Properties

Label 3150.2.m.i.2843.3
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.3
Root \(0.692297i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.i.1457.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.77786i q^{11} +(-0.692297 - 0.692297i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(2.39327 + 2.39327i) q^{17} +(1.25714 - 1.25714i) q^{22} +(-3.38459 + 3.38459i) q^{23} -0.979056i q^{26} +(-0.707107 - 0.707107i) q^{28} -4.42289 q^{29} -5.77786 q^{31} +(-0.707107 - 0.707107i) q^{32} +3.38459i q^{34} +(-5.91399 + 5.91399i) q^{37} +0.807922i q^{41} +(4.64173 + 4.64173i) q^{43} +1.77786 q^{44} -4.78654 q^{46} +(7.47016 + 7.47016i) q^{47} -1.00000i q^{49} +(0.692297 - 0.692297i) q^{52} +(-3.56484 + 3.56484i) q^{53} -1.00000i q^{56} +(-3.12745 - 3.12745i) q^{58} -5.89887 q^{59} +2.39327 q^{61} +(-4.08557 - 4.08557i) q^{62} -1.00000i q^{64} +(0.641735 - 0.641735i) q^{67} +(-2.39327 + 2.39327i) q^{68} +10.6854i q^{71} +(-5.70097 - 5.70097i) q^{73} -8.36365 q^{74} +(1.25714 + 1.25714i) q^{77} -16.3423i q^{79} +(-0.571287 + 0.571287i) q^{82} +(0.171134 - 0.171134i) q^{83} +6.56440i q^{86} +(1.25714 + 1.25714i) q^{88} -13.2340 q^{89} +0.979056 q^{91} +(-3.38459 - 3.38459i) q^{92} +10.5644i q^{94} +(-12.6413 + 12.6413i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 4q^{13} - 8q^{14} - 8q^{16} + 4q^{22} - 8q^{23} - 24q^{29} - 8q^{31} + 4q^{37} + 12q^{43} - 24q^{44} + 12q^{47} - 4q^{52} - 32q^{53} - 12q^{58} - 16q^{59} - 4q^{62} - 20q^{67} - 36q^{73} - 40q^{74} + 4q^{77} + 12q^{82} - 56q^{83} + 4q^{88} - 72q^{89} - 8q^{92} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.77786i 0.536046i −0.963412 0.268023i \(-0.913630\pi\)
0.963412 0.268023i \(-0.0863704\pi\)
\(12\) 0 0
\(13\) −0.692297 0.692297i −0.192009 0.192009i 0.604555 0.796564i \(-0.293351\pi\)
−0.796564 + 0.604555i \(0.793351\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 2.39327 + 2.39327i 0.580453 + 0.580453i 0.935028 0.354575i \(-0.115374\pi\)
−0.354575 + 0.935028i \(0.615374\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.25714 1.25714i 0.268023 0.268023i
\(23\) −3.38459 + 3.38459i −0.705737 + 0.705737i −0.965636 0.259899i \(-0.916311\pi\)
0.259899 + 0.965636i \(0.416311\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.979056i 0.192009i
\(27\) 0 0
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) −4.42289 −0.821310 −0.410655 0.911791i \(-0.634700\pi\)
−0.410655 + 0.911791i \(0.634700\pi\)
\(30\) 0 0
\(31\) −5.77786 −1.03774 −0.518868 0.854855i \(-0.673646\pi\)
−0.518868 + 0.854855i \(0.673646\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 3.38459i 0.580453i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.91399 + 5.91399i −0.972255 + 0.972255i −0.999625 0.0273707i \(-0.991287\pi\)
0.0273707 + 0.999625i \(0.491287\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.807922i 0.126176i 0.998008 + 0.0630881i \(0.0200949\pi\)
−0.998008 + 0.0630881i \(0.979905\pi\)
\(42\) 0 0
\(43\) 4.64173 + 4.64173i 0.707858 + 0.707858i 0.966084 0.258227i \(-0.0831381\pi\)
−0.258227 + 0.966084i \(0.583138\pi\)
\(44\) 1.77786 0.268023
\(45\) 0 0
\(46\) −4.78654 −0.705737
\(47\) 7.47016 + 7.47016i 1.08964 + 1.08964i 0.995566 + 0.0940694i \(0.0299876\pi\)
0.0940694 + 0.995566i \(0.470012\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.692297 0.692297i 0.0960044 0.0960044i
\(53\) −3.56484 + 3.56484i −0.489669 + 0.489669i −0.908202 0.418533i \(-0.862544\pi\)
0.418533 + 0.908202i \(0.362544\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −3.12745 3.12745i −0.410655 0.410655i
\(59\) −5.89887 −0.767968 −0.383984 0.923340i \(-0.625448\pi\)
−0.383984 + 0.923340i \(0.625448\pi\)
\(60\) 0 0
\(61\) 2.39327 0.306427 0.153213 0.988193i \(-0.451038\pi\)
0.153213 + 0.988193i \(0.451038\pi\)
\(62\) −4.08557 4.08557i −0.518868 0.518868i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.641735 0.641735i 0.0784004 0.0784004i −0.666819 0.745220i \(-0.732345\pi\)
0.745220 + 0.666819i \(0.232345\pi\)
\(68\) −2.39327 + 2.39327i −0.290227 + 0.290227i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.6854i 1.26813i 0.773282 + 0.634063i \(0.218614\pi\)
−0.773282 + 0.634063i \(0.781386\pi\)
\(72\) 0 0
\(73\) −5.70097 5.70097i −0.667248 0.667248i 0.289830 0.957078i \(-0.406401\pi\)
−0.957078 + 0.289830i \(0.906401\pi\)
\(74\) −8.36365 −0.972255
\(75\) 0 0
\(76\) 0 0
\(77\) 1.25714 + 1.25714i 0.143264 + 0.143264i
\(78\) 0 0
\(79\) 16.3423i 1.83865i −0.393500 0.919324i \(-0.628736\pi\)
0.393500 0.919324i \(-0.371264\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.571287 + 0.571287i −0.0630881 + 0.0630881i
\(83\) 0.171134 0.171134i 0.0187844 0.0187844i −0.697652 0.716437i \(-0.745772\pi\)
0.716437 + 0.697652i \(0.245772\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.56440i 0.707858i
\(87\) 0 0
\(88\) 1.25714 + 1.25714i 0.134012 + 0.134012i
\(89\) −13.2340 −1.40280 −0.701399 0.712769i \(-0.747441\pi\)
−0.701399 + 0.712769i \(0.747441\pi\)
\(90\) 0 0
\(91\) 0.979056 0.102633
\(92\) −3.38459 3.38459i −0.352868 0.352868i
\(93\) 0 0
\(94\) 10.5644i 1.08964i
\(95\) 0 0
\(96\) 0 0
\(97\) −12.6413 + 12.6413i −1.28353 + 1.28353i −0.344884 + 0.938645i \(0.612082\pi\)
−0.938645 + 0.344884i \(0.887918\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 12.6778i 1.26149i 0.775991 + 0.630744i \(0.217250\pi\)
−0.775991 + 0.630744i \(0.782750\pi\)
\(102\) 0 0
\(103\) −7.43472 7.43472i −0.732565 0.732565i 0.238563 0.971127i \(-0.423324\pi\)
−0.971127 + 0.238563i \(0.923324\pi\)
\(104\) 0.979056 0.0960044
\(105\) 0 0
\(106\) −5.04145 −0.489669
\(107\) −13.5138 13.5138i −1.30643 1.30643i −0.923972 0.382461i \(-0.875077\pi\)
−0.382461 0.923972i \(-0.624923\pi\)
\(108\) 0 0
\(109\) 3.30082i 0.316161i 0.987426 + 0.158081i \(0.0505306\pi\)
−0.987426 + 0.158081i \(0.949469\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) −5.84937 + 5.84937i −0.550263 + 0.550263i −0.926517 0.376254i \(-0.877212\pi\)
0.376254 + 0.926517i \(0.377212\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.42289i 0.410655i
\(117\) 0 0
\(118\) −4.17113 4.17113i −0.383984 0.383984i
\(119\) −3.38459 −0.310265
\(120\) 0 0
\(121\) 7.83920 0.712654
\(122\) 1.69230 + 1.69230i 0.153213 + 0.153213i
\(123\) 0 0
\(124\) 5.77786i 0.518868i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.615405 0.615405i 0.0546084 0.0546084i −0.679275 0.733884i \(-0.737706\pi\)
0.733884 + 0.679275i \(0.237706\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.52717i 0.570281i 0.958486 + 0.285141i \(0.0920403\pi\)
−0.958486 + 0.285141i \(0.907960\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.907550 0.0784004
\(135\) 0 0
\(136\) −3.38459 −0.290227
\(137\) 0.192517 + 0.192517i 0.0164478 + 0.0164478i 0.715283 0.698835i \(-0.246298\pi\)
−0.698835 + 0.715283i \(0.746298\pi\)
\(138\) 0 0
\(139\) 14.8694i 1.26121i −0.776104 0.630605i \(-0.782807\pi\)
0.776104 0.630605i \(-0.217193\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.55573 + 7.55573i −0.634063 + 0.634063i
\(143\) −1.23081 + 1.23081i −0.102926 + 0.102926i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.06239i 0.667248i
\(147\) 0 0
\(148\) −5.91399 5.91399i −0.486127 0.486127i
\(149\) 20.6467 1.69144 0.845721 0.533625i \(-0.179171\pi\)
0.845721 + 0.533625i \(0.179171\pi\)
\(150\) 0 0
\(151\) 6.01735 0.489685 0.244843 0.969563i \(-0.421264\pi\)
0.244843 + 0.969563i \(0.421264\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.77786i 0.143264i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.608522 0.608522i 0.0485654 0.0485654i −0.682407 0.730972i \(-0.739067\pi\)
0.730972 + 0.682407i \(0.239067\pi\)
\(158\) 11.5557 11.5557i 0.919324 0.919324i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.78654i 0.377232i
\(162\) 0 0
\(163\) −6.12745 6.12745i −0.479939 0.479939i 0.425173 0.905112i \(-0.360213\pi\)
−0.905112 + 0.425173i \(0.860213\pi\)
\(164\) −0.807922 −0.0630881
\(165\) 0 0
\(166\) 0.242020 0.0187844
\(167\) 6.18669 + 6.18669i 0.478741 + 0.478741i 0.904729 0.425988i \(-0.140073\pi\)
−0.425988 + 0.904729i \(0.640073\pi\)
\(168\) 0 0
\(169\) 12.0414i 0.926265i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.64173 + 4.64173i −0.353929 + 0.353929i
\(173\) −15.7720 + 15.7720i −1.19913 + 1.19913i −0.224697 + 0.974429i \(0.572139\pi\)
−0.974429 + 0.224697i \(0.927861\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.77786i 0.134012i
\(177\) 0 0
\(178\) −9.35783 9.35783i −0.701399 0.701399i
\(179\) 3.87899 0.289929 0.144965 0.989437i \(-0.453693\pi\)
0.144965 + 0.989437i \(0.453693\pi\)
\(180\) 0 0
\(181\) 23.6896 1.76084 0.880418 0.474198i \(-0.157262\pi\)
0.880418 + 0.474198i \(0.157262\pi\)
\(182\) 0.692297 + 0.692297i 0.0513165 + 0.0513165i
\(183\) 0 0
\(184\) 4.78654i 0.352868i
\(185\) 0 0
\(186\) 0 0
\(187\) 4.25491 4.25491i 0.311150 0.311150i
\(188\) −7.47016 + 7.47016i −0.544818 + 0.544818i
\(189\) 0 0
\(190\) 0 0
\(191\) 23.4720i 1.69837i 0.528095 + 0.849185i \(0.322907\pi\)
−0.528095 + 0.849185i \(0.677093\pi\)
\(192\) 0 0
\(193\) −18.1288 18.1288i −1.30494 1.30494i −0.925019 0.379921i \(-0.875951\pi\)
−0.379921 0.925019i \(-0.624049\pi\)
\(194\) −17.8775 −1.28353
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −9.58535 9.58535i −0.682928 0.682928i 0.277731 0.960659i \(-0.410418\pi\)
−0.960659 + 0.277731i \(0.910418\pi\)
\(198\) 0 0
\(199\) 2.46416i 0.174679i 0.996179 + 0.0873397i \(0.0278366\pi\)
−0.996179 + 0.0873397i \(0.972163\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −8.96456 + 8.96456i −0.630744 + 0.630744i
\(203\) 3.12745 3.12745i 0.219504 0.219504i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.5143i 0.732565i
\(207\) 0 0
\(208\) 0.692297 + 0.692297i 0.0480022 + 0.0480022i
\(209\) 0 0
\(210\) 0 0
\(211\) −5.57308 −0.383667 −0.191833 0.981428i \(-0.561443\pi\)
−0.191833 + 0.981428i \(0.561443\pi\)
\(212\) −3.56484 3.56484i −0.244834 0.244834i
\(213\) 0 0
\(214\) 19.1115i 1.30643i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.08557 4.08557i 0.277346 0.277346i
\(218\) −2.33403 + 2.33403i −0.158081 + 0.158081i
\(219\) 0 0
\(220\) 0 0
\(221\) 3.31371i 0.222904i
\(222\) 0 0
\(223\) 14.6854 + 14.6854i 0.983408 + 0.983408i 0.999865 0.0164565i \(-0.00523851\pi\)
−0.0164565 + 0.999865i \(0.505239\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −8.27226 −0.550263
\(227\) 19.5557 + 19.5557i 1.29796 + 1.29796i 0.929738 + 0.368221i \(0.120033\pi\)
0.368221 + 0.929738i \(0.379967\pi\)
\(228\) 0 0
\(229\) 24.3622i 1.60990i 0.593345 + 0.804948i \(0.297807\pi\)
−0.593345 + 0.804948i \(0.702193\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.12745 3.12745i 0.205327 0.205327i
\(233\) −14.7692 + 14.7692i −0.967562 + 0.967562i −0.999490 0.0319284i \(-0.989835\pi\)
0.0319284 + 0.999490i \(0.489835\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.89887i 0.383984i
\(237\) 0 0
\(238\) −2.39327 2.39327i −0.155133 0.155133i
\(239\) 1.47283 0.0952695 0.0476348 0.998865i \(-0.484832\pi\)
0.0476348 + 0.998865i \(0.484832\pi\)
\(240\) 0 0
\(241\) −21.5557 −1.38853 −0.694263 0.719721i \(-0.744270\pi\)
−0.694263 + 0.719721i \(0.744270\pi\)
\(242\) 5.54315 + 5.54315i 0.356327 + 0.356327i
\(243\) 0 0
\(244\) 2.39327i 0.153213i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.08557 4.08557i 0.259434 0.259434i
\(249\) 0 0
\(250\) 0 0
\(251\) 2.68541i 0.169502i 0.996402 + 0.0847509i \(0.0270095\pi\)
−0.996402 + 0.0847509i \(0.972991\pi\)
\(252\) 0 0
\(253\) 6.01735 + 6.01735i 0.378308 + 0.378308i
\(254\) 0.870315 0.0546084
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.9873 + 10.9873i 0.685368 + 0.685368i 0.961205 0.275836i \(-0.0889547\pi\)
−0.275836 + 0.961205i \(0.588955\pi\)
\(258\) 0 0
\(259\) 8.36365i 0.519692i
\(260\) 0 0
\(261\) 0 0
\(262\) −4.61541 + 4.61541i −0.285141 + 0.285141i
\(263\) 7.92911 7.92911i 0.488930 0.488930i −0.419038 0.907969i \(-0.637633\pi\)
0.907969 + 0.419038i \(0.137633\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.641735 + 0.641735i 0.0392002 + 0.0392002i
\(269\) 7.26420 0.442906 0.221453 0.975171i \(-0.428920\pi\)
0.221453 + 0.975171i \(0.428920\pi\)
\(270\) 0 0
\(271\) −17.5756 −1.06764 −0.533821 0.845597i \(-0.679244\pi\)
−0.533821 + 0.845597i \(0.679244\pi\)
\(272\) −2.39327 2.39327i −0.145113 0.145113i
\(273\) 0 0
\(274\) 0.272260i 0.0164478i
\(275\) 0 0
\(276\) 0 0
\(277\) 9.81287 9.81287i 0.589598 0.589598i −0.347924 0.937523i \(-0.613113\pi\)
0.937523 + 0.347924i \(0.113113\pi\)
\(278\) 10.5143 10.5143i 0.630605 0.630605i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.5849i 0.750753i −0.926872 0.375376i \(-0.877513\pi\)
0.926872 0.375376i \(-0.122487\pi\)
\(282\) 0 0
\(283\) −4.69918 4.69918i −0.279337 0.279337i 0.553507 0.832844i \(-0.313289\pi\)
−0.832844 + 0.553507i \(0.813289\pi\)
\(284\) −10.6854 −0.634063
\(285\) 0 0
\(286\) −1.74063 −0.102926
\(287\) −0.571287 0.571287i −0.0337220 0.0337220i
\(288\) 0 0
\(289\) 5.54452i 0.326148i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.70097 5.70097i 0.333624 0.333624i
\(293\) −3.39866 + 3.39866i −0.198552 + 0.198552i −0.799379 0.600827i \(-0.794838\pi\)
0.600827 + 0.799379i \(0.294838\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.36365i 0.486127i
\(297\) 0 0
\(298\) 14.5994 + 14.5994i 0.845721 + 0.845721i
\(299\) 4.68629 0.271015
\(300\) 0 0
\(301\) −6.56440 −0.378366
\(302\) 4.25491 + 4.25491i 0.244843 + 0.244843i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 15.5557 15.5557i 0.887812 0.887812i −0.106500 0.994313i \(-0.533965\pi\)
0.994313 + 0.106500i \(0.0339645\pi\)
\(308\) −1.25714 + 1.25714i −0.0716322 + 0.0716322i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.773651i 0.0438697i −0.999759 0.0219349i \(-0.993017\pi\)
0.999759 0.0219349i \(-0.00698264\pi\)
\(312\) 0 0
\(313\) 11.8548 + 11.8548i 0.670070 + 0.670070i 0.957732 0.287662i \(-0.0928779\pi\)
−0.287662 + 0.957732i \(0.592878\pi\)
\(314\) 0.860580 0.0485654
\(315\) 0 0
\(316\) 16.3423 0.919324
\(317\) 0.00911383 + 0.00911383i 0.000511884 + 0.000511884i 0.707363 0.706851i \(-0.249885\pi\)
−0.706851 + 0.707363i \(0.749885\pi\)
\(318\) 0 0
\(319\) 7.86330i 0.440260i
\(320\) 0 0
\(321\) 0 0
\(322\) 3.38459 3.38459i 0.188616 0.188616i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 8.66553i 0.479939i
\(327\) 0 0
\(328\) −0.571287 0.571287i −0.0315441 0.0315441i
\(329\) −10.5644 −0.582434
\(330\) 0 0
\(331\) −23.7977 −1.30804 −0.654021 0.756476i \(-0.726919\pi\)
−0.654021 + 0.756476i \(0.726919\pi\)
\(332\) 0.171134 + 0.171134i 0.00939221 + 0.00939221i
\(333\) 0 0
\(334\) 8.74930i 0.478741i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.828866 0.828866i 0.0451512 0.0451512i −0.684171 0.729322i \(-0.739836\pi\)
0.729322 + 0.684171i \(0.239836\pi\)
\(338\) 8.51459 8.51459i 0.463133 0.463133i
\(339\) 0 0
\(340\) 0 0
\(341\) 10.2723i 0.556274i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −6.56440 −0.353929
\(345\) 0 0
\(346\) −22.3050 −1.19913
\(347\) 5.17157 + 5.17157i 0.277625 + 0.277625i 0.832160 0.554535i \(-0.187104\pi\)
−0.554535 + 0.832160i \(0.687104\pi\)
\(348\) 0 0
\(349\) 4.20837i 0.225269i −0.993636 0.112634i \(-0.964071\pi\)
0.993636 0.112634i \(-0.0359289\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.25714 + 1.25714i −0.0670058 + 0.0670058i
\(353\) 2.22214 2.22214i 0.118272 0.118272i −0.645493 0.763766i \(-0.723348\pi\)
0.763766 + 0.645493i \(0.223348\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 13.2340i 0.701399i
\(357\) 0 0
\(358\) 2.74286 + 2.74286i 0.144965 + 0.144965i
\(359\) 22.7692 1.20171 0.600856 0.799357i \(-0.294827\pi\)
0.600856 + 0.799357i \(0.294827\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 16.7511 + 16.7511i 0.880418 + 0.880418i
\(363\) 0 0
\(364\) 0.979056i 0.0513165i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.13836 + 2.13836i −0.111622 + 0.111622i −0.760712 0.649090i \(-0.775150\pi\)
0.649090 + 0.760712i \(0.275150\pi\)
\(368\) 3.38459 3.38459i 0.176434 0.176434i
\(369\) 0 0
\(370\) 0 0
\(371\) 5.04145i 0.261739i
\(372\) 0 0
\(373\) −13.0263 13.0263i −0.674478 0.674478i 0.284267 0.958745i \(-0.408250\pi\)
−0.958745 + 0.284267i \(0.908250\pi\)
\(374\) 6.01735 0.311150
\(375\) 0 0
\(376\) −10.5644 −0.544818
\(377\) 3.06195 + 3.06195i 0.157699 + 0.157699i
\(378\) 0 0
\(379\) 27.4011i 1.40750i −0.710449 0.703749i \(-0.751508\pi\)
0.710449 0.703749i \(-0.248492\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −16.5972 + 16.5972i −0.849185 + 0.849185i
\(383\) −17.6715 + 17.6715i −0.902973 + 0.902973i −0.995692 0.0927190i \(-0.970444\pi\)
0.0927190 + 0.995692i \(0.470444\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 25.6380i 1.30494i
\(387\) 0 0
\(388\) −12.6413 12.6413i −0.641765 0.641765i
\(389\) 15.8356 0.802897 0.401449 0.915882i \(-0.368507\pi\)
0.401449 + 0.915882i \(0.368507\pi\)
\(390\) 0 0
\(391\) −16.2005 −0.819294
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 13.5557i 0.682928i
\(395\) 0 0
\(396\) 0 0
\(397\) 14.5575 14.5575i 0.730621 0.730621i −0.240122 0.970743i \(-0.577187\pi\)
0.970743 + 0.240122i \(0.0771874\pi\)
\(398\) −1.74242 + 1.74242i −0.0873397 + 0.0873397i
\(399\) 0 0
\(400\) 0 0
\(401\) 9.78102i 0.488441i −0.969720 0.244220i \(-0.921468\pi\)
0.969720 0.244220i \(-0.0785320\pi\)
\(402\) 0 0
\(403\) 4.00000 + 4.00000i 0.199254 + 0.199254i
\(404\) −12.6778 −0.630744
\(405\) 0 0
\(406\) 4.42289 0.219504
\(407\) 10.5143 + 10.5143i 0.521174 + 0.521174i
\(408\) 0 0
\(409\) 10.3907i 0.513789i 0.966439 + 0.256894i \(0.0826993\pi\)
−0.966439 + 0.256894i \(0.917301\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 7.43472 7.43472i 0.366282 0.366282i
\(413\) 4.17113 4.17113i 0.205248 0.205248i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.979056i 0.0480022i
\(417\) 0 0
\(418\) 0 0
\(419\) 32.8521 1.60493 0.802465 0.596700i \(-0.203522\pi\)
0.802465 + 0.596700i \(0.203522\pi\)
\(420\) 0 0
\(421\) 33.6560 1.64029 0.820146 0.572154i \(-0.193892\pi\)
0.820146 + 0.572154i \(0.193892\pi\)
\(422\) −3.94076 3.94076i −0.191833 0.191833i
\(423\) 0 0
\(424\) 5.04145i 0.244834i
\(425\) 0 0
\(426\) 0 0
\(427\) −1.69230 + 1.69230i −0.0818960 + 0.0818960i
\(428\) 13.5138 13.5138i 0.653216 0.653216i
\(429\) 0 0
\(430\) 0 0
\(431\) 28.4260i 1.36923i −0.728903 0.684617i \(-0.759969\pi\)
0.728903 0.684617i \(-0.240031\pi\)
\(432\) 0 0
\(433\) 8.84355 + 8.84355i 0.424994 + 0.424994i 0.886919 0.461925i \(-0.152841\pi\)
−0.461925 + 0.886919i \(0.652841\pi\)
\(434\) 5.77786 0.277346
\(435\) 0 0
\(436\) −3.30082 −0.158081
\(437\) 0 0
\(438\) 0 0
\(439\) 0.481506i 0.0229810i 0.999934 + 0.0114905i \(0.00365763\pi\)
−0.999934 + 0.0114905i \(0.996342\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.34315 2.34315i 0.111452 0.111452i
\(443\) 15.8570 15.8570i 0.753388 0.753388i −0.221722 0.975110i \(-0.571168\pi\)
0.975110 + 0.221722i \(0.0711677\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 20.7683i 0.983408i
\(447\) 0 0
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) −31.8986 −1.50539 −0.752694 0.658370i \(-0.771246\pi\)
−0.752694 + 0.658370i \(0.771246\pi\)
\(450\) 0 0
\(451\) 1.43638 0.0676363
\(452\) −5.84937 5.84937i −0.275131 0.275131i
\(453\) 0 0
\(454\) 27.6560i 1.29796i
\(455\) 0 0
\(456\) 0 0
\(457\) −20.5557 + 20.5557i −0.961556 + 0.961556i −0.999288 0.0377315i \(-0.987987\pi\)
0.0377315 + 0.999288i \(0.487987\pi\)
\(458\) −17.2266 + 17.2266i −0.804948 + 0.804948i
\(459\) 0 0
\(460\) 0 0
\(461\) 35.9849i 1.67599i 0.545682 + 0.837993i \(0.316271\pi\)
−0.545682 + 0.837993i \(0.683729\pi\)
\(462\) 0 0
\(463\) 12.8703 + 12.8703i 0.598134 + 0.598134i 0.939816 0.341682i \(-0.110996\pi\)
−0.341682 + 0.939816i \(0.610996\pi\)
\(464\) 4.42289 0.205327
\(465\) 0 0
\(466\) −20.8868 −0.967562
\(467\) −0.531630 0.531630i −0.0246009 0.0246009i 0.694699 0.719300i \(-0.255537\pi\)
−0.719300 + 0.694699i \(0.755537\pi\)
\(468\) 0 0
\(469\) 0.907550i 0.0419068i
\(470\) 0 0
\(471\) 0 0
\(472\) 4.17113 4.17113i 0.191992 0.191992i
\(473\) 8.25237 8.25237i 0.379445 0.379445i
\(474\) 0 0
\(475\) 0 0
\(476\) 3.38459i 0.155133i
\(477\) 0 0
\(478\) 1.04145 + 1.04145i 0.0476348 + 0.0476348i
\(479\) 23.0588 1.05358 0.526792 0.849994i \(-0.323395\pi\)
0.526792 + 0.849994i \(0.323395\pi\)
\(480\) 0 0
\(481\) 8.18848 0.373363
\(482\) −15.2422 15.2422i −0.694263 0.694263i
\(483\) 0 0
\(484\) 7.83920i 0.356327i
\(485\) 0 0
\(486\) 0 0
\(487\) 15.9291 15.9291i 0.721817 0.721817i −0.247158 0.968975i \(-0.579497\pi\)
0.968975 + 0.247158i \(0.0794967\pi\)
\(488\) −1.69230 + 1.69230i −0.0766067 + 0.0766067i
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3509i 0.512261i −0.966642 0.256130i \(-0.917552\pi\)
0.966642 0.256130i \(-0.0824477\pi\)
\(492\) 0 0
\(493\) −10.5852 10.5852i −0.476732 0.476732i
\(494\) 0 0
\(495\) 0 0
\(496\) 5.77786 0.259434
\(497\) −7.55573 7.55573i −0.338921 0.338921i
\(498\) 0 0
\(499\) 20.6319i 0.923610i 0.886982 + 0.461805i \(0.152798\pi\)
−0.886982 + 0.461805i \(0.847202\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.89887 + 1.89887i −0.0847509 + 0.0847509i
\(503\) 21.2982 21.2982i 0.949638 0.949638i −0.0491536 0.998791i \(-0.515652\pi\)
0.998791 + 0.0491536i \(0.0156524\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8.50982i 0.378308i
\(507\) 0 0
\(508\) 0.615405 + 0.615405i 0.0273042 + 0.0273042i
\(509\) 8.13328 0.360501 0.180251 0.983621i \(-0.442309\pi\)
0.180251 + 0.983621i \(0.442309\pi\)
\(510\) 0 0
\(511\) 8.06239 0.356659
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 15.5384i 0.685368i
\(515\) 0 0
\(516\) 0 0
\(517\) 13.2809 13.2809i 0.584095 0.584095i
\(518\) 5.91399 5.91399i 0.259846 0.259846i
\(519\) 0 0
\(520\) 0 0
\(521\) 19.2331i 0.842617i 0.906917 + 0.421308i \(0.138429\pi\)
−0.906917 + 0.421308i \(0.861571\pi\)
\(522\) 0 0
\(523\) 3.22635 + 3.22635i 0.141078 + 0.141078i 0.774119 0.633040i \(-0.218193\pi\)
−0.633040 + 0.774119i \(0.718193\pi\)
\(524\) −6.52717 −0.285141
\(525\) 0 0
\(526\) 11.2135 0.488930
\(527\) −13.8280 13.8280i −0.602357 0.602357i
\(528\) 0 0
\(529\) 0.0890385i 0.00387124i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.559322 0.559322i 0.0242269 0.0242269i
\(534\) 0 0
\(535\) 0 0
\(536\) 0.907550i 0.0392002i
\(537\) 0 0
\(538\) 5.13657 + 5.13657i 0.221453 + 0.221453i
\(539\) −1.77786 −0.0765780
\(540\) 0 0
\(541\) −12.9412 −0.556386 −0.278193 0.960525i \(-0.589735\pi\)
−0.278193 + 0.960525i \(0.589735\pi\)
\(542\) −12.4278 12.4278i −0.533821 0.533821i
\(543\) 0 0
\(544\) 3.38459i 0.145113i
\(545\) 0 0
\(546\) 0 0
\(547\) −7.15601 + 7.15601i −0.305969 + 0.305969i −0.843344 0.537375i \(-0.819416\pi\)
0.537375 + 0.843344i \(0.319416\pi\)
\(548\) −0.192517 + 0.192517i −0.00822390 + 0.00822390i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 11.5557 + 11.5557i 0.491400 + 0.491400i
\(554\) 13.8775 0.589598
\(555\) 0 0
\(556\) 14.8694 0.630605
\(557\) −19.5648 19.5648i −0.828989 0.828989i 0.158388 0.987377i \(-0.449370\pi\)
−0.987377 + 0.158388i \(0.949370\pi\)
\(558\) 0 0
\(559\) 6.42692i 0.271830i
\(560\) 0 0
\(561\) 0 0
\(562\) 8.89887 8.89887i 0.375376 0.375376i
\(563\) 0.0708861 0.0708861i 0.00298749 0.00298749i −0.705611 0.708599i \(-0.749328\pi\)
0.708599 + 0.705611i \(0.249328\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.64564i 0.279337i
\(567\) 0 0
\(568\) −7.55573 7.55573i −0.317031 0.317031i
\(569\) −20.2232 −0.847799 −0.423900 0.905709i \(-0.639339\pi\)
−0.423900 + 0.905709i \(0.639339\pi\)
\(570\) 0 0
\(571\) 34.9439 1.46236 0.731179 0.682186i \(-0.238971\pi\)
0.731179 + 0.682186i \(0.238971\pi\)
\(572\) −1.23081 1.23081i −0.0514628 0.0514628i
\(573\) 0 0
\(574\) 0.807922i 0.0337220i
\(575\) 0 0
\(576\) 0 0
\(577\) −32.2853 + 32.2853i −1.34405 + 1.34405i −0.452071 + 0.891982i \(0.649315\pi\)
−0.891982 + 0.452071i \(0.850685\pi\)
\(578\) 3.92057 3.92057i 0.163074 0.163074i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.242020i 0.0100407i
\(582\) 0 0
\(583\) 6.33781 + 6.33781i 0.262485 + 0.262485i
\(584\) 8.06239 0.333624
\(585\) 0 0
\(586\) −4.80642 −0.198552
\(587\) 9.40194 + 9.40194i 0.388060 + 0.388060i 0.873995 0.485935i \(-0.161521\pi\)
−0.485935 + 0.873995i \(0.661521\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 5.91399 5.91399i 0.243064 0.243064i
\(593\) −0.326416 + 0.326416i −0.0134043 + 0.0134043i −0.713777 0.700373i \(-0.753017\pi\)
0.700373 + 0.713777i \(0.253017\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.6467i 0.845721i
\(597\) 0 0
\(598\) 3.31371 + 3.31371i 0.135508 + 0.135508i
\(599\) 29.1288 1.19017 0.595085 0.803662i \(-0.297118\pi\)
0.595085 + 0.803662i \(0.297118\pi\)
\(600\) 0 0
\(601\) 45.0579 1.83795 0.918975 0.394315i \(-0.129018\pi\)
0.918975 + 0.394315i \(0.129018\pi\)
\(602\) −4.64173 4.64173i −0.189183 0.189183i
\(603\) 0 0
\(604\) 6.01735i 0.244843i
\(605\) 0 0
\(606\) 0 0
\(607\) −6.68541 + 6.68541i −0.271353 + 0.271353i −0.829645 0.558292i \(-0.811457\pi\)
0.558292 + 0.829645i \(0.311457\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.3431i 0.418439i
\(612\) 0 0
\(613\) 20.5112 + 20.5112i 0.828438 + 0.828438i 0.987301 0.158862i \(-0.0507826\pi\)
−0.158862 + 0.987301i \(0.550783\pi\)
\(614\) 21.9991 0.887812
\(615\) 0 0
\(616\) −1.77786 −0.0716322
\(617\) 4.29214 + 4.29214i 0.172795 + 0.172795i 0.788206 0.615411i \(-0.211010\pi\)
−0.615411 + 0.788206i \(0.711010\pi\)
\(618\) 0 0
\(619\) 8.16755i 0.328282i 0.986437 + 0.164141i \(0.0524851\pi\)
−0.986437 + 0.164141i \(0.947515\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0.547054 0.547054i 0.0219349 0.0219349i
\(623\) 9.35783 9.35783i 0.374913 0.374913i
\(624\) 0 0
\(625\) 0 0
\(626\) 16.7652i 0.670070i
\(627\) 0 0
\(628\) 0.608522 + 0.608522i 0.0242827 + 0.0242827i
\(629\) −28.3076 −1.12870
\(630\) 0 0
\(631\) 38.8694 1.54737 0.773684 0.633572i \(-0.218412\pi\)
0.773684 + 0.633572i \(0.218412\pi\)
\(632\) 11.5557 + 11.5557i 0.459662 + 0.459662i
\(633\) 0 0
\(634\) 0.0128889i 0.000511884i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.692297 + 0.692297i −0.0274298 + 0.0274298i
\(638\) −5.56019 + 5.56019i −0.220130 + 0.220130i
\(639\) 0 0
\(640\) 0 0
\(641\) 20.0751i 0.792918i 0.918052 + 0.396459i \(0.129761\pi\)
−0.918052 + 0.396459i \(0.870239\pi\)
\(642\) 0 0
\(643\) 13.6257 + 13.6257i 0.537347 + 0.537347i 0.922749 0.385402i \(-0.125937\pi\)
−0.385402 + 0.922749i \(0.625937\pi\)
\(644\) 4.78654 0.188616
\(645\) 0 0
\(646\) 0 0
\(647\) −1.47104 1.47104i −0.0578325 0.0578325i 0.677599 0.735432i \(-0.263021\pi\)
−0.735432 + 0.677599i \(0.763021\pi\)
\(648\) 0 0
\(649\) 10.4874i 0.411666i
\(650\) 0 0
\(651\) 0 0
\(652\) 6.12745 6.12745i 0.239970 0.239970i
\(653\) −4.09647 + 4.09647i −0.160307 + 0.160307i −0.782703 0.622396i \(-0.786160\pi\)
0.622396 + 0.782703i \(0.286160\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.807922i 0.0315441i
\(657\) 0 0
\(658\) −7.47016 7.47016i −0.291217 0.291217i
\(659\) 0.683757 0.0266354 0.0133177 0.999911i \(-0.495761\pi\)
0.0133177 + 0.999911i \(0.495761\pi\)
\(660\) 0 0
\(661\) −42.9776 −1.67163 −0.835817 0.549009i \(-0.815005\pi\)
−0.835817 + 0.549009i \(0.815005\pi\)
\(662\) −16.8275 16.8275i −0.654021 0.654021i
\(663\) 0 0
\(664\) 0.242020i 0.00939221i
\(665\) 0 0
\(666\) 0 0
\(667\) 14.9697 14.9697i 0.579629 0.579629i
\(668\) −6.18669 + 6.18669i −0.239370 + 0.239370i
\(669\) 0 0
\(670\) 0 0
\(671\) 4.25491i 0.164259i
\(672\) 0 0
\(673\) 24.6569 + 24.6569i 0.950452 + 0.950452i 0.998829 0.0483773i \(-0.0154050\pi\)
−0.0483773 + 0.998829i \(0.515405\pi\)
\(674\) 1.17219 0.0451512
\(675\) 0 0
\(676\) 12.0414 0.463133
\(677\) −31.2343 31.2343i −1.20043 1.20043i −0.974036 0.226394i \(-0.927306\pi\)
−0.226394 0.974036i \(-0.572694\pi\)
\(678\) 0 0
\(679\) 17.8775i 0.686075i
\(680\) 0 0
\(681\) 0 0
\(682\) −7.26358 + 7.26358i −0.278137 + 0.278137i
\(683\) 7.92000 7.92000i 0.303050 0.303050i −0.539156 0.842206i \(-0.681257\pi\)
0.842206 + 0.539156i \(0.181257\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −4.64173 4.64173i −0.176964 0.176964i
\(689\) 4.93586 0.188041
\(690\) 0 0
\(691\) 22.1227 0.841586 0.420793 0.907157i \(-0.361752\pi\)
0.420793 + 0.907157i \(0.361752\pi\)
\(692\) −15.7720 15.7720i −0.599563 0.599563i
\(693\) 0 0
\(694\) 7.31371i 0.277625i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.93358 + 1.93358i −0.0732394 + 0.0732394i
\(698\) 2.97577 2.97577i 0.112634 0.112634i
\(699\) 0 0
\(700\) 0 0
\(701\) 6.16352i 0.232793i −0.993203 0.116396i \(-0.962866\pi\)
0.993203 0.116396i \(-0.0371343\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.77786 −0.0670058
\(705\) 0 0
\(706\) 3.14257 0.118272
\(707\) −8.96456 8.96456i −0.337147 0.337147i
\(708\) 0 0
\(709\) 49.7215i 1.86733i 0.358146 + 0.933666i \(0.383409\pi\)
−0.358146 + 0.933666i \(0.616591\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 9.35783 9.35783i 0.350699 0.350699i
\(713\) 19.5557 19.5557i 0.732368 0.732368i
\(714\) 0 0
\(715\) 0 0
\(716\) 3.87899i 0.144965i
\(717\) 0 0
\(718\) 16.1002 + 16.1002i 0.600856 + 0.600856i
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) 10.5143 0.391572
\(722\) 13.4350 + 13.4350i 0.500000 + 0.500000i
\(723\) 0 0
\(724\) 23.6896i 0.880418i
\(725\) 0 0
\(726\) 0 0
\(727\) 15.9162 15.9162i 0.590300 0.590300i −0.347412 0.937712i \(-0.612940\pi\)
0.937712 + 0.347412i \(0.112940\pi\)
\(728\) −0.692297 + 0.692297i −0.0256582 + 0.0256582i
\(729\) 0 0
\(730\) 0 0
\(731\) 22.2178i 0.821757i
\(732\) 0 0
\(733\) 15.3578 + 15.3578i 0.567254 + 0.567254i 0.931358 0.364104i \(-0.118625\pi\)
−0.364104 + 0.931358i \(0.618625\pi\)
\(734\) −3.02410 −0.111622
\(735\) 0 0
\(736\) 4.78654 0.176434
\(737\) −1.14092 1.14092i −0.0420262 0.0420262i
\(738\) 0 0
\(739\) 45.6515i 1.67932i −0.543114 0.839659i \(-0.682755\pi\)
0.543114 0.839659i \(-0.317245\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 3.56484 3.56484i 0.130869 0.130869i
\(743\) 5.67508 5.67508i 0.208199 0.208199i −0.595303 0.803501i \(-0.702968\pi\)
0.803501 + 0.595303i \(0.202968\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 18.4220i 0.674478i
\(747\) 0 0
\(748\) 4.25491 + 4.25491i 0.155575 + 0.155575i
\(749\) 19.1115 0.698317
\(750\) 0 0
\(751\) −41.4364 −1.51203 −0.756017 0.654552i \(-0.772857\pi\)
−0.756017 + 0.654552i \(0.772857\pi\)
\(752\) −7.47016 7.47016i −0.272409 0.272409i
\(753\) 0 0
\(754\) 4.33026i 0.157699i
\(755\) 0 0
\(756\) 0 0
\(757\) 22.4109 22.4109i 0.814539 0.814539i −0.170772 0.985311i \(-0.554626\pi\)
0.985311 + 0.170772i \(0.0546261\pi\)
\(758\) 19.3755 19.3755i 0.703749 0.703749i
\(759\) 0 0
\(760\) 0 0
\(761\) 15.1675i 0.549823i 0.961470 + 0.274911i \(0.0886485\pi\)
−0.961470 + 0.274911i \(0.911351\pi\)
\(762\) 0 0
\(763\) −2.33403 2.33403i −0.0844976 0.0844976i
\(764\) −23.4720 −0.849185
\(765\) 0 0
\(766\) −24.9913 −0.902973
\(767\) 4.08378 + 4.08378i 0.147457 + 0.147457i
\(768\) 0 0
\(769\) 19.8686i 0.716481i −0.933629 0.358241i \(-0.883377\pi\)
0.933629 0.358241i \(-0.116623\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 18.1288 18.1288i 0.652470 0.652470i
\(773\) 0.293937 0.293937i 0.0105722 0.0105722i −0.701801 0.712373i \(-0.747620\pi\)
0.712373 + 0.701801i \(0.247620\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 17.8775i 0.641765i
\(777\) 0 0
\(778\) 11.1975 + 11.1975i 0.401449 + 0.401449i
\(779\) 0 0
\(780\) 0 0
\(781\) 18.9972 0.679774
\(782\) −11.4555 11.4555i −0.409647 0.409647i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −16.3076 + 16.3076i −0.581302 + 0.581302i −0.935261 0.353959i \(-0.884835\pi\)
0.353959 + 0.935261i \(0.384835\pi\)
\(788\) 9.58535 9.58535i 0.341464 0.341464i
\(789\) 0 0
\(790\) 0 0
\(791\) 8.27226i 0.294128i
\(792\) 0 0
\(793\) −1.65685 1.65685i −0.0588366 0.0588366i
\(794\) 20.5874 0.730621
\(795\) 0 0
\(796\) −2.46416 −0.0873397
\(797\) 22.1562 + 22.1562i 0.784813 + 0.784813i 0.980639 0.195826i \(-0.0627388\pi\)
−0.195826 + 0.980639i \(0.562739\pi\)
\(798\) 0 0
\(799\) 35.7562i 1.26496i
\(800\)