Properties

Label 920.2.e.b.369.1
Level $920$
Weight $2$
Character 920.369
Analytic conductor $7.346$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.1
Root \(-0.503254 - 0.503254i\) of defining polynomial
Character \(\chi\) \(=\) 920.369
Dual form 920.2.e.b.369.14

$q$-expansion

\(f(q)\) \(=\) \(q-2.98707i q^{3} +(0.274289 + 2.21918i) q^{5} -0.980560i q^{7} -5.92257 q^{9} +O(q^{10})\) \(q-2.98707i q^{3} +(0.274289 + 2.21918i) q^{5} -0.980560i q^{7} -5.92257 q^{9} -6.14721 q^{11} +6.37400i q^{13} +(6.62885 - 0.819321i) q^{15} +3.36098i q^{17} -1.08276 q^{19} -2.92900 q^{21} +1.00000i q^{23} +(-4.84953 + 1.21740i) q^{25} +8.72993i q^{27} +0.271042 q^{29} -8.77792 q^{31} +18.3621i q^{33} +(2.17604 - 0.268957i) q^{35} -8.84665i q^{37} +19.0396 q^{39} -4.85308 q^{41} -1.87756i q^{43} +(-1.62450 - 13.1433i) q^{45} +0.196089i q^{47} +6.03850 q^{49} +10.0395 q^{51} +1.93157i q^{53} +(-1.68612 - 13.6418i) q^{55} +3.23429i q^{57} -13.0036 q^{59} +6.00189 q^{61} +5.80744i q^{63} +(-14.1451 + 1.74832i) q^{65} +2.26847i q^{67} +2.98707 q^{69} +10.2677 q^{71} -1.38188i q^{73} +(3.63644 + 14.4859i) q^{75} +6.02771i q^{77} +4.67459 q^{79} +8.30917 q^{81} +15.7171i q^{83} +(-7.45862 + 0.921881i) q^{85} -0.809622i q^{87} +11.1548 q^{89} +6.25008 q^{91} +26.2202i q^{93} +(-0.296991 - 2.40285i) q^{95} -10.2868i q^{97} +36.4073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 14q + 2q^{5} - 4q^{9} - 14q^{11} - 6q^{15} + 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} - 20q^{31} - 2q^{35} + 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} - 14q^{51} - 38q^{55} + 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} - 28q^{71} - 24q^{75} + 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} - 14q^{91} - 30q^{95} + 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 2.98707i 1.72458i −0.506411 0.862292i \(-0.669028\pi\)
0.506411 0.862292i \(-0.330972\pi\)
\(4\) 0 0
\(5\) 0.274289 + 2.21918i 0.122666 + 0.992448i
\(6\) 0 0
\(7\) 0.980560i 0.370617i −0.982680 0.185308i \(-0.940672\pi\)
0.982680 0.185308i \(-0.0593284\pi\)
\(8\) 0 0
\(9\) −5.92257 −1.97419
\(10\) 0 0
\(11\) −6.14721 −1.85345 −0.926727 0.375734i \(-0.877391\pi\)
−0.926727 + 0.375734i \(0.877391\pi\)
\(12\) 0 0
\(13\) 6.37400i 1.76783i 0.467649 + 0.883914i \(0.345101\pi\)
−0.467649 + 0.883914i \(0.654899\pi\)
\(14\) 0 0
\(15\) 6.62885 0.819321i 1.71156 0.211548i
\(16\) 0 0
\(17\) 3.36098i 0.815157i 0.913170 + 0.407579i \(0.133627\pi\)
−0.913170 + 0.407579i \(0.866373\pi\)
\(18\) 0 0
\(19\) −1.08276 −0.248403 −0.124202 0.992257i \(-0.539637\pi\)
−0.124202 + 0.992257i \(0.539637\pi\)
\(20\) 0 0
\(21\) −2.92900 −0.639160
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −4.84953 + 1.21740i −0.969906 + 0.243479i
\(26\) 0 0
\(27\) 8.72993i 1.68008i
\(28\) 0 0
\(29\) 0.271042 0.0503313 0.0251657 0.999683i \(-0.491989\pi\)
0.0251657 + 0.999683i \(0.491989\pi\)
\(30\) 0 0
\(31\) −8.77792 −1.57656 −0.788280 0.615316i \(-0.789028\pi\)
−0.788280 + 0.615316i \(0.789028\pi\)
\(32\) 0 0
\(33\) 18.3621i 3.19644i
\(34\) 0 0
\(35\) 2.17604 0.268957i 0.367818 0.0454621i
\(36\) 0 0
\(37\) 8.84665i 1.45438i −0.686436 0.727190i \(-0.740826\pi\)
0.686436 0.727190i \(-0.259174\pi\)
\(38\) 0 0
\(39\) 19.0396 3.04877
\(40\) 0 0
\(41\) −4.85308 −0.757923 −0.378962 0.925412i \(-0.623719\pi\)
−0.378962 + 0.925412i \(0.623719\pi\)
\(42\) 0 0
\(43\) 1.87756i 0.286326i −0.989699 0.143163i \(-0.954273\pi\)
0.989699 0.143163i \(-0.0457273\pi\)
\(44\) 0 0
\(45\) −1.62450 13.1433i −0.242166 1.95928i
\(46\) 0 0
\(47\) 0.196089i 0.0286026i 0.999898 + 0.0143013i \(0.00455239\pi\)
−0.999898 + 0.0143013i \(0.995448\pi\)
\(48\) 0 0
\(49\) 6.03850 0.862643
\(50\) 0 0
\(51\) 10.0395 1.40581
\(52\) 0 0
\(53\) 1.93157i 0.265321i 0.991162 + 0.132661i \(0.0423521\pi\)
−0.991162 + 0.132661i \(0.957648\pi\)
\(54\) 0 0
\(55\) −1.68612 13.6418i −0.227356 1.83946i
\(56\) 0 0
\(57\) 3.23429i 0.428392i
\(58\) 0 0
\(59\) −13.0036 −1.69293 −0.846465 0.532444i \(-0.821274\pi\)
−0.846465 + 0.532444i \(0.821274\pi\)
\(60\) 0 0
\(61\) 6.00189 0.768464 0.384232 0.923237i \(-0.374466\pi\)
0.384232 + 0.923237i \(0.374466\pi\)
\(62\) 0 0
\(63\) 5.80744i 0.731668i
\(64\) 0 0
\(65\) −14.1451 + 1.74832i −1.75448 + 0.216852i
\(66\) 0 0
\(67\) 2.26847i 0.277138i 0.990353 + 0.138569i \(0.0442503\pi\)
−0.990353 + 0.138569i \(0.955750\pi\)
\(68\) 0 0
\(69\) 2.98707 0.359601
\(70\) 0 0
\(71\) 10.2677 1.21855 0.609277 0.792958i \(-0.291460\pi\)
0.609277 + 0.792958i \(0.291460\pi\)
\(72\) 0 0
\(73\) 1.38188i 0.161737i −0.996725 0.0808685i \(-0.974231\pi\)
0.996725 0.0808685i \(-0.0257694\pi\)
\(74\) 0 0
\(75\) 3.63644 + 14.4859i 0.419900 + 1.67269i
\(76\) 0 0
\(77\) 6.02771i 0.686921i
\(78\) 0 0
\(79\) 4.67459 0.525932 0.262966 0.964805i \(-0.415299\pi\)
0.262966 + 0.964805i \(0.415299\pi\)
\(80\) 0 0
\(81\) 8.30917 0.923241
\(82\) 0 0
\(83\) 15.7171i 1.72517i 0.505909 + 0.862587i \(0.331157\pi\)
−0.505909 + 0.862587i \(0.668843\pi\)
\(84\) 0 0
\(85\) −7.45862 + 0.921881i −0.809001 + 0.0999921i
\(86\) 0 0
\(87\) 0.809622i 0.0868006i
\(88\) 0 0
\(89\) 11.1548 1.18241 0.591206 0.806521i \(-0.298652\pi\)
0.591206 + 0.806521i \(0.298652\pi\)
\(90\) 0 0
\(91\) 6.25008 0.655187
\(92\) 0 0
\(93\) 26.2202i 2.71891i
\(94\) 0 0
\(95\) −0.296991 2.40285i −0.0304706 0.246527i
\(96\) 0 0
\(97\) 10.2868i 1.04447i −0.852802 0.522234i \(-0.825099\pi\)
0.852802 0.522234i \(-0.174901\pi\)
\(98\) 0 0
\(99\) 36.4073 3.65908
\(100\) 0 0
\(101\) −15.2625 −1.51868 −0.759339 0.650695i \(-0.774478\pi\)
−0.759339 + 0.650695i \(0.774478\pi\)
\(102\) 0 0
\(103\) 7.60795i 0.749634i 0.927099 + 0.374817i \(0.122294\pi\)
−0.927099 + 0.374817i \(0.877706\pi\)
\(104\) 0 0
\(105\) −0.803394 6.49998i −0.0784032 0.634333i
\(106\) 0 0
\(107\) 11.3081i 1.09320i 0.837395 + 0.546599i \(0.184078\pi\)
−0.837395 + 0.546599i \(0.815922\pi\)
\(108\) 0 0
\(109\) −3.45336 −0.330772 −0.165386 0.986229i \(-0.552887\pi\)
−0.165386 + 0.986229i \(0.552887\pi\)
\(110\) 0 0
\(111\) −26.4256 −2.50820
\(112\) 0 0
\(113\) 14.6889i 1.38181i −0.722944 0.690907i \(-0.757212\pi\)
0.722944 0.690907i \(-0.242788\pi\)
\(114\) 0 0
\(115\) −2.21918 + 0.274289i −0.206940 + 0.0255776i
\(116\) 0 0
\(117\) 37.7505i 3.49003i
\(118\) 0 0
\(119\) 3.29564 0.302111
\(120\) 0 0
\(121\) 26.7882 2.43530
\(122\) 0 0
\(123\) 14.4965i 1.30710i
\(124\) 0 0
\(125\) −4.03180 10.4281i −0.360615 0.932715i
\(126\) 0 0
\(127\) 1.19312i 0.105873i −0.998598 0.0529363i \(-0.983142\pi\)
0.998598 0.0529363i \(-0.0168580\pi\)
\(128\) 0 0
\(129\) −5.60841 −0.493793
\(130\) 0 0
\(131\) −11.7326 −1.02509 −0.512543 0.858662i \(-0.671296\pi\)
−0.512543 + 0.858662i \(0.671296\pi\)
\(132\) 0 0
\(133\) 1.06171i 0.0920623i
\(134\) 0 0
\(135\) −19.3733 + 2.39453i −1.66739 + 0.206088i
\(136\) 0 0
\(137\) 10.4665i 0.894210i −0.894481 0.447105i \(-0.852455\pi\)
0.894481 0.447105i \(-0.147545\pi\)
\(138\) 0 0
\(139\) −4.11349 −0.348902 −0.174451 0.984666i \(-0.555815\pi\)
−0.174451 + 0.984666i \(0.555815\pi\)
\(140\) 0 0
\(141\) 0.585732 0.0493275
\(142\) 0 0
\(143\) 39.1823i 3.27659i
\(144\) 0 0
\(145\) 0.0743441 + 0.601492i 0.00617394 + 0.0499512i
\(146\) 0 0
\(147\) 18.0374i 1.48770i
\(148\) 0 0
\(149\) −1.37793 −0.112885 −0.0564424 0.998406i \(-0.517976\pi\)
−0.0564424 + 0.998406i \(0.517976\pi\)
\(150\) 0 0
\(151\) −3.49384 −0.284325 −0.142162 0.989843i \(-0.545406\pi\)
−0.142162 + 0.989843i \(0.545406\pi\)
\(152\) 0 0
\(153\) 19.9057i 1.60928i
\(154\) 0 0
\(155\) −2.40769 19.4798i −0.193390 1.56465i
\(156\) 0 0
\(157\) 3.32373i 0.265262i −0.991165 0.132631i \(-0.957657\pi\)
0.991165 0.132631i \(-0.0423426\pi\)
\(158\) 0 0
\(159\) 5.76973 0.457569
\(160\) 0 0
\(161\) 0.980560 0.0772789
\(162\) 0 0
\(163\) 8.52075i 0.667397i 0.942680 + 0.333698i \(0.108297\pi\)
−0.942680 + 0.333698i \(0.891703\pi\)
\(164\) 0 0
\(165\) −40.7489 + 5.03654i −3.17230 + 0.392094i
\(166\) 0 0
\(167\) 15.6190i 1.20864i 0.796742 + 0.604319i \(0.206555\pi\)
−0.796742 + 0.604319i \(0.793445\pi\)
\(168\) 0 0
\(169\) −27.6278 −2.12522
\(170\) 0 0
\(171\) 6.41275 0.490395
\(172\) 0 0
\(173\) 8.42727i 0.640713i 0.947297 + 0.320357i \(0.103803\pi\)
−0.947297 + 0.320357i \(0.896197\pi\)
\(174\) 0 0
\(175\) 1.19373 + 4.75525i 0.0902375 + 0.359463i
\(176\) 0 0
\(177\) 38.8428i 2.91960i
\(178\) 0 0
\(179\) −10.8047 −0.807580 −0.403790 0.914852i \(-0.632307\pi\)
−0.403790 + 0.914852i \(0.632307\pi\)
\(180\) 0 0
\(181\) −15.4282 −1.14677 −0.573385 0.819286i \(-0.694370\pi\)
−0.573385 + 0.819286i \(0.694370\pi\)
\(182\) 0 0
\(183\) 17.9281i 1.32528i
\(184\) 0 0
\(185\) 19.6323 2.42654i 1.44340 0.178403i
\(186\) 0 0
\(187\) 20.6607i 1.51086i
\(188\) 0 0
\(189\) 8.56022 0.622664
\(190\) 0 0
\(191\) −22.2634 −1.61092 −0.805462 0.592648i \(-0.798083\pi\)
−0.805462 + 0.592648i \(0.798083\pi\)
\(192\) 0 0
\(193\) 16.1399i 1.16178i −0.813983 0.580889i \(-0.802705\pi\)
0.813983 0.580889i \(-0.197295\pi\)
\(194\) 0 0
\(195\) 5.22235 + 42.2522i 0.373980 + 3.02575i
\(196\) 0 0
\(197\) 13.9936i 0.997004i 0.866889 + 0.498502i \(0.166116\pi\)
−0.866889 + 0.498502i \(0.833884\pi\)
\(198\) 0 0
\(199\) 6.91926 0.490493 0.245246 0.969461i \(-0.421131\pi\)
0.245246 + 0.969461i \(0.421131\pi\)
\(200\) 0 0
\(201\) 6.77608 0.477948
\(202\) 0 0
\(203\) 0.265773i 0.0186536i
\(204\) 0 0
\(205\) −1.33115 10.7699i −0.0929714 0.752200i
\(206\) 0 0
\(207\) 5.92257i 0.411647i
\(208\) 0 0
\(209\) 6.65598 0.460404
\(210\) 0 0
\(211\) 12.9170 0.889246 0.444623 0.895718i \(-0.353338\pi\)
0.444623 + 0.895718i \(0.353338\pi\)
\(212\) 0 0
\(213\) 30.6704i 2.10150i
\(214\) 0 0
\(215\) 4.16665 0.514996i 0.284164 0.0351224i
\(216\) 0 0
\(217\) 8.60728i 0.584300i
\(218\) 0 0
\(219\) −4.12777 −0.278929
\(220\) 0 0
\(221\) −21.4229 −1.44106
\(222\) 0 0
\(223\) 26.6579i 1.78514i −0.450905 0.892572i \(-0.648899\pi\)
0.450905 0.892572i \(-0.351101\pi\)
\(224\) 0 0
\(225\) 28.7217 7.21012i 1.91478 0.480675i
\(226\) 0 0
\(227\) 9.44407i 0.626825i −0.949617 0.313412i \(-0.898528\pi\)
0.949617 0.313412i \(-0.101472\pi\)
\(228\) 0 0
\(229\) −14.1994 −0.938322 −0.469161 0.883113i \(-0.655444\pi\)
−0.469161 + 0.883113i \(0.655444\pi\)
\(230\) 0 0
\(231\) 18.0052 1.18465
\(232\) 0 0
\(233\) 9.41134i 0.616557i 0.951296 + 0.308279i \(0.0997529\pi\)
−0.951296 + 0.308279i \(0.900247\pi\)
\(234\) 0 0
\(235\) −0.435158 + 0.0537852i −0.0283866 + 0.00350856i
\(236\) 0 0
\(237\) 13.9633i 0.907014i
\(238\) 0 0
\(239\) 15.4781 1.00119 0.500597 0.865680i \(-0.333114\pi\)
0.500597 + 0.865680i \(0.333114\pi\)
\(240\) 0 0
\(241\) −3.51052 −0.226133 −0.113066 0.993587i \(-0.536067\pi\)
−0.113066 + 0.993587i \(0.536067\pi\)
\(242\) 0 0
\(243\) 1.36974i 0.0878689i
\(244\) 0 0
\(245\) 1.65630 + 13.4005i 0.105817 + 0.856129i
\(246\) 0 0
\(247\) 6.90153i 0.439134i
\(248\) 0 0
\(249\) 46.9480 2.97521
\(250\) 0 0
\(251\) −23.6649 −1.49372 −0.746859 0.664982i \(-0.768439\pi\)
−0.746859 + 0.664982i \(0.768439\pi\)
\(252\) 0 0
\(253\) 6.14721i 0.386472i
\(254\) 0 0
\(255\) 2.75372 + 22.2794i 0.172445 + 1.39519i
\(256\) 0 0
\(257\) 30.8326i 1.92328i 0.274311 + 0.961641i \(0.411550\pi\)
−0.274311 + 0.961641i \(0.588450\pi\)
\(258\) 0 0
\(259\) −8.67467 −0.539018
\(260\) 0 0
\(261\) −1.60527 −0.0993636
\(262\) 0 0
\(263\) 20.5880i 1.26951i −0.772714 0.634755i \(-0.781101\pi\)
0.772714 0.634755i \(-0.218899\pi\)
\(264\) 0 0
\(265\) −4.28650 + 0.529809i −0.263318 + 0.0325459i
\(266\) 0 0
\(267\) 33.3203i 2.03917i
\(268\) 0 0
\(269\) 17.0277 1.03820 0.519099 0.854714i \(-0.326268\pi\)
0.519099 + 0.854714i \(0.326268\pi\)
\(270\) 0 0
\(271\) 13.6709 0.830450 0.415225 0.909719i \(-0.363703\pi\)
0.415225 + 0.909719i \(0.363703\pi\)
\(272\) 0 0
\(273\) 18.6694i 1.12993i
\(274\) 0 0
\(275\) 29.8111 7.48360i 1.79768 0.451278i
\(276\) 0 0
\(277\) 16.2380i 0.975647i 0.872942 + 0.487824i \(0.162209\pi\)
−0.872942 + 0.487824i \(0.837791\pi\)
\(278\) 0 0
\(279\) 51.9879 3.11243
\(280\) 0 0
\(281\) −0.362407 −0.0216194 −0.0108097 0.999942i \(-0.503441\pi\)
−0.0108097 + 0.999942i \(0.503441\pi\)
\(282\) 0 0
\(283\) 6.80039i 0.404241i −0.979361 0.202120i \(-0.935217\pi\)
0.979361 0.202120i \(-0.0647833\pi\)
\(284\) 0 0
\(285\) −7.17747 + 0.887131i −0.425157 + 0.0525491i
\(286\) 0 0
\(287\) 4.75873i 0.280899i
\(288\) 0 0
\(289\) 5.70382 0.335519
\(290\) 0 0
\(291\) −30.7274 −1.80127
\(292\) 0 0
\(293\) 26.2172i 1.53162i 0.643065 + 0.765812i \(0.277663\pi\)
−0.643065 + 0.765812i \(0.722337\pi\)
\(294\) 0 0
\(295\) −3.56676 28.8574i −0.207665 1.68015i
\(296\) 0 0
\(297\) 53.6647i 3.11394i
\(298\) 0 0
\(299\) −6.37400 −0.368618
\(300\) 0 0
\(301\) −1.84106 −0.106117
\(302\) 0 0
\(303\) 45.5902i 2.61909i
\(304\) 0 0
\(305\) 1.64626 + 13.3193i 0.0942644 + 0.762660i
\(306\) 0 0
\(307\) 19.7146i 1.12517i 0.826738 + 0.562587i \(0.190194\pi\)
−0.826738 + 0.562587i \(0.809806\pi\)
\(308\) 0 0
\(309\) 22.7255 1.29281
\(310\) 0 0
\(311\) 15.1003 0.856258 0.428129 0.903718i \(-0.359173\pi\)
0.428129 + 0.903718i \(0.359173\pi\)
\(312\) 0 0
\(313\) 12.9813i 0.733747i −0.930271 0.366874i \(-0.880428\pi\)
0.930271 0.366874i \(-0.119572\pi\)
\(314\) 0 0
\(315\) −12.8878 + 1.59292i −0.726143 + 0.0897508i
\(316\) 0 0
\(317\) 17.3503i 0.974489i 0.873266 + 0.487244i \(0.161998\pi\)
−0.873266 + 0.487244i \(0.838002\pi\)
\(318\) 0 0
\(319\) −1.66616 −0.0932868
\(320\) 0 0
\(321\) 33.7781 1.88531
\(322\) 0 0
\(323\) 3.63915i 0.202488i
\(324\) 0 0
\(325\) −7.75968 30.9109i −0.430429 1.71463i
\(326\) 0 0
\(327\) 10.3154i 0.570444i
\(328\) 0 0
\(329\) 0.192277 0.0106006
\(330\) 0 0
\(331\) 0.984756 0.0541271 0.0270635 0.999634i \(-0.491384\pi\)
0.0270635 + 0.999634i \(0.491384\pi\)
\(332\) 0 0
\(333\) 52.3950i 2.87123i
\(334\) 0 0
\(335\) −5.03415 + 0.622218i −0.275045 + 0.0339954i
\(336\) 0 0
\(337\) 23.5575i 1.28326i 0.767015 + 0.641629i \(0.221741\pi\)
−0.767015 + 0.641629i \(0.778259\pi\)
\(338\) 0 0
\(339\) −43.8767 −2.38305
\(340\) 0 0
\(341\) 53.9598 2.92208
\(342\) 0 0
\(343\) 12.7850i 0.690327i
\(344\) 0 0
\(345\) 0.819321 + 6.62885i 0.0441108 + 0.356885i
\(346\) 0 0
\(347\) 26.0916i 1.40067i 0.713813 + 0.700337i \(0.246967\pi\)
−0.713813 + 0.700337i \(0.753033\pi\)
\(348\) 0 0
\(349\) 17.8609 0.956070 0.478035 0.878341i \(-0.341349\pi\)
0.478035 + 0.878341i \(0.341349\pi\)
\(350\) 0 0
\(351\) −55.6445 −2.97009
\(352\) 0 0
\(353\) 13.1080i 0.697667i 0.937185 + 0.348833i \(0.113422\pi\)
−0.937185 + 0.348833i \(0.886578\pi\)
\(354\) 0 0
\(355\) 2.81633 + 22.7859i 0.149475 + 1.20935i
\(356\) 0 0
\(357\) 9.84430i 0.521016i
\(358\) 0 0
\(359\) −22.1119 −1.16702 −0.583510 0.812106i \(-0.698321\pi\)
−0.583510 + 0.812106i \(0.698321\pi\)
\(360\) 0 0
\(361\) −17.8276 −0.938296
\(362\) 0 0
\(363\) 80.0183i 4.19987i
\(364\) 0 0
\(365\) 3.06665 0.379036i 0.160516 0.0198396i
\(366\) 0 0
\(367\) 7.98495i 0.416811i 0.978043 + 0.208406i \(0.0668274\pi\)
−0.978043 + 0.208406i \(0.933173\pi\)
\(368\) 0 0
\(369\) 28.7427 1.49629
\(370\) 0 0
\(371\) 1.89402 0.0983326
\(372\) 0 0
\(373\) 23.8712i 1.23600i −0.786177 0.618002i \(-0.787942\pi\)
0.786177 0.618002i \(-0.212058\pi\)
\(374\) 0 0
\(375\) −31.1493 + 12.0433i −1.60855 + 0.621911i
\(376\) 0 0
\(377\) 1.72762i 0.0889771i
\(378\) 0 0
\(379\) 34.5647 1.77547 0.887735 0.460355i \(-0.152278\pi\)
0.887735 + 0.460355i \(0.152278\pi\)
\(380\) 0 0
\(381\) −3.56394 −0.182586
\(382\) 0 0
\(383\) 12.3139i 0.629211i −0.949223 0.314606i \(-0.898128\pi\)
0.949223 0.314606i \(-0.101872\pi\)
\(384\) 0 0
\(385\) −13.3766 + 1.65334i −0.681734 + 0.0842619i
\(386\) 0 0
\(387\) 11.1200i 0.565262i
\(388\) 0 0
\(389\) 27.0447 1.37122 0.685611 0.727968i \(-0.259535\pi\)
0.685611 + 0.727968i \(0.259535\pi\)
\(390\) 0 0
\(391\) −3.36098 −0.169972
\(392\) 0 0
\(393\) 35.0462i 1.76785i
\(394\) 0 0
\(395\) 1.28219 + 10.3738i 0.0645140 + 0.521960i
\(396\) 0 0
\(397\) 9.07631i 0.455527i −0.973717 0.227763i \(-0.926859\pi\)
0.973717 0.227763i \(-0.0731413\pi\)
\(398\) 0 0
\(399\) 3.17141 0.158769
\(400\) 0 0
\(401\) 6.73762 0.336461 0.168230 0.985748i \(-0.446195\pi\)
0.168230 + 0.985748i \(0.446195\pi\)
\(402\) 0 0
\(403\) 55.9504i 2.78709i
\(404\) 0 0
\(405\) 2.27912 + 18.4395i 0.113250 + 0.916268i
\(406\) 0 0
\(407\) 54.3823i 2.69563i
\(408\) 0 0
\(409\) −25.7205 −1.27180 −0.635898 0.771773i \(-0.719370\pi\)
−0.635898 + 0.771773i \(0.719370\pi\)
\(410\) 0 0
\(411\) −31.2640 −1.54214
\(412\) 0 0
\(413\) 12.7509i 0.627428i
\(414\) 0 0
\(415\) −34.8791 + 4.31103i −1.71215 + 0.211620i
\(416\) 0 0
\(417\) 12.2873i 0.601711i
\(418\) 0 0
\(419\) 16.2666 0.794676 0.397338 0.917672i \(-0.369934\pi\)
0.397338 + 0.917672i \(0.369934\pi\)
\(420\) 0 0
\(421\) −18.9106 −0.921645 −0.460822 0.887492i \(-0.652445\pi\)
−0.460822 + 0.887492i \(0.652445\pi\)
\(422\) 0 0
\(423\) 1.16135i 0.0564669i
\(424\) 0 0
\(425\) −4.09164 16.2992i −0.198474 0.790626i
\(426\) 0 0
\(427\) 5.88522i 0.284806i
\(428\) 0 0
\(429\) −117.040 −5.65076
\(430\) 0 0
\(431\) −11.4086 −0.549535 −0.274767 0.961511i \(-0.588601\pi\)
−0.274767 + 0.961511i \(0.588601\pi\)
\(432\) 0 0
\(433\) 23.2756i 1.11856i 0.828980 + 0.559278i \(0.188922\pi\)
−0.828980 + 0.559278i \(0.811078\pi\)
\(434\) 0 0
\(435\) 1.79670 0.222071i 0.0861451 0.0106475i
\(436\) 0 0
\(437\) 1.08276i 0.0517956i
\(438\) 0 0
\(439\) 13.0581 0.623231 0.311615 0.950208i \(-0.399130\pi\)
0.311615 + 0.950208i \(0.399130\pi\)
\(440\) 0 0
\(441\) −35.7635 −1.70302
\(442\) 0 0
\(443\) 0.113844i 0.00540891i 0.999996 + 0.00270446i \(0.000860856\pi\)
−0.999996 + 0.00270446i \(0.999139\pi\)
\(444\) 0 0
\(445\) 3.05966 + 24.7546i 0.145042 + 1.17348i
\(446\) 0 0
\(447\) 4.11598i 0.194679i
\(448\) 0 0
\(449\) 11.0371 0.520874 0.260437 0.965491i \(-0.416133\pi\)
0.260437 + 0.965491i \(0.416133\pi\)
\(450\) 0 0
\(451\) 29.8329 1.40478
\(452\) 0 0
\(453\) 10.4363i 0.490342i
\(454\) 0 0
\(455\) 1.71433 + 13.8701i 0.0803691 + 0.650239i
\(456\) 0 0
\(457\) 30.1638i 1.41100i −0.708709 0.705501i \(-0.750722\pi\)
0.708709 0.705501i \(-0.249278\pi\)
\(458\) 0 0
\(459\) −29.3411 −1.36953
\(460\) 0 0
\(461\) −37.3908 −1.74146 −0.870732 0.491759i \(-0.836354\pi\)
−0.870732 + 0.491759i \(0.836354\pi\)
\(462\) 0 0
\(463\) 16.7365i 0.777810i 0.921278 + 0.388905i \(0.127147\pi\)
−0.921278 + 0.388905i \(0.872853\pi\)
\(464\) 0 0
\(465\) −58.1875 + 7.19194i −2.69838 + 0.333518i
\(466\) 0 0
\(467\) 18.2260i 0.843399i −0.906736 0.421699i \(-0.861434\pi\)
0.906736 0.421699i \(-0.138566\pi\)
\(468\) 0 0
\(469\) 2.22437 0.102712
\(470\) 0 0
\(471\) −9.92820 −0.457467
\(472\) 0 0
\(473\) 11.5418i 0.530692i
\(474\) 0 0
\(475\) 5.25090 1.31815i 0.240928 0.0604810i
\(476\) 0 0
\(477\) 11.4399i 0.523795i
\(478\) 0 0
\(479\) −3.31948 −0.151671 −0.0758355 0.997120i \(-0.524162\pi\)
−0.0758355 + 0.997120i \(0.524162\pi\)
\(480\) 0 0
\(481\) 56.3885 2.57110
\(482\) 0 0
\(483\) 2.92900i 0.133274i
\(484\) 0 0
\(485\) 22.8283 2.82157i 1.03658 0.128121i
\(486\) 0 0
\(487\) 19.7412i 0.894558i −0.894395 0.447279i \(-0.852393\pi\)
0.894395 0.447279i \(-0.147607\pi\)
\(488\) 0 0
\(489\) 25.4521 1.15098
\(490\) 0 0
\(491\) 18.1353 0.818432 0.409216 0.912437i \(-0.365802\pi\)
0.409216 + 0.912437i \(0.365802\pi\)
\(492\) 0 0
\(493\) 0.910968i 0.0410279i
\(494\) 0 0
\(495\) 9.98615 + 80.7945i 0.448844 + 3.63144i
\(496\) 0 0
\(497\) 10.0681i 0.451616i
\(498\) 0 0
\(499\) −14.9797 −0.670582 −0.335291 0.942115i \(-0.608835\pi\)
−0.335291 + 0.942115i \(0.608835\pi\)
\(500\) 0 0
\(501\) 46.6552 2.08440
\(502\) 0 0
\(503\) 7.90238i 0.352350i −0.984359 0.176175i \(-0.943628\pi\)
0.984359 0.176175i \(-0.0563724\pi\)
\(504\) 0 0
\(505\) −4.18635 33.8703i −0.186290 1.50721i
\(506\) 0 0
\(507\) 82.5262i 3.66512i
\(508\) 0 0
\(509\) 21.1882 0.939152 0.469576 0.882892i \(-0.344407\pi\)
0.469576 + 0.882892i \(0.344407\pi\)
\(510\) 0 0
\(511\) −1.35502 −0.0599425
\(512\) 0 0
\(513\) 9.45245i 0.417336i
\(514\) 0 0
\(515\) −16.8834 + 2.08678i −0.743973 + 0.0919546i
\(516\) 0 0
\(517\) 1.20540i 0.0530136i
\(518\) 0 0
\(519\) 25.1728 1.10496
\(520\) 0 0
\(521\) −11.1210 −0.487219 −0.243610 0.969873i \(-0.578332\pi\)
−0.243610 + 0.969873i \(0.578332\pi\)
\(522\) 0 0
\(523\) 16.2670i 0.711304i −0.934618 0.355652i \(-0.884259\pi\)
0.934618 0.355652i \(-0.115741\pi\)
\(524\) 0 0
\(525\) 14.2043 3.56575i 0.619925 0.155622i
\(526\) 0 0
\(527\) 29.5024i 1.28515i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 77.0151 3.34217
\(532\) 0 0
\(533\) 30.9335i 1.33988i
\(534\) 0 0
\(535\) −25.0948 + 3.10170i −1.08494 + 0.134098i
\(536\) 0 0
\(537\) 32.2743i 1.39274i
\(538\) 0 0
\(539\) −37.1200 −1.59887
\(540\) 0 0
\(541\) −13.8797 −0.596733 −0.298367 0.954451i \(-0.596442\pi\)
−0.298367 + 0.954451i \(0.596442\pi\)
\(542\) 0 0
\(543\) 46.0851i 1.97770i
\(544\) 0 0
\(545\) −0.947220 7.66363i −0.0405745 0.328274i
\(546\) 0 0
\(547\) 5.91647i 0.252970i 0.991969 + 0.126485i \(0.0403696\pi\)
−0.991969 + 0.126485i \(0.959630\pi\)
\(548\) 0 0
\(549\) −35.5467 −1.51709
\(550\) 0 0
\(551\) −0.293475 −0.0125025
\(552\) 0 0
\(553\) 4.58371i 0.194919i
\(554\) 0 0
\(555\) −7.24825 58.6431i −0.307671 2.48926i
\(556\) 0 0
\(557\) 28.2857i 1.19850i −0.800560 0.599252i \(-0.795465\pi\)
0.800560 0.599252i \(-0.204535\pi\)
\(558\) 0 0
\(559\) 11.9676 0.506175
\(560\) 0 0
\(561\) −61.7148 −2.60560
\(562\) 0 0
\(563\) 31.7025i 1.33610i 0.744117 + 0.668050i \(0.232871\pi\)
−0.744117 + 0.668050i \(0.767129\pi\)
\(564\) 0 0
\(565\) 32.5973 4.02900i 1.37138 0.169502i
\(566\) 0 0
\(567\) 8.14763i 0.342169i
\(568\) 0 0
\(569\) 24.0702 1.00907 0.504537 0.863390i \(-0.331663\pi\)
0.504537 + 0.863390i \(0.331663\pi\)
\(570\) 0 0
\(571\) 14.3935 0.602349 0.301175 0.953569i \(-0.402621\pi\)
0.301175 + 0.953569i \(0.402621\pi\)
\(572\) 0 0
\(573\) 66.5023i 2.77817i
\(574\) 0 0
\(575\) −1.21740 4.84953i −0.0507689 0.202239i
\(576\) 0 0
\(577\) 5.77998i 0.240624i −0.992736 0.120312i \(-0.961611\pi\)
0.992736 0.120312i \(-0.0383895\pi\)
\(578\) 0 0
\(579\) −48.2111 −2.00358
\(580\) 0 0
\(581\) 15.4115 0.639378
\(582\) 0 0
\(583\) 11.8738i 0.491761i
\(584\) 0 0
\(585\) 83.7751 10.3546i 3.46368 0.428108i
\(586\) 0 0
\(587\) 27.7897i 1.14700i 0.819204 + 0.573502i \(0.194416\pi\)
−0.819204 + 0.573502i \(0.805584\pi\)
\(588\) 0 0
\(589\) 9.50441 0.391623
\(590\) 0 0
\(591\) 41.7999 1.71942
\(592\) 0 0
\(593\) 22.1872i 0.911118i 0.890205 + 0.455559i \(0.150561\pi\)
−0.890205 + 0.455559i \(0.849439\pi\)
\(594\) 0 0
\(595\) 0.903960 + 7.31363i 0.0370587 + 0.299829i
\(596\) 0 0
\(597\) 20.6683i 0.845897i
\(598\) 0 0
\(599\) −15.1380 −0.618521 −0.309260 0.950977i \(-0.600081\pi\)
−0.309260 + 0.950977i \(0.600081\pi\)
\(600\) 0 0
\(601\) 20.5353 0.837652 0.418826 0.908067i \(-0.362442\pi\)
0.418826 + 0.908067i \(0.362442\pi\)
\(602\) 0 0
\(603\) 13.4352i 0.547123i
\(604\) 0 0
\(605\) 7.34773 + 59.4480i 0.298728 + 2.41690i
\(606\) 0 0
\(607\) 28.9906i 1.17669i 0.808610 + 0.588345i \(0.200220\pi\)
−0.808610 + 0.588345i \(0.799780\pi\)
\(608\) 0 0
\(609\) −0.793883 −0.0321698
\(610\) 0 0
\(611\) −1.24987 −0.0505644
\(612\) 0 0
\(613\) 9.03621i 0.364969i 0.983209 + 0.182485i \(0.0584139\pi\)
−0.983209 + 0.182485i \(0.941586\pi\)
\(614\) 0 0
\(615\) −32.1703 + 3.97623i −1.29723 + 0.160337i
\(616\) 0 0
\(617\) 4.42741i 0.178241i −0.996021 0.0891203i \(-0.971594\pi\)
0.996021 0.0891203i \(-0.0284056\pi\)
\(618\) 0 0
\(619\) −14.8403 −0.596483 −0.298241 0.954490i \(-0.596400\pi\)
−0.298241 + 0.954490i \(0.596400\pi\)
\(620\) 0 0
\(621\) −8.72993 −0.350320
\(622\) 0 0
\(623\) 10.9380i 0.438222i
\(624\) 0 0
\(625\) 22.0359 11.8076i 0.881436 0.472304i
\(626\) 0 0
\(627\) 19.8819i 0.794005i
\(628\) 0 0
\(629\) 29.7334 1.18555
\(630\) 0 0
\(631\) 41.8369 1.66550 0.832751 0.553648i \(-0.186765\pi\)
0.832751 + 0.553648i \(0.186765\pi\)
\(632\) 0 0
\(633\) 38.5841i 1.53358i
\(634\) 0 0
\(635\) 2.64776 0.327261i 0.105073 0.0129870i
\(636\) 0 0
\(637\) 38.4894i 1.52501i
\(638\) 0 0
\(639\) −60.8113 −2.40566
\(640\) 0 0
\(641\) 5.86478 0.231645 0.115822 0.993270i \(-0.463050\pi\)
0.115822 + 0.993270i \(0.463050\pi\)
\(642\) 0 0
\(643\) 0.460745i 0.0181700i 0.999959 + 0.00908500i \(0.00289188\pi\)
−0.999959 + 0.00908500i \(0.997108\pi\)
\(644\) 0 0
\(645\) −1.53833 12.4461i −0.0605716 0.490064i
\(646\) 0 0
\(647\) 15.5690i 0.612079i 0.952019 + 0.306040i \(0.0990040\pi\)
−0.952019 + 0.306040i \(0.900996\pi\)
\(648\) 0 0
\(649\) 79.9362 3.13777
\(650\) 0 0
\(651\) 25.7105 1.00767
\(652\) 0 0
\(653\) 29.4538i 1.15262i −0.817233 0.576308i \(-0.804493\pi\)
0.817233 0.576308i \(-0.195507\pi\)
\(654\) 0 0
\(655\) −3.21814 26.0369i −0.125743 1.01734i
\(656\) 0 0
\(657\) 8.18430i 0.319300i
\(658\) 0 0
\(659\) −22.5604 −0.878829 −0.439415 0.898284i \(-0.644814\pi\)
−0.439415 + 0.898284i \(0.644814\pi\)
\(660\) 0 0
\(661\) −39.7530 −1.54621 −0.773106 0.634277i \(-0.781298\pi\)
−0.773106 + 0.634277i \(0.781298\pi\)
\(662\) 0 0
\(663\) 63.9916i 2.48523i
\(664\) 0 0
\(665\) −2.35614 + 0.291217i −0.0913671 + 0.0112929i
\(666\) 0 0
\(667\) 0.271042i 0.0104948i
\(668\) 0 0
\(669\) −79.6289 −3.07863
\(670\) 0 0
\(671\) −36.8949 −1.42431
\(672\) 0 0
\(673\) 11.5047i 0.443475i 0.975106 + 0.221737i \(0.0711728\pi\)
−0.975106 + 0.221737i \(0.928827\pi\)
\(674\) 0 0
\(675\) −10.6278 42.3361i −0.409064 1.62952i
\(676\) 0 0
\(677\) 31.7703i 1.22103i −0.792005 0.610515i \(-0.790962\pi\)
0.792005 0.610515i \(-0.209038\pi\)
\(678\) 0 0
\(679\) −10.0868 −0.387098
\(680\) 0 0
\(681\) −28.2101 −1.08101
\(682\) 0 0
\(683\) 7.22683i 0.276527i 0.990395 + 0.138264i \(0.0441521\pi\)
−0.990395 + 0.138264i \(0.955848\pi\)
\(684\) 0 0
\(685\) 23.2270 2.87084i 0.887457 0.109689i
\(686\) 0 0
\(687\) 42.4145i 1.61822i
\(688\) 0 0
\(689\) −12.3118 −0.469043
\(690\) 0 0
\(691\) 3.29788 0.125457 0.0627286 0.998031i \(-0.480020\pi\)
0.0627286 + 0.998031i \(0.480020\pi\)
\(692\) 0 0
\(693\) 35.6996i 1.35611i
\(694\) 0 0
\(695\) −1.12829 9.12859i −0.0427984 0.346267i
\(696\) 0 0
\(697\) 16.3111i 0.617827i
\(698\) 0 0
\(699\) 28.1123 1.06331
\(700\) 0 0
\(701\) 18.7936 0.709824 0.354912 0.934900i \(-0.384511\pi\)
0.354912 + 0.934900i \(0.384511\pi\)
\(702\) 0 0
\(703\) 9.57884i 0.361273i
\(704\) 0 0
\(705\) 0.160660 + 1.29985i 0.00605081 + 0.0489550i
\(706\) 0 0
\(707\) 14.9658i 0.562848i
\(708\) 0 0
\(709\) −14.1039 −0.529685 −0.264842 0.964292i \(-0.585320\pi\)
−0.264842 + 0.964292i \(0.585320\pi\)
\(710\) 0 0
\(711\) −27.6856 −1.03829
\(712\) 0 0
\(713\) 8.77792i 0.328736i
\(714\) 0 0
\(715\) 86.9527 10.7473i 3.25185 0.401926i
\(716\) 0 0
\(717\) 46.2341i 1.72664i
\(718\) 0 0
\(719\) 23.5631 0.878754 0.439377 0.898303i \(-0.355199\pi\)
0.439377 + 0.898303i \(0.355199\pi\)
\(720\) 0 0
\(721\) 7.46005 0.277827
\(722\) 0 0
\(723\) 10.4862i 0.389985i
\(724\) 0 0
\(725\) −1.31443 + 0.329966i −0.0488166 + 0.0122546i
\(726\) 0 0
\(727\) 3.57021i 0.132412i 0.997806 + 0.0662059i \(0.0210894\pi\)
−0.997806 + 0.0662059i \(0.978911\pi\)
\(728\) 0 0
\(729\) 29.0190 1.07478
\(730\) 0 0
\(731\) 6.31045 0.233401
\(732\) 0 0
\(733\) 10.3158i 0.381022i 0.981685 + 0.190511i \(0.0610145\pi\)
−0.981685 + 0.190511i \(0.938985\pi\)
\(734\) 0 0
\(735\) 40.0283 4.94747i 1.47647 0.182490i
\(736\) 0 0
\(737\) 13.9448i 0.513663i
\(738\) 0 0
\(739\) 36.2056 1.33185 0.665923 0.746021i \(-0.268038\pi\)
0.665923 + 0.746021i \(0.268038\pi\)
\(740\) 0 0
\(741\) −20.6153 −0.757324
\(742\) 0 0
\(743\) 3.24466i 0.119035i 0.998227 + 0.0595174i \(0.0189562\pi\)
−0.998227 + 0.0595174i \(0.981044\pi\)
\(744\) 0 0
\(745\) −0.377953 3.05788i −0.0138471 0.112032i
\(746\) 0 0
\(747\) 93.0856i 3.40582i
\(748\) 0 0
\(749\) 11.0883 0.405157
\(750\) 0 0
\(751\) 26.9796 0.984499 0.492250 0.870454i \(-0.336175\pi\)
0.492250 + 0.870454i \(0.336175\pi\)
\(752\) 0 0
\(753\) 70.6888i 2.57604i
\(754\) 0 0
\(755\) −0.958324 7.75347i −0.0348770 0.282178i
\(756\) 0 0
\(757\) 11.7249i 0.426148i 0.977036 + 0.213074i \(0.0683476\pi\)
−0.977036 + 0.213074i \(0.931652\pi\)
\(758\) 0 0
\(759\) −18.3621 −0.666504
\(760\) 0 0
\(761\) −24.4303 −0.885599 −0.442800 0.896621i \(-0.646015\pi\)
−0.442800 + 0.896621i \(0.646015\pi\)
\(762\) 0 0
\(763\) 3.38623i 0.122590i
\(764\) 0 0
\(765\) 44.1742 5.45991i 1.59712 0.197403i
\(766\) 0 0
\(767\) 82.8852i 2.99281i
\(768\) 0 0
\(769\) −0.804588 −0.0290142 −0.0145071 0.999895i \(-0.504618\pi\)
−0.0145071 + 0.999895i \(0.504618\pi\)
\(770\) 0 0
\(771\) 92.0989 3.31686
\(772\) 0 0
\(773\) 6.02477i 0.216696i 0.994113 + 0.108348i \(0.0345561\pi\)
−0.994113 + 0.108348i \(0.965444\pi\)
\(774\) 0 0
\(775\) 42.5688 10.6862i 1.52912 0.383860i
\(776\) 0 0
\(777\) 25.9118i 0.929582i
\(778\) 0 0
\(779\) 5.25474 0.188270
\(780\) 0 0
\(781\) −63.1179 −2.25853
\(782\) 0 0
\(783\) 2.36618i 0.0845604i
\(784\) 0 0
\(785\) 7.37596 0.911664i 0.263259 0.0325387i
\(786\) 0 0
\(787\) 12.9326i 0.460996i 0.973073 + 0.230498i \(0.0740356\pi\)
−0.973073 + 0.230498i \(0.925964\pi\)
\(788\) 0 0
\(789\) −61.4977 −2.18938
\(790\) 0 0
\(791\) −14.4033 −0.512123
\(792\) 0 0
\(793\) 38.2561i 1.35851i
\(794\) 0 0
\(795\) 1.58258 + 12.8041i 0.0561282 + 0.454114i
\(796\) 0 0
\(797\) 36.3660i 1.28815i −0.764962 0.644075i \(-0.777242\pi\)
0.764962 0.644075i \(-0.222758\pi\)
\(798\) 0 0
\(799\) −0.659052 −0.0233156
\(800\) 0 0
\(801\) −66.0654 −2.33431
\(802\) 0 0
\(803\) 8.49472i 0.299772i