Properties

Label 756.2.ca.a.173.7
Level 756
Weight 2
Character 756.173
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ca (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 173.7
Character \(\chi\) \(=\) 756.173
Dual form 756.2.ca.a.437.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16896 + 1.27810i) q^{3} +(0.898527 - 0.753954i) q^{5} +(-1.31798 - 2.29411i) q^{7} +(-0.267080 - 2.98809i) q^{9} +O(q^{10})\) \(q+(-1.16896 + 1.27810i) q^{3} +(0.898527 - 0.753954i) q^{5} +(-1.31798 - 2.29411i) q^{7} +(-0.267080 - 2.98809i) q^{9} +(-2.05691 + 2.45133i) q^{11} +(1.12364 + 1.33911i) q^{13} +(-0.0867108 + 2.02975i) q^{15} +(-1.58225 + 2.74055i) q^{17} +(-5.76388 + 3.32778i) q^{19} +(4.47276 + 0.997209i) q^{21} +(-1.94528 + 5.34462i) q^{23} +(-0.629336 + 3.56914i) q^{25} +(4.13128 + 3.15159i) q^{27} +(3.84940 - 4.58754i) q^{29} +(-2.86246 - 3.41135i) q^{31} +(-0.728606 - 5.49443i) q^{33} +(-2.91389 - 1.06763i) q^{35} -9.50482 q^{37} +(-3.02500 - 0.129228i) q^{39} +(-7.74888 + 6.50209i) q^{41} +(3.80179 - 1.38374i) q^{43} +(-2.49286 - 2.48351i) q^{45} +(-6.48878 - 5.44473i) q^{47} +(-3.52588 + 6.04716i) q^{49} +(-1.65310 - 5.22586i) q^{51} +(11.7526 - 6.78537i) q^{53} +3.75340i q^{55} +(2.48449 - 11.2568i) q^{57} +(1.90381 + 10.7970i) q^{59} +(1.66901 - 1.98905i) q^{61} +(-6.50299 + 4.55094i) q^{63} +(2.01925 + 0.356048i) q^{65} +(-14.4248 - 5.25019i) q^{67} +(-4.55701 - 8.73390i) q^{69} +(2.08522 - 1.20391i) q^{71} -1.16715i q^{73} +(-3.82606 - 4.97653i) q^{75} +(8.33457 + 1.48798i) q^{77} +(-9.42995 + 3.43222i) q^{79} +(-8.85734 + 1.59612i) q^{81} +(5.29556 + 4.44350i) q^{83} +(0.644546 + 3.65540i) q^{85} +(1.36355 + 10.2826i) q^{87} +(5.74540 + 9.95133i) q^{89} +(1.59112 - 4.34267i) q^{91} +(7.70615 + 0.329207i) q^{93} +(-2.67001 + 7.33580i) q^{95} +(0.0688894 + 0.189272i) q^{97} +(7.87414 + 5.49152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q - 12q^{9} + O(q^{10}) \) \( 144q - 12q^{9} + 12q^{11} + 12q^{15} - 3q^{21} - 15q^{23} - 6q^{29} - 42q^{39} + 18q^{45} - 54q^{47} - 36q^{49} + 18q^{51} + 45q^{53} + 3q^{57} + 54q^{61} + 39q^{63} - 3q^{65} + 36q^{69} + 36q^{71} + 93q^{77} - 18q^{79} - 36q^{81} + 36q^{85} - 18q^{91} + 60q^{93} + 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.16896 + 1.27810i −0.674897 + 0.737912i
\(4\) 0 0
\(5\) 0.898527 0.753954i 0.401834 0.337178i −0.419368 0.907816i \(-0.637748\pi\)
0.821202 + 0.570638i \(0.193304\pi\)
\(6\) 0 0
\(7\) −1.31798 2.29411i −0.498148 0.867092i
\(8\) 0 0
\(9\) −0.267080 2.98809i −0.0890268 0.996029i
\(10\) 0 0
\(11\) −2.05691 + 2.45133i −0.620181 + 0.739103i −0.981102 0.193494i \(-0.938018\pi\)
0.360921 + 0.932597i \(0.382463\pi\)
\(12\) 0 0
\(13\) 1.12364 + 1.33911i 0.311643 + 0.371401i 0.899017 0.437914i \(-0.144283\pi\)
−0.587374 + 0.809316i \(0.699838\pi\)
\(14\) 0 0
\(15\) −0.0867108 + 2.02975i −0.0223886 + 0.524078i
\(16\) 0 0
\(17\) −1.58225 + 2.74055i −0.383753 + 0.664680i −0.991595 0.129378i \(-0.958702\pi\)
0.607842 + 0.794058i \(0.292035\pi\)
\(18\) 0 0
\(19\) −5.76388 + 3.32778i −1.32233 + 0.763445i −0.984099 0.177620i \(-0.943160\pi\)
−0.338226 + 0.941065i \(0.609827\pi\)
\(20\) 0 0
\(21\) 4.47276 + 0.997209i 0.976036 + 0.217609i
\(22\) 0 0
\(23\) −1.94528 + 5.34462i −0.405620 + 1.11443i 0.553850 + 0.832617i \(0.313158\pi\)
−0.959469 + 0.281814i \(0.909064\pi\)
\(24\) 0 0
\(25\) −0.629336 + 3.56914i −0.125867 + 0.713829i
\(26\) 0 0
\(27\) 4.13128 + 3.15159i 0.795065 + 0.606524i
\(28\) 0 0
\(29\) 3.84940 4.58754i 0.714816 0.851885i −0.279300 0.960204i \(-0.590102\pi\)
0.994116 + 0.108319i \(0.0345467\pi\)
\(30\) 0 0
\(31\) −2.86246 3.41135i −0.514114 0.612697i 0.445065 0.895498i \(-0.353181\pi\)
−0.959178 + 0.282801i \(0.908736\pi\)
\(32\) 0 0
\(33\) −0.728606 5.49443i −0.126834 0.956457i
\(34\) 0 0
\(35\) −2.91389 1.06763i −0.492537 0.180462i
\(36\) 0 0
\(37\) −9.50482 −1.56258 −0.781292 0.624166i \(-0.785439\pi\)
−0.781292 + 0.624166i \(0.785439\pi\)
\(38\) 0 0
\(39\) −3.02500 0.129228i −0.484388 0.0206931i
\(40\) 0 0
\(41\) −7.74888 + 6.50209i −1.21017 + 1.01546i −0.210893 + 0.977509i \(0.567637\pi\)
−0.999280 + 0.0379460i \(0.987919\pi\)
\(42\) 0 0
\(43\) 3.80179 1.38374i 0.579768 0.211018i −0.0354555 0.999371i \(-0.511288\pi\)
0.615223 + 0.788353i \(0.289066\pi\)
\(44\) 0 0
\(45\) −2.49286 2.48351i −0.371613 0.370220i
\(46\) 0 0
\(47\) −6.48878 5.44473i −0.946486 0.794196i 0.0322164 0.999481i \(-0.489743\pi\)
−0.978702 + 0.205285i \(0.934188\pi\)
\(48\) 0 0
\(49\) −3.52588 + 6.04716i −0.503697 + 0.863881i
\(50\) 0 0
\(51\) −1.65310 5.22586i −0.231481 0.731767i
\(52\) 0 0
\(53\) 11.7526 6.78537i 1.61434 0.932042i 0.625996 0.779826i \(-0.284693\pi\)
0.988347 0.152215i \(-0.0486407\pi\)
\(54\) 0 0
\(55\) 3.75340i 0.506108i
\(56\) 0 0
\(57\) 2.48449 11.2568i 0.329079 1.49101i
\(58\) 0 0
\(59\) 1.90381 + 10.7970i 0.247855 + 1.40565i 0.813769 + 0.581189i \(0.197412\pi\)
−0.565914 + 0.824464i \(0.691477\pi\)
\(60\) 0 0
\(61\) 1.66901 1.98905i 0.213695 0.254672i −0.648539 0.761181i \(-0.724620\pi\)
0.862235 + 0.506509i \(0.169064\pi\)
\(62\) 0 0
\(63\) −6.50299 + 4.55094i −0.819300 + 0.573365i
\(64\) 0 0
\(65\) 2.01925 + 0.356048i 0.250457 + 0.0441623i
\(66\) 0 0
\(67\) −14.4248 5.25019i −1.76227 0.641413i −0.762285 0.647242i \(-0.775922\pi\)
−0.999983 + 0.00582861i \(0.998145\pi\)
\(68\) 0 0
\(69\) −4.55701 8.73390i −0.548600 1.05144i
\(70\) 0 0
\(71\) 2.08522 1.20391i 0.247471 0.142877i −0.371135 0.928579i \(-0.621031\pi\)
0.618606 + 0.785702i \(0.287698\pi\)
\(72\) 0 0
\(73\) 1.16715i 0.136605i −0.997665 0.0683023i \(-0.978242\pi\)
0.997665 0.0683023i \(-0.0217582\pi\)
\(74\) 0 0
\(75\) −3.82606 4.97653i −0.441795 0.574640i
\(76\) 0 0
\(77\) 8.33457 + 1.48798i 0.949812 + 0.169571i
\(78\) 0 0
\(79\) −9.42995 + 3.43222i −1.06095 + 0.386155i −0.812786 0.582562i \(-0.802050\pi\)
−0.248167 + 0.968717i \(0.579828\pi\)
\(80\) 0 0
\(81\) −8.85734 + 1.59612i −0.984148 + 0.177347i
\(82\) 0 0
\(83\) 5.29556 + 4.44350i 0.581263 + 0.487738i 0.885362 0.464903i \(-0.153911\pi\)
−0.304098 + 0.952641i \(0.598355\pi\)
\(84\) 0 0
\(85\) 0.644546 + 3.65540i 0.0699108 + 0.396484i
\(86\) 0 0
\(87\) 1.36355 + 10.2826i 0.146188 + 1.10241i
\(88\) 0 0
\(89\) 5.74540 + 9.95133i 0.609011 + 1.05484i 0.991404 + 0.130839i \(0.0417670\pi\)
−0.382392 + 0.924000i \(0.624900\pi\)
\(90\) 0 0
\(91\) 1.59112 4.34267i 0.166795 0.455236i
\(92\) 0 0
\(93\) 7.70615 + 0.329207i 0.799090 + 0.0341371i
\(94\) 0 0
\(95\) −2.67001 + 7.33580i −0.273938 + 0.752637i
\(96\) 0 0
\(97\) 0.0688894 + 0.189272i 0.00699466 + 0.0192177i 0.943141 0.332393i \(-0.107856\pi\)
−0.936146 + 0.351611i \(0.885634\pi\)
\(98\) 0 0
\(99\) 7.87414 + 5.49152i 0.791381 + 0.551918i
\(100\) 0 0
\(101\) −5.45718 + 1.98625i −0.543010 + 0.197639i −0.598938 0.800795i \(-0.704410\pi\)
0.0559282 + 0.998435i \(0.482188\pi\)
\(102\) 0 0
\(103\) 3.40452 + 4.05735i 0.335457 + 0.399782i 0.907234 0.420627i \(-0.138190\pi\)
−0.571776 + 0.820410i \(0.693745\pi\)
\(104\) 0 0
\(105\) 4.77074 2.47623i 0.465577 0.241656i
\(106\) 0 0
\(107\) 8.16755 + 4.71554i 0.789587 + 0.455868i 0.839817 0.542870i \(-0.182662\pi\)
−0.0502303 + 0.998738i \(0.515996\pi\)
\(108\) 0 0
\(109\) −8.19677 14.1972i −0.785108 1.35985i −0.928934 0.370244i \(-0.879274\pi\)
0.143826 0.989603i \(-0.454059\pi\)
\(110\) 0 0
\(111\) 11.1107 12.1481i 1.05458 1.15305i
\(112\) 0 0
\(113\) 2.80986 7.72002i 0.264329 0.726238i −0.734534 0.678572i \(-0.762599\pi\)
0.998863 0.0476665i \(-0.0151785\pi\)
\(114\) 0 0
\(115\) 2.28171 + 6.26894i 0.212770 + 0.584582i
\(116\) 0 0
\(117\) 3.70126 3.71520i 0.342182 0.343470i
\(118\) 0 0
\(119\) 8.37249 + 0.0178916i 0.767505 + 0.00164012i
\(120\) 0 0
\(121\) 0.131995 + 0.748578i 0.0119995 + 0.0680526i
\(122\) 0 0
\(123\) 0.747793 17.5045i 0.0674262 1.57833i
\(124\) 0 0
\(125\) 5.05785 + 8.76046i 0.452388 + 0.783559i
\(126\) 0 0
\(127\) 2.19382 3.79980i 0.194670 0.337178i −0.752123 0.659023i \(-0.770970\pi\)
0.946792 + 0.321846i \(0.104303\pi\)
\(128\) 0 0
\(129\) −2.67557 + 6.47660i −0.235571 + 0.570233i
\(130\) 0 0
\(131\) 9.76335 + 3.55357i 0.853028 + 0.310477i 0.731274 0.682084i \(-0.238926\pi\)
0.121754 + 0.992560i \(0.461148\pi\)
\(132\) 0 0
\(133\) 15.2309 + 8.83704i 1.32069 + 0.766269i
\(134\) 0 0
\(135\) 6.08822 0.283006i 0.523991 0.0243573i
\(136\) 0 0
\(137\) −8.29360 1.46238i −0.708570 0.124940i −0.192263 0.981343i \(-0.561583\pi\)
−0.516307 + 0.856404i \(0.672694\pi\)
\(138\) 0 0
\(139\) −17.3552 + 3.06020i −1.47205 + 0.259563i −0.851398 0.524521i \(-0.824245\pi\)
−0.620655 + 0.784083i \(0.713133\pi\)
\(140\) 0 0
\(141\) 14.5440 1.92865i 1.22483 0.162422i
\(142\) 0 0
\(143\) −5.59382 −0.467779
\(144\) 0 0
\(145\) 7.02430i 0.583337i
\(146\) 0 0
\(147\) −3.60728 11.5753i −0.297524 0.954714i
\(148\) 0 0
\(149\) 18.3431 3.23438i 1.50272 0.264970i 0.639105 0.769119i \(-0.279305\pi\)
0.863617 + 0.504149i \(0.168194\pi\)
\(150\) 0 0
\(151\) 4.92670 + 4.13400i 0.400930 + 0.336420i 0.820853 0.571140i \(-0.193499\pi\)
−0.419923 + 0.907560i \(0.637943\pi\)
\(152\) 0 0
\(153\) 8.61158 + 3.99597i 0.696205 + 0.323055i
\(154\) 0 0
\(155\) −5.14400 0.907027i −0.413176 0.0728541i
\(156\) 0 0
\(157\) 3.87655 0.683541i 0.309383 0.0545525i −0.0168012 0.999859i \(-0.505348\pi\)
0.326184 + 0.945306i \(0.394237\pi\)
\(158\) 0 0
\(159\) −5.06590 + 22.9528i −0.401752 + 1.82028i
\(160\) 0 0
\(161\) 14.8250 2.58139i 1.16837 0.203442i
\(162\) 0 0
\(163\) 12.2039 21.1378i 0.955882 1.65564i 0.223547 0.974693i \(-0.428237\pi\)
0.732336 0.680944i \(-0.238430\pi\)
\(164\) 0 0
\(165\) −4.79722 4.38756i −0.373463 0.341571i
\(166\) 0 0
\(167\) −3.10807 1.13125i −0.240510 0.0875384i 0.218953 0.975735i \(-0.429736\pi\)
−0.459463 + 0.888197i \(0.651958\pi\)
\(168\) 0 0
\(169\) 1.72680 9.79314i 0.132830 0.753319i
\(170\) 0 0
\(171\) 11.4831 + 16.3342i 0.878136 + 1.24911i
\(172\) 0 0
\(173\) −1.16119 + 6.58546i −0.0882840 + 0.500683i 0.908316 + 0.418286i \(0.137369\pi\)
−0.996600 + 0.0823977i \(0.973742\pi\)
\(174\) 0 0
\(175\) 9.01746 3.26028i 0.681656 0.246454i
\(176\) 0 0
\(177\) −16.0251 10.1880i −1.20452 0.765777i
\(178\) 0 0
\(179\) −5.40867 3.12270i −0.404263 0.233401i 0.284059 0.958807i \(-0.408319\pi\)
−0.688322 + 0.725406i \(0.741652\pi\)
\(180\) 0 0
\(181\) −0.630501 0.364020i −0.0468648 0.0270574i 0.476385 0.879237i \(-0.341947\pi\)
−0.523249 + 0.852180i \(0.675280\pi\)
\(182\) 0 0
\(183\) 0.591204 + 4.45828i 0.0437031 + 0.329566i
\(184\) 0 0
\(185\) −8.54034 + 7.16620i −0.627898 + 0.526869i
\(186\) 0 0
\(187\) −3.46342 9.51567i −0.253271 0.695855i
\(188\) 0 0
\(189\) 1.78516 13.6313i 0.129851 0.991533i
\(190\) 0 0
\(191\) 0.849441 + 2.33382i 0.0614634 + 0.168869i 0.966623 0.256202i \(-0.0824712\pi\)
−0.905160 + 0.425071i \(0.860249\pi\)
\(192\) 0 0
\(193\) −13.6705 + 11.4709i −0.984027 + 0.825697i −0.984692 0.174303i \(-0.944233\pi\)
0.000664881 1.00000i \(0.499788\pi\)
\(194\) 0 0
\(195\) −2.81548 + 2.16460i −0.201621 + 0.155010i
\(196\) 0 0
\(197\) −4.49176 2.59332i −0.320025 0.184766i 0.331379 0.943498i \(-0.392486\pi\)
−0.651404 + 0.758731i \(0.725820\pi\)
\(198\) 0 0
\(199\) 18.4938 + 10.6774i 1.31099 + 0.756900i 0.982260 0.187524i \(-0.0600464\pi\)
0.328729 + 0.944424i \(0.393380\pi\)
\(200\) 0 0
\(201\) 23.5722 12.2991i 1.66266 0.867510i
\(202\) 0 0
\(203\) −15.5977 2.78468i −1.09475 0.195447i
\(204\) 0 0
\(205\) −2.06031 + 11.6846i −0.143898 + 0.816088i
\(206\) 0 0
\(207\) 16.4897 + 4.38523i 1.14612 + 0.304795i
\(208\) 0 0
\(209\) 3.69830 20.9741i 0.255817 1.45081i
\(210\) 0 0
\(211\) 15.7930 + 5.74820i 1.08724 + 0.395722i 0.822597 0.568625i \(-0.192524\pi\)
0.264641 + 0.964347i \(0.414747\pi\)
\(212\) 0 0
\(213\) −0.898826 + 4.07244i −0.0615865 + 0.279039i
\(214\) 0 0
\(215\) 2.37274 4.10970i 0.161819 0.280279i
\(216\) 0 0
\(217\) −4.05336 + 11.0629i −0.275160 + 0.750998i
\(218\) 0 0
\(219\) 1.49173 + 1.36435i 0.100802 + 0.0921941i
\(220\) 0 0
\(221\) −5.44777 + 0.960589i −0.366457 + 0.0646162i
\(222\) 0 0
\(223\) −0.0697119 0.0122921i −0.00466825 0.000823139i 0.171314 0.985217i \(-0.445199\pi\)
−0.175982 + 0.984393i \(0.556310\pi\)
\(224\) 0 0
\(225\) 10.8330 + 0.927264i 0.722200 + 0.0618176i
\(226\) 0 0
\(227\) −6.73735 5.65331i −0.447174 0.375223i 0.391212 0.920301i \(-0.372056\pi\)
−0.838386 + 0.545077i \(0.816500\pi\)
\(228\) 0 0
\(229\) −20.2872 + 3.57718i −1.34062 + 0.236387i −0.797525 0.603286i \(-0.793858\pi\)
−0.543092 + 0.839673i \(0.682747\pi\)
\(230\) 0 0
\(231\) −11.6445 + 8.91303i −0.766154 + 0.586434i
\(232\) 0 0
\(233\) 10.8947i 0.713734i −0.934155 0.356867i \(-0.883845\pi\)
0.934155 0.356867i \(-0.116155\pi\)
\(234\) 0 0
\(235\) −9.93542 −0.648115
\(236\) 0 0
\(237\) 6.63648 16.0645i 0.431086 1.04350i
\(238\) 0 0
\(239\) 4.63739 0.817697i 0.299968 0.0528924i −0.0216386 0.999766i \(-0.506888\pi\)
0.321606 + 0.946873i \(0.395777\pi\)
\(240\) 0 0
\(241\) −19.4671 3.43258i −1.25399 0.221112i −0.493086 0.869981i \(-0.664131\pi\)
−0.760900 + 0.648869i \(0.775242\pi\)
\(242\) 0 0
\(243\) 8.31384 13.1864i 0.533333 0.845905i
\(244\) 0 0
\(245\) 1.39119 + 8.09189i 0.0888796 + 0.516972i
\(246\) 0 0
\(247\) −10.9328 3.97921i −0.695637 0.253191i
\(248\) 0 0
\(249\) −11.8695 + 1.57399i −0.752200 + 0.0997478i
\(250\) 0 0
\(251\) −4.08899 + 7.08234i −0.258095 + 0.447033i −0.965731 0.259543i \(-0.916428\pi\)
0.707637 + 0.706576i \(0.249761\pi\)
\(252\) 0 0
\(253\) −9.10015 15.7619i −0.572121 0.990943i
\(254\) 0 0
\(255\) −5.42542 3.44921i −0.339753 0.215998i
\(256\) 0 0
\(257\) 3.36785 + 19.1000i 0.210081 + 1.19143i 0.889241 + 0.457438i \(0.151233\pi\)
−0.679160 + 0.733990i \(0.737656\pi\)
\(258\) 0 0
\(259\) 12.5271 + 21.8051i 0.778398 + 1.35490i
\(260\) 0 0
\(261\) −14.7361 10.2771i −0.912140 0.636138i
\(262\) 0 0
\(263\) −3.61617 9.93536i −0.222983 0.612640i 0.776872 0.629658i \(-0.216805\pi\)
−0.999855 + 0.0170178i \(0.994583\pi\)
\(264\) 0 0
\(265\) 5.44418 14.9577i 0.334433 0.918847i
\(266\) 0 0
\(267\) −19.4349 4.28947i −1.18940 0.262511i
\(268\) 0 0
\(269\) −1.21301 2.10099i −0.0739585 0.128100i 0.826674 0.562681i \(-0.190230\pi\)
−0.900633 + 0.434581i \(0.856897\pi\)
\(270\) 0 0
\(271\) −13.7260 7.92468i −0.833792 0.481390i 0.0213570 0.999772i \(-0.493201\pi\)
−0.855149 + 0.518382i \(0.826535\pi\)
\(272\) 0 0
\(273\) 3.69042 + 7.11001i 0.223354 + 0.430317i
\(274\) 0 0
\(275\) −7.45465 8.88411i −0.449532 0.535732i
\(276\) 0 0
\(277\) 6.24095 2.27152i 0.374982 0.136482i −0.147652 0.989039i \(-0.547172\pi\)
0.522634 + 0.852557i \(0.324949\pi\)
\(278\) 0 0
\(279\) −9.42891 + 9.46440i −0.564494 + 0.566619i
\(280\) 0 0
\(281\) 5.25557 + 14.4396i 0.313521 + 0.861392i 0.991939 + 0.126716i \(0.0404436\pi\)
−0.678418 + 0.734676i \(0.737334\pi\)
\(282\) 0 0
\(283\) −0.862835 + 2.37062i −0.0512902 + 0.140919i −0.962692 0.270598i \(-0.912779\pi\)
0.911402 + 0.411517i \(0.135001\pi\)
\(284\) 0 0
\(285\) −6.25476 11.9878i −0.370500 0.710095i
\(286\) 0 0
\(287\) 25.1293 + 9.20719i 1.48334 + 0.543483i
\(288\) 0 0
\(289\) 3.49294 + 6.04995i 0.205467 + 0.355879i
\(290\) 0 0
\(291\) −0.322437 0.133203i −0.0189016 0.00780851i
\(292\) 0 0
\(293\) −0.425049 2.41057i −0.0248316 0.140827i 0.969871 0.243617i \(-0.0783341\pi\)
−0.994703 + 0.102790i \(0.967223\pi\)
\(294\) 0 0
\(295\) 9.85108 + 8.26604i 0.573552 + 0.481267i
\(296\) 0 0
\(297\) −16.2232 + 3.64459i −0.941368 + 0.211481i
\(298\) 0 0
\(299\) −9.34282 + 3.40051i −0.540309 + 0.196657i
\(300\) 0 0
\(301\) −8.18512 6.89799i −0.471782 0.397593i
\(302\) 0 0
\(303\) 3.84058 9.29667i 0.220636 0.534080i
\(304\) 0 0
\(305\) 3.04558i 0.174389i
\(306\) 0 0
\(307\) 16.1947 9.34999i 0.924278 0.533632i 0.0392804 0.999228i \(-0.487493\pi\)
0.884997 + 0.465596i \(0.154160\pi\)
\(308\) 0 0
\(309\) −9.16544 0.391548i −0.521403 0.0222744i
\(310\) 0 0
\(311\) −0.473541 0.172355i −0.0268521 0.00977336i 0.328559 0.944483i \(-0.393437\pi\)
−0.355411 + 0.934710i \(0.615659\pi\)
\(312\) 0 0
\(313\) 18.4405 + 3.25157i 1.04232 + 0.183789i 0.668501 0.743712i \(-0.266936\pi\)
0.373821 + 0.927501i \(0.378048\pi\)
\(314\) 0 0
\(315\) −2.41192 + 8.99210i −0.135896 + 0.506647i
\(316\) 0 0
\(317\) 16.8363 20.0647i 0.945622 1.12695i −0.0461509 0.998934i \(-0.514696\pi\)
0.991772 0.128013i \(-0.0408600\pi\)
\(318\) 0 0
\(319\) 3.32770 + 18.8723i 0.186315 + 1.05665i
\(320\) 0 0
\(321\) −15.5744 + 4.92669i −0.869280 + 0.274981i
\(322\) 0 0
\(323\) 21.0616i 1.17190i
\(324\) 0 0
\(325\) −5.48661 + 3.16770i −0.304342 + 0.175712i
\(326\) 0 0
\(327\) 27.7271 + 6.11964i 1.53331 + 0.338417i
\(328\) 0 0
\(329\) −3.93876 + 22.0620i −0.217151 + 1.21632i
\(330\) 0 0
\(331\) 11.7118 + 9.82741i 0.643741 + 0.540163i 0.905165 0.425061i \(-0.139747\pi\)
−0.261423 + 0.965224i \(0.584192\pi\)
\(332\) 0 0
\(333\) 2.53855 + 28.4012i 0.139112 + 1.55638i
\(334\) 0 0
\(335\) −16.9195 + 6.15818i −0.924409 + 0.336457i
\(336\) 0 0
\(337\) −10.5844 + 8.88138i −0.576570 + 0.483800i −0.883819 0.467830i \(-0.845036\pi\)
0.307249 + 0.951629i \(0.400592\pi\)
\(338\) 0 0
\(339\) 6.58236 + 12.6156i 0.357504 + 0.685188i
\(340\) 0 0
\(341\) 14.2502 0.771690
\(342\) 0 0
\(343\) 18.5199 + 0.118730i 0.999979 + 0.00641079i
\(344\) 0 0
\(345\) −10.6796 4.41187i −0.574968 0.237527i
\(346\) 0 0
\(347\) −10.6235 12.6606i −0.570299 0.679656i 0.401393 0.915906i \(-0.368526\pi\)
−0.971692 + 0.236250i \(0.924082\pi\)
\(348\) 0 0
\(349\) 4.58698 5.46655i 0.245535 0.292618i −0.629175 0.777264i \(-0.716607\pi\)
0.874710 + 0.484646i \(0.161052\pi\)
\(350\) 0 0
\(351\) 0.421774 + 9.07349i 0.0225126 + 0.484307i
\(352\) 0 0
\(353\) 2.54561 14.4369i 0.135489 0.768396i −0.839029 0.544087i \(-0.816876\pi\)
0.974518 0.224310i \(-0.0720127\pi\)
\(354\) 0 0
\(355\) 0.965942 2.65390i 0.0512669 0.140855i
\(356\) 0 0
\(357\) −9.80994 + 10.6800i −0.519197 + 0.565244i
\(358\) 0 0
\(359\) 4.12351 2.38071i 0.217630 0.125649i −0.387222 0.921986i \(-0.626565\pi\)
0.604853 + 0.796337i \(0.293232\pi\)
\(360\) 0 0
\(361\) 12.6482 21.9074i 0.665696 1.15302i
\(362\) 0 0
\(363\) −1.11105 0.706353i −0.0583152 0.0370739i
\(364\) 0 0
\(365\) −0.879977 1.04872i −0.0460601 0.0548923i
\(366\) 0 0
\(367\) 3.85331 4.59220i 0.201141 0.239711i −0.656039 0.754727i \(-0.727770\pi\)
0.857181 + 0.515016i \(0.172214\pi\)
\(368\) 0 0
\(369\) 21.4984 + 21.4178i 1.11916 + 1.11496i
\(370\) 0 0
\(371\) −31.0560 18.0188i −1.61235 0.935489i
\(372\) 0 0
\(373\) −26.1862 + 21.9728i −1.35587 + 1.13771i −0.378634 + 0.925546i \(0.623606\pi\)
−0.977234 + 0.212162i \(0.931949\pi\)
\(374\) 0 0
\(375\) −17.1092 3.77615i −0.883513 0.195000i
\(376\) 0 0
\(377\) 10.4686 0.539159
\(378\) 0 0
\(379\) −8.62058 −0.442810 −0.221405 0.975182i \(-0.571064\pi\)
−0.221405 + 0.975182i \(0.571064\pi\)
\(380\) 0 0
\(381\) 2.29205 + 7.24572i 0.117425 + 0.371209i
\(382\) 0 0
\(383\) −10.7408 + 9.01256i −0.548827 + 0.460520i −0.874544 0.484947i \(-0.838839\pi\)
0.325717 + 0.945467i \(0.394394\pi\)
\(384\) 0 0
\(385\) 8.61070 4.94689i 0.438842 0.252117i
\(386\) 0 0
\(387\) −5.15012 10.9905i −0.261795 0.558679i
\(388\) 0 0
\(389\) −20.9070 + 24.9160i −1.06003 + 1.26329i −0.0965967 + 0.995324i \(0.530796\pi\)
−0.963429 + 0.267965i \(0.913649\pi\)
\(390\) 0 0
\(391\) −11.5692 13.7877i −0.585082 0.697274i
\(392\) 0 0
\(393\) −15.9547 + 8.32457i −0.804811 + 0.419919i
\(394\) 0 0
\(395\) −5.88533 + 10.1937i −0.296123 + 0.512900i
\(396\) 0 0
\(397\) −1.70486 + 0.984301i −0.0855645 + 0.0494007i −0.542172 0.840268i \(-0.682398\pi\)
0.456607 + 0.889668i \(0.349064\pi\)
\(398\) 0 0
\(399\) −29.0989 + 9.13656i −1.45677 + 0.457400i
\(400\) 0 0
\(401\) −8.46540 + 23.2585i −0.422742 + 1.16147i 0.527389 + 0.849624i \(0.323171\pi\)
−0.950131 + 0.311850i \(0.899051\pi\)
\(402\) 0 0
\(403\) 1.35177 7.66629i 0.0673366 0.381885i
\(404\) 0 0
\(405\) −6.75516 + 8.11218i −0.335666 + 0.403097i
\(406\) 0 0
\(407\) 19.5505 23.2994i 0.969085 1.15491i
\(408\) 0 0
\(409\) 20.4743 + 24.4003i 1.01239 + 1.20652i 0.978320 + 0.207097i \(0.0664016\pi\)
0.0340671 + 0.999420i \(0.489154\pi\)
\(410\) 0 0
\(411\) 11.5639 8.89058i 0.570407 0.438540i
\(412\) 0 0
\(413\) 22.2604 18.5978i 1.09536 0.915136i
\(414\) 0 0
\(415\) 8.10840 0.398026
\(416\) 0 0
\(417\) 16.3763 25.7590i 0.801951 1.26142i
\(418\) 0 0
\(419\) −28.8373 + 24.1974i −1.40879 + 1.18212i −0.451763 + 0.892138i \(0.649205\pi\)
−0.957032 + 0.289981i \(0.906351\pi\)
\(420\) 0 0
\(421\) 3.47410 1.26447i 0.169317 0.0616264i −0.255971 0.966685i \(-0.582395\pi\)
0.425288 + 0.905058i \(0.360173\pi\)
\(422\) 0 0
\(423\) −14.5363 + 20.8432i −0.706780 + 1.01343i
\(424\) 0 0
\(425\) −8.78563 7.37202i −0.426166 0.357595i
\(426\) 0 0
\(427\) −6.76282 1.20738i −0.327276 0.0584290i
\(428\) 0 0
\(429\) 6.53893 7.14946i 0.315703 0.345179i
\(430\) 0 0
\(431\) −4.28781 + 2.47557i −0.206536 + 0.119244i −0.599701 0.800224i \(-0.704714\pi\)
0.393164 + 0.919468i \(0.371380\pi\)
\(432\) 0 0
\(433\) 6.70918i 0.322423i −0.986920 0.161211i \(-0.948460\pi\)
0.986920 0.161211i \(-0.0515401\pi\)
\(434\) 0 0
\(435\) 8.97776 + 8.21111i 0.430451 + 0.393692i
\(436\) 0 0
\(437\) −6.57334 37.2792i −0.314445 1.78331i
\(438\) 0 0
\(439\) 0.243630 0.290347i 0.0116278 0.0138575i −0.760199 0.649690i \(-0.774899\pi\)
0.771827 + 0.635833i \(0.219343\pi\)
\(440\) 0 0
\(441\) 19.0111 + 8.92055i 0.905293 + 0.424788i
\(442\) 0 0
\(443\) 16.6943 + 2.94365i 0.793169 + 0.139857i 0.555530 0.831496i \(-0.312515\pi\)
0.237639 + 0.971353i \(0.423626\pi\)
\(444\) 0 0
\(445\) 12.6652 + 4.60977i 0.600390 + 0.218524i
\(446\) 0 0
\(447\) −17.3084 + 27.2251i −0.818659 + 1.28770i
\(448\) 0 0
\(449\) −15.9872 + 9.23020i −0.754481 + 0.435600i −0.827311 0.561744i \(-0.810130\pi\)
0.0728294 + 0.997344i \(0.476797\pi\)
\(450\) 0 0
\(451\) 32.3692i 1.52421i
\(452\) 0 0
\(453\) −11.0428 + 1.46436i −0.518834 + 0.0688016i
\(454\) 0 0
\(455\) −1.84451 5.10164i −0.0864719 0.239169i
\(456\) 0 0
\(457\) 1.87106 0.681010i 0.0875245 0.0318563i −0.297887 0.954601i \(-0.596282\pi\)
0.385411 + 0.922745i \(0.374060\pi\)
\(458\) 0 0
\(459\) −15.1738 + 6.33535i −0.708253 + 0.295709i
\(460\) 0 0
\(461\) −23.4896 19.7101i −1.09402 0.917992i −0.0970119 0.995283i \(-0.530928\pi\)
−0.997009 + 0.0772911i \(0.975373\pi\)
\(462\) 0 0
\(463\) 1.76880 + 10.0313i 0.0822029 + 0.466196i 0.997925 + 0.0643841i \(0.0205083\pi\)
−0.915722 + 0.401812i \(0.868381\pi\)
\(464\) 0 0
\(465\) 7.17239 5.51428i 0.332612 0.255718i
\(466\) 0 0
\(467\) −6.33793 10.9776i −0.293285 0.507984i 0.681300 0.732004i \(-0.261415\pi\)
−0.974584 + 0.224021i \(0.928082\pi\)
\(468\) 0 0
\(469\) 6.96701 + 40.0117i 0.321707 + 1.84757i
\(470\) 0 0
\(471\) −3.65789 + 5.75365i −0.168547 + 0.265114i
\(472\) 0 0
\(473\) −4.42794 + 12.1657i −0.203597 + 0.559377i
\(474\) 0 0
\(475\) −8.24990 22.6664i −0.378531 1.04001i
\(476\) 0 0
\(477\) −23.4142 33.3056i −1.07206 1.52496i
\(478\) 0 0
\(479\) −32.9769 + 12.0026i −1.50675 + 0.548413i −0.957798 0.287441i \(-0.907196\pi\)
−0.548953 + 0.835853i \(0.684973\pi\)
\(480\) 0 0
\(481\) −10.6800 12.7280i −0.486968 0.580346i
\(482\) 0 0
\(483\) −14.0305 + 21.9654i −0.638409 + 0.999458i
\(484\) 0 0
\(485\) 0.204601 + 0.118127i 0.00929046 + 0.00536385i
\(486\) 0 0
\(487\) −2.49812 4.32688i −0.113201 0.196070i 0.803858 0.594821i \(-0.202777\pi\)
−0.917059 + 0.398751i \(0.869444\pi\)
\(488\) 0 0
\(489\) 12.7504 + 40.3069i 0.576591 + 1.82274i
\(490\) 0 0
\(491\) 4.65547 12.7908i 0.210098 0.577241i −0.789222 0.614108i \(-0.789516\pi\)
0.999320 + 0.0368676i \(0.0117380\pi\)
\(492\) 0 0
\(493\) 6.48163 + 17.8081i 0.291918 + 0.802038i
\(494\) 0 0
\(495\) 11.2155 1.00246i 0.504098 0.0450572i
\(496\) 0 0
\(497\) −5.51017 3.19702i −0.247165 0.143406i
\(498\) 0 0
\(499\) −2.86951 16.2738i −0.128457 0.728515i −0.979194 0.202924i \(-0.934955\pi\)
0.850738 0.525591i \(-0.176156\pi\)
\(500\) 0 0
\(501\) 5.07905 2.65005i 0.226915 0.118396i
\(502\) 0 0
\(503\) −4.71614 8.16859i −0.210282 0.364219i 0.741521 0.670930i \(-0.234105\pi\)
−0.951803 + 0.306711i \(0.900772\pi\)
\(504\) 0 0
\(505\) −3.40588 + 5.89916i −0.151560 + 0.262509i
\(506\) 0 0
\(507\) 10.4981 + 13.6548i 0.466236 + 0.606430i
\(508\) 0 0
\(509\) 30.9222 + 11.2548i 1.37060 + 0.498858i 0.919316 0.393521i \(-0.128743\pi\)
0.451286 + 0.892379i \(0.350965\pi\)
\(510\) 0 0
\(511\) −2.67757 + 1.53828i −0.118449 + 0.0680493i
\(512\) 0 0
\(513\) −34.3000 4.41740i −1.51438 0.195033i
\(514\) 0 0
\(515\) 6.11811 + 1.07879i 0.269596 + 0.0475370i
\(516\) 0 0
\(517\) 26.6936 4.70681i 1.17399 0.207005i
\(518\) 0 0
\(519\) −7.05949 9.18224i −0.309877 0.403056i
\(520\) 0 0
\(521\) 4.48631 0.196549 0.0982745 0.995159i \(-0.468668\pi\)
0.0982745 + 0.995159i \(0.468668\pi\)
\(522\) 0 0
\(523\) 33.6813i 1.47278i −0.676556 0.736391i \(-0.736528\pi\)
0.676556 0.736391i \(-0.263472\pi\)
\(524\) 0 0
\(525\) −6.37405 + 15.3363i −0.278186 + 0.669333i
\(526\) 0 0
\(527\) 13.8781 2.44709i 0.604540 0.106597i
\(528\) 0 0
\(529\) −7.16183 6.00949i −0.311384 0.261282i
\(530\) 0 0
\(531\) 31.7540 8.57241i 1.37801 0.372011i
\(532\) 0 0
\(533\) −17.4140 3.07055i −0.754283 0.133000i
\(534\) 0 0
\(535\) 10.8941 1.92092i 0.470991 0.0830485i
\(536\) 0 0
\(537\) 10.3136 3.26253i 0.445066 0.140788i
\(538\) 0 0
\(539\) −7.57117 21.0815i −0.326114 0.908046i
\(540\) 0 0
\(541\) −13.5046 + 23.3907i −0.580610 + 1.00565i 0.414797 + 0.909914i \(0.363853\pi\)
−0.995407 + 0.0957324i \(0.969481\pi\)
\(542\) 0 0
\(543\) 1.20228 0.380320i 0.0515949 0.0163211i
\(544\) 0 0
\(545\) −18.0691 6.57660i −0.773994 0.281711i
\(546\) 0 0
\(547\) 7.54588 42.7948i 0.322638 1.82977i −0.203137 0.979150i \(-0.565114\pi\)
0.525775 0.850623i \(-0.323775\pi\)
\(548\) 0 0
\(549\) −6.38922 4.45592i −0.272685 0.190174i
\(550\) 0 0
\(551\) −6.92119 + 39.2520i −0.294853 + 1.67219i
\(552\) 0 0
\(553\) 20.3024 + 17.1098i 0.863344 + 0.727581i
\(554\) 0 0
\(555\) 0.824171 19.2924i 0.0349841 0.818916i
\(556\) 0 0
\(557\) 11.9269 + 6.88597i 0.505357 + 0.291768i 0.730923 0.682460i \(-0.239090\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(558\) 0 0
\(559\) 6.12483 + 3.53617i 0.259053 + 0.149564i
\(560\) 0 0
\(561\) 16.2106 + 6.69681i 0.684411 + 0.282740i
\(562\) 0 0
\(563\) 14.5706 12.2262i 0.614080 0.515274i −0.281857 0.959456i \(-0.590950\pi\)
0.895936 + 0.444183i \(0.146506\pi\)
\(564\) 0 0
\(565\) −3.29580 9.05515i −0.138656 0.380953i
\(566\) 0 0
\(567\) 15.3354 + 18.2161i 0.644028 + 0.765002i
\(568\) 0 0
\(569\) −5.30990 14.5888i −0.222603 0.611596i 0.777242 0.629201i \(-0.216618\pi\)
−0.999845 + 0.0176056i \(0.994396\pi\)
\(570\) 0 0
\(571\) 15.3842 12.9089i 0.643810 0.540220i −0.261376 0.965237i \(-0.584176\pi\)
0.905186 + 0.425017i \(0.139732\pi\)
\(572\) 0 0
\(573\) −3.97581 1.64246i −0.166092 0.0686149i
\(574\) 0 0
\(575\) −17.8515 10.3066i −0.744458 0.429813i
\(576\) 0 0
\(577\) −15.7602 9.09916i −0.656106 0.378803i 0.134686 0.990888i \(-0.456998\pi\)
−0.790792 + 0.612085i \(0.790331\pi\)
\(578\) 0 0
\(579\) 1.31925 30.8814i 0.0548263 1.28339i
\(580\) 0 0
\(581\) 3.21446 18.0050i 0.133358 0.746974i
\(582\) 0 0
\(583\) −7.54086 + 42.7663i −0.312310 + 1.77120i
\(584\) 0 0
\(585\) 0.524601 6.12879i 0.0216896 0.253394i
\(586\) 0 0
\(587\) 7.53824 42.7515i 0.311136 1.76454i −0.281974 0.959422i \(-0.590989\pi\)
0.593111 0.805121i \(-0.297900\pi\)
\(588\) 0 0
\(589\) 27.8511 + 10.1370i 1.14759 + 0.417687i
\(590\) 0 0
\(591\) 8.56520 2.70944i 0.352325 0.111452i
\(592\) 0 0
\(593\) −19.1883 + 33.2351i −0.787970 + 1.36480i 0.139239 + 0.990259i \(0.455534\pi\)
−0.927209 + 0.374544i \(0.877799\pi\)
\(594\) 0 0
\(595\) 7.53640 6.29639i 0.308962 0.258127i
\(596\) 0 0
\(597\) −35.2652 + 11.1555i −1.44331 + 0.456564i
\(598\) 0 0
\(599\) −9.42981 + 1.66273i −0.385291 + 0.0679373i −0.362939 0.931813i \(-0.618227\pi\)
−0.0223524 + 0.999750i \(0.507116\pi\)
\(600\) 0 0
\(601\) 22.7261 + 4.00723i 0.927018 + 0.163458i 0.616721 0.787181i \(-0.288460\pi\)
0.310297 + 0.950640i \(0.399572\pi\)
\(602\) 0 0
\(603\) −11.8355 + 44.5047i −0.481977 + 1.81237i
\(604\) 0 0
\(605\) 0.682994 + 0.573100i 0.0277677 + 0.0232998i
\(606\) 0 0
\(607\) 7.21768 1.27267i 0.292957 0.0516561i −0.0252384 0.999681i \(-0.508034\pi\)
0.318195 + 0.948025i \(0.396923\pi\)
\(608\) 0 0
\(609\) 21.7922 16.6803i 0.883064 0.675920i
\(610\) 0 0
\(611\) 14.8071i 0.599031i
\(612\) 0 0
\(613\) −19.3424 −0.781231 −0.390615 0.920554i \(-0.627738\pi\)
−0.390615 + 0.920554i \(0.627738\pi\)
\(614\) 0 0
\(615\) −12.5257 16.2921i −0.505084 0.656960i
\(616\) 0 0
\(617\) −18.4581 + 3.25466i −0.743094 + 0.131028i −0.532362 0.846517i \(-0.678696\pi\)
−0.210731 + 0.977544i \(0.567585\pi\)
\(618\) 0 0
\(619\) 36.0584 + 6.35806i 1.44931 + 0.255552i 0.842242 0.539099i \(-0.181235\pi\)
0.607066 + 0.794652i \(0.292346\pi\)
\(620\) 0 0
\(621\) −24.8806 + 15.9494i −0.998423 + 0.640027i
\(622\) 0 0
\(623\) 15.2571 26.2962i 0.611264 1.05353i
\(624\) 0 0
\(625\) −5.87859 2.13963i −0.235143 0.0855852i
\(626\) 0 0
\(627\) 22.4838 + 29.2446i 0.897918 + 1.16792i
\(628\) 0 0
\(629\) 15.0391 26.0484i 0.599646 1.03862i
\(630\) 0 0
\(631\) 11.0792 + 19.1897i 0.441056 + 0.763931i 0.997768 0.0667740i \(-0.0212707\pi\)
−0.556712 + 0.830706i \(0.687937\pi\)
\(632\) 0 0
\(633\) −25.8081 + 13.4657i −1.02578 + 0.535213i
\(634\) 0 0
\(635\) −0.893671 5.06826i −0.0354642 0.201128i
\(636\) 0 0
\(637\) −12.0596 + 2.07333i −0.477820 + 0.0821484i
\(638\) 0 0
\(639\) −4.15430 5.90929i −0.164341 0.233768i
\(640\) 0 0
\(641\) −16.1005 44.2359i −0.635933 1.74721i −0.664137 0.747611i \(-0.731201\pi\)
0.0282038 0.999602i \(-0.491021\pi\)
\(642\) 0 0
\(643\) 2.45049 6.73265i 0.0966377 0.265510i −0.881949 0.471345i \(-0.843769\pi\)
0.978587 + 0.205835i \(0.0659910\pi\)
\(644\) 0 0
\(645\) 2.47898 + 7.83666i 0.0976098 + 0.308568i
\(646\) 0 0
\(647\) −9.26911 16.0546i −0.364406 0.631170i 0.624274 0.781205i \(-0.285395\pi\)
−0.988681 + 0.150035i \(0.952061\pi\)
\(648\) 0 0
\(649\) −30.3830 17.5416i −1.19264 0.688569i
\(650\) 0 0
\(651\) −9.40128 18.1126i −0.368465 0.709890i
\(652\) 0 0
\(653\) 28.2615 + 33.6807i 1.10596 + 1.31803i 0.943522 + 0.331309i \(0.107490\pi\)
0.162434 + 0.986719i \(0.448065\pi\)
\(654\) 0 0
\(655\) 11.4519 4.16814i 0.447461 0.162863i
\(656\) 0 0
\(657\) −3.48755 + 0.311723i −0.136062 + 0.0121615i
\(658\) 0 0
\(659\) 12.0098 + 32.9965i 0.467834 + 1.28536i 0.919470 + 0.393160i \(0.128618\pi\)
−0.451636 + 0.892202i \(0.649160\pi\)
\(660\) 0 0
\(661\) 0.905052 2.48661i 0.0352025 0.0967180i −0.920846 0.389926i \(-0.872501\pi\)
0.956049 + 0.293208i \(0.0947228\pi\)
\(662\) 0 0
\(663\) 5.14048 8.08569i 0.199640 0.314022i
\(664\) 0 0
\(665\) 20.3481 3.54311i 0.789067 0.137396i
\(666\) 0 0
\(667\) 17.0305 + 29.4977i 0.659423 + 1.14215i
\(668\) 0 0
\(669\) 0.0972007 0.0747299i 0.00375800 0.00288922i
\(670\) 0 0
\(671\) 1.44281 + 8.18259i 0.0556991 + 0.315886i
\(672\) 0 0
\(673\) 8.03878 + 6.74534i 0.309872 + 0.260014i 0.784439 0.620206i \(-0.212951\pi\)
−0.474567 + 0.880219i \(0.657395\pi\)
\(674\) 0 0
\(675\) −13.8484 + 12.7617i −0.533027 + 0.491199i
\(676\) 0 0
\(677\) 41.3472 15.0491i 1.58910 0.578386i 0.611944 0.790901i \(-0.290388\pi\)
0.977158 + 0.212516i \(0.0681657\pi\)
\(678\) 0 0
\(679\) 0.343416 0.407496i 0.0131791 0.0156383i
\(680\) 0 0
\(681\) 15.1012 2.00254i 0.578678 0.0767374i
\(682\) 0 0
\(683\) 16.4121i 0.627990i 0.949425 + 0.313995i \(0.101667\pi\)
−0.949425 + 0.313995i \(0.898333\pi\)
\(684\) 0 0
\(685\) −8.55459 + 4.93900i −0.326854 + 0.188709i
\(686\) 0 0
\(687\) 19.1429 30.1107i 0.730346 1.14879i
\(688\) 0 0
\(689\) 22.2921 + 8.11365i 0.849260 + 0.309105i
\(690\) 0 0
\(691\) 0.661749 + 0.116684i 0.0251741 + 0.00443888i 0.186221 0.982508i \(-0.440376\pi\)
−0.161047 + 0.986947i \(0.551487\pi\)
\(692\) 0 0
\(693\) 2.22022 25.3018i 0.0843391 0.961137i
\(694\) 0 0
\(695\) −13.2869 + 15.8347i −0.504001 + 0.600645i
\(696\) 0 0
\(697\) −5.55855 31.5241i −0.210545 1.19406i
\(698\) 0 0
\(699\) 13.9245 + 12.7354i 0.526672 + 0.481697i
\(700\) 0 0
\(701\) 51.7991i 1.95643i 0.207606 + 0.978213i \(0.433433\pi\)
−0.207606 + 0.978213i \(0.566567\pi\)
\(702\) 0 0
\(703\) 54.7847 31.6300i 2.06624 1.19295i
\(704\) 0 0
\(705\) 11.6141 12.6985i 0.437411 0.478252i
\(706\) 0 0
\(707\) 11.7491 + 9.90154i 0.441871 + 0.372386i
\(708\) 0 0
\(709\) 13.4230 + 11.2632i 0.504110 + 0.422998i 0.859051 0.511890i \(-0.171055\pi\)
−0.354941 + 0.934889i \(0.615499\pi\)
\(710\) 0 0
\(711\) 12.7743 + 27.2609i 0.479075 + 1.02236i
\(712\) 0 0
\(713\) 23.8007 8.66274i 0.891343 0.324422i
\(714\) 0 0
\(715\) −5.02620 + 4.21748i −0.187969 + 0.157725i
\(716\) 0 0
\(717\) −4.37581 + 6.88290i −0.163418 + 0.257047i
\(718\) 0 0
\(719\) −17.9033 −0.667680 −0.333840 0.942630i \(-0.608344\pi\)
−0.333840 + 0.942630i \(0.608344\pi\)
\(720\) 0 0
\(721\) 4.82093 13.1578i 0.179541 0.490023i
\(722\) 0 0
\(723\) 27.1434 20.8684i 1.00947 0.776103i
\(724\) 0 0
\(725\) 13.9510 + 16.6262i 0.518128 + 0.617481i
\(726\) 0 0
\(727\) −20.1921 + 24.0641i −0.748885 + 0.892487i −0.997091 0.0762207i \(-0.975715\pi\)
0.248206 + 0.968707i \(0.420159\pi\)
\(728\) 0 0
\(729\) 7.13497 + 26.0402i 0.264258 + 0.964452i
\(730\) 0 0
\(731\) −2.22320 + 12.6084i −0.0822281 + 0.466339i
\(732\) 0 0
\(733\) −14.6996 + 40.3868i −0.542942 + 1.49172i 0.300119 + 0.953902i \(0.402974\pi\)
−0.843060 + 0.537819i \(0.819248\pi\)
\(734\) 0 0
\(735\) −11.9685 7.68099i −0.441464 0.283318i
\(736\) 0 0
\(737\) 42.5404 24.5607i 1.56700 0.904705i
\(738\) 0 0
\(739\) 9.24922 16.0201i 0.340238 0.589310i −0.644239 0.764825i \(-0.722826\pi\)
0.984477 + 0.175515i \(0.0561589\pi\)
\(740\) 0 0
\(741\) 17.8658 9.32169i 0.656317 0.342441i
\(742\) 0 0
\(743\) 2.62524 + 3.12864i 0.0963108 + 0.114779i 0.812047 0.583592i \(-0.198353\pi\)
−0.715736 + 0.698371i \(0.753909\pi\)
\(744\) 0 0
\(745\) 14.0432 16.7360i 0.514502 0.613159i
\(746\) 0 0
\(747\) 11.8632 17.0104i 0.434053 0.622377i
\(748\) 0 0
\(749\) 0.0533216 24.9522i 0.00194833 0.911734i
\(750\) 0 0
\(751\) −9.99749 + 8.38889i −0.364814 + 0.306115i −0.806706 0.590953i \(-0.798752\pi\)
0.441892 + 0.897068i \(0.354307\pi\)
\(752\) 0 0
\(753\) −4.27208 13.5051i −0.155683 0.492153i
\(754\) 0 0
\(755\) 7.54362 0.274540
\(756\) 0 0
\(757\) −13.3825 −0.486396 −0.243198 0.969977i \(-0.578196\pi\)
−0.243198 + 0.969977i \(0.578196\pi\)
\(758\) 0 0
\(759\) 30.7830 + 6.79410i 1.11735 + 0.246610i
\(760\) 0 0
\(761\) −36.7246 + 30.8156i −1.33127 + 1.11706i −0.347485 + 0.937686i \(0.612964\pi\)
−0.983780 + 0.179379i \(0.942591\pi\)
\(762\) 0 0
\(763\) −21.7668 + 37.5159i −0.788012 + 1.35817i
\(764\) 0 0
\(765\) 10.7505 2.90225i 0.388686 0.104931i
\(766\) 0 0
\(767\) −12.3192 + 14.6814i −0.444819 + 0.530115i
\(768\) 0 0
\(769\) 3.11190 + 3.70862i 0.112218 + 0.133736i 0.819229 0.573466i \(-0.194401\pi\)
−0.707011 + 0.707202i \(0.749957\pi\)
\(770\) 0 0
\(771\) −28.3486 18.0227i −1.02095 0.649071i
\(772\) 0 0
\(773\) 2.99946 5.19522i 0.107883 0.186859i −0.807029 0.590511i \(-0.798926\pi\)
0.914913 + 0.403652i \(0.132259\pi\)
\(774\) 0 0
\(775\) 13.9771 8.06966i 0.502071 0.289871i
\(776\) 0 0
\(777\) −42.5128 9.47830i −1.52514 0.340032i
\(778\)