Properties

Label 912.2.cc.c.641.3
Level $912$
Weight $2$
Character 912.641
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 641.3
Root \(-0.363139 + 1.69356i\) of defining polynomial
Character \(\chi\) \(=\) 912.641
Dual form 912.2.cc.c.737.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +O(q^{10})\) \(q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +(-2.33635 - 1.34889i) q^{11} +(-5.05419 + 0.891189i) q^{13} +(-5.81100 + 1.24602i) q^{15} +(-1.44531 - 3.97095i) q^{17} +(2.73048 - 3.39772i) q^{19} +(0.802750 - 5.78684i) q^{21} +(-1.69398 - 2.01881i) q^{23} +(-1.17620 - 6.67054i) q^{25} +(-2.08800 + 4.75818i) q^{27} +(3.54249 + 1.28936i) q^{29} +(-4.78254 + 2.76120i) q^{31} +(-1.75816 - 4.32933i) q^{33} +(11.3979 + 2.00975i) q^{35} +5.17636i q^{37} +(-7.85610 - 4.15918i) q^{39} +(0.289735 - 1.64317i) q^{41} +(-1.85806 - 1.55910i) q^{43} +(-9.26801 - 4.47940i) q^{45} +(-0.0440069 + 0.120908i) q^{47} +(-2.18866 + 3.79087i) q^{49} +(2.24935 - 6.96509i) q^{51} +(-6.53342 + 5.48219i) q^{53} +(8.69853 - 3.16600i) q^{55} +(7.34685 - 1.73892i) q^{57} +(-3.87665 + 1.41099i) q^{59} +(3.53369 - 2.96512i) q^{61} +(7.25390 - 7.05526i) q^{63} +(8.80484 - 15.2504i) q^{65} +(-3.81629 + 10.4852i) q^{67} +(-0.167450 - 4.56152i) q^{69} +(-9.91131 - 8.31658i) q^{71} +(-0.414656 + 2.35163i) q^{73} +(5.48930 - 10.3685i) q^{75} +9.09972i q^{77} +(-2.22246 - 0.391880i) q^{79} +(-7.91614 + 4.28191i) q^{81} +(-6.27861 + 3.62496i) q^{83} +(13.6253 + 4.95920i) q^{85} +(3.47002 + 5.53118i) q^{87} +(0.209662 + 1.18905i) q^{89} +(11.1272 + 13.2609i) q^{91} +(-9.47436 - 1.31428i) q^{93} +(2.90863 + 14.6709i) q^{95} +(3.13271 + 8.60706i) q^{97} +(2.20303 - 7.78777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(1\) \(-1\) \(1\)

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 0
\(3\) 1.36678 + 1.06392i 0.789109 + 0.614253i
\(4\) 0 0
\(5\) −2.20556 + 2.62849i −0.986357 + 1.17549i −0.00187711 + 0.999998i \(0.500598\pi\)
−0.984480 + 0.175496i \(0.943847\pi\)
\(6\) 0 0
\(7\) −1.68651 2.92113i −0.637442 1.10408i −0.985992 0.166792i \(-0.946659\pi\)
0.348550 0.937290i \(-0.386674\pi\)
\(8\) 0 0
\(9\) 0.736160 + 2.90828i 0.245387 + 0.969425i
\(10\) 0 0
\(11\) −2.33635 1.34889i −0.704437 0.406707i 0.104561 0.994519i \(-0.466656\pi\)
−0.808998 + 0.587811i \(0.799990\pi\)
\(12\) 0 0
\(13\) −5.05419 + 0.891189i −1.40178 + 0.247171i −0.822874 0.568224i \(-0.807631\pi\)
−0.578905 + 0.815395i \(0.696520\pi\)
\(14\) 0 0
\(15\) −5.81100 + 1.24602i −1.50039 + 0.321721i
\(16\) 0 0
\(17\) −1.44531 3.97095i −0.350538 0.963096i −0.982198 0.187850i \(-0.939848\pi\)
0.631659 0.775246i \(-0.282374\pi\)
\(18\) 0 0
\(19\) 2.73048 3.39772i 0.626414 0.779490i
\(20\) 0 0
\(21\) 0.802750 5.78684i 0.175174 1.26279i
\(22\) 0 0
\(23\) −1.69398 2.01881i −0.353220 0.420951i 0.559952 0.828525i \(-0.310819\pi\)
−0.913172 + 0.407574i \(0.866375\pi\)
\(24\) 0 0
\(25\) −1.17620 6.67054i −0.235239 1.33411i
\(26\) 0 0
\(27\) −2.08800 + 4.75818i −0.401836 + 0.915712i
\(28\) 0 0
\(29\) 3.54249 + 1.28936i 0.657823 + 0.239428i 0.649296 0.760536i \(-0.275064\pi\)
0.00852691 + 0.999964i \(0.497286\pi\)
\(30\) 0 0
\(31\) −4.78254 + 2.76120i −0.858970 + 0.495927i −0.863667 0.504062i \(-0.831838\pi\)
0.00469717 + 0.999989i \(0.498505\pi\)
\(32\) 0 0
\(33\) −1.75816 4.32933i −0.306057 0.753639i
\(34\) 0 0
\(35\) 11.3979 + 2.00975i 1.92659 + 0.339710i
\(36\) 0 0
\(37\) 5.17636i 0.850989i 0.904961 + 0.425494i \(0.139900\pi\)
−0.904961 + 0.425494i \(0.860100\pi\)
\(38\) 0 0
\(39\) −7.85610 4.15918i −1.25798 0.666002i
\(40\) 0 0
\(41\) 0.289735 1.64317i 0.0452490 0.256620i −0.953789 0.300478i \(-0.902854\pi\)
0.999038 + 0.0438581i \(0.0139649\pi\)
\(42\) 0 0
\(43\) −1.85806 1.55910i −0.283351 0.237760i 0.490023 0.871709i \(-0.336988\pi\)
−0.773374 + 0.633950i \(0.781433\pi\)
\(44\) 0 0
\(45\) −9.26801 4.47940i −1.38159 0.667749i
\(46\) 0 0
\(47\) −0.0440069 + 0.120908i −0.00641906 + 0.0176362i −0.942861 0.333187i \(-0.891876\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(48\) 0 0
\(49\) −2.18866 + 3.79087i −0.312665 + 0.541552i
\(50\) 0 0
\(51\) 2.24935 6.96509i 0.314972 0.975307i
\(52\) 0 0
\(53\) −6.53342 + 5.48219i −0.897434 + 0.753036i −0.969687 0.244350i \(-0.921425\pi\)
0.0722533 + 0.997386i \(0.476981\pi\)
\(54\) 0 0
\(55\) 8.69853 3.16600i 1.17291 0.426904i
\(56\) 0 0
\(57\) 7.34685 1.73892i 0.973113 0.230326i
\(58\) 0 0
\(59\) −3.87665 + 1.41099i −0.504697 + 0.183695i −0.581805 0.813328i \(-0.697653\pi\)
0.0771085 + 0.997023i \(0.475431\pi\)
\(60\) 0 0
\(61\) 3.53369 2.96512i 0.452443 0.379645i −0.387898 0.921702i \(-0.626799\pi\)
0.840342 + 0.542057i \(0.182354\pi\)
\(62\) 0 0
\(63\) 7.25390 7.05526i 0.913906 0.888880i
\(64\) 0 0
\(65\) 8.80484 15.2504i 1.09211 1.89158i
\(66\) 0 0
\(67\) −3.81629 + 10.4852i −0.466234 + 1.28097i 0.454490 + 0.890752i \(0.349821\pi\)
−0.920724 + 0.390215i \(0.872401\pi\)
\(68\) 0 0
\(69\) −0.167450 4.56152i −0.0201586 0.549143i
\(70\) 0 0
\(71\) −9.91131 8.31658i −1.17626 0.986996i −0.999996 0.00265261i \(-0.999156\pi\)
−0.176260 0.984344i \(-0.556400\pi\)
\(72\) 0 0
\(73\) −0.414656 + 2.35163i −0.0485318 + 0.275238i −0.999411 0.0343255i \(-0.989072\pi\)
0.950879 + 0.309563i \(0.100183\pi\)
\(74\) 0 0
\(75\) 5.48930 10.3685i 0.633850 1.19725i
\(76\) 0 0
\(77\) 9.09972i 1.03701i
\(78\) 0 0
\(79\) −2.22246 0.391880i −0.250046 0.0440899i 0.0472200 0.998885i \(-0.484964\pi\)
−0.297266 + 0.954795i \(0.596075\pi\)
\(80\) 0 0
\(81\) −7.91614 + 4.28191i −0.879571 + 0.475768i
\(82\) 0 0
\(83\) −6.27861 + 3.62496i −0.689167 + 0.397891i −0.803300 0.595575i \(-0.796924\pi\)
0.114133 + 0.993465i \(0.463591\pi\)
\(84\) 0 0
\(85\) 13.6253 + 4.95920i 1.47787 + 0.537901i
\(86\) 0 0
\(87\) 3.47002 + 5.53118i 0.372025 + 0.593005i
\(88\) 0 0
\(89\) 0.209662 + 1.18905i 0.0222241 + 0.126039i 0.993901 0.110273i \(-0.0351724\pi\)
−0.971677 + 0.236312i \(0.924061\pi\)
\(90\) 0 0
\(91\) 11.1272 + 13.2609i 1.16645 + 1.39012i
\(92\) 0 0
\(93\) −9.47436 1.31428i −0.982446 0.136285i
\(94\) 0 0
\(95\) 2.90863 + 14.6709i 0.298419 + 1.50520i
\(96\) 0 0
\(97\) 3.13271 + 8.60706i 0.318079 + 0.873914i 0.990959 + 0.134163i \(0.0428346\pi\)
−0.672880 + 0.739751i \(0.734943\pi\)
\(98\) 0 0
\(99\) 2.20303 7.78777i 0.221413 0.782700i
\(100\) 0 0
\(101\) 5.56915 0.981991i 0.554151 0.0977117i 0.110442 0.993883i \(-0.464773\pi\)
0.443709 + 0.896171i \(0.353662\pi\)
\(102\) 0 0
\(103\) −3.35680 1.93805i −0.330755 0.190961i 0.325421 0.945569i \(-0.394494\pi\)
−0.656176 + 0.754608i \(0.727827\pi\)
\(104\) 0 0
\(105\) 13.4401 + 14.8733i 1.31162 + 1.45148i
\(106\) 0 0
\(107\) 3.48940 + 6.04382i 0.337333 + 0.584278i 0.983930 0.178554i \(-0.0571419\pi\)
−0.646597 + 0.762832i \(0.723809\pi\)
\(108\) 0 0
\(109\) 3.68457 4.39110i 0.352918 0.420591i −0.560155 0.828388i \(-0.689258\pi\)
0.913073 + 0.407797i \(0.133703\pi\)
\(110\) 0 0
\(111\) −5.50722 + 7.07493i −0.522722 + 0.671523i
\(112\) 0 0
\(113\) −16.8907 −1.58895 −0.794474 0.607298i \(-0.792253\pi\)
−0.794474 + 0.607298i \(0.792253\pi\)
\(114\) 0 0
\(115\) 9.04260 0.843227
\(116\) 0 0
\(117\) −6.31251 14.0429i −0.583592 1.29827i
\(118\) 0 0
\(119\) −9.16212 + 10.9190i −0.839890 + 1.00094i
\(120\) 0 0
\(121\) −1.86097 3.22329i −0.169179 0.293026i
\(122\) 0 0
\(123\) 2.14420 1.93759i 0.193336 0.174707i
\(124\) 0 0
\(125\) 5.26986 + 3.04256i 0.471351 + 0.272134i
\(126\) 0 0
\(127\) −5.44679 + 0.960416i −0.483324 + 0.0852231i −0.410001 0.912085i \(-0.634472\pi\)
−0.0733234 + 0.997308i \(0.523361\pi\)
\(128\) 0 0
\(129\) −0.880802 4.10776i −0.0775503 0.361668i
\(130\) 0 0
\(131\) −5.04199 13.8528i −0.440521 1.21032i −0.939150 0.343506i \(-0.888385\pi\)
0.498629 0.866815i \(-0.333837\pi\)
\(132\) 0 0
\(133\) −14.5302 2.24577i −1.25992 0.194733i
\(134\) 0 0
\(135\) −7.90159 15.9827i −0.680061 1.37557i
\(136\) 0 0
\(137\) 12.8171 + 15.2748i 1.09503 + 1.30501i 0.948840 + 0.315756i \(0.102258\pi\)
0.146195 + 0.989256i \(0.453297\pi\)
\(138\) 0 0
\(139\) 0.280984 + 1.59354i 0.0238328 + 0.135162i 0.994403 0.105658i \(-0.0336948\pi\)
−0.970570 + 0.240820i \(0.922584\pi\)
\(140\) 0 0
\(141\) −0.188784 + 0.118434i −0.0158984 + 0.00997398i
\(142\) 0 0
\(143\) 13.0105 + 4.73543i 1.08799 + 0.395997i
\(144\) 0 0
\(145\) −11.2022 + 6.46761i −0.930295 + 0.537106i
\(146\) 0 0
\(147\) −7.02457 + 2.85272i −0.579377 + 0.235288i
\(148\) 0 0
\(149\) −23.7332 4.18480i −1.94430 0.342832i −0.999902 0.0140170i \(-0.995538\pi\)
−0.944394 0.328815i \(-0.893351\pi\)
\(150\) 0 0
\(151\) 14.7053i 1.19670i −0.801235 0.598349i \(-0.795824\pi\)
0.801235 0.598349i \(-0.204176\pi\)
\(152\) 0 0
\(153\) 10.4846 7.12660i 0.847633 0.576152i
\(154\) 0 0
\(155\) 3.29041 18.6609i 0.264292 1.49888i
\(156\) 0 0
\(157\) 11.7536 + 9.86243i 0.938038 + 0.787108i 0.977243 0.212124i \(-0.0680380\pi\)
−0.0392046 + 0.999231i \(0.512482\pi\)
\(158\) 0 0
\(159\) −14.7623 + 0.541913i −1.17073 + 0.0429765i
\(160\) 0 0
\(161\) −3.04028 + 8.35309i −0.239607 + 0.658316i
\(162\) 0 0
\(163\) −5.96235 + 10.3271i −0.467007 + 0.808880i −0.999290 0.0376868i \(-0.988001\pi\)
0.532283 + 0.846567i \(0.321334\pi\)
\(164\) 0 0
\(165\) 15.2573 + 4.92729i 1.18778 + 0.383589i
\(166\) 0 0
\(167\) 1.37759 1.15593i 0.106601 0.0894489i −0.587929 0.808912i \(-0.700057\pi\)
0.694530 + 0.719463i \(0.255612\pi\)
\(168\) 0 0
\(169\) 12.5346 4.56221i 0.964198 0.350939i
\(170\) 0 0
\(171\) 11.8916 + 5.43971i 0.909371 + 0.415985i
\(172\) 0 0
\(173\) 6.36766 2.31764i 0.484124 0.176207i −0.0884156 0.996084i \(-0.528180\pi\)
0.572540 + 0.819877i \(0.305958\pi\)
\(174\) 0 0
\(175\) −17.5018 + 14.6858i −1.32301 + 1.11014i
\(176\) 0 0
\(177\) −6.79969 2.19593i −0.511096 0.165056i
\(178\) 0 0
\(179\) 7.17879 12.4340i 0.536568 0.929363i −0.462518 0.886610i \(-0.653054\pi\)
0.999086 0.0427531i \(-0.0136129\pi\)
\(180\) 0 0
\(181\) −4.09139 + 11.2410i −0.304111 + 0.835537i 0.689664 + 0.724129i \(0.257758\pi\)
−0.993775 + 0.111408i \(0.964464\pi\)
\(182\) 0 0
\(183\) 7.98441 0.293102i 0.590225 0.0216667i
\(184\) 0 0
\(185\) −13.6060 11.4168i −1.00033 0.839379i
\(186\) 0 0
\(187\) −1.97964 + 11.2271i −0.144766 + 0.821008i
\(188\) 0 0
\(189\) 17.4207 1.92542i 1.26717 0.140054i
\(190\) 0 0
\(191\) 10.1652i 0.735526i 0.929919 + 0.367763i \(0.119876\pi\)
−0.929919 + 0.367763i \(0.880124\pi\)
\(192\) 0 0
\(193\) −12.3371 2.17537i −0.888046 0.156587i −0.289027 0.957321i \(-0.593332\pi\)
−0.599019 + 0.800734i \(0.704443\pi\)
\(194\) 0 0
\(195\) 28.2595 11.4763i 2.02370 0.821836i
\(196\) 0 0
\(197\) 19.9041 11.4916i 1.41811 0.818744i 0.421974 0.906608i \(-0.361338\pi\)
0.996132 + 0.0878643i \(0.0280042\pi\)
\(198\) 0 0
\(199\) 23.8117 + 8.66676i 1.68797 + 0.614370i 0.994367 0.105990i \(-0.0338011\pi\)
0.693601 + 0.720360i \(0.256023\pi\)
\(200\) 0 0
\(201\) −16.3714 + 10.2707i −1.15475 + 0.724437i
\(202\) 0 0
\(203\) −2.20807 12.5226i −0.154976 0.878913i
\(204\) 0 0
\(205\) 3.68002 + 4.38567i 0.257024 + 0.306309i
\(206\) 0 0
\(207\) 4.62422 6.41274i 0.321405 0.445716i
\(208\) 0 0
\(209\) −10.9625 + 4.25515i −0.758294 + 0.294335i
\(210\) 0 0
\(211\) 4.07273 + 11.1897i 0.280378 + 0.770333i 0.997317 + 0.0731972i \(0.0233202\pi\)
−0.716939 + 0.697136i \(0.754458\pi\)
\(212\) 0 0
\(213\) −4.69840 21.9117i −0.321929 1.50137i
\(214\) 0 0
\(215\) 8.19612 1.44520i 0.558971 0.0985616i
\(216\) 0 0
\(217\) 16.1316 + 9.31361i 1.09509 + 0.632249i
\(218\) 0 0
\(219\) −3.06868 + 2.77300i −0.207362 + 0.187382i
\(220\) 0 0
\(221\) 10.8437 + 18.7819i 0.729427 + 1.26341i
\(222\) 0 0
\(223\) −8.14222 + 9.70352i −0.545243 + 0.649796i −0.966355 0.257213i \(-0.917196\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(224\) 0 0
\(225\) 18.5339 8.33128i 1.23559 0.555419i
\(226\) 0 0
\(227\) 3.77953 0.250857 0.125428 0.992103i \(-0.459970\pi\)
0.125428 + 0.992103i \(0.459970\pi\)
\(228\) 0 0
\(229\) 15.3222 1.01252 0.506259 0.862381i \(-0.331028\pi\)
0.506259 + 0.862381i \(0.331028\pi\)
\(230\) 0 0
\(231\) −9.68135 + 12.4373i −0.636986 + 0.818313i
\(232\) 0 0
\(233\) 15.6260 18.6223i 1.02369 1.21999i 0.0484572 0.998825i \(-0.484570\pi\)
0.975236 0.221165i \(-0.0709860\pi\)
\(234\) 0 0
\(235\) −0.220745 0.382341i −0.0143998 0.0249412i
\(236\) 0 0
\(237\) −2.62068 2.90013i −0.170232 0.188384i
\(238\) 0 0
\(239\) 11.5689 + 6.67933i 0.748332 + 0.432050i 0.825091 0.565000i \(-0.191124\pi\)
−0.0767587 + 0.997050i \(0.524457\pi\)
\(240\) 0 0
\(241\) −21.6352 + 3.81487i −1.39365 + 0.245737i −0.819530 0.573037i \(-0.805765\pi\)
−0.574116 + 0.818774i \(0.694654\pi\)
\(242\) 0 0
\(243\) −15.3752 2.56970i −0.986319 0.164846i
\(244\) 0 0
\(245\) −5.13702 14.1138i −0.328192 0.901700i
\(246\) 0 0
\(247\) −10.7723 + 19.6061i −0.685427 + 1.24751i
\(248\) 0 0
\(249\) −12.4381 1.72541i −0.788234 0.109344i
\(250\) 0 0
\(251\) 4.35873 + 5.19453i 0.275121 + 0.327876i 0.885857 0.463958i \(-0.153571\pi\)
−0.610737 + 0.791834i \(0.709127\pi\)
\(252\) 0 0
\(253\) 1.23458 + 7.00166i 0.0776175 + 0.440191i
\(254\) 0 0
\(255\) 13.3466 + 21.2743i 0.835794 + 1.33225i
\(256\) 0 0
\(257\) 16.7251 + 6.08743i 1.04328 + 0.379724i 0.806123 0.591747i \(-0.201562\pi\)
0.237158 + 0.971471i \(0.423784\pi\)
\(258\) 0 0
\(259\) 15.1208 8.73000i 0.939561 0.542456i
\(260\) 0 0
\(261\) −1.14198 + 11.2517i −0.0706866 + 0.696463i
\(262\) 0 0
\(263\) −3.78041 0.666587i −0.233110 0.0411035i 0.0558728 0.998438i \(-0.482206\pi\)
−0.288983 + 0.957334i \(0.593317\pi\)
\(264\) 0 0
\(265\) 29.2643i 1.79769i
\(266\) 0 0
\(267\) −0.978490 + 1.84823i −0.0598826 + 0.113110i
\(268\) 0 0
\(269\) 0.457985 2.59736i 0.0279239 0.158364i −0.967657 0.252268i \(-0.918824\pi\)
0.995581 + 0.0939040i \(0.0299347\pi\)
\(270\) 0 0
\(271\) −10.7222 8.99702i −0.651329 0.546530i 0.256145 0.966638i \(-0.417548\pi\)
−0.907474 + 0.420108i \(0.861992\pi\)
\(272\) 0 0
\(273\) 1.09993 + 29.9632i 0.0665705 + 1.81345i
\(274\) 0 0
\(275\) −6.24984 + 17.1713i −0.376880 + 1.03547i
\(276\) 0 0
\(277\) −0.166629 + 0.288609i −0.0100117 + 0.0173408i −0.870988 0.491305i \(-0.836520\pi\)
0.860976 + 0.508645i \(0.169854\pi\)
\(278\) 0 0
\(279\) −11.5511 11.8763i −0.691544 0.711014i
\(280\) 0 0
\(281\) 1.92247 1.61315i 0.114685 0.0962323i −0.583642 0.812011i \(-0.698373\pi\)
0.698327 + 0.715779i \(0.253928\pi\)
\(282\) 0 0
\(283\) 24.7578 9.01110i 1.47170 0.535655i 0.523138 0.852248i \(-0.324761\pi\)
0.948561 + 0.316594i \(0.102539\pi\)
\(284\) 0 0
\(285\) −11.6332 + 23.1464i −0.689090 + 1.37107i
\(286\) 0 0
\(287\) −5.28855 + 1.92487i −0.312173 + 0.113622i
\(288\) 0 0
\(289\) −0.656761 + 0.551088i −0.0386330 + 0.0324169i
\(290\) 0 0
\(291\) −4.87548 + 15.0969i −0.285806 + 0.884995i
\(292\) 0 0
\(293\) −6.53329 + 11.3160i −0.381679 + 0.661087i −0.991302 0.131604i \(-0.957987\pi\)
0.609624 + 0.792691i \(0.291321\pi\)
\(294\) 0 0
\(295\) 4.84144 13.3017i 0.281879 0.774457i
\(296\) 0 0
\(297\) 11.2966 8.30030i 0.655495 0.481632i
\(298\) 0 0
\(299\) 10.3608 + 8.69378i 0.599183 + 0.502775i
\(300\) 0 0
\(301\) −1.42068 + 8.05706i −0.0818864 + 0.464401i
\(302\) 0 0
\(303\) 8.65654 + 4.58295i 0.497305 + 0.263284i
\(304\) 0 0
\(305\) 15.8280i 0.906310i
\(306\) 0 0
\(307\) −7.06477 1.24571i −0.403208 0.0710964i −0.0316333 0.999500i \(-0.510071\pi\)
−0.371575 + 0.928403i \(0.621182\pi\)
\(308\) 0 0
\(309\) −2.52607 6.22023i −0.143703 0.353857i
\(310\) 0 0
\(311\) 9.96292 5.75210i 0.564945 0.326171i −0.190183 0.981749i \(-0.560908\pi\)
0.755128 + 0.655577i \(0.227575\pi\)
\(312\) 0 0
\(313\) 16.6644 + 6.06533i 0.941925 + 0.342833i 0.766926 0.641736i \(-0.221785\pi\)
0.174999 + 0.984569i \(0.444008\pi\)
\(314\) 0 0
\(315\) 2.54574 + 34.6276i 0.143436 + 1.95104i
\(316\) 0 0
\(317\) −5.91797 33.5625i −0.332386 1.88506i −0.451653 0.892194i \(-0.649165\pi\)
0.119267 0.992862i \(-0.461946\pi\)
\(318\) 0 0
\(319\) −6.53729 7.79084i −0.366018 0.436203i
\(320\) 0 0
\(321\) −1.66089 + 11.9730i −0.0927019 + 0.668267i
\(322\) 0 0
\(323\) −17.4385 5.93183i −0.970307 0.330056i
\(324\) 0 0
\(325\) 11.8894 + 32.6659i 0.659507 + 1.81198i
\(326\) 0 0
\(327\) 9.70775 2.08158i 0.536840 0.115111i
\(328\) 0 0
\(329\) 0.427405 0.0753631i 0.0235636 0.00415490i
\(330\) 0 0
\(331\) −18.0961 10.4478i −0.994652 0.574263i −0.0879907 0.996121i \(-0.528045\pi\)
−0.906662 + 0.421858i \(0.861378\pi\)
\(332\) 0 0
\(333\) −15.0543 + 3.81063i −0.824970 + 0.208821i
\(334\) 0 0
\(335\) −19.1430 33.1567i −1.04590 1.81155i
\(336\) 0 0
\(337\) −19.1366 + 22.8061i −1.04244 + 1.24233i −0.0729092 + 0.997339i \(0.523228\pi\)
−0.969526 + 0.244988i \(0.921216\pi\)
\(338\) 0 0
\(339\) −23.0859 17.9704i −1.25385 0.976016i
\(340\) 0 0
\(341\) 14.8983 0.806788
\(342\) 0 0
\(343\) −8.84639 −0.477660
\(344\) 0 0
\(345\) 12.3592 + 9.62058i 0.665398 + 0.517955i
\(346\) 0 0
\(347\) −3.49226 + 4.16191i −0.187474 + 0.223423i −0.851592 0.524204i \(-0.824363\pi\)
0.664118 + 0.747628i \(0.268807\pi\)
\(348\) 0 0
\(349\) −8.07643 13.9888i −0.432322 0.748803i 0.564751 0.825261i \(-0.308972\pi\)
−0.997073 + 0.0764582i \(0.975639\pi\)
\(350\) 0 0
\(351\) 6.31270 25.9095i 0.336947 1.38295i
\(352\) 0 0
\(353\) 18.1153 + 10.4589i 0.964180 + 0.556670i 0.897457 0.441102i \(-0.145412\pi\)
0.0667232 + 0.997772i \(0.478746\pi\)
\(354\) 0 0
\(355\) 43.7200 7.70902i 2.32042 0.409152i
\(356\) 0 0
\(357\) −24.1395 + 5.17608i −1.27760 + 0.273947i
\(358\) 0 0
\(359\) −8.05343 22.1266i −0.425044 1.16780i −0.948785 0.315921i \(-0.897686\pi\)
0.523741 0.851877i \(-0.324536\pi\)
\(360\) 0 0
\(361\) −4.08900 18.5548i −0.215211 0.976568i
\(362\) 0 0
\(363\) 0.885785 6.38543i 0.0464917 0.335148i
\(364\) 0 0
\(365\) −5.26668 6.27659i −0.275671 0.328532i
\(366\) 0 0
\(367\) −3.11469 17.6643i −0.162586 0.922069i −0.951519 0.307590i \(-0.900477\pi\)
0.788933 0.614479i \(-0.210634\pi\)
\(368\) 0 0
\(369\) 4.99208 0.367005i 0.259877 0.0191055i
\(370\) 0 0
\(371\) 27.0329 + 9.83916i 1.40348 + 0.510824i
\(372\) 0 0
\(373\) 12.2615 7.07917i 0.634876 0.366546i −0.147762 0.989023i \(-0.547207\pi\)
0.782638 + 0.622477i \(0.213874\pi\)
\(374\) 0 0
\(375\) 3.96570 + 9.76519i 0.204788 + 0.504272i
\(376\) 0 0
\(377\) −19.0534 3.35964i −0.981303 0.173030i
\(378\) 0 0
\(379\) 1.25595i 0.0645137i 0.999480 + 0.0322569i \(0.0102695\pi\)
−0.999480 + 0.0322569i \(0.989731\pi\)
\(380\) 0 0
\(381\) −8.46635 4.48226i −0.433744 0.229633i
\(382\) 0 0
\(383\) −0.465296 + 2.63882i −0.0237755 + 0.134838i −0.994385 0.105822i \(-0.966253\pi\)
0.970610 + 0.240660i \(0.0773637\pi\)
\(384\) 0 0
\(385\) −23.9185 20.0700i −1.21900 1.02286i
\(386\) 0 0
\(387\) 3.16645 6.55149i 0.160960 0.333031i
\(388\) 0 0
\(389\) 11.2472 30.9013i 0.570253 1.56676i −0.233852 0.972272i \(-0.575133\pi\)
0.804106 0.594486i \(-0.202645\pi\)
\(390\) 0 0
\(391\) −5.56827 + 9.64452i −0.281599 + 0.487744i
\(392\) 0 0
\(393\) 7.84692 24.2979i 0.395825 1.22567i
\(394\) 0 0
\(395\) 5.93183 4.97739i 0.298463 0.250440i
\(396\) 0 0
\(397\) −2.19998 + 0.800726i −0.110414 + 0.0401873i −0.396636 0.917976i \(-0.629823\pi\)
0.286223 + 0.958163i \(0.407600\pi\)
\(398\) 0 0
\(399\) −17.4702 18.5284i −0.874603 0.927578i
\(400\) 0 0
\(401\) 12.8782 4.68726i 0.643104 0.234071i 0.000179351 1.00000i \(-0.499943\pi\)
0.642925 + 0.765929i \(0.277721\pi\)
\(402\) 0 0
\(403\) 21.7111 18.2178i 1.08151 0.907492i
\(404\) 0 0
\(405\) 6.20459 30.2515i 0.308308 1.50321i
\(406\) 0 0
\(407\) 6.98237 12.0938i 0.346103 0.599468i
\(408\) 0 0
\(409\) 7.27394 19.9850i 0.359673 0.988194i −0.619470 0.785020i \(-0.712652\pi\)
0.979143 0.203173i \(-0.0651254\pi\)
\(410\) 0 0
\(411\) 1.26696 + 34.5135i 0.0624947 + 1.70243i
\(412\) 0 0
\(413\) 10.6597 + 8.94454i 0.524529 + 0.440132i
\(414\) 0 0
\(415\) 4.31971 24.4983i 0.212046 1.20257i
\(416\) 0 0
\(417\) −1.31135 + 2.47696i −0.0642173 + 0.121297i
\(418\) 0 0
\(419\) 29.1990i 1.42646i 0.700928 + 0.713232i \(0.252770\pi\)
−0.700928 + 0.713232i \(0.747230\pi\)
\(420\) 0 0
\(421\) 7.45681 + 1.31484i 0.363423 + 0.0640812i 0.352378 0.935858i \(-0.385373\pi\)
0.0110448 + 0.999939i \(0.496484\pi\)
\(422\) 0 0
\(423\) −0.384029 0.0389766i −0.0186722 0.00189511i
\(424\) 0 0
\(425\) −24.7884 + 14.3116i −1.20241 + 0.694214i
\(426\) 0 0
\(427\) −14.6211 5.32165i −0.707565 0.257533i
\(428\) 0 0
\(429\) 12.7443 + 20.3144i 0.615302 + 0.980787i
\(430\) 0 0
\(431\) 4.16028 + 23.5941i 0.200394 + 1.13649i 0.904526 + 0.426419i \(0.140225\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(432\) 0 0
\(433\) −9.89407 11.7913i −0.475479 0.566654i 0.473984 0.880534i \(-0.342816\pi\)
−0.949463 + 0.313880i \(0.898371\pi\)
\(434\) 0 0
\(435\) −22.1920 3.07847i −1.06402 0.147601i
\(436\) 0 0
\(437\) −11.4847 + 0.243366i −0.549389 + 0.0116418i
\(438\) 0 0
\(439\) 7.60564 + 20.8963i 0.362997 + 0.997327i 0.977964 + 0.208774i \(0.0669472\pi\)
−0.614967 + 0.788553i \(0.710831\pi\)
\(440\) 0 0
\(441\) −12.6361 3.57454i −0.601718 0.170216i
\(442\) 0 0
\(443\) −30.8547 + 5.44051i −1.46595 + 0.258486i −0.848948 0.528476i \(-0.822764\pi\)
−0.617001 + 0.786963i \(0.711652\pi\)
\(444\) 0 0
\(445\) −3.58782 2.07143i −0.170079 0.0981952i
\(446\) 0 0
\(447\) −27.9857 30.9698i −1.32368 1.46482i
\(448\) 0 0
\(449\) −6.15216 10.6559i −0.290338 0.502881i 0.683551 0.729902i \(-0.260435\pi\)
−0.973890 + 0.227022i \(0.927101\pi\)
\(450\) 0 0
\(451\) −2.89339 + 3.44820i −0.136244 + 0.162370i
\(452\) 0 0
\(453\) 15.6452 20.0988i 0.735076 0.944326i
\(454\) 0 0
\(455\) −59.3979 −2.78462
\(456\) 0 0
\(457\) −37.8216 −1.76922 −0.884609 0.466334i \(-0.845575\pi\)
−0.884609 + 0.466334i \(0.845575\pi\)
\(458\) 0 0
\(459\) 21.9123 + 1.41431i 1.02278 + 0.0660142i
\(460\) 0 0
\(461\) −24.9818 + 29.7722i −1.16352 + 1.38663i −0.255970 + 0.966685i \(0.582395\pi\)
−0.907550 + 0.419945i \(0.862050\pi\)
\(462\) 0 0
\(463\) −12.3259 21.3492i −0.572835 0.992180i −0.996273 0.0862548i \(-0.972510\pi\)
0.423438 0.905925i \(-0.360823\pi\)
\(464\) 0 0
\(465\) 24.3509 22.0045i 1.12924 1.02043i
\(466\) 0 0
\(467\) −3.17931 1.83558i −0.147121 0.0849404i 0.424632 0.905366i \(-0.360403\pi\)
−0.571754 + 0.820425i \(0.693737\pi\)
\(468\) 0 0
\(469\) 37.0647 6.53551i 1.71149 0.301782i
\(470\) 0 0
\(471\) 5.57172 + 25.9846i 0.256731 + 1.19731i
\(472\) 0 0
\(473\) 2.23803 + 6.14892i 0.102905 + 0.282728i
\(474\) 0 0
\(475\) −25.8762 14.2174i −1.18728 0.652337i
\(476\) 0 0
\(477\) −20.7534 14.9652i −0.950231 0.685210i
\(478\) 0 0
\(479\) 16.6874 + 19.8872i 0.762465 + 0.908670i 0.998001 0.0631952i \(-0.0201291\pi\)
−0.235536 + 0.971866i \(0.575685\pi\)
\(480\) 0 0
\(481\) −4.61312 26.1623i −0.210340 1.19290i
\(482\) 0 0
\(483\) −13.0424 + 8.18221i −0.593449 + 0.372304i
\(484\) 0 0
\(485\) −29.5329 10.7491i −1.34102 0.488092i
\(486\) 0 0
\(487\) −8.59327 + 4.96133i −0.389398 + 0.224819i −0.681899 0.731446i \(-0.738846\pi\)
0.292501 + 0.956265i \(0.405512\pi\)
\(488\) 0 0
\(489\) −19.1364 + 7.77138i −0.865376 + 0.351434i
\(490\) 0 0
\(491\) −14.8971 2.62676i −0.672296 0.118544i −0.172929 0.984934i \(-0.555323\pi\)
−0.499367 + 0.866391i \(0.666434\pi\)
\(492\) 0 0
\(493\) 15.9305i 0.717476i
\(494\) 0 0
\(495\) 15.6111 + 22.9670i 0.701668 + 1.03229i
\(496\) 0 0
\(497\) −7.57822 + 42.9782i −0.339930 + 1.92784i
\(498\) 0 0
\(499\) −16.3136 13.6887i −0.730296 0.612791i 0.199917 0.979813i \(-0.435933\pi\)
−0.930212 + 0.367022i \(0.880377\pi\)
\(500\) 0 0
\(501\) 3.11268 0.114264i 0.139064 0.00510494i
\(502\) 0 0
\(503\) 1.99181 5.47245i 0.0888104 0.244004i −0.887334 0.461128i \(-0.847445\pi\)
0.976144 + 0.217123i \(0.0696673\pi\)
\(504\) 0 0
\(505\) −9.70195 + 16.8043i −0.431731 + 0.747780i
\(506\) 0 0
\(507\) 21.9858 + 7.10023i 0.976423 + 0.315332i
\(508\) 0 0
\(509\) −10.9586 + 9.19535i −0.485731 + 0.407577i −0.852493 0.522738i \(-0.824911\pi\)
0.366763 + 0.930315i \(0.380466\pi\)
\(510\) 0 0
\(511\) 7.56874 2.75480i 0.334821 0.121865i
\(512\) 0 0
\(513\) 10.4657 + 20.0865i 0.462073 + 0.886842i
\(514\) 0 0
\(515\) 12.4977 4.54881i 0.550717 0.200444i
\(516\) 0 0
\(517\) 0.265908 0.223123i 0.0116946 0.00981294i
\(518\) 0 0
\(519\) 11.1690 + 3.60697i 0.490263 + 0.158328i
\(520\) 0 0
\(521\) −5.93133 + 10.2734i −0.259856 + 0.450084i −0.966203 0.257781i \(-0.917009\pi\)
0.706347 + 0.707866i \(0.250342\pi\)
\(522\) 0 0
\(523\) −10.6971 + 29.3899i −0.467750 + 1.28513i 0.451787 + 0.892126i \(0.350787\pi\)
−0.919536 + 0.393005i \(0.871435\pi\)
\(524\) 0 0
\(525\) −39.5455 + 1.45169i −1.72591 + 0.0633568i
\(526\) 0 0
\(527\) 17.8768 + 15.0004i 0.778727 + 0.653430i
\(528\) 0 0
\(529\) 2.78789 15.8109i 0.121213 0.687431i
\(530\) 0 0
\(531\) −6.95737 10.2357i −0.301924 0.444190i
\(532\) 0 0
\(533\) 8.56309i 0.370909i
\(534\) 0 0
\(535\) −23.5822 4.15817i −1.01955 0.179774i
\(536\) 0 0
\(537\) 23.0406 9.35691i 0.994275 0.403780i
\(538\) 0 0
\(539\) 10.2270 5.90454i 0.440506 0.254326i
\(540\) 0 0
\(541\) −26.2388 9.55016i −1.12810 0.410593i −0.290495 0.956876i \(-0.593820\pi\)
−0.837601 + 0.546283i \(0.816042\pi\)
\(542\) 0 0
\(543\) −17.5515 + 11.0110i −0.753207 + 0.472529i
\(544\) 0 0
\(545\) 3.41540 + 19.3697i 0.146300 + 0.829706i
\(546\) 0 0
\(547\) −12.0859 14.4034i −0.516757 0.615847i 0.443054 0.896495i \(-0.353895\pi\)
−0.959811 + 0.280648i \(0.909451\pi\)
\(548\) 0 0
\(549\) 11.2248 + 8.09415i 0.479061 + 0.345450i
\(550\) 0 0
\(551\) 14.0536 8.51581i 0.598702 0.362786i
\(552\) 0 0
\(553\) 2.60348 + 7.15300i 0.110711 + 0.304177i
\(554\) 0 0
\(555\) −6.44985 30.0799i −0.273781 1.27682i
\(556\) 0 0
\(557\) −22.6372 + 3.99155i −0.959170 + 0.169128i −0.631251 0.775578i \(-0.717458\pi\)
−0.327919 + 0.944706i \(0.606347\pi\)
\(558\) 0 0
\(559\) 10.7804 + 6.22408i 0.455963 + 0.263250i
\(560\) 0 0
\(561\) −14.6504 + 13.2388i −0.618542 + 0.558942i
\(562\) 0 0
\(563\) −6.45057 11.1727i −0.271859 0.470874i 0.697479 0.716605i \(-0.254305\pi\)
−0.969338 + 0.245732i \(0.920972\pi\)
\(564\) 0 0
\(565\) 37.2536 44.3971i 1.56727 1.86780i
\(566\) 0 0
\(567\) 25.8587 + 15.9025i 1.08596 + 0.667844i
\(568\) 0 0
\(569\) −37.8380 −1.58625 −0.793125 0.609059i \(-0.791547\pi\)
−0.793125 + 0.609059i \(0.791547\pi\)
\(570\) 0 0
\(571\) −20.7087 −0.866632 −0.433316 0.901242i \(-0.642657\pi\)
−0.433316 + 0.901242i \(0.642657\pi\)
\(572\) 0 0
\(573\) −10.8149 + 13.8935i −0.451799 + 0.580411i
\(574\) 0 0
\(575\) −11.4741 + 13.6743i −0.478503 + 0.570258i
\(576\) 0 0
\(577\) −8.69281 15.0564i −0.361886 0.626805i 0.626385 0.779514i \(-0.284534\pi\)
−0.988271 + 0.152708i \(0.951200\pi\)
\(578\) 0 0
\(579\) −14.5477 16.0989i −0.604582 0.669049i
\(580\) 0 0
\(581\) 21.1779 + 12.2271i 0.878608 + 0.507265i
\(582\) 0 0
\(583\) 22.6593 3.99544i 0.938451 0.165474i
\(584\) 0 0
\(585\) 50.8342 + 14.3802i 2.10174 + 0.594546i
\(586\) 0 0
\(587\) 10.0782 + 27.6896i 0.415971 + 1.14287i 0.953964 + 0.299922i \(0.0969607\pi\)
−0.537992 + 0.842950i \(0.680817\pi\)
\(588\) 0 0
\(589\) −3.67683 + 23.7891i −0.151501 + 0.980214i
\(590\) 0 0
\(591\) 39.4306 + 5.46980i 1.62196 + 0.224998i
\(592\) 0 0
\(593\) −8.16230 9.72745i −0.335185 0.399458i 0.571956 0.820284i \(-0.306185\pi\)
−0.907141 + 0.420826i \(0.861740\pi\)
\(594\) 0 0
\(595\) −8.49279 48.1650i −0.348170 1.97457i
\(596\) 0 0
\(597\) 23.3246 + 37.1792i 0.954612 + 1.52164i
\(598\) 0 0
\(599\) 16.8817 + 6.14443i 0.689767 + 0.251055i 0.663035 0.748588i \(-0.269268\pi\)
0.0267313 + 0.999643i \(0.491490\pi\)
\(600\) 0 0
\(601\) 8.14038 4.69985i 0.332053 0.191711i −0.324699 0.945817i \(-0.605263\pi\)
0.656752 + 0.754106i \(0.271930\pi\)
\(602\) 0 0
\(603\) −33.3031 3.38006i −1.35621 0.137647i
\(604\) 0 0
\(605\) 12.5768 + 2.21764i 0.511321 + 0.0901597i
\(606\) 0 0
\(607\) 9.88885i 0.401376i 0.979655 + 0.200688i \(0.0643177\pi\)
−0.979655 + 0.200688i \(0.935682\pi\)
\(608\) 0 0
\(609\) 10.3050 19.4648i 0.417582 0.788752i
\(610\) 0 0
\(611\) 0.114667 0.650309i 0.00463893 0.0263087i
\(612\) 0 0
\(613\) −24.8777 20.8749i −1.00480 0.843129i −0.0171592 0.999853i \(-0.505462\pi\)
−0.987642 + 0.156724i \(0.949907\pi\)
\(614\) 0 0
\(615\) 0.363769 + 9.90947i 0.0146686 + 0.399589i
\(616\) 0 0
\(617\) 7.64721 21.0105i 0.307865 0.845852i −0.685207 0.728348i \(-0.740288\pi\)
0.993072 0.117504i \(-0.0374893\pi\)
\(618\) 0 0
\(619\) 9.39662 16.2754i 0.377682 0.654164i −0.613043 0.790050i \(-0.710055\pi\)
0.990725 + 0.135886i \(0.0433880\pi\)
\(620\) 0 0
\(621\) 13.1429 3.84500i 0.527406 0.154295i
\(622\) 0 0
\(623\) 3.11977 2.61780i 0.124991 0.104880i
\(624\) 0 0
\(625\) 12.2044 4.44205i 0.488178 0.177682i
\(626\) 0 0
\(627\) −19.5105 5.84738i −0.779173 0.233522i
\(628\) 0 0
\(629\) 20.5551 7.48143i 0.819584 0.298304i
\(630\) 0 0
\(631\) 22.1517 18.5875i 0.881846 0.739956i −0.0847122 0.996405i \(-0.526997\pi\)
0.966558 + 0.256449i \(0.0825526\pi\)
\(632\) 0 0
\(633\) −6.33844 + 19.6269i −0.251930 + 0.780100i
\(634\) 0 0
\(635\) 9.48879 16.4351i 0.376551 0.652206i
\(636\) 0 0
\(637\) 7.68350 21.1102i 0.304431 0.836418i
\(638\) 0 0
\(639\) 16.8906 34.9472i 0.668182 1.38249i
\(640\) 0 0
\(641\) 18.2950 + 15.3513i 0.722609 + 0.606341i 0.928106 0.372317i \(-0.121437\pi\)
−0.205497 + 0.978658i \(0.565881\pi\)
\(642\) 0 0
\(643\) −6.83453 + 38.7606i −0.269528 + 1.52857i 0.486297 + 0.873793i \(0.338347\pi\)
−0.755825 + 0.654774i \(0.772764\pi\)
\(644\) 0 0
\(645\) 12.7398 + 6.74473i 0.501631 + 0.265574i
\(646\) 0 0
\(647\) 24.3840i 0.958633i −0.877642 0.479317i \(-0.840885\pi\)
0.877642 0.479317i \(-0.159115\pi\)
\(648\) 0 0
\(649\) 10.9605 + 1.93263i 0.430237 + 0.0758624i
\(650\) 0 0
\(651\) 12.1395 + 29.8924i 0.475783 + 1.17157i
\(652\) 0 0
\(653\) 20.0643 11.5841i 0.785178 0.453323i −0.0530845 0.998590i \(-0.516905\pi\)
0.838262 + 0.545268i \(0.183572\pi\)
\(654\) 0 0
\(655\) 47.5322 + 17.3003i 1.85724 + 0.675979i
\(656\) 0 0
\(657\) −7.14445 + 0.525242i −0.278731 + 0.0204916i
\(658\) 0 0
\(659\) −3.15401 17.8873i −0.122863 0.696790i −0.982554 0.185976i \(-0.940455\pi\)
0.859691 0.510814i \(-0.170656\pi\)
\(660\) 0 0
\(661\) 22.4662 + 26.7742i 0.873835 + 1.04140i 0.998787 + 0.0492336i \(0.0156779\pi\)
−0.124952 + 0.992163i \(0.539878\pi\)
\(662\) 0 0
\(663\) −5.16141 + 37.2074i −0.200453 + 1.44502i
\(664\) 0 0
\(665\) 37.9501 33.2391i 1.47164 1.28896i
\(666\) 0 0
\(667\) −3.39794 9.33576i −0.131569 0.361482i
\(668\) 0 0
\(669\) −21.4523 + 4.59990i −0.829395 + 0.177842i
\(670\) 0 0
\(671\) −12.2556 + 2.16099i −0.473122 + 0.0834242i
\(672\) 0 0
\(673\) −8.97335 5.18077i −0.345897 0.199704i 0.316980 0.948432i \(-0.397331\pi\)
−0.662877 + 0.748729i \(0.730665\pi\)
\(674\) 0 0
\(675\) 34.1955 + 8.33153i 1.31619 + 0.320681i
\(676\) 0 0
\(677\) 2.66151 + 4.60988i 0.102290 + 0.177172i 0.912628 0.408791i \(-0.134050\pi\)
−0.810338 + 0.585963i \(0.800716\pi\)
\(678\) 0 0
\(679\) 19.8590 23.6670i 0.762117 0.908255i
\(680\) 0 0
\(681\) 5.16578 + 4.02111i 0.197953 + 0.154089i
\(682\) 0 0
\(683\) −29.5958 −1.13245 −0.566226 0.824250i \(-0.691597\pi\)
−0.566226 + 0.824250i \(0.691597\pi\)
\(684\) 0 0
\(685\) −68.4183 −2.61413
\(686\) 0 0
\(687\) 20.9420 + 16.3015i 0.798987 + 0.621942i
\(688\) 0 0
\(689\) 28.1354 33.5305i 1.07187 1.27741i
\(690\) 0 0
\(691\) −9.35680 16.2065i −0.355950 0.616523i 0.631330 0.775514i \(-0.282509\pi\)
−0.987280 + 0.158991i \(0.949176\pi\)
\(692\) 0 0
\(693\) −26.4645 + 6.69885i −1.00530 + 0.254468i
\(694\) 0 0
\(695\) −4.80833 2.77609i −0.182390 0.105303i
\(696\) 0 0
\(697\) −6.94369 + 1.22436i −0.263011 + 0.0463760i
\(698\) 0 0
\(699\) 41.1699 8.82782i 1.55719 0.333899i
\(700\) 0 0
\(701\) −9.40339 25.8356i −0.355161 0.975798i −0.980685 0.195593i \(-0.937337\pi\)
0.625524 0.780205i \(-0.284885\pi\)
\(702\) 0 0
\(703\) 17.5878 + 14.1339i 0.663337 + 0.533071i
\(704\) 0 0
\(705\) 0.105070 0.757429i 0.00395718 0.0285264i
\(706\) 0 0
\(707\) −12.2610 14.6120i −0.461121 0.549543i
\(708\) 0 0
\(709\) 7.22305 + 40.9640i 0.271267 + 1.53843i 0.750574 + 0.660786i \(0.229777\pi\)
−0.479307 + 0.877647i \(0.659112\pi\)
\(710\) 0 0
\(711\) −0.496392 6.75202i −0.0186161 0.253220i
\(712\) 0 0
\(713\) 13.6759 + 4.97762i 0.512166 + 0.186413i
\(714\) 0 0
\(715\) −41.1425 + 23.7536i −1.53864 + 0.888335i
\(716\) 0 0
\(717\) 8.70590 + 21.4375i 0.325128 + 0.800600i
\(718\) 0 0
\(719\) −26.6001 4.69031i −0.992015 0.174919i −0.345992 0.938237i \(-0.612458\pi\)
−0.646022 + 0.763318i \(0.723569\pi\)
\(720\) 0 0
\(721\) 13.0742i 0.486908i
\(722\) 0 0
\(723\) −33.6292 17.8040i −1.25068 0.662137i
\(724\) 0 0
\(725\) 4.43406 25.1468i 0.164677 0.933930i
\(726\) 0 0
\(727\) −23.4708 19.6943i −0.870483 0.730422i 0.0937165 0.995599i \(-0.470125\pi\)
−0.964200 + 0.265177i \(0.914570\pi\)
\(728\) 0 0
\(729\) −18.2805 19.8701i −0.677056 0.735931i
\(730\) 0 0
\(731\) −3.50562 + 9.63162i −0.129660 + 0.356238i
\(732\) 0 0
\(733\) −24.9658 + 43.2420i −0.922132 + 1.59718i −0.126023 + 0.992027i \(0.540221\pi\)
−0.796110 + 0.605152i \(0.793112\pi\)
\(734\) 0 0
\(735\) 7.99480 24.7558i 0.294893 0.913133i
\(736\) 0 0
\(737\) 23.0596 19.3493i 0.849410 0.712740i
\(738\) 0 0
\(739\) −32.2619 + 11.7424i −1.18677 + 0.431950i −0.858589 0.512664i \(-0.828659\pi\)
−0.328183 + 0.944614i \(0.606436\pi\)
\(740\) 0 0
\(741\) −35.5826 + 15.3363i −1.30716 + 0.563392i
\(742\) 0 0
\(743\) 27.6540 10.0652i 1.01453 0.369257i 0.219357 0.975645i \(-0.429604\pi\)
0.795169 + 0.606387i \(0.207382\pi\)
\(744\) 0 0
\(745\) 63.3446 53.1525i 2.32077 1.94736i
\(746\) 0 0
\(747\) −15.1644 15.5914i −0.554838 0.570459i
\(748\) 0 0
\(749\) 11.7698 20.3860i 0.430061 0.744887i
\(750\) 0 0
\(751\) −0.559448 + 1.53707i −0.0204145 + 0.0560885i −0.949481 0.313824i \(-0.898390\pi\)
0.929067 + 0.369912i \(0.120612\pi\)
\(752\) 0 0
\(753\) 0.430860 + 11.7371i 0.0157014 + 0.427724i
\(754\) 0 0
\(755\) 38.6526 + 32.4334i 1.40671 + 1.18037i
\(756\) 0 0
\(757\) 4.17165 23.6586i 0.151621 0.859887i −0.810189 0.586169i \(-0.800635\pi\)
0.961810 0.273718i \(-0.0882534\pi\)
\(758\) 0 0
\(759\) −5.76179 + 10.8832i −0.209140 + 0.395035i
\(760\) 0 0
\(761\) 12.8974i 0.467530i −0.972293 0.233765i \(-0.924895\pi\)
0.972293 0.233765i \(-0.0751047\pi\)
\(762\) 0 0
\(763\) −19.0410 3.35745i −0.689332 0.121548i
\(764\) 0 0
\(765\) −4.39233 + 43.2769i −0.158805 + 1.56468i
\(766\) 0 0
\(767\) 18.3359 10.5862i 0.662069 0.382246i
\(768\) 0 0
\(769\) 21.8210 + 7.94220i 0.786886 + 0.286403i 0.704041 0.710159i \(-0.251377\pi\)
0.0828452 + 0.996562i \(0.473599\pi\)
\(770\) 0 0
\(771\) 16.3829 + 26.1143i 0.590017 + 0.940482i
\(772\) 0 0
\(773\) 6.98308 + 39.6030i 0.251164 + 1.42442i 0.805730 + 0.592283i \(0.201773\pi\)
−0.554566 + 0.832140i \(0.687116\pi\)
\(774\) 0 0
\(775\) 24.0439 + 28.6544i 0.863683 + 1.02930i
\(776\) 0 0
\(777\) 29.9548 + 4.15532i 1.07462 + 0.149071i
\(778\) 0 0
\(779\) −4.79191 5.47107i −0.171688 0.196021i
\(780\) 0 0
\(781\) 11.9381 + 32.7998i 0.427181 + 1.17367i
\(782\) 0 0
\(783\) −13.5317 + 14.1636i −0.483584 + 0.506166i
\(784\) 0 0
\(785\) −51.8465 + 9.14194i −1.85048 + 0.326290i
\(786\) 0 0
\(787\) 40.4947 + 23.3796i 1.44348 + 0.833393i 0.998080 0.0619383i \(-0.0197282\pi\)
0.445400 + 0.895332i \(0.353062\pi\)
\(788\) 0 0
\(789\) −4.45778 4.93312i −0.158701 0.175624i
\(790\) 0 0
\(791\) 28.4865 + 49.3400i 1.01286 + 1.75433i
\(792\) 0 0
\(793\) −15.2175 + 18.1355i −0.540388 + 0.644009i