Properties

Label 300.2.x.a.53.3
Level $300$
Weight $2$
Character 300.53
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 53.3
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +O(q^{10})\) \(q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +(1.03855 + 0.337444i) q^{11} +(2.26685 - 4.44893i) q^{13} +(-1.59493 - 3.52933i) q^{15} +(2.19690 + 0.347955i) q^{17} +(-2.39954 - 3.30268i) q^{19} +(-2.21798 - 0.163656i) q^{21} +(-2.13422 - 4.18865i) q^{23} +(4.19701 + 2.71755i) q^{25} +(4.39017 - 2.77964i) q^{27} +(0.981024 + 0.712755i) q^{29} +(0.992266 - 0.720923i) q^{31} +(-0.732332 - 1.74385i) q^{33} +(2.52232 - 1.37171i) q^{35} +(6.47404 + 3.29869i) q^{37} +(-8.39948 + 2.06000i) q^{39} +(-8.57625 + 2.78659i) q^{41} +(1.48285 + 1.48285i) q^{43} +(-2.82455 + 6.08456i) q^{45} +(0.0645410 + 0.407496i) q^{47} +5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(-13.7949 + 2.18491i) q^{53} +(2.01325 + 1.38168i) q^{55} +(-1.61703 + 6.88343i) q^{57} +(3.76991 + 11.6026i) q^{59} +(0.344205 - 1.05936i) q^{61} +(2.29455 + 3.09413i) q^{63} +(7.68005 - 8.10400i) q^{65} +(-1.22742 + 7.74963i) q^{67} +(-3.07917 + 7.53776i) q^{69} +(-6.04759 + 8.32380i) q^{71} +(5.93345 - 3.02324i) q^{73} +(-1.18388 - 8.57895i) q^{75} +(1.24932 - 0.636563i) q^{77} +(-5.56738 + 7.66285i) q^{79} +(-8.61223 - 2.61331i) q^{81} +(2.79265 - 17.6321i) q^{83} +(4.49059 + 2.13819i) q^{85} +(-0.175018 - 2.09300i) q^{87} +(4.10757 - 12.6418i) q^{89} +(-1.98122 - 6.09757i) q^{91} +(-2.06808 - 0.485825i) q^{93} +(-3.05291 - 8.60274i) q^{95} +(-15.3339 + 2.42865i) q^{97} +(-1.45866 + 2.93331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\)

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
\(3\) −1.13130 1.31155i −0.653156 0.757223i
\(4\) 0 0
\(5\) 2.14441 + 0.633635i 0.959011 + 0.283370i
\(6\) 0 0
\(7\) 0.907947 0.907947i 0.343172 0.343172i −0.514387 0.857558i \(-0.671980\pi\)
0.857558 + 0.514387i \(0.171980\pi\)
\(8\) 0 0
\(9\) −0.440321 + 2.96751i −0.146774 + 0.989170i
\(10\) 0 0
\(11\) 1.03855 + 0.337444i 0.313133 + 0.101743i 0.461367 0.887209i \(-0.347359\pi\)
−0.148234 + 0.988952i \(0.547359\pi\)
\(12\) 0 0
\(13\) 2.26685 4.44893i 0.628710 1.23391i −0.328496 0.944505i \(-0.606542\pi\)
0.957206 0.289407i \(-0.0934581\pi\)
\(14\) 0 0
\(15\) −1.59493 3.52933i −0.411809 0.911270i
\(16\) 0 0
\(17\) 2.19690 + 0.347955i 0.532827 + 0.0843916i 0.417050 0.908884i \(-0.363064\pi\)
0.115777 + 0.993275i \(0.463064\pi\)
\(18\) 0 0
\(19\) −2.39954 3.30268i −0.550491 0.757686i 0.439587 0.898200i \(-0.355125\pi\)
−0.990079 + 0.140513i \(0.955125\pi\)
\(20\) 0 0
\(21\) −2.21798 0.163656i −0.484002 0.0357128i
\(22\) 0 0
\(23\) −2.13422 4.18865i −0.445016 0.873394i −0.999160 0.0409730i \(-0.986954\pi\)
0.554144 0.832421i \(-0.313046\pi\)
\(24\) 0 0
\(25\) 4.19701 + 2.71755i 0.839403 + 0.543510i
\(26\) 0 0
\(27\) 4.39017 2.77964i 0.844889 0.534942i
\(28\) 0 0
\(29\) 0.981024 + 0.712755i 0.182172 + 0.132355i 0.675134 0.737695i \(-0.264086\pi\)
−0.492962 + 0.870051i \(0.664086\pi\)
\(30\) 0 0
\(31\) 0.992266 0.720923i 0.178216 0.129482i −0.495101 0.868836i \(-0.664869\pi\)
0.673317 + 0.739354i \(0.264869\pi\)
\(32\) 0 0
\(33\) −0.732332 1.74385i −0.127483 0.303566i
\(34\) 0 0
\(35\) 2.52232 1.37171i 0.426350 0.231861i
\(36\) 0 0
\(37\) 6.47404 + 3.29869i 1.06432 + 0.542301i 0.896284 0.443480i \(-0.146256\pi\)
0.168040 + 0.985780i \(0.446256\pi\)
\(38\) 0 0
\(39\) −8.39948 + 2.06000i −1.34499 + 0.329864i
\(40\) 0 0
\(41\) −8.57625 + 2.78659i −1.33938 + 0.435193i −0.889108 0.457697i \(-0.848675\pi\)
−0.450277 + 0.892889i \(0.648675\pi\)
\(42\) 0 0
\(43\) 1.48285 + 1.48285i 0.226133 + 0.226133i 0.811075 0.584942i \(-0.198883\pi\)
−0.584942 + 0.811075i \(0.698883\pi\)
\(44\) 0 0
\(45\) −2.82455 + 6.08456i −0.421059 + 0.907033i
\(46\) 0 0
\(47\) 0.0645410 + 0.407496i 0.00941428 + 0.0594394i 0.991948 0.126644i \(-0.0404206\pi\)
−0.982534 + 0.186083i \(0.940421\pi\)
\(48\) 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 \(-0.958818\pi\)
−0.903240 + 0.429136i \(0.858818\pi\)
\(54\) 0 0
\(55\) 2.01325 + 1.38168i 0.271467 + 0.186305i
\(56\) 0 0
\(57\) −1.61703 + 6.88343i −0.214181 + 0.911732i
\(58\) 0 0
\(59\) 3.76991 + 11.6026i 0.490801 + 1.51053i 0.823400 + 0.567462i \(0.192075\pi\)
−0.332599 + 0.943068i \(0.607925\pi\)
\(60\) 0 0
\(61\) 0.344205 1.05936i 0.0440710 0.135637i −0.926600 0.376049i \(-0.877283\pi\)
0.970671 + 0.240412i \(0.0772826\pi\)
\(62\) 0 0
\(63\) 2.29455 + 3.09413i 0.289087 + 0.389824i
\(64\) 0 0
\(65\) 7.68005 8.10400i 0.952593 1.00518i
\(66\) 0 0
\(67\) −1.22742 + 7.74963i −0.149953 + 0.946768i 0.791877 + 0.610680i \(0.209104\pi\)
−0.941831 + 0.336088i \(0.890896\pi\)
\(68\) 0 0
\(69\) −3.07917 + 7.53776i −0.370689 + 0.907439i
\(70\) 0 0
\(71\) −6.04759 + 8.32380i −0.717717 + 0.987853i 0.281879 + 0.959450i \(0.409042\pi\)
−0.999597 + 0.0284034i \(0.990958\pi\)
\(72\) 0 0
\(73\) 5.93345 3.02324i 0.694458 0.353844i −0.0708692 0.997486i \(-0.522577\pi\)
0.765327 + 0.643642i \(0.222577\pi\)
\(74\) 0 0
\(75\) −1.18388 8.57895i −0.136703 0.990612i
\(76\) 0 0
\(77\) 1.24932 0.636563i 0.142374 0.0725431i
\(78\) 0 0
\(79\) −5.56738 + 7.66285i −0.626380 + 0.862138i −0.997798 0.0663280i \(-0.978872\pi\)
0.371418 + 0.928466i \(0.378872\pi\)
\(80\) 0 0
\(81\) −8.61223 2.61331i −0.956915 0.290368i
\(82\) 0 0
\(83\) 2.79265 17.6321i 0.306534 1.93538i −0.0444903 0.999010i \(-0.514166\pi\)
0.351024 0.936367i \(-0.385834\pi\)
\(84\) 0 0
\(85\) 4.49059 + 2.13819i 0.487073 + 0.231920i
\(86\) 0 0
\(87\) −0.175018 2.09300i −0.0187639 0.224393i
\(88\) 0 0
\(89\) 4.10757 12.6418i 0.435401 1.34003i −0.457274 0.889326i \(-0.651174\pi\)
0.892675 0.450701i \(-0.148826\pi\)
\(90\) 0 0
\(91\) −1.98122 6.09757i −0.207688 0.639199i
\(92\) 0 0
\(93\) −2.06808 0.485825i −0.214450 0.0503777i
\(94\) 0 0
\(95\) −3.05291 8.60274i −0.313221 0.882622i
\(96\) 0 0
\(97\) −15.3339 + 2.42865i −1.55692 + 0.246592i −0.874740 0.484592i \(-0.838968\pi\)
−0.682180 + 0.731184i \(0.738968\pi\)
\(98\) 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 0.965822 + 0.259207i \(0.0834613\pi\)
−0.838452 + 0.544976i \(0.816539\pi\)
\(104\) 0 0
\(105\) −4.65256 1.75633i −0.454043 0.171401i
\(106\) 0 0
\(107\) 6.56922 + 6.56922i 0.635071 + 0.635071i 0.949335 0.314265i \(-0.101758\pi\)
−0.314265 + 0.949335i \(0.601758\pi\)
\(108\) 0 0
\(109\) 18.5165 6.01639i 1.77356 0.576265i 0.775108 0.631829i \(-0.217696\pi\)
0.998455 + 0.0555636i \(0.0176956\pi\)
\(110\) 0 0
\(111\) −2.99769 12.2228i −0.284528 1.16014i
\(112\) 0 0
\(113\) −5.59661 2.85162i −0.526485 0.268258i 0.170482 0.985361i \(-0.445468\pi\)
−0.696967 + 0.717103i \(0.745468\pi\)
\(114\) 0 0
\(115\) −1.92258 10.3345i −0.179282 0.963698i
\(116\) 0 0
\(117\) 12.2041 + 8.68585i 1.12827 + 0.803007i
\(118\) 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
\(123\) 13.3571 + 8.09570i 1.20437 + 0.729964i
\(124\) 0 0
\(125\) 7.27820 + 8.48692i 0.650982 + 0.759093i
\(126\) 0 0
\(127\) −1.64120 3.22104i −0.145633 0.285821i 0.806655 0.591023i \(-0.201276\pi\)
−0.952287 + 0.305203i \(0.901276\pi\)
\(128\) 0 0
\(129\) 0.267283 3.62239i 0.0235329 0.318933i
\(130\) 0 0
\(131\) 6.57127 + 9.04457i 0.574134 + 0.790228i 0.993037 0.117803i \(-0.0375852\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(132\) 0 0
\(133\) −5.17731 0.820005i −0.448930 0.0711034i
\(134\) 0 0
\(135\) 11.1756 3.17894i 0.961844 0.273599i
\(136\) 0 0
\(137\) −5.59033 + 10.9716i −0.477615 + 0.937371i 0.518970 + 0.854792i \(0.326316\pi\)
−0.996585 + 0.0825788i \(0.973684\pi\)
\(138\) 0 0
\(139\) −15.7315 5.11149i −1.33433 0.433551i −0.446939 0.894565i \(-0.647486\pi\)
−0.887393 + 0.461014i \(0.847486\pi\)
\(140\) 0 0
\(141\) 0.461436 0.545649i 0.0388599 0.0459519i
\(142\) 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
\(147\) 7.01845 6.05389i 0.578872 0.499316i
\(148\) 0 0
\(149\) 7.21459 0.591042 0.295521 0.955336i \(-0.404507\pi\)
0.295521 + 0.955336i \(0.404507\pi\)
\(150\) 0 0
\(151\) −8.59485 −0.699439 −0.349719 0.936854i \(-0.613723\pi\)
−0.349719 + 0.936854i \(0.613723\pi\)
\(152\) 0 0
\(153\) −1.99990 + 6.36612i −0.161683 + 0.514670i
\(154\) 0 0
\(155\) 2.58463 0.917223i 0.207603 0.0736732i
\(156\) 0 0
\(157\) 9.22284 9.22284i 0.736063 0.736063i −0.235751 0.971814i \(-0.575755\pi\)
0.971814 + 0.235751i \(0.0757550\pi\)
\(158\) 0 0
\(159\) 18.4718 + 15.6210i 1.46491 + 1.23882i
\(160\) 0 0
\(161\) −5.74083 1.86531i −0.452441 0.147007i
\(162\) 0 0
\(163\) 0.429156 0.842267i 0.0336141 0.0659714i −0.873589 0.486665i \(-0.838213\pi\)
0.907203 + 0.420694i \(0.138213\pi\)
\(164\) 0 0
\(165\) −0.465457 4.20357i −0.0362357 0.327248i
\(166\) 0 0
\(167\) −23.0479 3.65042i −1.78350 0.282478i −0.824494 0.565871i \(-0.808540\pi\)
−0.959004 + 0.283393i \(0.908540\pi\)
\(168\) 0 0
\(169\) −7.01322 9.65287i −0.539479 0.742529i
\(170\) 0 0
\(171\) 10.8573 5.66641i 0.830278 0.433321i
\(172\) 0 0
\(173\) 1.70415 + 3.34458i 0.129564 + 0.254284i 0.946671 0.322203i \(-0.104423\pi\)
−0.817107 + 0.576487i \(0.804423\pi\)
\(174\) 0 0
\(175\) 6.27806 1.34328i 0.474576 0.101542i
\(176\) 0 0
\(177\) 10.9525 18.0704i 0.823239 1.35826i
\(178\) 0 0
\(179\) −8.16937 5.93539i −0.610607 0.443632i 0.239021 0.971014i \(-0.423174\pi\)
−0.849628 + 0.527382i \(0.823174\pi\)
\(180\) 0 0
\(181\) 9.96400 7.23927i 0.740618 0.538091i −0.152286 0.988336i \(-0.548664\pi\)
0.892905 + 0.450246i \(0.148664\pi\)
\(182\) 0 0
\(183\) −1.77880 + 0.747007i −0.131492 + 0.0552203i
\(184\) 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
\(189\) 1.46227 6.50981i 0.106365 0.473519i
\(190\) 0 0
\(191\) 12.2290 3.97343i 0.884858 0.287508i 0.168885 0.985636i \(-0.445983\pi\)
0.715973 + 0.698128i \(0.245983\pi\)
\(192\) 0 0
\(193\) −9.96950 9.96950i −0.717620 0.717620i 0.250497 0.968117i \(-0.419406\pi\)
−0.968117 + 0.250497i \(0.919406\pi\)
\(194\) 0 0
\(195\) −19.3172 0.904708i −1.38334 0.0647875i
\(196\) 0 0
\(197\) −1.20326 7.59705i −0.0857284 0.541268i −0.992751 0.120186i \(-0.961651\pi\)
0.907023 0.421081i \(-0.138349\pi\)
\(198\) 0 0
\(199\) 16.0864i 1.14033i 0.821530 + 0.570166i \(0.193121\pi\)
−0.821530 + 0.570166i \(0.806879\pi\)
\(200\) 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
\(207\) 13.3696 4.48898i 0.929252 0.312006i
\(208\) 0 0
\(209\) −1.37756 4.23969i −0.0952877 0.293265i
\(210\) 0 0
\(211\) −6.96750 + 21.4437i −0.479662 + 1.47625i 0.359903 + 0.932990i \(0.382810\pi\)
−0.839565 + 0.543259i \(0.817190\pi\)
\(212\) 0 0
\(213\) 17.7587 1.48500i 1.21681 0.101750i
\(214\) 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
\(219\) −10.6776 4.36181i −0.721528 0.294744i
\(220\) 0 0
\(221\) 6.52807 8.98512i 0.439126 0.604404i
\(222\) 0 0
\(223\) −10.1560 + 5.17474i −0.680097 + 0.346526i −0.759676 0.650302i \(-0.774642\pi\)
0.0795792 + 0.996829i \(0.474642\pi\)
\(224\) 0 0
\(225\) −9.91239 + 11.2581i −0.660826 + 0.750539i
\(226\) 0 0
\(227\) −12.6380 + 6.43937i −0.838812 + 0.427396i −0.819956 0.572426i \(-0.806002\pi\)
−0.0188557 + 0.999822i \(0.506002\pi\)
\(228\) 0 0
\(229\) 2.06221 2.83839i 0.136275 0.187566i −0.735425 0.677606i \(-0.763018\pi\)
0.871700 + 0.490039i \(0.163018\pi\)
\(230\) 0 0
\(231\) −2.24824 0.918407i −0.147924 0.0604267i
\(232\) 0 0
\(233\) 0.450064 2.84159i 0.0294847 0.186159i −0.968550 0.248818i \(-0.919958\pi\)
0.998035 + 0.0626588i \(0.0199580\pi\)
\(234\) 0 0
\(235\) −0.119801 + 0.914735i −0.00781496 + 0.0596708i
\(236\) 0 0
\(237\) 16.3486 1.36708i 1.06195 0.0888015i
\(238\) 0 0
\(239\) 4.44446 13.6787i 0.287488 0.884798i −0.698153 0.715948i \(-0.745995\pi\)
0.985642 0.168850i \(-0.0540054\pi\)
\(240\) 0 0
\(241\) 0.877493 + 2.70064i 0.0565243 + 0.173964i 0.975333 0.220740i \(-0.0708472\pi\)
−0.918808 + 0.394704i \(0.870847\pi\)
\(242\) 0 0
\(243\) 6.31553 + 14.2518i 0.405142 + 0.914254i
\(244\) 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
\(255\) −2.27586 8.30857i −0.142520 0.520303i
\(256\) 0 0
\(257\) −9.47863 9.47863i −0.591261 0.591261i 0.346711 0.937972i \(-0.387298\pi\)
−0.937972 + 0.346711i \(0.887298\pi\)
\(258\) 0 0
\(259\) 8.87311 2.88305i 0.551348 0.179144i
\(260\) 0 0
\(261\) −2.54707 + 2.59736i −0.157660 + 0.160772i
\(262\) 0 0
\(263\) −2.07596 1.05775i −0.128009 0.0652239i 0.388813 0.921317i \(-0.372885\pi\)
−0.516822 + 0.856093i \(0.672885\pi\)
\(264\) 0 0
\(265\) −30.9665 4.05562i −1.90226 0.249135i
\(266\) 0 0
\(267\) −21.2272 + 8.91438i −1.29908 + 0.545551i
\(268\) 0 0
\(269\) 22.3119 16.2105i 1.36038 0.988373i 0.361958 0.932194i \(-0.382108\pi\)
0.998421 0.0561787i \(-0.0178917\pi\)
\(270\) 0 0
\(271\) 25.5707 + 18.5782i 1.55331 + 1.12854i 0.941239 + 0.337740i \(0.109662\pi\)
0.612069 + 0.790805i \(0.290338\pi\)
\(272\) 0 0
\(273\) −5.75591 + 9.49665i −0.348363 + 0.574763i
\(274\) 0 0
\(275\) 3.44177 + 4.23855i 0.207546 + 0.255594i
\(276\) 0 0
\(277\) 3.14609 + 6.17455i 0.189030 + 0.370993i 0.965999 0.258547i \(-0.0832436\pi\)
−0.776969 + 0.629539i \(0.783244\pi\)
\(278\) 0 0
\(279\) 1.70243 + 3.26200i 0.101922 + 0.195291i
\(280\) 0 0
\(281\) −3.62737 4.99264i −0.216391 0.297836i 0.686998 0.726660i \(-0.258928\pi\)
−0.903388 + 0.428823i \(0.858928\pi\)
\(282\) 0 0
\(283\) 3.40261 + 0.538921i 0.202264 + 0.0320355i 0.256744 0.966479i \(-0.417350\pi\)
−0.0544801 + 0.998515i \(0.517350\pi\)
\(284\) 0 0
\(285\) −7.82916 + 13.7363i −0.463759 + 0.813669i
\(286\) 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
\(291\) 20.5325 + 17.3636i 1.20364 + 1.01787i
\(292\) 0 0
\(293\) −14.3870 + 14.3870i −0.840500 + 0.840500i −0.988924 0.148424i \(-0.952580\pi\)
0.148424 + 0.988924i \(0.452580\pi\)
\(294\) 0 0
\(295\) 0.732441 + 27.2695i 0.0426444 + 1.58769i
\(296\) 0 0
\(297\) 5.49736 1.40535i 0.318989 0.0815466i
\(298\) 0 0
\(299\) −23.4730 −1.35748
\(300\) 0 0
\(301\) 2.69270 0.155205
\(302\) 0 0
\(303\) 14.2779 12.3157i 0.820244 0.707516i
\(304\) 0 0
\(305\) 1.40936 2.05360i 0.0806999 0.117589i
\(306\) 0 0
\(307\) 21.8121 21.8121i 1.24488 1.24488i 0.286934 0.957950i \(-0.407364\pi\)
0.957950 0.286934i \(-0.0926362\pi\)
\(308\) 0 0
\(309\) 9.24191 10.9286i 0.525754 0.621705i
\(310\) 0 0
\(311\) 23.6419 + 7.68170i 1.34061 + 0.435589i 0.889522 0.456892i \(-0.151037\pi\)
0.451084 + 0.892481i \(0.351037\pi\)
\(312\) 0 0
\(313\) −5.16865 + 10.1440i −0.292149 + 0.573375i −0.989699 0.143161i \(-0.954273\pi\)
0.697550 + 0.716536i \(0.254273\pi\)
\(314\) 0 0
\(315\) 2.95992 + 8.08900i 0.166773 + 0.455764i
\(316\) 0 0
\(317\) −15.6631 2.48079i −0.879728 0.139335i −0.299799 0.954002i \(-0.596920\pi\)
−0.579929 + 0.814667i \(0.696920\pi\)
\(318\) 0 0
\(319\) 0.778322 + 1.07127i 0.0435777 + 0.0599795i
\(320\) 0 0
\(321\) 1.18410 16.0476i 0.0660898 0.895691i
\(322\) 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
\(327\) −28.8385 17.4790i −1.59478 0.966591i
\(328\) 0 0
\(329\) 0.428585 + 0.311385i 0.0236286 + 0.0171672i
\(330\) 0 0
\(331\) −10.2103 + 7.41821i −0.561209 + 0.407742i −0.831901 0.554924i \(-0.812747\pi\)
0.270693 + 0.962666i \(0.412747\pi\)
\(332\) 0 0
\(333\) −12.6395 + 17.7593i −0.692642 + 0.973203i
\(334\) 0 0
\(335\) −7.54253 + 15.8407i −0.412093 + 0.865468i
\(336\) 0 0
\(337\) 4.25752 + 2.16931i 0.231922 + 0.118170i 0.566090 0.824343i \(-0.308455\pi\)
−0.334168 + 0.942513i \(0.608455\pi\)
\(338\) 0 0
\(339\) 2.59141 + 10.5663i 0.140746 + 0.573881i
\(340\) 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
\(345\) −11.3792 + 14.2130i −0.612636 + 0.765202i
\(346\) 0 0
\(347\) −2.24653 14.1841i −0.120600 0.761440i −0.971662 0.236374i \(-0.924041\pi\)
0.851062 0.525066i \(-0.175959\pi\)
\(348\) 0 0
\(349\) 20.9612i 1.12203i 0.827807 + 0.561013i \(0.189588\pi\)
−0.827807 + 0.561013i \(0.810412\pi\)
\(350\) 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 \(-0.508245\pi\)
0.284281 + 0.958741i \(0.408245\pi\)
\(354\) 0 0
\(355\) −18.2428 + 14.0177i −0.968227 + 0.743982i
\(356\) 0 0
\(357\) −4.81574 1.13129i −0.254876 0.0598744i
\(358\) 0 0
\(359\) −2.41734 7.43981i −0.127582 0.392658i 0.866780 0.498690i \(-0.166185\pi\)
−0.994363 + 0.106032i \(0.966185\pi\)
\(360\) 0 0
\(361\) 0.721413 2.22028i 0.0379691 0.116857i
\(362\) 0 0
\(363\) 1.41554 + 16.9281i 0.0742967 + 0.888495i
\(364\) 0 0
\(365\) 14.6394 2.72344i 0.766261 0.142552i
\(366\) 0 0
\(367\) 2.47261 15.6115i 0.129069 0.814912i −0.835192 0.549959i \(-0.814643\pi\)
0.964261 0.264953i \(-0.0853565\pi\)
\(368\) 0 0
\(369\) −4.49294 26.6771i −0.233893 1.38875i
\(370\) 0 0
\(371\) −10.5413 + 14.5089i −0.547277 + 0.753262i
\(372\) 0 0
\(373\) −14.5011 + 7.38868i −0.750838 + 0.382571i −0.787144 0.616770i \(-0.788441\pi\)
0.0363057 + 0.999341i \(0.488441\pi\)
\(374\) 0 0
\(375\) 2.89719 19.1470i 0.149610 0.988745i
\(376\) 0 0
\(377\) 5.39483 2.74880i 0.277848 0.141571i
\(378\) 0 0
\(379\) 19.2777 26.5335i 0.990229 1.36293i 0.0590965 0.998252i \(-0.481178\pi\)
0.931133 0.364681i \(-0.118822\pi\)
\(380\) 0 0
\(381\) −2.36786 + 5.79647i −0.121309 + 0.296962i
\(382\) 0 0
\(383\) −2.51909 + 15.9049i −0.128720 + 0.812703i 0.835866 + 0.548933i \(0.184966\pi\)
−0.964586 + 0.263770i \(0.915034\pi\)
\(384\) 0 0
\(385\) 3.08242 0.573438i 0.157094 0.0292251i
\(386\) 0 0
\(387\) −5.05331 + 3.74745i −0.256874 + 0.190494i
\(388\) 0 0
\(389\) 7.88904 24.2800i 0.399990 1.23104i −0.525017 0.851092i \(-0.675941\pi\)
0.925007 0.379951i \(-0.124059\pi\)
\(390\) 0 0
\(391\) −3.23122 9.94467i −0.163410 0.502924i
\(392\) 0 0
\(393\) 4.42832 18.8507i 0.223379 0.950890i
\(394\) 0 0
\(395\) −16.7942 + 12.9046i −0.845009 + 0.649302i
\(396\) 0 0
\(397\) −2.82041 + 0.446710i −0.141553 + 0.0224197i −0.226809 0.973939i \(-0.572829\pi\)
0.0852560 + 0.996359i \(0.472829\pi\)
\(398\) 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
\(405\) −16.8123 11.0610i −0.835410 0.549627i
\(406\) 0 0
\(407\) 5.61046 + 5.61046i 0.278100 + 0.278100i
\(408\) 0 0
\(409\) 25.9665 8.43701i 1.28396 0.417183i 0.413986 0.910283i \(-0.364136\pi\)
0.869973 + 0.493100i \(0.164136\pi\)
\(410\) 0 0
\(411\) 20.7142 5.08023i 1.02176 0.250589i
\(412\) 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
\(417\) 11.0931 + 26.4153i 0.543232 + 1.29356i
\(418\) 0 0
\(419\) 14.7007 10.6807i 0.718178 0.521787i −0.167624 0.985851i \(-0.553609\pi\)
0.885802 + 0.464064i \(0.153609\pi\)
\(420\) 0 0
\(421\) −0.685185 0.497816i −0.0333939 0.0242621i 0.570963 0.820976i \(-0.306570\pi\)
−0.604357 + 0.796714i \(0.706570\pi\)
\(422\) 0 0
\(423\) −1.23767 + 0.0120971i −0.0601775 + 0.000588183i
\(424\) 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
\(429\) −9.41837 0.694947i −0.454723 0.0335524i
\(430\) 0 0
\(431\) 11.3436 + 15.6131i 0.546401 + 0.752057i 0.989518 0.144407i \(-0.0461274\pi\)
−0.443117 + 0.896464i \(0.646127\pi\)
\(432\) 0 0
\(433\) 14.7512 + 2.33636i 0.708897 + 0.112278i 0.500463 0.865758i \(-0.333163\pi\)
0.208434 + 0.978036i \(0.433163\pi\)
\(434\) 0 0
\(435\) 0.950886 4.59916i 0.0455915 0.220513i
\(436\) 0 0
\(437\) −8.71262 + 17.0995i −0.416781 + 0.817979i
\(438\) 0 0
\(439\) 3.77327 + 1.22601i 0.180088 + 0.0585143i 0.397673 0.917527i \(-0.369818\pi\)
−0.217585 + 0.976041i \(0.569818\pi\)
\(440\) 0 0
\(441\) −15.8799 2.35627i −0.756187 0.112204i
\(442\) 0 0
\(443\) 20.1922 20.1922i 0.959360 0.959360i −0.0398456 0.999206i \(-0.512687\pi\)
0.999206 + 0.0398456i \(0.0126866\pi\)
\(444\) 0 0
\(445\) 16.8186 24.5065i 0.797278 1.16172i
\(446\) 0 0
\(447\) −8.16186 9.46228i −0.386043 0.447551i
\(448\) 0 0
\(449\) −19.6086 −0.925387 −0.462693 0.886518i \(-0.653117\pi\)
−0.462693 + 0.886518i \(0.653117\pi\)
\(450\) 0 0
\(451\) −9.84714 −0.463684
\(452\) 0 0
\(453\) 9.72335 + 11.2726i 0.456843 + 0.529631i
\(454\) 0 0
\(455\) −0.384923 14.3311i −0.0180455 0.671851i
\(456\) 0 0
\(457\) 0.286369 0.286369i 0.0133958 0.0133958i −0.700377 0.713773i \(-0.746985\pi\)
0.713773 + 0.700377i \(0.246985\pi\)
\(458\) 0 0
\(459\) 10.6120 4.57902i 0.495324 0.213730i
\(460\) 0 0
\(461\) −7.31001 2.37517i −0.340461 0.110623i 0.133796 0.991009i \(-0.457283\pi\)
−0.474257 + 0.880386i \(0.657283\pi\)
\(462\) 0 0
\(463\) −2.82556 + 5.54548i −0.131315 + 0.257720i −0.947297 0.320358i \(-0.896197\pi\)
0.815982 + 0.578078i \(0.196197\pi\)
\(464\) 0 0
\(465\) −4.12698 2.35221i −0.191384 0.109081i
\(466\) 0 0
\(467\) −2.70390 0.428256i −0.125122 0.0198173i 0.0935595 0.995614i \(-0.470175\pi\)
−0.218681 + 0.975796i \(0.570175\pi\)
\(468\) 0 0
\(469\) 5.92182 + 8.15069i 0.273444 + 0.376364i
\(470\) 0 0
\(471\) −22.5300 1.66241i −1.03813 0.0765997i
\(472\) 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
\(477\) −0.409524 41.8987i −0.0187508 1.91841i
\(478\) 0 0
\(479\) 5.68590 + 4.13105i 0.259796 + 0.188753i 0.710057 0.704144i \(-0.248669\pi\)
−0.450261 + 0.892897i \(0.648669\pi\)
\(480\) 0 0
\(481\) 29.3513 21.3249i 1.33830 0.972334i
\(482\) 0 0
\(483\) 4.04816 + 9.63961i 0.184198 + 0.438617i
\(484\) 0 0
\(485\) −34.4211 4.50806i −1.56298 0.204700i
\(486\) 0 0
\(487\) 7.03443 + 3.58422i 0.318761 + 0.162417i 0.606049 0.795428i \(-0.292754\pi\)
−0.287288 + 0.957844i \(0.592754\pi\)
\(488\) 0 0
\(489\) −1.59018 + 0.389997i −0.0719104 + 0.0176363i
\(490\) 0 0
\(491\) 7.06686 2.29616i 0.318923 0.103624i −0.145181 0.989405i \(-0.546376\pi\)
0.464104 + 0.885781i \(0.346376\pi\)
\(492\) 0 0
\(493\) 1.90721 + 1.90721i 0.0858963 + 0.0858963i
\(494\) 0 0
\(495\) −4.98662 + 5.36597i −0.224132 + 0.241182i
\(496\) 0 0
\(497\) 2.06667 + 13.0485i 0.0927030 + 0.585303i
\(498\) 0 0
\(499\) 16.9596i 0.759216i 0.925147 + 0.379608i \(0.123941\pi\)
−0.925147 + 0.379608i \(0.876059\pi\)
\(500\) 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 \(-0.223731\pi\)
0.925397 + 0.378998i \(0.123731\pi\)
\(504\) 0 0
\(505\) −6.89793 + 23.3447i −0.306954 + 1.03882i
\(506\) 0 0
\(507\) −4.72616 + 20.1185i −0.209896 + 0.893493i
\(508\) 0 0
\(509\) 7.22530 + 22.2372i 0.320256 + 0.985646i 0.973537 + 0.228531i \(0.0733921\pi\)
−0.653281 + 0.757116i \(0.726608\pi\)
\(510\) 0 0
\(511\) 2.64231 8.13220i 0.116889 0.359747i
\(512\) 0 0
\(513\) −19.7146 7.82947i −0.870422 0.345679i
\(514\) 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
\(519\) 2.45868 6.01880i 0.107924 0.264196i
\(520\) 0 0
\(521\) 6.11512 8.41674i 0.267908 0.368744i −0.653774 0.756690i \(-0.726815\pi\)
0.921682 + 0.387946i \(0.126815\pi\)
\(522\) 0 0
\(523\) 29.8122 15.1901i 1.30360 0.664216i 0.342263 0.939604i \(-0.388806\pi\)
0.961333 + 0.275389i \(0.0888065\pi\)
\(524\) 0 0
\(525\) −8.86414 6.71433i −0.386863 0.293037i
\(526\) 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
\(531\) −36.0908 + 6.07839i −1.56621 + 0.263780i
\(532\) 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
\(537\) 1.45745 + 17.4292i 0.0628935 + 0.752127i
\(538\) 0 0
\(539\) −1.80575 + 5.55753i −0.0777792 + 0.239380i
\(540\) 0 0
\(541\) −0.727097 2.23777i −0.0312603 0.0962094i 0.934209 0.356726i \(-0.116107\pi\)
−0.965469 + 0.260517i \(0.916107\pi\)
\(542\) 0 0
\(543\) −20.7669 4.87849i −0.891194 0.209356i
\(544\) 0 0
\(545\) 43.5193 1.16890i 1.86416 0.0500701i
\(546\) 0 0
\(547\) −43.1229 + 6.82999i −1.84380 + 0.292029i −0.978038 0.208426i \(-0.933166\pi\)
−0.865762 + 0.500456i \(0.833166\pi\)
\(548\) 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
\(555\) 1.31652 28.1102i 0.0558832 1.19321i
\(556\) 0 0
\(557\) −3.81138 3.81138i −0.161493 0.161493i 0.621735 0.783228i \(-0.286428\pi\)
−0.783228 + 0.621735i \(0.786428\pi\)
\(558\) 0 0
\(559\) 9.95852 3.23572i 0.421200 0.136856i
\(560\) 0 0
\(561\) −1.00208 4.08589i −0.0423078 0.172507i
\(562\) 0 0
\(563\) −29.0405 14.7969i −1.22391 0.623615i −0.281981 0.959420i \(-0.590992\pi\)
−0.941931 + 0.335805i \(0.890992\pi\)
\(564\) 0 0
\(565\) −10.1946 9.66125i −0.428889 0.406452i
\(566\) 0 0
\(567\) −10.1922 + 5.44670i −0.428032 + 0.228740i
\(568\) 0 0
\(569\) −1.73598 + 1.26126i −0.0727760 + 0.0528749i −0.623578 0.781761i \(-0.714322\pi\)
0.550802 + 0.834636i \(0.314322\pi\)
\(570\) 0 0
\(571\) 4.09296 + 2.97371i 0.171285 + 0.124446i 0.670125 0.742248i \(-0.266240\pi\)
−0.498840 + 0.866694i \(0.666240\pi\)
\(572\) 0 0
\(573\) −19.0460 11.5438i −0.795658 0.482247i
\(574\) 0 0
\(575\) 2.42549 23.3797i 0.101150 0.975000i
\(576\) 0 0
\(577\) 10.9908 + 21.5708i 0.457555 + 0.898002i 0.998382 + 0.0568682i \(0.0181115\pi\)
−0.540827 + 0.841134i \(0.681889\pi\)
\(578\) 0 0
\(579\) −1.79699 + 24.3540i −0.0746804 + 1.01212i
\(580\) 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
\(585\) 20.6670 + 26.3590i 0.854476 + 1.08981i
\(586\) 0 0
\(587\) 12.2504 24.0428i 0.505628 0.992352i −0.487255 0.873260i \(-0.662002\pi\)
0.992883 0.119092i \(-0.0379983\pi\)
\(588\) 0 0
\(589\) −4.76196 1.54725i −0.196213 0.0637535i
\(590\) 0 0
\(591\) −8.60267 + 10.1727i −0.353866 + 0.418448i
\(592\) 0 0
\(593\) 7.14857 7.14857i 0.293556 0.293556i −0.544927 0.838483i \(-0.683443\pi\)
0.838483 + 0.544927i \(0.183443\pi\)
\(594\) 0 0
\(595\) 6.01858 2.13585i 0.246738 0.0875614i
\(596\) 0 0
\(597\) 21.0980 18.1985i 0.863485 0.744815i
\(598\) 0 0
\(599\) −20.6392 −0.843294 −0.421647 0.906760i \(-0.638548\pi\)
−0.421647 + 0.906760i \(0.638548\pi\)
\(600\) 0 0
\(601\) −7.30272 −0.297884 −0.148942 0.988846i \(-0.547587\pi\)
−0.148942 + 0.988846i \(0.547587\pi\)
\(602\) 0 0
\(603\) −22.4567 7.05471i −0.914506 0.287290i
\(604\) 0 0
\(605\) −13.3621 17.3895i −0.543245 0.706985i
\(606\) 0 0
\(607\) 10.3692 10.3692i 0.420872 0.420872i −0.464632 0.885504i \(-0.653813\pi\)
0.885504 + 0.464632i \(0.153813\pi\)
\(608\) 0 0
\(609\) −2.05924 1.74143i −0.0834446 0.0705661i
\(610\) 0 0
\(611\) 1.95923 + 0.636592i 0.0792619 + 0.0257537i
\(612\) 0 0
\(613\) −2.08080 + 4.08379i −0.0840425 + 0.164943i −0.929203 0.369570i \(-0.879505\pi\)
0.845160 + 0.534513i \(0.179505\pi\)
\(614\) 0 0
\(615\) 23.5133 + 25.8240i 0.948149 + 1.04132i
\(616\) 0 0
\(617\) 3.30490 + 0.523445i 0.133050 + 0.0210731i 0.222604 0.974909i \(-0.428544\pi\)
−0.0895540 + 0.995982i \(0.528544\pi\)
\(618\) 0 0
\(619\) −18.6414 25.6577i −0.749260 1.03127i −0.998032 0.0627063i \(-0.980027\pi\)
0.248772 0.968562i \(-0.419973\pi\)
\(620\) 0 0
\(621\) −21.0126 12.4565i −0.843205 0.499862i
\(622\) 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
\(627\) −4.00213 + 6.60310i −0.159830 + 0.263702i
\(628\) 0 0
\(629\) 13.0750 + 9.49957i 0.521336 + 0.378773i
\(630\) 0 0
\(631\) −2.88632 + 2.09703i −0.114902 + 0.0834815i −0.643753 0.765234i \(-0.722623\pi\)
0.528850 + 0.848715i \(0.322623\pi\)
\(632\) 0 0
\(633\) 36.0068 15.1211i 1.43114 0.601010i
\(634\) 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
\(639\) −22.0381 21.6114i −0.871813 0.854935i
\(640\) 0 0
\(641\) −26.6743 + 8.66700i −1.05357 + 0.342326i −0.784069 0.620674i \(-0.786859\pi\)
−0.269502 + 0.963000i \(0.586859\pi\)
\(642\) 0 0
\(643\) −4.46449 4.46449i −0.176062 0.176062i 0.613575 0.789637i \(-0.289731\pi\)
−0.789637 + 0.613575i \(0.789731\pi\)
\(644\) 0 0
\(645\) 2.86843 7.59853i 0.112945 0.299192i
\(646\) 0 0
\(647\) 2.38692 + 15.0704i 0.0938396 + 0.592480i 0.989135 + 0.147008i \(0.0469642\pi\)
−0.895296 + 0.445472i \(0.853036\pi\)
\(648\) 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 \(-0.691352\pi\)
−0.283068 + 0.959100i \(0.591352\pi\)
\(654\) 0 0
\(655\) 8.36055 + 23.5591i 0.326674 + 0.920529i
\(656\) 0 0
\(657\) 6.35888 + 18.9388i 0.248084 + 0.738872i
\(658\) 0 0
\(659\) −3.02628 9.31393i −0.117887 0.362819i 0.874651 0.484753i \(-0.161090\pi\)
−0.992538 + 0.121934i \(0.961090\pi\)
\(660\) 0 0
\(661\) −14.2639 + 43.8997i −0.554800 + 1.70750i 0.141671 + 0.989914i \(0.454753\pi\)
−0.696471 + 0.717585i \(0.745247\pi\)
\(662\) 0 0
\(663\) −19.1696 + 1.60298i −0.744487 + 0.0622546i
\(664\) 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
\(669\) 18.2764 + 7.46591i 0.706607 + 0.288649i
\(670\) 0 0
\(671\) 0.714946 0.984039i 0.0276002 0.0379884i
\(672\) 0 0
\(673\) −8.88482 + 4.52704i −0.342485 + 0.174505i −0.616769 0.787144i \(-0.711559\pi\)
0.274285 + 0.961648i \(0.411559\pi\)
\(674\) 0 0
\(675\) 25.9794 + 0.264307i 0.999948 + 0.0101732i
\(676\) 0 0
\(677\) 32.0266 16.3184i 1.23088 0.627167i 0.287154 0.957884i \(-0.407291\pi\)
0.943730 + 0.330718i \(0.107291\pi\)
\(678\) 0 0
\(679\) −11.7173 + 16.1274i −0.449668 + 0.618914i
\(680\) 0 0
\(681\) 22.7429 + 9.29046i 0.871510 + 0.356011i
\(682\) 0 0
\(683\) 4.75779 30.0395i 0.182052 1.14943i −0.712237 0.701939i \(-0.752318\pi\)
0.894289 0.447490i \(-0.147682\pi\)
\(684\) 0 0
\(685\) −18.9400 + 19.9855i −0.723660 + 0.763607i
\(686\) 0 0
\(687\) −6.05567 + 0.506380i −0.231038 + 0.0193196i
\(688\) 0 0
\(689\) −21.5505 + 66.3257i −0.821009 + 2.52681i
\(690\) 0 0
\(691\) −5.29160 16.2859i −0.201302 0.619543i −0.999845 0.0176058i \(-0.994396\pi\)
0.798543 0.601938i \(-0.205604\pi\)
\(692\) 0 0
\(693\) 1.33890 + 3.98768i 0.0508607 + 0.151479i
\(694\) 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
\(705\) 1.33525 0.877715i 0.0502885 0.0330567i
\(706\) 0 0
\(707\) 9.88417 + 9.88417i 0.371732 + 0.371732i
\(708\) 0 0
\(709\) −34.2516 + 11.1290i −1.28635 + 0.417959i −0.870811 0.491618i \(-0.836406\pi\)
−0.415535 + 0.909577i \(0.636406\pi\)
\(710\) 0 0
\(711\) −20.2881 19.8954i −0.760865 0.746135i
\(712\) 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
\(717\) −22.9682 + 9.64553i −0.857765 + 0.360219i
\(718\) 0 0
\(719\) −27.9485 + 20.3058i −1.04230 + 0.757278i −0.970734 0.240158i \(-0.922801\pi\)
−0.0715696 + 0.997436i \(0.522801\pi\)
\(720\) 0 0
\(721\) 8.58395 + 6.23660i 0.319683 + 0.232263i
\(722\) 0 0
\(723\) 2.54932 4.20611i 0.0948102 0.156427i
\(724\) 0 0
\(725\) 2.18042 + 5.65742i 0.0809788 + 0.210111i
\(726\) 0 0
\(727\) 14.5118 + 28.4810i 0.538212 + 1.05630i 0.986706 + 0.162515i \(0.0519607\pi\)
−0.448494 + 0.893786i \(0.648039\pi\)
\(728\) 0 0
\(729\) 11.5472 24.4062i 0.427673 0.903933i
\(730\) 0 0
\(731\) 2.74172 + 3.77365i 0.101406 + 0.139574i
\(732\) 0 0
\(733\) 20.6997 + 3.27851i 0.764560 + 0.121094i 0.526522 0.850161i \(-0.323496\pi\)
0.238038 + 0.971256i \(0.423496\pi\)
\(734\) 0 0
\(735\) 18.8864 8.53490i 0.696635 0.314815i
\(736\) 0 0
\(737\) −3.88980 + 7.63416i −0.143283 + 0.281208i
\(738\) 0 0
\(739\) −7.83354 2.54527i −0.288162 0.0936294i 0.161370 0.986894i \(-0.448409\pi\)
−0.449531 + 0.893265i \(0.648409\pi\)
\(740\) 0 0
\(741\) 26.9584 + 22.7977i 0.990340 + 0.837495i
\(742\) 0 0
\(743\) −30.1299 + 30.1299i −1.10536 + 1.10536i −0.111607 + 0.993752i \(0.535600\pi\)
−0.993752 + 0.111607i \(0.964400\pi\)
\(744\) 0 0
\(745\) 15.4711 + 4.57141i 0.566816 + 0.167484i
\(746\) 0 0
\(747\) 51.0938 + 16.0510i 1.86943 + 0.587276i
\(748\) 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
\(753\) 16.8494 14.5337i 0.614025 0.529638i
\(754\) 0 0
\(755\) −18.4309 5.44600i −0.670769 0.198200i
\(756\) 0 0
\(757\) −1.20647 + 1.20647i −0.0438498 + 0.0438498i −0.728692 0.684842i \(-0.759871\pi\)
0.684842 + 0.728692i \(0.259871\pi\)
\(758\) 0 0
\(759\) −5.74143 + 6.78925i −0.208401 + 0.246434i
\(760\) 0 0
\(761\) −41.1754 13.3787i −1.49261 0.484978i −0.554756 0.832013i \(-0.687189\pi\)
−0.937852 + 0.347035i \(0.887189\pi\)
\(762\) 0 0
\(763\) 11.3495 22.2746i 0.410878 0.806394i
\(764\) 0 0
\(765\) −8.32241 + 12.3844i −0.300898 + 0.447758i
\(766\) 0 0
\(767\) 60.1650 + 9.52920i 2.17243 + 0.344080i
\(768\) 0 0
\(769\) −19.1217 26.3187i −0.689545 0.949078i 0.310454 0.950589i \(-0.399519\pi\)
−0.999999 + 0.00151094i \(0.999519\pi\)
\(770\) 0 0
\(771\) −1.70851 + 23.1549i −0.0615306 + 0.833902i
\(772\) 0 0
\(773\) −7.28640 14.3004i −0.262074 0.514348i 0.722048 0.691843i \(-0.243201\pi\)
−0.984122 + 0.177494i \(0.943201\pi\)
\(774\) 0 0
\(775\) 6.12370 0.329194i 0.219970 0.0118250i
\(776\) 0 0
\(777\) −13.8194 8.37593i −0.495769 0.300485i
\(778\) 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
\(783\) 6.28806 + 0.402223i 0.224717 + 0.0143743i
\(784\) 0 0
\(785\) 25.6215 13.9337i 0.914470 0.497314i
\(786\) 0 0
\(787\) −2.48782 1.26761i −0.0886811 0.0451853i 0.409087 0.912495i \(-0.365847\pi\)
−0.497769 + 0.867310i \(0.665847\pi\)
\(788\) 0 0
\(789\) 0.961237 + 3.91936i 0.0342209 + 0.139533i
\(790\) 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
\(795\) 29.7133 + 45.2022i 1.05382 + 1.60316i
\(796\) 0 0
\(797\) −7.08694