Properties

Label 756.2.ba.a.71.13
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.13
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.726513 - 1.21333i) q^{2} +(-0.944358 + 1.76301i) q^{4} +(-0.256612 - 0.148155i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +O(q^{10})\) \(q+(-0.726513 - 1.21333i) q^{2} +(-0.944358 + 1.76301i) q^{4} +(-0.256612 - 0.148155i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +(0.00667042 + 0.418992i) q^{10} +(-2.21618 - 3.83853i) q^{11} +(-0.227431 + 0.393922i) q^{13} +(1.23585 + 0.687522i) q^{14} +(-2.21638 - 3.32982i) q^{16} +6.53822i q^{17} -1.47447i q^{19} +(0.503531 - 0.312497i) q^{20} +(-3.04734 + 5.47771i) q^{22} +(2.09235 - 3.62406i) q^{23} +(-2.45610 - 4.25409i) q^{25} +(0.643190 - 0.0102397i) q^{26} +(-0.0636644 - 1.99899i) q^{28} +(-5.71624 + 3.30027i) q^{29} +(-5.73985 - 3.31390i) q^{31} +(-2.42995 + 5.10836i) q^{32} +(7.93304 - 4.75010i) q^{34} +0.296310 q^{35} -7.53908 q^{37} +(-1.78902 + 1.07122i) q^{38} +(-0.744985 - 0.383919i) q^{40} +(-1.57065 - 0.906813i) q^{41} +(-8.80511 + 5.08363i) q^{43} +(8.86022 - 0.282183i) q^{44} +(-5.91731 + 0.0942044i) q^{46} +(-3.32792 - 5.76413i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.37724 + 6.07072i) q^{50} +(-0.479710 - 0.772966i) q^{52} -1.22675i q^{53} +1.31335i q^{55} +(-2.37918 + 1.52954i) q^{56} +(8.15725 + 4.53802i) q^{58} +(-6.57365 + 11.3859i) q^{59} +(1.86594 + 3.23190i) q^{61} +(0.149203 + 9.37195i) q^{62} +(7.96354 - 0.762941i) q^{64} +(0.116723 - 0.0673900i) q^{65} +(0.941252 + 0.543432i) q^{67} +(-11.5269 - 6.17442i) q^{68} +(-0.215273 - 0.359523i) q^{70} +1.66151 q^{71} +3.76397 q^{73} +(5.47723 + 9.14742i) q^{74} +(2.59949 + 1.39242i) q^{76} +(3.83853 + 2.21618i) q^{77} +(4.13444 - 2.38702i) q^{79} +(0.0754193 + 1.18284i) q^{80} +(0.0408277 + 2.56453i) q^{82} +(-4.93471 - 8.54717i) q^{83} +(0.968669 - 1.67778i) q^{85} +(12.5652 + 6.99022i) q^{86} +(-6.77945 - 10.5454i) q^{88} -11.2455i q^{89} -0.454862i q^{91} +(4.41331 + 7.11124i) q^{92} +(-4.57603 + 8.22559i) q^{94} +(-0.218449 + 0.378366i) q^{95} +(5.52923 + 9.57690i) q^{97} +(-1.41403 + 0.0225116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.726513 1.21333i −0.513722 0.857957i
\(3\) 0 0
\(4\) −0.944358 + 1.76301i −0.472179 + 0.881503i
\(5\) −0.256612 0.148155i −0.114760 0.0662569i 0.441521 0.897251i \(-0.354439\pi\)
−0.556281 + 0.830994i \(0.687772\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 2.82520 0.135024i 0.998860 0.0477382i
\(9\) 0 0
\(10\) 0.00667042 + 0.418992i 0.00210937 + 0.132497i
\(11\) −2.21618 3.83853i −0.668203 1.15736i −0.978406 0.206691i \(-0.933730\pi\)
0.310203 0.950670i \(-0.399603\pi\)
\(12\) 0 0
\(13\) −0.227431 + 0.393922i −0.0630780 + 0.109254i −0.895840 0.444377i \(-0.853425\pi\)
0.832762 + 0.553631i \(0.186758\pi\)
\(14\) 1.23585 + 0.687522i 0.330294 + 0.183748i
\(15\) 0 0
\(16\) −2.21638 3.32982i −0.554094 0.832454i
\(17\) 6.53822i 1.58575i 0.609384 + 0.792875i \(0.291417\pi\)
−0.609384 + 0.792875i \(0.708583\pi\)
\(18\) 0 0
\(19\) 1.47447i 0.338266i −0.985593 0.169133i \(-0.945903\pi\)
0.985593 0.169133i \(-0.0540967\pi\)
\(20\) 0.503531 0.312497i 0.112593 0.0698764i
\(21\) 0 0
\(22\) −3.04734 + 5.47771i −0.649695 + 1.16785i
\(23\) 2.09235 3.62406i 0.436285 0.755669i −0.561114 0.827738i \(-0.689627\pi\)
0.997400 + 0.0720699i \(0.0229605\pi\)
\(24\) 0 0
\(25\) −2.45610 4.25409i −0.491220 0.850818i
\(26\) 0.643190 0.0102397i 0.126140 0.00200817i
\(27\) 0 0
\(28\) −0.0636644 1.99899i −0.0120314 0.377773i
\(29\) −5.71624 + 3.30027i −1.06148 + 0.612845i −0.925841 0.377913i \(-0.876642\pi\)
−0.135638 + 0.990758i \(0.543308\pi\)
\(30\) 0 0
\(31\) −5.73985 3.31390i −1.03091 0.595195i −0.113663 0.993519i \(-0.536258\pi\)
−0.917244 + 0.398325i \(0.869592\pi\)
\(32\) −2.42995 + 5.10836i −0.429559 + 0.903039i
\(33\) 0 0
\(34\) 7.93304 4.75010i 1.36051 0.814635i
\(35\) 0.296310 0.0500855
\(36\) 0 0
\(37\) −7.53908 −1.23942 −0.619708 0.784832i \(-0.712749\pi\)
−0.619708 + 0.784832i \(0.712749\pi\)
\(38\) −1.78902 + 1.07122i −0.290217 + 0.173775i
\(39\) 0 0
\(40\) −0.744985 0.383919i −0.117792 0.0607029i
\(41\) −1.57065 0.906813i −0.245294 0.141620i 0.372314 0.928107i \(-0.378565\pi\)
−0.617607 + 0.786487i \(0.711898\pi\)
\(42\) 0 0
\(43\) −8.80511 + 5.08363i −1.34277 + 0.775247i −0.987213 0.159409i \(-0.949041\pi\)
−0.355554 + 0.934656i \(0.615708\pi\)
\(44\) 8.86022 0.282183i 1.33573 0.0425407i
\(45\) 0 0
\(46\) −5.91731 + 0.0942044i −0.872460 + 0.0138897i
\(47\) −3.32792 5.76413i −0.485427 0.840785i 0.514433 0.857531i \(-0.328003\pi\)
−0.999860 + 0.0167463i \(0.994669\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.37724 + 6.07072i −0.477614 + 0.858530i
\(51\) 0 0
\(52\) −0.479710 0.772966i −0.0665238 0.107191i
\(53\) 1.22675i 0.168508i −0.996444 0.0842538i \(-0.973149\pi\)
0.996444 0.0842538i \(-0.0268506\pi\)
\(54\) 0 0
\(55\) 1.31335i 0.177092i
\(56\) −2.37918 + 1.52954i −0.317932 + 0.204393i
\(57\) 0 0
\(58\) 8.15725 + 4.53802i 1.07110 + 0.595871i
\(59\) −6.57365 + 11.3859i −0.855817 + 1.48232i 0.0200684 + 0.999799i \(0.493612\pi\)
−0.875885 + 0.482520i \(0.839722\pi\)
\(60\) 0 0
\(61\) 1.86594 + 3.23190i 0.238909 + 0.413802i 0.960401 0.278620i \(-0.0898770\pi\)
−0.721493 + 0.692422i \(0.756544\pi\)
\(62\) 0.149203 + 9.37195i 0.0189488 + 1.19024i
\(63\) 0 0
\(64\) 7.96354 0.762941i 0.995442 0.0953676i
\(65\) 0.116723 0.0673900i 0.0144777 0.00835871i
\(66\) 0 0
\(67\) 0.941252 + 0.543432i 0.114992 + 0.0663908i 0.556393 0.830919i \(-0.312185\pi\)
−0.441401 + 0.897310i \(0.645518\pi\)
\(68\) −11.5269 6.17442i −1.39784 0.748758i
\(69\) 0 0
\(70\) −0.215273 0.359523i −0.0257300 0.0429712i
\(71\) 1.66151 0.197185 0.0985926 0.995128i \(-0.468566\pi\)
0.0985926 + 0.995128i \(0.468566\pi\)
\(72\) 0 0
\(73\) 3.76397 0.440539 0.220270 0.975439i \(-0.429306\pi\)
0.220270 + 0.975439i \(0.429306\pi\)
\(74\) 5.47723 + 9.14742i 0.636716 + 1.06337i
\(75\) 0 0
\(76\) 2.59949 + 1.39242i 0.298182 + 0.159722i
\(77\) 3.83853 + 2.21618i 0.437442 + 0.252557i
\(78\) 0 0
\(79\) 4.13444 2.38702i 0.465160 0.268560i −0.249051 0.968490i \(-0.580119\pi\)
0.714212 + 0.699930i \(0.246785\pi\)
\(80\) 0.0754193 + 1.18284i 0.00843214 + 0.132245i
\(81\) 0 0
\(82\) 0.0408277 + 2.56453i 0.00450866 + 0.283205i
\(83\) −4.93471 8.54717i −0.541655 0.938174i −0.998809 0.0487865i \(-0.984465\pi\)
0.457154 0.889387i \(-0.348869\pi\)
\(84\) 0 0
\(85\) 0.968669 1.67778i 0.105067 0.181981i
\(86\) 12.5652 + 6.99022i 1.35494 + 0.753774i
\(87\) 0 0
\(88\) −6.77945 10.5454i −0.722692 1.12414i
\(89\) 11.2455i 1.19202i −0.802976 0.596011i \(-0.796751\pi\)
0.802976 0.596011i \(-0.203249\pi\)
\(90\) 0 0
\(91\) 0.454862i 0.0476825i
\(92\) 4.41331 + 7.11124i 0.460119 + 0.741398i
\(93\) 0 0
\(94\) −4.57603 + 8.22559i −0.471982 + 0.848405i
\(95\) −0.218449 + 0.378366i −0.0224124 + 0.0388195i
\(96\) 0 0
\(97\) 5.52923 + 9.57690i 0.561408 + 0.972387i 0.997374 + 0.0724238i \(0.0230734\pi\)
−0.435966 + 0.899963i \(0.643593\pi\)
\(98\) −1.41403 + 0.0225116i −0.142839 + 0.00227402i
\(99\) 0 0
\(100\) 9.81942 0.312732i 0.981942 0.0312732i
\(101\) 8.89923 5.13797i 0.885506 0.511247i 0.0130363 0.999915i \(-0.495850\pi\)
0.872470 + 0.488668i \(0.162517\pi\)
\(102\) 0 0
\(103\) −6.75540 3.90023i −0.665629 0.384301i 0.128789 0.991672i \(-0.458891\pi\)
−0.794418 + 0.607371i \(0.792224\pi\)
\(104\) −0.589350 + 1.14362i −0.0577905 + 0.112141i
\(105\) 0 0
\(106\) −1.48846 + 0.891252i −0.144572 + 0.0865661i
\(107\) −3.24508 −0.313714 −0.156857 0.987621i \(-0.550136\pi\)
−0.156857 + 0.987621i \(0.550136\pi\)
\(108\) 0 0
\(109\) −9.77063 −0.935857 −0.467928 0.883766i \(-0.654999\pi\)
−0.467928 + 0.883766i \(0.654999\pi\)
\(110\) 1.59353 0.954166i 0.151937 0.0909762i
\(111\) 0 0
\(112\) 3.58435 + 1.77552i 0.338689 + 0.167771i
\(113\) 5.85142 + 3.37832i 0.550455 + 0.317805i 0.749306 0.662224i \(-0.230387\pi\)
−0.198850 + 0.980030i \(0.563721\pi\)
\(114\) 0 0
\(115\) −1.07384 + 0.619984i −0.100137 + 0.0578138i
\(116\) −0.420220 13.1944i −0.0390164 1.22507i
\(117\) 0 0
\(118\) 18.5907 0.295967i 1.71142 0.0272460i
\(119\) −3.26911 5.66226i −0.299679 0.519059i
\(120\) 0 0
\(121\) −4.32289 + 7.48747i −0.392990 + 0.680679i
\(122\) 2.56574 4.61202i 0.232292 0.417553i
\(123\) 0 0
\(124\) 11.2629 6.98987i 1.01144 0.627709i
\(125\) 2.93708i 0.262701i
\(126\) 0 0
\(127\) 17.2613i 1.53169i 0.643026 + 0.765844i \(0.277679\pi\)
−0.643026 + 0.765844i \(0.722321\pi\)
\(128\) −6.71131 9.10814i −0.593202 0.805054i
\(129\) 0 0
\(130\) −0.166567 0.0926642i −0.0146089 0.00812719i
\(131\) −0.624945 + 1.08244i −0.0546017 + 0.0945730i −0.892034 0.451968i \(-0.850722\pi\)
0.837433 + 0.546541i \(0.184056\pi\)
\(132\) 0 0
\(133\) 0.737233 + 1.27693i 0.0639262 + 0.110723i
\(134\) −0.0244671 1.53686i −0.00211363 0.132765i
\(135\) 0 0
\(136\) 0.882817 + 18.4718i 0.0757009 + 1.58394i
\(137\) 12.7469 7.35942i 1.08904 0.628758i 0.155720 0.987801i \(-0.450230\pi\)
0.933321 + 0.359043i \(0.116897\pi\)
\(138\) 0 0
\(139\) 4.89178 + 2.82427i 0.414915 + 0.239551i 0.692899 0.721034i \(-0.256333\pi\)
−0.277984 + 0.960586i \(0.589666\pi\)
\(140\) −0.279823 + 0.522396i −0.0236493 + 0.0441505i
\(141\) 0 0
\(142\) −1.20711 2.01597i −0.101298 0.169176i
\(143\) 2.01611 0.168596
\(144\) 0 0
\(145\) 1.95581 0.162421
\(146\) −2.73457 4.56695i −0.226315 0.377963i
\(147\) 0 0
\(148\) 7.11959 13.2914i 0.585227 1.09255i
\(149\) −16.2394 9.37583i −1.33038 0.768098i −0.345026 0.938593i \(-0.612130\pi\)
−0.985358 + 0.170496i \(0.945463\pi\)
\(150\) 0 0
\(151\) −18.6131 + 10.7463i −1.51471 + 0.874519i −0.514860 + 0.857274i \(0.672156\pi\)
−0.999851 + 0.0172443i \(0.994511\pi\)
\(152\) −0.199089 4.16567i −0.0161482 0.337880i
\(153\) 0 0
\(154\) −0.0997795 6.26751i −0.00804046 0.505050i
\(155\) 0.981942 + 1.70077i 0.0788715 + 0.136609i
\(156\) 0 0
\(157\) 10.4124 18.0347i 0.830996 1.43933i −0.0662526 0.997803i \(-0.521104\pi\)
0.897249 0.441525i \(-0.145562\pi\)
\(158\) −5.89997 3.28225i −0.469376 0.261122i
\(159\) 0 0
\(160\) 1.38038 0.950855i 0.109129 0.0751717i
\(161\) 4.18470i 0.329801i
\(162\) 0 0
\(163\) 11.1576i 0.873930i −0.899478 0.436965i \(-0.856053\pi\)
0.899478 0.436965i \(-0.143947\pi\)
\(164\) 3.08197 1.91270i 0.240661 0.149357i
\(165\) 0 0
\(166\) −6.78544 + 12.1971i −0.526652 + 0.946677i
\(167\) 8.54592 14.8020i 0.661303 1.14541i −0.318971 0.947765i \(-0.603337\pi\)
0.980274 0.197646i \(-0.0633295\pi\)
\(168\) 0 0
\(169\) 6.39655 + 11.0792i 0.492042 + 0.852242i
\(170\) −2.73946 + 0.0436126i −0.210107 + 0.00334494i
\(171\) 0 0
\(172\) −0.647293 20.3242i −0.0493556 1.54971i
\(173\) −4.04776 + 2.33697i −0.307745 + 0.177677i −0.645917 0.763408i \(-0.723525\pi\)
0.338172 + 0.941084i \(0.390192\pi\)
\(174\) 0 0
\(175\) 4.25409 + 2.45610i 0.321579 + 0.185664i
\(176\) −7.86973 + 15.8871i −0.593203 + 1.19754i
\(177\) 0 0
\(178\) −13.6446 + 8.17001i −1.02270 + 0.612368i
\(179\) 6.17066 0.461217 0.230608 0.973047i \(-0.425928\pi\)
0.230608 + 0.973047i \(0.425928\pi\)
\(180\) 0 0
\(181\) −3.95246 −0.293784 −0.146892 0.989153i \(-0.546927\pi\)
−0.146892 + 0.989153i \(0.546927\pi\)
\(182\) −0.551899 + 0.330463i −0.0409095 + 0.0244956i
\(183\) 0 0
\(184\) 5.42198 10.5212i 0.399714 0.775634i
\(185\) 1.93462 + 1.11695i 0.142236 + 0.0821199i
\(186\) 0 0
\(187\) 25.0972 14.4899i 1.83529 1.05960i
\(188\) 13.3049 0.423740i 0.970362 0.0309044i
\(189\) 0 0
\(190\) 0.617790 0.00983530i 0.0448192 0.000713528i
\(191\) −0.422858 0.732412i −0.0305970 0.0529955i 0.850321 0.526264i \(-0.176408\pi\)
−0.880918 + 0.473268i \(0.843074\pi\)
\(192\) 0 0
\(193\) 8.03323 13.9140i 0.578244 1.00155i −0.417436 0.908706i \(-0.637071\pi\)
0.995681 0.0928426i \(-0.0295953\pi\)
\(194\) 7.60292 13.6665i 0.545858 0.981200i
\(195\) 0 0
\(196\) 1.05463 + 1.69934i 0.0753306 + 0.121381i
\(197\) 18.1135i 1.29053i −0.763959 0.645265i \(-0.776747\pi\)
0.763959 0.645265i \(-0.223253\pi\)
\(198\) 0 0
\(199\) 17.5844i 1.24652i −0.782013 0.623262i \(-0.785807\pi\)
0.782013 0.623262i \(-0.214193\pi\)
\(200\) −7.51338 11.6870i −0.531277 0.826398i
\(201\) 0 0
\(202\) −12.6995 7.06493i −0.893532 0.497087i
\(203\) 3.30027 5.71624i 0.231634 0.401201i
\(204\) 0 0
\(205\) 0.268698 + 0.465398i 0.0187667 + 0.0325048i
\(206\) 0.175601 + 11.0301i 0.0122347 + 0.768505i
\(207\) 0 0
\(208\) 1.81576 0.115775i 0.125900 0.00802758i
\(209\) −5.65979 + 3.26768i −0.391496 + 0.226030i
\(210\) 0 0
\(211\) −13.2587 7.65494i −0.912770 0.526988i −0.0314486 0.999505i \(-0.510012\pi\)
−0.881321 + 0.472517i \(0.843345\pi\)
\(212\) 2.16277 + 1.15849i 0.148540 + 0.0795658i
\(213\) 0 0
\(214\) 2.35759 + 3.93736i 0.161162 + 0.269153i
\(215\) 3.01266 0.205462
\(216\) 0 0
\(217\) 6.62781 0.449925
\(218\) 7.09849 + 11.8550i 0.480770 + 0.802925i
\(219\) 0 0
\(220\) −2.31544 1.24027i −0.156107 0.0836193i
\(221\) −2.57555 1.48699i −0.173250 0.100026i
\(222\) 0 0
\(223\) 0.724566 0.418329i 0.0485206 0.0280134i −0.475543 0.879692i \(-0.657749\pi\)
0.524064 + 0.851679i \(0.324415\pi\)
\(224\) −0.449776 5.63895i −0.0300519 0.376768i
\(225\) 0 0
\(226\) −0.152103 9.55411i −0.0101177 0.635530i
\(227\) 9.95185 + 17.2371i 0.660527 + 1.14407i 0.980477 + 0.196633i \(0.0630006\pi\)
−0.319950 + 0.947435i \(0.603666\pi\)
\(228\) 0 0
\(229\) 12.8198 22.2046i 0.847158 1.46732i −0.0365756 0.999331i \(-0.511645\pi\)
0.883734 0.467990i \(-0.155022\pi\)
\(230\) 1.53241 + 0.852505i 0.101044 + 0.0562125i
\(231\) 0 0
\(232\) −15.7039 + 10.0958i −1.03101 + 0.662820i
\(233\) 9.73332i 0.637651i −0.947813 0.318825i \(-0.896712\pi\)
0.947813 0.318825i \(-0.103288\pi\)
\(234\) 0 0
\(235\) 1.97219i 0.128652i
\(236\) −13.8655 22.3418i −0.902569 1.45432i
\(237\) 0 0
\(238\) −4.49517 + 8.08023i −0.291378 + 0.523763i
\(239\) −8.89438 + 15.4055i −0.575330 + 0.996500i 0.420676 + 0.907211i \(0.361793\pi\)
−0.996006 + 0.0892892i \(0.971540\pi\)
\(240\) 0 0
\(241\) 10.0336 + 17.3787i 0.646319 + 1.11946i 0.983995 + 0.178195i \(0.0570259\pi\)
−0.337676 + 0.941262i \(0.609641\pi\)
\(242\) 12.2254 0.194631i 0.785881 0.0125113i
\(243\) 0 0
\(244\) −7.45997 + 0.237588i −0.477576 + 0.0152100i
\(245\) −0.256612 + 0.148155i −0.0163943 + 0.00946527i
\(246\) 0 0
\(247\) 0.580825 + 0.335339i 0.0369570 + 0.0213371i
\(248\) −16.6637 8.58743i −1.05815 0.545302i
\(249\) 0 0
\(250\) 3.56366 2.13383i 0.225386 0.134955i
\(251\) 1.79971 0.113597 0.0567984 0.998386i \(-0.481911\pi\)
0.0567984 + 0.998386i \(0.481911\pi\)
\(252\) 0 0
\(253\) −18.5481 −1.16611
\(254\) 20.9437 12.5405i 1.31412 0.786862i
\(255\) 0 0
\(256\) −6.17536 + 14.7602i −0.385960 + 0.922515i
\(257\) 25.2755 + 14.5928i 1.57664 + 0.910274i 0.995324 + 0.0965969i \(0.0307958\pi\)
0.581317 + 0.813677i \(0.302538\pi\)
\(258\) 0 0
\(259\) 6.52903 3.76954i 0.405694 0.234228i
\(260\) 0.00858069 + 0.269424i 0.000532152 + 0.0167089i
\(261\) 0 0
\(262\) 1.76739 0.0281371i 0.109190 0.00173831i
\(263\) 6.96390 + 12.0618i 0.429413 + 0.743764i 0.996821 0.0796720i \(-0.0253873\pi\)
−0.567409 + 0.823436i \(0.692054\pi\)
\(264\) 0 0
\(265\) −0.181750 + 0.314800i −0.0111648 + 0.0193380i
\(266\) 1.01373 1.82221i 0.0621556 0.111727i
\(267\) 0 0
\(268\) −1.84695 + 1.14624i −0.112821 + 0.0700176i
\(269\) 25.9733i 1.58362i 0.610766 + 0.791811i \(0.290862\pi\)
−0.610766 + 0.791811i \(0.709138\pi\)
\(270\) 0 0
\(271\) 16.7706i 1.01874i 0.860547 + 0.509371i \(0.170122\pi\)
−0.860547 + 0.509371i \(0.829878\pi\)
\(272\) 21.7711 14.4911i 1.32006 0.878655i
\(273\) 0 0
\(274\) −18.1902 10.1195i −1.09891 0.611343i
\(275\) −10.8863 + 18.8556i −0.656469 + 1.13704i
\(276\) 0 0
\(277\) 6.69523 + 11.5965i 0.402278 + 0.696765i 0.994000 0.109376i \(-0.0348853\pi\)
−0.591723 + 0.806142i \(0.701552\pi\)
\(278\) −0.127158 7.98723i −0.00762642 0.479042i
\(279\) 0 0
\(280\) 0.837135 0.0400090i 0.0500284 0.00239099i
\(281\) −11.2366 + 6.48745i −0.670319 + 0.387009i −0.796198 0.605037i \(-0.793158\pi\)
0.125878 + 0.992046i \(0.459825\pi\)
\(282\) 0 0
\(283\) 17.6067 + 10.1652i 1.04661 + 0.604260i 0.921698 0.387908i \(-0.126802\pi\)
0.124911 + 0.992168i \(0.460136\pi\)
\(284\) −1.56906 + 2.92925i −0.0931067 + 0.173819i
\(285\) 0 0
\(286\) −1.46473 2.44622i −0.0866113 0.144648i
\(287\) 1.81363 0.107055
\(288\) 0 0
\(289\) −25.7483 −1.51461
\(290\) −1.42092 2.37305i −0.0834392 0.139350i
\(291\) 0 0
\(292\) −3.55453 + 6.63589i −0.208013 + 0.388336i
\(293\) −13.3803 7.72510i −0.781684 0.451305i 0.0553431 0.998467i \(-0.482375\pi\)
−0.837027 + 0.547162i \(0.815708\pi\)
\(294\) 0 0
\(295\) 3.37376 1.94784i 0.196428 0.113408i
\(296\) −21.2994 + 1.01796i −1.23800 + 0.0591675i
\(297\) 0 0
\(298\) 0.422130 + 26.5155i 0.0244533 + 1.53600i
\(299\) 0.951731 + 1.64845i 0.0550400 + 0.0953321i
\(300\) 0 0
\(301\) 5.08363 8.80511i 0.293016 0.507518i
\(302\) 26.5615 + 14.7766i 1.52844 + 0.850297i
\(303\) 0 0
\(304\) −4.90970 + 3.26797i −0.281591 + 0.187431i
\(305\) 1.10579i 0.0633174i
\(306\) 0 0
\(307\) 25.1623i 1.43609i −0.695999 0.718043i \(-0.745038\pi\)
0.695999 0.718043i \(-0.254962\pi\)
\(308\) −7.53209 + 4.67449i −0.429180 + 0.266354i
\(309\) 0 0
\(310\) 1.35021 2.42706i 0.0766869 0.137848i
\(311\) −2.95532 + 5.11876i −0.167581 + 0.290258i −0.937569 0.347800i \(-0.886929\pi\)
0.769988 + 0.638058i \(0.220262\pi\)
\(312\) 0 0
\(313\) −1.83498 3.17828i −0.103719 0.179647i 0.809495 0.587127i \(-0.199741\pi\)
−0.913214 + 0.407480i \(0.866408\pi\)
\(314\) −29.4469 + 0.468798i −1.66178 + 0.0264558i
\(315\) 0 0
\(316\) 0.303936 + 9.54323i 0.0170977 + 0.536849i
\(317\) −21.2356 + 12.2604i −1.19271 + 0.688611i −0.958920 0.283676i \(-0.908446\pi\)
−0.233789 + 0.972287i \(0.575113\pi\)
\(318\) 0 0
\(319\) 25.3364 + 14.6280i 1.41857 + 0.819010i
\(320\) −2.15657 0.984058i −0.120556 0.0550105i
\(321\) 0 0
\(322\) 5.07744 3.04024i 0.282955 0.169426i
\(323\) 9.64038 0.536405
\(324\) 0 0
\(325\) 2.23437 0.123941
\(326\) −13.5379 + 8.10614i −0.749794 + 0.448957i
\(327\) 0 0
\(328\) −4.55984 2.34986i −0.251775 0.129749i
\(329\) 5.76413 + 3.32792i 0.317787 + 0.183474i
\(330\) 0 0
\(331\) 9.40387 5.42933i 0.516884 0.298423i −0.218775 0.975775i \(-0.570206\pi\)
0.735659 + 0.677352i \(0.236873\pi\)
\(332\) 19.7288 0.628331i 1.08276 0.0344841i
\(333\) 0 0
\(334\) −24.1684 + 0.384765i −1.32244 + 0.0210534i
\(335\) −0.161024 0.278902i −0.00879770 0.0152381i
\(336\) 0 0
\(337\) −2.58303 + 4.47395i −0.140707 + 0.243711i −0.927763 0.373170i \(-0.878271\pi\)
0.787056 + 0.616881i \(0.211604\pi\)
\(338\) 8.79553 15.8103i 0.478414 0.859967i
\(339\) 0 0
\(340\) 2.04317 + 3.29220i 0.110807 + 0.178545i
\(341\) 29.3768i 1.59084i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −24.1898 + 15.5512i −1.30423 + 0.838464i
\(345\) 0 0
\(346\) 5.77628 + 3.21344i 0.310535 + 0.172756i
\(347\) 4.05959 7.03141i 0.217930 0.377466i −0.736245 0.676715i \(-0.763403\pi\)
0.954175 + 0.299249i \(0.0967362\pi\)
\(348\) 0 0
\(349\) −7.98580 13.8318i −0.427470 0.740400i 0.569177 0.822215i \(-0.307262\pi\)
−0.996648 + 0.0818146i \(0.973928\pi\)
\(350\) −0.110582 6.94602i −0.00591083 0.371280i
\(351\) 0 0
\(352\) 24.9938 1.99357i 1.33217 0.106258i
\(353\) 23.8711 13.7820i 1.27053 0.733541i 0.295442 0.955361i \(-0.404533\pi\)
0.975088 + 0.221820i \(0.0711997\pi\)
\(354\) 0 0
\(355\) −0.426364 0.246161i −0.0226290 0.0130649i
\(356\) 19.8259 + 10.6198i 1.05077 + 0.562848i
\(357\) 0 0
\(358\) −4.48306 7.48707i −0.236937 0.395704i
\(359\) 7.06180 0.372708 0.186354 0.982483i \(-0.440333\pi\)
0.186354 + 0.982483i \(0.440333\pi\)
\(360\) 0 0
\(361\) 16.8259 0.885576
\(362\) 2.87151 + 4.79565i 0.150923 + 0.252054i
\(363\) 0 0
\(364\) 0.801924 + 0.429553i 0.0420322 + 0.0225147i
\(365\) −0.965879 0.557650i −0.0505564 0.0291888i
\(366\) 0 0
\(367\) −10.9395 + 6.31591i −0.571036 + 0.329688i −0.757563 0.652762i \(-0.773610\pi\)
0.186527 + 0.982450i \(0.440277\pi\)
\(368\) −16.7049 + 1.06513i −0.870803 + 0.0555236i
\(369\) 0 0
\(370\) −0.0502888 3.15881i −0.00261439 0.164219i
\(371\) 0.613377 + 1.06240i 0.0318449 + 0.0551570i
\(372\) 0 0
\(373\) −10.8851 + 18.8535i −0.563609 + 0.976199i 0.433569 + 0.901121i \(0.357254\pi\)
−0.997178 + 0.0750788i \(0.976079\pi\)
\(374\) −35.8144 19.9242i −1.85192 1.03025i
\(375\) 0 0
\(376\) −10.1803 15.8355i −0.525011 0.816652i
\(377\) 3.00234i 0.154628i
\(378\) 0 0
\(379\) 31.0746i 1.59620i 0.602527 + 0.798098i \(0.294160\pi\)
−0.602527 + 0.798098i \(0.705840\pi\)
\(380\) −0.460766 0.742440i −0.0236368 0.0380864i
\(381\) 0 0
\(382\) −0.581448 + 1.04518i −0.0297495 + 0.0534758i
\(383\) 11.0121 19.0735i 0.562692 0.974612i −0.434568 0.900639i \(-0.643099\pi\)
0.997260 0.0739726i \(-0.0235677\pi\)
\(384\) 0 0
\(385\) −0.656676 1.13740i −0.0334673 0.0579670i
\(386\) −22.7185 + 0.361682i −1.15634 + 0.0184091i
\(387\) 0 0
\(388\) −22.1057 + 0.704030i −1.12225 + 0.0357417i
\(389\) −23.3935 + 13.5062i −1.18610 + 0.684794i −0.957417 0.288708i \(-0.906774\pi\)
−0.228681 + 0.973502i \(0.573441\pi\)
\(390\) 0 0
\(391\) 23.6949 + 13.6802i 1.19830 + 0.691840i
\(392\) 1.29567 2.51421i 0.0654411 0.126987i
\(393\) 0 0
\(394\) −21.9777 + 13.1597i −1.10722 + 0.662974i
\(395\) −1.41459 −0.0711759
\(396\) 0 0
\(397\) −8.14977 −0.409025 −0.204513 0.978864i \(-0.565561\pi\)
−0.204513 + 0.978864i \(0.565561\pi\)
\(398\) −21.3357 + 12.7753i −1.06946 + 0.640366i
\(399\) 0 0
\(400\) −8.72170 + 17.6070i −0.436085 + 0.880351i
\(401\) −29.9154 17.2717i −1.49391 0.862507i −0.493930 0.869501i \(-0.664440\pi\)
−0.999976 + 0.00699448i \(0.997774\pi\)
\(402\) 0 0
\(403\) 2.61084 1.50737i 0.130055 0.0750874i
\(404\) 0.654212 + 20.5415i 0.0325483 + 1.02198i
\(405\) 0 0
\(406\) −9.33340 + 0.148589i −0.463209 + 0.00737435i
\(407\) 16.7079 + 28.9390i 0.828182 + 1.43445i
\(408\) 0 0
\(409\) −4.75787 + 8.24087i −0.235261 + 0.407485i −0.959349 0.282224i \(-0.908928\pi\)
0.724087 + 0.689708i \(0.242261\pi\)
\(410\) 0.369471 0.664138i 0.0182469 0.0327994i
\(411\) 0 0
\(412\) 13.2556 8.22659i 0.653059 0.405295i
\(413\) 13.1473i 0.646937i
\(414\) 0 0
\(415\) 2.92441i 0.143554i
\(416\) −1.45965 2.11901i −0.0715651 0.103893i
\(417\) 0 0
\(418\) 8.07670 + 4.49320i 0.395044 + 0.219770i
\(419\) −12.4203 + 21.5126i −0.606771 + 1.05096i 0.384998 + 0.922917i \(0.374202\pi\)
−0.991769 + 0.128040i \(0.959131\pi\)
\(420\) 0 0
\(421\) −6.76981 11.7257i −0.329940 0.571473i 0.652559 0.757738i \(-0.273695\pi\)
−0.982500 + 0.186264i \(0.940362\pi\)
\(422\) 0.344650 + 21.6487i 0.0167773 + 1.05384i
\(423\) 0 0
\(424\) −0.165641 3.46583i −0.00804425 0.168315i
\(425\) 27.8142 16.0585i 1.34919 0.778952i
\(426\) 0 0
\(427\) −3.23190 1.86594i −0.156403 0.0902991i
\(428\) 3.06452 5.72109i 0.148129 0.276539i
\(429\) 0 0
\(430\) −2.18874 3.65536i −0.105550 0.176277i
\(431\) −17.3938 −0.837829 −0.418914 0.908026i \(-0.637589\pi\)
−0.418914 + 0.908026i \(0.637589\pi\)
\(432\) 0 0
\(433\) −32.1442 −1.54475 −0.772377 0.635165i \(-0.780932\pi\)
−0.772377 + 0.635165i \(0.780932\pi\)
\(434\) −4.81519 8.04174i −0.231136 0.386016i
\(435\) 0 0
\(436\) 9.22698 17.2257i 0.441892 0.824960i
\(437\) −5.34355 3.08510i −0.255617 0.147580i
\(438\) 0 0
\(439\) 25.0879 14.4845i 1.19738 0.691309i 0.237411 0.971409i \(-0.423701\pi\)
0.959971 + 0.280100i \(0.0903678\pi\)
\(440\) 0.177334 + 3.71048i 0.00845407 + 0.176890i
\(441\) 0 0
\(442\) 0.0669493 + 4.20532i 0.00318445 + 0.200027i
\(443\) −3.31751 5.74609i −0.157619 0.273005i 0.776390 0.630252i \(-0.217049\pi\)
−0.934010 + 0.357248i \(0.883715\pi\)
\(444\) 0 0
\(445\) −1.66608 + 2.88573i −0.0789797 + 0.136797i
\(446\) −1.03398 0.575220i −0.0489603 0.0272374i
\(447\) 0 0
\(448\) −6.51515 + 4.64249i −0.307812 + 0.219337i
\(449\) 5.68888i 0.268475i 0.990949 + 0.134237i \(0.0428585\pi\)
−0.990949 + 0.134237i \(0.957142\pi\)
\(450\) 0 0
\(451\) 8.03864i 0.378525i
\(452\) −11.4818 + 7.12574i −0.540060 + 0.335167i
\(453\) 0 0
\(454\) 13.6842 24.5979i 0.642232 1.15444i
\(455\) −0.0673900 + 0.116723i −0.00315929 + 0.00547206i
\(456\) 0 0
\(457\) 16.5673 + 28.6953i 0.774984 + 1.34231i 0.934803 + 0.355165i \(0.115575\pi\)
−0.159819 + 0.987146i \(0.551091\pi\)
\(458\) −36.2554 + 0.577190i −1.69410 + 0.0269703i
\(459\) 0 0
\(460\) −0.0789419 2.47868i −0.00368068 0.115569i
\(461\) −3.69384 + 2.13264i −0.172039 + 0.0993270i −0.583547 0.812079i \(-0.698336\pi\)
0.411508 + 0.911406i \(0.365002\pi\)
\(462\) 0 0
\(463\) −20.3913 11.7729i −0.947665 0.547134i −0.0553099 0.998469i \(-0.517615\pi\)
−0.892355 + 0.451335i \(0.850948\pi\)
\(464\) 23.6586 + 11.7194i 1.09832 + 0.544059i
\(465\) 0 0
\(466\) −11.8098 + 7.07138i −0.547077 + 0.327575i
\(467\) −9.98701 −0.462144 −0.231072 0.972937i \(-0.574223\pi\)
−0.231072 + 0.972937i \(0.574223\pi\)
\(468\) 0 0
\(469\) −1.08686 −0.0501867
\(470\) 2.39293 1.43282i 0.110377 0.0660912i
\(471\) 0 0
\(472\) −17.0345 + 33.0551i −0.784078 + 1.52148i
\(473\) 39.0274 + 22.5325i 1.79448 + 1.03604i
\(474\) 0 0
\(475\) −6.27251 + 3.62144i −0.287803 + 0.166163i
\(476\) 13.0698 0.416252i 0.599054 0.0190789i
\(477\) 0 0
\(478\) 25.1539 0.400454i 1.15051 0.0183163i
\(479\) 7.07341 + 12.2515i 0.323192 + 0.559785i 0.981145 0.193274i \(-0.0619106\pi\)
−0.657953 + 0.753059i \(0.728577\pi\)
\(480\) 0 0
\(481\) 1.71462 2.96981i 0.0781799 0.135412i
\(482\) 13.7966 24.7999i 0.628418 1.12960i
\(483\) 0 0
\(484\) −9.11809 14.6921i −0.414459 0.667825i
\(485\) 3.27673i 0.148789i
\(486\) 0 0
\(487\) 37.5888i 1.70331i −0.524102 0.851656i \(-0.675599\pi\)
0.524102 0.851656i \(-0.324401\pi\)
\(488\) 5.70804 + 8.87882i 0.258391 + 0.401925i
\(489\) 0 0
\(490\) 0.366193 + 0.203719i 0.0165429 + 0.00920311i
\(491\) 1.91801 3.32210i 0.0865588 0.149924i −0.819496 0.573085i \(-0.805746\pi\)
0.906054 + 0.423161i \(0.139080\pi\)
\(492\) 0 0
\(493\) −21.5779 37.3740i −0.971820 1.68324i
\(494\) −0.0150981 0.948363i −0.000679294 0.0426689i
\(495\) 0 0
\(496\) 1.68697 + 26.4575i 0.0757470 + 1.18798i
\(497\) −1.43891 + 0.830756i −0.0645440 + 0.0372645i
\(498\) 0 0
\(499\) −8.09253 4.67223i −0.362272 0.209158i 0.307805 0.951449i \(-0.400405\pi\)
−0.670077 + 0.742292i \(0.733739\pi\)
\(500\) −5.17809 2.77366i −0.231571 0.124042i
\(501\) 0 0
\(502\) −1.30751 2.18365i −0.0583572 0.0974611i
\(503\) −3.43652 −0.153227 −0.0766134 0.997061i \(-0.524411\pi\)
−0.0766134 + 0.997061i \(0.524411\pi\)
\(504\) 0 0
\(505\) −3.04486 −0.135495
\(506\) 13.4754 + 22.5050i 0.599056 + 1.00047i
\(507\) 0 0
\(508\) −30.4317 16.3008i −1.35019 0.723231i
\(509\) −6.05939 3.49839i −0.268578 0.155063i 0.359663 0.933082i \(-0.382892\pi\)
−0.628241 + 0.778019i \(0.716225\pi\)
\(510\) 0 0
\(511\) −3.25969 + 1.88198i −0.144200 + 0.0832541i
\(512\) 22.3956 3.23073i 0.989755 0.142780i
\(513\) 0 0
\(514\) −0.657015 41.2694i −0.0289797 1.82032i
\(515\) 1.15568 + 2.00169i 0.0509252 + 0.0882050i
\(516\) 0 0
\(517\) −14.7505 + 25.5487i −0.648728 + 1.12363i
\(518\) −9.31713 5.18328i −0.409371 0.227740i
\(519\) 0 0
\(520\) 0.320667 0.206151i 0.0140622 0.00904032i
\(521\) 14.3013i 0.626553i −0.949662 0.313276i \(-0.898573\pi\)
0.949662 0.313276i \(-0.101427\pi\)
\(522\) 0 0
\(523\) 0.431887i 0.0188851i −0.999955 0.00944254i \(-0.996994\pi\)
0.999955 0.00944254i \(-0.00300570\pi\)
\(524\) −1.31817 2.12399i −0.0575845 0.0927870i
\(525\) 0 0
\(526\) 9.57567 17.2126i 0.417519 0.750506i
\(527\) 21.6670 37.5284i 0.943830 1.63476i
\(528\) 0 0
\(529\) 2.74413 + 4.75297i 0.119310 + 0.206651i
\(530\) 0.514000 0.00818296i 0.0223267 0.000355445i
\(531\) 0 0
\(532\) −2.94744 + 0.0938710i −0.127788 + 0.00406983i
\(533\) 0.714428 0.412475i 0.0309453 0.0178663i
\(534\) 0 0
\(535\) 0.832726 + 0.480774i 0.0360019 + 0.0207857i
\(536\) 2.73260 + 1.40821i 0.118031 + 0.0608256i
\(537\) 0 0
\(538\) 31.5143 18.8700i 1.35868 0.813542i
\(539\) −4.43236 −0.190915
\(540\) 0 0
\(541\) −10.1004 −0.434251 −0.217125 0.976144i \(-0.569668\pi\)
−0.217125 + 0.976144i \(0.569668\pi\)
\(542\) 20.3484 12.1841i 0.874037 0.523350i
\(543\) 0 0
\(544\) −33.3996 15.8876i −1.43199 0.681174i
\(545\) 2.50726 + 1.44757i 0.107399 + 0.0620070i
\(546\) 0 0
\(547\) 12.6249 7.28900i 0.539803 0.311655i −0.205196 0.978721i \(-0.565783\pi\)
0.744999 + 0.667066i \(0.232450\pi\)
\(548\) 0.937067 + 29.4228i 0.0400295 + 1.25688i
\(549\) 0 0
\(550\) 30.7872 0.490137i 1.31277 0.0208995i
\(551\) 4.86614 + 8.42840i 0.207305 + 0.359062i
\(552\) 0 0
\(553\) −2.38702 + 4.13444i −0.101506 + 0.175814i
\(554\) 9.20624 16.5486i 0.391135 0.703081i
\(555\) 0 0
\(556\) −9.59879 + 5.95711i −0.407079 + 0.252638i
\(557\) 0.720867i 0.0305441i −0.999883 0.0152720i \(-0.995139\pi\)
0.999883 0.0152720i \(-0.00486143\pi\)
\(558\) 0 0
\(559\) 4.62470i 0.195604i
\(560\) −0.656734 0.986658i −0.0277521 0.0416939i
\(561\) 0 0
\(562\) 16.0350 + 8.92053i 0.676395 + 0.376290i
\(563\) 17.1195 29.6518i 0.721499 1.24967i −0.238900 0.971044i \(-0.576787\pi\)
0.960399 0.278628i \(-0.0898798\pi\)
\(564\) 0 0
\(565\) −1.00103 1.73383i −0.0421136 0.0729429i
\(566\) −0.457671 28.7479i −0.0192374 1.20837i
\(567\) 0 0
\(568\) 4.69411 0.224344i 0.196960 0.00941327i
\(569\) 9.54066 5.50830i 0.399965 0.230920i −0.286504 0.958079i \(-0.592493\pi\)
0.686469 + 0.727159i \(0.259160\pi\)
\(570\) 0 0
\(571\) −8.18899 4.72792i −0.342699 0.197857i 0.318766 0.947833i \(-0.396732\pi\)
−0.661465 + 0.749976i \(0.730065\pi\)
\(572\) −1.90393 + 3.55441i −0.0796073 + 0.148618i
\(573\) 0 0
\(574\) −1.31762 2.20053i −0.0549965 0.0918486i
\(575\) −20.5561 −0.857249
\(576\) 0 0
\(577\) 34.2938 1.42767 0.713835 0.700314i \(-0.246957\pi\)
0.713835 + 0.700314i \(0.246957\pi\)
\(578\) 18.7065 + 31.2413i 0.778086 + 1.29947i
\(579\) 0 0
\(580\) −1.84698 + 3.44810i −0.0766918 + 0.143174i
\(581\) 8.54717 + 4.93471i 0.354596 + 0.204726i
\(582\) 0 0
\(583\) −4.70894 + 2.71870i −0.195024 + 0.112597i
\(584\) 10.6340 0.508226i 0.440037 0.0210306i
\(585\) 0 0
\(586\) 0.347809 + 21.8471i 0.0143679 + 0.902496i
\(587\) 1.53425 + 2.65739i 0.0633251 + 0.109682i 0.895950 0.444155i \(-0.146496\pi\)
−0.832625 + 0.553838i \(0.813163\pi\)
\(588\) 0 0
\(589\) −4.88624 + 8.46322i −0.201334 + 0.348721i
\(590\) −4.81445 2.67836i −0.198208 0.110266i
\(591\) 0 0
\(592\) 16.7094 + 25.1037i 0.686753 + 1.03176i
\(593\) 29.4946i 1.21120i 0.795770 + 0.605598i \(0.207066\pi\)
−0.795770 + 0.605598i \(0.792934\pi\)
\(594\) 0 0
\(595\) 1.93734i 0.0794231i
\(596\) 31.8655 19.7760i 1.30526 0.810057i
\(597\) 0 0
\(598\) 1.30867 2.35239i 0.0535155 0.0961962i
\(599\) −2.77278 + 4.80259i −0.113293 + 0.196228i −0.917096 0.398667i \(-0.869473\pi\)
0.803803 + 0.594895i \(0.202806\pi\)
\(600\) 0 0
\(601\) 9.01719 + 15.6182i 0.367819 + 0.637081i 0.989224 0.146408i \(-0.0467713\pi\)
−0.621405 + 0.783489i \(0.713438\pi\)
\(602\) −14.3769 + 0.228882i −0.585957 + 0.00932852i
\(603\) 0 0
\(604\) −1.36831 42.9633i −0.0556757 1.74815i
\(605\) 2.21861 1.28092i 0.0901994 0.0520767i
\(606\) 0 0
\(607\) −28.7368 16.5912i −1.16639 0.673417i −0.213564 0.976929i \(-0.568507\pi\)
−0.952827 + 0.303512i \(0.901841\pi\)
\(608\) 7.53210 + 3.58289i 0.305467 + 0.145305i
\(609\) 0 0
\(610\) −1.34169 + 0.803372i −0.0543236 + 0.0325276i
\(611\) 3.02749 0.122479
\(612\) 0 0
\(613\) 40.1767 1.62272 0.811361 0.584545i \(-0.198727\pi\)
0.811361 + 0.584545i \(0.198727\pi\)
\(614\) −30.5302 + 18.2807i −1.23210 + 0.737749i
\(615\) 0 0
\(616\) 11.1439 + 5.74286i 0.448999 + 0.231386i
\(617\) −1.00311 0.579145i −0.0403836 0.0233155i 0.479672 0.877448i \(-0.340756\pi\)
−0.520056 + 0.854132i \(0.674089\pi\)
\(618\) 0 0
\(619\) −26.7639 + 15.4521i −1.07573 + 0.621074i −0.929742 0.368213i \(-0.879970\pi\)
−0.145989 + 0.989286i \(0.546637\pi\)
\(620\) −3.92578 + 0.125030i −0.157663 + 0.00502131i
\(621\) 0 0
\(622\) 8.35784 0.133058i 0.335119 0.00533514i
\(623\) 5.62276 + 9.73890i 0.225271 + 0.390181i
\(624\) 0 0
\(625\) −11.8454 + 20.5168i −0.473814 + 0.820670i
\(626\) −2.52318 + 4.53551i −0.100847 + 0.181275i
\(627\) 0 0
\(628\) 21.9623 + 35.3883i 0.876392 + 1.41215i
\(629\) 49.2921i 1.96541i
\(630\) 0 0
\(631\) 20.8271i 0.829113i −0.910023 0.414557i \(-0.863937\pi\)
0.910023 0.414557i \(-0.136063\pi\)
\(632\) 11.3583 7.30206i 0.451809 0.290460i
\(633\) 0 0
\(634\) 30.3038 + 16.8585i 1.20352 + 0.669538i
\(635\) 2.55734 4.42944i 0.101485 0.175777i
\(636\) 0 0
\(637\) 0.227431 + 0.393922i 0.00901114 + 0.0156078i
\(638\) −0.658599 41.3689i −0.0260742 1.63781i
\(639\) 0 0
\(640\) 0.372786 + 3.33157i 0.0147357 + 0.131692i
\(641\) −9.86746 + 5.69698i −0.389741 + 0.225017i −0.682048 0.731307i \(-0.738910\pi\)
0.292307 + 0.956325i \(0.405577\pi\)
\(642\) 0 0
\(643\) −3.84437 2.21955i −0.151607 0.0875305i 0.422277 0.906467i \(-0.361231\pi\)
−0.573885 + 0.818936i \(0.694564\pi\)
\(644\) −7.37765 3.95186i −0.290720 0.155725i
\(645\) 0 0
\(646\) −7.00386 11.6970i −0.275563 0.460212i
\(647\) −23.4155 −0.920558 −0.460279 0.887774i \(-0.652251\pi\)
−0.460279 + 0.887774i \(0.652251\pi\)
\(648\) 0 0
\(649\) 58.2736 2.28744
\(650\) −1.62330 2.71104i −0.0636711 0.106336i
\(651\) 0 0
\(652\) 19.6709 + 10.5368i 0.770372 + 0.412652i
\(653\) −24.8536 14.3492i −0.972596 0.561528i −0.0725691 0.997363i \(-0.523120\pi\)
−0.900027 + 0.435835i \(0.856453\pi\)
\(654\) 0 0
\(655\) 0.320737 0.185178i 0.0125322 0.00723548i
\(656\) 0.461620 + 7.23981i 0.0180232 + 0.282667i
\(657\) 0 0
\(658\) −0.149834 9.41159i −0.00584113 0.366902i
\(659\) −9.63833 16.6941i −0.375456 0.650309i 0.614939 0.788574i \(-0.289181\pi\)
−0.990395 + 0.138266i \(0.955847\pi\)
\(660\) 0 0
\(661\) 23.0539 39.9305i 0.896692 1.55312i 0.0649955 0.997886i \(-0.479297\pi\)
0.831696 0.555231i \(-0.187370\pi\)
\(662\) −13.4196 7.46556i −0.521568 0.290157i
\(663\) 0 0
\(664\) −15.0956 23.4812i −0.585824 0.911247i
\(665\) 0.436899i 0.0169422i
\(666\) 0 0
\(667\) 27.6213i 1.06950i
\(668\) 18.0255 + 29.0448i 0.697429 + 1.12378i
\(669\) 0 0
\(670\) −0.221415 + 0.398002i −0.00855402 + 0.0153762i
\(671\) 8.27050 14.3249i 0.319279 0.553008i
\(672\) 0 0
\(673\) −11.8145 20.4632i −0.455414 0.788800i 0.543298 0.839540i \(-0.317175\pi\)
−0.998712 + 0.0507398i \(0.983842\pi\)
\(674\) 7.30500 0.116297i 0.281378 0.00447958i
\(675\) 0 0
\(676\) −25.5732 + 0.814465i −0.983586 + 0.0313256i
\(677\) 22.2416 12.8412i 0.854814 0.493527i −0.00745832 0.999972i \(-0.502374\pi\)
0.862272 + 0.506445i \(0.169041\pi\)
\(678\) 0 0
\(679\) −9.57690 5.52923i −0.367528 0.212192i
\(680\) 2.51015 4.87087i 0.0962597 0.186789i
\(681\) 0 0
\(682\) 35.6439 21.3426i 1.36487 0.817252i
\(683\) 5.57791 0.213433 0.106716 0.994290i \(-0.465966\pi\)
0.106716 + 0.994290i \(0.465966\pi\)
\(684\) 0 0
\(685\) −4.36134 −0.166638
\(686\) 1.21333 0.726513i 0.0463253 0.0277384i
\(687\) 0 0
\(688\) 36.4430 + 18.0522i 1.38938 + 0.688233i
\(689\) 0.483245 + 0.279002i 0.0184102 + 0.0106291i
\(690\) 0 0
\(691\) −38.5847 + 22.2769i −1.46783 + 0.847453i −0.999351 0.0360214i \(-0.988532\pi\)
−0.468480 + 0.883474i \(0.655198\pi\)
\(692\) −0.297564 9.34316i −0.0113117 0.355174i
\(693\) 0 0
\(694\) −11.4808 + 0.182776i −0.435805 + 0.00693808i
\(695\) −0.836859 1.44948i −0.0317439 0.0549820i
\(696\) 0 0
\(697\) 5.92894 10.2692i 0.224575 0.388975i
\(698\) −10.9808 + 19.7384i −0.415630 + 0.747111i
\(699\) 0 0
\(700\) −8.34750 + 5.18055i −0.315506 + 0.195806i
\(701\) 16.8238i 0.635428i −0.948187 0.317714i \(-0.897085\pi\)
0.948187 0.317714i \(-0.102915\pi\)
\(702\) 0 0
\(703\) 11.1161i 0.419252i
\(704\) −20.5772 28.8775i −0.775532 1.08836i
\(705\) 0 0
\(706\) −34.0648 18.9508i −1.28205 0.713223i
\(707\) −5.13797 + 8.89923i −0.193233 + 0.334690i
\(708\) 0 0
\(709\) −21.8146 37.7841i −0.819266 1.41901i −0.906224 0.422798i \(-0.861048\pi\)
0.0869576 0.996212i \(-0.472286\pi\)
\(710\) 0.0110830 + 0.696161i 0.000415937 + 0.0261265i
\(711\) 0 0
\(712\) −1.51842 31.7708i −0.0569050 1.19066i
\(713\) −24.0196 + 13.8677i −0.899540 + 0.519350i
\(714\) 0 0
\(715\) −0.517358 0.298697i −0.0193481 0.0111706i
\(716\) −5.82731 + 10.8789i −0.217777 + 0.406564i
\(717\) 0 0
\(718\) −5.13049 8.56832i −0.191468 0.319767i
\(719\) −22.2951 −0.831469 −0.415734 0.909486i \(-0.636475\pi\)
−0.415734 + 0.909486i \(0.636475\pi\)
\(720\) 0 0
\(721\) 7.80046 0.290504
\(722\) −12.2243 20.4155i −0.454940 0.759786i
\(723\) 0 0
\(724\) 3.73254 6.96821i 0.138719 0.258971i
\(725\) 28.0793 + 16.2116i 1.04284 + 0.602084i
\(726\) 0 0
\(727\) −20.6516 + 11.9232i −0.765925 + 0.442207i −0.831419 0.555646i \(-0.812471\pi\)
0.0654939 + 0.997853i \(0.479138\pi\)
\(728\) −0.0614173 1.28508i −0.00227628 0.0476281i
\(729\) 0 0
\(730\) 0.0251072 + 1.57707i 0.000929260 + 0.0583701i
\(731\) −33.2379 57.5697i −1.22935 2.12929i
\(732\) 0 0
\(733\) −3.96590 + 6.86914i −0.146484 + 0.253717i −0.929926 0.367748i \(-0.880129\pi\)
0.783442 + 0.621465i \(0.213462\pi\)
\(734\) 15.6110 + 8.68465i 0.576212 + 0.320556i
\(735\) 0 0
\(736\) 13.4287 + 19.4948i 0.494987 + 0.718587i
\(737\) 4.81737i 0.177450i
\(738\) 0 0
\(739\) 11.4276i 0.420372i 0.977661 + 0.210186i \(0.0674070\pi\)
−0.977661 + 0.210186i \(0.932593\pi\)
\(740\) −3.79616 + 2.35594i −0.139550 + 0.0866059i
\(741\) 0 0
\(742\) 0.843420 1.51608i 0.0309629 0.0556570i
\(743\) 4.19883 7.27258i 0.154040 0.266805i −0.778669 0.627435i \(-0.784105\pi\)
0.932709 + 0.360630i \(0.117438\pi\)
\(744\) 0 0
\(745\) 2.77815 + 4.81190i 0.101784 + 0.176294i
\(746\) 30.7838 0.490082i 1.12708 0.0179432i
\(747\) 0 0
\(748\) 1.84498 + 57.9301i 0.0674590 + 2.11813i
\(749\) 2.81032 1.62254i 0.102687 0.0592863i
\(750\) 0 0
\(751\) 23.7769 + 13.7276i 0.867632 + 0.500928i 0.866561 0.499072i \(-0.166326\pi\)
0.00107134 + 0.999999i \(0.499659\pi\)
\(752\) −11.8176 + 23.8568i −0.430942 + 0.869969i
\(753\) 0 0
\(754\) −3.64284 + 2.18124i −0.132664 + 0.0794359i
\(755\) 6.36845 0.231772
\(756\) 0 0
\(757\) 21.3239 0.775032 0.387516 0.921863i \(-0.373333\pi\)
0.387516 + 0.921863i \(0.373333\pi\)
\(758\) 37.7039 22.5761i 1.36947 0.820002i
\(759\) 0 0
\(760\) −0.566076 + 1.09846i −0.0205337 + 0.0398452i
\(761\) −20.3381 11.7422i −0.737254 0.425654i 0.0838162 0.996481i \(-0.473289\pi\)
−0.821070 + 0.570828i \(0.806622\pi\)
\(762\) 0 0
\(763\) 8.46162 4.88532i 0.306331 0.176860i
\(764\) 1.69058 0.0538421i 0.0611629 0.00194794i
\(765\) 0 0
\(766\) −31.1430 + 0.495801i −1.12524 + 0.0179140i
\(767\) −2.99010 5.17901i −0.107966 0.187003i
\(768\) 0 0
\(769\) 0.126197 0.218580i 0.00455079 0.00788219i −0.863741 0.503936i \(-0.831885\pi\)
0.868292 + 0.496054i \(0.165218\pi\)
\(770\) −0.902957 + 1.62310i −0.0325403 + 0.0584924i
\(771\) 0 0
\(772\) 16.9441 + 27.3024i 0.609833 + 0.982634i
\(773\) 44.8216i 1.61212i 0.591833 + 0.806061i \(0.298405\pi\)
−0.591833 + 0.806061i \(0.701595\pi\)
\(774\) 0 0
\(775\) 32.5571i 1.16949i
\(776\) 16.9143 + 26.3101i 0.607188 + 0.944478i
\(777\) 0 0
\(778\) 33.3833 + 18.5717i 1.19685 + 0.665827i
\(779\) −1.33707 + 2.31587i −0.0479054 + 0.0829745i
\(780\) 0 0
\(781\) −3.68221 6.37777i −0.131760 0.228215i
\(782\) −0.615929 38.6887i −0.0220256 1.38350i
\(783\) 0 0
\(784\) −3.99189 + 0.254529i −0.142568 + 0.00909031i
\(785\) −5.34387 + 3.08528i −0.190731 + 0.110118i
\(786\) 0 0
\(787\) −1.97648 1.14112i −0.0704538 0.0406765i 0.464359 0.885647i \(-0.346285\pi\)
−0.534813 + 0.844970i \(0.679618\pi\)
\(788\) 31.9341 + 17.1056i 1.13761 + 0.609362i
\(789\) 0 0