Properties

Label 405.4.b.e.244.2
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.2
Root \(-5.02371i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.e.244.15

$q$-expansion

\(f(q)\) \(=\) \(q-5.02371i q^{2} -17.2377 q^{4} +(5.75603 - 9.58479i) q^{5} -5.38197i q^{7} +46.4074i q^{8} +O(q^{10})\) \(q-5.02371i q^{2} -17.2377 q^{4} +(5.75603 - 9.58479i) q^{5} -5.38197i q^{7} +46.4074i q^{8} +(-48.1512 - 28.9166i) q^{10} -39.1018 q^{11} -86.6271i q^{13} -27.0375 q^{14} +95.2360 q^{16} +15.4194i q^{17} +26.8412 q^{19} +(-99.2205 + 165.219i) q^{20} +196.436i q^{22} +111.138i q^{23} +(-58.7363 - 110.341i) q^{25} -435.189 q^{26} +92.7727i q^{28} -49.2347 q^{29} -179.877 q^{31} -107.179i q^{32} +77.4624 q^{34} +(-51.5851 - 30.9788i) q^{35} +293.496i q^{37} -134.842i q^{38} +(444.805 + 267.122i) q^{40} +27.6032 q^{41} -60.5030i q^{43} +674.023 q^{44} +558.327 q^{46} +96.2351i q^{47} +314.034 q^{49} +(-554.319 + 295.074i) q^{50} +1493.25i q^{52} -251.203i q^{53} +(-225.071 + 374.782i) q^{55} +249.763 q^{56} +247.341i q^{58} +76.8462 q^{59} +490.091 q^{61} +903.648i q^{62} +223.452 q^{64} +(-830.302 - 498.628i) q^{65} -238.721i q^{67} -265.794i q^{68} +(-155.628 + 259.148i) q^{70} -640.447 q^{71} -769.257i q^{73} +1474.44 q^{74} -462.679 q^{76} +210.445i q^{77} -662.352 q^{79} +(548.181 - 912.817i) q^{80} -138.670i q^{82} +1302.14i q^{83} +(147.791 + 88.7543i) q^{85} -303.950 q^{86} -1814.61i q^{88} +995.544 q^{89} -466.224 q^{91} -1915.77i q^{92} +483.457 q^{94} +(154.499 - 257.267i) q^{95} -814.846i q^{97} -1577.62i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} - 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} - 3 q^{5} - 10 q^{10} - 90 q^{11} + 102 q^{14} + 146 q^{16} - 4 q^{19} + 6 q^{20} - 71 q^{25} - 468 q^{26} + 516 q^{29} + 38 q^{31} - 212 q^{34} - 267 q^{35} - 44 q^{40} - 576 q^{41} + 1644 q^{44} - 290 q^{46} + 4 q^{49} - 558 q^{50} + 15 q^{55} - 2430 q^{56} + 2202 q^{59} + 20 q^{61} + 322 q^{64} - 339 q^{65} - 636 q^{70} - 2952 q^{71} + 4080 q^{74} - 396 q^{76} + 218 q^{79} + 1266 q^{80} + 704 q^{85} - 6108 q^{86} + 4074 q^{89} - 942 q^{91} + 1078 q^{94} + 1692 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.02371i 1.77615i −0.459699 0.888075i \(-0.652043\pi\)
0.459699 0.888075i \(-0.347957\pi\)
\(3\) 0 0
\(4\) −17.2377 −2.15471
\(5\) 5.75603 9.58479i 0.514835 0.857289i
\(6\) 0 0
\(7\) 5.38197i 0.290599i −0.989388 0.145300i \(-0.953585\pi\)
0.989388 0.145300i \(-0.0464146\pi\)
\(8\) 46.4074i 2.05094i
\(9\) 0 0
\(10\) −48.1512 28.9166i −1.52267 0.914424i
\(11\) −39.1018 −1.07178 −0.535892 0.844286i \(-0.680025\pi\)
−0.535892 + 0.844286i \(0.680025\pi\)
\(12\) 0 0
\(13\) 86.6271i 1.84816i −0.382204 0.924078i \(-0.624835\pi\)
0.382204 0.924078i \(-0.375165\pi\)
\(14\) −27.0375 −0.516148
\(15\) 0 0
\(16\) 95.2360 1.48806
\(17\) 15.4194i 0.219985i 0.993932 + 0.109993i \(0.0350827\pi\)
−0.993932 + 0.109993i \(0.964917\pi\)
\(18\) 0 0
\(19\) 26.8412 0.324094 0.162047 0.986783i \(-0.448190\pi\)
0.162047 + 0.986783i \(0.448190\pi\)
\(20\) −99.2205 + 165.219i −1.10932 + 1.84721i
\(21\) 0 0
\(22\) 196.436i 1.90365i
\(23\) 111.138i 1.00756i 0.863831 + 0.503781i \(0.168058\pi\)
−0.863831 + 0.503781i \(0.831942\pi\)
\(24\) 0 0
\(25\) −58.7363 110.341i −0.469890 0.882725i
\(26\) −435.189 −3.28260
\(27\) 0 0
\(28\) 92.7727i 0.626157i
\(29\) −49.2347 −0.315264 −0.157632 0.987498i \(-0.550386\pi\)
−0.157632 + 0.987498i \(0.550386\pi\)
\(30\) 0 0
\(31\) −179.877 −1.04215 −0.521077 0.853510i \(-0.674470\pi\)
−0.521077 + 0.853510i \(0.674470\pi\)
\(32\) 107.179i 0.592085i
\(33\) 0 0
\(34\) 77.4624 0.390726
\(35\) −51.5851 30.9788i −0.249128 0.149611i
\(36\) 0 0
\(37\) 293.496i 1.30407i 0.758191 + 0.652033i \(0.226084\pi\)
−0.758191 + 0.652033i \(0.773916\pi\)
\(38\) 134.842i 0.575640i
\(39\) 0 0
\(40\) 444.805 + 267.122i 1.75825 + 1.05589i
\(41\) 27.6032 0.105144 0.0525719 0.998617i \(-0.483258\pi\)
0.0525719 + 0.998617i \(0.483258\pi\)
\(42\) 0 0
\(43\) 60.5030i 0.214573i −0.994228 0.107286i \(-0.965784\pi\)
0.994228 0.107286i \(-0.0342162\pi\)
\(44\) 674.023 2.30938
\(45\) 0 0
\(46\) 558.327 1.78958
\(47\) 96.2351i 0.298667i 0.988787 + 0.149333i \(0.0477127\pi\)
−0.988787 + 0.149333i \(0.952287\pi\)
\(48\) 0 0
\(49\) 314.034 0.915552
\(50\) −554.319 + 295.074i −1.56785 + 0.834595i
\(51\) 0 0
\(52\) 1493.25i 3.98224i
\(53\) 251.203i 0.651046i −0.945534 0.325523i \(-0.894460\pi\)
0.945534 0.325523i \(-0.105540\pi\)
\(54\) 0 0
\(55\) −225.071 + 374.782i −0.551792 + 0.918829i
\(56\) 249.763 0.596001
\(57\) 0 0
\(58\) 247.341i 0.559957i
\(59\) 76.8462 0.169568 0.0847841 0.996399i \(-0.472980\pi\)
0.0847841 + 0.996399i \(0.472980\pi\)
\(60\) 0 0
\(61\) 490.091 1.02868 0.514342 0.857585i \(-0.328036\pi\)
0.514342 + 0.857585i \(0.328036\pi\)
\(62\) 903.648i 1.85102i
\(63\) 0 0
\(64\) 223.452 0.436430
\(65\) −830.302 498.628i −1.58440 0.951495i
\(66\) 0 0
\(67\) 238.721i 0.435290i −0.976028 0.217645i \(-0.930163\pi\)
0.976028 0.217645i \(-0.0698374\pi\)
\(68\) 265.794i 0.474004i
\(69\) 0 0
\(70\) −155.628 + 259.148i −0.265731 + 0.442488i
\(71\) −640.447 −1.07052 −0.535261 0.844687i \(-0.679787\pi\)
−0.535261 + 0.844687i \(0.679787\pi\)
\(72\) 0 0
\(73\) 769.257i 1.23335i −0.787217 0.616676i \(-0.788479\pi\)
0.787217 0.616676i \(-0.211521\pi\)
\(74\) 1474.44 2.31622
\(75\) 0 0
\(76\) −462.679 −0.698328
\(77\) 210.445i 0.311460i
\(78\) 0 0
\(79\) −662.352 −0.943296 −0.471648 0.881787i \(-0.656341\pi\)
−0.471648 + 0.881787i \(0.656341\pi\)
\(80\) 548.181 912.817i 0.766106 1.27570i
\(81\) 0 0
\(82\) 138.670i 0.186751i
\(83\) 1302.14i 1.72203i 0.508578 + 0.861016i \(0.330171\pi\)
−0.508578 + 0.861016i \(0.669829\pi\)
\(84\) 0 0
\(85\) 147.791 + 88.7543i 0.188591 + 0.113256i
\(86\) −303.950 −0.381113
\(87\) 0 0
\(88\) 1814.61i 2.19816i
\(89\) 995.544 1.18570 0.592851 0.805312i \(-0.298002\pi\)
0.592851 + 0.805312i \(0.298002\pi\)
\(90\) 0 0
\(91\) −466.224 −0.537073
\(92\) 1915.77i 2.17100i
\(93\) 0 0
\(94\) 483.457 0.530477
\(95\) 154.499 257.267i 0.166855 0.277842i
\(96\) 0 0
\(97\) 814.846i 0.852939i −0.904502 0.426470i \(-0.859757\pi\)
0.904502 0.426470i \(-0.140243\pi\)
\(98\) 1577.62i 1.62616i
\(99\) 0 0
\(100\) 1012.48 + 1902.02i 1.01248 + 1.90202i
\(101\) −652.604 −0.642936 −0.321468 0.946920i \(-0.604176\pi\)
−0.321468 + 0.946920i \(0.604176\pi\)
\(102\) 0 0
\(103\) 153.955i 0.147278i −0.997285 0.0736391i \(-0.976539\pi\)
0.997285 0.0736391i \(-0.0234613\pi\)
\(104\) 4020.14 3.79045
\(105\) 0 0
\(106\) −1261.97 −1.15636
\(107\) 348.878i 0.315209i 0.987502 + 0.157604i \(0.0503770\pi\)
−0.987502 + 0.157604i \(0.949623\pi\)
\(108\) 0 0
\(109\) −1125.26 −0.988815 −0.494407 0.869230i \(-0.664615\pi\)
−0.494407 + 0.869230i \(0.664615\pi\)
\(110\) 1882.80 + 1130.69i 1.63198 + 0.980065i
\(111\) 0 0
\(112\) 512.557i 0.432430i
\(113\) 352.076i 0.293102i −0.989203 0.146551i \(-0.953183\pi\)
0.989203 0.146551i \(-0.0468173\pi\)
\(114\) 0 0
\(115\) 1065.24 + 639.715i 0.863773 + 0.518728i
\(116\) 848.692 0.679303
\(117\) 0 0
\(118\) 386.053i 0.301179i
\(119\) 82.9866 0.0639275
\(120\) 0 0
\(121\) 197.948 0.148721
\(122\) 2462.08i 1.82710i
\(123\) 0 0
\(124\) 3100.65 2.24554
\(125\) −1395.68 72.1493i −0.998666 0.0516259i
\(126\) 0 0
\(127\) 1502.08i 1.04951i −0.851252 0.524757i \(-0.824156\pi\)
0.851252 0.524757i \(-0.175844\pi\)
\(128\) 1979.99i 1.36725i
\(129\) 0 0
\(130\) −2504.96 + 4171.20i −1.69000 + 2.81414i
\(131\) −1574.71 −1.05025 −0.525127 0.851024i \(-0.675982\pi\)
−0.525127 + 0.851024i \(0.675982\pi\)
\(132\) 0 0
\(133\) 144.458i 0.0941814i
\(134\) −1199.26 −0.773140
\(135\) 0 0
\(136\) −715.573 −0.451175
\(137\) 892.298i 0.556454i 0.960515 + 0.278227i \(0.0897467\pi\)
−0.960515 + 0.278227i \(0.910253\pi\)
\(138\) 0 0
\(139\) −652.706 −0.398287 −0.199143 0.979970i \(-0.563816\pi\)
−0.199143 + 0.979970i \(0.563816\pi\)
\(140\) 889.206 + 534.002i 0.536797 + 0.322367i
\(141\) 0 0
\(142\) 3217.42i 1.90141i
\(143\) 3387.27i 1.98082i
\(144\) 0 0
\(145\) −283.397 + 471.905i −0.162309 + 0.270273i
\(146\) −3864.52 −2.19062
\(147\) 0 0
\(148\) 5059.19i 2.80988i
\(149\) −3437.85 −1.89020 −0.945101 0.326779i \(-0.894037\pi\)
−0.945101 + 0.326779i \(0.894037\pi\)
\(150\) 0 0
\(151\) 1670.92 0.900513 0.450256 0.892899i \(-0.351333\pi\)
0.450256 + 0.892899i \(0.351333\pi\)
\(152\) 1245.63i 0.664696i
\(153\) 0 0
\(154\) 1057.21 0.553199
\(155\) −1035.37 + 1724.08i −0.536537 + 0.893428i
\(156\) 0 0
\(157\) 666.105i 0.338605i −0.985564 0.169302i \(-0.945849\pi\)
0.985564 0.169302i \(-0.0541515\pi\)
\(158\) 3327.46i 1.67544i
\(159\) 0 0
\(160\) −1027.29 616.925i −0.507588 0.304826i
\(161\) 598.143 0.292797
\(162\) 0 0
\(163\) 889.255i 0.427312i −0.976909 0.213656i \(-0.931463\pi\)
0.976909 0.213656i \(-0.0685371\pi\)
\(164\) −475.815 −0.226554
\(165\) 0 0
\(166\) 6541.59 3.05859
\(167\) 403.862i 0.187137i 0.995613 + 0.0935683i \(0.0298273\pi\)
−0.995613 + 0.0935683i \(0.970173\pi\)
\(168\) 0 0
\(169\) −5307.25 −2.41568
\(170\) 445.876 742.461i 0.201160 0.334966i
\(171\) 0 0
\(172\) 1042.93i 0.462342i
\(173\) 236.061i 0.103742i −0.998654 0.0518712i \(-0.983481\pi\)
0.998654 0.0518712i \(-0.0165185\pi\)
\(174\) 0 0
\(175\) −593.850 + 316.117i −0.256519 + 0.136550i
\(176\) −3723.90 −1.59488
\(177\) 0 0
\(178\) 5001.33i 2.10599i
\(179\) −2404.31 −1.00395 −0.501973 0.864883i \(-0.667392\pi\)
−0.501973 + 0.864883i \(0.667392\pi\)
\(180\) 0 0
\(181\) −1218.41 −0.500354 −0.250177 0.968200i \(-0.580489\pi\)
−0.250177 + 0.968200i \(0.580489\pi\)
\(182\) 2342.18i 0.953921i
\(183\) 0 0
\(184\) −5157.64 −2.06645
\(185\) 2813.10 + 1689.37i 1.11796 + 0.671378i
\(186\) 0 0
\(187\) 602.925i 0.235777i
\(188\) 1658.87i 0.643539i
\(189\) 0 0
\(190\) −1292.43 776.156i −0.493490 0.296359i
\(191\) 175.943 0.0666533 0.0333267 0.999445i \(-0.489390\pi\)
0.0333267 + 0.999445i \(0.489390\pi\)
\(192\) 0 0
\(193\) 2215.26i 0.826207i −0.910684 0.413103i \(-0.864445\pi\)
0.910684 0.413103i \(-0.135555\pi\)
\(194\) −4093.55 −1.51495
\(195\) 0 0
\(196\) −5413.22 −1.97275
\(197\) 1054.08i 0.381218i −0.981666 0.190609i \(-0.938954\pi\)
0.981666 0.190609i \(-0.0610462\pi\)
\(198\) 0 0
\(199\) 3484.04 1.24109 0.620546 0.784170i \(-0.286911\pi\)
0.620546 + 0.784170i \(0.286911\pi\)
\(200\) 5120.62 2725.80i 1.81041 0.963715i
\(201\) 0 0
\(202\) 3278.49i 1.14195i
\(203\) 264.980i 0.0916155i
\(204\) 0 0
\(205\) 158.885 264.571i 0.0541316 0.0901386i
\(206\) −773.426 −0.261588
\(207\) 0 0
\(208\) 8250.01i 2.75017i
\(209\) −1049.54 −0.347359
\(210\) 0 0
\(211\) −4196.90 −1.36932 −0.684660 0.728863i \(-0.740049\pi\)
−0.684660 + 0.728863i \(0.740049\pi\)
\(212\) 4330.16i 1.40282i
\(213\) 0 0
\(214\) 1752.66 0.559858
\(215\) −579.908 348.257i −0.183951 0.110469i
\(216\) 0 0
\(217\) 968.091i 0.302849i
\(218\) 5653.01i 1.75628i
\(219\) 0 0
\(220\) 3879.70 6460.37i 1.18895 1.97981i
\(221\) 1335.73 0.406567
\(222\) 0 0
\(223\) 3034.56i 0.911251i −0.890172 0.455625i \(-0.849416\pi\)
0.890172 0.455625i \(-0.150584\pi\)
\(224\) −576.834 −0.172059
\(225\) 0 0
\(226\) −1768.73 −0.520593
\(227\) 3236.16i 0.946219i −0.881004 0.473109i \(-0.843132\pi\)
0.881004 0.473109i \(-0.156868\pi\)
\(228\) 0 0
\(229\) 2974.56 0.858360 0.429180 0.903219i \(-0.358803\pi\)
0.429180 + 0.903219i \(0.358803\pi\)
\(230\) 3213.75 5351.44i 0.921340 1.53419i
\(231\) 0 0
\(232\) 2284.86i 0.646587i
\(233\) 2927.42i 0.823097i −0.911388 0.411549i \(-0.864988\pi\)
0.911388 0.411549i \(-0.135012\pi\)
\(234\) 0 0
\(235\) 922.392 + 553.932i 0.256044 + 0.153764i
\(236\) −1324.65 −0.365370
\(237\) 0 0
\(238\) 416.901i 0.113545i
\(239\) −2878.69 −0.779110 −0.389555 0.921003i \(-0.627371\pi\)
−0.389555 + 0.921003i \(0.627371\pi\)
\(240\) 0 0
\(241\) −1117.58 −0.298713 −0.149357 0.988783i \(-0.547720\pi\)
−0.149357 + 0.988783i \(0.547720\pi\)
\(242\) 994.435i 0.264152i
\(243\) 0 0
\(244\) −8448.03 −2.21651
\(245\) 1807.59 3009.95i 0.471358 0.784893i
\(246\) 0 0
\(247\) 2325.17i 0.598976i
\(248\) 8347.60i 2.13739i
\(249\) 0 0
\(250\) −362.457 + 7011.49i −0.0916953 + 1.77378i
\(251\) −4612.00 −1.15979 −0.579894 0.814692i \(-0.696906\pi\)
−0.579894 + 0.814692i \(0.696906\pi\)
\(252\) 0 0
\(253\) 4345.71i 1.07989i
\(254\) −7546.04 −1.86410
\(255\) 0 0
\(256\) −8159.28 −1.99201
\(257\) 3787.72i 0.919345i 0.888089 + 0.459672i \(0.152033\pi\)
−0.888089 + 0.459672i \(0.847967\pi\)
\(258\) 0 0
\(259\) 1579.59 0.378960
\(260\) 14312.5 + 8595.18i 3.41393 + 2.05020i
\(261\) 0 0
\(262\) 7910.89i 1.86541i
\(263\) 4989.56i 1.16985i −0.811089 0.584923i \(-0.801125\pi\)
0.811089 0.584923i \(-0.198875\pi\)
\(264\) 0 0
\(265\) −2407.73 1445.93i −0.558135 0.335181i
\(266\) −725.717 −0.167280
\(267\) 0 0
\(268\) 4114.99i 0.937922i
\(269\) 5845.57 1.32495 0.662473 0.749086i \(-0.269507\pi\)
0.662473 + 0.749086i \(0.269507\pi\)
\(270\) 0 0
\(271\) 2766.09 0.620030 0.310015 0.950732i \(-0.399666\pi\)
0.310015 + 0.950732i \(0.399666\pi\)
\(272\) 1468.48i 0.327351i
\(273\) 0 0
\(274\) 4482.65 0.988346
\(275\) 2296.69 + 4314.51i 0.503621 + 0.946091i
\(276\) 0 0
\(277\) 1893.80i 0.410785i −0.978680 0.205393i \(-0.934153\pi\)
0.978680 0.205393i \(-0.0658471\pi\)
\(278\) 3279.01i 0.707417i
\(279\) 0 0
\(280\) 1437.65 2393.93i 0.306842 0.510945i
\(281\) 4484.38 0.952012 0.476006 0.879442i \(-0.342084\pi\)
0.476006 + 0.879442i \(0.342084\pi\)
\(282\) 0 0
\(283\) 5797.64i 1.21779i 0.793251 + 0.608894i \(0.208387\pi\)
−0.793251 + 0.608894i \(0.791613\pi\)
\(284\) 11039.8 2.30666
\(285\) 0 0
\(286\) 17016.7 3.51824
\(287\) 148.560i 0.0305547i
\(288\) 0 0
\(289\) 4675.24 0.951607
\(290\) 2370.71 + 1423.70i 0.480045 + 0.288285i
\(291\) 0 0
\(292\) 13260.2i 2.65752i
\(293\) 7910.26i 1.57721i −0.614900 0.788605i \(-0.710804\pi\)
0.614900 0.788605i \(-0.289196\pi\)
\(294\) 0 0
\(295\) 442.329 736.554i 0.0872996 0.145369i
\(296\) −13620.4 −2.67456
\(297\) 0 0
\(298\) 17270.8i 3.35728i
\(299\) 9627.59 1.86213
\(300\) 0 0
\(301\) −325.626 −0.0623546
\(302\) 8394.21i 1.59945i
\(303\) 0 0
\(304\) 2556.24 0.482272
\(305\) 2820.98 4697.42i 0.529602 0.881880i
\(306\) 0 0
\(307\) 4426.37i 0.822887i −0.911435 0.411443i \(-0.865025\pi\)
0.911435 0.411443i \(-0.134975\pi\)
\(308\) 3627.58i 0.671105i
\(309\) 0 0
\(310\) 8661.27 + 5201.42i 1.58686 + 0.952971i
\(311\) 9697.24 1.76810 0.884052 0.467389i \(-0.154805\pi\)
0.884052 + 0.467389i \(0.154805\pi\)
\(312\) 0 0
\(313\) 4523.09i 0.816806i 0.912802 + 0.408403i \(0.133914\pi\)
−0.912802 + 0.408403i \(0.866086\pi\)
\(314\) −3346.32 −0.601413
\(315\) 0 0
\(316\) 11417.4 2.03253
\(317\) 5322.21i 0.942981i 0.881871 + 0.471491i \(0.156284\pi\)
−0.881871 + 0.471491i \(0.843716\pi\)
\(318\) 0 0
\(319\) 1925.17 0.337895
\(320\) 1286.20 2141.74i 0.224689 0.374147i
\(321\) 0 0
\(322\) 3004.90i 0.520051i
\(323\) 413.874i 0.0712958i
\(324\) 0 0
\(325\) −9558.48 + 5088.15i −1.63141 + 0.868430i
\(326\) −4467.36 −0.758970
\(327\) 0 0
\(328\) 1280.99i 0.215643i
\(329\) 517.934 0.0867922
\(330\) 0 0
\(331\) −7833.11 −1.30075 −0.650373 0.759615i \(-0.725387\pi\)
−0.650373 + 0.759615i \(0.725387\pi\)
\(332\) 22445.9i 3.71048i
\(333\) 0 0
\(334\) 2028.89 0.332383
\(335\) −2288.09 1374.08i −0.373169 0.224102i
\(336\) 0 0
\(337\) 9928.08i 1.60480i −0.596787 0.802399i \(-0.703556\pi\)
0.596787 0.802399i \(-0.296444\pi\)
\(338\) 26662.1i 4.29061i
\(339\) 0 0
\(340\) −2547.58 1529.92i −0.406358 0.244034i
\(341\) 7033.49 1.11696
\(342\) 0 0
\(343\) 3536.14i 0.556658i
\(344\) 2807.79 0.440075
\(345\) 0 0
\(346\) −1185.90 −0.184262
\(347\) 4040.33i 0.625062i −0.949908 0.312531i \(-0.898823\pi\)
0.949908 0.312531i \(-0.101177\pi\)
\(348\) 0 0
\(349\) −4799.72 −0.736169 −0.368085 0.929792i \(-0.619986\pi\)
−0.368085 + 0.929792i \(0.619986\pi\)
\(350\) 1588.08 + 2983.33i 0.242533 + 0.455617i
\(351\) 0 0
\(352\) 4190.88i 0.634588i
\(353\) 3189.48i 0.480903i 0.970661 + 0.240451i \(0.0772955\pi\)
−0.970661 + 0.240451i \(0.922705\pi\)
\(354\) 0 0
\(355\) −3686.43 + 6138.55i −0.551142 + 0.917747i
\(356\) −17160.9 −2.55484
\(357\) 0 0
\(358\) 12078.5i 1.78316i
\(359\) 1159.83 0.170511 0.0852554 0.996359i \(-0.472829\pi\)
0.0852554 + 0.996359i \(0.472829\pi\)
\(360\) 0 0
\(361\) −6138.55 −0.894963
\(362\) 6120.96i 0.888703i
\(363\) 0 0
\(364\) 8036.62 1.15724
\(365\) −7373.16 4427.87i −1.05734 0.634973i
\(366\) 0 0
\(367\) 11875.2i 1.68904i −0.535524 0.844520i \(-0.679886\pi\)
0.535524 0.844520i \(-0.320114\pi\)
\(368\) 10584.4i 1.49932i
\(369\) 0 0
\(370\) 8486.91 14132.2i 1.19247 1.98567i
\(371\) −1351.97 −0.189194
\(372\) 0 0
\(373\) 2643.26i 0.366924i −0.983027 0.183462i \(-0.941270\pi\)
0.983027 0.183462i \(-0.0587305\pi\)
\(374\) −3028.92 −0.418774
\(375\) 0 0
\(376\) −4466.02 −0.612546
\(377\) 4265.06i 0.582657i
\(378\) 0 0
\(379\) −10452.7 −1.41667 −0.708335 0.705876i \(-0.750553\pi\)
−0.708335 + 0.705876i \(0.750553\pi\)
\(380\) −2663.19 + 4434.68i −0.359524 + 0.598669i
\(381\) 0 0
\(382\) 883.887i 0.118386i
\(383\) 10879.8i 1.45153i −0.687945 0.725763i \(-0.741487\pi\)
0.687945 0.725763i \(-0.258513\pi\)
\(384\) 0 0
\(385\) 2017.07 + 1211.33i 0.267011 + 0.160350i
\(386\) −11128.8 −1.46747
\(387\) 0 0
\(388\) 14046.1i 1.83784i
\(389\) −1677.66 −0.218665 −0.109333 0.994005i \(-0.534871\pi\)
−0.109333 + 0.994005i \(0.534871\pi\)
\(390\) 0 0
\(391\) −1713.68 −0.221649
\(392\) 14573.5i 1.87774i
\(393\) 0 0
\(394\) −5295.38 −0.677100
\(395\) −3812.52 + 6348.50i −0.485642 + 0.808678i
\(396\) 0 0
\(397\) 13147.5i 1.66210i −0.556199 0.831049i \(-0.687741\pi\)
0.556199 0.831049i \(-0.312259\pi\)
\(398\) 17502.8i 2.20437i
\(399\) 0 0
\(400\) −5593.81 10508.4i −0.699226 1.31355i
\(401\) −6521.91 −0.812191 −0.406095 0.913831i \(-0.633110\pi\)
−0.406095 + 0.913831i \(0.633110\pi\)
\(402\) 0 0
\(403\) 15582.2i 1.92606i
\(404\) 11249.4 1.38534
\(405\) 0 0
\(406\) 1331.18 0.162723
\(407\) 11476.2i 1.39768i
\(408\) 0 0
\(409\) −5642.67 −0.682181 −0.341091 0.940030i \(-0.610796\pi\)
−0.341091 + 0.940030i \(0.610796\pi\)
\(410\) −1329.13 798.191i −0.160100 0.0961459i
\(411\) 0 0
\(412\) 2653.83i 0.317342i
\(413\) 413.584i 0.0492764i
\(414\) 0 0
\(415\) 12480.8 + 7495.17i 1.47628 + 0.886562i
\(416\) −9284.59 −1.09427
\(417\) 0 0
\(418\) 5272.57i 0.616961i
\(419\) 9621.73 1.12184 0.560922 0.827869i \(-0.310447\pi\)
0.560922 + 0.827869i \(0.310447\pi\)
\(420\) 0 0
\(421\) 10030.3 1.16115 0.580577 0.814205i \(-0.302827\pi\)
0.580577 + 0.814205i \(0.302827\pi\)
\(422\) 21084.0i 2.43212i
\(423\) 0 0
\(424\) 11657.7 1.33525
\(425\) 1701.38 905.676i 0.194186 0.103369i
\(426\) 0 0
\(427\) 2637.66i 0.298935i
\(428\) 6013.85i 0.679183i
\(429\) 0 0
\(430\) −1749.54 + 2913.29i −0.196210 + 0.326724i
\(431\) 3867.23 0.432200 0.216100 0.976371i \(-0.430666\pi\)
0.216100 + 0.976371i \(0.430666\pi\)
\(432\) 0 0
\(433\) 2345.27i 0.260292i −0.991495 0.130146i \(-0.958455\pi\)
0.991495 0.130146i \(-0.0415446\pi\)
\(434\) 4863.41 0.537906
\(435\) 0 0
\(436\) 19396.9 2.13061
\(437\) 2983.08i 0.326545i
\(438\) 0 0
\(439\) 14117.9 1.53487 0.767437 0.641125i \(-0.221532\pi\)
0.767437 + 0.641125i \(0.221532\pi\)
\(440\) −17392.7 10445.0i −1.88446 1.13169i
\(441\) 0 0
\(442\) 6710.34i 0.722123i
\(443\) 17796.6i 1.90867i 0.298731 + 0.954337i \(0.403437\pi\)
−0.298731 + 0.954337i \(0.596563\pi\)
\(444\) 0 0
\(445\) 5730.38 9542.08i 0.610441 1.01649i
\(446\) −15244.7 −1.61852
\(447\) 0 0
\(448\) 1202.61i 0.126826i
\(449\) 11518.0 1.21062 0.605310 0.795990i \(-0.293049\pi\)
0.605310 + 0.795990i \(0.293049\pi\)
\(450\) 0 0
\(451\) −1079.33 −0.112691
\(452\) 6068.97i 0.631550i
\(453\) 0 0
\(454\) −16257.5 −1.68063
\(455\) −2683.60 + 4468.66i −0.276504 + 0.460427i
\(456\) 0 0
\(457\) 9857.71i 1.00902i −0.863405 0.504512i \(-0.831672\pi\)
0.863405 0.504512i \(-0.168328\pi\)
\(458\) 14943.3i 1.52458i
\(459\) 0 0
\(460\) −18362.2 11027.2i −1.86118 1.11771i
\(461\) −16081.6 −1.62472 −0.812358 0.583159i \(-0.801816\pi\)
−0.812358 + 0.583159i \(0.801816\pi\)
\(462\) 0 0
\(463\) 18895.8i 1.89668i 0.317263 + 0.948338i \(0.397236\pi\)
−0.317263 + 0.948338i \(0.602764\pi\)
\(464\) −4688.92 −0.469133
\(465\) 0 0
\(466\) −14706.5 −1.46194
\(467\) 10368.7i 1.02742i −0.857963 0.513712i \(-0.828270\pi\)
0.857963 0.513712i \(-0.171730\pi\)
\(468\) 0 0
\(469\) −1284.79 −0.126495
\(470\) 2782.79 4633.83i 0.273108 0.454772i
\(471\) 0 0
\(472\) 3566.23i 0.347774i
\(473\) 2365.77i 0.229976i
\(474\) 0 0
\(475\) −1576.55 2961.67i −0.152289 0.286086i
\(476\) −1430.50 −0.137745
\(477\) 0 0
\(478\) 14461.7i 1.38382i
\(479\) 9554.02 0.911345 0.455672 0.890148i \(-0.349399\pi\)
0.455672 + 0.890148i \(0.349399\pi\)
\(480\) 0 0
\(481\) 25424.7 2.41012
\(482\) 5614.42i 0.530559i
\(483\) 0 0
\(484\) −3412.17 −0.320451
\(485\) −7810.13 4690.28i −0.731216 0.439123i
\(486\) 0 0
\(487\) 17514.2i 1.62966i 0.579699 + 0.814831i \(0.303170\pi\)
−0.579699 + 0.814831i \(0.696830\pi\)
\(488\) 22743.8i 2.10977i
\(489\) 0 0
\(490\) −15121.1 9080.81i −1.39409 0.837203i
\(491\) −3866.54 −0.355386 −0.177693 0.984086i \(-0.556863\pi\)
−0.177693 + 0.984086i \(0.556863\pi\)
\(492\) 0 0
\(493\) 759.169i 0.0693534i
\(494\) −11681.0 −1.06387
\(495\) 0 0
\(496\) −17130.7 −1.55079
\(497\) 3446.87i 0.311093i
\(498\) 0 0
\(499\) −4855.96 −0.435637 −0.217818 0.975989i \(-0.569894\pi\)
−0.217818 + 0.975989i \(0.569894\pi\)
\(500\) 24058.3 + 1243.69i 2.15184 + 0.111239i
\(501\) 0 0
\(502\) 23169.3i 2.05996i
\(503\) 5481.79i 0.485927i 0.970035 + 0.242963i \(0.0781195\pi\)
−0.970035 + 0.242963i \(0.921881\pi\)
\(504\) 0 0
\(505\) −3756.41 + 6255.07i −0.331006 + 0.551182i
\(506\) −21831.6 −1.91805
\(507\) 0 0
\(508\) 25892.4i 2.26140i
\(509\) 20427.1 1.77881 0.889405 0.457120i \(-0.151119\pi\)
0.889405 + 0.457120i \(0.151119\pi\)
\(510\) 0 0
\(511\) −4140.12 −0.358411
\(512\) 25150.0i 2.17086i
\(513\) 0 0
\(514\) 19028.4 1.63289
\(515\) −1475.63 886.171i −0.126260 0.0758240i
\(516\) 0 0
\(517\) 3762.96i 0.320106i
\(518\) 7935.39i 0.673091i
\(519\) 0 0
\(520\) 23140.0 38532.2i 1.95146 3.24951i
\(521\) −5768.55 −0.485076 −0.242538 0.970142i \(-0.577980\pi\)
−0.242538 + 0.970142i \(0.577980\pi\)
\(522\) 0 0
\(523\) 1753.72i 0.146625i 0.997309 + 0.0733126i \(0.0233571\pi\)
−0.997309 + 0.0733126i \(0.976643\pi\)
\(524\) 27144.4 2.26299
\(525\) 0 0
\(526\) −25066.1 −2.07782
\(527\) 2773.58i 0.229258i
\(528\) 0 0
\(529\) −184.728 −0.0151827
\(530\) −7263.96 + 12095.7i −0.595332 + 0.991332i
\(531\) 0 0
\(532\) 2490.13i 0.202934i
\(533\) 2391.18i 0.194322i
\(534\) 0 0
\(535\) 3343.92 + 2008.15i 0.270225 + 0.162280i
\(536\) 11078.4 0.892751
\(537\) 0 0
\(538\) 29366.4i 2.35330i
\(539\) −12279.3 −0.981274
\(540\) 0 0
\(541\) 7146.18 0.567908 0.283954 0.958838i \(-0.408354\pi\)
0.283954 + 0.958838i \(0.408354\pi\)
\(542\) 13896.1i 1.10127i
\(543\) 0 0
\(544\) 1652.63 0.130250
\(545\) −6477.06 + 10785.4i −0.509076 + 0.847701i
\(546\) 0 0
\(547\) 7407.89i 0.579047i 0.957171 + 0.289523i \(0.0934968\pi\)
−0.957171 + 0.289523i \(0.906503\pi\)
\(548\) 15381.1i 1.19900i
\(549\) 0 0
\(550\) 21674.9 11537.9i 1.68040 0.894506i
\(551\) −1321.52 −0.102175
\(552\) 0 0
\(553\) 3564.76i 0.274121i
\(554\) −9513.91 −0.729616
\(555\) 0 0
\(556\) 11251.1 0.858192
\(557\) 11116.3i 0.845626i −0.906217 0.422813i \(-0.861043\pi\)
0.906217 0.422813i \(-0.138957\pi\)
\(558\) 0 0
\(559\) −5241.20 −0.396564
\(560\) −4912.75 2950.30i −0.370717 0.222630i
\(561\) 0 0
\(562\) 22528.2i 1.69092i
\(563\) 11206.6i 0.838901i 0.907778 + 0.419450i \(0.137777\pi\)
−0.907778 + 0.419450i \(0.862223\pi\)
\(564\) 0 0
\(565\) −3374.57 2026.56i −0.251273 0.150899i
\(566\) 29125.7 2.16298
\(567\) 0 0
\(568\) 29721.5i 2.19557i
\(569\) −15873.8 −1.16953 −0.584765 0.811203i \(-0.698813\pi\)
−0.584765 + 0.811203i \(0.698813\pi\)
\(570\) 0 0
\(571\) −2388.45 −0.175050 −0.0875250 0.996162i \(-0.527896\pi\)
−0.0875250 + 0.996162i \(0.527896\pi\)
\(572\) 58388.7i 4.26810i
\(573\) 0 0
\(574\) −746.320 −0.0542697
\(575\) 12263.1 6527.85i 0.889401 0.473444i
\(576\) 0 0
\(577\) 10429.0i 0.752455i −0.926527 0.376227i \(-0.877221\pi\)
0.926527 0.376227i \(-0.122779\pi\)
\(578\) 23487.1i 1.69020i
\(579\) 0 0
\(580\) 4885.10 8134.54i 0.349729 0.582359i
\(581\) 7008.09 0.500421
\(582\) 0 0
\(583\) 9822.50i 0.697781i
\(584\) 35699.2 2.52953
\(585\) 0 0
\(586\) −39738.9 −2.80136
\(587\) 3148.05i 0.221352i −0.993857 0.110676i \(-0.964698\pi\)
0.993857 0.110676i \(-0.0353016\pi\)
\(588\) 0 0
\(589\) −4828.10 −0.337756
\(590\) −3700.24 2222.13i −0.258197 0.155057i
\(591\) 0 0
\(592\) 27951.4i 1.94053i
\(593\) 12123.4i 0.839542i 0.907630 + 0.419771i \(0.137890\pi\)
−0.907630 + 0.419771i \(0.862110\pi\)
\(594\) 0 0
\(595\) 477.673 795.409i 0.0329121 0.0548043i
\(596\) 59260.6 4.07283
\(597\) 0 0
\(598\) 48366.2i 3.30743i
\(599\) 15842.8 1.08067 0.540333 0.841451i \(-0.318298\pi\)
0.540333 + 0.841451i \(0.318298\pi\)
\(600\) 0 0
\(601\) −25690.1 −1.74363 −0.871815 0.489836i \(-0.837057\pi\)
−0.871815 + 0.489836i \(0.837057\pi\)
\(602\) 1635.85i 0.110751i
\(603\) 0 0
\(604\) −28802.8 −1.94034
\(605\) 1139.40 1897.29i 0.0765670 0.127497i
\(606\) 0 0
\(607\) 14523.3i 0.971139i −0.874198 0.485570i \(-0.838612\pi\)
0.874198 0.485570i \(-0.161388\pi\)
\(608\) 2876.81i 0.191891i
\(609\) 0 0
\(610\) −23598.5 14171.8i −1.56635 0.940653i
\(611\) 8336.56 0.551982
\(612\) 0 0
\(613\) 26426.7i 1.74121i 0.491981 + 0.870606i \(0.336273\pi\)
−0.491981 + 0.870606i \(0.663727\pi\)
\(614\) −22236.8 −1.46157
\(615\) 0 0
\(616\) −9766.19 −0.638784
\(617\) 3757.77i 0.245190i 0.992457 + 0.122595i \(0.0391216\pi\)
−0.992457 + 0.122595i \(0.960878\pi\)
\(618\) 0 0
\(619\) 23480.5 1.52465 0.762327 0.647192i \(-0.224057\pi\)
0.762327 + 0.647192i \(0.224057\pi\)
\(620\) 17847.4 29719.1i 1.15608 1.92508i
\(621\) 0 0
\(622\) 48716.1i 3.14042i
\(623\) 5357.99i 0.344564i
\(624\) 0 0
\(625\) −8725.10 + 12962.0i −0.558407 + 0.829567i
\(626\) 22722.7 1.45077
\(627\) 0 0
\(628\) 11482.1i 0.729595i
\(629\) −4525.52 −0.286875
\(630\) 0 0
\(631\) 8654.12 0.545983 0.272991 0.962016i \(-0.411987\pi\)
0.272991 + 0.962016i \(0.411987\pi\)
\(632\) 30738.0i 1.93464i
\(633\) 0 0
\(634\) 26737.2 1.67488
\(635\) −14397.2 8646.04i −0.899738 0.540327i
\(636\) 0 0
\(637\) 27203.9i 1.69208i
\(638\) 9671.48i 0.600153i
\(639\) 0 0
\(640\) −18977.8 11396.9i −1.17213 0.703908i
\(641\) 19177.6 1.18170 0.590850 0.806781i \(-0.298792\pi\)
0.590850 + 0.806781i \(0.298792\pi\)
\(642\) 0 0
\(643\) 9835.57i 0.603230i −0.953430 0.301615i \(-0.902474\pi\)
0.953430 0.301615i \(-0.0975258\pi\)
\(644\) −10310.6 −0.630892
\(645\) 0 0
\(646\) 2079.18 0.126632
\(647\) 7621.18i 0.463090i 0.972824 + 0.231545i \(0.0743781\pi\)
−0.972824 + 0.231545i \(0.925622\pi\)
\(648\) 0 0
\(649\) −3004.82 −0.181741
\(650\) 25561.4 + 48019.1i 1.54246 + 2.89763i
\(651\) 0 0
\(652\) 15328.7i 0.920733i
\(653\) 4396.32i 0.263463i 0.991285 + 0.131731i \(0.0420537\pi\)
−0.991285 + 0.131731i \(0.957946\pi\)
\(654\) 0 0
\(655\) −9064.08 + 15093.3i −0.540707 + 0.900371i
\(656\) 2628.82 0.156460
\(657\) 0 0
\(658\) 2601.95i 0.154156i
\(659\) −10820.3 −0.639601 −0.319801 0.947485i \(-0.603616\pi\)
−0.319801 + 0.947485i \(0.603616\pi\)
\(660\) 0 0
\(661\) −28915.5 −1.70149 −0.850744 0.525581i \(-0.823848\pi\)
−0.850744 + 0.525581i \(0.823848\pi\)
\(662\) 39351.3i 2.31032i
\(663\) 0 0
\(664\) −60429.0 −3.53178
\(665\) −1384.60 831.507i −0.0807407 0.0484879i
\(666\) 0 0
\(667\) 5471.87i 0.317649i
\(668\) 6961.65i 0.403225i
\(669\) 0 0
\(670\) −6903.00 + 11494.7i −0.398039 + 0.662804i
\(671\) −19163.4 −1.10253
\(672\) 0 0
\(673\) 5061.16i 0.289886i −0.989440 0.144943i \(-0.953700\pi\)
0.989440 0.144943i \(-0.0462999\pi\)
\(674\) −49875.8 −2.85036
\(675\) 0 0
\(676\) 91484.6 5.20509
\(677\) 12059.3i 0.684601i 0.939591 + 0.342300i \(0.111206\pi\)
−0.939591 + 0.342300i \(0.888794\pi\)
\(678\) 0 0
\(679\) −4385.48 −0.247863
\(680\) −4118.86 + 6858.61i −0.232281 + 0.386788i
\(681\) 0 0
\(682\) 35334.2i 1.98390i
\(683\) 6110.33i 0.342321i 0.985243 + 0.171160i \(0.0547516\pi\)
−0.985243 + 0.171160i \(0.945248\pi\)
\(684\) 0 0
\(685\) 8552.49 + 5136.10i 0.477042 + 0.286482i
\(686\) −17764.5 −0.988708
\(687\) 0 0
\(688\) 5762.06i 0.319297i
\(689\) −21761.0 −1.20323
\(690\) 0 0
\(691\) 27209.7 1.49798 0.748991 0.662580i \(-0.230538\pi\)
0.748991 + 0.662580i \(0.230538\pi\)
\(692\) 4069.15i 0.223535i
\(693\) 0 0
\(694\) −20297.5 −1.11020
\(695\) −3757.00 + 6256.05i −0.205052 + 0.341447i
\(696\) 0 0
\(697\) 425.624i 0.0231300i
\(698\) 24112.4i 1.30755i
\(699\) 0 0
\(700\) 10236.6 5449.12i 0.552724 0.294225i
\(701\) −30424.7 −1.63927 −0.819633 0.572888i \(-0.805823\pi\)
−0.819633 + 0.572888i \(0.805823\pi\)
\(702\) 0 0
\(703\) 7877.77i 0.422640i
\(704\) −8737.37 −0.467759
\(705\) 0 0
\(706\) 16023.0 0.854156
\(707\) 3512.30i 0.186837i
\(708\) 0 0
\(709\) −1846.41 −0.0978045 −0.0489022 0.998804i \(-0.515572\pi\)
−0.0489022 + 0.998804i \(0.515572\pi\)
\(710\) 30838.3 + 18519.6i 1.63006 + 0.978911i
\(711\) 0 0
\(712\) 46200.6i 2.43180i
\(713\) 19991.2i 1.05004i
\(714\) 0 0
\(715\) 32466.3 + 19497.2i 1.69814 + 1.01980i
\(716\) 41444.6 2.16321
\(717\) 0 0
\(718\) 5826.64i 0.302853i
\(719\) −13301.3 −0.689923 −0.344961 0.938617i \(-0.612108\pi\)
−0.344961 + 0.938617i \(0.612108\pi\)
\(720\) 0 0
\(721\) −828.583 −0.0427989
\(722\) 30838.3i 1.58959i
\(723\) 0 0
\(724\) 21002.6 1.07812
\(725\) 2891.86 + 5432.59i 0.148140 + 0.278292i
\(726\) 0 0
\(727\) 25915.1i 1.32206i 0.750358 + 0.661031i \(0.229881\pi\)
−0.750358 + 0.661031i \(0.770119\pi\)
\(728\) 21636.3i 1.10150i
\(729\) 0 0
\(730\) −22244.3 + 37040.6i −1.12781 + 1.87799i
\(731\) 932.918 0.0472028
\(732\) 0 0
\(733\) 22247.8i 1.12106i 0.828132 + 0.560532i \(0.189403\pi\)
−0.828132 + 0.560532i \(0.810597\pi\)
\(734\) −59657.3 −2.99999
\(735\) 0 0
\(736\) 11911.7 0.596563
\(737\) 9334.41i 0.466536i
\(738\) 0 0
\(739\) 23675.6 1.17851 0.589256 0.807947i \(-0.299421\pi\)
0.589256 + 0.807947i \(0.299421\pi\)
\(740\) −48491.2 29120.8i −2.40888 1.44663i
\(741\) 0 0
\(742\) 6791.91i 0.336036i
\(743\) 33555.1i 1.65682i −0.560120 0.828411i \(-0.689245\pi\)
0.560120 0.828411i \(-0.310755\pi\)
\(744\) 0 0
\(745\) −19788.4 + 32951.1i −0.973142 + 1.62045i
\(746\) −13279.0 −0.651713
\(747\) 0 0
\(748\) 10393.0i 0.508030i
\(749\) 1877.65 0.0915993
\(750\) 0 0
\(751\) 21889.8 1.06361 0.531804 0.846868i \(-0.321514\pi\)
0.531804 + 0.846868i \(0.321514\pi\)
\(752\) 9165.04i 0.444434i
\(753\) 0 0
\(754\) 21426.4 1.03489
\(755\) 9617.86 16015.4i 0.463615 0.772000i
\(756\) 0 0
\(757\) 24362.3i 1.16970i −0.811141 0.584851i \(-0.801153\pi\)
0.811141 0.584851i \(-0.198847\pi\)
\(758\) 52511.2i 2.51622i
\(759\) 0 0
\(760\) 11939.1 + 7169.87i 0.569837 + 0.342209i
\(761\) −27685.3 −1.31878 −0.659391 0.751801i \(-0.729186\pi\)
−0.659391 + 0.751801i \(0.729186\pi\)
\(762\) 0 0
\(763\) 6056.14i 0.287349i
\(764\) −3032.85 −0.143619
\(765\) 0 0
\(766\) −54657.2 −2.57813
\(767\) 6656.96i 0.313388i
\(768\) 0 0
\(769\) 6996.11 0.328070 0.164035 0.986454i \(-0.447549\pi\)
0.164035 + 0.986454i \(0.447549\pi\)
\(770\) 6085.35 10133.2i 0.284806 0.474252i
\(771\) 0 0
\(772\) 38185.9i 1.78023i
\(773\) 19650.7i 0.914342i 0.889379 + 0.457171i \(0.151137\pi\)
−0.889379 + 0.457171i \(0.848863\pi\)
\(774\) 0 0
\(775\) 10565.3 + 19847.7i 0.489698 + 0.919936i
\(776\) 37814.9 1.74932
\(777\) 0 0
\(778\) 8428.08i 0.388382i
\(779\) 740.901 0.0340764
\(780\) 0 0
\(781\) 25042.6 1.14737
\(782\) 8609.05i 0.393681i
\(783\) 0 0
\(784\) 29907.4 1.36240
\(785\) −6384.47 3834.12i −0.290282 0.174326i
\(786\) 0 0
\(787\) 1312.96i 0.0594689i −0.999558 0.0297344i \(-0.990534\pi\)
0.999558 0.0297344i \(-0.00946616\pi\)
\(788\) 18169.8i 0.821413i
\(789\) 0 0
\(790\) 31893.0 + 19153.0i 1.43633 + 0.862573i
\(791\) −1894.86 −0.0851752
\(792\) 0 0
\(793\) 42455.1i 1.90117i
\(794\) −66049.1 −2.95214