Properties

Label 140.2.i.b.81.1
Level $140$
Weight $2$
Character 140.81
Analytic conductor $1.118$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 140.81
Dual form 140.2.i.b.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{11} -6.00000 q^{13} +3.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(7.50000 + 2.59808i) q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-3.00000 - 5.19615i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-9.00000 + 15.5885i) q^{39} +5.00000 q^{41} +1.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-2.00000 + 3.46410i) q^{53} +2.00000 q^{55} +(4.00000 - 6.92820i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(12.0000 - 10.3923i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(1.50000 - 2.59808i) q^{67} +27.0000 q^{69} +8.00000 q^{71} +(-7.00000 + 12.1244i) q^{73} +(1.50000 + 2.59808i) q^{75} +(5.00000 + 1.73205i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} -1.00000 q^{83} -2.00000 q^{85} +(4.50000 - 7.79423i) q^{87} +(-6.50000 - 11.2583i) q^{89} +(-3.00000 - 15.5885i) q^{91} +(3.00000 + 5.19615i) q^{93} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + q^{5} + q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + q^{5} + q^{7} - 6q^{9} + 2q^{11} - 12q^{13} + 6q^{15} - 2q^{17} + 15q^{21} + 9q^{23} - q^{25} - 18q^{27} + 6q^{29} - 2q^{31} - 6q^{33} - 4q^{35} - 8q^{37} - 18q^{39} + 10q^{41} + 2q^{43} + 6q^{45} - 8q^{47} - 13q^{49} + 6q^{51} - 4q^{53} + 4q^{55} + 8q^{59} - 7q^{61} + 24q^{63} - 6q^{65} + 3q^{67} + 54q^{69} + 16q^{71} - 14q^{73} + 3q^{75} + 10q^{77} - 4q^{79} - 9q^{81} - 2q^{83} - 4q^{85} + 9q^{87} - 13q^{89} - 6q^{91} + 6q^{93} - 20q^{97} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 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 \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 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 \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 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
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 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 \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 0 0
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 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 −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 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
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 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 \(0.472298\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) 0 0
\(75\) 1.50000 + 2.59808i 0.173205 + 0.300000i
\(76\) 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 \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 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 \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 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 \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) 0 0
\(105\) 1.50000 + 7.79423i 0.146385 + 0.760639i
\(106\) 0 0
\(107\) 7.50000 + 12.9904i 0.725052 + 1.25583i 0.958952 + 0.283567i \(0.0915178\pi\)
−0.233900 + 0.972261i \(0.575149\pi\)
\(108\) 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 \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 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
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 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
\(135\) −4.50000 7.79423i −0.387298 0.670820i
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 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
\(145\) 1.50000 + 2.59808i 0.124568 + 0.215758i
\(146\) 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
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 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 0.665771 0.746156i \(-0.268103\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 0 0
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 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 \(0.0414530\pi\)
−0.383304 + 0.923622i \(0.625214\pi\)
\(174\) 0 0
\(175\) −2.50000 0.866025i −0.188982 0.0654654i
\(176\) 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
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 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 −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) −18.0000 −1.28901
\(196\) 0 0
\(197\) 14.0000 0.997459 0.498729 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) 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
\(205\) 2.50000 + 4.33013i 0.174608 + 0.302429i
\(206\) 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
\(215\) 0.500000 + 0.866025i 0.0340997 + 0.0590624i
\(216\) 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 \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 6.00000 0.400000
\(226\) 0 0
\(227\) 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i \(-0.790954\pi\)
0.924734 + 0.380615i \(0.124288\pi\)
\(228\) 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 \(0.0340517\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(234\) 0 0
\(235\) 4.00000 6.92820i 0.260931 0.451946i
\(236\) 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
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 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
\(255\) −3.00000 + 5.19615i −0.187867 + 0.325396i
\(256\) 0 0
\(257\) −4.00000 6.92820i −0.249513 0.432169i 0.713878 0.700270i \(-0.246937\pi\)
−0.963391 + 0.268101i \(0.913604\pi\)
\(258\) 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 \(0.342277\pi\)
−0.999605 + 0.0280936i \(0.991056\pi\)
\(264\) 0 0
\(265\) −4.00000 −0.245718
\(266\) 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
\(275\) 1.00000 + 1.73205i 0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −9.00000 + 15.5885i −0.540758 + 0.936620i 0.458103 + 0.888899i \(0.348529\pi\)
−0.998861 + 0.0477206i \(0.984804\pi\)
\(278\) 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 −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 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 \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 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
\(305\) 3.50000 6.06218i 0.200409 0.347119i
\(306\) 0 0
\(307\) 1.00000 0.0570730 0.0285365 0.999593i \(-0.490915\pi\)
0.0285365 + 0.999593i \(0.490915\pi\)
\(308\) 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 0.916997 0.398894i \(-0.130606\pi\)
−0.803951 + 0.594696i \(0.797272\pi\)
\(314\) 0 0
\(315\) 15.0000 + 5.19615i 0.845154 + 0.292770i
\(316\) 0 0
\(317\) −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 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
\(325\) 3.00000 5.19615i 0.166410 0.288231i
\(326\) 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
\(335\) 3.00000 0.163908
\(336\) 0 0
\(337\) 28.0000 1.52526 0.762629 0.646837i \(-0.223908\pi\)
0.762629 + 0.646837i \(0.223908\pi\)
\(338\) 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
\(345\) 13.5000 + 23.3827i 0.726816 + 1.25888i
\(346\) 0 0
\(347\) −12.5000 + 21.6506i −0.671035 + 1.16227i 0.306576 + 0.951846i \(0.400817\pi\)
−0.977611 + 0.210421i \(0.932517\pi\)
\(348\) 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 \(-0.425866\pi\)
0.727245 0.686378i \(-0.240800\pi\)
\(354\) 0 0
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) 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
\(365\) −14.0000 −0.732793
\(366\) 0 0
\(367\) −0.500000 + 0.866025i −0.0260998 + 0.0452062i −0.878780 0.477227i \(-0.841642\pi\)
0.852680 + 0.522433i \(0.174975\pi\)
\(368\) 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 \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) 0 0
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) 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 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) 0 0
\(385\) 1.00000 + 5.19615i 0.0509647 + 0.264820i
\(386\) 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
\(395\) 2.00000 3.46410i 0.100631 0.174298i
\(396\) 0 0
\(397\) −5.00000 8.66025i −0.250943 0.434646i 0.712843 0.701324i \(-0.247407\pi\)
−0.963786 + 0.266678i \(0.914074\pi\)
\(398\) 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
\(405\) −9.00000 −0.447214
\(406\) 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
\(415\) −0.500000 0.866025i −0.0245440 0.0425115i
\(416\) 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
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 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 \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) 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 \(-0.824904\pi\)
−0.0264796 0.999649i \(-0.508430\pi\)
\(444\) 0 0
\(445\) 6.50000 11.2583i 0.308130 0.533696i
\(446\) 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
\(455\) 12.0000 10.3923i 0.562569 0.487199i
\(456\) 0 0
\(457\) −14.0000 24.2487i −0.654892 1.13431i −0.981921 0.189292i \(-0.939381\pi\)
0.327028 0.945015i \(-0.393953\pi\)
\(458\) 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 \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 0 0
\(465\) −3.00000 + 5.19615i −0.139122 + 0.240966i
\(466\) 0 0
\(467\) −2.50000 4.33013i −0.115686 0.200374i 0.802368 0.596830i \(-0.203573\pi\)
−0.918054 + 0.396456i \(0.870240\pi\)
\(468\) 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
\(485\) −5.00000 8.66025i −0.227038 0.393242i
\(486\) 0 0
\(487\) −16.0000 + 27.7128i −0.725029 + 1.25579i 0.233933 + 0.972253i \(0.424840\pi\)
−0.958962 + 0.283535i \(0.908493\pi\)
\(488\) 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
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) 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 \(-0.294397\pi\)
0.601935 + 0.798545i \(0.294397\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 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
\(515\) 6.50000 11.2583i 0.286424 0.496101i
\(516\) 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 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) 0 0
\(525\) −6.00000 + 5.19615i −0.261861 + 0.226779i
\(526\) 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
\(535\) −7.50000 + 12.9904i −0.324253 + 0.561623i
\(536\) 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
\(545\) −9.00000 −0.385518
\(546\) 0 0
\(547\) −15.0000 −0.641354 −0.320677 0.947189i \(-0.603910\pi\)
−0.320677 + 0.947189i \(0.603910\pi\)
\(548\) 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
\(555\) −12.0000 20.7846i −0.509372 0.882258i
\(556\) 0 0
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 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 −0.695925 0.718114i \(-0.745006\pi\)
0.969868 + 0.243632i \(0.0783389\pi\)
\(564\) 0 0
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) 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
\(575\) −9.00000 −0.375326
\(576\) 0 0
\(577\) −11.0000 + 19.0526i −0.457936 + 0.793168i −0.998852 0.0479084i \(-0.984744\pi\)
0.540916 + 0.841077i \(0.318078\pi\)
\(578\) 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
\(585\) −18.0000 + 31.1769i −0.744208 + 1.28901i
\(586\) 0 0
\(587\) 20.0000 0.825488 0.412744 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 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 \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) 0 0
\(595\) −1.00000 5.19615i −0.0409960 0.213021i
\(596\) 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
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) 0 0
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) 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 −0.799060 0.601251i \(-0.794669\pi\)
0.920229 + 0.391381i \(0.128002\pi\)
\(614\) 0 0
\(615\) 15.0000 0.604858
\(616\) 0 0
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 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
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 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
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) 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 \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) 0 0
\(647\) −0.500000 + 0.866025i −0.0196570 + 0.0340470i −0.875687 0.482880i \(-0.839591\pi\)
0.856030 + 0.516927i \(0.172924\pi\)
\(648\) 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 \(0.0650132\pi\)
−0.313953 + 0.949439i \(0.601653\pi\)
\(654\) 0 0
\(655\) −2.00000 + 3.46410i −0.0781465 + 0.135354i
\(656\) 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 \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 0 0
\(675\) 4.50000 7.79423i 0.173205 0.300000i
\(676\) 0 0
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 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 \(0.353882\pi\)
−0.997917 + 0.0645115i \(0.979451\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 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
\(695\) 5.00000 + 8.66025i 0.189661 + 0.328502i
\(696\) 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
\(705\) −12.0000 20.7846i −0.451946 0.782794i
\(706\) 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
\(715\) −12.0000 −0.448775
\(716\) 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
\(725\) −1.50000 + 2.59808i −0.0557086 + 0.0964901i
\(726\) 0 0
\(727\) 3.00000 0.111264 0.0556319 0.998451i \(-0.482283\pi\)
0.0556319 + 0.998451i \(0.482283\pi\)
\(728\) 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 \(-0.950578\pi\)
0.360061 0.932929i \(-0.382756\pi\)
\(734\) 0 0
\(735\) −19.5000 + 7.79423i −0.719268 + 0.287494i
\(736\) 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 \(-0.517525\pi\)
−0.0550297 + 0.998485i \(0.517525\pi\)
\(744\) 0 0
\(745\) 4.50000 7.79423i 0.164867 0.285558i
\(746\) 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
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 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
\(765\) 6.00000 + 10.3923i 0.216930 + 0.375735i
\(766\) 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 −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 0 0
\(775\) −1.00000 1.73205i −0.0359211 0.0622171i
\(776\) 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
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 5.50000 9.52628i 0.196054 0.339575i −0.751192 0.660084i \(-0.770521\pi\)
0.947245 + 0.320509i \(0.103854\pi\)
\(788\) 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
\(795\) −6.00000 + 10.3923i −0.212798 + 0.368577i
\(796\) 0 0
\(797\) 36.0000 1.27519