Properties

Label 245.2.e.b.116.1
Level $245$
Weight $2$
Character 245.116
Analytic conductor $1.956$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.2.e.b.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} -5.00000 q^{13} -1.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} -2.00000 q^{20} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +4.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{39} +12.0000 q^{41} -10.0000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.00000 - 1.73205i) q^{45} +(4.50000 + 7.79423i) q^{47} -4.00000 q^{48} +(-1.50000 - 2.59808i) q^{51} +(-5.00000 + 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-1.00000 + 1.73205i) q^{60} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(1.00000 - 1.73205i) q^{73} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} -3.00000 q^{85} +(1.50000 - 2.59808i) q^{87} +(-6.00000 - 10.3923i) q^{89} +12.0000 q^{92} +(2.00000 + 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + 2q^{4} - q^{5} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} + 2q^{4} - q^{5} + 2q^{9} + 3q^{11} - 2q^{12} - 10q^{13} - 2q^{15} - 4q^{16} + 3q^{17} + 2q^{19} - 4q^{20} + 6q^{23} - q^{25} + 10q^{27} + 6q^{29} - 4q^{31} - 3q^{33} + 8q^{36} - 2q^{37} - 5q^{39} + 24q^{41} - 20q^{43} - 6q^{44} + 2q^{45} + 9q^{47} - 8q^{48} - 3q^{51} - 10q^{52} - 12q^{53} - 6q^{55} + 4q^{57} - 2q^{60} + 8q^{61} - 16q^{64} + 5q^{65} + 4q^{67} - 6q^{68} + 12q^{69} + 2q^{73} + q^{75} + 8q^{76} + q^{79} - 4q^{80} - q^{81} - 24q^{83} - 6q^{85} + 3q^{87} - 12q^{89} + 24q^{92} + 4q^{93} + 2q^{95} + 2q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) −1.00000 1.73205i −0.288675 0.500000i
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 4.00000 0.666667
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 0 0
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −3.00000 5.19615i −0.452267 0.783349i
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) −4.00000 −0.577350
\(49\) 0 0
\(50\) 0 0
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) −5.00000 + 8.66025i −0.693375 + 1.20096i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) −1.00000 + 1.73205i −0.129099 + 0.223607i
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 2.50000 + 4.33013i 0.310087 + 0.537086i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) −2.00000 + 3.46410i −0.223607 + 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) 0 0
\(89\) −6.00000 10.3923i −0.635999 1.10158i −0.986303 0.164946i \(-0.947255\pi\)
0.350304 0.936636i \(-0.386078\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 12.0000 1.25109
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 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
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 5.00000 8.66025i 0.481125 0.833333i
\(109\) 3.50000 6.06218i 0.335239 0.580651i −0.648292 0.761392i \(-0.724516\pi\)
0.983531 + 0.180741i \(0.0578495\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 3.00000 5.19615i 0.279751 0.484544i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) −5.00000 8.66025i −0.462250 0.800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 6.00000 10.3923i 0.541002 0.937043i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) 0 0
\(135\) −2.50000 4.33013i −0.215166 0.372678i
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) 0 0
\(143\) −7.50000 + 12.9904i −0.627182 + 1.08631i
\(144\) 4.00000 6.92820i 0.333333 0.577350i
\(145\) −1.50000 2.59808i −0.124568 0.215758i
\(146\) 0 0
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 5.00000 + 8.66025i 0.400320 + 0.693375i
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) 0 0
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 12.0000 20.7846i 0.937043 1.62301i
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 0 0
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) −10.0000 + 17.3205i −0.762493 + 1.32068i
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −12.0000 −0.904534
\(177\) 0 0
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) −2.00000 3.46410i −0.149071 0.258199i
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 18.0000 1.31278
\(189\) 0 0
\(190\) 0 0
\(191\) −4.50000 7.79423i −0.325609 0.563971i 0.656027 0.754738i \(-0.272236\pi\)
−0.981635 + 0.190767i \(0.938902\pi\)
\(192\) −4.00000 + 6.92820i −0.288675 + 0.500000i
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 0 0
\(195\) 5.00000 0.358057
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0 0
\(201\) −2.00000 3.46410i −0.141069 0.244339i
\(202\) 0 0
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 0 0
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 10.0000 + 17.3205i 0.693375 + 1.20096i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 12.0000 + 20.7846i 0.824163 + 1.42749i
\(213\) 0 0
\(214\) 0 0
\(215\) 5.00000 + 8.66025i 0.340997 + 0.590624i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) −3.00000 + 5.19615i −0.202260 + 0.350325i
\(221\) −7.50000 + 12.9904i −0.504505 + 0.873828i
\(222\) 0 0
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.0000 20.7846i −0.786146 1.36165i −0.928312 0.371802i \(-0.878740\pi\)
0.142166 0.989843i \(-0.454593\pi\)
\(234\) 0 0
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) 0 0
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) −21.0000 −1.35838 −0.679189 0.733964i \(-0.737668\pi\)
−0.679189 + 0.733964i \(0.737668\pi\)
\(240\) 2.00000 + 3.46410i 0.129099 + 0.223607i
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 16.0000 1.02430
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 0 0
\(255\) −1.50000 + 2.59808i −0.0939336 + 0.162698i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 10.0000 0.620174
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) −3.00000 + 5.19615i −0.184988 + 0.320408i −0.943572 0.331166i \(-0.892558\pi\)
0.758585 + 0.651575i \(0.225891\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −12.0000 −0.727607
\(273\) 0 0
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) −6.50000 + 11.2583i −0.386385 + 0.669238i −0.991960 0.126550i \(-0.959610\pi\)
0.605575 + 0.795788i \(0.292943\pi\)
\(284\) 0 0
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 7.50000 12.9904i 0.435194 0.753778i
\(298\) 0 0
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) 0 0
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) 4.00000 6.92820i 0.229416 0.397360i
\(305\) 4.00000 6.92820i 0.229039 0.396708i
\(306\) 0 0
\(307\) −11.0000 −0.627803 −0.313902 0.949456i \(-0.601636\pi\)
−0.313902 + 0.949456i \(0.601636\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) 0 0
\(313\) −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i \(-0.986235\pi\)
0.462093 0.886831i \(-0.347098\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 4.00000 + 6.92820i 0.223607 + 0.387298i
\(321\) −6.00000 −0.334887
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 2.50000 4.33013i 0.138675 0.240192i
\(326\) 0 0
\(327\) −3.50000 6.06218i −0.193550 0.335239i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) −12.0000 + 20.7846i −0.658586 + 1.14070i
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.00000 5.19615i −0.161515 0.279751i
\(346\) 0 0
\(347\) 9.00000 15.5885i 0.483145 0.836832i −0.516667 0.856186i \(-0.672828\pi\)
0.999813 + 0.0193540i \(0.00616095\pi\)
\(348\) −3.00000 5.19615i −0.160817 0.278543i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −25.0000 −1.33440
\(352\) 0 0
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −24.0000 −1.27200
\(357\) 0 0
\(358\) 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
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) 12.0000 20.7846i 0.625543 1.08347i
\(369\) 12.0000 + 20.7846i 0.624695 + 1.08200i
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) 0 0
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −10.0000 17.3205i −0.508329 0.880451i
\(388\) 1.00000 1.73205i 0.0507673 0.0879316i
\(389\) 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i \(-0.809102\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 0.500000 0.866025i 0.0251577 0.0435745i
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) −12.5000 21.6506i −0.627357 1.08661i −0.988080 0.153941i \(-0.950803\pi\)
0.360723 0.932673i \(-0.382530\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) 0 0
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 10.0000 0.492665
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 0 0
\(417\) −7.00000 + 12.1244i −0.342791 + 0.593732i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 0 0
\(423\) −9.00000 + 15.5885i −0.437595 + 0.757937i
\(424\) 0 0
\(425\) 1.50000 + 2.59808i 0.0727607 + 0.126025i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 7.50000 + 12.9904i 0.362103 + 0.627182i
\(430\) 0 0
\(431\) −10.5000 + 18.1865i −0.505767 + 0.876014i 0.494211 + 0.869342i \(0.335457\pi\)
−0.999978 + 0.00667224i \(0.997876\pi\)
\(432\) −10.0000 17.3205i −0.481125 0.833333i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) −3.00000 −0.143839
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −6.00000 + 10.3923i −0.287019 + 0.497131i
\(438\) 0 0
\(439\) 13.0000 + 22.5167i 0.620456 + 1.07466i 0.989401 + 0.145210i \(0.0463858\pi\)
−0.368945 + 0.929451i \(0.620281\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i \(-0.0260248\pi\)
−0.569057 + 0.822298i \(0.692691\pi\)
\(444\) −2.00000 + 3.46410i −0.0949158 + 0.164399i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) −0.500000 0.866025i −0.0234920 0.0406894i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.00000 6.92820i −0.187112 0.324088i 0.757174 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329125i \(0.893246\pi\)
\(458\) 0 0
\(459\) 7.50000 12.9904i 0.350070 0.606339i
\(460\) −6.00000 10.3923i −0.279751 0.484544i
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −6.00000 10.3923i −0.278543 0.482451i
\(465\) 2.00000 3.46410i 0.0927478 0.160644i
\(466\) 0 0
\(467\) 7.50000 + 12.9904i 0.347059 + 0.601123i 0.985726 0.168360i \(-0.0538472\pi\)
−0.638667 + 0.769483i \(0.720514\pi\)
\(468\) −20.0000 −0.924500
\(469\) 0 0
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) −15.0000 + 25.9808i −0.689701 + 1.19460i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) −24.0000 −1.09888
\(478\) 0 0
\(479\) −15.0000 + 25.9808i −0.685367 + 1.18709i 0.287954 + 0.957644i \(0.407025\pi\)
−0.973321 + 0.229447i \(0.926308\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 4.00000 0.181818
\(485\) −0.500000 0.866025i −0.0227038 0.0393242i
\(486\) 0 0
\(487\) −19.0000 + 32.9090i −0.860972 + 1.49125i 0.0100195 + 0.999950i \(0.496811\pi\)
−0.870992 + 0.491298i \(0.836523\pi\)
\(488\) 0 0
\(489\) −2.00000 −0.0904431
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) −12.0000 20.7846i −0.541002 0.937043i
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 16.0000 0.718421
\(497\) 0 0
\(498\) 0 0
\(499\) 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i \(0.0774314\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) 0 0
\(503\) −27.0000 −1.20387 −0.601935 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) −16.0000 + 27.7128i −0.709885 + 1.22956i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 5.00000 + 8.66025i 0.220755 + 0.382360i
\(514\) 0 0
\(515\) 2.50000 4.33013i 0.110163 0.190808i
\(516\) 10.0000 + 17.3205i 0.440225 + 0.762493i
\(517\) 27.0000 1.18746
\(518\) 0 0
\(519\) −9.00000 −0.395056
\(520\) 0 0
\(521\) −21.0000 + 36.3731i −0.920027 + 1.59353i −0.120656 + 0.992694i \(0.538500\pi\)
−0.799370 + 0.600839i \(0.794833\pi\)
\(522\) 0 0
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) −6.00000 + 10.3923i −0.261116 + 0.452267i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −60.0000 −2.59889
\(534\) 0 0
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) 0 0
\(540\) −10.0000 −0.430331
\(541\) −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 0 0
\(543\) −10.0000 + 17.3205i −0.429141 + 0.743294i
\(544\) 0 0
\(545\) −7.00000 −0.299847
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −12.0000 20.7846i −0.512615 0.887875i
\(549\) −8.00000 + 13.8564i −0.341432 + 0.591377i
\(550\) 0 0
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.00000 + 1.73205i 0.0424476 + 0.0735215i
\(556\) −14.0000 + 24.2487i −0.593732 + 1.02837i
\(557\) 12.0000 20.7846i 0.508456 0.880672i −0.491496 0.870880i \(-0.663550\pi\)
0.999952 0.00979220i \(-0.00311700\pi\)
\(558\) 0 0
\(559\) 50.0000 2.11477
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(564\) 9.00000 15.5885i 0.378968 0.656392i
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 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
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 15.0000 + 25.9808i 0.627182 + 1.08631i
\(573\) −9.00000 −0.375980
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) −8.00000 13.8564i −0.333333 0.577350i
\(577\) −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i \(-0.879879\pi\)
0.783930 + 0.620850i \(0.213212\pi\)
\(578\) 0 0
\(579\) −2.00000 3.46410i −0.0831172 0.143963i
\(580\) −6.00000 −0.249136
\(581\) 0 0
\(582\) 0 0
\(583\) 18.0000 + 31.1769i 0.745484 + 1.29122i
\(584\) 0 0
\(585\) −5.00000 + 8.66025i −0.206725 + 0.358057i
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) −19.5000 33.7750i −0.800769 1.38697i −0.919111 0.394000i \(-0.871091\pi\)
0.118342 0.992973i \(-0.462242\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) 0 0
\(599\) −22.5000 + 38.9711i −0.919325 + 1.59232i −0.118882 + 0.992908i \(0.537931\pi\)
−0.800443 + 0.599409i \(0.795402\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) −1.00000 1.73205i −0.0406894 0.0704761i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −22.5000 38.9711i −0.910253 1.57660i
\(612\) 6.00000 10.3923i 0.242536 0.420084i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 0 0
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) 13.0000 22.5167i 0.522514 0.905021i −0.477143 0.878826i \(-0.658328\pi\)
0.999657 0.0261952i \(-0.00833914\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 15.0000 + 25.9808i 0.601929 + 1.04257i
\(622\) 0 0
\(623\) 0 0
\(624\) 20.0000 0.800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −14.0000 24.2487i −0.558661 0.967629i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 0 0
\(633\) −6.50000 + 11.2583i −0.258352 + 0.447478i
\(634\) 0 0
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) 24.0000 0.951662
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) −41.0000 −1.61688 −0.808441 0.588577i \(-0.799688\pi\)
−0.808441 + 0.588577i \(0.799688\pi\)
\(644\) 0 0
\(645\) 10.0000 0.393750
\(646\) 0 0
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) −24.0000 41.5692i −0.937043 1.62301i
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −15.0000 −0.584317 −0.292159 0.956370i \(-0.594373\pi\)
−0.292159 + 0.956370i \(0.594373\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) 16.0000 27.7128i 0.622328 1.07790i −0.366723 0.930330i \(-0.619520\pi\)
0.989051 0.147573i \(-0.0471463\pi\)
\(662\) 0 0
\(663\) 7.50000 + 12.9904i 0.291276 + 0.504505i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 3.00000 5.19615i 0.116073 0.201045i
\(669\) 9.50000 16.4545i 0.367291 0.636167i
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) 22.5000 + 38.9711i 0.864745 + 1.49778i 0.867300 + 0.497786i \(0.165853\pi\)
−0.00255466 + 0.999997i \(0.500813\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.50000 + 2.59808i 0.0574801 + 0.0995585i
\(682\) 0 0
\(683\) 12.0000 20.7846i 0.459167 0.795301i −0.539750 0.841825i \(-0.681481\pi\)
0.998917 + 0.0465244i \(0.0148145\pi\)
\(684\) 4.00000 + 6.92820i 0.152944 + 0.264906i
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) 20.0000 + 34.6410i 0.762493 + 1.32068i
\(689\) 30.0000 51.9615i 1.14291 1.97958i
\(690\) 0 0
\(691\) −14.0000 24.2487i −0.532585 0.922464i −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 0 0
\(695\) 7.00000 + 12.1244i 0.265525 + 0.459903i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) 2.00000 3.46410i 0.0754314 0.130651i
\(704\) −12.0000 + 20.7846i −0.452267 + 0.783349i
\(705\) −4.50000 7.79423i −0.169480 0.293548i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −17.5000 30.3109i −0.657226 1.13835i −0.981331 0.192328i \(-0.938396\pi\)
0.324104 0.946021i \(-0.394937\pi\)
\(710\) 0 0
\(711\) −1.00000 + 1.73205i −0.0375029 + 0.0649570i
\(712\) 0 0
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 15.0000 0.560968
\(716\) 12.0000 + 20.7846i 0.448461 + 0.776757i
\(717\) −10.5000 + 18.1865i −0.392130 + 0.679189i
\(718\) 0 0
\(719\) −15.0000 25.9808i −0.559406 0.968919i −0.997546 0.0700124i \(-0.977696\pi\)
0.438141 0.898906i \(-0.355637\pi\)
\(720\) −8.00000 −0.298142
\(721\) 0 0
\(722\) 0 0
\(723\) 5.00000 + 8.66025i 0.185952 + 0.322078i
\(724\) −20.0000 + 34.6410i −0.743294 + 1.28742i
\(725\) −1.50000 + 2.59808i −0.0557086 + 0.0964901i
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −15.0000 + 25.9808i −0.554795 + 0.960933i
\(732\) 8.00000 13.8564i 0.295689 0.512148i
\(733\) −15.5000 26.8468i −0.572506 0.991609i −0.996308 0.0858539i \(-0.972638\pi\)
0.423802 0.905755i \(-0.360695\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) 0 0
\(739\) 21.5000 37.2391i 0.790890 1.36986i −0.134526 0.990910i \(-0.542951\pi\)
0.925416 0.378952i \(-0.123715\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) −10.0000 −0.367359
\(742\) 0 0
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) 0 0
\(747\) −12.0000 20.7846i −0.439057 0.760469i
\(748\) −18.0000 −0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) −11.5000 19.9186i −0.419641 0.726839i 0.576262 0.817265i \(-0.304511\pi\)
−0.995903 + 0.0904254i \(0.971177\pi\)
\(752\) 18.0000 31.1769i 0.656392 1.13691i
\(753\) −9.00000 + 15.5885i −0.327978 + 0.568075i
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) 9.00000 15.5885i 0.326679 0.565825i
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −18.0000 −0.651217
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 0 0
\(767\) 0 0
\(768\) 8.00000 + 13.8564i 0.288675 + 0.500000i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) 10.5000 18.1865i 0.377659 0.654124i −0.613062 0.790034i \(-0.710063\pi\)
0.990721 + 0.135910i \(0.0433959\pi\)
\(774\) 0 0
\(775\) −2.00000 3.46410i −0.0718421 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.0000 + 20.7846i 0.429945 + 0.744686i
\(780\) 5.00000 8.66025i 0.179029 0.310087i
\(781\) 0 0
\(782\) 0 0
\(783\) 15.0000 0.536056
\(784\) 0 0
\(785\) −14.0000 −0.499681
\(786\) 0 0
\(787\) 2.50000 4.33013i 0.0891154 0.154352i −0.818022 0.575187i \(-0.804929\pi\)
0.907137 + 0.420834i \(0.138263\pi\)
\(788\) 0 0
\(789\) 3.00000 + 5.19615i 0.106803 + 0.184988i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −20.0000 34.6410i −0.710221 1.23014i
\(794\) 0 0