Properties

Label 700.2.i.a.501.1
Level $700$
Weight $2$
Character 700.501
Analytic conductor $5.590$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 700.501
Dual form 700.2.i.a.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{11} +6.00000 q^{13} +(1.00000 - 1.73205i) q^{17} +(7.50000 + 2.59808i) q^{21} +(-4.50000 - 7.79423i) q^{23} +9.00000 q^{27} +3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(3.00000 + 5.19615i) q^{33} +(4.00000 + 6.92820i) q^{37} +(-9.00000 + 15.5885i) q^{39} +5.00000 q^{41} -1.00000 q^{43} +(4.00000 + 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(2.00000 - 3.46410i) q^{53} +(4.00000 - 6.92820i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(-12.0000 + 10.3923i) q^{63} +(-1.50000 + 2.59808i) q^{67} +27.0000 q^{69} +8.00000 q^{71} +(7.00000 - 12.1244i) q^{73} +(-5.00000 - 1.73205i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +1.00000 q^{83} +(-4.50000 + 7.79423i) q^{87} +(-6.50000 - 11.2583i) q^{89} +(-3.00000 - 15.5885i) q^{91} +(-3.00000 - 5.19615i) q^{93} +10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} - q^{7} - 6q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - q^{7} - 6q^{9} + 2q^{11} + 12q^{13} + 2q^{17} + 15q^{21} - 9q^{23} + 18q^{27} + 6q^{29} - 2q^{31} + 6q^{33} + 8q^{37} - 18q^{39} + 10q^{41} - 2q^{43} + 8q^{47} - 13q^{49} + 6q^{51} + 4q^{53} + 8q^{59} - 7q^{61} - 24q^{63} - 3q^{67} + 54q^{69} + 16q^{71} + 14q^{73} - 10q^{77} - 4q^{79} - 9q^{81} + 2q^{83} - 9q^{87} - 13q^{89} - 6q^{91} - 6q^{93} + 20q^{97} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.50000 + 2.59808i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 0 0
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) 7.50000 + 2.59808i 1.63663 + 0.566947i
\(22\) 0 0
\(23\) −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i \(-0.779053\pi\)
−0.169701 0.985496i \(-0.554280\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i \(0.0617599\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(38\) 0 0
\(39\) −9.00000 + 15.5885i −1.44115 + 2.49615i
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0 0
\(53\) 2.00000 3.46410i 0.274721 0.475831i −0.695344 0.718677i \(-0.744748\pi\)
0.970065 + 0.242846i \(0.0780811\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) −12.0000 + 10.3923i −1.51186 + 1.30931i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 0 0
\(69\) 27.0000 3.25042
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.00000 1.73205i −0.569803 0.197386i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 1.00000 0.109764 0.0548821 0.998493i \(-0.482522\pi\)
0.0548821 + 0.998493i \(0.482522\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) 0 0
\(89\) −6.50000 11.2583i −0.688999 1.19338i −0.972162 0.234309i \(-0.924717\pi\)
0.283164 0.959072i \(-0.408616\pi\)
\(90\) 0 0
\(91\) −3.00000 15.5885i −0.314485 1.63411i
\(92\) 0 0
\(93\) −3.00000 5.19615i −0.311086 0.538816i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) −12.0000 −1.20605
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.50000 12.9904i −0.725052 1.25583i −0.958952 0.283567i \(-0.908482\pi\)
0.233900 0.972261i \(-0.424851\pi\)
\(108\) 0 0
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 0 0
\(111\) −24.0000 −2.27798
\(112\) 0 0
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −18.0000 31.1769i −1.66410 2.88231i
\(118\) 0 0
\(119\) −5.00000 1.73205i −0.458349 0.158777i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) −7.50000 + 12.9904i −0.676252 + 1.17130i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 1.50000 2.59808i 0.132068 0.228748i
\(130\) 0 0
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) −24.0000 −2.02116
\(142\) 0 0
\(143\) 6.00000 10.3923i 0.501745 0.869048i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.00000 20.7846i 0.247436 1.71429i
\(148\) 0 0
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 0 0
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) −18.0000 + 15.5885i −1.41860 + 1.22854i
\(162\) 0 0
\(163\) 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i \(-0.0652307\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.00000 13.8564i −0.608229 1.05348i −0.991532 0.129861i \(-0.958547\pi\)
0.383304 0.923622i \(-0.374786\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 + 20.7846i 0.901975 + 1.56227i
\(178\) 0 0
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 0 0
\(181\) 1.00000 0.0743294 0.0371647 0.999309i \(-0.488167\pi\)
0.0371647 + 0.999309i \(0.488167\pi\)
\(182\) 0 0
\(183\) 21.0000 1.55236
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) 0 0
\(189\) −4.50000 23.3827i −0.327327 1.70084i
\(190\) 0 0
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) 0 0
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.0000 −0.997459 −0.498729 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(198\) 0 0
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) 0 0
\(201\) −4.50000 7.79423i −0.317406 0.549762i
\(202\) 0 0
\(203\) −1.50000 7.79423i −0.105279 0.547048i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −27.0000 + 46.7654i −1.87663 + 3.25042i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) −12.0000 + 20.7846i −0.822226 + 1.42414i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 5.00000 + 1.73205i 0.339422 + 0.117579i
\(218\) 0 0
\(219\) 21.0000 + 36.3731i 1.41905 + 2.45786i
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.00000 + 3.46410i −0.132745 + 0.229920i −0.924734 0.380615i \(-0.875712\pi\)
0.791989 + 0.610535i \(0.209046\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 12.0000 10.3923i 0.789542 0.683763i
\(232\) 0 0
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 12.0000 0.779484
\(238\) 0 0
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −1.50000 + 2.59808i −0.0950586 + 0.164646i
\(250\) 0 0
\(251\) 30.0000 1.89358 0.946792 0.321847i \(-0.104304\pi\)
0.946792 + 0.321847i \(0.104304\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.00000 + 6.92820i 0.249513 + 0.432169i 0.963391 0.268101i \(-0.0863961\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(258\) 0 0
\(259\) 16.0000 13.8564i 0.994192 0.860995i
\(260\) 0 0
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) 0 0
\(263\) 8.50000 14.7224i 0.524132 0.907824i −0.475473 0.879730i \(-0.657723\pi\)
0.999605 0.0280936i \(-0.00894366\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 39.0000 2.38676
\(268\) 0 0
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 0 0
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 0 0
\(273\) 45.0000 + 15.5885i 2.72352 + 0.943456i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.00000 15.5885i 0.540758 0.936620i −0.458103 0.888899i \(-0.651471\pi\)
0.998861 0.0477206i \(-0.0151957\pi\)
\(278\) 0 0
\(279\) 12.0000 0.718421
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.50000 12.9904i −0.147570 0.766798i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −15.0000 + 25.9808i −0.879316 + 1.52302i
\(292\) 0 0
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.00000 15.5885i 0.522233 0.904534i
\(298\) 0 0
\(299\) −27.0000 46.7654i −1.56145 2.70451i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) 0 0
\(303\) 4.50000 + 7.79423i 0.258518 + 0.447767i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 −0.0570730 −0.0285365 0.999593i \(-0.509085\pi\)
−0.0285365 + 0.999593i \(0.509085\pi\)
\(308\) 0 0
\(309\) −39.0000 −2.21863
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −2.00000 3.46410i −0.113047 0.195803i 0.803951 0.594696i \(-0.202728\pi\)
−0.916997 + 0.398894i \(0.869394\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 + 8.66025i 0.280828 + 0.486408i 0.971589 0.236675i \(-0.0760576\pi\)
−0.690761 + 0.723083i \(0.742724\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) 45.0000 2.51166
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.5000 23.3827i −0.746552 1.29307i
\(328\) 0 0
\(329\) 16.0000 13.8564i 0.882109 0.763928i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) 0 0
\(333\) 24.0000 41.5692i 1.31519 2.27798i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −28.0000 −1.52526 −0.762629 0.646837i \(-0.776092\pi\)
−0.762629 + 0.646837i \(0.776092\pi\)
\(338\) 0 0
\(339\) −6.00000 + 10.3923i −0.325875 + 0.564433i
\(340\) 0 0
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.5000 21.6506i 0.671035 1.16227i −0.306576 0.951846i \(-0.599183\pi\)
0.977611 0.210421i \(-0.0674834\pi\)
\(348\) 0 0
\(349\) −17.0000 −0.909989 −0.454995 0.890494i \(-0.650359\pi\)
−0.454995 + 0.890494i \(0.650359\pi\)
\(350\) 0 0
\(351\) 54.0000 2.88231
\(352\) 0 0
\(353\) −18.0000 + 31.1769i −0.958043 + 1.65938i −0.230799 + 0.973002i \(0.574134\pi\)
−0.727245 + 0.686378i \(0.759200\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.0000 10.3923i 0.635107 0.550019i
\(358\) 0 0
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) −21.0000 −1.10221
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.500000 0.866025i 0.0260998 0.0452062i −0.852680 0.522433i \(-0.825025\pi\)
0.878780 + 0.477227i \(0.158358\pi\)
\(368\) 0 0
\(369\) −15.0000 25.9808i −0.780869 1.35250i
\(370\) 0 0
\(371\) −10.0000 3.46410i −0.519174 0.179847i
\(372\) 0 0
\(373\) 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i \(0.144109\pi\)
−0.0708063 + 0.997490i \(0.522557\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 24.0000 41.5692i 1.22956 2.12966i
\(382\) 0 0
\(383\) −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 0 0
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.00000 + 8.66025i 0.250943 + 0.434646i 0.963786 0.266678i \(-0.0859261\pi\)
−0.712843 + 0.701324i \(0.752593\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.5000 + 25.1147i 0.724095 + 1.25417i 0.959345 + 0.282235i \(0.0910758\pi\)
−0.235250 + 0.971935i \(0.575591\pi\)
\(402\) 0 0
\(403\) −6.00000 + 10.3923i −0.298881 + 0.517678i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.0000 0.793091
\(408\) 0 0
\(409\) −1.50000 + 2.59808i −0.0741702 + 0.128467i −0.900725 0.434389i \(-0.856964\pi\)
0.826555 + 0.562856i \(0.190297\pi\)
\(410\) 0 0
\(411\) −18.0000 31.1769i −0.887875 1.53784i
\(412\) 0 0
\(413\) −20.0000 6.92820i −0.984136 0.340915i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −15.0000 + 25.9808i −0.734553 + 1.27228i
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 0 0
\(423\) 24.0000 41.5692i 1.16692 2.02116i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −14.0000 + 12.1244i −0.677507 + 0.586739i
\(428\) 0 0
\(429\) 18.0000 + 31.1769i 0.869048 + 1.50524i
\(430\) 0 0
\(431\) −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i \(-0.879492\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(432\) 0 0
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i \(-0.197097\pi\)
−0.909798 + 0.415051i \(0.863764\pi\)
\(440\) 0 0
\(441\) 33.0000 + 25.9808i 1.57143 + 1.23718i
\(442\) 0 0
\(443\) 18.5000 + 32.0429i 0.878962 + 1.52241i 0.852482 + 0.522757i \(0.175096\pi\)
0.0264796 + 0.999649i \(0.491570\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 27.0000 1.27706
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) 0 0
\(453\) 15.0000 + 25.9808i 0.704761 + 1.22068i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.0000 + 24.2487i 0.654892 + 1.13431i 0.981921 + 0.189292i \(0.0606194\pi\)
−0.327028 + 0.945015i \(0.606047\pi\)
\(458\) 0 0
\(459\) 9.00000 15.5885i 0.420084 0.727607i
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.50000 + 4.33013i 0.115686 + 0.200374i 0.918054 0.396456i \(-0.129760\pi\)
−0.802368 + 0.596830i \(0.796427\pi\)
\(468\) 0 0
\(469\) 7.50000 + 2.59808i 0.346318 + 0.119968i
\(470\) 0 0
\(471\) −3.00000 5.19615i −0.138233 0.239426i
\(472\) 0 0
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −24.0000 −1.09888
\(478\) 0 0
\(479\) 15.0000 25.9808i 0.685367 1.18709i −0.287954 0.957644i \(-0.592975\pi\)
0.973321 0.229447i \(-0.0736918\pi\)
\(480\) 0 0
\(481\) 24.0000 + 41.5692i 1.09431 + 1.89539i
\(482\) 0 0
\(483\) −13.5000 70.1481i −0.614271 3.19185i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.0000 27.7128i 0.725029 1.25579i −0.233933 0.972253i \(-0.575160\pi\)
0.958962 0.283535i \(-0.0915071\pi\)
\(488\) 0 0
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) 3.00000 5.19615i 0.135113 0.234023i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.00000 20.7846i −0.179425 0.932317i
\(498\) 0 0
\(499\) 3.00000 + 5.19615i 0.134298 + 0.232612i 0.925329 0.379165i \(-0.123789\pi\)
−0.791031 + 0.611776i \(0.790455\pi\)
\(500\) 0 0
\(501\) −13.5000 + 23.3827i −0.603136 + 1.04466i
\(502\) 0 0
\(503\) −27.0000 −1.20387 −0.601935 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −34.5000 + 59.7558i −1.53220 + 2.65385i
\(508\) 0 0
\(509\) 20.5000 + 35.5070i 0.908647 + 1.57382i 0.815946 + 0.578128i \(0.196217\pi\)
0.0927004 + 0.995694i \(0.470450\pi\)
\(510\) 0 0
\(511\) −35.0000 12.1244i −1.54831 0.536350i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 48.0000 2.10697
\(520\) 0 0
\(521\) −7.00000 + 12.1244i −0.306676 + 0.531178i −0.977633 0.210318i \(-0.932550\pi\)
0.670957 + 0.741496i \(0.265883\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 + 3.46410i 0.0871214 + 0.150899i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) −48.0000 −2.08302
\(532\) 0 0
\(533\) 30.0000 1.29944
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 + 15.5885i 0.388379 + 0.672692i
\(538\) 0 0
\(539\) −2.00000 + 13.8564i −0.0861461 + 0.596838i
\(540\) 0 0
\(541\) −16.5000 28.5788i −0.709390 1.22870i −0.965084 0.261942i \(-0.915637\pi\)
0.255693 0.966758i \(-0.417696\pi\)
\(542\) 0 0
\(543\) −1.50000 + 2.59808i −0.0643712 + 0.111494i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.0000 0.641354 0.320677 0.947189i \(-0.396090\pi\)
0.320677 + 0.947189i \(0.396090\pi\)
\(548\) 0 0
\(549\) −21.0000 + 36.3731i −0.896258 + 1.55236i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −8.00000 + 6.92820i −0.340195 + 0.294617i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00000 + 1.73205i −0.0423714 + 0.0733893i −0.886433 0.462856i \(-0.846825\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) 0 0
\(563\) −6.50000 + 11.2583i −0.273942 + 0.474482i −0.969868 0.243632i \(-0.921661\pi\)
0.695925 + 0.718114i \(0.254994\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 22.5000 + 7.79423i 0.944911 + 0.327327i
\(568\) 0 0
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −12.0000 + 20.7846i −0.502184 + 0.869809i 0.497812 + 0.867285i \(0.334137\pi\)
−0.999997 + 0.00252413i \(0.999197\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000 19.0526i 0.457936 0.793168i −0.540916 0.841077i \(-0.681922\pi\)
0.998852 + 0.0479084i \(0.0152556\pi\)
\(578\) 0 0
\(579\) 3.00000 + 5.19615i 0.124676 + 0.215945i
\(580\) 0 0
\(581\) −0.500000 2.59808i −0.0207435 0.107786i
\(582\) 0 0
\(583\) −4.00000 6.92820i −0.165663 0.286937i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 21.0000 36.3731i 0.863825 1.49619i
\(592\) 0 0
\(593\) −18.0000 31.1769i −0.739171 1.28028i −0.952869 0.303383i \(-0.901884\pi\)
0.213697 0.976900i \(-0.431449\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −30.0000 51.9615i −1.22782 2.12664i
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i \(-0.160206\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(608\) 0 0
\(609\) 22.5000 + 7.79423i 0.911746 + 0.315838i
\(610\) 0 0
\(611\) 24.0000 + 41.5692i 0.970936 + 1.68171i
\(612\) 0 0
\(613\) −3.00000 + 5.19615i −0.121169 + 0.209871i −0.920229 0.391381i \(-0.871998\pi\)
0.799060 + 0.601251i \(0.205331\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −20.0000 −0.805170 −0.402585 0.915383i \(-0.631888\pi\)
−0.402585 + 0.915383i \(0.631888\pi\)
\(618\) 0 0
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 0 0
\(621\) −40.5000 70.1481i −1.62521 2.81494i
\(622\) 0 0
\(623\) −26.0000 + 22.5167i −1.04167 + 0.902111i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 0 0
\(633\) −6.00000 + 10.3923i −0.238479 + 0.413057i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −39.0000 + 15.5885i −1.54524 + 0.617637i
\(638\) 0 0
\(639\) −24.0000 41.5692i −0.949425 1.64445i
\(640\) 0 0
\(641\) 15.5000 26.8468i 0.612213 1.06038i −0.378653 0.925539i \(-0.623613\pi\)
0.990867 0.134846i \(-0.0430539\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.500000 0.866025i 0.0196570 0.0340470i −0.856030 0.516927i \(-0.827076\pi\)
0.875687 + 0.482880i \(0.160409\pi\)
\(648\) 0 0
\(649\) −8.00000 13.8564i −0.314027 0.543912i
\(650\) 0 0
\(651\) −12.0000 + 10.3923i −0.470317 + 0.407307i
\(652\) 0 0
\(653\) −17.0000 29.4449i −0.665261 1.15227i −0.979214 0.202828i \(-0.934987\pi\)
0.313953 0.949439i \(-0.398347\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −84.0000 −3.27715
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) −15.5000 + 26.8468i −0.602880 + 1.04422i 0.389503 + 0.921025i \(0.372647\pi\)
−0.992383 + 0.123194i \(0.960686\pi\)
\(662\) 0 0
\(663\) 18.0000 + 31.1769i 0.699062 + 1.21081i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −13.5000 23.3827i −0.522722 0.905381i
\(668\) 0 0
\(669\) 24.0000 41.5692i 0.927894 1.60716i
\(670\) 0 0
\(671\) −14.0000 −0.540464
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 0 0
\(679\) −5.00000 25.9808i −0.191882 0.997050i
\(680\) 0 0
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) 0 0
\(683\) 14.5000 25.1147i 0.554827 0.960989i −0.443090 0.896477i \(-0.646118\pi\)
0.997917 0.0645115i \(-0.0205489\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −42.0000 −1.60240
\(688\) 0 0
\(689\) 12.0000 20.7846i 0.457164 0.791831i
\(690\) 0 0
\(691\) 13.0000 + 22.5167i 0.494543 + 0.856574i 0.999980 0.00628943i \(-0.00200200\pi\)
−0.505437 + 0.862864i \(0.668669\pi\)
\(692\) 0 0
\(693\) 6.00000 + 31.1769i 0.227921 + 1.18431i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 5.00000 8.66025i 0.189389 0.328031i
\(698\) 0 0
\(699\) 54.0000 2.04247
\(700\) 0 0
\(701\) −29.0000 −1.09531 −0.547657 0.836703i \(-0.684480\pi\)
−0.547657 + 0.836703i \(0.684480\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.50000 2.59808i −0.282067 0.0977107i
\(708\) 0 0
\(709\) −15.5000 26.8468i −0.582115 1.00825i −0.995228 0.0975728i \(-0.968892\pi\)
0.413114 0.910679i \(-0.364441\pi\)
\(710\) 0 0
\(711\) −12.0000 + 20.7846i −0.450035 + 0.779484i
\(712\) 0 0
\(713\) 18.0000 0.674105
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 39.0000 67.5500i 1.45648 2.52270i
\(718\) 0 0
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0 0
\(721\) 26.0000 22.5167i 0.968291 0.838564i
\(722\) 0 0
\(723\) −15.0000 25.9808i −0.557856 0.966235i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −3.00000 −0.111264 −0.0556319 0.998451i \(-0.517717\pi\)
−0.0556319 + 0.998451i \(0.517717\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.00000 + 1.73205i −0.0369863 + 0.0640622i
\(732\) 0 0
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) 0 0
\(739\) −5.00000 + 8.66025i −0.183928 + 0.318573i −0.943215 0.332184i \(-0.892215\pi\)
0.759287 + 0.650756i \(0.225548\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.00000 0.110059 0.0550297 0.998485i \(-0.482475\pi\)
0.0550297 + 0.998485i \(0.482475\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) 0 0
\(749\) −30.0000 + 25.9808i −1.09618 + 0.949316i
\(750\) 0 0
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 0 0
\(753\) −45.0000 + 77.9423i −1.63989 + 2.84037i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) 27.0000 46.7654i 0.980038 1.69748i
\(760\) 0 0
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) 0 0
\(763\) 22.5000 + 7.79423i 0.814555 + 0.282170i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24.0000 41.5692i 0.866590 1.50098i
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 0 0
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 12.0000 + 62.3538i 0.430498 + 2.23693i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 8.00000 13.8564i 0.286263 0.495821i
\(782\) 0 0
\(783\) 27.0000 0.964901
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5.50000 + 9.52628i −0.196054 + 0.339575i −0.947245 0.320509i \(-0.896146\pi\)
0.751192 + 0.660084i \(0.229479\pi\)
\(788\) 0 0
\(789\) 25.5000 + 44.1673i 0.907824 + 1.57240i
\(790\) 0 0
\(791\) −2.00000 10.3923i −0.0711118 0.369508i
\(792\) 0 0
\(793\) −21.0000 36.3731i −0.745732 1.29165i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.0000 −1.27519 −0.637593 0.770374i \(-0.720070\pi\)
−0.637593 + 0.770374i \(0.720070\pi\)
\(798\) 0 0
\(799\) 16.0000