Properties

Label 1134.2.l.e.269.4
Level $1134$
Weight $2$
Character 1134.269
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.l (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: \(\Z[a_1, \ldots, a_{7}]\)
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 269.4
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1134.269
Dual form 1134.2.l.e.215.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(-3.67423 + 2.12132i) q^{11} +(-0.621320 + 0.358719i) q^{13} +(2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(1.22474 - 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +(-1.22474 + 2.12132i) q^{20} +(-2.12132 - 3.67423i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.358719 - 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +(1.52192 + 0.878680i) q^{29} +9.08052i q^{31} +1.00000i q^{32} +(2.12132 + 1.22474i) q^{34} +(-6.42090 + 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(-2.44949 - 4.24264i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(-1.22474 - 2.12132i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} -12.8418 q^{47} +(-1.74264 + 6.77962i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.621320 - 0.358719i) q^{52} +(-12.5446 - 7.24264i) q^{53} +10.3923i q^{55} +(-2.09077 + 1.62132i) q^{56} +(-0.878680 + 1.52192i) q^{58} +2.44949 q^{59} +4.18154i q^{61} -9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} +13.4853 q^{67} +(-1.22474 + 2.12132i) q^{68} +(-0.878680 - 6.42090i) q^{70} -12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(4.54026 - 2.62132i) q^{74} +(4.24264 - 2.44949i) q^{76} +(10.3923 + 4.24264i) q^{77} +0.757359 q^{79} +(1.22474 - 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +(7.64564 - 13.2426i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(-6.06218 - 3.50000i) q^{86} +(2.12132 + 3.67423i) q^{88} +(1.52192 + 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +(5.19615 + 3.00000i) q^{92} -12.8418i q^{94} +12.0000i q^{95} +(-2.74264 - 1.58346i) q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.22474 2.12132i 0.547723 0.948683i −0.450708 0.892672i \(-0.648828\pi\)
0.998430 0.0560116i \(-0.0178384\pi\)
\(6\) 0 0
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.12132 + 1.22474i 0.670820 + 0.387298i
\(11\) −3.67423 + 2.12132i −1.10782 + 0.639602i −0.938265 0.345918i \(-0.887568\pi\)
−0.169559 + 0.985520i \(0.554234\pi\)
\(12\) 0 0
\(13\) −0.621320 + 0.358719i −0.172323 + 0.0994909i −0.583681 0.811983i \(-0.698388\pi\)
0.411358 + 0.911474i \(0.365055\pi\)
\(14\) 2.09077 1.62132i 0.558782 0.433316i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.22474 2.12132i 0.297044 0.514496i −0.678414 0.734680i \(-0.737332\pi\)
0.975458 + 0.220184i \(0.0706658\pi\)
\(18\) 0 0
\(19\) −4.24264 + 2.44949i −0.973329 + 0.561951i −0.900249 0.435375i \(-0.856616\pi\)
−0.0730792 + 0.997326i \(0.523283\pi\)
\(20\) −1.22474 + 2.12132i −0.273861 + 0.474342i
\(21\) 0 0
\(22\) −2.12132 3.67423i −0.452267 0.783349i
\(23\) −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i \(-0.548456\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −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 0.634606 0.772836i \(-0.281162\pi\)
−0.351993 + 0.936003i \(0.614496\pi\)
\(30\) 0 0
\(31\) 9.08052i 1.63091i 0.578821 + 0.815455i \(0.303513\pi\)
−0.578821 + 0.815455i \(0.696487\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 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 0.566012 0.824397i \(-0.308485\pi\)
−0.996955 + 0.0779826i \(0.975152\pi\)
\(38\) −2.44949 4.24264i −0.397360 0.688247i
\(39\) 0 0
\(40\) −2.12132 1.22474i −0.335410 0.193649i
\(41\) −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
\(47\) −12.8418 −1.87317 −0.936584 0.350443i \(-0.886031\pi\)
−0.936584 + 0.350443i \(0.886031\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 0 0
\(52\) 0.621320 0.358719i 0.0861616 0.0497454i
\(53\) −12.5446 7.24264i −1.72314 0.994853i −0.912231 0.409675i \(-0.865642\pi\)
−0.810905 0.585178i \(-0.801025\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) −2.09077 + 1.62132i −0.279391 + 0.216658i
\(57\) 0 0
\(58\) −0.878680 + 1.52192i −0.115376 + 0.199838i
\(59\) 2.44949 0.318896 0.159448 0.987206i \(-0.449029\pi\)
0.159448 + 0.987206i \(0.449029\pi\)
\(60\) 0 0
\(61\) 4.18154i 0.535391i 0.963504 + 0.267696i \(0.0862622\pi\)
−0.963504 + 0.267696i \(0.913738\pi\)
\(62\) −9.08052 −1.15323
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.75736i 0.217974i
\(66\) 0 0
\(67\) 13.4853 1.64749 0.823745 0.566961i \(-0.191881\pi\)
0.823745 + 0.566961i \(0.191881\pi\)
\(68\) −1.22474 + 2.12132i −0.148522 + 0.257248i
\(69\) 0 0
\(70\) −0.878680 6.42090i −0.105022 0.767444i
\(71\) 12.7279i 1.51053i −0.655422 0.755263i \(-0.727509\pi\)
0.655422 0.755263i \(-0.272491\pi\)
\(72\) 0 0
\(73\) −4.75736 2.74666i −0.556807 0.321473i 0.195056 0.980792i \(-0.437511\pi\)
−0.751863 + 0.659320i \(0.770844\pi\)
\(74\) 4.54026 2.62132i 0.527795 0.304722i
\(75\) 0 0
\(76\) 4.24264 2.44949i 0.486664 0.280976i
\(77\) 10.3923 + 4.24264i 1.18431 + 0.483494i
\(78\) 0 0
\(79\) 0.757359 0.0852096 0.0426048 0.999092i \(-0.486434\pi\)
0.0426048 + 0.999092i \(0.486434\pi\)
\(80\) 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
\(86\) −6.06218 3.50000i −0.653701 0.377415i
\(87\) 0 0
\(88\) 2.12132 + 3.67423i 0.226134 + 0.391675i
\(89\) 1.52192 + 2.63604i 0.161323 + 0.279420i 0.935343 0.353741i \(-0.115091\pi\)
−0.774020 + 0.633161i \(0.781757\pi\)
\(90\) 0 0
\(91\) 1.75736 + 0.717439i 0.184221 + 0.0752080i
\(92\) 5.19615 + 3.00000i 0.541736 + 0.312772i
\(93\) 0 0
\(94\) 12.8418i 1.32453i
\(95\) 12.0000i 1.23117i
\(96\) 0 0
\(97\) −2.74264 1.58346i −0.278473 0.160776i 0.354259 0.935147i \(-0.384733\pi\)
−0.632732 + 0.774371i \(0.718066\pi\)
\(98\) −6.77962 1.74264i −0.684845 0.176033i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 3.67423 + 6.36396i 0.365600 + 0.633238i 0.988872 0.148767i \(-0.0475305\pi\)
−0.623272 + 0.782005i \(0.714197\pi\)
\(102\) 0 0
\(103\) −9.62132 5.55487i −0.948017 0.547338i −0.0555525 0.998456i \(-0.517692\pi\)
−0.892464 + 0.451118i \(0.851025\pi\)
\(104\) 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 −0.600415 0.799688i \(-0.704998\pi\)
0.392343 + 0.919819i \(0.371665\pi\)
\(108\) 0 0
\(109\) 8.86396 15.3528i 0.849013 1.47053i −0.0330761 0.999453i \(-0.510530\pi\)
0.882090 0.471082i \(-0.156136\pi\)
\(110\) −10.3923 −0.990867
\(111\) 0 0
\(112\) −1.62132 2.09077i −0.153200 0.197559i
\(113\) 8.87039 5.12132i 0.834456 0.481773i −0.0209200 0.999781i \(-0.506660\pi\)
0.855376 + 0.518008i \(0.173326\pi\)
\(114\) 0 0
\(115\) −12.7279 + 7.34847i −1.18688 + 0.685248i
\(116\) −1.52192 0.878680i −0.141307 0.0815834i
\(117\) 0 0
\(118\) 2.44949i 0.225494i
\(119\) −6.42090 + 0.878680i −0.588603 + 0.0805484i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −4.18154 −0.378579
\(123\) 0 0
\(124\) 9.08052i 0.815455i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) −7.72792 −0.685742 −0.342871 0.939382i \(-0.611399\pi\)
−0.342871 + 0.939382i \(0.611399\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −1.75736 −0.154131
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) 12.0000 + 4.89898i 1.04053 + 0.424795i
\(134\) 13.4853i 1.16495i
\(135\) 0 0
\(136\) −2.12132 1.22474i −0.181902 0.105021i
\(137\) 5.19615 3.00000i 0.443937 0.256307i −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) 0 0
\(139\) 6.98528 4.03295i 0.592484 0.342071i −0.173595 0.984817i \(-0.555538\pi\)
0.766079 + 0.642746i \(0.222205\pi\)
\(140\) 6.42090 0.878680i 0.542665 0.0742620i
\(141\) 0 0
\(142\) 12.7279 1.06810
\(143\) 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
\(149\) −14.0665 8.12132i −1.15238 0.665324i −0.202911 0.979197i \(-0.565040\pi\)
−0.949465 + 0.313873i \(0.898373\pi\)
\(150\) 0 0
\(151\) −4.37868 7.58410i −0.356332 0.617185i 0.631013 0.775772i \(-0.282639\pi\)
−0.987345 + 0.158587i \(0.949306\pi\)
\(152\) 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
\(157\) 10.3923i 0.829396i 0.909959 + 0.414698i \(0.136113\pi\)
−0.909959 + 0.414698i \(0.863887\pi\)
\(158\) 0.757359i 0.0602523i
\(159\) 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 0.989792 0.142518i \(-0.0455197\pi\)
−0.618320 + 0.785926i \(0.712186\pi\)
\(164\) 1.22474 + 2.12132i 0.0956365 + 0.165647i
\(165\) 0 0
\(166\) 13.2426 + 7.64564i 1.02783 + 0.593417i
\(167\) −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
\(173\) −20.7846 −1.58022 −0.790112 0.612962i \(-0.789978\pi\)
−0.790112 + 0.612962i \(0.789978\pi\)
\(174\) 0 0
\(175\) −1.00000 + 2.44949i −0.0755929 + 0.185164i
\(176\) −3.67423 + 2.12132i −0.276956 + 0.159901i
\(177\) 0 0
\(178\) −2.63604 + 1.52192i −0.197579 + 0.114073i
\(179\) 5.82655 + 3.36396i 0.435497 + 0.251434i 0.701686 0.712487i \(-0.252431\pi\)
−0.266189 + 0.963921i \(0.585764\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) −0.717439 + 1.75736i −0.0531801 + 0.130264i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −12.8418 −0.944148
\(186\) 0 0
\(187\) 10.3923i 0.759961i
\(188\) 12.8418 0.936584
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 21.2132i 1.53493i 0.641089 + 0.767467i \(0.278483\pi\)
−0.641089 + 0.767467i \(0.721517\pi\)
\(192\) 0 0
\(193\) −1.48528 −0.106913 −0.0534564 0.998570i \(-0.517024\pi\)
−0.0534564 + 0.998570i \(0.517024\pi\)
\(194\) 1.58346 2.74264i 0.113686 0.196910i
\(195\) 0 0
\(196\) 1.74264 6.77962i 0.124474 0.484258i
\(197\) 16.9706i 1.20910i 0.796566 + 0.604551i \(0.206648\pi\)
−0.796566 + 0.604551i \(0.793352\pi\)
\(198\) 0 0
\(199\) −18.1066 10.4539i −1.28354 0.741054i −0.306049 0.952016i \(-0.599007\pi\)
−0.977494 + 0.210962i \(0.932340\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) −6.36396 + 3.67423i −0.447767 + 0.258518i
\(203\) −0.630399 4.60660i −0.0442453 0.323320i
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 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 \(0.871613\pi\)
\(212\) 12.5446 + 7.24264i 0.861568 + 0.497427i
\(213\) 0 0
\(214\) −1.24264 2.15232i −0.0849452 0.147129i
\(215\) 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
\(220\) 10.3923i 0.700649i
\(221\) 1.75736i 0.118213i
\(222\) 0 0
\(223\) 9.00000 + 5.19615i 0.602685 + 0.347960i 0.770097 0.637927i \(-0.220208\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(224\) 2.09077 1.62132i 0.139695 0.108329i
\(225\) 0 0
\(226\) 5.12132 + 8.87039i 0.340665 + 0.590049i
\(227\) −12.5446 21.7279i −0.832616 1.44213i −0.895957 0.444141i \(-0.853509\pi\)
0.0633412 0.997992i \(-0.479824\pi\)
\(228\) 0 0
\(229\) 4.86396 + 2.80821i 0.321420 + 0.185572i 0.652025 0.758197i \(-0.273920\pi\)
−0.330606 + 0.943769i \(0.607253\pi\)
\(230\) −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 0.210398 0.977616i \(-0.432524\pi\)
0.951839 + 0.306598i \(0.0991908\pi\)
\(234\) 0 0
\(235\) −15.7279 + 27.2416i −1.02598 + 1.77704i
\(236\) −2.44949 −0.159448
\(237\) 0 0
\(238\) −0.878680 6.42090i −0.0569563 0.416205i
\(239\) 14.0665 8.12132i 0.909889 0.525325i 0.0294934 0.999565i \(-0.490611\pi\)
0.880395 + 0.474240i \(0.157277\pi\)
\(240\) 0 0
\(241\) 0.985281 0.568852i 0.0634676 0.0366430i −0.467930 0.883765i \(-0.655000\pi\)
0.531398 + 0.847122i \(0.321667\pi\)
\(242\) 6.06218 + 3.50000i 0.389692 + 0.224989i
\(243\) 0 0
\(244\) 4.18154i 0.267696i
\(245\) 12.2474 + 12.0000i 0.782461 + 0.766652i
\(246\) 0 0
\(247\) 1.75736 3.04384i 0.111818 0.193675i
\(248\) 9.08052 0.576614
\(249\) 0 0
\(250\) 9.79796i 0.619677i
\(251\) 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
\(254\) 7.72792i 0.484893i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.5446 + 21.7279i −0.782512 + 1.35535i 0.147962 + 0.988993i \(0.452729\pi\)
−0.930474 + 0.366358i \(0.880605\pi\)
\(258\) 0 0
\(259\) −5.24264 + 12.8418i −0.325762 + 0.797950i
\(260\) 1.75736i 0.108987i
\(261\) 0 0
\(262\) 0 0
\(263\) 5.82655 3.36396i 0.359281 0.207431i −0.309485 0.950904i \(-0.600157\pi\)
0.668765 + 0.743474i \(0.266823\pi\)
\(264\) 0 0
\(265\) −30.7279 + 17.7408i −1.88760 + 1.08981i
\(266\) −4.89898 + 12.0000i −0.300376 + 0.735767i
\(267\) 0 0
\(268\) −13.4853 −0.823745
\(269\) −4.89898 + 8.48528i −0.298696 + 0.517357i −0.975838 0.218496i \(-0.929885\pi\)
0.677142 + 0.735853i \(0.263218\pi\)
\(270\) 0 0
\(271\) −16.3492 + 9.43924i −0.993146 + 0.573393i −0.906213 0.422821i \(-0.861040\pi\)
−0.0869326 + 0.996214i \(0.527706\pi\)
\(272\) 1.22474 2.12132i 0.0742611 0.128624i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 3.67423 + 2.12132i 0.221565 + 0.127920i
\(276\) 0 0
\(277\) −11.8640 20.5490i −0.712836 1.23467i −0.963788 0.266669i \(-0.914077\pi\)
0.250952 0.968000i \(-0.419256\pi\)
\(278\) 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 0.811336 0.584580i \(-0.198741\pi\)
−0.100593 + 0.994928i \(0.532074\pi\)
\(282\) 0 0
\(283\) 6.03668i 0.358844i −0.983772 0.179422i \(-0.942577\pi\)
0.983772 0.179422i \(-0.0574227\pi\)
\(284\) 12.7279i 0.755263i
\(285\) 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
\(290\) 2.15232 + 3.72792i 0.126388 + 0.218911i
\(291\) 0 0
\(292\) 4.75736 + 2.74666i 0.278403 + 0.160736i
\(293\) −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
\(299\) 4.30463 0.248943
\(300\) 0 0
\(301\) 18.3492 2.51104i 1.05763 0.144734i
\(302\) 7.58410 4.37868i 0.436416 0.251965i
\(303\) 0 0
\(304\) −4.24264 + 2.44949i −0.243332 + 0.140488i
\(305\) 8.87039 + 5.12132i 0.507917 + 0.293246i
\(306\) 0 0
\(307\) 26.8213i 1.53077i 0.643571 + 0.765386i \(0.277452\pi\)
−0.643571 + 0.765386i \(0.722548\pi\)
\(308\) −10.3923 4.24264i −0.592157 0.241747i
\(309\) 0 0
\(310\) −11.1213 + 19.2627i −0.631649 + 1.09405i
\(311\) −17.1464 −0.972285 −0.486142 0.873880i \(-0.661596\pi\)
−0.486142 + 0.873880i \(0.661596\pi\)
\(312\) 0 0
\(313\) 20.1903i 1.14122i −0.821221 0.570611i \(-0.806707\pi\)
0.821221 0.570611i \(-0.193293\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) −0.757359 −0.0426048
\(317\) 22.2426i 1.24927i −0.780916 0.624636i \(-0.785248\pi\)
0.780916 0.624636i \(-0.214752\pi\)
\(318\) 0 0
\(319\) −7.45584 −0.417447
\(320\) −1.22474 + 2.12132i −0.0684653 + 0.118585i
\(321\) 0 0
\(322\) −15.7279 + 2.15232i −0.876483 + 0.119944i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 0.621320 + 0.358719i 0.0344647 + 0.0198982i
\(326\) −8.21449 + 4.74264i −0.454959 + 0.262671i
\(327\) 0 0
\(328\) −2.12132 + 1.22474i −0.117130 + 0.0676252i
\(329\) 20.8207 + 26.8492i 1.14788 + 1.48025i
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −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 \(0.634668\pi\)
\(338\) −10.8126 6.24264i −0.588126 0.339555i
\(339\) 0 0
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) −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
\(346\) 20.7846i 1.11739i
\(347\) 4.97056i 0.266834i 0.991060 + 0.133417i \(0.0425949\pi\)
−0.991060 + 0.133417i \(0.957405\pi\)
\(348\) 0 0
\(349\) 0.106602 + 0.0615465i 0.00570626 + 0.00329451i 0.502850 0.864373i \(-0.332285\pi\)
−0.497144 + 0.867668i \(0.665618\pi\)
\(350\) −2.44949 1.00000i −0.130931 0.0534522i
\(351\) 0 0
\(352\) −2.12132 3.67423i −0.113067 0.195837i
\(353\) −5.49333 9.51472i −0.292380 0.506417i 0.681992 0.731360i \(-0.261114\pi\)
−0.974372 + 0.224942i \(0.927781\pi\)
\(354\) 0 0
\(355\) −27.0000 15.5885i −1.43301 0.827349i
\(356\) −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 −0.793069 0.609132i \(-0.791518\pi\)
0.130989 + 0.991384i \(0.458185\pi\)
\(360\) 0 0
\(361\) 2.50000 4.33013i 0.131579 0.227901i
\(362\) 9.79796 0.514969
\(363\) 0 0
\(364\) −1.75736 0.717439i −0.0921107 0.0376040i
\(365\) −11.6531 + 6.72792i −0.609951 + 0.352156i
\(366\) 0 0
\(367\) 25.9706 14.9941i 1.35565 0.782686i 0.366618 0.930372i \(-0.380516\pi\)
0.989034 + 0.147685i \(0.0471823\pi\)
\(368\) −5.19615 3.00000i −0.270868 0.156386i
\(369\) 0 0
\(370\) 12.8418i 0.667613i
\(371\) 5.19615 + 37.9706i 0.269771 + 1.97133i
\(372\) 0 0
\(373\) 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) −10.3923 −0.537373
\(375\) 0 0
\(376\) 12.8418i 0.662265i
\(377\) −1.26080 −0.0649344
\(378\) 0 0
\(379\) −7.48528 −0.384493 −0.192247 0.981347i \(-0.561577\pi\)
−0.192247 + 0.981347i \(0.561577\pi\)
\(380\) 12.0000i 0.615587i
\(381\) 0 0
\(382\) −21.2132 −1.08536
\(383\) −2.74666 + 4.75736i −0.140348 + 0.243090i −0.927628 0.373506i \(-0.878155\pi\)
0.787280 + 0.616596i \(0.211489\pi\)
\(384\) 0 0
\(385\) 21.7279 16.8493i 1.10736 0.858718i
\(386\) 1.48528i 0.0755988i
\(387\) 0 0
\(388\) 2.74264 + 1.58346i 0.139236 + 0.0803882i
\(389\) −13.4361 + 7.75736i −0.681239 + 0.393314i −0.800322 0.599571i \(-0.795338\pi\)
0.119082 + 0.992884i \(0.462005\pi\)
\(390\) 0 0
\(391\) −12.7279 + 7.34847i −0.643679 + 0.371628i
\(392\) 6.77962 + 1.74264i 0.342422 + 0.0880166i
\(393\) 0 0
\(394\) −16.9706 −0.854965
\(395\) 0.927572 1.60660i 0.0466712 0.0808369i
\(396\) 0 0
\(397\) −13.1360 + 7.58410i −0.659279 + 0.380635i −0.792002 0.610518i \(-0.790961\pi\)
0.132723 + 0.991153i \(0.457628\pi\)
\(398\) 10.4539 18.1066i 0.524004 0.907602i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 17.1104 + 9.87868i 0.854451 + 0.493318i 0.862150 0.506653i \(-0.169117\pi\)
−0.00769892 + 0.999970i \(0.502451\pi\)
\(402\) 0 0
\(403\) −3.25736 5.64191i −0.162261 0.281044i
\(404\) −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
\(409\) 3.76127i 0.185983i 0.995667 + 0.0929915i \(0.0296430\pi\)
−0.995667 + 0.0929915i \(0.970357\pi\)
\(410\) 6.00000i 0.296319i
\(411\) 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
\(416\) −0.358719 0.621320i −0.0175877 0.0304627i
\(417\) 0 0
\(418\) 18.0000 + 10.3923i 0.880409 + 0.508304i
\(419\) −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
\(425\) −2.44949 −0.118818
\(426\) 0 0
\(427\) 8.74264 6.77962i 0.423086 0.328089i
\(428\) 2.15232 1.24264i 0.104036 0.0600653i
\(429\) 0 0
\(430\) −14.8492 + 8.57321i −0.716094 + 0.413437i
\(431\) 1.52192 + 0.878680i 0.0733082 + 0.0423245i 0.536206 0.844087i \(-0.319857\pi\)
−0.462898 + 0.886412i \(0.653190\pi\)
\(432\) 0 0
\(433\) 2.57258i 0.123630i 0.998088 + 0.0618152i \(0.0196889\pi\)
−0.998088 + 0.0618152i \(0.980311\pi\)
\(434\) 14.7224 + 18.9853i 0.706699 + 0.911323i
\(435\) 0 0
\(436\) −8.86396 + 15.3528i −0.424507 + 0.735267i
\(437\) 29.3939 1.40610
\(438\) 0 0
\(439\) 4.30463i 0.205449i 0.994710 + 0.102724i \(0.0327560\pi\)
−0.994710 + 0.102724i \(0.967244\pi\)
\(440\) 10.3923 0.495434
\(441\) 0 0
\(442\) −1.75736 −0.0835891
\(443\) 25.4558i 1.20944i −0.796437 0.604722i \(-0.793284\pi\)
0.796437 0.604722i \(-0.206716\pi\)
\(444\) 0 0
\(445\) 7.45584 0.353441
\(446\) −5.19615 + 9.00000i −0.246045 + 0.426162i
\(447\) 0 0
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) 5.27208i 0.248805i 0.992232 + 0.124402i \(0.0397014\pi\)
−0.992232 + 0.124402i \(0.960299\pi\)
\(450\) 0 0
\(451\) 9.00000 + 5.19615i 0.423793 + 0.244677i
\(452\) −8.87039 + 5.12132i −0.417228 + 0.240887i
\(453\) 0 0
\(454\) 21.7279 12.5446i 1.01974 0.588748i
\(455\) 3.67423 2.84924i 0.172251 0.133575i
\(456\) 0 0
\(457\) −23.0000 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(458\) −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 \(0.662530\pi\)
\(464\) 1.52192 + 0.878680i 0.0706533 + 0.0407917i
\(465\) 0 0
\(466\) 10.2426 + 17.7408i 0.474481 + 0.821825i
\(467\) −8.87039 15.3640i −0.410473 0.710959i 0.584469 0.811416i \(-0.301303\pi\)
−0.994941 + 0.100457i \(0.967970\pi\)
\(468\) 0 0
\(469\) −21.8640 28.1946i −1.00958 1.30191i
\(470\) −27.2416 15.7279i −1.25656 0.725475i
\(471\) 0 0
\(472\) 2.44949i 0.112747i
\(473\) 29.6985i 1.36554i
\(474\) 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
\(479\) −1.22474 2.12132i −0.0559600 0.0969256i 0.836688 0.547679i \(-0.184489\pi\)
−0.892648 + 0.450754i \(0.851155\pi\)
\(480\) 0 0
\(481\) 3.25736 + 1.88064i 0.148523 + 0.0857497i
\(482\) 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 −0.999998 0.00178012i \(-0.999433\pi\)
0.501541 + 0.865134i \(0.332767\pi\)
\(488\) 4.18154 0.189289
\(489\) 0 0
\(490\) −12.0000 + 12.2474i −0.542105 + 0.553283i
\(491\) 30.2854 17.4853i 1.36676 0.789100i 0.376248 0.926519i \(-0.377214\pi\)
0.990513 + 0.137419i \(0.0438808\pi\)
\(492\) 0 0
\(493\) 3.72792 2.15232i 0.167897 0.0969355i
\(494\) 3.04384 + 1.75736i 0.136949 + 0.0790673i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) −26.6112 + 20.6360i −1.19367 + 0.925653i
\(498\) 0 0
\(499\) 12.2279 21.1794i 0.547397 0.948119i −0.451055 0.892496i \(-0.648952\pi\)
0.998452 0.0556231i \(-0.0177145\pi\)
\(500\) −9.79796 −0.438178
\(501\) 0 0
\(502\) 15.2913i 0.682483i
\(503\) −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
\(506\) 25.4558i 1.13165i
\(507\) 0 0
\(508\) 7.72792 0.342871
\(509\) 4.60181 7.97056i 0.203971 0.353289i −0.745833 0.666133i \(-0.767948\pi\)
0.949805 + 0.312844i \(0.101282\pi\)
\(510\) 0 0
\(511\) 1.97056 + 14.3998i 0.0871726 + 0.637008i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −21.7279 12.5446i −0.958378 0.553320i
\(515\) −23.5673 + 13.6066i −1.03850 + 0.599579i
\(516\) 0 0
\(517\) 47.1838 27.2416i 2.07514 1.19808i
\(518\) −12.8418 5.24264i −0.564236 0.230348i
\(519\) 0 0
\(520\) 1.75736 0.0770653
\(521\) 14.9941 25.9706i 0.656904 1.13779i −0.324509 0.945883i \(-0.605199\pi\)
0.981413 0.191908i \(-0.0614676\pi\)
\(522\) 0 0
\(523\) 23.7426 13.7078i 1.03819 0.599401i 0.118872 0.992910i \(-0.462072\pi\)
0.919321 + 0.393508i \(0.128739\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 3.36396 + 5.82655i 0.146676 + 0.254050i
\(527\) 19.2627 + 11.1213i 0.839096 + 0.484452i
\(528\) 0 0
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) −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
\(535\) 6.08767i 0.263193i
\(536\) 13.4853i 0.582475i
\(537\) 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 0.918690 0.394980i \(-0.129248\pi\)
−0.801407 + 0.598119i \(0.795915\pi\)
\(542\) −9.43924 16.3492i −0.405450 0.702260i
\(543\) 0 0
\(544\) 2.12132 + 1.22474i 0.0909509 + 0.0525105i
\(545\) −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
\(551\) −8.60927 −0.366767
\(552\) 0 0
\(553\) −1.22792 1.58346i −0.0522166 0.0673358i
\(554\) 20.5490 11.8640i 0.873043 0.504051i
\(555\) 0 0
\(556\) −6.98528 + 4.03295i −0.296242 + 0.171035i
\(557\) −18.3712 10.6066i −0.778412 0.449416i 0.0574555 0.998348i \(-0.481701\pi\)
−0.835867 + 0.548932i \(0.815035\pi\)
\(558\) 0 0
\(559\) 5.02207i 0.212411i
\(560\) −6.42090 + 0.878680i −0.271332 + 0.0371310i
\(561\) 0 0
\(562\) −6.87868 + 11.9142i −0.290160 + 0.502571i
\(563\) −45.8739 −1.93335 −0.966676 0.256002i \(-0.917595\pi\)
−0.966676 + 0.256002i \(0.917595\pi\)
\(564\) 0 0
\(565\) 25.0892i 1.05551i
\(566\) 6.03668 0.253741
\(567\) 0 0
\(568\) −12.7279 −0.534052
\(569\) 10.2426i 0.429394i −0.976681 0.214697i \(-0.931124\pi\)
0.976681 0.214697i \(-0.0688764\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −1.52192 + 2.63604i −0.0636346 + 0.110218i
\(573\) 0 0
\(574\) −6.00000 2.44949i −0.250435 0.102240i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 23.7426 + 13.7078i 0.988419 + 0.570664i 0.904801 0.425834i \(-0.140019\pi\)
0.0836177 + 0.996498i \(0.473353\pi\)
\(578\) −9.52628 + 5.50000i −0.396241 + 0.228770i
\(579\) 0 0
\(580\) −3.72792 + 2.15232i −0.154794 + 0.0893701i
\(581\) −40.0834 + 5.48528i −1.66294 + 0.227568i
\(582\) 0 0
\(583\) 61.4558 2.54524
\(584\) −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
\(590\) 5.19615 + 3.00000i 0.213922 + 0.123508i
\(591\) 0 0
\(592\) −2.62132 4.54026i −0.107736 0.186604i
\(593\) 0.927572 + 1.60660i 0.0380908 + 0.0659752i 0.884442 0.466650i \(-0.154539\pi\)
−0.846352 + 0.532625i \(0.821206\pi\)
\(594\) 0 0
\(595\) −6.00000 + 14.6969i −0.245976 + 0.602516i
\(596\) 14.0665 + 8.12132i 0.576188 + 0.332662i
\(597\) 0 0
\(598\) 4.30463i 0.176030i
\(599\) 3.51472i 0.143608i −0.997419 0.0718038i \(-0.977124\pi\)
0.997419 0.0718038i \(-0.0228755\pi\)
\(600\) 0 0
\(601\) −35.9558 20.7591i −1.46667 0.846782i −0.467365 0.884065i \(-0.654796\pi\)
−0.999305 + 0.0372826i \(0.988130\pi\)
\(602\) 2.51104 + 18.3492i 0.102342 + 0.747859i
\(603\) 0 0
\(604\) 4.37868 + 7.58410i 0.178166 + 0.308592i
\(605\) −8.57321 14.8492i −0.348551 0.603708i
\(606\) 0 0
\(607\) −31.2426 18.0379i −1.26810 0.732138i −0.293471 0.955968i \(-0.594811\pi\)
−0.974628 + 0.223830i \(0.928144\pi\)
\(608\) −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 −0.426829 0.904332i \(-0.640369\pi\)
0.996589 0.0825214i \(-0.0262973\pi\)
\(614\) −26.8213 −1.08242
\(615\) 0 0
\(616\) 4.24264 10.3923i 0.170941 0.418718i
\(617\) 3.67423 2.12132i 0.147919 0.0854011i −0.424214 0.905562i \(-0.639449\pi\)
0.572133 + 0.820161i \(0.306116\pi\)
\(618\) 0 0
\(619\) 11.0147 6.35935i 0.442719 0.255604i −0.262031 0.965059i \(-0.584392\pi\)
0.704750 + 0.709455i \(0.251059\pi\)
\(620\) −19.2627 11.1213i −0.773608 0.446643i
\(621\) 0 0
\(622\) 17.1464i 0.687509i
\(623\) 3.04384 7.45584i 0.121949 0.298712i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 20.1903 0.806965
\(627\) 0 0
\(628\) 10.3923i 0.414698i
\(629\) −12.8418 −0.512036
\(630\) 0 0
\(631\) −14.7574 −0.587481 −0.293741 0.955885i \(-0.594900\pi\)
−0.293741 + 0.955885i \(0.594900\pi\)
\(632\) 0.757359i 0.0301261i
\(633\) 0 0
\(634\) 22.2426 0.883368
\(635\) −9.46473 + 16.3934i −0.375596 + 0.650552i
\(636\) 0 0
\(637\) −1.34924 4.83743i −0.0534589 0.191666i
\(638\) 7.45584i 0.295180i
\(639\) 0 0
\(640\) −2.12132 1.22474i −0.0838525 0.0484123i
\(641\) −28.7635 + 16.6066i −1.13609 + 0.655921i −0.945459 0.325741i \(-0.894386\pi\)
−0.190630 + 0.981662i \(0.561053\pi\)
\(642\) 0 0
\(643\) −1.50000 + 0.866025i −0.0591542 + 0.0341527i −0.529285 0.848444i \(-0.677540\pi\)
0.470131 + 0.882597i \(0.344207\pi\)
\(644\) −2.15232 15.7279i −0.0848132 0.619767i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) −10.3923 + 18.0000i −0.408564 + 0.707653i −0.994729 0.102538i \(-0.967304\pi\)
0.586165 + 0.810191i \(0.300637\pi\)
\(648\) 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
\(653\) 2.15232 + 1.24264i 0.0842267 + 0.0486283i 0.541522 0.840687i \(-0.317848\pi\)
−0.457295 + 0.889315i \(0.651182\pi\)
\(654\) 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 0.0754589 0.997149i \(-0.475958\pi\)
−0.825827 + 0.563924i \(0.809291\pi\)
\(660\) 0 0
\(661\) 4.89898i 0.190548i 0.995451 + 0.0952741i \(0.0303728\pi\)
−0.995451 + 0.0952741i \(0.969627\pi\)
\(662\) 10.0000i 0.388661i
\(663\) 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
\(668\) 0.297173 + 0.514719i 0.0114980 + 0.0199151i
\(669\) 0 0
\(670\) 28.6066 + 16.5160i 1.10517 + 0.638070i
\(671\) −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
\(677\) −14.6969 −0.564849 −0.282425 0.959289i \(-0.591139\pi\)
−0.282425 + 0.959289i \(0.591139\pi\)
\(678\) 0 0
\(679\) 1.13604 + 8.30153i 0.0435972 + 0.318584i
\(680\) −5.19615 + 3.00000i −0.199263 + 0.115045i
\(681\) 0 0
\(682\) 33.3640 19.2627i 1.27757 0.737607i
\(683\) 8.87039 + 5.12132i 0.339416 + 0.195962i 0.660014 0.751254i \(-0.270550\pi\)
−0.320598 + 0.947215i \(0.603884\pi\)
\(684\) 0 0
\(685\) 14.6969i 0.561541i
\(686\) 7.34847 + 17.0000i 0.280566 + 0.649063i
\(687\) 0 0
\(688\) −3.50000 + 6.06218i −0.133436 + 0.231118i
\(689\) 10.3923 0.395915
\(690\) 0 0
\(691\) 2.57258i 0.0978657i 0.998802 + 0.0489328i \(0.0155820\pi\)
−0.998802 + 0.0489328i \(0.984418\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) −4.97056 −0.188680
\(695\) 19.7574i 0.749439i
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) −0.0615465 + 0.106602i −0.00232957 + 0.00403493i
\(699\) 0 0
\(700\) 1.00000 2.44949i 0.0377964 0.0925820i
\(701\) 20.4853i 0.773718i 0.922139 + 0.386859i \(0.126440\pi\)
−0.922139 + 0.386859i \(0.873560\pi\)
\(702\) 0 0
\(703\) 22.2426 + 12.8418i 0.838897 + 0.484337i
\(704\) 3.67423 2.12132i 0.138478 0.0799503i
\(705\) 0 0
\(706\) 9.51472 5.49333i 0.358091 0.206744i
\(707\) 7.34847 18.0000i 0.276368 0.676960i
\(708\) 0 0
\(709\) 16.2132 0.608900 0.304450 0.952528i \(-0.401527\pi\)
0.304450 + 0.952528i \(0.401527\pi\)
\(710\) 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
\(716\) −5.82655 3.36396i −0.217748 0.125717i
\(717\) 0 0
\(718\) −7.24264 12.5446i −0.270293 0.468161i
\(719\) −26.3140 45.5772i −0.981346 1.69974i −0.657166 0.753746i \(-0.728245\pi\)
−0.324181 0.945995i \(-0.605089\pi\)
\(720\) 0 0
\(721\) 3.98528 + 29.1222i 0.148420 + 1.08457i
\(722\) 4.33013 + 2.50000i 0.161151 + 0.0930404i
\(723\) 0 0
\(724\) 9.79796i 0.364138i
\(725\) 1.75736i 0.0652667i
\(726\) 0 0
\(727\) 24.3198 + 14.0410i 0.901972 + 0.520754i 0.877839 0.478955i \(-0.158984\pi\)
0.0241323 + 0.999709i \(0.492318\pi\)
\(728\) 0.717439 1.75736i 0.0265901 0.0651321i
\(729\) 0 0
\(730\) −6.72792 11.6531i −0.249012 0.431301i
\(731\) 8.57321 + 14.8492i 0.317092 + 0.549219i
\(732\) 0 0
\(733\) −1.13604 0.655892i −0.0419606 0.0242259i 0.478873 0.877884i \(-0.341045\pi\)
−0.520834 + 0.853658i \(0.674379\pi\)
\(734\) 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 −0.777724 0.628606i \(-0.783626\pi\)
0.933251 + 0.359226i \(0.116959\pi\)
\(740\) 12.8418 0.472074
\(741\) 0 0
\(742\) −37.9706 + 5.19615i −1.39394 + 0.190757i
\(743\) 16.2189 9.36396i 0.595012 0.343530i −0.172065 0.985086i \(-0.555044\pi\)
0.767077 + 0.641555i \(0.221710\pi\)
\(744\) 0 0
\(745\) −34.4558 + 19.8931i −1.26236 + 0.728826i
\(746\) 19.0526 + 11.0000i 0.697564 + 0.402739i
\(747\) 0 0
\(748\) 10.3923i 0.379980i
\(749\) 6.08767 + 2.48528i 0.222439 + 0.0908102i
\(750\) 0 0
\(751\) −26.7279 + 46.2941i −0.975316 + 1.68930i −0.296427 + 0.955056i \(0.595795\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(752\) −12.8418 −0.468292
\(753\) 0 0
\(754\) 1.26080i 0.0459156i
\(755\) −21.4511 −0.780684
\(756\) 0 0
\(757\) 32.7574 1.19059 0.595293 0.803509i \(-0.297036\pi\)
0.595293 + 0.803509i \(0.297036\pi\)
\(758\) 7.48528i 0.271878i
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) −12.2474 + 21.2132i −0.443970 + 0.768978i −0.997980 0.0635319i \(-0.979764\pi\)
0.554010 + 0.832510i \(0.313097\pi\)
\(762\) 0 0
\(763\) −46.4706 + 6.35935i −1.68235 + 0.230224i
\(764\) 21.2132i 0.767467i
\(765\) 0 0
\(766\) −4.75736 2.74666i −0.171890 0.0992410i
\(767\) −1.52192 + 0.878680i −0.0549533 + 0.0317273i
\(768\) 0 0
\(769\) −34.9706 + 20.1903i −1.26107 + 0.728080i −0.973282 0.229614i \(-0.926254\pi\)
−0.287789 + 0.957694i \(0.592920\pi\)
\(770\) 16.8493 + 21.7279i 0.607205 + 0.783020i
\(771\) 0 0
\(772\) 1.48528 0.0534564
\(773\) 4.89898 8.48528i 0.176204 0.305194i −0.764373 0.644774i \(-0.776951\pi\)
0.940577 + 0.339580i \(0.110285\pi\)
\(774\) 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
\(779\) 10.3923 + 6.00000i 0.372343 + 0.214972i
\(780\) 0 0
\(781\) 27.0000 + 46.7654i 0.966136 + 1.67340i
\(782\) −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
\(787\) 28.2562i 1.00722i 0.863930 + 0.503612i \(0.167996\pi\)
−0.863930 + 0.503612i \(0.832004\pi\)
\(788\) 16.9706i