Properties

Label 2394.2.b.i.1709.5
Level $2394$
Weight $2$
Character 2394.1709
Analytic conductor $19.116$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1161862439\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 10x^{6} + 30x^{4} + 24x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1709.5
Root \(1.08784i\) of defining polynomial
Character \(\chi\) \(=\) 2394.1709
Dual form 2394.2.b.i.1709.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.15484i q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.15484i q^{5} -1.00000 q^{7} -1.00000 q^{8} -1.15484i q^{10} -2.90624i q^{11} -1.38329i q^{13} +1.00000 q^{14} +1.00000 q^{16} -2.90624i q^{17} +(3.79473 - 2.14477i) q^{19} +1.15484i q^{20} +2.90624i q^{22} +7.14888i q^{23} +3.66635 q^{25} +1.38329i q^{26} -1.00000 q^{28} -4.66635 q^{29} +4.06108i q^{31} -1.00000 q^{32} +2.90624i q^{34} -1.15484i q^{35} -6.55232i q^{37} +(-3.79473 + 2.14477i) q^{38} -1.15484i q^{40} -11.1869 q^{41} -2.04373 q^{43} -2.90624i q^{44} -7.14888i q^{46} -2.76658i q^{47} +1.00000 q^{49} -3.66635 q^{50} -1.38329i q^{52} -7.39997 q^{53} +3.35624 q^{55} +1.00000 q^{56} +4.66635 q^{58} -8.29954 q^{61} -4.06108i q^{62} +1.00000 q^{64} +1.59748 q^{65} -9.91547i q^{67} -2.90624i q^{68} +1.15484i q^{70} -6.06632 q^{71} +9.37643 q^{73} +6.55232i q^{74} +(3.79473 - 2.14477i) q^{76} +2.90624i q^{77} -12.1783i q^{79} +1.15484i q^{80} +11.1869 q^{82} -14.5262i q^{83} +3.35624 q^{85} +2.04373 q^{86} +2.90624i q^{88} +17.2533 q^{89} +1.38329i q^{91} +7.14888i q^{92} +2.76658i q^{94} +(2.47686 + 4.38230i) q^{95} -3.92142i q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8} + 8 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{32} - 12 q^{38} - 24 q^{41} - 32 q^{43} + 8 q^{49} + 24 q^{50} - 48 q^{53} + 8 q^{56} - 16 q^{58} + 8 q^{61} + 8 q^{64} - 16 q^{65} + 16 q^{71} - 16 q^{73} + 12 q^{76} + 24 q^{82} + 32 q^{86} + 8 q^{89} - 8 q^{95} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(1009\) \(1711\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.15484i 0.516459i 0.966084 + 0.258230i \(0.0831392\pi\)
−0.966084 + 0.258230i \(0.916861\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.15484i 0.365192i
\(11\) 2.90624i 0.876265i −0.898910 0.438133i \(-0.855640\pi\)
0.898910 0.438133i \(-0.144360\pi\)
\(12\) 0 0
\(13\) 1.38329i 0.383656i −0.981429 0.191828i \(-0.938558\pi\)
0.981429 0.191828i \(-0.0614416\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.90624i 0.704868i −0.935837 0.352434i \(-0.885354\pi\)
0.935837 0.352434i \(-0.114646\pi\)
\(18\) 0 0
\(19\) 3.79473 2.14477i 0.870571 0.492043i
\(20\) 1.15484i 0.258230i
\(21\) 0 0
\(22\) 2.90624i 0.619613i
\(23\) 7.14888i 1.49065i 0.666704 + 0.745323i \(0.267705\pi\)
−0.666704 + 0.745323i \(0.732295\pi\)
\(24\) 0 0
\(25\) 3.66635 0.733270
\(26\) 1.38329i 0.271286i
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −4.66635 −0.866519 −0.433260 0.901269i \(-0.642637\pi\)
−0.433260 + 0.901269i \(0.642637\pi\)
\(30\) 0 0
\(31\) 4.06108i 0.729392i 0.931127 + 0.364696i \(0.118827\pi\)
−0.931127 + 0.364696i \(0.881173\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.90624i 0.498417i
\(35\) 1.15484i 0.195203i
\(36\) 0 0
\(37\) 6.55232i 1.07719i −0.842563 0.538597i \(-0.818954\pi\)
0.842563 0.538597i \(-0.181046\pi\)
\(38\) −3.79473 + 2.14477i −0.615586 + 0.347927i
\(39\) 0 0
\(40\) 1.15484i 0.182596i
\(41\) −11.1869 −1.74711 −0.873553 0.486729i \(-0.838190\pi\)
−0.873553 + 0.486729i \(0.838190\pi\)
\(42\) 0 0
\(43\) −2.04373 −0.311666 −0.155833 0.987783i \(-0.549806\pi\)
−0.155833 + 0.987783i \(0.549806\pi\)
\(44\) 2.90624i 0.438133i
\(45\) 0 0
\(46\) 7.14888i 1.05405i
\(47\) 2.76658i 0.403548i −0.979432 0.201774i \(-0.935329\pi\)
0.979432 0.201774i \(-0.0646706\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −3.66635 −0.518500
\(51\) 0 0
\(52\) 1.38329i 0.191828i
\(53\) −7.39997 −1.01646 −0.508232 0.861220i \(-0.669701\pi\)
−0.508232 + 0.861220i \(0.669701\pi\)
\(54\) 0 0
\(55\) 3.35624 0.452556
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 4.66635 0.612722
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −8.29954 −1.06265 −0.531323 0.847169i \(-0.678305\pi\)
−0.531323 + 0.847169i \(0.678305\pi\)
\(62\) 4.06108i 0.515758i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.59748 0.198143
\(66\) 0 0
\(67\) 9.91547i 1.21137i −0.795706 0.605684i \(-0.792900\pi\)
0.795706 0.605684i \(-0.207100\pi\)
\(68\) 2.90624i 0.352434i
\(69\) 0 0
\(70\) 1.15484i 0.138030i
\(71\) −6.06632 −0.719940 −0.359970 0.932964i \(-0.617213\pi\)
−0.359970 + 0.932964i \(0.617213\pi\)
\(72\) 0 0
\(73\) 9.37643 1.09743 0.548714 0.836010i \(-0.315118\pi\)
0.548714 + 0.836010i \(0.315118\pi\)
\(74\) 6.55232i 0.761691i
\(75\) 0 0
\(76\) 3.79473 2.14477i 0.435285 0.246022i
\(77\) 2.90624i 0.331197i
\(78\) 0 0
\(79\) 12.1783i 1.37016i −0.728468 0.685080i \(-0.759767\pi\)
0.728468 0.685080i \(-0.240233\pi\)
\(80\) 1.15484i 0.129115i
\(81\) 0 0
\(82\) 11.1869 1.23539
\(83\) 14.5262i 1.59446i −0.603676 0.797230i \(-0.706298\pi\)
0.603676 0.797230i \(-0.293702\pi\)
\(84\) 0 0
\(85\) 3.35624 0.364036
\(86\) 2.04373 0.220381
\(87\) 0 0
\(88\) 2.90624i 0.309807i
\(89\) 17.2533 1.82884 0.914421 0.404765i \(-0.132647\pi\)
0.914421 + 0.404765i \(0.132647\pi\)
\(90\) 0 0
\(91\) 1.38329i 0.145008i
\(92\) 7.14888i 0.745323i
\(93\) 0 0
\(94\) 2.76658i 0.285351i
\(95\) 2.47686 + 4.38230i 0.254121 + 0.449614i
\(96\) 0 0
\(97\) 3.92142i 0.398160i −0.979983 0.199080i \(-0.936205\pi\)
0.979983 0.199080i \(-0.0637954\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 3.66635 0.366635
\(101\) 1.61175i 0.160375i 0.996780 + 0.0801873i \(0.0255519\pi\)
−0.996780 + 0.0801873i \(0.974448\pi\)
\(102\) 0 0
\(103\) 10.6603i 1.05039i −0.850982 0.525195i \(-0.823992\pi\)
0.850982 0.525195i \(-0.176008\pi\)
\(104\) 1.38329i 0.135643i
\(105\) 0 0
\(106\) 7.39997 0.718749
\(107\) −11.2226 −1.08493 −0.542467 0.840077i \(-0.682510\pi\)
−0.542467 + 0.840077i \(0.682510\pi\)
\(108\) 0 0
\(109\) 3.91282i 0.374780i 0.982286 + 0.187390i \(0.0600029\pi\)
−0.982286 + 0.187390i \(0.939997\pi\)
\(110\) −3.35624 −0.320005
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 11.4202 1.07432 0.537159 0.843481i \(-0.319498\pi\)
0.537159 + 0.843481i \(0.319498\pi\)
\(114\) 0 0
\(115\) −8.25581 −0.769858
\(116\) −4.66635 −0.433260
\(117\) 0 0
\(118\) 0 0
\(119\) 2.90624i 0.266415i
\(120\) 0 0
\(121\) 2.55375 0.232159
\(122\) 8.29954 0.751405
\(123\) 0 0
\(124\) 4.06108i 0.364696i
\(125\) 10.0082i 0.895164i
\(126\) 0 0
\(127\) 12.9145i 1.14597i −0.819564 0.572987i \(-0.805784\pi\)
0.819564 0.572987i \(-0.194216\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −1.59748 −0.140108
\(131\) 11.8101i 1.03186i −0.856632 0.515928i \(-0.827447\pi\)
0.856632 0.515928i \(-0.172553\pi\)
\(132\) 0 0
\(133\) −3.79473 + 2.14477i −0.329045 + 0.185975i
\(134\) 9.91547i 0.856566i
\(135\) 0 0
\(136\) 2.90624i 0.249208i
\(137\) 10.0551i 0.859068i −0.903051 0.429534i \(-0.858678\pi\)
0.903051 0.429534i \(-0.141322\pi\)
\(138\) 0 0
\(139\) −16.8663 −1.43058 −0.715289 0.698829i \(-0.753705\pi\)
−0.715289 + 0.698829i \(0.753705\pi\)
\(140\) 1.15484i 0.0976017i
\(141\) 0 0
\(142\) 6.06632 0.509074
\(143\) −4.02018 −0.336185
\(144\) 0 0
\(145\) 5.38888i 0.447522i
\(146\) −9.37643 −0.775998
\(147\) 0 0
\(148\) 6.55232i 0.538597i
\(149\) 14.2978i 1.17132i −0.810557 0.585659i \(-0.800836\pi\)
0.810557 0.585659i \(-0.199164\pi\)
\(150\) 0 0
\(151\) 6.64508i 0.540769i 0.962752 + 0.270385i \(0.0871508\pi\)
−0.962752 + 0.270385i \(0.912849\pi\)
\(152\) −3.79473 + 2.14477i −0.307793 + 0.173964i
\(153\) 0 0
\(154\) 2.90624i 0.234192i
\(155\) −4.68989 −0.376701
\(156\) 0 0
\(157\) 16.8201 1.34239 0.671196 0.741280i \(-0.265781\pi\)
0.671196 + 0.741280i \(0.265781\pi\)
\(158\) 12.1783i 0.968850i
\(159\) 0 0
\(160\) 1.15484i 0.0912980i
\(161\) 7.14888i 0.563411i
\(162\) 0 0
\(163\) 10.9100 0.854536 0.427268 0.904125i \(-0.359476\pi\)
0.427268 + 0.904125i \(0.359476\pi\)
\(164\) −11.1869 −0.873553
\(165\) 0 0
\(166\) 14.5262i 1.12745i
\(167\) 5.31251 0.411095 0.205547 0.978647i \(-0.434103\pi\)
0.205547 + 0.978647i \(0.434103\pi\)
\(168\) 0 0
\(169\) 11.0865 0.852808
\(170\) −3.35624 −0.257412
\(171\) 0 0
\(172\) −2.04373 −0.155833
\(173\) −11.2226 −0.853242 −0.426621 0.904430i \(-0.640296\pi\)
−0.426621 + 0.904430i \(0.640296\pi\)
\(174\) 0 0
\(175\) −3.66635 −0.277150
\(176\) 2.90624i 0.219066i
\(177\) 0 0
\(178\) −17.2533 −1.29319
\(179\) 15.3990 1.15098 0.575488 0.817810i \(-0.304812\pi\)
0.575488 + 0.817810i \(0.304812\pi\)
\(180\) 0 0
\(181\) 17.6276i 1.31025i 0.755520 + 0.655125i \(0.227384\pi\)
−0.755520 + 0.655125i \(0.772616\pi\)
\(182\) 1.38329i 0.102536i
\(183\) 0 0
\(184\) 7.14888i 0.527023i
\(185\) 7.56687 0.556327
\(186\) 0 0
\(187\) −8.44625 −0.617651
\(188\) 2.76658i 0.201774i
\(189\) 0 0
\(190\) −2.47686 4.38230i −0.179690 0.317925i
\(191\) 18.8244i 1.36208i −0.732245 0.681041i \(-0.761527\pi\)
0.732245 0.681041i \(-0.238473\pi\)
\(192\) 0 0
\(193\) 9.27201i 0.667414i −0.942677 0.333707i \(-0.891700\pi\)
0.942677 0.333707i \(-0.108300\pi\)
\(194\) 3.92142i 0.281542i
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 2.76658i 0.197111i 0.995132 + 0.0985555i \(0.0314222\pi\)
−0.995132 + 0.0985555i \(0.968578\pi\)
\(198\) 0 0
\(199\) −14.9302 −1.05837 −0.529186 0.848506i \(-0.677503\pi\)
−0.529186 + 0.848506i \(0.677503\pi\)
\(200\) −3.66635 −0.259250
\(201\) 0 0
\(202\) 1.61175i 0.113402i
\(203\) 4.66635 0.327513
\(204\) 0 0
\(205\) 12.9191i 0.902310i
\(206\) 10.6603i 0.742738i
\(207\) 0 0
\(208\) 1.38329i 0.0959141i
\(209\) −6.23322 11.0284i −0.431161 0.762851i
\(210\) 0 0
\(211\) 2.85935i 0.196846i 0.995145 + 0.0984228i \(0.0313798\pi\)
−0.995145 + 0.0984228i \(0.968620\pi\)
\(212\) −7.39997 −0.508232
\(213\) 0 0
\(214\) 11.2226 0.767164
\(215\) 2.36018i 0.160963i
\(216\) 0 0
\(217\) 4.06108i 0.275684i
\(218\) 3.91282i 0.265010i
\(219\) 0 0
\(220\) 3.35624 0.226278
\(221\) −4.02018 −0.270427
\(222\) 0 0
\(223\) 16.9297i 1.13370i −0.823822 0.566848i \(-0.808163\pi\)
0.823822 0.566848i \(-0.191837\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −11.4202 −0.759657
\(227\) 12.6889 0.842194 0.421097 0.907016i \(-0.361645\pi\)
0.421097 + 0.907016i \(0.361645\pi\)
\(228\) 0 0
\(229\) −5.55375 −0.367002 −0.183501 0.983020i \(-0.558743\pi\)
−0.183501 + 0.983020i \(0.558743\pi\)
\(230\) 8.25581 0.544372
\(231\) 0 0
\(232\) 4.66635 0.306361
\(233\) 13.6084i 0.891518i −0.895153 0.445759i \(-0.852934\pi\)
0.895153 0.445759i \(-0.147066\pi\)
\(234\) 0 0
\(235\) 3.19496 0.208416
\(236\) 0 0
\(237\) 0 0
\(238\) 2.90624i 0.188384i
\(239\) 21.7765i 1.40860i 0.709901 + 0.704301i \(0.248740\pi\)
−0.709901 + 0.704301i \(0.751260\pi\)
\(240\) 0 0
\(241\) 23.9379i 1.54197i 0.636850 + 0.770987i \(0.280237\pi\)
−0.636850 + 0.770987i \(0.719763\pi\)
\(242\) −2.55375 −0.164161
\(243\) 0 0
\(244\) −8.29954 −0.531323
\(245\) 1.15484i 0.0737799i
\(246\) 0 0
\(247\) −2.96684 5.24922i −0.188776 0.334000i
\(248\) 4.06108i 0.257879i
\(249\) 0 0
\(250\) 10.0082i 0.632976i
\(251\) 10.6936i 0.674974i −0.941330 0.337487i \(-0.890423\pi\)
0.941330 0.337487i \(-0.109577\pi\)
\(252\) 0 0
\(253\) 20.7764 1.30620
\(254\) 12.9145i 0.810326i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −13.3407 −0.832171 −0.416086 0.909325i \(-0.636598\pi\)
−0.416086 + 0.909325i \(0.636598\pi\)
\(258\) 0 0
\(259\) 6.55232i 0.407141i
\(260\) 1.59748 0.0990714
\(261\) 0 0
\(262\) 11.8101i 0.729633i
\(263\) 30.3555i 1.87180i −0.352262 0.935901i \(-0.614587\pi\)
0.352262 0.935901i \(-0.385413\pi\)
\(264\) 0 0
\(265\) 8.54577i 0.524963i
\(266\) 3.79473 2.14477i 0.232670 0.131504i
\(267\) 0 0
\(268\) 9.91547i 0.605684i
\(269\) −6.84367 −0.417266 −0.208633 0.977994i \(-0.566901\pi\)
−0.208633 + 0.977994i \(0.566901\pi\)
\(270\) 0 0
\(271\) −27.4865 −1.66968 −0.834842 0.550489i \(-0.814441\pi\)
−0.834842 + 0.550489i \(0.814441\pi\)
\(272\) 2.90624i 0.176217i
\(273\) 0 0
\(274\) 10.0551i 0.607452i
\(275\) 10.6553i 0.642539i
\(276\) 0 0
\(277\) −25.6191 −1.53930 −0.769652 0.638464i \(-0.779570\pi\)
−0.769652 + 0.638464i \(0.779570\pi\)
\(278\) 16.8663 1.01157
\(279\) 0 0
\(280\) 1.15484i 0.0690148i
\(281\) 8.79994 0.524961 0.262480 0.964937i \(-0.415460\pi\)
0.262480 + 0.964937i \(0.415460\pi\)
\(282\) 0 0
\(283\) −6.47686 −0.385009 −0.192505 0.981296i \(-0.561661\pi\)
−0.192505 + 0.981296i \(0.561661\pi\)
\(284\) −6.06632 −0.359970
\(285\) 0 0
\(286\) 4.02018 0.237718
\(287\) 11.1869 0.660344
\(288\) 0 0
\(289\) 8.55375 0.503162
\(290\) 5.38888i 0.316446i
\(291\) 0 0
\(292\) 9.37643 0.548714
\(293\) 4.64280 0.271235 0.135618 0.990761i \(-0.456698\pi\)
0.135618 + 0.990761i \(0.456698\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.55232i 0.380846i
\(297\) 0 0
\(298\) 14.2978i 0.828247i
\(299\) 9.88900 0.571895
\(300\) 0 0
\(301\) 2.04373 0.117799
\(302\) 6.64508i 0.382382i
\(303\) 0 0
\(304\) 3.79473 2.14477i 0.217643 0.123011i
\(305\) 9.58462i 0.548814i
\(306\) 0 0
\(307\) 12.3684i 0.705902i −0.935642 0.352951i \(-0.885178\pi\)
0.935642 0.352951i \(-0.114822\pi\)
\(308\) 2.90624i 0.165599i
\(309\) 0 0
\(310\) 4.68989 0.266368
\(311\) 4.71314i 0.267258i 0.991031 + 0.133629i \(0.0426630\pi\)
−0.991031 + 0.133629i \(0.957337\pi\)
\(312\) 0 0
\(313\) −9.17892 −0.518823 −0.259412 0.965767i \(-0.583529\pi\)
−0.259412 + 0.965767i \(0.583529\pi\)
\(314\) −16.8201 −0.949215
\(315\) 0 0
\(316\) 12.1783i 0.685080i
\(317\) −25.7117 −1.44411 −0.722056 0.691835i \(-0.756803\pi\)
−0.722056 + 0.691835i \(0.756803\pi\)
\(318\) 0 0
\(319\) 13.5615i 0.759301i
\(320\) 1.15484i 0.0645574i
\(321\) 0 0
\(322\) 7.14888i 0.398392i
\(323\) −6.23322 11.0284i −0.346825 0.613637i
\(324\) 0 0
\(325\) 5.07163i 0.281323i
\(326\) −10.9100 −0.604249
\(327\) 0 0
\(328\) 11.1869 0.617695
\(329\) 2.76658i 0.152527i
\(330\) 0 0
\(331\) 20.3473i 1.11839i −0.829036 0.559195i \(-0.811110\pi\)
0.829036 0.559195i \(-0.188890\pi\)
\(332\) 14.5262i 0.797230i
\(333\) 0 0
\(334\) −5.31251 −0.290688
\(335\) 11.4508 0.625622
\(336\) 0 0
\(337\) 34.8316i 1.89740i 0.316178 + 0.948700i \(0.397600\pi\)
−0.316178 + 0.948700i \(0.602400\pi\)
\(338\) −11.0865 −0.603026
\(339\) 0 0
\(340\) 3.35624 0.182018
\(341\) 11.8025 0.639141
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 2.04373 0.110191
\(345\) 0 0
\(346\) 11.2226 0.603333
\(347\) 12.9650i 0.695996i −0.937495 0.347998i \(-0.886862\pi\)
0.937495 0.347998i \(-0.113138\pi\)
\(348\) 0 0
\(349\) −9.12062 −0.488216 −0.244108 0.969748i \(-0.578495\pi\)
−0.244108 + 0.969748i \(0.578495\pi\)
\(350\) 3.66635 0.195975
\(351\) 0 0
\(352\) 2.90624i 0.154903i
\(353\) 22.1865i 1.18087i 0.807086 + 0.590434i \(0.201043\pi\)
−0.807086 + 0.590434i \(0.798957\pi\)
\(354\) 0 0
\(355\) 7.00562i 0.371820i
\(356\) 17.2533 0.914421
\(357\) 0 0
\(358\) −15.3990 −0.813863
\(359\) 5.29611i 0.279518i −0.990186 0.139759i \(-0.955367\pi\)
0.990186 0.139759i \(-0.0446328\pi\)
\(360\) 0 0
\(361\) 9.79994 16.2776i 0.515786 0.856717i
\(362\) 17.6276i 0.926487i
\(363\) 0 0
\(364\) 1.38329i 0.0725042i
\(365\) 10.8283i 0.566777i
\(366\) 0 0
\(367\) −24.3527 −1.27120 −0.635601 0.772018i \(-0.719248\pi\)
−0.635601 + 0.772018i \(0.719248\pi\)
\(368\) 7.14888i 0.372661i
\(369\) 0 0
\(370\) −7.56687 −0.393383
\(371\) 7.39997 0.384187
\(372\) 0 0
\(373\) 22.4235i 1.16105i −0.814244 0.580523i \(-0.802848\pi\)
0.814244 0.580523i \(-0.197152\pi\)
\(374\) 8.44625 0.436745
\(375\) 0 0
\(376\) 2.76658i 0.142676i
\(377\) 6.45492i 0.332445i
\(378\) 0 0
\(379\) 9.49186i 0.487564i 0.969830 + 0.243782i \(0.0783882\pi\)
−0.969830 + 0.243782i \(0.921612\pi\)
\(380\) 2.47686 + 4.38230i 0.127060 + 0.224807i
\(381\) 0 0
\(382\) 18.8244i 0.963138i
\(383\) 24.4086 1.24722 0.623611 0.781735i \(-0.285665\pi\)
0.623611 + 0.781735i \(0.285665\pi\)
\(384\) 0 0
\(385\) −3.35624 −0.171050
\(386\) 9.27201i 0.471933i
\(387\) 0 0
\(388\) 3.92142i 0.199080i
\(389\) 33.7656i 1.71198i 0.516990 + 0.855992i \(0.327053\pi\)
−0.516990 + 0.855992i \(0.672947\pi\)
\(390\) 0 0
\(391\) 20.7764 1.05071
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 2.76658i 0.139379i
\(395\) 14.0639 0.707632
\(396\) 0 0
\(397\) −5.46629 −0.274345 −0.137173 0.990547i \(-0.543802\pi\)
−0.137173 + 0.990547i \(0.543802\pi\)
\(398\) 14.9302 0.748382
\(399\) 0 0
\(400\) 3.66635 0.183317
\(401\) 36.2417 1.80983 0.904913 0.425597i \(-0.139936\pi\)
0.904913 + 0.425597i \(0.139936\pi\)
\(402\) 0 0
\(403\) 5.61766 0.279836
\(404\) 1.61175i 0.0801873i
\(405\) 0 0
\(406\) −4.66635 −0.231587
\(407\) −19.0426 −0.943908
\(408\) 0 0
\(409\) 17.8128i 0.880785i 0.897805 + 0.440393i \(0.145161\pi\)
−0.897805 + 0.440393i \(0.854839\pi\)
\(410\) 12.9191i 0.638029i
\(411\) 0 0
\(412\) 10.6603i 0.525195i
\(413\) 0 0
\(414\) 0 0
\(415\) 16.7754 0.823474
\(416\) 1.38329i 0.0678215i
\(417\) 0 0
\(418\) 6.23322 + 11.0284i 0.304877 + 0.539417i
\(419\) 4.75402i 0.232249i −0.993235 0.116124i \(-0.962953\pi\)
0.993235 0.116124i \(-0.0370472\pi\)
\(420\) 0 0
\(421\) 25.7821i 1.25654i −0.777995 0.628270i \(-0.783763\pi\)
0.777995 0.628270i \(-0.216237\pi\)
\(422\) 2.85935i 0.139191i
\(423\) 0 0
\(424\) 7.39997 0.359374
\(425\) 10.6553i 0.516858i
\(426\) 0 0
\(427\) 8.29954 0.401643
\(428\) −11.2226 −0.542467
\(429\) 0 0
\(430\) 2.36018i 0.113818i
\(431\) −14.4839 −0.697666 −0.348833 0.937185i \(-0.613422\pi\)
−0.348833 + 0.937185i \(0.613422\pi\)
\(432\) 0 0
\(433\) 5.77419i 0.277490i 0.990328 + 0.138745i \(0.0443068\pi\)
−0.990328 + 0.138745i \(0.955693\pi\)
\(434\) 4.06108i 0.194938i
\(435\) 0 0
\(436\) 3.91282i 0.187390i
\(437\) 15.3327 + 27.1281i 0.733462 + 1.29771i
\(438\) 0 0
\(439\) 27.6814i 1.32116i 0.750756 + 0.660580i \(0.229689\pi\)
−0.750756 + 0.660580i \(0.770311\pi\)
\(440\) −3.35624 −0.160003
\(441\) 0 0
\(442\) 4.02018 0.191221
\(443\) 10.2922i 0.488996i −0.969650 0.244498i \(-0.921377\pi\)
0.969650 0.244498i \(-0.0786232\pi\)
\(444\) 0 0
\(445\) 19.9247i 0.944523i
\(446\) 16.9297i 0.801644i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −29.6191 −1.39781 −0.698906 0.715213i \(-0.746330\pi\)
−0.698906 + 0.715213i \(0.746330\pi\)
\(450\) 0 0
\(451\) 32.5120i 1.53093i
\(452\) 11.4202 0.537159
\(453\) 0 0
\(454\) −12.6889 −0.595521
\(455\) −1.59748 −0.0748910
\(456\) 0 0
\(457\) −17.8664 −0.835755 −0.417878 0.908503i \(-0.637226\pi\)
−0.417878 + 0.908503i \(0.637226\pi\)
\(458\) 5.55375 0.259510
\(459\) 0 0
\(460\) −8.25581 −0.384929
\(461\) 14.3533i 0.668498i 0.942485 + 0.334249i \(0.108483\pi\)
−0.942485 + 0.334249i \(0.891517\pi\)
\(462\) 0 0
\(463\) −21.6840 −1.00774 −0.503870 0.863779i \(-0.668091\pi\)
−0.503870 + 0.863779i \(0.668091\pi\)
\(464\) −4.66635 −0.216630
\(465\) 0 0
\(466\) 13.6084i 0.630399i
\(467\) 10.1096i 0.467816i −0.972259 0.233908i \(-0.924848\pi\)
0.972259 0.233908i \(-0.0751515\pi\)
\(468\) 0 0
\(469\) 9.91547i 0.457854i
\(470\) −3.19496 −0.147372
\(471\) 0 0
\(472\) 0 0
\(473\) 5.93958i 0.273102i
\(474\) 0 0
\(475\) 13.9128 7.86346i 0.638363 0.360801i
\(476\) 2.90624i 0.133207i
\(477\) 0 0
\(478\) 21.7765i 0.996033i
\(479\) 17.0644i 0.779690i 0.920880 + 0.389845i \(0.127471\pi\)
−0.920880 + 0.389845i \(0.872529\pi\)
\(480\) 0 0
\(481\) −9.06377 −0.413272
\(482\) 23.9379i 1.09034i
\(483\) 0 0
\(484\) 2.55375 0.116080
\(485\) 4.52861 0.205634
\(486\) 0 0
\(487\) 19.5642i 0.886538i 0.896389 + 0.443269i \(0.146181\pi\)
−0.896389 + 0.443269i \(0.853819\pi\)
\(488\) 8.29954 0.375702
\(489\) 0 0
\(490\) 1.15484i 0.0521703i
\(491\) 6.86596i 0.309856i 0.987926 + 0.154928i \(0.0495146\pi\)
−0.987926 + 0.154928i \(0.950485\pi\)
\(492\) 0 0
\(493\) 13.5615i 0.610781i
\(494\) 2.96684 + 5.24922i 0.133484 + 0.236174i
\(495\) 0 0
\(496\) 4.06108i 0.182348i
\(497\) 6.06632 0.272112
\(498\) 0 0
\(499\) −10.7529 −0.481364 −0.240682 0.970604i \(-0.577371\pi\)
−0.240682 + 0.970604i \(0.577371\pi\)
\(500\) 10.0082i 0.447582i
\(501\) 0 0
\(502\) 10.6936i 0.477278i
\(503\) 9.00268i 0.401410i −0.979652 0.200705i \(-0.935677\pi\)
0.979652 0.200705i \(-0.0643232\pi\)
\(504\) 0 0
\(505\) −1.86131 −0.0828270
\(506\) −20.7764 −0.923623
\(507\) 0 0
\(508\) 12.9145i 0.572987i
\(509\) 31.1126 1.37904 0.689521 0.724266i \(-0.257821\pi\)
0.689521 + 0.724266i \(0.257821\pi\)
\(510\) 0 0
\(511\) −9.37643 −0.414789
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 13.3407 0.588434
\(515\) 12.3109 0.542484
\(516\) 0 0
\(517\) −8.04037 −0.353615
\(518\) 6.55232i 0.287892i
\(519\) 0 0
\(520\) −1.59748 −0.0700541
\(521\) −5.82094 −0.255020 −0.127510 0.991837i \(-0.540698\pi\)
−0.127510 + 0.991837i \(0.540698\pi\)
\(522\) 0 0
\(523\) 35.1010i 1.53486i 0.641134 + 0.767429i \(0.278464\pi\)
−0.641134 + 0.767429i \(0.721536\pi\)
\(524\) 11.8101i 0.515928i
\(525\) 0 0
\(526\) 30.3555i 1.32356i
\(527\) 11.8025 0.514125
\(528\) 0 0
\(529\) −28.1065 −1.22202
\(530\) 8.54577i 0.371205i
\(531\) 0 0
\(532\) −3.79473 + 2.14477i −0.164522 + 0.0929875i
\(533\) 15.4748i 0.670288i
\(534\) 0 0
\(535\) 12.9603i 0.560325i
\(536\) 9.91547i 0.428283i
\(537\) 0 0
\(538\) 6.84367 0.295052
\(539\) 2.90624i 0.125181i
\(540\) 0 0
\(541\) −3.04359 −0.130854 −0.0654270 0.997857i \(-0.520841\pi\)
−0.0654270 + 0.997857i \(0.520841\pi\)
\(542\) 27.4865 1.18065
\(543\) 0 0
\(544\) 2.90624i 0.124604i
\(545\) −4.51868 −0.193559
\(546\) 0 0
\(547\) 4.47609i 0.191384i −0.995411 0.0956919i \(-0.969494\pi\)
0.995411 0.0956919i \(-0.0305064\pi\)
\(548\) 10.0551i 0.429534i
\(549\) 0 0
\(550\) 10.6553i 0.454343i
\(551\) −17.7075 + 10.0082i −0.754366 + 0.426365i
\(552\) 0 0
\(553\) 12.1783i 0.517872i
\(554\) 25.6191 1.08845
\(555\) 0 0
\(556\) −16.8663 −0.715289
\(557\) 0.185529i 0.00786110i 0.999992 + 0.00393055i \(0.00125114\pi\)
−0.999992 + 0.00393055i \(0.998749\pi\)
\(558\) 0 0
\(559\) 2.82707i 0.119573i
\(560\) 1.15484i 0.0488008i
\(561\) 0 0
\(562\) −8.79994 −0.371203
\(563\) −2.62021 −0.110429 −0.0552144 0.998475i \(-0.517584\pi\)
−0.0552144 + 0.998475i \(0.517584\pi\)
\(564\) 0 0
\(565\) 13.1884i 0.554842i
\(566\) 6.47686 0.272243
\(567\) 0 0
\(568\) 6.06632 0.254537
\(569\) −25.1974 −1.05633 −0.528164 0.849142i \(-0.677119\pi\)
−0.528164 + 0.849142i \(0.677119\pi\)
\(570\) 0 0
\(571\) −27.2890 −1.14201 −0.571004 0.820947i \(-0.693446\pi\)
−0.571004 + 0.820947i \(0.693446\pi\)
\(572\) −4.02018 −0.168092
\(573\) 0 0
\(574\) −11.1869 −0.466934
\(575\) 26.2103i 1.09304i
\(576\) 0 0
\(577\) 8.11515 0.337838 0.168919 0.985630i \(-0.445972\pi\)
0.168919 + 0.985630i \(0.445972\pi\)
\(578\) −8.55375 −0.355789
\(579\) 0 0
\(580\) 5.38888i 0.223761i
\(581\) 14.5262i 0.602649i
\(582\) 0 0
\(583\) 21.5061i 0.890692i
\(584\) −9.37643 −0.387999
\(585\) 0 0
\(586\) −4.64280 −0.191792
\(587\) 5.49024i 0.226607i −0.993560 0.113303i \(-0.963857\pi\)
0.993560 0.113303i \(-0.0361432\pi\)
\(588\) 0 0
\(589\) 8.71008 + 15.4107i 0.358892 + 0.634987i
\(590\) 0 0
\(591\) 0 0
\(592\) 6.55232i 0.269299i
\(593\) 43.4133i 1.78277i 0.453247 + 0.891385i \(0.350266\pi\)
−0.453247 + 0.891385i \(0.649734\pi\)
\(594\) 0 0
\(595\) −3.35624 −0.137592
\(596\) 14.2978i 0.585659i
\(597\) 0 0
\(598\) −9.88900 −0.404391
\(599\) 36.7317 1.50082 0.750409 0.660974i \(-0.229857\pi\)
0.750409 + 0.660974i \(0.229857\pi\)
\(600\) 0 0
\(601\) 36.2991i 1.48067i −0.672238 0.740335i \(-0.734667\pi\)
0.672238 0.740335i \(-0.265333\pi\)
\(602\) −2.04373 −0.0832962
\(603\) 0 0
\(604\) 6.64508i 0.270385i
\(605\) 2.94917i 0.119901i
\(606\) 0 0
\(607\) 28.4176i 1.15343i 0.816944 + 0.576717i \(0.195666\pi\)
−0.816944 + 0.576717i \(0.804334\pi\)
\(608\) −3.79473 + 2.14477i −0.153897 + 0.0869818i
\(609\) 0 0
\(610\) 9.58462i 0.388070i
\(611\) −3.82699 −0.154824
\(612\) 0 0
\(613\) −8.46133 −0.341750 −0.170875 0.985293i \(-0.554659\pi\)
−0.170875 + 0.985293i \(0.554659\pi\)
\(614\) 12.3684i 0.499148i
\(615\) 0 0
\(616\) 2.90624i 0.117096i
\(617\) 21.6873i 0.873098i 0.899680 + 0.436549i \(0.143800\pi\)
−0.899680 + 0.436549i \(0.856200\pi\)
\(618\) 0 0
\(619\) 33.7075 1.35482 0.677410 0.735606i \(-0.263102\pi\)
0.677410 + 0.735606i \(0.263102\pi\)
\(620\) −4.68989 −0.188351
\(621\) 0 0
\(622\) 4.71314i 0.188980i
\(623\) −17.2533 −0.691237
\(624\) 0 0
\(625\) 6.77385 0.270954
\(626\) 9.17892 0.366863
\(627\) 0 0
\(628\) 16.8201 0.671196
\(629\) −19.0426 −0.759279
\(630\) 0 0
\(631\) 35.7780 1.42430 0.712150 0.702028i \(-0.247722\pi\)
0.712150 + 0.702028i \(0.247722\pi\)
\(632\) 12.1783i 0.484425i
\(633\) 0 0
\(634\) 25.7117 1.02114
\(635\) 14.9141 0.591849
\(636\) 0 0
\(637\) 1.38329i 0.0548080i
\(638\) 13.5615i 0.536907i
\(639\) 0 0
\(640\) 1.15484i 0.0456490i
\(641\) 43.1267 1.70340 0.851702 0.524027i \(-0.175571\pi\)
0.851702 + 0.524027i \(0.175571\pi\)
\(642\) 0 0
\(643\) 8.24028 0.324965 0.162482 0.986711i \(-0.448050\pi\)
0.162482 + 0.986711i \(0.448050\pi\)
\(644\) 7.14888i 0.281705i
\(645\) 0 0
\(646\) 6.23322 + 11.0284i 0.245243 + 0.433907i
\(647\) 8.02837i 0.315628i 0.987469 + 0.157814i \(0.0504446\pi\)
−0.987469 + 0.157814i \(0.949555\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 5.07163i 0.198926i
\(651\) 0 0
\(652\) 10.9100 0.427268
\(653\) 11.9881i 0.469130i −0.972100 0.234565i \(-0.924633\pi\)
0.972100 0.234565i \(-0.0753666\pi\)
\(654\) 0 0
\(655\) 13.6388 0.532912
\(656\) −11.1869 −0.436777
\(657\) 0 0
\(658\) 2.76658i 0.107853i
\(659\) 14.6688 0.571414 0.285707 0.958317i \(-0.407772\pi\)
0.285707 + 0.958317i \(0.407772\pi\)
\(660\) 0 0
\(661\) 41.6876i 1.62146i 0.585420 + 0.810730i \(0.300929\pi\)
−0.585420 + 0.810730i \(0.699071\pi\)
\(662\) 20.3473i 0.790821i
\(663\) 0 0
\(664\) 14.5262i 0.563727i
\(665\) −2.47686 4.38230i −0.0960485 0.169938i
\(666\) 0 0
\(667\) 33.3592i 1.29167i
\(668\) 5.31251 0.205547
\(669\) 0 0
\(670\) −11.4508 −0.442382
\(671\) 24.1205i 0.931160i
\(672\) 0 0
\(673\) 20.0337i 0.772241i −0.922448 0.386121i \(-0.873815\pi\)
0.922448 0.386121i \(-0.126185\pi\)
\(674\) 34.8316i 1.34166i
\(675\) 0 0
\(676\) 11.0865 0.426404
\(677\) −0.202607 −0.00778682 −0.00389341 0.999992i \(-0.501239\pi\)
−0.00389341 + 0.999992i \(0.501239\pi\)
\(678\) 0 0
\(679\) 3.92142i 0.150490i
\(680\) −3.35624 −0.128706
\(681\) 0 0
\(682\) −11.8025 −0.451941
\(683\) 36.3965 1.39267 0.696336 0.717716i \(-0.254812\pi\)
0.696336 + 0.717716i \(0.254812\pi\)
\(684\) 0 0
\(685\) 11.6120 0.443674
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −2.04373 −0.0779165
\(689\) 10.2363i 0.389973i
\(690\) 0 0
\(691\) −41.8443 −1.59183 −0.795916 0.605407i \(-0.793010\pi\)
−0.795916 + 0.605407i \(0.793010\pi\)
\(692\) −11.2226 −0.426621
\(693\) 0 0
\(694\) 12.9650i 0.492144i
\(695\) 19.4778i 0.738835i
\(696\) 0 0
\(697\) 32.5120i 1.23148i
\(698\) 9.12062 0.345221
\(699\) 0 0
\(700\) −3.66635 −0.138575
\(701\) 37.6920i 1.42361i −0.702378 0.711804i \(-0.747879\pi\)
0.702378 0.711804i \(-0.252121\pi\)
\(702\) 0 0
\(703\) −14.0532 24.8643i −0.530026 0.937774i
\(704\) 2.90624i 0.109533i
\(705\) 0 0
\(706\) 22.1865i 0.834999i
\(707\) 1.61175i 0.0606159i
\(708\) 0 0
\(709\) 35.5081 1.33353 0.666767 0.745266i \(-0.267677\pi\)
0.666767 + 0.745266i \(0.267677\pi\)
\(710\) 7.00562i 0.262916i
\(711\) 0 0
\(712\) −17.2533 −0.646593
\(713\) −29.0322 −1.08726
\(714\) 0 0
\(715\) 4.64266i 0.173626i
\(716\) 15.3990 0.575488
\(717\) 0 0
\(718\) 5.29611i 0.197649i
\(719\) 28.6288i 1.06768i −0.845587 0.533838i \(-0.820749\pi\)
0.845587 0.533838i \(-0.179251\pi\)
\(720\) 0 0
\(721\) 10.6603i 0.397010i
\(722\) −9.79994 + 16.2776i −0.364716 + 0.605791i
\(723\) 0 0
\(724\) 17.6276i 0.655125i
\(725\) −17.1085 −0.635392
\(726\) 0 0
\(727\) −17.7117 −0.656890 −0.328445 0.944523i \(-0.606524\pi\)
−0.328445 + 0.944523i \(0.606524\pi\)
\(728\) 1.38329i 0.0512682i
\(729\) 0 0
\(730\) 10.8283i 0.400772i
\(731\) 5.93958i 0.219683i
\(732\) 0 0
\(733\) 22.9197 0.846560 0.423280 0.905999i \(-0.360879\pi\)
0.423280 + 0.905999i \(0.360879\pi\)
\(734\) 24.3527 0.898876
\(735\) 0 0
\(736\) 7.14888i 0.263511i
\(737\) −28.8168 −1.06148
\(738\) 0 0
\(739\) −49.0215 −1.80328 −0.901642 0.432482i \(-0.857638\pi\)
−0.901642 + 0.432482i \(0.857638\pi\)
\(740\) 7.56687 0.278164
\(741\) 0 0
\(742\) −7.39997 −0.271661
\(743\) −15.1301 −0.555069 −0.277535 0.960716i \(-0.589517\pi\)
−0.277535 + 0.960716i \(0.589517\pi\)
\(744\) 0 0
\(745\) 16.5116 0.604939
\(746\) 22.4235i 0.820984i
\(747\) 0 0
\(748\) −8.44625 −0.308826
\(749\) 11.2226 0.410067
\(750\) 0 0
\(751\) 42.9079i 1.56573i −0.622190 0.782866i \(-0.713757\pi\)
0.622190 0.782866i \(-0.286243\pi\)
\(752\) 2.76658i 0.100887i
\(753\) 0 0
\(754\) 6.45492i 0.235074i
\(755\) −7.67400 −0.279285
\(756\) 0 0
\(757\) 15.4916 0.563051 0.281525 0.959554i \(-0.409160\pi\)
0.281525 + 0.959554i \(0.409160\pi\)
\(758\) 9.49186i 0.344760i
\(759\) 0 0
\(760\) −2.47686 4.38230i −0.0898452 0.158963i
\(761\) 1.98244i 0.0718633i −0.999354 0.0359317i \(-0.988560\pi\)
0.999354 0.0359317i \(-0.0114399\pi\)
\(762\) 0 0
\(763\) 3.91282i 0.141654i
\(764\) 18.8244i 0.681041i
\(765\) 0 0
\(766\) −24.4086 −0.881920
\(767\) 0 0
\(768\) 0 0
\(769\) 35.8443 1.29258 0.646289 0.763092i \(-0.276320\pi\)
0.646289 + 0.763092i \(0.276320\pi\)
\(770\) 3.35624 0.120951
\(771\) 0 0
\(772\) 9.27201i 0.333707i
\(773\) −23.0864 −0.830359 −0.415179 0.909740i \(-0.636281\pi\)
−0.415179 + 0.909740i \(0.636281\pi\)
\(774\) 0 0
\(775\) 14.8893i 0.534841i
\(776\) 3.92142i 0.140771i
\(777\) 0 0
\(778\) 33.7656i 1.21055i
\(779\) −42.4514 + 23.9934i −1.52098 + 0.859652i
\(780\) 0 0
\(781\) 17.6302i 0.630858i
\(782\) −20.7764 −0.742962
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 19.4245i 0.693291i
\(786\) 0 0
\(787\) 5.57646i 0.198779i 0.995049 + 0.0993896i \(0.0316890\pi\)
−0.995049 + 0.0993896i \(0.968311\pi\)
\(788\) 2.76658i 0.0985555i
\(789\) 0 0
\(790\) −14.0639 −0.500372
\(791\) −11.4202 −0.406054
\(792\) 0 0
\(793\) 11.4807i 0.407691i
\(794\) 5.46629 0.193991
\(795\) 0 0
\(796\) −14.9302 −0.529186
\(797\) 26.0404 0.922397 0.461199 0.887297i \(-0.347420\pi\)