Properties

Label 260.2.x.a.101.4
Level $260$
Weight $2$
Character 260.101
Analytic conductor $2.076$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.4
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 260.101
Dual form 260.2.x.a.121.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16612 + 2.01978i) q^{3} +1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +(-1.21969 + 2.11256i) q^{9} +O(q^{10})\) \(q+(1.16612 + 2.01978i) q^{3} +1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +(-1.21969 + 2.11256i) q^{9} +(1.50000 - 0.866025i) q^{11} +(-0.619491 + 3.55193i) q^{13} +(-2.01978 + 1.16612i) q^{15} +(0.346241 - 0.599706i) q^{17} +(-4.65213 - 2.68591i) q^{19} +0.932442i q^{21} +(-0.0535636 - 0.0927749i) q^{23} -1.00000 q^{25} +1.30752 q^{27} +(2.45174 + 4.24653i) q^{29} -7.86488i q^{31} +(3.49837 + 2.01978i) q^{33} +(-0.199902 + 0.346241i) q^{35} +(1.96128 - 1.13234i) q^{37} +(-7.89654 + 2.89075i) q^{39} +(6.69615 - 3.86603i) q^{41} +(3.00530 - 5.20533i) q^{43} +(-2.11256 - 1.21969i) q^{45} +3.46410i q^{47} +(-3.42008 - 5.92375i) q^{49} +1.61504 q^{51} +11.7189 q^{53} +(0.866025 + 1.50000i) q^{55} -12.5284i q^{57} +(-6.30059 - 3.63765i) q^{59} +(-4.34461 + 7.52509i) q^{61} +(-0.844610 + 0.487636i) q^{63} +(-3.55193 - 0.619491i) q^{65} +(-1.15009 + 0.664004i) q^{67} +(0.124924 - 0.216374i) q^{69} +(-3.35847 - 1.93902i) q^{71} -10.2251i q^{73} +(-1.16612 - 2.01978i) q^{75} +0.692481 q^{77} -13.1533 q^{79} +(5.18379 + 8.97859i) q^{81} -14.0791i q^{83} +(0.599706 + 0.346241i) q^{85} +(-5.71806 + 9.90396i) q^{87} +(0.300587 - 0.173544i) q^{89} +(-0.924532 + 1.10599i) q^{91} +(15.8854 - 9.17142i) q^{93} +(2.68591 - 4.65213i) q^{95} +(-7.66436 - 4.42502i) q^{97} +4.22512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 12 q^{11} - 8 q^{13} - 6 q^{15} + 6 q^{17} - 6 q^{23} - 8 q^{25} + 4 q^{27} - 6 q^{33} - 6 q^{35} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 10 q^{43} - 4 q^{49} + 24 q^{53} - 24 q^{59} - 4 q^{61} + 24 q^{63} - 54 q^{67} - 24 q^{69} - 36 q^{71} + 2 q^{75} + 12 q^{77} - 16 q^{79} + 8 q^{81} + 18 q^{85} - 6 q^{87} - 24 q^{89} + 24 q^{93} - 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(3\) 1.16612 + 2.01978i 0.673262 + 1.16612i 0.976974 + 0.213359i \(0.0684405\pi\)
−0.303712 + 0.952764i \(0.598226\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.346241 + 0.199902i 0.130867 + 0.0755559i 0.564004 0.825772i \(-0.309260\pi\)
−0.433137 + 0.901328i \(0.642594\pi\)
\(8\) 0 0
\(9\) −1.21969 + 2.11256i −0.406562 + 0.704187i
\(10\) 0 0
\(11\) 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i \(-0.582576\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) 0 0
\(13\) −0.619491 + 3.55193i −0.171816 + 0.985129i
\(14\) 0 0
\(15\) −2.01978 + 1.16612i −0.521506 + 0.301092i
\(16\) 0 0
\(17\) 0.346241 0.599706i 0.0839757 0.145450i −0.820979 0.570959i \(-0.806572\pi\)
0.904954 + 0.425509i \(0.139905\pi\)
\(18\) 0 0
\(19\) −4.65213 2.68591i −1.06727 0.616190i −0.139837 0.990175i \(-0.544658\pi\)
−0.927435 + 0.373985i \(0.877991\pi\)
\(20\) 0 0
\(21\) 0.932442i 0.203476i
\(22\) 0 0
\(23\) −0.0535636 0.0927749i −0.0111688 0.0193449i 0.860387 0.509641i \(-0.170222\pi\)
−0.871556 + 0.490296i \(0.836889\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 1.30752 0.251632
\(28\) 0 0
\(29\) 2.45174 + 4.24653i 0.455276 + 0.788562i 0.998704 0.0508943i \(-0.0162072\pi\)
−0.543428 + 0.839456i \(0.682874\pi\)
\(30\) 0 0
\(31\) 7.86488i 1.41257i −0.707925 0.706287i \(-0.750369\pi\)
0.707925 0.706287i \(-0.249631\pi\)
\(32\) 0 0
\(33\) 3.49837 + 2.01978i 0.608988 + 0.351599i
\(34\) 0 0
\(35\) −0.199902 + 0.346241i −0.0337896 + 0.0585254i
\(36\) 0 0
\(37\) 1.96128 1.13234i 0.322432 0.186156i −0.330044 0.943966i \(-0.607064\pi\)
0.652476 + 0.757809i \(0.273730\pi\)
\(38\) 0 0
\(39\) −7.89654 + 2.89075i −1.26446 + 0.462891i
\(40\) 0 0
\(41\) 6.69615 3.86603i 1.04576 0.603772i 0.124303 0.992244i \(-0.460331\pi\)
0.921460 + 0.388473i \(0.126997\pi\)
\(42\) 0 0
\(43\) 3.00530 5.20533i 0.458304 0.793806i −0.540567 0.841301i \(-0.681790\pi\)
0.998871 + 0.0474947i \(0.0151237\pi\)
\(44\) 0 0
\(45\) −2.11256 1.21969i −0.314922 0.181820i
\(46\) 0 0
\(47\) 3.46410i 0.505291i 0.967559 + 0.252646i \(0.0813007\pi\)
−0.967559 + 0.252646i \(0.918699\pi\)
\(48\) 0 0
\(49\) −3.42008 5.92375i −0.488583 0.846250i
\(50\) 0 0
\(51\) 1.61504 0.226150
\(52\) 0 0
\(53\) 11.7189 1.60972 0.804858 0.593468i \(-0.202242\pi\)
0.804858 + 0.593468i \(0.202242\pi\)
\(54\) 0 0
\(55\) 0.866025 + 1.50000i 0.116775 + 0.202260i
\(56\) 0 0
\(57\) 12.5284i 1.65943i
\(58\) 0 0
\(59\) −6.30059 3.63765i −0.820267 0.473581i 0.0302418 0.999543i \(-0.490372\pi\)
−0.850508 + 0.525961i \(0.823706\pi\)
\(60\) 0 0
\(61\) −4.34461 + 7.52509i −0.556270 + 0.963489i 0.441533 + 0.897245i \(0.354435\pi\)
−0.997803 + 0.0662436i \(0.978899\pi\)
\(62\) 0 0
\(63\) −0.844610 + 0.487636i −0.106411 + 0.0614364i
\(64\) 0 0
\(65\) −3.55193 0.619491i −0.440563 0.0768384i
\(66\) 0 0
\(67\) −1.15009 + 0.664004i −0.140506 + 0.0811210i −0.568605 0.822611i \(-0.692517\pi\)
0.428099 + 0.903732i \(0.359183\pi\)
\(68\) 0 0
\(69\) 0.124924 0.216374i 0.0150390 0.0260484i
\(70\) 0 0
\(71\) −3.35847 1.93902i −0.398577 0.230119i 0.287293 0.957843i \(-0.407245\pi\)
−0.685870 + 0.727724i \(0.740578\pi\)
\(72\) 0 0
\(73\) 10.2251i 1.19676i −0.801213 0.598380i \(-0.795811\pi\)
0.801213 0.598380i \(-0.204189\pi\)
\(74\) 0 0
\(75\) −1.16612 2.01978i −0.134652 0.233225i
\(76\) 0 0
\(77\) 0.692481 0.0789156
\(78\) 0 0
\(79\) −13.1533 −1.47986 −0.739932 0.672681i \(-0.765142\pi\)
−0.739932 + 0.672681i \(0.765142\pi\)
\(80\) 0 0
\(81\) 5.18379 + 8.97859i 0.575976 + 0.997621i
\(82\) 0 0
\(83\) 14.0791i 1.54539i −0.634780 0.772693i \(-0.718909\pi\)
0.634780 0.772693i \(-0.281091\pi\)
\(84\) 0 0
\(85\) 0.599706 + 0.346241i 0.0650473 + 0.0375551i
\(86\) 0 0
\(87\) −5.71806 + 9.90396i −0.613040 + 1.06182i
\(88\) 0 0
\(89\) 0.300587 0.173544i 0.0318622 0.0183956i −0.483984 0.875077i \(-0.660811\pi\)
0.515846 + 0.856681i \(0.327477\pi\)
\(90\) 0 0
\(91\) −0.924532 + 1.10599i −0.0969173 + 0.115939i
\(92\) 0 0
\(93\) 15.8854 9.17142i 1.64724 0.951032i
\(94\) 0 0
\(95\) 2.68591 4.65213i 0.275568 0.477298i
\(96\) 0 0
\(97\) −7.66436 4.42502i −0.778198 0.449293i 0.0575932 0.998340i \(-0.481657\pi\)
−0.835791 + 0.549047i \(0.814991\pi\)
\(98\) 0 0
\(99\) 4.22512i 0.424640i
\(100\) 0 0
\(101\) 2.05193 + 3.55405i 0.204175 + 0.353641i 0.949870 0.312646i \(-0.101216\pi\)
−0.745695 + 0.666288i \(0.767882\pi\)
\(102\) 0 0
\(103\) −11.2325 −1.10677 −0.553384 0.832926i \(-0.686664\pi\)
−0.553384 + 0.832926i \(0.686664\pi\)
\(104\) 0 0
\(105\) −0.932442 −0.0909970
\(106\) 0 0
\(107\) 8.80165 + 15.2449i 0.850888 + 1.47378i 0.880408 + 0.474216i \(0.157269\pi\)
−0.0295208 + 0.999564i \(0.509398\pi\)
\(108\) 0 0
\(109\) 15.1830i 1.45427i 0.686495 + 0.727134i \(0.259148\pi\)
−0.686495 + 0.727134i \(0.740852\pi\)
\(110\) 0 0
\(111\) 4.57418 + 2.64091i 0.434162 + 0.250664i
\(112\) 0 0
\(113\) −4.45011 + 7.70781i −0.418631 + 0.725090i −0.995802 0.0915332i \(-0.970823\pi\)
0.577171 + 0.816623i \(0.304157\pi\)
\(114\) 0 0
\(115\) 0.0927749 0.0535636i 0.00865131 0.00499483i
\(116\) 0 0
\(117\) −6.74809 5.64096i −0.623861 0.521507i
\(118\) 0 0
\(119\) 0.239765 0.138429i 0.0219792 0.0126897i
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) 0 0
\(123\) 15.6171 + 9.01652i 1.40814 + 0.812993i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.07829 + 10.5279i 0.539361 + 0.934201i 0.998939 + 0.0460632i \(0.0146676\pi\)
−0.459577 + 0.888138i \(0.651999\pi\)
\(128\) 0 0
\(129\) 14.0182 1.23423
\(130\) 0 0
\(131\) −2.11773 −0.185027 −0.0925135 0.995711i \(-0.529490\pi\)
−0.0925135 + 0.995711i \(0.529490\pi\)
\(132\) 0 0
\(133\) −1.07384 1.85994i −0.0931135 0.161277i
\(134\) 0 0
\(135\) 1.30752i 0.112533i
\(136\) 0 0
\(137\) 15.6171 + 9.01652i 1.33426 + 0.770334i 0.985949 0.167046i \(-0.0534230\pi\)
0.348308 + 0.937380i \(0.386756\pi\)
\(138\) 0 0
\(139\) 4.92008 8.52183i 0.417316 0.722812i −0.578353 0.815787i \(-0.696304\pi\)
0.995668 + 0.0929749i \(0.0296376\pi\)
\(140\) 0 0
\(141\) −6.99674 + 4.03957i −0.589232 + 0.340193i
\(142\) 0 0
\(143\) 2.14683 + 5.86440i 0.179527 + 0.490405i
\(144\) 0 0
\(145\) −4.24653 + 2.45174i −0.352655 + 0.203606i
\(146\) 0 0
\(147\) 7.97647 13.8156i 0.657888 1.13950i
\(148\) 0 0
\(149\) −7.69289 4.44149i −0.630226 0.363861i 0.150613 0.988593i \(-0.451875\pi\)
−0.780840 + 0.624731i \(0.785208\pi\)
\(150\) 0 0
\(151\) 4.43937i 0.361271i −0.983550 0.180636i \(-0.942185\pi\)
0.983550 0.180636i \(-0.0578155\pi\)
\(152\) 0 0
\(153\) 0.844610 + 1.46291i 0.0682827 + 0.118269i
\(154\) 0 0
\(155\) 7.86488 0.631723
\(156\) 0 0
\(157\) −4.16719 −0.332578 −0.166289 0.986077i \(-0.553178\pi\)
−0.166289 + 0.986077i \(0.553178\pi\)
\(158\) 0 0
\(159\) 13.6657 + 23.6697i 1.08376 + 1.87713i
\(160\) 0 0
\(161\) 0.0428299i 0.00337547i
\(162\) 0 0
\(163\) 3.20145 + 1.84836i 0.250757 + 0.144775i 0.620111 0.784514i \(-0.287088\pi\)
−0.369354 + 0.929289i \(0.620421\pi\)
\(164\) 0 0
\(165\) −2.01978 + 3.49837i −0.157240 + 0.272348i
\(166\) 0 0
\(167\) −18.6171 + 10.7486i −1.44063 + 0.831750i −0.997892 0.0648999i \(-0.979327\pi\)
−0.442741 + 0.896650i \(0.645994\pi\)
\(168\) 0 0
\(169\) −12.2325 4.40078i −0.940959 0.338522i
\(170\) 0 0
\(171\) 11.3483 6.55193i 0.867825 0.501039i
\(172\) 0 0
\(173\) −5.80589 + 10.0561i −0.441414 + 0.764551i −0.997795 0.0663766i \(-0.978856\pi\)
0.556381 + 0.830927i \(0.312189\pi\)
\(174\) 0 0
\(175\) −0.346241 0.199902i −0.0261733 0.0151112i
\(176\) 0 0
\(177\) 16.9678i 1.27538i
\(178\) 0 0
\(179\) −2.48516 4.30442i −0.185749 0.321728i 0.758079 0.652162i \(-0.226138\pi\)
−0.943829 + 0.330435i \(0.892805\pi\)
\(180\) 0 0
\(181\) −17.3695 −1.29107 −0.645534 0.763732i \(-0.723365\pi\)
−0.645534 + 0.763732i \(0.723365\pi\)
\(182\) 0 0
\(183\) −20.2654 −1.49806
\(184\) 0 0
\(185\) 1.13234 + 1.96128i 0.0832516 + 0.144196i
\(186\) 0 0
\(187\) 1.19941i 0.0877098i
\(188\) 0 0
\(189\) 0.452716 + 0.261376i 0.0329303 + 0.0190123i
\(190\) 0 0
\(191\) 10.2523 17.7575i 0.741832 1.28489i −0.209828 0.977738i \(-0.567290\pi\)
0.951660 0.307153i \(-0.0993762\pi\)
\(192\) 0 0
\(193\) −23.0428 + 13.3038i −1.65866 + 0.957626i −0.685322 + 0.728240i \(0.740338\pi\)
−0.973336 + 0.229386i \(0.926328\pi\)
\(194\) 0 0
\(195\) −2.89075 7.89654i −0.207011 0.565483i
\(196\) 0 0
\(197\) 0.353583 0.204141i 0.0251917 0.0145445i −0.487351 0.873206i \(-0.662037\pi\)
0.512543 + 0.858662i \(0.328704\pi\)
\(198\) 0 0
\(199\) 12.1998 21.1307i 0.864823 1.49792i −0.00240070 0.999997i \(-0.500764\pi\)
0.867223 0.497919i \(-0.165902\pi\)
\(200\) 0 0
\(201\) −2.68229 1.54862i −0.189194 0.109231i
\(202\) 0 0
\(203\) 1.96043i 0.137595i
\(204\) 0 0
\(205\) 3.86603 + 6.69615i 0.270015 + 0.467680i
\(206\) 0 0
\(207\) 0.261323 0.0181632
\(208\) 0 0
\(209\) −9.30426 −0.643589
\(210\) 0 0
\(211\) −0.880509 1.52509i −0.0606167 0.104991i 0.834125 0.551576i \(-0.185973\pi\)
−0.894741 + 0.446585i \(0.852640\pi\)
\(212\) 0 0
\(213\) 9.04452i 0.619721i
\(214\) 0 0
\(215\) 5.20533 + 3.00530i 0.355001 + 0.204960i
\(216\) 0 0
\(217\) 1.57221 2.72314i 0.106728 0.184859i
\(218\) 0 0
\(219\) 20.6525 11.9237i 1.39557 0.805732i
\(220\) 0 0
\(221\) 1.91562 + 1.60134i 0.128859 + 0.107718i
\(222\) 0 0
\(223\) 9.80263 5.65955i 0.656433 0.378991i −0.134484 0.990916i \(-0.542938\pi\)
0.790916 + 0.611924i \(0.209604\pi\)
\(224\) 0 0
\(225\) 1.21969 2.11256i 0.0813125 0.140837i
\(226\) 0 0
\(227\) −6.98084 4.03039i −0.463334 0.267506i 0.250111 0.968217i \(-0.419533\pi\)
−0.713445 + 0.700711i \(0.752866\pi\)
\(228\) 0 0
\(229\) 11.5715i 0.764666i −0.924025 0.382333i \(-0.875121\pi\)
0.924025 0.382333i \(-0.124879\pi\)
\(230\) 0 0
\(231\) 0.807519 + 1.39866i 0.0531308 + 0.0920253i
\(232\) 0 0
\(233\) −24.0900 −1.57819 −0.789094 0.614272i \(-0.789450\pi\)
−0.789094 + 0.614272i \(0.789450\pi\)
\(234\) 0 0
\(235\) −3.46410 −0.225973
\(236\) 0 0
\(237\) −15.3384 26.5669i −0.996336 1.72570i
\(238\) 0 0
\(239\) 30.7089i 1.98639i 0.116459 + 0.993196i \(0.462846\pi\)
−0.116459 + 0.993196i \(0.537154\pi\)
\(240\) 0 0
\(241\) 6.86541 + 3.96374i 0.442240 + 0.255327i 0.704547 0.709657i \(-0.251150\pi\)
−0.262308 + 0.964984i \(0.584483\pi\)
\(242\) 0 0
\(243\) −10.1286 + 17.5432i −0.649750 + 1.12540i
\(244\) 0 0
\(245\) 5.92375 3.42008i 0.378454 0.218501i
\(246\) 0 0
\(247\) 12.4221 14.8602i 0.790401 0.945529i
\(248\) 0 0
\(249\) 28.4368 16.4180i 1.80211 1.04045i
\(250\) 0 0
\(251\) 11.3112 19.5916i 0.713956 1.23661i −0.249405 0.968399i \(-0.580235\pi\)
0.963361 0.268209i \(-0.0864317\pi\)
\(252\) 0 0
\(253\) −0.160691 0.0927749i −0.0101025 0.00583271i
\(254\) 0 0
\(255\) 1.61504i 0.101138i
\(256\) 0 0
\(257\) 12.8982 + 22.3403i 0.804566 + 1.39355i 0.916584 + 0.399843i \(0.130935\pi\)
−0.112018 + 0.993706i \(0.535731\pi\)
\(258\) 0 0
\(259\) 0.905432 0.0562608
\(260\) 0 0
\(261\) −11.9614 −0.740393
\(262\) 0 0
\(263\) −0.795286 1.37748i −0.0490394 0.0849388i 0.840464 0.541868i \(-0.182283\pi\)
−0.889503 + 0.456929i \(0.848949\pi\)
\(264\) 0 0
\(265\) 11.7189i 0.719887i
\(266\) 0 0
\(267\) 0.701043 + 0.404747i 0.0429031 + 0.0247701i
\(268\) 0 0
\(269\) 13.9114 24.0952i 0.848192 1.46911i −0.0346278 0.999400i \(-0.511025\pi\)
0.882820 0.469712i \(-0.155642\pi\)
\(270\) 0 0
\(271\) −20.3520 + 11.7502i −1.23629 + 0.713774i −0.968335 0.249656i \(-0.919682\pi\)
−0.267959 + 0.963430i \(0.586349\pi\)
\(272\) 0 0
\(273\) −3.31197 0.577640i −0.200450 0.0349603i
\(274\) 0 0
\(275\) −1.50000 + 0.866025i −0.0904534 + 0.0522233i
\(276\) 0 0
\(277\) −1.49837 + 2.59525i −0.0900283 + 0.155934i −0.907523 0.420003i \(-0.862029\pi\)
0.817494 + 0.575936i \(0.195362\pi\)
\(278\) 0 0
\(279\) 16.6150 + 9.59270i 0.994716 + 0.574300i
\(280\) 0 0
\(281\) 24.6085i 1.46802i −0.679138 0.734011i \(-0.737646\pi\)
0.679138 0.734011i \(-0.262354\pi\)
\(282\) 0 0
\(283\) 4.08444 + 7.07446i 0.242795 + 0.420533i 0.961509 0.274772i \(-0.0886025\pi\)
−0.718715 + 0.695305i \(0.755269\pi\)
\(284\) 0 0
\(285\) 12.5284 0.742118
\(286\) 0 0
\(287\) 3.09131 0.182474
\(288\) 0 0
\(289\) 8.26023 + 14.3071i 0.485896 + 0.841597i
\(290\) 0 0
\(291\) 20.6405i 1.20997i
\(292\) 0 0
\(293\) −6.49837 3.75184i −0.379639 0.219185i 0.298022 0.954559i \(-0.403673\pi\)
−0.677661 + 0.735374i \(0.737006\pi\)
\(294\) 0 0
\(295\) 3.63765 6.30059i 0.211792 0.366834i
\(296\) 0 0
\(297\) 1.96128 1.13234i 0.113805 0.0657053i
\(298\) 0 0
\(299\) 0.362712 0.132781i 0.0209762 0.00767893i
\(300\) 0 0
\(301\) 2.08112 1.20153i 0.119953 0.0692552i
\(302\) 0 0
\(303\) −4.78561 + 8.28893i −0.274926 + 0.476186i
\(304\) 0 0
\(305\) −7.52509 4.34461i −0.430885 0.248772i
\(306\) 0 0
\(307\) 5.95293i 0.339752i −0.985465 0.169876i \(-0.945663\pi\)
0.985465 0.169876i \(-0.0543367\pi\)
\(308\) 0 0
\(309\) −13.0984 22.6872i −0.745144 1.29063i
\(310\) 0 0
\(311\) −17.9247 −1.01642 −0.508208 0.861235i \(-0.669692\pi\)
−0.508208 + 0.861235i \(0.669692\pi\)
\(312\) 0 0
\(313\) −17.0073 −0.961312 −0.480656 0.876909i \(-0.659601\pi\)
−0.480656 + 0.876909i \(0.659601\pi\)
\(314\) 0 0
\(315\) −0.487636 0.844610i −0.0274752 0.0475884i
\(316\) 0 0
\(317\) 3.09300i 0.173720i −0.996221 0.0868601i \(-0.972317\pi\)
0.996221 0.0868601i \(-0.0276833\pi\)
\(318\) 0 0
\(319\) 7.35521 + 4.24653i 0.411813 + 0.237760i
\(320\) 0 0
\(321\) −20.5276 + 35.5549i −1.14574 + 1.98448i
\(322\) 0 0
\(323\) −3.22151 + 1.85994i −0.179250 + 0.103490i
\(324\) 0 0
\(325\) 0.619491 3.55193i 0.0343632 0.197026i
\(326\) 0 0
\(327\) −30.6664 + 17.7053i −1.69586 + 0.979103i
\(328\) 0 0
\(329\) −0.692481 + 1.19941i −0.0381777 + 0.0661258i
\(330\) 0 0
\(331\) 19.5481 + 11.2861i 1.07446 + 0.620340i 0.929397 0.369082i \(-0.120328\pi\)
0.145064 + 0.989422i \(0.453661\pi\)
\(332\) 0 0
\(333\) 5.52442i 0.302736i
\(334\) 0 0
\(335\) −0.664004 1.15009i −0.0362784 0.0628360i
\(336\) 0 0
\(337\) 18.0603 0.983808 0.491904 0.870649i \(-0.336301\pi\)
0.491904 + 0.870649i \(0.336301\pi\)
\(338\) 0 0
\(339\) −20.7575 −1.12739
\(340\) 0 0
\(341\) −6.81119 11.7973i −0.368847 0.638861i
\(342\) 0 0
\(343\) 5.53335i 0.298773i
\(344\) 0 0
\(345\) 0.216374 + 0.124924i 0.0116492 + 0.00672566i
\(346\) 0 0
\(347\) −13.2359 + 22.9252i −0.710538 + 1.23069i 0.254118 + 0.967173i \(0.418215\pi\)
−0.964655 + 0.263514i \(0.915118\pi\)
\(348\) 0 0
\(349\) 10.7190 6.18860i 0.573773 0.331268i −0.184882 0.982761i \(-0.559190\pi\)
0.758655 + 0.651493i \(0.225857\pi\)
\(350\) 0 0
\(351\) −0.809996 + 4.64422i −0.0432344 + 0.247890i
\(352\) 0 0
\(353\) 16.6978 9.64047i 0.888733 0.513110i 0.0152053 0.999884i \(-0.495160\pi\)
0.873528 + 0.486774i \(0.161826\pi\)
\(354\) 0 0
\(355\) 1.93902 3.35847i 0.102912 0.178249i
\(356\) 0 0
\(357\) 0.559192 + 0.322849i 0.0295956 + 0.0170870i
\(358\) 0 0
\(359\) 26.5506i 1.40129i 0.713512 + 0.700643i \(0.247103\pi\)
−0.713512 + 0.700643i \(0.752897\pi\)
\(360\) 0 0
\(361\) 4.92820 + 8.53590i 0.259379 + 0.449258i
\(362\) 0 0
\(363\) −18.6580 −0.979290
\(364\) 0 0
\(365\) 10.2251 0.535207
\(366\) 0 0
\(367\) −3.68718 6.38638i −0.192469 0.333366i 0.753599 0.657335i \(-0.228316\pi\)
−0.946068 + 0.323968i \(0.894983\pi\)
\(368\) 0 0
\(369\) 18.8614i 0.981883i
\(370\) 0 0
\(371\) 4.05756 + 2.34263i 0.210658 + 0.121624i
\(372\) 0 0
\(373\) 14.1574 24.5214i 0.733044 1.26967i −0.222532 0.974925i \(-0.571432\pi\)
0.955576 0.294744i \(-0.0952344\pi\)
\(374\) 0 0
\(375\) 2.01978 1.16612i 0.104301 0.0602183i
\(376\) 0 0
\(377\) −16.6022 + 6.07772i −0.855059 + 0.313018i
\(378\) 0 0
\(379\) 9.02975 5.21333i 0.463827 0.267791i −0.249825 0.968291i \(-0.580373\pi\)
0.713652 + 0.700500i \(0.247040\pi\)
\(380\) 0 0
\(381\) −14.1761 + 24.5537i −0.726262 + 1.25792i
\(382\) 0 0
\(383\) −9.39811 5.42600i −0.480221 0.277256i 0.240288 0.970702i \(-0.422758\pi\)
−0.720509 + 0.693446i \(0.756092\pi\)
\(384\) 0 0
\(385\) 0.692481i 0.0352921i
\(386\) 0 0
\(387\) 7.33105 + 12.6978i 0.372658 + 0.645463i
\(388\) 0 0
\(389\) 20.2893 1.02871 0.514353 0.857578i \(-0.328032\pi\)
0.514353 + 0.857578i \(0.328032\pi\)
\(390\) 0 0
\(391\) −0.0741836 −0.00375163
\(392\) 0 0
\(393\) −2.46953 4.27736i −0.124572 0.215764i
\(394\) 0 0
\(395\) 13.1533i 0.661815i
\(396\) 0 0
\(397\) 21.8695 + 12.6263i 1.09760 + 0.633698i 0.935589 0.353091i \(-0.114870\pi\)
0.162008 + 0.986789i \(0.448203\pi\)
\(398\) 0 0
\(399\) 2.50445 4.33784i 0.125380 0.217164i
\(400\) 0 0
\(401\) 10.8377 6.25714i 0.541208 0.312467i −0.204360 0.978896i \(-0.565511\pi\)
0.745568 + 0.666429i \(0.232178\pi\)
\(402\) 0 0
\(403\) 27.9355 + 4.87223i 1.39157 + 0.242703i
\(404\) 0 0
\(405\) −8.97859 + 5.18379i −0.446149 + 0.257585i
\(406\) 0 0
\(407\) 1.96128 3.39703i 0.0972169 0.168385i
\(408\) 0 0
\(409\) 5.19248 + 2.99788i 0.256752 + 0.148236i 0.622852 0.782340i \(-0.285974\pi\)
−0.366100 + 0.930575i \(0.619307\pi\)
\(410\) 0 0
\(411\) 42.0575i 2.07454i
\(412\) 0 0
\(413\) −1.45435 2.51900i −0.0715637 0.123952i
\(414\) 0 0
\(415\) 14.0791 0.691118
\(416\) 0 0
\(417\) 22.9497 1.12385
\(418\) 0 0
\(419\) 5.48516 + 9.50057i 0.267968 + 0.464133i 0.968337 0.249647i \(-0.0803147\pi\)
−0.700369 + 0.713781i \(0.746981\pi\)
\(420\) 0 0
\(421\) 36.6085i 1.78419i 0.451848 + 0.892095i \(0.350765\pi\)
−0.451848 + 0.892095i \(0.649235\pi\)
\(422\) 0 0
\(423\) −7.31812 4.22512i −0.355819 0.205432i
\(424\) 0 0
\(425\) −0.346241 + 0.599706i −0.0167951 + 0.0290900i
\(426\) 0 0
\(427\) −3.00856 + 1.73699i −0.145595 + 0.0840590i
\(428\) 0 0
\(429\) −9.34135 + 11.1747i −0.451005 + 0.539521i
\(430\) 0 0
\(431\) −10.4873 + 6.05484i −0.505155 + 0.291651i −0.730840 0.682549i \(-0.760871\pi\)
0.225685 + 0.974200i \(0.427538\pi\)
\(432\) 0 0
\(433\) −4.50897 + 7.80977i −0.216687 + 0.375314i −0.953793 0.300464i \(-0.902859\pi\)
0.737106 + 0.675777i \(0.236192\pi\)
\(434\) 0 0
\(435\) −9.90396 5.71806i −0.474859 0.274160i
\(436\) 0 0
\(437\) 0.575468i 0.0275284i
\(438\) 0 0
\(439\) −6.07547 10.5230i −0.289966 0.502236i 0.683835 0.729637i \(-0.260311\pi\)
−0.973801 + 0.227400i \(0.926977\pi\)
\(440\) 0 0
\(441\) 16.6857 0.794557
\(442\) 0 0
\(443\) 15.3116 0.727476 0.363738 0.931501i \(-0.381500\pi\)
0.363738 + 0.931501i \(0.381500\pi\)
\(444\) 0 0
\(445\) 0.173544 + 0.300587i 0.00822678 + 0.0142492i
\(446\) 0 0
\(447\) 20.7173i 0.979895i
\(448\) 0 0
\(449\) −19.6929 11.3697i −0.929365 0.536569i −0.0427543 0.999086i \(-0.513613\pi\)
−0.886611 + 0.462516i \(0.846947\pi\)
\(450\) 0 0
\(451\) 6.69615 11.5981i 0.315310 0.546132i
\(452\) 0 0
\(453\) 8.96658 5.17686i 0.421287 0.243230i
\(454\) 0 0
\(455\) −1.10599 0.924532i −0.0518494 0.0433427i
\(456\) 0 0
\(457\) −9.30548 + 5.37252i −0.435292 + 0.251316i −0.701599 0.712572i \(-0.747530\pi\)
0.266307 + 0.963888i \(0.414197\pi\)
\(458\) 0 0
\(459\) 0.452716 0.784127i 0.0211310 0.0365999i
\(460\) 0 0
\(461\) 10.2973 + 5.94516i 0.479594 + 0.276894i 0.720247 0.693717i \(-0.244028\pi\)
−0.240653 + 0.970611i \(0.577362\pi\)
\(462\) 0 0
\(463\) 3.39726i 0.157884i −0.996879 0.0789420i \(-0.974846\pi\)
0.996879 0.0789420i \(-0.0251542\pi\)
\(464\) 0 0
\(465\) 9.17142 + 15.8854i 0.425315 + 0.736667i
\(466\) 0 0
\(467\) −6.39426 −0.295891 −0.147946 0.988996i \(-0.547266\pi\)
−0.147946 + 0.988996i \(0.547266\pi\)
\(468\) 0 0
\(469\) −0.530943 −0.0245167
\(470\) 0 0
\(471\) −4.85945 8.41682i −0.223912 0.387826i
\(472\) 0 0
\(473\) 10.4107i 0.478683i
\(474\) 0 0
\(475\) 4.65213 + 2.68591i 0.213454 + 0.123238i
\(476\) 0 0
\(477\) −14.2934 + 24.7569i −0.654450 + 1.13354i
\(478\) 0 0
\(479\) 14.1330 8.15968i 0.645752 0.372825i −0.141075 0.989999i \(-0.545056\pi\)
0.786827 + 0.617174i \(0.211722\pi\)
\(480\) 0 0
\(481\) 2.80702 + 7.66781i 0.127989 + 0.349622i
\(482\) 0 0
\(483\) 0.0865072 0.0499450i 0.00393622 0.00227258i
\(484\) 0 0
\(485\) 4.42502 7.66436i 0.200930 0.348021i
\(486\) 0 0
\(487\) −10.3356 5.96728i −0.468352 0.270403i 0.247197 0.968965i \(-0.420490\pi\)
−0.715550 + 0.698562i \(0.753824\pi\)
\(488\) 0 0
\(489\) 8.62166i 0.389885i
\(490\) 0 0
\(491\) −17.0259 29.4896i −0.768366 1.33085i −0.938448 0.345419i \(-0.887737\pi\)
0.170082 0.985430i \(-0.445597\pi\)
\(492\) 0 0
\(493\) 3.39557 0.152929
\(494\) 0 0
\(495\) −4.22512 −0.189905
\(496\) 0 0
\(497\) −0.775227 1.34273i −0.0347737 0.0602298i
\(498\) 0 0
\(499\) 12.5854i 0.563398i 0.959503 + 0.281699i \(0.0908979\pi\)
−0.959503 + 0.281699i \(0.909102\pi\)
\(500\) 0 0
\(501\) −43.4196 25.0683i −1.93985 1.11997i
\(502\) 0 0
\(503\) 9.09433 15.7518i 0.405496 0.702340i −0.588883 0.808218i \(-0.700432\pi\)
0.994379 + 0.105879i \(0.0337655\pi\)
\(504\) 0 0
\(505\) −3.55405 + 2.05193i −0.158153 + 0.0913098i
\(506\) 0 0
\(507\) −5.37592 29.8388i −0.238753 1.32519i
\(508\) 0 0
\(509\) −25.1265 + 14.5068i −1.11371 + 0.643001i −0.939788 0.341758i \(-0.888978\pi\)
−0.173923 + 0.984759i \(0.555644\pi\)
\(510\) 0 0
\(511\) 2.04402 3.54035i 0.0904223 0.156616i
\(512\) 0 0
\(513\) −6.08275 3.51187i −0.268560 0.155053i
\(514\) 0 0
\(515\) 11.2325i 0.494961i
\(516\) 0 0
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) 0 0
\(519\) −27.0815 −1.18875
\(520\) 0 0
\(521\) 35.0240 1.53443 0.767214 0.641391i \(-0.221642\pi\)
0.767214 + 0.641391i \(0.221642\pi\)
\(522\) 0 0
\(523\) 4.63870 + 8.03447i 0.202836 + 0.351323i 0.949441 0.313945i \(-0.101651\pi\)
−0.746605 + 0.665268i \(0.768317\pi\)
\(524\) 0 0
\(525\) 0.932442i 0.0406951i
\(526\) 0 0
\(527\) −4.71662 2.72314i −0.205459 0.118622i
\(528\) 0 0
\(529\) 11.4943 19.9086i 0.499751 0.865593i
\(530\) 0 0
\(531\) 15.3695 8.87358i 0.666979 0.385080i
\(532\) 0 0
\(533\) 9.58366 + 26.1793i 0.415114 + 1.13395i
\(534\) 0 0
\(535\) −15.2449 + 8.80165i −0.659095 + 0.380528i
\(536\) 0 0
\(537\) 5.79600 10.0390i 0.250116 0.433214i
\(538\) 0 0
\(539\) −10.2602 5.92375i −0.441940 0.255154i
\(540\) 0 0
\(541\) 24.3814i 1.04824i −0.851644 0.524120i \(-0.824394\pi\)
0.851644 0.524120i \(-0.175606\pi\)
\(542\) 0 0
\(543\) −20.2550 35.0827i −0.869226 1.50554i
\(544\) 0 0
\(545\) −15.1830 −0.650369
\(546\) 0 0
\(547\) 26.5270 1.13421 0.567106 0.823645i \(-0.308063\pi\)
0.567106 + 0.823645i \(0.308063\pi\)
\(548\) 0 0
\(549\) −10.5981 18.3565i −0.452317 0.783436i
\(550\) 0 0
\(551\) 26.3406i 1.12215i
\(552\) 0 0
\(553\) −4.55422 2.62938i −0.193665 0.111813i
\(554\) 0 0
\(555\) −2.64091 + 4.57418i −0.112100 + 0.194163i
\(556\) 0 0
\(557\) −2.78142 + 1.60586i −0.117853 + 0.0680423i −0.557768 0.829997i \(-0.688342\pi\)
0.439915 + 0.898039i \(0.355009\pi\)
\(558\) 0 0
\(559\) 16.6272 + 13.8993i 0.703257 + 0.587877i
\(560\) 0 0
\(561\) 2.42256 1.39866i 0.102280 0.0590516i
\(562\) 0 0
\(563\) −17.1426 + 29.6918i −0.722474 + 1.25136i 0.237531 + 0.971380i \(0.423662\pi\)
−0.960005 + 0.279982i \(0.909672\pi\)
\(564\) 0 0
\(565\) −7.70781 4.45011i −0.324270 0.187217i
\(566\) 0 0
\(567\) 4.14500i 0.174074i
\(568\) 0 0
\(569\) −17.8228 30.8701i −0.747172 1.29414i −0.949173 0.314755i \(-0.898078\pi\)
0.202001 0.979385i \(-0.435256\pi\)
\(570\) 0 0
\(571\) −4.53590 −0.189821 −0.0949107 0.995486i \(-0.530257\pi\)
−0.0949107 + 0.995486i \(0.530257\pi\)
\(572\) 0 0
\(573\) 47.8219 1.99779
\(574\) 0 0
\(575\) 0.0535636 + 0.0927749i 0.00223376 + 0.00386898i
\(576\) 0 0
\(577\) 18.4475i 0.767981i −0.923337 0.383991i \(-0.874550\pi\)
0.923337 0.383991i \(-0.125450\pi\)
\(578\) 0 0
\(579\) −53.7415 31.0277i −2.23342 1.28947i
\(580\) 0 0
\(581\) 2.81445 4.87477i 0.116763 0.202240i
\(582\) 0 0
\(583\) 17.5784 10.1489i 0.728021 0.420323i
\(584\) 0 0
\(585\) 5.64096 6.74809i 0.233225 0.278999i
\(586\) 0 0
\(587\) −37.2316 + 21.4957i −1.53671 + 0.887222i −0.537685 + 0.843146i \(0.680701\pi\)
−0.999028 + 0.0440760i \(0.985966\pi\)
\(588\) 0 0
\(589\) −21.1244 + 36.5885i −0.870414 + 1.50760i
\(590\) 0 0
\(591\) 0.824642 + 0.476107i 0.0339212 + 0.0195844i
\(592\) 0 0
\(593\) 12.8614i 0.528153i 0.964502 + 0.264076i \(0.0850671\pi\)
−0.964502 + 0.264076i \(0.914933\pi\)
\(594\) 0 0
\(595\) 0.138429 + 0.239765i 0.00567502 + 0.00982942i
\(596\) 0 0
\(597\) 56.9060 2.32901
\(598\) 0 0
\(599\) 28.3170 1.15700 0.578500 0.815682i \(-0.303638\pi\)
0.578500 + 0.815682i \(0.303638\pi\)
\(600\) 0 0
\(601\) 3.56734 + 6.17882i 0.145515 + 0.252039i 0.929565 0.368658i \(-0.120183\pi\)
−0.784050 + 0.620698i \(0.786849\pi\)
\(602\) 0 0
\(603\) 3.23951i 0.131923i
\(604\) 0 0
\(605\) −6.92820 4.00000i −0.281672 0.162623i
\(606\) 0 0
\(607\) 11.0901 19.2086i 0.450133 0.779653i −0.548261 0.836307i \(-0.684710\pi\)
0.998394 + 0.0566544i \(0.0180433\pi\)
\(608\) 0 0
\(609\) −3.95965 + 2.28610i −0.160453 + 0.0926376i
\(610\) 0 0
\(611\) −12.3043 2.14598i −0.497777 0.0868171i
\(612\) 0 0
\(613\) −0.279399 + 0.161311i −0.0112848 + 0.00651530i −0.505632 0.862749i \(-0.668741\pi\)
0.494347 + 0.869265i \(0.335407\pi\)
\(614\) 0 0
\(615\) −9.01652 + 15.6171i −0.363581 + 0.629741i
\(616\) 0 0
\(617\) −32.2150 18.5993i −1.29693 0.748781i −0.317055 0.948407i \(-0.602694\pi\)
−0.979872 + 0.199626i \(0.936027\pi\)
\(618\) 0 0
\(619\) 3.94911i 0.158728i 0.996846 + 0.0793641i \(0.0252890\pi\)
−0.996846 + 0.0793641i \(0.974711\pi\)
\(620\) 0 0
\(621\) −0.0700354 0.121305i −0.00281043 0.00486780i
\(622\) 0 0
\(623\) 0.138767 0.00555959
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −10.8499 18.7926i −0.433304 0.750504i
\(628\) 0 0
\(629\) 1.56825i 0.0625304i
\(630\) 0 0
\(631\) 29.0824 + 16.7908i 1.15775 + 0.668429i 0.950765 0.309914i \(-0.100300\pi\)
0.206989 + 0.978343i \(0.433634\pi\)
\(632\) 0 0
\(633\) 2.05356 3.55688i 0.0816218 0.141373i
\(634\) 0 0
\(635\) −10.5279 + 6.07829i −0.417787 + 0.241210i
\(636\) 0 0
\(637\) 23.1595 8.47818i 0.917612 0.335918i
\(638\) 0 0
\(639\) 8.19257 4.72998i 0.324093 0.187115i
\(640\) 0 0
\(641\) 16.5900 28.7347i 0.655266 1.13495i −0.326561 0.945176i \(-0.605890\pi\)
0.981827 0.189778i \(-0.0607767\pi\)
\(642\) 0 0
\(643\) 27.1643 + 15.6833i 1.07125 + 0.618489i 0.928524 0.371273i \(-0.121078\pi\)
0.142730 + 0.989762i \(0.454412\pi\)
\(644\) 0 0
\(645\) 14.0182i 0.551966i
\(646\) 0 0
\(647\) 9.79529 + 16.9659i 0.385092 + 0.667000i 0.991782 0.127939i \(-0.0408362\pi\)
−0.606690 + 0.794939i \(0.707503\pi\)
\(648\) 0 0
\(649\) −12.6012 −0.494639
\(650\) 0 0
\(651\) 7.33355 0.287424
\(652\) 0 0
\(653\) −3.55626 6.15962i −0.139167 0.241044i 0.788015 0.615657i \(-0.211109\pi\)
−0.927182 + 0.374612i \(0.877776\pi\)
\(654\) 0 0
\(655\) 2.11773i 0.0827466i
\(656\) 0 0
\(657\) 21.6012 + 12.4714i 0.842742 + 0.486557i
\(658\) 0 0
\(659\) −9.29211 + 16.0944i −0.361969 + 0.626949i −0.988285 0.152621i \(-0.951229\pi\)
0.626316 + 0.779570i \(0.284562\pi\)
\(660\) 0 0
\(661\) 14.5413 8.39540i 0.565590 0.326543i −0.189796 0.981823i \(-0.560783\pi\)
0.755386 + 0.655280i \(0.227449\pi\)
\(662\) 0 0
\(663\) −1.00050 + 5.73650i −0.0388563 + 0.222787i
\(664\) 0 0
\(665\) 1.85994 1.07384i 0.0721254 0.0416416i
\(666\) 0 0
\(667\) 0.262648 0.454919i 0.0101698 0.0176146i
\(668\) 0 0
\(669\) 22.8621 + 13.1995i 0.883902 + 0.510321i
\(670\) 0 0
\(671\) 15.0502i 0.581005i
\(672\) 0 0
\(673\) 11.2957 + 19.5647i 0.435417 + 0.754165i 0.997330 0.0730322i \(-0.0232676\pi\)
−0.561912 + 0.827197i \(0.689934\pi\)
\(674\) 0 0
\(675\) −1.30752 −0.0503264
\(676\) 0 0
\(677\) 5.31616 0.204317 0.102158 0.994768i \(-0.467425\pi\)
0.102158 + 0.994768i \(0.467425\pi\)
\(678\) 0 0
\(679\) −1.76914 3.06424i −0.0678935 0.117595i
\(680\) 0 0
\(681\) 18.7997i 0.720407i
\(682\) 0 0
\(683\) 3.42419 + 1.97695i 0.131023 + 0.0756461i 0.564079 0.825721i \(-0.309231\pi\)
−0.433056 + 0.901367i \(0.642565\pi\)
\(684\) 0 0
\(685\) −9.01652 + 15.6171i −0.344504 + 0.596698i
\(686\) 0 0
\(687\) 23.3719 13.4938i 0.891694 0.514820i
\(688\) 0 0
\(689\) −7.25976 + 41.6248i −0.276575 + 1.58578i
\(690\) 0 0
\(691\) −11.1493 + 6.43704i −0.424139 + 0.244877i −0.696846 0.717220i \(-0.745414\pi\)
0.272708 + 0.962097i \(0.412081\pi\)
\(692\) 0 0
\(693\) −0.844610 + 1.46291i −0.0320841 + 0.0555713i
\(694\) 0 0
\(695\) 8.52183 + 4.92008i 0.323251 + 0.186629i
\(696\) 0 0
\(697\) 5.35430i 0.202809i
\(698\) 0 0
\(699\) −28.0919 48.6566i −1.06253 1.84036i
\(700\) 0 0
\(701\) 34.9777 1.32109 0.660544 0.750787i \(-0.270326\pi\)
0.660544 + 0.750787i \(0.270326\pi\)
\(702\) 0 0
\(703\) −12.1655 −0.458830
\(704\) 0 0
\(705\) −4.03957 6.99674i −0.152139 0.263512i
\(706\) 0 0
\(707\) 1.64074i 0.0617065i
\(708\) 0 0
\(709\) −17.1183 9.88325i −0.642891 0.371173i 0.142836 0.989746i \(-0.454378\pi\)
−0.785727 + 0.618573i \(0.787711\pi\)
\(710\) 0 0
\(711\) 16.0429 27.7872i 0.601657 1.04210i
\(712\) 0 0
\(713\) −0.729664 + 0.421272i −0.0273261 + 0.0157767i
\(714\) 0 0
\(715\) −5.86440 + 2.14683i −0.219316 + 0.0802868i
\(716\) 0 0
\(717\) −62.0253 + 35.8103i −2.31638 + 1.33736i
\(718\) 0 0
\(719\) −22.1234 + 38.3188i −0.825062 + 1.42905i 0.0768099 + 0.997046i \(0.475527\pi\)
−0.901872 + 0.432004i \(0.857807\pi\)
\(720\) 0 0
\(721\) −3.88914 2.24539i −0.144839 0.0836228i
\(722\) 0 0
\(723\) 18.4889i 0.687608i
\(724\) 0 0
\(725\) −2.45174 4.24653i −0.0910553 0.157712i
\(726\) 0 0
\(727\) −31.4877 −1.16781 −0.583907 0.811821i \(-0.698477\pi\)
−0.583907 + 0.811821i \(0.698477\pi\)
\(728\) 0 0
\(729\) −16.1420 −0.597853
\(730\) 0 0
\(731\) −2.08112 3.60460i −0.0769728 0.133321i
\(732\) 0 0
\(733\) 42.4714i 1.56872i 0.620307 + 0.784359i \(0.287008\pi\)
−0.620307 + 0.784359i \(0.712992\pi\)
\(734\) 0 0
\(735\) 13.8156 + 7.97647i 0.509598 + 0.294216i
\(736\) 0 0
\(737\) −1.15009 + 1.99201i −0.0423640 + 0.0733767i
\(738\) 0 0
\(739\) −11.9368 + 6.89173i −0.439103 + 0.253516i −0.703217 0.710975i \(-0.748254\pi\)
0.264114 + 0.964492i \(0.414921\pi\)
\(740\) 0 0
\(741\) 44.5000 + 7.76123i 1.63475 + 0.285116i
\(742\) 0 0
\(743\) −13.8038 + 7.96961i −0.506411 + 0.292377i −0.731357 0.681995i \(-0.761113\pi\)
0.224946 + 0.974371i \(0.427779\pi\)
\(744\) 0 0
\(745\) 4.44149 7.69289i 0.162724 0.281846i
\(746\) 0 0
\(747\) 29.7430 + 17.1721i 1.08824 + 0.628296i
\(748\) 0 0
\(749\) 7.03787i 0.257158i
\(750\) 0 0
\(751\) −0.758540 1.31383i −0.0276795 0.0479423i 0.851854 0.523780i \(-0.175478\pi\)
−0.879533 + 0.475837i \(0.842145\pi\)
\(752\) 0 0
\(753\) 52.7610 1.92272
\(754\) 0 0
\(755\) 4.43937 0.161565
\(756\) 0 0
\(757\) −23.7414 41.1214i −0.862897 1.49458i −0.869120 0.494601i \(-0.835314\pi\)
0.00622310 0.999981i \(-0.498019\pi\)
\(758\) 0 0
\(759\) 0.432748i 0.0157078i
\(760\) 0 0
\(761\) −33.3805 19.2722i −1.21004 0.698618i −0.247274 0.968946i \(-0.579535\pi\)
−0.962768 + 0.270327i \(0.912868\pi\)
\(762\) 0 0
\(763\) −3.03512 + 5.25697i −0.109879 + 0.190315i
\(764\) 0 0
\(765\) −1.46291 + 0.844610i −0.0528916 + 0.0305370i
\(766\) 0 0
\(767\) 16.8238 20.1258i 0.607473 0.726700i
\(768\) 0 0
\(769\) 34.5236 19.9322i 1.24495 0.718775i 0.274856 0.961486i \(-0.411370\pi\)
0.970099 + 0.242711i \(0.0780366\pi\)
\(770\) 0 0
\(771\) −30.0817 + 52.1031i −1.08337 + 1.87645i
\(772\) 0 0
\(773\) 28.5396 + 16.4774i 1.02650 + 0.592650i 0.915980 0.401224i \(-0.131415\pi\)
0.110519 + 0.993874i \(0.464749\pi\)
\(774\) 0 0
\(775\) 7.86488i 0.282515i
\(776\) 0 0
\(777\) 1.05585 + 1.82878i 0.0378783 + 0.0656071i
\(778\) 0 0
\(779\) −41.5352 −1.48815
\(780\) 0 0
\(781\) −6.71695 −0.240351
\(782\) 0 0
\(783\) 3.20569 + 5.55242i 0.114562 + 0.198427i
\(784\) 0 0
\(785\) 4.16719i 0.148733i
\(786\) 0 0
\(787\) −0.934698 0.539648i −0.0333184 0.0192364i 0.483248 0.875483i \(-0.339457\pi\)
−0.516567 + 0.856247i \(0.672790\pi\)
\(788\) 0 0
\(789\) 1.85480 3.21261i 0.0660327 0.114372i
\(790\) 0 0
\(791\) −3.08162 + 1.77917i −0.109570 + 0.0632601i
\(792\) 0 0
\(793\) −24.0372 20.0935i −0.853584 0.713541i
\(794\) 0 0
\(795\) −23.6697