.177897i
\(766\) 0 0
\(767\) 10.2034 3.71374i 0.368425 0.134096i
\(768\) 0 0
\(769\) 9.50115 7.97241i 0.342620 0.287493i −0.455198 0.890390i \(-0.650432\pi\)
0.797819 + 0.602897i \(0.205987\pi\)
\(770\) 0 0
\(771\) 50.1721 + 17.0237i 1.80691 + 0.613095i
\(772\) 0 0
\(773\) −40.5127 + 23.3900i −1.45714 + 0.841280i −0.998870 0.0475339i \(-0.984864\pi\)
−0.458269 + 0.888813i \(0.651530\pi\)
\(774\) 0 0
\(775\) −29.2874 16.9091i −1.05204 0.607393i
\(776\) 0 0
\(777\) −3.41051 2.73648i −0.122351 0.0981707i
\(778\) 0 0
\(779\) −5.71724 32.4241i −0.204842 1.16171i
\(780\) 0 0
\(781\) 2.46509 + 2.06846i 0.0882080 + 0.0740153i
\(782\) 0 0
\(783\) −3.43178 2.51419i −0.122642 0.0898500i
\(784\) 0 0
\(785\) −4.85095 + 5.78114i −0.173138 + 0.206338i
\(786\) 0 0
\(787\) −19.7690 + 3.48581i −0.704690 + 0.124256i −0.514499 0.857491i \(-0.672022\pi\)
−0.190191 + 0.981747i \(0.560911\pi\)
\(788\) 0 0
\(789\) −8.16658 20.9921i −0.290738 0.747339i
\(790\) 0 0
\(791\) 3.38203 5.85785i 0.120251 0.208281i
\(792\) 0 0
\(793\) 4.54740 + 7.87632i 0.161483 + 0.279696i
\(794\) 0 0
\(795\) −15.2516 + 3.03582i −0.540917 + 0.107669i