Properties

Label 1960.2.q.o.961.1
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.o.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +(2.50000 + 4.33013i) q^{11} -5.00000 q^{13} -3.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +7.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-7.50000 + 12.9904i) q^{33} +(3.00000 - 5.19615i) q^{37} +(-7.50000 - 12.9904i) q^{39} -12.0000 q^{41} -2.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-10.5000 + 18.1865i) q^{51} -5.00000 q^{55} +6.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.50000 - 4.33013i) q^{65} +(-4.00000 - 6.92820i) q^{67} +6.00000 q^{69} +(-3.00000 - 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{75} +(1.50000 - 2.59808i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{83} -7.00000 q^{85} +(10.5000 + 18.1865i) q^{87} +(6.00000 - 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{95} +13.0000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} - q^{5} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{3} - q^{5} - 6q^{9} + 5q^{11} - 10q^{13} - 6q^{15} + 7q^{17} + 2q^{19} + 2q^{23} - q^{25} - 18q^{27} + 14q^{29} - 4q^{31} - 15q^{33} + 6q^{37} - 15q^{39} - 24q^{41} - 4q^{43} - 6q^{45} - q^{47} - 21q^{51} - 10q^{55} + 12q^{57} + 4q^{59} - 4q^{61} + 5q^{65} - 8q^{67} + 12q^{69} - 6q^{73} + 3q^{75} + 3q^{79} - 9q^{81} - 8q^{83} - 14q^{85} + 21q^{87} + 12q^{93} + 2q^{95} + 26q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −3.00000 −0.774597
\(16\) 0 0
\(17\) 3.50000 + 6.06218i 0.848875 + 1.47029i 0.882213 + 0.470850i \(0.156053\pi\)
−0.0333386 + 0.999444i \(0.510614\pi\)
\(18\) 0 0
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 1.73205i 0.208514 0.361158i −0.742732 0.669588i \(-0.766471\pi\)
0.951247 + 0.308431i \(0.0998038\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 7.00000 1.29987 0.649934 0.759991i \(-0.274797\pi\)
0.649934 + 0.759991i \(0.274797\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) −7.50000 + 12.9904i −1.30558 + 2.26134i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 0 0
\(39\) −7.50000 12.9904i −1.20096 2.08013i
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 0 0
\(47\) −0.500000 + 0.866025i −0.0729325 + 0.126323i −0.900185 0.435507i \(-0.856569\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −10.5000 + 18.1865i −1.47029 + 2.54662i
\(52\) 0 0
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.50000 4.33013i 0.310087 0.537086i
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.00000 5.19615i −0.351123 0.608164i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 0 0
\(75\) 1.50000 2.59808i 0.173205 0.300000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −7.00000 −0.759257
\(86\) 0 0
\(87\) 10.5000 + 18.1865i 1.12572 + 1.94980i
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 6.00000 10.3923i 0.622171 1.07763i
\(94\) 0 0
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) −30.0000 −3.01511
\(100\) 0 0
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i \(0.387925\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) 0 0
\(111\) 18.0000 1.70848
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 1.00000 + 1.73205i 0.0932505 + 0.161515i
\(116\) 0 0
\(117\) 15.0000 25.9808i 1.38675 2.40192i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) −18.0000 31.1769i −1.62301 2.81113i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 0 0
\(129\) −3.00000 5.19615i −0.264135 0.457496i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 4.50000 7.79423i 0.387298 0.670820i
\(136\) 0 0
\(137\) 4.00000 + 6.92820i 0.341743 + 0.591916i 0.984757 0.173939i \(-0.0556494\pi\)
−0.643013 + 0.765855i \(0.722316\pi\)
\(138\) 0 0
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) −12.5000 21.6506i −1.04530 1.81052i
\(144\) 0 0
\(145\) −3.50000 + 6.06218i −0.290659 + 0.503436i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.0000 19.0526i 0.901155 1.56085i 0.0751583 0.997172i \(-0.476054\pi\)
0.825997 0.563675i \(-0.190613\pi\)
\(150\) 0 0
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 0 0
\(153\) −42.0000 −3.39550
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −5.00000 8.66025i −0.399043 0.691164i 0.594565 0.804048i \(-0.297324\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.00000 12.1244i 0.548282 0.949653i −0.450110 0.892973i \(-0.648615\pi\)
0.998392 0.0566798i \(-0.0180514\pi\)
\(164\) 0 0
\(165\) −7.50000 12.9904i −0.583874 1.01130i
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) 0 0
\(173\) 3.50000 6.06218i 0.266100 0.460899i −0.701751 0.712422i \(-0.747598\pi\)
0.967851 + 0.251523i \(0.0809315\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0 0
\(179\) 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 0 0
\(183\) −12.0000 −0.887066
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) −17.5000 + 30.3109i −1.27973 + 2.21655i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.50000 11.2583i 0.470323 0.814624i −0.529101 0.848559i \(-0.677471\pi\)
0.999424 + 0.0339349i \(0.0108039\pi\)
\(192\) 0 0
\(193\) 4.00000 + 6.92820i 0.287926 + 0.498703i 0.973315 0.229475i \(-0.0737008\pi\)
−0.685388 + 0.728178i \(0.740368\pi\)
\(194\) 0 0
\(195\) 15.0000 1.07417
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0 0
\(201\) 12.0000 20.7846i 0.846415 1.46603i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 0 0
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) 0 0
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 9.00000 15.5885i 0.608164 1.05337i
\(220\) 0 0
\(221\) −17.5000 30.3109i −1.17718 2.03893i
\(222\) 0 0
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 0 0
\(225\) 6.00000 0.400000
\(226\) 0 0
\(227\) −4.50000 7.79423i −0.298675 0.517321i 0.677158 0.735838i \(-0.263211\pi\)
−0.975833 + 0.218517i \(0.929878\pi\)
\(228\) 0 0
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.0000 20.7846i 0.786146 1.36165i −0.142166 0.989843i \(-0.545407\pi\)
0.928312 0.371802i \(-0.121260\pi\)
\(234\) 0 0
\(235\) −0.500000 0.866025i −0.0326164 0.0564933i
\(236\) 0 0
\(237\) 9.00000 0.584613
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 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
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) 10.0000 0.628695
\(254\) 0 0
\(255\) −10.5000 18.1865i −0.657536 1.13888i
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −21.0000 + 36.3731i −1.29987 + 2.25144i
\(262\) 0 0
\(263\) 15.0000 + 25.9808i 0.924940 + 1.60204i 0.791658 + 0.610964i \(0.209218\pi\)
0.133281 + 0.991078i \(0.457449\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −13.0000 22.5167i −0.792624 1.37287i −0.924337 0.381577i \(-0.875381\pi\)
0.131713 0.991288i \(-0.457952\pi\)
\(270\) 0 0
\(271\) −6.00000 + 10.3923i −0.364474 + 0.631288i −0.988692 0.149963i \(-0.952085\pi\)
0.624218 + 0.781251i \(0.285418\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 0 0
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 19.0000 1.13344 0.566722 0.823909i \(-0.308211\pi\)
0.566722 + 0.823909i \(0.308211\pi\)
\(282\) 0 0
\(283\) 12.5000 + 21.6506i 0.743048 + 1.28700i 0.951101 + 0.308879i \(0.0999539\pi\)
−0.208053 + 0.978117i \(0.566713\pi\)
\(284\) 0 0
\(285\) −3.00000 + 5.19615i −0.177705 + 0.307794i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.0000 + 27.7128i −0.941176 + 1.63017i
\(290\) 0 0
\(291\) 19.5000 + 33.7750i 1.14311 + 1.97993i
\(292\) 0 0
\(293\) 13.0000 0.759468 0.379734 0.925096i \(-0.376015\pi\)
0.379734 + 0.925096i \(0.376015\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) −22.5000 38.9711i −1.30558 2.26134i
\(298\) 0 0
\(299\) −5.00000 + 8.66025i −0.289157 + 0.500835i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −27.0000 + 46.7654i −1.55111 + 2.68660i
\(304\) 0 0
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 0 0
\(307\) −17.0000 −0.970241 −0.485121 0.874447i \(-0.661224\pi\)
−0.485121 + 0.874447i \(0.661224\pi\)
\(308\) 0 0
\(309\) −39.0000 −2.21863
\(310\) 0 0
\(311\) 17.0000 + 29.4449i 0.963982 + 1.66967i 0.712327 + 0.701848i \(0.247641\pi\)
0.251655 + 0.967817i \(0.419025\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) 17.5000 + 30.3109i 0.979812 + 1.69708i
\(320\) 0 0
\(321\) −54.0000 −3.01399
\(322\) 0 0
\(323\) 14.0000 0.778981
\(324\) 0 0
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 0 0
\(327\) 7.50000 12.9904i 0.414751 0.718370i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.00000 10.3923i 0.329790 0.571213i −0.652680 0.757634i \(-0.726355\pi\)
0.982470 + 0.186421i \(0.0596888\pi\)
\(332\) 0 0
\(333\) 18.0000 + 31.1769i 0.986394 + 1.70848i
\(334\) 0 0
\(335\) 8.00000 0.437087
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 0 0
\(339\) 9.00000 + 15.5885i 0.488813 + 0.846649i
\(340\) 0 0
\(341\) 10.0000 17.3205i 0.541530 0.937958i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 0 0
\(347\) −13.0000 22.5167i −0.697877 1.20876i −0.969201 0.246270i \(-0.920795\pi\)
0.271325 0.962488i \(-0.412538\pi\)
\(348\) 0 0
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) 45.0000 2.40192
\(352\) 0 0
\(353\) −2.50000 4.33013i −0.133062 0.230469i 0.791794 0.610789i \(-0.209147\pi\)
−0.924855 + 0.380319i \(0.875814\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 3.50000 + 6.06218i 0.182699 + 0.316443i 0.942799 0.333363i \(-0.108183\pi\)
−0.760100 + 0.649806i \(0.774850\pi\)
\(368\) 0 0
\(369\) 36.0000 62.3538i 1.87409 3.24601i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.00000 + 13.8564i −0.414224 + 0.717458i −0.995347 0.0963587i \(-0.969280\pi\)
0.581122 + 0.813816i \(0.302614\pi\)
\(374\) 0 0
\(375\) 1.50000 + 2.59808i 0.0774597 + 0.134164i
\(376\) 0 0
\(377\) −35.0000 −1.80259
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −18.0000 31.1769i −0.922168 1.59724i
\(382\) 0 0
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6.00000 10.3923i 0.304997 0.528271i
\(388\) 0 0
\(389\) 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i \(-0.0424994\pi\)
−0.610835 + 0.791758i \(0.709166\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 0 0
\(395\) 1.50000 + 2.59808i 0.0754732 + 0.130723i
\(396\) 0 0
\(397\) 11.5000 19.9186i 0.577168 0.999685i −0.418634 0.908155i \(-0.637491\pi\)
0.995802 0.0915300i \(-0.0291757\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) 0 0
\(403\) 10.0000 + 17.3205i 0.498135 + 0.862796i
\(404\) 0 0
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) 30.0000 1.48704
\(408\) 0 0
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) −12.0000 + 20.7846i −0.591916 + 1.02523i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.00000 3.46410i 0.0981761 0.170046i
\(416\) 0 0
\(417\) 27.0000 + 46.7654i 1.32220 + 2.29011i
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) 3.50000 6.06218i 0.169775 0.294059i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 37.5000 64.9519i 1.81052 3.13591i
\(430\) 0 0
\(431\) 12.5000 + 21.6506i 0.602104 + 1.04287i 0.992502 + 0.122228i \(0.0390040\pi\)
−0.390398 + 0.920646i \(0.627663\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) −21.0000 −1.00687
\(436\) 0 0
\(437\) −2.00000 3.46410i −0.0956730 0.165710i
\(438\) 0 0
\(439\) 13.0000 22.5167i 0.620456 1.07466i −0.368945 0.929451i \(-0.620281\pi\)
0.989401 0.145210i \(-0.0463858\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.00000 + 5.19615i −0.142534 + 0.246877i −0.928450 0.371457i \(-0.878858\pi\)
0.785916 + 0.618333i \(0.212192\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 66.0000 3.12169
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) −30.0000 51.9615i −1.41264 2.44677i
\(452\) 0 0
\(453\) −28.5000 + 49.3634i −1.33905 + 2.31930i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.00000 6.92820i 0.187112 0.324088i −0.757174 0.653213i \(-0.773421\pi\)
0.944286 + 0.329125i \(0.106754\pi\)
\(458\) 0 0
\(459\) −31.5000 54.5596i −1.47029 2.54662i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −36.0000 −1.67306 −0.836531 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) 0 0
\(465\) 6.00000 + 10.3923i 0.278243 + 0.481932i
\(466\) 0 0
\(467\) −5.50000 + 9.52628i −0.254510 + 0.440824i −0.964762 0.263123i \(-0.915247\pi\)
0.710253 + 0.703947i \(0.248581\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 15.0000 25.9808i 0.691164 1.19713i
\(472\) 0 0
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.0000 29.4449i −0.776750 1.34537i −0.933806 0.357780i \(-0.883534\pi\)
0.157056 0.987590i \(-0.449800\pi\)
\(480\) 0 0
\(481\) −15.0000 + 25.9808i −0.683941 + 1.18462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.50000 + 11.2583i −0.295150 + 0.511214i
\(486\) 0 0
\(487\) −11.0000 19.0526i −0.498458 0.863354i 0.501541 0.865134i \(-0.332767\pi\)
−0.999998 + 0.00178012i \(0.999433\pi\)
\(488\) 0 0
\(489\) 42.0000 1.89931
\(490\) 0 0
\(491\) 9.00000 0.406164 0.203082 0.979162i \(-0.434904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(492\) 0 0
\(493\) 24.5000 + 42.4352i 1.10342 + 1.91119i
\(494\) 0 0
\(495\) 15.0000 25.9808i 0.674200 1.16775i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.500000 0.866025i 0.0223831 0.0387686i −0.854617 0.519259i \(-0.826208\pi\)
0.877000 + 0.480490i \(0.159541\pi\)
\(500\) 0 0
\(501\) −4.50000 7.79423i −0.201045 0.348220i
\(502\) 0 0
\(503\) 3.00000 0.133763 0.0668817 0.997761i \(-0.478695\pi\)
0.0668817 + 0.997761i \(0.478695\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) 18.0000 + 31.1769i 0.799408 + 1.38462i
\(508\) 0 0
\(509\) 7.00000 12.1244i 0.310270 0.537403i −0.668151 0.744026i \(-0.732914\pi\)
0.978421 + 0.206623i \(0.0662474\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −9.00000 + 15.5885i −0.397360 + 0.688247i
\(514\) 0 0
\(515\) −6.50000 11.2583i −0.286424 0.496101i
\(516\) 0 0
\(517\) −5.00000 −0.219900
\(518\) 0 0
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) −11.0000 19.0526i −0.481919 0.834708i 0.517866 0.855462i \(-0.326727\pi\)
−0.999785 + 0.0207541i \(0.993393\pi\)
\(522\) 0 0
\(523\) 22.0000 38.1051i 0.961993 1.66622i 0.244507 0.969648i \(-0.421374\pi\)
0.717486 0.696573i \(-0.245293\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.0000 24.2487i 0.609850 1.05629i
\(528\) 0 0
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 0 0
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 60.0000 2.59889
\(534\) 0 0
\(535\) −9.00000 15.5885i −0.389104 0.673948i
\(536\) 0 0
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −3.50000 + 6.06218i −0.150477 + 0.260633i −0.931403 0.363990i \(-0.881414\pi\)
0.780926 + 0.624623i \(0.214748\pi\)
\(542\) 0 0
\(543\) 12.0000 + 20.7846i 0.514969 + 0.891953i
\(544\) 0 0
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) −12.0000 20.7846i −0.512148 0.887066i
\(550\) 0 0
\(551\) 7.00000 12.1244i 0.298210 0.516515i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −9.00000 + 15.5885i −0.382029 + 0.661693i
\(556\) 0 0
\(557\) 8.00000 + 13.8564i 0.338971 + 0.587115i 0.984239 0.176841i \(-0.0565879\pi\)
−0.645269 + 0.763956i \(0.723255\pi\)
\(558\) 0 0
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) −105.000 −4.43310
\(562\) 0 0
\(563\) −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i \(-0.193529\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(564\) 0 0
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.0000 19.0526i 0.461144 0.798725i −0.537874 0.843025i \(-0.680772\pi\)
0.999018 + 0.0443003i \(0.0141058\pi\)
\(570\) 0 0
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 0 0
\(573\) 39.0000 1.62925
\(574\) 0 0
\(575\) −2.00000 −0.0834058
\(576\) 0 0
\(577\) 18.5000 + 32.0429i 0.770165 + 1.33397i 0.937472 + 0.348060i \(0.113160\pi\)
−0.167307 + 0.985905i \(0.553507\pi\)
\(578\) 0 0
\(579\) −12.0000 + 20.7846i −0.498703 + 0.863779i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 15.0000 + 25.9808i 0.620174 + 1.07417i
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −12.0000 20.7846i −0.493614 0.854965i
\(592\) 0 0
\(593\) −13.5000 + 23.3827i −0.554379 + 0.960212i 0.443573 + 0.896238i \(0.353711\pi\)
−0.997952 + 0.0639736i \(0.979623\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) 0 0
\(599\) −7.50000 12.9904i −0.306442 0.530773i 0.671140 0.741331i \(-0.265805\pi\)
−0.977581 + 0.210558i \(0.932472\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 48.0000 1.95471
\(604\) 0 0
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) −1.50000 + 2.59808i −0.0608831 + 0.105453i −0.894860 0.446346i \(-0.852725\pi\)
0.833977 + 0.551799i \(0.186058\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.50000 4.33013i 0.101139 0.175178i
\(612\) 0 0
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) 0 0
\(615\) 36.0000 1.45166
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −13.0000 22.5167i −0.522514 0.905021i −0.999657 0.0261952i \(-0.991661\pi\)
0.477143 0.878826i \(-0.341672\pi\)
\(620\) 0 0
\(621\) −9.00000 + 15.5885i −0.361158 + 0.625543i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 15.0000 + 25.9808i 0.599042 + 1.03757i
\(628\) 0 0
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) 7.50000 + 12.9904i 0.298098 + 0.516321i
\(634\) 0 0
\(635\) 6.00000 10.3923i 0.238103 0.412406i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 0 0
\(643\) 21.0000 0.828159 0.414080 0.910241i \(-0.364104\pi\)
0.414080 + 0.910241i \(0.364104\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 0 0
\(649\) −10.0000 + 17.3205i −0.392534 + 0.679889i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.0000 + 32.9090i −0.743527 + 1.28783i 0.207352 + 0.978266i \(0.433515\pi\)
−0.950880 + 0.309561i \(0.899818\pi\)
\(654\) 0 0
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) 0 0
\(657\) 36.0000 1.40449
\(658\) 0 0
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 0 0
\(663\) 52.5000 90.9327i 2.03893 3.53153i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.00000 12.1244i 0.271041 0.469457i
\(668\) 0 0
\(669\) −28.5000 49.3634i −1.10187 1.90850i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 4.50000 + 7.79423i 0.173205 + 0.300000i
\(676\) 0 0
\(677\) 14.5000 25.1147i 0.557280 0.965238i −0.440442 0.897781i \(-0.645178\pi\)
0.997722 0.0674566i \(-0.0214884\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.5000 23.3827i 0.517321 0.896026i
\(682\) 0 0
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) −8.00000 −0.305664
\(686\) 0 0
\(687\) −12.0000 −0.457829
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.00000 + 15.5885i −0.341389 + 0.591304i
\(696\) 0 0
\(697\) −42.0000 72.7461i −1.59086 2.75546i
\(698\) 0 0
\(699\) 72.0000 2.72329
\(700\) 0 0
\(701\) 35.0000 1.32193 0.660966 0.750416i \(-0.270147\pi\)
0.660966 + 0.750416i \(0.270147\pi\)
\(702\) 0 0
\(703\) −6.00000 10.3923i −0.226294 0.391953i
\(704\) 0 0
\(705\) 1.50000 2.59808i 0.0564933 0.0978492i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 12.5000 21.6506i 0.469447 0.813107i −0.529943 0.848034i \(-0.677787\pi\)
0.999390 + 0.0349269i \(0.0111198\pi\)
\(710\) 0 0
\(711\) 9.00000 + 15.5885i 0.337526 + 0.584613i
\(712\) 0 0
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 25.0000 0.934947
\(716\) 0 0
\(717\) 13.5000 + 23.3827i 0.504167 + 0.873242i
\(718\) 0 0
\(719\) 7.00000 12.1244i 0.261056 0.452162i −0.705467 0.708743i \(-0.749263\pi\)
0.966523 + 0.256581i \(0.0825960\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −33.0000 + 57.1577i −1.22728 + 2.12572i
\(724\) 0 0
\(725\) −3.50000 6.06218i −0.129987 0.225144i
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −7.00000 12.1244i −0.258904 0.448435i
\(732\) 0 0
\(733\) 16.5000 28.5788i 0.609441 1.05558i −0.381891 0.924207i \(-0.624727\pi\)
0.991333 0.131376i \(-0.0419396\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.0000 34.6410i 0.736709 1.27602i
\(738\) 0 0
\(739\) −25.5000 44.1673i −0.938033 1.62472i −0.769135 0.639087i \(-0.779313\pi\)
−0.168898 0.985634i \(-0.554021\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 11.0000 + 19.0526i 0.403009 + 0.698032i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.50000 2.59808i 0.0547358 0.0948051i −0.837359 0.546653i \(-0.815902\pi\)
0.892095 + 0.451848i \(0.149235\pi\)
\(752\) 0 0
\(753\) 9.00000 + 15.5885i 0.327978 + 0.568075i
\(754\) 0 0
\(755\) −19.0000 −0.691481
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) 0 0
\(759\) 15.0000 + 25.9808i 0.544466 + 0.943042i
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 21.0000 36.3731i 0.759257 1.31507i
\(766\) 0 0
\(767\) −10.0000 17.3205i −0.361079 0.625407i
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −54.0000 −1.94476
\(772\) 0 0
\(773\) 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i \(-0.0433959\pi\)
−0.613062 + 0.790034i \(0.710063\pi\)
\(774\) 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
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −63.0000 −2.25144
\(784\) 0 0
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) −8.50000 14.7224i −0.302992 0.524798i 0.673820 0.738896i \(-0.264652\pi\)
−0.976812 + 0.214097i \(0.931319\pi\)
\(788\) 0 0
\(789\) −45.0000 + 77.9423i −1.60204 + 2.77482i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 10.0000 17.3205i 0.355110 0.615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −39.0000 −1.38145 −0.690725 0.723117i \(-0.742709\pi\)
−0.690725 + 0.723117i \(0.742709\pi\)
\(798\) 0 0
\(799\) −7.00000 −0.247642
\(800\) 0 0