Properties

Label 1456.2.r.p.417.1
Level $1456$
Weight $2$
Character 1456.417
Analytic conductor $11.626$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 417.1
Root \(-0.132804 - 0.230024i\) of defining polynomial
Character \(\chi\) \(=\) 1456.417
Dual form 1456.2.r.p.625.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31364 + 2.27529i) q^{3} +(1.45130 + 2.51373i) q^{5} +(1.29536 - 2.30696i) q^{7} +(-1.95130 - 3.37975i) q^{9} +O(q^{10})\) \(q+(-1.31364 + 2.27529i) q^{3} +(1.45130 + 2.51373i) q^{5} +(1.29536 - 2.30696i) q^{7} +(-1.95130 - 3.37975i) q^{9} +(1.01828 - 1.76372i) q^{11} +1.00000 q^{13} -7.62594 q^{15} +(-1.99933 + 3.46294i) q^{17} +(3.48105 + 6.02935i) q^{19} +(3.54736 + 5.97783i) q^{21} +(-0.313640 - 0.543240i) q^{23} +(-1.71254 + 2.96621i) q^{25} +2.37138 q^{27} +1.09606 q^{29} +(-5.21624 + 9.03479i) q^{31} +(2.67531 + 4.63378i) q^{33} +(7.67901 - 0.0919110i) q^{35} +(1.54268 + 2.67201i) q^{37} +(-1.31364 + 2.27529i) q^{39} -0.521150 q^{41} -0.329024 q^{43} +(5.66384 - 9.81006i) q^{45} +(5.27284 + 9.13283i) q^{47} +(-3.64409 - 5.97667i) q^{49} +(-5.25280 - 9.09812i) q^{51} +(-3.55950 + 6.16523i) q^{53} +5.91133 q^{55} -18.2914 q^{57} +(1.01828 - 1.76372i) q^{59} +(-1.20041 - 2.07917i) q^{61} +(-10.3246 + 0.123576i) q^{63} +(1.45130 + 2.51373i) q^{65} +(7.34709 - 12.7255i) q^{67} +1.64804 q^{69} -3.60141 q^{71} +(-1.48786 + 2.57706i) q^{73} +(-4.49933 - 7.79307i) q^{75} +(-2.74978 - 4.63378i) q^{77} +(-4.38075 - 7.58769i) q^{79} +(2.73876 - 4.74367i) q^{81} -12.8039 q^{83} -11.6065 q^{85} +(-1.43983 + 2.49386i) q^{87} +(1.34049 + 2.32180i) q^{89} +(1.29536 - 2.30696i) q^{91} +(-13.7045 - 23.7369i) q^{93} +(-10.1041 + 17.5008i) q^{95} -2.32902 q^{97} -7.94789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.31364 + 2.27529i −0.758430 + 1.31364i 0.185220 + 0.982697i \(0.440700\pi\)
−0.943651 + 0.330943i \(0.892633\pi\)
\(4\) 0 0
\(5\) 1.45130 + 2.51373i 0.649041 + 1.12417i 0.983352 + 0.181709i \(0.0581630\pi\)
−0.334311 + 0.942463i \(0.608504\pi\)
\(6\) 0 0
\(7\) 1.29536 2.30696i 0.489599 0.871948i
\(8\) 0 0
\(9\) −1.95130 3.37975i −0.650433 1.12658i
\(10\) 0 0
\(11\) 1.01828 1.76372i 0.307024 0.531780i −0.670686 0.741741i \(-0.734000\pi\)
0.977710 + 0.209961i \(0.0673336\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −7.62594 −1.96901
\(16\) 0 0
\(17\) −1.99933 + 3.46294i −0.484909 + 0.839887i −0.999850 0.0173386i \(-0.994481\pi\)
0.514941 + 0.857226i \(0.327814\pi\)
\(18\) 0 0
\(19\) 3.48105 + 6.02935i 0.798608 + 1.38323i 0.920523 + 0.390688i \(0.127763\pi\)
−0.121915 + 0.992540i \(0.538904\pi\)
\(20\) 0 0
\(21\) 3.54736 + 5.97783i 0.774098 + 1.30447i
\(22\) 0 0
\(23\) −0.313640 0.543240i −0.0653985 0.113273i 0.831472 0.555566i \(-0.187499\pi\)
−0.896871 + 0.442293i \(0.854165\pi\)
\(24\) 0 0
\(25\) −1.71254 + 2.96621i −0.342509 + 0.593243i
\(26\) 0 0
\(27\) 2.37138 0.456373
\(28\) 0 0
\(29\) 1.09606 0.203534 0.101767 0.994808i \(-0.467550\pi\)
0.101767 + 0.994808i \(0.467550\pi\)
\(30\) 0 0
\(31\) −5.21624 + 9.03479i −0.936864 + 1.62270i −0.165589 + 0.986195i \(0.552953\pi\)
−0.771275 + 0.636502i \(0.780381\pi\)
\(32\) 0 0
\(33\) 2.67531 + 4.63378i 0.465712 + 0.806637i
\(34\) 0 0
\(35\) 7.67901 0.0919110i 1.29799 0.0155358i
\(36\) 0 0
\(37\) 1.54268 + 2.67201i 0.253616 + 0.439275i 0.964519 0.264015i \(-0.0850468\pi\)
−0.710903 + 0.703290i \(0.751713\pi\)
\(38\) 0 0
\(39\) −1.31364 + 2.27529i −0.210351 + 0.364338i
\(40\) 0 0
\(41\) −0.521150 −0.0813900 −0.0406950 0.999172i \(-0.512957\pi\)
−0.0406950 + 0.999172i \(0.512957\pi\)
\(42\) 0 0
\(43\) −0.329024 −0.0501757 −0.0250879 0.999685i \(-0.507987\pi\)
−0.0250879 + 0.999685i \(0.507987\pi\)
\(44\) 0 0
\(45\) 5.66384 9.81006i 0.844316 1.46240i
\(46\) 0 0
\(47\) 5.27284 + 9.13283i 0.769123 + 1.33216i 0.938039 + 0.346530i \(0.112640\pi\)
−0.168916 + 0.985630i \(0.554027\pi\)
\(48\) 0 0
\(49\) −3.64409 5.97667i −0.520585 0.853810i
\(50\) 0 0
\(51\) −5.25280 9.09812i −0.735540 1.27399i
\(52\) 0 0
\(53\) −3.55950 + 6.16523i −0.488935 + 0.846860i −0.999919 0.0127302i \(-0.995948\pi\)
0.510984 + 0.859590i \(0.329281\pi\)
\(54\) 0 0
\(55\) 5.91133 0.797084
\(56\) 0 0
\(57\) −18.2914 −2.42275
\(58\) 0 0
\(59\) 1.01828 1.76372i 0.132569 0.229616i −0.792097 0.610395i \(-0.791011\pi\)
0.924666 + 0.380779i \(0.124344\pi\)
\(60\) 0 0
\(61\) −1.20041 2.07917i −0.153696 0.266210i 0.778887 0.627164i \(-0.215784\pi\)
−0.932584 + 0.360954i \(0.882451\pi\)
\(62\) 0 0
\(63\) −10.3246 + 0.123576i −1.30077 + 0.0155691i
\(64\) 0 0
\(65\) 1.45130 + 2.51373i 0.180012 + 0.311789i
\(66\) 0 0
\(67\) 7.34709 12.7255i 0.897589 1.55467i 0.0670226 0.997751i \(-0.478650\pi\)
0.830567 0.556919i \(-0.188017\pi\)
\(68\) 0 0
\(69\) 1.64804 0.198401
\(70\) 0 0
\(71\) −3.60141 −0.427409 −0.213704 0.976898i \(-0.568553\pi\)
−0.213704 + 0.976898i \(0.568553\pi\)
\(72\) 0 0
\(73\) −1.48786 + 2.57706i −0.174141 + 0.301622i −0.939864 0.341550i \(-0.889048\pi\)
0.765722 + 0.643171i \(0.222382\pi\)
\(74\) 0 0
\(75\) −4.49933 7.79307i −0.519538 0.899866i
\(76\) 0 0
\(77\) −2.74978 4.63378i −0.313366 0.528068i
\(78\) 0 0
\(79\) −4.38075 7.58769i −0.492873 0.853681i 0.507093 0.861891i \(-0.330720\pi\)
−0.999966 + 0.00820995i \(0.997387\pi\)
\(80\) 0 0
\(81\) 2.73876 4.74367i 0.304306 0.527074i
\(82\) 0 0
\(83\) −12.8039 −1.40541 −0.702703 0.711483i \(-0.748024\pi\)
−0.702703 + 0.711483i \(0.748024\pi\)
\(84\) 0 0
\(85\) −11.6065 −1.25890
\(86\) 0 0
\(87\) −1.43983 + 2.49386i −0.154366 + 0.267370i
\(88\) 0 0
\(89\) 1.34049 + 2.32180i 0.142092 + 0.246110i 0.928284 0.371872i \(-0.121284\pi\)
−0.786192 + 0.617982i \(0.787950\pi\)
\(90\) 0 0
\(91\) 1.29536 2.30696i 0.135790 0.241835i
\(92\) 0 0
\(93\) −13.7045 23.7369i −1.42109 2.46141i
\(94\) 0 0
\(95\) −10.1041 + 17.5008i −1.03666 + 1.79554i
\(96\) 0 0
\(97\) −2.32902 −0.236477 −0.118238 0.992985i \(-0.537725\pi\)
−0.118238 + 0.992985i \(0.537725\pi\)
\(98\) 0 0
\(99\) −7.94789 −0.798793
\(100\) 0 0
\(101\) −0.726620 + 1.25854i −0.0723014 + 0.125230i −0.899910 0.436077i \(-0.856368\pi\)
0.827608 + 0.561306i \(0.189701\pi\)
\(102\) 0 0
\(103\) −5.81765 10.0765i −0.573230 0.992864i −0.996231 0.0867346i \(-0.972357\pi\)
0.423001 0.906129i \(-0.360977\pi\)
\(104\) 0 0
\(105\) −9.87833 + 17.5927i −0.964026 + 1.71687i
\(106\) 0 0
\(107\) 9.81297 + 16.9966i 0.948656 + 1.64312i 0.748261 + 0.663405i \(0.230889\pi\)
0.200395 + 0.979715i \(0.435777\pi\)
\(108\) 0 0
\(109\) 0.553378 0.958479i 0.0530040 0.0918057i −0.838306 0.545200i \(-0.816454\pi\)
0.891310 + 0.453394i \(0.149787\pi\)
\(110\) 0 0
\(111\) −8.10613 −0.769400
\(112\) 0 0
\(113\) −1.09606 −0.103109 −0.0515545 0.998670i \(-0.516418\pi\)
−0.0515545 + 0.998670i \(0.516418\pi\)
\(114\) 0 0
\(115\) 0.910371 1.57681i 0.0848926 0.147038i
\(116\) 0 0
\(117\) −1.95130 3.37975i −0.180398 0.312458i
\(118\) 0 0
\(119\) 5.39901 + 9.09812i 0.494926 + 0.834024i
\(120\) 0 0
\(121\) 3.42620 + 5.93436i 0.311473 + 0.539487i
\(122\) 0 0
\(123\) 0.684604 1.18577i 0.0617286 0.106917i
\(124\) 0 0
\(125\) 4.57134 0.408873
\(126\) 0 0
\(127\) −5.18143 −0.459778 −0.229889 0.973217i \(-0.573836\pi\)
−0.229889 + 0.973217i \(0.573836\pi\)
\(128\) 0 0
\(129\) 0.432219 0.748626i 0.0380548 0.0659128i
\(130\) 0 0
\(131\) 5.28335 + 9.15103i 0.461609 + 0.799530i 0.999041 0.0437770i \(-0.0139391\pi\)
−0.537433 + 0.843307i \(0.680606\pi\)
\(132\) 0 0
\(133\) 18.4187 0.220455i 1.59710 0.0191159i
\(134\) 0 0
\(135\) 3.44159 + 5.96101i 0.296205 + 0.513042i
\(136\) 0 0
\(137\) 2.93589 5.08510i 0.250830 0.434450i −0.712925 0.701241i \(-0.752630\pi\)
0.963754 + 0.266791i \(0.0859632\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −27.7065 −2.33331
\(142\) 0 0
\(143\) 1.01828 1.76372i 0.0851530 0.147489i
\(144\) 0 0
\(145\) 1.59072 + 2.75520i 0.132102 + 0.228807i
\(146\) 0 0
\(147\) 18.3857 0.440185i 1.51643 0.0363058i
\(148\) 0 0
\(149\) 5.05271 + 8.75155i 0.413934 + 0.716955i 0.995316 0.0966760i \(-0.0308211\pi\)
−0.581382 + 0.813631i \(0.697488\pi\)
\(150\) 0 0
\(151\) −0.0938631 + 0.162576i −0.00763847 + 0.0132302i −0.869819 0.493370i \(-0.835765\pi\)
0.862181 + 0.506601i \(0.169098\pi\)
\(152\) 0 0
\(153\) 15.6052 1.26160
\(154\) 0 0
\(155\) −30.2813 −2.43225
\(156\) 0 0
\(157\) 6.03590 10.4545i 0.481717 0.834358i −0.518063 0.855343i \(-0.673347\pi\)
0.999780 + 0.0209844i \(0.00668003\pi\)
\(158\) 0 0
\(159\) −9.35180 16.1978i −0.741646 1.28457i
\(160\) 0 0
\(161\) −1.65951 + 0.0198629i −0.130788 + 0.00156541i
\(162\) 0 0
\(163\) 7.45678 + 12.9155i 0.584060 + 1.01162i 0.994992 + 0.0999554i \(0.0318700\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(164\) 0 0
\(165\) −7.76536 + 13.4500i −0.604532 + 1.04708i
\(166\) 0 0
\(167\) −5.05664 −0.391294 −0.195647 0.980674i \(-0.562681\pi\)
−0.195647 + 0.980674i \(0.562681\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 13.5851 23.5302i 1.03888 1.79940i
\(172\) 0 0
\(173\) 0.297807 + 0.515817i 0.0226419 + 0.0392169i 0.877124 0.480263i \(-0.159459\pi\)
−0.854482 + 0.519480i \(0.826126\pi\)
\(174\) 0 0
\(175\) 4.62457 + 7.79307i 0.349584 + 0.589101i
\(176\) 0 0
\(177\) 2.67531 + 4.63378i 0.201089 + 0.348296i
\(178\) 0 0
\(179\) 4.03832 6.99458i 0.301838 0.522799i −0.674714 0.738079i \(-0.735733\pi\)
0.976552 + 0.215280i \(0.0690664\pi\)
\(180\) 0 0
\(181\) 1.89324 0.140724 0.0703618 0.997522i \(-0.477585\pi\)
0.0703618 + 0.997522i \(0.477585\pi\)
\(182\) 0 0
\(183\) 6.30761 0.466272
\(184\) 0 0
\(185\) −4.47780 + 7.75577i −0.329214 + 0.570216i
\(186\) 0 0
\(187\) 4.07177 + 7.05251i 0.297757 + 0.515730i
\(188\) 0 0
\(189\) 3.07179 5.47068i 0.223440 0.397933i
\(190\) 0 0
\(191\) 1.85087 + 3.20580i 0.133924 + 0.231964i 0.925186 0.379514i \(-0.123909\pi\)
−0.791262 + 0.611478i \(0.790575\pi\)
\(192\) 0 0
\(193\) −6.79373 + 11.7671i −0.489024 + 0.847014i −0.999920 0.0126285i \(-0.995980\pi\)
0.510897 + 0.859642i \(0.329313\pi\)
\(194\) 0 0
\(195\) −7.62594 −0.546105
\(196\) 0 0
\(197\) −9.70258 −0.691280 −0.345640 0.938367i \(-0.612338\pi\)
−0.345640 + 0.938367i \(0.612338\pi\)
\(198\) 0 0
\(199\) 13.1360 22.7522i 0.931185 1.61286i 0.149885 0.988703i \(-0.452109\pi\)
0.781299 0.624156i \(-0.214557\pi\)
\(200\) 0 0
\(201\) 19.3029 + 33.4335i 1.36152 + 2.35822i
\(202\) 0 0
\(203\) 1.41979 2.52857i 0.0996500 0.177471i
\(204\) 0 0
\(205\) −0.756345 1.31003i −0.0528255 0.0914964i
\(206\) 0 0
\(207\) −1.22401 + 2.12005i −0.0850747 + 0.147354i
\(208\) 0 0
\(209\) 14.1788 0.980765
\(210\) 0 0
\(211\) −10.0338 −0.690758 −0.345379 0.938463i \(-0.612250\pi\)
−0.345379 + 0.938463i \(0.612250\pi\)
\(212\) 0 0
\(213\) 4.73096 8.19426i 0.324160 0.561461i
\(214\) 0 0
\(215\) −0.477513 0.827077i −0.0325661 0.0564062i
\(216\) 0 0
\(217\) 14.0860 + 23.7369i 0.956218 + 1.61137i
\(218\) 0 0
\(219\) −3.90903 6.77065i −0.264148 0.457518i
\(220\) 0 0
\(221\) −1.99933 + 3.46294i −0.134490 + 0.232943i
\(222\) 0 0
\(223\) −17.4961 −1.17163 −0.585813 0.810446i \(-0.699225\pi\)
−0.585813 + 0.810446i \(0.699225\pi\)
\(224\) 0 0
\(225\) 13.3667 0.891116
\(226\) 0 0
\(227\) −4.75815 + 8.24136i −0.315810 + 0.546998i −0.979609 0.200912i \(-0.935609\pi\)
0.663800 + 0.747910i \(0.268943\pi\)
\(228\) 0 0
\(229\) −10.5585 18.2878i −0.697725 1.20849i −0.969254 0.246064i \(-0.920863\pi\)
0.271529 0.962430i \(-0.412471\pi\)
\(230\) 0 0
\(231\) 14.1554 0.169428i 0.931357 0.0111475i
\(232\) 0 0
\(233\) −7.08938 12.2792i −0.464441 0.804435i 0.534735 0.845020i \(-0.320411\pi\)
−0.999176 + 0.0405847i \(0.987078\pi\)
\(234\) 0 0
\(235\) −15.3050 + 26.5090i −0.998385 + 1.72925i
\(236\) 0 0
\(237\) 23.0189 1.49524
\(238\) 0 0
\(239\) 16.5275 1.06907 0.534536 0.845145i \(-0.320486\pi\)
0.534536 + 0.845145i \(0.320486\pi\)
\(240\) 0 0
\(241\) 6.84450 11.8550i 0.440893 0.763649i −0.556863 0.830604i \(-0.687995\pi\)
0.997756 + 0.0669552i \(0.0213284\pi\)
\(242\) 0 0
\(243\) 10.7526 + 18.6240i 0.689777 + 1.19473i
\(244\) 0 0
\(245\) 9.73503 17.8342i 0.621948 1.13938i
\(246\) 0 0
\(247\) 3.48105 + 6.02935i 0.221494 + 0.383639i
\(248\) 0 0
\(249\) 16.8197 29.1325i 1.06590 1.84620i
\(250\) 0 0
\(251\) 14.6603 0.925349 0.462674 0.886528i \(-0.346890\pi\)
0.462674 + 0.886528i \(0.346890\pi\)
\(252\) 0 0
\(253\) −1.27750 −0.0803155
\(254\) 0 0
\(255\) 15.2468 26.4082i 0.954791 1.65375i
\(256\) 0 0
\(257\) 0.876387 + 1.51795i 0.0546675 + 0.0946869i 0.892064 0.451909i \(-0.149257\pi\)
−0.837397 + 0.546596i \(0.815923\pi\)
\(258\) 0 0
\(259\) 8.16254 0.0976985i 0.507195 0.00607069i
\(260\) 0 0
\(261\) −2.13875 3.70442i −0.132385 0.229298i
\(262\) 0 0
\(263\) 13.4708 23.3321i 0.830645 1.43872i −0.0668823 0.997761i \(-0.521305\pi\)
0.897527 0.440959i \(-0.145361\pi\)
\(264\) 0 0
\(265\) −20.6636 −1.26936
\(266\) 0 0
\(267\) −7.04370 −0.431067
\(268\) 0 0
\(269\) 11.0346 19.1124i 0.672789 1.16530i −0.304321 0.952570i \(-0.598430\pi\)
0.977110 0.212735i \(-0.0682371\pi\)
\(270\) 0 0
\(271\) −4.48105 7.76141i −0.272204 0.471472i 0.697222 0.716856i \(-0.254419\pi\)
−0.969426 + 0.245384i \(0.921086\pi\)
\(272\) 0 0
\(273\) 3.54736 + 5.97783i 0.214696 + 0.361795i
\(274\) 0 0
\(275\) 3.48770 + 6.04088i 0.210316 + 0.364279i
\(276\) 0 0
\(277\) 3.76463 6.52052i 0.226194 0.391780i −0.730483 0.682931i \(-0.760705\pi\)
0.956677 + 0.291151i \(0.0940382\pi\)
\(278\) 0 0
\(279\) 40.7138 2.43747
\(280\) 0 0
\(281\) 29.7762 1.77630 0.888151 0.459553i \(-0.151990\pi\)
0.888151 + 0.459553i \(0.151990\pi\)
\(282\) 0 0
\(283\) 0.150726 0.261064i 0.00895970 0.0155187i −0.861511 0.507739i \(-0.830481\pi\)
0.870470 + 0.492221i \(0.163815\pi\)
\(284\) 0 0
\(285\) −26.5463 45.9795i −1.57247 2.72359i
\(286\) 0 0
\(287\) −0.675076 + 1.20227i −0.0398485 + 0.0709678i
\(288\) 0 0
\(289\) 0.505347 + 0.875286i 0.0297263 + 0.0514874i
\(290\) 0 0
\(291\) 3.05950 5.29921i 0.179351 0.310645i
\(292\) 0 0
\(293\) −19.2471 −1.12443 −0.562214 0.826992i \(-0.690050\pi\)
−0.562214 + 0.826992i \(0.690050\pi\)
\(294\) 0 0
\(295\) 5.91133 0.344171
\(296\) 0 0
\(297\) 2.41474 4.18245i 0.140117 0.242690i
\(298\) 0 0
\(299\) −0.313640 0.543240i −0.0181383 0.0314164i
\(300\) 0 0
\(301\) −0.426204 + 0.759044i −0.0245660 + 0.0437506i
\(302\) 0 0
\(303\) −1.90903 3.30654i −0.109671 0.189956i
\(304\) 0 0
\(305\) 3.48430 6.03499i 0.199511 0.345562i
\(306\) 0 0
\(307\) 3.57779 0.204195 0.102098 0.994774i \(-0.467445\pi\)
0.102098 + 0.994774i \(0.467445\pi\)
\(308\) 0 0
\(309\) 30.5692 1.73902
\(310\) 0 0
\(311\) −11.9153 + 20.6379i −0.675655 + 1.17027i 0.300622 + 0.953743i \(0.402806\pi\)
−0.976277 + 0.216526i \(0.930527\pi\)
\(312\) 0 0
\(313\) 9.04068 + 15.6589i 0.511009 + 0.885094i 0.999919 + 0.0127596i \(0.00406161\pi\)
−0.488909 + 0.872335i \(0.662605\pi\)
\(314\) 0 0
\(315\) −15.2947 25.7738i −0.861758 1.45219i
\(316\) 0 0
\(317\) 13.7741 + 23.8574i 0.773630 + 1.33997i 0.935561 + 0.353164i \(0.114894\pi\)
−0.161931 + 0.986802i \(0.551772\pi\)
\(318\) 0 0
\(319\) 1.11610 1.93314i 0.0624897 0.108235i
\(320\) 0 0
\(321\) −51.5628 −2.87796
\(322\) 0 0
\(323\) −27.8391 −1.54901
\(324\) 0 0
\(325\) −1.71254 + 2.96621i −0.0949948 + 0.164536i
\(326\) 0 0
\(327\) 1.45388 + 2.51819i 0.0803997 + 0.139256i
\(328\) 0 0
\(329\) 27.8993 0.333930i 1.53814 0.0184101i
\(330\) 0 0
\(331\) −9.09069 15.7455i −0.499669 0.865453i 0.500331 0.865834i \(-0.333212\pi\)
−1.00000 0.000381757i \(0.999878\pi\)
\(332\) 0 0
\(333\) 6.02048 10.4278i 0.329920 0.571439i
\(334\) 0 0
\(335\) 42.6513 2.33029
\(336\) 0 0
\(337\) −17.1381 −0.933572 −0.466786 0.884370i \(-0.654588\pi\)
−0.466786 + 0.884370i \(0.654588\pi\)
\(338\) 0 0
\(339\) 1.43983 2.49386i 0.0782010 0.135448i
\(340\) 0 0
\(341\) 10.6232 + 18.3999i 0.575279 + 0.996412i
\(342\) 0 0
\(343\) −18.5083 + 0.664840i −0.999355 + 0.0358980i
\(344\) 0 0
\(345\) 2.39180 + 4.14272i 0.128770 + 0.223037i
\(346\) 0 0
\(347\) 11.1344 19.2853i 0.597725 1.03529i −0.395431 0.918496i \(-0.629405\pi\)
0.993156 0.116794i \(-0.0372619\pi\)
\(348\) 0 0
\(349\) 19.9368 1.06719 0.533595 0.845740i \(-0.320841\pi\)
0.533595 + 0.845740i \(0.320841\pi\)
\(350\) 0 0
\(351\) 2.37138 0.126575
\(352\) 0 0
\(353\) −11.4576 + 19.8451i −0.609825 + 1.05625i 0.381444 + 0.924392i \(0.375427\pi\)
−0.991269 + 0.131856i \(0.957906\pi\)
\(354\) 0 0
\(355\) −5.22673 9.05296i −0.277406 0.480481i
\(356\) 0 0
\(357\) −27.7932 + 0.332661i −1.47097 + 0.0176063i
\(358\) 0 0
\(359\) 13.6157 + 23.5831i 0.718610 + 1.24467i 0.961551 + 0.274628i \(0.0885547\pi\)
−0.242940 + 0.970041i \(0.578112\pi\)
\(360\) 0 0
\(361\) −14.7354 + 25.5225i −0.775548 + 1.34329i
\(362\) 0 0
\(363\) −18.0032 −0.944923
\(364\) 0 0
\(365\) −8.63735 −0.452099
\(366\) 0 0
\(367\) −5.42822 + 9.40195i −0.283351 + 0.490778i −0.972208 0.234119i \(-0.924779\pi\)
0.688857 + 0.724897i \(0.258113\pi\)
\(368\) 0 0
\(369\) 1.01692 + 1.76136i 0.0529388 + 0.0916926i
\(370\) 0 0
\(371\) 9.61210 + 16.1978i 0.499035 + 0.840948i
\(372\) 0 0
\(373\) 1.18572 + 2.05373i 0.0613943 + 0.106338i 0.895089 0.445888i \(-0.147112\pi\)
−0.833695 + 0.552226i \(0.813779\pi\)
\(374\) 0 0
\(375\) −6.00510 + 10.4011i −0.310102 + 0.537112i
\(376\) 0 0
\(377\) 1.09606 0.0564501
\(378\) 0 0
\(379\) 29.2197 1.50092 0.750458 0.660918i \(-0.229833\pi\)
0.750458 + 0.660918i \(0.229833\pi\)
\(380\) 0 0
\(381\) 6.80654 11.7893i 0.348709 0.603982i
\(382\) 0 0
\(383\) −1.53297 2.65519i −0.0783313 0.135674i 0.824199 0.566301i \(-0.191626\pi\)
−0.902530 + 0.430627i \(0.858293\pi\)
\(384\) 0 0
\(385\) 7.65729 13.6372i 0.390252 0.695015i
\(386\) 0 0
\(387\) 0.642025 + 1.11202i 0.0326360 + 0.0565271i
\(388\) 0 0
\(389\) −13.8705 + 24.0244i −0.703261 + 1.21808i 0.264054 + 0.964508i \(0.414940\pi\)
−0.967315 + 0.253576i \(0.918393\pi\)
\(390\) 0 0
\(391\) 2.50828 0.126849
\(392\) 0 0
\(393\) −27.7617 −1.40039
\(394\) 0 0
\(395\) 12.7156 22.0240i 0.639790 1.10815i
\(396\) 0 0
\(397\) −8.61559 14.9226i −0.432404 0.748946i 0.564676 0.825313i \(-0.309001\pi\)
−0.997080 + 0.0763669i \(0.975668\pi\)
\(398\) 0 0
\(399\) −23.6939 + 42.1974i −1.18618 + 2.11251i
\(400\) 0 0
\(401\) −8.32201 14.4142i −0.415582 0.719808i 0.579908 0.814682i \(-0.303089\pi\)
−0.995489 + 0.0948737i \(0.969755\pi\)
\(402\) 0 0
\(403\) −5.21624 + 9.03479i −0.259839 + 0.450055i
\(404\) 0 0
\(405\) 15.8990 0.790029
\(406\) 0 0
\(407\) 6.28355 0.311464
\(408\) 0 0
\(409\) 6.81689 11.8072i 0.337073 0.583828i −0.646807 0.762653i \(-0.723896\pi\)
0.983881 + 0.178825i \(0.0572296\pi\)
\(410\) 0 0
\(411\) 7.71340 + 13.3600i 0.380474 + 0.659000i
\(412\) 0 0
\(413\) −2.74978 4.63378i −0.135308 0.228013i
\(414\) 0 0
\(415\) −18.5822 32.1854i −0.912167 1.57992i
\(416\) 0 0
\(417\) −5.25456 + 9.10116i −0.257317 + 0.445686i
\(418\) 0 0
\(419\) 10.8502 0.530066 0.265033 0.964239i \(-0.414617\pi\)
0.265033 + 0.964239i \(0.414617\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 20.5778 35.6418i 1.00053 1.73296i
\(424\) 0 0
\(425\) −6.84788 11.8609i −0.332171 0.575337i
\(426\) 0 0
\(427\) −6.35150 + 0.0760220i −0.307371 + 0.00367896i
\(428\) 0 0
\(429\) 2.67531 + 4.63378i 0.129165 + 0.223721i
\(430\) 0 0
\(431\) 0.604764 1.04748i 0.0291304 0.0504554i −0.851093 0.525016i \(-0.824060\pi\)
0.880223 + 0.474560i \(0.157393\pi\)
\(432\) 0 0
\(433\) −5.56422 −0.267399 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(434\) 0 0
\(435\) −8.35851 −0.400760
\(436\) 0 0
\(437\) 2.18359 3.78209i 0.104455 0.180922i
\(438\) 0 0
\(439\) −9.85960 17.0773i −0.470573 0.815057i 0.528860 0.848709i \(-0.322619\pi\)
−0.999434 + 0.0336522i \(0.989286\pi\)
\(440\) 0 0
\(441\) −13.0889 + 23.9784i −0.623282 + 1.14183i
\(442\) 0 0
\(443\) 11.1155 + 19.2526i 0.528113 + 0.914719i 0.999463 + 0.0327726i \(0.0104337\pi\)
−0.471350 + 0.881946i \(0.656233\pi\)
\(444\) 0 0
\(445\) −3.89091 + 6.73926i −0.184447 + 0.319471i
\(446\) 0 0
\(447\) −26.5498 −1.25576
\(448\) 0 0
\(449\) 18.4579 0.871082 0.435541 0.900169i \(-0.356557\pi\)
0.435541 + 0.900169i \(0.356557\pi\)
\(450\) 0 0
\(451\) −0.530678 + 0.919161i −0.0249886 + 0.0432816i
\(452\) 0 0
\(453\) −0.246605 0.427132i −0.0115865 0.0200684i
\(454\) 0 0
\(455\) 7.67901 0.0919110i 0.359997 0.00430886i
\(456\) 0 0
\(457\) 14.9910 + 25.9651i 0.701248 + 1.21460i 0.968029 + 0.250840i \(0.0807067\pi\)
−0.266781 + 0.963757i \(0.585960\pi\)
\(458\) 0 0
\(459\) −4.74118 + 8.21197i −0.221299 + 0.383302i
\(460\) 0 0
\(461\) 29.1498 1.35764 0.678821 0.734304i \(-0.262491\pi\)
0.678821 + 0.734304i \(0.262491\pi\)
\(462\) 0 0
\(463\) −1.55900 −0.0724530 −0.0362265 0.999344i \(-0.511534\pi\)
−0.0362265 + 0.999344i \(0.511534\pi\)
\(464\) 0 0
\(465\) 39.7787 68.8988i 1.84470 3.19511i
\(466\) 0 0
\(467\) 6.21156 + 10.7587i 0.287437 + 0.497855i 0.973197 0.229972i \(-0.0738635\pi\)
−0.685760 + 0.727827i \(0.740530\pi\)
\(468\) 0 0
\(469\) −19.8401 33.4335i −0.916132 1.54382i
\(470\) 0 0
\(471\) 15.8580 + 27.4668i 0.730697 + 1.26561i
\(472\) 0 0
\(473\) −0.335039 + 0.580305i −0.0154051 + 0.0266825i
\(474\) 0 0
\(475\) −23.8458 −1.09412
\(476\) 0 0
\(477\) 27.7826 1.27208
\(478\) 0 0
\(479\) 18.0279 31.2252i 0.823716 1.42672i −0.0791811 0.996860i \(-0.525231\pi\)
0.902897 0.429857i \(-0.141436\pi\)
\(480\) 0 0
\(481\) 1.54268 + 2.67201i 0.0703404 + 0.121833i
\(482\) 0 0
\(483\) 2.13480 3.80196i 0.0971369 0.172995i
\(484\) 0 0
\(485\) −3.38011 5.85453i −0.153483 0.265840i
\(486\) 0 0
\(487\) 3.65002 6.32202i 0.165398 0.286478i −0.771398 0.636352i \(-0.780442\pi\)
0.936797 + 0.349874i \(0.113776\pi\)
\(488\) 0 0
\(489\) −39.1821 −1.77188
\(490\) 0 0
\(491\) −4.49178 −0.202711 −0.101356 0.994850i \(-0.532318\pi\)
−0.101356 + 0.994850i \(0.532318\pi\)
\(492\) 0 0
\(493\) −2.19139 + 3.79560i −0.0986954 + 0.170945i
\(494\) 0 0
\(495\) −11.5348 19.9788i −0.518450 0.897981i
\(496\) 0 0
\(497\) −4.66512 + 8.30829i −0.209259 + 0.372678i
\(498\) 0 0
\(499\) 5.68369 + 9.84443i 0.254437 + 0.440697i 0.964742 0.263196i \(-0.0847766\pi\)
−0.710306 + 0.703893i \(0.751443\pi\)
\(500\) 0 0
\(501\) 6.64260 11.5053i 0.296770 0.514020i
\(502\) 0 0
\(503\) −17.1080 −0.762806 −0.381403 0.924409i \(-0.624559\pi\)
−0.381403 + 0.924409i \(0.624559\pi\)
\(504\) 0 0
\(505\) −4.21818 −0.187706
\(506\) 0 0
\(507\) −1.31364 + 2.27529i −0.0583408 + 0.101049i
\(508\) 0 0
\(509\) −1.64142 2.84303i −0.0727547 0.126015i 0.827353 0.561682i \(-0.189846\pi\)
−0.900108 + 0.435667i \(0.856512\pi\)
\(510\) 0 0
\(511\) 4.01784 + 6.77065i 0.177739 + 0.299516i
\(512\) 0 0
\(513\) 8.25490 + 14.2979i 0.364463 + 0.631268i
\(514\) 0 0
\(515\) 16.8863 29.2479i 0.744100 1.28882i
\(516\) 0 0
\(517\) 21.4770 0.944555
\(518\) 0 0
\(519\) −1.56485 −0.0686891
\(520\) 0 0
\(521\) 2.38530 4.13147i 0.104502 0.181003i −0.809033 0.587764i \(-0.800008\pi\)
0.913535 + 0.406761i \(0.133342\pi\)
\(522\) 0 0
\(523\) 12.7562 + 22.0944i 0.557789 + 0.966119i 0.997681 + 0.0680682i \(0.0216835\pi\)
−0.439892 + 0.898051i \(0.644983\pi\)
\(524\) 0 0
\(525\) −23.8065 + 0.284943i −1.03900 + 0.0124359i
\(526\) 0 0
\(527\) −20.8580 36.1271i −0.908588 1.57372i
\(528\) 0 0
\(529\) 11.3033 19.5778i 0.491446 0.851210i
\(530\) 0 0
\(531\) −7.94789 −0.344909
\(532\) 0 0
\(533\) −0.521150 −0.0225735
\(534\) 0 0
\(535\) −28.4831 + 49.3342i −1.23143 + 2.13290i
\(536\) 0 0
\(537\) 10.6098 + 18.3767i 0.457847 + 0.793013i
\(538\) 0 0
\(539\) −14.2519 + 0.341214i −0.613871 + 0.0146971i
\(540\) 0 0
\(541\) 8.25784 + 14.3030i 0.355032 + 0.614934i 0.987123 0.159960i \(-0.0511366\pi\)
−0.632091 + 0.774894i \(0.717803\pi\)
\(542\) 0 0
\(543\) −2.48704 + 4.30768i −0.106729 + 0.184860i
\(544\) 0 0
\(545\) 3.21247 0.137607
\(546\) 0 0
\(547\) −23.3317 −0.997591 −0.498796 0.866720i \(-0.666224\pi\)
−0.498796 + 0.866720i \(0.666224\pi\)
\(548\) 0 0
\(549\) −4.68471 + 8.11416i −0.199939 + 0.346304i
\(550\) 0 0
\(551\) 3.81545 + 6.60855i 0.162544 + 0.281534i
\(552\) 0 0
\(553\) −23.1791 + 0.277434i −0.985676 + 0.0117977i
\(554\) 0 0
\(555\) −11.7644 20.3766i −0.499372 0.864938i
\(556\) 0 0
\(557\) 10.0235 17.3613i 0.424711 0.735621i −0.571682 0.820475i \(-0.693709\pi\)
0.996393 + 0.0848540i \(0.0270424\pi\)
\(558\) 0 0
\(559\) −0.329024 −0.0139162
\(560\) 0 0
\(561\) −21.3953 −0.903312
\(562\) 0 0
\(563\) −20.2642 + 35.0986i −0.854034 + 1.47923i 0.0235047 + 0.999724i \(0.492518\pi\)
−0.877539 + 0.479506i \(0.840816\pi\)
\(564\) 0 0
\(565\) −1.59072 2.75520i −0.0669219 0.115912i
\(566\) 0 0
\(567\) −7.39576 12.4629i −0.310593 0.523394i
\(568\) 0 0
\(569\) 10.7252 + 18.5766i 0.449623 + 0.778770i 0.998361 0.0572245i \(-0.0182251\pi\)
−0.548739 + 0.835994i \(0.684892\pi\)
\(570\) 0 0
\(571\) −5.47793 + 9.48806i −0.229244 + 0.397063i −0.957584 0.288153i \(-0.906959\pi\)
0.728340 + 0.685216i \(0.240292\pi\)
\(572\) 0 0
\(573\) −9.72552 −0.406289
\(574\) 0 0
\(575\) 2.14849 0.0895982
\(576\) 0 0
\(577\) −17.3708 + 30.0870i −0.723154 + 1.25254i 0.236575 + 0.971613i \(0.423975\pi\)
−0.959729 + 0.280927i \(0.909358\pi\)
\(578\) 0 0
\(579\) −17.8490 30.9154i −0.741781 1.28480i
\(580\) 0 0
\(581\) −16.5856 + 29.5380i −0.688086 + 1.22544i
\(582\) 0 0
\(583\) 7.24915 + 12.5559i 0.300229 + 0.520012i
\(584\) 0 0
\(585\) 5.66384 9.81006i 0.234171 0.405596i
\(586\) 0 0
\(587\) 22.8463 0.942967 0.471483 0.881875i \(-0.343719\pi\)
0.471483 + 0.881875i \(0.343719\pi\)
\(588\) 0 0
\(589\) −72.6320 −2.99275
\(590\) 0 0
\(591\) 12.7457 22.0762i 0.524288 0.908094i
\(592\) 0 0
\(593\) −8.79676 15.2364i −0.361240 0.625686i 0.626925 0.779079i \(-0.284313\pi\)
−0.988165 + 0.153394i \(0.950980\pi\)
\(594\) 0 0
\(595\) −15.0346 + 26.7757i −0.616359 + 1.09770i
\(596\) 0 0
\(597\) 34.5119 + 59.7764i 1.41248 + 2.44648i
\(598\) 0 0
\(599\) 15.5036 26.8531i 0.633461 1.09719i −0.353378 0.935481i \(-0.614967\pi\)
0.986839 0.161706i \(-0.0516997\pi\)
\(600\) 0 0
\(601\) −1.43754 −0.0586385 −0.0293193 0.999570i \(-0.509334\pi\)
−0.0293193 + 0.999570i \(0.509334\pi\)
\(602\) 0 0
\(603\) −57.3455 −2.33529
\(604\) 0 0
\(605\) −9.94490 + 17.2251i −0.404318 + 0.700299i
\(606\) 0 0
\(607\) −16.5085 28.5936i −0.670061 1.16058i −0.977887 0.209136i \(-0.932935\pi\)
0.307826 0.951443i \(-0.400399\pi\)
\(608\) 0 0
\(609\) 3.88813 + 6.55208i 0.157555 + 0.265503i
\(610\) 0 0
\(611\) 5.27284 + 9.13283i 0.213316 + 0.369475i
\(612\) 0 0
\(613\) 21.5829 37.3826i 0.871723 1.50987i 0.0115102 0.999934i \(-0.496336\pi\)
0.860213 0.509935i \(-0.170331\pi\)
\(614\) 0 0
\(615\) 3.97426 0.160258
\(616\) 0 0
\(617\) 2.45772 0.0989441 0.0494721 0.998776i \(-0.484246\pi\)
0.0494721 + 0.998776i \(0.484246\pi\)
\(618\) 0 0
\(619\) 18.8894 32.7175i 0.759231 1.31503i −0.184013 0.982924i \(-0.558909\pi\)
0.943243 0.332102i \(-0.107758\pi\)
\(620\) 0 0
\(621\) −0.743761 1.28823i −0.0298461 0.0516949i
\(622\) 0 0
\(623\) 7.09271 0.0848936i 0.284163 0.00340119i
\(624\) 0 0
\(625\) 15.1971 + 26.3222i 0.607884 + 1.05289i
\(626\) 0 0
\(627\) −18.6258 + 32.2608i −0.743842 + 1.28837i
\(628\) 0 0
\(629\) −12.3374 −0.491922
\(630\) 0 0
\(631\) 28.4828 1.13388 0.566942 0.823758i \(-0.308126\pi\)
0.566942 + 0.823758i \(0.308126\pi\)
\(632\) 0 0
\(633\) 13.1809 22.8299i 0.523892 0.907407i
\(634\) 0 0
\(635\) −7.51981 13.0247i −0.298415 0.516869i
\(636\) 0 0
\(637\) −3.64409 5.97667i −0.144384 0.236804i
\(638\) 0 0
\(639\) 7.02743 + 12.1719i 0.278001 + 0.481512i
\(640\) 0 0
\(641\) 13.5961 23.5492i 0.537014 0.930136i −0.462049 0.886854i \(-0.652886\pi\)
0.999063 0.0432812i \(-0.0137811\pi\)
\(642\) 0 0
\(643\) 37.1664 1.46570 0.732849 0.680391i \(-0.238190\pi\)
0.732849 + 0.680391i \(0.238190\pi\)
\(644\) 0 0
\(645\) 2.50912 0.0987965
\(646\) 0 0
\(647\) 9.41593 16.3089i 0.370178 0.641168i −0.619414 0.785064i \(-0.712630\pi\)
0.989593 + 0.143896i \(0.0459632\pi\)
\(648\) 0 0
\(649\) −2.07380 3.59192i −0.0814036 0.140995i
\(650\) 0 0
\(651\) −72.5123 + 0.867909i −2.84198 + 0.0340161i
\(652\) 0 0
\(653\) 13.0092 + 22.5326i 0.509090 + 0.881770i 0.999945 + 0.0105286i \(0.00335143\pi\)
−0.490854 + 0.871242i \(0.663315\pi\)
\(654\) 0 0
\(655\) −15.3355 + 26.5618i −0.599206 + 1.03786i
\(656\) 0 0
\(657\) 11.6131 0.453069
\(658\) 0 0
\(659\) 33.3339 1.29851 0.649253 0.760573i \(-0.275082\pi\)
0.649253 + 0.760573i \(0.275082\pi\)
\(660\) 0 0
\(661\) −3.14920 + 5.45458i −0.122490 + 0.212159i −0.920749 0.390156i \(-0.872421\pi\)
0.798259 + 0.602314i \(0.205755\pi\)
\(662\) 0 0
\(663\) −5.25280 9.09812i −0.204002 0.353342i
\(664\) 0 0
\(665\) 27.2852 + 45.9795i 1.05807 + 1.78301i
\(666\) 0 0
\(667\) −0.343769 0.595426i −0.0133108 0.0230550i
\(668\) 0 0
\(669\) 22.9836 39.8088i 0.888597 1.53910i
\(670\) 0 0
\(671\) −4.88941 −0.188754
\(672\) 0 0
\(673\) 18.3188 0.706137 0.353068 0.935598i \(-0.385138\pi\)
0.353068 + 0.935598i \(0.385138\pi\)
\(674\) 0 0
\(675\) −4.06110 + 7.03403i −0.156312 + 0.270740i
\(676\) 0 0
\(677\) −12.1696 21.0783i −0.467715 0.810106i 0.531604 0.846993i \(-0.321589\pi\)
−0.999319 + 0.0368866i \(0.988256\pi\)
\(678\) 0 0
\(679\) −3.01692 + 5.37296i −0.115779 + 0.206195i
\(680\) 0 0
\(681\) −12.5010 21.6524i −0.479039 0.829720i
\(682\) 0 0
\(683\) 5.88409 10.1916i 0.225149 0.389969i −0.731215 0.682147i \(-0.761047\pi\)
0.956364 + 0.292178i \(0.0943799\pi\)
\(684\) 0 0
\(685\) 17.0434 0.651195
\(686\) 0 0
\(687\) 55.4802 2.11670
\(688\) 0 0
\(689\) −3.55950 + 6.16523i −0.135606 + 0.234877i
\(690\) 0 0
\(691\) 0.588923 + 1.02004i 0.0224037 + 0.0388043i 0.877010 0.480472i \(-0.159535\pi\)
−0.854606 + 0.519277i \(0.826201\pi\)
\(692\) 0 0
\(693\) −10.2954 + 18.3354i −0.391089 + 0.696506i
\(694\) 0 0
\(695\) 5.80520 + 10.0549i 0.220204 + 0.381404i
\(696\) 0 0
\(697\) 1.04195 1.80471i 0.0394668 0.0683584i
\(698\) 0 0
\(699\) 37.2516 1.40898
\(700\) 0 0
\(701\) −31.2867 −1.18168 −0.590841 0.806788i \(-0.701204\pi\)
−0.590841 + 0.806788i \(0.701204\pi\)
\(702\) 0 0
\(703\) −10.7403 + 18.6028i −0.405079 + 0.701617i
\(704\) 0 0
\(705\) −40.2104 69.6464i −1.51441 2.62304i
\(706\) 0 0
\(707\) 1.96217 + 3.30654i 0.0737950 + 0.124355i
\(708\) 0 0
\(709\) −7.68738 13.3149i −0.288706 0.500053i 0.684795 0.728735i \(-0.259892\pi\)
−0.973501 + 0.228682i \(0.926558\pi\)
\(710\) 0 0
\(711\) −17.0963 + 29.6117i −0.641162 + 1.11053i
\(712\) 0 0
\(713\) 6.54409 0.245078
\(714\) 0 0
\(715\) 5.91133 0.221071
\(716\) 0 0
\(717\) −21.7111 + 37.6048i −0.810817 + 1.40438i
\(718\) 0 0
\(719\) −5.57087 9.64904i −0.207759 0.359848i 0.743250 0.669014i \(-0.233283\pi\)
−0.951008 + 0.309166i \(0.899950\pi\)
\(720\) 0 0
\(721\) −30.7819 + 0.368433i −1.14638 + 0.0137211i
\(722\) 0 0
\(723\) 17.9824 + 31.1465i 0.668773 + 1.15835i
\(724\) 0 0
\(725\) −1.87706 + 3.25116i −0.0697121 + 0.120745i
\(726\) 0 0
\(727\) 6.24735 0.231702 0.115851 0.993267i \(-0.463041\pi\)
0.115851 + 0.993267i \(0.463041\pi\)
\(728\) 0 0
\(729\) −40.0674 −1.48398
\(730\) 0 0
\(731\) 0.657828 1.13939i 0.0243307 0.0421419i
\(732\) 0 0
\(733\) −15.4834 26.8181i −0.571894 0.990550i −0.996371 0.0851111i \(-0.972875\pi\)
0.424477 0.905439i \(-0.360458\pi\)
\(734\) 0 0
\(735\) 27.7897 + 45.5777i 1.02504 + 1.68116i
\(736\) 0 0
\(737\) −14.9628 25.9163i −0.551162 0.954641i
\(738\) 0 0
\(739\) 1.16872 2.02429i 0.0429921 0.0744646i −0.843729 0.536770i \(-0.819644\pi\)
0.886721 + 0.462305i \(0.152978\pi\)
\(740\) 0 0
\(741\) −18.2914 −0.671951
\(742\) 0 0
\(743\) −24.3612 −0.893726 −0.446863 0.894603i \(-0.647459\pi\)
−0.446863 + 0.894603i \(0.647459\pi\)
\(744\) 0 0
\(745\) −14.6660 + 25.4022i −0.537321 + 0.930666i
\(746\) 0 0
\(747\) 24.9842 + 43.2739i 0.914123 + 1.58331i
\(748\) 0 0
\(749\) 51.9216 0.621457i 1.89718 0.0227075i
\(750\) 0 0
\(751\) −6.01266 10.4142i −0.219405 0.380021i 0.735221 0.677827i \(-0.237078\pi\)
−0.954626 + 0.297806i \(0.903745\pi\)
\(752\) 0 0
\(753\) −19.2583 + 33.3564i −0.701813 + 1.21558i
\(754\) 0 0
\(755\) −0.544894 −0.0198307
\(756\) 0 0
\(757\) 25.9905 0.944641 0.472321 0.881427i \(-0.343416\pi\)
0.472321 + 0.881427i \(0.343416\pi\)
\(758\) 0 0
\(759\) 1.67817 2.90667i 0.0609137 0.105506i
\(760\) 0 0
\(761\) −6.66350 11.5415i −0.241552 0.418380i 0.719605 0.694384i \(-0.244323\pi\)
−0.961156 + 0.276004i \(0.910990\pi\)
\(762\) 0 0
\(763\) −1.49435 2.51819i −0.0540990 0.0911647i
\(764\) 0 0
\(765\) 22.6478 + 39.2271i 0.818833 + 1.41826i
\(766\) 0 0
\(767\) 1.01828 1.76372i 0.0367680 0.0636841i
\(768\) 0 0
\(769\) 9.24486 0.333378 0.166689 0.986010i \(-0.446692\pi\)
0.166689 + 0.986010i \(0.446692\pi\)
\(770\) 0 0
\(771\) −4.60503 −0.165846
\(772\) 0 0
\(773\) 5.07097 8.78317i 0.182390 0.315909i −0.760304 0.649568i \(-0.774950\pi\)
0.942694 + 0.333659i \(0.108283\pi\)
\(774\) 0 0
\(775\) −17.8661 30.9450i −0.641768 1.11158i
\(776\) 0 0
\(777\) −10.5003 + 18.7005i −0.376698 + 0.670876i
\(778\) 0 0
\(779\) −1.81415 3.14220i −0.0649987 0.112581i
\(780\) 0 0
\(781\) −3.66725 + 6.35186i −0.131225 + 0.227288i
\(782\) 0 0
\(783\) 2.59919 0.0928873
\(784\) 0 0
\(785\) 35.0396 1.25062
\(786\) 0 0
\(787\) 22.6411 39.2156i 0.807070 1.39789i −0.107815 0.994171i \(-0.534386\pi\)
0.914885 0.403715i \(-0.132281\pi\)
\(788\) 0 0
\(789\) 35.3916 + 61.3000i 1.25997 + 2.18234i
\(790\) 0 0
\(791\) −1.41979 + 2.52857i −0.0504821 + 0.0899056i
\(792\) 0 0
\(793\) −1.20041 2.07917i −0.0426277 0.0738334i
\(794\) 0 0
\(795\) 27.1445 47.0157i 0.962718 1.66748i
\(796\) 0 0
\(797\) 27.0784 0.959165