Properties

Label 2100.2.bc.a.1549.1
Level $2100$
Weight $2$
Character 2100.1549
Analytic conductor $16.769$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1549.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1549
Dual form 2100.2.bc.a.949.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{3} +(2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{3} +(2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -3.00000i q^{13} +(-6.92820 + 4.00000i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-6.92820 - 4.00000i) q^{23} +1.00000i q^{27} -4.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(1.73205 + 1.00000i) q^{33} +(-0.866025 - 0.500000i) q^{37} +(1.50000 + 2.59808i) q^{39} +6.00000 q^{41} +11.0000i q^{43} +(5.19615 + 3.00000i) q^{47} +(6.50000 - 2.59808i) q^{49} +(4.00000 - 6.92820i) q^{51} +(-10.3923 + 6.00000i) q^{53} -1.00000i q^{57} +(2.00000 + 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} +(0.866025 - 2.50000i) q^{63} +(-11.2583 + 6.50000i) q^{67} +8.00000 q^{69} -10.0000 q^{71} +(-9.52628 + 5.50000i) q^{73} +(-3.46410 - 4.00000i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +2.00000i q^{83} +(3.46410 - 2.00000i) q^{87} +(-1.50000 - 7.79423i) q^{91} +(2.59808 + 1.50000i) q^{93} -10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{9} - 4q^{11} - 2q^{19} - 8q^{21} - 16q^{29} - 6q^{31} + 6q^{39} + 24q^{41} + 26q^{49} + 16q^{51} + 8q^{59} + 12q^{61} + 32q^{69} - 40q^{71} - 6q^{79} - 2q^{81} - 6q^{91} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.59808 0.500000i 0.981981 0.188982i
\(8\) 0 0
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 3.00000i 0.832050i −0.909353 0.416025i \(-0.863423\pi\)
0.909353 0.416025i \(-0.136577\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.92820 + 4.00000i −1.68034 + 0.970143i −0.718900 + 0.695113i \(0.755354\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) −6.92820 4.00000i −1.44463 0.834058i −0.446476 0.894795i \(-0.647321\pi\)
−0.998154 + 0.0607377i \(0.980655\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −1.50000 2.59808i −0.269408 0.466628i 0.699301 0.714827i \(-0.253495\pi\)
−0.968709 + 0.248199i \(0.920161\pi\)
\(32\) 0 0
\(33\) 1.73205 + 1.00000i 0.301511 + 0.174078i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.866025 0.500000i −0.142374 0.0821995i 0.427121 0.904194i \(-0.359528\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 0 0
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 11.0000i 1.67748i 0.544529 + 0.838742i \(0.316708\pi\)
−0.544529 + 0.838742i \(0.683292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 + 3.00000i 0.757937 + 0.437595i 0.828554 0.559908i \(-0.189164\pi\)
−0.0706177 + 0.997503i \(0.522497\pi\)
\(48\) 0 0
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) 4.00000 6.92820i 0.560112 0.970143i
\(52\) 0 0
\(53\) −10.3923 + 6.00000i −1.42749 + 0.824163i −0.996922 0.0783936i \(-0.975021\pi\)
−0.430570 + 0.902557i \(0.641688\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 0 0
\(63\) 0.866025 2.50000i 0.109109 0.314970i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.2583 + 6.50000i −1.37542 + 0.794101i −0.991605 0.129307i \(-0.958725\pi\)
−0.383819 + 0.923408i \(0.625391\pi\)
\(68\) 0 0
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) 0 0
\(73\) −9.52628 + 5.50000i −1.11497 + 0.643726i −0.940111 0.340868i \(-0.889279\pi\)
−0.174855 + 0.984594i \(0.555946\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.46410 4.00000i −0.394771 0.455842i
\(78\) 0 0
\(79\) −1.50000 + 2.59808i −0.168763 + 0.292306i −0.937985 0.346675i \(-0.887311\pi\)
0.769222 + 0.638982i \(0.220644\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 2.00000i 0.219529i 0.993958 + 0.109764i \(0.0350096\pi\)
−0.993958 + 0.109764i \(0.964990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.46410 2.00000i 0.371391 0.214423i
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) −1.50000 7.79423i −0.157243 0.817057i
\(92\) 0 0
\(93\) 2.59808 + 1.50000i 0.269408 + 0.155543i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) −9.52628 5.50000i −0.938652 0.541931i −0.0491146 0.998793i \(-0.515640\pi\)
−0.889538 + 0.456862i \(0.848973\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 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
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.59808 1.50000i −0.240192 0.138675i
\(118\) 0 0
\(119\) −16.0000 + 13.8564i −1.46672 + 1.27021i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −5.19615 + 3.00000i −0.468521 + 0.270501i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 3.00000i 0.266207i −0.991102 0.133103i \(-0.957506\pi\)
0.991102 0.133103i \(-0.0424943\pi\)
\(128\) 0 0
\(129\) −5.50000 9.52628i −0.484248 0.838742i
\(130\) 0 0
\(131\) 1.00000 1.73205i 0.0873704 0.151330i −0.819028 0.573753i \(-0.805487\pi\)
0.906399 + 0.422423i \(0.138820\pi\)
\(132\) 0 0
\(133\) −0.866025 + 2.50000i −0.0750939 + 0.216777i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.46410 + 2.00000i −0.295958 + 0.170872i −0.640626 0.767853i \(-0.721325\pi\)
0.344668 + 0.938725i \(0.387992\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −5.19615 + 3.00000i −0.434524 + 0.250873i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.33013 + 5.50000i −0.357143 + 0.453632i
\(148\) 0 0
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 8.00000i 0.646762i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.73205 + 1.00000i −0.138233 + 0.0798087i −0.567521 0.823359i \(-0.692098\pi\)
0.429289 + 0.903167i \(0.358764\pi\)
\(158\) 0 0
\(159\) 6.00000 10.3923i 0.475831 0.824163i
\(160\) 0 0
\(161\) −20.0000 6.92820i −1.57622 0.546019i
\(162\) 0 0
\(163\) 3.46410 + 2.00000i 0.271329 + 0.156652i 0.629492 0.777007i \(-0.283263\pi\)
−0.358162 + 0.933659i \(0.616597\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 0 0
\(169\) 4.00000 0.307692
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) 0 0
\(173\) −13.8564 8.00000i −1.05348 0.608229i −0.129861 0.991532i \(-0.541453\pi\)
−0.923622 + 0.383304i \(0.874786\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.46410 2.00000i −0.260378 0.150329i
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −15.0000 −1.11494 −0.557471 0.830197i \(-0.688228\pi\)
−0.557471 + 0.830197i \(0.688228\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.443533i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 13.8564 + 8.00000i 1.01328 + 0.585018i
\(188\) 0 0
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) 9.52628 5.50000i 0.685717 0.395899i −0.116289 0.993215i \(-0.537100\pi\)
0.802005 + 0.597317i \(0.203766\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.00000i 0.569976i −0.958531 0.284988i \(-0.908010\pi\)
0.958531 0.284988i \(-0.0919897\pi\)
\(198\) 0 0
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) 0 0
\(201\) 6.50000 11.2583i 0.458475 0.794101i
\(202\) 0 0
\(203\) −10.3923 + 2.00000i −0.729397 + 0.140372i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −6.92820 + 4.00000i −0.481543 + 0.278019i
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 8.66025 5.00000i 0.593391 0.342594i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.19615 6.00000i −0.352738 0.407307i
\(218\) 0 0
\(219\) 5.50000 9.52628i 0.371656 0.643726i
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.5885 9.00000i 1.03464 0.597351i 0.116331 0.993210i \(-0.462887\pi\)
0.918311 + 0.395860i \(0.129553\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) 0 0
\(231\) 5.00000 + 1.73205i 0.328976 + 0.113961i
\(232\) 0 0
\(233\) −12.1244 7.00000i −0.794293 0.458585i 0.0471787 0.998886i \(-0.484977\pi\)
−0.841472 + 0.540301i \(0.818310\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3.00000i 0.194871i
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 0 0
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.59808 + 1.50000i 0.165312 + 0.0954427i
\(248\) 0 0
\(249\) −1.00000 1.73205i −0.0633724 0.109764i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000i 1.00591i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) 0 0
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) 0 0
\(263\) 10.3923 6.00000i 0.640817 0.369976i −0.144112 0.989561i \(-0.546033\pi\)
0.784929 + 0.619586i \(0.212699\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.00000 1.73205i −0.0609711 0.105605i 0.833929 0.551872i \(-0.186086\pi\)
−0.894900 + 0.446267i \(0.852753\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 0 0
\(273\) 5.19615 + 6.00000i 0.314485 + 0.363137i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −14.7224 + 8.50000i −0.884585 + 0.510716i −0.872167 0.489207i \(-0.837286\pi\)
−0.0124177 + 0.999923i \(0.503953\pi\)
\(278\) 0 0
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 0 0
\(283\) 16.4545 9.50000i 0.978117 0.564716i 0.0764162 0.997076i \(-0.475652\pi\)
0.901701 + 0.432360i \(0.142319\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 15.5885 3.00000i 0.920158 0.177084i
\(288\) 0 0
\(289\) 23.5000 40.7032i 1.38235 2.39431i
\(290\) 0 0
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) 0 0
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 0 0
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) 5.50000 + 28.5788i 0.317015 + 1.64726i
\(302\) 0 0
\(303\) 8.66025 + 5.00000i 0.497519 + 0.287242i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 23.0000i 1.31268i 0.754466 + 0.656340i \(0.227896\pi\)
−0.754466 + 0.656340i \(0.772104\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 1.00000 + 1.73205i 0.0567048 + 0.0982156i 0.892984 0.450088i \(-0.148607\pi\)
−0.836280 + 0.548303i \(0.815274\pi\)
\(312\) 0 0
\(313\) 14.7224 + 8.50000i 0.832161 + 0.480448i 0.854592 0.519300i \(-0.173807\pi\)
−0.0224310 + 0.999748i \(0.507141\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −20.7846 12.0000i −1.16738 0.673987i −0.214318 0.976764i \(-0.568753\pi\)
−0.953062 + 0.302777i \(0.902086\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000i 0.445132i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 9.52628 + 5.50000i 0.526804 + 0.304151i
\(328\) 0 0
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) 0 0
\(333\) −0.866025 + 0.500000i −0.0474579 + 0.0273998i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 21.0000i 1.14394i −0.820274 0.571971i \(-0.806179\pi\)
0.820274 0.571971i \(-0.193821\pi\)
\(338\) 0 0
\(339\) 7.00000 + 12.1244i 0.380188 + 0.658505i
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.7846 + 12.0000i −1.11578 + 0.644194i −0.940319 0.340293i \(-0.889474\pi\)
−0.175457 + 0.984487i \(0.556140\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 3.00000 0.160128
\(352\) 0 0
\(353\) −5.19615 + 3.00000i −0.276563 + 0.159674i −0.631867 0.775077i \(-0.717711\pi\)
0.355303 + 0.934751i \(0.384378\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 6.92820 20.0000i 0.366679 1.05851i
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.33013 + 2.50000i −0.226031 + 0.130499i −0.608740 0.793370i \(-0.708325\pi\)
0.382709 + 0.923869i \(0.374991\pi\)
\(368\) 0 0
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) 0 0
\(373\) 4.33013 + 2.50000i 0.224205 + 0.129445i 0.607896 0.794017i \(-0.292014\pi\)
−0.383691 + 0.923462i \(0.625347\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −13.0000 −0.667765 −0.333883 0.942615i \(-0.608359\pi\)
−0.333883 + 0.942615i \(0.608359\pi\)
\(380\) 0 0
\(381\) 1.50000 + 2.59808i 0.0768473 + 0.133103i
\(382\) 0 0
\(383\) 24.2487 + 14.0000i 1.23905 + 0.715367i 0.968900 0.247451i \(-0.0795931\pi\)
0.270151 + 0.962818i \(0.412926\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.52628 + 5.50000i 0.484248 + 0.279581i
\(388\) 0 0
\(389\) 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i \(-0.0850816\pi\)
−0.710980 + 0.703213i \(0.751748\pi\)
\(390\) 0 0
\(391\) 64.0000 3.23662
\(392\) 0 0
\(393\) 2.00000i 0.100887i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.59808 + 1.50000i 0.130394 + 0.0752828i 0.563778 0.825926i \(-0.309347\pi\)
−0.433384 + 0.901209i \(0.642681\pi\)
\(398\) 0 0
\(399\) −0.500000 2.59808i −0.0250313 0.130066i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) −7.79423 + 4.50000i −0.388258 + 0.224161i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.00000i 0.0991363i
\(408\) 0 0
\(409\) −9.50000 16.4545i −0.469745 0.813622i 0.529657 0.848212i \(-0.322321\pi\)
−0.999402 + 0.0345902i \(0.988987\pi\)
\(410\) 0 0
\(411\) 2.00000 3.46410i 0.0986527 0.170872i
\(412\) 0 0
\(413\) 6.92820 + 8.00000i 0.340915 + 0.393654i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.33013 + 2.50000i −0.212047 + 0.122426i
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.19615 15.0000i 0.251459 0.725901i
\(428\) 0 0
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) 0 0
\(433\) 25.0000i 1.20142i −0.799466 0.600712i \(-0.794884\pi\)
0.799466 0.600712i \(-0.205116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.92820 4.00000i 0.331421 0.191346i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) 3.46410 + 2.00000i 0.164584 + 0.0950229i 0.580030 0.814595i \(-0.303041\pi\)
−0.415445 + 0.909618i \(0.636374\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000i 0.567581i
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 0 0
\(453\) −6.92820 4.00000i −0.325515 0.187936i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.2583 + 6.50000i 0.526642 + 0.304057i 0.739648 0.672994i \(-0.234992\pi\)
−0.213006 + 0.977051i \(0.568325\pi\)
\(458\) 0 0
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) 11.0000i 0.511213i −0.966781 0.255607i \(-0.917725\pi\)
0.966781 0.255607i \(-0.0822752\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.4449 + 17.0000i 1.36255 + 0.786666i 0.989962 0.141332i \(-0.0451386\pi\)
0.372584 + 0.927999i \(0.378472\pi\)
\(468\) 0 0
\(469\) −26.0000 + 22.5167i −1.20057 + 1.03972i
\(470\) 0 0
\(471\) 1.00000 1.73205i 0.0460776 0.0798087i
\(472\) 0 0
\(473\) 19.0526 11.0000i 0.876038 0.505781i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000i 0.549442i
\(478\) 0 0
\(479\) −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i \(-0.945735\pi\)
0.345827 0.938298i \(-0.387598\pi\)
\(480\) 0 0
\(481\) −1.50000 + 2.59808i −0.0683941 + 0.118462i
\(482\) 0 0
\(483\) 20.7846 4.00000i 0.945732 0.182006i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.4545 9.50000i 0.745624 0.430486i −0.0784867 0.996915i \(-0.525009\pi\)
0.824110 + 0.566429i \(0.191675\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 27.7128 16.0000i 1.24812 0.720604i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −25.9808 + 5.00000i −1.16540 + 0.224281i
\(498\) 0 0
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) −1.00000 1.73205i −0.0446767 0.0773823i
\(502\) 0 0
\(503\) 30.0000i 1.33763i −0.743427 0.668817i \(-0.766801\pi\)
0.743427 0.668817i \(-0.233199\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.46410 + 2.00000i −0.153846 + 0.0888231i
\(508\) 0 0
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) −22.0000 + 19.0526i −0.973223 + 0.842836i
\(512\) 0 0
\(513\) −0.866025 0.500000i −0.0382360 0.0220755i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 12.0000i 0.527759i
\(518\) 0 0
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) 0 0
\(523\) 26.8468 + 15.5000i 1.17393 + 0.677768i 0.954602 0.297884i \(-0.0962809\pi\)
0.219326 + 0.975652i \(0.429614\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.7846 + 12.0000i 0.905392 + 0.522728i
\(528\) 0 0
\(529\) 20.5000 + 35.5070i 0.891304 + 1.54378i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 18.0000i 0.779667i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.19615 3.00000i −0.224231 0.129460i
\(538\) 0 0
\(539\) −11.0000 8.66025i −0.473804 0.373024i
\(540\) 0 0
\(541\) 7.50000 12.9904i 0.322450 0.558500i −0.658543 0.752543i \(-0.728827\pi\)
0.980993 + 0.194043i \(0.0621602\pi\)
\(542\) 0 0
\(543\) 12.9904 7.50000i 0.557471 0.321856i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000i 0.513083i 0.966533 + 0.256541i \(0.0825830\pi\)
−0.966533 + 0.256541i \(0.917417\pi\)
\(548\) 0 0
\(549\) −3.00000 5.19615i −0.128037 0.221766i
\(550\) 0 0
\(551\) 2.00000 3.46410i 0.0852029 0.147576i
\(552\) 0 0
\(553\) −2.59808 + 7.50000i −0.110481 + 0.318932i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.0526 + 11.0000i −0.807283 + 0.466085i −0.846011 0.533165i \(-0.821003\pi\)
0.0387286 + 0.999250i \(0.487669\pi\)
\(558\) 0 0
\(559\) 33.0000 1.39575
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) −39.8372 + 23.0000i −1.67894 + 0.969334i −0.716596 + 0.697489i \(0.754301\pi\)
−0.962341 + 0.271846i \(0.912366\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.73205 2.00000i −0.0727393 0.0839921i
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 10.5000 + 18.1865i 0.439411 + 0.761083i 0.997644 0.0686016i \(-0.0218537\pi\)
−0.558233 + 0.829684i \(0.688520\pi\)
\(572\) 0 0
\(573\) 6.00000i 0.250654i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 35.5070 20.5000i 1.47818 0.853426i 0.478482 0.878097i \(-0.341187\pi\)
0.999696 + 0.0246713i \(0.00785391\pi\)
\(578\) 0 0
\(579\) −5.50000 + 9.52628i −0.228572 + 0.395899i
\(580\) 0 0
\(581\) 1.00000 + 5.19615i 0.0414870 + 0.215573i
\(582\) 0 0
\(583\) 20.7846 + 12.0000i 0.860811 + 0.496989i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.0000i 1.32078i −0.750922 0.660391i \(-0.770391\pi\)
0.750922 0.660391i \(-0.229609\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) 0 0
\(591\) 4.00000 + 6.92820i 0.164538 + 0.284988i
\(592\) 0 0
\(593\) 5.19615 + 3.00000i 0.213380 + 0.123195i 0.602881 0.797831i \(-0.294019\pi\)
−0.389501 + 0.921026i \(0.627353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.92820 4.00000i −0.283552 0.163709i
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −1.00000 −0.0407909 −0.0203954 0.999792i \(-0.506493\pi\)
−0.0203954 + 0.999792i \(0.506493\pi\)
\(602\) 0 0
\(603\) 13.0000i 0.529401i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −2.59808 1.50000i −0.105453 0.0608831i 0.446346 0.894860i \(-0.352725\pi\)
−0.551799 + 0.833977i \(0.686058\pi\)
\(608\) 0 0
\(609\) 8.00000 6.92820i 0.324176 0.280745i
\(610\) 0 0
\(611\) 9.00000 15.5885i 0.364101 0.630641i
\(612\) 0 0
\(613\) −25.9808 + 15.0000i −1.04935 + 0.605844i −0.922468 0.386073i \(-0.873831\pi\)
−0.126885 + 0.991917i \(0.540498\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.0000i 1.04672i −0.852111 0.523360i \(-0.824678\pi\)
0.852111 0.523360i \(-0.175322\pi\)
\(618\) 0 0
\(619\) −5.50000 9.52628i −0.221064 0.382893i 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) 0 0
\(621\) 4.00000 6.92820i 0.160514 0.278019i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.73205 + 1.00000i −0.0691714 + 0.0399362i
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 3.46410 2.00000i 0.137686 0.0794929i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −7.79423 19.5000i −0.308819 0.772618i
\(638\) 0 0
\(639\) −5.00000 + 8.66025i −0.197797 + 0.342594i
\(640\) 0 0
\(641\) 20.0000 + 34.6410i 0.789953 + 1.36824i 0.925995 + 0.377535i \(0.123228\pi\)
−0.136043 + 0.990703i \(0.543438\pi\)
\(642\) 0 0
\(643\) 35.0000i 1.38027i 0.723683 + 0.690133i \(0.242448\pi\)
−0.723683 + 0.690133i \(0.757552\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.19615 + 3.00000i −0.204282 + 0.117942i −0.598651 0.801010i \(-0.704296\pi\)
0.394369 + 0.918952i \(0.370963\pi\)
\(648\) 0 0
\(649\) 4.00000 6.92820i 0.157014 0.271956i
\(650\) 0 0
\(651\) 7.50000 + 2.59808i 0.293948 + 0.101827i
\(652\) 0 0
\(653\) 5.19615 + 3.00000i 0.203341 + 0.117399i 0.598213 0.801337i \(-0.295878\pi\)
−0.394872 + 0.918736i \(0.629211\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.0000i 0.429151i
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) 14.5000 + 25.1147i 0.563985 + 0.976850i 0.997143 + 0.0755324i \(0.0240656\pi\)
−0.433159 + 0.901318i \(0.642601\pi\)
\(662\) 0 0
\(663\) −20.7846 12.0000i −0.807207 0.466041i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 27.7128 + 16.0000i 1.07304 + 0.619522i
\(668\) 0 0
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 1.00000i 0.0385472i −0.999814 0.0192736i \(-0.993865\pi\)
0.999814 0.0192736i \(-0.00613535\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.3923 + 6.00000i 0.399409 + 0.230599i 0.686229 0.727386i \(-0.259265\pi\)
−0.286820 + 0.957984i \(0.592598\pi\)
\(678\) 0 0
\(679\) −5.00000 25.9808i −0.191882 0.997050i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 0 0
\(683\) 31.1769 18.0000i 1.19295 0.688751i 0.233977 0.972242i \(-0.424826\pi\)
0.958975 + 0.283491i \(0.0914927\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.00000i 0.0381524i
\(688\) 0 0
\(689\) 18.0000 + 31.1769i 0.685745 + 1.18775i
\(690\) 0 0
\(691\) 21.5000 37.2391i 0.817899 1.41664i −0.0893292 0.996002i \(-0.528472\pi\)
0.907228 0.420640i \(-0.138194\pi\)
\(692\) 0 0
\(693\) −5.19615 + 1.00000i −0.197386 + 0.0379869i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −41.5692 + 24.0000i −1.57455 + 0.909065i
\(698\) 0 0
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 0 0
\(703\) 0.866025 0.500000i 0.0326628 0.0188579i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −17.3205 20.0000i −0.651405 0.752177i
\(708\) 0 0
\(709\) 7.00000 12.1244i 0.262891 0.455340i −0.704118 0.710083i \(-0.748658\pi\)
0.967009 + 0.254743i \(0.0819909\pi\)
\(710\) 0 0
\(711\) 1.50000 + 2.59808i 0.0562544 + 0.0974355i
\(712\) 0 0
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.5885 9.00000i 0.582162 0.336111i
\(718\) 0 0
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) −27.5000 9.52628i −1.02415 0.354777i
\(722\) 0 0
\(723\) 12.1244 + 7.00000i 0.450910 + 0.260333i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.0000i 0.853023i 0.904482 + 0.426511i \(0.140258\pi\)
−0.904482 + 0.426511i \(0.859742\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −44.0000 76.2102i −1.62740 2.81874i
\(732\) 0 0
\(733\) −38.9711 22.5000i −1.43943 0.831056i −0.441622 0.897201i \(-0.645597\pi\)
−0.997810 + 0.0661448i \(0.978930\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22.5167 + 13.0000i 0.829412 + 0.478861i
\(738\) 0 0
\(739\) −4.50000 7.79423i −0.165535 0.286715i 0.771310 0.636460i \(-0.219602\pi\)
−0.936845 + 0.349744i \(0.886268\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) 18.0000i 0.660356i −0.943919 0.330178i \(-0.892891\pi\)
0.943919 0.330178i \(-0.107109\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.73205 + 1.00000i 0.0633724 + 0.0365881i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i \(-0.921574\pi\)
0.696122 + 0.717923i \(0.254907\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 42.0000i 1.52652i −0.646094 0.763258i \(-0.723599\pi\)
0.646094 0.763258i \(-0.276401\pi\)
\(758\) 0 0
\(759\) −8.00000 13.8564i −0.290382 0.502956i
\(760\) 0 0
\(761\) −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i \(-0.879652\pi\)
0.784373 + 0.620289i \(0.212985\pi\)
\(762\) 0 0
\(763\) −19.0526 22.0000i −0.689749 0.796453i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.3923 6.00000i 0.375244 0.216647i
\(768\) 0 0
\(769\) −31.0000 −1.11789 −0.558944 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) 19.0526 11.0000i 0.685273 0.395643i −0.116566 0.993183i \(-0.537189\pi\)
0.801839 + 0.597540i \(0.203855\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.59808 0.500000i 0.0932055 0.0179374i
\(778\) 0 0
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 10.0000 + 17.3205i 0.357828 + 0.619777i
\(782\) 0 0
\(783\) 4.00000i 0.142948i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20.7846 + 12.0000i −0.740891 + 0.427754i −0.822393 0.568919i \(-0.807362\pi\)
0.0815020 + 0.996673i \(0.474028\pi\)
\(788\) 0 0
\(789\) −6.00000 + 10.3923i −0.213606 + 0.369976i
\(790\) 0 0
\(791\) −7.00000 36.3731i −0.248891 1.29328i
\(792\) 0 0
\(793\) −15.5885 9.00000i −0.553562 0.319599i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.0000i 1.70025i 0.526583 + 0.850124i \(0.323473\pi\)
−0.526583 + 0.850124i \(0.676527\pi\)
\(798\) 0 0
\(799\) −48.0000 −1.69812
\(800\) 0 0
\(801\) 0