Properties

Label 1008.2.cz.d.607.1
Level $1008$
Weight $2$
Character 1008.607
Analytic conductor $8.049$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cz (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 607.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1008.607
Dual form 1008.2.cz.d.367.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(3.00000 + 1.73205i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(1.50000 - 0.866025i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-1.50000 + 4.33013i) q^{21} +(-3.00000 + 1.73205i) q^{23} +(-2.50000 + 4.33013i) q^{25} +5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} -1.00000 q^{31} +(3.00000 + 5.19615i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(-1.50000 - 2.59808i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(-1.50000 + 0.866025i) q^{43} +9.00000 q^{47} +(-6.50000 + 2.59808i) q^{49} +3.00000 q^{51} +(4.50000 + 7.79423i) q^{53} +(7.50000 - 4.33013i) q^{57} +15.0000 q^{59} +1.73205i q^{61} +(-6.00000 + 5.19615i) q^{63} -15.5885i q^{67} -6.00000 q^{69} -10.3923i q^{71} +(1.50000 - 0.866025i) q^{73} +(-7.50000 + 4.33013i) q^{75} +(-3.00000 + 8.66025i) q^{77} -1.73205i q^{79} +(-4.50000 + 7.79423i) q^{81} +(4.50000 + 7.79423i) q^{83} -5.19615i q^{87} +(1.50000 + 0.866025i) q^{89} +(1.50000 - 4.33013i) q^{91} +(-1.50000 - 0.866025i) q^{93} +(-1.50000 + 0.866025i) q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 2 q + 3 q^{3} + q^{7} + 3 q^{9} + 6 q^{11} - 3 q^{13} + 3 q^{17} + 5 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} - 3 q^{29} - 2 q^{31} + 6 q^{33} - 7 q^{37} - 3 q^{39} - 3 q^{41} - 3 q^{43} + 18 q^{47} - 13 q^{49} + 6 q^{51} + 9 q^{53} + 15 q^{57} + 30 q^{59} - 12 q^{63} - 12 q^{69} + 3 q^{73} - 15 q^{75} - 6 q^{77} - 9 q^{81} + 9 q^{83} + 3 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0 0
\(5\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 3.00000 + 1.73205i 0.904534 + 0.522233i 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) 0 0
\(13\) −1.50000 0.866025i −0.416025 0.240192i 0.277350 0.960769i \(-0.410544\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 0.866025i 0.363803 0.210042i −0.306944 0.951727i \(-0.599307\pi\)
0.670748 + 0.741685i \(0.265973\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) −1.50000 + 4.33013i −0.327327 + 0.944911i
\(22\) 0 0
\(23\) −3.00000 + 1.73205i −0.625543 + 0.361158i −0.779024 0.626994i \(-0.784285\pi\)
0.153481 + 0.988152i \(0.450952\pi\)
\(24\) 0 0
\(25\) −2.50000 + 4.33013i −0.500000 + 0.866025i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 0 0
\(39\) −1.50000 2.59808i −0.240192 0.416025i
\(40\) 0 0
\(41\) −1.50000 0.866025i −0.234261 0.135250i 0.378275 0.925693i \(-0.376517\pi\)
−0.612536 + 0.790443i \(0.709851\pi\)
\(42\) 0 0
\(43\) −1.50000 + 0.866025i −0.228748 + 0.132068i −0.609994 0.792406i \(-0.708828\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.50000 4.33013i 0.993399 0.573539i
\(58\) 0 0
\(59\) 15.0000 1.95283 0.976417 0.215894i \(-0.0692665\pi\)
0.976417 + 0.215894i \(0.0692665\pi\)
\(60\) 0 0
\(61\) 1.73205i 0.221766i 0.993833 + 0.110883i \(0.0353679\pi\)
−0.993833 + 0.110883i \(0.964632\pi\)
\(62\) 0 0
\(63\) −6.00000 + 5.19615i −0.755929 + 0.654654i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.5885i 1.90443i −0.305424 0.952217i \(-0.598798\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 10.3923i 1.23334i −0.787222 0.616670i \(-0.788481\pi\)
0.787222 0.616670i \(-0.211519\pi\)
\(72\) 0 0
\(73\) 1.50000 0.866025i 0.175562 0.101361i −0.409644 0.912245i \(-0.634347\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) −7.50000 + 4.33013i −0.866025 + 0.500000i
\(76\) 0 0
\(77\) −3.00000 + 8.66025i −0.341882 + 0.986928i
\(78\) 0 0
\(79\) 1.73205i 0.194871i −0.995242 0.0974355i \(-0.968936\pi\)
0.995242 0.0974355i \(-0.0310640\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 5.19615i 0.557086i
\(88\) 0 0
\(89\) 1.50000 + 0.866025i 0.159000 + 0.0917985i 0.577389 0.816469i \(-0.304072\pi\)
−0.418389 + 0.908268i \(0.637405\pi\)
\(90\) 0 0
\(91\) 1.50000 4.33013i 0.157243 0.453921i
\(92\) 0 0
\(93\) −1.50000 0.866025i −0.155543 0.0898027i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.50000 + 0.866025i −0.152302 + 0.0879316i −0.574214 0.818705i \(-0.694692\pi\)
0.421912 + 0.906637i \(0.361359\pi\)
\(98\) 0 0
\(99\) 10.3923i 1.04447i
\(100\) 0 0
\(101\) −12.0000 6.92820i −1.19404 0.689382i −0.234823 0.972038i \(-0.575451\pi\)
−0.959221 + 0.282656i \(0.908784\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.50000 + 0.866025i 0.145010 + 0.0837218i 0.570750 0.821124i \(-0.306653\pi\)
−0.425739 + 0.904846i \(0.639986\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) −10.5000 + 6.06218i −0.996616 + 0.575396i
\(112\) 0 0
\(113\) 4.50000 7.79423i 0.423324 0.733219i −0.572938 0.819599i \(-0.694196\pi\)
0.996262 + 0.0863794i \(0.0275297\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.19615i 0.480384i
\(118\) 0 0
\(119\) 3.00000 + 3.46410i 0.275010 + 0.317554i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) −1.50000 2.59808i −0.135250 0.234261i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 0 0
\(129\) −3.00000 −0.264135
\(130\) 0 0
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) 12.5000 + 4.33013i 1.08389 + 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 0 0
\(141\) 13.5000 + 7.79423i 1.13691 + 0.656392i
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −12.0000 1.73205i −0.989743 0.142857i
\(148\) 0 0
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −15.0000 8.66025i −1.22068 0.704761i −0.255619 0.966778i \(-0.582279\pi\)
−0.965064 + 0.262016i \(0.915613\pi\)
\(152\) 0 0
\(153\) 4.50000 + 2.59808i 0.363803 + 0.210042i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.1244i 0.967629i 0.875171 + 0.483814i \(0.160749\pi\)
−0.875171 + 0.483814i \(0.839251\pi\)
\(158\) 0 0
\(159\) 15.5885i 1.23625i
\(160\) 0 0
\(161\) −6.00000 6.92820i −0.472866 0.546019i
\(162\) 0 0
\(163\) 13.5000 + 7.79423i 1.05740 + 0.610491i 0.924712 0.380667i \(-0.124305\pi\)
0.132689 + 0.991158i \(0.457639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.5000 + 18.1865i −0.812514 + 1.40732i 0.0985846 + 0.995129i \(0.468568\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(168\) 0 0
\(169\) −5.00000 8.66025i −0.384615 0.666173i
\(170\) 0 0
\(171\) 15.0000 1.14708
\(172\) 0 0
\(173\) 19.0526i 1.44854i −0.689517 0.724270i \(-0.742177\pi\)
0.689517 0.724270i \(-0.257823\pi\)
\(174\) 0 0
\(175\) −12.5000 4.33013i −0.944911 0.327327i
\(176\) 0 0
\(177\) 22.5000 + 12.9904i 1.69120 + 0.976417i
\(178\) 0 0
\(179\) 10.5000 6.06218i 0.784807 0.453108i −0.0533243 0.998577i \(-0.516982\pi\)
0.838131 + 0.545469i \(0.183648\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) 0 0
\(183\) −1.50000 + 2.59808i −0.110883 + 0.192055i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) 0 0
\(189\) −13.5000 + 2.59808i −0.981981 + 0.188982i
\(190\) 0 0
\(191\) 1.73205i 0.125327i −0.998035 0.0626634i \(-0.980041\pi\)
0.998035 0.0626634i \(-0.0199595\pi\)
\(192\) 0 0
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −0.500000 0.866025i −0.0354441 0.0613909i 0.847759 0.530381i \(-0.177951\pi\)
−0.883203 + 0.468990i \(0.844618\pi\)
\(200\) 0 0
\(201\) 13.5000 23.3827i 0.952217 1.64929i
\(202\) 0 0
\(203\) 6.00000 5.19615i 0.421117 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −9.00000 5.19615i −0.625543 0.361158i
\(208\) 0 0
\(209\) 15.0000 8.66025i 1.03757 0.599042i
\(210\) 0 0
\(211\) −10.5000 6.06218i −0.722850 0.417338i 0.0929509 0.995671i \(-0.470370\pi\)
−0.815801 + 0.578333i \(0.803703\pi\)
\(212\) 0 0
\(213\) 9.00000 15.5885i 0.616670 1.06810i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.500000 2.59808i −0.0339422 0.176369i
\(218\) 0 0
\(219\) 3.00000 0.202721
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 2.50000 + 4.33013i 0.167412 + 0.289967i 0.937509 0.347960i \(-0.113126\pi\)
−0.770097 + 0.637927i \(0.779792\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) 12.0000 6.92820i 0.792982 0.457829i −0.0480291 0.998846i \(-0.515294\pi\)
0.841011 + 0.541017i \(0.181961\pi\)
\(230\) 0 0
\(231\) −12.0000 + 10.3923i −0.789542 + 0.683763i
\(232\) 0 0
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.50000 2.59808i 0.0974355 0.168763i
\(238\) 0 0
\(239\) 19.5000 + 11.2583i 1.26135 + 0.728241i 0.973336 0.229385i \(-0.0736716\pi\)
0.288014 + 0.957626i \(0.407005\pi\)
\(240\) 0 0
\(241\) −18.0000 10.3923i −1.15948 0.669427i −0.208302 0.978065i \(-0.566794\pi\)
−0.951180 + 0.308637i \(0.900127\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.50000 + 4.33013i −0.477214 + 0.275519i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.0000 + 13.8564i −1.49708 + 0.864339i −0.999994 0.00336324i \(-0.998929\pi\)
−0.497085 + 0.867702i \(0.665596\pi\)
\(258\) 0 0
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) 0 0
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 0 0
\(263\) −27.0000 15.5885i −1.66489 0.961225i −0.970328 0.241794i \(-0.922264\pi\)
−0.694564 0.719431i \(-0.744403\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.50000 + 2.59808i 0.0917985 + 0.159000i
\(268\) 0 0
\(269\) 19.5000 11.2583i 1.18894 0.686433i 0.230871 0.972984i \(-0.425842\pi\)
0.958065 + 0.286552i \(0.0925091\pi\)
\(270\) 0 0
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 0 0
\(273\) 6.00000 5.19615i 0.363137 0.314485i
\(274\) 0 0
\(275\) −15.0000 + 8.66025i −0.904534 + 0.522233i
\(276\) 0 0
\(277\) 7.00000 12.1244i 0.420589 0.728482i −0.575408 0.817867i \(-0.695157\pi\)
0.995997 + 0.0893846i \(0.0284900\pi\)
\(278\) 0 0
\(279\) −1.50000 2.59808i −0.0898027 0.155543i
\(280\) 0 0
\(281\) −7.50000 12.9904i −0.447412 0.774941i 0.550804 0.834634i \(-0.314321\pi\)
−0.998217 + 0.0596933i \(0.980988\pi\)
\(282\) 0 0
\(283\) 31.0000 1.84276 0.921379 0.388664i \(-0.127063\pi\)
0.921379 + 0.388664i \(0.127063\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.50000 4.33013i 0.0885422 0.255599i
\(288\) 0 0
\(289\) −7.00000 + 12.1244i −0.411765 + 0.713197i
\(290\) 0 0
\(291\) −3.00000 −0.175863
\(292\) 0 0
\(293\) 22.5000 + 12.9904i 1.31446 + 0.758906i 0.982832 0.184503i \(-0.0590674\pi\)
0.331632 + 0.943409i \(0.392401\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −9.00000 + 15.5885i −0.522233 + 0.904534i
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) −3.00000 3.46410i −0.172917 0.199667i
\(302\) 0 0
\(303\) −12.0000 20.7846i −0.689382 1.19404i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 13.8564i 0.788263i
\(310\) 0 0
\(311\) 3.00000 0.170114 0.0850572 0.996376i \(-0.472893\pi\)
0.0850572 + 0.996376i \(0.472893\pi\)
\(312\) 0 0
\(313\) 29.4449i 1.66432i 0.554534 + 0.832161i \(0.312897\pi\)
−0.554534 + 0.832161i \(0.687103\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.0000 −1.17948 −0.589739 0.807594i \(-0.700769\pi\)
−0.589739 + 0.807594i \(0.700769\pi\)
\(318\) 0 0
\(319\) 10.3923i 0.581857i
\(320\) 0 0
\(321\) 1.50000 + 2.59808i 0.0837218 + 0.145010i
\(322\) 0 0
\(323\) 8.66025i 0.481869i
\(324\) 0 0
\(325\) 7.50000 4.33013i 0.416025 0.240192i
\(326\) 0 0
\(327\) 19.0526i 1.05361i
\(328\) 0 0
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) 0 0
\(331\) 5.19615i 0.285606i 0.989751 + 0.142803i \(0.0456116\pi\)
−0.989751 + 0.142803i \(0.954388\pi\)
\(332\) 0 0
\(333\) −21.0000 −1.15079
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.50000 + 9.52628i −0.299604 + 0.518930i −0.976045 0.217567i \(-0.930188\pi\)
0.676441 + 0.736497i \(0.263521\pi\)
\(338\) 0 0
\(339\) 13.5000 7.79423i 0.733219 0.423324i
\(340\) 0 0
\(341\) −3.00000 1.73205i −0.162459 0.0937958i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.5167i 1.20876i −0.796697 0.604379i \(-0.793421\pi\)
0.796697 0.604379i \(-0.206579\pi\)
\(348\) 0 0
\(349\) 22.5000 12.9904i 1.20440 0.695359i 0.242867 0.970059i \(-0.421912\pi\)
0.961530 + 0.274700i \(0.0885786\pi\)
\(350\) 0 0
\(351\) 4.50000 7.79423i 0.240192 0.416025i
\(352\) 0 0
\(353\) −18.0000 10.3923i −0.958043 0.553127i −0.0624731 0.998047i \(-0.519899\pi\)
−0.895570 + 0.444920i \(0.853232\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.50000 + 7.79423i 0.0793884 + 0.412514i
\(358\) 0 0
\(359\) −10.5000 6.06218i −0.554169 0.319950i 0.196633 0.980477i \(-0.436999\pi\)
−0.750802 + 0.660528i \(0.770333\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 1.73205i 0.0909091i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 0 0
\(369\) 5.19615i 0.270501i
\(370\) 0 0
\(371\) −18.0000 + 15.5885i −0.934513 + 0.809312i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.19615i 0.267615i
\(378\) 0 0
\(379\) 24.2487i 1.24557i 0.782392 + 0.622786i \(0.213999\pi\)
−0.782392 + 0.622786i \(0.786001\pi\)
\(380\) 0 0
\(381\) 9.00000 15.5885i 0.461084 0.798621i
\(382\) 0 0
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.50000 2.59808i −0.228748 0.132068i
\(388\) 0 0
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) −3.00000 + 5.19615i −0.151717 + 0.262781i
\(392\) 0 0
\(393\) 20.7846i 1.04844i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 13.5000 + 7.79423i 0.677546 + 0.391181i 0.798930 0.601424i \(-0.205400\pi\)
−0.121384 + 0.992606i \(0.538733\pi\)
\(398\) 0 0
\(399\) 15.0000 + 17.3205i 0.750939 + 0.867110i
\(400\) 0 0
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 0 0
\(403\) 1.50000 + 0.866025i 0.0747203 + 0.0431398i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.0000 + 12.1244i −1.04093 + 0.600982i
\(408\) 0 0
\(409\) 29.4449i 1.45595i −0.685601 0.727977i \(-0.740461\pi\)
0.685601 0.727977i \(-0.259539\pi\)
\(410\) 0 0
\(411\) 27.0000 15.5885i 1.33181 0.768922i
\(412\) 0 0
\(413\) 7.50000 + 38.9711i 0.369051 + 1.91764i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.50000 + 4.33013i −0.367277 + 0.212047i
\(418\) 0 0
\(419\) 7.50000 12.9904i 0.366399 0.634622i −0.622601 0.782540i \(-0.713924\pi\)
0.989000 + 0.147918i \(0.0472572\pi\)
\(420\) 0 0
\(421\) 2.50000 + 4.33013i 0.121843 + 0.211037i 0.920494 0.390756i \(-0.127786\pi\)
−0.798652 + 0.601793i \(0.794453\pi\)
\(422\) 0 0
\(423\) 13.5000 + 23.3827i 0.656392 + 1.13691i
\(424\) 0 0
\(425\) 8.66025i 0.420084i
\(426\) 0 0
\(427\) −4.50000 + 0.866025i −0.217770 + 0.0419099i
\(428\) 0 0
\(429\) 10.3923i 0.501745i
\(430\) 0 0
\(431\) 22.5000 12.9904i 1.08379 0.625725i 0.151871 0.988400i \(-0.451470\pi\)
0.931915 + 0.362676i \(0.118137\pi\)
\(432\) 0 0
\(433\) 13.8564i 0.665896i 0.942945 + 0.332948i \(0.108043\pi\)
−0.942945 + 0.332948i \(0.891957\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 17.3205i 0.828552i
\(438\) 0 0
\(439\) 25.0000 1.19318 0.596592 0.802544i \(-0.296521\pi\)
0.596592 + 0.802544i \(0.296521\pi\)
\(440\) 0 0
\(441\) −16.5000 12.9904i −0.785714 0.618590i
\(442\) 0 0
\(443\) 25.9808i 1.23438i 0.786813 + 0.617192i \(0.211730\pi\)
−0.786813 + 0.617192i \(0.788270\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 10.3923i 0.491539i
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 0 0
\(453\) −15.0000 25.9808i −0.704761 1.22068i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −0.0467780 −0.0233890 0.999726i \(-0.507446\pi\)
−0.0233890 + 0.999726i \(0.507446\pi\)
\(458\) 0 0
\(459\) 4.50000 + 7.79423i 0.210042 + 0.363803i
\(460\) 0 0
\(461\) −19.5000 + 11.2583i −0.908206 + 0.524353i −0.879853 0.475245i \(-0.842359\pi\)
−0.0283522 + 0.999598i \(0.509026\pi\)
\(462\) 0 0
\(463\) 31.5000 + 18.1865i 1.46393 + 0.845200i 0.999190 0.0402476i \(-0.0128147\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.50000 + 12.9904i −0.347059 + 0.601123i −0.985726 0.168360i \(-0.946153\pi\)
0.638667 + 0.769483i \(0.279486\pi\)
\(468\) 0 0
\(469\) 40.5000 7.79423i 1.87012 0.359904i
\(470\) 0 0
\(471\) −10.5000 + 18.1865i −0.483814 + 0.837991i
\(472\) 0 0
\(473\) −6.00000 −0.275880
\(474\) 0 0
\(475\) 12.5000 + 21.6506i 0.573539 + 0.993399i
\(476\) 0 0
\(477\) −13.5000 + 23.3827i −0.618123 + 1.07062i
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 10.5000 6.06218i 0.478759 0.276412i
\(482\) 0 0
\(483\) −3.00000 15.5885i −0.136505 0.709299i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −13.5000 + 7.79423i −0.611743 + 0.353190i −0.773647 0.633616i \(-0.781570\pi\)
0.161904 + 0.986807i \(0.448236\pi\)
\(488\) 0 0
\(489\) 13.5000 + 23.3827i 0.610491 + 1.05740i
\(490\) 0 0
\(491\) 7.50000 + 4.33013i 0.338470 + 0.195416i 0.659595 0.751621i \(-0.270728\pi\)
−0.321125 + 0.947037i \(0.604061\pi\)
\(492\) 0 0
\(493\) −4.50000 2.59808i −0.202670 0.117011i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 27.0000 5.19615i 1.21112 0.233079i
\(498\) 0 0
\(499\) −3.00000 + 1.73205i −0.134298 + 0.0775372i −0.565644 0.824650i \(-0.691372\pi\)
0.431346 + 0.902187i \(0.358039\pi\)
\(500\) 0 0
\(501\) −31.5000 + 18.1865i −1.40732 + 0.812514i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 17.3205i 0.769231i
\(508\) 0 0
\(509\) −30.0000 + 17.3205i −1.32973 + 0.767718i −0.985257 0.171080i \(-0.945274\pi\)
−0.344469 + 0.938798i \(0.611941\pi\)
\(510\) 0 0
\(511\) 3.00000 + 3.46410i 0.132712 + 0.153243i
\(512\) 0 0
\(513\) 22.5000 + 12.9904i 0.993399 + 0.573539i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 27.0000 + 15.5885i 1.18746 + 0.685580i
\(518\) 0 0
\(519\) 16.5000 28.5788i 0.724270 1.25447i
\(520\) 0 0
\(521\) 19.5000 11.2583i 0.854311 0.493236i −0.00779240 0.999970i \(-0.502480\pi\)
0.862103 + 0.506733i \(0.169147\pi\)
\(522\) 0 0
\(523\) 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i \(-0.741597\pi\)
0.972421 + 0.233233i \(0.0749303\pi\)
\(524\) 0 0
\(525\) −15.0000 17.3205i −0.654654 0.755929i
\(526\) 0 0
\(527\) −1.50000 + 0.866025i −0.0653410 + 0.0377247i
\(528\) 0 0
\(529\) −5.50000 + 9.52628i −0.239130 + 0.414186i
\(530\) 0 0
\(531\) 22.5000 + 38.9711i 0.976417 + 1.69120i
\(532\) 0 0
\(533\) 1.50000 + 2.59808i 0.0649722 + 0.112535i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.0000 0.906217
\(538\) 0 0
\(539\) −24.0000 3.46410i −1.03375 0.149209i
\(540\) 0 0
\(541\) −21.5000 + 37.2391i −0.924357 + 1.60103i −0.131765 + 0.991281i \(0.542065\pi\)
−0.792592 + 0.609753i \(0.791269\pi\)
\(542\) 0 0
\(543\) 12.0000 20.7846i 0.514969 0.891953i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −7.50000 + 4.33013i −0.320677 + 0.185143i −0.651694 0.758482i \(-0.725941\pi\)
0.331017 + 0.943625i \(0.392608\pi\)
\(548\) 0 0
\(549\) −4.50000 + 2.59808i −0.192055 + 0.110883i
\(550\) 0 0
\(551\) −15.0000 −0.639021
\(552\) 0 0
\(553\) 4.50000 0.866025i 0.191359 0.0368271i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i \(0.0797613\pi\)
−0.269642 + 0.962961i \(0.586905\pi\)
\(558\) 0 0
\(559\) 3.00000 0.126886
\(560\) 0 0
\(561\) 9.00000 + 5.19615i 0.379980 + 0.219382i
\(562\) 0 0
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −22.5000 7.79423i −0.944911 0.327327i
\(568\) 0 0
\(569\) 3.00000 0.125767 0.0628833 0.998021i \(-0.479970\pi\)
0.0628833 + 0.998021i \(0.479970\pi\)
\(570\) 0 0
\(571\) 39.8372i 1.66713i 0.552419 + 0.833567i \(0.313705\pi\)
−0.552419 + 0.833567i \(0.686295\pi\)
\(572\) 0 0
\(573\) 1.50000 2.59808i 0.0626634 0.108536i
\(574\) 0 0
\(575\) 17.3205i 0.722315i
\(576\) 0 0
\(577\) −22.5000 + 12.9904i −0.936687 + 0.540797i −0.888920 0.458062i \(-0.848544\pi\)
−0.0477669 + 0.998859i \(0.515210\pi\)
\(578\) 0 0
\(579\) −25.5000 14.7224i −1.05974 0.611843i
\(580\) 0 0
\(581\) −18.0000 + 15.5885i −0.746766 + 0.646718i
\(582\) 0 0
\(583\) 31.1769i 1.29122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.5000 23.3827i −0.557205 0.965107i −0.997728 0.0673658i \(-0.978541\pi\)
0.440524 0.897741i \(-0.354793\pi\)
\(588\) 0 0
\(589\) −2.50000 + 4.33013i −0.103011 + 0.178420i
\(590\) 0 0
\(591\) 9.00000 + 5.19615i 0.370211 + 0.213741i
\(592\) 0 0
\(593\) 7.50000 + 4.33013i 0.307988 + 0.177817i 0.646026 0.763316i \(-0.276430\pi\)
−0.338038 + 0.941133i \(0.609763\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.73205i 0.0708881i
\(598\) 0 0
\(599\) 36.3731i 1.48616i −0.669201 0.743082i \(-0.733363\pi\)
0.669201 0.743082i \(-0.266637\pi\)
\(600\) 0 0
\(601\) −31.5000 + 18.1865i −1.28491 + 0.741844i −0.977742 0.209811i \(-0.932715\pi\)
−0.307170 + 0.951655i \(0.599382\pi\)
\(602\) 0 0
\(603\) 40.5000 23.3827i 1.64929 0.952217i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) 0 0
\(609\) 13.5000 2.59808i 0.547048 0.105279i
\(610\) 0 0
\(611\) −13.5000 7.79423i −0.546152 0.315321i
\(612\) 0 0
\(613\) −17.5000 30.3109i −0.706818 1.22425i −0.966031 0.258425i \(-0.916796\pi\)
0.259213 0.965820i \(-0.416537\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.5000 + 23.3827i −0.543490 + 0.941351i 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) 0 0
\(621\) −9.00000 15.5885i −0.361158 0.625543i
\(622\) 0 0
\(623\) −1.50000 + 4.33013i −0.0600962 + 0.173483i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 0 0
\(627\) 30.0000 1.19808
\(628\) 0 0
\(629\) 12.1244i 0.483430i
\(630\) 0 0
\(631\) 31.1769i 1.24113i 0.784154 + 0.620567i \(0.213097\pi\)
−0.784154 + 0.620567i \(0.786903\pi\)
\(632\) 0 0
\(633\) −10.5000 18.1865i −0.417338 0.722850i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 12.0000 + 1.73205i 0.475457 + 0.0686264i
\(638\) 0 0
\(639\) 27.0000 15.5885i 1.06810 0.616670i
\(640\) 0 0
\(641\) −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) 0 0
\(643\) −6.50000 + 11.2583i −0.256335 + 0.443985i −0.965257 0.261301i \(-0.915848\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.50000 + 12.9904i 0.294855 + 0.510705i 0.974951 0.222419i \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) 0 0
\(649\) 45.0000 + 25.9808i 1.76640 + 1.01983i
\(650\) 0 0
\(651\) 1.50000 4.33013i 0.0587896 0.169711i
\(652\) 0 0
\(653\) −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i \(-0.966977\pi\)
0.407628 0.913148i \(-0.366356\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.50000 + 2.59808i 0.175562 + 0.101361i
\(658\) 0 0
\(659\) −19.5000 + 11.2583i −0.759612 + 0.438562i −0.829156 0.559017i \(-0.811179\pi\)
0.0695443 + 0.997579i \(0.477845\pi\)
\(660\) 0 0
\(661\) 8.66025i 0.336845i −0.985715 0.168422i \(-0.946133\pi\)
0.985715 0.168422i \(-0.0538673\pi\)
\(662\) 0 0
\(663\) −4.50000 2.59808i −0.174766 0.100901i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 + 5.19615i 0.348481 + 0.201196i
\(668\) 0 0
\(669\) 8.66025i 0.334825i
\(670\) 0 0
\(671\) −3.00000 + 5.19615i −0.115814 + 0.200595i
\(672\) 0 0
\(673\) −3.50000 6.06218i −0.134915 0.233680i 0.790650 0.612268i \(-0.209743\pi\)
−0.925565 + 0.378589i \(0.876409\pi\)
\(674\) 0 0
\(675\) −22.5000 12.9904i −0.866025 0.500000i
\(676\) 0 0
\(677\) 1.73205i 0.0665681i 0.999446 + 0.0332841i \(0.0105966\pi\)
−0.999446 + 0.0332841i \(0.989403\pi\)
\(678\) 0 0
\(679\) −3.00000 3.46410i −0.115129 0.132940i
\(680\) 0 0
\(681\) 18.0000 10.3923i 0.689761 0.398234i
\(682\) 0 0
\(683\) −37.5000 + 21.6506i −1.43490 + 0.828439i −0.997489 0.0708242i \(-0.977437\pi\)
−0.437409 + 0.899263i \(0.644104\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 24.0000 0.915657
\(688\) 0 0
\(689\) 15.5885i 0.593873i
\(690\) 0 0
\(691\) 5.00000 0.190209 0.0951045 0.995467i \(-0.469681\pi\)
0.0951045 + 0.995467i \(0.469681\pi\)
\(692\) 0 0
\(693\) −27.0000 + 5.19615i −1.02565 + 0.197386i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.00000 −0.113633
\(698\) 0 0
\(699\) 31.5000 18.1865i 1.19144 0.687878i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 17.5000 + 30.3109i 0.660025 + 1.14320i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.0000 34.6410i 0.451306 1.30281i
\(708\) 0 0
\(709\) −37.0000 −1.38956 −0.694782 0.719220i \(-0.744499\pi\)
−0.694782 + 0.719220i \(0.744499\pi\)
\(710\) 0 0
\(711\) 4.50000 2.59808i 0.168763 0.0974355i
\(712\) 0 0
\(713\) 3.00000 1.73205i 0.112351 0.0648658i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 19.5000 + 33.7750i 0.728241 + 1.26135i
\(718\) 0 0
\(719\) −13.5000 + 23.3827i −0.503465 + 0.872027i 0.496527 + 0.868021i \(0.334608\pi\)
−0.999992 + 0.00400572i \(0.998725\pi\)
\(720\) 0 0
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) 0 0
\(723\) −18.0000 31.1769i −0.669427 1.15948i
\(724\) 0 0
\(725\) 15.0000 0.557086
\(726\) 0 0
\(727\) −17.5000 30.3109i −0.649039 1.12417i −0.983353 0.181707i \(-0.941838\pi\)
0.334314 0.942462i \(-0.391496\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) 18.0000 10.3923i 0.664845 0.383849i −0.129275 0.991609i \(-0.541265\pi\)
0.794121 + 0.607760i \(0.207932\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27.0000 46.7654i 0.994558 1.72262i
\(738\) 0 0
\(739\) −13.5000 + 7.79423i −0.496606 + 0.286715i −0.727311 0.686308i \(-0.759230\pi\)
0.230705 + 0.973024i \(0.425897\pi\)
\(740\) 0 0
\(741\) −15.0000 −0.551039
\(742\) 0 0
\(743\) −10.5000 6.06218i −0.385208 0.222400i 0.294874 0.955536i \(-0.404722\pi\)
−0.680082 + 0.733136i \(0.738056\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −13.5000 + 23.3827i −0.493939 + 0.855528i
\(748\) 0 0
\(749\) −1.50000 + 4.33013i −0.0548088 + 0.158219i
\(750\) 0 0
\(751\) 15.0000 8.66025i 0.547358 0.316017i −0.200698 0.979653i \(-0.564321\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) −18.0000 10.3923i −0.653359 0.377217i
\(760\) 0 0
\(761\) −42.0000 + 24.2487i −1.52250 + 0.879015i −0.522852 + 0.852423i \(0.675132\pi\)
−0.999646 + 0.0265919i \(0.991535\pi\)
\(762\) 0 0
\(763\) 22.0000 19.0526i 0.796453 0.689749i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22.5000 12.9904i −0.812428 0.469055i
\(768\) 0 0
\(769\) 4.50000 + 2.59808i 0.162274 + 0.0936890i 0.578938 0.815372i \(-0.303467\pi\)
−0.416664 + 0.909061i \(0.636801\pi\)
\(770\) 0 0
\(771\) −48.0000 −1.72868
\(772\) 0 0
\(773\) −28.5000 + 16.4545i −1.02507 + 0.591827i −0.915570 0.402160i \(-0.868260\pi\)
−0.109504 + 0.993986i \(0.534926\pi\)
\(774\) 0 0
\(775\) 2.50000 4.33013i 0.0898027 0.155543i
\(776\) 0 0
\(777\) −21.0000 24.2487i −0.753371 0.869918i
\(778\) 0 0
\(779\) −7.50000 + 4.33013i −0.268715 + 0.155143i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 13.5000 7.79423i 0.482451 0.278543i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −13.0000 −0.463400 −0.231700 0.972787i \(-0.574429\pi\)
−0.231700 + 0.972787i \(0.574429\pi\)
\(788\) 0 0
\(789\) −27.0000 46.7654i −0.961225 1.66489i
\(790\) 0 0
\(791\) 22.5000 + 7.79423i 0.800008 + 0.277131i
\(792\) 0 0
\(793\) 1.50000 2.59808i 0.0532666 0.0922604i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.5000 + 16.4545i 1.00952 + 0.582848i 0.911052 0.412292i \(-0.135272\pi\)
0.0984702 + 0.995140i \(0.468605\pi\)
\(798\) 0