Properties

Label 3024.2.q.i.2881.2
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.2
Root \(1.19343 - 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.i.2305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.46043 + 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +O(q^{10})\) \(q+(-1.46043 + 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +(0.676857 + 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(-1.65514 + 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(-1.31415 + 2.27617i) q^{23} +(-1.76573 - 3.05833i) q^{25} +(-0.521720 + 0.903646i) q^{29} -3.27458 q^{31} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(0.904289 + 1.56627i) q^{41} +(2.17129 - 3.76078i) q^{43} +3.97914 q^{47} +(-6.96160 + 0.732185i) q^{49} +(3.22743 - 5.59008i) q^{53} -3.95402 q^{55} -12.2140 q^{59} +0.559734 q^{61} +4.28200 q^{65} -12.8118 q^{67} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-3.00371 + 1.95078i) q^{77} -0.767677 q^{79} +(-0.983707 + 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(-3.20356 - 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} -6.44514 q^{95} +(-4.14143 + 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{5} + 4q^{7} + O(q^{10}) \) \( 10q - 4q^{5} + 4q^{7} + 4q^{11} - 8q^{13} - 12q^{17} - q^{19} + 3q^{23} - q^{25} - 7q^{29} - 6q^{31} + 5q^{35} - 5q^{41} + 7q^{43} - 54q^{47} - 8q^{49} + 21q^{53} - 4q^{55} - 60q^{59} + 28q^{61} - 22q^{65} - 4q^{67} - 6q^{71} + 15q^{73} - 11q^{77} - 8q^{79} + 9q^{83} - 6q^{85} - 28q^{89} + 4q^{91} + 28q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −1.46043 + 2.52954i −0.653125 + 1.13125i 0.329235 + 0.944248i \(0.393209\pi\)
−0.982360 + 0.186998i \(0.940124\pi\)
\(6\) 0 0
\(7\) 0.138560 + 2.64212i 0.0523708 + 0.998628i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.676857 + 1.17235i 0.204080 + 0.353477i 0.949839 0.312738i \(-0.101246\pi\)
−0.745759 + 0.666216i \(0.767913\pi\)
\(12\) 0 0
\(13\) −0.733001 1.26960i −0.203298 0.352123i 0.746291 0.665620i \(-0.231833\pi\)
−0.949589 + 0.313497i \(0.898499\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.65514 + 2.86678i −0.401430 + 0.695297i −0.993899 0.110297i \(-0.964820\pi\)
0.592469 + 0.805593i \(0.298153\pi\)
\(18\) 0 0
\(19\) 1.10329 + 1.91096i 0.253113 + 0.438404i 0.964381 0.264516i \(-0.0852123\pi\)
−0.711268 + 0.702921i \(0.751879\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.31415 + 2.27617i −0.274019 + 0.474614i −0.969887 0.243555i \(-0.921686\pi\)
0.695868 + 0.718169i \(0.255020\pi\)
\(24\) 0 0
\(25\) −1.76573 3.05833i −0.353146 0.611666i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.521720 + 0.903646i −0.0968810 + 0.167803i −0.910392 0.413747i \(-0.864220\pi\)
0.813511 + 0.581549i \(0.197553\pi\)
\(30\) 0 0
\(31\) −3.27458 −0.588132 −0.294066 0.955785i \(-0.595009\pi\)
−0.294066 + 0.955785i \(0.595009\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.88572 3.50815i −1.16390 0.592985i
\(36\) 0 0
\(37\) 5.43773 + 9.41842i 0.893957 + 1.54838i 0.835090 + 0.550113i \(0.185415\pi\)
0.0588664 + 0.998266i \(0.481251\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.904289 + 1.56627i 0.141226 + 0.244611i 0.927959 0.372683i \(-0.121562\pi\)
−0.786732 + 0.617294i \(0.788229\pi\)
\(42\) 0 0
\(43\) 2.17129 3.76078i 0.331118 0.573514i −0.651613 0.758551i \(-0.725907\pi\)
0.982731 + 0.185038i \(0.0592408\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.97914 0.580417 0.290209 0.956963i \(-0.406275\pi\)
0.290209 + 0.956963i \(0.406275\pi\)
\(48\) 0 0
\(49\) −6.96160 + 0.732185i −0.994515 + 0.104598i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.22743 5.59008i 0.443322 0.767856i −0.554612 0.832109i \(-0.687133\pi\)
0.997934 + 0.0642533i \(0.0204666\pi\)
\(54\) 0 0
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −12.2140 −1.59013 −0.795064 0.606526i \(-0.792563\pi\)
−0.795064 + 0.606526i \(0.792563\pi\)
\(60\) 0 0
\(61\) 0.559734 0.0716666 0.0358333 0.999358i \(-0.488591\pi\)
0.0358333 + 0.999358i \(0.488591\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.28200 0.531117
\(66\) 0 0
\(67\) −12.8118 −1.56521 −0.782603 0.622521i \(-0.786109\pi\)
−0.782603 + 0.622521i \(0.786109\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.9177 1.53305 0.766525 0.642214i \(-0.221984\pi\)
0.766525 + 0.642214i \(0.221984\pi\)
\(72\) 0 0
\(73\) 5.22772 9.05467i 0.611858 1.05977i −0.379069 0.925368i \(-0.623756\pi\)
0.990927 0.134401i \(-0.0429109\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.00371 + 1.95078i −0.342304 + 0.222312i
\(78\) 0 0
\(79\) −0.767677 −0.0863704 −0.0431852 0.999067i \(-0.513751\pi\)
−0.0431852 + 0.999067i \(0.513751\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.983707 + 1.70383i −0.107976 + 0.187020i −0.914950 0.403567i \(-0.867770\pi\)
0.806974 + 0.590587i \(0.201104\pi\)
\(84\) 0 0
\(85\) −4.83443 8.37348i −0.524368 0.908232i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.20356 5.54872i −0.339576 0.588163i 0.644777 0.764371i \(-0.276950\pi\)
−0.984353 + 0.176208i \(0.943617\pi\)
\(90\) 0 0
\(91\) 3.25286 2.11259i 0.340992 0.221460i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.44514 −0.661258
\(96\) 0 0
\(97\) −4.14143 + 7.17316i −0.420498 + 0.728324i −0.995988 0.0894847i \(-0.971478\pi\)
0.575490 + 0.817809i \(0.304811\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.11331 14.0527i −0.807305 1.39829i −0.914724 0.404079i \(-0.867592\pi\)
0.107419 0.994214i \(-0.465741\pi\)
\(102\) 0 0
\(103\) −1.11342 + 1.92849i −0.109708 + 0.190020i −0.915652 0.401972i \(-0.868325\pi\)
0.805944 + 0.591992i \(0.201658\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.75403 15.1624i −0.846284 1.46581i −0.884501 0.466537i \(-0.845501\pi\)
0.0382175 0.999269i \(-0.487832\pi\)
\(108\) 0 0
\(109\) −7.79917 + 13.5086i −0.747025 + 1.29388i 0.202218 + 0.979341i \(0.435185\pi\)
−0.949243 + 0.314544i \(0.898148\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.844555 + 1.46281i 0.0794491 + 0.137610i 0.903012 0.429615i \(-0.141351\pi\)
−0.823563 + 0.567224i \(0.808017\pi\)
\(114\) 0 0
\(115\) −3.83845 6.64839i −0.357937 0.619966i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.80372 3.97585i −0.715366 0.364466i
\(120\) 0 0
\(121\) 4.58373 7.93925i 0.416703 0.721750i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.28942 −0.383657
\(126\) 0 0
\(127\) 3.96918 0.352208 0.176104 0.984372i \(-0.443650\pi\)
0.176104 + 0.984372i \(0.443650\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.66432 + 4.61473i −0.232782 + 0.403191i −0.958626 0.284669i \(-0.908116\pi\)
0.725844 + 0.687860i \(0.241450\pi\)
\(132\) 0 0
\(133\) −4.89611 + 3.17982i −0.424547 + 0.275725i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.74772 6.49124i −0.320189 0.554584i 0.660338 0.750969i \(-0.270413\pi\)
−0.980527 + 0.196385i \(0.937080\pi\)
\(138\) 0 0
\(139\) −7.03285 12.1812i −0.596518 1.03320i −0.993331 0.115300i \(-0.963217\pi\)
0.396812 0.917900i \(-0.370116\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.992275 1.71867i 0.0829782 0.143722i
\(144\) 0 0
\(145\) −1.52388 2.63943i −0.126551 0.219193i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.08986 1.88769i 0.0892846 0.154645i −0.817924 0.575326i \(-0.804875\pi\)
0.907209 + 0.420680i \(0.138209\pi\)
\(150\) 0 0
\(151\) 7.01387 + 12.1484i 0.570781 + 0.988621i 0.996486 + 0.0837595i \(0.0266927\pi\)
−0.425705 + 0.904862i \(0.639974\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.78231 8.28320i 0.384124 0.665322i
\(156\) 0 0
\(157\) 2.96623 0.236731 0.118365 0.992970i \(-0.462235\pi\)
0.118365 + 0.992970i \(0.462235\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.19601 3.15675i −0.488314 0.248787i
\(162\) 0 0
\(163\) 0.194278 + 0.336499i 0.0152170 + 0.0263566i 0.873534 0.486764i \(-0.161823\pi\)
−0.858317 + 0.513120i \(0.828489\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.64889 + 6.32006i 0.282360 + 0.489061i 0.971965 0.235124i \(-0.0755496\pi\)
−0.689606 + 0.724185i \(0.742216\pi\)
\(168\) 0 0
\(169\) 5.42542 9.39710i 0.417340 0.722854i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.05508 0.308302 0.154151 0.988047i \(-0.450736\pi\)
0.154151 + 0.988047i \(0.450736\pi\)
\(174\) 0 0
\(175\) 7.83582 5.08903i 0.592332 0.384695i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.29243 9.16675i 0.395575 0.685155i −0.597600 0.801795i \(-0.703879\pi\)
0.993174 + 0.116639i \(0.0372121\pi\)
\(180\) 0 0
\(181\) −19.6312 −1.45917 −0.729586 0.683889i \(-0.760287\pi\)
−0.729586 + 0.683889i \(0.760287\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −31.7657 −2.33546
\(186\) 0 0
\(187\) −4.48117 −0.327695
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.28714 0.599637 0.299818 0.953996i \(-0.403074\pi\)
0.299818 + 0.953996i \(0.403074\pi\)
\(192\) 0 0
\(193\) −18.7848 −1.35216 −0.676082 0.736827i \(-0.736323\pi\)
−0.676082 + 0.736827i \(0.736323\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.99634 −0.427222 −0.213611 0.976919i \(-0.568522\pi\)
−0.213611 + 0.976919i \(0.568522\pi\)
\(198\) 0 0
\(199\) −7.20434 + 12.4783i −0.510702 + 0.884562i 0.489221 + 0.872160i \(0.337281\pi\)
−0.999923 + 0.0124022i \(0.996052\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.45983 1.25324i −0.172646 0.0879601i
\(204\) 0 0
\(205\) −5.28261 −0.368954
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.49354 + 2.58690i −0.103311 + 0.178939i
\(210\) 0 0
\(211\) 6.92418 + 11.9930i 0.476680 + 0.825634i 0.999643 0.0267212i \(-0.00850663\pi\)
−0.522963 + 0.852356i \(0.675173\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.34204 + 10.9847i 0.432523 + 0.749153i
\(216\) 0 0
\(217\) −0.453726 8.65184i −0.0308010 0.587325i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.85287 0.326439
\(222\) 0 0
\(223\) −2.33756 + 4.04878i −0.156535 + 0.271126i −0.933617 0.358273i \(-0.883366\pi\)
0.777082 + 0.629399i \(0.216699\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.85631 17.0716i −0.654187 1.13308i −0.982097 0.188376i \(-0.939678\pi\)
0.327910 0.944709i \(-0.393656\pi\)
\(228\) 0 0
\(229\) −14.0364 + 24.3118i −0.927552 + 1.60657i −0.140148 + 0.990131i \(0.544758\pi\)
−0.787404 + 0.616437i \(0.788575\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.90113 + 11.9531i 0.452108 + 0.783074i 0.998517 0.0544448i \(-0.0173389\pi\)
−0.546409 + 0.837518i \(0.684006\pi\)
\(234\) 0 0
\(235\) −5.81127 + 10.0654i −0.379085 + 0.656595i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5.53069 + 9.57944i 0.357751 + 0.619642i 0.987585 0.157087i \(-0.0502104\pi\)
−0.629834 + 0.776730i \(0.716877\pi\)
\(240\) 0 0
\(241\) 11.5849 + 20.0656i 0.746247 + 1.29254i 0.949610 + 0.313435i \(0.101480\pi\)
−0.203362 + 0.979104i \(0.565187\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 8.31486 18.6790i 0.531217 1.19336i
\(246\) 0 0
\(247\) 1.61743 2.80147i 0.102915 0.178253i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.78402 −0.491323 −0.245662 0.969356i \(-0.579005\pi\)
−0.245662 + 0.969356i \(0.579005\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.18798 8.98585i 0.323618 0.560522i −0.657614 0.753355i \(-0.728434\pi\)
0.981232 + 0.192833i \(0.0617676\pi\)
\(258\) 0 0
\(259\) −24.1311 + 15.6721i −1.49944 + 0.973820i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.56654 + 16.5697i 0.589898 + 1.02173i 0.994245 + 0.107128i \(0.0341653\pi\)
−0.404347 + 0.914605i \(0.632501\pi\)
\(264\) 0 0
\(265\) 9.42689 + 16.3279i 0.579090 + 1.00301i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.41840 7.65290i 0.269395 0.466605i −0.699311 0.714818i \(-0.746510\pi\)
0.968706 + 0.248212i \(0.0798430\pi\)
\(270\) 0 0
\(271\) 9.16955 + 15.8821i 0.557010 + 0.964770i 0.997744 + 0.0671321i \(0.0213849\pi\)
−0.440734 + 0.897638i \(0.645282\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.39029 4.14011i 0.144140 0.249658i
\(276\) 0 0
\(277\) −2.55241 4.42091i −0.153360 0.265627i 0.779101 0.626899i \(-0.215676\pi\)
−0.932460 + 0.361272i \(0.882343\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.853180 1.47775i 0.0508964 0.0881552i −0.839455 0.543430i \(-0.817125\pi\)
0.890351 + 0.455274i \(0.150459\pi\)
\(282\) 0 0
\(283\) 12.4883 0.742352 0.371176 0.928562i \(-0.378955\pi\)
0.371176 + 0.928562i \(0.378955\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.01299 + 2.60626i −0.236879 + 0.153843i
\(288\) 0 0
\(289\) 3.02104 + 5.23260i 0.177708 + 0.307800i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.60202 + 4.50684i 0.152012 + 0.263292i 0.931967 0.362543i \(-0.118091\pi\)
−0.779955 + 0.625835i \(0.784758\pi\)
\(294\) 0 0
\(295\) 17.8377 30.8959i 1.03855 1.79883i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.85309 0.222830
\(300\) 0 0
\(301\) 10.2373 + 5.21571i 0.590067 + 0.300628i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.817453 + 1.41587i −0.0468072 + 0.0810725i
\(306\) 0 0
\(307\) −5.00136 −0.285442 −0.142721 0.989763i \(-0.545585\pi\)
−0.142721 + 0.989763i \(0.545585\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −32.3968 −1.83706 −0.918528 0.395355i \(-0.870621\pi\)
−0.918528 + 0.395355i \(0.870621\pi\)
\(312\) 0 0
\(313\) 1.51907 0.0858629 0.0429315 0.999078i \(-0.486330\pi\)
0.0429315 + 0.999078i \(0.486330\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.5089 1.20806 0.604029 0.796962i \(-0.293561\pi\)
0.604029 + 0.796962i \(0.293561\pi\)
\(318\) 0 0
\(319\) −1.41252 −0.0790860
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.30441 −0.406428
\(324\) 0 0
\(325\) −2.58856 + 4.48352i −0.143588 + 0.248701i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.551350 + 10.5134i 0.0303969 + 0.579621i
\(330\) 0 0
\(331\) −19.4780 −1.07061 −0.535305 0.844659i \(-0.679803\pi\)
−0.535305 + 0.844659i \(0.679803\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 18.7107 32.4079i 1.02228 1.77063i
\(336\) 0 0
\(337\) 4.84742 + 8.39598i 0.264056 + 0.457358i 0.967316 0.253575i \(-0.0816063\pi\)
−0.703260 + 0.710933i \(0.748273\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.21642 3.83896i −0.120026 0.207891i
\(342\) 0 0
\(343\) −2.89912 18.2919i −0.156538 0.987672i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.02604 0.108763 0.0543817 0.998520i \(-0.482681\pi\)
0.0543817 + 0.998520i \(0.482681\pi\)
\(348\) 0 0
\(349\) 8.14577 14.1089i 0.436033 0.755231i −0.561346 0.827581i \(-0.689716\pi\)
0.997379 + 0.0723497i \(0.0230498\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.53072 + 14.7756i 0.454045 + 0.786428i 0.998633 0.0522753i \(-0.0166473\pi\)
−0.544588 + 0.838704i \(0.683314\pi\)
\(354\) 0 0
\(355\) −18.8655 + 32.6759i −1.00127 + 1.73426i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.48363 + 2.56972i 0.0783030 + 0.135625i 0.902518 0.430652i \(-0.141717\pi\)
−0.824215 + 0.566277i \(0.808383\pi\)
\(360\) 0 0
\(361\) 7.06549 12.2378i 0.371868 0.644094i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.2695 + 26.4475i 0.799240 + 1.38432i
\(366\) 0 0
\(367\) −5.07874 8.79664i −0.265108 0.459181i 0.702484 0.711700i \(-0.252074\pi\)
−0.967592 + 0.252519i \(0.918741\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 15.2168 + 7.75270i 0.790019 + 0.402500i
\(372\) 0 0
\(373\) 12.7423 22.0703i 0.659771 1.14276i −0.320904 0.947112i \(-0.603987\pi\)
0.980675 0.195645i \(-0.0626799\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.52969 0.0787829
\(378\) 0 0
\(379\) −9.85497 −0.506216 −0.253108 0.967438i \(-0.581453\pi\)
−0.253108 + 0.967438i \(0.581453\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13.6563 23.6535i 0.697806 1.20864i −0.271419 0.962461i \(-0.587493\pi\)
0.969225 0.246175i \(-0.0791737\pi\)
\(384\) 0 0
\(385\) −0.547870 10.4470i −0.0279220 0.532428i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.09223 + 3.62385i 0.106080 + 0.183736i 0.914179 0.405311i \(-0.132837\pi\)
−0.808099 + 0.589047i \(0.799503\pi\)
\(390\) 0 0
\(391\) −4.35019 7.53475i −0.219999 0.381049i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.12114 1.94187i 0.0564107 0.0977062i
\(396\) 0 0
\(397\) 15.3354 + 26.5618i 0.769664 + 1.33310i 0.937745 + 0.347323i \(0.112909\pi\)
−0.168082 + 0.985773i \(0.553757\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.42402 + 5.93057i −0.170987 + 0.296158i −0.938765 0.344557i \(-0.888029\pi\)
0.767778 + 0.640716i \(0.221362\pi\)
\(402\) 0 0
\(403\) 2.40027 + 4.15739i 0.119566 + 0.207095i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.36113 + 12.7499i −0.364878 + 0.631987i
\(408\) 0 0
\(409\) −18.2698 −0.903384 −0.451692 0.892174i \(-0.649179\pi\)
−0.451692 + 0.892174i \(0.649179\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.69237 32.2709i −0.0832763 1.58795i
\(414\) 0 0
\(415\) −2.87328 4.97666i −0.141044 0.244295i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11.2310 + 19.4526i 0.548669 + 0.950322i 0.998366 + 0.0571410i \(0.0181984\pi\)
−0.449698 + 0.893181i \(0.648468\pi\)
\(420\) 0 0
\(421\) 10.4177 18.0440i 0.507728 0.879411i −0.492232 0.870464i \(-0.663819\pi\)
0.999960 0.00894684i \(-0.00284791\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.6901 0.567053
\(426\) 0 0
\(427\) 0.0775568 + 1.47888i 0.00375324 + 0.0715682i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.1213 + 17.5307i −0.487527 + 0.844422i −0.999897 0.0143427i \(-0.995434\pi\)
0.512370 + 0.858765i \(0.328768\pi\)
\(432\) 0 0
\(433\) −21.6764 −1.04170 −0.520851 0.853648i \(-0.674385\pi\)
−0.520851 + 0.853648i \(0.674385\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.79956 −0.277431
\(438\) 0 0
\(439\) 35.4781 1.69328 0.846639 0.532168i \(-0.178623\pi\)
0.846639 + 0.532168i \(0.178623\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −19.2063 −0.912517 −0.456258 0.889847i \(-0.650811\pi\)
−0.456258 + 0.889847i \(0.650811\pi\)
\(444\) 0 0
\(445\) 18.7143 0.887144
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 29.6082 1.39730 0.698648 0.715465i \(-0.253785\pi\)
0.698648 + 0.715465i \(0.253785\pi\)
\(450\) 0 0
\(451\) −1.22415 + 2.12029i −0.0576429 + 0.0998405i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.593314 + 11.3136i 0.0278150 + 0.530388i
\(456\) 0 0
\(457\) −9.56196 −0.447290 −0.223645 0.974671i \(-0.571796\pi\)
−0.223645 + 0.974671i \(0.571796\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.9187 + 18.9118i −0.508536 + 0.880809i 0.491416 + 0.870925i \(0.336480\pi\)
−0.999951 + 0.00988416i \(0.996854\pi\)
\(462\) 0 0
\(463\) −13.0744 22.6456i −0.607621 1.05243i −0.991631 0.129102i \(-0.958791\pi\)
0.384010 0.923329i \(-0.374543\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.4764 30.2699i −0.808709 1.40073i −0.913758 0.406258i \(-0.866833\pi\)
0.105049 0.994467i \(-0.466500\pi\)
\(468\) 0 0
\(469\) −1.77520 33.8502i −0.0819711 1.56306i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.87861 0.270299
\(474\) 0 0
\(475\) 3.89623 6.74848i 0.178771 0.309641i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14.9054 + 25.8170i 0.681047 + 1.17961i 0.974662 + 0.223684i \(0.0718083\pi\)
−0.293615 + 0.955924i \(0.594858\pi\)
\(480\) 0 0
\(481\) 7.97172 13.8074i 0.363479 0.629565i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −12.0965 20.9518i −0.549276 0.951374i
\(486\) 0 0
\(487\) 11.2253 19.4428i 0.508667 0.881037i −0.491283 0.871000i \(-0.663472\pi\)
0.999950 0.0100365i \(-0.00319477\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.5222 + 30.3494i 0.790767 + 1.36965i 0.925493 + 0.378765i \(0.123651\pi\)
−0.134726 + 0.990883i \(0.543016\pi\)
\(492\) 0 0
\(493\) −1.72704 2.99132i −0.0777819 0.134722i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.78988 + 34.1302i 0.0802871 + 1.53095i
\(498\) 0 0
\(499\) −4.46760 + 7.73811i −0.199997 + 0.346405i −0.948527 0.316696i \(-0.897427\pi\)
0.748530 + 0.663101i \(0.230760\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.6403 −0.563603 −0.281802 0.959473i \(-0.590932\pi\)
−0.281802 + 0.959473i \(0.590932\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14.0555 + 24.3449i −0.623000 + 1.07907i 0.365924 + 0.930645i \(0.380753\pi\)
−0.988924 + 0.148423i \(0.952580\pi\)
\(510\) 0 0
\(511\) 24.6479 + 12.5576i 1.09036 + 0.555517i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.25214 5.63287i −0.143306 0.248214i
\(516\) 0 0
\(517\) 2.69331 + 4.66495i 0.118452 + 0.205164i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.23768 + 7.33988i −0.185656 + 0.321566i −0.943797 0.330524i \(-0.892774\pi\)
0.758141 + 0.652090i \(0.226108\pi\)
\(522\) 0 0
\(523\) −16.7236 28.9662i −0.731273 1.26660i −0.956339 0.292259i \(-0.905593\pi\)
0.225066 0.974344i \(-0.427740\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.41988 9.38751i 0.236094 0.408926i
\(528\) 0 0
\(529\) 8.04603 + 13.9361i 0.349827 + 0.605919i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.32569 2.29616i 0.0574220 0.0994579i
\(534\) 0 0
\(535\) 51.1387 2.21092
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.57039 7.66586i −0.239934 0.330192i
\(540\) 0 0
\(541\) −9.12929 15.8124i −0.392499 0.679828i 0.600280 0.799790i \(-0.295056\pi\)
−0.992778 + 0.119962i \(0.961723\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −22.7803 39.4567i −0.975802 1.69014i
\(546\) 0 0
\(547\) 2.88599 4.99869i 0.123396 0.213728i −0.797709 0.603043i \(-0.793955\pi\)
0.921105 + 0.389315i \(0.127288\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.30244 −0.0980874
\(552\) 0 0
\(553\) −0.106369 2.02829i −0.00452329 0.0862518i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.6911 + 28.9098i −0.707223 + 1.22495i 0.258661 + 0.965968i \(0.416719\pi\)
−0.965883 + 0.258977i \(0.916614\pi\)
\(558\) 0 0
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.19131 0.0923528 0.0461764 0.998933i \(-0.485296\pi\)
0.0461764 + 0.998933i \(0.485296\pi\)
\(564\) 0 0
\(565\) −4.93367 −0.207561
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.9860 −0.795936 −0.397968 0.917399i \(-0.630284\pi\)
−0.397968 + 0.917399i \(0.630284\pi\)
\(570\) 0 0
\(571\) 21.7380 0.909709 0.454854 0.890566i \(-0.349691\pi\)
0.454854 + 0.890566i \(0.349691\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.28172 0.387074
\(576\) 0 0
\(577\) −15.4516 + 26.7629i −0.643258 + 1.11416i 0.341443 + 0.939903i \(0.389084\pi\)
−0.984701 + 0.174253i \(0.944249\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.63803 2.36299i −0.192418 0.0980333i
\(582\) 0 0
\(583\) 8.73804 0.361893
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.18332 + 15.9060i −0.379036 + 0.656510i −0.990922 0.134436i \(-0.957078\pi\)
0.611886 + 0.790946i \(0.290411\pi\)
\(588\) 0 0
\(589\) −3.61282 6.25759i −0.148864 0.257840i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −13.8775 24.0365i −0.569880 0.987061i −0.996577 0.0826662i \(-0.973656\pi\)
0.426698 0.904394i \(-0.359677\pi\)
\(594\) 0 0
\(595\) 21.4539 13.9334i 0.879524 0.571213i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0.402823 0.0164589 0.00822945 0.999966i \(-0.497380\pi\)
0.00822945 + 0.999966i \(0.497380\pi\)
\(600\) 0 0
\(601\) 12.3733 21.4312i 0.504717 0.874196i −0.495268 0.868740i \(-0.664930\pi\)
0.999985 0.00545577i \(-0.00173663\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13.3885 + 23.1895i 0.544318 + 0.942787i
\(606\) 0 0
\(607\) 12.0348 20.8449i 0.488479 0.846070i −0.511434 0.859323i \(-0.670885\pi\)
0.999912 + 0.0132531i \(0.00421872\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.91672 5.05190i −0.117998 0.204378i
\(612\) 0 0
\(613\) 10.1907 17.6509i 0.411600 0.712912i −0.583465 0.812138i \(-0.698303\pi\)
0.995065 + 0.0992261i \(0.0316367\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.9315 + 36.2544i 0.842669 + 1.45955i 0.887630 + 0.460558i \(0.152350\pi\)
−0.0449604 + 0.998989i \(0.514316\pi\)
\(618\) 0 0
\(619\) 7.41095 + 12.8361i 0.297871 + 0.515928i 0.975649 0.219339i \(-0.0703900\pi\)
−0.677777 + 0.735267i \(0.737057\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14.2165 9.23301i 0.569572 0.369913i
\(624\) 0 0
\(625\) 15.0930 26.1419i 0.603722 1.04568i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −36.0007 −1.43544
\(630\) 0 0
\(631\) 21.0294 0.837169 0.418585 0.908178i \(-0.362526\pi\)
0.418585 + 0.908178i \(0.362526\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.79673 + 10.0402i −0.230036 + 0.398434i
\(636\) 0 0
\(637\) 6.03244 + 8.30173i 0.239014 + 0.328926i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.96592 + 10.3333i 0.235640 + 0.408140i 0.959458 0.281850i \(-0.0909481\pi\)
−0.723819 + 0.689990i \(0.757615\pi\)
\(642\) 0 0
\(643\) 19.9678 + 34.5852i 0.787452 + 1.36391i 0.927524 + 0.373765i \(0.121933\pi\)
−0.140072 + 0.990141i \(0.544733\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.494477 0.856459i 0.0194399 0.0336709i −0.856142 0.516741i \(-0.827145\pi\)
0.875582 + 0.483070i \(0.160478\pi\)
\(648\) 0 0
\(649\) −8.26714 14.3191i −0.324514 0.562074i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.3573 19.6715i 0.444447 0.769804i −0.553567 0.832805i \(-0.686734\pi\)
0.998014 + 0.0630004i \(0.0200669\pi\)
\(654\) 0 0
\(655\) −7.78211 13.4790i −0.304072 0.526668i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.1943 + 33.2454i −0.747702 + 1.29506i 0.201220 + 0.979546i \(0.435509\pi\)
−0.948922 + 0.315512i \(0.897824\pi\)
\(660\) 0 0
\(661\) 33.9258 1.31956 0.659780 0.751459i \(-0.270649\pi\)
0.659780 + 0.751459i \(0.270649\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.893040 17.0288i −0.0346306 0.660350i
\(666\) 0 0
\(667\) −1.37124 2.37505i −0.0530944 0.0919623i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.378860 + 0.656205i 0.0146257 + 0.0253325i
\(672\) 0 0
\(673\) −16.1030 + 27.8912i −0.620725 + 1.07513i 0.368626 + 0.929578i \(0.379828\pi\)
−0.989351 + 0.145549i \(0.953505\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 37.9684 1.45924 0.729622 0.683850i \(-0.239696\pi\)
0.729622 + 0.683850i \(0.239696\pi\)
\(678\) 0 0
\(679\) −19.5262 9.94823i −0.749346 0.381778i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7.59357 13.1525i 0.290560 0.503265i −0.683382 0.730061i \(-0.739492\pi\)
0.973942 + 0.226796i \(0.0728251\pi\)
\(684\) 0 0
\(685\) 21.8932 0.836495
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.46285 −0.360506
\(690\) 0 0
\(691\) −2.69148 −0.102389 −0.0511943 0.998689i \(-0.516303\pi\)
−0.0511943 + 0.998689i \(0.516303\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 41.0840 1.55841
\(696\) 0 0
\(697\) −5.98689 −0.226770
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.8515 0.447625 0.223813 0.974632i \(-0.428150\pi\)
0.223813 + 0.974632i \(0.428150\pi\)
\(702\) 0 0
\(703\) −11.9988 + 20.7826i −0.452544 + 0.783829i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 36.0047 23.3835i 1.35410 0.879427i
\(708\) 0 0
\(709\) −41.0333 −1.54104 −0.770520 0.637416i \(-0.780003\pi\)
−0.770520 + 0.637416i \(0.780003\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.30328 7.45351i 0.161159 0.279136i
\(714\) 0 0
\(715\) 2.89830 + 5.02001i 0.108390 + 0.187738i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.4555 + 18.1094i 0.389923 + 0.675366i 0.992439 0.122741i \(-0.0391685\pi\)
−0.602516 + 0.798107i \(0.705835\pi\)
\(720\) 0 0
\(721\) −5.24958 2.67457i −0.195505 0.0996060i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.68487 0.136853
\(726\) 0 0
\(727\) −1.32165 + 2.28917i −0.0490173 + 0.0849005i −0.889493 0.456949i \(-0.848942\pi\)
0.840476 + 0.541849i \(0.182276\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.18756 + 12.4492i 0.265841 + 0.460451i
\(732\) 0 0
\(733\) −7.07446 + 12.2533i −0.261301 + 0.452587i −0.966588 0.256335i \(-0.917485\pi\)
0.705287 + 0.708922i \(0.250818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.67174 15.0199i −0.319428 0.553265i
\(738\) 0 0
\(739\) 7.85905 13.6123i 0.289100 0.500736i −0.684495 0.729017i \(-0.739977\pi\)
0.973595 + 0.228282i \(0.0733107\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.5496 + 18.2724i 0.387026 + 0.670348i 0.992048 0.125861i \(-0.0401692\pi\)
−0.605022 + 0.796208i \(0.706836\pi\)
\(744\) 0 0
\(745\) 3.18333 + 5.51368i 0.116628 + 0.202006i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 38.8480 25.2301i 1.41947 0.921888i
\(750\) 0 0
\(751\) 6.51848 11.2903i 0.237863 0.411990i −0.722238 0.691644i \(-0.756887\pi\)
0.960101 + 0.279654i \(0.0902199\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −40.9732 −1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.02038 + 5.23146i −0.109489 + 0.189640i −0.915563 0.402174i \(-0.868255\pi\)
0.806074 + 0.591814i \(0.201588\pi\)
\(762\) 0 0
\(763\) −36.7719 18.7346i −1.33123 0.678238i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.95288 + 15.5068i 0.323270 + 0.559920i
\(768\) 0 0
\(769\) 0.108129 + 0.187285i 0.00389924 + 0.00675368i 0.867968 0.496619i \(-0.165425\pi\)
−0.864069 + 0.503373i \(0.832092\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.8132 + 32.5854i −0.676663 + 1.17202i 0.299316 + 0.954154i \(0.403241\pi\)
−0.975980 + 0.217861i \(0.930092\pi\)
\(774\) 0 0
\(775\) 5.78202 + 10.0148i 0.207696 + 0.359741i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.99539 + 3.45612i −0.0714923 + 0.123828i
\(780\) 0 0
\(781\) 8.74345 + 15.1441i 0.312865 + 0.541898i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.33198 + 7.50321i −0.154615 + 0.267801i
\(786\) 0 0
\(787\) −30.8135 −1.09838 −0.549191 0.835697i \(-0.685064\pi\)
−0.549191 + 0.835697i \(0.685064\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.74791 + 2.43410i −0.133260 + 0.0865468i
\(792\) 0 0
\(793\) −0.410286 0.710636i −0.0145697 0.0252354i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.9792 + 31.1408i 0.636855 + 1.10306i 0.986119 + 0.166040i \(0.0530981\pi\)
−0.349264 + 0.937024i \(0.613569\pi\)
\(798\) 0 0
\(799\) −6.58602 + 11.4073i −0.232997 + 0.403562i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.1537 0.499472
\(804\) 0 0