Properties

Label 855.2.c.d.514.5
Level $855$
Weight $2$
Character 855.514
Analytic conductor $6.827$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.16516096.1
Defining polynomial: \(x^{6} + 9 x^{4} + 13 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 514.5
Root \(2.68667i\) of defining polynomial
Character \(\chi\) \(=\) 855.514
Dual form 855.2.c.d.514.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.82254i q^{2} -1.32164 q^{4} +(-1.94827 - 1.09737i) q^{5} -1.45033i q^{7} +1.23634i q^{8} +O(q^{10})\) \(q+1.82254i q^{2} -1.32164 q^{4} +(-1.94827 - 1.09737i) q^{5} -1.45033i q^{7} +1.23634i q^{8} +(2.00000 - 3.55080i) q^{10} +3.89655 q^{11} +3.05888i q^{13} +2.64327 q^{14} -4.89655 q^{16} +3.92301i q^{17} +1.00000 q^{19} +(2.57491 + 1.45033i) q^{20} +7.10160i q^{22} +5.37334i q^{23} +(2.59155 + 4.27596i) q^{25} -5.57491 q^{26} +1.91681i q^{28} +6.00000 q^{29} -8.43637 q^{31} -6.45146i q^{32} -7.14982 q^{34} +(-1.59155 + 2.82564i) q^{35} +5.95953i q^{37} +1.82254i q^{38} +(1.35673 - 2.40873i) q^{40} -10.4364 q^{41} -1.45033i q^{43} -5.14982 q^{44} -9.79310 q^{46} +4.90686i q^{47} +4.89655 q^{49} +(-7.79310 + 4.72319i) q^{50} -4.04272i q^{52} +4.23127i q^{53} +(-7.59155 - 4.27596i) q^{55} +1.79310 q^{56} +10.9352i q^{58} +3.35673 q^{59} +10.3329 q^{61} -15.3756i q^{62} +1.96491 q^{64} +(3.35673 - 5.95953i) q^{65} +9.84404i q^{67} -5.18479i q^{68} +(-5.14982 - 2.90066i) q^{70} -8.64327 q^{71} -2.43418i q^{73} -10.8615 q^{74} -1.32164 q^{76} -5.65127i q^{77} +12.4364 q^{79} +(9.53982 + 5.37334i) q^{80} -19.0207i q^{82} -12.6635i q^{83} +(4.30500 - 7.64310i) q^{85} +2.64327 q^{86} +4.81746i q^{88} +12.3662 q^{89} +4.43637 q^{91} -7.10160i q^{92} -8.94292 q^{94} +(-1.94827 - 1.09737i) q^{95} -3.05888i q^{97} +8.92414i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 8 q^{4} + q^{5} + O(q^{10}) \) \( 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.82254i 1.28873i 0.764719 + 0.644364i \(0.222878\pi\)
−0.764719 + 0.644364i \(0.777122\pi\)
\(3\) 0 0
\(4\) −1.32164 −0.660819
\(5\) −1.94827 1.09737i −0.871295 0.490760i
\(6\) 0 0
\(7\) 1.45033i 0.548172i −0.961705 0.274086i \(-0.911625\pi\)
0.961705 0.274086i \(-0.0883754\pi\)
\(8\) 1.23634i 0.437112i
\(9\) 0 0
\(10\) 2.00000 3.55080i 0.632456 1.12286i
\(11\) 3.89655 1.17485 0.587427 0.809277i \(-0.300141\pi\)
0.587427 + 0.809277i \(0.300141\pi\)
\(12\) 0 0
\(13\) 3.05888i 0.848380i 0.905573 + 0.424190i \(0.139441\pi\)
−0.905573 + 0.424190i \(0.860559\pi\)
\(14\) 2.64327 0.706445
\(15\) 0 0
\(16\) −4.89655 −1.22414
\(17\) 3.92301i 0.951469i 0.879589 + 0.475735i \(0.157818\pi\)
−0.879589 + 0.475735i \(0.842182\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 2.57491 + 1.45033i 0.575768 + 0.324303i
\(21\) 0 0
\(22\) 7.10160i 1.51407i
\(23\) 5.37334i 1.12042i 0.828351 + 0.560209i \(0.189279\pi\)
−0.828351 + 0.560209i \(0.810721\pi\)
\(24\) 0 0
\(25\) 2.59155 + 4.27596i 0.518310 + 0.855193i
\(26\) −5.57491 −1.09333
\(27\) 0 0
\(28\) 1.91681i 0.362242i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −8.43637 −1.51522 −0.757609 0.652709i \(-0.773632\pi\)
−0.757609 + 0.652709i \(0.773632\pi\)
\(32\) 6.45146i 1.14047i
\(33\) 0 0
\(34\) −7.14982 −1.22618
\(35\) −1.59155 + 2.82564i −0.269021 + 0.477620i
\(36\) 0 0
\(37\) 5.95953i 0.979741i 0.871795 + 0.489871i \(0.162956\pi\)
−0.871795 + 0.489871i \(0.837044\pi\)
\(38\) 1.82254i 0.295654i
\(39\) 0 0
\(40\) 1.35673 2.40873i 0.214517 0.380854i
\(41\) −10.4364 −1.62989 −0.814944 0.579540i \(-0.803232\pi\)
−0.814944 + 0.579540i \(0.803232\pi\)
\(42\) 0 0
\(43\) 1.45033i 0.221173i −0.993867 0.110586i \(-0.964727\pi\)
0.993867 0.110586i \(-0.0352729\pi\)
\(44\) −5.14982 −0.776365
\(45\) 0 0
\(46\) −9.79310 −1.44391
\(47\) 4.90686i 0.715739i 0.933772 + 0.357869i \(0.116497\pi\)
−0.933772 + 0.357869i \(0.883503\pi\)
\(48\) 0 0
\(49\) 4.89655 0.699507
\(50\) −7.79310 + 4.72319i −1.10211 + 0.667960i
\(51\) 0 0
\(52\) 4.04272i 0.560625i
\(53\) 4.23127i 0.581209i 0.956843 + 0.290605i \(0.0938564\pi\)
−0.956843 + 0.290605i \(0.906144\pi\)
\(54\) 0 0
\(55\) −7.59155 4.27596i −1.02364 0.576571i
\(56\) 1.79310 0.239613
\(57\) 0 0
\(58\) 10.9352i 1.43586i
\(59\) 3.35673 0.437008 0.218504 0.975836i \(-0.429882\pi\)
0.218504 + 0.975836i \(0.429882\pi\)
\(60\) 0 0
\(61\) 10.3329 1.32300 0.661498 0.749947i \(-0.269921\pi\)
0.661498 + 0.749947i \(0.269921\pi\)
\(62\) 15.3756i 1.95270i
\(63\) 0 0
\(64\) 1.96491 0.245614
\(65\) 3.35673 5.95953i 0.416351 0.739189i
\(66\) 0 0
\(67\) 9.84404i 1.20264i 0.799008 + 0.601320i \(0.205358\pi\)
−0.799008 + 0.601320i \(0.794642\pi\)
\(68\) 5.18479i 0.628749i
\(69\) 0 0
\(70\) −5.14982 2.90066i −0.615522 0.346695i
\(71\) −8.64327 −1.02577 −0.512884 0.858458i \(-0.671423\pi\)
−0.512884 + 0.858458i \(0.671423\pi\)
\(72\) 0 0
\(73\) 2.43418i 0.284899i −0.989802 0.142449i \(-0.954502\pi\)
0.989802 0.142449i \(-0.0454978\pi\)
\(74\) −10.8615 −1.26262
\(75\) 0 0
\(76\) −1.32164 −0.151602
\(77\) 5.65127i 0.644022i
\(78\) 0 0
\(79\) 12.4364 1.39920 0.699601 0.714534i \(-0.253361\pi\)
0.699601 + 0.714534i \(0.253361\pi\)
\(80\) 9.53982 + 5.37334i 1.06658 + 0.600757i
\(81\) 0 0
\(82\) 19.0207i 2.10048i
\(83\) 12.6635i 1.39000i −0.719011 0.694999i \(-0.755405\pi\)
0.719011 0.694999i \(-0.244595\pi\)
\(84\) 0 0
\(85\) 4.30500 7.64310i 0.466943 0.829011i
\(86\) 2.64327 0.285032
\(87\) 0 0
\(88\) 4.81746i 0.513543i
\(89\) 12.3662 1.31081 0.655407 0.755276i \(-0.272497\pi\)
0.655407 + 0.755276i \(0.272497\pi\)
\(90\) 0 0
\(91\) 4.43637 0.465058
\(92\) 7.10160i 0.740393i
\(93\) 0 0
\(94\) −8.94292 −0.922392
\(95\) −1.94827 1.09737i −0.199889 0.112588i
\(96\) 0 0
\(97\) 3.05888i 0.310582i −0.987869 0.155291i \(-0.950369\pi\)
0.987869 0.155291i \(-0.0496315\pi\)
\(98\) 8.92414i 0.901474i
\(99\) 0 0
\(100\) −3.42509 5.65127i −0.342509 0.565127i
\(101\) −3.35673 −0.334007 −0.167003 0.985956i \(-0.553409\pi\)
−0.167003 + 0.985956i \(0.553409\pi\)
\(102\) 0 0
\(103\) 13.0611i 1.28695i 0.765466 + 0.643476i \(0.222508\pi\)
−0.765466 + 0.643476i \(0.777492\pi\)
\(104\) −3.78181 −0.370837
\(105\) 0 0
\(106\) −7.71164 −0.749020
\(107\) 5.77099i 0.557903i −0.960305 0.278951i \(-0.910013\pi\)
0.960305 0.278951i \(-0.0899868\pi\)
\(108\) 0 0
\(109\) −6.64327 −0.636310 −0.318155 0.948039i \(-0.603063\pi\)
−0.318155 + 0.948039i \(0.603063\pi\)
\(110\) 7.79310 13.8359i 0.743043 1.31920i
\(111\) 0 0
\(112\) 7.10160i 0.671038i
\(113\) 9.41606i 0.885789i 0.896574 + 0.442894i \(0.146048\pi\)
−0.896574 + 0.442894i \(0.853952\pi\)
\(114\) 0 0
\(115\) 5.89655 10.4687i 0.549856 0.976215i
\(116\) −7.92982 −0.736266
\(117\) 0 0
\(118\) 6.11775i 0.563185i
\(119\) 5.68965 0.521569
\(120\) 0 0
\(121\) 4.18310 0.380282
\(122\) 18.8321i 1.70498i
\(123\) 0 0
\(124\) 11.1498 1.00128
\(125\) −0.356726 11.1746i −0.0319065 0.999491i
\(126\) 0 0
\(127\) 11.0934i 0.984383i −0.870487 0.492192i \(-0.836196\pi\)
0.870487 0.492192i \(-0.163804\pi\)
\(128\) 9.32179i 0.823938i
\(129\) 0 0
\(130\) 10.8615 + 6.11775i 0.952613 + 0.536562i
\(131\) −4.61000 −0.402778 −0.201389 0.979511i \(-0.564545\pi\)
−0.201389 + 0.979511i \(0.564545\pi\)
\(132\) 0 0
\(133\) 1.45033i 0.125759i
\(134\) −17.9411 −1.54988
\(135\) 0 0
\(136\) −4.85018 −0.415899
\(137\) 13.1808i 1.12612i −0.826417 0.563058i \(-0.809625\pi\)
0.826417 0.563058i \(-0.190375\pi\)
\(138\) 0 0
\(139\) −1.18310 −0.100349 −0.0501745 0.998740i \(-0.515978\pi\)
−0.0501745 + 0.998740i \(0.515978\pi\)
\(140\) 2.10345 3.73447i 0.177774 0.315620i
\(141\) 0 0
\(142\) 15.7527i 1.32194i
\(143\) 11.9191i 0.996722i
\(144\) 0 0
\(145\) −11.6896 6.58423i −0.970772 0.546791i
\(146\) 4.43637 0.367157
\(147\) 0 0
\(148\) 7.87634i 0.647431i
\(149\) 5.46018 0.447315 0.223658 0.974668i \(-0.428200\pi\)
0.223658 + 0.974668i \(0.428200\pi\)
\(150\) 0 0
\(151\) −5.07965 −0.413376 −0.206688 0.978407i \(-0.566268\pi\)
−0.206688 + 0.978407i \(0.566268\pi\)
\(152\) 1.23634i 0.100280i
\(153\) 0 0
\(154\) 10.2996 0.829969
\(155\) 16.4364 + 9.25784i 1.32020 + 0.743608i
\(156\) 0 0
\(157\) 6.11775i 0.488250i −0.969744 0.244125i \(-0.921499\pi\)
0.969744 0.244125i \(-0.0785007\pi\)
\(158\) 22.6657i 1.80319i
\(159\) 0 0
\(160\) −7.07965 + 12.5692i −0.559695 + 0.993683i
\(161\) 7.79310 0.614182
\(162\) 0 0
\(163\) 16.4365i 1.28740i −0.765277 0.643701i \(-0.777398\pi\)
0.765277 0.643701i \(-0.222602\pi\)
\(164\) 13.7931 1.07706
\(165\) 0 0
\(166\) 23.0796 1.79133
\(167\) 3.80329i 0.294308i −0.989114 0.147154i \(-0.952989\pi\)
0.989114 0.147154i \(-0.0470112\pi\)
\(168\) 0 0
\(169\) 3.64327 0.280252
\(170\) 13.9298 + 7.84602i 1.06837 + 0.601762i
\(171\) 0 0
\(172\) 1.91681i 0.146155i
\(173\) 11.3838i 0.865491i 0.901516 + 0.432746i \(0.142455\pi\)
−0.901516 + 0.432746i \(0.857545\pi\)
\(174\) 0 0
\(175\) 6.20155 3.75860i 0.468793 0.284123i
\(176\) −19.0796 −1.43818
\(177\) 0 0
\(178\) 22.5378i 1.68928i
\(179\) 10.0702 0.752680 0.376340 0.926482i \(-0.377182\pi\)
0.376340 + 0.926482i \(0.377182\pi\)
\(180\) 0 0
\(181\) 0.573097 0.0425980 0.0212990 0.999773i \(-0.493220\pi\)
0.0212990 + 0.999773i \(0.493220\pi\)
\(182\) 8.08545i 0.599333i
\(183\) 0 0
\(184\) −6.64327 −0.489749
\(185\) 6.53982 11.6108i 0.480817 0.853643i
\(186\) 0 0
\(187\) 15.2862i 1.11784i
\(188\) 6.48509i 0.472973i
\(189\) 0 0
\(190\) 2.00000 3.55080i 0.145095 0.257602i
\(191\) 3.18310 0.230321 0.115160 0.993347i \(-0.463262\pi\)
0.115160 + 0.993347i \(0.463262\pi\)
\(192\) 0 0
\(193\) 3.05888i 0.220183i 0.993921 + 0.110091i \(0.0351143\pi\)
−0.993921 + 0.110091i \(0.964886\pi\)
\(194\) 5.57491 0.400255
\(195\) 0 0
\(196\) −6.47146 −0.462247
\(197\) 21.4933i 1.53134i 0.643235 + 0.765669i \(0.277592\pi\)
−0.643235 + 0.765669i \(0.722408\pi\)
\(198\) 0 0
\(199\) 4.81690 0.341461 0.170731 0.985318i \(-0.445387\pi\)
0.170731 + 0.985318i \(0.445387\pi\)
\(200\) −5.28655 + 3.20404i −0.373815 + 0.226560i
\(201\) 0 0
\(202\) 6.11775i 0.430444i
\(203\) 8.70197i 0.610758i
\(204\) 0 0
\(205\) 20.3329 + 11.4526i 1.42011 + 0.799883i
\(206\) −23.8044 −1.65853
\(207\) 0 0
\(208\) 14.9779i 1.03853i
\(209\) 3.89655 0.269530
\(210\) 0 0
\(211\) 10.5066 0.723301 0.361650 0.932314i \(-0.382213\pi\)
0.361650 + 0.932314i \(0.382213\pi\)
\(212\) 5.59220i 0.384074i
\(213\) 0 0
\(214\) 10.5178 0.718984
\(215\) −1.59155 + 2.82564i −0.108543 + 0.192707i
\(216\) 0 0
\(217\) 12.2355i 0.830600i
\(218\) 12.1076i 0.820031i
\(219\) 0 0
\(220\) 10.0333 + 5.65127i 0.676443 + 0.381009i
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 16.8947i 1.13136i −0.824626 0.565678i \(-0.808615\pi\)
0.824626 0.565678i \(-0.191385\pi\)
\(224\) −9.35673 −0.625173
\(225\) 0 0
\(226\) −17.1611 −1.14154
\(227\) 17.1342i 1.13724i 0.822602 + 0.568618i \(0.192522\pi\)
−0.822602 + 0.568618i \(0.807478\pi\)
\(228\) 0 0
\(229\) −25.0464 −1.65511 −0.827555 0.561384i \(-0.810269\pi\)
−0.827555 + 0.561384i \(0.810269\pi\)
\(230\) 19.0796 + 10.7467i 1.25807 + 0.708615i
\(231\) 0 0
\(232\) 7.41804i 0.487018i
\(233\) 19.2986i 1.26429i −0.774849 0.632147i \(-0.782174\pi\)
0.774849 0.632147i \(-0.217826\pi\)
\(234\) 0 0
\(235\) 5.38465 9.55991i 0.351256 0.623620i
\(236\) −4.43637 −0.288783
\(237\) 0 0
\(238\) 10.3696i 0.672161i
\(239\) 18.7693 1.21408 0.607042 0.794669i \(-0.292356\pi\)
0.607042 + 0.794669i \(0.292356\pi\)
\(240\) 0 0
\(241\) −14.4364 −0.929929 −0.464964 0.885329i \(-0.653933\pi\)
−0.464964 + 0.885329i \(0.653933\pi\)
\(242\) 7.62385i 0.490079i
\(243\) 0 0
\(244\) −13.6564 −0.874260
\(245\) −9.53982 5.37334i −0.609477 0.343290i
\(246\) 0 0
\(247\) 3.05888i 0.194632i
\(248\) 10.4302i 0.662320i
\(249\) 0 0
\(250\) 20.3662 0.650145i 1.28807 0.0411188i
\(251\) 10.9762 0.692811 0.346406 0.938085i \(-0.387402\pi\)
0.346406 + 0.938085i \(0.387402\pi\)
\(252\) 0 0
\(253\) 20.9375i 1.31633i
\(254\) 20.2182 1.26860
\(255\) 0 0
\(256\) 20.9191 1.30745
\(257\) 17.6392i 1.10030i −0.835066 0.550150i \(-0.814570\pi\)
0.835066 0.550150i \(-0.185430\pi\)
\(258\) 0 0
\(259\) 8.64327 0.537067
\(260\) −4.43637 + 7.87634i −0.275132 + 0.488470i
\(261\) 0 0
\(262\) 8.40189i 0.519071i
\(263\) 1.68976i 0.104195i 0.998642 + 0.0520975i \(0.0165907\pi\)
−0.998642 + 0.0520975i \(0.983409\pi\)
\(264\) 0 0
\(265\) 4.64327 8.24367i 0.285234 0.506405i
\(266\) 2.64327 0.162070
\(267\) 0 0
\(268\) 13.0102i 0.794727i
\(269\) −27.1022 −1.65245 −0.826226 0.563339i \(-0.809516\pi\)
−0.826226 + 0.563339i \(0.809516\pi\)
\(270\) 0 0
\(271\) 23.9524 1.45500 0.727502 0.686105i \(-0.240681\pi\)
0.727502 + 0.686105i \(0.240681\pi\)
\(272\) 19.2092i 1.16473i
\(273\) 0 0
\(274\) 24.0226 1.45126
\(275\) 10.0981 + 16.6615i 0.608938 + 1.00473i
\(276\) 0 0
\(277\) 8.23549i 0.494822i −0.968911 0.247411i \(-0.920420\pi\)
0.968911 0.247411i \(-0.0795799\pi\)
\(278\) 2.15624i 0.129323i
\(279\) 0 0
\(280\) −3.49345 1.96770i −0.208774 0.117592i
\(281\) 10.4364 0.622582 0.311291 0.950315i \(-0.399239\pi\)
0.311291 + 0.950315i \(0.399239\pi\)
\(282\) 0 0
\(283\) 10.4687i 0.622302i −0.950361 0.311151i \(-0.899286\pi\)
0.950361 0.311151i \(-0.100714\pi\)
\(284\) 11.4233 0.677847
\(285\) 0 0
\(286\) −21.7229 −1.28450
\(287\) 15.1362i 0.893459i
\(288\) 0 0
\(289\) 1.61000 0.0947059
\(290\) 12.0000 21.3048i 0.704664 1.25106i
\(291\) 0 0
\(292\) 3.21710i 0.188266i
\(293\) 16.4668i 0.961999i 0.876721 + 0.481000i \(0.159726\pi\)
−0.876721 + 0.481000i \(0.840274\pi\)
\(294\) 0 0
\(295\) −6.53982 3.68358i −0.380763 0.214466i
\(296\) −7.36801 −0.428257
\(297\) 0 0
\(298\) 9.95137i 0.576467i
\(299\) −16.4364 −0.950540
\(300\) 0 0
\(301\) −2.10345 −0.121241
\(302\) 9.25784i 0.532729i
\(303\) 0 0
\(304\) −4.89655 −0.280836
\(305\) −20.1314 11.3391i −1.15272 0.649273i
\(306\) 0 0
\(307\) 7.87634i 0.449526i −0.974413 0.224763i \(-0.927839\pi\)
0.974413 0.224763i \(-0.0721609\pi\)
\(308\) 7.46893i 0.425582i
\(309\) 0 0
\(310\) −16.8727 + 29.9559i −0.958308 + 1.70138i
\(311\) −3.89655 −0.220953 −0.110477 0.993879i \(-0.535238\pi\)
−0.110477 + 0.993879i \(0.535238\pi\)
\(312\) 0 0
\(313\) 7.76901i 0.439130i 0.975598 + 0.219565i \(0.0704638\pi\)
−0.975598 + 0.219565i \(0.929536\pi\)
\(314\) 11.1498 0.629221
\(315\) 0 0
\(316\) −16.4364 −0.924618
\(317\) 19.0510i 1.07001i 0.844849 + 0.535005i \(0.179690\pi\)
−0.844849 + 0.535005i \(0.820310\pi\)
\(318\) 0 0
\(319\) 23.3793 1.30899
\(320\) −3.82819 2.15624i −0.214002 0.120537i
\(321\) 0 0
\(322\) 14.2032i 0.791514i
\(323\) 3.92301i 0.218282i
\(324\) 0 0
\(325\) −13.0796 + 7.92723i −0.725528 + 0.439724i
\(326\) 29.9560 1.65911
\(327\) 0 0
\(328\) 12.9029i 0.712444i
\(329\) 7.11655 0.392348
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 16.7365i 0.918536i
\(333\) 0 0
\(334\) 6.93164 0.379282
\(335\) 10.8026 19.1789i 0.590207 1.04785i
\(336\) 0 0
\(337\) 6.89249i 0.375458i 0.982221 + 0.187729i \(0.0601127\pi\)
−0.982221 + 0.187729i \(0.939887\pi\)
\(338\) 6.64000i 0.361168i
\(339\) 0 0
\(340\) −5.68965 + 10.1014i −0.308565 + 0.547826i
\(341\) −32.8727 −1.78016
\(342\) 0 0
\(343\) 17.2539i 0.931623i
\(344\) 1.79310 0.0966774
\(345\) 0 0
\(346\) −20.7473 −1.11538
\(347\) 30.5503i 1.64002i −0.572346 0.820012i \(-0.693967\pi\)
0.572346 0.820012i \(-0.306033\pi\)
\(348\) 0 0
\(349\) −16.7693 −0.897640 −0.448820 0.893622i \(-0.648156\pi\)
−0.448820 + 0.893622i \(0.648156\pi\)
\(350\) 6.85018 + 11.3025i 0.366157 + 0.604147i
\(351\) 0 0
\(352\) 25.1384i 1.33988i
\(353\) 29.0999i 1.54883i −0.632676 0.774417i \(-0.718044\pi\)
0.632676 0.774417i \(-0.281956\pi\)
\(354\) 0 0
\(355\) 16.8395 + 9.48489i 0.893746 + 0.503406i
\(356\) −16.3436 −0.866210
\(357\) 0 0
\(358\) 18.3533i 0.970000i
\(359\) −11.6896 −0.616956 −0.308478 0.951231i \(-0.599820\pi\)
−0.308478 + 0.951231i \(0.599820\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 1.04449i 0.0548972i
\(363\) 0 0
\(364\) −5.86328 −0.307319
\(365\) −2.67120 + 4.74244i −0.139817 + 0.248231i
\(366\) 0 0
\(367\) 4.20095i 0.219288i 0.993971 + 0.109644i \(0.0349710\pi\)
−0.993971 + 0.109644i \(0.965029\pi\)
\(368\) 26.3108i 1.37155i
\(369\) 0 0
\(370\) 21.1611 + 11.9191i 1.10011 + 0.619643i
\(371\) 6.13672 0.318603
\(372\) 0 0
\(373\) 16.9456i 0.877412i −0.898631 0.438706i \(-0.855437\pi\)
0.898631 0.438706i \(-0.144563\pi\)
\(374\) −27.8596 −1.44059
\(375\) 0 0
\(376\) −6.06655 −0.312858
\(377\) 18.3533i 0.945241i
\(378\) 0 0
\(379\) −10.3662 −0.532476 −0.266238 0.963907i \(-0.585781\pi\)
−0.266238 + 0.963907i \(0.585781\pi\)
\(380\) 2.57491 + 1.45033i 0.132090 + 0.0744002i
\(381\) 0 0
\(382\) 5.80131i 0.296821i
\(383\) 20.5907i 1.05214i −0.850442 0.526068i \(-0.823666\pi\)
0.850442 0.526068i \(-0.176334\pi\)
\(384\) 0 0
\(385\) −6.20155 + 11.0102i −0.316060 + 0.561133i
\(386\) −5.57491 −0.283756
\(387\) 0 0
\(388\) 4.04272i 0.205238i
\(389\) 8.10345 0.410861 0.205431 0.978672i \(-0.434141\pi\)
0.205431 + 0.978672i \(0.434141\pi\)
\(390\) 0 0
\(391\) −21.0796 −1.06604
\(392\) 6.05380i 0.305763i
\(393\) 0 0
\(394\) −39.1724 −1.97348
\(395\) −24.2295 13.6473i −1.21912 0.686672i
\(396\) 0 0
\(397\) 3.46891i 0.174100i −0.996204 0.0870499i \(-0.972256\pi\)
0.996204 0.0870499i \(-0.0277440\pi\)
\(398\) 8.77898i 0.440050i
\(399\) 0 0
\(400\) −12.6896 20.9375i −0.634482 1.04687i
\(401\) 15.9524 0.796625 0.398312 0.917250i \(-0.369596\pi\)
0.398312 + 0.917250i \(0.369596\pi\)
\(402\) 0 0
\(403\) 25.8058i 1.28548i
\(404\) 4.43637 0.220718
\(405\) 0 0
\(406\) 15.8596 0.787101
\(407\) 23.2216i 1.15105i
\(408\) 0 0
\(409\) 3.92982 0.194317 0.0971586 0.995269i \(-0.469025\pi\)
0.0971586 + 0.995269i \(0.469025\pi\)
\(410\) −20.8727 + 37.0575i −1.03083 + 1.83014i
\(411\) 0 0
\(412\) 17.2621i 0.850442i
\(413\) 4.86835i 0.239556i
\(414\) 0 0
\(415\) −13.8965 + 24.6719i −0.682155 + 1.21110i
\(416\) 19.7342 0.967549
\(417\) 0 0
\(418\) 7.10160i 0.347351i
\(419\) −34.2996 −1.67565 −0.837824 0.545941i \(-0.816172\pi\)
−0.837824 + 0.545941i \(0.816172\pi\)
\(420\) 0 0
\(421\) −26.0891 −1.27151 −0.635753 0.771893i \(-0.719310\pi\)
−0.635753 + 0.771893i \(0.719310\pi\)
\(422\) 19.1486i 0.932138i
\(423\) 0 0
\(424\) −5.23129 −0.254054
\(425\) −16.7746 + 10.1667i −0.813690 + 0.493156i
\(426\) 0 0
\(427\) 14.9861i 0.725229i
\(428\) 7.62715i 0.368672i
\(429\) 0 0
\(430\) −5.14982 2.90066i −0.248347 0.139882i
\(431\) −10.2996 −0.496117 −0.248058 0.968745i \(-0.579792\pi\)
−0.248058 + 0.968745i \(0.579792\pi\)
\(432\) 0 0
\(433\) 36.2319i 1.74119i −0.491999 0.870596i \(-0.663734\pi\)
0.491999 0.870596i \(-0.336266\pi\)
\(434\) −22.2996 −1.07042
\(435\) 0 0
\(436\) 8.78000 0.420486
\(437\) 5.37334i 0.257042i
\(438\) 0 0
\(439\) 24.0891 1.14971 0.574855 0.818255i \(-0.305058\pi\)
0.574855 + 0.818255i \(0.305058\pi\)
\(440\) 5.28655 9.38574i 0.252026 0.447448i
\(441\) 0 0
\(442\) 21.8704i 1.04027i
\(443\) 5.52337i 0.262423i 0.991354 + 0.131212i \(0.0418868\pi\)
−0.991354 + 0.131212i \(0.958113\pi\)
\(444\) 0 0
\(445\) −24.0927 13.5703i −1.14211 0.643295i
\(446\) 30.7913 1.45801
\(447\) 0 0
\(448\) 2.84977i 0.134639i
\(449\) 7.92982 0.374231 0.187116 0.982338i \(-0.440086\pi\)
0.187116 + 0.982338i \(0.440086\pi\)
\(450\) 0 0
\(451\) −40.6658 −1.91488
\(452\) 12.4446i 0.585346i
\(453\) 0 0
\(454\) −31.2277 −1.46559
\(455\) −8.64327 4.86835i −0.405203 0.228232i
\(456\) 0 0
\(457\) 22.6534i 1.05968i 0.848098 + 0.529840i \(0.177748\pi\)
−0.848098 + 0.529840i \(0.822252\pi\)
\(458\) 45.6479i 2.13299i
\(459\) 0 0
\(460\) −7.79310 + 13.8359i −0.363355 + 0.645101i
\(461\) −13.3900 −0.623634 −0.311817 0.950142i \(-0.600938\pi\)
−0.311817 + 0.950142i \(0.600938\pi\)
\(462\) 0 0
\(463\) 16.9029i 0.785546i −0.919635 0.392773i \(-0.871516\pi\)
0.919635 0.392773i \(-0.128484\pi\)
\(464\) −29.3793 −1.36390
\(465\) 0 0
\(466\) 35.1724 1.62933
\(467\) 22.2501i 1.02961i −0.857306 0.514807i \(-0.827864\pi\)
0.857306 0.514807i \(-0.172136\pi\)
\(468\) 0 0
\(469\) 14.2771 0.659254
\(470\) 17.4233 + 9.81371i 0.803676 + 0.452673i
\(471\) 0 0
\(472\) 4.15006i 0.191022i
\(473\) 5.65127i 0.259846i
\(474\) 0 0
\(475\) 2.59155 + 4.27596i 0.118908 + 0.196195i
\(476\) −7.51965 −0.344663
\(477\) 0 0
\(478\) 34.2077i 1.56462i
\(479\) 0.366196 0.0167319 0.00836597 0.999965i \(-0.497337\pi\)
0.00836597 + 0.999965i \(0.497337\pi\)
\(480\) 0 0
\(481\) −18.2295 −0.831192
\(482\) 26.3108i 1.19842i
\(483\) 0 0
\(484\) −5.52854 −0.251297
\(485\) −3.35673 + 5.95953i −0.152421 + 0.270608i
\(486\) 0 0
\(487\) 26.8461i 1.21651i 0.793740 + 0.608257i \(0.208131\pi\)
−0.793740 + 0.608257i \(0.791869\pi\)
\(488\) 12.7750i 0.578298i
\(489\) 0 0
\(490\) 9.79310 17.3867i 0.442407 0.785450i
\(491\) 23.7266 1.07076 0.535382 0.844610i \(-0.320168\pi\)
0.535382 + 0.844610i \(0.320168\pi\)
\(492\) 0 0
\(493\) 23.5381i 1.06010i
\(494\) −5.57491 −0.250827
\(495\) 0 0
\(496\) 41.3091 1.85483
\(497\) 12.5356i 0.562298i
\(498\) 0 0
\(499\) −6.81690 −0.305166 −0.152583 0.988291i \(-0.548759\pi\)
−0.152583 + 0.988291i \(0.548759\pi\)
\(500\) 0.471462 + 14.7688i 0.0210844 + 0.660482i
\(501\) 0 0
\(502\) 20.0045i 0.892845i
\(503\) 23.4102i 1.04381i 0.853004 + 0.521904i \(0.174778\pi\)
−0.853004 + 0.521904i \(0.825222\pi\)
\(504\) 0 0
\(505\) 6.53982 + 3.68358i 0.291018 + 0.163917i
\(506\) −38.1593 −1.69639
\(507\) 0 0
\(508\) 14.6615i 0.650499i
\(509\) 16.9204 0.749981 0.374991 0.927029i \(-0.377646\pi\)
0.374991 + 0.927029i \(0.377646\pi\)
\(510\) 0 0
\(511\) −3.53035 −0.156174
\(512\) 19.4823i 0.861003i
\(513\) 0 0
\(514\) 32.1480 1.41799
\(515\) 14.3329 25.4467i 0.631584 1.12131i
\(516\) 0 0
\(517\) 19.1198i 0.840888i
\(518\) 15.7527i 0.692133i
\(519\) 0 0
\(520\) 7.36801 + 4.15006i 0.323109 + 0.181992i
\(521\) 3.49345 0.153051 0.0765254 0.997068i \(-0.475617\pi\)
0.0765254 + 0.997068i \(0.475617\pi\)
\(522\) 0 0
\(523\) 14.9271i 0.652714i −0.945247 0.326357i \(-0.894179\pi\)
0.945247 0.326357i \(-0.105821\pi\)
\(524\) 6.09275 0.266163
\(525\) 0 0
\(526\) −3.07965 −0.134279
\(527\) 33.0960i 1.44168i
\(528\) 0 0
\(529\) −5.87275 −0.255337
\(530\) 15.0244 + 8.46253i 0.652618 + 0.367589i
\(531\) 0 0
\(532\) 1.91681i 0.0831041i
\(533\) 31.9236i 1.38276i
\(534\) 0 0
\(535\) −6.33292 + 11.2435i −0.273796 + 0.486098i
\(536\) −12.1706 −0.525689
\(537\) 0 0
\(538\) 49.3948i 2.12956i
\(539\) 19.0796 0.821819
\(540\) 0 0
\(541\) −12.6991 −0.545978 −0.272989 0.962017i \(-0.588012\pi\)
−0.272989 + 0.962017i \(0.588012\pi\)
\(542\) 43.6541i 1.87510i
\(543\) 0 0
\(544\) 25.3091 1.08512
\(545\) 12.9429 + 7.29014i 0.554414 + 0.312275i
\(546\) 0 0
\(547\) 31.8162i 1.36036i 0.733043 + 0.680182i \(0.238099\pi\)
−0.733043 + 0.680182i \(0.761901\pi\)
\(548\) 17.4203i 0.744158i
\(549\) 0 0
\(550\) −30.3662 + 18.4041i −1.29482 + 0.784756i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 18.0368i 0.767003i
\(554\) 15.0095 0.637691
\(555\) 0 0
\(556\) 1.56363 0.0663125
\(557\) 9.64731i 0.408770i −0.978891 0.204385i \(-0.934481\pi\)
0.978891 0.204385i \(-0.0655194\pi\)
\(558\) 0 0
\(559\) 4.43637 0.187639
\(560\) 7.79310 13.8359i 0.329319 0.584672i
\(561\) 0 0
\(562\) 19.0207i 0.802338i
\(563\) 4.28216i 0.180471i 0.995920 + 0.0902357i \(0.0287620\pi\)
−0.995920 + 0.0902357i \(0.971238\pi\)
\(564\) 0 0
\(565\) 10.3329 18.3451i 0.434709 0.771783i
\(566\) 19.0796 0.801977
\(567\) 0 0
\(568\) 10.6860i 0.448376i
\(569\) 42.2295 1.77035 0.885176 0.465257i \(-0.154038\pi\)
0.885176 + 0.465257i \(0.154038\pi\)
\(570\) 0 0
\(571\) −19.2200 −0.804332 −0.402166 0.915567i \(-0.631743\pi\)
−0.402166 + 0.915567i \(0.631743\pi\)
\(572\) 15.7527i 0.658653i
\(573\) 0 0
\(574\) −27.5862 −1.15143
\(575\) −22.9762 + 13.9253i −0.958174 + 0.580724i
\(576\) 0 0
\(577\) 40.7919i 1.69819i 0.528239 + 0.849096i \(0.322852\pi\)
−0.528239 + 0.849096i \(0.677148\pi\)
\(578\) 2.93428i 0.122050i
\(579\) 0 0
\(580\) 15.4495 + 8.70197i 0.641504 + 0.361329i
\(581\) −18.3662 −0.761958
\(582\) 0 0
\(583\) 16.4873i 0.682836i
\(584\) 3.00947 0.124533
\(585\) 0 0
\(586\) −30.0113 −1.23975
\(587\) 31.8851i 1.31604i −0.753001 0.658019i \(-0.771395\pi\)
0.753001 0.658019i \(-0.228605\pi\)
\(588\) 0 0
\(589\) −8.43637 −0.347615
\(590\) 6.71345 11.9191i 0.276388 0.490700i
\(591\) 0 0
\(592\) 29.1811i 1.19934i
\(593\) 38.8973i 1.59732i 0.601783 + 0.798660i \(0.294457\pi\)
−0.601783 + 0.798660i \(0.705543\pi\)
\(594\) 0 0
\(595\) −11.0850 6.24366i −0.454441 0.255965i
\(596\) −7.21637 −0.295594
\(597\) 0 0
\(598\) 29.9559i 1.22499i
\(599\) 28.1629 1.15071 0.575353 0.817905i \(-0.304865\pi\)
0.575353 + 0.817905i \(0.304865\pi\)
\(600\) 0 0
\(601\) −5.56363 −0.226945 −0.113473 0.993541i \(-0.536197\pi\)
−0.113473 + 0.993541i \(0.536197\pi\)
\(602\) 3.83361i 0.156246i
\(603\) 0 0
\(604\) 6.71345 0.273166
\(605\) −8.14982 4.59042i −0.331337 0.186627i
\(606\) 0 0
\(607\) 33.9986i 1.37996i −0.723828 0.689980i \(-0.757619\pi\)
0.723828 0.689980i \(-0.242381\pi\)
\(608\) 6.45146i 0.261641i
\(609\) 0 0
\(610\) 20.6658 36.6902i 0.836736 1.48554i
\(611\) −15.0095 −0.607218
\(612\) 0 0
\(613\) 17.5703i 0.709659i 0.934931 + 0.354830i \(0.115461\pi\)
−0.934931 + 0.354830i \(0.884539\pi\)
\(614\) 14.3549 0.579317
\(615\) 0 0
\(616\) 6.98690 0.281510
\(617\) 13.0791i 0.526544i −0.964722 0.263272i \(-0.915198\pi\)
0.964722 0.263272i \(-0.0848016\pi\)
\(618\) 0 0
\(619\) 18.9393 0.761234 0.380617 0.924733i \(-0.375712\pi\)
0.380617 + 0.924733i \(0.375712\pi\)
\(620\) −21.7229 12.2355i −0.872414 0.491390i
\(621\) 0 0
\(622\) 7.10160i 0.284748i
\(623\) 17.9350i 0.718552i
\(624\) 0 0
\(625\) −11.5677 + 22.1627i −0.462710 + 0.886510i
\(626\) −14.1593 −0.565919
\(627\) 0 0
\(628\) 8.08545i 0.322645i
\(629\) −23.3793 −0.932194
\(630\) 0 0
\(631\) 31.6896 1.26154 0.630772 0.775968i \(-0.282738\pi\)
0.630772 + 0.775968i \(0.282738\pi\)
\(632\) 15.3756i 0.611608i
\(633\) 0 0
\(634\) −34.7211 −1.37895
\(635\) −12.1736 + 21.6131i −0.483096 + 0.857688i
\(636\) 0 0
\(637\) 14.9779i 0.593448i
\(638\) 42.6096i 1.68693i
\(639\) 0 0
\(640\) −10.2295 + 18.1614i −0.404355 + 0.717893i
\(641\) −47.9750 −1.89490 −0.947449 0.319908i \(-0.896348\pi\)
−0.947449 + 0.319908i \(0.896348\pi\)
\(642\) 0 0
\(643\) 0.200927i 0.00792378i −0.999992 0.00396189i \(-0.998739\pi\)
0.999992 0.00396189i \(-0.00126111\pi\)
\(644\) −10.2996 −0.405863
\(645\) 0 0
\(646\) −7.14982 −0.281306
\(647\) 1.58798i 0.0624299i 0.999513 + 0.0312150i \(0.00993765\pi\)
−0.999513 + 0.0312150i \(0.990062\pi\)
\(648\) 0 0
\(649\) 13.0796 0.513421
\(650\) −14.4477 23.8381i −0.566684 0.935008i
\(651\) 0 0
\(652\) 21.7230i 0.850739i
\(653\) 33.5624i 1.31340i 0.754152 + 0.656700i \(0.228048\pi\)
−0.754152 + 0.656700i \(0.771952\pi\)
\(654\) 0 0
\(655\) 8.98155 + 5.05889i 0.350938 + 0.197667i
\(656\) 51.1022 1.99521
\(657\) 0 0
\(658\) 12.9702i 0.505630i
\(659\) 15.3567 0.598213 0.299107 0.954220i \(-0.403311\pi\)
0.299107 + 0.954220i \(0.403311\pi\)
\(660\) 0 0
\(661\) 12.8026 0.497962 0.248981 0.968508i \(-0.419904\pi\)
0.248981 + 0.968508i \(0.419904\pi\)
\(662\) 14.5803i 0.566679i
\(663\) 0 0
\(664\) 15.6564 0.607585
\(665\) −1.59155 + 2.82564i −0.0617176 + 0.109573i
\(666\) 0 0
\(667\) 32.2400i 1.24834i
\(668\) 5.02657i 0.194484i
\(669\) 0 0
\(670\) 34.9542 + 19.6881i 1.35040 + 0.760617i
\(671\) 40.2627 1.55433
\(672\) 0 0
\(673\) 7.82545i 0.301649i 0.988561 + 0.150824i \(0.0481928\pi\)
−0.988561 + 0.150824i \(0.951807\pi\)
\(674\) −12.5618 −0.483863
\(675\) 0 0
\(676\) −4.81509 −0.185196
\(677\) 21.6516i 0.832137i 0.909333 + 0.416069i \(0.136592\pi\)
−0.909333 + 0.416069i \(0.863408\pi\)
\(678\) 0 0
\(679\) −4.43637 −0.170252
\(680\) 9.44947 + 5.32245i 0.362371 + 0.204107i
\(681\) 0 0
\(682\) 59.9118i 2.29414i
\(683\) 6.38751i 0.244411i −0.992505 0.122206i \(-0.961003\pi\)
0.992505 0.122206i \(-0.0389967\pi\)
\(684\) 0 0
\(685\) −14.4643 + 25.6799i −0.552652 + 0.981179i
\(686\) 31.4458 1.20061
\(687\) 0 0
\(688\) 7.10160i 0.270746i
\(689\) −12.9429 −0.493086
\(690\) 0 0
\(691\) 44.4958 1.69270 0.846351 0.532626i \(-0.178795\pi\)
0.846351 + 0.532626i \(0.178795\pi\)
\(692\) 15.0452i 0.571933i
\(693\) 0 0
\(694\) 55.6789 2.11354
\(695\) 2.30500 + 1.29830i 0.0874336 + 0.0492473i
\(696\) 0 0
\(697\) 40.9420i 1.55079i
\(698\) 30.5626i 1.15681i
\(699\) 0 0
\(700\) −8.19620 + 4.96750i −0.309787 + 0.187754i
\(701\) −17.5160 −0.661571 −0.330785 0.943706i \(-0.607314\pi\)
−0.330785 + 0.943706i \(0.607314\pi\)
\(702\) 0 0
\(703\) 5.95953i 0.224768i
\(704\) 7.65638 0.288560
\(705\) 0 0
\(706\) 53.0357 1.99602
\(707\) 4.86835i 0.183093i
\(708\) 0 0
\(709\) −11.4269 −0.429146 −0.214573 0.976708i \(-0.568836\pi\)
−0.214573 + 0.976708i \(0.568836\pi\)
\(710\) −17.2865 + 30.6905i −0.648753 + 1.15180i
\(711\) 0 0
\(712\) 15.2888i 0.572973i
\(713\) 45.3315i 1.69768i
\(714\) 0 0
\(715\) 13.0796 23.2216i 0.489151 0.868439i
\(716\) −13.3091 −0.497385
\(717\) 0 0
\(718\) 21.3048i 0.795088i
\(719\) 15.8965 0.592841 0.296421 0.955057i \(-0.404207\pi\)
0.296421 + 0.955057i \(0.404207\pi\)
\(720\) 0 0
\(721\) 18.9429 0.705471
\(722\) 1.82254i 0.0678278i
\(723\) 0 0
\(724\) −0.757427 −0.0281495
\(725\) 15.5493 + 25.6558i 0.577486 + 0.952832i
\(726\) 0 0
\(727\) 41.9905i 1.55734i −0.627434 0.778670i \(-0.715895\pi\)
0.627434 0.778670i \(-0.284105\pi\)
\(728\) 5.48487i 0.203283i
\(729\) 0 0
\(730\) −8.64327 4.86835i −0.319902 0.180186i
\(731\) 5.68965 0.210439
\(732\) 0 0
\(733\) 0.632884i 0.0233761i −0.999932 0.0116881i \(-0.996279\pi\)
0.999932 0.0116881i \(-0.00372051\pi\)
\(734\) −7.65638 −0.282602
\(735\) 0 0
\(736\) 34.6658 1.27780
\(737\) 38.3578i 1.41293i
\(738\) 0 0
\(739\) 29.5493 1.08699 0.543494 0.839413i \(-0.317101\pi\)
0.543494 + 0.839413i \(0.317101\pi\)
\(740\) −8.64327 + 15.3453i −0.317733 + 0.564103i
\(741\) 0 0
\(742\) 11.1844i 0.410592i
\(743\) 31.3374i 1.14966i 0.818274 + 0.574829i \(0.194931\pi\)
−0.818274 + 0.574829i \(0.805069\pi\)
\(744\) 0 0
\(745\) −10.6379 5.99184i −0.389743 0.219524i
\(746\) 30.8840 1.13074
\(747\) 0 0
\(748\) 20.2028i 0.738688i
\(749\) −8.36983 −0.305827
\(750\) 0 0
\(751\) 25.0131 0.912741 0.456371 0.889790i \(-0.349149\pi\)
0.456371 + 0.889790i \(0.349149\pi\)
\(752\) 24.0267i 0.876163i
\(753\) 0 0
\(754\) −33.4495 −1.21816
\(755\) 9.89655 + 5.57426i 0.360172 + 0.202868i
\(756\) 0 0
\(757\) 32.0900i 1.16633i 0.812354 + 0.583165i \(0.198186\pi\)
−0.812354 + 0.583165i \(0.801814\pi\)
\(758\) 18.8928i 0.686216i
\(759\) 0 0
\(760\) 1.35673 2.40873i 0.0492136 0.0873739i
\(761\) 40.4922 1.46784 0.733921 0.679235i \(-0.237688\pi\)
0.733921 + 0.679235i \(0.237688\pi\)
\(762\) 0 0
\(763\) 9.63492i 0.348808i
\(764\) −4.20690 −0.152200
\(765\) 0 0
\(766\) 37.5273 1.35592
\(767\) 10.2678i 0.370749i
\(768\) 0 0
\(769\) −3.09398 −0.111572 −0.0557859 0.998443i \(-0.517766\pi\)
−0.0557859 + 0.998443i \(0.517766\pi\)
\(770\) −20.0665 11.3025i −0.723148 0.407316i
\(771\) 0 0
\(772\) 4.04272i 0.145501i
\(773\) 1.96350i 0.0706220i 0.999376 + 0.0353110i \(0.0112422\pi\)
−0.999376 + 0.0353110i \(0.988758\pi\)
\(774\) 0 0
\(775\) −21.8633 36.0736i −0.785352 1.29580i
\(776\) 3.78181 0.135759
\(777\) 0 0
\(778\) 14.7688i 0.529488i
\(779\) −10.4364 −0.373922
\(780\) 0 0
\(781\) −33.6789 −1.20513
\(782\) 38.4184i 1.37384i
\(783\) 0 0
\(784\) −23.9762 −0.856293
\(785\) −6.71345 + 11.9191i −0.239613 + 0.425410i
\(786\) 0 0
\(787\) 0.107331i 0.00382595i 0.999998 + 0.00191297i \(0.000608919\pi\)
−0.999998 + 0.00191297i \(0.999391\pi\)
\(788\) 28.4064i 1.01194i
\(789\) 0 0
\(790\) 24.8727 44.1591i 0.884933 1.57111i
\(791\) 13.6564 0.485565
\(792\) 0 0
\(793\) 31.6071i 1.12240i
\(794\) 6.32222 0.224367
\(795\) 0 0
\(796\) −6.36620 −0.225644
\(797\) 8.32068i 0.294734i −0.989082