Properties

Label 804.2.y.b.121.2
Level 804
Weight 2
Character 804.121
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 121.2
Character \(\chi\) = 804.121
Dual form 804.2.y.b.505.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(-2.07356 + 1.33260i) q^{5} +(4.33337 + 1.73482i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(-2.07356 + 1.33260i) q^{5} +(4.33337 + 1.73482i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-0.101141 - 2.12321i) q^{11} +(-3.24464 + 0.309826i) q^{13} +(-0.350785 + 2.43976i) q^{15} +(1.86970 + 7.70703i) q^{17} +(6.34431 - 2.53988i) q^{19} +(4.14885 - 2.13888i) q^{21} +(1.25405 + 0.241699i) q^{23} +(0.446774 - 0.978298i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(-3.89969 + 6.75447i) q^{29} +(6.64520 + 0.634540i) q^{31} +(-1.67085 - 1.31397i) q^{33} +(-11.2974 + 2.17739i) q^{35} +(-1.01966 - 1.76611i) q^{37} +(-1.89064 + 2.65503i) q^{39} +(6.72776 - 6.41491i) q^{41} +(2.12759 + 0.624716i) q^{43} +(1.61413 + 1.86281i) q^{45} +(0.0968303 + 0.279773i) q^{47} +(10.7024 + 10.2047i) q^{49} +(7.04898 + 3.63400i) q^{51} +(-2.36788 + 0.695274i) q^{53} +(3.03911 + 4.26784i) q^{55} +(2.23513 - 6.45798i) q^{57} +(3.15859 + 6.91636i) q^{59} +(-0.399313 + 8.38261i) q^{61} +(1.10046 - 4.53616i) q^{63} +(6.31510 - 4.96625i) q^{65} +(-3.88912 - 7.20241i) q^{67} +(1.00389 - 0.789472i) q^{69} +(2.12361 - 8.75365i) q^{71} +(0.736854 - 15.4685i) q^{73} +(-0.446774 - 0.978298i) q^{75} +(3.24511 - 9.37614i) q^{77} +(6.90329 + 9.69432i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-0.285490 - 0.147180i) q^{83} +(-14.1473 - 13.4895i) q^{85} +(2.55093 + 7.37043i) q^{87} +(-7.78897 - 8.98895i) q^{89} +(-14.5977 - 4.28628i) q^{91} +(4.83124 - 4.60657i) q^{93} +(-9.77070 + 13.7210i) q^{95} +(3.21956 + 5.57645i) q^{97} +(-2.08721 + 0.402276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{26}{33}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) −2.07356 + 1.33260i −0.927326 + 0.595956i −0.914774 0.403965i \(-0.867632\pi\)
−0.0125516 + 0.999921i \(0.503995\pi\)
\(6\) 0 0
\(7\) 4.33337 + 1.73482i 1.63786 + 0.655701i 0.993994 0.109436i \(-0.0349044\pi\)
0.643868 + 0.765137i \(0.277329\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) −0.101141 2.12321i −0.0304952 0.640173i −0.961440 0.275014i \(-0.911318\pi\)
0.930945 0.365159i \(-0.118985\pi\)
\(12\) 0 0
\(13\) −3.24464 + 0.309826i −0.899902 + 0.0859302i −0.534743 0.845015i \(-0.679591\pi\)
−0.365159 + 0.930945i \(0.618985\pi\)
\(14\) 0 0
\(15\) −0.350785 + 2.43976i −0.0905722 + 0.629944i
\(16\) 0 0
\(17\) 1.86970 + 7.70703i 0.453470 + 1.86923i 0.493031 + 0.870012i \(0.335889\pi\)
−0.0395612 + 0.999217i \(0.512596\pi\)
\(18\) 0 0
\(19\) 6.34431 2.53988i 1.45548 0.582688i 0.496979 0.867762i \(-0.334442\pi\)
0.958505 + 0.285074i \(0.0920182\pi\)
\(20\) 0 0
\(21\) 4.14885 2.13888i 0.905353 0.466742i
\(22\) 0 0
\(23\) 1.25405 + 0.241699i 0.261488 + 0.0503978i 0.318310 0.947987i \(-0.396885\pi\)
−0.0568219 + 0.998384i \(0.518097\pi\)
\(24\) 0 0
\(25\) 0.446774 0.978298i 0.0893548 0.195660i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) −3.89969 + 6.75447i −0.724155 + 1.25427i 0.235166 + 0.971955i \(0.424437\pi\)
−0.959321 + 0.282318i \(0.908897\pi\)
\(30\) 0 0
\(31\) 6.64520 + 0.634540i 1.19351 + 0.113967i 0.672839 0.739789i \(-0.265074\pi\)
0.520674 + 0.853755i \(0.325681\pi\)
\(32\) 0 0
\(33\) −1.67085 1.31397i −0.290858 0.228733i
\(34\) 0 0
\(35\) −11.2974 + 2.17739i −1.90960 + 0.368045i
\(36\) 0 0
\(37\) −1.01966 1.76611i −0.167632 0.290346i 0.769955 0.638098i \(-0.220279\pi\)
−0.937587 + 0.347752i \(0.886945\pi\)
\(38\) 0 0
\(39\) −1.89064 + 2.65503i −0.302744 + 0.425145i
\(40\) 0 0
\(41\) 6.72776 6.41491i 1.05070 1.00184i 0.0507051 0.998714i \(-0.483853\pi\)
0.999995 0.00312698i \(-0.000995352\pi\)
\(42\) 0 0
\(43\) 2.12759 + 0.624716i 0.324454 + 0.0952683i 0.439903 0.898045i \(-0.355013\pi\)
−0.115449 + 0.993313i \(0.536831\pi\)
\(44\) 0 0
\(45\) 1.61413 + 1.86281i 0.240621 + 0.277691i
\(46\) 0 0
\(47\) 0.0968303 + 0.279773i 0.0141241 + 0.0408090i 0.951843 0.306587i \(-0.0991871\pi\)
−0.937718 + 0.347396i \(0.887066\pi\)
\(48\) 0 0
\(49\) 10.7024 + 10.2047i 1.52891 + 1.45782i
\(50\) 0 0
\(51\) 7.04898 + 3.63400i 0.987055 + 0.508862i
\(52\) 0 0
\(53\) −2.36788 + 0.695274i −0.325254 + 0.0955032i −0.440283 0.897859i \(-0.645122\pi\)
0.115029 + 0.993362i \(0.463304\pi\)
\(54\) 0 0
\(55\) 3.03911 + 4.26784i 0.409794 + 0.575475i
\(56\) 0 0
\(57\) 2.23513 6.45798i 0.296050 0.855380i
\(58\) 0 0
\(59\) 3.15859 + 6.91636i 0.411214 + 0.900433i 0.996009 + 0.0892519i \(0.0284476\pi\)
−0.584795 + 0.811181i \(0.698825\pi\)
\(60\) 0 0
\(61\) −0.399313 + 8.38261i −0.0511268 + 1.07328i 0.816904 + 0.576773i \(0.195688\pi\)
−0.868031 + 0.496510i \(0.834615\pi\)
\(62\) 0 0
\(63\) 1.10046 4.53616i 0.138645 0.571502i
\(64\) 0 0
\(65\) 6.31510 4.96625i 0.783292 0.615987i
\(66\) 0 0
\(67\) −3.88912 7.20241i −0.475132 0.879915i
\(68\) 0 0
\(69\) 1.00389 0.789472i 0.120855 0.0950412i
\(70\) 0 0
\(71\) 2.12361 8.75365i 0.252026 1.03887i −0.695331 0.718690i \(-0.744742\pi\)
0.947358 0.320178i \(-0.103743\pi\)
\(72\) 0 0
\(73\) 0.736854 15.4685i 0.0862423 1.81045i −0.379141 0.925339i \(-0.623780\pi\)
0.465383 0.885109i \(-0.345917\pi\)
\(74\) 0 0
\(75\) −0.446774 0.978298i −0.0515890 0.112964i
\(76\) 0 0
\(77\) 3.24511 9.37614i 0.369815 1.06851i
\(78\) 0 0
\(79\) 6.90329 + 9.69432i 0.776681 + 1.09070i 0.993427 + 0.114468i \(0.0365164\pi\)
−0.216746 + 0.976228i \(0.569544\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) −0.285490 0.147180i −0.0313366 0.0161551i 0.442487 0.896775i \(-0.354096\pi\)
−0.473824 + 0.880620i \(0.657127\pi\)
\(84\) 0 0
\(85\) −14.1473 13.4895i −1.53449 1.46314i
\(86\) 0 0
\(87\) 2.55093 + 7.37043i 0.273488 + 0.790193i
\(88\) 0 0
\(89\) −7.78897 8.98895i −0.825629 0.952826i 0.173861 0.984770i \(-0.444376\pi\)
−0.999490 + 0.0319438i \(0.989830\pi\)
\(90\) 0 0
\(91\) −14.5977 4.28628i −1.53026 0.449325i
\(92\) 0 0
\(93\) 4.83124 4.60657i 0.500976 0.477680i
\(94\) 0 0
\(95\) −9.77070 + 13.7210i −1.00245 + 1.40775i
\(96\) 0 0
\(97\) 3.21956 + 5.57645i 0.326897 + 0.566202i 0.981894 0.189429i \(-0.0606636\pi\)
−0.654997 + 0.755631i \(0.727330\pi\)
\(98\) 0 0
\(99\) −2.08721 + 0.402276i −0.209772 + 0.0404303i
\(100\) 0 0
\(101\) −4.81416 3.78590i −0.479027 0.376711i 0.349250 0.937029i \(-0.386436\pi\)
−0.828277 + 0.560319i \(0.810679\pi\)
\(102\) 0 0
\(103\) −16.3237 1.55873i −1.60843 0.153586i −0.748191 0.663483i \(-0.769077\pi\)
−0.860235 + 0.509897i \(0.829683\pi\)
\(104\) 0 0
\(105\) −5.75263 + 9.96385i −0.561400 + 0.972373i
\(106\) 0 0
\(107\) −4.67973 3.00748i −0.452406 0.290744i 0.294527 0.955643i \(-0.404838\pi\)
−0.746933 + 0.664899i \(0.768474\pi\)
\(108\) 0 0
\(109\) −1.90863 + 4.17932i −0.182814 + 0.400306i −0.978745 0.205081i \(-0.934254\pi\)
0.795931 + 0.605387i \(0.206982\pi\)
\(110\) 0 0
\(111\) −2.00247 0.385945i −0.190066 0.0366323i
\(112\) 0 0
\(113\) 5.39668 2.78218i 0.507677 0.261725i −0.185305 0.982681i \(-0.559327\pi\)
0.692981 + 0.720956i \(0.256297\pi\)
\(114\) 0 0
\(115\) −2.92245 + 1.16997i −0.272520 + 0.109100i
\(116\) 0 0
\(117\) 0.768433 + 3.16752i 0.0710416 + 0.292838i
\(118\) 0 0
\(119\) −5.26819 + 36.6410i −0.482934 + 3.35888i
\(120\) 0 0
\(121\) 6.45238 0.616128i 0.586580 0.0560116i
\(122\) 0 0
\(123\) −0.442317 9.28538i −0.0398824 0.837234i
\(124\) 0 0
\(125\) −1.37666 9.57487i −0.123132 0.856403i
\(126\) 0 0
\(127\) −8.70362 3.48440i −0.772321 0.309191i −0.0481764 0.998839i \(-0.515341\pi\)
−0.724145 + 0.689648i \(0.757765\pi\)
\(128\) 0 0
\(129\) 1.86540 1.19882i 0.164239 0.105550i
\(130\) 0 0
\(131\) 2.67073 3.08218i 0.233343 0.269292i −0.626987 0.779030i \(-0.715712\pi\)
0.860330 + 0.509738i \(0.170258\pi\)
\(132\) 0 0
\(133\) 31.8985 2.76595
\(134\) 0 0
\(135\) 2.46485 0.212141
\(136\) 0 0
\(137\) −11.4023 + 13.1590i −0.974165 + 1.12425i 0.0180663 + 0.999837i \(0.494249\pi\)
−0.992231 + 0.124409i \(0.960296\pi\)
\(138\) 0 0
\(139\) −3.04668 + 1.95798i −0.258416 + 0.166074i −0.663434 0.748235i \(-0.730902\pi\)
0.405018 + 0.914309i \(0.367265\pi\)
\(140\) 0 0
\(141\) 0.274848 + 0.110033i 0.0231464 + 0.00926643i
\(142\) 0 0
\(143\) 0.985993 + 6.85773i 0.0824529 + 0.573472i
\(144\) 0 0
\(145\) −0.914730 19.2025i −0.0759642 1.59468i
\(146\) 0 0
\(147\) 14.7208 1.40566i 1.21415 0.115937i
\(148\) 0 0
\(149\) 0.797443 5.54634i 0.0653291 0.454374i −0.930732 0.365702i \(-0.880829\pi\)
0.996061 0.0886713i \(-0.0282621\pi\)
\(150\) 0 0
\(151\) −0.344209 1.41885i −0.0280113 0.115464i 0.956090 0.293075i \(-0.0946785\pi\)
−0.984101 + 0.177610i \(0.943163\pi\)
\(152\) 0 0
\(153\) 7.36249 2.94750i 0.595222 0.238291i
\(154\) 0 0
\(155\) −14.6248 + 7.53963i −1.17470 + 0.605598i
\(156\) 0 0
\(157\) −16.8430 3.24622i −1.34422 0.259077i −0.534138 0.845397i \(-0.679364\pi\)
−0.810079 + 0.586320i \(0.800576\pi\)
\(158\) 0 0
\(159\) −1.02518 + 2.24484i −0.0813022 + 0.178027i
\(160\) 0 0
\(161\) 5.01498 + 3.22293i 0.395236 + 0.254003i
\(162\) 0 0
\(163\) 0.813592 1.40918i 0.0637255 0.110376i −0.832402 0.554172i \(-0.813035\pi\)
0.896128 + 0.443796i \(0.146368\pi\)
\(164\) 0 0
\(165\) 5.21561 + 0.498031i 0.406035 + 0.0387716i
\(166\) 0 0
\(167\) −9.97108 7.84134i −0.771585 0.606781i 0.152793 0.988258i \(-0.451173\pi\)
−0.924378 + 0.381477i \(0.875416\pi\)
\(168\) 0 0
\(169\) −2.33337 + 0.449720i −0.179490 + 0.0345938i
\(170\) 0 0
\(171\) −3.41692 5.91827i −0.261298 0.452582i
\(172\) 0 0
\(173\) −6.35729 + 8.92757i −0.483336 + 0.678750i −0.982180 0.187941i \(-0.939819\pi\)
0.498844 + 0.866692i \(0.333758\pi\)
\(174\) 0 0
\(175\) 3.63321 3.46426i 0.274645 0.261873i
\(176\) 0 0
\(177\) 7.29547 + 2.14214i 0.548361 + 0.161013i
\(178\) 0 0
\(179\) −15.1818 17.5207i −1.13474 1.30956i −0.944758 0.327770i \(-0.893703\pi\)
−0.189981 0.981788i \(-0.560843\pi\)
\(180\) 0 0
\(181\) 1.12330 + 3.24556i 0.0834941 + 0.241240i 0.979018 0.203773i \(-0.0653203\pi\)
−0.895524 + 0.445013i \(0.853199\pi\)
\(182\) 0 0
\(183\) 6.07366 + 5.79122i 0.448978 + 0.428099i
\(184\) 0 0
\(185\) 4.46785 + 2.30334i 0.328483 + 0.169345i
\(186\) 0 0
\(187\) 16.1746 4.74928i 1.18280 0.347302i
\(188\) 0 0
\(189\) −2.70755 3.80222i −0.196945 0.276571i
\(190\) 0 0
\(191\) −4.10854 + 11.8708i −0.297283 + 0.858944i 0.693130 + 0.720812i \(0.256231\pi\)
−0.990414 + 0.138132i \(0.955890\pi\)
\(192\) 0 0
\(193\) 6.07807 + 13.3091i 0.437509 + 0.958011i 0.992049 + 0.125854i \(0.0401671\pi\)
−0.554540 + 0.832157i \(0.687106\pi\)
\(194\) 0 0
\(195\) 0.382270 8.02483i 0.0273749 0.574670i
\(196\) 0 0
\(197\) 2.18741 9.01665i 0.155847 0.642409i −0.839271 0.543714i \(-0.817018\pi\)
0.995118 0.0986958i \(-0.0314671\pi\)
\(198\) 0 0
\(199\) 0.646970 0.508783i 0.0458625 0.0360667i −0.594965 0.803752i \(-0.702834\pi\)
0.640827 + 0.767685i \(0.278592\pi\)
\(200\) 0 0
\(201\) −7.99005 1.77737i −0.563575 0.125366i
\(202\) 0 0
\(203\) −28.6166 + 22.5044i −2.00849 + 1.57950i
\(204\) 0 0
\(205\) −5.40195 + 22.2671i −0.377289 + 1.55520i
\(206\) 0 0
\(207\) 0.0607685 1.27569i 0.00422370 0.0886664i
\(208\) 0 0
\(209\) −6.03438 13.2134i −0.417407 0.913993i
\(210\) 0 0
\(211\) 2.53050 7.31140i 0.174207 0.503338i −0.823769 0.566925i \(-0.808133\pi\)
0.997976 + 0.0635874i \(0.0202542\pi\)
\(212\) 0 0
\(213\) −5.22490 7.33734i −0.358004 0.502746i
\(214\) 0 0
\(215\) −5.24418 + 1.53983i −0.357650 + 0.105016i
\(216\) 0 0
\(217\) 27.6953 + 14.2779i 1.88008 + 0.969250i
\(218\) 0 0
\(219\) −11.2078 10.6866i −0.757350 0.722132i
\(220\) 0 0
\(221\) −8.45436 24.4273i −0.568702 1.64316i
\(222\) 0 0
\(223\) −12.1065 13.9717i −0.810713 0.935613i 0.188204 0.982130i \(-0.439733\pi\)
−0.998918 + 0.0465169i \(0.985188\pi\)
\(224\) 0 0
\(225\) −1.03192 0.303000i −0.0687949 0.0202000i
\(226\) 0 0
\(227\) 12.3618 11.7870i 0.820485 0.782330i −0.158263 0.987397i \(-0.550590\pi\)
0.978748 + 0.205066i \(0.0657411\pi\)
\(228\) 0 0
\(229\) 15.7836 22.1650i 1.04301 1.46470i 0.164862 0.986317i \(-0.447282\pi\)
0.878149 0.478387i \(-0.158778\pi\)
\(230\) 0 0
\(231\) −4.96092 8.59256i −0.326404 0.565349i
\(232\) 0 0
\(233\) −15.0171 + 2.89431i −0.983805 + 0.189613i −0.655694 0.755026i \(-0.727624\pi\)
−0.328111 + 0.944639i \(0.606412\pi\)
\(234\) 0 0
\(235\) −0.573609 0.451091i −0.0374181 0.0294259i
\(236\) 0 0
\(237\) 11.8472 + 1.13127i 0.769557 + 0.0734838i
\(238\) 0 0
\(239\) −3.58145 + 6.20326i −0.231665 + 0.401256i −0.958298 0.285770i \(-0.907751\pi\)
0.726633 + 0.687026i \(0.241084\pi\)
\(240\) 0 0
\(241\) −15.4573 9.93380i −0.995692 0.639892i −0.0620397 0.998074i \(-0.519761\pi\)
−0.933652 + 0.358182i \(0.883397\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) −35.7909 6.89813i −2.28660 0.440705i
\(246\) 0 0
\(247\) −19.7981 + 10.2066i −1.25972 + 0.649432i
\(248\) 0 0
\(249\) −0.298188 + 0.119376i −0.0188969 + 0.00756517i
\(250\) 0 0
\(251\) 2.16104 + 8.90793i 0.136404 + 0.562264i 0.998461 + 0.0554533i \(0.0176604\pi\)
−0.862058 + 0.506810i \(0.830824\pi\)
\(252\) 0 0
\(253\) 0.386342 2.68707i 0.0242891 0.168935i
\(254\) 0 0
\(255\) −19.4592 + 1.85813i −1.21858 + 0.116360i
\(256\) 0 0
\(257\) −0.606523 12.7325i −0.0378339 0.794231i −0.935451 0.353456i \(-0.885007\pi\)
0.897617 0.440775i \(-0.145297\pi\)
\(258\) 0 0
\(259\) −1.35470 9.42214i −0.0841769 0.585463i
\(260\) 0 0
\(261\) 7.24070 + 2.89874i 0.448188 + 0.179427i
\(262\) 0 0
\(263\) 21.7052 13.9491i 1.33840 0.860136i 0.341580 0.939853i \(-0.389038\pi\)
0.996818 + 0.0797163i \(0.0254014\pi\)
\(264\) 0 0
\(265\) 3.98344 4.59713i 0.244701 0.282400i
\(266\) 0 0
\(267\) −11.8941 −0.727906
\(268\) 0 0
\(269\) 18.9708 1.15667 0.578336 0.815799i \(-0.303702\pi\)
0.578336 + 0.815799i \(0.303702\pi\)
\(270\) 0 0
\(271\) −4.17559 + 4.81889i −0.253649 + 0.292727i −0.868266 0.496099i \(-0.834765\pi\)
0.614617 + 0.788826i \(0.289311\pi\)
\(272\) 0 0
\(273\) −12.7988 + 8.22532i −0.774621 + 0.497819i
\(274\) 0 0
\(275\) −2.12232 0.849650i −0.127981 0.0512358i
\(276\) 0 0
\(277\) 2.38541 + 16.5909i 0.143325 + 0.996850i 0.926835 + 0.375470i \(0.122519\pi\)
−0.783509 + 0.621380i \(0.786572\pi\)
\(278\) 0 0
\(279\) −0.317630 6.66787i −0.0190160 0.399195i
\(280\) 0 0
\(281\) 32.6943 3.12193i 1.95038 0.186239i 0.956099 0.293044i \(-0.0946682\pi\)
0.994280 + 0.106805i \(0.0340621\pi\)
\(282\) 0 0
\(283\) 0.791944 5.50809i 0.0470762 0.327422i −0.952651 0.304066i \(-0.901656\pi\)
0.999727 0.0233563i \(-0.00743523\pi\)
\(284\) 0 0
\(285\) 3.97121 + 16.3696i 0.235234 + 0.969649i
\(286\) 0 0
\(287\) 40.2826 16.1267i 2.37781 0.951931i
\(288\) 0 0
\(289\) −40.7923 + 21.0299i −2.39955 + 1.23705i
\(290\) 0 0
\(291\) 6.32276 + 1.21861i 0.370647 + 0.0714363i
\(292\) 0 0
\(293\) −3.38464 + 7.41133i −0.197733 + 0.432975i −0.982362 0.186991i \(-0.940126\pi\)
0.784629 + 0.619966i \(0.212854\pi\)
\(294\) 0 0
\(295\) −15.7663 10.1324i −0.917948 0.589929i
\(296\) 0 0
\(297\) −1.06281 + 1.84084i −0.0616705 + 0.106816i
\(298\) 0 0
\(299\) −4.14384 0.395689i −0.239644 0.0228833i
\(300\) 0 0
\(301\) 8.13586 + 6.39811i 0.468943 + 0.368781i
\(302\) 0 0
\(303\) −6.01379 + 1.15906i −0.345483 + 0.0665865i
\(304\) 0 0
\(305\) −10.3426 17.9140i −0.592218 1.02575i
\(306\) 0 0
\(307\) 15.9492 22.3975i 0.910267 1.27829i −0.0498686 0.998756i \(-0.515880\pi\)
0.960135 0.279535i \(-0.0901803\pi\)
\(308\) 0 0
\(309\) −11.8678 + 11.3159i −0.675135 + 0.643740i
\(310\) 0 0
\(311\) 10.8757 + 3.19340i 0.616705 + 0.181081i 0.575140 0.818055i \(-0.304948\pi\)
0.0415648 + 0.999136i \(0.486766\pi\)
\(312\) 0 0
\(313\) −15.6498 18.0608i −0.884577 1.02086i −0.999622 0.0274959i \(-0.991247\pi\)
0.115045 0.993360i \(-0.463299\pi\)
\(314\) 0 0
\(315\) 3.76300 + 10.8725i 0.212021 + 0.612595i
\(316\) 0 0
\(317\) 11.5956 + 11.0564i 0.651275 + 0.620989i 0.941918 0.335842i \(-0.109021\pi\)
−0.290644 + 0.956831i \(0.593869\pi\)
\(318\) 0 0
\(319\) 14.7356 + 7.59673i 0.825035 + 0.425335i
\(320\) 0 0
\(321\) −5.33747 + 1.56722i −0.297909 + 0.0874738i
\(322\) 0 0
\(323\) 31.4369 + 44.1470i 1.74920 + 2.45640i
\(324\) 0 0
\(325\) −1.14652 + 3.31265i −0.0635974 + 0.183753i
\(326\) 0 0
\(327\) 1.90863 + 4.17932i 0.105548 + 0.231117i
\(328\) 0 0
\(329\) −0.0657539 + 1.38034i −0.00362513 + 0.0761008i
\(330\) 0 0
\(331\) −2.50370 + 10.3204i −0.137616 + 0.567259i 0.860693 + 0.509124i \(0.170031\pi\)
−0.998309 + 0.0581352i \(0.981485\pi\)
\(332\) 0 0
\(333\) −1.60302 + 1.26063i −0.0878449 + 0.0690820i
\(334\) 0 0
\(335\) 17.6623 + 9.75202i 0.964993 + 0.532810i
\(336\) 0 0
\(337\) 10.5273 8.27878i 0.573460 0.450974i −0.288836 0.957379i \(-0.593268\pi\)
0.862296 + 0.506405i \(0.169026\pi\)
\(338\) 0 0
\(339\) 1.43144 5.90048i 0.0777451 0.320470i
\(340\) 0 0
\(341\) 0.675161 14.1734i 0.0365620 0.767531i
\(342\) 0 0
\(343\) 15.1008 + 33.0661i 0.815366 + 1.78540i
\(344\) 0 0
\(345\) −1.02959 + 2.97481i −0.0554313 + 0.160158i
\(346\) 0 0
\(347\) −17.0162 23.8959i −0.913477 1.28280i −0.958874 0.283830i \(-0.908395\pi\)
0.0453971 0.998969i \(-0.485545\pi\)
\(348\) 0 0
\(349\) 25.2446 7.41247i 1.35131 0.396780i 0.475619 0.879652i \(-0.342224\pi\)
0.875691 + 0.482871i \(0.160406\pi\)
\(350\) 0 0
\(351\) 2.89707 + 1.49354i 0.154634 + 0.0797195i
\(352\) 0 0
\(353\) −4.48865 4.27992i −0.238907 0.227797i 0.561161 0.827706i \(-0.310355\pi\)
−0.800068 + 0.599910i \(0.795203\pi\)
\(354\) 0 0
\(355\) 7.26166 + 20.9812i 0.385409 + 1.11357i
\(356\) 0 0
\(357\) 24.2415 + 27.9762i 1.28300 + 1.48066i
\(358\) 0 0
\(359\) 34.3142 + 10.0755i 1.81103 + 0.531767i 0.998678 0.0513978i \(-0.0163676\pi\)
0.812354 + 0.583165i \(0.198186\pi\)
\(360\) 0 0
\(361\) 20.0484 19.1161i 1.05518 1.00611i
\(362\) 0 0
\(363\) 3.75977 5.27986i 0.197337 0.277121i
\(364\) 0 0
\(365\) 19.0854 + 33.0568i 0.998973 + 1.73027i
\(366\) 0 0
\(367\) 31.2365 6.02035i 1.63053 0.314260i 0.709785 0.704418i \(-0.248792\pi\)
0.920748 + 0.390158i \(0.127580\pi\)
\(368\) 0 0
\(369\) −7.30708 5.74635i −0.380391 0.299143i
\(370\) 0 0
\(371\) −11.4671 1.09498i −0.595343 0.0568483i
\(372\) 0 0
\(373\) −9.30706 + 16.1203i −0.481901 + 0.834678i −0.999784 0.0207740i \(-0.993387\pi\)
0.517883 + 0.855452i \(0.326720\pi\)
\(374\) 0 0
\(375\) −8.13773 5.22980i −0.420230 0.270066i
\(376\) 0 0
\(377\) 10.5604 23.1240i 0.543888 1.19095i
\(378\) 0 0
\(379\) −12.7336 2.45419i −0.654079 0.126063i −0.148593 0.988898i \(-0.547474\pi\)
−0.505486 + 0.862835i \(0.668687\pi\)
\(380\) 0 0
\(381\) −8.33299 + 4.29596i −0.426912 + 0.220088i
\(382\) 0 0
\(383\) 2.23341 0.894124i 0.114122 0.0456876i −0.313899 0.949456i \(-0.601635\pi\)
0.428021 + 0.903769i \(0.359211\pi\)
\(384\) 0 0
\(385\) 5.76568 + 23.7665i 0.293846 + 1.21125i
\(386\) 0 0
\(387\) 0.315570 2.19484i 0.0160413 0.111570i
\(388\) 0 0
\(389\) 34.5082 3.29514i 1.74964 0.167070i 0.829459 0.558568i \(-0.188649\pi\)
0.920179 + 0.391498i \(0.128043\pi\)
\(390\) 0 0
\(391\) 0.481929 + 10.1169i 0.0243722 + 0.511635i
\(392\) 0 0
\(393\) −0.580405 4.03680i −0.0292775 0.203630i
\(394\) 0 0
\(395\) −27.2331 10.9025i −1.37024 0.548563i
\(396\) 0 0
\(397\) −8.01695 + 5.15218i −0.402359 + 0.258581i −0.726133 0.687554i \(-0.758685\pi\)
0.323774 + 0.946134i \(0.395048\pi\)
\(398\) 0 0
\(399\) 20.8891 24.1073i 1.04576 1.20687i
\(400\) 0 0
\(401\) −21.7179 −1.08454 −0.542270 0.840204i \(-0.682435\pi\)
−0.542270 + 0.840204i \(0.682435\pi\)
\(402\) 0 0
\(403\) −21.7579 −1.08384
\(404\) 0 0
\(405\) 1.61413 1.86281i 0.0802070 0.0925638i
\(406\) 0 0
\(407\) −3.64670 + 2.34359i −0.180760 + 0.116167i
\(408\) 0 0
\(409\) −15.9079 6.36857i −0.786596 0.314906i −0.0566358 0.998395i \(-0.518037\pi\)
−0.729961 + 0.683489i \(0.760462\pi\)
\(410\) 0 0
\(411\) 2.47796 + 17.2346i 0.122229 + 0.850119i
\(412\) 0 0
\(413\) 1.68873 + 35.4508i 0.0830969 + 1.74442i
\(414\) 0 0
\(415\) 0.788114 0.0752558i 0.0386870 0.00369416i
\(416\) 0 0
\(417\) −0.515407 + 3.58474i −0.0252396 + 0.175545i
\(418\) 0 0
\(419\) 4.70058 + 19.3760i 0.229638 + 0.946582i 0.963591 + 0.267381i \(0.0861583\pi\)
−0.733953 + 0.679201i \(0.762327\pi\)
\(420\) 0 0
\(421\) −12.8116 + 5.12899i −0.624400 + 0.249972i −0.662216 0.749313i \(-0.730384\pi\)
0.0378166 + 0.999285i \(0.487960\pi\)
\(422\) 0 0
\(423\) 0.263145 0.135660i 0.0127945 0.00659604i
\(424\) 0 0
\(425\) 8.37511 + 1.61417i 0.406252 + 0.0782987i
\(426\) 0 0
\(427\) −16.2727 + 35.6322i −0.787491 + 1.72436i
\(428\) 0 0
\(429\) 5.82841 + 3.74569i 0.281399 + 0.180844i
\(430\) 0 0
\(431\) 3.97645 6.88741i 0.191539 0.331755i −0.754222 0.656620i \(-0.771986\pi\)
0.945760 + 0.324865i \(0.105319\pi\)
\(432\) 0 0
\(433\) −21.8410 2.08556i −1.04961 0.100226i −0.444031 0.896011i \(-0.646452\pi\)
−0.605578 + 0.795786i \(0.707058\pi\)
\(434\) 0 0
\(435\) −15.1113 11.8837i −0.724533 0.569779i
\(436\) 0 0
\(437\) 8.57000 1.65173i 0.409959 0.0790130i
\(438\) 0 0
\(439\) 4.81358 + 8.33737i 0.229740 + 0.397921i 0.957731 0.287666i \(-0.0928791\pi\)
−0.727991 + 0.685587i \(0.759546\pi\)
\(440\) 0 0
\(441\) 8.57773 12.0457i 0.408463 0.573607i
\(442\) 0 0
\(443\) 2.17686 2.07564i 0.103426 0.0986165i −0.636602 0.771192i \(-0.719661\pi\)
0.740028 + 0.672576i \(0.234812\pi\)
\(444\) 0 0
\(445\) 28.1296 + 8.25959i 1.33347 + 0.391542i
\(446\) 0 0
\(447\) −3.66943 4.23474i −0.173558 0.200297i
\(448\) 0 0
\(449\) −6.94453 20.0649i −0.327733 0.946921i −0.981706 0.190404i \(-0.939020\pi\)
0.653973 0.756518i \(-0.273101\pi\)
\(450\) 0 0
\(451\) −14.3007 13.6357i −0.673393 0.642079i
\(452\) 0 0
\(453\) −1.29770 0.669013i −0.0609714 0.0314330i
\(454\) 0 0
\(455\) 35.9812 10.5650i 1.68683 0.495297i
\(456\) 0 0
\(457\) 14.3128 + 20.0995i 0.669525 + 0.940216i 0.999994 0.00360062i \(-0.00114612\pi\)
−0.330468 + 0.943817i \(0.607207\pi\)
\(458\) 0 0
\(459\) 2.59384 7.49440i 0.121070 0.349809i
\(460\) 0 0
\(461\) −4.08804 8.95156i −0.190399 0.416916i 0.790225 0.612817i \(-0.209964\pi\)
−0.980624 + 0.195902i \(0.937237\pi\)
\(462\) 0 0
\(463\) −1.24041 + 26.0394i −0.0576468 + 1.21016i 0.765920 + 0.642936i \(0.222284\pi\)
−0.823567 + 0.567219i \(0.808019\pi\)
\(464\) 0 0
\(465\) −3.87916 + 15.9901i −0.179892 + 0.741524i
\(466\) 0 0
\(467\) −4.71579 + 3.70854i −0.218221 + 0.171611i −0.721285 0.692638i \(-0.756448\pi\)
0.503064 + 0.864249i \(0.332206\pi\)
\(468\) 0 0
\(469\) −4.35813 37.9577i −0.201240 1.75272i
\(470\) 0 0
\(471\) −13.4831 + 10.6033i −0.621271 + 0.488573i
\(472\) 0 0
\(473\) 1.11122 4.58051i 0.0510939 0.210612i
\(474\) 0 0
\(475\) 0.349713 7.34138i 0.0160459 0.336846i
\(476\) 0 0
\(477\) 1.02518 + 2.24484i 0.0469399 + 0.102784i
\(478\) 0 0
\(479\) −0.749908 + 2.16672i −0.0342642 + 0.0989998i −0.960836 0.277119i \(-0.910620\pi\)
0.926571 + 0.376119i \(0.122742\pi\)
\(480\) 0 0
\(481\) 3.85563 + 5.41447i 0.175801 + 0.246879i
\(482\) 0 0
\(483\) 5.71984 1.67950i 0.260262 0.0764198i
\(484\) 0 0
\(485\) −14.1071 7.27273i −0.640572 0.330238i
\(486\) 0 0
\(487\) −30.1200 28.7194i −1.36487 1.30140i −0.912216 0.409710i \(-0.865630\pi\)
−0.452651 0.891688i \(-0.649522\pi\)
\(488\) 0 0
\(489\) −0.532200 1.53769i −0.0240669 0.0695368i
\(490\) 0 0
\(491\) 2.14196 + 2.47195i 0.0966653 + 0.111558i 0.802021 0.597296i \(-0.203758\pi\)
−0.705356 + 0.708854i \(0.749213\pi\)
\(492\) 0 0
\(493\) −59.3481 17.4262i −2.67291 0.784836i
\(494\) 0 0
\(495\) 3.79189 3.61556i 0.170433 0.162507i
\(496\) 0 0
\(497\) 24.3884 34.2488i 1.09397 1.53627i
\(498\) 0 0
\(499\) 4.96471 + 8.59914i 0.222251 + 0.384950i 0.955491 0.295020i \(-0.0953262\pi\)
−0.733240 + 0.679970i \(0.761993\pi\)
\(500\) 0 0
\(501\) −12.4558 + 2.40065i −0.556482 + 0.107253i
\(502\) 0 0
\(503\) 19.6774 + 15.4745i 0.877374 + 0.689974i 0.951624 0.307265i \(-0.0994139\pi\)
−0.0742501 + 0.997240i \(0.523656\pi\)
\(504\) 0 0
\(505\) 15.0275 + 1.43496i 0.668717 + 0.0638547i
\(506\) 0 0
\(507\) −1.18816 + 2.05795i −0.0527679 + 0.0913966i
\(508\) 0 0
\(509\) −9.06152 5.82348i −0.401645 0.258121i 0.324188 0.945993i \(-0.394909\pi\)
−0.725833 + 0.687871i \(0.758545\pi\)
\(510\) 0 0
\(511\) 30.0281 65.7524i 1.32837 2.90871i
\(512\) 0 0
\(513\) −6.71034 1.29331i −0.296269 0.0571011i
\(514\) 0 0
\(515\) 35.9255 18.5209i 1.58307 0.816127i
\(516\) 0 0
\(517\) 0.584224 0.233888i 0.0256941 0.0102864i
\(518\) 0 0
\(519\) 2.58386 + 10.6508i 0.113419 + 0.467520i
\(520\) 0 0
\(521\) −0.480912 + 3.34482i −0.0210691 + 0.146539i −0.997640 0.0686549i \(-0.978129\pi\)
0.976571 + 0.215194i \(0.0690384\pi\)
\(522\) 0 0
\(523\) 0.688467 0.0657406i 0.0301046 0.00287464i −0.0799929 0.996795i \(-0.525490\pi\)
0.110097 + 0.993921i \(0.464884\pi\)
\(524\) 0 0
\(525\) −0.238866 5.01441i −0.0104250 0.218847i
\(526\) 0 0
\(527\) 7.53415 + 52.4012i 0.328193 + 2.28263i
\(528\) 0 0
\(529\) −19.8382 7.94203i −0.862532 0.345306i
\(530\) 0 0
\(531\) 6.39644 4.11074i 0.277582 0.178391i
\(532\) 0 0
\(533\) −19.8417 + 22.8985i −0.859438 + 0.991845i
\(534\) 0 0
\(535\) 13.7115 0.592799
\(536\) 0 0
\(537\) −23.1832 −1.00043
\(538\) 0 0
\(539\) 20.5843 23.7556i 0.886630 1.02323i
\(540\) 0 0
\(541\) 13.2756 8.53173i 0.570764 0.366808i −0.223200 0.974773i \(-0.571650\pi\)
0.793964 + 0.607965i \(0.208014\pi\)
\(542\) 0 0
\(543\) 3.18843 + 1.27646i 0.136829 + 0.0547780i
\(544\) 0 0
\(545\) −1.61169 11.2095i −0.0690371 0.480164i
\(546\) 0 0
\(547\) 0.538464 + 11.3038i 0.0230231 + 0.483314i 0.980706 + 0.195488i \(0.0626292\pi\)
−0.957683 + 0.287825i \(0.907068\pi\)
\(548\) 0 0
\(549\) 8.35411 0.797721i 0.356545 0.0340459i
\(550\) 0 0
\(551\) −7.58534 + 52.7572i −0.323146 + 2.24753i
\(552\) 0 0
\(553\) 13.0966 + 53.9851i 0.556926 + 2.29568i
\(554\) 0 0
\(555\) 4.66657 1.86821i 0.198085 0.0793012i
\(556\) 0 0
\(557\) 7.30490 3.76594i 0.309519 0.159568i −0.296468 0.955043i \(-0.595809\pi\)
0.605987 + 0.795475i \(0.292778\pi\)
\(558\) 0 0
\(559\) −7.09681 1.36780i −0.300163 0.0578517i
\(560\) 0 0
\(561\) 7.00282 15.3340i 0.295659 0.647404i
\(562\) 0 0
\(563\) 0.639741 + 0.411136i 0.0269618 + 0.0173273i 0.554052 0.832482i \(-0.313081\pi\)
−0.527090 + 0.849809i \(0.676717\pi\)
\(564\) 0 0
\(565\) −7.48282 + 12.9606i −0.314805 + 0.545258i
\(566\) 0 0
\(567\) −4.64660 0.443696i −0.195139 0.0186335i
\(568\) 0 0
\(569\) 30.6437 + 24.0985i 1.28465 + 1.01026i 0.998645 + 0.0520339i \(0.0165704\pi\)
0.286007 + 0.958228i \(0.407672\pi\)
\(570\) 0 0
\(571\) 33.4797 6.45268i 1.40108 0.270036i 0.567927 0.823079i \(-0.307746\pi\)
0.833153 + 0.553043i \(0.186533\pi\)
\(572\) 0 0
\(573\) 6.28086 + 10.8788i 0.262387 + 0.454467i
\(574\) 0 0
\(575\) 0.796733 1.11885i 0.0332260 0.0466594i
\(576\) 0 0
\(577\) −22.7097 + 21.6536i −0.945416 + 0.901452i −0.995255 0.0973052i \(-0.968978\pi\)
0.0498388 + 0.998757i \(0.484129\pi\)
\(578\) 0 0
\(579\) 14.0386 + 4.12212i 0.583426 + 0.171309i
\(580\) 0 0
\(581\) −0.981803 1.13306i −0.0407321 0.0470073i
\(582\) 0 0
\(583\) 1.71571 + 4.95720i 0.0710572 + 0.205306i
\(584\) 0 0
\(585\) −5.81443 5.54405i −0.240397 0.229218i
\(586\) 0 0
\(587\) −24.4988 12.6300i −1.01117 0.521296i −0.128713 0.991682i \(-0.541084\pi\)
−0.882461 + 0.470386i \(0.844115\pi\)
\(588\) 0 0
\(589\) 43.7709 12.8523i 1.80355 0.529570i
\(590\) 0 0
\(591\) −5.38187 7.55778i −0.221381 0.310886i
\(592\) 0 0
\(593\) −1.24223 + 3.58919i −0.0510124 + 0.147391i −0.967629 0.252377i \(-0.918788\pi\)
0.916617 + 0.399767i \(0.130909\pi\)
\(594\) 0 0
\(595\) −37.9039 82.9979i −1.55391 3.40258i
\(596\) 0 0
\(597\) 0.0391629 0.822129i 0.00160283 0.0336475i
\(598\) 0 0
\(599\) 4.69145 19.3384i 0.191688 0.790147i −0.792038 0.610471i \(-0.790980\pi\)
0.983726 0.179676i \(-0.0575048\pi\)
\(600\) 0 0
\(601\) −20.5711 + 16.1773i −0.839114 + 0.659887i −0.942298 0.334776i \(-0.891339\pi\)
0.103184 + 0.994662i \(0.467097\pi\)
\(602\) 0 0
\(603\) −6.57562 + 4.87455i −0.267780 + 0.198507i
\(604\) 0 0
\(605\) −12.5584 + 9.87602i −0.510571 + 0.401517i
\(606\) 0 0
\(607\) −3.89247 + 16.0450i −0.157990 + 0.651246i 0.836640 + 0.547753i \(0.184517\pi\)
−0.994630 + 0.103492i \(0.966998\pi\)
\(608\) 0 0
\(609\) −1.73224 + 36.3642i −0.0701940 + 1.47355i
\(610\) 0 0
\(611\) −0.400860 0.877762i −0.0162171 0.0355104i
\(612\) 0 0
\(613\) 9.03746 26.1120i 0.365020 1.05465i −0.601679 0.798738i \(-0.705501\pi\)
0.966699 0.255917i \(-0.0823773\pi\)
\(614\) 0 0
\(615\) 13.2909 + 18.6644i 0.535939 + 0.752621i
\(616\) 0 0
\(617\) 37.4452 10.9949i 1.50749 0.442638i 0.579413 0.815034i \(-0.303282\pi\)
0.928074 + 0.372397i \(0.121464\pi\)
\(618\) 0 0
\(619\) 17.3671 + 8.95337i 0.698044 + 0.359867i 0.770443 0.637509i \(-0.220035\pi\)
−0.0723991 + 0.997376i \(0.523066\pi\)
\(620\) 0 0
\(621\) −0.924305 0.881323i −0.0370911 0.0353663i
\(622\) 0 0
\(623\) −18.1583 52.4649i −0.727497 2.10196i
\(624\) 0 0
\(625\) 19.1355 + 22.0836i 0.765421 + 0.883343i
\(626\) 0 0
\(627\) −13.9377 4.09249i −0.556619 0.163438i
\(628\) 0 0
\(629\) 11.7050 11.1607i 0.466708 0.445005i
\(630\) 0 0
\(631\) −19.0864 + 26.8032i −0.759819 + 1.06702i 0.235641 + 0.971840i \(0.424281\pi\)
−0.995460 + 0.0951768i \(0.969658\pi\)
\(632\) 0 0
\(633\) −3.86846 6.70037i −0.153758 0.266316i
\(634\) 0 0
\(635\) 22.6908 4.37330i 0.900458 0.173549i
\(636\) 0 0
\(637\) −37.8871 29.7947i −1.50114 1.18051i
\(638\) 0 0
\(639\) −8.96677 0.856223i −0.354720 0.0338717i
\(640\) 0 0
\(641\) 7.78774 13.4888i 0.307597 0.532774i −0.670239 0.742145i \(-0.733808\pi\)
0.977836 + 0.209371i \(0.0671417\pi\)
\(642\) 0 0
\(643\) −23.2758 14.9584i −0.917907 0.589903i −0.00585732 0.999983i \(-0.501864\pi\)
−0.912050 + 0.410080i \(0.865501\pi\)
\(644\) 0 0
\(645\) −2.27048 + 4.97167i −0.0894002 + 0.195759i
\(646\) 0 0
\(647\) −42.9489 8.27773i −1.68850 0.325431i −0.747606 0.664142i \(-0.768797\pi\)
−0.940890 + 0.338711i \(0.890009\pi\)
\(648\) 0 0
\(649\) 14.3654 7.40590i 0.563893 0.290707i
\(650\) 0 0
\(651\) 28.9271 11.5807i 1.13374 0.453883i
\(652\) 0 0
\(653\) −1.39389 5.74569i −0.0545471 0.224846i 0.938013 0.346599i \(-0.112664\pi\)
−0.992560 + 0.121753i \(0.961148\pi\)
\(654\) 0 0
\(655\) −1.43061 + 9.95011i −0.0558986 + 0.388783i
\(656\) 0 0
\(657\) −15.4159 + 1.47204i −0.601431 + 0.0574297i
\(658\) 0 0
\(659\) −0.453962 9.52983i −0.0176838 0.371230i −0.990312 0.138862i \(-0.955656\pi\)
0.972628 0.232368i \(-0.0746474\pi\)
\(660\) 0 0
\(661\) 1.79977 + 12.5177i 0.0700031 + 0.486882i 0.994420 + 0.105498i \(0.0336435\pi\)
−0.924416 + 0.381385i \(0.875447\pi\)
\(662\) 0 0
\(663\) −23.9973 9.60708i −0.931978 0.373108i
\(664\) 0 0
\(665\) −66.1436 + 42.5079i −2.56494 + 1.64839i
\(666\) 0 0
\(667\) −6.52297 + 7.52791i −0.252571 + 0.291482i
\(668\) 0 0
\(669\) −18.4872 −0.714756
\(670\) 0 0
\(671\) 17.8384 0.688646
\(672\) 0 0
\(673\) −18.7931 + 21.6883i −0.724419 + 0.836024i −0.991831 0.127558i \(-0.959286\pi\)
0.267412 + 0.963582i \(0.413832\pi\)
\(674\) 0 0
\(675\) −0.904758 + 0.581453i −0.0348242 + 0.0223801i
\(676\) 0 0
\(677\) −19.3510 7.74696i −0.743718 0.297740i −0.0313141 0.999510i \(-0.509969\pi\)
−0.712404 + 0.701770i \(0.752393\pi\)
\(678\) 0 0
\(679\) 4.27743 + 29.7502i 0.164153 + 1.14171i
\(680\) 0 0
\(681\) −0.812730 17.0613i −0.0311439 0.653790i
\(682\) 0 0
\(683\) −12.7974 + 1.22200i −0.489679 + 0.0467586i −0.336975 0.941513i \(-0.609404\pi\)
−0.152703 + 0.988272i \(0.548798\pi\)
\(684\) 0 0
\(685\) 6.10780 42.4807i 0.233367 1.62310i
\(686\) 0 0
\(687\) −6.41511 26.4434i −0.244752 1.00888i
\(688\) 0 0
\(689\) 7.46752 2.98954i 0.284490 0.113893i
\(690\) 0 0
\(691\) 23.3325 12.0287i 0.887611 0.457595i 0.0467874 0.998905i \(-0.485102\pi\)
0.840823 + 0.541310i \(0.182071\pi\)
\(692\) 0 0
\(693\) −9.74253 1.87772i −0.370088 0.0713287i
\(694\) 0 0
\(695\) 3.70828 8.12001i 0.140663 0.308010i
\(696\) 0 0
\(697\) 62.0188 + 39.8571i 2.34913 + 1.50969i
\(698\) 0 0
\(699\) −7.64675 + 13.2446i −0.289227 + 0.500955i
\(700\) 0 0
\(701\) 7.20786 + 0.688267i 0.272237 + 0.0259955i 0.230282 0.973124i \(-0.426035\pi\)
0.0419554 + 0.999119i \(0.486641\pi\)
\(702\) 0 0
\(703\) −10.9548 8.61492i −0.413167 0.324918i
\(704\) 0 0
\(705\) −0.716545 + 0.138103i −0.0269867 + 0.00520125i
\(706\) 0 0
\(707\) −14.2937 24.7574i −0.537570 0.931098i
\(708\) 0 0
\(709\) −22.6780 + 31.8467i −0.851689 + 1.19603i 0.127249 + 0.991871i \(0.459385\pi\)
−0.978938 + 0.204159i \(0.934554\pi\)
\(710\) 0 0
\(711\) 8.61321 8.21267i 0.323020 0.307999i
\(712\) 0 0
\(713\) 8.18008 + 2.40189i 0.306346 + 0.0899514i
\(714\) 0 0
\(715\) −11.1831 12.9060i −0.418225 0.482657i
\(716\) 0 0
\(717\) 2.34276 + 6.76895i 0.0874919 + 0.252791i
\(718\) 0 0
\(719\) 1.46309 + 1.39505i 0.0545641 + 0.0520268i 0.716871 0.697206i \(-0.245574\pi\)
−0.662306 + 0.749233i \(0.730422\pi\)
\(720\) 0 0
\(721\) −68.0328 35.0733i −2.53367 1.30620i
\(722\) 0 0
\(723\) −17.6298 + 5.17659i −0.655661 + 0.192519i
\(724\) 0 0
\(725\) 4.86560 + 6.83278i 0.180704 + 0.253763i
\(726\) 0 0
\(727\) 7.06466 20.4120i 0.262014 0.757039i −0.734874 0.678204i \(-0.762759\pi\)
0.996888 0.0788352i \(-0.0251201\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) −0.836743 + 17.5654i −0.0309481 + 0.649680i
\(732\) 0 0
\(733\) −8.87629 + 36.5886i −0.327853 + 1.35143i 0.534520 + 0.845156i \(0.320493\pi\)
−0.862373 + 0.506274i \(0.831023\pi\)
\(734\) 0 0
\(735\) −28.6513 + 22.5316i −1.05682 + 0.831092i
\(736\) 0 0
\(737\) −14.8989 + 8.98590i −0.548808 + 0.331000i
\(738\) 0 0
\(739\) 2.56542 2.01747i 0.0943706 0.0742138i −0.569859 0.821743i \(-0.693002\pi\)
0.664230 + 0.747529i \(0.268760\pi\)
\(740\) 0 0
\(741\) −5.25134 + 21.6463i −0.192913 + 0.795197i
\(742\) 0 0
\(743\) 1.69006 35.4787i 0.0620023 1.30159i −0.726760 0.686891i \(-0.758975\pi\)
0.788763 0.614698i \(-0.210722\pi\)
\(744\) 0 0
\(745\) 5.73749 + 12.5634i 0.210205 + 0.460286i
\(746\) 0 0
\(747\) −0.105053 + 0.303530i −0.00384368 + 0.0111056i
\(748\) 0 0
\(749\) −15.0616 21.1510i −0.550338 0.772841i
\(750\) 0 0
\(751\) 4.19515 1.23181i 0.153083 0.0449493i −0.204293 0.978910i \(-0.565490\pi\)
0.357376 + 0.933960i \(0.383671\pi\)
\(752\) 0 0
\(753\) 8.14735 + 4.20025i 0.296906 + 0.153066i
\(754\) 0 0
\(755\) 2.60450 + 2.48338i 0.0947873 + 0.0903795i
\(756\) 0 0
\(757\) 10.6438 + 30.7532i 0.386855 + 1.11774i 0.955457 + 0.295131i \(0.0953634\pi\)
−0.568602 + 0.822613i \(0.692515\pi\)
\(758\) 0 0
\(759\) −1.77775 2.05164i −0.0645283 0.0744696i
\(760\) 0 0
\(761\) 24.4200 + 7.17035i 0.885223 + 0.259925i 0.692577 0.721344i \(-0.256475\pi\)
0.192645 + 0.981268i \(0.438293\pi\)
\(762\) 0 0
\(763\) −15.5212 + 14.7994i −0.561905 + 0.535775i
\(764\) 0 0
\(765\) −11.3388 + 15.9231i −0.409954 + 0.575700i
\(766\) 0 0
\(767\) −12.3914 21.4625i −0.447426 0.774965i
\(768\) 0 0
\(769\) −24.0309 + 4.63158i −0.866578 + 0.167019i −0.603119 0.797651i \(-0.706075\pi\)
−0.263459 + 0.964671i \(0.584863\pi\)
\(770\) 0 0
\(771\) −10.0198 7.87963i −0.360853 0.283778i
\(772\) 0 0
\(773\) −40.3696 3.85483i −1.45199 0.138649i −0.660960 0.750421i \(-0.729851\pi\)
−0.791034 + 0.611772i \(0.790457\pi\)
\(774\) 0 0
\(775\) 3.58967 6.21750i 0.128945 0.223339i
\(776\) 0 0
\(777\) −8.00792 5.14638i −0.287283 0.184625i
\(778\)