Properties

Label 1170.2.i.d.451.1
Level $1170$
Weight $2$
Character 1170.451
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1170.451
Dual form 1170.2.i.d.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(2.50000 + 2.59808i) q^{26} +(-1.00000 + 1.73205i) q^{28} +(1.50000 - 2.59808i) q^{29} +5.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(3.50000 - 6.06218i) q^{37} +2.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.50000 + 0.866025i) q^{52} +6.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(1.50000 + 2.59808i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.50000 + 4.33013i) q^{62} +1.00000 q^{64} +(1.00000 - 3.46410i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +2.00000 q^{70} +(-6.00000 - 10.3923i) q^{71} +14.0000 q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +6.00000 q^{77} +5.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(3.00000 + 5.19615i) q^{85} -1.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(-7.00000 + 1.73205i) q^{91} -3.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(-7.00000 - 12.1244i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 2q^{5} - 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 2q^{5} - 2q^{7} + 2q^{8} - q^{10} - 3q^{11} + 2q^{13} + 4q^{14} - q^{16} + 6q^{17} - 2q^{19} - q^{20} - 3q^{22} + 3q^{23} + 2q^{25} + 5q^{26} - 2q^{28} + 3q^{29} + 10q^{31} - q^{32} - 12q^{34} - 2q^{35} + 7q^{37} + 4q^{38} + 2q^{40} + 6q^{41} + q^{43} + 6q^{44} + 3q^{46} + 6q^{47} + 3q^{49} - q^{50} - 7q^{52} + 12q^{53} - 3q^{55} - 2q^{56} + 3q^{58} - 9q^{59} - 2q^{61} - 5q^{62} + 2q^{64} + 2q^{65} - 8q^{67} + 6q^{68} + 4q^{70} - 12q^{71} + 28q^{73} + 7q^{74} - 2q^{76} + 12q^{77} + 10q^{79} - q^{80} + 6q^{82} + 12q^{83} + 6q^{85} - 2q^{86} - 3q^{88} - 18q^{89} - 14q^{91} - 6q^{92} - 3q^{94} - 2q^{95} - 14q^{97} + 3q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.50000 + 2.59808i 0.490290 + 0.509525i
\(27\) 0 0
\(28\) −1.00000 + 1.73205i −0.188982 + 0.327327i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 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
\(34\) −6.00000 −1.02899
\(35\) −1.00000 1.73205i −0.169031 0.292770i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 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 0.452267
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) 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
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) 0 0
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) −2.50000 + 4.33013i −0.317500 + 0.549927i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 3.46410i 0.124035 0.429669i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) −6.00000 10.3923i −0.712069 1.23334i −0.964079 0.265615i \(-0.914425\pi\)
0.252010 0.967725i \(-0.418908\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) −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
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i \(0.569742\pi\)
−0.736644 + 0.676280i \(0.763591\pi\)
\(90\) 0 0
\(91\) −7.00000 + 1.73205i −0.733799 + 0.181568i
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) −7.00000 12.1244i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 1.00000 3.46410i 0.0980581 0.339683i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) 0 0
\(112\) 2.00000 0.188982
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) 9.00000 0.828517
\(119\) 6.00000 10.3923i 0.550019 0.952661i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) −2.50000 4.33013i −0.224507 0.388857i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.00000 + 12.1244i −0.621150 + 1.07586i 0.368122 + 0.929777i \(0.380001\pi\)
−0.989272 + 0.146085i \(0.953333\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.50000 + 2.59808i 0.219265 + 0.227866i
\(131\) −9.00000 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(132\) 0 0
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) −4.00000 6.92820i −0.345547 0.598506i
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 0 0
\(139\) −7.00000 12.1244i −0.593732 1.02837i −0.993724 0.111856i \(-0.964321\pi\)
0.399992 0.916519i \(-0.369013\pi\)
\(140\) −1.00000 + 1.73205i −0.0845154 + 0.146385i
\(141\) 0 0
\(142\) 12.0000 1.00702
\(143\) 7.50000 + 7.79423i 0.627182 + 0.651786i
\(144\) 0 0
\(145\) 1.50000 2.59808i 0.124568 0.215758i
\(146\) −7.00000 + 12.1244i −0.579324 + 1.00342i
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) 0 0
\(154\) −3.00000 + 5.19615i −0.241747 + 0.418718i
\(155\) 5.00000 0.401610
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) −2.50000 + 4.33013i −0.198889 + 0.344486i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 6.50000 + 11.2583i 0.509119 + 0.881820i 0.999944 + 0.0105623i \(0.00336213\pi\)
−0.490825 + 0.871258i \(0.663305\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −4.50000 + 7.79423i −0.348220 + 0.603136i −0.985933 0.167139i \(-0.946547\pi\)
0.637713 + 0.770274i \(0.279881\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −6.00000 −0.460179
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 0 0
\(175\) −1.00000 1.73205i −0.0755929 0.130931i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −9.00000 15.5885i −0.674579 1.16840i
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.00000 6.92820i 0.148250 0.513553i
\(183\) 0 0
\(184\) 1.50000 2.59808i 0.110581 0.191533i
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) −18.0000 −1.31629
\(188\) −1.50000 2.59808i −0.109399 0.189484i
\(189\) 0 0
\(190\) 2.00000 0.145095
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 12.0000 20.7846i 0.854965 1.48084i −0.0217133 0.999764i \(-0.506912\pi\)
0.876678 0.481078i \(-0.159755\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 3.00000 + 5.19615i 0.211079 + 0.365600i
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 0 0
\(208\) 2.50000 + 2.59808i 0.173344 + 0.180144i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0.500000 + 0.866025i 0.0340997 + 0.0590624i
\(216\) 0 0
\(217\) −5.00000 8.66025i −0.339422 0.587896i
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 0 0
\(220\) 3.00000 0.202260
\(221\) 21.0000 5.19615i 1.41261 0.349531i
\(222\) 0 0
\(223\) 5.00000 8.66025i 0.334825 0.579934i −0.648626 0.761107i \(-0.724656\pi\)
0.983451 + 0.181173i \(0.0579895\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 1.50000 + 2.59808i 0.0989071 + 0.171312i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) −4.50000 + 7.79423i −0.292925 + 0.507361i
\(237\) 0 0
\(238\) 6.00000 + 10.3923i 0.388922 + 0.673633i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 1.50000 2.59808i 0.0958315 0.165985i
\(246\) 0 0
\(247\) −7.00000 + 1.73205i −0.445399 + 0.110208i
\(248\) 5.00000 0.317500
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 7.50000 + 12.9904i 0.473396 + 0.819946i 0.999536 0.0304521i \(-0.00969471\pi\)
−0.526140 + 0.850398i \(0.676361\pi\)
\(252\) 0 0
\(253\) 4.50000 + 7.79423i 0.282913 + 0.490019i
\(254\) −7.00000 12.1244i −0.439219 0.760750i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5000 + 18.1865i −0.654972 + 1.13444i 0.326929 + 0.945049i \(0.393986\pi\)
−0.981901 + 0.189396i \(0.939347\pi\)
\(258\) 0 0
\(259\) −14.0000 −0.869918
\(260\) −3.50000 + 0.866025i −0.217061 + 0.0537086i
\(261\) 0 0
\(262\) 4.50000 7.79423i 0.278011 0.481529i
\(263\) −7.50000 + 12.9904i −0.462470 + 0.801021i −0.999083 0.0428069i \(-0.986370\pi\)
0.536614 + 0.843828i \(0.319703\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) −2.00000 3.46410i −0.122628 0.212398i
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) 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
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 14.0000 0.839664
\(279\) 0 0
\(280\) −1.00000 1.73205i −0.0597614 0.103510i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 15.5000 26.8468i 0.921379 1.59588i 0.124096 0.992270i \(-0.460397\pi\)
0.797283 0.603606i \(-0.206270\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) −10.5000 + 2.59808i −0.620878 + 0.153627i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 1.50000 + 2.59808i 0.0880830 + 0.152564i
\(291\) 0 0
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) −15.0000 25.9808i −0.876309 1.51781i −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 0 0
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) 3.50000 6.06218i 0.203433 0.352357i
\(297\) 0 0
\(298\) 9.00000 0.521356
\(299\) −7.50000 7.79423i −0.433736 0.450752i
\(300\) 0 0
\(301\) 1.00000 1.73205i 0.0576390 0.0998337i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) −1.00000 1.73205i −0.0572598 0.0991769i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) 0 0
\(310\) −2.50000 + 4.33013i −0.141990 + 0.245935i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 6.50000 11.2583i 0.366816 0.635344i
\(315\) 0 0
\(316\) −2.50000 4.33013i −0.140636 0.243589i
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 3.00000 5.19615i 0.167183 0.289570i
\(323\) 6.00000 10.3923i 0.333849 0.578243i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) −13.0000 −0.720003
\(327\) 0 0
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) −16.0000 27.7128i −0.879440 1.52323i −0.851957 0.523612i \(-0.824584\pi\)
−0.0274825 0.999622i \(-0.508749\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 0 0
\(334\) −4.50000 7.79423i −0.246229 0.426481i
\(335\) −4.00000 + 6.92820i −0.218543 + 0.378528i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 11.5000 6.06218i 0.625518 0.329739i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i \(-0.868702\pi\)
0.110885 0.993833i \(-0.464631\pi\)
\(348\) 0 0
\(349\) −4.00000 + 6.92820i −0.214115 + 0.370858i −0.952998 0.302975i \(-0.902020\pi\)
0.738883 + 0.673833i \(0.235353\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) −1.50000 2.59808i −0.0792775 0.137313i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 0 0
\(364\) 5.00000 + 5.19615i 0.262071 + 0.272352i
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −10.0000 + 17.3205i −0.521996 + 0.904123i 0.477677 + 0.878536i \(0.341479\pi\)
−0.999673 + 0.0255875i \(0.991854\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 3.50000 + 6.06218i 0.181956 + 0.315158i
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) 0 0
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) −7.50000 7.79423i −0.386270 0.401423i
\(378\) 0 0
\(379\) −19.0000 + 32.9090i −0.975964 + 1.69042i −0.299249 + 0.954175i \(0.596736\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(380\) −1.00000 + 1.73205i −0.0512989 + 0.0888523i
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 2.00000 + 3.46410i 0.101797 + 0.176318i
\(387\) 0 0
\(388\) −7.00000 + 12.1244i −0.355371 + 0.615521i
\(389\) −3.00000 −0.152106 −0.0760530 0.997104i \(-0.524232\pi\)
−0.0760530 + 0.997104i \(0.524232\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 0 0
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 5.00000 0.251577
\(396\) 0 0
\(397\) 15.5000 + 26.8468i 0.777923 + 1.34740i 0.933137 + 0.359521i \(0.117060\pi\)
−0.155214 + 0.987881i \(0.549607\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) 5.00000 17.3205i 0.249068 0.862796i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 3.00000 5.19615i 0.148888 0.257881i
\(407\) 10.5000 + 18.1865i 0.520466 + 0.901473i
\(408\) 0 0
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 3.00000 + 5.19615i 0.148159 + 0.256620i
\(411\) 0 0
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) −9.00000 + 15.5885i −0.442861 + 0.767058i
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) −3.50000 + 0.866025i −0.171602 + 0.0424604i
\(417\) 0 0
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) −10.0000 17.3205i −0.486792 0.843149i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) −2.00000 + 3.46410i −0.0967868 + 0.167640i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) −1.00000 −0.0482243
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) 20.0000 + 34.6410i 0.961139 + 1.66474i 0.719650 + 0.694337i \(0.244302\pi\)
0.241489 + 0.970404i \(0.422364\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) 2.00000 3.46410i 0.0954548 0.165333i −0.814344 0.580383i \(-0.802903\pi\)
0.909798 + 0.415051i \(0.136236\pi\)
\(440\) −1.50000 + 2.59808i −0.0715097 + 0.123858i
\(441\) 0 0
\(442\) −6.00000 + 20.7846i −0.285391 + 0.988623i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 5.00000 + 8.66025i 0.236757 + 0.410075i
\(447\) 0 0
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) 18.0000 + 31.1769i 0.849473 + 1.47133i 0.881680 + 0.471848i \(0.156413\pi\)
−0.0322072 + 0.999481i \(0.510254\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) 0 0
\(454\) 0 0
\(455\) −7.00000 + 1.73205i −0.328165 + 0.0811998i
\(456\) 0 0
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) −3.00000 −0.139876
\(461\) 7.50000 + 12.9904i 0.349310 + 0.605022i 0.986127 0.165992i \(-0.0530827\pi\)
−0.636817 + 0.771015i \(0.719749\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 10.5000 18.1865i 0.486403 0.842475i
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) −1.50000 + 2.59808i −0.0691898 + 0.119840i
\(471\) 0 0
\(472\) −4.50000 7.79423i −0.207129 0.358758i
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) −1.00000 1.73205i −0.0458831 0.0794719i
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 12.0000 20.7846i 0.548867 0.950666i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) 17.0000 0.774329
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −7.00000 12.1244i −0.317854 0.550539i
\(486\) 0 0
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 0 0
\(490\) 1.50000 + 2.59808i 0.0677631 + 0.117369i
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 2.00000 6.92820i 0.0899843 0.311715i
\(495\) 0 0
\(496\) −2.50000 + 4.33013i −0.112253 + 0.194428i
\(497\) −12.0000 + 20.7846i −0.538274 + 0.932317i
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) −15.0000 −0.669483
\(503\) 12.0000 + 20.7846i 0.535054 + 0.926740i 0.999161 + 0.0409609i \(0.0130419\pi\)
−0.464107 + 0.885779i \(0.653625\pi\)
\(504\) 0 0
\(505\) 3.00000 5.19615i 0.133498 0.231226i
\(506\) −9.00000 −0.400099
\(507\) 0 0
\(508\) 14.0000 0.621150
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) −14.0000 24.2487i −0.619324 1.07270i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −10.5000 18.1865i −0.463135 0.802174i
\(515\) 14.0000 0.616914
\(516\) 0 0
\(517\) −4.50000 + 7.79423i −0.197910 + 0.342790i
\(518\) 7.00000 12.1244i 0.307562 0.532714i
\(519\) 0 0
\(520\) 1.00000 3.46410i 0.0438529 0.151911i
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −5.50000 + 9.52628i −0.240498 + 0.416555i −0.960856 0.277047i \(-0.910644\pi\)
0.720358 + 0.693602i \(0.243977\pi\)
\(524\) 4.50000 + 7.79423i 0.196583 + 0.340492i
\(525\) 0 0
\(526\) −7.50000 12.9904i −0.327016 0.566408i
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −3.00000 + 5.19615i −0.130312 + 0.225706i
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) −15.0000 15.5885i −0.649722 0.675211i
\(534\) 0 0
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 0 0
\(538\) −18.0000 −0.776035
\(539\) 4.50000 + 7.79423i 0.193829 + 0.335721i
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −5.50000 9.52628i −0.236245 0.409189i
\(543\) 0 0
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 0 0
\(550\) −1.50000 2.59808i −0.0639602 0.110782i
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) −5.00000 8.66025i −0.212622 0.368271i
\(554\) −1.00000 −0.0424859
\(555\) 0 0
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −3.00000 + 5.19615i −0.127114 + 0.220168i −0.922557 0.385860i \(-0.873905\pi\)
0.795443 + 0.606028i \(0.207238\pi\)
\(558\) 0 0
\(559\) 3.50000 0.866025i 0.148034 0.0366290i
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i \(0.107454\pi\)
−0.184950 + 0.982748i \(0.559212\pi\)
\(564\) 0 0
\(565\) 7.50000 + 12.9904i 0.315527 + 0.546509i
\(566\) 15.5000 + 26.8468i 0.651514 + 1.12845i
\(567\) 0 0
\(568\) −6.00000 10.3923i −0.251754 0.436051i
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 3.00000 10.3923i 0.125436 0.434524i
\(573\) 0 0
\(574\) 6.00000 10.3923i 0.250435 0.433766i
\(575\) 1.50000 2.59808i 0.0625543 0.108347i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0 0
\(580\) −3.00000 −0.124568
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 9.00000 15.5885i 0.371470 0.643404i −0.618322 0.785925i \(-0.712187\pi\)
0.989792 + 0.142520i \(0.0455206\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 9.00000 0.370524
\(591\) 0 0
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) −27.0000 −1.10876 −0.554379 0.832265i \(-0.687044\pi\)
−0.554379 + 0.832265i \(0.687044\pi\)
\(594\) 0 0
\(595\) 6.00000 10.3923i 0.245976 0.426043i
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) 0 0
\(598\) 10.5000 2.59808i 0.429377 0.106243i
\(599\) −6.00000 −0.245153 −0.122577 0.992459i \(-0.539116\pi\)
−0.122577 + 0.992459i \(0.539116\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 1.00000 + 1.73205i 0.0407570 + 0.0705931i
\(603\) 0 0
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i \(-0.0193454\pi\)
−0.551678 + 0.834058i \(0.686012\pi\)
\(608\) −1.00000 + 1.73205i −0.0405554 + 0.0702439i
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) 3.00000 10.3923i 0.121367 0.420428i
\(612\) 0 0
\(613\) 15.5000 26.8468i 0.626039 1.08433i −0.362300 0.932062i \(-0.618008\pi\)
0.988339 0.152270i \(-0.0486583\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 10.5000 + 18.1865i 0.422714 + 0.732162i 0.996204 0.0870504i \(-0.0277441\pi\)
−0.573490 + 0.819213i \(0.694411\pi\)
\(618\) 0 0
\(619\) −46.0000 −1.84890 −0.924448 0.381308i \(-0.875474\pi\)
−0.924448 + 0.381308i \(0.875474\pi\)
\(620\) −2.50000 4.33013i −0.100402 0.173902i
\(621\) 0 0
\(622\) −6.00000 + 10.3923i −0.240578 + 0.416693i
\(623\) 36.0000 1.44231
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −4.00000 + 6.92820i −0.159872 + 0.276907i
\(627\) 0 0
\(628\) 6.50000 + 11.2583i 0.259378 + 0.449256i
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) 8.00000 + 13.8564i 0.318475 + 0.551615i 0.980170 0.198158i \(-0.0634960\pi\)
−0.661695 + 0.749773i \(0.730163\pi\)
\(632\) 5.00000 0.198889
\(633\) 0 0
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) −7.00000 + 12.1244i −0.277787 + 0.481140i
\(636\) 0 0
\(637\) −7.50000 7.79423i −0.297161 0.308819i
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) 0 0
\(643\) 8.00000 + 13.8564i 0.315489 + 0.546443i 0.979541 0.201243i \(-0.0644981\pi\)
−0.664052 + 0.747686i \(0.731165\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) 0 0
\(649\) 27.0000 1.05984
\(650\) 2.50000 + 2.59808i 0.0980581 + 0.101905i
\(651\) 0 0
\(652\) 6.50000 11.2583i 0.254560 0.440910i
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 0 0
\(655\) −9.00000 −0.351659
\(656\) 3.00000 + 5.19615i 0.117130 + 0.202876i
\(657\) 0 0
\(658\) 6.00000 0.233904
\(659\) 7.50000 + 12.9904i 0.292159 + 0.506033i 0.974320 0.225168i \(-0.0722932\pi\)
−0.682161 + 0.731202i \(0.738960\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) 32.0000 1.24372
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) −2.00000 + 3.46410i −0.0775567 + 0.134332i
\(666\) 0 0
\(667\) −4.50000 7.79423i −0.174241 0.301794i
\(668\) 9.00000 0.348220
\(669\) 0 0
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) 2.00000 3.46410i 0.0770943 0.133531i −0.824901 0.565278i \(-0.808769\pi\)
0.901995 + 0.431746i \(0.142102\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) 0 0
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 36.0000 1.38359 0.691796 0.722093i \(-0.256820\pi\)
0.691796 + 0.722093i \(0.256820\pi\)
\(678\) 0 0
\(679\) −14.0000 + 24.2487i −0.537271 + 0.930580i
\(680\) 3.00000 + 5.19615i 0.115045 + 0.199263i
\(681\) 0 0
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) 4.50000 + 7.79423i 0.171936 + 0.297802i
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) 23.0000 39.8372i 0.874961 1.51548i 0.0181572 0.999835i \(-0.494220\pi\)
0.856804 0.515642i \(-0.172447\pi\)
\(692\) 6.00000 10.3923i 0.228086 0.395056i
\(693\) 0 0
\(694\) 30.0000 1.13878
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) 0 0
\(697\) 36.0000 1.36360
\(698\) −4.00000 6.92820i −0.151402 0.262236i
\(699\) 0 0
\(700\) −1.00000 + 1.73205i −0.0377964 + 0.0654654i
\(701\) 21.0000 0.793159 0.396580 0.918000i \(-0.370197\pi\)
0.396580 + 0.918000i \(0.370197\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 15.0000 + 25.9808i 0.564532 + 0.977799i
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) −16.0000 27.7128i −0.600893 1.04078i −0.992686 0.120723i \(-0.961479\pi\)
0.391794 0.920053i \(-0.371855\pi\)
\(710\) 12.0000 0.450352
\(711\) 0 0
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) 7.50000 12.9904i 0.280877 0.486494i
\(714\) 0 0
\(715\) 7.50000 + 7.79423i 0.280484 + 0.291488i
\(716\) 3.00000 0.112115
\(717\) 0 0
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 18.0000 + 31.1769i 0.671287 + 1.16270i 0.977539 + 0.210752i \(0.0675914\pi\)
−0.306253 + 0.951950i \(0.599075\pi\)
\(720\) 0 0
\(721\) −14.0000 24.2487i −0.521387 0.903069i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) 0 0
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 1.50000 2.59808i 0.0557086 0.0964901i
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) −7.00000 + 1.73205i −0.259437 + 0.0641941i
\(729\) 0 0
\(730\) −7.00000 + 12.1244i −0.259082 + 0.448743i
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −10.0000 17.3205i −0.369107 0.639312i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) −7.00000 −0.257325
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) −4.50000 + 7.79423i −0.165089 + 0.285943i −0.936687 0.350168i \(-0.886124\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(744\) 0 0
\(745\) −4.50000 7.79423i −0.164867 0.285558i
\(746\) −25.0000 −0.915315
\(747\) 0 0
\(748\) 9.00000 + 15.5885i 0.329073 + 0.569970i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −20.5000 + 35.5070i −0.748056 + 1.29567i 0.200698 + 0.979653i \(0.435679\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 10.5000 2.59808i 0.382387 0.0946164i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −19.0000 + 32.9090i −0.690567 + 1.19610i 0.281086 + 0.959683i \(0.409305\pi\)
−0.971652 + 0.236414i \(0.924028\pi\)
\(758\) −19.0000 32.9090i −0.690111 1.19531i
\(759\) 0 0
\(760\) −1.00000 1.73205i −0.0362738 0.0628281i
\(761\) −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i \(-0.236457\pi\)
−0.954043 + 0.299670i \(0.903123\pi\)
\(762\) 0 0
\(763\) −14.0000 24.2487i −0.506834 0.877862i
\(764\) −6.00000 + 10.3923i −0.217072 + 0.375980i
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) −31.5000 + 7.79423i −1.13740 + 0.281433i
\(768\) 0 0
\(769\) 6.50000 11.2583i 0.234396 0.405986i −0.724701 0.689063i \(-0.758022\pi\)
0.959097 + 0.283078i \(0.0913554\pi\)
\(770\) −3.00000 + 5.19615i −0.108112 + 0.187256i
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i \(-0.835111\pi\)
0.00558380 0.999984i \(-0.498223\pi\)
\(774\) 0 0
\(775\) 5.00000 0.179605
\(776\) −7.00000 12.1244i −0.251285 0.435239i
\(777\) 0 0
\(778\) 1.50000 2.59808i 0.0537776 0.0931455i
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −9.00000 + 15.5885i −0.321839 + 0.557442i
\(783\) 0 0
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) −13.0000 −0.463990
\(786\) 0 0
\(787\) −17.5000 30.3109i −0.623808 1.08047i −0.988770 0.149444i \(-0.952252\pi\)
0.364963 0.931022i \(-0.381082\pi\)
\(788\) −24.0000 −0.854965
\(789\) 0 0
\(790\) −2.50000 + 4.33013i −0.0889460 + 0.154059i