Properties

Label 300.2.x.a.53.10
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 53.10
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.66741 - 0.468765i) q^{3} +(-0.354250 + 2.20783i) q^{5} +(-1.67035 + 1.67035i) q^{7} +(2.56052 - 1.56325i) q^{9} +O(q^{10})\) \(q+(1.66741 - 0.468765i) q^{3} +(-0.354250 + 2.20783i) q^{5} +(-1.67035 + 1.67035i) q^{7} +(2.56052 - 1.56325i) q^{9} +(5.27981 + 1.71551i) q^{11} +(-1.00207 + 1.96667i) q^{13} +(0.444271 + 3.84742i) q^{15} +(4.25837 + 0.674459i) q^{17} +(-4.59013 - 6.31777i) q^{19} +(-2.00216 + 3.56817i) q^{21} +(-1.53667 - 3.01588i) q^{23} +(-4.74901 - 1.56425i) q^{25} +(3.53664 - 3.80686i) q^{27} +(-0.409155 - 0.297269i) q^{29} +(2.41697 - 1.75603i) q^{31} +(9.60778 + 0.385478i) q^{33} +(-3.09613 - 4.27958i) q^{35} +(-7.68210 - 3.91423i) q^{37} +(-0.748954 + 3.74898i) q^{39} +(-4.48088 + 1.45593i) q^{41} +(5.88737 + 5.88737i) q^{43} +(2.54432 + 6.20697i) q^{45} +(0.527820 + 3.33252i) q^{47} +1.41984i q^{49} +(7.41661 - 0.871573i) q^{51} +(-5.21091 + 0.825328i) q^{53} +(-5.65793 + 11.0492i) q^{55} +(-10.6152 - 8.38263i) q^{57} +(-3.17139 - 9.76054i) q^{59} +(1.65928 - 5.10673i) q^{61} +(-1.66580 + 6.88815i) q^{63} +(-3.98709 - 2.90909i) q^{65} +(0.707187 - 4.46500i) q^{67} +(-3.97600 - 4.30838i) q^{69} +(6.04875 - 8.32540i) q^{71} +(-1.93067 + 0.983727i) q^{73} +(-8.65182 - 0.382074i) q^{75} +(-11.6847 + 5.95363i) q^{77} +(10.1110 - 13.9166i) q^{79} +(4.11252 - 8.00545i) q^{81} +(-1.93251 + 12.2014i) q^{83} +(-2.99762 + 9.16282i) q^{85} +(-0.821579 - 0.303872i) q^{87} +(-1.43321 + 4.41098i) q^{89} +(-1.61123 - 4.95884i) q^{91} +(3.20692 - 4.06102i) q^{93} +(15.5746 - 7.89614i) q^{95} +(-15.9942 + 2.53324i) q^{97} +(16.2008 - 3.86104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

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
\(3\) 1.66741 0.468765i 0.962680 0.270642i
\(4\) 0 0
\(5\) −0.354250 + 2.20783i −0.158426 + 0.987371i
\(6\) 0 0
\(7\) −1.67035 + 1.67035i −0.631334 + 0.631334i −0.948403 0.317068i \(-0.897302\pi\)
0.317068 + 0.948403i \(0.397302\pi\)
\(8\) 0 0
\(9\) 2.56052 1.56325i 0.853506 0.521082i
\(10\) 0 0
\(11\) 5.27981 + 1.71551i 1.59192 + 0.517247i 0.965092 0.261910i \(-0.0843522\pi\)
0.626830 + 0.779156i \(0.284352\pi\)
\(12\) 0 0
\(13\) −1.00207 + 1.96667i −0.277924 + 0.545456i −0.987202 0.159472i \(-0.949021\pi\)
0.709279 + 0.704928i \(0.249021\pi\)
\(14\) 0 0
\(15\) 0.444271 + 3.84742i 0.114710 + 0.993399i
\(16\) 0 0
\(17\) 4.25837 + 0.674459i 1.03281 + 0.163580i 0.649753 0.760146i \(-0.274872\pi\)
0.383053 + 0.923726i \(0.374872\pi\)
\(18\) 0 0
\(19\) −4.59013 6.31777i −1.05305 1.44940i −0.886137 0.463423i \(-0.846621\pi\)
−0.166911 0.985972i \(-0.553379\pi\)
\(20\) 0 0
\(21\) −2.00216 + 3.56817i −0.436908 + 0.778638i
\(22\) 0 0
\(23\) −1.53667 3.01588i −0.320418 0.628855i 0.673475 0.739210i \(-0.264801\pi\)
−0.993892 + 0.110355i \(0.964801\pi\)
\(24\) 0 0
\(25\) −4.74901 1.56425i −0.949803 0.312850i
\(26\) 0 0
\(27\) 3.53664 3.80686i 0.680627 0.732630i
\(28\) 0 0
\(29\) −0.409155 0.297269i −0.0759783 0.0552014i 0.549148 0.835725i \(-0.314952\pi\)
−0.625126 + 0.780524i \(0.714952\pi\)
\(30\) 0 0
\(31\) 2.41697 1.75603i 0.434101 0.315393i −0.349186 0.937054i \(-0.613542\pi\)
0.783287 + 0.621661i \(0.213542\pi\)
\(32\) 0 0
\(33\) 9.60778 + 0.385478i 1.67250 + 0.0671031i
\(34\) 0 0
\(35\) −3.09613 4.27958i −0.523342 0.723381i
\(36\) 0 0
\(37\) −7.68210 3.91423i −1.26293 0.643495i −0.311174 0.950353i \(-0.600722\pi\)
−0.951755 + 0.306858i \(0.900722\pi\)
\(38\) 0 0
\(39\) −0.748954 + 3.74898i −0.119929 + 0.600317i
\(40\) 0 0
\(41\) −4.48088 + 1.45593i −0.699796 + 0.227377i −0.637242 0.770664i \(-0.719925\pi\)
−0.0625543 + 0.998042i \(0.519925\pi\)
\(42\) 0 0
\(43\) 5.88737 + 5.88737i 0.897816 + 0.897816i 0.995243 0.0974269i \(-0.0310612\pi\)
−0.0974269 + 0.995243i \(0.531061\pi\)
\(44\) 0 0
\(45\) 2.54432 + 6.20697i 0.379284 + 0.925280i
\(46\) 0 0
\(47\) 0.527820 + 3.33252i 0.0769905 + 0.486099i 0.995812 + 0.0914252i \(0.0291423\pi\)
−0.918821 + 0.394673i \(0.870858\pi\)
\(48\) 0 0
\(49\) 1.41984i 0.202834i
\(50\) 0 0
\(51\) 7.41661 0.871573i 1.03853 0.122045i
\(52\) 0 0
\(53\) −5.21091 + 0.825328i −0.715774 + 0.113367i −0.503691 0.863884i \(-0.668025\pi\)
−0.212083 + 0.977252i \(0.568025\pi\)
\(54\) 0 0
\(55\) −5.65793 + 11.0492i −0.762916 + 1.48987i
\(56\) 0 0
\(57\) −10.6152 8.38263i −1.40601 1.11031i
\(58\) 0 0
\(59\) −3.17139 9.76054i −0.412880 1.27071i −0.914134 0.405413i \(-0.867128\pi\)
0.501254 0.865300i \(-0.332872\pi\)
\(60\) 0 0
\(61\) 1.65928 5.10673i 0.212449 0.653850i −0.786876 0.617111i \(-0.788303\pi\)
0.999325 0.0367391i \(-0.0116970\pi\)
\(62\) 0 0
\(63\) −1.66580 + 6.88815i −0.209871 + 0.867825i
\(64\) 0 0
\(65\) −3.98709 2.90909i −0.494537 0.360828i
\(66\) 0 0
\(67\) 0.707187 4.46500i 0.0863966 0.545487i −0.906085 0.423095i \(-0.860944\pi\)
0.992482 0.122392i \(-0.0390564\pi\)
\(68\) 0 0
\(69\) −3.97600 4.30838i −0.478654 0.518668i
\(70\) 0 0
\(71\) 6.04875 8.32540i 0.717855 0.988043i −0.281737 0.959492i \(-0.590911\pi\)
0.999592 0.0285511i \(-0.00908934\pi\)
\(72\) 0 0
\(73\) −1.93067 + 0.983727i −0.225968 + 0.115136i −0.563310 0.826246i \(-0.690472\pi\)
0.337342 + 0.941382i \(0.390472\pi\)
\(74\) 0 0
\(75\) −8.65182 0.382074i −0.999026 0.0441181i
\(76\) 0 0
\(77\) −11.6847 + 5.95363i −1.33159 + 0.678479i
\(78\) 0 0
\(79\) 10.1110 13.9166i 1.13757 1.56574i 0.364764 0.931100i \(-0.381150\pi\)
0.772811 0.634637i \(-0.218850\pi\)
\(80\) 0 0
\(81\) 4.11252 8.00545i 0.456946 0.889494i
\(82\) 0 0
\(83\) −1.93251 + 12.2014i −0.212121 + 1.33928i 0.619964 + 0.784630i \(0.287147\pi\)
−0.832085 + 0.554648i \(0.812853\pi\)
\(84\) 0 0
\(85\) −2.99762 + 9.16282i −0.325137 + 0.993847i
\(86\) 0 0
\(87\) −0.821579 0.303872i −0.0880826 0.0325785i
\(88\) 0 0
\(89\) −1.43321 + 4.41098i −0.151920 + 0.467563i −0.997836 0.0657541i \(-0.979055\pi\)
0.845915 + 0.533317i \(0.179055\pi\)
\(90\) 0 0
\(91\) −1.61123 4.95884i −0.168902 0.519828i
\(92\) 0 0
\(93\) 3.20692 4.06102i 0.332542 0.421108i
\(94\) 0 0
\(95\) 15.5746 7.89614i 1.59792 0.810127i
\(96\) 0 0
\(97\) −15.9942 + 2.53324i −1.62397 + 0.257211i −0.901048 0.433720i \(-0.857201\pi\)
−0.722921 + 0.690931i \(0.757201\pi\)
\(98\) 0 0
\(99\) 16.2008 3.86104i 1.62824 0.388049i
\(100\) 0 0
\(101\) 4.67239i 0.464920i 0.972606 + 0.232460i \(0.0746775\pi\)
−0.972606 + 0.232460i \(0.925322\pi\)
\(102\) 0 0
\(103\) −1.07022 6.75713i −0.105452 0.665800i −0.982622 0.185619i \(-0.940571\pi\)
0.877169 0.480181i \(-0.159429\pi\)
\(104\) 0 0
\(105\) −7.16864 5.68446i −0.699587 0.554746i
\(106\) 0 0
\(107\) 2.84075 + 2.84075i 0.274626 + 0.274626i 0.830959 0.556334i \(-0.187792\pi\)
−0.556334 + 0.830959i \(0.687792\pi\)
\(108\) 0 0
\(109\) −10.7758 + 3.50126i −1.03213 + 0.335360i −0.775633 0.631185i \(-0.782569\pi\)
−0.256499 + 0.966544i \(0.582569\pi\)
\(110\) 0 0
\(111\) −14.6441 2.92552i −1.38995 0.277678i
\(112\) 0 0
\(113\) −3.85613 1.96480i −0.362754 0.184833i 0.263108 0.964767i \(-0.415253\pi\)
−0.625862 + 0.779934i \(0.715253\pi\)
\(114\) 0 0
\(115\) 7.20292 2.32432i 0.671675 0.216744i
\(116\) 0 0
\(117\) 0.508576 + 6.60217i 0.0470179 + 0.610371i
\(118\) 0 0
\(119\) −8.23957 + 5.98640i −0.755320 + 0.548772i
\(120\) 0 0
\(121\) 16.0342 + 11.6495i 1.45765 + 1.05905i
\(122\) 0 0
\(123\) −6.78898 + 4.52811i −0.612142 + 0.408286i
\(124\) 0 0
\(125\) 5.13593 9.93087i 0.459372 0.888244i
\(126\) 0 0
\(127\) −0.759425 1.49046i −0.0673881 0.132257i 0.854855 0.518867i \(-0.173646\pi\)
−0.922243 + 0.386610i \(0.873646\pi\)
\(128\) 0 0
\(129\) 12.5765 + 7.05688i 1.10730 + 0.621323i
\(130\) 0 0
\(131\) 2.70065 + 3.71712i 0.235957 + 0.324767i 0.910531 0.413440i \(-0.135673\pi\)
−0.674575 + 0.738207i \(0.735673\pi\)
\(132\) 0 0
\(133\) 18.2200 + 2.88577i 1.57988 + 0.250228i
\(134\) 0 0
\(135\) 7.15203 + 9.15688i 0.615549 + 0.788099i
\(136\) 0 0
\(137\) 4.03906 7.92710i 0.345080 0.677258i −0.651610 0.758554i \(-0.725906\pi\)
0.996690 + 0.0812966i \(0.0259061\pi\)
\(138\) 0 0
\(139\) 3.53260 + 1.14781i 0.299631 + 0.0973561i 0.454975 0.890504i \(-0.349648\pi\)
−0.155343 + 0.987861i \(0.549648\pi\)
\(140\) 0 0
\(141\) 2.44226 + 5.30926i 0.205676 + 0.447121i
\(142\) 0 0
\(143\) −8.66458 + 8.66458i −0.724568 + 0.724568i
\(144\) 0 0
\(145\) 0.801262 0.798037i 0.0665412 0.0662734i
\(146\) 0 0
\(147\) 0.665570 + 2.36745i 0.0548953 + 0.195264i
\(148\) 0 0
\(149\) 16.5291 1.35411 0.677057 0.735931i \(-0.263255\pi\)
0.677057 + 0.735931i \(0.263255\pi\)
\(150\) 0 0
\(151\) −5.27383 −0.429178 −0.214589 0.976704i \(-0.568841\pi\)
−0.214589 + 0.976704i \(0.568841\pi\)
\(152\) 0 0
\(153\) 11.9580 4.92992i 0.966745 0.398560i
\(154\) 0 0
\(155\) 3.02081 + 5.95833i 0.242637 + 0.478585i
\(156\) 0 0
\(157\) 7.79069 7.79069i 0.621765 0.621765i −0.324218 0.945982i \(-0.605101\pi\)
0.945982 + 0.324218i \(0.105101\pi\)
\(158\) 0 0
\(159\) −8.30185 + 3.81885i −0.658379 + 0.302855i
\(160\) 0 0
\(161\) 7.60437 + 2.47081i 0.599308 + 0.194727i
\(162\) 0 0
\(163\) −7.02791 + 13.7931i −0.550469 + 1.08036i 0.433356 + 0.901223i \(0.357329\pi\)
−0.983825 + 0.179133i \(0.942671\pi\)
\(164\) 0 0
\(165\) −4.25463 + 21.0758i −0.331222 + 1.64075i
\(166\) 0 0
\(167\) 9.92370 + 1.57176i 0.767919 + 0.121626i 0.528090 0.849189i \(-0.322908\pi\)
0.239829 + 0.970815i \(0.422908\pi\)
\(168\) 0 0
\(169\) 4.77756 + 6.57575i 0.367505 + 0.505827i
\(170\) 0 0
\(171\) −21.6293 9.00126i −1.65404 0.688344i
\(172\) 0 0
\(173\) 6.65343 + 13.0581i 0.505851 + 0.992789i 0.992848 + 0.119385i \(0.0380923\pi\)
−0.486997 + 0.873404i \(0.661908\pi\)
\(174\) 0 0
\(175\) 10.5454 5.31968i 0.797156 0.402130i
\(176\) 0 0
\(177\) −9.86341 14.7882i −0.741379 1.11155i
\(178\) 0 0
\(179\) −12.3066 8.94125i −0.919837 0.668301i 0.0236465 0.999720i \(-0.492472\pi\)
−0.943483 + 0.331420i \(0.892472\pi\)
\(180\) 0 0
\(181\) 0.447095 0.324833i 0.0332323 0.0241447i −0.571045 0.820919i \(-0.693462\pi\)
0.604277 + 0.796774i \(0.293462\pi\)
\(182\) 0 0
\(183\) 0.372842 9.29283i 0.0275612 0.686946i
\(184\) 0 0
\(185\) 11.3633 15.5741i 0.835448 1.14503i
\(186\) 0 0
\(187\) 21.3263 + 10.8663i 1.55954 + 0.794623i
\(188\) 0 0
\(189\) 0.451355 + 12.2662i 0.0328312 + 0.892238i
\(190\) 0 0
\(191\) 20.5690 6.68327i 1.48832 0.483585i 0.551734 0.834020i \(-0.313966\pi\)
0.936587 + 0.350435i \(0.113966\pi\)
\(192\) 0 0
\(193\) −3.71609 3.71609i −0.267490 0.267490i 0.560598 0.828088i \(-0.310571\pi\)
−0.828088 + 0.560598i \(0.810571\pi\)
\(194\) 0 0
\(195\) −8.01179 2.98164i −0.573736 0.213520i
\(196\) 0 0
\(197\) 3.06376 + 19.3438i 0.218284 + 1.37819i 0.816726 + 0.577026i \(0.195787\pi\)
−0.598442 + 0.801166i \(0.704213\pi\)
\(198\) 0 0
\(199\) 1.77115i 0.125553i 0.998028 + 0.0627766i \(0.0199956\pi\)
−0.998028 + 0.0627766i \(0.980004\pi\)
\(200\) 0 0
\(201\) −0.913865 7.77649i −0.0644590 0.548512i
\(202\) 0 0
\(203\) 1.17998 0.186890i 0.0828182 0.0131171i
\(204\) 0 0
\(205\) −1.62708 10.4088i −0.113640 0.726980i
\(206\) 0 0
\(207\) −8.64924 5.32003i −0.601164 0.369768i
\(208\) 0 0
\(209\) −13.3968 41.2310i −0.926674 2.85201i
\(210\) 0 0
\(211\) 0.990096 3.04720i 0.0681610 0.209778i −0.911174 0.412021i \(-0.864823\pi\)
0.979335 + 0.202243i \(0.0648230\pi\)
\(212\) 0 0
\(213\) 6.18311 16.7173i 0.423659 1.14545i
\(214\) 0 0
\(215\) −15.0839 + 10.9127i −1.02871 + 0.744240i
\(216\) 0 0
\(217\) −1.10400 + 6.97039i −0.0749445 + 0.473181i
\(218\) 0 0
\(219\) −2.75809 + 2.54531i −0.186374 + 0.171996i
\(220\) 0 0
\(221\) −5.59361 + 7.69895i −0.376267 + 0.517887i
\(222\) 0 0
\(223\) −2.15039 + 1.09568i −0.144001 + 0.0733720i −0.524506 0.851407i \(-0.675750\pi\)
0.380505 + 0.924779i \(0.375750\pi\)
\(224\) 0 0
\(225\) −14.6052 + 3.41860i −0.973683 + 0.227906i
\(226\) 0 0
\(227\) −14.3886 + 7.33136i −0.955005 + 0.486599i −0.860794 0.508953i \(-0.830033\pi\)
−0.0942105 + 0.995552i \(0.530033\pi\)
\(228\) 0 0
\(229\) −10.1726 + 14.0013i −0.672222 + 0.925235i −0.999808 0.0195869i \(-0.993765\pi\)
0.327586 + 0.944821i \(0.393765\pi\)
\(230\) 0 0
\(231\) −16.6923 + 15.4045i −1.09827 + 1.01354i
\(232\) 0 0
\(233\) 2.40288 15.1712i 0.157418 0.993898i −0.774854 0.632140i \(-0.782177\pi\)
0.932272 0.361758i \(-0.117823\pi\)
\(234\) 0 0
\(235\) −7.54462 0.0152120i −0.492157 0.000992319i
\(236\) 0 0
\(237\) 10.3356 27.9443i 0.671367 1.81518i
\(238\) 0 0
\(239\) −6.17815 + 19.0144i −0.399631 + 1.22994i 0.525664 + 0.850692i \(0.323817\pi\)
−0.925296 + 0.379247i \(0.876183\pi\)
\(240\) 0 0
\(241\) 1.32659 + 4.08282i 0.0854532 + 0.262998i 0.984648 0.174550i \(-0.0558471\pi\)
−0.899195 + 0.437548i \(0.855847\pi\)
\(242\) 0 0
\(243\) 3.10458 15.2762i 0.199159 0.979967i
\(244\) 0 0
\(245\) −3.13476 0.502978i −0.200272 0.0321341i
\(246\) 0 0
\(247\) 17.0246 2.69643i 1.08325 0.171570i
\(248\) 0 0
\(249\) 2.49730 + 21.2506i 0.158260 + 1.34671i
\(250\) 0 0
\(251\) 7.64733i 0.482695i 0.970439 + 0.241347i \(0.0775893\pi\)
−0.970439 + 0.241347i \(0.922411\pi\)
\(252\) 0 0
\(253\) −2.93953 18.5595i −0.184807 1.16682i
\(254\) 0 0
\(255\) −0.703055 + 16.6834i −0.0440270 + 1.04475i
\(256\) 0 0
\(257\) 6.23777 + 6.23777i 0.389101 + 0.389101i 0.874367 0.485266i \(-0.161277\pi\)
−0.485266 + 0.874367i \(0.661277\pi\)
\(258\) 0 0
\(259\) 19.3700 6.29368i 1.20359 0.391070i
\(260\) 0 0
\(261\) −1.51236 0.121551i −0.0936124 0.00752384i
\(262\) 0 0
\(263\) −15.4727 7.88374i −0.954088 0.486132i −0.0936037 0.995610i \(-0.529839\pi\)
−0.860484 + 0.509478i \(0.829839\pi\)
\(264\) 0 0
\(265\) 0.0237862 11.7972i 0.00146118 0.724695i
\(266\) 0 0
\(267\) −0.322045 + 8.02676i −0.0197088 + 0.491230i
\(268\) 0 0
\(269\) −17.2020 + 12.4980i −1.04883 + 0.762017i −0.971989 0.235026i \(-0.924482\pi\)
−0.0768379 + 0.997044i \(0.524482\pi\)
\(270\) 0 0
\(271\) −7.79739 5.66514i −0.473658 0.344133i 0.325207 0.945643i \(-0.394566\pi\)
−0.798865 + 0.601510i \(0.794566\pi\)
\(272\) 0 0
\(273\) −5.01111 7.51314i −0.303286 0.454716i
\(274\) 0 0
\(275\) −22.3904 16.4059i −1.35019 0.989315i
\(276\) 0 0
\(277\) 14.6228 + 28.6988i 0.878596 + 1.72434i 0.664141 + 0.747608i \(0.268798\pi\)
0.214455 + 0.976734i \(0.431202\pi\)
\(278\) 0 0
\(279\) 3.44359 8.27468i 0.206162 0.495392i
\(280\) 0 0
\(281\) 1.62290 + 2.23373i 0.0968141 + 0.133253i 0.854676 0.519162i \(-0.173756\pi\)
−0.757862 + 0.652415i \(0.773756\pi\)
\(282\) 0 0
\(283\) −15.0519 2.38398i −0.894741 0.141713i −0.307903 0.951418i \(-0.599627\pi\)
−0.586838 + 0.809705i \(0.699627\pi\)
\(284\) 0 0
\(285\) 22.2678 20.4669i 1.31903 1.21236i
\(286\) 0 0
\(287\) 5.05274 9.91657i 0.298254 0.585356i
\(288\) 0 0
\(289\) 1.51085 + 0.490904i 0.0888733 + 0.0288767i
\(290\) 0 0
\(291\) −25.4815 + 11.7215i −1.49375 + 0.687126i
\(292\) 0 0
\(293\) −7.47364 + 7.47364i −0.436615 + 0.436615i −0.890871 0.454256i \(-0.849905\pi\)
0.454256 + 0.890871i \(0.349905\pi\)
\(294\) 0 0
\(295\) 22.6731 3.54421i 1.32008 0.206352i
\(296\) 0 0
\(297\) 25.2035 14.0323i 1.46246 0.814238i
\(298\) 0 0
\(299\) 7.47109 0.432064
\(300\) 0 0
\(301\) −19.6680 −1.13364
\(302\) 0 0
\(303\) 2.19025 + 7.79080i 0.125827 + 0.447570i
\(304\) 0 0
\(305\) 10.6870 + 5.47246i 0.611935 + 0.313352i
\(306\) 0 0
\(307\) 3.64430 3.64430i 0.207991 0.207991i −0.595422 0.803413i \(-0.703015\pi\)
0.803413 + 0.595422i \(0.203015\pi\)
\(308\) 0 0
\(309\) −4.95201 10.7652i −0.281710 0.612413i
\(310\) 0 0
\(311\) −7.97750 2.59205i −0.452363 0.146982i 0.0739696 0.997260i \(-0.476433\pi\)
−0.526332 + 0.850279i \(0.676433\pi\)
\(312\) 0 0
\(313\) 4.02979 7.90891i 0.227777 0.447038i −0.748626 0.662992i \(-0.769286\pi\)
0.976403 + 0.215954i \(0.0692863\pi\)
\(314\) 0 0
\(315\) −14.6177 6.11792i −0.823616 0.344706i
\(316\) 0 0
\(317\) 14.6748 + 2.32426i 0.824218 + 0.130543i 0.554276 0.832333i \(-0.312995\pi\)
0.269943 + 0.962876i \(0.412995\pi\)
\(318\) 0 0
\(319\) −1.65029 2.27143i −0.0923987 0.127176i
\(320\) 0 0
\(321\) 6.06834 + 3.40505i 0.338702 + 0.190051i
\(322\) 0 0
\(323\) −15.2854 29.9992i −0.850501 1.66920i
\(324\) 0 0
\(325\) 7.83519 7.77226i 0.434618 0.431127i
\(326\) 0 0
\(327\) −16.3264 + 10.8893i −0.902850 + 0.602182i
\(328\) 0 0
\(329\) −6.44814 4.68485i −0.355497 0.258284i
\(330\) 0 0
\(331\) −9.59179 + 6.96885i −0.527213 + 0.383042i −0.819314 0.573345i \(-0.805646\pi\)
0.292101 + 0.956387i \(0.405646\pi\)
\(332\) 0 0
\(333\) −25.7891 + 1.98657i −1.41323 + 0.108864i
\(334\) 0 0
\(335\) 9.60743 + 3.14307i 0.524910 + 0.171725i
\(336\) 0 0
\(337\) −9.98022 5.08518i −0.543657 0.277007i 0.160519 0.987033i \(-0.448683\pi\)
−0.704176 + 0.710026i \(0.748683\pi\)
\(338\) 0 0
\(339\) −7.35078 1.46851i −0.399240 0.0797583i
\(340\) 0 0
\(341\) 15.7736 5.12517i 0.854191 0.277543i
\(342\) 0 0
\(343\) −14.0641 14.0641i −0.759390 0.759390i
\(344\) 0 0
\(345\) 10.9207 7.25208i 0.587949 0.390439i
\(346\) 0 0
\(347\) 4.46050 + 28.1625i 0.239452 + 1.51184i 0.755424 + 0.655236i \(0.227431\pi\)
−0.515972 + 0.856606i \(0.672569\pi\)
\(348\) 0 0
\(349\) 24.5531i 1.31430i 0.753761 + 0.657149i \(0.228238\pi\)
−0.753761 + 0.657149i \(0.771762\pi\)
\(350\) 0 0
\(351\) 3.94287 + 10.7701i 0.210455 + 0.574867i
\(352\) 0 0
\(353\) −7.23776 + 1.14635i −0.385227 + 0.0610140i −0.346045 0.938218i \(-0.612475\pi\)
−0.0391827 + 0.999232i \(0.512475\pi\)
\(354\) 0 0
\(355\) 16.2383 + 16.3039i 0.861838 + 0.865320i
\(356\) 0 0
\(357\) −10.9325 + 13.8442i −0.578611 + 0.732713i
\(358\) 0 0
\(359\) −3.41890 10.5223i −0.180443 0.555345i 0.819397 0.573226i \(-0.194308\pi\)
−0.999840 + 0.0178804i \(0.994308\pi\)
\(360\) 0 0
\(361\) −12.9736 + 39.9287i −0.682821 + 2.10151i
\(362\) 0 0
\(363\) 32.1965 + 11.9083i 1.68988 + 0.625023i
\(364\) 0 0
\(365\) −1.48796 4.61108i −0.0778833 0.241355i
\(366\) 0 0
\(367\) 5.39806 34.0820i 0.281776 1.77907i −0.288366 0.957520i \(-0.593112\pi\)
0.570142 0.821546i \(-0.306888\pi\)
\(368\) 0 0
\(369\) −9.19741 + 10.7327i −0.478798 + 0.558719i
\(370\) 0 0
\(371\) 7.32548 10.0827i 0.380320 0.523465i
\(372\) 0 0
\(373\) 14.7942 7.53802i 0.766014 0.390304i −0.0268992 0.999638i \(-0.508563\pi\)
0.792913 + 0.609335i \(0.208563\pi\)
\(374\) 0 0
\(375\) 3.90846 18.9664i 0.201832 0.979420i
\(376\) 0 0
\(377\) 0.994631 0.506790i 0.0512261 0.0261010i
\(378\) 0 0
\(379\) −20.3628 + 28.0270i −1.04597 + 1.43965i −0.153711 + 0.988116i \(0.549122\pi\)
−0.892255 + 0.451532i \(0.850878\pi\)
\(380\) 0 0
\(381\) −1.96495 2.12921i −0.100667 0.109083i
\(382\) 0 0
\(383\) −3.45899 + 21.8392i −0.176746 + 1.11593i 0.726613 + 0.687047i \(0.241094\pi\)
−0.903359 + 0.428885i \(0.858906\pi\)
\(384\) 0 0
\(385\) −9.00530 27.9068i −0.458953 1.42226i
\(386\) 0 0
\(387\) 24.2781 + 5.87131i 1.23413 + 0.298455i
\(388\) 0 0
\(389\) −0.876383 + 2.69723i −0.0444344 + 0.136755i −0.970812 0.239840i \(-0.922905\pi\)
0.926378 + 0.376595i \(0.122905\pi\)
\(390\) 0 0
\(391\) −4.50961 13.8792i −0.228061 0.701899i
\(392\) 0 0
\(393\) 6.24555 + 4.93200i 0.315046 + 0.248787i
\(394\) 0 0
\(395\) 27.1436 + 27.2533i 1.36574 + 1.37126i
\(396\) 0 0
\(397\) −29.9879 + 4.74962i −1.50505 + 0.238377i −0.853846 0.520525i \(-0.825736\pi\)
−0.651205 + 0.758902i \(0.725736\pi\)
\(398\) 0 0
\(399\) 31.7331 3.72915i 1.58864 0.186691i
\(400\) 0 0
\(401\) 33.3974i 1.66779i −0.551925 0.833894i \(-0.686107\pi\)
0.551925 0.833894i \(-0.313893\pi\)
\(402\) 0 0
\(403\) 1.03157 + 6.51305i 0.0513859 + 0.324438i
\(404\) 0 0
\(405\) 16.2178 + 11.9157i 0.805869 + 0.592094i
\(406\) 0 0
\(407\) −33.8451 33.8451i −1.67764 1.67764i
\(408\) 0 0
\(409\) 15.7176 5.10695i 0.777184 0.252522i 0.106547 0.994308i \(-0.466021\pi\)
0.670637 + 0.741785i \(0.266021\pi\)
\(410\) 0 0
\(411\) 3.01882 15.1111i 0.148908 0.745375i
\(412\) 0 0
\(413\) 21.6009 + 11.0062i 1.06291 + 0.541580i
\(414\) 0 0
\(415\) −26.2540 8.58901i −1.28876 0.421618i
\(416\) 0 0
\(417\) 6.42835 + 0.257915i 0.314798 + 0.0126301i
\(418\) 0 0
\(419\) 0.401580 0.291765i 0.0196184 0.0142536i −0.577933 0.816084i \(-0.696140\pi\)
0.597551 + 0.801831i \(0.296140\pi\)
\(420\) 0 0
\(421\) −5.08407 3.69379i −0.247782 0.180025i 0.456961 0.889487i \(-0.348938\pi\)
−0.704743 + 0.709462i \(0.748938\pi\)
\(422\) 0 0
\(423\) 6.56105 + 7.70788i 0.319009 + 0.374770i
\(424\) 0 0
\(425\) −19.1680 9.86416i −0.929786 0.478482i
\(426\) 0 0
\(427\) 5.75847 + 11.3016i 0.278672 + 0.546924i
\(428\) 0 0
\(429\) −10.3858 + 18.5091i −0.501429 + 0.893626i
\(430\) 0 0
\(431\) 7.36561 + 10.1379i 0.354789 + 0.488325i 0.948688 0.316215i \(-0.102412\pi\)
−0.593899 + 0.804540i \(0.702412\pi\)
\(432\) 0 0
\(433\) −26.6433 4.21988i −1.28039 0.202795i −0.521074 0.853512i \(-0.674468\pi\)
−0.759320 + 0.650717i \(0.774468\pi\)
\(434\) 0 0
\(435\) 0.961941 1.70626i 0.0461216 0.0818089i
\(436\) 0 0
\(437\) −12.0001 + 23.5516i −0.574045 + 1.12663i
\(438\) 0 0
\(439\) −10.8500 3.52537i −0.517841 0.168257i 0.0384243 0.999262i \(-0.487766\pi\)
−0.556265 + 0.831005i \(0.687766\pi\)
\(440\) 0 0
\(441\) 2.21956 + 3.63552i 0.105693 + 0.173120i
\(442\) 0 0
\(443\) 15.4331 15.4331i 0.733251 0.733251i −0.238011 0.971262i \(-0.576496\pi\)
0.971262 + 0.238011i \(0.0764956\pi\)
\(444\) 0 0
\(445\) −9.23097 4.72688i −0.437590 0.224076i
\(446\) 0 0
\(447\) 27.5608 7.74825i 1.30358 0.366480i
\(448\) 0 0
\(449\) 34.8771 1.64595 0.822975 0.568077i \(-0.192312\pi\)
0.822975 + 0.568077i \(0.192312\pi\)
\(450\) 0 0
\(451\) −26.1558 −1.23163
\(452\) 0 0
\(453\) −8.79364 + 2.47218i −0.413161 + 0.116153i
\(454\) 0 0
\(455\) 11.5190 1.80064i 0.540021 0.0844152i
\(456\) 0 0
\(457\) 23.6405 23.6405i 1.10585 1.10585i 0.112165 0.993690i \(-0.464221\pi\)
0.993690 0.112165i \(-0.0357786\pi\)
\(458\) 0 0
\(459\) 17.6279 13.8257i 0.822800 0.645327i
\(460\) 0 0
\(461\) 11.6988 + 3.80117i 0.544868 + 0.177038i 0.568501 0.822682i \(-0.307523\pi\)
−0.0236333 + 0.999721i \(0.507523\pi\)
\(462\) 0 0
\(463\) 8.22226 16.1371i 0.382121 0.749955i −0.617200 0.786806i \(-0.711733\pi\)
0.999321 + 0.0368518i \(0.0117330\pi\)
\(464\) 0 0
\(465\) 7.82998 + 8.51895i 0.363107 + 0.395057i
\(466\) 0 0
\(467\) 16.3946 + 2.59664i 0.758650 + 0.120158i 0.523763 0.851864i \(-0.324528\pi\)
0.234887 + 0.972023i \(0.424528\pi\)
\(468\) 0 0
\(469\) 6.27688 + 8.63938i 0.289839 + 0.398930i
\(470\) 0 0
\(471\) 9.33828 16.6423i 0.430285 0.766836i
\(472\) 0 0
\(473\) 20.9843 + 41.1841i 0.964860 + 1.89365i
\(474\) 0 0
\(475\) 11.9160 + 37.1833i 0.546744 + 1.70609i
\(476\) 0 0
\(477\) −12.0525 + 10.2592i −0.551844 + 0.469737i
\(478\) 0 0
\(479\) 21.0507 + 15.2942i 0.961831 + 0.698811i 0.953575 0.301155i \(-0.0973721\pi\)
0.00825583 + 0.999966i \(0.497372\pi\)
\(480\) 0 0
\(481\) 15.3960 11.1858i 0.701996 0.510030i
\(482\) 0 0
\(483\) 13.8378 + 0.555194i 0.629644 + 0.0252622i
\(484\) 0 0
\(485\) 0.0730088 36.2099i 0.00331516 1.64421i
\(486\) 0 0
\(487\) 12.2935 + 6.26384i 0.557071 + 0.283842i 0.709773 0.704430i \(-0.248797\pi\)
−0.152702 + 0.988272i \(0.548797\pi\)
\(488\) 0 0
\(489\) −5.25272 + 26.2931i −0.237536 + 1.18902i
\(490\) 0 0
\(491\) −21.5354 + 6.99728i −0.971879 + 0.315783i −0.751574 0.659648i \(-0.770705\pi\)
−0.220305 + 0.975431i \(0.570705\pi\)
\(492\) 0 0
\(493\) −1.54184 1.54184i −0.0694409 0.0694409i
\(494\) 0 0
\(495\) 2.78537 + 37.1364i 0.125193 + 1.66916i
\(496\) 0 0
\(497\) 3.80280 + 24.0099i 0.170579 + 1.07699i
\(498\) 0 0
\(499\) 7.12077i 0.318770i −0.987217 0.159385i \(-0.949049\pi\)
0.987217 0.159385i \(-0.0509511\pi\)
\(500\) 0 0
\(501\) 17.2837 2.03111i 0.772178 0.0907434i
\(502\) 0 0
\(503\) −20.1311 + 3.18846i −0.897602 + 0.142166i −0.588153 0.808750i \(-0.700145\pi\)
−0.309449 + 0.950916i \(0.600145\pi\)
\(504\) 0 0
\(505\) −10.3158 1.65520i −0.459049 0.0736553i
\(506\) 0 0
\(507\) 11.0486 + 8.72492i 0.490687 + 0.387487i
\(508\) 0 0
\(509\) 0.874684 + 2.69200i 0.0387697 + 0.119321i 0.968568 0.248748i \(-0.0800191\pi\)
−0.929799 + 0.368069i \(0.880019\pi\)
\(510\) 0 0
\(511\) 1.58173 4.86808i 0.0699718 0.215351i
\(512\) 0 0
\(513\) −40.2845 4.86973i −1.77860 0.215004i
\(514\) 0 0
\(515\) 15.2977 + 0.0308443i 0.674098 + 0.00135916i
\(516\) 0 0
\(517\) −2.93020 + 18.5006i −0.128870 + 0.813654i
\(518\) 0 0
\(519\) 17.2152 + 18.6543i 0.755663 + 0.818834i
\(520\) 0 0
\(521\) −21.4218 + 29.4846i −0.938507 + 1.29174i 0.0179402 + 0.999839i \(0.494289\pi\)
−0.956447 + 0.291905i \(0.905711\pi\)
\(522\) 0 0
\(523\) −12.8556 + 6.55024i −0.562135 + 0.286422i −0.711878 0.702303i \(-0.752155\pi\)
0.149743 + 0.988725i \(0.452155\pi\)
\(524\) 0 0
\(525\) 15.0898 13.8134i 0.658573 0.602866i
\(526\) 0 0
\(527\) 11.4767 5.84769i 0.499934 0.254729i
\(528\) 0 0
\(529\) 6.78486 9.33856i 0.294994 0.406025i
\(530\) 0 0
\(531\) −23.3785 20.0344i −1.01454 0.869418i
\(532\) 0 0
\(533\) 1.62682 10.2713i 0.0704655 0.444901i
\(534\) 0 0
\(535\) −7.27822 + 5.26555i −0.314665 + 0.227650i
\(536\) 0 0
\(537\) −24.7115 9.13985i −1.06638 0.394414i
\(538\) 0 0
\(539\) −2.43575 + 7.49647i −0.104915 + 0.322896i
\(540\) 0 0
\(541\) −9.28677 28.5817i −0.399269 1.22882i −0.925586 0.378536i \(-0.876428\pi\)
0.526317 0.850288i \(-0.323572\pi\)
\(542\) 0 0
\(543\) 0.593220 0.751213i 0.0254575 0.0322376i
\(544\) 0 0
\(545\) −3.91286 25.0314i −0.167609 1.07223i
\(546\) 0 0
\(547\) −32.6302 + 5.16812i −1.39517 + 0.220973i −0.808329 0.588731i \(-0.799628\pi\)
−0.586839 + 0.809704i \(0.699628\pi\)
\(548\) 0 0
\(549\) −3.73447 15.6697i −0.159383 0.668769i
\(550\) 0 0
\(551\) 3.94945i 0.168252i
\(552\) 0 0
\(553\) 6.35668 + 40.1345i 0.270314 + 1.70669i
\(554\) 0 0
\(555\) 11.6467 31.2952i 0.494376 1.32841i
\(556\) 0 0
\(557\) −21.8255 21.8255i −0.924778 0.924778i 0.0725847 0.997362i \(-0.476875\pi\)
−0.997362 + 0.0725847i \(0.976875\pi\)
\(558\) 0 0
\(559\) −17.4781 + 5.67897i −0.739243 + 0.240195i
\(560\) 0 0
\(561\) 40.6535 + 8.12157i 1.71639 + 0.342893i
\(562\) 0 0
\(563\) 1.53782 + 0.783556i 0.0648112 + 0.0330230i 0.486096 0.873906i \(-0.338421\pi\)
−0.421285 + 0.906929i \(0.638421\pi\)
\(564\) 0 0
\(565\) 5.70397 7.81765i 0.239968 0.328891i
\(566\) 0 0
\(567\) 6.50258 + 20.2413i 0.273083 + 0.850054i
\(568\) 0 0
\(569\) −10.8632 + 7.89256i −0.455408 + 0.330873i −0.791727 0.610875i \(-0.790818\pi\)
0.336319 + 0.941748i \(0.390818\pi\)
\(570\) 0 0
\(571\) 13.8833 + 10.0868i 0.580999 + 0.422121i 0.839084 0.544001i \(-0.183091\pi\)
−0.258085 + 0.966122i \(0.583091\pi\)
\(572\) 0 0
\(573\) 31.1641 20.7858i 1.30190 0.868339i
\(574\) 0 0
\(575\) 2.58007 + 16.7262i 0.107596 + 0.697531i
\(576\) 0 0
\(577\) −5.02409 9.86033i −0.209156 0.410491i 0.762467 0.647027i \(-0.223988\pi\)
−0.971623 + 0.236536i \(0.923988\pi\)
\(578\) 0 0
\(579\) −7.93823 4.45428i −0.329902 0.185114i
\(580\) 0 0
\(581\) −17.1527 23.6086i −0.711613 0.979451i
\(582\) 0 0
\(583\) −28.9285 4.58182i −1.19810 0.189760i
\(584\) 0 0
\(585\) −14.7566 1.21597i −0.610112 0.0502743i
\(586\) 0 0
\(587\) 9.65285 18.9448i 0.398416 0.781935i −0.601440 0.798918i \(-0.705406\pi\)
0.999856 + 0.0169832i \(0.00540617\pi\)
\(588\) 0 0
\(589\) −22.1884 7.20945i −0.914258 0.297060i
\(590\) 0 0
\(591\) 14.1763 + 30.8180i 0.583134 + 1.26768i
\(592\) 0 0
\(593\) −12.3241 + 12.3241i −0.506090 + 0.506090i −0.913324 0.407234i \(-0.866493\pi\)
0.407234 + 0.913324i \(0.366493\pi\)
\(594\) 0 0
\(595\) −10.2981 20.3122i −0.422180 0.832720i
\(596\) 0 0
\(597\) 0.830251 + 2.95323i 0.0339799 + 0.120868i
\(598\) 0 0
\(599\) 13.1359 0.536716 0.268358 0.963319i \(-0.413519\pi\)
0.268358 + 0.963319i \(0.413519\pi\)
\(600\) 0 0
\(601\) 39.9534 1.62973 0.814867 0.579648i \(-0.196810\pi\)
0.814867 + 0.579648i \(0.196810\pi\)
\(602\) 0 0
\(603\) −5.16914 12.5382i −0.210503 0.510596i
\(604\) 0 0
\(605\) −31.4003 + 31.2739i −1.27660 + 1.27147i
\(606\) 0 0
\(607\) −8.63234 + 8.63234i −0.350376 + 0.350376i −0.860249 0.509874i \(-0.829692\pi\)
0.509874 + 0.860249i \(0.329692\pi\)
\(608\) 0 0
\(609\) 1.87990 0.864755i 0.0761774 0.0350416i
\(610\) 0 0
\(611\) −7.08288 2.30137i −0.286543 0.0931034i
\(612\) 0 0
\(613\) 12.3185 24.1765i 0.497541 0.976480i −0.496558 0.868004i \(-0.665403\pi\)
0.994099 0.108476i \(-0.0345971\pi\)
\(614\) 0 0
\(615\) −7.59228 16.5930i −0.306150 0.669094i
\(616\) 0 0
\(617\) −16.2868 2.57957i −0.655681 0.103850i −0.180275 0.983616i \(-0.557699\pi\)
−0.475406 + 0.879766i \(0.657699\pi\)
\(618\) 0 0
\(619\) −7.86705 10.8281i −0.316203 0.435216i 0.621100 0.783731i \(-0.286686\pi\)
−0.937303 + 0.348515i \(0.886686\pi\)
\(620\) 0 0
\(621\) −16.9157 4.81622i −0.678803 0.193268i
\(622\) 0 0
\(623\) −4.97392 9.76187i −0.199276 0.391101i
\(624\) 0 0
\(625\) 20.1063 + 14.8573i 0.804250 + 0.594291i
\(626\) 0 0
\(627\) −41.6656 62.4691i −1.66396 2.49478i
\(628\) 0 0
\(629\) −30.0732 21.8495i −1.19910 0.871196i
\(630\) 0 0
\(631\) 16.8778 12.2624i 0.671894 0.488160i −0.198764 0.980047i \(-0.563693\pi\)
0.870659 + 0.491887i \(0.163693\pi\)
\(632\) 0 0
\(633\) 0.222476 5.54506i 0.00884261 0.220396i
\(634\) 0 0
\(635\) 3.55970 1.14869i 0.141262 0.0455842i
\(636\) 0 0
\(637\) −2.79235 1.42277i −0.110637 0.0563723i
\(638\) 0 0
\(639\) 2.47330 30.7730i 0.0978421 1.21736i
\(640\) 0 0
\(641\) −19.5368 + 6.34790i −0.771658 + 0.250727i −0.668275 0.743915i \(-0.732967\pi\)
−0.103383 + 0.994642i \(0.532967\pi\)
\(642\) 0 0
\(643\) 20.8324 + 20.8324i 0.821549 + 0.821549i 0.986330 0.164781i \(-0.0526917\pi\)
−0.164781 + 0.986330i \(0.552692\pi\)
\(644\) 0 0
\(645\) −20.0356 + 25.2668i −0.788901 + 0.994878i
\(646\) 0 0
\(647\) −6.10259 38.5303i −0.239918 1.51478i −0.753905 0.656983i \(-0.771832\pi\)
0.513988 0.857798i \(-0.328168\pi\)
\(648\) 0 0
\(649\) 56.9743i 2.23644i
\(650\) 0 0
\(651\) 1.42665 + 12.1400i 0.0559149 + 0.475805i
\(652\) 0 0
\(653\) 32.1247 5.08805i 1.25714 0.199111i 0.507901 0.861415i \(-0.330421\pi\)
0.749235 + 0.662304i \(0.230421\pi\)
\(654\) 0 0
\(655\) −9.16347 + 4.64577i −0.358047 + 0.181525i
\(656\) 0 0
\(657\) −3.40571 + 5.53697i −0.132870 + 0.216018i
\(658\) 0 0
\(659\) −6.17031 18.9903i −0.240361 0.739755i −0.996365 0.0851880i \(-0.972851\pi\)
0.756004 0.654567i \(-0.227149\pi\)
\(660\) 0 0
\(661\) −4.21748 + 12.9801i −0.164041 + 0.504866i −0.998964 0.0455001i \(-0.985512\pi\)
0.834923 + 0.550366i \(0.185512\pi\)
\(662\) 0 0
\(663\) −5.71786 + 15.4594i −0.222063 + 0.600393i
\(664\) 0 0
\(665\) −12.8257 + 39.2044i −0.497361 + 1.52028i
\(666\) 0 0
\(667\) −0.267791 + 1.69077i −0.0103689 + 0.0654668i
\(668\) 0 0
\(669\) −3.07197 + 2.83497i −0.118769 + 0.109606i
\(670\) 0 0
\(671\) 17.5213 24.1161i 0.676404 0.930990i
\(672\) 0 0
\(673\) −1.04272 + 0.531291i −0.0401938 + 0.0204798i −0.473972 0.880540i \(-0.657180\pi\)
0.433778 + 0.901020i \(0.357180\pi\)
\(674\) 0 0
\(675\) −22.7504 + 12.5466i −0.875664 + 0.482920i
\(676\) 0 0
\(677\) 2.46293 1.25493i 0.0946581 0.0482307i −0.406020 0.913864i \(-0.633084\pi\)
0.500679 + 0.865633i \(0.333084\pi\)
\(678\) 0 0
\(679\) 22.4846 30.9474i 0.862881 1.18765i
\(680\) 0 0
\(681\) −20.5550 + 18.9693i −0.787670 + 0.726903i
\(682\) 0 0
\(683\) 4.28310 27.0424i 0.163888 1.03475i −0.759395 0.650630i \(-0.774505\pi\)
0.923283 0.384119i \(-0.125495\pi\)
\(684\) 0 0
\(685\) 16.0708 + 11.7257i 0.614035 + 0.448017i
\(686\) 0 0
\(687\) −10.3985 + 28.1145i −0.396728 + 1.07264i
\(688\) 0 0
\(689\) 3.59854 11.0752i 0.137094 0.421931i
\(690\) 0 0
\(691\) 6.92199 + 21.3037i 0.263325 + 0.810430i 0.992075 + 0.125650i \(0.0401017\pi\)
−0.728750 + 0.684780i \(0.759898\pi\)
\(692\) 0 0
\(693\) −20.6118 + 33.5104i −0.782977 + 1.27296i
\(694\) 0 0
\(695\) −3.78560 + 7.39276i −0.143596 + 0.280424i
\(696\) 0 0
\(697\) −20.0632 + 3.17770i −0.759948 + 0.120364i
\(698\) 0 0
\(699\) −3.10513 26.4230i −0.117447 0.999410i
\(700\) 0 0
\(701\) 19.9094i 0.751969i 0.926626 + 0.375985i \(0.122695\pi\)
−0.926626 + 0.375985i \(0.877305\pi\)
\(702\) 0 0
\(703\) 10.5326 + 66.5005i 0.397246 + 2.50811i
\(704\) 0 0
\(705\) −12.5871 + 3.51129i −0.474058 + 0.132243i
\(706\) 0 0
\(707\) −7.80455 7.80455i −0.293520 0.293520i
\(708\) 0 0
\(709\) −16.9259 + 5.49956i −0.635666 + 0.206540i −0.609083 0.793106i \(-0.708463\pi\)
−0.0265827 + 0.999647i \(0.508463\pi\)
\(710\) 0 0
\(711\) 4.13431 51.4396i 0.155049 1.92914i
\(712\) 0 0
\(713\) −9.01008 4.59086i −0.337430 0.171929i
\(714\) 0 0
\(715\) −16.0605 22.1993i −0.600627 0.830208i
\(716\) 0 0
\(717\) −1.38824 + 34.6009i −0.0518447 + 1.29219i
\(718\) 0 0
\(719\) −33.9545 + 24.6694i −1.26629 + 0.920014i −0.999048 0.0436153i \(-0.986112\pi\)
−0.267242 + 0.963629i \(0.586112\pi\)
\(720\) 0 0
\(721\) 13.0745 + 9.49915i 0.486918 + 0.353767i
\(722\) 0 0
\(723\) 4.12586 + 6.18589i 0.153442 + 0.230056i
\(724\) 0 0
\(725\) 1.47808 + 2.05175i 0.0548946 + 0.0762002i
\(726\) 0 0
\(727\) 11.3404 + 22.2569i 0.420594 + 0.825462i 0.999946 + 0.0103844i \(0.00330552\pi\)
−0.579352 + 0.815077i \(0.696694\pi\)
\(728\) 0 0
\(729\) −1.98433 26.9270i −0.0734935 0.997296i
\(730\) 0 0
\(731\) 21.0998 + 29.0414i 0.780405 + 1.07413i
\(732\) 0 0
\(733\) 30.1622 + 4.77723i 1.11407 + 0.176451i 0.686216 0.727398i \(-0.259270\pi\)
0.427852 + 0.903849i \(0.359270\pi\)
\(734\) 0 0
\(735\) −5.46271 + 0.630793i −0.201495 + 0.0232672i
\(736\) 0 0
\(737\) 11.3936 22.3612i 0.419688 0.823684i
\(738\) 0 0
\(739\) 18.0849 + 5.87616i 0.665266 + 0.216158i 0.622133 0.782911i \(-0.286266\pi\)
0.0431325 + 0.999069i \(0.486266\pi\)
\(740\) 0 0
\(741\) 27.1230 12.4766i 0.996388 0.458339i
\(742\) 0 0
\(743\) 21.7526 21.7526i 0.798025 0.798025i −0.184759 0.982784i \(-0.559150\pi\)
0.982784 + 0.184759i \(0.0591505\pi\)
\(744\) 0 0
\(745\) −5.85543 + 36.4934i −0.214526 + 1.33701i
\(746\) 0 0
\(747\) 14.1256 + 34.2629i 0.516828 + 1.25361i
\(748\) 0 0
\(749\) −9.49011 −0.346761
\(750\) 0 0
\(751\) −2.51184 −0.0916583 −0.0458292 0.998949i \(-0.514593\pi\)
−0.0458292 + 0.998949i \(0.514593\pi\)
\(752\) 0 0
\(753\) 3.58480 + 12.7512i 0.130637 + 0.464681i
\(754\) 0 0
\(755\) 1.86826 11.6437i 0.0679928 0.423758i
\(756\) 0 0
\(757\) 10.6543 10.6543i 0.387238 0.387238i −0.486463 0.873701i \(-0.661713\pi\)
0.873701 + 0.486463i \(0.161713\pi\)
\(758\) 0 0
\(759\) −13.6014 29.5683i −0.493700 1.07326i
\(760\) 0 0
\(761\) −25.2259 8.19638i −0.914437 0.297119i −0.186254 0.982502i \(-0.559635\pi\)
−0.728183 + 0.685383i \(0.759635\pi\)
\(762\) 0 0
\(763\) 12.1510 23.8477i 0.439896 0.863344i
\(764\) 0 0
\(765\) 6.64829 + 28.1476i 0.240370 + 1.01768i
\(766\) 0 0
\(767\) 22.3737 + 3.54365i 0.807867 + 0.127954i
\(768\) 0 0
\(769\) 12.4291 + 17.1072i 0.448206 + 0.616903i 0.972011 0.234935i \(-0.0754878\pi\)
−0.523805 + 0.851838i \(0.675488\pi\)
\(770\) 0 0
\(771\) 13.3250 + 7.47688i 0.479887 + 0.269273i
\(772\) 0 0
\(773\) −16.4953 32.3738i −0.593294 1.16441i −0.971134 0.238534i \(-0.923333\pi\)
0.377840 0.925871i \(-0.376667\pi\)
\(774\) 0 0
\(775\) −14.2251 + 4.55868i −0.510981 + 0.163753i
\(776\) 0 0
\(777\) 29.3474 19.5741i 1.05283 0.702218i
\(778\) 0 0
\(779\) 29.7660 + 21.6263i 1.06648 + 0.774842i
\(780\) 0 0
\(781\) 46.2186 33.5798i 1.65383 1.20158i
\(782\) 0 0
\(783\) −2.57870 + 0.506263i −0.0921551 + 0.0180924i
\(784\) 0 0
\(785\) 14.4406 + 19.9604i 0.515409 + 0.712416i
\(786\) 0 0
\(787\) −25.7846 13.1379i −0.919122 0.468316i −0.0706170 0.997504i \(-0.522497\pi\)
−0.848505 + 0.529188i \(0.822497\pi\)
\(788\) 0 0
\(789\) −29.4950 5.89237i −1.05005 0.209774i
\(790\) 0 0
\(791\) 9.72301 3.15920i 0.345710 0.112328i
\(792\) 0 0
\(793\) 8.38054 + 8.38054i 0.297602 + 0.297602i
\(794\) 0 0
\(795\) −5.49044 19.6819i −0.194726 0.698045i
\(796\) 0 0
\(797\) −1.30431 8.23509i