Properties

Label 1710.2.l.a.1261.1
Level $1710$
Weight $2$
Character 1710.1261
Analytic conductor $13.654$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1261
Dual form 1710.2.l.a.1531.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} -6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(3.00000 + 5.19615i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +5.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{35} +11.0000 q^{37} +(-0.500000 - 4.33013i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{44} -6.00000 q^{46} +(6.00000 - 10.3923i) q^{47} -6.00000 q^{49} +1.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(3.00000 + 5.19615i) q^{55} -1.00000 q^{56} -6.00000 q^{58} +(3.00000 + 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-2.50000 - 4.33013i) q^{62} +1.00000 q^{64} +5.00000 q^{65} +(0.500000 - 0.866025i) q^{67} +(0.500000 - 0.866025i) q^{70} +(0.500000 + 0.866025i) q^{73} +(-5.50000 - 9.52628i) q^{74} +(-3.50000 + 2.59808i) q^{76} +6.00000 q^{77} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(0.500000 - 0.866025i) q^{86} -6.00000 q^{88} +(-6.00000 + 10.3923i) q^{89} +(2.50000 - 4.33013i) q^{91} +(3.00000 + 5.19615i) q^{92} -12.0000 q^{94} +(-0.500000 - 4.33013i) q^{95} +(-7.00000 - 12.1244i) q^{97} +(3.00000 + 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - q^{5} - 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - q^{5} - 2q^{7} + 2q^{8} - q^{10} - 12q^{11} - 5q^{13} + q^{14} - q^{16} + 8q^{19} + 2q^{20} + 6q^{22} + 6q^{23} - q^{25} + 10q^{26} + q^{28} + 6q^{29} + 10q^{31} - q^{32} + q^{35} + 22q^{37} - q^{38} - q^{40} + 6q^{41} + q^{43} + 6q^{44} - 12q^{46} + 12q^{47} - 12q^{49} + 2q^{50} - 5q^{52} - 12q^{53} + 6q^{55} - 2q^{56} - 12q^{58} + 6q^{59} + 7q^{61} - 5q^{62} + 2q^{64} + 10q^{65} + q^{67} + q^{70} + q^{73} - 11q^{74} - 7q^{76} + 12q^{77} + 7q^{79} - q^{80} + 6q^{82} + 12q^{83} + q^{86} - 12q^{88} - 12q^{89} + 5q^{91} + 6q^{92} - 24q^{94} - q^{95} - 14q^{97} + 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 3.00000 + 5.19615i 0.639602 + 1.10782i
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 5.00000 0.980581
\(27\) 0 0
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.500000 + 0.866025i 0.0845154 + 0.146385i
\(36\) 0 0
\(37\) 11.0000 1.80839 0.904194 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −0.500000 4.33013i −0.0811107 0.702439i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −2.50000 4.33013i −0.317500 0.549927i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.0610847 0.105802i −0.833866 0.551967i \(-0.813877\pi\)
0.894951 + 0.446165i \(0.147211\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.500000 0.866025i 0.0597614 0.103510i
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 0 0
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) −5.50000 9.52628i −0.639362 1.10741i
\(75\) 0 0
\(76\) −3.50000 + 2.59808i −0.401478 + 0.298020i
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 3.50000 + 6.06218i 0.393781 + 0.682048i 0.992945 0.118578i \(-0.0378336\pi\)
−0.599164 + 0.800626i \(0.704500\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.0539164 0.0933859i
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) 2.50000 4.33013i 0.262071 0.453921i
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) 0 0
\(94\) −12.0000 −1.23771
\(95\) −0.500000 4.33013i −0.0512989 0.444262i
\(96\) 0 0
\(97\) −7.00000 12.1244i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) 3.00000 + 5.19615i 0.303046 + 0.524891i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) −2.50000 + 4.33013i −0.245145 + 0.424604i
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) −6.00000 −0.559503
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) −7.00000 −0.633750
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.00000 13.8564i 0.709885 1.22956i −0.255014 0.966937i \(-0.582080\pi\)
0.964899 0.262620i \(-0.0845865\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −2.50000 4.33013i −0.219265 0.379777i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) −4.00000 1.73205i −0.346844 0.150188i
\(134\) −1.00000 −0.0863868
\(135\) 0 0
\(136\) 0 0
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) 0.500000 0.866025i 0.0424094 0.0734553i −0.844042 0.536278i \(-0.819830\pi\)
0.886451 + 0.462822i \(0.153163\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) 15.0000 25.9808i 1.25436 2.17262i
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0.500000 0.866025i 0.0413803 0.0716728i
\(147\) 0 0
\(148\) −5.50000 + 9.52628i −0.452097 + 0.783055i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 4.00000 + 1.73205i 0.324443 + 0.140488i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) −2.50000 4.33013i −0.200805 0.347804i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 3.50000 6.06218i 0.278445 0.482281i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) −3.00000 + 5.19615i −0.236433 + 0.409514i
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −9.00000 + 15.5885i −0.696441 + 1.20627i 0.273252 + 0.961943i \(0.411901\pi\)
−0.969693 + 0.244328i \(0.921432\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 3.00000 + 5.19615i 0.226134 + 0.391675i
\(177\) 0 0
\(178\) 12.0000 0.899438
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) −13.0000 + 22.5167i −0.966282 + 1.67365i −0.260153 + 0.965567i \(0.583773\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) −5.00000 −0.370625
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −5.50000 9.52628i −0.404368 0.700386i
\(186\) 0 0
\(187\) 0 0
\(188\) 6.00000 + 10.3923i 0.437595 + 0.757937i
\(189\) 0 0
\(190\) −3.50000 + 2.59808i −0.253917 + 0.188484i
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −7.00000 + 12.1244i −0.502571 + 0.870478i
\(195\) 0 0
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) −3.00000 + 5.19615i −0.210559 + 0.364698i
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) −5.50000 9.52628i −0.383203 0.663727i
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) −24.0000 10.3923i −1.66011 0.718851i
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 0.500000 0.866025i 0.0340997 0.0590624i
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 0 0
\(220\) −6.00000 −0.404520
\(221\) 0 0
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 0 0
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −25.0000 −1.65205 −0.826023 0.563636i \(-0.809402\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(230\) 3.00000 + 5.19615i 0.197814 + 0.342624i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −6.00000 10.3923i −0.393073 0.680823i 0.599780 0.800165i \(-0.295255\pi\)
−0.992853 + 0.119342i \(0.961921\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) −6.00000 −0.390567
\(237\) 0 0
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) −12.5000 21.6506i −0.803530 1.39176i
\(243\) 0 0
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) 3.00000 + 5.19615i 0.191663 + 0.331970i
\(246\) 0 0
\(247\) −17.5000 + 12.9904i −1.11350 + 0.826558i
\(248\) 5.00000 0.317500
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 3.00000 5.19615i 0.189358 0.327978i −0.755678 0.654943i \(-0.772693\pi\)
0.945036 + 0.326965i \(0.106026\pi\)
\(252\) 0 0
\(253\) −18.0000 + 31.1769i −1.13165 + 1.96008i
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 0 0
\(259\) −11.0000 −0.683507
\(260\) −2.50000 + 4.33013i −0.155043 + 0.268543i
\(261\) 0 0
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0.500000 + 4.33013i 0.0306570 + 0.265497i
\(267\) 0 0
\(268\) 0.500000 + 0.866025i 0.0305424 + 0.0529009i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) −1.00000 −0.0599760
\(279\) 0 0
\(280\) 0.500000 + 0.866025i 0.0298807 + 0.0517549i
\(281\) 9.00000 15.5885i 0.536895 0.929929i −0.462174 0.886789i \(-0.652930\pi\)
0.999069 0.0431402i \(-0.0137362\pi\)
\(282\) 0 0
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −30.0000 −1.77394
\(287\) −3.00000 5.19615i −0.177084 0.306719i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 3.00000 + 5.19615i 0.176166 + 0.305129i
\(291\) 0 0
\(292\) −1.00000 −0.0585206
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) 11.0000 0.639362
\(297\) 0 0
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) 15.0000 + 25.9808i 0.867472 + 1.50251i
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) −4.00000 6.92820i −0.230174 0.398673i
\(303\) 0 0
\(304\) −0.500000 4.33013i −0.0286770 0.248350i
\(305\) −7.00000 −0.400819
\(306\) 0 0
\(307\) −10.0000 17.3205i −0.570730 0.988534i −0.996491 0.0836980i \(-0.973327\pi\)
0.425761 0.904836i \(-0.360006\pi\)
\(308\) −3.00000 + 5.19615i −0.170941 + 0.296078i
\(309\) 0 0
\(310\) −2.50000 + 4.33013i −0.141990 + 0.245935i
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) 0 0
\(313\) 11.0000 19.0526i 0.621757 1.07691i −0.367402 0.930062i \(-0.619753\pi\)
0.989158 0.146852i \(-0.0469141\pi\)
\(314\) 6.50000 11.2583i 0.366816 0.635344i
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) 0 0
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) −5.50000 9.52628i −0.304617 0.527612i
\(327\) 0 0
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) 0 0
\(331\) 29.0000 1.59398 0.796992 0.603990i \(-0.206423\pi\)
0.796992 + 0.603990i \(0.206423\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 0 0
\(334\) 18.0000 0.984916
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) −5.50000 9.52628i −0.299604 0.518930i 0.676441 0.736497i \(-0.263521\pi\)
−0.976045 + 0.217567i \(0.930188\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) −30.0000 −1.62459
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) 3.00000 5.19615i 0.159901 0.276956i
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 10.3923i −0.317999 0.550791i
\(357\) 0 0
\(358\) 9.00000 + 15.5885i 0.475665 + 0.823876i
\(359\) −3.00000 5.19615i −0.158334 0.274242i 0.775934 0.630814i \(-0.217279\pi\)
−0.934268 + 0.356572i \(0.883946\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 26.0000 1.36653
\(363\) 0 0
\(364\) 2.50000 + 4.33013i 0.131036 + 0.226960i
\(365\) 0.500000 0.866025i 0.0261712 0.0453298i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) −5.50000 + 9.52628i −0.285931 + 0.495248i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) 15.0000 + 25.9808i 0.772539 + 1.33808i
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 4.00000 + 1.73205i 0.205196 + 0.0888523i
\(381\) 0 0
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 0 0
\(385\) −3.00000 5.19615i −0.152894 0.264820i
\(386\) −2.50000 + 4.33013i −0.127247 + 0.220398i
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) 0 0
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 3.50000 6.06218i 0.176104 0.305021i
\(396\) 0 0
\(397\) 12.5000 + 21.6506i 0.627357 + 1.08661i 0.988080 + 0.153941i \(0.0491966\pi\)
−0.360723 + 0.932673i \(0.617470\pi\)
\(398\) −7.00000 −0.350878
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) −12.5000 + 21.6506i −0.622669 + 1.07849i
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) −66.0000 −3.27150
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −0.0494468 + 0.0856444i −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) −6.00000 −0.296319
\(411\) 0 0
\(412\) −5.50000 + 9.52628i −0.270966 + 0.469326i
\(413\) −3.00000 5.19615i −0.147620 0.255686i
\(414\) 0 0
\(415\) −3.00000 5.19615i −0.147264 0.255069i
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 0 0
\(418\) 3.00000 + 25.9808i 0.146735 + 1.27076i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i \(-0.948251\pi\)
0.353233 0.935536i \(-0.385082\pi\)
\(422\) 6.50000 11.2583i 0.316415 0.548047i
\(423\) 0 0
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.50000 + 6.06218i −0.169377 + 0.293369i
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) −1.00000 −0.0482243
\(431\) −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) 3.50000 6.06218i 0.168199 0.291330i −0.769588 0.638541i \(-0.779538\pi\)
0.937787 + 0.347212i \(0.112871\pi\)
\(434\) 2.50000 + 4.33013i 0.120004 + 0.207853i
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) 21.0000 15.5885i 1.00457 0.745697i
\(438\) 0 0
\(439\) −5.50000 9.52628i −0.262501 0.454665i 0.704405 0.709798i \(-0.251214\pi\)
−0.966906 + 0.255134i \(0.917881\pi\)
\(440\) 3.00000 + 5.19615i 0.143019 + 0.247717i
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) −18.0000 31.1769i −0.847587 1.46806i
\(452\) −9.00000 + 15.5885i −0.423324 + 0.733219i
\(453\) 0 0
\(454\) −9.00000 15.5885i −0.422391 0.731603i
\(455\) −5.00000 −0.234404
\(456\) 0 0
\(457\) 11.0000 0.514558 0.257279 0.966337i \(-0.417174\pi\)
0.257279 + 0.966337i \(0.417174\pi\)
\(458\) 12.5000 + 21.6506i 0.584087 + 1.01167i
\(459\) 0 0
\(460\) 3.00000 5.19615i 0.139876 0.242272i
\(461\) 18.0000 + 31.1769i 0.838344 + 1.45205i 0.891279 + 0.453456i \(0.149809\pi\)
−0.0529352 + 0.998598i \(0.516858\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −0.500000 + 0.866025i −0.0230879 + 0.0399893i
\(470\) 6.00000 + 10.3923i 0.276759 + 0.479361i
\(471\) 0 0
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 0 0
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 0 0
\(481\) −27.5000 + 47.6314i −1.25389 + 2.17180i
\(482\) 5.00000 0.227744
\(483\) 0 0
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −7.00000 + 12.1244i −0.317854 + 0.550539i
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 3.50000 6.06218i 0.158438 0.274422i
\(489\) 0 0
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 20.0000 + 8.66025i 0.899843 + 0.389643i
\(495\) 0 0
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.500000 + 0.866025i 0.0223831 + 0.0387686i 0.877000 0.480490i \(-0.159541\pi\)
−0.854617 + 0.519259i \(0.826208\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) −6.00000 −0.267793
\(503\) −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 36.0000 1.60040
\(507\) 0 0
\(508\) 8.00000 + 13.8564i 0.354943 + 0.614779i
\(509\) −18.0000 + 31.1769i −0.797836 + 1.38189i 0.123187 + 0.992384i \(0.460689\pi\)
−0.921023 + 0.389509i \(0.872645\pi\)
\(510\) 0 0
\(511\) −0.500000 0.866025i −0.0221187 0.0383107i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −5.50000 9.52628i −0.242359 0.419778i
\(516\) 0 0
\(517\) −36.0000 + 62.3538i −1.58328 + 2.74232i
\(518\) 5.50000 + 9.52628i 0.241656 + 0.418561i
\(519\) 0 0
\(520\) 5.00000 0.219265
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 0 0
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 0 0
\(532\) 3.50000 2.59808i 0.151744 0.112641i
\(533\) −30.0000 −1.29944
\(534\) 0 0
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) 0.500000 0.866025i 0.0215967 0.0374066i
\(537\) 0 0
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 0 0
\(545\) −7.00000 + 12.1244i −0.299847 + 0.519350i
\(546\) 0 0
\(547\) 6.50000 11.2583i 0.277920 0.481371i −0.692948 0.720988i \(-0.743688\pi\)
0.970868 + 0.239616i \(0.0770217\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) 21.0000 15.5885i 0.894630 0.664091i
\(552\) 0 0
\(553\) −3.50000 6.06218i −0.148835 0.257790i
\(554\) −7.00000 12.1244i −0.297402 0.515115i
\(555\) 0 0
\(556\) 0.500000 + 0.866025i 0.0212047 + 0.0367277i
\(557\) −6.00000 + 10.3923i −0.254228 + 0.440336i −0.964686 0.263404i \(-0.915155\pi\)
0.710457 + 0.703740i \(0.248488\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0.500000 0.866025i 0.0211289 0.0365963i
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 0 0
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 8.00000 13.8564i 0.336265 0.582428i
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 15.0000 + 25.9808i 0.627182 + 1.08631i
\(573\) 0 0
\(574\) −3.00000 + 5.19615i −0.125218 + 0.216883i
\(575\) 3.00000 + 5.19615i 0.125109 + 0.216695i
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −17.0000 −0.707107
\(579\) 0 0
\(580\) 3.00000 5.19615i 0.124568 0.215758i
\(581\) −6.00000 −0.248922
\(582\) 0 0
\(583\) 36.0000 62.3538i 1.49097 2.58243i
\(584\) 0.500000 + 0.866025i 0.0206901 + 0.0358364i
\(585\) 0 0
\(586\) −9.00000 15.5885i −0.371787 0.643953i
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) 0 0
\(589\) 20.0000 + 8.66025i 0.824086 + 0.356840i
\(590\) −6.00000 −0.247016
\(591\) 0 0
\(592\) −5.50000 9.52628i −0.226049 0.391528i
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) 0 0
\(598\) 15.0000 25.9808i 0.613396 1.06243i
\(599\) 24.0000 41.5692i 0.980613 1.69847i 0.320607 0.947212i \(-0.396113\pi\)
0.660006 0.751260i \(-0.270554\pi\)
\(600\) 0 0
\(601\) −1.00000 −0.0407909 −0.0203954 0.999792i \(-0.506493\pi\)
−0.0203954 + 0.999792i \(0.506493\pi\)
\(602\) −0.500000 + 0.866025i −0.0203785 + 0.0352966i
\(603\) 0 0
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −12.5000 21.6506i −0.508197 0.880223i
\(606\) 0 0
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −3.50000 + 2.59808i −0.141944 + 0.105366i
\(609\) 0 0
\(610\) 3.50000 + 6.06218i 0.141711 + 0.245450i
\(611\) 30.0000 + 51.9615i 1.21367 + 2.10214i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −10.0000 + 17.3205i −0.403567 + 0.698999i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −12.0000 + 20.7846i −0.483102 + 0.836757i −0.999812 0.0194037i \(-0.993823\pi\)
0.516710 + 0.856161i \(0.327157\pi\)
\(618\) 0 0
\(619\) 11.0000 0.442127 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) 5.00000 0.200805
\(621\) 0 0
\(622\) 3.00000 + 5.19615i 0.120289 + 0.208347i
\(623\) 6.00000 10.3923i 0.240385 0.416359i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) −13.0000 −0.518756
\(629\) 0 0
\(630\) 0 0
\(631\) 3.50000 6.06218i 0.139333 0.241331i −0.787911 0.615789i \(-0.788838\pi\)
0.927244 + 0.374457i \(0.122171\pi\)
\(632\) 3.50000 + 6.06218i 0.139223 + 0.241140i
\(633\) 0 0
\(634\) 18.0000 0.714871
\(635\) −16.0000 −0.634941
\(636\) 0 0
\(637\) 15.0000 25.9808i 0.594322 1.02940i
\(638\) 36.0000 1.42525
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −18.0000 31.1769i −0.710957 1.23141i −0.964498 0.264089i \(-0.914929\pi\)
0.253541 0.967325i \(-0.418405\pi\)
\(642\) 0 0
\(643\) −14.5000 25.1147i −0.571824 0.990429i −0.996379 0.0850262i \(-0.972903\pi\)
0.424555 0.905402i \(-0.360431\pi\)
\(644\) −3.00000 5.19615i −0.118217 0.204757i
\(645\) 0 0
\(646\) 0 0
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 0 0
\(649\) −18.0000 31.1769i −0.706562 1.22380i
\(650\) −2.50000 + 4.33013i −0.0980581 + 0.169842i
\(651\) 0 0
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 0 0
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) 0 0
\(658\) 12.0000 0.467809
\(659\) 15.0000 25.9808i 0.584317 1.01207i −0.410643 0.911796i \(-0.634696\pi\)
0.994960 0.100271i \(-0.0319709\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −14.5000 25.1147i −0.563559 0.976112i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0.500000 + 4.33013i 0.0193892 + 0.167915i
\(666\) 0 0
\(667\) −18.0000 31.1769i −0.696963 1.20717i
\(668\) −9.00000 15.5885i −0.348220 0.603136i
\(669\) 0 0
\(670\) 0.500000 + 0.866025i 0.0193167 + 0.0334575i
\(671\) −21.0000 + 36.3731i −0.810696 + 1.40417i
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −5.50000 + 9.52628i −0.211852 + 0.366939i
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) 0 0
\(679\) 7.00000 + 12.1244i 0.268635 + 0.465290i
\(680\) 0 0
\(681\) 0 0
\(682\) 15.0000 + 25.9808i 0.574380 + 0.994855i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) −6.50000 11.2583i −0.248171 0.429845i
\(687\) 0 0
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) −30.0000 51.9615i −1.14291 1.97958i
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −6.00000 + 10.3923i −0.227757 + 0.394486i
\(695\) −1.00000 −0.0379322
\(696\) 0 0
\(697\) 0 0
\(698\) 9.50000 + 16.4545i 0.359580 + 0.622811i
\(699\) 0 0
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) 0 0
\(703\) 44.0000 + 19.0526i 1.65949 + 0.718581i
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.00000 + 10.3923i −0.224860 + 0.389468i
\(713\) 15.0000 25.9808i 0.561754 0.972987i
\(714\) 0 0
\(715\) −30.0000 −1.12194
\(716\) 9.00000 15.5885i 0.336346 0.582568i
\(717\) 0 0
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i \(-0.880269\pi\)
0.146920 0.989148i \(-0.453064\pi\)
\(720\) 0 0
\(721\) −11.0000 −0.409661
\(722\) 5.50000 18.1865i 0.204689 0.676833i
\(723\) 0 0
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 0 0
\(727\) −17.5000 30.3109i −0.649039 1.12417i −0.983353 0.181707i \(-0.941838\pi\)
0.334314 0.942462i \(-0.391496\pi\)
\(728\) 2.50000 4.33013i 0.0926562 0.160485i
\(729\) 0 0
\(730\) −1.00000 −0.0370117
\(731\) 0 0
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 17.0000 0.627481
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −3.00000 + 5.19615i −0.110506 + 0.191403i
\(738\) 0 0
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 11.0000 0.404368
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) 9.00000 + 15.5885i 0.330178 + 0.571885i 0.982547 0.186017i \(-0.0595579\pi\)
−0.652369 + 0.757902i \(0.726225\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) −1.00000 1.73205i −0.0366126 0.0634149i
\(747\) 0 0
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −2.50000 + 4.33013i −0.0912263 + 0.158009i −0.908027 0.418911i \(-0.862412\pi\)
0.816801 + 0.576919i \(0.195745\pi\)
\(752\) −12.0000 −0.437595
\(753\) 0 0
\(754\) 15.0000 25.9808i 0.546268 0.946164i
\(755\) −4.00000 6.92820i −0.145575 0.252143i
\(756\) 0 0
\(757\) 15.5000 + 26.8468i 0.563357 + 0.975763i 0.997200 + 0.0747748i \(0.0238238\pi\)
−0.433843 + 0.900988i \(0.642843\pi\)
\(758\) 9.50000 + 16.4545i 0.345056 + 0.597654i
\(759\) 0 0
\(760\) −0.500000 4.33013i −0.0181369 0.157070i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 7.00000 + 12.1244i 0.253417 + 0.438931i
\(764\) 6.00000 10.3923i 0.217072 0.375980i
\(765\) 0 0
\(766\) −6.00000 + 10.3923i −0.216789 + 0.375489i
\(767\) −30.0000 −1.08324
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) −3.00000 + 5.19615i −0.108112 + 0.187256i
\(771\) 0 0
\(772\) 5.00000 0.179954
\(773\) −15.0000 + 25.9808i −0.539513 + 0.934463i 0.459418 + 0.888220i \(0.348058\pi\)
−0.998930 + 0.0462427i \(0.985275\pi\)
\(774\) 0 0
\(775\) −2.50000 + 4.33013i −0.0898027 + 0.155543i
\(776\) −7.00000 12.1244i −0.251285 0.435239i
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 3.00000 + 25.9808i 0.107486 + 0.930857i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 3.00000 + 5.19615i 0.107143 + 0.185577i
\(785\) 6.50000 11.2583i 0.231995 0.401827i
\(786\) 0 0
\(787\) 53.0000 1.88925 0.944623 0.328158i \(-0.106428\pi\)
0.944623 + 0.328158i \(0.106428\pi\)
\(788\) −9.00000 + 15.5885i −0.320612 + 0.555316i
\(789\) 0 0
\(790\) −7.00000 −0.249049
\(791\) −18.0000 −0.640006