Properties

Label 1680.2.di.a.529.2
Level $1680$
Weight $2$
Character 1680.529
Analytic conductor $13.415$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.di (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 529.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1680.529
Dual form 1680.2.di.a.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +1.00000i q^{13} +(-1.00000 - 2.00000i) q^{15} +(-1.73205 - 1.00000i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-2.59808 + 1.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000i q^{27} +(-3.00000 + 5.19615i) q^{31} +(-4.33013 + 2.50000i) q^{33} +(-0.767949 - 5.86603i) q^{35} +(4.33013 - 2.50000i) q^{37} +(-0.500000 + 0.866025i) q^{39} -9.00000 q^{41} -10.0000i q^{43} +(0.133975 - 2.23205i) q^{45} +(-11.2583 + 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.866025 + 0.500000i) q^{53} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-0.866025 + 2.50000i) q^{63} +(1.23205 - 1.86603i) q^{65} +(-5.19615 - 3.00000i) q^{67} -3.00000 q^{69} +2.00000 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-0.598076 + 4.96410i) q^{75} +(-12.9904 + 2.50000i) q^{77} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(-5.19615 + 3.00000i) q^{93} +(-0.937822 + 15.6244i) q^{95} -8.00000i q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} + 2q^{9} + O(q^{10}) \) \( 4q - 4q^{5} + 2q^{9} - 10q^{11} - 4q^{15} - 14q^{19} + 2q^{21} - 6q^{25} - 12q^{31} - 10q^{35} - 2q^{39} - 36q^{41} + 4q^{45} - 4q^{49} - 4q^{51} + 40q^{55} - 8q^{59} + 4q^{61} - 2q^{65} - 12q^{69} + 8q^{71} + 8q^{75} + 28q^{79} - 2q^{81} + 8q^{85} + 20q^{89} - 8q^{91} - 28q^{95} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) −1.86603 1.23205i −0.834512 0.550990i
\(6\) 0 0
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) 0 0
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 0 0
\(15\) −1.00000 2.00000i −0.258199 0.516398i
\(16\) 0 0
\(17\) −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) 0 0
\(23\) −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) 0 0
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) 0 0
\(33\) −4.33013 + 2.50000i −0.753778 + 0.435194i
\(34\) 0 0
\(35\) −0.767949 5.86603i −0.129807 0.991539i
\(36\) 0 0
\(37\) 4.33013 2.50000i 0.711868 0.410997i −0.0998840 0.994999i \(-0.531847\pi\)
0.811752 + 0.584002i \(0.198514\pi\)
\(38\) 0 0
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) 10.0000i 1.52499i −0.646997 0.762493i \(-0.723975\pi\)
0.646997 0.762493i \(-0.276025\pi\)
\(44\) 0 0
\(45\) 0.133975 2.23205i 0.0199718 0.332734i
\(46\) 0 0
\(47\) −11.2583 + 6.50000i −1.64220 + 0.948122i −0.662145 + 0.749375i \(0.730354\pi\)
−0.980051 + 0.198747i \(0.936313\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 0 0
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) 0 0
\(53\) 0.866025 + 0.500000i 0.118958 + 0.0686803i 0.558298 0.829640i \(-0.311454\pi\)
−0.439340 + 0.898321i \(0.644788\pi\)
\(54\) 0 0
\(55\) 10.0000 5.00000i 1.34840 0.674200i
\(56\) 0 0
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 0 0
\(63\) −0.866025 + 2.50000i −0.109109 + 0.314970i
\(64\) 0 0
\(65\) 1.23205 1.86603i 0.152817 0.231452i
\(66\) 0 0
\(67\) −5.19615 3.00000i −0.634811 0.366508i 0.147802 0.989017i \(-0.452780\pi\)
−0.782613 + 0.622509i \(0.786114\pi\)
\(68\) 0 0
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i \(-0.408542\pi\)
−0.688830 + 0.724923i \(0.741875\pi\)
\(74\) 0 0
\(75\) −0.598076 + 4.96410i −0.0690599 + 0.573205i
\(76\) 0 0
\(77\) −12.9904 + 2.50000i −1.48039 + 0.284901i
\(78\) 0 0
\(79\) 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i \(0.121990\pi\)
−0.139895 + 0.990166i \(0.544677\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 10.0000i 1.09764i 0.835940 + 0.548821i \(0.184923\pi\)
−0.835940 + 0.548821i \(0.815077\pi\)
\(84\) 0 0
\(85\) 2.00000 + 4.00000i 0.216930 + 0.433861i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 0 0
\(91\) −2.00000 + 1.73205i −0.209657 + 0.181568i
\(92\) 0 0
\(93\) −5.19615 + 3.00000i −0.538816 + 0.311086i
\(94\) 0 0
\(95\) −0.937822 + 15.6244i −0.0962185 + 1.60303i
\(96\) 0 0
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i \(-0.963634\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(102\) 0 0
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0 0
\(105\) 2.26795 5.46410i 0.221329 0.533242i
\(106\) 0 0
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 0 0
\(109\) −9.00000 + 15.5885i −0.862044 + 1.49310i 0.00790932 + 0.999969i \(0.497482\pi\)
−0.869953 + 0.493135i \(0.835851\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 6.69615 + 0.401924i 0.624419 + 0.0374796i
\(116\) 0 0
\(117\) −0.866025 + 0.500000i −0.0800641 + 0.0462250i
\(118\) 0 0
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) −7.79423 4.50000i −0.702782 0.405751i
\(124\) 0 0
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 9.00000i 0.798621i 0.916816 + 0.399310i \(0.130750\pi\)
−0.916816 + 0.399310i \(0.869250\pi\)
\(128\) 0 0
\(129\) 5.00000 8.66025i 0.440225 0.762493i
\(130\) 0 0
\(131\) −8.50000 14.7224i −0.742648 1.28630i −0.951285 0.308312i \(-0.900236\pi\)
0.208637 0.977993i \(-0.433097\pi\)
\(132\) 0 0
\(133\) 6.06218 17.5000i 0.525657 1.51744i
\(134\) 0 0
\(135\) 1.23205 1.86603i 0.106038 0.160602i
\(136\) 0 0
\(137\) −3.46410 2.00000i −0.295958 0.170872i 0.344668 0.938725i \(-0.387992\pi\)
−0.640626 + 0.767853i \(0.721325\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −13.0000 −1.09480
\(142\) 0 0
\(143\) −4.33013 2.50000i −0.362103 0.209061i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.33013 + 5.50000i −0.357143 + 0.453632i
\(148\) 0 0
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −11.0000 + 19.0526i −0.895167 + 1.55048i −0.0615699 + 0.998103i \(0.519611\pi\)
−0.833597 + 0.552372i \(0.813723\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 12.0000 6.00000i 0.963863 0.481932i
\(156\) 0 0
\(157\) 11.2583 + 6.50000i 0.898513 + 0.518756i 0.876717 0.481006i \(-0.159728\pi\)
0.0217953 + 0.999762i \(0.493062\pi\)
\(158\) 0 0
\(159\) 0.500000 + 0.866025i 0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) −7.50000 2.59808i −0.591083 0.204757i
\(162\) 0 0
\(163\) 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) 0 0
\(165\) 11.1603 + 0.669873i 0.868825 + 0.0521495i
\(166\) 0 0
\(167\) 19.0000i 1.47026i −0.677924 0.735132i \(-0.737120\pi\)
0.677924 0.735132i \(-0.262880\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 0 0
\(173\) 6.06218 3.50000i 0.460899 0.266100i −0.251523 0.967851i \(-0.580932\pi\)
0.712422 + 0.701751i \(0.247598\pi\)
\(174\) 0 0
\(175\) −5.79423 + 11.8923i −0.438003 + 0.898974i
\(176\) 0 0
\(177\) −3.46410 + 2.00000i −0.260378 + 0.150329i
\(178\) 0 0
\(179\) 5.50000 9.52628i 0.411089 0.712028i −0.583920 0.811811i \(-0.698482\pi\)
0.995009 + 0.0997838i \(0.0318151\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) −11.1603 0.669873i −0.820518 0.0492500i
\(186\) 0 0
\(187\) 8.66025 5.00000i 0.633300 0.365636i
\(188\) 0 0
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) 0 0
\(191\) −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i \(-0.970165\pi\)
0.416751 0.909021i \(-0.363169\pi\)
\(192\) 0 0
\(193\) 15.5885 + 9.00000i 1.12208 + 0.647834i 0.941932 0.335805i \(-0.109008\pi\)
0.180150 + 0.983639i \(0.442342\pi\)
\(194\) 0 0
\(195\) 2.00000 1.00000i 0.143223 0.0716115i
\(196\) 0 0
\(197\) 27.0000i 1.92367i 0.273629 + 0.961835i \(0.411776\pi\)
−0.273629 + 0.961835i \(0.588224\pi\)
\(198\) 0 0
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 0 0
\(201\) −3.00000 5.19615i −0.211604 0.366508i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 16.7942 + 11.0885i 1.17296 + 0.774451i
\(206\) 0 0
\(207\) −2.59808 1.50000i −0.180579 0.104257i
\(208\) 0 0
\(209\) 35.0000 2.42100
\(210\) 0 0
\(211\) −19.0000 −1.30801 −0.654007 0.756489i \(-0.726913\pi\)
−0.654007 + 0.756489i \(0.726913\pi\)
\(212\) 0 0
\(213\) 1.73205 + 1.00000i 0.118678 + 0.0685189i
\(214\) 0 0
\(215\) −12.3205 + 18.6603i −0.840252 + 1.27262i
\(216\) 0 0
\(217\) −15.5885 + 3.00000i −1.05821 + 0.203653i
\(218\) 0 0
\(219\) −2.00000 3.46410i −0.135147 0.234082i
\(220\) 0 0
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) 0 0
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 0 0
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 0 0
\(227\) −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i \(-0.487137\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(228\) 0 0
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 0 0
\(231\) −12.5000 4.33013i −0.822440 0.284901i
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 29.0167 + 1.74167i 1.89284 + 0.113614i
\(236\) 0 0
\(237\) 14.0000i 0.909398i
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 10.4019 11.6962i 0.664555 0.747240i
\(246\) 0 0
\(247\) 6.06218 3.50000i 0.385727 0.222700i
\(248\) 0 0
\(249\) −5.00000 + 8.66025i −0.316862 + 0.548821i
\(250\) 0 0
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 15.0000i 0.943042i
\(254\) 0 0
\(255\) −0.267949 + 4.46410i −0.0167796 + 0.279553i
\(256\) 0 0
\(257\) 8.66025 5.00000i 0.540212 0.311891i −0.204953 0.978772i \(-0.565704\pi\)
0.745165 + 0.666880i \(0.232371\pi\)
\(258\) 0 0
\(259\) 12.5000 + 4.33013i 0.776712 + 0.269061i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 20.7846 + 12.0000i 1.28163 + 0.739952i 0.977147 0.212565i \(-0.0681817\pi\)
0.304487 + 0.952517i \(0.401515\pi\)
\(264\) 0 0
\(265\) −1.00000 2.00000i −0.0614295 0.122859i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 0 0
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 0 0
\(273\) −2.59808 + 0.500000i −0.157243 + 0.0302614i
\(274\) 0 0
\(275\) −24.8205 2.99038i −1.49673 0.180327i
\(276\) 0 0
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −11.0000 −0.656205 −0.328102 0.944642i \(-0.606409\pi\)
−0.328102 + 0.944642i \(0.606409\pi\)
\(282\) 0 0
\(283\) 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i \(-0.0522041\pi\)
0.351895 + 0.936039i \(0.385537\pi\)
\(284\) 0 0
\(285\) −8.62436 + 13.0622i −0.510863 + 0.773737i
\(286\) 0 0
\(287\) −15.5885 18.0000i −0.920158 1.06251i
\(288\) 0 0
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) 4.00000 6.92820i 0.234484 0.406138i
\(292\) 0 0
\(293\) 1.00000i 0.0584206i 0.999573 + 0.0292103i \(0.00929925\pi\)
−0.999573 + 0.0292103i \(0.990701\pi\)
\(294\) 0 0
\(295\) 8.00000 4.00000i 0.465778 0.232889i
\(296\) 0 0
\(297\) −4.33013 2.50000i −0.251259 0.145065i
\(298\) 0 0
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) 0 0
\(301\) 20.0000 17.3205i 1.15278 0.998337i
\(302\) 0 0
\(303\) −6.92820 + 4.00000i −0.398015 + 0.229794i
\(304\) 0 0
\(305\) 0.267949 4.46410i 0.0153427 0.255614i
\(306\) 0 0
\(307\) 2.00000i 0.114146i 0.998370 + 0.0570730i \(0.0181768\pi\)
−0.998370 + 0.0570730i \(0.981823\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.0000 + 22.5167i −0.737162 + 1.27680i 0.216606 + 0.976259i \(0.430501\pi\)
−0.953768 + 0.300544i \(0.902832\pi\)
\(312\) 0 0
\(313\) −8.66025 + 5.00000i −0.489506 + 0.282617i −0.724370 0.689412i \(-0.757869\pi\)
0.234863 + 0.972028i \(0.424536\pi\)
\(314\) 0 0
\(315\) 4.69615 3.59808i 0.264598 0.202729i
\(316\) 0 0
\(317\) −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 14.0000i 0.778981i
\(324\) 0 0
\(325\) −4.59808 + 1.96410i −0.255055 + 0.108949i
\(326\) 0 0
\(327\) −15.5885 + 9.00000i −0.862044 + 0.497701i
\(328\) 0 0
\(329\) −32.5000 11.2583i −1.79178 0.620692i
\(330\) 0 0
\(331\) −7.50000 12.9904i −0.412237 0.714016i 0.582897 0.812546i \(-0.301919\pi\)
−0.995134 + 0.0985303i \(0.968586\pi\)
\(332\) 0 0
\(333\) 4.33013 + 2.50000i 0.237289 + 0.136999i
\(334\) 0 0
\(335\) 6.00000 + 12.0000i 0.327815 + 0.655630i
\(336\) 0 0
\(337\) 14.0000i 0.762629i 0.924445 + 0.381314i \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) 0 0
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 0 0
\(345\) 5.59808 + 3.69615i 0.301390 + 0.198994i
\(346\) 0 0
\(347\) 13.8564 + 8.00000i 0.743851 + 0.429463i 0.823468 0.567363i \(-0.192036\pi\)
−0.0796169 + 0.996826i \(0.525370\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) −3.73205 2.46410i −0.198077 0.130781i
\(356\) 0 0
\(357\) 1.73205 5.00000i 0.0916698 0.264628i
\(358\) 0 0
\(359\) 14.0000 + 24.2487i 0.738892 + 1.27980i 0.952995 + 0.302987i \(0.0979839\pi\)
−0.214103 + 0.976811i \(0.568683\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) 0 0
\(367\) 32.0429 + 18.5000i 1.67263 + 0.965692i 0.966159 + 0.257948i \(0.0830464\pi\)
0.706469 + 0.707744i \(0.250287\pi\)
\(368\) 0 0
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) 0 0
\(371\) 0.500000 + 2.59808i 0.0259587 + 0.134885i
\(372\) 0 0
\(373\) 5.19615 3.00000i 0.269047 0.155334i −0.359408 0.933181i \(-0.617021\pi\)
0.628454 + 0.777847i \(0.283688\pi\)
\(374\) 0 0
\(375\) 7.23205 8.52628i 0.373461 0.440295i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) −4.50000 + 7.79423i −0.230542 + 0.399310i
\(382\) 0 0
\(383\) 7.79423 4.50000i 0.398266 0.229939i −0.287469 0.957790i \(-0.592814\pi\)
0.685736 + 0.727851i \(0.259481\pi\)
\(384\) 0 0
\(385\) 27.3205 + 11.3397i 1.39238 + 0.577927i
\(386\) 0 0
\(387\) 8.66025 5.00000i 0.440225 0.254164i
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 17.0000i 0.857537i
\(394\) 0 0
\(395\) 1.87564 31.2487i 0.0943739 1.57229i
\(396\) 0 0
\(397\) 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i \(-0.650684\pi\)
0.542834 + 0.839840i \(0.317351\pi\)
\(398\) 0 0
\(399\) 14.0000 12.1244i 0.700877 0.606977i
\(400\) 0 0
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 0 0
\(403\) −5.19615 3.00000i −0.258839 0.149441i
\(404\) 0 0
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) 0 0
\(407\) 25.0000i 1.23920i
\(408\) 0 0
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) 0 0
\(411\) −2.00000 3.46410i −0.0986527 0.170872i
\(412\) 0 0
\(413\) −10.3923 + 2.00000i −0.511372 + 0.0984136i
\(414\) 0 0
\(415\) 12.3205 18.6603i 0.604790 0.915996i
\(416\) 0 0
\(417\) −6.92820 4.00000i −0.339276 0.195881i
\(418\) 0 0
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) −11.2583 6.50000i −0.547399 0.316041i
\(424\) 0 0
\(425\) 1.19615 9.92820i 0.0580219 0.481589i
\(426\) 0 0
\(427\) −1.73205 + 5.00000i −0.0838198 + 0.241967i
\(428\) 0 0
\(429\) −2.50000 4.33013i −0.120701 0.209061i
\(430\) 0 0
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) 0 0
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.1865 + 10.5000i 0.869980 + 0.502283i
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) 5.19615 3.00000i 0.246877 0.142534i −0.371457 0.928450i \(-0.621142\pi\)
0.618333 + 0.785916i \(0.287808\pi\)
\(444\) 0 0
\(445\) 1.33975 22.3205i 0.0635100 1.05809i
\(446\) 0 0
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 22.5000 38.9711i 1.05948 1.83508i
\(452\) 0 0
\(453\) −19.0526 + 11.0000i −0.895167 + 0.516825i
\(454\) 0 0
\(455\) 5.86603 0.767949i 0.275004 0.0360020i
\(456\) 0 0
\(457\) 32.9090 19.0000i 1.53942 0.888783i 0.540544 0.841316i \(-0.318219\pi\)
0.998873 0.0474665i \(-0.0151147\pi\)
\(458\) 0 0
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 15.0000i 0.697109i 0.937288 + 0.348555i \(0.113327\pi\)
−0.937288 + 0.348555i \(0.886673\pi\)
\(464\) 0 0
\(465\) 13.3923 + 0.803848i 0.621053 + 0.0372775i
\(466\) 0 0
\(467\) 1.73205 1.00000i 0.0801498 0.0462745i −0.459390 0.888235i \(-0.651932\pi\)
0.539539 + 0.841960i \(0.318598\pi\)
\(468\) 0 0
\(469\) −3.00000 15.5885i −0.138527 0.719808i
\(470\) 0 0
\(471\) 6.50000 + 11.2583i 0.299504 + 0.518756i
\(472\) 0 0
\(473\) 43.3013 + 25.0000i 1.99099 + 1.14950i
\(474\) 0 0
\(475\) 21.0000 28.0000i 0.963546 1.28473i
\(476\) 0 0
\(477\) 1.00000i 0.0457869i
\(478\) 0 0
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 0 0
\(483\) −5.19615 6.00000i −0.236433 0.273009i
\(484\) 0 0
\(485\) −9.85641 + 14.9282i −0.447556 + 0.677855i
\(486\) 0 0
\(487\) −20.7846 12.0000i −0.941841 0.543772i −0.0513038 0.998683i \(-0.516338\pi\)
−0.890537 + 0.454911i \(0.849671\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 9.33013 + 6.16025i 0.419358 + 0.276883i
\(496\) 0 0
\(497\) 3.46410 + 4.00000i 0.155386 + 0.179425i
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 0 0
\(501\) 9.50000 16.4545i 0.424429 0.735132i
\(502\) 0 0
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 0 0
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 0 0
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) 0 0
\(509\) 7.00000 + 12.1244i 0.310270 + 0.537403i 0.978421 0.206623i \(-0.0662474\pi\)
−0.668151 + 0.744026i \(0.732914\pi\)
\(510\) 0 0
\(511\) −2.00000 10.3923i −0.0884748 0.459728i
\(512\) 0 0
\(513\) 6.06218 3.50000i 0.267652 0.154529i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 65.0000i 2.85870i
\(518\) 0 0
\(519\) 7.00000 0.307266
\(520\) 0 0
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 0 0
\(523\) −10.3923 + 6.00000i −0.454424 + 0.262362i −0.709697 0.704507i \(-0.751168\pi\)
0.255273 + 0.966869i \(0.417835\pi\)
\(524\) 0 0
\(525\) −10.9641 + 7.40192i −0.478513 + 0.323046i
\(526\) 0 0
\(527\) 10.3923 6.00000i 0.452696 0.261364i
\(528\) 0 0
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 9.00000i 0.389833i
\(534\) 0 0
\(535\) −26.7846 1.60770i −1.15800 0.0695067i
\(536\) 0 0
\(537\) 9.52628 5.50000i 0.411089 0.237343i
\(538\) 0 0
\(539\) −27.5000 21.6506i −1.18451 0.932559i
\(540\) 0 0
\(541\) −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i \(-0.194071\pi\)
−0.905811 + 0.423681i \(0.860738\pi\)
\(542\) 0 0
\(543\) −1.73205 1.00000i −0.0743294 0.0429141i
\(544\) 0 0
\(545\) 36.0000 18.0000i 1.54207 0.771035i
\(546\) 0 0
\(547\) 14.0000i 0.598597i −0.954160 0.299298i \(-0.903247\pi\)
0.954160 0.299298i \(-0.0967526\pi\)
\(548\) 0 0
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −12.1244 + 35.0000i −0.515580 + 1.48835i
\(554\) 0 0
\(555\) −9.33013 6.16025i −0.396042 0.261488i
\(556\) 0 0
\(557\) −33.7750 19.5000i −1.43109 0.826242i −0.433888 0.900967i \(-0.642859\pi\)
−0.997204 + 0.0747252i \(0.976192\pi\)
\(558\) 0 0
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 0 0
\(563\) 25.9808 + 15.0000i 1.09496 + 0.632175i 0.934892 0.354932i \(-0.115496\pi\)
0.160066 + 0.987106i \(0.448829\pi\)
\(564\) 0 0
\(565\) 7.39230 11.1962i 0.310997 0.471026i
\(566\) 0 0
\(567\) −2.59808 + 0.500000i −0.109109 + 0.0209980i
\(568\) 0 0
\(569\) −1.50000 2.59808i −0.0628833 0.108917i 0.832870 0.553469i \(-0.186696\pi\)
−0.895753 + 0.444552i \(0.853363\pi\)
\(570\) 0 0
\(571\) −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) 0 0
\(573\) 16.0000i 0.668410i
\(574\) 0 0
\(575\) −12.0000 9.00000i −0.500435 0.375326i
\(576\) 0 0
\(577\) 20.7846 + 12.0000i 0.865275 + 0.499567i 0.865775 0.500433i \(-0.166826\pi\)
−0.000500448 1.00000i \(0.500159\pi\)
\(578\) 0 0
\(579\) 9.00000 + 15.5885i 0.374027 + 0.647834i
\(580\) 0 0
\(581\) −20.0000 + 17.3205i −0.829740 + 0.718576i
\(582\) 0 0
\(583\) −4.33013 + 2.50000i −0.179336 + 0.103539i
\(584\) 0 0
\(585\) 2.23205 + 0.133975i 0.0922839 + 0.00553917i
\(586\) 0 0
\(587\) 2.00000i 0.0825488i 0.999148 + 0.0412744i \(0.0131418\pi\)
−0.999148 + 0.0412744i \(0.986858\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) −13.5000 + 23.3827i −0.555316 + 0.961835i
\(592\) 0 0
\(593\) −29.4449 + 17.0000i −1.20916 + 0.698106i −0.962575 0.271016i \(-0.912640\pi\)
−0.246581 + 0.969122i \(0.579307\pi\)
\(594\) 0 0
\(595\) −4.53590 + 10.9282i −0.185954 + 0.448013i
\(596\) 0 0
\(597\) 12.1244 7.00000i 0.496217 0.286491i
\(598\) 0 0
\(599\) 14.0000 24.2487i 0.572024 0.990775i −0.424333 0.905506i \(-0.639492\pi\)
0.996358 0.0852695i \(-0.0271751\pi\)
\(600\) 0 0
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) 0 0
\(603\) 6.00000i 0.244339i
\(604\) 0 0
\(605\) −1.87564 + 31.2487i −0.0762558 + 1.27044i
\(606\) 0 0
\(607\) 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i \(-0.581682\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.50000 11.2583i −0.262962 0.455463i
\(612\) 0 0
\(613\) −16.4545 9.50000i −0.664590 0.383701i 0.129433 0.991588i \(-0.458684\pi\)
−0.794024 + 0.607887i \(0.792017\pi\)
\(614\) 0 0
\(615\) 9.00000 + 18.0000i 0.362915 + 0.725830i
\(616\) 0 0
\(617\) 30.0000i 1.20775i −0.797077 0.603877i \(-0.793622\pi\)
0.797077 0.603877i \(-0.206378\pi\)
\(618\) 0 0
\(619\) −7.50000 + 12.9904i −0.301450 + 0.522127i −0.976465 0.215677i \(-0.930804\pi\)
0.675014 + 0.737805i \(0.264137\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 0 0
\(623\) −8.66025 + 25.0000i −0.346966 + 1.00160i
\(624\) 0 0
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 0 0
\(627\) 30.3109 + 17.5000i 1.21050 + 0.698883i
\(628\) 0 0
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 0 0
\(633\) −16.4545 9.50000i −0.654007 0.377591i
\(634\) 0 0
\(635\) 11.0885 16.7942i 0.440032 0.666459i
\(636\) 0 0
\(637\) −6.92820 1.00000i −0.274505 0.0396214i
\(638\) 0 0
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) 38.0000i 1.49857i −0.662246 0.749287i \(-0.730396\pi\)
0.662246 0.749287i \(-0.269604\pi\)
\(644\) 0 0
\(645\) −20.0000 + 10.0000i −0.787499 + 0.393750i
\(646\) 0 0
\(647\) 0.866025 + 0.500000i 0.0340470 + 0.0196570i 0.516927 0.856030i \(-0.327076\pi\)
−0.482880 + 0.875687i \(0.660409\pi\)
\(648\) 0 0
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) 0 0
\(651\) −15.0000 5.19615i −0.587896 0.203653i
\(652\) 0 0
\(653\) 4.33013 2.50000i 0.169451 0.0978326i −0.412876 0.910787i \(-0.635476\pi\)
0.582327 + 0.812955i \(0.302142\pi\)
\(654\) 0 0
\(655\) −2.27757 + 37.9449i −0.0889920 + 1.48263i
\(656\) 0 0
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) 0 0
\(663\) 1.73205 1.00000i 0.0672673 0.0388368i
\(664\) 0 0
\(665\) −32.8731 + 25.1865i −1.27476 + 0.976692i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) 0 0
\(675\) −4.59808 + 1.96410i −0.176980 + 0.0755983i
\(676\) 0 0
\(677\) −28.5788 + 16.5000i −1.09837 + 0.634147i −0.935793 0.352549i \(-0.885315\pi\)
−0.162581 + 0.986695i \(0.551982\pi\)
\(678\) 0 0
\(679\) 16.0000 13.8564i 0.614024 0.531760i
\(680\) 0 0
\(681\) −7.00000 12.1244i −0.268241 0.464606i
\(682\) 0 0
\(683\) −3.46410 2.00000i −0.132550 0.0765279i 0.432259 0.901750i \(-0.357717\pi\)
−0.564809 + 0.825222i \(0.691050\pi\)
\(684\) 0 0
\(685\) 4.00000 + 8.00000i 0.152832 + 0.305664i
\(686\) 0 0
\(687\) 4.00000i 0.152610i
\(688\) 0 0
\(689\) −0.500000 + 0.866025i −0.0190485 + 0.0329929i
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 0 0
\(693\) −8.66025 10.0000i −0.328976 0.379869i
\(694\) 0 0
\(695\) 14.9282 + 9.85641i 0.566259 + 0.373875i
\(696\) 0 0
\(697\) 15.5885 + 9.00000i 0.590455 + 0.340899i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −30.3109 17.5000i −1.14320 0.660025i
\(704\) 0 0
\(705\) 24.2583 + 16.0167i 0.913622 + 0.603222i
\(706\) 0 0
\(707\) −20.7846 + 4.00000i −0.781686 + 0.150435i
\(708\) 0 0
\(709\) 8.00000 + 13.8564i 0.300446 + 0.520388i 0.976237 0.216705i \(-0.0695310\pi\)
−0.675791 + 0.737093i \(0.736198\pi\)
\(710\) 0 0
\(711\) −7.00000 + 12.1244i −0.262521 + 0.454699i
\(712\) 0 0
\(713\) 18.0000i 0.674105i
\(714\) 0 0
\(715\) 5.00000 + 10.0000i 0.186989 + 0.373979i
\(716\) 0 0
\(717\) 17.3205 + 10.0000i 0.646846 + 0.373457i
\(718\) 0 0
\(719\) 1.00000 + 1.73205i 0.0372937 + 0.0645946i 0.884070 0.467355i \(-0.154793\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0.866025 0.500000i 0.0322078 0.0185952i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 53.0000i 1.96566i 0.184510 + 0.982831i \(0.440930\pi\)
−0.184510 + 0.982831i \(0.559070\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) −18.1865 + 10.5000i −0.671735 + 0.387826i −0.796734 0.604331i \(-0.793441\pi\)
0.124999 + 0.992157i \(0.460107\pi\)
\(734\) 0 0
\(735\) 14.8564 4.92820i 0.547987 0.181780i
\(736\) 0 0
\(737\) 25.9808 15.0000i 0.957014 0.552532i
\(738\) 0 0
\(739\) −23.5000 + 40.7032i −0.864461 + 1.49729i 0.00311943 + 0.999995i \(0.499007\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) 0 0
\(743\) 31.0000i 1.13728i 0.822587 + 0.568640i \(0.192530\pi\)
−0.822587 + 0.568640i \(0.807470\pi\)
\(744\) 0 0
\(745\) −0.803848 + 13.3923i −0.0294507 + 0.490656i
\(746\) 0 0
\(747\) −8.66025 + 5.00000i −0.316862 + 0.182940i
\(748\) 0 0
\(749\) 30.0000 + 10.3923i 1.09618 + 0.379727i
\(750\) 0 0
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 0 0
\(753\) 2.59808 + 1.50000i 0.0946792 + 0.0546630i
\(754\) 0 0
\(755\) 44.0000 22.0000i 1.60132 0.800662i
\(756\) 0 0
\(757\) 26.0000i 0.944986i 0.881334 + 0.472493i \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) 0 0
\(759\) 7.50000 12.9904i 0.272233 0.471521i
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 0 0
\(763\) −46.7654 + 9.00000i −1.69302 + 0.325822i
\(764\) 0 0
\(765\) −2.46410 + 3.73205i −0.0890898 + 0.134933i
\(766\) 0 0
\(767\) −3.46410 2.00000i −0.125081 0.0722158i
\(768\) 0 0
\(769\) −51.0000 −1.83911 −0.919554 0.392965i \(-0.871449\pi\)
−0.919554 + 0.392965i \(0.871449\pi\)
\(770\) 0 0
\(771\) 10.0000 0.360141
\(772\) 0 0
\(773\) 32.0429 + 18.5000i 1.15250 + 0.665399i 0.949496 0.313778i \(-0.101595\pi\)
0.203008 + 0.979177i \(0.434928\pi\)
\(774\) 0 0
\(775\) −29.7846 3.58846i −1.06989 0.128901i
\(776\) 0 0
\(777\) 8.66025 + 10.0000i 0.310685 + 0.358748i
\(778\) 0 0
\(779\) 31.5000 + 54.5596i 1.12860 + 1.95480i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −13.0000 26.0000i −0.463990 0.927980i
\(786\) 0 0
\(787\) −32.9090 19.0000i −1.17308 0.677277i −0.218675 0.975798i \(-0.570173\pi\)
−0.954403 + 0.298521i \(0.903507\pi\)
\(788\) 0 0
\(789\) 12.0000 + 20.7846i 0.427211 + 0.739952i
\(790\) 0 0
\(791\) −12.0000 + 10.3923i −0.426671 + 0.369508i
\(792\) 0 0
\(793\) −1.73205 + 1.00000i −0.0615069 + 0.0355110i
\(794\) 0 0
\(795\) 0.133975 2.23205i 0.00475159 0.0791627i
\(796\) 0 0
\(797\) 30.0000i 1.06265i 0.847167 + 0.531327i \(0.178307\pi\)
−0.847167 + 0.531327i \(0.821693\pi\)
\(798\) 0 0
\(799\) 26.0000 0.919814
\(800\) 0 0
\(801\) −5.00000 + 8.66025i −0.176666 + 0.305995i
\(802\) 0 0
\(803\) 17.3205 10.0000i 0.611227 0.352892i
\(804\) 0 0