Properties

Label 768.2.o.b.95.6
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.6
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.602068 - 1.62404i) q^{3} +(-0.378520 + 0.156788i) q^{5} +(2.01144 + 2.01144i) q^{7} +(-2.27503 + 1.95557i) q^{9} +O(q^{10})\) \(q+(-0.602068 - 1.62404i) q^{3} +(-0.378520 + 0.156788i) q^{5} +(2.01144 + 2.01144i) q^{7} +(-2.27503 + 1.95557i) q^{9} +(-0.709852 + 0.294030i) q^{11} +(-2.08393 + 5.03104i) q^{13} +(0.482526 + 0.520336i) q^{15} -6.33777 q^{17} +(-0.646487 - 0.267784i) q^{19} +(2.05564 - 4.47769i) q^{21} +(1.61798 + 1.61798i) q^{23} +(-3.41684 + 3.41684i) q^{25} +(4.54565 + 2.51736i) q^{27} +(-2.04571 + 4.93879i) q^{29} -5.75464i q^{31} +(0.904897 + 0.975803i) q^{33} +(-1.07674 - 0.446001i) q^{35} +(2.50232 + 6.04113i) q^{37} +(9.42529 + 0.355354i) q^{39} +(5.52228 - 5.52228i) q^{41} +(0.406593 + 0.981601i) q^{43} +(0.554534 - 1.09692i) q^{45} +10.4826i q^{47} +1.09178i q^{49} +(3.81577 + 10.2928i) q^{51} +(-0.674566 - 1.62855i) q^{53} +(0.222593 - 0.222593i) q^{55} +(-0.0456628 + 1.21115i) q^{57} +(3.35082 + 8.08960i) q^{59} +(-4.14715 - 1.71781i) q^{61} +(-8.50959 - 0.642573i) q^{63} -2.23109i q^{65} +(2.65183 - 6.40208i) q^{67} +(1.65353 - 3.60179i) q^{69} +(-1.97014 + 1.97014i) q^{71} +(9.48914 + 9.48914i) q^{73} +(7.60626 + 3.49192i) q^{75} +(-2.01925 - 0.836400i) q^{77} -8.75751 q^{79} +(1.35150 - 8.89795i) q^{81} +(6.60293 - 15.9409i) q^{83} +(2.39898 - 0.993689i) q^{85} +(9.25246 + 0.348838i) q^{87} +(6.11535 + 6.11535i) q^{89} +(-14.3113 + 5.92795i) q^{91} +(-9.34579 + 3.46469i) q^{93} +0.286694 q^{95} -5.09195 q^{97} +(1.03994 - 2.05709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) −0.602068 1.62404i −0.347604 0.937641i
\(4\) 0 0
\(5\) −0.378520 + 0.156788i −0.169279 + 0.0701179i −0.465714 0.884935i \(-0.654202\pi\)
0.296434 + 0.955053i \(0.404202\pi\)
\(6\) 0 0
\(7\) 2.01144 + 2.01144i 0.760253 + 0.760253i 0.976368 0.216115i \(-0.0693386\pi\)
−0.216115 + 0.976368i \(0.569339\pi\)
\(8\) 0 0
\(9\) −2.27503 + 1.95557i −0.758343 + 0.651856i
\(10\) 0 0
\(11\) −0.709852 + 0.294030i −0.214028 + 0.0886534i −0.487122 0.873334i \(-0.661953\pi\)
0.273093 + 0.961988i \(0.411953\pi\)
\(12\) 0 0
\(13\) −2.08393 + 5.03104i −0.577977 + 1.39536i 0.316648 + 0.948543i \(0.397443\pi\)
−0.894625 + 0.446817i \(0.852557\pi\)
\(14\) 0 0
\(15\) 0.482526 + 0.520336i 0.124588 + 0.134350i
\(16\) 0 0
\(17\) −6.33777 −1.53714 −0.768568 0.639768i \(-0.779030\pi\)
−0.768568 + 0.639768i \(0.779030\pi\)
\(18\) 0 0
\(19\) −0.646487 0.267784i −0.148314 0.0614338i 0.307291 0.951615i \(-0.400577\pi\)
−0.455606 + 0.890182i \(0.650577\pi\)
\(20\) 0 0
\(21\) 2.05564 4.47769i 0.448577 0.977112i
\(22\) 0 0
\(23\) 1.61798 + 1.61798i 0.337371 + 0.337371i 0.855377 0.518006i \(-0.173325\pi\)
−0.518006 + 0.855377i \(0.673325\pi\)
\(24\) 0 0
\(25\) −3.41684 + 3.41684i −0.683368 + 0.683368i
\(26\) 0 0
\(27\) 4.54565 + 2.51736i 0.874810 + 0.484465i
\(28\) 0 0
\(29\) −2.04571 + 4.93879i −0.379879 + 0.917110i 0.612108 + 0.790774i \(0.290322\pi\)
−0.991988 + 0.126336i \(0.959678\pi\)
\(30\) 0 0
\(31\) 5.75464i 1.03356i −0.856117 0.516782i \(-0.827130\pi\)
0.856117 0.516782i \(-0.172870\pi\)
\(32\) 0 0
\(33\) 0.904897 + 0.975803i 0.157522 + 0.169866i
\(34\) 0 0
\(35\) −1.07674 0.446001i −0.182002 0.0753879i
\(36\) 0 0
\(37\) 2.50232 + 6.04113i 0.411379 + 0.993156i 0.984768 + 0.173873i \(0.0556282\pi\)
−0.573389 + 0.819283i \(0.694372\pi\)
\(38\) 0 0
\(39\) 9.42529 + 0.355354i 1.50925 + 0.0569021i
\(40\) 0 0
\(41\) 5.52228 5.52228i 0.862435 0.862435i −0.129185 0.991620i \(-0.541236\pi\)
0.991620 + 0.129185i \(0.0412361\pi\)
\(42\) 0 0
\(43\) 0.406593 + 0.981601i 0.0620048 + 0.149693i 0.951845 0.306579i \(-0.0991844\pi\)
−0.889840 + 0.456272i \(0.849184\pi\)
\(44\) 0 0
\(45\) 0.554534 1.09692i 0.0826651 0.163519i
\(46\) 0 0
\(47\) 10.4826i 1.52904i 0.644597 + 0.764522i \(0.277025\pi\)
−0.644597 + 0.764522i \(0.722975\pi\)
\(48\) 0 0
\(49\) 1.09178i 0.155969i
\(50\) 0 0
\(51\) 3.81577 + 10.2928i 0.534315 + 1.44128i
\(52\) 0 0
\(53\) −0.674566 1.62855i −0.0926588 0.223698i 0.870755 0.491718i \(-0.163631\pi\)
−0.963413 + 0.268020i \(0.913631\pi\)
\(54\) 0 0
\(55\) 0.222593 0.222593i 0.0300144 0.0300144i
\(56\) 0 0
\(57\) −0.0456628 + 1.21115i −0.00604819 + 0.160420i
\(58\) 0 0
\(59\) 3.35082 + 8.08960i 0.436240 + 1.05318i 0.977237 + 0.212152i \(0.0680472\pi\)
−0.540997 + 0.841025i \(0.681953\pi\)
\(60\) 0 0
\(61\) −4.14715 1.71781i −0.530988 0.219943i 0.101048 0.994882i \(-0.467781\pi\)
−0.632036 + 0.774939i \(0.717781\pi\)
\(62\) 0 0
\(63\) −8.50959 0.642573i −1.07211 0.0809566i
\(64\) 0 0
\(65\) 2.23109i 0.276732i
\(66\) 0 0
\(67\) 2.65183 6.40208i 0.323972 0.782138i −0.675043 0.737778i \(-0.735875\pi\)
0.999016 0.0443601i \(-0.0141249\pi\)
\(68\) 0 0
\(69\) 1.65353 3.60179i 0.199061 0.433605i
\(70\) 0 0
\(71\) −1.97014 + 1.97014i −0.233813 + 0.233813i −0.814282 0.580469i \(-0.802869\pi\)
0.580469 + 0.814282i \(0.302869\pi\)
\(72\) 0 0
\(73\) 9.48914 + 9.48914i 1.11062 + 1.11062i 0.993067 + 0.117554i \(0.0375052\pi\)
0.117554 + 0.993067i \(0.462495\pi\)
\(74\) 0 0
\(75\) 7.60626 + 3.49192i 0.878295 + 0.403212i
\(76\) 0 0
\(77\) −2.01925 0.836400i −0.230115 0.0953166i
\(78\) 0 0
\(79\) −8.75751 −0.985297 −0.492649 0.870228i \(-0.663971\pi\)
−0.492649 + 0.870228i \(0.663971\pi\)
\(80\) 0 0
\(81\) 1.35150 8.89795i 0.150167 0.988661i
\(82\) 0 0
\(83\) 6.60293 15.9409i 0.724766 1.74974i 0.0654719 0.997854i \(-0.479145\pi\)
0.659294 0.751885i \(-0.270855\pi\)
\(84\) 0 0
\(85\) 2.39898 0.993689i 0.260206 0.107781i
\(86\) 0 0
\(87\) 9.25246 + 0.348838i 0.991968 + 0.0373993i
\(88\) 0 0
\(89\) 6.11535 + 6.11535i 0.648226 + 0.648226i 0.952564 0.304338i \(-0.0984353\pi\)
−0.304338 + 0.952564i \(0.598435\pi\)
\(90\) 0 0
\(91\) −14.3113 + 5.92795i −1.50024 + 0.621418i
\(92\) 0 0
\(93\) −9.34579 + 3.46469i −0.969113 + 0.359271i
\(94\) 0 0
\(95\) 0.286694 0.0294142
\(96\) 0 0
\(97\) −5.09195 −0.517009 −0.258505 0.966010i \(-0.583230\pi\)
−0.258505 + 0.966010i \(0.583230\pi\)
\(98\) 0 0
\(99\) 1.03994 2.05709i 0.104518 0.206745i
\(100\) 0 0
\(101\) −2.33659 + 0.967847i −0.232499 + 0.0963044i −0.495892 0.868384i \(-0.665159\pi\)
0.263392 + 0.964689i \(0.415159\pi\)
\(102\) 0 0
\(103\) −6.15411 6.15411i −0.606383 0.606383i 0.335616 0.941999i \(-0.391055\pi\)
−0.941999 + 0.335616i \(0.891055\pi\)
\(104\) 0 0
\(105\) −0.0760526 + 2.01720i −0.00742198 + 0.196858i
\(106\) 0 0
\(107\) 1.19264 0.494009i 0.115297 0.0477576i −0.324289 0.945958i \(-0.605125\pi\)
0.439586 + 0.898200i \(0.355125\pi\)
\(108\) 0 0
\(109\) 0.933827 2.25446i 0.0894444 0.215938i −0.872827 0.488030i \(-0.837716\pi\)
0.962271 + 0.272092i \(0.0877156\pi\)
\(110\) 0 0
\(111\) 8.30449 7.70104i 0.788227 0.730951i
\(112\) 0 0
\(113\) −7.02329 −0.660696 −0.330348 0.943859i \(-0.607166\pi\)
−0.330348 + 0.943859i \(0.607166\pi\)
\(114\) 0 0
\(115\) −0.866116 0.358757i −0.0807657 0.0334543i
\(116\) 0 0
\(117\) −5.09756 15.5210i −0.471270 1.43492i
\(118\) 0 0
\(119\) −12.7481 12.7481i −1.16861 1.16861i
\(120\) 0 0
\(121\) −7.36074 + 7.36074i −0.669158 + 0.669158i
\(122\) 0 0
\(123\) −12.2932 5.64363i −1.10844 0.508869i
\(124\) 0 0
\(125\) 1.54156 3.72167i 0.137882 0.332876i
\(126\) 0 0
\(127\) 5.12307i 0.454599i 0.973825 + 0.227299i \(0.0729896\pi\)
−0.973825 + 0.227299i \(0.927010\pi\)
\(128\) 0 0
\(129\) 1.34937 1.25131i 0.118805 0.110172i
\(130\) 0 0
\(131\) −13.0406 5.40161i −1.13937 0.471941i −0.268412 0.963304i \(-0.586499\pi\)
−0.870955 + 0.491363i \(0.836499\pi\)
\(132\) 0 0
\(133\) −0.761739 1.83900i −0.0660512 0.159462i
\(134\) 0 0
\(135\) −2.11531 0.240166i −0.182057 0.0206702i
\(136\) 0 0
\(137\) 5.19191 5.19191i 0.443575 0.443575i −0.449637 0.893211i \(-0.648447\pi\)
0.893211 + 0.449637i \(0.148447\pi\)
\(138\) 0 0
\(139\) −2.91660 7.04129i −0.247383 0.597234i 0.750598 0.660759i \(-0.229766\pi\)
−0.997980 + 0.0635252i \(0.979766\pi\)
\(140\) 0 0
\(141\) 17.0242 6.31124i 1.43370 0.531502i
\(142\) 0 0
\(143\) 4.18403i 0.349886i
\(144\) 0 0
\(145\) 2.19018i 0.181884i
\(146\) 0 0
\(147\) 1.77310 0.657327i 0.146243 0.0542154i
\(148\) 0 0
\(149\) 7.55828 + 18.2473i 0.619199 + 1.49488i 0.852636 + 0.522506i \(0.175003\pi\)
−0.233437 + 0.972372i \(0.574997\pi\)
\(150\) 0 0
\(151\) −8.19627 + 8.19627i −0.667003 + 0.667003i −0.957021 0.290018i \(-0.906339\pi\)
0.290018 + 0.957021i \(0.406339\pi\)
\(152\) 0 0
\(153\) 14.4186 12.3940i 1.16568 1.00199i
\(154\) 0 0
\(155\) 0.902261 + 2.17825i 0.0724713 + 0.174961i
\(156\) 0 0
\(157\) 1.42476 + 0.590154i 0.113708 + 0.0470994i 0.438812 0.898579i \(-0.355399\pi\)
−0.325104 + 0.945678i \(0.605399\pi\)
\(158\) 0 0
\(159\) −2.23869 + 2.07602i −0.177540 + 0.164639i
\(160\) 0 0
\(161\) 6.50892i 0.512975i
\(162\) 0 0
\(163\) −0.927085 + 2.23818i −0.0726149 + 0.175308i −0.956019 0.293303i \(-0.905245\pi\)
0.883405 + 0.468611i \(0.155245\pi\)
\(164\) 0 0
\(165\) −0.495516 0.227484i −0.0385759 0.0177096i
\(166\) 0 0
\(167\) 13.4441 13.4441i 1.04033 1.04033i 0.0411813 0.999152i \(-0.486888\pi\)
0.999152 0.0411813i \(-0.0131121\pi\)
\(168\) 0 0
\(169\) −11.7763 11.7763i −0.905866 0.905866i
\(170\) 0 0
\(171\) 1.99445 0.655035i 0.152519 0.0500918i
\(172\) 0 0
\(173\) −5.11484 2.11864i −0.388874 0.161077i 0.179675 0.983726i \(-0.442495\pi\)
−0.568550 + 0.822649i \(0.692495\pi\)
\(174\) 0 0
\(175\) −13.7455 −1.03906
\(176\) 0 0
\(177\) 11.1204 10.3124i 0.835863 0.775125i
\(178\) 0 0
\(179\) −2.02160 + 4.88057i −0.151101 + 0.364791i −0.981247 0.192756i \(-0.938257\pi\)
0.830145 + 0.557547i \(0.188257\pi\)
\(180\) 0 0
\(181\) −8.06344 + 3.33999i −0.599351 + 0.248259i −0.661668 0.749797i \(-0.730151\pi\)
0.0623171 + 0.998056i \(0.480151\pi\)
\(182\) 0 0
\(183\) −0.292922 + 7.76939i −0.0216535 + 0.574330i
\(184\) 0 0
\(185\) −1.89436 1.89436i −0.139276 0.139276i
\(186\) 0 0
\(187\) 4.49888 1.86350i 0.328991 0.136272i
\(188\) 0 0
\(189\) 4.07979 + 14.2068i 0.296761 + 1.03339i
\(190\) 0 0
\(191\) 10.8066 0.781940 0.390970 0.920404i \(-0.372140\pi\)
0.390970 + 0.920404i \(0.372140\pi\)
\(192\) 0 0
\(193\) −5.82359 −0.419192 −0.209596 0.977788i \(-0.567215\pi\)
−0.209596 + 0.977788i \(0.567215\pi\)
\(194\) 0 0
\(195\) −3.62338 + 1.34327i −0.259476 + 0.0961933i
\(196\) 0 0
\(197\) 19.4552 8.05861i 1.38613 0.574152i 0.440014 0.897991i \(-0.354974\pi\)
0.946112 + 0.323839i \(0.104974\pi\)
\(198\) 0 0
\(199\) 1.63519 + 1.63519i 0.115916 + 0.115916i 0.762685 0.646770i \(-0.223880\pi\)
−0.646770 + 0.762685i \(0.723880\pi\)
\(200\) 0 0
\(201\) −11.9938 0.452193i −0.845979 0.0318952i
\(202\) 0 0
\(203\) −14.0489 + 5.81925i −0.986040 + 0.408431i
\(204\) 0 0
\(205\) −1.22447 + 2.95612i −0.0855205 + 0.206465i
\(206\) 0 0
\(207\) −6.84500 0.516877i −0.475760 0.0359254i
\(208\) 0 0
\(209\) 0.537647 0.0371898
\(210\) 0 0
\(211\) −13.4379 5.56618i −0.925106 0.383192i −0.131286 0.991344i \(-0.541911\pi\)
−0.793820 + 0.608153i \(0.791911\pi\)
\(212\) 0 0
\(213\) 4.38575 + 2.01343i 0.300507 + 0.137958i
\(214\) 0 0
\(215\) −0.307807 0.307807i −0.0209923 0.0209923i
\(216\) 0 0
\(217\) 11.5751 11.5751i 0.785771 0.785771i
\(218\) 0 0
\(219\) 9.69766 21.1239i 0.655307 1.42742i
\(220\) 0 0
\(221\) 13.2075 31.8856i 0.888430 2.14486i
\(222\) 0 0
\(223\) 0.106627i 0.00714024i 0.999994 + 0.00357012i \(0.00113641\pi\)
−0.999994 + 0.00357012i \(0.998864\pi\)
\(224\) 0 0
\(225\) 1.09154 14.4553i 0.0727694 0.963684i
\(226\) 0 0
\(227\) 21.0312 + 8.71141i 1.39589 + 0.578196i 0.948681 0.316233i \(-0.102418\pi\)
0.447208 + 0.894430i \(0.352418\pi\)
\(228\) 0 0
\(229\) 1.56199 + 3.77098i 0.103219 + 0.249193i 0.967049 0.254591i \(-0.0819407\pi\)
−0.863830 + 0.503784i \(0.831941\pi\)
\(230\) 0 0
\(231\) −0.142624 + 3.78291i −0.00938397 + 0.248898i
\(232\) 0 0
\(233\) 4.47635 4.47635i 0.293255 0.293255i −0.545110 0.838365i \(-0.683512\pi\)
0.838365 + 0.545110i \(0.183512\pi\)
\(234\) 0 0
\(235\) −1.64355 3.96788i −0.107213 0.258836i
\(236\) 0 0
\(237\) 5.27262 + 14.2226i 0.342493 + 0.923855i
\(238\) 0 0
\(239\) 8.68031i 0.561483i −0.959783 0.280741i \(-0.909420\pi\)
0.959783 0.280741i \(-0.0905803\pi\)
\(240\) 0 0
\(241\) 4.55656i 0.293514i 0.989173 + 0.146757i \(0.0468835\pi\)
−0.989173 + 0.146757i \(0.953117\pi\)
\(242\) 0 0
\(243\) −15.2643 + 3.16227i −0.979208 + 0.202860i
\(244\) 0 0
\(245\) −0.171179 0.413262i −0.0109362 0.0264023i
\(246\) 0 0
\(247\) 2.69446 2.69446i 0.171445 0.171445i
\(248\) 0 0
\(249\) −29.8641 1.12594i −1.89256 0.0713536i
\(250\) 0 0
\(251\) −0.750992 1.81305i −0.0474022 0.114439i 0.898405 0.439168i \(-0.144727\pi\)
−0.945807 + 0.324729i \(0.894727\pi\)
\(252\) 0 0
\(253\) −1.62426 0.672789i −0.102116 0.0422979i
\(254\) 0 0
\(255\) −3.05814 3.29777i −0.191508 0.206515i
\(256\) 0 0
\(257\) 13.4127i 0.836663i 0.908294 + 0.418332i \(0.137385\pi\)
−0.908294 + 0.418332i \(0.862615\pi\)
\(258\) 0 0
\(259\) −7.11811 + 17.1846i −0.442298 + 1.06780i
\(260\) 0 0
\(261\) −5.00409 15.2364i −0.309745 0.943110i
\(262\) 0 0
\(263\) −18.7027 + 18.7027i −1.15326 + 1.15326i −0.167359 + 0.985896i \(0.553524\pi\)
−0.985896 + 0.167359i \(0.946476\pi\)
\(264\) 0 0
\(265\) 0.510674 + 0.510674i 0.0313705 + 0.0313705i
\(266\) 0 0
\(267\) 6.24973 13.6134i 0.382477 0.833130i
\(268\) 0 0
\(269\) −6.20132 2.56867i −0.378101 0.156615i 0.185535 0.982638i \(-0.440598\pi\)
−0.563636 + 0.826023i \(0.690598\pi\)
\(270\) 0 0
\(271\) 26.4006 1.60372 0.801860 0.597512i \(-0.203844\pi\)
0.801860 + 0.597512i \(0.203844\pi\)
\(272\) 0 0
\(273\) 18.2436 + 19.6732i 1.10416 + 1.19068i
\(274\) 0 0
\(275\) 1.42079 3.43010i 0.0856772 0.206843i
\(276\) 0 0
\(277\) 11.8110 4.89227i 0.709654 0.293948i 0.00149230 0.999999i \(-0.499525\pi\)
0.708161 + 0.706051i \(0.249525\pi\)
\(278\) 0 0
\(279\) 11.2536 + 13.0920i 0.673736 + 0.783796i
\(280\) 0 0
\(281\) 10.9033 + 10.9033i 0.650433 + 0.650433i 0.953097 0.302664i \(-0.0978760\pi\)
−0.302664 + 0.953097i \(0.597876\pi\)
\(282\) 0 0
\(283\) 8.86260 3.67101i 0.526827 0.218219i −0.103386 0.994641i \(-0.532968\pi\)
0.630213 + 0.776423i \(0.282968\pi\)
\(284\) 0 0
\(285\) −0.172609 0.465603i −0.0102245 0.0275800i
\(286\) 0 0
\(287\) 22.2155 1.31134
\(288\) 0 0
\(289\) 23.1674 1.36279
\(290\) 0 0
\(291\) 3.06570 + 8.26954i 0.179715 + 0.484769i
\(292\) 0 0
\(293\) −20.0666 + 8.31184i −1.17230 + 0.485583i −0.881952 0.471338i \(-0.843771\pi\)
−0.290348 + 0.956921i \(0.593771\pi\)
\(294\) 0 0
\(295\) −2.53671 2.53671i −0.147693 0.147693i
\(296\) 0 0
\(297\) −3.96691 0.450392i −0.230184 0.0261344i
\(298\) 0 0
\(299\) −11.5118 + 4.76836i −0.665747 + 0.275761i
\(300\) 0 0
\(301\) −1.15660 + 2.79227i −0.0666650 + 0.160944i
\(302\) 0 0
\(303\) 2.97861 + 3.21201i 0.171117 + 0.184525i
\(304\) 0 0
\(305\) 1.83911 0.105307
\(306\) 0 0
\(307\) −0.548682 0.227272i −0.0313149 0.0129711i 0.366971 0.930232i \(-0.380395\pi\)
−0.398286 + 0.917261i \(0.630395\pi\)
\(308\) 0 0
\(309\) −6.28934 + 13.6997i −0.357788 + 0.779351i
\(310\) 0 0
\(311\) −8.31914 8.31914i −0.471735 0.471735i 0.430741 0.902476i \(-0.358252\pi\)
−0.902476 + 0.430741i \(0.858252\pi\)
\(312\) 0 0
\(313\) 5.90243 5.90243i 0.333625 0.333625i −0.520336 0.853961i \(-0.674193\pi\)
0.853961 + 0.520336i \(0.174193\pi\)
\(314\) 0 0
\(315\) 3.32180 1.09098i 0.187162 0.0614696i
\(316\) 0 0
\(317\) 0.432895 1.04510i 0.0243138 0.0586987i −0.911256 0.411840i \(-0.864886\pi\)
0.935570 + 0.353141i \(0.114886\pi\)
\(318\) 0 0
\(319\) 4.10731i 0.229965i
\(320\) 0 0
\(321\) −1.52034 1.63948i −0.0848573 0.0915066i
\(322\) 0 0
\(323\) 4.09729 + 1.69715i 0.227979 + 0.0944321i
\(324\) 0 0
\(325\) −10.0698 24.3107i −0.558573 1.34852i
\(326\) 0 0
\(327\) −4.22356 0.159237i −0.233564 0.00880584i
\(328\) 0 0
\(329\) −21.0851 + 21.0851i −1.16246 + 1.16246i
\(330\) 0 0
\(331\) 6.16978 + 14.8952i 0.339122 + 0.818713i 0.997801 + 0.0662882i \(0.0211157\pi\)
−0.658679 + 0.752424i \(0.728884\pi\)
\(332\) 0 0
\(333\) −17.5067 8.85029i −0.959361 0.484993i
\(334\) 0 0
\(335\) 2.83909i 0.155116i
\(336\) 0 0
\(337\) 17.2474i 0.939527i 0.882792 + 0.469763i \(0.155661\pi\)
−0.882792 + 0.469763i \(0.844339\pi\)
\(338\) 0 0
\(339\) 4.22850 + 11.4061i 0.229661 + 0.619496i
\(340\) 0 0
\(341\) 1.69204 + 4.08494i 0.0916291 + 0.221212i
\(342\) 0 0
\(343\) 11.8840 11.8840i 0.641677 0.641677i
\(344\) 0 0
\(345\) −0.0611757 + 1.62261i −0.00329359 + 0.0873581i
\(346\) 0 0
\(347\) 3.34246 + 8.06942i 0.179433 + 0.433189i 0.987848 0.155424i \(-0.0496743\pi\)
−0.808415 + 0.588613i \(0.799674\pi\)
\(348\) 0 0
\(349\) 22.7745 + 9.43351i 1.21909 + 0.504964i 0.897121 0.441785i \(-0.145655\pi\)
0.321971 + 0.946750i \(0.395655\pi\)
\(350\) 0 0
\(351\) −22.1377 + 17.6234i −1.18162 + 0.940666i
\(352\) 0 0
\(353\) 7.05617i 0.375562i −0.982211 0.187781i \(-0.939870\pi\)
0.982211 0.187781i \(-0.0601295\pi\)
\(354\) 0 0
\(355\) 0.436843 1.05463i 0.0231852 0.0559741i
\(356\) 0 0
\(357\) −13.0282 + 28.3786i −0.689525 + 1.50195i
\(358\) 0 0
\(359\) −17.9832 + 17.9832i −0.949116 + 0.949116i −0.998767 0.0496509i \(-0.984189\pi\)
0.0496509 + 0.998767i \(0.484189\pi\)
\(360\) 0 0
\(361\) −13.0888 13.0888i −0.688884 0.688884i
\(362\) 0 0
\(363\) 16.3858 + 7.52249i 0.860032 + 0.394828i
\(364\) 0 0
\(365\) −5.07962 2.10405i −0.265879 0.110131i
\(366\) 0 0
\(367\) 9.28729 0.484792 0.242396 0.970177i \(-0.422067\pi\)
0.242396 + 0.970177i \(0.422067\pi\)
\(368\) 0 0
\(369\) −1.76414 + 23.3625i −0.0918376 + 1.21621i
\(370\) 0 0
\(371\) 1.91887 4.63257i 0.0996230 0.240511i
\(372\) 0 0
\(373\) −31.7209 + 13.1392i −1.64244 + 0.680323i −0.996541 0.0830975i \(-0.973519\pi\)
−0.645902 + 0.763420i \(0.723519\pi\)
\(374\) 0 0
\(375\) −6.97227 0.262869i −0.360046 0.0135745i
\(376\) 0 0
\(377\) −20.5841 20.5841i −1.06014 1.06014i
\(378\) 0 0
\(379\) 28.0588 11.6223i 1.44128 0.596999i 0.481174 0.876625i \(-0.340211\pi\)
0.960109 + 0.279626i \(0.0902105\pi\)
\(380\) 0 0
\(381\) 8.32008 3.08444i 0.426251 0.158021i
\(382\) 0 0
\(383\) 5.32676 0.272185 0.136092 0.990696i \(-0.456546\pi\)
0.136092 + 0.990696i \(0.456546\pi\)
\(384\) 0 0
\(385\) 0.895464 0.0456371
\(386\) 0 0
\(387\) −2.84460 1.43805i −0.144599 0.0731002i
\(388\) 0 0
\(389\) −20.0435 + 8.30227i −1.01624 + 0.420942i −0.827729 0.561128i \(-0.810367\pi\)
−0.188515 + 0.982070i \(0.560367\pi\)
\(390\) 0 0
\(391\) −10.2544 10.2544i −0.518585 0.518585i
\(392\) 0 0
\(393\) −0.921090 + 24.4307i −0.0464628 + 1.23237i
\(394\) 0 0
\(395\) 3.31490 1.37308i 0.166791 0.0690869i
\(396\) 0 0
\(397\) 2.65193 6.40233i 0.133097 0.321323i −0.843255 0.537514i \(-0.819363\pi\)
0.976351 + 0.216191i \(0.0693634\pi\)
\(398\) 0 0
\(399\) −2.52800 + 2.34430i −0.126558 + 0.117362i
\(400\) 0 0
\(401\) −5.61080 −0.280190 −0.140095 0.990138i \(-0.544741\pi\)
−0.140095 + 0.990138i \(0.544741\pi\)
\(402\) 0 0
\(403\) 28.9519 + 11.9923i 1.44220 + 0.597377i
\(404\) 0 0
\(405\) 0.883522 + 3.57995i 0.0439026 + 0.177889i
\(406\) 0 0
\(407\) −3.55255 3.55255i −0.176093 0.176093i
\(408\) 0 0
\(409\) −0.683364 + 0.683364i −0.0337902 + 0.0337902i −0.723800 0.690010i \(-0.757606\pi\)
0.690010 + 0.723800i \(0.257606\pi\)
\(410\) 0 0
\(411\) −11.5578 5.30600i −0.570102 0.261725i
\(412\) 0 0
\(413\) −9.53177 + 23.0117i −0.469028 + 1.13233i
\(414\) 0 0
\(415\) 7.06921i 0.347014i
\(416\) 0 0
\(417\) −9.67936 + 8.97601i −0.474000 + 0.439557i
\(418\) 0 0
\(419\) 16.8772 + 6.99075i 0.824503 + 0.341521i 0.754724 0.656042i \(-0.227771\pi\)
0.0697790 + 0.997562i \(0.477771\pi\)
\(420\) 0 0
\(421\) 7.36473 + 17.7800i 0.358935 + 0.866546i 0.995450 + 0.0952818i \(0.0303752\pi\)
−0.636515 + 0.771264i \(0.719625\pi\)
\(422\) 0 0
\(423\) −20.4994 23.8482i −0.996717 1.15954i
\(424\) 0 0
\(425\) 21.6552 21.6552i 1.05043 1.05043i
\(426\) 0 0
\(427\) −4.88648 11.7970i −0.236473 0.570897i
\(428\) 0 0
\(429\) −6.79505 + 2.51907i −0.328068 + 0.121622i
\(430\) 0 0
\(431\) 18.7398i 0.902664i −0.892356 0.451332i \(-0.850949\pi\)
0.892356 0.451332i \(-0.149051\pi\)
\(432\) 0 0
\(433\) 2.88137i 0.138470i −0.997600 0.0692349i \(-0.977944\pi\)
0.997600 0.0692349i \(-0.0220558\pi\)
\(434\) 0 0
\(435\) −3.55694 + 1.31864i −0.170542 + 0.0632237i
\(436\) 0 0
\(437\) −0.612733 1.47927i −0.0293110 0.0707630i
\(438\) 0 0
\(439\) 6.54440 6.54440i 0.312347 0.312347i −0.533471 0.845818i \(-0.679113\pi\)
0.845818 + 0.533471i \(0.179113\pi\)
\(440\) 0 0
\(441\) −2.13505 2.48383i −0.101669 0.118278i
\(442\) 0 0
\(443\) −5.97491 14.4247i −0.283877 0.685339i 0.716042 0.698057i \(-0.245952\pi\)
−0.999919 + 0.0127177i \(0.995952\pi\)
\(444\) 0 0
\(445\) −3.27360 1.35597i −0.155184 0.0642791i
\(446\) 0 0
\(447\) 25.0838 23.2611i 1.18642 1.10021i
\(448\) 0 0
\(449\) 2.52116i 0.118981i 0.998229 + 0.0594905i \(0.0189476\pi\)
−0.998229 + 0.0594905i \(0.981052\pi\)
\(450\) 0 0
\(451\) −2.29628 + 5.54372i −0.108128 + 0.261043i
\(452\) 0 0
\(453\) 18.2458 + 8.37638i 0.857263 + 0.393557i
\(454\) 0 0
\(455\) 4.48770 4.48770i 0.210387 0.210387i
\(456\) 0 0
\(457\) 26.6180 + 26.6180i 1.24514 + 1.24514i 0.957842 + 0.287295i \(0.0927560\pi\)
0.287295 + 0.957842i \(0.407244\pi\)
\(458\) 0 0
\(459\) −28.8093 15.9544i −1.34470 0.744689i
\(460\) 0 0
\(461\) −16.9365 7.01532i −0.788810 0.326736i −0.0483450 0.998831i \(-0.515395\pi\)
−0.740465 + 0.672095i \(0.765395\pi\)
\(462\) 0 0
\(463\) 22.1078 1.02744 0.513719 0.857959i \(-0.328268\pi\)
0.513719 + 0.857959i \(0.328268\pi\)
\(464\) 0 0
\(465\) 2.99435 2.77677i 0.138860 0.128769i
\(466\) 0 0
\(467\) −11.0935 + 26.7822i −0.513348 + 1.23933i 0.428577 + 0.903505i \(0.359015\pi\)
−0.941924 + 0.335825i \(0.890985\pi\)
\(468\) 0 0
\(469\) 18.2114 7.54340i 0.840923 0.348322i
\(470\) 0 0
\(471\) 0.100634 2.66918i 0.00463696 0.122989i
\(472\) 0 0
\(473\) −0.577241 0.577241i −0.0265416 0.0265416i
\(474\) 0 0
\(475\) 3.12392 1.29397i 0.143335 0.0593714i
\(476\) 0 0
\(477\) 4.71939 + 2.38583i 0.216086 + 0.109240i
\(478\) 0 0
\(479\) −11.5288 −0.526765 −0.263382 0.964692i \(-0.584838\pi\)
−0.263382 + 0.964692i \(0.584838\pi\)
\(480\) 0 0
\(481\) −35.6078 −1.62358
\(482\) 0 0
\(483\) 10.5708 3.91881i 0.480986 0.178312i
\(484\) 0 0
\(485\) 1.92741 0.798358i 0.0875190 0.0362516i
\(486\) 0 0
\(487\) 24.3533 + 24.3533i 1.10355 + 1.10355i 0.993979 + 0.109575i \(0.0349489\pi\)
0.109575 + 0.993979i \(0.465051\pi\)
\(488\) 0 0
\(489\) 4.19307 + 0.158088i 0.189617 + 0.00714897i
\(490\) 0 0
\(491\) −13.2408 + 5.48453i −0.597550 + 0.247513i −0.660895 0.750478i \(-0.729823\pi\)
0.0633450 + 0.997992i \(0.479823\pi\)
\(492\) 0 0
\(493\) 12.9653 31.3009i 0.583926 1.40972i
\(494\) 0 0
\(495\) −0.0711093 + 0.941700i −0.00319613 + 0.0423263i
\(496\) 0 0
\(497\) −7.92564 −0.355513
\(498\) 0 0
\(499\) 6.79930 + 2.81636i 0.304378 + 0.126078i 0.529645 0.848220i \(-0.322325\pi\)
−0.225266 + 0.974297i \(0.572325\pi\)
\(500\) 0 0
\(501\) −29.9280 13.7395i −1.33708 0.613835i
\(502\) 0 0
\(503\) 20.7317 + 20.7317i 0.924383 + 0.924383i 0.997335 0.0729527i \(-0.0232422\pi\)
−0.0729527 + 0.997335i \(0.523242\pi\)
\(504\) 0 0
\(505\) 0.732700 0.732700i 0.0326047 0.0326047i
\(506\) 0 0
\(507\) −12.0350 + 26.2153i −0.534495 + 1.16426i
\(508\) 0 0
\(509\) 7.27710 17.5685i 0.322552 0.778708i −0.676553 0.736394i \(-0.736527\pi\)
0.999104 0.0423143i \(-0.0134731\pi\)
\(510\) 0 0
\(511\) 38.1737i 1.68870i
\(512\) 0 0
\(513\) −2.26460 2.84469i −0.0999844 0.125596i
\(514\) 0 0
\(515\) 3.29435 + 1.36456i 0.145166 + 0.0601299i
\(516\) 0 0
\(517\) −3.08220 7.44109i −0.135555 0.327259i
\(518\) 0 0
\(519\) −0.361273 + 9.58229i −0.0158581 + 0.420616i
\(520\) 0 0
\(521\) −12.9964 + 12.9964i −0.569382 + 0.569382i −0.931955 0.362573i \(-0.881898\pi\)
0.362573 + 0.931955i \(0.381898\pi\)
\(522\) 0 0
\(523\) 13.8611 + 33.4638i 0.606105 + 1.46327i 0.867203 + 0.497955i \(0.165916\pi\)
−0.261097 + 0.965313i \(0.584084\pi\)
\(524\) 0 0
\(525\) 8.27575 + 22.3233i 0.361183 + 0.974270i
\(526\) 0 0
\(527\) 36.4716i 1.58873i
\(528\) 0 0
\(529\) 17.7643i 0.772361i
\(530\) 0 0
\(531\) −23.4430 11.8513i −1.01734 0.514303i
\(532\) 0 0
\(533\) 16.2748 + 39.2909i 0.704940 + 1.70188i
\(534\) 0 0
\(535\) −0.373985 + 0.373985i −0.0161688 + 0.0161688i
\(536\) 0 0
\(537\) 9.14339 + 0.344725i 0.394566 + 0.0148760i
\(538\) 0 0
\(539\) −0.321017 0.775003i −0.0138272 0.0333817i
\(540\) 0 0
\(541\) −0.814609 0.337422i −0.0350228 0.0145069i 0.365103 0.930967i \(-0.381034\pi\)
−0.400126 + 0.916460i \(0.631034\pi\)
\(542\) 0 0
\(543\) 10.2790 + 11.0845i 0.441115 + 0.475680i
\(544\) 0 0
\(545\) 0.999771i 0.0428255i
\(546\) 0 0
\(547\) 11.6045 28.0158i 0.496173 1.19787i −0.455356 0.890310i \(-0.650488\pi\)
0.951529 0.307559i \(-0.0995121\pi\)
\(548\) 0 0
\(549\) 12.7942 4.20198i 0.546042 0.179336i
\(550\) 0 0
\(551\) 2.64506 2.64506i 0.112683 0.112683i
\(552\) 0 0
\(553\) −17.6152 17.6152i −0.749075 0.749075i
\(554\) 0 0
\(555\) −1.93598 + 4.21705i −0.0821780 + 0.179004i
\(556\) 0 0
\(557\) 9.67547 + 4.00771i 0.409963 + 0.169812i 0.578127 0.815947i \(-0.303784\pi\)
−0.168164 + 0.985759i \(0.553784\pi\)
\(558\) 0 0
\(559\) −5.78579 −0.244713
\(560\) 0 0
\(561\) −5.73503 6.18442i −0.242133 0.261106i
\(562\) 0 0
\(563\) 7.67115 18.5198i 0.323300 0.780516i −0.675758 0.737124i \(-0.736183\pi\)
0.999058 0.0433923i \(-0.0138165\pi\)
\(564\) 0 0
\(565\) 2.65846 1.10117i 0.111842 0.0463266i
\(566\) 0 0
\(567\) 20.6162 15.1792i 0.865797 0.637467i
\(568\) 0 0
\(569\) 3.36174 + 3.36174i 0.140932 + 0.140932i 0.774053 0.633121i \(-0.218227\pi\)
−0.633121 + 0.774053i \(0.718227\pi\)
\(570\) 0 0
\(571\) −14.6718 + 6.07726i −0.613996 + 0.254325i −0.667936 0.744219i \(-0.732822\pi\)
0.0539402 + 0.998544i \(0.482822\pi\)
\(572\) 0 0
\(573\) −6.50632 17.5504i −0.271806 0.733179i
\(574\) 0 0
\(575\) −11.0567 −0.461097
\(576\) 0 0
\(577\) 11.1656 0.464830 0.232415 0.972617i \(-0.425337\pi\)
0.232415 + 0.972617i \(0.425337\pi\)
\(578\) 0 0
\(579\) 3.50620 + 9.45777i 0.145713 + 0.393051i
\(580\) 0 0
\(581\) 45.3455 18.7827i 1.88125 0.779239i
\(582\) 0 0
\(583\) 0.957684 + 0.957684i 0.0396632 + 0.0396632i
\(584\) 0 0
\(585\) 4.36305 + 5.07579i 0.180390 + 0.209858i
\(586\) 0 0
\(587\) 31.3098 12.9689i 1.29229 0.535286i 0.372625 0.927982i \(-0.378458\pi\)
0.919668 + 0.392696i \(0.128458\pi\)
\(588\) 0 0
\(589\) −1.54100 + 3.72030i −0.0634958 + 0.153292i
\(590\) 0 0
\(591\) −24.8009 26.7442i −1.02017 1.10011i
\(592\) 0 0
\(593\) 21.0070 0.862656 0.431328 0.902195i \(-0.358045\pi\)
0.431328 + 0.902195i \(0.358045\pi\)
\(594\) 0 0
\(595\) 6.82414 + 2.82665i 0.279763 + 0.115881i
\(596\) 0 0
\(597\) 1.67113 3.64012i 0.0683947 0.148980i
\(598\) 0 0
\(599\) 4.73031 + 4.73031i 0.193275 + 0.193275i 0.797110 0.603835i \(-0.206361\pi\)
−0.603835 + 0.797110i \(0.706361\pi\)
\(600\) 0 0
\(601\) 22.8135 22.8135i 0.930581 0.930581i −0.0671615 0.997742i \(-0.521394\pi\)
0.997742 + 0.0671615i \(0.0213943\pi\)
\(602\) 0 0
\(603\) 6.48672 + 19.7507i 0.264160 + 0.804312i
\(604\) 0 0
\(605\) 1.63211 3.94027i 0.0663548 0.160195i
\(606\) 0 0
\(607\) 20.5708i 0.834943i −0.908690 0.417472i \(-0.862916\pi\)
0.908690 0.417472i \(-0.137084\pi\)
\(608\) 0 0
\(609\) 17.9091 + 19.3124i 0.725714 + 0.782579i
\(610\) 0 0
\(611\) −52.7384 21.8450i −2.13357 0.883753i
\(612\) 0 0
\(613\) 1.90289 + 4.59399i 0.0768571 + 0.185550i 0.957638 0.287974i \(-0.0929818\pi\)
−0.880781 + 0.473524i \(0.842982\pi\)
\(614\) 0 0
\(615\) 5.53808 + 0.208798i 0.223317 + 0.00841953i
\(616\) 0 0
\(617\) 2.85391 2.85391i 0.114894 0.114894i −0.647322 0.762216i \(-0.724111\pi\)
0.762216 + 0.647322i \(0.224111\pi\)
\(618\) 0 0
\(619\) −12.0551 29.1035i −0.484534 1.16977i −0.957434 0.288652i \(-0.906793\pi\)
0.472901 0.881116i \(-0.343207\pi\)
\(620\) 0 0
\(621\) 3.28173 + 11.4278i 0.131691 + 0.458580i
\(622\) 0 0
\(623\) 24.6013i 0.985631i
\(624\) 0 0
\(625\) 22.5103i 0.900411i
\(626\) 0 0
\(627\) −0.323700 0.873161i −0.0129273 0.0348707i
\(628\) 0 0
\(629\) −15.8591 38.2873i −0.632345 1.52662i
\(630\) 0 0
\(631\) −27.3014 + 27.3014i −1.08685 + 1.08685i −0.0910003 + 0.995851i \(0.529006\pi\)
−0.995851 + 0.0910003i \(0.970994\pi\)
\(632\) 0 0
\(633\) −0.949152 + 25.1750i −0.0377254 + 1.00062i
\(634\) 0 0
\(635\) −0.803237 1.93919i −0.0318755 0.0769543i
\(636\) 0 0
\(637\) −5.49280 2.27519i −0.217633 0.0901464i
\(638\) 0 0
\(639\) 0.629379 8.33487i 0.0248979 0.329722i
\(640\) 0 0
\(641\) 34.3968i 1.35859i −0.733865 0.679295i \(-0.762286\pi\)
0.733865 0.679295i \(-0.237714\pi\)
\(642\) 0 0
\(643\) 10.4779 25.2960i 0.413210 0.997576i −0.571061 0.820908i \(-0.693468\pi\)
0.984270 0.176669i \(-0.0565321\pi\)
\(644\) 0 0
\(645\) −0.314571 + 0.685213i −0.0123862 + 0.0269802i
\(646\) 0 0
\(647\) 26.7097 26.7097i 1.05007 1.05007i 0.0513899 0.998679i \(-0.483635\pi\)
0.998679 0.0513899i \(-0.0163651\pi\)
\(648\) 0 0
\(649\) −4.75718 4.75718i −0.186735 0.186735i
\(650\) 0 0
\(651\) −25.7675 11.8295i −1.00991 0.463634i
\(652\) 0 0
\(653\) 40.0093 + 16.5724i 1.56569 + 0.648528i 0.986065 0.166358i \(-0.0532008\pi\)
0.579620 + 0.814887i \(0.303201\pi\)
\(654\) 0 0
\(655\) 5.78306 0.225963
\(656\) 0 0
\(657\) −40.1447 3.03139i −1.56620 0.118266i
\(658\) 0 0
\(659\) 6.33558 15.2955i 0.246799 0.595826i −0.751129 0.660155i \(-0.770491\pi\)
0.997929 + 0.0643286i \(0.0204906\pi\)
\(660\) 0 0
\(661\) 13.2351 5.48218i 0.514787 0.213232i −0.110138 0.993916i \(-0.535129\pi\)
0.624926 + 0.780684i \(0.285129\pi\)
\(662\) 0 0
\(663\) −59.7354 2.25215i −2.31993 0.0874663i
\(664\) 0 0
\(665\) 0.576668 + 0.576668i 0.0223622 + 0.0223622i
\(666\) 0 0
\(667\) −11.3007 + 4.68092i −0.437567 + 0.181246i
\(668\) 0 0
\(669\) 0.173166 0.0641964i 0.00669499 0.00248198i
\(670\) 0 0
\(671\) 3.44895 0.133145
\(672\) 0 0
\(673\) 20.2651 0.781160 0.390580 0.920569i \(-0.372274\pi\)
0.390580 + 0.920569i \(0.372274\pi\)
\(674\) 0 0
\(675\) −24.1331 + 6.93035i −0.928885 + 0.266749i
\(676\) 0 0
\(677\) −36.6561 + 15.1834i −1.40881 + 0.583547i −0.952022 0.306030i \(-0.900999\pi\)
−0.456785 + 0.889577i \(0.650999\pi\)
\(678\) 0 0
\(679\) −10.2422 10.2422i −0.393058 0.393058i
\(680\) 0 0
\(681\) 1.48548 39.4004i 0.0569237 1.50983i
\(682\) 0 0
\(683\) 24.0996 9.98236i 0.922144 0.381965i 0.129451 0.991586i \(-0.458678\pi\)
0.792693 + 0.609621i \(0.208678\pi\)
\(684\) 0 0
\(685\) −1.15121 + 2.77927i −0.0439856 + 0.106191i
\(686\) 0 0
\(687\) 5.18381 4.80713i 0.197775 0.183403i
\(688\) 0 0
\(689\) 9.59903 0.365694
\(690\) 0 0
\(691\) −13.6860 5.66894i −0.520641 0.215657i 0.106857 0.994274i \(-0.465921\pi\)
−0.627499 + 0.778618i \(0.715921\pi\)
\(692\) 0 0
\(693\) 6.22948 2.04595i 0.236638 0.0777190i
\(694\) 0 0
\(695\) 2.20798 + 2.20798i 0.0837536 + 0.0837536i
\(696\) 0 0
\(697\) −34.9990 + 34.9990i −1.32568 + 1.32568i
\(698\) 0 0
\(699\) −9.96484 4.57471i −0.376905 0.173031i
\(700\) 0 0
\(701\) −15.2498 + 36.8163i −0.575977 + 1.39053i 0.320419 + 0.947276i \(0.396176\pi\)
−0.896396 + 0.443255i \(0.853824\pi\)
\(702\) 0 0
\(703\) 4.57559i 0.172572i
\(704\) 0 0
\(705\) −5.45447 + 5.05813i −0.205427 + 0.190500i
\(706\) 0 0
\(707\) −6.64668 2.75314i −0.249974 0.103543i
\(708\) 0 0
\(709\) −11.6037 28.0139i −0.435788 1.05209i −0.977389 0.211449i \(-0.932182\pi\)
0.541601 0.840636i \(-0.317818\pi\)
\(710\) 0 0
\(711\) 19.9236 17.1259i 0.747193 0.642272i
\(712\) 0 0
\(713\) 9.31087 9.31087i 0.348695 0.348695i
\(714\) 0 0
\(715\) 0.656007 + 1.58374i 0.0245333 + 0.0592286i
\(716\) 0 0
\(717\) −14.0972 + 5.22614i −0.526469 + 0.195174i
\(718\) 0 0
\(719\) 44.6170i 1.66393i −0.554826 0.831967i \(-0.687215\pi\)
0.554826 0.831967i \(-0.312785\pi\)
\(720\) 0 0
\(721\) 24.7573i 0.922008i
\(722\) 0 0
\(723\) 7.40004 2.74336i 0.275211 0.102027i
\(724\) 0 0
\(725\) −9.88517 23.8649i −0.367126 0.886321i
\(726\) 0 0
\(727\) 15.5081 15.5081i 0.575162 0.575162i −0.358405 0.933566i \(-0.616679\pi\)
0.933566 + 0.358405i \(0.116679\pi\)
\(728\) 0 0
\(729\) 14.3258 + 22.8860i 0.530587 + 0.847631i
\(730\) 0 0
\(731\) −2.57689 6.22117i −0.0953098 0.230098i
\(732\) 0 0
\(733\) −43.3401 17.9520i −1.60080 0.663074i −0.609273 0.792961i \(-0.708538\pi\)
−0.991529 + 0.129887i \(0.958538\pi\)
\(734\) 0 0
\(735\) −0.568093 + 0.526813i −0.0209544 + 0.0194318i
\(736\) 0 0
\(737\) 5.32424i 0.196121i
\(738\) 0 0
\(739\) −18.0170 + 43.4968i −0.662765 + 1.60006i 0.130686 + 0.991424i \(0.458282\pi\)
−0.793452 + 0.608633i \(0.791718\pi\)
\(740\) 0 0
\(741\) −5.99817 2.75367i −0.220348 0.101159i
\(742\) 0 0
\(743\) −3.20365 + 3.20365i −0.117530 + 0.117530i −0.763426 0.645895i \(-0.776484\pi\)
0.645895 + 0.763426i \(0.276484\pi\)
\(744\) 0 0
\(745\) −5.72193 5.72193i −0.209635 0.209635i
\(746\) 0 0
\(747\) 16.1516 + 49.1784i 0.590958 + 1.79935i
\(748\) 0 0
\(749\) 3.39260 + 1.40526i 0.123963 + 0.0513471i
\(750\) 0 0
\(751\) −53.3838 −1.94800 −0.974001 0.226542i \(-0.927258\pi\)
−0.974001 + 0.226542i \(0.927258\pi\)
\(752\) 0 0
\(753\) −2.49233 + 2.31123i −0.0908255 + 0.0842257i
\(754\) 0 0
\(755\) 1.81738 4.38754i 0.0661411 0.159679i
\(756\) 0 0
\(757\) 40.7929 16.8970i 1.48264 0.614130i 0.512941 0.858424i \(-0.328556\pi\)
0.969701 + 0.244294i \(0.0785560\pi\)
\(758\) 0 0
\(759\) −0.114725 + 3.04293i −0.00416425 + 0.110451i
\(760\) 0 0
\(761\) −2.82203 2.82203i −0.102299 0.102299i 0.654105 0.756404i \(-0.273045\pi\)
−0.756404 + 0.654105i \(0.773045\pi\)
\(762\) 0 0
\(763\) 6.41304 2.65637i 0.232168 0.0961670i
\(764\) 0 0
\(765\) −3.51451 + 6.95203i −0.127067 + 0.251351i
\(766\) 0 0
\(767\) −47.6820 −1.72170
\(768\) 0 0
\(769\) 11.4430 0.412645 0.206322 0.978484i \(-0.433850\pi\)
0.206322 + 0.978484i \(0.433850\pi\)
\(770\) 0 0
\(771\) 21.7828 8.07538i 0.784490 0.290828i
\(772\) 0 0
\(773\) 17.4059 7.20975i 0.626046 0.259317i −0.0470263 0.998894i \(-0.514974\pi\)
0.673072 + 0.739577i \(0.264974\pi\)
\(774\) 0 0
\(775\) 19.6627 + 19.6627i 0.706305 + 0.706305i
\(776\) 0 0
\(777\) 32.1942 + 1.21379i 1.15496 + 0.0435444i
\(778\) 0 0
\(779\) −5.04886 + 2.09131i −0.180894 + 0.0749289i
\(780\) 0 0
\(781\) 0.819227 1.97779i 0.0293142 0.0707708i
\(782\) 0 0
\(783\) −21.7318