Properties

Label 525.2.j.b.218.12
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.12
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.79963 + 1.79963i) q^{2} +(1.66094 - 0.491204i) q^{3} +4.47734i q^{4} +(3.87306 + 2.10509i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-4.45829 + 4.45829i) q^{8} +(2.51744 - 1.63172i) q^{9} +O(q^{10})\) \(q+(1.79963 + 1.79963i) q^{2} +(1.66094 - 0.491204i) q^{3} +4.47734i q^{4} +(3.87306 + 2.10509i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-4.45829 + 4.45829i) q^{8} +(2.51744 - 1.63172i) q^{9} +1.56870i q^{11} +(2.19929 + 7.43658i) q^{12} +(-2.21881 - 2.21881i) q^{13} +2.54506 q^{14} -7.09187 q^{16} +(-3.60725 - 3.60725i) q^{17} +(7.46695 + 1.59396i) q^{18} +1.68040i q^{19} +(0.827127 - 1.52180i) q^{21} +(-2.82308 + 2.82308i) q^{22} +(-0.995850 + 0.995850i) q^{23} +(-5.21502 + 9.59488i) q^{24} -7.98606i q^{26} +(3.37980 - 3.94676i) q^{27} +(3.16595 + 3.16595i) q^{28} -8.91955 q^{29} +2.74834 q^{31} +(-3.84616 - 3.84616i) q^{32} +(0.770553 + 2.60552i) q^{33} -12.9834i q^{34} +(7.30576 + 11.2714i) q^{36} +(-0.440360 + 0.440360i) q^{37} +(-3.02410 + 3.02410i) q^{38} +(-4.77519 - 2.59542i) q^{39} -6.44292i q^{41} +(4.22719 - 1.25015i) q^{42} +(5.47734 + 5.47734i) q^{43} -7.02360 q^{44} -3.58432 q^{46} +(-3.69358 - 3.69358i) q^{47} +(-11.7792 + 3.48356i) q^{48} -1.00000i q^{49} +(-7.76331 - 4.21952i) q^{51} +(9.93435 - 9.93435i) q^{52} +(-2.83358 + 2.83358i) q^{53} +(13.1851 - 1.02033i) q^{54} +6.30497i q^{56} +(0.825420 + 2.79104i) q^{57} +(-16.0519 - 16.0519i) q^{58} +5.54871 q^{59} +7.40665 q^{61} +(4.94599 + 4.94599i) q^{62} +(0.626296 - 2.93390i) q^{63} +0.340400i q^{64} +(-3.30226 + 6.07568i) q^{66} +(3.75240 - 3.75240i) q^{67} +(16.1509 - 16.1509i) q^{68} +(-1.16488 + 2.14321i) q^{69} +3.61943i q^{71} +(-3.94878 + 18.4981i) q^{72} +(5.89737 + 5.89737i) q^{73} -1.58497 q^{74} -7.52372 q^{76} +(1.10924 + 1.10924i) q^{77} +(-3.92279 - 13.2644i) q^{78} -17.0572i q^{79} +(3.67497 - 8.21551i) q^{81} +(11.5949 - 11.5949i) q^{82} +(-3.21312 + 3.21312i) q^{83} +(6.81359 + 3.70333i) q^{84} +19.7144i q^{86} +(-14.8148 + 4.38132i) q^{87} +(-6.99372 - 6.99372i) q^{88} -9.40273 q^{89} -3.13787 q^{91} +(-4.45876 - 4.45876i) q^{92} +(4.56482 - 1.35000i) q^{93} -13.2941i q^{94} +(-8.27749 - 4.49899i) q^{96} +(-4.39640 + 4.39640i) q^{97} +(1.79963 - 1.79963i) q^{98} +(2.55968 + 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79963 + 1.79963i 1.27253 + 1.27253i 0.944756 + 0.327775i \(0.106299\pi\)
0.327775 + 0.944756i \(0.393701\pi\)
\(3\) 1.66094 0.491204i 0.958944 0.283597i
\(4\) 4.47734i 2.23867i
\(5\) 0 0
\(6\) 3.87306 + 2.10509i 1.58117 + 0.859399i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) −4.45829 + 4.45829i −1.57624 + 1.57624i
\(9\) 2.51744 1.63172i 0.839146 0.543907i
\(10\) 0 0
\(11\) 1.56870i 0.472981i 0.971634 + 0.236491i \(0.0759973\pi\)
−0.971634 + 0.236491i \(0.924003\pi\)
\(12\) 2.19929 + 7.43658i 0.634880 + 2.14676i
\(13\) −2.21881 2.21881i −0.615386 0.615386i 0.328958 0.944345i \(-0.393303\pi\)
−0.944345 + 0.328958i \(0.893303\pi\)
\(14\) 2.54506 0.680196
\(15\) 0 0
\(16\) −7.09187 −1.77297
\(17\) −3.60725 3.60725i −0.874886 0.874886i 0.118114 0.993000i \(-0.462315\pi\)
−0.993000 + 0.118114i \(0.962315\pi\)
\(18\) 7.46695 + 1.59396i 1.75998 + 0.375700i
\(19\) 1.68040i 0.385510i 0.981247 + 0.192755i \(0.0617423\pi\)
−0.981247 + 0.192755i \(0.938258\pi\)
\(20\) 0 0
\(21\) 0.827127 1.52180i 0.180494 0.332083i
\(22\) −2.82308 + 2.82308i −0.601883 + 0.601883i
\(23\) −0.995850 + 0.995850i −0.207649 + 0.207649i −0.803268 0.595618i \(-0.796907\pi\)
0.595618 + 0.803268i \(0.296907\pi\)
\(24\) −5.21502 + 9.59488i −1.06451 + 1.95855i
\(25\) 0 0
\(26\) 7.98606i 1.56620i
\(27\) 3.37980 3.94676i 0.650443 0.759555i
\(28\) 3.16595 + 3.16595i 0.598309 + 0.598309i
\(29\) −8.91955 −1.65632 −0.828159 0.560493i \(-0.810612\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(30\) 0 0
\(31\) 2.74834 0.493616 0.246808 0.969064i \(-0.420618\pi\)
0.246808 + 0.969064i \(0.420618\pi\)
\(32\) −3.84616 3.84616i −0.679912 0.679912i
\(33\) 0.770553 + 2.60552i 0.134136 + 0.453562i
\(34\) 12.9834i 2.22664i
\(35\) 0 0
\(36\) 7.30576 + 11.2714i 1.21763 + 1.87857i
\(37\) −0.440360 + 0.440360i −0.0723947 + 0.0723947i −0.742377 0.669982i \(-0.766302\pi\)
0.669982 + 0.742377i \(0.266302\pi\)
\(38\) −3.02410 + 3.02410i −0.490574 + 0.490574i
\(39\) −4.77519 2.59542i −0.764643 0.415599i
\(40\) 0 0
\(41\) 6.44292i 1.00622i −0.864224 0.503108i \(-0.832190\pi\)
0.864224 0.503108i \(-0.167810\pi\)
\(42\) 4.22719 1.25015i 0.652270 0.192902i
\(43\) 5.47734 + 5.47734i 0.835286 + 0.835286i 0.988234 0.152948i \(-0.0488768\pi\)
−0.152948 + 0.988234i \(0.548877\pi\)
\(44\) −7.02360 −1.05885
\(45\) 0 0
\(46\) −3.58432 −0.528480
\(47\) −3.69358 3.69358i −0.538763 0.538763i 0.384402 0.923166i \(-0.374408\pi\)
−0.923166 + 0.384402i \(0.874408\pi\)
\(48\) −11.7792 + 3.48356i −1.70018 + 0.502808i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −7.76331 4.21952i −1.08708 0.590851i
\(52\) 9.93435 9.93435i 1.37765 1.37765i
\(53\) −2.83358 + 2.83358i −0.389222 + 0.389222i −0.874410 0.485188i \(-0.838751\pi\)
0.485188 + 0.874410i \(0.338751\pi\)
\(54\) 13.1851 1.02033i 1.79427 0.138849i
\(55\) 0 0
\(56\) 6.30497i 0.842537i
\(57\) 0.825420 + 2.79104i 0.109330 + 0.369683i
\(58\) −16.0519 16.0519i −2.10772 2.10772i
\(59\) 5.54871 0.722381 0.361191 0.932492i \(-0.382370\pi\)
0.361191 + 0.932492i \(0.382370\pi\)
\(60\) 0 0
\(61\) 7.40665 0.948325 0.474162 0.880437i \(-0.342751\pi\)
0.474162 + 0.880437i \(0.342751\pi\)
\(62\) 4.94599 + 4.94599i 0.628141 + 0.628141i
\(63\) 0.626296 2.93390i 0.0789058 0.369636i
\(64\) 0.340400i 0.0425500i
\(65\) 0 0
\(66\) −3.30226 + 6.07568i −0.406480 + 0.747864i
\(67\) 3.75240 3.75240i 0.458429 0.458429i −0.439711 0.898139i \(-0.644919\pi\)
0.898139 + 0.439711i \(0.144919\pi\)
\(68\) 16.1509 16.1509i 1.95858 1.95858i
\(69\) −1.16488 + 2.14321i −0.140235 + 0.258012i
\(70\) 0 0
\(71\) 3.61943i 0.429548i 0.976664 + 0.214774i \(0.0689015\pi\)
−0.976664 + 0.214774i \(0.931099\pi\)
\(72\) −3.94878 + 18.4981i −0.465368 + 2.18003i
\(73\) 5.89737 + 5.89737i 0.690235 + 0.690235i 0.962284 0.272049i \(-0.0877011\pi\)
−0.272049 + 0.962284i \(0.587701\pi\)
\(74\) −1.58497 −0.184249
\(75\) 0 0
\(76\) −7.52372 −0.863030
\(77\) 1.10924 + 1.10924i 0.126410 + 0.126410i
\(78\) −3.92279 13.2644i −0.444168 1.50189i
\(79\) 17.0572i 1.91909i −0.281558 0.959544i \(-0.590851\pi\)
0.281558 0.959544i \(-0.409149\pi\)
\(80\) 0 0
\(81\) 3.67497 8.21551i 0.408330 0.912834i
\(82\) 11.5949 11.5949i 1.28044 1.28044i
\(83\) −3.21312 + 3.21312i −0.352686 + 0.352686i −0.861108 0.508422i \(-0.830229\pi\)
0.508422 + 0.861108i \(0.330229\pi\)
\(84\) 6.81359 + 3.70333i 0.743423 + 0.404066i
\(85\) 0 0
\(86\) 19.7144i 2.12585i
\(87\) −14.8148 + 4.38132i −1.58832 + 0.469727i
\(88\) −6.99372 6.99372i −0.745533 0.745533i
\(89\) −9.40273 −0.996688 −0.498344 0.866979i \(-0.666058\pi\)
−0.498344 + 0.866979i \(0.666058\pi\)
\(90\) 0 0
\(91\) −3.13787 −0.328938
\(92\) −4.45876 4.45876i −0.464858 0.464858i
\(93\) 4.56482 1.35000i 0.473350 0.139988i
\(94\) 13.2941i 1.37119i
\(95\) 0 0
\(96\) −8.27749 4.49899i −0.844818 0.459176i
\(97\) −4.39640 + 4.39640i −0.446386 + 0.446386i −0.894151 0.447765i \(-0.852220\pi\)
0.447765 + 0.894151i \(0.352220\pi\)
\(98\) 1.79963 1.79963i 0.181790 0.181790i
\(99\) 2.55968 + 3.94911i 0.257258 + 0.396900i
\(100\) 0 0
\(101\) 1.01132i 0.100630i −0.998733 0.0503152i \(-0.983977\pi\)
0.998733 0.0503152i \(-0.0160226\pi\)
\(102\) −6.37751 21.5647i −0.631468 2.13522i
\(103\) 4.03058 + 4.03058i 0.397145 + 0.397145i 0.877225 0.480080i \(-0.159392\pi\)
−0.480080 + 0.877225i \(0.659392\pi\)
\(104\) 19.7842 1.94000
\(105\) 0 0
\(106\) −10.1988 −0.990593
\(107\) −2.81760 2.81760i −0.272388 0.272388i 0.557673 0.830061i \(-0.311694\pi\)
−0.830061 + 0.557673i \(0.811694\pi\)
\(108\) 17.6710 + 15.1325i 1.70039 + 1.45613i
\(109\) 6.42246i 0.615160i 0.951522 + 0.307580i \(0.0995192\pi\)
−0.951522 + 0.307580i \(0.900481\pi\)
\(110\) 0 0
\(111\) −0.515104 + 0.947718i −0.0488915 + 0.0899534i
\(112\) −5.01471 + 5.01471i −0.473845 + 0.473845i
\(113\) −3.29246 + 3.29246i −0.309729 + 0.309729i −0.844804 0.535075i \(-0.820283\pi\)
0.535075 + 0.844804i \(0.320283\pi\)
\(114\) −3.53739 + 6.50830i −0.331307 + 0.609558i
\(115\) 0 0
\(116\) 39.9358i 3.70795i
\(117\) −9.20618 1.96523i −0.851112 0.181686i
\(118\) 9.98563 + 9.98563i 0.919252 + 0.919252i
\(119\) −5.10142 −0.467646
\(120\) 0 0
\(121\) 8.53918 0.776289
\(122\) 13.3292 + 13.3292i 1.20677 + 1.20677i
\(123\) −3.16479 10.7013i −0.285360 0.964904i
\(124\) 12.3052i 1.10504i
\(125\) 0 0
\(126\) 6.40703 4.15283i 0.570784 0.369963i
\(127\) −14.2818 + 14.2818i −1.26730 + 1.26730i −0.319826 + 0.947476i \(0.603624\pi\)
−0.947476 + 0.319826i \(0.896376\pi\)
\(128\) −8.30492 + 8.30492i −0.734058 + 0.734058i
\(129\) 11.7880 + 6.40703i 1.03788 + 0.564108i
\(130\) 0 0
\(131\) 4.89729i 0.427878i 0.976847 + 0.213939i \(0.0686294\pi\)
−0.976847 + 0.213939i \(0.931371\pi\)
\(132\) −11.6658 + 3.45002i −1.01538 + 0.300286i
\(133\) 1.18822 + 1.18822i 0.103032 + 0.103032i
\(134\) 13.5059 1.16673
\(135\) 0 0
\(136\) 32.1643 2.75807
\(137\) 4.55880 + 4.55880i 0.389485 + 0.389485i 0.874504 0.485019i \(-0.161187\pi\)
−0.485019 + 0.874504i \(0.661187\pi\)
\(138\) −5.95334 + 1.76064i −0.506782 + 0.149875i
\(139\) 10.2045i 0.865536i 0.901505 + 0.432768i \(0.142463\pi\)
−0.901505 + 0.432768i \(0.857537\pi\)
\(140\) 0 0
\(141\) −7.94911 4.32050i −0.669435 0.363852i
\(142\) −6.51364 + 6.51364i −0.546613 + 0.546613i
\(143\) 3.48065 3.48065i 0.291066 0.291066i
\(144\) −17.8533 + 11.5720i −1.48778 + 0.964329i
\(145\) 0 0
\(146\) 21.2262i 1.75669i
\(147\) −0.491204 1.66094i −0.0405139 0.136992i
\(148\) −1.97164 1.97164i −0.162068 0.162068i
\(149\) −0.923124 −0.0756253 −0.0378126 0.999285i \(-0.512039\pi\)
−0.0378126 + 0.999285i \(0.512039\pi\)
\(150\) 0 0
\(151\) −13.7310 −1.11741 −0.558705 0.829366i \(-0.688702\pi\)
−0.558705 + 0.829366i \(0.688702\pi\)
\(152\) −7.49171 7.49171i −0.607658 0.607658i
\(153\) −14.9670 3.19499i −1.21001 0.258300i
\(154\) 3.99244i 0.321720i
\(155\) 0 0
\(156\) 11.6205 21.3801i 0.930389 1.71178i
\(157\) 13.7211 13.7211i 1.09506 1.09506i 0.100086 0.994979i \(-0.468088\pi\)
0.994979 0.100086i \(-0.0319118\pi\)
\(158\) 30.6967 30.6967i 2.44210 2.44210i
\(159\) −3.31453 + 6.09826i −0.262859 + 0.483624i
\(160\) 0 0
\(161\) 1.40834i 0.110993i
\(162\) 21.3985 8.17128i 1.68122 0.641997i
\(163\) −6.60566 6.60566i −0.517395 0.517395i 0.399387 0.916782i \(-0.369223\pi\)
−0.916782 + 0.399387i \(0.869223\pi\)
\(164\) 28.8471 2.25258
\(165\) 0 0
\(166\) −11.5649 −0.897607
\(167\) 3.11442 + 3.11442i 0.241001 + 0.241001i 0.817264 0.576263i \(-0.195490\pi\)
−0.576263 + 0.817264i \(0.695490\pi\)
\(168\) 3.09703 + 10.4722i 0.238941 + 0.807946i
\(169\) 3.15379i 0.242599i
\(170\) 0 0
\(171\) 2.74195 + 4.23030i 0.209682 + 0.323499i
\(172\) −24.5239 + 24.5239i −1.86993 + 1.86993i
\(173\) −8.12870 + 8.12870i −0.618013 + 0.618013i −0.945022 0.327008i \(-0.893960\pi\)
0.327008 + 0.945022i \(0.393960\pi\)
\(174\) −34.5460 18.7764i −2.61892 1.42344i
\(175\) 0 0
\(176\) 11.1250i 0.838580i
\(177\) 9.21608 2.72555i 0.692723 0.204865i
\(178\) −16.9214 16.9214i −1.26832 1.26832i
\(179\) 16.5980 1.24059 0.620297 0.784367i \(-0.287012\pi\)
0.620297 + 0.784367i \(0.287012\pi\)
\(180\) 0 0
\(181\) 11.6532 0.866174 0.433087 0.901352i \(-0.357424\pi\)
0.433087 + 0.901352i \(0.357424\pi\)
\(182\) −5.64700 5.64700i −0.418583 0.418583i
\(183\) 12.3020 3.63818i 0.909390 0.268942i
\(184\) 8.87958i 0.654611i
\(185\) 0 0
\(186\) 10.6445 + 5.78550i 0.780491 + 0.424213i
\(187\) 5.65869 5.65869i 0.413805 0.413805i
\(188\) 16.5374 16.5374i 1.20611 1.20611i
\(189\) −0.400905 5.18066i −0.0291615 0.376838i
\(190\) 0 0
\(191\) 12.8543i 0.930108i −0.885282 0.465054i \(-0.846035\pi\)
0.885282 0.465054i \(-0.153965\pi\)
\(192\) 0.167206 + 0.565384i 0.0120671 + 0.0408031i
\(193\) 8.06158 + 8.06158i 0.580285 + 0.580285i 0.934982 0.354696i \(-0.115416\pi\)
−0.354696 + 0.934982i \(0.615416\pi\)
\(194\) −15.8238 −1.13608
\(195\) 0 0
\(196\) 4.47734 0.319810
\(197\) 18.7512 + 18.7512i 1.33597 + 1.33597i 0.899929 + 0.436036i \(0.143618\pi\)
0.436036 + 0.899929i \(0.356382\pi\)
\(198\) −2.50045 + 11.7134i −0.177699 + 0.832436i
\(199\) 4.20728i 0.298246i 0.988819 + 0.149123i \(0.0476451\pi\)
−0.988819 + 0.149123i \(0.952355\pi\)
\(200\) 0 0
\(201\) 4.38931 8.07570i 0.309598 0.569616i
\(202\) 1.82001 1.82001i 0.128055 0.128055i
\(203\) −6.30707 + 6.30707i −0.442670 + 0.442670i
\(204\) 18.8922 34.7590i 1.32272 2.43361i
\(205\) 0 0
\(206\) 14.5071i 1.01076i
\(207\) −0.882040 + 4.13194i −0.0613060 + 0.287190i
\(208\) 15.7355 + 15.7355i 1.09106 + 1.09106i
\(209\) −2.63605 −0.182339
\(210\) 0 0
\(211\) −21.5211 −1.48158 −0.740788 0.671739i \(-0.765548\pi\)
−0.740788 + 0.671739i \(0.765548\pi\)
\(212\) −12.6869 12.6869i −0.871338 0.871338i
\(213\) 1.77788 + 6.01166i 0.121818 + 0.411912i
\(214\) 10.1413i 0.693244i
\(215\) 0 0
\(216\) 2.52769 + 32.6639i 0.171988 + 2.22250i
\(217\) 1.94337 1.94337i 0.131924 0.131924i
\(218\) −11.5581 + 11.5581i −0.782810 + 0.782810i
\(219\) 12.6920 + 6.89836i 0.857645 + 0.466148i
\(220\) 0 0
\(221\) 16.0076i 1.07679i
\(222\) −2.63254 + 0.778544i −0.176684 + 0.0522525i
\(223\) −12.4001 12.4001i −0.830375 0.830375i 0.157193 0.987568i \(-0.449756\pi\)
−0.987568 + 0.157193i \(0.949756\pi\)
\(224\) −5.43929 −0.363428
\(225\) 0 0
\(226\) −11.8504 −0.788279
\(227\) 8.70556 + 8.70556i 0.577809 + 0.577809i 0.934299 0.356490i \(-0.116027\pi\)
−0.356490 + 0.934299i \(0.616027\pi\)
\(228\) −12.4964 + 3.69568i −0.827597 + 0.244753i
\(229\) 4.46342i 0.294951i 0.989066 + 0.147476i \(0.0471148\pi\)
−0.989066 + 0.147476i \(0.952885\pi\)
\(230\) 0 0
\(231\) 2.38724 + 1.29752i 0.157069 + 0.0853703i
\(232\) 39.7659 39.7659i 2.61076 2.61076i
\(233\) 5.64161 5.64161i 0.369594 0.369594i −0.497735 0.867329i \(-0.665835\pi\)
0.867329 + 0.497735i \(0.165835\pi\)
\(234\) −13.0310 20.1044i −0.851865 1.31427i
\(235\) 0 0
\(236\) 24.8435i 1.61717i
\(237\) −8.37859 28.3310i −0.544248 1.84030i
\(238\) −9.18066 9.18066i −0.595094 0.595094i
\(239\) 11.8594 0.767124 0.383562 0.923515i \(-0.374697\pi\)
0.383562 + 0.923515i \(0.374697\pi\)
\(240\) 0 0
\(241\) −18.0723 −1.16414 −0.582071 0.813138i \(-0.697757\pi\)
−0.582071 + 0.813138i \(0.697757\pi\)
\(242\) 15.3674 + 15.3674i 0.987851 + 0.987851i
\(243\) 2.06841 15.4506i 0.132689 0.991158i
\(244\) 33.1621i 2.12298i
\(245\) 0 0
\(246\) 13.5629 24.9538i 0.864741 1.59100i
\(247\) 3.72849 3.72849i 0.237238 0.237238i
\(248\) −12.2529 + 12.2529i −0.778059 + 0.778059i
\(249\) −3.75850 + 6.91510i −0.238185 + 0.438226i
\(250\) 0 0
\(251\) 3.19253i 0.201511i 0.994911 + 0.100755i \(0.0321259\pi\)
−0.994911 + 0.100755i \(0.967874\pi\)
\(252\) 13.1360 + 2.80414i 0.827493 + 0.176644i
\(253\) −1.56219 1.56219i −0.0982141 0.0982141i
\(254\) −51.4038 −3.22536
\(255\) 0 0
\(256\) −29.2108 −1.82567
\(257\) −11.8118 11.8118i −0.736799 0.736799i 0.235158 0.971957i \(-0.424439\pi\)
−0.971957 + 0.235158i \(0.924439\pi\)
\(258\) 9.68378 + 32.7443i 0.602886 + 2.03857i
\(259\) 0.622763i 0.0386966i
\(260\) 0 0
\(261\) −22.4544 + 14.5542i −1.38989 + 0.900883i
\(262\) −8.81331 + 8.81331i −0.544488 + 0.544488i
\(263\) −13.1502 + 13.1502i −0.810874 + 0.810874i −0.984765 0.173891i \(-0.944366\pi\)
0.173891 + 0.984765i \(0.444366\pi\)
\(264\) −15.0515 8.18080i −0.926356 0.503493i
\(265\) 0 0
\(266\) 4.27672i 0.262223i
\(267\) −15.6174 + 4.61866i −0.955767 + 0.282658i
\(268\) 16.8008 + 16.8008i 1.02627 + 1.02627i
\(269\) −29.3405 −1.78892 −0.894461 0.447146i \(-0.852441\pi\)
−0.894461 + 0.447146i \(0.852441\pi\)
\(270\) 0 0
\(271\) 3.18366 0.193394 0.0966968 0.995314i \(-0.469172\pi\)
0.0966968 + 0.995314i \(0.469172\pi\)
\(272\) 25.5821 + 25.5821i 1.55114 + 1.55114i
\(273\) −5.21181 + 1.54133i −0.315433 + 0.0932858i
\(274\) 16.4083i 0.991263i
\(275\) 0 0
\(276\) −9.59588 5.21556i −0.577604 0.313940i
\(277\) −16.8636 + 16.8636i −1.01324 + 1.01324i −0.0133247 + 0.999911i \(0.504242\pi\)
−0.999911 + 0.0133247i \(0.995758\pi\)
\(278\) −18.3644 + 18.3644i −1.10142 + 1.10142i
\(279\) 6.91877 4.48452i 0.414216 0.268481i
\(280\) 0 0
\(281\) 24.8052i 1.47975i 0.672742 + 0.739877i \(0.265116\pi\)
−0.672742 + 0.739877i \(0.734884\pi\)
\(282\) −6.53014 22.0808i −0.388864 1.31489i
\(283\) −5.41918 5.41918i −0.322137 0.322137i 0.527449 0.849586i \(-0.323148\pi\)
−0.849586 + 0.527449i \(0.823148\pi\)
\(284\) −16.2054 −0.961615
\(285\) 0 0
\(286\) 12.5277 0.740781
\(287\) −4.55583 4.55583i −0.268922 0.268922i
\(288\) −15.9583 3.40661i −0.940354 0.200736i
\(289\) 9.02446i 0.530850i
\(290\) 0 0
\(291\) −5.14262 + 9.46168i −0.301466 + 0.554653i
\(292\) −26.4045 + 26.4045i −1.54521 + 1.54521i
\(293\) −8.60739 + 8.60739i −0.502849 + 0.502849i −0.912322 0.409473i \(-0.865712\pi\)
0.409473 + 0.912322i \(0.365712\pi\)
\(294\) 2.10509 3.87306i 0.122771 0.225882i
\(295\) 0 0
\(296\) 3.92650i 0.228223i
\(297\) 6.19129 + 5.30190i 0.359255 + 0.307647i
\(298\) −1.66128 1.66128i −0.0962355 0.0962355i
\(299\) 4.41920 0.255569
\(300\) 0 0
\(301\) 7.74612 0.446479
\(302\) −24.7107 24.7107i −1.42194 1.42194i
\(303\) −0.496766 1.67975i −0.0285385 0.0964989i
\(304\) 11.9172i 0.683497i
\(305\) 0 0
\(306\) −21.1853 32.6849i −1.21108 1.86847i
\(307\) 11.8525 11.8525i 0.676457 0.676457i −0.282740 0.959197i \(-0.591243\pi\)
0.959197 + 0.282740i \(0.0912434\pi\)
\(308\) −4.96644 + 4.96644i −0.282989 + 0.282989i
\(309\) 8.67440 + 4.71471i 0.493469 + 0.268211i
\(310\) 0 0
\(311\) 29.2800i 1.66032i −0.557528 0.830158i \(-0.688250\pi\)
0.557528 0.830158i \(-0.311750\pi\)
\(312\) 32.8603 9.71807i 1.86035 0.550177i
\(313\) −1.22577 1.22577i −0.0692848 0.0692848i 0.671615 0.740900i \(-0.265601\pi\)
−0.740900 + 0.671615i \(0.765601\pi\)
\(314\) 49.3859 2.78701
\(315\) 0 0
\(316\) 76.3710 4.29620
\(317\) 4.30159 + 4.30159i 0.241601 + 0.241601i 0.817512 0.575911i \(-0.195353\pi\)
−0.575911 + 0.817512i \(0.695353\pi\)
\(318\) −16.9395 + 5.00968i −0.949922 + 0.280929i
\(319\) 13.9921i 0.783408i
\(320\) 0 0
\(321\) −6.06388 3.29585i −0.338453 0.183956i
\(322\) −2.53450 + 2.53450i −0.141242 + 0.141242i
\(323\) 6.06162 6.06162i 0.337278 0.337278i
\(324\) 36.7836 + 16.4541i 2.04353 + 0.914116i
\(325\) 0 0
\(326\) 23.7755i 1.31680i
\(327\) 3.15474 + 10.6673i 0.174458 + 0.589904i
\(328\) 28.7244 + 28.7244i 1.58604 + 1.58604i
\(329\) −5.22351 −0.287981
\(330\) 0 0
\(331\) 33.2602 1.82815 0.914074 0.405548i \(-0.132919\pi\)
0.914074 + 0.405548i \(0.132919\pi\)
\(332\) −14.3862 14.3862i −0.789547 0.789547i
\(333\) −0.390034 + 1.82712i −0.0213737 + 0.100126i
\(334\) 11.2096i 0.613363i
\(335\) 0 0
\(336\) −5.86588 + 10.7924i −0.320010 + 0.588772i
\(337\) −10.3056 + 10.3056i −0.561383 + 0.561383i −0.929700 0.368317i \(-0.879934\pi\)
0.368317 + 0.929700i \(0.379934\pi\)
\(338\) 5.67565 5.67565i 0.308715 0.308715i
\(339\) −3.85131 + 7.08585i −0.209174 + 0.384851i
\(340\) 0 0
\(341\) 4.31132i 0.233471i
\(342\) −2.67849 + 12.5475i −0.144836 + 0.678489i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −48.8391 −2.63323
\(345\) 0 0
\(346\) −29.2573 −1.57288
\(347\) −19.2241 19.2241i −1.03200 1.03200i −0.999471 0.0325323i \(-0.989643\pi\)
−0.0325323 0.999471i \(-0.510357\pi\)
\(348\) −19.6166 66.3310i −1.05156 3.55571i
\(349\) 30.1301i 1.61283i −0.591353 0.806413i \(-0.701406\pi\)
0.591353 0.806413i \(-0.298594\pi\)
\(350\) 0 0
\(351\) −16.2562 + 1.25799i −0.867694 + 0.0671463i
\(352\) 6.03348 6.03348i 0.321586 0.321586i
\(353\) 17.0339 17.0339i 0.906625 0.906625i −0.0893729 0.995998i \(-0.528486\pi\)
0.995998 + 0.0893729i \(0.0284863\pi\)
\(354\) 21.4905 + 11.6805i 1.14221 + 0.620814i
\(355\) 0 0
\(356\) 42.0992i 2.23125i
\(357\) −8.47314 + 2.50584i −0.448446 + 0.132623i
\(358\) 29.8703 + 29.8703i 1.57869 + 1.57869i
\(359\) 0.737982 0.0389492 0.0194746 0.999810i \(-0.493801\pi\)
0.0194746 + 0.999810i \(0.493801\pi\)
\(360\) 0 0
\(361\) 16.1763 0.851382
\(362\) 20.9714 + 20.9714i 1.10223 + 1.10223i
\(363\) 14.1831 4.19448i 0.744417 0.220153i
\(364\) 14.0493i 0.736383i
\(365\) 0 0
\(366\) 28.6864 + 15.5917i 1.49946 + 0.814990i
\(367\) −23.2923 + 23.2923i −1.21585 + 1.21585i −0.246776 + 0.969073i \(0.579371\pi\)
−0.969073 + 0.246776i \(0.920629\pi\)
\(368\) 7.06244 7.06244i 0.368155 0.368155i
\(369\) −10.5131 16.2196i −0.547288 0.844361i
\(370\) 0 0
\(371\) 4.00728i 0.208048i
\(372\) 6.04438 + 20.4382i 0.313387 + 1.05967i
\(373\) 5.28110 + 5.28110i 0.273445 + 0.273445i 0.830485 0.557040i \(-0.188063\pi\)
−0.557040 + 0.830485i \(0.688063\pi\)
\(374\) 20.3671 1.05316
\(375\) 0 0
\(376\) 32.9341 1.69844
\(377\) 19.7908 + 19.7908i 1.01928 + 1.01928i
\(378\) 8.60180 10.0448i 0.442429 0.516647i
\(379\) 3.38353i 0.173800i −0.996217 0.0869000i \(-0.972304\pi\)
0.996217 0.0869000i \(-0.0276961\pi\)
\(380\) 0 0
\(381\) −16.7059 + 30.7364i −0.855868 + 1.57467i
\(382\) 23.1331 23.1331i 1.18359 1.18359i
\(383\) −2.86741 + 2.86741i −0.146518 + 0.146518i −0.776561 0.630043i \(-0.783037\pi\)
0.630043 + 0.776561i \(0.283037\pi\)
\(384\) −9.71455 + 17.8734i −0.495744 + 0.912097i
\(385\) 0 0
\(386\) 29.0157i 1.47686i
\(387\) 22.7263 + 4.85136i 1.15524 + 0.246609i
\(388\) −19.6841 19.6841i −0.999311 0.999311i
\(389\) −10.2102 −0.517675 −0.258838 0.965921i \(-0.583339\pi\)
−0.258838 + 0.965921i \(0.583339\pi\)
\(390\) 0 0
\(391\) 7.18455 0.363339
\(392\) 4.45829 + 4.45829i 0.225178 + 0.225178i
\(393\) 2.40557 + 8.13410i 0.121345 + 0.410311i
\(394\) 67.4903i 3.40011i
\(395\) 0 0
\(396\) −17.6815 + 11.4606i −0.888528 + 0.575915i
\(397\) 24.0534 24.0534i 1.20721 1.20721i 0.235280 0.971928i \(-0.424399\pi\)
0.971928 0.235280i \(-0.0756009\pi\)
\(398\) −7.57156 + 7.57156i −0.379528 + 0.379528i
\(399\) 2.55723 + 1.38991i 0.128021 + 0.0695823i
\(400\) 0 0
\(401\) 20.0912i 1.00331i −0.865068 0.501654i \(-0.832725\pi\)
0.865068 0.501654i \(-0.167275\pi\)
\(402\) 22.4324 6.63414i 1.11883 0.330881i
\(403\) −6.09803 6.09803i −0.303765 0.303765i
\(404\) 4.52803 0.225278
\(405\) 0 0
\(406\) −22.7008 −1.12662
\(407\) −0.690793 0.690793i −0.0342413 0.0342413i
\(408\) 53.4229 15.7992i 2.64483 0.782179i
\(409\) 33.5102i 1.65697i 0.560008 + 0.828487i \(0.310798\pi\)
−0.560008 + 0.828487i \(0.689202\pi\)
\(410\) 0 0
\(411\) 9.81120 + 5.33259i 0.483951 + 0.263037i
\(412\) −18.0463 + 18.0463i −0.889077 + 0.889077i
\(413\) 3.92353 3.92353i 0.193064 0.193064i
\(414\) −9.02331 + 5.84862i −0.443471 + 0.287444i
\(415\) 0 0
\(416\) 17.0678i 0.836817i
\(417\) 5.01251 + 16.9491i 0.245463 + 0.830000i
\(418\) −4.74391 4.74391i −0.232032 0.232032i
\(419\) 25.8773 1.26419 0.632093 0.774892i \(-0.282196\pi\)
0.632093 + 0.774892i \(0.282196\pi\)
\(420\) 0 0
\(421\) 10.4030 0.507013 0.253507 0.967334i \(-0.418416\pi\)
0.253507 + 0.967334i \(0.418416\pi\)
\(422\) −38.7301 38.7301i −1.88535 1.88535i
\(423\) −15.3252 3.27146i −0.745138 0.159064i
\(424\) 25.2658i 1.22702i
\(425\) 0 0
\(426\) −7.61923 + 14.0183i −0.369153 + 0.679188i
\(427\) 5.23730 5.23730i 0.253450 0.253450i
\(428\) 12.6154 12.6154i 0.609786 0.609786i
\(429\) 4.07143 7.49085i 0.196571 0.361662i
\(430\) 0 0
\(431\) 0.449005i 0.0216278i 0.999942 + 0.0108139i \(0.00344224\pi\)
−0.999942 + 0.0108139i \(0.996558\pi\)
\(432\) −23.9691 + 27.9899i −1.15321 + 1.34667i
\(433\) 17.7813 + 17.7813i 0.854517 + 0.854517i 0.990686 0.136169i \(-0.0434790\pi\)
−0.136169 + 0.990686i \(0.543479\pi\)
\(434\) 6.99469 0.335756
\(435\) 0 0
\(436\) −28.7555 −1.37714
\(437\) −1.67343 1.67343i −0.0800509 0.0800509i
\(438\) 10.4264 + 35.2554i 0.498192 + 1.68457i
\(439\) 29.5293i 1.40936i −0.709526 0.704679i \(-0.751091\pi\)
0.709526 0.704679i \(-0.248909\pi\)
\(440\) 0 0
\(441\) −1.63172 2.51744i −0.0777010 0.119878i
\(442\) −28.8077 + 28.8077i −1.37024 + 1.37024i
\(443\) 15.5643 15.5643i 0.739483 0.739483i −0.232995 0.972478i \(-0.574853\pi\)
0.972478 + 0.232995i \(0.0748525\pi\)
\(444\) −4.24325 2.30630i −0.201376 0.109452i
\(445\) 0 0
\(446\) 44.6313i 2.11336i
\(447\) −1.53325 + 0.453443i −0.0725204 + 0.0214471i
\(448\) 0.240699 + 0.240699i 0.0113720 + 0.0113720i
\(449\) 16.3214 0.770252 0.385126 0.922864i \(-0.374158\pi\)
0.385126 + 0.922864i \(0.374158\pi\)
\(450\) 0 0
\(451\) 10.1070 0.475921
\(452\) −14.7415 14.7415i −0.693380 0.693380i
\(453\) −22.8063 + 6.74471i −1.07153 + 0.316894i
\(454\) 31.3336i 1.47056i
\(455\) 0 0
\(456\) −16.1232 8.76332i −0.755040 0.410380i
\(457\) 20.6299 20.6299i 0.965028 0.965028i −0.0343811 0.999409i \(-0.510946\pi\)
0.999409 + 0.0343811i \(0.0109460\pi\)
\(458\) −8.03251 + 8.03251i −0.375335 + 0.375335i
\(459\) −26.4287 + 2.04518i −1.23359 + 0.0954609i
\(460\) 0 0
\(461\) 15.2893i 0.712094i −0.934468 0.356047i \(-0.884124\pi\)
0.934468 0.356047i \(-0.115876\pi\)
\(462\) 1.96110 + 6.63120i 0.0912388 + 0.308511i
\(463\) −0.492195 0.492195i −0.0228743 0.0228743i 0.695577 0.718451i \(-0.255149\pi\)
−0.718451 + 0.695577i \(0.755149\pi\)
\(464\) 63.2563 2.93660
\(465\) 0 0
\(466\) 20.3056 0.940640
\(467\) 9.00044 + 9.00044i 0.416491 + 0.416491i 0.883992 0.467501i \(-0.154846\pi\)
−0.467501 + 0.883992i \(0.654846\pi\)
\(468\) 8.79901 41.2192i 0.406734 1.90536i
\(469\) 5.30669i 0.245040i
\(470\) 0 0
\(471\) 16.0501 29.5298i 0.739548 1.36066i
\(472\) −24.7378 + 24.7378i −1.13865 + 1.13865i
\(473\) −8.59230 + 8.59230i −0.395075 + 0.395075i
\(474\) 35.9070 66.0637i 1.64926 3.03441i
\(475\) 0 0
\(476\) 22.8408i 1.04690i
\(477\) −2.50974 + 11.7570i −0.114913 + 0.538314i
\(478\) 21.3426 + 21.3426i 0.976188 + 0.976188i
\(479\) −22.7572 −1.03980 −0.519901 0.854226i \(-0.674031\pi\)
−0.519901 + 0.854226i \(0.674031\pi\)
\(480\) 0 0
\(481\) 1.95415 0.0891015
\(482\) −32.5235 32.5235i −1.48141 1.48141i
\(483\) 0.691785 + 2.33917i 0.0314773 + 0.106436i
\(484\) 38.2328i 1.73785i
\(485\) 0 0
\(486\) 31.5278 24.0830i 1.43013 1.09243i
\(487\) 11.4919 11.4919i 0.520746 0.520746i −0.397051 0.917797i \(-0.629966\pi\)
0.917797 + 0.397051i \(0.129966\pi\)
\(488\) −33.0210 + 33.0210i −1.49479 + 1.49479i
\(489\) −14.2163 7.72687i −0.642884 0.349421i
\(490\) 0 0
\(491\) 0.301729i 0.0136168i −0.999977 0.00680841i \(-0.997833\pi\)
0.999977 0.00680841i \(-0.00216720\pi\)
\(492\) 47.9133 14.1698i 2.16010 0.638826i
\(493\) 32.1750 + 32.1750i 1.44909 + 1.44909i
\(494\) 13.4198 0.603785
\(495\) 0 0
\(496\) −19.4909 −0.875165
\(497\) 2.55933 + 2.55933i 0.114801 + 0.114801i
\(498\) −19.2085 + 5.68071i −0.860754 + 0.254559i
\(499\) 20.2207i 0.905202i −0.891713 0.452601i \(-0.850496\pi\)
0.891713 0.452601i \(-0.149504\pi\)
\(500\) 0 0
\(501\) 6.70268 + 3.64305i 0.299454 + 0.162759i
\(502\) −5.74537 + 5.74537i −0.256428 + 0.256428i
\(503\) 23.8859 23.8859i 1.06502 1.06502i 0.0672882 0.997734i \(-0.478565\pi\)
0.997734 0.0672882i \(-0.0214347\pi\)
\(504\) 10.2880 + 15.8724i 0.458262 + 0.707012i
\(505\) 0 0
\(506\) 5.62273i 0.249961i
\(507\) −1.54915 5.23825i −0.0688004 0.232639i
\(508\) −63.9443 63.9443i −2.83707 2.83707i
\(509\) −11.7721 −0.521788 −0.260894 0.965368i \(-0.584017\pi\)
−0.260894 + 0.965368i \(0.584017\pi\)
\(510\) 0 0
\(511\) 8.34014 0.368946
\(512\) −35.9587 35.9587i −1.58917 1.58917i
\(513\) 6.63215 + 5.67942i 0.292816 + 0.250752i
\(514\) 42.5137i 1.87520i
\(515\) 0 0
\(516\) −28.6864 + 52.7789i −1.26285 + 2.32346i
\(517\) 5.79412 5.79412i 0.254825 0.254825i
\(518\) −1.12074 + 1.12074i −0.0492426 + 0.0492426i
\(519\) −9.50842 + 17.4941i −0.417373 + 0.767907i
\(520\) 0 0
\(521\) 29.7872i 1.30500i 0.757789 + 0.652500i \(0.226280\pi\)
−0.757789 + 0.652500i \(0.773720\pi\)
\(522\) −66.6018 14.2174i −2.91508 0.622279i
\(523\) −17.4673 17.4673i −0.763792 0.763792i 0.213214 0.977006i \(-0.431607\pi\)
−0.977006 + 0.213214i \(0.931607\pi\)
\(524\) −21.9268 −0.957877
\(525\) 0 0
\(526\) −47.3309 −2.06373
\(527\) −9.91393 9.91393i −0.431858 0.431858i
\(528\) −5.46466 18.4780i −0.237819 0.804151i
\(529\) 21.0166i 0.913764i
\(530\) 0 0
\(531\) 13.9685 9.05395i 0.606183 0.392908i
\(532\) −5.32007 + 5.32007i −0.230654 + 0.230654i
\(533\) −14.2956 + 14.2956i −0.619211 + 0.619211i
\(534\) −36.4174 19.7936i −1.57593 0.856553i
\(535\) 0 0
\(536\) 33.4586i 1.44519i
\(537\) 27.5683 8.15302i 1.18966 0.351829i
\(538\) −52.8021 52.8021i −2.27646 2.27646i
\(539\) 1.56870 0.0675687
\(540\) 0 0
\(541\) −23.1117 −0.993650 −0.496825 0.867851i \(-0.665501\pi\)
−0.496825 + 0.867851i \(0.665501\pi\)
\(542\) 5.72941 + 5.72941i 0.246099 + 0.246099i
\(543\) 19.3552 5.72409i 0.830612 0.245644i
\(544\) 27.7481i 1.18969i
\(545\) 0 0
\(546\) −12.1532 6.60549i −0.520107 0.282689i
\(547\) 25.6689 25.6689i 1.09752 1.09752i 0.102823 0.994700i \(-0.467213\pi\)
0.994700 0.102823i \(-0.0327874\pi\)
\(548\) −20.4113 + 20.4113i −0.871928 + 0.871928i
\(549\) 18.6458 12.0856i 0.795783 0.515801i
\(550\) 0 0
\(551\) 14.9884i 0.638528i
\(552\) −4.36169 14.7484i −0.185646 0.627735i
\(553\) −12.0613 12.0613i −0.512898 0.512898i
\(554\) −60.6965 −2.57875
\(555\) 0 0
\(556\) −45.6891 −1.93765
\(557\) 10.5779 + 10.5779i 0.448199 + 0.448199i 0.894756 0.446556i \(-0.147350\pi\)
−0.446556 + 0.894756i \(0.647350\pi\)
\(558\) 20.5217 + 4.38074i 0.868753 + 0.185452i
\(559\) 24.3063i 1.02805i
\(560\) 0 0
\(561\) 6.61917 12.1783i 0.279462 0.514169i
\(562\) −44.6402 + 44.6402i −1.88303 + 1.88303i
\(563\) 10.9216 10.9216i 0.460291 0.460291i −0.438460 0.898751i \(-0.644476\pi\)
0.898751 + 0.438460i \(0.144476\pi\)
\(564\) 19.3444 35.5908i 0.814544 1.49864i
\(565\) 0 0
\(566\) 19.5050i 0.819858i
\(567\) −3.21064 8.40784i −0.134834 0.353096i
\(568\) −16.1365 16.1365i −0.677072 0.677072i
\(569\) 42.0710 1.76371 0.881854 0.471523i \(-0.156295\pi\)
0.881854 + 0.471523i \(0.156295\pi\)
\(570\) 0 0
\(571\) 10.8342 0.453399 0.226699 0.973965i \(-0.427207\pi\)
0.226699 + 0.973965i \(0.427207\pi\)
\(572\) 15.5840 + 15.5840i 0.651601 + 0.651601i
\(573\) −6.31411 21.3503i −0.263776 0.891921i
\(574\) 16.3976i 0.684424i
\(575\) 0 0
\(576\) 0.555438 + 0.856936i 0.0231433 + 0.0357057i
\(577\) −14.6975 + 14.6975i −0.611865 + 0.611865i −0.943432 0.331567i \(-0.892423\pi\)
0.331567 + 0.943432i \(0.392423\pi\)
\(578\) −16.2407 + 16.2407i −0.675523 + 0.675523i
\(579\) 17.3497 + 9.42991i 0.721028 + 0.391894i
\(580\) 0 0
\(581\) 4.54404i 0.188519i
\(582\) −26.2823 + 7.77271i −1.08944 + 0.322189i
\(583\) −4.44503 4.44503i −0.184094 0.184094i
\(584\) −52.5844 −2.17596
\(585\) 0 0
\(586\) −30.9802 −1.27978
\(587\) −4.89737 4.89737i −0.202136 0.202136i 0.598779 0.800915i \(-0.295653\pi\)
−0.800915 + 0.598779i \(0.795653\pi\)
\(588\) 7.43658 2.19929i 0.306680 0.0906971i
\(589\) 4.61831i 0.190294i
\(590\) 0 0
\(591\) 40.3552 + 21.9339i 1.65999 + 0.902240i
\(592\) 3.12297 3.12297i 0.128353 0.128353i
\(593\) 22.5635 22.5635i 0.926573 0.926573i −0.0709102 0.997483i \(-0.522590\pi\)
0.997483 + 0.0709102i \(0.0225904\pi\)
\(594\) 1.60059 + 20.6835i 0.0656729 + 0.848654i
\(595\) 0 0
\(596\) 4.13314i 0.169300i
\(597\) 2.06664 + 6.98804i 0.0845818 + 0.286002i
\(598\) 7.95292 + 7.95292i 0.325219 + 0.325219i
\(599\) 6.81971 0.278646 0.139323 0.990247i \(-0.455507\pi\)
0.139323 + 0.990247i \(0.455507\pi\)
\(600\) 0 0
\(601\) −8.46733 −0.345390 −0.172695 0.984975i \(-0.555247\pi\)
−0.172695 + 0.984975i \(0.555247\pi\)
\(602\) 13.9402 + 13.9402i 0.568158 + 0.568158i
\(603\) 3.32356 15.5693i 0.135346 0.634031i
\(604\) 61.4782i 2.50151i
\(605\) 0 0
\(606\) 2.12893 3.91692i 0.0864817 0.159114i
\(607\) −6.30295 + 6.30295i −0.255829 + 0.255829i −0.823355 0.567526i \(-0.807900\pi\)
0.567526 + 0.823355i \(0.307900\pi\)
\(608\) 6.46309 6.46309i 0.262113 0.262113i
\(609\) −7.37760 + 13.5737i −0.298956 + 0.550035i
\(610\) 0 0
\(611\) 16.3907i 0.663095i
\(612\) 14.3051 67.0125i 0.578248 2.70882i
\(613\) 5.24728 + 5.24728i 0.211935 + 0.211935i 0.805089 0.593154i \(-0.202117\pi\)
−0.593154 + 0.805089i \(0.702117\pi\)
\(614\) 42.6601 1.72162
\(615\) 0 0
\(616\) −9.89062 −0.398504
\(617\) 2.10719 + 2.10719i 0.0848323 + 0.0848323i 0.748250 0.663417i \(-0.230895\pi\)
−0.663417 + 0.748250i \(0.730895\pi\)
\(618\) 7.12596 + 24.0954i 0.286648 + 0.969261i
\(619\) 21.0734i 0.847012i −0.905893 0.423506i \(-0.860799\pi\)
0.905893 0.423506i \(-0.139201\pi\)
\(620\) 0 0
\(621\) 0.564612 + 7.29616i 0.0226571 + 0.292785i
\(622\) 52.6932 52.6932i 2.11280 2.11280i
\(623\) −6.64874 + 6.64874i −0.266376 + 0.266376i
\(624\) 33.8650 + 18.4063i 1.35569 + 0.736844i
\(625\) 0 0
\(626\) 4.41188i 0.176334i
\(627\) −4.37831 + 1.29484i −0.174853 + 0.0517108i
\(628\) 61.4341 + 61.4341i 2.45149 + 2.45149i
\(629\) 3.17697 0.126674
\(630\) 0 0
\(631\) −11.6376 −0.463287 −0.231643 0.972801i \(-0.574410\pi\)
−0.231643 + 0.972801i \(0.574410\pi\)
\(632\) 76.0461 + 76.0461i 3.02495 + 3.02495i
\(633\) −35.7453 + 10.5713i −1.42075 + 0.420170i
\(634\) 15.4825i 0.614890i
\(635\) 0 0
\(636\) −27.3040 14.8403i −1.08267 0.588455i
\(637\) −2.21881 + 2.21881i −0.0879123 + 0.0879123i
\(638\) 25.1806 25.1806i 0.996910 0.996910i
\(639\) 5.90591 + 9.11170i 0.233634 + 0.360453i
\(640\) 0 0
\(641\) 36.1036i 1.42601i 0.701161 + 0.713003i \(0.252665\pi\)
−0.701161 + 0.713003i \(0.747335\pi\)
\(642\) −4.98144 16.8441i −0.196602 0.664782i
\(643\) 21.0115 + 21.0115i 0.828614 + 0.828614i 0.987325 0.158711i \(-0.0507337\pi\)
−0.158711 + 0.987325i \(0.550734\pi\)
\(644\) −6.30563 −0.248477
\(645\) 0 0
\(646\) 21.8173 0.858392
\(647\) −18.9025 18.9025i −0.743133 0.743133i 0.230046 0.973180i \(-0.426112\pi\)
−0.973180 + 0.230046i \(0.926112\pi\)
\(648\) 20.2430 + 53.0112i 0.795221 + 2.08248i
\(649\) 8.70428i 0.341673i
\(650\) 0 0
\(651\) 2.27322 4.18241i 0.0890947 0.163921i
\(652\) 29.5757 29.5757i 1.15828 1.15828i
\(653\) −12.2864 + 12.2864i −0.480803 + 0.480803i −0.905388 0.424585i \(-0.860420\pi\)
0.424585 + 0.905388i \(0.360420\pi\)
\(654\) −13.5199 + 24.8746i −0.528668 + 0.972674i
\(655\) 0 0
\(656\) 45.6924i 1.78399i
\(657\) 24.4691 + 5.22339i 0.954631 + 0.203784i
\(658\) −9.40038 9.40038i −0.366465 0.366465i
\(659\) 0.708622 0.0276040 0.0138020 0.999905i \(-0.495607\pi\)
0.0138020 + 0.999905i \(0.495607\pi\)
\(660\) 0 0
\(661\) 17.4206 0.677582 0.338791 0.940862i \(-0.389982\pi\)
0.338791 + 0.940862i \(0.389982\pi\)
\(662\) 59.8561 + 59.8561i 2.32637 + 2.32637i
\(663\) 7.86299 + 26.5876i 0.305373 + 1.03258i
\(664\) 28.6500i 1.11184i
\(665\) 0 0
\(666\) −3.99006 + 2.58623i −0.154612 + 0.100214i
\(667\) 8.88253 8.88253i 0.343933 0.343933i
\(668\) −13.9443 + 13.9443i −0.539522 + 0.539522i
\(669\) −26.6869 14.5049i −1.03177 0.560791i
\(670\) 0 0
\(671\) 11.6188i 0.448540i
\(672\) −9.03434 + 2.67181i −0.348507 + 0.103067i
\(673\) 8.20389 + 8.20389i 0.316237 + 0.316237i 0.847320 0.531083i \(-0.178215\pi\)
−0.531083 + 0.847320i \(0.678215\pi\)
\(674\) −37.0926 −1.42875
\(675\) 0 0
\(676\) 14.1206 0.543099
\(677\) −32.8605 32.8605i −1.26293 1.26293i −0.949666 0.313264i \(-0.898578\pi\)
−0.313264 0.949666i \(-0.601422\pi\)
\(678\) −19.6828 + 5.82098i −0.755915 + 0.223554i
\(679\) 6.21744i 0.238604i
\(680\) 0 0
\(681\) 18.7356 + 10.1832i 0.717951 + 0.390221i
\(682\) −7.75878 + 7.75878i −0.297099 + 0.297099i
\(683\) 28.4978 28.4978i 1.09044 1.09044i 0.0949562 0.995481i \(-0.469729\pi\)
0.995481 0.0949562i \(-0.0302711\pi\)
\(684\) −18.9405 + 12.2766i −0.724208 + 0.469408i
\(685\) 0 0
\(686\) 2.54506i 0.0971709i
\(687\) 2.19245 + 7.41347i 0.0836473 + 0.282842i
\(688\) −38.8446 38.8446i −1.48093 1.48093i
\(689\) 12.5743 0.479043
\(690\) 0 0
\(691\) 5.79939 0.220619 0.110310 0.993897i \(-0.464816\pi\)
0.110310 + 0.993897i \(0.464816\pi\)
\(692\) −36.3949 36.3949i −1.38353 1.38353i
\(693\) 4.60241 + 0.982471i 0.174831 + 0.0373210i
\(694\) 69.1925i 2.62651i
\(695\) 0 0
\(696\) 46.5156 85.5820i 1.76317 3.24398i
\(697\) −23.2412 + 23.2412i −0.880324 + 0.880324i
\(698\) 54.2230 54.2230i 2.05237 2.05237i
\(699\) 6.59919 12.1416i 0.249604 0.459236i
\(700\) 0 0
\(701\) 4.92775i 0.186118i −0.995661 0.0930592i \(-0.970335\pi\)
0.995661 0.0930592i \(-0.0296646\pi\)
\(702\) −31.5191 26.9913i −1.18961 1.01872i
\(703\) −0.739981 0.739981i −0.0279089 0.0279089i
\(704\) −0.533986 −0.0201254
\(705\) 0 0
\(706\) 61.3096 2.30742
\(707\) −0.715113 0.715113i −0.0268946 0.0268946i
\(708\) 12.2032 + 41.2635i 0.458625 + 1.55078i
\(709\) 17.1922i 0.645666i 0.946456 + 0.322833i \(0.104635\pi\)
−0.946456 + 0.322833i \(0.895365\pi\)
\(710\) 0 0
\(711\) −27.8326 42.9405i −1.04381 1.61039i
\(712\) 41.9201 41.9201i 1.57102 1.57102i
\(713\) −2.73693 + 2.73693i −0.102499 + 0.102499i
\(714\) −19.7581 10.7389i −0.739428 0.401895i
\(715\) 0 0
\(716\) 74.3149i 2.77728i
\(717\) 19.6978 5.82541i 0.735628 0.217554i
\(718\) 1.32809 + 1.32809i 0.0495640 + 0.0495640i
\(719\) 12.2556 0.457059 0.228529 0.973537i \(-0.426608\pi\)
0.228529 + 0.973537i \(0.426608\pi\)
\(720\) 0 0
\(721\) 5.70011 0.212283
\(722\) 29.1113 + 29.1113i 1.08341 + 1.08341i
\(723\) −30.0170 + 8.87721i −1.11635 + 0.330147i
\(724\) 52.1752i 1.93908i
\(725\) 0 0
\(726\) 33.0728 + 17.9757i 1.22745 + 0.667142i
\(727\) −5.83842 + 5.83842i −0.216535 + 0.216535i −0.807037 0.590501i \(-0.798930\pi\)
0.590501 + 0.807037i \(0.298930\pi\)
\(728\) 13.9895 13.9895i 0.518486 0.518486i
\(729\) −4.15390 26.6786i −0.153848 0.988094i
\(730\) 0 0
\(731\) 39.5162i 1.46156i
\(732\) 16.2894 + 55.0802i 0.602072 + 2.03582i
\(733\) −13.5940 13.5940i −0.502105 0.502105i 0.409987 0.912091i \(-0.365533\pi\)
−0.912091 + 0.409987i \(0.865533\pi\)
\(734\) −83.8351 −3.09441
\(735\) 0 0
\(736\) 7.66040 0.282366
\(737\) 5.88639 + 5.88639i 0.216828 + 0.216828i
\(738\) 10.2698 48.1090i 0.378035 1.77092i
\(739\) 15.1801i 0.558411i 0.960231 + 0.279205i \(0.0900710\pi\)
−0.960231 + 0.279205i \(0.909929\pi\)
\(740\) 0 0
\(741\) 4.36134 8.02424i 0.160218 0.294778i
\(742\) −7.21162 + 7.21162i −0.264747 + 0.264747i
\(743\) 34.4215 34.4215i 1.26280 1.26280i 0.313073 0.949729i \(-0.398642\pi\)
0.949729 0.313073i \(-0.101358\pi\)
\(744\) −14.3326 + 26.3700i −0.525459 + 0.966770i
\(745\) 0 0
\(746\) 19.0080i 0.695934i
\(747\) −2.84591 + 13.3317i −0.104126 + 0.487783i
\(748\) 25.3359 + 25.3359i 0.926371 + 0.926371i
\(749\) −3.98469 −0.145597
\(750\) 0 0
\(751\) −22.2515 −0.811970 −0.405985 0.913880i \(-0.633071\pi\)
−0.405985 + 0.913880i \(0.633071\pi\)
\(752\) 26.1944 + 26.1944i 0.955210 + 0.955210i
\(753\) 1.56818 + 5.30260i 0.0571478 + 0.193237i
\(754\) 71.2321i 2.59412i
\(755\) 0 0
\(756\) 23.1956 1.79498i 0.843615 0.0652830i
\(757\) 1.88407 1.88407i 0.0684777 0.0684777i −0.672038 0.740516i \(-0.734581\pi\)
0.740516 + 0.672038i \(0.234581\pi\)
\(758\) 6.08909 6.08909i 0.221166 0.221166i
\(759\) −3.36206 1.82735i −0.122035 0.0663286i
\(760\) 0 0
\(761\) 35.6674i 1.29294i −0.762938 0.646472i \(-0.776244\pi\)
0.762938 0.646472i \(-0.223756\pi\)
\(762\) −85.3786 + 25.2498i −3.09294 + 0.914703i
\(763\) 4.54137 + 4.54137i 0.164409 + 0.164409i
\(764\) 57.5532 2.08220
\(765\) 0 0
\(766\) −10.3206 −0.372897
\(767\) −12.3115 12.3115i −0.444543 0.444543i
\(768\) −48.5173 + 14.3485i −1.75072 + 0.517755i
\(769\) 31.7331i 1.14432i 0.820141 + 0.572162i \(0.193895\pi\)
−0.820141 + 0.572162i \(0.806105\pi\)
\(770\) 0 0
\(771\) −25.4207 13.8167i −0.915503 0.497595i
\(772\) −36.0944 + 36.0944i −1.29907 + 1.29907i
\(773\) −4.97844 + 4.97844i −0.179062 + 0.179062i −0.790947 0.611885i \(-0.790412\pi\)
0.611885 + 0.790947i \(0.290412\pi\)
\(774\) 32.1683 + 49.6296i 1.15627 + 1.78390i
\(775\) 0 0
\(776\) 39.2008i 1.40723i
\(777\) 0.305904 + 1.03437i 0.0109742 + 0.0371079i
\(778\) −18.3745 18.3745i −0.658758 0.658758i