Properties

Label 2646.2.h.q.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.q.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.93185 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.93185 q^{5} +1.00000 q^{8} +(0.965926 + 1.67303i) q^{10} -5.46410 q^{11} +(1.22474 + 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.15660 - 5.46739i) q^{17} +(-0.965926 + 1.67303i) q^{19} +(0.965926 - 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +5.92820 q^{23} -1.26795 q^{25} +(1.22474 - 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} +(-3.67423 + 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.15660 + 5.46739i) q^{34} +(4.00000 - 6.92820i) q^{37} +1.93185 q^{38} -1.93185 q^{40} +(-2.82843 - 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.96410 - 5.13397i) q^{46} +(4.76028 + 8.24504i) q^{47} +(0.633975 + 1.09808i) q^{50} -2.44949 q^{52} +(1.63397 + 2.83013i) q^{53} +10.5558 q^{55} +0.732051 q^{58} +(-2.50026 + 4.33057i) q^{59} +(-1.48356 - 2.56961i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(-2.36603 - 4.09808i) q^{65} +(7.09808 - 12.2942i) q^{67} +6.31319 q^{68} +11.1962 q^{71} +(4.76028 + 8.24504i) q^{73} -8.00000 q^{74} +(-0.965926 - 1.67303i) q^{76} +(5.06218 + 8.76795i) q^{79} +(0.965926 + 1.67303i) q^{80} +(-2.82843 + 4.89898i) q^{82} +(4.94975 - 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} -1.80385 q^{86} -5.46410 q^{88} +(-6.64136 + 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +(4.76028 - 8.24504i) q^{94} +(1.86603 - 3.23205i) q^{95} +(1.93185 - 3.34607i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.93185 −0.863950 −0.431975 0.901886i \(-0.642183\pi\)
−0.431975 + 0.901886i \(0.642183\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.965926 + 1.67303i 0.305453 + 0.529059i
\(11\) −5.46410 −1.64749 −0.823744 0.566961i \(-0.808119\pi\)
−0.823744 + 0.566961i \(0.808119\pi\)
\(12\) 0 0
\(13\) 1.22474 + 2.12132i 0.339683 + 0.588348i 0.984373 0.176096i \(-0.0563468\pi\)
−0.644690 + 0.764444i \(0.723014\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.15660 5.46739i −0.765587 1.32604i −0.939936 0.341352i \(-0.889115\pi\)
0.174349 0.984684i \(-0.444218\pi\)
\(18\) 0 0
\(19\) −0.965926 + 1.67303i −0.221599 + 0.383820i −0.955294 0.295659i \(-0.904461\pi\)
0.733695 + 0.679479i \(0.237794\pi\)
\(20\) 0.965926 1.67303i 0.215988 0.374101i
\(21\) 0 0
\(22\) 2.73205 + 4.73205i 0.582475 + 1.00888i
\(23\) 5.92820 1.23612 0.618058 0.786133i \(-0.287920\pi\)
0.618058 + 0.786133i \(0.287920\pi\)
\(24\) 0 0
\(25\) −1.26795 −0.253590
\(26\) 1.22474 2.12132i 0.240192 0.416025i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.366025 + 0.633975i −0.0679692 + 0.117726i −0.898007 0.439981i \(-0.854985\pi\)
0.830038 + 0.557707i \(0.188319\pi\)
\(30\) 0 0
\(31\) −3.67423 + 6.36396i −0.659912 + 1.14300i 0.320726 + 0.947172i \(0.396073\pi\)
−0.980638 + 0.195829i \(0.937260\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.15660 + 5.46739i −0.541352 + 0.937649i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 1.93185 0.313388
\(39\) 0 0
\(40\) −1.93185 −0.305453
\(41\) −2.82843 4.89898i −0.441726 0.765092i 0.556092 0.831121i \(-0.312300\pi\)
−0.997818 + 0.0660290i \(0.978967\pi\)
\(42\) 0 0
\(43\) 0.901924 1.56218i 0.137542 0.238230i −0.789024 0.614363i \(-0.789413\pi\)
0.926566 + 0.376133i \(0.122746\pi\)
\(44\) 2.73205 4.73205i 0.411872 0.713384i
\(45\) 0 0
\(46\) −2.96410 5.13397i −0.437033 0.756963i
\(47\) 4.76028 + 8.24504i 0.694358 + 1.20266i 0.970397 + 0.241517i \(0.0776449\pi\)
−0.276039 + 0.961147i \(0.589022\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.633975 + 1.09808i 0.0896575 + 0.155291i
\(51\) 0 0
\(52\) −2.44949 −0.339683
\(53\) 1.63397 + 2.83013i 0.224444 + 0.388748i 0.956152 0.292870i \(-0.0946102\pi\)
−0.731709 + 0.681617i \(0.761277\pi\)
\(54\) 0 0
\(55\) 10.5558 1.42335
\(56\) 0 0
\(57\) 0 0
\(58\) 0.732051 0.0961230
\(59\) −2.50026 + 4.33057i −0.325506 + 0.563793i −0.981615 0.190874i \(-0.938868\pi\)
0.656109 + 0.754666i \(0.272201\pi\)
\(60\) 0 0
\(61\) −1.48356 2.56961i −0.189951 0.329005i 0.755283 0.655399i \(-0.227500\pi\)
−0.945234 + 0.326394i \(0.894166\pi\)
\(62\) 7.34847 0.933257
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.36603 4.09808i −0.293469 0.508304i
\(66\) 0 0
\(67\) 7.09808 12.2942i 0.867168 1.50198i 0.00228979 0.999997i \(-0.499271\pi\)
0.864878 0.501982i \(-0.167396\pi\)
\(68\) 6.31319 0.765587
\(69\) 0 0
\(70\) 0 0
\(71\) 11.1962 1.32874 0.664369 0.747404i \(-0.268700\pi\)
0.664369 + 0.747404i \(0.268700\pi\)
\(72\) 0 0
\(73\) 4.76028 + 8.24504i 0.557148 + 0.965009i 0.997733 + 0.0672983i \(0.0214379\pi\)
−0.440584 + 0.897711i \(0.645229\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) −0.965926 1.67303i −0.110799 0.191910i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.06218 + 8.76795i 0.569540 + 0.986471i 0.996611 + 0.0822537i \(0.0262118\pi\)
−0.427072 + 0.904218i \(0.640455\pi\)
\(80\) 0.965926 + 1.67303i 0.107994 + 0.187051i
\(81\) 0 0
\(82\) −2.82843 + 4.89898i −0.312348 + 0.541002i
\(83\) 4.94975 8.57321i 0.543305 0.941033i −0.455406 0.890284i \(-0.650506\pi\)
0.998711 0.0507487i \(-0.0161607\pi\)
\(84\) 0 0
\(85\) 6.09808 + 10.5622i 0.661429 + 1.14563i
\(86\) −1.80385 −0.194514
\(87\) 0 0
\(88\) −5.46410 −0.582475
\(89\) −6.64136 + 11.5032i −0.703983 + 1.21933i 0.263074 + 0.964776i \(0.415264\pi\)
−0.967057 + 0.254559i \(0.918070\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.96410 + 5.13397i −0.309029 + 0.535254i
\(93\) 0 0
\(94\) 4.76028 8.24504i 0.490985 0.850411i
\(95\) 1.86603 3.23205i 0.191450 0.331601i
\(96\) 0 0
\(97\) 1.93185 3.34607i 0.196150 0.339741i −0.751127 0.660158i \(-0.770489\pi\)
0.947277 + 0.320416i \(0.103823\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.633975 1.09808i 0.0633975 0.109808i
\(101\) −1.55291 −0.154521 −0.0772604 0.997011i \(-0.524617\pi\)
−0.0772604 + 0.997011i \(0.524617\pi\)
\(102\) 0 0
\(103\) −8.38375 −0.826075 −0.413037 0.910714i \(-0.635532\pi\)
−0.413037 + 0.910714i \(0.635532\pi\)
\(104\) 1.22474 + 2.12132i 0.120096 + 0.208013i
\(105\) 0 0
\(106\) 1.63397 2.83013i 0.158706 0.274886i
\(107\) 8.46410 14.6603i 0.818256 1.41726i −0.0887109 0.996057i \(-0.528275\pi\)
0.906966 0.421203i \(-0.138392\pi\)
\(108\) 0 0
\(109\) 10.2942 + 17.8301i 0.986008 + 1.70782i 0.637367 + 0.770560i \(0.280023\pi\)
0.348641 + 0.937256i \(0.386643\pi\)
\(110\) −5.27792 9.14162i −0.503230 0.871619i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.33013 + 2.30385i 0.125128 + 0.216728i 0.921783 0.387706i \(-0.126733\pi\)
−0.796655 + 0.604434i \(0.793399\pi\)
\(114\) 0 0
\(115\) −11.4524 −1.06794
\(116\) −0.366025 0.633975i −0.0339846 0.0588631i
\(117\) 0 0
\(118\) 5.00052 0.460335
\(119\) 0 0
\(120\) 0 0
\(121\) 18.8564 1.71422
\(122\) −1.48356 + 2.56961i −0.134316 + 0.232641i
\(123\) 0 0
\(124\) −3.67423 6.36396i −0.329956 0.571501i
\(125\) 12.1087 1.08304
\(126\) 0 0
\(127\) 7.92820 0.703514 0.351757 0.936091i \(-0.385584\pi\)
0.351757 + 0.936091i \(0.385584\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −2.36603 + 4.09808i −0.207514 + 0.359425i
\(131\) 0.240237 0.0209896 0.0104948 0.999945i \(-0.496659\pi\)
0.0104948 + 0.999945i \(0.496659\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −14.1962 −1.22636
\(135\) 0 0
\(136\) −3.15660 5.46739i −0.270676 0.468824i
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0.915158 + 1.58510i 0.0776227 + 0.134446i 0.902224 0.431268i \(-0.141934\pi\)
−0.824601 + 0.565715i \(0.808600\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.59808 9.69615i −0.469780 0.813683i
\(143\) −6.69213 11.5911i −0.559624 0.969297i
\(144\) 0 0
\(145\) 0.707107 1.22474i 0.0587220 0.101710i
\(146\) 4.76028 8.24504i 0.393963 0.682365i
\(147\) 0 0
\(148\) 4.00000 + 6.92820i 0.328798 + 0.569495i
\(149\) −18.3923 −1.50676 −0.753378 0.657588i \(-0.771577\pi\)
−0.753378 + 0.657588i \(0.771577\pi\)
\(150\) 0 0
\(151\) 3.39230 0.276062 0.138031 0.990428i \(-0.455923\pi\)
0.138031 + 0.990428i \(0.455923\pi\)
\(152\) −0.965926 + 1.67303i −0.0783469 + 0.135701i
\(153\) 0 0
\(154\) 0 0
\(155\) 7.09808 12.2942i 0.570131 0.987496i
\(156\) 0 0
\(157\) 12.1781 21.0931i 0.971918 1.68341i 0.282166 0.959366i \(-0.408947\pi\)
0.689752 0.724046i \(-0.257720\pi\)
\(158\) 5.06218 8.76795i 0.402725 0.697541i
\(159\) 0 0
\(160\) 0.965926 1.67303i 0.0763631 0.132265i
\(161\) 0 0
\(162\) 0 0
\(163\) 10.4641 18.1244i 0.819612 1.41961i −0.0863569 0.996264i \(-0.527523\pi\)
0.905969 0.423345i \(-0.139144\pi\)
\(164\) 5.65685 0.441726
\(165\) 0 0
\(166\) −9.89949 −0.768350
\(167\) 8.05558 + 13.9527i 0.623359 + 1.07969i 0.988856 + 0.148877i \(0.0475659\pi\)
−0.365497 + 0.930813i \(0.619101\pi\)
\(168\) 0 0
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) 6.09808 10.5622i 0.467701 0.810082i
\(171\) 0 0
\(172\) 0.901924 + 1.56218i 0.0687710 + 0.119115i
\(173\) 7.26054 + 12.5756i 0.552008 + 0.956107i 0.998130 + 0.0611340i \(0.0194717\pi\)
−0.446121 + 0.894973i \(0.647195\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.73205 + 4.73205i 0.205936 + 0.356692i
\(177\) 0 0
\(178\) 13.2827 0.995582
\(179\) 1.09808 + 1.90192i 0.0820741 + 0.142156i 0.904141 0.427235i \(-0.140512\pi\)
−0.822067 + 0.569391i \(0.807179\pi\)
\(180\) 0 0
\(181\) 8.72552 0.648563 0.324281 0.945961i \(-0.394878\pi\)
0.324281 + 0.945961i \(0.394878\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 5.92820 0.437033
\(185\) −7.72741 + 13.3843i −0.568130 + 0.984030i
\(186\) 0 0
\(187\) 17.2480 + 29.8744i 1.26130 + 2.18463i
\(188\) −9.52056 −0.694358
\(189\) 0 0
\(190\) −3.73205 −0.270751
\(191\) 1.59808 + 2.76795i 0.115633 + 0.200282i 0.918033 0.396505i \(-0.129777\pi\)
−0.802400 + 0.596787i \(0.796444\pi\)
\(192\) 0 0
\(193\) 10.1340 17.5526i 0.729459 1.26346i −0.227652 0.973742i \(-0.573105\pi\)
0.957112 0.289718i \(-0.0935617\pi\)
\(194\) −3.86370 −0.277398
\(195\) 0 0
\(196\) 0 0
\(197\) 7.66025 0.545771 0.272885 0.962047i \(-0.412022\pi\)
0.272885 + 0.962047i \(0.412022\pi\)
\(198\) 0 0
\(199\) −1.55291 2.68973i −0.110083 0.190670i 0.805720 0.592296i \(-0.201778\pi\)
−0.915804 + 0.401626i \(0.868445\pi\)
\(200\) −1.26795 −0.0896575
\(201\) 0 0
\(202\) 0.776457 + 1.34486i 0.0546313 + 0.0946242i
\(203\) 0 0
\(204\) 0 0
\(205\) 5.46410 + 9.46410i 0.381629 + 0.661002i
\(206\) 4.19187 + 7.26054i 0.292062 + 0.505866i
\(207\) 0 0
\(208\) 1.22474 2.12132i 0.0849208 0.147087i
\(209\) 5.27792 9.14162i 0.365081 0.632339i
\(210\) 0 0
\(211\) −2.36603 4.09808i −0.162884 0.282123i 0.773018 0.634384i \(-0.218746\pi\)
−0.935902 + 0.352261i \(0.885413\pi\)
\(212\) −3.26795 −0.224444
\(213\) 0 0
\(214\) −16.9282 −1.15719
\(215\) −1.74238 + 3.01790i −0.118830 + 0.205819i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.2942 17.8301i 0.697213 1.20761i
\(219\) 0 0
\(220\) −5.27792 + 9.14162i −0.355837 + 0.616328i
\(221\) 7.73205 13.3923i 0.520114 0.900864i
\(222\) 0 0
\(223\) −10.3664 + 17.9551i −0.694183 + 1.20236i 0.276272 + 0.961079i \(0.410901\pi\)
−0.970455 + 0.241281i \(0.922432\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.33013 2.30385i 0.0884787 0.153250i
\(227\) 0.896575 0.0595078 0.0297539 0.999557i \(-0.490528\pi\)
0.0297539 + 0.999557i \(0.490528\pi\)
\(228\) 0 0
\(229\) 18.0430 1.19232 0.596158 0.802867i \(-0.296693\pi\)
0.596158 + 0.802867i \(0.296693\pi\)
\(230\) 5.72620 + 9.91808i 0.377575 + 0.653979i
\(231\) 0 0
\(232\) −0.366025 + 0.633975i −0.0240307 + 0.0416225i
\(233\) −9.69615 + 16.7942i −0.635216 + 1.10023i 0.351253 + 0.936280i \(0.385756\pi\)
−0.986469 + 0.163946i \(0.947578\pi\)
\(234\) 0 0
\(235\) −9.19615 15.9282i −0.599891 1.03904i
\(236\) −2.50026 4.33057i −0.162753 0.281896i
\(237\) 0 0
\(238\) 0 0
\(239\) −2.76795 4.79423i −0.179044 0.310113i 0.762510 0.646977i \(-0.223967\pi\)
−0.941553 + 0.336864i \(0.890634\pi\)
\(240\) 0 0
\(241\) −12.7279 −0.819878 −0.409939 0.912113i \(-0.634450\pi\)
−0.409939 + 0.912113i \(0.634450\pi\)
\(242\) −9.42820 16.3301i −0.606068 1.04974i
\(243\) 0 0
\(244\) 2.96713 0.189951
\(245\) 0 0
\(246\) 0 0
\(247\) −4.73205 −0.301093
\(248\) −3.67423 + 6.36396i −0.233314 + 0.404112i
\(249\) 0 0
\(250\) −6.05437 10.4865i −0.382912 0.663223i
\(251\) 1.93185 0.121937 0.0609687 0.998140i \(-0.480581\pi\)
0.0609687 + 0.998140i \(0.480581\pi\)
\(252\) 0 0
\(253\) −32.3923 −2.03649
\(254\) −3.96410 6.86603i −0.248730 0.430813i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −20.7327 −1.29327 −0.646636 0.762799i \(-0.723825\pi\)
−0.646636 + 0.762799i \(0.723825\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.73205 0.293469
\(261\) 0 0
\(262\) −0.120118 0.208051i −0.00742094 0.0128534i
\(263\) 14.6603 0.903990 0.451995 0.892020i \(-0.350712\pi\)
0.451995 + 0.892020i \(0.350712\pi\)
\(264\) 0 0
\(265\) −3.15660 5.46739i −0.193908 0.335859i
\(266\) 0 0
\(267\) 0 0
\(268\) 7.09808 + 12.2942i 0.433584 + 0.750990i
\(269\) 0.0185824 + 0.0321856i 0.00113299 + 0.00196239i 0.866591 0.499018i \(-0.166306\pi\)
−0.865458 + 0.500981i \(0.832973\pi\)
\(270\) 0 0
\(271\) 2.50026 4.33057i 0.151880 0.263064i −0.780039 0.625731i \(-0.784801\pi\)
0.931919 + 0.362668i \(0.118134\pi\)
\(272\) −3.15660 + 5.46739i −0.191397 + 0.331509i
\(273\) 0 0
\(274\) 0 0
\(275\) 6.92820 0.417786
\(276\) 0 0
\(277\) −5.80385 −0.348719 −0.174360 0.984682i \(-0.555786\pi\)
−0.174360 + 0.984682i \(0.555786\pi\)
\(278\) 0.915158 1.58510i 0.0548875 0.0950680i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.69615 2.93782i 0.101184 0.175256i −0.810989 0.585062i \(-0.801070\pi\)
0.912173 + 0.409806i \(0.134404\pi\)
\(282\) 0 0
\(283\) 8.55463 14.8171i 0.508520 0.880783i −0.491431 0.870916i \(-0.663526\pi\)
0.999951 0.00986623i \(-0.00314057\pi\)
\(284\) −5.59808 + 9.69615i −0.332185 + 0.575361i
\(285\) 0 0
\(286\) −6.69213 + 11.5911i −0.395714 + 0.685397i
\(287\) 0 0
\(288\) 0 0
\(289\) −11.4282 + 19.7942i −0.672247 + 1.16437i
\(290\) −1.41421 −0.0830455
\(291\) 0 0
\(292\) −9.52056 −0.557148
\(293\) −2.19067 3.79435i −0.127980 0.221668i 0.794914 0.606723i \(-0.207516\pi\)
−0.922894 + 0.385054i \(0.874183\pi\)
\(294\) 0 0
\(295\) 4.83013 8.36603i 0.281221 0.487089i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) 9.19615 + 15.9282i 0.532719 + 0.922696i
\(299\) 7.26054 + 12.5756i 0.419888 + 0.727267i
\(300\) 0 0
\(301\) 0 0
\(302\) −1.69615 2.93782i −0.0976026 0.169053i
\(303\) 0 0
\(304\) 1.93185 0.110799
\(305\) 2.86603 + 4.96410i 0.164108 + 0.284244i
\(306\) 0 0
\(307\) 29.0793 1.65964 0.829822 0.558028i \(-0.188442\pi\)
0.829822 + 0.558028i \(0.188442\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −14.1962 −0.806287
\(311\) 10.5051 18.1953i 0.595688 1.03176i −0.397762 0.917489i \(-0.630213\pi\)
0.993449 0.114273i \(-0.0364537\pi\)
\(312\) 0 0
\(313\) −0.896575 1.55291i −0.0506774 0.0877759i 0.839574 0.543245i \(-0.182805\pi\)
−0.890251 + 0.455470i \(0.849471\pi\)
\(314\) −24.3562 −1.37450
\(315\) 0 0
\(316\) −10.1244 −0.569540
\(317\) 0.705771 + 1.22243i 0.0396401 + 0.0686586i 0.885165 0.465278i \(-0.154046\pi\)
−0.845525 + 0.533936i \(0.820712\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) −1.93185 −0.107994
\(321\) 0 0
\(322\) 0 0
\(323\) 12.1962 0.678612
\(324\) 0 0
\(325\) −1.55291 2.68973i −0.0861402 0.149199i
\(326\) −20.9282 −1.15911
\(327\) 0 0
\(328\) −2.82843 4.89898i −0.156174 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0263 22.5622i −0.715989 1.24013i −0.962577 0.271009i \(-0.912643\pi\)
0.246588 0.969120i \(-0.420691\pi\)
\(332\) 4.94975 + 8.57321i 0.271653 + 0.470516i
\(333\) 0 0
\(334\) 8.05558 13.9527i 0.440782 0.763456i
\(335\) −13.7124 + 23.7506i −0.749190 + 1.29764i
\(336\) 0 0
\(337\) −6.66025 11.5359i −0.362807 0.628400i 0.625615 0.780132i \(-0.284848\pi\)
−0.988422 + 0.151732i \(0.951515\pi\)
\(338\) −7.00000 −0.380750
\(339\) 0 0
\(340\) −12.1962 −0.661429
\(341\) 20.0764 34.7733i 1.08720 1.88308i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.901924 1.56218i 0.0486285 0.0842270i
\(345\) 0 0
\(346\) 7.26054 12.5756i 0.390329 0.676069i
\(347\) −16.8564 + 29.1962i −0.904899 + 1.56733i −0.0838470 + 0.996479i \(0.526721\pi\)
−0.821052 + 0.570853i \(0.806613\pi\)
\(348\) 0 0
\(349\) −12.3998 + 21.4770i −0.663744 + 1.14964i 0.315881 + 0.948799i \(0.397700\pi\)
−0.979624 + 0.200839i \(0.935633\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.73205 4.73205i 0.145619 0.252219i
\(353\) 19.6975 1.04839 0.524195 0.851598i \(-0.324366\pi\)
0.524195 + 0.851598i \(0.324366\pi\)
\(354\) 0 0
\(355\) −21.6293 −1.14796
\(356\) −6.64136 11.5032i −0.351992 0.609667i
\(357\) 0 0
\(358\) 1.09808 1.90192i 0.0580351 0.100520i
\(359\) −0.0358984 + 0.0621778i −0.00189464 + 0.00328162i −0.866971 0.498358i \(-0.833936\pi\)
0.865077 + 0.501640i \(0.167270\pi\)
\(360\) 0 0
\(361\) 7.63397 + 13.2224i 0.401788 + 0.695917i
\(362\) −4.36276 7.55652i −0.229302 0.397162i
\(363\) 0 0
\(364\) 0 0
\(365\) −9.19615 15.9282i −0.481349 0.833720i
\(366\) 0 0
\(367\) −14.4195 −0.752694 −0.376347 0.926479i \(-0.622820\pi\)
−0.376347 + 0.926479i \(0.622820\pi\)
\(368\) −2.96410 5.13397i −0.154514 0.267627i
\(369\) 0 0
\(370\) 15.4548 0.803457
\(371\) 0 0
\(372\) 0 0
\(373\) −5.12436 −0.265329 −0.132665 0.991161i \(-0.542353\pi\)
−0.132665 + 0.991161i \(0.542353\pi\)
\(374\) 17.2480 29.8744i 0.891871 1.54477i
\(375\) 0 0
\(376\) 4.76028 + 8.24504i 0.245493 + 0.425206i
\(377\) −1.79315 −0.0923520
\(378\) 0 0
\(379\) 17.5167 0.899770 0.449885 0.893086i \(-0.351465\pi\)
0.449885 + 0.893086i \(0.351465\pi\)
\(380\) 1.86603 + 3.23205i 0.0957251 + 0.165801i
\(381\) 0 0
\(382\) 1.59808 2.76795i 0.0817647 0.141621i
\(383\) −19.5216 −0.997507 −0.498753 0.866744i \(-0.666209\pi\)
−0.498753 + 0.866744i \(0.666209\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −20.2679 −1.03161
\(387\) 0 0
\(388\) 1.93185 + 3.34607i 0.0980749 + 0.169871i
\(389\) 29.1244 1.47666 0.738332 0.674438i \(-0.235614\pi\)
0.738332 + 0.674438i \(0.235614\pi\)
\(390\) 0 0
\(391\) −18.7129 32.4118i −0.946354 1.63913i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.83013 6.63397i −0.192959 0.334215i
\(395\) −9.77938 16.9384i −0.492054 0.852262i
\(396\) 0 0
\(397\) 0.947343 1.64085i 0.0475458 0.0823518i −0.841273 0.540610i \(-0.818193\pi\)
0.888819 + 0.458259i \(0.151527\pi\)
\(398\) −1.55291 + 2.68973i −0.0778406 + 0.134824i
\(399\) 0 0
\(400\) 0.633975 + 1.09808i 0.0316987 + 0.0549038i
\(401\) −13.0526 −0.651814 −0.325907 0.945402i \(-0.605670\pi\)
−0.325907 + 0.945402i \(0.605670\pi\)
\(402\) 0 0
\(403\) −18.0000 −0.896644
\(404\) 0.776457 1.34486i 0.0386302 0.0669094i
\(405\) 0 0
\(406\) 0 0
\(407\) −21.8564 + 37.8564i −1.08338 + 1.87647i
\(408\) 0 0
\(409\) −13.1440 + 22.7661i −0.649930 + 1.12571i 0.333209 + 0.942853i \(0.391869\pi\)
−0.983139 + 0.182859i \(0.941465\pi\)
\(410\) 5.46410 9.46410i 0.269853 0.467399i
\(411\) 0 0
\(412\) 4.19187 7.26054i 0.206519 0.357701i
\(413\) 0 0
\(414\) 0 0
\(415\) −9.56218 + 16.5622i −0.469389 + 0.813005i
\(416\) −2.44949 −0.120096
\(417\) 0 0
\(418\) −10.5558 −0.516303
\(419\) −2.13990 3.70642i −0.104541 0.181070i 0.809010 0.587796i \(-0.200004\pi\)
−0.913551 + 0.406725i \(0.866671\pi\)
\(420\) 0 0
\(421\) 5.02628 8.70577i 0.244966 0.424293i −0.717156 0.696913i \(-0.754557\pi\)
0.962122 + 0.272619i \(0.0878899\pi\)
\(422\) −2.36603 + 4.09808i −0.115176 + 0.199491i
\(423\) 0 0
\(424\) 1.63397 + 2.83013i 0.0793528 + 0.137443i
\(425\) 4.00240 + 6.93237i 0.194145 + 0.336269i
\(426\) 0 0
\(427\) 0 0
\(428\) 8.46410 + 14.6603i 0.409128 + 0.708630i
\(429\) 0 0
\(430\) 3.48477 0.168050
\(431\) 7.39230 + 12.8038i 0.356075 + 0.616740i 0.987301 0.158859i \(-0.0507815\pi\)
−0.631226 + 0.775599i \(0.717448\pi\)
\(432\) 0 0
\(433\) −28.7375 −1.38104 −0.690519 0.723314i \(-0.742618\pi\)
−0.690519 + 0.723314i \(0.742618\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −20.5885 −0.986008
\(437\) −5.72620 + 9.91808i −0.273922 + 0.474446i
\(438\) 0 0
\(439\) −0.656339 1.13681i −0.0313253 0.0542571i 0.849938 0.526883i \(-0.176639\pi\)
−0.881263 + 0.472626i \(0.843306\pi\)
\(440\) 10.5558 0.503230
\(441\) 0 0
\(442\) −15.4641 −0.735552
\(443\) 7.49038 + 12.9737i 0.355879 + 0.616400i 0.987268 0.159066i \(-0.0508483\pi\)
−0.631389 + 0.775466i \(0.717515\pi\)
\(444\) 0 0
\(445\) 12.8301 22.2224i 0.608206 1.05344i
\(446\) 20.7327 0.981723
\(447\) 0 0
\(448\) 0 0
\(449\) −17.7846 −0.839308 −0.419654 0.907684i \(-0.637849\pi\)
−0.419654 + 0.907684i \(0.637849\pi\)
\(450\) 0 0
\(451\) 15.4548 + 26.7685i 0.727739 + 1.26048i
\(452\) −2.66025 −0.125128
\(453\) 0 0
\(454\) −0.448288 0.776457i −0.0210392 0.0364409i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.8660 + 22.2846i 0.601847 + 1.04243i 0.992541 + 0.121909i \(0.0389017\pi\)
−0.390694 + 0.920521i \(0.627765\pi\)
\(458\) −9.02150 15.6257i −0.421547 0.730141i
\(459\) 0 0
\(460\) 5.72620 9.91808i 0.266986 0.462433i
\(461\) −10.9162 + 18.9074i −0.508418 + 0.880605i 0.491535 + 0.870858i \(0.336436\pi\)
−0.999952 + 0.00974723i \(0.996897\pi\)
\(462\) 0 0
\(463\) 5.33013 + 9.23205i 0.247712 + 0.429050i 0.962891 0.269892i \(-0.0869880\pi\)
−0.715179 + 0.698942i \(0.753655\pi\)
\(464\) 0.732051 0.0339846
\(465\) 0 0
\(466\) 19.3923 0.898331
\(467\) 2.39872 4.15471i 0.111000 0.192257i −0.805174 0.593039i \(-0.797928\pi\)
0.916174 + 0.400782i \(0.131261\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.19615 + 15.9282i −0.424187 + 0.734713i
\(471\) 0 0
\(472\) −2.50026 + 4.33057i −0.115084 + 0.199331i
\(473\) −4.92820 + 8.53590i −0.226599 + 0.392481i
\(474\) 0 0
\(475\) 1.22474 2.12132i 0.0561951 0.0973329i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.76795 + 4.79423i −0.126603 + 0.219283i
\(479\) 16.1112 0.736137 0.368069 0.929799i \(-0.380019\pi\)
0.368069 + 0.929799i \(0.380019\pi\)
\(480\) 0 0
\(481\) 19.5959 0.893497
\(482\) 6.36396 + 11.0227i 0.289870 + 0.502070i
\(483\) 0 0
\(484\) −9.42820 + 16.3301i −0.428555 + 0.742279i
\(485\) −3.73205 + 6.46410i −0.169464 + 0.293520i
\(486\) 0 0
\(487\) −1.16025 2.00962i −0.0525761 0.0910645i 0.838540 0.544841i \(-0.183410\pi\)
−0.891116 + 0.453776i \(0.850077\pi\)
\(488\) −1.48356 2.56961i −0.0671578 0.116321i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.46410 16.3923i −0.427109 0.739774i 0.569506 0.821987i \(-0.307135\pi\)
−0.996615 + 0.0822129i \(0.973801\pi\)
\(492\) 0 0
\(493\) 4.62158 0.208145
\(494\) 2.36603 + 4.09808i 0.106453 + 0.184381i
\(495\) 0 0
\(496\) 7.34847 0.329956
\(497\) 0 0
\(498\) 0 0
\(499\) −27.3205 −1.22303 −0.611517 0.791231i \(-0.709440\pi\)
−0.611517 + 0.791231i \(0.709440\pi\)
\(500\) −6.05437 + 10.4865i −0.270760 + 0.468970i
\(501\) 0 0
\(502\) −0.965926 1.67303i −0.0431114 0.0746711i
\(503\) 19.1427 0.853529 0.426764 0.904363i \(-0.359653\pi\)
0.426764 + 0.904363i \(0.359653\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 16.1962 + 28.0526i 0.720007 + 1.24709i
\(507\) 0 0
\(508\) −3.96410 + 6.86603i −0.175879 + 0.304631i
\(509\) 21.7680 0.964850 0.482425 0.875937i \(-0.339756\pi\)
0.482425 + 0.875937i \(0.339756\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.3664 + 17.9551i 0.457241 + 0.791964i
\(515\) 16.1962 0.713688
\(516\) 0 0
\(517\) −26.0106 45.0518i −1.14395 1.98137i
\(518\) 0 0
\(519\) 0 0
\(520\) −2.36603 4.09808i −0.103757 0.179713i
\(521\) 16.2635 + 28.1691i 0.712515 + 1.23411i 0.963910 + 0.266228i \(0.0857773\pi\)
−0.251395 + 0.967885i \(0.580889\pi\)
\(522\) 0 0
\(523\) 3.70642 6.41971i 0.162070 0.280714i −0.773541 0.633747i \(-0.781516\pi\)
0.935611 + 0.353032i \(0.114849\pi\)
\(524\) −0.120118 + 0.208051i −0.00524739 + 0.00908875i
\(525\) 0 0
\(526\) −7.33013 12.6962i −0.319609 0.553579i
\(527\) 46.3923 2.02088
\(528\) 0 0
\(529\) 12.1436 0.527982
\(530\) −3.15660 + 5.46739i −0.137114 + 0.237488i
\(531\) 0 0
\(532\) 0 0
\(533\) 6.92820 12.0000i 0.300094 0.519778i
\(534\) 0 0
\(535\) −16.3514 + 28.3214i −0.706932 + 1.22444i
\(536\) 7.09808 12.2942i 0.306590 0.531030i
\(537\) 0 0
\(538\) 0.0185824 0.0321856i 0.000801143 0.00138762i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.63397 + 14.9545i −0.371204 + 0.642943i −0.989751 0.142804i \(-0.954388\pi\)
0.618547 + 0.785747i \(0.287721\pi\)
\(542\) −5.00052 −0.214791
\(543\) 0 0
\(544\) 6.31319 0.270676
\(545\) −19.8869 34.4452i −0.851862 1.47547i
\(546\) 0 0
\(547\) 2.26795 3.92820i 0.0969705 0.167958i −0.813459 0.581623i \(-0.802418\pi\)
0.910429 + 0.413665i \(0.135751\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −3.46410 6.00000i −0.147710 0.255841i
\(551\) −0.707107 1.22474i −0.0301238 0.0521759i
\(552\) 0 0
\(553\) 0 0
\(554\) 2.90192 + 5.02628i 0.123291 + 0.213546i
\(555\) 0 0
\(556\) −1.83032 −0.0776227
\(557\) 13.5622 + 23.4904i 0.574648 + 0.995319i 0.996080 + 0.0884593i \(0.0281943\pi\)
−0.421432 + 0.906860i \(0.638472\pi\)
\(558\) 0 0
\(559\) 4.41851 0.186883
\(560\) 0 0
\(561\) 0 0
\(562\) −3.39230 −0.143096
\(563\) 4.31199 7.46859i 0.181729 0.314763i −0.760741 0.649056i \(-0.775164\pi\)
0.942469 + 0.334293i \(0.108497\pi\)
\(564\) 0 0
\(565\) −2.56961 4.45069i −0.108104 0.187242i
\(566\) −17.1093 −0.719156
\(567\) 0 0
\(568\) 11.1962 0.469780
\(569\) 6.53590 + 11.3205i 0.273999 + 0.474580i 0.969882 0.243575i \(-0.0783201\pi\)
−0.695883 + 0.718155i \(0.744987\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 13.3843 0.559624
\(573\) 0 0
\(574\) 0 0
\(575\) −7.51666 −0.313466
\(576\) 0 0
\(577\) −8.90138 15.4176i −0.370569 0.641845i 0.619084 0.785325i \(-0.287504\pi\)
−0.989653 + 0.143480i \(0.954171\pi\)
\(578\) 22.8564 0.950701
\(579\) 0 0
\(580\) 0.707107 + 1.22474i 0.0293610 + 0.0508548i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.92820 15.4641i −0.369768 0.640458i
\(584\) 4.76028 + 8.24504i 0.196982 + 0.341182i
\(585\) 0 0
\(586\) −2.19067 + 3.79435i −0.0904958 + 0.156743i
\(587\) 16.6102 28.7697i 0.685577 1.18745i −0.287679 0.957727i \(-0.592883\pi\)
0.973255 0.229727i \(-0.0737832\pi\)
\(588\) 0 0
\(589\) −7.09808 12.2942i −0.292471 0.506575i
\(590\) −9.66025 −0.397706
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 10.7453 18.6114i 0.441257 0.764279i −0.556526 0.830830i \(-0.687866\pi\)
0.997783 + 0.0665510i \(0.0211995\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.19615 15.9282i 0.376689 0.652445i
\(597\) 0 0
\(598\) 7.26054 12.5756i 0.296905 0.514255i
\(599\) 4.19615 7.26795i 0.171450 0.296960i −0.767477 0.641077i \(-0.778488\pi\)
0.938927 + 0.344116i \(0.111821\pi\)
\(600\) 0 0
\(601\) −8.72552 + 15.1130i −0.355921 + 0.616474i −0.987275 0.159021i \(-0.949166\pi\)
0.631354 + 0.775495i \(0.282500\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.69615 + 2.93782i −0.0690155 + 0.119538i
\(605\) −36.4278 −1.48100
\(606\) 0 0
\(607\) −12.9038 −0.523749 −0.261874 0.965102i \(-0.584341\pi\)
−0.261874 + 0.965102i \(0.584341\pi\)
\(608\) −0.965926 1.67303i −0.0391735 0.0678504i
\(609\) 0 0
\(610\) 2.86603 4.96410i 0.116042 0.200991i
\(611\) −11.6603 + 20.1962i −0.471723 + 0.817049i
\(612\) 0 0
\(613\) 19.2224 + 33.2942i 0.776387 + 1.34474i 0.934012 + 0.357242i \(0.116283\pi\)
−0.157625 + 0.987499i \(0.550384\pi\)
\(614\) −14.5397 25.1834i −0.586773 1.01632i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.8038 + 18.7128i 0.434947 + 0.753349i 0.997291 0.0735534i \(-0.0234339\pi\)
−0.562345 + 0.826903i \(0.690101\pi\)
\(618\) 0 0
\(619\) −14.5582 −0.585145 −0.292572 0.956243i \(-0.594511\pi\)
−0.292572 + 0.956243i \(0.594511\pi\)
\(620\) 7.09808 + 12.2942i 0.285066 + 0.493748i
\(621\) 0 0
\(622\) −21.0101 −0.842430
\(623\) 0 0
\(624\) 0 0
\(625\) −17.0526 −0.682102
\(626\) −0.896575 + 1.55291i −0.0358344 + 0.0620669i
\(627\) 0 0
\(628\) 12.1781 + 21.0931i 0.485959 + 0.841706i
\(629\) −50.5055 −2.01379
\(630\) 0 0
\(631\) −28.1244 −1.11961 −0.559806 0.828623i \(-0.689125\pi\)
−0.559806 + 0.828623i \(0.689125\pi\)
\(632\) 5.06218 + 8.76795i 0.201363 + 0.348770i
\(633\) 0 0
\(634\) 0.705771 1.22243i 0.0280298 0.0485490i
\(635\) −15.3161 −0.607801
\(636\) 0 0
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) 0.965926 + 1.67303i 0.0381816 + 0.0661324i
\(641\) −35.0526 −1.38449 −0.692246 0.721661i \(-0.743379\pi\)
−0.692246 + 0.721661i \(0.743379\pi\)
\(642\) 0 0
\(643\) 6.50266 + 11.2629i 0.256440 + 0.444167i 0.965286 0.261197i \(-0.0841171\pi\)
−0.708846 + 0.705364i \(0.750784\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.09808 10.5622i −0.239926 0.415563i
\(647\) 0.568406 + 0.984508i 0.0223463 + 0.0387050i 0.876982 0.480523i \(-0.159553\pi\)
−0.854636 + 0.519228i \(0.826220\pi\)
\(648\) 0 0
\(649\) 13.6617 23.6627i 0.536267 0.928842i
\(650\) −1.55291 + 2.68973i −0.0609103 + 0.105500i
\(651\) 0 0
\(652\) 10.4641 + 18.1244i 0.409806 + 0.709805i
\(653\) 6.67949 0.261389 0.130694 0.991423i \(-0.458279\pi\)
0.130694 + 0.991423i \(0.458279\pi\)
\(654\) 0 0
\(655\) −0.464102 −0.0181340
\(656\) −2.82843 + 4.89898i −0.110432 + 0.191273i
\(657\) 0 0
\(658\) 0 0
\(659\) −7.43782 + 12.8827i −0.289736 + 0.501838i −0.973747 0.227634i \(-0.926901\pi\)
0.684010 + 0.729472i \(0.260234\pi\)
\(660\) 0 0
\(661\) 16.8504 29.1858i 0.655406 1.13520i −0.326385 0.945237i \(-0.605831\pi\)
0.981792 0.189960i \(-0.0608359\pi\)
\(662\) −13.0263 + 22.5622i −0.506281 + 0.876904i
\(663\) 0 0
\(664\) 4.94975 8.57321i 0.192087 0.332705i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.16987 + 3.75833i −0.0840178 + 0.145523i
\(668\) −16.1112 −0.623359
\(669\) 0 0
\(670\) 27.4249 1.05951
\(671\) 8.10634 + 14.0406i 0.312942 + 0.542031i
\(672\) 0 0
\(673\) −11.0885 + 19.2058i −0.427429 + 0.740328i −0.996644 0.0818605i \(-0.973914\pi\)
0.569215 + 0.822189i \(0.307247\pi\)
\(674\) −6.66025 + 11.5359i −0.256543 + 0.444346i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) −7.91688 13.7124i −0.304270 0.527012i 0.672828 0.739799i \(-0.265079\pi\)
−0.977099 + 0.212787i \(0.931746\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.09808 + 10.5622i 0.233851 + 0.405041i
\(681\) 0 0
\(682\) −40.1528 −1.53753
\(683\) −17.1962 29.7846i −0.657992 1.13968i −0.981135 0.193326i \(-0.938073\pi\)
0.323142 0.946350i \(-0.395261\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.80385 −0.0687710
\(689\) −4.00240 + 6.93237i −0.152479 + 0.264102i
\(690\) 0 0
\(691\) 12.1273 + 21.0052i 0.461345 + 0.799074i 0.999028 0.0440735i \(-0.0140336\pi\)
−0.537683 + 0.843147i \(0.680700\pi\)
\(692\) −14.5211 −0.552008
\(693\) 0 0
\(694\) 33.7128 1.27972
\(695\) −1.76795 3.06218i −0.0670621 0.116155i
\(696\) 0 0
\(697\) −17.8564 + 30.9282i −0.676360 + 1.17149i
\(698\) 24.7995 0.938675
\(699\) 0 0
\(700\) 0 0
\(701\) −27.4641 −1.03730 −0.518652 0.854985i \(-0.673566\pi\)
−0.518652 + 0.854985i \(0.673566\pi\)
\(702\) 0 0
\(703\) 7.72741 + 13.3843i 0.291445 + 0.504797i
\(704\) −5.46410 −0.205936
\(705\) 0 0
\(706\) −9.84873 17.0585i −0.370662 0.642005i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.7321 + 25.5167i 0.553274 + 0.958298i 0.998036 + 0.0626494i \(0.0199550\pi\)
−0.444762 + 0.895649i \(0.646712\pi\)
\(710\) 10.8147 + 18.7315i 0.405867 + 0.702982i
\(711\) 0 0
\(712\) −6.64136 + 11.5032i −0.248896 + 0.431100i
\(713\) −21.7816 + 37.7269i −0.815728 + 1.41288i
\(714\) 0 0
\(715\) 12.9282 + 22.3923i 0.483487 + 0.837425i
\(716\) −2.19615 −0.0820741
\(717\) 0 0
\(718\) 0.0717968 0.00267943
\(719\) −9.93666 + 17.2108i −0.370575 + 0.641855i −0.989654 0.143474i \(-0.954173\pi\)
0.619079 + 0.785329i \(0.287506\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7.63397 13.2224i 0.284107 0.492088i
\(723\) 0 0
\(724\) −4.36276 + 7.55652i −0.162141 + 0.280836i
\(725\) 0.464102 0.803848i 0.0172363 0.0298541i
\(726\) 0 0
\(727\) 12.0580 20.8850i 0.447206 0.774583i −0.550997 0.834507i \(-0.685753\pi\)
0.998203 + 0.0599240i \(0.0190858\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −9.19615 + 15.9282i −0.340365 + 0.589529i
\(731\) −11.3880 −0.421202
\(732\) 0 0
\(733\) −8.06918 −0.298042 −0.149021 0.988834i \(-0.547612\pi\)
−0.149021 + 0.988834i \(0.547612\pi\)
\(734\) 7.20977 + 12.4877i 0.266117 + 0.460929i
\(735\) 0 0
\(736\) −2.96410 + 5.13397i −0.109258 + 0.189241i
\(737\) −38.7846 + 67.1769i −1.42865 + 2.47449i
\(738\) 0 0
\(739\) 21.9282 + 37.9808i 0.806642 + 1.39714i 0.915177 + 0.403052i \(0.132051\pi\)
−0.108535 + 0.994093i \(0.534616\pi\)
\(740\) −7.72741 13.3843i −0.284065 0.492015i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.1244 + 17.5359i 0.371427 + 0.643330i 0.989785 0.142566i \(-0.0455354\pi\)
−0.618359 + 0.785896i \(0.712202\pi\)
\(744\) 0 0
\(745\) 35.5312 1.30176
\(746\) 2.56218 + 4.43782i 0.0938080 + 0.162480i
\(747\) 0 0
\(748\) −34.4959 −1.26130
\(749\) 0 0
\(750\) 0 0
\(751\) 12.1769 0.444342 0.222171 0.975008i \(-0.428686\pi\)
0.222171 + 0.975008i \(0.428686\pi\)
\(752\) 4.76028 8.24504i 0.173590 0.300666i
\(753\) 0 0
\(754\) 0.896575 + 1.55291i 0.0326514 + 0.0565538i
\(755\) −6.55343 −0.238504
\(756\) 0 0
\(757\) −28.2487 −1.02672 −0.513358 0.858174i \(-0.671599\pi\)
−0.513358 + 0.858174i \(0.671599\pi\)
\(758\) −8.75833 15.1699i −0.318117 0.550995i
\(759\) 0 0
\(760\) 1.86603 3.23205i 0.0676879 0.117239i
\(761\) −5.48099 −0.198686 −0.0993428 0.995053i \(-0.531674\pi\)
−0.0993428 + 0.995053i \(0.531674\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.19615 −0.115633
\(765\) 0 0
\(766\) 9.76079 + 16.9062i 0.352672 + 0.610846i
\(767\) −12.2487 −0.442275
\(768\) 0 0
\(769\) −2.20925 3.82654i −0.0796677 0.137989i 0.823439 0.567405i \(-0.192053\pi\)
−0.903107 + 0.429416i \(0.858719\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.1340 + 17.5526i 0.364730 + 0.631730i
\(773\) 1.81173 + 3.13801i 0.0651635 + 0.112867i 0.896767 0.442504i \(-0.145910\pi\)
−0.831603 + 0.555371i \(0.812576\pi\)
\(774\) 0 0
\(775\) 4.65874 8.06918i 0.167347 0.289853i
\(776\) 1.93185 3.34607i 0.0693494 0.120117i
\(777\) 0 0
\(778\) −14.5622 25.2224i −0.522079 0.904268i
\(779\) 10.9282 0.391544
\(780\) 0 0
\(781\) −61.1769 −2.18908
\(782\) −18.7129 + 32.4118i −0.669174 + 1.15904i
\(783\) 0 0
\(784\) 0 0
\(785\) −23.5263 + 40.7487i −0.839689 + 1.45438i
\(786\) 0 0
\(787\) 3.95164 6.84443i 0.140861 0.243978i −0.786960 0.617004i \(-0.788346\pi\)
0.927821 + 0.373026i \(0.121680\pi\)
\(788\) −3.83013 + 6.63397i −0.136443 + 0.236326i
\(789\) 0 0
\(790\) −9.77938 + 16.9384i −0.347935 + 0.602640i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.63397 6.29423i 0.129046 0.223515i