Properties

Label 322.2.c.a.321.3
Level $322$
Weight $2$
Character 322.321
Analytic conductor $2.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 8 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 321.3
Root \(1.16372i\) of defining polynomial
Character \(\chi\) \(=\) 322.321
Dual form 322.2.c.a.321.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -1.41421i q^{6} -2.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -1.41421i q^{6} -2.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.74166i q^{11} +1.41421i q^{12} +4.24264i q^{13} +2.64575 q^{14} +1.00000 q^{16} -1.00000 q^{18} -5.29150 q^{19} -3.74166i q^{21} -3.74166i q^{22} +(-3.00000 - 3.74166i) q^{23} -1.41421i q^{24} -5.00000 q^{25} -4.24264i q^{26} +5.65685i q^{27} -2.64575 q^{28} +6.00000 q^{29} +8.48528i q^{31} -1.00000 q^{32} -5.29150 q^{33} +1.00000 q^{36} +11.2250i q^{37} +5.29150 q^{38} -6.00000 q^{39} -5.65685i q^{41} +3.74166i q^{42} -11.2250i q^{43} +3.74166i q^{44} +(3.00000 + 3.74166i) q^{46} +2.82843i q^{47} +1.41421i q^{48} +7.00000 q^{49} +5.00000 q^{50} +4.24264i q^{52} +3.74166i q^{53} -5.65685i q^{54} +2.64575 q^{56} -7.48331i q^{57} -6.00000 q^{58} -9.89949i q^{59} +10.5830 q^{61} -8.48528i q^{62} -2.64575 q^{63} +1.00000 q^{64} +5.29150 q^{66} +11.2250i q^{67} +(5.29150 - 4.24264i) q^{69} +6.00000 q^{71} -1.00000 q^{72} -8.48528i q^{73} -11.2250i q^{74} -7.07107i q^{75} -5.29150 q^{76} -9.89949i q^{77} +6.00000 q^{78} -5.00000 q^{81} +5.65685i q^{82} +15.8745 q^{83} -3.74166i q^{84} +11.2250i q^{86} +8.48528i q^{87} -3.74166i q^{88} +15.8745 q^{89} -11.2250i q^{91} +(-3.00000 - 3.74166i) q^{92} -12.0000 q^{93} -2.82843i q^{94} -1.41421i q^{96} -5.29150 q^{97} -7.00000 q^{98} +3.74166i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + 4q^{16} - 4q^{18} - 12q^{23} - 20q^{25} + 24q^{29} - 4q^{32} + 4q^{36} - 24q^{39} + 12q^{46} + 28q^{49} + 20q^{50} - 24q^{58} + 4q^{64} + 24q^{71} - 4q^{72} + 24q^{78} - 20q^{81} - 12q^{92} - 48q^{93} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.41421i 0.816497i 0.912871 + 0.408248i \(0.133860\pi\)
−0.912871 + 0.408248i \(0.866140\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.41421i 0.577350i
\(7\) −2.64575 −1.00000
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.74166i 1.12815i 0.825723 + 0.564076i \(0.190768\pi\)
−0.825723 + 0.564076i \(0.809232\pi\)
\(12\) 1.41421i 0.408248i
\(13\) 4.24264i 1.17670i 0.808608 + 0.588348i \(0.200222\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(14\) 2.64575 0.707107
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.29150 −1.21395 −0.606977 0.794719i \(-0.707618\pi\)
−0.606977 + 0.794719i \(0.707618\pi\)
\(20\) 0 0
\(21\) 3.74166i 0.816497i
\(22\) 3.74166i 0.797724i
\(23\) −3.00000 3.74166i −0.625543 0.780189i
\(24\) 1.41421i 0.288675i
\(25\) −5.00000 −1.00000
\(26\) 4.24264i 0.832050i
\(27\) 5.65685i 1.08866i
\(28\) −2.64575 −0.500000
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 8.48528i 1.52400i 0.647576 + 0.762001i \(0.275783\pi\)
−0.647576 + 0.762001i \(0.724217\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.29150 −0.921132
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 11.2250i 1.84537i 0.385550 + 0.922687i \(0.374012\pi\)
−0.385550 + 0.922687i \(0.625988\pi\)
\(38\) 5.29150 0.858395
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) 5.65685i 0.883452i −0.897150 0.441726i \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 3.74166i 0.577350i
\(43\) 11.2250i 1.71179i −0.517148 0.855896i \(-0.673006\pi\)
0.517148 0.855896i \(-0.326994\pi\)
\(44\) 3.74166i 0.564076i
\(45\) 0 0
\(46\) 3.00000 + 3.74166i 0.442326 + 0.551677i
\(47\) 2.82843i 0.412568i 0.978492 + 0.206284i \(0.0661372\pi\)
−0.978492 + 0.206284i \(0.933863\pi\)
\(48\) 1.41421i 0.204124i
\(49\) 7.00000 1.00000
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 4.24264i 0.588348i
\(53\) 3.74166i 0.513956i 0.966417 + 0.256978i \(0.0827268\pi\)
−0.966417 + 0.256978i \(0.917273\pi\)
\(54\) 5.65685i 0.769800i
\(55\) 0 0
\(56\) 2.64575 0.353553
\(57\) 7.48331i 0.991189i
\(58\) −6.00000 −0.787839
\(59\) 9.89949i 1.28880i −0.764687 0.644402i \(-0.777106\pi\)
0.764687 0.644402i \(-0.222894\pi\)
\(60\) 0 0
\(61\) 10.5830 1.35501 0.677507 0.735516i \(-0.263060\pi\)
0.677507 + 0.735516i \(0.263060\pi\)
\(62\) 8.48528i 1.07763i
\(63\) −2.64575 −0.333333
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.29150 0.651339
\(67\) 11.2250i 1.37135i 0.727908 + 0.685674i \(0.240493\pi\)
−0.727908 + 0.685674i \(0.759507\pi\)
\(68\) 0 0
\(69\) 5.29150 4.24264i 0.637022 0.510754i
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −1.00000 −0.117851
\(73\) 8.48528i 0.993127i −0.868000 0.496564i \(-0.834595\pi\)
0.868000 0.496564i \(-0.165405\pi\)
\(74\) 11.2250i 1.30488i
\(75\) 7.07107i 0.816497i
\(76\) −5.29150 −0.606977
\(77\) 9.89949i 1.12815i
\(78\) 6.00000 0.679366
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −5.00000 −0.555556
\(82\) 5.65685i 0.624695i
\(83\) 15.8745 1.74245 0.871227 0.490881i \(-0.163325\pi\)
0.871227 + 0.490881i \(0.163325\pi\)
\(84\) 3.74166i 0.408248i
\(85\) 0 0
\(86\) 11.2250i 1.21042i
\(87\) 8.48528i 0.909718i
\(88\) 3.74166i 0.398862i
\(89\) 15.8745 1.68269 0.841347 0.540495i \(-0.181763\pi\)
0.841347 + 0.540495i \(0.181763\pi\)
\(90\) 0 0
\(91\) 11.2250i 1.17670i
\(92\) −3.00000 3.74166i −0.312772 0.390095i
\(93\) −12.0000 −1.24434
\(94\) 2.82843i 0.291730i
\(95\) 0 0
\(96\) 1.41421i 0.144338i
\(97\) −5.29150 −0.537271 −0.268635 0.963242i \(-0.586573\pi\)
−0.268635 + 0.963242i \(0.586573\pi\)
\(98\) −7.00000 −0.707107
\(99\) 3.74166i 0.376051i
\(100\) −5.00000 −0.500000
\(101\) 9.89949i 0.985037i −0.870302 0.492518i \(-0.836076\pi\)
0.870302 0.492518i \(-0.163924\pi\)
\(102\) 0 0
\(103\) −5.29150 −0.521387 −0.260694 0.965422i \(-0.583951\pi\)
−0.260694 + 0.965422i \(0.583951\pi\)
\(104\) 4.24264i 0.416025i
\(105\) 0 0
\(106\) 3.74166i 0.363422i
\(107\) 3.74166i 0.361720i 0.983509 + 0.180860i \(0.0578880\pi\)
−0.983509 + 0.180860i \(0.942112\pi\)
\(108\) 5.65685i 0.544331i
\(109\) 11.2250i 1.07516i 0.843214 + 0.537579i \(0.180661\pi\)
−0.843214 + 0.537579i \(0.819339\pi\)
\(110\) 0 0
\(111\) −15.8745 −1.50674
\(112\) −2.64575 −0.250000
\(113\) 7.48331i 0.703971i −0.936005 0.351986i \(-0.885507\pi\)
0.936005 0.351986i \(-0.114493\pi\)
\(114\) 7.48331i 0.700877i
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 4.24264i 0.392232i
\(118\) 9.89949i 0.911322i
\(119\) 0 0
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) −10.5830 −0.958140
\(123\) 8.00000 0.721336
\(124\) 8.48528i 0.762001i
\(125\) 0 0
\(126\) 2.64575 0.235702
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 15.8745 1.39767
\(130\) 0 0
\(131\) 7.07107i 0.617802i 0.951094 + 0.308901i \(0.0999612\pi\)
−0.951094 + 0.308901i \(0.900039\pi\)
\(132\) −5.29150 −0.460566
\(133\) 14.0000 1.21395
\(134\) 11.2250i 0.969690i
\(135\) 0 0
\(136\) 0 0
\(137\) 7.48331i 0.639343i −0.947528 0.319671i \(-0.896427\pi\)
0.947528 0.319671i \(-0.103573\pi\)
\(138\) −5.29150 + 4.24264i −0.450443 + 0.361158i
\(139\) 4.24264i 0.359856i −0.983680 0.179928i \(-0.942414\pi\)
0.983680 0.179928i \(-0.0575865\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) −6.00000 −0.503509
\(143\) −15.8745 −1.32749
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 8.48528i 0.702247i
\(147\) 9.89949i 0.816497i
\(148\) 11.2250i 0.922687i
\(149\) 3.74166i 0.306529i 0.988185 + 0.153264i \(0.0489786\pi\)
−0.988185 + 0.153264i \(0.951021\pi\)
\(150\) 7.07107i 0.577350i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 5.29150 0.429198
\(153\) 0 0
\(154\) 9.89949i 0.797724i
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) −21.1660 −1.68923 −0.844616 0.535373i \(-0.820171\pi\)
−0.844616 + 0.535373i \(0.820171\pi\)
\(158\) 0 0
\(159\) −5.29150 −0.419643
\(160\) 0 0
\(161\) 7.93725 + 9.89949i 0.625543 + 0.780189i
\(162\) 5.00000 0.392837
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 5.65685i 0.441726i
\(165\) 0 0
\(166\) −15.8745 −1.23210
\(167\) 19.7990i 1.53209i 0.642786 + 0.766046i \(0.277779\pi\)
−0.642786 + 0.766046i \(0.722221\pi\)
\(168\) 3.74166i 0.288675i
\(169\) −5.00000 −0.384615
\(170\) 0 0
\(171\) −5.29150 −0.404651
\(172\) 11.2250i 0.855896i
\(173\) 9.89949i 0.752645i −0.926489 0.376322i \(-0.877189\pi\)
0.926489 0.376322i \(-0.122811\pi\)
\(174\) 8.48528i 0.643268i
\(175\) 13.2288 1.00000
\(176\) 3.74166i 0.282038i
\(177\) 14.0000 1.05230
\(178\) −15.8745 −1.18984
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 10.5830 0.786629 0.393314 0.919404i \(-0.371328\pi\)
0.393314 + 0.919404i \(0.371328\pi\)
\(182\) 11.2250i 0.832050i
\(183\) 14.9666i 1.10637i
\(184\) 3.00000 + 3.74166i 0.221163 + 0.275839i
\(185\) 0 0
\(186\) 12.0000 0.879883
\(187\) 0 0
\(188\) 2.82843i 0.206284i
\(189\) 14.9666i 1.08866i
\(190\) 0 0
\(191\) 14.9666i 1.08295i 0.840718 + 0.541474i \(0.182133\pi\)
−0.840718 + 0.541474i \(0.817867\pi\)
\(192\) 1.41421i 0.102062i
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 5.29150 0.379908
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 3.74166i 0.265908i
\(199\) 10.5830 0.750209 0.375105 0.926982i \(-0.377607\pi\)
0.375105 + 0.926982i \(0.377607\pi\)
\(200\) 5.00000 0.353553
\(201\) −15.8745 −1.11970
\(202\) 9.89949i 0.696526i
\(203\) −15.8745 −1.11417
\(204\) 0 0
\(205\) 0 0
\(206\) 5.29150 0.368676
\(207\) −3.00000 3.74166i −0.208514 0.260063i
\(208\) 4.24264i 0.294174i
\(209\) 19.7990i 1.36952i
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 3.74166i 0.256978i
\(213\) 8.48528i 0.581402i
\(214\) 3.74166i 0.255774i
\(215\) 0 0
\(216\) 5.65685i 0.384900i
\(217\) 22.4499i 1.52400i
\(218\) 11.2250i 0.760251i
\(219\) 12.0000 0.810885
\(220\) 0 0
\(221\) 0 0
\(222\) 15.8745 1.06543
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 2.64575 0.176777
\(225\) −5.00000 −0.333333
\(226\) 7.48331i 0.497783i
\(227\) 15.8745 1.05363 0.526814 0.849981i \(-0.323386\pi\)
0.526814 + 0.849981i \(0.323386\pi\)
\(228\) 7.48331i 0.495595i
\(229\) 10.5830 0.699345 0.349672 0.936872i \(-0.386293\pi\)
0.349672 + 0.936872i \(0.386293\pi\)
\(230\) 0 0
\(231\) 14.0000 0.921132
\(232\) −6.00000 −0.393919
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 4.24264i 0.277350i
\(235\) 0 0
\(236\) 9.89949i 0.644402i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −5.29150 −0.340856 −0.170428 0.985370i \(-0.554515\pi\)
−0.170428 + 0.985370i \(0.554515\pi\)
\(242\) 3.00000 0.192847
\(243\) 9.89949i 0.635053i
\(244\) 10.5830 0.677507
\(245\) 0 0
\(246\) −8.00000 −0.510061
\(247\) 22.4499i 1.42846i
\(248\) 8.48528i 0.538816i
\(249\) 22.4499i 1.42271i
\(250\) 0 0
\(251\) −15.8745 −1.00199 −0.500995 0.865450i \(-0.667033\pi\)
−0.500995 + 0.865450i \(0.667033\pi\)
\(252\) −2.64575 −0.166667
\(253\) 14.0000 11.2250i 0.880172 0.705708i
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.82843i 0.176432i 0.996101 + 0.0882162i \(0.0281166\pi\)
−0.996101 + 0.0882162i \(0.971883\pi\)
\(258\) −15.8745 −0.988304
\(259\) 29.6985i 1.84537i
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 7.07107i 0.436852i
\(263\) 7.48331i 0.461441i −0.973020 0.230720i \(-0.925892\pi\)
0.973020 0.230720i \(-0.0741083\pi\)
\(264\) 5.29150 0.325669
\(265\) 0 0
\(266\) −14.0000 −0.858395
\(267\) 22.4499i 1.37391i
\(268\) 11.2250i 0.685674i
\(269\) 18.3848i 1.12094i −0.828175 0.560470i \(-0.810621\pi\)
0.828175 0.560470i \(-0.189379\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 15.8745 0.960769
\(274\) 7.48331i 0.452084i
\(275\) 18.7083i 1.12815i
\(276\) 5.29150 4.24264i 0.318511 0.255377i
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 4.24264i 0.254457i
\(279\) 8.48528i 0.508001i
\(280\) 0 0
\(281\) 14.9666i 0.892834i 0.894825 + 0.446417i \(0.147300\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 4.00000 0.238197
\(283\) 26.4575 1.57274 0.786368 0.617758i \(-0.211959\pi\)
0.786368 + 0.617758i \(0.211959\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 15.8745 0.938679
\(287\) 14.9666i 0.883452i
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 7.48331i 0.438680i
\(292\) 8.48528i 0.496564i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 9.89949i 0.577350i
\(295\) 0 0
\(296\) 11.2250i 0.652438i
\(297\) −21.1660 −1.22818
\(298\) 3.74166i 0.216748i
\(299\) 15.8745 12.7279i 0.918046 0.736075i
\(300\) 7.07107i 0.408248i
\(301\) 29.6985i 1.71179i
\(302\) −2.00000 −0.115087
\(303\) 14.0000 0.804279
\(304\) −5.29150 −0.303488
\(305\) 0 0
\(306\) 0 0
\(307\) 29.6985i 1.69498i −0.530810 0.847491i \(-0.678112\pi\)
0.530810 0.847491i \(-0.321888\pi\)
\(308\) 9.89949i 0.564076i
\(309\) 7.48331i 0.425711i
\(310\) 0 0
\(311\) 28.2843i 1.60385i 0.597422 + 0.801927i \(0.296192\pi\)
−0.597422 + 0.801927i \(0.703808\pi\)
\(312\) 6.00000 0.339683
\(313\) 26.4575 1.49547 0.747734 0.663999i \(-0.231142\pi\)
0.747734 + 0.663999i \(0.231142\pi\)
\(314\) 21.1660 1.19447
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 5.29150 0.296733
\(319\) 22.4499i 1.25696i
\(320\) 0 0
\(321\) −5.29150 −0.295343
\(322\) −7.93725 9.89949i −0.442326 0.551677i
\(323\) 0 0
\(324\) −5.00000 −0.277778
\(325\) 21.2132i 1.17670i
\(326\) 4.00000 0.221540
\(327\) −15.8745 −0.877862
\(328\) 5.65685i 0.312348i
\(329\) 7.48331i 0.412568i
\(330\) 0 0
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) 15.8745 0.871227
\(333\) 11.2250i 0.615125i
\(334\) 19.7990i 1.08335i
\(335\) 0 0
\(336\) 3.74166i 0.204124i
\(337\) 22.4499i 1.22293i 0.791273 + 0.611463i \(0.209419\pi\)
−0.791273 + 0.611463i \(0.790581\pi\)
\(338\) 5.00000 0.271964
\(339\) 10.5830 0.574790
\(340\) 0 0
\(341\) −31.7490 −1.71931
\(342\) 5.29150 0.286132
\(343\) −18.5203 −1.00000
\(344\) 11.2250i 0.605210i
\(345\) 0 0
\(346\) 9.89949i 0.532200i
\(347\) 24.0000 1.28839 0.644194 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) 8.48528i 0.454859i
\(349\) 4.24264i 0.227103i 0.993532 + 0.113552i \(0.0362227\pi\)
−0.993532 + 0.113552i \(0.963777\pi\)
\(350\) −13.2288 −0.707107
\(351\) −24.0000 −1.28103
\(352\) 3.74166i 0.199431i
\(353\) 28.2843i 1.50542i 0.658352 + 0.752710i \(0.271254\pi\)
−0.658352 + 0.752710i \(0.728746\pi\)
\(354\) −14.0000 −0.744092
\(355\) 0 0
\(356\) 15.8745 0.841347
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 29.9333i 1.57982i −0.613225 0.789908i \(-0.710128\pi\)
0.613225 0.789908i \(-0.289872\pi\)
\(360\) 0 0
\(361\) 9.00000 0.473684
\(362\) −10.5830 −0.556230
\(363\) 4.24264i 0.222681i
\(364\) 11.2250i 0.588348i
\(365\) 0 0
\(366\) 14.9666i 0.782318i
\(367\) −5.29150 −0.276214 −0.138107 0.990417i \(-0.544102\pi\)
−0.138107 + 0.990417i \(0.544102\pi\)
\(368\) −3.00000 3.74166i −0.156386 0.195047i
\(369\) 5.65685i 0.294484i
\(370\) 0 0
\(371\) 9.89949i 0.513956i
\(372\) −12.0000 −0.622171
\(373\) 11.2250i 0.581207i 0.956844 + 0.290604i \(0.0938561\pi\)
−0.956844 + 0.290604i \(0.906144\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 2.82843i 0.145865i
\(377\) 25.4558i 1.31104i
\(378\) 14.9666i 0.769800i
\(379\) 11.2250i 0.576588i 0.957542 + 0.288294i \(0.0930881\pi\)
−0.957542 + 0.288294i \(0.906912\pi\)
\(380\) 0 0
\(381\) 11.3137i 0.579619i
\(382\) 14.9666i 0.765759i
\(383\) −15.8745 −0.811149 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(384\) 1.41421i 0.0721688i
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) 11.2250i 0.570597i
\(388\) −5.29150 −0.268635
\(389\) 18.7083i 0.948548i −0.880377 0.474274i \(-0.842711\pi\)
0.880377 0.474274i \(-0.157289\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −7.00000 −0.353553
\(393\) −10.0000 −0.504433
\(394\) −6.00000 −0.302276
\(395\) 0 0
\(396\) 3.74166i 0.188025i
\(397\) 12.7279i 0.638796i 0.947621 + 0.319398i \(0.103481\pi\)
−0.947621 + 0.319398i \(0.896519\pi\)
\(398\) −10.5830 −0.530478
\(399\) 19.7990i 0.991189i
\(400\) −5.00000 −0.250000
\(401\) 14.9666i 0.747398i 0.927550 + 0.373699i \(0.121911\pi\)
−0.927550 + 0.373699i \(0.878089\pi\)
\(402\) 15.8745 0.791748
\(403\) −36.0000 −1.79329
\(404\) 9.89949i 0.492518i
\(405\) 0 0
\(406\) 15.8745 0.787839
\(407\) −42.0000 −2.08186
\(408\) 0 0
\(409\) 8.48528i 0.419570i −0.977748 0.209785i \(-0.932724\pi\)
0.977748 0.209785i \(-0.0672764\pi\)
\(410\) 0 0
\(411\) 10.5830 0.522021
\(412\) −5.29150 −0.260694
\(413\) 26.1916i 1.28880i
\(414\) 3.00000 + 3.74166i 0.147442 + 0.183892i
\(415\) 0 0
\(416\) 4.24264i 0.208013i
\(417\) 6.00000 0.293821
\(418\) 19.7990i 0.968400i
\(419\) −15.8745 −0.775520 −0.387760 0.921760i \(-0.626751\pi\)
−0.387760 + 0.921760i \(0.626751\pi\)
\(420\) 0 0
\(421\) 11.2250i 0.547072i −0.961862 0.273536i \(-0.911807\pi\)
0.961862 0.273536i \(-0.0881932\pi\)
\(422\) 16.0000 0.778868
\(423\) 2.82843i 0.137523i
\(424\) 3.74166i 0.181711i
\(425\) 0 0
\(426\) 8.48528i 0.411113i
\(427\) −28.0000 −1.35501
\(428\) 3.74166i 0.180860i
\(429\) 22.4499i 1.08389i
\(430\) 0 0
\(431\) 29.9333i 1.44183i −0.693021 0.720917i \(-0.743721\pi\)
0.693021 0.720917i \(-0.256279\pi\)
\(432\) 5.65685i 0.272166i
\(433\) −21.1660 −1.01717 −0.508587 0.861011i \(-0.669832\pi\)
−0.508587 + 0.861011i \(0.669832\pi\)
\(434\) 22.4499i 1.07763i
\(435\) 0 0
\(436\) 11.2250i 0.537579i
\(437\) 15.8745 + 19.7990i 0.759381 + 0.947114i
\(438\) −12.0000 −0.573382
\(439\) 16.9706i 0.809961i −0.914325 0.404980i \(-0.867278\pi\)
0.914325 0.404980i \(-0.132722\pi\)
\(440\) 0 0
\(441\) 7.00000 0.333333
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) −15.8745 −0.753371
\(445\) 0 0
\(446\) 0 0
\(447\) −5.29150 −0.250279
\(448\) −2.64575 −0.125000
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 5.00000 0.235702
\(451\) 21.1660 0.996669
\(452\) 7.48331i 0.351986i
\(453\) 2.82843i 0.132891i
\(454\) −15.8745 −0.745028
\(455\) 0 0
\(456\) 7.48331i 0.350438i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −10.5830 −0.494511
\(459\) 0 0
\(460\) 0 0
\(461\) 15.5563i 0.724531i 0.932075 + 0.362266i \(0.117997\pi\)
−0.932075 + 0.362266i \(0.882003\pi\)
\(462\) −14.0000 −0.651339
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 15.8745 0.734585 0.367292 0.930106i \(-0.380285\pi\)
0.367292 + 0.930106i \(0.380285\pi\)
\(468\) 4.24264i 0.196116i
\(469\) 29.6985i 1.37135i
\(470\) 0 0
\(471\) 29.9333i 1.37925i
\(472\) 9.89949i 0.455661i
\(473\) 42.0000 1.93116
\(474\) 0 0
\(475\) 26.4575 1.21395
\(476\) 0 0
\(477\) 3.74166i 0.171319i
\(478\) 6.00000 0.274434
\(479\) −15.8745 −0.725325 −0.362662 0.931921i \(-0.618132\pi\)
−0.362662 + 0.931921i \(0.618132\pi\)
\(480\) 0 0
\(481\) −47.6235 −2.17145
\(482\) 5.29150 0.241021
\(483\) −14.0000 + 11.2250i −0.637022 + 0.510754i
\(484\) −3.00000 −0.136364
\(485\) 0 0
\(486\) 9.89949i 0.449050i
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −10.5830 −0.479070
\(489\) 5.65685i 0.255812i
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 8.00000 0.360668
\(493\) 0 0
\(494\) 22.4499i 1.01007i
\(495\) 0 0
\(496\) 8.48528i 0.381000i
\(497\) −15.8745 −0.712069
\(498\) 22.4499i 1.00601i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) −28.0000 −1.25095
\(502\) 15.8745 0.708514
\(503\) 15.8745 0.707809 0.353905 0.935282i \(-0.384854\pi\)
0.353905 + 0.935282i \(0.384854\pi\)
\(504\) 2.64575 0.117851
\(505\) 0 0
\(506\) −14.0000 + 11.2250i −0.622376 + 0.499011i
\(507\) 7.07107i 0.314037i
\(508\) 8.00000 0.354943
\(509\) 32.5269i 1.44173i 0.693075 + 0.720865i \(0.256255\pi\)
−0.693075 + 0.720865i \(0.743745\pi\)
\(510\) 0 0
\(511\) 22.4499i 0.993127i
\(512\) −1.00000 −0.0441942
\(513\) 29.9333i 1.32159i
\(514\) 2.82843i 0.124757i
\(515\) 0 0
\(516\) 15.8745 0.698836
\(517\) −10.5830 −0.465440
\(518\) 29.6985i 1.30488i
\(519\) 14.0000 0.614532
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −6.00000 −0.262613
\(523\) 26.4575 1.15691 0.578453 0.815716i \(-0.303657\pi\)
0.578453 + 0.815716i \(0.303657\pi\)
\(524\) 7.07107i 0.308901i
\(525\) 18.7083i 0.816497i
\(526\) 7.48331i 0.326288i
\(527\) 0 0
\(528\) −5.29150 −0.230283
\(529\) −5.00000 + 22.4499i −0.217391 + 0.976085i
\(530\) 0 0
\(531\) 9.89949i 0.429601i
\(532\) 14.0000 0.606977
\(533\) 24.0000 1.03956
\(534\) 22.4499i 0.971504i
\(535\) 0 0
\(536\) 11.2250i 0.484845i
\(537\) 16.9706i 0.732334i
\(538\) 18.3848i 0.792624i
\(539\) 26.1916i 1.12815i
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 0 0
\(543\) 14.9666i 0.642280i
\(544\) 0 0
\(545\) 0 0
\(546\) −15.8745 −0.679366
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 7.48331i 0.319671i
\(549\) 10.5830 0.451672
\(550\) 18.7083i 0.797724i
\(551\) −31.7490 −1.35255
\(552\) −5.29150 + 4.24264i −0.225221 + 0.180579i
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.24264i 0.179928i
\(557\) 3.74166i 0.158539i 0.996853 + 0.0792696i \(0.0252588\pi\)
−0.996853 + 0.0792696i \(0.974741\pi\)
\(558\) 8.48528i 0.359211i
\(559\) 47.6235 2.01426
\(560\) 0 0
\(561\) 0 0
\(562\) 14.9666i 0.631329i
\(563\) −15.8745 −0.669031 −0.334515 0.942390i \(-0.608573\pi\)
−0.334515 + 0.942390i \(0.608573\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −26.4575 −1.11209
\(567\) 13.2288 0.555556
\(568\) −6.00000 −0.251754
\(569\) 14.9666i 0.627434i 0.949517 + 0.313717i \(0.101574\pi\)
−0.949517 + 0.313717i \(0.898426\pi\)
\(570\) 0 0
\(571\) 33.6749i 1.40925i −0.709579 0.704626i \(-0.751115\pi\)
0.709579 0.704626i \(-0.248885\pi\)
\(572\) −15.8745 −0.663747
\(573\) −21.1660 −0.884223
\(574\) 14.9666i 0.624695i
\(575\) 15.0000 + 18.7083i 0.625543 + 0.780189i
\(576\) 1.00000 0.0416667
\(577\) 8.48528i 0.353247i 0.984278 + 0.176623i \(0.0565175\pi\)
−0.984278 + 0.176623i \(0.943483\pi\)
\(578\) 17.0000 0.707107
\(579\) 22.6274i 0.940363i
\(580\) 0 0
\(581\) −42.0000 −1.74245
\(582\) 7.48331i 0.310193i
\(583\) −14.0000 −0.579821
\(584\) 8.48528i 0.351123i
\(585\) 0 0
\(586\) 0 0
\(587\) 35.3553i 1.45927i −0.683836 0.729636i \(-0.739690\pi\)
0.683836 0.729636i \(-0.260310\pi\)
\(588\) 9.89949i 0.408248i
\(589\) 44.8999i 1.85007i
\(590\) 0 0
\(591\) 8.48528i 0.349038i
\(592\) 11.2250i 0.461344i
\(593\) 19.7990i 0.813047i 0.913640 + 0.406524i \(0.133259\pi\)
−0.913640 + 0.406524i \(0.866741\pi\)
\(594\) 21.1660 0.868452
\(595\) 0 0
\(596\) 3.74166i 0.153264i
\(597\) 14.9666i 0.612543i
\(598\) −15.8745 + 12.7279i −0.649157 + 0.520483i
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 7.07107i 0.288675i
\(601\) 25.4558i 1.03837i 0.854663 + 0.519183i \(0.173764\pi\)
−0.854663 + 0.519183i \(0.826236\pi\)
\(602\) 29.6985i 1.21042i
\(603\) 11.2250i 0.457116i
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) −14.0000 −0.568711
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 5.29150 0.214599
\(609\) 22.4499i 0.909718i
\(610\) 0 0
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) 11.2250i 0.453372i 0.973968 + 0.226686i \(0.0727892\pi\)
−0.973968 + 0.226686i \(0.927211\pi\)
\(614\) 29.6985i 1.19853i
\(615\) 0 0
\(616\) 9.89949i 0.398862i
\(617\) 7.48331i 0.301267i −0.988590 0.150633i \(-0.951869\pi\)
0.988590 0.150633i \(-0.0481313\pi\)
\(618\) 7.48331i 0.301023i
\(619\) −5.29150 −0.212683 −0.106342 0.994330i \(-0.533914\pi\)
−0.106342 + 0.994330i \(0.533914\pi\)
\(620\) 0 0
\(621\) 21.1660 16.9706i 0.849363 0.681005i
\(622\) 28.2843i 1.13410i
\(623\) −42.0000 −1.68269
\(624\) −6.00000 −0.240192
\(625\) 25.0000 1.00000
\(626\) −26.4575 −1.05745
\(627\) 28.0000 1.11821
\(628\) −21.1660 −0.844616
\(629\) 0 0
\(630\) 0 0
\(631\) 22.4499i 0.893718i 0.894604 + 0.446859i \(0.147457\pi\)
−0.894604 + 0.446859i \(0.852543\pi\)
\(632\) 0 0
\(633\) 22.6274i 0.899359i
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) −5.29150 −0.209822
\(637\) 29.6985i 1.17670i
\(638\) 22.4499i 0.888802i
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 29.9333i 1.18229i −0.806564 0.591146i \(-0.798676\pi\)
0.806564 0.591146i \(-0.201324\pi\)
\(642\) 5.29150 0.208839
\(643\) −5.29150 −0.208676 −0.104338 0.994542i \(-0.533272\pi\)
−0.104338 + 0.994542i \(0.533272\pi\)
\(644\) 7.93725 + 9.89949i 0.312772 + 0.390095i
\(645\) 0 0
\(646\) 0 0
\(647\) 31.1127i 1.22317i −0.791180 0.611583i \(-0.790533\pi\)
0.791180 0.611583i \(-0.209467\pi\)
\(648\) 5.00000 0.196419
\(649\) 37.0405 1.45397
\(650\) 21.2132i 0.832050i
\(651\) 31.7490 1.24434
\(652\) −4.00000 −0.156652
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 15.8745 0.620742
\(655\) 0 0
\(656\) 5.65685i 0.220863i
\(657\) 8.48528i 0.331042i
\(658\) 7.48331i 0.291730i
\(659\) 18.7083i 0.728771i −0.931248 0.364386i \(-0.881279\pi\)
0.931248 0.364386i \(-0.118721\pi\)
\(660\) 0 0
\(661\) −21.1660 −0.823262 −0.411631 0.911351i \(-0.635041\pi\)
−0.411631 + 0.911351i \(0.635041\pi\)
\(662\) −32.0000 −1.24372
\(663\) 0 0
\(664\) −15.8745 −0.616050
\(665\) 0 0
\(666\) 11.2250i 0.434959i
\(667\) −18.0000 22.4499i −0.696963 0.869265i
\(668\) 19.7990i 0.766046i
\(669\) 0 0
\(670\) 0 0
\(671\) 39.5980i 1.52866i
\(672\) 3.74166i 0.144338i
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 22.4499i 0.864740i
\(675\) 28.2843i 1.08866i
\(676\) −5.00000 −0.192308
\(677\) 31.7490 1.22021 0.610107 0.792319i \(-0.291126\pi\)
0.610107 + 0.792319i \(0.291126\pi\)
\(678\) −10.5830 −0.406438
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) 22.4499i 0.860284i
\(682\) 31.7490 1.21573
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −5.29150 −0.202326
\(685\) 0 0
\(686\) 18.5203 0.707107
\(687\) 14.9666i 0.571013i
\(688\) 11.2250i 0.427948i
\(689\) −15.8745 −0.604771
\(690\) 0 0
\(691\) 29.6985i 1.12978i −0.825165 0.564892i \(-0.808918\pi\)
0.825165 0.564892i \(-0.191082\pi\)
\(692\) 9.89949i 0.376322i
\(693\) 9.89949i 0.376051i
\(694\) −24.0000 −0.911028
\(695\) 0 0
\(696\) 8.48528i 0.321634i
\(697\) 0 0
\(698\) 4.24264i 0.160586i
\(699\) 25.4558i 0.962828i
\(700\) 13.2288 0.500000
\(701\) 26.1916i 0.989243i 0.869108 + 0.494622i \(0.164693\pi\)
−0.869108 + 0.494622i \(0.835307\pi\)
\(702\) 24.0000 0.905822
\(703\) 59.3970i 2.24020i
\(704\) 3.74166i 0.141019i
\(705\) 0 0
\(706\) 28.2843i 1.06449i
\(707\) 26.1916i 0.985037i
\(708\) 14.0000 0.526152
\(709\) 11.2250i 0.421563i −0.977533 0.210781i \(-0.932399\pi\)
0.977533 0.210781i \(-0.0676008\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −15.8745 −0.594922
\(713\) 31.7490 25.4558i 1.18901 0.953329i
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 8.48528i 0.316889i
\(718\) 29.9333i 1.11710i
\(719\) 19.7990i 0.738378i 0.929354 + 0.369189i \(0.120364\pi\)
−0.929354 + 0.369189i \(0.879636\pi\)
\(720\) 0 0
\(721\) 14.0000 0.521387
\(722\) −9.00000 −0.334945
\(723\) 7.48331i 0.278307i
\(724\) 10.5830 0.393314
\(725\) −30.0000 −1.11417
\(726\) 4.24264i 0.157459i
\(727\) 10.5830 0.392502 0.196251 0.980554i \(-0.437123\pi\)
0.196251 + 0.980554i \(0.437123\pi\)
\(728\) 11.2250i 0.416025i
\(729\) −29.0000 −1.07407
\(730\) 0 0
\(731\) 0 0
\(732\) 14.9666i 0.553183i
\(733\) −21.1660 −0.781784 −0.390892 0.920436i \(-0.627833\pi\)
−0.390892 + 0.920436i \(0.627833\pi\)
\(734\) 5.29150 0.195313
\(735\) 0 0
\(736\) 3.00000 + 3.74166i 0.110581 + 0.137919i
\(737\) −42.0000 −1.54709
\(738\) 5.65685i 0.208232i
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) 31.7490 1.16633
\(742\) 9.89949i 0.363422i
\(743\) 7.48331i 0.274536i −0.990534 0.137268i \(-0.956168\pi\)
0.990534 0.137268i \(-0.0438322\pi\)
\(744\) 12.0000 0.439941
\(745\) 0 0
\(746\) 11.2250i 0.410975i
\(747\) 15.8745 0.580818
\(748\) 0 0
\(749\) 9.89949i 0.361720i
\(750\) 0 0
\(751\) 22.4499i 0.819210i −0.912263 0.409605i \(-0.865667\pi\)
0.912263 0.409605i \(-0.134333\pi\)
\(752\) 2.82843i 0.103142i
\(753\) 22.4499i 0.818121i
\(754\) 25.4558i 0.927047i
\(755\) 0 0
\(756\) 14.9666i 0.544331i
\(757\) 33.6749i 1.22394i −0.790883 0.611968i \(-0.790378\pi\)
0.790883 0.611968i \(-0.209622\pi\)
\(758\) 11.2250i 0.407709i
\(759\) 15.8745 + 19.7990i 0.576208 + 0.718658i
\(760\) 0 0
\(761\) 2.82843i 0.102530i 0.998685 + 0.0512652i \(0.0163254\pi\)
−0.998685 + 0.0512652i \(0.983675\pi\)
\(762\) 11.3137i 0.409852i
\(763\) 29.6985i 1.07516i
\(764\) 14.9666i 0.541474i
\(765\) 0 0
\(766\) 15.8745 0.573569
\(767\) 42.0000 1.51653
\(768\) 1.41421i 0.0510310i
\(769\) −21.1660 −0.763266 −0.381633 0.924314i \(-0.624638\pi\)
−0.381633 + 0.924314i \(0.624638\pi\)
\(770\) 0 0
\(771\) −4.00000 −0.144056
\(772\) −16.0000 −0.575853
\(773\) −31.7490 −1.14193 −0.570966 0.820973i \(-0.693431\pi\)
−0.570966 + 0.820973i \(0.693431\pi\)
\(774\) 11.2250i 0.403473i
\(775\) 42.4264i 1.52400i
\(776\) 5.29150 0.189954
\(777\) 42.0000 1.50674
\(778\) 18.7083i 0.670725i
\(779\) 29.9333i 1.07247i
\(780\) 0 0
\(781\) 22.4499i 0.803322i
\(782\) 0 0
\(783\) 33.9411i 1.21296i
\(784\) 7.00000 0.250000
\(785\) 0 0
\(786\) 10.0000 0.356688
\(787\) 26.4575 0.943108 0.471554 0.881837i \(-0.343693\pi\)
0.471554 + 0.881837i \(0.343693\pi\)
\(788\) 6.00000 0.213741
\(789\) 10.5830 0.376765
\(790\) 0 0
\(791\) 19.7990i 0.703971i
\(792\) 3.74166i 0.132954i
\(793\) 44.8999i 1.59444i
\(794\) 12.7279i 0.451697i
\(795\) 0 0
\(796\) 10.5830 0.375105
\(797\) −31.7490 −1.12461 −0.562304 0.826931i \(-0.690085\pi\)
−0.562304 + 0.826931i \(0.690085\pi\)