Properties

Label 1134.2.t.f.593.1
Level $1134$
Weight $2$
Character 1134.593
Analytic conductor $9.055$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1134.593
Dual form 1134.2.t.f.1025.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.44949 q^{5} +(2.62132 + 0.358719i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.44949 q^{5} +(2.62132 + 0.358719i) q^{7} +1.00000i q^{8} +(2.12132 - 1.22474i) q^{10} +4.24264i q^{11} +(0.621320 - 0.358719i) q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.22474 + 2.12132i) q^{17} +(-4.24264 - 2.44949i) q^{19} +(-1.22474 + 2.12132i) q^{20} +(-2.12132 - 3.67423i) q^{22} -6.00000i q^{23} +1.00000 q^{25} +(-0.358719 + 0.621320i) q^{26} +(1.62132 - 2.09077i) q^{28} +(-1.52192 - 0.878680i) q^{29} +(7.86396 + 4.54026i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.12132 - 1.22474i) q^{34} +(-6.42090 - 0.878680i) q^{35} +(-2.62132 + 4.54026i) q^{37} +4.89898 q^{38} -2.44949i q^{40} +(-1.22474 - 2.12132i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(3.67423 + 2.12132i) q^{44} +(3.00000 + 5.19615i) q^{46} +(6.42090 + 11.1213i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-0.866025 + 0.500000i) q^{50} -0.717439i q^{52} +(-12.5446 + 7.24264i) q^{53} -10.3923i q^{55} +(-0.358719 + 2.62132i) q^{56} +1.75736 q^{58} +(-1.22474 + 2.12132i) q^{59} +(-3.62132 + 2.09077i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(-1.52192 + 0.878680i) q^{65} +(-6.74264 + 11.6786i) q^{67} +2.44949 q^{68} +(6.00000 - 2.44949i) q^{70} +12.7279i q^{71} +(-4.75736 + 2.74666i) q^{73} -5.24264i q^{74} +(-4.24264 + 2.44949i) q^{76} +(-1.52192 + 11.1213i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(1.22474 + 2.12132i) q^{80} +(2.12132 + 1.22474i) q^{82} +(7.64564 - 13.2426i) q^{83} +(-3.00000 - 5.19615i) q^{85} -7.00000i q^{86} -4.24264 q^{88} +(1.52192 - 2.63604i) q^{89} +(1.75736 - 0.717439i) q^{91} +(-5.19615 - 3.00000i) q^{92} +(-11.1213 - 6.42090i) q^{94} +(10.3923 + 6.00000i) q^{95} +(2.74264 + 1.58346i) q^{97} +(-6.77962 + 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 4 q^{7} - 12 q^{13} - 4 q^{16} + 8 q^{25} - 4 q^{28} + 12 q^{31} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} + 48 q^{58} - 12 q^{61} - 8 q^{64} - 20 q^{67} + 48 q^{70} - 72 q^{73} - 20 q^{79} - 24 q^{85} + 48 q^{91} - 72 q^{94} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.44949 −1.09545 −0.547723 0.836660i \(-0.684505\pi\)
−0.547723 + 0.836660i \(0.684505\pi\)
\(6\) 0 0
\(7\) 2.62132 + 0.358719i 0.990766 + 0.135583i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.12132 1.22474i 0.670820 0.387298i
\(11\) 4.24264i 1.27920i 0.768706 + 0.639602i \(0.220901\pi\)
−0.768706 + 0.639602i \(0.779099\pi\)
\(12\) 0 0
\(13\) 0.621320 0.358719i 0.172323 0.0994909i −0.411358 0.911474i \(-0.634945\pi\)
0.583681 + 0.811983i \(0.301612\pi\)
\(14\) −2.44949 + 1.00000i −0.654654 + 0.267261i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.22474 + 2.12132i 0.297044 + 0.514496i 0.975458 0.220184i \(-0.0706658\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(18\) 0 0
\(19\) −4.24264 2.44949i −0.973329 0.561951i −0.0730792 0.997326i \(-0.523283\pi\)
−0.900249 + 0.435375i \(0.856616\pi\)
\(20\) −1.22474 + 2.12132i −0.273861 + 0.474342i
\(21\) 0 0
\(22\) −2.12132 3.67423i −0.452267 0.783349i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −0.358719 + 0.621320i −0.0703507 + 0.121851i
\(27\) 0 0
\(28\) 1.62132 2.09077i 0.306401 0.395118i
\(29\) −1.52192 0.878680i −0.282613 0.163167i 0.351993 0.936003i \(-0.385504\pi\)
−0.634606 + 0.772836i \(0.718838\pi\)
\(30\) 0 0
\(31\) 7.86396 + 4.54026i 1.41241 + 0.815455i 0.995615 0.0935461i \(-0.0298203\pi\)
0.416794 + 0.909001i \(0.363154\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −2.12132 1.22474i −0.363803 0.210042i
\(35\) −6.42090 0.878680i −1.08533 0.148524i
\(36\) 0 0
\(37\) −2.62132 + 4.54026i −0.430942 + 0.746414i −0.996955 0.0779826i \(-0.975152\pi\)
0.566012 + 0.824397i \(0.308485\pi\)
\(38\) 4.89898 0.794719
\(39\) 0 0
\(40\) 2.44949i 0.387298i
\(41\) −1.22474 2.12132i −0.191273 0.331295i 0.754399 0.656416i \(-0.227928\pi\)
−0.945672 + 0.325121i \(0.894595\pi\)
\(42\) 0 0
\(43\) −3.50000 + 6.06218i −0.533745 + 0.924473i 0.465478 + 0.885059i \(0.345882\pi\)
−0.999223 + 0.0394140i \(0.987451\pi\)
\(44\) 3.67423 + 2.12132i 0.553912 + 0.319801i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 6.42090 + 11.1213i 0.936584 + 1.62221i 0.771784 + 0.635884i \(0.219364\pi\)
0.164800 + 0.986327i \(0.447302\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0 0
\(52\) 0.717439i 0.0994909i
\(53\) −12.5446 + 7.24264i −1.72314 + 0.994853i −0.810905 + 0.585178i \(0.801025\pi\)
−0.912231 + 0.409675i \(0.865642\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) −0.358719 + 2.62132i −0.0479359 + 0.350289i
\(57\) 0 0
\(58\) 1.75736 0.230753
\(59\) −1.22474 + 2.12132i −0.159448 + 0.276172i −0.934670 0.355517i \(-0.884305\pi\)
0.775222 + 0.631689i \(0.217638\pi\)
\(60\) 0 0
\(61\) −3.62132 + 2.09077i −0.463663 + 0.267696i −0.713583 0.700571i \(-0.752929\pi\)
0.249920 + 0.968266i \(0.419596\pi\)
\(62\) −9.08052 −1.15323
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.52192 + 0.878680i −0.188771 + 0.108987i
\(66\) 0 0
\(67\) −6.74264 + 11.6786i −0.823745 + 1.42677i 0.0791303 + 0.996864i \(0.474786\pi\)
−0.902875 + 0.429903i \(0.858548\pi\)
\(68\) 2.44949 0.297044
\(69\) 0 0
\(70\) 6.00000 2.44949i 0.717137 0.292770i
\(71\) 12.7279i 1.51053i 0.655422 + 0.755263i \(0.272491\pi\)
−0.655422 + 0.755263i \(0.727509\pi\)
\(72\) 0 0
\(73\) −4.75736 + 2.74666i −0.556807 + 0.321473i −0.751863 0.659320i \(-0.770844\pi\)
0.195056 + 0.980792i \(0.437511\pi\)
\(74\) 5.24264i 0.609445i
\(75\) 0 0
\(76\) −4.24264 + 2.44949i −0.486664 + 0.280976i
\(77\) −1.52192 + 11.1213i −0.173439 + 1.26739i
\(78\) 0 0
\(79\) −0.378680 0.655892i −0.0426048 0.0737937i 0.843937 0.536443i \(-0.180232\pi\)
−0.886541 + 0.462649i \(0.846899\pi\)
\(80\) 1.22474 + 2.12132i 0.136931 + 0.237171i
\(81\) 0 0
\(82\) 2.12132 + 1.22474i 0.234261 + 0.135250i
\(83\) 7.64564 13.2426i 0.839218 1.45357i −0.0513309 0.998682i \(-0.516346\pi\)
0.890549 0.454887i \(-0.150320\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 7.00000i 0.754829i
\(87\) 0 0
\(88\) −4.24264 −0.452267
\(89\) 1.52192 2.63604i 0.161323 0.279420i −0.774020 0.633161i \(-0.781757\pi\)
0.935343 + 0.353741i \(0.115091\pi\)
\(90\) 0 0
\(91\) 1.75736 0.717439i 0.184221 0.0752080i
\(92\) −5.19615 3.00000i −0.541736 0.312772i
\(93\) 0 0
\(94\) −11.1213 6.42090i −1.14708 0.662265i
\(95\) 10.3923 + 6.00000i 1.06623 + 0.615587i
\(96\) 0 0
\(97\) 2.74264 + 1.58346i 0.278473 + 0.160776i 0.632732 0.774371i \(-0.281934\pi\)
−0.354259 + 0.935147i \(0.615267\pi\)
\(98\) −6.77962 + 1.74264i −0.684845 + 0.176033i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −7.34847 −0.731200 −0.365600 0.930772i \(-0.619136\pi\)
−0.365600 + 0.930772i \(0.619136\pi\)
\(102\) 0 0
\(103\) 11.1097i 1.09468i −0.836912 0.547338i \(-0.815641\pi\)
0.836912 0.547338i \(-0.184359\pi\)
\(104\) 0.358719 + 0.621320i 0.0351753 + 0.0609255i
\(105\) 0 0
\(106\) 7.24264 12.5446i 0.703467 1.21844i
\(107\) −2.15232 1.24264i −0.208072 0.120131i 0.392343 0.919819i \(-0.371665\pi\)
−0.600415 + 0.799688i \(0.704998\pi\)
\(108\) 0 0
\(109\) 8.86396 + 15.3528i 0.849013 + 1.47053i 0.882090 + 0.471082i \(0.156136\pi\)
−0.0330761 + 0.999453i \(0.510530\pi\)
\(110\) 5.19615 + 9.00000i 0.495434 + 0.858116i
\(111\) 0 0
\(112\) −1.00000 2.44949i −0.0944911 0.231455i
\(113\) −8.87039 + 5.12132i −0.834456 + 0.481773i −0.855376 0.518008i \(-0.826674\pi\)
0.0209200 + 0.999781i \(0.493340\pi\)
\(114\) 0 0
\(115\) 14.6969i 1.37050i
\(116\) −1.52192 + 0.878680i −0.141307 + 0.0815834i
\(117\) 0 0
\(118\) 2.44949i 0.225494i
\(119\) 2.44949 + 6.00000i 0.224544 + 0.550019i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 2.09077 3.62132i 0.189289 0.327859i
\(123\) 0 0
\(124\) 7.86396 4.54026i 0.706205 0.407727i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) −7.72792 −0.685742 −0.342871 0.939382i \(-0.611399\pi\)
−0.342871 + 0.939382i \(0.611399\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0.878680 1.52192i 0.0770653 0.133481i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −10.2426 7.94282i −0.888150 0.688729i
\(134\) 13.4853i 1.16495i
\(135\) 0 0
\(136\) −2.12132 + 1.22474i −0.181902 + 0.105021i
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) −6.98528 + 4.03295i −0.592484 + 0.342071i −0.766079 0.642746i \(-0.777795\pi\)
0.173595 + 0.984817i \(0.444462\pi\)
\(140\) −3.97141 + 5.12132i −0.335645 + 0.432831i
\(141\) 0 0
\(142\) −6.36396 11.0227i −0.534052 0.925005i
\(143\) 1.52192 + 2.63604i 0.127269 + 0.220437i
\(144\) 0 0
\(145\) 3.72792 + 2.15232i 0.309587 + 0.178740i
\(146\) 2.74666 4.75736i 0.227315 0.393722i
\(147\) 0 0
\(148\) 2.62132 + 4.54026i 0.215471 + 0.373207i
\(149\) 16.2426i 1.33065i −0.746554 0.665324i \(-0.768293\pi\)
0.746554 0.665324i \(-0.231707\pi\)
\(150\) 0 0
\(151\) 8.75736 0.712664 0.356332 0.934359i \(-0.384027\pi\)
0.356332 + 0.934359i \(0.384027\pi\)
\(152\) 2.44949 4.24264i 0.198680 0.344124i
\(153\) 0 0
\(154\) −4.24264 10.3923i −0.341882 0.837436i
\(155\) −19.2627 11.1213i −1.54722 0.893286i
\(156\) 0 0
\(157\) 9.00000 + 5.19615i 0.718278 + 0.414698i 0.814119 0.580699i \(-0.197221\pi\)
−0.0958404 + 0.995397i \(0.530554\pi\)
\(158\) 0.655892 + 0.378680i 0.0521800 + 0.0301261i
\(159\) 0 0
\(160\) −2.12132 1.22474i −0.167705 0.0968246i
\(161\) 2.15232 15.7279i 0.169626 1.23953i
\(162\) 0 0
\(163\) 4.74264 8.21449i 0.371472 0.643409i −0.618320 0.785926i \(-0.712186\pi\)
0.989792 + 0.142518i \(0.0455197\pi\)
\(164\) −2.44949 −0.191273
\(165\) 0 0
\(166\) 15.2913i 1.18683i
\(167\) −0.297173 0.514719i −0.0229959 0.0398301i 0.854298 0.519783i \(-0.173987\pi\)
−0.877294 + 0.479953i \(0.840654\pi\)
\(168\) 0 0
\(169\) −6.24264 + 10.8126i −0.480203 + 0.831736i
\(170\) 5.19615 + 3.00000i 0.398527 + 0.230089i
\(171\) 0 0
\(172\) 3.50000 + 6.06218i 0.266872 + 0.462237i
\(173\) 10.3923 + 18.0000i 0.790112 + 1.36851i 0.925897 + 0.377776i \(0.123311\pi\)
−0.135785 + 0.990738i \(0.543356\pi\)
\(174\) 0 0
\(175\) 2.62132 + 0.358719i 0.198153 + 0.0271166i
\(176\) 3.67423 2.12132i 0.276956 0.159901i
\(177\) 0 0
\(178\) 3.04384i 0.228145i
\(179\) 5.82655 3.36396i 0.435497 0.251434i −0.266189 0.963921i \(-0.585764\pi\)
0.701686 + 0.712487i \(0.252431\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i 0.931345 + 0.364138i \(0.118636\pi\)
−0.931345 + 0.364138i \(0.881364\pi\)
\(182\) −1.16320 + 1.50000i −0.0862220 + 0.111187i
\(183\) 0 0
\(184\) 6.00000 0.442326
\(185\) 6.42090 11.1213i 0.472074 0.817656i
\(186\) 0 0
\(187\) −9.00000 + 5.19615i −0.658145 + 0.379980i
\(188\) 12.8418 0.936584
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) −18.3712 + 10.6066i −1.32929 + 0.767467i −0.985190 0.171466i \(-0.945150\pi\)
−0.344101 + 0.938933i \(0.611816\pi\)
\(192\) 0 0
\(193\) 0.742641 1.28629i 0.0534564 0.0925893i −0.838059 0.545580i \(-0.816310\pi\)
0.891515 + 0.452990i \(0.149643\pi\)
\(194\) −3.16693 −0.227372
\(195\) 0 0
\(196\) 5.00000 4.89898i 0.357143 0.349927i
\(197\) 16.9706i 1.20910i −0.796566 0.604551i \(-0.793352\pi\)
0.796566 0.604551i \(-0.206648\pi\)
\(198\) 0 0
\(199\) −18.1066 + 10.4539i −1.28354 + 0.741054i −0.977494 0.210962i \(-0.932340\pi\)
−0.306049 + 0.952016i \(0.599007\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 6.36396 3.67423i 0.447767 0.258518i
\(203\) −3.67423 2.84924i −0.257881 0.199978i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 5.55487 + 9.62132i 0.387026 + 0.670349i
\(207\) 0 0
\(208\) −0.621320 0.358719i −0.0430808 0.0248727i
\(209\) 10.3923 18.0000i 0.718851 1.24509i
\(210\) 0 0
\(211\) −1.74264 3.01834i −0.119968 0.207791i 0.799787 0.600284i \(-0.204946\pi\)
−0.919755 + 0.392493i \(0.871613\pi\)
\(212\) 14.4853i 0.994853i
\(213\) 0 0
\(214\) 2.48528 0.169890
\(215\) 8.57321 14.8492i 0.584688 1.01271i
\(216\) 0 0
\(217\) 18.9853 + 14.7224i 1.28880 + 0.999424i
\(218\) −15.3528 8.86396i −1.03982 0.600343i
\(219\) 0 0
\(220\) −9.00000 5.19615i −0.606780 0.350325i
\(221\) 1.52192 + 0.878680i 0.102375 + 0.0591064i
\(222\) 0 0
\(223\) −9.00000 5.19615i −0.602685 0.347960i 0.167412 0.985887i \(-0.446459\pi\)
−0.770097 + 0.637927i \(0.779792\pi\)
\(224\) 2.09077 + 1.62132i 0.139695 + 0.108329i
\(225\) 0 0
\(226\) 5.12132 8.87039i 0.340665 0.590049i
\(227\) 25.0892 1.66523 0.832616 0.553851i \(-0.186842\pi\)
0.832616 + 0.553851i \(0.186842\pi\)
\(228\) 0 0
\(229\) 5.61642i 0.371143i 0.982631 + 0.185572i \(0.0594137\pi\)
−0.982631 + 0.185572i \(0.940586\pi\)
\(230\) −7.34847 12.7279i −0.484544 0.839254i
\(231\) 0 0
\(232\) 0.878680 1.52192i 0.0576881 0.0999188i
\(233\) 17.7408 + 10.2426i 1.16224 + 0.671018i 0.951839 0.306598i \(-0.0991908\pi\)
0.210398 + 0.977616i \(0.432524\pi\)
\(234\) 0 0
\(235\) −15.7279 27.2416i −1.02598 1.77704i
\(236\) 1.22474 + 2.12132i 0.0797241 + 0.138086i
\(237\) 0 0
\(238\) −5.12132 3.97141i −0.331966 0.257428i
\(239\) −14.0665 + 8.12132i −0.909889 + 0.525325i −0.880395 0.474240i \(-0.842723\pi\)
−0.0294934 + 0.999565i \(0.509389\pi\)
\(240\) 0 0
\(241\) 1.13770i 0.0732860i −0.999328 0.0366430i \(-0.988334\pi\)
0.999328 0.0366430i \(-0.0116664\pi\)
\(242\) 6.06218 3.50000i 0.389692 0.224989i
\(243\) 0 0
\(244\) 4.18154i 0.267696i
\(245\) −16.5160 4.60660i −1.05517 0.294305i
\(246\) 0 0
\(247\) −3.51472 −0.223636
\(248\) −4.54026 + 7.86396i −0.288307 + 0.499362i
\(249\) 0 0
\(250\) −8.48528 + 4.89898i −0.536656 + 0.309839i
\(251\) 15.2913 0.965177 0.482589 0.875847i \(-0.339697\pi\)
0.482589 + 0.875847i \(0.339697\pi\)
\(252\) 0 0
\(253\) 25.4558 1.60040
\(254\) 6.69258 3.86396i 0.419930 0.242446i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 25.0892 1.56502 0.782512 0.622636i \(-0.213938\pi\)
0.782512 + 0.622636i \(0.213938\pi\)
\(258\) 0 0
\(259\) −8.50000 + 10.9612i −0.528164 + 0.681093i
\(260\) 1.75736i 0.108987i
\(261\) 0 0
\(262\) 0 0
\(263\) 6.72792i 0.414861i −0.978250 0.207431i \(-0.933490\pi\)
0.978250 0.207431i \(-0.0665102\pi\)
\(264\) 0 0
\(265\) 30.7279 17.7408i 1.88760 1.08981i
\(266\) 12.8418 + 1.75736i 0.787381 + 0.107751i
\(267\) 0 0
\(268\) 6.74264 + 11.6786i 0.411872 + 0.713384i
\(269\) −4.89898 8.48528i −0.298696 0.517357i 0.677142 0.735853i \(-0.263218\pi\)
−0.975838 + 0.218496i \(0.929885\pi\)
\(270\) 0 0
\(271\) −16.3492 9.43924i −0.993146 0.573393i −0.0869326 0.996214i \(-0.527706\pi\)
−0.906213 + 0.422821i \(0.861040\pi\)
\(272\) 1.22474 2.12132i 0.0742611 0.128624i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 4.24264i 0.255841i
\(276\) 0 0
\(277\) 23.7279 1.42567 0.712836 0.701330i \(-0.247410\pi\)
0.712836 + 0.701330i \(0.247410\pi\)
\(278\) 4.03295 6.98528i 0.241881 0.418949i
\(279\) 0 0
\(280\) 0.878680 6.42090i 0.0525112 0.383722i
\(281\) −11.9142 6.87868i −0.710743 0.410348i 0.100593 0.994928i \(-0.467926\pi\)
−0.811336 + 0.584580i \(0.801259\pi\)
\(282\) 0 0
\(283\) −5.22792 3.01834i −0.310768 0.179422i 0.336502 0.941683i \(-0.390756\pi\)
−0.647270 + 0.762261i \(0.724089\pi\)
\(284\) 11.0227 + 6.36396i 0.654077 + 0.377632i
\(285\) 0 0
\(286\) −2.63604 1.52192i −0.155872 0.0899929i
\(287\) −2.44949 6.00000i −0.144589 0.354169i
\(288\) 0 0
\(289\) 5.50000 9.52628i 0.323529 0.560369i
\(290\) −4.30463 −0.252777
\(291\) 0 0
\(292\) 5.49333i 0.321473i
\(293\) −6.42090 11.1213i −0.375113 0.649714i 0.615231 0.788347i \(-0.289063\pi\)
−0.990344 + 0.138632i \(0.955729\pi\)
\(294\) 0 0
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) −4.54026 2.62132i −0.263897 0.152361i
\(297\) 0 0
\(298\) 8.12132 + 14.0665i 0.470455 + 0.814853i
\(299\) −2.15232 3.72792i −0.124472 0.215591i
\(300\) 0 0
\(301\) −11.3492 + 14.6354i −0.654159 + 0.843570i
\(302\) −7.58410 + 4.37868i −0.436416 + 0.251965i
\(303\) 0 0
\(304\) 4.89898i 0.280976i
\(305\) 8.87039 5.12132i 0.507917 0.293246i
\(306\) 0 0
\(307\) 26.8213i 1.53077i −0.643571 0.765386i \(-0.722548\pi\)
0.643571 0.765386i \(-0.277452\pi\)
\(308\) 8.87039 + 6.87868i 0.505437 + 0.391949i
\(309\) 0 0
\(310\) 22.2426 1.26330
\(311\) 8.57321 14.8492i 0.486142 0.842023i −0.513731 0.857951i \(-0.671737\pi\)
0.999873 + 0.0159282i \(0.00507031\pi\)
\(312\) 0 0
\(313\) 17.4853 10.0951i 0.988327 0.570611i 0.0835529 0.996503i \(-0.473373\pi\)
0.904774 + 0.425893i \(0.140040\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) −0.757359 −0.0426048
\(317\) 19.2627 11.1213i 1.08190 0.624636i 0.150492 0.988611i \(-0.451914\pi\)
0.931408 + 0.363976i \(0.118581\pi\)
\(318\) 0 0
\(319\) 3.72792 6.45695i 0.208724 0.361520i
\(320\) 2.44949 0.136931
\(321\) 0 0
\(322\) 6.00000 + 14.6969i 0.334367 + 0.819028i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 0.621320 0.358719i 0.0344647 0.0198982i
\(326\) 9.48528i 0.525341i
\(327\) 0 0
\(328\) 2.12132 1.22474i 0.117130 0.0676252i
\(329\) 12.8418 + 31.4558i 0.707991 + 1.73422i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) −7.64564 13.2426i −0.419609 0.726784i
\(333\) 0 0
\(334\) 0.514719 + 0.297173i 0.0281642 + 0.0162606i
\(335\) 16.5160 28.6066i 0.902367 1.56295i
\(336\) 0 0
\(337\) 10.7279 + 18.5813i 0.584387 + 1.01219i 0.994952 + 0.100357i \(0.0319984\pi\)
−0.410564 + 0.911832i \(0.634668\pi\)
\(338\) 12.4853i 0.679110i
\(339\) 0 0
\(340\) −6.00000 −0.325396
\(341\) −19.2627 + 33.3640i −1.04313 + 1.80676i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) −6.06218 3.50000i −0.326851 0.188707i
\(345\) 0 0
\(346\) −18.0000 10.3923i −0.967686 0.558694i
\(347\) 4.30463 + 2.48528i 0.231085 + 0.133417i 0.611072 0.791575i \(-0.290738\pi\)
−0.379988 + 0.924992i \(0.624072\pi\)
\(348\) 0 0
\(349\) −0.106602 0.0615465i −0.00570626 0.00329451i 0.497144 0.867668i \(-0.334382\pi\)
−0.502850 + 0.864373i \(0.667715\pi\)
\(350\) −2.44949 + 1.00000i −0.130931 + 0.0534522i
\(351\) 0 0
\(352\) −2.12132 + 3.67423i −0.113067 + 0.195837i
\(353\) 10.9867 0.584760 0.292380 0.956302i \(-0.405553\pi\)
0.292380 + 0.956302i \(0.405553\pi\)
\(354\) 0 0
\(355\) 31.1769i 1.65470i
\(356\) −1.52192 2.63604i −0.0806615 0.139710i
\(357\) 0 0
\(358\) −3.36396 + 5.82655i −0.177791 + 0.307943i
\(359\) −12.5446 7.24264i −0.662080 0.382252i 0.130989 0.991384i \(-0.458185\pi\)
−0.793069 + 0.609132i \(0.791518\pi\)
\(360\) 0 0
\(361\) 2.50000 + 4.33013i 0.131579 + 0.227901i
\(362\) −4.89898 8.48528i −0.257485 0.445976i
\(363\) 0 0
\(364\) 0.257359 1.88064i 0.0134893 0.0985722i
\(365\) 11.6531 6.72792i 0.609951 0.352156i
\(366\) 0 0
\(367\) 29.9882i 1.56537i −0.622416 0.782686i \(-0.713849\pi\)
0.622416 0.782686i \(-0.286151\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) 0 0
\(370\) 12.8418i 0.667613i
\(371\) −35.4815 + 14.4853i −1.84211 + 0.752038i
\(372\) 0 0
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 5.19615 9.00000i 0.268687 0.465379i
\(375\) 0 0
\(376\) −11.1213 + 6.42090i −0.573538 + 0.331132i
\(377\) −1.26080 −0.0649344
\(378\) 0 0
\(379\) −7.48528 −0.384493 −0.192247 0.981347i \(-0.561577\pi\)
−0.192247 + 0.981347i \(0.561577\pi\)
\(380\) 10.3923 6.00000i 0.533114 0.307794i
\(381\) 0 0
\(382\) 10.6066 18.3712i 0.542681 0.939951i
\(383\) 5.49333 0.280696 0.140348 0.990102i \(-0.455178\pi\)
0.140348 + 0.990102i \(0.455178\pi\)
\(384\) 0 0
\(385\) 3.72792 27.2416i 0.189993 1.38836i
\(386\) 1.48528i 0.0755988i
\(387\) 0 0
\(388\) 2.74264 1.58346i 0.139236 0.0803882i
\(389\) 15.5147i 0.786627i 0.919404 + 0.393314i \(0.128671\pi\)
−0.919404 + 0.393314i \(0.871329\pi\)
\(390\) 0 0
\(391\) 12.7279 7.34847i 0.643679 0.371628i
\(392\) −1.88064 + 6.74264i −0.0949865 + 0.340555i
\(393\) 0 0
\(394\) 8.48528 + 14.6969i 0.427482 + 0.740421i
\(395\) 0.927572 + 1.60660i 0.0466712 + 0.0808369i
\(396\) 0 0
\(397\) −13.1360 7.58410i −0.659279 0.380635i 0.132723 0.991153i \(-0.457628\pi\)
−0.792002 + 0.610518i \(0.790961\pi\)
\(398\) 10.4539 18.1066i 0.524004 0.907602i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 19.7574i 0.986635i 0.869849 + 0.493318i \(0.164216\pi\)
−0.869849 + 0.493318i \(0.835784\pi\)
\(402\) 0 0
\(403\) 6.51472 0.324521
\(404\) −3.67423 + 6.36396i −0.182800 + 0.316619i
\(405\) 0 0
\(406\) 4.60660 + 0.630399i 0.228622 + 0.0312862i
\(407\) −19.2627 11.1213i −0.954816 0.551263i
\(408\) 0 0
\(409\) 3.25736 + 1.88064i 0.161066 + 0.0929915i 0.578366 0.815777i \(-0.303690\pi\)
−0.417300 + 0.908769i \(0.637024\pi\)
\(410\) −5.19615 3.00000i −0.256620 0.148159i
\(411\) 0 0
\(412\) −9.62132 5.55487i −0.474008 0.273669i
\(413\) −3.97141 + 5.12132i −0.195420 + 0.252004i
\(414\) 0 0
\(415\) −18.7279 + 32.4377i −0.919318 + 1.59230i
\(416\) 0.717439 0.0351753
\(417\) 0 0
\(418\) 20.7846i 1.01661i
\(419\) −3.97141 6.87868i −0.194016 0.336045i 0.752562 0.658522i \(-0.228818\pi\)
−0.946577 + 0.322476i \(0.895485\pi\)
\(420\) 0 0
\(421\) 11.7279 20.3134i 0.571584 0.990012i −0.424820 0.905278i \(-0.639662\pi\)
0.996404 0.0847344i \(-0.0270042\pi\)
\(422\) 3.01834 + 1.74264i 0.146931 + 0.0848304i
\(423\) 0 0
\(424\) −7.24264 12.5446i −0.351734 0.609221i
\(425\) 1.22474 + 2.12132i 0.0594089 + 0.102899i
\(426\) 0 0
\(427\) −10.2426 + 4.18154i −0.495676 + 0.202359i
\(428\) −2.15232 + 1.24264i −0.104036 + 0.0600653i
\(429\) 0 0
\(430\) 17.1464i 0.826874i
\(431\) 1.52192 0.878680i 0.0733082 0.0423245i −0.462898 0.886412i \(-0.653190\pi\)
0.536206 + 0.844087i \(0.319857\pi\)
\(432\) 0 0
\(433\) 2.57258i 0.123630i −0.998088 0.0618152i \(-0.980311\pi\)
0.998088 0.0618152i \(-0.0196889\pi\)
\(434\) −23.8030 3.25736i −1.14258 0.156358i
\(435\) 0 0
\(436\) 17.7279 0.849013
\(437\) −14.6969 + 25.4558i −0.703050 + 1.21772i
\(438\) 0 0
\(439\) −3.72792 + 2.15232i −0.177924 + 0.102724i −0.586317 0.810082i \(-0.699423\pi\)
0.408393 + 0.912806i \(0.366089\pi\)
\(440\) 10.3923 0.495434
\(441\) 0 0
\(442\) −1.75736 −0.0835891
\(443\) 22.0454 12.7279i 1.04741 0.604722i 0.125486 0.992095i \(-0.459951\pi\)
0.921923 + 0.387374i \(0.126618\pi\)
\(444\) 0 0
\(445\) −3.72792 + 6.45695i −0.176720 + 0.306089i
\(446\) 10.3923 0.492090
\(447\) 0 0
\(448\) −2.62132 0.358719i −0.123846 0.0169479i
\(449\) 5.27208i 0.248805i −0.992232 0.124402i \(-0.960299\pi\)
0.992232 0.124402i \(-0.0397014\pi\)
\(450\) 0 0
\(451\) 9.00000 5.19615i 0.423793 0.244677i
\(452\) 10.2426i 0.481773i
\(453\) 0 0
\(454\) −21.7279 + 12.5446i −1.01974 + 0.588748i
\(455\) −4.30463 + 1.75736i −0.201804 + 0.0823863i
\(456\) 0 0
\(457\) 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) −2.80821 4.86396i −0.131219 0.227278i
\(459\) 0 0
\(460\) 12.7279 + 7.34847i 0.593442 + 0.342624i
\(461\) −10.7255 + 18.5772i −0.499538 + 0.865225i −1.00000 0.000533648i \(-0.999830\pi\)
0.500462 + 0.865758i \(0.333163\pi\)
\(462\) 0 0
\(463\) 11.0000 + 19.0526i 0.511213 + 0.885448i 0.999916 + 0.0129968i \(0.00413714\pi\)
−0.488702 + 0.872451i \(0.662530\pi\)
\(464\) 1.75736i 0.0815834i
\(465\) 0 0
\(466\) −20.4853 −0.948962
\(467\) −8.87039 + 15.3640i −0.410473 + 0.710959i −0.994941 0.100457i \(-0.967970\pi\)
0.584469 + 0.811416i \(0.301303\pi\)
\(468\) 0 0
\(469\) −21.8640 + 28.1946i −1.00958 + 1.30191i
\(470\) 27.2416 + 15.7279i 1.25656 + 0.725475i
\(471\) 0 0
\(472\) −2.12132 1.22474i −0.0976417 0.0563735i
\(473\) −25.7196 14.8492i −1.18259 0.682769i
\(474\) 0 0
\(475\) −4.24264 2.44949i −0.194666 0.112390i
\(476\) 6.42090 + 0.878680i 0.294301 + 0.0402742i
\(477\) 0 0
\(478\) 8.12132 14.0665i 0.371461 0.643389i
\(479\) 2.44949 0.111920 0.0559600 0.998433i \(-0.482178\pi\)
0.0559600 + 0.998433i \(0.482178\pi\)
\(480\) 0 0
\(481\) 3.76127i 0.171499i
\(482\) 0.568852 + 0.985281i 0.0259105 + 0.0448783i
\(483\) 0 0
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) −6.71807 3.87868i −0.305052 0.176122i
\(486\) 0 0
\(487\) −11.0000 19.0526i −0.498458 0.863354i 0.501541 0.865134i \(-0.332767\pi\)
−0.999998 + 0.00178012i \(0.999433\pi\)
\(488\) −2.09077 3.62132i −0.0946447 0.163929i
\(489\) 0 0
\(490\) 16.6066 4.26858i 0.750210 0.192835i
\(491\) −30.2854 + 17.4853i −1.36676 + 0.789100i −0.990513 0.137419i \(-0.956119\pi\)
−0.376248 + 0.926519i \(0.622786\pi\)
\(492\) 0 0
\(493\) 4.30463i 0.193871i
\(494\) 3.04384 1.75736i 0.136949 0.0790673i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) −4.56575 + 33.3640i −0.204802 + 1.49658i
\(498\) 0 0
\(499\) −24.4558 −1.09479 −0.547397 0.836873i \(-0.684381\pi\)
−0.547397 + 0.836873i \(0.684381\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) 0 0
\(502\) −13.2426 + 7.64564i −0.591048 + 0.341242i
\(503\) −0.594346 −0.0265006 −0.0132503 0.999912i \(-0.504218\pi\)
−0.0132503 + 0.999912i \(0.504218\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) −22.0454 + 12.7279i −0.980038 + 0.565825i
\(507\) 0 0
\(508\) −3.86396 + 6.69258i −0.171436 + 0.296935i
\(509\) −9.20361 −0.407943 −0.203971 0.978977i \(-0.565385\pi\)
−0.203971 + 0.978977i \(0.565385\pi\)
\(510\) 0 0
\(511\) −13.4558 + 5.49333i −0.595251 + 0.243010i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −21.7279 + 12.5446i −0.958378 + 0.553320i
\(515\) 27.2132i 1.19916i
\(516\) 0 0
\(517\) −47.1838 + 27.2416i −2.07514 + 1.19808i
\(518\) 1.88064 13.7426i 0.0826305 0.603817i
\(519\) 0 0
\(520\) −0.878680 1.52192i −0.0385327 0.0667405i
\(521\) 14.9941 + 25.9706i 0.656904 + 1.13779i 0.981413 + 0.191908i \(0.0614676\pi\)
−0.324509 + 0.945883i \(0.605199\pi\)
\(522\) 0 0
\(523\) 23.7426 + 13.7078i 1.03819 + 0.599401i 0.919321 0.393508i \(-0.128739\pi\)
0.118872 + 0.992910i \(0.462072\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 3.36396 + 5.82655i 0.146676 + 0.254050i
\(527\) 22.2426i 0.968905i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −17.7408 + 30.7279i −0.770610 + 1.33474i
\(531\) 0 0
\(532\) −12.0000 + 4.89898i −0.520266 + 0.212398i
\(533\) −1.52192 0.878680i −0.0659216 0.0380598i
\(534\) 0 0
\(535\) 5.27208 + 3.04384i 0.227932 + 0.131596i
\(536\) −11.6786 6.74264i −0.504439 0.291238i
\(537\) 0 0
\(538\) 8.48528 + 4.89898i 0.365826 + 0.211210i
\(539\) −7.97887 + 28.6066i −0.343674 + 1.23217i
\(540\) 0 0
\(541\) 2.72792 4.72490i 0.117283 0.203139i −0.801407 0.598119i \(-0.795915\pi\)
0.918690 + 0.394980i \(0.129248\pi\)
\(542\) 18.8785 0.810900
\(543\) 0 0
\(544\) 2.44949i 0.105021i
\(545\) −21.7122 37.6066i −0.930048 1.61089i
\(546\) 0 0
\(547\) −19.9853 + 34.6155i −0.854509 + 1.48005i 0.0225909 + 0.999745i \(0.492808\pi\)
−0.877100 + 0.480308i \(0.840525\pi\)
\(548\) −5.19615 3.00000i −0.221969 0.128154i
\(549\) 0 0
\(550\) −2.12132 3.67423i −0.0904534 0.156670i
\(551\) 4.30463 + 7.45584i 0.183384 + 0.317630i
\(552\) 0 0
\(553\) −0.757359 1.85514i −0.0322062 0.0788887i
\(554\) −20.5490 + 11.8640i −0.873043 + 0.504051i
\(555\) 0 0
\(556\) 8.06591i 0.342071i
\(557\) −18.3712 + 10.6066i −0.778412 + 0.449416i −0.835867 0.548932i \(-0.815035\pi\)
0.0574555 + 0.998348i \(0.481701\pi\)
\(558\) 0 0
\(559\) 5.02207i 0.212411i
\(560\) 2.44949 + 6.00000i 0.103510 + 0.253546i
\(561\) 0 0
\(562\) 13.7574 0.580319
\(563\) 22.9369 39.7279i 0.966676 1.67433i 0.261634 0.965167i \(-0.415739\pi\)
0.705043 0.709165i \(-0.250928\pi\)
\(564\) 0 0
\(565\) 21.7279 12.5446i 0.914101 0.527756i
\(566\) 6.03668 0.253741
\(567\) 0 0
\(568\) −12.7279 −0.534052
\(569\) 8.87039 5.12132i 0.371866 0.214697i −0.302407 0.953179i \(-0.597790\pi\)
0.674273 + 0.738482i \(0.264457\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) 3.04384 0.127269
\(573\) 0 0
\(574\) 5.12132 + 3.97141i 0.213760 + 0.165763i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 23.7426 13.7078i 0.988419 0.570664i 0.0836177 0.996498i \(-0.473353\pi\)
0.904801 + 0.425834i \(0.140019\pi\)
\(578\) 11.0000i 0.457540i
\(579\) 0 0
\(580\) 3.72792 2.15232i 0.154794 0.0893701i
\(581\) 24.7921 31.9706i 1.02855 1.32636i
\(582\) 0 0
\(583\) −30.7279 53.2223i −1.27262 2.20424i
\(584\) −2.74666 4.75736i −0.113658 0.196861i
\(585\) 0 0
\(586\) 11.1213 + 6.42090i 0.459418 + 0.265245i
\(587\) −16.2189 + 28.0919i −0.669424 + 1.15948i 0.308642 + 0.951178i \(0.400126\pi\)
−0.978065 + 0.208298i \(0.933208\pi\)
\(588\) 0 0
\(589\) −22.2426 38.5254i −0.916492 1.58741i
\(590\) 6.00000i 0.247016i
\(591\) 0 0
\(592\) 5.24264 0.215471
\(593\) 0.927572 1.60660i 0.0380908 0.0659752i −0.846352 0.532625i \(-0.821206\pi\)
0.884442 + 0.466650i \(0.154539\pi\)
\(594\) 0 0
\(595\) −6.00000 14.6969i −0.245976 0.602516i
\(596\) −14.0665 8.12132i −0.576188 0.332662i
\(597\) 0 0
\(598\) 3.72792 + 2.15232i 0.152446 + 0.0880148i
\(599\) −3.04384 1.75736i −0.124368 0.0718038i 0.436526 0.899692i \(-0.356209\pi\)
−0.560893 + 0.827888i \(0.689542\pi\)
\(600\) 0 0
\(601\) 35.9558 + 20.7591i 1.46667 + 0.846782i 0.999305 0.0372826i \(-0.0118702\pi\)
0.467365 + 0.884065i \(0.345204\pi\)
\(602\) 2.51104 18.3492i 0.102342 0.747859i
\(603\) 0 0
\(604\) 4.37868 7.58410i 0.178166 0.308592i
\(605\) 17.1464 0.697101
\(606\) 0 0
\(607\) 36.0759i 1.46428i −0.681157 0.732138i \(-0.738523\pi\)
0.681157 0.732138i \(-0.261477\pi\)
\(608\) −2.44949 4.24264i −0.0993399 0.172062i
\(609\) 0 0
\(610\) −5.12132 + 8.87039i −0.207356 + 0.359151i
\(611\) 7.97887 + 4.60660i 0.322790 + 0.186363i
\(612\) 0 0
\(613\) 14.1066 + 24.4334i 0.569760 + 0.986854i 0.996589 + 0.0825214i \(0.0262973\pi\)
−0.426829 + 0.904332i \(0.640369\pi\)
\(614\) 13.4106 + 23.2279i 0.541210 + 0.937403i
\(615\) 0 0
\(616\) −11.1213 1.52192i −0.448091 0.0613198i
\(617\) −3.67423 + 2.12132i −0.147919 + 0.0854011i −0.572133 0.820161i \(-0.693884\pi\)
0.424214 + 0.905562i \(0.360551\pi\)
\(618\) 0 0
\(619\) 12.7187i 0.511208i −0.966782 0.255604i \(-0.917726\pi\)
0.966782 0.255604i \(-0.0822743\pi\)
\(620\) −19.2627 + 11.1213i −0.773608 + 0.446643i
\(621\) 0 0
\(622\) 17.1464i 0.687509i
\(623\) 4.93503 6.36396i 0.197718 0.254967i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −10.0951 + 17.4853i −0.403483 + 0.698852i
\(627\) 0 0
\(628\) 9.00000 5.19615i 0.359139 0.207349i
\(629\) −12.8418 −0.512036
\(630\) 0 0
\(631\) −14.7574 −0.587481 −0.293741 0.955885i \(-0.594900\pi\)
−0.293741 + 0.955885i \(0.594900\pi\)
\(632\) 0.655892 0.378680i 0.0260900 0.0150631i
\(633\) 0 0
\(634\) −11.1213 + 19.2627i −0.441684 + 0.765019i
\(635\) 18.9295 0.751193
\(636\) 0 0
\(637\) 4.86396 1.25024i 0.192717 0.0495362i
\(638\) 7.45584i 0.295180i
\(639\) 0 0
\(640\) −2.12132 + 1.22474i −0.0838525 + 0.0484123i
\(641\) 33.2132i 1.31184i 0.754829 + 0.655921i \(0.227720\pi\)
−0.754829 + 0.655921i \(0.772280\pi\)
\(642\) 0 0
\(643\) 1.50000 0.866025i 0.0591542 0.0341527i −0.470131 0.882597i \(-0.655793\pi\)
0.529285 + 0.848444i \(0.322460\pi\)
\(644\) −12.5446 9.72792i −0.494327 0.383334i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −10.3923 18.0000i −0.408564 0.707653i 0.586165 0.810191i \(-0.300637\pi\)
−0.994729 + 0.102538i \(0.967304\pi\)
\(648\) 0 0
\(649\) −9.00000 5.19615i −0.353281 0.203967i
\(650\) −0.358719 + 0.621320i −0.0140701 + 0.0243702i
\(651\) 0 0
\(652\) −4.74264 8.21449i −0.185736 0.321704i
\(653\) 2.48528i 0.0972566i 0.998817 + 0.0486283i \(0.0154850\pi\)
−0.998817 + 0.0486283i \(0.984515\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.22474 + 2.12132i −0.0478183 + 0.0828236i
\(657\) 0 0
\(658\) −26.8492 20.8207i −1.04669 0.811674i
\(659\) 19.2627 + 11.1213i 0.750368 + 0.433225i 0.825827 0.563924i \(-0.190709\pi\)
−0.0754589 + 0.997149i \(0.524042\pi\)
\(660\) 0 0
\(661\) 4.24264 + 2.44949i 0.165020 + 0.0952741i 0.580235 0.814449i \(-0.302961\pi\)
−0.415216 + 0.909723i \(0.636294\pi\)
\(662\) 8.66025 + 5.00000i 0.336590 + 0.194331i
\(663\) 0 0
\(664\) 13.2426 + 7.64564i 0.513914 + 0.296708i
\(665\) 25.0892 + 19.4558i 0.972919 + 0.754465i
\(666\) 0 0
\(667\) −5.27208 + 9.13151i −0.204136 + 0.353573i
\(668\) −0.594346 −0.0229959
\(669\) 0 0
\(670\) 33.0321i 1.27614i
\(671\) −8.87039 15.3640i −0.342437 0.593119i
\(672\) 0 0
\(673\) 22.7279 39.3659i 0.876097 1.51744i 0.0205075 0.999790i \(-0.493472\pi\)
0.855590 0.517655i \(-0.173195\pi\)
\(674\) −18.5813 10.7279i −0.715725 0.413224i
\(675\) 0 0
\(676\) 6.24264 + 10.8126i 0.240102 + 0.415868i
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) 6.62132 + 5.13461i 0.254103 + 0.197048i
\(680\) 5.19615 3.00000i 0.199263 0.115045i
\(681\) 0 0
\(682\) 38.5254i 1.47521i
\(683\) 8.87039 5.12132i 0.339416 0.195962i −0.320598 0.947215i \(-0.603884\pi\)
0.660014 + 0.751254i \(0.270550\pi\)
\(684\) 0 0
\(685\) 14.6969i 0.561541i
\(686\) −18.3967 + 2.13604i −0.702388 + 0.0815543i
\(687\) 0 0
\(688\) 7.00000 0.266872
\(689\) −5.19615 + 9.00000i −0.197958 + 0.342873i
\(690\) 0 0
\(691\) −2.22792 + 1.28629i −0.0847541 + 0.0489328i −0.541778 0.840522i \(-0.682249\pi\)
0.457024 + 0.889454i \(0.348915\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) −4.97056 −0.188680
\(695\) 17.1104 9.87868i 0.649034 0.374720i
\(696\) 0 0
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) 0.123093 0.00465914
\(699\) 0 0
\(700\) 1.62132 2.09077i 0.0612801 0.0790237i
\(701\) 20.4853i 0.773718i −0.922139 0.386859i \(-0.873560\pi\)
0.922139 0.386859i \(-0.126440\pi\)
\(702\) 0 0
\(703\) 22.2426 12.8418i 0.838897 0.484337i
\(704\) 4.24264i 0.159901i
\(705\) 0 0
\(706\) −9.51472 + 5.49333i −0.358091 + 0.206744i
\(707\) −19.2627 2.63604i −0.724448 0.0991384i
\(708\) 0 0
\(709\) −8.10660 14.0410i −0.304450 0.527323i 0.672689 0.739925i \(-0.265139\pi\)
−0.977139 + 0.212603i \(0.931806\pi\)
\(710\) 15.5885 + 27.0000i 0.585024 + 1.01329i
\(711\) 0 0
\(712\) 2.63604 + 1.52192i 0.0987897 + 0.0570363i
\(713\) 27.2416 47.1838i 1.02020 1.76705i
\(714\) 0 0
\(715\) −3.72792 6.45695i −0.139416 0.241476i
\(716\) 6.72792i 0.251434i
\(717\) 0 0
\(718\) 14.4853 0.540586
\(719\) −26.3140 + 45.5772i −0.981346 + 1.69974i −0.324181 + 0.945995i \(0.605089\pi\)
−0.657166 + 0.753746i \(0.728245\pi\)
\(720\) 0 0
\(721\) 3.98528 29.1222i 0.148420 1.08457i
\(722\) −4.33013 2.50000i −0.161151 0.0930404i
\(723\) 0 0
\(724\) 8.48528 + 4.89898i 0.315353 + 0.182069i
\(725\) −1.52192 0.878680i −0.0565226 0.0326333i
\(726\) 0 0
\(727\) −24.3198 14.0410i −0.901972 0.520754i −0.0241323 0.999709i \(-0.507682\pi\)
−0.877839 + 0.478955i \(0.841016\pi\)
\(728\) 0.717439 + 1.75736i 0.0265901 + 0.0651321i
\(729\) 0 0
\(730\) −6.72792 + 11.6531i −0.249012 + 0.431301i
\(731\) −17.1464 −0.634184
\(732\) 0 0
\(733\) 1.31178i 0.0484519i −0.999707 0.0242259i \(-0.992288\pi\)
0.999707 0.0242259i \(-0.00771211\pi\)
\(734\) 14.9941 + 25.9706i 0.553443 + 0.958591i
\(735\) 0 0
\(736\) 3.00000 5.19615i 0.110581 0.191533i
\(737\) −49.5481 28.6066i −1.82513 1.05374i
\(738\) 0 0
\(739\) 4.22792 + 7.32298i 0.155527 + 0.269380i 0.933251 0.359226i \(-0.116959\pi\)
−0.777724 + 0.628606i \(0.783626\pi\)
\(740\) −6.42090 11.1213i −0.236037 0.408828i
\(741\) 0 0
\(742\) 23.4853 30.2854i 0.862172 1.11181i
\(743\) −16.2189 + 9.36396i −0.595012 + 0.343530i −0.767077 0.641555i \(-0.778290\pi\)
0.172065 + 0.985086i \(0.444956\pi\)
\(744\) 0 0
\(745\) 39.7862i 1.45765i
\(746\) 19.0526 11.0000i 0.697564 0.402739i
\(747\) 0 0
\(748\) 10.3923i 0.379980i
\(749\) −5.19615 4.02944i −0.189863 0.147232i
\(750\) 0 0
\(751\) 53.4558 1.95063 0.975316 0.220815i \(-0.0708717\pi\)
0.975316 + 0.220815i \(0.0708717\pi\)
\(752\) 6.42090 11.1213i 0.234146 0.405553i
\(753\) 0 0
\(754\) 1.09188 0.630399i 0.0397640 0.0229578i
\(755\) −21.4511 −0.780684
\(756\) 0 0
\(757\) 32.7574 1.19059 0.595293 0.803509i \(-0.297036\pi\)
0.595293 + 0.803509i \(0.297036\pi\)
\(758\) 6.48244 3.74264i 0.235453 0.135939i
\(759\) 0 0
\(760\) −6.00000 + 10.3923i −0.217643 + 0.376969i
\(761\) 24.4949 0.887939 0.443970 0.896042i \(-0.353570\pi\)
0.443970 + 0.896042i \(0.353570\pi\)
\(762\) 0 0
\(763\) 17.7279 + 43.4244i 0.641794 + 1.57207i
\(764\) 21.2132i 0.767467i
\(765\) 0 0
\(766\) −4.75736 + 2.74666i −0.171890 + 0.0992410i
\(767\) 1.75736i 0.0634546i
\(768\) 0 0
\(769\) 34.9706 20.1903i 1.26107 0.728080i 0.287789 0.957694i \(-0.407080\pi\)
0.973282 + 0.229614i \(0.0737465\pi\)
\(770\) 10.3923 + 25.4558i 0.374513 + 0.917365i
\(771\) 0 0
\(772\) −0.742641 1.28629i −0.0267282 0.0462946i
\(773\) 4.89898 + 8.48528i 0.176204 + 0.305194i 0.940577 0.339580i \(-0.110285\pi\)
−0.764373 + 0.644774i \(0.776951\pi\)
\(774\) 0 0
\(775\) 7.86396 + 4.54026i 0.282482 + 0.163091i
\(776\) −1.58346 + 2.74264i −0.0568431 + 0.0984551i
\(777\) 0 0
\(778\) −7.75736 13.4361i −0.278115 0.481709i
\(779\) 12.0000i 0.429945i
\(780\) 0 0
\(781\) −54.0000 −1.93227
\(782\) −7.34847 + 12.7279i −0.262781 + 0.455150i
\(783\) 0 0
\(784\) −1.74264 6.77962i −0.0622372 0.242129i
\(785\) −22.0454 12.7279i −0.786834 0.454279i
\(786\) 0 0
\(787\) 24.4706 + 14.1281i 0.872281 + 0.503612i 0.868106 0.496379i \(-0.165338\pi\)
0.00417567 + 0.999991i \(0.498671\pi\)
\(788\) −14.6969 8.48528i −0.523557 0.302276i</