Properties

Label 576.2.bb.e.49.3
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.3
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45211 + 0.944122i) q^{3} +(-0.491749 + 0.131764i) q^{5} +(2.40518 - 1.38863i) q^{7} +(1.21727 - 2.74194i) q^{9} +O(q^{10})\) \(q+(-1.45211 + 0.944122i) q^{3} +(-0.491749 + 0.131764i) q^{5} +(2.40518 - 1.38863i) q^{7} +(1.21727 - 2.74194i) q^{9} +(-1.06358 + 3.96934i) q^{11} +(-0.596329 - 2.22553i) q^{13} +(0.589675 - 0.655607i) q^{15} +2.87908 q^{17} +(3.48018 - 3.48018i) q^{19} +(-2.18156 + 4.28723i) q^{21} +(3.85945 + 2.22826i) q^{23} +(-4.10567 + 2.37041i) q^{25} +(0.821118 + 5.13086i) q^{27} +(5.88383 + 1.57657i) q^{29} +(1.28296 - 2.22216i) q^{31} +(-2.20310 - 6.76808i) q^{33} +(-0.999773 + 0.999773i) q^{35} +(7.64112 + 7.64112i) q^{37} +(2.96711 + 2.66872i) q^{39} +(4.84731 + 2.79860i) q^{41} +(-0.911456 + 3.40160i) q^{43} +(-0.237302 + 1.50874i) q^{45} +(4.94233 + 8.56037i) q^{47} +(0.356586 - 0.617625i) q^{49} +(-4.18075 + 2.71820i) q^{51} +(-2.86564 - 2.86564i) q^{53} -2.09206i q^{55} +(-1.76790 + 8.33934i) q^{57} +(-2.15652 + 0.577838i) q^{59} +(4.79709 + 1.28538i) q^{61} +(-0.879800 - 8.28520i) q^{63} +(0.586489 + 1.01583i) q^{65} +(-3.96319 - 14.7908i) q^{67} +(-7.70811 + 0.408113i) q^{69} -13.2447i q^{71} -11.3768i q^{73} +(3.72395 - 7.31836i) q^{75} +(2.95384 + 11.0239i) q^{77} +(1.56750 + 2.71499i) q^{79} +(-6.03652 - 6.67536i) q^{81} +(-11.0286 - 2.95510i) q^{83} +(-1.41578 + 0.379358i) q^{85} +(-10.0325 + 3.26570i) q^{87} +2.37475i q^{89} +(-4.52472 - 4.52472i) q^{91} +(0.234979 + 4.43810i) q^{93} +(-1.25282 + 2.16994i) q^{95} +(-5.04313 - 8.73496i) q^{97} +(9.58904 + 7.74803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −1.45211 + 0.944122i −0.838378 + 0.545089i
\(4\) 0 0
\(5\) −0.491749 + 0.131764i −0.219917 + 0.0589266i −0.367095 0.930183i \(-0.619648\pi\)
0.147178 + 0.989110i \(0.452981\pi\)
\(6\) 0 0
\(7\) 2.40518 1.38863i 0.909072 0.524853i 0.0289393 0.999581i \(-0.490787\pi\)
0.880132 + 0.474728i \(0.157454\pi\)
\(8\) 0 0
\(9\) 1.21727 2.74194i 0.405756 0.913981i
\(10\) 0 0
\(11\) −1.06358 + 3.96934i −0.320682 + 1.19680i 0.597900 + 0.801570i \(0.296002\pi\)
−0.918582 + 0.395230i \(0.870665\pi\)
\(12\) 0 0
\(13\) −0.596329 2.22553i −0.165392 0.617251i −0.997990 0.0633733i \(-0.979814\pi\)
0.832598 0.553878i \(-0.186853\pi\)
\(14\) 0 0
\(15\) 0.589675 0.655607i 0.152253 0.169277i
\(16\) 0 0
\(17\) 2.87908 0.698279 0.349139 0.937071i \(-0.386474\pi\)
0.349139 + 0.937071i \(0.386474\pi\)
\(18\) 0 0
\(19\) 3.48018 3.48018i 0.798409 0.798409i −0.184436 0.982845i \(-0.559046\pi\)
0.982845 + 0.184436i \(0.0590457\pi\)
\(20\) 0 0
\(21\) −2.18156 + 4.28723i −0.476054 + 0.935550i
\(22\) 0 0
\(23\) 3.85945 + 2.22826i 0.804752 + 0.464624i 0.845130 0.534561i \(-0.179523\pi\)
−0.0403783 + 0.999184i \(0.512856\pi\)
\(24\) 0 0
\(25\) −4.10567 + 2.37041i −0.821134 + 0.474082i
\(26\) 0 0
\(27\) 0.821118 + 5.13086i 0.158024 + 0.987435i
\(28\) 0 0
\(29\) 5.88383 + 1.57657i 1.09260 + 0.292761i 0.759748 0.650218i \(-0.225323\pi\)
0.332852 + 0.942979i \(0.391989\pi\)
\(30\) 0 0
\(31\) 1.28296 2.22216i 0.230427 0.399112i −0.727507 0.686101i \(-0.759321\pi\)
0.957934 + 0.286989i \(0.0926543\pi\)
\(32\) 0 0
\(33\) −2.20310 6.76808i −0.383510 1.17817i
\(34\) 0 0
\(35\) −0.999773 + 0.999773i −0.168993 + 0.168993i
\(36\) 0 0
\(37\) 7.64112 + 7.64112i 1.25619 + 1.25619i 0.952896 + 0.303297i \(0.0980873\pi\)
0.303297 + 0.952896i \(0.401913\pi\)
\(38\) 0 0
\(39\) 2.96711 + 2.66872i 0.475118 + 0.427337i
\(40\) 0 0
\(41\) 4.84731 + 2.79860i 0.757023 + 0.437067i 0.828226 0.560394i \(-0.189350\pi\)
−0.0712028 + 0.997462i \(0.522684\pi\)
\(42\) 0 0
\(43\) −0.911456 + 3.40160i −0.138996 + 0.518739i 0.860954 + 0.508683i \(0.169868\pi\)
−0.999949 + 0.0100559i \(0.996799\pi\)
\(44\) 0 0
\(45\) −0.237302 + 1.50874i −0.0353748 + 0.224910i
\(46\) 0 0
\(47\) 4.94233 + 8.56037i 0.720913 + 1.24866i 0.960634 + 0.277817i \(0.0896108\pi\)
−0.239721 + 0.970842i \(0.577056\pi\)
\(48\) 0 0
\(49\) 0.356586 0.617625i 0.0509409 0.0882322i
\(50\) 0 0
\(51\) −4.18075 + 2.71820i −0.585422 + 0.380624i
\(52\) 0 0
\(53\) −2.86564 2.86564i −0.393626 0.393626i 0.482352 0.875978i \(-0.339783\pi\)
−0.875978 + 0.482352i \(0.839783\pi\)
\(54\) 0 0
\(55\) 2.09206i 0.282093i
\(56\) 0 0
\(57\) −1.76790 + 8.33934i −0.234165 + 1.10457i
\(58\) 0 0
\(59\) −2.15652 + 0.577838i −0.280755 + 0.0752281i −0.396449 0.918057i \(-0.629758\pi\)
0.115694 + 0.993285i \(0.463091\pi\)
\(60\) 0 0
\(61\) 4.79709 + 1.28538i 0.614204 + 0.164575i 0.552491 0.833519i \(-0.313677\pi\)
0.0617124 + 0.998094i \(0.480344\pi\)
\(62\) 0 0
\(63\) −0.879800 8.28520i −0.110844 1.04384i
\(64\) 0 0
\(65\) 0.586489 + 1.01583i 0.0727450 + 0.125998i
\(66\) 0 0
\(67\) −3.96319 14.7908i −0.484181 1.80699i −0.583721 0.811955i \(-0.698404\pi\)
0.0995397 0.995034i \(-0.468263\pi\)
\(68\) 0 0
\(69\) −7.70811 + 0.408113i −0.927947 + 0.0491310i
\(70\) 0 0
\(71\) 13.2447i 1.57186i −0.618317 0.785929i \(-0.712185\pi\)
0.618317 0.785929i \(-0.287815\pi\)
\(72\) 0 0
\(73\) 11.3768i 1.33155i −0.746152 0.665776i \(-0.768101\pi\)
0.746152 0.665776i \(-0.231899\pi\)
\(74\) 0 0
\(75\) 3.72395 7.31836i 0.430004 0.845051i
\(76\) 0 0
\(77\) 2.95384 + 11.0239i 0.336621 + 1.25629i
\(78\) 0 0
\(79\) 1.56750 + 2.71499i 0.176358 + 0.305460i 0.940630 0.339433i \(-0.110235\pi\)
−0.764273 + 0.644893i \(0.776902\pi\)
\(80\) 0 0
\(81\) −6.03652 6.67536i −0.670724 0.741707i
\(82\) 0 0
\(83\) −11.0286 2.95510i −1.21055 0.324365i −0.403569 0.914949i \(-0.632231\pi\)
−0.806976 + 0.590584i \(0.798897\pi\)
\(84\) 0 0
\(85\) −1.41578 + 0.379358i −0.153563 + 0.0411472i
\(86\) 0 0
\(87\) −10.0325 + 3.26570i −1.07559 + 0.350119i
\(88\) 0 0
\(89\) 2.37475i 0.251723i 0.992048 + 0.125862i \(0.0401696\pi\)
−0.992048 + 0.125862i \(0.959830\pi\)
\(90\) 0 0
\(91\) −4.52472 4.52472i −0.474319 0.474319i
\(92\) 0 0
\(93\) 0.234979 + 4.43810i 0.0243662 + 0.460210i
\(94\) 0 0
\(95\) −1.25282 + 2.16994i −0.128536 + 0.222631i
\(96\) 0 0
\(97\) −5.04313 8.73496i −0.512052 0.886900i −0.999902 0.0139730i \(-0.995552\pi\)
0.487850 0.872927i \(-0.337781\pi\)
\(98\) 0 0
\(99\) 9.58904 + 7.74803i 0.963735 + 0.778706i
\(100\) 0 0
\(101\) 1.55666 5.80953i 0.154893 0.578070i −0.844221 0.535995i \(-0.819937\pi\)
0.999114 0.0420749i \(-0.0133968\pi\)
\(102\) 0 0
\(103\) 11.7431 + 6.77986i 1.15708 + 0.668039i 0.950602 0.310412i \(-0.100467\pi\)
0.206476 + 0.978452i \(0.433800\pi\)
\(104\) 0 0
\(105\) 0.507877 2.39569i 0.0495637 0.233796i
\(106\) 0 0
\(107\) −2.81971 2.81971i −0.272592 0.272592i 0.557551 0.830143i \(-0.311741\pi\)
−0.830143 + 0.557551i \(0.811741\pi\)
\(108\) 0 0
\(109\) 3.20455 3.20455i 0.306940 0.306940i −0.536781 0.843721i \(-0.680360\pi\)
0.843721 + 0.536781i \(0.180360\pi\)
\(110\) 0 0
\(111\) −18.3099 3.88163i −1.73790 0.368428i
\(112\) 0 0
\(113\) −5.07913 + 8.79731i −0.477804 + 0.827581i −0.999676 0.0254424i \(-0.991901\pi\)
0.521872 + 0.853024i \(0.325234\pi\)
\(114\) 0 0
\(115\) −2.19149 0.587207i −0.204357 0.0547573i
\(116\) 0 0
\(117\) −6.82817 1.07397i −0.631265 0.0992882i
\(118\) 0 0
\(119\) 6.92469 3.99797i 0.634785 0.366493i
\(120\) 0 0
\(121\) −5.09817 2.94343i −0.463470 0.267584i
\(122\) 0 0
\(123\) −9.68107 + 0.512573i −0.872912 + 0.0462171i
\(124\) 0 0
\(125\) 3.50655 3.50655i 0.313636 0.313636i
\(126\) 0 0
\(127\) −7.32268 −0.649783 −0.324892 0.945751i \(-0.605328\pi\)
−0.324892 + 0.945751i \(0.605328\pi\)
\(128\) 0 0
\(129\) −1.88799 5.80004i −0.166228 0.510665i
\(130\) 0 0
\(131\) 5.31322 + 19.8292i 0.464218 + 1.73249i 0.659468 + 0.751733i \(0.270782\pi\)
−0.195250 + 0.980754i \(0.562552\pi\)
\(132\) 0 0
\(133\) 3.53777 13.2031i 0.306764 1.14486i
\(134\) 0 0
\(135\) −1.07985 2.41490i −0.0929384 0.207842i
\(136\) 0 0
\(137\) −10.0888 + 5.82479i −0.861947 + 0.497646i −0.864664 0.502351i \(-0.832469\pi\)
0.00271649 + 0.999996i \(0.499135\pi\)
\(138\) 0 0
\(139\) 11.5413 3.09248i 0.978918 0.262300i 0.266329 0.963882i \(-0.414189\pi\)
0.712589 + 0.701582i \(0.247522\pi\)
\(140\) 0 0
\(141\) −15.2589 7.76447i −1.28503 0.653886i
\(142\) 0 0
\(143\) 9.46813 0.791765
\(144\) 0 0
\(145\) −3.10110 −0.257533
\(146\) 0 0
\(147\) 0.0653099 + 1.23352i 0.00538667 + 0.101739i
\(148\) 0 0
\(149\) 1.01009 0.270654i 0.0827502 0.0221728i −0.217206 0.976126i \(-0.569694\pi\)
0.299957 + 0.953953i \(0.403028\pi\)
\(150\) 0 0
\(151\) −11.0495 + 6.37943i −0.899195 + 0.519150i −0.876939 0.480602i \(-0.840418\pi\)
−0.0222559 + 0.999752i \(0.507085\pi\)
\(152\) 0 0
\(153\) 3.50461 7.89427i 0.283331 0.638214i
\(154\) 0 0
\(155\) −0.338097 + 1.26179i −0.0271566 + 0.101350i
\(156\) 0 0
\(157\) −2.95544 11.0299i −0.235870 0.880279i −0.977755 0.209751i \(-0.932735\pi\)
0.741885 0.670527i \(-0.233932\pi\)
\(158\) 0 0
\(159\) 6.86675 + 1.45572i 0.544569 + 0.115446i
\(160\) 0 0
\(161\) 12.3769 0.975436
\(162\) 0 0
\(163\) 4.61842 4.61842i 0.361742 0.361742i −0.502712 0.864454i \(-0.667664\pi\)
0.864454 + 0.502712i \(0.167664\pi\)
\(164\) 0 0
\(165\) 1.97516 + 3.03791i 0.153766 + 0.236501i
\(166\) 0 0
\(167\) 6.85336 + 3.95679i 0.530329 + 0.306186i 0.741150 0.671339i \(-0.234280\pi\)
−0.210821 + 0.977525i \(0.567614\pi\)
\(168\) 0 0
\(169\) 6.66095 3.84570i 0.512381 0.295823i
\(170\) 0 0
\(171\) −5.30615 13.7788i −0.405772 1.05369i
\(172\) 0 0
\(173\) −20.9267 5.60729i −1.59103 0.426315i −0.648711 0.761035i \(-0.724691\pi\)
−0.942317 + 0.334721i \(0.891358\pi\)
\(174\) 0 0
\(175\) −6.58325 + 11.4025i −0.497647 + 0.861949i
\(176\) 0 0
\(177\) 2.58596 2.87511i 0.194373 0.216106i
\(178\) 0 0
\(179\) −4.24438 + 4.24438i −0.317240 + 0.317240i −0.847706 0.530466i \(-0.822017\pi\)
0.530466 + 0.847706i \(0.322017\pi\)
\(180\) 0 0
\(181\) 10.0752 + 10.0752i 0.748886 + 0.748886i 0.974270 0.225384i \(-0.0723638\pi\)
−0.225384 + 0.974270i \(0.572364\pi\)
\(182\) 0 0
\(183\) −8.17946 + 2.66252i −0.604643 + 0.196819i
\(184\) 0 0
\(185\) −4.76434 2.75069i −0.350281 0.202235i
\(186\) 0 0
\(187\) −3.06213 + 11.4280i −0.223925 + 0.835700i
\(188\) 0 0
\(189\) 9.09981 + 11.2004i 0.661914 + 0.814710i
\(190\) 0 0
\(191\) −5.46820 9.47119i −0.395665 0.685312i 0.597521 0.801853i \(-0.296152\pi\)
−0.993186 + 0.116542i \(0.962819\pi\)
\(192\) 0 0
\(193\) −9.82326 + 17.0144i −0.707094 + 1.22472i 0.258837 + 0.965921i \(0.416661\pi\)
−0.965931 + 0.258801i \(0.916673\pi\)
\(194\) 0 0
\(195\) −1.81071 0.921381i −0.129668 0.0659815i
\(196\) 0 0
\(197\) −17.9489 17.9489i −1.27881 1.27881i −0.941336 0.337472i \(-0.890428\pi\)
−0.337472 0.941336i \(-0.609572\pi\)
\(198\) 0 0
\(199\) 10.7912i 0.764966i 0.923963 + 0.382483i \(0.124931\pi\)
−0.923963 + 0.382483i \(0.875069\pi\)
\(200\) 0 0
\(201\) 19.7194 + 17.7362i 1.39090 + 1.25102i
\(202\) 0 0
\(203\) 16.3409 4.37854i 1.14691 0.307313i
\(204\) 0 0
\(205\) −2.75242 0.737508i −0.192237 0.0515098i
\(206\) 0 0
\(207\) 10.8077 7.87002i 0.751190 0.547004i
\(208\) 0 0
\(209\) 10.1126 + 17.5155i 0.699501 + 1.21157i
\(210\) 0 0
\(211\) −2.28982 8.54571i −0.157637 0.588311i −0.998865 0.0476299i \(-0.984833\pi\)
0.841228 0.540681i \(-0.181833\pi\)
\(212\) 0 0
\(213\) 12.5046 + 19.2328i 0.856802 + 1.31781i
\(214\) 0 0
\(215\) 1.79283i 0.122270i
\(216\) 0 0
\(217\) 7.12625i 0.483762i
\(218\) 0 0
\(219\) 10.7411 + 16.5204i 0.725814 + 1.11634i
\(220\) 0 0
\(221\) −1.71688 6.40747i −0.115490 0.431013i
\(222\) 0 0
\(223\) −7.53363 13.0486i −0.504489 0.873800i −0.999987 0.00519105i \(-0.998348\pi\)
0.495498 0.868609i \(-0.334986\pi\)
\(224\) 0 0
\(225\) 1.50183 + 14.1429i 0.100122 + 0.942863i
\(226\) 0 0
\(227\) −5.94741 1.59360i −0.394743 0.105771i 0.0559866 0.998432i \(-0.482170\pi\)
−0.450730 + 0.892660i \(0.648836\pi\)
\(228\) 0 0
\(229\) 4.03435 1.08100i 0.266597 0.0714345i −0.123044 0.992401i \(-0.539266\pi\)
0.389641 + 0.920967i \(0.372599\pi\)
\(230\) 0 0
\(231\) −14.6972 13.2191i −0.967005 0.869756i
\(232\) 0 0
\(233\) 1.71937i 0.112640i −0.998413 0.0563200i \(-0.982063\pi\)
0.998413 0.0563200i \(-0.0179367\pi\)
\(234\) 0 0
\(235\) −3.55834 3.55834i −0.232120 0.232120i
\(236\) 0 0
\(237\) −4.83947 2.46256i −0.314357 0.159961i
\(238\) 0 0
\(239\) −4.99586 + 8.65308i −0.323155 + 0.559721i −0.981137 0.193312i \(-0.938077\pi\)
0.657982 + 0.753034i \(0.271410\pi\)
\(240\) 0 0
\(241\) 10.9017 + 18.8822i 0.702238 + 1.21631i 0.967679 + 0.252184i \(0.0811489\pi\)
−0.265442 + 0.964127i \(0.585518\pi\)
\(242\) 0 0
\(243\) 15.0681 + 3.99418i 0.966617 + 0.256226i
\(244\) 0 0
\(245\) −0.0939703 + 0.350702i −0.00600354 + 0.0224055i
\(246\) 0 0
\(247\) −9.82059 5.66992i −0.624869 0.360768i
\(248\) 0 0
\(249\) 18.8047 6.12119i 1.19170 0.387915i
\(250\) 0 0
\(251\) −0.351987 0.351987i −0.0222172 0.0222172i 0.695911 0.718128i \(-0.255001\pi\)
−0.718128 + 0.695911i \(0.755001\pi\)
\(252\) 0 0
\(253\) −12.9495 + 12.9495i −0.814131 + 0.814131i
\(254\) 0 0
\(255\) 1.69772 1.88754i 0.106315 0.118203i
\(256\) 0 0
\(257\) 5.69516 9.86431i 0.355254 0.615319i −0.631907 0.775044i \(-0.717728\pi\)
0.987161 + 0.159726i \(0.0510609\pi\)
\(258\) 0 0
\(259\) 28.9889 + 7.76756i 1.80129 + 0.482653i
\(260\) 0 0
\(261\) 11.4851 14.2140i 0.710907 0.879826i
\(262\) 0 0
\(263\) −4.43754 + 2.56201i −0.273630 + 0.157980i −0.630536 0.776160i \(-0.717165\pi\)
0.356906 + 0.934140i \(0.383832\pi\)
\(264\) 0 0
\(265\) 1.78676 + 1.03159i 0.109760 + 0.0633700i
\(266\) 0 0
\(267\) −2.24206 3.44841i −0.137212 0.211039i
\(268\) 0 0
\(269\) 8.67269 8.67269i 0.528784 0.528784i −0.391426 0.920210i \(-0.628018\pi\)
0.920210 + 0.391426i \(0.128018\pi\)
\(270\) 0 0
\(271\) 19.6128 1.19139 0.595696 0.803210i \(-0.296876\pi\)
0.595696 + 0.803210i \(0.296876\pi\)
\(272\) 0 0
\(273\) 10.8423 + 2.29852i 0.656205 + 0.139113i
\(274\) 0 0
\(275\) −5.04225 18.8179i −0.304059 1.13476i
\(276\) 0 0
\(277\) 4.36219 16.2799i 0.262099 0.978165i −0.701904 0.712272i \(-0.747666\pi\)
0.964002 0.265893i \(-0.0856669\pi\)
\(278\) 0 0
\(279\) −4.53133 6.22278i −0.271283 0.372548i
\(280\) 0 0
\(281\) −14.0437 + 8.10816i −0.837780 + 0.483692i −0.856509 0.516132i \(-0.827371\pi\)
0.0187292 + 0.999825i \(0.494038\pi\)
\(282\) 0 0
\(283\) 0.905572 0.242647i 0.0538307 0.0144239i −0.231803 0.972763i \(-0.574463\pi\)
0.285634 + 0.958339i \(0.407796\pi\)
\(284\) 0 0
\(285\) −0.229457 4.33381i −0.0135919 0.256713i
\(286\) 0 0
\(287\) 15.5449 0.917584
\(288\) 0 0
\(289\) −8.71092 −0.512407
\(290\) 0 0
\(291\) 15.5701 + 7.92282i 0.912733 + 0.464444i
\(292\) 0 0
\(293\) 9.76797 2.61732i 0.570651 0.152905i 0.0380557 0.999276i \(-0.487884\pi\)
0.532595 + 0.846370i \(0.321217\pi\)
\(294\) 0 0
\(295\) 0.984330 0.568303i 0.0573099 0.0330879i
\(296\) 0 0
\(297\) −21.2395 2.19779i −1.23244 0.127529i
\(298\) 0 0
\(299\) 2.65755 9.91811i 0.153690 0.573579i
\(300\) 0 0
\(301\) 2.53135 + 9.44713i 0.145905 + 0.544524i
\(302\) 0 0
\(303\) 3.22446 + 9.90578i 0.185240 + 0.569072i
\(304\) 0 0
\(305\) −2.52833 −0.144772
\(306\) 0 0
\(307\) −16.1653 + 16.1653i −0.922603 + 0.922603i −0.997213 0.0746101i \(-0.976229\pi\)
0.0746101 + 0.997213i \(0.476229\pi\)
\(308\) 0 0
\(309\) −23.4533 + 1.24175i −1.33421 + 0.0706409i
\(310\) 0 0
\(311\) −11.8457 6.83912i −0.671708 0.387811i 0.125015 0.992155i \(-0.460102\pi\)
−0.796724 + 0.604344i \(0.793435\pi\)
\(312\) 0 0
\(313\) −22.5829 + 13.0383i −1.27646 + 0.736966i −0.976196 0.216890i \(-0.930409\pi\)
−0.300266 + 0.953855i \(0.597075\pi\)
\(314\) 0 0
\(315\) 1.52433 + 3.95831i 0.0858863 + 0.223026i
\(316\) 0 0
\(317\) −14.9639 4.00957i −0.840457 0.225200i −0.187187 0.982324i \(-0.559937\pi\)
−0.653270 + 0.757125i \(0.726604\pi\)
\(318\) 0 0
\(319\) −12.5159 + 21.6781i −0.700753 + 1.21374i
\(320\) 0 0
\(321\) 6.75670 + 1.43239i 0.377122 + 0.0799483i
\(322\) 0 0
\(323\) 10.0197 10.0197i 0.557512 0.557512i
\(324\) 0 0
\(325\) 7.72375 + 7.72375i 0.428437 + 0.428437i
\(326\) 0 0
\(327\) −1.62788 + 7.67885i −0.0900222 + 0.424641i
\(328\) 0 0
\(329\) 23.7744 + 13.7261i 1.31072 + 0.756747i
\(330\) 0 0
\(331\) 2.82670 10.5494i 0.155370 0.579847i −0.843704 0.536809i \(-0.819630\pi\)
0.999073 0.0430383i \(-0.0137038\pi\)
\(332\) 0 0
\(333\) 30.2528 11.6502i 1.65784 0.638429i
\(334\) 0 0
\(335\) 3.89779 + 6.75118i 0.212959 + 0.368856i
\(336\) 0 0
\(337\) −2.81502 + 4.87577i −0.153344 + 0.265600i −0.932455 0.361287i \(-0.882338\pi\)
0.779111 + 0.626886i \(0.215671\pi\)
\(338\) 0 0
\(339\) −0.930260 17.5700i −0.0505248 0.954272i
\(340\) 0 0
\(341\) 7.45597 + 7.45597i 0.403763 + 0.403763i
\(342\) 0 0
\(343\) 17.4602i 0.942760i
\(344\) 0 0
\(345\) 3.73668 1.21634i 0.201176 0.0654855i
\(346\) 0 0
\(347\) −1.40004 + 0.375139i −0.0751579 + 0.0201385i −0.296202 0.955125i \(-0.595720\pi\)
0.221044 + 0.975264i \(0.429054\pi\)
\(348\) 0 0
\(349\) 4.05103 + 1.08547i 0.216847 + 0.0581039i 0.365607 0.930769i \(-0.380861\pi\)
−0.148760 + 0.988873i \(0.547528\pi\)
\(350\) 0 0
\(351\) 10.9292 4.88711i 0.583360 0.260854i
\(352\) 0 0
\(353\) −5.70555 9.88230i −0.303676 0.525982i 0.673290 0.739379i \(-0.264881\pi\)
−0.976966 + 0.213397i \(0.931547\pi\)
\(354\) 0 0
\(355\) 1.74517 + 6.51307i 0.0926242 + 0.345678i
\(356\) 0 0
\(357\) −6.28086 + 12.3433i −0.332419 + 0.653275i
\(358\) 0 0
\(359\) 1.05572i 0.0557189i 0.999612 + 0.0278594i \(0.00886909\pi\)
−0.999612 + 0.0278594i \(0.991131\pi\)
\(360\) 0 0
\(361\) 5.22336i 0.274914i
\(362\) 0 0
\(363\) 10.1821 0.539099i 0.534420 0.0282953i
\(364\) 0 0
\(365\) 1.49905 + 5.59452i 0.0784638 + 0.292831i
\(366\) 0 0
\(367\) −4.67503 8.09739i −0.244035 0.422680i 0.717825 0.696223i \(-0.245138\pi\)
−0.961860 + 0.273543i \(0.911804\pi\)
\(368\) 0 0
\(369\) 13.5741 9.88442i 0.706638 0.514562i
\(370\) 0 0
\(371\) −10.8717 2.91306i −0.564430 0.151239i
\(372\) 0 0
\(373\) 5.80682 1.55593i 0.300666 0.0805631i −0.105332 0.994437i \(-0.533591\pi\)
0.405998 + 0.913874i \(0.366924\pi\)
\(374\) 0 0
\(375\) −1.78130 + 8.40253i −0.0919860 + 0.433905i
\(376\) 0 0
\(377\) 14.0348i 0.722828i
\(378\) 0 0
\(379\) −6.35334 6.35334i −0.326349 0.326349i 0.524847 0.851196i \(-0.324122\pi\)
−0.851196 + 0.524847i \(0.824122\pi\)
\(380\) 0 0
\(381\) 10.6334 6.91350i 0.544764 0.354190i
\(382\) 0 0
\(383\) 10.8961 18.8725i 0.556762 0.964341i −0.441002 0.897506i \(-0.645377\pi\)
0.997764 0.0668344i \(-0.0212899\pi\)
\(384\) 0 0
\(385\) −2.90510 5.03178i −0.148058 0.256443i
\(386\) 0 0
\(387\) 8.21751 + 6.63982i 0.417720 + 0.337521i
\(388\) 0 0
\(389\) −1.30926 + 4.88623i −0.0663822 + 0.247742i −0.991141 0.132811i \(-0.957600\pi\)
0.924759 + 0.380553i \(0.124266\pi\)
\(390\) 0 0
\(391\) 11.1117 + 6.41532i 0.561941 + 0.324437i
\(392\) 0 0
\(393\) −26.4366 23.7779i −1.33355 1.19944i
\(394\) 0 0
\(395\) −1.12855 1.12855i −0.0567837 0.0567837i
\(396\) 0 0
\(397\) 2.11018 2.11018i 0.105907 0.105907i −0.652168 0.758075i \(-0.726140\pi\)
0.758075 + 0.652168i \(0.226140\pi\)
\(398\) 0 0
\(399\) 7.32813 + 22.5126i 0.366865 + 1.12704i
\(400\) 0 0
\(401\) 4.22120 7.31133i 0.210797 0.365110i −0.741168 0.671320i \(-0.765728\pi\)
0.951964 + 0.306210i \(0.0990609\pi\)
\(402\) 0 0
\(403\) −5.71055 1.53014i −0.284463 0.0762216i
\(404\) 0 0
\(405\) 3.84802 + 2.48721i 0.191210 + 0.123590i
\(406\) 0 0
\(407\) −38.4572 + 22.2032i −1.90625 + 1.10057i
\(408\) 0 0
\(409\) 34.4821 + 19.9082i 1.70503 + 0.984399i 0.940490 + 0.339822i \(0.110367\pi\)
0.764539 + 0.644577i \(0.222967\pi\)
\(410\) 0 0
\(411\) 9.15082 17.9834i 0.451377 0.887053i
\(412\) 0 0
\(413\) −4.38441 + 4.38441i −0.215743 + 0.215743i
\(414\) 0 0
\(415\) 5.81268 0.285333
\(416\) 0 0
\(417\) −13.8396 + 15.3870i −0.677727 + 0.753505i
\(418\) 0 0
\(419\) 1.69652 + 6.33148i 0.0828802 + 0.309313i 0.994904 0.100823i \(-0.0321477\pi\)
−0.912024 + 0.410137i \(0.865481\pi\)
\(420\) 0 0
\(421\) −8.71468 + 32.5236i −0.424727 + 1.58510i 0.339790 + 0.940501i \(0.389644\pi\)
−0.764518 + 0.644603i \(0.777023\pi\)
\(422\) 0 0
\(423\) 29.4882 3.13134i 1.43377 0.152251i
\(424\) 0 0
\(425\) −11.8205 + 6.82459i −0.573380 + 0.331041i
\(426\) 0 0
\(427\) 13.3228 3.56982i 0.644733 0.172756i
\(428\) 0 0
\(429\) −13.7488 + 8.93907i −0.663798 + 0.431582i
\(430\) 0 0
\(431\) −19.0914 −0.919602 −0.459801 0.888022i \(-0.652079\pi\)
−0.459801 + 0.888022i \(0.652079\pi\)
\(432\) 0 0
\(433\) −4.98594 −0.239609 −0.119805 0.992797i \(-0.538227\pi\)
−0.119805 + 0.992797i \(0.538227\pi\)
\(434\) 0 0
\(435\) 4.50315 2.92782i 0.215910 0.140378i
\(436\) 0 0
\(437\) 21.1863 5.67687i 1.01348 0.271561i
\(438\) 0 0
\(439\) 11.1893 6.46017i 0.534038 0.308327i −0.208621 0.977997i \(-0.566898\pi\)
0.742659 + 0.669670i \(0.233564\pi\)
\(440\) 0 0
\(441\) −1.25943 1.72955i −0.0599730 0.0823597i
\(442\) 0 0
\(443\) −3.84803 + 14.3610i −0.182825 + 0.682314i 0.812260 + 0.583295i \(0.198237\pi\)
−0.995086 + 0.0990185i \(0.968430\pi\)
\(444\) 0 0
\(445\) −0.312907 1.16778i −0.0148332 0.0553583i
\(446\) 0 0
\(447\) −1.21124 + 1.34667i −0.0572898 + 0.0636954i
\(448\) 0 0
\(449\) −3.60684 −0.170217 −0.0851086 0.996372i \(-0.527124\pi\)
−0.0851086 + 0.996372i \(0.527124\pi\)
\(450\) 0 0
\(451\) −16.2641 + 16.2641i −0.765846 + 0.765846i
\(452\) 0 0
\(453\) 10.0222 19.6957i 0.470882 0.925385i
\(454\) 0 0
\(455\) 2.82122 + 1.62883i 0.132261 + 0.0763608i
\(456\) 0 0
\(457\) −4.13238 + 2.38583i −0.193304 + 0.111604i −0.593529 0.804813i \(-0.702266\pi\)
0.400224 + 0.916417i \(0.368932\pi\)
\(458\) 0 0
\(459\) 2.36406 + 14.7721i 0.110345 + 0.689505i
\(460\) 0 0
\(461\) 22.7740 + 6.10228i 1.06069 + 0.284212i 0.746664 0.665202i \(-0.231655\pi\)
0.314029 + 0.949413i \(0.398321\pi\)
\(462\) 0 0
\(463\) −15.9602 + 27.6439i −0.741735 + 1.28472i 0.209970 + 0.977708i \(0.432663\pi\)
−0.951705 + 0.307014i \(0.900670\pi\)
\(464\) 0 0
\(465\) −0.700332 2.15147i −0.0324771 0.0997721i
\(466\) 0 0
\(467\) −7.26104 + 7.26104i −0.336001 + 0.336001i −0.854860 0.518859i \(-0.826357\pi\)
0.518859 + 0.854860i \(0.326357\pi\)
\(468\) 0 0
\(469\) −30.0712 30.0712i −1.38856 1.38856i
\(470\) 0 0
\(471\) 14.7052 + 13.2263i 0.677579 + 0.609436i
\(472\) 0 0
\(473\) −12.5327 7.23576i −0.576254 0.332700i
\(474\) 0 0
\(475\) −6.03903 + 22.5380i −0.277090 + 1.03411i
\(476\) 0 0
\(477\) −11.3457 + 4.36917i −0.519483 + 0.200051i
\(478\) 0 0
\(479\) −13.4733 23.3364i −0.615609 1.06627i −0.990277 0.139107i \(-0.955577\pi\)
0.374669 0.927159i \(-0.377756\pi\)
\(480\) 0 0
\(481\) 12.4489 21.5622i 0.567622 0.983151i
\(482\) 0 0
\(483\) −17.9727 + 11.6853i −0.817784 + 0.531699i
\(484\) 0 0
\(485\) 3.63091 + 3.63091i 0.164871 + 0.164871i
\(486\) 0 0
\(487\) 33.3405i 1.51080i −0.655264 0.755400i \(-0.727442\pi\)
0.655264 0.755400i \(-0.272558\pi\)
\(488\) 0 0
\(489\) −2.34612 + 11.0668i −0.106095 + 0.500459i
\(490\) 0 0
\(491\) −22.4169 + 6.00659i −1.01166 + 0.271074i −0.726323 0.687353i \(-0.758772\pi\)
−0.285338 + 0.958427i \(0.592106\pi\)
\(492\) 0 0
\(493\) 16.9400 + 4.53906i 0.762939 + 0.204429i
\(494\) 0 0
\(495\) −5.73631 2.54660i −0.257828 0.114461i
\(496\) 0 0
\(497\) −18.3920 31.8559i −0.824994 1.42893i
\(498\) 0 0
\(499\) −4.03564 15.0612i −0.180660 0.674233i −0.995518 0.0945722i \(-0.969852\pi\)
0.814858 0.579661i \(-0.196815\pi\)
\(500\) 0 0
\(501\) −13.6876 + 0.724700i −0.611515 + 0.0323772i
\(502\) 0 0
\(503\) 26.2715i 1.17139i −0.810533 0.585693i \(-0.800822\pi\)
0.810533 0.585693i \(-0.199178\pi\)
\(504\) 0 0
\(505\) 3.06194i 0.136255i
\(506\) 0 0
\(507\) −6.04165 + 11.8731i −0.268319 + 0.527305i
\(508\) 0 0
\(509\) −7.08716 26.4496i −0.314133 1.17236i −0.924794 0.380468i \(-0.875763\pi\)
0.610661 0.791892i \(-0.290904\pi\)
\(510\) 0 0
\(511\) −15.7981 27.3632i −0.698869 1.21048i
\(512\) 0 0
\(513\) 20.7140 + 14.9987i 0.914545 + 0.662209i
\(514\) 0 0
\(515\) −6.66798 1.78668i −0.293826 0.0787305i
\(516\) 0 0
\(517\) −39.2356 + 10.5131i −1.72558 + 0.462368i
\(518\) 0 0
\(519\) 35.6819 11.6149i 1.56626 0.509839i
\(520\) 0 0
\(521\) 13.9069i 0.609272i −0.952469 0.304636i \(-0.901465\pi\)
0.952469 0.304636i \(-0.0985348\pi\)
\(522\) 0 0
\(523\) −14.8539 14.8539i −0.649517 0.649517i 0.303359 0.952876i \(-0.401892\pi\)
−0.952876 + 0.303359i \(0.901892\pi\)
\(524\) 0 0
\(525\) −1.20574 22.7731i −0.0526230 0.993901i
\(526\) 0 0
\(527\) 3.69375 6.39777i 0.160902 0.278691i
\(528\) 0 0
\(529\) −1.56975 2.71888i −0.0682499 0.118212i
\(530\) 0 0
\(531\) −1.04066 + 6.61645i −0.0451610 + 0.287129i
\(532\) 0 0
\(533\) 3.33777 12.4567i 0.144575 0.539561i
\(534\) 0 0
\(535\) 1.75813 + 1.01506i 0.0760105 + 0.0438847i
\(536\) 0 0
\(537\) 2.15611 10.1705i 0.0930430 0.438891i
\(538\) 0 0
\(539\) 2.07230 + 2.07230i 0.0892605 + 0.0892605i
\(540\) 0 0
\(541\) −30.6206 + 30.6206i −1.31648 + 1.31648i −0.399939 + 0.916542i \(0.630969\pi\)
−0.916542 + 0.399939i \(0.869031\pi\)
\(542\) 0 0
\(543\) −24.1426 5.11813i −1.03606 0.219640i
\(544\) 0 0
\(545\) −1.15359 + 1.99808i −0.0494144 + 0.0855882i
\(546\) 0 0
\(547\) −0.751802 0.201445i −0.0321447 0.00861315i 0.242711 0.970099i \(-0.421963\pi\)
−0.274856 + 0.961486i \(0.588630\pi\)
\(548\) 0 0
\(549\) 9.36376 11.5887i 0.399636 0.494593i
\(550\) 0 0
\(551\) 25.9635 14.9901i 1.10608 0.638598i
\(552\) 0 0
\(553\) 7.54023 + 4.35336i 0.320643 + 0.185124i
\(554\) 0 0
\(555\) 9.51535 0.503799i 0.403904 0.0213851i
\(556\) 0 0
\(557\) −15.1991 + 15.1991i −0.644006 + 0.644006i −0.951538 0.307532i \(-0.900497\pi\)
0.307532 + 0.951538i \(0.400497\pi\)
\(558\) 0 0
\(559\) 8.11390 0.343181
\(560\) 0 0
\(561\) −6.34289 19.4858i −0.267797 0.822692i
\(562\) 0 0
\(563\) −2.92996 10.9348i −0.123483 0.460846i 0.876298 0.481770i \(-0.160006\pi\)
−0.999781 + 0.0209240i \(0.993339\pi\)
\(564\) 0 0
\(565\) 1.33849 4.99532i 0.0563107 0.210155i
\(566\) 0 0
\(567\) −23.7885 7.67294i −0.999023 0.322233i
\(568\) 0 0
\(569\) 38.8985 22.4581i 1.63071 0.941491i 0.646835 0.762630i \(-0.276092\pi\)
0.983874 0.178861i \(-0.0572413\pi\)
\(570\) 0 0
\(571\) −22.0647 + 5.91221i −0.923378 + 0.247418i −0.689029 0.724734i \(-0.741963\pi\)
−0.234349 + 0.972152i \(0.575296\pi\)
\(572\) 0 0
\(573\) 16.8824 + 8.59061i 0.705273 + 0.358878i
\(574\) 0 0
\(575\) −21.1275 −0.881079
\(576\) 0 0
\(577\) −13.2304 −0.550790 −0.275395 0.961331i \(-0.588809\pi\)
−0.275395 + 0.961331i \(0.588809\pi\)
\(578\) 0 0
\(579\) −1.79916 33.9812i −0.0747707 1.41221i
\(580\) 0 0
\(581\) −30.6293 + 8.20709i −1.27072 + 0.340487i
\(582\) 0 0
\(583\) 14.4225 8.32685i 0.597320 0.344863i
\(584\) 0 0
\(585\) 3.49926 0.371584i 0.144677 0.0153631i
\(586\) 0 0
\(587\) 0.899168 3.35574i 0.0371126 0.138506i −0.944884 0.327406i \(-0.893825\pi\)
0.981996 + 0.188900i \(0.0604922\pi\)
\(588\) 0 0
\(589\) −3.26857 12.1985i −0.134679 0.502630i
\(590\) 0 0
\(591\) 43.0098 + 9.11790i 1.76919 + 0.375060i
\(592\) 0 0
\(593\) −43.3013 −1.77817 −0.889086 0.457740i \(-0.848659\pi\)
−0.889086 + 0.457740i \(0.848659\pi\)
\(594\) 0 0
\(595\) −2.87842 + 2.87842i −0.118004 + 0.118004i
\(596\) 0 0
\(597\) −10.1882 15.6700i −0.416974 0.641331i
\(598\) 0 0
\(599\) 15.9727 + 9.22187i 0.652629 + 0.376795i 0.789463 0.613799i \(-0.210359\pi\)
−0.136834 + 0.990594i \(0.543693\pi\)
\(600\) 0 0
\(601\) −17.7246 + 10.2333i −0.723003 + 0.417426i −0.815857 0.578254i \(-0.803734\pi\)
0.0928541 + 0.995680i \(0.470401\pi\)
\(602\) 0 0
\(603\) −45.3799 7.13756i −1.84801 0.290664i
\(604\) 0 0
\(605\) 2.89486 + 0.775674i 0.117693 + 0.0315357i
\(606\) 0 0
\(607\) 8.07865 13.9926i 0.327902 0.567944i −0.654193 0.756328i \(-0.726992\pi\)
0.982095 + 0.188384i \(0.0603249\pi\)
\(608\) 0 0
\(609\) −19.5950 + 21.7859i −0.794029 + 0.882811i
\(610\) 0 0
\(611\) 16.1041 16.1041i 0.651503 0.651503i
\(612\) 0 0
\(613\) 22.2010 + 22.2010i 0.896689 + 0.896689i 0.995142 0.0984526i \(-0.0313893\pi\)
−0.0984526 + 0.995142i \(0.531389\pi\)
\(614\) 0 0
\(615\) 4.69312 1.52767i 0.189245 0.0616017i
\(616\) 0 0
\(617\) 0.887087 + 0.512160i 0.0357128 + 0.0206188i 0.517750 0.855532i \(-0.326770\pi\)
−0.482037 + 0.876151i \(0.660103\pi\)
\(618\) 0 0
\(619\) 2.14654 8.01100i 0.0862768 0.321989i −0.909276 0.416193i \(-0.863364\pi\)
0.995553 + 0.0942040i \(0.0300306\pi\)
\(620\) 0 0
\(621\) −8.26381 + 21.6320i −0.331615 + 0.868062i
\(622\) 0 0
\(623\) 3.29766 + 5.71171i 0.132118 + 0.228835i
\(624\) 0 0
\(625\) 10.5897 18.3420i 0.423590 0.733679i
\(626\) 0 0
\(627\) −31.2214 15.8870i −1.24686 0.634465i
\(628\) 0 0
\(629\) 21.9994 + 21.9994i 0.877172 + 0.877172i
\(630\) 0 0
\(631\) 17.1003i 0.680750i −0.940290 0.340375i \(-0.889446\pi\)
0.940290 0.340375i \(-0.110554\pi\)
\(632\) 0 0
\(633\) 11.3933 + 10.2475i 0.452842 + 0.407301i
\(634\) 0 0
\(635\) 3.60092 0.964865i 0.142898 0.0382895i
\(636\) 0 0
\(637\) −1.58719 0.425285i −0.0628866 0.0168504i
\(638\) 0 0
\(639\) −36.3162 16.1224i −1.43665 0.637790i
\(640\) 0 0
\(641\) −4.96926 8.60701i −0.196274 0.339956i 0.751044 0.660253i \(-0.229551\pi\)
−0.947317 + 0.320296i \(0.896217\pi\)
\(642\) 0 0
\(643\) 8.95763 + 33.4303i 0.353254 + 1.31836i 0.882667 + 0.469999i \(0.155746\pi\)
−0.529413 + 0.848364i \(0.677588\pi\)
\(644\) 0 0
\(645\) 1.69265 + 2.60340i 0.0666481 + 0.102509i
\(646\) 0 0
\(647\) 41.6750i 1.63841i 0.573498 + 0.819207i \(0.305586\pi\)
−0.573498 + 0.819207i \(0.694414\pi\)
\(648\) 0 0
\(649\) 9.17454i 0.360132i
\(650\) 0 0
\(651\) 6.72805 + 10.3481i 0.263693 + 0.405575i
\(652\) 0 0
\(653\) 10.9418 + 40.8352i 0.428184 + 1.59800i 0.756871 + 0.653565i \(0.226727\pi\)
−0.328687 + 0.944439i \(0.606606\pi\)
\(654\) 0 0
\(655\) −5.22555 9.05091i −0.204179 0.353648i
\(656\) 0 0
\(657\) −31.1945 13.8486i −1.21701 0.540285i
\(658\) 0 0
\(659\) 25.4089 + 6.80828i 0.989789 + 0.265213i 0.717162 0.696907i \(-0.245441\pi\)
0.272627 + 0.962120i \(0.412108\pi\)
\(660\) 0 0
\(661\) −12.8649 + 3.44715i −0.500388 + 0.134079i −0.500180 0.865921i \(-0.666733\pi\)
−0.000208061 1.00000i \(0.500066\pi\)
\(662\) 0 0
\(663\) 8.54254 + 7.68344i 0.331765 + 0.298400i
\(664\) 0 0
\(665\) 6.95879i 0.269850i
\(666\) 0 0
\(667\) 19.1954 + 19.1954i 0.743247 + 0.743247i
\(668\) 0 0
\(669\) 23.2592 + 11.8354i 0.899251 + 0.457584i
\(670\) 0 0
\(671\) −10.2042 + 17.6742i −0.393928 + 0.682303i
\(672\) 0 0
\(673\) −6.35961 11.0152i −0.245145 0.424604i 0.717027 0.697045i \(-0.245502\pi\)
−0.962172 + 0.272441i \(0.912169\pi\)
\(674\) 0 0
\(675\) −15.5335 19.1193i −0.597885 0.735900i
\(676\) 0 0
\(677\) −11.3408 + 42.3243i −0.435861 + 1.62665i 0.303137 + 0.952947i \(0.401966\pi\)
−0.738998 + 0.673708i \(0.764701\pi\)
\(678\) 0 0
\(679\) −24.2592 14.0061i −0.930984 0.537504i
\(680\) 0 0
\(681\) 10.1409 3.30098i 0.388599 0.126494i
\(682\) 0 0
\(683\) −4.22715 4.22715i −0.161748 0.161748i 0.621593 0.783340i \(-0.286486\pi\)
−0.783340 + 0.621593i \(0.786486\pi\)
\(684\) 0 0
\(685\) 4.19368 4.19368i 0.160232 0.160232i
\(686\) 0 0
\(687\) −4.83773 + 5.37865i −0.184571 + 0.205208i
\(688\) 0 0
\(689\) −4.66870 + 8.08643i −0.177863 + 0.308069i
\(690\) 0 0
\(691\) 3.57753 + 0.958595i 0.136096 + 0.0364667i 0.326224 0.945293i \(-0.394224\pi\)
−0.190128 + 0.981759i \(0.560890\pi\)
\(692\) 0 0
\(693\) 33.8225 + 5.31975i 1.28481 + 0.202081i
\(694\) 0 0
\(695\) −5.26794 + 3.04145i −0.199824 + 0.115369i
\(696\) 0 0
\(697\) 13.9558 + 8.05738i 0.528613 + 0.305195i
\(698\) 0 0
\(699\) 1.62330 + 2.49673i 0.0613988 + 0.0944349i
\(700\) 0 0
\(701\) 22.6596 22.6596i 0.855842 0.855842i −0.135003 0.990845i \(-0.543104\pi\)
0.990845 + 0.135003i \(0.0431044\pi\)
\(702\) 0 0
\(703\) 53.1850 2.00591
\(704\) 0 0
\(705\) 8.52661 + 1.80761i 0.321131 + 0.0680784i
\(706\) 0 0
\(707\) −4.32325 16.1346i −0.162592 0.606803i
\(708\) 0 0
\(709\) 5.72683 21.3728i 0.215076 0.802673i −0.771064 0.636757i \(-0.780275\pi\)
0.986140 0.165916i \(-0.0530580\pi\)
\(710\) 0 0
\(711\) 9.35242 0.993128i 0.350743 0.0372452i
\(712\) 0 0
\(713\) 9.90308 5.71755i 0.370873 0.214124i
\(714\) 0 0
\(715\) −4.65595 + 1.24756i −0.174122 + 0.0466560i
\(716\) 0 0
\(717\) −0.915008 17.2820i −0.0341716 0.645407i
\(718\) 0 0
\(719\) −8.65067 −0.322616 −0.161308 0.986904i \(-0.551571\pi\)
−0.161308 + 0.986904i \(0.551571\pi\)
\(720\) 0 0
\(721\) 37.6589 1.40249
\(722\) 0 0
\(723\) −33.6576 17.1266i −1.25174 0.636947i
\(724\) 0 0
\(725\) −27.8942 + 7.47422i −1.03596 + 0.277586i
\(726\) 0 0
\(727\) −2.70356 + 1.56090i −0.100269 + 0.0578905i −0.549296 0.835628i \(-0.685104\pi\)
0.449027 + 0.893518i \(0.351771\pi\)
\(728\) 0 0
\(729\) −25.6515 + 8.42609i −0.950057 + 0.312077i
\(730\) 0 0
\(731\) −2.62415 + 9.79347i −0.0970578 + 0.362225i
\(732\) 0 0
\(733\) −0.888818 3.31711i −0.0328292 0.122520i 0.947567 0.319558i \(-0.103534\pi\)
−0.980396 + 0.197038i \(0.936868\pi\)
\(734\) 0 0
\(735\) −0.194650 0.597978i −0.00717976 0.0220568i
\(736\) 0 0
\(737\) 62.9250 2.31787
\(738\) 0 0
\(739\) −11.1765 + 11.1765i −0.411133 + 0.411133i −0.882133 0.471000i \(-0.843893\pi\)
0.471000 + 0.882133i \(0.343893\pi\)
\(740\) 0 0
\(741\) 19.6137 1.03847i 0.720528 0.0381490i
\(742\) 0 0
\(743\) 8.55561 + 4.93958i 0.313875 + 0.181216i 0.648659 0.761079i \(-0.275330\pi\)
−0.334784 + 0.942295i \(0.608663\pi\)
\(744\) 0 0
\(745\) −0.461051 + 0.266188i −0.0168916 + 0.00975237i
\(746\) 0 0
\(747\) −21.5275 + 26.6426i −0.787649 + 0.974803i
\(748\) 0 0
\(749\) −10.6974 2.86637i −0.390876 0.104735i
\(750\) 0 0
\(751\) 23.4223 40.5685i 0.854690 1.48037i −0.0222416 0.999753i \(-0.507080\pi\)
0.876932 0.480615i \(-0.159586\pi\)
\(752\) 0 0
\(753\) 0.843443 + 0.178806i 0.0307368 + 0.00651606i
\(754\) 0 0
\(755\) 4.59300 4.59300i 0.167156 0.167156i
\(756\) 0 0
\(757\) −14.0064 14.0064i −0.509071 0.509071i 0.405170 0.914241i \(-0.367212\pi\)
−0.914241 + 0.405170i \(0.867212\pi\)
\(758\) 0 0
\(759\) 6.57826 31.0302i 0.238776 1.12632i
\(760\) 0 0
\(761\) −24.1008 13.9146i −0.873655 0.504405i −0.00509371 0.999987i \(-0.501621\pi\)
−0.868561 + 0.495582i \(0.834955\pi\)
\(762\) 0 0
\(763\) 3.25757 12.1574i 0.117932 0.440129i
\(764\) 0 0
\(765\) −0.683209 + 4.34378i −0.0247015 + 0.157050i
\(766\) 0 0
\(767\) 2.57199 + 4.45482i 0.0928693 + 0.160854i
\(768\) 0 0
\(769\) 8.70836 15.0833i 0.314031 0.543918i −0.665200 0.746666i \(-0.731654\pi\)
0.979231 + 0.202747i \(0.0649869\pi\)
\(770\) 0 0
\(771\) 1.04309 + 19.7010i 0.0375659 + 0.709515i
\(772\) 0 0
\(773\) 2.74550 + 2.74550i 0.0987489 + 0.0987489i 0.754755 0.656006i \(-0.227756\pi\)
−0.656006 + 0.754755i \(0.727756\pi\)
\(774\) 0 0
\(775\) 12.1646i 0.436966i
\(776\) 0 0
\(777\) −49.4288 + 16.0897i −1.77325 + 0.577215i
\(778\) 0 0
\(779\) 26.6092 7.12991i 0.953373 0.255455i
\(780\) 0 0
\(781\) 52.5727 + 14.0868i 1.88120 + 0.504066i
\(782\) 0 0
\(783\) −3.25783 + 31.4837i −0.116425 + 1.12513i
\(784\) 0 0
\(785\) 2.90667 + 5.03451i 0.103744 + 0.179689i
\(786\) 0 0
\(787\) −0.187023 0.697981i −0.00666666 0.0248803i 0.962512 0.271238i \(-0.0874330\pi\)
−0.969179 + 0.246357i \(0.920766\pi\)
\(788\) 0 0
\(789\) 4.02495 7.90991i 0.143292 0.281600i
\(790\) 0 0
\(791\) 28.2121i 1.00311i
\(792\) 0 0
\(793\) 11.4426i 0.406337i
\(794\) 0 0
\(795\) −3.56853 + 0.188939i −0.126563 + 0.00670097i
\(796\) 0 0