Properties

Label 483.2.h.a.160.8
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
Defining polynomial: \(x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.8
Root \(0.599676 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.a.160.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +3.33513 q^{5} -1.00000i q^{6} +(2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +3.33513 q^{5} -1.00000i q^{6} +(2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} -3.33513 q^{10} -4.27156i q^{11} -1.00000i q^{12} -3.12311i q^{13} +(-2.60399 - 0.468213i) q^{14} +3.33513i q^{15} -1.00000 q^{16} -3.33513 q^{17} +1.00000 q^{18} +1.46228 q^{19} -3.33513 q^{20} +(-0.468213 + 2.60399i) q^{21} +4.27156i q^{22} +(1.56155 + 4.53448i) q^{23} +3.00000i q^{24} +6.12311 q^{25} +3.12311i q^{26} -1.00000i q^{27} +(-2.60399 - 0.468213i) q^{28} +8.24621 q^{29} -3.33513i q^{30} -10.2462i q^{31} -5.00000 q^{32} +4.27156 q^{33} +3.33513 q^{34} +(8.68466 + 1.56155i) q^{35} +1.00000 q^{36} -1.87285i q^{37} -1.46228 q^{38} +3.12311 q^{39} +10.0054 q^{40} +11.1231i q^{41} +(0.468213 - 2.60399i) q^{42} -0.936426i q^{43} +4.27156i q^{44} -3.33513 q^{45} +(-1.56155 - 4.53448i) q^{46} +7.12311i q^{47} -1.00000i q^{48} +(6.56155 + 2.43845i) q^{49} -6.12311 q^{50} -3.33513i q^{51} +3.12311i q^{52} +10.0054i q^{53} +1.00000i q^{54} -14.2462i q^{55} +(7.81198 + 1.40464i) q^{56} +1.46228i q^{57} -8.24621 q^{58} -7.12311i q^{59} -3.33513i q^{60} -1.87285 q^{61} +10.2462i q^{62} +(-2.60399 - 0.468213i) q^{63} +7.00000 q^{64} -10.4160i q^{65} -4.27156 q^{66} +4.68213i q^{67} +3.33513 q^{68} +(-4.53448 + 1.56155i) q^{69} +(-8.68466 - 1.56155i) q^{70} -11.1231 q^{71} -3.00000 q^{72} -6.24621i q^{73} +1.87285i q^{74} +6.12311i q^{75} -1.46228 q^{76} +(2.00000 - 11.1231i) q^{77} -3.12311 q^{78} +16.1498i q^{79} -3.33513 q^{80} +1.00000 q^{81} -11.1231i q^{82} -17.0862 q^{83} +(0.468213 - 2.60399i) q^{84} -11.1231 q^{85} +0.936426i q^{86} +8.24621i q^{87} -12.8147i q^{88} +10.0054 q^{89} +3.33513 q^{90} +(1.46228 - 8.13254i) q^{91} +(-1.56155 - 4.53448i) q^{92} +10.2462 q^{93} -7.12311i q^{94} +4.87689 q^{95} -5.00000i q^{96} +1.87285 q^{97} +(-6.56155 - 2.43845i) q^{98} +4.27156i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 8q^{4} + 24q^{8} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 8q^{4} + 24q^{8} - 8q^{9} - 8q^{16} + 8q^{18} - 4q^{23} + 16q^{25} - 40q^{32} + 20q^{35} + 8q^{36} - 8q^{39} + 4q^{46} + 36q^{49} - 16q^{50} + 56q^{64} - 20q^{70} - 56q^{71} - 24q^{72} + 16q^{77} + 8q^{78} + 8q^{81} - 56q^{85} + 4q^{92} + 16q^{93} + 72q^{95} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 3.33513 1.49152 0.745758 0.666217i \(-0.232087\pi\)
0.745758 + 0.666217i \(0.232087\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 2.60399 + 0.468213i 0.984217 + 0.176968i
\(8\) 3.00000 1.06066
\(9\) −1.00000 −0.333333
\(10\) −3.33513 −1.05466
\(11\) 4.27156i 1.28792i −0.765058 0.643962i \(-0.777290\pi\)
0.765058 0.643962i \(-0.222710\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.12311i 0.866194i −0.901347 0.433097i \(-0.857421\pi\)
0.901347 0.433097i \(-0.142579\pi\)
\(14\) −2.60399 0.468213i −0.695946 0.125135i
\(15\) 3.33513i 0.861127i
\(16\) −1.00000 −0.250000
\(17\) −3.33513 −0.808888 −0.404444 0.914563i \(-0.632535\pi\)
−0.404444 + 0.914563i \(0.632535\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.46228 0.335470 0.167735 0.985832i \(-0.446355\pi\)
0.167735 + 0.985832i \(0.446355\pi\)
\(20\) −3.33513 −0.745758
\(21\) −0.468213 + 2.60399i −0.102172 + 0.568238i
\(22\) 4.27156i 0.910699i
\(23\) 1.56155 + 4.53448i 0.325606 + 0.945505i
\(24\) 3.00000i 0.612372i
\(25\) 6.12311 1.22462
\(26\) 3.12311i 0.612491i
\(27\) 1.00000i 0.192450i
\(28\) −2.60399 0.468213i −0.492108 0.0884840i
\(29\) 8.24621 1.53128 0.765641 0.643268i \(-0.222422\pi\)
0.765641 + 0.643268i \(0.222422\pi\)
\(30\) 3.33513i 0.608909i
\(31\) 10.2462i 1.84027i −0.391597 0.920137i \(-0.628077\pi\)
0.391597 0.920137i \(-0.371923\pi\)
\(32\) −5.00000 −0.883883
\(33\) 4.27156 0.743583
\(34\) 3.33513 0.571970
\(35\) 8.68466 + 1.56155i 1.46798 + 0.263951i
\(36\) 1.00000 0.166667
\(37\) 1.87285i 0.307895i −0.988079 0.153948i \(-0.950801\pi\)
0.988079 0.153948i \(-0.0491987\pi\)
\(38\) −1.46228 −0.237213
\(39\) 3.12311 0.500097
\(40\) 10.0054 1.58199
\(41\) 11.1231i 1.73714i 0.495569 + 0.868569i \(0.334960\pi\)
−0.495569 + 0.868569i \(0.665040\pi\)
\(42\) 0.468213 2.60399i 0.0722469 0.401805i
\(43\) 0.936426i 0.142804i −0.997448 0.0714018i \(-0.977253\pi\)
0.997448 0.0714018i \(-0.0227473\pi\)
\(44\) 4.27156i 0.643962i
\(45\) −3.33513 −0.497172
\(46\) −1.56155 4.53448i −0.230238 0.668573i
\(47\) 7.12311i 1.03901i 0.854467 + 0.519506i \(0.173884\pi\)
−0.854467 + 0.519506i \(0.826116\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.56155 + 2.43845i 0.937365 + 0.348350i
\(50\) −6.12311 −0.865938
\(51\) 3.33513i 0.467012i
\(52\) 3.12311i 0.433097i
\(53\) 10.0054i 1.37435i 0.726493 + 0.687173i \(0.241149\pi\)
−0.726493 + 0.687173i \(0.758851\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 14.2462i 1.92096i
\(56\) 7.81198 + 1.40464i 1.04392 + 0.187703i
\(57\) 1.46228i 0.193684i
\(58\) −8.24621 −1.08278
\(59\) 7.12311i 0.927349i −0.886006 0.463675i \(-0.846531\pi\)
0.886006 0.463675i \(-0.153469\pi\)
\(60\) 3.33513i 0.430564i
\(61\) −1.87285 −0.239794 −0.119897 0.992786i \(-0.538256\pi\)
−0.119897 + 0.992786i \(0.538256\pi\)
\(62\) 10.2462i 1.30127i
\(63\) −2.60399 0.468213i −0.328072 0.0589893i
\(64\) 7.00000 0.875000
\(65\) 10.4160i 1.29194i
\(66\) −4.27156 −0.525792
\(67\) 4.68213i 0.572013i 0.958228 + 0.286007i \(0.0923280\pi\)
−0.958228 + 0.286007i \(0.907672\pi\)
\(68\) 3.33513 0.404444
\(69\) −4.53448 + 1.56155i −0.545888 + 0.187989i
\(70\) −8.68466 1.56155i −1.03802 0.186641i
\(71\) −11.1231 −1.32007 −0.660035 0.751235i \(-0.729459\pi\)
−0.660035 + 0.751235i \(0.729459\pi\)
\(72\) −3.00000 −0.353553
\(73\) 6.24621i 0.731064i −0.930799 0.365532i \(-0.880887\pi\)
0.930799 0.365532i \(-0.119113\pi\)
\(74\) 1.87285i 0.217715i
\(75\) 6.12311i 0.707035i
\(76\) −1.46228 −0.167735
\(77\) 2.00000 11.1231i 0.227921 1.26760i
\(78\) −3.12311 −0.353622
\(79\) 16.1498i 1.81700i 0.417890 + 0.908498i \(0.362770\pi\)
−0.417890 + 0.908498i \(0.637230\pi\)
\(80\) −3.33513 −0.372879
\(81\) 1.00000 0.111111
\(82\) 11.1231i 1.22834i
\(83\) −17.0862 −1.87546 −0.937729 0.347368i \(-0.887075\pi\)
−0.937729 + 0.347368i \(0.887075\pi\)
\(84\) 0.468213 2.60399i 0.0510862 0.284119i
\(85\) −11.1231 −1.20647
\(86\) 0.936426i 0.100977i
\(87\) 8.24621i 0.884087i
\(88\) 12.8147i 1.36605i
\(89\) 10.0054 1.06057 0.530285 0.847819i \(-0.322085\pi\)
0.530285 + 0.847819i \(0.322085\pi\)
\(90\) 3.33513 0.351554
\(91\) 1.46228 8.13254i 0.153289 0.852522i
\(92\) −1.56155 4.53448i −0.162803 0.472753i
\(93\) 10.2462 1.06248
\(94\) 7.12311i 0.734692i
\(95\) 4.87689 0.500359
\(96\) 5.00000i 0.510310i
\(97\) 1.87285 0.190159 0.0950797 0.995470i \(-0.469689\pi\)
0.0950797 + 0.995470i \(0.469689\pi\)
\(98\) −6.56155 2.43845i −0.662817 0.246320i
\(99\) 4.27156i 0.429308i
\(100\) −6.12311 −0.612311
\(101\) 3.12311i 0.310761i 0.987855 + 0.155380i \(0.0496603\pi\)
−0.987855 + 0.155380i \(0.950340\pi\)
\(102\) 3.33513i 0.330227i
\(103\) −5.20798 −0.513158 −0.256579 0.966523i \(-0.582595\pi\)
−0.256579 + 0.966523i \(0.582595\pi\)
\(104\) 9.36932i 0.918737i
\(105\) −1.56155 + 8.68466i −0.152392 + 0.847536i
\(106\) 10.0054i 0.971810i
\(107\) 9.06897i 0.876730i −0.898797 0.438365i \(-0.855558\pi\)
0.898797 0.438365i \(-0.144442\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 12.2888i 1.17706i −0.808477 0.588528i \(-0.799708\pi\)
0.808477 0.588528i \(-0.200292\pi\)
\(110\) 14.2462i 1.35832i
\(111\) 1.87285 0.177763
\(112\) −2.60399 0.468213i −0.246054 0.0442420i
\(113\) 8.95369i 0.842292i 0.906993 + 0.421146i \(0.138372\pi\)
−0.906993 + 0.421146i \(0.861628\pi\)
\(114\) 1.46228i 0.136955i
\(115\) 5.20798 + 15.1231i 0.485647 + 1.41024i
\(116\) −8.24621 −0.765641
\(117\) 3.12311i 0.288731i
\(118\) 7.12311i 0.655735i
\(119\) −8.68466 1.56155i −0.796121 0.143147i
\(120\) 10.0054i 0.913364i
\(121\) −7.24621 −0.658746
\(122\) 1.87285 0.169560
\(123\) −11.1231 −1.00294
\(124\) 10.2462i 0.920137i
\(125\) 3.74571 0.335026
\(126\) 2.60399 + 0.468213i 0.231982 + 0.0417117i
\(127\) −6.24621 −0.554262 −0.277131 0.960832i \(-0.589384\pi\)
−0.277131 + 0.960832i \(0.589384\pi\)
\(128\) 3.00000 0.265165
\(129\) 0.936426 0.0824477
\(130\) 10.4160i 0.913541i
\(131\) 12.0000i 1.04844i −0.851581 0.524222i \(-0.824356\pi\)
0.851581 0.524222i \(-0.175644\pi\)
\(132\) −4.27156 −0.371791
\(133\) 3.80776 + 0.684658i 0.330175 + 0.0593674i
\(134\) 4.68213i 0.404475i
\(135\) 3.33513i 0.287042i
\(136\) −10.0054 −0.857956
\(137\) 14.8028i 1.26469i 0.774687 + 0.632345i \(0.217907\pi\)
−0.774687 + 0.632345i \(0.782093\pi\)
\(138\) 4.53448 1.56155i 0.386001 0.132928i
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) −8.68466 1.56155i −0.733988 0.131975i
\(141\) −7.12311 −0.599874
\(142\) 11.1231 0.933430
\(143\) −13.3405 −1.11559
\(144\) 1.00000 0.0833333
\(145\) 27.5022 2.28393
\(146\) 6.24621i 0.516940i
\(147\) −2.43845 + 6.56155i −0.201120 + 0.541188i
\(148\) 1.87285i 0.153948i
\(149\) 0.410574i 0.0336355i 0.999859 + 0.0168177i \(0.00535351\pi\)
−0.999859 + 0.0168177i \(0.994646\pi\)
\(150\) 6.12311i 0.499949i
\(151\) −20.4924 −1.66765 −0.833825 0.552029i \(-0.813854\pi\)
−0.833825 + 0.552029i \(0.813854\pi\)
\(152\) 4.38684 0.355820
\(153\) 3.33513 0.269629
\(154\) −2.00000 + 11.1231i −0.161165 + 0.896325i
\(155\) 34.1725i 2.74480i
\(156\) −3.12311 −0.250049
\(157\) −15.2134 −1.21416 −0.607080 0.794641i \(-0.707659\pi\)
−0.607080 + 0.794641i \(0.707659\pi\)
\(158\) 16.1498i 1.28481i
\(159\) −10.0054 −0.793480
\(160\) −16.6757 −1.31833
\(161\) 1.94317 + 12.5389i 0.153143 + 0.988204i
\(162\) −1.00000 −0.0785674
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 11.1231i 0.868569i
\(165\) 14.2462 1.10907
\(166\) 17.0862 1.32615
\(167\) 5.75379i 0.445242i 0.974905 + 0.222621i \(0.0714612\pi\)
−0.974905 + 0.222621i \(0.928539\pi\)
\(168\) −1.40464 + 7.81198i −0.108370 + 0.602707i
\(169\) 3.24621 0.249709
\(170\) 11.1231 0.853103
\(171\) −1.46228 −0.111823
\(172\) 0.936426i 0.0714018i
\(173\) 3.12311i 0.237445i −0.992927 0.118723i \(-0.962120\pi\)
0.992927 0.118723i \(-0.0378799\pi\)
\(174\) 8.24621i 0.625144i
\(175\) 15.9445 + 2.86692i 1.20529 + 0.216719i
\(176\) 4.27156i 0.321981i
\(177\) 7.12311 0.535405
\(178\) −10.0054 −0.749936
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 3.33513 0.248586
\(181\) −12.2888 −0.913421 −0.456710 0.889615i \(-0.650972\pi\)
−0.456710 + 0.889615i \(0.650972\pi\)
\(182\) −1.46228 + 8.13254i −0.108391 + 0.602824i
\(183\) 1.87285i 0.138445i
\(184\) 4.68466 + 13.6035i 0.345358 + 1.00286i
\(185\) 6.24621i 0.459231i
\(186\) −10.2462 −0.751289
\(187\) 14.2462i 1.04179i
\(188\) 7.12311i 0.519506i
\(189\) 0.468213 2.60399i 0.0340575 0.189413i
\(190\) −4.87689 −0.353807
\(191\) 3.45041i 0.249663i −0.992178 0.124832i \(-0.960161\pi\)
0.992178 0.124832i \(-0.0398390\pi\)
\(192\) 7.00000i 0.505181i
\(193\) 25.6155 1.84385 0.921923 0.387373i \(-0.126617\pi\)
0.921923 + 0.387373i \(0.126617\pi\)
\(194\) −1.87285 −0.134463
\(195\) 10.4160 0.745903
\(196\) −6.56155 2.43845i −0.468682 0.174175i
\(197\) 18.4924 1.31753 0.658765 0.752349i \(-0.271079\pi\)
0.658765 + 0.752349i \(0.271079\pi\)
\(198\) 4.27156i 0.303566i
\(199\) −5.20798 −0.369184 −0.184592 0.982815i \(-0.559096\pi\)
−0.184592 + 0.982815i \(0.559096\pi\)
\(200\) 18.3693 1.29891
\(201\) −4.68213 −0.330252
\(202\) 3.12311i 0.219741i
\(203\) 21.4731 + 3.86098i 1.50711 + 0.270988i
\(204\) 3.33513i 0.233506i
\(205\) 37.0970i 2.59097i
\(206\) 5.20798 0.362857
\(207\) −1.56155 4.53448i −0.108535 0.315168i
\(208\) 3.12311i 0.216548i
\(209\) 6.24621i 0.432059i
\(210\) 1.56155 8.68466i 0.107757 0.599298i
\(211\) −10.2462 −0.705378 −0.352689 0.935741i \(-0.614733\pi\)
−0.352689 + 0.935741i \(0.614733\pi\)
\(212\) 10.0054i 0.687173i
\(213\) 11.1231i 0.762143i
\(214\) 9.06897i 0.619942i
\(215\) 3.12311i 0.212994i
\(216\) 3.00000i 0.204124i
\(217\) 4.79741 26.6811i 0.325669 1.81123i
\(218\) 12.2888i 0.832304i
\(219\) 6.24621 0.422080
\(220\) 14.2462i 0.960479i
\(221\) 10.4160i 0.700654i
\(222\) −1.87285 −0.125698
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) −13.0200 2.34107i −0.869933 0.156419i
\(225\) −6.12311 −0.408207
\(226\) 8.95369i 0.595591i
\(227\) −6.67026 −0.442721 −0.221360 0.975192i \(-0.571050\pi\)
−0.221360 + 0.975192i \(0.571050\pi\)
\(228\) 1.46228i 0.0968418i
\(229\) −12.2888 −0.812068 −0.406034 0.913858i \(-0.633089\pi\)
−0.406034 + 0.913858i \(0.633089\pi\)
\(230\) −5.20798 15.1231i −0.343404 0.997188i
\(231\) 11.1231 + 2.00000i 0.731847 + 0.131590i
\(232\) 24.7386 1.62417
\(233\) −3.75379 −0.245919 −0.122959 0.992412i \(-0.539239\pi\)
−0.122959 + 0.992412i \(0.539239\pi\)
\(234\) 3.12311i 0.204164i
\(235\) 23.7565i 1.54970i
\(236\) 7.12311i 0.463675i
\(237\) −16.1498 −1.04904
\(238\) 8.68466 + 1.56155i 0.562943 + 0.101220i
\(239\) −1.36932 −0.0885737 −0.0442869 0.999019i \(-0.514102\pi\)
−0.0442869 + 0.999019i \(0.514102\pi\)
\(240\) 3.33513i 0.215282i
\(241\) −11.4677 −0.738698 −0.369349 0.929291i \(-0.620419\pi\)
−0.369349 + 0.929291i \(0.620419\pi\)
\(242\) 7.24621 0.465804
\(243\) 1.00000i 0.0641500i
\(244\) 1.87285 0.119897
\(245\) 21.8836 + 8.13254i 1.39809 + 0.519569i
\(246\) 11.1231 0.709183
\(247\) 4.56685i 0.290582i
\(248\) 30.7386i 1.95191i
\(249\) 17.0862i 1.08280i
\(250\) −3.74571 −0.236899
\(251\) 0.821147 0.0518303 0.0259152 0.999664i \(-0.491750\pi\)
0.0259152 + 0.999664i \(0.491750\pi\)
\(252\) 2.60399 + 0.468213i 0.164036 + 0.0294947i
\(253\) 19.3693 6.67026i 1.21774 0.419356i
\(254\) 6.24621 0.391922
\(255\) 11.1231i 0.696556i
\(256\) −17.0000 −1.06250
\(257\) 17.3693i 1.08347i −0.840550 0.541734i \(-0.817768\pi\)
0.840550 0.541734i \(-0.182232\pi\)
\(258\) −0.936426 −0.0582994
\(259\) 0.876894 4.87689i 0.0544876 0.303035i
\(260\) 10.4160i 0.645971i
\(261\) −8.24621 −0.510428
\(262\) 12.0000i 0.741362i
\(263\) 20.5366i 1.26634i 0.774011 + 0.633172i \(0.218247\pi\)
−0.774011 + 0.633172i \(0.781753\pi\)
\(264\) 12.8147 0.788689
\(265\) 33.3693i 2.04986i
\(266\) −3.80776 0.684658i −0.233469 0.0419791i
\(267\) 10.0054i 0.612320i
\(268\) 4.68213i 0.286007i
\(269\) 6.63068i 0.404280i 0.979357 + 0.202140i \(0.0647896\pi\)
−0.979357 + 0.202140i \(0.935210\pi\)
\(270\) 3.33513i 0.202970i
\(271\) 16.4924i 1.00184i −0.865493 0.500922i \(-0.832994\pi\)
0.865493 0.500922i \(-0.167006\pi\)
\(272\) 3.33513 0.202222
\(273\) 8.13254 + 1.46228i 0.492204 + 0.0885012i
\(274\) 14.8028i 0.894270i
\(275\) 26.1552i 1.57722i
\(276\) 4.53448 1.56155i 0.272944 0.0939944i
\(277\) 16.2462 0.976140 0.488070 0.872804i \(-0.337701\pi\)
0.488070 + 0.872804i \(0.337701\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 10.2462i 0.613425i
\(280\) 26.0540 + 4.68466i 1.55702 + 0.279962i
\(281\) 22.2942i 1.32996i 0.746860 + 0.664981i \(0.231560\pi\)
−0.746860 + 0.664981i \(0.768440\pi\)
\(282\) 7.12311 0.424175
\(283\) 19.3697 1.15141 0.575703 0.817659i \(-0.304728\pi\)
0.575703 + 0.817659i \(0.304728\pi\)
\(284\) 11.1231 0.660035
\(285\) 4.87689i 0.288882i
\(286\) 13.3405 0.788842
\(287\) −5.20798 + 28.9645i −0.307418 + 1.70972i
\(288\) 5.00000 0.294628
\(289\) −5.87689 −0.345700
\(290\) −27.5022 −1.61498
\(291\) 1.87285i 0.109789i
\(292\) 6.24621i 0.365532i
\(293\) 9.18425 0.536550 0.268275 0.963342i \(-0.413546\pi\)
0.268275 + 0.963342i \(0.413546\pi\)
\(294\) 2.43845 6.56155i 0.142213 0.382678i
\(295\) 23.7565i 1.38316i
\(296\) 5.61856i 0.326572i
\(297\) −4.27156 −0.247861
\(298\) 0.410574i 0.0237839i
\(299\) 14.1617 4.87689i 0.818991 0.282038i
\(300\) 6.12311i 0.353518i
\(301\) 0.438447 2.43845i 0.0252717 0.140550i
\(302\) 20.4924 1.17921
\(303\) −3.12311 −0.179418
\(304\) −1.46228 −0.0838675
\(305\) −6.24621 −0.357657
\(306\) −3.33513 −0.190657
\(307\) 2.24621i 0.128198i −0.997944 0.0640990i \(-0.979583\pi\)
0.997944 0.0640990i \(-0.0204174\pi\)
\(308\) −2.00000 + 11.1231i −0.113961 + 0.633798i
\(309\) 5.20798i 0.296272i
\(310\) 34.1725i 1.94087i
\(311\) 2.63068i 0.149172i −0.997215 0.0745862i \(-0.976236\pi\)
0.997215 0.0745862i \(-0.0237636\pi\)
\(312\) 9.36932 0.530433
\(313\) −14.3922 −0.813497 −0.406749 0.913540i \(-0.633337\pi\)
−0.406749 + 0.913540i \(0.633337\pi\)
\(314\) 15.2134 0.858541
\(315\) −8.68466 1.56155i −0.489325 0.0879835i
\(316\) 16.1498i 0.908498i
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 10.0054 0.561075
\(319\) 35.2242i 1.97218i
\(320\) 23.3459 1.30508
\(321\) 9.06897 0.506181
\(322\) −1.94317 12.5389i −0.108288 0.698766i
\(323\) −4.87689 −0.271358
\(324\) −1.00000 −0.0555556
\(325\) 19.1231i 1.06076i
\(326\) −12.0000 −0.664619
\(327\) 12.2888 0.679573
\(328\) 33.3693i 1.84251i
\(329\) −3.33513 + 18.5485i −0.183872 + 1.02261i
\(330\) −14.2462 −0.784228
\(331\) −16.4924 −0.906506 −0.453253 0.891382i \(-0.649737\pi\)
−0.453253 + 0.891382i \(0.649737\pi\)
\(332\) 17.0862 0.937729
\(333\) 1.87285i 0.102632i
\(334\) 5.75379i 0.314833i
\(335\) 15.6155i 0.853167i
\(336\) 0.468213 2.60399i 0.0255431 0.142059i
\(337\) 6.67026i 0.363352i −0.983358 0.181676i \(-0.941848\pi\)
0.983358 0.181676i \(-0.0581523\pi\)
\(338\) −3.24621 −0.176571
\(339\) −8.95369 −0.486298
\(340\) 11.1231 0.603235
\(341\) −43.7673 −2.37013
\(342\) 1.46228 0.0790710
\(343\) 15.9445 + 9.42190i 0.860923 + 0.508735i
\(344\) 2.80928i 0.151466i
\(345\) −15.1231 + 5.20798i −0.814201 + 0.280388i
\(346\) 3.12311i 0.167899i
\(347\) −16.4924 −0.885360 −0.442680 0.896680i \(-0.645972\pi\)
−0.442680 + 0.896680i \(0.645972\pi\)
\(348\) 8.24621i 0.442043i
\(349\) 9.36932i 0.501528i 0.968048 + 0.250764i \(0.0806818\pi\)
−0.968048 + 0.250764i \(0.919318\pi\)
\(350\) −15.9445 2.86692i −0.852270 0.153243i
\(351\) −3.12311 −0.166699
\(352\) 21.3578i 1.13837i
\(353\) 17.3693i 0.924475i 0.886756 + 0.462238i \(0.152953\pi\)
−0.886756 + 0.462238i \(0.847047\pi\)
\(354\) −7.12311 −0.378589
\(355\) −37.0970 −1.96891
\(356\) −10.0054 −0.530285
\(357\) 1.56155 8.68466i 0.0826461 0.459641i
\(358\) 4.00000 0.211407
\(359\) 25.3341i 1.33708i −0.743676 0.668540i \(-0.766919\pi\)
0.743676 0.668540i \(-0.233081\pi\)
\(360\) −10.0054 −0.527331
\(361\) −16.8617 −0.887460
\(362\) 12.2888 0.645886
\(363\) 7.24621i 0.380327i
\(364\) −1.46228 + 8.13254i −0.0766443 + 0.426261i
\(365\) 20.8319i 1.09039i
\(366\) 1.87285i 0.0978956i
\(367\) −12.6994 −0.662903 −0.331452 0.943472i \(-0.607538\pi\)
−0.331452 + 0.943472i \(0.607538\pi\)
\(368\) −1.56155 4.53448i −0.0814016 0.236376i
\(369\) 11.1231i 0.579046i
\(370\) 6.24621i 0.324725i
\(371\) −4.68466 + 26.0540i −0.243215 + 1.35266i
\(372\) −10.2462 −0.531241
\(373\) 15.2134i 0.787719i −0.919171 0.393860i \(-0.871140\pi\)
0.919171 0.393860i \(-0.128860\pi\)
\(374\) 14.2462i 0.736654i
\(375\) 3.74571i 0.193427i
\(376\) 21.3693i 1.10204i
\(377\) 25.7538i 1.32639i
\(378\) −0.468213 + 2.60399i −0.0240823 + 0.133935i
\(379\) 21.7684i 1.11817i 0.829112 + 0.559083i \(0.188847\pi\)
−0.829112 + 0.559083i \(0.811153\pi\)
\(380\) −4.87689 −0.250179
\(381\) 6.24621i 0.320003i
\(382\) 3.45041i 0.176538i
\(383\) −16.2651 −0.831107 −0.415554 0.909569i \(-0.636412\pi\)
−0.415554 + 0.909569i \(0.636412\pi\)
\(384\) 3.00000i 0.153093i
\(385\) 6.67026 37.0970i 0.339948 1.89064i
\(386\) −25.6155 −1.30380
\(387\) 0.936426i 0.0476012i
\(388\) −1.87285 −0.0950797
\(389\) 14.5722i 0.738842i 0.929262 + 0.369421i \(0.120444\pi\)
−0.929262 + 0.369421i \(0.879556\pi\)
\(390\) −10.4160 −0.527433
\(391\) −5.20798 15.1231i −0.263379 0.764808i
\(392\) 19.6847 + 7.31534i 0.994225 + 0.369481i
\(393\) 12.0000 0.605320
\(394\) −18.4924 −0.931635
\(395\) 53.8617i 2.71008i
\(396\) 4.27156i 0.214654i
\(397\) 20.4924i 1.02849i −0.857645 0.514243i \(-0.828073\pi\)
0.857645 0.514243i \(-0.171927\pi\)
\(398\) 5.20798 0.261053
\(399\) −0.684658 + 3.80776i −0.0342758 + 0.190627i
\(400\) −6.12311 −0.306155
\(401\) 11.8782i 0.593171i −0.955006 0.296586i \(-0.904152\pi\)
0.955006 0.296586i \(-0.0958480\pi\)
\(402\) 4.68213 0.233524
\(403\) −32.0000 −1.59403
\(404\) 3.12311i 0.155380i
\(405\) 3.33513 0.165724
\(406\) −21.4731 3.86098i −1.06569 0.191617i
\(407\) −8.00000 −0.396545
\(408\) 10.0054i 0.495341i
\(409\) 1.36932i 0.0677084i 0.999427 + 0.0338542i \(0.0107782\pi\)
−0.999427 + 0.0338542i \(0.989222\pi\)
\(410\) 37.0970i 1.83209i
\(411\) −14.8028 −0.730169
\(412\) 5.20798 0.256579
\(413\) 3.33513 18.5485i 0.164111 0.912713i
\(414\) 1.56155 + 4.53448i 0.0767461 + 0.222858i
\(415\) −56.9848 −2.79728
\(416\) 15.6155i 0.765614i
\(417\) 12.0000 0.587643
\(418\) 6.24621i 0.305512i
\(419\) 9.59482 0.468738 0.234369 0.972148i \(-0.424698\pi\)
0.234369 + 0.972148i \(0.424698\pi\)
\(420\) 1.56155 8.68466i 0.0761960 0.423768i
\(421\) 25.6294i 1.24910i 0.780986 + 0.624549i \(0.214717\pi\)
−0.780986 + 0.624549i \(0.785283\pi\)
\(422\) 10.2462 0.498778
\(423\) 7.12311i 0.346337i
\(424\) 30.0162i 1.45771i
\(425\) −20.4214 −0.990582
\(426\) 11.1231i 0.538916i
\(427\) −4.87689 0.876894i −0.236009 0.0424359i
\(428\) 9.06897i 0.438365i
\(429\) 13.3405i 0.644087i
\(430\) 3.12311i 0.150610i
\(431\) 28.8492i 1.38962i −0.719195 0.694809i \(-0.755489\pi\)
0.719195 0.694809i \(-0.244511\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 18.1379 0.871654 0.435827 0.900031i \(-0.356456\pi\)
0.435827 + 0.900031i \(0.356456\pi\)
\(434\) −4.79741 + 26.6811i −0.230283 + 1.28073i
\(435\) 27.5022i 1.31863i
\(436\) 12.2888i 0.588528i
\(437\) 2.28343 + 6.63068i 0.109231 + 0.317189i
\(438\) −6.24621 −0.298456
\(439\) 21.7538i 1.03825i 0.854698 + 0.519126i \(0.173742\pi\)
−0.854698 + 0.519126i \(0.826258\pi\)
\(440\) 42.7386i 2.03748i
\(441\) −6.56155 2.43845i −0.312455 0.116117i
\(442\) 10.4160i 0.495437i
\(443\) 29.3693 1.39538 0.697689 0.716401i \(-0.254212\pi\)
0.697689 + 0.716401i \(0.254212\pi\)
\(444\) −1.87285 −0.0888817
\(445\) 33.3693 1.58186
\(446\) 4.00000i 0.189405i
\(447\) −0.410574 −0.0194195
\(448\) 18.2279 + 3.27749i 0.861190 + 0.154847i
\(449\) 1.50758 0.0711470 0.0355735 0.999367i \(-0.488674\pi\)
0.0355735 + 0.999367i \(0.488674\pi\)
\(450\) 6.12311 0.288646
\(451\) 47.5130 2.23730
\(452\) 8.95369i 0.421146i
\(453\) 20.4924i 0.962818i
\(454\) 6.67026 0.313051
\(455\) 4.87689 27.1231i 0.228632 1.27155i
\(456\) 4.38684i 0.205433i
\(457\) 29.6056i 1.38489i 0.721470 + 0.692446i \(0.243467\pi\)
−0.721470 + 0.692446i \(0.756533\pi\)
\(458\) 12.2888 0.574219
\(459\) 3.33513i 0.155671i
\(460\) −5.20798 15.1231i −0.242824 0.705118i
\(461\) 9.36932i 0.436373i 0.975907 + 0.218186i \(0.0700140\pi\)
−0.975907 + 0.218186i \(0.929986\pi\)
\(462\) −11.1231 2.00000i −0.517494 0.0930484i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −8.24621 −0.382821
\(465\) 34.1725 1.58471
\(466\) 3.75379 0.173891
\(467\) −6.67026 −0.308663 −0.154332 0.988019i \(-0.549322\pi\)
−0.154332 + 0.988019i \(0.549322\pi\)
\(468\) 3.12311i 0.144366i
\(469\) −2.19224 + 12.1922i −0.101228 + 0.562985i
\(470\) 23.7565i 1.09581i
\(471\) 15.2134i 0.700996i
\(472\) 21.3693i 0.983603i
\(473\) −4.00000 −0.183920
\(474\) 16.1498 0.741785
\(475\) 8.95369 0.410823
\(476\) 8.68466 + 1.56155i 0.398061 + 0.0715737i
\(477\) 10.0054i 0.458116i
\(478\) 1.36932 0.0626311
\(479\) 5.84912 0.267253 0.133626 0.991032i \(-0.457338\pi\)
0.133626 + 0.991032i \(0.457338\pi\)
\(480\) 16.6757i 0.761136i
\(481\) −5.84912 −0.266697
\(482\) 11.4677 0.522338
\(483\) −12.5389 + 1.94317i −0.570540 + 0.0884171i
\(484\) 7.24621 0.329373
\(485\) 6.24621 0.283626
\(486\) 1.00000i 0.0453609i
\(487\) −14.2462 −0.645557 −0.322779 0.946474i \(-0.604617\pi\)
−0.322779 + 0.946474i \(0.604617\pi\)
\(488\) −5.61856 −0.254340
\(489\) 12.0000i 0.542659i
\(490\) −21.8836 8.13254i −0.988602 0.367391i
\(491\) −32.4924 −1.46636 −0.733181 0.680033i \(-0.761965\pi\)
−0.733181 + 0.680033i \(0.761965\pi\)
\(492\) 11.1231 0.501468
\(493\) −27.5022 −1.23864
\(494\) 4.56685i 0.205472i
\(495\) 14.2462i 0.640320i
\(496\) 10.2462i 0.460068i
\(497\) −28.9645 5.20798i −1.29923 0.233610i
\(498\) 17.0862i 0.765652i
\(499\) 5.75379 0.257575 0.128787 0.991672i \(-0.458891\pi\)
0.128787 + 0.991672i \(0.458891\pi\)
\(500\) −3.74571 −0.167513
\(501\) −5.75379 −0.257060
\(502\) −0.821147 −0.0366496
\(503\) 34.1725 1.52368 0.761838 0.647768i \(-0.224297\pi\)
0.761838 + 0.647768i \(0.224297\pi\)
\(504\) −7.81198 1.40464i −0.347973 0.0625676i
\(505\) 10.4160i 0.463505i
\(506\) −19.3693 + 6.67026i −0.861071 + 0.296529i
\(507\) 3.24621i 0.144169i
\(508\) 6.24621 0.277131
\(509\) 15.6155i 0.692146i −0.938208 0.346073i \(-0.887515\pi\)
0.938208 0.346073i \(-0.112485\pi\)
\(510\) 11.1231i 0.492539i
\(511\) 2.92456 16.2651i 0.129375 0.719525i
\(512\) 11.0000 0.486136
\(513\) 1.46228i 0.0645612i
\(514\) 17.3693i 0.766128i
\(515\) −17.3693 −0.765384
\(516\) −0.936426 −0.0412239
\(517\) 30.4268 1.33817
\(518\) −0.876894 + 4.87689i −0.0385285 + 0.214278i
\(519\) 3.12311 0.137089
\(520\) 31.2479i 1.37031i
\(521\) −3.33513 −0.146115 −0.0730574 0.997328i \(-0.523276\pi\)
−0.0730574 + 0.997328i \(0.523276\pi\)
\(522\) 8.24621 0.360927
\(523\) −11.8782 −0.519400 −0.259700 0.965689i \(-0.583624\pi\)
−0.259700 + 0.965689i \(0.583624\pi\)
\(524\) 12.0000i 0.524222i
\(525\) −2.86692 + 15.9445i −0.125123 + 0.695876i
\(526\) 20.5366i 0.895440i
\(527\) 34.1725i 1.48858i
\(528\) −4.27156 −0.185896
\(529\) −18.1231 + 14.1617i −0.787961 + 0.615725i
\(530\) 33.3693i 1.44947i
\(531\) 7.12311i 0.309116i
\(532\) −3.80776 0.684658i −0.165088 0.0296837i
\(533\) 34.7386 1.50470
\(534\) 10.0054i 0.432976i
\(535\) 30.2462i 1.30766i
\(536\) 14.0464i 0.606712i
\(537\) 4.00000i 0.172613i
\(538\) 6.63068i 0.285869i
\(539\) 10.4160 28.0281i 0.448648 1.20725i
\(540\) 3.33513i 0.143521i
\(541\) 22.8769 0.983555 0.491777 0.870721i \(-0.336347\pi\)
0.491777 + 0.870721i \(0.336347\pi\)
\(542\) 16.4924i 0.708410i
\(543\) 12.2888i 0.527364i
\(544\) 16.6757 0.714963
\(545\) 40.9848i 1.75560i
\(546\) −8.13254 1.46228i −0.348041 0.0625798i
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 14.8028i 0.632345i
\(549\) 1.87285 0.0799314
\(550\) 26.1552i 1.11526i
\(551\) 12.0583 0.513699
\(552\) −13.6035 + 4.68466i −0.579001 + 0.199392i
\(553\) −7.56155 + 42.0540i −0.321550 + 1.78832i
\(554\) −16.2462 −0.690235
\(555\) 6.24621 0.265137
\(556\) 12.0000i 0.508913i
\(557\) 15.8545i 0.671777i 0.941902 + 0.335889i \(0.109037\pi\)
−0.941902 + 0.335889i \(0.890963\pi\)
\(558\) 10.2462i 0.433757i
\(559\) −2.92456 −0.123696
\(560\) −8.68466 1.56155i −0.366994 0.0659877i
\(561\) −14.2462 −0.601476
\(562\) 22.2942i 0.940425i
\(563\) −0.821147 −0.0346072 −0.0173036 0.999850i \(-0.505508\pi\)
−0.0173036 + 0.999850i \(0.505508\pi\)
\(564\) 7.12311 0.299937
\(565\) 29.8617i 1.25629i
\(566\) −19.3697 −0.814168
\(567\) 2.60399 + 0.468213i 0.109357 + 0.0196631i
\(568\) −33.3693 −1.40015
\(569\) 0.641132i 0.0268777i 0.999910 + 0.0134388i \(0.00427784\pi\)
−0.999910 + 0.0134388i \(0.995722\pi\)
\(570\) 4.87689i 0.204271i
\(571\) 24.6929i 1.03337i −0.856177 0.516683i \(-0.827166\pi\)
0.856177 0.516683i \(-0.172834\pi\)
\(572\) 13.3405 0.557796
\(573\) 3.45041 0.144143
\(574\) 5.20798 28.9645i 0.217377 1.20895i
\(575\) 9.56155 + 27.7651i 0.398744 + 1.15789i
\(576\) −7.00000 −0.291667
\(577\) 27.1231i 1.12915i −0.825382 0.564575i \(-0.809040\pi\)
0.825382 0.564575i \(-0.190960\pi\)
\(578\) 5.87689 0.244447
\(579\) 25.6155i 1.06455i
\(580\) −27.5022 −1.14197
\(581\) −44.4924 8.00000i −1.84586 0.331896i
\(582\) 1.87285i 0.0776322i
\(583\) 42.7386 1.77005
\(584\) 18.7386i 0.775410i
\(585\) 10.4160i 0.430647i
\(586\) −9.18425 −0.379398
\(587\) 32.4924i 1.34111i 0.741862 + 0.670553i \(0.233943\pi\)
−0.741862 + 0.670553i \(0.766057\pi\)
\(588\) 2.43845 6.56155i 0.100560 0.270594i
\(589\) 14.9828i 0.617356i
\(590\) 23.7565i 0.978040i
\(591\) 18.4924i 0.760677i
\(592\) 1.87285i 0.0769738i
\(593\) 17.3693i 0.713272i 0.934243 + 0.356636i \(0.116076\pi\)
−0.934243 + 0.356636i \(0.883924\pi\)
\(594\) 4.27156 0.175264
\(595\) −28.9645 5.20798i −1.18743 0.213507i
\(596\) 0.410574i 0.0168177i
\(597\) 5.20798i 0.213149i
\(598\) −14.1617 + 4.87689i −0.579114 + 0.199431i
\(599\) −14.6307 −0.597794 −0.298897 0.954285i \(-0.596619\pi\)
−0.298897 + 0.954285i \(0.596619\pi\)
\(600\) 18.3693i 0.749924i
\(601\) 33.3693i 1.36116i −0.732672 0.680581i \(-0.761727\pi\)
0.732672 0.680581i \(-0.238273\pi\)
\(602\) −0.438447 + 2.43845i −0.0178698 + 0.0993837i
\(603\) 4.68213i 0.190671i
\(604\) 20.4924 0.833825
\(605\) −24.1671 −0.982531
\(606\) 3.12311 0.126867
\(607\) 22.7386i 0.922933i −0.887158 0.461466i \(-0.847324\pi\)
0.887158 0.461466i \(-0.152676\pi\)
\(608\) −7.31140 −0.296516
\(609\) −3.86098 + 21.4731i −0.156455 + 0.870133i
\(610\) 6.24621 0.252902
\(611\) 22.2462 0.899985
\(612\) −3.33513 −0.134815
\(613\) 41.8944i 1.69210i 0.533103 + 0.846050i \(0.321026\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(614\) 2.24621i 0.0906497i
\(615\) −37.0970 −1.49590
\(616\) 6.00000 33.3693i 0.241747 1.34449i
\(617\) 11.0571i 0.445142i −0.974916 0.222571i \(-0.928555\pi\)
0.974916 0.222571i \(-0.0714449\pi\)
\(618\) 5.20798i 0.209496i
\(619\) 29.7856 1.19719 0.598593 0.801053i \(-0.295727\pi\)
0.598593 + 0.801053i \(0.295727\pi\)
\(620\) 34.1725i 1.37240i
\(621\) 4.53448 1.56155i 0.181963 0.0626630i
\(622\) 2.63068i 0.105481i
\(623\) 26.0540 + 4.68466i 1.04383 + 0.187687i
\(624\) −3.12311 −0.125024
\(625\) −18.1231 −0.724924
\(626\) 14.3922 0.575229
\(627\) 6.24621 0.249450
\(628\) 15.2134 0.607080
\(629\) 6.24621i 0.249053i
\(630\) 8.68466 + 1.56155i 0.346005 + 0.0622138i
\(631\) 9.47954i 0.377375i 0.982037 + 0.188687i \(0.0604233\pi\)
−0.982037 + 0.188687i \(0.939577\pi\)
\(632\) 48.4494i 1.92721i
\(633\) 10.2462i 0.407250i
\(634\) 14.0000 0.556011
\(635\) −20.8319 −0.826690
\(636\) 10.0054 0.396740
\(637\) 7.61553 20.4924i 0.301738 0.811939i
\(638\) 35.2242i 1.39454i
\(639\) 11.1231 0.440023
\(640\) 10.0054 0.395498
\(641\) 46.0507i 1.81889i −0.415820 0.909447i \(-0.636505\pi\)
0.415820 0.909447i \(-0.363495\pi\)
\(642\) −9.06897 −0.357924
\(643\) −35.6347 −1.40530 −0.702649 0.711537i \(-0.747999\pi\)
−0.702649 + 0.711537i \(0.747999\pi\)
\(644\) −1.94317 12.5389i −0.0765715 0.494102i
\(645\) 3.12311 0.122972
\(646\) 4.87689 0.191879
\(647\) 35.6155i 1.40019i 0.714049 + 0.700095i \(0.246859\pi\)
−0.714049 + 0.700095i \(0.753141\pi\)
\(648\) 3.00000 0.117851
\(649\) −30.4268 −1.19435
\(650\) 19.1231i 0.750070i
\(651\) 26.6811 + 4.79741i 1.04571 + 0.188025i
\(652\) −12.0000 −0.469956
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) −12.2888 −0.480531
\(655\) 40.0216i 1.56377i
\(656\) 11.1231i 0.434284i
\(657\) 6.24621i 0.243688i
\(658\) 3.33513 18.5485i 0.130017 0.723096i
\(659\) 24.2824i 0.945906i 0.881088 + 0.472953i \(0.156812\pi\)
−0.881088 + 0.472953i \(0.843188\pi\)
\(660\) −14.2462 −0.554533
\(661\) 38.1487 1.48381 0.741907 0.670503i \(-0.233922\pi\)
0.741907 + 0.670503i \(0.233922\pi\)
\(662\) 16.4924 0.640996
\(663\) −10.4160 −0.404523
\(664\) −51.2587 −1.98922
\(665\) 12.6994 + 2.28343i 0.492461 + 0.0885475i
\(666\) 1.87285i 0.0725716i
\(667\) 12.8769 + 37.3923i 0.498595 + 1.44784i
\(668\) 5.75379i 0.222621i
\(669\) 4.00000 0.154649
\(670\) 15.6155i 0.603280i
\(671\) 8.00000i 0.308837i
\(672\) 2.34107 13.0200i 0.0903086 0.502256i
\(673\) −13.1231 −0.505859 −0.252929 0.967485i \(-0.581394\pi\)
−0.252929 + 0.967485i \(0.581394\pi\)
\(674\) 6.67026i 0.256929i
\(675\) 6.12311i 0.235678i
\(676\) −3.24621 −0.124854
\(677\) 9.18425 0.352979 0.176490 0.984302i \(-0.443526\pi\)
0.176490 + 0.984302i \(0.443526\pi\)
\(678\) 8.95369 0.343864
\(679\) 4.87689 + 0.876894i 0.187158 + 0.0336521i
\(680\) −33.3693 −1.27965
\(681\) 6.67026i 0.255605i
\(682\) 43.7673 1.67594
\(683\) 7.12311 0.272558 0.136279 0.990670i \(-0.456486\pi\)
0.136279 + 0.990670i \(0.456486\pi\)
\(684\) 1.46228 0.0559116
\(685\) 49.3693i 1.88630i
\(686\) −15.9445 9.42190i −0.608765 0.359730i
\(687\) 12.2888i 0.468848i
\(688\) 0.936426i 0.0357009i
\(689\) 31.2479 1.19045
\(690\) 15.1231 5.20798i 0.575727 0.198265i
\(691\) 2.24621i 0.0854499i −0.999087 0.0427250i \(-0.986396\pi\)
0.999087 0.0427250i \(-0.0136039\pi\)
\(692\) 3.12311i 0.118723i
\(693\) −2.00000 + 11.1231i −0.0759737 + 0.422532i
\(694\) 16.4924 0.626044
\(695\) 40.0216i 1.51811i
\(696\) 24.7386i 0.937715i
\(697\) 37.0970i 1.40515i
\(698\) 9.36932i 0.354634i
\(699\) 3.75379i 0.141981i
\(700\) −15.9445 2.86692i −0.602646 0.108359i
\(701\) 13.7511i 0.519372i −0.965693 0.259686i \(-0.916381\pi\)
0.965693 0.259686i \(-0.0836191\pi\)
\(702\) 3.12311 0.117874
\(703\) 2.73863i 0.103290i
\(704\) 29.9009i 1.12693i
\(705\) −23.7565 −0.894721
\(706\) 17.3693i 0.653703i
\(707\) −1.46228 + 8.13254i −0.0549947 + 0.305856i
\(708\) −7.12311 −0.267703
\(709\) 27.7328i 1.04153i 0.853701 + 0.520763i \(0.174352\pi\)
−0.853701 + 0.520763i \(0.825648\pi\)
\(710\) 37.0970 1.39223
\(711\) 16.1498i 0.605665i
\(712\) 30.0162 1.12490
\(713\) 46.4613 16.0000i 1.73999 0.599205i
\(714\) −1.56155 + 8.68466i −0.0584396 + 0.325015i
\(715\) −44.4924 −1.66392
\(716\) 4.00000 0.149487
\(717\) 1.36932i 0.0511381i
\(718\) 25.3341i 0.945459i
\(719\) 2.63068i 0.0981079i −0.998796 0.0490540i \(-0.984379\pi\)
0.998796 0.0490540i \(-0.0156206\pi\)
\(720\) 3.33513 0.124293
\(721\) −13.5616 2.43845i −0.505059 0.0908125i
\(722\) 16.8617 0.627529
\(723\) 11.4677i 0.426487i
\(724\) 12.2888 0.456710
\(725\) 50.4924 1.87524
\(726\) 7.24621i 0.268932i
\(727\) 52.7210 1.95531 0.977656 0.210209i \(-0.0674145\pi\)
0.977656 + 0.210209i \(0.0674145\pi\)
\(728\) 4.38684 24.3976i 0.162587 0.904236i
\(729\) −1.00000 −0.0370370
\(730\) 20.8319i 0.771025i
\(731\) 3.12311i 0.115512i
\(732\) 1.87285i 0.0692226i
\(733\) 8.54312 0.315547 0.157774 0.987475i \(-0.449568\pi\)
0.157774 + 0.987475i \(0.449568\pi\)
\(734\) 12.6994 0.468743
\(735\) −8.13254 + 21.8836i −0.299973 + 0.807190i
\(736\) −7.80776 22.6724i −0.287798 0.835717i
\(737\) 20.0000 0.736709
\(738\) 11.1231i 0.409447i
\(739\) 14.7386 0.542169 0.271085 0.962555i \(-0.412618\pi\)
0.271085 + 0.962555i \(0.412618\pi\)
\(740\) 6.24621i 0.229615i
\(741\) 4.56685 0.167768
\(742\) 4.68466 26.0540i 0.171979 0.956472i
\(743\) 7.19612i 0.264000i 0.991250 + 0.132000i \(0.0421399\pi\)
−0.991250 + 0.132000i \(0.957860\pi\)
\(744\) 30.7386 1.12693
\(745\) 1.36932i 0.0501679i
\(746\) 15.2134i 0.557001i
\(747\) 17.0862 0.625153
\(748\) 14.2462i 0.520893i
\(749\) 4.24621 23.6155i 0.155153 0.862893i
\(750\) 3.74571i 0.136774i
\(751\) 3.03984i 0.110925i −0.998461 0.0554626i \(-0.982337\pi\)
0.998461 0.0554626i \(-0.0176634\pi\)
\(752\) 7.12311i 0.259753i
\(753\) 0.821147i 0.0299243i
\(754\) 25.7538i 0.937898i
\(755\) −68.3449 −2.48733
\(756\) −0.468213 + 2.60399i −0.0170287 + 0.0947063i
\(757\) 12.2888i 0.446645i 0.974745 + 0.223322i \(0.0716903\pi\)
−0.974745 + 0.223322i \(0.928310\pi\)
\(758\) 21.7684i 0.790663i
\(759\) 6.67026 + 19.3693i 0.242115 + 0.703062i
\(760\) 14.6307 0.530711
\(761\) 20.8769i 0.756787i 0.925645 + 0.378393i \(0.123523\pi\)
−0.925645 + 0.378393i \(0.876477\pi\)
\(762\) 6.24621i 0.226276i
\(763\) 5.75379 32.0000i 0.208301 1.15848i
\(764\) 3.45041i 0.124832i
\(765\) 11.1231 0.402157
\(766\) 16.2651 0.587681
\(767\) −22.2462 −0.803264
\(768\) 17.0000i 0.613435i
\(769\) 37.3276 1.34607 0.673034 0.739612i \(-0.264991\pi\)
0.673034 + 0.739612i \(0.264991\pi\)
\(770\) −6.67026 + 37.0970i −0.240380 + 1.33688i
\(771\) 17.3693 0.625541
\(772\) −25.6155 −0.921923
\(773\) −14.5722 −0.524127 −0.262064 0.965051i \(-0.584403\pi\)
−0.262064 + 0.965051i \(0.584403\pi\)
\(774\) 0.936426i 0.0336592i
\(775\) 62.7386i 2.25364i
\(776\) 5.61856 0.201694
\(777\) 4.87689 + 0.876894i 0.174958 + 0.0314584i
\(778\) 14.5722i 0.522440i
\(779\) 16.2651i 0.582757i
\(780\) −10.4160 −0.372952
\(781\) 47.5130i 1.70015i
\(782\) 5.20798 + 15.1231i 0.186237 + 0.540801i
\(783\) 8.24621i 0.294696i
\(784\) −6.56155 2.43845i −0.234341 0.0870874i
\(785\) −50.7386 −1.81094
\(786\) −12.0000 −0.428026
\(787\) −29.7856 −1.06174 −0.530872 0.847452i \(-0.678135\pi\)
−0.530872 + 0.847452i \(0.678135\pi\)
\(788\) −18.4924