Properties

Label 2352.2.bl.t.31.2
Level $2352$
Weight $2$
Character 2352.31
Analytic conductor $18.781$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(1.60021 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 2352.31
Dual form 2352.2.bl.t.607.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.45849 + 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.45849 + 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.05870 - 1.76594i) q^{11} -2.93015i q^{13} +1.68412i q^{15} +(-1.74192 - 1.00570i) q^{17} +(0.848820 + 1.47020i) q^{19} +(-1.38435 + 0.799257i) q^{23} +(-1.08187 + 1.87385i) q^{25} -1.00000 q^{27} +7.94028 q^{29} +(-2.47683 + 4.29000i) q^{31} +(-3.05870 + 1.76594i) q^{33} +(5.23317 + 9.06412i) q^{37} +(-2.53759 - 1.46508i) q^{39} -2.86237i q^{41} +11.7518i q^{43} +(1.45849 + 0.842061i) q^{45} +(-3.35159 - 5.80513i) q^{47} +(-1.74192 + 1.00570i) q^{51} +(-1.46054 + 2.52974i) q^{53} +5.94812 q^{55} +1.69764 q^{57} +(-3.87766 + 6.71630i) q^{59} +(-10.9055 + 6.29627i) q^{61} +(2.46737 + 4.27361i) q^{65} +(-1.47393 - 0.850976i) q^{67} +1.59851i q^{69} -6.13052i q^{71} +(2.10588 + 1.21583i) q^{73} +(1.08187 + 1.87385i) q^{75} +(0.749517 - 0.432734i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.5319 q^{83} +3.38744 q^{85} +(3.97014 - 6.87648i) q^{87} +(-13.8033 + 7.96936i) q^{89} +(2.47683 + 4.29000i) q^{93} +(-2.47600 - 1.42952i) q^{95} +9.82270i q^{97} +3.53188i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 4q^{9} + 24q^{23} + 12q^{25} - 8q^{27} + 16q^{29} - 16q^{31} - 8q^{47} - 8q^{53} + 64q^{55} + 24q^{59} - 48q^{61} + 8q^{65} - 48q^{67} - 48q^{73} - 12q^{75} - 24q^{79} - 4q^{81} - 64q^{85} + 8q^{87} - 48q^{89} + 16q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −1.45849 + 0.842061i −0.652258 + 0.376581i −0.789321 0.613981i \(-0.789567\pi\)
0.137063 + 0.990562i \(0.456234\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.05870 1.76594i −0.922233 0.532451i −0.0378860 0.999282i \(-0.512062\pi\)
−0.884347 + 0.466831i \(0.845396\pi\)
\(12\) 0 0
\(13\) 2.93015i 0.812678i −0.913722 0.406339i \(-0.866805\pi\)
0.913722 0.406339i \(-0.133195\pi\)
\(14\) 0 0
\(15\) 1.68412i 0.434839i
\(16\) 0 0
\(17\) −1.74192 1.00570i −0.422478 0.243918i 0.273659 0.961827i \(-0.411766\pi\)
−0.696137 + 0.717909i \(0.745099\pi\)
\(18\) 0 0
\(19\) 0.848820 + 1.47020i 0.194733 + 0.337287i 0.946813 0.321785i \(-0.104283\pi\)
−0.752080 + 0.659072i \(0.770949\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.38435 + 0.799257i −0.288658 + 0.166657i −0.637336 0.770586i \(-0.719964\pi\)
0.348679 + 0.937242i \(0.386630\pi\)
\(24\) 0 0
\(25\) −1.08187 + 1.87385i −0.216373 + 0.374769i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.94028 1.47447 0.737237 0.675635i \(-0.236130\pi\)
0.737237 + 0.675635i \(0.236130\pi\)
\(30\) 0 0
\(31\) −2.47683 + 4.29000i −0.444853 + 0.770507i −0.998042 0.0625483i \(-0.980077\pi\)
0.553189 + 0.833056i \(0.313411\pi\)
\(32\) 0 0
\(33\) −3.05870 + 1.76594i −0.532451 + 0.307411i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.23317 + 9.06412i 0.860328 + 1.49013i 0.871612 + 0.490196i \(0.163075\pi\)
−0.0112836 + 0.999936i \(0.503592\pi\)
\(38\) 0 0
\(39\) −2.53759 1.46508i −0.406339 0.234600i
\(40\) 0 0
\(41\) 2.86237i 0.447027i −0.974701 0.223514i \(-0.928247\pi\)
0.974701 0.223514i \(-0.0717527\pi\)
\(42\) 0 0
\(43\) 11.7518i 1.79214i 0.443917 + 0.896068i \(0.353589\pi\)
−0.443917 + 0.896068i \(0.646411\pi\)
\(44\) 0 0
\(45\) 1.45849 + 0.842061i 0.217419 + 0.125527i
\(46\) 0 0
\(47\) −3.35159 5.80513i −0.488880 0.846765i 0.511038 0.859558i \(-0.329261\pi\)
−0.999918 + 0.0127930i \(0.995928\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.74192 + 1.00570i −0.243918 + 0.140826i
\(52\) 0 0
\(53\) −1.46054 + 2.52974i −0.200621 + 0.347486i −0.948729 0.316091i \(-0.897629\pi\)
0.748108 + 0.663578i \(0.230963\pi\)
\(54\) 0 0
\(55\) 5.94812 0.802045
\(56\) 0 0
\(57\) 1.69764 0.224858
\(58\) 0 0
\(59\) −3.87766 + 6.71630i −0.504828 + 0.874388i 0.495156 + 0.868804i \(0.335111\pi\)
−0.999984 + 0.00558422i \(0.998222\pi\)
\(60\) 0 0
\(61\) −10.9055 + 6.29627i −1.39630 + 0.806155i −0.994003 0.109353i \(-0.965122\pi\)
−0.402299 + 0.915508i \(0.631789\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.46737 + 4.27361i 0.306039 + 0.530076i
\(66\) 0 0
\(67\) −1.47393 0.850976i −0.180070 0.103963i 0.407256 0.913314i \(-0.366486\pi\)
−0.587325 + 0.809351i \(0.699819\pi\)
\(68\) 0 0
\(69\) 1.59851i 0.192438i
\(70\) 0 0
\(71\) 6.13052i 0.727558i −0.931485 0.363779i \(-0.881486\pi\)
0.931485 0.363779i \(-0.118514\pi\)
\(72\) 0 0
\(73\) 2.10588 + 1.21583i 0.246475 + 0.142302i 0.618149 0.786061i \(-0.287883\pi\)
−0.371674 + 0.928363i \(0.621216\pi\)
\(74\) 0 0
\(75\) 1.08187 + 1.87385i 0.124923 + 0.216373i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.749517 0.432734i 0.0843272 0.0486863i −0.457243 0.889342i \(-0.651163\pi\)
0.541571 + 0.840655i \(0.317830\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −14.5319 −1.59508 −0.797540 0.603266i \(-0.793866\pi\)
−0.797540 + 0.603266i \(0.793866\pi\)
\(84\) 0 0
\(85\) 3.38744 0.367419
\(86\) 0 0
\(87\) 3.97014 6.87648i 0.425644 0.737237i
\(88\) 0 0
\(89\) −13.8033 + 7.96936i −1.46315 + 0.844751i −0.999156 0.0410870i \(-0.986918\pi\)
−0.463995 + 0.885838i \(0.653585\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.47683 + 4.29000i 0.256836 + 0.444853i
\(94\) 0 0
\(95\) −2.47600 1.42952i −0.254032 0.146665i
\(96\) 0 0
\(97\) 9.82270i 0.997344i 0.866791 + 0.498672i \(0.166179\pi\)
−0.866791 + 0.498672i \(0.833821\pi\)
\(98\) 0 0
\(99\) 3.53188i 0.354967i
\(100\) 0 0
\(101\) 8.16458 + 4.71382i 0.812406 + 0.469043i 0.847791 0.530331i \(-0.177932\pi\)
−0.0353847 + 0.999374i \(0.511266\pi\)
\(102\) 0 0
\(103\) −7.83133 13.5643i −0.771644 1.33653i −0.936662 0.350236i \(-0.886102\pi\)
0.165018 0.986291i \(-0.447232\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.4365 + 9.48961i −1.58898 + 0.917395i −0.595499 + 0.803356i \(0.703046\pi\)
−0.993476 + 0.114039i \(0.963621\pi\)
\(108\) 0 0
\(109\) −5.27950 + 9.14437i −0.505685 + 0.875872i 0.494294 + 0.869295i \(0.335427\pi\)
−0.999978 + 0.00657678i \(0.997907\pi\)
\(110\) 0 0
\(111\) 10.4663 0.993422
\(112\) 0 0
\(113\) 15.4530 1.45369 0.726846 0.686800i \(-0.240985\pi\)
0.726846 + 0.686800i \(0.240985\pi\)
\(114\) 0 0
\(115\) 1.34605 2.33142i 0.125520 0.217406i
\(116\) 0 0
\(117\) −2.53759 + 1.46508i −0.234600 + 0.135446i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.737095 + 1.27669i 0.0670086 + 0.116062i
\(122\) 0 0
\(123\) −2.47889 1.43119i −0.223514 0.129046i
\(124\) 0 0
\(125\) 12.0646i 1.07909i
\(126\) 0 0
\(127\) 2.16478i 0.192094i 0.995377 + 0.0960468i \(0.0306198\pi\)
−0.995377 + 0.0960468i \(0.969380\pi\)
\(128\) 0 0
\(129\) 10.1774 + 5.87591i 0.896068 + 0.517345i
\(130\) 0 0
\(131\) −7.66096 13.2692i −0.669341 1.15933i −0.978089 0.208189i \(-0.933243\pi\)
0.308748 0.951144i \(-0.400090\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.45849 0.842061i 0.125527 0.0724731i
\(136\) 0 0
\(137\) −6.43068 + 11.1383i −0.549410 + 0.951607i 0.448905 + 0.893580i \(0.351814\pi\)
−0.998315 + 0.0580272i \(0.981519\pi\)
\(138\) 0 0
\(139\) 0.743971 0.0631028 0.0315514 0.999502i \(-0.489955\pi\)
0.0315514 + 0.999502i \(0.489955\pi\)
\(140\) 0 0
\(141\) −6.70319 −0.564510
\(142\) 0 0
\(143\) −5.17447 + 8.96245i −0.432711 + 0.749478i
\(144\) 0 0
\(145\) −11.5808 + 6.68620i −0.961737 + 0.555259i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.65131 + 6.32425i 0.299127 + 0.518103i 0.975936 0.218055i \(-0.0699713\pi\)
−0.676810 + 0.736158i \(0.736638\pi\)
\(150\) 0 0
\(151\) −5.44161 3.14172i −0.442832 0.255669i 0.261966 0.965077i \(-0.415629\pi\)
−0.704798 + 0.709408i \(0.748962\pi\)
\(152\) 0 0
\(153\) 2.01140i 0.162612i
\(154\) 0 0
\(155\) 8.34259i 0.670093i
\(156\) 0 0
\(157\) 7.71761 + 4.45576i 0.615932 + 0.355608i 0.775283 0.631613i \(-0.217607\pi\)
−0.159352 + 0.987222i \(0.550940\pi\)
\(158\) 0 0
\(159\) 1.46054 + 2.52974i 0.115829 + 0.200621i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.209698 0.121069i 0.0164248 0.00948287i −0.491765 0.870728i \(-0.663648\pi\)
0.508190 + 0.861245i \(0.330315\pi\)
\(164\) 0 0
\(165\) 2.97406 5.15123i 0.231530 0.401022i
\(166\) 0 0
\(167\) 5.82817 0.450997 0.225499 0.974243i \(-0.427599\pi\)
0.225499 + 0.974243i \(0.427599\pi\)
\(168\) 0 0
\(169\) 4.41421 0.339555
\(170\) 0 0
\(171\) 0.848820 1.47020i 0.0649109 0.112429i
\(172\) 0 0
\(173\) 14.5436 8.39673i 1.10573 0.638392i 0.168008 0.985786i \(-0.446267\pi\)
0.937719 + 0.347394i \(0.112933\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.87766 + 6.71630i 0.291463 + 0.504828i
\(178\) 0 0
\(179\) 18.3943 + 10.6199i 1.37485 + 0.793771i 0.991534 0.129846i \(-0.0414482\pi\)
0.383317 + 0.923617i \(0.374782\pi\)
\(180\) 0 0
\(181\) 2.74444i 0.203993i 0.994785 + 0.101996i \(0.0325230\pi\)
−0.994785 + 0.101996i \(0.967477\pi\)
\(182\) 0 0
\(183\) 12.5925i 0.930868i
\(184\) 0 0
\(185\) −15.2651 8.81331i −1.12231 0.647967i
\(186\) 0 0
\(187\) 3.55201 + 6.15225i 0.259748 + 0.449897i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.39364 + 0.804618i −0.100840 + 0.0582201i −0.549572 0.835446i \(-0.685209\pi\)
0.448732 + 0.893666i \(0.351876\pi\)
\(192\) 0 0
\(193\) −2.00555 + 3.47371i −0.144362 + 0.250043i −0.929135 0.369741i \(-0.879446\pi\)
0.784773 + 0.619784i \(0.212780\pi\)
\(194\) 0 0
\(195\) 4.93473 0.353384
\(196\) 0 0
\(197\) 11.7413 0.836534 0.418267 0.908324i \(-0.362638\pi\)
0.418267 + 0.908324i \(0.362638\pi\)
\(198\) 0 0
\(199\) 8.68015 15.0345i 0.615319 1.06576i −0.375009 0.927021i \(-0.622360\pi\)
0.990328 0.138743i \(-0.0443063\pi\)
\(200\) 0 0
\(201\) −1.47393 + 0.850976i −0.103963 + 0.0600232i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.41029 + 4.17475i 0.168342 + 0.291577i
\(206\) 0 0
\(207\) 1.38435 + 0.799257i 0.0962192 + 0.0555522i
\(208\) 0 0
\(209\) 5.99586i 0.414743i
\(210\) 0 0
\(211\) 24.1172i 1.66030i 0.557543 + 0.830148i \(0.311744\pi\)
−0.557543 + 0.830148i \(0.688256\pi\)
\(212\) 0 0
\(213\) −5.30918 3.06526i −0.363779 0.210028i
\(214\) 0 0
\(215\) −9.89576 17.1400i −0.674885 1.16893i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2.10588 1.21583i 0.142302 0.0821582i
\(220\) 0 0
\(221\) −2.94685 + 5.10409i −0.198226 + 0.343338i
\(222\) 0 0
\(223\) 20.1154 1.34702 0.673512 0.739176i \(-0.264785\pi\)
0.673512 + 0.739176i \(0.264785\pi\)
\(224\) 0 0
\(225\) 2.16373 0.144249
\(226\) 0 0
\(227\) −8.79465 + 15.2328i −0.583721 + 1.01103i 0.411312 + 0.911494i \(0.365071\pi\)
−0.995034 + 0.0995403i \(0.968263\pi\)
\(228\) 0 0
\(229\) −3.45722 + 1.99602i −0.228459 + 0.131901i −0.609861 0.792508i \(-0.708775\pi\)
0.381402 + 0.924409i \(0.375441\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.63484 2.83162i −0.107102 0.185506i 0.807493 0.589877i \(-0.200824\pi\)
−0.914595 + 0.404371i \(0.867490\pi\)
\(234\) 0 0
\(235\) 9.77655 + 5.64449i 0.637752 + 0.368206i
\(236\) 0 0
\(237\) 0.865467i 0.0562181i
\(238\) 0 0
\(239\) 28.9127i 1.87021i −0.354371 0.935105i \(-0.615305\pi\)
0.354371 0.935105i \(-0.384695\pi\)
\(240\) 0 0
\(241\) 5.29374 + 3.05634i 0.341000 + 0.196876i 0.660714 0.750638i \(-0.270254\pi\)
−0.319714 + 0.947514i \(0.603587\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.30791 2.48717i 0.274105 0.158255i
\(248\) 0 0
\(249\) −7.26593 + 12.5850i −0.460460 + 0.797540i
\(250\) 0 0
\(251\) −27.7471 −1.75138 −0.875691 0.482872i \(-0.839594\pi\)
−0.875691 + 0.482872i \(0.839594\pi\)
\(252\) 0 0
\(253\) 5.64576 0.354946
\(254\) 0 0
\(255\) 1.69372 2.93361i 0.106065 0.183710i
\(256\) 0 0
\(257\) 2.47889 1.43119i 0.154629 0.0892749i −0.420689 0.907205i \(-0.638212\pi\)
0.575318 + 0.817930i \(0.304878\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.97014 6.87648i −0.245746 0.425644i
\(262\) 0 0
\(263\) −16.8466 9.72639i −1.03881 0.599755i −0.119311 0.992857i \(-0.538069\pi\)
−0.919495 + 0.393102i \(0.871402\pi\)
\(264\) 0 0
\(265\) 4.91947i 0.302201i
\(266\) 0 0
\(267\) 15.9387i 0.975434i
\(268\) 0 0
\(269\) −14.4480 8.34156i −0.880910 0.508594i −0.00995197 0.999950i \(-0.503168\pi\)
−0.870959 + 0.491357i \(0.836501\pi\)
\(270\) 0 0
\(271\) 9.95283 + 17.2388i 0.604591 + 1.04718i 0.992116 + 0.125324i \(0.0399969\pi\)
−0.387525 + 0.921859i \(0.626670\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.61820 3.82102i 0.399092 0.230416i
\(276\) 0 0
\(277\) 7.16373 12.4079i 0.430427 0.745521i −0.566483 0.824073i \(-0.691696\pi\)
0.996910 + 0.0785522i \(0.0250297\pi\)
\(278\) 0 0
\(279\) 4.95367 0.296568
\(280\) 0 0
\(281\) 16.5450 0.986992 0.493496 0.869748i \(-0.335719\pi\)
0.493496 + 0.869748i \(0.335719\pi\)
\(282\) 0 0
\(283\) 14.9295 25.8587i 0.887469 1.53714i 0.0446112 0.999004i \(-0.485795\pi\)
0.842858 0.538137i \(-0.180872\pi\)
\(284\) 0 0
\(285\) −2.47600 + 1.42952i −0.146665 + 0.0846773i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −6.47714 11.2187i −0.381009 0.659926i
\(290\) 0 0
\(291\) 8.50671 + 4.91135i 0.498672 + 0.287908i
\(292\) 0 0
\(293\) 6.40183i 0.373999i 0.982360 + 0.187000i \(0.0598763\pi\)
−0.982360 + 0.187000i \(0.940124\pi\)
\(294\) 0 0
\(295\) 13.0609i 0.760436i
\(296\) 0 0
\(297\) 3.05870 + 1.76594i 0.177484 + 0.102470i
\(298\) 0 0
\(299\) 2.34194 + 4.05637i 0.135438 + 0.234586i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 8.16458 4.71382i 0.469043 0.270802i
\(304\) 0 0
\(305\) 10.6037 18.3661i 0.607166 1.05164i
\(306\) 0 0
\(307\) −11.6511 −0.664961 −0.332480 0.943110i \(-0.607886\pi\)
−0.332480 + 0.943110i \(0.607886\pi\)
\(308\) 0 0
\(309\) −15.6627 −0.891017
\(310\) 0 0
\(311\) −11.5386 + 19.9855i −0.654295 + 1.13327i 0.327775 + 0.944756i \(0.393701\pi\)
−0.982070 + 0.188516i \(0.939632\pi\)
\(312\) 0 0
\(313\) 22.4738 12.9752i 1.27029 0.733404i 0.295249 0.955420i \(-0.404597\pi\)
0.975043 + 0.222017i \(0.0712640\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.2715 17.7907i −0.576904 0.999227i −0.995832 0.0912073i \(-0.970927\pi\)
0.418928 0.908019i \(-0.362406\pi\)
\(318\) 0 0
\(319\) −24.2869 14.0221i −1.35981 0.785085i
\(320\) 0 0
\(321\) 18.9792i 1.05932i
\(322\) 0 0
\(323\) 3.41462i 0.189995i
\(324\) 0 0
\(325\) 5.49065 + 3.17003i 0.304566 + 0.175842i
\(326\) 0 0
\(327\) 5.27950 + 9.14437i 0.291957 + 0.505685i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −28.3851 + 16.3882i −1.56019 + 0.900775i −0.562951 + 0.826490i \(0.690334\pi\)
−0.997237 + 0.0742851i \(0.976333\pi\)
\(332\) 0 0
\(333\) 5.23317 9.06412i 0.286776 0.496711i
\(334\) 0 0
\(335\) 2.86630 0.156602
\(336\) 0 0
\(337\) −33.2791 −1.81283 −0.906414 0.422391i \(-0.861191\pi\)
−0.906414 + 0.422391i \(0.861191\pi\)
\(338\) 0 0
\(339\) 7.72648 13.3827i 0.419645 0.726846i
\(340\) 0 0
\(341\) 15.1518 8.74789i 0.820515 0.473725i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.34605 2.33142i −0.0724687 0.125520i
\(346\) 0 0
\(347\) 8.36516 + 4.82963i 0.449065 + 0.259268i 0.707435 0.706778i \(-0.249852\pi\)
−0.258370 + 0.966046i \(0.583185\pi\)
\(348\) 0 0
\(349\) 11.9525i 0.639802i −0.947451 0.319901i \(-0.896350\pi\)
0.947451 0.319901i \(-0.103650\pi\)
\(350\) 0 0
\(351\) 2.93015i 0.156400i
\(352\) 0 0
\(353\) −11.1916 6.46148i −0.595669 0.343910i 0.171667 0.985155i \(-0.445085\pi\)
−0.767336 + 0.641245i \(0.778418\pi\)
\(354\) 0 0
\(355\) 5.16227 + 8.94132i 0.273985 + 0.474556i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.58077 5.53146i 0.505654 0.291939i −0.225392 0.974268i \(-0.572366\pi\)
0.731045 + 0.682329i \(0.239033\pi\)
\(360\) 0 0
\(361\) 8.05901 13.9586i 0.424158 0.734664i
\(362\) 0 0
\(363\) 1.47419 0.0773749
\(364\) 0 0
\(365\) −4.09522 −0.214353
\(366\) 0 0
\(367\) −5.94438 + 10.2960i −0.310294 + 0.537445i −0.978426 0.206598i \(-0.933761\pi\)
0.668132 + 0.744043i \(0.267094\pi\)
\(368\) 0 0
\(369\) −2.47889 + 1.43119i −0.129046 + 0.0745045i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 4.76290 + 8.24959i 0.246614 + 0.427148i 0.962584 0.270983i \(-0.0873487\pi\)
−0.715970 + 0.698131i \(0.754015\pi\)
\(374\) 0 0
\(375\) −10.4483 6.03230i −0.539545 0.311507i
\(376\) 0 0
\(377\) 23.2662i 1.19827i
\(378\) 0 0
\(379\) 4.52128i 0.232243i −0.993235 0.116121i \(-0.962954\pi\)
0.993235 0.116121i \(-0.0370461\pi\)
\(380\) 0 0
\(381\) 1.87476 + 1.08239i 0.0960468 + 0.0554526i
\(382\) 0 0
\(383\) −1.17157 2.02922i −0.0598646 0.103688i 0.834540 0.550947i \(-0.185734\pi\)
−0.894404 + 0.447259i \(0.852400\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.1774 5.87591i 0.517345 0.298689i
\(388\) 0 0
\(389\) −9.04905 + 15.6734i −0.458805 + 0.794674i −0.998898 0.0469316i \(-0.985056\pi\)
0.540093 + 0.841605i \(0.318389\pi\)
\(390\) 0 0
\(391\) 3.21524 0.162602
\(392\) 0 0
\(393\) −15.3219 −0.772888
\(394\) 0 0
\(395\) −0.728777 + 1.26228i −0.0366687 + 0.0635121i
\(396\) 0 0
\(397\) −2.43793 + 1.40754i −0.122356 + 0.0706425i −0.559929 0.828541i \(-0.689172\pi\)
0.437573 + 0.899183i \(0.355838\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.04121 5.26753i −0.151871 0.263048i 0.780044 0.625724i \(-0.215196\pi\)
−0.931915 + 0.362676i \(0.881863\pi\)
\(402\) 0 0
\(403\) 12.5704 + 7.25750i 0.626174 + 0.361522i
\(404\) 0 0
\(405\) 1.68412i 0.0836847i
\(406\) 0 0
\(407\) 36.9659i 1.83233i
\(408\) 0 0
\(409\) 7.28566 + 4.20638i 0.360253 + 0.207992i 0.669192 0.743090i \(-0.266641\pi\)
−0.308939 + 0.951082i \(0.599974\pi\)
\(410\) 0 0
\(411\) 6.43068 + 11.1383i 0.317202 + 0.549410i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 21.1946 12.2367i 1.04040 0.600677i
\(416\) 0 0
\(417\) 0.371985 0.644298i 0.0182162 0.0315514i
\(418\) 0 0
\(419\) −18.6496 −0.911094 −0.455547 0.890212i \(-0.650556\pi\)
−0.455547 + 0.890212i \(0.650556\pi\)
\(420\) 0 0
\(421\) −22.6274 −1.10279 −0.551396 0.834243i \(-0.685905\pi\)
−0.551396 + 0.834243i \(0.685905\pi\)
\(422\) 0 0
\(423\) −3.35159 + 5.80513i −0.162960 + 0.282255i
\(424\) 0 0
\(425\) 3.76904 2.17606i 0.182825 0.105554i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 5.17447 + 8.96245i 0.249826 + 0.432711i
\(430\) 0 0
\(431\) 13.7759 + 7.95352i 0.663561 + 0.383107i 0.793633 0.608397i \(-0.208187\pi\)
−0.130071 + 0.991505i \(0.541521\pi\)
\(432\) 0 0
\(433\) 14.4650i 0.695146i 0.937653 + 0.347573i \(0.112994\pi\)
−0.937653 + 0.347573i \(0.887006\pi\)
\(434\) 0 0
\(435\) 13.3724i 0.641158i
\(436\) 0 0
\(437\) −2.35013 1.35685i −0.112422 0.0649070i
\(438\) 0 0
\(439\) 10.8981 + 18.8760i 0.520136 + 0.900901i 0.999726 + 0.0234089i \(0.00745195\pi\)
−0.479590 + 0.877493i \(0.659215\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.2743 + 5.93187i −0.488147 + 0.281832i −0.723805 0.690004i \(-0.757609\pi\)
0.235658 + 0.971836i \(0.424275\pi\)
\(444\) 0 0
\(445\) 13.4214 23.2465i 0.636235 1.10199i
\(446\) 0 0
\(447\) 7.30262 0.345402
\(448\) 0 0
\(449\) −38.6472 −1.82388 −0.911938 0.410329i \(-0.865414\pi\)
−0.911938 + 0.410329i \(0.865414\pi\)
\(450\) 0 0
\(451\) −5.05478 + 8.75513i −0.238020 + 0.412263i
\(452\) 0 0
\(453\) −5.44161 + 3.14172i −0.255669 + 0.147611i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.47189 16.4058i −0.443076 0.767431i 0.554840 0.831957i \(-0.312780\pi\)
−0.997916 + 0.0645264i \(0.979446\pi\)
\(458\) 0 0
\(459\) 1.74192 + 1.00570i 0.0813058 + 0.0469419i
\(460\) 0 0
\(461\) 24.5269i 1.14233i 0.820834 + 0.571167i \(0.193509\pi\)
−0.820834 + 0.571167i \(0.806491\pi\)
\(462\) 0 0
\(463\) 7.59791i 0.353105i 0.984291 + 0.176552i \(0.0564945\pi\)
−0.984291 + 0.176552i \(0.943505\pi\)
\(464\) 0 0
\(465\) −7.22489 4.17129i −0.335046 0.193439i
\(466\) 0 0
\(467\) 5.50941 + 9.54258i 0.254945 + 0.441578i 0.964881 0.262689i \(-0.0846092\pi\)
−0.709935 + 0.704267i \(0.751276\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 7.71761 4.45576i 0.355608 0.205311i
\(472\) 0 0
\(473\) 20.7530 35.9453i 0.954225 1.65277i
\(474\) 0 0
\(475\) −3.67323 −0.168540
\(476\) 0 0
\(477\) 2.92109 0.133747
\(478\) 0 0
\(479\) −18.1014 + 31.3525i −0.827073 + 1.43253i 0.0732525 + 0.997313i \(0.476662\pi\)
−0.900325 + 0.435218i \(0.856671\pi\)
\(480\) 0 0
\(481\) 26.5593 15.3340i 1.21100 0.699170i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.27131 14.3263i −0.375581 0.650525i
\(486\) 0 0
\(487\) −15.0792 8.70596i −0.683302 0.394505i 0.117796 0.993038i \(-0.462417\pi\)
−0.801098 + 0.598533i \(0.795751\pi\)
\(488\) 0 0
\(489\) 0.242138i 0.0109499i
\(490\) 0 0
\(491\) 21.5154i 0.970977i −0.874243 0.485489i \(-0.838642\pi\)
0.874243 0.485489i \(-0.161358\pi\)
\(492\) 0 0
\(493\) −13.8313 7.98552i −0.622932 0.359650i
\(494\) 0 0
\(495\) −2.97406 5.15123i −0.133674 0.231530i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 31.5566 18.2192i 1.41267 0.815604i 0.417029 0.908893i \(-0.363071\pi\)
0.995639 + 0.0932893i \(0.0297381\pi\)
\(500\) 0 0
\(501\) 2.91409 5.04734i 0.130192 0.225499i
\(502\) 0 0
\(503\) −39.5840 −1.76496 −0.882482 0.470347i \(-0.844129\pi\)
−0.882482 + 0.470347i \(0.844129\pi\)
\(504\) 0 0
\(505\) −15.8773 −0.706531
\(506\) 0 0
\(507\) 2.20711 3.82282i 0.0980211 0.169777i
\(508\) 0 0
\(509\) 30.4632 17.5879i 1.35026 0.779572i 0.361972 0.932189i \(-0.382104\pi\)
0.988285 + 0.152617i \(0.0487702\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.848820 1.47020i −0.0374763 0.0649109i
\(514\) 0 0
\(515\) 22.8439 + 13.1889i 1.00662 + 0.581173i
\(516\) 0 0
\(517\) 23.6749i 1.04122i
\(518\) 0 0
\(519\) 16.7935i 0.737151i
\(520\) 0 0
\(521\) −16.9510 9.78669i −0.742638 0.428762i 0.0803894 0.996764i \(-0.474384\pi\)
−0.823028 + 0.568001i \(0.807717\pi\)
\(522\) 0 0
\(523\) 4.33120 + 7.50186i 0.189390 + 0.328033i 0.945047 0.326934i \(-0.106016\pi\)
−0.755657 + 0.654968i \(0.772682\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.62889 4.98189i 0.375880 0.217015i
\(528\) 0 0
\(529\) −10.2224 + 17.7057i −0.444451 + 0.769812i
\(530\) 0 0
\(531\) 7.75532 0.336552
\(532\) 0 0
\(533\) −8.38718 −0.363289
\(534\) 0 0
\(535\) 15.9817 27.6811i 0.690948 1.19676i
\(536\) 0 0
\(537\) 18.3943 10.6199i 0.793771 0.458284i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.5453 21.7290i −0.539363 0.934204i −0.998938 0.0460651i \(-0.985332\pi\)
0.459576 0.888139i \(-0.348001\pi\)
\(542\) 0 0
\(543\) 2.37676 + 1.37222i 0.101996 + 0.0588876i
\(544\) 0 0
\(545\) 17.7827i 0.761726i
\(546\) 0 0
\(547\) 0.523032i 0.0223632i 0.999937 + 0.0111816i \(0.00355929\pi\)
−0.999937 + 0.0111816i \(0.996441\pi\)
\(548\) 0 0
\(549\) 10.9055 + 6.29627i 0.465434 + 0.268718i
\(550\) 0 0
\(551\) 6.73987 + 11.6738i 0.287128 + 0.497320i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −15.2651 + 8.81331i −0.647967 + 0.374104i
\(556\) 0 0
\(557\) −11.0670 + 19.1685i −0.468922 + 0.812197i −0.999369 0.0355210i \(-0.988691\pi\)
0.530447 + 0.847718i \(0.322024\pi\)
\(558\) 0 0
\(559\) 34.4346 1.45643
\(560\) 0 0
\(561\) 7.10401 0.299932
\(562\) 0 0
\(563\) 5.30382 9.18648i 0.223529 0.387164i −0.732348 0.680931i \(-0.761575\pi\)
0.955877 + 0.293767i \(0.0949088\pi\)
\(564\) 0 0
\(565\) −22.5380 + 13.0123i −0.948182 + 0.547433i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.19939 9.00561i −0.217970 0.377535i 0.736217 0.676745i \(-0.236610\pi\)
−0.954187 + 0.299210i \(0.903277\pi\)
\(570\) 0 0
\(571\) 18.4912 + 10.6759i 0.773832 + 0.446772i 0.834240 0.551402i \(-0.185907\pi\)
−0.0604077 + 0.998174i \(0.519240\pi\)
\(572\) 0 0
\(573\) 1.60924i 0.0672268i
\(574\) 0 0
\(575\) 3.45875i 0.144240i
\(576\) 0 0
\(577\) −0.798556 0.461047i −0.0332443 0.0191936i 0.483286 0.875463i \(-0.339443\pi\)
−0.516530 + 0.856269i \(0.672777\pi\)
\(578\) 0 0
\(579\) 2.00555 + 3.47371i 0.0833476 + 0.144362i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 8.93473 5.15847i 0.370039 0.213642i
\(584\) 0 0
\(585\) 2.46737 4.27361i 0.102013 0.176692i
\(586\) 0 0
\(587\) −9.11149 −0.376071 −0.188036 0.982162i \(-0.560212\pi\)
−0.188036 + 0.982162i \(0.560212\pi\)
\(588\) 0 0
\(589\) −8.40955 −0.346509
\(590\) 0 0
\(591\) 5.87066 10.1683i 0.241486 0.418267i
\(592\) 0 0
\(593\) 10.5720 6.10377i 0.434142 0.250652i −0.266968 0.963705i \(-0.586022\pi\)
0.701110 + 0.713054i \(0.252688\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.68015 15.0345i −0.355255 0.615319i
\(598\) 0 0
\(599\) −30.4985 17.6083i −1.24614 0.719457i −0.275800 0.961215i \(-0.588943\pi\)
−0.970337 + 0.241758i \(0.922276\pi\)
\(600\) 0 0
\(601\) 30.6430i 1.24995i 0.780644 + 0.624976i \(0.214891\pi\)
−0.780644 + 0.624976i \(0.785109\pi\)
\(602\) 0 0
\(603\) 1.70195i 0.0693088i
\(604\) 0 0
\(605\) −2.15010 1.24136i −0.0874138 0.0504684i
\(606\) 0 0
\(607\) −4.98251 8.62996i −0.202234 0.350279i 0.747014 0.664808i \(-0.231487\pi\)
−0.949248 + 0.314529i \(0.898153\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17.0099 + 9.82067i −0.688147 + 0.397302i
\(612\) 0 0
\(613\) 7.56293 13.0994i 0.305464 0.529079i −0.671901 0.740641i \(-0.734522\pi\)
0.977365 + 0.211562i \(0.0678551\pi\)
\(614\) 0 0
\(615\) 4.82058 0.194385
\(616\) 0 0
\(617\) 11.7055 0.471245 0.235622 0.971845i \(-0.424287\pi\)
0.235622 + 0.971845i \(0.424287\pi\)
\(618\) 0 0
\(619\) 3.63382 6.29396i 0.146055 0.252975i −0.783711 0.621126i \(-0.786676\pi\)
0.929766 + 0.368150i \(0.120009\pi\)
\(620\) 0 0
\(621\) 1.38435 0.799257i 0.0555522 0.0320731i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 4.74981 + 8.22691i 0.189992 + 0.329077i
\(626\) 0 0
\(627\) −5.19257 2.99793i −0.207371 0.119726i
\(628\) 0 0
\(629\) 21.0520i 0.839397i
\(630\) 0 0
\(631\) 1.40366i 0.0558789i −0.999610 0.0279395i \(-0.991105\pi\)
0.999610 0.0279395i \(-0.00889456\pi\)
\(632\) 0 0
\(633\) 20.8861 + 12.0586i 0.830148 + 0.479286i
\(634\) 0 0
\(635\) −1.82288 3.15732i −0.0723388 0.125295i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −5.30918 + 3.06526i −0.210028 + 0.121260i
\(640\) 0 0
\(641\) 16.6136 28.7756i 0.656198 1.13657i −0.325394 0.945579i \(-0.605497\pi\)
0.981592 0.190990i \(-0.0611697\pi\)
\(642\) 0 0
\(643\) −46.2604 −1.82433 −0.912166 0.409820i \(-0.865591\pi\)
−0.912166 + 0.409820i \(0.865591\pi\)
\(644\) 0 0
\(645\) −19.7915 −0.779290
\(646\) 0 0
\(647\) 17.3166 29.9932i 0.680786 1.17916i −0.293955 0.955819i \(-0.594972\pi\)
0.974741 0.223337i \(-0.0716950\pi\)
\(648\) 0 0
\(649\) 23.7212 13.6954i 0.931138 0.537593i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.11432 7.12620i −0.161006 0.278870i 0.774224 0.632912i \(-0.218140\pi\)
−0.935230 + 0.354042i \(0.884807\pi\)
\(654\) 0 0
\(655\) 22.3469 + 12.9020i 0.873166 + 0.504123i
\(656\) 0 0
\(657\) 2.43166i 0.0948681i
\(658\) 0 0
\(659\) 10.9381i 0.426087i 0.977043 + 0.213044i \(0.0683376\pi\)
−0.977043 + 0.213044i \(0.931662\pi\)
\(660\) 0 0
\(661\) −21.8198 12.5977i −0.848692 0.489993i 0.0115171 0.999934i \(-0.496334\pi\)
−0.860209 + 0.509941i \(0.829667\pi\)
\(662\) 0 0
\(663\) 2.94685 + 5.10409i 0.114446 + 0.198226i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −10.9922 + 6.34632i −0.425618 + 0.245731i
\(668\) 0 0
\(669\) 10.0577 17.4204i 0.388852 0.673512i
\(670\) 0 0
\(671\) 44.4754 1.71695
\(672\) 0 0
\(673\) 11.5831 0.446497 0.223248 0.974762i \(-0.428334\pi\)
0.223248 + 0.974762i \(0.428334\pi\)
\(674\) 0 0
\(675\) 1.08187 1.87385i 0.0416410 0.0721243i
\(676\) 0 0
\(677\) 30.1066 17.3820i 1.15709 0.668046i 0.206485 0.978450i \(-0.433798\pi\)
0.950605 + 0.310404i \(0.100464\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 8.79465 + 15.2328i 0.337012 + 0.583721i
\(682\) 0 0
\(683\) 10.1924 + 5.88459i 0.390002 + 0.225167i 0.682161 0.731202i \(-0.261040\pi\)
−0.292159 + 0.956370i \(0.594374\pi\)
\(684\) 0 0
\(685\) 21.6601i 0.827591i
\(686\) 0 0
\(687\) 3.99205i 0.152306i
\(688\) 0 0
\(689\) 7.41251 + 4.27962i 0.282394 + 0.163040i
\(690\) 0 0
\(691\) 5.65157 + 9.78880i 0.214996 + 0.372383i 0.953271 0.302116i \(-0.0976929\pi\)
−0.738276 + 0.674499i \(0.764360\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.08508 + 0.626469i −0.0411593 + 0.0237633i
\(696\) 0 0
\(697\) −2.87868 + 4.98602i −0.109038 + 0.188859i
\(698\) 0 0
\(699\) −3.26967 −0.123670
\(700\) 0 0
\(701\) 24.9265 0.941462 0.470731 0.882277i \(-0.343990\pi\)
0.470731 + 0.882277i \(0.343990\pi\)
\(702\) 0 0
\(703\) −8.88404 + 15.3876i −0.335068 + 0.580355i
\(704\) 0 0
\(705\) 9.77655 5.64449i 0.368206 0.212584i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −22.1190 38.3113i −0.830697 1.43881i −0.897486 0.441043i \(-0.854609\pi\)
0.0667887 0.997767i \(-0.478725\pi\)
\(710\) 0 0
\(711\) −0.749517 0.432734i −0.0281091 0.0162288i
\(712\) 0 0
\(713\) 7.91851i 0.296551i
\(714\) 0 0
\(715\) 17.4289i 0.651804i
\(716\) 0 0
\(717\) −25.0392 14.4564i −0.935105 0.539883i
\(718\) 0 0
\(719\) −2.70319 4.68205i −0.100812 0.174611i 0.811208 0.584758i \(-0.198811\pi\)
−0.912019 + 0.410147i \(0.865477\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 5.29374 3.05634i 0.196876 0.113667i
\(724\) 0 0
\(725\) −8.59031 + 14.8789i −0.319036 + 0.552587i
\(726\) 0 0
\(727\) 36.5459 1.35541 0.677706 0.735333i \(-0.262974\pi\)
0.677706 + 0.735333i \(0.262974\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 11.8188 20.4707i 0.437133 0.757137i
\(732\) 0 0
\(733\) 23.6637 13.6622i 0.874038 0.504626i 0.00535017 0.999986i \(-0.498297\pi\)
0.868688 + 0.495359i \(0.164964\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.00555 + 5.20576i 0.110711 + 0.191757i
\(738\) 0 0
\(739\) 15.4043 + 8.89369i 0.566657 + 0.327160i 0.755813 0.654787i \(-0.227242\pi\)
−0.189156 + 0.981947i \(0.560575\pi\)
\(740\) 0 0
\(741\) 4.97434i 0.182737i
\(742\) 0 0
\(743\) 30.1701i 1.10683i −0.832904 0.553417i \(-0.813324\pi\)
0.832904 0.553417i \(-0.186676\pi\)
\(744\) 0 0
\(745\) −10.6508 6.14925i −0.390216 0.225291i
\(746\) 0 0
\(747\) 7.26593 + 12.5850i 0.265847 + 0.460460i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 37.2330 21.4965i 1.35865 0.784418i 0.369210 0.929346i \(-0.379628\pi\)
0.989442 + 0.144928i \(0.0462950\pi\)
\(752\) 0 0
\(753\) −13.8736 + 24.0297i −0.505581 + 0.875691i
\(754\) 0 0
\(755\) 10.5821 0.385121
\(756\) 0 0
\(757\) −13.2021 −0.479839 −0.239919 0.970793i \(-0.577121\pi\)
−0.239919 + 0.970793i \(0.577121\pi\)
\(758\) 0 0
\(759\) 2.82288 4.88937i 0.102464 0.177473i
\(760\) 0 0
\(761\) −15.7032 + 9.06624i −0.569240 + 0.328651i −0.756846 0.653593i \(-0.773261\pi\)
0.187605 + 0.982244i \(0.439927\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.69372 2.93361i −0.0612365 0.106065i
\(766\) 0 0
\(767\) 19.6798 + 11.3621i 0.710596 + 0.410263i
\(768\) 0 0
\(769\) 45.0980i 1.62628i −0.582070 0.813139i \(-0.697757\pi\)
0.582070 0.813139i \(-0.302243\pi\)
\(770\) 0 0
\(771\) 2.86237i 0.103086i
\(772\) 0 0
\(773\) 31.2176 + 18.0235i 1.12282 + 0.648259i 0.942119 0.335279i \(-0.108831\pi\)
0.180699 + 0.983538i \(0.442164\pi\)
\(774\) 0 0
\(775\) −5.35920 9.28241i −0.192508 0.333434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.20826 2.42964i 0.150776 0.0870508i
\(780\) 0 0
\(781\) −10.8261 + 18.7514i −0.387389 + 0.670978i
\(782\) 0 0
\(783\) −7.94028 −0.283762
\(784\) 0 0
\(785\) −15.0081 −0.535662
\(786\) 0 0
\(787\) −13.1922 + 22.8496i −0.470251 + 0.814499i −0.999421 0.0340166i \(-0.989170\pi\)
0.529170 + 0.848516i \(0.322503\pi\)
\(788\) 0 0
\(789\) −16.8466 + 9.72639i −0.599755 + 0.346269i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 18.4490 + 31.9547i 0.655145 + 1.13474i
\(794\) 0 0
\(795\) −4.26039 2.45974i −0.151100 0.0872379i
\(796\) 0 0
\(797\) 52.8839i 1.87324i 0.350344 + 0.936621i \(0.386065\pi\)
−0.350344 + 0.936621i \(0.613935\pi\)
\(798\) 0 0
\(799\) 13.4828i 0.476986i
\(800\) 0 0