Properties

Label 2352.2.bl.q.607.3
Level $2352$
Weight $2$
Character 2352.607
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 607.3
Root \(1.60021 + 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 2352.607
Dual form 2352.2.bl.q.31.3

$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 \(-0.210433\pi\)
−0.137063 + 0.990562i \(0.543766\pi\)
\(6\) 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 −0.884347 0.466831i \(-0.845396\pi\)
−0.0378860 + 0.999282i \(0.512062\pi\)
\(12\) 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 \(-0.588234\pi\)
0.696137 + 0.717909i \(0.254901\pi\)
\(18\) 0 0
\(19\) −0.848820 + 1.47020i −0.194733 + 0.337287i −0.946813 0.321785i \(-0.895717\pi\)
0.752080 + 0.659072i \(0.229051\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.38435 0.799257i −0.288658 0.166657i 0.348679 0.937242i \(-0.386630\pi\)
−0.637336 + 0.770586i \(0.719964\pi\)
\(24\) 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 \(-0.0199227\pi\)
−0.553189 + 0.833056i \(0.686589\pi\)
\(32\) 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 −0.0112836 0.999936i \(-0.503592\pi\)
0.871612 0.490196i \(-0.163075\pi\)
\(38\) 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 \(-0.646411\pi\)
0.443917 0.896068i \(-0.353589\pi\)
\(44\) 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 \(-0.670739\pi\)
0.999918 + 0.0127930i \(0.00407224\pi\)
\(48\) 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 0.748108 0.663578i \(-0.230963\pi\)
−0.948729 + 0.316091i \(0.897629\pi\)
\(54\) 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 0.999984 + 0.00558422i \(0.00177752\pi\)
−0.495156 + 0.868804i \(0.664889\pi\)
\(60\) 0 0
\(61\) 10.9055 + 6.29627i 1.39630 + 0.806155i 0.994003 0.109353i \(-0.0348779\pi\)
0.402299 + 0.915508i \(0.368211\pi\)
\(62\) 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 −0.587325 0.809351i \(-0.699819\pi\)
0.407256 + 0.913314i \(0.366486\pi\)
\(68\) 0 0
\(69\) 1.59851i 0.192438i
\(70\) 0 0
\(71\) 6.13052i 0.727558i 0.931485 + 0.363779i \(0.118514\pi\)
−0.931485 + 0.363779i \(0.881486\pi\)
\(72\) 0 0
\(73\) −2.10588 + 1.21583i −0.246475 + 0.142302i −0.618149 0.786061i \(-0.712117\pi\)
0.371674 + 0.928363i \(0.378784\pi\)
\(74\) 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 0.541571 0.840655i \(-0.317830\pi\)
−0.457243 + 0.889342i \(0.651163\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 14.5319 1.59508 0.797540 0.603266i \(-0.206134\pi\)
0.797540 + 0.603266i \(0.206134\pi\)
\(84\) 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 \(-0.0130821\pi\)
0.463995 + 0.885838i \(0.346415\pi\)
\(90\) 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 \(-0.822068\pi\)
0.0353847 + 0.999374i \(0.488734\pi\)
\(102\) 0 0
\(103\) 7.83133 13.5643i 0.771644 1.33653i −0.165018 0.986291i \(-0.552768\pi\)
0.936662 0.350236i \(-0.113898\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.4365 9.48961i −1.58898 0.917395i −0.993476 0.114039i \(-0.963621\pi\)
−0.595499 0.803356i \(-0.703046\pi\)
\(108\) 0 0
\(109\) −5.27950 9.14437i −0.505685 0.875872i −0.999978 0.00657678i \(-0.997907\pi\)
0.494294 0.869295i \(-0.335427\pi\)
\(110\) 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 \(-0.969380\pi\)
0.995377 0.0960468i \(-0.0306198\pi\)
\(128\) 0 0
\(129\) −10.1774 + 5.87591i −0.896068 + 0.517345i
\(130\) 0 0
\(131\) 7.66096 13.2692i 0.669341 1.15933i −0.308748 0.951144i \(-0.599910\pi\)
0.978089 0.208189i \(-0.0667568\pi\)
\(132\) 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 −0.998315 0.0580272i \(-0.981519\pi\)
0.448905 0.893580i \(-0.351814\pi\)
\(138\) 0 0
\(139\) −0.743971 −0.0631028 −0.0315514 0.999502i \(-0.510045\pi\)
−0.0315514 + 0.999502i \(0.510045\pi\)
\(140\) 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 −0.676810 0.736158i \(-0.736638\pi\)
0.975936 + 0.218055i \(0.0699713\pi\)
\(150\) 0 0
\(151\) −5.44161 + 3.14172i −0.442832 + 0.255669i −0.704798 0.709408i \(-0.748962\pi\)
0.261966 + 0.965077i \(0.415629\pi\)
\(152\) 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 \(-0.782393\pi\)
0.159352 + 0.987222i \(0.449060\pi\)
\(158\) 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 0.508190 0.861245i \(-0.330315\pi\)
−0.491765 + 0.870728i \(0.663648\pi\)
\(164\) 0 0
\(165\) 2.97406 + 5.15123i 0.231530 + 0.401022i
\(166\) 0 0
\(167\) −5.82817 −0.450997 −0.225499 0.974243i \(-0.572401\pi\)
−0.225499 + 0.974243i \(0.572401\pi\)
\(168\) 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 \(-0.553733\pi\)
−0.937719 + 0.347394i \(0.887067\pi\)
\(174\) 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 0.383317 0.923617i \(-0.374782\pi\)
0.991534 + 0.129846i \(0.0414482\pi\)
\(180\) 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 0.448732 0.893666i \(-0.351876\pi\)
−0.549572 + 0.835446i \(0.685209\pi\)
\(192\) 0 0
\(193\) −2.00555 3.47371i −0.144362 0.250043i 0.784773 0.619784i \(-0.212780\pi\)
−0.929135 + 0.369741i \(0.879446\pi\)
\(194\) 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 −0.990328 0.138743i \(-0.955694\pi\)
0.375009 0.927021i \(-0.377640\pi\)
\(200\) 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 \(-0.688256\pi\)
0.557543 0.830148i \(-0.311744\pi\)
\(212\) 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 \(-0.735215\pi\)
−0.673512 + 0.739176i \(0.735215\pi\)
\(224\) 0 0
\(225\) 2.16373 0.144249
\(226\) 0 0
\(227\) 8.79465 + 15.2328i 0.583721 + 1.01103i 0.995034 + 0.0995403i \(0.0317372\pi\)
−0.411312 + 0.911494i \(0.634929\pi\)
\(228\) 0 0
\(229\) 3.45722 + 1.99602i 0.228459 + 0.131901i 0.609861 0.792508i \(-0.291225\pi\)
−0.381402 + 0.924409i \(0.624559\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.63484 + 2.83162i −0.107102 + 0.185506i −0.914595 0.404371i \(-0.867490\pi\)
0.807493 + 0.589877i \(0.200824\pi\)
\(234\) 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 \(0.384695\pi\)
−0.354371 + 0.935105i \(0.615305\pi\)
\(240\) 0 0
\(241\) −5.29374 + 3.05634i −0.341000 + 0.196876i −0.660714 0.750638i \(-0.729746\pi\)
0.319714 + 0.947514i \(0.396413\pi\)
\(242\) 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 \(-0.160406\pi\)
0.875691 + 0.482872i \(0.160406\pi\)
\(252\) 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 \(-0.361788\pi\)
−0.575318 + 0.817930i \(0.695122\pi\)
\(258\) 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 −0.919495 0.393102i \(-0.871402\pi\)
−0.119311 + 0.992857i \(0.538069\pi\)
\(264\) 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 \(-0.496832\pi\)
0.870959 + 0.491357i \(0.163499\pi\)
\(270\) 0 0
\(271\) −9.95283 + 17.2388i −0.604591 + 1.04718i 0.387525 + 0.921859i \(0.373330\pi\)
−0.992116 + 0.125324i \(0.960003\pi\)
\(272\) 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 0.996910 0.0785522i \(-0.0250297\pi\)
−0.566483 + 0.824073i \(0.691696\pi\)
\(278\) 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 −0.842858 0.538137i \(-0.819128\pi\)
−0.0446112 0.999004i \(-0.514205\pi\)
\(284\) 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 \(-0.392114\pi\)
0.332480 + 0.943110i \(0.392114\pi\)
\(308\) 0 0
\(309\) −15.6627 −0.891017
\(310\) 0 0
\(311\) 11.5386 + 19.9855i 0.654295 + 1.13327i 0.982070 + 0.188516i \(0.0603678\pi\)
−0.327775 + 0.944756i \(0.606299\pi\)
\(312\) 0 0
\(313\) −22.4738 12.9752i −1.27029 0.733404i −0.295249 0.955420i \(-0.595403\pi\)
−0.975043 + 0.222017i \(0.928736\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.2715 + 17.7907i −0.576904 + 0.999227i 0.418928 + 0.908019i \(0.362406\pi\)
−0.995832 + 0.0912073i \(0.970927\pi\)
\(318\) 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 −0.997237 0.0742851i \(-0.976333\pi\)
−0.562951 0.826490i \(-0.690334\pi\)
\(332\) 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 −0.258370 0.966046i \(-0.583185\pi\)
0.707435 + 0.706778i \(0.249852\pi\)
\(348\) 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 \(-0.554915\pi\)
0.767336 + 0.641245i \(0.221582\pi\)
\(354\) 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 0.731045 0.682329i \(-0.239033\pi\)
−0.225392 + 0.974268i \(0.572366\pi\)
\(360\) 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 \(-0.0662391\pi\)
−0.668132 + 0.744043i \(0.732906\pi\)
\(368\) 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 −0.715970 0.698131i \(-0.754015\pi\)
0.962584 + 0.270983i \(0.0873487\pi\)
\(374\) 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 \(0.0370461\pi\)
−0.993235 + 0.116121i \(0.962954\pi\)
\(380\) 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 \(-0.814266\pi\)
0.894404 + 0.447259i \(0.147600\pi\)
\(384\) 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 0.540093 0.841605i \(-0.318389\pi\)
−0.998898 + 0.0469316i \(0.985056\pi\)
\(390\) 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 \(-0.310828\pi\)
−0.437573 + 0.899183i \(0.644162\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.04121 + 5.26753i −0.151871 + 0.263048i −0.931915 0.362676i \(-0.881863\pi\)
0.780044 + 0.625724i \(0.215196\pi\)
\(402\) 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 \(-0.733359\pi\)
0.308939 + 0.951082i \(0.400026\pi\)
\(410\) 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 \(-0.349444\pi\)
0.455547 + 0.890212i \(0.349444\pi\)
\(420\) 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 −0.130071 0.991505i \(-0.541521\pi\)
0.793633 + 0.608397i \(0.208187\pi\)
\(432\) 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 0.479590 + 0.877493i \(0.340785\pi\)
−0.999726 + 0.0234089i \(0.992548\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.2743 5.93187i −0.488147 0.281832i 0.235658 0.971836i \(-0.424275\pi\)
−0.723805 + 0.690004i \(0.757609\pi\)
\(444\) 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 −0.997916 0.0645264i \(-0.979446\pi\)
0.554840 + 0.831957i \(0.312780\pi\)
\(458\) 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 \(-0.943505\pi\)
0.984291 0.176552i \(-0.0564945\pi\)
\(464\) 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 \(-0.915391\pi\)
0.709935 + 0.704267i \(0.248724\pi\)
\(468\) 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 0.900325 + 0.435218i \(0.143329\pi\)
−0.0732525 + 0.997313i \(0.523338\pi\)
\(480\) 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 −0.801098 0.598533i \(-0.795751\pi\)
0.117796 + 0.993038i \(0.462417\pi\)
\(488\) 0 0
\(489\) 0.242138i 0.0109499i
\(490\) 0 0
\(491\) 21.5154i 0.970977i 0.874243 + 0.485489i \(0.161358\pi\)
−0.874243 + 0.485489i \(0.838642\pi\)
\(492\) 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 0.995639 0.0932893i \(-0.0297381\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(500\) 0 0
\(501\) 2.91409 + 5.04734i 0.130192 + 0.225499i
\(502\) 0 0
\(503\) 39.5840 1.76496 0.882482 0.470347i \(-0.155871\pi\)
0.882482 + 0.470347i \(0.155871\pi\)
\(504\) 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 \(-0.617896\pi\)
−0.988285 + 0.152617i \(0.951230\pi\)
\(510\) 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 \(-0.525616\pi\)
0.823028 + 0.568001i \(0.192283\pi\)
\(522\) 0 0
\(523\) −4.33120 + 7.50186i −0.189390 + 0.328033i −0.945047 0.326934i \(-0.893984\pi\)
0.755657 + 0.654968i \(0.227318\pi\)
\(524\) 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 0.459576 + 0.888139i \(0.348001\pi\)
−0.998938 + 0.0460651i \(0.985332\pi\)
\(542\) 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 \(-0.996441\pi\)
0.999937 0.0111816i \(-0.00355929\pi\)
\(548\) 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 0.530447 0.847718i \(-0.322024\pi\)
−0.999369 + 0.0355210i \(0.988691\pi\)
\(558\) 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 \(-0.238425\pi\)
−0.955877 + 0.293767i \(0.905091\pi\)
\(564\) 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 −0.954187 0.299210i \(-0.903277\pi\)
0.736217 + 0.676745i \(0.236610\pi\)
\(570\) 0 0
\(571\) 18.4912 10.6759i 0.773832 0.446772i −0.0604077 0.998174i \(-0.519240\pi\)
0.834240 + 0.551402i \(0.185907\pi\)
\(572\) 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 \(-0.660557\pi\)
0.516530 + 0.856269i \(0.327223\pi\)
\(578\) 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 \(-0.439788\pi\)
0.188036 + 0.982162i \(0.439788\pi\)
\(588\) 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 \(-0.413978\pi\)
−0.701110 + 0.713054i \(0.747312\pi\)
\(594\) 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 −0.970337 0.241758i \(-0.922276\pi\)
−0.275800 + 0.961215i \(0.588943\pi\)
\(600\) 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 \(-0.768513\pi\)
0.949248 + 0.314529i \(0.101847\pi\)
\(608\) 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 0.977365 0.211562i \(-0.0678551\pi\)
−0.671901 + 0.740641i \(0.734522\pi\)
\(614\) 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 \(-0.213324\pi\)
−0.929766 + 0.368150i \(0.879991\pi\)
\(620\) 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 \(0.00889456\pi\)
−0.999610 + 0.0279395i \(0.991105\pi\)
\(632\) 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 0.981592 + 0.190990i \(0.0611697\pi\)
−0.325394 + 0.945579i \(0.605497\pi\)
\(642\) 0 0
\(643\) 46.2604 1.82433 0.912166 0.409820i \(-0.134409\pi\)
0.912166 + 0.409820i \(0.134409\pi\)
\(644\) 0 0
\(645\) −19.7915 −0.779290
\(646\) 0 0
\(647\) −17.3166 29.9932i −0.680786 1.17916i −0.974741 0.223337i \(-0.928305\pi\)
0.293955 0.955819i \(-0.405028\pi\)
\(648\) 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 −0.935230 0.354042i \(-0.884807\pi\)
0.774224 + 0.632912i \(0.218140\pi\)
\(654\) 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 \(-0.931662\pi\)
0.977043 0.213044i \(-0.0683376\pi\)
\(660\) 0 0
\(661\) 21.8198 12.5977i 0.848692 0.489993i −0.0115171 0.999934i \(-0.503666\pi\)
0.860209 + 0.509941i \(0.170333\pi\)
\(662\) 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 \(-0.566202\pi\)
−0.950605 + 0.310404i \(0.899536\pi\)
\(678\) 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 −0.292159 0.956370i \(-0.594374\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(684\) 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 \(-0.902307\pi\)
0.738276 + 0.674499i \(0.235640\pi\)
\(692\) 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 0.0667887 + 0.997767i \(0.478725\pi\)
−0.897486 + 0.441043i \(0.854609\pi\)
\(710\) 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 \(-0.801189\pi\)
0.912019 + 0.410147i \(0.134523\pi\)
\(720\) 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 \(-0.737026\pi\)
−0.677706 + 0.735333i \(0.737026\pi\)
\(728\) 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 \(-0.501703\pi\)
−0.868688 + 0.495359i \(0.835036\pi\)
\(734\) 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 −0.189156 0.981947i \(-0.560575\pi\)
0.755813 + 0.654787i \(0.227242\pi\)
\(740\) 0 0
\(741\) 4.97434i 0.182737i
\(742\) 0 0
\(743\) 30.1701i 1.10683i 0.832904 + 0.553417i \(0.186676\pi\)
−0.832904 + 0.553417i \(0.813324\pi\)
\(744\) 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 0.989442 0.144928i \(-0.0462950\pi\)
0.369210 + 0.929346i \(0.379628\pi\)
\(752\) 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 \(-0.226739\pi\)
−0.187605 + 0.982244i \(0.560073\pi\)
\(762\) 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 \(-0.891169\pi\)
−0.180699 + 0.983538i \(0.557836\pi\)
\(774\) 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 \(-0.0108299\pi\)
−0.529170 + 0.848516i \(0.677497\pi\)
\(788\) 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