Properties

Label 420.2.bh.b.341.1
Level $420$
Weight $2$
Character 420.341
Analytic conductor $3.354$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.bh (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.35371688489\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.29471584693248.1
Defining polynomial: \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 341.1
Root \(-1.31611 + 1.12599i\) of defining polynomial
Character \(\chi\) \(=\) 420.341
Dual form 420.2.bh.b.101.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63319 - 0.576792i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73439 + 1.99797i) q^{7} +(2.33462 + 1.88402i) q^{9} +O(q^{10})\) \(q+(-1.63319 - 0.576792i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73439 + 1.99797i) q^{7} +(2.33462 + 1.88402i) q^{9} +(3.38064 - 1.95181i) q^{11} -6.06329i q^{13} +(-1.31611 + 1.12599i) q^{15} +(-1.53296 - 2.65516i) q^{17} +(-2.94930 - 1.70278i) q^{19} +(3.98500 - 2.26269i) q^{21} +(-2.48871 - 1.43686i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.72620 - 4.42356i) q^{27} -7.97997i q^{29} +(-5.63161 + 3.25141i) q^{31} +(-6.64702 + 1.23776i) q^{33} +(0.863098 + 2.50101i) q^{35} +(-0.0654987 + 0.113447i) q^{37} +(-3.49726 + 9.90252i) q^{39} +12.3654 q^{41} +4.43247 q^{43} +(2.79892 - 1.07983i) q^{45} +(5.02960 - 8.71153i) q^{47} +(-0.983778 - 6.93053i) q^{49} +(0.972138 + 5.22058i) q^{51} +(-4.64119 + 2.67959i) q^{53} -3.90363i q^{55} +(3.83462 + 4.48210i) q^{57} +(-1.28860 - 2.23193i) q^{59} +(7.44930 + 4.30086i) q^{61} +(-7.81337 + 1.39688i) q^{63} +(-5.25097 - 3.03165i) q^{65} +(7.99884 + 13.8544i) q^{67} +(3.23578 + 3.78214i) q^{69} -3.63245i q^{71} +(-6.72468 + 3.88250i) q^{73} +(0.317079 + 1.70278i) q^{75} +(-1.96368 + 10.1396i) q^{77} +(-1.22311 + 2.11848i) q^{79} +(1.90093 + 8.79696i) q^{81} -7.63648 q^{83} -3.06592 q^{85} +(-4.60278 + 13.0328i) q^{87} +(-4.11874 + 7.13387i) q^{89} +(12.1143 + 10.5161i) q^{91} +(11.0729 - 2.06191i) q^{93} +(-2.94930 + 1.70278i) q^{95} -5.74985i q^{97} +(11.5698 + 1.81245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(241\) \(281\) \(337\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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
\(3\) −1.63319 0.576792i −0.942923 0.333011i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −1.73439 + 1.99797i −0.655538 + 0.755162i
\(8\) 0 0
\(9\) 2.33462 + 1.88402i 0.778208 + 0.628007i
\(10\) 0 0
\(11\) 3.38064 1.95181i 1.01930 0.588494i 0.105400 0.994430i \(-0.466388\pi\)
0.913902 + 0.405936i \(0.133054\pi\)
\(12\) 0 0
\(13\) 6.06329i 1.68166i −0.541303 0.840828i \(-0.682069\pi\)
0.541303 0.840828i \(-0.317931\pi\)
\(14\) 0 0
\(15\) −1.31611 + 1.12599i −0.339819 + 0.290729i
\(16\) 0 0
\(17\) −1.53296 2.65516i −0.371797 0.643971i 0.618045 0.786143i \(-0.287925\pi\)
−0.989842 + 0.142171i \(0.954592\pi\)
\(18\) 0 0
\(19\) −2.94930 1.70278i −0.676616 0.390645i 0.121963 0.992535i \(-0.461081\pi\)
−0.798579 + 0.601890i \(0.794415\pi\)
\(20\) 0 0
\(21\) 3.98500 2.26269i 0.869599 0.493759i
\(22\) 0 0
\(23\) −2.48871 1.43686i −0.518933 0.299606i 0.217565 0.976046i \(-0.430189\pi\)
−0.736498 + 0.676440i \(0.763522\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −2.72620 4.42356i −0.524657 0.851314i
\(28\) 0 0
\(29\) 7.97997i 1.48184i −0.671591 0.740922i \(-0.734389\pi\)
0.671591 0.740922i \(-0.265611\pi\)
\(30\) 0 0
\(31\) −5.63161 + 3.25141i −1.01147 + 0.583971i −0.911621 0.411032i \(-0.865168\pi\)
−0.0998461 + 0.995003i \(0.531835\pi\)
\(32\) 0 0
\(33\) −6.64702 + 1.23776i −1.15710 + 0.215466i
\(34\) 0 0
\(35\) 0.863098 + 2.50101i 0.145890 + 0.422748i
\(36\) 0 0
\(37\) −0.0654987 + 0.113447i −0.0107679 + 0.0186506i −0.871359 0.490646i \(-0.836761\pi\)
0.860591 + 0.509296i \(0.170094\pi\)
\(38\) 0 0
\(39\) −3.49726 + 9.90252i −0.560009 + 1.58567i
\(40\) 0 0
\(41\) 12.3654 1.93116 0.965579 0.260108i \(-0.0837583\pi\)
0.965579 + 0.260108i \(0.0837583\pi\)
\(42\) 0 0
\(43\) 4.43247 0.675945 0.337972 0.941156i \(-0.390259\pi\)
0.337972 + 0.941156i \(0.390259\pi\)
\(44\) 0 0
\(45\) 2.79892 1.07983i 0.417239 0.160972i
\(46\) 0 0
\(47\) 5.02960 8.71153i 0.733643 1.27071i −0.221674 0.975121i \(-0.571152\pi\)
0.955316 0.295586i \(-0.0955148\pi\)
\(48\) 0 0
\(49\) −0.983778 6.93053i −0.140540 0.990075i
\(50\) 0 0
\(51\) 0.972138 + 5.22058i 0.136127 + 0.731028i
\(52\) 0 0
\(53\) −4.64119 + 2.67959i −0.637516 + 0.368070i −0.783657 0.621194i \(-0.786648\pi\)
0.146141 + 0.989264i \(0.453315\pi\)
\(54\) 0 0
\(55\) 3.90363i 0.526365i
\(56\) 0 0
\(57\) 3.83462 + 4.48210i 0.507908 + 0.593668i
\(58\) 0 0
\(59\) −1.28860 2.23193i −0.167762 0.290572i 0.769871 0.638200i \(-0.220321\pi\)
−0.937633 + 0.347628i \(0.886987\pi\)
\(60\) 0 0
\(61\) 7.44930 + 4.30086i 0.953785 + 0.550668i 0.894255 0.447558i \(-0.147706\pi\)
0.0595306 + 0.998226i \(0.481040\pi\)
\(62\) 0 0
\(63\) −7.81337 + 1.39688i −0.984392 + 0.175990i
\(64\) 0 0
\(65\) −5.25097 3.03165i −0.651302 0.376030i
\(66\) 0 0
\(67\) 7.99884 + 13.8544i 0.977213 + 1.69258i 0.672429 + 0.740162i \(0.265251\pi\)
0.304785 + 0.952421i \(0.401415\pi\)
\(68\) 0 0
\(69\) 3.23578 + 3.78214i 0.389542 + 0.455316i
\(70\) 0 0
\(71\) 3.63245i 0.431093i −0.976494 0.215547i \(-0.930847\pi\)
0.976494 0.215547i \(-0.0691533\pi\)
\(72\) 0 0
\(73\) −6.72468 + 3.88250i −0.787064 + 0.454412i −0.838928 0.544242i \(-0.816817\pi\)
0.0518638 + 0.998654i \(0.483484\pi\)
\(74\) 0 0
\(75\) 0.317079 + 1.70278i 0.0366131 + 0.196620i
\(76\) 0 0
\(77\) −1.96368 + 10.1396i −0.223783 + 1.15552i
\(78\) 0 0
\(79\) −1.22311 + 2.11848i −0.137610 + 0.238348i −0.926591 0.376069i \(-0.877275\pi\)
0.788981 + 0.614417i \(0.210609\pi\)
\(80\) 0 0
\(81\) 1.90093 + 8.79696i 0.211214 + 0.977440i
\(82\) 0 0
\(83\) −7.63648 −0.838213 −0.419106 0.907937i \(-0.637657\pi\)
−0.419106 + 0.907937i \(0.637657\pi\)
\(84\) 0 0
\(85\) −3.06592 −0.332545
\(86\) 0 0
\(87\) −4.60278 + 13.0328i −0.493470 + 1.39726i
\(88\) 0 0
\(89\) −4.11874 + 7.13387i −0.436586 + 0.756189i −0.997424 0.0717367i \(-0.977146\pi\)
0.560838 + 0.827926i \(0.310479\pi\)
\(90\) 0 0
\(91\) 12.1143 + 10.5161i 1.26992 + 1.10239i
\(92\) 0 0
\(93\) 11.0729 2.06191i 1.14820 0.213810i
\(94\) 0 0
\(95\) −2.94930 + 1.70278i −0.302592 + 0.174702i
\(96\) 0 0
\(97\) 5.74985i 0.583809i −0.956447 0.291904i \(-0.905711\pi\)
0.956447 0.291904i \(-0.0942889\pi\)
\(98\) 0 0
\(99\) 11.5698 + 1.81245i 1.16281 + 0.182158i
\(100\) 0 0
\(101\) −4.54502 7.87220i −0.452246 0.783313i 0.546279 0.837603i \(-0.316044\pi\)
−0.998525 + 0.0542901i \(0.982710\pi\)
\(102\) 0 0
\(103\) −0.853234 0.492615i −0.0840717 0.0485388i 0.457375 0.889274i \(-0.348790\pi\)
−0.541446 + 0.840735i \(0.682123\pi\)
\(104\) 0 0
\(105\) 0.0329582 4.58246i 0.00321640 0.447202i
\(106\) 0 0
\(107\) −1.11849 0.645758i −0.108128 0.0624278i 0.444961 0.895550i \(-0.353218\pi\)
−0.553089 + 0.833122i \(0.686551\pi\)
\(108\) 0 0
\(109\) 3.68547 + 6.38342i 0.353004 + 0.611421i 0.986774 0.162101i \(-0.0518269\pi\)
−0.633770 + 0.773521i \(0.718494\pi\)
\(110\) 0 0
\(111\) 0.172407 0.147502i 0.0163642 0.0140002i
\(112\) 0 0
\(113\) 4.52778i 0.425938i 0.977059 + 0.212969i \(0.0683133\pi\)
−0.977059 + 0.212969i \(0.931687\pi\)
\(114\) 0 0
\(115\) −2.48871 + 1.43686i −0.232074 + 0.133988i
\(116\) 0 0
\(117\) 11.4234 14.1555i 1.05609 1.30868i
\(118\) 0 0
\(119\) 7.96368 + 1.54228i 0.730030 + 0.141381i
\(120\) 0 0
\(121\) 2.11916 3.67050i 0.192651 0.333681i
\(122\) 0 0
\(123\) −20.1951 7.13229i −1.82093 0.643097i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −0.700855 −0.0621908 −0.0310954 0.999516i \(-0.509900\pi\)
−0.0310954 + 0.999516i \(0.509900\pi\)
\(128\) 0 0
\(129\) −7.23906 2.55661i −0.637364 0.225097i
\(130\) 0 0
\(131\) −2.66028 + 4.60774i −0.232430 + 0.402580i −0.958523 0.285016i \(-0.908001\pi\)
0.726093 + 0.687597i \(0.241334\pi\)
\(132\) 0 0
\(133\) 8.51735 2.93933i 0.738548 0.254873i
\(134\) 0 0
\(135\) −5.19401 + 0.149178i −0.447029 + 0.0128392i
\(136\) 0 0
\(137\) 3.39919 1.96252i 0.290412 0.167670i −0.347715 0.937600i \(-0.613042\pi\)
0.638128 + 0.769930i \(0.279709\pi\)
\(138\) 0 0
\(139\) 16.1726i 1.37174i −0.727724 0.685870i \(-0.759422\pi\)
0.727724 0.685870i \(-0.240578\pi\)
\(140\) 0 0
\(141\) −13.2390 + 11.3265i −1.11493 + 0.953868i
\(142\) 0 0
\(143\) −11.8344 20.4978i −0.989645 1.71411i
\(144\) 0 0
\(145\) −6.91086 3.98999i −0.573915 0.331350i
\(146\) 0 0
\(147\) −2.39077 + 11.8863i −0.197188 + 0.980366i
\(148\) 0 0
\(149\) 17.4366 + 10.0670i 1.42846 + 0.824721i 0.996999 0.0774116i \(-0.0246655\pi\)
0.431459 + 0.902132i \(0.357999\pi\)
\(150\) 0 0
\(151\) −2.38980 4.13926i −0.194479 0.336848i 0.752250 0.658877i \(-0.228968\pi\)
−0.946730 + 0.322029i \(0.895635\pi\)
\(152\) 0 0
\(153\) 1.42350 9.08693i 0.115083 0.734635i
\(154\) 0 0
\(155\) 6.50282i 0.522319i
\(156\) 0 0
\(157\) 6.62784 3.82658i 0.528959 0.305395i −0.211633 0.977349i \(-0.567878\pi\)
0.740592 + 0.671955i \(0.234545\pi\)
\(158\) 0 0
\(159\) 9.12551 1.69929i 0.723700 0.134762i
\(160\) 0 0
\(161\) 7.18721 2.48030i 0.566431 0.195475i
\(162\) 0 0
\(163\) 4.23749 7.33954i 0.331906 0.574877i −0.650980 0.759095i \(-0.725642\pi\)
0.982885 + 0.184218i \(0.0589751\pi\)
\(164\) 0 0
\(165\) −2.25158 + 6.37537i −0.175285 + 0.496322i
\(166\) 0 0
\(167\) 20.5669 1.59152 0.795759 0.605614i \(-0.207072\pi\)
0.795759 + 0.605614i \(0.207072\pi\)
\(168\) 0 0
\(169\) −23.7635 −1.82796
\(170\) 0 0
\(171\) −3.67743 9.53190i −0.281220 0.728922i
\(172\) 0 0
\(173\) −8.30340 + 14.3819i −0.631296 + 1.09344i 0.355991 + 0.934489i \(0.384143\pi\)
−0.987287 + 0.158948i \(0.949190\pi\)
\(174\) 0 0
\(175\) 2.59749 + 0.503041i 0.196352 + 0.0380263i
\(176\) 0 0
\(177\) 0.817179 + 4.38842i 0.0614229 + 0.329854i
\(178\) 0 0
\(179\) 0.336240 0.194128i 0.0251318 0.0145098i −0.487381 0.873189i \(-0.662048\pi\)
0.512513 + 0.858679i \(0.328715\pi\)
\(180\) 0 0
\(181\) 20.6789i 1.53705i 0.639820 + 0.768524i \(0.279009\pi\)
−0.639820 + 0.768524i \(0.720991\pi\)
\(182\) 0 0
\(183\) −9.68543 11.3208i −0.715968 0.836859i
\(184\) 0 0
\(185\) 0.0654987 + 0.113447i 0.00481556 + 0.00834079i
\(186\) 0 0
\(187\) −10.3648 5.98410i −0.757947 0.437601i
\(188\) 0 0
\(189\) 13.5664 + 2.22531i 0.986812 + 0.161868i
\(190\) 0 0
\(191\) −15.2933 8.82961i −1.10659 0.638888i −0.168644 0.985677i \(-0.553939\pi\)
−0.937943 + 0.346789i \(0.887272\pi\)
\(192\) 0 0
\(193\) 10.6903 + 18.5161i 0.769505 + 1.33282i 0.937832 + 0.347090i \(0.112830\pi\)
−0.168327 + 0.985731i \(0.553837\pi\)
\(194\) 0 0
\(195\) 6.82720 + 7.97997i 0.488906 + 0.571458i
\(196\) 0 0
\(197\) 22.5070i 1.60356i −0.597619 0.801780i \(-0.703886\pi\)
0.597619 0.801780i \(-0.296114\pi\)
\(198\) 0 0
\(199\) −8.48532 + 4.89900i −0.601509 + 0.347281i −0.769635 0.638484i \(-0.779562\pi\)
0.168126 + 0.985765i \(0.446228\pi\)
\(200\) 0 0
\(201\) −5.07253 27.2405i −0.357789 1.92140i
\(202\) 0 0
\(203\) 15.9438 + 13.8404i 1.11903 + 0.971405i
\(204\) 0 0
\(205\) 6.18272 10.7088i 0.431820 0.747935i
\(206\) 0 0
\(207\) −3.10314 8.04332i −0.215683 0.559049i
\(208\) 0 0
\(209\) −13.2940 −0.919568
\(210\) 0 0
\(211\) −1.96291 −0.135132 −0.0675660 0.997715i \(-0.521523\pi\)
−0.0675660 + 0.997715i \(0.521523\pi\)
\(212\) 0 0
\(213\) −2.09517 + 5.93249i −0.143559 + 0.406488i
\(214\) 0 0
\(215\) 2.21623 3.83863i 0.151146 0.261792i
\(216\) 0 0
\(217\) 3.27118 16.8910i 0.222062 1.14664i
\(218\) 0 0
\(219\) 13.2221 2.46212i 0.893465 0.166374i
\(220\) 0 0
\(221\) −16.0990 + 9.29478i −1.08294 + 0.625234i
\(222\) 0 0
\(223\) 1.78864i 0.119776i 0.998205 + 0.0598882i \(0.0190744\pi\)
−0.998205 + 0.0598882i \(0.980926\pi\)
\(224\) 0 0
\(225\) 0.464299 2.96385i 0.0309532 0.197590i
\(226\) 0 0
\(227\) 13.7981 + 23.8990i 0.915813 + 1.58623i 0.805707 + 0.592315i \(0.201786\pi\)
0.110106 + 0.993920i \(0.464881\pi\)
\(228\) 0 0
\(229\) −8.37613 4.83596i −0.553510 0.319569i 0.197026 0.980398i \(-0.436872\pi\)
−0.750537 + 0.660829i \(0.770205\pi\)
\(230\) 0 0
\(231\) 9.05553 15.4273i 0.595810 1.01504i
\(232\) 0 0
\(233\) −0.516767 0.298355i −0.0338545 0.0195459i 0.482977 0.875633i \(-0.339555\pi\)
−0.516832 + 0.856087i \(0.672889\pi\)
\(234\) 0 0
\(235\) −5.02960 8.71153i −0.328095 0.568277i
\(236\) 0 0
\(237\) 3.21949 2.75441i 0.209128 0.178918i
\(238\) 0 0
\(239\) 8.90983i 0.576329i −0.957581 0.288165i \(-0.906955\pi\)
0.957581 0.288165i \(-0.0930450\pi\)
\(240\) 0 0
\(241\) 1.82543 1.05391i 0.117586 0.0678886i −0.440053 0.897972i \(-0.645040\pi\)
0.557640 + 0.830083i \(0.311707\pi\)
\(242\) 0 0
\(243\) 1.96943 15.4635i 0.126339 0.991987i
\(244\) 0 0
\(245\) −6.49390 2.61329i −0.414880 0.166957i
\(246\) 0 0
\(247\) −10.3245 + 17.8825i −0.656930 + 1.13784i
\(248\) 0 0
\(249\) 12.4718 + 4.40466i 0.790370 + 0.279134i
\(250\) 0 0
\(251\) 29.8229 1.88241 0.941204 0.337840i \(-0.109696\pi\)
0.941204 + 0.337840i \(0.109696\pi\)
\(252\) 0 0
\(253\) −11.2179 −0.705266
\(254\) 0 0
\(255\) 5.00723 + 1.76839i 0.313565 + 0.110741i
\(256\) 0 0
\(257\) −6.78489 + 11.7518i −0.423230 + 0.733055i −0.996253 0.0864836i \(-0.972437\pi\)
0.573024 + 0.819539i \(0.305770\pi\)
\(258\) 0 0
\(259\) −0.113064 0.327626i −0.00702543 0.0203577i
\(260\) 0 0
\(261\) 15.0344 18.6302i 0.930608 1.15318i
\(262\) 0 0
\(263\) 10.5291 6.07897i 0.649252 0.374846i −0.138918 0.990304i \(-0.544362\pi\)
0.788169 + 0.615458i \(0.211029\pi\)
\(264\) 0 0
\(265\) 5.35918i 0.329212i
\(266\) 0 0
\(267\) 10.8415 9.27532i 0.663486 0.567640i
\(268\) 0 0
\(269\) −11.2201 19.4338i −0.684101 1.18490i −0.973718 0.227756i \(-0.926861\pi\)
0.289617 0.957143i \(-0.406472\pi\)
\(270\) 0 0
\(271\) −7.19179 4.15218i −0.436870 0.252227i 0.265399 0.964139i \(-0.414496\pi\)
−0.702269 + 0.711912i \(0.747830\pi\)
\(272\) 0 0
\(273\) −13.7193 24.1622i −0.830332 1.46237i
\(274\) 0 0
\(275\) −3.38064 1.95181i −0.203860 0.117699i
\(276\) 0 0
\(277\) −3.02848 5.24547i −0.181963 0.315170i 0.760586 0.649238i \(-0.224912\pi\)
−0.942549 + 0.334068i \(0.891579\pi\)
\(278\) 0 0
\(279\) −19.2734 3.01925i −1.15387 0.180758i
\(280\) 0 0
\(281\) 17.5771i 1.04856i 0.851545 + 0.524282i \(0.175666\pi\)
−0.851545 + 0.524282i \(0.824334\pi\)
\(282\) 0 0
\(283\) 7.10845 4.10407i 0.422554 0.243961i −0.273616 0.961839i \(-0.588220\pi\)
0.696169 + 0.717878i \(0.254886\pi\)
\(284\) 0 0
\(285\) 5.79892 1.07983i 0.343498 0.0639637i
\(286\) 0 0
\(287\) −21.4465 + 24.7058i −1.26595 + 1.45834i
\(288\) 0 0
\(289\) 3.80008 6.58193i 0.223534 0.387172i
\(290\) 0 0
\(291\) −3.31647 + 9.39060i −0.194415 + 0.550487i
\(292\) 0 0
\(293\) 3.88610 0.227028 0.113514 0.993536i \(-0.463789\pi\)
0.113514 + 0.993536i \(0.463789\pi\)
\(294\) 0 0
\(295\) −2.57721 −0.150051
\(296\) 0 0
\(297\) −17.8503 9.63343i −1.03578 0.558988i
\(298\) 0 0
\(299\) −8.71210 + 15.0898i −0.503834 + 0.872666i
\(300\) 0 0
\(301\) −7.68763 + 8.85594i −0.443108 + 0.510448i
\(302\) 0 0
\(303\) 2.88226 + 15.4783i 0.165581 + 0.889207i
\(304\) 0 0
\(305\) 7.44930 4.30086i 0.426546 0.246266i
\(306\) 0 0
\(307\) 0.119756i 0.00683482i −0.999994 0.00341741i \(-0.998912\pi\)
0.999994 0.00341741i \(-0.00108780\pi\)
\(308\) 0 0
\(309\) 1.10936 + 1.29667i 0.0631092 + 0.0737651i
\(310\) 0 0
\(311\) 6.57207 + 11.3832i 0.372668 + 0.645480i 0.989975 0.141243i \(-0.0451097\pi\)
−0.617307 + 0.786722i \(0.711776\pi\)
\(312\) 0 0
\(313\) 20.1517 + 11.6346i 1.13904 + 0.657625i 0.946192 0.323604i \(-0.104895\pi\)
0.192847 + 0.981229i \(0.438228\pi\)
\(314\) 0 0
\(315\) −2.69695 + 7.46502i −0.151956 + 0.420606i
\(316\) 0 0
\(317\) −30.0933 17.3744i −1.69021 0.975841i −0.954344 0.298709i \(-0.903444\pi\)
−0.735861 0.677132i \(-0.763223\pi\)
\(318\) 0 0
\(319\) −15.5754 26.9774i −0.872056 1.51045i
\(320\) 0 0
\(321\) 1.45423 + 1.69978i 0.0811674 + 0.0948725i
\(322\) 0 0
\(323\) 10.4412i 0.580962i
\(324\) 0 0
\(325\) −5.25097 + 3.03165i −0.291271 + 0.168166i
\(326\) 0 0
\(327\) −2.33717 12.5511i −0.129246 0.694077i
\(328\) 0 0
\(329\) 8.68208 + 25.1582i 0.478659 + 1.38702i
\(330\) 0 0
\(331\) 12.8024 22.1744i 0.703684 1.21882i −0.263481 0.964665i \(-0.584871\pi\)
0.967165 0.254151i \(-0.0817961\pi\)
\(332\) 0 0
\(333\) −0.366651 + 0.141455i −0.0200924 + 0.00775169i
\(334\) 0 0
\(335\) 15.9977 0.874046
\(336\) 0 0
\(337\) 26.5502 1.44628 0.723140 0.690702i \(-0.242698\pi\)
0.723140 + 0.690702i \(0.242698\pi\)
\(338\) 0 0
\(339\) 2.61159 7.39473i 0.141842 0.401627i
\(340\) 0 0
\(341\) −12.6923 + 21.9837i −0.687327 + 1.19048i
\(342\) 0 0
\(343\) 15.5532 + 10.0547i 0.839796 + 0.542902i
\(344\) 0 0
\(345\) 4.89331 0.911197i 0.263447 0.0490572i
\(346\) 0 0
\(347\) 16.6519 9.61397i 0.893920 0.516105i 0.0186975 0.999825i \(-0.494048\pi\)
0.875223 + 0.483720i \(0.160715\pi\)
\(348\) 0 0
\(349\) 1.40475i 0.0751943i −0.999293 0.0375972i \(-0.988030\pi\)
0.999293 0.0375972i \(-0.0119704\pi\)
\(350\) 0 0
\(351\) −26.8213 + 16.5297i −1.43162 + 0.882292i
\(352\) 0 0
\(353\) 9.43705 + 16.3454i 0.502283 + 0.869980i 0.999997 + 0.00263867i \(0.000839917\pi\)
−0.497713 + 0.867342i \(0.665827\pi\)
\(354\) 0 0
\(355\) −3.14580 1.81623i −0.166962 0.0963953i
\(356\) 0 0
\(357\) −12.1166 7.11222i −0.641281 0.376419i
\(358\) 0 0
\(359\) −19.1592 11.0615i −1.01118 0.583806i −0.0996440 0.995023i \(-0.531770\pi\)
−0.911537 + 0.411217i \(0.865104\pi\)
\(360\) 0 0
\(361\) −3.70108 6.41046i −0.194794 0.337392i
\(362\) 0 0
\(363\) −5.57811 + 4.77230i −0.292775 + 0.250481i
\(364\) 0 0
\(365\) 7.76499i 0.406438i
\(366\) 0 0
\(367\) −11.3631 + 6.56047i −0.593147 + 0.342454i −0.766341 0.642434i \(-0.777925\pi\)
0.173194 + 0.984888i \(0.444591\pi\)
\(368\) 0 0
\(369\) 28.8687 + 23.2968i 1.50284 + 1.21278i
\(370\) 0 0
\(371\) 2.69589 13.9204i 0.139964 0.722712i
\(372\) 0 0
\(373\) −7.38003 + 12.7826i −0.382123 + 0.661857i −0.991366 0.131127i \(-0.958140\pi\)
0.609242 + 0.792984i \(0.291474\pi\)
\(374\) 0 0
\(375\) 1.63319 + 0.576792i 0.0843376 + 0.0297854i
\(376\) 0 0
\(377\) −48.3849 −2.49195
\(378\) 0 0
\(379\) 29.9980 1.54089 0.770447 0.637505i \(-0.220033\pi\)
0.770447 + 0.637505i \(0.220033\pi\)
\(380\) 0 0
\(381\) 1.14463 + 0.404247i 0.0586411 + 0.0207102i
\(382\) 0 0
\(383\) 7.72052 13.3723i 0.394500 0.683294i −0.598537 0.801095i \(-0.704251\pi\)
0.993037 + 0.117801i \(0.0375844\pi\)
\(384\) 0 0
\(385\) 7.79934 + 6.77042i 0.397491 + 0.345052i
\(386\) 0 0
\(387\) 10.3481 + 8.35086i 0.526025 + 0.424498i
\(388\) 0 0
\(389\) 7.53666 4.35129i 0.382124 0.220619i −0.296618 0.954996i \(-0.595859\pi\)
0.678742 + 0.734377i \(0.262525\pi\)
\(390\) 0 0
\(391\) 8.81059i 0.445570i
\(392\) 0 0
\(393\) 7.00245 5.99089i 0.353227 0.302201i
\(394\) 0 0
\(395\) 1.22311 + 2.11848i 0.0615411 + 0.106592i
\(396\) 0 0
\(397\) 23.3904 + 13.5044i 1.17393 + 0.677768i 0.954602 0.297883i \(-0.0962806\pi\)
0.219327 + 0.975651i \(0.429614\pi\)
\(398\) 0 0
\(399\) −15.6058 0.112241i −0.781269 0.00561909i
\(400\) 0 0
\(401\) −4.30215 2.48385i −0.214839 0.124037i 0.388719 0.921356i \(-0.372918\pi\)
−0.603558 + 0.797319i \(0.706251\pi\)
\(402\) 0 0
\(403\) 19.7143 + 34.1461i 0.982037 + 1.70094i
\(404\) 0 0
\(405\) 8.56885 + 2.75223i 0.425790 + 0.136759i
\(406\) 0 0
\(407\) 0.511365i 0.0253474i
\(408\) 0 0
\(409\) −7.00387 + 4.04369i −0.346319 + 0.199947i −0.663063 0.748564i \(-0.730744\pi\)
0.316744 + 0.948511i \(0.397410\pi\)
\(410\) 0 0
\(411\) −6.68349 + 1.24455i −0.329672 + 0.0613891i
\(412\) 0 0
\(413\) 6.69427 + 1.29644i 0.329403 + 0.0637937i
\(414\) 0 0
\(415\) −3.81824 + 6.61339i −0.187430 + 0.324638i
\(416\) 0 0
\(417\) −9.32820 + 26.4129i −0.456804 + 1.29345i
\(418\) 0 0
\(419\) 7.60294 0.371428 0.185714 0.982604i \(-0.440540\pi\)
0.185714 + 0.982604i \(0.440540\pi\)
\(420\) 0 0
\(421\) −4.43892 −0.216340 −0.108170 0.994132i \(-0.534499\pi\)
−0.108170 + 0.994132i \(0.534499\pi\)
\(422\) 0 0
\(423\) 28.1549 10.8623i 1.36894 0.528141i
\(424\) 0 0
\(425\) −1.53296 + 2.65516i −0.0743594 + 0.128794i
\(426\) 0 0
\(427\) −21.5130 + 7.42413i −1.04109 + 0.359279i
\(428\) 0 0
\(429\) 7.50490 + 40.3029i 0.362340 + 1.94584i
\(430\) 0 0
\(431\) −4.24065 + 2.44834i −0.204265 + 0.117932i −0.598643 0.801016i \(-0.704293\pi\)
0.394378 + 0.918948i \(0.370960\pi\)
\(432\) 0 0
\(433\) 18.6390i 0.895732i 0.894101 + 0.447866i \(0.147816\pi\)
−0.894101 + 0.447866i \(0.852184\pi\)
\(434\) 0 0
\(435\) 8.98536 + 10.5025i 0.430815 + 0.503558i
\(436\) 0 0
\(437\) 4.89331 + 8.47547i 0.234079 + 0.405437i
\(438\) 0 0
\(439\) −2.87038 1.65722i −0.136996 0.0790946i 0.429936 0.902860i \(-0.358536\pi\)
−0.566932 + 0.823765i \(0.691870\pi\)
\(440\) 0 0
\(441\) 10.7605 18.0336i 0.512405 0.858744i
\(442\) 0 0
\(443\) 0.707683 + 0.408581i 0.0336231 + 0.0194123i 0.516717 0.856156i \(-0.327154\pi\)
−0.483094 + 0.875568i \(0.660487\pi\)
\(444\) 0 0
\(445\) 4.11874 + 7.13387i 0.195247 + 0.338178i
\(446\) 0 0
\(447\) −22.6707 26.4986i −1.07229 1.25334i
\(448\) 0 0
\(449\) 5.17892i 0.244408i 0.992505 + 0.122204i \(0.0389962\pi\)
−0.992505 + 0.122204i \(0.961004\pi\)
\(450\) 0 0
\(451\) 41.8032 24.1351i 1.96843 1.13648i
\(452\) 0 0
\(453\) 1.51551 + 8.13862i 0.0712051 + 0.382386i
\(454\) 0 0
\(455\) 15.1644 5.23322i 0.710917 0.245337i
\(456\) 0 0
\(457\) −6.01889 + 10.4250i −0.281552 + 0.487662i −0.971767 0.235942i \(-0.924183\pi\)
0.690215 + 0.723604i \(0.257516\pi\)
\(458\) 0 0
\(459\) −7.56611 + 14.0196i −0.353156 + 0.654380i
\(460\) 0 0
\(461\) −23.0451 −1.07332 −0.536658 0.843800i \(-0.680314\pi\)
−0.536658 + 0.843800i \(0.680314\pi\)
\(462\) 0 0
\(463\) 27.8549 1.29453 0.647263 0.762267i \(-0.275914\pi\)
0.647263 + 0.762267i \(0.275914\pi\)
\(464\) 0 0
\(465\) 3.75077 10.6203i 0.173938 0.492507i
\(466\) 0 0
\(467\) 1.10822 1.91950i 0.0512825 0.0888240i −0.839245 0.543754i \(-0.817002\pi\)
0.890527 + 0.454930i \(0.150336\pi\)
\(468\) 0 0
\(469\) −41.5538 8.04748i −1.91878 0.371598i
\(470\) 0 0
\(471\) −13.0317 + 2.42666i −0.600467 + 0.111815i
\(472\) 0 0
\(473\) 14.9846 8.65135i 0.688992 0.397790i
\(474\) 0 0
\(475\) 3.40556i 0.156258i
\(476\) 0 0
\(477\) −15.8838 2.48826i −0.727271 0.113930i
\(478\) 0 0
\(479\) 3.53276 + 6.11892i 0.161416 + 0.279581i 0.935377 0.353653i \(-0.115061\pi\)
−0.773961 + 0.633234i \(0.781727\pi\)
\(480\) 0 0
\(481\) 0.687863 + 0.397138i 0.0313638 + 0.0181079i
\(482\) 0 0
\(483\) −13.1687 0.0947128i −0.599197 0.00430958i
\(484\) 0 0
\(485\) −4.97952 2.87493i −0.226108 0.130544i
\(486\) 0 0
\(487\) −4.62036 8.00270i −0.209368 0.362637i 0.742147 0.670237i \(-0.233807\pi\)
−0.951516 + 0.307600i \(0.900474\pi\)
\(488\) 0 0
\(489\) −11.1540 + 9.54273i −0.504402 + 0.431537i
\(490\) 0 0
\(491\) 14.0713i 0.635031i 0.948253 + 0.317515i \(0.102848\pi\)
−0.948253 + 0.317515i \(0.897152\pi\)
\(492\) 0 0
\(493\) −21.1881 + 12.2330i −0.954265 + 0.550945i
\(494\) 0 0
\(495\) 7.35452 9.11350i 0.330561 0.409622i
\(496\) 0 0
\(497\) 7.25754 + 6.30010i 0.325545 + 0.282598i
\(498\) 0 0
\(499\) −6.50255 + 11.2627i −0.291094 + 0.504190i −0.974069 0.226252i \(-0.927353\pi\)
0.682975 + 0.730442i \(0.260686\pi\)
\(500\) 0 0
\(501\) −33.5897 11.8628i −1.50068 0.529993i
\(502\) 0 0
\(503\) 0.580122 0.0258664 0.0129332 0.999916i \(-0.495883\pi\)
0.0129332 + 0.999916i \(0.495883\pi\)
\(504\) 0 0
\(505\) −9.09003 −0.404501
\(506\) 0 0
\(507\) 38.8104 + 13.7066i 1.72363 + 0.608732i
\(508\) 0 0
\(509\) −9.86251 + 17.0824i −0.437148 + 0.757163i −0.997468 0.0711133i \(-0.977345\pi\)
0.560320 + 0.828276i \(0.310678\pi\)
\(510\) 0 0
\(511\) 3.90611 20.1695i 0.172796 0.892245i
\(512\) 0 0
\(513\) 0.508034 + 17.6885i 0.0224302 + 0.780967i
\(514\) 0 0
\(515\) −0.853234 + 0.492615i −0.0375980 + 0.0217072i
\(516\) 0 0
\(517\) 39.2674i 1.72698i
\(518\) 0 0
\(519\) 21.8564 18.6991i 0.959390 0.820799i
\(520\) 0 0
\(521\) −18.0051 31.1857i −0.788818 1.36627i −0.926692 0.375822i \(-0.877360\pi\)
0.137874 0.990450i \(-0.455973\pi\)
\(522\) 0 0
\(523\) −18.5387 10.7033i −0.810640 0.468023i 0.0365378 0.999332i \(-0.488367\pi\)
−0.847178 + 0.531309i \(0.821700\pi\)
\(524\) 0 0
\(525\) −3.95205 2.31977i −0.172481 0.101243i
\(526\) 0 0
\(527\) 17.2660 + 9.96855i 0.752121 + 0.434237i
\(528\) 0 0
\(529\) −7.37087 12.7667i −0.320472 0.555075i
\(530\) 0 0
\(531\) 1.19659 7.63846i 0.0519277 0.331481i
\(532\) 0 0
\(533\) 74.9754i 3.24754i
\(534\) 0 0
\(535\) −1.11849 + 0.645758i −0.0483564 + 0.0279186i
\(536\) 0 0
\(537\) −0.661116 + 0.123108i −0.0285293 + 0.00531251i
\(538\) 0 0
\(539\) −16.8529 21.5095i −0.725906 0.926479i
\(540\) 0 0
\(541\) −2.32759 + 4.03151i −0.100071 + 0.173328i −0.911714 0.410826i \(-0.865240\pi\)
0.811643 + 0.584154i \(0.198574\pi\)
\(542\) 0 0
\(543\) 11.9274 33.7725i 0.511854 1.44932i
\(544\) 0 0
\(545\) 7.37094 0.315736
\(546\) 0 0
\(547\) 7.34057 0.313860 0.156930 0.987610i \(-0.449840\pi\)
0.156930 + 0.987610i \(0.449840\pi\)
\(548\) 0 0
\(549\) 9.28841 + 24.0755i 0.396420 + 1.02752i
\(550\) 0 0
\(551\) −13.5881 + 23.5353i −0.578874 + 1.00264i
\(552\) 0 0
\(553\) −2.11132 6.11800i −0.0897825 0.260164i
\(554\) 0 0
\(555\) −0.0415365 0.223060i −0.00176313 0.00946836i
\(556\) 0 0
\(557\) 27.9154 16.1169i 1.18281 0.682897i 0.226149 0.974093i \(-0.427386\pi\)
0.956663 + 0.291196i \(0.0940531\pi\)
\(558\) 0 0
\(559\) 26.8753i 1.13671i
\(560\) 0 0
\(561\) 13.4761 + 15.7515i 0.568960 + 0.665028i
\(562\) 0 0
\(563\) 11.4830 + 19.8892i 0.483952 + 0.838230i 0.999830 0.0184324i \(-0.00586756\pi\)
−0.515878 + 0.856662i \(0.672534\pi\)
\(564\) 0 0
\(565\) 3.92118 + 2.26389i 0.164965 + 0.0952426i
\(566\) 0 0
\(567\) −20.8730 11.4594i −0.876585 0.481248i
\(568\) 0 0
\(569\) 16.0347 + 9.25765i 0.672211 + 0.388101i 0.796914 0.604093i \(-0.206465\pi\)
−0.124703 + 0.992194i \(0.539798\pi\)
\(570\) 0 0
\(571\) −21.9408 38.0025i −0.918193 1.59036i −0.802158 0.597112i \(-0.796315\pi\)
−0.116035 0.993245i \(-0.537019\pi\)
\(572\) 0 0
\(573\) 19.8841 + 23.2415i 0.830670 + 0.970928i
\(574\) 0 0
\(575\) 2.87372i 0.119842i
\(576\) 0 0
\(577\) 14.6663 8.46761i 0.610568 0.352511i −0.162620 0.986689i \(-0.551994\pi\)
0.773188 + 0.634177i \(0.218661\pi\)
\(578\) 0 0
\(579\) −6.77934 36.4065i −0.281740 1.51300i
\(580\) 0 0
\(581\) 13.2446 15.2575i 0.549480 0.632987i
\(582\) 0 0
\(583\) −10.4601 + 18.1175i −0.433214 + 0.750349i
\(584\) 0 0
\(585\) −6.54734 16.9707i −0.270699 0.701651i
\(586\) 0 0
\(587\) −15.3959 −0.635456 −0.317728 0.948182i \(-0.602920\pi\)
−0.317728 + 0.948182i \(0.602920\pi\)
\(588\) 0 0
\(589\) 22.1458 0.912500
\(590\) 0 0
\(591\) −12.9819 + 36.7583i −0.534003 + 1.51203i
\(592\) 0 0
\(593\) −2.37500 + 4.11363i −0.0975297 + 0.168926i −0.910662 0.413153i \(-0.864427\pi\)
0.813132 + 0.582079i \(0.197761\pi\)
\(594\) 0 0
\(595\) 5.31750 6.12561i 0.217996 0.251126i
\(596\) 0 0
\(597\) 16.6839 3.10674i 0.682825 0.127151i
\(598\) 0 0
\(599\) 19.2300 11.1024i 0.785716 0.453634i −0.0527360 0.998608i \(-0.516794\pi\)
0.838452 + 0.544975i \(0.183461\pi\)
\(600\) 0 0
\(601\) 42.5924i 1.73738i 0.495357 + 0.868689i \(0.335037\pi\)
−0.495357 + 0.868689i \(0.664963\pi\)
\(602\) 0 0
\(603\) −7.42770 + 47.4148i −0.302479 + 1.93088i
\(604\) 0 0
\(605\) −2.11916 3.67050i −0.0861562 0.149227i
\(606\) 0 0
\(607\) 16.2862 + 9.40283i 0.661035 + 0.381649i 0.792671 0.609649i \(-0.208690\pi\)
−0.131636 + 0.991298i \(0.542023\pi\)
\(608\) 0 0
\(609\) −18.0562 31.8002i −0.731673 1.28861i
\(610\) 0 0
\(611\) −52.8205 30.4960i −2.13689 1.23373i
\(612\) 0 0
\(613\) −7.74783 13.4196i −0.312932 0.542014i 0.666064 0.745895i \(-0.267978\pi\)
−0.978996 + 0.203881i \(0.934645\pi\)
\(614\) 0 0
\(615\) −16.2743 + 13.9234i −0.656244 + 0.561444i
\(616\) 0 0
\(617\) 17.7219i 0.713459i −0.934208 0.356729i \(-0.883892\pi\)
0.934208 0.356729i \(-0.116108\pi\)
\(618\) 0 0
\(619\) 5.96204 3.44219i 0.239635 0.138353i −0.375374 0.926873i \(-0.622486\pi\)
0.615009 + 0.788520i \(0.289152\pi\)
\(620\) 0 0
\(621\) 0.428695 + 14.9261i 0.0172029 + 0.598965i
\(622\) 0 0
\(623\) −7.10976 20.6021i −0.284847 0.825404i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 21.7117 + 7.66789i 0.867082 + 0.306226i
\(628\) 0 0
\(629\) 0.401627 0.0160139
\(630\) 0 0
\(631\) −49.6754 −1.97755 −0.988774 0.149421i \(-0.952259\pi\)
−0.988774 + 0.149421i \(0.952259\pi\)
\(632\) 0 0
\(633\) 3.20580 + 1.13219i 0.127419 + 0.0450004i
\(634\) 0 0
\(635\) −0.350427 + 0.606958i −0.0139063 + 0.0240864i
\(636\) 0 0
\(637\) −42.0218 + 5.96493i −1.66496 + 0.236339i
\(638\) 0 0
\(639\) 6.84362 8.48041i 0.270729 0.335480i
\(640\) 0 0
\(641\) 23.3007 13.4527i 0.920324 0.531349i 0.0365856 0.999331i \(-0.488352\pi\)
0.883738 + 0.467981i \(0.155019\pi\)
\(642\) 0 0
\(643\) 13.9638i 0.550679i −0.961347 0.275339i \(-0.911210\pi\)
0.961347 0.275339i \(-0.0887902\pi\)
\(644\) 0 0
\(645\) −5.83362 + 4.99091i −0.229699 + 0.196517i
\(646\) 0 0
\(647\) −15.3377 26.5656i −0.602985 1.04440i −0.992366 0.123324i \(-0.960644\pi\)
0.389381 0.921077i \(-0.372689\pi\)
\(648\) 0 0
\(649\) −8.71262 5.03023i −0.342000 0.197454i
\(650\) 0 0
\(651\) −15.0851 + 25.6994i −0.591230 + 1.00724i
\(652\) 0 0
\(653\) 11.3602 + 6.55879i 0.444557 + 0.256665i 0.705529 0.708681i \(-0.250710\pi\)
−0.260971 + 0.965347i \(0.584043\pi\)
\(654\) 0 0
\(655\) 2.66028 + 4.60774i 0.103946 + 0.180039i
\(656\) 0 0
\(657\) −23.0143 3.60527i −0.897873 0.140655i
\(658\) 0 0
\(659\) 37.1306i 1.44640i −0.690638 0.723201i \(-0.742670\pi\)
0.690638 0.723201i \(-0.257330\pi\)
\(660\) 0 0
\(661\) 4.41297 2.54783i 0.171645 0.0990992i −0.411716 0.911312i \(-0.635071\pi\)
0.583361 + 0.812213i \(0.301737\pi\)
\(662\) 0 0
\(663\) 31.6539 5.89436i 1.22934 0.228918i
\(664\) 0 0
\(665\) 1.71314 8.84591i 0.0664326 0.343030i
\(666\) 0 0
\(667\) −11.4661 + 19.8599i −0.443969 + 0.768977i
\(668\) 0 0
\(669\) 1.03168 2.92120i 0.0398869 0.112940i
\(670\) 0 0
\(671\) 33.5779 1.29626
\(672\) 0 0
\(673\) 29.0339 1.11918 0.559588 0.828771i \(-0.310960\pi\)
0.559588 + 0.828771i \(0.310960\pi\)
\(674\) 0 0
\(675\) −2.46781 + 4.57273i −0.0949862 + 0.176005i
\(676\) 0 0
\(677\) 12.4783 21.6131i 0.479581 0.830658i −0.520145 0.854078i \(-0.674122\pi\)
0.999726 + 0.0234197i \(0.00745540\pi\)
\(678\) 0 0
\(679\) 11.4880 + 9.97249i 0.440870 + 0.382709i
\(680\) 0 0
\(681\) −8.75019 46.9903i −0.335308 1.80067i
\(682\) 0 0
\(683\) 29.3107 16.9226i 1.12154 0.647524i 0.179749 0.983712i \(-0.442471\pi\)
0.941795 + 0.336189i \(0.109138\pi\)
\(684\) 0 0
\(685\) 3.92505i 0.149968i
\(686\) 0 0
\(687\) 10.8905 + 12.7293i 0.415498 + 0.485654i
\(688\) 0 0
\(689\) 16.2472 + 28.1409i 0.618967 + 1.07208i
\(690\) 0 0
\(691\) 9.82503 + 5.67249i 0.373762 + 0.215792i 0.675101 0.737726i \(-0.264100\pi\)
−0.301339 + 0.953517i \(0.597434\pi\)
\(692\) 0 0
\(693\) −23.6878 + 19.9726i −0.899823 + 0.758696i
\(694\) 0 0
\(695\) −14.0059 8.08629i −0.531273 0.306730i
\(696\) 0 0
\(697\) −18.9557 32.8323i −0.717999 1.24361i
\(698\) 0 0
\(699\) 0.671890 + 0.785338i 0.0254132 + 0.0297042i
\(700\) 0 0
\(701\) 23.1947i 0.876052i 0.898962 + 0.438026i \(0.144322\pi\)
−0.898962 + 0.438026i \(0.855678\pi\)
\(702\) 0 0
\(703\) 0.386351 0.223060i 0.0145715 0.00841285i
\(704\) 0 0
\(705\) 3.18956 + 17.1286i 0.120126 + 0.645101i
\(706\) 0 0
\(707\) 23.6113 + 4.57266i 0.887993 + 0.171972i
\(708\) 0 0
\(709\) 7.29490 12.6351i 0.273966 0.474522i −0.695908 0.718131i \(-0.744998\pi\)
0.969874 + 0.243609i \(0.0783312\pi\)
\(710\) 0 0
\(711\) −6.84675 + 2.64150i −0.256773 + 0.0990639i
\(712\) 0 0
\(713\) 18.6873 0.699844
\(714\) 0 0
\(715\) −23.6689 −0.885165
\(716\) 0 0
\(717\) −5.13912 + 14.5515i −0.191924 + 0.543434i
\(718\) 0 0
\(719\) 9.35171 16.1976i 0.348760 0.604070i −0.637270 0.770641i \(-0.719936\pi\)
0.986029 + 0.166571i \(0.0532696\pi\)
\(720\) 0 0
\(721\) 2.46407 0.850351i 0.0917668 0.0316687i
\(722\) 0 0
\(723\) −3.58917 + 0.668348i −0.133483 + 0.0248561i
\(724\) 0 0
\(725\) −6.91086 + 3.98999i −0.256663 + 0.148184i
\(726\) 0 0
\(727\) 23.0483i 0.854815i 0.904059 + 0.427407i \(0.140573\pi\)
−0.904059 + 0.427407i \(0.859427\pi\)
\(728\) 0 0
\(729\) −12.1357 + 24.1190i −0.449470 + 0.893295i
\(730\) 0 0
\(731\) −6.79479 11.7689i −0.251314 0.435289i
\(732\) 0 0
\(733\) 15.4109 + 8.89746i 0.569213 + 0.328635i 0.756835 0.653606i \(-0.226745\pi\)
−0.187622 + 0.982241i \(0.560078\pi\)
\(734\) 0 0
\(735\) 9.09846 + 8.01362i 0.335602 + 0.295587i
\(736\) 0 0
\(737\) 54.0824 + 31.2245i 1.99215 + 1.15017i
\(738\) 0 0
\(739\) 6.97258 + 12.0769i 0.256491 + 0.444255i 0.965299 0.261146i \(-0.0841004\pi\)
−0.708809 + 0.705401i \(0.750767\pi\)
\(740\) 0 0
\(741\) 27.1763 23.2504i 0.998345 0.854127i
\(742\) 0 0
\(743\) 30.8975i 1.13352i 0.823883 + 0.566760i \(0.191803\pi\)
−0.823883 + 0.566760i \(0.808197\pi\)
\(744\) 0 0
\(745\) 17.4366 10.0670i 0.638826 0.368826i
\(746\) 0 0
\(747\) −17.8283 14.3873i −0.652304 0.526404i
\(748\) 0 0
\(749\) 3.23010 1.11471i 0.118025 0.0407305i
\(750\) 0 0
\(751\) −11.7085 + 20.2797i −0.427249 + 0.740017i −0.996628 0.0820583i \(-0.973851\pi\)
0.569378 + 0.822076i \(0.307184\pi\)
\(752\) 0 0
\(753\) −48.7065 17.2016i −1.77497 0.626862i
\(754\) 0 0
\(755\) −4.77961 −0.173948
\(756\) 0 0
\(757\) 25.7901 0.937357 0.468679 0.883369i \(-0.344730\pi\)
0.468679 + 0.883369i \(0.344730\pi\)
\(758\) 0 0
\(759\) 18.3210 + 6.47041i 0.665011 + 0.234861i
\(760\) 0 0
\(761\) 9.03119 15.6425i 0.327380 0.567039i −0.654611 0.755966i \(-0.727168\pi\)
0.981991 + 0.188927i \(0.0605008\pi\)
\(762\) 0 0
\(763\) −19.1459 3.70788i −0.693129 0.134234i
\(764\) 0 0
\(765\) −7.15776 5.77625i −0.258789 0.208841i
\(766\) 0 0
\(767\) −13.5328 + 7.81318i −0.488642 + 0.282118i
\(768\) 0 0
\(769\) 46.2208i 1.66677i 0.552696 + 0.833383i \(0.313599\pi\)
−0.552696 + 0.833383i \(0.686401\pi\)
\(770\) 0 0
\(771\) 17.8593 15.2794i 0.643188 0.550275i
\(772\) 0 0
\(773\) −2.03651 3.52734i −0.0732482 0.126870i 0.827075 0.562092i \(-0.190003\pi\)
−0.900323 + 0.435222i \(0.856670\pi\)
\(774\) 0 0
\(775\) 5.63161 + 3.25141i 0.202293 + 0.116794i
\(776\) 0 0
\(777\) −0.00431744 + 0.600290i −0.000154887 + 0.0215353i
\(778\) 0 0
\(779\) −36.4694 21.0556i −1.30665 0.754397i
\(780\) 0 0
\(781\) −7.08988 12.2800i −0.253696 0.439414i
\(782\) 0 0
\(783\) −35.2998 + 21.7550i −1.26151 + 0.777459i
\(784\) 0 0
\(785\) 7.65317i 0.273153i
\(786\) 0 0
\(787\) 10.0876 5.82407i 0.359584 0.207606i −0.309314 0.950960i \(-0.600100\pi\)
0.668898 + 0.743354i \(0.266766\pi\)
\(788\) 0 0
\(789\) −20.7023 + 3.85503i −0.737022 + 0.137243i
\(790\) 0 0
\(791\) −9.04638 7.85295i −0.321652 0.279219i
\(792\) 0 0
\(793\) 26.0774 45.1673i 0.926034 1.60394i