Properties

Label 864.2.w.a.107.7
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +O(q^{10})\) \(q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +(-0.775695 - 1.50966i) q^{10} +(-4.23612 - 1.75466i) q^{11} +(-0.644097 - 1.55499i) q^{13} +(-4.56533 + 0.374940i) q^{14} +(-3.78704 + 1.28775i) q^{16} -5.75819 q^{17} +(4.00625 - 1.65944i) q^{19} +(-0.544443 + 2.33777i) q^{20} +(2.96349 + 5.76757i) q^{22} +(4.82067 - 4.82067i) q^{23} +(-2.51702 - 2.51702i) q^{25} +(-0.727835 + 2.26626i) q^{26} +(5.26669 + 3.77196i) q^{28} +(-1.52718 - 3.68694i) q^{29} +10.9561i q^{31} +(5.26234 + 2.07553i) q^{32} +(6.21019 + 5.26755i) q^{34} +(3.59147 - 1.48764i) q^{35} +(1.67353 - 4.04025i) q^{37} +(-5.83877 - 1.87518i) q^{38} +(2.72575 - 2.02322i) q^{40} +(-2.75672 - 2.75672i) q^{41} +(3.26736 - 7.88810i) q^{43} +(2.08001 - 8.93129i) q^{44} +(-9.60899 + 0.789163i) q^{46} +3.05588i q^{47} -3.49141i q^{49} +(0.412047 + 5.01715i) q^{50} +(2.85813 - 1.77834i) q^{52} +(3.81361 - 9.20688i) q^{53} +(-3.89116 - 3.89116i) q^{55} +(-2.22954 - 8.88597i) q^{56} +(-1.72573 + 5.37340i) q^{58} +(-2.49029 + 6.01210i) q^{59} +(4.36611 - 1.80850i) q^{61} +(10.0225 - 11.8161i) q^{62} +(-3.77673 - 7.05240i) q^{64} -2.02000i q^{65} +(-4.89651 - 11.8212i) q^{67} +(-1.87895 - 11.3621i) q^{68} +(-5.23427 - 1.68104i) q^{70} +(0.814206 + 0.814206i) q^{71} +(-6.13068 + 6.13068i) q^{73} +(-5.50089 + 2.82647i) q^{74} +(4.58169 + 7.36364i) q^{76} +(-13.7210 + 5.68342i) q^{77} -7.99746 q^{79} +(-4.79054 - 0.311461i) q^{80} +(0.451287 + 5.49495i) q^{82} +(4.51997 + 10.9122i) q^{83} +(-6.38472 - 2.64464i) q^{85} +(-10.7398 + 5.51834i) q^{86} +(-10.4136 + 7.72958i) q^{88} +(6.05533 - 6.05533i) q^{89} +(-5.03667 - 2.08626i) q^{91} +(11.0852 + 7.93912i) q^{92} +(2.79550 - 3.29576i) q^{94} +5.20430 q^{95} +11.5086 q^{97} +(-3.19392 + 3.76548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07850 0.914792i −0.762612 0.646856i
\(3\) 0 0
\(4\) 0.326309 + 1.97320i 0.163155 + 0.986601i
\(5\) 1.10881 + 0.459283i 0.495873 + 0.205397i 0.616582 0.787291i \(-0.288517\pi\)
−0.120709 + 0.992688i \(0.538517\pi\)
\(6\) 0 0
\(7\) 2.29035 2.29035i 0.865671 0.865671i −0.126319 0.991990i \(-0.540316\pi\)
0.991990 + 0.126319i \(0.0403161\pi\)
\(8\) 1.45315 2.42660i 0.513765 0.857931i
\(9\) 0 0
\(10\) −0.775695 1.50966i −0.245296 0.477397i
\(11\) −4.23612 1.75466i −1.27724 0.529050i −0.362082 0.932146i \(-0.617934\pi\)
−0.915158 + 0.403096i \(0.867934\pi\)
\(12\) 0 0
\(13\) −0.644097 1.55499i −0.178640 0.431276i 0.809041 0.587752i \(-0.199987\pi\)
−0.987682 + 0.156476i \(0.949987\pi\)
\(14\) −4.56533 + 0.374940i −1.22014 + 0.100207i
\(15\) 0 0
\(16\) −3.78704 + 1.28775i −0.946761 + 0.321937i
\(17\) −5.75819 −1.39657 −0.698284 0.715821i \(-0.746053\pi\)
−0.698284 + 0.715821i \(0.746053\pi\)
\(18\) 0 0
\(19\) 4.00625 1.65944i 0.919096 0.380702i 0.127564 0.991830i \(-0.459284\pi\)
0.791531 + 0.611128i \(0.209284\pi\)
\(20\) −0.544443 + 2.33777i −0.121741 + 0.522740i
\(21\) 0 0
\(22\) 2.96349 + 5.76757i 0.631819 + 1.22965i
\(23\) 4.82067 4.82067i 1.00518 1.00518i 0.00519281 0.999987i \(-0.498347\pi\)
0.999987 0.00519281i \(-0.00165293\pi\)
\(24\) 0 0
\(25\) −2.51702 2.51702i −0.503405 0.503405i
\(26\) −0.727835 + 2.26626i −0.142740 + 0.444451i
\(27\) 0 0
\(28\) 5.26669 + 3.77196i 0.995310 + 0.712833i
\(29\) −1.52718 3.68694i −0.283590 0.684647i 0.716324 0.697768i \(-0.245823\pi\)
−0.999914 + 0.0131208i \(0.995823\pi\)
\(30\) 0 0
\(31\) 10.9561i 1.96777i 0.178802 + 0.983885i \(0.442778\pi\)
−0.178802 + 0.983885i \(0.557222\pi\)
\(32\) 5.26234 + 2.07553i 0.930258 + 0.366905i
\(33\) 0 0
\(34\) 6.21019 + 5.26755i 1.06504 + 0.903378i
\(35\) 3.59147 1.48764i 0.607070 0.251457i
\(36\) 0 0
\(37\) 1.67353 4.04025i 0.275126 0.664213i −0.724561 0.689210i \(-0.757958\pi\)
0.999688 + 0.0249970i \(0.00795762\pi\)
\(38\) −5.83877 1.87518i −0.947173 0.304195i
\(39\) 0 0
\(40\) 2.72575 2.02322i 0.430979 0.319899i
\(41\) −2.75672 2.75672i −0.430528 0.430528i 0.458280 0.888808i \(-0.348466\pi\)
−0.888808 + 0.458280i \(0.848466\pi\)
\(42\) 0 0
\(43\) 3.26736 7.88810i 0.498268 1.20292i −0.452148 0.891943i \(-0.649342\pi\)
0.950416 0.310982i \(-0.100658\pi\)
\(44\) 2.08001 8.93129i 0.313573 1.34644i
\(45\) 0 0
\(46\) −9.60899 + 0.789163i −1.41677 + 0.116356i
\(47\) 3.05588i 0.445746i 0.974847 + 0.222873i \(0.0715436\pi\)
−0.974847 + 0.222873i \(0.928456\pi\)
\(48\) 0 0
\(49\) 3.49141i 0.498773i
\(50\) 0.412047 + 5.01715i 0.0582722 + 0.709533i
\(51\) 0 0
\(52\) 2.85813 1.77834i 0.396351 0.246611i
\(53\) 3.81361 9.20688i 0.523840 1.26466i −0.411661 0.911337i \(-0.635051\pi\)
0.935501 0.353325i \(-0.114949\pi\)
\(54\) 0 0
\(55\) −3.89116 3.89116i −0.524683 0.524683i
\(56\) −2.22954 8.88597i −0.297935 1.18744i
\(57\) 0 0
\(58\) −1.72573 + 5.37340i −0.226599 + 0.705562i
\(59\) −2.49029 + 6.01210i −0.324208 + 0.782708i 0.674792 + 0.738008i \(0.264233\pi\)
−0.999000 + 0.0447004i \(0.985767\pi\)
\(60\) 0 0
\(61\) 4.36611 1.80850i 0.559023 0.231555i −0.0852381 0.996361i \(-0.527165\pi\)
0.644261 + 0.764806i \(0.277165\pi\)
\(62\) 10.0225 11.8161i 1.27286 1.50065i
\(63\) 0 0
\(64\) −3.77673 7.05240i −0.472092 0.881549i
\(65\) 2.02000i 0.250550i
\(66\) 0 0
\(67\) −4.89651 11.8212i −0.598204 1.44419i −0.875410 0.483381i \(-0.839409\pi\)
0.277207 0.960810i \(-0.410591\pi\)
\(68\) −1.87895 11.3621i −0.227857 1.37785i
\(69\) 0 0
\(70\) −5.23427 1.68104i −0.625615 0.200923i
\(71\) 0.814206 + 0.814206i 0.0966285 + 0.0966285i 0.753769 0.657140i \(-0.228234\pi\)
−0.657140 + 0.753769i \(0.728234\pi\)
\(72\) 0 0
\(73\) −6.13068 + 6.13068i −0.717541 + 0.717541i −0.968101 0.250560i \(-0.919385\pi\)
0.250560 + 0.968101i \(0.419385\pi\)
\(74\) −5.50089 + 2.82647i −0.639465 + 0.328570i
\(75\) 0 0
\(76\) 4.58169 + 7.36364i 0.525555 + 0.844667i
\(77\) −13.7210 + 5.68342i −1.56365 + 0.647686i
\(78\) 0 0
\(79\) −7.99746 −0.899785 −0.449892 0.893083i \(-0.648538\pi\)
−0.449892 + 0.893083i \(0.648538\pi\)
\(80\) −4.79054 0.311461i −0.535598 0.0348223i
\(81\) 0 0
\(82\) 0.451287 + 5.49495i 0.0498363 + 0.606816i
\(83\) 4.51997 + 10.9122i 0.496131 + 1.19777i 0.951551 + 0.307490i \(0.0994891\pi\)
−0.455420 + 0.890277i \(0.650511\pi\)
\(84\) 0 0
\(85\) −6.38472 2.64464i −0.692520 0.286851i
\(86\) −10.7398 + 5.51834i −1.15810 + 0.595058i
\(87\) 0 0
\(88\) −10.4136 + 7.72958i −1.11009 + 0.823976i
\(89\) 6.05533 6.05533i 0.641864 0.641864i −0.309150 0.951013i \(-0.600044\pi\)
0.951013 + 0.309150i \(0.100044\pi\)
\(90\) 0 0
\(91\) −5.03667 2.08626i −0.527987 0.218699i
\(92\) 11.0852 + 7.93912i 1.15571 + 0.827711i
\(93\) 0 0
\(94\) 2.79550 3.29576i 0.288334 0.339932i
\(95\) 5.20430 0.533950
\(96\) 0 0
\(97\) 11.5086 1.16852 0.584262 0.811565i \(-0.301384\pi\)
0.584262 + 0.811565i \(0.301384\pi\)
\(98\) −3.19392 + 3.76548i −0.322634 + 0.380371i
\(99\) 0 0
\(100\) 4.14526 5.78792i 0.414526 0.578792i
\(101\) 0.407683 + 0.168868i 0.0405660 + 0.0168030i 0.402874 0.915255i \(-0.368011\pi\)
−0.362308 + 0.932058i \(0.618011\pi\)
\(102\) 0 0
\(103\) −1.14131 + 1.14131i −0.112456 + 0.112456i −0.761096 0.648639i \(-0.775338\pi\)
0.648639 + 0.761096i \(0.275338\pi\)
\(104\) −4.70929 0.696661i −0.461784 0.0683132i
\(105\) 0 0
\(106\) −12.5354 + 6.44092i −1.21754 + 0.625598i
\(107\) 8.61819 + 3.56977i 0.833152 + 0.345103i 0.758150 0.652081i \(-0.226104\pi\)
0.0750020 + 0.997183i \(0.476104\pi\)
\(108\) 0 0
\(109\) −3.95363 9.54490i −0.378689 0.914236i −0.992212 0.124559i \(-0.960248\pi\)
0.613523 0.789677i \(-0.289752\pi\)
\(110\) 0.636998 + 7.75620i 0.0607353 + 0.739524i
\(111\) 0 0
\(112\) −5.72427 + 11.6231i −0.540892 + 1.09828i
\(113\) −9.49602 −0.893310 −0.446655 0.894706i \(-0.647385\pi\)
−0.446655 + 0.894706i \(0.647385\pi\)
\(114\) 0 0
\(115\) 7.55924 3.13114i 0.704903 0.291980i
\(116\) 6.77674 4.21652i 0.629204 0.391494i
\(117\) 0 0
\(118\) 8.18559 4.20592i 0.753545 0.387187i
\(119\) −13.1883 + 13.1883i −1.20897 + 1.20897i
\(120\) 0 0
\(121\) 7.08774 + 7.08774i 0.644340 + 0.644340i
\(122\) −6.36324 2.04362i −0.576100 0.185021i
\(123\) 0 0
\(124\) −21.6185 + 3.57507i −1.94140 + 0.321051i
\(125\) −3.93128 9.49095i −0.351624 0.848896i
\(126\) 0 0
\(127\) 17.3638i 1.54079i −0.637568 0.770394i \(-0.720059\pi\)
0.637568 0.770394i \(-0.279941\pi\)
\(128\) −2.37828 + 11.0609i −0.210213 + 0.977656i
\(129\) 0 0
\(130\) −1.84788 + 2.17857i −0.162070 + 0.191073i
\(131\) 12.9137 5.34903i 1.12827 0.467347i 0.261081 0.965317i \(-0.415921\pi\)
0.867194 + 0.497970i \(0.165921\pi\)
\(132\) 0 0
\(133\) 5.37500 12.9764i 0.466072 1.12520i
\(134\) −5.53309 + 17.2284i −0.477986 + 1.48831i
\(135\) 0 0
\(136\) −8.36750 + 13.9728i −0.717507 + 1.19816i
\(137\) −1.43528 1.43528i −0.122624 0.122624i 0.643132 0.765756i \(-0.277635\pi\)
−0.765756 + 0.643132i \(0.777635\pi\)
\(138\) 0 0
\(139\) 1.00602 2.42876i 0.0853298 0.206004i −0.875455 0.483300i \(-0.839438\pi\)
0.960785 + 0.277295i \(0.0894381\pi\)
\(140\) 4.10734 + 6.60127i 0.347133 + 0.557909i
\(141\) 0 0
\(142\) −0.133289 1.62295i −0.0111853 0.136195i
\(143\) 7.71729i 0.645352i
\(144\) 0 0
\(145\) 4.78951i 0.397747i
\(146\) 12.2202 1.00362i 1.01135 0.0830599i
\(147\) 0 0
\(148\) 8.51832 + 1.98383i 0.700201 + 0.163070i
\(149\) −2.21125 + 5.33842i −0.181152 + 0.437341i −0.988205 0.153140i \(-0.951062\pi\)
0.807052 + 0.590480i \(0.201062\pi\)
\(150\) 0 0
\(151\) 7.88070 + 7.88070i 0.641322 + 0.641322i 0.950880 0.309558i \(-0.100181\pi\)
−0.309558 + 0.950880i \(0.600181\pi\)
\(152\) 1.79487 12.1329i 0.145583 0.984112i
\(153\) 0 0
\(154\) 19.9972 + 6.42231i 1.61142 + 0.517525i
\(155\) −5.03194 + 12.1482i −0.404175 + 0.975765i
\(156\) 0 0
\(157\) −12.8602 + 5.32685i −1.02635 + 0.425129i −0.831394 0.555683i \(-0.812457\pi\)
−0.194957 + 0.980812i \(0.562457\pi\)
\(158\) 8.62523 + 7.31602i 0.686187 + 0.582031i
\(159\) 0 0
\(160\) 4.88166 + 4.71826i 0.385929 + 0.373011i
\(161\) 22.0821i 1.74031i
\(162\) 0 0
\(163\) 2.99107 + 7.22108i 0.234278 + 0.565598i 0.996672 0.0815153i \(-0.0259759\pi\)
−0.762394 + 0.647114i \(0.775976\pi\)
\(164\) 4.54003 6.33912i 0.354517 0.495002i
\(165\) 0 0
\(166\) 5.10760 15.9036i 0.396427 1.23436i
\(167\) 10.0758 + 10.0758i 0.779690 + 0.779690i 0.979778 0.200088i \(-0.0641227\pi\)
−0.200088 + 0.979778i \(0.564123\pi\)
\(168\) 0 0
\(169\) 7.18926 7.18926i 0.553020 0.553020i
\(170\) 4.46661 + 8.69293i 0.342573 + 0.666717i
\(171\) 0 0
\(172\) 16.6310 + 3.87320i 1.26810 + 0.295328i
\(173\) 7.96435 3.29894i 0.605518 0.250814i −0.0587927 0.998270i \(-0.518725\pi\)
0.664311 + 0.747456i \(0.268725\pi\)
\(174\) 0 0
\(175\) −11.5297 −0.871566
\(176\) 18.3019 + 1.18992i 1.37956 + 0.0896932i
\(177\) 0 0
\(178\) −12.0700 + 0.991282i −0.904687 + 0.0742997i
\(179\) 2.93955 + 7.09670i 0.219712 + 0.530432i 0.994850 0.101360i \(-0.0323195\pi\)
−0.775138 + 0.631793i \(0.782319\pi\)
\(180\) 0 0
\(181\) −8.77358 3.63414i −0.652135 0.270123i 0.0319896 0.999488i \(-0.489816\pi\)
−0.684125 + 0.729365i \(0.739816\pi\)
\(182\) 3.52354 + 6.85754i 0.261182 + 0.508314i
\(183\) 0 0
\(184\) −4.69268 18.7030i −0.345949 1.37880i
\(185\) 3.71123 3.71123i 0.272855 0.272855i
\(186\) 0 0
\(187\) 24.3924 + 10.1037i 1.78375 + 0.738854i
\(188\) −6.02987 + 0.997164i −0.439774 + 0.0727256i
\(189\) 0 0
\(190\) −5.61282 4.76086i −0.407197 0.345389i
\(191\) 11.3188 0.819002 0.409501 0.912310i \(-0.365703\pi\)
0.409501 + 0.912310i \(0.365703\pi\)
\(192\) 0 0
\(193\) −1.00738 −0.0725131 −0.0362565 0.999343i \(-0.511543\pi\)
−0.0362565 + 0.999343i \(0.511543\pi\)
\(194\) −12.4120 10.5280i −0.891131 0.755867i
\(195\) 0 0
\(196\) 6.88926 1.13928i 0.492090 0.0813772i
\(197\) 4.85159 + 2.00959i 0.345661 + 0.143178i 0.548758 0.835981i \(-0.315101\pi\)
−0.203097 + 0.979159i \(0.565101\pi\)
\(198\) 0 0
\(199\) −11.9610 + 11.9610i −0.847891 + 0.847891i −0.989870 0.141979i \(-0.954653\pi\)
0.141979 + 0.989870i \(0.454653\pi\)
\(200\) −9.76540 + 2.45020i −0.690518 + 0.173255i
\(201\) 0 0
\(202\) −0.285206 0.555069i −0.0200670 0.0390545i
\(203\) −11.9422 4.94660i −0.838175 0.347184i
\(204\) 0 0
\(205\) −1.79056 4.32279i −0.125058 0.301917i
\(206\) 2.27496 0.186837i 0.158504 0.0130175i
\(207\) 0 0
\(208\) 4.44166 + 5.05937i 0.307973 + 0.350804i
\(209\) −19.8827 −1.37532
\(210\) 0 0
\(211\) 9.78520 4.05316i 0.673641 0.279031i −0.0195249 0.999809i \(-0.506215\pi\)
0.693166 + 0.720778i \(0.256215\pi\)
\(212\) 19.4114 + 4.52074i 1.33318 + 0.310485i
\(213\) 0 0
\(214\) −6.02909 11.7338i −0.412140 0.802109i
\(215\) 7.24574 7.24574i 0.494155 0.494155i
\(216\) 0 0
\(217\) 25.0933 + 25.0933i 1.70344 + 1.70344i
\(218\) −4.46763 + 13.9109i −0.302586 + 0.942164i
\(219\) 0 0
\(220\) 6.40831 8.94775i 0.432048 0.603257i
\(221\) 3.70884 + 8.95392i 0.249483 + 0.602306i
\(222\) 0 0
\(223\) 11.6867i 0.782596i 0.920264 + 0.391298i \(0.127974\pi\)
−0.920264 + 0.391298i \(0.872026\pi\)
\(224\) 16.8063 7.29891i 1.12292 0.487679i
\(225\) 0 0
\(226\) 10.2414 + 8.68688i 0.681249 + 0.577843i
\(227\) 27.4221 11.3586i 1.82007 0.753897i 0.844029 0.536297i \(-0.180177\pi\)
0.976038 0.217600i \(-0.0698227\pi\)
\(228\) 0 0
\(229\) −4.97093 + 12.0009i −0.328488 + 0.793040i 0.670217 + 0.742165i \(0.266201\pi\)
−0.998705 + 0.0508750i \(0.983799\pi\)
\(230\) −11.0170 3.53821i −0.726437 0.233303i
\(231\) 0 0
\(232\) −11.1659 1.65181i −0.733079 0.108447i
\(233\) 15.1524 + 15.1524i 0.992666 + 0.992666i 0.999973 0.00730690i \(-0.00232588\pi\)
−0.00730690 + 0.999973i \(0.502326\pi\)
\(234\) 0 0
\(235\) −1.40351 + 3.38838i −0.0915552 + 0.221034i
\(236\) −12.6757 2.95204i −0.825117 0.192162i
\(237\) 0 0
\(238\) 26.2881 2.15898i 1.70400 0.139946i
\(239\) 23.6477i 1.52964i −0.644241 0.764822i \(-0.722827\pi\)
0.644241 0.764822i \(-0.277173\pi\)
\(240\) 0 0
\(241\) 15.2836i 0.984506i 0.870452 + 0.492253i \(0.163826\pi\)
−0.870452 + 0.492253i \(0.836174\pi\)
\(242\) −1.16029 14.1279i −0.0745863 0.908177i
\(243\) 0 0
\(244\) 4.99324 + 8.02508i 0.319659 + 0.513753i
\(245\) 1.60354 3.87130i 0.102447 0.247328i
\(246\) 0 0
\(247\) −5.16082 5.16082i −0.328375 0.328375i
\(248\) 26.5860 + 15.9208i 1.68821 + 1.01097i
\(249\) 0 0
\(250\) −4.44238 + 13.8323i −0.280961 + 0.874829i
\(251\) −4.23813 + 10.2317i −0.267508 + 0.645822i −0.999365 0.0356366i \(-0.988654\pi\)
0.731857 + 0.681459i \(0.238654\pi\)
\(252\) 0 0
\(253\) −28.8796 + 11.9623i −1.81564 + 0.752065i
\(254\) −15.8843 + 18.7268i −0.996668 + 1.17502i
\(255\) 0 0
\(256\) 12.6834 9.75352i 0.792713 0.609595i
\(257\) 24.2953i 1.51550i 0.652544 + 0.757751i \(0.273702\pi\)
−0.652544 + 0.757751i \(0.726298\pi\)
\(258\) 0 0
\(259\) −5.42063 13.0866i −0.336822 0.813159i
\(260\) 3.98587 0.659146i 0.247193 0.0408785i
\(261\) 0 0
\(262\) −18.8206 6.04444i −1.16274 0.373427i
\(263\) 17.0847 + 17.0847i 1.05349 + 1.05349i 0.998486 + 0.0550047i \(0.0175174\pi\)
0.0550047 + 0.998486i \(0.482483\pi\)
\(264\) 0 0
\(265\) 8.45712 8.45712i 0.519517 0.519517i
\(266\) −17.6676 + 9.07800i −1.08327 + 0.556608i
\(267\) 0 0
\(268\) 21.7279 13.5192i 1.32724 0.825814i
\(269\) −27.5091 + 11.3947i −1.67726 + 0.694745i −0.999190 0.0402507i \(-0.987184\pi\)
−0.678072 + 0.734995i \(0.737184\pi\)
\(270\) 0 0
\(271\) −1.03250 −0.0627197 −0.0313598 0.999508i \(-0.509984\pi\)
−0.0313598 + 0.999508i \(0.509984\pi\)
\(272\) 21.8065 7.41510i 1.32222 0.449607i
\(273\) 0 0
\(274\) 0.234960 + 2.86092i 0.0141945 + 0.172835i
\(275\) 6.24590 + 15.0789i 0.376642 + 0.909294i
\(276\) 0 0
\(277\) 6.98129 + 2.89174i 0.419465 + 0.173748i 0.582425 0.812885i \(-0.302104\pi\)
−0.162960 + 0.986633i \(0.552104\pi\)
\(278\) −3.30680 + 1.69910i −0.198329 + 0.101905i
\(279\) 0 0
\(280\) 1.60904 10.8768i 0.0961586 0.650014i
\(281\) −5.66031 + 5.66031i −0.337666 + 0.337666i −0.855488 0.517822i \(-0.826743\pi\)
0.517822 + 0.855488i \(0.326743\pi\)
\(282\) 0 0
\(283\) −8.97137 3.71606i −0.533292 0.220897i 0.0997521 0.995012i \(-0.468195\pi\)
−0.633045 + 0.774115i \(0.718195\pi\)
\(284\) −1.34091 + 1.87228i −0.0795683 + 0.111099i
\(285\) 0 0
\(286\) 7.05972 8.32307i 0.417450 0.492154i
\(287\) −12.6277 −0.745391
\(288\) 0 0
\(289\) 16.1568 0.950401
\(290\) −4.38141 + 5.16547i −0.257285 + 0.303327i
\(291\) 0 0
\(292\) −14.0976 10.0966i −0.824997 0.590856i
\(293\) −12.4522 5.15788i −0.727467 0.301327i −0.0119561 0.999929i \(-0.503806\pi\)
−0.715510 + 0.698602i \(0.753806\pi\)
\(294\) 0 0
\(295\) −5.52250 + 5.52250i −0.321533 + 0.321533i
\(296\) −7.37218 9.93205i −0.428499 0.577289i
\(297\) 0 0
\(298\) 7.26837 3.73464i 0.421045 0.216342i
\(299\) −10.6011 4.39110i −0.613075 0.253944i
\(300\) 0 0
\(301\) −10.5831 25.5499i −0.610001 1.47267i
\(302\) −1.29010 15.7085i −0.0742370 0.903923i
\(303\) 0 0
\(304\) −13.0349 + 11.4434i −0.747602 + 0.656325i
\(305\) 5.67178 0.324765
\(306\) 0 0
\(307\) −15.2016 + 6.29670i −0.867600 + 0.359372i −0.771675 0.636017i \(-0.780581\pi\)
−0.0959250 + 0.995389i \(0.530581\pi\)
\(308\) −15.6918 25.2197i −0.894125 1.43703i
\(309\) 0 0
\(310\) 16.5400 8.49858i 0.939408 0.482687i
\(311\) −14.4880 + 14.4880i −0.821542 + 0.821542i −0.986329 0.164787i \(-0.947306\pi\)
0.164787 + 0.986329i \(0.447306\pi\)
\(312\) 0 0
\(313\) 7.88864 + 7.88864i 0.445893 + 0.445893i 0.893986 0.448094i \(-0.147897\pi\)
−0.448094 + 0.893986i \(0.647897\pi\)
\(314\) 18.7426 + 6.01938i 1.05771 + 0.339693i
\(315\) 0 0
\(316\) −2.60965 15.7806i −0.146804 0.887728i
\(317\) 2.14940 + 5.18912i 0.120722 + 0.291450i 0.972676 0.232168i \(-0.0745819\pi\)
−0.851953 + 0.523618i \(0.824582\pi\)
\(318\) 0 0
\(319\) 18.2980i 1.02449i
\(320\) −0.948623 9.55433i −0.0530297 0.534103i
\(321\) 0 0
\(322\) −20.2005 + 23.8154i −1.12573 + 1.32718i
\(323\) −23.0687 + 9.55539i −1.28358 + 0.531676i
\(324\) 0 0
\(325\) −2.29273 + 5.53515i −0.127178 + 0.307035i
\(326\) 3.37993 10.5241i 0.187197 0.582877i
\(327\) 0 0
\(328\) −10.6954 + 2.68353i −0.590554 + 0.148173i
\(329\) 6.99905 + 6.99905i 0.385870 + 0.385870i
\(330\) 0 0
\(331\) 4.79808 11.5836i 0.263726 0.636692i −0.735437 0.677593i \(-0.763023\pi\)
0.999163 + 0.0409015i \(0.0130230\pi\)
\(332\) −20.0570 + 12.4796i −1.10077 + 0.684905i
\(333\) 0 0
\(334\) −1.64945 20.0840i −0.0902540 1.09895i
\(335\) 15.3563i 0.839005i
\(336\) 0 0
\(337\) 34.5409i 1.88156i 0.339011 + 0.940782i \(0.389907\pi\)
−0.339011 + 0.940782i \(0.610093\pi\)
\(338\) −14.3303 + 1.17691i −0.779464 + 0.0640155i
\(339\) 0 0
\(340\) 3.13501 13.4613i 0.170020 0.730042i
\(341\) 19.2242 46.4113i 1.04105 2.51331i
\(342\) 0 0
\(343\) 8.03590 + 8.03590i 0.433898 + 0.433898i
\(344\) −14.3933 19.3911i −0.776034 1.04550i
\(345\) 0 0
\(346\) −11.6074 3.72783i −0.624016 0.200409i
\(347\) 13.4976 32.5861i 0.724590 1.74932i 0.0647598 0.997901i \(-0.479372\pi\)
0.659830 0.751415i \(-0.270628\pi\)
\(348\) 0 0
\(349\) 19.4574 8.05954i 1.04153 0.431417i 0.204671 0.978831i \(-0.434388\pi\)
0.836862 + 0.547414i \(0.184388\pi\)
\(350\) 12.4348 + 10.5473i 0.664667 + 0.563778i
\(351\) 0 0
\(352\) −18.6501 18.0258i −0.994052 0.960779i
\(353\) 28.8838i 1.53733i −0.639653 0.768664i \(-0.720922\pi\)
0.639653 0.768664i \(-0.279078\pi\)
\(354\) 0 0
\(355\) 0.528846 + 1.27675i 0.0280682 + 0.0677627i
\(356\) 13.9243 + 9.97248i 0.737986 + 0.528540i
\(357\) 0 0
\(358\) 3.32171 10.3428i 0.175558 0.546636i
\(359\) 21.9015 + 21.9015i 1.15592 + 1.15592i 0.985345 + 0.170574i \(0.0545623\pi\)
0.170574 + 0.985345i \(0.445438\pi\)
\(360\) 0 0
\(361\) −0.138774 + 0.138774i −0.00730389 + 0.00730389i
\(362\) 6.13780 + 11.9454i 0.322595 + 0.627837i
\(363\) 0 0
\(364\) 2.47309 10.6191i 0.129625 0.556594i
\(365\) −9.61344 + 3.98202i −0.503191 + 0.208428i
\(366\) 0 0
\(367\) 4.27993 0.223411 0.111705 0.993741i \(-0.464369\pi\)
0.111705 + 0.993741i \(0.464369\pi\)
\(368\) −12.0483 + 24.4639i −0.628060 + 1.27527i
\(369\) 0 0
\(370\) −7.39756 + 0.607544i −0.384581 + 0.0315847i
\(371\) −12.3525 29.8215i −0.641308 1.54825i
\(372\) 0 0
\(373\) −1.63995 0.679288i −0.0849132 0.0351722i 0.339823 0.940490i \(-0.389633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(374\) −17.0644 33.2108i −0.882378 1.71729i
\(375\) 0 0
\(376\) 7.41539 + 4.44065i 0.382420 + 0.229009i
\(377\) −4.74949 + 4.74949i −0.244611 + 0.244611i
\(378\) 0 0
\(379\) 24.5928 + 10.1867i 1.26325 + 0.523254i 0.910904 0.412618i \(-0.135385\pi\)
0.352342 + 0.935871i \(0.385385\pi\)
\(380\) 1.69821 + 10.2691i 0.0871165 + 0.526795i
\(381\) 0 0
\(382\) −12.2073 10.3544i −0.624581 0.529777i
\(383\) −8.94049 −0.456838 −0.228419 0.973563i \(-0.573356\pi\)
−0.228419 + 0.973563i \(0.573356\pi\)
\(384\) 0 0
\(385\) −17.8242 −0.908406
\(386\) 1.08646 + 0.921547i 0.0552994 + 0.0469055i
\(387\) 0 0
\(388\) 3.75537 + 22.7088i 0.190650 + 1.15287i
\(389\) −26.3896 10.9309i −1.33801 0.554221i −0.405079 0.914282i \(-0.632756\pi\)
−0.932929 + 0.360061i \(0.882756\pi\)
\(390\) 0 0
\(391\) −27.7584 + 27.7584i −1.40380 + 1.40380i
\(392\) −8.47225 5.07353i −0.427913 0.256252i
\(393\) 0 0
\(394\) −3.39406 6.60553i −0.170990 0.332782i
\(395\) −8.86763 3.67309i −0.446179 0.184813i
\(396\) 0 0
\(397\) −5.22517 12.6147i −0.262244 0.633113i 0.736833 0.676075i \(-0.236320\pi\)
−0.999077 + 0.0429622i \(0.986320\pi\)
\(398\) 23.8417 1.95806i 1.19507 0.0981486i
\(399\) 0 0
\(400\) 12.7734 + 6.29079i 0.638669 + 0.314539i
\(401\) 5.30249 0.264794 0.132397 0.991197i \(-0.457733\pi\)
0.132397 + 0.991197i \(0.457733\pi\)
\(402\) 0 0
\(403\) 17.0366 7.05678i 0.848652 0.351523i
\(404\) −0.200180 + 0.859544i −0.00995931 + 0.0427639i
\(405\) 0 0
\(406\) 8.35446 + 16.2595i 0.414625 + 0.806945i
\(407\) −14.1785 + 14.1785i −0.702804 + 0.702804i
\(408\) 0 0
\(409\) −22.2095 22.2095i −1.09819 1.09819i −0.994622 0.103568i \(-0.966974\pi\)
−0.103568 0.994622i \(-0.533026\pi\)
\(410\) −2.02334 + 6.30010i −0.0999259 + 0.311140i
\(411\) 0 0
\(412\) −2.62445 1.87961i −0.129297 0.0926018i
\(413\) 8.06617 + 19.4735i 0.396910 + 0.958226i
\(414\) 0 0
\(415\) 14.1754i 0.695844i
\(416\) −0.162034 9.51971i −0.00794438 0.466742i
\(417\) 0 0
\(418\) 21.4434 + 18.1885i 1.04883 + 0.889631i
\(419\) 19.3284 8.00610i 0.944256 0.391124i 0.143187 0.989696i \(-0.454265\pi\)
0.801069 + 0.598572i \(0.204265\pi\)
\(420\) 0 0
\(421\) −8.19769 + 19.7910i −0.399531 + 0.964554i 0.588246 + 0.808682i \(0.299819\pi\)
−0.987777 + 0.155872i \(0.950181\pi\)
\(422\) −14.2611 4.58011i −0.694220 0.222956i
\(423\) 0 0
\(424\) −16.7996 22.6330i −0.815862 1.09916i
\(425\) 14.4935 + 14.4935i 0.703039 + 0.703039i
\(426\) 0 0
\(427\) 5.85782 14.1420i 0.283480 0.684380i
\(428\) −4.23168 + 18.1703i −0.204546 + 0.878293i
\(429\) 0 0
\(430\) −14.4428 + 1.18616i −0.696496 + 0.0572015i
\(431\) 4.03116i 0.194174i −0.995276 0.0970871i \(-0.969047\pi\)
0.995276 0.0970871i \(-0.0309526\pi\)
\(432\) 0 0
\(433\) 19.5320i 0.938650i 0.883025 + 0.469325i \(0.155503\pi\)
−0.883025 + 0.469325i \(0.844497\pi\)
\(434\) −4.10787 50.0181i −0.197184 2.40095i
\(435\) 0 0
\(436\) 17.5439 10.9159i 0.840201 0.522776i
\(437\) 11.3132 27.3124i 0.541182 1.30653i
\(438\) 0 0
\(439\) −2.79500 2.79500i −0.133398 0.133398i 0.637255 0.770653i \(-0.280070\pi\)
−0.770653 + 0.637255i \(0.780070\pi\)
\(440\) −15.0967 + 3.78784i −0.719706 + 0.180578i
\(441\) 0 0
\(442\) 4.19101 13.0496i 0.199346 0.620706i
\(443\) −7.32465 + 17.6833i −0.348005 + 0.840157i 0.648851 + 0.760916i \(0.275250\pi\)
−0.996855 + 0.0792418i \(0.974750\pi\)
\(444\) 0 0
\(445\) 9.49530 3.93308i 0.450120 0.186446i
\(446\) 10.6909 12.6040i 0.506227 0.596817i
\(447\) 0 0
\(448\) −24.8025 7.50241i −1.17181 0.354456i
\(449\) 32.9730i 1.55609i −0.628208 0.778045i \(-0.716211\pi\)
0.628208 0.778045i \(-0.283789\pi\)
\(450\) 0 0
\(451\) 6.84071 + 16.5149i 0.322117 + 0.777658i
\(452\) −3.09864 18.7375i −0.145748 0.881340i
\(453\) 0 0
\(454\) −39.9654 12.8353i −1.87567 0.602391i
\(455\) −4.62651 4.62651i −0.216894 0.216894i
\(456\) 0 0
\(457\) −16.3157 + 16.3157i −0.763214 + 0.763214i −0.976902 0.213688i \(-0.931452\pi\)
0.213688 + 0.976902i \(0.431452\pi\)
\(458\) 16.3394 8.39554i 0.763492 0.392298i
\(459\) 0 0
\(460\) 8.64502 + 13.8942i 0.403076 + 0.647819i
\(461\) 12.1576 5.03583i 0.566234 0.234542i −0.0811549 0.996702i \(-0.525861\pi\)
0.647389 + 0.762160i \(0.275861\pi\)
\(462\) 0 0
\(463\) −7.60945 −0.353641 −0.176821 0.984243i \(-0.556581\pi\)
−0.176821 + 0.984243i \(0.556581\pi\)
\(464\) 10.5313 + 11.9960i 0.488905 + 0.556899i
\(465\) 0 0
\(466\) −2.48051 30.2031i −0.114907 1.39913i
\(467\) 1.94882 + 4.70488i 0.0901809 + 0.217716i 0.962534 0.271160i \(-0.0874072\pi\)
−0.872353 + 0.488876i \(0.837407\pi\)
\(468\) 0 0
\(469\) −38.2894 15.8600i −1.76804 0.732347i
\(470\) 4.61335 2.37043i 0.212798 0.109340i
\(471\) 0 0
\(472\) 10.9702 + 14.7794i 0.504943 + 0.680276i
\(473\) −27.6819 + 27.6819i −1.27281 + 1.27281i
\(474\) 0 0
\(475\) −14.2607 5.90696i −0.654324 0.271030i
\(476\) −30.3266 21.7197i −1.39002 0.995520i
\(477\) 0 0
\(478\) −21.6328 + 25.5040i −0.989460 + 1.16653i
\(479\) 8.04063 0.367386 0.183693 0.982984i \(-0.441195\pi\)
0.183693 + 0.982984i \(0.441195\pi\)
\(480\) 0 0
\(481\) −7.36045 −0.335608
\(482\) 13.9814 16.4834i 0.636833 0.750796i
\(483\) 0 0
\(484\) −11.6727 + 16.2983i −0.530579 + 0.740833i
\(485\) 12.7608 + 5.28571i 0.579440 + 0.240012i
\(486\) 0 0
\(487\) 13.0819 13.0819i 0.592796 0.592796i −0.345590 0.938386i \(-0.612321\pi\)
0.938386 + 0.345590i \(0.112321\pi\)
\(488\) 1.95609 13.2228i 0.0885481 0.598568i
\(489\) 0 0
\(490\) −5.27085 + 2.70827i −0.238113 + 0.122347i
\(491\) −1.59917 0.662398i −0.0721696 0.0298936i 0.346307 0.938121i \(-0.387436\pi\)
−0.418476 + 0.908228i \(0.637436\pi\)
\(492\) 0 0
\(493\) 8.79380 + 21.2301i 0.396053 + 0.956156i
\(494\) 0.844847 + 10.2870i 0.0380115 + 0.462834i
\(495\) 0 0
\(496\) −14.1087 41.4912i −0.633498 1.86301i
\(497\) 3.72963 0.167297
\(498\) 0 0
\(499\) 13.5962 5.63174i 0.608651 0.252111i −0.0570007 0.998374i \(-0.518154\pi\)
0.665652 + 0.746263i \(0.268154\pi\)
\(500\) 17.4447 10.8542i 0.780152 0.485414i
\(501\) 0 0
\(502\) 13.9307 7.15790i 0.621759 0.319472i
\(503\) −25.4762 + 25.4762i −1.13593 + 1.13593i −0.146752 + 0.989173i \(0.546882\pi\)
−0.989173 + 0.146752i \(0.953118\pi\)
\(504\) 0 0
\(505\) 0.374484 + 0.374484i 0.0166643 + 0.0166643i
\(506\) 42.0896 + 13.5175i 1.87111 + 0.600927i
\(507\) 0 0
\(508\) 34.2623 5.66597i 1.52014 0.251387i
\(509\) 5.65965 + 13.6636i 0.250860 + 0.605629i 0.998274 0.0587294i \(-0.0187049\pi\)
−0.747414 + 0.664358i \(0.768705\pi\)
\(510\) 0 0
\(511\) 28.0828i 1.24231i
\(512\) −22.6015 1.08355i −0.998853 0.0478868i
\(513\) 0 0
\(514\) 22.2252 26.2024i 0.980311 1.15574i
\(515\) −1.78967 + 0.741307i −0.0788624 + 0.0326659i
\(516\) 0 0
\(517\) 5.36204 12.9451i 0.235822 0.569325i
\(518\) −6.12535 + 19.0726i −0.269133 + 0.838000i
\(519\) 0 0
\(520\) −4.90173 2.93536i −0.214955 0.128724i
\(521\) −6.11420 6.11420i −0.267868 0.267868i 0.560373 0.828241i \(-0.310658\pi\)
−0.828241 + 0.560373i \(0.810658\pi\)
\(522\) 0 0
\(523\) −3.45240 + 8.33482i −0.150963 + 0.364456i −0.981211 0.192937i \(-0.938199\pi\)
0.830248 + 0.557394i \(0.188199\pi\)
\(524\) 14.7686 + 23.7359i 0.645168 + 1.03691i
\(525\) 0 0
\(526\) −2.79684 34.0548i −0.121948 1.48486i
\(527\) 63.0872i 2.74812i
\(528\) 0 0
\(529\) 23.4777i 1.02077i
\(530\) −16.8575 + 1.38446i −0.732242 + 0.0601373i
\(531\) 0 0
\(532\) 27.3590 + 6.37164i 1.18616 + 0.276246i
\(533\) −2.51107 + 6.06227i −0.108767 + 0.262586i
\(534\) 0 0
\(535\) 7.91637 + 7.91637i 0.342254 + 0.342254i
\(536\) −35.8006 5.29611i −1.54635 0.228757i
\(537\) 0 0
\(538\) 40.0923 + 12.8761i 1.72850 + 0.555126i
\(539\) −6.12624 + 14.7901i −0.263876 + 0.637053i
\(540\) 0 0
\(541\) 8.67432 3.59302i 0.372938 0.154476i −0.188339 0.982104i \(-0.560310\pi\)
0.561277 + 0.827628i \(0.310310\pi\)
\(542\) 1.11354 + 0.944520i 0.0478308 + 0.0405706i
\(543\) 0 0
\(544\) −30.3016 11.9513i −1.29917 0.512408i
\(545\) 12.3993i 0.531127i
\(546\) 0 0
\(547\) −8.99937 21.7264i −0.384785 0.928954i −0.991026 0.133673i \(-0.957323\pi\)
0.606240 0.795282i \(-0.292677\pi\)
\(548\) 2.36374 3.30043i 0.100974 0.140988i
\(549\) 0 0
\(550\) 7.05792 21.9763i 0.300951 0.937072i
\(551\) −12.2365 12.2365i −0.521293 0.521293i
\(552\) 0 0
\(553\) −18.3170 + 18.3170i −0.778918 + 0.778918i
\(554\) −4.88395 9.50517i −0.207499 0.403836i
\(555\) 0 0
\(556\) 5.12070 + 1.19256i 0.217166 + 0.0505759i
\(557\) −12.0218 + 4.97960i −0.509380 + 0.210992i −0.622545 0.782584i \(-0.713901\pi\)
0.113165 + 0.993576i \(0.463901\pi\)
\(558\) 0 0
\(559\) −14.3704 −0.607803
\(560\) −11.6854 + 10.2587i −0.493797 + 0.433507i
\(561\) 0 0
\(562\) 11.2826 0.926616i 0.475929 0.0390869i
\(563\) −3.87198 9.34780i −0.163185 0.393963i 0.821044 0.570865i \(-0.193392\pi\)
−0.984228 + 0.176903i \(0.943392\pi\)
\(564\) 0 0
\(565\) −10.5292 4.36135i −0.442969 0.183484i
\(566\) 6.27616 + 12.2147i 0.263807 + 0.513422i
\(567\) 0 0
\(568\) 3.15891 0.792589i 0.132545 0.0332563i
\(569\) 27.9604 27.9604i 1.17216 1.17216i 0.190469 0.981693i \(-0.438999\pi\)
0.981693 0.190469i \(-0.0610008\pi\)
\(570\) 0 0
\(571\) −1.06863 0.442642i −0.0447209 0.0185240i 0.360211 0.932871i \(-0.382705\pi\)
−0.404932 + 0.914347i \(0.632705\pi\)
\(572\) −15.2278 + 2.51822i −0.636705 + 0.105292i
\(573\) 0 0
\(574\) 13.6190 + 11.5518i 0.568445 + 0.482161i
\(575\) −24.2675 −1.01202
\(576\) 0 0
\(577\) 39.9542 1.66332 0.831658 0.555288i \(-0.187392\pi\)
0.831658 + 0.555288i \(0.187392\pi\)
\(578\) −17.4251 14.7801i −0.724787 0.614772i
\(579\) 0 0
\(580\) 9.45066 1.56286i 0.392417 0.0648943i
\(581\) 35.3450 + 14.6404i 1.46636 + 0.607386i
\(582\) 0 0
\(583\) −32.3099 + 32.3099i −1.33814 + 1.33814i
\(584\) 5.96790 + 23.7854i 0.246954 + 0.984248i
\(585\) 0 0
\(586\) 8.71129 + 16.9540i 0.359860 + 0.700361i
\(587\) −6.65416 2.75624i −0.274646 0.113762i 0.241109 0.970498i \(-0.422489\pi\)
−0.515756 + 0.856736i \(0.672489\pi\)
\(588\) 0 0
\(589\) 18.1810 + 43.8927i 0.749134 + 1.80857i
\(590\) 11.0079 0.904056i 0.453190 0.0372194i
\(591\) 0 0
\(592\) −1.13490 + 17.4557i −0.0466439 + 0.717425i
\(593\) −30.4542 −1.25060 −0.625302 0.780383i \(-0.715024\pi\)
−0.625302 + 0.780383i \(0.715024\pi\)
\(594\) 0 0
\(595\) −20.6804 + 8.56610i −0.847814 + 0.351176i
\(596\) −11.2553 2.62126i −0.461036 0.107371i
\(597\) 0 0
\(598\) 7.41626 + 14.4336i 0.303273 + 0.590232i
\(599\) 27.7991 27.7991i 1.13584 1.13584i 0.146654 0.989188i \(-0.453150\pi\)
0.989188 0.146654i \(-0.0468502\pi\)
\(600\) 0 0
\(601\) 10.9042 + 10.9042i 0.444792 + 0.444792i 0.893619 0.448827i \(-0.148158\pi\)
−0.448827 + 0.893619i \(0.648158\pi\)
\(602\) −11.9590 + 37.2369i −0.487413 + 1.51766i
\(603\) 0 0
\(604\) −12.9787 + 18.1217i −0.528094 + 0.737363i
\(605\) 4.60365 + 11.1142i 0.187165 + 0.451857i
\(606\) 0 0
\(607\) 12.2609i 0.497654i −0.968548 0.248827i \(-0.919955\pi\)
0.968548 0.248827i \(-0.0800451\pi\)
\(608\) 24.5264 0.417462i 0.994678 0.0169303i
\(609\) 0 0
\(610\) −6.11700 5.18850i −0.247670 0.210076i
\(611\) 4.75186 1.96829i 0.192240 0.0796283i
\(612\) 0 0
\(613\) 12.0970 29.2047i 0.488593 1.17957i −0.466835 0.884344i \(-0.654606\pi\)
0.955428 0.295224i \(-0.0953942\pi\)
\(614\) 22.1550 + 7.11532i 0.894104 + 0.287151i
\(615\) 0 0
\(616\) −6.14724 + 41.5542i −0.247679 + 1.67426i
\(617\) 20.3519 + 20.3519i 0.819336 + 0.819336i 0.986012 0.166676i \(-0.0533033\pi\)
−0.166676 + 0.986012i \(0.553303\pi\)
\(618\) 0 0
\(619\) 17.1759 41.4663i 0.690358 1.66667i −0.0537006 0.998557i \(-0.517102\pi\)
0.744059 0.668114i \(-0.232898\pi\)
\(620\) −25.6127 5.96496i −1.02863 0.239559i
\(621\) 0 0
\(622\) 28.8789 2.37175i 1.15794 0.0950986i
\(623\) 27.7377i 1.11129i
\(624\) 0 0
\(625\) 5.46885i 0.218754i
\(626\) −1.29140 15.7243i −0.0516148 0.628471i
\(627\) 0 0
\(628\) −14.7073 23.6375i −0.586886 0.943237i
\(629\) −9.63649 + 23.2646i −0.384232 + 0.927619i
\(630\) 0 0
\(631\) −12.5561 12.5561i −0.499851 0.499851i 0.411540 0.911392i \(-0.364991\pi\)
−0.911392 + 0.411540i \(0.864991\pi\)
\(632\) −11.6215 + 19.4066i −0.462278 + 0.771953i
\(633\) 0 0
\(634\) 2.42884 7.56270i 0.0964617 0.300353i
\(635\) 7.97489 19.2531i 0.316474 0.764036i
\(636\) 0 0
\(637\) −5.42910 + 2.24881i −0.215109 + 0.0891010i
\(638\) 16.7389 19.7343i 0.662699 0.781290i
\(639\) 0 0
\(640\) −7.71714 + 11.1721i −0.305047 + 0.441616i
\(641\) 23.6971i 0.935980i −0.883734 0.467990i \(-0.844978\pi\)
0.883734 0.467990i \(-0.155022\pi\)
\(642\) 0 0
\(643\) 14.2539 + 34.4119i 0.562118 + 1.35707i 0.908069 + 0.418820i \(0.137556\pi\)
−0.345952 + 0.938252i \(0.612444\pi\)
\(644\) 43.5723 7.20558i 1.71699 0.283940i
\(645\) 0 0
\(646\) 33.6207 + 10.7977i 1.32279 + 0.424828i
\(647\) −9.10926 9.10926i −0.358122 0.358122i 0.504998 0.863120i \(-0.331493\pi\)
−0.863120 + 0.504998i \(0.831493\pi\)
\(648\) 0 0
\(649\) 21.0984 21.0984i 0.828183 0.828183i
\(650\) 7.53621 3.87226i 0.295595 0.151883i
\(651\) 0 0
\(652\) −13.2726 + 8.25828i −0.519796 + 0.323419i
\(653\) −45.0078 + 18.6428i −1.76129 + 0.729551i −0.764951 + 0.644089i \(0.777237\pi\)
−0.996341 + 0.0854621i \(0.972763\pi\)
\(654\) 0 0
\(655\) 16.7755 0.655473
\(656\) 13.9898 + 6.88987i 0.546210 + 0.269004i
\(657\) 0 0
\(658\) −1.14577 13.9511i −0.0446668 0.543871i
\(659\) 7.19109 + 17.3608i 0.280125 + 0.676281i 0.999838 0.0179900i \(-0.00572670\pi\)
−0.719713 + 0.694271i \(0.755727\pi\)
\(660\) 0 0
\(661\) 33.0166 + 13.6759i 1.28420 + 0.531931i 0.917250 0.398312i \(-0.130404\pi\)
0.366945 + 0.930243i \(0.380404\pi\)
\(662\) −15.7713 + 8.10362i −0.612969 + 0.314956i
\(663\) 0 0
\(664\) 33.0476 + 4.88884i 1.28250 + 0.189724i
\(665\) 11.9197 11.9197i 0.462225 0.462225i
\(666\) 0 0
\(667\) −25.1355 10.4115i −0.973252 0.403134i
\(668\) −16.5938 + 23.1695i −0.642033 + 0.896453i
\(669\) 0 0
\(670\) −14.0478 + 16.5617i −0.542715 + 0.639836i
\(671\) −21.6687 −0.836510
\(672\) 0 0
\(673\) 24.2342 0.934159 0.467080 0.884215i \(-0.345306\pi\)
0.467080 + 0.884215i \(0.345306\pi\)
\(674\) 31.5978 37.2523i 1.21710 1.43490i
\(675\) 0 0
\(676\) 16.5318 + 11.8399i 0.635838 + 0.455382i
\(677\) 13.5836 + 5.62649i 0.522058 + 0.216244i 0.628121 0.778116i \(-0.283824\pi\)
−0.106062 + 0.994359i \(0.533824\pi\)
\(678\) 0 0
\(679\) 26.3588 26.3588i 1.01156 1.01156i
\(680\) −15.6954 + 11.6501i −0.601891 + 0.446761i
\(681\) 0 0
\(682\) −63.1900 + 32.4683i −2.41967 + 1.24328i
\(683\) −36.2049 14.9966i −1.38534 0.573828i −0.439438 0.898273i \(-0.644822\pi\)
−0.945905 + 0.324445i \(0.894822\pi\)
\(684\) 0 0
\(685\) −0.932246 2.25064i −0.0356193 0.0859926i
\(686\) −1.31551 16.0179i −0.0502263 0.611565i
\(687\) 0 0
\(688\) −2.21575 + 34.0801i −0.0844745 + 1.29929i
\(689\) −16.7729 −0.638997
\(690\) 0 0
\(691\) 27.6470 11.4518i 1.05174 0.435645i 0.211228 0.977437i \(-0.432254\pi\)
0.840513 + 0.541792i \(0.182254\pi\)
\(692\) 9.10832 + 14.6388i 0.346246 + 0.556483i
\(693\) 0 0
\(694\) −44.3667 + 22.7965i −1.68414 + 0.865344i
\(695\) 2.23097 2.23097i 0.0846256 0.0846256i
\(696\) 0 0
\(697\) 15.8738 + 15.8738i 0.601261 + 0.601261i
\(698\) −28.3576 9.10734i −1.07335 0.344718i
\(699\) 0 0
\(700\) −3.76226 22.7505i −0.142200 0.859887i
\(701\) 12.3452 + 29.8040i 0.466272 + 1.12568i 0.965778 + 0.259369i \(0.0835147\pi\)
−0.499506 + 0.866310i \(0.666485\pi\)
\(702\) 0 0
\(703\) 18.9634i 0.715217i
\(704\) 3.62416 + 36.5017i 0.136590 + 1.37571i
\(705\) 0 0
\(706\) −26.4227 + 31.1510i −0.994430 + 1.17239i
\(707\) 1.32050 0.546971i 0.0496627 0.0205710i
\(708\) 0 0
\(709\) 6.65689 16.0712i 0.250005 0.603565i −0.748199 0.663474i \(-0.769081\pi\)
0.998204 + 0.0599095i \(0.0190812\pi\)
\(710\) 0.597600 1.86075i 0.0224275 0.0698328i
\(711\) 0 0
\(712\) −5.89456 23.4931i −0.220908 0.880442i
\(713\) 52.8157 + 52.8157i 1.97796 + 1.97796i
\(714\) 0 0
\(715\) −3.54442 + 8.55698i −0.132554 + 0.320013i
\(716\) −13.0440 + 8.11604i −0.487478 + 0.303311i
\(717\) 0 0
\(718\) −3.58537 43.6561i −0.133805 1.62923i
\(719\) 9.06929i 0.338228i −0.985597 0.169114i \(-0.945909\pi\)
0.985597 0.169114i \(-0.0540905\pi\)
\(720\) 0 0
\(721\) 5.22799i 0.194701i
\(722\) 0.276616 0.0227178i 0.0102946 0.000845470i
\(723\) 0 0
\(724\) 4.30798 18.4979i 0.160105 0.687469i
\(725\) −5.43616 + 13.1241i −0.201894 + 0.487415i
\(726\) 0 0
\(727\) 4.93965 + 4.93965i 0.183201 + 0.183201i 0.792749 0.609548i \(-0.208649\pi\)
−0.609548 + 0.792749i \(0.708649\pi\)
\(728\) −12.3815 + 9.19033i −0.458890 + 0.340616i
\(729\) 0 0
\(730\) 14.0108 + 4.49971i 0.518562 + 0.166542i
\(731\) −18.8141 + 45.4212i −0.695864 + 1.67997i
\(732\) 0 0
\(733\) 18.9279 7.84021i 0.699119 0.289585i −0.00467439 0.999989i \(-0.501488\pi\)
0.703794 + 0.710404i \(0.251488\pi\)
\(734\) −4.61589 3.91525i −0.170376 0.144515i
\(735\) 0 0
\(736\) 35.3734 15.3626i 1.30388 0.566271i
\(737\) 58.6678i 2.16106i
\(738\) 0 0
\(739\) −8.94853 21.6037i −0.329177 0.794704i −0.998654 0.0518708i \(-0.983482\pi\)
0.669477 0.742833i \(-0.266518\pi\)
\(740\) 8.53402 + 6.11200i 0.313717 + 0.224682i
\(741\) 0 0
\(742\) −13.9584 + 43.4623i −0.512429 + 1.59555i
\(743\) 34.2959 + 34.2959i 1.25819 + 1.25819i 0.951955 + 0.306239i \(0.0990708\pi\)
0.306239 + 0.951955i \(0.400929\pi\)
\(744\) 0 0
\(745\) −4.90369 + 4.90369i −0.179657 + 0.179657i
\(746\) 1.14727 + 2.23282i 0.0420045 + 0.0817494i
\(747\) 0 0
\(748\) −11.9771 + 51.4281i −0.437926 + 1.88040i
\(749\) 27.9147 11.5626i 1.01998 0.422490i
\(750\) 0 0
\(751\) −8.46502 −0.308893 −0.154446 0.988001i \(-0.549359\pi\)
−0.154446 + 0.988001i \(0.549359\pi\)
\(752\) −3.93521 11.5728i −0.143502 0.422015i
\(753\) 0 0
\(754\) 9.46711 0.777511i 0.344772 0.0283153i
\(755\) 5.11870 + 12.3576i 0.186289 + 0.449740i
\(756\) 0 0
\(757\) −38.2928 15.8614i −1.39178 0.576493i −0.444173 0.895941i \(-0.646502\pi\)
−0.947604 + 0.319449i \(0.896502\pi\)
\(758\) −17.2045 33.4836i −0.624897 1.21618i
\(759\) 0 0
\(760\) 7.56261 12.6287i 0.274325 0.458092i
\(761\) 0.833887 0.833887i 0.0302284 0.0302284i −0.691831 0.722059i \(-0.743196\pi\)
0.722059 + 0.691831i \(0.243196\pi\)
\(762\) 0 0
\(763\) −30.9164 12.8060i −1.11925 0.463608i
\(764\) 3.69344 + 22.3343i 0.133624 + 0.808028i
\(765\) 0 0
\(766\) 9.64229 + 8.17870i 0.348390 + 0.295508i
\(767\) 10.9527 0.395480
\(768\) 0 0
\(769\) −32.1393 −1.15897 −0.579486 0.814982i \(-0.696747\pi\)
−0.579486 + 0.814982i \(0.696747\pi\)
\(770\) 19.2234 + 16.3055i 0.692762 + 0.587608i
\(771\) 0 0
\(772\) −0.328719 1.98777i −0.0118309 0.0715415i
\(773\) 28.3337 + 11.7362i 1.01909 + 0.422122i 0.828764 0.559598i \(-0.189045\pi\)
0.190329 + 0.981720i \(0.439045\pi\)
\(774\) 0 0
\(775\) 27.5767 27.5767i 0.990585 0.990585i
\(776\) 16.7237 27.9268i 0.600347 1.00251i
\(777\) 0 0
\(778\) 18.4616 + 35.9300i 0.661880 + 1.28815i
\(779\) −15.6187 6.46949i −0.559599 0.231794i
\(780\) 0 0
\(781\) −2.02042 4.87773i −0.0722964 0.174539i
\(782\) 55.3304 4.54415i 1.97861 0.162499i
\(783\) 0 0
\(784\) 4.49606 + 13.2221i 0.160574 + 0.472219i
\(785\) −16.7059 −0.596261
\(786\) 0 0
\(787\) 17.1011 7.08351i 0.609588 0.252500i −0.0564642 0.998405i \(-0.517983\pi\)
0.666052 + 0.745905i \(0.267983\pi\)
\(788\) −2.38221 + 10.2289i −0.0848628 + 0.364390i