Properties

Label 1680.2.bg.l.1201.1
Level 1680
Weight 2
Character 1680.1201
Analytic conductor 13.415
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.bg (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.1
Root \(0.500000 + 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 1680.1201
Dual form 1680.2.bg.l.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -3.00000 q^{13} -1.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.50000 + 2.59808i) q^{39} -6.00000 q^{41} -1.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 + 3.46410i) q^{53} +6.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} -4.00000 q^{69} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(12.0000 + 10.3923i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000 q^{83} -4.00000 q^{85} +(-4.00000 + 6.92820i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-1.50000 + 7.79423i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(0.500000 - 0.866025i) q^{95} -6.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - q^{5} + q^{7} - q^{9} - 6q^{11} - 6q^{13} - 2q^{15} + 4q^{17} + q^{19} - 4q^{21} - 4q^{23} - q^{25} - 2q^{27} - 16q^{29} + q^{31} + 6q^{33} - 5q^{35} - 7q^{37} - 3q^{39} - 12q^{41} - 2q^{43} - q^{45} + 2q^{47} - 13q^{49} - 4q^{51} - 4q^{53} + 12q^{55} + 2q^{57} - 8q^{59} + 14q^{61} - 5q^{63} + 3q^{65} + 7q^{67} - 8q^{69} - 12q^{71} - q^{73} + q^{75} + 24q^{77} - q^{79} - q^{81} - 4q^{83} - 8q^{85} - 8q^{87} + 12q^{89} - 3q^{91} - q^{93} + q^{95} - 12q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) −2.50000 + 0.866025i −0.422577 + 0.146385i
\(36\) 0 0
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 0 0
\(39\) −1.50000 + 2.59808i −0.240192 + 0.416025i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) −2.00000 + 3.46410i −0.274721 + 0.475831i −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 0 0
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 0 0
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) 0 0
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −0.500000 + 0.866025i −0.0585206 + 0.101361i −0.893801 0.448463i \(-0.851972\pi\)
0.835281 + 0.549823i \(0.185305\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 12.0000 + 10.3923i 1.36753 + 1.18431i
\(78\) 0 0
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −4.00000 + 6.92820i −0.428845 + 0.742781i
\(88\) 0 0
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) 0 0
\(91\) −1.50000 + 7.79423i −0.157243 + 0.817057i
\(92\) 0 0
\(93\) −0.500000 0.866025i −0.0518476 0.0898027i
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 0 0
\(103\) −9.50000 16.4545i −0.936063 1.62131i −0.772728 0.634738i \(-0.781108\pi\)
−0.163335 0.986571i \(-0.552225\pi\)
\(104\) 0 0
\(105\) −0.500000 + 2.59808i −0.0487950 + 0.253546i
\(106\) 0 0
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0 0
\(109\) 7.50000 12.9904i 0.718370 1.24425i −0.243276 0.969957i \(-0.578222\pi\)
0.961645 0.274296i \(-0.0884447\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −2.00000 + 3.46410i −0.186501 + 0.323029i
\(116\) 0 0
\(117\) 1.50000 + 2.59808i 0.138675 + 0.240192i
\(118\) 0 0
\(119\) −8.00000 6.92820i −0.733359 0.635107i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 0 0
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) −0.500000 + 0.866025i −0.0440225 + 0.0762493i
\(130\) 0 0
\(131\) 1.00000 + 1.73205i 0.0873704 + 0.151330i 0.906399 0.422423i \(-0.138820\pi\)
−0.819028 + 0.573753i \(0.805487\pi\)
\(132\) 0 0
\(133\) 2.50000 0.866025i 0.216777 0.0750939i
\(134\) 0 0
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) −4.00000 + 6.92820i −0.341743 + 0.591916i −0.984757 0.173939i \(-0.944351\pi\)
0.643013 + 0.765855i \(0.277684\pi\)
\(138\) 0 0
\(139\) −21.0000 −1.78120 −0.890598 0.454791i \(-0.849714\pi\)
−0.890598 + 0.454791i \(0.849714\pi\)
\(140\) 0 0
\(141\) 2.00000 0.168430
\(142\) 0 0
\(143\) 9.00000 15.5885i 0.752618 1.30357i
\(144\) 0 0
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) 0 0
\(147\) −5.50000 + 4.33013i −0.453632 + 0.357143i
\(148\) 0 0
\(149\) 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i \(-0.114277\pi\)
−0.772399 + 0.635138i \(0.780943\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) −5.00000 + 8.66025i −0.399043 + 0.691164i −0.993608 0.112884i \(-0.963991\pi\)
0.594565 + 0.804048i \(0.297324\pi\)
\(158\) 0 0
\(159\) 2.00000 + 3.46410i 0.158610 + 0.274721i
\(160\) 0 0
\(161\) −10.0000 + 3.46410i −0.788110 + 0.273009i
\(162\) 0 0
\(163\) −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i \(-0.322397\pi\)
−0.999410 + 0.0343508i \(0.989064\pi\)
\(164\) 0 0
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0.500000 0.866025i 0.0382360 0.0662266i
\(172\) 0 0
\(173\) −12.0000 20.7846i −0.912343 1.58022i −0.810745 0.585399i \(-0.800938\pi\)
−0.101598 0.994826i \(-0.532395\pi\)
\(174\) 0 0
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 0 0
\(177\) 4.00000 + 6.92820i 0.300658 + 0.520756i
\(178\) 0 0
\(179\) 9.00000 15.5885i 0.672692 1.16514i −0.304446 0.952529i \(-0.598471\pi\)
0.977138 0.212607i \(-0.0681952\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) 0 0
\(187\) 12.0000 + 20.7846i 0.877527 + 1.51992i
\(188\) 0 0
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) 0 0
\(191\) 5.00000 + 8.66025i 0.361787 + 0.626634i 0.988255 0.152813i \(-0.0488333\pi\)
−0.626468 + 0.779447i \(0.715500\pi\)
\(192\) 0 0
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) 0 0
\(195\) 3.00000 0.214834
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 0 0
\(201\) −3.50000 6.06218i −0.246871 0.427593i
\(202\) 0 0
\(203\) −4.00000 + 20.7846i −0.280745 + 1.45879i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 0 0
\(207\) −2.00000 + 3.46410i −0.139010 + 0.240772i
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) 0 0
\(215\) 0.500000 + 0.866025i 0.0340997 + 0.0590624i
\(216\) 0 0
\(217\) −2.00000 1.73205i −0.135769 0.117579i
\(218\) 0 0
\(219\) 0.500000 + 0.866025i 0.0337869 + 0.0585206i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −5.00000 + 8.66025i −0.331862 + 0.574801i −0.982877 0.184263i \(-0.941010\pi\)
0.651015 + 0.759065i \(0.274343\pi\)
\(228\) 0 0
\(229\) −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i \(-0.307988\pi\)
−0.996832 + 0.0795401i \(0.974655\pi\)
\(230\) 0 0
\(231\) 15.0000 5.19615i 0.986928 0.341882i
\(232\) 0 0
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0 0
\(235\) 1.00000 1.73205i 0.0652328 0.112987i
\(236\) 0 0
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) −14.0000 −0.905585 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 0 0
\(241\) 9.00000 15.5885i 0.579741 1.00414i −0.415768 0.909471i \(-0.636487\pi\)
0.995509 0.0946700i \(-0.0301796\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 0 0
\(247\) −1.50000 2.59808i −0.0954427 0.165312i
\(248\) 0 0
\(249\) −1.00000 + 1.73205i −0.0633724 + 0.109764i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 24.0000 1.50887
\(254\) 0 0
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) 0 0
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 0 0
\(261\) 4.00000 + 6.92820i 0.247594 + 0.428845i
\(262\) 0 0
\(263\) 2.00000 3.46410i 0.123325 0.213606i −0.797752 0.602986i \(-0.793977\pi\)
0.921077 + 0.389380i \(0.127311\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 0 0
\(273\) 6.00000 + 5.19615i 0.363137 + 0.314485i
\(274\) 0 0
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) 0 0
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) −3.50000 + 6.06218i −0.208053 + 0.360359i −0.951101 0.308879i \(-0.900046\pi\)
0.743048 + 0.669238i \(0.233379\pi\)
\(284\) 0 0
\(285\) −0.500000 0.866025i −0.0296174 0.0512989i
\(286\) 0 0
\(287\) −3.00000 + 15.5885i −0.177084 + 0.920158i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −3.00000 + 5.19615i −0.175863 + 0.304604i
\(292\) 0 0
\(293\) −16.0000 −0.934730 −0.467365 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) 3.00000 5.19615i 0.174078 0.301511i
\(298\) 0 0
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) −0.500000 + 2.59808i −0.0288195 + 0.149751i
\(302\) 0 0
\(303\) −5.00000 8.66025i −0.287242 0.497519i
\(304\) 0 0
\(305\) 7.00000 12.1244i 0.400819 0.694239i
\(306\) 0 0
\(307\) −3.00000 −0.171219 −0.0856095 0.996329i \(-0.527284\pi\)
−0.0856095 + 0.996329i \(0.527284\pi\)
\(308\) 0 0
\(309\) −19.0000 −1.08087
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) −5.50000 9.52628i −0.310878 0.538457i 0.667674 0.744453i \(-0.267290\pi\)
−0.978553 + 0.205996i \(0.933957\pi\)
\(314\) 0 0
\(315\) 2.00000 + 1.73205i 0.112687 + 0.0975900i
\(316\) 0 0
\(317\) −10.0000 17.3205i −0.561656 0.972817i −0.997352 0.0727229i \(-0.976831\pi\)
0.435696 0.900094i \(-0.356502\pi\)
\(318\) 0 0
\(319\) 24.0000 41.5692i 1.34374 2.32743i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) 0 0
\(327\) −7.50000 12.9904i −0.414751 0.718370i
\(328\) 0 0
\(329\) 5.00000 1.73205i 0.275659 0.0954911i
\(330\) 0 0
\(331\) −4.50000 7.79423i −0.247342 0.428410i 0.715445 0.698669i \(-0.246224\pi\)
−0.962788 + 0.270259i \(0.912891\pi\)
\(332\) 0 0
\(333\) −3.50000 + 6.06218i −0.191799 + 0.332205i
\(334\) 0 0
\(335\) −7.00000 −0.382451
\(336\) 0 0
\(337\) 25.0000 1.36184 0.680918 0.732359i \(-0.261581\pi\)
0.680918 + 0.732359i \(0.261581\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 2.00000 + 3.46410i 0.107676 + 0.186501i
\(346\) 0 0
\(347\) 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i \(-0.692036\pi\)
0.996826 + 0.0796169i \(0.0253697\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 3.00000 0.160128
\(352\) 0 0
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 0 0
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) 0 0
\(357\) −10.0000 + 3.46410i −0.529256 + 0.183340i
\(358\) 0 0
\(359\) −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) −25.0000 −1.31216
\(364\) 0 0
\(365\) 1.00000 0.0523424
\(366\) 0 0
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) 0 0
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 0 0
\(371\) 8.00000 + 6.92820i 0.415339 + 0.359694i
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) 0 0
\(381\) −2.50000 + 4.33013i −0.128079 + 0.221839i
\(382\) 0 0
\(383\) 14.0000 + 24.2487i 0.715367 + 1.23905i 0.962818 + 0.270151i \(0.0870736\pi\)
−0.247451 + 0.968900i \(0.579593\pi\)
\(384\) 0 0
\(385\) 3.00000 15.5885i 0.152894 0.794461i
\(386\) 0 0
\(387\) 0.500000 + 0.866025i 0.0254164 + 0.0440225i
\(388\) 0 0
\(389\) −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
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 0 0
\(395\) −0.500000 + 0.866025i −0.0251577 + 0.0435745i
\(396\) 0 0
\(397\) 18.5000 + 32.0429i 0.928488 + 1.60819i 0.785853 + 0.618414i \(0.212224\pi\)
0.142636 + 0.989775i \(0.454442\pi\)
\(398\) 0 0
\(399\) 0.500000 2.59808i 0.0250313 0.130066i
\(400\) 0 0
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 0 0
\(403\) −1.50000 + 2.59808i −0.0747203 + 0.129419i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 42.0000 2.08186
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 0 0
\(411\) 4.00000 + 6.92820i 0.197305 + 0.341743i
\(412\) 0 0
\(413\) 16.0000 + 13.8564i 0.787309 + 0.681829i
\(414\) 0 0
\(415\) 1.00000 + 1.73205i 0.0490881 + 0.0850230i
\(416\) 0 0
\(417\) −10.5000 + 18.1865i −0.514187 + 0.890598i
\(418\) 0 0
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) 0 0
\(423\) 1.00000 1.73205i 0.0486217 0.0842152i
\(424\) 0 0
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 35.0000 12.1244i 1.69377 0.586739i
\(428\) 0 0
\(429\) −9.00000 15.5885i −0.434524 0.752618i
\(430\) 0 0
\(431\) −1.00000 + 1.73205i −0.0481683 + 0.0834300i −0.889104 0.457705i \(-0.848672\pi\)
0.840936 + 0.541135i \(0.182005\pi\)
\(432\) 0 0
\(433\) −5.00000 −0.240285 −0.120142 0.992757i \(-0.538335\pi\)
−0.120142 + 0.992757i \(0.538335\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) 2.00000 3.46410i 0.0956730 0.165710i
\(438\) 0 0
\(439\) 8.00000 + 13.8564i 0.381819 + 0.661330i 0.991322 0.131453i \(-0.0419644\pi\)
−0.609503 + 0.792784i \(0.708631\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) 0 0
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) 0 0
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 0 0
\(455\) 7.50000 2.59808i 0.351605 0.121800i
\(456\) 0 0
\(457\) 7.50000 + 12.9904i 0.350835 + 0.607664i 0.986396 0.164386i \(-0.0525644\pi\)
−0.635561 + 0.772051i \(0.719231\pi\)
\(458\) 0 0
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) −8.00000 −0.372597 −0.186299 0.982493i \(-0.559649\pi\)
−0.186299 + 0.982493i \(0.559649\pi\)
\(462\) 0 0
\(463\) −3.00000 −0.139422 −0.0697109 0.997567i \(-0.522208\pi\)
−0.0697109 + 0.997567i \(0.522208\pi\)
\(464\) 0 0
\(465\) −0.500000 + 0.866025i −0.0231869 + 0.0401610i
\(466\) 0 0
\(467\) 11.0000 + 19.0526i 0.509019 + 0.881647i 0.999945 + 0.0104461i \(0.00332515\pi\)
−0.490926 + 0.871201i \(0.663342\pi\)
\(468\) 0 0
\(469\) −14.0000 12.1244i −0.646460 0.559851i
\(470\) 0 0
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) 0 0
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 4.00000 0.183147
\(478\) 0 0
\(479\) −2.00000 + 3.46410i −0.0913823 + 0.158279i −0.908093 0.418769i \(-0.862462\pi\)
0.816711 + 0.577047i \(0.195795\pi\)
\(480\) 0 0
\(481\) 10.5000 + 18.1865i 0.478759 + 0.829235i
\(482\) 0 0
\(483\) −2.00000 + 10.3923i −0.0910032 + 0.472866i
\(484\) 0 0
\(485\) 3.00000 + 5.19615i 0.136223 + 0.235945i
\(486\) 0 0
\(487\) −6.50000 + 11.2583i −0.294543 + 0.510164i −0.974879 0.222737i \(-0.928501\pi\)
0.680335 + 0.732901i \(0.261834\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −16.0000 + 27.7128i −0.720604 + 1.24812i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 0 0
\(497\) −3.00000 + 15.5885i −0.134568 + 0.699238i
\(498\) 0 0
\(499\) 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i \(0.0581915\pi\)
−0.334227 + 0.942493i \(0.608475\pi\)
\(500\) 0 0
\(501\) 5.00000 8.66025i 0.223384 0.386912i
\(502\) 0 0
\(503\) 2.00000 0.0891756 0.0445878 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) −2.00000 + 3.46410i −0.0888231 + 0.153846i
\(508\) 0 0
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 0 0
\(511\) 2.00000 + 1.73205i 0.0884748 + 0.0766214i
\(512\) 0 0
\(513\) −0.500000 0.866025i −0.0220755 0.0382360i
\(514\) 0 0
\(515\) −9.50000 + 16.4545i −0.418620 + 0.725071i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −2.00000 + 3.46410i −0.0876216 + 0.151765i −0.906505 0.422194i \(-0.861260\pi\)
0.818884 + 0.573959i \(0.194593\pi\)
\(522\) 0 0
\(523\) 5.50000 + 9.52628i 0.240498 + 0.416555i 0.960856 0.277047i \(-0.0893559\pi\)
−0.720358 + 0.693602i \(0.756023\pi\)
\(524\) 0 0
\(525\) 2.50000 0.866025i 0.109109 0.0377964i
\(526\) 0 0
\(527\) −2.00000 3.46410i −0.0871214 0.150899i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) 0 0
\(537\) −9.00000 15.5885i −0.388379 0.672692i
\(538\) 0 0
\(539\) 33.0000 25.9808i 1.42141 1.11907i
\(540\) 0 0
\(541\) 1.50000 + 2.59808i 0.0644900 + 0.111700i 0.896468 0.443109i \(-0.146125\pi\)
−0.831978 + 0.554809i \(0.812791\pi\)
\(542\) 0 0
\(543\) 6.50000 11.2583i 0.278942 0.483141i
\(544\) 0 0
\(545\) −15.0000 −0.642529
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 0 0
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) 0 0
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) 0 0
\(553\) −2.50000 + 0.866025i −0.106311 + 0.0368271i
\(554\) 0 0
\(555\) 3.50000 + 6.06218i 0.148567 + 0.257325i
\(556\) 0 0
\(557\) 5.00000 8.66025i 0.211857 0.366947i −0.740439 0.672124i \(-0.765382\pi\)
0.952296 + 0.305177i \(0.0987156\pi\)
\(558\) 0 0
\(559\) 3.00000 0.126886
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 0 0
\(563\) −13.0000 + 22.5167i −0.547885 + 0.948964i 0.450535 + 0.892759i \(0.351233\pi\)
−0.998419 + 0.0562051i \(0.982100\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −1.50000 + 2.59808i −0.0627730 + 0.108726i −0.895704 0.444651i \(-0.853328\pi\)
0.832931 + 0.553377i \(0.186661\pi\)
\(572\) 0 0
\(573\) 10.0000 0.417756
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 14.5000 25.1147i 0.603643 1.04554i −0.388621 0.921397i \(-0.627049\pi\)
0.992264 0.124143i \(-0.0396180\pi\)
\(578\) 0 0
\(579\) −4.50000 7.79423i −0.187014 0.323917i
\(580\) 0 0
\(581\) −1.00000 + 5.19615i −0.0414870 + 0.215573i
\(582\) 0 0
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) 0 0
\(585\) 1.50000 2.59808i 0.0620174 0.107417i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 1.00000 0.0412043
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 0 0
\(593\) 9.00000 + 15.5885i 0.369586 + 0.640141i 0.989501 0.144528i \(-0.0461663\pi\)
−0.619915 + 0.784669i \(0.712833\pi\)
\(594\) 0 0
\(595\) −2.00000 + 10.3923i −0.0819920 + 0.426043i
\(596\) 0 0
\(597\) −4.00000 6.92820i −0.163709 0.283552i
\(598\) 0 0
\(599\) −2.00000 + 3.46410i −0.0817178 + 0.141539i −0.903988 0.427558i \(-0.859374\pi\)
0.822270 + 0.569097i \(0.192707\pi\)
\(600\) 0 0
\(601\) −33.0000 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(602\) 0 0
\(603\) −7.00000 −0.285062
\(604\) 0 0
\(605\) −12.5000 + 21.6506i −0.508197 + 0.880223i
\(606\) 0 0
\(607\) 17.5000 + 30.3109i 0.710303 + 1.23028i 0.964743 + 0.263193i \(0.0847754\pi\)
−0.254440 + 0.967088i \(0.581891\pi\)
\(608\) 0 0
\(609\) 16.0000 + 13.8564i 0.648353 + 0.561490i
\(610\) 0 0
\(611\) −3.00000 5.19615i −0.121367 0.210214i
\(612\) 0 0
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 0 0
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 1.50000 2.59808i 0.0602901 0.104425i −0.834305 0.551303i \(-0.814131\pi\)
0.894595 + 0.446878i \(0.147464\pi\)
\(620\) 0 0
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) 0 0
\(623\) 30.0000 10.3923i 1.20192 0.416359i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) 0 0
\(629\) −28.0000 −1.11643
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 0 0
\(633\) 10.0000 17.3205i 0.397464 0.688428i
\(634\) 0 0
\(635\) 2.50000 + 4.33013i 0.0992095 + 0.171836i
\(636\) 0 0
\(637\) 19.5000 + 7.79423i 0.772618 + 0.308819i
\(638\) 0 0
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0 0
\(641\) −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 0 0
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 0 0
\(645\) 1.00000 0.0393750
\(646\) 0 0
\(647\) 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i \(-0.632575\pi\)
0.994270 0.106897i \(-0.0340916\pi\)
\(648\) 0 0
\(649\) −24.0000 41.5692i −0.942082 1.63173i
\(650\) 0 0
\(651\) −2.50000 + 0.866025i −0.0979827 + 0.0339422i
\(652\) 0 0
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) 0 0
\(655\) 1.00000 1.73205i 0.0390732 0.0676768i
\(656\) 0 0
\(657\) 1.00000 0.0390137
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i \(-0.980947\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(662\) 0 0
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 0 0
\(665\) −2.00000 1.73205i −0.0775567 0.0671660i
\(666\) 0 0
\(667\) 16.0000 + 27.7128i 0.619522 + 1.07304i
\(668\) 0 0
\(669\) 12.0000 20.7846i 0.463947 0.803579i
\(670\) 0 0
\(671\) −84.0000 −3.24278
\(672\) 0 0
\(673\) −37.0000 −1.42625 −0.713123 0.701039i \(-0.752720\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) 0 0
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 0 0
\(677\) −8.00000 13.8564i −0.307465 0.532545i 0.670342 0.742052i \(-0.266147\pi\)
−0.977807 + 0.209507i \(0.932814\pi\)
\(678\) 0 0
\(679\) −3.00000 + 15.5885i −0.115129 + 0.598230i
\(680\) 0 0
\(681\) 5.00000 + 8.66025i 0.191600 + 0.331862i
\(682\) 0 0
\(683\) −24.0000 + 41.5692i −0.918334 + 1.59060i −0.116390 + 0.993204i \(0.537132\pi\)
−0.801945 + 0.597398i \(0.796201\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) −13.0000 −0.495981
\(688\) 0 0
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 13.5000 + 23.3827i 0.513564 + 0.889519i 0.999876 + 0.0157341i \(0.00500851\pi\)
−0.486312 + 0.873785i \(0.661658\pi\)
\(692\) 0 0
\(693\) 3.00000 15.5885i 0.113961 0.592157i
\(694\) 0 0
\(695\) 10.5000 + 18.1865i 0.398288 + 0.689855i
\(696\) 0 0
\(697\) −12.0000 + 20.7846i −0.454532 + 0.787273i
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) 0 0
\(703\) 3.50000 6.06218i 0.132005 0.228639i
\(704\) 0 0
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) 0 0
\(707\) −20.0000 17.3205i −0.752177 0.651405i
\(708\) 0 0
\(709\) 13.0000 + 22.5167i 0.488225 + 0.845631i 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) 0 0
\(711\) −0.500000 + 0.866025i −0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 0 0
\(717\) −7.00000 + 12.1244i −0.261420 + 0.452792i
\(718\) 0 0
\(719\) −17.0000 29.4449i −0.633993 1.09811i −0.986728 0.162385i \(-0.948081\pi\)
0.352735 0.935723i \(-0.385252\pi\)
\(720\) 0 0
\(721\) −47.5000 + 16.4545i −1.76899 + 0.612797i
\(722\) 0 0
\(723\) −9.00000 15.5885i −0.334714 0.579741i
\(724\) 0 0
\(725\) 4.00000 6.92820i 0.148556 0.257307i
\(726\) 0 0
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.00000 + 3.46410i −0.0739727 + 0.128124i
\(732\) 0 0
\(733\) 21.5000 + 37.2391i 0.794121 + 1.37546i 0.923396 + 0.383849i \(0.125402\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) 0 0
\(735\) 6.50000 + 2.59808i 0.239756 + 0.0958315i
\(736\) 0 0
\(737\) 21.0000 + 36.3731i 0.773545 + 1.33982i
\(738\) 0 0
\(739\) 20.5000 35.5070i 0.754105 1.30615i −0.191714 0.981451i \(-0.561404\pi\)
0.945818 0.324697i \(-0.105262\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 0 0
\(747\) 1.00000 + 1.73205i 0.0365881 + 0.0633724i
\(748\) 0 0
\(749\) 30.0000 10.3923i 1.09618 0.379727i
\(750\) 0 0
\(751\) 14.5000 + 25.1147i 0.529113 + 0.916450i 0.999424 + 0.0339490i \(0.0108084\pi\)
−0.470311 + 0.882501i \(0.655858\pi\)
\(752\) 0 0
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 12.0000 20.7846i 0.435572 0.754434i
\(760\) 0 0
\(761\) 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 0 0
\(763\) −30.0000 25.9808i −1.08607 0.940567i
\(764\) 0 0
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 0 0
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) 0 0
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 0 0
\(775\) 0.500000 + 0.866025i 0.0179605 + 0.0311086i
\(776\) 0 0
\(777\) −3.50000 + 18.1865i −0.125562 + 0.652438i
\(778\) 0 0
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i \(0.359855\pi\)
−0.996531 + 0.0832226i \(0.973479\pi\)
\(788\) 0 0
\(789\) −2.00000 3.46410i −0.0712019 0.123325i
\(790\) 0 0
\(791\) −3.00000 + 15.5885i −0.106668 + 0.554262i
\(792\) 0 0
\(793\) −21.0000 36.3731i −0.745732 1.29165i
\(794\) 0 0
\(795\) 2.00000 3.46410i 0.0709327 0.122859i
\(796\) 0 0
\(797\) −36.0000 −1.27519 −0.637593 0.770374i \(-0.720070\pi\)
−0.637593 + 0.770374i \(0.720070\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 6.00000 10.3923i 0.212000 0.367194i
\(802\) 0 0
\(803\) −3.00000 5.19615i −0.105868 0.183368i
\(804\) 0 0
\(805\) 8.00000 + 6.92820i 0.281963 + 0.244187i
\(806\) 0 0
\(807\) −5.00000 8.66025i −0.176008 0.304855i
\(808\) 0 0
\(809\) 21.0000 36.3731i 0.738321 1.27881i −0.214930