Properties

Label 1600.2.l.f.1201.6
Level $1600$
Weight $2$
Character 1600.1201
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1201.6
Root \(0.719139 - 1.21772i\) of defining polynomial
Character \(\chi\) \(=\) 1600.1201
Dual form 1600.2.l.f.401.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.66783 - 1.66783i) q^{3} -1.87372i q^{7} -2.56332i q^{9} +O(q^{10})\) \(q+(1.66783 - 1.66783i) q^{3} -1.87372i q^{7} -2.56332i q^{9} +(3.29695 + 3.29695i) q^{11} +(-1.90022 + 1.90022i) q^{13} -2.57148 q^{17} +(5.76636 - 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} -7.58574i q^{23} +(0.728312 + 0.728312i) q^{27} +(6.45786 - 6.45786i) q^{29} +0.799135 q^{31} +10.9975 q^{33} +(-2.69652 - 2.69652i) q^{37} +6.33850i q^{39} +0.946984i q^{41} +(0.829986 + 0.829986i) q^{43} +1.52421 q^{47} +3.48919 q^{49} +(-4.28879 + 4.28879i) q^{51} +(-6.97225 - 6.97225i) q^{53} -19.2346i q^{57} +(-6.84418 - 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} -4.80293 q^{63} +(-3.73647 + 3.73647i) q^{67} +(-12.6517 - 12.6517i) q^{69} +9.34417i q^{71} +0.886316i q^{73} +(6.17755 - 6.17755i) q^{77} -3.07575 q^{79} +10.1194 q^{81} +(-0.989393 + 0.989393i) q^{83} -21.5412i q^{87} +10.0942i q^{89} +(3.56048 + 3.56048i) q^{91} +(1.33282 - 1.33282i) q^{93} +7.16829 q^{97} +(8.45113 - 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{3} + O(q^{10}) \) \( 12q - 2q^{3} + 2q^{11} - 4q^{13} - 8q^{17} + 14q^{19} - 20q^{21} + 10q^{27} + 4q^{31} + 28q^{33} + 8q^{37} - 8q^{47} + 4q^{49} - 10q^{51} - 16q^{53} - 20q^{59} + 4q^{61} + 8q^{63} - 50q^{67} - 8q^{77} - 12q^{79} - 8q^{81} + 2q^{83} - 44q^{93} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 1.66783 1.66783i 0.962922 0.962922i −0.0364144 0.999337i \(-0.511594\pi\)
0.999337 + 0.0364144i \(0.0115936\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.87372i 0.708198i −0.935208 0.354099i \(-0.884788\pi\)
0.935208 0.354099i \(-0.115212\pi\)
\(8\) 0 0
\(9\) 2.56332i 0.854439i
\(10\) 0 0
\(11\) 3.29695 + 3.29695i 0.994068 + 0.994068i 0.999983 0.00591443i \(-0.00188263\pi\)
−0.00591443 + 0.999983i \(0.501883\pi\)
\(12\) 0 0
\(13\) −1.90022 + 1.90022i −0.527027 + 0.527027i −0.919685 0.392658i \(-0.871556\pi\)
0.392658 + 0.919685i \(0.371556\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.57148 −0.623675 −0.311838 0.950135i \(-0.600944\pi\)
−0.311838 + 0.950135i \(0.600944\pi\)
\(18\) 0 0
\(19\) 5.76636 5.76636i 1.32289 1.32289i 0.411472 0.911422i \(-0.365015\pi\)
0.911422 0.411472i \(-0.134985\pi\)
\(20\) 0 0
\(21\) −3.12504 3.12504i −0.681940 0.681940i
\(22\) 0 0
\(23\) 7.58574i 1.58174i −0.611987 0.790868i \(-0.709629\pi\)
0.611987 0.790868i \(-0.290371\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.728312 + 0.728312i 0.140164 + 0.140164i
\(28\) 0 0
\(29\) 6.45786 6.45786i 1.19919 1.19919i 0.224787 0.974408i \(-0.427831\pi\)
0.974408 0.224787i \(-0.0721685\pi\)
\(30\) 0 0
\(31\) 0.799135 0.143529 0.0717644 0.997422i \(-0.477137\pi\)
0.0717644 + 0.997422i \(0.477137\pi\)
\(32\) 0 0
\(33\) 10.9975 1.91442
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.69652 2.69652i −0.443305 0.443305i 0.449816 0.893121i \(-0.351489\pi\)
−0.893121 + 0.449816i \(0.851489\pi\)
\(38\) 0 0
\(39\) 6.33850i 1.01497i
\(40\) 0 0
\(41\) 0.946984i 0.147894i 0.997262 + 0.0739471i \(0.0235596\pi\)
−0.997262 + 0.0739471i \(0.976440\pi\)
\(42\) 0 0
\(43\) 0.829986 + 0.829986i 0.126572 + 0.126572i 0.767555 0.640983i \(-0.221473\pi\)
−0.640983 + 0.767555i \(0.721473\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.52421 0.222329 0.111165 0.993802i \(-0.464542\pi\)
0.111165 + 0.993802i \(0.464542\pi\)
\(48\) 0 0
\(49\) 3.48919 0.498456
\(50\) 0 0
\(51\) −4.28879 + 4.28879i −0.600551 + 0.600551i
\(52\) 0 0
\(53\) −6.97225 6.97225i −0.957712 0.957712i 0.0414296 0.999141i \(-0.486809\pi\)
−0.999141 + 0.0414296i \(0.986809\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 19.2346i 2.54769i
\(58\) 0 0
\(59\) −6.84418 6.84418i −0.891036 0.891036i 0.103585 0.994621i \(-0.466969\pi\)
−0.994621 + 0.103585i \(0.966969\pi\)
\(60\) 0 0
\(61\) −6.87247 + 6.87247i −0.879930 + 0.879930i −0.993527 0.113597i \(-0.963763\pi\)
0.113597 + 0.993527i \(0.463763\pi\)
\(62\) 0 0
\(63\) −4.80293 −0.605112
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.73647 + 3.73647i −0.456483 + 0.456483i −0.897499 0.441016i \(-0.854618\pi\)
0.441016 + 0.897499i \(0.354618\pi\)
\(68\) 0 0
\(69\) −12.6517 12.6517i −1.52309 1.52309i
\(70\) 0 0
\(71\) 9.34417i 1.10895i 0.832201 + 0.554475i \(0.187081\pi\)
−0.832201 + 0.554475i \(0.812919\pi\)
\(72\) 0 0
\(73\) 0.886316i 0.103735i 0.998654 + 0.0518677i \(0.0165174\pi\)
−0.998654 + 0.0518677i \(0.983483\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.17755 6.17755i 0.703997 0.703997i
\(78\) 0 0
\(79\) −3.07575 −0.346049 −0.173024 0.984918i \(-0.555354\pi\)
−0.173024 + 0.984918i \(0.555354\pi\)
\(80\) 0 0
\(81\) 10.1194 1.12437
\(82\) 0 0
\(83\) −0.989393 + 0.989393i −0.108600 + 0.108600i −0.759319 0.650719i \(-0.774468\pi\)
0.650719 + 0.759319i \(0.274468\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 21.5412i 2.30946i
\(88\) 0 0
\(89\) 10.0942i 1.06998i 0.844859 + 0.534990i \(0.179684\pi\)
−0.844859 + 0.534990i \(0.820316\pi\)
\(90\) 0 0
\(91\) 3.56048 + 3.56048i 0.373239 + 0.373239i
\(92\) 0 0
\(93\) 1.33282 1.33282i 0.138207 0.138207i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.16829 0.727830 0.363915 0.931432i \(-0.381440\pi\)
0.363915 + 0.931432i \(0.381440\pi\)
\(98\) 0 0
\(99\) 8.45113 8.45113i 0.849371 0.849371i
\(100\) 0 0
\(101\) −1.05091 1.05091i −0.104570 0.104570i 0.652886 0.757456i \(-0.273558\pi\)
−0.757456 + 0.652886i \(0.773558\pi\)
\(102\) 0 0
\(103\) 8.20690i 0.808649i 0.914616 + 0.404325i \(0.132493\pi\)
−0.914616 + 0.404325i \(0.867507\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.85743 2.85743i −0.276238 0.276238i 0.555367 0.831605i \(-0.312578\pi\)
−0.831605 + 0.555367i \(0.812578\pi\)
\(108\) 0 0
\(109\) −11.3735 + 11.3735i −1.08939 + 1.08939i −0.0937940 + 0.995592i \(0.529900\pi\)
−0.995592 + 0.0937940i \(0.970100\pi\)
\(110\) 0 0
\(111\) −8.99467 −0.853736
\(112\) 0 0
\(113\) 3.54221 0.333223 0.166611 0.986023i \(-0.446717\pi\)
0.166611 + 0.986023i \(0.446717\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.87088 + 4.87088i 0.450313 + 0.450313i
\(118\) 0 0
\(119\) 4.81822i 0.441685i
\(120\) 0 0
\(121\) 10.7398i 0.976343i
\(122\) 0 0
\(123\) 1.57941 + 1.57941i 0.142411 + 0.142411i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 18.0693 1.60339 0.801693 0.597735i \(-0.203933\pi\)
0.801693 + 0.597735i \(0.203933\pi\)
\(128\) 0 0
\(129\) 2.76855 0.243757
\(130\) 0 0
\(131\) 6.39614 6.39614i 0.558834 0.558834i −0.370142 0.928975i \(-0.620691\pi\)
0.928975 + 0.370142i \(0.120691\pi\)
\(132\) 0 0
\(133\) −10.8045 10.8045i −0.936871 0.936871i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.7357i 0.917212i 0.888640 + 0.458606i \(0.151651\pi\)
−0.888640 + 0.458606i \(0.848349\pi\)
\(138\) 0 0
\(139\) 2.31086 + 2.31086i 0.196005 + 0.196005i 0.798285 0.602280i \(-0.205741\pi\)
−0.602280 + 0.798285i \(0.705741\pi\)
\(140\) 0 0
\(141\) 2.54213 2.54213i 0.214086 0.214086i
\(142\) 0 0
\(143\) −12.5299 −1.04780
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.81938 5.81938i 0.479974 0.479974i
\(148\) 0 0
\(149\) 1.38743 + 1.38743i 0.113663 + 0.113663i 0.761651 0.647988i \(-0.224389\pi\)
−0.647988 + 0.761651i \(0.724389\pi\)
\(150\) 0 0
\(151\) 5.68590i 0.462712i 0.972869 + 0.231356i \(0.0743163\pi\)
−0.972869 + 0.231356i \(0.925684\pi\)
\(152\) 0 0
\(153\) 6.59152i 0.532892i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.48874 2.48874i 0.198623 0.198623i −0.600787 0.799409i \(-0.705146\pi\)
0.799409 + 0.600787i \(0.205146\pi\)
\(158\) 0 0
\(159\) −23.2571 −1.84440
\(160\) 0 0
\(161\) −14.2135 −1.12018
\(162\) 0 0
\(163\) 12.7091 12.7091i 0.995451 0.995451i −0.00453842 0.999990i \(-0.501445\pi\)
0.999990 + 0.00453842i \(0.00144463\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.00982i 0.387672i −0.981034 0.193836i \(-0.937907\pi\)
0.981034 0.193836i \(-0.0620929\pi\)
\(168\) 0 0
\(169\) 5.77830i 0.444485i
\(170\) 0 0
\(171\) −14.7810 14.7810i −1.13033 1.13033i
\(172\) 0 0
\(173\) −6.19546 + 6.19546i −0.471032 + 0.471032i −0.902249 0.431216i \(-0.858085\pi\)
0.431216 + 0.902249i \(0.358085\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −22.8299 −1.71600
\(178\) 0 0
\(179\) 5.51628 5.51628i 0.412306 0.412306i −0.470235 0.882541i \(-0.655831\pi\)
0.882541 + 0.470235i \(0.155831\pi\)
\(180\) 0 0
\(181\) 11.8993 + 11.8993i 0.884470 + 0.884470i 0.993985 0.109515i \(-0.0349298\pi\)
−0.109515 + 0.993985i \(0.534930\pi\)
\(182\) 0 0
\(183\) 22.9242i 1.69461i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −8.47804 8.47804i −0.619976 0.619976i
\(188\) 0 0
\(189\) 1.36465 1.36465i 0.0992637 0.0992637i
\(190\) 0 0
\(191\) −11.1278 −0.805180 −0.402590 0.915380i \(-0.631890\pi\)
−0.402590 + 0.915380i \(0.631890\pi\)
\(192\) 0 0
\(193\) −20.7821 −1.49593 −0.747965 0.663738i \(-0.768969\pi\)
−0.747965 + 0.663738i \(0.768969\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.0309 + 14.0309i 0.999663 + 0.999663i 1.00000 0.000337236i \(-0.000107346\pi\)
−0.000337236 1.00000i \(0.500107\pi\)
\(198\) 0 0
\(199\) 3.24727i 0.230193i 0.993354 + 0.115096i \(0.0367177\pi\)
−0.993354 + 0.115096i \(0.963282\pi\)
\(200\) 0 0
\(201\) 12.4636i 0.879115i
\(202\) 0 0
\(203\) −12.1002 12.1002i −0.849267 0.849267i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −19.4447 −1.35150
\(208\) 0 0
\(209\) 38.0228 2.63009
\(210\) 0 0
\(211\) 10.1821 10.1821i 0.700964 0.700964i −0.263654 0.964617i \(-0.584928\pi\)
0.964617 + 0.263654i \(0.0849276\pi\)
\(212\) 0 0
\(213\) 15.5845 + 15.5845i 1.06783 + 1.06783i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.49735i 0.101647i
\(218\) 0 0
\(219\) 1.47822 + 1.47822i 0.0998892 + 0.0998892i
\(220\) 0 0
\(221\) 4.88638 4.88638i 0.328694 0.328694i
\(222\) 0 0
\(223\) 24.0469 1.61030 0.805151 0.593070i \(-0.202084\pi\)
0.805151 + 0.593070i \(0.202084\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.9863 + 11.9863i −0.795562 + 0.795562i −0.982392 0.186830i \(-0.940179\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(228\) 0 0
\(229\) −20.1972 20.1972i −1.33467 1.33467i −0.901140 0.433529i \(-0.857268\pi\)
−0.433529 0.901140i \(-0.642732\pi\)
\(230\) 0 0
\(231\) 20.6062i 1.35579i
\(232\) 0 0
\(233\) 10.0655i 0.659410i −0.944084 0.329705i \(-0.893051\pi\)
0.944084 0.329705i \(-0.106949\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.12983 + 5.12983i −0.333218 + 0.333218i
\(238\) 0 0
\(239\) −0.992801 −0.0642189 −0.0321095 0.999484i \(-0.510223\pi\)
−0.0321095 + 0.999484i \(0.510223\pi\)
\(240\) 0 0
\(241\) 14.1229 0.909738 0.454869 0.890558i \(-0.349686\pi\)
0.454869 + 0.890558i \(0.349686\pi\)
\(242\) 0 0
\(243\) 14.6924 14.6924i 0.942520 0.942520i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 21.9148i 1.39440i
\(248\) 0 0
\(249\) 3.30028i 0.209147i
\(250\) 0 0
\(251\) −1.56681 1.56681i −0.0988961 0.0988961i 0.655928 0.754824i \(-0.272278\pi\)
−0.754824 + 0.655928i \(0.772278\pi\)
\(252\) 0 0
\(253\) 25.0098 25.0098i 1.57235 1.57235i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.2593 −0.639960 −0.319980 0.947424i \(-0.603676\pi\)
−0.319980 + 0.947424i \(0.603676\pi\)
\(258\) 0 0
\(259\) −5.05251 + 5.05251i −0.313948 + 0.313948i
\(260\) 0 0
\(261\) −16.5535 16.5535i −1.02464 1.02464i
\(262\) 0 0
\(263\) 19.0630i 1.17548i 0.809051 + 0.587739i \(0.199982\pi\)
−0.809051 + 0.587739i \(0.800018\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 16.8354 + 16.8354i 1.03031 + 1.03031i
\(268\) 0 0
\(269\) 3.48459 3.48459i 0.212459 0.212459i −0.592852 0.805311i \(-0.701998\pi\)
0.805311 + 0.592852i \(0.201998\pi\)
\(270\) 0 0
\(271\) 30.0045 1.82264 0.911322 0.411695i \(-0.135063\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(272\) 0 0
\(273\) 11.8765 0.718801
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.43732 + 8.43732i 0.506949 + 0.506949i 0.913589 0.406639i \(-0.133299\pi\)
−0.406639 + 0.913589i \(0.633299\pi\)
\(278\) 0 0
\(279\) 2.04844i 0.122637i
\(280\) 0 0
\(281\) 6.44714i 0.384604i −0.981336 0.192302i \(-0.938405\pi\)
0.981336 0.192302i \(-0.0615954\pi\)
\(282\) 0 0
\(283\) −2.61000 2.61000i −0.155148 0.155148i 0.625264 0.780413i \(-0.284991\pi\)
−0.780413 + 0.625264i \(0.784991\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.77438 0.104738
\(288\) 0 0
\(289\) −10.3875 −0.611029
\(290\) 0 0
\(291\) 11.9555 11.9555i 0.700844 0.700844i
\(292\) 0 0
\(293\) −7.52428 7.52428i −0.439573 0.439573i 0.452295 0.891868i \(-0.350605\pi\)
−0.891868 + 0.452295i \(0.850605\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.80242i 0.278665i
\(298\) 0 0
\(299\) 14.4146 + 14.4146i 0.833618 + 0.833618i
\(300\) 0 0
\(301\) 1.55516 1.55516i 0.0896377 0.0896377i
\(302\) 0 0
\(303\) −3.50549 −0.201385
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12.7130 + 12.7130i −0.725571 + 0.725571i −0.969734 0.244163i \(-0.921487\pi\)
0.244163 + 0.969734i \(0.421487\pi\)
\(308\) 0 0
\(309\) 13.6877 + 13.6877i 0.778667 + 0.778667i
\(310\) 0 0
\(311\) 11.9313i 0.676563i 0.941045 + 0.338281i \(0.109846\pi\)
−0.941045 + 0.338281i \(0.890154\pi\)
\(312\) 0 0
\(313\) 34.3458i 1.94134i 0.240414 + 0.970670i \(0.422717\pi\)
−0.240414 + 0.970670i \(0.577283\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.1112 + 17.1112i −0.961060 + 0.961060i −0.999270 0.0382097i \(-0.987835\pi\)
0.0382097 + 0.999270i \(0.487835\pi\)
\(318\) 0 0
\(319\) 42.5825 2.38416
\(320\) 0 0
\(321\) −9.53141 −0.531992
\(322\) 0 0
\(323\) −14.8281 + 14.8281i −0.825056 + 0.825056i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 37.9382i 2.09799i
\(328\) 0 0
\(329\) 2.85594i 0.157453i
\(330\) 0 0
\(331\) −9.80246 9.80246i −0.538792 0.538792i 0.384382 0.923174i \(-0.374415\pi\)
−0.923174 + 0.384382i \(0.874415\pi\)
\(332\) 0 0
\(333\) −6.91203 + 6.91203i −0.378777 + 0.378777i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6.07501 0.330927 0.165463 0.986216i \(-0.447088\pi\)
0.165463 + 0.986216i \(0.447088\pi\)
\(338\) 0 0
\(339\) 5.90780 5.90780i 0.320868 0.320868i
\(340\) 0 0
\(341\) 2.63471 + 2.63471i 0.142677 + 0.142677i
\(342\) 0 0
\(343\) 19.6538i 1.06120i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.77231 5.77231i −0.309874 0.309874i 0.534987 0.844860i \(-0.320317\pi\)
−0.844860 + 0.534987i \(0.820317\pi\)
\(348\) 0 0
\(349\) −7.58851 + 7.58851i −0.406203 + 0.406203i −0.880412 0.474209i \(-0.842734\pi\)
0.474209 + 0.880412i \(0.342734\pi\)
\(350\) 0 0
\(351\) −2.76791 −0.147740
\(352\) 0 0
\(353\) −16.2285 −0.863753 −0.431877 0.901933i \(-0.642148\pi\)
−0.431877 + 0.901933i \(0.642148\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 8.03597 + 8.03597i 0.425309 + 0.425309i
\(358\) 0 0
\(359\) 6.77298i 0.357464i 0.983898 + 0.178732i \(0.0571996\pi\)
−0.983898 + 0.178732i \(0.942800\pi\)
\(360\) 0 0
\(361\) 47.5019i 2.50010i
\(362\) 0 0
\(363\) 17.9121 + 17.9121i 0.940142 + 0.940142i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6.35705 0.331835 0.165918 0.986140i \(-0.446941\pi\)
0.165918 + 0.986140i \(0.446941\pi\)
\(368\) 0 0
\(369\) 2.42742 0.126367
\(370\) 0 0
\(371\) −13.0640 + 13.0640i −0.678250 + 0.678250i
\(372\) 0 0
\(373\) 9.20937 + 9.20937i 0.476843 + 0.476843i 0.904121 0.427278i \(-0.140527\pi\)
−0.427278 + 0.904121i \(0.640527\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.5428i 1.26402i
\(378\) 0 0
\(379\) −5.41600 5.41600i −0.278201 0.278201i 0.554189 0.832391i \(-0.313028\pi\)
−0.832391 + 0.554189i \(0.813028\pi\)
\(380\) 0 0
\(381\) 30.1365 30.1365i 1.54394 1.54394i
\(382\) 0 0
\(383\) −28.1626 −1.43904 −0.719520 0.694472i \(-0.755638\pi\)
−0.719520 + 0.694472i \(0.755638\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.12752 2.12752i 0.108148 0.108148i
\(388\) 0 0
\(389\) 9.59783 + 9.59783i 0.486629 + 0.486629i 0.907241 0.420611i \(-0.138184\pi\)
−0.420611 + 0.907241i \(0.638184\pi\)
\(390\) 0 0
\(391\) 19.5066i 0.986490i
\(392\) 0 0
\(393\) 21.3354i 1.07623i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 10.4884 10.4884i 0.526399 0.526399i −0.393098 0.919497i \(-0.628597\pi\)
0.919497 + 0.393098i \(0.128597\pi\)
\(398\) 0 0
\(399\) −36.0402 −1.80427
\(400\) 0 0
\(401\) −2.44221 −0.121958 −0.0609791 0.998139i \(-0.519422\pi\)
−0.0609791 + 0.998139i \(0.519422\pi\)
\(402\) 0 0
\(403\) −1.51853 + 1.51853i −0.0756436 + 0.0756436i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 17.7806i 0.881350i
\(408\) 0 0
\(409\) 24.6628i 1.21950i 0.792596 + 0.609748i \(0.208729\pi\)
−0.792596 + 0.609748i \(0.791271\pi\)
\(410\) 0 0
\(411\) 17.9053 + 17.9053i 0.883204 + 0.883204i
\(412\) 0 0
\(413\) −12.8240 + 12.8240i −0.631030 + 0.631030i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.70826 0.377475
\(418\) 0 0
\(419\) −19.1661 + 19.1661i −0.936326 + 0.936326i −0.998091 0.0617649i \(-0.980327\pi\)
0.0617649 + 0.998091i \(0.480327\pi\)
\(420\) 0 0
\(421\) −7.43469 7.43469i −0.362345 0.362345i 0.502331 0.864676i \(-0.332476\pi\)
−0.864676 + 0.502331i \(0.832476\pi\)
\(422\) 0 0
\(423\) 3.90704i 0.189967i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.8771 + 12.8771i 0.623164 + 0.623164i
\(428\) 0 0
\(429\) −20.8977 + 20.8977i −1.00895 + 1.00895i
\(430\) 0 0
\(431\) −22.5647 −1.08690 −0.543451 0.839441i \(-0.682883\pi\)
−0.543451 + 0.839441i \(0.682883\pi\)
\(432\) 0 0
\(433\) 26.4811 1.27260 0.636301 0.771441i \(-0.280464\pi\)
0.636301 + 0.771441i \(0.280464\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −43.7421 43.7421i −2.09247 2.09247i
\(438\) 0 0
\(439\) 0.765288i 0.0365252i −0.999833 0.0182626i \(-0.994187\pi\)
0.999833 0.0182626i \(-0.00581349\pi\)
\(440\) 0 0
\(441\) 8.94390i 0.425900i
\(442\) 0 0
\(443\) −20.2685 20.2685i −0.962985 0.962985i 0.0363537 0.999339i \(-0.488426\pi\)
−0.999339 + 0.0363537i \(0.988426\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.62800 0.218897
\(448\) 0 0
\(449\) −35.2717 −1.66457 −0.832287 0.554345i \(-0.812969\pi\)
−0.832287 + 0.554345i \(0.812969\pi\)
\(450\) 0 0
\(451\) −3.12216 + 3.12216i −0.147017 + 0.147017i
\(452\) 0 0
\(453\) 9.48312 + 9.48312i 0.445556 + 0.445556i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.01188i 0.421558i 0.977534 + 0.210779i \(0.0676000\pi\)
−0.977534 + 0.210779i \(0.932400\pi\)
\(458\) 0 0
\(459\) −1.87284 1.87284i −0.0874167 0.0874167i
\(460\) 0 0
\(461\) −22.8247 + 22.8247i −1.06305 + 1.06305i −0.0651807 + 0.997873i \(0.520762\pi\)
−0.997873 + 0.0651807i \(0.979238\pi\)
\(462\) 0 0
\(463\) −3.72721 −0.173218 −0.0866090 0.996242i \(-0.527603\pi\)
−0.0866090 + 0.996242i \(0.527603\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.23477 3.23477i 0.149687 0.149687i −0.628291 0.777978i \(-0.716245\pi\)
0.777978 + 0.628291i \(0.216245\pi\)
\(468\) 0 0
\(469\) 7.00109 + 7.00109i 0.323280 + 0.323280i
\(470\) 0 0
\(471\) 8.30158i 0.382517i
\(472\) 0 0
\(473\) 5.47284i 0.251642i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −17.8721 + 17.8721i −0.818307 + 0.818307i
\(478\) 0 0
\(479\) 11.0636 0.505508 0.252754 0.967531i \(-0.418664\pi\)
0.252754 + 0.967531i \(0.418664\pi\)
\(480\) 0 0
\(481\) 10.2480 0.467267
\(482\) 0 0
\(483\) −23.7057 + 23.7057i −1.07865 + 1.07865i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.68176i 0.302779i 0.988474 + 0.151390i \(0.0483748\pi\)
−0.988474 + 0.151390i \(0.951625\pi\)
\(488\) 0 0
\(489\) 42.3932i 1.91708i
\(490\) 0 0
\(491\) 18.4274 + 18.4274i 0.831618 + 0.831618i 0.987738 0.156120i \(-0.0498986\pi\)
−0.156120 + 0.987738i \(0.549899\pi\)
\(492\) 0 0
\(493\) −16.6063 + 16.6063i −0.747908 + 0.747908i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.5083 0.785356
\(498\) 0 0
\(499\) −8.84615 + 8.84615i −0.396008 + 0.396008i −0.876822 0.480814i \(-0.840341\pi\)
0.480814 + 0.876822i \(0.340341\pi\)
\(500\) 0 0
\(501\) −8.35554 8.35554i −0.373298 0.373298i
\(502\) 0 0
\(503\) 16.8746i 0.752401i −0.926538 0.376201i \(-0.877230\pi\)
0.926538 0.376201i \(-0.122770\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 9.63723 + 9.63723i 0.428004 + 0.428004i
\(508\) 0 0
\(509\) 20.5691 20.5691i 0.911707 0.911707i −0.0846994 0.996407i \(-0.526993\pi\)
0.996407 + 0.0846994i \(0.0269930\pi\)
\(510\) 0 0
\(511\) 1.66070 0.0734652
\(512\) 0 0
\(513\) 8.39943 0.370844
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.02526 + 5.02526i 0.221011 + 0.221011i
\(518\) 0 0
\(519\) 20.6660i 0.907135i
\(520\) 0 0
\(521\) 12.6708i 0.555118i 0.960709 + 0.277559i \(0.0895253\pi\)
−0.960709 + 0.277559i \(0.910475\pi\)
\(522\) 0 0
\(523\) 27.8509 + 27.8509i 1.21784 + 1.21784i 0.968388 + 0.249448i \(0.0802491\pi\)
0.249448 + 0.968388i \(0.419751\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.05496 −0.0895154
\(528\) 0 0
\(529\) −34.5435 −1.50189
\(530\) 0 0
\(531\) −17.5438 + 17.5438i −0.761336 + 0.761336i
\(532\) 0 0
\(533\) −1.79948 1.79948i −0.0779442 0.0779442i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 18.4005i 0.794038i
\(538\) 0 0
\(539\) 11.5037 + 11.5037i 0.495499 + 0.495499i
\(540\) 0 0
\(541\) −23.4122 + 23.4122i −1.00657 + 1.00657i −0.00659048 + 0.999978i \(0.502098\pi\)
−0.999978 + 0.00659048i \(0.997902\pi\)
\(542\) 0 0
\(543\) 39.6921 1.70335
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17.3745 + 17.3745i −0.742878 + 0.742878i −0.973131 0.230253i \(-0.926045\pi\)
0.230253 + 0.973131i \(0.426045\pi\)
\(548\) 0 0
\(549\) 17.6163 + 17.6163i 0.751846 + 0.751846i
\(550\) 0 0
\(551\) 74.4767i 3.17282i
\(552\) 0 0
\(553\) 5.76308i 0.245071i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.8889 22.8889i 0.969832 0.969832i −0.0297261 0.999558i \(-0.509464\pi\)
0.999558 + 0.0297261i \(0.00946351\pi\)
\(558\) 0 0
\(559\) −3.15432 −0.133413
\(560\) 0 0
\(561\) −28.2799 −1.19398
\(562\) 0 0
\(563\) −19.2489 + 19.2489i −0.811246 + 0.811246i −0.984821 0.173574i \(-0.944468\pi\)
0.173574 + 0.984821i \(0.444468\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 18.9608i 0.796278i
\(568\) 0 0
\(569\) 34.4274i 1.44327i 0.692273 + 0.721635i \(0.256609\pi\)
−0.692273 + 0.721635i \(0.743391\pi\)
\(570\) 0 0
\(571\) −5.85059 5.85059i −0.244840 0.244840i 0.574009 0.818849i \(-0.305387\pi\)
−0.818849 + 0.574009i \(0.805387\pi\)
\(572\) 0 0
\(573\) −18.5593 + 18.5593i −0.775326 + 0.775326i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 32.5042 1.35317 0.676585 0.736365i \(-0.263459\pi\)
0.676585 + 0.736365i \(0.263459\pi\)
\(578\) 0 0
\(579\) −34.6611 + 34.6611i −1.44047 + 1.44047i
\(580\) 0 0
\(581\) 1.85384 + 1.85384i 0.0769103 + 0.0769103i
\(582\) 0 0
\(583\) 45.9743i 1.90406i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.7519 + 14.7519i 0.608875 + 0.608875i 0.942652 0.333777i \(-0.108323\pi\)
−0.333777 + 0.942652i \(0.608323\pi\)
\(588\) 0 0
\(589\) 4.60810 4.60810i 0.189873 0.189873i
\(590\) 0 0
\(591\) 46.8024 1.92520
\(592\) 0 0
\(593\) −20.5310 −0.843108 −0.421554 0.906803i \(-0.638515\pi\)
−0.421554 + 0.906803i \(0.638515\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.41590 + 5.41590i 0.221658 + 0.221658i
\(598\) 0 0
\(599\) 12.3998i 0.506644i −0.967382 0.253322i \(-0.918477\pi\)
0.967382 0.253322i \(-0.0815232\pi\)
\(600\) 0 0
\(601\) 12.3980i 0.505723i 0.967502 + 0.252862i \(0.0813718\pi\)
−0.967502 + 0.252862i \(0.918628\pi\)
\(602\) 0 0
\(603\) 9.57777 + 9.57777i 0.390037 + 0.390037i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −4.90398 −0.199046 −0.0995232 0.995035i \(-0.531732\pi\)
−0.0995232 + 0.995035i \(0.531732\pi\)
\(608\) 0 0
\(609\) −40.3621 −1.63556
\(610\) 0 0
\(611\) −2.89635 + 2.89635i −0.117174 + 0.117174i
\(612\) 0 0
\(613\) −0.408547 0.408547i −0.0165011 0.0165011i 0.698808 0.715309i \(-0.253714\pi\)
−0.715309 + 0.698808i \(0.753714\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.17186i 0.248470i −0.992253 0.124235i \(-0.960352\pi\)
0.992253 0.124235i \(-0.0396476\pi\)
\(618\) 0 0
\(619\) −18.5138 18.5138i −0.744132 0.744132i 0.229238 0.973370i \(-0.426377\pi\)
−0.973370 + 0.229238i \(0.926377\pi\)
\(620\) 0 0
\(621\) 5.52479 5.52479i 0.221702 0.221702i
\(622\) 0 0
\(623\) 18.9136 0.757757
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 63.4156 63.4156i 2.53258 2.53258i
\(628\) 0 0
\(629\) 6.93404 + 6.93404i 0.276478 + 0.276478i
\(630\) 0 0
\(631\) 20.7940i 0.827795i 0.910323 + 0.413897i \(0.135833\pi\)
−0.910323 + 0.413897i \(0.864167\pi\)
\(632\) 0 0
\(633\) 33.9640i 1.34995i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.63024 + 6.63024i −0.262700 + 0.262700i
\(638\) 0 0
\(639\) 23.9521 0.947530
\(640\) 0 0
\(641\) 16.1179 0.636620 0.318310 0.947987i \(-0.396885\pi\)
0.318310 + 0.947987i \(0.396885\pi\)
\(642\) 0 0
\(643\) −10.3733 + 10.3733i −0.409082 + 0.409082i −0.881419 0.472336i \(-0.843411\pi\)
0.472336 + 0.881419i \(0.343411\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.5724i 1.28055i 0.768145 + 0.640276i \(0.221180\pi\)
−0.768145 + 0.640276i \(0.778820\pi\)
\(648\) 0 0
\(649\) 45.1298i 1.77150i
\(650\) 0 0
\(651\) −2.49733 2.49733i −0.0978780 0.0978780i
\(652\) 0 0
\(653\) 4.31962 4.31962i 0.169040 0.169040i −0.617517 0.786557i \(-0.711861\pi\)
0.786557 + 0.617517i \(0.211861\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.27191 0.0886356
\(658\) 0 0
\(659\) 4.19711 4.19711i 0.163496 0.163496i −0.620617 0.784114i \(-0.713118\pi\)
0.784114 + 0.620617i \(0.213118\pi\)
\(660\) 0 0
\(661\) 21.2310 + 21.2310i 0.825790 + 0.825790i 0.986931 0.161141i \(-0.0515175\pi\)
−0.161141 + 0.986931i \(0.551518\pi\)
\(662\) 0 0
\(663\) 16.2993i 0.633013i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −48.9877 48.9877i −1.89681 1.89681i
\(668\) 0 0
\(669\) 40.1062 40.1062i 1.55060 1.55060i
\(670\) 0 0
\(671\) −45.3164 −1.74942
\(672\) 0 0
\(673\) −6.08317 −0.234489 −0.117244 0.993103i \(-0.537406\pi\)
−0.117244 + 0.993103i \(0.537406\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.42443 8.42443i −0.323777 0.323777i 0.526437 0.850214i \(-0.323528\pi\)
−0.850214 + 0.526437i \(0.823528\pi\)
\(678\) 0 0
\(679\) 13.4313i 0.515447i
\(680\) 0 0
\(681\) 39.9824i 1.53213i
\(682\) 0 0
\(683\) −14.7609 14.7609i −0.564812 0.564812i 0.365859 0.930670i \(-0.380775\pi\)
−0.930670 + 0.365859i \(0.880775\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −67.3710 −2.57036
\(688\) 0 0
\(689\) 26.4977 1.00948
\(690\) 0 0
\(691\) 4.06268 4.06268i 0.154552 0.154552i −0.625596 0.780147i \(-0.715144\pi\)
0.780147 + 0.625596i \(0.215144\pi\)
\(692\) 0 0
\(693\) −15.8350 15.8350i −0.601523 0.601523i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.43515i 0.0922379i
\(698\) 0 0
\(699\) −16.7875 16.7875i −0.634961 0.634961i
\(700\) 0 0
\(701\) 11.1049 11.1049i 0.419428 0.419428i −0.465578 0.885007i \(-0.654154\pi\)
0.885007 + 0.465578i \(0.154154\pi\)
\(702\) 0 0
\(703\) −31.0982 −1.17289
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.96911 + 1.96911i −0.0740561 + 0.0740561i
\(708\) 0 0
\(709\) 13.0114 + 13.0114i 0.488652 + 0.488652i 0.907881 0.419229i \(-0.137700\pi\)
−0.419229 + 0.907881i \(0.637700\pi\)
\(710\) 0 0
\(711\) 7.88412i 0.295678i
\(712\) 0 0
\(713\) 6.06203i 0.227025i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.65582 + 1.65582i −0.0618378 + 0.0618378i
\(718\) 0 0
\(719\) 50.0570 1.86681 0.933406 0.358821i \(-0.116821\pi\)
0.933406 + 0.358821i \(0.116821\pi\)
\(720\) 0 0
\(721\) 15.3774 0.572684
\(722\) 0 0
\(723\) 23.5547 23.5547i 0.876007 0.876007i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 27.7141i 1.02786i −0.857832 0.513930i \(-0.828189\pi\)
0.857832 0.513930i \(-0.171811\pi\)
\(728\) 0 0
\(729\) 18.6509i 0.690775i
\(730\) 0 0
\(731\) −2.13429 2.13429i −0.0789396 0.0789396i
\(732\) 0 0
\(733\) 16.8860 16.8860i 0.623698 0.623698i −0.322777 0.946475i \(-0.604616\pi\)
0.946475 + 0.322777i \(0.104616\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24.6379 −0.907550
\(738\) 0 0
\(739\) 23.6286 23.6286i 0.869193 0.869193i −0.123190 0.992383i \(-0.539312\pi\)
0.992383 + 0.123190i \(0.0393124\pi\)
\(740\) 0 0
\(741\) 36.5501 + 36.5501i 1.34270 + 1.34270i
\(742\) 0 0
\(743\) 6.53356i 0.239693i 0.992792 + 0.119846i \(0.0382402\pi\)
−0.992792 + 0.119846i \(0.961760\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.53613 + 2.53613i 0.0927921 + 0.0927921i
\(748\) 0 0
\(749\) −5.35401 + 5.35401i −0.195631 + 0.195631i
\(750\) 0 0
\(751\) 22.8483 0.833746 0.416873 0.908965i \(-0.363126\pi\)
0.416873 + 0.908965i \(0.363126\pi\)
\(752\) 0 0
\(753\) −5.22634 −0.190459
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.0190 24.0190i −0.872985 0.872985i 0.119811 0.992797i \(-0.461771\pi\)
−0.992797 + 0.119811i \(0.961771\pi\)
\(758\) 0 0
\(759\) 83.4243i 3.02811i
\(760\) 0 0
\(761\) 5.51772i 0.200017i −0.994987 0.100009i \(-0.968113\pi\)
0.994987 0.100009i \(-0.0318871\pi\)
\(762\) 0 0
\(763\) 21.3107 + 21.3107i 0.771501 + 0.771501i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.0109 0.939200
\(768\) 0 0
\(769\) 14.0124 0.505299 0.252649 0.967558i \(-0.418698\pi\)
0.252649 + 0.967558i \(0.418698\pi\)
\(770\) 0 0
\(771\) −17.1108 + 17.1108i −0.616231 + 0.616231i
\(772\) 0 0
\(773\) 0.753043 + 0.753043i 0.0270851 + 0.0270851i 0.720520 0.693435i \(-0.243903\pi\)
−0.693435 + 0.720520i \(0.743903\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16.8535i 0.604614i
\(778\) 0 0
\(779\) 5.46066 + 5.46066i 0.195648 + 0.195648i
\(780\) 0 0
\(781\) −30.8073 + 30.8073i −1.10237 + 1.10237i
\(782\) 0 0
\(783\) 9.40668 0.336167
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 29.2752 29.2752i 1.04355 1.04355i 0.0445395 0.999008i \(-0.485818\pi\)
0.999008 0.0445395i \(-0.0141821\pi\)
\(788\) 0 0
\(789\) 31.7939 + 31.7939i 1.13189 + 1.13189i
\(790\) 0 0
\(791\) 6.63709i 0.235988i
\(792\) 0 0
\(793\) 26.1185i 0.927494i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.09658 + 6.09658i −0.215952 + 0.215952i −0.806790 0.590838i \(-0.798797\pi\)
0.590838 + 0.806790i \(0.298797\pi\)
\(798\) 0 0
\(799\) −3.91948 −0.138661
\(800\) 0 0
\(801\) 25.8745 0.914232
\(802\) 0 0
\(803\) −2.92214 + 2.92214i −0.103120 + 0.103120i