Properties

Label 2205.2.d.l.1324.2
Level $2205$
Weight $2$
Character 2205.1324
Analytic conductor $17.607$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.6070136457\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1324.2
Root \(1.45161 + 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 2205.1324
Dual form 2205.2.d.l.1324.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +O(q^{10})\) \(q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +(4.21432 - 0.592104i) q^{10} -2.00000 q^{11} +6.42864i q^{13} -4.61285 q^{16} -4.42864i q^{17} -2.42864 q^{19} +(-0.504684 - 3.59210i) q^{20} +3.80642i q^{22} -1.37778i q^{23} +(-4.80642 + 1.37778i) q^{25} +12.2351 q^{26} +0.755569 q^{29} -5.18421 q^{31} +7.34122i q^{32} -8.42864 q^{34} -7.61285i q^{37} +4.62222i q^{38} +(1.59210 - 0.223688i) q^{40} -8.23506 q^{41} +10.1017i q^{43} +3.24443 q^{44} -2.62222 q^{46} -2.75557i q^{47} +(2.62222 + 9.14764i) q^{50} -10.4286i q^{52} -9.18421i q^{53} +(-0.622216 - 4.42864i) q^{55} -1.43801i q^{58} -14.1017 q^{59} -6.85728 q^{61} +9.86665i q^{62} +4.74620 q^{64} +(-14.2351 + 2.00000i) q^{65} -2.75557i q^{67} +7.18421i q^{68} -2.00000 q^{71} +1.57136i q^{73} -14.4889 q^{74} +3.93978 q^{76} +4.85728 q^{79} +(-1.43509 - 10.2143i) q^{80} +15.6731i q^{82} +11.6128i q^{83} +(9.80642 - 1.37778i) q^{85} +19.2257 q^{86} +1.43801i q^{88} -4.62222 q^{89} +2.23506i q^{92} -5.24443 q^{94} +(-0.755569 - 5.37778i) q^{95} -11.9398i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} + 12 q^{10} - 12 q^{11} + 26 q^{16} + 12 q^{19} - 30 q^{20} - 2 q^{25} + 20 q^{26} + 4 q^{29} - 4 q^{31} - 24 q^{34} - 4 q^{40} + 4 q^{41} + 20 q^{44} - 16 q^{46} + 16 q^{50} - 4 q^{55} - 32 q^{59} + 12 q^{61} - 26 q^{64} - 32 q^{65} - 12 q^{71} - 88 q^{74} - 4 q^{76} - 24 q^{79} + 46 q^{80} + 32 q^{85} + 8 q^{86} - 28 q^{89} - 32 q^{94} - 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).

\(n\) \(442\) \(1081\) \(1226\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90321i 1.34577i −0.739745 0.672887i \(-0.765054\pi\)
0.739745 0.672887i \(-0.234946\pi\)
\(3\) 0 0
\(4\) −1.62222 −0.811108
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) 0 0
\(7\) 0 0
\(8\) 0.719004i 0.254206i
\(9\) 0 0
\(10\) 4.21432 0.592104i 1.33268 0.187240i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 6.42864i 1.78298i 0.453037 + 0.891492i \(0.350341\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.61285 −1.15321
\(17\) 4.42864i 1.07410i −0.843550 0.537051i \(-0.819538\pi\)
0.843550 0.537051i \(-0.180462\pi\)
\(18\) 0 0
\(19\) −2.42864 −0.557168 −0.278584 0.960412i \(-0.589865\pi\)
−0.278584 + 0.960412i \(0.589865\pi\)
\(20\) −0.504684 3.59210i −0.112851 0.803219i
\(21\) 0 0
\(22\) 3.80642i 0.811532i
\(23\) 1.37778i 0.287288i −0.989629 0.143644i \(-0.954118\pi\)
0.989629 0.143644i \(-0.0458820\pi\)
\(24\) 0 0
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) 12.2351 2.39949
\(27\) 0 0
\(28\) 0 0
\(29\) 0.755569 0.140306 0.0701528 0.997536i \(-0.477651\pi\)
0.0701528 + 0.997536i \(0.477651\pi\)
\(30\) 0 0
\(31\) −5.18421 −0.931111 −0.465556 0.885019i \(-0.654145\pi\)
−0.465556 + 0.885019i \(0.654145\pi\)
\(32\) 7.34122i 1.29776i
\(33\) 0 0
\(34\) −8.42864 −1.44550
\(35\) 0 0
\(36\) 0 0
\(37\) 7.61285i 1.25154i −0.780006 0.625772i \(-0.784784\pi\)
0.780006 0.625772i \(-0.215216\pi\)
\(38\) 4.62222i 0.749822i
\(39\) 0 0
\(40\) 1.59210 0.223688i 0.251734 0.0353681i
\(41\) −8.23506 −1.28610 −0.643050 0.765824i \(-0.722331\pi\)
−0.643050 + 0.765824i \(0.722331\pi\)
\(42\) 0 0
\(43\) 10.1017i 1.54050i 0.637744 + 0.770248i \(0.279868\pi\)
−0.637744 + 0.770248i \(0.720132\pi\)
\(44\) 3.24443 0.489116
\(45\) 0 0
\(46\) −2.62222 −0.386625
\(47\) 2.75557i 0.401941i −0.979597 0.200971i \(-0.935590\pi\)
0.979597 0.200971i \(-0.0644095\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.62222 + 9.14764i 0.370837 + 1.29367i
\(51\) 0 0
\(52\) 10.4286i 1.44619i
\(53\) 9.18421i 1.26155i −0.775967 0.630774i \(-0.782737\pi\)
0.775967 0.630774i \(-0.217263\pi\)
\(54\) 0 0
\(55\) −0.622216 4.42864i −0.0838995 0.597158i
\(56\) 0 0
\(57\) 0 0
\(58\) 1.43801i 0.188820i
\(59\) −14.1017 −1.83589 −0.917943 0.396712i \(-0.870151\pi\)
−0.917943 + 0.396712i \(0.870151\pi\)
\(60\) 0 0
\(61\) −6.85728 −0.877985 −0.438992 0.898491i \(-0.644664\pi\)
−0.438992 + 0.898491i \(0.644664\pi\)
\(62\) 9.86665i 1.25307i
\(63\) 0 0
\(64\) 4.74620 0.593275
\(65\) −14.2351 + 2.00000i −1.76564 + 0.248069i
\(66\) 0 0
\(67\) 2.75557i 0.336646i −0.985732 0.168323i \(-0.946165\pi\)
0.985732 0.168323i \(-0.0538352\pi\)
\(68\) 7.18421i 0.871213i
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 1.57136i 0.183914i 0.995763 + 0.0919569i \(0.0293122\pi\)
−0.995763 + 0.0919569i \(0.970688\pi\)
\(74\) −14.4889 −1.68430
\(75\) 0 0
\(76\) 3.93978 0.451923
\(77\) 0 0
\(78\) 0 0
\(79\) 4.85728 0.546487 0.273243 0.961945i \(-0.411904\pi\)
0.273243 + 0.961945i \(0.411904\pi\)
\(80\) −1.43509 10.2143i −0.160448 1.14200i
\(81\) 0 0
\(82\) 15.6731i 1.73080i
\(83\) 11.6128i 1.27468i 0.770585 + 0.637338i \(0.219964\pi\)
−0.770585 + 0.637338i \(0.780036\pi\)
\(84\) 0 0
\(85\) 9.80642 1.37778i 1.06366 0.149442i
\(86\) 19.2257 2.07316
\(87\) 0 0
\(88\) 1.43801i 0.153292i
\(89\) −4.62222 −0.489954 −0.244977 0.969529i \(-0.578780\pi\)
−0.244977 + 0.969529i \(0.578780\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.23506i 0.233021i
\(93\) 0 0
\(94\) −5.24443 −0.540922
\(95\) −0.755569 5.37778i −0.0775197 0.551749i
\(96\) 0 0
\(97\) 11.9398i 1.21230i −0.795350 0.606150i \(-0.792713\pi\)
0.795350 0.606150i \(-0.207287\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 7.79706 2.23506i 0.779706 0.223506i
\(101\) 1.47949 0.147215 0.0736076 0.997287i \(-0.476549\pi\)
0.0736076 + 0.997287i \(0.476549\pi\)
\(102\) 0 0
\(103\) 8.85728i 0.872734i 0.899769 + 0.436367i \(0.143735\pi\)
−0.899769 + 0.436367i \(0.856265\pi\)
\(104\) 4.62222 0.453246
\(105\) 0 0
\(106\) −17.4795 −1.69776
\(107\) 1.76494i 0.170623i 0.996354 + 0.0853114i \(0.0271885\pi\)
−0.996354 + 0.0853114i \(0.972811\pi\)
\(108\) 0 0
\(109\) −5.61285 −0.537613 −0.268807 0.963194i \(-0.586629\pi\)
−0.268807 + 0.963194i \(0.586629\pi\)
\(110\) −8.42864 + 1.18421i −0.803639 + 0.112910i
\(111\) 0 0
\(112\) 0 0
\(113\) 11.2859i 1.06169i 0.847469 + 0.530845i \(0.178125\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(114\) 0 0
\(115\) 3.05086 0.428639i 0.284494 0.0399708i
\(116\) −1.22570 −0.113803
\(117\) 0 0
\(118\) 26.8385i 2.47069i
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 13.0509i 1.18157i
\(123\) 0 0
\(124\) 8.40990 0.755232
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) 0 0
\(127\) 12.8573i 1.14090i 0.821333 + 0.570450i \(0.193231\pi\)
−0.821333 + 0.570450i \(0.806769\pi\)
\(128\) 5.64941i 0.499342i
\(129\) 0 0
\(130\) 3.80642 + 27.0923i 0.333845 + 2.37616i
\(131\) −2.10171 −0.183627 −0.0918136 0.995776i \(-0.529266\pi\)
−0.0918136 + 0.995776i \(0.529266\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.24443 −0.453050
\(135\) 0 0
\(136\) −3.18421 −0.273044
\(137\) 15.9398i 1.36183i 0.732364 + 0.680914i \(0.238417\pi\)
−0.732364 + 0.680914i \(0.761583\pi\)
\(138\) 0 0
\(139\) 11.6731 0.990097 0.495048 0.868865i \(-0.335150\pi\)
0.495048 + 0.868865i \(0.335150\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.80642i 0.319428i
\(143\) 12.8573i 1.07518i
\(144\) 0 0
\(145\) 0.235063 + 1.67307i 0.0195209 + 0.138941i
\(146\) 2.99063 0.247506
\(147\) 0 0
\(148\) 12.3497i 1.01514i
\(149\) −21.2257 −1.73888 −0.869438 0.494041i \(-0.835519\pi\)
−0.869438 + 0.494041i \(0.835519\pi\)
\(150\) 0 0
\(151\) 16.8573 1.37183 0.685913 0.727684i \(-0.259403\pi\)
0.685913 + 0.727684i \(0.259403\pi\)
\(152\) 1.74620i 0.141636i
\(153\) 0 0
\(154\) 0 0
\(155\) −1.61285 11.4795i −0.129547 0.922055i
\(156\) 0 0
\(157\) 10.4286i 0.832296i −0.909297 0.416148i \(-0.863380\pi\)
0.909297 0.416148i \(-0.136620\pi\)
\(158\) 9.24443i 0.735447i
\(159\) 0 0
\(160\) −16.2558 + 2.28391i −1.28513 + 0.180559i
\(161\) 0 0
\(162\) 0 0
\(163\) 20.8573i 1.63367i 0.576873 + 0.816834i \(0.304273\pi\)
−0.576873 + 0.816834i \(0.695727\pi\)
\(164\) 13.3590 1.04317
\(165\) 0 0
\(166\) 22.1017 1.71543
\(167\) 15.3461i 1.18752i −0.804642 0.593760i \(-0.797643\pi\)
0.804642 0.593760i \(-0.202357\pi\)
\(168\) 0 0
\(169\) −28.3274 −2.17903
\(170\) −2.62222 18.6637i −0.201115 1.43144i
\(171\) 0 0
\(172\) 16.3872i 1.24951i
\(173\) 2.06022i 0.156636i 0.996928 + 0.0783179i \(0.0249549\pi\)
−0.996928 + 0.0783179i \(0.975045\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.22570 0.695413
\(177\) 0 0
\(178\) 8.79706i 0.659367i
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 12.1017 0.899513 0.449757 0.893151i \(-0.351511\pi\)
0.449757 + 0.893151i \(0.351511\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.990632 −0.0730304
\(185\) 16.8573 2.36842i 1.23937 0.174129i
\(186\) 0 0
\(187\) 8.85728i 0.647708i
\(188\) 4.47013i 0.326017i
\(189\) 0 0
\(190\) −10.2351 + 1.43801i −0.742530 + 0.104324i
\(191\) −0.488863 −0.0353729 −0.0176864 0.999844i \(-0.505630\pi\)
−0.0176864 + 0.999844i \(0.505630\pi\)
\(192\) 0 0
\(193\) 22.9590i 1.65262i −0.563212 0.826312i \(-0.690435\pi\)
0.563212 0.826312i \(-0.309565\pi\)
\(194\) −22.7239 −1.63148
\(195\) 0 0
\(196\) 0 0
\(197\) 1.18421i 0.0843713i −0.999110 0.0421857i \(-0.986568\pi\)
0.999110 0.0421857i \(-0.0134321\pi\)
\(198\) 0 0
\(199\) 8.79706 0.623607 0.311803 0.950147i \(-0.399067\pi\)
0.311803 + 0.950147i \(0.399067\pi\)
\(200\) 0.990632 + 3.45584i 0.0700483 + 0.244365i
\(201\) 0 0
\(202\) 2.81579i 0.198118i
\(203\) 0 0
\(204\) 0 0
\(205\) −2.56199 18.2351i −0.178937 1.27359i
\(206\) 16.8573 1.17450
\(207\) 0 0
\(208\) 29.6543i 2.05616i
\(209\) 4.85728 0.335985
\(210\) 0 0
\(211\) 23.2257 1.59892 0.799461 0.600717i \(-0.205118\pi\)
0.799461 + 0.600717i \(0.205118\pi\)
\(212\) 14.8988i 1.02325i
\(213\) 0 0
\(214\) 3.35905 0.229620
\(215\) −22.3684 + 3.14272i −1.52551 + 0.214332i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.6824i 0.723506i
\(219\) 0 0
\(220\) 1.00937 + 7.18421i 0.0680516 + 0.484359i
\(221\) 28.4701 1.91511
\(222\) 0 0
\(223\) 15.2257i 1.01959i 0.860297 + 0.509794i \(0.170278\pi\)
−0.860297 + 0.509794i \(0.829722\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 21.4795 1.42879
\(227\) 14.3684i 0.953665i 0.878994 + 0.476833i \(0.158215\pi\)
−0.878994 + 0.476833i \(0.841785\pi\)
\(228\) 0 0
\(229\) −5.61285 −0.370907 −0.185454 0.982653i \(-0.559375\pi\)
−0.185454 + 0.982653i \(0.559375\pi\)
\(230\) −0.815792 5.80642i −0.0537917 0.382864i
\(231\) 0 0
\(232\) 0.543257i 0.0356666i
\(233\) 23.2859i 1.52551i −0.646687 0.762756i \(-0.723846\pi\)
0.646687 0.762756i \(-0.276154\pi\)
\(234\) 0 0
\(235\) 6.10171 0.857279i 0.398032 0.0559227i
\(236\) 22.8760 1.48910
\(237\) 0 0
\(238\) 0 0
\(239\) −8.48886 −0.549099 −0.274549 0.961573i \(-0.588529\pi\)
−0.274549 + 0.961573i \(0.588529\pi\)
\(240\) 0 0
\(241\) 7.24443 0.466655 0.233327 0.972398i \(-0.425039\pi\)
0.233327 + 0.972398i \(0.425039\pi\)
\(242\) 13.3225i 0.856402i
\(243\) 0 0
\(244\) 11.1240 0.712140
\(245\) 0 0
\(246\) 0 0
\(247\) 15.6128i 0.993422i
\(248\) 3.72746i 0.236694i
\(249\) 0 0
\(250\) −19.4400 + 8.65233i −1.22949 + 0.547221i
\(251\) 27.6128 1.74291 0.871454 0.490478i \(-0.163178\pi\)
0.871454 + 0.490478i \(0.163178\pi\)
\(252\) 0 0
\(253\) 2.75557i 0.173241i
\(254\) 24.4701 1.53539
\(255\) 0 0
\(256\) 20.2444 1.26528
\(257\) 0.428639i 0.0267378i 0.999911 + 0.0133689i \(0.00425558\pi\)
−0.999911 + 0.0133689i \(0.995744\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 23.0923 3.24443i 1.43213 0.201211i
\(261\) 0 0
\(262\) 4.00000i 0.247121i
\(263\) 9.37778i 0.578259i 0.957290 + 0.289129i \(0.0933658\pi\)
−0.957290 + 0.289129i \(0.906634\pi\)
\(264\) 0 0
\(265\) 20.3368 2.85728i 1.24928 0.175521i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.47013i 0.273056i
\(269\) −1.74620 −0.106468 −0.0532339 0.998582i \(-0.516953\pi\)
−0.0532339 + 0.998582i \(0.516953\pi\)
\(270\) 0 0
\(271\) 2.69535 0.163731 0.0818653 0.996643i \(-0.473912\pi\)
0.0818653 + 0.996643i \(0.473912\pi\)
\(272\) 20.4286i 1.23867i
\(273\) 0 0
\(274\) 30.3368 1.83271
\(275\) 9.61285 2.75557i 0.579677 0.166167i
\(276\) 0 0
\(277\) 5.12399i 0.307870i 0.988081 + 0.153935i \(0.0491947\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(278\) 22.2163i 1.33245i
\(279\) 0 0
\(280\) 0 0
\(281\) −23.9813 −1.43060 −0.715301 0.698816i \(-0.753710\pi\)
−0.715301 + 0.698816i \(0.753710\pi\)
\(282\) 0 0
\(283\) 2.36842i 0.140788i −0.997519 0.0703939i \(-0.977574\pi\)
0.997519 0.0703939i \(-0.0224256\pi\)
\(284\) 3.24443 0.192522
\(285\) 0 0
\(286\) −24.4701 −1.44695
\(287\) 0 0
\(288\) 0 0
\(289\) −2.61285 −0.153697
\(290\) 3.18421 0.447375i 0.186983 0.0262708i
\(291\) 0 0
\(292\) 2.54909i 0.149174i
\(293\) 8.42864i 0.492406i 0.969218 + 0.246203i \(0.0791831\pi\)
−0.969218 + 0.246203i \(0.920817\pi\)
\(294\) 0 0
\(295\) −4.38715 31.2257i −0.255430 1.81803i
\(296\) −5.47367 −0.318150
\(297\) 0 0
\(298\) 40.3970i 2.34014i
\(299\) 8.85728 0.512230
\(300\) 0 0
\(301\) 0 0
\(302\) 32.0830i 1.84617i
\(303\) 0 0
\(304\) 11.2029 0.642533
\(305\) −2.13335 15.1842i −0.122155 0.869445i
\(306\) 0 0
\(307\) 22.5718i 1.28824i −0.764923 0.644121i \(-0.777223\pi\)
0.764923 0.644121i \(-0.222777\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −21.8479 + 3.06959i −1.24088 + 0.174341i
\(311\) −24.0830 −1.36562 −0.682810 0.730596i \(-0.739242\pi\)
−0.682810 + 0.730596i \(0.739242\pi\)
\(312\) 0 0
\(313\) 9.65433i 0.545695i −0.962057 0.272848i \(-0.912035\pi\)
0.962057 0.272848i \(-0.0879655\pi\)
\(314\) −19.8479 −1.12008
\(315\) 0 0
\(316\) −7.87955 −0.443260
\(317\) 6.04149i 0.339324i −0.985502 0.169662i \(-0.945732\pi\)
0.985502 0.169662i \(-0.0542676\pi\)
\(318\) 0 0
\(319\) −1.51114 −0.0846075
\(320\) 1.47658 + 10.5096i 0.0825433 + 0.587505i
\(321\) 0 0
\(322\) 0 0
\(323\) 10.7556i 0.598456i
\(324\) 0 0
\(325\) −8.85728 30.8988i −0.491313 1.71396i
\(326\) 39.6958 2.19855
\(327\) 0 0
\(328\) 5.92104i 0.326935i
\(329\) 0 0
\(330\) 0 0
\(331\) 13.5111 0.742639 0.371320 0.928505i \(-0.378905\pi\)
0.371320 + 0.928505i \(0.378905\pi\)
\(332\) 18.8385i 1.03390i
\(333\) 0 0
\(334\) −29.2070 −1.59813
\(335\) 6.10171 0.857279i 0.333372 0.0468382i
\(336\) 0 0
\(337\) 10.4889i 0.571365i −0.958324 0.285682i \(-0.907780\pi\)
0.958324 0.285682i \(-0.0922202\pi\)
\(338\) 53.9131i 2.93248i
\(339\) 0 0
\(340\) −15.9081 + 2.23506i −0.862740 + 0.121213i
\(341\) 10.3684 0.561481
\(342\) 0 0
\(343\) 0 0
\(344\) 7.26317 0.391604
\(345\) 0 0
\(346\) 3.92104 0.210796
\(347\) 16.7239i 0.897787i −0.893585 0.448894i \(-0.851818\pi\)
0.893585 0.448894i \(-0.148182\pi\)
\(348\) 0 0
\(349\) −16.3684 −0.876181 −0.438091 0.898931i \(-0.644345\pi\)
−0.438091 + 0.898931i \(0.644345\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 14.6824i 0.782577i
\(353\) 0.549086i 0.0292249i 0.999893 + 0.0146124i \(0.00465145\pi\)
−0.999893 + 0.0146124i \(0.995349\pi\)
\(354\) 0 0
\(355\) −0.622216 4.42864i −0.0330238 0.235048i
\(356\) 7.49823 0.397405
\(357\) 0 0
\(358\) 19.0321i 1.00588i
\(359\) −0.285442 −0.0150651 −0.00753253 0.999972i \(-0.502398\pi\)
−0.00753253 + 0.999972i \(0.502398\pi\)
\(360\) 0 0
\(361\) −13.1017 −0.689564
\(362\) 23.0321i 1.21054i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.47949 + 0.488863i −0.182125 + 0.0255882i
\(366\) 0 0
\(367\) 1.71456i 0.0894992i 0.998998 + 0.0447496i \(0.0142490\pi\)
−0.998998 + 0.0447496i \(0.985751\pi\)
\(368\) 6.35551i 0.331304i
\(369\) 0 0
\(370\) −4.50760 32.0830i −0.234339 1.66791i
\(371\) 0 0
\(372\) 0 0
\(373\) 16.0000i 0.828449i 0.910175 + 0.414224i \(0.135947\pi\)
−0.910175 + 0.414224i \(0.864053\pi\)
\(374\) 16.8573 0.871669
\(375\) 0 0
\(376\) −1.98126 −0.102176
\(377\) 4.85728i 0.250163i
\(378\) 0 0
\(379\) 4.85728 0.249502 0.124751 0.992188i \(-0.460187\pi\)
0.124751 + 0.992188i \(0.460187\pi\)
\(380\) 1.22570 + 8.72393i 0.0628768 + 0.447528i
\(381\) 0 0
\(382\) 0.930409i 0.0476039i
\(383\) 8.38715i 0.428563i −0.976772 0.214282i \(-0.931259\pi\)
0.976772 0.214282i \(-0.0687411\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −43.6958 −2.22406
\(387\) 0 0
\(388\) 19.3689i 0.983307i
\(389\) 8.95899 0.454239 0.227119 0.973867i \(-0.427069\pi\)
0.227119 + 0.973867i \(0.427069\pi\)
\(390\) 0 0
\(391\) −6.10171 −0.308577
\(392\) 0 0
\(393\) 0 0
\(394\) −2.25380 −0.113545
\(395\) 1.51114 + 10.7556i 0.0760336 + 0.541171i
\(396\) 0 0
\(397\) 2.54909i 0.127935i −0.997952 0.0639675i \(-0.979625\pi\)
0.997952 0.0639675i \(-0.0203754\pi\)
\(398\) 16.7427i 0.839234i
\(399\) 0 0
\(400\) 22.1713 6.35551i 1.10857 0.317775i
\(401\) −0.958989 −0.0478896 −0.0239448 0.999713i \(-0.507623\pi\)
−0.0239448 + 0.999713i \(0.507623\pi\)
\(402\) 0 0
\(403\) 33.3274i 1.66016i
\(404\) −2.40006 −0.119407
\(405\) 0 0
\(406\) 0 0
\(407\) 15.2257i 0.754710i
\(408\) 0 0
\(409\) −31.9813 −1.58137 −0.790686 0.612222i \(-0.790276\pi\)
−0.790686 + 0.612222i \(0.790276\pi\)
\(410\) −34.7052 + 4.87601i −1.71397 + 0.240809i
\(411\) 0 0
\(412\) 14.3684i 0.707881i
\(413\) 0 0
\(414\) 0 0
\(415\) −25.7146 + 3.61285i −1.26228 + 0.177348i
\(416\) −47.1941 −2.31388
\(417\) 0 0
\(418\) 9.24443i 0.452160i
\(419\) 0.470127 0.0229672 0.0114836 0.999934i \(-0.496345\pi\)
0.0114836 + 0.999934i \(0.496345\pi\)
\(420\) 0 0
\(421\) −33.6128 −1.63819 −0.819095 0.573658i \(-0.805524\pi\)
−0.819095 + 0.573658i \(0.805524\pi\)
\(422\) 44.2034i 2.15179i
\(423\) 0 0
\(424\) −6.60348 −0.320693
\(425\) 6.10171 + 21.2859i 0.295976 + 1.03252i
\(426\) 0 0
\(427\) 0 0
\(428\) 2.86311i 0.138394i
\(429\) 0 0
\(430\) 5.98126 + 42.5718i 0.288442 + 2.05300i
\(431\) −11.7146 −0.564270 −0.282135 0.959375i \(-0.591043\pi\)
−0.282135 + 0.959375i \(0.591043\pi\)
\(432\) 0 0
\(433\) 0.0602231i 0.00289414i 0.999999 + 0.00144707i \(0.000460616\pi\)
−0.999999 + 0.00144707i \(0.999539\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.10525 0.436062
\(437\) 3.34614i 0.160068i
\(438\) 0 0
\(439\) −22.4286 −1.07046 −0.535230 0.844706i \(-0.679775\pi\)
−0.535230 + 0.844706i \(0.679775\pi\)
\(440\) −3.18421 + 0.447375i −0.151801 + 0.0213278i
\(441\) 0 0
\(442\) 54.1847i 2.57730i
\(443\) 23.9496i 1.13788i 0.822379 + 0.568940i \(0.192647\pi\)
−0.822379 + 0.568940i \(0.807353\pi\)
\(444\) 0 0
\(445\) −1.43801 10.2351i −0.0681681 0.485189i
\(446\) 28.9777 1.37214
\(447\) 0 0
\(448\) 0 0
\(449\) 29.4291 1.38885 0.694423 0.719567i \(-0.255660\pi\)
0.694423 + 0.719567i \(0.255660\pi\)
\(450\) 0 0
\(451\) 16.4701 0.775548
\(452\) 18.3082i 0.861145i
\(453\) 0 0
\(454\) 27.3461 1.28342
\(455\) 0 0
\(456\) 0 0
\(457\) 3.14272i 0.147010i 0.997295 + 0.0735051i \(0.0234185\pi\)
−0.997295 + 0.0735051i \(0.976581\pi\)
\(458\) 10.6824i 0.499158i
\(459\) 0 0
\(460\) −4.94914 + 0.695346i −0.230755 + 0.0324207i
\(461\) −3.37778 −0.157319 −0.0786596 0.996902i \(-0.525064\pi\)
−0.0786596 + 0.996902i \(0.525064\pi\)
\(462\) 0 0
\(463\) 20.8573i 0.969320i 0.874703 + 0.484660i \(0.161057\pi\)
−0.874703 + 0.484660i \(0.838943\pi\)
\(464\) −3.48532 −0.161802
\(465\) 0 0
\(466\) −44.3180 −2.05299
\(467\) 14.3684i 0.664891i 0.943122 + 0.332446i \(0.107874\pi\)
−0.943122 + 0.332446i \(0.892126\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.63158 11.6128i −0.0752593 0.535661i
\(471\) 0 0
\(472\) 10.1392i 0.466694i
\(473\) 20.2034i 0.928954i
\(474\) 0 0
\(475\) 11.6731 3.34614i 0.535597 0.153532i
\(476\) 0 0
\(477\) 0 0
\(478\) 16.1561i 0.738963i
\(479\) −6.36842 −0.290980 −0.145490 0.989360i \(-0.546476\pi\)
−0.145490 + 0.989360i \(0.546476\pi\)
\(480\) 0 0
\(481\) 48.9403 2.23148
\(482\) 13.7877i 0.628012i
\(483\) 0 0
\(484\) 11.3555 0.516160
\(485\) 26.4385 3.71456i 1.20051 0.168669i
\(486\) 0 0
\(487\) 17.3274i 0.785180i −0.919714 0.392590i \(-0.871579\pi\)
0.919714 0.392590i \(-0.128421\pi\)
\(488\) 4.93041i 0.223189i
\(489\) 0 0
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 3.34614i 0.150703i
\(494\) −29.7146 −1.33692
\(495\) 0 0
\(496\) 23.9140 1.07377
\(497\) 0 0
\(498\) 0 0
\(499\) −23.3461 −1.04512 −0.522558 0.852603i \(-0.675022\pi\)
−0.522558 + 0.852603i \(0.675022\pi\)
\(500\) 7.37487 + 16.5698i 0.329814 + 0.741025i
\(501\) 0 0
\(502\) 52.5531i 2.34556i
\(503\) 0.387152i 0.0172623i 0.999963 + 0.00863113i \(0.00274741\pi\)
−0.999963 + 0.00863113i \(0.997253\pi\)
\(504\) 0 0
\(505\) 0.460282 + 3.27607i 0.0204823 + 0.145783i
\(506\) 5.24443 0.233143
\(507\) 0 0
\(508\) 20.8573i 0.925392i
\(509\) 29.9496 1.32749 0.663747 0.747957i \(-0.268965\pi\)
0.663747 + 0.747957i \(0.268965\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 27.2306i 1.20343i
\(513\) 0 0
\(514\) 0.815792 0.0359830
\(515\) −19.6128 + 2.75557i −0.864245 + 0.121425i
\(516\) 0 0
\(517\) 5.51114i 0.242380i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.43801 + 10.2351i 0.0630608 + 0.448837i
\(521\) −18.5205 −0.811398 −0.405699 0.914007i \(-0.632972\pi\)
−0.405699 + 0.914007i \(0.632972\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) 3.40943 0.148942
\(525\) 0 0
\(526\) 17.8479 0.778206
\(527\) 22.9590i 1.00011i
\(528\) 0 0
\(529\) 21.1017 0.917466
\(530\) −5.43801 38.7052i −0.236212 1.68125i
\(531\) 0 0
\(532\) 0 0
\(533\) 52.9403i 2.29310i
\(534\) 0 0
\(535\) −3.90813 + 0.549086i −0.168963 + 0.0237390i
\(536\) −1.98126 −0.0855776
\(537\) 0 0
\(538\) 3.32339i 0.143282i
\(539\) 0 0
\(540\) 0 0
\(541\) 14.5906 0.627298 0.313649 0.949539i \(-0.398449\pi\)
0.313649 + 0.949539i \(0.398449\pi\)
\(542\) 5.12981i 0.220344i
\(543\) 0 0
\(544\) 32.5116 1.39392
\(545\) −1.74620 12.4286i −0.0747990 0.532384i
\(546\) 0 0
\(547\) 18.7556i 0.801930i 0.916093 + 0.400965i \(0.131325\pi\)
−0.916093 + 0.400965i \(0.868675\pi\)
\(548\) 25.8578i 1.10459i
\(549\) 0 0
\(550\) −5.24443 18.2953i −0.223623 0.780114i
\(551\) −1.83500 −0.0781738
\(552\) 0 0
\(553\) 0 0
\(554\) 9.75203 0.414324
\(555\) 0 0
\(556\) −18.9362 −0.803075
\(557\) 31.8765i 1.35065i 0.737520 + 0.675325i \(0.235997\pi\)
−0.737520 + 0.675325i \(0.764003\pi\)
\(558\) 0 0
\(559\) −64.9403 −2.74668
\(560\) 0 0
\(561\) 0 0
\(562\) 45.6414i 1.92527i
\(563\) 2.01874i 0.0850796i −0.999095 0.0425398i \(-0.986455\pi\)
0.999095 0.0425398i \(-0.0135449\pi\)
\(564\) 0 0
\(565\) −24.9906 + 3.51114i −1.05136 + 0.147715i
\(566\) −4.50760 −0.189468
\(567\) 0 0
\(568\) 1.43801i 0.0603375i
\(569\) −28.9590 −1.21402 −0.607012 0.794693i \(-0.707632\pi\)
−0.607012 + 0.794693i \(0.707632\pi\)
\(570\) 0 0
\(571\) 8.97773 0.375706 0.187853 0.982197i \(-0.439847\pi\)
0.187853 + 0.982197i \(0.439847\pi\)
\(572\) 20.8573i 0.872087i
\(573\) 0 0
\(574\) 0 0
\(575\) 1.89829 + 6.62222i 0.0791642 + 0.276165i
\(576\) 0 0
\(577\) 28.6766i 1.19382i 0.802307 + 0.596911i \(0.203606\pi\)
−0.802307 + 0.596911i \(0.796394\pi\)
\(578\) 4.97280i 0.206841i
\(579\) 0 0
\(580\) −0.381323 2.71408i −0.0158336 0.112696i
\(581\) 0 0
\(582\) 0 0
\(583\) 18.3684i 0.760742i
\(584\) 1.12981 0.0467520
\(585\) 0 0
\(586\) 16.0415 0.662668
\(587\) 45.2070i 1.86589i −0.360018 0.932945i \(-0.617229\pi\)
0.360018 0.932945i \(-0.382771\pi\)
\(588\) 0 0
\(589\) 12.5906 0.518786
\(590\) −59.4291 + 8.34968i −2.44666 + 0.343751i
\(591\) 0 0
\(592\) 35.1169i 1.44330i
\(593\) 18.2636i 0.749998i −0.927025 0.374999i \(-0.877643\pi\)
0.927025 0.374999i \(-0.122357\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 34.4327 1.41042
\(597\) 0 0
\(598\) 16.8573i 0.689345i
\(599\) −22.7368 −0.929002 −0.464501 0.885573i \(-0.653766\pi\)
−0.464501 + 0.885573i \(0.653766\pi\)
\(600\) 0 0
\(601\) −0.488863 −0.0199411 −0.00997056 0.999950i \(-0.503174\pi\)
−0.00997056 + 0.999950i \(0.503174\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −27.3461 −1.11270
\(605\) −2.17775 15.5002i −0.0885383 0.630174i
\(606\) 0 0
\(607\) 20.2034i 0.820032i 0.912078 + 0.410016i \(0.134477\pi\)
−0.912078 + 0.410016i \(0.865523\pi\)
\(608\) 17.8292i 0.723069i
\(609\) 0 0
\(610\) −28.8988 + 4.06022i −1.17008 + 0.164394i
\(611\) 17.7146 0.716654
\(612\) 0 0
\(613\) 10.3684i 0.418776i −0.977833 0.209388i \(-0.932853\pi\)
0.977833 0.209388i \(-0.0671472\pi\)
\(614\) −42.9590 −1.73368
\(615\) 0 0
\(616\) 0 0
\(617\) 39.2859i 1.58159i 0.612080 + 0.790796i \(0.290333\pi\)
−0.612080 + 0.790796i \(0.709667\pi\)
\(618\) 0 0
\(619\) 42.8988 1.72425 0.862123 0.506698i \(-0.169134\pi\)
0.862123 + 0.506698i \(0.169134\pi\)
\(620\) 2.61639 + 18.6222i 0.105077 + 0.747886i
\(621\) 0 0
\(622\) 45.8350i 1.83782i
\(623\) 0 0
\(624\) 0 0
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) −18.3742 −0.734383
\(627\) 0 0
\(628\) 16.9175i 0.675082i
\(629\) −33.7146 −1.34429
\(630\) 0 0
\(631\) 15.3461 0.610920 0.305460 0.952205i \(-0.401190\pi\)
0.305460 + 0.952205i \(0.401190\pi\)
\(632\) 3.49240i 0.138920i
\(633\) 0 0
\(634\) −11.4982 −0.456653
\(635\) −28.4701 + 4.00000i −1.12980 + 0.158735i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.87601i 0.113863i
\(639\) 0 0
\(640\) −12.5096 + 1.75758i −0.494486 + 0.0694743i
\(641\) −30.6735 −1.21153 −0.605766 0.795643i \(-0.707133\pi\)
−0.605766 + 0.795643i \(0.707133\pi\)
\(642\) 0 0
\(643\) 49.0607i 1.93477i −0.253320 0.967383i \(-0.581523\pi\)
0.253320 0.967383i \(-0.418477\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 20.4701 0.805386
\(647\) 15.3461i 0.603319i −0.953416 0.301660i \(-0.902459\pi\)
0.953416 0.301660i \(-0.0975406\pi\)
\(648\) 0 0
\(649\) 28.2034 1.10708
\(650\) −58.8069 + 16.8573i −2.30660 + 0.661197i
\(651\) 0 0
\(652\) 33.8350i 1.32508i
\(653\) 19.4697i 0.761906i −0.924594 0.380953i \(-0.875596\pi\)
0.924594 0.380953i \(-0.124404\pi\)
\(654\) 0 0
\(655\) −0.653858 4.65386i −0.0255484 0.181841i
\(656\) 37.9871 1.48315
\(657\) 0 0
\(658\) 0 0
\(659\) 30.9403 1.20526 0.602631 0.798020i \(-0.294119\pi\)
0.602631 + 0.798020i \(0.294119\pi\)
\(660\) 0 0
\(661\) −47.7975 −1.85911 −0.929554 0.368685i \(-0.879808\pi\)
−0.929554 + 0.368685i \(0.879808\pi\)
\(662\) 25.7146i 0.999425i
\(663\) 0 0
\(664\) 8.34968 0.324030
\(665\) 0 0
\(666\) 0 0
\(667\) 1.04101i 0.0403081i
\(668\) 24.8948i 0.963207i
\(669\) 0 0
\(670\) −1.63158 11.6128i −0.0630336 0.448643i
\(671\) 13.7146 0.529445
\(672\) 0 0
\(673\) 27.8163i 1.07224i −0.844142 0.536119i \(-0.819890\pi\)
0.844142 0.536119i \(-0.180110\pi\)
\(674\) −19.9625 −0.768928
\(675\) 0 0
\(676\) 45.9532 1.76743
\(677\) 19.0005i 0.730248i −0.930959 0.365124i \(-0.881027\pi\)
0.930959 0.365124i \(-0.118973\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.990632 7.05086i −0.0379890 0.270388i
\(681\) 0 0
\(682\) 19.7333i 0.755627i
\(683\) 4.52051i 0.172972i 0.996253 + 0.0864862i \(0.0275638\pi\)
−0.996253 + 0.0864862i \(0.972436\pi\)
\(684\) 0 0
\(685\) −35.2958 + 4.95899i −1.34858 + 0.189473i
\(686\) 0 0
\(687\) 0 0
\(688\) 46.5977i 1.77652i
\(689\) 59.0420 2.24932
\(690\) 0 0
\(691\) 1.18421 0.0450494 0.0225247 0.999746i \(-0.492830\pi\)
0.0225247 + 0.999746i \(0.492830\pi\)
\(692\) 3.34213i 0.127049i
\(693\) 0 0
\(694\) −31.8292 −1.20822
\(695\) 3.63158 + 25.8479i 0.137754 + 0.980467i
\(696\) 0 0
\(697\) 36.4701i 1.38140i
\(698\) 31.1526i 1.17914i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.6735 1.00745 0.503723 0.863865i \(-0.331963\pi\)
0.503723 + 0.863865i \(0.331963\pi\)
\(702\) 0 0
\(703\) 18.4889i 0.697321i
\(704\) −9.49240 −0.357758
\(705\) 0 0
\(706\) 1.04503 0.0393301
\(707\) 0 0
\(708\) 0 0
\(709\) 18.2034 0.683644 0.341822 0.939765i \(-0.388956\pi\)
0.341822 + 0.939765i \(0.388956\pi\)
\(710\) −8.42864 + 1.18421i −0.316321 + 0.0444425i
\(711\) 0 0
\(712\) 3.32339i 0.124549i
\(713\) 7.14272i 0.267497i
\(714\) 0 0
\(715\) 28.4701 4.00000i 1.06472 0.149592i
\(716\) −16.2222 −0.606250
\(717\) 0 0
\(718\) 0.543257i 0.0202742i
\(719\) −4.85728 −0.181146 −0.0905730 0.995890i \(-0.528870\pi\)
−0.0905730 + 0.995890i \(0.528870\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 24.9353i 0.927997i
\(723\) 0 0
\(724\) −19.6316 −0.729602
\(725\) −3.63158 + 1.04101i −0.134874 + 0.0386622i
\(726\) 0 0
\(727\) 21.0607i 0.781098i −0.920582 0.390549i \(-0.872285\pi\)
0.920582 0.390549i \(-0.127715\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.930409 + 6.62222i 0.0344360 + 0.245099i
\(731\) 44.7368 1.65465
\(732\) 0 0
\(733\) 9.45091i 0.349077i 0.984650 + 0.174539i \(0.0558434\pi\)
−0.984650 + 0.174539i \(0.944157\pi\)
\(734\) 3.26317 0.120446
\(735\) 0 0
\(736\) 10.1146 0.372830
\(737\) 5.51114i 0.203005i
\(738\) 0 0
\(739\) 8.20342 0.301768 0.150884 0.988551i \(-0.451788\pi\)
0.150884 + 0.988551i \(0.451788\pi\)
\(740\) −27.3461 + 3.84208i −1.00526 + 0.141238i
\(741\) 0 0
\(742\) 0 0
\(743\) 8.33677i 0.305847i 0.988238 + 0.152923i \(0.0488687\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(744\) 0 0
\(745\) −6.60348 47.0005i −0.241933 1.72196i
\(746\) 30.4514 1.11490
\(747\) 0 0
\(748\) 14.3684i 0.525361i
\(749\) 0 0
\(750\) 0 0
\(751\) −25.9180 −0.945760 −0.472880 0.881127i \(-0.656786\pi\)
−0.472880 + 0.881127i \(0.656786\pi\)
\(752\) 12.7110i 0.463523i
\(753\) 0 0
\(754\) 9.24443 0.336662
\(755\) 5.24443 + 37.3274i 0.190864 + 1.35848i
\(756\) 0 0
\(757\) 8.94025i 0.324939i 0.986714 + 0.162470i \(0.0519459\pi\)
−0.986714 + 0.162470i \(0.948054\pi\)
\(758\) 9.24443i 0.335773i
\(759\) 0 0
\(760\) −3.86665 + 0.543257i −0.140258 + 0.0197060i
\(761\) −0.825636 −0.0299293 −0.0149646 0.999888i \(-0.504764\pi\)
−0.0149646 + 0.999888i \(0.504764\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.793040 0.0286912
\(765\) 0 0
\(766\) −15.9625 −0.576750
\(767\) 90.6548i 3.27336i
\(768\) 0 0
\(769\) 21.2257 0.765418 0.382709 0.923869i \(-0.374991\pi\)
0.382709 + 0.923869i \(0.374991\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 37.2444i 1.34046i
\(773\) 29.4893i 1.06066i −0.847792 0.530329i \(-0.822068\pi\)
0.847792 0.530329i \(-0.177932\pi\)
\(774\) 0 0
\(775\) 24.9175 7.14272i 0.895063 0.256574i
\(776\) −8.58474 −0.308174
\(777\) 0 0
\(778\) 17.0509i 0.611303i
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 11.6128i 0.415275i
\(783\) 0 0
\(784\) 0 0
\(785\) 23.0923 3.24443i 0.824201 0.115799i
\(786\) 0 0
\(787\) 34.4514i 1.22806i 0.789283 + 0.614030i \(0.210453\pi\)
−0.789283 + 0.614030i \(0.789547\pi\)
\(788\) 1.92104i 0.0684343i
\(789\) 0 0
\(790\) 20.4701 2.87601i 0.728294 0.102324i
\(791\) 0 0
\(792\) 0 0
\(793\) 44.0830i 1.56543i
\(794\) −4.85145 −0.172172
\(795\) 0 0
\(796\) −14.2707 −0.505812
\(797\) 18.9175i 0.670092i 0.942202 + 0.335046i \(0.108752\pi\)
−0.942202 + 0.335046i \(0.891248\pi\)