Properties

Label 300.2.x.a.17.6
Level $300$
Weight $2$
Character 300.17
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 17.6
Character \(\chi\) \(=\) 300.17
Dual form 300.2.x.a.53.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +O(q^{10})\) \(q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +(-1.03855 + 0.337444i) q^{11} +(2.26685 + 4.44893i) q^{13} +(-2.45001 - 2.99958i) q^{15} +(-2.19690 + 0.347955i) q^{17} +(-2.39954 + 3.30268i) q^{19} +(-0.841039 + 2.05885i) q^{21} +(2.13422 - 4.18865i) q^{23} +(4.19701 - 2.71755i) q^{25} +(-4.82925 - 1.91789i) q^{27} +(-0.981024 + 0.712755i) q^{29} +(0.992266 + 0.720923i) q^{31} +(-1.23537 - 1.43220i) q^{33} +(-2.52232 - 1.37171i) q^{35} +(6.47404 - 3.29869i) q^{37} +(-5.58448 + 6.60366i) q^{39} +(8.57625 + 2.78659i) q^{41} +(1.48285 - 1.48285i) q^{43} +(3.14709 - 5.92417i) q^{45} +(-0.0645410 + 0.407496i) q^{47} -5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(13.7949 + 2.18491i) q^{53} +(2.01325 - 1.38168i) q^{55} +(-6.88343 - 1.61703i) q^{57} +(-3.76991 + 11.6026i) q^{59} +(0.344205 + 1.05936i) q^{61} +(-3.85191 + 0.0376491i) q^{63} +(-7.68005 - 8.10400i) q^{65} +(-1.22742 - 7.74963i) q^{67} +(8.12035 + 0.599171i) q^{69} +(6.04759 + 8.32380i) q^{71} +(5.93345 + 3.02324i) q^{73} +(7.15447 + 4.87992i) q^{75} +(-1.24932 - 0.636563i) q^{77} +(-5.56738 - 7.66285i) q^{79} +(-0.175918 - 8.99828i) q^{81} +(-2.79265 - 17.6321i) q^{83} +(4.49059 - 2.13819i) q^{85} +(-1.79615 - 1.08864i) q^{87} +(-4.10757 - 12.6418i) q^{89} +(-1.98122 + 6.09757i) q^{91} +(-0.485825 + 2.06808i) q^{93} +(3.05291 - 8.60274i) q^{95} +(-15.3339 - 2.42865i) q^{97} +(1.45866 - 2.93331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\)

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
\(3\) 0.670639 + 1.59695i 0.387194 + 0.921998i
\(4\) 0 0
\(5\) −2.14441 + 0.633635i −0.959011 + 0.283370i
\(6\) 0 0
\(7\) 0.907947 + 0.907947i 0.343172 + 0.343172i 0.857558 0.514387i \(-0.171980\pi\)
−0.514387 + 0.857558i \(0.671980\pi\)
\(8\) 0 0
\(9\) −2.10049 + 2.14195i −0.700162 + 0.713984i
\(10\) 0 0
\(11\) −1.03855 + 0.337444i −0.313133 + 0.101743i −0.461367 0.887209i \(-0.652641\pi\)
0.148234 + 0.988952i \(0.452641\pi\)
\(12\) 0 0
\(13\) 2.26685 + 4.44893i 0.628710 + 1.23391i 0.957206 + 0.289407i \(0.0934581\pi\)
−0.328496 + 0.944505i \(0.606542\pi\)
\(14\) 0 0
\(15\) −2.45001 2.99958i −0.632590 0.774487i
\(16\) 0 0
\(17\) −2.19690 + 0.347955i −0.532827 + 0.0843916i −0.417050 0.908884i \(-0.636936\pi\)
−0.115777 + 0.993275i \(0.536936\pi\)
\(18\) 0 0
\(19\) −2.39954 + 3.30268i −0.550491 + 0.757686i −0.990079 0.140513i \(-0.955125\pi\)
0.439587 + 0.898200i \(0.355125\pi\)
\(20\) 0 0
\(21\) −0.841039 + 2.05885i −0.183530 + 0.449278i
\(22\) 0 0
\(23\) 2.13422 4.18865i 0.445016 0.873394i −0.554144 0.832421i \(-0.686954\pi\)
0.999160 0.0409730i \(-0.0130458\pi\)
\(24\) 0 0
\(25\) 4.19701 2.71755i 0.839403 0.543510i
\(26\) 0 0
\(27\) −4.82925 1.91789i −0.929390 0.369098i
\(28\) 0 0
\(29\) −0.981024 + 0.712755i −0.182172 + 0.132355i −0.675134 0.737695i \(-0.735914\pi\)
0.492962 + 0.870051i \(0.335914\pi\)
\(30\) 0 0
\(31\) 0.992266 + 0.720923i 0.178216 + 0.129482i 0.673317 0.739354i \(-0.264869\pi\)
−0.495101 + 0.868836i \(0.664869\pi\)
\(32\) 0 0
\(33\) −1.23537 1.43220i −0.215050 0.249314i
\(34\) 0 0
\(35\) −2.52232 1.37171i −0.426350 0.231861i
\(36\) 0 0
\(37\) 6.47404 3.29869i 1.06432 0.542301i 0.168040 0.985780i \(-0.446256\pi\)
0.896284 + 0.443480i \(0.146256\pi\)
\(38\) 0 0
\(39\) −5.58448 + 6.60366i −0.894233 + 1.05743i
\(40\) 0 0
\(41\) 8.57625 + 2.78659i 1.33938 + 0.435193i 0.889108 0.457697i \(-0.151325\pi\)
0.450277 + 0.892889i \(0.351325\pi\)
\(42\) 0 0
\(43\) 1.48285 1.48285i 0.226133 0.226133i −0.584942 0.811075i \(-0.698883\pi\)
0.811075 + 0.584942i \(0.198883\pi\)
\(44\) 0 0
\(45\) 3.14709 5.92417i 0.469141 0.883123i
\(46\) 0 0
\(47\) −0.0645410 + 0.407496i −0.00941428 + 0.0594394i −0.991948 0.126644i \(-0.959579\pi\)
0.982534 + 0.186083i \(0.0595794\pi\)
\(48\) 0 0
\(49\) 5.35127i 0.764466i
\(50\) 0 0
\(51\) −2.02900 3.27499i −0.284116 0.458590i
\(52\) 0 0
\(53\) 13.7949 + 2.18491i 1.89488 + 0.300120i 0.991642 0.129017i \(-0.0411821\pi\)
0.903240 + 0.429136i \(0.141182\pi\)
\(54\) 0 0
\(55\) 2.01325 1.38168i 0.271467 0.186305i
\(56\) 0 0
\(57\) −6.88343 1.61703i −0.911732 0.214181i
\(58\) 0 0
\(59\) −3.76991 + 11.6026i −0.490801 + 1.51053i 0.332599 + 0.943068i \(0.392075\pi\)
−0.823400 + 0.567462i \(0.807925\pi\)
\(60\) 0 0
\(61\) 0.344205 + 1.05936i 0.0440710 + 0.135637i 0.970671 0.240412i \(-0.0772826\pi\)
−0.926600 + 0.376049i \(0.877283\pi\)
\(62\) 0 0
\(63\) −3.85191 + 0.0376491i −0.485295 + 0.00474334i
\(64\) 0 0
\(65\) −7.68005 8.10400i −0.952593 1.00518i
\(66\) 0 0
\(67\) −1.22742 7.74963i −0.149953 0.946768i −0.941831 0.336088i \(-0.890896\pi\)
0.791877 0.610680i \(-0.209104\pi\)
\(68\) 0 0
\(69\) 8.12035 + 0.599171i 0.977575 + 0.0721317i
\(70\) 0 0
\(71\) 6.04759 + 8.32380i 0.717717 + 0.987853i 0.999597 + 0.0284034i \(0.00904228\pi\)
−0.281879 + 0.959450i \(0.590958\pi\)
\(72\) 0 0
\(73\) 5.93345 + 3.02324i 0.694458 + 0.353844i 0.765327 0.643642i \(-0.222577\pi\)
−0.0708692 + 0.997486i \(0.522577\pi\)
\(74\) 0 0
\(75\) 7.15447 + 4.87992i 0.826127 + 0.563484i
\(76\) 0 0
\(77\) −1.24932 0.636563i −0.142374 0.0725431i
\(78\) 0 0
\(79\) −5.56738 7.66285i −0.626380 0.862138i 0.371418 0.928466i \(-0.378872\pi\)
−0.997798 + 0.0663280i \(0.978872\pi\)
\(80\) 0 0
\(81\) −0.175918 8.99828i −0.0195464 0.999809i
\(82\) 0 0
\(83\) −2.79265 17.6321i −0.306534 1.93538i −0.351024 0.936367i \(-0.614166\pi\)
0.0444903 0.999010i \(-0.485834\pi\)
\(84\) 0 0
\(85\) 4.49059 2.13819i 0.487073 0.231920i
\(86\) 0 0
\(87\) −1.79615 1.08864i −0.192567 0.116715i
\(88\) 0 0
\(89\) −4.10757 12.6418i −0.435401 1.34003i −0.892675 0.450701i \(-0.851174\pi\)
0.457274 0.889326i \(-0.348826\pi\)
\(90\) 0 0
\(91\) −1.98122 + 6.09757i −0.207688 + 0.639199i
\(92\) 0 0
\(93\) −0.485825 + 2.06808i −0.0503777 + 0.214450i
\(94\) 0 0
\(95\) 3.05291 8.60274i 0.313221 0.882622i
\(96\) 0 0
\(97\) −15.3339 2.42865i −1.55692 0.246592i −0.682180 0.731184i \(-0.738968\pi\)
−0.874740 + 0.484592i \(0.838968\pi\)
\(98\) 0 0
\(99\) 1.45866 2.93331i 0.146601 0.294809i
\(100\) 0 0
\(101\) 10.8863i 1.08323i 0.840628 + 0.541613i \(0.182186\pi\)
−0.840628 + 0.541613i \(0.817814\pi\)
\(102\) 0 0
\(103\) 1.29267 8.16157i 0.127370 0.804184i −0.838452 0.544976i \(-0.816539\pi\)
0.965822 0.259207i \(-0.0834613\pi\)
\(104\) 0 0
\(105\) 0.498977 4.94793i 0.0486952 0.482869i
\(106\) 0 0
\(107\) −6.56922 + 6.56922i −0.635071 + 0.635071i −0.949335 0.314265i \(-0.898242\pi\)
0.314265 + 0.949335i \(0.398242\pi\)
\(108\) 0 0
\(109\) 18.5165 + 6.01639i 1.77356 + 0.576265i 0.998455 0.0555636i \(-0.0176956\pi\)
0.775108 + 0.631829i \(0.217696\pi\)
\(110\) 0 0
\(111\) 9.60957 + 8.12647i 0.912100 + 0.771330i
\(112\) 0 0
\(113\) 5.59661 2.85162i 0.526485 0.268258i −0.170482 0.985361i \(-0.554532\pi\)
0.696967 + 0.717103i \(0.254532\pi\)
\(114\) 0 0
\(115\) −1.92258 + 10.3345i −0.179282 + 0.963698i
\(116\) 0 0
\(117\) −14.2909 4.48945i −1.32119 0.415050i
\(118\) 0 0
\(119\) −2.31060 1.67875i −0.211812 0.153890i
\(120\) 0 0
\(121\) −7.93448 + 5.76474i −0.721316 + 0.524067i
\(122\) 0 0
\(123\) 1.30153 + 15.5646i 0.117355 + 1.40341i
\(124\) 0 0
\(125\) −7.27820 + 8.48692i −0.650982 + 0.759093i
\(126\) 0 0
\(127\) −1.64120 + 3.22104i −0.145633 + 0.285821i −0.952287 0.305203i \(-0.901276\pi\)
0.806655 + 0.591023i \(0.201276\pi\)
\(128\) 0 0
\(129\) 3.36250 + 1.37358i 0.296052 + 0.120937i
\(130\) 0 0
\(131\) −6.57127 + 9.04457i −0.574134 + 0.790228i −0.993037 0.117803i \(-0.962415\pi\)
0.418903 + 0.908031i \(0.362415\pi\)
\(132\) 0 0
\(133\) −5.17731 + 0.820005i −0.448930 + 0.0711034i
\(134\) 0 0
\(135\) 11.5712 + 1.05276i 0.995887 + 0.0906075i
\(136\) 0 0
\(137\) 5.59033 + 10.9716i 0.477615 + 0.937371i 0.996585 + 0.0825788i \(0.0263156\pi\)
−0.518970 + 0.854792i \(0.673684\pi\)
\(138\) 0 0
\(139\) −15.7315 + 5.11149i −1.33433 + 0.433551i −0.887393 0.461014i \(-0.847486\pi\)
−0.446939 + 0.894565i \(0.647486\pi\)
\(140\) 0 0
\(141\) −0.694034 + 0.170214i −0.0584482 + 0.0143346i
\(142\) 0 0
\(143\) −3.85549 3.85549i −0.322412 0.322412i
\(144\) 0 0
\(145\) 1.65209 2.15005i 0.137199 0.178552i
\(146\) 0 0
\(147\) 8.54569 3.58877i 0.704837 0.295997i
\(148\) 0 0
\(149\) −7.21459 −0.591042 −0.295521 0.955336i \(-0.595493\pi\)
−0.295521 + 0.955336i \(0.595493\pi\)
\(150\) 0 0
\(151\) −8.59485 −0.699439 −0.349719 0.936854i \(-0.613723\pi\)
−0.349719 + 0.936854i \(0.613723\pi\)
\(152\) 0 0
\(153\) 3.86926 5.43654i 0.312811 0.439518i
\(154\) 0 0
\(155\) −2.58463 0.917223i −0.207603 0.0736732i
\(156\) 0 0
\(157\) 9.22284 + 9.22284i 0.736063 + 0.736063i 0.971814 0.235751i \(-0.0757550\pi\)
−0.235751 + 0.971814i \(0.575755\pi\)
\(158\) 0 0
\(159\) 5.76225 + 23.4951i 0.456977 + 1.86328i
\(160\) 0 0
\(161\) 5.74083 1.86531i 0.452441 0.147007i
\(162\) 0 0
\(163\) 0.429156 + 0.842267i 0.0336141 + 0.0659714i 0.907203 0.420694i \(-0.138213\pi\)
−0.873589 + 0.486665i \(0.838213\pi\)
\(164\) 0 0
\(165\) 3.55663 + 2.28845i 0.276884 + 0.178156i
\(166\) 0 0
\(167\) 23.0479 3.65042i 1.78350 0.282478i 0.824494 0.565871i \(-0.191460\pi\)
0.959004 + 0.283393i \(0.0914601\pi\)
\(168\) 0 0
\(169\) −7.01322 + 9.65287i −0.539479 + 0.742529i
\(170\) 0 0
\(171\) −2.03399 12.0769i −0.155543 0.923545i
\(172\) 0 0
\(173\) −1.70415 + 3.34458i −0.129564 + 0.254284i −0.946671 0.322203i \(-0.895577\pi\)
0.817107 + 0.576487i \(0.195577\pi\)
\(174\) 0 0
\(175\) 6.27806 + 1.34328i 0.474576 + 0.101542i
\(176\) 0 0
\(177\) −21.0570 + 1.76080i −1.58274 + 0.132350i
\(178\) 0 0
\(179\) 8.16937 5.93539i 0.610607 0.443632i −0.239021 0.971014i \(-0.576826\pi\)
0.849628 + 0.527382i \(0.176826\pi\)
\(180\) 0 0
\(181\) 9.96400 + 7.23927i 0.740618 + 0.538091i 0.892905 0.450246i \(-0.148664\pi\)
−0.152286 + 0.988336i \(0.548664\pi\)
\(182\) 0 0
\(183\) −1.46090 + 1.26012i −0.107993 + 0.0931510i
\(184\) 0 0
\(185\) −11.7928 + 11.1759i −0.867027 + 0.821670i
\(186\) 0 0
\(187\) 2.16417 1.10270i 0.158260 0.0806373i
\(188\) 0 0
\(189\) −2.64336 6.12605i −0.192276 0.445604i
\(190\) 0 0
\(191\) −12.2290 3.97343i −0.884858 0.287508i −0.168885 0.985636i \(-0.554017\pi\)
−0.715973 + 0.698128i \(0.754017\pi\)
\(192\) 0 0
\(193\) −9.96950 + 9.96950i −0.717620 + 0.717620i −0.968117 0.250497i \(-0.919406\pi\)
0.250497 + 0.968117i \(0.419406\pi\)
\(194\) 0 0
\(195\) 7.79112 17.6995i 0.557934 1.26749i
\(196\) 0 0
\(197\) 1.20326 7.59705i 0.0857284 0.541268i −0.907023 0.421081i \(-0.861651\pi\)
0.992751 0.120186i \(-0.0383493\pi\)
\(198\) 0 0
\(199\) 16.0864i 1.14033i −0.821530 0.570166i \(-0.806879\pi\)
0.821530 0.570166i \(-0.193121\pi\)
\(200\) 0 0
\(201\) 11.5526 7.15733i 0.814858 0.504839i
\(202\) 0 0
\(203\) −1.53786 0.243573i −0.107937 0.0170955i
\(204\) 0 0
\(205\) −20.1567 0.541395i −1.40780 0.0378127i
\(206\) 0 0
\(207\) 4.48898 + 13.3696i 0.312006 + 0.929252i
\(208\) 0 0
\(209\) 1.37756 4.23969i 0.0952877 0.293265i
\(210\) 0 0
\(211\) −6.96750 21.4437i −0.479662 1.47625i −0.839565 0.543259i \(-0.817190\pi\)
0.359903 0.932990i \(-0.382810\pi\)
\(212\) 0 0
\(213\) −9.23692 + 15.2400i −0.632903 + 1.04422i
\(214\) 0 0
\(215\) −2.24026 + 4.11944i −0.152785 + 0.280943i
\(216\) 0 0
\(217\) 0.246365 + 1.55548i 0.0167243 + 0.105593i
\(218\) 0 0
\(219\) −0.848758 + 11.5029i −0.0573538 + 0.777295i
\(220\) 0 0
\(221\) −6.52807 8.98512i −0.439126 0.604404i
\(222\) 0 0
\(223\) −10.1560 5.17474i −0.680097 0.346526i 0.0795792 0.996829i \(-0.474642\pi\)
−0.759676 + 0.650302i \(0.774642\pi\)
\(224\) 0 0
\(225\) −2.99491 + 14.6980i −0.199661 + 0.979865i
\(226\) 0 0
\(227\) 12.6380 + 6.43937i 0.838812 + 0.427396i 0.819956 0.572426i \(-0.193998\pi\)
0.0188557 + 0.999822i \(0.493998\pi\)
\(228\) 0 0
\(229\) 2.06221 + 2.83839i 0.136275 + 0.187566i 0.871700 0.490039i \(-0.163018\pi\)
−0.735425 + 0.677606i \(0.763018\pi\)
\(230\) 0 0
\(231\) 0.178711 2.42201i 0.0117583 0.159357i
\(232\) 0 0
\(233\) −0.450064 2.84159i −0.0294847 0.186159i 0.968550 0.248818i \(-0.0800420\pi\)
−0.998035 + 0.0626588i \(0.980042\pi\)
\(234\) 0 0
\(235\) −0.119801 0.914735i −0.00781496 0.0596708i
\(236\) 0 0
\(237\) 8.50346 14.0298i 0.552359 0.911335i
\(238\) 0 0
\(239\) −4.44446 13.6787i −0.287488 0.884798i −0.985642 0.168850i \(-0.945995\pi\)
0.698153 0.715948i \(-0.254005\pi\)
\(240\) 0 0
\(241\) 0.877493 2.70064i 0.0565243 0.173964i −0.918808 0.394704i \(-0.870847\pi\)
0.975333 + 0.220740i \(0.0708472\pi\)
\(242\) 0 0
\(243\) 14.2518 6.31553i 0.914254 0.405142i
\(244\) 0 0
\(245\) 3.39075 + 11.4753i 0.216627 + 0.733131i
\(246\) 0 0
\(247\) −20.1328 3.18872i −1.28102 0.202893i
\(248\) 0 0
\(249\) 26.2847 16.2845i 1.66573 1.03199i
\(250\) 0 0
\(251\) 12.8469i 0.810891i 0.914119 + 0.405445i \(0.132884\pi\)
−0.914119 + 0.405445i \(0.867116\pi\)
\(252\) 0 0
\(253\) −0.803054 + 5.07028i −0.0504876 + 0.318766i
\(254\) 0 0
\(255\) 6.42615 + 5.73728i 0.402421 + 0.359283i
\(256\) 0 0
\(257\) 9.47863 9.47863i 0.591261 0.591261i −0.346711 0.937972i \(-0.612702\pi\)
0.937972 + 0.346711i \(0.112702\pi\)
\(258\) 0 0
\(259\) 8.87311 + 2.88305i 0.551348 + 0.179144i
\(260\) 0 0
\(261\) 0.533938 3.59844i 0.0330500 0.222738i
\(262\) 0 0
\(263\) 2.07596 1.05775i 0.128009 0.0652239i −0.388813 0.921317i \(-0.627115\pi\)
0.516822 + 0.856093i \(0.327115\pi\)
\(264\) 0 0
\(265\) −30.9665 + 4.05562i −1.90226 + 0.249135i
\(266\) 0 0
\(267\) 17.4336 15.0377i 1.06692 0.920289i
\(268\) 0 0
\(269\) −22.3119 16.2105i −1.36038 0.988373i −0.998421 0.0561787i \(-0.982108\pi\)
−0.361958 0.932194i \(-0.617892\pi\)
\(270\) 0 0
\(271\) 25.5707 18.5782i 1.55331 1.12854i 0.612069 0.790805i \(-0.290338\pi\)
0.941239 0.337740i \(-0.109662\pi\)
\(272\) 0 0
\(273\) −11.0662 + 0.925364i −0.669756 + 0.0560056i
\(274\) 0 0
\(275\) −3.44177 + 4.23855i −0.207546 + 0.255594i
\(276\) 0 0
\(277\) 3.14609 6.17455i 0.189030 0.370993i −0.776969 0.629539i \(-0.783244\pi\)
0.965999 + 0.258547i \(0.0832436\pi\)
\(278\) 0 0
\(279\) −3.62842 + 0.611097i −0.217228 + 0.0365854i
\(280\) 0 0
\(281\) 3.62737 4.99264i 0.216391 0.297836i −0.686998 0.726660i \(-0.741072\pi\)
0.903388 + 0.428823i \(0.141072\pi\)
\(282\) 0 0
\(283\) 3.40261 0.538921i 0.202264 0.0320355i −0.0544801 0.998515i \(-0.517350\pi\)
0.256744 + 0.966479i \(0.417350\pi\)
\(284\) 0 0
\(285\) 15.7855 0.894002i 0.935054 0.0529561i
\(286\) 0 0
\(287\) 5.25670 + 10.3169i 0.310293 + 0.608985i
\(288\) 0 0
\(289\) −11.4626 + 3.72444i −0.674274 + 0.219085i
\(290\) 0 0
\(291\) −6.40508 26.1162i −0.375473 1.53096i
\(292\) 0 0
\(293\) 14.3870 + 14.3870i 0.840500 + 0.840500i 0.988924 0.148424i \(-0.0474199\pi\)
−0.148424 + 0.988924i \(0.547420\pi\)
\(294\) 0 0
\(295\) 0.732441 27.2695i 0.0426444 1.58769i
\(296\) 0 0
\(297\) 5.66258 + 0.362213i 0.328576 + 0.0210177i
\(298\) 0 0
\(299\) 23.4730 1.35748
\(300\) 0 0
\(301\) 2.69270 0.155205
\(302\) 0 0
\(303\) −17.3848 + 7.30077i −0.998732 + 0.419418i
\(304\) 0 0
\(305\) −1.40936 2.05360i −0.0806999 0.117589i
\(306\) 0 0
\(307\) 21.8121 + 21.8121i 1.24488 + 1.24488i 0.957950 + 0.286934i \(0.0926362\pi\)
0.286934 + 0.957950i \(0.407364\pi\)
\(308\) 0 0
\(309\) 13.9005 3.40915i 0.790773 0.193940i
\(310\) 0 0
\(311\) −23.6419 + 7.68170i −1.34061 + 0.435589i −0.889522 0.456892i \(-0.848963\pi\)
−0.451084 + 0.892481i \(0.648963\pi\)
\(312\) 0 0
\(313\) −5.16865 10.1440i −0.292149 0.573375i 0.697550 0.716536i \(-0.254273\pi\)
−0.989699 + 0.143161i \(0.954273\pi\)
\(314\) 0 0
\(315\) 8.23623 2.52144i 0.464059 0.142067i
\(316\) 0 0
\(317\) 15.6631 2.48079i 0.879728 0.139335i 0.299799 0.954002i \(-0.403080\pi\)
0.579929 + 0.814667i \(0.303080\pi\)
\(318\) 0 0
\(319\) 0.778322 1.07127i 0.0435777 0.0599795i
\(320\) 0 0
\(321\) −14.8963 6.08513i −0.831429 0.339639i
\(322\) 0 0
\(323\) 4.12236 8.09060i 0.229375 0.450173i
\(324\) 0 0
\(325\) 21.6042 + 12.5120i 1.19838 + 0.694040i
\(326\) 0 0
\(327\) 2.81006 + 33.6048i 0.155397 + 1.85835i
\(328\) 0 0
\(329\) −0.428585 + 0.311385i −0.0236286 + 0.0171672i
\(330\) 0 0
\(331\) −10.2103 7.41821i −0.561209 0.407742i 0.270693 0.962666i \(-0.412747\pi\)
−0.831901 + 0.554924i \(0.812747\pi\)
\(332\) 0 0
\(333\) −6.53299 + 20.7959i −0.358006 + 1.13961i
\(334\) 0 0
\(335\) 7.54253 + 15.8407i 0.412093 + 0.865468i
\(336\) 0 0
\(337\) 4.25752 2.16931i 0.231922 0.118170i −0.334168 0.942513i \(-0.608455\pi\)
0.566090 + 0.824343i \(0.308455\pi\)
\(338\) 0 0
\(339\) 8.30719 + 7.02510i 0.451185 + 0.381551i
\(340\) 0 0
\(341\) −1.27378 0.413878i −0.0689793 0.0224127i
\(342\) 0 0
\(343\) 11.2143 11.2143i 0.605515 0.605515i
\(344\) 0 0
\(345\) −17.7930 + 3.86047i −0.957945 + 0.207840i
\(346\) 0 0
\(347\) 2.24653 14.1841i 0.120600 0.761440i −0.851062 0.525066i \(-0.824041\pi\)
0.971662 0.236374i \(-0.0759592\pi\)
\(348\) 0 0
\(349\) 20.9612i 1.12203i −0.827807 0.561013i \(-0.810412\pi\)
0.827807 0.561013i \(-0.189588\pi\)
\(350\) 0 0
\(351\) −2.41461 25.8326i −0.128882 1.37884i
\(352\) 0 0
\(353\) −4.85452 0.768881i −0.258380 0.0409234i 0.0259004 0.999665i \(-0.491755\pi\)
−0.284281 + 0.958741i \(0.591755\pi\)
\(354\) 0 0
\(355\) −18.2428 14.0177i −0.968227 0.743982i
\(356\) 0 0
\(357\) 1.13129 4.81574i 0.0598744 0.254876i
\(358\) 0 0
\(359\) 2.41734 7.43981i 0.127582 0.392658i −0.866780 0.498690i \(-0.833815\pi\)
0.994363 + 0.106032i \(0.0338146\pi\)
\(360\) 0 0
\(361\) 0.721413 + 2.22028i 0.0379691 + 0.116857i
\(362\) 0 0
\(363\) −14.5272 8.80489i −0.762478 0.462137i
\(364\) 0 0
\(365\) −14.6394 2.72344i −0.766261 0.142552i
\(366\) 0 0
\(367\) 2.47261 + 15.6115i 0.129069 + 0.814912i 0.964261 + 0.264953i \(0.0853565\pi\)
−0.835192 + 0.549959i \(0.814643\pi\)
\(368\) 0 0
\(369\) −23.9830 + 12.5167i −1.24851 + 0.651594i
\(370\) 0 0
\(371\) 10.5413 + 14.5089i 0.547277 + 0.753262i
\(372\) 0 0
\(373\) −14.5011 7.38868i −0.750838 0.382571i 0.0363057 0.999341i \(-0.488441\pi\)
−0.787144 + 0.616770i \(0.788441\pi\)
\(374\) 0 0
\(375\) −18.4342 5.93124i −0.951939 0.306288i
\(376\) 0 0
\(377\) −5.39483 2.74880i −0.277848 0.141571i
\(378\) 0 0
\(379\) 19.2777 + 26.5335i 0.990229 + 1.36293i 0.931133 + 0.364681i \(0.118822\pi\)
0.0590965 + 0.998252i \(0.481178\pi\)
\(380\) 0 0
\(381\) −6.24448 0.460757i −0.319914 0.0236053i
\(382\) 0 0
\(383\) 2.51909 + 15.9049i 0.128720 + 0.812703i 0.964586 + 0.263770i \(0.0849659\pi\)
−0.835866 + 0.548933i \(0.815034\pi\)
\(384\) 0 0
\(385\) 3.08242 + 0.573438i 0.157094 + 0.0292251i
\(386\) 0 0
\(387\) 0.0614883 + 6.29091i 0.00312563 + 0.319785i
\(388\) 0 0
\(389\) −7.88904 24.2800i −0.399990 1.23104i −0.925007 0.379951i \(-0.875941\pi\)
0.525017 0.851092i \(-0.324059\pi\)
\(390\) 0 0
\(391\) −3.23122 + 9.94467i −0.163410 + 0.502924i
\(392\) 0 0
\(393\) −18.8507 4.42832i −0.950890 0.223379i
\(394\) 0 0
\(395\) 16.7942 + 12.9046i 0.845009 + 0.649302i
\(396\) 0 0
\(397\) −2.82041 0.446710i −0.141553 0.0224197i 0.0852560 0.996359i \(-0.472829\pi\)
−0.226809 + 0.973939i \(0.572829\pi\)
\(398\) 0 0
\(399\) −4.78161 7.71796i −0.239380 0.386381i
\(400\) 0 0
\(401\) 27.6582i 1.38119i −0.723244 0.690593i \(-0.757350\pi\)
0.723244 0.690593i \(-0.242650\pi\)
\(402\) 0 0
\(403\) −0.958028 + 6.04875i −0.0477228 + 0.301310i
\(404\) 0 0
\(405\) 6.07886 + 19.1846i 0.302061 + 0.953289i
\(406\) 0 0
\(407\) −5.61046 + 5.61046i −0.278100 + 0.278100i
\(408\) 0 0
\(409\) 25.9665 + 8.43701i 1.28396 + 0.417183i 0.869973 0.493100i \(-0.164136\pi\)
0.413986 + 0.910283i \(0.364136\pi\)
\(410\) 0 0
\(411\) −13.7721 + 16.2855i −0.679325 + 0.803304i
\(412\) 0 0
\(413\) −13.9574 + 7.11166i −0.686800 + 0.349942i
\(414\) 0 0
\(415\) 17.1609 + 36.0410i 0.842397 + 1.76918i
\(416\) 0 0
\(417\) −18.7130 21.6945i −0.916378 1.06238i
\(418\) 0 0
\(419\) −14.7007 10.6807i −0.718178 0.521787i 0.167624 0.985851i \(-0.446391\pi\)
−0.885802 + 0.464064i \(0.846391\pi\)
\(420\) 0 0
\(421\) −0.685185 + 0.497816i −0.0333939 + 0.0242621i −0.604357 0.796714i \(-0.706570\pi\)
0.570963 + 0.820976i \(0.306570\pi\)
\(422\) 0 0
\(423\) −0.737270 0.994184i −0.0358473 0.0483389i
\(424\) 0 0
\(425\) −8.27485 + 7.43057i −0.401389 + 0.360435i
\(426\) 0 0
\(427\) −0.649318 + 1.27436i −0.0314227 + 0.0616705i
\(428\) 0 0
\(429\) 3.57137 8.74265i 0.172427 0.422099i
\(430\) 0 0
\(431\) −11.3436 + 15.6131i −0.546401 + 0.752057i −0.989518 0.144407i \(-0.953873\pi\)
0.443117 + 0.896464i \(0.353873\pi\)
\(432\) 0 0
\(433\) 14.7512 2.33636i 0.708897 0.112278i 0.208434 0.978036i \(-0.433163\pi\)
0.500463 + 0.865758i \(0.333163\pi\)
\(434\) 0 0
\(435\) 4.54148 + 1.19640i 0.217747 + 0.0573629i
\(436\) 0 0
\(437\) 8.71262 + 17.0995i 0.416781 + 0.817979i
\(438\) 0 0
\(439\) 3.77327 1.22601i 0.180088 0.0585143i −0.217585 0.976041i \(-0.569818\pi\)
0.397673 + 0.917527i \(0.369818\pi\)
\(440\) 0 0
\(441\) 11.4622 + 11.2403i 0.545817 + 0.535250i
\(442\) 0 0
\(443\) −20.1922 20.1922i −0.959360 0.959360i 0.0398456 0.999206i \(-0.487313\pi\)
−0.999206 + 0.0398456i \(0.987313\pi\)
\(444\) 0 0
\(445\) 16.8186 + 24.5065i 0.797278 + 1.16172i
\(446\) 0 0
\(447\) −4.83839 11.5213i −0.228848 0.544940i
\(448\) 0 0
\(449\) 19.6086 0.925387 0.462693 0.886518i \(-0.346883\pi\)
0.462693 + 0.886518i \(0.346883\pi\)
\(450\) 0 0
\(451\) −9.84714 −0.463684
\(452\) 0 0
\(453\) −5.76404 13.7255i −0.270818 0.644882i
\(454\) 0 0
\(455\) 0.384923 14.3311i 0.0180455 0.671851i
\(456\) 0 0
\(457\) 0.286369 + 0.286369i 0.0133958 + 0.0133958i 0.713773 0.700377i \(-0.246985\pi\)
−0.700377 + 0.713773i \(0.746985\pi\)
\(458\) 0 0
\(459\) 11.2767 + 2.53305i 0.526353 + 0.118233i
\(460\) 0 0
\(461\) 7.31001 2.37517i 0.340461 0.110623i −0.133796 0.991009i \(-0.542717\pi\)
0.474257 + 0.880386i \(0.342717\pi\)
\(462\) 0 0
\(463\) −2.82556 5.54548i −0.131315 0.257720i 0.815982 0.578078i \(-0.196197\pi\)
−0.947297 + 0.320358i \(0.896197\pi\)
\(464\) 0 0
\(465\) −0.268596 4.74265i −0.0124559 0.219935i
\(466\) 0 0
\(467\) 2.70390 0.428256i 0.125122 0.0198173i −0.0935595 0.995614i \(-0.529825\pi\)
0.218681 + 0.975796i \(0.429825\pi\)
\(468\) 0 0
\(469\) 5.92182 8.15069i 0.273444 0.376364i
\(470\) 0 0
\(471\) −8.54320 + 20.9136i −0.393650 + 0.963647i
\(472\) 0 0
\(473\) −1.03963 + 2.04039i −0.0478023 + 0.0938172i
\(474\) 0 0
\(475\) −1.09570 + 20.3822i −0.0502740 + 0.935202i
\(476\) 0 0
\(477\) −33.6561 + 24.9588i −1.54101 + 1.14278i
\(478\) 0 0
\(479\) −5.68590 + 4.13105i −0.259796 + 0.188753i −0.710057 0.704144i \(-0.751331\pi\)
0.450261 + 0.892897i \(0.351331\pi\)
\(480\) 0 0
\(481\) 29.3513 + 21.3249i 1.33830 + 0.972334i
\(482\) 0 0
\(483\) 6.82883 + 7.91686i 0.310723 + 0.360230i
\(484\) 0 0
\(485\) 34.4211 4.50806i 1.56298 0.204700i
\(486\) 0 0
\(487\) 7.03443 3.58422i 0.318761 0.162417i −0.287288 0.957844i \(-0.592754\pi\)
0.606049 + 0.795428i \(0.292754\pi\)
\(488\) 0 0
\(489\) −1.05725 + 1.25020i −0.0478104 + 0.0565359i
\(490\) 0 0
\(491\) −7.06686 2.29616i −0.318923 0.103624i 0.145181 0.989405i \(-0.453624\pi\)
−0.464104 + 0.885781i \(0.653624\pi\)
\(492\) 0 0
\(493\) 1.90721 1.90721i 0.0858963 0.0858963i
\(494\) 0 0
\(495\) −1.26932 + 7.21449i −0.0570519 + 0.324267i
\(496\) 0 0
\(497\) −2.06667 + 13.0485i −0.0927030 + 0.585303i
\(498\) 0 0
\(499\) 16.9596i 0.759216i −0.925147 0.379608i \(-0.876059\pi\)
0.925147 0.379608i \(-0.123941\pi\)
\(500\) 0 0
\(501\) 21.2863 + 34.3581i 0.951004 + 1.53501i
\(502\) 0 0
\(503\) −37.8665 5.99747i −1.68839 0.267414i −0.762988 0.646412i \(-0.776269\pi\)
−0.925397 + 0.378998i \(0.876269\pi\)
\(504\) 0 0
\(505\) −6.89793 23.3447i −0.306954 1.03882i
\(506\) 0 0
\(507\) −20.1185 4.72616i −0.893493 0.209896i
\(508\) 0 0
\(509\) −7.22530 + 22.2372i −0.320256 + 0.985646i 0.653281 + 0.757116i \(0.273392\pi\)
−0.973537 + 0.228531i \(0.926608\pi\)
\(510\) 0 0
\(511\) 2.64231 + 8.13220i 0.116889 + 0.359747i
\(512\) 0 0
\(513\) 17.9221 11.3474i 0.791282 0.501001i
\(514\) 0 0
\(515\) 2.39945 + 18.3209i 0.105732 + 0.807313i
\(516\) 0 0
\(517\) −0.0704782 0.444982i −0.00309963 0.0195703i
\(518\) 0 0
\(519\) −6.48399 0.478430i −0.284616 0.0210008i
\(520\) 0 0
\(521\) −6.11512 8.41674i −0.267908 0.368744i 0.653774 0.756690i \(-0.273185\pi\)
−0.921682 + 0.387946i \(0.873185\pi\)
\(522\) 0 0
\(523\) 29.8122 + 15.1901i 1.30360 + 0.664216i 0.961333 0.275389i \(-0.0888065\pi\)
0.342263 + 0.939604i \(0.388806\pi\)
\(524\) 0 0
\(525\) 2.06517 + 10.9266i 0.0901314 + 0.476875i
\(526\) 0 0
\(527\) −2.43076 1.23853i −0.105886 0.0539514i
\(528\) 0 0
\(529\) 0.529182 + 0.728357i 0.0230079 + 0.0316677i
\(530\) 0 0
\(531\) −16.9336 32.4461i −0.734854 1.40804i
\(532\) 0 0
\(533\) 7.04366 + 44.4719i 0.305095 + 1.92629i
\(534\) 0 0
\(535\) 9.92464 18.2496i 0.429079 0.788999i
\(536\) 0 0
\(537\) 14.9572 + 9.06555i 0.645451 + 0.391207i
\(538\) 0 0
\(539\) 1.80575 + 5.55753i 0.0777792 + 0.239380i
\(540\) 0 0
\(541\) −0.727097 + 2.23777i −0.0312603 + 0.0962094i −0.965469 0.260517i \(-0.916107\pi\)
0.934209 + 0.356726i \(0.116107\pi\)
\(542\) 0 0
\(543\) −4.87849 + 20.7669i −0.209356 + 0.891194i
\(544\) 0 0
\(545\) −43.5193 1.16890i −1.86416 0.0500701i
\(546\) 0 0
\(547\) −43.1229 6.82999i −1.84380 0.292029i −0.865762 0.500456i \(-0.833166\pi\)
−0.978038 + 0.208426i \(0.933166\pi\)
\(548\) 0 0
\(549\) −2.99209 1.48789i −0.127699 0.0635016i
\(550\) 0 0
\(551\) 4.95029i 0.210889i
\(552\) 0 0
\(553\) 1.90257 12.0123i 0.0809055 0.510817i
\(554\) 0 0
\(555\) −25.7561 11.3375i −1.09329 0.481252i
\(556\) 0 0
\(557\) 3.81138 3.81138i 0.161493 0.161493i −0.621735 0.783228i \(-0.713572\pi\)
0.783228 + 0.621735i \(0.213572\pi\)
\(558\) 0 0
\(559\) 9.95852 + 3.23572i 0.421200 + 0.136856i
\(560\) 0 0
\(561\) 3.21233 + 2.71655i 0.135625 + 0.114693i
\(562\) 0 0
\(563\) 29.0405 14.7969i 1.22391 0.623615i 0.281981 0.959420i \(-0.409008\pi\)
0.941931 + 0.335805i \(0.109008\pi\)
\(564\) 0 0
\(565\) −10.1946 + 9.66125i −0.428889 + 0.406452i
\(566\) 0 0
\(567\) 8.01024 8.32968i 0.336398 0.349814i
\(568\) 0 0
\(569\) 1.73598 + 1.26126i 0.0727760 + 0.0528749i 0.623578 0.781761i \(-0.285678\pi\)
−0.550802 + 0.834636i \(0.685678\pi\)
\(570\) 0 0
\(571\) 4.09296 2.97371i 0.171285 0.124446i −0.498840 0.866694i \(-0.666240\pi\)
0.670125 + 0.742248i \(0.266240\pi\)
\(572\) 0 0
\(573\) −1.85586 22.1938i −0.0775297 0.927158i
\(574\) 0 0
\(575\) −2.42549 23.3797i −0.101150 0.975000i
\(576\) 0 0
\(577\) 10.9908 21.5708i 0.457555 0.898002i −0.540827 0.841134i \(-0.681889\pi\)
0.998382 0.0568682i \(-0.0181115\pi\)
\(578\) 0 0
\(579\) −22.6067 9.23483i −0.939502 0.383786i
\(580\) 0 0
\(581\) 13.4734 18.5446i 0.558973 0.769360i
\(582\) 0 0
\(583\) −15.0640 + 2.38590i −0.623886 + 0.0988138i
\(584\) 0 0
\(585\) 33.4902 + 0.572036i 1.38465 + 0.0236508i
\(586\) 0 0
\(587\) −12.2504 24.0428i −0.505628 0.992352i −0.992883 0.119092i \(-0.962002\pi\)
0.487255 0.873260i \(-0.337998\pi\)
\(588\) 0 0
\(589\) −4.76196 + 1.54725i −0.196213 + 0.0637535i
\(590\) 0 0
\(591\) 12.9391 3.17335i 0.532241 0.130534i
\(592\) 0 0
\(593\) −7.14857 7.14857i −0.293556 0.293556i 0.544927 0.838483i \(-0.316557\pi\)
−0.838483 + 0.544927i \(0.816557\pi\)
\(594\) 0 0
\(595\) 6.01858 + 2.13585i 0.246738 + 0.0875614i
\(596\) 0 0
\(597\) 25.6891 10.7881i 1.05138 0.441529i
\(598\) 0 0
\(599\) 20.6392 0.843294 0.421647 0.906760i \(-0.361452\pi\)
0.421647 + 0.906760i \(0.361452\pi\)
\(600\) 0 0
\(601\) −7.30272 −0.297884 −0.148942 0.988846i \(-0.547587\pi\)
−0.148942 + 0.988846i \(0.547587\pi\)
\(602\) 0 0
\(603\) 19.1775 + 13.6489i 0.780969 + 0.555827i
\(604\) 0 0
\(605\) 13.3621 17.3895i 0.543245 0.706985i
\(606\) 0 0
\(607\) 10.3692 + 10.3692i 0.420872 + 0.420872i 0.885504 0.464632i \(-0.153813\pi\)
−0.464632 + 0.885504i \(0.653813\pi\)
\(608\) 0 0
\(609\) −0.642376 2.61923i −0.0260304 0.106137i
\(610\) 0 0
\(611\) −1.95923 + 0.636592i −0.0792619 + 0.0257537i
\(612\) 0 0
\(613\) −2.08080 4.08379i −0.0840425 0.164943i 0.845160 0.534513i \(-0.179505\pi\)
−0.929203 + 0.369570i \(0.879505\pi\)
\(614\) 0 0
\(615\) −12.6533 32.5523i −0.510230 1.31263i
\(616\) 0 0
\(617\) −3.30490 + 0.523445i −0.133050 + 0.0210731i −0.222604 0.974909i \(-0.571456\pi\)
0.0895540 + 0.995982i \(0.471456\pi\)
\(618\) 0 0
\(619\) −18.6414 + 25.6577i −0.749260 + 1.03127i 0.248772 + 0.968562i \(0.419973\pi\)
−0.998032 + 0.0627063i \(0.980027\pi\)
\(620\) 0 0
\(621\) −18.3401 + 16.1349i −0.735962 + 0.647469i
\(622\) 0 0
\(623\) 7.74862 15.2075i 0.310442 0.609277i
\(624\) 0 0
\(625\) 10.2299 22.8112i 0.409194 0.912447i
\(626\) 0 0
\(627\) 7.69441 0.643413i 0.307285 0.0256954i
\(628\) 0 0
\(629\) −13.0750 + 9.49957i −0.521336 + 0.378773i
\(630\) 0 0
\(631\) −2.88632 2.09703i −0.114902 0.0834815i 0.528850 0.848715i \(-0.322623\pi\)
−0.643753 + 0.765234i \(0.722623\pi\)
\(632\) 0 0
\(633\) 29.5719 25.5077i 1.17538 1.01384i
\(634\) 0 0
\(635\) 1.47845 7.94715i 0.0586705 0.315373i
\(636\) 0 0
\(637\) 23.8074 12.1305i 0.943285 0.480628i
\(638\) 0 0
\(639\) −30.5321 4.53037i −1.20783 0.179219i
\(640\) 0 0
\(641\) 26.6743 + 8.66700i 1.05357 + 0.342326i 0.784069 0.620674i \(-0.213141\pi\)
0.269502 + 0.963000i \(0.413141\pi\)
\(642\) 0 0
\(643\) −4.46449 + 4.46449i −0.176062 + 0.176062i −0.789637 0.613575i \(-0.789731\pi\)
0.613575 + 0.789637i \(0.289731\pi\)
\(644\) 0 0
\(645\) −8.08094 0.814927i −0.318187 0.0320877i
\(646\) 0 0
\(647\) −2.38692 + 15.0704i −0.0938396 + 0.592480i 0.895296 + 0.445472i \(0.146964\pi\)
−0.989135 + 0.147008i \(0.953036\pi\)
\(648\) 0 0
\(649\) 13.3220i 0.522933i
\(650\) 0 0
\(651\) −2.31881 + 1.43660i −0.0908812 + 0.0563048i
\(652\) 0 0
\(653\) 21.6865 + 3.43481i 0.848660 + 0.134415i 0.565592 0.824685i \(-0.308648\pi\)
0.283068 + 0.959100i \(0.408648\pi\)
\(654\) 0 0
\(655\) 8.36055 23.5591i 0.326674 0.920529i
\(656\) 0 0
\(657\) −18.9388 + 6.35888i −0.738872 + 0.248084i
\(658\) 0 0
\(659\) 3.02628 9.31393i 0.117887 0.362819i −0.874651 0.484753i \(-0.838910\pi\)
0.992538 + 0.121934i \(0.0389095\pi\)
\(660\) 0 0
\(661\) −14.2639 43.8997i −0.554800 1.70750i −0.696471 0.717585i \(-0.745247\pi\)
0.141671 0.989914i \(-0.454753\pi\)
\(662\) 0 0
\(663\) 9.97079 16.4508i 0.387233 0.638895i
\(664\) 0 0
\(665\) 10.5827 5.03895i 0.410380 0.195402i
\(666\) 0 0
\(667\) 0.891759 + 5.63034i 0.0345290 + 0.218008i
\(668\) 0 0
\(669\) 1.45278 19.6890i 0.0561677 0.761221i
\(670\) 0 0
\(671\) −0.714946 0.984039i −0.0276002 0.0379884i
\(672\) 0 0
\(673\) −8.88482 4.52704i −0.342485 0.174505i 0.274285 0.961648i \(-0.411559\pi\)
−0.616769 + 0.787144i \(0.711559\pi\)
\(674\) 0 0
\(675\) −25.4804 + 5.07433i −0.980741 + 0.195311i
\(676\) 0 0
\(677\) −32.0266 16.3184i −1.23088 0.627167i −0.287154 0.957884i \(-0.592709\pi\)
−0.943730 + 0.330718i \(0.892709\pi\)
\(678\) 0 0
\(679\) −11.7173 16.1274i −0.449668 0.618914i
\(680\) 0 0
\(681\) −1.80782 + 24.5007i −0.0692757 + 0.938868i
\(682\) 0 0
\(683\) −4.75779 30.0395i −0.182052 1.14943i −0.894289 0.447490i \(-0.852318\pi\)
0.712237 0.701939i \(-0.247682\pi\)
\(684\) 0 0
\(685\) −18.9400 19.9855i −0.723660 0.763607i
\(686\) 0 0
\(687\) −3.14976 + 5.19678i −0.120171 + 0.198270i
\(688\) 0 0
\(689\) 21.5505 + 66.3257i 0.821009 + 2.52681i
\(690\) 0 0
\(691\) −5.29160 + 16.2859i −0.201302 + 0.619543i 0.798543 + 0.601938i \(0.205604\pi\)
−0.999845 + 0.0176058i \(0.994396\pi\)
\(692\) 0 0
\(693\) 3.98768 1.33890i 0.151479 0.0508607i
\(694\) 0 0
\(695\) 30.4961 20.9292i 1.15678 0.793889i
\(696\) 0 0
\(697\) −19.8108 3.13772i −0.750387 0.118850i
\(698\) 0 0
\(699\) 4.23605 2.62441i 0.160222 0.0992644i
\(700\) 0 0
\(701\) 36.7694i 1.38876i 0.719609 + 0.694380i \(0.244321\pi\)
−0.719609 + 0.694380i \(0.755679\pi\)
\(702\) 0 0
\(703\) −4.64018 + 29.2970i −0.175008 + 1.10496i
\(704\) 0 0
\(705\) 1.38044 0.804773i 0.0519904 0.0303095i
\(706\) 0 0
\(707\) −9.88417 + 9.88417i −0.371732 + 0.371732i
\(708\) 0 0
\(709\) −34.2516 11.1290i −1.28635 0.417959i −0.415535 0.909577i \(-0.636406\pi\)
−0.870811 + 0.491618i \(0.836406\pi\)
\(710\) 0 0
\(711\) 28.1077 + 4.17063i 1.05412 + 0.156411i
\(712\) 0 0
\(713\) 5.13741 2.61764i 0.192398 0.0980315i
\(714\) 0 0
\(715\) 10.7107 + 5.82478i 0.400558 + 0.217835i
\(716\) 0 0
\(717\) 18.8635 16.2710i 0.704469 0.607652i
\(718\) 0 0
\(719\) 27.9485 + 20.3058i 1.04230 + 0.757278i 0.970734 0.240158i \(-0.0771992\pi\)
0.0715696 + 0.997436i \(0.477199\pi\)
\(720\) 0 0
\(721\) 8.58395 6.23660i 0.319683 0.232263i
\(722\) 0 0
\(723\) 4.90127 0.409848i 0.182280 0.0152424i
\(724\) 0 0
\(725\) −2.18042 + 5.65742i −0.0809788 + 0.210111i
\(726\) 0 0
\(727\) 14.5118 28.4810i 0.538212 1.05630i −0.448494 0.893786i \(-0.648039\pi\)
0.986706 0.162515i \(-0.0519607\pi\)
\(728\) 0 0
\(729\) 19.6434 + 18.5240i 0.727533 + 0.686072i
\(730\) 0 0
\(731\) −2.74172 + 3.77365i −0.101406 + 0.139574i
\(732\) 0 0
\(733\) 20.6997 3.27851i 0.764560 0.121094i 0.238038 0.971256i \(-0.423496\pi\)
0.526522 + 0.850161i \(0.323496\pi\)
\(734\) 0 0
\(735\) −16.0515 + 13.1106i −0.592069 + 0.483594i
\(736\) 0 0
\(737\) 3.88980 + 7.63416i 0.143283 + 0.281208i
\(738\) 0 0
\(739\) −7.83354 + 2.54527i −0.288162 + 0.0936294i −0.449531 0.893265i \(-0.648409\pi\)
0.161370 + 0.986894i \(0.448409\pi\)
\(740\) 0 0
\(741\) −8.40961 34.2895i −0.308935 1.25966i
\(742\) 0 0
\(743\) 30.1299 + 30.1299i 1.10536 + 1.10536i 0.993752 + 0.111607i \(0.0355998\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(744\) 0 0
\(745\) 15.4711 4.57141i 0.566816 0.167484i
\(746\) 0 0
\(747\) 43.6331 + 31.0543i 1.59645 + 1.13622i
\(748\) 0 0
\(749\) −11.9290 −0.435876
\(750\) 0 0
\(751\) −26.7528 −0.976225 −0.488113 0.872781i \(-0.662314\pi\)
−0.488113 + 0.872781i \(0.662314\pi\)
\(752\) 0 0
\(753\) −20.5159 + 8.61565i −0.747640 + 0.313972i
\(754\) 0 0
\(755\) 18.4309 5.44600i 0.670769 0.198200i
\(756\) 0 0
\(757\) −1.20647 1.20647i −0.0438498 0.0438498i 0.684842 0.728692i \(-0.259871\pi\)
−0.728692 + 0.684842i \(0.759871\pi\)
\(758\) 0 0
\(759\) −8.63554 + 2.11790i −0.313450 + 0.0768747i
\(760\) 0 0
\(761\) 41.1754 13.3787i 1.49261 0.484978i 0.554756 0.832013i \(-0.312811\pi\)
0.937852 + 0.347035i \(0.112811\pi\)
\(762\) 0 0
\(763\) 11.3495 + 22.2746i 0.410878 + 0.806394i
\(764\) 0 0
\(765\) −4.85251 + 14.1099i −0.175443 + 0.510144i
\(766\) 0 0
\(767\) −60.1650 + 9.52920i −2.17243 + 0.344080i
\(768\) 0 0
\(769\) −19.1217 + 26.3187i −0.689545 + 0.949078i −0.999999 0.00151094i \(-0.999519\pi\)
0.310454 + 0.950589i \(0.399519\pi\)
\(770\) 0 0
\(771\) 21.4936 + 8.78014i 0.774074 + 0.316209i
\(772\) 0 0
\(773\) 7.28640 14.3004i 0.262074 0.514348i −0.722048 0.691843i \(-0.756799\pi\)
0.984122 + 0.177494i \(0.0567992\pi\)
\(774\) 0 0
\(775\) 6.12370 + 0.329194i 0.219970 + 0.0118250i
\(776\) 0 0
\(777\) 1.34658 + 16.1034i 0.0483082 + 0.577706i
\(778\) 0 0
\(779\) −29.7822 + 21.6381i −1.06706 + 0.775264i
\(780\) 0 0
\(781\) −9.08951 6.60392i −0.325248 0.236307i
\(782\) 0 0
\(783\) 6.10460 1.56058i 0.218161 0.0557707i
\(784\) 0 0
\(785\) −25.6215 13.9337i −0.914470 0.497314i
\(786\) 0 0
\(787\) −2.48782 + 1.26761i −0.0886811 + 0.0451853i −0.497769 0.867310i \(-0.665847\pi\)
0.409087 + 0.912495i \(0.365847\pi\)
\(788\) 0 0
\(789\) 3.08140 + 2.60583i 0.109701 + 0.0927700i
\(790\) 0 0
\(791\) 7.67054 + 2.49231i 0.272733 + 0.0886164i
\(792\) 0 0
\(793\) −3.93274 + 3.93274i −0.139656 + 0.139656i
\(794\) 0 0
\(795\) −27.2440 46.7320i −0.966244 1.65741i
\(796\) 0 0
\(797\) 7.08694 &min