Properties

Label 384.3.l.a.223.6
Level $384$
Weight $3$
Character 384.223
Analytic conductor $10.463$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 223.6
Root \(-1.96679 + 0.362960i\) of defining polynomial
Character \(\chi\) \(=\) 384.223
Dual form 384.3.l.a.31.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{3} +(-1.69930 + 1.69930i) q^{5} -5.74280 q^{7} -3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{3} +(-1.69930 + 1.69930i) q^{5} -5.74280 q^{7} -3.00000i q^{9} +(5.59560 + 5.59560i) q^{11} +(13.5782 + 13.5782i) q^{13} +4.16243i q^{15} +19.7023 q^{17} +(21.6943 - 21.6943i) q^{19} +(-7.03347 + 7.03347i) q^{21} +24.9257 q^{23} +19.2247i q^{25} +(-3.67423 - 3.67423i) q^{27} +(-1.50581 - 1.50581i) q^{29} -2.20037i q^{31} +13.7064 q^{33} +(9.75877 - 9.75877i) q^{35} +(-27.6956 + 27.6956i) q^{37} +33.2596 q^{39} +51.3127i q^{41} +(-21.4400 - 21.4400i) q^{43} +(5.09791 + 5.09791i) q^{45} -76.5216i q^{47} -16.0202 q^{49} +(24.1303 - 24.1303i) q^{51} +(56.5145 - 56.5145i) q^{53} -19.0173 q^{55} -53.1400i q^{57} +(48.0041 + 48.0041i) q^{59} +(51.5587 + 51.5587i) q^{61} +17.2284i q^{63} -46.1469 q^{65} +(-63.4445 + 63.4445i) q^{67} +(30.5276 - 30.5276i) q^{69} +43.4856 q^{71} +73.9992i q^{73} +(23.5454 + 23.5454i) q^{75} +(-32.1344 - 32.1344i) q^{77} -4.12659i q^{79} -9.00000 q^{81} +(-38.4428 + 38.4428i) q^{83} +(-33.4803 + 33.4803i) q^{85} -3.68846 q^{87} -52.9839i q^{89} +(-77.9767 - 77.9767i) q^{91} +(-2.69489 - 2.69489i) q^{93} +73.7305i q^{95} +23.1008 q^{97} +(16.7868 - 16.7868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} - 128q^{23} - 32q^{29} - 96q^{35} + 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} + 160q^{53} - 256q^{55} + 128q^{59} + 32q^{61} - 32q^{65} - 320q^{67} - 96q^{69} + 512q^{71} - 192q^{75} - 224q^{77} - 144q^{81} + 160q^{83} - 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 0 0
\(5\) −1.69930 + 1.69930i −0.339861 + 0.339861i −0.856315 0.516454i \(-0.827252\pi\)
0.516454 + 0.856315i \(0.327252\pi\)
\(6\) 0 0
\(7\) −5.74280 −0.820400 −0.410200 0.911996i \(-0.634541\pi\)
−0.410200 + 0.911996i \(0.634541\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 5.59560 + 5.59560i 0.508691 + 0.508691i 0.914125 0.405434i \(-0.132879\pi\)
−0.405434 + 0.914125i \(0.632879\pi\)
\(12\) 0 0
\(13\) 13.5782 + 13.5782i 1.04447 + 1.04447i 0.998964 + 0.0455110i \(0.0144916\pi\)
0.0455110 + 0.998964i \(0.485508\pi\)
\(14\) 0 0
\(15\) 4.16243i 0.277495i
\(16\) 0 0
\(17\) 19.7023 1.15896 0.579481 0.814986i \(-0.303255\pi\)
0.579481 + 0.814986i \(0.303255\pi\)
\(18\) 0 0
\(19\) 21.6943 21.6943i 1.14181 1.14181i 0.153687 0.988120i \(-0.450885\pi\)
0.988120 0.153687i \(-0.0491147\pi\)
\(20\) 0 0
\(21\) −7.03347 + 7.03347i −0.334927 + 0.334927i
\(22\) 0 0
\(23\) 24.9257 1.08373 0.541863 0.840467i \(-0.317719\pi\)
0.541863 + 0.840467i \(0.317719\pi\)
\(24\) 0 0
\(25\) 19.2247i 0.768989i
\(26\) 0 0
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 0 0
\(29\) −1.50581 1.50581i −0.0519245 0.0519245i 0.680668 0.732592i \(-0.261690\pi\)
−0.732592 + 0.680668i \(0.761690\pi\)
\(30\) 0 0
\(31\) 2.20037i 0.0709796i −0.999370 0.0354898i \(-0.988701\pi\)
0.999370 0.0354898i \(-0.0112991\pi\)
\(32\) 0 0
\(33\) 13.7064 0.415344
\(34\) 0 0
\(35\) 9.75877 9.75877i 0.278822 0.278822i
\(36\) 0 0
\(37\) −27.6956 + 27.6956i −0.748530 + 0.748530i −0.974203 0.225673i \(-0.927542\pi\)
0.225673 + 0.974203i \(0.427542\pi\)
\(38\) 0 0
\(39\) 33.2596 0.852810
\(40\) 0 0
\(41\) 51.3127i 1.25153i 0.780012 + 0.625764i \(0.215213\pi\)
−0.780012 + 0.625764i \(0.784787\pi\)
\(42\) 0 0
\(43\) −21.4400 21.4400i −0.498606 0.498606i 0.412398 0.911004i \(-0.364691\pi\)
−0.911004 + 0.412398i \(0.864691\pi\)
\(44\) 0 0
\(45\) 5.09791 + 5.09791i 0.113287 + 0.113287i
\(46\) 0 0
\(47\) 76.5216i 1.62812i −0.580781 0.814060i \(-0.697253\pi\)
0.580781 0.814060i \(-0.302747\pi\)
\(48\) 0 0
\(49\) −16.0202 −0.326944
\(50\) 0 0
\(51\) 24.1303 24.1303i 0.473144 0.473144i
\(52\) 0 0
\(53\) 56.5145 56.5145i 1.06631 1.06631i 0.0686712 0.997639i \(-0.478124\pi\)
0.997639 0.0686712i \(-0.0218759\pi\)
\(54\) 0 0
\(55\) −19.0173 −0.345768
\(56\) 0 0
\(57\) 53.1400i 0.932281i
\(58\) 0 0
\(59\) 48.0041 + 48.0041i 0.813628 + 0.813628i 0.985176 0.171547i \(-0.0548767\pi\)
−0.171547 + 0.985176i \(0.554877\pi\)
\(60\) 0 0
\(61\) 51.5587 + 51.5587i 0.845224 + 0.845224i 0.989533 0.144308i \(-0.0460957\pi\)
−0.144308 + 0.989533i \(0.546096\pi\)
\(62\) 0 0
\(63\) 17.2284i 0.273467i
\(64\) 0 0
\(65\) −46.1469 −0.709952
\(66\) 0 0
\(67\) −63.4445 + 63.4445i −0.946934 + 0.946934i −0.998661 0.0517277i \(-0.983527\pi\)
0.0517277 + 0.998661i \(0.483527\pi\)
\(68\) 0 0
\(69\) 30.5276 30.5276i 0.442429 0.442429i
\(70\) 0 0
\(71\) 43.4856 0.612473 0.306237 0.951955i \(-0.400930\pi\)
0.306237 + 0.951955i \(0.400930\pi\)
\(72\) 0 0
\(73\) 73.9992i 1.01369i 0.862038 + 0.506844i \(0.169188\pi\)
−0.862038 + 0.506844i \(0.830812\pi\)
\(74\) 0 0
\(75\) 23.5454 + 23.5454i 0.313939 + 0.313939i
\(76\) 0 0
\(77\) −32.1344 32.1344i −0.417330 0.417330i
\(78\) 0 0
\(79\) 4.12659i 0.0522354i −0.999659 0.0261177i \(-0.991686\pi\)
0.999659 0.0261177i \(-0.00831446\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −38.4428 + 38.4428i −0.463166 + 0.463166i −0.899692 0.436526i \(-0.856209\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(84\) 0 0
\(85\) −33.4803 + 33.4803i −0.393886 + 0.393886i
\(86\) 0 0
\(87\) −3.68846 −0.0423961
\(88\) 0 0
\(89\) 52.9839i 0.595325i −0.954671 0.297662i \(-0.903793\pi\)
0.954671 0.297662i \(-0.0962070\pi\)
\(90\) 0 0
\(91\) −77.9767 77.9767i −0.856887 0.856887i
\(92\) 0 0
\(93\) −2.69489 2.69489i −0.0289773 0.0289773i
\(94\) 0 0
\(95\) 73.7305i 0.776111i
\(96\) 0 0
\(97\) 23.1008 0.238153 0.119077 0.992885i \(-0.462007\pi\)
0.119077 + 0.992885i \(0.462007\pi\)
\(98\) 0 0
\(99\) 16.7868 16.7868i 0.169564 0.169564i
\(100\) 0 0
\(101\) −16.1216 + 16.1216i −0.159619 + 0.159619i −0.782398 0.622779i \(-0.786004\pi\)
0.622779 + 0.782398i \(0.286004\pi\)
\(102\) 0 0
\(103\) −98.8380 −0.959592 −0.479796 0.877380i \(-0.659289\pi\)
−0.479796 + 0.877380i \(0.659289\pi\)
\(104\) 0 0
\(105\) 23.9040i 0.227657i
\(106\) 0 0
\(107\) −15.6655 15.6655i −0.146406 0.146406i 0.630104 0.776511i \(-0.283012\pi\)
−0.776511 + 0.630104i \(0.783012\pi\)
\(108\) 0 0
\(109\) −84.6938 84.6938i −0.777008 0.777008i 0.202313 0.979321i \(-0.435154\pi\)
−0.979321 + 0.202313i \(0.935154\pi\)
\(110\) 0 0
\(111\) 67.8401i 0.611172i
\(112\) 0 0
\(113\) 63.8537 0.565077 0.282538 0.959256i \(-0.408824\pi\)
0.282538 + 0.959256i \(0.408824\pi\)
\(114\) 0 0
\(115\) −42.3563 + 42.3563i −0.368316 + 0.368316i
\(116\) 0 0
\(117\) 40.7345 40.7345i 0.348158 0.348158i
\(118\) 0 0
\(119\) −113.147 −0.950812
\(120\) 0 0
\(121\) 58.3785i 0.482467i
\(122\) 0 0
\(123\) 62.8449 + 62.8449i 0.510934 + 0.510934i
\(124\) 0 0
\(125\) −75.1513 75.1513i −0.601210 0.601210i
\(126\) 0 0
\(127\) 36.8901i 0.290473i 0.989397 + 0.145237i \(0.0463944\pi\)
−0.989397 + 0.145237i \(0.953606\pi\)
\(128\) 0 0
\(129\) −52.5172 −0.407110
\(130\) 0 0
\(131\) 40.4136 40.4136i 0.308500 0.308500i −0.535827 0.844328i \(-0.680000\pi\)
0.844328 + 0.535827i \(0.180000\pi\)
\(132\) 0 0
\(133\) −124.586 + 124.586i −0.936738 + 0.936738i
\(134\) 0 0
\(135\) 12.4873 0.0924984
\(136\) 0 0
\(137\) 253.499i 1.85036i −0.379531 0.925179i \(-0.623915\pi\)
0.379531 0.925179i \(-0.376085\pi\)
\(138\) 0 0
\(139\) −67.8065 67.8065i −0.487816 0.487816i 0.419800 0.907617i \(-0.362100\pi\)
−0.907617 + 0.419800i \(0.862100\pi\)
\(140\) 0 0
\(141\) −93.7194 93.7194i −0.664677 0.664677i
\(142\) 0 0
\(143\) 151.956i 1.06263i
\(144\) 0 0
\(145\) 5.11766 0.0352942
\(146\) 0 0
\(147\) −19.6207 + 19.6207i −0.133474 + 0.133474i
\(148\) 0 0
\(149\) 43.9337 43.9337i 0.294857 0.294857i −0.544138 0.838996i \(-0.683143\pi\)
0.838996 + 0.544138i \(0.183143\pi\)
\(150\) 0 0
\(151\) −223.084 −1.47738 −0.738688 0.674047i \(-0.764554\pi\)
−0.738688 + 0.674047i \(0.764554\pi\)
\(152\) 0 0
\(153\) 59.1070i 0.386320i
\(154\) 0 0
\(155\) 3.73909 + 3.73909i 0.0241232 + 0.0241232i
\(156\) 0 0
\(157\) 78.8526 + 78.8526i 0.502246 + 0.502246i 0.912135 0.409889i \(-0.134433\pi\)
−0.409889 + 0.912135i \(0.634433\pi\)
\(158\) 0 0
\(159\) 138.432i 0.870639i
\(160\) 0 0
\(161\) −143.143 −0.889089
\(162\) 0 0
\(163\) −52.2425 + 52.2425i −0.320506 + 0.320506i −0.848961 0.528455i \(-0.822772\pi\)
0.528455 + 0.848961i \(0.322772\pi\)
\(164\) 0 0
\(165\) −23.2913 + 23.2913i −0.141159 + 0.141159i
\(166\) 0 0
\(167\) 96.5201 0.577965 0.288982 0.957334i \(-0.406683\pi\)
0.288982 + 0.957334i \(0.406683\pi\)
\(168\) 0 0
\(169\) 199.734i 1.18186i
\(170\) 0 0
\(171\) −65.0830 65.0830i −0.380602 0.380602i
\(172\) 0 0
\(173\) 46.3076 + 46.3076i 0.267674 + 0.267674i 0.828162 0.560488i \(-0.189386\pi\)
−0.560488 + 0.828162i \(0.689386\pi\)
\(174\) 0 0
\(175\) 110.404i 0.630879i
\(176\) 0 0
\(177\) 117.585 0.664325
\(178\) 0 0
\(179\) 93.5440 93.5440i 0.522592 0.522592i −0.395761 0.918353i \(-0.629519\pi\)
0.918353 + 0.395761i \(0.129519\pi\)
\(180\) 0 0
\(181\) 115.810 115.810i 0.639836 0.639836i −0.310679 0.950515i \(-0.600556\pi\)
0.950515 + 0.310679i \(0.100556\pi\)
\(182\) 0 0
\(183\) 126.292 0.690123
\(184\) 0 0
\(185\) 94.1266i 0.508792i
\(186\) 0 0
\(187\) 110.246 + 110.246i 0.589553 + 0.589553i
\(188\) 0 0
\(189\) 21.1004 + 21.1004i 0.111642 + 0.111642i
\(190\) 0 0
\(191\) 35.2964i 0.184798i 0.995722 + 0.0923991i \(0.0294535\pi\)
−0.995722 + 0.0923991i \(0.970546\pi\)
\(192\) 0 0
\(193\) −364.339 −1.88777 −0.943884 0.330277i \(-0.892858\pi\)
−0.943884 + 0.330277i \(0.892858\pi\)
\(194\) 0 0
\(195\) −56.5182 + 56.5182i −0.289837 + 0.289837i
\(196\) 0 0
\(197\) −130.582 + 130.582i −0.662851 + 0.662851i −0.956051 0.293200i \(-0.905280\pi\)
0.293200 + 0.956051i \(0.405280\pi\)
\(198\) 0 0
\(199\) −12.7493 −0.0640670 −0.0320335 0.999487i \(-0.510198\pi\)
−0.0320335 + 0.999487i \(0.510198\pi\)
\(200\) 0 0
\(201\) 155.407i 0.773168i
\(202\) 0 0
\(203\) 8.64756 + 8.64756i 0.0425988 + 0.0425988i
\(204\) 0 0
\(205\) −87.1958 87.1958i −0.425346 0.425346i
\(206\) 0 0
\(207\) 74.7771i 0.361242i
\(208\) 0 0
\(209\) 242.786 1.16165
\(210\) 0 0
\(211\) −8.59499 + 8.59499i −0.0407345 + 0.0407345i −0.727181 0.686446i \(-0.759170\pi\)
0.686446 + 0.727181i \(0.259170\pi\)
\(212\) 0 0
\(213\) 53.2588 53.2588i 0.250041 0.250041i
\(214\) 0 0
\(215\) 72.8663 0.338913
\(216\) 0 0
\(217\) 12.6363i 0.0582317i
\(218\) 0 0
\(219\) 90.6302 + 90.6302i 0.413837 + 0.413837i
\(220\) 0 0
\(221\) 267.522 + 267.522i 1.21051 + 1.21051i
\(222\) 0 0
\(223\) 50.5909i 0.226865i −0.993546 0.113433i \(-0.963815\pi\)
0.993546 0.113433i \(-0.0361846\pi\)
\(224\) 0 0
\(225\) 57.6742 0.256330
\(226\) 0 0
\(227\) −31.7175 + 31.7175i −0.139725 + 0.139725i −0.773509 0.633785i \(-0.781501\pi\)
0.633785 + 0.773509i \(0.281501\pi\)
\(228\) 0 0
\(229\) 169.826 169.826i 0.741599 0.741599i −0.231287 0.972886i \(-0.574294\pi\)
0.972886 + 0.231287i \(0.0742936\pi\)
\(230\) 0 0
\(231\) −78.7129 −0.340749
\(232\) 0 0
\(233\) 363.082i 1.55829i 0.626844 + 0.779145i \(0.284346\pi\)
−0.626844 + 0.779145i \(0.715654\pi\)
\(234\) 0 0
\(235\) 130.033 + 130.033i 0.553334 + 0.553334i
\(236\) 0 0
\(237\) −5.05402 5.05402i −0.0213250 0.0213250i
\(238\) 0 0
\(239\) 27.6282i 0.115599i −0.998328 0.0577996i \(-0.981592\pi\)
0.998328 0.0577996i \(-0.0184084\pi\)
\(240\) 0 0
\(241\) 368.121 1.52747 0.763737 0.645527i \(-0.223362\pi\)
0.763737 + 0.645527i \(0.223362\pi\)
\(242\) 0 0
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 27.2233 27.2233i 0.111115 0.111115i
\(246\) 0 0
\(247\) 589.139 2.38518
\(248\) 0 0
\(249\) 94.1651i 0.378173i
\(250\) 0 0
\(251\) −329.839 329.839i −1.31410 1.31410i −0.918365 0.395734i \(-0.870490\pi\)
−0.395734 0.918365i \(-0.629510\pi\)
\(252\) 0 0
\(253\) 139.474 + 139.474i 0.551281 + 0.551281i
\(254\) 0 0
\(255\) 82.0096i 0.321606i
\(256\) 0 0
\(257\) 23.6762 0.0921252 0.0460626 0.998939i \(-0.485333\pi\)
0.0460626 + 0.998939i \(0.485333\pi\)
\(258\) 0 0
\(259\) 159.050 159.050i 0.614094 0.614094i
\(260\) 0 0
\(261\) −4.51743 + 4.51743i −0.0173082 + 0.0173082i
\(262\) 0 0
\(263\) 243.854 0.927202 0.463601 0.886044i \(-0.346557\pi\)
0.463601 + 0.886044i \(0.346557\pi\)
\(264\) 0 0
\(265\) 192.071i 0.724794i
\(266\) 0 0
\(267\) −64.8918 64.8918i −0.243040 0.243040i
\(268\) 0 0
\(269\) −234.293 234.293i −0.870976 0.870976i 0.121603 0.992579i \(-0.461197\pi\)
−0.992579 + 0.121603i \(0.961197\pi\)
\(270\) 0 0
\(271\) 30.9533i 0.114219i −0.998368 0.0571094i \(-0.981812\pi\)
0.998368 0.0571094i \(-0.0181884\pi\)
\(272\) 0 0
\(273\) −191.003 −0.699646
\(274\) 0 0
\(275\) −107.574 + 107.574i −0.391178 + 0.391178i
\(276\) 0 0
\(277\) 41.4479 41.4479i 0.149631 0.149631i −0.628322 0.777953i \(-0.716258\pi\)
0.777953 + 0.628322i \(0.216258\pi\)
\(278\) 0 0
\(279\) −6.60110 −0.0236599
\(280\) 0 0
\(281\) 93.3971i 0.332374i −0.986094 0.166187i \(-0.946854\pi\)
0.986094 0.166187i \(-0.0531455\pi\)
\(282\) 0 0
\(283\) −40.0982 40.0982i −0.141690 0.141690i 0.632704 0.774394i \(-0.281945\pi\)
−0.774394 + 0.632704i \(0.781945\pi\)
\(284\) 0 0
\(285\) 90.3011 + 90.3011i 0.316846 + 0.316846i
\(286\) 0 0
\(287\) 294.678i 1.02675i
\(288\) 0 0
\(289\) 99.1824 0.343192
\(290\) 0 0
\(291\) 28.2926 28.2926i 0.0972256 0.0972256i
\(292\) 0 0
\(293\) −141.326 + 141.326i −0.482340 + 0.482340i −0.905878 0.423538i \(-0.860788\pi\)
0.423538 + 0.905878i \(0.360788\pi\)
\(294\) 0 0
\(295\) −163.147 −0.553041
\(296\) 0 0
\(297\) 41.1191i 0.138448i
\(298\) 0 0
\(299\) 338.445 + 338.445i 1.13192 + 1.13192i
\(300\) 0 0
\(301\) 123.126 + 123.126i 0.409056 + 0.409056i
\(302\) 0 0
\(303\) 39.4896i 0.130329i
\(304\) 0 0
\(305\) −175.228 −0.574517
\(306\) 0 0
\(307\) 285.548 285.548i 0.930125 0.930125i −0.0675885 0.997713i \(-0.521530\pi\)
0.997713 + 0.0675885i \(0.0215305\pi\)
\(308\) 0 0
\(309\) −121.051 + 121.051i −0.391752 + 0.391752i
\(310\) 0 0
\(311\) −365.454 −1.17509 −0.587547 0.809190i \(-0.699906\pi\)
−0.587547 + 0.809190i \(0.699906\pi\)
\(312\) 0 0
\(313\) 461.508i 1.47447i −0.675638 0.737234i \(-0.736132\pi\)
0.675638 0.737234i \(-0.263868\pi\)
\(314\) 0 0
\(315\) −29.2763 29.2763i −0.0929406 0.0929406i
\(316\) 0 0
\(317\) 319.216 + 319.216i 1.00699 + 1.00699i 0.999975 + 0.00701388i \(0.00223261\pi\)
0.00701388 + 0.999975i \(0.497767\pi\)
\(318\) 0 0
\(319\) 16.8518i 0.0528270i
\(320\) 0 0
\(321\) −38.3724 −0.119540
\(322\) 0 0
\(323\) 427.429 427.429i 1.32331 1.32331i
\(324\) 0 0
\(325\) −261.037 + 261.037i −0.803190 + 0.803190i
\(326\) 0 0
\(327\) −207.457 −0.634424
\(328\) 0 0
\(329\) 439.448i 1.33571i
\(330\) 0 0
\(331\) 85.7864 + 85.7864i 0.259173 + 0.259173i 0.824718 0.565544i \(-0.191334\pi\)
−0.565544 + 0.824718i \(0.691334\pi\)
\(332\) 0 0
\(333\) 83.0869 + 83.0869i 0.249510 + 0.249510i
\(334\) 0 0
\(335\) 215.623i 0.643651i
\(336\) 0 0
\(337\) 258.256 0.766339 0.383170 0.923678i \(-0.374832\pi\)
0.383170 + 0.923678i \(0.374832\pi\)
\(338\) 0 0
\(339\) 78.2045 78.2045i 0.230692 0.230692i
\(340\) 0 0
\(341\) 12.3124 12.3124i 0.0361067 0.0361067i
\(342\) 0 0
\(343\) 373.398 1.08862
\(344\) 0 0
\(345\) 103.751i 0.300729i
\(346\) 0 0
\(347\) −27.7237 27.7237i −0.0798953 0.0798953i 0.666030 0.745925i \(-0.267992\pi\)
−0.745925 + 0.666030i \(0.767992\pi\)
\(348\) 0 0
\(349\) −321.089 321.089i −0.920027 0.920027i 0.0770037 0.997031i \(-0.475465\pi\)
−0.997031 + 0.0770037i \(0.975465\pi\)
\(350\) 0 0
\(351\) 99.7788i 0.284270i
\(352\) 0 0
\(353\) −241.363 −0.683748 −0.341874 0.939746i \(-0.611062\pi\)
−0.341874 + 0.939746i \(0.611062\pi\)
\(354\) 0 0
\(355\) −73.8953 + 73.8953i −0.208156 + 0.208156i
\(356\) 0 0
\(357\) −138.576 + 138.576i −0.388167 + 0.388167i
\(358\) 0 0
\(359\) −363.821 −1.01343 −0.506714 0.862114i \(-0.669140\pi\)
−0.506714 + 0.862114i \(0.669140\pi\)
\(360\) 0 0
\(361\) 580.287i 1.60744i
\(362\) 0 0
\(363\) −71.4988 71.4988i −0.196966 0.196966i
\(364\) 0 0
\(365\) −125.747 125.747i −0.344513 0.344513i
\(366\) 0 0
\(367\) 411.402i 1.12099i 0.828159 + 0.560493i \(0.189388\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(368\) 0 0
\(369\) 153.938 0.417176
\(370\) 0 0
\(371\) −324.551 + 324.551i −0.874801 + 0.874801i
\(372\) 0 0
\(373\) 225.677 225.677i 0.605033 0.605033i −0.336611 0.941644i \(-0.609281\pi\)
0.941644 + 0.336611i \(0.109281\pi\)
\(374\) 0 0
\(375\) −184.082 −0.490886
\(376\) 0 0
\(377\) 40.8923i 0.108468i
\(378\) 0 0
\(379\) 157.180 + 157.180i 0.414724 + 0.414724i 0.883381 0.468656i \(-0.155262\pi\)
−0.468656 + 0.883381i \(0.655262\pi\)
\(380\) 0 0
\(381\) 45.1810 + 45.1810i 0.118585 + 0.118585i
\(382\) 0 0
\(383\) 703.356i 1.83644i 0.396072 + 0.918219i \(0.370373\pi\)
−0.396072 + 0.918219i \(0.629627\pi\)
\(384\) 0 0
\(385\) 109.212 0.283668
\(386\) 0 0
\(387\) −64.3201 + 64.3201i −0.166202 + 0.166202i
\(388\) 0 0
\(389\) −10.7401 + 10.7401i −0.0276095 + 0.0276095i −0.720777 0.693167i \(-0.756215\pi\)
0.693167 + 0.720777i \(0.256215\pi\)
\(390\) 0 0
\(391\) 491.095 1.25600
\(392\) 0 0
\(393\) 98.9926i 0.251890i
\(394\) 0 0
\(395\) 7.01234 + 7.01234i 0.0177528 + 0.0177528i
\(396\) 0 0
\(397\) −365.020 365.020i −0.919446 0.919446i 0.0775433 0.996989i \(-0.475292\pi\)
−0.996989 + 0.0775433i \(0.975292\pi\)
\(398\) 0 0
\(399\) 305.173i 0.764844i
\(400\) 0 0
\(401\) 341.735 0.852207 0.426104 0.904674i \(-0.359886\pi\)
0.426104 + 0.904674i \(0.359886\pi\)
\(402\) 0 0
\(403\) 29.8770 29.8770i 0.0741364 0.0741364i
\(404\) 0 0
\(405\) 15.2937 15.2937i 0.0377623 0.0377623i
\(406\) 0 0
\(407\) −309.947 −0.761541
\(408\) 0 0
\(409\) 368.259i 0.900389i −0.892931 0.450194i \(-0.851355\pi\)
0.892931 0.450194i \(-0.148645\pi\)
\(410\) 0 0
\(411\) −310.472 310.472i −0.755405 0.755405i
\(412\) 0 0
\(413\) −275.678 275.678i −0.667501 0.667501i
\(414\) 0 0
\(415\) 130.652i 0.314824i
\(416\) 0 0
\(417\) −166.091 −0.398300
\(418\) 0 0
\(419\) −407.140 + 407.140i −0.971694 + 0.971694i −0.999610 0.0279165i \(-0.991113\pi\)
0.0279165 + 0.999610i \(0.491113\pi\)
\(420\) 0 0
\(421\) −57.5576 + 57.5576i −0.136716 + 0.136716i −0.772153 0.635437i \(-0.780820\pi\)
0.635437 + 0.772153i \(0.280820\pi\)
\(422\) 0 0
\(423\) −229.565 −0.542706
\(424\) 0 0
\(425\) 378.772i 0.891229i
\(426\) 0 0
\(427\) −296.091 296.091i −0.693422 0.693422i
\(428\) 0 0
\(429\) 186.107 + 186.107i 0.433817 + 0.433817i
\(430\) 0 0
\(431\) 796.565i 1.84818i −0.382177 0.924089i \(-0.624826\pi\)
0.382177 0.924089i \(-0.375174\pi\)
\(432\) 0 0
\(433\) −335.804 −0.775529 −0.387764 0.921758i \(-0.626753\pi\)
−0.387764 + 0.921758i \(0.626753\pi\)
\(434\) 0 0
\(435\) 6.26782 6.26782i 0.0144088 0.0144088i
\(436\) 0 0
\(437\) 540.746 540.746i 1.23741 1.23741i
\(438\) 0 0
\(439\) −285.630 −0.650638 −0.325319 0.945604i \(-0.605472\pi\)
−0.325319 + 0.945604i \(0.605472\pi\)
\(440\) 0 0
\(441\) 48.0607i 0.108981i
\(442\) 0 0
\(443\) −111.596 111.596i −0.251909 0.251909i 0.569844 0.821753i \(-0.307004\pi\)
−0.821753 + 0.569844i \(0.807004\pi\)
\(444\) 0 0
\(445\) 90.0358 + 90.0358i 0.202328 + 0.202328i
\(446\) 0 0
\(447\) 107.615i 0.240750i
\(448\) 0 0
\(449\) −99.6741 −0.221991 −0.110996 0.993821i \(-0.535404\pi\)
−0.110996 + 0.993821i \(0.535404\pi\)
\(450\) 0 0
\(451\) −287.125 + 287.125i −0.636641 + 0.636641i
\(452\) 0 0
\(453\) −273.221 + 273.221i −0.603137 + 0.603137i
\(454\) 0 0
\(455\) 265.012 0.582445
\(456\) 0 0
\(457\) 32.1643i 0.0703813i 0.999381 + 0.0351907i \(0.0112039\pi\)
−0.999381 + 0.0351907i \(0.988796\pi\)
\(458\) 0 0
\(459\) −72.3910 72.3910i −0.157715 0.157715i
\(460\) 0 0
\(461\) −165.361 165.361i −0.358701 0.358701i 0.504633 0.863334i \(-0.331628\pi\)
−0.863334 + 0.504633i \(0.831628\pi\)
\(462\) 0 0
\(463\) 923.215i 1.99398i 0.0774991 + 0.996992i \(0.475307\pi\)
−0.0774991 + 0.996992i \(0.524693\pi\)
\(464\) 0 0
\(465\) 9.15887 0.0196965
\(466\) 0 0
\(467\) −507.842 + 507.842i −1.08746 + 1.08746i −0.0916660 + 0.995790i \(0.529219\pi\)
−0.995790 + 0.0916660i \(0.970781\pi\)
\(468\) 0 0
\(469\) 364.349 364.349i 0.776864 0.776864i
\(470\) 0 0
\(471\) 193.149 0.410082
\(472\) 0 0
\(473\) 239.940i 0.507272i
\(474\) 0 0
\(475\) 417.068 + 417.068i 0.878037 + 0.878037i
\(476\) 0 0
\(477\) −169.543 169.543i −0.355437 0.355437i
\(478\) 0 0
\(479\) 52.3866i 0.109367i −0.998504 0.0546833i \(-0.982585\pi\)
0.998504 0.0546833i \(-0.0174149\pi\)
\(480\) 0 0
\(481\) −752.112 −1.56364
\(482\) 0 0
\(483\) −175.314 + 175.314i −0.362969 + 0.362969i
\(484\) 0 0
\(485\) −39.2554 + 39.2554i −0.0809389 + 0.0809389i
\(486\) 0 0
\(487\) −715.733 −1.46968 −0.734839 0.678241i \(-0.762742\pi\)
−0.734839 + 0.678241i \(0.762742\pi\)
\(488\) 0 0
\(489\) 127.968i 0.261692i
\(490\) 0 0
\(491\) 22.3258 + 22.3258i 0.0454701 + 0.0454701i 0.729476 0.684006i \(-0.239764\pi\)
−0.684006 + 0.729476i \(0.739764\pi\)
\(492\) 0 0
\(493\) −29.6680 29.6680i −0.0601784 0.0601784i
\(494\) 0 0
\(495\) 57.0518i 0.115256i
\(496\) 0 0
\(497\) −249.729 −0.502473
\(498\) 0 0
\(499\) −84.0984 + 84.0984i −0.168534 + 0.168534i −0.786335 0.617801i \(-0.788024\pi\)
0.617801 + 0.786335i \(0.288024\pi\)
\(500\) 0 0
\(501\) 118.213 118.213i 0.235953 0.235953i
\(502\) 0 0
\(503\) 327.870 0.651829 0.325914 0.945399i \(-0.394328\pi\)
0.325914 + 0.945399i \(0.394328\pi\)
\(504\) 0 0
\(505\) 54.7909i 0.108497i
\(506\) 0 0
\(507\) 244.623 + 244.623i 0.482490 + 0.482490i
\(508\) 0 0
\(509\) −34.6224 34.6224i −0.0680205 0.0680205i 0.672278 0.740299i \(-0.265316\pi\)
−0.740299 + 0.672278i \(0.765316\pi\)
\(510\) 0 0
\(511\) 424.963i 0.831630i
\(512\) 0 0
\(513\) −159.420 −0.310760
\(514\) 0 0
\(515\) 167.956 167.956i 0.326128 0.326128i
\(516\) 0 0
\(517\) 428.184 428.184i 0.828210 0.828210i
\(518\) 0 0
\(519\) 113.430 0.218555
\(520\) 0 0
\(521\) 235.719i 0.452436i −0.974077 0.226218i \(-0.927364\pi\)
0.974077 0.226218i \(-0.0726362\pi\)
\(522\) 0 0
\(523\) 185.851 + 185.851i 0.355356 + 0.355356i 0.862098 0.506742i \(-0.169150\pi\)
−0.506742 + 0.862098i \(0.669150\pi\)
\(524\) 0 0
\(525\) −135.216 135.216i −0.257555 0.257555i
\(526\) 0 0
\(527\) 43.3524i 0.0822626i
\(528\) 0 0
\(529\) 92.2900 0.174461
\(530\) 0 0
\(531\) 144.012 144.012i 0.271209 0.271209i
\(532\) 0 0
\(533\) −696.732 + 696.732i −1.30719 + 1.30719i
\(534\) 0 0
\(535\) 53.2408 0.0995155
\(536\) 0 0
\(537\) 229.135i 0.426695i
\(538\) 0 0
\(539\) −89.6428 89.6428i −0.166313 0.166313i
\(540\) 0 0
\(541\) 315.952 + 315.952i 0.584015 + 0.584015i 0.936004 0.351989i \(-0.114494\pi\)
−0.351989 + 0.936004i \(0.614494\pi\)
\(542\) 0 0
\(543\) 283.676i 0.522424i
\(544\) 0 0
\(545\) 287.841 0.528149
\(546\) 0 0
\(547\) 550.957 550.957i 1.00723 1.00723i 0.00725954 0.999974i \(-0.497689\pi\)
0.999974 0.00725954i \(-0.00231080\pi\)
\(548\) 0 0
\(549\) 154.676 154.676i 0.281741 0.281741i
\(550\) 0 0
\(551\) −65.3350 −0.118575
\(552\) 0 0
\(553\) 23.6982i 0.0428539i
\(554\) 0 0
\(555\) −115.281 115.281i −0.207714 0.207714i
\(556\) 0 0
\(557\) −2.35545 2.35545i −0.00422882 0.00422882i 0.704989 0.709218i \(-0.250952\pi\)
−0.709218 + 0.704989i \(0.750952\pi\)
\(558\) 0 0
\(559\) 582.233i 1.04156i
\(560\) 0 0
\(561\) 270.048 0.481368
\(562\) 0 0
\(563\) −269.210 + 269.210i −0.478170 + 0.478170i −0.904546 0.426376i \(-0.859790\pi\)
0.426376 + 0.904546i \(0.359790\pi\)
\(564\) 0 0
\(565\) −108.507 + 108.507i −0.192047 + 0.192047i
\(566\) 0 0
\(567\) 51.6852 0.0911556
\(568\) 0 0
\(569\) 342.558i 0.602035i 0.953619 + 0.301018i \(0.0973263\pi\)
−0.953619 + 0.301018i \(0.902674\pi\)
\(570\) 0 0
\(571\) −153.948 153.948i −0.269610 0.269610i 0.559333 0.828943i \(-0.311057\pi\)
−0.828943 + 0.559333i \(0.811057\pi\)
\(572\) 0 0
\(573\) 43.2291 + 43.2291i 0.0754435 + 0.0754435i
\(574\) 0 0
\(575\) 479.190i 0.833373i
\(576\) 0 0
\(577\) 563.693 0.976938 0.488469 0.872581i \(-0.337556\pi\)
0.488469 + 0.872581i \(0.337556\pi\)
\(578\) 0 0
\(579\) −446.223 + 446.223i −0.770678 + 0.770678i
\(580\) 0 0
\(581\) 220.769 220.769i 0.379981 0.379981i
\(582\) 0 0
\(583\) 632.465 1.08484
\(584\) 0 0
\(585\) 138.441i 0.236651i
\(586\) 0 0
\(587\) −176.603 176.603i −0.300857 0.300857i 0.540492 0.841349i \(-0.318238\pi\)
−0.841349 + 0.540492i \(0.818238\pi\)
\(588\) 0 0
\(589\) −47.7355 47.7355i −0.0810450 0.0810450i
\(590\) 0 0
\(591\) 319.858i 0.541215i
\(592\) 0 0
\(593\) −996.597 −1.68060 −0.840301 0.542120i \(-0.817622\pi\)
−0.840301 + 0.542120i \(0.817622\pi\)
\(594\) 0 0
\(595\) 192.271 192.271i 0.323144 0.323144i
\(596\) 0 0
\(597\) −15.6147 + 15.6147i −0.0261553 + 0.0261553i
\(598\) 0 0
\(599\) −854.031 −1.42576 −0.712880 0.701286i \(-0.752610\pi\)
−0.712880 + 0.701286i \(0.752610\pi\)
\(600\) 0 0
\(601\) 345.733i 0.575263i 0.957741 + 0.287631i \(0.0928678\pi\)
−0.957741 + 0.287631i \(0.907132\pi\)
\(602\) 0 0
\(603\) 190.334 + 190.334i 0.315645 + 0.315645i
\(604\) 0 0
\(605\) 99.2029 + 99.2029i 0.163972 + 0.163972i
\(606\) 0 0
\(607\) 526.354i 0.867141i −0.901120 0.433570i \(-0.857254\pi\)
0.901120 0.433570i \(-0.142746\pi\)
\(608\) 0 0
\(609\) 21.1821 0.0347818
\(610\) 0 0
\(611\) 1039.02 1039.02i 1.70053 1.70053i
\(612\) 0 0
\(613\) −410.567 + 410.567i −0.669767 + 0.669767i −0.957662 0.287895i \(-0.907045\pi\)
0.287895 + 0.957662i \(0.407045\pi\)
\(614\) 0 0
\(615\) −213.585 −0.347293
\(616\) 0 0
\(617\) 514.755i 0.834287i −0.908841 0.417144i \(-0.863031\pi\)
0.908841 0.417144i \(-0.136969\pi\)
\(618\) 0 0
\(619\) −314.214 314.214i −0.507615 0.507615i 0.406179 0.913794i \(-0.366861\pi\)
−0.913794 + 0.406179i \(0.866861\pi\)
\(620\) 0 0
\(621\) −91.5828 91.5828i −0.147476 0.147476i
\(622\) 0 0
\(623\) 304.276i 0.488404i
\(624\) 0 0
\(625\) −225.209 −0.360334
\(626\) 0 0
\(627\) 297.350 297.350i 0.474243 0.474243i
\(628\) 0 0
\(629\) −545.669 + 545.669i −0.867518 + 0.867518i
\(630\) 0 0
\(631\) −230.081 −0.364629 −0.182315 0.983240i \(-0.558359\pi\)
−0.182315 + 0.983240i \(0.558359\pi\)
\(632\) 0 0
\(633\) 21.0533i 0.0332596i
\(634\) 0 0
\(635\) −62.6875 62.6875i −0.0987205 0.0987205i
\(636\) 0 0
\(637\) −217.526 217.526i −0.341484 0.341484i
\(638\) 0 0
\(639\) 130.457i 0.204158i
\(640\) 0 0
\(641\) 746.825 1.16509 0.582547 0.812797i \(-0.302056\pi\)
0.582547 + 0.812797i \(0.302056\pi\)
\(642\) 0 0
\(643\) −548.092 + 548.092i −0.852398 + 0.852398i −0.990428 0.138030i \(-0.955923\pi\)
0.138030 + 0.990428i \(0.455923\pi\)
\(644\) 0 0
\(645\) 89.2426 89.2426i 0.138361 0.138361i
\(646\) 0 0
\(647\) 1055.00 1.63060 0.815302 0.579036i \(-0.196571\pi\)
0.815302 + 0.579036i \(0.196571\pi\)
\(648\) 0 0
\(649\) 537.223i 0.827771i
\(650\) 0 0
\(651\) 15.4762 + 15.4762i 0.0237730 + 0.0237730i
\(652\) 0 0
\(653\) 854.888 + 854.888i 1.30917 + 1.30917i 0.922015 + 0.387155i \(0.126542\pi\)
0.387155 + 0.922015i \(0.373458\pi\)
\(654\) 0 0
\(655\) 137.350i 0.209694i
\(656\) 0 0
\(657\) 221.998 0.337896
\(658\) 0 0
\(659\) 768.766 768.766i 1.16656 1.16656i 0.183556 0.983009i \(-0.441239\pi\)
0.983009 0.183556i \(-0.0587607\pi\)
\(660\) 0 0
\(661\) −312.323 + 312.323i −0.472500 + 0.472500i −0.902723 0.430223i \(-0.858435\pi\)
0.430223 + 0.902723i \(0.358435\pi\)
\(662\) 0 0
\(663\) 655.292 0.988374
\(664\) 0 0
\(665\) 423.420i 0.636721i
\(666\) 0 0
\(667\) −37.5333 37.5333i −0.0562719 0.0562719i
\(668\) 0 0
\(669\) −61.9610 61.9610i −0.0926173 0.0926173i
\(670\) 0 0
\(671\) 577.004i 0.859916i
\(672\) 0 0
\(673\) 740.565 1.10039 0.550197 0.835035i \(-0.314553\pi\)
0.550197 + 0.835035i \(0.314553\pi\)
\(674\) 0 0
\(675\) 70.6362 70.6362i 0.104646 0.104646i
\(676\) 0 0
\(677\) 547.118 547.118i 0.808151 0.808151i −0.176203 0.984354i \(-0.556381\pi\)
0.984354 + 0.176203i \(0.0563814\pi\)
\(678\) 0 0
\(679\) −132.664 −0.195381
\(680\) 0 0
\(681\) 77.6918i 0.114085i
\(682\) 0 0
\(683\) 407.623 + 407.623i 0.596813 + 0.596813i 0.939463 0.342650i \(-0.111324\pi\)
−0.342650 + 0.939463i \(0.611324\pi\)
\(684\) 0 0
\(685\) 430.772 + 430.772i 0.628864 + 0.628864i
\(686\) 0 0
\(687\) 415.987i 0.605513i
\(688\) 0 0
\(689\) 1534.73 2.22747
\(690\) 0 0
\(691\) −17.6037 + 17.6037i −0.0254757 + 0.0254757i −0.719730 0.694254i \(-0.755734\pi\)
0.694254 + 0.719730i \(0.255734\pi\)
\(692\) 0 0
\(693\) −96.4033 + 96.4033i −0.139110 + 0.139110i
\(694\) 0 0
\(695\) 230.448 0.331579
\(696\) 0 0
\(697\) 1010.98i 1.45047i
\(698\) 0 0
\(699\) 444.682 + 444.682i 0.636169 + 0.636169i
\(700\) 0 0
\(701\) −164.273 164.273i −0.234341 0.234341i 0.580161 0.814502i \(-0.302990\pi\)
−0.814502 + 0.580161i \(0.802990\pi\)
\(702\) 0 0
\(703\) 1201.68i 1.70935i
\(704\) 0 0
\(705\) 318.516 0.451795
\(706\) 0 0
\(707\) 92.5829 92.5829i 0.130952 0.130952i
\(708\) 0 0
\(709\) −422.796 + 422.796i −0.596327 + 0.596327i −0.939333 0.343006i \(-0.888555\pi\)
0.343006 + 0.939333i \(0.388555\pi\)
\(710\) 0 0
\(711\) −12.3798 −0.0174118
\(712\) 0 0
\(713\) 54.8457i 0.0769224i
\(714\) 0 0
\(715\) −258.220 258.220i −0.361146 0.361146i
\(716\) 0 0
\(717\) −33.8375 33.8375i −0.0471932 0.0471932i
\(718\) 0 0
\(719\) 1029.00i 1.43115i −0.698534 0.715577i \(-0.746164\pi\)
0.698534 0.715577i \(-0.253836\pi\)
\(720\) 0 0
\(721\) 567.607 0.787250
\(722\) 0 0
\(723\) 450.855 450.855i 0.623589 0.623589i
\(724\) 0 0
\(725\) 28.9488 28.9488i 0.0399293 0.0399293i
\(726\) 0 0
\(727\) −475.001 −0.653372 −0.326686 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −422.419 422.419i −0.577865 0.577865i
\(732\) 0 0
\(733\) 344.939 + 344.939i 0.470586 + 0.470586i 0.902104 0.431519i \(-0.142022\pi\)
−0.431519 + 0.902104i \(0.642022\pi\)
\(734\) 0 0
\(735\) 66.6831i 0.0907253i
\(736\) 0 0
\(737\) −710.021 −0.963393
\(738\) 0 0
\(739\) −363.340 + 363.340i −0.491665 + 0.491665i −0.908831 0.417166i \(-0.863024\pi\)
0.417166 + 0.908831i \(0.363024\pi\)
\(740\) 0 0
\(741\) 721.544 721.544i 0.973744 0.973744i
\(742\) 0 0
\(743\) 271.667 0.365636 0.182818 0.983147i \(-0.441478\pi\)
0.182818 + 0.983147i \(0.441478\pi\)
\(744\) 0 0
\(745\) 149.314i 0.200421i
\(746\) 0 0
\(747\) 115.328 + 115.328i 0.154389 + 0.154389i
\(748\) 0 0
\(749\) 89.9637 + 89.9637i 0.120112 + 0.120112i
\(750\) 0 0
\(751\) 1105.27i 1.47173i −0.677128 0.735866i \(-0.736776\pi\)
0.677128 0.735866i \(-0.263224\pi\)
\(752\) 0 0
\(753\) −807.937 −1.07296
\(754\) 0 0
\(755\) 379.087 379.087i 0.502102 0.502102i
\(756\) 0 0
\(757\) −554.565 + 554.565i −0.732583 + 0.732583i −0.971131 0.238548i \(-0.923329\pi\)
0.238548 + 0.971131i \(0.423329\pi\)
\(758\) 0 0
\(759\) 341.641 0.450119
\(760\) 0 0
\(761\) 188.496i 0.247695i 0.992301 + 0.123847i \(0.0395234\pi\)
−0.992301 + 0.123847i \(0.960477\pi\)
\(762\) 0 0
\(763\) 486.380 + 486.380i 0.637457 + 0.637457i
\(764\) 0 0
\(765\) 100.441 + 100.441i 0.131295 + 0.131295i
\(766\) 0 0
\(767\) 1303.62i 1.69963i
\(768\) 0 0
\(769\) −593.354 −0.771592 −0.385796 0.922584i \(-0.626073\pi\)
−0.385796 + 0.922584i \(0.626073\pi\)
\(770\) 0 0
\(771\) 28.9973 28.9973i 0.0376100 0.0376100i
\(772\) 0 0
\(773\) −514.720 + 514.720i −0.665873 + 0.665873i −0.956758 0.290885i \(-0.906050\pi\)
0.290885 + 0.956758i \(0.406050\pi\)
\(774\) 0 0
\(775\) 42.3015 0.0545826
\(776\) 0 0
\(777\) 389.592i 0.501406i
\(778\) 0 0
\(779\) 1113.19 + 1113.19i 1.42900 + 1.42900i
\(780\) 0 0
\(781\) 243.328 + 243.328i 0.311560 + 0.311560i
\(782\) 0 0
\(783\) 11.0654i 0.0141320i
\(784\) 0 0
\(785\) −267.989 −0.341387
\(786\) 0 0
\(787\) −96.1835 + 96.1835i −0.122215 + 0.122215i −0.765569 0.643354i \(-0.777542\pi\)
0.643354 + 0.765569i \(0.277542\pi\)
\(788\) 0 0
\(789\) 298.659 298.659i 0.378529 0.378529i
\(790\) 0 0
\(791\) −366.699 −0.463589
\(792\) 0 0
\(793\) 1400.15i 1.76563i
\(794\) 0 0