Properties

Label 280.2.q.a.121.1
Level $280$
Weight $2$
Character 280.121
Analytic conductor $2.236$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 280.121
Dual form 280.2.q.a.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{15} +(-2.00000 - 3.46410i) q^{17} +(1.00000 - 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(-2.00000 + 3.46410i) q^{37} +1.00000 q^{41} +9.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(5.50000 + 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(5.00000 + 8.66025i) q^{53} -2.00000 q^{55} -2.00000 q^{57} +(5.00000 + 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(-4.00000 + 3.46410i) q^{63} +(-2.50000 - 4.33013i) q^{67} +1.00000 q^{69} +14.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(1.00000 + 5.19615i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +11.0000 q^{83} -4.00000 q^{85} +(-4.50000 - 7.79423i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-2.00000 + 3.46410i) q^{93} +(-1.00000 - 1.73205i) q^{95} -18.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + q^{5} - 5q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} + q^{5} - 5q^{7} + 2q^{9} - 2q^{11} - 2q^{15} - 4q^{17} + 2q^{19} + q^{21} - q^{23} - q^{25} - 10q^{27} + 18q^{29} - 4q^{31} - 2q^{33} - 4q^{35} - 4q^{37} + 2q^{41} + 18q^{43} - 2q^{45} + 11q^{49} - 4q^{51} + 10q^{53} - 4q^{55} - 4q^{57} + 10q^{59} - 9q^{61} - 8q^{63} - 5q^{67} + 2q^{69} + 28q^{71} - 12q^{73} - q^{75} + 2q^{77} - 14q^{79} - q^{81} + 22q^{83} - 8q^{85} - 9q^{87} + 15q^{89} - 4q^{93} - 2q^{95} - 36q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 0 0
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.00000 0.156174 0.0780869 0.996947i \(-0.475119\pi\)
0.0780869 + 0.996947i \(0.475119\pi\)
\(42\) 0 0
\(43\) 9.00000 1.37249 0.686244 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i \(0.0743197\pi\)
−0.286064 + 0.958211i \(0.592347\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) 5.00000 + 8.66025i 0.650945 + 1.12747i 0.982894 + 0.184172i \(0.0589603\pi\)
−0.331949 + 0.943297i \(0.607706\pi\)
\(60\) 0 0
\(61\) −4.50000 + 7.79423i −0.576166 + 0.997949i 0.419748 + 0.907641i \(0.362118\pi\)
−0.995914 + 0.0903080i \(0.971215\pi\)
\(62\) 0 0
\(63\) −4.00000 + 3.46410i −0.503953 + 0.436436i
\(64\) 0 0
\(65\) 0 0
\(66\) 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
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i \(-0.918847\pi\)
0.265429 0.964130i \(-0.414486\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 1.00000 + 5.19615i 0.113961 + 0.592157i
\(78\) 0 0
\(79\) −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 0 0
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) 2.50000 + 0.866025i 0.243975 + 0.0845154i
\(106\) 0 0
\(107\) −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 + 10.3923i 0.183340 + 0.952661i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −0.500000 0.866025i −0.0450835 0.0780869i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −4.50000 7.79423i −0.396203 0.686244i
\(130\) 0 0
\(131\) 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 0 0
\(133\) −4.00000 + 3.46410i −0.346844 + 0.300376i
\(134\) 0 0
\(135\) −2.50000 + 4.33013i −0.215166 + 0.372678i
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) 0 0
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 0 0
\(149\) 2.50000 4.33013i 0.204808 0.354738i −0.745264 0.666770i \(-0.767676\pi\)
0.950072 + 0.312032i \(0.101010\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) −8.00000 −0.646762
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) 5.00000 8.66025i 0.396526 0.686803i
\(160\) 0 0
\(161\) 2.00000 1.73205i 0.157622 0.136505i
\(162\) 0 0
\(163\) 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i \(-0.546888\pi\)
0.930033 0.367477i \(-0.119778\pi\)
\(164\) 0 0
\(165\) 1.00000 + 1.73205i 0.0778499 + 0.134840i
\(166\) 0 0
\(167\) 17.0000 1.31550 0.657750 0.753237i \(-0.271508\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 0 0
\(173\) −8.00000 + 13.8564i −0.608229 + 1.05348i 0.383304 + 0.923622i \(0.374786\pi\)
−0.991532 + 0.129861i \(0.958547\pi\)
\(174\) 0 0
\(175\) 0.500000 + 2.59808i 0.0377964 + 0.196396i
\(176\) 0 0
\(177\) 5.00000 8.66025i 0.375823 0.650945i
\(178\) 0 0
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 9.00000 0.665299
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 0 0
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) 0 0
\(189\) 12.5000 + 4.33013i 0.909241 + 0.314970i
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0 0
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) 0 0
\(203\) −22.5000 7.79423i −1.57919 0.547048i
\(204\) 0 0
\(205\) 0.500000 0.866025i 0.0349215 0.0604858i
\(206\) 0 0
\(207\) 1.00000 + 1.73205i 0.0695048 + 0.120386i
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) −7.00000 12.1244i −0.479632 0.830747i
\(214\) 0 0
\(215\) 4.50000 7.79423i 0.306897 0.531562i
\(216\) 0 0
\(217\) 2.00000 + 10.3923i 0.135769 + 0.705476i
\(218\) 0 0
\(219\) −6.00000 + 10.3923i −0.405442 + 0.702247i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 4.00000 3.46410i 0.263181 0.227921i
\(232\) 0 0
\(233\) −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i \(-0.917731\pi\)
0.704737 + 0.709468i \(0.251065\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 14.0000 0.909398
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 0 0
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 0 0
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −5.50000 9.52628i −0.348548 0.603703i
\(250\) 0 0
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 2.00000 0.125739
\(254\) 0 0
\(255\) 2.00000 + 3.46410i 0.125245 + 0.216930i
\(256\) 0 0
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0 0
\(263\) 0.500000 + 0.866025i 0.0308313 + 0.0534014i 0.881029 0.473062i \(-0.156851\pi\)
−0.850198 + 0.526463i \(0.823518\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) 0 0
\(269\) 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 0 0
\(271\) −11.0000 + 19.0526i −0.668202 + 1.15736i 0.310204 + 0.950670i \(0.399603\pi\)
−0.978406 + 0.206691i \(0.933731\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) 14.0000 + 24.2487i 0.841178 + 1.45696i 0.888899 + 0.458103i \(0.151471\pi\)
−0.0477206 + 0.998861i \(0.515196\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 0 0
\(285\) −1.00000 + 1.73205i −0.0592349 + 0.102598i
\(286\) 0 0
\(287\) −2.50000 0.866025i −0.147570 0.0511199i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) 0 0
\(297\) 5.00000 + 8.66025i 0.290129 + 0.502519i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −22.5000 7.79423i −1.29688 0.449252i
\(302\) 0 0
\(303\) −1.50000 + 2.59808i −0.0861727 + 0.149256i
\(304\) 0 0
\(305\) 4.50000 + 7.79423i 0.257669 + 0.446296i
\(306\) 0 0
\(307\) 21.0000 1.19853 0.599267 0.800549i \(-0.295459\pi\)
0.599267 + 0.800549i \(0.295459\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) −13.0000 22.5167i −0.737162 1.27680i −0.953768 0.300544i \(-0.902832\pi\)
0.216606 0.976259i \(-0.430501\pi\)
\(312\) 0 0
\(313\) −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i \(-0.982689\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(314\) 0 0
\(315\) 1.00000 + 5.19615i 0.0563436 + 0.292770i
\(316\) 0 0
\(317\) 8.00000 13.8564i 0.449325 0.778253i −0.549017 0.835811i \(-0.684998\pi\)
0.998342 + 0.0575576i \(0.0183313\pi\)
\(318\) 0 0
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0 0
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.500000 0.866025i 0.0276501 0.0478913i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0 0
\(333\) 4.00000 + 6.92820i 0.219199 + 0.379663i
\(334\) 0 0
\(335\) −5.00000 −0.273179
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0 0
\(339\) −1.00000 1.73205i −0.0543125 0.0940721i
\(340\) 0 0
\(341\) −4.00000 + 6.92820i −0.216612 + 0.375183i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0.500000 0.866025i 0.0269191 0.0466252i
\(346\) 0 0
\(347\) 3.50000 + 6.06218i 0.187890 + 0.325435i 0.944547 0.328378i \(-0.106502\pi\)
−0.756657 + 0.653812i \(0.773169\pi\)
\(348\) 0 0
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) 0 0
\(355\) 7.00000 12.1244i 0.371521 0.643494i
\(356\) 0 0
\(357\) 8.00000 6.92820i 0.423405 0.366679i
\(358\) 0 0
\(359\) −6.00000 + 10.3923i −0.316668 + 0.548485i −0.979791 0.200026i \(-0.935897\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 0 0
\(367\) −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i \(-0.225150\pi\)
−0.942799 + 0.333363i \(0.891817\pi\)
\(368\) 0 0
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 0 0
\(371\) −5.00000 25.9808i −0.259587 1.34885i
\(372\) 0 0
\(373\) 14.0000 24.2487i 0.724893 1.25555i −0.234126 0.972206i \(-0.575223\pi\)
0.959018 0.283344i \(-0.0914439\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) 0 0
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 0 0
\(383\) −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i \(0.346930\pi\)
−0.999088 + 0.0427020i \(0.986403\pi\)
\(384\) 0 0
\(385\) 5.00000 + 1.73205i 0.254824 + 0.0882735i
\(386\) 0 0
\(387\) 9.00000 15.5885i 0.457496 0.792406i
\(388\) 0 0
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −8.00000 −0.403547
\(394\) 0 0
\(395\) 7.00000 + 12.1244i 0.352208 + 0.610043i
\(396\) 0 0
\(397\) −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i \(-0.881443\pi\)
0.780870 + 0.624694i \(0.214776\pi\)
\(398\) 0 0
\(399\) 5.00000 + 1.73205i 0.250313 + 0.0867110i
\(400\) 0 0
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) 10.5000 + 18.1865i 0.519192 + 0.899266i 0.999751 + 0.0223042i \(0.00710022\pi\)
−0.480560 + 0.876962i \(0.659566\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) 0 0
\(413\) −5.00000 25.9808i −0.246034 1.27843i
\(414\) 0 0
\(415\) 5.50000 9.52628i 0.269984 0.467627i
\(416\) 0 0
\(417\) 1.00000 + 1.73205i 0.0489702 + 0.0848189i
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 18.0000 15.5885i 0.871081 0.754378i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.00000 12.1244i −0.337178 0.584010i 0.646723 0.762725i \(-0.276139\pi\)
−0.983901 + 0.178716i \(0.942806\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) −9.00000 −0.431517
\(436\) 0 0
\(437\) 1.00000 + 1.73205i 0.0478365 + 0.0828552i
\(438\) 0 0
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) 13.0000 5.19615i 0.619048 0.247436i
\(442\) 0 0
\(443\) 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i \(-0.749178\pi\)
0.966591 + 0.256323i \(0.0825112\pi\)
\(444\) 0 0
\(445\) −7.50000 12.9904i −0.355534 0.615803i
\(446\) 0 0
\(447\) −5.00000 −0.236492
\(448\) 0 0
\(449\) −41.0000 −1.93491 −0.967455 0.253044i \(-0.918568\pi\)
−0.967455 + 0.253044i \(0.918568\pi\)
\(450\) 0 0
\(451\) −1.00000 1.73205i −0.0470882 0.0815591i
\(452\) 0 0
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.00000 + 6.92820i −0.187112 + 0.324088i −0.944286 0.329125i \(-0.893246\pi\)
0.757174 + 0.653213i \(0.226579\pi\)
\(458\) 0 0
\(459\) 10.0000 + 17.3205i 0.466760 + 0.808452i
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 39.0000 1.81248 0.906242 0.422760i \(-0.138939\pi\)
0.906242 + 0.422760i \(0.138939\pi\)
\(464\) 0 0
\(465\) 2.00000 + 3.46410i 0.0927478 + 0.160644i
\(466\) 0 0
\(467\) 3.50000 6.06218i 0.161961 0.280524i −0.773611 0.633661i \(-0.781552\pi\)
0.935572 + 0.353137i \(0.114885\pi\)
\(468\) 0 0
\(469\) 2.50000 + 12.9904i 0.115439 + 0.599840i
\(470\) 0 0
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) −9.00000 15.5885i −0.413820 0.716758i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 20.0000 0.915737
\(478\) 0 0
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −2.50000 0.866025i −0.113754 0.0394055i
\(484\) 0 0
\(485\) −9.00000 + 15.5885i −0.408669 + 0.707835i
\(486\) 0 0
\(487\) 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i \(-0.108650\pi\)
−0.761052 + 0.648691i \(0.775317\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) −18.0000 31.1769i −0.810679 1.40414i
\(494\) 0 0
\(495\) −2.00000 + 3.46410i −0.0898933 + 0.155700i
\(496\) 0 0
\(497\) −35.0000 12.1244i −1.56996 0.543852i
\(498\) 0 0
\(499\) 19.0000 32.9090i 0.850557 1.47321i −0.0301498 0.999545i \(-0.509598\pi\)
0.880707 0.473662i \(-0.157068\pi\)
\(500\) 0 0
\(501\) −8.50000 14.7224i −0.379752 0.657750i
\(502\) 0 0
\(503\) −23.0000 −1.02552 −0.512760 0.858532i \(-0.671377\pi\)
−0.512760 + 0.858532i \(0.671377\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 6.50000 + 11.2583i 0.288675 + 0.500000i
\(508\) 0 0
\(509\) 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i \(-0.725464\pi\)
0.982988 + 0.183669i \(0.0587976\pi\)
\(510\) 0 0
\(511\) 6.00000 + 31.1769i 0.265424 + 1.37919i
\(512\) 0 0
\(513\) −5.00000 + 8.66025i −0.220755 + 0.382360i
\(514\) 0 0
\(515\) −6.50000 11.2583i −0.286424 0.496101i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 0 0
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) 0 0
\(525\) 2.00000 1.73205i 0.0872872 0.0755929i
\(526\) 0 0
\(527\) −8.00000 + 13.8564i −0.348485 + 0.603595i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 20.0000 0.867926
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.50000 + 7.79423i 0.194552 + 0.336974i
\(536\) 0 0
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 0 0
\(539\) 2.00000 13.8564i 0.0861461 0.596838i
\(540\) 0 0
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) 0 0
\(543\) 12.5000 + 21.6506i 0.536426 + 0.929118i
\(544\) 0 0
\(545\) 1.00000 0.0428353
\(546\) 0 0
\(547\) −35.0000 −1.49649 −0.748246 0.663421i \(-0.769104\pi\)
−0.748246 + 0.663421i \(0.769104\pi\)
\(548\) 0 0
\(549\) 9.00000 + 15.5885i 0.384111 + 0.665299i
\(550\) 0 0
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) 0 0
\(553\) 28.0000 24.2487i 1.19068 1.03116i
\(554\) 0 0
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) 0 0
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 0 0
\(563\) 22.5000 + 38.9711i 0.948262 + 1.64244i 0.749085 + 0.662474i \(0.230494\pi\)
0.199177 + 0.979963i \(0.436173\pi\)
\(564\) 0 0
\(565\) 1.00000 1.73205i 0.0420703 0.0728679i
\(566\) 0 0
\(567\) 0.500000 + 2.59808i 0.0209980 + 0.109109i
\(568\) 0 0
\(569\) −23.0000 + 39.8372i −0.964210 + 1.67006i −0.252488 + 0.967600i \(0.581249\pi\)
−0.711722 + 0.702461i \(0.752085\pi\)
\(570\) 0 0
\(571\) 13.0000 + 22.5167i 0.544033 + 0.942293i 0.998667 + 0.0516146i \(0.0164367\pi\)
−0.454634 + 0.890678i \(0.650230\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −1.00000 1.73205i −0.0416305 0.0721062i 0.844459 0.535620i \(-0.179922\pi\)
−0.886090 + 0.463513i \(0.846589\pi\)
\(578\) 0 0
\(579\) 7.00000 12.1244i 0.290910 0.503871i
\(580\) 0 0
\(581\) −27.5000 9.52628i −1.14089 0.395217i
\(582\) 0 0
\(583\) 10.0000 17.3205i 0.414158 0.717342i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −9.00000 15.5885i −0.370211 0.641223i
\(592\) 0 0
\(593\) −9.00000 + 15.5885i −0.369586 + 0.640141i −0.989501 0.144528i \(-0.953834\pi\)
0.619915 + 0.784669i \(0.287167\pi\)
\(594\) 0 0
\(595\) 10.0000 + 3.46410i 0.409960 + 0.142014i
\(596\) 0 0
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) −2.00000 3.46410i −0.0817178 0.141539i 0.822270 0.569097i \(-0.192707\pi\)
−0.903988 + 0.427558i \(0.859374\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −10.0000 −0.407231
\(604\) 0 0
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) 0 0
\(607\) −13.5000 + 23.3827i −0.547948 + 0.949074i 0.450467 + 0.892793i \(0.351258\pi\)
−0.998415 + 0.0562808i \(0.982076\pi\)
\(608\) 0 0
\(609\) 4.50000 + 23.3827i 0.182349 + 0.947514i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 10.0000 + 17.3205i 0.403896 + 0.699569i 0.994192 0.107618i \(-0.0343224\pi\)
−0.590296 + 0.807187i \(0.700989\pi\)
\(614\) 0 0
\(615\) −1.00000 −0.0403239
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) 17.0000 + 29.4449i 0.683288 + 1.18349i 0.973972 + 0.226670i \(0.0727838\pi\)
−0.290684 + 0.956819i \(0.593883\pi\)
\(620\) 0 0
\(621\) 2.50000 4.33013i 0.100322 0.173762i
\(622\) 0 0
\(623\) −30.0000 + 25.9808i −1.20192 + 1.04090i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 2.00000 + 3.46410i 0.0798723 + 0.138343i
\(628\) 0 0
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −2.00000 −0.0796187 −0.0398094 0.999207i \(-0.512675\pi\)
−0.0398094 + 0.999207i \(0.512675\pi\)
\(632\) 0 0
\(633\) −1.00000 1.73205i −0.0397464 0.0688428i
\(634\) 0 0
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 14.0000 24.2487i 0.553831 0.959264i
\(640\) 0 0
\(641\) 9.50000 + 16.4545i 0.375227 + 0.649913i 0.990361 0.138510i \(-0.0442313\pi\)
−0.615134 + 0.788423i \(0.710898\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) −9.00000 −0.354375
\(646\) 0 0
\(647\) −11.5000 19.9186i −0.452112 0.783080i 0.546405 0.837521i \(-0.315996\pi\)
−0.998517 + 0.0544405i \(0.982662\pi\)
\(648\) 0 0
\(649\) 10.0000 17.3205i 0.392534 0.679889i
\(650\) 0 0
\(651\) 8.00000 6.92820i 0.313545 0.271538i
\(652\) 0 0
\(653\) −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i \(0.415448\pi\)
−0.966910 + 0.255119i \(0.917885\pi\)
\(654\) 0 0
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) 0 0
\(657\) −24.0000 −0.936329
\(658\) 0 0
\(659\) 2.00000 0.0779089 0.0389545 0.999241i \(-0.487597\pi\)
0.0389545 + 0.999241i \(0.487597\pi\)
\(660\) 0 0
\(661\) 1.50000 + 2.59808i 0.0583432 + 0.101053i 0.893722 0.448622i \(-0.148085\pi\)
−0.835379 + 0.549675i \(0.814752\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00000 + 5.19615i 0.0387783 + 0.201498i
\(666\) 0 0
\(667\) −4.50000 + 7.79423i −0.174241 + 0.301794i
\(668\) 0 0
\(669\) 2.00000 + 3.46410i 0.0773245 + 0.133930i
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) 0 0
\(677\) 12.0000 20.7846i 0.461197 0.798817i −0.537823 0.843057i \(-0.680753\pi\)
0.999021 + 0.0442400i \(0.0140866\pi\)
\(678\) 0 0
\(679\) 45.0000 + 15.5885i 1.72694 + 0.598230i
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 0 0
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) 0 0
\(693\) 10.0000 + 3.46410i 0.379869 + 0.131590i
\(694\) 0 0
\(695\) −1.00000 + 1.73205i −0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) 0 0
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) 4.00000 + 6.92820i 0.150863 + 0.261302i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.50000 + 7.79423i 0.0564133 + 0.293132i
\(708\) 0 0
\(709\) −10.5000 + 18.1865i −0.394336 + 0.683010i −0.993016 0.117978i \(-0.962359\pi\)
0.598680 + 0.800988i \(0.295692\pi\)
\(710\) 0 0
\(711\) 14.0000 + 24.2487i 0.525041 + 0.909398i
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) 0 0
\(719\) 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i \(-0.546936\pi\)
0.930087 0.367338i \(-0.119731\pi\)
\(720\) 0 0
\(721\) −26.0000 + 22.5167i −0.968291 + 0.838564i
\(722\) 0 0
\(723\) 11.0000 19.0526i 0.409094 0.708572i
\(724\) 0 0
\(725\) −4.50000 7.79423i −0.167126 0.289470i
\(726\) 0 0
\(727\) −31.0000 −1.14973 −0.574863 0.818250i \(-0.694945\pi\)
−0.574863 + 0.818250i \(0.694945\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −18.0000 31.1769i −0.665754 1.15312i
\(732\) 0 0
\(733\) 13.0000 22.5167i 0.480166 0.831672i −0.519575 0.854425i \(-0.673910\pi\)
0.999741 + 0.0227529i \(0.00724310\pi\)
\(734\) 0 0
\(735\) −5.50000 4.33013i −0.202871 0.159719i
\(736\) 0 0
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 0 0
\(739\) −5.00000 8.66025i −0.183928 0.318573i 0.759287 0.650756i \(-0.225548\pi\)
−0.943215 + 0.332184i \(0.892215\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27.0000 0.990534 0.495267 0.868741i \(-0.335070\pi\)
0.495267 + 0.868741i \(0.335070\pi\)
\(744\) 0 0
\(745\) −2.50000 4.33013i −0.0915929 0.158644i
\(746\) 0 0
\(747\) 11.0000 19.0526i 0.402469 0.697097i
\(748\) 0 0
\(749\) 18.0000 15.5885i 0.657706 0.569590i
\(750\) 0 0
\(751\) −6.00000 + 10.3923i −0.218943 + 0.379221i −0.954485 0.298259i \(-0.903594\pi\)
0.735542 + 0.677479i \(0.236928\pi\)
\(752\) 0 0
\(753\) −4.00000 6.92820i −0.145768 0.252478i
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −24.0000 −0.872295 −0.436147 0.899875i \(-0.643657\pi\)
−0.436147 + 0.899875i \(0.643657\pi\)
\(758\) 0 0
\(759\) −1.00000 1.73205i −0.0362977 0.0628695i
\(760\) 0 0
\(761\) 3.00000 5.19615i 0.108750 0.188360i −0.806514 0.591215i \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) 0 0
\(763\) −0.500000 2.59808i −0.0181012 0.0940567i
\(764\) 0 0
\(765\) −4.00000 + 6.92820i −0.144620 + 0.250490i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(774\) 0 0
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 0 0
\(777\) −10.0000 3.46410i −0.358748 0.124274i
\(778\) 0 0
\(779\) 1.00000 1.73205i 0.0358287 0.0620572i
\(780\) 0 0
\(781\) −14.0000 24.2487i −0.500959 0.867687i
\(782\) 0 0
\(783\) −45.0000 −1.60817
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −22.5000 38.9711i −0.802038 1.38917i −0.918272 0.395949i \(-0.870416\pi\)
0.116234 0.993222i \(-0.462918\pi\)
\(788\) 0 0
\(789\) 0.500000 0.866025i 0.0178005 0.0308313i
\(790\) 0 0
\(791\) −5.00000 1.73205i −0.177780 0.0615846i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −5.00000 8.66025i −0.177332 0.307148i
\(796\) 0 0
\(797\) 8.00000 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)