Properties

Label 405.4.b.f.244.13
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 244.13
Root \(3.08740i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.f.244.4

$q$-expansion

\(f(q)\) \(=\) \(q+3.08740i q^{2} -1.53204 q^{4} +(5.83763 + 9.53531i) q^{5} -31.3204i q^{7} +19.9692i q^{8} +O(q^{10})\) \(q+3.08740i q^{2} -1.53204 q^{4} +(5.83763 + 9.53531i) q^{5} -31.3204i q^{7} +19.9692i q^{8} +(-29.4393 + 18.0231i) q^{10} +19.1937 q^{11} +20.9909i q^{13} +96.6986 q^{14} -73.9092 q^{16} +6.19137i q^{17} +96.6654 q^{19} +(-8.94350 - 14.6085i) q^{20} +59.2586i q^{22} +162.986i q^{23} +(-56.8442 + 111.327i) q^{25} -64.8074 q^{26} +47.9842i q^{28} +7.64922 q^{29} +225.025 q^{31} -68.4339i q^{32} -19.1153 q^{34} +(298.650 - 182.837i) q^{35} +155.911i q^{37} +298.445i q^{38} +(-190.412 + 116.573i) q^{40} +315.221 q^{41} +192.759i q^{43} -29.4056 q^{44} -503.202 q^{46} -318.312i q^{47} -637.967 q^{49} +(-343.711 - 175.501i) q^{50} -32.1590i q^{52} +277.459i q^{53} +(112.046 + 183.018i) q^{55} +625.442 q^{56} +23.6162i q^{58} -429.292 q^{59} -89.9348 q^{61} +694.741i q^{62} -379.991 q^{64} +(-200.155 + 122.537i) q^{65} +583.304i q^{67} -9.48546i q^{68} +(564.490 + 922.051i) q^{70} -132.605 q^{71} -259.933i q^{73} -481.361 q^{74} -148.096 q^{76} -601.153i q^{77} -124.649 q^{79} +(-431.454 - 704.747i) q^{80} +973.214i q^{82} +36.7198i q^{83} +(-59.0367 + 36.1429i) q^{85} -595.123 q^{86} +383.282i q^{88} +333.424 q^{89} +657.443 q^{91} -249.701i q^{92} +982.757 q^{94} +(564.296 + 921.735i) q^{95} -1029.25i q^{97} -1969.66i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} + 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} + 3 q^{5} - 10 q^{10} + 90 q^{11} - 102 q^{14} + 146 q^{16} - 4 q^{19} - 6 q^{20} - 71 q^{25} + 468 q^{26} - 516 q^{29} + 38 q^{31} - 212 q^{34} + 267 q^{35} - 44 q^{40} + 576 q^{41} - 1644 q^{44} - 290 q^{46} + 4 q^{49} + 558 q^{50} + 15 q^{55} + 2430 q^{56} - 2202 q^{59} + 20 q^{61} + 322 q^{64} + 339 q^{65} - 636 q^{70} + 2952 q^{71} - 4080 q^{74} - 396 q^{76} + 218 q^{79} - 1266 q^{80} + 704 q^{85} + 6108 q^{86} - 4074 q^{89} - 942 q^{91} + 1078 q^{94} - 1692 q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.08740i 1.09156i 0.837928 + 0.545781i \(0.183767\pi\)
−0.837928 + 0.545781i \(0.816233\pi\)
\(3\) 0 0
\(4\) −1.53204 −0.191506
\(5\) 5.83763 + 9.53531i 0.522133 + 0.852864i
\(6\) 0 0
\(7\) 31.3204i 1.69114i −0.533863 0.845571i \(-0.679260\pi\)
0.533863 0.845571i \(-0.320740\pi\)
\(8\) 19.9692i 0.882521i
\(9\) 0 0
\(10\) −29.4393 + 18.0231i −0.930953 + 0.569940i
\(11\) 19.1937 0.526101 0.263051 0.964782i \(-0.415271\pi\)
0.263051 + 0.964782i \(0.415271\pi\)
\(12\) 0 0
\(13\) 20.9909i 0.447833i 0.974608 + 0.223917i \(0.0718843\pi\)
−0.974608 + 0.223917i \(0.928116\pi\)
\(14\) 96.6986 1.84598
\(15\) 0 0
\(16\) −73.9092 −1.15483
\(17\) 6.19137i 0.0883311i 0.999024 + 0.0441656i \(0.0140629\pi\)
−0.999024 + 0.0441656i \(0.985937\pi\)
\(18\) 0 0
\(19\) 96.6654 1.16719 0.583594 0.812046i \(-0.301646\pi\)
0.583594 + 0.812046i \(0.301646\pi\)
\(20\) −8.94350 14.6085i −0.0999914 0.163328i
\(21\) 0 0
\(22\) 59.2586i 0.574271i
\(23\) 162.986i 1.47760i 0.673923 + 0.738801i \(0.264608\pi\)
−0.673923 + 0.738801i \(0.735392\pi\)
\(24\) 0 0
\(25\) −56.8442 + 111.327i −0.454754 + 0.890617i
\(26\) −64.8074 −0.488837
\(27\) 0 0
\(28\) 47.9842i 0.323863i
\(29\) 7.64922 0.0489802 0.0244901 0.999700i \(-0.492204\pi\)
0.0244901 + 0.999700i \(0.492204\pi\)
\(30\) 0 0
\(31\) 225.025 1.30373 0.651865 0.758335i \(-0.273987\pi\)
0.651865 + 0.758335i \(0.273987\pi\)
\(32\) 68.4339i 0.378048i
\(33\) 0 0
\(34\) −19.1153 −0.0964188
\(35\) 298.650 182.837i 1.44231 0.883001i
\(36\) 0 0
\(37\) 155.911i 0.692748i 0.938097 + 0.346374i \(0.112587\pi\)
−0.938097 + 0.346374i \(0.887413\pi\)
\(38\) 298.445i 1.27406i
\(39\) 0 0
\(40\) −190.412 + 116.573i −0.752670 + 0.460793i
\(41\) 315.221 1.20071 0.600357 0.799732i \(-0.295025\pi\)
0.600357 + 0.799732i \(0.295025\pi\)
\(42\) 0 0
\(43\) 192.759i 0.683614i 0.939770 + 0.341807i \(0.111039\pi\)
−0.939770 + 0.341807i \(0.888961\pi\)
\(44\) −29.4056 −0.100751
\(45\) 0 0
\(46\) −503.202 −1.61289
\(47\) 318.312i 0.987885i −0.869495 0.493942i \(-0.835555\pi\)
0.869495 0.493942i \(-0.164445\pi\)
\(48\) 0 0
\(49\) −637.967 −1.85996
\(50\) −343.711 175.501i −0.972163 0.496392i
\(51\) 0 0
\(52\) 32.1590i 0.0857625i
\(53\) 277.459i 0.719093i 0.933127 + 0.359547i \(0.117069\pi\)
−0.933127 + 0.359547i \(0.882931\pi\)
\(54\) 0 0
\(55\) 112.046 + 183.018i 0.274695 + 0.448693i
\(56\) 625.442 1.49247
\(57\) 0 0
\(58\) 23.6162i 0.0534648i
\(59\) −429.292 −0.947272 −0.473636 0.880721i \(-0.657059\pi\)
−0.473636 + 0.880721i \(0.657059\pi\)
\(60\) 0 0
\(61\) −89.9348 −0.188770 −0.0943850 0.995536i \(-0.530088\pi\)
−0.0943850 + 0.995536i \(0.530088\pi\)
\(62\) 694.741i 1.42310i
\(63\) 0 0
\(64\) −379.991 −0.742169
\(65\) −200.155 + 122.537i −0.381941 + 0.233829i
\(66\) 0 0
\(67\) 583.304i 1.06361i 0.846867 + 0.531805i \(0.178486\pi\)
−0.846867 + 0.531805i \(0.821514\pi\)
\(68\) 9.48546i 0.0169159i
\(69\) 0 0
\(70\) 564.490 + 922.051i 0.963850 + 1.57437i
\(71\) −132.605 −0.221653 −0.110826 0.993840i \(-0.535350\pi\)
−0.110826 + 0.993840i \(0.535350\pi\)
\(72\) 0 0
\(73\) 259.933i 0.416752i −0.978049 0.208376i \(-0.933182\pi\)
0.978049 0.208376i \(-0.0668177\pi\)
\(74\) −481.361 −0.756176
\(75\) 0 0
\(76\) −148.096 −0.223523
\(77\) 601.153i 0.889712i
\(78\) 0 0
\(79\) −124.649 −0.177520 −0.0887601 0.996053i \(-0.528290\pi\)
−0.0887601 + 0.996053i \(0.528290\pi\)
\(80\) −431.454 704.747i −0.602976 0.984914i
\(81\) 0 0
\(82\) 973.214i 1.31065i
\(83\) 36.7198i 0.0485605i 0.999705 + 0.0242802i \(0.00772940\pi\)
−0.999705 + 0.0242802i \(0.992271\pi\)
\(84\) 0 0
\(85\) −59.0367 + 36.1429i −0.0753344 + 0.0461206i
\(86\) −595.123 −0.746207
\(87\) 0 0
\(88\) 383.282i 0.464295i
\(89\) 333.424 0.397111 0.198555 0.980090i \(-0.436375\pi\)
0.198555 + 0.980090i \(0.436375\pi\)
\(90\) 0 0
\(91\) 657.443 0.757349
\(92\) 249.701i 0.282969i
\(93\) 0 0
\(94\) 982.757 1.07834
\(95\) 564.296 + 921.735i 0.609427 + 0.995452i
\(96\) 0 0
\(97\) 1029.25i 1.07736i −0.842510 0.538681i \(-0.818923\pi\)
0.842510 0.538681i \(-0.181077\pi\)
\(98\) 1969.66i 2.03026i
\(99\) 0 0
\(100\) 87.0879 170.558i 0.0870879 0.170558i
\(101\) −926.962 −0.913230 −0.456615 0.889664i \(-0.650938\pi\)
−0.456615 + 0.889664i \(0.650938\pi\)
\(102\) 0 0
\(103\) 1687.60i 1.61441i −0.590271 0.807205i \(-0.700979\pi\)
0.590271 0.807205i \(-0.299021\pi\)
\(104\) −419.171 −0.395222
\(105\) 0 0
\(106\) −856.627 −0.784934
\(107\) 750.833i 0.678372i 0.940719 + 0.339186i \(0.110152\pi\)
−0.940719 + 0.339186i \(0.889848\pi\)
\(108\) 0 0
\(109\) −401.243 −0.352589 −0.176294 0.984338i \(-0.556411\pi\)
−0.176294 + 0.984338i \(0.556411\pi\)
\(110\) −565.049 + 345.929i −0.489775 + 0.299846i
\(111\) 0 0
\(112\) 2314.86i 1.95298i
\(113\) 220.450i 0.183524i −0.995781 0.0917620i \(-0.970750\pi\)
0.995781 0.0917620i \(-0.0292499\pi\)
\(114\) 0 0
\(115\) −1554.12 + 951.449i −1.26019 + 0.771505i
\(116\) −11.7189 −0.00937997
\(117\) 0 0
\(118\) 1325.40i 1.03401i
\(119\) 193.916 0.149380
\(120\) 0 0
\(121\) −962.603 −0.723218
\(122\) 277.665i 0.206054i
\(123\) 0 0
\(124\) −344.748 −0.249671
\(125\) −1393.37 + 107.859i −0.997017 + 0.0771774i
\(126\) 0 0
\(127\) 1185.99i 0.828659i 0.910127 + 0.414329i \(0.135984\pi\)
−0.910127 + 0.414329i \(0.864016\pi\)
\(128\) 1720.65i 1.18817i
\(129\) 0 0
\(130\) −378.321 617.958i −0.255238 0.416912i
\(131\) 2770.80 1.84799 0.923993 0.382408i \(-0.124905\pi\)
0.923993 + 0.382408i \(0.124905\pi\)
\(132\) 0 0
\(133\) 3027.60i 1.97388i
\(134\) −1800.89 −1.16100
\(135\) 0 0
\(136\) −123.637 −0.0779541
\(137\) 1321.94i 0.824384i −0.911097 0.412192i \(-0.864763\pi\)
0.911097 0.412192i \(-0.135237\pi\)
\(138\) 0 0
\(139\) 1810.45 1.10475 0.552374 0.833596i \(-0.313722\pi\)
0.552374 + 0.833596i \(0.313722\pi\)
\(140\) −457.544 + 280.114i −0.276211 + 0.169100i
\(141\) 0 0
\(142\) 409.405i 0.241947i
\(143\) 402.893i 0.235606i
\(144\) 0 0
\(145\) 44.6533 + 72.9377i 0.0255742 + 0.0417734i
\(146\) 802.518 0.454910
\(147\) 0 0
\(148\) 238.863i 0.132665i
\(149\) −254.768 −0.140076 −0.0700382 0.997544i \(-0.522312\pi\)
−0.0700382 + 0.997544i \(0.522312\pi\)
\(150\) 0 0
\(151\) 2844.74 1.53313 0.766563 0.642170i \(-0.221966\pi\)
0.766563 + 0.642170i \(0.221966\pi\)
\(152\) 1930.33i 1.03007i
\(153\) 0 0
\(154\) 1856.00 0.971175
\(155\) 1313.61 + 2145.68i 0.680720 + 1.11190i
\(156\) 0 0
\(157\) 1745.14i 0.887115i −0.896246 0.443558i \(-0.853716\pi\)
0.896246 0.443558i \(-0.146284\pi\)
\(158\) 384.841i 0.193774i
\(159\) 0 0
\(160\) 652.539 399.492i 0.322423 0.197391i
\(161\) 5104.77 2.49884
\(162\) 0 0
\(163\) 2607.78i 1.25311i −0.779378 0.626554i \(-0.784465\pi\)
0.779378 0.626554i \(-0.215535\pi\)
\(164\) −482.933 −0.229943
\(165\) 0 0
\(166\) −113.369 −0.0530067
\(167\) 1223.32i 0.566847i 0.958995 + 0.283423i \(0.0914701\pi\)
−0.958995 + 0.283423i \(0.908530\pi\)
\(168\) 0 0
\(169\) 1756.38 0.799445
\(170\) −111.588 182.270i −0.0503434 0.0822321i
\(171\) 0 0
\(172\) 295.315i 0.130916i
\(173\) 2789.93i 1.22610i 0.790045 + 0.613048i \(0.210057\pi\)
−0.790045 + 0.613048i \(0.789943\pi\)
\(174\) 0 0
\(175\) 3486.81 + 1780.38i 1.50616 + 0.769054i
\(176\) −1418.59 −0.607558
\(177\) 0 0
\(178\) 1029.41i 0.433471i
\(179\) 769.584 0.321349 0.160674 0.987007i \(-0.448633\pi\)
0.160674 + 0.987007i \(0.448633\pi\)
\(180\) 0 0
\(181\) 2302.38 0.945495 0.472747 0.881198i \(-0.343262\pi\)
0.472747 + 0.881198i \(0.343262\pi\)
\(182\) 2029.79i 0.826693i
\(183\) 0 0
\(184\) −3254.69 −1.30402
\(185\) −1486.66 + 910.152i −0.590820 + 0.361707i
\(186\) 0 0
\(187\) 118.835i 0.0464711i
\(188\) 487.668i 0.189185i
\(189\) 0 0
\(190\) −2845.76 + 1742.21i −1.08660 + 0.665227i
\(191\) 4228.96 1.60208 0.801039 0.598612i \(-0.204281\pi\)
0.801039 + 0.598612i \(0.204281\pi\)
\(192\) 0 0
\(193\) 4364.09i 1.62764i −0.581119 0.813818i \(-0.697385\pi\)
0.581119 0.813818i \(-0.302615\pi\)
\(194\) 3177.69 1.17601
\(195\) 0 0
\(196\) 977.393 0.356193
\(197\) 1031.50i 0.373052i −0.982450 0.186526i \(-0.940277\pi\)
0.982450 0.186526i \(-0.0597228\pi\)
\(198\) 0 0
\(199\) −1271.59 −0.452966 −0.226483 0.974015i \(-0.572723\pi\)
−0.226483 + 0.974015i \(0.572723\pi\)
\(200\) −2223.11 1135.13i −0.785988 0.401330i
\(201\) 0 0
\(202\) 2861.90i 0.996846i
\(203\) 239.577i 0.0828324i
\(204\) 0 0
\(205\) 1840.14 + 3005.73i 0.626932 + 1.02405i
\(206\) 5210.30 1.76223
\(207\) 0 0
\(208\) 1551.42i 0.517172i
\(209\) 1855.36 0.614059
\(210\) 0 0
\(211\) 346.295 0.112986 0.0564928 0.998403i \(-0.482008\pi\)
0.0564928 + 0.998403i \(0.482008\pi\)
\(212\) 425.080i 0.137710i
\(213\) 0 0
\(214\) −2318.12 −0.740484
\(215\) −1838.01 + 1125.25i −0.583030 + 0.356938i
\(216\) 0 0
\(217\) 7047.86i 2.20479i
\(218\) 1238.80i 0.384872i
\(219\) 0 0
\(220\) −171.659 280.391i −0.0526056 0.0859271i
\(221\) −129.963 −0.0395576
\(222\) 0 0
\(223\) 4039.33i 1.21297i −0.795093 0.606487i \(-0.792578\pi\)
0.795093 0.606487i \(-0.207422\pi\)
\(224\) −2143.38 −0.639332
\(225\) 0 0
\(226\) 680.618 0.200328
\(227\) 862.451i 0.252171i 0.992019 + 0.126086i \(0.0402414\pi\)
−0.992019 + 0.126086i \(0.959759\pi\)
\(228\) 0 0
\(229\) −958.217 −0.276510 −0.138255 0.990397i \(-0.544149\pi\)
−0.138255 + 0.990397i \(0.544149\pi\)
\(230\) −2937.51 4798.19i −0.842145 1.37558i
\(231\) 0 0
\(232\) 152.749i 0.0432260i
\(233\) 1159.05i 0.325887i 0.986635 + 0.162944i \(0.0520989\pi\)
−0.986635 + 0.162944i \(0.947901\pi\)
\(234\) 0 0
\(235\) 3035.20 1858.19i 0.842531 0.515807i
\(236\) 657.694 0.181408
\(237\) 0 0
\(238\) 598.697i 0.163058i
\(239\) −4046.40 −1.09515 −0.547573 0.836758i \(-0.684448\pi\)
−0.547573 + 0.836758i \(0.684448\pi\)
\(240\) 0 0
\(241\) −2425.49 −0.648296 −0.324148 0.946006i \(-0.605078\pi\)
−0.324148 + 0.946006i \(0.605078\pi\)
\(242\) 2971.94i 0.789436i
\(243\) 0 0
\(244\) 137.784 0.0361505
\(245\) −3724.21 6083.21i −0.971147 1.58629i
\(246\) 0 0
\(247\) 2029.09i 0.522705i
\(248\) 4493.55i 1.15057i
\(249\) 0 0
\(250\) −333.003 4301.90i −0.0842438 1.08831i
\(251\) −7272.75 −1.82889 −0.914445 0.404709i \(-0.867373\pi\)
−0.914445 + 0.404709i \(0.867373\pi\)
\(252\) 0 0
\(253\) 3128.29i 0.777368i
\(254\) −3661.63 −0.904532
\(255\) 0 0
\(256\) 2272.43 0.554792
\(257\) 3234.18i 0.784990i −0.919754 0.392495i \(-0.871612\pi\)
0.919754 0.392495i \(-0.128388\pi\)
\(258\) 0 0
\(259\) 4883.20 1.17153
\(260\) 306.646 187.732i 0.0731438 0.0447795i
\(261\) 0 0
\(262\) 8554.58i 2.01719i
\(263\) 1056.62i 0.247733i 0.992299 + 0.123866i \(0.0395294\pi\)
−0.992299 + 0.123866i \(0.960471\pi\)
\(264\) 0 0
\(265\) −2645.66 + 1619.70i −0.613289 + 0.375462i
\(266\) 9347.41 2.15461
\(267\) 0 0
\(268\) 893.647i 0.203687i
\(269\) −1528.13 −0.346363 −0.173182 0.984890i \(-0.555405\pi\)
−0.173182 + 0.984890i \(0.555405\pi\)
\(270\) 0 0
\(271\) −7368.77 −1.65174 −0.825869 0.563862i \(-0.809315\pi\)
−0.825869 + 0.563862i \(0.809315\pi\)
\(272\) 457.599i 0.102008i
\(273\) 0 0
\(274\) 4081.35 0.899865
\(275\) −1091.05 + 2136.78i −0.239247 + 0.468555i
\(276\) 0 0
\(277\) 1854.32i 0.402221i 0.979569 + 0.201111i \(0.0644551\pi\)
−0.979569 + 0.201111i \(0.935545\pi\)
\(278\) 5589.57i 1.20590i
\(279\) 0 0
\(280\) 3651.10 + 5963.78i 0.779267 + 1.27287i
\(281\) −415.132 −0.0881306 −0.0440653 0.999029i \(-0.514031\pi\)
−0.0440653 + 0.999029i \(0.514031\pi\)
\(282\) 0 0
\(283\) 4116.22i 0.864607i 0.901728 + 0.432303i \(0.142299\pi\)
−0.901728 + 0.432303i \(0.857701\pi\)
\(284\) 203.157 0.0424477
\(285\) 0 0
\(286\) −1243.89 −0.257178
\(287\) 9872.84i 2.03058i
\(288\) 0 0
\(289\) 4874.67 0.992198
\(290\) −225.188 + 137.863i −0.0455982 + 0.0279158i
\(291\) 0 0
\(292\) 398.229i 0.0798103i
\(293\) 4906.20i 0.978236i −0.872218 0.489118i \(-0.837319\pi\)
0.872218 0.489118i \(-0.162681\pi\)
\(294\) 0 0
\(295\) −2506.05 4093.43i −0.494602 0.807894i
\(296\) −3113.42 −0.611364
\(297\) 0 0
\(298\) 786.570i 0.152902i
\(299\) −3421.22 −0.661720
\(300\) 0 0
\(301\) 6037.28 1.15609
\(302\) 8782.86i 1.67350i
\(303\) 0 0
\(304\) −7144.46 −1.34790
\(305\) −525.006 857.556i −0.0985631 0.160995i
\(306\) 0 0
\(307\) 6909.30i 1.28448i −0.766504 0.642239i \(-0.778006\pi\)
0.766504 0.642239i \(-0.221994\pi\)
\(308\) 920.994i 0.170385i
\(309\) 0 0
\(310\) −6624.57 + 4055.64i −1.21371 + 0.743048i
\(311\) 5373.87 0.979820 0.489910 0.871773i \(-0.337030\pi\)
0.489910 + 0.871773i \(0.337030\pi\)
\(312\) 0 0
\(313\) 2392.60i 0.432070i 0.976386 + 0.216035i \(0.0693125\pi\)
−0.976386 + 0.216035i \(0.930687\pi\)
\(314\) 5387.94 0.968340
\(315\) 0 0
\(316\) 190.968 0.0339961
\(317\) 1183.68i 0.209723i −0.994487 0.104861i \(-0.966560\pi\)
0.994487 0.104861i \(-0.0334399\pi\)
\(318\) 0 0
\(319\) 146.817 0.0257685
\(320\) −2218.24 3623.33i −0.387511 0.632969i
\(321\) 0 0
\(322\) 15760.5i 2.72763i
\(323\) 598.492i 0.103099i
\(324\) 0 0
\(325\) −2336.86 1193.21i −0.398848 0.203654i
\(326\) 8051.25 1.36784
\(327\) 0 0
\(328\) 6294.70i 1.05965i
\(329\) −9969.66 −1.67065
\(330\) 0 0
\(331\) −9386.43 −1.55868 −0.779342 0.626598i \(-0.784447\pi\)
−0.779342 + 0.626598i \(0.784447\pi\)
\(332\) 56.2563i 0.00929960i
\(333\) 0 0
\(334\) −3776.88 −0.618748
\(335\) −5561.98 + 3405.11i −0.907115 + 0.555346i
\(336\) 0 0
\(337\) 12171.6i 1.96745i −0.179685 0.983724i \(-0.557508\pi\)
0.179685 0.983724i \(-0.442492\pi\)
\(338\) 5422.65i 0.872644i
\(339\) 0 0
\(340\) 90.4468 55.3726i 0.0144270 0.00883235i
\(341\) 4319.05 0.685893
\(342\) 0 0
\(343\) 9238.47i 1.45432i
\(344\) −3849.23 −0.603304
\(345\) 0 0
\(346\) −8613.64 −1.33836
\(347\) 2785.57i 0.430943i 0.976510 + 0.215471i \(0.0691288\pi\)
−0.976510 + 0.215471i \(0.930871\pi\)
\(348\) 0 0
\(349\) 3359.76 0.515311 0.257656 0.966237i \(-0.417050\pi\)
0.257656 + 0.966237i \(0.417050\pi\)
\(350\) −5496.76 + 10765.2i −0.839469 + 1.64407i
\(351\) 0 0
\(352\) 1313.50i 0.198891i
\(353\) 5427.68i 0.818375i −0.912450 0.409188i \(-0.865812\pi\)
0.912450 0.409188i \(-0.134188\pi\)
\(354\) 0 0
\(355\) −774.100 1264.43i −0.115732 0.189040i
\(356\) −510.820 −0.0760489
\(357\) 0 0
\(358\) 2376.01i 0.350772i
\(359\) −3920.74 −0.576404 −0.288202 0.957570i \(-0.593057\pi\)
−0.288202 + 0.957570i \(0.593057\pi\)
\(360\) 0 0
\(361\) 2485.20 0.362327
\(362\) 7108.37i 1.03207i
\(363\) 0 0
\(364\) −1007.23 −0.145037
\(365\) 2478.54 1517.39i 0.355433 0.217600i
\(366\) 0 0
\(367\) 1677.21i 0.238554i −0.992861 0.119277i \(-0.961942\pi\)
0.992861 0.119277i \(-0.0380577\pi\)
\(368\) 12046.1i 1.70638i
\(369\) 0 0
\(370\) −2810.00 4589.92i −0.394825 0.644916i
\(371\) 8690.13 1.21609
\(372\) 0 0
\(373\) 956.336i 0.132754i 0.997795 + 0.0663769i \(0.0211440\pi\)
−0.997795 + 0.0663769i \(0.978856\pi\)
\(374\) −366.892 −0.0507260
\(375\) 0 0
\(376\) 6356.43 0.871829
\(377\) 160.564i 0.0219349i
\(378\) 0 0
\(379\) −10019.0 −1.35789 −0.678943 0.734191i \(-0.737562\pi\)
−0.678943 + 0.734191i \(0.737562\pi\)
\(380\) −864.527 1412.14i −0.116709 0.190635i
\(381\) 0 0
\(382\) 13056.5i 1.74877i
\(383\) 12886.2i 1.71920i −0.510967 0.859600i \(-0.670713\pi\)
0.510967 0.859600i \(-0.329287\pi\)
\(384\) 0 0
\(385\) 5732.18 3509.31i 0.758803 0.464548i
\(386\) 13473.7 1.77667
\(387\) 0 0
\(388\) 1576.85i 0.206321i
\(389\) −688.486 −0.0897369 −0.0448684 0.998993i \(-0.514287\pi\)
−0.0448684 + 0.998993i \(0.514287\pi\)
\(390\) 0 0
\(391\) −1009.11 −0.130518
\(392\) 12739.7i 1.64145i
\(393\) 0 0
\(394\) 3184.65 0.407209
\(395\) −727.654 1188.57i −0.0926892 0.151401i
\(396\) 0 0
\(397\) 7893.06i 0.997837i 0.866649 + 0.498918i \(0.166269\pi\)
−0.866649 + 0.498918i \(0.833731\pi\)
\(398\) 3925.90i 0.494441i
\(399\) 0 0
\(400\) 4201.31 8228.10i 0.525164 1.02851i
\(401\) −4192.82 −0.522144 −0.261072 0.965319i \(-0.584076\pi\)
−0.261072 + 0.965319i \(0.584076\pi\)
\(402\) 0 0
\(403\) 4723.47i 0.583853i
\(404\) 1420.15 0.174889
\(405\) 0 0
\(406\) 739.669 0.0904166
\(407\) 2992.51i 0.364455i
\(408\) 0 0
\(409\) −9010.03 −1.08928 −0.544642 0.838668i \(-0.683335\pi\)
−0.544642 + 0.838668i \(0.683335\pi\)
\(410\) −9279.89 + 5681.26i −1.11781 + 0.684335i
\(411\) 0 0
\(412\) 2585.48i 0.309169i
\(413\) 13445.6i 1.60197i
\(414\) 0 0
\(415\) −350.134 + 214.356i −0.0414155 + 0.0253550i
\(416\) 1436.49 0.169302
\(417\) 0 0
\(418\) 5728.25i 0.670283i
\(419\) 6859.80 0.799817 0.399908 0.916555i \(-0.369042\pi\)
0.399908 + 0.916555i \(0.369042\pi\)
\(420\) 0 0
\(421\) 12594.6 1.45801 0.729007 0.684507i \(-0.239982\pi\)
0.729007 + 0.684507i \(0.239982\pi\)
\(422\) 1069.15i 0.123331i
\(423\) 0 0
\(424\) −5540.63 −0.634615
\(425\) −689.268 351.944i −0.0786692 0.0401689i
\(426\) 0 0
\(427\) 2816.79i 0.319237i
\(428\) 1150.31i 0.129912i
\(429\) 0 0
\(430\) −3474.11 5674.68i −0.389619 0.636413i
\(431\) 8470.15 0.946619 0.473310 0.880896i \(-0.343059\pi\)
0.473310 + 0.880896i \(0.343059\pi\)
\(432\) 0 0
\(433\) 8182.86i 0.908183i 0.890955 + 0.454092i \(0.150036\pi\)
−0.890955 + 0.454092i \(0.849964\pi\)
\(434\) 21759.6 2.40666
\(435\) 0 0
\(436\) 614.723 0.0675227
\(437\) 15755.1i 1.72464i
\(438\) 0 0
\(439\) −8353.58 −0.908189 −0.454094 0.890954i \(-0.650037\pi\)
−0.454094 + 0.890954i \(0.650037\pi\)
\(440\) −3654.71 + 2237.46i −0.395981 + 0.242424i
\(441\) 0 0
\(442\) 401.247i 0.0431795i
\(443\) 2222.59i 0.238371i 0.992872 + 0.119186i \(0.0380284\pi\)
−0.992872 + 0.119186i \(0.961972\pi\)
\(444\) 0 0
\(445\) 1946.40 + 3179.30i 0.207345 + 0.338681i
\(446\) 12471.0 1.32404
\(447\) 0 0
\(448\) 11901.5i 1.25511i
\(449\) −5455.02 −0.573360 −0.286680 0.958026i \(-0.592552\pi\)
−0.286680 + 0.958026i \(0.592552\pi\)
\(450\) 0 0
\(451\) 6050.25 0.631697
\(452\) 337.739i 0.0351459i
\(453\) 0 0
\(454\) −2662.73 −0.275260
\(455\) 3837.91 + 6268.93i 0.395437 + 0.645916i
\(456\) 0 0
\(457\) 6974.13i 0.713865i −0.934130 0.356932i \(-0.883823\pi\)
0.934130 0.356932i \(-0.116177\pi\)
\(458\) 2958.40i 0.301827i
\(459\) 0 0
\(460\) 2380.98 1457.66i 0.241334 0.147748i
\(461\) −5623.10 −0.568099 −0.284050 0.958810i \(-0.591678\pi\)
−0.284050 + 0.958810i \(0.591678\pi\)
\(462\) 0 0
\(463\) 2881.60i 0.289242i 0.989487 + 0.144621i \(0.0461963\pi\)
−0.989487 + 0.144621i \(0.953804\pi\)
\(464\) −565.348 −0.0565638
\(465\) 0 0
\(466\) −3578.45 −0.355726
\(467\) 16877.2i 1.67234i 0.548468 + 0.836172i \(0.315211\pi\)
−0.548468 + 0.836172i \(0.684789\pi\)
\(468\) 0 0
\(469\) 18269.3 1.79872
\(470\) 5736.97 + 9370.89i 0.563035 + 0.919675i
\(471\) 0 0
\(472\) 8572.61i 0.835988i
\(473\) 3699.75i 0.359650i
\(474\) 0 0
\(475\) −5494.87 + 10761.5i −0.530783 + 1.03952i
\(476\) −297.088 −0.0286072
\(477\) 0 0
\(478\) 12492.9i 1.19542i
\(479\) −19088.2 −1.82079 −0.910397 0.413736i \(-0.864224\pi\)
−0.910397 + 0.413736i \(0.864224\pi\)
\(480\) 0 0
\(481\) −3272.72 −0.310235
\(482\) 7488.45i 0.707655i
\(483\) 0 0
\(484\) 1474.75 0.138500
\(485\) 9814.18 6008.35i 0.918843 0.562526i
\(486\) 0 0
\(487\) 12553.6i 1.16809i −0.811722 0.584044i \(-0.801470\pi\)
0.811722 0.584044i \(-0.198530\pi\)
\(488\) 1795.92i 0.166593i
\(489\) 0 0
\(490\) 18781.3 11498.1i 1.73154 1.06007i
\(491\) −1569.32 −0.144241 −0.0721205 0.997396i \(-0.522977\pi\)
−0.0721205 + 0.997396i \(0.522977\pi\)
\(492\) 0 0
\(493\) 47.3592i 0.00432647i
\(494\) −6264.63 −0.570565
\(495\) 0 0
\(496\) −16631.4 −1.50559
\(497\) 4153.25i 0.374846i
\(498\) 0 0
\(499\) 10714.7 0.961232 0.480616 0.876931i \(-0.340413\pi\)
0.480616 + 0.876931i \(0.340413\pi\)
\(500\) 2134.71 165.244i 0.190934 0.0147799i
\(501\) 0 0
\(502\) 22453.9i 1.99635i
\(503\) 19016.8i 1.68572i −0.538130 0.842862i \(-0.680869\pi\)
0.538130 0.842862i \(-0.319131\pi\)
\(504\) 0 0
\(505\) −5411.26 8838.87i −0.476827 0.778861i
\(506\) −9658.30 −0.848545
\(507\) 0 0
\(508\) 1816.99i 0.158693i
\(509\) 16411.5 1.42913 0.714563 0.699571i \(-0.246625\pi\)
0.714563 + 0.699571i \(0.246625\pi\)
\(510\) 0 0
\(511\) −8141.21 −0.704786
\(512\) 6749.35i 0.582582i
\(513\) 0 0
\(514\) 9985.20 0.856865
\(515\) 16091.8 9851.58i 1.37687 0.842937i
\(516\) 0 0
\(517\) 6109.58i 0.519727i
\(518\) 15076.4i 1.27880i
\(519\) 0 0
\(520\) −2446.96 3996.93i −0.206359 0.337071i
\(521\) 9319.21 0.783651 0.391826 0.920040i \(-0.371844\pi\)
0.391826 + 0.920040i \(0.371844\pi\)
\(522\) 0 0
\(523\) 19719.6i 1.64871i 0.566071 + 0.824357i \(0.308463\pi\)
−0.566071 + 0.824357i \(0.691537\pi\)
\(524\) −4244.99 −0.353900
\(525\) 0 0
\(526\) −3262.19 −0.270415
\(527\) 1393.21i 0.115160i
\(528\) 0 0
\(529\) −14397.3 −1.18331
\(530\) −5000.67 8168.21i −0.409840 0.669442i
\(531\) 0 0
\(532\) 4638.41i 0.378009i
\(533\) 6616.78i 0.537719i
\(534\) 0 0
\(535\) −7159.42 + 4383.08i −0.578559 + 0.354200i
\(536\) −11648.1 −0.938658
\(537\) 0 0
\(538\) 4717.95i 0.378077i
\(539\) −12244.9 −0.978527
\(540\) 0 0
\(541\) 16592.1 1.31857 0.659287 0.751891i \(-0.270858\pi\)
0.659287 + 0.751891i \(0.270858\pi\)
\(542\) 22750.4i 1.80297i
\(543\) 0 0
\(544\) 423.700 0.0333934
\(545\) −2342.31 3825.98i −0.184098 0.300710i
\(546\) 0 0
\(547\) 12264.5i 0.958667i −0.877633 0.479333i \(-0.840878\pi\)
0.877633 0.479333i \(-0.159122\pi\)
\(548\) 2025.26i 0.157874i
\(549\) 0 0
\(550\) −6597.09 3368.51i −0.511456 0.261152i
\(551\) 739.415 0.0571690
\(552\) 0 0
\(553\) 3904.05i 0.300212i
\(554\) −5725.03 −0.439049
\(555\) 0 0
\(556\) −2773.68 −0.211565
\(557\) 1623.54i 0.123504i 0.998092 + 0.0617518i \(0.0196687\pi\)
−0.998092 + 0.0617518i \(0.980331\pi\)
\(558\) 0 0
\(559\) −4046.18 −0.306145
\(560\) −22072.9 + 13513.3i −1.66563 + 1.01972i
\(561\) 0 0
\(562\) 1281.68i 0.0961999i
\(563\) 6842.29i 0.512199i −0.966650 0.256100i \(-0.917562\pi\)
0.966650 0.256100i \(-0.0824375\pi\)
\(564\) 0 0
\(565\) 2102.06 1286.91i 0.156521 0.0958240i
\(566\) −12708.4 −0.943771
\(567\) 0 0
\(568\) 2648.02i 0.195613i
\(569\) −9076.58 −0.668735 −0.334367 0.942443i \(-0.608523\pi\)
−0.334367 + 0.942443i \(0.608523\pi\)
\(570\) 0 0
\(571\) −5501.59 −0.403213 −0.201606 0.979467i \(-0.564616\pi\)
−0.201606 + 0.979467i \(0.564616\pi\)
\(572\) 617.250i 0.0451198i
\(573\) 0 0
\(574\) 30481.4 2.21650
\(575\) −18144.7 9264.80i −1.31598 0.671946i
\(576\) 0 0
\(577\) 13600.1i 0.981245i −0.871372 0.490622i \(-0.836769\pi\)
0.871372 0.490622i \(-0.163231\pi\)
\(578\) 15050.1i 1.08304i
\(579\) 0 0
\(580\) −68.4108 111.744i −0.00489759 0.00799984i
\(581\) 1150.08 0.0821226
\(582\) 0 0
\(583\) 5325.46i 0.378316i
\(584\) 5190.65 0.367792
\(585\) 0 0
\(586\) 15147.4 1.06780
\(587\) 21216.1i 1.49179i −0.666062 0.745896i \(-0.732021\pi\)
0.666062 0.745896i \(-0.267979\pi\)
\(588\) 0 0
\(589\) 21752.1 1.52170
\(590\) 12638.1 7737.17i 0.881866 0.539889i
\(591\) 0 0
\(592\) 11523.3i 0.800007i
\(593\) 14973.6i 1.03692i 0.855103 + 0.518458i \(0.173494\pi\)
−0.855103 + 0.518458i \(0.826506\pi\)
\(594\) 0 0
\(595\) 1132.01 + 1849.05i 0.0779965 + 0.127401i
\(596\) 390.315 0.0268254
\(597\) 0 0
\(598\) 10562.7i 0.722307i
\(599\) −17904.8 −1.22132 −0.610659 0.791894i \(-0.709095\pi\)
−0.610659 + 0.791894i \(0.709095\pi\)
\(600\) 0 0
\(601\) 16455.0 1.11683 0.558414 0.829562i \(-0.311410\pi\)
0.558414 + 0.829562i \(0.311410\pi\)
\(602\) 18639.5i 1.26194i
\(603\) 0 0
\(604\) −4358.27 −0.293602
\(605\) −5619.31 9178.71i −0.377616 0.616806i
\(606\) 0 0
\(607\) 5457.49i 0.364930i 0.983212 + 0.182465i \(0.0584077\pi\)
−0.983212 + 0.182465i \(0.941592\pi\)
\(608\) 6615.19i 0.441253i
\(609\) 0 0
\(610\) 2647.62 1620.90i 0.175736 0.107588i
\(611\) 6681.66 0.442408
\(612\) 0 0
\(613\) 10945.3i 0.721167i −0.932727 0.360584i \(-0.882578\pi\)
0.932727 0.360584i \(-0.117422\pi\)
\(614\) 21331.8 1.40209
\(615\) 0 0
\(616\) 12004.5 0.785189
\(617\) 25534.0i 1.66606i −0.553225 0.833032i \(-0.686603\pi\)
0.553225 0.833032i \(-0.313397\pi\)
\(618\) 0 0
\(619\) 7895.81 0.512697 0.256349 0.966584i \(-0.417480\pi\)
0.256349 + 0.966584i \(0.417480\pi\)
\(620\) −2012.51 3287.27i −0.130362 0.212936i
\(621\) 0 0
\(622\) 16591.3i 1.06953i
\(623\) 10443.0i 0.671570i
\(624\) 0 0
\(625\) −9162.46 12656.6i −0.586398 0.810023i
\(626\) −7386.93 −0.471631
\(627\) 0 0
\(628\) 2673.63i 0.169887i
\(629\) −965.305 −0.0611912
\(630\) 0 0
\(631\) −5659.61 −0.357061 −0.178531 0.983934i \(-0.557134\pi\)
−0.178531 + 0.983934i \(0.557134\pi\)
\(632\) 2489.14i 0.156665i
\(633\) 0 0
\(634\) 3654.50 0.228925
\(635\) −11308.8 + 6923.37i −0.706733 + 0.432670i
\(636\) 0 0
\(637\) 13391.5i 0.832952i
\(638\) 453.282i 0.0281279i
\(639\) 0 0
\(640\) 16407.0 10044.5i 1.01335 0.620383i
\(641\) 16082.9 0.991010 0.495505 0.868605i \(-0.334983\pi\)
0.495505 + 0.868605i \(0.334983\pi\)
\(642\) 0 0
\(643\) 66.7491i 0.00409382i −0.999998 0.00204691i \(-0.999348\pi\)
0.999998 0.00204691i \(-0.000651552\pi\)
\(644\) −7820.74 −0.478541
\(645\) 0 0
\(646\) −1847.78 −0.112539
\(647\) 1263.42i 0.0767697i 0.999263 + 0.0383849i \(0.0122213\pi\)
−0.999263 + 0.0383849i \(0.987779\pi\)
\(648\) 0 0
\(649\) −8239.69 −0.498361
\(650\) 3683.93 7214.82i 0.222301 0.435367i
\(651\) 0 0
\(652\) 3995.23i 0.239977i
\(653\) 21867.4i 1.31047i 0.755425 + 0.655235i \(0.227430\pi\)
−0.755425 + 0.655235i \(0.772570\pi\)
\(654\) 0 0
\(655\) 16174.9 + 26420.5i 0.964895 + 1.57608i
\(656\) −23297.7 −1.38662
\(657\) 0 0
\(658\) 30780.3i 1.82362i
\(659\) 362.493 0.0214275 0.0107138 0.999943i \(-0.496590\pi\)
0.0107138 + 0.999943i \(0.496590\pi\)
\(660\) 0 0
\(661\) −398.741 −0.0234633 −0.0117316 0.999931i \(-0.503734\pi\)
−0.0117316 + 0.999931i \(0.503734\pi\)
\(662\) 28979.7i 1.70140i
\(663\) 0 0
\(664\) −733.263 −0.0428556
\(665\) 28869.1 17674.0i 1.68345 1.03063i
\(666\) 0 0
\(667\) 1246.71i 0.0723732i
\(668\) 1874.18i 0.108554i
\(669\) 0 0
\(670\) −10512.9 17172.1i −0.606194 0.990171i
\(671\) −1726.18 −0.0993121
\(672\) 0 0
\(673\) 3104.18i 0.177797i 0.996041 + 0.0888986i \(0.0283347\pi\)
−0.996041 + 0.0888986i \(0.971665\pi\)
\(674\) 37578.7 2.14759
\(675\) 0 0
\(676\) −2690.85 −0.153098
\(677\) 24565.4i 1.39457i 0.716794 + 0.697285i \(0.245609\pi\)
−0.716794 + 0.697285i \(0.754391\pi\)
\(678\) 0 0
\(679\) −32236.4 −1.82197
\(680\) −721.744 1178.91i −0.0407024 0.0664842i
\(681\) 0 0
\(682\) 13334.6i 0.748694i
\(683\) 8921.93i 0.499836i −0.968267 0.249918i \(-0.919596\pi\)
0.968267 0.249918i \(-0.0804037\pi\)
\(684\) 0 0
\(685\) 12605.1 7716.97i 0.703087 0.430438i
\(686\) −28522.9 −1.58747
\(687\) 0 0
\(688\) 14246.6i 0.789459i
\(689\) −5824.12 −0.322034
\(690\) 0 0
\(691\) −6688.21 −0.368207 −0.184104 0.982907i \(-0.558938\pi\)
−0.184104 + 0.982907i \(0.558938\pi\)
\(692\) 4274.30i 0.234804i
\(693\) 0 0
\(694\) −8600.17 −0.470400
\(695\) 10568.7 + 17263.2i 0.576825 + 0.942200i
\(696\) 0 0
\(697\) 1951.65i 0.106060i
\(698\) 10372.9i 0.562494i
\(699\) 0 0
\(700\) −5341.95 2727.63i −0.288438 0.147278i
\(701\) −33422.0 −1.80076 −0.900380 0.435105i \(-0.856711\pi\)
−0.900380 + 0.435105i \(0.856711\pi\)
\(702\) 0 0
\(703\) 15071.2i 0.808567i
\(704\) −7293.42 −0.390456
\(705\) 0 0
\(706\) 16757.4 0.893306
\(707\) 29032.8i 1.54440i
\(708\) 0 0
\(709\) −29293.5 −1.55168 −0.775840 0.630929i \(-0.782674\pi\)
−0.775840 + 0.630929i \(0.782674\pi\)
\(710\) 3903.81 2389.96i 0.206348 0.126329i
\(711\) 0 0
\(712\) 6658.20i 0.350459i
\(713\) 36675.8i 1.92639i
\(714\) 0 0
\(715\) −3841.71 + 2351.94i −0.200939 + 0.123017i
\(716\) −1179.04 −0.0615401
\(717\) 0 0
\(718\) 12104.9i 0.629180i
\(719\) 29311.2 1.52034 0.760169 0.649725i \(-0.225116\pi\)
0.760169 + 0.649725i \(0.225116\pi\)
\(720\) 0 0
\(721\) −52856.3 −2.73020
\(722\) 7672.81i 0.395502i
\(723\) 0 0
\(724\) −3527.35 −0.181067
\(725\) −434.814 + 851.566i −0.0222739 + 0.0436226i
\(726\) 0 0
\(727\) 4931.68i 0.251590i 0.992056 + 0.125795i \(0.0401481\pi\)
−0.992056 + 0.125795i \(0.959852\pi\)
\(728\) 13128.6i 0.668377i
\(729\) 0 0
\(730\) 4684.80 + 7652.26i 0.237524 + 0.387976i
\(731\) −1193.44 −0.0603844
\(732\) 0 0
\(733\) 8225.55i 0.414485i −0.978290 0.207243i \(-0.933551\pi\)
0.978290 0.207243i \(-0.0664489\pi\)
\(734\) 5178.21 0.260397
\(735\) 0 0
\(736\) 11153.8 0.558604
\(737\) 11195.7i 0.559566i
\(738\) 0 0
\(739\) −17847.1 −0.888382 −0.444191 0.895932i \(-0.646509\pi\)
−0.444191 + 0.895932i \(0.646509\pi\)
\(740\) 2277.63 1394.39i 0.113145 0.0692688i
\(741\) 0 0
\(742\) 26829.9i 1.32743i
\(743\) 23810.6i 1.17568i −0.808979 0.587838i \(-0.799979\pi\)
0.808979 0.587838i \(-0.200021\pi\)
\(744\) 0 0
\(745\) −1487.24 2429.29i −0.0731385 0.119466i
\(746\) −2952.59 −0.144909
\(747\) 0 0
\(748\) 182.061i 0.00889947i
\(749\) 23516.4 1.14722
\(750\) 0 0
\(751\) 21295.8 1.03475 0.517374 0.855759i \(-0.326909\pi\)
0.517374 + 0.855759i \(0.326909\pi\)
\(752\) 23526.2i 1.14084i
\(753\) 0 0
\(754\) −495.726 −0.0239433
\(755\) 16606.5 + 27125.5i 0.800495 + 1.30755i
\(756\) 0 0
\(757\) 13423.0i 0.644472i 0.946659 + 0.322236i \(0.104435\pi\)
−0.946659 + 0.322236i \(0.895565\pi\)
\(758\) 30932.5i 1.48222i
\(759\) 0 0
\(760\) −18406.3 + 11268.5i −0.878508 + 0.537832i
\(761\) 24100.2 1.14801 0.574003 0.818853i \(-0.305390\pi\)
0.574003 + 0.818853i \(0.305390\pi\)
\(762\) 0 0
\(763\) 12567.1i 0.596277i
\(764\) −6478.96 −0.306807
\(765\) 0 0
\(766\) 39784.8 1.87661
\(767\) 9011.23i 0.424220i
\(768\) 0 0
\(769\) 986.759 0.0462724 0.0231362 0.999732i \(-0.492635\pi\)
0.0231362 + 0.999732i \(0.492635\pi\)
\(770\) 10834.6 + 17697.6i 0.507082 + 0.828280i
\(771\) 0 0
\(772\) 6685.98i 0.311701i
\(773\) 7277.05i 0.338599i −0.985565 0.169300i \(-0.945849\pi\)
0.985565 0.169300i \(-0.0541505\pi\)
\(774\) 0 0
\(775\) −12791.4 + 25051.3i −0.592876 + 1.16112i
\(776\) 20553.2 0.950794
\(777\) 0 0
\(778\) 2125.63i 0.0979533i
\(779\) 30471.0 1.40146
\(780\) 0 0
\(781\) −2545.18 −0.116612
\(782\) 3115.51i 0.142469i
\(783\) 0 0
\(784\) 47151.6 2.14794
\(785\) 16640.4 10187.5i 0.756588 0.463192i
\(786\) 0 0
\(787\) 4939.44i 0.223726i 0.993724 + 0.111863i \(0.0356817\pi\)
−0.993724 + 0.111863i \(0.964318\pi\)
\(788\) 1580.30i 0.0714415i
\(789\) 0 0
\(790\) 3669.58 2246.56i 0.165263 0.101176i
\(791\) −6904.59 −0.310365
\(792\) 0 0
\(793\) 1887.81i 0.0845375i
\(794\) −24369.0 −1.08920