Properties

Label 384.3.l.a.223.3
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 223.3
Root \(-1.25564 + 1.55672i\) of defining polynomial
Character \(\chi\) \(=\) 384.223
Dual form 384.3.l.a.31.3

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

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

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
\(5\) −0.909023 + 0.909023i −0.181805 + 0.181805i −0.792142 0.610337i \(-0.791034\pi\)
0.610337 + 0.792142i \(0.291034\pi\)
\(6\) 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 0.969021 + 0.246980i \(0.0794382\pi\)
0.246980 + 0.969021i \(0.420562\pi\)
\(12\) 0 0
\(13\) −8.32795 8.32795i −0.640612 0.640612i 0.310094 0.950706i \(-0.399639\pi\)
−0.950706 + 0.310094i \(0.899639\pi\)
\(14\) 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 −0.994459 0.105123i \(-0.966476\pi\)
0.105123 + 0.994459i \(0.466476\pi\)
\(20\) 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 −0.964739 0.263209i \(-0.915219\pi\)
−0.263209 0.964739i \(-0.584781\pi\)
\(30\) 0 0
\(31\) 45.5687i 1.46996i 0.678089 + 0.734980i \(0.262808\pi\)
−0.678089 + 0.734980i \(0.737192\pi\)
\(32\) 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 −0.830868 0.556470i \(-0.812156\pi\)
0.556470 + 0.830868i \(0.312156\pi\)
\(38\) 0 0
\(39\) 20.3992 0.523057
\(40\) 0 0
\(41\) 28.4661i 0.694295i −0.937811 0.347148i \(-0.887150\pi\)
0.937811 0.347148i \(-0.112850\pi\)
\(42\) 0 0
\(43\) −22.7354 22.7354i −0.528730 0.528730i 0.391464 0.920194i \(-0.371969\pi\)
−0.920194 + 0.391464i \(0.871969\pi\)
\(44\) 0 0
\(45\) 2.72707 + 2.72707i 0.0606015 + 0.0606015i
\(46\) 0 0
\(47\) 10.7746i 0.229247i 0.993409 + 0.114623i \(0.0365661\pi\)
−0.993409 + 0.114623i \(0.963434\pi\)
\(48\) 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 −0.980384 0.197097i \(-0.936849\pi\)
0.197097 + 0.980384i \(0.436849\pi\)
\(54\) 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 0.862716 0.505689i \(-0.168762\pi\)
−0.505689 + 0.862716i \(0.668762\pi\)
\(60\) 0 0
\(61\) 68.7531 + 68.7531i 1.12710 + 1.12710i 0.990647 + 0.136453i \(0.0435703\pi\)
0.136453 + 0.990647i \(0.456430\pi\)
\(62\) 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 −0.0123779 + 0.999923i \(0.503940\pi\)
−0.999923 + 0.0123779i \(0.996060\pi\)
\(68\) 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 \(-0.959265\pi\)
0.991823 0.127624i \(-0.0407351\pi\)
\(74\) 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 \(0.0126798\pi\)
−0.999207 + 0.0398242i \(0.987320\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 72.0774 72.0774i 0.868402 0.868402i −0.123894 0.992296i \(-0.539538\pi\)
0.992296 + 0.123894i \(0.0395382\pi\)
\(84\) 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 \(0.0189902\pi\)
−0.998221 + 0.0596240i \(0.981010\pi\)
\(90\) 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 −0.100753 0.994912i \(-0.532125\pi\)
0.994912 + 0.100753i \(0.0321251\pi\)
\(102\) 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 0.568197 0.822892i \(-0.307641\pi\)
−0.822892 + 0.568197i \(0.807641\pi\)
\(108\) 0 0
\(109\) 132.413 + 132.413i 1.21480 + 1.21480i 0.969430 + 0.245366i \(0.0789082\pi\)
0.245366 + 0.969430i \(0.421092\pi\)
\(110\) 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 \(-0.875897\pi\)
0.924954 0.380078i \(-0.124103\pi\)
\(128\) 0 0
\(129\) 55.6901 0.431706
\(130\) 0 0
\(131\) 54.5082 54.5082i 0.416093 0.416093i −0.467762 0.883855i \(-0.654939\pi\)
0.883855 + 0.467762i \(0.154939\pi\)
\(132\) 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 \(-0.969828\pi\)
0.995511 0.0946471i \(-0.0301723\pi\)
\(138\) 0 0
\(139\) −3.64066 3.64066i −0.0261918 0.0261918i 0.693890 0.720081i \(-0.255896\pi\)
−0.720081 + 0.693890i \(0.755896\pi\)
\(140\) 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 −0.640571 0.767899i \(-0.721302\pi\)
0.767899 + 0.640571i \(0.221302\pi\)
\(150\) 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 0.368000 0.929826i \(-0.380043\pi\)
−0.929826 + 0.368000i \(0.880043\pi\)
\(158\) 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 −0.762431 0.647070i \(-0.775994\pi\)
0.647070 + 0.762431i \(0.275994\pi\)
\(164\) 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 0.994272 0.106876i \(-0.0340849\pi\)
−0.106876 + 0.994272i \(0.534085\pi\)
\(174\) 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 −0.962320 0.271921i \(-0.912341\pi\)
0.271921 + 0.962320i \(0.412341\pi\)
\(180\) 0 0
\(181\) −122.965 + 122.965i −0.679364 + 0.679364i −0.959856 0.280493i \(-0.909502\pi\)
0.280493 + 0.959856i \(0.409502\pi\)
\(182\) 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 \(0.169553\pi\)
−0.861456 + 0.507832i \(0.830447\pi\)
\(192\) 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 −0.776758 0.629800i \(-0.783137\pi\)
0.629800 + 0.776758i \(0.283137\pi\)
\(198\) 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 −0.724310 0.689474i \(-0.757842\pi\)
0.689474 + 0.724310i \(0.257842\pi\)
\(212\) 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 \(0.333131\pi\)
−0.500549 + 0.865708i \(0.666869\pi\)
\(224\) 0 0
\(225\) 70.0421 0.311298
\(226\) 0 0
\(227\) 49.7286 49.7286i 0.219069 0.219069i −0.589037 0.808106i \(-0.700493\pi\)
0.808106 + 0.589037i \(0.200493\pi\)
\(228\) 0 0
\(229\) 191.870 191.870i 0.837861 0.837861i −0.150716 0.988577i \(-0.548158\pi\)
0.988577 + 0.150716i \(0.0481579\pi\)
\(230\) 0 0
\(231\) 21.4513 0.0928627
\(232\) 0 0
\(233\) 298.610i 1.28159i −0.767712 0.640795i \(-0.778605\pi\)
0.767712 0.640795i \(-0.221395\pi\)
\(234\) 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 \(0.173127\pi\)
−0.855700 + 0.517473i \(0.826873\pi\)
\(240\) 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 0.304303 0.952575i \(-0.401576\pi\)
−0.952575 + 0.304303i \(0.901576\pi\)
\(252\) 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 0.704289 0.709913i \(-0.251266\pi\)
−0.709913 + 0.704289i \(0.751266\pi\)
\(270\) 0 0
\(271\) 166.098i 0.612909i 0.951885 + 0.306454i \(0.0991427\pi\)
−0.951885 + 0.306454i \(0.900857\pi\)
\(272\) 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 −0.160338 + 0.987062i \(0.551259\pi\)
−0.987062 + 0.160338i \(0.948741\pi\)
\(278\) 0 0
\(279\) 136.706 0.489986
\(280\) 0 0
\(281\) 402.790i 1.43342i 0.697374 + 0.716708i \(0.254352\pi\)
−0.697374 + 0.716708i \(0.745648\pi\)
\(282\) 0 0
\(283\) 192.406 + 192.406i 0.679881 + 0.679881i 0.959973 0.280092i \(-0.0903649\pi\)
−0.280092 + 0.959973i \(0.590365\pi\)
\(284\) 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 −0.566704 0.823921i \(-0.691782\pi\)
0.823921 + 0.566704i \(0.191782\pi\)
\(294\) 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 −0.501703 0.865040i \(-0.667293\pi\)
0.865040 + 0.501703i \(0.167293\pi\)
\(308\) 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 \(-0.715171\pi\)
0.625661 0.780095i \(-0.284829\pi\)
\(314\) 0 0
\(315\) −1.78545 1.78545i −0.00566809 0.00566809i
\(316\) 0 0
\(317\) −257.361 257.361i −0.811863 0.811863i 0.173050 0.984913i \(-0.444638\pi\)
−0.984913 + 0.173050i \(0.944638\pi\)
\(318\) 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 0.868667 0.495396i \(-0.164977\pi\)
−0.495396 + 0.868667i \(0.664977\pi\)
\(332\) 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 0.861994 0.506918i \(-0.169215\pi\)
−0.506918 + 0.861994i \(0.669215\pi\)
\(348\) 0 0
\(349\) −115.371 115.371i −0.330575 0.330575i 0.522230 0.852805i \(-0.325100\pi\)
−0.852805 + 0.522230i \(0.825100\pi\)
\(350\) 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 \(0.0572832\pi\)
−0.983851 + 0.178991i \(0.942717\pi\)
\(368\) 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 −0.233062 0.972462i \(-0.574874\pi\)
0.972462 + 0.233062i \(0.0748745\pi\)
\(374\) 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 0.724104 0.689691i \(-0.242253\pi\)
−0.689691 + 0.724104i \(0.742253\pi\)
\(380\) 0 0
\(381\) 118.237 + 118.237i 0.310333 + 0.310333i
\(382\) 0 0
\(383\) 121.974i 0.318470i 0.987241 + 0.159235i \(0.0509027\pi\)
−0.987241 + 0.159235i \(0.949097\pi\)
\(384\) 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 −0.340563 0.940222i \(-0.610618\pi\)
0.940222 + 0.340563i \(0.110618\pi\)
\(390\) 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 0.804695 0.593689i \(-0.202329\pi\)
−0.593689 + 0.804695i \(0.702329\pi\)
\(398\) 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 \(0.185086\pi\)
−0.835659 + 0.549248i \(0.814914\pi\)
\(410\) 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 −0.396307 0.918118i \(-0.629708\pi\)
0.918118 + 0.396307i \(0.129708\pi\)
\(420\) 0 0
\(421\) 61.2101 61.2101i 0.145392 0.145392i −0.630664 0.776056i \(-0.717217\pi\)
0.776056 + 0.630664i \(0.217217\pi\)
\(422\) 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 \(-0.802527\pi\)
0.813657 0.581345i \(-0.197473\pi\)
\(432\) 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 0.283746 0.958899i \(-0.408423\pi\)
−0.958899 + 0.283746i \(0.908423\pi\)
\(444\) 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 \(-0.752486\pi\)
0.712609 0.701562i \(-0.247514\pi\)
\(458\) 0 0
\(459\) −14.4592 14.4592i −0.0315015 0.0315015i
\(460\) 0 0
\(461\) 393.690 + 393.690i 0.853991 + 0.853991i 0.990622 0.136631i \(-0.0436273\pi\)
−0.136631 + 0.990622i \(0.543627\pi\)
\(462\) 0 0
\(463\) 395.861i 0.854991i −0.904018 0.427495i \(-0.859396\pi\)
0.904018 0.427495i \(-0.140604\pi\)
\(464\) 0 0
\(465\) 101.465 0.218205
\(466\) 0 0
\(467\) 83.1457 83.1457i 0.178042 0.178042i −0.612460 0.790502i \(-0.709820\pi\)
0.790502 + 0.612460i \(0.209820\pi\)
\(468\) 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 \(0.148183\pi\)
−0.893584 + 0.448896i \(0.851817\pi\)
\(480\) 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 0.999993 0.00379588i \(-0.00120827\pi\)
−0.00379588 + 0.999993i \(0.501208\pi\)
\(492\) 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 −0.918170 0.396188i \(-0.870333\pi\)
0.396188 + 0.918170i \(0.370333\pi\)
\(500\) 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 0.986894 0.161371i \(-0.0515916\pi\)
−0.161371 + 0.986894i \(0.551592\pi\)
\(510\) 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 \(0.124199\pi\)
−0.924839 + 0.380358i \(0.875801\pi\)
\(522\) 0 0
\(523\) −564.600 564.600i −1.07954 1.07954i −0.996550 0.0829913i \(-0.973553\pi\)
−0.0829913 0.996550i \(-0.526447\pi\)
\(524\) 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 0.733899 0.679259i \(-0.237699\pi\)
−0.679259 + 0.733899i \(0.737699\pi\)
\(542\) 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 −0.568965 0.822362i \(-0.692656\pi\)
0.822362 + 0.568965i \(0.192656\pi\)
\(548\) 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 0.650767 0.759277i \(-0.274447\pi\)
−0.759277 + 0.650767i \(0.774447\pi\)
\(558\) 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 −0.903471 0.428649i \(-0.858990\pi\)
0.428649 + 0.903471i \(0.358990\pi\)
\(564\) 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 \(-0.910518\pi\)
0.960746 0.277429i \(-0.0894825\pi\)
\(570\) 0 0
\(571\) 670.572 + 670.572i 1.17438 + 1.17438i 0.981154 + 0.193228i \(0.0618956\pi\)
0.193228 + 0.981154i \(0.438104\pi\)
\(572\) 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 0.967711 0.252064i \(-0.0811093\pi\)
−0.252064 + 0.967711i \(0.581109\pi\)
\(588\) 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 \(0.102387\pi\)
−0.948712 + 0.316140i \(0.897613\pi\)
\(602\) 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 \(0.0478512\pi\)
−0.988722 + 0.149763i \(0.952149\pi\)
\(608\) 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 −0.750657 0.660693i \(-0.770263\pi\)
0.660693 + 0.750657i \(0.270263\pi\)
\(614\) 0 0
\(615\) −63.3838 −0.103063
\(616\) 0 0
\(617\) 579.674i 0.939504i 0.882798 + 0.469752i \(0.155657\pi\)
−0.882798 + 0.469752i \(0.844343\pi\)
\(618\) 0 0
\(619\) −91.1070 91.1070i −0.147184 0.147184i 0.629675 0.776859i \(-0.283188\pi\)
−0.776859 + 0.629675i \(0.783188\pi\)
\(620\) 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 −0.535787 + 0.844353i \(0.679985\pi\)
−0.844353 + 0.535787i \(0.820015\pi\)
\(644\) 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 0.160549 0.987028i \(-0.448674\pi\)
−0.987028 + 0.160549i \(0.948674\pi\)
\(654\) 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 −0.998745 0.0500862i \(-0.984050\pi\)
0.0500862 + 0.998745i \(0.484050\pi\)
\(660\) 0 0
\(661\) 326.893 326.893i 0.494544 0.494544i −0.415191 0.909734i \(-0.636285\pi\)
0.909734 + 0.415191i \(0.136285\pi\)
\(662\) 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 −0.607885 0.794025i \(-0.707982\pi\)
0.794025 + 0.607885i \(0.207982\pi\)
\(678\) 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 0.0857647 0.996315i \(-0.472667\pi\)
−0.996315 + 0.0857647i \(0.972667\pi\)
\(684\) 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 −0.352176 0.935934i \(-0.614558\pi\)
0.935934 + 0.352176i \(0.114558\pi\)
\(692\) 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 0.291086 0.956697i \(-0.405983\pi\)
−0.956697 + 0.291086i \(0.905983\pi\)
\(702\) 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 −0.176081 + 0.984376i \(0.556342\pi\)
−0.984376 + 0.176081i \(0.943658\pi\)
\(710\) 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 \(-0.835593\pi\)
0.869553 0.493840i \(-0.164407\pi\)
\(720\) 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 0.769662 0.638452i \(-0.220425\pi\)
−0.638452 + 0.769662i \(0.720425\pi\)
\(734\) 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 −0.223268 + 0.974757i \(0.571673\pi\)
−0.974757 + 0.223268i \(0.928327\pi\)
\(740\) 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 \(0.276600\pi\)
−0.645618 + 0.763661i \(0.723400\pi\)
\(752\) 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 −0.963177 0.268869i \(-0.913350\pi\)
0.268869 + 0.963177i \(0.413350\pi\)
\(758\) 0 0
\(759\) 759.435 1.00057
\(760\) 0 0
\(761\) 788.107i 1.03562i −0.855495 0.517810i \(-0.826747\pi\)
0.855495 0.517810i \(-0.173253\pi\)
\(762\) 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 −0.862684 0.505743i \(-0.831218\pi\)
0.505743 + 0.862684i \(0.331218\pi\)
\(774\) 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 −0.843356 0.537354i \(-0.819424\pi\)
0.537354 + 0.843356i \(0.319424\pi\)
\(788\) 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
\(795\)