Properties

Label 108.3.f.c.91.5
Level 108
Weight 3
Character 108.91
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.5
Root \(0.186266 + 1.99131i\) of \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Character \(\chi\) \(=\) 108.91
Dual form 108.3.f.c.19.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})\) \(q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(-15.1205 + 8.72982i) q^{11} +(-0.892255 + 1.54543i) q^{13} +(0.683395 + 0.963628i) q^{14} +(14.8994 - 5.83166i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(8.13306 - 23.2084i) q^{20} +(-20.2002 - 28.4835i) q^{22} +(6.86778 + 3.96511i) q^{23} +(-6.39933 - 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 - 5.49956i) q^{29} +(27.6558 + 15.9671i) q^{31} +(14.3879 + 28.5830i) q^{32} +(3.15108 + 33.6871i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(-38.8420 + 3.63326i) q^{38} +(47.7301 + 11.8725i) q^{40} +(2.66948 - 4.62368i) q^{41} +(-33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(9.64117 - 5.56633i) q^{47} +(-24.3255 + 42.1331i) q^{49} +(20.8796 - 14.8076i) q^{50} +(2.36067 - 6.73638i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-3.40100 - 3.28069i) q^{56} +(10.3599 - 7.34713i) q^{58} +(20.8974 + 12.0651i) q^{59} +(-37.9460 - 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 - 9.50141i) q^{65} +(-31.8200 - 18.3713i) q^{67} +(-66.4945 + 12.5495i) q^{68} +(-7.23150 + 0.676431i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(10.8562 + 116.060i) q^{74} +(-14.4699 - 76.6696i) q^{76} +(-5.15652 + 8.93136i) q^{77} +(32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(66.0281 - 38.1214i) q^{83} +(-52.0037 + 90.0730i) q^{85} +(-45.3319 - 63.9207i) q^{86} +(100.529 + 96.9724i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(-29.9360 - 10.4906i) q^{92} +(12.8801 + 18.1617i) q^{94} +(-103.856 - 59.9614i) q^{95} +(13.0585 + 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.186266 + 1.99131i 0.0931330 + 0.995654i
\(3\) 0 0
\(4\) −3.93061 + 0.741826i −0.982652 + 0.185456i
\(5\) −3.07403 + 5.32438i −0.614806 + 1.06488i 0.375612 + 0.926777i \(0.377432\pi\)
−0.990418 + 0.138099i \(0.955901\pi\)
\(6\) 0 0
\(7\) 0.511543 0.295340i 0.0730776 0.0421914i −0.463016 0.886350i \(-0.653233\pi\)
0.536094 + 0.844159i \(0.319899\pi\)
\(8\) −2.20934 7.68888i −0.276168 0.961109i
\(9\) 0 0
\(10\) −11.1751 5.12959i −1.11751 0.512959i
\(11\) −15.1205 + 8.72982i −1.37459 + 0.793620i −0.991502 0.130092i \(-0.958473\pi\)
−0.383088 + 0.923712i \(0.625139\pi\)
\(12\) 0 0
\(13\) −0.892255 + 1.54543i −0.0686350 + 0.118879i −0.898301 0.439381i \(-0.855198\pi\)
0.829666 + 0.558261i \(0.188531\pi\)
\(14\) 0.683395 + 0.963628i 0.0488140 + 0.0688306i
\(15\) 0 0
\(16\) 14.8994 5.83166i 0.931212 0.364479i
\(17\) 16.9171 0.995123 0.497562 0.867429i \(-0.334229\pi\)
0.497562 + 0.867429i \(0.334229\pi\)
\(18\) 0 0
\(19\) 19.5058i 1.02662i 0.858203 + 0.513310i \(0.171581\pi\)
−0.858203 + 0.513310i \(0.828419\pi\)
\(20\) 8.13306 23.2084i 0.406653 1.16042i
\(21\) 0 0
\(22\) −20.2002 28.4835i −0.918190 1.29470i
\(23\) 6.86778 + 3.96511i 0.298599 + 0.172396i 0.641813 0.766861i \(-0.278182\pi\)
−0.343214 + 0.939257i \(0.611516\pi\)
\(24\) 0 0
\(25\) −6.39933 11.0840i −0.255973 0.443359i
\(26\) −3.24362 1.48889i −0.124755 0.0572651i
\(27\) 0 0
\(28\) −1.79159 + 1.54034i −0.0639852 + 0.0550122i
\(29\) −3.17517 5.49956i −0.109489 0.189640i 0.806075 0.591814i \(-0.201588\pi\)
−0.915563 + 0.402174i \(0.868255\pi\)
\(30\) 0 0
\(31\) 27.6558 + 15.9671i 0.892124 + 0.515068i 0.874637 0.484779i \(-0.161100\pi\)
0.0174873 + 0.999847i \(0.494433\pi\)
\(32\) 14.3879 + 28.5830i 0.449621 + 0.893219i
\(33\) 0 0
\(34\) 3.15108 + 33.6871i 0.0926788 + 0.990798i
\(35\) 3.63153i 0.103758i
\(36\) 0 0
\(37\) 58.2834 1.57523 0.787614 0.616169i \(-0.211316\pi\)
0.787614 + 0.616169i \(0.211316\pi\)
\(38\) −38.8420 + 3.63326i −1.02216 + 0.0956122i
\(39\) 0 0
\(40\) 47.7301 + 11.8725i 1.19325 + 0.296812i
\(41\) 2.66948 4.62368i 0.0651093 0.112773i −0.831633 0.555325i \(-0.812594\pi\)
0.896742 + 0.442553i \(0.145927\pi\)
\(42\) 0 0
\(43\) −33.9324 + 19.5909i −0.789126 + 0.455602i −0.839655 0.543121i \(-0.817243\pi\)
0.0505290 + 0.998723i \(0.483909\pi\)
\(44\) 52.9567 45.5303i 1.20356 1.03478i
\(45\) 0 0
\(46\) −6.61653 + 14.4144i −0.143838 + 0.313357i
\(47\) 9.64117 5.56633i 0.205131 0.118433i −0.393915 0.919147i \(-0.628880\pi\)
0.599047 + 0.800714i \(0.295546\pi\)
\(48\) 0 0
\(49\) −24.3255 + 42.1331i −0.496440 + 0.859859i
\(50\) 20.8796 14.8076i 0.417592 0.296152i
\(51\) 0 0
\(52\) 2.36067 6.73638i 0.0453974 0.129546i
\(53\) −35.8770 −0.676925 −0.338462 0.940980i \(-0.609907\pi\)
−0.338462 + 0.940980i \(0.609907\pi\)
\(54\) 0 0
\(55\) 107.343i 1.95169i
\(56\) −3.40100 3.28069i −0.0607322 0.0585837i
\(57\) 0 0
\(58\) 10.3599 7.34713i 0.178619 0.126675i
\(59\) 20.8974 + 12.0651i 0.354194 + 0.204494i 0.666531 0.745477i \(-0.267778\pi\)
−0.312337 + 0.949971i \(0.601112\pi\)
\(60\) 0 0
\(61\) −37.9460 65.7244i −0.622066 1.07745i −0.989100 0.147243i \(-0.952960\pi\)
0.367034 0.930207i \(-0.380373\pi\)
\(62\) −26.6441 + 58.0454i −0.429743 + 0.936216i
\(63\) 0 0
\(64\) −54.2376 + 33.9747i −0.847463 + 0.530855i
\(65\) −5.48564 9.50141i −0.0843944 0.146175i
\(66\) 0 0
\(67\) −31.8200 18.3713i −0.474925 0.274198i 0.243374 0.969933i \(-0.421746\pi\)
−0.718299 + 0.695734i \(0.755079\pi\)
\(68\) −66.4945 + 12.5495i −0.977860 + 0.184552i
\(69\) 0 0
\(70\) −7.23150 + 0.676431i −0.103307 + 0.00966331i
\(71\) 87.8370i 1.23714i −0.785730 0.618570i \(-0.787712\pi\)
0.785730 0.618570i \(-0.212288\pi\)
\(72\) 0 0
\(73\) −60.0423 −0.822498 −0.411249 0.911523i \(-0.634907\pi\)
−0.411249 + 0.911523i \(0.634907\pi\)
\(74\) 10.8562 + 116.060i 0.146706 + 1.56838i
\(75\) 0 0
\(76\) −14.4699 76.6696i −0.190393 1.00881i
\(77\) −5.15652 + 8.93136i −0.0669678 + 0.115992i
\(78\) 0 0
\(79\) 32.1841 18.5815i 0.407394 0.235209i −0.282275 0.959333i \(-0.591089\pi\)
0.689669 + 0.724124i \(0.257756\pi\)
\(80\) −14.7512 + 97.2567i −0.184391 + 1.21571i
\(81\) 0 0
\(82\) 9.70439 + 4.45452i 0.118346 + 0.0543234i
\(83\) 66.0281 38.1214i 0.795520 0.459294i −0.0463824 0.998924i \(-0.514769\pi\)
0.841902 + 0.539630i \(0.181436\pi\)
\(84\) 0 0
\(85\) −52.0037 + 90.0730i −0.611808 + 1.05968i
\(86\) −45.3319 63.9207i −0.527115 0.743264i
\(87\) 0 0
\(88\) 100.529 + 96.9724i 1.14237 + 1.10196i
\(89\) 27.5873 0.309969 0.154985 0.987917i \(-0.450467\pi\)
0.154985 + 0.987917i \(0.450467\pi\)
\(90\) 0 0
\(91\) 1.05407i 0.0115832i
\(92\) −29.9360 10.4906i −0.325391 0.114028i
\(93\) 0 0
\(94\) 12.8801 + 18.1617i 0.137022 + 0.193210i
\(95\) −103.856 59.9614i −1.09322 0.631172i
\(96\) 0 0
\(97\) 13.0585 + 22.6180i 0.134624 + 0.233176i 0.925454 0.378861i \(-0.123684\pi\)
−0.790830 + 0.612036i \(0.790351\pi\)
\(98\) −88.4309 40.5917i −0.902357 0.414201i
\(99\) 0 0
\(100\) 33.3757 + 38.8196i 0.333757 + 0.388196i
\(101\) 12.8831 + 22.3142i 0.127556 + 0.220933i 0.922729 0.385449i \(-0.125953\pi\)
−0.795173 + 0.606382i \(0.792620\pi\)
\(102\) 0 0
\(103\) −16.9947 9.81187i −0.164997 0.0952609i 0.415228 0.909717i \(-0.363702\pi\)
−0.580225 + 0.814457i \(0.697035\pi\)
\(104\) 13.8539 + 3.44605i 0.133211 + 0.0331351i
\(105\) 0 0
\(106\) −6.68267 71.4422i −0.0630441 0.673983i
\(107\) 183.200i 1.71215i 0.516850 + 0.856076i \(0.327105\pi\)
−0.516850 + 0.856076i \(0.672895\pi\)
\(108\) 0 0
\(109\) 100.841 0.925147 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(110\) 213.753 19.9943i 1.94321 0.181767i
\(111\) 0 0
\(112\) 5.89936 7.38353i 0.0526729 0.0659243i
\(113\) 9.12484 15.8047i 0.0807508 0.139865i −0.822822 0.568299i \(-0.807602\pi\)
0.903573 + 0.428435i \(0.140935\pi\)
\(114\) 0 0
\(115\) −42.2235 + 24.3778i −0.367161 + 0.211981i
\(116\) 16.5601 + 19.2612i 0.142759 + 0.166045i
\(117\) 0 0
\(118\) −20.1329 + 43.8606i −0.170618 + 0.371700i
\(119\) 8.65383 4.99629i 0.0727212 0.0419856i
\(120\) 0 0
\(121\) 91.9194 159.209i 0.759664 1.31578i
\(122\) 123.810 87.8044i 1.01483 0.719708i
\(123\) 0 0
\(124\) −120.549 42.2447i −0.972170 0.340683i
\(125\) −75.0146 −0.600117
\(126\) 0 0
\(127\) 164.386i 1.29438i 0.762331 + 0.647188i \(0.224055\pi\)
−0.762331 + 0.647188i \(0.775945\pi\)
\(128\) −77.7567 101.675i −0.607474 0.794339i
\(129\) 0 0
\(130\) 17.8984 12.6934i 0.137680 0.0976414i
\(131\) 123.421 + 71.2570i 0.942143 + 0.543947i 0.890631 0.454726i \(-0.150263\pi\)
0.0515116 + 0.998672i \(0.483596\pi\)
\(132\) 0 0
\(133\) 5.76083 + 9.97805i 0.0433145 + 0.0750229i
\(134\) 30.6559 66.7853i 0.228775 0.498398i
\(135\) 0 0
\(136\) −37.3757 130.073i −0.274821 0.956422i
\(137\) 3.08176 + 5.33777i 0.0224946 + 0.0389618i 0.877054 0.480393i \(-0.159506\pi\)
−0.854559 + 0.519354i \(0.826172\pi\)
\(138\) 0 0
\(139\) 103.168 + 59.5642i 0.742218 + 0.428519i 0.822875 0.568222i \(-0.192369\pi\)
−0.0806575 + 0.996742i \(0.525702\pi\)
\(140\) −2.69397 14.2741i −0.0192426 0.101958i
\(141\) 0 0
\(142\) 174.910 16.3610i 1.23176 0.115219i
\(143\) 31.1569i 0.217880i
\(144\) 0 0
\(145\) 39.0423 0.269257
\(146\) −11.1838 119.563i −0.0766017 0.818923i
\(147\) 0 0
\(148\) −229.089 + 43.2361i −1.54790 + 0.292136i
\(149\) 103.365 179.034i 0.693726 1.20157i −0.276882 0.960904i \(-0.589301\pi\)
0.970608 0.240665i \(-0.0773657\pi\)
\(150\) 0 0
\(151\) 127.422 73.5670i 0.843853 0.487199i −0.0147190 0.999892i \(-0.504685\pi\)
0.858572 + 0.512693i \(0.171352\pi\)
\(152\) 149.977 43.0949i 0.986694 0.283519i
\(153\) 0 0
\(154\) −18.7456 8.60461i −0.121724 0.0558741i
\(155\) −170.030 + 98.1668i −1.09697 + 0.633334i
\(156\) 0 0
\(157\) 31.4395 54.4548i 0.200251 0.346846i −0.748358 0.663295i \(-0.769157\pi\)
0.948609 + 0.316449i \(0.102491\pi\)
\(158\) 42.9963 + 60.6274i 0.272129 + 0.383718i
\(159\) 0 0
\(160\) −196.416 11.2586i −1.22760 0.0703665i
\(161\) 4.68422 0.0290946
\(162\) 0 0
\(163\) 143.325i 0.879292i 0.898171 + 0.439646i \(0.144896\pi\)
−0.898171 + 0.439646i \(0.855104\pi\)
\(164\) −7.06272 + 20.1542i −0.0430654 + 0.122891i
\(165\) 0 0
\(166\) 88.2102 + 124.382i 0.531386 + 0.749287i
\(167\) −150.531 86.9089i −0.901381 0.520413i −0.0237332 0.999718i \(-0.507555\pi\)
−0.877648 + 0.479306i \(0.840889\pi\)
\(168\) 0 0
\(169\) 82.9078 + 143.600i 0.490578 + 0.849707i
\(170\) −189.050 86.7777i −1.11206 0.510457i
\(171\) 0 0
\(172\) 118.842 102.176i 0.690942 0.594047i
\(173\) 125.806 + 217.902i 0.727201 + 1.25955i 0.958062 + 0.286562i \(0.0925125\pi\)
−0.230861 + 0.972987i \(0.574154\pi\)
\(174\) 0 0
\(175\) −6.54707 3.77995i −0.0374118 0.0215997i
\(176\) −174.377 + 218.246i −0.990777 + 1.24004i
\(177\) 0 0
\(178\) 5.13857 + 54.9347i 0.0288684 + 0.308622i
\(179\) 96.0059i 0.536346i 0.963371 + 0.268173i \(0.0864199\pi\)
−0.963371 + 0.268173i \(0.913580\pi\)
\(180\) 0 0
\(181\) −328.757 −1.81634 −0.908170 0.418603i \(-0.862520\pi\)
−0.908170 + 0.418603i \(0.862520\pi\)
\(182\) −2.09898 + 0.196338i −0.0115329 + 0.00107878i
\(183\) 0 0
\(184\) 15.3140 61.5658i 0.0832282 0.334597i
\(185\) −179.165 + 310.323i −0.968460 + 1.67742i
\(186\) 0 0
\(187\) −255.795 + 147.683i −1.36789 + 0.789749i
\(188\) −33.7664 + 29.0312i −0.179609 + 0.154421i
\(189\) 0 0
\(190\) 100.057 217.978i 0.526614 1.14725i
\(191\) 0.351914 0.203178i 0.00184248 0.00106376i −0.499078 0.866557i \(-0.666328\pi\)
0.500921 + 0.865493i \(0.332995\pi\)
\(192\) 0 0
\(193\) −31.2230 + 54.0798i −0.161777 + 0.280206i −0.935506 0.353311i \(-0.885056\pi\)
0.773729 + 0.633517i \(0.218389\pi\)
\(194\) −42.6071 + 30.2165i −0.219624 + 0.155755i
\(195\) 0 0
\(196\) 64.3588 183.654i 0.328361 0.937010i
\(197\) 207.861 1.05513 0.527566 0.849514i \(-0.323105\pi\)
0.527566 + 0.849514i \(0.323105\pi\)
\(198\) 0 0
\(199\) 299.128i 1.50316i −0.659643 0.751579i \(-0.729293\pi\)
0.659643 0.751579i \(-0.270707\pi\)
\(200\) −71.0849 + 73.6919i −0.355425 + 0.368460i
\(201\) 0 0
\(202\) −42.0348 + 29.8107i −0.208093 + 0.147578i
\(203\) −3.24848 1.87551i −0.0160024 0.00923896i
\(204\) 0 0
\(205\) 16.4121 + 28.4266i 0.0800592 + 0.138667i
\(206\) 16.3729 35.6692i 0.0794802 0.173152i
\(207\) 0 0
\(208\) −4.28163 + 28.2293i −0.0205848 + 0.135718i
\(209\) −170.282 294.937i −0.814746 1.41118i
\(210\) 0 0
\(211\) −141.744 81.8360i −0.671773 0.387848i 0.124975 0.992160i \(-0.460115\pi\)
−0.796748 + 0.604311i \(0.793448\pi\)
\(212\) 141.019 26.6145i 0.665182 0.125540i
\(213\) 0 0
\(214\) −364.808 + 34.1240i −1.70471 + 0.159458i
\(215\) 240.892i 1.12043i
\(216\) 0 0
\(217\) 18.8629 0.0869257
\(218\) 18.7833 + 200.805i 0.0861617 + 0.921126i
\(219\) 0 0
\(220\) 79.6297 + 421.923i 0.361953 + 1.91783i
\(221\) −15.0944 + 26.1442i −0.0683003 + 0.118300i
\(222\) 0 0
\(223\) 330.681 190.919i 1.48287 0.856138i 0.483063 0.875586i \(-0.339524\pi\)
0.999811 + 0.0194478i \(0.00619081\pi\)
\(224\) 15.8017 + 10.3721i 0.0705434 + 0.0463042i
\(225\) 0 0
\(226\) 33.1717 + 15.2265i 0.146777 + 0.0673739i
\(227\) 51.5472 29.7608i 0.227080 0.131105i −0.382144 0.924103i \(-0.624814\pi\)
0.609224 + 0.792998i \(0.291481\pi\)
\(228\) 0 0
\(229\) 64.4366 111.608i 0.281383 0.487369i −0.690343 0.723482i \(-0.742540\pi\)
0.971726 + 0.236113i \(0.0758736\pi\)
\(230\) −56.4084 79.5393i −0.245254 0.345823i
\(231\) 0 0
\(232\) −35.2704 + 36.5639i −0.152028 + 0.157603i
\(233\) −14.9939 −0.0643513 −0.0321757 0.999482i \(-0.510244\pi\)
−0.0321757 + 0.999482i \(0.510244\pi\)
\(234\) 0 0
\(235\) 68.4443i 0.291252i
\(236\) −91.0899 31.9211i −0.385974 0.135259i
\(237\) 0 0
\(238\) 11.5611 + 16.3018i 0.0485759 + 0.0684949i
\(239\) 315.244 + 182.006i 1.31901 + 0.761532i 0.983570 0.180529i \(-0.0577811\pi\)
0.335442 + 0.942061i \(0.391114\pi\)
\(240\) 0 0
\(241\) −40.5235 70.1888i −0.168147 0.291240i 0.769621 0.638501i \(-0.220445\pi\)
−0.937769 + 0.347261i \(0.887112\pi\)
\(242\) 334.156 + 153.385i 1.38081 + 0.633820i
\(243\) 0 0
\(244\) 197.907 + 230.188i 0.811095 + 0.943393i
\(245\) −149.555 259.037i −0.610428 1.05729i
\(246\) 0 0
\(247\) −30.1448 17.4041i −0.122044 0.0704620i
\(248\) 61.6679 247.919i 0.248661 0.999674i
\(249\) 0 0
\(250\) −13.9727 149.377i −0.0558907 0.597508i
\(251\) 281.883i 1.12304i −0.827463 0.561520i \(-0.810217\pi\)
0.827463 0.561520i \(-0.189783\pi\)
\(252\) 0 0
\(253\) −138.459 −0.547268
\(254\) −327.342 + 30.6195i −1.28875 + 0.120549i
\(255\) 0 0
\(256\) 187.984 173.776i 0.734311 0.678813i
\(257\) 37.6564 65.2227i 0.146523 0.253785i −0.783417 0.621496i \(-0.786525\pi\)
0.929940 + 0.367711i \(0.119858\pi\)
\(258\) 0 0
\(259\) 29.8145 17.2134i 0.115114 0.0664610i
\(260\) 28.6103 + 33.2769i 0.110040 + 0.127988i
\(261\) 0 0
\(262\) −118.905 + 259.041i −0.453838 + 0.988708i
\(263\) 105.914 61.1497i 0.402716 0.232508i −0.284939 0.958546i \(-0.591973\pi\)
0.687655 + 0.726037i \(0.258640\pi\)
\(264\) 0 0
\(265\) 110.287 191.023i 0.416178 0.720841i
\(266\) −18.7963 + 13.3302i −0.0706628 + 0.0501134i
\(267\) 0 0
\(268\) 138.700 + 48.6054i 0.517538 + 0.181364i
\(269\) −280.452 −1.04257 −0.521287 0.853382i \(-0.674548\pi\)
−0.521287 + 0.853382i \(0.674548\pi\)
\(270\) 0 0
\(271\) 81.4468i 0.300542i −0.988645 0.150271i \(-0.951985\pi\)
0.988645 0.150271i \(-0.0480146\pi\)
\(272\) 252.054 98.6547i 0.926670 0.362701i
\(273\) 0 0
\(274\) −10.0551 + 7.13098i −0.0366975 + 0.0260255i
\(275\) 193.522 + 111.730i 0.703716 + 0.406291i
\(276\) 0 0
\(277\) 224.861 + 389.471i 0.811774 + 1.40603i 0.911622 + 0.411031i \(0.134831\pi\)
−0.0998479 + 0.995003i \(0.531836\pi\)
\(278\) −99.3939 + 216.534i −0.357532 + 0.778901i
\(279\) 0 0
\(280\) 27.9224 8.02330i 0.0997229 0.0286546i
\(281\) 37.8649 + 65.5838i 0.134750 + 0.233394i 0.925502 0.378743i \(-0.123643\pi\)
−0.790752 + 0.612137i \(0.790310\pi\)
\(282\) 0 0
\(283\) −322.061 185.942i −1.13803 0.657039i −0.192084 0.981378i \(-0.561525\pi\)
−0.945941 + 0.324339i \(0.894858\pi\)
\(284\) 65.1597 + 345.253i 0.229436 + 1.21568i
\(285\) 0 0
\(286\) 62.0429 5.80347i 0.216933 0.0202919i
\(287\) 3.15361i 0.0109882i
\(288\) 0 0
\(289\) −2.81196 −0.00972996
\(290\) 7.27226 + 77.7453i 0.0250768 + 0.268087i
\(291\) 0 0
\(292\) 236.003 44.5409i 0.808229 0.152537i
\(293\) 66.3946 114.999i 0.226603 0.392488i −0.730196 0.683237i \(-0.760571\pi\)
0.956799 + 0.290750i \(0.0939047\pi\)
\(294\) 0 0
\(295\) −128.479 + 74.1772i −0.435521 + 0.251448i
\(296\) −128.768 448.134i −0.435027 1.51397i
\(297\) 0 0
\(298\) 375.765 + 172.484i 1.26096 + 0.578806i
\(299\) −12.2556 + 7.07579i −0.0409887 + 0.0236648i
\(300\) 0 0
\(301\) −11.5719 + 20.0432i −0.0384450 + 0.0665886i
\(302\) 170.229 + 240.033i 0.563672 + 0.794811i
\(303\) 0 0
\(304\) 113.751 + 290.624i 0.374181 + 0.956000i
\(305\) 466.589 1.52980
\(306\) 0 0
\(307\) 336.514i 1.09614i 0.836434 + 0.548068i \(0.184637\pi\)
−0.836434 + 0.548068i \(0.815363\pi\)
\(308\) 13.6428 38.9309i 0.0442947 0.126399i
\(309\) 0 0
\(310\) −227.151 320.296i −0.732745 1.03321i
\(311\) −304.206 175.634i −0.978156 0.564738i −0.0764428 0.997074i \(-0.524356\pi\)
−0.901713 + 0.432336i \(0.857690\pi\)
\(312\) 0 0
\(313\) −95.4299 165.289i −0.304888 0.528081i 0.672349 0.740235i \(-0.265286\pi\)
−0.977236 + 0.212154i \(0.931952\pi\)
\(314\) 114.292 + 52.4626i 0.363988 + 0.167078i
\(315\) 0 0
\(316\) −112.719 + 96.9117i −0.356706 + 0.306683i
\(317\) 202.797 + 351.255i 0.639738 + 1.10806i 0.985490 + 0.169733i \(0.0542906\pi\)
−0.345752 + 0.938326i \(0.612376\pi\)
\(318\) 0 0
\(319\) 96.0203 + 55.4374i 0.301004 + 0.173785i
\(320\) −14.1661 393.221i −0.0442692 1.22882i
\(321\) 0 0
\(322\) 0.872512 + 9.32773i 0.00270966 + 0.0289681i
\(323\) 329.981i 1.02161i
\(324\) 0 0
\(325\) 22.8393 0.0702749
\(326\) −285.403 + 26.6965i −0.875470 + 0.0818911i
\(327\) 0 0
\(328\) −41.4487 10.3100i −0.126368 0.0314330i
\(329\) 3.28792 5.69484i 0.00999368 0.0173096i
\(330\) 0 0
\(331\) 384.104 221.763i 1.16044 0.669978i 0.209027 0.977910i \(-0.432970\pi\)
0.951408 + 0.307932i \(0.0996370\pi\)
\(332\) −231.251 + 198.822i −0.696541 + 0.598860i
\(333\) 0 0
\(334\) 145.024 315.941i 0.434203 0.945931i
\(335\) 195.631 112.948i 0.583974 0.337158i
\(336\) 0 0
\(337\) −254.239 + 440.356i −0.754420 + 1.30669i 0.191243 + 0.981543i \(0.438748\pi\)
−0.945662 + 0.325150i \(0.894585\pi\)
\(338\) −270.510 + 191.843i −0.800325 + 0.567582i
\(339\) 0 0
\(340\) 137.588 392.619i 0.404670 1.15476i
\(341\) −557.560 −1.63507
\(342\) 0 0
\(343\) 57.6805i 0.168165i
\(344\) 225.600 + 217.619i 0.655814 + 0.632614i
\(345\) 0 0
\(346\) −410.476 + 291.106i −1.18635 + 0.841346i
\(347\) −492.773 284.503i −1.42010 0.819893i −0.423790 0.905761i \(-0.639300\pi\)
−0.996307 + 0.0858678i \(0.972634\pi\)
\(348\) 0 0
\(349\) −206.901 358.363i −0.592840 1.02683i −0.993848 0.110754i \(-0.964673\pi\)
0.401008 0.916074i \(-0.368660\pi\)
\(350\) 6.30755 13.7413i 0.0180216 0.0392609i
\(351\) 0 0
\(352\) −467.076 306.586i −1.32692 0.870982i
\(353\) −62.3070 107.919i −0.176507 0.305719i 0.764175 0.645009i \(-0.223147\pi\)
−0.940682 + 0.339290i \(0.889813\pi\)
\(354\) 0 0
\(355\) 467.677 + 270.014i 1.31740 + 0.760602i
\(356\) −108.435 + 20.4649i −0.304592 + 0.0574858i
\(357\) 0 0
\(358\) −191.177 + 17.8826i −0.534015 + 0.0499515i
\(359\) 303.196i 0.844557i 0.906466 + 0.422278i \(0.138770\pi\)
−0.906466 + 0.422278i \(0.861230\pi\)
\(360\) 0 0
\(361\) −19.4752 −0.0539480
\(362\) −61.2363 654.657i −0.169161 1.80844i
\(363\) 0 0
\(364\) −0.781939 4.14315i −0.00214818 0.0113823i
\(365\) 184.572 319.688i 0.505677 0.875858i
\(366\) 0 0
\(367\) −615.571 + 355.400i −1.67730 + 0.968392i −0.713936 + 0.700211i \(0.753089\pi\)
−0.963369 + 0.268181i \(0.913578\pi\)
\(368\) 125.449 + 19.0273i 0.340894 + 0.0517045i
\(369\) 0 0
\(370\) −651.321 298.970i −1.76033 0.808027i
\(371\) −18.3527 + 10.5959i −0.0494681 + 0.0285604i
\(372\) 0 0
\(373\) 166.740 288.803i 0.447025 0.774271i −0.551166 0.834396i \(-0.685817\pi\)
0.998191 + 0.0601254i \(0.0191501\pi\)
\(374\) −341.728 481.857i −0.913712 1.28839i
\(375\) 0 0
\(376\) −64.0995 61.8318i −0.170477 0.164446i
\(377\) 11.3323 0.0300590
\(378\) 0 0
\(379\) 662.686i 1.74851i −0.485465 0.874256i \(-0.661350\pi\)
0.485465 0.874256i \(-0.338650\pi\)
\(380\) 452.699 + 158.642i 1.19131 + 0.417478i
\(381\) 0 0
\(382\) 0.470139 + 0.662924i 0.00123073 + 0.00173540i
\(383\) 69.9008 + 40.3572i 0.182509 + 0.105371i 0.588471 0.808518i \(-0.299730\pi\)
−0.405962 + 0.913890i \(0.633064\pi\)
\(384\) 0 0
\(385\) −31.7026 54.9106i −0.0823445 0.142625i
\(386\) −113.505 52.1013i −0.294055 0.134977i
\(387\) 0 0
\(388\) −68.1066 79.2155i −0.175533 0.204164i
\(389\) 346.006 + 599.301i 0.889476 + 1.54062i 0.840495 + 0.541819i \(0.182264\pi\)
0.0489809 + 0.998800i \(0.484403\pi\)
\(390\) 0 0
\(391\) 116.183 + 67.0782i 0.297143 + 0.171556i
\(392\) 377.700 + 93.9497i 0.963519 + 0.239668i
\(393\) 0 0
\(394\) 38.7174 + 413.915i 0.0982675 + 1.05055i
\(395\) 228.481i 0.578432i
\(396\) 0 0
\(397\) 657.713 1.65671 0.828354 0.560206i \(-0.189278\pi\)
0.828354 + 0.560206i \(0.189278\pi\)
\(398\) 595.657 55.7175i 1.49662 0.139994i
\(399\) 0 0
\(400\) −159.984 127.826i −0.399960 0.319564i
\(401\) −296.433 + 513.437i −0.739235 + 1.28039i 0.213606 + 0.976920i \(0.431479\pi\)
−0.952840 + 0.303472i \(0.901854\pi\)
\(402\) 0 0
\(403\) −49.3521 + 28.4935i −0.122462 + 0.0707034i
\(404\) −67.1918 78.1515i −0.166316 0.193444i
\(405\) 0 0
\(406\) 3.12963 6.81806i 0.00770846 0.0167933i
\(407\) −881.274 + 508.804i −2.16529 + 1.25013i
\(408\) 0 0
\(409\) −161.594 + 279.889i −0.395095 + 0.684325i −0.993113 0.117157i \(-0.962622\pi\)
0.598018 + 0.801483i \(0.295955\pi\)
\(410\) −53.5492 + 37.9765i −0.130608 + 0.0926257i
\(411\) 0 0
\(412\) 74.0781 + 25.9596i 0.179801 + 0.0630086i
\(413\) 14.2533 0.0345115
\(414\) 0 0
\(415\) 468.745i 1.12951i
\(416\) −57.0107 3.26788i −0.137045 0.00785549i
\(417\) 0 0
\(418\) 555.592 394.020i 1.32917 0.942632i
\(419\) 222.744 + 128.601i 0.531608 + 0.306924i 0.741671 0.670764i \(-0.234033\pi\)
−0.210063 + 0.977688i \(0.567367\pi\)
\(420\) 0 0
\(421\) 41.9905 + 72.7297i 0.0997400 + 0.172755i 0.911577 0.411129i \(-0.134866\pi\)
−0.811837 + 0.583884i \(0.801532\pi\)
\(422\) 136.559 297.499i 0.323598 0.704975i
\(423\) 0 0
\(424\) 79.2646 + 275.854i 0.186945 + 0.650599i
\(425\) −108.258 187.509i −0.254725 0.441197i
\(426\) 0 0
\(427\) −38.8221 22.4139i −0.0909182 0.0524917i
\(428\) −135.903 720.089i −0.317530 1.68245i
\(429\) 0 0
\(430\) 479.690 44.8700i 1.11556 0.104349i
\(431\) 144.348i 0.334914i 0.985879 + 0.167457i \(0.0535555\pi\)
−0.985879 + 0.167457i \(0.946445\pi\)
\(432\) 0 0
\(433\) 395.353 0.913057 0.456528 0.889709i \(-0.349093\pi\)
0.456528 + 0.889709i \(0.349093\pi\)
\(434\) 3.51351 + 37.5618i 0.00809566 + 0.0865479i
\(435\) 0 0
\(436\) −396.367 + 74.8065i −0.909098 + 0.171574i
\(437\) −77.3426 + 133.961i −0.176985 + 0.306548i
\(438\) 0 0
\(439\) −194.776 + 112.454i −0.443682 + 0.256160i −0.705158 0.709050i \(-0.749124\pi\)
0.261476 + 0.965210i \(0.415791\pi\)
\(440\) −825.346 + 237.157i −1.87579 + 0.538994i
\(441\) 0 0
\(442\) −54.8727 25.1877i −0.124146 0.0569858i
\(443\) 369.184 213.148i 0.833373 0.481148i −0.0216335 0.999766i \(-0.506887\pi\)
0.855006 + 0.518618i \(0.173553\pi\)
\(444\) 0 0
\(445\) −84.8041 + 146.885i −0.190571 + 0.330079i
\(446\) 441.772 + 622.926i 0.990521 + 1.39669i
\(447\) 0 0
\(448\) −17.7108 + 33.3981i −0.0395331 + 0.0745493i
\(449\) 406.744 0.905888 0.452944 0.891539i \(-0.350374\pi\)
0.452944 + 0.891539i \(0.350374\pi\)
\(450\) 0 0
\(451\) 93.2163i 0.206688i
\(452\) −24.1419 + 68.8911i −0.0534112 + 0.152414i
\(453\) 0 0
\(454\) 68.8644 + 97.1029i 0.151684 + 0.213883i
\(455\) −5.61228 3.24025i −0.0123347 0.00712144i
\(456\) 0 0
\(457\) −159.600 276.435i −0.349234 0.604891i 0.636879 0.770963i \(-0.280225\pi\)
−0.986114 + 0.166072i \(0.946892\pi\)
\(458\) 234.247 + 107.524i 0.511457 + 0.234770i
\(459\) 0 0
\(460\) 147.880 127.142i 0.321479 0.276396i
\(461\) −293.888 509.029i −0.637501 1.10418i −0.985979 0.166867i \(-0.946635\pi\)
0.348478 0.937317i \(-0.386698\pi\)
\(462\) 0 0
\(463\) 230.088 + 132.841i 0.496950 + 0.286914i 0.727453 0.686157i \(-0.240704\pi\)
−0.230503 + 0.973072i \(0.574037\pi\)
\(464\) −79.3797 63.4236i −0.171077 0.136689i
\(465\) 0 0
\(466\) −2.79285 29.8574i −0.00599323 0.0640716i
\(467\) 794.598i 1.70149i −0.525575 0.850747i \(-0.676150\pi\)
0.525575 0.850747i \(-0.323850\pi\)
\(468\) 0 0
\(469\) −21.7031 −0.0462752
\(470\) −136.294 + 12.7489i −0.289987 + 0.0271252i
\(471\) 0 0
\(472\) 46.5978 187.334i 0.0987241 0.396894i
\(473\) 342.050 592.447i 0.723149 1.25253i
\(474\) 0 0
\(475\) 216.201 124.824i 0.455161 0.262787i
\(476\) −30.3084 + 26.0581i −0.0636732 + 0.0547439i
\(477\) 0 0
\(478\) −303.711 + 661.649i −0.635378 + 1.38420i
\(479\) 572.964 330.801i 1.19617 0.690607i 0.236468 0.971639i \(-0.424010\pi\)
0.959698 + 0.281033i \(0.0906769\pi\)
\(480\) 0 0
\(481\) −52.0037 + 90.0730i −0.108116 + 0.187262i
\(482\) 132.219 93.7686i 0.274314 0.194541i
\(483\) 0 0
\(484\) −243.194 + 693.977i −0.502467 + 1.43384i
\(485\) −160.569 −0.331071
\(486\) 0 0
\(487\) 57.1525i 0.117356i 0.998277 + 0.0586781i \(0.0186886\pi\)
−0.998277 + 0.0586781i \(0.981311\pi\)
\(488\) −421.511 + 436.970i −0.863753 + 0.895430i
\(489\) 0 0
\(490\) 487.965 346.060i 0.995847 0.706244i
\(491\) −48.6600 28.0939i −0.0991040 0.0572177i 0.449629 0.893215i \(-0.351556\pi\)
−0.548733 + 0.835998i \(0.684890\pi\)
\(492\) 0 0
\(493\) −53.7147 93.0366i −0.108955 0.188715i
\(494\) 29.0420 63.2694i 0.0587895 0.128076i
\(495\) 0 0
\(496\) 505.170 + 76.6208i 1.01849 + 0.154477i
\(497\) −25.9417 44.9324i −0.0521967 0.0904073i
\(498\) 0 0
\(499\) 522.225 + 301.507i 1.04654 + 0.604222i 0.921679 0.387952i \(-0.126817\pi\)
0.124863 + 0.992174i \(0.460151\pi\)
\(500\) 294.853 55.6477i 0.589706 0.111295i
\(501\) 0 0
\(502\) 561.316 52.5052i 1.11816 0.104592i
\(503\) 549.354i 1.09216i 0.837734 + 0.546078i \(0.183880\pi\)
−0.837734 + 0.546078i \(0.816120\pi\)
\(504\) 0 0
\(505\) −158.413 −0.313688
\(506\) −25.7902 275.714i −0.0509687 0.544890i
\(507\) 0 0
\(508\) −121.946 646.136i −0.240050 1.27192i
\(509\) 119.464 206.918i 0.234704 0.406519i −0.724483 0.689293i \(-0.757921\pi\)
0.959187 + 0.282774i \(0.0912547\pi\)
\(510\) 0 0
\(511\) −30.7143 + 17.7329i −0.0601062 + 0.0347023i
\(512\) 381.057 + 341.964i 0.744252 + 0.667899i
\(513\) 0 0
\(514\) 136.893 + 62.8366i 0.266328 + 0.122250i
\(515\) 104.484 60.3240i 0.202882 0.117134i
\(516\) 0 0
\(517\) −97.1862 + 168.331i −0.187981 + 0.325593i
\(518\) 39.8306 + 56.1636i 0.0768931 + 0.108424i
\(519\) 0 0
\(520\) −60.9355 + 63.1703i −0.117184 + 0.121481i
\(521\) 567.711 1.08966 0.544828 0.838548i \(-0.316595\pi\)
0.544828 + 0.838548i \(0.316595\pi\)
\(522\) 0 0
\(523\) 941.999i 1.80114i −0.434706 0.900572i \(-0.643148\pi\)
0.434706 0.900572i \(-0.356852\pi\)
\(524\) −537.979 188.527i −1.02668 0.359784i
\(525\) 0 0
\(526\) 141.496 + 199.518i 0.269004 + 0.379312i
\(527\) 467.856 + 270.117i 0.887773 + 0.512556i
\(528\) 0 0
\(529\) −233.056 403.664i −0.440559 0.763071i
\(530\) 400.928 + 184.034i 0.756468 + 0.347235i
\(531\) 0 0
\(532\) −30.0456 34.9463i −0.0564766 0.0656885i
\(533\) 4.76372 + 8.25100i 0.00893755 + 0.0154803i
\(534\) 0 0
\(535\) −975.428 563.163i −1.82323 1.05264i
\(536\) −70.9532 + 285.248i −0.132375 + 0.532180i
\(537\) 0 0
\(538\) −52.2387 558.467i −0.0970980 1.03804i
\(539\) 849.430i 1.57594i
\(540\) 0 0
\(541\) −242.245 −0.447772 −0.223886 0.974615i \(-0.571874\pi\)
−0.223886 + 0.974615i \(0.571874\pi\)
\(542\) 162.186 15.1708i 0.299235 0.0279904i
\(543\) 0 0
\(544\) 243.401 + 483.542i 0.447428 + 0.888863i
\(545\) −309.988 + 536.915i −0.568786 + 0.985166i
\(546\) 0 0
\(547\) −170.503 + 98.4402i −0.311706 + 0.179964i −0.647690 0.761904i \(-0.724265\pi\)
0.335983 + 0.941868i \(0.390931\pi\)
\(548\) −16.0729 18.6945i −0.0293301 0.0341141i
\(549\) 0 0
\(550\) −186.442 + 406.173i −0.338986 + 0.738497i
\(551\) 107.273 61.9342i 0.194688 0.112403i
\(552\) 0 0
\(553\) 10.9757 19.0105i 0.0198476 0.0343770i
\(554\) −733.673 + 520.313i −1.32432 + 0.939194i
\(555\) 0 0
\(556\) −449.700 157.591i −0.808814 0.283437i
\(557\) −958.121 −1.72015 −0.860073 0.510171i \(-0.829582\pi\)
−0.860073 + 0.510171i \(0.829582\pi\)
\(558\) 0 0
\(559\) 69.9202i 0.125081i
\(560\) 21.1779 + 54.1076i 0.0378176 + 0.0966208i
\(561\) 0 0
\(562\) −123.545 + 87.6166i −0.219830 + 0.155901i
\(563\) −165.774 95.7097i −0.294448 0.169999i 0.345498 0.938419i \(-0.387710\pi\)
−0.639946 + 0.768420i \(0.721043\pi\)
\(564\) 0 0
\(565\) 56.1001 + 97.1682i 0.0992922 + 0.171979i
\(566\) 310.279 675.957i 0.548196 1.19427i
\(567\) 0 0
\(568\) −675.368 + 194.062i −1.18903 + 0.341658i
\(569\) −228.215 395.280i −0.401081 0.694693i 0.592775 0.805368i \(-0.298032\pi\)
−0.993857 + 0.110675i \(0.964699\pi\)
\(570\) 0 0
\(571\) −842.764 486.570i −1.47594 0.852136i −0.476312 0.879276i \(-0.658027\pi\)
−0.999632 + 0.0271399i \(0.991360\pi\)
\(572\) 23.1130 + 122.466i 0.0404073 + 0.214101i
\(573\) 0 0
\(574\) 6.27982 0.587411i 0.0109404 0.00102336i
\(575\) 101.496i 0.176515i
\(576\) 0 0
\(577\) 138.527 0.240081 0.120040 0.992769i \(-0.461698\pi\)
0.120040 + 0.992769i \(0.461698\pi\)
\(578\) −0.523773 5.59948i −0.000906181 0.00968768i
\(579\) 0 0
\(580\) −153.460 + 28.9626i −0.264586 + 0.0499355i
\(581\) 22.5175 39.0015i 0.0387565 0.0671282i
\(582\) 0 0
\(583\) 542.478 313.200i 0.930494 0.537221i
\(584\) 132.654 + 461.658i 0.227147 + 0.790510i
\(585\) 0 0
\(586\) 241.365 + 110.792i 0.411886 + 0.189064i
\(587\) −620.808 + 358.424i −1.05759 + 0.610602i −0.924766 0.380537i \(-0.875739\pi\)
−0.132829 + 0.991139i \(0.542406\pi\)
\(588\) 0 0
\(589\) −311.451 + 539.449i −0.528779 + 0.915872i
\(590\) −171.641 242.024i −0.290917 0.410210i
\(591\) 0 0
\(592\) 868.387 339.889i 1.46687 0.574137i
\(593\) −542.129 −0.914214 −0.457107 0.889412i \(-0.651114\pi\)
−0.457107 + 0.889412i \(0.651114\pi\)
\(594\) 0 0
\(595\) 61.4350i 0.103252i
\(596\) −273.477 + 780.391i −0.458853 + 1.30938i
\(597\) 0 0
\(598\) −16.3729 23.0867i −0.0273794 0.0386066i
\(599\) 245.527 + 141.755i 0.409895 + 0.236653i 0.690744 0.723099i \(-0.257283\pi\)
−0.280850 + 0.959752i \(0.590616\pi\)
\(600\) 0 0
\(601\) 377.424 + 653.717i 0.627993 + 1.08772i 0.987954 + 0.154748i \(0.0494567\pi\)
−0.359961 + 0.932967i \(0.617210\pi\)
\(602\) −42.0676 19.3099i −0.0698797 0.0320763i
\(603\) 0 0
\(604\) −446.272 + 383.688i −0.738860 + 0.635245i
\(605\) 565.126 + 978.827i 0.934093 + 1.61790i
\(606\) 0 0
\(607\) 77.2227 + 44.5845i 0.127220 + 0.0734506i 0.562260 0.826961i \(-0.309932\pi\)
−0.435039 + 0.900411i \(0.643266\pi\)
\(608\) −557.534 + 280.647i −0.916997 + 0.461590i
\(609\) 0 0
\(610\) 86.9097 + 929.122i 0.142475 + 1.52315i
\(611\) 19.8664i 0.0325145i
\(612\) 0 0
\(613\) −316.779 −0.516769 −0.258385 0.966042i \(-0.583190\pi\)
−0.258385 + 0.966042i \(0.583190\pi\)
\(614\) −670.103 + 62.6811i −1.09137 + 0.102087i
\(615\) 0 0
\(616\) 80.0646 + 19.9154i 0.129975 + 0.0323302i
\(617\) −534.934 + 926.533i −0.866992 + 1.50167i −0.00193565 + 0.999998i \(0.500616\pi\)
−0.865056 + 0.501675i \(0.832717\pi\)
\(618\) 0 0
\(619\) 578.542 334.021i 0.934640 0.539615i 0.0463638 0.998925i \(-0.485237\pi\)
0.888276 + 0.459310i \(0.151903\pi\)
\(620\) 595.498 511.988i 0.960481 0.825787i
\(621\) 0 0
\(622\) 293.077 638.483i 0.471185 1.02650i
\(623\) 14.1121 8.14762i 0.0226518 0.0130780i
\(624\) 0 0
\(625\) 390.580 676.505i 0.624929 1.08241i
\(626\) 311.367 220.818i 0.497391 0.352744i
\(627\) 0 0
\(628\) −83.1804 + 237.363i −0.132453 + 0.377967i
\(629\) 985.986 1.56755
\(630\) 0 0
\(631\) 150.631i 0.238718i 0.992851 + 0.119359i \(0.0380839\pi\)
−0.992851 + 0.119359i \(0.961916\pi\)
\(632\) −213.977 206.407i −0.338571 0.326593i
\(633\) 0 0
\(634\) −661.682 + 469.258i −1.04366 + 0.740155i
\(635\) −875.252 505.327i −1.37835 0.795790i
\(636\) 0 0
\(637\) −43.4092 75.1869i −0.0681463 0.118033i
\(638\) −92.5075 + 201.532i −0.144996 + 0.315881i
\(639\) 0 0
\(640\) 780.385 101.453i 1.21935 0.158520i
\(641\) −351.521 608.852i −0.548395 0.949847i −0.998385 0.0568139i \(-0.981906\pi\)
0.449990 0.893034i \(-0.351427\pi\)
\(642\) 0 0
\(643\) 742.057 + 428.427i 1.15405 + 0.666293i 0.949872 0.312639i \(-0.101213\pi\)
0.204182 + 0.978933i \(0.434546\pi\)
\(644\) −18.4119 + 3.47488i −0.0285898 + 0.00539577i
\(645\) 0 0
\(646\) −657.094 + 61.4643i −1.01717 + 0.0951459i
\(647\) 156.257i 0.241510i −0.992682 0.120755i \(-0.961468\pi\)
0.992682 0.120755i \(-0.0385316\pi\)
\(648\) 0 0
\(649\) −421.306 −0.649162
\(650\) 4.25419 + 45.4802i 0.00654491 + 0.0699695i
\(651\) 0 0
\(652\) −106.322 563.353i −0.163070 0.864038i
\(653\) 441.773 765.173i 0.676528 1.17178i −0.299492 0.954099i \(-0.596817\pi\)
0.976020 0.217682i \(-0.0698495\pi\)
\(654\) 0 0
\(655\) −758.798 + 438.092i −1.15847 + 0.668843i
\(656\) 12.8099 84.4574i 0.0195273 0.128746i
\(657\) 0 0
\(658\) 11.9526 + 5.48650i 0.0181651 + 0.00833815i
\(659\) 379.533 219.123i 0.575922 0.332509i −0.183589 0.983003i \(-0.558772\pi\)
0.759511 + 0.650494i \(0.225438\pi\)
\(660\) 0 0
\(661\) 233.924 405.168i 0.353894 0.612963i −0.633034 0.774124i \(-0.718191\pi\)
0.986928 + 0.161161i \(0.0515239\pi\)
\(662\) 513.143 + 723.562i 0.775140 + 1.09299i
\(663\) 0 0
\(664\) −438.989 423.459i −0.661128 0.637739i
\(665\) −70.8359 −0.106520
\(666\) 0 0
\(667\) 50.3597i 0.0755018i
\(668\) 656.149 + 229.938i 0.982259 + 0.344218i
\(669\) 0 0
\(670\) 261.353 + 368.524i 0.390079 + 0.550035i
\(671\) 1147.52 + 662.524i 1.71017 + 0.987368i
\(672\) 0 0
\(673\) 273.302 + 473.372i 0.406094 + 0.703376i 0.994448 0.105227i \(-0.0335571\pi\)
−0.588354 + 0.808604i \(0.700224\pi\)
\(674\) −924.240 424.246i −1.37128 0.629444i
\(675\) 0 0
\(676\) −432.405 502.934i −0.639652 0.743986i
\(677\) −227.606 394.225i −0.336198 0.582312i 0.647516 0.762052i \(-0.275808\pi\)
−0.983714 + 0.179740i \(0.942475\pi\)
\(678\) 0 0
\(679\) 13.3600 + 7.71341i 0.0196760 + 0.0113600i
\(680\) 807.454 + 200.848i 1.18743 + 0.295364i
\(681\) 0 0
\(682\) −103.854 1110.27i −0.152279 1.62797i
\(683\) 123.214i 0.180400i −0.995924 0.0902002i \(-0.971249\pi\)
0.995924 0.0902002i \(-0.0287507\pi\)
\(684\) 0 0
\(685\) −37.8937 −0.0553193
\(686\) −114.860 + 10.7439i −0.167434 + 0.0156617i
\(687\) 0 0
\(688\) −391.325 + 489.774i −0.568786 + 0.711881i
\(689\) 32.0115 55.4455i 0.0464607 0.0804724i
\(690\) 0 0
\(691\) −163.326 + 94.2965i −0.236362 + 0.136464i −0.613504 0.789692i \(-0.710240\pi\)
0.377141 + 0.926156i \(0.376907\pi\)
\(692\) −656.139 763.162i −0.948177 1.10283i
\(693\) 0 0
\(694\) 474.746 1034.26i 0.684071 1.49028i
\(695\) −634.285 + 366.204i −0.912640 + 0.526913i
\(696\) 0 0
\(697\) 45.1599 78.2192i 0.0647918 0.112223i
\(698\) 675.073 478.754i 0.967153 0.685895i
\(699\) 0 0
\(700\) 28.5381 + 10.0007i 0.0407686 + 0.0142868i
\(701\) 810.064 1.15558 0.577792 0.816184i \(-0.303915\pi\)
0.577792 + 0.816184i \(0.303915\pi\)
\(702\) 0 0
\(703\) 1136.86i 1.61716i
\(704\) 523.506 987.199i 0.743616 1.40227i
\(705\) 0 0
\(706\) 203.294 144.174i 0.287952 0.204212i
\(707\) 13.1806 + 7.60980i 0.0186429 + 0.0107635i
\(708\) 0 0
\(709\) −651.819 1128.98i −0.919349 1.59236i −0.800406 0.599459i \(-0.795382\pi\)
−0.118944 0.992901i \(-0.537951\pi\)
\(710\) −450.568 + 981.583i −0.634602 + 1.38251i
\(711\) 0 0
\(712\) −60.9497 212.115i −0.0856035 0.297914i
\(713\) 126.623 + 219.317i 0.177592 + 0.307598i
\(714\) 0 0
\(715\) 165.891 + 95.7772i 0.232015 + 0.133954i
\(716\) −71.2197 377.362i −0.0994688 0.527042i
\(717\) 0 0
\(718\) −603.756 + 56.4751i −0.840886 + 0.0786561i
\(719\) 788.981i 1.09733i 0.836042 + 0.548666i \(0.184864\pi\)
−0.836042 + 0.548666i \(0.815136\pi\)
\(720\) 0 0
\(721\) −11.5913 −0.0160768
\(722\) −3.62757 38.7812i −0.00502434 0.0537135i
\(723\) 0 0
\(724\) 1292.22 243.881i 1.78483 0.336852i
\(725\) −40.6380 + 70.3870i −0.0560524 + 0.0970856i
\(726\) 0 0
\(727\) −232.676 + 134.335i −0.320049 + 0.184780i −0.651414 0.758722i \(-0.725824\pi\)
0.331365 + 0.943502i \(0.392491\pi\)
\(728\) 8.10464 2.32881i 0.0111327 0.00319891i
\(729\) 0 0
\(730\) 670.977 + 307.992i 0.919146 + 0.421907i
\(731\) −574.038 + 331.421i −0.785277 + 0.453380i
\(732\) 0 0
\(733\) −36.8343 + 63.7989i −0.0502514 + 0.0870380i −0.890057 0.455849i \(-0.849336\pi\)
0.839806 + 0.542887i \(0.182669\pi\)
\(734\) −822.370 1159.59i −1.12040 1.57982i
\(735\) 0 0
\(736\) −14.5222 + 253.351i −0.0197313 + 0.344227i
\(737\) 641.512 0.870437
\(738\) 0 0
\(739\) 448.249i 0.606562i 0.952901 + 0.303281i \(0.0980820\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(740\) 474.022 1352.67i 0.640571 1.82793i
\(741\) 0 0
\(742\) −24.5182 34.5721i −0.0330434 0.0465932i
\(743\) −656.602 379.089i −0.883718 0.510215i −0.0118352 0.999930i \(-0.503767\pi\)
−0.871882 + 0.489715i \(0.837101\pi\)
\(744\) 0 0
\(745\) 635.496 + 1100.71i 0.853015 + 1.47746i
\(746\) 606.153 + 278.237i 0.812538 + 0.372972i
\(747\) 0 0
\(748\) 895.874 770.240i 1.19769 1.02973i
\(749\) 54.1063 + 93.7149i 0.0722381 + 0.125120i
\(750\) 0 0
\(751\) 1141.58 + 659.091i 1.52008 + 0.877618i 0.999720 + 0.0236697i \(0.00753501\pi\)
0.520358 + 0.853948i \(0.325798\pi\)
\(752\) 111.187 139.159i 0.147855 0.185052i
\(753\) 0 0
\(754\) 2.11081 + 22.5660i 0.00279949 + 0.0299284i
\(755\) 904.589i 1.19813i
\(756\) 0 0
\(757\) 587.874 0.776583 0.388292 0.921537i \(-0.373065\pi\)
0.388292 + 0.921537i \(0.373065\pi\)
\(758\) 1319.61 123.436i 1.74091 0.162844i
\(759\) 0 0
\(760\) −231.582 + 931.012i −0.304713 + 1.22502i
\(761\) 188.496 326.485i 0.247695 0.429021i −0.715191 0.698929i \(-0.753660\pi\)
0.962886 + 0.269908i \(0.0869934\pi\)
\(762\) 0 0
\(763\) 51.5845 29.7823i 0.0676075 0.0390332i
\(764\) −1.23252 + 1.05967i −0.00161324 + 0.00138701i
\(765\) 0 0
\(766\) −67.3435 + 146.711i −0.0879158 + 0.191529i
\(767\) −37.2917 + 21.5304i −0.0486202 + 0.0280709i
\(768\) 0 0
\(769\) 643.939 1115.34i 0.837372 1.45037i −0.0547122 0.998502i \(-0.517424\pi\)
0.892084 0.451869i \(-0.149243\pi\)
\(770\) 103.439 73.3576i 0.134336 0.0952697i
\(771\) 0 0
\(772\) 82.6075 235.728i 0.107005 0.305348i
\(773\) −778.578 −1.00722 −0.503608 0.863932i \(-0.667994\pi\)
−0.503608 + 0.863932i \(0.667994\pi\)
\(774\) 0 0
\(775\) 408.715i 0.527375i
\(776\) 145.057 150.376i 0.186929 0.193784i
\(777\) 0 0
\(778\) −1128.94 + 800.634i −1.45108 + 1.02909i
\(779\) 90.1884 + 52.0703i 0.115775 + 0.0668425i
\(780\) 0 0
\(781\) 766.801 + 1328.14i 0.981819 + 1.70056i
\(782\) −111.932 + 243.850i −0.143136 + 0.311829i