Properties

Label 108.3.f.c.19.5
Level 108
Weight 3
Character 108.19
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 19.5
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 \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.5

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.990418 0.138099i \(-0.955901\pi\)
0.375612 0.926777i \(-0.377432\pi\)
\(6\) 0 0
\(7\) 0.511543 + 0.295340i 0.0730776 + 0.0421914i 0.536094 0.844159i \(-0.319899\pi\)
−0.463016 + 0.886350i \(0.653233\pi\)
\(8\) −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 −0.383088 0.923712i \(-0.625139\pi\)
−0.991502 + 0.130092i \(0.958473\pi\)
\(12\) 0 0
\(13\) −0.892255 1.54543i −0.0686350 0.118879i 0.829666 0.558261i \(-0.188531\pi\)
−0.898301 + 0.439381i \(0.855198\pi\)
\(14\) 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 \(-0.828419\pi\)
0.858203 0.513310i \(-0.171581\pi\)
\(20\) 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 −0.343214 0.939257i \(-0.611516\pi\)
0.641813 + 0.766861i \(0.278182\pi\)
\(24\) 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 −0.915563 0.402174i \(-0.868255\pi\)
0.806075 + 0.591814i \(0.201588\pi\)
\(30\) 0 0
\(31\) 27.6558 15.9671i 0.892124 0.515068i 0.0174873 0.999847i \(-0.494433\pi\)
0.874637 + 0.484779i \(0.161100\pi\)
\(32\) 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 0.896742 0.442553i \(-0.145927\pi\)
−0.831633 + 0.555325i \(0.812594\pi\)
\(42\) 0 0
\(43\) −33.9324 19.5909i −0.789126 0.455602i 0.0505290 0.998723i \(-0.483909\pi\)
−0.839655 + 0.543121i \(0.817243\pi\)
\(44\) 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 0.599047 0.800714i \(-0.295546\pi\)
−0.393915 + 0.919147i \(0.628880\pi\)
\(48\) 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 −0.312337 0.949971i \(-0.601112\pi\)
0.666531 + 0.745477i \(0.267778\pi\)
\(60\) 0 0
\(61\) −37.9460 + 65.7244i −0.622066 + 1.07745i 0.367034 + 0.930207i \(0.380373\pi\)
−0.989100 + 0.147243i \(0.952960\pi\)
\(62\) −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 −0.718299 0.695734i \(-0.755079\pi\)
0.243374 + 0.969933i \(0.421746\pi\)
\(68\) −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 \(0.212288\pi\)
−0.785730 + 0.618570i \(0.787712\pi\)
\(72\) 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 0.689669 0.724124i \(-0.257756\pi\)
−0.282275 + 0.959333i \(0.591089\pi\)
\(80\) −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 0.841902 0.539630i \(-0.181436\pi\)
−0.0463824 + 0.998924i \(0.514769\pi\)
\(84\) 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 −0.790830 0.612036i \(-0.790351\pi\)
0.925454 + 0.378861i \(0.123684\pi\)
\(98\) −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 −0.795173 0.606382i \(-0.792620\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(102\) 0 0
\(103\) −16.9947 + 9.81187i −0.164997 + 0.0952609i −0.580225 0.814457i \(-0.697035\pi\)
0.415228 + 0.909717i \(0.363702\pi\)
\(104\) 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 \(-0.672895\pi\)
0.516850 0.856076i \(-0.327105\pi\)
\(108\) 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 0.903573 0.428435i \(-0.140935\pi\)
−0.822822 + 0.568299i \(0.807602\pi\)
\(114\) 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 \(-0.775945\pi\)
0.762331 0.647188i \(-0.224055\pi\)
\(128\) −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 0.0515116 0.998672i \(-0.483596\pi\)
0.890631 + 0.454726i \(0.150263\pi\)
\(132\) 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 −0.854559 0.519354i \(-0.826172\pi\)
0.877054 + 0.480393i \(0.159506\pi\)
\(138\) 0 0
\(139\) 103.168 59.5642i 0.742218 0.428519i −0.0806575 0.996742i \(-0.525702\pi\)
0.822875 + 0.568222i \(0.192369\pi\)
\(140\) −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 0.970608 + 0.240665i \(0.0773657\pi\)
−0.276882 + 0.960904i \(0.589301\pi\)
\(150\) 0 0
\(151\) 127.422 + 73.5670i 0.843853 + 0.487199i 0.858572 0.512693i \(-0.171352\pi\)
−0.0147190 + 0.999892i \(0.504685\pi\)
\(152\) 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 0.948609 0.316449i \(-0.102491\pi\)
−0.748358 + 0.663295i \(0.769157\pi\)
\(158\) 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 \(-0.855104\pi\)
0.898171 0.439646i \(-0.144896\pi\)
\(164\) −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 −0.877648 0.479306i \(-0.840889\pi\)
−0.0237332 + 0.999718i \(0.507555\pi\)
\(168\) 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 −0.230861 0.972987i \(-0.574154\pi\)
0.958062 0.286562i \(-0.0925125\pi\)
\(174\) 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 \(-0.913580\pi\)
0.963371 0.268173i \(-0.0864199\pi\)
\(180\) 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 0.500921 0.865493i \(-0.332995\pi\)
−0.499078 + 0.866557i \(0.666328\pi\)
\(192\) 0 0
\(193\) −31.2230 54.0798i −0.161777 0.280206i 0.773729 0.633517i \(-0.218389\pi\)
−0.935506 + 0.353311i \(0.885056\pi\)
\(194\) −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 \(0.270707\pi\)
−0.659643 + 0.751579i \(0.729293\pi\)
\(200\) −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 −0.796748 0.604311i \(-0.793448\pi\)
0.124975 + 0.992160i \(0.460115\pi\)
\(212\) 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 0.999811 0.0194478i \(-0.00619081\pi\)
0.483063 + 0.875586i \(0.339524\pi\)
\(224\) 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 0.609224 0.792998i \(-0.291481\pi\)
−0.382144 + 0.924103i \(0.624814\pi\)
\(228\) 0 0
\(229\) 64.4366 + 111.608i 0.281383 + 0.487369i 0.971726 0.236113i \(-0.0758736\pi\)
−0.690343 + 0.723482i \(0.742540\pi\)
\(230\) −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 0.335442 0.942061i \(-0.391114\pi\)
0.983570 + 0.180529i \(0.0577811\pi\)
\(240\) 0 0
\(241\) −40.5235 + 70.1888i −0.168147 + 0.291240i −0.937769 0.347261i \(-0.887112\pi\)
0.769621 + 0.638501i \(0.220445\pi\)
\(242\) 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 \(0.189783\pi\)
−0.827463 + 0.561520i \(0.810217\pi\)
\(252\) 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 0.929940 0.367711i \(-0.119858\pi\)
−0.783417 + 0.621496i \(0.786525\pi\)
\(258\) 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 0.687655 0.726037i \(-0.258640\pi\)
−0.284939 + 0.958546i \(0.591973\pi\)
\(264\) 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 \(0.0480146\pi\)
−0.988645 + 0.150271i \(0.951985\pi\)
\(272\) 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 −0.0998479 0.995003i \(-0.531836\pi\)
0.911622 0.411031i \(-0.134831\pi\)
\(278\) −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 −0.790752 0.612137i \(-0.790310\pi\)
0.925502 + 0.378743i \(0.123643\pi\)
\(282\) 0 0
\(283\) −322.061 + 185.942i −1.13803 + 0.657039i −0.945941 0.324339i \(-0.894858\pi\)
−0.192084 + 0.981378i \(0.561525\pi\)
\(284\) 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 0.956799 0.290750i \(-0.0939047\pi\)
−0.730196 + 0.683237i \(0.760571\pi\)
\(294\) 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 \(-0.815363\pi\)
0.836434 0.548068i \(-0.184637\pi\)
\(308\) 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 −0.901713 0.432336i \(-0.857690\pi\)
−0.0764428 + 0.997074i \(0.524356\pi\)
\(312\) 0 0
\(313\) −95.4299 + 165.289i −0.304888 + 0.528081i −0.977236 0.212154i \(-0.931952\pi\)
0.672349 + 0.740235i \(0.265286\pi\)
\(314\) 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 −0.345752 0.938326i \(-0.612376\pi\)
0.985490 0.169733i \(-0.0542906\pi\)
\(318\) 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 0.951408 0.307932i \(-0.0996370\pi\)
0.209027 + 0.977910i \(0.432970\pi\)
\(332\) −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 −0.945662 0.325150i \(-0.894585\pi\)
0.191243 0.981543i \(-0.438748\pi\)
\(338\) −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 −0.996307 0.0858678i \(-0.972634\pi\)
−0.423790 + 0.905761i \(0.639300\pi\)
\(348\) 0 0
\(349\) −206.901 + 358.363i −0.592840 + 1.02683i 0.401008 + 0.916074i \(0.368660\pi\)
−0.993848 + 0.110754i \(0.964673\pi\)
\(350\) 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 −0.940682 0.339290i \(-0.889813\pi\)
0.764175 + 0.645009i \(0.223147\pi\)
\(354\) 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 \(-0.861230\pi\)
0.906466 0.422278i \(-0.138770\pi\)
\(360\) 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 −0.963369 0.268181i \(-0.913578\pi\)
−0.713936 0.700211i \(1.24691\pi\)
\(368\) 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 0.998191 0.0601254i \(-0.0191501\pi\)
−0.551166 + 0.834396i \(0.685817\pi\)
\(374\) −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 \(0.338650\pi\)
−0.485465 + 0.874256i \(0.661350\pi\)
\(380\) 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 −0.405962 0.913890i \(-0.633064\pi\)
0.588471 + 0.808518i \(0.299730\pi\)
\(384\) 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 0.0489809 0.998800i \(-0.484403\pi\)
0.840495 0.541819i \(-0.182264\pi\)
\(390\) 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 −0.952840 0.303472i \(-0.901854\pi\)
0.213606 0.976920i \(-0.431479\pi\)
\(402\) 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 0.598018 0.801483i \(-0.295955\pi\)
−0.993113 + 0.117157i \(0.962622\pi\)
\(410\) −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 −0.210063 0.977688i \(-0.567367\pi\)
0.741671 + 0.670764i \(0.234033\pi\)
\(420\) 0 0
\(421\) 41.9905 72.7297i 0.0997400 0.172755i −0.811837 0.583884i \(-0.801532\pi\)
0.911577 + 0.411129i \(0.134866\pi\)
\(422\) 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 \(-0.946445\pi\)
0.985879 0.167457i \(-0.0535555\pi\)
\(432\) 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 0.261476 0.965210i \(-0.415791\pi\)
−0.705158 + 0.709050i \(0.749124\pi\)
\(440\) −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 0.855006 0.518618i \(-0.173553\pi\)
−0.0216335 + 0.999766i \(0.506887\pi\)
\(444\) 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 −0.986114 0.166072i \(-0.946892\pi\)
0.636879 + 0.770963i \(0.280225\pi\)
\(458\) 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 0.348478 + 0.937317i \(0.386698\pi\)
−0.985979 + 0.166867i \(0.946635\pi\)
\(462\) 0 0
\(463\) 230.088 132.841i 0.496950 0.286914i −0.230503 0.973072i \(-0.574037\pi\)
0.727453 + 0.686157i \(0.240704\pi\)
\(464\) −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 \(0.323850\pi\)
−0.525575 + 0.850747i \(0.676150\pi\)
\(468\) 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 0.959698 0.281033i \(-0.0906769\pi\)
0.236468 + 0.971639i \(0.424010\pi\)
\(480\) 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 \(-0.981311\pi\)
0.998277 0.0586781i \(-0.0186886\pi\)
\(488\) −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 −0.548733 0.835998i \(-0.684890\pi\)
0.449629 + 0.893215i \(0.351556\pi\)
\(492\) 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 0.124863 0.992174i \(-0.460151\pi\)
0.921679 + 0.387952i \(0.126817\pi\)
\(500\) 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 \(-0.816120\pi\)
0.837734 0.546078i \(-0.183880\pi\)
\(504\) 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 0.959187 0.282774i \(-0.0912547\pi\)
−0.724483 + 0.689293i \(0.757921\pi\)
\(510\) 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 \(0.356852\pi\)
−0.434706 + 0.900572i \(0.643148\pi\)
\(524\) −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 0.335983 0.941868i \(-0.390931\pi\)
−0.647690 + 0.761904i \(0.724265\pi\)
\(548\) −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 −0.639946 0.768420i \(-0.721043\pi\)
0.345498 + 0.938419i \(0.387710\pi\)
\(564\) 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 −0.993857 0.110675i \(-0.964699\pi\)
0.592775 + 0.805368i \(0.298032\pi\)
\(570\) 0 0
\(571\) −842.764 + 486.570i −1.47594 + 0.852136i −0.999632 0.0271399i \(-0.991360\pi\)
−0.476312 + 0.879276i \(0.658027\pi\)
\(572\) 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 −0.132829 0.991139i \(-0.542406\pi\)
−0.924766 + 0.380537i \(0.875739\pi\)
\(588\) 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 −0.280850 0.959752i \(-0.590616\pi\)
0.690744 + 0.723099i \(0.257283\pi\)
\(600\) 0 0
\(601\) 377.424 653.717i 0.627993 1.08772i −0.359961 0.932967i \(-0.617210\pi\)
0.987954 0.154748i \(-0.0494567\pi\)
\(602\) −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 −0.435039 0.900411i \(-0.643266\pi\)
0.562260 + 0.826961i \(0.309932\pi\)
\(608\) −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 −0.865056 0.501675i \(-0.832717\pi\)
−0.00193565 0.999998i \(-0.500616\pi\)
\(618\) 0 0
\(619\) 578.542 + 334.021i 0.934640 + 0.539615i 0.888276 0.459310i \(-0.151903\pi\)
0.0463638 + 0.998925i \(0.485237\pi\)
\(620\) 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 \(-0.961916\pi\)
0.992851 0.119359i \(-0.0380839\pi\)
\(632\) −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 0.449990 + 0.893034i \(0.351427\pi\)
−0.998385 + 0.0568139i \(0.981906\pi\)
\(642\) 0 0
\(643\) 742.057 428.427i 1.15405 0.666293i 0.204182 0.978933i \(-0.434546\pi\)
0.949872 + 0.312639i \(0.101213\pi\)
\(644\) −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 \(0.0385316\pi\)
−0.992682 + 0.120755i \(0.961468\pi\)
\(648\) 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 0.976020 + 0.217682i \(0.0698495\pi\)
−0.299492 + 0.954099i \(0.596817\pi\)
\(654\) 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 0.759511 0.650494i \(-0.225438\pi\)
−0.183589 + 0.983003i \(0.558772\pi\)
\(660\) 0 0
\(661\) 233.924 + 405.168i 0.353894 + 0.612963i 0.986928 0.161161i \(-0.0515239\pi\)
−0.633034 + 0.774124i \(0.718191\pi\)
\(662\) 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 −0.588354 0.808604i \(-0.700224\pi\)
0.994448 + 0.105227i \(0.0335571\pi\)
\(674\) −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 −0.983714 0.179740i \(-0.942475\pi\)
0.647516 + 0.762052i \(0.275808\pi\)
\(678\) 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 \(0.0287507\pi\)
−0.995924 + 0.0902002i \(0.971249\pi\)
\(684\) 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 0.377141 0.926156i \(-0.376907\pi\)
−0.613504 + 0.789692i \(0.710240\pi\)
\(692\) −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 −0.118944 + 0.992901i \(0.537951\pi\)
−0.800406 + 0.599459i \(0.795382\pi\)
\(710\) −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 \(-0.815136\pi\)
0.836042 0.548666i \(-0.184864\pi\)
\(720\) 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 0.331365 0.943502i \(-0.392491\pi\)
−0.651414 + 0.758722i \(0.725824\pi\)
\(728\) 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 0.839806 0.542887i \(-0.182669\pi\)
−0.890057 + 0.455849i \(0.849336\pi\)
\(734\) −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 \(-0.901918\pi\)
0.952901 0.303281i \(-0.0980820\pi\)
\(740\) 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 −0.871882 0.489715i \(-0.837101\pi\)
−0.0118352 + 0.999930i \(0.503767\pi\)
\(744\) 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 0.520358 0.853948i \(-0.325798\pi\)
0.999720 0.0236697i \(-0.00753501\pi\)
\(752\) 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 0.962886 0.269908i \(-0.0869934\pi\)
−0.715191 + 0.698929i \(0.753660\pi\)
\(762\) 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 0.892084 + 0.451869i \(0.149243\pi\)
−0.0547122 + 0.998502i \(0.517424\pi\)
\(770\) 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 &minu