Properties

Label 768.2.o.b.95.12
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 95.12
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57410 - 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(2.01144 + 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +O(q^{10})\) \(q+(1.57410 - 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(2.01144 + 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +(0.709852 - 0.294030i) q^{11} +(-2.08393 + 5.03104i) q^{13} +(0.482526 - 0.520336i) q^{15} +6.33777 q^{17} +(-0.646487 - 0.267784i) q^{19} +(4.61976 + 1.71265i) q^{21} +(-1.61798 - 1.61798i) q^{23} +(-3.41684 + 3.41684i) q^{25} +(1.43422 - 4.99430i) q^{27} +(2.04571 - 4.93879i) q^{29} -5.75464i q^{31} +(0.904897 - 0.975803i) q^{33} +(1.07674 + 0.446001i) q^{35} +(2.50232 + 6.04113i) q^{37} +(0.355354 + 9.42529i) q^{39} +(-5.52228 + 5.52228i) q^{41} +(0.406593 + 0.981601i) q^{43} +(0.383525 - 1.16775i) q^{45} -10.4826i q^{47} +1.09178i q^{49} +(9.97628 - 4.57996i) q^{51} +(0.674566 + 1.62855i) q^{53} +(0.222593 - 0.222593i) q^{55} +(-1.21115 + 0.0456628i) q^{57} +(-3.35082 - 8.08960i) q^{59} +(-4.14715 - 1.71781i) q^{61} +(8.50959 - 0.642573i) q^{63} +2.23109i q^{65} +(2.65183 - 6.40208i) q^{67} +(-3.71607 - 1.37763i) q^{69} +(1.97014 - 1.97014i) q^{71} +(9.48914 + 9.48914i) q^{73} +(-2.90928 + 7.84760i) q^{75} +(2.01925 + 0.836400i) q^{77} -8.75751 q^{79} +(-1.35150 - 8.89795i) q^{81} +(-6.60293 + 15.9409i) q^{83} +(2.39898 - 0.993689i) q^{85} +(-0.348838 - 9.25246i) q^{87} +(-6.11535 - 6.11535i) q^{89} +(-14.3113 + 5.92795i) q^{91} +(-4.15856 - 9.05837i) q^{93} -0.286694 q^{95} -5.09195 q^{97} +(0.719237 - 2.18993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) 1.57410 0.722645i 0.908806 0.417219i
\(4\) 0 0
\(5\) 0.378520 0.156788i 0.169279 0.0701179i −0.296434 0.955053i \(-0.595798\pi\)
0.465714 + 0.884935i \(0.345798\pi\)
\(6\) 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
\(9\) 1.95557 2.27503i 0.651856 0.758343i
\(10\) 0 0
\(11\) 0.709852 0.294030i 0.214028 0.0886534i −0.273093 0.961988i \(-0.588047\pi\)
0.487122 + 0.873334i \(0.338047\pi\)
\(12\) 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 \(-0.220970\pi\)
0.768568 + 0.639768i \(0.220970\pi\)
\(18\) 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
\(21\) 4.61976 + 1.71265i 1.00811 + 0.373730i
\(22\) 0 0
\(23\) −1.61798 1.61798i −0.337371 0.337371i 0.518006 0.855377i \(-0.326675\pi\)
−0.855377 + 0.518006i \(0.826675\pi\)
\(24\) 0 0
\(25\) −3.41684 + 3.41684i −0.683368 + 0.683368i
\(26\) 0 0
\(27\) 1.43422 4.99430i 0.276016 0.961153i
\(28\) 0 0
\(29\) 2.04571 4.93879i 0.379879 0.917110i −0.612108 0.790774i \(-0.709678\pi\)
0.991988 0.126336i \(-0.0403217\pi\)
\(30\) 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
\(39\) 0.355354 + 9.42529i 0.0569021 + 1.50925i
\(40\) 0 0
\(41\) −5.52228 + 5.52228i −0.862435 + 0.862435i −0.991620 0.129185i \(-0.958764\pi\)
0.129185 + 0.991620i \(0.458764\pi\)
\(42\) 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
\(45\) 0.383525 1.16775i 0.0571725 0.174079i
\(46\) 0 0
\(47\) 10.4826i 1.52904i −0.644597 0.764522i \(-0.722975\pi\)
0.644597 0.764522i \(-0.277025\pi\)
\(48\) 0 0
\(49\) 1.09178i 0.155969i
\(50\) 0 0
\(51\) 9.97628 4.57996i 1.39696 0.641323i
\(52\) 0 0
\(53\) 0.674566 + 1.62855i 0.0926588 + 0.223698i 0.963413 0.268020i \(-0.0863692\pi\)
−0.870755 + 0.491718i \(0.836369\pi\)
\(54\) 0 0
\(55\) 0.222593 0.222593i 0.0300144 0.0300144i
\(56\) 0 0
\(57\) −1.21115 + 0.0456628i −0.160420 + 0.00604819i
\(58\) 0 0
\(59\) −3.35082 8.08960i −0.436240 1.05318i −0.977237 0.212152i \(-0.931953\pi\)
0.540997 0.841025i \(1.68195\pi\)
\(60\) 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
\(69\) −3.71607 1.37763i −0.447363 0.165847i
\(70\) 0 0
\(71\) 1.97014 1.97014i 0.233813 0.233813i −0.580469 0.814282i \(-0.697131\pi\)
0.814282 + 0.580469i \(0.197131\pi\)
\(72\) 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
\(75\) −2.90928 + 7.84760i −0.335934 + 0.906163i
\(76\) 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 \(0.520855\pi\)
−0.659294 + 0.751885i \(0.729145\pi\)
\(84\) 0 0
\(85\) 2.39898 0.993689i 0.260206 0.107781i
\(86\) 0 0
\(87\) −0.348838 9.25246i −0.0373993 0.991968i
\(88\) 0 0
\(89\) −6.11535 6.11535i −0.648226 0.648226i 0.304338 0.952564i \(-0.401565\pi\)
−0.952564 + 0.304338i \(0.901565\pi\)
\(90\) 0 0
\(91\) −14.3113 + 5.92795i −1.50024 + 0.621418i
\(92\) 0 0
\(93\) −4.15856 9.05837i −0.431223 0.939310i
\(94\) 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
\(99\) 0.719237 2.18993i 0.0722860 0.220096i
\(100\) 0 0
\(101\) 2.33659 0.967847i 0.232499 0.0963044i −0.263392 0.964689i \(-0.584841\pi\)
0.495892 + 0.868384i \(0.334841\pi\)
\(102\) 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
\(105\) 2.01720 0.0760526i 0.196858 0.00742198i
\(106\) 0 0
\(107\) −1.19264 + 0.494009i −0.115297 + 0.0477576i −0.439586 0.898200i \(-0.644875\pi\)
0.324289 + 0.945958i \(0.394875\pi\)
\(108\) 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 \(-0.392834\pi\)
0.330348 + 0.943859i \(0.392834\pi\)
\(114\) 0 0
\(115\) −0.866116 0.358757i −0.0807657 0.0334543i
\(116\) 0 0
\(117\) 7.37050 + 14.5795i 0.681403 + 1.34788i
\(118\) 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
\(123\) −4.70196 + 12.6833i −0.423962 + 1.14361i
\(124\) 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 0.870955 0.491363i \(-0.163501\pi\)
0.268412 + 0.963304i \(0.413501\pi\)
\(132\) 0 0
\(133\) −0.761739 1.83900i −0.0660512 0.159462i
\(134\) 0 0
\(135\) −0.240166 2.11531i −0.0206702 0.182057i
\(136\) 0 0
\(137\) −5.19191 + 5.19191i −0.443575 + 0.443575i −0.893211 0.449637i \(-0.851553\pi\)
0.449637 + 0.893211i \(0.351553\pi\)
\(138\) 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
\(141\) −7.57520 16.5006i −0.637947 1.38960i
\(142\) 0 0
\(143\) 4.18403i 0.349886i
\(144\) 0 0
\(145\) 2.19018i 0.181884i
\(146\) 0 0
\(147\) 0.788970 + 1.71857i 0.0650732 + 0.141745i
\(148\) 0 0
\(149\) −7.55828 18.2473i −0.619199 1.49488i −0.852636 0.522506i \(-0.824997\pi\)
0.233437 0.972372i \(1.57500\pi\)
\(150\) 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
\(153\) 12.3940 14.4186i 1.00199 1.16568i
\(154\) 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
\(165\) 0.189527 0.511239i 0.0147547 0.0397999i
\(166\) 0 0
\(167\) −13.4441 + 13.4441i −1.04033 + 1.04033i −0.0411813 + 0.999152i \(0.513112\pi\)
−0.999152 + 0.0411813i \(0.986888\pi\)
\(168\) 0 0
\(169\) −11.7763 11.7763i −0.905866 0.905866i
\(170\) 0 0
\(171\) −1.87347 + 0.947107i −0.143268 + 0.0724271i
\(172\) 0 0
\(173\) 5.11484 + 2.11864i 0.388874 + 0.161077i 0.568550 0.822649i \(-0.307505\pi\)
−0.179675 + 0.983726i \(0.557505\pi\)
\(174\) 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 −0.830145 0.557547i \(-0.811743\pi\)
0.981247 + 0.192756i \(0.0617426\pi\)
\(180\) 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
\(183\) −7.76939 + 0.292922i −0.574330 + 0.0216535i
\(184\) 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
\(189\) 12.9306 7.16089i 0.940561 0.520878i
\(190\) 0 0
\(191\) −10.8066 −0.781940 −0.390970 0.920404i \(-0.627860\pi\)
−0.390970 + 0.920404i \(0.627860\pi\)
\(192\) 0 0
\(193\) −5.82359 −0.419192 −0.209596 0.977788i \(-0.567215\pi\)
−0.209596 + 0.977788i \(0.567215\pi\)
\(194\) 0 0
\(195\) 1.61228 + 3.51195i 0.115458 + 0.251496i
\(196\) 0 0
\(197\) −19.4552 + 8.05861i −1.38613 + 0.574152i −0.946112 0.323839i \(-0.895026\pi\)
−0.440014 + 0.897991i \(0.645026\pi\)
\(198\) 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
\(201\) −0.452193 11.9938i −0.0318952 0.845979i
\(202\) 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
\(213\) 1.67748 4.52491i 0.114939 0.310041i
\(214\) 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
\(219\) 21.7941 + 8.07956i 1.47271 + 0.545966i
\(220\) 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 −0.447208 0.894430i \(-0.647582\pi\)
−0.948681 + 0.316233i \(0.897582\pi\)
\(228\) 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
\(231\) 3.78291 0.142624i 0.248898 0.00938397i
\(232\) 0 0
\(233\) −4.47635 + 4.47635i −0.293255 + 0.293255i −0.838365 0.545110i \(-0.816488\pi\)
0.545110 + 0.838365i \(0.316488\pi\)
\(234\) 0 0
\(235\) −1.64355 3.96788i −0.107213 0.258836i
\(236\) 0 0
\(237\) −13.7852 + 6.32857i −0.895444 + 0.411085i
\(238\) 0 0
\(239\) 8.68031i 0.561483i 0.959783 + 0.280741i \(0.0905803\pi\)
−0.959783 + 0.280741i \(0.909420\pi\)
\(240\) 0 0
\(241\) 4.55656i 0.293514i 0.989173 + 0.146757i \(0.0468835\pi\)
−0.989173 + 0.146757i \(0.953117\pi\)
\(242\) 0 0
\(243\) −8.55745 13.0296i −0.548961 0.835848i
\(244\) 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
\(249\) 1.12594 + 29.8641i 0.0713536 + 1.89256i
\(250\) 0 0
\(251\) 0.750992 + 1.81305i 0.0474022 + 0.114439i 0.945807 0.324729i \(-0.105273\pi\)
−0.898405 + 0.439168i \(0.855273\pi\)
\(252\) 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 \(-0.862615\pi\)
0.908294 0.418332i \(-0.137385\pi\)
\(258\) 0 0
\(259\) −7.11811 + 17.1846i −0.442298 + 1.06780i
\(260\) 0 0
\(261\) −7.23535 14.3122i −0.447857 0.885903i
\(262\) 0 0
\(263\) 18.7027 18.7027i 1.15326 1.15326i 0.167359 0.985896i \(-0.446476\pi\)
0.985896 0.167359i \(-0.0535240\pi\)
\(264\) 0 0
\(265\) 0.510674 + 0.510674i 0.0313705 + 0.0313705i
\(266\) 0 0
\(267\) −14.0454 5.20693i −0.859564 0.318659i
\(268\) 0 0
\(269\) 6.20132 + 2.56867i 0.378101 + 0.156615i 0.563636 0.826023i \(-0.309402\pi\)
−0.185535 + 0.982638i \(0.559402\pi\)
\(270\) 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
\(279\) −13.0920 11.2536i −0.783796 0.673736i
\(280\) 0 0
\(281\) −10.9033 10.9033i −0.650433 0.650433i 0.302664 0.953097i \(-0.402124\pi\)
−0.953097 + 0.302664i \(0.902124\pi\)
\(282\) 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
\(285\) −0.451284 + 0.207178i −0.0267318 + 0.0122722i
\(286\) 0 0
\(287\) −22.2155 −1.31134
\(288\) 0 0
\(289\) 23.1674 1.36279
\(290\) 0 0
\(291\) −8.01523 + 3.67967i −0.469861 + 0.215706i
\(292\) 0 0
\(293\) 20.0666 8.31184i 1.17230 0.485583i 0.290348 0.956921i \(-0.406229\pi\)
0.881952 + 0.471338i \(0.156229\pi\)
\(294\) 0 0
\(295\) −2.53671 2.53671i −0.147693 0.147693i
\(296\) 0 0
\(297\) −0.450392 3.96691i −0.0261344 0.230184i
\(298\) 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
\(309\) −14.1344 5.23994i −0.804079 0.298090i
\(310\) 0 0
\(311\) 8.31914 + 8.31914i 0.471735 + 0.471735i 0.902476 0.430741i \(-0.141748\pi\)
−0.430741 + 0.902476i \(0.641748\pi\)
\(312\) 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
\(315\) 3.12031 1.57743i 0.175809 0.0888782i
\(316\) 0 0
\(317\) −0.432895 + 1.04510i −0.0243138 + 0.0586987i −0.935570 0.353141i \(-0.885114\pi\)
0.911256 + 0.411840i \(0.135114\pi\)
\(318\) 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
\(327\) −0.159237 4.22356i −0.00880584 0.233564i
\(328\) 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
\(333\) 18.6372 + 6.12100i 1.02131 + 0.335429i
\(334\) 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
\(339\) 11.0553 5.07535i 0.600444 0.275655i
\(340\) 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
\(345\) −1.62261 + 0.0611757i −0.0873581 + 0.00329359i
\(346\) 0 0
\(347\) −3.34246 8.06942i −0.179433 0.433189i 0.808415 0.588613i \(-0.200326\pi\)
−0.987848 + 0.155424i \(0.950326\pi\)
\(348\) 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 \(0.0601295\pi\)
−0.982211 + 0.187781i \(0.939870\pi\)
\(354\) 0 0
\(355\) 0.436843 1.05463i 0.0231852 0.0559741i
\(356\) 0 0
\(357\) 29.2790 + 10.8544i 1.54961 + 0.574474i
\(358\) 0 0
\(359\) 17.9832 17.9832i 0.949116 0.949116i −0.0496509 0.998767i \(-0.515811\pi\)
0.998767 + 0.0496509i \(0.0158109\pi\)
\(360\) 0 0
\(361\) −13.0888 13.0888i −0.688884 0.688884i
\(362\) 0 0
\(363\) −6.26732 + 16.9057i −0.328949 + 0.887320i
\(364\) 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
\(375\) 0.262869 + 6.97227i 0.0135745 + 0.360046i
\(376\) 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
\(381\) 3.70216 + 8.06421i 0.189667 + 0.413142i
\(382\) 0 0
\(383\) −5.32676 −0.272185 −0.136092 0.990696i \(-0.543454\pi\)
−0.136092 + 0.990696i \(0.543454\pi\)
\(384\) 0 0
\(385\) 0.895464 0.0456371
\(386\) 0 0
\(387\) 3.02829 + 0.994579i 0.153937 + 0.0505573i
\(388\) 0 0
\(389\) 20.0435 8.30227i 1.01624 0.420942i 0.188515 0.982070i \(-0.439633\pi\)
0.827729 + 0.561128i \(0.189633\pi\)
\(390\) 0 0
\(391\) −10.2544 10.2544i −0.518585 0.518585i
\(392\) 0 0
\(393\) 24.4307 0.921090i 1.23237 0.0464628i
\(394\) 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 \(-0.455259\pi\)
0.140095 + 0.990138i \(0.455259\pi\)
\(402\) 0 0
\(403\) 28.9519 + 11.9923i 1.44220 + 0.597377i
\(404\) 0 0
\(405\) −1.90666 3.15615i −0.0947429 0.156831i
\(406\) 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
\(411\) −4.42067 + 11.9245i −0.218055 + 0.588191i
\(412\) 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 −0.0697790 0.997562i \(-0.522229\pi\)
−0.754724 + 0.656042i \(0.772229\pi\)
\(420\) 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
\(423\) −23.8482 20.4994i −1.15954 0.996717i
\(424\) 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
\(429\) 3.02357 + 6.58608i 0.145979 + 0.317979i
\(430\) 0 0
\(431\) 18.7398i 0.902664i 0.892356 + 0.451332i \(0.149051\pi\)
−0.892356 + 0.451332i \(0.850949\pi\)
\(432\) 0 0
\(433\) 2.88137i 0.138470i −0.997600 0.0692349i \(-0.977944\pi\)
0.997600 0.0692349i \(-0.0220558\pi\)
\(434\) 0 0
\(435\) −1.58272 3.44755i −0.0758856 0.165297i
\(436\) 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
\(441\) 2.48383 + 2.13505i 0.118278 + 0.101669i
\(442\) 0 0
\(443\) 5.97491 + 14.4247i 0.283877 + 0.685339i 0.999919 0.0127177i \(-0.00404829\pi\)
−0.716042 + 0.698057i \(0.754048\pi\)
\(444\) 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 \(-0.981052\pi\)
0.998229 0.0594905i \(-0.0189476\pi\)
\(450\) 0 0
\(451\) −2.29628 + 5.54372i −0.108128 + 0.261043i
\(452\) 0 0
\(453\) −6.97874 + 18.8247i −0.327890 + 0.884463i
\(454\) 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
\(459\) 9.08976 31.6527i 0.424274 1.47742i
\(460\) 0 0
\(461\) 16.9365 + 7.01532i 0.788810 + 0.326736i 0.740465 0.672095i \(-0.234605\pi\)
0.0483450 + 0.998831i \(0.484605\pi\)
\(462\) 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 \(-0.640985\pi\)
0.941924 0.335825i \(-0.109015\pi\)
\(468\) 0 0
\(469\) 18.2114 7.54340i 0.840923 0.348322i
\(470\) 0 0
\(471\) 2.66918 0.100634i 0.122989 0.00463696i
\(472\) 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
\(477\) 5.02415 + 1.65008i 0.230040 + 0.0755519i
\(478\) 0 0
\(479\) 11.5288 0.526765 0.263382 0.964692i \(-0.415162\pi\)
0.263382 + 0.964692i \(0.415162\pi\)
\(480\) 0 0
\(481\) −35.6078 −1.62358
\(482\) 0 0
\(483\) −4.70364 10.2457i −0.214023 0.466194i
\(484\) 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
\(489\) 0.158088 + 4.19307i 0.00714897 + 0.189617i
\(490\) 0 0
\(491\) 13.2408 5.48453i 0.597550 0.247513i −0.0633450 0.997992i \(-0.520177\pi\)
0.660895 + 0.750478i \(0.270177\pi\)
\(492\) 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
\(501\) −11.4470 + 30.8776i −0.511414 + 1.37951i
\(502\) 0 0
\(503\) −20.7317 20.7317i −0.924383 0.924383i 0.0729527 0.997335i \(-0.476758\pi\)
−0.997335 + 0.0729527i \(0.976758\pi\)
\(504\) 0 0
\(505\) 0.732700 0.732700i 0.0326047 0.0326047i
\(506\) 0 0
\(507\) −27.0470 10.0269i −1.20120 0.445312i
\(508\) 0 0
\(509\) −7.27710 + 17.5685i −0.322552 + 0.778708i 0.676553 + 0.736394i \(0.263473\pi\)
−0.999104 + 0.0423143i \(0.986527\pi\)
\(510\) 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
\(519\) 9.58229 0.361273i 0.420616 0.0158581i
\(520\) 0 0
\(521\) 12.9964 12.9964i 0.569382 0.569382i −0.362573 0.931955i \(-0.618102\pi\)
0.931955 + 0.362573i \(0.118102\pi\)
\(522\) 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
\(525\) −21.6368 + 9.93314i −0.944308 + 0.433518i
\(526\) 0 0
\(527\) 36.4716i 1.58873i
\(528\) 0 0
\(529\) 17.7643i 0.772361i
\(530\) 0 0
\(531\) −24.9568 8.19656i −1.08303 0.355700i
\(532\) 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
\(537\) −0.344725 9.14339i −0.0148760 0.394566i
\(538\) 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
\(549\) −12.0181 + 6.07560i −0.512920 + 0.259300i
\(550\) 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
\(555\) 4.35085 + 1.61296i 0.184683 + 0.0684662i
\(556\) 0 0
\(557\) −9.67547 4.00771i −0.409963 0.169812i 0.168164 0.985759i \(-0.446216\pi\)
−0.578127 + 0.815947i \(0.696216\pi\)
\(558\) 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 \(0.263817\pi\)
−0.999058 + 0.0433923i \(0.986183\pi\)
\(564\) 0 0
\(565\) 2.65846 1.10117i 0.111842 0.0463266i
\(566\) 0 0
\(567\) 15.1792 20.6162i 0.637467 0.865797i
\(568\) 0 0
\(569\) −3.36174 3.36174i −0.140932 0.140932i 0.633121 0.774053i \(-0.281773\pi\)
−0.774053 + 0.633121i \(0.781773\pi\)
\(570\) 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
\(573\) −17.0107 + 7.80935i −0.710631 + 0.326240i
\(574\) 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
\(579\) −9.16691 + 4.20839i −0.380964 + 0.174895i
\(580\) 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
\(585\) 5.07579 + 4.36305i 0.209858 + 0.180390i
\(586\) 0 0
\(587\) −31.3098 + 12.9689i −1.29229 + 0.535286i −0.919668 0.392696i \(-0.871542\pi\)
−0.372625 + 0.927982i \(0.621542\pi\)
\(588\) 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 \(-0.641955\pi\)
−0.431328 + 0.902195i \(0.641955\pi\)
\(594\) 0 0
\(595\) 6.82414 + 2.82665i 0.279763 + 0.115881i
\(596\) 0 0
\(597\) 3.75562 + 1.39229i 0.153707 + 0.0569827i
\(598\) 0 0
\(599\) −4.73031 4.73031i −0.193275 0.193275i 0.603835 0.797110i \(-0.293639\pi\)
−0.797110 + 0.603835i \(0.793639\pi\)
\(600\) 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
\(603\) −9.37907 18.5527i −0.381945 0.755523i
\(604\) 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
\(615\) 0.208798 + 5.53808i 0.00841953 + 0.223317i
\(616\) 0 0
\(617\) −2.85391 + 2.85391i −0.114894 + 0.114894i −0.762216 0.647322i \(-0.775889\pi\)
0.647322 + 0.762216i \(0.275889\pi\)
\(618\) 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
\(621\) −10.4012 + 5.76012i −0.417385 + 0.231146i
\(622\) 0 0
\(623\) 24.6013i 0.985631i
\(624\) 0 0
\(625\) 22.5103i 0.900411i
\(626\) 0 0
\(627\) −0.846308 + 0.388528i −0.0337983 + 0.0155163i
\(628\) 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
\(633\) −25.1750 + 0.949152i −1.00062 + 0.0377254i
\(634\) 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 \(0.237714\pi\)
−0.733865 + 0.679295i \(0.762286\pi\)
\(642\) 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
\(645\) 0.706954 + 0.262083i 0.0278363 + 0.0103195i
\(646\) 0 0
\(647\) −26.7097 + 26.7097i −1.05007 + 1.05007i −0.0513899 + 0.998679i \(0.516365\pi\)
−0.998679 + 0.0513899i \(0.983635\pi\)
\(648\) 0 0
\(649\) −4.75718 4.75718i −0.186735 0.186735i
\(650\) 0 0
\(651\) 9.85567 26.5851i 0.386274 1.04195i
\(652\) 0 0
\(653\) −40.0093 16.5724i −1.56569 0.648528i −0.579620 0.814887i \(-0.696799\pi\)
−0.986065 + 0.166358i \(0.946799\pi\)
\(654\) 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 −0.997929 0.0643286i \(-0.979509\pi\)
0.751129 + 0.660155i \(0.229509\pi\)
\(660\) 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
\(663\) 2.25215 + 59.7354i 0.0874663 + 2.31993i
\(664\) 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
\(669\) 0.0770531 + 0.167841i 0.00297905 + 0.00648909i
\(670\) 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
\(675\) 12.1642 + 21.9652i 0.468201 + 0.845441i
\(676\) 0 0
\(677\) 36.6561 15.1834i 1.40881 0.583547i 0.456785 0.889577i \(-0.349001\pi\)
0.952022 + 0.306030i \(0.0990009\pi\)
\(678\) 0 0
\(679\) −10.2422 10.2422i −0.393058 0.393058i
\(680\) 0 0
\(681\) −39.4004 + 1.48548i −1.50983 + 0.0569237i
\(682\) 0 0
\(683\) −24.0996 + 9.98236i −0.922144 + 0.381965i −0.792693 0.609621i \(-0.791322\pi\)
−0.129451 + 0.991586i \(0.541322\pi\)
\(684\) 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
\(693\) 5.85161 2.95821i 0.222284 0.112373i
\(694\) 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
\(699\) −3.81140 + 10.2810i −0.144160 + 0.388864i
\(700\) 0 0
\(701\) 15.2498 36.8163i 0.575977 1.39053i −0.320419 0.947276i \(-0.603824\pi\)
0.896396 0.443255i \(-0.146176\pi\)
\(702\) 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
\(711\) −17.1259 + 19.9236i −0.642272 + 0.747193i
\(712\) 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
\(717\) 6.27278 + 13.6637i 0.234261 + 0.510279i
\(718\) 0 0
\(719\) 44.6170i 1.66393i 0.554826 + 0.831967i \(0.312785\pi\)
−0.554826 + 0.831967i \(0.687215\pi\)
\(720\) 0 0
\(721\) 24.7573i 0.922008i
\(722\) 0 0
\(723\) 3.29277 + 7.17247i 0.122460 + 0.266747i
\(724\) 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
\(729\) −22.8860 14.3258i −0.847631 0.530587i
\(730\) 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
\(741\) 2.29421 6.18849i 0.0842799 0.227340i
\(742\) 0 0
\(743\) 3.20365 3.20365i 0.117530 0.117530i −0.645895 0.763426i \(-0.723516\pi\)
0.763426 + 0.645895i \(0.223516\pi\)
\(744\) 0 0
\(745\) −5.72193 5.72193i −0.209635 0.209635i
\(746\) 0 0
\(747\) 23.3535 + 46.1954i 0.854459 + 1.69020i
\(748\) 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
\(759\) −3.04293 + 0.114725i −0.110451 + 0.00416425i
\(760\) 0 0
\(761\) 2.82203 + 2.82203i 0.102299 + 0.102299i 0.756404 0.654105i \(-0.226955\pi\)
−0.654105 + 0.756404i \(0.726955\pi\)
\(762\) 0 0
\(763\) 6.41304 2.65637i 0.232168 0.0961670i
\(764\) 0 0
\(765\) 2.43069 7.40097i 0.0878819 0.267582i
\(766\) 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
\(771\) −9.69264 21.1130i −0.349072 0.760365i
\(772\) 0 0
\(773\) −17.4059 + 7.20975i −0.626046 + 0.259317i −0.673072 0.739577i \(-0.735026\pi\)
0.0470263 + 0.998894i \(0.485026\pi\)
\(774\) 0 0
\(775\) 19.6627 + 19.6627i 0.706305 + 0.706305i
\(776\) 0 0
\(777\) 1.21379 + 32.1942i 0.0435444 + 1.15496i
\(778\) 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 17.3002<