Properties

Label 320.2.o.e.287.1
Level $320$
Weight $2$
Character 320.287
Analytic conductor $2.555$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.49787136.1
Defining polynomial: \(x^{8} + 3 x^{6} + 5 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.1
Root \(1.09445 + 0.895644i\) of defining polynomial
Character \(\chi\) \(=\) 320.287
Dual form 320.2.o.e.223.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.18890 + 2.18890i) q^{3} +(0.456850 - 2.18890i) q^{5} +(1.79129 - 1.79129i) q^{7} -6.58258i q^{9} +O(q^{10})\) \(q+(-2.18890 + 2.18890i) q^{3} +(0.456850 - 2.18890i) q^{5} +(1.79129 - 1.79129i) q^{7} -6.58258i q^{9} +0.913701 q^{11} +(1.73205 + 1.73205i) q^{13} +(3.79129 + 5.79129i) q^{15} +(3.00000 + 3.00000i) q^{17} -3.46410i q^{19} +7.84190i q^{21} +(3.79129 + 3.79129i) q^{23} +(-4.58258 - 2.00000i) q^{25} +(7.84190 + 7.84190i) q^{27} +5.29150 q^{29} -7.58258i q^{31} +(-2.00000 + 2.00000i) q^{33} +(-3.10260 - 4.73930i) q^{35} +(5.19615 - 5.19615i) q^{37} -7.58258 q^{39} +1.58258 q^{41} +(-0.361500 + 0.361500i) q^{43} +(-14.4086 - 3.00725i) q^{45} +(-3.79129 + 3.79129i) q^{47} +0.582576i q^{49} -13.1334 q^{51} +(-2.64575 - 2.64575i) q^{53} +(0.417424 - 2.00000i) q^{55} +(7.58258 + 7.58258i) q^{57} -5.29150i q^{59} -6.20520i q^{61} +(-11.7913 - 11.7913i) q^{63} +(4.58258 - 3.00000i) q^{65} +(0.361500 + 0.361500i) q^{67} -16.5975 q^{69} -4.41742i q^{71} +(-8.58258 + 8.58258i) q^{73} +(14.4086 - 5.65300i) q^{75} +(1.63670 - 1.63670i) q^{77} +12.0000 q^{79} -14.5826 q^{81} +(-3.10260 + 3.10260i) q^{83} +(7.93725 - 5.19615i) q^{85} +(-11.5826 + 11.5826i) q^{87} +15.1652i q^{89} +6.20520 q^{91} +(16.5975 + 16.5975i) q^{93} +(-7.58258 - 1.58258i) q^{95} +(-8.58258 - 8.58258i) q^{97} -6.01450i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{7} + O(q^{10}) \) \( 8q - 4q^{7} + 12q^{15} + 24q^{17} + 12q^{23} - 16q^{33} - 24q^{39} - 24q^{41} - 12q^{47} + 40q^{55} + 24q^{57} - 76q^{63} - 32q^{73} + 96q^{79} - 80q^{81} - 56q^{87} - 24q^{95} - 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) −2.18890 + 2.18890i −1.26376 + 1.26376i −0.314508 + 0.949255i \(0.601839\pi\)
−0.949255 + 0.314508i \(0.898161\pi\)
\(4\) 0 0
\(5\) 0.456850 2.18890i 0.204310 0.978906i
\(6\) 0 0
\(7\) 1.79129 1.79129i 0.677043 0.677043i −0.282287 0.959330i \(-0.591093\pi\)
0.959330 + 0.282287i \(0.0910930\pi\)
\(8\) 0 0
\(9\) 6.58258i 2.19419i
\(10\) 0 0
\(11\) 0.913701 0.275491 0.137746 0.990468i \(-0.456014\pi\)
0.137746 + 0.990468i \(0.456014\pi\)
\(12\) 0 0
\(13\) 1.73205 + 1.73205i 0.480384 + 0.480384i 0.905254 0.424870i \(-0.139680\pi\)
−0.424870 + 0.905254i \(0.639680\pi\)
\(14\) 0 0
\(15\) 3.79129 + 5.79129i 0.978906 + 1.49530i
\(16\) 0 0
\(17\) 3.00000 + 3.00000i 0.727607 + 0.727607i 0.970143 0.242536i \(-0.0779791\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 7.84190i 1.71124i
\(22\) 0 0
\(23\) 3.79129 + 3.79129i 0.790538 + 0.790538i 0.981582 0.191043i \(-0.0611871\pi\)
−0.191043 + 0.981582i \(0.561187\pi\)
\(24\) 0 0
\(25\) −4.58258 2.00000i −0.916515 0.400000i
\(26\) 0 0
\(27\) 7.84190 + 7.84190i 1.50918 + 1.50918i
\(28\) 0 0
\(29\) 5.29150 0.982607 0.491304 0.870988i \(-0.336521\pi\)
0.491304 + 0.870988i \(0.336521\pi\)
\(30\) 0 0
\(31\) 7.58258i 1.36187i −0.732343 0.680935i \(-0.761573\pi\)
0.732343 0.680935i \(-0.238427\pi\)
\(32\) 0 0
\(33\) −2.00000 + 2.00000i −0.348155 + 0.348155i
\(34\) 0 0
\(35\) −3.10260 4.73930i −0.524435 0.801088i
\(36\) 0 0
\(37\) 5.19615 5.19615i 0.854242 0.854242i −0.136410 0.990652i \(-0.543557\pi\)
0.990652 + 0.136410i \(0.0435565\pi\)
\(38\) 0 0
\(39\) −7.58258 −1.21418
\(40\) 0 0
\(41\) 1.58258 0.247157 0.123578 0.992335i \(-0.460563\pi\)
0.123578 + 0.992335i \(0.460563\pi\)
\(42\) 0 0
\(43\) −0.361500 + 0.361500i −0.0551282 + 0.0551282i −0.734133 0.679005i \(-0.762411\pi\)
0.679005 + 0.734133i \(0.262411\pi\)
\(44\) 0 0
\(45\) −14.4086 3.00725i −2.14791 0.448295i
\(46\) 0 0
\(47\) −3.79129 + 3.79129i −0.553016 + 0.553016i −0.927310 0.374294i \(-0.877885\pi\)
0.374294 + 0.927310i \(0.377885\pi\)
\(48\) 0 0
\(49\) 0.582576i 0.0832251i
\(50\) 0 0
\(51\) −13.1334 −1.83904
\(52\) 0 0
\(53\) −2.64575 2.64575i −0.363422 0.363422i 0.501649 0.865071i \(-0.332727\pi\)
−0.865071 + 0.501649i \(0.832727\pi\)
\(54\) 0 0
\(55\) 0.417424 2.00000i 0.0562855 0.269680i
\(56\) 0 0
\(57\) 7.58258 + 7.58258i 1.00434 + 1.00434i
\(58\) 0 0
\(59\) 5.29150i 0.688895i −0.938806 0.344447i \(-0.888066\pi\)
0.938806 0.344447i \(-0.111934\pi\)
\(60\) 0 0
\(61\) 6.20520i 0.794495i −0.917712 0.397247i \(-0.869965\pi\)
0.917712 0.397247i \(-0.130035\pi\)
\(62\) 0 0
\(63\) −11.7913 11.7913i −1.48556 1.48556i
\(64\) 0 0
\(65\) 4.58258 3.00000i 0.568399 0.372104i
\(66\) 0 0
\(67\) 0.361500 + 0.361500i 0.0441643 + 0.0441643i 0.728844 0.684680i \(-0.240058\pi\)
−0.684680 + 0.728844i \(0.740058\pi\)
\(68\) 0 0
\(69\) −16.5975 −1.99811
\(70\) 0 0
\(71\) 4.41742i 0.524252i −0.965034 0.262126i \(-0.915576\pi\)
0.965034 0.262126i \(-0.0844236\pi\)
\(72\) 0 0
\(73\) −8.58258 + 8.58258i −1.00451 + 1.00451i −0.00452474 + 0.999990i \(0.501440\pi\)
−0.999990 + 0.00452474i \(0.998560\pi\)
\(74\) 0 0
\(75\) 14.4086 5.65300i 1.66376 0.652753i
\(76\) 0 0
\(77\) 1.63670 1.63670i 0.186519 0.186519i
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) −14.5826 −1.62029
\(82\) 0 0
\(83\) −3.10260 + 3.10260i −0.340555 + 0.340555i −0.856576 0.516021i \(-0.827413\pi\)
0.516021 + 0.856576i \(0.327413\pi\)
\(84\) 0 0
\(85\) 7.93725 5.19615i 0.860916 0.563602i
\(86\) 0 0
\(87\) −11.5826 + 11.5826i −1.24178 + 1.24178i
\(88\) 0 0
\(89\) 15.1652i 1.60750i 0.594965 + 0.803751i \(0.297166\pi\)
−0.594965 + 0.803751i \(0.702834\pi\)
\(90\) 0 0
\(91\) 6.20520 0.650482
\(92\) 0 0
\(93\) 16.5975 + 16.5975i 1.72108 + 1.72108i
\(94\) 0 0
\(95\) −7.58258 1.58258i −0.777956 0.162369i
\(96\) 0 0
\(97\) −8.58258 8.58258i −0.871429 0.871429i 0.121200 0.992628i \(-0.461326\pi\)
−0.992628 + 0.121200i \(0.961326\pi\)
\(98\) 0 0
\(99\) 6.01450i 0.604480i
\(100\) 0 0
\(101\) 17.5112i 1.74243i 0.490901 + 0.871215i \(0.336668\pi\)
−0.490901 + 0.871215i \(0.663332\pi\)
\(102\) 0 0
\(103\) −3.37386 3.37386i −0.332437 0.332437i 0.521075 0.853511i \(-0.325531\pi\)
−0.853511 + 0.521075i \(0.825531\pi\)
\(104\) 0 0
\(105\) 17.1652 + 3.58258i 1.67515 + 0.349624i
\(106\) 0 0
\(107\) 0.361500 + 0.361500i 0.0349475 + 0.0349475i 0.724365 0.689417i \(-0.242133\pi\)
−0.689417 + 0.724365i \(0.742133\pi\)
\(108\) 0 0
\(109\) −9.66930 −0.926151 −0.463076 0.886319i \(-0.653254\pi\)
−0.463076 + 0.886319i \(0.653254\pi\)
\(110\) 0 0
\(111\) 22.7477i 2.15912i
\(112\) 0 0
\(113\) 4.58258 4.58258i 0.431092 0.431092i −0.457907 0.889000i \(-0.651401\pi\)
0.889000 + 0.457907i \(0.151401\pi\)
\(114\) 0 0
\(115\) 10.0308 6.56670i 0.935377 0.612348i
\(116\) 0 0
\(117\) 11.4014 11.4014i 1.05406 1.05406i
\(118\) 0 0
\(119\) 10.7477 0.985243
\(120\) 0 0
\(121\) −10.1652 −0.924105
\(122\) 0 0
\(123\) −3.46410 + 3.46410i −0.312348 + 0.312348i
\(124\) 0 0
\(125\) −6.47135 + 9.11710i −0.578815 + 0.815459i
\(126\) 0 0
\(127\) 5.79129 5.79129i 0.513894 0.513894i −0.401823 0.915717i \(-0.631623\pi\)
0.915717 + 0.401823i \(0.131623\pi\)
\(128\) 0 0
\(129\) 1.58258i 0.139338i
\(130\) 0 0
\(131\) −6.01450 −0.525490 −0.262745 0.964865i \(-0.584628\pi\)
−0.262745 + 0.964865i \(0.584628\pi\)
\(132\) 0 0
\(133\) −6.20520 6.20520i −0.538059 0.538059i
\(134\) 0 0
\(135\) 20.7477 13.5826i 1.78568 1.16900i
\(136\) 0 0
\(137\) −6.16515 6.16515i −0.526724 0.526724i 0.392870 0.919594i \(-0.371482\pi\)
−0.919594 + 0.392870i \(0.871482\pi\)
\(138\) 0 0
\(139\) 22.8027i 1.93410i 0.254585 + 0.967050i \(0.418061\pi\)
−0.254585 + 0.967050i \(0.581939\pi\)
\(140\) 0 0
\(141\) 16.5975i 1.39776i
\(142\) 0 0
\(143\) 1.58258 + 1.58258i 0.132342 + 0.132342i
\(144\) 0 0
\(145\) 2.41742 11.5826i 0.200756 0.961881i
\(146\) 0 0
\(147\) −1.27520 1.27520i −0.105177 0.105177i
\(148\) 0 0
\(149\) 0.913701 0.0748533 0.0374266 0.999299i \(-0.488084\pi\)
0.0374266 + 0.999299i \(0.488084\pi\)
\(150\) 0 0
\(151\) 14.7477i 1.20015i −0.799943 0.600077i \(-0.795137\pi\)
0.799943 0.600077i \(-0.204863\pi\)
\(152\) 0 0
\(153\) 19.7477 19.7477i 1.59651 1.59651i
\(154\) 0 0
\(155\) −16.5975 3.46410i −1.33314 0.278243i
\(156\) 0 0
\(157\) 4.47315 4.47315i 0.356996 0.356996i −0.505708 0.862705i \(-0.668769\pi\)
0.862705 + 0.505708i \(0.168769\pi\)
\(158\) 0 0
\(159\) 11.5826 0.918558
\(160\) 0 0
\(161\) 13.5826 1.07046
\(162\) 0 0
\(163\) −0.361500 + 0.361500i −0.0283149 + 0.0283149i −0.721122 0.692808i \(-0.756374\pi\)
0.692808 + 0.721122i \(0.256374\pi\)
\(164\) 0 0
\(165\) 3.46410 + 5.29150i 0.269680 + 0.411943i
\(166\) 0 0
\(167\) −15.7913 + 15.7913i −1.22197 + 1.22197i −0.255035 + 0.966932i \(0.582087\pi\)
−0.966932 + 0.255035i \(0.917913\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.538462i
\(170\) 0 0
\(171\) −22.8027 −1.74377
\(172\) 0 0
\(173\) −8.66025 8.66025i −0.658427 0.658427i 0.296581 0.955008i \(-0.404154\pi\)
−0.955008 + 0.296581i \(0.904154\pi\)
\(174\) 0 0
\(175\) −11.7913 + 4.62614i −0.891338 + 0.349703i
\(176\) 0 0
\(177\) 11.5826 + 11.5826i 0.870600 + 0.870600i
\(178\) 0 0
\(179\) 19.1479i 1.43118i 0.698520 + 0.715591i \(0.253843\pi\)
−0.698520 + 0.715591i \(0.746157\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 13.5826 + 13.5826i 1.00405 + 1.00405i
\(184\) 0 0
\(185\) −9.00000 13.7477i −0.661693 1.01075i
\(186\) 0 0
\(187\) 2.74110 + 2.74110i 0.200449 + 0.200449i
\(188\) 0 0
\(189\) 28.0942 2.04355
\(190\) 0 0
\(191\) 4.41742i 0.319634i 0.987147 + 0.159817i \(0.0510903\pi\)
−0.987147 + 0.159817i \(0.948910\pi\)
\(192\) 0 0
\(193\) −4.16515 + 4.16515i −0.299814 + 0.299814i −0.840941 0.541127i \(-0.817998\pi\)
0.541127 + 0.840941i \(0.317998\pi\)
\(194\) 0 0
\(195\) −3.46410 + 16.5975i −0.248069 + 1.18857i
\(196\) 0 0
\(197\) −2.64575 + 2.64575i −0.188502 + 0.188502i −0.795048 0.606546i \(-0.792554\pi\)
0.606546 + 0.795048i \(0.292554\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) −1.58258 −0.111626
\(202\) 0 0
\(203\) 9.47860 9.47860i 0.665268 0.665268i
\(204\) 0 0
\(205\) 0.723000 3.46410i 0.0504965 0.241943i
\(206\) 0 0
\(207\) 24.9564 24.9564i 1.73459 1.73459i
\(208\) 0 0
\(209\) 3.16515i 0.218938i
\(210\) 0 0
\(211\) 23.5257 1.61958 0.809788 0.586722i \(-0.199582\pi\)
0.809788 + 0.586722i \(0.199582\pi\)
\(212\) 0 0
\(213\) 9.66930 + 9.66930i 0.662530 + 0.662530i
\(214\) 0 0
\(215\) 0.626136 + 0.956439i 0.0427022 + 0.0652286i
\(216\) 0 0
\(217\) −13.5826 13.5826i −0.922045 0.922045i
\(218\) 0 0
\(219\) 37.5728i 2.53894i
\(220\) 0 0
\(221\) 10.3923i 0.699062i
\(222\) 0 0
\(223\) 1.37386 + 1.37386i 0.0920007 + 0.0920007i 0.751609 0.659609i \(-0.229278\pi\)
−0.659609 + 0.751609i \(0.729278\pi\)
\(224\) 0 0
\(225\) −13.1652 + 30.1652i −0.877677 + 2.01101i
\(226\) 0 0
\(227\) 11.8582 + 11.8582i 0.787057 + 0.787057i 0.981011 0.193954i \(-0.0621312\pi\)
−0.193954 + 0.981011i \(0.562131\pi\)
\(228\) 0 0
\(229\) 3.46410 0.228914 0.114457 0.993428i \(-0.463487\pi\)
0.114457 + 0.993428i \(0.463487\pi\)
\(230\) 0 0
\(231\) 7.16515i 0.471432i
\(232\) 0 0
\(233\) −12.1652 + 12.1652i −0.796966 + 0.796966i −0.982616 0.185650i \(-0.940561\pi\)
0.185650 + 0.982616i \(0.440561\pi\)
\(234\) 0 0
\(235\) 6.56670 + 10.0308i 0.428364 + 0.654338i
\(236\) 0 0
\(237\) −26.2668 + 26.2668i −1.70621 + 1.70621i
\(238\) 0 0
\(239\) −15.1652 −0.980952 −0.490476 0.871455i \(-0.663177\pi\)
−0.490476 + 0.871455i \(0.663177\pi\)
\(240\) 0 0
\(241\) 16.7477 1.07882 0.539408 0.842045i \(-0.318648\pi\)
0.539408 + 0.842045i \(0.318648\pi\)
\(242\) 0 0
\(243\) 8.39410 8.39410i 0.538482 0.538482i
\(244\) 0 0
\(245\) 1.27520 + 0.266150i 0.0814696 + 0.0170037i
\(246\) 0 0
\(247\) 6.00000 6.00000i 0.381771 0.381771i
\(248\) 0 0
\(249\) 13.5826i 0.860761i
\(250\) 0 0
\(251\) 12.9427 0.816936 0.408468 0.912773i \(-0.366063\pi\)
0.408468 + 0.912773i \(0.366063\pi\)
\(252\) 0 0
\(253\) 3.46410 + 3.46410i 0.217786 + 0.217786i
\(254\) 0 0
\(255\) −6.00000 + 28.7477i −0.375735 + 1.80025i
\(256\) 0 0
\(257\) 7.74773 + 7.74773i 0.483290 + 0.483290i 0.906181 0.422891i \(-0.138985\pi\)
−0.422891 + 0.906181i \(0.638985\pi\)
\(258\) 0 0
\(259\) 18.6156i 1.15672i
\(260\) 0 0
\(261\) 34.8317i 2.15603i
\(262\) 0 0
\(263\) 14.2087 + 14.2087i 0.876147 + 0.876147i 0.993133 0.116987i \(-0.0373235\pi\)
−0.116987 + 0.993133i \(0.537324\pi\)
\(264\) 0 0
\(265\) −7.00000 + 4.58258i −0.430007 + 0.281505i
\(266\) 0 0
\(267\) −33.1950 33.1950i −2.03150 2.03150i
\(268\) 0 0
\(269\) −13.3241 −0.812385 −0.406193 0.913788i \(-0.633144\pi\)
−0.406193 + 0.913788i \(0.633144\pi\)
\(270\) 0 0
\(271\) 18.7477i 1.13884i −0.822046 0.569422i \(-0.807167\pi\)
0.822046 0.569422i \(-0.192833\pi\)
\(272\) 0 0
\(273\) −13.5826 + 13.5826i −0.822055 + 0.822055i
\(274\) 0 0
\(275\) −4.18710 1.82740i −0.252492 0.110196i
\(276\) 0 0
\(277\) −21.7937 + 21.7937i −1.30945 + 1.30945i −0.387646 + 0.921808i \(0.626712\pi\)
−0.921808 + 0.387646i \(0.873288\pi\)
\(278\) 0 0
\(279\) −49.9129 −2.98821
\(280\) 0 0
\(281\) 16.7477 0.999086 0.499543 0.866289i \(-0.333501\pi\)
0.499543 + 0.866289i \(0.333501\pi\)
\(282\) 0 0
\(283\) −22.4412 + 22.4412i −1.33399 + 1.33399i −0.432226 + 0.901765i \(0.642272\pi\)
−0.901765 + 0.432226i \(0.857728\pi\)
\(284\) 0 0
\(285\) 20.0616 13.1334i 1.18835 0.777956i
\(286\) 0 0
\(287\) 2.83485 2.83485i 0.167336 0.167336i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 37.5728 2.20256
\(292\) 0 0
\(293\) −18.1389 18.1389i −1.05968 1.05968i −0.998102 0.0615814i \(-0.980386\pi\)
−0.0615814 0.998102i \(-0.519614\pi\)
\(294\) 0 0
\(295\) −11.5826 2.41742i −0.674364 0.140748i
\(296\) 0 0
\(297\) 7.16515 + 7.16515i 0.415764 + 0.415764i
\(298\) 0 0
\(299\) 13.1334i 0.759525i
\(300\) 0 0
\(301\) 1.29510i 0.0746484i
\(302\) 0 0
\(303\) −38.3303 38.3303i −2.20202 2.20202i
\(304\) 0 0
\(305\) −13.5826 2.83485i −0.777736 0.162323i
\(306\) 0 0
\(307\) −6.56670 6.56670i −0.374782 0.374782i 0.494434 0.869215i \(-0.335375\pi\)
−0.869215 + 0.494434i \(0.835375\pi\)
\(308\) 0 0
\(309\) 14.7701 0.840242
\(310\) 0 0
\(311\) 19.5826i 1.11043i −0.831708 0.555213i \(-0.812637\pi\)
0.831708 0.555213i \(-0.187363\pi\)
\(312\) 0 0
\(313\) −6.58258 + 6.58258i −0.372069 + 0.372069i −0.868230 0.496161i \(-0.834742\pi\)
0.496161 + 0.868230i \(0.334742\pi\)
\(314\) 0 0
\(315\) −31.1968 + 20.4231i −1.75774 + 1.15071i
\(316\) 0 0
\(317\) 14.1425 14.1425i 0.794320 0.794320i −0.187874 0.982193i \(-0.560160\pi\)
0.982193 + 0.187874i \(0.0601596\pi\)
\(318\) 0 0
\(319\) 4.83485 0.270700
\(320\) 0 0
\(321\) −1.58258 −0.0883308
\(322\) 0 0
\(323\) 10.3923 10.3923i 0.578243 0.578243i
\(324\) 0 0
\(325\) −4.47315 11.4014i −0.248126 0.632433i
\(326\) 0 0
\(327\) 21.1652 21.1652i 1.17044 1.17044i
\(328\) 0 0
\(329\) 13.5826i 0.748832i
\(330\) 0 0
\(331\) −9.66930 −0.531473 −0.265737 0.964046i \(-0.585615\pi\)
−0.265737 + 0.964046i \(0.585615\pi\)
\(332\) 0 0
\(333\) −34.2041 34.2041i −1.87437 1.87437i
\(334\) 0 0
\(335\) 0.956439 0.626136i 0.0522559 0.0342095i
\(336\) 0 0
\(337\) 1.00000 + 1.00000i 0.0544735 + 0.0544735i 0.733819 0.679345i \(-0.237736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(338\) 0 0
\(339\) 20.0616i 1.08960i
\(340\) 0 0
\(341\) 6.92820i 0.375183i
\(342\) 0 0
\(343\) 13.5826 + 13.5826i 0.733390 + 0.733390i
\(344\) 0 0
\(345\) −7.58258 + 36.3303i −0.408232 + 1.95596i
\(346\) 0 0
\(347\) 1.27520 + 1.27520i 0.0684564 + 0.0684564i 0.740506 0.672050i \(-0.234586\pi\)
−0.672050 + 0.740506i \(0.734586\pi\)
\(348\) 0 0
\(349\) −10.3923 −0.556287 −0.278144 0.960539i \(-0.589719\pi\)
−0.278144 + 0.960539i \(0.589719\pi\)
\(350\) 0 0
\(351\) 27.1652i 1.44997i
\(352\) 0 0
\(353\) 24.1652 24.1652i 1.28618 1.28618i 0.349093 0.937088i \(-0.386490\pi\)
0.937088 0.349093i \(-0.113510\pi\)
\(354\) 0 0
\(355\) −9.66930 2.01810i −0.513193 0.107110i
\(356\) 0 0
\(357\) −23.5257 + 23.5257i −1.24511 + 1.24511i
\(358\) 0 0
\(359\) −27.1652 −1.43372 −0.716861 0.697216i \(-0.754422\pi\)
−0.716861 + 0.697216i \(0.754422\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 0 0
\(363\) 22.2505 22.2505i 1.16785 1.16785i
\(364\) 0 0
\(365\) 14.8655 + 22.7074i 0.778094 + 1.18856i
\(366\) 0 0
\(367\) −16.5390 + 16.5390i −0.863330 + 0.863330i −0.991723 0.128394i \(-0.959018\pi\)
0.128394 + 0.991723i \(0.459018\pi\)
\(368\) 0 0
\(369\) 10.4174i 0.542309i
\(370\) 0 0
\(371\) −9.47860 −0.492105
\(372\) 0 0
\(373\) 5.19615 + 5.19615i 0.269047 + 0.269047i 0.828716 0.559669i \(-0.189072\pi\)
−0.559669 + 0.828716i \(0.689072\pi\)
\(374\) 0 0
\(375\) −5.79129 34.1216i −0.299061 1.76203i
\(376\) 0 0
\(377\) 9.16515 + 9.16515i 0.472029 + 0.472029i
\(378\) 0 0
\(379\) 10.3923i 0.533817i −0.963722 0.266908i \(-0.913998\pi\)
0.963722 0.266908i \(-0.0860021\pi\)
\(380\) 0 0
\(381\) 25.3531i 1.29888i
\(382\) 0 0
\(383\) 17.3739 + 17.3739i 0.887763 + 0.887763i 0.994308 0.106545i \(-0.0339788\pi\)
−0.106545 + 0.994308i \(0.533979\pi\)
\(384\) 0 0
\(385\) −2.83485 4.33030i −0.144477 0.220693i
\(386\) 0 0
\(387\) 2.37960 + 2.37960i 0.120962 + 0.120962i
\(388\) 0 0
\(389\) 35.5547 1.80270 0.901348 0.433096i \(-0.142579\pi\)
0.901348 + 0.433096i \(0.142579\pi\)
\(390\) 0 0
\(391\) 22.7477i 1.15040i
\(392\) 0 0
\(393\) 13.1652 13.1652i 0.664094 0.664094i
\(394\) 0 0
\(395\) 5.48220 26.2668i 0.275840 1.32163i
\(396\) 0 0
\(397\) 7.93725 7.93725i 0.398359 0.398359i −0.479295 0.877654i \(-0.659107\pi\)
0.877654 + 0.479295i \(0.159107\pi\)
\(398\) 0 0
\(399\) 27.1652 1.35996
\(400\) 0 0
\(401\) −24.3303 −1.21500 −0.607499 0.794321i \(-0.707827\pi\)
−0.607499 + 0.794321i \(0.707827\pi\)
\(402\) 0 0
\(403\) 13.1334 13.1334i 0.654222 0.654222i
\(404\) 0 0
\(405\) −6.66205 + 31.9198i −0.331040 + 1.58611i
\(406\) 0 0
\(407\) 4.74773 4.74773i 0.235336 0.235336i
\(408\) 0 0
\(409\) 16.4174i 0.811789i 0.913920 + 0.405895i \(0.133040\pi\)
−0.913920 + 0.405895i \(0.866960\pi\)
\(410\) 0 0
\(411\) 26.9898 1.33131
\(412\) 0 0
\(413\) −9.47860 9.47860i −0.466412 0.466412i
\(414\) 0 0
\(415\) 5.37386 + 8.20871i 0.263793 + 0.402950i
\(416\) 0 0
\(417\) −49.9129 49.9129i −2.44424 2.44424i
\(418\) 0 0
\(419\) 20.9753i 1.02471i 0.858773 + 0.512355i \(0.171227\pi\)
−0.858773 + 0.512355i \(0.828773\pi\)
\(420\) 0 0
\(421\) 13.1334i 0.640083i −0.947404 0.320042i \(-0.896303\pi\)
0.947404 0.320042i \(-0.103697\pi\)
\(422\) 0 0
\(423\) 24.9564 + 24.9564i 1.21342 + 1.21342i
\(424\) 0 0
\(425\) −7.74773 19.7477i −0.375820 0.957905i
\(426\) 0 0
\(427\) −11.1153 11.1153i −0.537907 0.537907i
\(428\) 0 0
\(429\) −6.92820 −0.334497
\(430\) 0 0
\(431\) 10.7477i 0.517700i −0.965918 0.258850i \(-0.916656\pi\)
0.965918 0.258850i \(-0.0833435\pi\)
\(432\) 0 0
\(433\) −5.41742 + 5.41742i −0.260345 + 0.260345i −0.825194 0.564849i \(-0.808934\pi\)
0.564849 + 0.825194i \(0.308934\pi\)
\(434\) 0 0
\(435\) 20.0616 + 30.6446i 0.961881 + 1.46930i
\(436\) 0 0
\(437\) 13.1334 13.1334i 0.628256 0.628256i
\(438\) 0 0
\(439\) 25.4955 1.21683 0.608416 0.793618i \(-0.291805\pi\)
0.608416 + 0.793618i \(0.291805\pi\)
\(440\) 0 0
\(441\) 3.83485 0.182612
\(442\) 0 0
\(443\) 14.4086 14.4086i 0.684574 0.684574i −0.276454 0.961027i \(-0.589159\pi\)
0.961027 + 0.276454i \(0.0891592\pi\)
\(444\) 0 0
\(445\) 33.1950 + 6.92820i 1.57359 + 0.328428i
\(446\) 0 0
\(447\) −2.00000 + 2.00000i −0.0945968 + 0.0945968i
\(448\) 0 0
\(449\) 19.5826i 0.924159i 0.886839 + 0.462079i \(0.152897\pi\)
−0.886839 + 0.462079i \(0.847103\pi\)
\(450\) 0 0
\(451\) 1.44600 0.0680895
\(452\) 0 0
\(453\) 32.2813 + 32.2813i 1.51671 + 1.51671i
\(454\) 0 0
\(455\) 2.83485 13.5826i 0.132900 0.636761i
\(456\) 0 0
\(457\) 12.5826 + 12.5826i 0.588588 + 0.588588i 0.937249 0.348661i \(-0.113364\pi\)
−0.348661 + 0.937249i \(0.613364\pi\)
\(458\) 0 0
\(459\) 47.0514i 2.19617i
\(460\) 0 0
\(461\) 3.65480i 0.170221i −0.996372 0.0851106i \(-0.972876\pi\)
0.996372 0.0851106i \(-0.0271243\pi\)
\(462\) 0 0
\(463\) −12.2087 12.2087i −0.567387 0.567387i 0.364009 0.931396i \(-0.381408\pi\)
−0.931396 + 0.364009i \(0.881408\pi\)
\(464\) 0 0
\(465\) 43.9129 28.7477i 2.03641 1.33314i
\(466\) 0 0
\(467\) −16.2360 16.2360i −0.751313 0.751313i 0.223411 0.974724i \(-0.428281\pi\)
−0.974724 + 0.223411i \(0.928281\pi\)
\(468\) 0 0
\(469\) 1.29510 0.0598022
\(470\) 0 0
\(471\) 19.5826i 0.902317i
\(472\) 0 0
\(473\) −0.330303 + 0.330303i −0.0151873 + 0.0151873i
\(474\) 0 0
\(475\) −6.92820 + 15.8745i −0.317888 + 0.728372i
\(476\) 0 0
\(477\) −17.4159 + 17.4159i −0.797417 + 0.797417i
\(478\) 0 0
\(479\) 33.4955 1.53045 0.765223 0.643765i \(-0.222629\pi\)
0.765223 + 0.643765i \(0.222629\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) −29.7309 + 29.7309i −1.35280 + 1.35280i
\(484\) 0 0
\(485\) −22.7074 + 14.8655i −1.03109 + 0.675006i
\(486\) 0 0
\(487\) −13.3739 + 13.3739i −0.606028 + 0.606028i −0.941906 0.335878i \(-0.890967\pi\)
0.335878 + 0.941906i \(0.390967\pi\)
\(488\) 0 0
\(489\) 1.58258i 0.0715665i
\(490\) 0 0
\(491\) −27.1805 −1.22664 −0.613320 0.789835i \(-0.710166\pi\)
−0.613320 + 0.789835i \(0.710166\pi\)
\(492\) 0 0
\(493\) 15.8745 + 15.8745i 0.714952 + 0.714952i
\(494\) 0 0
\(495\) −13.1652 2.74773i −0.591730 0.123501i
\(496\) 0 0
\(497\) −7.91288 7.91288i −0.354941 0.354941i
\(498\) 0 0
\(499\) 24.2487i 1.08552i −0.839887 0.542761i \(-0.817379\pi\)
0.839887 0.542761i \(-0.182621\pi\)
\(500\) 0 0
\(501\) 69.1311i 3.08855i
\(502\) 0 0
\(503\) −14.5390 14.5390i −0.648263 0.648263i 0.304310 0.952573i \(-0.401574\pi\)
−0.952573 + 0.304310i \(0.901574\pi\)
\(504\) 0 0
\(505\) 38.3303 + 8.00000i 1.70568 + 0.355995i
\(506\) 0 0
\(507\) 15.3223 + 15.3223i 0.680488 + 0.680488i
\(508\) 0 0
\(509\) −3.84550 −0.170449 −0.0852244 0.996362i \(-0.527161\pi\)
−0.0852244 + 0.996362i \(0.527161\pi\)
\(510\) 0 0
\(511\) 30.7477i 1.36020i
\(512\) 0 0
\(513\) 27.1652 27.1652i 1.19937 1.19937i
\(514\) 0 0
\(515\) −8.92640 + 5.84370i −0.393344 + 0.257504i
\(516\) 0 0
\(517\) −3.46410 + 3.46410i −0.152351 + 0.152351i
\(518\) 0 0
\(519\) 37.9129 1.66419
\(520\) 0 0
\(521\) −14.8348 −0.649927 −0.324963 0.945727i \(-0.605352\pi\)
−0.324963 + 0.945727i \(0.605352\pi\)
\(522\) 0 0
\(523\) −23.8872 + 23.8872i −1.04451 + 1.04451i −0.0455529 + 0.998962i \(0.514505\pi\)
−0.998962 + 0.0455529i \(0.985495\pi\)
\(524\) 0 0
\(525\) 15.6838 35.9361i 0.684497 1.56838i
\(526\) 0 0
\(527\) 22.7477 22.7477i 0.990907 0.990907i
\(528\) 0 0
\(529\) 5.74773i 0.249901i
\(530\) 0 0
\(531\) −34.8317 −1.51157
\(532\) 0 0
\(533\) 2.74110 + 2.74110i 0.118730 + 0.118730i
\(534\) 0 0
\(535\) 0.956439 0.626136i 0.0413505 0.0270702i
\(536\) 0 0
\(537\) −41.9129 41.9129i −1.80867 1.80867i
\(538\) 0 0
\(539\) 0.532300i 0.0229278i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −15.1652 15.1652i −0.650799 0.650799i
\(544\) 0 0
\(545\) −4.41742 + 21.1652i −0.189222 + 0.906615i
\(546\) 0 0
\(547\) −23.1642 23.1642i −0.990430 0.990430i 0.00952449 0.999955i \(-0.496968\pi\)
−0.999955 + 0.00952449i \(0.996968\pi\)
\(548\) 0 0
\(549\) −40.8462 −1.74327
\(550\) 0 0
\(551\) 18.3303i 0.780897i
\(552\) 0 0
\(553\) 21.4955 21.4955i 0.914080 0.914080i
\(554\) 0 0
\(555\) 49.7925 + 10.3923i 2.11357 + 0.441129i
\(556\) 0 0
\(557\) 20.8800 20.8800i 0.884712 0.884712i −0.109297 0.994009i \(-0.534860\pi\)
0.994009 + 0.109297i \(0.0348599\pi\)
\(558\) 0 0
\(559\) −1.25227 −0.0529655
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) 11.6675 11.6675i 0.491727 0.491727i −0.417123 0.908850i \(-0.636962\pi\)
0.908850 + 0.417123i \(0.136962\pi\)
\(564\) 0 0
\(565\) −7.93725 12.1244i −0.333923 0.510075i
\(566\) 0 0
\(567\) −26.1216 + 26.1216i −1.09700 + 1.09700i
\(568\) 0 0
\(569\) 22.7477i 0.953634i −0.879002 0.476817i \(-0.841790\pi\)
0.879002 0.476817i \(-0.158210\pi\)
\(570\) 0 0
\(571\) 8.22330 0.344135 0.172067 0.985085i \(-0.444955\pi\)
0.172067 + 0.985085i \(0.444955\pi\)
\(572\) 0 0
\(573\) −9.66930 9.66930i −0.403941 0.403941i
\(574\) 0 0
\(575\) −9.79129 24.9564i −0.408325 1.04076i
\(576\) 0 0
\(577\) 15.7477 + 15.7477i 0.655586 + 0.655586i 0.954333 0.298746i \(-0.0965684\pi\)
−0.298746 + 0.954333i \(0.596568\pi\)
\(578\) 0 0
\(579\) 18.2342i 0.757788i
\(580\) 0 0
\(581\) 11.1153i 0.461141i
\(582\) 0 0
\(583\) −2.41742 2.41742i −0.100119 0.100119i
\(584\) 0 0
\(585\) −19.7477 30.1652i −0.816468 1.24718i
\(586\) 0 0
\(587\) 4.54860 + 4.54860i 0.187741 + 0.187741i 0.794719 0.606978i \(-0.207618\pi\)
−0.606978 + 0.794719i \(0.707618\pi\)
\(588\) 0 0
\(589\) −26.2668 −1.08231
\(590\) 0 0
\(591\) 11.5826i 0.476444i
\(592\) 0 0
\(593\) −18.1652 + 18.1652i −0.745953 + 0.745953i −0.973717 0.227763i \(-0.926859\pi\)
0.227763 + 0.973717i \(0.426859\pi\)
\(594\) 0 0
\(595\) 4.91010 23.5257i 0.201295 0.964460i
\(596\) 0 0
\(597\) 8.75560 8.75560i 0.358343 0.358343i
\(598\) 0 0
\(599\) 5.66970 0.231658 0.115829 0.993269i \(-0.463048\pi\)
0.115829 + 0.993269i \(0.463048\pi\)
\(600\) 0 0
\(601\) 24.7477 1.00948 0.504740 0.863271i \(-0.331588\pi\)
0.504740 + 0.863271i \(0.331588\pi\)
\(602\) 0 0
\(603\) 2.37960 2.37960i 0.0969049 0.0969049i
\(604\) 0 0
\(605\) −4.64395 + 22.2505i −0.188803 + 0.904612i
\(606\) 0 0
\(607\) 7.37386 7.37386i 0.299296 0.299296i −0.541442 0.840738i \(-0.682121\pi\)
0.840738 + 0.541442i \(0.182121\pi\)
\(608\) 0 0
\(609\) 41.4955i 1.68148i
\(610\) 0 0
\(611\) −13.1334 −0.531321
\(612\) 0 0
\(613\) 8.66025 + 8.66025i 0.349784 + 0.349784i 0.860029 0.510245i \(-0.170445\pi\)
−0.510245 + 0.860029i \(0.670445\pi\)
\(614\) 0 0
\(615\) 6.00000 + 9.16515i 0.241943 + 0.369575i
\(616\) 0 0
\(617\) 3.00000 + 3.00000i 0.120775 + 0.120775i 0.764911 0.644136i \(-0.222783\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) 2.01810i 0.0811143i 0.999177 + 0.0405572i \(0.0129133\pi\)
−0.999177 + 0.0405572i \(0.987087\pi\)
\(620\) 0 0
\(621\) 59.4618i 2.38612i
\(622\) 0 0
\(623\) 27.1652 + 27.1652i 1.08835 + 1.08835i
\(624\) 0 0
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) 0 0
\(627\) 6.92820 + 6.92820i 0.276686 + 0.276686i
\(628\) 0 0
\(629\) 31.1769 1.24310
\(630\) 0 0
\(631\) 17.0780i 0.679866i 0.940450 + 0.339933i \(0.110404\pi\)
−0.940450 + 0.339933i \(0.889596\pi\)
\(632\) 0 0
\(633\) −51.4955 + 51.4955i −2.04676 + 2.04676i
\(634\) 0 0
\(635\) −10.0308 15.3223i −0.398060 0.608047i
\(636\) 0 0
\(637\) −1.00905 + 1.00905i −0.0399800 + 0.0399800i
\(638\) 0 0
\(639\) −29.0780 −1.15031
\(640\) 0 0
\(641\) −19.9129 −0.786511 −0.393256 0.919429i \(-0.628651\pi\)
−0.393256 + 0.919429i \(0.628651\pi\)
\(642\) 0 0
\(643\) 10.7538 10.7538i 0.424089 0.424089i −0.462520 0.886609i \(-0.653055\pi\)
0.886609 + 0.462520i \(0.153055\pi\)
\(644\) 0 0
\(645\) −3.46410 0.723000i −0.136399 0.0284681i
\(646\) 0 0
\(647\) −32.5390 + 32.5390i −1.27924 + 1.27924i −0.338148 + 0.941093i \(0.609800\pi\)
−0.941093 + 0.338148i \(0.890200\pi\)
\(648\) 0 0
\(649\) 4.83485i 0.189784i
\(650\) 0 0
\(651\) 59.4618 2.33049
\(652\) 0 0
\(653\) −4.47315 4.47315i −0.175048 0.175048i 0.614145 0.789193i \(-0.289501\pi\)
−0.789193 + 0.614145i \(0.789501\pi\)
\(654\) 0 0
\(655\) −2.74773 + 13.1652i −0.107363 + 0.514405i
\(656\) 0 0
\(657\) 56.4955 + 56.4955i 2.20410 + 2.20410i
\(658\) 0 0
\(659\) 38.4865i 1.49922i 0.661879 + 0.749611i \(0.269759\pi\)
−0.661879 + 0.749611i \(0.730241\pi\)
\(660\) 0 0
\(661\) 37.9542i 1.47625i 0.674665 + 0.738124i \(0.264288\pi\)
−0.674665 + 0.738124i \(0.735712\pi\)
\(662\) 0 0
\(663\) −22.7477 22.7477i −0.883449 0.883449i
\(664\) 0 0
\(665\) −16.4174 + 10.7477i −0.636640 + 0.416779i
\(666\) 0 0
\(667\) 20.0616 + 20.0616i 0.776789 + 0.776789i
\(668\) 0 0
\(669\) −6.01450 −0.232534
\(670\) 0 0
\(671\) 5.66970i 0.218876i
\(672\) 0 0
\(673\) −9.41742 + 9.41742i −0.363015 + 0.363015i −0.864922 0.501907i \(-0.832632\pi\)
0.501907 + 0.864922i \(0.332632\pi\)
\(674\) 0 0
\(675\) −20.2523 51.6199i −0.779512 1.98685i
\(676\) 0 0
\(677\) 2.45505 2.45505i 0.0943553 0.0943553i −0.658354 0.752709i \(-0.728747\pi\)
0.752709 + 0.658354i \(0.228747\pi\)
\(678\) 0 0
\(679\) −30.7477 −1.17999
\(680\) 0 0
\(681\) −51.9129 −1.98931
\(682\) 0 0
\(683\) 32.8335 32.8335i 1.25634 1.25634i 0.303512 0.952828i \(-0.401841\pi\)
0.952828 0.303512i \(-0.0981592\pi\)
\(684\) 0 0
\(685\) −16.3115 + 10.6784i −0.623229 + 0.407999i
\(686\) 0 0
\(687\) −7.58258 + 7.58258i −0.289293 + 0.289293i
\(688\) 0 0
\(689\) 9.16515i 0.349164i
\(690\) 0 0
\(691\) −15.1515 −0.576391 −0.288195 0.957572i \(-0.593055\pi\)
−0.288195 + 0.957572i \(0.593055\pi\)
\(692\) 0 0
\(693\) −10.7737 10.7737i −0.409259 0.409259i
\(694\) 0 0
\(695\) 49.9129 + 10.4174i 1.89330 + 0.395155i
\(696\) 0 0
\(697\) 4.74773 + 4.74773i 0.179833 + 0.179833i
\(698\) 0 0
\(699\) 53.2566i 2.01435i
\(700\) 0 0
\(701\) 25.1624i 0.950371i −0.879886 0.475186i \(-0.842381\pi\)
0.879886 0.475186i \(-0.157619\pi\)
\(702\) 0 0
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) 0 0
\(705\) −36.3303 7.58258i −1.36828 0.285576i
\(706\) 0 0
\(707\) 31.3676 + 31.3676i 1.17970 + 1.17970i
\(708\) 0 0
\(709\) 36.6591 1.37676 0.688381 0.725349i \(-0.258322\pi\)
0.688381 + 0.725349i \(0.258322\pi\)
\(710\) 0 0
\(711\) 78.9909i 2.96239i
\(712\) 0 0
\(713\) 28.7477 28.7477i 1.07661 1.07661i
\(714\) 0 0
\(715\) 4.18710 2.74110i 0.156589 0.102511i
\(716\) 0 0
\(717\) 33.1950 33.1950i 1.23969 1.23969i
\(718\) 0 0
\(719\) −51.8258 −1.93277 −0.966387 0.257091i \(-0.917236\pi\)
−0.966387 + 0.257091i \(0.917236\pi\)
\(720\) 0 0
\(721\) −12.0871 −0.450148
\(722\) 0 0
\(723\) −36.6591 + 36.6591i −1.36337 + 1.36337i
\(724\) 0 0
\(725\) −24.2487 10.5830i −0.900575 0.393043i
\(726\) 0 0
\(727\) 16.9564 16.9564i 0.628880 0.628880i −0.318907 0.947786i \(-0.603316\pi\)
0.947786 + 0.318907i \(0.103316\pi\)
\(728\) 0 0
\(729\) 7.00000i 0.259259i
\(730\) 0 0
\(731\) −2.16900 −0.0802234
\(732\) 0 0
\(733\) −14.1425 14.1425i −0.522364 0.522364i 0.395921 0.918285i \(-0.370425\pi\)
−0.918285 + 0.395921i \(0.870425\pi\)
\(734\) 0 0
\(735\) −3.37386 + 2.20871i −0.124447 + 0.0814696i
\(736\) 0 0
\(737\) 0.330303 + 0.330303i 0.0121669 + 0.0121669i
\(738\) 0 0
\(739\) 29.7309i 1.09367i −0.837241 0.546835i \(-0.815833\pi\)
0.837241 0.546835i \(-0.184167\pi\)
\(740\) 0 0
\(741\) 26.2668i 0.964935i
\(742\) 0 0
\(743\) −21.7913 21.7913i −0.799445 0.799445i 0.183563 0.983008i \(-0.441237\pi\)
−0.983008 + 0.183563i \(0.941237\pi\)
\(744\) 0 0
\(745\) 0.417424 2.00000i 0.0152932 0.0732743i
\(746\) 0 0
\(747\) 20.4231 + 20.4231i 0.747243 + 0.747243i
\(748\) 0 0
\(749\) 1.29510 0.0473220
\(750\) 0 0
\(751\) 41.0780i 1.49896i 0.662028 + 0.749479i \(0.269696\pi\)
−0.662028 + 0.749479i \(0.730304\pi\)
\(752\) 0 0
\(753\) −28.3303 + 28.3303i −1.03241 + 1.03241i
\(754\) 0 0
\(755\) −32.2813 6.73750i −1.17484 0.245203i
\(756\) 0 0
\(757\) −27.2759 + 27.2759i −0.991358 + 0.991358i −0.999963 0.00860486i \(-0.997261\pi\)
0.00860486 + 0.999963i \(0.497261\pi\)
\(758\) 0 0
\(759\) −15.1652 −0.550460
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) −17.3205 + 17.3205i −0.627044 + 0.627044i
\(764\) 0 0
\(765\) −34.2041 52.2476i −1.23665 1.88902i
\(766\) 0 0
\(767\) 9.16515 9.16515i 0.330934 0.330934i
\(768\) 0 0
\(769\) 17.4955i 0.630902i −0.948942 0.315451i \(-0.897844\pi\)
0.948942 0.315451i \(-0.102156\pi\)
\(770\) 0 0
\(771\) −33.9180 −1.22153
\(772\) 0 0
\(773\) −31.4630 31.4630i −1.13164 1.13164i −0.989904 0.141740i \(-0.954730\pi\)
−0.141740 0.989904i \(-0.545270\pi\)
\(774\) 0 0
\(775\) −15.1652 + 34.7477i −0.544748 + 1.24818i
\(776\) 0 0
\(777\) 40.7477 + 40.7477i 1.46182 + 1.46182i
\(778\) 0 0
\(779\) 5.48220i 0.196420i
\(780\) 0 0
\(781\) 4.03620i 0.144427i
\(782\) 0 0
\(783\) 41.4955 + 41.4955i 1.48293 + 1.48293i
\(784\) 0 0
\(785\) −7.74773 11.8348i −0.276528 0.422404i
\(786\) 0 0
\(787\) −18.9771 18.9771i −0.676461 0.676461i 0.282737 0.959198i \(-0.408758\pi\)
−0.959198 + 0.282737i \(0.908758\pi\)
\(788\) 0 0
\(789\) −62.2029 −2.21448
\(790\) 0 0
\(791\) 16.4174i 0.583736i
\(792\) 0 0
\(793\) 10.7477 10.7477i 0.381663 0.381663i
\(794\) 0 0
\(795\) 5.29150 25.3531i 0.187670 0.899182i
\(796\) 0 0
\(797\) 3.17805 3.17805i 0.112572 0.112572i −0.648577 0.761149i \(-0.724635\pi\)
0.761149 + 0.648577i \(0.224635\pi\)