Properties

Label 294.2.e.b.79.1
Level $294$
Weight $2$
Character 294.79
Analytic conductor $2.348$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.34760181943\)
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 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.2.e.b.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +1.00000 q^{27} -5.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.50000 + 2.59808i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(4.00000 + 6.92820i) q^{38} +(0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} -4.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} +(-0.500000 + 0.866025i) q^{54} -5.00000 q^{55} -8.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} -4.00000 q^{69} +2.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +(2.00000 - 3.46410i) q^{75} -8.00000 q^{76} +(-1.50000 + 2.59808i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(2.50000 + 4.33013i) q^{87} +(-2.50000 - 4.33013i) q^{88} +(-3.00000 + 5.19615i) q^{89} -1.00000 q^{90} -4.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} -7.00000 q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} + 2q^{6} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} + 2q^{6} + 2q^{8} - q^{9} + q^{10} - 5q^{11} - q^{12} - 2q^{15} - q^{16} - 4q^{17} - q^{18} + 8q^{19} - 2q^{20} + 10q^{22} + 4q^{23} - q^{24} + 4q^{25} + 2q^{27} - 10q^{29} + q^{30} + 3q^{31} - q^{32} - 5q^{33} + 8q^{34} + 2q^{36} + 4q^{37} + 8q^{38} + q^{40} + 4q^{43} - 5q^{44} + q^{45} + 4q^{46} - 6q^{47} + 2q^{48} - 8q^{50} - 4q^{51} + 9q^{53} - q^{54} - 10q^{55} - 16q^{57} + 5q^{58} - 11q^{59} + q^{60} - 6q^{61} - 6q^{62} + 2q^{64} - 5q^{66} + 2q^{67} - 4q^{68} - 8q^{69} + 4q^{71} - q^{72} + 10q^{73} + 4q^{74} + 4q^{75} - 16q^{76} - 3q^{79} + q^{80} - q^{81} + 14q^{83} - 8q^{85} - 2q^{86} + 5q^{87} - 5q^{88} - 6q^{89} - 2q^{90} - 8q^{92} + 3q^{93} - 6q^{94} - 8q^{95} - q^{96} - 14q^{97} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 4.00000 6.92820i 0.917663 1.58944i 0.114708 0.993399i \(-0.463407\pi\)
0.802955 0.596040i \(-0.203260\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 4.00000 + 6.92820i 0.648886 + 1.12390i
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) −4.00000 −0.565685
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) −5.50000 9.52628i −0.716039 1.24022i −0.962557 0.271078i \(-0.912620\pi\)
0.246518 0.969138i \(-0.420713\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −3.00000 −0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.50000 4.33013i −0.307729 0.533002i
\(67\) 1.00000 + 1.73205i 0.122169 + 0.211604i 0.920623 0.390453i \(-0.127682\pi\)
−0.798454 + 0.602056i \(0.794348\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) 0 0
\(79\) −1.50000 + 2.59808i −0.168763 + 0.292306i −0.937985 0.346675i \(-0.887311\pi\)
0.769222 + 0.638982i \(0.220644\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 2.50000 + 4.33013i 0.268028 + 0.464238i
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 2.50000 4.33013i 0.238366 0.412861i
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 4.00000 6.92820i 0.374634 0.648886i
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) 2.50000 + 4.33013i 0.232119 + 0.402042i
\(117\) 0 0
\(118\) 11.0000 1.01263
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −3.00000 5.19615i −0.271607 0.470438i
\(123\) 0 0
\(124\) 1.50000 2.59808i 0.134704 0.233314i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) 0 0
\(131\) 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i \(-0.819423\pi\)
0.887041 + 0.461690i \(0.152757\pi\)
\(132\) 5.00000 0.435194
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 2.00000 3.46410i 0.170251 0.294884i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −1.00000 + 1.73205i −0.0839181 + 0.145350i
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −2.50000 + 4.33013i −0.207614 + 0.359597i
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) −9.50000 16.4545i −0.773099 1.33905i −0.935857 0.352381i \(-0.885372\pi\)
0.162758 0.986666i \(-0.447961\pi\)
\(152\) 4.00000 6.92820i 0.324443 0.561951i
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) −1.50000 2.59808i −0.119334 0.206692i
\(159\) 4.50000 7.79423i 0.356873 0.618123i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 2.50000 + 4.33013i 0.194625 + 0.337100i
\(166\) −3.50000 + 6.06218i −0.271653 + 0.470516i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 4.00000 + 6.92820i 0.305888 + 0.529813i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 11.0000 19.0526i 0.836315 1.44854i −0.0566411 0.998395i \(-0.518039\pi\)
0.892956 0.450145i \(-0.148628\pi\)
\(174\) −5.00000 −0.379049
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) −5.50000 + 9.52628i −0.413405 + 0.716039i
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) −10.0000 + 17.3205i −0.731272 + 1.26660i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −2.50000 + 4.33013i −0.177667 + 0.307729i
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 1.00000 1.73205i 0.0705346 0.122169i
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) 0 0
\(209\) −40.0000 −2.76686
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) −1.00000 1.73205i −0.0685189 0.118678i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 2.50000 + 4.33013i 0.168550 + 0.291937i
\(221\) 0 0
\(222\) 2.00000 3.46410i 0.134231 0.232495i
\(223\) 7.00000 0.468755 0.234377 0.972146i \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 4.00000 + 6.92820i 0.264906 + 0.458831i
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) 0 0
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −5.50000 + 9.52628i −0.358020 + 0.620108i
\(237\) 3.00000 0.194871
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i \(-0.868727\pi\)
0.110963 0.993825i \(-0.464606\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) −3.50000 6.06218i −0.221803 0.384175i
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) −4.50000 + 7.79423i −0.282355 + 0.489053i
\(255\) 2.00000 + 3.46410i 0.125245 + 0.216930i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 2.00000 0.124515
\(259\) 0 0
\(260\) 0 0
\(261\) 2.50000 4.33013i 0.154746 0.268028i
\(262\) 0.500000 + 0.866025i 0.0308901 + 0.0535032i
\(263\) 15.0000 + 25.9808i 0.924940 + 1.60204i 0.791658 + 0.610964i \(0.209218\pi\)
0.133281 + 0.991078i \(0.457449\pi\)
\(264\) −2.50000 + 4.33013i −0.153864 + 0.266501i
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 1.00000 1.73205i 0.0610847 0.105802i
\(269\) 15.5000 + 26.8468i 0.945052 + 1.63688i 0.755648 + 0.654978i \(0.227322\pi\)
0.189404 + 0.981899i \(0.439344\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 7.50000 12.9904i 0.455593 0.789109i −0.543130 0.839649i \(-0.682761\pi\)
0.998722 + 0.0505395i \(0.0160941\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 10.0000 17.3205i 0.603023 1.04447i
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) −7.00000 + 12.1244i −0.419832 + 0.727171i
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) −4.00000 + 6.92820i −0.236940 + 0.410391i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −2.50000 4.33013i −0.146805 0.254274i
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 0 0
\(295\) −11.0000 −0.640445
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 19.0000 1.09333
\(303\) 5.00000 8.66025i 0.287242 0.497519i
\(304\) 4.00000 + 6.92820i 0.229416 + 0.397360i
\(305\) 3.00000 + 5.19615i 0.171780 + 0.297531i
\(306\) −2.00000 + 3.46410i −0.114332 + 0.198030i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) −16.0000 27.7128i −0.907277 1.57145i −0.817832 0.575458i \(-0.804824\pi\)
−0.0894452 0.995992i \(-0.528509\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) 4.50000 + 7.79423i 0.252347 + 0.437079i
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 3.00000 0.167444
\(322\) 0 0
\(323\) −32.0000 −1.78053
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 0 0
\(329\) 0 0
\(330\) −5.00000 −0.275241
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −3.50000 6.06218i −0.192087 0.332705i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) −7.00000 + 12.1244i −0.383023 + 0.663415i
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) −8.00000 13.8564i −0.434500 0.752577i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) −8.00000 −0.432590
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) 11.0000 + 19.0526i 0.591364 + 1.02427i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 2.50000 4.33013i 0.134014 0.232119i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) −5.50000 9.52628i −0.292322 0.506316i
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) 8.50000 + 14.7224i 0.443696 + 0.768505i 0.997960 0.0638362i \(-0.0203335\pi\)
−0.554264 + 0.832341i \(0.687000\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 0 0
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) −3.00000 −0.155543
\(373\) 16.0000 27.7128i 0.828449 1.43492i −0.0708063 0.997490i \(-0.522557\pi\)
0.899255 0.437425i \(-0.144109\pi\)
\(374\) −10.0000 17.3205i −0.517088 0.895622i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −4.00000 + 6.92820i −0.205196 + 0.355409i
\(381\) −4.50000 7.79423i −0.230542 0.399310i
\(382\) −12.0000 20.7846i −0.613973 1.06343i
\(383\) −17.0000 + 29.4449i −0.868659 + 1.50456i −0.00529229 + 0.999986i \(0.501685\pi\)
−0.863367 + 0.504576i \(0.831649\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) 3.50000 + 6.06218i 0.177686 + 0.307760i
\(389\) 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i \(-0.150521\pi\)
−0.839561 + 0.543266i \(0.817187\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) −1.00000 −0.0504433
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 1.50000 + 2.59808i 0.0754732 + 0.130723i
\(396\) −2.50000 4.33013i −0.125630 0.217597i
\(397\) 18.0000 31.1769i 0.903394 1.56472i 0.0803356 0.996768i \(-0.474401\pi\)
0.823058 0.567957i \(-0.192266\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 1.00000 + 1.73205i 0.0498755 + 0.0863868i
\(403\) 0 0
\(404\) 5.00000 8.66025i 0.248759 0.430864i
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) 1.00000 1.73205i 0.0493264 0.0854358i
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 3.50000 6.06218i 0.171808 0.297581i
\(416\) 0 0
\(417\) −7.00000 12.1244i −0.342791 0.593732i
\(418\) 20.0000 34.6410i 0.978232 1.69435i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) −1.00000 + 1.73205i −0.0486792 + 0.0843149i
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 8.00000 13.8564i 0.388057 0.672134i
\(426\) 2.00000 0.0969003
\(427\) 0 0
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) 1.00000 + 1.73205i 0.0482243 + 0.0835269i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 5.00000 0.239732
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −16.0000 27.7128i −0.765384 1.32568i
\(438\) 5.00000 + 8.66025i 0.238909 + 0.413803i
\(439\) 7.50000 12.9904i 0.357955 0.619997i −0.629664 0.776868i \(-0.716807\pi\)
0.987619 + 0.156871i \(0.0501406\pi\)
\(440\) −5.00000 −0.238366
\(441\) 0 0
\(442\) 0 0
\(443\) −8.50000 + 14.7224i −0.403847 + 0.699484i −0.994187 0.107671i \(-0.965661\pi\)
0.590339 + 0.807155i \(0.298994\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −3.50000 + 6.06218i −0.165730 + 0.287052i
\(447\) −18.0000 −0.851371
\(448\) 0 0
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 2.00000 3.46410i 0.0942809 0.163299i
\(451\) 0 0
\(452\) −8.00000 13.8564i −0.376288 0.651751i
\(453\) −9.50000 + 16.4545i −0.446349 + 0.773099i
\(454\) −3.00000 −0.140797
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) −10.0000 17.3205i −0.467269 0.809334i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) −2.00000 + 3.46410i −0.0932505 + 0.161515i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 2.50000 4.33013i 0.116060 0.201021i
\(465\) −1.50000 2.59808i −0.0695608 0.120483i
\(466\) 2.00000 + 3.46410i 0.0926482 + 0.160471i
\(467\) −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −6.00000 −0.276759
\(471\) −2.00000 + 3.46410i −0.0921551 + 0.159617i
\(472\) −5.50000 9.52628i −0.253158 0.438483i
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) −1.50000 + 2.59808i −0.0688973 + 0.119334i
\(475\) 32.0000 1.46826
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 19.0000 + 32.9090i 0.868132 + 1.50365i 0.863903 + 0.503658i \(0.168013\pi\)
0.00422900 + 0.999991i \(0.498654\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 0 0
\(482\) 25.0000 1.13872
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) −3.50000 + 6.06218i −0.158927 + 0.275269i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −2.50000 4.33013i −0.113286 0.196217i 0.803807 0.594890i \(-0.202804\pi\)
−0.917093 + 0.398673i \(0.869471\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 9.00000 0.406164 0.203082 0.979162i \(-0.434904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(492\) 0 0
\(493\) 10.0000 + 17.3205i 0.450377 + 0.780076i
\(494\) 0 0
\(495\) 2.50000 4.33013i 0.112367 0.194625i
\(496\) −3.00000 −0.134704
\(497\) 0 0
\(498\) 7.00000 0.313678
\(499\) −5.00000 + 8.66025i −0.223831 + 0.387686i −0.955968 0.293471i \(-0.905190\pi\)
0.732137 + 0.681157i \(0.238523\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) −7.00000 12.1244i −0.312737 0.541676i
\(502\) 10.5000 18.1865i 0.468638 0.811705i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 10.0000 17.3205i 0.444554 0.769991i
\(507\) 6.50000 + 11.2583i 0.288675 + 0.500000i
\(508\) −4.50000 7.79423i −0.199655 0.345813i
\(509\) 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i \(-0.725464\pi\)
0.982988 + 0.183669i \(0.0587976\pi\)
\(510\) −4.00000 −0.177123
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 4.00000 6.92820i 0.176604 0.305888i
\(514\) −3.00000 5.19615i −0.132324 0.229192i
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 30.0000 1.31940
\(518\) 0 0
\(519\) −22.0000 −0.965693
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 2.50000 + 4.33013i 0.109422 + 0.189525i
\(523\) 4.00000 6.92820i 0.174908 0.302949i −0.765222 0.643767i \(-0.777371\pi\)
0.940129 + 0.340818i \(0.110704\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) −2.50000 4.33013i −0.108799 0.188445i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 11.0000 0.477359
\(532\) 0 0
\(533\) 0 0
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 1.50000 + 2.59808i 0.0648507 + 0.112325i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −31.0000 −1.33650
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i \(-0.706865\pi\)
0.992036 + 0.125952i \(0.0401986\pi\)
\(542\) 7.50000 + 12.9904i 0.322153 + 0.557985i
\(543\) 0 0
\(544\) −2.00000 + 3.46410i −0.0857493 + 0.148522i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) −3.00000 5.19615i −0.128037 0.221766i
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) −20.0000 + 34.6410i −0.852029 + 1.47576i
\(552\) −4.00000 −0.170251
\(553\) 0 0
\(554\) −16.0000 −0.679775
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i \(-0.00465919\pi\)
−0.512622 + 0.858614i \(0.671326\pi\)
\(558\) 1.50000 2.59808i 0.0635001 0.109985i
\(559\) 0 0
\(560\) 0 0
\(561\) 20.0000 0.844401
\(562\) −1.00000 + 1.73205i −0.0421825 + 0.0730622i
\(563\) 8.50000 + 14.7224i 0.358232 + 0.620477i 0.987666 0.156578i \(-0.0500463\pi\)
−0.629433 + 0.777055i \(0.716713\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 8.00000 13.8564i 0.336563 0.582943i
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) 2.00000 0.0839181
\(569\) −12.0000 + 20.7846i −0.503066 + 0.871336i 0.496928 + 0.867792i \(0.334461\pi\)
−0.999994 + 0.00354413i \(0.998872\pi\)
\(570\) −4.00000 6.92820i −0.167542 0.290191i
\(571\) 15.0000 + 25.9808i 0.627730 + 1.08726i 0.988006 + 0.154415i \(0.0493493\pi\)
−0.360276 + 0.932846i \(0.617317\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 16.0000 0.667246
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −2.50000 + 4.33013i −0.103896 + 0.179954i
\(580\) 5.00000 0.207614
\(581\) 0 0
\(582\) −7.00000 −0.290159
\(583\) 22.5000 38.9711i 0.931855 1.61402i
\(584\) 5.00000 + 8.66025i 0.206901 + 0.358364i
\(585\) 0 0
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) −35.0000 −1.44460 −0.722302 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 5.50000 9.52628i 0.226431 0.392191i
\(591\) −1.00000 1.73205i −0.0411345 0.0712470i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) −2.00000 + 3.46410i −0.0818546 + 0.141776i
\(598\) 0 0
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) −35.0000 −1.42768 −0.713840 0.700309i \(-0.753046\pi\)
−0.713840 + 0.700309i \(0.753046\pi\)
\(602\) 0 0
\(603\) −2.00000 −0.0814463
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 5.00000 + 8.66025i 0.203111 + 0.351799i
\(607\) −13.5000 + 23.3827i −0.547948 + 0.949074i 0.450467 + 0.892793i \(0.351258\pi\)
−0.998415 + 0.0562808i \(0.982076\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) −6.00000 −0.242933
\(611\) 0 0
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) −6.00000 10.3923i −0.242338 0.419741i 0.719042 0.694967i \(-0.244581\pi\)
−0.961380 + 0.275225i \(0.911248\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 4.00000 6.92820i 0.160904 0.278693i
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) −1.50000 2.59808i −0.0602414 0.104341i
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 32.0000 1.28308
\(623\) 0 0
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) 20.0000 + 34.6410i 0.798723 + 1.38343i
\(628\) −2.00000 + 3.46410i −0.0798087 + 0.138233i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) −1.50000 + 2.59808i −0.0596668 + 0.103346i
\(633\) −1.00000 1.73205i −0.0397464 0.0688428i
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) 4.50000 7.79423i 0.178577 0.309305i
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) −25.0000 −0.989759
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) −1.50000 + 2.59808i −0.0592003 + 0.102538i
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 0 0
\(645\) −2.00000 −0.0787499
\(646\) 16.0000 27.7128i 0.629512 1.09035i
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −27.5000 + 47.6314i −1.07947 + 1.86970i
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) −0.500000 0.866025i −0.0195366 0.0338384i
\(656\) 0 0
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 2.50000 4.33013i 0.0973124 0.168550i
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 2.00000 + 3.46410i 0.0777322 + 0.134636i
\(663\) 0 0
\(664\) 7.00000 0.271653
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −10.0000 + 17.3205i −0.387202 + 0.670653i
\(668\) −7.00000 12.1244i −0.270838 0.469105i
\(669\) −3.50000 6.06218i −0.135318 0.234377i
\(670\) −1.00000 + 1.73205i −0.0386334 + 0.0669150i
\(671\) 30.0000 1.15814
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −4.50000 + 7.79423i −0.173334 + 0.300222i
\(675\) 2.00000 + 3.46410i 0.0769800 + 0.133333i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 16.0000 0.614476
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 1.50000 2.59808i 0.0574801 0.0995585i
\(682\) 7.50000 + 12.9904i 0.287190 + 0.497427i
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 4.00000 6.92820i 0.152944 0.264906i
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 20.0000 0.763048
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 0 0
\(690\) −2.00000 3.46410i −0.0761387 0.131876i
\(691\) 4.00000 6.92820i 0.152167 0.263561i −0.779857 0.625958i \(-0.784708\pi\)
0.932024 + 0.362397i \(0.118041\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 7.00000 12.1244i 0.265525 0.459903i
\(696\) 2.50000 + 4.33013i 0.0947623 + 0.164133i
\(697\) 0 0
\(698\) −7.00000 + 12.1244i −0.264954 + 0.458914i
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 0 0
\(703\) −16.0000 27.7128i −0.603451 1.04521i
\(704\) −2.50000 4.33013i −0.0942223 0.163198i
\(705\) 3.00000 5.19615i 0.112987 0.195698i
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 11.0000 0.413405
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 1.00000 + 1.73205i 0.0375293 + 0.0650027i
\(711\) −1.50000 2.59808i −0.0562544 0.0974355i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −5.00000 8.66025i −0.186598 0.323198i
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) 45.0000 1.67473
\(723\) −12.5000 + 21.6506i −0.464880 + 0.805196i
\(724\) 0 0
\(725\) −10.0000 17.3205i −0.371391 0.643268i
\(726\) −7.00000 + 12.1244i −0.259794 + 0.449977i
\(727\) −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
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) −3.00000 5.19615i −0.110883 0.192055i
\(733\) −3.00000 + 5.19615i −0.110808 + 0.191924i −0.916096 0.400959i \(-0.868677\pi\)
0.805289 + 0.592883i \(0.202010\pi\)
\(734\) −17.0000 −0.627481
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) 0 0
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) 0 0
\(742\) 0 0
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) 16.0000 + 27.7128i 0.585802 + 1.01464i
\(747\) −3.50000 + 6.06218i −0.128058 + 0.221803i
\(748\) 20.0000 0.731272
\(749\) 0 0
\(750\) 9.00000 0.328634
\(751\) −22.5000 + 38.9711i −0.821037 + 1.42208i 0.0838743 + 0.996476i \(0.473271\pi\)
−0.904911 + 0.425601i \(0.860063\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 10.5000 + 18.1865i 0.382641 + 0.662754i
\(754\) 0 0
\(755\) −19.0000 −0.691481
\(756\) 0 0
\(757\) −54.0000 −1.96266 −0.981332 0.192323i \(-0.938398\pi\)
−0.981332 + 0.192323i \(0.938398\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) 10.0000 + 17.3205i 0.362977 + 0.628695i
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) 4.00000 6.92820i 0.145000 0.251147i −0.784373 0.620289i \(-0.787015\pi\)
0.929373 + 0.369142i \(0.120348\pi\)
\(762\) 9.00000 0.326036
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) −17.0000 29.4449i −0.614235 1.06389i
\(767\) 0 0
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) 5.00000 + 8.66025i 0.179838 + 0.311488i 0.941825 0.336104i \(-0.109109\pi\)
−0.761987 + 0.647592i \(0.775776\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) −6.00000 + 10.3923i −0.215526 + 0.373303i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) −2.00000 −0.0717035
\(779\) 0 0
\(780\) 0 0
\(781\) −5.00000 8.66025i −0.178914 0.309888i
\(782\) 8.00000 13.8564i 0.286079 0.495504i
\(783\) −5.00000 −0.178685
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0.500000 0.866025i 0.0178344 0.0308901i
\(787\) −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i \(-0.270624\pi\)