Properties

Label 804.2.g.b.401.4
Level 804
Weight 2
Character 804.401
Analytic conductor 6.420
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-5})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 401.4
Root \(-1.58114 - 0.707107i\)
Character \(\chi\) = 804.401
Dual form 804.2.g.b.401.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.58114 + 0.707107i) q^{3} -3.16228 q^{5} -1.41421i q^{7} +(2.00000 + 2.23607i) q^{9} +O(q^{10})\) \(q+(1.58114 + 0.707107i) q^{3} -3.16228 q^{5} -1.41421i q^{7} +(2.00000 + 2.23607i) q^{9} -3.16228 q^{11} +4.24264i q^{13} +(-5.00000 - 2.23607i) q^{15} +6.70820i q^{17} -3.00000 q^{19} +(1.00000 - 2.23607i) q^{21} +6.70820i q^{23} +5.00000 q^{25} +(1.58114 + 4.94975i) q^{27} -2.23607i q^{29} -4.24264i q^{31} +(-5.00000 - 2.23607i) q^{33} +4.47214i q^{35} +5.00000 q^{37} +(-3.00000 + 6.70820i) q^{39} -12.6491 q^{41} +11.3137i q^{43} +(-6.32456 - 7.07107i) q^{45} -2.23607i q^{47} +5.00000 q^{49} +(-4.74342 + 10.6066i) q^{51} +10.0000 q^{55} +(-4.74342 - 2.12132i) q^{57} -2.23607i q^{59} -2.82843i q^{61} +(3.16228 - 2.82843i) q^{63} -13.4164i q^{65} +(-7.00000 - 4.24264i) q^{67} +(-4.74342 + 10.6066i) q^{69} -13.4164i q^{71} +5.00000 q^{73} +(7.90569 + 3.53553i) q^{75} +4.47214i q^{77} -14.1421i q^{79} +(-1.00000 + 8.94427i) q^{81} +4.47214i q^{83} -21.2132i q^{85} +(1.58114 - 3.53553i) q^{87} +2.23607i q^{89} +6.00000 q^{91} +(3.00000 - 6.70820i) q^{93} +9.48683 q^{95} +8.48528i q^{97} +(-6.32456 - 7.07107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{9} + O(q^{10}) \) \( 4q + 8q^{9} - 20q^{15} - 12q^{19} + 4q^{21} + 20q^{25} - 20q^{33} + 20q^{37} - 12q^{39} + 20q^{49} + 40q^{55} - 28q^{67} + 20q^{73} - 4q^{81} + 24q^{91} + 12q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) 1.58114 + 0.707107i 0.912871 + 0.408248i
\(4\) 0 0
\(5\) −3.16228 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(6\) 0 0
\(7\) 1.41421i 0.534522i −0.963624 0.267261i \(-0.913881\pi\)
0.963624 0.267261i \(-0.0861187\pi\)
\(8\) 0 0
\(9\) 2.00000 + 2.23607i 0.666667 + 0.745356i
\(10\) 0 0
\(11\) −3.16228 −0.953463 −0.476731 0.879049i \(-0.658179\pi\)
−0.476731 + 0.879049i \(0.658179\pi\)
\(12\) 0 0
\(13\) 4.24264i 1.17670i 0.808608 + 0.588348i \(0.200222\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(14\) 0 0
\(15\) −5.00000 2.23607i −1.29099 0.577350i
\(16\) 0 0
\(17\) 6.70820i 1.62698i 0.581580 + 0.813489i \(0.302435\pi\)
−0.581580 + 0.813489i \(0.697565\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0 0
\(21\) 1.00000 2.23607i 0.218218 0.487950i
\(22\) 0 0
\(23\) 6.70820i 1.39876i 0.714751 + 0.699379i \(0.246540\pi\)
−0.714751 + 0.699379i \(0.753460\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 1.58114 + 4.94975i 0.304290 + 0.952579i
\(28\) 0 0
\(29\) 2.23607i 0.415227i −0.978211 0.207614i \(-0.933430\pi\)
0.978211 0.207614i \(-0.0665697\pi\)
\(30\) 0 0
\(31\) 4.24264i 0.762001i −0.924575 0.381000i \(-0.875580\pi\)
0.924575 0.381000i \(-0.124420\pi\)
\(32\) 0 0
\(33\) −5.00000 2.23607i −0.870388 0.389249i
\(34\) 0 0
\(35\) 4.47214i 0.755929i
\(36\) 0 0
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 0 0
\(39\) −3.00000 + 6.70820i −0.480384 + 1.07417i
\(40\) 0 0
\(41\) −12.6491 −1.97546 −0.987730 0.156174i \(-0.950084\pi\)
−0.987730 + 0.156174i \(0.950084\pi\)
\(42\) 0 0
\(43\) 11.3137i 1.72532i 0.505781 + 0.862662i \(0.331205\pi\)
−0.505781 + 0.862662i \(0.668795\pi\)
\(44\) 0 0
\(45\) −6.32456 7.07107i −0.942809 1.05409i
\(46\) 0 0
\(47\) 2.23607i 0.326164i −0.986613 0.163082i \(-0.947856\pi\)
0.986613 0.163082i \(-0.0521435\pi\)
\(48\) 0 0
\(49\) 5.00000 0.714286
\(50\) 0 0
\(51\) −4.74342 + 10.6066i −0.664211 + 1.48522i
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 10.0000 1.34840
\(56\) 0 0
\(57\) −4.74342 2.12132i −0.628281 0.280976i
\(58\) 0 0
\(59\) 2.23607i 0.291111i −0.989350 0.145556i \(-0.953503\pi\)
0.989350 0.145556i \(-0.0464970\pi\)
\(60\) 0 0
\(61\) 2.82843i 0.362143i −0.983470 0.181071i \(-0.942043\pi\)
0.983470 0.181071i \(-0.0579565\pi\)
\(62\) 0 0
\(63\) 3.16228 2.82843i 0.398410 0.356348i
\(64\) 0 0
\(65\) 13.4164i 1.66410i
\(66\) 0 0
\(67\) −7.00000 4.24264i −0.855186 0.518321i
\(68\) 0 0
\(69\) −4.74342 + 10.6066i −0.571040 + 1.27688i
\(70\) 0 0
\(71\) 13.4164i 1.59223i −0.605142 0.796117i \(-0.706884\pi\)
0.605142 0.796117i \(-0.293116\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) 0 0
\(75\) 7.90569 + 3.53553i 0.912871 + 0.408248i
\(76\) 0 0
\(77\) 4.47214i 0.509647i
\(78\) 0 0
\(79\) 14.1421i 1.59111i −0.605878 0.795557i \(-0.707178\pi\)
0.605878 0.795557i \(-0.292822\pi\)
\(80\) 0 0
\(81\) −1.00000 + 8.94427i −0.111111 + 0.993808i
\(82\) 0 0
\(83\) 4.47214i 0.490881i 0.969412 + 0.245440i \(0.0789325\pi\)
−0.969412 + 0.245440i \(0.921067\pi\)
\(84\) 0 0
\(85\) 21.2132i 2.30089i
\(86\) 0 0
\(87\) 1.58114 3.53553i 0.169516 0.379049i
\(88\) 0 0
\(89\) 2.23607i 0.237023i 0.992953 + 0.118511i \(0.0378122\pi\)
−0.992953 + 0.118511i \(0.962188\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 3.00000 6.70820i 0.311086 0.695608i
\(94\) 0 0
\(95\) 9.48683 0.973329
\(96\) 0 0
\(97\) 8.48528i 0.861550i 0.902459 + 0.430775i \(0.141760\pi\)
−0.902459 + 0.430775i \(0.858240\pi\)
\(98\) 0 0
\(99\) −6.32456 7.07107i −0.635642 0.710669i
\(100\) 0 0
\(101\) −3.16228 −0.314658 −0.157329 0.987546i \(-0.550288\pi\)
−0.157329 + 0.987546i \(0.550288\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) −3.16228 + 7.07107i −0.308607 + 0.690066i
\(106\) 0 0
\(107\) 11.1803i 1.08084i 0.841394 + 0.540422i \(0.181735\pi\)
−0.841394 + 0.540422i \(0.818265\pi\)
\(108\) 0 0
\(109\) 12.7279i 1.21911i 0.792742 + 0.609557i \(0.208653\pi\)
−0.792742 + 0.609557i \(0.791347\pi\)
\(110\) 0 0
\(111\) 7.90569 + 3.53553i 0.750375 + 0.335578i
\(112\) 0 0
\(113\) 9.48683 0.892446 0.446223 0.894922i \(-0.352769\pi\)
0.446223 + 0.894922i \(0.352769\pi\)
\(114\) 0 0
\(115\) 21.2132i 1.97814i
\(116\) 0 0
\(117\) −9.48683 + 8.48528i −0.877058 + 0.784465i
\(118\) 0 0
\(119\) 9.48683 0.869657
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) −20.0000 8.94427i −1.80334 0.806478i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) −8.00000 + 17.8885i −0.704361 + 1.57500i
\(130\) 0 0
\(131\) 8.94427i 0.781465i −0.920504 0.390732i \(-0.872222\pi\)
0.920504 0.390732i \(-0.127778\pi\)
\(132\) 0 0
\(133\) 4.24264i 0.367884i
\(134\) 0 0
\(135\) −5.00000 15.6525i −0.430331 1.34715i
\(136\) 0 0
\(137\) 22.1359 1.89120 0.945601 0.325330i \(-0.105475\pi\)
0.945601 + 0.325330i \(0.105475\pi\)
\(138\) 0 0
\(139\) 14.1421i 1.19952i 0.800180 + 0.599760i \(0.204737\pi\)
−0.800180 + 0.599760i \(0.795263\pi\)
\(140\) 0 0
\(141\) 1.58114 3.53553i 0.133156 0.297746i
\(142\) 0 0
\(143\) 13.4164i 1.12194i
\(144\) 0 0
\(145\) 7.07107i 0.587220i
\(146\) 0 0
\(147\) 7.90569 + 3.53553i 0.652051 + 0.291606i
\(148\) 0 0
\(149\) 15.6525i 1.28230i 0.767415 + 0.641150i \(0.221543\pi\)
−0.767415 + 0.641150i \(0.778457\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 0 0
\(153\) −15.0000 + 13.4164i −1.21268 + 1.08465i
\(154\) 0 0
\(155\) 13.4164i 1.07763i
\(156\) 0 0
\(157\) −21.0000 −1.67598 −0.837991 0.545684i \(-0.816270\pi\)
−0.837991 + 0.545684i \(0.816270\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 9.48683 0.747667
\(162\) 0 0
\(163\) 3.00000 0.234978 0.117489 0.993074i \(-0.462515\pi\)
0.117489 + 0.993074i \(0.462515\pi\)
\(164\) 0 0
\(165\) 15.8114 + 7.07107i 1.23091 + 0.550482i
\(166\) 0 0
\(167\) 4.47214i 0.346064i −0.984916 0.173032i \(-0.944644\pi\)
0.984916 0.173032i \(-0.0553564\pi\)
\(168\) 0 0
\(169\) −5.00000 −0.384615
\(170\) 0 0
\(171\) −6.00000 6.70820i −0.458831 0.512989i
\(172\) 0 0
\(173\) 15.6525i 1.19004i −0.803712 0.595018i \(-0.797145\pi\)
0.803712 0.595018i \(-0.202855\pi\)
\(174\) 0 0
\(175\) 7.07107i 0.534522i
\(176\) 0 0
\(177\) 1.58114 3.53553i 0.118846 0.265747i
\(178\) 0 0
\(179\) 9.48683 0.709079 0.354540 0.935041i \(-0.384638\pi\)
0.354540 + 0.935041i \(0.384638\pi\)
\(180\) 0 0
\(181\) −19.0000 −1.41226 −0.706129 0.708083i \(-0.749560\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 0 0
\(183\) 2.00000 4.47214i 0.147844 0.330590i
\(184\) 0 0
\(185\) −15.8114 −1.16248
\(186\) 0 0
\(187\) 21.2132i 1.55126i
\(188\) 0 0
\(189\) 7.00000 2.23607i 0.509175 0.162650i
\(190\) 0 0
\(191\) 9.48683 0.686443 0.343222 0.939254i \(-0.388482\pi\)
0.343222 + 0.939254i \(0.388482\pi\)
\(192\) 0 0
\(193\) −23.0000 −1.65558 −0.827788 0.561041i \(-0.810401\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 0 0
\(195\) 9.48683 21.2132i 0.679366 1.51911i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 13.0000 0.921546 0.460773 0.887518i \(-0.347572\pi\)
0.460773 + 0.887518i \(0.347572\pi\)
\(200\) 0 0
\(201\) −8.06797 11.6580i −0.569071 0.822288i
\(202\) 0 0
\(203\) −3.16228 −0.221948
\(204\) 0 0
\(205\) 40.0000 2.79372
\(206\) 0 0
\(207\) −15.0000 + 13.4164i −1.04257 + 0.932505i
\(208\) 0 0
\(209\) 9.48683 0.656218
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) 0 0
\(213\) 9.48683 21.2132i 0.650027 1.45350i
\(214\) 0 0
\(215\) 35.7771i 2.43998i
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 0 0
\(219\) 7.90569 + 3.53553i 0.534217 + 0.238909i
\(220\) 0 0
\(221\) −28.4605 −1.91446
\(222\) 0 0
\(223\) −3.00000 −0.200895 −0.100447 0.994942i \(-0.532027\pi\)
−0.100447 + 0.994942i \(0.532027\pi\)
\(224\) 0 0
\(225\) 10.0000 + 11.1803i 0.666667 + 0.745356i
\(226\) 0 0
\(227\) 2.23607i 0.148413i −0.997243 0.0742065i \(-0.976358\pi\)
0.997243 0.0742065i \(-0.0236424\pi\)
\(228\) 0 0
\(229\) 12.7279i 0.841085i 0.907273 + 0.420542i \(0.138160\pi\)
−0.907273 + 0.420542i \(0.861840\pi\)
\(230\) 0 0
\(231\) −3.16228 + 7.07107i −0.208063 + 0.465242i
\(232\) 0 0
\(233\) 9.48683 0.621503 0.310752 0.950491i \(-0.399419\pi\)
0.310752 + 0.950491i \(0.399419\pi\)
\(234\) 0 0
\(235\) 7.07107i 0.461266i
\(236\) 0 0
\(237\) 10.0000 22.3607i 0.649570 1.45248i
\(238\) 0 0
\(239\) 12.6491 0.818203 0.409101 0.912489i \(-0.365842\pi\)
0.409101 + 0.912489i \(0.365842\pi\)
\(240\) 0 0
\(241\) 19.0000 1.22390 0.611949 0.790897i \(-0.290386\pi\)
0.611949 + 0.790897i \(0.290386\pi\)
\(242\) 0 0
\(243\) −7.90569 + 13.4350i −0.507151 + 0.861858i
\(244\) 0 0
\(245\) −15.8114 −1.01015
\(246\) 0 0
\(247\) 12.7279i 0.809858i
\(248\) 0 0
\(249\) −3.16228 + 7.07107i −0.200401 + 0.448111i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 21.2132i 1.33366i
\(254\) 0 0
\(255\) 15.0000 33.5410i 0.939336 2.10042i
\(256\) 0 0
\(257\) 15.6525i 0.976375i 0.872739 + 0.488187i \(0.162342\pi\)
−0.872739 + 0.488187i \(0.837658\pi\)
\(258\) 0 0
\(259\) 7.07107i 0.439375i
\(260\) 0 0
\(261\) 5.00000 4.47214i 0.309492 0.276818i
\(262\) 0 0
\(263\) 4.47214i 0.275764i 0.990449 + 0.137882i \(0.0440294\pi\)
−0.990449 + 0.137882i \(0.955971\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.58114 + 3.53553i −0.0967641 + 0.216371i
\(268\) 0 0
\(269\) 17.8885i 1.09068i −0.838214 0.545342i \(-0.816400\pi\)
0.838214 0.545342i \(-0.183600\pi\)
\(270\) 0 0
\(271\) 7.07107i 0.429537i −0.976665 0.214768i \(-0.931100\pi\)
0.976665 0.214768i \(-0.0688997\pi\)
\(272\) 0 0
\(273\) 9.48683 + 4.24264i 0.574169 + 0.256776i
\(274\) 0 0
\(275\) −15.8114 −0.953463
\(276\) 0 0
\(277\) 4.00000 0.240337 0.120168 0.992754i \(-0.461657\pi\)
0.120168 + 0.992754i \(0.461657\pi\)
\(278\) 0 0
\(279\) 9.48683 8.48528i 0.567962 0.508001i
\(280\) 0 0
\(281\) 6.32456 0.377291 0.188646 0.982045i \(-0.439590\pi\)
0.188646 + 0.982045i \(0.439590\pi\)
\(282\) 0 0
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) 0 0
\(285\) 15.0000 + 6.70820i 0.888523 + 0.397360i
\(286\) 0 0
\(287\) 17.8885i 1.05593i
\(288\) 0 0
\(289\) −28.0000 −1.64706
\(290\) 0 0
\(291\) −6.00000 + 13.4164i −0.351726 + 0.786484i
\(292\) 0 0
\(293\) 26.8328i 1.56759i 0.621020 + 0.783795i \(0.286719\pi\)
−0.621020 + 0.783795i \(0.713281\pi\)
\(294\) 0 0
\(295\) 7.07107i 0.411693i
\(296\) 0 0
\(297\) −5.00000 15.6525i −0.290129 0.908249i
\(298\) 0 0
\(299\) −28.4605 −1.64591
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 0 0
\(303\) −5.00000 2.23607i −0.287242 0.128459i
\(304\) 0 0
\(305\) 8.94427i 0.512148i
\(306\) 0 0
\(307\) −11.0000 −0.627803 −0.313902 0.949456i \(-0.601636\pi\)
−0.313902 + 0.949456i \(0.601636\pi\)
\(308\) 0 0
\(309\) 15.8114 + 7.07107i 0.899478 + 0.402259i
\(310\) 0 0
\(311\) −18.9737 −1.07590 −0.537949 0.842977i \(-0.680801\pi\)
−0.537949 + 0.842977i \(0.680801\pi\)
\(312\) 0 0
\(313\) 24.0416i 1.35891i −0.733716 0.679457i \(-0.762216\pi\)
0.733716 0.679457i \(-0.237784\pi\)
\(314\) 0 0
\(315\) −10.0000 + 8.94427i −0.563436 + 0.503953i
\(316\) 0 0
\(317\) 4.47214i 0.251180i 0.992082 + 0.125590i \(0.0400824\pi\)
−0.992082 + 0.125590i \(0.959918\pi\)
\(318\) 0 0
\(319\) 7.07107i 0.395904i
\(320\) 0 0
\(321\) −7.90569 + 17.6777i −0.441253 + 0.986671i
\(322\) 0 0
\(323\) 20.1246i 1.11976i
\(324\) 0 0
\(325\) 21.2132i 1.17670i
\(326\) 0 0
\(327\) −9.00000 + 20.1246i −0.497701 + 1.11289i
\(328\) 0 0
\(329\) −3.16228 −0.174342
\(330\) 0 0
\(331\) 7.07107i 0.388661i −0.980936 0.194331i \(-0.937747\pi\)
0.980936 0.194331i \(-0.0622534\pi\)
\(332\) 0 0
\(333\) 10.0000 + 11.1803i 0.547997 + 0.612679i
\(334\) 0 0
\(335\) 22.1359 + 13.4164i 1.20942 + 0.733017i
\(336\) 0 0
\(337\) 22.6274i 1.23259i 0.787514 + 0.616297i \(0.211368\pi\)
−0.787514 + 0.616297i \(0.788632\pi\)
\(338\) 0 0
\(339\) 15.0000 + 6.70820i 0.814688 + 0.364340i
\(340\) 0 0
\(341\) 13.4164i 0.726539i
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) 15.0000 33.5410i 0.807573 1.80579i
\(346\) 0 0
\(347\) −6.32456 −0.339520 −0.169760 0.985485i \(-0.554299\pi\)
−0.169760 + 0.985485i \(0.554299\pi\)
\(348\) 0 0
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) 0 0
\(351\) −21.0000 + 6.70820i −1.12090 + 0.358057i
\(352\) 0 0
\(353\) −6.32456 −0.336622 −0.168311 0.985734i \(-0.553831\pi\)
−0.168311 + 0.985734i \(0.553831\pi\)
\(354\) 0 0
\(355\) 42.4264i 2.25176i
\(356\) 0 0
\(357\) 15.0000 + 6.70820i 0.793884 + 0.355036i
\(358\) 0 0
\(359\) 20.1246i 1.06214i −0.847329 0.531068i \(-0.821791\pi\)
0.847329 0.531068i \(-0.178209\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 0 0
\(363\) −1.58114 0.707107i −0.0829883 0.0371135i
\(364\) 0 0
\(365\) −15.8114 −0.827606
\(366\) 0 0
\(367\) 33.9411i 1.77171i 0.463960 + 0.885856i \(0.346428\pi\)
−0.463960 + 0.885856i \(0.653572\pi\)
\(368\) 0 0
\(369\) −25.2982 28.2843i −1.31697 1.47242i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 11.3137i 0.585802i 0.956143 + 0.292901i \(0.0946206\pi\)
−0.956143 + 0.292901i \(0.905379\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.48683 0.488597
\(378\) 0 0
\(379\) 5.65685i 0.290573i 0.989390 + 0.145287i \(0.0464104\pi\)
−0.989390 + 0.145287i \(0.953590\pi\)
\(380\) 0 0
\(381\) −7.90569 3.53553i −0.405021 0.181131i
\(382\) 0 0
\(383\) 31.6228 1.61585 0.807924 0.589286i \(-0.200591\pi\)
0.807924 + 0.589286i \(0.200591\pi\)
\(384\) 0 0
\(385\) 14.1421i 0.720750i
\(386\) 0 0
\(387\) −25.2982 + 22.6274i −1.28598 + 1.15022i
\(388\) 0 0
\(389\) 8.94427i 0.453493i −0.973954 0.226746i \(-0.927191\pi\)
0.973954 0.226746i \(-0.0728088\pi\)
\(390\) 0 0
\(391\) −45.0000 −2.27575
\(392\) 0 0
\(393\) 6.32456 14.1421i 0.319032 0.713376i
\(394\) 0 0
\(395\) 44.7214i 2.25018i
\(396\) 0 0
\(397\) −21.0000 −1.05396 −0.526980 0.849878i \(-0.676676\pi\)
−0.526980 + 0.849878i \(0.676676\pi\)
\(398\) 0 0
\(399\) −3.00000 + 6.70820i −0.150188 + 0.335830i
\(400\) 0 0
\(401\) −15.8114 −0.789583 −0.394792 0.918771i \(-0.629183\pi\)
−0.394792 + 0.918771i \(0.629183\pi\)
\(402\) 0 0
\(403\) 18.0000 0.896644
\(404\) 0 0
\(405\) 3.16228 28.2843i 0.157135 1.40546i
\(406\) 0 0
\(407\) −15.8114 −0.783741
\(408\) 0 0
\(409\) 33.9411i 1.67828i 0.543915 + 0.839140i \(0.316941\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 35.0000 + 15.6525i 1.72642 + 0.772080i
\(412\) 0 0
\(413\) −3.16228 −0.155606
\(414\) 0 0
\(415\) 14.1421i 0.694210i
\(416\) 0 0
\(417\) −10.0000 + 22.3607i −0.489702 + 1.09501i
\(418\) 0 0
\(419\) 11.1803i 0.546195i −0.961986 0.273098i \(-0.911952\pi\)
0.961986 0.273098i \(-0.0880482\pi\)
\(420\) 0 0
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 0 0
\(423\) 5.00000 4.47214i 0.243108 0.217443i
\(424\) 0 0
\(425\) 33.5410i 1.62698i
\(426\) 0 0
\(427\) −4.00000 −0.193574
\(428\) 0 0
\(429\) 9.48683 21.2132i 0.458029 1.02418i
\(430\) 0 0
\(431\) 15.6525i 0.753953i 0.926223 + 0.376977i \(0.123036\pi\)
−0.926223 + 0.376977i \(0.876964\pi\)
\(432\) 0 0
\(433\) 4.24264i 0.203888i −0.994790 0.101944i \(-0.967494\pi\)
0.994790 0.101944i \(-0.0325063\pi\)
\(434\) 0 0
\(435\) −5.00000 + 11.1803i −0.239732 + 0.536056i
\(436\) 0 0
\(437\) 20.1246i 0.962691i
\(438\) 0 0
\(439\) 13.0000 0.620456 0.310228 0.950662i \(-0.399595\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(440\) 0 0
\(441\) 10.0000 + 11.1803i 0.476190 + 0.532397i
\(442\) 0 0
\(443\) 28.4605 1.35220 0.676100 0.736810i \(-0.263669\pi\)
0.676100 + 0.736810i \(0.263669\pi\)
\(444\) 0 0
\(445\) 7.07107i 0.335201i
\(446\) 0 0
\(447\) −11.0680 + 24.7487i −0.523497 + 1.17058i
\(448\) 0 0
\(449\) 6.70820i 0.316580i 0.987393 + 0.158290i \(0.0505980\pi\)
−0.987393 + 0.158290i \(0.949402\pi\)
\(450\) 0 0
\(451\) 40.0000 1.88353
\(452\) 0 0
\(453\) 17.3925 + 7.77817i 0.817172 + 0.365451i
\(454\) 0 0
\(455\) −18.9737 −0.889499
\(456\) 0 0
\(457\) 35.0000 1.63723 0.818615 0.574342i \(-0.194742\pi\)
0.818615 + 0.574342i \(0.194742\pi\)
\(458\) 0 0
\(459\) −33.2039 + 10.6066i −1.54983 + 0.495074i
\(460\) 0 0
\(461\) 24.5967i 1.14558i 0.819700 + 0.572792i \(0.194140\pi\)
−0.819700 + 0.572792i \(0.805860\pi\)
\(462\) 0 0
\(463\) 8.48528i 0.394344i 0.980369 + 0.197172i \(0.0631758\pi\)
−0.980369 + 0.197172i \(0.936824\pi\)
\(464\) 0 0
\(465\) −9.48683 + 21.2132i −0.439941 + 0.983739i
\(466\) 0 0
\(467\) 26.8328i 1.24167i −0.783939 0.620837i \(-0.786793\pi\)
0.783939 0.620837i \(-0.213207\pi\)
\(468\) 0 0
\(469\) −6.00000 + 9.89949i −0.277054 + 0.457116i
\(470\) 0 0
\(471\) −33.2039 14.8492i −1.52996 0.684217i
\(472\) 0 0
\(473\) 35.7771i 1.64503i
\(474\) 0 0
\(475\) −15.0000 −0.688247
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.6525i 0.715180i 0.933879 + 0.357590i \(0.116401\pi\)
−0.933879 + 0.357590i \(0.883599\pi\)
\(480\) 0 0
\(481\) 21.2132i 0.967239i
\(482\) 0 0
\(483\) 15.0000 + 6.70820i 0.682524 + 0.305234i
\(484\) 0 0
\(485\) 26.8328i 1.21842i
\(486\) 0 0
\(487\) 43.8406i 1.98661i 0.115529 + 0.993304i \(0.463144\pi\)
−0.115529 + 0.993304i \(0.536856\pi\)
\(488\) 0 0
\(489\) 4.74342 + 2.12132i 0.214505 + 0.0959294i
\(490\) 0 0
\(491\) 2.23607i 0.100912i −0.998726 0.0504562i \(-0.983932\pi\)
0.998726 0.0504562i \(-0.0160675\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 20.0000 + 22.3607i 0.898933 + 1.00504i
\(496\) 0 0
\(497\) −18.9737 −0.851085
\(498\) 0 0
\(499\) 26.8701i 1.20287i −0.798922 0.601434i \(-0.794596\pi\)
0.798922 0.601434i \(-0.205404\pi\)
\(500\) 0 0
\(501\) 3.16228 7.07107i 0.141280 0.315912i
\(502\) 0 0
\(503\) 34.7851 1.55099 0.775494 0.631354i \(-0.217501\pi\)
0.775494 + 0.631354i \(0.217501\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) −7.90569 3.53553i −0.351104 0.157019i
\(508\) 0 0
\(509\) 29.0689i 1.28846i 0.764834 + 0.644228i \(0.222821\pi\)
−0.764834 + 0.644228i \(0.777179\pi\)
\(510\) 0 0
\(511\) 7.07107i 0.312806i
\(512\) 0 0
\(513\) −4.74342 14.8492i −0.209427 0.655610i
\(514\) 0 0
\(515\) −31.6228 −1.39347
\(516\) 0 0
\(517\) 7.07107i 0.310985i
\(518\) 0 0
\(519\) 11.0680 24.7487i 0.485830 1.08635i
\(520\) 0 0
\(521\) 9.48683 0.415626 0.207813 0.978169i \(-0.433365\pi\)
0.207813 + 0.978169i \(0.433365\pi\)
\(522\) 0 0
\(523\) 37.0000 1.61790 0.808949 0.587879i \(-0.200037\pi\)
0.808949 + 0.587879i \(0.200037\pi\)
\(524\) 0 0
\(525\) 5.00000 11.1803i 0.218218 0.487950i
\(526\) 0 0
\(527\) 28.4605 1.23976
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 5.00000 4.47214i 0.216982 0.194074i
\(532\) 0 0
\(533\) 53.6656i 2.32452i
\(534\) 0 0
\(535\) 35.3553i 1.52854i
\(536\) 0 0
\(537\) 15.0000 + 6.70820i 0.647298 + 0.289480i
\(538\) 0 0
\(539\) −15.8114 −0.681045
\(540\) 0 0
\(541\) 24.0416i 1.03363i −0.856097 0.516815i \(-0.827117\pi\)
0.856097 0.516815i \(-0.172883\pi\)
\(542\) 0 0
\(543\) −30.0416 13.4350i −1.28921 0.576552i
\(544\) 0 0
\(545\) 40.2492i 1.72409i
\(546\) 0 0
\(547\) 16.9706i 0.725609i −0.931865 0.362804i \(-0.881819\pi\)
0.931865 0.362804i \(-0.118181\pi\)
\(548\) 0 0
\(549\) 6.32456 5.65685i 0.269925 0.241429i
\(550\) 0 0
\(551\) 6.70820i 0.285779i
\(552\) 0 0
\(553\) −20.0000 −0.850487
\(554\) 0 0
\(555\) −25.0000 11.1803i −1.06119 0.474579i
\(556\) 0 0
\(557\) 17.8885i 0.757962i 0.925404 + 0.378981i \(0.123725\pi\)
−0.925404 + 0.378981i \(0.876275\pi\)
\(558\) 0 0
\(559\) −48.0000 −2.03018
\(560\) 0 0
\(561\) 15.0000 33.5410i 0.633300 1.41610i
\(562\) 0 0
\(563\) −6.32456 −0.266548 −0.133274 0.991079i \(-0.542549\pi\)
−0.133274 + 0.991079i \(0.542549\pi\)
\(564\) 0 0
\(565\) −30.0000 −1.26211
\(566\) 0 0
\(567\) 12.6491 + 1.41421i 0.531213 + 0.0593914i
\(568\) 0 0
\(569\) 38.0132i 1.59359i −0.604247 0.796797i \(-0.706526\pi\)
0.604247 0.796797i \(-0.293474\pi\)
\(570\) 0 0
\(571\) −31.0000 −1.29731 −0.648655 0.761083i \(-0.724668\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 0 0
\(573\) 15.0000 + 6.70820i 0.626634 + 0.280239i
\(574\) 0 0
\(575\) 33.5410i 1.39876i
\(576\) 0 0
\(577\) 8.48528i 0.353247i 0.984278 + 0.176623i \(0.0565175\pi\)
−0.984278 + 0.176623i \(0.943483\pi\)
\(578\) 0 0
\(579\) −36.3662 16.2635i −1.51133 0.675886i
\(580\) 0 0
\(581\) 6.32456 0.262387
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 30.0000 26.8328i 1.24035 1.10940i
\(586\) 0 0
\(587\) −31.6228 −1.30521 −0.652606 0.757698i \(-0.726324\pi\)
−0.652606 + 0.757698i \(0.726324\pi\)
\(588\) 0 0
\(589\) 12.7279i 0.524445i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18.9737 −0.779155 −0.389578 0.920994i \(-0.627379\pi\)
−0.389578 + 0.920994i \(0.627379\pi\)
\(594\) 0 0
\(595\) −30.0000 −1.22988
\(596\) 0 0
\(597\) 20.5548 + 9.19239i 0.841252 + 0.376219i
\(598\) 0 0
\(599\) 28.4605 1.16286 0.581432 0.813595i \(-0.302493\pi\)
0.581432 + 0.813595i \(0.302493\pi\)
\(600\) 0 0
\(601\) 29.0000 1.18293 0.591467 0.806329i \(-0.298549\pi\)
0.591467 + 0.806329i \(0.298549\pi\)
\(602\) 0 0
\(603\) −4.51317 24.1378i −0.183790 0.982965i
\(604\) 0 0
\(605\) 3.16228 0.128565
\(606\) 0 0
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 0 0
\(609\) −5.00000 2.23607i −0.202610 0.0906100i
\(610\) 0 0
\(611\) 9.48683 0.383796
\(612\) 0 0
\(613\) −15.0000 −0.605844 −0.302922 0.953015i \(-0.597962\pi\)
−0.302922 + 0.953015i \(0.597962\pi\)
\(614\) 0 0
\(615\) 63.2456 + 28.2843i 2.55031 + 1.14053i
\(616\) 0 0
\(617\) 38.0132i 1.53035i 0.643821 + 0.765176i \(0.277348\pi\)
−0.643821 + 0.765176i \(0.722652\pi\)
\(618\) 0 0
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) 0 0
\(621\) −33.2039 + 10.6066i −1.33243 + 0.425628i
\(622\) 0 0
\(623\) 3.16228 0.126694
\(624\) 0 0
\(625\) −25.0000 −1.00000
\(626\) 0 0
\(627\) 15.0000 + 6.70820i 0.599042 + 0.267900i
\(628\) 0 0
\(629\) 33.5410i 1.33737i
\(630\) 0 0
\(631\) 16.9706i 0.675587i 0.941220 + 0.337794i \(0.109681\pi\)
−0.941220 + 0.337794i \(0.890319\pi\)
\(632\) 0 0
\(633\) 41.1096 + 18.3848i 1.63396 + 0.730729i
\(634\) 0 0
\(635\) 15.8114 0.627456
\(636\) 0 0
\(637\) 21.2132i 0.840498i
\(638\) 0 0
\(639\) 30.0000 26.8328i 1.18678 1.06149i
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −10.0000 −0.394362 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) 0 0
\(645\) 25.2982 56.5685i 0.996116 2.22738i
\(646\) 0 0
\(647\) −44.2719 −1.74051 −0.870254 0.492604i \(-0.836045\pi\)
−0.870254 + 0.492604i \(0.836045\pi\)
\(648\) 0 0
\(649\) 7.07107i 0.277564i
\(650\) 0 0
\(651\) −9.48683 4.24264i −0.371818 0.166282i
\(652\) 0 0
\(653\) 25.2982 0.989996 0.494998 0.868894i \(-0.335169\pi\)
0.494998 + 0.868894i \(0.335169\pi\)
\(654\) 0 0
\(655\) 28.2843i 1.10516i
\(656\) 0 0
\(657\) 10.0000 + 11.1803i 0.390137 + 0.436187i
\(658\) 0 0
\(659\) 29.0689i 1.13236i 0.824281 + 0.566181i \(0.191580\pi\)
−0.824281 + 0.566181i \(0.808420\pi\)
\(660\) 0 0
\(661\) 49.4975i 1.92523i 0.270876 + 0.962614i \(0.412687\pi\)
−0.270876 + 0.962614i \(0.587313\pi\)
\(662\) 0 0
\(663\) −45.0000 20.1246i −1.74766 0.781575i
\(664\) 0 0
\(665\) 13.4164i 0.520266i
\(666\) 0 0
\(667\) 15.0000 0.580802
\(668\) 0 0
\(669\) −4.74342 2.12132i −0.183391 0.0820150i
\(670\) 0 0
\(671\) 8.94427i 0.345290i
\(672\) 0 0
\(673\) 1.41421i 0.0545139i −0.999628 0.0272570i \(-0.991323\pi\)
0.999628 0.0272570i \(-0.00867724\pi\)
\(674\) 0 0
\(675\) 7.90569 + 24.7487i 0.304290 + 0.952579i
\(676\) 0 0
\(677\) 15.8114 0.607681 0.303841 0.952723i \(-0.401731\pi\)
0.303841 + 0.952723i \(0.401731\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) 1.58114 3.53553i 0.0605894 0.135482i
\(682\) 0 0
\(683\) 6.32456 0.242002 0.121001 0.992652i \(-0.461390\pi\)
0.121001 + 0.992652i \(0.461390\pi\)
\(684\) 0 0
\(685\) −70.0000 −2.67456
\(686\) 0 0
\(687\) −9.00000 + 20.1246i −0.343371 + 0.767802i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 47.0000 1.78796 0.893982 0.448103i \(-0.147900\pi\)
0.893982 + 0.448103i \(0.147900\pi\)
\(692\) 0 0
\(693\) −10.0000 + 8.94427i −0.379869 + 0.339765i
\(694\) 0 0
\(695\) 44.7214i 1.69638i
\(696\) 0 0
\(697\) 84.8528i 3.21403i
\(698\) 0 0
\(699\) 15.0000 + 6.70820i 0.567352 + 0.253728i
\(700\) 0 0
\(701\) −9.48683 −0.358313 −0.179156 0.983821i \(-0.557337\pi\)
−0.179156 + 0.983821i \(0.557337\pi\)
\(702\) 0 0
\(703\) −15.0000 −0.565736
\(704\) 0 0
\(705\) −5.00000 + 11.1803i −0.188311 + 0.421076i
\(706\) 0 0
\(707\) 4.47214i 0.168192i
\(708\) 0 0
\(709\) 2.00000 0.0751116 0.0375558 0.999295i \(-0.488043\pi\)
0.0375558 + 0.999295i \(0.488043\pi\)
\(710\) 0 0
\(711\) 31.6228 28.2843i 1.18595 1.06074i
\(712\) 0 0
\(713\) 28.4605 1.06585
\(714\) 0 0
\(715\) 42.4264i 1.58666i
\(716\) 0 0
\(717\) 20.0000 + 8.94427i 0.746914 + 0.334030i
\(718\) 0 0
\(719\) 42.4853i 1.58443i −0.610239 0.792217i \(-0.708927\pi\)
0.610239 0.792217i \(-0.291073\pi\)
\(720\) 0 0
\(721\) 14.1421i 0.526681i
\(722\) 0 0
\(723\) 30.0416 + 13.4350i 1.11726 + 0.499654i
\(724\) 0 0
\(725\) 11.1803i 0.415227i
\(726\) 0 0
\(727\) 8.48528i 0.314702i −0.987543 0.157351i \(-0.949705\pi\)
0.987543 0.157351i \(-0.0502953\pi\)
\(728\) 0 0
\(729\) −22.0000 + 15.6525i −0.814815 + 0.579721i
\(730\) 0 0
\(731\) −75.8947 −2.80707
\(732\) 0 0
\(733\) 1.41421i 0.0522352i −0.999659 0.0261176i \(-0.991686\pi\)
0.999659 0.0261176i \(-0.00831443\pi\)
\(734\) 0 0
\(735\) −25.0000 11.1803i −0.922139 0.412393i
\(736\) 0 0
\(737\) 22.1359 + 13.4164i 0.815388 + 0.494200i
\(738\) 0 0
\(739\) 28.2843i 1.04045i −0.854028 0.520227i \(-0.825847\pi\)
0.854028 0.520227i \(-0.174153\pi\)
\(740\) 0 0
\(741\) 9.00000 20.1246i 0.330623 0.739296i
\(742\) 0 0
\(743\) 31.3050i 1.14847i 0.818691 + 0.574234i \(0.194700\pi\)
−0.818691 + 0.574234i \(0.805300\pi\)
\(744\) 0 0
\(745\) 49.4975i 1.81345i
\(746\) 0 0
\(747\) −10.0000 + 8.94427i −0.365881 + 0.327254i
\(748\) 0 0
\(749\) 15.8114 0.577736
\(750\) 0 0
\(751\) −17.0000 −0.620339 −0.310169 0.950681i \(-0.600386\pi\)
−0.310169 + 0.950681i \(0.600386\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −34.7851 −1.26596
\(756\) 0 0
\(757\) 15.5563i 0.565405i −0.959208 0.282703i \(-0.908769\pi\)
0.959208 0.282703i \(-0.0912309\pi\)
\(758\) 0 0
\(759\) 15.0000 33.5410i 0.544466 1.21746i
\(760\) 0 0
\(761\) 42.4853i 1.54009i −0.637989 0.770045i \(-0.720234\pi\)
0.637989 0.770045i \(-0.279766\pi\)
\(762\) 0 0
\(763\) 18.0000 0.651644
\(764\) 0 0
\(765\) 47.4342 42.4264i 1.71499 1.53393i
\(766\) 0 0
\(767\) 9.48683 0.342550
\(768\) 0 0
\(769\) 36.7696i 1.32594i −0.748644 0.662972i \(-0.769295\pi\)
0.748644 0.662972i \(-0.230705\pi\)
\(770\) 0 0
\(771\) −11.0680 + 24.7487i −0.398603 + 0.891304i
\(772\) 0 0
\(773\) 29.0689i 1.04554i −0.852475 0.522768i \(-0.824900\pi\)
0.852475 0.522768i \(-0.175100\pi\)
\(774\) 0 0
\(775\) 21.2132i 0.762001i
\(776\) 0 0
\(777\) 5.00000 11.1803i 0.179374 0.401092i
\(778\) 0 0
\(779\) 37.9473 1.35960
\(780\) 0 0
\(781\) 42.4264i 1.51814i
\(782\) 0 0
\(783\) 11.0680 3.53553i 0.395537 0.126350i
\(784\) 0 0
\(785\) 66.4078 2.37020
\(786\) 0 0
\(787\) 19.7990i 0.705758i 0.935669 + 0.352879i \(0.114797\pi\)
−0.935669 + 0.352879i \(0.885203\pi\)
\(788\) 0 0
\(789\) −3.16228 + 7.07107i −0.112580 + 0.251737i
\(790\) 0 0
\(791\) 13.4164i 0.477033i
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.8328i 0.950467i −0.879860 0.475234i \(-0.842364\pi\)
0.879860 0.475234i \(-0.157636\pi\)
\(798\) 0 0
\(799\) 15.0000 0.530662
\(800\) 0 0
\(801\) −5.00000 + 4.47214i −0.176666 + 0.158015i
\(802\) 0 0
\(803\) −15.8114 −0.557972
\(804\) 0 0
\(805\) −30.0000 −1.05736
\(806\) 0 0
\(807\) 12.6491 28.2843i 0.445270 0.995654i
\(808\) 0 0
\(809\) 28.4605 1.00062