Properties

Label 384.3.l.a.31.3
Level $384$
Weight $3$
Character 384.31
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 31.3
Root \(-1.25564 - 1.55672i\) of defining polynomial
Character \(\chi\) \(=\) 384.31
Dual form 384.3.l.a.223.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(-0.909023 - 0.909023i) q^{5} -0.654713 q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(-0.909023 - 0.909023i) q^{5} -0.654713 q^{7} +3.00000i q^{9} +(13.3760 - 13.3760i) q^{11} +(-8.32795 + 8.32795i) q^{13} +2.22664i q^{15} -3.93529 q^{17} +(-16.8974 - 16.8974i) q^{19} +(0.801857 + 0.801857i) q^{21} -23.1787 q^{23} -23.3474i q^{25} +(3.67423 - 3.67423i) q^{27} +(-35.6105 + 35.6105i) q^{29} -45.5687i q^{31} -32.7644 q^{33} +(0.595149 + 0.595149i) q^{35} +(-10.1527 - 10.1527i) q^{37} +20.3992 q^{39} +28.4661i q^{41} +(-22.7354 + 22.7354i) q^{43} +(2.72707 - 2.72707i) q^{45} -10.7746i q^{47} -48.5714 q^{49} +(4.81973 + 4.81973i) q^{51} +(-41.5142 - 41.5142i) q^{53} -24.3182 q^{55} +41.3900i q^{57} +(21.0646 - 21.0646i) q^{59} +(68.7531 - 68.7531i) q^{61} -1.96414i q^{63} +15.1406 q^{65} +(-67.8242 - 67.8242i) q^{67} +(28.3880 + 28.3880i) q^{69} +33.3094 q^{71} +18.6331i q^{73} +(-28.5946 + 28.5946i) q^{75} +(-8.75745 + 8.75745i) q^{77} -6.29222i q^{79} -9.00000 q^{81} +(72.0774 + 72.0774i) q^{83} +(3.57727 + 3.57727i) q^{85} +87.2275 q^{87} -10.6131i q^{89} +(5.45242 - 5.45242i) q^{91} +(-55.8101 + 55.8101i) q^{93} +30.7202i q^{95} +143.631 q^{97} +(40.1280 + 40.1280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} - 128q^{23} - 32q^{29} - 96q^{35} + 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} + 160q^{53} - 256q^{55} + 128q^{59} + 32q^{61} - 32q^{65} - 320q^{67} - 96q^{69} + 512q^{71} - 192q^{75} - 224q^{77} - 144q^{81} + 160q^{83} - 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.909023 0.909023i −0.181805 0.181805i 0.610337 0.792142i \(-0.291034\pi\)
−0.792142 + 0.610337i \(0.791034\pi\)
\(6\) 0 0
\(7\) −0.654713 −0.0935305 −0.0467652 0.998906i \(-0.514891\pi\)
−0.0467652 + 0.998906i \(0.514891\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 13.3760 13.3760i 1.21600 1.21600i 0.246980 0.969021i \(-0.420562\pi\)
0.969021 0.246980i \(-0.0794382\pi\)
\(12\) 0 0
\(13\) −8.32795 + 8.32795i −0.640612 + 0.640612i −0.950706 0.310094i \(-0.899639\pi\)
0.310094 + 0.950706i \(0.399639\pi\)
\(14\) 0 0
\(15\) 2.22664i 0.148443i
\(16\) 0 0
\(17\) −3.93529 −0.231488 −0.115744 0.993279i \(-0.536925\pi\)
−0.115744 + 0.993279i \(0.536925\pi\)
\(18\) 0 0
\(19\) −16.8974 16.8974i −0.889336 0.889336i 0.105123 0.994459i \(-0.466476\pi\)
−0.994459 + 0.105123i \(0.966476\pi\)
\(20\) 0 0
\(21\) 0.801857 + 0.801857i 0.0381837 + 0.0381837i
\(22\) 0 0
\(23\) −23.1787 −1.00777 −0.503884 0.863771i \(-0.668096\pi\)
−0.503884 + 0.863771i \(0.668096\pi\)
\(24\) 0 0
\(25\) 23.3474i 0.933894i
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) −35.6105 + 35.6105i −1.22795 + 1.22795i −0.263209 + 0.964739i \(0.584781\pi\)
−0.964739 + 0.263209i \(0.915219\pi\)
\(30\) 0 0
\(31\) 45.5687i 1.46996i −0.678089 0.734980i \(-0.737192\pi\)
0.678089 0.734980i \(-0.262808\pi\)
\(32\) 0 0
\(33\) −32.7644 −0.992860
\(34\) 0 0
\(35\) 0.595149 + 0.595149i 0.0170043 + 0.0170043i
\(36\) 0 0
\(37\) −10.1527 10.1527i −0.274398 0.274398i 0.556470 0.830868i \(-0.312156\pi\)
−0.830868 + 0.556470i \(0.812156\pi\)
\(38\) 0 0
\(39\) 20.3992 0.523057
\(40\) 0 0
\(41\) 28.4661i 0.694295i 0.937811 + 0.347148i \(0.112850\pi\)
−0.937811 + 0.347148i \(0.887150\pi\)
\(42\) 0 0
\(43\) −22.7354 + 22.7354i −0.528730 + 0.528730i −0.920194 0.391464i \(-0.871969\pi\)
0.391464 + 0.920194i \(0.371969\pi\)
\(44\) 0 0
\(45\) 2.72707 2.72707i 0.0606015 0.0606015i
\(46\) 0 0
\(47\) 10.7746i 0.229247i −0.993409 0.114623i \(-0.963434\pi\)
0.993409 0.114623i \(-0.0365661\pi\)
\(48\) 0 0
\(49\) −48.5714 −0.991252
\(50\) 0 0
\(51\) 4.81973 + 4.81973i 0.0945045 + 0.0945045i
\(52\) 0 0
\(53\) −41.5142 41.5142i −0.783287 0.783287i 0.197097 0.980384i \(-0.436849\pi\)
−0.980384 + 0.197097i \(0.936849\pi\)
\(54\) 0 0
\(55\) −24.3182 −0.442149
\(56\) 0 0
\(57\) 41.3900i 0.726140i
\(58\) 0 0
\(59\) 21.0646 21.0646i 0.357027 0.357027i −0.505689 0.862716i \(-0.668762\pi\)
0.862716 + 0.505689i \(0.168762\pi\)
\(60\) 0 0
\(61\) 68.7531 68.7531i 1.12710 1.12710i 0.136453 0.990647i \(-0.456430\pi\)
0.990647 0.136453i \(-0.0435703\pi\)
\(62\) 0 0
\(63\) 1.96414i 0.0311768i
\(64\) 0 0
\(65\) 15.1406 0.232932
\(66\) 0 0
\(67\) −67.8242 67.8242i −1.01230 1.01230i −0.999923 0.0123779i \(-0.996060\pi\)
−0.0123779 0.999923i \(-0.503940\pi\)
\(68\) 0 0
\(69\) 28.3880 + 28.3880i 0.411420 + 0.411420i
\(70\) 0 0
\(71\) 33.3094 0.469147 0.234573 0.972098i \(-0.424631\pi\)
0.234573 + 0.972098i \(0.424631\pi\)
\(72\) 0 0
\(73\) 18.6331i 0.255248i 0.991823 + 0.127624i \(0.0407351\pi\)
−0.991823 + 0.127624i \(0.959265\pi\)
\(74\) 0 0
\(75\) −28.5946 + 28.5946i −0.381261 + 0.381261i
\(76\) 0 0
\(77\) −8.75745 + 8.75745i −0.113733 + 0.113733i
\(78\) 0 0
\(79\) 6.29222i 0.0796483i −0.999207 0.0398242i \(-0.987320\pi\)
0.999207 0.0398242i \(-0.0126798\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 72.0774 + 72.0774i 0.868402 + 0.868402i 0.992296 0.123894i \(-0.0395382\pi\)
−0.123894 + 0.992296i \(0.539538\pi\)
\(84\) 0 0
\(85\) 3.57727 + 3.57727i 0.0420855 + 0.0420855i
\(86\) 0 0
\(87\) 87.2275 1.00262
\(88\) 0 0
\(89\) 10.6131i 0.119248i −0.998221 0.0596240i \(-0.981010\pi\)
0.998221 0.0596240i \(-0.0189902\pi\)
\(90\) 0 0
\(91\) 5.45242 5.45242i 0.0599167 0.0599167i
\(92\) 0 0
\(93\) −55.8101 + 55.8101i −0.600108 + 0.600108i
\(94\) 0 0
\(95\) 30.7202i 0.323371i
\(96\) 0 0
\(97\) 143.631 1.48073 0.740366 0.672204i \(-0.234652\pi\)
0.740366 + 0.672204i \(0.234652\pi\)
\(98\) 0 0
\(99\) 40.1280 + 40.1280i 0.405334 + 0.405334i
\(100\) 0 0
\(101\) 90.3100 + 90.3100i 0.894159 + 0.894159i 0.994912 0.100753i \(-0.0321251\pi\)
−0.100753 + 0.994912i \(0.532125\pi\)
\(102\) 0 0
\(103\) −95.1656 −0.923938 −0.461969 0.886896i \(-0.652857\pi\)
−0.461969 + 0.886896i \(0.652857\pi\)
\(104\) 0 0
\(105\) 1.45781i 0.0138839i
\(106\) 0 0
\(107\) −27.2524 + 27.2524i −0.254695 + 0.254695i −0.822892 0.568197i \(-0.807641\pi\)
0.568197 + 0.822892i \(0.307641\pi\)
\(108\) 0 0
\(109\) 132.413 132.413i 1.21480 1.21480i 0.245366 0.969430i \(-0.421092\pi\)
0.969430 0.245366i \(-0.0789082\pi\)
\(110\) 0 0
\(111\) 24.8690i 0.224045i
\(112\) 0 0
\(113\) 37.9551 0.335886 0.167943 0.985797i \(-0.446288\pi\)
0.167943 + 0.985797i \(0.446288\pi\)
\(114\) 0 0
\(115\) 21.0699 + 21.0699i 0.183217 + 0.183217i
\(116\) 0 0
\(117\) −24.9838 24.9838i −0.213537 0.213537i
\(118\) 0 0
\(119\) 2.57649 0.0216512
\(120\) 0 0
\(121\) 236.835i 1.95731i
\(122\) 0 0
\(123\) 34.8637 34.8637i 0.283445 0.283445i
\(124\) 0 0
\(125\) −43.9488 + 43.9488i −0.351591 + 0.351591i
\(126\) 0 0
\(127\) 96.5399i 0.760157i 0.924954 + 0.380078i \(0.124103\pi\)
−0.924954 + 0.380078i \(0.875897\pi\)
\(128\) 0 0
\(129\) 55.6901 0.431706
\(130\) 0 0
\(131\) 54.5082 + 54.5082i 0.416093 + 0.416093i 0.883855 0.467762i \(-0.154939\pi\)
−0.467762 + 0.883855i \(0.654939\pi\)
\(132\) 0 0
\(133\) 11.0629 + 11.0629i 0.0831801 + 0.0831801i
\(134\) 0 0
\(135\) −6.67992 −0.0494809
\(136\) 0 0
\(137\) 25.9333i 0.189294i 0.995511 + 0.0946471i \(0.0301723\pi\)
−0.995511 + 0.0946471i \(0.969828\pi\)
\(138\) 0 0
\(139\) −3.64066 + 3.64066i −0.0261918 + 0.0261918i −0.720081 0.693890i \(-0.755896\pi\)
0.693890 + 0.720081i \(0.255896\pi\)
\(140\) 0 0
\(141\) −13.1961 + 13.1961i −0.0935896 + 0.0935896i
\(142\) 0 0
\(143\) 222.789i 1.55797i
\(144\) 0 0
\(145\) 64.7415 0.446493
\(146\) 0 0
\(147\) 59.4875 + 59.4875i 0.404677 + 0.404677i
\(148\) 0 0
\(149\) 18.9718 + 18.9718i 0.127328 + 0.127328i 0.767899 0.640571i \(-0.221302\pi\)
−0.640571 + 0.767899i \(0.721302\pi\)
\(150\) 0 0
\(151\) −103.209 −0.683503 −0.341751 0.939790i \(-0.611020\pi\)
−0.341751 + 0.939790i \(0.611020\pi\)
\(152\) 0 0
\(153\) 11.8059i 0.0771626i
\(154\) 0 0
\(155\) −41.4230 + 41.4230i −0.267245 + 0.267245i
\(156\) 0 0
\(157\) −88.2067 + 88.2067i −0.561826 + 0.561826i −0.929826 0.368000i \(-0.880043\pi\)
0.368000 + 0.929826i \(0.380043\pi\)
\(158\) 0 0
\(159\) 101.689i 0.639551i
\(160\) 0 0
\(161\) 15.1754 0.0942571
\(162\) 0 0
\(163\) −18.8038 18.8038i −0.115361 0.115361i 0.647070 0.762431i \(-0.275994\pi\)
−0.762431 + 0.647070i \(0.775994\pi\)
\(164\) 0 0
\(165\) 29.7836 + 29.7836i 0.180507 + 0.180507i
\(166\) 0 0
\(167\) 267.105 1.59943 0.799715 0.600380i \(-0.204984\pi\)
0.799715 + 0.600380i \(0.204984\pi\)
\(168\) 0 0
\(169\) 30.2905i 0.179234i
\(170\) 0 0
\(171\) 50.6922 50.6922i 0.296445 0.296445i
\(172\) 0 0
\(173\) 153.520 153.520i 0.887396 0.887396i −0.106876 0.994272i \(-0.534085\pi\)
0.994272 + 0.106876i \(0.0340849\pi\)
\(174\) 0 0
\(175\) 15.2858i 0.0873476i
\(176\) 0 0
\(177\) −51.5975 −0.291511
\(178\) 0 0
\(179\) −123.581 123.581i −0.690399 0.690399i 0.271921 0.962320i \(-0.412341\pi\)
−0.962320 + 0.271921i \(0.912341\pi\)
\(180\) 0 0
\(181\) −122.965 122.965i −0.679364 0.679364i 0.280493 0.959856i \(-0.409502\pi\)
−0.959856 + 0.280493i \(0.909502\pi\)
\(182\) 0 0
\(183\) −168.410 −0.920273
\(184\) 0 0
\(185\) 18.4581i 0.0997737i
\(186\) 0 0
\(187\) −52.6385 + 52.6385i −0.281489 + 0.281489i
\(188\) 0 0
\(189\) −2.40557 + 2.40557i −0.0127279 + 0.0127279i
\(190\) 0 0
\(191\) 193.992i 1.01566i −0.861456 0.507832i \(-0.830447\pi\)
0.861456 0.507832i \(-0.169553\pi\)
\(192\) 0 0
\(193\) 141.555 0.733444 0.366722 0.930331i \(-0.380480\pi\)
0.366722 + 0.930331i \(0.380480\pi\)
\(194\) 0 0
\(195\) −18.5434 18.5434i −0.0950942 0.0950942i
\(196\) 0 0
\(197\) −28.9507 28.9507i −0.146958 0.146958i 0.629800 0.776758i \(-0.283137\pi\)
−0.776758 + 0.629800i \(0.783137\pi\)
\(198\) 0 0
\(199\) −27.6253 −0.138821 −0.0694104 0.997588i \(-0.522112\pi\)
−0.0694104 + 0.997588i \(0.522112\pi\)
\(200\) 0 0
\(201\) 166.135i 0.826541i
\(202\) 0 0
\(203\) 23.3147 23.3147i 0.114851 0.114851i
\(204\) 0 0
\(205\) 25.8763 25.8763i 0.126226 0.126226i
\(206\) 0 0
\(207\) 69.5360i 0.335923i
\(208\) 0 0
\(209\) −452.039 −2.16287
\(210\) 0 0
\(211\) −7.35041 7.35041i −0.0348361 0.0348361i 0.689474 0.724310i \(-0.257842\pi\)
−0.724310 + 0.689474i \(0.757842\pi\)
\(212\) 0 0
\(213\) −40.7955 40.7955i −0.191528 0.191528i
\(214\) 0 0
\(215\) 41.3340 0.192251
\(216\) 0 0
\(217\) 29.8345i 0.137486i
\(218\) 0 0
\(219\) 22.8208 22.8208i 0.104205 0.104205i
\(220\) 0 0
\(221\) 32.7729 32.7729i 0.148294 0.148294i
\(222\) 0 0
\(223\) 386.106i 1.73142i −0.500549 0.865708i \(-0.666869\pi\)
0.500549 0.865708i \(-0.333131\pi\)
\(224\) 0 0
\(225\) 70.0421 0.311298
\(226\) 0 0
\(227\) 49.7286 + 49.7286i 0.219069 + 0.219069i 0.808106 0.589037i \(-0.200493\pi\)
−0.589037 + 0.808106i \(0.700493\pi\)
\(228\) 0 0
\(229\) 191.870 + 191.870i 0.837861 + 0.837861i 0.988577 0.150716i \(-0.0481579\pi\)
−0.150716 + 0.988577i \(0.548158\pi\)
\(230\) 0 0
\(231\) 21.4513 0.0928627
\(232\) 0 0
\(233\) 298.610i 1.28159i 0.767712 + 0.640795i \(0.221395\pi\)
−0.767712 + 0.640795i \(0.778605\pi\)
\(234\) 0 0
\(235\) −9.79435 + 9.79435i −0.0416781 + 0.0416781i
\(236\) 0 0
\(237\) −7.70636 + 7.70636i −0.0325163 + 0.0325163i
\(238\) 0 0
\(239\) 247.352i 1.03495i −0.855700 0.517473i \(-0.826873\pi\)
0.855700 0.517473i \(-0.173127\pi\)
\(240\) 0 0
\(241\) −220.337 −0.914260 −0.457130 0.889400i \(-0.651123\pi\)
−0.457130 + 0.889400i \(0.651123\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 44.1525 + 44.1525i 0.180214 + 0.180214i
\(246\) 0 0
\(247\) 281.441 1.13944
\(248\) 0 0
\(249\) 176.553i 0.709047i
\(250\) 0 0
\(251\) −162.716 + 162.716i −0.648272 + 0.648272i −0.952575 0.304303i \(-0.901576\pi\)
0.304303 + 0.952575i \(0.401576\pi\)
\(252\) 0 0
\(253\) −310.038 + 310.038i −1.22545 + 1.22545i
\(254\) 0 0
\(255\) 8.76249i 0.0343627i
\(256\) 0 0
\(257\) 101.165 0.393637 0.196819 0.980440i \(-0.436939\pi\)
0.196819 + 0.980440i \(0.436939\pi\)
\(258\) 0 0
\(259\) 6.64713 + 6.64713i 0.0256646 + 0.0256646i
\(260\) 0 0
\(261\) −106.831 106.831i −0.409316 0.409316i
\(262\) 0 0
\(263\) −323.635 −1.23055 −0.615276 0.788312i \(-0.710955\pi\)
−0.615276 + 0.788312i \(0.710955\pi\)
\(264\) 0 0
\(265\) 75.4747i 0.284810i
\(266\) 0 0
\(267\) −12.9983 + 12.9983i −0.0486828 + 0.0486828i
\(268\) 0 0
\(269\) −1.51275 + 1.51275i −0.00562361 + 0.00562361i −0.709913 0.704289i \(-0.751266\pi\)
0.704289 + 0.709913i \(0.251266\pi\)
\(270\) 0 0
\(271\) 166.098i 0.612909i −0.951885 0.306454i \(-0.900857\pi\)
0.951885 0.306454i \(-0.0991427\pi\)
\(272\) 0 0
\(273\) −13.3556 −0.0489218
\(274\) 0 0
\(275\) −312.294 312.294i −1.13562 1.13562i
\(276\) 0 0
\(277\) −317.830 317.830i −1.14740 1.14740i −0.987062 0.160338i \(-0.948741\pi\)
−0.160338 0.987062i \(-0.551259\pi\)
\(278\) 0 0
\(279\) 136.706 0.489986
\(280\) 0 0
\(281\) 402.790i 1.43342i −0.697374 0.716708i \(-0.745648\pi\)
0.697374 0.716708i \(-0.254352\pi\)
\(282\) 0 0
\(283\) 192.406 192.406i 0.679881 0.679881i −0.280092 0.959973i \(-0.590365\pi\)
0.959973 + 0.280092i \(0.0903649\pi\)
\(284\) 0 0
\(285\) 37.6244 37.6244i 0.132016 0.132016i
\(286\) 0 0
\(287\) 18.6371i 0.0649378i
\(288\) 0 0
\(289\) −273.513 −0.946413
\(290\) 0 0
\(291\) −175.911 175.911i −0.604506 0.604506i
\(292\) 0 0
\(293\) 75.3645 + 75.3645i 0.257217 + 0.257217i 0.823921 0.566704i \(-0.191782\pi\)
−0.566704 + 0.823921i \(0.691782\pi\)
\(294\) 0 0
\(295\) −38.2964 −0.129818
\(296\) 0 0
\(297\) 98.2932i 0.330953i
\(298\) 0 0
\(299\) 193.031 193.031i 0.645588 0.645588i
\(300\) 0 0
\(301\) 14.8852 14.8852i 0.0494524 0.0494524i
\(302\) 0 0
\(303\) 221.214i 0.730078i
\(304\) 0 0
\(305\) −124.996 −0.409824
\(306\) 0 0
\(307\) 111.544 + 111.544i 0.363337 + 0.363337i 0.865040 0.501703i \(-0.167293\pi\)
−0.501703 + 0.865040i \(0.667293\pi\)
\(308\) 0 0
\(309\) 116.554 + 116.554i 0.377196 + 0.377196i
\(310\) 0 0
\(311\) −224.484 −0.721813 −0.360906 0.932602i \(-0.617533\pi\)
−0.360906 + 0.932602i \(0.617533\pi\)
\(312\) 0 0
\(313\) 488.339i 1.56019i 0.625661 + 0.780095i \(0.284829\pi\)
−0.625661 + 0.780095i \(0.715171\pi\)
\(314\) 0 0
\(315\) −1.78545 + 1.78545i −0.00566809 + 0.00566809i
\(316\) 0 0
\(317\) −257.361 + 257.361i −0.811863 + 0.811863i −0.984913 0.173050i \(-0.944638\pi\)
0.173050 + 0.984913i \(0.444638\pi\)
\(318\) 0 0
\(319\) 952.652i 2.98637i
\(320\) 0 0
\(321\) 66.7545 0.207958
\(322\) 0 0
\(323\) 66.4962 + 66.4962i 0.205871 + 0.205871i
\(324\) 0 0
\(325\) 194.436 + 194.436i 0.598263 + 0.598263i
\(326\) 0 0
\(327\) −324.344 −0.991877
\(328\) 0 0
\(329\) 7.05427i 0.0214416i
\(330\) 0 0
\(331\) 123.553 123.553i 0.373271 0.373271i −0.495396 0.868667i \(-0.664977\pi\)
0.868667 + 0.495396i \(0.164977\pi\)
\(332\) 0 0
\(333\) 30.4582 30.4582i 0.0914661 0.0914661i
\(334\) 0 0
\(335\) 123.307i 0.368082i
\(336\) 0 0
\(337\) −246.234 −0.730665 −0.365333 0.930877i \(-0.619045\pi\)
−0.365333 + 0.930877i \(0.619045\pi\)
\(338\) 0 0
\(339\) −46.4853 46.4853i −0.137125 0.137125i
\(340\) 0 0
\(341\) −609.528 609.528i −1.78747 1.78747i
\(342\) 0 0
\(343\) 63.8813 0.186243
\(344\) 0 0
\(345\) 51.6106i 0.149596i
\(346\) 0 0
\(347\) 123.212 123.212i 0.355076 0.355076i −0.506918 0.861994i \(-0.669215\pi\)
0.861994 + 0.506918i \(0.169215\pi\)
\(348\) 0 0
\(349\) −115.371 + 115.371i −0.330575 + 0.330575i −0.852805 0.522230i \(-0.825100\pi\)
0.522230 + 0.852805i \(0.325100\pi\)
\(350\) 0 0
\(351\) 61.1977i 0.174352i
\(352\) 0 0
\(353\) 650.544 1.84290 0.921451 0.388495i \(-0.127005\pi\)
0.921451 + 0.388495i \(0.127005\pi\)
\(354\) 0 0
\(355\) −30.2790 30.2790i −0.0852930 0.0852930i
\(356\) 0 0
\(357\) −3.15554 3.15554i −0.00883906 0.00883906i
\(358\) 0 0
\(359\) 94.4878 0.263197 0.131599 0.991303i \(-0.457989\pi\)
0.131599 + 0.991303i \(0.457989\pi\)
\(360\) 0 0
\(361\) 210.044i 0.581838i
\(362\) 0 0
\(363\) −290.063 + 290.063i −0.799070 + 0.799070i
\(364\) 0 0
\(365\) 16.9379 16.9379i 0.0464053 0.0464053i
\(366\) 0 0
\(367\) 131.379i 0.357982i −0.983851 0.178991i \(-0.942717\pi\)
0.983851 0.178991i \(-0.0572832\pi\)
\(368\) 0 0
\(369\) −85.3983 −0.231432
\(370\) 0 0
\(371\) 27.1799 + 27.1799i 0.0732612 + 0.0732612i
\(372\) 0 0
\(373\) 275.796 + 275.796i 0.739400 + 0.739400i 0.972462 0.233062i \(-0.0748745\pi\)
−0.233062 + 0.972462i \(0.574874\pi\)
\(374\) 0 0
\(375\) 107.652 0.287073
\(376\) 0 0
\(377\) 593.125i 1.57328i
\(378\) 0 0
\(379\) 13.0427 13.0427i 0.0344135 0.0344135i −0.689691 0.724104i \(-0.742253\pi\)
0.724104 + 0.689691i \(0.242253\pi\)
\(380\) 0 0
\(381\) 118.237 118.237i 0.310333 0.310333i
\(382\) 0 0
\(383\) 121.974i 0.318470i −0.987241 0.159235i \(-0.949097\pi\)
0.987241 0.159235i \(-0.0509027\pi\)
\(384\) 0 0
\(385\) 15.9214 0.0413544
\(386\) 0 0
\(387\) −68.2062 68.2062i −0.176243 0.176243i
\(388\) 0 0
\(389\) 233.267 + 233.267i 0.599659 + 0.599659i 0.940222 0.340563i \(-0.110618\pi\)
−0.340563 + 0.940222i \(0.610618\pi\)
\(390\) 0 0
\(391\) 91.2149 0.233286
\(392\) 0 0
\(393\) 133.517i 0.339738i
\(394\) 0 0
\(395\) −5.71977 + 5.71977i −0.0144804 + 0.0144804i
\(396\) 0 0
\(397\) 83.7693 83.7693i 0.211006 0.211006i −0.593689 0.804695i \(-0.702329\pi\)
0.804695 + 0.593689i \(0.202329\pi\)
\(398\) 0 0
\(399\) 27.0986i 0.0679162i
\(400\) 0 0
\(401\) 589.134 1.46916 0.734581 0.678521i \(-0.237379\pi\)
0.734581 + 0.678521i \(0.237379\pi\)
\(402\) 0 0
\(403\) 379.494 + 379.494i 0.941673 + 0.941673i
\(404\) 0 0
\(405\) 8.18120 + 8.18120i 0.0202005 + 0.0202005i
\(406\) 0 0
\(407\) −271.606 −0.667337
\(408\) 0 0
\(409\) 449.285i 1.09850i −0.835659 0.549248i \(-0.814914\pi\)
0.835659 0.549248i \(-0.185086\pi\)
\(410\) 0 0
\(411\) 31.7617 31.7617i 0.0772790 0.0772790i
\(412\) 0 0
\(413\) −13.7913 + 13.7913i −0.0333929 + 0.0333929i
\(414\) 0 0
\(415\) 131.040i 0.315759i
\(416\) 0 0
\(417\) 8.91777 0.0213855
\(418\) 0 0
\(419\) 218.639 + 218.639i 0.521811 + 0.521811i 0.918118 0.396307i \(-0.129708\pi\)
−0.396307 + 0.918118i \(0.629708\pi\)
\(420\) 0 0
\(421\) 61.2101 + 61.2101i 0.145392 + 0.145392i 0.776056 0.630664i \(-0.217217\pi\)
−0.630664 + 0.776056i \(0.717217\pi\)
\(422\) 0 0
\(423\) 32.3238 0.0764156
\(424\) 0 0
\(425\) 91.8787i 0.216185i
\(426\) 0 0
\(427\) −45.0136 + 45.0136i −0.105418 + 0.105418i
\(428\) 0 0
\(429\) 272.860 272.860i 0.636038 0.636038i
\(430\) 0 0
\(431\) 501.119i 1.16269i 0.813657 + 0.581345i \(0.197473\pi\)
−0.813657 + 0.581345i \(0.802527\pi\)
\(432\) 0 0
\(433\) 75.5505 0.174482 0.0872408 0.996187i \(-0.472195\pi\)
0.0872408 + 0.996187i \(0.472195\pi\)
\(434\) 0 0
\(435\) −79.2918 79.2918i −0.182280 0.182280i
\(436\) 0 0
\(437\) 391.659 + 391.659i 0.896245 + 0.896245i
\(438\) 0 0
\(439\) 717.251 1.63383 0.816915 0.576758i \(-0.195682\pi\)
0.816915 + 0.576758i \(0.195682\pi\)
\(440\) 0 0
\(441\) 145.714i 0.330417i
\(442\) 0 0
\(443\) −299.093 + 299.093i −0.675153 + 0.675153i −0.958899 0.283746i \(-0.908423\pi\)
0.283746 + 0.958899i \(0.408423\pi\)
\(444\) 0 0
\(445\) −9.64753 + 9.64753i −0.0216798 + 0.0216798i
\(446\) 0 0
\(447\) 46.4714i 0.103963i
\(448\) 0 0
\(449\) −44.5560 −0.0992339 −0.0496170 0.998768i \(-0.515800\pi\)
−0.0496170 + 0.998768i \(0.515800\pi\)
\(450\) 0 0
\(451\) 380.763 + 380.763i 0.844263 + 0.844263i
\(452\) 0 0
\(453\) 126.405 + 126.405i 0.279039 + 0.279039i
\(454\) 0 0
\(455\) −9.91275 −0.0217863
\(456\) 0 0
\(457\) 641.227i 1.40312i 0.712609 + 0.701562i \(0.247514\pi\)
−0.712609 + 0.701562i \(0.752486\pi\)
\(458\) 0 0
\(459\) −14.4592 + 14.4592i −0.0315015 + 0.0315015i
\(460\) 0 0
\(461\) 393.690 393.690i 0.853991 0.853991i −0.136631 0.990622i \(-0.543627\pi\)
0.990622 + 0.136631i \(0.0436273\pi\)
\(462\) 0 0
\(463\) 395.861i 0.854991i 0.904018 + 0.427495i \(0.140604\pi\)
−0.904018 + 0.427495i \(0.859396\pi\)
\(464\) 0 0
\(465\) 101.465 0.218205
\(466\) 0 0
\(467\) 83.1457 + 83.1457i 0.178042 + 0.178042i 0.790502 0.612460i \(-0.209820\pi\)
−0.612460 + 0.790502i \(0.709820\pi\)
\(468\) 0 0
\(469\) 44.4054 + 44.4054i 0.0946810 + 0.0946810i
\(470\) 0 0
\(471\) 216.061 0.458729
\(472\) 0 0
\(473\) 608.217i 1.28587i
\(474\) 0 0
\(475\) −394.509 + 394.509i −0.830546 + 0.830546i
\(476\) 0 0
\(477\) 124.543 124.543i 0.261096 0.261096i
\(478\) 0 0
\(479\) 430.043i 0.897793i −0.893584 0.448896i \(-0.851817\pi\)
0.893584 0.448896i \(-0.148183\pi\)
\(480\) 0 0
\(481\) 169.103 0.351565
\(482\) 0 0
\(483\) −18.5860 18.5860i −0.0384803 0.0384803i
\(484\) 0 0
\(485\) −130.564 130.564i −0.269204 0.269204i
\(486\) 0 0
\(487\) 573.790 1.17821 0.589107 0.808055i \(-0.299480\pi\)
0.589107 + 0.808055i \(0.299480\pi\)
\(488\) 0 0
\(489\) 46.0597i 0.0941916i
\(490\) 0 0
\(491\) 489.133 489.133i 0.996197 0.996197i −0.00379588 0.999993i \(-0.501208\pi\)
0.999993 + 0.00379588i \(0.00120827\pi\)
\(492\) 0 0
\(493\) 140.138 140.138i 0.284255 0.284255i
\(494\) 0 0
\(495\) 72.9546i 0.147383i
\(496\) 0 0
\(497\) −21.8081 −0.0438795
\(498\) 0 0
\(499\) −260.469 260.469i −0.521982 0.521982i 0.396188 0.918170i \(-0.370333\pi\)
−0.918170 + 0.396188i \(0.870333\pi\)
\(500\) 0 0
\(501\) −327.135 327.135i −0.652965 0.652965i
\(502\) 0 0
\(503\) −975.416 −1.93920 −0.969598 0.244701i \(-0.921310\pi\)
−0.969598 + 0.244701i \(0.921310\pi\)
\(504\) 0 0
\(505\) 164.188i 0.325124i
\(506\) 0 0
\(507\) 37.0981 37.0981i 0.0731719 0.0731719i
\(508\) 0 0
\(509\) 420.191 420.191i 0.825523 0.825523i −0.161371 0.986894i \(-0.551592\pi\)
0.986894 + 0.161371i \(0.0515916\pi\)
\(510\) 0 0
\(511\) 12.1994i 0.0238735i
\(512\) 0 0
\(513\) −124.170 −0.242047
\(514\) 0 0
\(515\) 86.5077 + 86.5077i 0.167976 + 0.167976i
\(516\) 0 0
\(517\) −144.121 144.121i −0.278764 0.278764i
\(518\) 0 0
\(519\) −376.044 −0.724556
\(520\) 0 0
\(521\) 396.333i 0.760716i −0.924839 0.380358i \(-0.875801\pi\)
0.924839 0.380358i \(-0.124199\pi\)
\(522\) 0 0
\(523\) −564.600 + 564.600i −1.07954 + 1.07954i −0.0829913 + 0.996550i \(0.526447\pi\)
−0.996550 + 0.0829913i \(0.973553\pi\)
\(524\) 0 0
\(525\) 18.7212 18.7212i 0.0356595 0.0356595i
\(526\) 0 0
\(527\) 179.326i 0.340278i
\(528\) 0 0
\(529\) 8.25115 0.0155976
\(530\) 0 0
\(531\) 63.1938 + 63.1938i 0.119009 + 0.119009i
\(532\) 0 0
\(533\) −237.064 237.064i −0.444773 0.444773i
\(534\) 0 0
\(535\) 49.5461 0.0926095
\(536\) 0 0
\(537\) 302.711i 0.563708i
\(538\) 0 0
\(539\) −649.691 + 649.691i −1.20536 + 1.20536i
\(540\) 0 0
\(541\) 29.5601 29.5601i 0.0546398 0.0546398i −0.679259 0.733899i \(-0.737699\pi\)
0.733899 + 0.679259i \(0.237699\pi\)
\(542\) 0 0
\(543\) 301.201i 0.554698i
\(544\) 0 0
\(545\) −240.733 −0.441711
\(546\) 0 0
\(547\) 138.608 + 138.608i 0.253397 + 0.253397i 0.822362 0.568965i \(-0.192656\pi\)
−0.568965 + 0.822362i \(0.692656\pi\)
\(548\) 0 0
\(549\) 206.259 + 206.259i 0.375700 + 0.375700i
\(550\) 0 0
\(551\) 1203.45 2.18412
\(552\) 0 0
\(553\) 4.11960i 0.00744955i
\(554\) 0 0
\(555\) 22.6065 22.6065i 0.0407324 0.0407324i
\(556\) 0 0
\(557\) −60.4400 + 60.4400i −0.108510 + 0.108510i −0.759277 0.650767i \(-0.774447\pi\)
0.650767 + 0.759277i \(0.274447\pi\)
\(558\) 0 0
\(559\) 378.678i 0.677421i
\(560\) 0 0
\(561\) 128.938 0.229835
\(562\) 0 0
\(563\) −267.325 267.325i −0.474822 0.474822i 0.428649 0.903471i \(-0.358990\pi\)
−0.903471 + 0.428649i \(0.858990\pi\)
\(564\) 0 0
\(565\) −34.5021 34.5021i −0.0610656 0.0610656i
\(566\) 0 0
\(567\) 5.89242 0.0103923
\(568\) 0 0
\(569\) 315.715i 0.554859i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.960746 + 0.277429i \(0.910518\pi\)
\(570\) 0 0
\(571\) 670.572 670.572i 1.17438 1.17438i 0.193228 0.981154i \(-0.438104\pi\)
0.981154 0.193228i \(-0.0618956\pi\)
\(572\) 0 0
\(573\) −237.591 + 237.591i −0.414643 + 0.414643i
\(574\) 0 0
\(575\) 541.161i 0.941149i
\(576\) 0 0
\(577\) 413.628 0.716859 0.358430 0.933557i \(-0.383312\pi\)
0.358430 + 0.933557i \(0.383312\pi\)
\(578\) 0 0
\(579\) −173.368 173.368i −0.299427 0.299427i
\(580\) 0 0
\(581\) −47.1900 47.1900i −0.0812220 0.0812220i
\(582\) 0 0
\(583\) −1110.59 −1.90495
\(584\) 0 0
\(585\) 45.4218i 0.0776441i
\(586\) 0 0
\(587\) 420.085 420.085i 0.715647 0.715647i −0.252064 0.967711i \(-0.581109\pi\)
0.967711 + 0.252064i \(0.0811093\pi\)
\(588\) 0 0
\(589\) −769.993 + 769.993i −1.30729 + 1.30729i
\(590\) 0 0
\(591\) 70.9145i 0.119991i
\(592\) 0 0
\(593\) −740.798 −1.24924 −0.624619 0.780930i \(-0.714746\pi\)
−0.624619 + 0.780930i \(0.714746\pi\)
\(594\) 0 0
\(595\) −2.34209 2.34209i −0.00393628 0.00393628i
\(596\) 0 0
\(597\) 33.8340 + 33.8340i 0.0566733 + 0.0566733i
\(598\) 0 0
\(599\) 435.161 0.726479 0.363240 0.931696i \(-0.381671\pi\)
0.363240 + 0.931696i \(0.381671\pi\)
\(600\) 0 0
\(601\) 380.001i 0.632280i −0.948712 0.316140i \(-0.897613\pi\)
0.948712 0.316140i \(-0.102387\pi\)
\(602\) 0 0
\(603\) 203.473 203.473i 0.337434 0.337434i
\(604\) 0 0
\(605\) −215.288 + 215.288i −0.355849 + 0.355849i
\(606\) 0 0
\(607\) 181.813i 0.299527i −0.988722 0.149763i \(-0.952149\pi\)
0.988722 0.149763i \(-0.0478512\pi\)
\(608\) 0 0
\(609\) −57.1090 −0.0937751
\(610\) 0 0
\(611\) 89.7303 + 89.7303i 0.146858 + 0.146858i
\(612\) 0 0
\(613\) −55.1479 55.1479i −0.0899640 0.0899640i 0.660693 0.750657i \(-0.270263\pi\)
−0.750657 + 0.660693i \(0.770263\pi\)
\(614\) 0 0
\(615\) −63.3838 −0.103063
\(616\) 0 0
\(617\) 579.674i 0.939504i −0.882798 0.469752i \(-0.844343\pi\)
0.882798 0.469752i \(-0.155657\pi\)
\(618\) 0 0
\(619\) −91.1070 + 91.1070i −0.147184 + 0.147184i −0.776859 0.629675i \(-0.783188\pi\)
0.629675 + 0.776859i \(0.283188\pi\)
\(620\) 0 0
\(621\) −85.1639 + 85.1639i −0.137140 + 0.137140i
\(622\) 0 0
\(623\) 6.94852i 0.0111533i
\(624\) 0 0
\(625\) −503.783 −0.806053
\(626\) 0 0
\(627\) 553.633 + 553.633i 0.882987 + 0.882987i
\(628\) 0 0
\(629\) 39.9540 + 39.9540i 0.0635199 + 0.0635199i
\(630\) 0 0
\(631\) −693.474 −1.09901 −0.549504 0.835491i \(-0.685183\pi\)
−0.549504 + 0.835491i \(0.685183\pi\)
\(632\) 0 0
\(633\) 18.0048i 0.0284435i
\(634\) 0 0
\(635\) 87.7570 87.7570i 0.138200 0.138200i
\(636\) 0 0
\(637\) 404.500 404.500i 0.635007 0.635007i
\(638\) 0 0
\(639\) 99.9283i 0.156382i
\(640\) 0 0
\(641\) −218.329 −0.340607 −0.170304 0.985392i \(-0.554475\pi\)
−0.170304 + 0.985392i \(0.554475\pi\)
\(642\) 0 0
\(643\) −887.430 887.430i −1.38014 1.38014i −0.844353 0.535787i \(-0.820015\pi\)
−0.535787 0.844353i \(-0.679985\pi\)
\(644\) 0 0
\(645\) −50.6236 50.6236i −0.0784861 0.0784861i
\(646\) 0 0
\(647\) −223.177 −0.344941 −0.172470 0.985015i \(-0.555175\pi\)
−0.172470 + 0.985015i \(0.555175\pi\)
\(648\) 0 0
\(649\) 563.520i 0.868290i
\(650\) 0 0
\(651\) 36.5396 36.5396i 0.0561284 0.0561284i
\(652\) 0 0
\(653\) −539.691 + 539.691i −0.826479 + 0.826479i −0.987028 0.160549i \(-0.948674\pi\)
0.160549 + 0.987028i \(0.448674\pi\)
\(654\) 0 0
\(655\) 99.0983i 0.151295i
\(656\) 0 0
\(657\) −55.8994 −0.0850828
\(658\) 0 0
\(659\) −625.166 625.166i −0.948659 0.948659i 0.0500862 0.998745i \(-0.484050\pi\)
−0.998745 + 0.0500862i \(0.984050\pi\)
\(660\) 0 0
\(661\) 326.893 + 326.893i 0.494544 + 0.494544i 0.909734 0.415191i \(-0.136285\pi\)
−0.415191 + 0.909734i \(0.636285\pi\)
\(662\) 0 0
\(663\) −80.2770 −0.121081
\(664\) 0 0
\(665\) 20.1129i 0.0302450i
\(666\) 0 0
\(667\) 825.404 825.404i 1.23749 1.23749i
\(668\) 0 0
\(669\) −472.881 + 472.881i −0.706848 + 0.706848i
\(670\) 0 0
\(671\) 1839.28i 2.74111i
\(672\) 0 0
\(673\) 422.147 0.627262 0.313631 0.949545i \(-0.398455\pi\)
0.313631 + 0.949545i \(0.398455\pi\)
\(674\) 0 0
\(675\) −85.7837 85.7837i −0.127087 0.127087i
\(676\) 0 0
\(677\) 126.017 + 126.017i 0.186140 + 0.186140i 0.794025 0.607885i \(-0.207982\pi\)
−0.607885 + 0.794025i \(0.707982\pi\)
\(678\) 0 0
\(679\) −94.0372 −0.138494
\(680\) 0 0
\(681\) 121.810i 0.178869i
\(682\) 0 0
\(683\) −621.906 + 621.906i −0.910551 + 0.910551i −0.996315 0.0857647i \(-0.972667\pi\)
0.0857647 + 0.996315i \(0.472667\pi\)
\(684\) 0 0
\(685\) 23.5740 23.5740i 0.0344145 0.0344145i
\(686\) 0 0
\(687\) 469.984i 0.684111i
\(688\) 0 0
\(689\) 691.456 1.00357
\(690\) 0 0
\(691\) 403.376 + 403.376i 0.583758 + 0.583758i 0.935934 0.352176i \(-0.114558\pi\)
−0.352176 + 0.935934i \(0.614558\pi\)
\(692\) 0 0
\(693\) −26.2724 26.2724i −0.0379110 0.0379110i
\(694\) 0 0
\(695\) 6.61889 0.00952359
\(696\) 0 0
\(697\) 112.022i 0.160721i
\(698\) 0 0
\(699\) 365.722 365.722i 0.523207 0.523207i
\(700\) 0 0
\(701\) −466.593 + 466.593i −0.665611 + 0.665611i −0.956697 0.291086i \(-0.905983\pi\)
0.291086 + 0.956697i \(0.405983\pi\)
\(702\) 0 0
\(703\) 343.109i 0.488065i
\(704\) 0 0
\(705\) 23.9912 0.0340300
\(706\) 0 0
\(707\) −59.1272 59.1272i −0.0836311 0.0836311i
\(708\) 0 0
\(709\) −822.764 822.764i −1.16046 1.16046i −0.984376 0.176081i \(-0.943658\pi\)
−0.176081 0.984376i \(-0.556342\pi\)
\(710\) 0 0
\(711\) 18.8767 0.0265494
\(712\) 0 0
\(713\) 1056.22i 1.48138i
\(714\) 0 0
\(715\) 202.521 202.521i 0.283246 0.283246i
\(716\) 0 0
\(717\) −302.943 + 302.943i −0.422515 + 0.422515i
\(718\) 0 0
\(719\) 710.142i 0.987681i 0.869553 + 0.493840i \(0.164407\pi\)
−0.869553 + 0.493840i \(0.835593\pi\)
\(720\) 0 0
\(721\) 62.3062 0.0864164
\(722\) 0 0
\(723\) 269.856 + 269.856i 0.373245 + 0.373245i
\(724\) 0 0
\(725\) 831.411 + 831.411i 1.14677 + 1.14677i
\(726\) 0 0
\(727\) −214.095 −0.294490 −0.147245 0.989100i \(-0.547041\pi\)
−0.147245 + 0.989100i \(0.547041\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 89.4704 89.4704i 0.122395 0.122395i
\(732\) 0 0
\(733\) 96.1768 96.1768i 0.131210 0.131210i −0.638452 0.769662i \(-0.720425\pi\)
0.769662 + 0.638452i \(0.220425\pi\)
\(734\) 0 0
\(735\) 108.151i 0.147144i
\(736\) 0 0
\(737\) −1814.43 −2.46192
\(738\) 0 0
\(739\) −885.341 885.341i −1.19803 1.19803i −0.974757 0.223268i \(-0.928327\pi\)
−0.223268 0.974757i \(-0.571673\pi\)
\(740\) 0 0
\(741\) −344.694 344.694i −0.465174 0.465174i
\(742\) 0 0
\(743\) 906.258 1.21973 0.609864 0.792506i \(-0.291224\pi\)
0.609864 + 0.792506i \(0.291224\pi\)
\(744\) 0 0
\(745\) 34.4917i 0.0462976i
\(746\) 0 0
\(747\) −216.232 + 216.232i −0.289467 + 0.289467i
\(748\) 0 0
\(749\) 17.8425 17.8425i 0.0238218 0.0238218i
\(750\) 0 0
\(751\) 1147.02i 1.52732i −0.645618 0.763661i \(-0.723400\pi\)
0.645618 0.763661i \(-0.276600\pi\)
\(752\) 0 0
\(753\) 398.572 0.529312
\(754\) 0 0
\(755\) 93.8192 + 93.8192i 0.124264 + 0.124264i
\(756\) 0 0
\(757\) −525.591 525.591i −0.694308 0.694308i 0.268869 0.963177i \(-0.413350\pi\)
−0.963177 + 0.268869i \(0.913350\pi\)
\(758\) 0 0
\(759\) 759.435 1.00057
\(760\) 0 0
\(761\) 788.107i 1.03562i 0.855495 + 0.517810i \(0.173253\pi\)
−0.855495 + 0.517810i \(0.826747\pi\)
\(762\) 0 0
\(763\) −86.6925 + 86.6925i −0.113621 + 0.113621i
\(764\) 0 0
\(765\) −10.7318 + 10.7318i −0.0140285 + 0.0140285i
\(766\) 0 0
\(767\) 350.850i 0.457431i
\(768\) 0 0
\(769\) −768.187 −0.998943 −0.499471 0.866330i \(-0.666472\pi\)
−0.499471 + 0.866330i \(0.666472\pi\)
\(770\) 0 0
\(771\) −123.901 123.901i −0.160702 0.160702i
\(772\) 0 0
\(773\) −275.915 275.915i −0.356941 0.356941i 0.505743 0.862684i \(-0.331218\pi\)
−0.862684 + 0.505743i \(0.831218\pi\)
\(774\) 0 0
\(775\) −1063.91 −1.37279
\(776\) 0 0
\(777\) 16.2821i 0.0209551i
\(778\) 0 0
\(779\) 481.003 481.003i 0.617462 0.617462i
\(780\) 0 0
\(781\) 445.547 445.547i 0.570483 0.570483i
\(782\) 0 0
\(783\) 261.683i 0.334205i
\(784\) 0 0
\(785\) 160.364 0.204285
\(786\) 0 0
\(787\) −240.824 240.824i −0.306002 0.306002i 0.537354 0.843356i \(-0.319424\pi\)
−0.843356 + 0.537354i \(0.819424\pi\)
\(788\) 0 0
\(789\) 396.371 + 396.371i 0.502371 + 0.502371i
\(790\) 0 0
\(791\) −24.8497 −0.0314156
\(792\) 0 0
\(793\) 1145.14i 1.44407i
\(794\) 0 0