Properties

Label 600.2.d.g.349.7
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.214798336.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.7
Root \(-0.565036 + 1.29643i\) of \(x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16\)
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.g.349.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +3.93012i q^{11} +(0.731395 + 1.86147i) q^{12} +3.46733 q^{13} +(5.51937 + 3.76149i) q^{14} +(-2.93012 + 2.72294i) q^{16} +3.51575i q^{17} +(0.796431 - 1.16863i) q^{18} -5.44133i q^{19} -4.72294i q^{21} +(4.59286 + 3.13007i) q^{22} +7.11585i q^{23} +(2.75787 + 0.627801i) q^{24} +(2.76149 - 4.05203i) q^{26} -1.00000 q^{27} +(8.79159 - 3.45433i) q^{28} -3.66998i q^{29} +5.23414 q^{31} +(0.848464 + 5.59286i) q^{32} -3.93012i q^{33} +(4.10861 + 2.80005i) q^{34} +(-0.731395 - 1.86147i) q^{36} -0.414376 q^{37} +(-6.35890 - 4.33364i) q^{38} -3.46733 q^{39} +3.00454 q^{41} +(-5.51937 - 3.76149i) q^{42} -5.34450 q^{43} +(7.31580 - 2.87447i) q^{44} +(8.31580 + 5.66728i) q^{46} -0.925579i q^{47} +(2.93012 - 2.72294i) q^{48} -15.3061 q^{49} -3.51575i q^{51} +(-2.53599 - 6.45433i) q^{52} +0.233196 q^{53} +(-0.796431 + 1.16863i) q^{54} +(2.96506 - 13.0253i) q^{56} +5.44133i q^{57} +(-4.28885 - 2.92288i) q^{58} +14.3805i q^{59} +0.118290i q^{61} +(4.16863 - 6.11677i) q^{62} +4.72294i q^{63} +(7.21173 + 3.46279i) q^{64} +(-4.59286 - 3.13007i) q^{66} +13.4504 q^{67} +(6.54445 - 2.57140i) q^{68} -7.11585i q^{69} +2.19027 q^{71} +(-2.75787 - 0.627801i) q^{72} +0.563219i q^{73} +(-0.330022 + 0.484253i) q^{74} +(-10.1289 + 3.97976i) q^{76} -18.5617 q^{77} +(-2.76149 + 4.05203i) q^{78} +10.2746 q^{79} +1.00000 q^{81} +(2.39291 - 3.51120i) q^{82} -11.3490 q^{83} +(-8.79159 + 3.45433i) q^{84} +(-4.25653 + 6.24575i) q^{86} +3.66998i q^{87} +(2.46733 - 10.8388i) q^{88} -8.88265 q^{89} +16.3760i q^{91} +(13.2459 - 5.20449i) q^{92} -5.23414 q^{93} +(-1.08166 - 0.737160i) q^{94} +(-0.848464 - 5.59286i) q^{96} +7.27462i q^{97} +(-12.1903 + 17.8872i) q^{98} +3.93012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + 4q^{12} + 6q^{14} + 8q^{16} - 2q^{18} + 20q^{22} + 8q^{24} - 2q^{26} - 8q^{27} + 24q^{28} + 8q^{31} - 12q^{32} - 12q^{34} - 4q^{36} + 14q^{38} - 6q^{42} - 8q^{43} + 12q^{44} + 20q^{46} - 8q^{48} + 24q^{52} + 8q^{53} + 2q^{54} + 8q^{56} - 20q^{58} + 26q^{62} + 32q^{64} - 20q^{66} + 24q^{67} + 36q^{68} - 40q^{71} - 8q^{72} - 8q^{74} - 20q^{76} - 24q^{77} + 2q^{78} + 16q^{79} + 8q^{81} - 16q^{82} - 32q^{83} - 24q^{84} - 18q^{86} - 8q^{88} + 28q^{92} - 8q^{93} + 4q^{94} + 12q^{96} - 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.796431 1.16863i 0.563162 0.826347i
\(3\) −1.00000 −0.577350
\(4\) −0.731395 1.86147i −0.365697 0.930734i
\(5\) 0 0
\(6\) −0.796431 + 1.16863i −0.325142 + 0.477091i
\(7\) 4.72294i 1.78510i 0.450947 + 0.892551i \(0.351086\pi\)
−0.450947 + 0.892551i \(0.648914\pi\)
\(8\) −2.75787 0.627801i −0.975056 0.221961i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.93012i 1.18498i 0.805579 + 0.592488i \(0.201854\pi\)
−0.805579 + 0.592488i \(0.798146\pi\)
\(12\) 0.731395 + 1.86147i 0.211135 + 0.537359i
\(13\) 3.46733 0.961665 0.480833 0.876812i \(-0.340334\pi\)
0.480833 + 0.876812i \(0.340334\pi\)
\(14\) 5.51937 + 3.76149i 1.47511 + 1.00530i
\(15\) 0 0
\(16\) −2.93012 + 2.72294i −0.732531 + 0.680734i
\(17\) 3.51575i 0.852694i 0.904560 + 0.426347i \(0.140200\pi\)
−0.904560 + 0.426347i \(0.859800\pi\)
\(18\) 0.796431 1.16863i 0.187721 0.275449i
\(19\) 5.44133i 1.24833i −0.781294 0.624163i \(-0.785440\pi\)
0.781294 0.624163i \(-0.214560\pi\)
\(20\) 0 0
\(21\) 4.72294i 1.03063i
\(22\) 4.59286 + 3.13007i 0.979202 + 0.667334i
\(23\) 7.11585i 1.48376i 0.670534 + 0.741878i \(0.266065\pi\)
−0.670534 + 0.741878i \(0.733935\pi\)
\(24\) 2.75787 + 0.627801i 0.562949 + 0.128149i
\(25\) 0 0
\(26\) 2.76149 4.05203i 0.541573 0.794669i
\(27\) −1.00000 −0.192450
\(28\) 8.79159 3.45433i 1.66145 0.652807i
\(29\) 3.66998i 0.681498i −0.940154 0.340749i \(-0.889319\pi\)
0.940154 0.340749i \(-0.110681\pi\)
\(30\) 0 0
\(31\) 5.23414 0.940079 0.470039 0.882645i \(-0.344240\pi\)
0.470039 + 0.882645i \(0.344240\pi\)
\(32\) 0.848464 + 5.59286i 0.149989 + 0.988688i
\(33\) 3.93012i 0.684147i
\(34\) 4.10861 + 2.80005i 0.704621 + 0.480205i
\(35\) 0 0
\(36\) −0.731395 1.86147i −0.121899 0.310245i
\(37\) −0.414376 −0.0681231 −0.0340615 0.999420i \(-0.510844\pi\)
−0.0340615 + 0.999420i \(0.510844\pi\)
\(38\) −6.35890 4.33364i −1.03155 0.703010i
\(39\) −3.46733 −0.555218
\(40\) 0 0
\(41\) 3.00454 0.469231 0.234616 0.972088i \(-0.424617\pi\)
0.234616 + 0.972088i \(0.424617\pi\)
\(42\) −5.51937 3.76149i −0.851657 0.580411i
\(43\) −5.34450 −0.815029 −0.407514 0.913199i \(-0.633604\pi\)
−0.407514 + 0.913199i \(0.633604\pi\)
\(44\) 7.31580 2.87447i 1.10290 0.433343i
\(45\) 0 0
\(46\) 8.31580 + 5.66728i 1.22610 + 0.835595i
\(47\) 0.925579i 0.135010i −0.997719 0.0675048i \(-0.978496\pi\)
0.997719 0.0675048i \(-0.0215038\pi\)
\(48\) 2.93012 2.72294i 0.422927 0.393022i
\(49\) −15.3061 −2.18659
\(50\) 0 0
\(51\) 3.51575i 0.492303i
\(52\) −2.53599 6.45433i −0.351679 0.895055i
\(53\) 0.233196 0.0320320 0.0160160 0.999872i \(-0.494902\pi\)
0.0160160 + 0.999872i \(0.494902\pi\)
\(54\) −0.796431 + 1.16863i −0.108381 + 0.159030i
\(55\) 0 0
\(56\) 2.96506 13.0253i 0.396223 1.74057i
\(57\) 5.44133i 0.720721i
\(58\) −4.28885 2.92288i −0.563153 0.383794i
\(59\) 14.3805i 1.87219i 0.351752 + 0.936093i \(0.385586\pi\)
−0.351752 + 0.936093i \(0.614414\pi\)
\(60\) 0 0
\(61\) 0.118290i 0.0151454i 0.999971 + 0.00757271i \(0.00241049\pi\)
−0.999971 + 0.00757271i \(0.997590\pi\)
\(62\) 4.16863 6.11677i 0.529417 0.776831i
\(63\) 4.72294i 0.595034i
\(64\) 7.21173 + 3.46279i 0.901467 + 0.432849i
\(65\) 0 0
\(66\) −4.59286 3.13007i −0.565342 0.385285i
\(67\) 13.4504 1.64323 0.821615 0.570043i \(-0.193073\pi\)
0.821615 + 0.570043i \(0.193073\pi\)
\(68\) 6.54445 2.57140i 0.793631 0.311828i
\(69\) 7.11585i 0.856647i
\(70\) 0 0
\(71\) 2.19027 0.259937 0.129969 0.991518i \(-0.458512\pi\)
0.129969 + 0.991518i \(0.458512\pi\)
\(72\) −2.75787 0.627801i −0.325019 0.0739870i
\(73\) 0.563219i 0.0659197i 0.999457 + 0.0329599i \(0.0104934\pi\)
−0.999457 + 0.0329599i \(0.989507\pi\)
\(74\) −0.330022 + 0.484253i −0.0383643 + 0.0562933i
\(75\) 0 0
\(76\) −10.1289 + 3.97976i −1.16186 + 0.456509i
\(77\) −18.5617 −2.11530
\(78\) −2.76149 + 4.05203i −0.312678 + 0.458802i
\(79\) 10.2746 1.15599 0.577993 0.816042i \(-0.303836\pi\)
0.577993 + 0.816042i \(0.303836\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.39291 3.51120i 0.264253 0.387747i
\(83\) −11.3490 −1.24572 −0.622860 0.782334i \(-0.714029\pi\)
−0.622860 + 0.782334i \(0.714029\pi\)
\(84\) −8.79159 + 3.45433i −0.959241 + 0.376898i
\(85\) 0 0
\(86\) −4.25653 + 6.24575i −0.458993 + 0.673496i
\(87\) 3.66998i 0.393463i
\(88\) 2.46733 10.8388i 0.263019 1.15542i
\(89\) −8.88265 −0.941559 −0.470780 0.882251i \(-0.656027\pi\)
−0.470780 + 0.882251i \(0.656027\pi\)
\(90\) 0 0
\(91\) 16.3760i 1.71667i
\(92\) 13.2459 5.20449i 1.38098 0.542606i
\(93\) −5.23414 −0.542755
\(94\) −1.08166 0.737160i −0.111565 0.0760322i
\(95\) 0 0
\(96\) −0.848464 5.59286i −0.0865960 0.570819i
\(97\) 7.27462i 0.738626i 0.929305 + 0.369313i \(0.120407\pi\)
−0.929305 + 0.369313i \(0.879593\pi\)
\(98\) −12.1903 + 17.8872i −1.23140 + 1.80688i
\(99\) 3.93012i 0.394992i
\(100\) 0 0
\(101\) 4.23320i 0.421219i −0.977570 0.210609i \(-0.932455\pi\)
0.977570 0.210609i \(-0.0675448\pi\)
\(102\) −4.10861 2.80005i −0.406813 0.277246i
\(103\) 0.0429270i 0.00422972i −0.999998 0.00211486i \(-0.999327\pi\)
0.999998 0.00211486i \(-0.000673181\pi\)
\(104\) −9.56247 2.17679i −0.937677 0.213452i
\(105\) 0 0
\(106\) 0.185725 0.272520i 0.0180392 0.0264695i
\(107\) −15.4728 −1.49581 −0.747907 0.663804i \(-0.768941\pi\)
−0.747907 + 0.663804i \(0.768941\pi\)
\(108\) 0.731395 + 1.86147i 0.0703785 + 0.179120i
\(109\) 12.9561i 1.24097i −0.784217 0.620486i \(-0.786935\pi\)
0.784217 0.620486i \(-0.213065\pi\)
\(110\) 0 0
\(111\) 0.414376 0.0393309
\(112\) −12.8602 13.8388i −1.21518 1.30764i
\(113\) 3.86025i 0.363141i −0.983378 0.181571i \(-0.941882\pi\)
0.983378 0.181571i \(-0.0581181\pi\)
\(114\) 6.35890 + 4.33364i 0.595566 + 0.405883i
\(115\) 0 0
\(116\) −6.83154 + 2.68420i −0.634293 + 0.249222i
\(117\) 3.46733 0.320555
\(118\) 16.8055 + 11.4531i 1.54708 + 1.05434i
\(119\) −16.6046 −1.52215
\(120\) 0 0
\(121\) −4.44587 −0.404170
\(122\) 0.138237 + 0.0942095i 0.0125154 + 0.00852933i
\(123\) −3.00454 −0.270911
\(124\) −3.82822 9.74318i −0.343784 0.874963i
\(125\) 0 0
\(126\) 5.51937 + 3.76149i 0.491704 + 0.335100i
\(127\) 18.3805i 1.63101i −0.578751 0.815505i \(-0.696460\pi\)
0.578751 0.815505i \(-0.303540\pi\)
\(128\) 9.79037 5.66998i 0.865355 0.501160i
\(129\) 5.34450 0.470557
\(130\) 0 0
\(131\) 3.41892i 0.298713i 0.988783 + 0.149356i \(0.0477201\pi\)
−0.988783 + 0.149356i \(0.952280\pi\)
\(132\) −7.31580 + 2.87447i −0.636758 + 0.250191i
\(133\) 25.6990 2.22839
\(134\) 10.7123 15.7186i 0.925404 1.35788i
\(135\) 0 0
\(136\) 2.20719 9.69599i 0.189265 0.831424i
\(137\) 16.3714i 1.39871i −0.714776 0.699354i \(-0.753471\pi\)
0.714776 0.699354i \(-0.246529\pi\)
\(138\) −8.31580 5.66728i −0.707888 0.482431i
\(139\) 1.95707i 0.165997i −0.996550 0.0829984i \(-0.973550\pi\)
0.996550 0.0829984i \(-0.0264496\pi\)
\(140\) 0 0
\(141\) 0.925579i 0.0779478i
\(142\) 1.74440 2.55962i 0.146387 0.214798i
\(143\) 13.6271i 1.13955i
\(144\) −2.93012 + 2.72294i −0.244177 + 0.226911i
\(145\) 0 0
\(146\) 0.658194 + 0.448565i 0.0544726 + 0.0371235i
\(147\) 15.3061 1.26243
\(148\) 0.303073 + 0.771348i 0.0249124 + 0.0634044i
\(149\) 12.0968i 0.991011i 0.868605 + 0.495505i \(0.165017\pi\)
−0.868605 + 0.495505i \(0.834983\pi\)
\(150\) 0 0
\(151\) −4.87178 −0.396460 −0.198230 0.980156i \(-0.563519\pi\)
−0.198230 + 0.980156i \(0.563519\pi\)
\(152\) −3.41607 + 15.0065i −0.277080 + 1.21719i
\(153\) 3.51575i 0.284231i
\(154\) −14.7831 + 21.6918i −1.19126 + 1.74797i
\(155\) 0 0
\(156\) 2.53599 + 6.45433i 0.203042 + 0.516760i
\(157\) 21.6561 1.72835 0.864173 0.503195i \(-0.167842\pi\)
0.864173 + 0.503195i \(0.167842\pi\)
\(158\) 8.18303 12.0072i 0.651007 0.955245i
\(159\) −0.233196 −0.0184937
\(160\) 0 0
\(161\) −33.6077 −2.64866
\(162\) 0.796431 1.16863i 0.0625735 0.0918163i
\(163\) −16.2362 −1.27172 −0.635860 0.771804i \(-0.719355\pi\)
−0.635860 + 0.771804i \(0.719355\pi\)
\(164\) −2.19751 5.59286i −0.171597 0.436729i
\(165\) 0 0
\(166\) −9.03873 + 13.2628i −0.701542 + 1.02940i
\(167\) 6.69238i 0.517872i −0.965894 0.258936i \(-0.916628\pi\)
0.965894 0.258936i \(-0.0833719\pi\)
\(168\) −2.96506 + 13.0253i −0.228759 + 1.00492i
\(169\) −0.977595 −0.0751996
\(170\) 0 0
\(171\) 5.44133i 0.416109i
\(172\) 3.90894 + 9.94861i 0.298054 + 0.758575i
\(173\) 22.4220 1.70471 0.852355 0.522963i \(-0.175173\pi\)
0.852355 + 0.522963i \(0.175173\pi\)
\(174\) 4.28885 + 2.92288i 0.325137 + 0.221583i
\(175\) 0 0
\(176\) −10.7015 11.5157i −0.806654 0.868032i
\(177\) 14.3805i 1.08091i
\(178\) −7.07442 + 10.3805i −0.530250 + 0.778054i
\(179\) 0.148842i 0.0111250i −0.999985 0.00556249i \(-0.998229\pi\)
0.999985 0.00556249i \(-0.00177060\pi\)
\(180\) 0 0
\(181\) 10.3929i 0.772499i −0.922394 0.386250i \(-0.873770\pi\)
0.922394 0.386250i \(-0.126230\pi\)
\(182\) 19.1375 + 13.0424i 1.41856 + 0.966763i
\(183\) 0.118290i 0.00874422i
\(184\) 4.46733 19.6246i 0.329336 1.44675i
\(185\) 0 0
\(186\) −4.16863 + 6.11677i −0.305659 + 0.448504i
\(187\) −13.8173 −1.01042
\(188\) −1.72294 + 0.676964i −0.125658 + 0.0493726i
\(189\) 4.72294i 0.343543i
\(190\) 0 0
\(191\) 6.23320 0.451018 0.225509 0.974241i \(-0.427595\pi\)
0.225509 + 0.974241i \(0.427595\pi\)
\(192\) −7.21173 3.46279i −0.520462 0.249905i
\(193\) 0.391971i 0.0282147i 0.999900 + 0.0141074i \(0.00449066\pi\)
−0.999900 + 0.0141074i \(0.995509\pi\)
\(194\) 8.50135 + 5.79374i 0.610361 + 0.415966i
\(195\) 0 0
\(196\) 11.1948 + 28.4918i 0.799630 + 2.03513i
\(197\) −5.96616 −0.425071 −0.212536 0.977153i \(-0.568172\pi\)
−0.212536 + 0.977153i \(0.568172\pi\)
\(198\) 4.59286 + 3.13007i 0.326401 + 0.222445i
\(199\) 17.9322 1.27118 0.635591 0.772026i \(-0.280757\pi\)
0.635591 + 0.772026i \(0.280757\pi\)
\(200\) 0 0
\(201\) −13.4504 −0.948719
\(202\) −4.94704 3.37145i −0.348073 0.237214i
\(203\) 17.3331 1.21654
\(204\) −6.54445 + 2.57140i −0.458203 + 0.180034i
\(205\) 0 0
\(206\) −0.0501658 0.0341884i −0.00349521 0.00238202i
\(207\) 7.11585i 0.494586i
\(208\) −10.1597 + 9.44133i −0.704450 + 0.654638i
\(209\) 21.3851 1.47924
\(210\) 0 0
\(211\) 6.51575i 0.448563i −0.974524 0.224281i \(-0.927997\pi\)
0.974524 0.224281i \(-0.0720034\pi\)
\(212\) −0.170558 0.434087i −0.0117140 0.0298132i
\(213\) −2.19027 −0.150075
\(214\) −12.3230 + 18.0820i −0.842385 + 1.23606i
\(215\) 0 0
\(216\) 2.75787 + 0.627801i 0.187650 + 0.0427164i
\(217\) 24.7205i 1.67814i
\(218\) −15.1409 10.3187i −1.02547 0.698868i
\(219\) 0.563219i 0.0380588i
\(220\) 0 0
\(221\) 12.1903i 0.820006i
\(222\) 0.330022 0.484253i 0.0221496 0.0325009i
\(223\) 3.14640i 0.210699i −0.994435 0.105349i \(-0.966404\pi\)
0.994435 0.105349i \(-0.0335961\pi\)
\(224\) −26.4147 + 4.00724i −1.76491 + 0.267745i
\(225\) 0 0
\(226\) −4.51120 3.07442i −0.300081 0.204507i
\(227\) 3.92103 0.260248 0.130124 0.991498i \(-0.458462\pi\)
0.130124 + 0.991498i \(0.458462\pi\)
\(228\) 10.1289 3.97976i 0.670800 0.263566i
\(229\) 25.6899i 1.69764i 0.528683 + 0.848820i \(0.322686\pi\)
−0.528683 + 0.848820i \(0.677314\pi\)
\(230\) 0 0
\(231\) 18.5617 1.22127
\(232\) −2.30401 + 10.1213i −0.151266 + 0.664498i
\(233\) 25.7565i 1.68737i −0.536841 0.843683i \(-0.680383\pi\)
0.536841 0.843683i \(-0.319617\pi\)
\(234\) 2.76149 4.05203i 0.180524 0.264890i
\(235\) 0 0
\(236\) 26.7689 10.5179i 1.74251 0.684654i
\(237\) −10.2746 −0.667409
\(238\) −13.2245 + 19.4047i −0.857214 + 1.25782i
\(239\) 15.8727 1.02672 0.513360 0.858173i \(-0.328400\pi\)
0.513360 + 0.858173i \(0.328400\pi\)
\(240\) 0 0
\(241\) 28.1664 1.81436 0.907178 0.420748i \(-0.138232\pi\)
0.907178 + 0.420748i \(0.138232\pi\)
\(242\) −3.54083 + 5.19558i −0.227613 + 0.333985i
\(243\) −1.00000 −0.0641500
\(244\) 0.220192 0.0865164i 0.0140964 0.00553864i
\(245\) 0 0
\(246\) −2.39291 + 3.51120i −0.152567 + 0.223866i
\(247\) 18.8669i 1.20047i
\(248\) −14.4351 3.28600i −0.916629 0.208661i
\(249\) 11.3490 0.719216
\(250\) 0 0
\(251\) 4.66004i 0.294139i 0.989126 + 0.147070i \(0.0469842\pi\)
−0.989126 + 0.147070i \(0.953016\pi\)
\(252\) 8.79159 3.45433i 0.553818 0.217602i
\(253\) −27.9662 −1.75822
\(254\) −21.4801 14.6388i −1.34778 0.918522i
\(255\) 0 0
\(256\) 1.17125 15.9571i 0.0732029 0.997317i
\(257\) 3.33996i 0.208341i −0.994559 0.104170i \(-0.966781\pi\)
0.994559 0.104170i \(-0.0332187\pi\)
\(258\) 4.25653 6.24575i 0.265000 0.388843i
\(259\) 1.95707i 0.121607i
\(260\) 0 0
\(261\) 3.66998i 0.227166i
\(262\) 3.99546 + 2.72294i 0.246840 + 0.168224i
\(263\) 27.5932i 1.70147i −0.525595 0.850735i \(-0.676157\pi\)
0.525595 0.850735i \(-0.323843\pi\)
\(264\) −2.46733 + 10.8388i −0.151854 + 0.667081i
\(265\) 0 0
\(266\) 20.4675 30.0327i 1.25494 1.84142i
\(267\) 8.88265 0.543609
\(268\) −9.83756 25.0375i −0.600925 1.52941i
\(269\) 21.8727i 1.33360i −0.745235 0.666802i \(-0.767663\pi\)
0.745235 0.666802i \(-0.232337\pi\)
\(270\) 0 0
\(271\) −8.78583 −0.533701 −0.266850 0.963738i \(-0.585983\pi\)
−0.266850 + 0.963738i \(0.585983\pi\)
\(272\) −9.57315 10.3016i −0.580458 0.624625i
\(273\) 16.3760i 0.991120i
\(274\) −19.1322 13.0387i −1.15582 0.787699i
\(275\) 0 0
\(276\) −13.2459 + 5.20449i −0.797311 + 0.313274i
\(277\) 10.3838 0.623904 0.311952 0.950098i \(-0.399017\pi\)
0.311952 + 0.950098i \(0.399017\pi\)
\(278\) −2.28710 1.55867i −0.137171 0.0934831i
\(279\) 5.23414 0.313360
\(280\) 0 0
\(281\) 17.0584 1.01762 0.508811 0.860878i \(-0.330085\pi\)
0.508811 + 0.860878i \(0.330085\pi\)
\(282\) 1.08166 + 0.737160i 0.0644119 + 0.0438972i
\(283\) −3.54724 −0.210862 −0.105431 0.994427i \(-0.533622\pi\)
−0.105431 + 0.994427i \(0.533622\pi\)
\(284\) −1.60195 4.07712i −0.0950583 0.241932i
\(285\) 0 0
\(286\) 15.9250 + 10.8530i 0.941664 + 0.641752i
\(287\) 14.1903i 0.837625i
\(288\) 0.848464 + 5.59286i 0.0499962 + 0.329563i
\(289\) 4.63952 0.272913
\(290\) 0 0
\(291\) 7.27462i 0.426446i
\(292\) 1.04841 0.411935i 0.0613537 0.0241067i
\(293\) 5.72538 0.334480 0.167240 0.985916i \(-0.446515\pi\)
0.167240 + 0.985916i \(0.446515\pi\)
\(294\) 12.1903 17.8872i 0.710951 1.04320i
\(295\) 0 0
\(296\) 1.14280 + 0.260146i 0.0664238 + 0.0151207i
\(297\) 3.93012i 0.228049i
\(298\) 14.1367 + 9.63429i 0.818918 + 0.558099i
\(299\) 24.6730i 1.42688i
\(300\) 0 0
\(301\) 25.2417i 1.45491i
\(302\) −3.88004 + 5.69331i −0.223271 + 0.327613i
\(303\) 4.23320i 0.243191i
\(304\) 14.8164 + 15.9438i 0.849778 + 0.914437i
\(305\) 0 0
\(306\) 4.10861 + 2.80005i 0.234874 + 0.160068i
\(307\) −12.3760 −0.706335 −0.353168 0.935560i \(-0.614895\pi\)
−0.353168 + 0.935560i \(0.614895\pi\)
\(308\) 13.5759 + 34.5520i 0.773561 + 1.96879i
\(309\) 0.0429270i 0.00244203i
\(310\) 0 0
\(311\) −18.2746 −1.03626 −0.518129 0.855302i \(-0.673371\pi\)
−0.518129 + 0.855302i \(0.673371\pi\)
\(312\) 9.56247 + 2.17679i 0.541368 + 0.123237i
\(313\) 12.7114i 0.718491i 0.933243 + 0.359246i \(0.116966\pi\)
−0.933243 + 0.359246i \(0.883034\pi\)
\(314\) 17.2476 25.3080i 0.973338 1.42821i
\(315\) 0 0
\(316\) −7.51481 19.1259i −0.422741 1.07591i
\(317\) −15.8602 −0.890800 −0.445400 0.895332i \(-0.646939\pi\)
−0.445400 + 0.895332i \(0.646939\pi\)
\(318\) −0.185725 + 0.272520i −0.0104149 + 0.0152822i
\(319\) 14.4235 0.807559
\(320\) 0 0
\(321\) 15.4728 0.863609
\(322\) −26.7662 + 39.2750i −1.49162 + 2.18871i
\(323\) 19.1303 1.06444
\(324\) −0.731395 1.86147i −0.0406330 0.103415i
\(325\) 0 0
\(326\) −12.9310 + 18.9742i −0.716185 + 1.05088i
\(327\) 12.9561i 0.716476i
\(328\) −8.28615 1.88625i −0.457526 0.104151i
\(329\) 4.37145 0.241006
\(330\) 0 0
\(331\) 23.0315i 1.26593i −0.774182 0.632963i \(-0.781839\pi\)
0.774182 0.632963i \(-0.218161\pi\)
\(332\) 8.30063 + 21.1259i 0.455556 + 1.15943i
\(333\) −0.414376 −0.0227077
\(334\) −7.82092 5.33002i −0.427942 0.291646i
\(335\) 0 0
\(336\) 12.8602 + 13.8388i 0.701584 + 0.754968i
\(337\) 0.860247i 0.0468606i −0.999725 0.0234303i \(-0.992541\pi\)
0.999725 0.0234303i \(-0.00745878\pi\)
\(338\) −0.778587 + 1.14245i −0.0423496 + 0.0621409i
\(339\) 3.86025i 0.209660i
\(340\) 0 0
\(341\) 20.5708i 1.11397i
\(342\) −6.35890 4.33364i −0.343850 0.234337i
\(343\) 39.2293i 2.11818i
\(344\) 14.7395 + 3.35528i 0.794698 + 0.180905i
\(345\) 0 0
\(346\) 17.8576 26.2030i 0.960028 1.40868i
\(347\) 32.2856 1.73318 0.866591 0.499019i \(-0.166306\pi\)
0.866591 + 0.499019i \(0.166306\pi\)
\(348\) 6.83154 2.68420i 0.366209 0.143888i
\(349\) 0.742899i 0.0397665i 0.999802 + 0.0198832i \(0.00632945\pi\)
−0.999802 + 0.0198832i \(0.993671\pi\)
\(350\) 0 0
\(351\) −3.46733 −0.185073
\(352\) −21.9806 + 3.33457i −1.17157 + 0.177733i
\(353\) 32.6392i 1.73721i 0.495506 + 0.868604i \(0.334982\pi\)
−0.495506 + 0.868604i \(0.665018\pi\)
\(354\) −16.8055 11.4531i −0.893204 0.608726i
\(355\) 0 0
\(356\) 6.49672 + 16.5348i 0.344326 + 0.876341i
\(357\) 16.6046 0.878811
\(358\) −0.173941 0.118542i −0.00919309 0.00626517i
\(359\) 2.71056 0.143058 0.0715290 0.997439i \(-0.477212\pi\)
0.0715290 + 0.997439i \(0.477212\pi\)
\(360\) 0 0
\(361\) −10.6080 −0.558317
\(362\) −12.1455 8.27724i −0.638352 0.435042i
\(363\) 4.44587 0.233348
\(364\) 30.4834 11.9773i 1.59776 0.627782i
\(365\) 0 0
\(366\) −0.138237 0.0942095i −0.00722575 0.00492441i
\(367\) 0.680008i 0.0354961i 0.999842 + 0.0177481i \(0.00564968\pi\)
−0.999842 + 0.0177481i \(0.994350\pi\)
\(368\) −19.3760 20.8503i −1.01004 1.08690i
\(369\) 3.00454 0.156410
\(370\) 0 0
\(371\) 1.10137i 0.0571803i
\(372\) 3.82822 + 9.74318i 0.198484 + 0.505160i
\(373\) −3.47642 −0.180002 −0.0900012 0.995942i \(-0.528687\pi\)
−0.0900012 + 0.995942i \(0.528687\pi\)
\(374\) −11.0045 + 16.1473i −0.569031 + 0.834959i
\(375\) 0 0
\(376\) −0.581079 + 2.55263i −0.0299669 + 0.131642i
\(377\) 12.7250i 0.655373i
\(378\) −5.51937 3.76149i −0.283886 0.193470i
\(379\) 23.0650i 1.18477i −0.805655 0.592385i \(-0.798187\pi\)
0.805655 0.592385i \(-0.201813\pi\)
\(380\) 0 0
\(381\) 18.3805i 0.941664i
\(382\) 4.96431 7.28430i 0.253996 0.372697i
\(383\) 9.81544i 0.501545i 0.968046 + 0.250773i \(0.0806847\pi\)
−0.968046 + 0.250773i \(0.919315\pi\)
\(384\) −9.79037 + 5.66998i −0.499613 + 0.289345i
\(385\) 0 0
\(386\) 0.458070 + 0.312178i 0.0233151 + 0.0158895i
\(387\) −5.34450 −0.271676
\(388\) 13.5415 5.32062i 0.687464 0.270114i
\(389\) 9.86175i 0.500010i 0.968244 + 0.250005i \(0.0804323\pi\)
−0.968244 + 0.250005i \(0.919568\pi\)
\(390\) 0 0
\(391\) −25.0175 −1.26519
\(392\) 42.2123 + 9.60919i 2.13204 + 0.485337i
\(393\) 3.41892i 0.172462i
\(394\) −4.75164 + 6.97224i −0.239384 + 0.351256i
\(395\) 0 0
\(396\) 7.31580 2.87447i 0.367633 0.144448i
\(397\) −12.7783 −0.641326 −0.320663 0.947193i \(-0.603906\pi\)
−0.320663 + 0.947193i \(0.603906\pi\)
\(398\) 14.2818 20.9561i 0.715881 1.05044i
\(399\) −25.6990 −1.28656
\(400\) 0 0
\(401\) 3.17325 0.158465 0.0792323 0.996856i \(-0.474753\pi\)
0.0792323 + 0.996856i \(0.474753\pi\)
\(402\) −10.7123 + 15.7186i −0.534282 + 0.783971i
\(403\) 18.1485 0.904041
\(404\) −7.87996 + 3.09614i −0.392043 + 0.154039i
\(405\) 0 0
\(406\) 13.8046 20.2560i 0.685111 1.00529i
\(407\) 1.62855i 0.0807243i
\(408\) −2.20719 + 9.69599i −0.109272 + 0.480023i
\(409\) −12.1125 −0.598923 −0.299461 0.954108i \(-0.596807\pi\)
−0.299461 + 0.954108i \(0.596807\pi\)
\(410\) 0 0
\(411\) 16.3714i 0.807544i
\(412\) −0.0799071 + 0.0313965i −0.00393674 + 0.00154680i
\(413\) −67.9184 −3.34204
\(414\) 8.31580 + 5.66728i 0.408699 + 0.278532i
\(415\) 0 0
\(416\) 2.94191 + 19.3923i 0.144239 + 0.950787i
\(417\) 1.95707i 0.0958383i
\(418\) 17.0317 24.9913i 0.833050 1.22236i
\(419\) 4.24767i 0.207512i −0.994603 0.103756i \(-0.966914\pi\)
0.994603 0.103756i \(-0.0330862\pi\)
\(420\) 0 0
\(421\) 3.77928i 0.184191i −0.995750 0.0920953i \(-0.970644\pi\)
0.995750 0.0920953i \(-0.0293564\pi\)
\(422\) −7.61450 5.18934i −0.370668 0.252613i
\(423\) 0.925579i 0.0450032i
\(424\) −0.643126 0.146401i −0.0312329 0.00710985i
\(425\) 0 0
\(426\) −1.74440 + 2.55962i −0.0845164 + 0.124014i
\(427\) −0.558674 −0.0270361
\(428\) 11.3167 + 28.8022i 0.547015 + 1.39220i
\(429\) 13.6271i 0.657920i
\(430\) 0 0
\(431\) 25.6271 1.23441 0.617206 0.786802i \(-0.288265\pi\)
0.617206 + 0.786802i \(0.288265\pi\)
\(432\) 2.93012 2.72294i 0.140976 0.131007i
\(433\) 2.03149i 0.0976274i 0.998808 + 0.0488137i \(0.0155441\pi\)
−0.998808 + 0.0488137i \(0.984456\pi\)
\(434\) 28.8891 + 19.6882i 1.38672 + 0.945063i
\(435\) 0 0
\(436\) −24.1174 + 9.47605i −1.15501 + 0.453820i
\(437\) 38.7196 1.85221
\(438\) −0.658194 0.448565i −0.0314497 0.0214333i
\(439\) 22.4864 1.07322 0.536608 0.843832i \(-0.319706\pi\)
0.536608 + 0.843832i \(0.319706\pi\)
\(440\) 0 0
\(441\) −15.3061 −0.728863
\(442\) 14.2459 + 9.70871i 0.677609 + 0.461796i
\(443\) −3.39385 −0.161247 −0.0806234 0.996745i \(-0.525691\pi\)
−0.0806234 + 0.996745i \(0.525691\pi\)
\(444\) −0.303073 0.771348i −0.0143832 0.0366066i
\(445\) 0 0
\(446\) −3.67698 2.50589i −0.174110 0.118657i
\(447\) 12.0968i 0.572160i
\(448\) −16.3545 + 34.0605i −0.772679 + 1.60921i
\(449\) 2.17780 0.102777 0.0513883 0.998679i \(-0.483635\pi\)
0.0513883 + 0.998679i \(0.483635\pi\)
\(450\) 0 0
\(451\) 11.8082i 0.556028i
\(452\) −7.18572 + 2.82336i −0.337988 + 0.132800i
\(453\) 4.87178 0.228896
\(454\) 3.12283 4.58224i 0.146562 0.215055i
\(455\) 0 0
\(456\) 3.41607 15.0065i 0.159972 0.702743i
\(457\) 3.57653i 0.167303i −0.996495 0.0836516i \(-0.973342\pi\)
0.996495 0.0836516i \(-0.0266583\pi\)
\(458\) 30.0221 + 20.4603i 1.40284 + 0.956046i
\(459\) 3.51575i 0.164101i
\(460\) 0 0
\(461\) 13.1158i 0.610866i 0.952214 + 0.305433i \(0.0988012\pi\)
−0.952214 + 0.305433i \(0.901199\pi\)
\(462\) 14.7831 21.6918i 0.687774 1.00919i
\(463\) 3.21417i 0.149375i 0.997207 + 0.0746877i \(0.0237960\pi\)
−0.997207 + 0.0746877i \(0.976204\pi\)
\(464\) 9.99311 + 10.7535i 0.463919 + 0.499218i
\(465\) 0 0
\(466\) −30.0999 20.5133i −1.39435 0.950261i
\(467\) −30.3016 −1.40219 −0.701095 0.713068i \(-0.747305\pi\)
−0.701095 + 0.713068i \(0.747305\pi\)
\(468\) −2.53599 6.45433i −0.117226 0.298352i
\(469\) 63.5254i 2.93333i
\(470\) 0 0
\(471\) −21.6561 −0.997861
\(472\) 9.02811 39.6597i 0.415552 1.82549i
\(473\) 21.0045i 0.965790i
\(474\) −8.18303 + 12.0072i −0.375859 + 0.551511i
\(475\) 0 0
\(476\) 12.1446 + 30.9090i 0.556645 + 1.41671i
\(477\) 0.233196 0.0106773
\(478\) 12.6415 18.5493i 0.578210 0.848427i
\(479\) −35.0896 −1.60328 −0.801642 0.597804i \(-0.796040\pi\)
−0.801642 + 0.597804i \(0.796040\pi\)
\(480\) 0 0
\(481\) −1.43678 −0.0655116
\(482\) 22.4326 32.9161i 1.02178 1.49929i
\(483\) 33.6077 1.52920
\(484\) 3.25169 + 8.27584i 0.147804 + 0.376175i
\(485\) 0 0
\(486\) −0.796431 + 1.16863i −0.0361269 + 0.0530102i
\(487\) 36.9117i 1.67263i 0.548250 + 0.836315i \(0.315294\pi\)
−0.548250 + 0.836315i \(0.684706\pi\)
\(488\) 0.0742623 0.326228i 0.00336169 0.0147676i
\(489\) 16.2362 0.734228
\(490\) 0 0
\(491\) 20.9867i 0.947116i −0.880763 0.473558i \(-0.842969\pi\)
0.880763 0.473558i \(-0.157031\pi\)
\(492\) 2.19751 + 5.59286i 0.0990713 + 0.252146i
\(493\) 12.9027 0.581109
\(494\) −22.0484 15.0262i −0.992006 0.676060i
\(495\) 0 0
\(496\) −15.3367 + 14.2522i −0.688637 + 0.639943i
\(497\) 10.3445i 0.464014i
\(498\) 9.03873 13.2628i 0.405035 0.594322i
\(499\) 15.9906i 0.715836i −0.933753 0.357918i \(-0.883487\pi\)
0.933753 0.357918i \(-0.116513\pi\)
\(500\) 0 0
\(501\) 6.69238i 0.298994i
\(502\) 5.44587 + 3.71140i 0.243061 + 0.165648i
\(503\) 37.6023i 1.67660i 0.545206 + 0.838302i \(0.316451\pi\)
−0.545206 + 0.838302i \(0.683549\pi\)
\(504\) 2.96506 13.0253i 0.132074 0.580191i
\(505\) 0 0
\(506\) −22.2731 + 32.6821i −0.990161 + 1.45290i
\(507\) 0.977595 0.0434165
\(508\) −34.2148 + 13.4434i −1.51804 + 0.596456i
\(509\) 12.8579i 0.569917i 0.958540 + 0.284958i \(0.0919797\pi\)
−0.958540 + 0.284958i \(0.908020\pi\)
\(510\) 0 0
\(511\) −2.66004 −0.117673
\(512\) −17.7151 14.0775i −0.782904 0.622142i
\(513\) 5.44133i 0.240240i
\(514\) −3.90317 2.66004i −0.172162 0.117330i
\(515\) 0 0
\(516\) −3.90894 9.94861i −0.172081 0.437963i
\(517\) 3.63764 0.159983
\(518\) −2.28710 1.55867i −0.100489 0.0684842i
\(519\) −22.4220 −0.984215
\(520\) 0 0
\(521\) 37.0015 1.62107 0.810534 0.585692i \(-0.199177\pi\)
0.810534 + 0.585692i \(0.199177\pi\)
\(522\) −4.28885 2.92288i −0.187718 0.127931i
\(523\) −17.4952 −0.765013 −0.382506 0.923953i \(-0.624939\pi\)
−0.382506 + 0.923953i \(0.624939\pi\)
\(524\) 6.36421 2.50058i 0.278022 0.109238i
\(525\) 0 0
\(526\) −32.2463 21.9761i −1.40600 0.958203i
\(527\) 18.4019i 0.801600i
\(528\) 10.7015 + 11.5157i 0.465722 + 0.501159i
\(529\) −27.6353 −1.20153
\(530\) 0 0
\(531\) 14.3805i 0.624062i
\(532\) −18.7961 47.8379i −0.814916 2.07404i
\(533\) 10.4178 0.451243
\(534\) 7.07442 10.3805i 0.306140 0.449210i
\(535\) 0 0
\(536\) −37.0945 8.44418i −1.60224 0.364733i
\(537\) 0.148842i 0.00642301i
\(538\) −25.5611 17.4201i −1.10202 0.751035i
\(539\) 60.1549i 2.59106i
\(540\) 0 0
\(541\) 38.1225i 1.63901i 0.573069 + 0.819507i \(0.305753\pi\)
−0.573069 + 0.819507i \(0.694247\pi\)
\(542\) −6.99731 + 10.2674i −0.300560 + 0.441022i
\(543\) 10.3929i 0.446003i
\(544\) −19.6631 + 2.98298i −0.843048 + 0.127894i
\(545\) 0 0
\(546\) −19.1375 13.0424i −0.819009 0.558161i
\(547\) −35.7406 −1.52816 −0.764078 0.645124i \(-0.776806\pi\)
−0.764078 + 0.645124i \(0.776806\pi\)
\(548\) −30.4749 + 11.9740i −1.30182 + 0.511504i
\(549\) 0.118290i 0.00504848i
\(550\) 0 0
\(551\) −19.9695 −0.850731
\(552\) −4.46733 + 19.6246i −0.190142 + 0.835279i
\(553\) 48.5264i 2.06355i
\(554\) 8.27000 12.1349i 0.351359 0.515561i
\(555\) 0 0
\(556\) −3.64303 + 1.43139i −0.154499 + 0.0607046i
\(557\) 2.65516 0.112503 0.0562514 0.998417i \(-0.482085\pi\)
0.0562514 + 0.998417i \(0.482085\pi\)
\(558\) 4.16863 6.11677i 0.176472 0.258944i
\(559\) −18.5312 −0.783785
\(560\) 0 0
\(561\) 13.8173 0.583368
\(562\) 13.5859 19.9350i 0.573086 0.840908i
\(563\) 20.3107 0.855992 0.427996 0.903781i \(-0.359220\pi\)
0.427996 + 0.903781i \(0.359220\pi\)
\(564\) 1.72294 0.676964i 0.0725487 0.0285053i
\(565\) 0 0
\(566\) −2.82513 + 4.14541i −0.118749 + 0.174245i
\(567\) 4.72294i 0.198345i
\(568\) −6.04049 1.37505i −0.253453 0.0576959i
\(569\) 28.4274 1.19174 0.595868 0.803082i \(-0.296808\pi\)
0.595868 + 0.803082i \(0.296808\pi\)
\(570\) 0 0
\(571\) 16.1485i 0.675794i −0.941183 0.337897i \(-0.890284\pi\)
0.941183 0.337897i \(-0.109716\pi\)
\(572\) 25.3663 9.96675i 1.06062 0.416731i
\(573\) −6.23320 −0.260396
\(574\) 16.5832 + 11.3016i 0.692169 + 0.471719i
\(575\) 0 0
\(576\) 7.21173 + 3.46279i 0.300489 + 0.144283i
\(577\) 30.3600i 1.26390i −0.775008 0.631952i \(-0.782254\pi\)
0.775008 0.631952i \(-0.217746\pi\)
\(578\) 3.69506 5.42189i 0.153694 0.225521i
\(579\) 0.391971i 0.0162898i
\(580\) 0 0
\(581\) 53.6008i 2.22374i
\(582\) −8.50135 5.79374i −0.352392 0.240158i
\(583\) 0.916490i 0.0379571i
\(584\) 0.353589 1.55329i 0.0146316 0.0642754i
\(585\) 0 0
\(586\) 4.55987 6.69085i 0.188366 0.276396i
\(587\) −2.74070 −0.113121 −0.0565604 0.998399i \(-0.518013\pi\)
−0.0565604 + 0.998399i \(0.518013\pi\)
\(588\) −11.1948 28.4918i −0.461666 1.17498i
\(589\) 28.4807i 1.17352i
\(590\) 0 0
\(591\) 5.96616 0.245415
\(592\) 1.21417 1.12832i 0.0499022 0.0463737i
\(593\) 22.2586i 0.914053i 0.889453 + 0.457027i \(0.151086\pi\)
−0.889453 + 0.457027i \(0.848914\pi\)
\(594\) −4.59286 3.13007i −0.188447 0.128428i
\(595\) 0 0
\(596\) 22.5179 8.84755i 0.922367 0.362410i
\(597\) −17.9322 −0.733917
\(598\) 28.8336 + 19.6504i 1.17910 + 0.803563i
\(599\) −48.4526 −1.97972 −0.989860 0.142046i \(-0.954632\pi\)
−0.989860 + 0.142046i \(0.954632\pi\)
\(600\) 0 0
\(601\) 5.26553 0.214786 0.107393 0.994217i \(-0.465750\pi\)
0.107393 + 0.994217i \(0.465750\pi\)
\(602\) −29.4983 20.1033i −1.20226 0.819349i
\(603\) 13.4504 0.547743
\(604\) 3.56319 + 9.06866i 0.144984 + 0.368998i
\(605\) 0 0
\(606\) 4.94704 + 3.37145i 0.200960 + 0.136956i
\(607\) 7.38288i 0.299662i −0.988712 0.149831i \(-0.952127\pi\)
0.988712 0.149831i \(-0.0478730\pi\)
\(608\) 30.4326 4.61677i 1.23420 0.187235i
\(609\) −17.3331 −0.702371
\(610\) 0 0
\(611\) 3.20929i 0.129834i
\(612\) 6.54445 2.57140i 0.264544 0.103943i
\(613\) −2.64607 −0.106874 −0.0534369 0.998571i \(-0.517018\pi\)
−0.0534369 + 0.998571i \(0.517018\pi\)
\(614\) −9.85663 + 14.4630i −0.397781 + 0.583678i
\(615\) 0 0
\(616\) 51.1909 + 11.6531i 2.06254 + 0.469515i
\(617\) 21.0136i 0.845977i −0.906135 0.422989i \(-0.860981\pi\)
0.906135 0.422989i \(-0.139019\pi\)
\(618\) 0.0501658 + 0.0341884i 0.00201796 + 0.00137526i
\(619\) 24.0874i 0.968154i −0.875025 0.484077i \(-0.839155\pi\)
0.875025 0.484077i \(-0.160845\pi\)
\(620\) 0 0
\(621\) 7.11585i 0.285549i
\(622\) −14.5545 + 21.3563i −0.583581 + 0.856309i
\(623\) 41.9522i 1.68078i
\(624\) 10.1597 9.44133i 0.406714 0.377956i
\(625\) 0 0
\(626\) 14.8549 + 10.1238i 0.593723 + 0.404627i
\(627\) −21.3851 −0.854038
\(628\) −15.8392 40.3121i −0.632051 1.60863i
\(629\) 1.45684i 0.0580881i
\(630\) 0 0
\(631\) 25.2094 1.00357 0.501785 0.864992i \(-0.332677\pi\)
0.501785 + 0.864992i \(0.332677\pi\)
\(632\) −28.3361 6.45042i −1.12715 0.256584i
\(633\) 6.51575i 0.258978i
\(634\) −12.6316 + 18.5348i −0.501665 + 0.736110i
\(635\) 0 0
\(636\) 0.170558 + 0.434087i 0.00676308 + 0.0172127i
\(637\) −53.0714 −2.10277
\(638\) 11.4873 16.8557i 0.454786 0.667324i
\(639\) 2.19027 0.0866457
\(640\) 0 0
\(641\) −18.4755 −0.729738 −0.364869 0.931059i \(-0.618886\pi\)
−0.364869 + 0.931059i \(0.618886\pi\)
\(642\) 12.3230 18.0820i 0.486351 0.713640i
\(643\) −0.636984 −0.0251202 −0.0125601 0.999921i \(-0.503998\pi\)
−0.0125601 + 0.999921i \(0.503998\pi\)
\(644\) 24.5805 + 62.5596i 0.968607 + 2.46519i
\(645\) 0 0
\(646\) 15.2360 22.3563i 0.599452 0.879596i
\(647\) 32.0182i 1.25876i −0.777096 0.629382i \(-0.783308\pi\)
0.777096 0.629382i \(-0.216692\pi\)
\(648\) −2.75787 0.627801i −0.108340 0.0246623i
\(649\) −56.5173 −2.21850
\(650\) 0 0
\(651\) 24.7205i 0.968873i
\(652\) 11.8751 + 30.2232i 0.465065 + 1.18363i
\(653\) −25.9769 −1.01656 −0.508278 0.861193i \(-0.669718\pi\)
−0.508278 + 0.861193i \(0.669718\pi\)
\(654\) 15.1409 + 10.3187i 0.592057 + 0.403492i
\(655\) 0 0
\(656\) −8.80369 + 8.18118i −0.343726 + 0.319421i
\(657\) 0.563219i 0.0219732i
\(658\) 3.48156 5.10861i 0.135725 0.199154i
\(659\) 21.3422i 0.831372i 0.909508 + 0.415686i \(0.136459\pi\)
−0.909508 + 0.415686i \(0.863541\pi\)
\(660\) 0 0
\(661\) 14.8397i 0.577198i 0.957450 + 0.288599i \(0.0931895\pi\)
−0.957450 + 0.288599i \(0.906810\pi\)
\(662\) −26.9153 18.3430i −1.04609 0.712921i
\(663\) 12.1903i 0.473431i
\(664\) 31.2992 + 7.12494i 1.21465 + 0.276501i
\(665\) 0 0
\(666\) −0.330022 + 0.484253i −0.0127881 + 0.0187644i
\(667\) 26.1150 1.01118
\(668\) −12.4577 + 4.89477i −0.482001 + 0.189384i
\(669\) 3.14640i 0.121647i
\(670\) 0 0
\(671\) −0.464893 −0.0179470
\(672\) 26.4147 4.00724i 1.01897 0.154583i
\(673\) 18.1167i 0.698347i 0.937058 + 0.349174i \(0.113538\pi\)
−0.937058 + 0.349174i \(0.886462\pi\)
\(674\) −1.00531 0.685127i −0.0387231 0.0263901i
\(675\) 0 0
\(676\) 0.715008 + 1.81976i 0.0275003 + 0.0699908i
\(677\) 30.5617 1.17458 0.587291 0.809376i \(-0.300194\pi\)
0.587291 + 0.809376i \(0.300194\pi\)
\(678\) 4.51120 + 3.07442i 0.173252 + 0.118072i
\(679\) −34.3576 −1.31852
\(680\) 0 0
\(681\) −3.92103 −0.150254
\(682\) 24.0397 + 16.3832i 0.920527 + 0.627346i
\(683\) −22.2027 −0.849564 −0.424782 0.905296i \(-0.639649\pi\)
−0.424782 + 0.905296i \(0.639649\pi\)
\(684\) −10.1289 + 3.97976i −0.387286 + 0.152170i
\(685\) 0 0
\(686\) −45.8445 31.2434i −1.75035 1.19288i
\(687\) 25.6899i 0.980132i
\(688\) 15.6600 14.5527i 0.597034 0.554818i
\(689\) 0.808569 0.0308040
\(690\) 0 0
\(691\) 12.6890i 0.482712i −0.970437 0.241356i \(-0.922408\pi\)
0.970437 0.241356i \(-0.0775922\pi\)
\(692\) −16.3993 41.7378i −0.623408 1.58663i
\(693\) −18.5617 −0.705101
\(694\) 25.7133 37.7299i 0.976062 1.43221i
\(695\) 0 0
\(696\) 2.30401 10.1213i 0.0873334 0.383648i
\(697\) 10.5632i 0.400110i
\(698\) 0.868174 + 0.591668i 0.0328609 + 0.0223950i
\(699\) 25.7565i 0.974202i
\(700\) 0 0
\(701\) 34.9241i 1.31906i 0.751676 + 0.659532i \(0.229246\pi\)
−0.751676 + 0.659532i \(0.770754\pi\)
\(702\) −2.76149 + 4.05203i −0.104226 + 0.152934i
\(703\) 2.25476i 0.0850398i
\(704\) −13.6092 + 28.3430i −0.512916 + 1.06822i
\(705\) 0 0
\(706\) 38.1431 + 25.9949i 1.43554 + 0.978330i
\(707\) 19.9931 0.751918
\(708\) −26.7689 + 10.5179i −1.00604 + 0.395285i
\(709\) 5.65610i 0.212419i −0.994344 0.106210i \(-0.966129\pi\)
0.994344 0.106210i \(-0.0338715\pi\)
\(710\) 0 0
\(711\) 10.2746 0.385328
\(712\) 24.4972 + 5.57653i 0.918073 + 0.208989i
\(713\) 37.2453i 1.39485i
\(714\) 13.2245 19.4047i 0.494913 0.726203i
\(715\) 0 0
\(716\) −0.277065 + 0.108862i −0.0103544 + 0.00406838i
\(717\) −15.8727 −0.592778
\(718\) 2.15878 3.16764i 0.0805648 0.118215i
\(719\) 20.0844 0.749020 0.374510 0.927223i \(-0.377811\pi\)
0.374510 + 0.927223i \(0.377811\pi\)
\(720\) 0 0
\(721\) 0.202741 0.00755048
\(722\) −8.44856 + 12.3969i −0.314423 + 0.461364i
\(723\) −28.1664 −1.04752
\(724\) −19.3461 + 7.60132i −0.718991 + 0.282501i
\(725\) 0 0
\(726\) 3.54083 5.19558i 0.131413 0.192826i
\(727\) 13.0424i 0.483715i −0.970312 0.241857i \(-0.922243\pi\)
0.970312 0.241857i \(-0.0777566\pi\)
\(728\) 10.2809 45.1629i 0.381034 1.67385i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 18.7899i 0.694970i
\(732\) −0.220192 + 0.0865164i −0.00813854 + 0.00319774i
\(733\) −34.8917 −1.28876 −0.644378 0.764707i \(-0.722884\pi\)
−0.644378 + 0.764707i \(0.722884\pi\)
\(734\) 0.794678 + 0.541580i 0.0293321 + 0.0199901i
\(735\) 0 0
\(736\) −39.7980 + 6.03754i −1.46697 + 0.222547i
\(737\) 52.8618i 1.94719i
\(738\) 2.39291 3.51120i 0.0880843 0.129249i
\(739\) 41.5040i 1.52675i 0.645957 + 0.763374i \(0.276459\pi\)
−0.645957 + 0.763374i \(0.723541\pi\)
\(740\) 0 0
\(741\) 18.8669i 0.693093i
\(742\) 1.28710 + 0.877166i 0.0472508 + 0.0322018i
\(743\) 7.63764i 0.280198i 0.990138 + 0.140099i \(0.0447421\pi\)
−0.990138 + 0.140099i \(0.955258\pi\)
\(744\) 14.4351 + 3.28600i 0.529216 + 0.120470i
\(745\) 0 0
\(746\) −2.76873 + 4.06265i −0.101370 + 0.148744i
\(747\) −11.3490 −0.415240
\(748\) 10.1059 + 25.7205i 0.369509 + 0.940434i
\(749\) 73.0771i 2.67018i
\(750\) 0 0
\(751\) −19.4029 −0.708023 −0.354012 0.935241i \(-0.615183\pi\)
−0.354012 + 0.935241i \(0.615183\pi\)
\(752\) 2.52029 + 2.71206i 0.0919056 + 0.0988987i
\(753\) 4.66004i 0.169821i
\(754\) −14.8709 10.1346i −0.541565 0.369081i
\(755\) 0 0
\(756\) −8.79159 + 3.45433i −0.319747 + 0.125633i
\(757\) 43.7959 1.59179 0.795894 0.605436i \(-0.207001\pi\)
0.795894 + 0.605436i \(0.207001\pi\)
\(758\) −26.9545 18.3697i −0.979030 0.667217i
\(759\) 27.9662 1.01511
\(760\) 0 0
\(761\) 9.95519 0.360875 0.180438 0.983586i \(-0.442249\pi\)
0.180438 + 0.983586i \(0.442249\pi\)
\(762\) 21.4801 + 14.6388i 0.778140 + 0.530309i
\(763\) 61.1910 2.21526
\(764\) −4.55893 11.6029i −0.164936 0.419778i
\(765\) 0 0
\(766\) 11.4706 + 7.81732i 0.414450 + 0.282451i
\(767\) 49.8621i 1.80042i
\(768\) −1.17125 + 15.9571i −0.0422637 + 0.575801i
\(769\) 17.9008 0.645520 0.322760 0.946481i \(-0.395389\pi\)
0.322760 + 0.946481i \(0.395389\pi\)
\(770\) 0 0
\(771\) 3.33996i 0.120286i
\(772\) 0.729642 0.286686i 0.0262604 0.0103180i
\(773\) 20.8182 0.748777 0.374389 0.927272i \(-0.377853\pi\)
0.374389 + 0.927272i \(0.377853\pi\)
\(774\) −4.25653 + 6.24575i −0.152998 + 0.224499i
\(775\) 0 0
\(776\) 4.56701 20.0625i 0.163946 0.720201i
\(777\) 1.95707i 0.0702096i
\(778\) 11.5247 + 7.85420i 0.413182 + 0.281587i
\(779\) 16.3487i 0.585753i
\(780\) 0 0
\(781\) 8.60803i 0.308019i
\(782\) −19.9247 + 29.2362i −0.712507 + 1.04549i
\(783\) 3.66998i 0.131154i
\(784\) 44.8488 41.6776i 1.60174 1.48848i
\(785\) 0 0
\(786\) −3.99546 2.72294i −0.142513 0.0971239i
\(787\) −27.2047 −0.969744 −0.484872 0.874585i \(-0.661134\pi\)
−0.484872 + 0.874585i \(0.661134\pi\)