Properties

Label 570.2.m.a.37.4
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.4
Root \(2.19691 - 2.19691i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.a.493.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.25884 + 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.25884 + 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-2.19691 - 0.416642i) q^{10} -3.82217 q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.0891314 + 0.0891314i) q^{13} -4.39382 q^{14} +(0.416642 - 2.19691i) q^{15} -1.00000 q^{16} +(-1.83065 - 1.83065i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.70268 + 3.41987i) q^{19} +(1.84806 - 1.25884i) q^{20} -4.39382i q^{21} +(2.70268 - 2.70268i) q^{22} +(2.58922 - 2.58922i) q^{23} -1.00000i q^{24} +(-1.83065 + 4.65282i) q^{25} -0.126051 q^{26} +(0.707107 - 0.707107i) q^{27} +(3.10690 - 3.10690i) q^{28} -3.60048 q^{29} +(1.25884 + 1.84806i) q^{30} +3.60048i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.70268 + 2.70268i) q^{33} +2.58893 q^{34} +(-1.83065 + 9.65282i) q^{35} +1.00000 q^{36} +(-7.07188 + 7.07188i) q^{37} +(-4.32930 - 0.507128i) q^{38} -0.126051i q^{39} +(-0.416642 + 2.19691i) q^{40} +11.2134i q^{41} +(3.10690 + 3.10690i) q^{42} +(7.93755 - 7.93755i) q^{43} +3.82217i q^{44} +(-1.84806 + 1.25884i) q^{45} +3.66171i q^{46} +(-0.463170 - 0.463170i) q^{47} +(0.707107 + 0.707107i) q^{48} +12.3056i q^{49} +(-1.99558 - 4.58450i) q^{50} +2.58893i q^{51} +(0.0891314 - 0.0891314i) q^{52} +(3.21910 + 3.21910i) q^{53} +1.00000i q^{54} +(-4.81150 - 7.06360i) q^{55} +4.39382i q^{56} +(0.507128 - 4.32930i) q^{57} +(2.54592 - 2.54592i) q^{58} -9.40851 q^{59} +(-2.19691 - 0.416642i) q^{60} +8.21380 q^{61} +(-2.54592 - 2.54592i) q^{62} +(-3.10690 + 3.10690i) q^{63} +1.00000i q^{64} +(-0.0525181 + 0.276922i) q^{65} -3.82217 q^{66} +(8.78764 - 8.78764i) q^{67} +(-1.83065 + 1.83065i) q^{68} -3.66171 q^{69} +(-5.53111 - 8.12004i) q^{70} +1.66657i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-3.64373 + 3.64373i) q^{73} -10.0011i q^{74} +(4.58450 - 1.99558i) q^{75} +(3.41987 - 2.70268i) q^{76} +(-11.8751 - 11.8751i) q^{77} +(0.0891314 + 0.0891314i) q^{78} +8.82758 q^{79} +(-1.25884 - 1.84806i) q^{80} -1.00000 q^{81} +(-7.92907 - 7.92907i) q^{82} +(-0.347181 + 0.347181i) q^{83} -4.39382 q^{84} +(1.07866 - 5.68764i) q^{85} +11.2254i q^{86} +(2.54592 + 2.54592i) q^{87} +(-2.70268 - 2.70268i) q^{88} +9.79832 q^{89} +(0.416642 - 2.19691i) q^{90} +0.553844i q^{91} +(-2.58922 - 2.58922i) q^{92} +(2.54592 - 2.54592i) q^{93} +0.655021 q^{94} +(-2.91788 + 9.29978i) q^{95} -1.00000 q^{96} +(6.88409 - 6.88409i) q^{97} +(-8.70140 - 8.70140i) q^{98} -3.82217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.25884 + 1.84806i 0.562970 + 0.826477i
\(6\) 1.00000 0.408248
\(7\) 3.10690 + 3.10690i 1.17430 + 1.17430i 0.981175 + 0.193123i \(0.0618615\pi\)
0.193123 + 0.981175i \(0.438138\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −2.19691 0.416642i −0.694724 0.131754i
\(11\) −3.82217 −1.15243 −0.576214 0.817299i \(-0.695470\pi\)
−0.576214 + 0.817299i \(0.695470\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 0.0891314 + 0.0891314i 0.0247206 + 0.0247206i 0.719359 0.694638i \(-0.244436\pi\)
−0.694638 + 0.719359i \(0.744436\pi\)
\(14\) −4.39382 −1.17430
\(15\) 0.416642 2.19691i 0.107576 0.567239i
\(16\) −1.00000 −0.250000
\(17\) −1.83065 1.83065i −0.443998 0.443998i 0.449355 0.893353i \(-0.351654\pi\)
−0.893353 + 0.449355i \(0.851654\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 2.70268 + 3.41987i 0.620038 + 0.784572i
\(20\) 1.84806 1.25884i 0.413239 0.281485i
\(21\) 4.39382i 0.958810i
\(22\) 2.70268 2.70268i 0.576214 0.576214i
\(23\) 2.58922 2.58922i 0.539890 0.539890i −0.383607 0.923497i \(-0.625318\pi\)
0.923497 + 0.383607i \(0.125318\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.83065 + 4.65282i −0.366130 + 0.930564i
\(26\) −0.126051 −0.0247206
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 3.10690 3.10690i 0.587149 0.587149i
\(29\) −3.60048 −0.668591 −0.334296 0.942468i \(-0.608498\pi\)
−0.334296 + 0.942468i \(0.608498\pi\)
\(30\) 1.25884 + 1.84806i 0.229832 + 0.337408i
\(31\) 3.60048i 0.646664i 0.946286 + 0.323332i \(0.104803\pi\)
−0.946286 + 0.323332i \(0.895197\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 2.70268 + 2.70268i 0.470477 + 0.470477i
\(34\) 2.58893 0.443998
\(35\) −1.83065 + 9.65282i −0.309436 + 1.63162i
\(36\) 1.00000 0.166667
\(37\) −7.07188 + 7.07188i −1.16261 + 1.16261i −0.178707 + 0.983902i \(0.557192\pi\)
−0.983902 + 0.178707i \(0.942808\pi\)
\(38\) −4.32930 0.507128i −0.702305 0.0822670i
\(39\) 0.126051i 0.0201843i
\(40\) −0.416642 + 2.19691i −0.0658769 + 0.347362i
\(41\) 11.2134i 1.75124i 0.483002 + 0.875619i \(0.339546\pi\)
−0.483002 + 0.875619i \(0.660454\pi\)
\(42\) 3.10690 + 3.10690i 0.479405 + 0.479405i
\(43\) 7.93755 7.93755i 1.21046 1.21046i 0.239591 0.970874i \(-0.422987\pi\)
0.970874 0.239591i \(-0.0770132\pi\)
\(44\) 3.82217i 0.576214i
\(45\) −1.84806 + 1.25884i −0.275492 + 0.187657i
\(46\) 3.66171i 0.539890i
\(47\) −0.463170 0.463170i −0.0675603 0.0675603i 0.672519 0.740080i \(-0.265212\pi\)
−0.740080 + 0.672519i \(0.765212\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 12.3056i 1.75795i
\(50\) −1.99558 4.58450i −0.282217 0.648347i
\(51\) 2.58893i 0.362523i
\(52\) 0.0891314 0.0891314i 0.0123603 0.0123603i
\(53\) 3.21910 + 3.21910i 0.442178 + 0.442178i 0.892743 0.450566i \(-0.148778\pi\)
−0.450566 + 0.892743i \(0.648778\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −4.81150 7.06360i −0.648782 0.952455i
\(56\) 4.39382i 0.587149i
\(57\) 0.507128 4.32930i 0.0671707 0.573430i
\(58\) 2.54592 2.54592i 0.334296 0.334296i
\(59\) −9.40851 −1.22488 −0.612442 0.790516i \(-0.709813\pi\)
−0.612442 + 0.790516i \(0.709813\pi\)
\(60\) −2.19691 0.416642i −0.283620 0.0537882i
\(61\) 8.21380 1.05167 0.525834 0.850587i \(-0.323753\pi\)
0.525834 + 0.850587i \(0.323753\pi\)
\(62\) −2.54592 2.54592i −0.323332 0.323332i
\(63\) −3.10690 + 3.10690i −0.391432 + 0.391432i
\(64\) 1.00000i 0.125000i
\(65\) −0.0525181 + 0.276922i −0.00651406 + 0.0343480i
\(66\) −3.82217 −0.470477
\(67\) 8.78764 8.78764i 1.07358 1.07358i 0.0765120 0.997069i \(-0.475622\pi\)
0.997069 0.0765120i \(-0.0243783\pi\)
\(68\) −1.83065 + 1.83065i −0.221999 + 0.221999i
\(69\) −3.66171 −0.440818
\(70\) −5.53111 8.12004i −0.661094 0.970530i
\(71\) 1.66657i 0.197785i 0.995098 + 0.0988926i \(0.0315300\pi\)
−0.995098 + 0.0988926i \(0.968470\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −3.64373 + 3.64373i −0.426466 + 0.426466i −0.887423 0.460957i \(-0.847506\pi\)
0.460957 + 0.887423i \(0.347506\pi\)
\(74\) 10.0011i 1.16261i
\(75\) 4.58450 1.99558i 0.529373 0.230429i
\(76\) 3.41987 2.70268i 0.392286 0.310019i
\(77\) −11.8751 11.8751i −1.35329 1.35329i
\(78\) 0.0891314 + 0.0891314i 0.0100921 + 0.0100921i
\(79\) 8.82758 0.993180 0.496590 0.867985i \(-0.334585\pi\)
0.496590 + 0.867985i \(0.334585\pi\)
\(80\) −1.25884 1.84806i −0.140742 0.206619i
\(81\) −1.00000 −0.111111
\(82\) −7.92907 7.92907i −0.875619 0.875619i
\(83\) −0.347181 + 0.347181i −0.0381081 + 0.0381081i −0.725904 0.687796i \(-0.758578\pi\)
0.687796 + 0.725904i \(0.258578\pi\)
\(84\) −4.39382 −0.479405
\(85\) 1.07866 5.68764i 0.116997 0.616911i
\(86\) 11.2254i 1.21046i
\(87\) 2.54592 + 2.54592i 0.272951 + 0.272951i
\(88\) −2.70268 2.70268i −0.288107 0.288107i
\(89\) 9.79832 1.03862 0.519310 0.854586i \(-0.326189\pi\)
0.519310 + 0.854586i \(0.326189\pi\)
\(90\) 0.416642 2.19691i 0.0439179 0.231575i
\(91\) 0.553844i 0.0580587i
\(92\) −2.58922 2.58922i −0.269945 0.269945i
\(93\) 2.54592 2.54592i 0.264000 0.264000i
\(94\) 0.655021 0.0675603
\(95\) −2.91788 + 9.29978i −0.299368 + 0.954138i
\(96\) −1.00000 −0.102062
\(97\) 6.88409 6.88409i 0.698973 0.698973i −0.265216 0.964189i \(-0.585443\pi\)
0.964189 + 0.265216i \(0.0854432\pi\)
\(98\) −8.70140 8.70140i −0.878974 0.878974i
\(99\) 3.82217i 0.384143i
\(100\) 4.65282 + 1.83065i 0.465282 + 0.183065i
\(101\) −3.89174 −0.387242 −0.193621 0.981076i \(-0.562023\pi\)
−0.193621 + 0.981076i \(0.562023\pi\)
\(102\) −1.83065 1.83065i −0.181261 0.181261i
\(103\) −9.40518 9.40518i −0.926720 0.926720i 0.0707726 0.997492i \(-0.477454\pi\)
−0.997492 + 0.0707726i \(0.977454\pi\)
\(104\) 0.126051i 0.0123603i
\(105\) 8.12004 5.53111i 0.792435 0.539781i
\(106\) −4.55250 −0.442178
\(107\) 7.00983 7.00983i 0.677666 0.677666i −0.281806 0.959472i \(-0.590933\pi\)
0.959472 + 0.281806i \(0.0909333\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −17.7935 −1.70431 −0.852153 0.523293i \(-0.824703\pi\)
−0.852153 + 0.523293i \(0.824703\pi\)
\(110\) 8.39696 + 1.59248i 0.800619 + 0.151837i
\(111\) 10.0011 0.949267
\(112\) −3.10690 3.10690i −0.293574 0.293574i
\(113\) 12.4493 + 12.4493i 1.17114 + 1.17114i 0.981939 + 0.189197i \(0.0605884\pi\)
0.189197 + 0.981939i \(0.439412\pi\)
\(114\) 2.70268 + 3.41987i 0.253129 + 0.320300i
\(115\) 8.04445 + 1.52562i 0.750148 + 0.142265i
\(116\) 3.60048i 0.334296i
\(117\) −0.0891314 + 0.0891314i −0.00824020 + 0.00824020i
\(118\) 6.65282 6.65282i 0.612442 0.612442i
\(119\) 11.3753i 1.04277i
\(120\) 1.84806 1.25884i 0.168704 0.114916i
\(121\) 3.60898 0.328089
\(122\) −5.80803 + 5.80803i −0.525834 + 0.525834i
\(123\) 7.92907 7.92907i 0.714940 0.714940i
\(124\) 3.60048 0.323332
\(125\) −10.9032 + 2.47400i −0.975210 + 0.221281i
\(126\) 4.39382i 0.391432i
\(127\) −0.0636986 + 0.0636986i −0.00565234 + 0.00565234i −0.709927 0.704275i \(-0.751272\pi\)
0.704275 + 0.709927i \(0.251272\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −11.2254 −0.988340
\(130\) −0.158678 0.232949i −0.0139170 0.0204310i
\(131\) 2.44811 0.213893 0.106946 0.994265i \(-0.465893\pi\)
0.106946 + 0.994265i \(0.465893\pi\)
\(132\) 2.70268 2.70268i 0.235238 0.235238i
\(133\) −2.22823 + 19.0221i −0.193212 + 1.64943i
\(134\) 12.4276i 1.07358i
\(135\) 2.19691 + 0.416642i 0.189080 + 0.0358588i
\(136\) 2.58893i 0.221999i
\(137\) 3.02688 + 3.02688i 0.258604 + 0.258604i 0.824486 0.565882i \(-0.191464\pi\)
−0.565882 + 0.824486i \(0.691464\pi\)
\(138\) 2.58922 2.58922i 0.220409 0.220409i
\(139\) 3.96170i 0.336027i 0.985785 + 0.168013i \(0.0537352\pi\)
−0.985785 + 0.168013i \(0.946265\pi\)
\(140\) 9.65282 + 1.83065i 0.815812 + 0.154718i
\(141\) 0.655021i 0.0551627i
\(142\) −1.17844 1.17844i −0.0988926 0.0988926i
\(143\) −0.340675 0.340675i −0.0284887 0.0284887i
\(144\) 1.00000i 0.0833333i
\(145\) −4.53242 6.65389i −0.376397 0.552576i
\(146\) 5.15301i 0.426466i
\(147\) 8.70140 8.70140i 0.717679 0.717679i
\(148\) 7.07188 + 7.07188i 0.581305 + 0.581305i
\(149\) 22.3940i 1.83459i −0.398211 0.917294i \(-0.630369\pi\)
0.398211 0.917294i \(-0.369631\pi\)
\(150\) −1.83065 + 4.65282i −0.149472 + 0.379901i
\(151\) 11.2995i 0.919539i −0.888038 0.459769i \(-0.847932\pi\)
0.888038 0.459769i \(-0.152068\pi\)
\(152\) −0.507128 + 4.32930i −0.0411335 + 0.351152i
\(153\) 1.83065 1.83065i 0.147999 0.147999i
\(154\) 16.7939 1.35329
\(155\) −6.65389 + 4.53242i −0.534454 + 0.364053i
\(156\) −0.126051 −0.0100921
\(157\) −4.57916 4.57916i −0.365457 0.365457i 0.500361 0.865817i \(-0.333201\pi\)
−0.865817 + 0.500361i \(0.833201\pi\)
\(158\) −6.24204 + 6.24204i −0.496590 + 0.496590i
\(159\) 4.55250i 0.361037i
\(160\) 2.19691 + 0.416642i 0.173681 + 0.0329384i
\(161\) 16.0889 1.26798
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 7.54592 7.54592i 0.591042 0.591042i −0.346871 0.937913i \(-0.612756\pi\)
0.937913 + 0.346871i \(0.112756\pi\)
\(164\) 11.2134 0.875619
\(165\) −1.59248 + 8.39696i −0.123974 + 0.653702i
\(166\) 0.490988i 0.0381081i
\(167\) 15.1275 15.1275i 1.17060 1.17060i 0.188531 0.982067i \(-0.439627\pi\)
0.982067 0.188531i \(-0.0603726\pi\)
\(168\) 3.10690 3.10690i 0.239702 0.239702i
\(169\) 12.9841i 0.998778i
\(170\) 3.25904 + 4.78449i 0.249957 + 0.366954i
\(171\) −3.41987 + 2.70268i −0.261524 + 0.206679i
\(172\) −7.93755 7.93755i −0.605232 0.605232i
\(173\) −2.32458 2.32458i −0.176735 0.176735i 0.613196 0.789931i \(-0.289884\pi\)
−0.789931 + 0.613196i \(0.789884\pi\)
\(174\) −3.60048 −0.272951
\(175\) −20.1435 + 8.76820i −1.52270 + 0.662813i
\(176\) 3.82217 0.288107
\(177\) 6.65282 + 6.65282i 0.500056 + 0.500056i
\(178\) −6.92846 + 6.92846i −0.519310 + 0.519310i
\(179\) −0.515834 −0.0385553 −0.0192776 0.999814i \(-0.506137\pi\)
−0.0192776 + 0.999814i \(0.506137\pi\)
\(180\) 1.25884 + 1.84806i 0.0938283 + 0.137746i
\(181\) 4.86127i 0.361336i −0.983544 0.180668i \(-0.942174\pi\)
0.983544 0.180668i \(-0.0578259\pi\)
\(182\) −0.391627 0.391627i −0.0290293 0.0290293i
\(183\) −5.80803 5.80803i −0.429342 0.429342i
\(184\) 3.66171 0.269945
\(185\) −21.9716 4.16690i −1.61538 0.306356i
\(186\) 3.60048i 0.264000i
\(187\) 6.99705 + 6.99705i 0.511675 + 0.511675i
\(188\) −0.463170 + 0.463170i −0.0337801 + 0.0337801i
\(189\) 4.39382 0.319603
\(190\) −4.51269 8.63919i −0.327385 0.626753i
\(191\) −15.3369 −1.10974 −0.554870 0.831937i \(-0.687232\pi\)
−0.554870 + 0.831937i \(0.687232\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 17.1600 + 17.1600i 1.23521 + 1.23521i 0.961938 + 0.273268i \(0.0881046\pi\)
0.273268 + 0.961938i \(0.411895\pi\)
\(194\) 9.73557i 0.698973i
\(195\) 0.232949 0.158678i 0.0166819 0.0113631i
\(196\) 12.3056 0.878974
\(197\) −6.25052 6.25052i −0.445331 0.445331i 0.448468 0.893799i \(-0.351970\pi\)
−0.893799 + 0.448468i \(0.851970\pi\)
\(198\) 2.70268 + 2.70268i 0.192071 + 0.192071i
\(199\) 10.4094i 0.737904i 0.929448 + 0.368952i \(0.120283\pi\)
−0.929448 + 0.368952i \(0.879717\pi\)
\(200\) −4.58450 + 1.99558i −0.324173 + 0.141109i
\(201\) −12.4276 −0.876575
\(202\) 2.75187 2.75187i 0.193621 0.193621i
\(203\) −11.1863 11.1863i −0.785125 0.785125i
\(204\) 2.58893 0.181261
\(205\) −20.7230 + 14.1159i −1.44736 + 0.985894i
\(206\) 13.3009 0.926720
\(207\) 2.58922 + 2.58922i 0.179963 + 0.179963i
\(208\) −0.0891314 0.0891314i −0.00618015 0.00618015i
\(209\) −10.3301 13.0713i −0.714549 0.904162i
\(210\) −1.83065 + 9.65282i −0.126327 + 0.666108i
\(211\) 13.0551i 0.898752i −0.893343 0.449376i \(-0.851646\pi\)
0.893343 0.449376i \(-0.148354\pi\)
\(212\) 3.21910 3.21910i 0.221089 0.221089i
\(213\) 1.17844 1.17844i 0.0807455 0.0807455i
\(214\) 9.91340i 0.677666i
\(215\) 24.6612 + 4.67697i 1.68188 + 0.318967i
\(216\) 1.00000 0.0680414
\(217\) −11.1863 + 11.1863i −0.759376 + 0.759376i
\(218\) 12.5819 12.5819i 0.852153 0.852153i
\(219\) 5.15301 0.348208
\(220\) −7.06360 + 4.81150i −0.476228 + 0.324391i
\(221\) 0.326337i 0.0219518i
\(222\) −7.07188 + 7.07188i −0.474633 + 0.474633i
\(223\) 11.5414 + 11.5414i 0.772872 + 0.772872i 0.978608 0.205736i \(-0.0659587\pi\)
−0.205736 + 0.978608i \(0.565959\pi\)
\(224\) 4.39382 0.293574
\(225\) −4.65282 1.83065i −0.310188 0.122043i
\(226\) −17.6060 −1.17114
\(227\) 16.4312 16.4312i 1.09058 1.09058i 0.0951099 0.995467i \(-0.469680\pi\)
0.995467 0.0951099i \(-0.0303202\pi\)
\(228\) −4.32930 0.507128i −0.286715 0.0335854i
\(229\) 15.5194i 1.02555i 0.858522 + 0.512777i \(0.171383\pi\)
−0.858522 + 0.512777i \(0.828617\pi\)
\(230\) −6.76706 + 4.60950i −0.446207 + 0.303942i
\(231\) 16.7939i 1.10496i
\(232\) −2.54592 2.54592i −0.167148 0.167148i
\(233\) −1.69112 + 1.69112i −0.110789 + 0.110789i −0.760328 0.649539i \(-0.774962\pi\)
0.649539 + 0.760328i \(0.274962\pi\)
\(234\) 0.126051i 0.00824020i
\(235\) 0.272909 1.43902i 0.0178026 0.0938714i
\(236\) 9.40851i 0.612442i
\(237\) −6.24204 6.24204i −0.405464 0.405464i
\(238\) 8.04354 + 8.04354i 0.521385 + 0.521385i
\(239\) 12.9971i 0.840714i 0.907359 + 0.420357i \(0.138095\pi\)
−0.907359 + 0.420357i \(0.861905\pi\)
\(240\) −0.416642 + 2.19691i −0.0268941 + 0.141810i
\(241\) 8.64001i 0.556552i −0.960501 0.278276i \(-0.910237\pi\)
0.960501 0.278276i \(-0.0897630\pi\)
\(242\) −2.55194 + 2.55194i −0.164045 + 0.164045i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 8.21380i 0.525834i
\(245\) −22.7416 + 15.4908i −1.45290 + 0.989672i
\(246\) 11.2134i 0.714940i
\(247\) −0.0639239 + 0.545712i −0.00406738 + 0.0347228i
\(248\) −2.54592 + 2.54592i −0.161666 + 0.161666i
\(249\) 0.490988 0.0311151
\(250\) 5.96033 9.45910i 0.376964 0.598246i
\(251\) 23.6590 1.49334 0.746670 0.665194i \(-0.231651\pi\)
0.746670 + 0.665194i \(0.231651\pi\)
\(252\) 3.10690 + 3.10690i 0.195716 + 0.195716i
\(253\) −9.89644 + 9.89644i −0.622184 + 0.622184i
\(254\) 0.0900835i 0.00565234i
\(255\) −4.78449 + 3.25904i −0.299617 + 0.204089i
\(256\) 1.00000 0.0625000
\(257\) 8.63732 8.63732i 0.538781 0.538781i −0.384390 0.923171i \(-0.625588\pi\)
0.923171 + 0.384390i \(0.125588\pi\)
\(258\) 7.93755 7.93755i 0.494170 0.494170i
\(259\) −43.9432 −2.73050
\(260\) 0.276922 + 0.0525181i 0.0171740 + 0.00325703i
\(261\) 3.60048i 0.222864i
\(262\) −1.73108 + 1.73108i −0.106946 + 0.106946i
\(263\) 10.9291 10.9291i 0.673915 0.673915i −0.284701 0.958616i \(-0.591894\pi\)
0.958616 + 0.284701i \(0.0918943\pi\)
\(264\) 3.82217i 0.235238i
\(265\) −1.89676 + 10.0014i −0.116517 + 0.614383i
\(266\) −11.8751 15.0263i −0.728109 0.921321i
\(267\) −6.92846 6.92846i −0.424015 0.424015i
\(268\) −8.78764 8.78764i −0.536790 0.536790i
\(269\) −13.8523 −0.844591 −0.422296 0.906458i \(-0.638776\pi\)
−0.422296 + 0.906458i \(0.638776\pi\)
\(270\) −1.84806 + 1.25884i −0.112469 + 0.0766105i
\(271\) 14.8370 0.901284 0.450642 0.892705i \(-0.351195\pi\)
0.450642 + 0.892705i \(0.351195\pi\)
\(272\) 1.83065 + 1.83065i 0.110999 + 0.110999i
\(273\) 0.391627 0.391627i 0.0237024 0.0237024i
\(274\) −4.28065 −0.258604
\(275\) 6.99705 17.7839i 0.421938 1.07241i
\(276\) 3.66171i 0.220409i
\(277\) −8.95723 8.95723i −0.538188 0.538188i 0.384808 0.922996i \(-0.374268\pi\)
−0.922996 + 0.384808i \(0.874268\pi\)
\(278\) −2.80134 2.80134i −0.168013 0.168013i
\(279\) −3.60048 −0.215555
\(280\) −8.12004 + 5.53111i −0.485265 + 0.330547i
\(281\) 6.13940i 0.366246i −0.983090 0.183123i \(-0.941379\pi\)
0.983090 0.183123i \(-0.0586207\pi\)
\(282\) −0.463170 0.463170i −0.0275814 0.0275814i
\(283\) −22.7963 + 22.7963i −1.35510 + 1.35510i −0.475246 + 0.879853i \(0.657641\pi\)
−0.879853 + 0.475246i \(0.842359\pi\)
\(284\) 1.66657 0.0988926
\(285\) 8.63919 4.51269i 0.511742 0.267308i
\(286\) 0.481788 0.0284887
\(287\) −34.8389 + 34.8389i −2.05647 + 2.05647i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 10.2974i 0.605732i
\(290\) 7.90992 + 1.50011i 0.464486 + 0.0880894i
\(291\) −9.73557 −0.570709
\(292\) 3.64373 + 3.64373i 0.213233 + 0.213233i
\(293\) 0.341431 + 0.341431i 0.0199466 + 0.0199466i 0.717010 0.697063i \(-0.245510\pi\)
−0.697063 + 0.717010i \(0.745510\pi\)
\(294\) 12.3056i 0.717679i
\(295\) −11.8438 17.3875i −0.689572 1.01234i
\(296\) −10.0011 −0.581305
\(297\) −2.70268 + 2.70268i −0.156826 + 0.156826i
\(298\) 15.8349 + 15.8349i 0.917294 + 0.917294i
\(299\) 0.461562 0.0266928
\(300\) −1.99558 4.58450i −0.115215 0.264686i
\(301\) 49.3223 2.84289
\(302\) 7.98994 + 7.98994i 0.459769 + 0.459769i
\(303\) 2.75187 + 2.75187i 0.158091 + 0.158091i
\(304\) −2.70268 3.41987i −0.155009 0.196143i
\(305\) 10.3398 + 15.1796i 0.592058 + 0.869181i
\(306\) 2.58893i 0.147999i
\(307\) −18.0543 + 18.0543i −1.03041 + 1.03041i −0.0308888 + 0.999523i \(0.509834\pi\)
−0.999523 + 0.0308888i \(0.990166\pi\)
\(308\) −11.8751 + 11.8751i −0.676646 + 0.676646i
\(309\) 13.3009i 0.756664i
\(310\) 1.50011 7.90992i 0.0852005 0.449253i
\(311\) 5.73086 0.324967 0.162484 0.986711i \(-0.448049\pi\)
0.162484 + 0.986711i \(0.448049\pi\)
\(312\) 0.0891314 0.0891314i 0.00504607 0.00504607i
\(313\) 22.1761 22.1761i 1.25347 1.25347i 0.299312 0.954155i \(-0.403243\pi\)
0.954155 0.299312i \(-0.0967572\pi\)
\(314\) 6.47591 0.365457
\(315\) −9.65282 1.83065i −0.543875 0.103145i
\(316\) 8.82758i 0.496590i
\(317\) 11.0630 11.0630i 0.621359 0.621359i −0.324520 0.945879i \(-0.605203\pi\)
0.945879 + 0.324520i \(0.105203\pi\)
\(318\) 3.21910 + 3.21910i 0.180518 + 0.180518i
\(319\) 13.7616 0.770503
\(320\) −1.84806 + 1.25884i −0.103310 + 0.0703712i
\(321\) −9.91340 −0.553312
\(322\) −11.3766 + 11.3766i −0.633991 + 0.633991i
\(323\) 1.31292 11.2082i 0.0730527 0.623643i
\(324\) 1.00000i 0.0555556i
\(325\) −0.577881 + 0.251544i −0.0320550 + 0.0139531i
\(326\) 10.6715i 0.591042i
\(327\) 12.5819 + 12.5819i 0.695780 + 0.695780i
\(328\) −7.92907 + 7.92907i −0.437810 + 0.437810i
\(329\) 2.87804i 0.158672i
\(330\) −4.81150 7.06360i −0.264864 0.388838i
\(331\) 11.7959i 0.648364i −0.945995 0.324182i \(-0.894911\pi\)
0.945995 0.324182i \(-0.105089\pi\)
\(332\) 0.347181 + 0.347181i 0.0190540 + 0.0190540i
\(333\) −7.07188 7.07188i −0.387537 0.387537i
\(334\) 21.3935i 1.17060i
\(335\) 27.3023 + 5.17786i 1.49168 + 0.282897i
\(336\) 4.39382i 0.239702i
\(337\) −10.9001 + 10.9001i −0.593765 + 0.593765i −0.938646 0.344881i \(-0.887919\pi\)
0.344881 + 0.938646i \(0.387919\pi\)
\(338\) 9.18115 + 9.18115i 0.499389 + 0.499389i
\(339\) 17.6060i 0.956229i
\(340\) −5.68764 1.07866i −0.308456 0.0584983i
\(341\) 13.7616i 0.745234i
\(342\) 0.507128 4.32930i 0.0274223 0.234102i
\(343\) −16.4841 + 16.4841i −0.890057 + 0.890057i
\(344\) 11.2254 0.605232
\(345\) −4.60950 6.76706i −0.248167 0.364326i
\(346\) 3.28746 0.176735
\(347\) 15.9014 + 15.9014i 0.853630 + 0.853630i 0.990578 0.136948i \(-0.0437295\pi\)
−0.136948 + 0.990578i \(0.543729\pi\)
\(348\) 2.54592 2.54592i 0.136476 0.136476i
\(349\) 14.0170i 0.750311i −0.926962 0.375155i \(-0.877589\pi\)
0.926962 0.375155i \(-0.122411\pi\)
\(350\) 8.04354 20.4436i 0.429945 1.09276i
\(351\) 0.126051 0.00672810
\(352\) −2.70268 + 2.70268i −0.144053 + 0.144053i
\(353\) −1.70112 + 1.70112i −0.0905412 + 0.0905412i −0.750927 0.660386i \(-0.770393\pi\)
0.660386 + 0.750927i \(0.270393\pi\)
\(354\) −9.40851 −0.500056
\(355\) −3.07992 + 2.09794i −0.163465 + 0.111347i
\(356\) 9.79832i 0.519310i
\(357\) −8.04354 + 8.04354i −0.425709 + 0.425709i
\(358\) 0.364750 0.364750i 0.0192776 0.0192776i
\(359\) 36.9693i 1.95117i 0.219633 + 0.975583i \(0.429514\pi\)
−0.219633 + 0.975583i \(0.570486\pi\)
\(360\) −2.19691 0.416642i −0.115787 0.0219590i
\(361\) −4.39102 + 18.4856i −0.231106 + 0.972929i
\(362\) 3.43744 + 3.43744i 0.180668 + 0.180668i
\(363\) −2.55194 2.55194i −0.133942 0.133942i
\(364\) 0.553844 0.0290293
\(365\) −11.3207 2.14696i −0.592552 0.112377i
\(366\) 8.21380 0.429342
\(367\) −11.7866 11.7866i −0.615255 0.615255i 0.329055 0.944311i \(-0.393270\pi\)
−0.944311 + 0.329055i \(0.893270\pi\)
\(368\) −2.58922 + 2.58922i −0.134972 + 0.134972i
\(369\) −11.2134 −0.583746
\(370\) 18.4827 12.5898i 0.960871 0.654514i
\(371\) 20.0029i 1.03850i
\(372\) −2.54592 2.54592i −0.132000 0.132000i
\(373\) 9.29229 + 9.29229i 0.481137 + 0.481137i 0.905495 0.424358i \(-0.139500\pi\)
−0.424358 + 0.905495i \(0.639500\pi\)
\(374\) −9.89533 −0.511675
\(375\) 9.45910 + 5.96033i 0.488466 + 0.307790i
\(376\) 0.655021i 0.0337801i
\(377\) −0.320915 0.320915i −0.0165280 0.0165280i
\(378\) −3.10690 + 3.10690i −0.159802 + 0.159802i
\(379\) 9.08999 0.466921 0.233461 0.972366i \(-0.424995\pi\)
0.233461 + 0.972366i \(0.424995\pi\)
\(380\) 9.29978 + 2.91788i 0.477069 + 0.149684i
\(381\) 0.0900835 0.00461512
\(382\) 10.8448 10.8448i 0.554870 0.554870i
\(383\) 2.91923 + 2.91923i 0.149166 + 0.149166i 0.777745 0.628579i \(-0.216363\pi\)
−0.628579 + 0.777745i \(0.716363\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 6.99705 36.8947i 0.356603 1.88033i
\(386\) −24.2679 −1.23521
\(387\) 7.93755 + 7.93755i 0.403488 + 0.403488i
\(388\) −6.88409 6.88409i −0.349487 0.349487i
\(389\) 25.2850i 1.28200i 0.767540 + 0.641001i \(0.221481\pi\)
−0.767540 + 0.641001i \(0.778519\pi\)
\(390\) −0.0525181 + 0.276922i −0.00265936 + 0.0140225i
\(391\) −9.47991 −0.479420
\(392\) −8.70140 + 8.70140i −0.439487 + 0.439487i
\(393\) −1.73108 1.73108i −0.0873213 0.0873213i
\(394\) 8.83957 0.445331
\(395\) 11.1125 + 16.3139i 0.559130 + 0.820841i
\(396\) −3.82217 −0.192071
\(397\) 11.4572 + 11.4572i 0.575020 + 0.575020i 0.933527 0.358507i \(-0.116714\pi\)
−0.358507 + 0.933527i \(0.616714\pi\)
\(398\) −7.36057 7.36057i −0.368952 0.368952i
\(399\) 15.0263 11.8751i 0.752255 0.594498i
\(400\) 1.83065 4.65282i 0.0915324 0.232641i
\(401\) 7.22311i 0.360705i 0.983602 + 0.180352i \(0.0577238\pi\)
−0.983602 + 0.180352i \(0.942276\pi\)
\(402\) 8.78764 8.78764i 0.438287 0.438287i
\(403\) −0.320915 + 0.320915i −0.0159859 + 0.0159859i
\(404\) 3.89174i 0.193621i
\(405\) −1.25884 1.84806i −0.0625522 0.0918308i
\(406\) 15.8198 0.785125
\(407\) 27.0299 27.0299i 1.33982 1.33982i
\(408\) −1.83065 + 1.83065i −0.0906306 + 0.0906306i
\(409\) 17.4019 0.860470 0.430235 0.902717i \(-0.358431\pi\)
0.430235 + 0.902717i \(0.358431\pi\)
\(410\) 4.67197 24.6348i 0.230732 1.21663i
\(411\) 4.28065i 0.211149i
\(412\) −9.40518 + 9.40518i −0.463360 + 0.463360i
\(413\) −29.2313 29.2313i −1.43838 1.43838i
\(414\) −3.66171 −0.179963
\(415\) −1.07866 0.204566i −0.0529491 0.0100418i
\(416\) 0.126051 0.00618015
\(417\) 2.80134 2.80134i 0.137182 0.137182i
\(418\) 16.5473 + 1.93833i 0.809356 + 0.0948068i
\(419\) 1.67485i 0.0818218i 0.999163 + 0.0409109i \(0.0130260\pi\)
−0.999163 + 0.0409109i \(0.986974\pi\)
\(420\) −5.53111 8.12004i −0.269891 0.396217i
\(421\) 26.3045i 1.28200i −0.767540 0.641001i \(-0.778520\pi\)
0.767540 0.641001i \(-0.221480\pi\)
\(422\) 9.23137 + 9.23137i 0.449376 + 0.449376i
\(423\) 0.463170 0.463170i 0.0225201 0.0225201i
\(424\) 4.55250i 0.221089i
\(425\) 11.8690 5.16640i 0.575729 0.250607i
\(426\) 1.66657i 0.0807455i
\(427\) 25.5194 + 25.5194i 1.23497 + 1.23497i
\(428\) −7.00983 7.00983i −0.338833 0.338833i
\(429\) 0.481788i 0.0232609i
\(430\) −20.7452 + 14.1310i −1.00042 + 0.681455i
\(431\) 9.18675i 0.442510i −0.975216 0.221255i \(-0.928985\pi\)
0.975216 0.221255i \(-0.0710154\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −7.28482 7.28482i −0.350086 0.350086i 0.510055 0.860142i \(-0.329625\pi\)
−0.860142 + 0.510055i \(0.829625\pi\)
\(434\) 15.8198i 0.759376i
\(435\) −1.50011 + 7.90992i −0.0719247 + 0.379251i
\(436\) 17.7935i 0.852153i
\(437\) 15.8526 + 1.85696i 0.758335 + 0.0888302i
\(438\) −3.64373 + 3.64373i −0.174104 + 0.174104i
\(439\) −11.5269 −0.550148 −0.275074 0.961423i \(-0.588702\pi\)
−0.275074 + 0.961423i \(0.588702\pi\)
\(440\) 1.59248 8.39696i 0.0759183 0.400309i
\(441\) −12.3056 −0.585983
\(442\) 0.230755 + 0.230755i 0.0109759 + 0.0109759i
\(443\) 1.68879 1.68879i 0.0802367 0.0802367i −0.665849 0.746086i \(-0.731931\pi\)
0.746086 + 0.665849i \(0.231931\pi\)
\(444\) 10.0011i 0.474633i
\(445\) 12.3345 + 18.1079i 0.584712 + 0.858396i
\(446\) −16.3221 −0.772872
\(447\) −15.8349 + 15.8349i −0.748967 + 0.748967i
\(448\) −3.10690 + 3.10690i −0.146787 + 0.146787i
\(449\) 10.9876 0.518538 0.259269 0.965805i \(-0.416518\pi\)
0.259269 + 0.965805i \(0.416518\pi\)
\(450\) 4.58450 1.99558i 0.216116 0.0940723i
\(451\) 42.8595i 2.01818i
\(452\) 12.4493 12.4493i 0.585568 0.585568i
\(453\) −7.98994 + 7.98994i −0.375400 + 0.375400i
\(454\) 23.2372i 1.09058i
\(455\) −1.02354 + 0.697201i −0.0479842 + 0.0326853i
\(456\) 3.41987 2.70268i 0.160150 0.126565i
\(457\) −24.3188 24.3188i −1.13759 1.13759i −0.988882 0.148703i \(-0.952490\pi\)
−0.148703 0.988882i \(-0.547510\pi\)
\(458\) −10.9739 10.9739i −0.512777 0.512777i
\(459\) −2.58893 −0.120841
\(460\) 1.52562 8.04445i 0.0711325 0.375074i
\(461\) 20.8769 0.972332 0.486166 0.873866i \(-0.338395\pi\)
0.486166 + 0.873866i \(0.338395\pi\)
\(462\) −11.8751 11.8751i −0.552479 0.552479i
\(463\) −16.5161 + 16.5161i −0.767568 + 0.767568i −0.977678 0.210110i \(-0.932618\pi\)
0.210110 + 0.977678i \(0.432618\pi\)
\(464\) 3.60048 0.167148
\(465\) 7.90992 + 1.50011i 0.366814 + 0.0695659i
\(466\) 2.39161i 0.110789i
\(467\) −14.6317 14.6317i −0.677074 0.677074i 0.282263 0.959337i \(-0.408915\pi\)
−0.959337 + 0.282263i \(0.908915\pi\)
\(468\) 0.0891314 + 0.0891314i 0.00412010 + 0.00412010i
\(469\) 54.6046 2.52141
\(470\) 0.824566 + 1.21052i 0.0380344 + 0.0558370i
\(471\) 6.47591i 0.298394i
\(472\) −6.65282 6.65282i −0.306221 0.306221i
\(473\) −30.3387 + 30.3387i −1.39497 + 1.39497i
\(474\) 8.82758 0.405464
\(475\) −20.8597 + 6.31451i −0.957109 + 0.289730i
\(476\) −11.3753 −0.521385
\(477\) −3.21910 + 3.21910i −0.147393 + 0.147393i
\(478\) −9.19036 9.19036i −0.420357 0.420357i
\(479\) 28.1296i 1.28527i −0.766171 0.642636i \(-0.777841\pi\)
0.766171 0.642636i \(-0.222159\pi\)
\(480\) −1.25884 1.84806i −0.0574579 0.0843520i
\(481\) −1.26065 −0.0574808
\(482\) 6.10941 + 6.10941i 0.278276 + 0.278276i
\(483\) −11.3766 11.3766i −0.517652 0.517652i
\(484\) 3.60898i 0.164045i
\(485\) 21.3882 + 4.05625i 0.971186 + 0.184185i
\(486\) −1.00000 −0.0453609
\(487\) 11.6398 11.6398i 0.527451 0.527451i −0.392361 0.919811i \(-0.628342\pi\)
0.919811 + 0.392361i \(0.128342\pi\)
\(488\) 5.80803 + 5.80803i 0.262917 + 0.262917i
\(489\) −10.6715 −0.482584
\(490\) 5.12704 27.0344i 0.231616 1.22129i
\(491\) 5.55189 0.250553 0.125277 0.992122i \(-0.460018\pi\)
0.125277 + 0.992122i \(0.460018\pi\)
\(492\) −7.92907 7.92907i −0.357470 0.357470i
\(493\) 6.59121 + 6.59121i 0.296853 + 0.296853i
\(494\) −0.340675 0.431077i −0.0153277 0.0193951i
\(495\) 7.06360 4.81150i 0.317485 0.216261i
\(496\) 3.60048i 0.161666i
\(497\) −5.17786 + 5.17786i −0.232259 + 0.232259i
\(498\) −0.347181 + 0.347181i −0.0155576 + 0.0155576i
\(499\) 27.8562i 1.24701i −0.781818 0.623507i \(-0.785707\pi\)
0.781818 0.623507i \(-0.214293\pi\)
\(500\) 2.47400 + 10.9032i 0.110641 + 0.487605i
\(501\) −21.3935 −0.955789
\(502\) −16.7294 + 16.7294i −0.746670 + 0.746670i
\(503\) 20.5340 20.5340i 0.915564 0.915564i −0.0811388 0.996703i \(-0.525856\pi\)
0.996703 + 0.0811388i \(0.0258557\pi\)
\(504\) −4.39382 −0.195716
\(505\) −4.89907 7.19216i −0.218006 0.320047i
\(506\) 13.9957i 0.622184i
\(507\) −9.18115 + 9.18115i −0.407749 + 0.407749i
\(508\) 0.0636986 + 0.0636986i 0.00282617 + 0.00282617i
\(509\) 27.6636 1.22617 0.613085 0.790017i \(-0.289928\pi\)
0.613085 + 0.790017i \(0.289928\pi\)
\(510\) 1.07866 5.68764i 0.0477637 0.251853i
\(511\) −22.6414 −1.00160
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.32930 + 0.507128i 0.191143 + 0.0223902i
\(514\) 12.2150i 0.538781i
\(515\) 5.54173 29.2209i 0.244198 1.28763i
\(516\) 11.2254i 0.494170i
\(517\) 1.77031 + 1.77031i 0.0778583 + 0.0778583i
\(518\) 31.0725 31.0725i 1.36525 1.36525i
\(519\) 3.28746i 0.144303i
\(520\) −0.232949 + 0.158678i −0.0102155 + 0.00695848i
\(521\) 23.2591i 1.01900i 0.860471 + 0.509500i \(0.170170\pi\)
−0.860471 + 0.509500i \(0.829830\pi\)
\(522\) 2.54592 + 2.54592i 0.111432 + 0.111432i
\(523\) 8.81162 + 8.81162i 0.385305 + 0.385305i 0.873009 0.487704i \(-0.162165\pi\)
−0.487704 + 0.873009i \(0.662165\pi\)
\(524\) 2.44811i 0.106946i
\(525\) 20.4436 + 8.04354i 0.892234 + 0.351049i
\(526\) 15.4560i 0.673915i
\(527\) 6.59121 6.59121i 0.287117 0.287117i
\(528\) −2.70268 2.70268i −0.117619 0.117619i
\(529\) 9.59187i 0.417038i
\(530\) −5.73086 8.41329i −0.248933 0.365450i
\(531\) 9.40851i 0.408294i
\(532\) 19.0221 + 2.22823i 0.824715 + 0.0966059i
\(533\) −0.999466 + 0.999466i −0.0432917 + 0.0432917i
\(534\) 9.79832 0.424015
\(535\) 21.7788 + 4.13034i 0.941581 + 0.178570i
\(536\) 12.4276 0.536790
\(537\) 0.364750 + 0.364750i 0.0157401 + 0.0157401i
\(538\) 9.79507 9.79507i 0.422296 0.422296i
\(539\) 47.0342i 2.02591i
\(540\) 0.416642 2.19691i 0.0179294 0.0945399i
\(541\) −16.3738 −0.703966 −0.351983 0.936006i \(-0.614493\pi\)
−0.351983 + 0.936006i \(0.614493\pi\)
\(542\) −10.4913 + 10.4913i −0.450642 + 0.450642i
\(543\) −3.43744 + 3.43744i −0.147515 + 0.147515i
\(544\) −2.58893 −0.110999
\(545\) −22.3991 32.8834i −0.959473 1.40857i
\(546\) 0.553844i 0.0237024i
\(547\) −20.3289 + 20.3289i −0.869199 + 0.869199i −0.992384 0.123185i \(-0.960689\pi\)
0.123185 + 0.992384i \(0.460689\pi\)
\(548\) 3.02688 3.02688i 0.129302 0.129302i
\(549\) 8.21380i 0.350556i
\(550\) 7.62743 + 17.5228i 0.325235 + 0.747173i
\(551\) −9.73094 12.3132i −0.414552 0.524558i
\(552\) −2.58922 2.58922i −0.110205 0.110205i
\(553\) 27.4264 + 27.4264i 1.16629 + 1.16629i
\(554\) 12.6674 0.538188
\(555\) 12.5898 + 18.4827i 0.534409 + 0.784548i
\(556\) 3.96170 0.168013
\(557\) −12.6433 12.6433i −0.535713 0.535713i 0.386554 0.922267i \(-0.373665\pi\)
−0.922267 + 0.386554i \(0.873665\pi\)
\(558\) 2.54592 2.54592i 0.107777 0.107777i
\(559\) 1.41497 0.0598468
\(560\) 1.83065 9.65282i 0.0773590 0.407906i
\(561\) 9.89533i 0.417781i
\(562\) 4.34121 + 4.34121i 0.183123 + 0.183123i
\(563\) −20.5997 20.5997i −0.868176 0.868176i 0.124095 0.992270i \(-0.460397\pi\)
−0.992270 + 0.124095i \(0.960397\pi\)
\(564\) 0.655021 0.0275814
\(565\) −7.33541 + 38.6789i −0.308603 + 1.62723i
\(566\) 32.2388i 1.35510i
\(567\) −3.10690 3.10690i −0.130477 0.130477i
\(568\) −1.17844 + 1.17844i −0.0494463 + 0.0494463i
\(569\) −39.5742 −1.65904 −0.829519 0.558478i \(-0.811386\pi\)
−0.829519 + 0.558478i \(0.811386\pi\)
\(570\) −2.91788 + 9.29978i −0.122217 + 0.389525i
\(571\) −15.5508 −0.650780 −0.325390 0.945580i \(-0.605496\pi\)
−0.325390 + 0.945580i \(0.605496\pi\)
\(572\) −0.340675 + 0.340675i −0.0142444 + 0.0142444i
\(573\) 10.8448 + 10.8448i 0.453049 + 0.453049i
\(574\) 49.2696i 2.05647i
\(575\) 7.30722 + 16.7871i 0.304732 + 0.700072i
\(576\) −1.00000 −0.0416667
\(577\) 2.21358 + 2.21358i 0.0921525 + 0.0921525i 0.751680 0.659528i \(-0.229244\pi\)
−0.659528 + 0.751680i \(0.729244\pi\)
\(578\) 7.28140 + 7.28140i 0.302866 + 0.302866i
\(579\) 24.2679i 1.00854i
\(580\) −6.65389 + 4.53242i −0.276288 + 0.188198i
\(581\) −2.15731 −0.0895004
\(582\) 6.88409 6.88409i 0.285355 0.285355i
\(583\) −12.3040 12.3040i −0.509578 0.509578i
\(584\) −5.15301 −0.213233
\(585\) −0.276922 0.0525181i −0.0114493 0.00217135i
\(586\) −0.482856 −0.0199466
\(587\) −0.773553 0.773553i −0.0319279 0.0319279i 0.690963 0.722891i \(-0.257187\pi\)
−0.722891 + 0.690963i \(0.757187\pi\)
\(588\) −8.70140 8.70140i −0.358840 0.358840i
\(589\) −12.3132 + 9.73094i −0.507355 + 0.400956i
\(590\) 20.6696 + 3.91998i 0.850955 + 0.161383i
\(591\) 8.83957i 0.363611i
\(592\) 7.07188 7.07188i 0.290652 0.290652i
\(593\) 6.83126 6.83126i 0.280526 0.280526i −0.552793 0.833319i \(-0.686438\pi\)
0.833319 + 0.552793i \(0.186438\pi\)
\(594\) 3.82217i 0.156826i
\(595\) 21.0222 14.3196i 0.861826 0.587048i
\(596\) −22.3940 −0.917294
\(597\) 7.36057 7.36057i 0.301248 0.301248i
\(598\) −0.326373 + 0.326373i −0.0133464 + 0.0133464i
\(599\) 4.89411 0.199968 0.0999840 0.994989i \(-0.468121\pi\)
0.0999840 + 0.994989i \(0.468121\pi\)
\(600\) 4.65282 + 1.83065i 0.189951 + 0.0747359i
\(601\) 18.8596i 0.769299i 0.923063 + 0.384650i \(0.125678\pi\)
−0.923063 + 0.384650i \(0.874322\pi\)
\(602\) −34.8761 + 34.8761i −1.42145 + 1.42145i
\(603\) 8.78764 + 8.78764i 0.357860 + 0.357860i
\(604\) −11.2995 −0.459769
\(605\) 4.54313 + 6.66962i 0.184705 + 0.271159i
\(606\) −3.89174 −0.158091
\(607\) 16.5646 16.5646i 0.672335 0.672335i −0.285919 0.958254i \(-0.592299\pi\)
0.958254 + 0.285919i \(0.0922988\pi\)
\(608\) 4.32930 + 0.507128i 0.175576 + 0.0205668i
\(609\) 15.8198i 0.641052i
\(610\) −18.0450 3.42221i −0.730619 0.138561i
\(611\) 0.0825659i 0.00334026i
\(612\) −1.83065 1.83065i −0.0739996 0.0739996i
\(613\) 29.1371 29.1371i 1.17684 1.17684i 0.196291 0.980546i \(-0.437110\pi\)
0.980546 0.196291i \(-0.0628899\pi\)
\(614\) 25.5326i 1.03041i
\(615\) 24.6348 + 4.67197i 0.993372 + 0.188392i
\(616\) 16.7939i 0.676646i
\(617\) 18.0432 + 18.0432i 0.726393 + 0.726393i 0.969899 0.243506i \(-0.0782977\pi\)
−0.243506 + 0.969899i \(0.578298\pi\)
\(618\) −9.40518 9.40518i −0.378332 0.378332i
\(619\) 2.38578i 0.0958924i 0.998850 + 0.0479462i \(0.0152676\pi\)
−0.998850 + 0.0479462i \(0.984732\pi\)
\(620\) 4.53242 + 6.65389i 0.182026 + 0.267227i
\(621\) 3.66171i 0.146939i
\(622\) −4.05233 + 4.05233i −0.162484 + 0.162484i
\(623\) 30.4424 + 30.4424i 1.21965 + 1.21965i
\(624\) 0.126051i 0.00504607i
\(625\) −18.2974 17.0354i −0.731898 0.681414i
\(626\) 31.3617i 1.25347i
\(627\) −1.93833 + 16.5473i −0.0774094 + 0.660836i
\(628\) −4.57916 + 4.57916i −0.182728 + 0.182728i
\(629\) 25.8923 1.03239
\(630\) 8.12004 5.53111i 0.323510 0.220365i
\(631\) −14.5023 −0.577326 −0.288663 0.957431i \(-0.593211\pi\)
−0.288663 + 0.957431i \(0.593211\pi\)
\(632\) 6.24204 + 6.24204i 0.248295 + 0.248295i
\(633\) −9.23137 + 9.23137i −0.366914 + 0.366914i
\(634\) 15.6454i 0.621359i
\(635\) −0.197905 0.0375326i −0.00785363 0.00148943i
\(636\) −4.55250 −0.180518
\(637\) −1.09682 + 1.09682i −0.0434575 + 0.0434575i
\(638\) −9.73094 + 9.73094i −0.385252 + 0.385252i
\(639\) −1.66657 −0.0659284
\(640\) 0.416642 2.19691i 0.0164692 0.0868405i
\(641\) 12.7084i 0.501950i 0.967994 + 0.250975i \(0.0807512\pi\)
−0.967994 + 0.250975i \(0.919249\pi\)
\(642\) 7.00983 7.00983i 0.276656 0.276656i
\(643\) −1.79680 + 1.79680i −0.0708588 + 0.0708588i −0.741648 0.670789i \(-0.765956\pi\)
0.670789 + 0.741648i \(0.265956\pi\)
\(644\) 16.0889i 0.633991i
\(645\) −14.1310 20.7452i −0.556406 0.816841i
\(646\) 6.99705 + 8.85380i 0.275295 + 0.348348i
\(647\) 7.42896 + 7.42896i 0.292063 + 0.292063i 0.837895 0.545832i \(-0.183786\pi\)
−0.545832 + 0.837895i \(0.683786\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 35.9609 1.41159
\(650\) 0.230755 0.586492i 0.00905095 0.0230041i
\(651\) 15.8198 0.620028
\(652\) −7.54592 7.54592i −0.295521 0.295521i
\(653\) −32.4125 + 32.4125i −1.26840 + 1.26840i −0.321486 + 0.946914i \(0.604182\pi\)
−0.946914 + 0.321486i \(0.895818\pi\)
\(654\) −17.7935 −0.695780
\(655\) 3.08178 + 4.52426i 0.120415 + 0.176777i
\(656\) 11.2134i 0.437810i
\(657\) −3.64373 3.64373i −0.142155 0.142155i
\(658\) 2.03508 + 2.03508i 0.0793358 + 0.0793358i
\(659\) −41.3365 −1.61024 −0.805122 0.593110i \(-0.797900\pi\)
−0.805122 + 0.593110i \(0.797900\pi\)
\(660\) 8.39696 + 1.59248i 0.326851 + 0.0619871i
\(661\) 2.43023i 0.0945250i −0.998883 0.0472625i \(-0.984950\pi\)
0.998883 0.0472625i \(-0.0150497\pi\)
\(662\) 8.34099 + 8.34099i 0.324182 + 0.324182i
\(663\) −0.230755 + 0.230755i −0.00896177 + 0.00896177i
\(664\) −0.490988 −0.0190540
\(665\) −37.9590 + 19.8279i −1.47199 + 0.768894i
\(666\) 10.0011 0.387537
\(667\) −9.32242 + 9.32242i −0.360966 + 0.360966i
\(668\) −15.1275 15.1275i −0.585299 0.585299i
\(669\) 16.3221i 0.631047i
\(670\) −22.9669 + 15.6443i −0.887290 + 0.604394i
\(671\) −31.3945 −1.21197
\(672\) −3.10690 3.10690i −0.119851 0.119851i
\(673\) −19.4040 19.4040i −0.747968 0.747968i 0.226129 0.974097i \(-0.427393\pi\)
−0.974097 + 0.226129i \(0.927393\pi\)
\(674\) 15.4150i 0.593765i
\(675\) 1.99558 + 4.58450i 0.0768097 + 0.176458i
\(676\) −12.9841 −0.499389
\(677\) −18.9654 + 18.9654i −0.728899 + 0.728899i −0.970401 0.241501i \(-0.922360\pi\)
0.241501 + 0.970401i \(0.422360\pi\)
\(678\) 12.4493 + 12.4493i 0.478114 + 0.478114i
\(679\) 42.7763 1.64160
\(680\) 4.78449 3.25904i 0.183477 0.124979i
\(681\) −23.2372 −0.890452
\(682\) 9.73094 + 9.73094i 0.372617 + 0.372617i
\(683\) 11.9597 + 11.9597i 0.457626 + 0.457626i 0.897876 0.440249i \(-0.145110\pi\)
−0.440249 + 0.897876i \(0.645110\pi\)
\(684\) 2.70268 + 3.41987i 0.103340 + 0.130762i
\(685\) −1.78350 + 9.40420i −0.0681440 + 0.359316i
\(686\) 23.3120i 0.890057i
\(687\) 10.9739 10.9739i 0.418680 0.418680i
\(688\) −7.93755 + 7.93755i −0.302616 + 0.302616i
\(689\) 0.573846i 0.0218618i
\(690\) 8.04445 + 1.52562i 0.306247 + 0.0580795i
\(691\) 3.66130 0.139282 0.0696412 0.997572i \(-0.477815\pi\)
0.0696412 + 0.997572i \(0.477815\pi\)
\(692\) −2.32458 + 2.32458i −0.0883674 + 0.0883674i
\(693\) 11.8751 11.8751i 0.451098 0.451098i
\(694\) −22.4879 −0.853630
\(695\) −7.32145 + 4.98714i −0.277718 + 0.189173i
\(696\) 3.60048i 0.136476i
\(697\) 20.5278 20.5278i 0.777546 0.777546i
\(698\) 9.91149 + 9.91149i 0.375155 + 0.375155i
\(699\) 2.39161 0.0904590
\(700\) 8.76820 + 20.1435i 0.331407 + 0.761352i
\(701\) −25.2380 −0.953225 −0.476612 0.879113i \(-0.658136\pi\)
−0.476612 + 0.879113i \(0.658136\pi\)
\(702\) −0.0891314 + 0.0891314i −0.00336405 + 0.00336405i
\(703\) −43.2979 5.07186i −1.63301 0.191289i
\(704\) 3.82217i 0.144053i
\(705\) −1.21052 + 0.824566i −0.0455907 + 0.0310550i
\(706\) 2.40574i 0.0905412i
\(707\) −12.0912 12.0912i −0.454737 0.454737i
\(708\) 6.65282 6.65282i 0.250028 0.250028i
\(709\) 7.14208i 0.268226i −0.990966 0.134113i \(-0.957181\pi\)
0.990966 0.134113i \(-0.0428186\pi\)
\(710\) 0.694362 3.66130i 0.0260589 0.137406i
\(711\) 8.82758i 0.331060i
\(712\) 6.92846 + 6.92846i 0.259655 + 0.259655i
\(713\) 9.32242 + 9.32242i 0.349128 + 0.349128i
\(714\) 11.3753i 0.425709i
\(715\) 0.200733 1.05844i 0.00750699 0.0395836i
\(716\) 0.515834i 0.0192776i
\(717\) 9.19036 9.19036i 0.343220 0.343220i
\(718\) −26.1412 26.1412i −0.975583 0.975583i
\(719\) 30.1848i 1.12570i 0.826558 + 0.562852i \(0.190296\pi\)
−0.826558 + 0.562852i \(0.809704\pi\)
\(720\) 1.84806 1.25884i 0.0688731 0.0469142i
\(721\) 58.4419i 2.17649i
\(722\) −9.96641 16.1762i −0.370911 0.602017i
\(723\) −6.10941 + 6.10941i −0.227211 + 0.227211i
\(724\) −4.86127 −0.180668
\(725\) 6.59121 16.7524i 0.244791 0.622167i
\(726\) 3.60898 0.133942
\(727\) 10.1806 + 10.1806i 0.377576 + 0.377576i 0.870227 0.492651i \(-0.163972\pi\)
−0.492651 + 0.870227i \(0.663972\pi\)
\(728\) −0.391627 + 0.391627i −0.0145147 + 0.0145147i
\(729\) 1.00000i 0.0370370i
\(730\) 9.52307 6.48681i 0.352465 0.240088i
\(731\) −29.0617 −1.07489
\(732\) −5.80803 + 5.80803i −0.214671 + 0.214671i
\(733\) −12.6028 + 12.6028i −0.465495 + 0.465495i −0.900451 0.434957i \(-0.856764\pi\)
0.434957 + 0.900451i \(0.356764\pi\)
\(734\) 16.6688 0.615255
\(735\) 27.0344 + 5.12704i 0.997178 + 0.189114i
\(736\) 3.66171i 0.134972i
\(737\) −33.5878 + 33.5878i −1.23722 + 1.23722i
\(738\) 7.92907 7.92907i 0.291873 0.291873i
\(739\) 30.9906i 1.14001i −0.821642 0.570003i \(-0.806942\pi\)
0.821642 0.570003i \(-0.193058\pi\)
\(740\) −4.16690 + 21.9716i −0.153178 + 0.807692i
\(741\) 0.431077 0.340675i 0.0158360 0.0125150i
\(742\) −14.1442 14.1442i −0.519248 0.519248i
\(743\) 33.1976 + 33.1976i 1.21790 + 1.21790i 0.968366 + 0.249536i \(0.0802779\pi\)
0.249536 + 0.968366i \(0.419722\pi\)
\(744\) 3.60048 0.132000
\(745\) 41.3854 28.1904i 1.51625 1.03282i
\(746\) −13.1413 −0.481137
\(747\) −0.347181 0.347181i −0.0127027 0.0127027i
\(748\) 6.99705 6.99705i 0.255838 0.255838i
\(749\) 43.5577 1.59156
\(750\) −10.9032 + 2.47400i −0.398128 + 0.0903378i
\(751\) 11.6085i 0.423600i 0.977313 + 0.211800i \(0.0679325\pi\)
−0.977313 + 0.211800i \(0.932067\pi\)
\(752\) 0.463170 + 0.463170i 0.0168901 + 0.0168901i
\(753\) −16.7294 16.7294i −0.609654 0.609654i
\(754\) 0.453843 0.0165280
\(755\) 20.8821 14.2242i 0.759978 0.517673i
\(756\) 4.39382i 0.159802i
\(757\) 33.9555 + 33.9555i 1.23413 + 1.23413i 0.962362 + 0.271772i \(0.0876098\pi\)
0.271772 + 0.962362i \(0.412390\pi\)
\(758\) −6.42759 + 6.42759i −0.233461 + 0.233461i
\(759\) 13.9957 0.508011
\(760\) −8.63919 + 4.51269i −0.313376 + 0.163692i
\(761\) −1.91340 −0.0693607 −0.0346803 0.999398i \(-0.511041\pi\)
−0.0346803 + 0.999398i \(0.511041\pi\)
\(762\) −0.0636986 + 0.0636986i −0.00230756 + 0.00230756i
\(763\) −55.2825 55.2825i −2.00136 2.00136i
\(764\) 15.3369i 0.554870i
\(765\) 5.68764 + 1.07866i 0.205637 + 0.0389989i
\(766\) −4.12842 −0.149166
\(767\) −0.838593 0.838593i −0.0302798 0.0302798i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 17.5747i 0.633760i 0.948466 + 0.316880i \(0.102635\pi\)
−0.948466 + 0.316880i \(0.897365\pi\)
\(770\) 21.1408 + 31.0362i 0.761863 + 1.11847i
\(771\) −12.2150 −0.439913
\(772\) 17.1600 17.1600i 0.617603 0.617603i
\(773\) −28.9882 28.9882i −1.04263 1.04263i −0.999050 0.0435843i \(-0.986122\pi\)
−0.0435843 0.999050i \(-0.513878\pi\)
\(774\) −11.2254 −0.403488
\(775\) −16.7524 6.59121i −0.601763 0.236763i
\(776\) 9.73557 0.349487
\(777\) 31.0725 + 31.0725i 1.11472 + 1.11472i
\(778\) −17.8792 17.8792i −0.641001 0.641001i