Properties

Label 108.3.k.a.77.2
Level 108
Weight 3
Character 108.77
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 77.2
Character \(\chi\) \(=\) 108.77
Dual form 108.3.k.a.101.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.47205 + 2.61402i) q^{3} +(-4.32861 - 0.763252i) q^{5} +(-2.73772 + 2.29722i) q^{7} +(-4.66616 - 7.69591i) q^{9} +O(q^{10})\) \(q+(-1.47205 + 2.61402i) q^{3} +(-4.32861 - 0.763252i) q^{5} +(-2.73772 + 2.29722i) q^{7} +(-4.66616 - 7.69591i) q^{9} +(-14.4582 + 2.54938i) q^{11} +(-3.67778 + 1.33860i) q^{13} +(8.36707 - 10.1915i) q^{15} +(-5.96626 - 3.44462i) q^{17} +(14.1412 + 24.4932i) q^{19} +(-1.97492 - 10.5381i) q^{21} +(0.832583 - 0.992234i) q^{23} +(-5.33796 - 1.94286i) q^{25} +(26.9860 - 0.868674i) q^{27} +(-12.9959 + 35.7059i) q^{29} +(41.7175 + 35.0052i) q^{31} +(14.6191 - 41.5469i) q^{33} +(13.6039 - 7.85422i) q^{35} +(18.5334 - 32.1007i) q^{37} +(1.91473 - 11.5842i) q^{39} +(-14.0768 - 38.6757i) q^{41} +(-0.615899 - 3.49294i) q^{43} +(14.3241 + 36.8741i) q^{45} +(-27.5222 - 32.7997i) q^{47} +(-6.29086 + 35.6773i) q^{49} +(17.7869 - 10.5253i) q^{51} +47.8007i q^{53} +64.5299 q^{55} +(-84.8421 + 0.910069i) q^{57} +(-61.1091 - 10.7752i) q^{59} +(-8.50896 + 7.13987i) q^{61} +(30.4539 + 10.3501i) q^{63} +(16.9414 - 2.98722i) q^{65} +(-105.153 + 38.2727i) q^{67} +(1.36811 + 3.63700i) q^{69} +(90.9885 + 52.5322i) q^{71} +(-48.5118 - 84.0248i) q^{73} +(12.9364 - 11.0935i) q^{75} +(33.7262 - 40.1933i) q^{77} +(-104.299 - 37.9616i) q^{79} +(-37.4540 + 71.8206i) q^{81} +(-44.8984 + 123.357i) q^{83} +(23.1965 + 19.4642i) q^{85} +(-74.2053 - 86.5322i) q^{87} +(87.8638 - 50.7282i) q^{89} +(6.99367 - 12.1134i) q^{91} +(-152.914 + 57.5210i) q^{93} +(-42.5172 - 116.815i) q^{95} +(-28.7527 - 163.065i) q^{97} +(87.0842 + 99.3734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(1\)

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
\(3\) −1.47205 + 2.61402i −0.490682 + 0.871339i
\(4\) 0 0
\(5\) −4.32861 0.763252i −0.865723 0.152650i −0.276887 0.960903i \(-0.589303\pi\)
−0.588836 + 0.808252i \(0.700414\pi\)
\(6\) 0 0
\(7\) −2.73772 + 2.29722i −0.391103 + 0.328175i −0.817043 0.576577i \(-0.804388\pi\)
0.425939 + 0.904752i \(0.359944\pi\)
\(8\) 0 0
\(9\) −4.66616 7.69591i −0.518462 0.855101i
\(10\) 0 0
\(11\) −14.4582 + 2.54938i −1.31438 + 0.231762i −0.786519 0.617566i \(-0.788119\pi\)
−0.527866 + 0.849328i \(0.677008\pi\)
\(12\) 0 0
\(13\) −3.67778 + 1.33860i −0.282906 + 0.102969i −0.479576 0.877500i \(-0.659209\pi\)
0.196670 + 0.980470i \(0.436987\pi\)
\(14\) 0 0
\(15\) 8.36707 10.1915i 0.557805 0.679435i
\(16\) 0 0
\(17\) −5.96626 3.44462i −0.350956 0.202625i 0.314150 0.949373i \(-0.398280\pi\)
−0.665106 + 0.746749i \(0.731614\pi\)
\(18\) 0 0
\(19\) 14.1412 + 24.4932i 0.744272 + 1.28912i 0.950534 + 0.310620i \(0.100537\pi\)
−0.206263 + 0.978497i \(0.566130\pi\)
\(20\) 0 0
\(21\) −1.97492 10.5381i −0.0940438 0.501813i
\(22\) 0 0
\(23\) 0.832583 0.992234i 0.0361993 0.0431406i −0.747641 0.664103i \(-0.768814\pi\)
0.783840 + 0.620962i \(0.213258\pi\)
\(24\) 0 0
\(25\) −5.33796 1.94286i −0.213519 0.0777144i
\(26\) 0 0
\(27\) 26.9860 0.868674i 0.999482 0.0321731i
\(28\) 0 0
\(29\) −12.9959 + 35.7059i −0.448134 + 1.23124i 0.485887 + 0.874021i \(0.338496\pi\)
−0.934021 + 0.357217i \(0.883726\pi\)
\(30\) 0 0
\(31\) 41.7175 + 35.0052i 1.34573 + 1.12920i 0.980115 + 0.198431i \(0.0635846\pi\)
0.365612 + 0.930767i \(0.380860\pi\)
\(32\) 0 0
\(33\) 14.6191 41.5469i 0.443003 1.25900i
\(34\) 0 0
\(35\) 13.6039 7.85422i 0.388683 0.224406i
\(36\) 0 0
\(37\) 18.5334 32.1007i 0.500902 0.867588i −0.499097 0.866546i \(-0.666335\pi\)
0.999999 0.00104187i \(-0.000331638\pi\)
\(38\) 0 0
\(39\) 1.91473 11.5842i 0.0490957 0.297032i
\(40\) 0 0
\(41\) −14.0768 38.6757i −0.343336 0.943309i −0.984419 0.175837i \(-0.943737\pi\)
0.641083 0.767472i \(-0.278485\pi\)
\(42\) 0 0
\(43\) −0.615899 3.49294i −0.0143232 0.0812311i 0.976808 0.214116i \(-0.0686870\pi\)
−0.991131 + 0.132885i \(0.957576\pi\)
\(44\) 0 0
\(45\) 14.3241 + 36.8741i 0.318313 + 0.819424i
\(46\) 0 0
\(47\) −27.5222 32.7997i −0.585578 0.697865i 0.389171 0.921165i \(-0.372761\pi\)
−0.974750 + 0.223300i \(0.928317\pi\)
\(48\) 0 0
\(49\) −6.29086 + 35.6773i −0.128385 + 0.728107i
\(50\) 0 0
\(51\) 17.7869 10.5253i 0.348763 0.206377i
\(52\) 0 0
\(53\) 47.8007i 0.901900i 0.892549 + 0.450950i \(0.148915\pi\)
−0.892549 + 0.450950i \(0.851085\pi\)
\(54\) 0 0
\(55\) 64.5299 1.17327
\(56\) 0 0
\(57\) −84.8421 + 0.910069i −1.48846 + 0.0159661i
\(58\) 0 0
\(59\) −61.1091 10.7752i −1.03575 0.182630i −0.370174 0.928962i \(-0.620702\pi\)
−0.665574 + 0.746332i \(0.731813\pi\)
\(60\) 0 0
\(61\) −8.50896 + 7.13987i −0.139491 + 0.117047i −0.709863 0.704339i \(-0.751243\pi\)
0.570372 + 0.821386i \(0.306799\pi\)
\(62\) 0 0
\(63\) 30.4539 + 10.3501i 0.483395 + 0.164287i
\(64\) 0 0
\(65\) 16.9414 2.98722i 0.260636 0.0459572i
\(66\) 0 0
\(67\) −105.153 + 38.2727i −1.56945 + 0.571235i −0.972877 0.231321i \(-0.925695\pi\)
−0.596577 + 0.802556i \(0.703473\pi\)
\(68\) 0 0
\(69\) 1.36811 + 3.63700i 0.0198277 + 0.0527101i
\(70\) 0 0
\(71\) 90.9885 + 52.5322i 1.28153 + 0.739890i 0.977128 0.212654i \(-0.0682107\pi\)
0.304400 + 0.952544i \(0.401544\pi\)
\(72\) 0 0
\(73\) −48.5118 84.0248i −0.664545 1.15102i −0.979409 0.201888i \(-0.935292\pi\)
0.314864 0.949137i \(-0.398041\pi\)
\(74\) 0 0
\(75\) 12.9364 11.0935i 0.172485 0.147914i
\(76\) 0 0
\(77\) 33.7262 40.1933i 0.438002 0.521991i
\(78\) 0 0
\(79\) −104.299 37.9616i −1.32024 0.480527i −0.416702 0.909043i \(-0.636814\pi\)
−0.903534 + 0.428516i \(0.859037\pi\)
\(80\) 0 0
\(81\) −37.4540 + 71.8206i −0.462395 + 0.886674i
\(82\) 0 0
\(83\) −44.8984 + 123.357i −0.540945 + 1.48623i 0.304679 + 0.952455i \(0.401451\pi\)
−0.845624 + 0.533779i \(0.820771\pi\)
\(84\) 0 0
\(85\) 23.1965 + 19.4642i 0.272900 + 0.228990i
\(86\) 0 0
\(87\) −74.2053 86.5322i −0.852934 0.994623i
\(88\) 0 0
\(89\) 87.8638 50.7282i 0.987233 0.569979i 0.0827871 0.996567i \(-0.473618\pi\)
0.904446 + 0.426588i \(0.140285\pi\)
\(90\) 0 0
\(91\) 6.99367 12.1134i 0.0768535 0.133114i
\(92\) 0 0
\(93\) −152.914 + 57.5210i −1.64424 + 0.618506i
\(94\) 0 0
\(95\) −42.5172 116.815i −0.447549 1.22963i
\(96\) 0 0
\(97\) −28.7527 163.065i −0.296420 1.68108i −0.661376 0.750055i \(-0.730027\pi\)
0.364956 0.931025i \(-0.381084\pi\)
\(98\) 0 0
\(99\) 87.0842 + 99.3734i 0.879638 + 1.00377i
\(100\) 0 0
\(101\) 14.2076 + 16.9319i 0.140669 + 0.167643i 0.831779 0.555107i \(-0.187323\pi\)
−0.691110 + 0.722749i \(0.742878\pi\)
\(102\) 0 0
\(103\) −4.91300 + 27.8630i −0.0476991 + 0.270515i −0.999325 0.0367451i \(-0.988301\pi\)
0.951626 + 0.307260i \(0.0994121\pi\)
\(104\) 0 0
\(105\) 0.505467 + 47.1226i 0.00481397 + 0.448787i
\(106\) 0 0
\(107\) 67.0830i 0.626944i −0.949597 0.313472i \(-0.898508\pi\)
0.949597 0.313472i \(-0.101492\pi\)
\(108\) 0 0
\(109\) 82.0479 0.752733 0.376367 0.926471i \(-0.377173\pi\)
0.376367 + 0.926471i \(0.377173\pi\)
\(110\) 0 0
\(111\) 56.6299 + 95.7003i 0.510179 + 0.862165i
\(112\) 0 0
\(113\) 139.573 + 24.6104i 1.23516 + 0.217791i 0.752839 0.658205i \(-0.228684\pi\)
0.482317 + 0.875997i \(0.339795\pi\)
\(114\) 0 0
\(115\) −4.36126 + 3.65953i −0.0379240 + 0.0318220i
\(116\) 0 0
\(117\) 27.4628 + 22.0577i 0.234725 + 0.188527i
\(118\) 0 0
\(119\) 24.2470 4.27540i 0.203757 0.0359278i
\(120\) 0 0
\(121\) 88.8384 32.3345i 0.734202 0.267228i
\(122\) 0 0
\(123\) 121.820 + 20.1354i 0.990410 + 0.163703i
\(124\) 0 0
\(125\) 116.786 + 67.4265i 0.934289 + 0.539412i
\(126\) 0 0
\(127\) 36.1258 + 62.5718i 0.284455 + 0.492691i 0.972477 0.232999i \(-0.0748539\pi\)
−0.688022 + 0.725690i \(0.741521\pi\)
\(128\) 0 0
\(129\) 10.0372 + 3.53180i 0.0778079 + 0.0273783i
\(130\) 0 0
\(131\) 80.4893 95.9234i 0.614422 0.732239i −0.365679 0.930741i \(-0.619163\pi\)
0.980101 + 0.198502i \(0.0636076\pi\)
\(132\) 0 0
\(133\) −94.9809 34.5702i −0.714142 0.259927i
\(134\) 0 0
\(135\) −117.475 16.8370i −0.870186 0.124718i
\(136\) 0 0
\(137\) −44.4879 + 122.229i −0.324729 + 0.892186i 0.664693 + 0.747117i \(0.268563\pi\)
−0.989422 + 0.145069i \(0.953660\pi\)
\(138\) 0 0
\(139\) −64.7192 54.3058i −0.465606 0.390689i 0.379583 0.925158i \(-0.376067\pi\)
−0.845189 + 0.534468i \(0.820512\pi\)
\(140\) 0 0
\(141\) 126.253 23.6608i 0.895410 0.167807i
\(142\) 0 0
\(143\) 49.7615 28.7298i 0.347983 0.200908i
\(144\) 0 0
\(145\) 83.5068 144.638i 0.575909 0.997503i
\(146\) 0 0
\(147\) −84.0005 68.9630i −0.571432 0.469136i
\(148\) 0 0
\(149\) 48.8305 + 134.161i 0.327722 + 0.900408i 0.988687 + 0.149992i \(0.0479247\pi\)
−0.660966 + 0.750416i \(0.729853\pi\)
\(150\) 0 0
\(151\) 7.41354 + 42.0443i 0.0490963 + 0.278439i 0.999466 0.0326849i \(-0.0104058\pi\)
−0.950369 + 0.311124i \(0.899295\pi\)
\(152\) 0 0
\(153\) 1.33002 + 61.9889i 0.00869292 + 0.405156i
\(154\) 0 0
\(155\) −153.861 183.365i −0.992654 1.18300i
\(156\) 0 0
\(157\) −11.8042 + 66.9447i −0.0751857 + 0.426399i 0.923860 + 0.382730i \(0.125016\pi\)
−0.999046 + 0.0436696i \(0.986095\pi\)
\(158\) 0 0
\(159\) −124.952 70.3649i −0.785861 0.442546i
\(160\) 0 0
\(161\) 4.62909i 0.0287521i
\(162\) 0 0
\(163\) −52.2555 −0.320586 −0.160293 0.987069i \(-0.551244\pi\)
−0.160293 + 0.987069i \(0.551244\pi\)
\(164\) 0 0
\(165\) −94.9911 + 168.682i −0.575704 + 1.02232i
\(166\) 0 0
\(167\) −205.761 36.2813i −1.23210 0.217253i −0.480575 0.876953i \(-0.659572\pi\)
−0.751529 + 0.659700i \(0.770683\pi\)
\(168\) 0 0
\(169\) −117.727 + 98.7850i −0.696611 + 0.584526i
\(170\) 0 0
\(171\) 122.513 223.118i 0.716448 1.30478i
\(172\) 0 0
\(173\) 285.514 50.3439i 1.65037 0.291005i 0.730409 0.683010i \(-0.239329\pi\)
0.919963 + 0.392005i \(0.128218\pi\)
\(174\) 0 0
\(175\) 19.0771 6.94348i 0.109012 0.0396770i
\(176\) 0 0
\(177\) 118.122 143.879i 0.667356 0.812874i
\(178\) 0 0
\(179\) −84.3915 48.7235i −0.471461 0.272198i 0.245390 0.969424i \(-0.421084\pi\)
−0.716851 + 0.697226i \(0.754417\pi\)
\(180\) 0 0
\(181\) 18.6602 + 32.3205i 0.103095 + 0.178566i 0.912958 0.408053i \(-0.133792\pi\)
−0.809863 + 0.586619i \(0.800459\pi\)
\(182\) 0 0
\(183\) −6.13813 32.7528i −0.0335417 0.178977i
\(184\) 0 0
\(185\) −104.725 + 124.806i −0.566080 + 0.674628i
\(186\) 0 0
\(187\) 95.0432 + 34.5929i 0.508252 + 0.184989i
\(188\) 0 0
\(189\) −71.8847 + 64.3711i −0.380342 + 0.340588i
\(190\) 0 0
\(191\) −119.816 + 329.191i −0.627307 + 1.72351i 0.0610446 + 0.998135i \(0.480557\pi\)
−0.688352 + 0.725377i \(0.741665\pi\)
\(192\) 0 0
\(193\) 8.46714 + 7.10477i 0.0438712 + 0.0368123i 0.664460 0.747324i \(-0.268662\pi\)
−0.620588 + 0.784136i \(0.713106\pi\)
\(194\) 0 0
\(195\) −17.1298 + 48.6823i −0.0878453 + 0.249653i
\(196\) 0 0
\(197\) −275.483 + 159.050i −1.39839 + 0.807362i −0.994224 0.107323i \(-0.965772\pi\)
−0.404167 + 0.914685i \(0.632439\pi\)
\(198\) 0 0
\(199\) −88.3486 + 153.024i −0.443963 + 0.768966i −0.997979 0.0635397i \(-0.979761\pi\)
0.554017 + 0.832506i \(0.313094\pi\)
\(200\) 0 0
\(201\) 54.7453 331.212i 0.272365 1.64782i
\(202\) 0 0
\(203\) −46.4453 127.607i −0.228794 0.628608i
\(204\) 0 0
\(205\) 31.4137 + 178.156i 0.153238 + 0.869054i
\(206\) 0 0
\(207\) −11.5211 1.77756i −0.0556575 0.00858726i
\(208\) 0 0
\(209\) −266.899 318.077i −1.27703 1.52190i
\(210\) 0 0
\(211\) −36.0058 + 204.199i −0.170644 + 0.967768i 0.772409 + 0.635125i \(0.219051\pi\)
−0.943053 + 0.332643i \(0.892060\pi\)
\(212\) 0 0
\(213\) −271.259 + 160.515i −1.27352 + 0.753594i
\(214\) 0 0
\(215\) 15.5897i 0.0725100i
\(216\) 0 0
\(217\) −194.626 −0.896893
\(218\) 0 0
\(219\) 291.054 3.12203i 1.32901 0.0142558i
\(220\) 0 0
\(221\) 26.5535 + 4.68210i 0.120152 + 0.0211860i
\(222\) 0 0
\(223\) 316.844 265.863i 1.42082 1.19221i 0.469926 0.882706i \(-0.344281\pi\)
0.950897 0.309506i \(-0.100164\pi\)
\(224\) 0 0
\(225\) 9.95571 + 50.1462i 0.0442476 + 0.222872i
\(226\) 0 0
\(227\) 94.9127 16.7357i 0.418117 0.0737254i 0.0393683 0.999225i \(-0.487465\pi\)
0.378749 + 0.925499i \(0.376354\pi\)
\(228\) 0 0
\(229\) 189.133 68.8386i 0.825906 0.300605i 0.105729 0.994395i \(-0.466283\pi\)
0.720178 + 0.693790i \(0.244060\pi\)
\(230\) 0 0
\(231\) 55.4194 + 147.327i 0.239911 + 0.637780i
\(232\) 0 0
\(233\) −303.285 175.101i −1.30165 0.751508i −0.320964 0.947092i \(-0.604007\pi\)
−0.980687 + 0.195583i \(0.937340\pi\)
\(234\) 0 0
\(235\) 94.0985 + 162.983i 0.400419 + 0.693547i
\(236\) 0 0
\(237\) 252.765 216.757i 1.06652 0.914587i
\(238\) 0 0
\(239\) −100.663 + 119.965i −0.421183 + 0.501947i −0.934357 0.356338i \(-0.884025\pi\)
0.513174 + 0.858285i \(0.328470\pi\)
\(240\) 0 0
\(241\) 324.419 + 118.079i 1.34614 + 0.489954i 0.911740 0.410768i \(-0.134739\pi\)
0.434397 + 0.900721i \(0.356961\pi\)
\(242\) 0 0
\(243\) −132.606 203.629i −0.545705 0.837978i
\(244\) 0 0
\(245\) 54.4614 149.632i 0.222292 0.610741i
\(246\) 0 0
\(247\) −84.7946 71.1512i −0.343298 0.288061i
\(248\) 0 0
\(249\) −256.366 298.953i −1.02958 1.20062i
\(250\) 0 0
\(251\) 22.8819 13.2109i 0.0911628 0.0526329i −0.453726 0.891141i \(-0.649905\pi\)
0.544888 + 0.838509i \(0.316572\pi\)
\(252\) 0 0
\(253\) −9.50810 + 16.4685i −0.0375814 + 0.0650930i
\(254\) 0 0
\(255\) −85.0261 + 31.9839i −0.333436 + 0.125427i
\(256\) 0 0
\(257\) 40.6520 + 111.691i 0.158179 + 0.434593i 0.993313 0.115453i \(-0.0368321\pi\)
−0.835134 + 0.550047i \(0.814610\pi\)
\(258\) 0 0
\(259\) 23.0033 + 130.458i 0.0888159 + 0.503700i
\(260\) 0 0
\(261\) 335.430 66.5942i 1.28517 0.255150i
\(262\) 0 0
\(263\) 110.151 + 131.272i 0.418823 + 0.499134i 0.933663 0.358152i \(-0.116593\pi\)
−0.514840 + 0.857286i \(0.672149\pi\)
\(264\) 0 0
\(265\) 36.4840 206.911i 0.137675 0.780796i
\(266\) 0 0
\(267\) 3.26466 + 304.351i 0.0122272 + 1.13989i
\(268\) 0 0
\(269\) 147.131i 0.546957i 0.961878 + 0.273478i \(0.0881742\pi\)
−0.961878 + 0.273478i \(0.911826\pi\)
\(270\) 0 0
\(271\) 42.2256 0.155814 0.0779071 0.996961i \(-0.475176\pi\)
0.0779071 + 0.996961i \(0.475176\pi\)
\(272\) 0 0
\(273\) 21.3696 + 36.1130i 0.0782769 + 0.132282i
\(274\) 0 0
\(275\) 82.1306 + 14.4818i 0.298657 + 0.0526612i
\(276\) 0 0
\(277\) −241.990 + 203.054i −0.873611 + 0.733046i −0.964855 0.262782i \(-0.915360\pi\)
0.0912446 + 0.995829i \(0.470916\pi\)
\(278\) 0 0
\(279\) 74.7359 484.394i 0.267871 1.73618i
\(280\) 0 0
\(281\) 425.296 74.9912i 1.51351 0.266872i 0.645631 0.763650i \(-0.276594\pi\)
0.867878 + 0.496777i \(0.165483\pi\)
\(282\) 0 0
\(283\) −51.4917 + 18.7414i −0.181949 + 0.0662242i −0.431388 0.902166i \(-0.641976\pi\)
0.249439 + 0.968391i \(0.419754\pi\)
\(284\) 0 0
\(285\) 367.943 + 60.8165i 1.29103 + 0.213391i
\(286\) 0 0
\(287\) 127.385 + 73.5457i 0.443850 + 0.256257i
\(288\) 0 0
\(289\) −120.769 209.178i −0.417886 0.723801i
\(290\) 0 0
\(291\) 468.579 + 164.879i 1.61024 + 0.566594i
\(292\) 0 0
\(293\) −90.3507 + 107.676i −0.308364 + 0.367494i −0.897863 0.440275i \(-0.854881\pi\)
0.589499 + 0.807769i \(0.299325\pi\)
\(294\) 0 0
\(295\) 256.294 + 93.2833i 0.868792 + 0.316214i
\(296\) 0 0
\(297\) −387.956 + 81.3570i −1.30625 + 0.273929i
\(298\) 0 0
\(299\) −1.73385 + 4.76371i −0.00579883 + 0.0159321i
\(300\) 0 0
\(301\) 9.71021 + 8.14784i 0.0322598 + 0.0270692i
\(302\) 0 0
\(303\) −65.1745 + 12.2142i −0.215097 + 0.0403110i
\(304\) 0 0
\(305\) 42.2815 24.4113i 0.138628 0.0800369i
\(306\) 0 0
\(307\) −213.941 + 370.556i −0.696876 + 1.20702i 0.272669 + 0.962108i \(0.412094\pi\)
−0.969544 + 0.244916i \(0.921240\pi\)
\(308\) 0 0
\(309\) −65.6022 53.8584i −0.212305 0.174299i
\(310\) 0 0
\(311\) 142.432 + 391.327i 0.457979 + 1.25829i 0.926987 + 0.375094i \(0.122389\pi\)
−0.469008 + 0.883194i \(0.655388\pi\)
\(312\) 0 0
\(313\) 25.1171 + 142.446i 0.0802462 + 0.455099i 0.998282 + 0.0586003i \(0.0186638\pi\)
−0.918035 + 0.396499i \(0.870225\pi\)
\(314\) 0 0
\(315\) −123.923 68.0454i −0.393407 0.216017i
\(316\) 0 0
\(317\) −348.939 415.849i −1.10075 1.31183i −0.946106 0.323858i \(-0.895020\pi\)
−0.154648 0.987970i \(-0.549424\pi\)
\(318\) 0 0
\(319\) 96.8698 549.376i 0.303667 1.72218i
\(320\) 0 0
\(321\) 175.356 + 98.7493i 0.546280 + 0.307630i
\(322\) 0 0
\(323\) 194.844i 0.603231i
\(324\) 0 0
\(325\) 22.2325 0.0684078
\(326\) 0 0
\(327\) −120.778 + 214.475i −0.369353 + 0.655886i
\(328\) 0 0
\(329\) 150.696 + 26.5718i 0.458043 + 0.0807654i
\(330\) 0 0
\(331\) 169.745 142.433i 0.512825 0.430311i −0.349297 0.937012i \(-0.613580\pi\)
0.862122 + 0.506701i \(0.169135\pi\)
\(332\) 0 0
\(333\) −333.524 + 7.15600i −1.00157 + 0.0214895i
\(334\) 0 0
\(335\) 484.380 85.4093i 1.44591 0.254953i
\(336\) 0 0
\(337\) 36.2922 13.2093i 0.107692 0.0391967i −0.287612 0.957747i \(-0.592861\pi\)
0.395304 + 0.918550i \(0.370639\pi\)
\(338\) 0 0
\(339\) −269.789 + 328.617i −0.795839 + 0.969373i
\(340\) 0 0
\(341\) −692.403 399.759i −2.03051 1.17231i
\(342\) 0 0
\(343\) −152.295 263.783i −0.444009 0.769046i
\(344\) 0 0
\(345\) −3.14609 16.7874i −0.00911911 0.0486591i
\(346\) 0 0
\(347\) 134.499 160.290i 0.387607 0.461932i −0.536593 0.843841i \(-0.680289\pi\)
0.924200 + 0.381910i \(0.124733\pi\)
\(348\) 0 0
\(349\) −262.851 95.6701i −0.753156 0.274126i −0.0632228 0.997999i \(-0.520138\pi\)
−0.689933 + 0.723873i \(0.742360\pi\)
\(350\) 0 0
\(351\) −98.0857 + 39.3183i −0.279447 + 0.112018i
\(352\) 0 0
\(353\) −28.7312 + 78.9384i −0.0813916 + 0.223622i −0.973713 0.227780i \(-0.926853\pi\)
0.892321 + 0.451401i \(0.149076\pi\)
\(354\) 0 0
\(355\) −353.759 296.839i −0.996503 0.836166i
\(356\) 0 0
\(357\) −24.5168 + 69.6757i −0.0686745 + 0.195170i
\(358\) 0 0
\(359\) −221.262 + 127.746i −0.616330 + 0.355838i −0.775439 0.631423i \(-0.782471\pi\)
0.159109 + 0.987261i \(0.449138\pi\)
\(360\) 0 0
\(361\) −219.445 + 380.090i −0.607880 + 1.05288i
\(362\) 0 0
\(363\) −46.2513 + 279.823i −0.127414 + 0.770862i
\(364\) 0 0
\(365\) 145.857 + 400.738i 0.399607 + 1.09791i
\(366\) 0 0
\(367\) −44.7221 253.632i −0.121859 0.691095i −0.983124 0.182940i \(-0.941439\pi\)
0.861265 0.508155i \(-0.169672\pi\)
\(368\) 0 0
\(369\) −231.960 + 288.800i −0.628617 + 0.782657i
\(370\) 0 0
\(371\) −109.809 130.865i −0.295981 0.352736i
\(372\) 0 0
\(373\) 83.5846 474.032i 0.224087 1.27086i −0.640335 0.768096i \(-0.721204\pi\)
0.864422 0.502767i \(-0.167684\pi\)
\(374\) 0 0
\(375\) −348.168 + 206.026i −0.928449 + 0.549402i
\(376\) 0 0
\(377\) 148.715i 0.394469i
\(378\) 0 0
\(379\) −370.571 −0.977759 −0.488880 0.872351i \(-0.662594\pi\)
−0.488880 + 0.872351i \(0.662594\pi\)
\(380\) 0 0
\(381\) −216.743 + 2.32492i −0.568878 + 0.00610214i
\(382\) 0 0
\(383\) 481.807 + 84.9556i 1.25798 + 0.221816i 0.762606 0.646863i \(-0.223919\pi\)
0.495375 + 0.868679i \(0.335031\pi\)
\(384\) 0 0
\(385\) −176.665 + 148.240i −0.458870 + 0.385038i
\(386\) 0 0
\(387\) −24.0074 + 21.0385i −0.0620347 + 0.0543630i
\(388\) 0 0
\(389\) 309.685 54.6057i 0.796104 0.140375i 0.239221 0.970965i \(-0.423108\pi\)
0.556884 + 0.830591i \(0.311997\pi\)
\(390\) 0 0
\(391\) −8.38528 + 3.05199i −0.0214457 + 0.00780560i
\(392\) 0 0
\(393\) 132.261 + 351.604i 0.336543 + 0.894666i
\(394\) 0 0
\(395\) 422.495 + 243.927i 1.06961 + 0.617538i
\(396\) 0 0
\(397\) −44.8022 77.5996i −0.112852 0.195465i 0.804067 0.594538i \(-0.202665\pi\)
−0.916919 + 0.399073i \(0.869332\pi\)
\(398\) 0 0
\(399\) 230.184 197.393i 0.576901 0.494719i
\(400\) 0 0
\(401\) −55.2456 + 65.8392i −0.137770 + 0.164187i −0.830518 0.556992i \(-0.811955\pi\)
0.692748 + 0.721180i \(0.256400\pi\)
\(402\) 0 0
\(403\) −200.286 72.8980i −0.496987 0.180888i
\(404\) 0 0
\(405\) 216.941 282.297i 0.535657 0.697030i
\(406\) 0 0
\(407\) −186.123 + 511.369i −0.457305 + 1.25643i
\(408\) 0 0
\(409\) 479.987 + 402.757i 1.17356 + 0.984736i 1.00000 8.63705e-5i \(-2.74926e-5\pi\)
0.173563 + 0.984823i \(0.444472\pi\)
\(410\) 0 0
\(411\) −254.021 296.219i −0.618057 0.720729i
\(412\) 0 0
\(413\) 192.053 110.882i 0.465019 0.268479i
\(414\) 0 0
\(415\) 288.501 499.698i 0.695183 1.20409i
\(416\) 0 0
\(417\) 237.226 89.2362i 0.568887 0.213996i
\(418\) 0 0
\(419\) −120.491 331.047i −0.287569 0.790089i −0.996405 0.0847157i \(-0.973002\pi\)
0.708836 0.705373i \(-0.249220\pi\)
\(420\) 0 0
\(421\) 26.8471 + 152.258i 0.0637699 + 0.361657i 0.999949 + 0.0101329i \(0.00322545\pi\)
−0.936179 + 0.351524i \(0.885663\pi\)
\(422\) 0 0
\(423\) −124.000 + 364.857i −0.293145 + 0.862545i
\(424\) 0 0
\(425\) 25.1553 + 29.9789i 0.0591888 + 0.0705385i
\(426\) 0 0
\(427\) 6.89332 39.0940i 0.0161436 0.0915549i
\(428\) 0 0
\(429\) 1.84894 + 172.369i 0.00430988 + 0.401793i
\(430\) 0 0
\(431\) 226.253i 0.524949i −0.964939 0.262474i \(-0.915461\pi\)
0.964939 0.262474i \(-0.0845386\pi\)
\(432\) 0 0
\(433\) −648.539 −1.49778 −0.748890 0.662695i \(-0.769413\pi\)
−0.748890 + 0.662695i \(0.769413\pi\)
\(434\) 0 0
\(435\) 255.160 + 431.202i 0.586575 + 0.991269i
\(436\) 0 0
\(437\) 36.0767 + 6.36129i 0.0825553 + 0.0145567i
\(438\) 0 0
\(439\) 231.313 194.095i 0.526909 0.442129i −0.340123 0.940381i \(-0.610469\pi\)
0.867032 + 0.498252i \(0.166024\pi\)
\(440\) 0 0
\(441\) 303.923 118.062i 0.689168 0.267714i
\(442\) 0 0
\(443\) 458.869 80.9110i 1.03582 0.182643i 0.370215 0.928946i \(-0.379284\pi\)
0.665606 + 0.746303i \(0.268173\pi\)
\(444\) 0 0
\(445\) −419.047 + 152.521i −0.941678 + 0.342743i
\(446\) 0 0
\(447\) −422.579 69.8472i −0.945367 0.156258i
\(448\) 0 0
\(449\) 35.8903 + 20.7213i 0.0799339 + 0.0461498i 0.539434 0.842028i \(-0.318638\pi\)
−0.459500 + 0.888178i \(0.651971\pi\)
\(450\) 0 0
\(451\) 302.124 + 523.295i 0.669899 + 1.16030i
\(452\) 0 0
\(453\) −120.817 42.5120i −0.266705 0.0938455i
\(454\) 0 0
\(455\) −39.5185 + 47.0963i −0.0868538 + 0.103508i
\(456\) 0 0
\(457\) 405.966 + 147.760i 0.888329 + 0.323325i 0.745566 0.666432i \(-0.232179\pi\)
0.142763 + 0.989757i \(0.454401\pi\)
\(458\) 0 0
\(459\) −163.998 87.7739i −0.357294 0.191229i
\(460\) 0 0
\(461\) 224.994 618.167i 0.488057 1.34093i −0.414380 0.910104i \(-0.636002\pi\)
0.902437 0.430822i \(-0.141776\pi\)
\(462\) 0 0
\(463\) −415.550 348.688i −0.897516 0.753105i 0.0721872 0.997391i \(-0.477002\pi\)
−0.969703 + 0.244286i \(0.921447\pi\)
\(464\) 0 0
\(465\) 705.810 132.274i 1.51787 0.284461i
\(466\) 0 0
\(467\) −71.4291 + 41.2396i −0.152953 + 0.0883075i −0.574523 0.818488i \(-0.694812\pi\)
0.421570 + 0.906796i \(0.361479\pi\)
\(468\) 0 0
\(469\) 199.960 346.341i 0.426354 0.738467i
\(470\) 0 0
\(471\) −157.618 129.402i −0.334646 0.274739i
\(472\) 0 0
\(473\) 17.8096 + 48.9315i 0.0376525 + 0.103449i
\(474\) 0 0
\(475\) −27.8981 158.218i −0.0587329 0.333091i
\(476\) 0 0
\(477\) 367.870 223.046i 0.771216 0.467601i
\(478\) 0 0
\(479\) 54.1626 + 64.5485i 0.113074 + 0.134757i 0.819613 0.572918i \(-0.194189\pi\)
−0.706538 + 0.707675i \(0.749744\pi\)
\(480\) 0 0
\(481\) −25.1915 + 142.868i −0.0523732 + 0.297023i
\(482\) 0 0
\(483\) −12.1005 6.81424i −0.0250528 0.0141082i
\(484\) 0 0
\(485\) 727.790i 1.50060i
\(486\) 0 0
\(487\) 566.361 1.16296 0.581479 0.813561i \(-0.302474\pi\)
0.581479 + 0.813561i \(0.302474\pi\)
\(488\) 0 0
\(489\) 76.9225 136.597i 0.157306 0.279339i
\(490\) 0 0
\(491\) −754.890 133.107i −1.53745 0.271095i −0.660188 0.751100i \(-0.729524\pi\)
−0.877266 + 0.480005i \(0.840635\pi\)
\(492\) 0 0
\(493\) 200.530 168.265i 0.406755 0.341308i
\(494\) 0 0
\(495\) −301.107 496.616i −0.608297 1.00327i
\(496\) 0 0
\(497\) −369.779 + 65.2021i −0.744023 + 0.131191i
\(498\) 0 0
\(499\) −207.387 + 75.4828i −0.415606 + 0.151268i −0.541355 0.840794i \(-0.682089\pi\)
0.125750 + 0.992062i \(0.459866\pi\)
\(500\) 0 0
\(501\) 397.730 484.456i 0.793873 0.966978i
\(502\) 0 0
\(503\) 783.399 + 452.296i 1.55745 + 0.899196i 0.997500 + 0.0706721i \(0.0225144\pi\)
0.559954 + 0.828524i \(0.310819\pi\)
\(504\) 0 0
\(505\) −48.5757 84.1357i −0.0961896 0.166605i
\(506\) 0 0
\(507\) −84.9253 453.157i −0.167506 0.893801i
\(508\) 0 0
\(509\) 220.212 262.439i 0.432637 0.515596i −0.505044 0.863093i \(-0.668524\pi\)
0.937681 + 0.347497i \(0.112968\pi\)
\(510\) 0 0
\(511\) 325.835 + 118.594i 0.637643 + 0.232083i
\(512\) 0 0
\(513\) 402.890 + 648.690i 0.785361 + 1.26450i
\(514\) 0 0
\(515\) 42.5330 116.858i 0.0825884 0.226910i
\(516\) 0 0
\(517\) 481.541 + 404.061i 0.931414 + 0.781549i
\(518\) 0 0
\(519\) −288.691 + 820.448i −0.556244 + 1.58082i
\(520\) 0 0
\(521\) −120.568 + 69.6099i −0.231416 + 0.133608i −0.611225 0.791457i \(-0.709323\pi\)
0.379809 + 0.925065i \(0.375990\pi\)
\(522\) 0 0
\(523\) −12.3821 + 21.4464i −0.0236751 + 0.0410065i −0.877620 0.479357i \(-0.840870\pi\)
0.853945 + 0.520363i \(0.174203\pi\)
\(524\) 0 0
\(525\) −9.93195 + 60.0888i −0.0189180 + 0.114455i
\(526\) 0 0
\(527\) −128.318 352.551i −0.243488 0.668977i
\(528\) 0 0
\(529\) 91.5686 + 519.311i 0.173097 + 0.981684i
\(530\) 0 0
\(531\) 202.220 + 520.569i 0.380828 + 0.980355i
\(532\) 0 0
\(533\) 103.543 + 123.397i 0.194264 + 0.231514i
\(534\) 0 0
\(535\) −51.2012 + 290.376i −0.0957032 + 0.542760i
\(536\) 0 0
\(537\) 251.592 148.878i 0.468514 0.277239i
\(538\) 0 0
\(539\) 531.868i 0.986768i
\(540\) 0 0
\(541\) 476.086 0.880011 0.440006 0.897995i \(-0.354976\pi\)
0.440006 + 0.897995i \(0.354976\pi\)
\(542\) 0 0
\(543\) −111.955 + 1.20090i −0.206179 + 0.00221160i
\(544\) 0 0
\(545\) −355.154 62.6232i −0.651658 0.114905i
\(546\) 0 0
\(547\) −225.822 + 189.487i −0.412836 + 0.346411i −0.825430 0.564504i \(-0.809067\pi\)
0.412594 + 0.910915i \(0.364623\pi\)
\(548\) 0 0
\(549\) 94.6519 + 32.1684i 0.172408 + 0.0585946i
\(550\) 0 0
\(551\) −1058.33 + 186.612i −1.92074 + 0.338679i
\(552\) 0 0
\(553\) 372.747 135.669i 0.674046 0.245333i
\(554\) 0 0
\(555\) −172.085 457.473i −0.310064 0.824275i
\(556\) 0 0
\(557\) −756.664 436.860i −1.35846 0.784309i −0.369047 0.929411i \(-0.620316\pi\)
−0.989417 + 0.145101i \(0.953649\pi\)
\(558\) 0 0
\(559\) 6.94078 + 12.0218i 0.0124164 + 0.0215059i
\(560\) 0 0
\(561\) −230.334 + 197.522i −0.410578 + 0.352089i
\(562\) 0 0
\(563\) −327.795 + 390.651i −0.582230 + 0.693874i −0.974093 0.226149i \(-0.927386\pi\)
0.391863 + 0.920024i \(0.371831\pi\)
\(564\) 0 0
\(565\) −585.372 213.058i −1.03606 0.377094i
\(566\) 0 0
\(567\) −62.4494 282.665i −0.110140 0.498527i
\(568\) 0 0
\(569\) −303.435 + 833.680i −0.533277 + 1.46517i 0.321871 + 0.946784i \(0.395688\pi\)
−0.855148 + 0.518384i \(0.826534\pi\)
\(570\) 0 0
\(571\) 403.162 + 338.293i 0.706063 + 0.592457i 0.923491 0.383619i \(-0.125323\pi\)
−0.217429 + 0.976076i \(0.569767\pi\)
\(572\) 0 0
\(573\) −684.136 797.784i −1.19395 1.39229i
\(574\) 0 0
\(575\) −6.37207 + 3.67892i −0.0110819 + 0.00639812i
\(576\) 0 0
\(577\) 68.5779 118.780i 0.118853 0.205859i −0.800461 0.599385i \(-0.795412\pi\)
0.919313 + 0.393527i \(0.128745\pi\)
\(578\) 0 0
\(579\) −31.0360 + 11.6747i −0.0536028 + 0.0201635i
\(580\) 0 0
\(581\) −160.460 440.860i −0.276179 0.758796i
\(582\) 0 0
\(583\) −121.862 691.114i −0.209026 1.18544i
\(584\) 0 0
\(585\) −102.040 116.440i −0.174428 0.199043i
\(586\) 0 0
\(587\) −115.043 137.103i −0.195985 0.233566i 0.659098 0.752057i \(-0.270938\pi\)
−0.855083 + 0.518491i \(0.826494\pi\)
\(588\) 0 0
\(589\) −267.454 + 1516.81i −0.454082 + 2.57523i
\(590\) 0 0
\(591\) −10.2358 954.247i −0.0173195 1.61463i
\(592\) 0 0
\(593\) 52.0285i 0.0877377i 0.999037 + 0.0438689i \(0.0139684\pi\)
−0.999037 + 0.0438689i \(0.986032\pi\)
\(594\) 0 0
\(595\) −108.219 −0.181881
\(596\) 0 0
\(597\) −269.954 456.203i −0.452185 0.764160i
\(598\) 0 0
\(599\) 114.494 + 20.1884i 0.191142 + 0.0337035i 0.268400 0.963308i \(-0.413505\pi\)
−0.0772575 + 0.997011i \(0.524616\pi\)
\(600\) 0 0
\(601\) −402.677 + 337.886i −0.670011 + 0.562206i −0.913069 0.407806i \(-0.866294\pi\)
0.243057 + 0.970012i \(0.421850\pi\)
\(602\) 0 0
\(603\) 785.206 + 630.665i 1.30217 + 1.04588i
\(604\) 0 0
\(605\) −409.227 + 72.1577i −0.676408 + 0.119269i
\(606\) 0 0
\(607\) 80.4769 29.2912i 0.132581 0.0482557i −0.274877 0.961479i \(-0.588637\pi\)
0.407459 + 0.913224i \(0.366415\pi\)
\(608\) 0 0
\(609\) 401.937 + 66.4353i 0.659995 + 0.109089i
\(610\) 0 0
\(611\) 145.126 + 83.7886i 0.237522 + 0.137134i
\(612\) 0 0
\(613\) 81.6463 + 141.416i 0.133191 + 0.230694i 0.924905 0.380198i \(-0.124144\pi\)
−0.791714 + 0.610892i \(0.790811\pi\)
\(614\) 0 0
\(615\) −511.946 180.138i −0.832432 0.292908i
\(616\) 0 0
\(617\) 179.054 213.388i 0.290200 0.345847i −0.601171 0.799120i \(-0.705299\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(618\) 0 0
\(619\) −669.731 243.762i −1.08196 0.393800i −0.261321 0.965252i \(-0.584158\pi\)
−0.820636 + 0.571452i \(0.806380\pi\)
\(620\) 0 0
\(621\) 21.6062 27.4997i 0.0347926 0.0442829i
\(622\) 0 0
\(623\) −124.013 + 340.722i −0.199057 + 0.546906i
\(624\) 0 0
\(625\) −345.270 289.716i −0.552432 0.463545i
\(626\) 0 0
\(627\) 1224.35 229.452i 1.95271 0.365953i
\(628\) 0 0
\(629\) −221.150 + 127.681i −0.351590 + 0.202990i
\(630\) 0 0
\(631\) −311.029 + 538.718i −0.492914 + 0.853753i −0.999967 0.00816241i \(-0.997402\pi\)
0.507052 + 0.861915i \(0.330735\pi\)
\(632\) 0 0
\(633\) −480.777 394.710i −0.759522 0.623555i
\(634\) 0 0
\(635\) −108.617 298.422i −0.171050 0.469956i
\(636\) 0 0
\(637\) −24.6212 139.634i −0.0386518 0.219206i
\(638\) 0 0
\(639\) −20.2834 945.362i −0.0317425 1.47944i
\(640\) 0 0
\(641\) 163.405 + 194.738i 0.254921 + 0.303804i 0.878294 0.478122i \(-0.158682\pi\)
−0.623372 + 0.781925i \(0.714238\pi\)
\(642\) 0 0
\(643\) 36.8378 208.917i 0.0572905 0.324910i −0.942671 0.333724i \(-0.891695\pi\)
0.999961 + 0.00881399i \(0.00280562\pi\)
\(644\) 0 0
\(645\) −40.7516 22.9487i −0.0631808 0.0355794i
\(646\) 0 0
\(647\) 330.267i 0.510459i 0.966880 + 0.255230i \(0.0821511\pi\)
−0.966880 + 0.255230i \(0.917849\pi\)
\(648\) 0 0
\(649\) 911.000 1.40370
\(650\) 0 0
\(651\) 286.498 508.755i 0.440089 0.781497i
\(652\) 0 0
\(653\) 329.228 + 58.0518i 0.504178 + 0.0889002i 0.419952 0.907546i \(-0.362047\pi\)
0.0842262 + 0.996447i \(0.473158\pi\)
\(654\) 0 0
\(655\) −421.621 + 353.782i −0.643696 + 0.540125i
\(656\) 0 0
\(657\) −420.284 + 765.415i −0.639701 + 1.16502i
\(658\) 0 0
\(659\) −1021.20 + 180.064i −1.54962 + 0.273239i −0.881993 0.471262i \(-0.843799\pi\)
−0.667622 + 0.744501i \(0.732688\pi\)
\(660\) 0 0
\(661\) 397.057 144.517i 0.600692 0.218634i −0.0237335 0.999718i \(-0.507555\pi\)
0.624426 + 0.781084i \(0.285333\pi\)
\(662\) 0 0
\(663\) −51.3271 + 62.5191i −0.0774165 + 0.0942972i
\(664\) 0 0
\(665\) 384.750 + 222.136i 0.578572 + 0.334038i
\(666\) 0 0
\(667\) 24.6085 + 42.6231i 0.0368942 + 0.0639027i
\(668\) 0 0
\(669\) 228.562 + 1219.60i 0.341648 + 1.82302i
\(670\) 0 0
\(671\) 104.822 124.922i 0.156218 0.186173i
\(672\) 0 0
\(673\) −14.3659 5.22876i −0.0213460 0.00776932i 0.331325 0.943517i \(-0.392504\pi\)
−0.352671 + 0.935747i \(0.614727\pi\)
\(674\) 0 0
\(675\) −145.738 47.7931i −0.215908 0.0708046i
\(676\) 0 0
\(677\) 103.653 284.784i 0.153106 0.420655i −0.839299 0.543670i \(-0.817034\pi\)
0.992405 + 0.123015i \(0.0392564\pi\)
\(678\) 0 0
\(679\) 453.313 + 380.375i 0.667618 + 0.560198i
\(680\) 0 0
\(681\) −95.9686 + 272.739i −0.140923 + 0.400498i
\(682\) 0 0
\(683\) 688.686 397.613i 1.00833 0.582157i 0.0976243 0.995223i \(-0.468876\pi\)
0.910701 + 0.413067i \(0.135542\pi\)
\(684\) 0 0
\(685\) 285.863 495.129i 0.417318 0.722816i
\(686\) 0 0
\(687\) −98.4667 + 595.729i −0.143329 + 0.867146i
\(688\) 0 0
\(689\) −63.9861 175.800i −0.0928680 0.255153i
\(690\) 0 0
\(691\) 8.31097 + 47.1339i 0.0120275 + 0.0682111i 0.990231 0.139438i \(-0.0445297\pi\)
−0.978203 + 0.207650i \(0.933419\pi\)
\(692\) 0 0
\(693\) −466.695 72.0053i −0.673442 0.103904i
\(694\) 0 0
\(695\) 238.695 + 284.466i 0.343447 + 0.409304i
\(696\) 0 0
\(697\) −49.2372 + 279.238i −0.0706416 + 0.400629i
\(698\) 0 0
\(699\) 904.167 535.033i 1.29352 0.765427i
\(700\) 0 0
\(701\) 32.9301i 0.0469759i −0.999724 0.0234880i \(-0.992523\pi\)
0.999724 0.0234880i \(-0.00747714\pi\)
\(702\) 0 0
\(703\) 1048.33 1.49123
\(704\) 0 0
\(705\) −564.559 + 6.05581i −0.800793 + 0.00858980i
\(706\) 0 0
\(707\) −77.7927 13.7170i −0.110032 0.0194016i
\(708\) 0 0
\(709\) 705.725 592.173i 0.995380 0.835223i 0.00904260 0.999959i \(-0.497122\pi\)
0.986338 + 0.164736i \(0.0526772\pi\)
\(710\) 0 0
\(711\) 194.525 + 979.808i 0.273593 + 1.37807i
\(712\) 0 0
\(713\) 69.4666 12.2488i 0.0974286 0.0171793i
\(714\) 0 0
\(715\) −237.327 + 86.3798i −0.331925 + 0.120811i
\(716\) 0 0
\(717\) −165.411 439.729i −0.230698 0.613290i
\(718\) 0 0
\(719\) 406.335 + 234.597i 0.565139 + 0.326283i 0.755205 0.655488i \(-0.227537\pi\)
−0.190067 + 0.981771i \(0.560870\pi\)
\(720\) 0 0
\(721\) −50.5571 87.5675i −0.0701209 0.121453i
\(722\) 0 0
\(723\) −786.220 + 674.219i −1.08744 + 0.932530i
\(724\) 0 0
\(725\) 138.743 165.348i 0.191370 0.228066i
\(726\) 0 0
\(727\) 53.3053 + 19.4016i 0.0733223 + 0.0266871i 0.378421 0.925634i \(-0.376467\pi\)
−0.305099 + 0.952321i \(0.598689\pi\)
\(728\) 0 0
\(729\) 727.491 46.8841i 0.997930 0.0643129i
\(730\) 0 0
\(731\) −8.35723 + 22.9613i −0.0114326 + 0.0314108i
\(732\) 0 0
\(733\) −773.970 649.438i −1.05589 0.886000i −0.0621924 0.998064i \(-0.519809\pi\)
−0.993701 + 0.112064i \(0.964254\pi\)
\(734\) 0 0
\(735\) 310.970 + 362.628i 0.423088 + 0.493371i
\(736\) 0 0
\(737\) 1422.76 821.432i 1.93048 1.11456i
\(738\) 0 0
\(739\) 368.682 638.576i 0.498893 0.864108i −0.501106 0.865386i \(-0.667073\pi\)
0.999999 + 0.00127777i \(0.000406727\pi\)
\(740\) 0 0
\(741\) 310.812 116.917i 0.419449 0.157782i
\(742\) 0 0
\(743\) −31.4911 86.5211i −0.0423837 0.116448i 0.916695 0.399587i \(-0.130847\pi\)
−0.959079 + 0.283139i \(0.908624\pi\)
\(744\) 0 0
\(745\) −108.970 618.000i −0.146269 0.829531i
\(746\) 0 0
\(747\) 1158.85 230.071i 1.55134 0.307993i
\(748\) 0 0
\(749\) 154.105 + 183.655i 0.205747 + 0.245200i
\(750\) 0 0
\(751\) −65.4270 + 371.055i −0.0871199 + 0.494081i 0.909759 + 0.415137i \(0.136266\pi\)
−0.996879 + 0.0789448i \(0.974845\pi\)
\(752\) 0 0
\(753\) 0.850199 + 79.2606i 0.00112908 + 0.105260i
\(754\) 0 0
\(755\) 187.652i 0.248545i
\(756\) 0 0
\(757\) 98.9786 0.130751 0.0653755 0.997861i \(-0.479175\pi\)
0.0653755 + 0.997861i \(0.479175\pi\)
\(758\) 0 0
\(759\) −29.0526 49.0968i −0.0382775 0.0646861i
\(760\) 0 0
\(761\) −1035.32 182.555i −1.36047 0.239888i −0.554669 0.832071i \(-0.687155\pi\)
−0.805804 + 0.592183i \(0.798266\pi\)
\(762\) 0 0
\(763\) −224.625 + 188.482i −0.294396 + 0.247028i
\(764\) 0 0
\(765\) 41.5560 269.341i 0.0543216 0.352080i
\(766\) 0 0
\(767\) 239.169 42.1720i 0.311824 0.0549830i
\(768\) 0 0
\(769\) 14.0610 5.11778i 0.0182848 0.00665511i −0.332862 0.942976i \(-0.608014\pi\)
0.351146 + 0.936321i \(0.385792\pi\)
\(770\) 0 0
\(771\) −351.802 58.1486i −0.456294 0.0754198i
\(772\) 0 0
\(773\) 453.509 + 261.834i 0.586687 + 0.338724i 0.763787 0.645469i \(-0.223338\pi\)
−0.177099 + 0.984193i \(0.556671\pi\)
\(774\) 0 0
\(775\) −154.677 267.908i −0.199583 0.345687i
\(776\) 0 0
\(777\) −374.882 131.910i −0.482473 0.169768i
\(778\) 0 0
\(779\) 748.229 891.705i 0.960499 1.14468i
\(780\) 0 0
\(781\) −1449.46 527.559i −1.85590 0.675492i
\(782\) 0 0
\(783\) −319.691 + 974.850i −0.408289 + 1.24502i
\(784\) 0 0
\(785\) 102.191 280.768i 0.130180 0.357667i