Properties

Label 260.2.x.a.121.4
Level $260$
Weight $2$
Character 260.121
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 121.4
Root \(1.40994 + 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 260.121
Dual form 260.2.x.a.101.4

$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

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

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 −0.303712 0.952764i \(-0.598226\pi\)
0.976974 0.213359i \(-0.0684405\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.346241 0.199902i 0.130867 0.0755559i −0.433137 0.901328i \(-0.642594\pi\)
0.564004 + 0.825772i \(0.309260\pi\)
\(8\) 0 0
\(9\) −1.21969 2.11256i −0.406562 0.704187i
\(10\) 0 0
\(11\) 1.50000 + 0.866025i 0.452267 + 0.261116i 0.708787 0.705422i \(-0.249243\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(12\) 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 0.904954 0.425509i \(-0.139905\pi\)
−0.820979 + 0.570959i \(0.806572\pi\)
\(18\) 0 0
\(19\) −4.65213 + 2.68591i −1.06727 + 0.616190i −0.927435 0.373985i \(-0.877991\pi\)
−0.139837 + 0.990175i \(0.544658\pi\)
\(20\) 0 0
\(21\) 0.932442i 0.203476i
\(22\) 0 0
\(23\) −0.0535636 + 0.0927749i −0.0111688 + 0.0193449i −0.871556 0.490296i \(-0.836889\pi\)
0.860387 + 0.509641i \(0.170222\pi\)
\(24\) 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 −0.543428 0.839456i \(-0.682874\pi\)
0.998704 + 0.0508943i \(0.0162072\pi\)
\(30\) 0 0
\(31\) 7.86488i 1.41257i 0.707925 + 0.706287i \(0.249631\pi\)
−0.707925 + 0.706287i \(0.750369\pi\)
\(32\) 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 0.652476 0.757809i \(-0.273730\pi\)
−0.330044 + 0.943966i \(0.607064\pi\)
\(38\) 0 0
\(39\) −7.89654 2.89075i −1.26446 0.462891i
\(40\) 0 0
\(41\) 6.69615 + 3.86603i 1.04576 + 0.603772i 0.921460 0.388473i \(-0.126997\pi\)
0.124303 + 0.992244i \(0.460331\pi\)
\(42\) 0 0
\(43\) 3.00530 + 5.20533i 0.458304 + 0.793806i 0.998871 0.0474947i \(-0.0151237\pi\)
−0.540567 + 0.841301i \(0.681790\pi\)
\(44\) 0 0
\(45\) −2.11256 + 1.21969i −0.314922 + 0.181820i
\(46\) 0 0
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 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 −0.850508 0.525961i \(-0.823706\pi\)
0.0302418 + 0.999543i \(0.490372\pi\)
\(60\) 0 0
\(61\) −4.34461 7.52509i −0.556270 0.963489i −0.997803 0.0662436i \(-0.978899\pi\)
0.441533 0.897245i \(-0.354435\pi\)
\(62\) 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 0.428099 0.903732i \(-0.359183\pi\)
−0.568605 + 0.822611i \(0.692517\pi\)
\(68\) 0 0
\(69\) 0.124924 + 0.216374i 0.0150390 + 0.0260484i
\(70\) 0 0
\(71\) −3.35847 + 1.93902i −0.398577 + 0.230119i −0.685870 0.727724i \(-0.740578\pi\)
0.287293 + 0.957843i \(0.407245\pi\)
\(72\) 0 0
\(73\) 10.2251i 1.19676i 0.801213 + 0.598380i \(0.204189\pi\)
−0.801213 + 0.598380i \(0.795811\pi\)
\(74\) 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 \(0.281091\pi\)
−0.634780 + 0.772693i \(0.718909\pi\)
\(84\) 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 0.515846 0.856681i \(-0.327477\pi\)
−0.483984 + 0.875077i \(0.660811\pi\)
\(90\) 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 −0.835791 0.549047i \(-0.814991\pi\)
0.0575932 + 0.998340i \(0.481657\pi\)
\(98\) 0 0
\(99\) 4.22512i 0.424640i
\(100\) 0 0
\(101\) 2.05193 3.55405i 0.204175 0.353641i −0.745695 0.666288i \(-0.767882\pi\)
0.949870 + 0.312646i \(0.101216\pi\)
\(102\) 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 −0.0295208 0.999564i \(-0.509398\pi\)
0.880408 0.474216i \(-0.157269\pi\)
\(108\) 0 0
\(109\) 15.1830i 1.45427i −0.686495 0.727134i \(-0.740852\pi\)
0.686495 0.727134i \(-0.259148\pi\)
\(110\) 0 0
\(111\) 4.57418 2.64091i 0.434162 0.250664i
\(112\) 0 0
\(113\) −4.45011 7.70781i −0.418631 0.725090i 0.577171 0.816623i \(-0.304157\pi\)
−0.995802 + 0.0915332i \(0.970823\pi\)
\(114\) 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 −0.459577 0.888138i \(-0.651999\pi\)
0.998939 0.0460632i \(-0.0146676\pi\)
\(128\) 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 0.348308 0.937380i \(-0.386756\pi\)
0.985949 + 0.167046i \(0.0534230\pi\)
\(138\) 0 0
\(139\) 4.92008 + 8.52183i 0.417316 + 0.722812i 0.995668 0.0929749i \(-0.0296376\pi\)
−0.578353 + 0.815787i \(0.696304\pi\)
\(140\) 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 −0.780840 0.624731i \(-0.785208\pi\)
0.150613 + 0.988593i \(0.451875\pi\)
\(150\) 0 0
\(151\) 4.43937i 0.361271i 0.983550 + 0.180636i \(0.0578155\pi\)
−0.983550 + 0.180636i \(0.942185\pi\)
\(152\) 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 −0.369354 0.929289i \(-0.620421\pi\)
0.620111 + 0.784514i \(0.287088\pi\)
\(164\) 0 0
\(165\) −2.01978 3.49837i −0.157240 0.272348i
\(166\) 0 0
\(167\) −18.6171 10.7486i −1.44063 0.831750i −0.442741 0.896650i \(-0.645994\pi\)
−0.997892 + 0.0648999i \(0.979327\pi\)
\(168\) 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 0.556381 0.830927i \(-0.312189\pi\)
−0.997795 + 0.0663766i \(0.978856\pi\)
\(174\) 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 −0.943829 0.330435i \(-0.892805\pi\)
0.758079 + 0.652162i \(0.226138\pi\)
\(180\) 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 0.951660 + 0.307153i \(0.0993762\pi\)
−0.209828 + 0.977738i \(0.567290\pi\)
\(192\) 0 0
\(193\) −23.0428 13.3038i −1.65866 0.957626i −0.973336 0.229386i \(-0.926328\pi\)
−0.685322 0.728240i \(-0.740338\pi\)
\(194\) 0 0
\(195\) −2.89075 + 7.89654i −0.207011 + 0.565483i
\(196\) 0 0
\(197\) 0.353583 + 0.204141i 0.0251917 + 0.0145445i 0.512543 0.858662i \(-0.328704\pi\)
−0.487351 + 0.873206i \(0.662037\pi\)
\(198\) 0 0
\(199\) 12.1998 + 21.1307i 0.864823 + 1.49792i 0.867223 + 0.497919i \(0.165902\pi\)
−0.00240070 + 0.999997i \(0.500764\pi\)
\(200\) 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 −0.894741 0.446585i \(-0.852640\pi\)
0.834125 + 0.551576i \(0.185973\pi\)
\(212\) 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 0.790916 0.611924i \(-0.209604\pi\)
−0.134484 + 0.990916i \(0.542938\pi\)
\(224\) 0 0
\(225\) 1.21969 + 2.11256i 0.0813125 + 0.140837i
\(226\) 0 0
\(227\) −6.98084 + 4.03039i −0.463334 + 0.267506i −0.713445 0.700711i \(-0.752866\pi\)
0.250111 + 0.968217i \(0.419533\pi\)
\(228\) 0 0
\(229\) 11.5715i 0.764666i 0.924025 + 0.382333i \(0.124879\pi\)
−0.924025 + 0.382333i \(0.875121\pi\)
\(230\) 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 \(-0.537154\pi\)
0.116459 0.993196i \(-0.462846\pi\)
\(240\) 0 0
\(241\) 6.86541 3.96374i 0.442240 0.255327i −0.262308 0.964984i \(-0.584483\pi\)
0.704547 + 0.709657i \(0.251150\pi\)
\(242\) 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 0.963361 + 0.268209i \(0.0864317\pi\)
−0.249405 + 0.968399i \(0.580235\pi\)
\(252\) 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 −0.112018 0.993706i \(-0.535731\pi\)
0.916584 0.399843i \(-0.130935\pi\)
\(258\) 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 −0.889503 0.456929i \(-0.848949\pi\)
0.840464 + 0.541868i \(0.182283\pi\)
\(264\) 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 0.882820 + 0.469712i \(0.155642\pi\)
−0.0346278 + 0.999400i \(0.511025\pi\)
\(270\) 0 0
\(271\) −20.3520 11.7502i −1.23629 0.713774i −0.267959 0.963430i \(-0.586349\pi\)
−0.968335 + 0.249656i \(0.919682\pi\)
\(272\) 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 0.817494 0.575936i \(-0.195362\pi\)
−0.907523 + 0.420003i \(0.862029\pi\)
\(278\) 0 0
\(279\) 16.6150 9.59270i 0.994716 0.574300i
\(280\) 0 0
\(281\) 24.6085i 1.46802i 0.679138 + 0.734011i \(0.262354\pi\)
−0.679138 + 0.734011i \(0.737646\pi\)
\(282\) 0 0
\(283\) 4.08444 7.07446i 0.242795 0.420533i −0.718715 0.695305i \(-0.755269\pi\)
0.961509 + 0.274772i \(0.0886025\pi\)
\(284\) 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 −0.677661 0.735374i \(-0.737006\pi\)
0.298022 + 0.954559i \(0.403673\pi\)
\(294\) 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 \(0.0543367\pi\)
−0.985465 + 0.169876i \(0.945663\pi\)
\(308\) 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 \(0.0276833\pi\)
−0.996221 + 0.0868601i \(0.972317\pi\)
\(318\) 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 0.145064 0.989422i \(-0.453661\pi\)
0.929397 + 0.369082i \(0.120328\pi\)
\(332\) 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 −0.964655 0.263514i \(-0.915118\pi\)
0.254118 0.967173i \(-0.418215\pi\)
\(348\) 0 0
\(349\) 10.7190 + 6.18860i 0.573773 + 0.331268i 0.758655 0.651493i \(-0.225857\pi\)
−0.184882 + 0.982761i \(0.559190\pi\)
\(350\) 0 0
\(351\) −0.809996 4.64422i −0.0432344 0.247890i
\(352\) 0 0
\(353\) 16.6978 + 9.64047i 0.888733 + 0.513110i 0.873528 0.486774i \(-0.161826\pi\)
0.0152053 + 0.999884i \(0.495160\pi\)
\(354\) 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 \(-0.752897\pi\)
0.713512 0.700643i \(-0.247103\pi\)
\(360\) 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 −0.946068 0.323968i \(-0.894983\pi\)
0.753599 + 0.657335i \(0.228316\pi\)
\(368\) 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 0.955576 + 0.294744i \(0.0952344\pi\)
−0.222532 + 0.974925i \(0.571432\pi\)
\(374\) 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 0.713652 0.700500i \(-0.247040\pi\)
−0.249825 + 0.968291i \(0.580373\pi\)
\(380\) 0 0
\(381\) −14.1761 24.5537i −0.726262 1.25792i
\(382\) 0 0
\(383\) −9.39811 + 5.42600i −0.480221 + 0.277256i −0.720509 0.693446i \(-0.756092\pi\)
0.240288 + 0.970702i \(0.422758\pi\)
\(384\) 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 0.162008 0.986789i \(-0.448203\pi\)
0.935589 + 0.353091i \(0.114870\pi\)
\(398\) 0 0
\(399\) 2.50445 + 4.33784i 0.125380 + 0.217164i
\(400\) 0 0
\(401\) 10.8377 + 6.25714i 0.541208 + 0.312467i 0.745568 0.666429i \(-0.232178\pi\)
−0.204360 + 0.978896i \(0.565511\pi\)
\(402\) 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 −0.366100 0.930575i \(-0.619307\pi\)
0.622852 + 0.782340i \(0.285974\pi\)
\(410\) 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 −0.700369 0.713781i \(-0.746981\pi\)
0.968337 + 0.249647i \(0.0803147\pi\)
\(420\) 0 0
\(421\) 36.6085i 1.78419i −0.451848 0.892095i \(-0.649235\pi\)
0.451848 0.892095i \(-0.350765\pi\)
\(422\) 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 0.225685 0.974200i \(-0.427538\pi\)
−0.730840 + 0.682549i \(0.760871\pi\)
\(432\) 0 0
\(433\) −4.50897 7.80977i −0.216687 0.375314i 0.737106 0.675777i \(-0.236192\pi\)
−0.953793 + 0.300464i \(0.902859\pi\)
\(434\) 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 −0.973801 0.227400i \(-0.926977\pi\)
0.683835 + 0.729637i \(0.260311\pi\)
\(440\) 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 −0.886611 0.462516i \(-0.846947\pi\)
−0.0427543 + 0.999086i \(0.513613\pi\)
\(450\) 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 0.266307 0.963888i \(-0.414197\pi\)
−0.701599 + 0.712572i \(0.747530\pi\)
\(458\) 0 0
\(459\) 0.452716 + 0.784127i 0.0211310 + 0.0365999i
\(460\) 0 0
\(461\) 10.2973 5.94516i 0.479594 0.276894i −0.240653 0.970611i \(-0.577362\pi\)
0.720247 + 0.693717i \(0.244028\pi\)
\(462\) 0 0
\(463\) 3.39726i 0.157884i 0.996879 + 0.0789420i \(0.0251542\pi\)
−0.996879 + 0.0789420i \(0.974846\pi\)
\(464\) 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 0.786827 0.617174i \(-0.211722\pi\)
−0.141075 + 0.989999i \(0.545056\pi\)
\(480\) 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 −0.715550 0.698562i \(-0.753824\pi\)
0.247197 + 0.968965i \(0.420490\pi\)
\(488\) 0 0
\(489\) 8.62166i 0.389885i
\(490\) 0 0
\(491\) −17.0259 + 29.4896i −0.768366 + 1.33085i 0.170082 + 0.985430i \(0.445597\pi\)
−0.938448 + 0.345419i \(0.887737\pi\)
\(492\) 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 \(-0.909102\pi\)
0.959503 0.281699i \(-0.0908979\pi\)
\(500\) 0 0
\(501\) −43.4196 + 25.0683i −1.93985 + 1.11997i
\(502\) 0 0
\(503\) 9.09433 + 15.7518i 0.405496 + 0.702340i 0.994379 0.105879i \(-0.0337655\pi\)
−0.588883 + 0.808218i \(0.700432\pi\)
\(504\) 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 −0.173923 0.984759i \(-0.555644\pi\)
−0.939788 + 0.341758i \(0.888978\pi\)
\(510\) 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 −0.746605 0.665268i \(-0.768317\pi\)
0.949441 + 0.313945i \(0.101651\pi\)
\(524\) 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 \(0.175606\pi\)
−0.851644 + 0.524120i \(0.824394\pi\)
\(542\) 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 0.439915 0.898039i \(-0.355009\pi\)
−0.557768 + 0.829997i \(0.688342\pi\)
\(558\) 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 −0.960005 0.279982i \(-0.909672\pi\)
0.237531 0.971380i \(-0.423662\pi\)
\(564\) 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 0.202001 + 0.979385i \(0.435256\pi\)
−0.949173 + 0.314755i \(0.898078\pi\)
\(570\) 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 \(0.125450\pi\)
−0.923337 + 0.383991i \(0.874550\pi\)
\(578\) 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 −0.999028 0.0440760i \(-0.985966\pi\)
−0.537685 0.843146i \(-0.680701\pi\)
\(588\) 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 \(-0.914933\pi\)
0.964502 0.264076i \(-0.0850671\pi\)
\(594\) 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 −0.784050 0.620698i \(-0.786849\pi\)
0.929565 + 0.368658i \(0.120183\pi\)
\(602\) 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 0.998394 0.0566544i \(-0.0180433\pi\)
−0.548261 + 0.836307i \(0.684710\pi\)
\(608\) 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 0.494347 0.869265i \(-0.335407\pi\)
−0.505632 + 0.862749i \(0.668741\pi\)
\(614\) 0 0
\(615\) −9.01652 15.6171i −0.363581 0.629741i
\(616\) 0 0
\(617\) −32.2150 + 18.5993i −1.29693 + 0.748781i −0.979872 0.199626i \(-0.936027\pi\)
−0.317055 + 0.948407i \(0.602694\pi\)
\(618\) 0 0
\(619\) 3.94911i 0.158728i −0.996846 0.0793641i \(-0.974711\pi\)
0.996846 0.0793641i \(-0.0252890\pi\)
\(620\) 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 0.206989 0.978343i \(-0.433634\pi\)
0.950765 + 0.309914i \(0.100300\pi\)
\(632\) 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 0.981827 + 0.189778i \(0.0607767\pi\)
−0.326561 + 0.945176i \(0.605890\pi\)
\(642\) 0 0
\(643\) 27.1643 15.6833i 1.07125 0.618489i 0.142730 0.989762i \(-0.454412\pi\)
0.928524 + 0.371273i \(0.121078\pi\)
\(644\) 0 0
\(645\) 14.0182i 0.551966i
\(646\) 0 0
\(647\) 9.79529 16.9659i 0.385092 0.667000i −0.606690 0.794939i \(-0.707503\pi\)
0.991782 + 0.127939i \(0.0408362\pi\)
\(648\) 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 −0.927182 0.374612i \(-0.877776\pi\)
0.788015 + 0.615657i \(0.211109\pi\)
\(654\) 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 0.626316 0.779570i \(-0.284562\pi\)
−0.988285 + 0.152621i \(0.951229\pi\)
\(660\) 0 0
\(661\) 14.5413 + 8.39540i 0.565590 + 0.326543i 0.755386 0.655280i \(-0.227449\pi\)
−0.189796 + 0.981823i \(0.560783\pi\)
\(662\) 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 −0.561912 0.827197i \(-0.689934\pi\)
0.997330 + 0.0730322i \(0.0232676\pi\)
\(674\) 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 −0.433056 0.901367i \(-0.642565\pi\)
0.564079 + 0.825721i \(0.309231\pi\)
\(684\) 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 0.272708 0.962097i \(-0.412081\pi\)
−0.696846 + 0.717220i \(0.745414\pi\)
\(692\) 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 −0.785727 0.618573i \(-0.787711\pi\)
0.142836 + 0.989746i \(0.454378\pi\)
\(710\) 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 −0.901872 0.432004i \(-0.857807\pi\)
0.0768099 0.997046i \(-0.475527\pi\)
\(720\) 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 \(-0.712992\pi\)
0.620307 0.784359i \(-0.287008\pi\)
\(734\) 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 0.264114 0.964492i \(-0.414921\pi\)
−0.703217 + 0.710975i \(0.748254\pi\)
\(740\) 0 0
\(741\) 44.5000 7.76123i 1.63475 0.285116i
\(742\) 0 0
\(743\) −13.8038 7.96961i −0.506411 0.292377i 0.224946 0.974371i \(-0.427779\pi\)
−0.731357 + 0.681995i \(0.761113\pi\)
\(744\) 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 −0.879533 0.475837i \(-0.842145\pi\)
0.851854 + 0.523780i \(0.175478\pi\)
\(752\) 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 0.00622310 + 0.999981i \(0.498019\pi\)
−0.869120 + 0.494601i \(0.835314\pi\)
\(758\) 0 0
\(759\) 0.432748i 0.0157078i
\(760\) 0 0
\(761\) −33.3805 + 19.2722i −1.21004 + 0.698618i −0.962768 0.270327i \(-0.912868\pi\)
−0.247274 + 0.968946i \(0.579535\pi\)
\(762\) 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 0.970099 0.242711i \(-0.0780366\pi\)
0.274856 + 0.961486i \(0.411370\pi\)
\(770\) 0 0
\(771\) −30.0817 52.1031i −1.08337 1.87645i
\(772\) 0 0
\(773\) 28.5396 16.4774i 1.02650 0.592650i 0.110519 0.993874i \(-0.464749\pi\)
0.915980 + 0.401224i \(0.131415\pi\)
\(774\) 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 −0.516567 0.856247i \(-0.672790\pi\)
0.483248 + 0.875483i \(0.339457\pi\)
\(788\) 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
\(795\)