Properties

Label 354.2.c.a.353.10
Level 354
Weight 2
Character 354.353
Analytic conductor 2.827
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: 10.0.41542366334681088.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.10
Root \(-1.64288 + 0.548592i\)
Character \(\chi\) = 354.353
Dual form 354.2.c.a.353.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.64288 + 0.548592i) q^{3} +1.00000 q^{4} -2.54852i q^{5} +(-1.64288 - 0.548592i) q^{6} -0.0900537 q^{7} -1.00000 q^{8} +(2.39809 + 1.80254i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.64288 + 0.548592i) q^{3} +1.00000 q^{4} -2.54852i q^{5} +(-1.64288 - 0.548592i) q^{6} -0.0900537 q^{7} -1.00000 q^{8} +(2.39809 + 1.80254i) q^{9} +2.54852i q^{10} +2.40488 q^{11} +(1.64288 + 0.548592i) q^{12} -2.81820i q^{13} +0.0900537 q^{14} +(1.39809 - 4.18690i) q^{15} +1.00000 q^{16} -3.17124i q^{17} +(-2.39809 - 1.80254i) q^{18} -2.49493 q^{19} -2.54852i q^{20} +(-0.147947 - 0.0494027i) q^{21} -2.40488 q^{22} +3.09208 q^{23} +(-1.64288 - 0.548592i) q^{24} -1.49493 q^{25} +2.81820i q^{26} +(2.95092 + 4.27692i) q^{27} -0.0900537 q^{28} +6.21894i q^{29} +(-1.39809 + 4.18690i) q^{30} +2.16964i q^{31} -1.00000 q^{32} +(3.95092 + 1.31930i) q^{33} +3.17124i q^{34} +0.229503i q^{35} +(2.39809 + 1.80254i) q^{36} -11.5857i q^{37} +2.49493 q^{38} +(1.54604 - 4.62996i) q^{39} +2.54852i q^{40} +0.762149i q^{41} +(0.147947 + 0.0494027i) q^{42} +7.62643i q^{43} +2.40488 q^{44} +(4.59380 - 6.11158i) q^{45} -3.09208 q^{46} +7.90184 q^{47} +(1.64288 + 0.548592i) q^{48} -6.99189 q^{49} +1.49493 q^{50} +(1.73971 - 5.20995i) q^{51} -2.81820i q^{52} +3.58035i q^{53} +(-2.95092 - 4.27692i) q^{54} -6.12887i q^{55} +0.0900537 q^{56} +(-4.09887 - 1.36870i) q^{57} -6.21894i q^{58} +(-7.57687 - 1.26134i) q^{59} +(1.39809 - 4.18690i) q^{60} +3.56445i q^{61} -2.16964i q^{62} +(-0.215957 - 0.162325i) q^{63} +1.00000 q^{64} -7.18223 q^{65} +(-3.95092 - 1.31930i) q^{66} +14.5015i q^{67} -3.17124i q^{68} +(5.07991 + 1.69629i) q^{69} -0.229503i q^{70} -4.84841i q^{71} +(-2.39809 - 1.80254i) q^{72} +6.03117i q^{73} +11.5857i q^{74} +(-2.45599 - 0.820106i) q^{75} -2.49493 q^{76} -0.216568 q^{77} +(-1.54604 + 4.62996i) q^{78} -11.0840 q^{79} -2.54852i q^{80} +(2.50171 + 8.64531i) q^{81} -0.762149i q^{82} -1.68527 q^{83} +(-0.147947 - 0.0494027i) q^{84} -8.08194 q^{85} -7.62643i q^{86} +(-3.41166 + 10.2170i) q^{87} -2.40488 q^{88} -8.62144 q^{89} +(-4.59380 + 6.11158i) q^{90} +0.253790i q^{91} +3.09208 q^{92} +(-1.19025 + 3.56445i) q^{93} -7.90184 q^{94} +6.35837i q^{95} +(-1.64288 - 0.548592i) q^{96} +0.394771i q^{97} +6.99189 q^{98} +(5.76712 + 4.33488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + 4q^{11} - q^{12} + 2q^{14} - 7q^{15} + 10q^{16} - 3q^{18} - 6q^{19} - 3q^{21} - 4q^{22} - 8q^{23} + q^{24} + 4q^{25} - 10q^{27} - 2q^{28} + 7q^{30} - 10q^{32} + 3q^{36} + 6q^{38} - 4q^{39} + 3q^{42} + 4q^{44} - 11q^{45} + 8q^{46} - q^{48} + 8q^{49} - 4q^{50} + 2q^{51} + 10q^{54} + 2q^{56} - 3q^{57} + 20q^{59} - 7q^{60} - 19q^{63} + 10q^{64} + 16q^{65} + 14q^{69} - 3q^{72} - 4q^{75} - 6q^{76} + 48q^{77} + 4q^{78} + 6q^{79} + 7q^{81} + 12q^{83} - 3q^{84} - 4q^{85} - 15q^{87} - 4q^{88} - 16q^{89} + 11q^{90} - 8q^{92} - 52q^{93} + q^{96} - 8q^{98} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.64288 + 0.548592i 0.948516 + 0.316730i
\(4\) 1.00000 0.500000
\(5\) 2.54852i 1.13973i −0.821738 0.569865i \(-0.806995\pi\)
0.821738 0.569865i \(-0.193005\pi\)
\(6\) −1.64288 0.548592i −0.670702 0.223962i
\(7\) −0.0900537 −0.0340371 −0.0170186 0.999855i \(-0.505417\pi\)
−0.0170186 + 0.999855i \(0.505417\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.39809 + 1.80254i 0.799365 + 0.600846i
\(10\) 2.54852i 0.805911i
\(11\) 2.40488 0.725098 0.362549 0.931965i \(-0.381907\pi\)
0.362549 + 0.931965i \(0.381907\pi\)
\(12\) 1.64288 + 0.548592i 0.474258 + 0.158365i
\(13\) 2.81820i 0.781628i −0.920470 0.390814i \(-0.872194\pi\)
0.920470 0.390814i \(-0.127806\pi\)
\(14\) 0.0900537 0.0240679
\(15\) 1.39809 4.18690i 0.360986 1.08105i
\(16\) 1.00000 0.250000
\(17\) 3.17124i 0.769138i −0.923096 0.384569i \(-0.874350\pi\)
0.923096 0.384569i \(-0.125650\pi\)
\(18\) −2.39809 1.80254i −0.565236 0.424862i
\(19\) −2.49493 −0.572376 −0.286188 0.958173i \(-0.592388\pi\)
−0.286188 + 0.958173i \(0.592388\pi\)
\(20\) 2.54852i 0.569865i
\(21\) −0.147947 0.0494027i −0.0322847 0.0107806i
\(22\) −2.40488 −0.512721
\(23\) 3.09208 0.644744 0.322372 0.946613i \(-0.395520\pi\)
0.322372 + 0.946613i \(0.395520\pi\)
\(24\) −1.64288 0.548592i −0.335351 0.111981i
\(25\) −1.49493 −0.298986
\(26\) 2.81820i 0.552695i
\(27\) 2.95092 + 4.27692i 0.567904 + 0.823094i
\(28\) −0.0900537 −0.0170186
\(29\) 6.21894i 1.15483i 0.816451 + 0.577414i \(0.195938\pi\)
−0.816451 + 0.577414i \(0.804062\pi\)
\(30\) −1.39809 + 4.18690i −0.255256 + 0.764420i
\(31\) 2.16964i 0.389679i 0.980835 + 0.194839i \(0.0624186\pi\)
−0.980835 + 0.194839i \(0.937581\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.95092 + 1.31930i 0.687767 + 0.229660i
\(34\) 3.17124i 0.543863i
\(35\) 0.229503i 0.0387931i
\(36\) 2.39809 + 1.80254i 0.399682 + 0.300423i
\(37\) 11.5857i 1.90467i −0.305054 0.952335i \(-0.598674\pi\)
0.305054 0.952335i \(-0.401326\pi\)
\(38\) 2.49493 0.404731
\(39\) 1.54604 4.62996i 0.247565 0.741387i
\(40\) 2.54852i 0.402956i
\(41\) 0.762149i 0.119028i 0.998227 + 0.0595138i \(0.0189550\pi\)
−0.998227 + 0.0595138i \(0.981045\pi\)
\(42\) 0.147947 + 0.0494027i 0.0228288 + 0.00762301i
\(43\) 7.62643i 1.16302i 0.813539 + 0.581510i \(0.197538\pi\)
−0.813539 + 0.581510i \(0.802462\pi\)
\(44\) 2.40488 0.362549
\(45\) 4.59380 6.11158i 0.684803 0.911061i
\(46\) −3.09208 −0.455903
\(47\) 7.90184 1.15260 0.576301 0.817238i \(-0.304496\pi\)
0.576301 + 0.817238i \(0.304496\pi\)
\(48\) 1.64288 + 0.548592i 0.237129 + 0.0791824i
\(49\) −6.99189 −0.998841
\(50\) 1.49493 0.211415
\(51\) 1.73971 5.20995i 0.243609 0.729539i
\(52\) 2.81820i 0.390814i
\(53\) 3.58035i 0.491799i 0.969295 + 0.245899i \(0.0790833\pi\)
−0.969295 + 0.245899i \(0.920917\pi\)
\(54\) −2.95092 4.27692i −0.401569 0.582016i
\(55\) 6.12887i 0.826416i
\(56\) 0.0900537 0.0120339
\(57\) −4.09887 1.36870i −0.542908 0.181288i
\(58\) 6.21894i 0.816587i
\(59\) −7.57687 1.26134i −0.986425 0.164212i
\(60\) 1.39809 4.18690i 0.180493 0.540526i
\(61\) 3.56445i 0.456382i 0.973616 + 0.228191i \(0.0732810\pi\)
−0.973616 + 0.228191i \(0.926719\pi\)
\(62\) 2.16964i 0.275545i
\(63\) −0.215957 0.162325i −0.0272081 0.0204511i
\(64\) 1.00000 0.125000
\(65\) −7.18223 −0.890846
\(66\) −3.95092 1.31930i −0.486324 0.162394i
\(67\) 14.5015i 1.77165i 0.464023 + 0.885823i \(0.346405\pi\)
−0.464023 + 0.885823i \(0.653595\pi\)
\(68\) 3.17124i 0.384569i
\(69\) 5.07991 + 1.69629i 0.611550 + 0.204209i
\(70\) 0.229503i 0.0274309i
\(71\) 4.84841i 0.575401i −0.957720 0.287700i \(-0.907109\pi\)
0.957720 0.287700i \(-0.0928907\pi\)
\(72\) −2.39809 1.80254i −0.282618 0.212431i
\(73\) 6.03117i 0.705895i 0.935643 + 0.352948i \(0.114821\pi\)
−0.935643 + 0.352948i \(0.885179\pi\)
\(74\) 11.5857i 1.34681i
\(75\) −2.45599 0.820106i −0.283593 0.0946977i
\(76\) −2.49493 −0.286188
\(77\) −0.216568 −0.0246802
\(78\) −1.54604 + 4.62996i −0.175055 + 0.524240i
\(79\) −11.0840 −1.24704 −0.623522 0.781806i \(-0.714299\pi\)
−0.623522 + 0.781806i \(0.714299\pi\)
\(80\) 2.54852i 0.284933i
\(81\) 2.50171 + 8.64531i 0.277968 + 0.960590i
\(82\) 0.762149i 0.0841653i
\(83\) −1.68527 −0.184982 −0.0924911 0.995714i \(-0.529483\pi\)
−0.0924911 + 0.995714i \(0.529483\pi\)
\(84\) −0.147947 0.0494027i −0.0161424 0.00539028i
\(85\) −8.08194 −0.876610
\(86\) 7.62643i 0.822379i
\(87\) −3.41166 + 10.2170i −0.365768 + 1.09537i
\(88\) −2.40488 −0.256361
\(89\) −8.62144 −0.913871 −0.456936 0.889500i \(-0.651053\pi\)
−0.456936 + 0.889500i \(0.651053\pi\)
\(90\) −4.59380 + 6.11158i −0.484229 + 0.644217i
\(91\) 0.253790i 0.0266044i
\(92\) 3.09208 0.322372
\(93\) −1.19025 + 3.56445i −0.123423 + 0.369617i
\(94\) −7.90184 −0.815012
\(95\) 6.35837i 0.652355i
\(96\) −1.64288 0.548592i −0.167676 0.0559904i
\(97\) 0.394771i 0.0400829i 0.999799 + 0.0200415i \(0.00637982\pi\)
−0.999799 + 0.0200415i \(0.993620\pi\)
\(98\) 6.99189 0.706288
\(99\) 5.76712 + 4.33488i 0.579617 + 0.435672i
\(100\) −1.49493 −0.149493
\(101\) −6.21657 −0.618572 −0.309286 0.950969i \(-0.600090\pi\)
−0.309286 + 0.950969i \(0.600090\pi\)
\(102\) −1.73971 + 5.20995i −0.172257 + 0.515862i
\(103\) 9.59563i 0.945485i −0.881201 0.472743i \(-0.843264\pi\)
0.881201 0.472743i \(-0.156736\pi\)
\(104\) 2.81820i 0.276347i
\(105\) −0.125904 + 0.377046i −0.0122869 + 0.0367959i
\(106\) 3.58035i 0.347754i
\(107\) 7.04711i 0.681270i 0.940196 + 0.340635i \(0.110642\pi\)
−0.940196 + 0.340635i \(0.889358\pi\)
\(108\) 2.95092 + 4.27692i 0.283952 + 0.411547i
\(109\) 10.0881i 0.966264i 0.875548 + 0.483132i \(0.160501\pi\)
−0.875548 + 0.483132i \(0.839499\pi\)
\(110\) 6.12887i 0.584364i
\(111\) 6.35579 19.0338i 0.603265 1.80661i
\(112\) −0.0900537 −0.00850928
\(113\) −13.2519 −1.24664 −0.623318 0.781969i \(-0.714216\pi\)
−0.623318 + 0.781969i \(0.714216\pi\)
\(114\) 4.09887 + 1.36870i 0.383894 + 0.128190i
\(115\) 7.88022i 0.734834i
\(116\) 6.21894i 0.577414i
\(117\) 5.07991 6.75831i 0.469638 0.624806i
\(118\) 7.57687 + 1.26134i 0.697508 + 0.116116i
\(119\) 0.285582i 0.0261792i
\(120\) −1.39809 + 4.18690i −0.127628 + 0.382210i
\(121\) −5.21657 −0.474233
\(122\) 3.56445i 0.322710i
\(123\) −0.418109 + 1.25212i −0.0376996 + 0.112900i
\(124\) 2.16964i 0.194839i
\(125\) 8.93272i 0.798967i
\(126\) 0.215957 + 0.162325i 0.0192390 + 0.0144611i
\(127\) −2.96557 −0.263152 −0.131576 0.991306i \(-0.542004\pi\)
−0.131576 + 0.991306i \(0.542004\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.18380 + 12.5293i −0.368363 + 1.10314i
\(130\) 7.18223 0.629923
\(131\) 5.28039 0.461350 0.230675 0.973031i \(-0.425907\pi\)
0.230675 + 0.973031i \(0.425907\pi\)
\(132\) 3.95092 + 1.31930i 0.343883 + 0.114830i
\(133\) 0.224678 0.0194820
\(134\) 14.5015i 1.25274i
\(135\) 10.8998 7.52046i 0.938106 0.647258i
\(136\) 3.17124i 0.271931i
\(137\) 8.64237i 0.738368i 0.929356 + 0.369184i \(0.120363\pi\)
−0.929356 + 0.369184i \(0.879637\pi\)
\(138\) −5.07991 1.69629i −0.432431 0.144398i
\(139\) 1.00194 0.0849833 0.0424916 0.999097i \(-0.486470\pi\)
0.0424916 + 0.999097i \(0.486470\pi\)
\(140\) 0.229503i 0.0193966i
\(141\) 12.9818 + 4.33488i 1.09326 + 0.365063i
\(142\) 4.84841i 0.406870i
\(143\) 6.77743i 0.566757i
\(144\) 2.39809 + 1.80254i 0.199841 + 0.150212i
\(145\) 15.8491 1.31619
\(146\) 6.03117i 0.499143i
\(147\) −11.4868 3.83569i −0.947417 0.316363i
\(148\) 11.5857i 0.952335i
\(149\) −21.1213 −1.73033 −0.865164 0.501489i \(-0.832786\pi\)
−0.865164 + 0.501489i \(0.832786\pi\)
\(150\) 2.45599 + 0.820106i 0.200531 + 0.0669614i
\(151\) 18.8555i 1.53444i −0.641383 0.767221i \(-0.721639\pi\)
0.641383 0.767221i \(-0.278361\pi\)
\(152\) 2.49493 0.202366
\(153\) 5.71627 7.60492i 0.462133 0.614822i
\(154\) 0.216568 0.0174516
\(155\) 5.52936 0.444129
\(156\) 1.54604 4.62996i 0.123782 0.370693i
\(157\) 15.3653i 1.22628i 0.789973 + 0.613141i \(0.210094\pi\)
−0.789973 + 0.613141i \(0.789906\pi\)
\(158\) 11.0840 0.881794
\(159\) −1.96415 + 5.88208i −0.155767 + 0.466479i
\(160\) 2.54852i 0.201478i
\(161\) −0.278454 −0.0219452
\(162\) −2.50171 8.64531i −0.196553 0.679240i
\(163\) 22.4341 1.75718 0.878589 0.477579i \(-0.158486\pi\)
0.878589 + 0.477579i \(0.158486\pi\)
\(164\) 0.762149i 0.0595138i
\(165\) 3.36224 10.0690i 0.261750 0.783869i
\(166\) 1.68527 0.130802
\(167\) 14.3138i 1.10763i −0.832639 0.553817i \(-0.813171\pi\)
0.832639 0.553817i \(-0.186829\pi\)
\(168\) 0.147947 + 0.0494027i 0.0114144 + 0.00381150i
\(169\) 5.05774 0.389057
\(170\) 8.08194 0.619857
\(171\) −5.98308 4.49721i −0.457537 0.343910i
\(172\) 7.62643i 0.581510i
\(173\) 4.77735 0.363215 0.181608 0.983371i \(-0.441870\pi\)
0.181608 + 0.983371i \(0.441870\pi\)
\(174\) 3.41166 10.2170i 0.258637 0.774546i
\(175\) 0.134624 0.0101766
\(176\) 2.40488 0.181274
\(177\) −11.7559 6.22883i −0.883629 0.468188i
\(178\) 8.62144 0.646205
\(179\) 0.495022 0.0369997 0.0184998 0.999829i \(-0.494111\pi\)
0.0184998 + 0.999829i \(0.494111\pi\)
\(180\) 4.59380 6.11158i 0.342401 0.455530i
\(181\) 19.6569 1.46108 0.730542 0.682868i \(-0.239267\pi\)
0.730542 + 0.682868i \(0.239267\pi\)
\(182\) 0.253790i 0.0188121i
\(183\) −1.95543 + 5.85596i −0.144550 + 0.432885i
\(184\) −3.09208 −0.227951
\(185\) −29.5262 −2.17081
\(186\) 1.19025 3.56445i 0.0872731 0.261358i
\(187\) 7.62643i 0.557700i
\(188\) 7.90184 0.576301
\(189\) −0.265741 0.385153i −0.0193298 0.0280158i
\(190\) 6.35837i 0.461285i
\(191\) 24.2458 1.75437 0.877183 0.480155i \(-0.159420\pi\)
0.877183 + 0.480155i \(0.159420\pi\)
\(192\) 1.64288 + 0.548592i 0.118564 + 0.0395912i
\(193\) 7.81178 0.562304 0.281152 0.959663i \(-0.409283\pi\)
0.281152 + 0.959663i \(0.409283\pi\)
\(194\) 0.394771i 0.0283429i
\(195\) −11.7995 3.94011i −0.844981 0.282157i
\(196\) −6.99189 −0.499421
\(197\) 14.1485i 1.00804i 0.863692 + 0.504020i \(0.168146\pi\)
−0.863692 + 0.504020i \(0.831854\pi\)
\(198\) −5.76712 4.33488i −0.409851 0.308067i
\(199\) 7.12946 0.505394 0.252697 0.967545i \(-0.418682\pi\)
0.252697 + 0.967545i \(0.418682\pi\)
\(200\) 1.49493 0.105708
\(201\) −7.95543 + 23.8243i −0.561133 + 1.68043i
\(202\) 6.21657 0.437396
\(203\) 0.560039i 0.0393070i
\(204\) 1.73971 5.20995i 0.121804 0.364770i
\(205\) 1.94235 0.135659
\(206\) 9.59563i 0.668559i
\(207\) 7.41511 + 5.57360i 0.515386 + 0.387392i
\(208\) 2.81820i 0.195407i
\(209\) −6.00000 −0.415029
\(210\) 0.125904 0.377046i 0.00868818 0.0260186i
\(211\) 18.1479i 1.24935i 0.780883 + 0.624677i \(0.214769\pi\)
−0.780883 + 0.624677i \(0.785231\pi\)
\(212\) 3.58035i 0.245899i
\(213\) 2.65980 7.96535i 0.182246 0.545777i
\(214\) 7.04711i 0.481731i
\(215\) 19.4361 1.32553
\(216\) −2.95092 4.27692i −0.200785 0.291008i
\(217\) 0.195384i 0.0132635i
\(218\) 10.0881i 0.683252i
\(219\) −3.30865 + 9.90848i −0.223578 + 0.669553i
\(220\) 6.12887i 0.413208i
\(221\) −8.93718 −0.601180
\(222\) −6.35579 + 19.0338i −0.426573 + 1.27747i
\(223\) 19.4889 1.30508 0.652538 0.757756i \(-0.273704\pi\)
0.652538 + 0.757756i \(0.273704\pi\)
\(224\) 0.0900537 0.00601697
\(225\) −3.58498 2.69467i −0.238999 0.179645i
\(226\) 13.2519 0.881504
\(227\) 1.03534 0.0687182 0.0343591 0.999410i \(-0.489061\pi\)
0.0343591 + 0.999410i \(0.489061\pi\)
\(228\) −4.09887 1.36870i −0.271454 0.0906442i
\(229\) 10.7961i 0.713427i −0.934214 0.356714i \(-0.883897\pi\)
0.934214 0.356714i \(-0.116103\pi\)
\(230\) 7.88022i 0.519606i
\(231\) −0.355795 0.118807i −0.0234096 0.00781696i
\(232\) 6.21894i 0.408293i
\(233\) 9.44022 0.618449 0.309225 0.950989i \(-0.399930\pi\)
0.309225 + 0.950989i \(0.399930\pi\)
\(234\) −5.07991 + 6.75831i −0.332084 + 0.441805i
\(235\) 20.1380i 1.31366i
\(236\) −7.57687 1.26134i −0.493213 0.0821061i
\(237\) −18.2096 6.08058i −1.18284 0.394976i
\(238\) 0.285582i 0.0185115i
\(239\) 10.1040i 0.653573i 0.945098 + 0.326786i \(0.105966\pi\)
−0.945098 + 0.326786i \(0.894034\pi\)
\(240\) 1.39809 4.18690i 0.0902466 0.270263i
\(241\) −16.8918 −1.08810 −0.544048 0.839054i \(-0.683109\pi\)
−0.544048 + 0.839054i \(0.683109\pi\)
\(242\) 5.21657 0.335334
\(243\) −0.632739 + 15.5756i −0.0405902 + 0.999176i
\(244\) 3.56445i 0.228191i
\(245\) 17.8189i 1.13841i
\(246\) 0.418109 1.25212i 0.0266576 0.0798321i
\(247\) 7.03122i 0.447386i
\(248\) 2.16964i 0.137772i
\(249\) −2.76869 0.924524i −0.175459 0.0585893i
\(250\) 8.93272i 0.564955i
\(251\) 23.6479i 1.49264i −0.665587 0.746320i \(-0.731819\pi\)
0.665587 0.746320i \(-0.268181\pi\)
\(252\) −0.215957 0.162325i −0.0136040 0.0102255i
\(253\) 7.43608 0.467502
\(254\) 2.96557 0.186076
\(255\) −13.2776 4.43369i −0.831478 0.277648i
\(256\) 1.00000 0.0625000
\(257\) 22.4410i 1.39983i 0.714227 + 0.699914i \(0.246778\pi\)
−0.714227 + 0.699914i \(0.753222\pi\)
\(258\) 4.18380 12.5293i 0.260472 0.780040i
\(259\) 1.04333i 0.0648295i
\(260\) −7.18223 −0.445423
\(261\) −11.2099 + 14.9136i −0.693874 + 0.923129i
\(262\) −5.28039 −0.326224
\(263\) 1.14864i 0.0708282i −0.999373 0.0354141i \(-0.988725\pi\)
0.999373 0.0354141i \(-0.0112750\pi\)
\(264\) −3.95092 1.31930i −0.243162 0.0811970i
\(265\) 9.12458 0.560518
\(266\) −0.224678 −0.0137759
\(267\) −14.1640 4.72965i −0.866821 0.289450i
\(268\) 14.5015i 0.885823i
\(269\) −9.58711 −0.584536 −0.292268 0.956336i \(-0.594410\pi\)
−0.292268 + 0.956336i \(0.594410\pi\)
\(270\) −10.8998 + 7.52046i −0.663341 + 0.457681i
\(271\) −10.6508 −0.646992 −0.323496 0.946229i \(-0.604858\pi\)
−0.323496 + 0.946229i \(0.604858\pi\)
\(272\) 3.17124i 0.192284i
\(273\) −0.139227 + 0.416945i −0.00842639 + 0.0252347i
\(274\) 8.64237i 0.522105i
\(275\) −3.59512 −0.216794
\(276\) 5.07991 + 1.69629i 0.305775 + 0.102105i
\(277\) −22.3887 −1.34521 −0.672605 0.740002i \(-0.734825\pi\)
−0.672605 + 0.740002i \(0.734825\pi\)
\(278\) −1.00194 −0.0600923
\(279\) −3.91086 + 5.20300i −0.234137 + 0.311496i
\(280\) 0.229503i 0.0137154i
\(281\) 31.5953i 1.88482i −0.334463 0.942409i \(-0.608555\pi\)
0.334463 0.942409i \(-0.391445\pi\)
\(282\) −12.9818 4.33488i −0.773052 0.258138i
\(283\) 9.11894i 0.542065i −0.962570 0.271032i \(-0.912635\pi\)
0.962570 0.271032i \(-0.0873650\pi\)
\(284\) 4.84841i 0.287700i
\(285\) −3.48815 + 10.4460i −0.206620 + 0.618769i
\(286\) 6.77743i 0.400758i
\(287\) 0.0686344i 0.00405136i
\(288\) −2.39809 1.80254i −0.141309 0.106216i
\(289\) 6.94326 0.408427
\(290\) −15.8491 −0.930689
\(291\) −0.216568 + 0.648561i −0.0126954 + 0.0380193i
\(292\) 6.03117i 0.352948i
\(293\) 24.3784i 1.42420i −0.702079 0.712099i \(-0.747744\pi\)
0.702079 0.712099i \(-0.252256\pi\)
\(294\) 11.4868 + 3.83569i 0.669925 + 0.223702i
\(295\) −3.21454 + 19.3098i −0.187158 + 1.12426i
\(296\) 11.5857i 0.673403i
\(297\) 7.09659 + 10.2855i 0.411786 + 0.596824i
\(298\) 21.1213 1.22353
\(299\) 8.71411i 0.503950i
\(300\) −2.45599 0.820106i −0.141797 0.0473489i
\(301\) 0.686789i 0.0395858i
\(302\) 18.8555i 1.08501i
\(303\) −10.2131 3.41036i −0.586725 0.195920i
\(304\) −2.49493 −0.143094
\(305\) 9.08406 0.520152
\(306\) −5.71627 + 7.60492i −0.326778 + 0.434745i
\(307\) 8.37649 0.478071 0.239036 0.971011i \(-0.423169\pi\)
0.239036 + 0.971011i \(0.423169\pi\)
\(308\) −0.216568 −0.0123401
\(309\) 5.26408 15.7644i 0.299463 0.896808i
\(310\) −5.52936 −0.314047
\(311\) 27.9904i 1.58719i 0.608447 + 0.793594i \(0.291793\pi\)
−0.608447 + 0.793594i \(0.708207\pi\)
\(312\) −1.54604 + 4.62996i −0.0875274 + 0.262120i
\(313\) 13.0090i 0.735315i −0.929961 0.367657i \(-0.880160\pi\)
0.929961 0.367657i \(-0.119840\pi\)
\(314\) 15.3653i 0.867112i
\(315\) −0.413689 + 0.550371i −0.0233087 + 0.0310099i
\(316\) −11.0840 −0.623522
\(317\) 14.2111i 0.798174i −0.916913 0.399087i \(-0.869327\pi\)
0.916913 0.399087i \(-0.130673\pi\)
\(318\) 1.96415 5.88208i 0.110144 0.329850i
\(319\) 14.9558i 0.837363i
\(320\) 2.54852i 0.142466i
\(321\) −3.86599 + 11.5775i −0.215778 + 0.646195i
\(322\) 0.278454 0.0155176
\(323\) 7.91201i 0.440236i
\(324\) 2.50171 + 8.64531i 0.138984 + 0.480295i
\(325\) 4.21301i 0.233696i
\(326\) −22.4341 −1.24251
\(327\) −5.53424 + 16.5735i −0.306044 + 0.916517i
\(328\) 0.762149i 0.0420826i
\(329\) −0.711590 −0.0392312
\(330\) −3.36224 + 10.0690i −0.185085 + 0.554279i
\(331\) −22.8299 −1.25484 −0.627422 0.778679i \(-0.715890\pi\)
−0.627422 + 0.778679i \(0.715890\pi\)
\(332\) −1.68527 −0.0924911
\(333\) 20.8836 27.7835i 1.14441 1.52253i
\(334\) 14.3138i 0.783215i
\(335\) 36.9574 2.01920
\(336\) −0.147947 0.0494027i −0.00807119 0.00269514i
\(337\) 24.9076i 1.35680i −0.734692 0.678400i \(-0.762673\pi\)
0.734692 0.678400i \(-0.237327\pi\)
\(338\) −5.05774 −0.275105
\(339\) −21.7713 7.26989i −1.18245 0.394846i
\(340\) −8.08194 −0.438305
\(341\) 5.21772i 0.282555i
\(342\) 5.98308 + 4.49721i 0.323528 + 0.243181i
\(343\) 1.26002 0.0680348
\(344\) 7.62643i 0.411190i
\(345\) 4.32302 12.9462i 0.232744 0.697002i
\(346\) −4.77735 −0.256832
\(347\) 26.9745 1.44807 0.724033 0.689766i \(-0.242287\pi\)
0.724033 + 0.689766i \(0.242287\pi\)
\(348\) −3.41166 + 10.2170i −0.182884 + 0.547686i
\(349\) 24.7901i 1.32698i 0.748184 + 0.663491i \(0.230926\pi\)
−0.748184 + 0.663491i \(0.769074\pi\)
\(350\) −0.134624 −0.00719596
\(351\) 12.0532 8.31628i 0.643354 0.443890i
\(352\) −2.40488 −0.128180
\(353\) 18.8958 1.00572 0.502860 0.864368i \(-0.332281\pi\)
0.502860 + 0.864368i \(0.332281\pi\)
\(354\) 11.7559 + 6.22883i 0.624820 + 0.331059i
\(355\) −12.3563 −0.655802
\(356\) −8.62144 −0.456936
\(357\) −0.156668 + 0.469176i −0.00829174 + 0.0248314i
\(358\) −0.495022 −0.0261627
\(359\) 24.5978i 1.29822i 0.760694 + 0.649111i \(0.224859\pi\)
−0.760694 + 0.649111i \(0.775141\pi\)
\(360\) −4.59380 + 6.11158i −0.242114 + 0.322109i
\(361\) −12.7753 −0.672385
\(362\) −19.6569 −1.03314
\(363\) −8.57018 2.86177i −0.449818 0.150204i
\(364\) 0.253790i 0.0133022i
\(365\) 15.3705 0.804531
\(366\) 1.95543 5.85596i 0.102212 0.306096i
\(367\) 19.6069i 1.02347i −0.859143 0.511735i \(-0.829003\pi\)
0.859143 0.511735i \(-0.170997\pi\)
\(368\) 3.09208 0.161186
\(369\) −1.37380 + 1.82770i −0.0715173 + 0.0951465i
\(370\) 29.5262 1.53500
\(371\) 0.322424i 0.0167394i
\(372\) −1.19025 + 3.56445i −0.0617114 + 0.184808i
\(373\) −5.00294 −0.259043 −0.129521 0.991577i \(-0.541344\pi\)
−0.129521 + 0.991577i \(0.541344\pi\)
\(374\) 7.62643i 0.394353i
\(375\) 4.90042 14.6754i 0.253056 0.757833i
\(376\) −7.90184 −0.407506
\(377\) 17.5262 0.902646
\(378\) 0.265741 + 0.385153i 0.0136683 + 0.0198101i
\(379\) 1.41105 0.0724807 0.0362403 0.999343i \(-0.488462\pi\)
0.0362403 + 0.999343i \(0.488462\pi\)
\(380\) 6.35837i 0.326177i
\(381\) −4.87207 1.62689i −0.249604 0.0833479i
\(382\) −24.2458 −1.24052
\(383\) 32.4479i 1.65801i −0.559241 0.829005i \(-0.688907\pi\)
0.559241 0.829005i \(-0.311093\pi\)
\(384\) −1.64288 0.548592i −0.0838378 0.0279952i
\(385\) 0.551927i 0.0281288i
\(386\) −7.81178 −0.397609
\(387\) −13.7469 + 18.2889i −0.698796 + 0.929677i
\(388\) 0.394771i 0.0200415i
\(389\) 2.14262i 0.108635i −0.998524 0.0543176i \(-0.982702\pi\)
0.998524 0.0543176i \(-0.0172983\pi\)
\(390\) 11.7995 + 3.94011i 0.597492 + 0.199515i
\(391\) 9.80573i 0.495897i
\(392\) 6.99189 0.353144
\(393\) 8.67504 + 2.89678i 0.437598 + 0.146123i
\(394\) 14.1485i 0.712792i
\(395\) 28.2477i 1.42129i
\(396\) 5.76712 + 4.33488i 0.289809 + 0.217836i
\(397\) 24.1710i 1.21311i −0.795043 0.606553i \(-0.792552\pi\)
0.795043 0.606553i \(-0.207448\pi\)
\(398\) −7.12946 −0.357367
\(399\) 0.369118 + 0.123256i 0.0184790 + 0.00617054i
\(400\) −1.49493 −0.0747465
\(401\) 13.4312 0.670722 0.335361 0.942090i \(-0.391142\pi\)
0.335361 + 0.942090i \(0.391142\pi\)
\(402\) 7.95543 23.8243i 0.396781 1.18825i
\(403\) 6.11448 0.304584
\(404\) −6.21657 −0.309286
\(405\) 22.0327 6.37565i 1.09481 0.316809i
\(406\) 0.560039i 0.0277943i
\(407\) 27.8621i 1.38107i
\(408\) −1.73971 + 5.20995i −0.0861287 + 0.257931i
\(409\) 0.0382281i 0.00189026i 1.00000 0.000945129i \(0.000300844\pi\)
−1.00000 0.000945129i \(0.999699\pi\)
\(410\) −1.94235 −0.0959257
\(411\) −4.74113 + 14.1984i −0.233863 + 0.700353i
\(412\) 9.59563i 0.472743i
\(413\) 0.682326 + 0.113588i 0.0335751 + 0.00558931i
\(414\) −7.41511 5.57360i −0.364433 0.273927i
\(415\) 4.29493i 0.210830i
\(416\) 2.81820i 0.138174i
\(417\) 1.64606 + 0.549655i 0.0806080 + 0.0269167i
\(418\) 6.00000 0.293470
\(419\) −16.4059 −0.801480 −0.400740 0.916192i \(-0.631247\pi\)
−0.400740 + 0.916192i \(0.631247\pi\)
\(420\) −0.125904 + 0.377046i −0.00614347 + 0.0183980i
\(421\) 18.1688i 0.885491i 0.896647 + 0.442746i \(0.145995\pi\)
−0.896647 + 0.442746i \(0.854005\pi\)
\(422\) 18.1479i 0.883427i
\(423\) 18.9493 + 14.2434i 0.921349 + 0.692536i
\(424\) 3.58035i 0.173877i
\(425\) 4.74078i 0.229961i
\(426\) −2.65980 + 7.96535i −0.128868 + 0.385922i
\(427\) 0.320992i 0.0155339i
\(428\) 7.04711i 0.340635i
\(429\) 3.71804 11.1345i 0.179509 0.537578i
\(430\) −19.4361 −0.937291
\(431\) 33.4322 1.61037 0.805186 0.593022i \(-0.202065\pi\)
0.805186 + 0.593022i \(0.202065\pi\)
\(432\) 2.95092 + 4.27692i 0.141976 + 0.205774i
\(433\) 13.7095 0.658835 0.329418 0.944184i \(-0.393148\pi\)
0.329418 + 0.944184i \(0.393148\pi\)
\(434\) 0.195384i 0.00937874i
\(435\) 26.0381 + 8.69467i 1.24843 + 0.416877i
\(436\) 10.0881i 0.483132i
\(437\) −7.71453 −0.369036
\(438\) 3.30865 9.90848i 0.158093 0.473445i
\(439\) −35.8086 −1.70905 −0.854526 0.519409i \(-0.826152\pi\)
−0.854526 + 0.519409i \(0.826152\pi\)
\(440\) 6.12887i 0.292182i
\(441\) −16.7672 12.6031i −0.798439 0.600150i
\(442\) 8.93718 0.425098
\(443\) −9.77441 −0.464396 −0.232198 0.972669i \(-0.574592\pi\)
−0.232198 + 0.972669i \(0.574592\pi\)
\(444\) 6.35579 19.0338i 0.301633 0.903305i
\(445\) 21.9719i 1.04157i
\(446\) −19.4889 −0.922828
\(447\) −34.6998 11.5870i −1.64124 0.548046i
\(448\) −0.0900537 −0.00425464
\(449\) 21.4713i 1.01329i −0.862154 0.506646i \(-0.830885\pi\)
0.862154 0.506646i \(-0.169115\pi\)
\(450\) 3.58498 + 2.69467i 0.168998 + 0.127028i
\(451\) 1.83287i 0.0863067i
\(452\) −13.2519 −0.623318
\(453\) 10.3440 30.9774i 0.486003 1.45544i
\(454\) −1.03534 −0.0485911
\(455\) 0.646787 0.0303218
\(456\) 4.09887 + 1.36870i 0.191947 + 0.0640952i
\(457\) 19.2356i 0.899803i 0.893078 + 0.449902i \(0.148541\pi\)
−0.893078 + 0.449902i \(0.851459\pi\)
\(458\) 10.7961i 0.504469i
\(459\) 13.5631 9.35806i 0.633073 0.436797i
\(460\) 7.88022i 0.367417i
\(461\) 24.1597i 1.12523i 0.826718 + 0.562616i \(0.190205\pi\)
−0.826718 + 0.562616i \(0.809795\pi\)
\(462\) 0.355795 + 0.118807i 0.0165531 + 0.00552742i
\(463\) 3.60000i 0.167306i 0.996495 + 0.0836532i \(0.0266588\pi\)
−0.996495 + 0.0836532i \(0.973341\pi\)
\(464\) 6.21894i 0.288707i
\(465\) 9.08406 + 3.03336i 0.421263 + 0.140669i
\(466\) −9.44022 −0.437310
\(467\) −35.4938 −1.64246 −0.821229 0.570599i \(-0.806711\pi\)
−0.821229 + 0.570599i \(0.806711\pi\)
\(468\) 5.07991 6.75831i 0.234819 0.312403i
\(469\) 1.30592i 0.0603017i
\(470\) 20.1380i 0.928894i
\(471\) −8.42926 + 25.2433i −0.388400 + 1.16315i
\(472\) 7.57687 + 1.26134i 0.348754 + 0.0580578i
\(473\) 18.3406i 0.843303i
\(474\) 18.2096 + 6.08058i 0.836395 + 0.279290i
\(475\) 3.72975 0.171133
\(476\) 0.285582i 0.0130896i
\(477\) −6.45372 + 8.58602i −0.295495 + 0.393127i
\(478\) 10.1040i 0.462146i
\(479\) 20.5292i 0.938004i −0.883197 0.469002i \(-0.844614\pi\)
0.883197 0.469002i \(-0.155386\pi\)
\(480\) −1.39809 + 4.18690i −0.0638140 + 0.191105i
\(481\) −32.6507 −1.48874
\(482\) 16.8918 0.769400
\(483\) −0.457465 0.152757i −0.0208154 0.00695070i
\(484\) −5.21657 −0.237117
\(485\) 1.00608 0.0456837
\(486\) 0.632739 15.5756i 0.0287016 0.706524i
\(487\) 11.9099 0.539691 0.269846 0.962904i \(-0.413027\pi\)
0.269846 + 0.962904i \(0.413027\pi\)
\(488\) 3.56445i 0.161355i
\(489\) 36.8565 + 12.3072i 1.66671 + 0.556550i
\(490\) 17.8189i 0.804978i
\(491\) 22.3000i 1.00638i 0.864175 + 0.503192i \(0.167841\pi\)
−0.864175 + 0.503192i \(0.832159\pi\)
\(492\) −0.418109 + 1.25212i −0.0188498 + 0.0564498i
\(493\) 19.7217 0.888222
\(494\) 7.03122i 0.316349i
\(495\) 11.0475 14.6976i 0.496549 0.660608i
\(496\) 2.16964i 0.0974197i
\(497\) 0.436618i 0.0195850i
\(498\) 2.76869 + 0.924524i 0.124068 + 0.0414289i
\(499\) −7.29667 −0.326644 −0.163322 0.986573i \(-0.552221\pi\)
−0.163322 + 0.986573i \(0.552221\pi\)
\(500\) 8.93272i 0.399484i
\(501\) 7.85242 23.5158i 0.350820 1.05061i
\(502\) 23.6479i 1.05546i
\(503\) −26.0707 −1.16243 −0.581217 0.813748i \(-0.697423\pi\)
−0.581217 + 0.813748i \(0.697423\pi\)
\(504\) 0.215957 + 0.162325i 0.00961951 + 0.00723054i
\(505\) 15.8430i 0.705005i
\(506\) −7.43608 −0.330574
\(507\) 8.30925 + 2.77464i 0.369027 + 0.123226i
\(508\) −2.96557 −0.131576
\(509\) −12.3401 −0.546966 −0.273483 0.961877i \(-0.588176\pi\)
−0.273483 + 0.961877i \(0.588176\pi\)
\(510\) 13.2776 + 4.43369i 0.587944 + 0.196327i
\(511\) 0.543130i 0.0240266i
\(512\) −1.00000 −0.0441942
\(513\) −7.36234 10.6706i −0.325055 0.471120i
\(514\) 22.4410i 0.989828i
\(515\) −24.4546 −1.07760
\(516\) −4.18380 + 12.5293i −0.184181 + 0.551571i
\(517\) 19.0029 0.835748
\(518\) 1.04333i 0.0458414i
\(519\) 7.84860 + 2.62082i 0.344516 + 0.115041i
\(520\) 7.18223 0.314962
\(521\) 34.2123i 1.49887i 0.662079 + 0.749434i \(0.269674\pi\)
−0.662079 + 0.749434i \(0.730326\pi\)
\(522\) 11.2099 14.9136i 0.490643 0.652751i
\(523\) 25.1911 1.10153 0.550765 0.834660i \(-0.314336\pi\)
0.550765 + 0.834660i \(0.314336\pi\)
\(524\) 5.28039 0.230675
\(525\) 0.221171 + 0.0738536i 0.00965269 + 0.00322324i
\(526\) 1.14864i 0.0500831i
\(527\) 6.88044 0.299717
\(528\) 3.95092 + 1.31930i 0.171942 + 0.0574150i
\(529\) −13.4390 −0.584305
\(530\) −9.12458 −0.396346
\(531\) −15.8965 16.6824i −0.689847 0.723955i
\(532\) 0.224678 0.00974102
\(533\) 2.14789 0.0930354
\(534\) 14.1640 + 4.72965i 0.612935 + 0.204672i
\(535\) 17.9597 0.776464
\(536\) 14.5015i 0.626372i
\(537\) 0.813260 + 0.271565i 0.0350948 + 0.0117189i
\(538\) 9.58711 0.413329
\(539\) −16.8146 −0.724258
\(540\) 10.8998 7.52046i 0.469053 0.323629i
\(541\) 31.3137i 1.34628i −0.739514 0.673141i \(-0.764945\pi\)
0.739514 0.673141i \(-0.235055\pi\)
\(542\) 10.6508 0.457493
\(543\) 32.2939 + 10.7836i 1.38586 + 0.462769i
\(544\) 3.17124i 0.135966i
\(545\) 25.7097 1.10128
\(546\) 0.139227 0.416945i 0.00595836 0.0178436i
\(547\) −41.1416 −1.75909 −0.879544 0.475818i \(-0.842152\pi\)
−0.879544 + 0.475818i \(0.842152\pi\)
\(548\) 8.64237i 0.369184i
\(549\) −6.42506 + 8.54790i −0.274215 + 0.364815i
\(550\) 3.59512 0.153297
\(551\) 15.5158i 0.660996i
\(552\) −5.07991 1.69629i −0.216216 0.0721989i
\(553\) 0.998153 0.0424458
\(554\) 22.3887 0.951207
\(555\) −48.5080 16.1978i −2.05905 0.687560i
\(556\) 1.00194 0.0424916
\(557\) 28.9042i 1.22471i −0.790582 0.612356i \(-0.790222\pi\)
0.790582 0.612356i \(-0.209778\pi\)
\(558\) 3.91086 5.20300i 0.165560 0.220261i
\(559\) 21.4928 0.909049
\(560\) 0.229503i 0.00969829i
\(561\) 4.18380 12.5293i 0.176640 0.528987i
\(562\) 31.5953i 1.33277i
\(563\) −46.5072 −1.96005 −0.980023 0.198883i \(-0.936269\pi\)
−0.980023 + 0.198883i \(0.936269\pi\)
\(564\) 12.9818 + 4.33488i 0.546630 + 0.182531i
\(565\) 33.7727i 1.42083i
\(566\) 9.11894i 0.383298i
\(567\) −0.225289 0.778543i −0.00946123 0.0326957i
\(568\) 4.84841i 0.203435i
\(569\) 26.9664 1.13049 0.565246 0.824922i \(-0.308781\pi\)
0.565246 + 0.824922i \(0.308781\pi\)
\(570\) 3.48815 10.4460i 0.146102 0.437536i
\(571\) 14.2679i 0.597095i −0.954395 0.298547i \(-0.903498\pi\)
0.954395 0.298547i \(-0.0965021\pi\)
\(572\) 6.77743i 0.283378i
\(573\) 39.8329 + 13.3011i 1.66404 + 0.555660i
\(574\) 0.0686344i 0.00286474i
\(575\) −4.62245 −0.192769
\(576\) 2.39809 + 1.80254i 0.0999206 + 0.0751058i
\(577\) 35.9765 1.49772 0.748860 0.662728i \(-0.230601\pi\)
0.748860 + 0.662728i \(0.230601\pi\)
\(578\) −6.94326 −0.288802
\(579\) 12.8338 + 4.28548i 0.533355 + 0.178098i
\(580\) 15.8491 0.658097
\(581\) 0.151765 0.00629626
\(582\) 0.216568 0.648561i 0.00897704 0.0268837i
\(583\) 8.61030i 0.356602i
\(584\) 6.03117i 0.249572i
\(585\) −17.2237 12.9462i −0.712111 0.535261i
\(586\) 24.3784i 1.00706i
\(587\) 21.6537 0.893742 0.446871 0.894598i \(-0.352538\pi\)
0.446871 + 0.894598i \(0.352538\pi\)
\(588\) −11.4868 3.83569i −0.473709 0.158181i
\(589\) 5.41310i 0.223043i
\(590\) 3.21454 19.3098i 0.132340 0.794971i
\(591\) −7.76176 + 23.2443i −0.319276 + 0.956142i
\(592\) 11.5857i 0.476168i
\(593\) 39.6547i 1.62842i −0.580567 0.814212i \(-0.697169\pi\)
0.580567 0.814212i \(-0.302831\pi\)
\(594\) −7.09659 10.2855i −0.291177 0.422018i
\(595\) 0.727809 0.0298373
\(596\) −21.1213 −0.865164
\(597\) 11.7128 + 3.91116i 0.479374 + 0.160073i
\(598\) 8.71411i 0.356347i
\(599\) 8.17342i 0.333957i 0.985961 + 0.166978i \(0.0534010\pi\)
−0.985961 + 0.166978i \(0.946599\pi\)
\(600\) 2.45599 + 0.820106i 0.100265 + 0.0334807i
\(601\) 32.7522i 1.33599i −0.744165 0.667996i \(-0.767153\pi\)
0.744165 0.667996i \(-0.232847\pi\)
\(602\) 0.686789i 0.0279914i
\(603\) −26.1396 + 34.7761i −1.06449 + 1.41619i
\(604\) 18.8555i 0.767221i
\(605\) 13.2945i 0.540498i
\(606\) 10.2131 + 3.41036i 0.414877 + 0.138536i
\(607\) −12.9889 −0.527205 −0.263603 0.964631i \(-0.584911\pi\)
−0.263603 + 0.964631i \(0.584911\pi\)
\(608\) 2.49493 0.101183
\(609\) 0.307233 0.920075i 0.0124497 0.0372833i
\(610\) −9.08406 −0.367803
\(611\) 22.2690i 0.900906i
\(612\) 5.71627 7.60492i 0.231067 0.307411i
\(613\) 26.0490i 1.05211i −0.850451 0.526054i \(-0.823671\pi\)
0.850451 0.526054i \(-0.176329\pi\)
\(614\) −8.37649 −0.338048
\(615\) 3.19104 + 1.06556i 0.128675 + 0.0429674i
\(616\) 0.216568 0.00872578
\(617\) 29.7818i 1.19897i −0.800386 0.599485i \(-0.795372\pi\)
0.800386 0.599485i \(-0.204628\pi\)
\(618\) −5.26408 + 15.7644i −0.211752 + 0.634139i
\(619\) −17.1132 −0.687839 −0.343920 0.938999i \(-0.611755\pi\)
−0.343920 + 0.938999i \(0.611755\pi\)
\(620\) 5.52936 0.222065
\(621\) 9.12448 + 13.2246i 0.366153 + 0.530685i
\(622\) 27.9904i 1.12231i
\(623\) 0.776393 0.0311055
\(624\) 1.54604 4.62996i 0.0618912 0.185347i
\(625\) −30.2398 −1.20959
\(626\) 13.0090i 0.519946i
\(627\) −9.85727 3.29155i −0.393661 0.131452i
\(628\) 15.3653i 0.613141i
\(629\) −36.7409 −1.46495
\(630\) 0.413689 0.550371i 0.0164817 0.0219273i
\(631\) −13.0597 −0.519898 −0.259949 0.965622i \(-0.583706\pi\)
−0.259949 + 0.965622i \(0.583706\pi\)
\(632\) 11.0840 0.440897
\(633\) −9.95580 + 29.8148i −0.395707 + 1.18503i
\(634\) 14.2111i 0.564394i
\(635\) 7.55780i 0.299922i
\(636\) −1.96415 + 5.88208i −0.0778836 + 0.233240i
\(637\) 19.7046i 0.780723i
\(638\) 14.9558i 0.592105i
\(639\) 8.73945 11.6270i 0.345727 0.459955i
\(640\) 2.54852i 0.100739i
\(641\) 16.0393i 0.633514i −0.948507 0.316757i \(-0.897406\pi\)
0.948507 0.316757i \(-0.102594\pi\)
\(642\) 3.86599 11.5775i 0.152578 0.456929i
\(643\) 39.0313 1.53924 0.769622 0.638500i \(-0.220445\pi\)
0.769622 + 0.638500i \(0.220445\pi\)
\(644\) −0.278454 −0.0109726
\(645\) 31.9311 + 10.6625i 1.25729 + 0.419834i
\(646\) 7.91201i 0.311294i
\(647\) 10.0658i 0.395726i 0.980230 + 0.197863i \(0.0634001\pi\)
−0.980230 + 0.197863i \(0.936600\pi\)
\(648\) −2.50171 8.64531i −0.0982766 0.339620i
\(649\) −18.2214 3.03336i −0.715254 0.119070i
\(650\) 4.21301i 0.165248i
\(651\) 0.107186 0.320992i 0.00420096 0.0125807i
\(652\) 22.4341 0.878589
\(653\) 17.2684i 0.675766i 0.941188 + 0.337883i \(0.109711\pi\)
−0.941188 + 0.337883i \(0.890289\pi\)
\(654\) 5.53424 16.5735i 0.216406 0.648075i
\(655\) 13.4572i 0.525815i
\(656\) 0.762149i 0.0297569i
\(657\) −10.8714 + 14.4633i −0.424134 + 0.564268i
\(658\) 0.711590 0.0277407
\(659\) 8.90478 0.346881 0.173440 0.984844i \(-0.444512\pi\)
0.173440 + 0.984844i \(0.444512\pi\)
\(660\) 3.36224 10.0690i 0.130875 0.391934i
\(661\) −23.3948 −0.909953 −0.454977 0.890503i \(-0.650352\pi\)
−0.454977 + 0.890503i \(0.650352\pi\)
\(662\) 22.8299 0.887309
\(663\) −14.6827 4.90286i −0.570229 0.190411i
\(664\) 1.68527 0.0654011
\(665\) 0.572595i 0.0222043i
\(666\) −20.8836 + 27.7835i −0.809223 + 1.07659i
\(667\) 19.2295i 0.744568i
\(668\) 14.3138i 0.553817i
\(669\) 32.0179 + 10.6915i 1.23789 + 0.413356i
\(670\) −36.9574 −1.42779
\(671\) 8.57207i 0.330921i
\(672\) 0.147947 + 0.0494027i 0.00570719 + 0.00190575i
\(673\) 46.3809i 1.78785i −0.448216 0.893925i \(-0.647940\pi\)
0.448216 0.893925i \(-0.352060\pi\)
\(674\) 24.9076i 0.959403i
\(675\) −4.41142 6.39370i −0.169796 0.246094i
\(676\) 5.05774 0.194529
\(677\) 1.46357i 0.0562496i −0.999604 0.0281248i \(-0.991046\pi\)
0.999604 0.0281248i \(-0.00895358\pi\)
\(678\) 21.7713 + 7.26989i 0.836121 + 0.279198i
\(679\) 0.0355506i 0.00136431i
\(680\) 8.08194 0.309928
\(681\) 1.70094 + 0.567981i 0.0651803 + 0.0217651i
\(682\) 5.21772i 0.199797i
\(683\) −5.74279 −0.219742 −0.109871 0.993946i \(-0.535044\pi\)
−0.109871 + 0.993946i \(0.535044\pi\)
\(684\) −5.98308 4.49721i −0.228769 0.171955i
\(685\) 22.0252 0.841540
\(686\) −1.26002 −0.0481079
\(687\) 5.92266 17.7367i 0.225964 0.676697i
\(688\) 7.62643i 0.290755i
\(689\) 10.0901 0.384404
\(690\) −4.32302 + 12.9462i −0.164575 + 0.492855i
\(691\) 13.4494i 0.511640i 0.966724 + 0.255820i \(0.0823455\pi\)
−0.966724 + 0.255820i \(0.917655\pi\)
\(692\) 4.77735 0.181608
\(693\) −0.519351 0.390372i −0.0197285 0.0148290i
\(694\) −26.9745 −1.02394
\(695\) 2.55345i 0.0968581i
\(696\) 3.41166 10.2170i 0.129319 0.387273i
\(697\) 2.41695 0.0915487
\(698\) 24.7901i 0.938319i
\(699\) 15.5091 + 5.17883i 0.586609 + 0.195881i
\(700\) 0.134624 0.00508831
\(701\) 43.2164 1.63226 0.816130 0.577868i \(-0.196115\pi\)
0.816130 + 0.577868i \(0.196115\pi\)
\(702\) −12.0532 + 8.31628i −0.454920 + 0.313878i
\(703\) 28.9054i 1.09019i
\(704\) 2.40488 0.0906372
\(705\) 11.0475 33.0842i 0.416073 1.24602i
\(706\) −18.8958 −0.711151
\(707\) 0.559825 0.0210544
\(708\) −11.7559 6.22883i −0.441814 0.234094i
\(709\) −48.6141 −1.82574 −0.912871 0.408249i \(-0.866140\pi\)
−0.912871 + 0.408249i \(0.866140\pi\)
\(710\) 12.3563 0.463722
\(711\) −26.5804 19.9793i −0.996843 0.749282i
\(712\) 8.62144 0.323102
\(713\) 6.70871i 0.251243i
\(714\) 0.156668 0.469176i 0.00586314 0.0175585i
\(715\) −17.2724 −0.645950
\(716\) 0.495022 0.0184998
\(717\) −5.54296 + 16.5996i −0.207006 + 0.619924i
\(718\) 24.5978i 0.917982i
\(719\) 45.3674 1.69192 0.845959 0.533248i \(-0.179029\pi\)
0.845959 + 0.533248i \(0.179029\pi\)
\(720\) 4.59380 6.11158i 0.171201 0.227765i
\(721\) 0.864122i 0.0321816i
\(722\) 12.7753 0.475448
\(723\) −27.7511 9.26669i −1.03208 0.344632i
\(724\) 19.6569 0.730542
\(725\) 9.29688i 0.345278i
\(726\) 8.57018 + 2.86177i 0.318069 + 0.106210i
\(727\) −3.48894 −0.129398 −0.0646988 0.997905i \(-0.520609\pi\)
−0.0646988 + 0.997905i \(0.520609\pi\)
\(728\) 0.253790i 0.00940607i
\(729\) −9.58416 + 25.2417i −0.354969 + 0.934878i
\(730\) −15.3705 −0.568889
\(731\) 24.1852 0.894523
\(732\) −1.95543 + 5.85596i −0.0722748 + 0.216443i
\(733\) −10.4331 −0.385357 −0.192678 0.981262i \(-0.561717\pi\)
−0.192678 + 0.981262i \(0.561717\pi\)
\(734\) 19.6069i 0.723702i
\(735\) −9.77532 + 29.2743i −0.360568 + 1.07980i
\(736\) −3.09208 −0.113976
\(737\) 34.8744i 1.28462i
\(738\) 1.37380 1.82770i 0.0505704 0.0672787i
\(739\) 51.5614i 1.89672i 0.317201 + 0.948358i \(0.397257\pi\)
−0.317201 + 0.948358i \(0.602743\pi\)
\(740\) −29.5262 −1.08541
\(741\) −3.85727 + 11.5514i −0.141700 + 0.424352i
\(742\) 0.322424i 0.0118366i
\(743\) 30.2886i 1.11118i 0.831456 + 0.555591i \(0.187508\pi\)
−0.831456 + 0.555591i \(0.812492\pi\)
\(744\) 1.19025 3.56445i 0.0436366 0.130679i
\(745\) 53.8281i 1.97211i
\(746\) 5.00294 0.183171
\(747\) −4.04143 3.03776i −0.147868 0.111146i
\(748\) 7.62643i 0.278850i
\(749\) 0.634619i 0.0231885i
\(750\) −4.90042 + 14.6754i −0.178938 + 0.535869i
\(751\) 15.9239i 0.581071i −0.956864 0.290535i \(-0.906167\pi\)
0.956864 0.290535i \(-0.0938334\pi\)
\(752\) 7.90184 0.288150
\(753\) 12.9730 38.8506i 0.472764 1.41579i
\(754\) −17.5262 −0.638267
\(755\) −48.0536 −1.74885
\(756\) −0.265741 0.385153i −0.00966492 0.0140079i
\(757\) −34.0455 −1.23740 −0.618702 0.785626i \(-0.712341\pi\)
−0.618702 + 0.785626i \(0.712341\pi\)
\(758\) −1.41105 −0.0512516
\(759\) 12.2166 + 4.07937i 0.443433 + 0.148072i
\(760\) 6.35837i 0.230642i
\(761\) 37.6293i 1.36406i 0.731324 + 0.682030i \(0.238903\pi\)
−0.731324 + 0.682030i \(0.761097\pi\)
\(762\) 4.87207 + 1.62689i 0.176496 + 0.0589359i
\(763\) 0.908470i 0.0328888i
\(764\) 24.2458 0.877183
\(765\) −19.3813 14.5680i −0.700731 0.526708i
\(766\) 32.4479i 1.17239i
\(767\) −3.55470 + 21.3532i −0.128353 + 0.771018i
\(768\) 1.64288 + 0.548592i 0.0592822 + 0.0197956i
\(769\) 47.2538i 1.70401i −0.523530 0.852007i \(-0.675385\pi\)
0.523530 0.852007i \(-0.324615\pi\)
\(770\) 0.551927i 0.0198901i
\(771\) −12.3109 + 36.8677i −0.443367 + 1.32776i
\(772\) 7.81178 0.281152
\(773\) −51.6780 −1.85873 −0.929365 0.369163i \(-0.879645\pi\)
−0.929365 + 0.369163i \(0.879645\pi\)
\(774\) 13.7469 18.2889i 0.494123 0.657381i
\(775\) 3.24346i 0.116509i
\(776\) 0.394771i 0.0141715i
\(777\) −0.572363 + 1.71407i −0.0205334 + 0.0614918i
\(778\) 2.14262i 0.0768166i
\(779\) 1.90151i 0.0681286i
\(780\) −11.7995 3.94011i −0.422491 0.141079i
\(781\) 11.6598i 0.417222i
\(782\) 9.80573i 0.350652i
\(783\) −26.5979 + 18.3516i −0.950533 + 0.655832i
\(784\)