Properties

Label 1323.2.g.h.361.1
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 361.1
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.1

$q$-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 \(-0.384573\pi\)
0.354728 + 0.934969i \(0.384573\pi\)
\(6\) 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 −0.556991 0.830518i \(-0.688044\pi\)
0.997746 + 0.0671096i \(0.0213777\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −7.05696 + 12.2230i −1.76424 + 3.05575i
\(17\) 1.40027 2.42534i 0.339615 0.588230i −0.644745 0.764397i \(-0.723037\pi\)
0.984360 + 0.176167i \(0.0563699\pi\)
\(18\) 0 0
\(19\) −0.312846 0.541866i −0.0717719 0.124313i 0.827906 0.560867i \(-0.189532\pi\)
−0.899678 + 0.436554i \(0.856199\pi\)
\(20\) −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 \(-0.934143\pi\)
0.311435 0.950267i \(-0.399190\pi\)
\(32\) −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 \(0.452950\pi\)
−0.930219 + 0.367004i \(0.880384\pi\)
\(42\) 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 \(-0.531152\pi\)
0.910737 0.412988i \(-0.135515\pi\)
\(48\) 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 0.975629 0.219425i \(-0.0704182\pi\)
−0.677842 + 0.735207i \(0.737085\pi\)
\(60\) 0 0
\(61\) 0.192507 0.333432i 0.0246480 0.0426916i −0.853438 0.521194i \(-0.825487\pi\)
0.878086 + 0.478502i \(0.158820\pi\)
\(62\) 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 −0.852003 0.523538i \(-0.824612\pi\)
0.879398 + 0.476087i \(0.157945\pi\)
\(74\) 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 \(0.111894\pi\)
−0.171225 + 0.985232i \(0.554772\pi\)
\(84\) 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 0.789289 0.614022i \(-0.210449\pi\)
−0.926403 + 0.376534i \(0.877116\pi\)
\(90\) 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 \(0.0957089\pi\)
−0.221079 + 0.975256i \(0.570958\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.67023 + 11.5532i 0.667023 + 1.15532i
\(101\) −9.83776 −0.978894 −0.489447 0.872033i \(-0.662801\pi\)
−0.489447 + 0.872033i \(0.662801\pi\)
\(102\) 0 0
\(103\) 11.0579 1.08957 0.544786 0.838575i \(-0.316611\pi\)
0.544786 + 0.838575i \(0.316611\pi\)
\(104\) 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 \(-0.324804\pi\)
0.523024 + 0.852318i \(0.324804\pi\)
\(132\) 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 −0.648375 0.761321i \(-0.724551\pi\)
0.983511 + 0.180849i \(0.0578845\pi\)
\(140\) 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 0.871839 0.489793i \(-0.162928\pi\)
−0.860093 + 0.510138i \(0.829594\pi\)
\(158\) 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 −0.921229 0.389020i \(-0.872814\pi\)
0.797516 + 0.603298i \(0.206147\pi\)
\(168\) 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 −0.997278 0.0737284i \(-0.976510\pi\)
0.562490 + 0.826804i \(0.309844\pi\)
\(174\) 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 \(-0.462172\pi\)
0.118560 + 0.992947i \(0.462172\pi\)
\(182\) 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 −0.956062 0.293164i \(-0.905292\pi\)
0.731919 + 0.681392i \(0.238625\pi\)
\(200\) −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 \(0.0224538\pi\)
−0.437717 + 0.899113i \(0.644213\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.32625 7.49328i −0.287778 0.498446i
\(227\) −17.0700 −1.13298 −0.566489 0.824070i \(-0.691698\pi\)
−0.566489 + 0.824070i \(0.691698\pi\)
\(228\) 0 0
\(229\) 19.7894 1.30772 0.653861 0.756615i \(-0.273148\pi\)
0.653861 + 0.756615i \(0.273148\pi\)
\(230\) −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 \(-0.107679\pi\)
0.943326 + 0.331869i \(0.107679\pi\)
\(242\) 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 \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(252\) 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 \(-0.226396\pi\)
0.757550 + 0.652778i \(0.226396\pi\)
\(258\) 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 −0.999171 0.0407073i \(-0.987039\pi\)
0.534839 + 0.844954i \(0.320372\pi\)
\(270\) 0 0
\(271\) 2.33910 + 4.05144i 0.142090 + 0.246108i 0.928284 0.371873i \(-0.121284\pi\)
−0.786193 + 0.617981i \(0.787951\pi\)
\(272\) 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 \(-0.884480\pi\)
0.159992 0.987118i \(-0.448853\pi\)
\(284\) −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 \(-0.647350\pi\)
0.998159 0.0606487i \(-0.0193169\pi\)
\(294\) 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 \(-0.711875\pi\)
−0.617551 + 0.786531i \(0.711875\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 32.0032 1.81766
\(311\) 2.24724 + 3.89234i 0.127429 + 0.220714i 0.922680 0.385567i \(-0.125994\pi\)
−0.795251 + 0.606281i \(0.792661\pi\)
\(312\) 0 0
\(313\) −4.30102 + 7.44958i −0.243108 + 0.421075i −0.961598 0.274462i \(-0.911500\pi\)
0.718490 + 0.695537i \(0.244834\pi\)
\(314\) −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 0.813444 0.581643i \(-0.197590\pi\)
−0.910440 + 0.413642i \(0.864256\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −13.4947 23.3734i −0.719268 1.24581i
\(353\) 2.75401 0.146581 0.0732907 0.997311i \(-0.476650\pi\)
0.0732907 + 0.997311i \(0.476650\pi\)
\(354\) 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 \(-0.714767\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(368\) −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 \(-0.327925\pi\)
0.514643 + 0.857405i \(0.327925\pi\)
\(384\) 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 0.998512 0.0545313i \(-0.0173665\pi\)
−0.546482 + 0.837471i \(0.684033\pi\)
\(398\) −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 0.968466 0.249147i \(-0.0801502\pi\)
−0.700000 + 0.714142i \(0.746817\pi\)
\(410\) −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 −0.859915 0.510438i \(-0.829483\pi\)
0.872009 + 0.489489i \(0.162817\pi\)
\(420\) 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 \(-0.797476\pi\)
−0.804330 + 0.594183i \(0.797476\pi\)
\(434\) 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 −1.00000 0.000574559i \(-0.999817\pi\)
0.500498 + 0.865738i \(0.333150\pi\)
\(440\) 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 0.596058 0.802941i \(-0.296733\pi\)
−0.993397 + 0.114731i \(0.963400\pi\)
\(462\) 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 0.755563 0.655076i \(-0.227363\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(468\) 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 \(-0.301559\pi\)
0.583817 + 0.811885i \(0.301559\pi\)
\(480\) 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 \(-0.458748\pi\)
0.129236 + 0.991614i \(0.458748\pi\)
\(504\) 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 \(-0.688103\pi\)
−0.557144 + 0.830416i \(0.688103\pi\)
\(510\) 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 −0.774975 0.631992i \(-0.782237\pi\)
0.934809 + 0.355152i \(0.115571\pi\)
\(522\) 0 0
\(523\) −8.38637 14.5256i −0.366710 0.635161i 0.622339 0.782748i \(-0.286183\pi\)
−0.989049 + 0.147587i \(0.952849\pi\)
\(524\) −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 \(0.0314427\pi\)
−0.412155 + 0.911114i \(0.635224\pi\)
\(564\) 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 \(-0.559443\pi\)
0.943799 0.330519i \(-0.107224\pi\)
\(578\) −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 0.727605 0.685996i \(-0.240633\pi\)
−0.957893 + 0.287126i \(0.907300\pi\)
\(588\) 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 0.994520 0.104547i \(-0.0333392\pi\)
−0.587800 + 0.809006i \(0.700006\pi\)
\(594\) 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 \(-0.998937\pi\)
0.497105 0.867690i \(-0.334396\pi\)
\(602\) 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 \(-0.385965\pi\)
0.350637 + 0.936512i \(0.385965\pi\)
\(608\) −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 \(-0.262255\pi\)
0.679366 + 0.733800i \(0.262255\pi\)
\(620\) −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 \(0.341718\pi\)
−0.999653 + 0.0263376i \(0.991616\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.37883 4.12026i 0.0935938 0.162109i
\(647\) 0.00801958 0.0138903i 0.000315282 0.000546085i −0.865868 0.500273i \(-0.833233\pi\)
0.866183 + 0.499727i \(0.166566\pi\)
\(648\) 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 0.809802 0.586703i \(-0.199574\pi\)
−0.913001 + 0.407958i \(0.866241\pi\)
\(662\) 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 \(0.399708\pi\)
−0.978338 + 0.207014i \(0.933625\pi\)
\(678\) 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 −0.795979 0.605324i \(-0.793043\pi\)
0.922216 + 0.386676i \(0.126377\pi\)
\(692\) 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 \(-0.857351\pi\)
0.0753825 0.997155i \(-0.475982\pi\)
\(720\) 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 \(0.00884060\pi\)
−0.475758 + 0.879576i \(0.657826\pi\)
\(728\) 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 \(-0.652872\pi\)
−0.462010 + 0.886875i \(0.652872\pi\)
\(734\) 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 \(-0.422380\pi\)
0.241442 + 0.970415i \(0.422380\pi\)
\(762\) 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 \(-0.385676\pi\)
0.635022 0.772494i \(-0.280991\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.1088 19.2410i 0.399814 0.692498i
\(773\) 1.18021 2.04418i 0.0424491 0.0735240i −0.844020 0.536311i \(-0.819817\pi\)
0.886469 + 0.462787i \(0.153151\pi\)
\(774\) 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 0.880507 0.474034i \(-0.157203\pi\)
−0.850779 + 0.525524i \(0.823869\pi\)
\(788\) −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
\(797\)