Properties

Label 605.2.g.e.81.1
Level $605$
Weight $2$
Character 605.81
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} + 5 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(1.69513 - 1.23158i\) of defining polynomial
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.e.366.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} +O(q^{10})\) \(q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} -2.09529 q^{10} +4.57255 q^{12} +(2.46735 + 1.79264i) q^{13} +(1.98595 - 6.11211i) q^{14} +(-0.591149 - 1.81937i) q^{15} +(2.48141 - 1.80285i) q^{16} +(-0.375259 + 0.272641i) q^{17} +(0.427051 + 1.31433i) q^{18} +(2.43988 - 7.50919i) q^{19} +(1.93376 + 1.40496i) q^{20} +5.86752 q^{21} -1.39026 q^{23} +(-1.26552 - 0.919451i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.97470 - 6.07750i) q^{26} +(3.62218 - 2.63167i) q^{27} +(-5.93120 + 4.30927i) q^{28} +(-1.15004 - 3.53947i) q^{29} +(-1.23863 + 3.81211i) q^{30} +(8.47564 + 6.15791i) q^{31} -8.06206 q^{32} +0.971892 q^{34} +(2.48141 + 1.80285i) q^{35} +(0.487169 - 1.49935i) q^{36} +(0.569992 + 1.75425i) q^{37} +(-13.3841 + 9.72412i) q^{38} +(4.72004 - 3.42931i) q^{39} +(-0.252684 - 0.777682i) q^{40} +(1.36203 - 4.19190i) q^{41} +(-9.94619 - 7.22633i) q^{42} +1.31478 q^{43} -0.659557 q^{45} +(2.35666 + 1.71222i) q^{46} +(-0.920927 + 2.83432i) q^{47} +(-1.81316 - 5.58034i) q^{48} +(-1.94781 + 1.41517i) q^{49} +(-1.69513 + 1.23158i) q^{50} +(0.274201 + 0.843905i) q^{51} +(-2.25268 + 6.93305i) q^{52} +(-3.38828 - 2.46173i) q^{53} -9.38118 q^{54} +2.50805 q^{56} +(-12.2196 - 8.87809i) q^{57} +(-2.40968 + 7.41623i) q^{58} +(0.869890 + 2.67725i) q^{59} +(3.69927 - 2.68768i) q^{60} +(-1.63209 + 1.18578i) q^{61} +(-6.78332 - 20.8769i) q^{62} +(0.625136 - 1.92397i) q^{63} +(8.70342 + 6.32340i) q^{64} +3.04981 q^{65} -6.75753 q^{67} +(-0.896964 - 0.651683i) q^{68} +(-0.821848 + 2.52939i) q^{69} +(-1.98595 - 6.11211i) q^{70} +(5.27637 - 3.83351i) q^{71} +(-0.436320 + 0.317005i) q^{72} +(3.05179 + 9.39245i) q^{73} +(1.19430 - 3.67568i) q^{74} +(-1.54765 - 1.12443i) q^{75} +18.8726 q^{76} -12.2245 q^{78} +(-9.35051 - 6.79354i) q^{79} +(0.947813 - 2.91707i) q^{80} +(-3.25817 - 10.0276i) q^{81} +(-7.47150 + 5.42836i) q^{82} +(7.21531 - 5.24223i) q^{83} +(4.33392 + 13.3384i) q^{84} +(-0.143336 + 0.441143i) q^{85} +(-2.22872 - 1.61926i) q^{86} -7.11945 q^{87} -6.76978 q^{89} +(1.11803 + 0.812299i) q^{90} +(-2.89065 + 8.89651i) q^{91} +(-1.02689 - 3.16043i) q^{92} +(16.2139 - 11.7801i) q^{93} +(5.05179 - 3.67034i) q^{94} +(-2.43988 - 7.50919i) q^{95} +(-4.76588 + 14.6679i) q^{96} +(-12.4219 - 9.02506i) q^{97} +5.04469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} + O(q^{10}) \) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} - 2q^{10} + 16q^{12} - 3q^{13} + 14q^{14} - 5q^{15} - q^{16} - 12q^{17} - 10q^{18} - 5q^{19} + 2q^{20} + 20q^{21} + 10q^{23} + 2q^{24} - 2q^{25} + 5q^{26} + 5q^{27} - 19q^{28} - 21q^{29} - 7q^{30} + 15q^{31} - 16q^{32} + 4q^{34} - q^{35} + 15q^{36} - 31q^{37} - 20q^{38} + 14q^{39} - q^{40} - 3q^{41} - 21q^{42} + 38q^{43} + 7q^{46} - 5q^{47} + 5q^{48} - 4q^{49} - 3q^{50} - 6q^{51} - 17q^{52} - 2q^{53} - 16q^{54} + 22q^{56} - 40q^{57} + 2q^{58} + 18q^{59} + 4q^{60} - 6q^{61} + 5q^{62} + 30q^{63} + 29q^{64} - 2q^{65} - 38q^{67} + 14q^{68} + 9q^{69} - 14q^{70} + 15q^{71} - 5q^{72} + 2q^{73} + 20q^{74} - 5q^{75} - 16q^{78} + 3q^{79} - 4q^{80} - 12q^{81} - 22q^{82} + 38q^{83} + 17q^{84} - 13q^{85} + 2q^{86} - 38q^{87} - 16q^{89} - 36q^{91} + q^{92} + 40q^{93} + 18q^{94} + 5q^{95} + 17q^{96} - 56q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69513 1.23158i −1.19864 0.870861i −0.204487 0.978869i \(-0.565553\pi\)
−0.994150 + 0.108009i \(0.965553\pi\)
\(3\) 0.591149 1.81937i 0.341300 1.05041i −0.622235 0.782830i \(-0.713775\pi\)
0.963535 0.267582i \(-0.0862247\pi\)
\(4\) 0.738630 + 2.27327i 0.369315 + 1.13663i
\(5\) 0.809017 0.587785i 0.361803 0.262866i
\(6\) −3.24278 + 2.35601i −1.32386 + 0.961839i
\(7\) 0.947813 + 2.91707i 0.358239 + 1.10255i 0.954107 + 0.299465i \(0.0968082\pi\)
−0.595868 + 0.803083i \(0.703192\pi\)
\(8\) 0.252684 0.777682i 0.0893373 0.274952i
\(9\) −0.533593 0.387678i −0.177864 0.129226i
\(10\) −2.09529 −0.662590
\(11\) 0 0
\(12\) 4.57255 1.31998
\(13\) 2.46735 + 1.79264i 0.684320 + 0.497188i 0.874788 0.484506i \(-0.161001\pi\)
−0.190468 + 0.981693i \(0.561001\pi\)
\(14\) 1.98595 6.11211i 0.530766 1.63353i
\(15\) −0.591149 1.81937i −0.152634 0.469759i
\(16\) 2.48141 1.80285i 0.620351 0.450712i
\(17\) −0.375259 + 0.272641i −0.0910136 + 0.0661252i −0.632361 0.774674i \(-0.717914\pi\)
0.541348 + 0.840799i \(0.317914\pi\)
\(18\) 0.427051 + 1.31433i 0.100657 + 0.309790i
\(19\) 2.43988 7.50919i 0.559747 1.72273i −0.123317 0.992367i \(-0.539353\pi\)
0.683065 0.730358i \(-0.260647\pi\)
\(20\) 1.93376 + 1.40496i 0.432402 + 0.314158i
\(21\) 5.86752 1.28040
\(22\) 0 0
\(23\) −1.39026 −0.289889 −0.144944 0.989440i \(-0.546300\pi\)
−0.144944 + 0.989440i \(0.546300\pi\)
\(24\) −1.26552 0.919451i −0.258322 0.187682i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) −1.97470 6.07750i −0.387270 1.19189i
\(27\) 3.62218 2.63167i 0.697089 0.506465i
\(28\) −5.93120 + 4.30927i −1.12089 + 0.814375i
\(29\) −1.15004 3.53947i −0.213558 0.657263i −0.999253 0.0386491i \(-0.987695\pi\)
0.785695 0.618614i \(-0.212305\pi\)
\(30\) −1.23863 + 3.81211i −0.226142 + 0.695993i
\(31\) 8.47564 + 6.15791i 1.52227 + 1.10599i 0.960348 + 0.278804i \(0.0899380\pi\)
0.561922 + 0.827190i \(0.310062\pi\)
\(32\) −8.06206 −1.42518
\(33\) 0 0
\(34\) 0.971892 0.166678
\(35\) 2.48141 + 1.80285i 0.419434 + 0.304737i
\(36\) 0.487169 1.49935i 0.0811948 0.249892i
\(37\) 0.569992 + 1.75425i 0.0937061 + 0.288398i 0.986914 0.161246i \(-0.0515511\pi\)
−0.893208 + 0.449643i \(0.851551\pi\)
\(38\) −13.3841 + 9.72412i −2.17119 + 1.57746i
\(39\) 4.72004 3.42931i 0.755811 0.549129i
\(40\) −0.252684 0.777682i −0.0399529 0.122962i
\(41\) 1.36203 4.19190i 0.212714 0.654665i −0.786594 0.617470i \(-0.788158\pi\)
0.999308 0.0371953i \(-0.0118424\pi\)
\(42\) −9.94619 7.22633i −1.53473 1.11505i
\(43\) 1.31478 0.200502 0.100251 0.994962i \(-0.468035\pi\)
0.100251 + 0.994962i \(0.468035\pi\)
\(44\) 0 0
\(45\) −0.659557 −0.0983210
\(46\) 2.35666 + 1.71222i 0.347471 + 0.252453i
\(47\) −0.920927 + 2.83432i −0.134331 + 0.413428i −0.995485 0.0949152i \(-0.969742\pi\)
0.861154 + 0.508344i \(0.169742\pi\)
\(48\) −1.81316 5.58034i −0.261707 0.805453i
\(49\) −1.94781 + 1.41517i −0.278259 + 0.202167i
\(50\) −1.69513 + 1.23158i −0.239727 + 0.174172i
\(51\) 0.274201 + 0.843905i 0.0383959 + 0.118170i
\(52\) −2.25268 + 6.93305i −0.312391 + 0.961441i
\(53\) −3.38828 2.46173i −0.465416 0.338144i 0.330236 0.943898i \(-0.392872\pi\)
−0.795652 + 0.605754i \(0.792872\pi\)
\(54\) −9.38118 −1.27662
\(55\) 0 0
\(56\) 2.50805 0.335152
\(57\) −12.2196 8.87809i −1.61853 1.17593i
\(58\) −2.40968 + 7.41623i −0.316406 + 0.973799i
\(59\) 0.869890 + 2.67725i 0.113250 + 0.348548i 0.991578 0.129511i \(-0.0413407\pi\)
−0.878328 + 0.478059i \(0.841341\pi\)
\(60\) 3.69927 2.68768i 0.477574 0.346978i
\(61\) −1.63209 + 1.18578i −0.208967 + 0.151824i −0.687346 0.726330i \(-0.741225\pi\)
0.478379 + 0.878154i \(0.341225\pi\)
\(62\) −6.78332 20.8769i −0.861482 2.65137i
\(63\) 0.625136 1.92397i 0.0787598 0.242398i
\(64\) 8.70342 + 6.32340i 1.08793 + 0.790426i
\(65\) 3.04981 0.378283
\(66\) 0 0
\(67\) −6.75753 −0.825564 −0.412782 0.910830i \(-0.635443\pi\)
−0.412782 + 0.910830i \(0.635443\pi\)
\(68\) −0.896964 0.651683i −0.108773 0.0790281i
\(69\) −0.821848 + 2.52939i −0.0989389 + 0.304503i
\(70\) −1.98595 6.11211i −0.237366 0.730537i
\(71\) 5.27637 3.83351i 0.626190 0.454953i −0.228888 0.973453i \(-0.573509\pi\)
0.855078 + 0.518499i \(0.173509\pi\)
\(72\) −0.436320 + 0.317005i −0.0514209 + 0.0373594i
\(73\) 3.05179 + 9.39245i 0.357185 + 1.09930i 0.954732 + 0.297469i \(0.0961424\pi\)
−0.597546 + 0.801834i \(0.703858\pi\)
\(74\) 1.19430 3.67568i 0.138835 0.427289i
\(75\) −1.54765 1.12443i −0.178707 0.129838i
\(76\) 18.8726 2.16483
\(77\) 0 0
\(78\) −12.2245 −1.38416
\(79\) −9.35051 6.79354i −1.05201 0.764333i −0.0794197 0.996841i \(-0.525307\pi\)
−0.972594 + 0.232508i \(0.925307\pi\)
\(80\) 0.947813 2.91707i 0.105969 0.326138i
\(81\) −3.25817 10.0276i −0.362019 1.11418i
\(82\) −7.47150 + 5.42836i −0.825089 + 0.599462i
\(83\) 7.21531 5.24223i 0.791983 0.575409i −0.116568 0.993183i \(-0.537189\pi\)
0.908551 + 0.417773i \(0.137189\pi\)
\(84\) 4.33392 + 13.3384i 0.472870 + 1.45534i
\(85\) −0.143336 + 0.441143i −0.0155470 + 0.0478487i
\(86\) −2.22872 1.61926i −0.240329 0.174609i
\(87\) −7.11945 −0.763285
\(88\) 0 0
\(89\) −6.76978 −0.717595 −0.358797 0.933415i \(-0.616813\pi\)
−0.358797 + 0.933415i \(0.616813\pi\)
\(90\) 1.11803 + 0.812299i 0.117851 + 0.0856239i
\(91\) −2.89065 + 8.89651i −0.303023 + 0.932608i
\(92\) −1.02689 3.16043i −0.107060 0.329497i
\(93\) 16.2139 11.7801i 1.68130 1.22154i
\(94\) 5.05179 3.67034i 0.521053 0.378567i
\(95\) −2.43988 7.50919i −0.250327 0.770426i
\(96\) −4.76588 + 14.6679i −0.486415 + 1.49703i
\(97\) −12.4219 9.02506i −1.26126 0.916356i −0.262437 0.964949i \(-0.584526\pi\)
−0.998819 + 0.0485933i \(0.984526\pi\)
\(98\) 5.04469 0.509591
\(99\) 0 0
\(100\) 2.39026 0.239026
\(101\) 9.49186 + 6.89624i 0.944476 + 0.686202i 0.949494 0.313786i \(-0.101597\pi\)
−0.00501815 + 0.999987i \(0.501597\pi\)
\(102\) 0.574532 1.76823i 0.0568872 0.175081i
\(103\) 4.29165 + 13.2083i 0.422868 + 1.30146i 0.905021 + 0.425368i \(0.139855\pi\)
−0.482152 + 0.876087i \(0.660145\pi\)
\(104\) 2.01756 1.46584i 0.197838 0.143738i
\(105\) 4.74692 3.44884i 0.463252 0.336572i
\(106\) 2.71174 + 8.34589i 0.263388 + 0.810625i
\(107\) 2.26231 6.96269i 0.218706 0.673108i −0.780164 0.625576i \(-0.784864\pi\)
0.998870 0.0475327i \(-0.0151358\pi\)
\(108\) 8.65794 + 6.29036i 0.833111 + 0.605290i
\(109\) 7.43306 0.711958 0.355979 0.934494i \(-0.384147\pi\)
0.355979 + 0.934494i \(0.384147\pi\)
\(110\) 0 0
\(111\) 3.52859 0.334919
\(112\) 7.61093 + 5.52967i 0.719165 + 0.522504i
\(113\) −0.938299 + 2.88779i −0.0882677 + 0.271660i −0.985441 0.170019i \(-0.945617\pi\)
0.897173 + 0.441679i \(0.145617\pi\)
\(114\) 9.77976 + 30.0990i 0.915958 + 2.81903i
\(115\) −1.12474 + 0.817172i −0.104883 + 0.0762017i
\(116\) 7.19671 5.22872i 0.668198 0.485474i
\(117\) −0.621596 1.91308i −0.0574666 0.176864i
\(118\) 1.82268 5.60962i 0.167791 0.516407i
\(119\) −1.15099 0.836242i −0.105511 0.0766581i
\(120\) −1.56426 −0.142797
\(121\) 0 0
\(122\) 4.22699 0.382693
\(123\) −6.82145 4.95608i −0.615070 0.446874i
\(124\) −7.73823 + 23.8158i −0.694914 + 2.13873i
\(125\) −0.309017 0.951057i −0.0276393 0.0850651i
\(126\) −3.42922 + 2.49147i −0.305499 + 0.221958i
\(127\) −0.365350 + 0.265442i −0.0324196 + 0.0235542i −0.603877 0.797077i \(-0.706378\pi\)
0.571457 + 0.820632i \(0.306378\pi\)
\(128\) −1.98299 6.10301i −0.175273 0.539435i
\(129\) 0.777230 2.39207i 0.0684313 0.210610i
\(130\) −5.16983 3.75610i −0.453424 0.329432i
\(131\) −0.629003 −0.0549563 −0.0274781 0.999622i \(-0.508748\pi\)
−0.0274781 + 0.999622i \(0.508748\pi\)
\(132\) 0 0
\(133\) 24.2173 2.09991
\(134\) 11.4549 + 8.32246i 0.989551 + 0.718951i
\(135\) 1.38355 4.25813i 0.119077 0.366481i
\(136\) 0.117206 + 0.360724i 0.0100504 + 0.0309318i
\(137\) −9.04756 + 6.57343i −0.772985 + 0.561606i −0.902865 0.429923i \(-0.858541\pi\)
0.129880 + 0.991530i \(0.458541\pi\)
\(138\) 4.50829 3.27547i 0.383771 0.278826i
\(139\) 0.733901 + 2.25872i 0.0622487 + 0.191582i 0.977345 0.211655i \(-0.0678852\pi\)
−0.915096 + 0.403236i \(0.867885\pi\)
\(140\) −2.26552 + 6.97254i −0.191471 + 0.589287i
\(141\) 4.61227 + 3.35101i 0.388423 + 0.282206i
\(142\) −13.6654 −1.14678
\(143\) 0 0
\(144\) −2.02298 −0.168582
\(145\) −3.01085 2.18751i −0.250038 0.181663i
\(146\) 6.39440 19.6799i 0.529205 1.62872i
\(147\) 1.42327 + 4.38036i 0.117389 + 0.361286i
\(148\) −3.56688 + 2.59149i −0.293196 + 0.213019i
\(149\) −7.05490 + 5.12569i −0.577960 + 0.419913i −0.837988 0.545688i \(-0.816268\pi\)
0.260028 + 0.965601i \(0.416268\pi\)
\(150\) 1.23863 + 3.81211i 0.101134 + 0.311258i
\(151\) −3.68825 + 11.3513i −0.300145 + 0.923753i 0.681299 + 0.732005i \(0.261415\pi\)
−0.981444 + 0.191747i \(0.938585\pi\)
\(152\) −5.22324 3.79490i −0.423660 0.307807i
\(153\) 0.305932 0.0247332
\(154\) 0 0
\(155\) 10.4765 0.841490
\(156\) 11.2821 + 8.19692i 0.903291 + 0.656279i
\(157\) 1.19754 3.68565i 0.0955741 0.294147i −0.891829 0.452373i \(-0.850578\pi\)
0.987403 + 0.158226i \(0.0505776\pi\)
\(158\) 7.48350 + 23.0318i 0.595355 + 1.83232i
\(159\) −6.48177 + 4.70928i −0.514037 + 0.373470i
\(160\) −6.52234 + 4.73876i −0.515637 + 0.374632i
\(161\) −1.31770 4.05547i −0.103850 0.319616i
\(162\) −6.82682 + 21.0108i −0.536366 + 1.65076i
\(163\) 8.03857 + 5.84036i 0.629629 + 0.457452i 0.856272 0.516526i \(-0.172775\pi\)
−0.226643 + 0.973978i \(0.572775\pi\)
\(164\) 10.5354 0.822674
\(165\) 0 0
\(166\) −18.6871 −1.45040
\(167\) 11.2615 + 8.18198i 0.871443 + 0.633140i 0.930974 0.365086i \(-0.118960\pi\)
−0.0595308 + 0.998226i \(0.518960\pi\)
\(168\) 1.48263 4.56306i 0.114387 0.352048i
\(169\) −1.14294 3.51761i −0.0879185 0.270585i
\(170\) 0.786277 0.571264i 0.0603047 0.0438139i
\(171\) −4.21305 + 3.06096i −0.322180 + 0.234077i
\(172\) 0.971136 + 2.98885i 0.0740484 + 0.227898i
\(173\) −3.34700 + 10.3010i −0.254468 + 0.783171i 0.739466 + 0.673193i \(0.235078\pi\)
−0.993934 + 0.109977i \(0.964922\pi\)
\(174\) 12.0684 + 8.76819i 0.914901 + 0.664715i
\(175\) 3.06719 0.231857
\(176\) 0 0
\(177\) 5.38513 0.404771
\(178\) 11.4756 + 8.33754i 0.860136 + 0.624925i
\(179\) 7.02502 21.6208i 0.525075 1.61601i −0.239093 0.970997i \(-0.576850\pi\)
0.764168 0.645018i \(-0.223150\pi\)
\(180\) −0.487169 1.49935i −0.0363114 0.111755i
\(181\) −1.94028 + 1.40969i −0.144220 + 0.104782i −0.657556 0.753406i \(-0.728410\pi\)
0.513336 + 0.858188i \(0.328410\pi\)
\(182\) 15.8568 11.5207i 1.17539 0.853968i
\(183\) 1.19257 + 3.67034i 0.0881570 + 0.271319i
\(184\) −0.351296 + 1.08118i −0.0258979 + 0.0797054i
\(185\) 1.49226 + 1.08419i 0.109713 + 0.0797112i
\(186\) −41.9927 −3.07906
\(187\) 0 0
\(188\) −7.12340 −0.519527
\(189\) 11.1099 + 8.07181i 0.808126 + 0.587138i
\(190\) −5.11227 + 15.7340i −0.370883 + 1.14146i
\(191\) 5.32938 + 16.4022i 0.385621 + 1.18682i 0.936029 + 0.351923i \(0.114472\pi\)
−0.550408 + 0.834896i \(0.685528\pi\)
\(192\) 16.6496 12.0967i 1.20158 0.873001i
\(193\) −2.09190 + 1.51986i −0.150579 + 0.109402i −0.660524 0.750805i \(-0.729666\pi\)
0.509945 + 0.860207i \(0.329666\pi\)
\(194\) 9.94165 + 30.5973i 0.713769 + 2.19676i
\(195\) 1.80289 5.54873i 0.129108 0.397353i
\(196\) −4.65577 3.38262i −0.332555 0.241615i
\(197\) −0.144731 −0.0103116 −0.00515582 0.999987i \(-0.501641\pi\)
−0.00515582 + 0.999987i \(0.501641\pi\)
\(198\) 0 0
\(199\) −7.54177 −0.534622 −0.267311 0.963610i \(-0.586135\pi\)
−0.267311 + 0.963610i \(0.586135\pi\)
\(200\) −0.661536 0.480634i −0.0467776 0.0339859i
\(201\) −3.99470 + 12.2944i −0.281765 + 0.867183i
\(202\) −7.59663 23.3800i −0.534497 1.64501i
\(203\) 9.23485 6.70951i 0.648159 0.470915i
\(204\) −1.71589 + 1.24667i −0.120136 + 0.0872842i
\(205\) −1.36203 4.19190i −0.0951285 0.292775i
\(206\) 8.99226 27.6753i 0.626520 1.92823i
\(207\) 0.741831 + 0.538972i 0.0515608 + 0.0374611i
\(208\) 9.35435 0.648607
\(209\) 0 0
\(210\) −12.2942 −0.848379
\(211\) −1.83551 1.33357i −0.126362 0.0918070i 0.522809 0.852450i \(-0.324884\pi\)
−0.649171 + 0.760643i \(0.724884\pi\)
\(212\) 3.09349 9.52078i 0.212462 0.653890i
\(213\) −3.85544 11.8658i −0.264170 0.813033i
\(214\) −12.4100 + 9.01642i −0.848333 + 0.616350i
\(215\) 1.06368 0.772808i 0.0725423 0.0527051i
\(216\) −1.13133 3.48188i −0.0769774 0.236912i
\(217\) −9.92973 + 30.5606i −0.674074 + 2.07459i
\(218\) −12.6000 9.15443i −0.853379 0.620016i
\(219\) 18.8924 1.27663
\(220\) 0 0
\(221\) −1.41464 −0.0951591
\(222\) −5.98141 4.34575i −0.401446 0.291667i
\(223\) 2.65127 8.15976i 0.177542 0.546418i −0.822199 0.569201i \(-0.807253\pi\)
0.999740 + 0.0227830i \(0.00725268\pi\)
\(224\) −7.64132 23.5176i −0.510557 1.57133i
\(225\) −0.533593 + 0.387678i −0.0355729 + 0.0258452i
\(226\) 5.14709 3.73958i 0.342379 0.248753i
\(227\) −1.91603 5.89692i −0.127171 0.391392i 0.867119 0.498101i \(-0.165969\pi\)
−0.994290 + 0.106708i \(0.965969\pi\)
\(228\) 11.1565 34.3362i 0.738857 2.27397i
\(229\) −18.7416 13.6166i −1.23848 0.899808i −0.240983 0.970529i \(-0.577470\pi\)
−0.997496 + 0.0707216i \(0.977470\pi\)
\(230\) 2.91300 0.192077
\(231\) 0 0
\(232\) −3.04318 −0.199794
\(233\) −22.5414 16.3773i −1.47674 1.07291i −0.978590 0.205818i \(-0.934014\pi\)
−0.498146 0.867093i \(-0.665986\pi\)
\(234\) −1.30243 + 4.00846i −0.0851423 + 0.262041i
\(235\) 0.920927 + 2.83432i 0.0600747 + 0.184891i
\(236\) −5.44358 + 3.95499i −0.354347 + 0.257448i
\(237\) −17.8875 + 12.9960i −1.16192 + 0.844182i
\(238\) 0.921171 + 2.83507i 0.0597107 + 0.183771i
\(239\) 5.03272 15.4891i 0.325540 1.00191i −0.645657 0.763628i \(-0.723416\pi\)
0.971196 0.238280i \(-0.0765837\pi\)
\(240\) −4.74692 3.44884i −0.306412 0.222622i
\(241\) −4.39063 −0.282826 −0.141413 0.989951i \(-0.545164\pi\)
−0.141413 + 0.989951i \(0.545164\pi\)
\(242\) 0 0
\(243\) −6.73820 −0.432256
\(244\) −3.90111 2.83432i −0.249743 0.181449i
\(245\) −0.743998 + 2.28979i −0.0475323 + 0.146289i
\(246\) 5.45942 + 16.8024i 0.348080 + 1.07128i
\(247\) 19.4813 14.1540i 1.23956 0.900596i
\(248\) 6.93056 5.03534i 0.440091 0.319745i
\(249\) −5.27222 16.2262i −0.334114 1.02830i
\(250\) −0.647481 + 1.99274i −0.0409503 + 0.126032i
\(251\) 2.15739 + 1.56744i 0.136173 + 0.0989357i 0.653787 0.756679i \(-0.273179\pi\)
−0.517613 + 0.855615i \(0.673179\pi\)
\(252\) 4.83545 0.304605
\(253\) 0 0
\(254\) 0.946229 0.0593717
\(255\) 0.717868 + 0.521562i 0.0449547 + 0.0326615i
\(256\) 2.49388 7.67536i 0.155867 0.479710i
\(257\) −6.68486 20.5739i −0.416990 1.28336i −0.910459 0.413600i \(-0.864271\pi\)
0.493469 0.869764i \(-0.335729\pi\)
\(258\) −4.26354 + 3.09764i −0.265436 + 0.192851i
\(259\) −4.57703 + 3.32541i −0.284403 + 0.206631i
\(260\) 2.25268 + 6.93305i 0.139706 + 0.429969i
\(261\) −0.758519 + 2.33448i −0.0469512 + 0.144501i
\(262\) 1.06624 + 0.774670i 0.0658726 + 0.0478593i
\(263\) −22.1392 −1.36516 −0.682581 0.730810i \(-0.739142\pi\)
−0.682581 + 0.730810i \(0.739142\pi\)
\(264\) 0 0
\(265\) −4.18814 −0.257276
\(266\) −41.0515 29.8257i −2.51703 1.82873i
\(267\) −4.00194 + 12.3167i −0.244915 + 0.753771i
\(268\) −4.99131 15.3617i −0.304893 0.938364i
\(269\) −16.7615 + 12.1780i −1.02197 + 0.742503i −0.966685 0.255967i \(-0.917606\pi\)
−0.0552828 + 0.998471i \(0.517606\pi\)
\(270\) −7.58953 + 5.51412i −0.461884 + 0.335578i
\(271\) 0.130749 + 0.402403i 0.00794242 + 0.0244443i 0.954949 0.296769i \(-0.0959093\pi\)
−0.947007 + 0.321214i \(0.895909\pi\)
\(272\) −0.439638 + 1.35307i −0.0266570 + 0.0820417i
\(273\) 14.4772 + 10.5183i 0.876202 + 0.636598i
\(274\) 23.4325 1.41561
\(275\) 0 0
\(276\) −6.35702 −0.382648
\(277\) −6.93534 5.03882i −0.416704 0.302753i 0.359606 0.933104i \(-0.382911\pi\)
−0.776310 + 0.630351i \(0.782911\pi\)
\(278\) 1.53774 4.73267i 0.0922274 0.283847i
\(279\) −2.13525 6.57164i −0.127834 0.393434i
\(280\) 2.02905 1.47419i 0.121259 0.0880999i
\(281\) −5.67208 + 4.12101i −0.338368 + 0.245839i −0.743973 0.668210i \(-0.767061\pi\)
0.405605 + 0.914049i \(0.367061\pi\)
\(282\) −3.69134 11.3608i −0.219816 0.676525i
\(283\) −3.07570 + 9.46603i −0.182831 + 0.562697i −0.999904 0.0138373i \(-0.995595\pi\)
0.817073 + 0.576534i \(0.195595\pi\)
\(284\) 12.6119 + 9.16306i 0.748377 + 0.543728i
\(285\) −15.1043 −0.894702
\(286\) 0 0
\(287\) 13.5190 0.798002
\(288\) 4.30186 + 3.12548i 0.253489 + 0.184171i
\(289\) −5.18680 + 15.9633i −0.305106 + 0.939020i
\(290\) 2.40968 + 7.41623i 0.141501 + 0.435496i
\(291\) −23.7631 + 17.2649i −1.39302 + 1.01209i
\(292\) −19.0974 + 13.8751i −1.11759 + 0.811978i
\(293\) −6.74302 20.7529i −0.393931 1.21240i −0.929791 0.368089i \(-0.880012\pi\)
0.535859 0.844307i \(-0.319988\pi\)
\(294\) 2.98216 9.17815i 0.173923 0.535280i
\(295\) 2.27740 + 1.65463i 0.132596 + 0.0963363i
\(296\) 1.50828 0.0876670
\(297\) 0 0
\(298\) 18.2717 1.05845
\(299\) −3.43025 2.49222i −0.198377 0.144129i
\(300\) 1.41300 4.34876i 0.0815794 0.251076i
\(301\) 1.24617 + 3.83530i 0.0718278 + 0.221063i
\(302\) 20.2321 14.6995i 1.16423 0.845859i
\(303\) 18.1579 13.1925i 1.04314 0.757889i
\(304\) −7.48357 23.0321i −0.429212 1.32098i
\(305\) −0.623402 + 1.91863i −0.0356959 + 0.109861i
\(306\) −0.518595 0.376781i −0.0296461 0.0215391i
\(307\) 30.8674 1.76170 0.880849 0.473397i \(-0.156972\pi\)
0.880849 + 0.473397i \(0.156972\pi\)
\(308\) 0 0
\(309\) 26.5678 1.51139
\(310\) −17.7590 12.9026i −1.00864 0.732821i
\(311\) −5.99957 + 18.4648i −0.340204 + 1.04704i 0.623897 + 0.781507i \(0.285549\pi\)
−0.964101 + 0.265535i \(0.914451\pi\)
\(312\) −1.47423 4.53722i −0.0834619 0.256869i
\(313\) −0.850657 + 0.618038i −0.0480820 + 0.0349336i −0.611567 0.791193i \(-0.709460\pi\)
0.563485 + 0.826127i \(0.309460\pi\)
\(314\) −6.56916 + 4.77278i −0.370719 + 0.269343i
\(315\) −0.625136 1.92397i −0.0352225 0.108404i
\(316\) 8.53698 26.2741i 0.480243 1.47804i
\(317\) 19.2800 + 14.0078i 1.08287 + 0.786754i 0.978182 0.207750i \(-0.0666142\pi\)
0.104692 + 0.994505i \(0.466614\pi\)
\(318\) 16.7873 0.941385
\(319\) 0 0
\(320\) 10.7580 0.601391
\(321\) −11.3303 8.23196i −0.632397 0.459463i
\(322\) −2.76097 + 8.49741i −0.153863 + 0.473542i
\(323\) 1.13173 + 3.48310i 0.0629710 + 0.193805i
\(324\) 20.3889 14.8134i 1.13272 0.822966i
\(325\) 2.46735 1.79264i 0.136864 0.0994375i
\(326\) −6.43351 19.8003i −0.356319 1.09664i
\(327\) 4.39404 13.5235i 0.242991 0.747850i
\(328\) −2.91580 2.11845i −0.160998 0.116972i
\(329\) −9.14077 −0.503947
\(330\) 0 0
\(331\) 25.6693 1.41091 0.705457 0.708753i \(-0.250742\pi\)
0.705457 + 0.708753i \(0.250742\pi\)
\(332\) 17.2464 + 12.5303i 0.946521 + 0.687688i
\(333\) 0.375942 1.15703i 0.0206015 0.0634049i
\(334\) −9.01295 27.7390i −0.493167 1.51781i
\(335\) −5.46696 + 3.97198i −0.298692 + 0.217012i
\(336\) 14.5597 10.5782i 0.794296 0.577090i
\(337\) 7.38308 + 22.7228i 0.402182 + 1.23779i 0.923225 + 0.384259i \(0.125543\pi\)
−0.521043 + 0.853530i \(0.674457\pi\)
\(338\) −2.39480 + 7.37043i −0.130260 + 0.400898i
\(339\) 4.69927 + 3.41422i 0.255230 + 0.185435i
\(340\) −1.10871 −0.0601282
\(341\) 0 0
\(342\) 10.9115 0.590026
\(343\) 11.3955 + 8.27934i 0.615301 + 0.447042i
\(344\) 0.332224 1.02248i 0.0179123 0.0551285i
\(345\) 0.821848 + 2.52939i 0.0442468 + 0.136178i
\(346\) 18.3601 13.3394i 0.987047 0.717132i
\(347\) −0.268717 + 0.195234i −0.0144255 + 0.0104807i −0.594975 0.803744i \(-0.702838\pi\)
0.580549 + 0.814225i \(0.302838\pi\)
\(348\) −5.25864 16.1844i −0.281892 0.867576i
\(349\) −0.377460 + 1.16170i −0.0202050 + 0.0621845i −0.960651 0.277760i \(-0.910408\pi\)
0.940446 + 0.339944i \(0.110408\pi\)
\(350\) −5.19927 3.77749i −0.277913 0.201916i
\(351\) 13.6548 0.728840
\(352\) 0 0
\(353\) −25.7038 −1.36808 −0.684039 0.729446i \(-0.739778\pi\)
−0.684039 + 0.729446i \(0.739778\pi\)
\(354\) −9.12849 6.63224i −0.485174 0.352499i
\(355\) 2.01539 6.20274i 0.106966 0.329207i
\(356\) −5.00036 15.3895i −0.265019 0.815643i
\(357\) −2.20184 + 1.59973i −0.116534 + 0.0846666i
\(358\) −38.5361 + 27.9981i −2.03670 + 1.47975i
\(359\) 5.54113 + 17.0538i 0.292450 + 0.900067i 0.984066 + 0.177802i \(0.0568988\pi\)
−0.691617 + 0.722265i \(0.743101\pi\)
\(360\) −0.166660 + 0.512925i −0.00878373 + 0.0270335i
\(361\) −35.0635 25.4751i −1.84545 1.34080i
\(362\) 5.02517 0.264117
\(363\) 0 0
\(364\) −22.3593 −1.17195
\(365\) 7.98970 + 5.80485i 0.418200 + 0.303840i
\(366\) 2.49878 7.69045i 0.130613 0.401986i
\(367\) −2.62383 8.07533i −0.136963 0.421529i 0.858927 0.512098i \(-0.171131\pi\)
−0.995890 + 0.0905689i \(0.971131\pi\)
\(368\) −3.44979 + 2.50642i −0.179833 + 0.130656i
\(369\) −2.35188 + 1.70874i −0.122434 + 0.0889535i
\(370\) −1.19430 3.67568i −0.0620887 0.191089i
\(371\) 3.96957 12.2171i 0.206090 0.634280i
\(372\) 38.7553 + 28.1574i 2.00937 + 1.45989i
\(373\) −35.8450 −1.85598 −0.927991 0.372604i \(-0.878465\pi\)
−0.927991 + 0.372604i \(0.878465\pi\)
\(374\) 0 0
\(375\) −1.91300 −0.0987867
\(376\) 1.97150 + 1.43238i 0.101672 + 0.0738692i
\(377\) 3.50742 10.7947i 0.180641 0.555957i
\(378\) −8.89160 27.3655i −0.457334 1.40753i
\(379\) −14.1995 + 10.3166i −0.729380 + 0.529926i −0.889367 0.457193i \(-0.848855\pi\)
0.159987 + 0.987119i \(0.448855\pi\)
\(380\) 15.2682 11.0930i 0.783244 0.569060i
\(381\) 0.266961 + 0.821622i 0.0136768 + 0.0420930i
\(382\) 11.1666 34.3673i 0.571334 1.75839i
\(383\) 17.4950 + 12.7109i 0.893954 + 0.649496i 0.936906 0.349581i \(-0.113676\pi\)
−0.0429517 + 0.999077i \(0.513676\pi\)
\(384\) −12.2759 −0.626450
\(385\) 0 0
\(386\) 5.41788 0.275763
\(387\) −0.701557 0.509711i −0.0356622 0.0259101i
\(388\) 11.3412 34.9046i 0.575761 1.77201i
\(389\) 11.0448 + 33.9923i 0.559992 + 1.72348i 0.682381 + 0.730996i \(0.260944\pi\)
−0.122389 + 0.992482i \(0.539056\pi\)
\(390\) −9.88986 + 7.18541i −0.500793 + 0.363847i
\(391\) 0.521706 0.379041i 0.0263838 0.0191689i
\(392\) 0.608369 + 1.87237i 0.0307273 + 0.0945689i
\(393\) −0.371834 + 1.14439i −0.0187566 + 0.0577268i
\(394\) 0.245337 + 0.178248i 0.0123599 + 0.00898001i
\(395\) −11.5579 −0.581539
\(396\) 0 0
\(397\) −20.0447 −1.00601 −0.503007 0.864282i \(-0.667773\pi\)
−0.503007 + 0.864282i \(0.667773\pi\)
\(398\) 12.7843 + 9.28831i 0.640817 + 0.465581i
\(399\) 14.3161 44.0603i 0.716699 2.20577i
\(400\) −0.947813 2.91707i −0.0473906 0.145853i
\(401\) 16.9074 12.2839i 0.844315 0.613431i −0.0792579 0.996854i \(-0.525255\pi\)
0.923573 + 0.383424i \(0.125255\pi\)
\(402\) 21.9132 15.9208i 1.09293 0.794059i
\(403\) 9.87349 + 30.3875i 0.491834 + 1.51371i
\(404\) −8.66604 + 26.6713i −0.431152 + 1.32695i
\(405\) −8.53000 6.19741i −0.423859 0.307952i
\(406\) −23.9176 −1.18701
\(407\) 0 0
\(408\) 0.725576 0.0359214
\(409\) 19.0104 + 13.8119i 0.940005 + 0.682954i 0.948422 0.317011i \(-0.102679\pi\)
−0.00841691 + 0.999965i \(0.502679\pi\)
\(410\) −2.85386 + 8.78327i −0.140942 + 0.433775i
\(411\) 6.61105 + 20.3467i 0.326099 + 1.00363i
\(412\) −26.8561 + 19.5121i −1.32311 + 0.961294i
\(413\) −6.98522 + 5.07506i −0.343720 + 0.249727i
\(414\) −0.593711 1.82725i −0.0291793 0.0898046i
\(415\) 2.75600 8.48210i 0.135287 0.416370i
\(416\) −19.8919 14.4523i −0.975283 0.708584i
\(417\) 4.54328 0.222485
\(418\) 0 0
\(419\) −10.1128 −0.494043 −0.247022 0.969010i \(-0.579452\pi\)
−0.247022 + 0.969010i \(0.579452\pi\)
\(420\) 11.3464 + 8.24361i 0.553646 + 0.402247i
\(421\) 2.75731 8.48612i 0.134383 0.413588i −0.861111 0.508418i \(-0.830231\pi\)
0.995494 + 0.0948296i \(0.0302306\pi\)
\(422\) 1.46901 + 4.52116i 0.0715105 + 0.220087i
\(423\) 1.59020 1.15535i 0.0773184 0.0561751i
\(424\) −2.77061 + 2.01296i −0.134552 + 0.0977581i
\(425\) 0.143336 + 0.441143i 0.00695282 + 0.0213986i
\(426\) −8.07828 + 24.8624i −0.391394 + 1.20459i
\(427\) −5.00592 3.63701i −0.242253 0.176007i
\(428\) 17.4991 0.845850
\(429\) 0 0
\(430\) −2.75485 −0.132851
\(431\) −14.2486 10.3522i −0.686331 0.498649i 0.189121 0.981954i \(-0.439436\pi\)
−0.875452 + 0.483305i \(0.839436\pi\)
\(432\) 4.24360 13.0605i 0.204170 0.628372i
\(433\) 2.82564 + 8.69644i 0.135792 + 0.417924i 0.995712 0.0925038i \(-0.0294870\pi\)
−0.859921 + 0.510428i \(0.829487\pi\)
\(434\) 54.4700 39.5748i 2.61465 1.89965i
\(435\) −5.75975 + 4.18470i −0.276159 + 0.200641i
\(436\) 5.49028 + 16.8973i 0.262937 + 0.809236i
\(437\) −3.39206 + 10.4397i −0.162264 + 0.499398i
\(438\) −32.0250 23.2675i −1.53021 1.11177i
\(439\) −6.46946 −0.308770 −0.154385 0.988011i \(-0.549340\pi\)
−0.154385 + 0.988011i \(0.549340\pi\)
\(440\) 0 0
\(441\) 1.58797 0.0756176
\(442\) 2.39800 + 1.74225i 0.114061 + 0.0828703i
\(443\) −12.6339 + 38.8832i −0.600255 + 1.84739i −0.0736507 + 0.997284i \(0.523465\pi\)
−0.526604 + 0.850111i \(0.676535\pi\)
\(444\) 2.60632 + 8.02143i 0.123690 + 0.380680i
\(445\) −5.47686 + 3.97918i −0.259628 + 0.188631i
\(446\) −14.5437 + 10.5666i −0.688662 + 0.500342i
\(447\) 5.15502 + 15.8655i 0.243824 + 0.750413i
\(448\) −10.1966 + 31.3819i −0.481743 + 1.48265i
\(449\) 9.83826 + 7.14791i 0.464296 + 0.337331i 0.795214 0.606329i \(-0.207358\pi\)
−0.330918 + 0.943659i \(0.607358\pi\)
\(450\) 1.38197 0.0651465
\(451\) 0 0
\(452\) −7.25777 −0.341377
\(453\) 18.4718 + 13.4206i 0.867882 + 0.630553i
\(454\) −4.01464 + 12.3558i −0.188416 + 0.579886i
\(455\) 2.89065 + 8.89651i 0.135516 + 0.417075i
\(456\) −9.99204 + 7.25964i −0.467920 + 0.339964i
\(457\) −8.01121 + 5.82049i −0.374749 + 0.272271i −0.759177 0.650884i \(-0.774398\pi\)
0.384429 + 0.923155i \(0.374398\pi\)
\(458\) 14.9995 + 46.1636i 0.700880 + 2.15709i
\(459\) −0.641753 + 1.97511i −0.0299544 + 0.0921903i
\(460\) −2.68842 1.95325i −0.125348 0.0910709i
\(461\) 3.12529 0.145559 0.0727796 0.997348i \(-0.476813\pi\)
0.0727796 + 0.997348i \(0.476813\pi\)
\(462\) 0 0
\(463\) −24.3518 −1.13173 −0.565863 0.824499i \(-0.691457\pi\)
−0.565863 + 0.824499i \(0.691457\pi\)
\(464\) −9.23485 6.70951i −0.428717 0.311481i
\(465\) 6.19315 19.0606i 0.287200 0.883912i
\(466\) 18.0406 + 55.5232i 0.835714 + 2.57206i
\(467\) −26.8381 + 19.4990i −1.24192 + 0.902307i −0.997725 0.0674196i \(-0.978523\pi\)
−0.244194 + 0.969726i \(0.578523\pi\)
\(468\) 3.88981 2.82611i 0.179806 0.130637i
\(469\) −6.40487 19.7122i −0.295749 0.910223i
\(470\) 1.92961 5.93874i 0.0890064 0.273934i
\(471\) −5.99763 4.35753i −0.276356 0.200784i
\(472\) 2.30185 0.105951
\(473\) 0 0
\(474\) 46.3273 2.12788
\(475\) −6.38769 4.64093i −0.293088 0.212941i
\(476\) 1.05085 3.23418i 0.0481655 0.148238i
\(477\) 0.853604 + 2.62712i 0.0390838 + 0.120288i
\(478\) −27.6072 + 20.0578i −1.26273 + 0.917424i
\(479\) −13.9941 + 10.1673i −0.639409 + 0.464558i −0.859647 0.510888i \(-0.829317\pi\)
0.220238 + 0.975446i \(0.429317\pi\)
\(480\) 4.76588 + 14.6679i 0.217531 + 0.669493i
\(481\) −1.73837 + 5.35015i −0.0792628 + 0.243946i
\(482\) 7.44269 + 5.40743i 0.339005 + 0.246302i
\(483\) −8.15736 −0.371173
\(484\) 0 0
\(485\) −15.3543 −0.697205
\(486\) 11.4221 + 8.29865i 0.518118 + 0.376435i
\(487\) 2.36108 7.26665i 0.106991 0.329283i −0.883202 0.468993i \(-0.844617\pi\)
0.990192 + 0.139710i \(0.0446170\pi\)
\(488\) 0.509758 + 1.56887i 0.0230756 + 0.0710195i
\(489\) 15.3778 11.1726i 0.695406 0.505242i
\(490\) 4.08124 2.96519i 0.184372 0.133954i
\(491\) 9.47332 + 29.1559i 0.427525 + 1.31579i 0.900556 + 0.434741i \(0.143160\pi\)
−0.473030 + 0.881046i \(0.656840\pi\)
\(492\) 6.22797 19.1677i 0.280778 0.864147i
\(493\) 1.39657 + 1.01467i 0.0628983 + 0.0456983i
\(494\) −50.4551 −2.27008
\(495\) 0 0
\(496\) 32.1333 1.44283
\(497\) 16.1836 + 11.7581i 0.725934 + 0.527422i
\(498\) −11.0469 + 33.9987i −0.495021 + 1.52352i
\(499\) −11.5814 35.6440i −0.518456 1.59564i −0.776905 0.629618i \(-0.783211\pi\)
0.258449 0.966025i \(-0.416789\pi\)
\(500\) 1.93376 1.40496i 0.0864803 0.0628316i
\(501\) 21.5433 15.6521i 0.962482 0.699284i
\(502\) −1.72663 5.31401i −0.0770631 0.237176i
\(503\) −2.61952 + 8.06206i −0.116799 + 0.359469i −0.992318 0.123714i \(-0.960520\pi\)
0.875519 + 0.483183i \(0.160520\pi\)
\(504\) −1.33828 0.972314i −0.0596115 0.0433103i
\(505\) 11.7326 0.522093
\(506\) 0 0
\(507\) −7.07548 −0.314233
\(508\) −0.873280 0.634475i −0.0387455 0.0281503i
\(509\) −0.524474 + 1.61417i −0.0232469 + 0.0715466i −0.962007 0.273025i \(-0.911976\pi\)
0.938760 + 0.344572i \(0.111976\pi\)
\(510\) −0.574532 1.76823i −0.0254407 0.0782985i
\(511\) −24.5059 + 17.8046i −1.08408 + 0.787628i
\(512\) −24.0633 + 17.4830i −1.06346 + 0.772649i
\(513\) −10.9240 33.6206i −0.482306 1.48438i
\(514\) −14.0067 + 43.1083i −0.617811 + 1.90143i
\(515\) 11.2357 + 8.16319i 0.495103 + 0.359713i
\(516\) 6.01190 0.264659
\(517\) 0 0
\(518\) 11.8542 0.520843
\(519\) 16.7627 + 12.1788i 0.735803 + 0.534592i
\(520\) 0.770639 2.37178i 0.0337948 0.104010i
\(521\) −11.4623 35.2775i −0.502174 1.54553i −0.805470 0.592637i \(-0.798087\pi\)
0.303295 0.952897i \(-0.401913\pi\)
\(522\) 4.16090 3.02307i 0.182117 0.132316i
\(523\) −14.6285 + 10.6282i −0.639659 + 0.464740i −0.859733 0.510744i \(-0.829370\pi\)
0.220074 + 0.975483i \(0.429370\pi\)
\(524\) −0.464601 1.42989i −0.0202962 0.0624652i
\(525\) 1.81316 5.58034i 0.0791329 0.243546i
\(526\) 37.5288 + 27.2663i 1.63633 + 1.18887i
\(527\) −4.85946 −0.211681
\(528\) 0 0
\(529\) −21.0672 −0.915965
\(530\) 7.09944 + 5.15804i 0.308380 + 0.224051i
\(531\) 0.573742 1.76580i 0.0248983 0.0766291i
\(532\) 17.8877 + 55.0526i 0.775528 + 2.38683i
\(533\) 10.8752 7.90127i 0.471056 0.342242i
\(534\) 21.9529 15.9497i 0.949994 0.690211i
\(535\) −2.26231 6.96269i −0.0978084 0.301023i
\(536\) −1.70752 + 5.25521i −0.0737536 + 0.226990i
\(537\) −35.1834 25.5622i −1.51827 1.10309i
\(538\) 43.4111 1.87159
\(539\) 0 0
\(540\) 10.7018 0.460532
\(541\) 9.50790 + 6.90789i 0.408776 + 0.296993i 0.773106 0.634277i \(-0.218702\pi\)
−0.364330 + 0.931270i \(0.618702\pi\)
\(542\) 0.273957 0.843154i 0.0117675 0.0362165i
\(543\) 1.41776 + 4.36342i 0.0608419 + 0.187252i
\(544\) 3.02536 2.19805i 0.129711 0.0942407i
\(545\) 6.01347 4.36904i 0.257589 0.187149i
\(546\) −11.5866 35.6598i −0.495860 1.52610i
\(547\) 6.72324 20.6920i 0.287465 0.884726i −0.698184 0.715918i \(-0.746008\pi\)
0.985649 0.168808i \(-0.0539917\pi\)
\(548\) −21.6260 15.7122i −0.923816 0.671192i
\(549\) 1.33057 0.0567874
\(550\) 0 0
\(551\) −29.3845 −1.25182
\(552\) 1.75939 + 1.27827i 0.0748847 + 0.0544069i
\(553\) 10.9547 33.7151i 0.465841 1.43371i
\(554\) 5.55057 + 17.0829i 0.235821 + 0.725783i
\(555\) 2.85469 2.07405i 0.121175 0.0880385i
\(556\) −4.59259 + 3.33671i −0.194769 + 0.141508i
\(557\) −1.49389 4.59771i −0.0632980 0.194811i 0.914406 0.404798i \(-0.132658\pi\)
−0.977704 + 0.209986i \(0.932658\pi\)
\(558\) −4.47399 + 13.7695i −0.189399 + 0.582910i
\(559\) 3.24402 + 2.35692i 0.137208 + 0.0996872i
\(560\) 9.40763 0.397545
\(561\) 0 0
\(562\) 14.6903 0.619672
\(563\) 3.86062 + 2.80491i 0.162706 + 0.118213i 0.666159 0.745810i \(-0.267937\pi\)
−0.503453 + 0.864023i \(0.667937\pi\)
\(564\) −4.21099 + 12.9601i −0.177315 + 0.545718i
\(565\) 0.938299 + 2.88779i 0.0394745 + 0.121490i
\(566\) 16.8719 12.2582i 0.709179 0.515249i
\(567\) 26.1631 19.0086i 1.09875 0.798286i
\(568\) −1.64799 5.07200i −0.0691483 0.212816i
\(569\) −11.0377 + 33.9705i −0.462724 + 1.42412i 0.399098 + 0.916908i \(0.369323\pi\)
−0.861822 + 0.507210i \(0.830677\pi\)
\(570\) 25.6037 + 18.6022i 1.07242 + 0.779161i
\(571\) 33.9838 1.42218 0.711090 0.703101i \(-0.248202\pi\)
0.711090 + 0.703101i \(0.248202\pi\)
\(572\) 0 0
\(573\) 32.9920 1.37826
\(574\) −22.9165 16.6498i −0.956515 0.694949i
\(575\) −0.429613 + 1.32221i −0.0179161 + 0.0551401i
\(576\) −2.19264 6.74825i −0.0913599 0.281177i
\(577\) 16.7126 12.1424i 0.695755 0.505495i −0.182792 0.983152i \(-0.558514\pi\)
0.878547 + 0.477656i \(0.158514\pi\)
\(578\) 28.4525 20.6719i 1.18347 0.859839i
\(579\) 1.52855 + 4.70441i 0.0635245 + 0.195508i
\(580\) 2.74890 8.46024i 0.114142 0.351292i
\(581\) 22.1307 + 16.0789i 0.918136 + 0.667065i
\(582\) 61.5447 2.55111
\(583\) 0 0
\(584\) 8.07548 0.334166
\(585\) −1.62736 1.18235i −0.0672830 0.0488840i
\(586\) −14.1286 + 43.4834i −0.583647 + 1.79628i
\(587\) 4.12848 + 12.7062i 0.170401 + 0.524439i 0.999394 0.0348197i \(-0.0110857\pi\)
−0.828993 + 0.559259i \(0.811086\pi\)
\(588\) −8.90648 + 6.47094i −0.367297 + 0.266857i
\(589\) 66.9205 48.6206i 2.75741 2.00338i
\(590\) −1.82268 5.60962i −0.0750384 0.230944i
\(591\) −0.0855575 + 0.263319i −0.00351936 + 0.0108315i
\(592\) 4.57703 + 3.32541i 0.188115 + 0.136673i
\(593\) −20.8062 −0.854410 −0.427205 0.904155i \(-0.640502\pi\)
−0.427205 + 0.904155i \(0.640502\pi\)
\(594\) 0 0
\(595\) −1.42270 −0.0583250
\(596\) −16.8630 12.2517i −0.690737 0.501850i
\(597\) −4.45830 + 13.7213i −0.182466 + 0.561573i
\(598\) 2.74534 + 8.44928i 0.112265 + 0.345517i
\(599\) 11.5250 8.37338i 0.470897 0.342127i −0.326894 0.945061i \(-0.606002\pi\)
0.797791 + 0.602934i \(0.206002\pi\)
\(600\) −1.26552 + 0.919451i −0.0516645 + 0.0375364i
\(601\) 6.41093 + 19.7308i 0.261507 + 0.804836i 0.992478 + 0.122427i \(0.0390677\pi\)
−0.730970 + 0.682409i \(0.760932\pi\)
\(602\) 2.61108 8.03609i 0.106420 0.327526i
\(603\) 3.60577 + 2.61975i 0.146838 + 0.106684i
\(604\) −28.5287 −1.16082
\(605\) 0 0
\(606\) −47.0276 −1.91037
\(607\) 14.4991 + 10.5342i 0.588502 + 0.427572i 0.841779 0.539822i \(-0.181508\pi\)
−0.253277 + 0.967394i \(0.581508\pi\)
\(608\) −19.6705 + 60.5395i −0.797743 + 2.45520i
\(609\) −6.74790 20.7679i −0.273439 0.841558i
\(610\) 3.41970 2.48456i 0.138460 0.100597i
\(611\) −7.35316 + 5.34238i −0.297477 + 0.216130i
\(612\) 0.225971 + 0.695467i 0.00913433 + 0.0281126i
\(613\) 8.71486 26.8216i 0.351990 1.08331i −0.605745 0.795659i \(-0.707125\pi\)
0.957734 0.287654i \(-0.0928753\pi\)
\(614\) −52.3243 38.0158i −2.11164 1.53419i
\(615\) −8.43178 −0.340002
\(616\) 0 0
\(617\) −4.72930 −0.190394 −0.0951972 0.995458i \(-0.530348\pi\)
−0.0951972 + 0.995458i \(0.530348\pi\)
\(618\) −45.0358 32.7205i −1.81161 1.31621i
\(619\) −9.28827 + 28.5864i −0.373327 + 1.14898i 0.571273 + 0.820760i \(0.306450\pi\)
−0.944600 + 0.328223i \(0.893550\pi\)
\(620\) 7.73823 + 23.8158i 0.310775 + 0.956467i
\(621\) −5.03576 + 3.65869i −0.202078 + 0.146818i
\(622\) 32.9109 23.9112i 1.31961 0.958752i
\(623\) −6.41648 19.7479i −0.257071 0.791183i
\(624\) 5.52981 17.0190i 0.221369 0.681305i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 2.20314 0.0880551
\(627\) 0 0
\(628\) 9.26301 0.369634
\(629\) −0.692177 0.502896i −0.0275989 0.0200518i
\(630\) −1.30984 + 4.03129i −0.0521855 + 0.160610i
\(631\) −9.79694 30.1519i −0.390010 1.20033i −0.932780 0.360446i \(-0.882624\pi\)
0.542770 0.839882i \(-0.317376\pi\)
\(632\) −7.64594 + 5.55510i −0.304139 + 0.220970i
\(633\) −3.51132 + 2.55112i −0.139562 + 0.101398i
\(634\) −15.4304 47.4899i −0.612820 1.88607i
\(635\) −0.139551 + 0.429495i −0.00553792 + 0.0170440i
\(636\) −15.4931 11.2564i −0.614341 0.446345i
\(637\) −7.34282 −0.290933
\(638\) 0 0
\(639\) −4.30160 −0.170169
\(640\) −5.19153 3.77187i −0.205213 0.149096i
\(641\) −5.85814 + 18.0295i −0.231383 + 0.712123i 0.766198 + 0.642605i \(0.222146\pi\)
−0.997581 + 0.0695181i \(0.977854\pi\)
\(642\) 9.06801 + 27.9085i 0.357886 + 1.10146i
\(643\) 29.3259 21.3065i 1.15650 0.840248i 0.167170 0.985928i \(-0.446537\pi\)
0.989332 + 0.145680i \(0.0465370\pi\)
\(644\) 8.24589 5.99099i 0.324933 0.236078i
\(645\) −0.777230 2.39207i −0.0306034 0.0941876i
\(646\) 2.37130 7.29812i 0.0932976 0.287141i
\(647\) 28.2767 + 20.5442i 1.11167 + 0.807676i 0.982926 0.184002i \(-0.0589052\pi\)
0.128745 + 0.991678i \(0.458905\pi\)
\(648\) −8.62158 −0.338688
\(649\) 0 0
\(650\) −6.39026 −0.250646
\(651\) 49.7310 + 36.1317i 1.94911 + 1.41611i
\(652\) −7.33919 + 22.5877i −0.287425 + 0.884602i
\(653\) −9.20539 28.3313i −0.360235 1.10869i −0.952912 0.303248i \(-0.901929\pi\)
0.592677 0.805440i \(-0.298071\pi\)
\(654\) −24.1037 + 17.5124i −0.942531 + 0.684789i
\(655\) −0.508874 + 0.369719i −0.0198834 + 0.0144461i
\(656\) −4.17761 12.8573i −0.163108 0.501995i
\(657\) 2.01283 6.19486i 0.0785280 0.241684i
\(658\) 15.4948 + 11.2576i 0.604050 + 0.438868i
\(659\) 7.30532 0.284575 0.142287 0.989825i \(-0.454554\pi\)
0.142287 + 0.989825i \(0.454554\pi\)
\(660\) 0 0
\(661\) −22.7352 −0.884296 −0.442148 0.896942i \(-0.645783\pi\)
−0.442148 + 0.896942i \(0.645783\pi\)
\(662\) −43.5128 31.6139i −1.69117 1.22871i
\(663\) −0.836263 + 2.57375i −0.0324778 + 0.0999563i
\(664\) −2.25359 6.93584i −0.0874563 0.269163i
\(665\) 19.5922 14.2346i 0.759755 0.551994i
\(666\) −2.06225 + 1.49831i −0.0799106 + 0.0580584i
\(667\) 1.59886 + 4.92077i 0.0619079 + 0.190533i
\(668\) −10.2817 + 31.6439i −0.397812 + 1.22434i
\(669\) −13.2783 9.64726i −0.513369 0.372985i
\(670\) 14.1590 0.547010
\(671\) 0 0
\(672\) −47.3043 −1.82480
\(673\) −14.3561 10.4303i −0.553387 0.402059i 0.275646 0.961259i \(-0.411108\pi\)
−0.829033 + 0.559200i \(0.811108\pi\)
\(674\) 15.4697 47.6109i 0.595872 1.83390i
\(675\) −1.38355 4.25813i −0.0532528 0.163895i
\(676\) 7.15227 5.19643i 0.275087 0.199863i
\(677\) 6.60332 4.79759i 0.253786 0.184387i −0.453617 0.891197i \(-0.649867\pi\)
0.707403 + 0.706810i \(0.249867\pi\)
\(678\) −3.76097 11.5751i −0.144439 0.444539i
\(679\) 14.5530 44.7897i 0.558494 1.71887i
\(680\) 0.306850 + 0.222940i 0.0117672 + 0.00854934i
\(681\) −11.8613 −0.454527
\(682\) 0 0
\(683\) −6.19100 −0.236892 −0.118446 0.992960i \(-0.537791\pi\)
−0.118446 + 0.992960i \(0.537791\pi\)
\(684\) −10.0703 7.31648i −0.385046 0.279753i
\(685\) −3.45586 + 10.6360i −0.132042 + 0.406382i
\(686\) −9.12020 28.0691i −0.348211 1.07168i
\(687\) −35.8526 + 26.0484i −1.36786 + 0.993810i
\(688\) 3.26250 2.37035i 0.124382 0.0903686i
\(689\) −3.94709 12.1479i −0.150372 0.462798i
\(690\) 1.72201 5.29981i 0.0655559 0.201760i
\(691\) −19.0969 13.8747i −0.726482 0.527820i 0.161967 0.986796i \(-0.448216\pi\)
−0.888448 + 0.458976i \(0.848216\pi\)
\(692\) −25.8892 −0.984158
\(693\) 0 0
\(694\) 0.695956 0.0264181
\(695\) 1.92138 + 1.39596i 0.0728820 + 0.0529519i
\(696\) −1.79897 + 5.53666i −0.0681898 + 0.209867i
\(697\) 0.631772 + 1.94439i 0.0239301 + 0.0736492i
\(698\) 2.07058 1.50436i 0.0783724 0.0569409i
\(699\) −43.1216 + 31.3297i −1.63101 + 1.18500i
\(700\) 2.26552 + 6.97254i 0.0856284 + 0.263537i
\(701\) −11.5042 + 35.4063i −0.434508 + 1.33728i 0.459082 + 0.888394i \(0.348178\pi\)
−0.893590 + 0.448884i \(0.851822\pi\)
\(702\) −23.1467 16.8170i −0.873614 0.634718i
\(703\) 14.5637 0.549282
\(704\) 0 0
\(705\) 5.70108 0.214715
\(706\) 43.5713 + 31.6564i 1.63983 + 1.19140i
\(707\) −11.1203 + 34.2247i −0.418222 + 1.28715i
\(708\) 3.97762 + 12.2419i 0.149488 + 0.460077i
\(709\) −14.7676 + 10.7293i −0.554609 + 0.402947i −0.829482 0.558534i \(-0.811364\pi\)
0.274873 + 0.961480i \(0.411364\pi\)
\(710\) −11.0555 + 8.03232i −0.414907 + 0.301448i
\(711\) 2.35566 + 7.24997i 0.0883441 + 0.271895i
\(712\) −1.71062 + 5.26473i −0.0641080 + 0.197304i
\(713\) −11.7833 8.56108i −0.441289 0.320615i
\(714\) 5.70259 0.213414
\(715\) 0 0
\(716\) 54.3388 2.03074
\(717\) −25.2053 18.3127i −0.941310 0.683902i
\(718\) 11.6103 35.7328i 0.433292 1.33354i
\(719\) 2.95849 + 9.10531i 0.110333 + 0.339571i 0.990945 0.134268i \(-0.0428682\pi\)
−0.880612 + 0.473838i \(0.842868\pi\)
\(720\) −1.63663 + 1.18908i −0.0609935 + 0.0443144i
\(721\) −34.4619 + 25.0380i −1.28343 + 0.932465i
\(722\) 28.0624 + 86.3673i 1.04438 + 3.21426i
\(723\) −2.59552 + 7.98818i −0.0965283 + 0.297084i
\(724\) −4.63776 3.36953i −0.172361 0.125228i
\(725\) −3.72162 −0.138217
\(726\) 0 0
\(727\) −14.0175 −0.519882 −0.259941 0.965625i \(-0.583703\pi\)
−0.259941 + 0.965625i \(0.583703\pi\)
\(728\) 6.18823 + 4.49601i 0.229351 + 0.166633i
\(729\) 5.79123 17.8236i 0.214490 0.660132i
\(730\) −6.39440 19.6799i −0.236667 0.728388i
\(731\) −0.493383 + 0.358463i −0.0182484 + 0.0132582i
\(732\) −7.46281 + 5.42205i −0.275833 + 0.200405i
\(733\) −2.87006 8.83314i −0.106008 0.326260i 0.883958 0.467567i \(-0.154869\pi\)
−0.989966 + 0.141307i \(0.954869\pi\)
\(734\) −5.49771 + 16.9202i −0.202924 + 0.624536i
\(735\) 3.72616 + 2.70721i 0.137441 + 0.0998571i
\(736\) 11.2083 0.413145
\(737\) 0 0
\(738\) 6.09119 0.224220
\(739\) −31.5182 22.8993i −1.15942 0.842365i −0.169712 0.985494i \(-0.554284\pi\)
−0.989704 + 0.143129i \(0.954284\pi\)
\(740\) −1.36243 + 4.19312i −0.0500838 + 0.154142i
\(741\) −14.2350 43.8107i −0.522935 1.60943i
\(742\) −21.7753 + 15.8207i −0.799396 + 0.580795i
\(743\) 37.1578 26.9968i 1.36319 0.990415i 0.364954 0.931025i \(-0.381085\pi\)
0.998235 0.0593894i \(-0.0189154\pi\)
\(744\) −5.06416 15.5859i −0.185661 0.571406i
\(745\) −2.69473 + 8.29354i −0.0987274 + 0.303852i
\(746\) 60.7618 + 44.1460i 2.22465 + 1.61630i
\(747\) −5.88233 −0.215223
\(748\) 0 0
\(749\) 22.4549 0.820483
\(750\) 3.24278 + 2.35601i 0.118409 + 0.0860295i
\(751\) 7.16698 22.0577i 0.261527 0.804896i −0.730947 0.682435i \(-0.760921\pi\)
0.992473 0.122462i \(-0.0390788\pi\)
\(752\) 2.82465 + 8.69339i 0.103005 + 0.317015i
\(753\) 4.12708 2.99850i 0.150399 0.109271i
\(754\) −19.2401 + 13.9788i −0.700684 + 0.509077i
\(755\) 3.68825 + 11.3513i 0.134229 + 0.413115i
\(756\) −10.1433 + 31.2179i −0.368908 + 1.13538i
\(757\) 5.27642 + 3.83355i 0.191775 + 0.139333i 0.679530 0.733648i \(-0.262184\pi\)
−0.487755 + 0.872981i \(0.662184\pi\)
\(758\) 36.7757 1.33575
\(759\) 0 0
\(760\) −6.45628 −0.234194
\(761\) −5.31267 3.85988i −0.192584 0.139921i 0.487315 0.873226i \(-0.337976\pi\)
−0.679899 + 0.733306i \(0.737976\pi\)
\(762\) 0.559362 1.72154i 0.0202635 0.0623648i
\(763\) 7.04515 + 21.6827i 0.255051 + 0.784968i
\(764\) −33.3501 + 24.2302i −1.20656 + 0.876620i
\(765\) 0.247504 0.179823i 0.00894854 0.00650150i
\(766\) −14.0018 43.0932i −0.505906 1.55702i
\(767\) −2.65300 + 8.16511i −0.0957944 + 0.294825i
\(768\) −12.4901 9.07456i −0.450696 0.327450i
\(769\) −12.5950 −0.454188 −0.227094 0.973873i \(-0.572922\pi\)
−0.227094 + 0.973873i \(0.572922\pi\)
\(770\) 0 0
\(771\) −41.3832 −1.49038
\(772\) −5.00019 3.63285i −0.179961 0.130749i
\(773\) 6.78131 20.8707i 0.243907 0.750668i −0.751907 0.659269i \(-0.770866\pi\)
0.995814 0.0913995i \(-0.0291340\pi\)
\(774\) 0.561478 + 1.72805i 0.0201819 + 0.0621136i
\(775\) 8.47564 6.15791i 0.304454 0.221199i
\(776\) −10.1574 + 7.37982i −0.364631 + 0.264920i
\(777\) 3.34444 + 10.2931i 0.119981 + 0.369264i
\(778\) 23.1420 71.2239i 0.829682 2.55350i