Properties

Label 1400.2.x.a.993.7
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: 16.0.29960650073923649536.7
Defining polynomial: \(x^{16} - 7 x^{12} + 40 x^{8} - 112 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{22} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.7
Root \(1.38588 + 0.281691i\) of defining polynomial
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.a.657.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.66757 - 1.66757i) q^{3} +(-1.34308 + 2.27950i) q^{7} -2.56155i q^{9} +O(q^{10})\) \(q+(1.66757 - 1.66757i) q^{3} +(-1.34308 + 2.27950i) q^{7} -2.56155i q^{9} +1.56155 q^{11} +(2.60399 - 2.60399i) q^{13} +(2.60399 + 2.60399i) q^{17} +2.64861 q^{19} +(1.56155 + 6.04090i) q^{21} +(0.794156 + 0.794156i) q^{23} +(0.731140 + 0.731140i) q^{27} -6.68466i q^{29} -9.43318i q^{31} +(2.60399 - 2.60399i) q^{33} +(2.82843 - 2.82843i) q^{37} -8.68466i q^{39} +2.64861i q^{41} +(6.45101 + 6.45101i) q^{43} +(1.66757 + 1.66757i) q^{47} +(-3.39228 - 6.12311i) q^{49} +8.68466 q^{51} +(-7.24517 - 7.24517i) q^{53} +(4.41674 - 4.41674i) q^{57} +12.0818 q^{59} +9.43318i q^{61} +(5.83907 + 3.44037i) q^{63} +(-3.62258 + 3.62258i) q^{67} +2.64861 q^{69} +6.24621 q^{71} +(-6.67026 + 6.67026i) q^{73} +(-2.09729 + 3.55957i) q^{77} -11.8078i q^{79} +10.1231 q^{81} +(-9.47954 + 9.47954i) q^{83} +(-11.1471 - 11.1471i) q^{87} -9.43318 q^{89} +(2.43845 + 9.43318i) q^{91} +(-15.7304 - 15.7304i) q^{93} +(-5.52855 - 5.52855i) q^{97} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{11} - 8q^{21} + 40q^{51} - 32q^{71} + 96q^{81} + 72q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.66757 1.66757i 0.962770 0.962770i −0.0365617 0.999331i \(-0.511641\pi\)
0.999331 + 0.0365617i \(0.0116405\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.34308 + 2.27950i −0.507636 + 0.861572i
\(8\) 0 0
\(9\) 2.56155i 0.853851i
\(10\) 0 0
\(11\) 1.56155 0.470826 0.235413 0.971895i \(-0.424356\pi\)
0.235413 + 0.971895i \(0.424356\pi\)
\(12\) 0 0
\(13\) 2.60399 2.60399i 0.722218 0.722218i −0.246839 0.969057i \(-0.579392\pi\)
0.969057 + 0.246839i \(0.0793919\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.60399 + 2.60399i 0.631561 + 0.631561i 0.948459 0.316899i \(-0.102641\pi\)
−0.316899 + 0.948459i \(0.602641\pi\)
\(18\) 0 0
\(19\) 2.64861 0.607634 0.303817 0.952730i \(-0.401739\pi\)
0.303817 + 0.952730i \(0.401739\pi\)
\(20\) 0 0
\(21\) 1.56155 + 6.04090i 0.340759 + 1.31823i
\(22\) 0 0
\(23\) 0.794156 + 0.794156i 0.165593 + 0.165593i 0.785039 0.619446i \(-0.212643\pi\)
−0.619446 + 0.785039i \(0.712643\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.731140 + 0.731140i 0.140708 + 0.140708i
\(28\) 0 0
\(29\) 6.68466i 1.24131i −0.784084 0.620655i \(-0.786867\pi\)
0.784084 0.620655i \(-0.213133\pi\)
\(30\) 0 0
\(31\) 9.43318i 1.69425i −0.531395 0.847124i \(-0.678332\pi\)
0.531395 0.847124i \(-0.321668\pi\)
\(32\) 0 0
\(33\) 2.60399 2.60399i 0.453297 0.453297i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.82843 2.82843i 0.464991 0.464991i −0.435297 0.900287i \(-0.643356\pi\)
0.900287 + 0.435297i \(0.143356\pi\)
\(38\) 0 0
\(39\) 8.68466i 1.39066i
\(40\) 0 0
\(41\) 2.64861i 0.413644i 0.978379 + 0.206822i \(0.0663121\pi\)
−0.978379 + 0.206822i \(0.933688\pi\)
\(42\) 0 0
\(43\) 6.45101 + 6.45101i 0.983770 + 0.983770i 0.999870 0.0161006i \(-0.00512520\pi\)
−0.0161006 + 0.999870i \(0.505125\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.66757 + 1.66757i 0.243240 + 0.243240i 0.818189 0.574949i \(-0.194978\pi\)
−0.574949 + 0.818189i \(0.694978\pi\)
\(48\) 0 0
\(49\) −3.39228 6.12311i −0.484612 0.874729i
\(50\) 0 0
\(51\) 8.68466 1.21610
\(52\) 0 0
\(53\) −7.24517 7.24517i −0.995200 0.995200i 0.00478852 0.999989i \(-0.498476\pi\)
−0.999989 + 0.00478852i \(0.998476\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.41674 4.41674i 0.585011 0.585011i
\(58\) 0 0
\(59\) 12.0818 1.57292 0.786458 0.617644i \(-0.211913\pi\)
0.786458 + 0.617644i \(0.211913\pi\)
\(60\) 0 0
\(61\) 9.43318i 1.20779i 0.797062 + 0.603897i \(0.206386\pi\)
−0.797062 + 0.603897i \(0.793614\pi\)
\(62\) 0 0
\(63\) 5.83907 + 3.44037i 0.735654 + 0.433445i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.62258 + 3.62258i −0.442569 + 0.442569i −0.892875 0.450306i \(-0.851315\pi\)
0.450306 + 0.892875i \(0.351315\pi\)
\(68\) 0 0
\(69\) 2.64861 0.318856
\(70\) 0 0
\(71\) 6.24621 0.741289 0.370644 0.928775i \(-0.379137\pi\)
0.370644 + 0.928775i \(0.379137\pi\)
\(72\) 0 0
\(73\) −6.67026 + 6.67026i −0.780695 + 0.780695i −0.979948 0.199253i \(-0.936149\pi\)
0.199253 + 0.979948i \(0.436149\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.09729 + 3.55957i −0.239008 + 0.405650i
\(78\) 0 0
\(79\) 11.8078i 1.32848i −0.747521 0.664239i \(-0.768756\pi\)
0.747521 0.664239i \(-0.231244\pi\)
\(80\) 0 0
\(81\) 10.1231 1.12479
\(82\) 0 0
\(83\) −9.47954 + 9.47954i −1.04052 + 1.04052i −0.0413712 + 0.999144i \(0.513173\pi\)
−0.999144 + 0.0413712i \(0.986827\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −11.1471 11.1471i −1.19510 1.19510i
\(88\) 0 0
\(89\) −9.43318 −0.999915 −0.499957 0.866050i \(-0.666651\pi\)
−0.499957 + 0.866050i \(0.666651\pi\)
\(90\) 0 0
\(91\) 2.43845 + 9.43318i 0.255619 + 0.988866i
\(92\) 0 0
\(93\) −15.7304 15.7304i −1.63117 1.63117i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.52855 5.52855i −0.561339 0.561339i 0.368348 0.929688i \(-0.379923\pi\)
−0.929688 + 0.368348i \(0.879923\pi\)
\(98\) 0 0
\(99\) 4.00000i 0.402015i
\(100\) 0 0
\(101\) 16.2177i 1.61373i −0.590739 0.806863i \(-0.701164\pi\)
0.590739 0.806863i \(-0.298836\pi\)
\(102\) 0 0
\(103\) −8.74840 + 8.74840i −0.862006 + 0.862006i −0.991571 0.129565i \(-0.958642\pi\)
0.129565 + 0.991571i \(0.458642\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.03427 2.03427i 0.196660 0.196660i −0.601906 0.798567i \(-0.705592\pi\)
0.798567 + 0.601906i \(0.205592\pi\)
\(108\) 0 0
\(109\) 2.68466i 0.257144i −0.991700 0.128572i \(-0.958961\pi\)
0.991700 0.128572i \(-0.0410393\pi\)
\(110\) 0 0
\(111\) 9.43318i 0.895358i
\(112\) 0 0
\(113\) 1.24012 + 1.24012i 0.116660 + 0.116660i 0.763027 0.646367i \(-0.223712\pi\)
−0.646367 + 0.763027i \(0.723712\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.67026 6.67026i −0.616666 0.616666i
\(118\) 0 0
\(119\) −9.43318 + 2.43845i −0.864738 + 0.223532i
\(120\) 0 0
\(121\) −8.56155 −0.778323
\(122\) 0 0
\(123\) 4.41674 + 4.41674i 0.398244 + 0.398244i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.27944 + 9.27944i −0.823417 + 0.823417i −0.986596 0.163180i \(-0.947825\pi\)
0.163180 + 0.986596i \(0.447825\pi\)
\(128\) 0 0
\(129\) 21.5150 1.89429
\(130\) 0 0
\(131\) 21.5150i 1.87977i 0.341489 + 0.939886i \(0.389069\pi\)
−0.341489 + 0.939886i \(0.610931\pi\)
\(132\) 0 0
\(133\) −3.55730 + 6.03753i −0.308457 + 0.523520i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.0736 10.0736i 0.860645 0.860645i −0.130768 0.991413i \(-0.541744\pi\)
0.991413 + 0.130768i \(0.0417443\pi\)
\(138\) 0 0
\(139\) 12.0818 1.02476 0.512382 0.858758i \(-0.328763\pi\)
0.512382 + 0.858758i \(0.328763\pi\)
\(140\) 0 0
\(141\) 5.56155 0.468367
\(142\) 0 0
\(143\) 4.06627 4.06627i 0.340039 0.340039i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −15.8675 4.55383i −1.30873 0.375593i
\(148\) 0 0
\(149\) 4.24621i 0.347863i 0.984758 + 0.173932i \(0.0556472\pi\)
−0.984758 + 0.173932i \(0.944353\pi\)
\(150\) 0 0
\(151\) −16.6847 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(152\) 0 0
\(153\) 6.67026 6.67026i 0.539259 0.539259i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 13.3405 + 13.3405i 1.06469 + 1.06469i 0.997758 + 0.0669325i \(0.0213212\pi\)
0.0669325 + 0.997758i \(0.478679\pi\)
\(158\) 0 0
\(159\) −24.1636 −1.91630
\(160\) 0 0
\(161\) −2.87689 + 0.743668i −0.226731 + 0.0586093i
\(162\) 0 0
\(163\) −7.69113 7.69113i −0.602415 0.602415i 0.338537 0.940953i \(-0.390068\pi\)
−0.940953 + 0.338537i \(0.890068\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.0081 + 15.0081i 1.16136 + 1.16136i 0.984178 + 0.177183i \(0.0566986\pi\)
0.177183 + 0.984178i \(0.443301\pi\)
\(168\) 0 0
\(169\) 0.561553i 0.0431964i
\(170\) 0 0
\(171\) 6.78456i 0.518829i
\(172\) 0 0
\(173\) 1.14171 1.14171i 0.0868028 0.0868028i −0.662372 0.749175i \(-0.730450\pi\)
0.749175 + 0.662372i \(0.230450\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 20.1472 20.1472i 1.51436 1.51436i
\(178\) 0 0
\(179\) 2.24621i 0.167890i 0.996470 + 0.0839449i \(0.0267520\pi\)
−0.996470 + 0.0839449i \(0.973248\pi\)
\(180\) 0 0
\(181\) 17.3790i 1.29177i −0.763434 0.645886i \(-0.776488\pi\)
0.763434 0.645886i \(-0.223512\pi\)
\(182\) 0 0
\(183\) 15.7304 + 15.7304i 1.16283 + 1.16283i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 4.06627 + 4.06627i 0.297355 + 0.297355i
\(188\) 0 0
\(189\) −2.64861 + 0.684658i −0.192658 + 0.0498016i
\(190\) 0 0
\(191\) 10.4384 0.755300 0.377650 0.925949i \(-0.376732\pi\)
0.377650 + 0.925949i \(0.376732\pi\)
\(192\) 0 0
\(193\) −1.24012 1.24012i −0.0892655 0.0892655i 0.661064 0.750330i \(-0.270105\pi\)
−0.750330 + 0.661064i \(0.770105\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.3188 + 17.3188i −1.23391 + 1.23391i −0.271461 + 0.962449i \(0.587507\pi\)
−0.962449 + 0.271461i \(0.912493\pi\)
\(198\) 0 0
\(199\) −5.29723 −0.375511 −0.187755 0.982216i \(-0.560121\pi\)
−0.187755 + 0.982216i \(0.560121\pi\)
\(200\) 0 0
\(201\) 12.0818i 0.852184i
\(202\) 0 0
\(203\) 15.2377 + 8.97802i 1.06948 + 0.630133i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.03427 2.03427i 0.141392 0.141392i
\(208\) 0 0
\(209\) 4.13595 0.286090
\(210\) 0 0
\(211\) −25.1771 −1.73326 −0.866631 0.498950i \(-0.833719\pi\)
−0.866631 + 0.498950i \(0.833719\pi\)
\(212\) 0 0
\(213\) 10.4160 10.4160i 0.713690 0.713690i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 21.5030 + 12.6695i 1.45972 + 0.860061i
\(218\) 0 0
\(219\) 22.2462i 1.50326i
\(220\) 0 0
\(221\) 13.5616 0.912249
\(222\) 0 0
\(223\) 2.07814 2.07814i 0.139163 0.139163i −0.634094 0.773256i \(-0.718627\pi\)
0.773256 + 0.634094i \(0.218627\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.25699 1.25699i −0.0834295 0.0834295i 0.664160 0.747590i \(-0.268789\pi\)
−0.747590 + 0.664160i \(0.768789\pi\)
\(228\) 0 0
\(229\) 2.64861 0.175025 0.0875127 0.996163i \(-0.472108\pi\)
0.0875127 + 0.996163i \(0.472108\pi\)
\(230\) 0 0
\(231\) 2.43845 + 9.43318i 0.160438 + 0.620658i
\(232\) 0 0
\(233\) −16.9706 16.9706i −1.11178 1.11178i −0.992910 0.118869i \(-0.962073\pi\)
−0.118869 0.992910i \(-0.537927\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −19.6902 19.6902i −1.27902 1.27902i
\(238\) 0 0
\(239\) 19.8078i 1.28126i 0.767851 + 0.640629i \(0.221326\pi\)
−0.767851 + 0.640629i \(0.778674\pi\)
\(240\) 0 0
\(241\) 26.8122i 1.72713i −0.504241 0.863563i \(-0.668228\pi\)
0.504241 0.863563i \(-0.331772\pi\)
\(242\) 0 0
\(243\) 14.6875 14.6875i 0.942205 0.942205i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.89697 6.89697i 0.438844 0.438844i
\(248\) 0 0
\(249\) 31.6155i 2.00355i
\(250\) 0 0
\(251\) 12.0818i 0.762596i 0.924452 + 0.381298i \(0.124523\pi\)
−0.924452 + 0.381298i \(0.875477\pi\)
\(252\) 0 0
\(253\) 1.24012 + 1.24012i 0.0779654 + 0.0779654i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.4160 + 10.4160i 0.649730 + 0.649730i 0.952928 0.303197i \(-0.0980542\pi\)
−0.303197 + 0.952928i \(0.598054\pi\)
\(258\) 0 0
\(259\) 2.64861 + 10.2462i 0.164577 + 0.636669i
\(260\) 0 0
\(261\) −17.1231 −1.05989
\(262\) 0 0
\(263\) 5.21089 + 5.21089i 0.321317 + 0.321317i 0.849272 0.527955i \(-0.177041\pi\)
−0.527955 + 0.849272i \(0.677041\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −15.7304 + 15.7304i −0.962688 + 0.962688i
\(268\) 0 0
\(269\) −5.29723 −0.322978 −0.161489 0.986875i \(-0.551630\pi\)
−0.161489 + 0.986875i \(0.551630\pi\)
\(270\) 0 0
\(271\) 4.13595i 0.251241i 0.992078 + 0.125621i \(0.0400922\pi\)
−0.992078 + 0.125621i \(0.959908\pi\)
\(272\) 0 0
\(273\) 19.7967 + 11.6642i 1.19815 + 0.705948i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7.24517 + 7.24517i −0.435320 + 0.435320i −0.890433 0.455114i \(-0.849599\pi\)
0.455114 + 0.890433i \(0.349599\pi\)
\(278\) 0 0
\(279\) −24.1636 −1.44664
\(280\) 0 0
\(281\) 0.438447 0.0261556 0.0130778 0.999914i \(-0.495837\pi\)
0.0130778 + 0.999914i \(0.495837\pi\)
\(282\) 0 0
\(283\) −2.07814 + 2.07814i −0.123533 + 0.123533i −0.766170 0.642638i \(-0.777840\pi\)
0.642638 + 0.766170i \(0.277840\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.03753 3.55730i −0.356384 0.209981i
\(288\) 0 0
\(289\) 3.43845i 0.202262i
\(290\) 0 0
\(291\) −18.4384 −1.08088
\(292\) 0 0
\(293\) 14.4822 14.4822i 0.846062 0.846062i −0.143578 0.989639i \(-0.545861\pi\)
0.989639 + 0.143578i \(0.0458606\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.14171 + 1.14171i 0.0662489 + 0.0662489i
\(298\) 0 0
\(299\) 4.13595 0.239188
\(300\) 0 0
\(301\) −23.3693 + 6.04090i −1.34699 + 0.348191i
\(302\) 0 0
\(303\) −27.0442 27.0442i −1.55365 1.55365i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 18.3432 + 18.3432i 1.04690 + 1.04690i 0.998845 + 0.0480587i \(0.0153035\pi\)
0.0480587 + 0.998845i \(0.484697\pi\)
\(308\) 0 0
\(309\) 29.1771i 1.65983i
\(310\) 0 0
\(311\) 14.7304i 0.835285i −0.908612 0.417642i \(-0.862857\pi\)
0.908612 0.417642i \(-0.137143\pi\)
\(312\) 0 0
\(313\) 6.99083 6.99083i 0.395145 0.395145i −0.481372 0.876517i \(-0.659861\pi\)
0.876517 + 0.481372i \(0.159861\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.4218 + 10.4218i −0.585346 + 0.585346i −0.936367 0.351021i \(-0.885834\pi\)
0.351021 + 0.936367i \(0.385834\pi\)
\(318\) 0 0
\(319\) 10.4384i 0.584441i
\(320\) 0 0
\(321\) 6.78456i 0.378677i
\(322\) 0 0
\(323\) 6.89697 + 6.89697i 0.383758 + 0.383758i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.47685 4.47685i −0.247570 0.247570i
\(328\) 0 0
\(329\) −6.04090 + 1.56155i −0.333045 + 0.0860912i
\(330\) 0 0
\(331\) −22.7386 −1.24983 −0.624914 0.780693i \(-0.714866\pi\)
−0.624914 + 0.780693i \(0.714866\pi\)
\(332\) 0 0
\(333\) −7.24517 7.24517i −0.397033 0.397033i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.17662 3.17662i 0.173042 0.173042i −0.615273 0.788314i \(-0.710954\pi\)
0.788314 + 0.615273i \(0.210954\pi\)
\(338\) 0 0
\(339\) 4.13595 0.224634
\(340\) 0 0
\(341\) 14.7304i 0.797696i
\(342\) 0 0
\(343\) 18.5137 + 0.491087i 0.999648 + 0.0265162i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.6962 13.6962i 0.735249 0.735249i −0.236405 0.971655i \(-0.575969\pi\)
0.971655 + 0.236405i \(0.0759693\pi\)
\(348\) 0 0
\(349\) −2.64861 −0.141777 −0.0708885 0.997484i \(-0.522583\pi\)
−0.0708885 + 0.997484i \(0.522583\pi\)
\(350\) 0 0
\(351\) 3.80776 0.203243
\(352\) 0 0
\(353\) −22.6148 + 22.6148i −1.20366 + 1.20366i −0.230620 + 0.973044i \(0.574075\pi\)
−0.973044 + 0.230620i \(0.925925\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −11.6642 + 19.7967i −0.617334 + 1.04775i
\(358\) 0 0
\(359\) 26.7386i 1.41121i 0.708605 + 0.705606i \(0.249325\pi\)
−0.708605 + 0.705606i \(0.750675\pi\)
\(360\) 0 0
\(361\) −11.9848 −0.630781
\(362\) 0 0
\(363\) −14.2770 + 14.2770i −0.749346 + 0.749346i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8.33783 8.33783i −0.435231 0.435231i 0.455172 0.890403i \(-0.349578\pi\)
−0.890403 + 0.455172i \(0.849578\pi\)
\(368\) 0 0
\(369\) 6.78456 0.353190
\(370\) 0 0
\(371\) 26.2462 6.78456i 1.36264 0.352237i
\(372\) 0 0
\(373\) −14.1421 14.1421i −0.732252 0.732252i 0.238813 0.971065i \(-0.423242\pi\)
−0.971065 + 0.238813i \(0.923242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17.4068 17.4068i −0.896496 0.896496i
\(378\) 0 0
\(379\) 26.2462i 1.34818i −0.738650 0.674089i \(-0.764537\pi\)
0.738650 0.674089i \(-0.235463\pi\)
\(380\) 0 0
\(381\) 30.9481i 1.58552i
\(382\) 0 0
\(383\) −14.2770 + 14.2770i −0.729518 + 0.729518i −0.970524 0.241005i \(-0.922523\pi\)
0.241005 + 0.970524i \(0.422523\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.5246 16.5246i 0.839993 0.839993i
\(388\) 0 0
\(389\) 20.4384i 1.03627i 0.855299 + 0.518135i \(0.173374\pi\)
−0.855299 + 0.518135i \(0.826626\pi\)
\(390\) 0 0
\(391\) 4.13595i 0.209164i
\(392\) 0 0
\(393\) 35.8776 + 35.8776i 1.80979 + 1.80979i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0200 13.0200i −0.653453 0.653453i 0.300370 0.953823i \(-0.402890\pi\)
−0.953823 + 0.300370i \(0.902890\pi\)
\(398\) 0 0
\(399\) 4.13595 + 16.0000i 0.207056 + 0.801002i
\(400\) 0 0
\(401\) 0.930870 0.0464854 0.0232427 0.999730i \(-0.492601\pi\)
0.0232427 + 0.999730i \(0.492601\pi\)
\(402\) 0 0
\(403\) −24.5639 24.5639i −1.22362 1.22362i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.41674 4.41674i 0.218930 0.218930i
\(408\) 0 0
\(409\) −30.9481 −1.53029 −0.765144 0.643860i \(-0.777332\pi\)
−0.765144 + 0.643860i \(0.777332\pi\)
\(410\) 0 0
\(411\) 33.5968i 1.65721i
\(412\) 0 0
\(413\) −16.2268 + 27.5405i −0.798468 + 1.35518i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 20.1472 20.1472i 0.986612 0.986612i
\(418\) 0 0
\(419\) 6.78456 0.331448 0.165724 0.986172i \(-0.447004\pi\)
0.165724 + 0.986172i \(0.447004\pi\)
\(420\) 0 0
\(421\) −10.6847 −0.520738 −0.260369 0.965509i \(-0.583844\pi\)
−0.260369 + 0.965509i \(0.583844\pi\)
\(422\) 0 0
\(423\) 4.27156 4.27156i 0.207690 0.207690i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −21.5030 12.6695i −1.04060 0.613120i
\(428\) 0 0
\(429\) 13.5616i 0.654758i
\(430\) 0 0
\(431\) −18.4384 −0.888149 −0.444074 0.895990i \(-0.646467\pi\)
−0.444074 + 0.895990i \(0.646467\pi\)
\(432\) 0 0
\(433\) −14.1617 + 14.1617i −0.680567 + 0.680567i −0.960128 0.279561i \(-0.909811\pi\)
0.279561 + 0.960128i \(0.409811\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.10341 + 2.10341i 0.100620 + 0.100620i
\(438\) 0 0
\(439\) 29.4608 1.40609 0.703044 0.711146i \(-0.251824\pi\)
0.703044 + 0.711146i \(0.251824\pi\)
\(440\) 0 0
\(441\) −15.6847 + 8.68951i −0.746888 + 0.413786i
\(442\) 0 0
\(443\) −16.1764 16.1764i −0.768564 0.768564i 0.209289 0.977854i \(-0.432885\pi\)
−0.977854 + 0.209289i \(0.932885\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 7.08084 + 7.08084i 0.334912 + 0.334912i
\(448\) 0 0
\(449\) 20.0540i 0.946406i 0.880954 + 0.473203i \(0.156902\pi\)
−0.880954 + 0.473203i \(0.843098\pi\)
\(450\) 0 0
\(451\) 4.13595i 0.194754i
\(452\) 0 0
\(453\) −27.8228 + 27.8228i −1.30723 + 1.30723i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.0442 27.0442i 1.26507 1.26507i 0.316470 0.948603i \(-0.397502\pi\)
0.948603 0.316470i \(-0.102498\pi\)
\(458\) 0 0
\(459\) 3.80776i 0.177731i
\(460\) 0 0
\(461\) 36.2454i 1.68812i 0.536252 + 0.844058i \(0.319840\pi\)
−0.536252 + 0.844058i \(0.680160\pi\)
\(462\) 0 0
\(463\) −3.97078 3.97078i −0.184538 0.184538i 0.608792 0.793330i \(-0.291654\pi\)
−0.793330 + 0.608792i \(0.791654\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.25699 1.25699i −0.0581667 0.0581667i 0.677425 0.735592i \(-0.263096\pi\)
−0.735592 + 0.677425i \(0.763096\pi\)
\(468\) 0 0
\(469\) −3.39228 13.1231i −0.156641 0.605969i
\(470\) 0 0
\(471\) 44.4924 2.05010
\(472\) 0 0
\(473\) 10.0736 + 10.0736i 0.463184 + 0.463184i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −18.5589 + 18.5589i −0.849752 + 0.849752i
\(478\) 0 0
\(479\) 1.16128 0.0530601 0.0265301 0.999648i \(-0.491554\pi\)
0.0265301 + 0.999648i \(0.491554\pi\)
\(480\) 0 0
\(481\) 14.7304i 0.671649i
\(482\) 0 0
\(483\) −3.55730 + 6.03753i −0.161863 + 0.274717i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −7.69113 + 7.69113i −0.348518 + 0.348518i −0.859557 0.511039i \(-0.829261\pi\)
0.511039 + 0.859557i \(0.329261\pi\)
\(488\) 0 0
\(489\) −25.6509 −1.15997
\(490\) 0 0
\(491\) 4.68466 0.211416 0.105708 0.994397i \(-0.466289\pi\)
0.105708 + 0.994397i \(0.466289\pi\)
\(492\) 0 0
\(493\) 17.4068 17.4068i 0.783963 0.783963i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.38915 + 14.2383i −0.376305 + 0.638674i
\(498\) 0 0
\(499\) 16.1922i 0.724864i 0.932010 + 0.362432i \(0.118053\pi\)
−0.932010 + 0.362432i \(0.881947\pi\)
\(500\) 0 0
\(501\) 50.0540 2.23625
\(502\) 0 0
\(503\) −12.0835 + 12.0835i −0.538778 + 0.538778i −0.923170 0.384392i \(-0.874411\pi\)
0.384392 + 0.923170i \(0.374411\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.936426 0.936426i −0.0415882 0.0415882i
\(508\) 0 0
\(509\) −17.3790 −0.770311 −0.385156 0.922852i \(-0.625852\pi\)
−0.385156 + 0.922852i \(0.625852\pi\)
\(510\) 0 0
\(511\) −6.24621 24.1636i −0.276316 1.06893i
\(512\) 0 0
\(513\) 1.93651 + 1.93651i 0.0854989 + 0.0854989i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2.60399 + 2.60399i 0.114523 + 0.114523i
\(518\) 0 0
\(519\) 3.80776i 0.167142i
\(520\) 0 0
\(521\) 38.8940i 1.70398i 0.523561 + 0.851988i \(0.324603\pi\)
−0.523561 + 0.851988i \(0.675397\pi\)
\(522\) 0 0
\(523\) −3.86098 + 3.86098i −0.168829 + 0.168829i −0.786465 0.617635i \(-0.788091\pi\)
0.617635 + 0.786465i \(0.288091\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.5639 24.5639i 1.07002 1.07002i
\(528\) 0 0
\(529\) 21.7386i 0.945158i
\(530\) 0 0
\(531\) 30.9481i 1.34304i
\(532\) 0 0
\(533\) 6.89697 + 6.89697i 0.298741 + 0.298741i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.74571 + 3.74571i 0.161639 + 0.161639i
\(538\) 0 0
\(539\) −5.29723 9.56155i −0.228168 0.411845i
\(540\) 0 0
\(541\) −28.9309 −1.24384 −0.621918 0.783083i \(-0.713646\pi\)
−0.621918 + 0.783083i \(0.713646\pi\)
\(542\) 0 0
\(543\) −28.9807 28.9807i −1.24368 1.24368i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 9.62763 9.62763i 0.411648 0.411648i −0.470664 0.882312i \(-0.655986\pi\)
0.882312 + 0.470664i \(0.155986\pi\)
\(548\) 0 0
\(549\) 24.1636 1.03128
\(550\) 0 0
\(551\) 17.7051i 0.754262i
\(552\) 0 0
\(553\) 26.9159 + 15.8588i 1.14458 + 0.674383i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.5690 + 30.5690i −1.29525 + 1.29525i −0.363754 + 0.931495i \(0.618505\pi\)
−0.931495 + 0.363754i \(0.881495\pi\)
\(558\) 0 0
\(559\) 33.5968 1.42099
\(560\) 0 0
\(561\) 13.5616 0.572569
\(562\) 0 0
\(563\) 15.0981 15.0981i 0.636309 0.636309i −0.313334 0.949643i \(-0.601446\pi\)
0.949643 + 0.313334i \(0.101446\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −13.5961 + 23.0757i −0.570983 + 0.969087i
\(568\) 0 0
\(569\) 36.7386i 1.54016i −0.637945 0.770082i \(-0.720215\pi\)
0.637945 0.770082i \(-0.279785\pi\)
\(570\) 0 0
\(571\) −21.7538 −0.910368 −0.455184 0.890397i \(-0.650426\pi\)
−0.455184 + 0.890397i \(0.650426\pi\)
\(572\) 0 0
\(573\) 17.4068 17.4068i 0.727179 0.727179i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −12.1988 12.1988i −0.507843 0.507843i 0.406021 0.913864i \(-0.366916\pi\)
−0.913864 + 0.406021i \(0.866916\pi\)
\(578\) 0 0
\(579\) −4.13595 −0.171884
\(580\) 0 0
\(581\) −8.87689 34.3404i −0.368276 1.42468i
\(582\) 0 0
\(583\) −11.3137 11.3137i −0.468566 0.468566i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.73384 5.73384i −0.236661 0.236661i 0.578805 0.815466i \(-0.303519\pi\)
−0.815466 + 0.578805i \(0.803519\pi\)
\(588\) 0 0
\(589\) 24.9848i 1.02948i
\(590\) 0 0
\(591\) 57.7603i 2.37594i
\(592\) 0 0
\(593\) 30.7473 30.7473i 1.26264 1.26264i 0.312833 0.949808i \(-0.398722\pi\)
0.949808 0.312833i \(-0.101278\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.83348 + 8.83348i −0.361530 + 0.361530i
\(598\) 0 0
\(599\) 23.3153i 0.952639i −0.879272 0.476320i \(-0.841971\pi\)
0.879272 0.476320i \(-0.158029\pi\)
\(600\) 0 0
\(601\) 25.6509i 1.04632i 0.852234 + 0.523161i \(0.175248\pi\)
−0.852234 + 0.523161i \(0.824752\pi\)
\(602\) 0 0
\(603\) 9.27944 + 9.27944i 0.377888 + 0.377888i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 12.0835 + 12.0835i 0.490456 + 0.490456i 0.908450 0.417994i \(-0.137267\pi\)
−0.417994 + 0.908450i \(0.637267\pi\)
\(608\) 0 0
\(609\) 40.3813 10.4384i 1.63633 0.422987i
\(610\) 0 0
\(611\) 8.68466 0.351344
\(612\) 0 0
\(613\) −9.72540 9.72540i −0.392805 0.392805i 0.482881 0.875686i \(-0.339590\pi\)
−0.875686 + 0.482881i \(0.839590\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(618\) 0 0
\(619\) −29.7869 −1.19724 −0.598618 0.801035i \(-0.704283\pi\)
−0.598618 + 0.801035i \(0.704283\pi\)
\(620\) 0 0
\(621\) 1.16128i 0.0466005i
\(622\) 0 0
\(623\) 12.6695 21.5030i 0.507593 0.861498i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 6.89697 6.89697i 0.275438 0.275438i
\(628\) 0 0
\(629\) 14.7304 0.587340
\(630\) 0 0
\(631\) −19.8078 −0.788535 −0.394267 0.918996i \(-0.629002\pi\)
−0.394267 + 0.918996i \(0.629002\pi\)
\(632\) 0 0
\(633\) −41.9844 + 41.9844i −1.66873 + 1.66873i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −24.7780 7.11104i −0.981740 0.281750i
\(638\) 0 0
\(639\) 16.0000i 0.632950i
\(640\) 0 0
\(641\) 44.7386 1.76707 0.883535 0.468365i \(-0.155157\pi\)
0.883535 + 0.468365i \(0.155157\pi\)
\(642\) 0 0
\(643\) 15.8292 15.8292i 0.624244 0.624244i −0.322370 0.946614i \(-0.604479\pi\)
0.946614 + 0.322370i \(0.104479\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.55498 + 6.55498i 0.257703 + 0.257703i 0.824119 0.566416i \(-0.191671\pi\)
−0.566416 + 0.824119i \(0.691671\pi\)
\(648\) 0 0
\(649\) 18.8664 0.740569
\(650\) 0 0
\(651\) 56.9848 14.7304i 2.23341 0.577330i
\(652\) 0 0
\(653\) −14.1421 14.1421i −0.553425 0.553425i 0.374003 0.927428i \(-0.377985\pi\)
−0.927428 + 0.374003i \(0.877985\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 17.0862 + 17.0862i 0.666597 + 0.666597i
\(658\) 0 0
\(659\) 26.9309i 1.04908i −0.851387 0.524539i \(-0.824238\pi\)
0.851387 0.524539i \(-0.175762\pi\)
\(660\) 0 0
\(661\) 8.27190i 0.321740i 0.986976 + 0.160870i \(0.0514299\pi\)
−0.986976 + 0.160870i \(0.948570\pi\)
\(662\) 0 0
\(663\) 22.6148 22.6148i 0.878285 0.878285i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.30866 5.30866i 0.205552 0.205552i
\(668\) 0 0
\(669\) 6.93087i 0.267963i
\(670\) 0 0
\(671\) 14.7304i 0.568661i
\(672\) 0 0
\(673\) 33.3974 + 33.3974i 1.28738 + 1.28738i 0.936376 + 0.351000i \(0.114158\pi\)
0.351000 + 0.936376i \(0.385842\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.3034 15.3034i −0.588157 0.588157i 0.348975 0.937132i \(-0.386530\pi\)
−0.937132 + 0.348975i \(0.886530\pi\)
\(678\) 0 0
\(679\) 20.0276 5.17708i 0.768590 0.198678i
\(680\) 0 0
\(681\) −4.19224 −0.160647
\(682\) 0 0
\(683\) 15.2845 + 15.2845i 0.584845 + 0.584845i 0.936231 0.351386i \(-0.114290\pi\)
−0.351386 + 0.936231i \(0.614290\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.41674 4.41674i 0.168509 0.168509i
\(688\) 0 0
\(689\) −37.7327 −1.43750
\(690\) 0 0
\(691\) 6.78456i 0.258097i −0.991638 0.129048i \(-0.958808\pi\)
0.991638 0.129048i \(-0.0411923\pi\)
\(692\) 0 0
\(693\) 9.11802 + 5.37231i 0.346365 + 0.204077i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.89697 + 6.89697i −0.261241 + 0.261241i
\(698\) 0 0
\(699\) −56.5991 −2.14077
\(700\) 0 0
\(701\) 40.9309 1.54594 0.772969 0.634444i \(-0.218771\pi\)
0.772969 + 0.634444i \(0.218771\pi\)
\(702\) 0 0
\(703\) 7.49141 7.49141i 0.282544 0.282544i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 36.9684 + 21.7817i 1.39034 + 0.819185i
\(708\) 0 0
\(709\) 29.8078i 1.11945i −0.828677 0.559727i \(-0.810906\pi\)
0.828677 0.559727i \(-0.189094\pi\)
\(710\) 0 0
\(711\) −30.2462 −1.13432
\(712\) 0 0
\(713\) 7.49141 7.49141i 0.280556 0.280556i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 33.0308 + 33.0308i 1.23356 + 1.23356i
\(718\) 0 0
\(719\) 28.2995 1.05539 0.527697 0.849433i \(-0.323056\pi\)
0.527697 + 0.849433i \(0.323056\pi\)
\(720\) 0 0
\(721\) −8.19224 31.6918i −0.305095 1.18026i
\(722\) 0 0
\(723\) −44.7111 44.7111i −1.66282 1.66282i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −6.55498 6.55498i −0.243111 0.243111i 0.575025 0.818136i \(-0.304992\pi\)
−0.818136 + 0.575025i \(0.804992\pi\)
\(728\) 0 0
\(729\) 18.6155i 0.689464i
\(730\) 0 0
\(731\) 33.5968i 1.24262i
\(732\) 0 0
\(733\) 3.42514 3.42514i 0.126510 0.126510i −0.641017 0.767527i \(-0.721487\pi\)
0.767527 + 0.641017i \(0.221487\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.65685 + 5.65685i −0.208373 + 0.208373i
\(738\) 0 0
\(739\) 39.4233i 1.45021i −0.688639 0.725105i \(-0.741791\pi\)
0.688639 0.725105i \(-0.258209\pi\)
\(740\) 0 0
\(741\) 23.0023i 0.845011i
\(742\) 0 0
\(743\) 16.5246 + 16.5246i 0.606229 + 0.606229i 0.941958 0.335730i \(-0.108983\pi\)
−0.335730 + 0.941958i \(0.608983\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 24.2824 + 24.2824i 0.888445 + 0.888445i
\(748\) 0 0
\(749\) 1.90495 + 7.36932i 0.0696052 + 0.269269i
\(750\) 0 0
\(751\) 34.4384 1.25668 0.628338 0.777940i \(-0.283735\pi\)
0.628338 + 0.777940i \(0.283735\pi\)
\(752\) 0 0
\(753\) 20.1472 + 20.1472i 0.734204 + 0.734204i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −12.9020 + 12.9020i −0.468932 + 0.468932i −0.901568 0.432637i \(-0.857583\pi\)
0.432637 + 0.901568i \(0.357583\pi\)
\(758\) 0 0
\(759\) 4.13595 0.150125
\(760\) 0 0
\(761\) 4.13595i 0.149928i −0.997186 0.0749640i \(-0.976116\pi\)
0.997186 0.0749640i \(-0.0238842\pi\)
\(762\) 0 0
\(763\) 6.11969 + 3.60571i 0.221548 + 0.130535i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 31.4609 31.4609i 1.13599 1.13599i
\(768\) 0 0
\(769\) 34.7580 1.25341 0.626703 0.779258i \(-0.284404\pi\)
0.626703 + 0.779258i \(0.284404\pi\)
\(770\) 0 0
\(771\) 34.7386 1.25108
\(772\) 0 0
\(773\) 32.2096 32.2096i 1.15850 1.15850i 0.173701 0.984799i \(-0.444428\pi\)
0.984799 0.173701i \(-0.0555725\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 21.5030 + 12.6695i 0.771415 + 0.454516i
\(778\) 0 0
\(779\) 7.01515i 0.251344i
\(780\) 0 0
\(781\) 9.75379 0.349018
\(782\) 0 0
\(783\) 4.88742 4.88742i 0.174662 0.174662i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15.4187 15.4187i −0.549616 0.549616i 0.376714 0.926330i \(-0.377054\pi\)
−0.926330 + 0.376714i \(0.877054\pi\)
\(788\) 0 0
\(789\) 17.3790 0.618709
\(790\) 0 0
\(791\) −4.49242 + 1.16128i −0.159732 + 0.0412903i
\(792\) 0 0
\(793\) 24.5639 + 24.5639i 0.872290 + 0.872290i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.96286 1.96286i −0.0695281 0.0695281i 0.671488 0.741016i \(-0.265656\pi\)
−0.741016 + 0.671488i \(0.765656\pi\)
\(798\) 0 0
\(799\) 8.68466i 0.307241i
\(800\) 0 0
\(801\) 24.1636i 0.853778i
\(802\) 0 0
\(803\) −10.4160 + 10.4160i −0.367572 + 0.367572i