Properties

Label 1323.2.g.h.361.2
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} -1.58639 q^{5} +9.15528 q^{8} +O(q^{10})\) \(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} -1.58639 q^{5} +9.15528 q^{8} +(2.15363 - 3.73020i) q^{10} +1.34875 q^{11} +(-1.58916 + 2.75251i) q^{13} +(-7.05696 + 12.2230i) q^{16} +(-1.40027 + 2.42534i) q^{17} +(0.312846 + 0.541866i) q^{19} +(4.26101 + 7.38028i) q^{20} +(-1.83102 + 3.17142i) q^{22} +0.284867 q^{23} -2.48336 q^{25} +(-4.31479 - 7.47343i) q^{26} +(-2.27396 - 3.93861i) q^{29} +(3.71502 + 6.43461i) q^{31} +(-10.0053 - 17.3297i) q^{32} +(-3.80191 - 6.58511i) q^{34} +(-4.01126 - 6.94770i) q^{37} -1.69884 q^{38} -14.5239 q^{40} +(5.01329 - 8.68327i) q^{41} +(-3.12937 - 5.42022i) q^{43} +(-3.62271 - 6.27472i) q^{44} +(-0.386726 + 0.669829i) q^{46} +(-5.57383 + 9.65415i) q^{47} +(3.37132 - 5.83930i) q^{50} +17.0738 q^{52} +(1.39349 - 2.41359i) q^{53} -2.13965 q^{55} +12.3482 q^{58} +(-2.28734 - 3.96180i) q^{59} +(-0.192507 + 0.333432i) q^{61} -20.1736 q^{62} +26.1036 q^{64} +(2.52104 - 4.36656i) q^{65} +(1.26958 + 2.19898i) q^{67} +15.0443 q^{68} +1.45208 q^{71} +(-0.234067 + 0.405416i) q^{73} +21.7822 q^{74} +(1.68059 - 2.91087i) q^{76} +(7.85620 - 13.6073i) q^{79} +(11.1951 - 19.3905i) q^{80} +(13.6117 + 23.5762i) q^{82} +(-6.99338 - 12.1129i) q^{83} +(2.22138 - 3.84754i) q^{85} +16.9933 q^{86} +12.3482 q^{88} +(1.29353 + 2.24046i) q^{89} +(-0.765146 - 1.32527i) q^{92} +(-15.1337 - 26.2123i) q^{94} +(-0.496297 - 0.859612i) q^{95} +(-7.22962 - 12.5221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35757 + 2.35137i −0.959944 + 1.66267i −0.237320 + 0.971432i \(0.576269\pi\)
−0.722624 + 0.691241i \(0.757064\pi\)
\(3\) 0 0
\(4\) −2.68597 4.65224i −1.34299 2.32612i
\(5\) −1.58639 −0.709457 −0.354728 0.934969i \(-0.615427\pi\)
−0.354728 + 0.934969i \(0.615427\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 9.15528 3.23688
\(9\) 0 0
\(10\) 2.15363 3.73020i 0.681039 1.17959i
\(11\) 1.34875 0.406664 0.203332 0.979110i \(-0.434823\pi\)
0.203332 + 0.979110i \(0.434823\pi\)
\(12\) 0 0
\(13\) −1.58916 + 2.75251i −0.440754 + 0.763409i −0.997746 0.0671096i \(-0.978622\pi\)
0.556991 + 0.830518i \(0.311956\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −7.05696 + 12.2230i −1.76424 + 3.05575i
\(17\) −1.40027 + 2.42534i −0.339615 + 0.588230i −0.984360 0.176167i \(-0.943630\pi\)
0.644745 + 0.764397i \(0.276963\pi\)
\(18\) 0 0
\(19\) 0.312846 + 0.541866i 0.0717719 + 0.124313i 0.899678 0.436554i \(-0.143801\pi\)
−0.827906 + 0.560867i \(0.810468\pi\)
\(20\) 4.26101 + 7.38028i 0.952791 + 1.65028i
\(21\) 0 0
\(22\) −1.83102 + 3.17142i −0.390375 + 0.676149i
\(23\) 0.284867 0.0593989 0.0296995 0.999559i \(-0.490545\pi\)
0.0296995 + 0.999559i \(0.490545\pi\)
\(24\) 0 0
\(25\) −2.48336 −0.496671
\(26\) −4.31479 7.47343i −0.846199 1.46566i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.27396 3.93861i −0.422264 0.731382i 0.573897 0.818928i \(-0.305431\pi\)
−0.996161 + 0.0875454i \(0.972098\pi\)
\(30\) 0 0
\(31\) 3.71502 + 6.43461i 0.667238 + 1.15569i 0.978673 + 0.205423i \(0.0658569\pi\)
−0.311435 + 0.950267i \(0.600810\pi\)
\(32\) −10.0053 17.3297i −1.76870 3.06348i
\(33\) 0 0
\(34\) −3.80191 6.58511i −0.652023 1.12934i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.01126 6.94770i −0.659447 1.14220i −0.980759 0.195222i \(-0.937457\pi\)
0.321312 0.946973i \(-0.395876\pi\)
\(38\) −1.69884 −0.275588
\(39\) 0 0
\(40\) −14.5239 −2.29643
\(41\) 5.01329 8.68327i 0.782944 1.35610i −0.147275 0.989096i \(-0.547050\pi\)
0.930219 0.367004i \(-0.119616\pi\)
\(42\) 0 0
\(43\) −3.12937 5.42022i −0.477224 0.826576i 0.522435 0.852679i \(-0.325024\pi\)
−0.999659 + 0.0261027i \(0.991690\pi\)
\(44\) −3.62271 6.27472i −0.546144 0.945950i
\(45\) 0 0
\(46\) −0.386726 + 0.669829i −0.0570197 + 0.0987609i
\(47\) −5.57383 + 9.65415i −0.813026 + 1.40820i 0.0977106 + 0.995215i \(0.468848\pi\)
−0.910737 + 0.412988i \(0.864485\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.37132 5.83930i 0.476777 0.825802i
\(51\) 0 0
\(52\) 17.0738 2.36771
\(53\) 1.39349 2.41359i 0.191410 0.331532i −0.754308 0.656521i \(-0.772027\pi\)
0.945718 + 0.324989i \(0.105361\pi\)
\(54\) 0 0
\(55\) −2.13965 −0.288510
\(56\) 0 0
\(57\) 0 0
\(58\) 12.3482 1.62140
\(59\) −2.28734 3.96180i −0.297787 0.515782i 0.677842 0.735207i \(-0.262915\pi\)
−0.975629 + 0.219425i \(0.929582\pi\)
\(60\) 0 0
\(61\) −0.192507 + 0.333432i −0.0246480 + 0.0426916i −0.878086 0.478502i \(-0.841180\pi\)
0.853438 + 0.521194i \(0.174513\pi\)
\(62\) −20.1736 −2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) 2.52104 4.36656i 0.312696 0.541605i
\(66\) 0 0
\(67\) 1.26958 + 2.19898i 0.155104 + 0.268648i 0.933097 0.359625i \(-0.117095\pi\)
−0.777993 + 0.628273i \(0.783762\pi\)
\(68\) 15.0443 1.82439
\(69\) 0 0
\(70\) 0 0
\(71\) 1.45208 0.172330 0.0861651 0.996281i \(-0.472539\pi\)
0.0861651 + 0.996281i \(0.472539\pi\)
\(72\) 0 0
\(73\) −0.234067 + 0.405416i −0.0273955 + 0.0474503i −0.879398 0.476087i \(-0.842055\pi\)
0.852003 + 0.523538i \(0.175388\pi\)
\(74\) 21.7822 2.53213
\(75\) 0 0
\(76\) 1.68059 2.91087i 0.192777 0.333900i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.85620 13.6073i 0.883892 1.53095i 0.0369135 0.999318i \(-0.488247\pi\)
0.846978 0.531627i \(-0.178419\pi\)
\(80\) 11.1951 19.3905i 1.25165 2.16792i
\(81\) 0 0
\(82\) 13.6117 + 23.5762i 1.50317 + 2.60356i
\(83\) −6.99338 12.1129i −0.767623 1.32956i −0.938848 0.344331i \(-0.888106\pi\)
0.171225 0.985232i \(-0.445228\pi\)
\(84\) 0 0
\(85\) 2.22138 3.84754i 0.240942 0.417324i
\(86\) 16.9933 1.83243
\(87\) 0 0
\(88\) 12.3482 1.31632
\(89\) 1.29353 + 2.24046i 0.137114 + 0.237488i 0.926403 0.376534i \(-0.122884\pi\)
−0.789289 + 0.614022i \(0.789551\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.765146 1.32527i −0.0797719 0.138169i
\(93\) 0 0
\(94\) −15.1337 26.2123i −1.56092 2.70359i
\(95\) −0.496297 0.859612i −0.0509190 0.0881944i
\(96\) 0 0
\(97\) −7.22962 12.5221i −0.734057 1.27142i −0.955136 0.296168i \(-0.904291\pi\)
0.221079 0.975256i \(-0.429042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.67023 + 11.5532i 0.667023 + 1.15532i
\(101\) 9.83776 0.978894 0.489447 0.872033i \(-0.337199\pi\)
0.489447 + 0.872033i \(0.337199\pi\)
\(102\) 0 0
\(103\) −11.0579 −1.08957 −0.544786 0.838575i \(-0.683389\pi\)
−0.544786 + 0.838575i \(0.683389\pi\)
\(104\) −14.5492 + 25.2000i −1.42667 + 2.47106i
\(105\) 0 0
\(106\) 3.78350 + 6.55322i 0.367486 + 0.636505i
\(107\) −0.962153 1.66650i −0.0930149 0.161106i 0.815764 0.578386i \(-0.196317\pi\)
−0.908778 + 0.417279i \(0.862984\pi\)
\(108\) 0 0
\(109\) 9.30341 16.1140i 0.891105 1.54344i 0.0525523 0.998618i \(-0.483264\pi\)
0.838553 0.544821i \(-0.183402\pi\)
\(110\) 2.90472 5.03112i 0.276954 0.479698i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.59338 + 2.75982i −0.149893 + 0.259622i −0.931188 0.364540i \(-0.881226\pi\)
0.781295 + 0.624162i \(0.214560\pi\)
\(114\) 0 0
\(115\) −0.451911 −0.0421410
\(116\) −12.2156 + 21.1580i −1.13419 + 1.96447i
\(117\) 0 0
\(118\) 12.4209 1.14344
\(119\) 0 0
\(120\) 0 0
\(121\) −9.18087 −0.834624
\(122\) −0.522682 0.905312i −0.0473214 0.0819631i
\(123\) 0 0
\(124\) 19.9569 34.5664i 1.79218 3.10415i
\(125\) 11.8715 1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) −15.4267 + 26.7199i −1.36354 + 2.36173i
\(129\) 0 0
\(130\) 6.84495 + 11.8558i 0.600341 + 1.03982i
\(131\) −11.9726 −1.04605 −0.523024 0.852318i \(-0.675196\pi\)
−0.523024 + 0.852318i \(0.675196\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.89415 −0.595564
\(135\) 0 0
\(136\) −12.8199 + 22.2046i −1.09929 + 1.90403i
\(137\) −16.5505 −1.41401 −0.707003 0.707211i \(-0.749953\pi\)
−0.707003 + 0.707211i \(0.749953\pi\)
\(138\) 0 0
\(139\) −3.95119 + 6.84367i −0.335136 + 0.580472i −0.983511 0.180849i \(-0.942116\pi\)
0.648375 + 0.761321i \(0.275449\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.97130 + 3.41438i −0.165427 + 0.286529i
\(143\) −2.14339 + 3.71245i −0.179239 + 0.310451i
\(144\) 0 0
\(145\) 3.60739 + 6.24819i 0.299578 + 0.518884i
\(146\) −0.635523 1.10076i −0.0525962 0.0910994i
\(147\) 0 0
\(148\) −21.5483 + 37.3227i −1.77126 + 3.06791i
\(149\) 13.6685 1.11977 0.559885 0.828570i \(-0.310845\pi\)
0.559885 + 0.828570i \(0.310845\pi\)
\(150\) 0 0
\(151\) 3.89963 0.317348 0.158674 0.987331i \(-0.449278\pi\)
0.158674 + 0.987331i \(0.449278\pi\)
\(152\) 2.86420 + 4.96093i 0.232317 + 0.402385i
\(153\) 0 0
\(154\) 0 0
\(155\) −5.89349 10.2078i −0.473376 0.819912i
\(156\) 0 0
\(157\) −0.147176 0.254917i −0.0117459 0.0203446i 0.860093 0.510138i \(-0.170406\pi\)
−0.871839 + 0.489793i \(0.837072\pi\)
\(158\) 21.3306 + 36.9457i 1.69697 + 2.93925i
\(159\) 0 0
\(160\) 15.8723 + 27.4917i 1.25482 + 2.17341i
\(161\) 0 0
\(162\) 0 0
\(163\) −5.35455 9.27436i −0.419401 0.726424i 0.576478 0.817112i \(-0.304427\pi\)
−0.995879 + 0.0906886i \(0.971093\pi\)
\(164\) −53.8622 −4.20593
\(165\) 0 0
\(166\) 37.9759 2.94750
\(167\) 1.59872 2.76907i 0.123713 0.214277i −0.797516 0.603298i \(-0.793853\pi\)
0.921229 + 0.389020i \(0.127186\pi\)
\(168\) 0 0
\(169\) 1.44913 + 2.50997i 0.111472 + 0.193074i
\(170\) 6.03133 + 10.4466i 0.462582 + 0.801215i
\(171\) 0 0
\(172\) −16.8108 + 29.1171i −1.28181 + 2.22016i
\(173\) 5.71875 9.90517i 0.434789 0.753076i −0.562490 0.826804i \(-0.690156\pi\)
0.997278 + 0.0737284i \(0.0234898\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −9.51809 + 16.4858i −0.717453 + 1.24266i
\(177\) 0 0
\(178\) −7.02421 −0.526487
\(179\) 0.549275 0.951372i 0.0410547 0.0711089i −0.844768 0.535133i \(-0.820262\pi\)
0.885823 + 0.464024i \(0.153595\pi\)
\(180\) 0 0
\(181\) −3.19013 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.60804 0.192267
\(185\) 6.36343 + 11.0218i 0.467849 + 0.810338i
\(186\) 0 0
\(187\) −1.88861 + 3.27118i −0.138109 + 0.239212i
\(188\) 59.8846 4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) 1.93407 3.34992i 0.139945 0.242391i −0.787531 0.616275i \(-0.788641\pi\)
0.927475 + 0.373884i \(0.121974\pi\)
\(192\) 0 0
\(193\) 2.06793 + 3.58175i 0.148853 + 0.257820i 0.930804 0.365520i \(-0.119109\pi\)
−0.781951 + 0.623340i \(0.785775\pi\)
\(194\) 39.2588 2.81862
\(195\) 0 0
\(196\) 0 0
\(197\) 0.889267 0.0633576 0.0316788 0.999498i \(-0.489915\pi\)
0.0316788 + 0.999498i \(0.489915\pi\)
\(198\) 0 0
\(199\) 3.16193 5.47663i 0.224143 0.388228i −0.731919 0.681392i \(-0.761375\pi\)
0.956062 + 0.293164i \(0.0947083\pi\)
\(200\) −22.7358 −1.60767
\(201\) 0 0
\(202\) −13.3554 + 23.1323i −0.939684 + 1.62758i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.95305 + 13.7751i −0.555465 + 0.962093i
\(206\) 15.0119 26.0014i 1.04593 1.81160i
\(207\) 0 0
\(208\) −22.4293 38.8487i −1.55519 2.69367i
\(209\) 0.421952 + 0.730843i 0.0291870 + 0.0505535i
\(210\) 0 0
\(211\) 5.71291 9.89505i 0.393293 0.681204i −0.599589 0.800308i \(-0.704669\pi\)
0.992882 + 0.119105i \(0.0380025\pi\)
\(212\) −14.9715 −1.02825
\(213\) 0 0
\(214\) 5.22475 0.357156
\(215\) 4.96441 + 8.59860i 0.338570 + 0.586420i
\(216\) 0 0
\(217\) 0 0
\(218\) 25.2600 + 43.7516i 1.71082 + 2.96323i
\(219\) 0 0
\(220\) 5.74705 + 9.95417i 0.387466 + 0.671110i
\(221\) −4.45051 7.70850i −0.299373 0.518530i
\(222\) 0 0
\(223\) −8.35953 14.4791i −0.559796 0.969595i −0.997513 0.0704822i \(-0.977546\pi\)
0.437717 0.899113i \(-0.355787\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.32625 7.49328i −0.287778 0.498446i
\(227\) 17.0700 1.13298 0.566489 0.824070i \(-0.308302\pi\)
0.566489 + 0.824070i \(0.308302\pi\)
\(228\) 0 0
\(229\) −19.7894 −1.30772 −0.653861 0.756615i \(-0.726852\pi\)
−0.653861 + 0.756615i \(0.726852\pi\)
\(230\) 0.613500 1.06261i 0.0404530 0.0700666i
\(231\) 0 0
\(232\) −20.8187 36.0591i −1.36682 2.36740i
\(233\) 2.96579 + 5.13691i 0.194296 + 0.336530i 0.946669 0.322207i \(-0.104425\pi\)
−0.752374 + 0.658736i \(0.771091\pi\)
\(234\) 0 0
\(235\) 8.84228 15.3153i 0.576807 0.999058i
\(236\) −12.2875 + 21.2826i −0.799847 + 1.38538i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0277 17.3685i 0.648637 1.12347i −0.334812 0.942285i \(-0.608673\pi\)
0.983449 0.181187i \(-0.0579939\pi\)
\(240\) 0 0
\(241\) −29.2887 −1.88665 −0.943326 0.331869i \(-0.892321\pi\)
−0.943326 + 0.331869i \(0.892321\pi\)
\(242\) 12.4636 21.5877i 0.801193 1.38771i
\(243\) 0 0
\(244\) 2.06827 0.132408
\(245\) 0 0
\(246\) 0 0
\(247\) −1.98865 −0.126535
\(248\) 34.0121 + 58.9107i 2.15977 + 3.74083i
\(249\) 0 0
\(250\) −16.1164 + 27.9144i −1.01929 + 1.76546i
\(251\) −22.7856 −1.43821 −0.719106 0.694901i \(-0.755448\pi\)
−0.719106 + 0.694901i \(0.755448\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) 11.3681 19.6901i 0.713297 1.23547i
\(255\) 0 0
\(256\) −15.7821 27.3354i −0.986381 1.70846i
\(257\) −24.2889 −1.51510 −0.757550 0.652778i \(-0.773604\pi\)
−0.757550 + 0.652778i \(0.773604\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −27.0857 −1.67979
\(261\) 0 0
\(262\) 16.2536 28.1520i 1.00415 1.73924i
\(263\) 8.61155 0.531011 0.265506 0.964109i \(-0.414461\pi\)
0.265506 + 0.964109i \(0.414461\pi\)
\(264\) 0 0
\(265\) −2.21062 + 3.82890i −0.135797 + 0.235208i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.82011 11.8128i 0.416605 0.721581i
\(269\) 7.61561 13.1906i 0.464332 0.804247i −0.534839 0.844954i \(-0.679628\pi\)
0.999171 + 0.0407073i \(0.0129611\pi\)
\(270\) 0 0
\(271\) −2.33910 4.05144i −0.142090 0.246108i 0.786193 0.617981i \(-0.212049\pi\)
−0.928284 + 0.371873i \(0.878716\pi\)
\(272\) −19.7633 34.2310i −1.19832 2.07556i
\(273\) 0 0
\(274\) 22.4684 38.9164i 1.35737 2.35103i
\(275\) −3.34943 −0.201978
\(276\) 0 0
\(277\) −16.3907 −0.984824 −0.492412 0.870362i \(-0.663885\pi\)
−0.492412 + 0.870362i \(0.663885\pi\)
\(278\) −10.7280 18.5815i −0.643423 1.11444i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.75702 3.04325i −0.104815 0.181545i 0.808848 0.588018i \(-0.200092\pi\)
−0.913663 + 0.406473i \(0.866758\pi\)
\(282\) 0 0
\(283\) 13.0354 + 22.5780i 0.774874 + 1.34212i 0.934865 + 0.355002i \(0.115520\pi\)
−0.159992 + 0.987118i \(0.551147\pi\)
\(284\) −3.90025 6.75543i −0.231437 0.400861i
\(285\) 0 0
\(286\) −5.81958 10.0798i −0.344119 0.596031i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.57850 + 7.93019i 0.269323 + 0.466482i
\(290\) −19.5891 −1.15031
\(291\) 0 0
\(292\) 2.51479 0.147167
\(293\) −9.44192 + 16.3539i −0.551603 + 0.955404i 0.446556 + 0.894756i \(0.352650\pi\)
−0.998159 + 0.0606487i \(0.980683\pi\)
\(294\) 0 0
\(295\) 3.62863 + 6.28497i 0.211267 + 0.365925i
\(296\) −36.7242 63.6082i −2.13455 3.69715i
\(297\) 0 0
\(298\) −18.5559 + 32.1398i −1.07492 + 1.86181i
\(299\) −0.452700 + 0.784099i −0.0261803 + 0.0453456i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.29401 + 9.16950i −0.304636 + 0.527645i
\(303\) 0 0
\(304\) −8.83097 −0.506491
\(305\) 0.305392 0.528954i 0.0174867 0.0302878i
\(306\) 0 0
\(307\) 21.6407 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 32.0032 1.81766
\(311\) −2.24724 3.89234i −0.127429 0.220714i 0.795251 0.606281i \(-0.207339\pi\)
−0.922680 + 0.385567i \(0.874006\pi\)
\(312\) 0 0
\(313\) 4.30102 7.44958i 0.243108 0.421075i −0.718490 0.695537i \(-0.755166\pi\)
0.961598 + 0.274462i \(0.0884997\pi\)
\(314\) 0.799206 0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) −4.03128 + 6.98237i −0.226419 + 0.392169i −0.956744 0.290930i \(-0.906035\pi\)
0.730325 + 0.683100i \(0.239369\pi\)
\(318\) 0 0
\(319\) −3.06701 5.31221i −0.171719 0.297427i
\(320\) −41.4105 −2.31492
\(321\) 0 0
\(322\) 0 0
\(323\) −1.75228 −0.0974992
\(324\) 0 0
\(325\) 3.94646 6.83546i 0.218910 0.379163i
\(326\) 29.0766 1.61041
\(327\) 0 0
\(328\) 45.8981 79.4978i 2.53430 4.38953i
\(329\) 0 0
\(330\) 0 0
\(331\) 11.4513 19.8342i 0.629419 1.09019i −0.358249 0.933626i \(-0.616626\pi\)
0.987668 0.156560i \(-0.0500405\pi\)
\(332\) −37.5681 + 65.0698i −2.06182 + 3.57117i
\(333\) 0 0
\(334\) 4.34075 + 7.51840i 0.237515 + 0.411388i
\(335\) −2.01405 3.48844i −0.110039 0.190594i
\(336\) 0 0
\(337\) −6.81891 + 11.8107i −0.371450 + 0.643369i −0.989789 0.142542i \(-0.954472\pi\)
0.618339 + 0.785911i \(0.287806\pi\)
\(338\) −7.86916 −0.428026
\(339\) 0 0
\(340\) −23.8662 −1.29433
\(341\) 5.01065 + 8.67869i 0.271342 + 0.469978i
\(342\) 0 0
\(343\) 0 0
\(344\) −28.6502 49.6237i −1.54472 2.67553i
\(345\) 0 0
\(346\) 15.5272 + 26.8938i 0.834746 + 1.44582i
\(347\) −1.41282 2.44707i −0.0758440 0.131366i 0.825609 0.564243i \(-0.190832\pi\)
−0.901453 + 0.432877i \(0.857498\pi\)
\(348\) 0 0
\(349\) 1.81202 + 3.13851i 0.0969951 + 0.168000i 0.910440 0.413642i \(-0.135744\pi\)
−0.813444 + 0.581643i \(0.802410\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −13.4947 23.3734i −0.719268 1.24581i
\(353\) −2.75401 −0.146581 −0.0732907 0.997311i \(-0.523350\pi\)
−0.0732907 + 0.997311i \(0.523350\pi\)
\(354\) 0 0
\(355\) −2.30357 −0.122261
\(356\) 6.94877 12.0356i 0.368284 0.637887i
\(357\) 0 0
\(358\) 1.49135 + 2.58310i 0.0788205 + 0.136521i
\(359\) −8.40076 14.5505i −0.443375 0.767948i 0.554562 0.832142i \(-0.312886\pi\)
−0.997937 + 0.0641941i \(0.979552\pi\)
\(360\) 0 0
\(361\) 9.30425 16.1154i 0.489698 0.848181i
\(362\) 4.33081 7.50119i 0.227622 0.394254i
\(363\) 0 0
\(364\) 0 0
\(365\) 0.371322 0.643149i 0.0194359 0.0336640i
\(366\) 0 0
\(367\) 23.9339 1.24934 0.624670 0.780889i \(-0.285233\pi\)
0.624670 + 0.780889i \(0.285233\pi\)
\(368\) −2.01030 + 3.48193i −0.104794 + 0.181508i
\(369\) 0 0
\(370\) −34.5551 −1.79644
\(371\) 0 0
\(372\) 0 0
\(373\) −19.1606 −0.992098 −0.496049 0.868295i \(-0.665216\pi\)
−0.496049 + 0.868295i \(0.665216\pi\)
\(374\) −5.12784 8.88168i −0.265154 0.459261i
\(375\) 0 0
\(376\) −51.0299 + 88.3865i −2.63167 + 4.55818i
\(377\) 14.4548 0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) −2.66608 + 4.61779i −0.136767 + 0.236888i
\(381\) 0 0
\(382\) 5.25127 + 9.09546i 0.268678 + 0.465364i
\(383\) −20.1435 −1.02929 −0.514643 0.857405i \(-0.672075\pi\)
−0.514643 + 0.857405i \(0.672075\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −11.2294 −0.571561
\(387\) 0 0
\(388\) −38.8372 + 67.2679i −1.97166 + 3.41501i
\(389\) −13.3947 −0.679139 −0.339570 0.940581i \(-0.610281\pi\)
−0.339570 + 0.940581i \(0.610281\pi\)
\(390\) 0 0
\(391\) −0.398891 + 0.690899i −0.0201728 + 0.0349402i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.20724 + 2.09100i −0.0608198 + 0.105343i
\(395\) −12.4630 + 21.5866i −0.627083 + 1.08614i
\(396\) 0 0
\(397\) −9.00664 15.6000i −0.452031 0.782940i 0.546482 0.837471i \(-0.315967\pi\)
−0.998512 + 0.0545313i \(0.982634\pi\)
\(398\) 8.58506 + 14.8698i 0.430330 + 0.745354i
\(399\) 0 0
\(400\) 17.5249 30.3541i 0.876247 1.51770i
\(401\) −28.8675 −1.44157 −0.720787 0.693157i \(-0.756219\pi\)
−0.720787 + 0.693157i \(0.756219\pi\)
\(402\) 0 0
\(403\) −23.6151 −1.17635
\(404\) −26.4240 45.7676i −1.31464 2.27703i
\(405\) 0 0
\(406\) 0 0
\(407\) −5.41019 9.37073i −0.268173 0.464490i
\(408\) 0 0
\(409\) −5.42937 9.40395i −0.268465 0.464995i 0.700000 0.714142i \(-0.253183\pi\)
−0.968466 + 0.249147i \(0.919850\pi\)
\(410\) −21.5936 37.4012i −1.06643 1.84711i
\(411\) 0 0
\(412\) 29.7014 + 51.4443i 1.46328 + 2.53448i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.0943 + 19.2158i 0.544595 + 0.943267i
\(416\) 63.6001 3.11825
\(417\) 0 0
\(418\) −2.29131 −0.112072
\(419\) −0.247572 + 0.428807i −0.0120947 + 0.0209486i −0.872009 0.489489i \(-0.837183\pi\)
0.859915 + 0.510438i \(0.170517\pi\)
\(420\) 0 0
\(421\) 9.50320 + 16.4600i 0.463158 + 0.802212i 0.999116 0.0420318i \(-0.0133831\pi\)
−0.535959 + 0.844244i \(0.680050\pi\)
\(422\) 15.5113 + 26.8664i 0.755079 + 1.30784i
\(423\) 0 0
\(424\) 12.7578 22.0971i 0.619572 1.07313i
\(425\) 3.47737 6.02298i 0.168677 0.292157i
\(426\) 0 0
\(427\) 0 0
\(428\) −5.16864 + 8.95234i −0.249835 + 0.432728i
\(429\) 0 0
\(430\) −26.9580 −1.30003
\(431\) −8.46073 + 14.6544i −0.407539 + 0.705878i −0.994613 0.103655i \(-0.966946\pi\)
0.587074 + 0.809533i \(0.300280\pi\)
\(432\) 0 0
\(433\) 33.4740 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −99.9548 −4.78697
\(437\) 0.0891197 + 0.154360i 0.00426317 + 0.00738403i
\(438\) 0 0
\(439\) 10.4657 18.1272i 0.499502 0.865163i −0.500498 0.865738i \(-0.666850\pi\)
1.00000 0.000574559i \(0.000182888\pi\)
\(440\) −19.5891 −0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) −15.4290 + 26.7238i −0.733054 + 1.26969i 0.222517 + 0.974929i \(0.428573\pi\)
−0.955572 + 0.294759i \(0.904761\pi\)
\(444\) 0 0
\(445\) −2.05205 3.55425i −0.0972763 0.168487i
\(446\) 45.3945 2.14949
\(447\) 0 0
\(448\) 0 0
\(449\) 33.2789 1.57053 0.785263 0.619162i \(-0.212528\pi\)
0.785263 + 0.619162i \(0.212528\pi\)
\(450\) 0 0
\(451\) 6.76168 11.7116i 0.318395 0.551477i
\(452\) 17.1191 0.805217
\(453\) 0 0
\(454\) −23.1737 + 40.1380i −1.08760 + 1.88377i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.8952 + 20.6031i −0.556434 + 0.963772i 0.441356 + 0.897332i \(0.354498\pi\)
−0.997790 + 0.0664402i \(0.978836\pi\)
\(458\) 26.8654 46.5323i 1.25534 2.17431i
\(459\) 0 0
\(460\) 1.21382 + 2.10240i 0.0565947 + 0.0980249i
\(461\) 8.53122 + 14.7765i 0.397339 + 0.688211i 0.993397 0.114731i \(-0.0366005\pi\)
−0.596058 + 0.802941i \(0.703267\pi\)
\(462\) 0 0
\(463\) 18.1243 31.3922i 0.842306 1.45892i −0.0456338 0.998958i \(-0.514531\pi\)
0.887940 0.459959i \(-0.152136\pi\)
\(464\) 64.1889 2.97990
\(465\) 0 0
\(466\) −16.1051 −0.746052
\(467\) 4.09580 + 7.09413i 0.189531 + 0.328277i 0.945094 0.326799i \(-0.105970\pi\)
−0.755563 + 0.655076i \(0.772637\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0080 + 41.5830i 1.10740 + 1.91808i
\(471\) 0 0
\(472\) −20.9413 36.2714i −0.963900 1.66952i
\(473\) −4.22074 7.31054i −0.194070 0.336139i
\(474\) 0 0
\(475\) −0.776909 1.34565i −0.0356470 0.0617425i
\(476\) 0 0
\(477\) 0 0
\(478\) 27.2265 + 47.1577i 1.24531 + 2.15694i
\(479\) −25.5549 −1.16763 −0.583817 0.811885i \(-0.698441\pi\)
−0.583817 + 0.811885i \(0.698441\pi\)
\(480\) 0 0
\(481\) 25.4982 1.16262
\(482\) 39.7614 68.8687i 1.81108 3.13688i
\(483\) 0 0
\(484\) 24.6596 + 42.7116i 1.12089 + 1.94144i
\(485\) 11.4690 + 19.8649i 0.520782 + 0.902020i
\(486\) 0 0
\(487\) 3.46140 5.99533i 0.156851 0.271674i −0.776880 0.629648i \(-0.783199\pi\)
0.933732 + 0.357974i \(0.116532\pi\)
\(488\) −1.76246 + 3.05266i −0.0797826 + 0.138188i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.7262 + 32.4348i −0.845103 + 1.46376i 0.0404294 + 0.999182i \(0.487127\pi\)
−0.885532 + 0.464578i \(0.846206\pi\)
\(492\) 0 0
\(493\) 12.7366 0.573628
\(494\) 2.69973 4.67607i 0.121467 0.210386i
\(495\) 0 0
\(496\) −104.867 −4.70867
\(497\) 0 0
\(498\) 0 0
\(499\) 25.6250 1.14713 0.573566 0.819159i \(-0.305560\pi\)
0.573566 + 0.819159i \(0.305560\pi\)
\(500\) −31.8867 55.2293i −1.42601 2.46993i
\(501\) 0 0
\(502\) 30.9329 53.5774i 1.38060 2.39127i
\(503\) −5.79692 −0.258472 −0.129236 0.991614i \(-0.541252\pi\)
−0.129236 + 0.991614i \(0.541252\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) −0.521598 + 0.903434i −0.0231878 + 0.0401625i
\(507\) 0 0
\(508\) 22.4920 + 38.9573i 0.997921 + 1.72845i
\(509\) 25.1395 1.11429 0.557144 0.830416i \(-0.311897\pi\)
0.557144 + 0.830416i \(0.311897\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 23.9940 1.06039
\(513\) 0 0
\(514\) 32.9738 57.1123i 1.45441 2.51911i
\(515\) 17.5423 0.773004
\(516\) 0 0
\(517\) −7.51771 + 13.0211i −0.330629 + 0.572665i
\(518\) 0 0
\(519\) 0 0
\(520\) 23.0808 39.9771i 1.01216 1.75311i
\(521\) −3.64828 + 6.31900i −0.159834 + 0.276841i −0.934809 0.355152i \(-0.884429\pi\)
0.774975 + 0.631992i \(0.217763\pi\)
\(522\) 0 0
\(523\) 8.38637 + 14.5256i 0.366710 + 0.635161i 0.989049 0.147587i \(-0.0471506\pi\)
−0.622339 + 0.782748i \(0.713817\pi\)
\(524\) 32.1580 + 55.6993i 1.40483 + 2.43324i
\(525\) 0 0
\(526\) −11.6908 + 20.2490i −0.509741 + 0.882898i
\(527\) −20.8081 −0.906416
\(528\) 0 0
\(529\) −22.9189 −0.996472
\(530\) −6.00212 10.3960i −0.260716 0.451573i
\(531\) 0 0
\(532\) 0 0
\(533\) 15.9339 + 27.5982i 0.690172 + 1.19541i
\(534\) 0 0
\(535\) 1.52635 + 2.64372i 0.0659900 + 0.114298i
\(536\) 11.6234 + 20.1322i 0.502053 + 0.869581i
\(537\) 0 0
\(538\) 20.6774 + 35.8143i 0.891466 + 1.54406i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.64908 + 4.58834i 0.113893 + 0.197268i 0.917337 0.398112i \(-0.130335\pi\)
−0.803444 + 0.595381i \(0.797001\pi\)
\(542\) 12.7019 0.545595
\(543\) 0 0
\(544\) 56.0404 2.40271
\(545\) −14.7589 + 25.5631i −0.632200 + 1.09500i
\(546\) 0 0
\(547\) 16.4325 + 28.4619i 0.702603 + 1.21694i 0.967550 + 0.252681i \(0.0813123\pi\)
−0.264947 + 0.964263i \(0.585354\pi\)
\(548\) 44.4542 + 76.9970i 1.89899 + 3.28915i
\(549\) 0 0
\(550\) 4.54708 7.87577i 0.193888 0.335824i
\(551\) 1.42280 2.46436i 0.0606133 0.104985i
\(552\) 0 0
\(553\) 0 0
\(554\) 22.2515 38.5408i 0.945376 1.63744i
\(555\) 0 0
\(556\) 42.4512 1.80033
\(557\) −9.40798 + 16.2951i −0.398629 + 0.690446i −0.993557 0.113333i \(-0.963847\pi\)
0.594928 + 0.803779i \(0.297181\pi\)
\(558\) 0 0
\(559\) 19.8923 0.841354
\(560\) 0 0
\(561\) 0 0
\(562\) 9.54108 0.402466
\(563\) −13.8325 23.9586i −0.582970 1.00973i −0.995125 0.0986197i \(-0.968557\pi\)
0.412155 0.911114i \(-0.364776\pi\)
\(564\) 0 0
\(565\) 2.52773 4.37816i 0.106343 0.184191i
\(566\) −70.7856 −2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) −20.0916 + 34.7996i −0.842282 + 1.45888i 0.0456782 + 0.998956i \(0.485455\pi\)
−0.887961 + 0.459920i \(0.847878\pi\)
\(570\) 0 0
\(571\) 3.40565 + 5.89875i 0.142522 + 0.246855i 0.928446 0.371468i \(-0.121146\pi\)
−0.785924 + 0.618323i \(0.787812\pi\)
\(572\) 23.0283 0.962862
\(573\) 0 0
\(574\) 0 0
\(575\) −0.707427 −0.0295017
\(576\) 0 0
\(577\) −18.2111 + 31.5425i −0.758138 + 1.31313i 0.185661 + 0.982614i \(0.440557\pi\)
−0.943799 + 0.330519i \(0.892776\pi\)
\(578\) −24.8625 −1.03414
\(579\) 0 0
\(580\) 19.3787 33.5649i 0.804658 1.39371i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.87947 3.25534i 0.0778397 0.134822i
\(584\) −2.14295 + 3.71170i −0.0886759 + 0.153591i
\(585\) 0 0
\(586\) −25.6361 44.4030i −1.05902 1.83427i
\(587\) 5.57943 + 9.66385i 0.230288 + 0.398870i 0.957893 0.287126i \(-0.0927000\pi\)
−0.727605 + 0.685996i \(0.759367\pi\)
\(588\) 0 0
\(589\) −2.32446 + 4.02609i −0.0957779 + 0.165892i
\(590\) −19.7044 −0.811218
\(591\) 0 0
\(592\) 113.229 4.65369
\(593\) −9.90427 17.1547i −0.406720 0.704459i 0.587800 0.809006i \(-0.299994\pi\)
−0.994520 + 0.104547i \(0.966661\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36.7133 63.5893i −1.50384 2.60472i
\(597\) 0 0
\(598\) −1.22914 2.12893i −0.0502633 0.0870586i
\(599\) −9.06600 15.7028i −0.370427 0.641598i 0.619204 0.785230i \(-0.287455\pi\)
−0.989631 + 0.143632i \(0.954122\pi\)
\(600\) 0 0
\(601\) 12.3285 + 21.3536i 0.502889 + 0.871030i 0.999994 + 0.00333942i \(0.00106297\pi\)
−0.497105 + 0.867690i \(0.665604\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −10.4743 18.1420i −0.426194 0.738189i
\(605\) 14.5645 0.592130
\(606\) 0 0
\(607\) −17.2775 −0.701273 −0.350637 0.936512i \(-0.614035\pi\)
−0.350637 + 0.936512i \(0.614035\pi\)
\(608\) 6.26024 10.8431i 0.253886 0.439744i
\(609\) 0 0
\(610\) 0.829179 + 1.43618i 0.0335725 + 0.0581492i
\(611\) −17.7154 30.6840i −0.716689 1.24134i
\(612\) 0 0
\(613\) −9.77828 + 16.9365i −0.394941 + 0.684058i −0.993094 0.117324i \(-0.962568\pi\)
0.598153 + 0.801382i \(0.295902\pi\)
\(614\) −29.3787 + 50.8855i −1.18563 + 2.05357i
\(615\) 0 0
\(616\) 0 0
\(617\) −10.8723 + 18.8314i −0.437702 + 0.758122i −0.997512 0.0704988i \(-0.977541\pi\)
0.559810 + 0.828621i \(0.310874\pi\)
\(618\) 0 0
\(619\) −33.8048 −1.35873 −0.679366 0.733800i \(-0.737745\pi\)
−0.679366 + 0.733800i \(0.737745\pi\)
\(620\) −31.6595 + 54.8359i −1.27148 + 2.20226i
\(621\) 0 0
\(622\) 12.2031 0.489300
\(623\) 0 0
\(624\) 0 0
\(625\) −6.41615 −0.256646
\(626\) 11.6778 + 20.2266i 0.466740 + 0.808418i
\(627\) 0 0
\(628\) −0.790623 + 1.36940i −0.0315493 + 0.0546450i
\(629\) 22.4674 0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) 71.9258 124.579i 2.86105 4.95549i
\(633\) 0 0
\(634\) −10.9454 18.9581i −0.434699 0.752921i
\(635\) 13.2843 0.527169
\(636\) 0 0
\(637\) 0 0
\(638\) 16.6547 0.659365
\(639\) 0 0
\(640\) 24.4729 42.3883i 0.967375 1.67554i
\(641\) −15.9180 −0.628724 −0.314362 0.949303i \(-0.601791\pi\)
−0.314362 + 0.949303i \(0.601791\pi\)
\(642\) 0 0
\(643\) 13.2527 22.9544i 0.522636 0.905231i −0.477017 0.878894i \(-0.658282\pi\)
0.999653 0.0263376i \(-0.00838450\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.37883 4.12026i 0.0935938 0.162109i
\(647\) −0.00801958 + 0.0138903i −0.000315282 + 0.000546085i −0.866183 0.499727i \(-0.833434\pi\)
0.865868 + 0.500273i \(0.166767\pi\)
\(648\) 0 0
\(649\) −3.08506 5.34348i −0.121099 0.209750i
\(650\) 10.7152 + 18.5592i 0.420283 + 0.727951i
\(651\) 0 0
\(652\) −28.7644 + 49.8214i −1.12650 + 1.95115i
\(653\) 33.2879 1.30266 0.651328 0.758796i \(-0.274212\pi\)
0.651328 + 0.758796i \(0.274212\pi\)
\(654\) 0 0
\(655\) 18.9932 0.742126
\(656\) 70.7571 + 122.555i 2.76260 + 4.78497i
\(657\) 0 0
\(658\) 0 0
\(659\) −19.4156 33.6288i −0.756324 1.30999i −0.944713 0.327897i \(-0.893660\pi\)
0.188389 0.982094i \(-0.439673\pi\)
\(660\) 0 0
\(661\) 2.65322 + 4.59551i 0.103198 + 0.178745i 0.913001 0.407958i \(-0.133759\pi\)
−0.809802 + 0.586703i \(0.800426\pi\)
\(662\) 31.0917 + 53.8525i 1.20842 + 2.09304i
\(663\) 0 0
\(664\) −64.0264 110.897i −2.48471 4.30364i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.647777 1.12198i −0.0250820 0.0434433i
\(668\) −17.1765 −0.664579
\(669\) 0 0
\(670\) 10.9368 0.422527
\(671\) −0.259644 + 0.449717i −0.0100235 + 0.0173611i
\(672\) 0 0
\(673\) −3.03565 5.25789i −0.117016 0.202677i 0.801568 0.597903i \(-0.203999\pi\)
−0.918584 + 0.395227i \(0.870666\pi\)
\(674\) −18.5142 32.0676i −0.713142 1.23520i
\(675\) 0 0
\(676\) 7.78465 13.4834i 0.299410 0.518593i
\(677\) 17.3925 30.1247i 0.668449 1.15779i −0.309889 0.950773i \(-0.600292\pi\)
0.978338 0.207014i \(-0.0663747\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 20.3373 35.2253i 0.779901 1.35083i
\(681\) 0 0
\(682\) −27.2091 −1.04189
\(683\) 9.71206 16.8218i 0.371622 0.643667i −0.618194 0.786026i \(-0.712135\pi\)
0.989815 + 0.142358i \(0.0454686\pi\)
\(684\) 0 0
\(685\) 26.2556 1.00318
\(686\) 0 0
\(687\) 0 0
\(688\) 88.3352 3.36775
\(689\) 4.42895 + 7.67117i 0.168730 + 0.292248i
\(690\) 0 0
\(691\) −3.31837 + 5.74759i −0.126237 + 0.218649i −0.922216 0.386676i \(-0.873623\pi\)
0.795979 + 0.605324i \(0.206957\pi\)
\(692\) −61.4416 −2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) 6.26814 10.8567i 0.237764 0.411820i
\(696\) 0 0
\(697\) 14.0399 + 24.3178i 0.531799 + 0.921103i
\(698\) −9.83974 −0.372440
\(699\) 0 0
\(700\) 0 0
\(701\) 13.9153 0.525574 0.262787 0.964854i \(-0.415358\pi\)
0.262787 + 0.964854i \(0.415358\pi\)
\(702\) 0 0
\(703\) 2.50982 4.34713i 0.0946595 0.163955i
\(704\) 35.2072 1.32692
\(705\) 0 0
\(706\) 3.73876 6.47571i 0.140710 0.243717i
\(707\) 0 0
\(708\) 0 0
\(709\) −17.0778 + 29.5796i −0.641370 + 1.11089i 0.343757 + 0.939059i \(0.388300\pi\)
−0.985127 + 0.171827i \(0.945033\pi\)
\(710\) 3.12725 5.41655i 0.117364 0.203280i
\(711\) 0 0
\(712\) 11.8426 + 20.5120i 0.443821 + 0.768721i
\(713\) 1.05829 + 1.83301i 0.0396332 + 0.0686467i
\(714\) 0 0
\(715\) 3.40025 5.88941i 0.127162 0.220251i
\(716\) −5.90135 −0.220544
\(717\) 0 0
\(718\) 45.6183 1.70246
\(719\) 22.1450 + 38.3563i 0.825870 + 1.43045i 0.901253 + 0.433294i \(0.142649\pi\)
−0.0753825 + 0.997155i \(0.524018\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 25.2623 + 43.7556i 0.940165 + 1.62841i
\(723\) 0 0
\(724\) 8.56860 + 14.8413i 0.318450 + 0.551571i
\(725\) 5.64705 + 9.78099i 0.209726 + 0.363257i
\(726\) 0 0
\(727\) −14.1247 24.4647i −0.523857 0.907346i −0.999614 0.0277700i \(-0.991159\pi\)
0.475758 0.879576i \(-0.342174\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.00819 + 1.74623i 0.0373147 + 0.0646310i
\(731\) 17.5278 0.648290
\(732\) 0 0
\(733\) 25.0169 0.924020 0.462010 0.886875i \(-0.347128\pi\)
0.462010 + 0.886875i \(0.347128\pi\)
\(734\) −32.4919 + 56.2776i −1.19930 + 2.07724i
\(735\) 0 0
\(736\) −2.85018 4.93666i −0.105059 0.181968i
\(737\) 1.71235 + 2.96587i 0.0630752 + 0.109249i
\(738\) 0 0
\(739\) −16.0115 + 27.7327i −0.588992 + 1.02016i 0.405373 + 0.914151i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(740\) 34.1840 59.2084i 1.25663 2.17655i
\(741\) 0 0
\(742\) 0 0
\(743\) −19.4031 + 33.6072i −0.711833 + 1.23293i 0.252336 + 0.967640i \(0.418801\pi\)
−0.964169 + 0.265290i \(0.914532\pi\)
\(744\) 0 0
\(745\) −21.6837 −0.794428
\(746\) 26.0118 45.0537i 0.952359 1.64953i
\(747\) 0 0
\(748\) 20.2911 0.741915
\(749\) 0 0
\(750\) 0 0
\(751\) 21.6991 0.791811 0.395905 0.918291i \(-0.370431\pi\)
0.395905 + 0.918291i \(0.370431\pi\)
\(752\) −78.6685 136.258i −2.86874 4.96881i
\(753\) 0 0
\(754\) −19.6233 + 33.9885i −0.714638 + 1.23779i
\(755\) −6.18635 −0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) −13.6802 + 23.6949i −0.496889 + 0.860637i
\(759\) 0 0
\(760\) −4.54374 7.86999i −0.164819 0.285475i
\(761\) −13.3210 −0.482884 −0.241442 0.970415i \(-0.577620\pi\)
−0.241442 + 0.970415i \(0.577620\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.7795 −0.751775
\(765\) 0 0
\(766\) 27.3462 47.3649i 0.988057 1.71137i
\(767\) 14.5398 0.525003
\(768\) 0 0
\(769\) −27.3568 + 47.3833i −0.986510 + 1.70869i −0.351488 + 0.936192i \(0.614324\pi\)
−0.635022 + 0.772494i \(0.719009\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.1088 19.2410i 0.399814 0.692498i
\(773\) −1.18021 + 2.04418i −0.0424491 + 0.0735240i −0.886469 0.462787i \(-0.846849\pi\)
0.844020 + 0.536311i \(0.180183\pi\)
\(774\) 0 0
\(775\) −9.22573 15.9794i −0.331398 0.573998i
\(776\) −66.1892 114.643i −2.37606 4.11545i
\(777\) 0 0
\(778\) 18.1842 31.4960i 0.651936 1.12919i
\(779\) 6.27356 0.224774
\(780\) 0 0
\(781\) 1.95850 0.0700805
\(782\) −1.08304 1.87588i −0.0387295 0.0670814i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.233479 + 0.404398i 0.00833323 + 0.0144336i
\(786\) 0 0
\(787\) −0.833971 1.44448i −0.0297278 0.0514901i 0.850779 0.525524i \(-0.176131\pi\)
−0.880507 + 0.474034i \(0.842797\pi\)
\(788\) −2.38855 4.13708i −0.0850884 0.147377i
\(789\) 0 0
\(790\) −33.8388 58.6105i −1.20393 2.08527i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.611849 1.05975i −0.0217274 0.0376330i
\(794\) 48.9085 1.73570
\(795\) 0 0
\(796\) −33.9715 −1.20409
\(797\) −14.3148 + 24.7939i