Properties

Label 1134.2.t.f.1025.4
Level $1134$
Weight $2$
Character 1134.1025
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 1025.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1025
Dual form 1134.2.t.f.593.4

$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

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

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 \(-0.315495\pi\)
0.547723 + 0.836660i \(0.315495\pi\)
\(6\) 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 0.583681 0.811983i \(-0.301612\pi\)
−0.411358 + 0.911474i \(0.634945\pi\)
\(14\) 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 \(-0.929334\pi\)
0.678414 + 0.734680i \(0.262668\pi\)
\(18\) 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
\(23\) 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 \(-0.614496\pi\)
0.634606 + 0.772836i \(0.281162\pi\)
\(30\) 0 0
\(31\) 7.86396 4.54026i 1.41241 0.815455i 0.416794 0.909001i \(-0.363154\pi\)
0.995615 + 0.0935461i \(0.0298203\pi\)
\(32\) −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 0.566012 0.824397i \(-0.308485\pi\)
−0.996955 + 0.0779826i \(0.975152\pi\)
\(38\) −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 \(-0.772072\pi\)
0.945672 + 0.325121i \(0.105405\pi\)
\(42\) 0 0
\(43\) −3.50000 6.06218i −0.533745 0.924473i −0.999223 0.0394140i \(-0.987451\pi\)
0.465478 0.885059i \(-0.345882\pi\)
\(44\) −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 −0.164800 + 0.986327i \(0.552698\pi\)
−0.771784 + 0.635884i \(0.780636\pi\)
\(48\) 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 0.912231 + 0.409675i \(0.134358\pi\)
0.810905 + 0.585178i \(0.198975\pi\)
\(54\) 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 \(-0.115695\pi\)
−0.775222 + 0.631689i \(0.782362\pi\)
\(60\) 0 0
\(61\) −3.62132 2.09077i −0.463663 0.267696i 0.249920 0.968266i \(-0.419596\pi\)
−0.713583 + 0.700571i \(0.752929\pi\)
\(62\) 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 −0.902875 0.429903i \(-0.858548\pi\)
0.0791303 0.996864i \(-0.474786\pi\)
\(68\) −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 0.195056 0.980792i \(-0.437511\pi\)
−0.751863 + 0.659320i \(0.770844\pi\)
\(74\) 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 −0.886541 0.462649i \(-0.846899\pi\)
0.843937 + 0.536443i \(0.180232\pi\)
\(80\) −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 −0.890549 0.454887i \(-0.849680\pi\)
0.0513309 0.998682i \(-0.483654\pi\)
\(84\) 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 \(-0.218243\pi\)
−0.935343 + 0.353741i \(0.884909\pi\)
\(90\) 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 −0.354259 0.935147i \(-0.615267\pi\)
0.632732 + 0.774371i \(0.281934\pi\)
\(98\) 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 \(-0.380864\pi\)
0.365600 + 0.930772i \(0.380864\pi\)
\(102\) 0 0
\(103\) 11.1097i 1.09468i 0.836912 + 0.547338i \(0.184359\pi\)
−0.836912 + 0.547338i \(0.815641\pi\)
\(104\) −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 \(-0.628335\pi\)
0.600415 + 0.799688i \(0.295002\pi\)
\(108\) 0 0
\(109\) 8.86396 15.3528i 0.849013 1.47053i −0.0330761 0.999453i \(-0.510530\pi\)
0.882090 0.471082i \(-0.156136\pi\)
\(110\) −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 \(-0.173326\pi\)
−0.0209200 + 0.999781i \(0.506660\pi\)
\(114\) 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 0.173595 0.984817i \(-0.444462\pi\)
−0.766079 + 0.642746i \(0.777795\pi\)
\(140\) 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 −0.0958404 0.995397i \(-0.530554\pi\)
0.814119 + 0.580699i \(0.197221\pi\)
\(158\) −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 0.989792 0.142518i \(-0.0455197\pi\)
−0.618320 + 0.785926i \(0.712186\pi\)
\(164\) 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 \(-0.826013\pi\)
0.877294 + 0.479953i \(0.159346\pi\)
\(168\) 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 0.135785 + 0.990738i \(0.456644\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(174\) 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 \(-0.414236\pi\)
−0.701686 + 0.712487i \(0.747569\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) 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 \(-0.0548503\pi\)
0.344101 + 0.938933i \(0.388184\pi\)
\(192\) 0 0
\(193\) 0.742641 + 1.28629i 0.0534564 + 0.0925893i 0.891515 0.452990i \(-0.149643\pi\)
−0.838059 + 0.545580i \(0.816310\pi\)
\(194\) 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 −0.306049 0.952016i \(-0.599007\pi\)
−0.977494 + 0.210962i \(0.932340\pi\)
\(200\) 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 −0.919755 0.392493i \(-0.871613\pi\)
0.799787 + 0.600284i \(0.204946\pi\)
\(212\) 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 −0.770097 0.637927i \(-0.779792\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) −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 \(-0.813158\pi\)
−0.832616 + 0.553851i \(0.813158\pi\)
\(228\) 0 0
\(229\) 5.61642i 0.371143i −0.982631 0.185572i \(-0.940586\pi\)
0.982631 0.185572i \(-0.0594137\pi\)
\(230\) 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 \(-0.900809\pi\)
−0.210398 + 0.977616i \(0.567476\pi\)
\(234\) 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 \(-0.157277\pi\)
0.0294934 + 0.999565i \(0.490611\pi\)
\(240\) 0 0
\(241\) 1.13770i 0.0732860i 0.999328 + 0.0366430i \(0.0116664\pi\)
−0.999328 + 0.0366430i \(0.988334\pi\)
\(242\) −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 \(-0.660303\pi\)
−0.482589 + 0.875847i \(0.660303\pi\)
\(252\) 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 \(-0.786062\pi\)
−0.782512 + 0.622636i \(0.786062\pi\)
\(258\) 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 \(-0.736782\pi\)
0.975838 + 0.218496i \(0.0701150\pi\)
\(270\) 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
\(275\) 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 \(-0.532074\pi\)
0.811336 + 0.584580i \(0.198741\pi\)
\(282\) 0 0
\(283\) −5.22792 + 3.01834i −0.310768 + 0.179422i −0.647270 0.762261i \(-0.724089\pi\)
0.336502 + 0.941683i \(0.390756\pi\)
\(284\) −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 \(-0.710937\pi\)
0.990344 + 0.138632i \(0.0442706\pi\)
\(294\) 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 \(0.277452\pi\)
−0.643571 + 0.765386i \(0.722548\pi\)
\(308\) −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 \(-0.328263\pi\)
−0.999873 + 0.0159282i \(0.994930\pi\)
\(312\) 0 0
\(313\) 17.4853 + 10.0951i 0.988327 + 0.570611i 0.904774 0.425893i \(-0.140040\pi\)
0.0835529 + 0.996503i \(0.473373\pi\)
\(314\) 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 \(-0.548086\pi\)
−0.931408 + 0.363976i \(0.881419\pi\)
\(318\) 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 −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) 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 −0.410564 0.911832i \(-0.634668\pi\)
0.994952 0.100357i \(-0.0319984\pi\)
\(338\) 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 \(-0.709262\pi\)
0.379988 + 0.924992i \(0.375928\pi\)
\(348\) 0 0
\(349\) −0.106602 + 0.0615465i −0.00570626 + 0.00329451i −0.502850 0.864373i \(-0.667715\pi\)
0.497144 + 0.867668i \(0.334382\pi\)
\(350\) 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 \(-0.594447\pi\)
−0.292380 + 0.956302i \(0.594447\pi\)
\(354\) 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 \(-0.541815\pi\)
0.793069 + 0.609132i \(0.208482\pi\)
\(360\) 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 \(0.286151\pi\)
−0.622416 + 0.782686i \(0.713849\pi\)
\(368\) 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 \(-0.544822\pi\)
−0.140348 + 0.990102i \(0.544822\pi\)
\(384\) 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 −0.792002 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
\(401\) 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 −0.417300 0.908769i \(-0.637024\pi\)
0.578366 + 0.815777i \(0.303690\pi\)
\(410\) 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 \(-0.771182\pi\)
0.946577 + 0.322476i \(0.104515\pi\)
\(420\) 0 0
\(421\) 11.7279 + 20.3134i 0.571584 + 0.990012i 0.996404 + 0.0847344i \(0.0270042\pi\)
−0.424820 + 0.905278i \(0.639662\pi\)
\(422\) −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 \(-0.346810\pi\)
−0.536206 + 0.844087i \(0.680143\pi\)
\(432\) 0 0
\(433\) 2.57258i 0.123630i 0.998088 + 0.0618152i \(0.0196889\pi\)
−0.998088 + 0.0618152i \(0.980311\pi\)
\(434\) 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 0.408393 0.912806i \(-0.366089\pi\)
−0.586317 + 0.810082i \(0.699423\pi\)
\(440\) −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 \(-0.540049\pi\)
−0.921923 + 0.387374i \(0.873382\pi\)
\(444\) 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 −0.461067 0.887365i \(-0.652533\pi\)
0.999014 0.0443868i \(-0.0141334\pi\)
\(458\) 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 \(-0.000169865\pi\)
−0.500462 + 0.865758i \(0.666837\pi\)
\(462\) 0 0
\(463\) 11.0000 19.0526i 0.511213 0.885448i −0.488702 0.872451i \(-0.662530\pi\)
0.999916 0.0129968i \(-0.00413714\pi\)
\(464\) 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 \(-0.0320304\pi\)
−0.584469 + 0.811416i \(0.698697\pi\)
\(468\) 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 \(-0.517822\pi\)
−0.0559600 + 0.998433i \(0.517822\pi\)
\(480\) 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 −0.999998 0.00178012i \(-0.999433\pi\)
0.501541 + 0.865134i \(0.332767\pi\)
\(488\) 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 \(-0.0438808\pi\)
0.376248 + 0.926519i \(0.377214\pi\)
\(492\) 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 \(-0.495782\pi\)
0.0132503 + 0.999912i \(0.495782\pi\)
\(504\) 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 \(-0.434615\pi\)
0.203971 + 0.978977i \(0.434615\pi\)
\(510\) 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 0.324509 + 0.945883i \(0.394801\pi\)
−0.981413 + 0.191908i \(0.938532\pi\)
\(522\) 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
\(527\) 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 0.918690 0.394980i \(-0.129248\pi\)
−0.801407 + 0.598119i \(0.795915\pi\)
\(542\) −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 −0.877100 0.480308i \(-0.840525\pi\)
0.0225909 0.999745i \(-0.492808\pi\)
\(548\) 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 \(-0.184965\pi\)
−0.0574555 + 0.998348i \(0.518299\pi\)
\(558\) 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 −0.705043 0.709165i \(-0.749072\pi\)
−0.261634 0.965167i \(-0.584261\pi\)
\(564\) 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 \(-0.402210\pi\)
−0.674273 + 0.738482i \(0.735543\pi\)
\(570\) 0 0
\(571\) 11.0000 + 19.0526i 0.460336 + 0.797325i 0.998978 0.0452101i \(-0.0143957\pi\)
−0.538642 + 0.842535i \(0.681062\pi\)
\(572\) −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 0.904801 0.425834i \(-0.140019\pi\)
0.0836177 + 0.996498i \(0.473353\pi\)
\(578\) 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 0.978065 + 0.208298i \(0.0667923\pi\)
−0.308642 + 0.951178i \(0.599874\pi\)
\(588\) 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 \(-0.178794\pi\)
−0.884442 + 0.466650i \(0.845461\pi\)
\(594\) 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 \(-0.643791\pi\)
0.560893 + 0.827888i \(0.310458\pi\)
\(600\) 0 0
\(601\) 35.9558 20.7591i 1.46667 0.846782i 0.467365 0.884065i \(-0.345204\pi\)
0.999305 + 0.0372826i \(0.0118702\pi\)
\(602\) −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 \(0.261477\pi\)
−0.681157 + 0.732138i \(0.738523\pi\)
\(608\) 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 \(-0.0262973\pi\)
\(614\) −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 \(-0.306116\pi\)
−0.424214 + 0.905562i \(0.639449\pi\)
\(618\) 0 0
\(619\) 12.7187i 0.511208i 0.966782 + 0.255604i \(0.0822743\pi\)
−0.966782 + 0.255604i \(0.917726\pi\)
\(620\) 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 0.529285 0.848444i \(-0.322460\pi\)
−0.470131 + 0.882597i \(0.655793\pi\)
\(644\) 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 \(-0.699363\pi\)
0.994729 + 0.102538i \(0.0326965\pi\)
\(648\) 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 \(-0.809291\pi\)
0.0754589 + 0.997149i \(0.475958\pi\)
\(660\) 0 0
\(661\) 4.24264 2.44949i 0.165020 0.0952741i −0.415216 0.909723i \(-0.636294\pi\)
0.580235 + 0.814449i \(0.302961\pi\)
\(662\) −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 0.855590 + 0.517655i \(0.173195\pi\)
0.0205075 + 0.999790i \(0.493472\pi\)
\(674\) 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 \(-0.924472\pi\)
0.689557 + 0.724232i \(0.257805\pi\)
\(678\) 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 \(-0.396116\pi\)
−0.660014 + 0.751254i \(0.729450\pi\)
\(684\) 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 0.457024 0.889454i \(-0.348915\pi\)
−0.541778 + 0.840522i \(0.682249\pi\)
\(692\) −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 −0.977139 0.212603i \(-0.931806\pi\)
0.672689 + 0.739925i \(0.265139\pi\)
\(710\) −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 0.657166 + 0.753746i \(0.271755\pi\)
0.324181 + 0.945995i \(0.394911\pi\)
\(720\) 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 −0.877839 0.478955i \(-0.841016\pi\)
−0.0241323 + 0.999709i \(0.507682\pi\)
\(728\) −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 \(0.00771211\pi\)
−0.999707 + 0.0242259i \(0.992288\pi\)
\(734\) −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 \(0.116959\pi\)
\(740\) 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 \(-0.221710\pi\)
−0.172065 + 0.985086i \(0.555044\pi\)
\(744\) 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 \(-0.646430\pi\)
−0.443970 + 0.896042i \(0.646430\pi\)
\(762\) 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 0.973282 0.229614i \(-0.0737465\pi\)
0.287789 + 0.957694i \(0.407080\pi\)
\(770\) −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 \(-0.889715\pi\)
0.764373 + 0.644774i \(0.223049\pi\)
\(774\) 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 0.00417567 0.999991i \(-0.498671\pi\)
0.868106 + 0.496379i \(0.165338\pi\)
\(788\) 14.6969 8.48528i 0.523557 0.302276i