Properties

Label 570.2.m.a.37.9
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 37.9
Root \(-2.19691 + 2.19691i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.a.493.9

$q$-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} +(0.507128 + 4.32930i) 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} +(-4.32930 + 0.507128i) 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} +(-9.72236 - 0.689653i) 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 0.694638 0.719359i \(-0.255564\pi\)
−0.719359 + 0.694638i \(0.755564\pi\)
\(14\) 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 \(-0.391502\pi\)
0.334296 + 0.942468i \(0.391502\pi\)
\(30\) 1.25884 + 1.84806i 0.229832 + 0.337408i
\(31\) 3.60048i 0.646664i −0.946286 0.323332i \(-0.895197\pi\)
0.946286 0.323332i \(-0.104803\pi\)
\(32\) −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 \(-0.442808\pi\)
0.983902 0.178707i \(-0.0571915\pi\)
\(38\) 0.507128 + 4.32930i 0.0822670 + 0.702305i
\(39\) 0.126051i 0.0201843i
\(40\) 0.416642 2.19691i 0.0658769 0.347362i
\(41\) 11.2134i 1.75124i −0.483002 0.875619i \(-0.660454\pi\)
0.483002 0.875619i \(-0.339546\pi\)
\(42\) 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 0.450566 0.892743i \(-0.351222\pi\)
−0.892743 + 0.450566i \(0.851222\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −4.81150 7.06360i −0.648782 0.952455i
\(56\) 4.39382i 0.587149i
\(57\) −4.32930 + 0.507128i −0.573430 + 0.0671707i
\(58\) 2.54592 2.54592i 0.334296 0.334296i
\(59\) 9.40851 1.22488 0.612442 0.790516i \(-0.290187\pi\)
0.612442 + 0.790516i \(0.290187\pi\)
\(60\) 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 \(0.524378\pi\)
−0.997069 + 0.0765120i \(0.975622\pi\)
\(68\) −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 \(-0.968470\pi\)
0.995098 0.0988926i \(-0.0315300\pi\)
\(72\) 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 \(-0.665415\pi\)
−0.496590 + 0.867985i \(0.665415\pi\)
\(80\) −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 \(-0.673811\pi\)
−0.519310 + 0.854586i \(0.673811\pi\)
\(90\) −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
\(95\) −9.72236 0.689653i −0.997494 0.0707569i
\(96\) −1.00000 −0.102062
\(97\) −6.88409 + 6.88409i −0.698973 + 0.698973i −0.964189 0.265216i \(-0.914557\pi\)
0.265216 + 0.964189i \(0.414557\pi\)
\(98\) 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 0.997492 0.0707726i \(-0.0225465\pi\)
−0.0707726 + 0.997492i \(0.522546\pi\)
\(104\) 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 −0.959472 0.281806i \(-0.909067\pi\)
0.281806 + 0.959472i \(0.409067\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 17.7935 1.70431 0.852153 0.523293i \(-0.175297\pi\)
0.852153 + 0.523293i \(0.175297\pi\)
\(110\) −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 \(-0.939412\pi\)
−0.189197 0.981939i \(-0.560588\pi\)
\(114\) −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 −0.704275 0.709927i \(-0.748728\pi\)
0.709927 + 0.704275i \(0.248728\pi\)
\(128\) 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
\(133\) −19.0221 + 2.22823i −1.64943 + 0.193212i
\(134\) 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 \(0.152068\pi\)
−0.888038 + 0.459769i \(0.847932\pi\)
\(152\) 4.32930 0.507128i 0.351152 0.0411335i
\(153\) 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 \(0.560373\pi\)
−0.982067 + 0.188531i \(0.939627\pi\)
\(168\) 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 0.789931 0.613196i \(-0.210116\pi\)
−0.613196 + 0.789931i \(0.710116\pi\)
\(174\) 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 \(-0.493863\pi\)
0.0192776 + 0.999814i \(0.493863\pi\)
\(180\) 1.25884 + 1.84806i 0.0938283 + 0.137746i
\(181\) 4.86127i 0.361336i 0.983544 + 0.180668i \(0.0578259\pi\)
−0.983544 + 0.180668i \(0.942174\pi\)
\(182\) −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
\(190\) −7.36241 + 6.38709i −0.534125 + 0.463368i
\(191\) −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 \(-0.911895\pi\)
−0.273268 0.961938i \(-0.588105\pi\)
\(194\) 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 \(0.148354\pi\)
−0.893343 + 0.449376i \(0.851646\pi\)
\(212\) −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 0.205736 0.978608i \(-0.434041\pi\)
−0.978608 + 0.205736i \(0.934041\pi\)
\(224\) −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 \(0.530320\pi\)
−0.995467 + 0.0951099i \(0.969680\pi\)
\(228\) 0.507128 + 4.32930i 0.0335854 + 0.286715i
\(229\) 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 \(0.0897630\pi\)
−0.960501 + 0.278276i \(0.910237\pi\)
\(242\) 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
\(247\) 0.545712 0.0639239i 0.0347228 0.00406738i
\(248\) −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 −0.923171 0.384390i \(-0.874412\pi\)
0.384390 + 0.923171i \(0.374412\pi\)
\(258\) 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 \(-0.361224\pi\)
0.422296 + 0.906458i \(0.361224\pi\)
\(270\) −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 \(0.0586207\pi\)
−0.983090 + 0.183123i \(0.941379\pi\)
\(282\) −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
\(285\) −6.38709 7.36241i −0.378339 0.436111i
\(286\) 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 0.697063 0.717010i \(-0.254490\pi\)
−0.717010 + 0.697063i \(0.754490\pi\)
\(294\) 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 \(-0.490166\pi\)
0.999523 0.0308888i \(-0.00983377\pi\)
\(308\) −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 −0.945879 0.324520i \(-0.894797\pi\)
0.324520 + 0.945879i \(0.394797\pi\)
\(318\) −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
\(323\) 11.2082 1.31292i 0.623643 0.0730527i
\(324\) 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 \(0.105089\pi\)
−0.945995 + 0.324182i \(0.894911\pi\)
\(332\) 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 −0.344881 0.938646i \(-0.612081\pi\)
0.938646 + 0.344881i \(0.112081\pi\)
\(338\) −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
\(342\) −4.32930 + 0.507128i −0.234102 + 0.0274223i
\(343\) −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 0.424358 0.905495i \(-0.360500\pi\)
−0.905495 + 0.424358i \(0.860500\pi\)
\(374\) 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 \(-0.575005\pi\)
−0.233461 + 0.972366i \(0.575005\pi\)
\(380\) −0.689653 + 9.72236i −0.0353785 + 0.498747i
\(381\) 0.0900835 0.00461512
\(382\) −10.8448 + 10.8448i −0.554870 + 0.554870i
\(383\) −2.91923 2.91923i −0.149166 0.149166i 0.628579 0.777745i \(-0.283637\pi\)
−0.777745 + 0.628579i \(0.783637\pi\)
\(384\) 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 \(-0.942276\pi\)
0.983602 0.180352i \(-0.0577238\pi\)
\(402\) −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 \(-0.641569\pi\)
−0.430235 + 0.902717i \(0.641569\pi\)
\(410\) 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
\(418\) −1.93833 16.5473i −0.0948068 0.809356i
\(419\) 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 \(0.221480\pi\)
−0.767540 + 0.641001i \(0.778520\pi\)
\(422\) 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 \(0.0710154\pi\)
−0.975216 + 0.221255i \(0.928985\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 7.28482 + 7.28482i 0.350086 + 0.350086i 0.860142 0.510055i \(-0.170375\pi\)
−0.510055 + 0.860142i \(0.670375\pi\)
\(434\) 15.8198i 0.759376i
\(435\) −1.50011 + 7.90992i −0.0719247 + 0.379251i
\(436\) 17.7935i 0.852153i
\(437\) 1.85696 + 15.8526i 0.0888302 + 0.758335i
\(438\) −3.64373 + 3.64373i −0.174104 + 0.174104i
\(439\) 11.5269 0.550148 0.275074 0.961423i \(-0.411298\pi\)
0.275074 + 0.961423i \(0.411298\pi\)
\(440\) −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 \(-0.583482\pi\)
−0.259269 + 0.965805i \(0.583482\pi\)
\(450\) −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
\(475\) −10.9644 18.8357i −0.503080 0.864240i
\(476\) −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 −0.919811 0.392361i \(-0.871658\pi\)
0.392361 + 0.919811i \(0.371658\pi\)
\(488\) −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 \(-0.710072\pi\)
−0.613085 + 0.790017i \(0.710072\pi\)
\(510\) 1.07866 5.68764i 0.0477637 0.251853i
\(511\) −22.6414 −1.00160
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.507128 4.32930i −0.0223902 0.191143i
\(514\) 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 \(-0.829830\pi\)
0.860471 0.509500i \(-0.170170\pi\)
\(522\) 2.54592 + 2.54592i 0.111432 + 0.111432i
\(523\) −8.81162 8.81162i −0.385305 0.385305i 0.487704 0.873009i \(-0.337835\pi\)
−0.873009 + 0.487704i \(0.837835\pi\)
\(524\) 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
\(532\) 2.22823 + 19.0221i 0.0966059 + 0.824715i
\(533\) −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 −0.123185 0.992384i \(-0.539311\pi\)
0.992384 + 0.123185i \(0.0393108\pi\)
\(548\) 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 0.992270 0.124095i \(-0.0396027\pi\)
−0.124095 + 0.992270i \(0.539603\pi\)
\(564\) −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 \(-0.188614\pi\)
0.829519 + 0.558478i \(0.188614\pi\)
\(570\) −9.72236 0.689653i −0.407225 0.0288864i
\(571\) −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 \(-0.531879\pi\)
−0.0999840 + 0.994989i \(0.531879\pi\)
\(600\) 4.65282 + 1.83065i 0.189951 + 0.0747359i
\(601\) 18.8596i 0.769299i −0.923063 0.384650i \(-0.874322\pi\)
0.923063 0.384650i \(-0.125678\pi\)
\(602\) 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 −0.958254 0.285919i \(-0.907701\pi\)
0.285919 + 0.958254i \(0.407701\pi\)
\(608\) −0.507128 4.32930i −0.0205668 0.175576i
\(609\) 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
\(627\) 16.5473 1.93833i 0.660836 0.0774094i
\(628\) −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 \(-0.919249\pi\)
0.967994 0.250975i \(-0.0807512\pi\)
\(642\) −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 \(-0.202100\pi\)
0.805122 + 0.593110i \(0.202100\pi\)
\(660\) −8.39696 1.59248i −0.326851 0.0619871i
\(661\) 2.43023i 0.0945250i 0.998883 + 0.0472625i \(0.0150497\pi\)
−0.998883 + 0.0472625i \(0.984950\pi\)
\(662\) 8.34099 + 8.34099i 0.324182 + 0.324182i
\(663\) −0.230755 + 0.230755i −0.00896177 + 0.00896177i
\(664\) 0.490988 0.0190540
\(665\) −28.0637 32.3491i −1.08826 1.25444i
\(666\) 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 0.974097 0.226129i \(-0.0726071\pi\)
−0.226129 + 0.974097i \(0.572607\pi\)
\(674\) 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 −0.241501 0.970401i \(-0.577640\pi\)
0.970401 + 0.241501i \(0.0776398\pi\)
\(678\) −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 0.440249 0.897876i \(-0.354890\pi\)
−0.897876 + 0.440249i \(0.854890\pi\)
\(684\) −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
\(703\) 5.07186 + 43.2979i 0.191289 + 1.63301i
\(704\) 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
\(722\) −16.1762 9.96641i −0.602017 0.370911i
\(723\) −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 \(-0.919722\pi\)
−0.249536 0.968366i \(-0.580278\pi\)
\(744\) −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 \(-0.932067\pi\)
0.977313 0.211800i \(-0.0679325\pi\)
\(752\) 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
\(760\) 6.38709 + 7.36241i 0.231684 + 0.267063i
\(761\) −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 \(0.0138777\pi\)
0.0435843 + 0.999050i \(0.486122\pi\)
\(774\) 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