Properties

Label 1680.2.t.k.1009.5
Level $1680$
Weight $2$
Character 1680.1009
Analytic conductor $13.415$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.t (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1009.5
Root \(1.45161 + 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 1680.1009
Dual form 1680.2.t.k.1009.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{3} +(0.311108 + 2.21432i) q^{5} -1.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +(0.311108 + 2.21432i) q^{5} -1.00000i q^{7} -1.00000 q^{9} -2.00000 q^{11} -6.42864i q^{13} +(-2.21432 + 0.311108i) q^{15} -4.42864i q^{17} -2.42864 q^{19} +1.00000 q^{21} -1.37778i q^{23} +(-4.80642 + 1.37778i) q^{25} -1.00000i q^{27} -0.755569 q^{29} -5.18421 q^{31} -2.00000i q^{33} +(2.21432 - 0.311108i) q^{35} -7.61285i q^{37} +6.42864 q^{39} -8.23506 q^{41} -10.1017i q^{43} +(-0.311108 - 2.21432i) q^{45} +2.75557i q^{47} -1.00000 q^{49} +4.42864 q^{51} +9.18421i q^{53} +(-0.622216 - 4.42864i) q^{55} -2.42864i q^{57} +14.1017 q^{59} +6.85728 q^{61} +1.00000i q^{63} +(14.2351 - 2.00000i) q^{65} +2.75557i q^{67} +1.37778 q^{69} -2.00000 q^{71} -1.57136i q^{73} +(-1.37778 - 4.80642i) q^{75} +2.00000i q^{77} -4.85728 q^{79} +1.00000 q^{81} -11.6128i q^{83} +(9.80642 - 1.37778i) q^{85} -0.755569i q^{87} -4.62222 q^{89} -6.42864 q^{91} -5.18421i q^{93} +(-0.755569 - 5.37778i) q^{95} +11.9398i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{5} - 6 q^{9} - 12 q^{11} + 12 q^{19} + 6 q^{21} - 2 q^{25} - 4 q^{29} - 4 q^{31} + 12 q^{39} + 4 q^{41} - 2 q^{45} - 6 q^{49} - 4 q^{55} + 32 q^{59} - 12 q^{61} + 32 q^{65} + 8 q^{69} - 12 q^{71} - 8 q^{75} + 24 q^{79} + 6 q^{81} + 32 q^{85} - 28 q^{89} - 12 q^{91} - 4 q^{95} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\) \(1\)

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
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 6.42864i 1.78298i −0.453037 0.891492i \(-0.649659\pi\)
0.453037 0.891492i \(-0.350341\pi\)
\(14\) 0 0
\(15\) −2.21432 + 0.311108i −0.571735 + 0.0803277i
\(16\) 0 0
\(17\) 4.42864i 1.07410i −0.843550 0.537051i \(-0.819538\pi\)
0.843550 0.537051i \(-0.180462\pi\)
\(18\) 0 0
\(19\) −2.42864 −0.557168 −0.278584 0.960412i \(-0.589865\pi\)
−0.278584 + 0.960412i \(0.589865\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 1.37778i 0.287288i −0.989629 0.143644i \(-0.954118\pi\)
0.989629 0.143644i \(-0.0458820\pi\)
\(24\) 0 0
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −0.755569 −0.140306 −0.0701528 0.997536i \(-0.522349\pi\)
−0.0701528 + 0.997536i \(0.522349\pi\)
\(30\) 0 0
\(31\) −5.18421 −0.931111 −0.465556 0.885019i \(-0.654145\pi\)
−0.465556 + 0.885019i \(0.654145\pi\)
\(32\) 0 0
\(33\) 2.00000i 0.348155i
\(34\) 0 0
\(35\) 2.21432 0.311108i 0.374288 0.0525868i
\(36\) 0 0
\(37\) 7.61285i 1.25154i −0.780006 0.625772i \(-0.784784\pi\)
0.780006 0.625772i \(-0.215216\pi\)
\(38\) 0 0
\(39\) 6.42864 1.02941
\(40\) 0 0
\(41\) −8.23506 −1.28610 −0.643050 0.765824i \(-0.722331\pi\)
−0.643050 + 0.765824i \(0.722331\pi\)
\(42\) 0 0
\(43\) 10.1017i 1.54050i −0.637744 0.770248i \(-0.720132\pi\)
0.637744 0.770248i \(-0.279868\pi\)
\(44\) 0 0
\(45\) −0.311108 2.21432i −0.0463772 0.330091i
\(46\) 0 0
\(47\) 2.75557i 0.401941i 0.979597 + 0.200971i \(0.0644095\pi\)
−0.979597 + 0.200971i \(0.935590\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 4.42864 0.620134
\(52\) 0 0
\(53\) 9.18421i 1.26155i 0.775967 + 0.630774i \(0.217263\pi\)
−0.775967 + 0.630774i \(0.782737\pi\)
\(54\) 0 0
\(55\) −0.622216 4.42864i −0.0838995 0.597158i
\(56\) 0 0
\(57\) 2.42864i 0.321681i
\(58\) 0 0
\(59\) 14.1017 1.83589 0.917943 0.396712i \(-0.129849\pi\)
0.917943 + 0.396712i \(0.129849\pi\)
\(60\) 0 0
\(61\) 6.85728 0.877985 0.438992 0.898491i \(-0.355336\pi\)
0.438992 + 0.898491i \(0.355336\pi\)
\(62\) 0 0
\(63\) 1.00000i 0.125988i
\(64\) 0 0
\(65\) 14.2351 2.00000i 1.76564 0.248069i
\(66\) 0 0
\(67\) 2.75557i 0.336646i 0.985732 + 0.168323i \(0.0538352\pi\)
−0.985732 + 0.168323i \(0.946165\pi\)
\(68\) 0 0
\(69\) 1.37778 0.165866
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 1.57136i 0.183914i −0.995763 0.0919569i \(-0.970688\pi\)
0.995763 0.0919569i \(-0.0293122\pi\)
\(74\) 0 0
\(75\) −1.37778 4.80642i −0.159093 0.554998i
\(76\) 0 0
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) −4.85728 −0.546487 −0.273243 0.961945i \(-0.588096\pi\)
−0.273243 + 0.961945i \(0.588096\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 11.6128i 1.27468i −0.770585 0.637338i \(-0.780036\pi\)
0.770585 0.637338i \(-0.219964\pi\)
\(84\) 0 0
\(85\) 9.80642 1.37778i 1.06366 0.149442i
\(86\) 0 0
\(87\) 0.755569i 0.0810055i
\(88\) 0 0
\(89\) −4.62222 −0.489954 −0.244977 0.969529i \(-0.578780\pi\)
−0.244977 + 0.969529i \(0.578780\pi\)
\(90\) 0 0
\(91\) −6.42864 −0.673905
\(92\) 0 0
\(93\) 5.18421i 0.537577i
\(94\) 0 0
\(95\) −0.755569 5.37778i −0.0775197 0.551749i
\(96\) 0 0
\(97\) 11.9398i 1.21230i 0.795350 + 0.606150i \(0.207287\pi\)
−0.795350 + 0.606150i \(0.792713\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 1.47949 0.147215 0.0736076 0.997287i \(-0.476549\pi\)
0.0736076 + 0.997287i \(0.476549\pi\)
\(102\) 0 0
\(103\) 8.85728i 0.872734i 0.899769 + 0.436367i \(0.143735\pi\)
−0.899769 + 0.436367i \(0.856265\pi\)
\(104\) 0 0
\(105\) 0.311108 + 2.21432i 0.0303610 + 0.216095i
\(106\) 0 0
\(107\) 1.76494i 0.170623i 0.996354 + 0.0853114i \(0.0271885\pi\)
−0.996354 + 0.0853114i \(0.972811\pi\)
\(108\) 0 0
\(109\) −5.61285 −0.537613 −0.268807 0.963194i \(-0.586629\pi\)
−0.268807 + 0.963194i \(0.586629\pi\)
\(110\) 0 0
\(111\) 7.61285 0.722580
\(112\) 0 0
\(113\) 11.2859i 1.06169i −0.847469 0.530845i \(-0.821875\pi\)
0.847469 0.530845i \(-0.178125\pi\)
\(114\) 0 0
\(115\) 3.05086 0.428639i 0.284494 0.0399708i
\(116\) 0 0
\(117\) 6.42864i 0.594328i
\(118\) 0 0
\(119\) −4.42864 −0.405973
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 8.23506i 0.742531i
\(124\) 0 0
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) 0 0
\(127\) 12.8573i 1.14090i −0.821333 0.570450i \(-0.806769\pi\)
0.821333 0.570450i \(-0.193231\pi\)
\(128\) 0 0
\(129\) 10.1017 0.889406
\(130\) 0 0
\(131\) 2.10171 0.183627 0.0918136 0.995776i \(-0.470734\pi\)
0.0918136 + 0.995776i \(0.470734\pi\)
\(132\) 0 0
\(133\) 2.42864i 0.210590i
\(134\) 0 0
\(135\) 2.21432 0.311108i 0.190578 0.0267759i
\(136\) 0 0
\(137\) 15.9398i 1.36183i −0.732364 0.680914i \(-0.761583\pi\)
0.732364 0.680914i \(-0.238417\pi\)
\(138\) 0 0
\(139\) 11.6731 0.990097 0.495048 0.868865i \(-0.335150\pi\)
0.495048 + 0.868865i \(0.335150\pi\)
\(140\) 0 0
\(141\) −2.75557 −0.232061
\(142\) 0 0
\(143\) 12.8573i 1.07518i
\(144\) 0 0
\(145\) −0.235063 1.67307i −0.0195209 0.138941i
\(146\) 0 0
\(147\) 1.00000i 0.0824786i
\(148\) 0 0
\(149\) 21.2257 1.73888 0.869438 0.494041i \(-0.164481\pi\)
0.869438 + 0.494041i \(0.164481\pi\)
\(150\) 0 0
\(151\) −16.8573 −1.37183 −0.685913 0.727684i \(-0.740597\pi\)
−0.685913 + 0.727684i \(0.740597\pi\)
\(152\) 0 0
\(153\) 4.42864i 0.358034i
\(154\) 0 0
\(155\) −1.61285 11.4795i −0.129547 0.922055i
\(156\) 0 0
\(157\) 10.4286i 0.832296i 0.909297 + 0.416148i \(0.136620\pi\)
−0.909297 + 0.416148i \(0.863380\pi\)
\(158\) 0 0
\(159\) −9.18421 −0.728355
\(160\) 0 0
\(161\) −1.37778 −0.108585
\(162\) 0 0
\(163\) 20.8573i 1.63367i −0.576873 0.816834i \(-0.695727\pi\)
0.576873 0.816834i \(-0.304273\pi\)
\(164\) 0 0
\(165\) 4.42864 0.622216i 0.344769 0.0484394i
\(166\) 0 0
\(167\) 15.3461i 1.18752i 0.804642 + 0.593760i \(0.202357\pi\)
−0.804642 + 0.593760i \(0.797643\pi\)
\(168\) 0 0
\(169\) −28.3274 −2.17903
\(170\) 0 0
\(171\) 2.42864 0.185723
\(172\) 0 0
\(173\) 2.06022i 0.156636i 0.996928 + 0.0783179i \(0.0249549\pi\)
−0.996928 + 0.0783179i \(0.975045\pi\)
\(174\) 0 0
\(175\) 1.37778 + 4.80642i 0.104151 + 0.363331i
\(176\) 0 0
\(177\) 14.1017i 1.05995i
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) −12.1017 −0.899513 −0.449757 0.893151i \(-0.648489\pi\)
−0.449757 + 0.893151i \(0.648489\pi\)
\(182\) 0 0
\(183\) 6.85728i 0.506905i
\(184\) 0 0
\(185\) 16.8573 2.36842i 1.23937 0.174129i
\(186\) 0 0
\(187\) 8.85728i 0.647708i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) −0.488863 −0.0353729 −0.0176864 0.999844i \(-0.505630\pi\)
−0.0176864 + 0.999844i \(0.505630\pi\)
\(192\) 0 0
\(193\) 22.9590i 1.65262i −0.563212 0.826312i \(-0.690435\pi\)
0.563212 0.826312i \(-0.309565\pi\)
\(194\) 0 0
\(195\) 2.00000 + 14.2351i 0.143223 + 1.01939i
\(196\) 0 0
\(197\) 1.18421i 0.0843713i 0.999110 + 0.0421857i \(0.0134321\pi\)
−0.999110 + 0.0421857i \(0.986568\pi\)
\(198\) 0 0
\(199\) 8.79706 0.623607 0.311803 0.950147i \(-0.399067\pi\)
0.311803 + 0.950147i \(0.399067\pi\)
\(200\) 0 0
\(201\) −2.75557 −0.194363
\(202\) 0 0
\(203\) 0.755569i 0.0530305i
\(204\) 0 0
\(205\) −2.56199 18.2351i −0.178937 1.27359i
\(206\) 0 0
\(207\) 1.37778i 0.0957626i
\(208\) 0 0
\(209\) 4.85728 0.335985
\(210\) 0 0
\(211\) −23.2257 −1.59892 −0.799461 0.600717i \(-0.794882\pi\)
−0.799461 + 0.600717i \(0.794882\pi\)
\(212\) 0 0
\(213\) 2.00000i 0.137038i
\(214\) 0 0
\(215\) 22.3684 3.14272i 1.52551 0.214332i
\(216\) 0 0
\(217\) 5.18421i 0.351927i
\(218\) 0 0
\(219\) 1.57136 0.106183
\(220\) 0 0
\(221\) −28.4701 −1.91511
\(222\) 0 0
\(223\) 15.2257i 1.01959i 0.860297 + 0.509794i \(0.170278\pi\)
−0.860297 + 0.509794i \(0.829722\pi\)
\(224\) 0 0
\(225\) 4.80642 1.37778i 0.320428 0.0918523i
\(226\) 0 0
\(227\) 14.3684i 0.953665i −0.878994 0.476833i \(-0.841785\pi\)
0.878994 0.476833i \(-0.158215\pi\)
\(228\) 0 0
\(229\) 5.61285 0.370907 0.185454 0.982653i \(-0.440625\pi\)
0.185454 + 0.982653i \(0.440625\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) 23.2859i 1.52551i 0.646687 + 0.762756i \(0.276154\pi\)
−0.646687 + 0.762756i \(0.723846\pi\)
\(234\) 0 0
\(235\) −6.10171 + 0.857279i −0.398032 + 0.0559227i
\(236\) 0 0
\(237\) 4.85728i 0.315514i
\(238\) 0 0
\(239\) −8.48886 −0.549099 −0.274549 0.961573i \(-0.588529\pi\)
−0.274549 + 0.961573i \(0.588529\pi\)
\(240\) 0 0
\(241\) −7.24443 −0.466655 −0.233327 0.972398i \(-0.574961\pi\)
−0.233327 + 0.972398i \(0.574961\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −0.311108 2.21432i −0.0198759 0.141468i
\(246\) 0 0
\(247\) 15.6128i 0.993422i
\(248\) 0 0
\(249\) 11.6128 0.735934
\(250\) 0 0
\(251\) −27.6128 −1.74291 −0.871454 0.490478i \(-0.836822\pi\)
−0.871454 + 0.490478i \(0.836822\pi\)
\(252\) 0 0
\(253\) 2.75557i 0.173241i
\(254\) 0 0
\(255\) 1.37778 + 9.80642i 0.0862802 + 0.614102i
\(256\) 0 0
\(257\) 0.428639i 0.0267378i 0.999911 + 0.0133689i \(0.00425558\pi\)
−0.999911 + 0.0133689i \(0.995744\pi\)
\(258\) 0 0
\(259\) −7.61285 −0.473039
\(260\) 0 0
\(261\) 0.755569 0.0467685
\(262\) 0 0
\(263\) 9.37778i 0.578259i 0.957290 + 0.289129i \(0.0933658\pi\)
−0.957290 + 0.289129i \(0.906634\pi\)
\(264\) 0 0
\(265\) −20.3368 + 2.85728i −1.24928 + 0.175521i
\(266\) 0 0
\(267\) 4.62222i 0.282875i
\(268\) 0 0
\(269\) −1.74620 −0.106468 −0.0532339 0.998582i \(-0.516953\pi\)
−0.0532339 + 0.998582i \(0.516953\pi\)
\(270\) 0 0
\(271\) 2.69535 0.163731 0.0818653 0.996643i \(-0.473912\pi\)
0.0818653 + 0.996643i \(0.473912\pi\)
\(272\) 0 0
\(273\) 6.42864i 0.389079i
\(274\) 0 0
\(275\) 9.61285 2.75557i 0.579677 0.166167i
\(276\) 0 0
\(277\) 5.12399i 0.307870i 0.988081 + 0.153935i \(0.0491947\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(278\) 0 0
\(279\) 5.18421 0.310370
\(280\) 0 0
\(281\) 23.9813 1.43060 0.715301 0.698816i \(-0.246290\pi\)
0.715301 + 0.698816i \(0.246290\pi\)
\(282\) 0 0
\(283\) 2.36842i 0.140788i −0.997519 0.0703939i \(-0.977574\pi\)
0.997519 0.0703939i \(-0.0224256\pi\)
\(284\) 0 0
\(285\) 5.37778 0.755569i 0.318552 0.0447560i
\(286\) 0 0
\(287\) 8.23506i 0.486100i
\(288\) 0 0
\(289\) −2.61285 −0.153697
\(290\) 0 0
\(291\) −11.9398 −0.699922
\(292\) 0 0
\(293\) 8.42864i 0.492406i 0.969218 + 0.246203i \(0.0791831\pi\)
−0.969218 + 0.246203i \(0.920817\pi\)
\(294\) 0 0
\(295\) 4.38715 + 31.2257i 0.255430 + 1.81803i
\(296\) 0 0
\(297\) 2.00000i 0.116052i
\(298\) 0 0
\(299\) −8.85728 −0.512230
\(300\) 0 0
\(301\) −10.1017 −0.582253
\(302\) 0 0
\(303\) 1.47949i 0.0849947i
\(304\) 0 0
\(305\) 2.13335 + 15.1842i 0.122155 + 0.869445i
\(306\) 0 0
\(307\) 22.5718i 1.28824i −0.764923 0.644121i \(-0.777223\pi\)
0.764923 0.644121i \(-0.222777\pi\)
\(308\) 0 0
\(309\) −8.85728 −0.503873
\(310\) 0 0
\(311\) 24.0830 1.36562 0.682810 0.730596i \(-0.260758\pi\)
0.682810 + 0.730596i \(0.260758\pi\)
\(312\) 0 0
\(313\) 9.65433i 0.545695i 0.962057 + 0.272848i \(0.0879655\pi\)
−0.962057 + 0.272848i \(0.912035\pi\)
\(314\) 0 0
\(315\) −2.21432 + 0.311108i −0.124763 + 0.0175289i
\(316\) 0 0
\(317\) 6.04149i 0.339324i 0.985502 + 0.169662i \(0.0542676\pi\)
−0.985502 + 0.169662i \(0.945732\pi\)
\(318\) 0 0
\(319\) 1.51114 0.0846075
\(320\) 0 0
\(321\) −1.76494 −0.0985092
\(322\) 0 0
\(323\) 10.7556i 0.598456i
\(324\) 0 0
\(325\) 8.85728 + 30.8988i 0.491313 + 1.71396i
\(326\) 0 0
\(327\) 5.61285i 0.310391i
\(328\) 0 0
\(329\) 2.75557 0.151919
\(330\) 0 0
\(331\) −13.5111 −0.742639 −0.371320 0.928505i \(-0.621095\pi\)
−0.371320 + 0.928505i \(0.621095\pi\)
\(332\) 0 0
\(333\) 7.61285i 0.417181i
\(334\) 0 0
\(335\) −6.10171 + 0.857279i −0.333372 + 0.0468382i
\(336\) 0 0
\(337\) 10.4889i 0.571365i −0.958324 0.285682i \(-0.907780\pi\)
0.958324 0.285682i \(-0.0922202\pi\)
\(338\) 0 0
\(339\) 11.2859 0.612967
\(340\) 0 0
\(341\) 10.3684 0.561481
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0.428639 + 3.05086i 0.0230772 + 0.164253i
\(346\) 0 0
\(347\) 16.7239i 0.897787i −0.893585 0.448894i \(-0.851818\pi\)
0.893585 0.448894i \(-0.148182\pi\)
\(348\) 0 0
\(349\) 16.3684 0.876181 0.438091 0.898931i \(-0.355655\pi\)
0.438091 + 0.898931i \(0.355655\pi\)
\(350\) 0 0
\(351\) −6.42864 −0.343135
\(352\) 0 0
\(353\) 0.549086i 0.0292249i 0.999893 + 0.0146124i \(0.00465145\pi\)
−0.999893 + 0.0146124i \(0.995349\pi\)
\(354\) 0 0
\(355\) −0.622216 4.42864i −0.0330238 0.235048i
\(356\) 0 0
\(357\) 4.42864i 0.234388i
\(358\) 0 0
\(359\) −0.285442 −0.0150651 −0.00753253 0.999972i \(-0.502398\pi\)
−0.00753253 + 0.999972i \(0.502398\pi\)
\(360\) 0 0
\(361\) −13.1017 −0.689564
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 3.47949 0.488863i 0.182125 0.0255882i
\(366\) 0 0
\(367\) 1.71456i 0.0894992i 0.998998 + 0.0447496i \(0.0142490\pi\)
−0.998998 + 0.0447496i \(0.985751\pi\)
\(368\) 0 0
\(369\) 8.23506 0.428700
\(370\) 0 0
\(371\) 9.18421 0.476820
\(372\) 0 0
\(373\) 16.0000i 0.828449i 0.910175 + 0.414224i \(0.135947\pi\)
−0.910175 + 0.414224i \(0.864053\pi\)
\(374\) 0 0
\(375\) 10.2143 4.54617i 0.527465 0.234763i
\(376\) 0 0
\(377\) 4.85728i 0.250163i
\(378\) 0 0
\(379\) −4.85728 −0.249502 −0.124751 0.992188i \(-0.539813\pi\)
−0.124751 + 0.992188i \(0.539813\pi\)
\(380\) 0 0
\(381\) 12.8573 0.658698
\(382\) 0 0
\(383\) 8.38715i 0.428563i 0.976772 + 0.214282i \(0.0687411\pi\)
−0.976772 + 0.214282i \(0.931259\pi\)
\(384\) 0 0
\(385\) −4.42864 + 0.622216i −0.225704 + 0.0317110i
\(386\) 0 0
\(387\) 10.1017i 0.513499i
\(388\) 0 0
\(389\) −8.95899 −0.454239 −0.227119 0.973867i \(-0.572931\pi\)
−0.227119 + 0.973867i \(0.572931\pi\)
\(390\) 0 0
\(391\) −6.10171 −0.308577
\(392\) 0 0
\(393\) 2.10171i 0.106017i
\(394\) 0 0
\(395\) −1.51114 10.7556i −0.0760336 0.541171i
\(396\) 0 0
\(397\) 2.54909i 0.127935i 0.997952 + 0.0639675i \(0.0203754\pi\)
−0.997952 + 0.0639675i \(0.979625\pi\)
\(398\) 0 0
\(399\) −2.42864 −0.121584
\(400\) 0 0
\(401\) 0.958989 0.0478896 0.0239448 0.999713i \(-0.492377\pi\)
0.0239448 + 0.999713i \(0.492377\pi\)
\(402\) 0 0
\(403\) 33.3274i 1.66016i
\(404\) 0 0
\(405\) 0.311108 + 2.21432i 0.0154591 + 0.110030i
\(406\) 0 0
\(407\) 15.2257i 0.754710i
\(408\) 0 0
\(409\) 31.9813 1.58137 0.790686 0.612222i \(-0.209724\pi\)
0.790686 + 0.612222i \(0.209724\pi\)
\(410\) 0 0
\(411\) 15.9398 0.786251
\(412\) 0 0
\(413\) 14.1017i 0.693900i
\(414\) 0 0
\(415\) 25.7146 3.61285i 1.26228 0.177348i
\(416\) 0 0
\(417\) 11.6731i 0.571633i
\(418\) 0 0
\(419\) −0.470127 −0.0229672 −0.0114836 0.999934i \(-0.503655\pi\)
−0.0114836 + 0.999934i \(0.503655\pi\)
\(420\) 0 0
\(421\) −33.6128 −1.63819 −0.819095 0.573658i \(-0.805524\pi\)
−0.819095 + 0.573658i \(0.805524\pi\)
\(422\) 0 0
\(423\) 2.75557i 0.133980i
\(424\) 0 0
\(425\) 6.10171 + 21.2859i 0.295976 + 1.03252i
\(426\) 0 0
\(427\) 6.85728i 0.331847i
\(428\) 0 0
\(429\) −12.8573 −0.620755
\(430\) 0 0
\(431\) −11.7146 −0.564270 −0.282135 0.959375i \(-0.591043\pi\)
−0.282135 + 0.959375i \(0.591043\pi\)
\(432\) 0 0
\(433\) 0.0602231i 0.00289414i −0.999999 0.00144707i \(-0.999539\pi\)
0.999999 0.00144707i \(-0.000460616\pi\)
\(434\) 0 0
\(435\) 1.67307 0.235063i 0.0802176 0.0112704i
\(436\) 0 0
\(437\) 3.34614i 0.160068i
\(438\) 0 0
\(439\) −22.4286 −1.07046 −0.535230 0.844706i \(-0.679775\pi\)
−0.535230 + 0.844706i \(0.679775\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 23.9496i 1.13788i 0.822379 + 0.568940i \(0.192647\pi\)
−0.822379 + 0.568940i \(0.807353\pi\)
\(444\) 0 0
\(445\) −1.43801 10.2351i −0.0681681 0.485189i
\(446\) 0 0
\(447\) 21.2257i 1.00394i
\(448\) 0 0
\(449\) −29.4291 −1.38885 −0.694423 0.719567i \(-0.744340\pi\)
−0.694423 + 0.719567i \(0.744340\pi\)
\(450\) 0 0
\(451\) 16.4701 0.775548
\(452\) 0 0
\(453\) 16.8573i 0.792024i
\(454\) 0 0
\(455\) −2.00000 14.2351i −0.0937614 0.667350i
\(456\) 0 0
\(457\) 3.14272i 0.147010i 0.997295 + 0.0735051i \(0.0234185\pi\)
−0.997295 + 0.0735051i \(0.976581\pi\)
\(458\) 0 0
\(459\) −4.42864 −0.206711
\(460\) 0 0
\(461\) −3.37778 −0.157319 −0.0786596 0.996902i \(-0.525064\pi\)
−0.0786596 + 0.996902i \(0.525064\pi\)
\(462\) 0 0
\(463\) 20.8573i 0.969320i −0.874703 0.484660i \(-0.838943\pi\)
0.874703 0.484660i \(-0.161057\pi\)
\(464\) 0 0
\(465\) 11.4795 1.61285i 0.532349 0.0747940i
\(466\) 0 0
\(467\) 14.3684i 0.664891i −0.943122 0.332446i \(-0.892126\pi\)
0.943122 0.332446i \(-0.107874\pi\)
\(468\) 0 0
\(469\) 2.75557 0.127240
\(470\) 0 0
\(471\) −10.4286 −0.480526
\(472\) 0 0
\(473\) 20.2034i 0.928954i
\(474\) 0 0
\(475\) 11.6731 3.34614i 0.535597 0.153532i
\(476\) 0 0
\(477\) 9.18421i 0.420516i
\(478\) 0 0
\(479\) 6.36842 0.290980 0.145490 0.989360i \(-0.453524\pi\)
0.145490 + 0.989360i \(0.453524\pi\)
\(480\) 0 0
\(481\) −48.9403 −2.23148
\(482\) 0 0
\(483\) 1.37778i 0.0626914i
\(484\) 0 0
\(485\) −26.4385 + 3.71456i −1.20051 + 0.168669i
\(486\) 0 0
\(487\) 17.3274i 0.785180i 0.919714 + 0.392590i \(0.128421\pi\)
−0.919714 + 0.392590i \(0.871579\pi\)
\(488\) 0 0
\(489\) 20.8573 0.943199
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 3.34614i 0.150703i
\(494\) 0 0
\(495\) 0.622216 + 4.42864i 0.0279665 + 0.199053i
\(496\) 0 0
\(497\) 2.00000i 0.0897123i
\(498\) 0 0
\(499\) 23.3461 1.04512 0.522558 0.852603i \(-0.324978\pi\)
0.522558 + 0.852603i \(0.324978\pi\)
\(500\) 0 0
\(501\) −15.3461 −0.685615
\(502\) 0 0
\(503\) 0.387152i 0.0172623i −0.999963 0.00863113i \(-0.997253\pi\)
0.999963 0.00863113i \(-0.00274741\pi\)
\(504\) 0 0
\(505\) 0.460282 + 3.27607i 0.0204823 + 0.145783i
\(506\) 0 0
\(507\) 28.3274i 1.25806i
\(508\) 0 0
\(509\) 29.9496 1.32749 0.663747 0.747957i \(-0.268965\pi\)
0.663747 + 0.747957i \(0.268965\pi\)
\(510\) 0 0
\(511\) −1.57136 −0.0695129
\(512\) 0 0
\(513\) 2.42864i 0.107227i
\(514\) 0 0
\(515\) −19.6128 + 2.75557i −0.864245 + 0.121425i
\(516\) 0 0
\(517\) 5.51114i 0.242380i
\(518\) 0 0
\(519\) −2.06022 −0.0904338
\(520\) 0 0
\(521\) −18.5205 −0.811398 −0.405699 0.914007i \(-0.632972\pi\)
−0.405699 + 0.914007i \(0.632972\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) 0 0
\(525\) −4.80642 + 1.37778i −0.209770 + 0.0601314i
\(526\) 0 0
\(527\) 22.9590i 1.00011i
\(528\) 0 0
\(529\) 21.1017 0.917466
\(530\) 0 0
\(531\) −14.1017 −0.611962
\(532\) 0 0
\(533\) 52.9403i 2.29310i
\(534\) 0 0
\(535\) −3.90813 + 0.549086i −0.168963 + 0.0237390i
\(536\) 0 0
\(537\) 10.0000i 0.431532i
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 14.5906 0.627298 0.313649 0.949539i \(-0.398449\pi\)
0.313649 + 0.949539i \(0.398449\pi\)
\(542\) 0 0
\(543\) 12.1017i 0.519334i
\(544\) 0 0
\(545\) −1.74620 12.4286i −0.0747990 0.532384i
\(546\) 0 0
\(547\) 18.7556i 0.801930i −0.916093 0.400965i \(-0.868675\pi\)
0.916093 0.400965i \(-0.131325\pi\)
\(548\) 0 0
\(549\) −6.85728 −0.292662
\(550\) 0 0
\(551\) 1.83500 0.0781738
\(552\) 0 0
\(553\) 4.85728i 0.206553i
\(554\) 0 0
\(555\) 2.36842 + 16.8573i 0.100534 + 0.715552i
\(556\) 0 0
\(557\) 31.8765i 1.35065i −0.737520 0.675325i \(-0.764003\pi\)
0.737520 0.675325i \(-0.235997\pi\)
\(558\) 0 0
\(559\) −64.9403 −2.74668
\(560\) 0 0
\(561\) −8.85728 −0.373955
\(562\) 0 0
\(563\) 2.01874i 0.0850796i 0.999095 + 0.0425398i \(0.0135449\pi\)
−0.999095 + 0.0425398i \(0.986455\pi\)
\(564\) 0 0
\(565\) 24.9906 3.51114i 1.05136 0.147715i
\(566\) 0 0
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 28.9590 1.21402 0.607012 0.794693i \(-0.292368\pi\)
0.607012 + 0.794693i \(0.292368\pi\)
\(570\) 0 0
\(571\) −8.97773 −0.375706 −0.187853 0.982197i \(-0.560153\pi\)
−0.187853 + 0.982197i \(0.560153\pi\)
\(572\) 0 0
\(573\) 0.488863i 0.0204225i
\(574\) 0 0
\(575\) 1.89829 + 6.62222i 0.0791642 + 0.276165i
\(576\) 0 0
\(577\) 28.6766i 1.19382i −0.802307 0.596911i \(-0.796394\pi\)
0.802307 0.596911i \(-0.203606\pi\)
\(578\) 0 0
\(579\) 22.9590 0.954143
\(580\) 0 0
\(581\) −11.6128 −0.481782
\(582\) 0 0
\(583\) 18.3684i 0.760742i
\(584\) 0 0
\(585\) −14.2351 + 2.00000i −0.588547 + 0.0826898i
\(586\) 0 0
\(587\) 45.2070i 1.86589i 0.360018 + 0.932945i \(0.382771\pi\)
−0.360018 + 0.932945i \(0.617229\pi\)
\(588\) 0 0
\(589\) 12.5906 0.518786
\(590\) 0 0
\(591\) −1.18421 −0.0487118
\(592\) 0 0
\(593\) 18.2636i 0.749998i −0.927025 0.374999i \(-0.877643\pi\)
0.927025 0.374999i \(-0.122357\pi\)
\(594\) 0 0
\(595\) −1.37778 9.80642i −0.0564837 0.402024i
\(596\) 0 0
\(597\) 8.79706i 0.360040i
\(598\) 0 0
\(599\) −22.7368 −0.929002 −0.464501 0.885573i \(-0.653766\pi\)
−0.464501 + 0.885573i \(0.653766\pi\)
\(600\) 0 0
\(601\) 0.488863 0.0199411 0.00997056 0.999950i \(-0.496826\pi\)
0.00997056 + 0.999950i \(0.496826\pi\)
\(602\) 0 0
\(603\) 2.75557i 0.112215i
\(604\) 0 0
\(605\) −2.17775 15.5002i −0.0885383 0.630174i
\(606\) 0 0
\(607\) 20.2034i 0.820032i 0.912078 + 0.410016i \(0.134477\pi\)
−0.912078 + 0.410016i \(0.865523\pi\)
\(608\) 0 0
\(609\) −0.755569 −0.0306172
\(610\) 0 0
\(611\) 17.7146 0.716654
\(612\) 0 0
\(613\) 10.3684i 0.418776i −0.977833 0.209388i \(-0.932853\pi\)
0.977833 0.209388i \(-0.0671472\pi\)
\(614\) 0 0
\(615\) 18.2351 2.56199i 0.735309 0.103310i
\(616\) 0 0
\(617\) 39.2859i 1.58159i −0.612080 0.790796i \(-0.709667\pi\)
0.612080 0.790796i \(-0.290333\pi\)
\(618\) 0 0
\(619\) 42.8988 1.72425 0.862123 0.506698i \(-0.169134\pi\)
0.862123 + 0.506698i \(0.169134\pi\)
\(620\) 0 0
\(621\) −1.37778 −0.0552886
\(622\) 0 0
\(623\) 4.62222i 0.185185i
\(624\) 0 0
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) 0 0
\(627\) 4.85728i 0.193981i
\(628\) 0 0
\(629\) −33.7146 −1.34429
\(630\) 0 0
\(631\) −15.3461 −0.610920 −0.305460 0.952205i \(-0.598810\pi\)
−0.305460 + 0.952205i \(0.598810\pi\)
\(632\) 0 0
\(633\) 23.2257i 0.923139i
\(634\) 0 0
\(635\) 28.4701 4.00000i 1.12980 0.158735i
\(636\) 0 0
\(637\) 6.42864i 0.254712i
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) 30.6735 1.21153 0.605766 0.795643i \(-0.292867\pi\)
0.605766 + 0.795643i \(0.292867\pi\)
\(642\) 0 0
\(643\) 49.0607i 1.93477i −0.253320 0.967383i \(-0.581523\pi\)
0.253320 0.967383i \(-0.418477\pi\)
\(644\) 0 0
\(645\) 3.14272 + 22.3684i 0.123745 + 0.880756i
\(646\) 0 0
\(647\) 15.3461i 0.603319i 0.953416 + 0.301660i \(0.0975406\pi\)
−0.953416 + 0.301660i \(0.902459\pi\)
\(648\) 0 0
\(649\) −28.2034 −1.10708
\(650\) 0 0
\(651\) −5.18421 −0.203185
\(652\) 0 0
\(653\) 19.4697i 0.761906i 0.924594 + 0.380953i \(0.124404\pi\)
−0.924594 + 0.380953i \(0.875596\pi\)
\(654\) 0 0
\(655\) 0.653858 + 4.65386i 0.0255484 + 0.181841i
\(656\) 0 0
\(657\) 1.57136i 0.0613046i
\(658\) 0 0
\(659\) 30.9403 1.20526 0.602631 0.798020i \(-0.294119\pi\)
0.602631 + 0.798020i \(0.294119\pi\)
\(660\) 0 0
\(661\) 47.7975 1.85911 0.929554 0.368685i \(-0.120192\pi\)
0.929554 + 0.368685i \(0.120192\pi\)
\(662\) 0 0
\(663\) 28.4701i 1.10569i
\(664\) 0 0
\(665\) −5.37778 + 0.755569i −0.208542 + 0.0292997i
\(666\) 0 0
\(667\) 1.04101i 0.0403081i
\(668\) 0 0
\(669\) −15.2257 −0.588659
\(670\) 0 0
\(671\) −13.7146 −0.529445
\(672\) 0 0
\(673\) 27.8163i 1.07224i −0.844142 0.536119i \(-0.819890\pi\)
0.844142 0.536119i \(-0.180110\pi\)
\(674\) 0 0
\(675\) 1.37778 + 4.80642i 0.0530309 + 0.184999i
\(676\) 0 0
\(677\) 19.0005i 0.730248i −0.930959 0.365124i \(-0.881027\pi\)
0.930959 0.365124i \(-0.118973\pi\)
\(678\) 0 0
\(679\) 11.9398 0.458207
\(680\) 0 0
\(681\) 14.3684 0.550599
\(682\) 0 0
\(683\) 4.52051i 0.172972i 0.996253 + 0.0864862i \(0.0275638\pi\)
−0.996253 + 0.0864862i \(0.972436\pi\)
\(684\) 0 0
\(685\) 35.2958 4.95899i 1.34858 0.189473i
\(686\) 0 0
\(687\) 5.61285i 0.214143i
\(688\) 0 0
\(689\) 59.0420 2.24932
\(690\) 0 0
\(691\) 1.18421 0.0450494 0.0225247 0.999746i \(-0.492830\pi\)
0.0225247 + 0.999746i \(0.492830\pi\)
\(692\) 0 0
\(693\) 2.00000i 0.0759737i
\(694\) 0 0
\(695\) 3.63158 + 25.8479i 0.137754 + 0.980467i
\(696\) 0 0
\(697\) 36.4701i 1.38140i
\(698\) 0 0
\(699\) −23.2859 −0.880754
\(700\) 0 0
\(701\) −26.6735 −1.00745 −0.503723 0.863865i \(-0.668037\pi\)
−0.503723 + 0.863865i \(0.668037\pi\)
\(702\) 0 0
\(703\) 18.4889i 0.697321i
\(704\) 0 0
\(705\) −0.857279 6.10171i −0.0322870 0.229804i
\(706\) 0 0
\(707\) 1.47949i 0.0556421i
\(708\) 0 0
\(709\) 18.2034 0.683644 0.341822 0.939765i \(-0.388956\pi\)
0.341822 + 0.939765i \(0.388956\pi\)
\(710\) 0 0
\(711\) 4.85728 0.182162
\(712\) 0 0
\(713\) 7.14272i 0.267497i
\(714\) 0 0
\(715\) −28.4701 + 4.00000i −1.06472 + 0.149592i
\(716\) 0 0
\(717\) 8.48886i 0.317022i
\(718\) 0 0
\(719\) 4.85728 0.181146 0.0905730 0.995890i \(-0.471130\pi\)
0.0905730 + 0.995890i \(0.471130\pi\)
\(720\) 0 0
\(721\) 8.85728 0.329862
\(722\) 0 0
\(723\) 7.24443i 0.269423i
\(724\) 0 0
\(725\) 3.63158 1.04101i 0.134874 0.0386622i
\(726\) 0 0
\(727\) 21.0607i 0.781098i −0.920582 0.390549i \(-0.872285\pi\)
0.920582 0.390549i \(-0.127715\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −44.7368 −1.65465
\(732\) 0 0
\(733\) 9.45091i 0.349077i −0.984650 0.174539i \(-0.944157\pi\)
0.984650 0.174539i \(-0.0558434\pi\)
\(734\) 0 0
\(735\) 2.21432 0.311108i 0.0816764 0.0114754i
\(736\) 0 0
\(737\) 5.51114i 0.203005i
\(738\) 0 0
\(739\) −8.20342 −0.301768 −0.150884 0.988551i \(-0.548212\pi\)
−0.150884 + 0.988551i \(0.548212\pi\)
\(740\) 0 0
\(741\) −15.6128 −0.573552
\(742\) 0 0
\(743\) 8.33677i 0.305847i 0.988238 + 0.152923i \(0.0488687\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(744\) 0 0
\(745\) 6.60348 + 47.0005i 0.241933 + 1.72196i
\(746\) 0 0
\(747\) 11.6128i 0.424892i
\(748\) 0 0
\(749\) 1.76494 0.0644894
\(750\) 0 0
\(751\) 25.9180 0.945760 0.472880 0.881127i \(-0.343214\pi\)
0.472880 + 0.881127i \(0.343214\pi\)
\(752\) 0 0
\(753\) 27.6128i 1.00627i
\(754\) 0 0
\(755\) −5.24443 37.3274i −0.190864 1.35848i
\(756\) 0 0
\(757\) 8.94025i 0.324939i 0.986714 + 0.162470i \(0.0519459\pi\)
−0.986714 + 0.162470i \(0.948054\pi\)
\(758\) 0 0
\(759\) −2.75557 −0.100021
\(760\) 0 0
\(761\) −0.825636 −0.0299293 −0.0149646 0.999888i \(-0.504764\pi\)
−0.0149646 + 0.999888i \(0.504764\pi\)
\(762\) 0 0
\(763\) 5.61285i 0.203199i
\(764\) 0 0
\(765\) −9.80642 + 1.37778i −0.354552 + 0.0498139i
\(766\) 0 0
\(767\) 90.6548i 3.27336i
\(768\) 0 0
\(769\) −21.2257 −0.765418 −0.382709 0.923869i \(-0.625009\pi\)
−0.382709 + 0.923869i \(0.625009\pi\)
\(770\) 0 0
\(771\) −0.428639 −0.0154371
\(772\) 0 0
\(773\) 29.4893i 1.06066i −0.847792 0.530329i \(-0.822068\pi\)
0.847792 0.530329i \(-0.177932\pi\)
\(774\) 0 0
\(775\) 24.9175 7.14272i 0.895063 0.256574i
\(776\) 0 0
\(777\) 7.61285i 0.273109i
\(778\) 0 0
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 0.755569i 0.0270018i
\(784\) 0 0
\(785\) −23.0923 + 3.24443i −0.824201 + 0.115799i
\(786\) 0 0
\(787\) 34.4514i 1.22806i 0.789283 + 0.614030i \(0.210453\pi\)
−0.789283 + 0.614030i \(0.789547\pi\)
\(788\) 0 0
\(789\) −9.37778 −0.333858
\(790\) 0 0
\(791\) −11.2859 −0.401281
\(792\) 0 0
\(793\) 44.0830i 1.56543i
\(794\) 0 0
\(795\) −2.85728 20.3368i −0.101337 0.721271i
\(796\) 0 0
\(797\) 18.9175i 0.670092i 0.942202 + 0.335046i \(0.108752\pi\)
−0.942202 + 0.335046i \(0.891248\pi\)
\(798\) 0 0
\(799\) 12.2034 0.431726
\(800\) 0 0
\(801\) 4.62222 0.163318
\(802\) 0