Properties

Label 384.3.l.a.223.7
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 223.7
Root \(-0.455024 + 1.94755i\) of defining polynomial
Character \(\chi\) \(=\) 384.223
Dual form 384.3.l.a.31.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{3} +(3.40572 - 3.40572i) q^{5} +12.1303 q^{7} -3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{3} +(3.40572 - 3.40572i) q^{5} +12.1303 q^{7} -3.00000i q^{9} +(-9.81086 - 9.81086i) q^{11} +(7.76859 + 7.76859i) q^{13} -8.34229i q^{15} +9.73087 q^{17} +(-11.2823 + 11.2823i) q^{19} +(14.8566 - 14.8566i) q^{21} -20.2635 q^{23} +1.80207i q^{25} +(-3.67423 - 3.67423i) q^{27} +(16.4069 + 16.4069i) q^{29} -26.3542i q^{31} -24.0316 q^{33} +(41.3125 - 41.3125i) q^{35} +(23.7263 - 23.7263i) q^{37} +19.0291 q^{39} -24.7452i q^{41} +(-29.8844 - 29.8844i) q^{43} +(-10.2172 - 10.2172i) q^{45} -31.3325i q^{47} +98.1448 q^{49} +(11.9178 - 11.9178i) q^{51} +(-36.8742 + 36.8742i) q^{53} -66.8262 q^{55} +27.6359i q^{57} +(14.1325 + 14.1325i) q^{59} +(42.5199 + 42.5199i) q^{61} -36.3910i q^{63} +52.9153 q^{65} +(-48.7789 + 48.7789i) q^{67} +(-24.8176 + 24.8176i) q^{69} +7.73935 q^{71} +85.4163i q^{73} +(2.20708 + 2.20708i) q^{75} +(-119.009 - 119.009i) q^{77} +105.294i q^{79} -9.00000 q^{81} +(62.1229 - 62.1229i) q^{83} +(33.1407 - 33.1407i) q^{85} +40.1885 q^{87} -127.172i q^{89} +(94.2355 + 94.2355i) q^{91} +(-32.2771 - 32.2771i) q^{93} +76.8489i q^{95} -147.348 q^{97} +(-29.4326 + 29.4326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} - 128q^{23} - 32q^{29} - 96q^{35} + 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} + 160q^{53} - 256q^{55} + 128q^{59} + 32q^{61} - 32q^{65} - 320q^{67} - 96q^{69} + 512q^{71} - 192q^{75} - 224q^{77} - 144q^{81} + 160q^{83} - 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

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
\(5\) 3.40572 3.40572i 0.681145 0.681145i −0.279113 0.960258i \(-0.590040\pi\)
0.960258 + 0.279113i \(0.0900405\pi\)
\(6\) 0 0
\(7\) 12.1303 1.73290 0.866452 0.499261i \(-0.166395\pi\)
0.866452 + 0.499261i \(0.166395\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −9.81086 9.81086i −0.891896 0.891896i 0.102805 0.994702i \(-0.467218\pi\)
−0.994702 + 0.102805i \(0.967218\pi\)
\(12\) 0 0
\(13\) 7.76859 + 7.76859i 0.597584 + 0.597584i 0.939669 0.342085i \(-0.111133\pi\)
−0.342085 + 0.939669i \(0.611133\pi\)
\(14\) 0 0
\(15\) 8.34229i 0.556153i
\(16\) 0 0
\(17\) 9.73087 0.572404 0.286202 0.958169i \(-0.407607\pi\)
0.286202 + 0.958169i \(0.407607\pi\)
\(18\) 0 0
\(19\) −11.2823 + 11.2823i −0.593806 + 0.593806i −0.938657 0.344851i \(-0.887929\pi\)
0.344851 + 0.938657i \(0.387929\pi\)
\(20\) 0 0
\(21\) 14.8566 14.8566i 0.707455 0.707455i
\(22\) 0 0
\(23\) −20.2635 −0.881020 −0.440510 0.897748i \(-0.645202\pi\)
−0.440510 + 0.897748i \(0.645202\pi\)
\(24\) 0 0
\(25\) 1.80207i 0.0720830i
\(26\) 0 0
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 0 0
\(29\) 16.4069 + 16.4069i 0.565754 + 0.565754i 0.930936 0.365182i \(-0.118993\pi\)
−0.365182 + 0.930936i \(0.618993\pi\)
\(30\) 0 0
\(31\) 26.3542i 0.850134i −0.905162 0.425067i \(-0.860251\pi\)
0.905162 0.425067i \(-0.139749\pi\)
\(32\) 0 0
\(33\) −24.0316 −0.728230
\(34\) 0 0
\(35\) 41.3125 41.3125i 1.18036 1.18036i
\(36\) 0 0
\(37\) 23.7263 23.7263i 0.641250 0.641250i −0.309613 0.950863i \(-0.600199\pi\)
0.950863 + 0.309613i \(0.100199\pi\)
\(38\) 0 0
\(39\) 19.0291 0.487925
\(40\) 0 0
\(41\) 24.7452i 0.603542i −0.953380 0.301771i \(-0.902422\pi\)
0.953380 0.301771i \(-0.0975779\pi\)
\(42\) 0 0
\(43\) −29.8844 29.8844i −0.694987 0.694987i 0.268338 0.963325i \(-0.413526\pi\)
−0.963325 + 0.268338i \(0.913526\pi\)
\(44\) 0 0
\(45\) −10.2172 10.2172i −0.227048 0.227048i
\(46\) 0 0
\(47\) 31.3325i 0.666648i −0.942812 0.333324i \(-0.891830\pi\)
0.942812 0.333324i \(-0.108170\pi\)
\(48\) 0 0
\(49\) 98.1448 2.00295
\(50\) 0 0
\(51\) 11.9178 11.9178i 0.233683 0.233683i
\(52\) 0 0
\(53\) −36.8742 + 36.8742i −0.695739 + 0.695739i −0.963489 0.267750i \(-0.913720\pi\)
0.267750 + 0.963489i \(0.413720\pi\)
\(54\) 0 0
\(55\) −66.8262 −1.21502
\(56\) 0 0
\(57\) 27.6359i 0.484841i
\(58\) 0 0
\(59\) 14.1325 + 14.1325i 0.239534 + 0.239534i 0.816657 0.577123i \(-0.195825\pi\)
−0.577123 + 0.816657i \(0.695825\pi\)
\(60\) 0 0
\(61\) 42.5199 + 42.5199i 0.697048 + 0.697048i 0.963773 0.266725i \(-0.0859414\pi\)
−0.266725 + 0.963773i \(0.585941\pi\)
\(62\) 0 0
\(63\) 36.3910i 0.577634i
\(64\) 0 0
\(65\) 52.9153 0.814082
\(66\) 0 0
\(67\) −48.7789 + 48.7789i −0.728044 + 0.728044i −0.970230 0.242186i \(-0.922136\pi\)
0.242186 + 0.970230i \(0.422136\pi\)
\(68\) 0 0
\(69\) −24.8176 + 24.8176i −0.359675 + 0.359675i
\(70\) 0 0
\(71\) 7.73935 0.109005 0.0545025 0.998514i \(-0.482643\pi\)
0.0545025 + 0.998514i \(0.482643\pi\)
\(72\) 0 0
\(73\) 85.4163i 1.17009i 0.811002 + 0.585043i \(0.198923\pi\)
−0.811002 + 0.585043i \(0.801077\pi\)
\(74\) 0 0
\(75\) 2.20708 + 2.20708i 0.0294278 + 0.0294278i
\(76\) 0 0
\(77\) −119.009 119.009i −1.54557 1.54557i
\(78\) 0 0
\(79\) 105.294i 1.33283i 0.745581 + 0.666416i \(0.232172\pi\)
−0.745581 + 0.666416i \(0.767828\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 62.1229 62.1229i 0.748469 0.748469i −0.225723 0.974192i \(-0.572474\pi\)
0.974192 + 0.225723i \(0.0724743\pi\)
\(84\) 0 0
\(85\) 33.1407 33.1407i 0.389890 0.389890i
\(86\) 0 0
\(87\) 40.1885 0.461937
\(88\) 0 0
\(89\) 127.172i 1.42890i −0.699685 0.714451i \(-0.746676\pi\)
0.699685 0.714451i \(-0.253324\pi\)
\(90\) 0 0
\(91\) 94.2355 + 94.2355i 1.03555 + 1.03555i
\(92\) 0 0
\(93\) −32.2771 32.2771i −0.347066 0.347066i
\(94\) 0 0
\(95\) 76.8489i 0.808936i
\(96\) 0 0
\(97\) −147.348 −1.51905 −0.759525 0.650478i \(-0.774569\pi\)
−0.759525 + 0.650478i \(0.774569\pi\)
\(98\) 0 0
\(99\) −29.4326 + 29.4326i −0.297299 + 0.297299i
\(100\) 0 0
\(101\) −12.7690 + 12.7690i −0.126426 + 0.126426i −0.767489 0.641063i \(-0.778494\pi\)
0.641063 + 0.767489i \(0.278494\pi\)
\(102\) 0 0
\(103\) −17.7621 −0.172448 −0.0862240 0.996276i \(-0.527480\pi\)
−0.0862240 + 0.996276i \(0.527480\pi\)
\(104\) 0 0
\(105\) 101.195i 0.963759i
\(106\) 0 0
\(107\) 15.8889 + 15.8889i 0.148494 + 0.148494i 0.777445 0.628951i \(-0.216515\pi\)
−0.628951 + 0.777445i \(0.716515\pi\)
\(108\) 0 0
\(109\) 79.3257 + 79.3257i 0.727758 + 0.727758i 0.970173 0.242414i \(-0.0779394\pi\)
−0.242414 + 0.970173i \(0.577939\pi\)
\(110\) 0 0
\(111\) 58.1172i 0.523579i
\(112\) 0 0
\(113\) −167.538 −1.48263 −0.741317 0.671155i \(-0.765799\pi\)
−0.741317 + 0.671155i \(0.765799\pi\)
\(114\) 0 0
\(115\) −69.0118 + 69.0118i −0.600102 + 0.600102i
\(116\) 0 0
\(117\) 23.3058 23.3058i 0.199195 0.199195i
\(118\) 0 0
\(119\) 118.039 0.991921
\(120\) 0 0
\(121\) 71.5059i 0.590958i
\(122\) 0 0
\(123\) −30.3066 30.3066i −0.246395 0.246395i
\(124\) 0 0
\(125\) 91.2805 + 91.2805i 0.730244 + 0.730244i
\(126\) 0 0
\(127\) 198.247i 1.56100i 0.625156 + 0.780500i \(0.285035\pi\)
−0.625156 + 0.780500i \(0.714965\pi\)
\(128\) 0 0
\(129\) −73.2016 −0.567454
\(130\) 0 0
\(131\) −134.339 + 134.339i −1.02549 + 1.02549i −0.0258197 + 0.999667i \(0.508220\pi\)
−0.999667 + 0.0258197i \(0.991780\pi\)
\(132\) 0 0
\(133\) −136.858 + 136.858i −1.02901 + 1.02901i
\(134\) 0 0
\(135\) −25.0269 −0.185384
\(136\) 0 0
\(137\) 255.937i 1.86816i 0.357069 + 0.934078i \(0.383776\pi\)
−0.357069 + 0.934078i \(0.616224\pi\)
\(138\) 0 0
\(139\) 21.7231 + 21.7231i 0.156281 + 0.156281i 0.780917 0.624635i \(-0.214752\pi\)
−0.624635 + 0.780917i \(0.714752\pi\)
\(140\) 0 0
\(141\) −38.3743 38.3743i −0.272158 0.272158i
\(142\) 0 0
\(143\) 152.433i 1.06597i
\(144\) 0 0
\(145\) 111.755 0.770722
\(146\) 0 0
\(147\) 120.202 120.202i 0.817703 0.817703i
\(148\) 0 0
\(149\) 34.2444 34.2444i 0.229828 0.229828i −0.582793 0.812621i \(-0.698040\pi\)
0.812621 + 0.582793i \(0.198040\pi\)
\(150\) 0 0
\(151\) −14.4645 −0.0957913 −0.0478956 0.998852i \(-0.515251\pi\)
−0.0478956 + 0.998852i \(0.515251\pi\)
\(152\) 0 0
\(153\) 29.1926i 0.190801i
\(154\) 0 0
\(155\) −89.7550 89.7550i −0.579064 0.579064i
\(156\) 0 0
\(157\) −31.4652 31.4652i −0.200415 0.200415i 0.599763 0.800178i \(-0.295262\pi\)
−0.800178 + 0.599763i \(0.795262\pi\)
\(158\) 0 0
\(159\) 90.3229i 0.568068i
\(160\) 0 0
\(161\) −245.802 −1.52672
\(162\) 0 0
\(163\) −31.4002 + 31.4002i −0.192640 + 0.192640i −0.796836 0.604196i \(-0.793494\pi\)
0.604196 + 0.796836i \(0.293494\pi\)
\(164\) 0 0
\(165\) −81.8450 + 81.8450i −0.496030 + 0.496030i
\(166\) 0 0
\(167\) 36.4796 0.218441 0.109220 0.994018i \(-0.465165\pi\)
0.109220 + 0.994018i \(0.465165\pi\)
\(168\) 0 0
\(169\) 48.2981i 0.285788i
\(170\) 0 0
\(171\) 33.8469 + 33.8469i 0.197935 + 0.197935i
\(172\) 0 0
\(173\) −97.6419 97.6419i −0.564404 0.564404i 0.366151 0.930555i \(-0.380675\pi\)
−0.930555 + 0.366151i \(0.880675\pi\)
\(174\) 0 0
\(175\) 21.8598i 0.124913i
\(176\) 0 0
\(177\) 34.6175 0.195579
\(178\) 0 0
\(179\) −89.7427 + 89.7427i −0.501356 + 0.501356i −0.911859 0.410503i \(-0.865353\pi\)
0.410503 + 0.911859i \(0.365353\pi\)
\(180\) 0 0
\(181\) 115.497 115.497i 0.638108 0.638108i −0.311981 0.950088i \(-0.600992\pi\)
0.950088 + 0.311981i \(0.100992\pi\)
\(182\) 0 0
\(183\) 104.152 0.569137
\(184\) 0 0
\(185\) 161.610i 0.873569i
\(186\) 0 0
\(187\) −95.4682 95.4682i −0.510525 0.510525i
\(188\) 0 0
\(189\) −44.5697 44.5697i −0.235818 0.235818i
\(190\) 0 0
\(191\) 62.6278i 0.327894i 0.986469 + 0.163947i \(0.0524227\pi\)
−0.986469 + 0.163947i \(0.947577\pi\)
\(192\) 0 0
\(193\) 223.342 1.15721 0.578607 0.815607i \(-0.303597\pi\)
0.578607 + 0.815607i \(0.303597\pi\)
\(194\) 0 0
\(195\) 64.8078 64.8078i 0.332348 0.332348i
\(196\) 0 0
\(197\) −29.0959 + 29.0959i −0.147695 + 0.147695i −0.777087 0.629393i \(-0.783304\pi\)
0.629393 + 0.777087i \(0.283304\pi\)
\(198\) 0 0
\(199\) 11.6967 0.0587776 0.0293888 0.999568i \(-0.490644\pi\)
0.0293888 + 0.999568i \(0.490644\pi\)
\(200\) 0 0
\(201\) 119.484i 0.594445i
\(202\) 0 0
\(203\) 199.021 + 199.021i 0.980398 + 0.980398i
\(204\) 0 0
\(205\) −84.2755 84.2755i −0.411100 0.411100i
\(206\) 0 0
\(207\) 60.7904i 0.293673i
\(208\) 0 0
\(209\) 221.378 1.05923
\(210\) 0 0
\(211\) 0.215765 0.215765i 0.00102258 0.00102258i −0.706595 0.707618i \(-0.749770\pi\)
0.707618 + 0.706595i \(0.249770\pi\)
\(212\) 0 0
\(213\) 9.47873 9.47873i 0.0445011 0.0445011i
\(214\) 0 0
\(215\) −203.556 −0.946773
\(216\) 0 0
\(217\) 319.684i 1.47320i
\(218\) 0 0
\(219\) 104.613 + 104.613i 0.477686 + 0.477686i
\(220\) 0 0
\(221\) 75.5951 + 75.5951i 0.342059 + 0.342059i
\(222\) 0 0
\(223\) 371.347i 1.66523i −0.553850 0.832617i \(-0.686842\pi\)
0.553850 0.832617i \(-0.313158\pi\)
\(224\) 0 0
\(225\) 5.40622 0.0240277
\(226\) 0 0
\(227\) 209.823 209.823i 0.924330 0.924330i −0.0730018 0.997332i \(-0.523258\pi\)
0.997332 + 0.0730018i \(0.0232579\pi\)
\(228\) 0 0
\(229\) −152.751 + 152.751i −0.667037 + 0.667037i −0.957029 0.289992i \(-0.906347\pi\)
0.289992 + 0.957029i \(0.406347\pi\)
\(230\) 0 0
\(231\) −291.511 −1.26195
\(232\) 0 0
\(233\) 272.899i 1.17124i 0.810586 + 0.585619i \(0.199149\pi\)
−0.810586 + 0.585619i \(0.800851\pi\)
\(234\) 0 0
\(235\) −106.710 106.710i −0.454084 0.454084i
\(236\) 0 0
\(237\) 128.958 + 128.958i 0.544126 + 0.544126i
\(238\) 0 0
\(239\) 104.650i 0.437866i −0.975740 0.218933i \(-0.929742\pi\)
0.975740 0.218933i \(-0.0702576\pi\)
\(240\) 0 0
\(241\) 148.875 0.617737 0.308869 0.951105i \(-0.400050\pi\)
0.308869 + 0.951105i \(0.400050\pi\)
\(242\) 0 0
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 334.254 334.254i 1.36430 1.36430i
\(246\) 0 0
\(247\) −175.295 −0.709698
\(248\) 0 0
\(249\) 152.169i 0.611122i
\(250\) 0 0
\(251\) −143.712 143.712i −0.572558 0.572558i 0.360284 0.932843i \(-0.382680\pi\)
−0.932843 + 0.360284i \(0.882680\pi\)
\(252\) 0 0
\(253\) 198.802 + 198.802i 0.785778 + 0.785778i
\(254\) 0 0
\(255\) 81.1777i 0.318344i
\(256\) 0 0
\(257\) 134.023 0.521489 0.260745 0.965408i \(-0.416032\pi\)
0.260745 + 0.965408i \(0.416032\pi\)
\(258\) 0 0
\(259\) 287.807 287.807i 1.11122 1.11122i
\(260\) 0 0
\(261\) 49.2206 49.2206i 0.188585 0.188585i
\(262\) 0 0
\(263\) 290.386 1.10413 0.552066 0.833801i \(-0.313840\pi\)
0.552066 + 0.833801i \(0.313840\pi\)
\(264\) 0 0
\(265\) 251.166i 0.947798i
\(266\) 0 0
\(267\) −155.754 155.754i −0.583347 0.583347i
\(268\) 0 0
\(269\) 74.2628 + 74.2628i 0.276070 + 0.276070i 0.831538 0.555468i \(-0.187461\pi\)
−0.555468 + 0.831538i \(0.687461\pi\)
\(270\) 0 0
\(271\) 70.8329i 0.261376i 0.991424 + 0.130688i \(0.0417186\pi\)
−0.991424 + 0.130688i \(0.958281\pi\)
\(272\) 0 0
\(273\) 230.829 0.845527
\(274\) 0 0
\(275\) 17.6799 17.6799i 0.0642906 0.0642906i
\(276\) 0 0
\(277\) 96.6953 96.6953i 0.349081 0.349081i −0.510686 0.859767i \(-0.670609\pi\)
0.859767 + 0.510686i \(0.170609\pi\)
\(278\) 0 0
\(279\) −79.0625 −0.283378
\(280\) 0 0
\(281\) 138.151i 0.491640i −0.969316 0.245820i \(-0.920943\pi\)
0.969316 0.245820i \(-0.0790572\pi\)
\(282\) 0 0
\(283\) 295.011 + 295.011i 1.04244 + 1.04244i 0.999059 + 0.0433821i \(0.0138133\pi\)
0.0433821 + 0.999059i \(0.486187\pi\)
\(284\) 0 0
\(285\) 94.1203 + 94.1203i 0.330247 + 0.330247i
\(286\) 0 0
\(287\) 300.168i 1.04588i
\(288\) 0 0
\(289\) −194.310 −0.672353
\(290\) 0 0
\(291\) −180.464 + 180.464i −0.620150 + 0.620150i
\(292\) 0 0
\(293\) 33.4759 33.4759i 0.114252 0.114252i −0.647669 0.761922i \(-0.724256\pi\)
0.761922 + 0.647669i \(0.224256\pi\)
\(294\) 0 0
\(295\) 96.2630 0.326315
\(296\) 0 0
\(297\) 72.0948i 0.242743i
\(298\) 0 0
\(299\) −157.418 157.418i −0.526483 0.526483i
\(300\) 0 0
\(301\) −362.508 362.508i −1.20434 1.20434i
\(302\) 0 0
\(303\) 31.2776i 0.103226i
\(304\) 0 0
\(305\) 289.622 0.949582
\(306\) 0 0
\(307\) 92.6638 92.6638i 0.301836 0.301836i −0.539896 0.841732i \(-0.681536\pi\)
0.841732 + 0.539896i \(0.181536\pi\)
\(308\) 0 0
\(309\) −21.7541 + 21.7541i −0.0704016 + 0.0704016i
\(310\) 0 0
\(311\) −18.5610 −0.0596817 −0.0298408 0.999555i \(-0.509500\pi\)
−0.0298408 + 0.999555i \(0.509500\pi\)
\(312\) 0 0
\(313\) 55.1534i 0.176209i −0.996111 0.0881045i \(-0.971919\pi\)
0.996111 0.0881045i \(-0.0280809\pi\)
\(314\) 0 0
\(315\) −123.938 123.938i −0.393453 0.393453i
\(316\) 0 0
\(317\) −62.2977 62.2977i −0.196523 0.196523i 0.601985 0.798507i \(-0.294377\pi\)
−0.798507 + 0.601985i \(0.794377\pi\)
\(318\) 0 0
\(319\) 321.931i 1.00919i
\(320\) 0 0
\(321\) 38.9197 0.121245
\(322\) 0 0
\(323\) −109.787 + 109.787i −0.339897 + 0.339897i
\(324\) 0 0
\(325\) −13.9996 + 13.9996i −0.0430756 + 0.0430756i
\(326\) 0 0
\(327\) 194.307 0.594212
\(328\) 0 0
\(329\) 380.073i 1.15524i
\(330\) 0 0
\(331\) −373.767 373.767i −1.12921 1.12921i −0.990307 0.138899i \(-0.955644\pi\)
−0.138899 0.990307i \(-0.544356\pi\)
\(332\) 0 0
\(333\) −71.1788 71.1788i −0.213750 0.213750i
\(334\) 0 0
\(335\) 332.255i 0.991807i
\(336\) 0 0
\(337\) −519.936 −1.54284 −0.771419 0.636328i \(-0.780453\pi\)
−0.771419 + 0.636328i \(0.780453\pi\)
\(338\) 0 0
\(339\) −205.191 + 205.191i −0.605283 + 0.605283i
\(340\) 0 0
\(341\) −258.557 + 258.557i −0.758231 + 0.758231i
\(342\) 0 0
\(343\) 596.142 1.73802
\(344\) 0 0
\(345\) 169.044i 0.489981i
\(346\) 0 0
\(347\) −122.160 122.160i −0.352045 0.352045i 0.508825 0.860870i \(-0.330080\pi\)
−0.860870 + 0.508825i \(0.830080\pi\)
\(348\) 0 0
\(349\) 279.483 + 279.483i 0.800810 + 0.800810i 0.983222 0.182412i \(-0.0583906\pi\)
−0.182412 + 0.983222i \(0.558391\pi\)
\(350\) 0 0
\(351\) 57.0872i 0.162642i
\(352\) 0 0
\(353\) −212.266 −0.601320 −0.300660 0.953731i \(-0.597207\pi\)
−0.300660 + 0.953731i \(0.597207\pi\)
\(354\) 0 0
\(355\) 26.3581 26.3581i 0.0742482 0.0742482i
\(356\) 0 0
\(357\) 144.567 144.567i 0.404950 0.404950i
\(358\) 0 0
\(359\) −435.033 −1.21179 −0.605895 0.795545i \(-0.707185\pi\)
−0.605895 + 0.795545i \(0.707185\pi\)
\(360\) 0 0
\(361\) 106.419i 0.294789i
\(362\) 0 0
\(363\) 87.5765 + 87.5765i 0.241258 + 0.241258i
\(364\) 0 0
\(365\) 290.905 + 290.905i 0.796999 + 0.796999i
\(366\) 0 0
\(367\) 125.535i 0.342058i 0.985266 + 0.171029i \(0.0547091\pi\)
−0.985266 + 0.171029i \(0.945291\pi\)
\(368\) 0 0
\(369\) −74.2357 −0.201181
\(370\) 0 0
\(371\) −447.295 + 447.295i −1.20565 + 1.20565i
\(372\) 0 0
\(373\) 302.389 302.389i 0.810694 0.810694i −0.174044 0.984738i \(-0.555683\pi\)
0.984738 + 0.174044i \(0.0556835\pi\)
\(374\) 0 0
\(375\) 223.591 0.596242
\(376\) 0 0
\(377\) 254.917i 0.676171i
\(378\) 0 0
\(379\) −189.784 189.784i −0.500751 0.500751i 0.410921 0.911671i \(-0.365207\pi\)
−0.911671 + 0.410921i \(0.865207\pi\)
\(380\) 0 0
\(381\) 242.802 + 242.802i 0.637275 + 0.637275i
\(382\) 0 0
\(383\) 639.916i 1.67080i 0.549644 + 0.835399i \(0.314763\pi\)
−0.549644 + 0.835399i \(0.685237\pi\)
\(384\) 0 0
\(385\) −810.623 −2.10551
\(386\) 0 0
\(387\) −89.6533 + 89.6533i −0.231662 + 0.231662i
\(388\) 0 0
\(389\) −499.333 + 499.333i −1.28363 + 1.28363i −0.345046 + 0.938586i \(0.612137\pi\)
−0.938586 + 0.345046i \(0.887863\pi\)
\(390\) 0 0
\(391\) −197.181 −0.504300
\(392\) 0 0
\(393\) 329.061i 0.837306i
\(394\) 0 0
\(395\) 358.601 + 358.601i 0.907851 + 0.907851i
\(396\) 0 0
\(397\) −492.518 492.518i −1.24060 1.24060i −0.959753 0.280846i \(-0.909385\pi\)
−0.280846 0.959753i \(-0.590615\pi\)
\(398\) 0 0
\(399\) 335.233i 0.840182i
\(400\) 0 0
\(401\) 705.045 1.75822 0.879109 0.476621i \(-0.158138\pi\)
0.879109 + 0.476621i \(0.158138\pi\)
\(402\) 0 0
\(403\) 204.735 204.735i 0.508026 0.508026i
\(404\) 0 0
\(405\) −30.6515 + 30.6515i −0.0756828 + 0.0756828i
\(406\) 0 0
\(407\) −465.550 −1.14386
\(408\) 0 0
\(409\) 279.815i 0.684144i −0.939674 0.342072i \(-0.888871\pi\)
0.939674 0.342072i \(-0.111129\pi\)
\(410\) 0 0
\(411\) 313.458 + 313.458i 0.762671 + 0.762671i
\(412\) 0 0
\(413\) 171.432 + 171.432i 0.415090 + 0.415090i
\(414\) 0 0
\(415\) 423.147i 1.01963i
\(416\) 0 0
\(417\) 53.2106 0.127603
\(418\) 0 0
\(419\) 573.583 573.583i 1.36893 1.36893i 0.506968 0.861965i \(-0.330766\pi\)
0.861965 0.506968i \(-0.169234\pi\)
\(420\) 0 0
\(421\) 213.341 213.341i 0.506749 0.506749i −0.406778 0.913527i \(-0.633348\pi\)
0.913527 + 0.406778i \(0.133348\pi\)
\(422\) 0 0
\(423\) −93.9974 −0.222216
\(424\) 0 0
\(425\) 17.5358i 0.0412606i
\(426\) 0 0
\(427\) 515.781 + 515.781i 1.20792 + 1.20792i
\(428\) 0 0
\(429\) −186.692 186.692i −0.435178 0.435178i
\(430\) 0 0
\(431\) 166.900i 0.387239i −0.981077 0.193619i \(-0.937977\pi\)
0.981077 0.193619i \(-0.0620227\pi\)
\(432\) 0 0
\(433\) 233.153 0.538459 0.269230 0.963076i \(-0.413231\pi\)
0.269230 + 0.963076i \(0.413231\pi\)
\(434\) 0 0
\(435\) 136.871 136.871i 0.314646 0.314646i
\(436\) 0 0
\(437\) 228.619 228.619i 0.523155 0.523155i
\(438\) 0 0
\(439\) 440.480 1.00337 0.501686 0.865050i \(-0.332713\pi\)
0.501686 + 0.865050i \(0.332713\pi\)
\(440\) 0 0
\(441\) 294.434i 0.667651i
\(442\) 0 0
\(443\) 312.524 + 312.524i 0.705473 + 0.705473i 0.965580 0.260107i \(-0.0837579\pi\)
−0.260107 + 0.965580i \(0.583758\pi\)
\(444\) 0 0
\(445\) −433.114 433.114i −0.973290 0.973290i
\(446\) 0 0
\(447\) 83.8814i 0.187654i
\(448\) 0 0
\(449\) −734.338 −1.63550 −0.817748 0.575576i \(-0.804778\pi\)
−0.817748 + 0.575576i \(0.804778\pi\)
\(450\) 0 0
\(451\) −242.772 + 242.772i −0.538297 + 0.538297i
\(452\) 0 0
\(453\) −17.7153 + 17.7153i −0.0391066 + 0.0391066i
\(454\) 0 0
\(455\) 641.880 1.41073
\(456\) 0 0
\(457\) 692.749i 1.51586i −0.652335 0.757931i \(-0.726211\pi\)
0.652335 0.757931i \(-0.273789\pi\)
\(458\) 0 0
\(459\) −35.7535 35.7535i −0.0778944 0.0778944i
\(460\) 0 0
\(461\) −298.447 298.447i −0.647391 0.647391i 0.304971 0.952362i \(-0.401353\pi\)
−0.952362 + 0.304971i \(0.901353\pi\)
\(462\) 0 0
\(463\) 281.830i 0.608705i −0.952560 0.304352i \(-0.901560\pi\)
0.952560 0.304352i \(-0.0984400\pi\)
\(464\) 0 0
\(465\) −219.854 −0.472804
\(466\) 0 0
\(467\) −198.116 + 198.116i −0.424232 + 0.424232i −0.886658 0.462426i \(-0.846979\pi\)
0.462426 + 0.886658i \(0.346979\pi\)
\(468\) 0 0
\(469\) −591.704 + 591.704i −1.26163 + 1.26163i
\(470\) 0 0
\(471\) −77.0737 −0.163638
\(472\) 0 0
\(473\) 586.384i 1.23971i
\(474\) 0 0
\(475\) −20.3316 20.3316i −0.0428033 0.0428033i
\(476\) 0 0
\(477\) 110.622 + 110.622i 0.231913 + 0.231913i
\(478\) 0 0
\(479\) 917.713i 1.91589i 0.286945 + 0.957947i \(0.407360\pi\)
−0.286945 + 0.957947i \(0.592640\pi\)
\(480\) 0 0
\(481\) 368.639 0.766401
\(482\) 0 0
\(483\) −301.045 + 301.045i −0.623282 + 0.623282i
\(484\) 0 0
\(485\) −501.826 + 501.826i −1.03469 + 1.03469i
\(486\) 0 0
\(487\) −426.183 −0.875119 −0.437559 0.899190i \(-0.644157\pi\)
−0.437559 + 0.899190i \(0.644157\pi\)
\(488\) 0 0
\(489\) 76.9146i 0.157290i
\(490\) 0 0
\(491\) 266.299 + 266.299i 0.542361 + 0.542361i 0.924220 0.381859i \(-0.124716\pi\)
−0.381859 + 0.924220i \(0.624716\pi\)
\(492\) 0 0
\(493\) 159.653 + 159.653i 0.323840 + 0.323840i
\(494\) 0 0
\(495\) 200.479i 0.405007i
\(496\) 0 0
\(497\) 93.8809 0.188895
\(498\) 0 0
\(499\) 264.104 264.104i 0.529266 0.529266i −0.391088 0.920353i \(-0.627901\pi\)
0.920353 + 0.391088i \(0.127901\pi\)
\(500\) 0 0
\(501\) 44.6782 44.6782i 0.0891781 0.0891781i
\(502\) 0 0
\(503\) −574.766 −1.14268 −0.571338 0.820715i \(-0.693575\pi\)
−0.571338 + 0.820715i \(0.693575\pi\)
\(504\) 0 0
\(505\) 86.9756i 0.172229i
\(506\) 0 0
\(507\) −59.1528 59.1528i −0.116672 0.116672i
\(508\) 0 0
\(509\) −170.592 170.592i −0.335152 0.335152i 0.519387 0.854539i \(-0.326160\pi\)
−0.854539 + 0.519387i \(0.826160\pi\)
\(510\) 0 0
\(511\) 1036.13i 2.02765i
\(512\) 0 0
\(513\) 82.9077 0.161614
\(514\) 0 0
\(515\) −60.4930 + 60.4930i −0.117462 + 0.117462i
\(516\) 0 0
\(517\) −307.398 + 307.398i −0.594581 + 0.594581i
\(518\) 0 0
\(519\) −239.173 −0.460834
\(520\) 0 0
\(521\) 37.1210i 0.0712496i −0.999365 0.0356248i \(-0.988658\pi\)
0.999365 0.0356248i \(-0.0113421\pi\)
\(522\) 0 0
\(523\) 199.555 + 199.555i 0.381558 + 0.381558i 0.871663 0.490105i \(-0.163042\pi\)
−0.490105 + 0.871663i \(0.663042\pi\)
\(524\) 0 0
\(525\) 26.7726 + 26.7726i 0.0509955 + 0.0509955i
\(526\) 0 0
\(527\) 256.449i 0.486620i
\(528\) 0 0
\(529\) −118.392 −0.223804
\(530\) 0 0
\(531\) 42.3976 42.3976i 0.0798448 0.0798448i
\(532\) 0 0
\(533\) 192.236 192.236i 0.360667 0.360667i
\(534\) 0 0
\(535\) 108.226 0.202292
\(536\) 0 0
\(537\) 219.824i 0.409355i
\(538\) 0 0
\(539\) −962.884 962.884i −1.78643 1.78643i
\(540\) 0 0
\(541\) −278.121 278.121i −0.514086 0.514086i 0.401690 0.915776i \(-0.368423\pi\)
−0.915776 + 0.401690i \(0.868423\pi\)
\(542\) 0 0
\(543\) 282.910i 0.521013i
\(544\) 0 0
\(545\) 540.323 0.991418
\(546\) 0 0
\(547\) −724.938 + 724.938i −1.32530 + 1.32530i −0.415876 + 0.909421i \(0.636525\pi\)
−0.909421 + 0.415876i \(0.863475\pi\)
\(548\) 0 0
\(549\) 127.560 127.560i 0.232349 0.232349i
\(550\) 0 0
\(551\) −370.215 −0.671897
\(552\) 0 0
\(553\) 1277.25i 2.30967i
\(554\) 0 0
\(555\) −197.931 197.931i −0.356633 0.356633i
\(556\) 0 0
\(557\) −268.298 268.298i −0.481685 0.481685i 0.423985 0.905669i \(-0.360631\pi\)
−0.905669 + 0.423985i \(0.860631\pi\)
\(558\) 0 0
\(559\) 464.320i 0.830625i
\(560\) 0 0
\(561\) −233.848 −0.416842
\(562\) 0 0
\(563\) 78.4662 78.4662i 0.139372 0.139372i −0.633979 0.773350i \(-0.718579\pi\)
0.773350 + 0.633979i \(0.218579\pi\)
\(564\) 0 0
\(565\) −570.587 + 570.587i −1.00989 + 1.00989i
\(566\) 0 0
\(567\) −109.173 −0.192545
\(568\) 0 0
\(569\) 801.999i 1.40949i −0.709461 0.704744i \(-0.751062\pi\)
0.709461 0.704744i \(-0.248938\pi\)
\(570\) 0 0
\(571\) −79.9964 79.9964i −0.140099 0.140099i 0.633579 0.773678i \(-0.281585\pi\)
−0.773678 + 0.633579i \(0.781585\pi\)
\(572\) 0 0
\(573\) 76.7031 + 76.7031i 0.133862 + 0.133862i
\(574\) 0 0
\(575\) 36.5163i 0.0635066i
\(576\) 0 0
\(577\) −237.186 −0.411068 −0.205534 0.978650i \(-0.565893\pi\)
−0.205534 + 0.978650i \(0.565893\pi\)
\(578\) 0 0
\(579\) 273.537 273.537i 0.472430 0.472430i
\(580\) 0 0
\(581\) 753.571 753.571i 1.29702 1.29702i
\(582\) 0 0
\(583\) 723.534 1.24105
\(584\) 0 0
\(585\) 158.746i 0.271361i
\(586\) 0 0
\(587\) 267.958 + 267.958i 0.456487 + 0.456487i 0.897500 0.441014i \(-0.145381\pi\)
−0.441014 + 0.897500i \(0.645381\pi\)
\(588\) 0 0
\(589\) 297.336 + 297.336i 0.504815 + 0.504815i
\(590\) 0 0
\(591\) 71.2701i 0.120592i
\(592\) 0 0
\(593\) −607.086 −1.02375 −0.511877 0.859059i \(-0.671050\pi\)
−0.511877 + 0.859059i \(0.671050\pi\)
\(594\) 0 0
\(595\) 402.007 402.007i 0.675642 0.675642i
\(596\) 0 0
\(597\) 14.3255 14.3255i 0.0239958 0.0239958i
\(598\) 0 0
\(599\) 575.392 0.960587 0.480294 0.877108i \(-0.340530\pi\)
0.480294 + 0.877108i \(0.340530\pi\)
\(600\) 0 0
\(601\) 310.094i 0.515963i −0.966150 0.257981i \(-0.916943\pi\)
0.966150 0.257981i \(-0.0830573\pi\)
\(602\) 0 0
\(603\) 146.337 + 146.337i 0.242681 + 0.242681i
\(604\) 0 0
\(605\) 243.529 + 243.529i 0.402528 + 0.402528i
\(606\) 0 0
\(607\) 556.510i 0.916820i −0.888741 0.458410i \(-0.848419\pi\)
0.888741 0.458410i \(-0.151581\pi\)
\(608\) 0 0
\(609\) 487.499 0.800492
\(610\) 0 0
\(611\) 243.409 243.409i 0.398378 0.398378i
\(612\) 0 0
\(613\) 326.241 326.241i 0.532204 0.532204i −0.389024 0.921228i \(-0.627188\pi\)
0.921228 + 0.389024i \(0.127188\pi\)
\(614\) 0 0
\(615\) −206.432 −0.335662
\(616\) 0 0
\(617\) 502.068i 0.813725i −0.913490 0.406862i \(-0.866623\pi\)
0.913490 0.406862i \(-0.133377\pi\)
\(618\) 0 0
\(619\) −304.429 304.429i −0.491808 0.491808i 0.417067 0.908876i \(-0.363058\pi\)
−0.908876 + 0.417067i \(0.863058\pi\)
\(620\) 0 0
\(621\) 74.4527 + 74.4527i 0.119892 + 0.119892i
\(622\) 0 0
\(623\) 1542.64i 2.47615i
\(624\) 0 0
\(625\) 576.701 0.922721
\(626\) 0 0
\(627\) 271.132 271.132i 0.432428 0.432428i
\(628\) 0 0
\(629\) 230.877 230.877i 0.367054 0.367054i
\(630\) 0 0
\(631\) 8.60592 0.0136385 0.00681927 0.999977i \(-0.497829\pi\)
0.00681927 + 0.999977i \(0.497829\pi\)
\(632\) 0 0
\(633\) 0.528515i 0.000834936i
\(634\) 0 0
\(635\) 675.174 + 675.174i 1.06327 + 1.06327i
\(636\) 0 0
\(637\) 762.446 + 762.446i 1.19693 + 1.19693i
\(638\) 0 0
\(639\) 23.2181i 0.0363350i
\(640\) 0 0
\(641\) −445.780 −0.695445 −0.347722 0.937598i \(-0.613045\pi\)
−0.347722 + 0.937598i \(0.613045\pi\)
\(642\) 0 0
\(643\) 118.001 118.001i 0.183517 0.183517i −0.609369 0.792886i \(-0.708577\pi\)
0.792886 + 0.609369i \(0.208577\pi\)
\(644\) 0 0
\(645\) −249.304 + 249.304i −0.386519 + 0.386519i
\(646\) 0 0
\(647\) 1081.35 1.67132 0.835662 0.549243i \(-0.185084\pi\)
0.835662 + 0.549243i \(0.185084\pi\)
\(648\) 0 0
\(649\) 277.305i 0.427280i
\(650\) 0 0
\(651\) −391.532 391.532i −0.601431 0.601431i
\(652\) 0 0
\(653\) 586.227 + 586.227i 0.897744 + 0.897744i 0.995236 0.0974927i \(-0.0310823\pi\)
−0.0974927 + 0.995236i \(0.531082\pi\)
\(654\) 0 0
\(655\) 915.041i 1.39701i
\(656\) 0 0
\(657\) 256.249 0.390029
\(658\) 0 0
\(659\) −469.999 + 469.999i −0.713201 + 0.713201i −0.967204 0.254003i \(-0.918253\pi\)
0.254003 + 0.967204i \(0.418253\pi\)
\(660\) 0 0
\(661\) 884.745 884.745i 1.33849 1.33849i 0.440976 0.897519i \(-0.354632\pi\)
0.897519 0.440976i \(-0.145368\pi\)
\(662\) 0 0
\(663\) 185.170 0.279290
\(664\) 0 0
\(665\) 932.202i 1.40181i
\(666\) 0 0
\(667\) −332.460 332.460i −0.498441 0.498441i
\(668\) 0 0
\(669\) −454.805 454.805i −0.679829 0.679829i
\(670\) 0 0
\(671\) 834.314i 1.24339i
\(672\) 0 0
\(673\) 684.329 1.01683 0.508417 0.861111i \(-0.330231\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(674\) 0 0
\(675\) 6.62125 6.62125i 0.00980925 0.00980925i
\(676\) 0 0
\(677\) 383.762 383.762i 0.566857 0.566857i −0.364390 0.931246i \(-0.618722\pi\)
0.931246 + 0.364390i \(0.118722\pi\)
\(678\) 0 0
\(679\) −1787.38 −2.63237
\(680\) 0 0
\(681\) 513.959i 0.754712i
\(682\) 0 0
\(683\) −903.626 903.626i −1.32302 1.32302i −0.911315 0.411709i \(-0.864932\pi\)
−0.411709 0.911315i \(-0.635068\pi\)
\(684\) 0 0
\(685\) 871.652 + 871.652i 1.27248 + 1.27248i
\(686\) 0 0
\(687\) 374.163i 0.544633i
\(688\) 0 0
\(689\) −572.920 −0.831524
\(690\) 0 0
\(691\) 63.6870 63.6870i 0.0921665 0.0921665i −0.659520 0.751687i \(-0.729241\pi\)
0.751687 + 0.659520i \(0.229241\pi\)
\(692\) 0 0
\(693\) −357.027 + 357.027i −0.515190 + 0.515190i
\(694\) 0 0
\(695\) 147.966 0.212901
\(696\) 0 0
\(697\) 240.793i 0.345470i
\(698\) 0 0
\(699\) 334.231 + 334.231i 0.478156 + 0.478156i
\(700\) 0 0
\(701\) −218.312 218.312i −0.311430 0.311430i 0.534033 0.845463i \(-0.320676\pi\)
−0.845463 + 0.534033i \(0.820676\pi\)
\(702\) 0 0
\(703\) 535.374i 0.761557i
\(704\) 0 0
\(705\) −261.384 −0.370758
\(706\) 0 0
\(707\) −154.893 + 154.893i −0.219084 + 0.219084i
\(708\) 0 0
\(709\) 822.199 822.199i 1.15966 1.15966i 0.175112 0.984548i \(-0.443971\pi\)
0.984548 0.175112i \(-0.0560288\pi\)
\(710\) 0 0
\(711\) 315.881 0.444277
\(712\) 0 0
\(713\) 534.026i 0.748985i
\(714\) 0 0
\(715\) −519.145 519.145i −0.726077 0.726077i
\(716\) 0 0
\(717\) −128.169 128.169i −0.178758 0.178758i
\(718\) 0 0
\(719\) 340.913i 0.474149i 0.971491 + 0.237074i \(0.0761885\pi\)
−0.971491 + 0.237074i \(0.923811\pi\)
\(720\) 0 0
\(721\) −215.461 −0.298836
\(722\) 0 0
\(723\) 182.334 182.334i 0.252190 0.252190i
\(724\) 0 0
\(725\) −29.5664 + 29.5664i −0.0407813 + 0.0407813i
\(726\) 0 0
\(727\) −803.090 −1.10466 −0.552331 0.833625i \(-0.686262\pi\)
−0.552331 + 0.833625i \(0.686262\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −290.802 290.802i −0.397813 0.397813i
\(732\) 0 0
\(733\) −481.592 481.592i −0.657015 0.657015i 0.297658 0.954673i \(-0.403795\pi\)
−0.954673 + 0.297658i \(0.903795\pi\)
\(734\) 0 0
\(735\) 818.752i 1.11395i
\(736\) 0 0
\(737\) 957.127 1.29868
\(738\) 0 0
\(739\) −173.622 + 173.622i −0.234941 + 0.234941i −0.814752 0.579810i \(-0.803127\pi\)
0.579810 + 0.814752i \(0.303127\pi\)
\(740\) 0 0
\(741\) −214.692 + 214.692i −0.289733 + 0.289733i
\(742\) 0 0
\(743\) 1316.22 1.77149 0.885744 0.464173i \(-0.153649\pi\)
0.885744 + 0.464173i \(0.153649\pi\)
\(744\) 0 0
\(745\) 233.254i 0.313093i
\(746\) 0 0
\(747\) −186.369 186.369i −0.249490 0.249490i
\(748\) 0 0
\(749\) 192.737 + 192.737i 0.257326 + 0.257326i
\(750\) 0 0
\(751\) 322.977i 0.430062i −0.976607 0.215031i \(-0.931015\pi\)
0.976607 0.215031i \(-0.0689853\pi\)
\(752\) 0 0
\(753\) −352.021 −0.467492
\(754\) 0 0
\(755\) −49.2621 + 49.2621i −0.0652478 + 0.0652478i
\(756\) 0 0
\(757\) 80.2744 80.2744i 0.106043 0.106043i −0.652095 0.758138i \(-0.726110\pi\)
0.758138 + 0.652095i \(0.226110\pi\)
\(758\) 0 0
\(759\) 486.963 0.641585
\(760\) 0 0
\(761\) 596.664i 0.784053i −0.919954 0.392027i \(-0.871774\pi\)
0.919954 0.392027i \(-0.128226\pi\)
\(762\) 0 0
\(763\) 962.246 + 962.246i 1.26113 + 1.26113i
\(764\) 0 0
\(765\) −99.4220 99.4220i −0.129963 0.129963i
\(766\) 0 0
\(767\) 219.580i 0.286284i
\(768\) 0 0
\(769\) 1515.31 1.97050 0.985249 0.171129i \(-0.0547416\pi\)
0.985249 + 0.171129i \(0.0547416\pi\)
\(770\) 0 0
\(771\) 164.144 164.144i 0.212897 0.212897i
\(772\) 0 0
\(773\) −607.901 + 607.901i −0.786418 + 0.786418i −0.980905 0.194487i \(-0.937696\pi\)
0.194487 + 0.980905i \(0.437696\pi\)
\(774\) 0 0
\(775\) 47.4922 0.0612802
\(776\) 0 0
\(777\) 704.981i 0.907311i
\(778\) 0 0
\(779\) 279.184 + 279.184i 0.358387 + 0.358387i
\(780\) 0 0
\(781\) −75.9297 75.9297i −0.0972211 0.0972211i
\(782\) 0 0
\(783\) 120.565i 0.153979i
\(784\) 0 0
\(785\) −214.324 −0.273024
\(786\) 0 0
\(787\) −356.009 + 356.009i −0.452362 + 0.452362i −0.896138 0.443776i \(-0.853639\pi\)
0.443776 + 0.896138i \(0.353639\pi\)
\(788\) 0 0
\(789\) 355.649 355.649i 0.450760 0.450760i
\(790\) 0 0
\(791\) −2032.29 −2.56926
\(792\) 0 0
\(793\) 660.640i 0.833089i
\(794\) 0 0