Properties

Label 804.2.ba.b.41.14
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.14
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +O(q^{10})\) \(q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +(2.41940 - 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(-2.29636 - 0.905215i) q^{15} +(-3.53951 + 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-2.65838 - 0.367831i) q^{21} +(-0.357259 + 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-3.33982 + 3.98065i) q^{27} +(-2.14642 + 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(-0.666088 - 4.46445i) q^{33} +(-2.20559 - 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(-4.15976 + 2.43116i) q^{39} +(-1.45686 - 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.44281 + 3.50866i) q^{45} +(-5.86207 + 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(0.650925 + 6.45468i) q^{51} +(-1.34621 - 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(-0.0465258 + 0.136771i) q^{57} +(0.862133 + 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(-1.68171 + 4.33343i) q^{63} +(-3.22916 + 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.114010 + 0.608910i) q^{69} +(-3.54925 - 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(2.54766 - 4.46724i) q^{75} +(-1.85030 - 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(5.37492 + 7.21874i) q^{81} +(-3.35310 + 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(1.23127 + 4.11248i) q^{87} +(4.10997 - 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-3.28504 - 5.05248i) q^{93} +(-0.0280235 + 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.79029 - 0.660540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) 0.399410 1.68537i 0.230599 0.973049i
\(4\) 0 0
\(5\) 0.202812 1.41059i 0.0907002 0.630834i −0.892871 0.450313i \(-0.851312\pi\)
0.983571 0.180521i \(-0.0577784\pi\)
\(6\) 0 0
\(7\) −0.147283 1.54242i −0.0556679 0.582980i −0.979673 0.200600i \(-0.935711\pi\)
0.924005 0.382380i \(-0.124895\pi\)
\(8\) 0 0
\(9\) −2.68094 1.34631i −0.893648 0.448769i
\(10\) 0 0
\(11\) 2.41940 0.968583i 0.729477 0.292039i 0.0229619 0.999736i \(-0.492690\pi\)
0.706515 + 0.707698i \(0.250266\pi\)
\(12\) 0 0
\(13\) −1.91962 2.01323i −0.532405 0.558371i 0.401515 0.915853i \(-0.368484\pi\)
−0.933920 + 0.357482i \(0.883635\pi\)
\(14\) 0 0
\(15\) −2.29636 0.905215i −0.592917 0.233726i
\(16\) 0 0
\(17\) −3.53951 + 1.22504i −0.858458 + 0.297115i −0.720612 0.693339i \(-0.756139\pi\)
−0.137846 + 0.990454i \(0.544018\pi\)
\(18\) 0 0
\(19\) −0.0830309 0.00792849i −0.0190486 0.00181892i 0.0855274 0.996336i \(-0.472742\pi\)
−0.104576 + 0.994517i \(0.533349\pi\)
\(20\) 0 0
\(21\) −2.65838 0.367831i −0.580105 0.0802673i
\(22\) 0 0
\(23\) −0.357259 + 0.0170183i −0.0744936 + 0.00354857i −0.0847956 0.996398i \(-0.527024\pi\)
0.0103020 + 0.999947i \(0.496721\pi\)
\(24\) 0 0
\(25\) 2.84884 + 0.836495i 0.569768 + 0.167299i
\(26\) 0 0
\(27\) −3.33982 + 3.98065i −0.642748 + 0.766077i
\(28\) 0 0
\(29\) −2.14642 + 1.23924i −0.398581 + 0.230121i −0.685872 0.727723i \(-0.740579\pi\)
0.287291 + 0.957843i \(0.407245\pi\)
\(30\) 0 0
\(31\) 2.40107 2.51817i 0.431245 0.452277i −0.471875 0.881666i \(-0.656422\pi\)
0.903120 + 0.429389i \(0.141271\pi\)
\(32\) 0 0
\(33\) −0.666088 4.46445i −0.115951 0.777161i
\(34\) 0 0
\(35\) −2.20559 0.105065i −0.372813 0.0177593i
\(36\) 0 0
\(37\) 3.28486 5.68954i 0.540027 0.935354i −0.458875 0.888501i \(-0.651747\pi\)
0.998902 0.0468534i \(-0.0149193\pi\)
\(38\) 0 0
\(39\) −4.15976 + 2.43116i −0.666094 + 0.389297i
\(40\) 0 0
\(41\) −1.45686 0.280786i −0.227523 0.0438514i 0.0742156 0.997242i \(-0.476355\pi\)
−0.301738 + 0.953391i \(0.597567\pi\)
\(42\) 0 0
\(43\) −6.93510 6.00930i −1.05759 0.916409i −0.0609383 0.998142i \(-0.519409\pi\)
−0.996654 + 0.0817323i \(0.973955\pi\)
\(44\) 0 0
\(45\) −2.44281 + 3.50866i −0.364153 + 0.523040i
\(46\) 0 0
\(47\) −5.86207 + 11.3708i −0.855071 + 1.65861i −0.107716 + 0.994182i \(0.534354\pi\)
−0.747355 + 0.664425i \(0.768677\pi\)
\(48\) 0 0
\(49\) 4.51613 0.870413i 0.645162 0.124345i
\(50\) 0 0
\(51\) 0.650925 + 6.45468i 0.0911478 + 0.903836i
\(52\) 0 0
\(53\) −1.34621 1.55361i −0.184916 0.213405i 0.655721 0.755003i \(-0.272365\pi\)
−0.840637 + 0.541598i \(0.817819\pi\)
\(54\) 0 0
\(55\) −0.875587 3.60922i −0.118064 0.486667i
\(56\) 0 0
\(57\) −0.0465258 + 0.136771i −0.00616249 + 0.0181158i
\(58\) 0 0
\(59\) 0.862133 + 2.93616i 0.112240 + 0.382255i 0.996384 0.0849590i \(-0.0270759\pi\)
−0.884144 + 0.467214i \(0.845258\pi\)
\(60\) 0 0
\(61\) 4.16017 10.3916i 0.532655 1.33051i −0.381209 0.924489i \(-0.624492\pi\)
0.913864 0.406020i \(-0.133084\pi\)
\(62\) 0 0
\(63\) −1.68171 + 4.33343i −0.211876 + 0.545961i
\(64\) 0 0
\(65\) −3.22916 + 2.29948i −0.400529 + 0.285215i
\(66\) 0 0
\(67\) 8.16291 + 0.605750i 0.997258 + 0.0740041i
\(68\) 0 0
\(69\) −0.114010 + 0.608910i −0.0137252 + 0.0733042i
\(70\) 0 0
\(71\) −3.54925 1.22841i −0.421219 0.145785i 0.108232 0.994126i \(-0.465481\pi\)
−0.529451 + 0.848340i \(0.677602\pi\)
\(72\) 0 0
\(73\) −3.48722 1.39607i −0.408148 0.163398i 0.158498 0.987359i \(-0.449335\pi\)
−0.566646 + 0.823962i \(0.691759\pi\)
\(74\) 0 0
\(75\) 2.54766 4.46724i 0.294178 0.515833i
\(76\) 0 0
\(77\) −1.85030 3.58908i −0.210861 0.409014i
\(78\) 0 0
\(79\) −2.37878 + 0.577087i −0.267634 + 0.0649273i −0.367330 0.930091i \(-0.619728\pi\)
0.0996961 + 0.995018i \(0.468213\pi\)
\(80\) 0 0
\(81\) 5.37492 + 7.21874i 0.597213 + 0.802082i
\(82\) 0 0
\(83\) −3.35310 + 4.26381i −0.368051 + 0.468014i −0.934439 0.356124i \(-0.884098\pi\)
0.566388 + 0.824139i \(0.308340\pi\)
\(84\) 0 0
\(85\) 1.01017 + 5.24124i 0.109568 + 0.568493i
\(86\) 0 0
\(87\) 1.23127 + 4.11248i 0.132006 + 0.440904i
\(88\) 0 0
\(89\) 4.10997 6.39524i 0.435656 0.677894i −0.552122 0.833763i \(-0.686182\pi\)
0.987778 + 0.155870i \(0.0498180\pi\)
\(90\) 0 0
\(91\) −2.82253 + 3.25737i −0.295881 + 0.341465i
\(92\) 0 0
\(93\) −3.28504 5.05248i −0.340643 0.523917i
\(94\) 0 0
\(95\) −0.0280235 + 0.115514i −0.00287515 + 0.0118515i
\(96\) 0 0
\(97\) 1.05636 + 0.609890i 0.107257 + 0.0619250i 0.552669 0.833401i \(-0.313609\pi\)
−0.445412 + 0.895326i \(0.646943\pi\)
\(98\) 0 0
\(99\) −7.79029 0.660540i −0.782954 0.0663868i
\(100\) 0 0
\(101\) 6.68674 9.39021i 0.665355 0.934360i −0.334613 0.942356i \(-0.608606\pi\)
0.999968 + 0.00799517i \(0.00254497\pi\)
\(102\) 0 0
\(103\) 0.528083 + 0.503526i 0.0520335 + 0.0496139i 0.715650 0.698459i \(-0.246131\pi\)
−0.663616 + 0.748073i \(0.730979\pi\)
\(104\) 0 0
\(105\) −1.05801 + 3.67527i −0.103251 + 0.358670i
\(106\) 0 0
\(107\) 6.25579 0.899446i 0.604770 0.0869527i 0.166874 0.985978i \(-0.446633\pi\)
0.437896 + 0.899026i \(0.355724\pi\)
\(108\) 0 0
\(109\) 3.35712 11.4333i 0.321554 1.09511i −0.627138 0.778908i \(-0.715774\pi\)
0.948692 0.316203i \(-0.102408\pi\)
\(110\) 0 0
\(111\) −8.27697 7.80865i −0.785616 0.741165i
\(112\) 0 0
\(113\) 6.30125 4.95536i 0.592772 0.466161i −0.276147 0.961115i \(-0.589058\pi\)
0.868919 + 0.494954i \(0.164815\pi\)
\(114\) 0 0
\(115\) −0.0484505 + 0.507396i −0.00451803 + 0.0473149i
\(116\) 0 0
\(117\) 2.43595 + 7.98176i 0.225204 + 0.737914i
\(118\) 0 0
\(119\) 2.41083 + 5.27899i 0.221001 + 0.483924i
\(120\) 0 0
\(121\) −3.04572 + 2.90409i −0.276883 + 0.264008i
\(122\) 0 0
\(123\) −1.05511 + 2.34319i −0.0951361 + 0.211278i
\(124\) 0 0
\(125\) 4.71775 10.3304i 0.421969 0.923983i
\(126\) 0 0
\(127\) 11.8766 1.13408i 1.05388 0.100633i 0.446292 0.894887i \(-0.352744\pi\)
0.607586 + 0.794254i \(0.292138\pi\)
\(128\) 0 0
\(129\) −12.8978 + 9.28804i −1.13559 + 0.817766i
\(130\) 0 0
\(131\) 3.67671 + 5.72108i 0.321236 + 0.499853i 0.963889 0.266305i \(-0.0858027\pi\)
−0.642653 + 0.766157i \(0.722166\pi\)
\(132\) 0 0
\(133\) 0.129236i 0.0112062i
\(134\) 0 0
\(135\) 4.93771 + 5.51843i 0.424970 + 0.474951i
\(136\) 0 0
\(137\) −1.14559 + 0.736228i −0.0978746 + 0.0629002i −0.588663 0.808379i \(-0.700345\pi\)
0.490788 + 0.871279i \(0.336709\pi\)
\(138\) 0 0
\(139\) 10.8784 + 1.56408i 0.922694 + 0.132663i 0.587258 0.809400i \(-0.300207\pi\)
0.335436 + 0.942063i \(0.391116\pi\)
\(140\) 0 0
\(141\) 16.8227 + 14.4214i 1.41673 + 1.21450i
\(142\) 0 0
\(143\) −6.59431 3.01152i −0.551444 0.251836i
\(144\) 0 0
\(145\) 1.31273 + 3.27905i 0.109017 + 0.272310i
\(146\) 0 0
\(147\) 0.336818 7.95900i 0.0277803 0.656448i
\(148\) 0 0
\(149\) 15.7872 7.20977i 1.29334 0.590648i 0.354516 0.935050i \(-0.384646\pi\)
0.938822 + 0.344403i \(0.111919\pi\)
\(150\) 0 0
\(151\) 0.992148 + 2.86662i 0.0807399 + 0.233283i 0.978145 0.207926i \(-0.0666712\pi\)
−0.897405 + 0.441208i \(0.854550\pi\)
\(152\) 0 0
\(153\) 11.1385 + 1.48101i 0.900495 + 0.119733i
\(154\) 0 0
\(155\) −3.06514 3.89764i −0.246198 0.313066i
\(156\) 0 0
\(157\) 0.328555 + 6.89723i 0.0262216 + 0.550459i 0.973311 + 0.229489i \(0.0737056\pi\)
−0.947090 + 0.320969i \(0.895991\pi\)
\(158\) 0 0
\(159\) −3.15610 + 1.64834i −0.250295 + 0.130722i
\(160\) 0 0
\(161\) 0.0788676 + 0.548536i 0.00621564 + 0.0432307i
\(162\) 0 0
\(163\) 3.61487 + 6.26113i 0.283138 + 0.490410i 0.972156 0.234335i \(-0.0752912\pi\)
−0.689018 + 0.724744i \(0.741958\pi\)
\(164\) 0 0
\(165\) −6.43259 + 0.0341313i −0.500776 + 0.00265712i
\(166\) 0 0
\(167\) 2.39412 + 1.70485i 0.185263 + 0.131925i 0.668925 0.743329i \(-0.266755\pi\)
−0.483663 + 0.875254i \(0.660694\pi\)
\(168\) 0 0
\(169\) 0.250374 5.25600i 0.0192596 0.404308i
\(170\) 0 0
\(171\) 0.211927 + 0.133041i 0.0162065 + 0.0101739i
\(172\) 0 0
\(173\) −5.89177 1.42933i −0.447943 0.108670i 0.00544065 0.999985i \(-0.498268\pi\)
−0.453384 + 0.891315i \(0.649783\pi\)
\(174\) 0 0
\(175\) 0.870640 4.51731i 0.0658142 0.341477i
\(176\) 0 0
\(177\) 5.29285 0.280284i 0.397835 0.0210675i
\(178\) 0 0
\(179\) 4.82757 + 3.10249i 0.360829 + 0.231891i 0.708476 0.705735i \(-0.249383\pi\)
−0.347647 + 0.937626i \(0.613019\pi\)
\(180\) 0 0
\(181\) 20.1033 + 10.3640i 1.49427 + 0.770348i 0.995352 0.0963033i \(-0.0307019\pi\)
0.498915 + 0.866651i \(0.333732\pi\)
\(182\) 0 0
\(183\) −15.8521 11.1619i −1.17182 0.825114i
\(184\) 0 0
\(185\) −7.35939 5.78748i −0.541073 0.425504i
\(186\) 0 0
\(187\) −7.37695 + 6.39217i −0.539456 + 0.467442i
\(188\) 0 0
\(189\) 6.63174 + 4.56512i 0.482388 + 0.332064i
\(190\) 0 0
\(191\) 24.0016 12.3737i 1.73669 0.895328i 0.770527 0.637407i \(-0.219993\pi\)
0.966166 0.257921i \(-0.0830374\pi\)
\(192\) 0 0
\(193\) 2.62247 0.770026i 0.188769 0.0554277i −0.185981 0.982553i \(-0.559546\pi\)
0.374751 + 0.927126i \(0.377728\pi\)
\(194\) 0 0
\(195\) 2.58571 + 6.36077i 0.185167 + 0.455504i
\(196\) 0 0
\(197\) −0.305616 + 0.883020i −0.0217743 + 0.0629126i −0.955364 0.295430i \(-0.904537\pi\)
0.933590 + 0.358343i \(0.116658\pi\)
\(198\) 0 0
\(199\) 0.0656217 + 0.0921528i 0.00465180 + 0.00653254i 0.816895 0.576786i \(-0.195693\pi\)
−0.812244 + 0.583319i \(0.801754\pi\)
\(200\) 0 0
\(201\) 4.28126 13.5156i 0.301977 0.953315i
\(202\) 0 0
\(203\) 2.22756 + 3.12817i 0.156344 + 0.219555i
\(204\) 0 0
\(205\) −0.691541 + 1.99808i −0.0482993 + 0.139552i
\(206\) 0 0
\(207\) 0.980702 + 0.435354i 0.0681635 + 0.0302592i
\(208\) 0 0
\(209\) −0.208565 + 0.0612401i −0.0144267 + 0.00423607i
\(210\) 0 0
\(211\) −18.2747 + 9.42126i −1.25808 + 0.648587i −0.952778 0.303668i \(-0.901789\pi\)
−0.305305 + 0.952255i \(0.598758\pi\)
\(212\) 0 0
\(213\) −3.48793 + 5.49117i −0.238989 + 0.376248i
\(214\) 0 0
\(215\) −9.88316 + 8.56381i −0.674026 + 0.584047i
\(216\) 0 0
\(217\) −4.23772 3.33258i −0.287675 0.226230i
\(218\) 0 0
\(219\) −3.74572 + 5.31965i −0.253113 + 0.359468i
\(220\) 0 0
\(221\) 9.26079 + 4.77427i 0.622948 + 0.321152i
\(222\) 0 0
\(223\) −5.19600 3.33927i −0.347950 0.223614i 0.354979 0.934874i \(-0.384488\pi\)
−0.702928 + 0.711261i \(0.748125\pi\)
\(224\) 0 0
\(225\) −6.51140 6.07801i −0.434093 0.405200i
\(226\) 0 0
\(227\) −4.20062 + 21.7949i −0.278805 + 1.44658i 0.524704 + 0.851285i \(0.324176\pi\)
−0.803509 + 0.595292i \(0.797036\pi\)
\(228\) 0 0
\(229\) 4.93842 + 1.19805i 0.326340 + 0.0791693i 0.395582 0.918431i \(-0.370543\pi\)
−0.0692419 + 0.997600i \(0.522058\pi\)
\(230\) 0 0
\(231\) −6.78796 + 1.68493i −0.446615 + 0.110860i
\(232\) 0 0
\(233\) −0.859288 + 18.0387i −0.0562938 + 1.18175i 0.777211 + 0.629240i \(0.216634\pi\)
−0.833505 + 0.552512i \(0.813669\pi\)
\(234\) 0 0
\(235\) 14.8507 + 10.5751i 0.968750 + 0.689844i
\(236\) 0 0
\(237\) 0.0224955 + 4.23962i 0.00146124 + 0.275393i
\(238\) 0 0
\(239\) −11.4331 19.8027i −0.739545 1.28093i −0.952700 0.303911i \(-0.901707\pi\)
0.213156 0.977018i \(-0.431626\pi\)
\(240\) 0 0
\(241\) −2.88317 20.0529i −0.185722 1.29172i −0.842934 0.538017i \(-0.819174\pi\)
0.657213 0.753705i \(-0.271735\pi\)
\(242\) 0 0
\(243\) 14.3130 6.17549i 0.918182 0.396158i
\(244\) 0 0
\(245\) −0.311869 6.54693i −0.0199246 0.418268i
\(246\) 0 0
\(247\) 0.143425 + 0.182380i 0.00912595 + 0.0116046i
\(248\) 0 0
\(249\) 5.84684 + 7.35422i 0.370529 + 0.466055i
\(250\) 0 0
\(251\) 2.54986 + 7.36734i 0.160946 + 0.465022i 0.996423 0.0845023i \(-0.0269300\pi\)
−0.835477 + 0.549525i \(0.814809\pi\)
\(252\) 0 0
\(253\) −0.847869 + 0.387209i −0.0533050 + 0.0243436i
\(254\) 0 0
\(255\) 9.23690 + 0.390898i 0.578437 + 0.0244790i
\(256\) 0 0
\(257\) 10.2940 + 25.7132i 0.642122 + 1.60394i 0.788724 + 0.614748i \(0.210742\pi\)
−0.146602 + 0.989196i \(0.546834\pi\)
\(258\) 0 0
\(259\) −9.25947 4.22866i −0.575355 0.262756i
\(260\) 0 0
\(261\) 7.42284 0.432586i 0.459462 0.0267764i
\(262\) 0 0
\(263\) −6.22844 0.895514i −0.384062 0.0552198i −0.0524201 0.998625i \(-0.516693\pi\)
−0.331642 + 0.943405i \(0.607603\pi\)
\(264\) 0 0
\(265\) −2.46453 + 1.58386i −0.151395 + 0.0972957i
\(266\) 0 0
\(267\) −9.13678 9.48114i −0.559162 0.580236i
\(268\) 0 0
\(269\) 13.0797i 0.797486i 0.917063 + 0.398743i \(0.130553\pi\)
−0.917063 + 0.398743i \(0.869447\pi\)
\(270\) 0 0
\(271\) 4.10696 + 6.39055i 0.249480 + 0.388199i 0.943295 0.331954i \(-0.107708\pi\)
−0.693815 + 0.720153i \(0.744072\pi\)
\(272\) 0 0
\(273\) 4.36253 + 6.05803i 0.264032 + 0.366649i
\(274\) 0 0
\(275\) 7.70270 0.735519i 0.464491 0.0443535i
\(276\) 0 0
\(277\) 6.98148 15.2873i 0.419477 0.918526i −0.575442 0.817843i \(-0.695170\pi\)
0.994919 0.100683i \(-0.0321028\pi\)
\(278\) 0 0
\(279\) −9.82737 + 3.51850i −0.588349 + 0.210647i
\(280\) 0 0
\(281\) 14.5570 13.8800i 0.868396 0.828013i −0.117896 0.993026i \(-0.537615\pi\)
0.986291 + 0.165012i \(0.0527664\pi\)
\(282\) 0 0
\(283\) 0.488456 + 1.06957i 0.0290357 + 0.0635793i 0.923594 0.383372i \(-0.125237\pi\)
−0.894558 + 0.446951i \(0.852510\pi\)
\(284\) 0 0
\(285\) 0.183492 + 0.0933675i 0.0108691 + 0.00553061i
\(286\) 0 0
\(287\) −0.218519 + 2.28844i −0.0128988 + 0.135082i
\(288\) 0 0
\(289\) −2.33548 + 1.83664i −0.137381 + 0.108038i
\(290\) 0 0
\(291\) 1.44981 1.53676i 0.0849894 0.0900866i
\(292\) 0 0
\(293\) −0.126387 + 0.430435i −0.00738362 + 0.0251463i −0.963102 0.269135i \(-0.913262\pi\)
0.955719 + 0.294282i \(0.0950803\pi\)
\(294\) 0 0
\(295\) 4.31656 0.620627i 0.251320 0.0361343i
\(296\) 0 0
\(297\) −4.22477 + 12.8657i −0.245146 + 0.746543i
\(298\) 0 0
\(299\) 0.720061 + 0.686577i 0.0416422 + 0.0397058i
\(300\) 0 0
\(301\) −8.24744 + 11.5819i −0.475375 + 0.667570i
\(302\) 0 0
\(303\) −13.1552 15.0202i −0.755748 0.862886i
\(304\) 0 0
\(305\) −13.8145 7.97583i −0.791018 0.456694i
\(306\) 0 0
\(307\) −7.26725 + 29.9560i −0.414764 + 1.70968i 0.254859 + 0.966978i \(0.417971\pi\)
−0.669623 + 0.742701i \(0.733544\pi\)
\(308\) 0 0
\(309\) 1.05955 0.688902i 0.0602756 0.0391903i
\(310\) 0 0
\(311\) −4.38634 + 5.06210i −0.248726 + 0.287045i −0.866360 0.499421i \(-0.833546\pi\)
0.617633 + 0.786466i \(0.288092\pi\)
\(312\) 0 0
\(313\) 10.4654 16.2844i 0.591538 0.920450i −0.408433 0.912788i \(-0.633925\pi\)
0.999971 0.00766215i \(-0.00243896\pi\)
\(314\) 0 0
\(315\) 5.77161 + 3.25107i 0.325194 + 0.183177i
\(316\) 0 0
\(317\) −1.11635 5.79218i −0.0627005 0.325321i 0.937012 0.349297i \(-0.113580\pi\)
−0.999713 + 0.0239760i \(0.992367\pi\)
\(318\) 0 0
\(319\) −3.99276 + 5.07721i −0.223552 + 0.284269i
\(320\) 0 0
\(321\) 0.982721 10.9026i 0.0548502 0.608522i
\(322\) 0 0
\(323\) 0.303602 0.0736529i 0.0168928 0.00409816i
\(324\) 0 0
\(325\) −3.78462 7.34113i −0.209933 0.407213i
\(326\) 0 0
\(327\) −17.9285 10.2246i −0.991447 0.565419i
\(328\) 0 0
\(329\) 18.4020 + 7.36705i 1.01453 + 0.406158i
\(330\) 0 0
\(331\) −0.801830 0.277516i −0.0440726 0.0152537i 0.304943 0.952371i \(-0.401363\pi\)
−0.349015 + 0.937117i \(0.613484\pi\)
\(332\) 0 0
\(333\) −16.4664 + 10.8309i −0.902352 + 0.593530i
\(334\) 0 0
\(335\) 2.51000 11.3916i 0.137136 0.622392i
\(336\) 0 0
\(337\) −3.49556 + 2.48918i −0.190415 + 0.135594i −0.671289 0.741196i \(-0.734259\pi\)
0.480874 + 0.876790i \(0.340320\pi\)
\(338\) 0 0
\(339\) −5.83484 12.5992i −0.316905 0.684293i
\(340\) 0 0
\(341\) 3.37010 8.41811i 0.182501 0.455866i
\(342\) 0 0
\(343\) −5.06338 17.2443i −0.273397 0.931104i
\(344\) 0 0
\(345\) 0.835799 + 0.284316i 0.0449979 + 0.0153070i
\(346\) 0 0
\(347\) −5.13930 21.1845i −0.275892 1.13724i −0.926037 0.377433i \(-0.876807\pi\)
0.650145 0.759810i \(-0.274708\pi\)
\(348\) 0 0
\(349\) −11.2600 12.9947i −0.602732 0.695590i 0.369600 0.929191i \(-0.379495\pi\)
−0.972333 + 0.233601i \(0.924949\pi\)
\(350\) 0 0
\(351\) 14.4252 0.917488i 0.769958 0.0489719i
\(352\) 0 0
\(353\) −33.7883 + 6.51216i −1.79837 + 0.346607i −0.975224 0.221221i \(-0.928996\pi\)
−0.823147 + 0.567829i \(0.807784\pi\)
\(354\) 0 0
\(355\) −2.45261 + 4.75740i −0.130171 + 0.252496i
\(356\) 0 0
\(357\) 9.85996 1.95467i 0.521844 0.103452i
\(358\) 0 0
\(359\) −9.21787 7.98733i −0.486501 0.421555i 0.376762 0.926310i \(-0.377037\pi\)
−0.863263 + 0.504755i \(0.831583\pi\)
\(360\) 0 0
\(361\) −18.6498 3.59446i −0.981569 0.189182i
\(362\) 0 0
\(363\) 3.67797 + 6.29308i 0.193043 + 0.330301i
\(364\) 0 0
\(365\) −2.67653 + 4.63589i −0.140096 + 0.242653i
\(366\) 0 0
\(367\) −12.5256 0.596669i −0.653832 0.0311459i −0.281955 0.959428i \(-0.590983\pi\)
−0.371877 + 0.928282i \(0.621286\pi\)
\(368\) 0 0
\(369\) 3.52772 + 2.71414i 0.183646 + 0.141293i
\(370\) 0 0
\(371\) −2.19805 + 2.30525i −0.114117 + 0.119682i
\(372\) 0 0
\(373\) 17.8677 10.3159i 0.925152 0.534137i 0.0398769 0.999205i \(-0.487303\pi\)
0.885275 + 0.465068i \(0.153970\pi\)
\(374\) 0 0
\(375\) −15.5263 12.0772i −0.801774 0.623666i
\(376\) 0 0
\(377\) 6.61519 + 1.94239i 0.340700 + 0.100038i
\(378\) 0 0
\(379\) 3.61034 0.171982i 0.185451 0.00883410i 0.0453489 0.998971i \(-0.485560\pi\)
0.140102 + 0.990137i \(0.455257\pi\)
\(380\) 0 0
\(381\) 2.83229 20.4694i 0.145103 1.04868i
\(382\) 0 0
\(383\) −33.6647 3.21459i −1.72019 0.164258i −0.812234 0.583332i \(-0.801749\pi\)
−0.907952 + 0.419075i \(0.862355\pi\)
\(384\) 0 0
\(385\) −5.43798 + 1.88210i −0.277145 + 0.0959208i
\(386\) 0 0
\(387\) 10.5023 + 25.4474i 0.533860 + 1.29356i
\(388\) 0 0
\(389\) −5.78914 6.07148i −0.293521 0.307836i 0.560417 0.828211i \(-0.310641\pi\)
−0.853938 + 0.520374i \(0.825792\pi\)
\(390\) 0 0
\(391\) 1.24367 0.497891i 0.0628952 0.0251795i
\(392\) 0 0
\(393\) 11.1106 3.91157i 0.560458 0.197312i
\(394\) 0 0
\(395\) 0.331586 + 3.47252i 0.0166839 + 0.174722i
\(396\) 0 0
\(397\) −0.615406 + 4.28024i −0.0308864 + 0.214819i −0.999420 0.0340648i \(-0.989155\pi\)
0.968533 + 0.248884i \(0.0800638\pi\)
\(398\) 0 0
\(399\) 0.217811 + 0.0516182i 0.0109042 + 0.00258414i
\(400\) 0 0
\(401\) −8.18648 −0.408813 −0.204407 0.978886i \(-0.565526\pi\)
−0.204407 + 0.978886i \(0.565526\pi\)
\(402\) 0 0
\(403\) −9.67881 −0.482136
\(404\) 0 0
\(405\) 11.2728 6.11775i 0.560148 0.303993i
\(406\) 0 0
\(407\) 2.43660 16.9469i 0.120778 0.840029i
\(408\) 0 0
\(409\) 0.349654 + 3.66174i 0.0172893 + 0.181062i 0.999991 0.00413133i \(-0.00131505\pi\)
−0.982702 + 0.185193i \(0.940709\pi\)
\(410\) 0 0
\(411\) 0.783255 + 2.22480i 0.0386351 + 0.109741i
\(412\) 0 0
\(413\) 4.40181 1.76222i 0.216599 0.0867131i
\(414\) 0 0
\(415\) 5.33444 + 5.59460i 0.261857 + 0.274628i
\(416\) 0 0
\(417\) 6.98099 17.7094i 0.341860 0.867234i
\(418\) 0 0
\(419\) 19.7012 6.81865i 0.962466 0.333113i 0.199750 0.979847i \(-0.435987\pi\)
0.762716 + 0.646734i \(0.223866\pi\)
\(420\) 0 0
\(421\) −2.93353 0.280118i −0.142972 0.0136521i 0.0233249 0.999728i \(-0.492575\pi\)
−0.166296 + 0.986076i \(0.553181\pi\)
\(422\) 0 0
\(423\) 31.0245 22.5924i 1.50846 1.09848i
\(424\) 0 0
\(425\) −11.1082 + 0.529151i −0.538829 + 0.0256676i
\(426\) 0 0
\(427\) −16.6409 4.88622i −0.805312 0.236461i
\(428\) 0 0
\(429\) −7.70935 + 9.91102i −0.372211 + 0.478508i
\(430\) 0 0
\(431\) 0.139674 0.0806411i 0.00672788 0.00388434i −0.496632 0.867961i \(-0.665430\pi\)
0.503360 + 0.864077i \(0.332097\pi\)
\(432\) 0 0
\(433\) −9.23625 + 9.68670i −0.443866 + 0.465513i −0.907218 0.420661i \(-0.861798\pi\)
0.463352 + 0.886174i \(0.346647\pi\)
\(434\) 0 0
\(435\) 6.05074 0.902758i 0.290111 0.0432840i
\(436\) 0 0
\(437\) 0.0297984 + 0.00141947i 0.00142545 + 6.79027e-5i
\(438\) 0 0
\(439\) 10.2184 17.6988i 0.487699 0.844719i −0.512201 0.858865i \(-0.671170\pi\)
0.999900 + 0.0141468i \(0.00450321\pi\)
\(440\) 0 0
\(441\) −13.2793 3.74657i −0.632349 0.178408i
\(442\) 0 0
\(443\) −2.47875 0.477739i −0.117769 0.0226981i 0.130026 0.991511i \(-0.458494\pi\)
−0.247795 + 0.968812i \(0.579706\pi\)
\(444\) 0 0
\(445\) −8.18749 7.09450i −0.388124 0.336312i
\(446\) 0 0
\(447\) −5.84557 29.4869i −0.276486 1.39468i
\(448\) 0 0
\(449\) −15.3573 + 29.7891i −0.724757 + 1.40583i 0.181623 + 0.983368i \(0.441865\pi\)
−0.906380 + 0.422464i \(0.861165\pi\)
\(450\) 0 0
\(451\) −3.79668 + 0.731751i −0.178779 + 0.0344568i
\(452\) 0 0
\(453\) 5.22760 0.527180i 0.245614 0.0247691i
\(454\) 0 0
\(455\) 4.02236 + 4.64206i 0.188571 + 0.217623i
\(456\) 0 0
\(457\) 1.47064 + 6.06204i 0.0687935 + 0.283571i 0.995810 0.0914510i \(-0.0291505\pi\)
−0.927016 + 0.375021i \(0.877635\pi\)
\(458\) 0 0
\(459\) 6.94488 18.1810i 0.324159 0.848615i
\(460\) 0 0
\(461\) 0.207098 + 0.705312i 0.00964552 + 0.0328496i 0.964175 0.265266i \(-0.0854599\pi\)
−0.954530 + 0.298116i \(0.903642\pi\)
\(462\) 0 0
\(463\) 2.50929 6.26790i 0.116616 0.291294i −0.858564 0.512707i \(-0.828643\pi\)
0.975180 + 0.221413i \(0.0710670\pi\)
\(464\) 0 0
\(465\) −7.79321 + 3.60913i −0.361401 + 0.167370i
\(466\) 0 0
\(467\) −16.6138 + 11.8307i −0.768796 + 0.547457i −0.895807 0.444444i \(-0.853401\pi\)
0.127010 + 0.991901i \(0.459462\pi\)
\(468\) 0 0
\(469\) −0.267940 12.6799i −0.0123723 0.585501i
\(470\) 0 0
\(471\) 11.7556 + 2.20108i 0.541670 + 0.101420i
\(472\) 0 0
\(473\) −22.5993 7.82169i −1.03912 0.359642i
\(474\) 0 0
\(475\) −0.229910 0.0920419i −0.0105490 0.00422317i
\(476\) 0 0
\(477\) 1.51748 + 5.97756i 0.0694807 + 0.273694i
\(478\) 0 0
\(479\) 9.11674 + 17.6840i 0.416554 + 0.808003i 0.999991 0.00415563i \(-0.00132278\pi\)
−0.583437 + 0.812158i \(0.698292\pi\)
\(480\) 0 0
\(481\) −17.7600 + 4.30854i −0.809788 + 0.196452i
\(482\) 0 0
\(483\) 0.955987 + 0.0861696i 0.0434989 + 0.00392085i
\(484\) 0 0
\(485\) 1.07455 1.36640i 0.0487926 0.0620449i
\(486\) 0 0
\(487\) −1.09713 5.69243i −0.0497155 0.257949i 0.948564 0.316586i \(-0.102537\pi\)
−0.998279 + 0.0586373i \(0.981324\pi\)
\(488\) 0 0
\(489\) 11.9961 3.59163i 0.542484 0.162419i
\(490\) 0 0
\(491\) 18.9279 29.4524i 0.854204 1.32917i −0.0886844 0.996060i \(-0.528266\pi\)
0.942889 0.333108i \(-0.108097\pi\)
\(492\) 0 0
\(493\) 6.07918 7.01575i 0.273793 0.315973i
\(494\) 0 0
\(495\) −2.51171 + 10.8549i −0.112893 + 0.487893i
\(496\) 0 0
\(497\) −1.37198 + 5.65536i −0.0615416 + 0.253678i
\(498\) 0 0
\(499\) 29.2314 + 16.8767i 1.30858 + 0.755507i 0.981859 0.189615i \(-0.0607240\pi\)
0.326718 + 0.945122i \(0.394057\pi\)
\(500\) 0 0
\(501\) 3.82953 3.35405i 0.171091 0.149848i
\(502\) 0 0
\(503\) 9.88721 13.8846i 0.440849 0.619086i −0.533046 0.846086i \(-0.678953\pi\)
0.973895 + 0.227001i \(0.0728920\pi\)
\(504\) 0 0
\(505\) −11.8896 11.3367i −0.529079 0.504475i
\(506\) 0 0
\(507\) −8.75831 2.52127i −0.388970 0.111974i
\(508\) 0 0
\(509\) −27.9399 + 4.01716i −1.23842 + 0.178057i −0.730237 0.683194i \(-0.760590\pi\)
−0.508179 + 0.861251i \(0.669681\pi\)
\(510\) 0 0
\(511\) −1.63972 + 5.58437i −0.0725369 + 0.247038i
\(512\) 0 0
\(513\) 0.308869 0.304038i 0.0136369 0.0134236i
\(514\) 0 0
\(515\) 0.817369 0.642786i 0.0360176 0.0283245i
\(516\) 0 0
\(517\) −3.16912 + 33.1885i −0.139378 + 1.45963i
\(518\) 0 0
\(519\) −4.76218 + 9.35893i −0.209036 + 0.410811i
\(520\) 0 0
\(521\) 5.69828 + 12.4775i 0.249646 + 0.546649i 0.992420 0.122894i \(-0.0392174\pi\)
−0.742774 + 0.669543i \(0.766490\pi\)
\(522\) 0 0
\(523\) 0.277148 0.264260i 0.0121188 0.0115553i −0.683995 0.729486i \(-0.739759\pi\)
0.696114 + 0.717931i \(0.254911\pi\)
\(524\) 0 0
\(525\) −7.26560 3.27161i −0.317097 0.142785i
\(526\) 0 0
\(527\) −5.41377 + 11.8545i −0.235827 + 0.516390i
\(528\) 0 0
\(529\) −22.7685 + 2.17413i −0.989935 + 0.0945274i
\(530\) 0 0
\(531\) 1.64163 9.03236i 0.0712408 0.391971i
\(532\) 0 0
\(533\) 2.23131 + 3.47199i 0.0966489 + 0.150389i
\(534\) 0 0
\(535\) 9.00675i 0.389396i
\(536\) 0 0
\(537\) 7.15702 6.89708i 0.308848 0.297631i
\(538\) 0 0
\(539\) 10.0833 6.48013i 0.434317 0.279119i
\(540\) 0 0
\(541\) −16.3582 2.35195i −0.703294 0.101118i −0.218616 0.975811i \(-0.570154\pi\)
−0.484678 + 0.874693i \(0.661063\pi\)
\(542\) 0 0
\(543\) 25.4966 29.7420i 1.09416 1.27635i
\(544\) 0 0
\(545\) −15.4468 7.05432i −0.661669 0.302174i
\(546\) 0 0
\(547\) 1.10381 + 2.75718i 0.0471955 + 0.117889i 0.950093 0.311968i \(-0.100988\pi\)
−0.902897 + 0.429857i \(0.858564\pi\)
\(548\) 0 0
\(549\) −25.1435 + 22.2584i −1.07310 + 0.949967i
\(550\) 0 0
\(551\) 0.188045 0.0858772i 0.00801098 0.00365849i
\(552\) 0 0
\(553\) 1.24047 + 3.58409i 0.0527500 + 0.152411i
\(554\) 0 0
\(555\) −12.6935 + 10.0917i −0.538807 + 0.428369i
\(556\) 0 0
\(557\) −24.7197 31.4337i −1.04741 1.33189i −0.941314 0.337531i \(-0.890408\pi\)
−0.106094 0.994356i \(-0.533834\pi\)
\(558\) 0 0
\(559\) 1.21460 + 25.4975i 0.0513720 + 1.07843i
\(560\) 0 0
\(561\) 7.82674 + 14.9860i 0.330445 + 0.632709i
\(562\) 0 0
\(563\) 3.39797 + 23.6334i 0.143208 + 0.996030i 0.927014 + 0.375026i \(0.122366\pi\)
−0.783807 + 0.621005i \(0.786725\pi\)
\(564\) 0 0
\(565\) −5.71200 9.89348i −0.240306 0.416222i
\(566\) 0 0
\(567\) 10.3427 9.35359i 0.434353 0.392814i
\(568\) 0 0
\(569\) −0.941694 0.670577i −0.0394778 0.0281120i 0.560148 0.828393i \(-0.310744\pi\)
−0.599626 + 0.800281i \(0.704684\pi\)
\(570\) 0 0
\(571\) −2.14806 + 45.0934i −0.0898936 + 1.88710i 0.282848 + 0.959165i \(0.408721\pi\)
−0.372742 + 0.927935i \(0.621582\pi\)
\(572\) 0 0
\(573\) −11.2678 45.3937i −0.470717 1.89635i
\(574\) 0 0
\(575\) −1.03201 0.250362i −0.0430377 0.0104408i
\(576\) 0 0
\(577\) −5.19434 + 26.9508i −0.216243 + 1.12198i 0.697779 + 0.716313i \(0.254172\pi\)
−0.914022 + 0.405664i \(0.867040\pi\)
\(578\) 0 0
\(579\) −0.250340 4.72739i −0.0104038 0.196463i
\(580\) 0 0
\(581\) 7.07045 + 4.54390i 0.293332 + 0.188513i
\(582\) 0 0
\(583\) −4.76183 2.45489i −0.197215 0.101671i
\(584\) 0 0
\(585\) 11.7530 1.81733i 0.485927 0.0751372i
\(586\) 0 0
\(587\) −2.28824 1.79949i −0.0944459 0.0742730i 0.569820 0.821770i \(-0.307013\pi\)
−0.664265 + 0.747497i \(0.731256\pi\)
\(588\) 0 0
\(589\) −0.219328 + 0.190049i −0.00903727 + 0.00783084i
\(590\) 0 0
\(591\) 1.36615 + 0.867763i 0.0561959 + 0.0356950i
\(592\) 0 0
\(593\) 8.77838 4.52557i 0.360485 0.185843i −0.268464 0.963290i \(-0.586516\pi\)
0.628948 + 0.777447i \(0.283486\pi\)
\(594\) 0 0
\(595\) 7.93542 2.33005i 0.325321 0.0955227i
\(596\) 0 0
\(597\) 0.181522 0.0737902i 0.00742918 0.00302003i
\(598\) 0 0
\(599\) −12.1844 + 35.2044i −0.497839 + 1.43841i 0.364080 + 0.931368i \(0.381383\pi\)
−0.861920 + 0.507045i \(0.830738\pi\)
\(600\) 0 0
\(601\) −7.04162 9.88857i −0.287234 0.403363i 0.645597 0.763678i \(-0.276609\pi\)
−0.932831 + 0.360315i \(0.882669\pi\)
\(602\) 0 0
\(603\) −21.0688 12.6138i −0.857987 0.513672i
\(604\) 0 0
\(605\) 3.47876 + 4.88524i 0.141432 + 0.198613i
\(606\) 0 0
\(607\) 3.42463 9.89481i 0.139001 0.401618i −0.853918 0.520407i \(-0.825780\pi\)
0.992919 + 0.118789i \(0.0379014\pi\)
\(608\) 0 0
\(609\) 6.16183 2.50484i 0.249690 0.101501i
\(610\) 0 0
\(611\) 34.1451 10.0259i 1.38136 0.405604i
\(612\) 0 0
\(613\) −27.7057 + 14.2833i −1.11902 + 0.576896i −0.915558 0.402187i \(-0.868250\pi\)
−0.203464 + 0.979082i \(0.565220\pi\)
\(614\) 0 0
\(615\) 3.09129 + 1.96355i 0.124653 + 0.0791781i
\(616\) 0 0
\(617\) 29.9576 25.9584i 1.20605 1.04505i 0.208292 0.978067i \(-0.433209\pi\)
0.997754 0.0669789i \(-0.0213360\pi\)
\(618\) 0 0
\(619\) 20.8262 + 16.3779i 0.837075 + 0.658283i 0.941783 0.336220i \(-0.109149\pi\)
−0.104709 + 0.994503i \(0.533391\pi\)
\(620\) 0 0
\(621\) 1.12543 1.47896i 0.0451621 0.0593487i
\(622\) 0 0
\(623\) −10.4695 5.39739i −0.419451 0.216242i
\(624\) 0 0
\(625\) −1.12631 0.723833i −0.0450522 0.0289533i
\(626\) 0 0
\(627\) 0.0199095 + 0.375968i 0.000795109 + 0.0150147i
\(628\) 0 0
\(629\) −4.65689 + 24.1623i −0.185682 + 0.963412i
\(630\) 0 0
\(631\) 28.0316 + 6.80039i 1.11592 + 0.270719i 0.750989 0.660315i \(-0.229577\pi\)
0.364931 + 0.931034i \(0.381092\pi\)
\(632\) 0 0
\(633\) 8.57922 + 34.5626i 0.340994 + 1.37374i
\(634\) 0 0
\(635\) 0.809000 16.9830i 0.0321042 0.673950i
\(636\) 0 0
\(637\) −10.4216 7.42117i −0.412918 0.294038i
\(638\) 0 0
\(639\) 7.86153 + 8.07167i 0.310997 + 0.319310i
\(640\) 0 0
\(641\) −4.54237 7.86762i −0.179413 0.310752i 0.762267 0.647263i \(-0.224087\pi\)
−0.941680 + 0.336511i \(0.890753\pi\)
\(642\) 0 0
\(643\) 4.62181 + 32.1454i 0.182267 + 1.26769i 0.851387 + 0.524538i \(0.175762\pi\)
−0.669120 + 0.743154i \(0.733329\pi\)
\(644\) 0 0
\(645\) 10.4858 + 20.0773i 0.412876 + 0.790541i
\(646\) 0 0
\(647\) 2.07032 + 43.4613i 0.0813926 + 1.70864i 0.558260 + 0.829666i \(0.311469\pi\)
−0.476867 + 0.878975i \(0.658228\pi\)
\(648\) 0 0
\(649\) 4.92976 + 6.26870i 0.193510 + 0.246068i
\(650\) 0 0
\(651\) −7.30921 + 5.81106i −0.286471 + 0.227753i
\(652\) 0 0
\(653\) 13.5176 + 39.0564i 0.528983 + 1.52840i 0.820394 + 0.571798i \(0.193754\pi\)
−0.291411 + 0.956598i \(0.594125\pi\)
\(654\) 0 0
\(655\) 8.81576 4.02602i 0.344460 0.157310i
\(656\) 0 0
\(657\) 7.46949 + 8.43765i 0.291413 + 0.329184i
\(658\) 0 0
\(659\) 15.5343 + 38.8029i 0.605132 + 1.51155i 0.841708 + 0.539933i \(0.181551\pi\)
−0.236576 + 0.971613i \(0.576025\pi\)
\(660\) 0 0
\(661\) 27.5555 + 12.5842i 1.07178 + 0.489468i 0.871563 0.490283i \(-0.163107\pi\)
0.200222 + 0.979751i \(0.435834\pi\)
\(662\) 0 0
\(663\) 11.7453 13.7010i 0.456148 0.532101i
\(664\) 0 0
\(665\) 0.182299 + 0.0262107i 0.00706926 + 0.00101641i
\(666\) 0 0
\(667\) 0.745739 0.479257i 0.0288751 0.0185569i
\(668\) 0 0
\(669\) −7.70323 + 7.42344i −0.297824 + 0.287007i
\(670\) 0 0
\(671\) 29.1709i 1.12613i
\(672\) 0 0
\(673\) −25.0388 38.9611i −0.965174 1.50184i −0.861832 0.507195i \(-0.830683\pi\)
−0.103343 0.994646i \(-0.532954\pi\)
\(674\) 0 0
\(675\) −12.8444 + 8.54651i −0.494381 + 0.328955i
\(676\) 0 0
\(677\) 21.2689 2.03094i 0.817432 0.0780553i 0.322041 0.946726i \(-0.395631\pi\)
0.495391 + 0.868670i \(0.335025\pi\)
\(678\) 0 0
\(679\) 0.785123 1.71918i 0.0301302 0.0659760i
\(680\) 0 0
\(681\) 35.0547 + 15.7847i 1.34330 + 0.604870i
\(682\) 0 0
\(683\) 5.96693 5.68946i 0.228318 0.217701i −0.567281 0.823524i \(-0.692005\pi\)
0.795599 + 0.605823i \(0.207156\pi\)
\(684\) 0 0
\(685\) 0.806174 + 1.76527i 0.0308023 + 0.0674477i
\(686\) 0 0
\(687\) 3.99161 7.84456i 0.152289 0.299288i
\(688\) 0 0
\(689\) −0.543575 + 5.69257i −0.0207086 + 0.216870i
\(690\) 0 0
\(691\) −11.6624 + 9.17143i −0.443659 + 0.348898i −0.814863 0.579654i \(-0.803188\pi\)
0.371203 + 0.928552i \(0.378945\pi\)
\(692\) 0 0
\(693\) 0.128549 + 12.1132i 0.00488317 + 0.460142i
\(694\) 0 0
\(695\) 4.41254 15.0277i 0.167377 0.570034i
\(696\) 0 0
\(697\) 5.50053 0.790857i 0.208347 0.0299558i
\(698\) 0 0
\(699\) 30.0586 + 8.65303i 1.13692 + 0.327288i
\(700\) 0 0
\(701\) 2.13427 + 2.03502i 0.0806103 + 0.0768618i 0.729313 0.684180i \(-0.239840\pi\)
−0.648703 + 0.761042i \(0.724688\pi\)
\(702\) 0 0
\(703\) −0.317854 + 0.446364i −0.0119881 + 0.0168349i
\(704\) 0 0
\(705\) 23.7545 20.8051i 0.894645 0.783564i
\(706\) 0 0
\(707\) −15.4685 8.93074i −0.581753 0.335875i
\(708\) 0 0
\(709\) 1.26490 5.21399i 0.0475043 0.195815i −0.943115 0.332467i \(-0.892119\pi\)
0.990619 + 0.136652i \(0.0436341\pi\)
\(710\) 0 0
\(711\) 7.15432 + 1.65543i 0.268308 + 0.0620836i
\(712\) 0 0
\(713\) −0.814948 + 0.940501i −0.0305201 + 0.0352220i
\(714\) 0 0
\(715\) −5.58542 + 8.69108i −0.208883 + 0.325028i
\(716\) 0 0
\(717\) −37.9413 + 11.3596i −1.41695 + 0.424232i
\(718\) 0 0
\(719\) −6.71790 34.8558i −0.250535 1.29990i −0.861303 0.508092i \(-0.830351\pi\)
0.610768 0.791810i \(-0.290861\pi\)
\(720\) 0 0
\(721\) 0.698871 0.888687i 0.0260273 0.0330964i
\(722\) 0 0
\(723\) −34.9481 3.15011i −1.29974 0.117154i
\(724\) 0 0
\(725\) −7.15144 + 1.73492i −0.265598 + 0.0644333i
\(726\) 0 0
\(727\) 4.27368 + 8.28979i 0.158502 + 0.307451i 0.954692 0.297596i \(-0.0961847\pi\)
−0.796190 + 0.605047i \(0.793154\pi\)
\(728\) 0 0
\(729\) −4.69123 26.5893i −0.173749 0.984790i
\(730\) 0 0
\(731\) 31.9085 + 12.7742i 1.18018 + 0.472472i
\(732\) 0 0
\(733\) −37.0304 12.8163i −1.36775 0.473382i −0.458151 0.888874i \(-0.651488\pi\)
−0.909597 + 0.415493i \(0.863609\pi\)
\(734\) 0 0
\(735\) −11.1586 2.08929i −0.411590 0.0770647i
\(736\) 0 0
\(737\) 20.3361 6.44090i 0.749089 0.237254i
\(738\) 0 0
\(739\) −4.98582 + 3.55039i −0.183406 + 0.130603i −0.668073 0.744096i \(-0.732880\pi\)
0.484666 + 0.874699i \(0.338941\pi\)
\(740\) 0 0
\(741\) 0.364664 0.168881i 0.0133963 0.00620398i
\(742\) 0 0
\(743\) 16.6185 41.5110i 0.609674 1.52289i −0.226263 0.974066i \(-0.572651\pi\)
0.835937 0.548825i \(-0.184925\pi\)
\(744\) 0 0
\(745\) −6.96818 23.7315i −0.255295 0.869453i
\(746\) 0 0
\(747\) 14.7299 6.91675i 0.538938 0.253071i
\(748\) 0 0
\(749\) −2.30870 9.51658i −0.0843580 0.347728i
\(750\) 0 0
\(751\) 25.8809 + 29.8682i 0.944408 + 1.08990i 0.995830 + 0.0912277i \(0.0290791\pi\)
−0.0514223 + 0.998677i \(0.516375\pi\)
\(752\) 0 0
\(753\) 13.4351 1.35487i 0.489603 0.0493743i
\(754\) 0 0
\(755\) 4.24484 0.818127i 0.154486 0.0297747i
\(756\) 0 0
\(757\) −12.3112 + 23.8803i −0.447457 + 0.867946i 0.551962 + 0.833869i \(0.313879\pi\)
−0.999419 + 0.0340765i \(0.989151\pi\)
\(758\) 0 0
\(759\) 0.313943 + 1.58363i 0.0113954 + 0.0574820i
\(760\) 0 0
\(761\) 25.0471 + 21.7035i 0.907958 + 0.786750i 0.977523 0.210827i \(-0.0676157\pi\)
−0.0695652 + 0.997577i \(0.522161\pi\)
\(762\) 0 0
\(763\) −18.1294 3.49416i −0.656329 0.126497i
\(764\) 0 0
\(765\) 4.34812 15.4115i 0.157206 0.557203i
\(766\) 0 0
\(767\) 4.25621 7.37197i 0.153683 0.266186i
\(768\) 0 0
\(769\) 3.40997 + 0.162437i 0.122966 + 0.00585762i 0.108975 0.994044i \(-0.465243\pi\)
0.0139916 + 0.999902i \(0.495546\pi\)
\(770\) 0 0
\(771\) 47.4477 7.07911i 1.70879 0.254948i
\(772\) 0 0
\(773\) −11.5079 + 12.0691i −0.413910 + 0.434096i −0.897376 0.441267i \(-0.854529\pi\)
0.483466 + 0.875363i \(0.339378\pi\)