Properties

Label 4020.2.g.c.1609.9
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.9
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.28

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-0.599682 - 2.15415i) q^{5}\) \(+0.0778518i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-0.599682 - 2.15415i) q^{5}\) \(+0.0778518i q^{7}\) \(-1.00000 q^{9}\) \(-4.03380 q^{11}\) \(-0.176152i q^{13}\) \(+(-2.15415 + 0.599682i) q^{15}\) \(-7.72106i q^{17}\) \(-1.88421 q^{19}\) \(+0.0778518 q^{21}\) \(-2.47191i q^{23}\) \(+(-4.28076 + 2.58362i) q^{25}\) \(+1.00000i q^{27}\) \(+6.84971 q^{29}\) \(-7.45359 q^{31}\) \(+4.03380i q^{33}\) \(+(0.167705 - 0.0466864i) q^{35}\) \(-3.67413i q^{37}\) \(-0.176152 q^{39}\) \(-0.0931527 q^{41}\) \(+6.63231i q^{43}\) \(+(0.599682 + 2.15415i) q^{45}\) \(+8.43872i q^{47}\) \(+6.99394 q^{49}\) \(-7.72106 q^{51}\) \(-1.60464i q^{53}\) \(+(2.41900 + 8.68943i) q^{55}\) \(+1.88421i q^{57}\) \(-0.795026 q^{59}\) \(-5.94662 q^{61}\) \(-0.0778518i q^{63}\) \(+(-0.379458 + 0.105635i) q^{65}\) \(-1.00000i q^{67}\) \(-2.47191 q^{69}\) \(+10.2043 q^{71}\) \(-0.963933i q^{73}\) \(+(2.58362 + 4.28076i) q^{75}\) \(-0.314039i q^{77}\) \(-13.7522 q^{79}\) \(+1.00000 q^{81}\) \(+5.08460i q^{83}\) \(+(-16.6324 + 4.63019i) q^{85}\) \(-6.84971i q^{87}\) \(-12.5250 q^{89}\) \(+0.0137137 q^{91}\) \(+7.45359i q^{93}\) \(+(1.12993 + 4.05887i) q^{95}\) \(+13.8335i q^{97}\) \(+4.03380 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −0.599682 2.15415i −0.268186 0.963367i
\(6\) 0 0
\(7\) 0.0778518i 0.0294252i 0.999892 + 0.0147126i \(0.00468334\pi\)
−0.999892 + 0.0147126i \(0.995317\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −4.03380 −1.21624 −0.608119 0.793846i \(-0.708075\pi\)
−0.608119 + 0.793846i \(0.708075\pi\)
\(12\) 0 0
\(13\) 0.176152i 0.0488557i −0.999702 0.0244278i \(-0.992224\pi\)
0.999702 0.0244278i \(-0.00777640\pi\)
\(14\) 0 0
\(15\) −2.15415 + 0.599682i −0.556200 + 0.154837i
\(16\) 0 0
\(17\) 7.72106i 1.87263i −0.351158 0.936316i \(-0.614212\pi\)
0.351158 0.936316i \(-0.385788\pi\)
\(18\) 0 0
\(19\) −1.88421 −0.432267 −0.216133 0.976364i \(-0.569345\pi\)
−0.216133 + 0.976364i \(0.569345\pi\)
\(20\) 0 0
\(21\) 0.0778518 0.0169887
\(22\) 0 0
\(23\) 2.47191i 0.515429i −0.966221 0.257715i \(-0.917031\pi\)
0.966221 0.257715i \(-0.0829695\pi\)
\(24\) 0 0
\(25\) −4.28076 + 2.58362i −0.856152 + 0.516723i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.84971 1.27196 0.635980 0.771706i \(-0.280596\pi\)
0.635980 + 0.771706i \(0.280596\pi\)
\(30\) 0 0
\(31\) −7.45359 −1.33870 −0.669352 0.742945i \(-0.733428\pi\)
−0.669352 + 0.742945i \(0.733428\pi\)
\(32\) 0 0
\(33\) 4.03380i 0.702195i
\(34\) 0 0
\(35\) 0.167705 0.0466864i 0.0283473 0.00789144i
\(36\) 0 0
\(37\) 3.67413i 0.604024i −0.953304 0.302012i \(-0.902342\pi\)
0.953304 0.302012i \(-0.0976582\pi\)
\(38\) 0 0
\(39\) −0.176152 −0.0282068
\(40\) 0 0
\(41\) −0.0931527 −0.0145480 −0.00727401 0.999974i \(-0.502315\pi\)
−0.00727401 + 0.999974i \(0.502315\pi\)
\(42\) 0 0
\(43\) 6.63231i 1.01142i 0.862704 + 0.505709i \(0.168769\pi\)
−0.862704 + 0.505709i \(0.831231\pi\)
\(44\) 0 0
\(45\) 0.599682 + 2.15415i 0.0893954 + 0.321122i
\(46\) 0 0
\(47\) 8.43872i 1.23091i 0.788170 + 0.615457i \(0.211029\pi\)
−0.788170 + 0.615457i \(0.788971\pi\)
\(48\) 0 0
\(49\) 6.99394 0.999134
\(50\) 0 0
\(51\) −7.72106 −1.08117
\(52\) 0 0
\(53\) 1.60464i 0.220415i −0.993909 0.110207i \(-0.964849\pi\)
0.993909 0.110207i \(-0.0351515\pi\)
\(54\) 0 0
\(55\) 2.41900 + 8.68943i 0.326178 + 1.17168i
\(56\) 0 0
\(57\) 1.88421i 0.249569i
\(58\) 0 0
\(59\) −0.795026 −0.103504 −0.0517518 0.998660i \(-0.516480\pi\)
−0.0517518 + 0.998660i \(0.516480\pi\)
\(60\) 0 0
\(61\) −5.94662 −0.761387 −0.380693 0.924701i \(-0.624315\pi\)
−0.380693 + 0.924701i \(0.624315\pi\)
\(62\) 0 0
\(63\) 0.0778518i 0.00980841i
\(64\) 0 0
\(65\) −0.379458 + 0.105635i −0.0470660 + 0.0131024i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −2.47191 −0.297583
\(70\) 0 0
\(71\) 10.2043 1.21103 0.605514 0.795834i \(-0.292967\pi\)
0.605514 + 0.795834i \(0.292967\pi\)
\(72\) 0 0
\(73\) 0.963933i 0.112820i −0.998408 0.0564099i \(-0.982035\pi\)
0.998408 0.0564099i \(-0.0179654\pi\)
\(74\) 0 0
\(75\) 2.58362 + 4.28076i 0.298330 + 0.494300i
\(76\) 0 0
\(77\) 0.314039i 0.0357880i
\(78\) 0 0
\(79\) −13.7522 −1.54725 −0.773623 0.633646i \(-0.781557\pi\)
−0.773623 + 0.633646i \(0.781557\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.08460i 0.558108i 0.960275 + 0.279054i \(0.0900208\pi\)
−0.960275 + 0.279054i \(0.909979\pi\)
\(84\) 0 0
\(85\) −16.6324 + 4.63019i −1.80403 + 0.502214i
\(86\) 0 0
\(87\) 6.84971i 0.734366i
\(88\) 0 0
\(89\) −12.5250 −1.32764 −0.663822 0.747891i \(-0.731067\pi\)
−0.663822 + 0.747891i \(0.731067\pi\)
\(90\) 0 0
\(91\) 0.0137137 0.00143759
\(92\) 0 0
\(93\) 7.45359i 0.772901i
\(94\) 0 0
\(95\) 1.12993 + 4.05887i 0.115928 + 0.416431i
\(96\) 0 0
\(97\) 13.8335i 1.40458i 0.711890 + 0.702291i \(0.247839\pi\)
−0.711890 + 0.702291i \(0.752161\pi\)
\(98\) 0 0
\(99\) 4.03380 0.405412
\(100\) 0 0
\(101\) 15.7346 1.56566 0.782828 0.622239i \(-0.213777\pi\)
0.782828 + 0.622239i \(0.213777\pi\)
\(102\) 0 0
\(103\) 13.3508i 1.31550i −0.753237 0.657749i \(-0.771509\pi\)
0.753237 0.657749i \(-0.228491\pi\)
\(104\) 0 0
\(105\) −0.0466864 0.167705i −0.00455612 0.0163663i
\(106\) 0 0
\(107\) 4.89148i 0.472877i 0.971646 + 0.236438i \(0.0759801\pi\)
−0.971646 + 0.236438i \(0.924020\pi\)
\(108\) 0 0
\(109\) −13.4979 −1.29286 −0.646430 0.762973i \(-0.723739\pi\)
−0.646430 + 0.762973i \(0.723739\pi\)
\(110\) 0 0
\(111\) −3.67413 −0.348733
\(112\) 0 0
\(113\) 8.95878i 0.842771i 0.906882 + 0.421385i \(0.138456\pi\)
−0.906882 + 0.421385i \(0.861544\pi\)
\(114\) 0 0
\(115\) −5.32488 + 1.48236i −0.496548 + 0.138231i
\(116\) 0 0
\(117\) 0.176152i 0.0162852i
\(118\) 0 0
\(119\) 0.601099 0.0551026
\(120\) 0 0
\(121\) 5.27156 0.479233
\(122\) 0 0
\(123\) 0.0931527i 0.00839930i
\(124\) 0 0
\(125\) 8.13261 + 7.67207i 0.727403 + 0.686211i
\(126\) 0 0
\(127\) 8.12676i 0.721133i 0.932733 + 0.360567i \(0.117417\pi\)
−0.932733 + 0.360567i \(0.882583\pi\)
\(128\) 0 0
\(129\) 6.63231 0.583942
\(130\) 0 0
\(131\) −4.45229 −0.388998 −0.194499 0.980903i \(-0.562308\pi\)
−0.194499 + 0.980903i \(0.562308\pi\)
\(132\) 0 0
\(133\) 0.146689i 0.0127195i
\(134\) 0 0
\(135\) 2.15415 0.599682i 0.185400 0.0516125i
\(136\) 0 0
\(137\) 2.00903i 0.171643i −0.996311 0.0858217i \(-0.972648\pi\)
0.996311 0.0858217i \(-0.0273515\pi\)
\(138\) 0 0
\(139\) −14.3601 −1.21801 −0.609003 0.793168i \(-0.708430\pi\)
−0.609003 + 0.793168i \(0.708430\pi\)
\(140\) 0 0
\(141\) 8.43872 0.710669
\(142\) 0 0
\(143\) 0.710561i 0.0594201i
\(144\) 0 0
\(145\) −4.10765 14.7553i −0.341122 1.22536i
\(146\) 0 0
\(147\) 6.99394i 0.576850i
\(148\) 0 0
\(149\) −4.93926 −0.404640 −0.202320 0.979319i \(-0.564848\pi\)
−0.202320 + 0.979319i \(0.564848\pi\)
\(150\) 0 0
\(151\) 2.01310 0.163824 0.0819118 0.996640i \(-0.473897\pi\)
0.0819118 + 0.996640i \(0.473897\pi\)
\(152\) 0 0
\(153\) 7.72106i 0.624211i
\(154\) 0 0
\(155\) 4.46979 + 16.0562i 0.359022 + 1.28966i
\(156\) 0 0
\(157\) 9.56781i 0.763595i 0.924246 + 0.381797i \(0.124695\pi\)
−0.924246 + 0.381797i \(0.875305\pi\)
\(158\) 0 0
\(159\) −1.60464 −0.127256
\(160\) 0 0
\(161\) 0.192443 0.0151666
\(162\) 0 0
\(163\) 14.5402i 1.13888i −0.822033 0.569439i \(-0.807160\pi\)
0.822033 0.569439i \(-0.192840\pi\)
\(164\) 0 0
\(165\) 8.68943 2.41900i 0.676471 0.188319i
\(166\) 0 0
\(167\) 11.5213i 0.891542i 0.895147 + 0.445771i \(0.147070\pi\)
−0.895147 + 0.445771i \(0.852930\pi\)
\(168\) 0 0
\(169\) 12.9690 0.997613
\(170\) 0 0
\(171\) 1.88421 0.144089
\(172\) 0 0
\(173\) 4.32812i 0.329061i −0.986372 0.164530i \(-0.947389\pi\)
0.986372 0.164530i \(-0.0526109\pi\)
\(174\) 0 0
\(175\) −0.201139 0.333265i −0.0152047 0.0251925i
\(176\) 0 0
\(177\) 0.795026i 0.0597578i
\(178\) 0 0
\(179\) −0.803651 −0.0600677 −0.0300338 0.999549i \(-0.509562\pi\)
−0.0300338 + 0.999549i \(0.509562\pi\)
\(180\) 0 0
\(181\) 1.58419 0.117752 0.0588760 0.998265i \(-0.481248\pi\)
0.0588760 + 0.998265i \(0.481248\pi\)
\(182\) 0 0
\(183\) 5.94662i 0.439587i
\(184\) 0 0
\(185\) −7.91465 + 2.20331i −0.581897 + 0.161991i
\(186\) 0 0
\(187\) 31.1452i 2.27757i
\(188\) 0 0
\(189\) −0.0778518 −0.00566289
\(190\) 0 0
\(191\) −7.17923 −0.519471 −0.259736 0.965680i \(-0.583635\pi\)
−0.259736 + 0.965680i \(0.583635\pi\)
\(192\) 0 0
\(193\) 10.4401i 0.751492i 0.926723 + 0.375746i \(0.122613\pi\)
−0.926723 + 0.375746i \(0.877387\pi\)
\(194\) 0 0
\(195\) 0.105635 + 0.379458i 0.00756468 + 0.0271735i
\(196\) 0 0
\(197\) 17.5284i 1.24884i −0.781087 0.624422i \(-0.785335\pi\)
0.781087 0.624422i \(-0.214665\pi\)
\(198\) 0 0
\(199\) 4.68951 0.332430 0.166215 0.986090i \(-0.446845\pi\)
0.166215 + 0.986090i \(0.446845\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 0.533262i 0.0374277i
\(204\) 0 0
\(205\) 0.0558621 + 0.200665i 0.00390158 + 0.0140151i
\(206\) 0 0
\(207\) 2.47191i 0.171810i
\(208\) 0 0
\(209\) 7.60052 0.525739
\(210\) 0 0
\(211\) 24.4865 1.68572 0.842860 0.538133i \(-0.180870\pi\)
0.842860 + 0.538133i \(0.180870\pi\)
\(212\) 0 0
\(213\) 10.2043i 0.699188i
\(214\) 0 0
\(215\) 14.2870 3.97728i 0.974367 0.271248i
\(216\) 0 0
\(217\) 0.580276i 0.0393917i
\(218\) 0 0
\(219\) −0.963933 −0.0651365
\(220\) 0 0
\(221\) −1.36008 −0.0914887
\(222\) 0 0
\(223\) 8.35896i 0.559758i −0.960035 0.279879i \(-0.909706\pi\)
0.960035 0.279879i \(-0.0902943\pi\)
\(224\) 0 0
\(225\) 4.28076 2.58362i 0.285384 0.172241i
\(226\) 0 0
\(227\) 20.3926i 1.35350i 0.736212 + 0.676751i \(0.236613\pi\)
−0.736212 + 0.676751i \(0.763387\pi\)
\(228\) 0 0
\(229\) 6.28122 0.415074 0.207537 0.978227i \(-0.433455\pi\)
0.207537 + 0.978227i \(0.433455\pi\)
\(230\) 0 0
\(231\) −0.314039 −0.0206622
\(232\) 0 0
\(233\) 17.2508i 1.13014i 0.825043 + 0.565070i \(0.191151\pi\)
−0.825043 + 0.565070i \(0.808849\pi\)
\(234\) 0 0
\(235\) 18.1783 5.06055i 1.18582 0.330114i
\(236\) 0 0
\(237\) 13.7522i 0.893303i
\(238\) 0 0
\(239\) 16.1232 1.04292 0.521461 0.853275i \(-0.325387\pi\)
0.521461 + 0.853275i \(0.325387\pi\)
\(240\) 0 0
\(241\) 10.5061 0.676757 0.338379 0.941010i \(-0.390122\pi\)
0.338379 + 0.941010i \(0.390122\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −4.19414 15.0660i −0.267954 0.962533i
\(246\) 0 0
\(247\) 0.331906i 0.0211187i
\(248\) 0 0
\(249\) 5.08460 0.322224
\(250\) 0 0
\(251\) −23.0076 −1.45223 −0.726114 0.687574i \(-0.758675\pi\)
−0.726114 + 0.687574i \(0.758675\pi\)
\(252\) 0 0
\(253\) 9.97121i 0.626884i
\(254\) 0 0
\(255\) 4.63019 + 16.6324i 0.289954 + 1.04156i
\(256\) 0 0
\(257\) 10.9038i 0.680163i −0.940396 0.340082i \(-0.889545\pi\)
0.940396 0.340082i \(-0.110455\pi\)
\(258\) 0 0
\(259\) 0.286038 0.0177735
\(260\) 0 0
\(261\) −6.84971 −0.423986
\(262\) 0 0
\(263\) 9.75034i 0.601232i 0.953745 + 0.300616i \(0.0971922\pi\)
−0.953745 + 0.300616i \(0.902808\pi\)
\(264\) 0 0
\(265\) −3.45665 + 0.962276i −0.212340 + 0.0591122i
\(266\) 0 0
\(267\) 12.5250i 0.766515i
\(268\) 0 0
\(269\) −10.3564 −0.631442 −0.315721 0.948852i \(-0.602246\pi\)
−0.315721 + 0.948852i \(0.602246\pi\)
\(270\) 0 0
\(271\) 0.270042 0.0164039 0.00820194 0.999966i \(-0.497389\pi\)
0.00820194 + 0.999966i \(0.497389\pi\)
\(272\) 0 0
\(273\) 0.0137137i 0.000829993i
\(274\) 0 0
\(275\) 17.2677 10.4218i 1.04128 0.628458i
\(276\) 0 0
\(277\) 25.9341i 1.55823i 0.626883 + 0.779113i \(0.284330\pi\)
−0.626883 + 0.779113i \(0.715670\pi\)
\(278\) 0 0
\(279\) 7.45359 0.446235
\(280\) 0 0
\(281\) −10.2757 −0.612996 −0.306498 0.951871i \(-0.599157\pi\)
−0.306498 + 0.951871i \(0.599157\pi\)
\(282\) 0 0
\(283\) 0.341083i 0.0202753i 0.999949 + 0.0101377i \(0.00322697\pi\)
−0.999949 + 0.0101377i \(0.996773\pi\)
\(284\) 0 0
\(285\) 4.05887 1.12993i 0.240427 0.0669310i
\(286\) 0 0
\(287\) 0.00725211i 0.000428079i
\(288\) 0 0
\(289\) −42.6148 −2.50675
\(290\) 0 0
\(291\) 13.8335 0.810936
\(292\) 0 0
\(293\) 6.82592i 0.398775i −0.979921 0.199387i \(-0.936105\pi\)
0.979921 0.199387i \(-0.0638952\pi\)
\(294\) 0 0
\(295\) 0.476763 + 1.71261i 0.0277582 + 0.0997119i
\(296\) 0 0
\(297\) 4.03380i 0.234065i
\(298\) 0 0
\(299\) −0.435432 −0.0251817
\(300\) 0 0
\(301\) −0.516337 −0.0297612
\(302\) 0 0
\(303\) 15.7346i 0.903932i
\(304\) 0 0
\(305\) 3.56609 + 12.8099i 0.204193 + 0.733495i
\(306\) 0 0
\(307\) 12.0892i 0.689968i 0.938609 + 0.344984i \(0.112116\pi\)
−0.938609 + 0.344984i \(0.887884\pi\)
\(308\) 0 0
\(309\) −13.3508 −0.759503
\(310\) 0 0
\(311\) −14.4102 −0.817128 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(312\) 0 0
\(313\) 6.05120i 0.342034i 0.985268 + 0.171017i \(0.0547053\pi\)
−0.985268 + 0.171017i \(0.945295\pi\)
\(314\) 0 0
\(315\) −0.167705 + 0.0466864i −0.00944910 + 0.00263048i
\(316\) 0 0
\(317\) 4.43387i 0.249031i −0.992218 0.124515i \(-0.960262\pi\)
0.992218 0.124515i \(-0.0397376\pi\)
\(318\) 0 0
\(319\) −27.6304 −1.54700
\(320\) 0 0
\(321\) 4.89148 0.273016
\(322\) 0 0
\(323\) 14.5481i 0.809477i
\(324\) 0 0
\(325\) 0.455108 + 0.754063i 0.0252449 + 0.0418279i
\(326\) 0 0
\(327\) 13.4979i 0.746433i
\(328\) 0 0
\(329\) −0.656970 −0.0362199
\(330\) 0 0
\(331\) −11.5281 −0.633643 −0.316821 0.948485i \(-0.602616\pi\)
−0.316821 + 0.948485i \(0.602616\pi\)
\(332\) 0 0
\(333\) 3.67413i 0.201341i
\(334\) 0 0
\(335\) −2.15415 + 0.599682i −0.117694 + 0.0327642i
\(336\) 0 0
\(337\) 9.88171i 0.538291i −0.963099 0.269146i \(-0.913259\pi\)
0.963099 0.269146i \(-0.0867413\pi\)
\(338\) 0 0
\(339\) 8.95878 0.486574
\(340\) 0 0
\(341\) 30.0663 1.62818
\(342\) 0 0
\(343\) 1.08945i 0.0588250i
\(344\) 0 0
\(345\) 1.48236 + 5.32488i 0.0798077 + 0.286682i
\(346\) 0 0
\(347\) 25.9320i 1.39210i −0.717992 0.696051i \(-0.754939\pi\)
0.717992 0.696051i \(-0.245061\pi\)
\(348\) 0 0
\(349\) −30.1666 −1.61478 −0.807390 0.590018i \(-0.799121\pi\)
−0.807390 + 0.590018i \(0.799121\pi\)
\(350\) 0 0
\(351\) 0.176152 0.00940228
\(352\) 0 0
\(353\) 17.6545i 0.939652i −0.882759 0.469826i \(-0.844317\pi\)
0.882759 0.469826i \(-0.155683\pi\)
\(354\) 0 0
\(355\) −6.11934 21.9817i −0.324781 1.16667i
\(356\) 0 0
\(357\) 0.601099i 0.0318135i
\(358\) 0 0
\(359\) 6.56411 0.346440 0.173220 0.984883i \(-0.444583\pi\)
0.173220 + 0.984883i \(0.444583\pi\)
\(360\) 0 0
\(361\) −15.4498 −0.813146
\(362\) 0 0
\(363\) 5.27156i 0.276685i
\(364\) 0 0
\(365\) −2.07646 + 0.578054i −0.108687 + 0.0302567i
\(366\) 0 0
\(367\) 17.8986i 0.934299i 0.884178 + 0.467149i \(0.154719\pi\)
−0.884178 + 0.467149i \(0.845281\pi\)
\(368\) 0 0
\(369\) 0.0931527 0.00484934
\(370\) 0 0
\(371\) 0.124924 0.00648575
\(372\) 0 0
\(373\) 27.6803i 1.43323i −0.697469 0.716615i \(-0.745691\pi\)
0.697469 0.716615i \(-0.254309\pi\)
\(374\) 0 0
\(375\) 7.67207 8.13261i 0.396184 0.419966i
\(376\) 0 0
\(377\) 1.20659i 0.0621424i
\(378\) 0 0
\(379\) −2.80412 −0.144038 −0.0720189 0.997403i \(-0.522944\pi\)
−0.0720189 + 0.997403i \(0.522944\pi\)
\(380\) 0 0
\(381\) 8.12676 0.416346
\(382\) 0 0
\(383\) 26.6124i 1.35983i 0.733290 + 0.679916i \(0.237984\pi\)
−0.733290 + 0.679916i \(0.762016\pi\)
\(384\) 0 0
\(385\) −0.676488 + 0.188324i −0.0344770 + 0.00959786i
\(386\) 0 0
\(387\) 6.63231i 0.337139i
\(388\) 0 0
\(389\) −14.1640 −0.718144 −0.359072 0.933310i \(-0.616907\pi\)
−0.359072 + 0.933310i \(0.616907\pi\)
\(390\) 0 0
\(391\) −19.0858 −0.965210
\(392\) 0 0
\(393\) 4.45229i 0.224588i
\(394\) 0 0
\(395\) 8.24697 + 29.6244i 0.414950 + 1.49057i
\(396\) 0 0
\(397\) 17.3011i 0.868316i −0.900837 0.434158i \(-0.857046\pi\)
0.900837 0.434158i \(-0.142954\pi\)
\(398\) 0 0
\(399\) −0.146689 −0.00734363
\(400\) 0 0
\(401\) 28.8970 1.44305 0.721524 0.692389i \(-0.243442\pi\)
0.721524 + 0.692389i \(0.243442\pi\)
\(402\) 0 0
\(403\) 1.31296i 0.0654033i
\(404\) 0 0
\(405\) −0.599682 2.15415i −0.0297985 0.107041i
\(406\) 0 0
\(407\) 14.8207i 0.734636i
\(408\) 0 0
\(409\) −32.7055 −1.61718 −0.808592 0.588370i \(-0.799770\pi\)
−0.808592 + 0.588370i \(0.799770\pi\)
\(410\) 0 0
\(411\) −2.00903 −0.0990983
\(412\) 0 0
\(413\) 0.0618942i 0.00304562i
\(414\) 0 0
\(415\) 10.9530 3.04915i 0.537663 0.149677i
\(416\) 0 0
\(417\) 14.3601i 0.703216i
\(418\) 0 0
\(419\) −21.4604 −1.04841 −0.524204 0.851593i \(-0.675637\pi\)
−0.524204 + 0.851593i \(0.675637\pi\)
\(420\) 0 0
\(421\) 8.40929 0.409844 0.204922 0.978778i \(-0.434306\pi\)
0.204922 + 0.978778i \(0.434306\pi\)
\(422\) 0 0
\(423\) 8.43872i 0.410305i
\(424\) 0 0
\(425\) 19.9483 + 33.0520i 0.967633 + 1.60326i
\(426\) 0 0
\(427\) 0.462955i 0.0224040i
\(428\) 0 0
\(429\) 0.710561 0.0343062
\(430\) 0 0
\(431\) −9.99239 −0.481317 −0.240658 0.970610i \(-0.577363\pi\)
−0.240658 + 0.970610i \(0.577363\pi\)
\(432\) 0 0
\(433\) 8.63842i 0.415136i 0.978221 + 0.207568i \(0.0665548\pi\)
−0.978221 + 0.207568i \(0.933445\pi\)
\(434\) 0 0
\(435\) −14.7553 + 4.10765i −0.707464 + 0.196947i
\(436\) 0 0
\(437\) 4.65759i 0.222803i
\(438\) 0 0
\(439\) −9.55805 −0.456181 −0.228090 0.973640i \(-0.573248\pi\)
−0.228090 + 0.973640i \(0.573248\pi\)
\(440\) 0 0
\(441\) −6.99394 −0.333045
\(442\) 0 0
\(443\) 10.9529i 0.520390i −0.965556 0.260195i \(-0.916213\pi\)
0.965556 0.260195i \(-0.0837868\pi\)
\(444\) 0 0
\(445\) 7.51100 + 26.9807i 0.356056 + 1.27901i
\(446\) 0 0
\(447\) 4.93926i 0.233619i
\(448\) 0 0
\(449\) 13.1449 0.620346 0.310173 0.950680i \(-0.399613\pi\)
0.310173 + 0.950680i \(0.399613\pi\)
\(450\) 0 0
\(451\) 0.375760 0.0176938
\(452\) 0 0
\(453\) 2.01310i 0.0945836i
\(454\) 0 0
\(455\) −0.00822388 0.0295415i −0.000385542 0.00138493i
\(456\) 0 0
\(457\) 39.5239i 1.84885i −0.381364 0.924425i \(-0.624546\pi\)
0.381364 0.924425i \(-0.375454\pi\)
\(458\) 0 0
\(459\) 7.72106 0.360388
\(460\) 0 0
\(461\) 5.13801 0.239301 0.119650 0.992816i \(-0.461823\pi\)
0.119650 + 0.992816i \(0.461823\pi\)
\(462\) 0 0
\(463\) 40.6052i 1.88708i 0.331255 + 0.943541i \(0.392528\pi\)
−0.331255 + 0.943541i \(0.607472\pi\)
\(464\) 0 0
\(465\) 16.0562 4.46979i 0.744588 0.207281i
\(466\) 0 0
\(467\) 38.8979i 1.79998i −0.435910 0.899990i \(-0.643573\pi\)
0.435910 0.899990i \(-0.356427\pi\)
\(468\) 0 0
\(469\) 0.0778518 0.00359486
\(470\) 0 0
\(471\) 9.56781 0.440862
\(472\) 0 0
\(473\) 26.7534i 1.23012i
\(474\) 0 0
\(475\) 8.06584 4.86807i 0.370086 0.223362i
\(476\) 0 0
\(477\) 1.60464i 0.0734715i
\(478\) 0 0
\(479\) 21.2898 0.972756 0.486378 0.873748i \(-0.338318\pi\)
0.486378 + 0.873748i \(0.338318\pi\)
\(480\) 0 0
\(481\) −0.647205 −0.0295100
\(482\) 0 0
\(483\) 0.192443i 0.00875646i
\(484\) 0 0
\(485\) 29.7995 8.29572i 1.35313 0.376689i
\(486\) 0 0
\(487\) 11.0189i 0.499312i 0.968335 + 0.249656i \(0.0803176\pi\)
−0.968335 + 0.249656i \(0.919682\pi\)
\(488\) 0 0
\(489\) −14.5402 −0.657532
\(490\) 0 0
\(491\) 19.5214 0.880989 0.440495 0.897755i \(-0.354803\pi\)
0.440495 + 0.897755i \(0.354803\pi\)
\(492\) 0 0
\(493\) 52.8870i 2.38191i
\(494\) 0 0
\(495\) −2.41900 8.68943i −0.108726 0.390561i
\(496\) 0 0
\(497\) 0.794424i 0.0356348i
\(498\) 0 0
\(499\) −15.7073 −0.703157 −0.351579 0.936158i \(-0.614355\pi\)
−0.351579 + 0.936158i \(0.614355\pi\)
\(500\) 0 0
\(501\) 11.5213 0.514732
\(502\) 0 0
\(503\) 11.1273i 0.496144i −0.968742 0.248072i \(-0.920203\pi\)
0.968742 0.248072i \(-0.0797969\pi\)
\(504\) 0 0
\(505\) −9.43579 33.8948i −0.419887 1.50830i
\(506\) 0 0
\(507\) 12.9690i 0.575972i
\(508\) 0 0
\(509\) −39.8436 −1.76604 −0.883019 0.469338i \(-0.844493\pi\)
−0.883019 + 0.469338i \(0.844493\pi\)
\(510\) 0 0
\(511\) 0.0750439 0.00331975
\(512\) 0 0
\(513\) 1.88421i 0.0831897i
\(514\) 0 0
\(515\) −28.7598 + 8.00627i −1.26731 + 0.352798i
\(516\) 0 0
\(517\) 34.0401i 1.49708i
\(518\) 0 0
\(519\) −4.32812 −0.189983
\(520\) 0 0
\(521\) 5.17332 0.226647 0.113324 0.993558i \(-0.463850\pi\)
0.113324 + 0.993558i \(0.463850\pi\)
\(522\) 0 0
\(523\) 42.9653i 1.87874i −0.342902 0.939371i \(-0.611410\pi\)
0.342902 0.939371i \(-0.388590\pi\)
\(524\) 0 0
\(525\) −0.333265 + 0.201139i −0.0145449 + 0.00877844i
\(526\) 0 0
\(527\) 57.5496i 2.50690i
\(528\) 0 0
\(529\) 16.8896 0.734332
\(530\) 0 0
\(531\) 0.795026 0.0345012
\(532\) 0 0
\(533\) 0.0164090i 0.000710753i
\(534\) 0 0
\(535\) 10.5370 2.93333i 0.455554 0.126819i
\(536\) 0 0
\(537\) 0.803651i 0.0346801i
\(538\) 0 0
\(539\) −28.2122 −1.21518
\(540\) 0 0
\(541\) −42.3274 −1.81980 −0.909899 0.414830i \(-0.863841\pi\)
−0.909899 + 0.414830i \(0.863841\pi\)
\(542\) 0 0
\(543\) 1.58419i 0.0679841i
\(544\) 0 0
\(545\) 8.09443 + 29.0765i 0.346727 + 1.24550i
\(546\) 0 0
\(547\) 0.119998i 0.00513075i −0.999997 0.00256537i \(-0.999183\pi\)
0.999997 0.00256537i \(-0.000816585\pi\)
\(548\) 0 0
\(549\) 5.94662 0.253796
\(550\) 0 0
\(551\) −12.9063 −0.549825
\(552\) 0 0
\(553\) 1.07064i 0.0455281i
\(554\) 0 0
\(555\) 2.20331 + 7.91465i 0.0935254 + 0.335958i
\(556\) 0 0
\(557\) 1.87818i 0.0795812i −0.999208 0.0397906i \(-0.987331\pi\)
0.999208 0.0397906i \(-0.0126691\pi\)
\(558\) 0 0
\(559\) 1.16829 0.0494135
\(560\) 0 0
\(561\) 31.1452 1.31495
\(562\) 0 0
\(563\) 0.0755137i 0.00318252i 0.999999 + 0.00159126i \(0.000506515\pi\)
−0.999999 + 0.00159126i \(0.999493\pi\)
\(564\) 0 0
\(565\) 19.2986 5.37242i 0.811898 0.226019i
\(566\) 0 0
\(567\) 0.0778518i 0.00326947i
\(568\) 0 0
\(569\) 14.7697 0.619179 0.309589 0.950870i \(-0.399808\pi\)
0.309589 + 0.950870i \(0.399808\pi\)
\(570\) 0 0
\(571\) 7.45240 0.311873 0.155937 0.987767i \(-0.450160\pi\)
0.155937 + 0.987767i \(0.450160\pi\)
\(572\) 0 0
\(573\) 7.17923i 0.299917i
\(574\) 0 0
\(575\) 6.38648 + 10.5817i 0.266335 + 0.441286i
\(576\) 0 0
\(577\) 16.8741i 0.702477i 0.936286 + 0.351239i \(0.114239\pi\)
−0.936286 + 0.351239i \(0.885761\pi\)
\(578\) 0 0
\(579\) 10.4401 0.433874
\(580\) 0 0
\(581\) −0.395846 −0.0164224
\(582\) 0 0
\(583\) 6.47281i 0.268076i
\(584\) 0 0
\(585\) 0.379458 0.105635i 0.0156887 0.00436747i
\(586\) 0 0
\(587\) 31.7975i 1.31242i −0.754576 0.656212i \(-0.772158\pi\)
0.754576 0.656212i \(-0.227842\pi\)
\(588\) 0 0
\(589\) 14.0441 0.578677
\(590\) 0 0
\(591\) −17.5284 −0.721020
\(592\) 0 0
\(593\) 11.0814i 0.455059i 0.973771 + 0.227530i \(0.0730649\pi\)
−0.973771 + 0.227530i \(0.926935\pi\)
\(594\) 0 0
\(595\) −0.360468 1.29486i −0.0147778 0.0530841i
\(596\) 0 0
\(597\) 4.68951i 0.191929i
\(598\) 0 0
\(599\) −4.51312 −0.184401 −0.0922005 0.995740i \(-0.529390\pi\)
−0.0922005 + 0.995740i \(0.529390\pi\)
\(600\) 0 0
\(601\) −1.03044 −0.0420325 −0.0210163 0.999779i \(-0.506690\pi\)
−0.0210163 + 0.999779i \(0.506690\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −3.16126 11.3558i −0.128524 0.461677i
\(606\) 0 0
\(607\) 16.2834i 0.660924i −0.943819 0.330462i \(-0.892795\pi\)
0.943819 0.330462i \(-0.107205\pi\)
\(608\) 0 0
\(609\) 0.533262 0.0216089
\(610\) 0 0
\(611\) 1.48650 0.0601372
\(612\) 0 0
\(613\) 24.9121i 1.00619i −0.864231 0.503095i \(-0.832195\pi\)
0.864231 0.503095i \(-0.167805\pi\)
\(614\) 0 0
\(615\) 0.200665 0.0558621i 0.00809161 0.00225258i
\(616\) 0 0
\(617\) 1.55603i 0.0626433i −0.999509 0.0313217i \(-0.990028\pi\)
0.999509 0.0313217i \(-0.00997163\pi\)
\(618\) 0 0
\(619\) −34.3980 −1.38257 −0.691286 0.722582i \(-0.742955\pi\)
−0.691286 + 0.722582i \(0.742955\pi\)
\(620\) 0 0
\(621\) 2.47191 0.0991945
\(622\) 0 0
\(623\) 0.975091i 0.0390662i
\(624\) 0 0
\(625\) 11.6498 22.1197i 0.465994 0.884788i
\(626\) 0 0
\(627\) 7.60052i 0.303535i
\(628\) 0 0
\(629\) −28.3682 −1.13111
\(630\) 0 0
\(631\) −12.4889 −0.497176 −0.248588 0.968609i \(-0.579967\pi\)
−0.248588 + 0.968609i \(0.579967\pi\)
\(632\) 0 0
\(633\) 24.4865i 0.973251i
\(634\) 0 0
\(635\) 17.5063 4.87347i 0.694716 0.193398i
\(636\) 0 0
\(637\) 1.23199i 0.0488134i
\(638\) 0 0
\(639\) −10.2043 −0.403676
\(640\) 0 0
\(641\) 41.0882 1.62289 0.811443 0.584431i \(-0.198682\pi\)
0.811443 + 0.584431i \(0.198682\pi\)
\(642\) 0 0
\(643\) 37.2853i 1.47039i 0.677857 + 0.735194i \(0.262909\pi\)
−0.677857 + 0.735194i \(0.737091\pi\)
\(644\) 0 0
\(645\) −3.97728 14.2870i −0.156605 0.562551i
\(646\) 0 0
\(647\) 4.45446i 0.175123i −0.996159 0.0875614i \(-0.972093\pi\)
0.996159 0.0875614i \(-0.0279074\pi\)
\(648\) 0 0
\(649\) 3.20698 0.125885
\(650\) 0 0
\(651\) −0.580276 −0.0227428
\(652\) 0 0
\(653\) 31.2109i 1.22138i −0.791872 0.610688i \(-0.790893\pi\)
0.791872 0.610688i \(-0.209107\pi\)
\(654\) 0 0
\(655\) 2.66996 + 9.59091i 0.104324 + 0.374748i
\(656\) 0 0
\(657\) 0.963933i 0.0376066i
\(658\) 0 0
\(659\) −13.1330 −0.511591 −0.255795 0.966731i \(-0.582337\pi\)
−0.255795 + 0.966731i \(0.582337\pi\)
\(660\) 0 0
\(661\) −34.1253 −1.32732 −0.663660 0.748034i \(-0.730998\pi\)
−0.663660 + 0.748034i \(0.730998\pi\)
\(662\) 0 0
\(663\) 1.36008i 0.0528211i
\(664\) 0 0
\(665\) −0.315991 + 0.0879668i −0.0122536 + 0.00341121i
\(666\) 0 0
\(667\) 16.9319i 0.655605i
\(668\) 0 0
\(669\) −8.35896 −0.323176
\(670\) 0 0
\(671\) 23.9875 0.926027
\(672\) 0 0
\(673\) 22.8699i 0.881571i −0.897612 0.440786i \(-0.854700\pi\)
0.897612 0.440786i \(-0.145300\pi\)
\(674\) 0 0
\(675\) −2.58362 4.28076i −0.0994435 0.164767i
\(676\) 0 0
\(677\) 46.7344i 1.79615i −0.439843 0.898075i \(-0.644966\pi\)
0.439843 0.898075i \(-0.355034\pi\)
\(678\) 0 0
\(679\) −1.07697 −0.0413301
\(680\) 0 0
\(681\) 20.3926 0.781445
\(682\) 0 0
\(683\) 31.1832i 1.19319i 0.802542 + 0.596596i \(0.203481\pi\)
−0.802542 + 0.596596i \(0.796519\pi\)
\(684\) 0 0
\(685\) −4.32777 + 1.20478i −0.165356 + 0.0460324i
\(686\) 0 0
\(687\) 6.28122i 0.239643i
\(688\) 0 0
\(689\) −0.282660 −0.0107685
\(690\) 0 0
\(691\) 5.21574 0.198416 0.0992080 0.995067i \(-0.468369\pi\)
0.0992080 + 0.995067i \(0.468369\pi\)
\(692\) 0 0
\(693\) 0.314039i 0.0119293i
\(694\) 0 0
\(695\) 8.61149 + 30.9338i 0.326652 + 1.17339i
\(696\) 0 0
\(697\) 0.719238i 0.0272431i
\(698\) 0 0
\(699\) 17.2508 0.652487
\(700\) 0 0
\(701\) 44.2520 1.67137 0.835687 0.549206i \(-0.185070\pi\)
0.835687 + 0.549206i \(0.185070\pi\)
\(702\) 0 0
\(703\) 6.92283i 0.261099i
\(704\) 0 0
\(705\) −5.06055 18.1783i −0.190592 0.684635i
\(706\) 0 0
\(707\) 1.22497i 0.0460698i
\(708\) 0 0
\(709\) −9.48585 −0.356249 −0.178124 0.984008i \(-0.557003\pi\)
−0.178124 + 0.984008i \(0.557003\pi\)
\(710\) 0 0
\(711\) 13.7522 0.515749
\(712\) 0 0
\(713\) 18.4246i 0.690008i
\(714\) 0 0
\(715\) 1.53066 0.426111i 0.0572434 0.0159356i
\(716\) 0 0
\(717\) 16.1232i 0.602131i
\(718\) 0 0
\(719\) −38.6200 −1.44028 −0.720141 0.693828i \(-0.755923\pi\)
−0.720141 + 0.693828i \(0.755923\pi\)
\(720\) 0 0
\(721\) 1.03939 0.0387088
\(722\) 0 0
\(723\) 10.5061i 0.390726i
\(724\) 0 0
\(725\) −29.3220 + 17.6970i −1.08899 + 0.657251i
\(726\) 0 0
\(727\) 43.5732i 1.61604i 0.589155 + 0.808020i \(0.299461\pi\)
−0.589155 + 0.808020i \(0.700539\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 51.2085 1.89401
\(732\) 0 0
\(733\) 5.25802i 0.194209i 0.995274 + 0.0971047i \(0.0309582\pi\)
−0.995274 + 0.0971047i \(0.969042\pi\)
\(734\) 0 0
\(735\) −15.0660 + 4.19414i −0.555719 + 0.154703i
\(736\) 0 0
\(737\) 4.03380i 0.148587i
\(738\) 0 0
\(739\) −26.6880 −0.981735 −0.490867 0.871234i \(-0.663320\pi\)
−0.490867 + 0.871234i \(0.663320\pi\)
\(740\) 0 0
\(741\) 0.331906 0.0121929
\(742\) 0 0
\(743\) 11.6192i 0.426268i 0.977023 + 0.213134i \(0.0683671\pi\)
−0.977023 + 0.213134i \(0.931633\pi\)
\(744\) 0 0
\(745\) 2.96199 + 10.6399i 0.108519 + 0.389817i
\(746\) 0 0
\(747\) 5.08460i 0.186036i
\(748\) 0 0
\(749\) −0.380810 −0.0139145
\(750\) 0 0
\(751\) 13.4994 0.492598 0.246299 0.969194i \(-0.420785\pi\)
0.246299 + 0.969194i \(0.420785\pi\)
\(752\) 0 0
\(753\) 23.0076i 0.838444i
\(754\) 0 0
\(755\) −1.20722 4.33653i −0.0439352 0.157822i
\(756\) 0 0
\(757\) 51.7616i 1.88131i −0.339371 0.940653i \(-0.610214\pi\)
0.339371 0.940653i \(-0.389786\pi\)
\(758\) 0 0
\(759\) 9.97121 0.361932
\(760\) 0 0
\(761\) −51.3327 −1.86081 −0.930404 0.366537i \(-0.880543\pi\)
−0.930404 + 0.366537i \(0.880543\pi\)
\(762\) 0 0
\(763\) 1.05083i 0.0380427i
\(764\) 0 0
\(765\) 16.6324 4.63019i 0.601344 0.167405i
\(766\) 0 0
\(767\) 0.140045i 0.00505674i
\(768\) 0 0
\(769\) −40.1613 −1.44825 −0.724127 0.689667i \(-0.757757\pi\)
−0.724127 + 0.689667i \(0.757757\pi\)
\(770\) 0 0
\(771\) −10.9038 −0.392692
\(772\) 0 0
\(773\) 35.3015i 1.26971i 0.772633 + 0.634853i \(0.218939\pi\)
−0.772633 + 0.634853i \(0.781061\pi\)
\(774\) 0 0
\(775\) 31.9071 19.2572i 1.14614 0.691740i
\(776\) 0 0
\(777\) 0.286038i 0.0102616i
\(778\) 0 0
\(779\) 0.175519 0.00628862
\(780\) 0 0
\(781\) −41.1622 −1.47290
\(782\) 0 0
\(783\) 6.84971i 0.244789i
\(784\) 0 0
\(785\) 20.6105 5.73765i 0.735622 0.204786i
\(786\) 0 0
\(787\) 37.9520i 1.35284i −0.736515 0.676421i \(-0.763530\pi\)
0.736515 0.676421i \(-0.236470\pi\)
\(788\) 0 0
\(789\) 9.75034 0.347121
\(790\) 0 0
\(791\) −0.697457 −0.0247987
\(792\)