Properties

Label 216.2.q.b.49.4
Level $216$
Weight $2$
Character 216.49
Analytic conductor $1.725$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.q (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 49.4
Character \(\chi\) \(=\) 216.49
Dual form 216.2.q.b.97.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.10062 + 1.33740i) q^{3} +(3.74067 - 1.36149i) q^{5} +(-0.452652 - 2.56712i) q^{7} +(-0.577279 + 2.94393i) q^{9} +O(q^{10})\) \(q+(1.10062 + 1.33740i) q^{3} +(3.74067 - 1.36149i) q^{5} +(-0.452652 - 2.56712i) q^{7} +(-0.577279 + 2.94393i) q^{9} +(-4.99402 - 1.81767i) q^{11} +(-0.0404003 - 0.0338999i) q^{13} +(5.93792 + 3.50429i) q^{15} +(-1.69081 + 2.92857i) q^{17} +(1.23206 + 2.13399i) q^{19} +(2.93506 - 3.43079i) q^{21} +(-0.964125 + 5.46782i) q^{23} +(8.30876 - 6.97187i) q^{25} +(-4.57258 + 2.46810i) q^{27} +(-6.29991 + 5.28625i) q^{29} +(-0.115728 + 0.656323i) q^{31} +(-3.06555 - 8.67957i) q^{33} +(-5.18834 - 8.98646i) q^{35} +(2.67730 - 4.63722i) q^{37} +(0.000872395 - 0.0913423i) q^{39} +(-5.31122 - 4.45664i) q^{41} +(-0.0524095 - 0.0190755i) q^{43} +(1.84874 + 11.7983i) q^{45} +(-0.0794772 - 0.450737i) q^{47} +(0.192660 - 0.0701224i) q^{49} +(-5.77762 + 0.961949i) q^{51} +1.38667 q^{53} -21.1558 q^{55} +(-1.49797 + 3.99646i) q^{57} +(3.99339 - 1.45348i) q^{59} +(0.457339 + 2.59370i) q^{61} +(7.81873 + 0.149364i) q^{63} +(-0.197279 - 0.0718037i) q^{65} +(7.16941 + 6.01585i) q^{67} +(-8.37380 + 4.72856i) q^{69} +(7.18697 - 12.4482i) q^{71} +(-7.15357 - 12.3903i) q^{73} +(18.4690 + 3.43876i) q^{75} +(-2.40563 + 13.6430i) q^{77} +(5.93415 - 4.97935i) q^{79} +(-8.33350 - 3.39894i) q^{81} +(1.83808 - 1.54234i) q^{83} +(-2.33755 + 13.2569i) q^{85} +(-14.0036 - 2.60735i) q^{87} +(2.04047 + 3.53420i) q^{89} +(-0.0687377 + 0.119057i) q^{91} +(-1.00514 + 0.567588i) q^{93} +(7.51413 + 6.30511i) q^{95} +(-11.8711 - 4.32074i) q^{97} +(8.23406 - 13.6528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 3q^{7} - 6q^{9} + O(q^{10}) \) \( 30q + 3q^{7} - 6q^{9} - 3q^{11} - 12q^{13} + 15q^{15} + 6q^{17} - 9q^{19} + 30q^{21} - 12q^{23} + 24q^{25} - 15q^{27} - 9q^{29} + 27q^{31} - 30q^{33} - 18q^{35} - 15q^{37} - 21q^{39} - 15q^{41} - 30q^{43} + 15q^{45} - 18q^{47} + 15q^{49} - 6q^{51} - 18q^{53} + 54q^{55} - 72q^{57} - 12q^{59} + 6q^{61} - 54q^{63} - 54q^{65} - 45q^{67} + 9q^{69} - 36q^{73} + 69q^{75} + 12q^{77} + 45q^{79} - 30q^{81} - 3q^{83} + 57q^{85} - 60q^{87} + 36q^{89} - 39q^{91} + 30q^{93} + 51q^{95} - 84q^{97} + 162q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\)

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 0
\(3\) 1.10062 + 1.33740i 0.635442 + 0.772148i
\(4\) 0 0
\(5\) 3.74067 1.36149i 1.67288 0.608879i 0.680573 0.732680i \(-0.261731\pi\)
0.992307 + 0.123801i \(0.0395085\pi\)
\(6\) 0 0
\(7\) −0.452652 2.56712i −0.171086 0.970278i −0.942565 0.334023i \(-0.891594\pi\)
0.771479 0.636255i \(-0.219517\pi\)
\(8\) 0 0
\(9\) −0.577279 + 2.94393i −0.192426 + 0.981311i
\(10\) 0 0
\(11\) −4.99402 1.81767i −1.50575 0.548050i −0.548211 0.836340i \(-0.684691\pi\)
−0.957543 + 0.288291i \(0.906913\pi\)
\(12\) 0 0
\(13\) −0.0404003 0.0338999i −0.0112050 0.00940214i 0.637168 0.770725i \(-0.280106\pi\)
−0.648373 + 0.761323i \(0.724550\pi\)
\(14\) 0 0
\(15\) 5.93792 + 3.50429i 1.53316 + 0.904805i
\(16\) 0 0
\(17\) −1.69081 + 2.92857i −0.410082 + 0.710284i −0.994898 0.100882i \(-0.967833\pi\)
0.584816 + 0.811166i \(0.301167\pi\)
\(18\) 0 0
\(19\) 1.23206 + 2.13399i 0.282653 + 0.489570i 0.972037 0.234826i \(-0.0754521\pi\)
−0.689384 + 0.724396i \(0.742119\pi\)
\(20\) 0 0
\(21\) 2.93506 3.43079i 0.640484 0.748660i
\(22\) 0 0
\(23\) −0.964125 + 5.46782i −0.201034 + 1.14012i 0.702526 + 0.711658i \(0.252055\pi\)
−0.903560 + 0.428462i \(0.859056\pi\)
\(24\) 0 0
\(25\) 8.30876 6.97187i 1.66175 1.39437i
\(26\) 0 0
\(27\) −4.57258 + 2.46810i −0.879994 + 0.474985i
\(28\) 0 0
\(29\) −6.29991 + 5.28625i −1.16986 + 0.981632i −0.999993 0.00383417i \(-0.998780\pi\)
−0.169871 + 0.985466i \(0.554335\pi\)
\(30\) 0 0
\(31\) −0.115728 + 0.656323i −0.0207853 + 0.117879i −0.993435 0.114397i \(-0.963506\pi\)
0.972650 + 0.232276i \(0.0746174\pi\)
\(32\) 0 0
\(33\) −3.06555 8.67957i −0.533644 1.51092i
\(34\) 0 0
\(35\) −5.18834 8.98646i −0.876989 1.51899i
\(36\) 0 0
\(37\) 2.67730 4.63722i 0.440145 0.762353i −0.557555 0.830140i \(-0.688260\pi\)
0.997700 + 0.0677866i \(0.0215937\pi\)
\(38\) 0 0
\(39\) 0.000872395 0.0913423i 0.000139695 0.0146265i
\(40\) 0 0
\(41\) −5.31122 4.45664i −0.829473 0.696010i 0.125697 0.992069i \(-0.459883\pi\)
−0.955170 + 0.296058i \(0.904328\pi\)
\(42\) 0 0
\(43\) −0.0524095 0.0190755i −0.00799237 0.00290898i 0.338021 0.941139i \(-0.390243\pi\)
−0.346013 + 0.938230i \(0.612465\pi\)
\(44\) 0 0
\(45\) 1.84874 + 11.7983i 0.275593 + 1.75878i
\(46\) 0 0
\(47\) −0.0794772 0.450737i −0.0115929 0.0657468i 0.978462 0.206425i \(-0.0661829\pi\)
−0.990055 + 0.140678i \(0.955072\pi\)
\(48\) 0 0
\(49\) 0.192660 0.0701224i 0.0275228 0.0100175i
\(50\) 0 0
\(51\) −5.77762 + 0.961949i −0.809028 + 0.134700i
\(52\) 0 0
\(53\) 1.38667 0.190474 0.0952370 0.995455i \(-0.469639\pi\)
0.0952370 + 0.995455i \(0.469639\pi\)
\(54\) 0 0
\(55\) −21.1558 −2.85264
\(56\) 0 0
\(57\) −1.49797 + 3.99646i −0.198411 + 0.529344i
\(58\) 0 0
\(59\) 3.99339 1.45348i 0.519895 0.189226i −0.0687257 0.997636i \(-0.521893\pi\)
0.588621 + 0.808409i \(0.299671\pi\)
\(60\) 0 0
\(61\) 0.457339 + 2.59370i 0.0585563 + 0.332089i 0.999987 0.00511752i \(-0.00162896\pi\)
−0.941431 + 0.337207i \(0.890518\pi\)
\(62\) 0 0
\(63\) 7.81873 + 0.149364i 0.985067 + 0.0188181i
\(64\) 0 0
\(65\) −0.197279 0.0718037i −0.0244694 0.00890615i
\(66\) 0 0
\(67\) 7.16941 + 6.01585i 0.875882 + 0.734953i 0.965328 0.261039i \(-0.0840651\pi\)
−0.0894458 + 0.995992i \(0.528510\pi\)
\(68\) 0 0
\(69\) −8.37380 + 4.72856i −1.00809 + 0.569252i
\(70\) 0 0
\(71\) 7.18697 12.4482i 0.852937 1.47733i −0.0256094 0.999672i \(-0.508153\pi\)
0.878546 0.477658i \(-0.158514\pi\)
\(72\) 0 0
\(73\) −7.15357 12.3903i −0.837262 1.45018i −0.892176 0.451689i \(-0.850822\pi\)
0.0549141 0.998491i \(-0.482512\pi\)
\(74\) 0 0
\(75\) 18.4690 + 3.43876i 2.13261 + 0.397074i
\(76\) 0 0
\(77\) −2.40563 + 13.6430i −0.274147 + 1.55476i
\(78\) 0 0
\(79\) 5.93415 4.97935i 0.667644 0.560220i −0.244723 0.969593i \(-0.578697\pi\)
0.912367 + 0.409373i \(0.134253\pi\)
\(80\) 0 0
\(81\) −8.33350 3.39894i −0.925944 0.377660i
\(82\) 0 0
\(83\) 1.83808 1.54234i 0.201756 0.169293i −0.536312 0.844020i \(-0.680183\pi\)
0.738068 + 0.674727i \(0.235738\pi\)
\(84\) 0 0
\(85\) −2.33755 + 13.2569i −0.253542 + 1.43791i
\(86\) 0 0
\(87\) −14.0036 2.60735i −1.50135 0.279538i
\(88\) 0 0
\(89\) 2.04047 + 3.53420i 0.216290 + 0.374625i 0.953671 0.300852i \(-0.0972711\pi\)
−0.737381 + 0.675477i \(0.763938\pi\)
\(90\) 0 0
\(91\) −0.0687377 + 0.119057i −0.00720567 + 0.0124806i
\(92\) 0 0
\(93\) −1.00514 + 0.567588i −0.104228 + 0.0588561i
\(94\) 0 0
\(95\) 7.51413 + 6.30511i 0.770934 + 0.646890i
\(96\) 0 0
\(97\) −11.8711 4.32074i −1.20533 0.438705i −0.340250 0.940335i \(-0.610512\pi\)
−0.865082 + 0.501630i \(0.832734\pi\)
\(98\) 0 0
\(99\) 8.23406 13.6528i 0.827554 1.37215i
\(100\) 0 0
\(101\) 1.52514 + 8.64948i 0.151757 + 0.860655i 0.961691 + 0.274135i \(0.0883915\pi\)
−0.809934 + 0.586520i \(0.800497\pi\)
\(102\) 0 0
\(103\) 6.59095 2.39891i 0.649426 0.236372i 0.00376127 0.999993i \(-0.498803\pi\)
0.645664 + 0.763621i \(0.276581\pi\)
\(104\) 0 0
\(105\) 6.30812 16.8295i 0.615609 1.64240i
\(106\) 0 0
\(107\) −9.10320 −0.880040 −0.440020 0.897988i \(-0.645029\pi\)
−0.440020 + 0.897988i \(0.645029\pi\)
\(108\) 0 0
\(109\) 14.5496 1.39360 0.696801 0.717264i \(-0.254606\pi\)
0.696801 + 0.717264i \(0.254606\pi\)
\(110\) 0 0
\(111\) 9.14850 1.52319i 0.868337 0.144574i
\(112\) 0 0
\(113\) 14.0868 5.12716i 1.32517 0.482323i 0.420059 0.907497i \(-0.362009\pi\)
0.905112 + 0.425174i \(0.139787\pi\)
\(114\) 0 0
\(115\) 3.83793 + 21.7660i 0.357889 + 2.02969i
\(116\) 0 0
\(117\) 0.123121 0.0993662i 0.0113826 0.00918641i
\(118\) 0 0
\(119\) 8.28334 + 3.01489i 0.759332 + 0.276374i
\(120\) 0 0
\(121\) 13.2098 + 11.0843i 1.20089 + 1.00767i
\(122\) 0 0
\(123\) 0.114689 12.0083i 0.0103412 1.08275i
\(124\) 0 0
\(125\) 11.6363 20.1547i 1.04079 1.80269i
\(126\) 0 0
\(127\) −1.00053 1.73296i −0.0887824 0.153776i 0.818214 0.574913i \(-0.194964\pi\)
−0.906997 + 0.421138i \(0.861631\pi\)
\(128\) 0 0
\(129\) −0.0321713 0.0910872i −0.00283252 0.00801978i
\(130\) 0 0
\(131\) 0.156341 0.886652i 0.0136595 0.0774671i −0.977216 0.212247i \(-0.931922\pi\)
0.990876 + 0.134780i \(0.0430328\pi\)
\(132\) 0 0
\(133\) 4.92049 4.12878i 0.426661 0.358011i
\(134\) 0 0
\(135\) −13.7442 + 15.4579i −1.18292 + 1.33040i
\(136\) 0 0
\(137\) −10.5185 + 8.82610i −0.898659 + 0.754065i −0.969928 0.243393i \(-0.921740\pi\)
0.0712687 + 0.997457i \(0.477295\pi\)
\(138\) 0 0
\(139\) 0.00441448 0.0250358i 0.000374432 0.00212351i −0.984620 0.174710i \(-0.944101\pi\)
0.984994 + 0.172586i \(0.0552124\pi\)
\(140\) 0 0
\(141\) 0.515342 0.602383i 0.0433996 0.0507298i
\(142\) 0 0
\(143\) 0.140141 + 0.242731i 0.0117192 + 0.0202982i
\(144\) 0 0
\(145\) −16.3687 + 28.3514i −1.35935 + 2.35446i
\(146\) 0 0
\(147\) 0.305827 + 0.180485i 0.0252241 + 0.0148862i
\(148\) 0 0
\(149\) 9.35550 + 7.85019i 0.766432 + 0.643113i 0.939793 0.341746i \(-0.111018\pi\)
−0.173360 + 0.984858i \(0.555463\pi\)
\(150\) 0 0
\(151\) 2.76321 + 1.00573i 0.224867 + 0.0818448i 0.451996 0.892020i \(-0.350712\pi\)
−0.227130 + 0.973864i \(0.572934\pi\)
\(152\) 0 0
\(153\) −7.64546 6.66825i −0.618099 0.539096i
\(154\) 0 0
\(155\) 0.460682 + 2.61265i 0.0370028 + 0.209853i
\(156\) 0 0
\(157\) −11.3273 + 4.12280i −0.904016 + 0.329035i −0.751861 0.659322i \(-0.770844\pi\)
−0.152155 + 0.988357i \(0.548621\pi\)
\(158\) 0 0
\(159\) 1.52620 + 1.85453i 0.121035 + 0.147074i
\(160\) 0 0
\(161\) 14.4729 1.14063
\(162\) 0 0
\(163\) −10.3746 −0.812605 −0.406302 0.913739i \(-0.633182\pi\)
−0.406302 + 0.913739i \(0.633182\pi\)
\(164\) 0 0
\(165\) −23.2844 28.2937i −1.81269 2.20266i
\(166\) 0 0
\(167\) −4.57455 + 1.66500i −0.353989 + 0.128842i −0.512893 0.858453i \(-0.671426\pi\)
0.158904 + 0.987294i \(0.449204\pi\)
\(168\) 0 0
\(169\) −2.25694 12.7998i −0.173611 0.984597i
\(170\) 0 0
\(171\) −6.99355 + 2.39519i −0.534810 + 0.183165i
\(172\) 0 0
\(173\) −14.4101 5.24484i −1.09558 0.398758i −0.269894 0.962890i \(-0.586989\pi\)
−0.825685 + 0.564132i \(0.809211\pi\)
\(174\) 0 0
\(175\) −21.6586 18.1737i −1.63723 1.37380i
\(176\) 0 0
\(177\) 6.33908 + 3.74104i 0.476474 + 0.281194i
\(178\) 0 0
\(179\) −8.10111 + 14.0315i −0.605505 + 1.04877i 0.386466 + 0.922304i \(0.373696\pi\)
−0.991971 + 0.126462i \(0.959638\pi\)
\(180\) 0 0
\(181\) 4.93187 + 8.54226i 0.366583 + 0.634941i 0.989029 0.147722i \(-0.0471941\pi\)
−0.622446 + 0.782663i \(0.713861\pi\)
\(182\) 0 0
\(183\) −2.96546 + 3.46632i −0.219213 + 0.256238i
\(184\) 0 0
\(185\) 3.70136 20.9914i 0.272129 1.54332i
\(186\) 0 0
\(187\) 13.7672 11.5520i 1.00675 0.844767i
\(188\) 0 0
\(189\) 8.40567 + 10.6212i 0.611423 + 0.772576i
\(190\) 0 0
\(191\) 10.4067 8.73226i 0.753003 0.631844i −0.183293 0.983058i \(-0.558676\pi\)
0.936295 + 0.351214i \(0.114231\pi\)
\(192\) 0 0
\(193\) −0.599757 + 3.40139i −0.0431715 + 0.244838i −0.998755 0.0498825i \(-0.984115\pi\)
0.955584 + 0.294720i \(0.0952264\pi\)
\(194\) 0 0
\(195\) −0.121099 0.342869i −0.00867205 0.0245534i
\(196\) 0 0
\(197\) −0.413665 0.716488i −0.0294724 0.0510477i 0.850913 0.525307i \(-0.176049\pi\)
−0.880385 + 0.474259i \(0.842716\pi\)
\(198\) 0 0
\(199\) 1.28337 2.22286i 0.0909755 0.157574i −0.816946 0.576714i \(-0.804335\pi\)
0.907922 + 0.419139i \(0.137668\pi\)
\(200\) 0 0
\(201\) −0.154814 + 16.2095i −0.0109198 + 1.14333i
\(202\) 0 0
\(203\) 16.4221 + 13.7798i 1.15260 + 0.967150i
\(204\) 0 0
\(205\) −25.9352 9.43965i −1.81139 0.659294i
\(206\) 0 0
\(207\) −15.5403 5.99478i −1.08013 0.416666i
\(208\) 0 0
\(209\) −2.27403 12.8966i −0.157298 0.892080i
\(210\) 0 0
\(211\) −16.6574 + 6.06281i −1.14674 + 0.417381i −0.844345 0.535801i \(-0.820010\pi\)
−0.302400 + 0.953181i \(0.597788\pi\)
\(212\) 0 0
\(213\) 24.5583 4.08886i 1.68271 0.280164i
\(214\) 0 0
\(215\) −0.222018 −0.0151415
\(216\) 0 0
\(217\) 1.73724 0.117932
\(218\) 0 0
\(219\) 8.69750 23.2042i 0.587722 1.56800i
\(220\) 0 0
\(221\) 0.167588 0.0609970i 0.0112732 0.00410310i
\(222\) 0 0
\(223\) 3.62276 + 20.5457i 0.242598 + 1.37584i 0.826005 + 0.563663i \(0.190608\pi\)
−0.583407 + 0.812180i \(0.698281\pi\)
\(224\) 0 0
\(225\) 15.7283 + 28.4851i 1.04855 + 1.89901i
\(226\) 0 0
\(227\) −3.39434 1.23544i −0.225290 0.0819989i 0.226909 0.973916i \(-0.427138\pi\)
−0.452199 + 0.891917i \(0.649360\pi\)
\(228\) 0 0
\(229\) −3.11755 2.61593i −0.206013 0.172866i 0.533943 0.845520i \(-0.320710\pi\)
−0.739957 + 0.672655i \(0.765154\pi\)
\(230\) 0 0
\(231\) −20.8938 + 11.7984i −1.37471 + 0.776281i
\(232\) 0 0
\(233\) −12.2458 + 21.2104i −0.802252 + 1.38954i 0.115879 + 0.993263i \(0.463031\pi\)
−0.918131 + 0.396277i \(0.870302\pi\)
\(234\) 0 0
\(235\) −0.910974 1.57785i −0.0594254 0.102928i
\(236\) 0 0
\(237\) 13.1906 + 2.45598i 0.856823 + 0.159533i
\(238\) 0 0
\(239\) 3.92957 22.2857i 0.254183 1.44154i −0.543978 0.839100i \(-0.683082\pi\)
0.798161 0.602444i \(-0.205806\pi\)
\(240\) 0 0
\(241\) 8.75006 7.34218i 0.563641 0.472951i −0.315888 0.948797i \(-0.602302\pi\)
0.879529 + 0.475845i \(0.157858\pi\)
\(242\) 0 0
\(243\) −4.62626 14.8862i −0.296774 0.954948i
\(244\) 0 0
\(245\) 0.625206 0.524610i 0.0399429 0.0335161i
\(246\) 0 0
\(247\) 0.0225664 0.127980i 0.00143586 0.00814319i
\(248\) 0 0
\(249\) 4.08575 + 0.760731i 0.258924 + 0.0482094i
\(250\) 0 0
\(251\) 1.27111 + 2.20163i 0.0802317 + 0.138965i 0.903349 0.428905i \(-0.141101\pi\)
−0.823118 + 0.567871i \(0.807767\pi\)
\(252\) 0 0
\(253\) 14.7536 25.5540i 0.927550 1.60656i
\(254\) 0 0
\(255\) −20.3025 + 11.4645i −1.27139 + 0.717937i
\(256\) 0 0
\(257\) −13.7955 11.5758i −0.860539 0.722078i 0.101545 0.994831i \(-0.467621\pi\)
−0.962084 + 0.272753i \(0.912066\pi\)
\(258\) 0 0
\(259\) −13.1162 4.77389i −0.814998 0.296635i
\(260\) 0 0
\(261\) −11.9256 21.5982i −0.738174 1.33689i
\(262\) 0 0
\(263\) 0.130638 + 0.740886i 0.00805550 + 0.0456850i 0.988571 0.150759i \(-0.0481717\pi\)
−0.980515 + 0.196444i \(0.937061\pi\)
\(264\) 0 0
\(265\) 5.18709 1.88795i 0.318640 0.115976i
\(266\) 0 0
\(267\) −2.48086 + 6.61874i −0.151826 + 0.405060i
\(268\) 0 0
\(269\) 0.748703 0.0456493 0.0228246 0.999739i \(-0.492734\pi\)
0.0228246 + 0.999739i \(0.492734\pi\)
\(270\) 0 0
\(271\) 28.7361 1.74559 0.872795 0.488086i \(-0.162305\pi\)
0.872795 + 0.488086i \(0.162305\pi\)
\(272\) 0 0
\(273\) −0.234881 + 0.0391067i −0.0142156 + 0.00236684i
\(274\) 0 0
\(275\) −54.1667 + 19.7151i −3.26638 + 1.18886i
\(276\) 0 0
\(277\) 2.02567 + 11.4881i 0.121711 + 0.690255i 0.983207 + 0.182492i \(0.0584163\pi\)
−0.861497 + 0.507763i \(0.830473\pi\)
\(278\) 0 0
\(279\) −1.86537 0.719576i −0.111677 0.0430799i
\(280\) 0 0
\(281\) −7.59722 2.76516i −0.453212 0.164956i 0.105320 0.994438i \(-0.466413\pi\)
−0.558533 + 0.829483i \(0.688635\pi\)
\(282\) 0 0
\(283\) 24.9217 + 20.9118i 1.48144 + 1.24308i 0.904628 + 0.426201i \(0.140148\pi\)
0.576813 + 0.816876i \(0.304296\pi\)
\(284\) 0 0
\(285\) −0.162258 + 16.9889i −0.00961136 + 1.00634i
\(286\) 0 0
\(287\) −9.03658 + 15.6518i −0.533412 + 0.923897i
\(288\) 0 0
\(289\) 2.78230 + 4.81909i 0.163665 + 0.283476i
\(290\) 0 0
\(291\) −7.28704 20.6320i −0.427174 1.20947i
\(292\) 0 0
\(293\) 0.929693 5.27255i 0.0543132 0.308026i −0.945534 0.325524i \(-0.894459\pi\)
0.999847 + 0.0174987i \(0.00557030\pi\)
\(294\) 0 0
\(295\) 12.9591 10.8740i 0.754506 0.633106i
\(296\) 0 0
\(297\) 27.3218 4.01425i 1.58537 0.232930i
\(298\) 0 0
\(299\) 0.224310 0.188218i 0.0129722 0.0108849i
\(300\) 0 0
\(301\) −0.0252457 + 0.143176i −0.00145514 + 0.00825251i
\(302\) 0 0
\(303\) −9.88922 + 11.5595i −0.568121 + 0.664076i
\(304\) 0 0
\(305\) 5.24206 + 9.07952i 0.300160 + 0.519892i
\(306\) 0 0
\(307\) −3.29583 + 5.70854i −0.188103 + 0.325804i −0.944618 0.328173i \(-0.893567\pi\)
0.756515 + 0.653977i \(0.226900\pi\)
\(308\) 0 0
\(309\) 10.4624 + 6.17445i 0.595186 + 0.351252i
\(310\) 0 0
\(311\) 20.3382 + 17.0658i 1.15327 + 0.967712i 0.999791 0.0204396i \(-0.00650659\pi\)
0.153483 + 0.988151i \(0.450951\pi\)
\(312\) 0 0
\(313\) 17.9416 + 6.53022i 1.01412 + 0.369110i 0.795014 0.606591i \(-0.207463\pi\)
0.219107 + 0.975701i \(0.429686\pi\)
\(314\) 0 0
\(315\) 29.4507 10.0864i 1.65936 0.568306i
\(316\) 0 0
\(317\) −1.36707 7.75306i −0.0767825 0.435455i −0.998829 0.0483765i \(-0.984595\pi\)
0.922047 0.387079i \(-0.126516\pi\)
\(318\) 0 0
\(319\) 41.0706 14.9485i 2.29951 0.836953i
\(320\) 0 0
\(321\) −10.0192 12.1746i −0.559214 0.679521i
\(322\) 0 0
\(323\) −8.33271 −0.463645
\(324\) 0 0
\(325\) −0.572022 −0.0317301
\(326\) 0 0
\(327\) 16.0136 + 19.4587i 0.885554 + 1.07607i
\(328\) 0 0
\(329\) −1.12112 + 0.408054i −0.0618093 + 0.0224967i
\(330\) 0 0
\(331\) 1.21881 + 6.91220i 0.0669917 + 0.379929i 0.999808 + 0.0195775i \(0.00623212\pi\)
−0.932817 + 0.360351i \(0.882657\pi\)
\(332\) 0 0
\(333\) 12.1061 + 10.5588i 0.663411 + 0.578616i
\(334\) 0 0
\(335\) 35.0090 + 12.7422i 1.91274 + 0.696182i
\(336\) 0 0
\(337\) −27.0600 22.7060i −1.47405 1.23688i −0.912269 0.409592i \(-0.865671\pi\)
−0.561783 0.827284i \(-0.689885\pi\)
\(338\) 0 0
\(339\) 22.3612 + 13.1966i 1.21449 + 0.716740i
\(340\) 0 0
\(341\) 1.77093 3.06734i 0.0959011 0.166106i
\(342\) 0 0
\(343\) −9.39073 16.2652i −0.507052 0.878240i
\(344\) 0 0
\(345\) −24.8857 + 29.0889i −1.33980 + 1.56609i
\(346\) 0 0
\(347\) −0.838421 + 4.75492i −0.0450088 + 0.255258i −0.999007 0.0445550i \(-0.985813\pi\)
0.953998 + 0.299813i \(0.0969241\pi\)
\(348\) 0 0
\(349\) −14.1473 + 11.8710i −0.757288 + 0.635440i −0.937419 0.348203i \(-0.886792\pi\)
0.180131 + 0.983643i \(0.442348\pi\)
\(350\) 0 0
\(351\) 0.268402 + 0.0552982i 0.0143262 + 0.00295160i
\(352\) 0 0
\(353\) 14.8590 12.4682i 0.790867 0.663616i −0.155093 0.987900i \(-0.549568\pi\)
0.945960 + 0.324284i \(0.105123\pi\)
\(354\) 0 0
\(355\) 9.93597 56.3497i 0.527347 2.99073i
\(356\) 0 0
\(357\) 5.08468 + 14.3964i 0.269110 + 0.761937i
\(358\) 0 0
\(359\) −9.99948 17.3196i −0.527752 0.914094i −0.999477 0.0323477i \(-0.989702\pi\)
0.471724 0.881746i \(-0.343632\pi\)
\(360\) 0 0
\(361\) 6.46407 11.1961i 0.340214 0.589268i
\(362\) 0 0
\(363\) −0.285249 + 29.8664i −0.0149717 + 1.56758i
\(364\) 0 0
\(365\) −43.6285 36.6087i −2.28362 1.91619i
\(366\) 0 0
\(367\) −34.6495 12.6114i −1.80869 0.658309i −0.997270 0.0738470i \(-0.976472\pi\)
−0.811421 0.584462i \(-0.801305\pi\)
\(368\) 0 0
\(369\) 16.1861 13.0632i 0.842615 0.680041i
\(370\) 0 0
\(371\) −0.627679 3.55975i −0.0325875 0.184813i
\(372\) 0 0
\(373\) −8.12357 + 2.95674i −0.420623 + 0.153094i −0.543655 0.839309i \(-0.682960\pi\)
0.123033 + 0.992403i \(0.460738\pi\)
\(374\) 0 0
\(375\) 39.7621 6.62022i 2.05331 0.341867i
\(376\) 0 0
\(377\) 0.433722 0.0223378
\(378\) 0 0
\(379\) 5.55752 0.285471 0.142735 0.989761i \(-0.454410\pi\)
0.142735 + 0.989761i \(0.454410\pi\)
\(380\) 0 0
\(381\) 1.21647 3.24544i 0.0623215 0.166269i
\(382\) 0 0
\(383\) −6.70080 + 2.43889i −0.342395 + 0.124622i −0.507494 0.861656i \(-0.669428\pi\)
0.165099 + 0.986277i \(0.447206\pi\)
\(384\) 0 0
\(385\) 9.57619 + 54.3093i 0.488048 + 2.76786i
\(386\) 0 0
\(387\) 0.0864118 0.143278i 0.00439256 0.00728324i
\(388\) 0 0
\(389\) 28.6659 + 10.4335i 1.45342 + 0.529002i 0.943544 0.331246i \(-0.107469\pi\)
0.509876 + 0.860248i \(0.329691\pi\)
\(390\) 0 0
\(391\) −14.3828 12.0686i −0.727368 0.610334i
\(392\) 0 0
\(393\) 1.35788 0.766775i 0.0684960 0.0386787i
\(394\) 0 0
\(395\) 15.4184 26.7054i 0.775783 1.34370i
\(396\) 0 0
\(397\) 3.04665 + 5.27696i 0.152907 + 0.264843i 0.932295 0.361699i \(-0.117803\pi\)
−0.779388 + 0.626542i \(0.784470\pi\)
\(398\) 0 0
\(399\) 10.9374 + 2.03645i 0.547556 + 0.101950i
\(400\) 0 0
\(401\) −2.45733 + 13.9362i −0.122713 + 0.695941i 0.859927 + 0.510418i \(0.170509\pi\)
−0.982640 + 0.185523i \(0.940602\pi\)
\(402\) 0 0
\(403\) 0.0269247 0.0225925i 0.00134122 0.00112541i
\(404\) 0 0
\(405\) −35.8005 1.36832i −1.77894 0.0679926i
\(406\) 0 0
\(407\) −21.7994 + 18.2919i −1.08056 + 0.906695i
\(408\) 0 0
\(409\) 2.50869 14.2275i 0.124047 0.703503i −0.857823 0.513945i \(-0.828184\pi\)
0.981870 0.189558i \(-0.0607054\pi\)
\(410\) 0 0
\(411\) −23.3809 4.35333i −1.15330 0.214734i
\(412\) 0 0
\(413\) −5.53885 9.59358i −0.272549 0.472069i
\(414\) 0 0
\(415\) 4.77579 8.27192i 0.234435 0.406053i
\(416\) 0 0
\(417\) 0.0383415 0.0216509i 0.00187759 0.00106025i
\(418\) 0 0
\(419\) −17.6121 14.7783i −0.860405 0.721966i 0.101650 0.994820i \(-0.467588\pi\)
−0.962055 + 0.272855i \(0.912032\pi\)
\(420\) 0 0
\(421\) −29.3391 10.6785i −1.42990 0.520441i −0.492996 0.870031i \(-0.664098\pi\)
−0.936902 + 0.349591i \(0.886321\pi\)
\(422\) 0 0
\(423\) 1.37282 + 0.0262256i 0.0667489 + 0.00127513i
\(424\) 0 0
\(425\) 6.36910 + 36.1210i 0.308947 + 1.75212i
\(426\) 0 0
\(427\) 6.45131 2.34809i 0.312201 0.113632i
\(428\) 0 0
\(429\) −0.170387 + 0.454579i −0.00822638 + 0.0219473i
\(430\) 0 0
\(431\) 11.9923 0.577649 0.288825 0.957382i \(-0.406736\pi\)
0.288825 + 0.957382i \(0.406736\pi\)
\(432\) 0 0
\(433\) −6.69798 −0.321885 −0.160942 0.986964i \(-0.551453\pi\)
−0.160942 + 0.986964i \(0.551453\pi\)
\(434\) 0 0
\(435\) −55.9329 + 9.31259i −2.68178 + 0.446505i
\(436\) 0 0
\(437\) −12.8561 + 4.67924i −0.614991 + 0.223838i
\(438\) 0 0
\(439\) −1.65291 9.37410i −0.0788889 0.447401i −0.998509 0.0545918i \(-0.982614\pi\)
0.919620 0.392810i \(-0.128497\pi\)
\(440\) 0 0
\(441\) 0.0952174 + 0.607658i 0.00453416 + 0.0289361i
\(442\) 0 0
\(443\) −14.1355 5.14490i −0.671598 0.244442i −0.0163624 0.999866i \(-0.505209\pi\)
−0.655236 + 0.755424i \(0.727431\pi\)
\(444\) 0 0
\(445\) 12.4445 + 10.4422i 0.589928 + 0.495008i
\(446\) 0 0
\(447\) −0.202020 + 21.1521i −0.00955523 + 1.00046i
\(448\) 0 0
\(449\) −11.1437 + 19.3014i −0.525902 + 0.910889i 0.473642 + 0.880717i \(0.342939\pi\)
−0.999545 + 0.0301722i \(0.990394\pi\)
\(450\) 0 0
\(451\) 18.4236 + 31.9106i 0.867534 + 1.50261i
\(452\) 0 0
\(453\) 1.69618 + 4.80243i 0.0796935 + 0.225638i
\(454\) 0 0
\(455\) −0.0950297 + 0.538940i −0.00445506 + 0.0252659i
\(456\) 0 0
\(457\) −14.9820 + 12.5714i −0.700830 + 0.588066i −0.922010 0.387167i \(-0.873454\pi\)
0.221179 + 0.975233i \(0.429009\pi\)
\(458\) 0 0
\(459\) 0.503382 17.5642i 0.0234959 0.819828i
\(460\) 0 0
\(461\) 30.9993 26.0115i 1.44378 1.21148i 0.506814 0.862055i \(-0.330823\pi\)
0.936966 0.349420i \(-0.113621\pi\)
\(462\) 0 0
\(463\) −2.40694 + 13.6505i −0.111860 + 0.634390i 0.876397 + 0.481590i \(0.159940\pi\)
−0.988257 + 0.152801i \(0.951171\pi\)
\(464\) 0 0
\(465\) −2.98713 + 3.49165i −0.138525 + 0.161921i
\(466\) 0 0
\(467\) 15.8137 + 27.3901i 0.731769 + 1.26746i 0.956126 + 0.292955i \(0.0946385\pi\)
−0.224357 + 0.974507i \(0.572028\pi\)
\(468\) 0 0
\(469\) 12.1981 21.1278i 0.563257 0.975590i
\(470\) 0 0
\(471\) −17.9809 10.6115i −0.828514 0.488952i
\(472\) 0 0
\(473\) 0.227061 + 0.190527i 0.0104403 + 0.00876043i
\(474\) 0 0
\(475\) 25.1147 + 9.14102i 1.15234 + 0.419419i
\(476\) 0 0
\(477\) −0.800496 + 4.08227i −0.0366522 + 0.186914i
\(478\) 0 0
\(479\) −6.33650 35.9361i −0.289522 1.64196i −0.688669 0.725076i \(-0.741805\pi\)
0.399147 0.916887i \(-0.369306\pi\)
\(480\) 0 0
\(481\) −0.265365 + 0.0965849i −0.0120996 + 0.00440389i
\(482\) 0 0
\(483\) 15.9292 + 19.3561i 0.724803 + 0.880734i
\(484\) 0 0
\(485\) −50.2887 −2.28349
\(486\) 0 0
\(487\) 0.637186 0.0288737 0.0144368 0.999896i \(-0.495404\pi\)
0.0144368 + 0.999896i \(0.495404\pi\)
\(488\) 0 0
\(489\) −11.4185 13.8751i −0.516364 0.627452i
\(490\) 0 0
\(491\) 16.6019 6.04262i 0.749235 0.272699i 0.0609515 0.998141i \(-0.480587\pi\)
0.688284 + 0.725441i \(0.258364\pi\)
\(492\) 0 0
\(493\) −4.82921 27.3878i −0.217497 1.23349i
\(494\) 0 0
\(495\) 12.2128 62.2812i 0.548923 2.79933i
\(496\) 0 0
\(497\) −35.2092 12.8151i −1.57935 0.574835i
\(498\) 0 0
\(499\) −7.39153 6.20223i −0.330891 0.277650i 0.462172 0.886790i \(-0.347070\pi\)
−0.793063 + 0.609140i \(0.791515\pi\)
\(500\) 0 0
\(501\) −7.26160 4.28547i −0.324424 0.191461i
\(502\) 0 0
\(503\) −12.0802 + 20.9235i −0.538628 + 0.932931i 0.460351 + 0.887737i \(0.347724\pi\)
−0.998978 + 0.0451934i \(0.985610\pi\)
\(504\) 0 0
\(505\) 17.4813 + 30.2784i 0.777906 + 1.34737i
\(506\) 0 0
\(507\) 14.6344 17.1061i 0.649935 0.759708i
\(508\) 0 0
\(509\) −3.31124 + 18.7790i −0.146768 + 0.832362i 0.819163 + 0.573561i \(0.194439\pi\)
−0.965931 + 0.258801i \(0.916673\pi\)
\(510\) 0 0
\(511\) −28.5694 + 23.9725i −1.26383 + 1.06048i
\(512\) 0 0
\(513\) −10.9006 6.71699i −0.481272 0.296562i
\(514\) 0 0
\(515\) 21.3885 17.9471i 0.942490 0.790843i
\(516\) 0 0
\(517\) −0.422383 + 2.39546i −0.0185764 + 0.105352i
\(518\) 0 0
\(519\) −8.84555 25.0446i −0.388277 1.09934i
\(520\) 0 0
\(521\) 14.4319 + 24.9968i 0.632273 + 1.09513i 0.987086 + 0.160191i \(0.0512111\pi\)
−0.354813 + 0.934937i \(0.615456\pi\)
\(522\) 0 0
\(523\) −7.76804 + 13.4546i −0.339673 + 0.588330i −0.984371 0.176107i \(-0.943650\pi\)
0.644698 + 0.764437i \(0.276983\pi\)
\(524\) 0 0
\(525\) 0.467690 48.9685i 0.0204117 2.13716i
\(526\) 0 0
\(527\) −1.72642 1.44864i −0.0752040 0.0631036i
\(528\) 0 0
\(529\) −7.35461 2.67686i −0.319766 0.116385i
\(530\) 0 0
\(531\) 1.97364 + 12.5953i 0.0856485 + 0.546591i
\(532\) 0 0
\(533\) 0.0634953 + 0.360100i 0.00275028 + 0.0155976i
\(534\) 0 0
\(535\) −34.0521 + 12.3940i −1.47220 + 0.535837i
\(536\) 0 0
\(537\) −27.6820 + 4.60894i −1.19457 + 0.198890i
\(538\) 0 0
\(539\) −1.08961 −0.0469327
\(540\) 0 0
\(541\) −6.78149 −0.291559 −0.145779 0.989317i \(-0.546569\pi\)
−0.145779 + 0.989317i \(0.546569\pi\)
\(542\) 0 0
\(543\) −5.99631 + 15.9977i −0.257326 + 0.686525i
\(544\) 0 0
\(545\) 54.4255 19.8092i 2.33133 0.848535i
\(546\) 0 0
\(547\) 1.14447 + 6.49059i 0.0489339 + 0.277518i 0.999450 0.0331570i \(-0.0105561\pi\)
−0.950516 + 0.310675i \(0.899445\pi\)
\(548\) 0 0
\(549\) −7.89969 0.150911i −0.337151 0.00644073i
\(550\) 0 0
\(551\) −19.0426 6.93095i −0.811243 0.295268i
\(552\) 0 0
\(553\) −15.4687 12.9797i −0.657794 0.551955i
\(554\) 0 0
\(555\) 32.1477 18.1534i 1.36460 0.770567i
\(556\) 0 0
\(557\) 0.421123 0.729407i 0.0178436 0.0309060i −0.856966 0.515373i \(-0.827653\pi\)
0.874809 + 0.484467i \(0.160987\pi\)
\(558\) 0 0
\(559\) 0.00147070 + 0.00254733i 6.22041e−5 + 0.000107741i
\(560\) 0 0
\(561\) 30.6020 + 5.69784i 1.29202 + 0.240563i
\(562\) 0 0
\(563\) 7.13172 40.4460i 0.300566 1.70460i −0.343108 0.939296i \(-0.611480\pi\)
0.643674 0.765300i \(-0.277409\pi\)
\(564\) 0 0
\(565\) 45.7134 38.3581i 1.92318 1.61374i
\(566\) 0 0
\(567\) −4.95330 + 22.9316i −0.208019 + 0.963036i
\(568\) 0 0
\(569\) −13.5383 + 11.3600i −0.567555 + 0.476235i −0.880834 0.473426i \(-0.843017\pi\)
0.313278 + 0.949661i \(0.398573\pi\)
\(570\) 0 0
\(571\) −7.49724 + 42.5189i −0.313750 + 1.77936i 0.265397 + 0.964139i \(0.414497\pi\)
−0.579147 + 0.815223i \(0.696614\pi\)
\(572\) 0 0
\(573\) 23.1323 + 4.30704i 0.966367 + 0.179929i
\(574\) 0 0
\(575\) 30.1103 + 52.1526i 1.25569 + 2.17491i
\(576\) 0 0
\(577\) 8.83839 15.3085i 0.367947 0.637303i −0.621297 0.783575i \(-0.713394\pi\)
0.989244 + 0.146272i \(0.0467275\pi\)
\(578\) 0 0
\(579\) −5.20913 + 2.94152i −0.216484 + 0.122245i
\(580\) 0 0
\(581\) −4.79137 4.02043i −0.198779 0.166796i
\(582\) 0 0
\(583\) −6.92507 2.52052i −0.286807 0.104389i
\(584\) 0 0
\(585\) 0.325270 0.539326i 0.0134483 0.0222984i
\(586\) 0 0
\(587\) 2.91945 + 16.5570i 0.120499 + 0.683381i 0.983880 + 0.178830i \(0.0572311\pi\)
−0.863381 + 0.504552i \(0.831658\pi\)
\(588\) 0 0
\(589\) −1.54317 + 0.561667i −0.0635851 + 0.0231431i
\(590\) 0 0
\(591\) 0.502945 1.34182i 0.0206884 0.0551949i
\(592\) 0 0
\(593\) 30.6747 1.25966 0.629829 0.776734i \(-0.283125\pi\)
0.629829 + 0.776734i \(0.283125\pi\)
\(594\) 0 0
\(595\) 35.0900 1.43855
\(596\) 0 0
\(597\) 4.38535 0.730142i 0.179480 0.0298827i
\(598\) 0 0
\(599\) 10.8656 3.95476i 0.443957 0.161587i −0.110362 0.993891i \(-0.535201\pi\)
0.554319 + 0.832304i \(0.312979\pi\)
\(600\) 0 0
\(601\) 5.36971 + 30.4531i 0.219035 + 1.24221i 0.873766 + 0.486347i \(0.161671\pi\)
−0.654731 + 0.755862i \(0.727218\pi\)
\(602\) 0 0
\(603\) −21.8490 + 17.6334i −0.889760 + 0.718089i
\(604\) 0 0
\(605\) 64.5049 + 23.4779i 2.62250 + 0.954511i
\(606\) 0 0
\(607\) −12.3480 10.3612i −0.501190 0.420549i 0.356826 0.934171i \(-0.383859\pi\)
−0.858016 + 0.513622i \(0.828303\pi\)
\(608\) 0 0
\(609\) −0.354614 + 37.1292i −0.0143697 + 1.50455i
\(610\) 0 0
\(611\) −0.0120690 + 0.0209042i −0.000488261 + 0.000845694i
\(612\) 0 0
\(613\) 7.76761 + 13.4539i 0.313731 + 0.543398i 0.979167 0.203057i \(-0.0650877\pi\)
−0.665436 + 0.746455i \(0.731754\pi\)
\(614\) 0 0
\(615\) −15.9202 45.0752i −0.641964 1.81761i
\(616\) 0 0
\(617\) −5.72338 + 32.4589i −0.230415 + 1.30675i 0.621644 + 0.783300i \(0.286465\pi\)
−0.852059 + 0.523446i \(0.824646\pi\)
\(618\) 0 0
\(619\) −19.0195 + 15.9593i −0.764460 + 0.641458i −0.939284 0.343142i \(-0.888509\pi\)
0.174824 + 0.984600i \(0.444064\pi\)
\(620\) 0 0
\(621\) −9.08657 27.3816i −0.364631 1.09879i
\(622\) 0 0
\(623\) 8.14908 6.83789i 0.326486 0.273954i
\(624\) 0 0
\(625\) 6.66999 37.8274i 0.266799 1.51309i
\(626\) 0 0
\(627\) 14.7451 17.2356i 0.588864 0.688322i
\(628\) 0 0
\(629\) 9.05362 + 15.6813i 0.360991 + 0.625256i
\(630\) 0 0
\(631\) −19.5573 + 33.8742i −0.778563 + 1.34851i 0.154207 + 0.988039i \(0.450718\pi\)
−0.932770 + 0.360472i \(0.882616\pi\)
\(632\) 0 0
\(633\) −26.4419 15.6048i −1.05097 0.620235i
\(634\) 0 0
\(635\) −6.10206 5.12024i −0.242153 0.203191i
\(636\) 0 0
\(637\) −0.0101607 0.00369818i −0.000402580 0.000146527i
\(638\) 0 0
\(639\) 32.4978 + 28.3441i 1.28559 + 1.12127i
\(640\) 0 0
\(641\) −8.31018 47.1293i −0.328232 1.86150i −0.485913 0.874007i \(-0.661513\pi\)
0.157681 0.987490i \(-0.449598\pi\)
\(642\) 0 0
\(643\) −41.2546 + 15.0155i −1.62692 + 0.592152i −0.984684 0.174351i \(-0.944217\pi\)
−0.642241 + 0.766503i \(0.721995\pi\)
\(644\) 0 0
\(645\) −0.244357 0.296927i −0.00962154 0.0116915i
\(646\) 0 0
\(647\) 15.9642 0.627618 0.313809 0.949486i \(-0.398395\pi\)
0.313809 + 0.949486i \(0.398395\pi\)
\(648\) 0 0
\(649\) −22.5850 −0.886539
\(650\) 0 0
\(651\) 1.91204 + 2.32339i 0.0749388 + 0.0910608i
\(652\) 0 0
\(653\) 13.8697 5.04816i 0.542763 0.197550i −0.0560649 0.998427i \(-0.517855\pi\)
0.598828 + 0.800877i \(0.295633\pi\)
\(654\) 0 0
\(655\) −0.622352 3.52953i −0.0243173 0.137910i
\(656\) 0 0
\(657\) 40.6059 13.9069i 1.58419 0.542562i
\(658\) 0 0
\(659\) 9.91286 + 3.60799i 0.386150 + 0.140547i 0.527798 0.849370i \(-0.323018\pi\)
−0.141648 + 0.989917i \(0.545240\pi\)
\(660\) 0 0
\(661\) 25.1093 + 21.0692i 0.976640 + 0.819499i 0.983579 0.180477i \(-0.0577643\pi\)
−0.00693878 + 0.999976i \(0.502209\pi\)
\(662\) 0 0
\(663\) 0.266028 + 0.156998i 0.0103317 + 0.00609728i
\(664\) 0 0
\(665\) 12.7847 22.1437i 0.495767 0.858694i
\(666\) 0 0
\(667\) −22.8304 39.5434i −0.883996 1.53113i
\(668\) 0 0
\(669\) −23.4906 + 27.4581i −0.908198 + 1.06159i
\(670\) 0 0
\(671\) 2.43054 13.7843i 0.0938300 0.532136i
\(672\) 0 0
\(673\) 15.6106 13.0988i 0.601743 0.504922i −0.290262 0.956947i \(-0.593743\pi\)
0.892005 + 0.452025i \(0.149298\pi\)
\(674\) 0 0
\(675\) −20.7852 + 52.3863i −0.800024 + 2.01635i
\(676\) 0 0
\(677\) 8.95863 7.51718i 0.344308 0.288909i −0.454192 0.890904i \(-0.650072\pi\)
0.798500 + 0.601995i \(0.205627\pi\)
\(678\) 0 0
\(679\) −5.71835 + 32.4304i −0.219450 + 1.24456i
\(680\) 0 0
\(681\) −2.08360 5.89934i −0.0798436 0.226063i
\(682\) 0 0
\(683\) −22.7585 39.4189i −0.870830 1.50832i −0.861140 0.508368i \(-0.830249\pi\)
−0.00968953 0.999953i \(-0.503084\pi\)
\(684\) 0 0
\(685\) −27.3297 + 47.3365i −1.04422 + 1.80863i
\(686\) 0 0
\(687\) 0.0673196 7.04855i 0.00256840 0.268919i
\(688\) 0 0
\(689\) −0.0560220 0.0470080i −0.00213427 0.00179086i
\(690\) 0 0
\(691\) 4.68876 + 1.70657i 0.178369 + 0.0649210i 0.429661 0.902990i \(-0.358633\pi\)
−0.251292 + 0.967911i \(0.580855\pi\)
\(692\) 0 0
\(693\) −38.7754 14.9578i −1.47295 0.568201i
\(694\) 0 0
\(695\) −0.0175729 0.0996610i −0.000666579 0.00378036i
\(696\) 0 0
\(697\) 22.0319 8.01895i 0.834517 0.303739i
\(698\) 0 0
\(699\) −41.8448 + 6.96698i −1.58272 + 0.263516i
\(700\) 0 0
\(701\) 25.9484 0.980059 0.490029 0.871706i \(-0.336986\pi\)
0.490029 + 0.871706i \(0.336986\pi\)
\(702\) 0 0
\(703\) 13.1943 0.497634
\(704\) 0 0
\(705\) 1.10759 2.95495i 0.0417141 0.111290i
\(706\) 0 0
\(707\) 21.5139 7.83040i 0.809112 0.294493i
\(708\) 0 0
\(709\) −1.73503 9.83985i −0.0651605 0.369543i −0.999899 0.0142073i \(-0.995478\pi\)
0.934739 0.355336i \(-0.115634\pi\)
\(710\) 0 0
\(711\) 11.2332 + 20.3442i 0.421278 + 0.762968i
\(712\) 0 0
\(713\) −3.47708 1.26556i −0.130218 0.0473954i
\(714\) 0 0
\(715\) 0.854700 + 0.717178i 0.0319640 + 0.0268209i
\(716\) 0 0
\(717\) 34.1299 19.2727i 1.27460 0.719751i
\(718\) 0 0
\(719\) 5.41746 9.38332i 0.202037 0.349939i −0.747147 0.664658i \(-0.768577\pi\)
0.949185 + 0.314719i \(0.101910\pi\)
\(720\) 0 0
\(721\) −9.14168 15.8339i −0.340454 0.589684i
\(722\) 0 0
\(723\) 19.4499 + 3.62141i 0.723350 + 0.134682i
\(724\) 0 0
\(725\) −15.4893 + 87.8443i −0.575259 + 3.26246i
\(726\) 0 0
\(727\) 13.4070 11.2498i 0.497237 0.417232i −0.359374 0.933194i \(-0.617010\pi\)
0.856612 + 0.515962i \(0.172565\pi\)
\(728\) 0 0
\(729\) 14.8170 22.5711i 0.548778 0.835968i
\(730\) 0 0
\(731\) 0.144479 0.121232i 0.00534373 0.00448392i
\(732\) 0 0
\(733\) −4.10784 + 23.2967i −0.151727 + 0.860484i 0.809991 + 0.586442i \(0.199472\pi\)
−0.961718 + 0.274042i \(0.911639\pi\)
\(734\) 0 0
\(735\) 1.38973 + 0.258755i 0.0512609 + 0.00954433i
\(736\) 0 0
\(737\) −24.8693 43.0749i −0.916073 1.58668i
\(738\) 0 0
\(739\) −1.39583 + 2.41766i −0.0513466 + 0.0889349i −0.890556 0.454873i \(-0.849685\pi\)
0.839210 + 0.543808i \(0.183018\pi\)
\(740\) 0 0
\(741\) 0.195998 0.110677i 0.00720016 0.00406583i
\(742\) 0 0
\(743\) −28.2480 23.7029i −1.03632 0.869576i −0.0447304 0.998999i \(-0.514243\pi\)
−0.991589 + 0.129423i \(0.958687\pi\)
\(744\) 0 0
\(745\) 45.6839 + 16.6276i 1.67373 + 0.609187i
\(746\) 0 0
\(747\) 3.47945 + 6.30156i 0.127306 + 0.230562i
\(748\) 0 0
\(749\) 4.12058 + 23.3690i 0.150563 + 0.853884i
\(750\) 0 0
\(751\) 11.4717 4.17535i 0.418608 0.152361i −0.124124 0.992267i \(-0.539612\pi\)
0.542732 + 0.839906i \(0.317390\pi\)
\(752\) 0 0
\(753\) −1.54545 + 4.12313i −0.0563193 + 0.150255i
\(754\) 0 0
\(755\) 11.7055 0.426009
\(756\) 0 0
\(757\) 17.4136 0.632907 0.316453 0.948608i \(-0.397508\pi\)
0.316453 + 0.948608i \(0.397508\pi\)
\(758\) 0 0
\(759\) 50.4139 8.39370i 1.82991 0.304672i
\(760\) 0 0
\(761\) 19.1950 6.98639i 0.695816 0.253256i 0.0301929 0.999544i \(-0.490388\pi\)
0.665624 + 0.746288i \(0.268166\pi\)
\(762\) 0 0
\(763\) −6.58592 37.3506i −0.238426 1.35218i
\(764\) 0 0
\(765\) −37.6780 14.5345i −1.36225 0.525496i
\(766\) 0 0
\(767\) −0.210607 0.0766547i −0.00760458 0.00276784i
\(768\) 0 0
\(769\) −12.7022 10.6584i −0.458052 0.384351i 0.384362 0.923183i \(-0.374422\pi\)
−0.842414 + 0.538831i \(0.818866\pi\)
\(770\) 0 0
\(771\) 0.297896 31.1906i 0.0107285 1.12330i
\(772\) 0 0
\(773\) −9.24355 + 16.0103i −0.332467 + 0.575850i −0.982995 0.183632i \(-0.941214\pi\)
0.650528 + 0.759482i \(0.274548\pi\)
\(774\) 0 0
\(775\) 3.61425 + 6.26007i 0.129828 + 0.224868i
\(776\) 0 0
\(777\) −8.05128 22.7958i −0.288838 0.817794i
\(778\) 0 0
\(779\) 2.96668 16.8249i 0.106292 0.602814i
\(780\) 0 0
\(781\) −58.5187 + 49.1030i −2.09396 + 1.75704i
\(782\) 0 0
\(783\) 15.7599 39.7206i 0.563212 1.41950i
\(784\) 0 0
\(785\) −36.7585 + 30.8441i −1.31197 + 1.10087i
\(786\) 0 0
\(787\) 6.19112 35.1116i 0.220690 1.25159i −0.650066 0.759877i \(-0.725259\pi\)
0.870756 0.491715i \(-0.163630\pi\)
\(788\) 0 0
\(789\) −0.847078 + 0.990148i −0.0301568 + 0.0352502i
\(790\) 0 0
\(791\) −19.5384 33.8415i −0.694706 1.20327i
\(792\) 0 0
\(793\) 0.0694495 0.120290i 0.00246622 0.00427163i
\(794\) 0 0
\(795\) 8.23394 + 4.85930i 0.292028 + 0.172342i
\(796\) 0