Properties

Label 4020.2.g.c.1609.12
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.12
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.31

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(0.145309 + 2.23134i) q^{5}\) \(-1.12842i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(0.145309 + 2.23134i) q^{5}\) \(-1.12842i q^{7}\) \(-1.00000 q^{9}\) \(+6.26399 q^{11}\) \(-0.929302i q^{13}\) \(+(2.23134 - 0.145309i) q^{15}\) \(-1.84970i q^{17}\) \(-5.56412 q^{19}\) \(-1.12842 q^{21}\) \(-6.60354i q^{23}\) \(+(-4.95777 + 0.648470i) q^{25}\) \(+1.00000i q^{27}\) \(+2.69947 q^{29}\) \(-10.1966 q^{31}\) \(-6.26399i q^{33}\) \(+(2.51789 - 0.163970i) q^{35}\) \(-3.96694i q^{37}\) \(-0.929302 q^{39}\) \(+6.94365 q^{41}\) \(-8.50773i q^{43}\) \(+(-0.145309 - 2.23134i) q^{45}\) \(+2.02625i q^{47}\) \(+5.72667 q^{49}\) \(-1.84970 q^{51}\) \(-12.2342i q^{53}\) \(+(0.910217 + 13.9771i) q^{55}\) \(+5.56412i q^{57}\) \(-10.5150 q^{59}\) \(+13.6403 q^{61}\) \(+1.12842i q^{63}\) \(+(2.07359 - 0.135036i) q^{65}\) \(-1.00000i q^{67}\) \(-6.60354 q^{69}\) \(+1.79047 q^{71}\) \(+8.93411i q^{73}\) \(+(0.648470 + 4.95777i) q^{75}\) \(-7.06842i q^{77}\) \(-0.0306733 q^{79}\) \(+1.00000 q^{81}\) \(+14.1845i q^{83}\) \(+(4.12731 - 0.268779i) q^{85}\) \(-2.69947i q^{87}\) \(-5.95555 q^{89}\) \(-1.04864 q^{91}\) \(+10.1966i q^{93}\) \(+(-0.808518 - 12.4154i) q^{95}\) \(-12.2239i q^{97}\) \(-6.26399 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 0.145309 + 2.23134i 0.0649844 + 0.997886i
\(6\) 0 0
\(7\) 1.12842i 0.426503i −0.976997 0.213252i \(-0.931595\pi\)
0.976997 0.213252i \(-0.0684054\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 6.26399 1.88866 0.944332 0.328994i \(-0.106710\pi\)
0.944332 + 0.328994i \(0.106710\pi\)
\(12\) 0 0
\(13\) 0.929302i 0.257742i −0.991661 0.128871i \(-0.958865\pi\)
0.991661 0.128871i \(-0.0411353\pi\)
\(14\) 0 0
\(15\) 2.23134 0.145309i 0.576130 0.0375187i
\(16\) 0 0
\(17\) 1.84970i 0.448618i −0.974518 0.224309i \(-0.927987\pi\)
0.974518 0.224309i \(-0.0720125\pi\)
\(18\) 0 0
\(19\) −5.56412 −1.27650 −0.638248 0.769831i \(-0.720340\pi\)
−0.638248 + 0.769831i \(0.720340\pi\)
\(20\) 0 0
\(21\) −1.12842 −0.246242
\(22\) 0 0
\(23\) 6.60354i 1.37693i −0.725268 0.688467i \(-0.758284\pi\)
0.725268 0.688467i \(-0.241716\pi\)
\(24\) 0 0
\(25\) −4.95777 + 0.648470i −0.991554 + 0.129694i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 2.69947 0.501279 0.250640 0.968080i \(-0.419359\pi\)
0.250640 + 0.968080i \(0.419359\pi\)
\(30\) 0 0
\(31\) −10.1966 −1.83136 −0.915682 0.401905i \(-0.868348\pi\)
−0.915682 + 0.401905i \(0.868348\pi\)
\(32\) 0 0
\(33\) 6.26399i 1.09042i
\(34\) 0 0
\(35\) 2.51789 0.163970i 0.425602 0.0277160i
\(36\) 0 0
\(37\) 3.96694i 0.652161i −0.945342 0.326080i \(-0.894272\pi\)
0.945342 0.326080i \(-0.105728\pi\)
\(38\) 0 0
\(39\) −0.929302 −0.148807
\(40\) 0 0
\(41\) 6.94365 1.08442 0.542208 0.840245i \(-0.317589\pi\)
0.542208 + 0.840245i \(0.317589\pi\)
\(42\) 0 0
\(43\) 8.50773i 1.29742i −0.761037 0.648709i \(-0.775309\pi\)
0.761037 0.648709i \(-0.224691\pi\)
\(44\) 0 0
\(45\) −0.145309 2.23134i −0.0216615 0.332629i
\(46\) 0 0
\(47\) 2.02625i 0.295559i 0.989020 + 0.147779i \(0.0472126\pi\)
−0.989020 + 0.147779i \(0.952787\pi\)
\(48\) 0 0
\(49\) 5.72667 0.818095
\(50\) 0 0
\(51\) −1.84970 −0.259010
\(52\) 0 0
\(53\) 12.2342i 1.68049i −0.542203 0.840247i \(-0.682410\pi\)
0.542203 0.840247i \(-0.317590\pi\)
\(54\) 0 0
\(55\) 0.910217 + 13.9771i 0.122734 + 1.88467i
\(56\) 0 0
\(57\) 5.56412i 0.736985i
\(58\) 0 0
\(59\) −10.5150 −1.36893 −0.684467 0.729044i \(-0.739965\pi\)
−0.684467 + 0.729044i \(0.739965\pi\)
\(60\) 0 0
\(61\) 13.6403 1.74646 0.873232 0.487305i \(-0.162020\pi\)
0.873232 + 0.487305i \(0.162020\pi\)
\(62\) 0 0
\(63\) 1.12842i 0.142168i
\(64\) 0 0
\(65\) 2.07359 0.135036i 0.257197 0.0167492i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −6.60354 −0.794973
\(70\) 0 0
\(71\) 1.79047 0.212489 0.106245 0.994340i \(-0.466117\pi\)
0.106245 + 0.994340i \(0.466117\pi\)
\(72\) 0 0
\(73\) 8.93411i 1.04566i 0.852437 + 0.522829i \(0.175124\pi\)
−0.852437 + 0.522829i \(0.824876\pi\)
\(74\) 0 0
\(75\) 0.648470 + 4.95777i 0.0748789 + 0.572474i
\(76\) 0 0
\(77\) 7.06842i 0.805521i
\(78\) 0 0
\(79\) −0.0306733 −0.00345101 −0.00172551 0.999999i \(-0.500549\pi\)
−0.00172551 + 0.999999i \(0.500549\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 14.1845i 1.55695i 0.627674 + 0.778476i \(0.284007\pi\)
−0.627674 + 0.778476i \(0.715993\pi\)
\(84\) 0 0
\(85\) 4.12731 0.268779i 0.447670 0.0291532i
\(86\) 0 0
\(87\) 2.69947i 0.289414i
\(88\) 0 0
\(89\) −5.95555 −0.631287 −0.315644 0.948878i \(-0.602220\pi\)
−0.315644 + 0.948878i \(0.602220\pi\)
\(90\) 0 0
\(91\) −1.04864 −0.109928
\(92\) 0 0
\(93\) 10.1966i 1.05734i
\(94\) 0 0
\(95\) −0.808518 12.4154i −0.0829522 1.27380i
\(96\) 0 0
\(97\) 12.2239i 1.24115i −0.784147 0.620576i \(-0.786899\pi\)
0.784147 0.620576i \(-0.213101\pi\)
\(98\) 0 0
\(99\) −6.26399 −0.629555
\(100\) 0 0
\(101\) −5.60500 −0.557719 −0.278859 0.960332i \(-0.589956\pi\)
−0.278859 + 0.960332i \(0.589956\pi\)
\(102\) 0 0
\(103\) 8.34053i 0.821817i 0.911677 + 0.410909i \(0.134788\pi\)
−0.911677 + 0.410909i \(0.865212\pi\)
\(104\) 0 0
\(105\) −0.163970 2.51789i −0.0160019 0.245721i
\(106\) 0 0
\(107\) 3.33167i 0.322084i 0.986948 + 0.161042i \(0.0514855\pi\)
−0.986948 + 0.161042i \(0.948514\pi\)
\(108\) 0 0
\(109\) 5.52141 0.528855 0.264427 0.964406i \(-0.414817\pi\)
0.264427 + 0.964406i \(0.414817\pi\)
\(110\) 0 0
\(111\) −3.96694 −0.376525
\(112\) 0 0
\(113\) 10.4110i 0.979385i −0.871895 0.489692i \(-0.837109\pi\)
0.871895 0.489692i \(-0.162891\pi\)
\(114\) 0 0
\(115\) 14.7348 0.959556i 1.37402 0.0894791i
\(116\) 0 0
\(117\) 0.929302i 0.0859140i
\(118\) 0 0
\(119\) −2.08724 −0.191337
\(120\) 0 0
\(121\) 28.2376 2.56705
\(122\) 0 0
\(123\) 6.94365i 0.626087i
\(124\) 0 0
\(125\) −2.16737 10.9683i −0.193855 0.981030i
\(126\) 0 0
\(127\) 8.02001i 0.711661i −0.934551 0.355830i \(-0.884198\pi\)
0.934551 0.355830i \(-0.115802\pi\)
\(128\) 0 0
\(129\) −8.50773 −0.749064
\(130\) 0 0
\(131\) 4.87634 0.426048 0.213024 0.977047i \(-0.431669\pi\)
0.213024 + 0.977047i \(0.431669\pi\)
\(132\) 0 0
\(133\) 6.27867i 0.544429i
\(134\) 0 0
\(135\) −2.23134 + 0.145309i −0.192043 + 0.0125062i
\(136\) 0 0
\(137\) 6.55953i 0.560419i −0.959939 0.280209i \(-0.909596\pi\)
0.959939 0.280209i \(-0.0904039\pi\)
\(138\) 0 0
\(139\) −11.9185 −1.01091 −0.505456 0.862852i \(-0.668676\pi\)
−0.505456 + 0.862852i \(0.668676\pi\)
\(140\) 0 0
\(141\) 2.02625 0.170641
\(142\) 0 0
\(143\) 5.82113i 0.486788i
\(144\) 0 0
\(145\) 0.392259 + 6.02344i 0.0325753 + 0.500220i
\(146\) 0 0
\(147\) 5.72667i 0.472327i
\(148\) 0 0
\(149\) 7.26428 0.595113 0.297557 0.954704i \(-0.403828\pi\)
0.297557 + 0.954704i \(0.403828\pi\)
\(150\) 0 0
\(151\) 15.7162 1.27897 0.639484 0.768805i \(-0.279148\pi\)
0.639484 + 0.768805i \(0.279148\pi\)
\(152\) 0 0
\(153\) 1.84970i 0.149539i
\(154\) 0 0
\(155\) −1.48166 22.7521i −0.119010 1.82749i
\(156\) 0 0
\(157\) 12.8287i 1.02385i −0.859032 0.511923i \(-0.828933\pi\)
0.859032 0.511923i \(-0.171067\pi\)
\(158\) 0 0
\(159\) −12.2342 −0.970234
\(160\) 0 0
\(161\) −7.45157 −0.587266
\(162\) 0 0
\(163\) 20.9223i 1.63876i −0.573249 0.819381i \(-0.694317\pi\)
0.573249 0.819381i \(-0.305683\pi\)
\(164\) 0 0
\(165\) 13.9771 0.910217i 1.08812 0.0708603i
\(166\) 0 0
\(167\) 11.6346i 0.900311i −0.892950 0.450155i \(-0.851369\pi\)
0.892950 0.450155i \(-0.148631\pi\)
\(168\) 0 0
\(169\) 12.1364 0.933569
\(170\) 0 0
\(171\) 5.56412 0.425499
\(172\) 0 0
\(173\) 11.2044i 0.851857i −0.904757 0.425928i \(-0.859948\pi\)
0.904757 0.425928i \(-0.140052\pi\)
\(174\) 0 0
\(175\) 0.731747 + 5.59445i 0.0553149 + 0.422901i
\(176\) 0 0
\(177\) 10.5150i 0.790354i
\(178\) 0 0
\(179\) −9.33753 −0.697920 −0.348960 0.937138i \(-0.613465\pi\)
−0.348960 + 0.937138i \(0.613465\pi\)
\(180\) 0 0
\(181\) −14.0490 −1.04425 −0.522125 0.852869i \(-0.674861\pi\)
−0.522125 + 0.852869i \(0.674861\pi\)
\(182\) 0 0
\(183\) 13.6403i 1.00832i
\(184\) 0 0
\(185\) 8.85159 0.576433i 0.650782 0.0423802i
\(186\) 0 0
\(187\) 11.5865i 0.847289i
\(188\) 0 0
\(189\) 1.12842 0.0820806
\(190\) 0 0
\(191\) 16.7184 1.20970 0.604850 0.796340i \(-0.293233\pi\)
0.604850 + 0.796340i \(0.293233\pi\)
\(192\) 0 0
\(193\) 9.43446i 0.679107i 0.940587 + 0.339554i \(0.110276\pi\)
−0.940587 + 0.339554i \(0.889724\pi\)
\(194\) 0 0
\(195\) −0.135036 2.07359i −0.00967015 0.148493i
\(196\) 0 0
\(197\) 5.96186i 0.424765i −0.977187 0.212382i \(-0.931878\pi\)
0.977187 0.212382i \(-0.0681222\pi\)
\(198\) 0 0
\(199\) −7.76009 −0.550098 −0.275049 0.961430i \(-0.588694\pi\)
−0.275049 + 0.961430i \(0.588694\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 3.04614i 0.213797i
\(204\) 0 0
\(205\) 1.00898 + 15.4936i 0.0704700 + 1.08212i
\(206\) 0 0
\(207\) 6.60354i 0.458978i
\(208\) 0 0
\(209\) −34.8536 −2.41087
\(210\) 0 0
\(211\) −15.5083 −1.06763 −0.533816 0.845601i \(-0.679243\pi\)
−0.533816 + 0.845601i \(0.679243\pi\)
\(212\) 0 0
\(213\) 1.79047i 0.122681i
\(214\) 0 0
\(215\) 18.9837 1.23625i 1.29467 0.0843118i
\(216\) 0 0
\(217\) 11.5061i 0.781082i
\(218\) 0 0
\(219\) 8.93411 0.603711
\(220\) 0 0
\(221\) −1.71893 −0.115628
\(222\) 0 0
\(223\) 23.4454i 1.57002i −0.619483 0.785010i \(-0.712658\pi\)
0.619483 0.785010i \(-0.287342\pi\)
\(224\) 0 0
\(225\) 4.95777 0.648470i 0.330518 0.0432313i
\(226\) 0 0
\(227\) 0.207600i 0.0137789i −0.999976 0.00688945i \(-0.997807\pi\)
0.999976 0.00688945i \(-0.00219300\pi\)
\(228\) 0 0
\(229\) 2.26426 0.149627 0.0748134 0.997198i \(-0.476164\pi\)
0.0748134 + 0.997198i \(0.476164\pi\)
\(230\) 0 0
\(231\) −7.06842 −0.465068
\(232\) 0 0
\(233\) 7.58804i 0.497109i −0.968618 0.248554i \(-0.920045\pi\)
0.968618 0.248554i \(-0.0799555\pi\)
\(234\) 0 0
\(235\) −4.52125 + 0.294433i −0.294934 + 0.0192067i
\(236\) 0 0
\(237\) 0.0306733i 0.00199244i
\(238\) 0 0
\(239\) −6.66454 −0.431094 −0.215547 0.976494i \(-0.569153\pi\)
−0.215547 + 0.976494i \(0.569153\pi\)
\(240\) 0 0
\(241\) 3.97697 0.256179 0.128090 0.991763i \(-0.459115\pi\)
0.128090 + 0.991763i \(0.459115\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 0.832138 + 12.7781i 0.0531634 + 0.816366i
\(246\) 0 0
\(247\) 5.17074i 0.329006i
\(248\) 0 0
\(249\) 14.1845 0.898907
\(250\) 0 0
\(251\) −12.7120 −0.802376 −0.401188 0.915996i \(-0.631403\pi\)
−0.401188 + 0.915996i \(0.631403\pi\)
\(252\) 0 0
\(253\) 41.3645i 2.60056i
\(254\) 0 0
\(255\) −0.268779 4.12731i −0.0168316 0.258462i
\(256\) 0 0
\(257\) 9.22292i 0.575310i 0.957734 + 0.287655i \(0.0928756\pi\)
−0.957734 + 0.287655i \(0.907124\pi\)
\(258\) 0 0
\(259\) −4.47638 −0.278149
\(260\) 0 0
\(261\) −2.69947 −0.167093
\(262\) 0 0
\(263\) 4.58502i 0.282725i 0.989958 + 0.141362i \(0.0451482\pi\)
−0.989958 + 0.141362i \(0.954852\pi\)
\(264\) 0 0
\(265\) 27.2986 1.77774i 1.67694 0.109206i
\(266\) 0 0
\(267\) 5.95555i 0.364474i
\(268\) 0 0
\(269\) 14.1482 0.862629 0.431315 0.902202i \(-0.358050\pi\)
0.431315 + 0.902202i \(0.358050\pi\)
\(270\) 0 0
\(271\) 15.3501 0.932453 0.466226 0.884666i \(-0.345613\pi\)
0.466226 + 0.884666i \(0.345613\pi\)
\(272\) 0 0
\(273\) 1.04864i 0.0634668i
\(274\) 0 0
\(275\) −31.0554 + 4.06201i −1.87271 + 0.244948i
\(276\) 0 0
\(277\) 9.60094i 0.576865i 0.957500 + 0.288432i \(0.0931340\pi\)
−0.957500 + 0.288432i \(0.906866\pi\)
\(278\) 0 0
\(279\) 10.1966 0.610454
\(280\) 0 0
\(281\) −10.0081 −0.597034 −0.298517 0.954404i \(-0.596492\pi\)
−0.298517 + 0.954404i \(0.596492\pi\)
\(282\) 0 0
\(283\) 14.4995i 0.861908i −0.902374 0.430954i \(-0.858177\pi\)
0.902374 0.430954i \(-0.141823\pi\)
\(284\) 0 0
\(285\) −12.4154 + 0.808518i −0.735427 + 0.0478925i
\(286\) 0 0
\(287\) 7.83536i 0.462507i
\(288\) 0 0
\(289\) 13.5786 0.798742
\(290\) 0 0
\(291\) −12.2239 −0.716579
\(292\) 0 0
\(293\) 30.2685i 1.76831i 0.467198 + 0.884153i \(0.345264\pi\)
−0.467198 + 0.884153i \(0.654736\pi\)
\(294\) 0 0
\(295\) −1.52792 23.4625i −0.0889592 1.36604i
\(296\) 0 0
\(297\) 6.26399i 0.363473i
\(298\) 0 0
\(299\) −6.13668 −0.354893
\(300\) 0 0
\(301\) −9.60031 −0.553352
\(302\) 0 0
\(303\) 5.60500i 0.321999i
\(304\) 0 0
\(305\) 1.98207 + 30.4362i 0.113493 + 1.74277i
\(306\) 0 0
\(307\) 12.3548i 0.705124i −0.935788 0.352562i \(-0.885311\pi\)
0.935788 0.352562i \(-0.114689\pi\)
\(308\) 0 0
\(309\) 8.34053 0.474476
\(310\) 0 0
\(311\) 1.22589 0.0695140 0.0347570 0.999396i \(-0.488934\pi\)
0.0347570 + 0.999396i \(0.488934\pi\)
\(312\) 0 0
\(313\) 29.0382i 1.64133i 0.571407 + 0.820667i \(0.306398\pi\)
−0.571407 + 0.820667i \(0.693602\pi\)
\(314\) 0 0
\(315\) −2.51789 + 0.163970i −0.141867 + 0.00923868i
\(316\) 0 0
\(317\) 5.85567i 0.328887i −0.986386 0.164444i \(-0.947417\pi\)
0.986386 0.164444i \(-0.0525829\pi\)
\(318\) 0 0
\(319\) 16.9095 0.946748
\(320\) 0 0
\(321\) 3.33167 0.185956
\(322\) 0 0
\(323\) 10.2919i 0.572659i
\(324\) 0 0
\(325\) 0.602624 + 4.60726i 0.0334276 + 0.255565i
\(326\) 0 0
\(327\) 5.52141i 0.305334i
\(328\) 0 0
\(329\) 2.28646 0.126057
\(330\) 0 0
\(331\) 10.6855 0.587328 0.293664 0.955909i \(-0.405125\pi\)
0.293664 + 0.955909i \(0.405125\pi\)
\(332\) 0 0
\(333\) 3.96694i 0.217387i
\(334\) 0 0
\(335\) 2.23134 0.145309i 0.121911 0.00793910i
\(336\) 0 0
\(337\) 18.7175i 1.01961i −0.860291 0.509804i \(-0.829718\pi\)
0.860291 0.509804i \(-0.170282\pi\)
\(338\) 0 0
\(339\) −10.4110 −0.565448
\(340\) 0 0
\(341\) −63.8714 −3.45883
\(342\) 0 0
\(343\) 14.3610i 0.775423i
\(344\) 0 0
\(345\) −0.959556 14.7348i −0.0516608 0.793292i
\(346\) 0 0
\(347\) 8.82254i 0.473619i 0.971556 + 0.236809i \(0.0761017\pi\)
−0.971556 + 0.236809i \(0.923898\pi\)
\(348\) 0 0
\(349\) 33.8915 1.81417 0.907086 0.420945i \(-0.138302\pi\)
0.907086 + 0.420945i \(0.138302\pi\)
\(350\) 0 0
\(351\) 0.929302 0.0496025
\(352\) 0 0
\(353\) 5.88350i 0.313147i 0.987666 + 0.156574i \(0.0500448\pi\)
−0.987666 + 0.156574i \(0.949955\pi\)
\(354\) 0 0
\(355\) 0.260172 + 3.99514i 0.0138085 + 0.212040i
\(356\) 0 0
\(357\) 2.08724i 0.110468i
\(358\) 0 0
\(359\) −9.66040 −0.509857 −0.254928 0.966960i \(-0.582052\pi\)
−0.254928 + 0.966960i \(0.582052\pi\)
\(360\) 0 0
\(361\) 11.9594 0.629441
\(362\) 0 0
\(363\) 28.2376i 1.48209i
\(364\) 0 0
\(365\) −19.9351 + 1.29821i −1.04345 + 0.0679515i
\(366\) 0 0
\(367\) 19.9664i 1.04224i 0.853484 + 0.521119i \(0.174485\pi\)
−0.853484 + 0.521119i \(0.825515\pi\)
\(368\) 0 0
\(369\) −6.94365 −0.361472
\(370\) 0 0
\(371\) −13.8053 −0.716736
\(372\) 0 0
\(373\) 22.7056i 1.17565i 0.808988 + 0.587825i \(0.200016\pi\)
−0.808988 + 0.587825i \(0.799984\pi\)
\(374\) 0 0
\(375\) −10.9683 + 2.16737i −0.566398 + 0.111922i
\(376\) 0 0
\(377\) 2.50862i 0.129201i
\(378\) 0 0
\(379\) −20.8020 −1.06852 −0.534262 0.845319i \(-0.679411\pi\)
−0.534262 + 0.845319i \(0.679411\pi\)
\(380\) 0 0
\(381\) −8.02001 −0.410878
\(382\) 0 0
\(383\) 2.80878i 0.143522i −0.997422 0.0717610i \(-0.977138\pi\)
0.997422 0.0717610i \(-0.0228619\pi\)
\(384\) 0 0
\(385\) 15.7721 1.02711i 0.803818 0.0523463i
\(386\) 0 0
\(387\) 8.50773i 0.432472i
\(388\) 0 0
\(389\) 4.10035 0.207896 0.103948 0.994583i \(-0.466852\pi\)
0.103948 + 0.994583i \(0.466852\pi\)
\(390\) 0 0
\(391\) −12.2146 −0.617717
\(392\) 0 0
\(393\) 4.87634i 0.245979i
\(394\) 0 0
\(395\) −0.00445711 0.0684425i −0.000224262 0.00344372i
\(396\) 0 0
\(397\) 10.0390i 0.503843i −0.967748 0.251921i \(-0.918938\pi\)
0.967748 0.251921i \(-0.0810624\pi\)
\(398\) 0 0
\(399\) 6.27867 0.314326
\(400\) 0 0
\(401\) 25.2690 1.26187 0.630936 0.775835i \(-0.282671\pi\)
0.630936 + 0.775835i \(0.282671\pi\)
\(402\) 0 0
\(403\) 9.47572i 0.472019i
\(404\) 0 0
\(405\) 0.145309 + 2.23134i 0.00722048 + 0.110876i
\(406\) 0 0
\(407\) 24.8489i 1.23171i
\(408\) 0 0
\(409\) −38.6571 −1.91147 −0.955735 0.294230i \(-0.904937\pi\)
−0.955735 + 0.294230i \(0.904937\pi\)
\(410\) 0 0
\(411\) −6.55953 −0.323558
\(412\) 0 0
\(413\) 11.8653i 0.583854i
\(414\) 0 0
\(415\) −31.6505 + 2.06114i −1.55366 + 0.101178i
\(416\) 0 0
\(417\) 11.9185i 0.583650i
\(418\) 0 0
\(419\) 7.77628 0.379896 0.189948 0.981794i \(-0.439168\pi\)
0.189948 + 0.981794i \(0.439168\pi\)
\(420\) 0 0
\(421\) −13.5152 −0.658690 −0.329345 0.944210i \(-0.606828\pi\)
−0.329345 + 0.944210i \(0.606828\pi\)
\(422\) 0 0
\(423\) 2.02625i 0.0985196i
\(424\) 0 0
\(425\) 1.19947 + 9.17039i 0.0581831 + 0.444829i
\(426\) 0 0
\(427\) 15.3920i 0.744872i
\(428\) 0 0
\(429\) −5.82113 −0.281047
\(430\) 0 0
\(431\) 24.4327 1.17688 0.588440 0.808541i \(-0.299742\pi\)
0.588440 + 0.808541i \(0.299742\pi\)
\(432\) 0 0
\(433\) 13.0026i 0.624863i 0.949940 + 0.312431i \(0.101143\pi\)
−0.949940 + 0.312431i \(0.898857\pi\)
\(434\) 0 0
\(435\) 6.02344 0.392259i 0.288802 0.0188074i
\(436\) 0 0
\(437\) 36.7429i 1.75765i
\(438\) 0 0
\(439\) 26.6723 1.27300 0.636500 0.771277i \(-0.280381\pi\)
0.636500 + 0.771277i \(0.280381\pi\)
\(440\) 0 0
\(441\) −5.72667 −0.272698
\(442\) 0 0
\(443\) 34.3767i 1.63329i −0.577141 0.816644i \(-0.695832\pi\)
0.577141 0.816644i \(-0.304168\pi\)
\(444\) 0 0
\(445\) −0.865398 13.2889i −0.0410238 0.629953i
\(446\) 0 0
\(447\) 7.26428i 0.343589i
\(448\) 0 0
\(449\) −24.4317 −1.15300 −0.576501 0.817097i \(-0.695582\pi\)
−0.576501 + 0.817097i \(0.695582\pi\)
\(450\) 0 0
\(451\) 43.4949 2.04810
\(452\) 0 0
\(453\) 15.7162i 0.738412i
\(454\) 0 0
\(455\) −0.152378 2.33988i −0.00714358 0.109695i
\(456\) 0 0
\(457\) 19.0286i 0.890119i 0.895501 + 0.445059i \(0.146817\pi\)
−0.895501 + 0.445059i \(0.853183\pi\)
\(458\) 0 0
\(459\) 1.84970 0.0863366
\(460\) 0 0
\(461\) 20.4848 0.954074 0.477037 0.878883i \(-0.341711\pi\)
0.477037 + 0.878883i \(0.341711\pi\)
\(462\) 0 0
\(463\) 5.07492i 0.235852i −0.993022 0.117926i \(-0.962375\pi\)
0.993022 0.117926i \(-0.0376245\pi\)
\(464\) 0 0
\(465\) −22.7521 + 1.48166i −1.05510 + 0.0687104i
\(466\) 0 0
\(467\) 25.8385i 1.19566i −0.801622 0.597832i \(-0.796029\pi\)
0.801622 0.597832i \(-0.203971\pi\)
\(468\) 0 0
\(469\) −1.12842 −0.0521057
\(470\) 0 0
\(471\) −12.8287 −0.591117
\(472\) 0 0
\(473\) 53.2923i 2.45038i
\(474\) 0 0
\(475\) 27.5856 3.60816i 1.26571 0.165554i
\(476\) 0 0
\(477\) 12.2342i 0.560165i
\(478\) 0 0
\(479\) 2.47132 0.112918 0.0564589 0.998405i \(-0.482019\pi\)
0.0564589 + 0.998405i \(0.482019\pi\)
\(480\) 0 0
\(481\) −3.68648 −0.168089
\(482\) 0 0
\(483\) 7.45157i 0.339058i
\(484\) 0 0
\(485\) 27.2758 1.77625i 1.23853 0.0806554i
\(486\) 0 0
\(487\) 23.8384i 1.08022i −0.841595 0.540110i \(-0.818383\pi\)
0.841595 0.540110i \(-0.181617\pi\)
\(488\) 0 0
\(489\) −20.9223 −0.946140
\(490\) 0 0
\(491\) −23.9747 −1.08196 −0.540982 0.841034i \(-0.681947\pi\)
−0.540982 + 0.841034i \(0.681947\pi\)
\(492\) 0 0
\(493\) 4.99321i 0.224883i
\(494\) 0 0
\(495\) −0.910217 13.9771i −0.0409112 0.628224i
\(496\) 0 0
\(497\) 2.02040i 0.0906273i
\(498\) 0 0
\(499\) −28.8330 −1.29074 −0.645371 0.763869i \(-0.723297\pi\)
−0.645371 + 0.763869i \(0.723297\pi\)
\(500\) 0 0
\(501\) −11.6346 −0.519795
\(502\) 0 0
\(503\) 7.31901i 0.326339i 0.986598 + 0.163169i \(0.0521717\pi\)
−0.986598 + 0.163169i \(0.947828\pi\)
\(504\) 0 0
\(505\) −0.814460 12.5067i −0.0362430 0.556540i
\(506\) 0 0
\(507\) 12.1364i 0.538996i
\(508\) 0 0
\(509\) −27.1764 −1.20457 −0.602286 0.798280i \(-0.705743\pi\)
−0.602286 + 0.798280i \(0.705743\pi\)
\(510\) 0 0
\(511\) 10.0814 0.445977
\(512\) 0 0
\(513\) 5.56412i 0.245662i
\(514\) 0 0
\(515\) −18.6106 + 1.21196i −0.820080 + 0.0534052i
\(516\) 0 0
\(517\) 12.6924i 0.558211i
\(518\) 0 0
\(519\) −11.2044 −0.491820
\(520\) 0 0
\(521\) 36.7097 1.60828 0.804141 0.594439i \(-0.202626\pi\)
0.804141 + 0.594439i \(0.202626\pi\)
\(522\) 0 0
\(523\) 23.1431i 1.01198i 0.862541 + 0.505988i \(0.168872\pi\)
−0.862541 + 0.505988i \(0.831128\pi\)
\(524\) 0 0
\(525\) 5.59445 0.731747i 0.244162 0.0319361i
\(526\) 0 0
\(527\) 18.8606i 0.821583i
\(528\) 0 0
\(529\) −20.6067 −0.895945
\(530\) 0 0
\(531\) 10.5150 0.456311
\(532\) 0 0
\(533\) 6.45274i 0.279499i
\(534\) 0 0
\(535\) −7.43409 + 0.484123i −0.321404 + 0.0209304i
\(536\) 0 0
\(537\) 9.33753i 0.402944i
\(538\) 0 0
\(539\) 35.8718 1.54511
\(540\) 0 0
\(541\) 11.1264 0.478362 0.239181 0.970975i \(-0.423121\pi\)
0.239181 + 0.970975i \(0.423121\pi\)
\(542\) 0 0
\(543\) 14.0490i 0.602898i
\(544\) 0 0
\(545\) 0.802312 + 12.3201i 0.0343673 + 0.527737i
\(546\) 0 0
\(547\) 39.2846i 1.67969i 0.542829 + 0.839843i \(0.317353\pi\)
−0.542829 + 0.839843i \(0.682647\pi\)
\(548\) 0 0
\(549\) −13.6403 −0.582155
\(550\) 0 0
\(551\) −15.0202 −0.639881
\(552\) 0 0
\(553\) 0.0346124i 0.00147187i
\(554\) 0 0
\(555\) −0.576433 8.85159i −0.0244682 0.375729i
\(556\) 0 0
\(557\) 8.00977i 0.339385i −0.985497 0.169692i \(-0.945723\pi\)
0.985497 0.169692i \(-0.0542774\pi\)
\(558\) 0 0
\(559\) −7.90625 −0.334399
\(560\) 0 0
\(561\) −11.5865 −0.489182
\(562\) 0 0
\(563\) 10.0007i 0.421478i 0.977542 + 0.210739i \(0.0675871\pi\)
−0.977542 + 0.210739i \(0.932413\pi\)
\(564\) 0 0
\(565\) 23.2305 1.51282i 0.977315 0.0636447i
\(566\) 0 0
\(567\) 1.12842i 0.0473892i
\(568\) 0 0
\(569\) −14.2167 −0.595994 −0.297997 0.954567i \(-0.596319\pi\)
−0.297997 + 0.954567i \(0.596319\pi\)
\(570\) 0 0
\(571\) 43.1228 1.80463 0.902317 0.431072i \(-0.141865\pi\)
0.902317 + 0.431072i \(0.141865\pi\)
\(572\) 0 0
\(573\) 16.7184i 0.698420i
\(574\) 0 0
\(575\) 4.28220 + 32.7388i 0.178580 + 1.36530i
\(576\) 0 0
\(577\) 28.1240i 1.17082i 0.810739 + 0.585408i \(0.199066\pi\)
−0.810739 + 0.585408i \(0.800934\pi\)
\(578\) 0 0
\(579\) 9.43446 0.392083
\(580\) 0 0
\(581\) 16.0061 0.664045
\(582\) 0 0
\(583\) 76.6348i 3.17389i
\(584\) 0 0
\(585\) −2.07359 + 0.135036i −0.0857324 + 0.00558306i
\(586\) 0 0
\(587\) 16.9796i 0.700825i 0.936595 + 0.350412i \(0.113959\pi\)
−0.936595 + 0.350412i \(0.886041\pi\)
\(588\) 0 0
\(589\) 56.7350 2.33773
\(590\) 0 0
\(591\) −5.96186 −0.245238
\(592\) 0 0
\(593\) 10.5640i 0.433811i −0.976193 0.216905i \(-0.930404\pi\)
0.976193 0.216905i \(-0.0695963\pi\)
\(594\) 0 0
\(595\) −0.303296 4.65735i −0.0124339 0.190933i
\(596\) 0 0
\(597\) 7.76009i 0.317599i
\(598\) 0 0
\(599\) −4.96729 −0.202958 −0.101479 0.994838i \(-0.532357\pi\)
−0.101479 + 0.994838i \(0.532357\pi\)
\(600\) 0 0
\(601\) −32.3830 −1.32093 −0.660465 0.750857i \(-0.729641\pi\)
−0.660465 + 0.750857i \(0.729641\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 4.10318 + 63.0076i 0.166818 + 2.56162i
\(606\) 0 0
\(607\) 10.8553i 0.440604i 0.975432 + 0.220302i \(0.0707042\pi\)
−0.975432 + 0.220302i \(0.929296\pi\)
\(608\) 0 0
\(609\) −3.04614 −0.123436
\(610\) 0 0
\(611\) 1.88300 0.0761779
\(612\) 0 0
\(613\) 3.95967i 0.159930i −0.996798 0.0799648i \(-0.974519\pi\)
0.996798 0.0799648i \(-0.0254808\pi\)
\(614\) 0 0
\(615\) 15.4936 1.00898i 0.624764 0.0406859i
\(616\) 0 0
\(617\) 25.4694i 1.02536i −0.858580 0.512680i \(-0.828653\pi\)
0.858580 0.512680i \(-0.171347\pi\)
\(618\) 0 0
\(619\) 24.4008 0.980751 0.490375 0.871511i \(-0.336860\pi\)
0.490375 + 0.871511i \(0.336860\pi\)
\(620\) 0 0
\(621\) 6.60354 0.264991
\(622\) 0 0
\(623\) 6.72037i 0.269246i
\(624\) 0 0
\(625\) 24.1590 6.42993i 0.966359 0.257197i
\(626\) 0 0
\(627\) 34.8536i 1.39192i
\(628\) 0 0
\(629\) −7.33764 −0.292571
\(630\) 0 0
\(631\) −25.6736 −1.02205 −0.511025 0.859566i \(-0.670734\pi\)
−0.511025 + 0.859566i \(0.670734\pi\)
\(632\) 0 0
\(633\) 15.5083i 0.616398i
\(634\) 0 0
\(635\) 17.8954 1.16538i 0.710157 0.0462468i
\(636\) 0 0
\(637\) 5.32180i 0.210857i
\(638\) 0 0
\(639\) −1.79047 −0.0708297
\(640\) 0 0
\(641\) −37.4047 −1.47740 −0.738698 0.674037i \(-0.764559\pi\)
−0.738698 + 0.674037i \(0.764559\pi\)
\(642\) 0 0
\(643\) 48.6927i 1.92025i 0.279565 + 0.960127i \(0.409810\pi\)
−0.279565 + 0.960127i \(0.590190\pi\)
\(644\) 0 0
\(645\) −1.23625 18.9837i −0.0486774 0.747481i
\(646\) 0 0
\(647\) 10.1853i 0.400427i 0.979752 + 0.200213i \(0.0641636\pi\)
−0.979752 + 0.200213i \(0.935836\pi\)
\(648\) 0 0
\(649\) −65.8657 −2.58545
\(650\) 0 0
\(651\) 11.5061 0.450958
\(652\) 0 0
\(653\) 41.1225i 1.60925i 0.593784 + 0.804625i \(0.297633\pi\)
−0.593784 + 0.804625i \(0.702367\pi\)
\(654\) 0 0
\(655\) 0.708578 + 10.8808i 0.0276864 + 0.425147i
\(656\) 0 0
\(657\) 8.93411i 0.348553i
\(658\) 0 0
\(659\) −1.45845 −0.0568133 −0.0284067 0.999596i \(-0.509043\pi\)
−0.0284067 + 0.999596i \(0.509043\pi\)
\(660\) 0 0
\(661\) 22.1037 0.859733 0.429866 0.902893i \(-0.358561\pi\)
0.429866 + 0.902893i \(0.358561\pi\)
\(662\) 0 0
\(663\) 1.71893i 0.0667577i
\(664\) 0 0
\(665\) −14.0098 + 0.912349i −0.543279 + 0.0353794i
\(666\) 0 0
\(667\) 17.8261i 0.690228i
\(668\) 0 0
\(669\) −23.4454 −0.906452
\(670\) 0 0
\(671\) 85.4428 3.29848
\(672\) 0 0
\(673\) 3.54542i 0.136666i 0.997663 + 0.0683330i \(0.0217680\pi\)
−0.997663 + 0.0683330i \(0.978232\pi\)
\(674\) 0 0
\(675\) −0.648470 4.95777i −0.0249596 0.190825i
\(676\) 0 0
\(677\) 4.69231i 0.180340i −0.995926 0.0901701i \(-0.971259\pi\)
0.995926 0.0901701i \(-0.0287411\pi\)
\(678\) 0 0
\(679\) −13.7937 −0.529355
\(680\) 0 0
\(681\) −0.207600 −0.00795525
\(682\) 0 0
\(683\) 29.9186i 1.14480i 0.819973 + 0.572402i \(0.193988\pi\)
−0.819973 + 0.572402i \(0.806012\pi\)
\(684\) 0 0
\(685\) 14.6366 0.953162i 0.559234 0.0364184i
\(686\) 0 0
\(687\) 2.26426i 0.0863870i
\(688\) 0 0
\(689\) −11.3692 −0.433134
\(690\) 0 0
\(691\) 12.1635 0.462720 0.231360 0.972868i \(-0.425682\pi\)
0.231360 + 0.972868i \(0.425682\pi\)
\(692\) 0 0
\(693\) 7.06842i 0.268507i
\(694\) 0 0
\(695\) −1.73187 26.5942i −0.0656934 1.00877i
\(696\) 0 0
\(697\) 12.8437i 0.486488i
\(698\) 0 0
\(699\) −7.58804 −0.287006
\(700\) 0 0
\(701\) 7.77478 0.293649 0.146825 0.989163i \(-0.453095\pi\)
0.146825 + 0.989163i \(0.453095\pi\)
\(702\) 0 0
\(703\) 22.0725i 0.832480i
\(704\) 0 0
\(705\) 0.294433 + 4.52125i 0.0110890 + 0.170280i
\(706\) 0 0
\(707\) 6.32480i 0.237869i
\(708\) 0 0
\(709\) 29.3401 1.10189 0.550945 0.834541i \(-0.314267\pi\)
0.550945 + 0.834541i \(0.314267\pi\)
\(710\) 0 0
\(711\) 0.0306733 0.00115034
\(712\) 0 0
\(713\) 67.3336i 2.52166i
\(714\) 0 0
\(715\) 12.9889 0.845866i 0.485759 0.0316336i
\(716\) 0 0
\(717\) 6.66454i 0.248892i
\(718\) 0 0
\(719\) −5.33213 −0.198855 −0.0994274 0.995045i \(-0.531701\pi\)
−0.0994274 + 0.995045i \(0.531701\pi\)
\(720\) 0 0
\(721\) 9.41163 0.350508
\(722\) 0 0
\(723\) 3.97697i 0.147905i
\(724\) 0 0
\(725\) −13.3834 + 1.75053i −0.497046 + 0.0650129i
\(726\) 0 0
\(727\) 10.7400i 0.398323i −0.979967 0.199162i \(-0.936178\pi\)
0.979967 0.199162i \(-0.0638219\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −15.7368 −0.582045
\(732\) 0 0
\(733\) 21.6453i 0.799487i 0.916627 + 0.399744i \(0.130901\pi\)
−0.916627 + 0.399744i \(0.869099\pi\)
\(734\) 0 0
\(735\) 12.7781 0.832138i 0.471329 0.0306939i
\(736\) 0 0
\(737\) 6.26399i 0.230737i
\(738\) 0 0
\(739\) −2.20629 −0.0811595 −0.0405798 0.999176i \(-0.512920\pi\)
−0.0405798 + 0.999176i \(0.512920\pi\)
\(740\) 0 0
\(741\) 5.17074 0.189952
\(742\) 0 0
\(743\) 11.8727i 0.435567i −0.975997 0.217784i \(-0.930117\pi\)
0.975997 0.217784i \(-0.0698827\pi\)
\(744\) 0 0
\(745\) 1.05557 + 16.2091i 0.0386731 + 0.593855i
\(746\) 0 0
\(747\) 14.1845i 0.518984i
\(748\) 0 0
\(749\) 3.75952 0.137370
\(750\) 0 0
\(751\) 21.2180 0.774254 0.387127 0.922026i \(-0.373467\pi\)
0.387127 + 0.922026i \(0.373467\pi\)
\(752\) 0 0
\(753\) 12.7120i 0.463252i
\(754\) 0 0
\(755\) 2.28371 + 35.0682i 0.0831129 + 1.27626i
\(756\) 0 0
\(757\) 29.2197i 1.06201i 0.847370 + 0.531004i \(0.178185\pi\)
−0.847370 + 0.531004i \(0.821815\pi\)
\(758\) 0 0
\(759\) −41.3645 −1.50144
\(760\) 0 0
\(761\) −20.0081 −0.725294 −0.362647 0.931927i \(-0.618127\pi\)
−0.362647 + 0.931927i \(0.618127\pi\)
\(762\) 0 0
\(763\) 6.23047i 0.225558i
\(764\) 0 0
\(765\) −4.12731 + 0.268779i −0.149223 + 0.00971772i
\(766\) 0 0
\(767\) 9.77158i 0.352831i
\(768\) 0 0
\(769\) −6.34941 −0.228965 −0.114483 0.993425i \(-0.536521\pi\)
−0.114483 + 0.993425i \(0.536521\pi\)
\(770\) 0 0
\(771\) 9.22292 0.332155
\(772\) 0 0
\(773\) 51.7531i 1.86143i −0.365746 0.930715i \(-0.619186\pi\)
0.365746 0.930715i \(-0.380814\pi\)
\(774\) 0 0
\(775\) 50.5524 6.61219i 1.81590 0.237517i
\(776\) 0 0
\(777\) 4.47638i 0.160589i
\(778\) 0 0
\(779\) −38.6352 −1.38425
\(780\) 0 0
\(781\) 11.2155 0.401321
\(782\) 0 0
\(783\) 2.69947i 0.0964713i
\(784\) 0 0
\(785\) 28.6253 1.86414i 1.02168 0.0665339i
\(786\) 0 0
\(787\) 35.9857i 1.28275i 0.767227 + 0.641375i \(0.221636\pi\)
−0.767227 + 0.641375i \(0.778364\pi\)
\(788\) 0 0
\(789\) 4.58502 0.163231
\(790\) 0 0
\(791\) −11.7480 −0.417711
\(792\) 0