Properties

Label 700.2.i.d.401.3
Level $700$
Weight $2$
Character 700.401
Analytic conductor $5.590$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} - 2 x^{3} + 19 x^{2} - 12 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 401.3
Root \(-0.956115 + 1.65604i\) of defining polynomial
Character \(\chi\) \(=\) 700.401
Dual form 700.2.i.d.501.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28442 + 2.22469i) q^{3} +(2.58392 + 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +O(q^{10})\) \(q+(1.28442 + 2.22469i) q^{3} +(2.58392 + 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +(0.784425 + 1.35866i) q^{11} +5.56885 q^{13} +(-3.58392 - 6.20753i) q^{17} +(-1.58392 + 2.74343i) q^{19} +(2.05378 + 6.47880i) q^{21} +(-2.86834 + 4.96812i) q^{23} -1.53871 q^{27} +1.96986 q^{29} +(-0.484931 - 0.839925i) q^{31} +(-2.01507 + 3.49020i) q^{33} +(3.35327 - 5.80804i) q^{37} +(7.15277 + 12.3890i) q^{39} -8.87439 q^{41} -4.59899 q^{43} +(-0.200506 + 0.347286i) q^{47} +(6.35327 + 2.93869i) q^{49} +(9.20655 - 15.9462i) q^{51} +(-4.76936 - 8.26077i) q^{53} -8.13770 q^{57} +(2.28442 + 3.95674i) q^{59} +(-7.65277 + 13.2550i) q^{61} +(-6.42212 + 7.03032i) q^{63} +(-0.431150 - 0.746774i) q^{67} -14.7367 q^{69} -12.1377 q^{71} +(-2.00000 - 3.46410i) q^{73} +(1.25429 + 3.95674i) q^{77} +(6.43719 - 11.1495i) q^{79} +(3.42212 + 5.92729i) q^{81} +17.1076 q^{83} +(2.53014 + 4.38233i) q^{87} +(2.79949 - 4.84887i) q^{89} +(14.3895 + 3.16673i) q^{91} +(1.24571 - 2.15764i) q^{93} +0.233174 q^{97} -5.64627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{3} + 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 6 q - q^{3} + 4 q^{7} - 8 q^{9} - 4 q^{11} + 16 q^{13} - 10 q^{17} + 2 q^{19} - 11 q^{21} + 3 q^{23} + 20 q^{27} + 3 q^{31} - 18 q^{33} - 6 q^{37} + 14 q^{39} + 22 q^{41} - 22 q^{43} - 4 q^{47} + 12 q^{49} + 3 q^{51} - 14 q^{53} - 14 q^{57} + 5 q^{59} - 17 q^{61} + 5 q^{63} - 20 q^{67} - 48 q^{69} - 38 q^{71} - 12 q^{73} - 13 q^{77} + q^{79} - 23 q^{81} + 56 q^{83} + 27 q^{87} + 14 q^{89} + 17 q^{91} + 28 q^{93} + 30 q^{97} + 42 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.28442 + 2.22469i 0.741563 + 1.28442i 0.951783 + 0.306771i \(0.0992485\pi\)
−0.210220 + 0.977654i \(0.567418\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.58392 + 0.568650i 0.976630 + 0.214929i
\(8\) 0 0
\(9\) −1.79949 + 3.11682i −0.599831 + 1.03894i
\(10\) 0 0
\(11\) 0.784425 + 1.35866i 0.236513 + 0.409652i 0.959711 0.280988i \(-0.0906621\pi\)
−0.723198 + 0.690640i \(0.757329\pi\)
\(12\) 0 0
\(13\) 5.56885 1.54452 0.772260 0.635306i \(-0.219126\pi\)
0.772260 + 0.635306i \(0.219126\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.58392 6.20753i −0.869228 1.50555i −0.862787 0.505568i \(-0.831283\pi\)
−0.00644117 0.999979i \(-0.502050\pi\)
\(18\) 0 0
\(19\) −1.58392 + 2.74343i −0.363376 + 0.629386i −0.988514 0.151129i \(-0.951709\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(20\) 0 0
\(21\) 2.05378 + 6.47880i 0.448172 + 1.41379i
\(22\) 0 0
\(23\) −2.86834 + 4.96812i −0.598091 + 1.03592i 0.395012 + 0.918676i \(0.370741\pi\)
−0.993103 + 0.117248i \(0.962593\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.53871 −0.296125
\(28\) 0 0
\(29\) 1.96986 0.365794 0.182897 0.983132i \(-0.441453\pi\)
0.182897 + 0.983132i \(0.441453\pi\)
\(30\) 0 0
\(31\) −0.484931 0.839925i −0.0870961 0.150855i 0.819186 0.573527i \(-0.194425\pi\)
−0.906282 + 0.422673i \(0.861092\pi\)
\(32\) 0 0
\(33\) −2.01507 + 3.49020i −0.350779 + 0.607566i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.35327 5.80804i 0.551275 0.954836i −0.446908 0.894580i \(-0.647475\pi\)
0.998183 0.0602563i \(-0.0191918\pi\)
\(38\) 0 0
\(39\) 7.15277 + 12.3890i 1.14536 + 1.98382i
\(40\) 0 0
\(41\) −8.87439 −1.38595 −0.692973 0.720963i \(-0.743700\pi\)
−0.692973 + 0.720963i \(0.743700\pi\)
\(42\) 0 0
\(43\) −4.59899 −0.701339 −0.350670 0.936499i \(-0.614046\pi\)
−0.350670 + 0.936499i \(0.614046\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.200506 + 0.347286i −0.0292468 + 0.0506569i −0.880278 0.474458i \(-0.842644\pi\)
0.851032 + 0.525115i \(0.175978\pi\)
\(48\) 0 0
\(49\) 6.35327 + 2.93869i 0.907611 + 0.419813i
\(50\) 0 0
\(51\) 9.20655 15.9462i 1.28917 2.23292i
\(52\) 0 0
\(53\) −4.76936 8.26077i −0.655121 1.13470i −0.981863 0.189590i \(-0.939284\pi\)
0.326742 0.945114i \(-0.394049\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8.13770 −1.07786
\(58\) 0 0
\(59\) 2.28442 + 3.95674i 0.297407 + 0.515124i 0.975542 0.219814i \(-0.0705449\pi\)
−0.678135 + 0.734937i \(0.737212\pi\)
\(60\) 0 0
\(61\) −7.65277 + 13.2550i −0.979837 + 1.69713i −0.316886 + 0.948464i \(0.602637\pi\)
−0.662951 + 0.748663i \(0.730696\pi\)
\(62\) 0 0
\(63\) −6.42212 + 7.03032i −0.809112 + 0.885737i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.431150 0.746774i −0.0526734 0.0912330i 0.838486 0.544922i \(-0.183441\pi\)
−0.891160 + 0.453689i \(0.850108\pi\)
\(68\) 0 0
\(69\) −14.7367 −1.77409
\(70\) 0 0
\(71\) −12.1377 −1.44048 −0.720240 0.693725i \(-0.755968\pi\)
−0.720240 + 0.693725i \(0.755968\pi\)
\(72\) 0 0
\(73\) −2.00000 3.46410i −0.234082 0.405442i 0.724923 0.688830i \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.25429 + 3.95674i 0.142939 + 0.450912i
\(78\) 0 0
\(79\) 6.43719 11.1495i 0.724241 1.25442i −0.235045 0.971985i \(-0.575524\pi\)
0.959286 0.282437i \(-0.0911430\pi\)
\(80\) 0 0
\(81\) 3.42212 + 5.92729i 0.380236 + 0.658588i
\(82\) 0 0
\(83\) 17.1076 1.87780 0.938899 0.344192i \(-0.111847\pi\)
0.938899 + 0.344192i \(0.111847\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.53014 + 4.38233i 0.271259 + 0.469835i
\(88\) 0 0
\(89\) 2.79949 4.84887i 0.296746 0.513979i −0.678644 0.734468i \(-0.737432\pi\)
0.975389 + 0.220489i \(0.0707653\pi\)
\(90\) 0 0
\(91\) 14.3895 + 3.16673i 1.50842 + 0.331963i
\(92\) 0 0
\(93\) 1.24571 2.15764i 0.129175 0.223737i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.233174 0.0236752 0.0118376 0.999930i \(-0.496232\pi\)
0.0118376 + 0.999930i \(0.496232\pi\)
\(98\) 0 0
\(99\) −5.64627 −0.567472
\(100\) 0 0
\(101\) −6.25176 10.8284i −0.622073 1.07746i −0.989099 0.147251i \(-0.952957\pi\)
0.367026 0.930211i \(-0.380376\pi\)
\(102\) 0 0
\(103\) −1.68544 + 2.91926i −0.166071 + 0.287643i −0.937035 0.349235i \(-0.886441\pi\)
0.770964 + 0.636879i \(0.219775\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.86834 15.3604i 0.857335 1.48495i −0.0171265 0.999853i \(-0.505452\pi\)
0.874462 0.485095i \(-0.161215\pi\)
\(108\) 0 0
\(109\) −2.95226 5.11347i −0.282775 0.489782i 0.689292 0.724484i \(-0.257922\pi\)
−0.972067 + 0.234702i \(0.924588\pi\)
\(110\) 0 0
\(111\) 17.2281 1.63522
\(112\) 0 0
\(113\) 15.6412 1.47140 0.735701 0.677307i \(-0.236853\pi\)
0.735701 + 0.677307i \(0.236853\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.0211 + 17.3571i −0.926452 + 1.60466i
\(118\) 0 0
\(119\) −5.73064 18.0777i −0.525327 1.65718i
\(120\) 0 0
\(121\) 4.26936 7.39474i 0.388123 0.672249i
\(122\) 0 0
\(123\) −11.3985 19.7428i −1.02777 1.78014i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.8744 1.14242 0.571209 0.820805i \(-0.306475\pi\)
0.571209 + 0.820805i \(0.306475\pi\)
\(128\) 0 0
\(129\) −5.90705 10.2313i −0.520087 0.900817i
\(130\) 0 0
\(131\) 0.114058 0.197554i 0.00996526 0.0172603i −0.861000 0.508605i \(-0.830161\pi\)
0.870965 + 0.491345i \(0.163495\pi\)
\(132\) 0 0
\(133\) −5.65277 + 6.18810i −0.490157 + 0.536576i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.83821 + 8.38002i 0.413356 + 0.715953i 0.995254 0.0973082i \(-0.0310233\pi\)
−0.581899 + 0.813261i \(0.697690\pi\)
\(138\) 0 0
\(139\) −12.3709 −1.04928 −0.524642 0.851323i \(-0.675801\pi\)
−0.524642 + 0.851323i \(0.675801\pi\)
\(140\) 0 0
\(141\) −1.03014 −0.0867533
\(142\) 0 0
\(143\) 4.36834 + 7.56619i 0.365299 + 0.632717i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1.62263 + 17.9086i 0.133832 + 1.47708i
\(148\) 0 0
\(149\) −5.95479 + 10.3140i −0.487836 + 0.844956i −0.999902 0.0139898i \(-0.995547\pi\)
0.512067 + 0.858946i \(0.328880\pi\)
\(150\) 0 0
\(151\) −4.98493 8.63415i −0.405668 0.702637i 0.588731 0.808329i \(-0.299628\pi\)
−0.994399 + 0.105692i \(0.966294\pi\)
\(152\) 0 0
\(153\) 25.7970 2.08556
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.02111 + 10.4289i 0.480537 + 0.832315i 0.999751 0.0223299i \(-0.00710841\pi\)
−0.519214 + 0.854645i \(0.673775\pi\)
\(158\) 0 0
\(159\) 12.2518 21.2207i 0.971628 1.68291i
\(160\) 0 0
\(161\) −10.2367 + 11.2061i −0.806764 + 0.883167i
\(162\) 0 0
\(163\) 8.36834 14.4944i 0.655459 1.13529i −0.326319 0.945260i \(-0.605808\pi\)
0.981778 0.190029i \(-0.0608582\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.76683 −0.523633 −0.261816 0.965118i \(-0.584321\pi\)
−0.261816 + 0.965118i \(0.584321\pi\)
\(168\) 0 0
\(169\) 18.0121 1.38555
\(170\) 0 0
\(171\) −5.70051 9.87357i −0.435929 0.755050i
\(172\) 0 0
\(173\) −2.34723 + 4.06552i −0.178457 + 0.309096i −0.941352 0.337426i \(-0.890444\pi\)
0.762895 + 0.646522i \(0.223777\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.86834 + 10.1643i −0.441092 + 0.763993i
\(178\) 0 0
\(179\) −5.73669 9.93623i −0.428780 0.742669i 0.567985 0.823039i \(-0.307723\pi\)
−0.996765 + 0.0803699i \(0.974390\pi\)
\(180\) 0 0
\(181\) 0.832162 0.0618541 0.0309271 0.999522i \(-0.490154\pi\)
0.0309271 + 0.999522i \(0.490154\pi\)
\(182\) 0 0
\(183\) −39.3176 −2.90644
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.62263 9.73868i 0.411167 0.712163i
\(188\) 0 0
\(189\) −3.97590 0.874988i −0.289204 0.0636460i
\(190\) 0 0
\(191\) −3.46986 + 6.00998i −0.251070 + 0.434867i −0.963821 0.266551i \(-0.914116\pi\)
0.712750 + 0.701418i \(0.247449\pi\)
\(192\) 0 0
\(193\) −9.83821 17.0403i −0.708169 1.22659i −0.965535 0.260272i \(-0.916188\pi\)
0.257366 0.966314i \(-0.417145\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −16.0422 −1.14296 −0.571481 0.820616i \(-0.693631\pi\)
−0.571481 + 0.820616i \(0.693631\pi\)
\(198\) 0 0
\(199\) 5.33821 + 9.24604i 0.378415 + 0.655435i 0.990832 0.135101i \(-0.0431358\pi\)
−0.612417 + 0.790535i \(0.709802\pi\)
\(200\) 0 0
\(201\) 1.10756 1.91835i 0.0781213 0.135310i
\(202\) 0 0
\(203\) 5.08996 + 1.12016i 0.357245 + 0.0786199i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −10.3231 17.8802i −0.717508 1.24276i
\(208\) 0 0
\(209\) −4.96986 −0.343772
\(210\) 0 0
\(211\) 11.3658 0.782455 0.391227 0.920294i \(-0.372051\pi\)
0.391227 + 0.920294i \(0.372051\pi\)
\(212\) 0 0
\(213\) −15.5900 27.0026i −1.06821 1.85019i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.775398 2.44605i −0.0526375 0.166049i
\(218\) 0 0
\(219\) 5.13770 8.89876i 0.347174 0.601322i
\(220\) 0 0
\(221\) −19.9583 34.5688i −1.34254 2.32535i
\(222\) 0 0
\(223\) −6.04222 −0.404617 −0.202309 0.979322i \(-0.564844\pi\)
−0.202309 + 0.979322i \(0.564844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −10.8206 18.7418i −0.718189 1.24394i −0.961717 0.274046i \(-0.911638\pi\)
0.243528 0.969894i \(-0.421695\pi\)
\(228\) 0 0
\(229\) 2.71558 4.70351i 0.179450 0.310817i −0.762242 0.647292i \(-0.775901\pi\)
0.941692 + 0.336475i \(0.109235\pi\)
\(230\) 0 0
\(231\) −7.19148 + 7.87253i −0.473165 + 0.517975i
\(232\) 0 0
\(233\) 3.46986 6.00998i 0.227318 0.393727i −0.729694 0.683774i \(-0.760338\pi\)
0.957012 + 0.290047i \(0.0936709\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 33.0724 2.14828
\(238\) 0 0
\(239\) 1.69446 0.109606 0.0548028 0.998497i \(-0.482547\pi\)
0.0548028 + 0.998497i \(0.482547\pi\)
\(240\) 0 0
\(241\) 7.46733 + 12.9338i 0.481013 + 0.833139i 0.999763 0.0217871i \(-0.00693559\pi\)
−0.518749 + 0.854926i \(0.673602\pi\)
\(242\) 0 0
\(243\) −11.0990 + 19.2240i −0.712000 + 1.23322i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.82061 + 15.2777i −0.561242 + 0.972099i
\(248\) 0 0
\(249\) 21.9734 + 38.0590i 1.39251 + 2.41189i
\(250\) 0 0
\(251\) 8.90958 0.562368 0.281184 0.959654i \(-0.409273\pi\)
0.281184 + 0.959654i \(0.409273\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.83216 + 8.36955i −0.301422 + 0.522078i −0.976458 0.215706i \(-0.930795\pi\)
0.675036 + 0.737785i \(0.264128\pi\)
\(258\) 0 0
\(259\) 11.9673 13.1007i 0.743614 0.814036i
\(260\) 0 0
\(261\) −3.54475 + 6.13969i −0.219415 + 0.380038i
\(262\) 0 0
\(263\) 3.05125 + 5.28492i 0.188148 + 0.325882i 0.944633 0.328129i \(-0.106418\pi\)
−0.756485 + 0.654011i \(0.773085\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 14.3830 0.880223
\(268\) 0 0
\(269\) −11.2668 19.5147i −0.686951 1.18983i −0.972820 0.231565i \(-0.925616\pi\)
0.285869 0.958269i \(-0.407718\pi\)
\(270\) 0 0
\(271\) −2.23064 + 3.86359i −0.135502 + 0.234696i −0.925789 0.378040i \(-0.876598\pi\)
0.790287 + 0.612737i \(0.209931\pi\)
\(272\) 0 0
\(273\) 11.4372 + 36.0795i 0.692210 + 2.18363i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −3.25429 5.63659i −0.195531 0.338670i 0.751543 0.659684i \(-0.229310\pi\)
−0.947074 + 0.321014i \(0.895976\pi\)
\(278\) 0 0
\(279\) 3.49052 0.208972
\(280\) 0 0
\(281\) −11.1980 −0.668015 −0.334008 0.942570i \(-0.608401\pi\)
−0.334008 + 0.942570i \(0.608401\pi\)
\(282\) 0 0
\(283\) 3.82314 + 6.62187i 0.227262 + 0.393629i 0.956996 0.290102i \(-0.0936893\pi\)
−0.729734 + 0.683731i \(0.760356\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.9307 5.04642i −1.35356 0.297881i
\(288\) 0 0
\(289\) −17.1890 + 29.7721i −1.01111 + 1.75130i
\(290\) 0 0
\(291\) 0.299494 + 0.518739i 0.0175567 + 0.0304090i
\(292\) 0 0
\(293\) 6.12561 0.357862 0.178931 0.983862i \(-0.442736\pi\)
0.178931 + 0.983862i \(0.442736\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.20700 2.09059i −0.0700374 0.121308i
\(298\) 0 0
\(299\) −15.9734 + 27.6667i −0.923764 + 1.60001i
\(300\) 0 0
\(301\) −11.8834 2.61521i −0.684949 0.150738i
\(302\) 0 0
\(303\) 16.0598 27.8164i 0.922613 1.59801i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 26.4080 1.50719 0.753593 0.657341i \(-0.228319\pi\)
0.753593 + 0.657341i \(0.228319\pi\)
\(308\) 0 0
\(309\) −8.65927 −0.492608
\(310\) 0 0
\(311\) 9.67641 + 16.7600i 0.548699 + 0.950374i 0.998364 + 0.0571771i \(0.0182100\pi\)
−0.449665 + 0.893197i \(0.648457\pi\)
\(312\) 0 0
\(313\) −4.35327 + 7.54009i −0.246062 + 0.426191i −0.962430 0.271531i \(-0.912470\pi\)
0.716368 + 0.697723i \(0.245803\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.63770 + 13.2289i −0.428976 + 0.743008i −0.996782 0.0801539i \(-0.974459\pi\)
0.567807 + 0.823162i \(0.307792\pi\)
\(318\) 0 0
\(319\) 1.54521 + 2.67638i 0.0865150 + 0.149848i
\(320\) 0 0
\(321\) 45.5629 2.54307
\(322\) 0 0
\(323\) 22.7065 1.26343
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 7.58392 13.1357i 0.419392 0.726408i
\(328\) 0 0
\(329\) −0.715575 + 0.783342i −0.0394509 + 0.0431870i
\(330\) 0 0
\(331\) −8.37439 + 14.5049i −0.460298 + 0.797259i −0.998976 0.0452526i \(-0.985591\pi\)
0.538678 + 0.842512i \(0.318924\pi\)
\(332\) 0 0
\(333\) 12.0684 + 20.9031i 0.661344 + 1.14548i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −31.2453 −1.70204 −0.851019 0.525135i \(-0.824015\pi\)
−0.851019 + 0.525135i \(0.824015\pi\)
\(338\) 0 0
\(339\) 20.0900 + 34.7968i 1.09114 + 1.88990i
\(340\) 0 0
\(341\) 0.760783 1.31772i 0.0411987 0.0713583i
\(342\) 0 0
\(343\) 14.7453 + 11.2061i 0.796169 + 0.605074i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.05125 10.4811i −0.324848 0.562654i 0.656633 0.754210i \(-0.271980\pi\)
−0.981482 + 0.191556i \(0.938647\pi\)
\(348\) 0 0
\(349\) −3.87439 −0.207391 −0.103696 0.994609i \(-0.533067\pi\)
−0.103696 + 0.994609i \(0.533067\pi\)
\(350\) 0 0
\(351\) −8.56885 −0.457371
\(352\) 0 0
\(353\) 1.28190 + 2.22031i 0.0682284 + 0.118175i 0.898122 0.439747i \(-0.144932\pi\)
−0.829893 + 0.557922i \(0.811599\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 32.8568 35.9684i 1.73897 1.90365i
\(358\) 0 0
\(359\) −10.4196 + 18.0473i −0.549925 + 0.952498i 0.448354 + 0.893856i \(0.352010\pi\)
−0.998279 + 0.0586422i \(0.981323\pi\)
\(360\) 0 0
\(361\) 4.48240 + 7.76375i 0.235916 + 0.408618i
\(362\) 0 0
\(363\) 21.9347 1.15127
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7.91608 + 13.7111i 0.413216 + 0.715711i 0.995239 0.0974609i \(-0.0310721\pi\)
−0.582023 + 0.813172i \(0.697739\pi\)
\(368\) 0 0
\(369\) 15.9694 27.6598i 0.831334 1.43991i
\(370\) 0 0
\(371\) −7.62614 24.0572i −0.395930 1.24899i
\(372\) 0 0
\(373\) −11.2518 + 19.4886i −0.582594 + 1.00908i 0.412577 + 0.910923i \(0.364629\pi\)
−0.995171 + 0.0981594i \(0.968704\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.9699 0.564977
\(378\) 0 0
\(379\) −7.36581 −0.378356 −0.189178 0.981943i \(-0.560582\pi\)
−0.189178 + 0.981943i \(0.560582\pi\)
\(380\) 0 0
\(381\) 16.5362 + 28.6415i 0.847174 + 1.46735i
\(382\) 0 0
\(383\) −16.8266 + 29.1446i −0.859802 + 1.48922i 0.0123162 + 0.999924i \(0.496080\pi\)
−0.872118 + 0.489296i \(0.837254\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.27585 14.3342i 0.420685 0.728648i
\(388\) 0 0
\(389\) −8.74273 15.1429i −0.443274 0.767773i 0.554656 0.832080i \(-0.312850\pi\)
−0.997930 + 0.0643065i \(0.979516\pi\)
\(390\) 0 0
\(391\) 41.1196 2.07951
\(392\) 0 0
\(393\) 0.585994 0.0295595
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3.79949 6.58092i 0.190691 0.330287i −0.754788 0.655968i \(-0.772260\pi\)
0.945479 + 0.325682i \(0.105594\pi\)
\(398\) 0 0
\(399\) −21.0272 4.62750i −1.05267 0.231665i
\(400\) 0 0
\(401\) −5.42212 + 9.39139i −0.270768 + 0.468984i −0.969059 0.246830i \(-0.920611\pi\)
0.698291 + 0.715814i \(0.253944\pi\)
\(402\) 0 0
\(403\) −2.70051 4.67741i −0.134522 0.232999i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.5216 0.521535
\(408\) 0 0
\(409\) 8.43466 + 14.6093i 0.417067 + 0.722382i 0.995643 0.0932469i \(-0.0297246\pi\)
−0.578576 + 0.815629i \(0.696391\pi\)
\(410\) 0 0
\(411\) −12.4286 + 21.5270i −0.613059 + 1.06185i
\(412\) 0 0
\(413\) 3.65277 + 11.5229i 0.179741 + 0.567006i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −15.8895 27.5213i −0.778110 1.34773i
\(418\) 0 0
\(419\) −4.03014 −0.196885 −0.0984426 0.995143i \(-0.531386\pi\)
−0.0984426 + 0.995143i \(0.531386\pi\)
\(420\) 0 0
\(421\) 25.1196 1.22426 0.612128 0.790758i \(-0.290314\pi\)
0.612128 + 0.790758i \(0.290314\pi\)
\(422\) 0 0
\(423\) −0.721618 1.24988i −0.0350863 0.0607712i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −27.3116 + 29.8981i −1.32170 + 1.44687i
\(428\) 0 0
\(429\) −11.2216 + 19.4364i −0.541785 + 0.938399i
\(430\) 0 0
\(431\) −15.1201 26.1888i −0.728310 1.26147i −0.957597 0.288111i \(-0.906973\pi\)
0.229288 0.973359i \(-0.426360\pi\)
\(432\) 0 0
\(433\) −22.9769 −1.10420 −0.552099 0.833778i \(-0.686173\pi\)
−0.552099 + 0.833778i \(0.686173\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.08645 15.7382i −0.434664 0.752860i
\(438\) 0 0
\(439\) −5.97590 + 10.3506i −0.285214 + 0.494006i −0.972661 0.232229i \(-0.925398\pi\)
0.687447 + 0.726235i \(0.258731\pi\)
\(440\) 0 0
\(441\) −20.5920 + 14.5138i −0.980573 + 0.691135i
\(442\) 0 0
\(443\) 7.05378 12.2175i 0.335135 0.580471i −0.648376 0.761321i \(-0.724551\pi\)
0.983511 + 0.180849i \(0.0578847\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −30.5939 −1.44704
\(448\) 0 0
\(449\) 37.9468 1.79082 0.895409 0.445245i \(-0.146883\pi\)
0.895409 + 0.445245i \(0.146883\pi\)
\(450\) 0 0
\(451\) −6.96129 12.0573i −0.327794 0.567756i
\(452\) 0 0
\(453\) 12.8055 22.1798i 0.601657 1.04210i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.27287 16.0611i 0.433767 0.751306i −0.563428 0.826165i \(-0.690518\pi\)
0.997194 + 0.0748598i \(0.0238509\pi\)
\(458\) 0 0
\(459\) 5.51462 + 9.55159i 0.257400 + 0.445830i
\(460\) 0 0
\(461\) −23.2453 −1.08264 −0.541320 0.840817i \(-0.682075\pi\)
−0.541320 + 0.840817i \(0.682075\pi\)
\(462\) 0 0
\(463\) 7.59393 0.352920 0.176460 0.984308i \(-0.443535\pi\)
0.176460 + 0.984308i \(0.443535\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.0839 + 24.3941i −0.651726 + 1.12882i 0.330978 + 0.943639i \(0.392621\pi\)
−0.982704 + 0.185184i \(0.940712\pi\)
\(468\) 0 0
\(469\) −0.689404 2.17478i −0.0318337 0.100422i
\(470\) 0 0
\(471\) −15.4673 + 26.7902i −0.712697 + 1.23443i
\(472\) 0 0
\(473\) −3.60756 6.24848i −0.165876 0.287305i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 34.3297 1.57185
\(478\) 0 0
\(479\) 17.0900 + 29.6007i 0.780860 + 1.35249i 0.931441 + 0.363892i \(0.118552\pi\)
−0.150581 + 0.988598i \(0.548114\pi\)
\(480\) 0 0
\(481\) 18.6739 32.3441i 0.851456 1.47476i
\(482\) 0 0
\(483\) −38.0784 8.38002i −1.73263 0.381304i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5.75176 + 9.96234i 0.260637 + 0.451436i 0.966411 0.257000i \(-0.0827341\pi\)
−0.705774 + 0.708437i \(0.749401\pi\)
\(488\) 0 0
\(489\) 42.9940 1.94426
\(490\) 0 0
\(491\) −25.5337 −1.15232 −0.576159 0.817338i \(-0.695449\pi\)
−0.576159 + 0.817338i \(0.695449\pi\)
\(492\) 0 0
\(493\) −7.05982 12.2280i −0.317958 0.550720i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −31.3628 6.90210i −1.40682 0.309602i
\(498\) 0 0
\(499\) 5.69798 9.86919i 0.255076 0.441805i −0.709840 0.704363i \(-0.751233\pi\)
0.964916 + 0.262558i \(0.0845660\pi\)
\(500\) 0 0
\(501\) −8.69148 15.0541i −0.388307 0.672567i
\(502\) 0 0
\(503\) −2.49649 −0.111313 −0.0556564 0.998450i \(-0.517725\pi\)
−0.0556564 + 0.998450i \(0.517725\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.1352 + 40.0713i 1.02747 + 1.77963i
\(508\) 0 0
\(509\) −5.77188 + 9.99720i −0.255834 + 0.443118i −0.965122 0.261801i \(-0.915683\pi\)
0.709287 + 0.704919i \(0.249017\pi\)
\(510\) 0 0
\(511\) −3.19798 10.0883i −0.141470 0.446278i
\(512\) 0 0
\(513\) 2.43719 4.22134i 0.107605 0.186377i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −0.629127 −0.0276690
\(518\) 0 0
\(519\) −12.0594 −0.529348
\(520\) 0 0
\(521\) −11.8744 20.5670i −0.520226 0.901058i −0.999723 0.0235150i \(-0.992514\pi\)
0.479497 0.877543i \(-0.340819\pi\)
\(522\) 0 0
\(523\) −8.06885 + 13.9757i −0.352826 + 0.611113i −0.986743 0.162288i \(-0.948113\pi\)
0.633917 + 0.773401i \(0.281446\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.47590 + 6.02044i −0.151413 + 0.262255i
\(528\) 0 0
\(529\) −4.95479 8.58195i −0.215426 0.373128i
\(530\) 0 0
\(531\) −16.4432 −0.713576
\(532\) 0 0
\(533\) −49.4201 −2.14062
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 14.7367 25.5247i 0.635935 1.10147i
\(538\) 0 0
\(539\) 0.990974 + 10.9371i 0.0426843 + 0.471096i
\(540\) 0 0
\(541\) 0.769355 1.33256i 0.0330772 0.0572913i −0.849013 0.528372i \(-0.822803\pi\)
0.882090 + 0.471081i \(0.156136\pi\)
\(542\) 0 0
\(543\) 1.06885 + 1.85130i 0.0458687 + 0.0794470i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −14.3779 −0.614755 −0.307377 0.951588i \(-0.599451\pi\)
−0.307377 + 0.951588i \(0.599451\pi\)
\(548\) 0 0
\(549\) −27.5422 47.7045i −1.17547 2.03598i
\(550\) 0 0
\(551\) −3.12010 + 5.40417i −0.132921 + 0.230226i
\(552\) 0 0
\(553\) 22.9734 25.1490i 0.976927 1.06944i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.46733 + 14.6658i 0.358772 + 0.621412i 0.987756 0.156007i \(-0.0498621\pi\)
−0.628984 + 0.777419i \(0.716529\pi\)
\(558\) 0 0
\(559\) −25.6111 −1.08323
\(560\) 0 0
\(561\) 28.8874 1.21963
\(562\) 0 0
\(563\) −0.332162 0.575322i −0.0139990 0.0242469i 0.858941 0.512074i \(-0.171123\pi\)
−0.872940 + 0.487828i \(0.837789\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 5.47194 + 17.2616i 0.229800 + 0.724921i
\(568\) 0 0
\(569\) 20.5186 35.5392i 0.860184 1.48988i −0.0115674 0.999933i \(-0.503682\pi\)
0.871751 0.489949i \(-0.162985\pi\)
\(570\) 0 0
\(571\) 14.3146 + 24.7936i 0.599046 + 1.03758i 0.992962 + 0.118432i \(0.0377866\pi\)
−0.393916 + 0.919146i \(0.628880\pi\)
\(572\) 0 0
\(573\) −17.8271 −0.744738
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −15.7302 27.2455i −0.654856 1.13424i −0.981930 0.189246i \(-0.939396\pi\)
0.327073 0.944999i \(-0.393938\pi\)
\(578\) 0 0
\(579\) 25.2729 43.7739i 1.05030 1.81918i
\(580\) 0 0
\(581\) 44.2046 + 9.72821i 1.83391 + 0.403594i
\(582\) 0 0
\(583\) 7.48240 12.9599i 0.309889 0.536744i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.53871 −0.393705 −0.196852 0.980433i \(-0.563072\pi\)
−0.196852 + 0.980433i \(0.563072\pi\)
\(588\) 0 0
\(589\) 3.07236 0.126595
\(590\) 0 0
\(591\) −20.6050 35.6890i −0.847578 1.46805i
\(592\) 0 0
\(593\) −4.96986 + 8.60805i −0.204088 + 0.353490i −0.949842 0.312731i \(-0.898756\pi\)
0.745754 + 0.666221i \(0.232089\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −13.7130 + 23.7517i −0.561238 + 0.972092i
\(598\) 0 0
\(599\) −4.70655 8.15198i −0.192304 0.333081i 0.753709 0.657208i \(-0.228263\pi\)
−0.946014 + 0.324127i \(0.894929\pi\)
\(600\) 0 0
\(601\) −3.00506 −0.122579 −0.0612894 0.998120i \(-0.519521\pi\)
−0.0612894 + 0.998120i \(0.519521\pi\)
\(602\) 0 0
\(603\) 3.10341 0.126381
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 9.41608 16.3091i 0.382187 0.661967i −0.609188 0.793026i \(-0.708504\pi\)
0.991375 + 0.131059i \(0.0418377\pi\)
\(608\) 0 0
\(609\) 4.04566 + 12.7623i 0.163939 + 0.517156i
\(610\) 0 0
\(611\) −1.11659 + 1.93399i −0.0451723 + 0.0782407i
\(612\) 0 0
\(613\) −7.91959 13.7171i −0.319869 0.554030i 0.660591 0.750746i \(-0.270306\pi\)
−0.980461 + 0.196716i \(0.936972\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.778912 −0.0313578 −0.0156789 0.999877i \(-0.504991\pi\)
−0.0156789 + 0.999877i \(0.504991\pi\)
\(618\) 0 0
\(619\) −4.97338 8.61414i −0.199897 0.346231i 0.748598 0.663024i \(-0.230727\pi\)
−0.948495 + 0.316793i \(0.897394\pi\)
\(620\) 0 0
\(621\) 4.41355 7.64450i 0.177110 0.306763i
\(622\) 0 0
\(623\) 9.99097 10.9371i 0.400280 0.438187i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −6.38341 11.0564i −0.254929 0.441550i
\(628\) 0 0
\(629\) −48.0715 −1.91673
\(630\) 0 0
\(631\) −12.5638 −0.500157 −0.250078 0.968226i \(-0.580456\pi\)
−0.250078 + 0.968226i \(0.580456\pi\)
\(632\) 0 0
\(633\) 14.5985 + 25.2854i 0.580240 + 1.00500i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 35.3804 + 16.3651i 1.40182 + 0.648410i
\(638\) 0 0
\(639\) 21.8417 37.8310i 0.864045 1.49657i
\(640\) 0 0
\(641\) 5.76033 + 9.97718i 0.227519 + 0.394075i 0.957072 0.289849i \(-0.0936052\pi\)
−0.729553 + 0.683924i \(0.760272\pi\)
\(642\) 0 0
\(643\) −9.74175 −0.384177 −0.192088 0.981378i \(-0.561526\pi\)
−0.192088 + 0.981378i \(0.561526\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.8769 + 22.3035i 0.506244 + 0.876840i 0.999974 + 0.00722479i \(0.00229974\pi\)
−0.493730 + 0.869615i \(0.664367\pi\)
\(648\) 0 0
\(649\) −3.58392 + 6.20753i −0.140681 + 0.243667i
\(650\) 0 0
\(651\) 4.44577 4.86679i 0.174243 0.190745i
\(652\) 0 0
\(653\) 7.59646 13.1575i 0.297272 0.514891i −0.678239 0.734842i \(-0.737256\pi\)
0.975511 + 0.219951i \(0.0705897\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.3960 0.561640
\(658\) 0 0
\(659\) −14.6894 −0.572218 −0.286109 0.958197i \(-0.592362\pi\)
−0.286109 + 0.958197i \(0.592362\pi\)
\(660\) 0 0
\(661\) −2.16784 3.75481i −0.0843191 0.146045i 0.820782 0.571242i \(-0.193538\pi\)
−0.905101 + 0.425197i \(0.860205\pi\)
\(662\) 0 0
\(663\) 51.2699 88.8020i 1.99116 3.44879i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.65024 + 9.78650i −0.218778 + 0.378935i
\(668\) 0 0
\(669\) −7.76078 13.4421i −0.300049 0.519700i
\(670\) 0 0
\(671\) −24.0121 −0.926976
\(672\) 0 0
\(673\) 34.1971 1.31820 0.659100 0.752055i \(-0.270937\pi\)
0.659100 + 0.752055i \(0.270937\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.04521 + 15.6668i −0.347636 + 0.602122i −0.985829 0.167754i \(-0.946349\pi\)
0.638193 + 0.769876i \(0.279682\pi\)
\(678\) 0 0
\(679\) 0.602502 + 0.132594i 0.0231219 + 0.00508850i
\(680\) 0 0
\(681\) 27.7965 48.1450i 1.06516 1.84492i
\(682\) 0 0
\(683\) 12.0628 + 20.8934i 0.461570 + 0.799464i 0.999039 0.0438200i \(-0.0139528\pi\)
−0.537469 + 0.843284i \(0.680619\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 13.9518 0.532295
\(688\) 0 0
\(689\) −26.5598 46.0030i −1.01185 1.75257i
\(690\) 0 0
\(691\) −8.72415 + 15.1107i −0.331882 + 0.574837i −0.982881 0.184242i \(-0.941017\pi\)
0.650999 + 0.759079i \(0.274350\pi\)
\(692\) 0 0
\(693\) −14.5895 3.21075i −0.554210 0.121966i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 31.8051 + 55.0880i 1.20470 + 2.08661i
\(698\) 0 0
\(699\) 17.8271 0.674283
\(700\) 0 0
\(701\) 20.7015 0.781885 0.390942 0.920415i \(-0.372149\pi\)
0.390942 + 0.920415i \(0.372149\pi\)
\(702\) 0 0
\(703\) 10.6226 + 18.3989i 0.400640 + 0.693929i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.99649 31.5347i −0.375957 1.18598i
\(708\) 0 0
\(709\) −3.54774 + 6.14486i −0.133238 + 0.230775i −0.924923 0.380154i \(-0.875871\pi\)
0.791685 + 0.610930i \(0.209204\pi\)
\(710\) 0 0
\(711\) 23.1674 + 40.1271i 0.868845 + 1.50488i
\(712\) 0 0
\(713\) 5.56379 0.208366
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.17641 + 3.76965i 0.0812795 + 0.140780i
\(718\) 0 0
\(719\) −26.2216 + 45.4172i −0.977901 + 1.69377i −0.307893 + 0.951421i \(0.599624\pi\)
−0.670008 + 0.742354i \(0.733709\pi\)
\(720\) 0 0
\(721\) −6.01507 + 6.58471i −0.224013 + 0.245227i
\(722\) 0 0
\(723\) −19.1825 + 33.2250i −0.713403 + 1.23565i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −29.9045 −1.10910 −0.554549 0.832151i \(-0.687109\pi\)
−0.554549 + 0.832151i \(0.687109\pi\)
\(728\) 0 0
\(729\) −36.4905 −1.35150
\(730\) 0 0
\(731\) 16.4824 + 28.5484i 0.609624 + 1.05590i
\(732\) 0 0
\(733\) −2.79047 + 4.83323i −0.103068 + 0.178519i −0.912947 0.408077i \(-0.866199\pi\)
0.809879 + 0.586597i \(0.199533\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.676410 1.17158i 0.0249159 0.0431556i
\(738\) 0 0
\(739\) −20.3744 35.2895i −0.749484 1.29814i −0.948070 0.318061i \(-0.896968\pi\)
0.198586 0.980083i \(-0.436365\pi\)
\(740\) 0 0
\(741\) −45.3176 −1.66478
\(742\) 0 0
\(743\) 50.5327 1.85387 0.926933 0.375226i \(-0.122435\pi\)
0.926933 + 0.375226i \(0.122435\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −30.7850 + 53.3211i −1.12636 + 1.95092i
\(748\) 0 0
\(749\) 31.6498 34.6471i 1.15646 1.26598i
\(750\) 0 0
\(751\) 15.3568 26.5987i 0.560377 0.970602i −0.437086 0.899420i \(-0.643990\pi\)
0.997463 0.0711821i \(-0.0226771\pi\)
\(752\) 0 0
\(753\) 11.4437 + 19.8211i 0.417031 + 0.722319i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −20.7116 −0.752776 −0.376388 0.926462i \(-0.622834\pi\)
−0.376388 + 0.926462i \(0.622834\pi\)
\(758\) 0 0
\(759\) −11.5598 20.0222i −0.419595 0.726760i
\(760\) 0 0
\(761\) 17.1764 29.7504i 0.622644 1.07845i −0.366347 0.930478i \(-0.619392\pi\)
0.988991 0.147973i \(-0.0472750\pi\)
\(762\) 0 0
\(763\) −4.72063 14.8916i −0.170898 0.539112i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.7216 + 22.0345i 0.459351 + 0.795619i
\(768\) 0 0
\(769\) 46.8392 1.68906 0.844532 0.535505i \(-0.179879\pi\)
0.844532 + 0.535505i \(0.179879\pi\)
\(770\) 0 0
\(771\) −24.8262 −0.894094
\(772\) 0 0
\(773\) −16.6653 28.8652i −0.599409 1.03821i −0.992908 0.118883i \(-0.962069\pi\)
0.393499 0.919325i \(-0.371265\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 44.5161 + 9.79677i 1.59700 + 0.351457i
\(778\) 0 0
\(779\) 14.0563 24.3462i 0.503620 0.872295i
\(780\) 0 0
\(781\) −9.52111 16.4911i −0.340692 0.590096i
\(782\) 0 0
\(783\) −3.03105 −0.108321
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.20402 7.28158i −0.149857 0.259560i 0.781317 0.624134i \(-0.214548\pi\)
−0.931175 + 0.364574i \(0.881215\pi\)
\(788\) 0 0
\(789\) −7.83821 + 13.5762i −0.279047 + 0.483324i
\(790\) 0 0
\(791\) 40.4156 + 8.89438i 1.43701 + 0.316248i
\(792\) 0 0
\(793\) −42.6171 + 73.8150i −1.51338 + 2.62125i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.2935 0.577144 0.288572 0.957458i \(-0.406820\pi\)
0.288572 + 0.957458i \(0.406820\pi\)
\(798\) 0 0
\(799\) 2.87439 0.101688
\(800\) 0