Properties

Label 804.2.ba.b.41.2
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 41.2
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +O(q^{10})\) \(q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +(-2.41940 + 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(0.819678 - 2.32826i) q^{15} +(3.53951 - 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-0.269274 + 2.67016i) q^{21} +(0.357259 - 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-4.32601 - 2.87847i) q^{27} +(2.14642 - 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(4.43676 - 0.830725i) q^{33} +(2.20559 + 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(2.58332 + 4.06701i) q^{39} +(1.45686 + 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.17681 + 3.67961i) q^{45} +(5.86207 - 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(-6.42619 + 0.889171i) q^{51} +(1.34621 + 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(0.138398 + 0.0414362i) q^{57} +(-0.862133 - 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(1.35684 - 4.44587i) q^{63} +(3.22916 - 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.612710 - 0.0914151i) q^{69} +(3.54925 + 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(-4.55840 - 2.38072i) q^{75} +(1.85030 + 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(6.38033 + 6.34755i) q^{81} +(3.35310 - 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(-4.06414 + 1.38251i) q^{87} +(-4.10997 + 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-4.92754 + 3.46963i) q^{93} +(0.0280235 - 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.81780 - 0.0829650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −1.69899 0.336812i −0.980911 0.194459i
\(4\) 0 0
\(5\) −0.202812 + 1.41059i −0.0907002 + 0.630834i 0.892871 + 0.450313i \(0.148688\pi\)
−0.983571 + 0.180521i \(0.942222\pi\)
\(6\) 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
\(9\) 2.77312 + 1.14448i 0.924372 + 0.381493i
\(10\) 0 0
\(11\) −2.41940 + 0.968583i −0.729477 + 0.292039i −0.706515 0.707698i \(-0.749734\pi\)
−0.0229619 + 0.999736i \(0.507310\pi\)
\(12\) 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
\(15\) 0.819678 2.32826i 0.211640 0.601154i
\(16\) 0 0
\(17\) 3.53951 1.22504i 0.858458 0.297115i 0.137846 0.990454i \(-0.455982\pi\)
0.720612 + 0.693339i \(0.243861\pi\)
\(18\) 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
\(21\) −0.269274 + 2.67016i −0.0587603 + 0.582677i
\(22\) 0 0
\(23\) 0.357259 0.0170183i 0.0744936 0.00354857i −0.0103020 0.999947i \(-0.503279\pi\)
0.0847956 + 0.996398i \(0.472976\pi\)
\(24\) 0 0
\(25\) 2.84884 + 0.836495i 0.569768 + 0.167299i
\(26\) 0 0
\(27\) −4.32601 2.87847i −0.832541 0.553963i
\(28\) 0 0
\(29\) 2.14642 1.23924i 0.398581 0.230121i −0.287291 0.957843i \(-0.592755\pi\)
0.685872 + 0.727723i \(0.259421\pi\)
\(30\) 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
\(33\) 4.43676 0.830725i 0.772342 0.144611i
\(34\) 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
\(39\) 2.58332 + 4.06701i 0.413662 + 0.651243i
\(40\) 0 0
\(41\) 1.45686 + 0.280786i 0.227523 + 0.0438514i 0.301738 0.953391i \(-0.402433\pi\)
−0.0742156 + 0.997242i \(0.523645\pi\)
\(42\) 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
\(45\) −2.17681 + 3.67961i −0.324500 + 0.548524i
\(46\) 0 0
\(47\) 5.86207 11.3708i 0.855071 1.65861i 0.107716 0.994182i \(-0.465646\pi\)
0.747355 0.664425i \(-0.231323\pi\)
\(48\) 0 0
\(49\) 4.51613 0.870413i 0.645162 0.124345i
\(50\) 0 0
\(51\) −6.42619 + 0.889171i −0.899847 + 0.124509i
\(52\) 0 0
\(53\) 1.34621 + 1.55361i 0.184916 + 0.213405i 0.840637 0.541598i \(-0.182181\pi\)
−0.655721 + 0.755003i \(0.727635\pi\)
\(54\) 0 0
\(55\) −0.875587 3.60922i −0.118064 0.486667i
\(56\) 0 0
\(57\) 0.138398 + 0.0414362i 0.0183313 + 0.00548836i
\(58\) 0 0
\(59\) −0.862133 2.93616i −0.112240 0.382255i 0.884144 0.467214i \(-0.154742\pi\)
−0.996384 + 0.0849590i \(0.972924\pi\)
\(60\) 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
\(63\) 1.35684 4.44587i 0.170945 0.560127i
\(64\) 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
\(69\) −0.612710 0.0914151i −0.0737616 0.0110051i
\(70\) 0 0
\(71\) 3.54925 + 1.22841i 0.421219 + 0.145785i 0.529451 0.848340i \(-0.322398\pi\)
−0.108232 + 0.994126i \(0.534519\pi\)
\(72\) 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
\(75\) −4.55840 2.38072i −0.526359 0.274902i
\(76\) 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
\(81\) 6.38033 + 6.34755i 0.708926 + 0.705283i
\(82\) 0 0
\(83\) 3.35310 4.26381i 0.368051 0.468014i −0.566388 0.824139i \(-0.691660\pi\)
0.934439 + 0.356124i \(0.115902\pi\)
\(84\) 0 0
\(85\) 1.01017 + 5.24124i 0.109568 + 0.568493i
\(86\) 0 0
\(87\) −4.06414 + 1.38251i −0.435721 + 0.148221i
\(88\) 0 0
\(89\) −4.10997 + 6.39524i −0.435656 + 0.677894i −0.987778 0.155870i \(-0.950182\pi\)
0.552122 + 0.833763i \(0.313818\pi\)
\(90\) 0 0
\(91\) −2.82253 + 3.25737i −0.295881 + 0.341465i
\(92\) 0 0
\(93\) −4.92754 + 3.46963i −0.510962 + 0.359784i
\(94\) 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
\(99\) −7.81780 0.0829650i −0.785719 0.00833829i
\(100\) 0 0
\(101\) −6.68674 + 9.39021i −0.665355 + 0.934360i −0.999968 0.00799517i \(-0.997455\pi\)
0.334613 + 0.942356i \(0.391394\pi\)
\(102\) 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
\(105\) −3.71188 0.921374i −0.362243 0.0899169i
\(106\) 0 0
\(107\) −6.25579 + 0.899446i −0.604770 + 0.0869527i −0.437896 0.899026i \(-0.644276\pi\)
−0.166874 + 0.985978i \(0.553367\pi\)
\(108\) 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
\(111\) −7.49724 + 8.56007i −0.711606 + 0.812486i
\(112\) 0 0
\(113\) −6.30125 + 4.95536i −0.592772 + 0.466161i −0.868919 0.494954i \(-0.835185\pi\)
0.276147 + 0.961115i \(0.410942\pi\)
\(114\) 0 0
\(115\) −0.0484505 + 0.507396i −0.00451803 + 0.0473149i
\(116\) 0 0
\(117\) −3.01921 7.77989i −0.279126 0.719251i
\(118\) 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
\(123\) −2.38061 0.967738i −0.214652 0.0872580i
\(124\) 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
\(129\) 9.75864 + 12.5455i 0.859200 + 1.10457i
\(130\) 0 0
\(131\) −3.67671 5.72108i −0.321236 0.499853i 0.642653 0.766157i \(-0.277834\pi\)
−0.963889 + 0.266305i \(0.914197\pi\)
\(132\) 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 −0.490788 0.871279i \(-0.663291\pi\)
0.588663 + 0.808379i \(0.299655\pi\)
\(138\) 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
\(141\) −13.7894 + 17.3445i −1.16128 + 1.46067i
\(142\) 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
\(147\) −7.96602 0.0422677i −0.657026 0.00348618i
\(148\) 0 0
\(149\) −15.7872 + 7.20977i −1.29334 + 0.590648i −0.938822 0.344403i \(-0.888081\pi\)
−0.354516 + 0.935050i \(0.615354\pi\)
\(150\) 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
\(153\) 11.2175 + 0.653730i 0.906881 + 0.0528509i
\(154\) 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
\(159\) −1.76392 3.09299i −0.139888 0.245290i
\(160\) 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
\(165\) 0.271982 + 6.42693i 0.0211738 + 0.500336i
\(166\) 0 0
\(167\) −2.39412 1.70485i −0.185263 0.131925i 0.483663 0.875254i \(-0.339306\pi\)
−0.668925 + 0.743329i \(0.733245\pi\)
\(168\) 0 0
\(169\) 0.250374 5.25600i 0.0192596 0.404308i
\(170\) 0 0
\(171\) −0.221180 0.117014i −0.0169141 0.00894827i
\(172\) 0 0
\(173\) 5.89177 + 1.42933i 0.447943 + 0.108670i 0.453384 0.891315i \(-0.350217\pi\)
−0.00544065 + 0.999985i \(0.501732\pi\)
\(174\) 0 0
\(175\) 0.870640 4.51731i 0.0658142 0.341477i
\(176\) 0 0
\(177\) 0.475820 + 5.27887i 0.0357648 + 0.396784i
\(178\) 0 0
\(179\) −4.82757 3.10249i −0.360829 0.231891i 0.347647 0.937626i \(-0.386981\pi\)
−0.708476 + 0.705735i \(0.750617\pi\)
\(180\) 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
\(183\) −10.5681 + 16.2540i −0.781216 + 1.20153i
\(184\) 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
\(189\) −3.80267 + 7.09648i −0.276604 + 0.516193i
\(190\) 0 0
\(191\) −24.0016 + 12.3737i −1.73669 + 0.895328i −0.770527 + 0.637407i \(0.780007\pi\)
−0.966166 + 0.257921i \(0.916963\pi\)
\(192\) 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
\(195\) −6.26080 + 2.81916i −0.448345 + 0.201884i
\(196\) 0 0
\(197\) 0.305616 0.883020i 0.0217743 0.0629126i −0.933590 0.358343i \(-0.883342\pi\)
0.955364 + 0.295430i \(0.0954630\pi\)
\(198\) 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
\(201\) −13.6647 3.77853i −0.963830 0.266517i
\(202\) 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
\(207\) 1.01020 + 0.361681i 0.0702135 + 0.0251386i
\(208\) 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
\(213\) −5.61639 3.28248i −0.384829 0.224912i
\(214\) 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
\(219\) 5.45452 + 3.54644i 0.368583 + 0.239646i
\(220\) 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
\(225\) 6.94281 + 5.58013i 0.462854 + 0.372009i
\(226\) 0 0
\(227\) 4.20062 21.7949i 0.278805 1.44658i −0.524704 0.851285i \(-0.675824\pi\)
0.803509 0.595292i \(-0.202964\pi\)
\(228\) 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
\(231\) −1.93479 6.72101i −0.127300 0.442210i
\(232\) 0 0
\(233\) 0.859288 18.0387i 0.0562938 1.18175i −0.777211 0.629240i \(-0.783366\pi\)
0.833505 0.552512i \(-0.186331\pi\)
\(234\) 0 0
\(235\) 14.8507 + 10.5751i 0.968750 + 0.689844i
\(236\) 0 0
\(237\) 4.23589 0.179259i 0.275151 0.0116442i
\(238\) 0 0
\(239\) 11.4331 + 19.8027i 0.739545 + 1.28093i 0.952700 + 0.303911i \(0.0982925\pi\)
−0.213156 + 0.977018i \(0.568374\pi\)
\(240\) 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
\(243\) −8.70218 12.9334i −0.558245 0.829676i
\(244\) 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
\(249\) −7.13298 + 6.11480i −0.452034 + 0.387510i
\(250\) 0 0
\(251\) −2.54986 7.36734i −0.160946 0.465022i 0.835477 0.549525i \(-0.185191\pi\)
−0.996423 + 0.0845023i \(0.973070\pi\)
\(252\) 0 0
\(253\) −0.847869 + 0.387209i −0.0533050 + 0.0243436i
\(254\) 0 0
\(255\) 0.0490542 9.24504i 0.00307190 0.578947i
\(256\) 0 0
\(257\) −10.2940 25.7132i −0.642122 1.60394i −0.788724 0.614748i \(-0.789258\pi\)
0.146602 0.989196i \(-0.453166\pi\)
\(258\) 0 0
\(259\) −9.25947 4.22866i −0.575355 0.262756i
\(260\) 0 0
\(261\) 7.37057 0.980013i 0.456227 0.0606613i
\(262\) 0 0
\(263\) 6.22844 + 0.895514i 0.384062 + 0.0552198i 0.331642 0.943405i \(-0.392397\pi\)
0.0524201 + 0.998625i \(0.483307\pi\)
\(264\) 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 \(-0.869447\pi\)
0.917063 0.398743i \(-0.130553\pi\)
\(270\) 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
\(273\) 5.89256 4.58357i 0.356634 0.277410i
\(274\) 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
\(279\) 9.54044 4.23520i 0.571171 0.253555i
\(280\) 0 0
\(281\) −14.5570 + 13.8800i −0.868396 + 0.828013i −0.986291 0.165012i \(-0.947234\pi\)
0.117896 + 0.993026i \(0.462385\pi\)
\(282\) 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
\(285\) −0.0865182 + 0.186819i −0.00512490 + 0.0110662i
\(286\) 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
\(291\) −1.58932 1.39199i −0.0931679 0.0815999i
\(292\) 0 0
\(293\) 0.126387 0.430435i 0.00738362 0.0251463i −0.955719 0.294282i \(-0.904920\pi\)
0.963102 + 0.269135i \(0.0867379\pi\)
\(294\) 0 0
\(295\) 4.31656 0.620627i 0.251320 0.0361343i
\(296\) 0 0
\(297\) 13.2544 + 2.77409i 0.769099 + 0.160969i
\(298\) 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
\(303\) 14.5234 13.7017i 0.834348 0.787140i
\(304\) 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
\(309\) −0.727612 1.03335i −0.0413924 0.0587852i
\(310\) 0 0
\(311\) 4.38634 5.06210i 0.248726 0.287045i −0.617633 0.786466i \(-0.711908\pi\)
0.866360 + 0.499421i \(0.166454\pi\)
\(312\) 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
\(315\) 5.99611 + 2.81561i 0.337843 + 0.158642i
\(316\) 0 0
\(317\) 1.11635 + 5.79218i 0.0627005 + 0.325321i 0.999713 0.0239760i \(-0.00763251\pi\)
−0.937012 + 0.349297i \(0.886420\pi\)
\(318\) 0 0
\(319\) −3.99276 + 5.07721i −0.223552 + 0.284269i
\(320\) 0 0
\(321\) 10.9314 + 0.578878i 0.610134 + 0.0323098i
\(322\) 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
\(327\) −9.55458 + 18.2943i −0.528369 + 1.01168i
\(328\) 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
\(333\) 15.6208 12.0183i 0.856017 0.658598i
\(334\) 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
\(339\) 12.3748 6.29676i 0.672106 0.341993i
\(340\) 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
\(345\) 0.253214 0.845741i 0.0136326 0.0455332i
\(346\) 0 0
\(347\) 5.13930 + 21.1845i 0.275892 + 1.13724i 0.926037 + 0.377433i \(0.123193\pi\)
−0.650145 + 0.759810i \(0.725292\pi\)
\(348\) 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
\(351\) 2.50923 + 14.2348i 0.133933 + 0.759800i
\(352\) 0 0
\(353\) 33.7883 6.51216i 1.79837 0.346607i 0.823147 0.567829i \(-0.192216\pi\)
0.975224 + 0.221221i \(0.0710044\pi\)
\(354\) 0 0
\(355\) −2.45261 + 4.75740i −0.130171 + 0.252496i
\(356\) 0 0
\(357\) 2.31795 + 9.78093i 0.122679 + 0.517662i
\(358\) 0 0
\(359\) 9.21787 + 7.98733i 0.486501 + 0.421555i 0.863263 0.504755i \(-0.168417\pi\)
−0.376762 + 0.926310i \(0.622963\pi\)
\(360\) 0 0
\(361\) −18.6498 3.59446i −0.981569 0.189182i
\(362\) 0 0
\(363\) 6.15277 3.90817i 0.322937 0.205126i
\(364\) 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
\(369\) 3.71867 + 2.44599i 0.193586 + 0.127333i
\(370\) 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
\(375\) 11.4948 15.9623i 0.593590 0.824289i
\(376\) 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
\(381\) −20.5602 2.07340i −1.05333 0.106224i
\(382\) 0 0
\(383\) 33.6647 + 3.21459i 1.72019 + 0.164258i 0.907952 0.419075i \(-0.137645\pi\)
0.812234 + 0.583332i \(0.198251\pi\)
\(384\) 0 0
\(385\) −5.43798 + 1.88210i −0.277145 + 0.0959208i
\(386\) 0 0
\(387\) −12.3543 24.6016i −0.628005 1.25057i
\(388\) 0 0
\(389\) 5.78914 + 6.07148i 0.293521 + 0.307836i 0.853938 0.520374i \(-0.174208\pi\)
−0.560417 + 0.828211i \(0.689359\pi\)
\(390\) 0 0
\(391\) 1.24367 0.497891i 0.0628952 0.0251795i
\(392\) 0 0
\(393\) 4.31976 + 10.9584i 0.217903 + 0.552778i
\(394\) 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
\(399\) 0.0435284 0.219571i 0.00217914 0.0109923i
\(400\) 0 0
\(401\) 8.18648 0.408813 0.204407 0.978886i \(-0.434474\pi\)
0.204407 + 0.978886i \(0.434474\pi\)
\(402\) 0 0
\(403\) −9.67881 −0.482136
\(404\) 0 0
\(405\) −10.2478 + 7.71266i −0.509216 + 0.383245i
\(406\) 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
\(411\) −2.19432 + 0.864992i −0.108238 + 0.0426669i
\(412\) 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
\(417\) −17.9555 6.32133i −0.879283 0.309557i
\(418\) 0 0
\(419\) −19.7012 + 6.81865i −0.962466 + 0.333113i −0.762716 0.646734i \(-0.776134\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(420\) 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
\(423\) 29.2699 24.8236i 1.42315 1.20697i
\(424\) 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
\(429\) −10.1893 7.33757i −0.491945 0.354261i
\(430\) 0 0
\(431\) −0.139674 + 0.0806411i −0.00672788 + 0.00388434i −0.503360 0.864077i \(-0.667903\pi\)
0.496632 + 0.867961i \(0.334570\pi\)
\(432\) 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
\(435\) −1.12589 6.01321i −0.0539825 0.288312i
\(436\) 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
\(441\) 13.5199 + 2.75486i 0.643806 + 0.131184i
\(442\) 0 0
\(443\) 2.47875 + 0.477739i 0.117769 + 0.0226981i 0.247795 0.968812i \(-0.420294\pi\)
−0.130026 + 0.991511i \(0.541506\pi\)
\(444\) 0 0
\(445\) −8.18749 7.09450i −0.388124 0.336312i
\(446\) 0 0
\(447\) 29.2506 6.93199i 1.38351 0.327872i
\(448\) 0 0
\(449\) 15.3573 29.7891i 0.724757 1.40583i −0.181623 0.983368i \(-0.558135\pi\)
0.906380 0.422464i \(-0.138835\pi\)
\(450\) 0 0
\(451\) −3.79668 + 0.731751i −0.178779 + 0.0344568i
\(452\) 0 0
\(453\) −0.720133 5.20452i −0.0338348 0.244530i
\(454\) 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
\(459\) −18.8382 4.88887i −0.879292 0.228193i
\(460\) 0 0
\(461\) −0.207098 0.705312i −0.00964552 0.0328496i 0.954530 0.298116i \(-0.0963583\pi\)
−0.964175 + 0.265266i \(0.914540\pi\)
\(462\) 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
\(465\) −3.89486 7.65441i −0.180620 0.354965i
\(466\) 0 0
\(467\) 16.6138 11.8307i 0.768796 0.547457i −0.127010 0.991901i \(-0.540538\pi\)
0.895807 + 0.444444i \(0.146599\pi\)
\(468\) 0 0
\(469\) −0.267940 12.6799i −0.0123723 0.585501i
\(470\) 0 0
\(471\) 1.76486 11.8290i 0.0813204 0.545050i
\(472\) 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
\(477\) 1.95512 + 5.84905i 0.0895190 + 0.267810i
\(478\) 0 0
\(479\) −9.11674 17.6840i −0.416554 0.808003i 0.583437 0.812158i \(-0.301708\pi\)
−0.999991 + 0.00415563i \(0.998677\pi\)
\(480\) 0 0
\(481\) −17.7600 + 4.30854i −0.809788 + 0.196452i
\(482\) 0 0
\(483\) −0.0507587 + 0.958520i −0.00230960 + 0.0436142i
\(484\) 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
\(489\) −4.03278 11.8551i −0.182369 0.536107i
\(490\) 0 0
\(491\) −18.9279 + 29.4524i −0.854204 + 1.32917i 0.0886844 + 0.996060i \(0.471734\pi\)
−0.942889 + 0.333108i \(0.891903\pi\)
\(492\) 0 0
\(493\) 6.07918 7.01575i 0.273793 0.315973i
\(494\) 0 0
\(495\) 1.70257 11.0109i 0.0765250 0.494902i
\(496\) 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
\(501\) 3.49337 + 3.70288i 0.156072 + 0.165432i
\(502\) 0 0
\(503\) −9.88721 + 13.8846i −0.440849 + 0.619086i −0.973895 0.227001i \(-0.927108\pi\)
0.533046 + 0.846086i \(0.321047\pi\)
\(504\) 0 0
\(505\) −11.8896 11.3367i −0.529079 0.504475i
\(506\) 0 0
\(507\) −2.19567 + 8.84555i −0.0975131 + 0.392845i
\(508\) 0 0
\(509\) 27.9399 4.01716i 1.23842 0.178057i 0.508179 0.861251i \(-0.330319\pi\)
0.730237 + 0.683194i \(0.239410\pi\)
\(510\) 0 0
\(511\) −1.63972 + 5.58437i −0.0725369 + 0.247038i
\(512\) 0 0
\(513\) 0.336371 + 0.273301i 0.0148511 + 0.0120665i
\(514\) 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
\(519\) −9.52863 4.41283i −0.418261 0.193702i
\(520\) 0 0
\(521\) −5.69828 12.4775i −0.249646 0.546649i 0.742774 0.669543i \(-0.233510\pi\)
−0.992420 + 0.122894i \(0.960783\pi\)
\(522\) 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
\(525\) −3.00069 + 7.38161i −0.130961 + 0.322160i
\(526\) 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
\(531\) 0.969575 9.12899i 0.0420760 0.396165i
\(532\) 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
\(543\) −30.6645 24.3793i −1.31594 1.04622i
\(544\) 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
\(549\) 23.4296 24.0559i 0.999951 1.02668i
\(550\) 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
\(555\) −10.5542 12.3116i −0.448001 0.522598i
\(556\) 0 0
\(557\) 24.7197 + 31.4337i 1.04741 + 1.33189i 0.941314 + 0.337531i \(0.109592\pi\)
0.106094 + 0.994356i \(0.466166\pi\)
\(558\) 0 0
\(559\) 1.21460 + 25.4975i 0.0513720 + 1.07843i
\(560\) 0 0
\(561\) 14.6863 8.37556i 0.620056 0.353616i
\(562\) 0 0
\(563\) −3.39797 23.6334i −0.143208 0.996030i −0.927014 0.375026i \(-0.877634\pi\)
0.783807 0.621005i \(-0.213275\pi\)
\(564\) 0 0
\(565\) −5.71200 9.89348i −0.240306 0.416222i
\(566\) 0 0
\(567\) 8.85087 10.7760i 0.371702 0.452551i
\(568\) 0 0
\(569\) 0.941694 + 0.670577i 0.0394778 + 0.0281120i 0.599626 0.800281i \(-0.295316\pi\)
−0.560148 + 0.828393i \(0.689256\pi\)
\(570\) 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
\(573\) 44.9460 12.9387i 1.87765 0.540522i
\(574\) 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
\(579\) −4.71490 + 0.424985i −0.195944 + 0.0176618i
\(580\) 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
\(585\) 11.5866 2.68100i 0.479045 0.110846i
\(586\) 0 0
\(587\) 2.28824 + 1.79949i 0.0944459 + 0.0742730i 0.664265 0.747497i \(-0.268744\pi\)
−0.569820 + 0.821770i \(0.692987\pi\)
\(588\) 0 0
\(589\) −0.219328 + 0.190049i −0.00903727 + 0.00783084i
\(590\) 0 0
\(591\) −0.816650 + 1.39731i −0.0335925 + 0.0574774i
\(592\) 0 0
\(593\) −8.77838 + 4.52557i −0.360485 + 0.185843i −0.628948 0.777447i \(-0.716514\pi\)
0.268464 + 0.963290i \(0.413484\pi\)
\(594\) 0 0
\(595\) 7.93542 2.33005i 0.325321 0.0955227i
\(596\) 0 0
\(597\) −0.0804523 0.178669i −0.00329269 0.00731242i
\(598\) 0 0
\(599\) 12.1844 35.2044i 0.497839 1.43841i −0.364080 0.931368i \(-0.618617\pi\)
0.861920 0.507045i \(-0.169262\pi\)
\(600\) 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
\(603\) 21.9434 + 11.0221i 0.893605 + 0.448854i
\(604\) 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
\(609\) 2.73099 + 6.06499i 0.110665 + 0.245766i
\(610\) 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
\(615\) 1.84790 3.16179i 0.0745143 0.127496i
\(616\) 0 0
\(617\) −29.9576 + 25.9584i −1.20605 + 1.04505i −0.208292 + 0.978067i \(0.566791\pi\)
−0.997754 + 0.0669789i \(0.978664\pi\)
\(618\) 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
\(621\) −1.59449 0.954738i −0.0639848 0.0383123i
\(622\) 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
\(627\) −0.374975 + 0.0337990i −0.0149751 + 0.00134980i
\(628\) 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
\(633\) 34.2217 9.85146i 1.36019 0.391561i
\(634\) 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
\(639\) 8.43660 + 7.46856i 0.333747 + 0.295452i
\(640\) 0 0
\(641\) 4.54237 + 7.86762i 0.179413 + 0.310752i 0.941680 0.336511i \(-0.109247\pi\)
−0.762267 + 0.647263i \(0.775913\pi\)
\(642\) 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
\(645\) −19.6758 + 11.2210i −0.774732 + 0.441828i
\(646\) 0 0
\(647\) −2.07032 43.4613i −0.0813926 1.70864i −0.558260 0.829666i \(-0.688531\pi\)
0.476867 0.878975i \(-0.341772\pi\)
\(648\) 0 0
\(649\) 4.92976 + 6.26870i 0.193510 + 0.246068i
\(650\) 0 0
\(651\) 6.07738 + 7.08932i 0.238191 + 0.277853i
\(652\) 0 0
\(653\) −13.5176 39.0564i −0.528983 1.52840i −0.820394 0.571798i \(-0.806246\pi\)
0.291411 0.956598i \(-0.405875\pi\)
\(654\) 0 0
\(655\) 8.81576 4.02602i 0.344460 0.157310i
\(656\) 0 0
\(657\) −8.07268 7.86251i −0.314945 0.306746i
\(658\) 0 0
\(659\) −15.5343 38.8029i −0.605132 1.51155i −0.841708 0.539933i \(-0.818449\pi\)
0.236576 0.971613i \(-0.423975\pi\)
\(660\) 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
\(663\) 14.1259 + 11.2306i 0.548606 + 0.436159i
\(664\) 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
\(675\) −9.91629 11.8190i −0.381678 0.454914i
\(676\) 0 0
\(677\) −21.2689 + 2.03094i −0.817432 + 0.0780553i −0.495391 0.868670i \(-0.664975\pi\)
−0.322041 + 0.946726i \(0.604369\pi\)
\(678\) 0 0
\(679\) 0.785123 1.71918i 0.0301302 0.0659760i
\(680\) 0 0
\(681\) −14.4776 + 35.6144i −0.554782 + 1.36475i
\(682\) 0 0
\(683\) −5.96693 + 5.68946i −0.228318 + 0.217701i −0.795599 0.605823i \(-0.792844\pi\)
0.567281 + 0.823524i \(0.307995\pi\)
\(684\) 0 0
\(685\) 0.806174 + 1.76527i 0.0308023 + 0.0674477i
\(686\) 0 0
\(687\) −7.98680 3.69879i −0.304715 0.141118i
\(688\) 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
\(693\) 1.02347 + 12.0706i 0.0388782 + 0.458523i
\(694\) 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
\(699\) −7.53556 + 30.3580i −0.285021 + 1.14825i
\(700\) 0 0
\(701\) −2.13427 2.03502i −0.0806103 0.0768618i 0.648703 0.761042i \(-0.275312\pi\)
−0.729313 + 0.684180i \(0.760160\pi\)
\(702\) 0 0
\(703\) −0.317854 + 0.446364i −0.0119881 + 0.0168349i
\(704\) 0 0
\(705\) −21.6693 22.9689i −0.816111 0.865057i
\(706\) 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
\(711\) −7.25710 1.12214i −0.272163 0.0420836i
\(712\) 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
\(717\) −12.7549 37.4953i −0.476340 1.40029i
\(718\) 0 0
\(719\) 6.71790 + 34.8558i 0.250535 + 1.29990i 0.861303 + 0.508092i \(0.169649\pi\)
−0.610768 + 0.791810i \(0.709139\pi\)
\(720\) 0 0
\(721\) 0.698871 0.888687i 0.0260273 0.0330964i
\(722\) 0 0
\(723\) −1.85559 + 35.0407i −0.0690102 + 1.30318i
\(724\) 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
\(729\) 10.4288 + 24.9046i 0.386251 + 0.922394i
\(730\) 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
\(735\) 1.67523 11.2282i 0.0617916 0.414158i
\(736\) 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
\(741\) −0.182250 0.358169i −0.00669513 0.0131577i
\(742\) 0 0
\(743\) −16.6185 + 41.5110i −0.609674 + 1.52289i 0.226263 + 0.974066i \(0.427349\pi\)
−0.835937 + 0.548825i \(0.815075\pi\)
\(744\) 0 0
\(745\) −6.96818 23.7315i −0.255295 0.869453i
\(746\) 0 0
\(747\) 14.1784 7.98649i 0.518760 0.292211i
\(748\) 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
\(753\) 1.85077 + 13.3758i 0.0674459 + 0.487443i
\(754\) 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
\(759\) 1.57093 0.372290i 0.0570213 0.0135133i
\(760\) 0 0
\(761\) −25.0471 21.7035i −0.907958 0.786750i 0.0695652 0.997577i \(-0.477839\pi\)
−0.977523 + 0.210827i \(0.932384\pi\)
\(762\) 0 0
\(763\) −18.1294 3.49416i −0.656329 0.126497i
\(764\) 0 0
\(765\) −3.19719 + 15.6907i −0.115594 + 0.567298i
\(766\) 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
\(771\) 8.82886 + 47.1535i 0.317964 + 1.69819i
\(772\) 0 0
\(773\) 11.5079 12.0691i 0.413910 0.434096i −0.483466 0.875363i \(-0.660622\pi\)
0.897376 + 0.441267i