Properties

Label 260.2.i.a.81.1
Level $260$
Weight $2$
Character 260.81
Analytic conductor $2.076$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
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 \(\chi\) \(=\) 260.81
Dual form 260.2.i.a.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} -1.00000 q^{21} +(-4.50000 - 7.79423i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-3.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{49} -3.00000 q^{51} +6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 1.73205i) q^{63} +(-1.00000 + 3.46410i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-4.50000 + 7.79423i) q^{69} +(-4.50000 + 7.79423i) q^{71} +2.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} -3.00000 q^{77} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{85} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(-2.50000 - 2.59808i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(2.50000 - 4.33013i) q^{95} +(-8.50000 + 14.7224i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9} - 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 5 q^{19} - 2 q^{21} - 9 q^{23} + 2 q^{25} - 10 q^{27} + 9 q^{29} + 16 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 7 q^{39} - 3 q^{41} + q^{43} - 2 q^{45} + 6 q^{49} - 6 q^{51} + 12 q^{53} + 3 q^{55} + 10 q^{57} - 9 q^{59} + q^{61} - 2 q^{63} - 2 q^{65} - 5 q^{67} - 9 q^{69} - 9 q^{71} + 4 q^{73} - q^{75} - 6 q^{77} + 16 q^{79} - q^{81} - 3 q^{85} + 9 q^{87} - 3 q^{89} - 5 q^{91} - 8 q^{93} + 5 q^{95} - 17 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) 0 0
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 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
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) −0.500000 + 0.866025i −0.0845154 + 0.146385i
\(36\) 0 0
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0 0
\(39\) −3.50000 + 0.866025i −0.560449 + 0.138675i
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) 0 0
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) −1.00000 1.73205i −0.125988 0.218218i
\(64\) 0 0
\(65\) −1.00000 + 3.46410i −0.124035 + 0.429669i
\(66\) 0 0
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) −4.50000 + 7.79423i −0.541736 + 0.938315i
\(70\) 0 0
\(71\) −4.50000 + 7.79423i −0.534052 + 0.925005i 0.465157 + 0.885228i \(0.345998\pi\)
−0.999209 + 0.0397765i \(0.987335\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 0 0
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −1.50000 + 2.59808i −0.162698 + 0.281801i
\(86\) 0 0
\(87\) 4.50000 7.79423i 0.482451 0.835629i
\(88\) 0 0
\(89\) −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) 0 0
\(91\) −2.50000 2.59808i −0.262071 0.272352i
\(92\) 0 0
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 0 0
\(95\) 2.50000 4.33013i 0.256495 0.444262i
\(96\) 0 0
\(97\) −8.50000 + 14.7224i −0.863044 + 1.49484i 0.00593185 + 0.999982i \(0.498112\pi\)
−0.868976 + 0.494854i \(0.835222\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 1.00000 0.0975900
\(106\) 0 0
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) 0 0
\(115\) 4.50000 + 7.79423i 0.419627 + 0.726816i
\(116\) 0 0
\(117\) −5.00000 5.19615i −0.462250 0.480384i
\(118\) 0 0
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −1.50000 + 2.59808i −0.135250 + 0.234261i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.50000 14.7224i −0.754253 1.30640i −0.945745 0.324910i \(-0.894666\pi\)
0.191492 0.981494i \(-0.438667\pi\)
\(128\) 0 0
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 2.50000 + 4.33013i 0.216777 + 0.375470i
\(134\) 0 0
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −10.5000 + 2.59808i −0.878054 + 0.217262i
\(144\) 0 0
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) 0 0
\(147\) 3.00000 5.19615i 0.247436 0.428571i
\(148\) 0 0
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 0 0
\(153\) −3.00000 5.19615i −0.242536 0.420084i
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 0 0
\(163\) 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i \(0.0304244\pi\)
−0.415068 + 0.909790i \(0.636242\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) 5.00000 + 8.66025i 0.382360 + 0.662266i
\(172\) 0 0
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 0 0
\(177\) 9.00000 0.676481
\(178\) 0 0
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 0 0
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 0 0
\(187\) −9.00000 −0.658145
\(188\) 0 0
\(189\) −2.50000 + 4.33013i −0.181848 + 0.314970i
\(190\) 0 0
\(191\) 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i \(-0.798717\pi\)
0.915177 + 0.403051i \(0.132050\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 0 0
\(195\) 3.50000 0.866025i 0.250640 0.0620174i
\(196\) 0 0
\(197\) 1.50000 + 2.59808i 0.106871 + 0.185105i 0.914501 0.404584i \(-0.132584\pi\)
−0.807630 + 0.589689i \(0.799250\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) 0 0
\(203\) 9.00000 0.631676
\(204\) 0 0
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) 0 0
\(207\) −18.0000 −1.25109
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) 12.5000 + 21.6506i 0.860535 + 1.49049i 0.871413 + 0.490550i \(0.163204\pi\)
−0.0108774 + 0.999941i \(0.503462\pi\)
\(212\) 0 0
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) −0.500000 + 0.866025i −0.0340997 + 0.0590624i
\(216\) 0 0
\(217\) 4.00000 6.92820i 0.271538 0.470317i
\(218\) 0 0
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 0 0
\(221\) −7.50000 7.79423i −0.504505 0.524297i
\(222\) 0 0
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) 0 0
\(225\) 1.00000 1.73205i 0.0666667 0.115470i
\(226\) 0 0
\(227\) −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i \(-0.999189\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 1.50000 + 2.59808i 0.0986928 + 0.170941i
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4.00000 6.92820i −0.259828 0.450035i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 0 0
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 0 0
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) 0 0
\(247\) 12.5000 + 12.9904i 0.795356 + 0.826558i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.50000 + 7.79423i −0.284037 + 0.491967i −0.972375 0.233423i \(-0.925007\pi\)
0.688338 + 0.725390i \(0.258341\pi\)
\(252\) 0 0
\(253\) −13.5000 + 23.3827i −0.848738 + 1.47006i
\(254\) 0 0
\(255\) 3.00000 0.187867
\(256\) 0 0
\(257\) 13.5000 + 23.3827i 0.842107 + 1.45857i 0.888110 + 0.459631i \(0.152018\pi\)
−0.0460033 + 0.998941i \(0.514648\pi\)
\(258\) 0 0
\(259\) 7.00000 0.434959
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) −1.50000 + 2.59808i −0.0917985 + 0.159000i
\(268\) 0 0
\(269\) 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170321i \(-0.0544803\pi\)
\(270\) 0 0
\(271\) 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i \(-0.0374643\pi\)
−0.598235 + 0.801321i \(0.704131\pi\)
\(272\) 0 0
\(273\) −1.00000 + 3.46410i −0.0605228 + 0.209657i
\(274\) 0 0
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 0 0
\(277\) 9.50000 16.4545i 0.570800 0.988654i −0.425684 0.904872i \(-0.639967\pi\)
0.996484 0.0837823i \(-0.0267000\pi\)
\(278\) 0 0
\(279\) 8.00000 13.8564i 0.478947 0.829561i
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) −8.50000 14.7224i −0.505273 0.875158i −0.999981 0.00609896i \(-0.998059\pi\)
0.494709 0.869059i \(-0.335275\pi\)
\(284\) 0 0
\(285\) −5.00000 −0.296174
\(286\) 0 0
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) 0 0
\(293\) 1.50000 2.59808i 0.0876309 0.151781i −0.818878 0.573967i \(-0.805404\pi\)
0.906509 + 0.422186i \(0.138737\pi\)
\(294\) 0 0
\(295\) 4.50000 7.79423i 0.262000 0.453798i
\(296\) 0 0
\(297\) 7.50000 + 12.9904i 0.435194 + 0.753778i
\(298\) 0 0
\(299\) −31.5000 + 7.79423i −1.82169 + 0.450752i
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) 0 0
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) 0 0
\(305\) −0.500000 + 0.866025i −0.0286299 + 0.0495885i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) −4.00000 6.92820i −0.227552 0.394132i
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) 13.5000 23.3827i 0.755855 1.30918i
\(320\) 0 0
\(321\) 1.50000 2.59808i 0.0837218 0.145010i
\(322\) 0 0
\(323\) 7.50000 + 12.9904i 0.417311 + 0.722804i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) 0 0
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i \(-0.658457\pi\)
0.999667 0.0257885i \(-0.00820965\pi\)
\(332\) 0 0
\(333\) 14.0000 0.767195
\(334\) 0 0
\(335\) 2.50000 + 4.33013i 0.136590 + 0.236580i
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) −15.0000 −0.814688
\(340\) 0 0
\(341\) −12.0000 20.7846i −0.649836 1.12555i
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 4.50000 7.79423i 0.242272 0.419627i
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) −17.5000 30.3109i −0.936754 1.62250i −0.771477 0.636257i \(-0.780482\pi\)
−0.165277 0.986247i \(-0.552852\pi\)
\(350\) 0 0
\(351\) −5.00000 + 17.3205i −0.266880 + 0.924500i
\(352\) 0 0
\(353\) 13.5000 + 23.3827i 0.718532 + 1.24453i 0.961581 + 0.274521i \(0.0885192\pi\)
−0.243049 + 0.970014i \(0.578147\pi\)
\(354\) 0 0
\(355\) 4.50000 7.79423i 0.238835 0.413675i
\(356\) 0 0
\(357\) −1.50000 + 2.59808i −0.0793884 + 0.137505i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −2.50000 + 4.33013i −0.129445 + 0.224205i −0.923462 0.383691i \(-0.874653\pi\)
0.794017 + 0.607896i \(0.207986\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 31.5000 7.79423i 1.62233 0.401423i
\(378\) 0 0
\(379\) −5.50000 9.52628i −0.282516 0.489332i 0.689488 0.724297i \(-0.257836\pi\)
−0.972004 + 0.234965i \(0.924502\pi\)
\(380\) 0 0
\(381\) −8.50000 + 14.7224i −0.435468 + 0.754253i
\(382\) 0 0
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 0 0
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) 0 0
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) −27.0000 −1.36545
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) −14.5000 + 25.1147i −0.727734 + 1.26047i 0.230105 + 0.973166i \(0.426093\pi\)
−0.957839 + 0.287307i \(0.907240\pi\)
\(398\) 0 0
\(399\) 2.50000 4.33013i 0.125157 0.216777i
\(400\) 0 0
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 0 0
\(403\) 8.00000 27.7128i 0.398508 1.38047i
\(404\) 0 0
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 0 0
\(407\) 10.5000 18.1865i 0.520466 0.901473i
\(408\) 0 0
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 0 0
\(411\) −3.00000 −0.147979
\(412\) 0 0
\(413\) 4.50000 + 7.79423i 0.221431 + 0.383529i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 10.5000 + 18.1865i 0.512959 + 0.888470i 0.999887 + 0.0150285i \(0.00478389\pi\)
−0.486928 + 0.873442i \(0.661883\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.50000 2.59808i 0.0727607 0.126025i
\(426\) 0 0
\(427\) −0.500000 0.866025i −0.0241967 0.0419099i
\(428\) 0 0
\(429\) 7.50000 + 7.79423i 0.362103 + 0.376309i
\(430\) 0 0
\(431\) −1.50000 2.59808i −0.0722525 0.125145i 0.827636 0.561266i \(-0.189685\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(432\) 0 0
\(433\) −2.50000 + 4.33013i −0.120142 + 0.208093i −0.919824 0.392332i \(-0.871668\pi\)
0.799681 + 0.600425i \(0.205002\pi\)
\(434\) 0 0
\(435\) −4.50000 + 7.79423i −0.215758 + 0.373705i
\(436\) 0 0
\(437\) 45.0000 2.15264
\(438\) 0 0
\(439\) 0.500000 + 0.866025i 0.0238637 + 0.0413331i 0.877711 0.479191i \(-0.159070\pi\)
−0.853847 + 0.520524i \(0.825737\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) 1.50000 + 2.59808i 0.0711068 + 0.123161i
\(446\) 0 0
\(447\) −9.00000 −0.425685
\(448\) 0 0
\(449\) −7.50000 + 12.9904i −0.353947 + 0.613054i −0.986937 0.161106i \(-0.948494\pi\)
0.632990 + 0.774160i \(0.281827\pi\)
\(450\) 0 0
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) 0 0
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) 0 0
\(455\) 2.50000 + 2.59808i 0.117202 + 0.121800i
\(456\) 0 0
\(457\) −20.5000 35.5070i −0.958950 1.66095i −0.725059 0.688686i \(-0.758188\pi\)
−0.233890 0.972263i \(-0.575146\pi\)
\(458\) 0 0
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 0 0
\(461\) −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i \(-0.946917\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −5.00000 −0.230879
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 6.00000 10.3923i 0.274721 0.475831i
\(478\) 0 0
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) 0 0
\(481\) 24.5000 6.06218i 1.11710 0.276412i
\(482\) 0 0
\(483\) 4.50000 + 7.79423i 0.204757 + 0.354650i
\(484\) 0 0
\(485\) 8.50000 14.7224i 0.385965 0.668511i
\(486\) 0 0
\(487\) −17.5000 + 30.3109i −0.793001 + 1.37352i 0.131100 + 0.991369i \(0.458149\pi\)
−0.924101 + 0.382148i \(0.875184\pi\)
\(488\) 0 0
\(489\) −1.00000 −0.0452216
\(490\) 0 0
\(491\) −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 0 0
\(493\) 27.0000 1.21602
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) 4.50000 + 7.79423i 0.201853 + 0.349619i
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 7.50000 12.9904i 0.335075 0.580367i
\(502\) 0 0
\(503\) −19.5000 + 33.7750i −0.869462 + 1.50595i −0.00691465 + 0.999976i \(0.502201\pi\)
−0.862547 + 0.505976i \(0.831132\pi\)
\(504\) 0 0
\(505\) 7.50000 + 12.9904i 0.333746 + 0.578064i
\(506\) 0 0
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) 0 0
\(509\) 16.5000 + 28.5788i 0.731350 + 1.26673i 0.956306 + 0.292366i \(0.0944425\pi\)
−0.224957 + 0.974369i \(0.572224\pi\)
\(510\) 0 0
\(511\) 1.00000 1.73205i 0.0442374 0.0766214i
\(512\) 0 0
\(513\) 12.5000 21.6506i 0.551888 0.955899i
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −2.50000 4.33013i −0.109317 0.189343i 0.806177 0.591675i \(-0.201533\pi\)
−0.915494 + 0.402332i \(0.868200\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) 9.00000 + 15.5885i 0.390567 + 0.676481i
\(532\) 0 0
\(533\) −10.5000 + 2.59808i −0.454805 + 0.112535i
\(534\) 0 0
\(535\) −1.50000 2.59808i −0.0648507 0.112325i
\(536\) 0 0
\(537\) −7.50000 + 12.9904i −0.323649 + 0.560576i
\(538\) 0 0
\(539\) 9.00000 15.5885i 0.387657 0.671442i
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 0 0
\(543\) 5.00000 + 8.66025i 0.214571 + 0.371647i
\(544\) 0 0
\(545\) −14.0000 −0.599694
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) −45.0000 −1.91706
\(552\) 0 0
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) 0 0
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) 0 0
\(557\) 19.5000 + 33.7750i 0.826242 + 1.43109i 0.900967 + 0.433888i \(0.142859\pi\)
−0.0747252 + 0.997204i \(0.523808\pi\)
\(558\) 0 0
\(559\) −2.50000 2.59808i −0.105739 0.109887i
\(560\) 0 0
\(561\) 4.50000 + 7.79423i 0.189990 + 0.329073i
\(562\) 0 0
\(563\) 16.5000 28.5788i 0.695392 1.20445i −0.274656 0.961542i \(-0.588564\pi\)
0.970048 0.242912i \(-0.0781026\pi\)
\(564\) 0 0
\(565\) −7.50000 + 12.9904i −0.315527 + 0.546509i
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) 16.5000 + 28.5788i 0.691716 + 1.19809i 0.971275 + 0.237959i \(0.0764783\pi\)
−0.279559 + 0.960128i \(0.590188\pi\)
\(570\) 0 0
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −4.50000 7.79423i −0.187663 0.325042i
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 0 0
\(579\) −2.50000 + 4.33013i −0.103896 + 0.179954i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 0 0
\(585\) 5.00000 + 5.19615i 0.206725 + 0.214834i
\(586\) 0 0
\(587\) 13.5000 + 23.3827i 0.557205 + 0.965107i 0.997728 + 0.0673658i \(0.0214594\pi\)
−0.440524 + 0.897741i \(0.645207\pi\)
\(588\) 0 0
\(589\) −20.0000 + 34.6410i −0.824086 + 1.42736i
\(590\) 0 0
\(591\) 1.50000 2.59808i 0.0617018 0.106871i
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 1.50000 + 2.59808i 0.0614940 + 0.106511i
\(596\) 0 0
\(597\) −7.00000 −0.286491
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0.500000 + 0.866025i 0.0203954 + 0.0353259i 0.876043 0.482233i \(-0.160174\pi\)
−0.855648 + 0.517559i \(0.826841\pi\)
\(602\) 0 0
\(603\) −10.0000 −0.407231
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) 0 0
\(609\) −4.50000 7.79423i −0.182349 0.315838i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −14.5000 25.1147i −0.585649 1.01437i −0.994794 0.101905i \(-0.967506\pi\)
0.409145 0.912470i \(-0.365827\pi\)
\(614\) 0 0
\(615\) 1.50000 2.59808i 0.0604858 0.104765i
\(616\) 0 0
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) 22.5000 + 38.9711i 0.902894 + 1.56386i
\(622\) 0 0
\(623\) −3.00000 −0.120192
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −7.50000 12.9904i −0.299521 0.518786i
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) 3.50000 6.06218i 0.139333 0.241331i −0.787911 0.615789i \(-0.788838\pi\)
0.927244 + 0.374457i \(0.122171\pi\)
\(632\) 0 0
\(633\) 12.5000 21.6506i 0.496830 0.860535i
\(634\) 0 0
\(635\) 8.50000 + 14.7224i 0.337312 + 0.584242i
\(636\) 0 0
\(637\) 21.0000 5.19615i 0.832050 0.205879i
\(638\) 0 0
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) 0 0
\(641\) −1.50000 + 2.59808i −0.0592464 + 0.102618i −0.894127 0.447813i \(-0.852203\pi\)
0.834881 + 0.550431i \(0.185536\pi\)
\(642\) 0 0
\(643\) 12.5000 21.6506i 0.492952 0.853818i −0.507015 0.861937i \(-0.669251\pi\)
0.999967 + 0.00811944i \(0.00258453\pi\)
\(644\) 0 0
\(645\) 1.00000 0.0393750
\(646\) 0 0
\(647\) 13.5000 + 23.3827i 0.530740 + 0.919268i 0.999357 + 0.0358667i \(0.0114192\pi\)
−0.468617 + 0.883402i \(0.655247\pi\)
\(648\) 0 0
\(649\) 27.0000 1.05984
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 0 0
\(653\) 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i \(0.0105021\pi\)
−0.471160 + 0.882048i \(0.656165\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 3.46410i 0.0780274 0.135147i
\(658\) 0 0
\(659\) −22.5000 + 38.9711i −0.876476 + 1.51810i −0.0212930 + 0.999773i \(0.506778\pi\)
−0.855183 + 0.518327i \(0.826555\pi\)
\(660\) 0 0
\(661\) −17.5000 30.3109i −0.680671 1.17896i −0.974776 0.223184i \(-0.928355\pi\)
0.294105 0.955773i \(-0.404978\pi\)
\(662\) 0 0
\(663\) −3.00000 + 10.3923i −0.116510 + 0.403604i
\(664\) 0 0
\(665\) −2.50000 4.33013i −0.0969458 0.167915i
\(666\) 0 0
\(667\) 40.5000 70.1481i 1.56817 2.71614i
\(668\) 0 0
\(669\) 9.50000 16.4545i 0.367291 0.636167i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) 0 0
\(675\) −5.00000 −0.192450
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 8.50000 + 14.7224i 0.326200 + 0.564995i
\(680\) 0 0
\(681\) 15.0000 0.574801
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) −1.50000 + 2.59808i −0.0573121 + 0.0992674i
\(686\) 0 0
\(687\) 11.0000 + 19.0526i 0.419676 + 0.726900i
\(688\) 0 0
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) −11.5000 19.9186i −0.437481 0.757739i 0.560014 0.828483i \(-0.310796\pi\)
−0.997494 + 0.0707446i \(0.977462\pi\)
\(692\) 0 0
\(693\) −3.00000 + 5.19615i −0.113961 + 0.197386i
\(694\) 0 0
\(695\) 2.50000 4.33013i 0.0948304 0.164251i
\(696\) 0 0
\(697\) −9.00000 −0.340899
\(698\) 0 0
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −35.0000 −1.32005
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.0000 −0.564133
\(708\) 0 0
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 0 0
\(711\) 8.00000 13.8564i 0.300023 0.519656i
\(712\) 0 0
\(713\) −36.0000 62.3538i −1.34821 2.33517i
\(714\) 0 0
\(715\) 10.5000 2.59808i 0.392678 0.0971625i
\(716\) 0 0
\(717\) −12.0000 20.7846i −0.448148 0.776215i
\(718\) 0 0
\(719\) −22.5000 + 38.9711i −0.839108 + 1.45338i 0.0515326 + 0.998671i \(0.483589\pi\)
−0.890641 + 0.454707i \(0.849744\pi\)
\(720\) 0 0
\(721\) 4.00000 6.92820i 0.148968 0.258020i
\(722\) 0 0
\(723\) 23.0000 0.855379
\(724\) 0 0
\(725\) 4.50000 + 7.79423i 0.167126 + 0.289470i
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) −3.00000 + 5.19615i −0.110657 + 0.191663i
\(736\) 0 0
\(737\) −7.50000 + 12.9904i −0.276266 + 0.478507i
\(738\) 0 0
\(739\) −5.50000 9.52628i −0.202321 0.350430i 0.746955 0.664875i \(-0.231515\pi\)
−0.949276 + 0.314445i \(0.898182\pi\)
\(740\) 0 0
\(741\) 5.00000 17.3205i 0.183680 0.636285i
\(742\) 0 0
\(743\) −16.5000 28.5788i −0.605326 1.04846i −0.992000 0.126239i \(-0.959709\pi\)
0.386674 0.922217i \(-0.373624\pi\)
\(744\) 0 0
\(745\) −4.50000 + 7.79423i −0.164867 + 0.285558i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.00000 0.109618
\(750\) 0 0
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 0 0
\(753\) 9.00000 0.327978
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) −2.50000 4.33013i −0.0908640 0.157381i 0.817011 0.576622i \(-0.195630\pi\)
−0.907875 + 0.419241i \(0.862296\pi\)
\(758\) 0 0
\(759\) 27.0000 0.980038
\(760\) 0 0
\(761\) 4.50000 7.79423i 0.163125 0.282541i −0.772863 0.634573i \(-0.781176\pi\)
0.935988 + 0.352032i \(0.114509\pi\)
\(762\) 0 0
\(763\) 7.00000 12.1244i 0.253417 0.438931i
\(764\) 0 0
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 0 0
\(767\) 22.5000 + 23.3827i 0.812428 + 0.844300i
\(768\) 0 0
\(769\) −5.50000 9.52628i −0.198335 0.343526i 0.749654 0.661830i \(-0.230220\pi\)
−0.947989 + 0.318304i \(0.896887\pi\)
\(770\) 0 0
\(771\) 13.5000 23.3827i 0.486191 0.842107i
\(772\) 0 0
\(773\) 7.50000 12.9904i 0.269756 0.467232i −0.699043 0.715080i \(-0.746390\pi\)
0.968799 + 0.247849i \(0.0797235\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) 0 0
\(777\) −3.50000 6.06218i −0.125562 0.217479i
\(778\) 0 0
\(779\) 15.0000 0.537431
\(780\) 0 0
\(781\) 27.0000 0.966136
\(782\) 0 0
\(783\) −22.5000 38.9711i −0.804084 1.39272i
\(784\) 0 0
\(785\) −14.0000 −0.499681
\(786\) 0 0
\(787\) 24.5000 42.4352i 0.873331 1.51265i 0.0148003 0.999890i \(-0.495289\pi\)
0.858530 0.512763i \(-0.171378\pi\)
\(788\) 0 0
\(789\) 1.50000 2.59808i 0.0534014 0.0924940i
\(790\) 0 0
\(791\) −7.50000 12.9904i −0.266669 0.461885i
\(792\) 0 0
\(793\) −2.50000 2.59808i −0.0887776 0.0922604i
\(794\) 0 0
\(795\) 3.00000 + 5.19615i 0.106399 +