Properties

Label 1400.2.bh.g.849.3
Level $1400$
Weight $2$
Character 1400.849
Analytic conductor $11.179$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 849.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1400.849
Dual form 1400.2.bh.g.249.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.358719 - 0.207107i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(0.358719 - 0.207107i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(-0.414214 - 0.717439i) q^{11} +2.00000i q^{13} +(6.63103 - 3.82843i) q^{17} +(-2.82843 + 4.89898i) q^{19} +(-1.08579 - 0.148586i) q^{21} +(4.83743 + 2.79289i) q^{23} +2.41421i q^{27} +7.82843 q^{29} +(-0.414214 - 0.717439i) q^{31} +(-0.297173 - 0.171573i) q^{33} +(4.89898 + 2.82843i) q^{37} +(0.414214 + 0.717439i) q^{39} +5.82843 q^{41} -6.89949i q^{43} +(10.0951 + 5.82843i) q^{47} +(1.74264 + 6.77962i) q^{49} +(1.58579 - 2.74666i) q^{51} +(-4.89898 + 2.82843i) q^{53} +2.34315i q^{57} +(-2.00000 - 3.46410i) q^{59} +(-3.32843 + 5.76500i) q^{61} +(6.92820 - 2.82843i) q^{63} +(11.1713 - 6.44975i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(3.16693 - 1.82843i) q^{73} +(-0.297173 + 2.17157i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(-3.74264 - 6.48244i) q^{81} -4.75736i q^{83} +(2.80821 - 1.62132i) q^{87} +(-2.67157 + 4.62730i) q^{89} +(3.24264 - 4.18154i) q^{91} +(-0.297173 - 0.171573i) q^{93} -6.00000i q^{97} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{11} - 20q^{21} + 40q^{29} + 8q^{31} - 8q^{39} + 24q^{41} - 20q^{49} + 24q^{51} - 16q^{59} - 4q^{61} - 72q^{69} - 96q^{71} - 16q^{79} + 4q^{81} - 44q^{89} - 8q^{91} + 64q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.358719 0.207107i 0.207107 0.119573i −0.392859 0.919599i \(-0.628514\pi\)
0.599966 + 0.800025i \(0.295181\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.09077 1.62132i −0.790237 0.612801i
\(8\) 0 0
\(9\) −1.41421 + 2.44949i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) −0.414214 0.717439i −0.124890 0.216316i 0.796800 0.604243i \(-0.206524\pi\)
−0.921690 + 0.387927i \(0.873191\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.63103 3.82843i 1.60826 0.928530i 0.618502 0.785783i \(-0.287740\pi\)
0.989759 0.142747i \(-0.0455934\pi\)
\(18\) 0 0
\(19\) −2.82843 + 4.89898i −0.648886 + 1.12390i 0.334504 + 0.942394i \(0.391431\pi\)
−0.983389 + 0.181509i \(0.941902\pi\)
\(20\) 0 0
\(21\) −1.08579 0.148586i −0.236938 0.0324242i
\(22\) 0 0
\(23\) 4.83743 + 2.79289i 1.00867 + 0.582358i 0.910803 0.412841i \(-0.135463\pi\)
0.0978712 + 0.995199i \(0.468797\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.41421i 0.464616i
\(28\) 0 0
\(29\) 7.82843 1.45370 0.726851 0.686795i \(-0.240983\pi\)
0.726851 + 0.686795i \(0.240983\pi\)
\(30\) 0 0
\(31\) −0.414214 0.717439i −0.0743950 0.128856i 0.826428 0.563042i \(-0.190369\pi\)
−0.900823 + 0.434187i \(0.857036\pi\)
\(32\) 0 0
\(33\) −0.297173 0.171573i −0.0517312 0.0298670i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.89898 + 2.82843i 0.805387 + 0.464991i 0.845351 0.534211i \(-0.179391\pi\)
−0.0399642 + 0.999201i \(0.512724\pi\)
\(38\) 0 0
\(39\) 0.414214 + 0.717439i 0.0663273 + 0.114882i
\(40\) 0 0
\(41\) 5.82843 0.910247 0.455124 0.890428i \(-0.349595\pi\)
0.455124 + 0.890428i \(0.349595\pi\)
\(42\) 0 0
\(43\) 6.89949i 1.05216i −0.850434 0.526082i \(-0.823661\pi\)
0.850434 0.526082i \(-0.176339\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.0951 + 5.82843i 1.47253 + 0.850163i 0.999523 0.0308969i \(-0.00983637\pi\)
0.473004 + 0.881060i \(0.343170\pi\)
\(48\) 0 0
\(49\) 1.74264 + 6.77962i 0.248949 + 0.968517i
\(50\) 0 0
\(51\) 1.58579 2.74666i 0.222055 0.384610i
\(52\) 0 0
\(53\) −4.89898 + 2.82843i −0.672927 + 0.388514i −0.797185 0.603736i \(-0.793678\pi\)
0.124258 + 0.992250i \(0.460345\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.34315i 0.310357i
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) −3.32843 + 5.76500i −0.426161 + 0.738133i −0.996528 0.0832569i \(-0.973468\pi\)
0.570367 + 0.821390i \(0.306801\pi\)
\(62\) 0 0
\(63\) 6.92820 2.82843i 0.872872 0.356348i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 11.1713 6.44975i 1.36479 0.787962i 0.374533 0.927213i \(-0.377803\pi\)
0.990257 + 0.139251i \(0.0444696\pi\)
\(68\) 0 0
\(69\) 2.31371 0.278538
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 3.16693 1.82843i 0.370661 0.214001i −0.303086 0.952963i \(-0.598017\pi\)
0.673747 + 0.738962i \(0.264684\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.297173 + 2.17157i −0.0338660 + 0.247474i
\(78\) 0 0
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) 0 0
\(83\) 4.75736i 0.522188i −0.965313 0.261094i \(-0.915917\pi\)
0.965313 0.261094i \(-0.0840833\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.80821 1.62132i 0.301072 0.173824i
\(88\) 0 0
\(89\) −2.67157 + 4.62730i −0.283186 + 0.490493i −0.972168 0.234286i \(-0.924725\pi\)
0.688982 + 0.724779i \(0.258058\pi\)
\(90\) 0 0
\(91\) 3.24264 4.18154i 0.339921 0.438345i
\(92\) 0 0
\(93\) −0.297173 0.171573i −0.0308154 0.0177913i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 0 0
\(99\) 2.34315 0.235495
\(100\) 0 0
\(101\) 5.74264 + 9.94655i 0.571414 + 0.989718i 0.996421 + 0.0845282i \(0.0269383\pi\)
−0.425007 + 0.905190i \(0.639728\pi\)
\(102\) 0 0
\(103\) −6.56948 3.79289i −0.647310 0.373725i 0.140115 0.990135i \(-0.455253\pi\)
−0.787425 + 0.616410i \(0.788586\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.83743 2.79289i −0.467652 0.269999i 0.247604 0.968861i \(-0.420357\pi\)
−0.715256 + 0.698862i \(0.753690\pi\)
\(108\) 0 0
\(109\) 9.15685 + 15.8601i 0.877068 + 1.51913i 0.854544 + 0.519379i \(0.173837\pi\)
0.0225237 + 0.999746i \(0.492830\pi\)
\(110\) 0 0
\(111\) 2.34315 0.222402
\(112\) 0 0
\(113\) 11.3137i 1.06430i 0.846649 + 0.532152i \(0.178617\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.89898 2.82843i −0.452911 0.261488i
\(118\) 0 0
\(119\) −20.0711 2.74666i −1.83991 0.251786i
\(120\) 0 0
\(121\) 5.15685 8.93193i 0.468805 0.811994i
\(122\) 0 0
\(123\) 2.09077 1.20711i 0.188518 0.108841i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 4.34315i 0.385392i 0.981259 + 0.192696i \(0.0617231\pi\)
−0.981259 + 0.192696i \(0.938277\pi\)
\(128\) 0 0
\(129\) −1.42893 2.47498i −0.125810 0.217910i
\(130\) 0 0
\(131\) −6.82843 + 11.8272i −0.596602 + 1.03335i 0.396716 + 0.917941i \(0.370150\pi\)
−0.993319 + 0.115404i \(0.963184\pi\)
\(132\) 0 0
\(133\) 13.8564 5.65685i 1.20150 0.490511i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.46410 2.00000i 0.295958 0.170872i −0.344668 0.938725i \(-0.612008\pi\)
0.640626 + 0.767853i \(0.278675\pi\)
\(138\) 0 0
\(139\) −2.48528 −0.210799 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(140\) 0 0
\(141\) 4.82843 0.406627
\(142\) 0 0
\(143\) 1.43488 0.828427i 0.119991 0.0692766i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.02922 + 2.07107i 0.167368 + 0.170819i
\(148\) 0 0
\(149\) 2.32843 4.03295i 0.190752 0.330392i −0.754748 0.656015i \(-0.772241\pi\)
0.945500 + 0.325623i \(0.105574\pi\)
\(150\) 0 0
\(151\) 5.58579 + 9.67487i 0.454565 + 0.787329i 0.998663 0.0516921i \(-0.0164614\pi\)
−0.544098 + 0.839022i \(0.683128\pi\)
\(152\) 0 0
\(153\) 21.6569i 1.75085i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.13770 + 0.656854i −0.0907987 + 0.0524227i −0.544712 0.838623i \(-0.683361\pi\)
0.453913 + 0.891046i \(0.350028\pi\)
\(158\) 0 0
\(159\) −1.17157 + 2.02922i −0.0929118 + 0.160928i
\(160\) 0 0
\(161\) −5.58579 13.6823i −0.440222 1.07832i
\(162\) 0 0
\(163\) 13.5592 + 7.82843i 1.06204 + 0.613170i 0.925996 0.377533i \(-0.123227\pi\)
0.136045 + 0.990703i \(0.456561\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.07107i 0.160264i −0.996784 0.0801320i \(-0.974466\pi\)
0.996784 0.0801320i \(-0.0255342\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −8.00000 13.8564i −0.611775 1.05963i
\(172\) 0 0
\(173\) −8.95743 5.17157i −0.681021 0.393187i 0.119219 0.992868i \(-0.461961\pi\)
−0.800239 + 0.599681i \(0.795294\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.43488 0.828427i −0.107852 0.0622684i
\(178\) 0 0
\(179\) −3.24264 5.61642i −0.242366 0.419791i 0.719022 0.694988i \(-0.244590\pi\)
−0.961388 + 0.275197i \(0.911257\pi\)
\(180\) 0 0
\(181\) −4.17157 −0.310071 −0.155035 0.987909i \(-0.549549\pi\)
−0.155035 + 0.987909i \(0.549549\pi\)
\(182\) 0 0
\(183\) 2.75736i 0.203830i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.49333 3.17157i −0.401712 0.231928i
\(188\) 0 0
\(189\) 3.91421 5.04757i 0.284717 0.367156i
\(190\) 0 0
\(191\) 2.75736 4.77589i 0.199516 0.345571i −0.748856 0.662733i \(-0.769397\pi\)
0.948371 + 0.317162i \(0.102730\pi\)
\(192\) 0 0
\(193\) −4.60181 + 2.65685i −0.331245 + 0.191245i −0.656394 0.754418i \(-0.727919\pi\)
0.325149 + 0.945663i \(0.394586\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.343146i 0.0244481i −0.999925 0.0122241i \(-0.996109\pi\)
0.999925 0.0122241i \(-0.00389114\pi\)
\(198\) 0 0
\(199\) −11.6569 20.1903i −0.826332 1.43125i −0.900897 0.434034i \(-0.857090\pi\)
0.0745642 0.997216i \(-0.476243\pi\)
\(200\) 0 0
\(201\) 2.67157 4.62730i 0.188438 0.326385i
\(202\) 0 0
\(203\) −16.3674 12.6924i −1.14877 0.890831i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −13.6823 + 7.89949i −0.950987 + 0.549053i
\(208\) 0 0
\(209\) 4.68629 0.324158
\(210\) 0 0
\(211\) 26.6274 1.83311 0.916553 0.399912i \(-0.130959\pi\)
0.916553 + 0.399912i \(0.130959\pi\)
\(212\) 0 0
\(213\) −4.30463 + 2.48528i −0.294949 + 0.170289i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.297173 + 2.17157i −0.0201734 + 0.147416i
\(218\) 0 0
\(219\) 0.757359 1.31178i 0.0511776 0.0886422i
\(220\) 0 0
\(221\) 7.65685 + 13.2621i 0.515056 + 0.892103i
\(222\) 0 0
\(223\) 14.9706i 1.00250i −0.865302 0.501252i \(-0.832873\pi\)
0.865302 0.501252i \(-0.167127\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.1244 + 7.00000i −0.804722 + 0.464606i −0.845120 0.534577i \(-0.820471\pi\)
0.0403978 + 0.999184i \(0.487137\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0.343146 + 0.840532i 0.0225773 + 0.0553029i
\(232\) 0 0
\(233\) −10.0951 5.82843i −0.661354 0.381833i 0.131439 0.991324i \(-0.458040\pi\)
−0.792793 + 0.609491i \(0.791374\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.65685i 0.107624i
\(238\) 0 0
\(239\) 30.4853 1.97193 0.985964 0.166955i \(-0.0533936\pi\)
0.985964 + 0.166955i \(0.0533936\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) −8.95743 5.17157i −0.574619 0.331757i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −9.79796 5.65685i −0.623429 0.359937i
\(248\) 0 0
\(249\) −0.985281 1.70656i −0.0624397 0.108149i
\(250\) 0 0
\(251\) −27.4558 −1.73300 −0.866499 0.499179i \(-0.833635\pi\)
−0.866499 + 0.499179i \(0.833635\pi\)
\(252\) 0 0
\(253\) 4.62742i 0.290923i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.2621 + 7.65685i 0.827265 + 0.477621i 0.852915 0.522050i \(-0.174832\pi\)
−0.0256506 + 0.999671i \(0.508166\pi\)
\(258\) 0 0
\(259\) −5.65685 13.8564i −0.351500 0.860995i
\(260\) 0 0
\(261\) −11.0711 + 19.1757i −0.685282 + 1.18694i
\(262\) 0 0
\(263\) −13.6208 + 7.86396i −0.839893 + 0.484913i −0.857228 0.514937i \(-0.827815\pi\)
0.0173347 + 0.999850i \(0.494482\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.21320i 0.135446i
\(268\) 0 0
\(269\) −3.32843 5.76500i −0.202938 0.351499i 0.746536 0.665345i \(-0.231716\pi\)
−0.949474 + 0.313847i \(0.898382\pi\)
\(270\) 0 0
\(271\) 1.65685 2.86976i 0.100647 0.174325i −0.811305 0.584624i \(-0.801242\pi\)
0.911951 + 0.410298i \(0.134575\pi\)
\(272\) 0 0
\(273\) 0.297173 2.17157i 0.0179857 0.131430i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −24.7921 + 14.3137i −1.48961 + 0.860027i −0.999930 0.0118739i \(-0.996220\pi\)
−0.489682 + 0.871901i \(0.662887\pi\)
\(278\) 0 0
\(279\) 2.34315 0.140280
\(280\) 0 0
\(281\) 2.68629 0.160251 0.0801254 0.996785i \(-0.474468\pi\)
0.0801254 + 0.996785i \(0.474468\pi\)
\(282\) 0 0
\(283\) 15.5885 9.00000i 0.926638 0.534994i 0.0408910 0.999164i \(-0.486980\pi\)
0.885747 + 0.464169i \(0.153647\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.1859 9.44975i −0.719311 0.557801i
\(288\) 0 0
\(289\) 20.8137 36.0504i 1.22434 2.12061i
\(290\) 0 0
\(291\) −1.24264 2.15232i −0.0728449 0.126171i
\(292\) 0 0
\(293\) 16.9706i 0.991431i 0.868485 + 0.495715i \(0.165094\pi\)
−0.868485 + 0.495715i \(0.834906\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 0 0
\(299\) −5.58579 + 9.67487i −0.323034 + 0.559512i
\(300\) 0 0
\(301\) −11.1863 + 14.4253i −0.644767 + 0.831458i
\(302\) 0 0
\(303\) 4.11999 + 2.37868i 0.236687 + 0.136652i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.75736i 0.271517i −0.990742 0.135758i \(-0.956653\pi\)
0.990742 0.135758i \(-0.0433471\pi\)
\(308\) 0 0
\(309\) −3.14214 −0.178750
\(310\) 0 0
\(311\) −10.8284 18.7554i −0.614024 1.06352i −0.990555 0.137116i \(-0.956217\pi\)
0.376531 0.926404i \(-0.377117\pi\)
\(312\) 0 0
\(313\) −18.1610 10.4853i −1.02652 0.592663i −0.110536 0.993872i \(-0.535257\pi\)
−0.915987 + 0.401209i \(0.868590\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −19.0526 11.0000i −1.07010 0.617822i −0.141890 0.989882i \(-0.545318\pi\)
−0.928208 + 0.372061i \(0.878651\pi\)
\(318\) 0 0
\(319\) −3.24264 5.61642i −0.181553 0.314459i
\(320\) 0 0
\(321\) −2.31371 −0.129139
\(322\) 0 0
\(323\) 43.3137i 2.41004i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 6.56948 + 3.79289i 0.363293 + 0.209747i
\(328\) 0 0
\(329\) −11.6569 28.5533i −0.642663 1.57420i
\(330\) 0 0
\(331\) −13.2426 + 22.9369i −0.727881 + 1.26073i 0.229896 + 0.973215i \(0.426162\pi\)
−0.957777 + 0.287512i \(0.907172\pi\)
\(332\) 0 0
\(333\) −13.8564 + 8.00000i −0.759326 + 0.438397i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 24.9706i 1.36023i −0.733104 0.680117i \(-0.761929\pi\)
0.733104 0.680117i \(-0.238071\pi\)
\(338\) 0 0
\(339\) 2.34315 + 4.05845i 0.127262 + 0.220425i
\(340\) 0 0
\(341\) −0.343146 + 0.594346i −0.0185824 + 0.0321856i
\(342\) 0 0
\(343\) 7.34847 17.0000i 0.396780 0.917914i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.85951 + 5.69239i −0.529286 + 0.305583i −0.740726 0.671808i \(-0.765518\pi\)
0.211440 + 0.977391i \(0.432185\pi\)
\(348\) 0 0
\(349\) −9.82843 −0.526104 −0.263052 0.964782i \(-0.584729\pi\)
−0.263052 + 0.964782i \(0.584729\pi\)
\(350\) 0 0
\(351\) −4.82843 −0.257722
\(352\) 0 0
\(353\) 29.1477 16.8284i 1.55138 0.895687i 0.553345 0.832952i \(-0.313351\pi\)
0.998030 0.0627345i \(-0.0199821\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.76874 + 3.17157i −0.411165 + 0.167857i
\(358\) 0 0
\(359\) −3.24264 + 5.61642i −0.171140 + 0.296423i −0.938819 0.344412i \(-0.888078\pi\)
0.767679 + 0.640835i \(0.221412\pi\)
\(360\) 0 0
\(361\) −6.50000 11.2583i −0.342105 0.592544i
\(362\) 0 0
\(363\) 4.27208i 0.224226i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −18.6938 + 10.7929i −0.975810 + 0.563384i −0.901003 0.433814i \(-0.857168\pi\)
−0.0748078 + 0.997198i \(0.523834\pi\)
\(368\) 0 0
\(369\) −8.24264 + 14.2767i −0.429095 + 0.743214i
\(370\) 0 0
\(371\) 14.8284 + 2.02922i 0.769854 + 0.105352i
\(372\) 0 0
\(373\) −10.3923 6.00000i −0.538093 0.310668i 0.206213 0.978507i \(-0.433886\pi\)
−0.744306 + 0.667839i \(0.767219\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.6569i 0.806369i
\(378\) 0 0
\(379\) −4.68629 −0.240719 −0.120359 0.992730i \(-0.538405\pi\)
−0.120359 + 0.992730i \(0.538405\pi\)
\(380\) 0 0
\(381\) 0.899495 + 1.55797i 0.0460825 + 0.0798173i
\(382\) 0 0
\(383\) 0.778985 + 0.449747i 0.0398043 + 0.0229810i 0.519770 0.854306i \(-0.326018\pi\)
−0.479966 + 0.877287i \(0.659351\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.9002 + 9.75736i 0.859088 + 0.495994i
\(388\) 0 0
\(389\) 2.65685 + 4.60181i 0.134708 + 0.233321i 0.925486 0.378782i \(-0.123657\pi\)
−0.790778 + 0.612103i \(0.790324\pi\)
\(390\) 0 0
\(391\) 42.7696 2.16295
\(392\) 0 0
\(393\) 5.65685i 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −21.3280 12.3137i −1.07042 0.618007i −0.142124 0.989849i \(-0.545393\pi\)
−0.928296 + 0.371842i \(0.878726\pi\)
\(398\) 0 0
\(399\) 3.79899 4.89898i 0.190187 0.245256i
\(400\) 0 0
\(401\) 16.1569 27.9845i 0.806835 1.39748i −0.108211 0.994128i \(-0.534512\pi\)
0.915045 0.403351i \(-0.132155\pi\)
\(402\) 0 0
\(403\) 1.43488 0.828427i 0.0714764 0.0412669i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.68629i 0.232291i
\(408\) 0 0
\(409\) −12.5711 21.7737i −0.621599 1.07664i −0.989188 0.146653i \(-0.953150\pi\)
0.367589 0.929988i \(-0.380183\pi\)
\(410\) 0 0
\(411\) 0.828427 1.43488i 0.0408633 0.0707773i
\(412\) 0 0
\(413\) −1.43488 + 10.4853i −0.0706057 + 0.515947i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.891519 + 0.514719i −0.0436579 + 0.0252059i
\(418\) 0 0
\(419\) 15.3137 0.748124 0.374062 0.927404i \(-0.377965\pi\)
0.374062 + 0.927404i \(0.377965\pi\)
\(420\) 0 0
\(421\) 27.3431 1.33262 0.666312 0.745673i \(-0.267872\pi\)
0.666312 + 0.745673i \(0.267872\pi\)
\(422\) 0 0
\(423\) −28.5533 + 16.4853i −1.38831 + 0.801542i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16.3059 6.65685i 0.789098 0.322148i
\(428\) 0 0
\(429\) 0.343146 0.594346i 0.0165672 0.0286953i
\(430\) 0 0
\(431\) 0.414214 + 0.717439i 0.0199520 + 0.0345578i 0.875829 0.482622i \(-0.160315\pi\)
−0.855877 + 0.517179i \(0.826982\pi\)
\(432\) 0 0
\(433\) 19.3137i 0.928158i −0.885794 0.464079i \(-0.846385\pi\)
0.885794 0.464079i \(-0.153615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −27.3647 + 15.7990i −1.30903 + 0.755768i
\(438\) 0 0
\(439\) −9.17157 + 15.8856i −0.437735 + 0.758180i −0.997514 0.0704621i \(-0.977553\pi\)
0.559779 + 0.828642i \(0.310886\pi\)
\(440\) 0 0
\(441\) −19.0711 5.31925i −0.908146 0.253297i
\(442\) 0 0
\(443\) 13.4977 + 7.79289i 0.641294 + 0.370252i 0.785113 0.619353i \(-0.212605\pi\)
−0.143819 + 0.989604i \(0.545938\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.92893i 0.0912354i
\(448\) 0 0
\(449\) 7.48528 0.353252 0.176626 0.984278i \(-0.443482\pi\)
0.176626 + 0.984278i \(0.443482\pi\)
\(450\) 0 0
\(451\) −2.41421 4.18154i −0.113681 0.196901i
\(452\) 0 0
\(453\) 4.00746 + 2.31371i 0.188287 + 0.108708i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.0892 + 14.4853i 1.17363 + 0.677593i 0.954531 0.298111i \(-0.0963565\pi\)
0.219094 + 0.975704i \(0.429690\pi\)
\(458\) 0 0
\(459\) 9.24264 + 16.0087i 0.431410 + 0.747223i
\(460\) 0 0
\(461\) 1.31371 0.0611855 0.0305928 0.999532i \(-0.490261\pi\)
0.0305928 + 0.999532i \(0.490261\pi\)
\(462\) 0 0
\(463\) 14.8995i 0.692438i 0.938154 + 0.346219i \(0.112535\pi\)
−0.938154 + 0.346219i \(0.887465\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −32.7964 18.9350i −1.51764 0.876209i −0.999785 0.0207390i \(-0.993398\pi\)
−0.517853 0.855470i \(-0.673269\pi\)
\(468\) 0 0
\(469\) −33.8137 4.62730i −1.56137 0.213669i
\(470\) 0 0
\(471\) −0.272078 + 0.471253i −0.0125367 + 0.0217142i
\(472\) 0 0
\(473\) −4.94997 + 2.85786i −0.227600 + 0.131405i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 16.0000i 0.732590i
\(478\) 0 0
\(479\) −0.757359 1.31178i −0.0346046 0.0599370i 0.848204 0.529669i \(-0.177684\pi\)
−0.882809 + 0.469732i \(0.844351\pi\)
\(480\) 0 0
\(481\) −5.65685 + 9.79796i −0.257930 + 0.446748i
\(482\) 0 0
\(483\) −4.83743 3.75126i −0.220111 0.170688i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 33.1552 19.1421i 1.50240 0.867413i 0.502407 0.864631i \(-0.332448\pi\)
0.999996 0.00278182i \(-0.000885482\pi\)
\(488\) 0 0
\(489\) 6.48528 0.293275
\(490\) 0 0
\(491\) 1.51472 0.0683583 0.0341791 0.999416i \(-0.489118\pi\)
0.0341791 + 0.999416i \(0.489118\pi\)
\(492\) 0 0
\(493\) 51.9105 29.9706i 2.33793 1.34981i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 25.0892 + 19.4558i 1.12541 + 0.872714i
\(498\) 0 0
\(499\) 22.0711 38.2282i 0.988037 1.71133i 0.360461 0.932774i \(-0.382619\pi\)
0.627576 0.778555i \(-0.284047\pi\)
\(500\) 0 0
\(501\) −0.428932 0.742932i −0.0191633 0.0331918i
\(502\) 0 0
\(503\) 3.92893i 0.175182i −0.996157 0.0875912i \(-0.972083\pi\)
0.996157 0.0875912i \(-0.0279169\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.22848 1.86396i 0.143382 0.0827814i
\(508\) 0 0
\(509\) −16.7426 + 28.9991i −0.742105 + 1.28536i 0.209431 + 0.977823i \(0.432839\pi\)
−0.951535 + 0.307539i \(0.900494\pi\)
\(510\) 0 0
\(511\) −9.58579 1.31178i −0.424050 0.0580299i
\(512\) 0 0
\(513\) −11.8272 6.82843i −0.522183 0.301482i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.65685i 0.424708i
\(518\) 0 0
\(519\) −4.28427 −0.188059
\(520\) 0 0
\(521\) −18.3137 31.7203i −0.802338 1.38969i −0.918073 0.396410i \(-0.870256\pi\)
0.115735 0.993280i \(-0.463078\pi\)
\(522\) 0 0
\(523\) −24.1977 13.9706i −1.05809 0.610890i −0.133189 0.991091i \(-0.542522\pi\)
−0.924904 + 0.380201i \(0.875855\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.49333 3.17157i −0.239293 0.138156i
\(528\) 0 0
\(529\) 4.10051 + 7.10228i 0.178283 + 0.308795i
\(530\) 0 0
\(531\) 11.3137 0.490973
\(532\) 0 0
\(533\) 11.6569i 0.504914i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.32640 1.34315i −0.100391 0.0579610i
\(538\) 0 0
\(539\) 4.14214 4.05845i 0.178414 0.174810i
\(540\) 0 0
\(541\) 11.7426 20.3389i 0.504856 0.874435i −0.495129 0.868820i \(-0.664879\pi\)
0.999984 0.00561582i \(-0.00178758\pi\)
\(542\) 0 0
\(543\) −1.49642 + 0.863961i −0.0642177 + 0.0370761i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.27208i 0.0971470i 0.998820 + 0.0485735i \(0.0154675\pi\)
−0.998820 + 0.0485735i \(0.984532\pi\)
\(548\) 0 0
\(549\) −9.41421 16.3059i −0.401789 0.695919i
\(550\) 0 0
\(551\) −22.1421 + 38.3513i −0.943287 + 1.63382i
\(552\) 0 0
\(553\) 9.79796 4.00000i 0.416652 0.170097i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.9941 8.65685i 0.635321 0.366803i −0.147489 0.989064i \(-0.547119\pi\)
0.782810 + 0.622261i \(0.213786\pi\)
\(558\) 0 0
\(559\) 13.7990 0.583635
\(560\) 0 0
\(561\) −2.62742 −0.110930
\(562\) 0 0
\(563\) −3.52565 + 2.03553i −0.148588 + 0.0857875i −0.572451 0.819939i \(-0.694007\pi\)
0.423863 + 0.905727i \(0.360674\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.68512 + 19.6213i −0.112764 + 0.824018i
\(568\) 0 0
\(569\) −18.3137 + 31.7203i −0.767751 + 1.32978i 0.171029 + 0.985266i \(0.445291\pi\)
−0.938780 + 0.344517i \(0.888043\pi\)
\(570\) 0 0
\(571\) 10.4853 + 18.1610i 0.438795 + 0.760016i 0.997597 0.0692856i \(-0.0220720\pi\)
−0.558801 + 0.829301i \(0.688739\pi\)
\(572\) 0 0
\(573\) 2.28427i 0.0954268i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19.2987 11.1421i 0.803417 0.463853i −0.0412474 0.999149i \(-0.513133\pi\)
0.844665 + 0.535296i \(0.179800\pi\)
\(578\) 0 0
\(579\) −1.10051 + 1.90613i −0.0457354 + 0.0792161i
\(580\) 0 0
\(581\) −7.71320 + 9.94655i −0.319998 + 0.412652i
\(582\) 0 0
\(583\) 4.05845 + 2.34315i 0.168084 + 0.0970432i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.6863i 0.936363i 0.883632 + 0.468182i \(0.155091\pi\)
−0.883632 + 0.468182i \(0.844909\pi\)
\(588\) 0 0
\(589\) 4.68629 0.193095
\(590\) 0 0
\(591\) −0.0710678 0.123093i −0.00292334 0.00506337i
\(592\) 0 0
\(593\) −25.9298 14.9706i −1.06481 0.614767i −0.138050 0.990425i \(-0.544083\pi\)
−0.926758 + 0.375658i \(0.877417\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.36308 4.82843i −0.342278 0.197614i
\(598\) 0 0
\(599\) 21.3137 + 36.9164i 0.870855 + 1.50836i 0.861114 + 0.508412i \(0.169767\pi\)
0.00974040 + 0.999953i \(0.496899\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 36.4853i 1.48580i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 23.5928 + 13.6213i 0.957603 + 0.552872i 0.895434 0.445193i \(-0.146865\pi\)
0.0621685 + 0.998066i \(0.480198\pi\)
\(608\) 0 0
\(609\) −8.50000 1.16320i −0.344437 0.0471352i
\(610\) 0 0
\(611\) −11.6569 + 20.1903i −0.471586 + 0.816811i
\(612\) 0 0
\(613\) 33.7495 19.4853i 1.36313 0.787003i 0.373090 0.927795i \(-0.378298\pi\)
0.990039 + 0.140792i \(0.0449649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.6863i 0.510731i 0.966845 + 0.255365i \(0.0821958\pi\)
−0.966845 + 0.255365i \(0.917804\pi\)
\(618\) 0 0
\(619\) 19.7279 + 34.1698i 0.792932 + 1.37340i 0.924144 + 0.382044i \(0.124780\pi\)
−0.131212 + 0.991354i \(0.541887\pi\)
\(620\) 0 0
\(621\) −6.74264 + 11.6786i −0.270573 + 0.468646i
\(622\) 0 0
\(623\) 13.0880 5.34315i 0.524359 0.214069i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.68106 0.970563i 0.0671352 0.0387605i
\(628\) 0 0
\(629\) 43.3137 1.72703
\(630\) 0 0
\(631\) −1.51472 −0.0603000 −0.0301500 0.999545i \(-0.509598\pi\)
−0.0301500 + 0.999545i \(0.509598\pi\)
\(632\) 0 0
\(633\) 9.55177 5.51472i 0.379649 0.219190i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.5592 + 3.48528i −0.537236 + 0.138092i
\(638\) 0 0
\(639\) 16.9706 29.3939i 0.671345 1.16280i
\(640\) 0 0
\(641\) −7.05635 12.2220i −0.278709 0.482738i 0.692355 0.721557i \(-0.256573\pi\)
−0.971064 + 0.238819i \(0.923240\pi\)
\(642\) 0 0
\(643\) 26.0000i 1.02534i 0.858586 + 0.512670i \(0.171344\pi\)
−0.858586 + 0.512670i \(0.828656\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.9764 10.3787i 0.706725 0.408028i −0.103122 0.994669i \(-0.532883\pi\)
0.809847 + 0.586641i \(0.199550\pi\)
\(648\) 0 0
\(649\) −1.65685 + 2.86976i −0.0650372 + 0.112648i
\(650\) 0 0
\(651\) 0.343146 + 0.840532i 0.0134489 + 0.0329430i
\(652\) 0 0
\(653\) 13.5592 + 7.82843i 0.530614 + 0.306350i 0.741266 0.671211i \(-0.234226\pi\)
−0.210653 + 0.977561i \(0.567559\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 10.3431i 0.403525i
\(658\) 0 0
\(659\) −12.6863 −0.494188 −0.247094 0.968992i \(-0.579476\pi\)
−0.247094 + 0.968992i \(0.579476\pi\)
\(660\) 0 0
\(661\) 25.1569 + 43.5729i 0.978488 + 1.69479i 0.667907 + 0.744244i \(0.267190\pi\)
0.310581 + 0.950547i \(0.399476\pi\)
\(662\) 0 0
\(663\) 5.49333 + 3.17157i 0.213343 + 0.123174i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 37.8695 + 21.8640i 1.46631 + 0.846576i
\(668\) 0 0
\(669\) −3.10051 5.37023i −0.119872 0.207625i
\(670\) 0 0
\(671\) 5.51472 0.212893
\(672\) 0 0
\(673\) 5.65685i 0.218056i −0.994039 0.109028i \(-0.965226\pi\)
0.994039 0.109028i \(-0.0347738\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.8931 + 11.4853i 0.764554 + 0.441415i 0.830928 0.556380i \(-0.187810\pi\)
−0.0663747 + 0.997795i \(0.521143\pi\)
\(678\) 0 0
\(679\) −9.72792 + 12.5446i −0.373323 + 0.481418i
\(680\) 0 0
\(681\) −2.89949 + 5.02207i −0.111109 + 0.192446i
\(682\) 0 0
\(683\) −1.67050 + 0.964466i −0.0639201 + 0.0369043i −0.531619 0.846983i \(-0.678416\pi\)
0.467699 + 0.883888i \(0.345083\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.79899i 0.221245i
\(688\) 0 0
\(689\) −5.65685 9.79796i −0.215509 0.373273i
\(690\) 0 0
\(691\) 21.3848 37.0395i 0.813515 1.40905i −0.0968739 0.995297i \(-0.530884\pi\)
0.910389 0.413753i \(-0.135782\pi\)
\(692\) 0 0
\(693\) −4.89898 3.79899i −0.186097 0.144312i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 38.6485 22.3137i 1.46392 0.845192i
\(698\) 0 0
\(699\) −4.82843 −0.182628
\(700\) 0 0
\(701\) −11.0000 −0.415464 −0.207732 0.978186i \(-0.566608\pi\)
−0.207732 + 0.978186i \(0.566608\pi\)
\(702\) 0 0
\(703\) −27.7128 + 16.0000i −1.04521 + 0.603451i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.11999 30.1066i 0.154948 1.13228i
\(708\) 0 0
\(709\) −17.7132 + 30.6802i −0.665233 + 1.15222i 0.313989 + 0.949427i \(0.398335\pi\)
−0.979222 + 0.202791i \(0.934999\pi\)
\(710\) 0 0
\(711\) −5.65685 9.79796i −0.212149 0.367452i
\(712\) 0 0
\(713\) 4.62742i 0.173298i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.9357 6.31371i 0.408400 0.235790i
\(718\) 0 0
\(719\) −12.8995 + 22.3426i −0.481070 + 0.833238i −0.999764 0.0217223i \(-0.993085\pi\)
0.518694 + 0.854960i \(0.326418\pi\)
\(720\) 0 0
\(721\) 7.58579 + 18.5813i 0.282509 + 0.692004i
\(722\) 0 0
\(723\) 3.58719 + 2.07107i 0.133409 + 0.0770238i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 38.0711i 1.41198i −0.708223 0.705989i \(-0.750503\pi\)
0.708223 0.705989i \(-0.249497\pi\)
\(728\) 0 0
\(729\) 18.1716 0.673021
\(730\) 0 0
\(731\) −26.4142 45.7508i −0.976965 1.69215i
\(732\) 0 0
\(733\) −6.63103 3.82843i −0.244923 0.141406i 0.372514 0.928026i \(-0.378496\pi\)
−0.617437 + 0.786620i \(0.711829\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.25460 5.34315i −0.340898 0.196817i
\(738\) 0 0
\(739\) 8.41421 + 14.5738i 0.309522 + 0.536108i 0.978258 0.207392i \(-0.0664977\pi\)
−0.668736 + 0.743500i \(0.733164\pi\)
\(740\) 0 0
\(741\) −4.68629 −0.172155
\(742\) 0 0
\(743\) 10.7574i 0.394649i −0.980338 0.197325i \(-0.936775\pi\)
0.980338 0.197325i \(-0.0632253\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 11.6531 + 6.72792i 0.426365 + 0.246162i
\(748\) 0 0
\(749\) 5.58579 + 13.6823i 0.204100 + 0.499941i
\(750\) 0 0
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) 0 0
\(753\) −9.84895 + 5.68629i −0.358916 + 0.207220i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 6.00000i 0.218074i −0.994038 0.109037i \(-0.965223\pi\)
0.994038 0.109037i \(-0.0347767\pi\)
\(758\) 0 0
\(759\) −0.958369 1.65994i −0.0347866 0.0602522i
\(760\) 0 0
\(761\) 21.9706 38.0541i 0.796432 1.37946i −0.125493 0.992094i \(-0.540051\pi\)
0.921926 0.387367i \(-0.126615\pi\)
\(762\) 0 0
\(763\) 6.56948 48.0061i 0.237831 1.73794i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.92820 4.00000i 0.250163 0.144432i
\(768\) 0 0
\(769\) −43.2548 −1.55981 −0.779905 0.625898i \(-0.784732\pi\)
−0.779905 + 0.625898i \(0.784732\pi\)
\(770\) 0 0
\(771\) 6.34315 0.228443
\(772\) 0 0
\(773\) 21.0818 12.1716i 0.758259 0.437781i −0.0704113 0.997518i \(-0.522431\pi\)
0.828670 + 0.559737i \(0.189098\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −4.89898 3.79899i −0.175750 0.136288i
\(778\) 0 0
\(779\) −16.4853 + 28.5533i −0.590647 + 1.02303i
\(780\) 0 0
\(781\) 4.97056 + 8.60927i 0.177861 + 0.308064i
\(782\) 0 0
\(783\) 18.8995i 0.675413i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.37333 0.792893i 0.0489540 0.0282636i −0.475323 0.879811i \(-0.657669\pi\)
0.524277 + 0.851548i \(0.324336\pi\)
\(788\) 0 0
\(789\) −3.25736 + 5.64191i −0.115965 + 0.200857i
\(790\) 0 0
\(791\) 18.3431 23.6544i 0.652207 0.841052i
\(792\) 0 0
\(793\) −11.5300 6.65685i −0.409443 0.236392i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 35.3137i 1.25088i 0.780274 + 0.625438i \(0.215080\pi\)
−0.780274 + 0.625438i \(0.784920\pi\)
\(798\) 0 0
\(799\) 89.2548 3.15761
\(800\) 0