Properties

Label 105.3.k.c.62.4
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 16
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 62.4
Root \(1.97320 - 0.817327i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +(-4.65877 + 1.81544i) q^{10} -2.58936i q^{11} +(2.56399 + 8.62705i) q^{12} +(8.94114 + 8.94114i) q^{13} +(1.29468 - 6.87923i) q^{14} +(14.8831 + 1.86906i) q^{15} -5.00000 q^{16} +(-0.581460 - 0.581460i) q^{17} +(-1.85519 + 8.80672i) q^{18} +16.5793 q^{19} +(-6.03161 + 13.7339i) q^{20} +(-13.2460 + 16.2955i) q^{21} +(1.83095 + 1.83095i) q^{22} +(-26.5115 - 26.5115i) q^{23} +(-18.4643 - 10.0035i) q^{24} +(16.9155 + 18.4083i) q^{25} -12.6447 q^{26} +(17.4790 - 20.5787i) q^{27} +(-11.8466 - 17.3395i) q^{28} +11.5528 q^{29} +(-11.8456 + 9.20232i) q^{30} -30.8307i q^{31} +(23.3345 - 23.3345i) q^{32} +(-2.21303 - 7.44617i) q^{33} +0.822309 q^{34} +(-34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 - 41.4929i) q^{37} +(-11.7233 + 11.7233i) q^{38} +(33.3536 + 18.0702i) q^{39} +(-12.7081 - 32.6114i) q^{40} +17.1489 q^{41} +(-2.15633 - 20.8890i) q^{42} +(-25.1548 + 25.1548i) q^{43} +7.76807 q^{44} +(44.3965 - 7.34521i) q^{45} +37.4929 q^{46} +(-45.2473 - 45.2473i) q^{47} +(-14.3784 + 4.27331i) q^{48} +(17.8128 - 45.6476i) q^{49} +(-24.9777 - 1.05561i) q^{50} +(-2.16905 - 1.17514i) q^{51} +(-26.8234 + 26.8234i) q^{52} +(-34.1600 - 34.1600i) q^{53} +(2.19185 + 26.9109i) q^{54} +(5.20600 - 11.8540i) q^{55} +(48.1546 + 9.06275i) q^{56} +(47.6769 - 14.1697i) q^{57} +(-8.16905 + 8.16905i) q^{58} +47.6223i q^{59} +(-5.60717 + 44.6493i) q^{60} +78.9936i q^{61} +(21.8006 + 21.8006i) q^{62} +(-24.1641 + 58.1816i) q^{63} +13.0000i q^{64} +(22.9557 + 58.9087i) q^{65} +(6.83008 + 3.70039i) q^{66} +(72.4786 + 72.4786i) q^{67} +(1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 - 28.8899i) q^{70} +49.0193i q^{71} +(-61.6470 - 12.9863i) q^{72} +(26.0359 + 26.0359i) q^{73} +58.6798 q^{74} +(64.3765 + 38.4795i) q^{75} +49.7380i q^{76} +(10.2250 + 14.9660i) q^{77} +(-36.3621 + 10.8069i) q^{78} -75.8024i q^{79} +(-22.8898 - 10.0527i) q^{80} +(32.6762 - 74.1166i) q^{81} +(-12.1261 + 12.1261i) q^{82} +(53.6785 - 53.6785i) q^{83} +(-48.8865 - 39.7380i) q^{84} +(-1.49286 - 3.83095i) q^{85} -35.5742i q^{86} +(33.2221 - 9.87373i) q^{87} +(-12.8167 + 12.8167i) q^{88} +14.0533i q^{89} +(-26.1992 + 36.5869i) q^{90} +(-86.9857 - 16.3708i) q^{91} +(79.5344 - 79.5344i) q^{92} +(-26.3499 - 88.6594i) q^{93} +63.9894 q^{94} +(75.8995 + 33.3333i) q^{95} +(47.1596 - 87.0458i) q^{96} +(-25.9664 + 25.9664i) q^{97} +(19.6822 + 44.8733i) q^{98} +(-12.7279 - 19.5214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.353553 + 0.353553i −0.861430 0.507877i \(-0.830431\pi\)
0.507877 + 0.861430i \(0.330431\pi\)
\(3\) 2.87568 0.854662i 0.958561 0.284887i
\(4\) 3.00000i 0.750000i
\(5\) 4.57796 + 2.01054i 0.915592 + 0.402108i
\(6\) −1.42908 + 2.63775i −0.238180 + 0.439625i
\(7\) −5.77983 + 3.94887i −0.825689 + 0.564125i
\(8\) −4.94975 4.94975i −0.618718 0.618718i
\(9\) 7.53910 4.91548i 0.837678 0.546164i
\(10\) −4.65877 + 1.81544i −0.465877 + 0.181544i
\(11\) 2.58936i 0.235396i −0.993049 0.117698i \(-0.962449\pi\)
0.993049 0.117698i \(-0.0375515\pi\)
\(12\) 2.56399 + 8.62705i 0.213666 + 0.718921i
\(13\) 8.94114 + 8.94114i 0.687780 + 0.687780i 0.961741 0.273961i \(-0.0883338\pi\)
−0.273961 + 0.961741i \(0.588334\pi\)
\(14\) 1.29468 6.87923i 0.0924770 0.491374i
\(15\) 14.8831 + 1.86906i 0.992207 + 0.124604i
\(16\) −5.00000 −0.312500
\(17\) −0.581460 0.581460i −0.0342036 0.0342036i 0.689798 0.724002i \(-0.257699\pi\)
−0.724002 + 0.689798i \(0.757699\pi\)
\(18\) −1.85519 + 8.80672i −0.103066 + 0.489262i
\(19\) 16.5793 0.872596 0.436298 0.899802i \(-0.356289\pi\)
0.436298 + 0.899802i \(0.356289\pi\)
\(20\) −6.03161 + 13.7339i −0.301581 + 0.686694i
\(21\) −13.2460 + 16.2955i −0.630762 + 0.775977i
\(22\) 1.83095 + 1.83095i 0.0832251 + 0.0832251i
\(23\) −26.5115 26.5115i −1.15267 1.15267i −0.986015 0.166657i \(-0.946703\pi\)
−0.166657 0.986015i \(-0.553297\pi\)
\(24\) −18.4643 10.0035i −0.769344 0.416814i
\(25\) 16.9155 + 18.4083i 0.676619 + 0.736333i
\(26\) −12.6447 −0.486334
\(27\) 17.4790 20.5787i 0.647370 0.762176i
\(28\) −11.8466 17.3395i −0.423094 0.619267i
\(29\) 11.5528 0.398372 0.199186 0.979962i \(-0.436170\pi\)
0.199186 + 0.979962i \(0.436170\pi\)
\(30\) −11.8456 + 9.20232i −0.394852 + 0.306744i
\(31\) 30.8307i 0.994539i −0.867596 0.497270i \(-0.834336\pi\)
0.867596 0.497270i \(-0.165664\pi\)
\(32\) 23.3345 23.3345i 0.729204 0.729204i
\(33\) −2.21303 7.44617i −0.0670614 0.225642i
\(34\) 0.822309 0.0241856
\(35\) −34.3992 + 6.45724i −0.982834 + 0.184493i
\(36\) 14.7464 + 22.6173i 0.409623 + 0.628259i
\(37\) −41.4929 41.4929i −1.12143 1.12143i −0.991527 0.129902i \(-0.958534\pi\)
−0.129902 0.991527i \(-0.541466\pi\)
\(38\) −11.7233 + 11.7233i −0.308509 + 0.308509i
\(39\) 33.3536 + 18.0702i 0.855219 + 0.463339i
\(40\) −12.7081 32.6114i −0.317703 0.815285i
\(41\) 17.1489 0.418267 0.209133 0.977887i \(-0.432936\pi\)
0.209133 + 0.977887i \(0.432936\pi\)
\(42\) −2.15633 20.8890i −0.0513413 0.497357i
\(43\) −25.1548 + 25.1548i −0.584994 + 0.584994i −0.936272 0.351277i \(-0.885748\pi\)
0.351277 + 0.936272i \(0.385748\pi\)
\(44\) 7.76807 0.176547
\(45\) 44.3965 7.34521i 0.986589 0.163227i
\(46\) 37.4929 0.815062
\(47\) −45.2473 45.2473i −0.962709 0.962709i 0.0366205 0.999329i \(-0.488341\pi\)
−0.999329 + 0.0366205i \(0.988341\pi\)
\(48\) −14.3784 + 4.27331i −0.299550 + 0.0890273i
\(49\) 17.8128 45.6476i 0.363526 0.931584i
\(50\) −24.9777 1.05561i −0.499554 0.0211122i
\(51\) −2.16905 1.17514i −0.0425304 0.0230420i
\(52\) −26.8234 + 26.8234i −0.515835 + 0.515835i
\(53\) −34.1600 34.1600i −0.644528 0.644528i 0.307137 0.951665i \(-0.400629\pi\)
−0.951665 + 0.307137i \(0.900629\pi\)
\(54\) 2.19185 + 26.9109i 0.0405897 + 0.498350i
\(55\) 5.20600 11.8540i 0.0946545 0.215527i
\(56\) 48.1546 + 9.06275i 0.859904 + 0.161835i
\(57\) 47.6769 14.1697i 0.836436 0.248592i
\(58\) −8.16905 + 8.16905i −0.140846 + 0.140846i
\(59\) 47.6223i 0.807158i 0.914945 + 0.403579i \(0.132234\pi\)
−0.914945 + 0.403579i \(0.867766\pi\)
\(60\) −5.60717 + 44.6493i −0.0934529 + 0.744155i
\(61\) 78.9936i 1.29498i 0.762075 + 0.647488i \(0.224181\pi\)
−0.762075 + 0.647488i \(0.775819\pi\)
\(62\) 21.8006 + 21.8006i 0.351623 + 0.351623i
\(63\) −24.1641 + 58.1816i −0.383557 + 0.923517i
\(64\) 13.0000i 0.203125i
\(65\) 22.9557 + 58.9087i 0.353165 + 0.906288i
\(66\) 6.83008 + 3.70039i 0.103486 + 0.0560665i
\(67\) 72.4786 + 72.4786i 1.08177 + 1.08177i 0.996345 + 0.0854251i \(0.0272248\pi\)
0.0854251 + 0.996345i \(0.472775\pi\)
\(68\) 1.74438 1.74438i 0.0256527 0.0256527i
\(69\) −98.8969 53.5802i −1.43329 0.776524i
\(70\) 19.7579 28.8899i 0.282256 0.412712i
\(71\) 49.0193i 0.690413i 0.938527 + 0.345207i \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(72\) −61.6470 12.9863i −0.856209 0.180365i
\(73\) 26.0359 + 26.0359i 0.356656 + 0.356656i 0.862579 0.505923i \(-0.168848\pi\)
−0.505923 + 0.862579i \(0.668848\pi\)
\(74\) 58.6798 0.792970
\(75\) 64.3765 + 38.4795i 0.858353 + 0.513060i
\(76\) 49.7380i 0.654447i
\(77\) 10.2250 + 14.9660i 0.132793 + 0.194364i
\(78\) −36.3621 + 10.8069i −0.466181 + 0.138550i
\(79\) 75.8024i 0.959524i −0.877399 0.479762i \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(80\) −22.8898 10.0527i −0.286123 0.125659i
\(81\) 32.6762 74.1166i 0.403410 0.915019i
\(82\) −12.1261 + 12.1261i −0.147880 + 0.147880i
\(83\) 53.6785 53.6785i 0.646729 0.646729i −0.305472 0.952201i \(-0.598814\pi\)
0.952201 + 0.305472i \(0.0988143\pi\)
\(84\) −48.8865 39.7380i −0.581983 0.473071i
\(85\) −1.49286 3.83095i −0.0175630 0.0450700i
\(86\) 35.5742i 0.413654i
\(87\) 33.2221 9.87373i 0.381864 0.113491i
\(88\) −12.8167 + 12.8167i −0.145644 + 0.145644i
\(89\) 14.0533i 0.157903i 0.996878 + 0.0789514i \(0.0251572\pi\)
−0.996878 + 0.0789514i \(0.974843\pi\)
\(90\) −26.1992 + 36.5869i −0.291102 + 0.406521i
\(91\) −86.9857 16.3708i −0.955887 0.179899i
\(92\) 79.5344 79.5344i 0.864504 0.864504i
\(93\) −26.3499 88.6594i −0.283332 0.953327i
\(94\) 63.9894 0.680738
\(95\) 75.8995 + 33.3333i 0.798942 + 0.350877i
\(96\) 47.1596 87.0458i 0.491245 0.906727i
\(97\) −25.9664 + 25.9664i −0.267695 + 0.267695i −0.828171 0.560476i \(-0.810618\pi\)
0.560476 + 0.828171i \(0.310618\pi\)
\(98\) 19.6822 + 44.8733i 0.200839 + 0.457891i
\(99\) −12.7279 19.5214i −0.128565 0.197186i
\(100\) −55.2250 + 50.7464i −0.552250 + 0.507464i
\(101\) 23.6924 0.234579 0.117289 0.993098i \(-0.462580\pi\)
0.117289 + 0.993098i \(0.462580\pi\)
\(102\) 2.36470 0.702797i 0.0231833 0.00689016i
\(103\) −78.6519 78.6519i −0.763611 0.763611i 0.213362 0.976973i \(-0.431559\pi\)
−0.976973 + 0.213362i \(0.931559\pi\)
\(104\) 88.5128i 0.851085i
\(105\) −93.4024 + 47.9687i −0.889547 + 0.456844i
\(106\) 48.3095 0.455750
\(107\) −124.868 + 124.868i −1.16699 + 1.16699i −0.184083 + 0.982911i \(0.558931\pi\)
−0.982911 + 0.184083i \(0.941069\pi\)
\(108\) 61.7362 + 52.4370i 0.571632 + 0.485528i
\(109\) 72.9857i 0.669594i 0.942290 + 0.334797i \(0.108668\pi\)
−0.942290 + 0.334797i \(0.891332\pi\)
\(110\) 4.70083 + 12.0632i 0.0427348 + 0.109666i
\(111\) −154.783 83.8579i −1.39444 0.755477i
\(112\) 28.8991 19.7444i 0.258028 0.176289i
\(113\) 51.8276 + 51.8276i 0.458651 + 0.458651i 0.898212 0.439562i \(-0.144866\pi\)
−0.439562 + 0.898212i \(0.644866\pi\)
\(114\) −23.6931 + 43.7321i −0.207834 + 0.383615i
\(115\) −68.0662 174.671i −0.591880 1.51888i
\(116\) 34.6583i 0.298779i
\(117\) 111.358 + 23.4582i 0.951779 + 0.200498i
\(118\) −33.6740 33.6740i −0.285373 0.285373i
\(119\) 5.65685 + 1.06463i 0.0475366 + 0.00894644i
\(120\) −64.4162 82.9189i −0.536802 0.690991i
\(121\) 114.295 0.944589
\(122\) −55.8569 55.8569i −0.457843 0.457843i
\(123\) 49.3149 14.6565i 0.400934 0.119159i
\(124\) 92.4922 0.745905
\(125\) 40.4278 + 118.282i 0.323422 + 0.946255i
\(126\) −24.0540 58.2272i −0.190905 0.462121i
\(127\) 21.6476 + 21.6476i 0.170454 + 0.170454i 0.787179 0.616725i \(-0.211541\pi\)
−0.616725 + 0.787179i \(0.711541\pi\)
\(128\) 84.1457 + 84.1457i 0.657388 + 0.657388i
\(129\) −50.8383 + 93.8359i −0.394095 + 0.727410i
\(130\) −57.8869 25.4226i −0.445284 0.195559i
\(131\) −217.662 −1.66154 −0.830771 0.556614i \(-0.812100\pi\)
−0.830771 + 0.556614i \(0.812100\pi\)
\(132\) 22.3385 6.63908i 0.169231 0.0502960i
\(133\) −95.8256 + 65.4696i −0.720493 + 0.492253i
\(134\) −102.500 −0.764927
\(135\) 121.393 59.0665i 0.899204 0.437530i
\(136\) 5.75616i 0.0423247i
\(137\) −32.1683 + 32.1683i −0.234805 + 0.234805i −0.814695 0.579890i \(-0.803096\pi\)
0.579890 + 0.814695i \(0.303096\pi\)
\(138\) 107.818 32.0437i 0.781287 0.232201i
\(139\) 112.569 0.809851 0.404925 0.914350i \(-0.367298\pi\)
0.404925 + 0.914350i \(0.367298\pi\)
\(140\) −19.3717 103.198i −0.138369 0.737125i
\(141\) −168.788 91.4457i −1.19708 0.648551i
\(142\) −34.6619 34.6619i −0.244098 0.244098i
\(143\) 23.1518 23.1518i 0.161901 0.161901i
\(144\) −37.6955 + 24.5774i −0.261774 + 0.170676i
\(145\) 52.8882 + 23.2273i 0.364746 + 0.160188i
\(146\) −36.8203 −0.252194
\(147\) 12.2106 146.492i 0.0830654 0.996544i
\(148\) 124.479 124.479i 0.841071 0.841071i
\(149\) 24.7386 0.166031 0.0830155 0.996548i \(-0.473545\pi\)
0.0830155 + 0.996548i \(0.473545\pi\)
\(150\) −72.7301 + 18.3119i −0.484868 + 0.122079i
\(151\) −116.676 −0.772690 −0.386345 0.922354i \(-0.626263\pi\)
−0.386345 + 0.922354i \(0.626263\pi\)
\(152\) −82.0634 82.0634i −0.539891 0.539891i
\(153\) −7.24185 1.52554i −0.0473323 0.00997082i
\(154\) −17.8128 3.35238i −0.115667 0.0217687i
\(155\) 61.9863 141.142i 0.399912 0.910593i
\(156\) −54.2107 + 100.061i −0.347505 + 0.641414i
\(157\) −142.879 + 142.879i −0.910055 + 0.910055i −0.996276 0.0862209i \(-0.972521\pi\)
0.0862209 + 0.996276i \(0.472521\pi\)
\(158\) 53.6004 + 53.6004i 0.339243 + 0.339243i
\(159\) −127.429 69.0380i −0.801437 0.434202i
\(160\) 153.740 59.9096i 0.960872 0.374435i
\(161\) 257.922 + 48.5412i 1.60200 + 0.301498i
\(162\) 29.3028 + 75.5139i 0.180881 + 0.466135i
\(163\) 97.1548 97.1548i 0.596041 0.596041i −0.343215 0.939257i \(-0.611516\pi\)
0.939257 + 0.343215i \(0.111516\pi\)
\(164\) 51.4468i 0.313700i
\(165\) 4.83966 38.5377i 0.0293312 0.233562i
\(166\) 75.9128i 0.457306i
\(167\) 207.245 + 207.245i 1.24099 + 1.24099i 0.959592 + 0.281396i \(0.0907974\pi\)
0.281396 + 0.959592i \(0.409203\pi\)
\(168\) 146.223 15.0943i 0.870375 0.0898473i
\(169\) 9.11189i 0.0539165i
\(170\) 3.76450 + 1.65328i 0.0221441 + 0.00972520i
\(171\) 124.993 81.4952i 0.730954 0.476580i
\(172\) −75.4643 75.4643i −0.438746 0.438746i
\(173\) −115.444 + 115.444i −0.667307 + 0.667307i −0.957092 0.289785i \(-0.906416\pi\)
0.289785 + 0.957092i \(0.406416\pi\)
\(174\) −16.5098 + 30.4734i −0.0948840 + 0.175134i
\(175\) −170.461 39.5999i −0.974061 0.226285i
\(176\) 12.9468i 0.0735613i
\(177\) 40.7010 + 136.947i 0.229949 + 0.773710i
\(178\) −9.93722 9.93722i −0.0558271 0.0558271i
\(179\) −236.871 −1.32330 −0.661650 0.749813i \(-0.730143\pi\)
−0.661650 + 0.749813i \(0.730143\pi\)
\(180\) 22.0356 + 133.189i 0.122420 + 0.739941i
\(181\) 227.866i 1.25893i 0.777030 + 0.629463i \(0.216725\pi\)
−0.777030 + 0.629463i \(0.783275\pi\)
\(182\) 73.0841 49.9323i 0.401561 0.274353i
\(183\) 67.5128 + 227.160i 0.368923 + 1.24131i
\(184\) 262.450i 1.42636i
\(185\) −106.530 273.376i −0.575837 1.47771i
\(186\) 81.3238 + 44.0595i 0.437225 + 0.236879i
\(187\) −1.50561 + 1.50561i −0.00805138 + 0.00805138i
\(188\) 135.742 135.742i 0.722032 0.722032i
\(189\) −19.7627 + 187.964i −0.104565 + 0.994518i
\(190\) −77.2393 + 30.0988i −0.406523 + 0.158415i
\(191\) 370.941i 1.94210i −0.238872 0.971051i \(-0.576778\pi\)
0.238872 0.971051i \(-0.423222\pi\)
\(192\) 11.1106 + 37.3839i 0.0578678 + 0.194708i
\(193\) 81.6333 81.6333i 0.422971 0.422971i −0.463255 0.886225i \(-0.653318\pi\)
0.886225 + 0.463255i \(0.153318\pi\)
\(194\) 36.7220i 0.189289i
\(195\) 116.360 + 149.783i 0.596720 + 0.768120i
\(196\) 136.943 + 53.4383i 0.698688 + 0.272645i
\(197\) −182.194 + 182.194i −0.924845 + 0.924845i −0.997367 0.0725218i \(-0.976895\pi\)
0.0725218 + 0.997367i \(0.476895\pi\)
\(198\) 22.8037 + 4.80374i 0.115170 + 0.0242613i
\(199\) 31.2360 0.156965 0.0784824 0.996915i \(-0.474993\pi\)
0.0784824 + 0.996915i \(0.474993\pi\)
\(200\) 7.38926 174.844i 0.0369463 0.874220i
\(201\) 270.370 + 146.481i 1.34512 + 0.728760i
\(202\) −16.7531 + 16.7531i −0.0829360 + 0.0829360i
\(203\) −66.7731 + 45.6205i −0.328931 + 0.224731i
\(204\) 3.52543 6.50714i 0.0172815 0.0318978i
\(205\) 78.5071 + 34.4786i 0.382962 + 0.168188i
\(206\) 111.231 0.539954
\(207\) −330.189 69.5562i −1.59512 0.336020i
\(208\) −44.7057 44.7057i −0.214931 0.214931i
\(209\) 42.9298i 0.205406i
\(210\) 32.1265 99.9644i 0.152983 0.476021i
\(211\) −96.5905 −0.457775 −0.228887 0.973453i \(-0.573509\pi\)
−0.228887 + 0.973453i \(0.573509\pi\)
\(212\) 102.480 102.480i 0.483396 0.483396i
\(213\) 41.8950 + 140.964i 0.196690 + 0.661803i
\(214\) 176.590i 0.825189i
\(215\) −165.732 + 64.5829i −0.770847 + 0.300386i
\(216\) −188.376 + 15.3429i −0.872112 + 0.0710320i
\(217\) 121.747 + 178.196i 0.561044 + 0.821181i
\(218\) −51.6087 51.6087i −0.236737 0.236737i
\(219\) 97.1228 + 52.6190i 0.443483 + 0.240270i
\(220\) 35.5619 + 15.6180i 0.161645 + 0.0709909i
\(221\) 10.3978i 0.0470491i
\(222\) 168.744 50.1514i 0.760110 0.225907i
\(223\) −79.9490 79.9490i −0.358516 0.358516i 0.504750 0.863266i \(-0.331585\pi\)
−0.863266 + 0.504750i \(0.831585\pi\)
\(224\) −42.7244 + 227.015i −0.190734 + 1.01346i
\(225\) 218.013 + 55.6347i 0.968948 + 0.247265i
\(226\) −73.2952 −0.324315
\(227\) −56.7824 56.7824i −0.250143 0.250143i 0.570886 0.821029i \(-0.306600\pi\)
−0.821029 + 0.570886i \(0.806600\pi\)
\(228\) 42.5092 + 143.031i 0.186444 + 0.627327i
\(229\) 153.812 0.671668 0.335834 0.941921i \(-0.390982\pi\)
0.335834 + 0.941921i \(0.390982\pi\)
\(230\) 171.641 + 75.3808i 0.746265 + 0.327743i
\(231\) 42.1949 + 34.2986i 0.182662 + 0.148479i
\(232\) −57.1833 57.1833i −0.246480 0.246480i
\(233\) −50.2938 50.2938i −0.215853 0.215853i 0.590895 0.806748i \(-0.298775\pi\)
−0.806748 + 0.590895i \(0.798775\pi\)
\(234\) −95.3296 + 62.1547i −0.407392 + 0.265618i
\(235\) −116.169 298.112i −0.494336 1.26856i
\(236\) −142.867 −0.605368
\(237\) −64.7854 217.984i −0.273356 0.919762i
\(238\) −4.75280 + 3.24720i −0.0199698 + 0.0136437i
\(239\) 131.741 0.551216 0.275608 0.961270i \(-0.411121\pi\)
0.275608 + 0.961270i \(0.411121\pi\)
\(240\) −74.4155 9.34529i −0.310065 0.0389387i
\(241\) 103.031i 0.427516i −0.976887 0.213758i \(-0.931430\pi\)
0.976887 0.213758i \(-0.0685704\pi\)
\(242\) −80.8189 + 80.8189i −0.333963 + 0.333963i
\(243\) 30.6217 241.063i 0.126015 0.992028i
\(244\) −236.981 −0.971232
\(245\) 173.322 173.160i 0.707439 0.706775i
\(246\) −24.5071 + 45.2346i −0.0996225 + 0.183881i
\(247\) 148.238 + 148.238i 0.600154 + 0.600154i
\(248\) −152.604 + 152.604i −0.615340 + 0.615340i
\(249\) 108.485 200.239i 0.435684 0.804174i
\(250\) −112.225 55.0512i −0.448899 0.220205i
\(251\) −363.395 −1.44779 −0.723895 0.689910i \(-0.757650\pi\)
−0.723895 + 0.689910i \(0.757650\pi\)
\(252\) −174.545 72.4924i −0.692638 0.287668i
\(253\) −68.6476 + 68.6476i −0.271334 + 0.271334i
\(254\) −30.6144 −0.120529
\(255\) −7.56715 9.74072i −0.0296751 0.0381989i
\(256\) −171.000 −0.667969
\(257\) 86.9159 + 86.9159i 0.338194 + 0.338194i 0.855687 0.517493i \(-0.173135\pi\)
−0.517493 + 0.855687i \(0.673135\pi\)
\(258\) −30.4039 102.300i −0.117845 0.396512i
\(259\) 403.672 + 75.9714i 1.55858 + 0.293326i
\(260\) −176.726 + 68.8671i −0.679716 + 0.264874i
\(261\) 87.0976 56.7874i 0.333707 0.217576i
\(262\) 153.910 153.910i 0.587444 0.587444i
\(263\) −97.6009 97.6009i −0.371106 0.371106i 0.496774 0.867880i \(-0.334518\pi\)
−0.867880 + 0.496774i \(0.834518\pi\)
\(264\) −25.9027 + 47.8106i −0.0981164 + 0.181101i
\(265\) −87.7032 225.063i −0.330955 0.849295i
\(266\) 21.4649 114.053i 0.0806951 0.428770i
\(267\) 12.0109 + 40.4130i 0.0449845 + 0.151359i
\(268\) −217.436 + 217.436i −0.811327 + 0.811327i
\(269\) 119.813i 0.445403i 0.974887 + 0.222701i \(0.0714875\pi\)
−0.974887 + 0.222701i \(0.928512\pi\)
\(270\) −44.0712 + 127.604i −0.163227 + 0.472607i
\(271\) 246.646i 0.910132i −0.890458 0.455066i \(-0.849616\pi\)
0.890458 0.455066i \(-0.150384\pi\)
\(272\) 2.90730 + 2.90730i 0.0106886 + 0.0106886i
\(273\) −264.135 + 27.2662i −0.967527 + 0.0998761i
\(274\) 45.4929i 0.166032i
\(275\) 47.6657 43.8002i 0.173330 0.159273i
\(276\) 160.741 296.691i 0.582393 1.07497i
\(277\) 51.1833 + 51.1833i 0.184777 + 0.184777i 0.793434 0.608656i \(-0.208291\pi\)
−0.608656 + 0.793434i \(0.708291\pi\)
\(278\) −79.5985 + 79.5985i −0.286325 + 0.286325i
\(279\) −151.548 232.436i −0.543182 0.833104i
\(280\) 202.229 + 138.306i 0.722246 + 0.493949i
\(281\) 6.33365i 0.0225397i −0.999936 0.0112698i \(-0.996413\pi\)
0.999936 0.0112698i \(-0.00358738\pi\)
\(282\) 184.013 54.6893i 0.652529 0.193934i
\(283\) 242.152 + 242.152i 0.855661 + 0.855661i 0.990823 0.135163i \(-0.0431558\pi\)
−0.135163 + 0.990823i \(0.543156\pi\)
\(284\) −147.058 −0.517810
\(285\) 246.752 + 30.9877i 0.865795 + 0.108729i
\(286\) 32.7416i 0.114481i
\(287\) −99.1178 + 67.7190i −0.345358 + 0.235955i
\(288\) 61.2211 290.622i 0.212573 1.00910i
\(289\) 288.324i 0.997660i
\(290\) −53.8218 + 20.9734i −0.185592 + 0.0723221i
\(291\) −52.4786 + 96.8635i −0.180339 + 0.332864i
\(292\) −78.1076 + 78.1076i −0.267492 + 0.267492i
\(293\) 333.360 333.360i 1.13775 1.13775i 0.148895 0.988853i \(-0.452428\pi\)
0.988853 0.148895i \(-0.0475717\pi\)
\(294\) 94.9513 + 112.220i 0.322963 + 0.381700i
\(295\) −95.7464 + 218.013i −0.324564 + 0.739027i
\(296\) 410.758i 1.38770i
\(297\) −53.2857 45.2594i −0.179413 0.152388i
\(298\) −17.4929 + 17.4929i −0.0587009 + 0.0587009i
\(299\) 474.085i 1.58557i
\(300\) −115.439 + 193.129i −0.384795 + 0.643765i
\(301\) 46.0572 244.723i 0.153014 0.813034i
\(302\) 82.5025 82.5025i 0.273187 0.273187i
\(303\) 68.1319 20.2490i 0.224858 0.0668285i
\(304\) −82.8966 −0.272686
\(305\) −158.820 + 361.630i −0.520720 + 1.18567i
\(306\) 6.19947 4.04204i 0.0202597 0.0132093i
\(307\) 115.748 115.748i 0.377030 0.377030i −0.492999 0.870030i \(-0.664099\pi\)
0.870030 + 0.492999i \(0.164099\pi\)
\(308\) −44.8981 + 30.6751i −0.145773 + 0.0995946i
\(309\) −293.399 158.957i −0.949511 0.514424i
\(310\) 55.9714 + 143.633i 0.180553 + 0.463333i
\(311\) 87.4973 0.281342 0.140671 0.990056i \(-0.455074\pi\)
0.140671 + 0.990056i \(0.455074\pi\)
\(312\) −75.6486 254.535i −0.242463 0.815817i
\(313\) 74.9574 + 74.9574i 0.239481 + 0.239481i 0.816635 0.577154i \(-0.195837\pi\)
−0.577154 + 0.816635i \(0.695837\pi\)
\(314\) 202.061i 0.643506i
\(315\) −227.599 + 217.770i −0.722535 + 0.691334i
\(316\) 227.407 0.719643
\(317\) 393.091 393.091i 1.24003 1.24003i 0.280048 0.959986i \(-0.409650\pi\)
0.959986 0.280048i \(-0.0903503\pi\)
\(318\) 138.923 41.2883i 0.436864 0.129838i
\(319\) 29.9143i 0.0937751i
\(320\) −26.1370 + 59.5135i −0.0816781 + 0.185980i
\(321\) −252.361 + 465.802i −0.786173 + 1.45110i
\(322\) −216.702 + 148.055i −0.672988 + 0.459797i
\(323\) −9.64022 9.64022i −0.0298459 0.0298459i
\(324\) 222.350 + 98.0286i 0.686265 + 0.302557i
\(325\) −13.3478 + 315.835i −0.0410703 + 0.971801i
\(326\) 137.398i 0.421465i
\(327\) 62.3781 + 209.884i 0.190759 + 0.641846i
\(328\) −84.8829 84.8829i −0.258789 0.258789i
\(329\) 440.198 + 82.8456i 1.33799 + 0.251810i
\(330\) 23.8281 + 30.6724i 0.0722063 + 0.0929466i
\(331\) 244.986 0.740138 0.370069 0.929004i \(-0.379334\pi\)
0.370069 + 0.929004i \(0.379334\pi\)
\(332\) 161.035 + 161.035i 0.485047 + 0.485047i
\(333\) −516.776 108.862i −1.55188 0.326912i
\(334\) −293.089 −0.877511
\(335\) 186.083 + 477.525i 0.555472 + 1.42545i
\(336\) 66.2300 81.4776i 0.197113 0.242493i
\(337\) −333.576 333.576i −0.989840 0.989840i 0.0101086 0.999949i \(-0.496782\pi\)
−0.999949 + 0.0101086i \(0.996782\pi\)
\(338\) 6.44308 + 6.44308i 0.0190624 + 0.0190624i
\(339\) 193.335 + 104.745i 0.570309 + 0.308981i
\(340\) 11.4929 4.47857i 0.0338025 0.0131723i
\(341\) −79.8317 −0.234111
\(342\) −30.7577 + 146.009i −0.0899348 + 0.426928i
\(343\) 77.3019 + 334.176i 0.225370 + 0.974273i
\(344\) 249.019 0.723894
\(345\) −345.021 444.124i −1.00006 1.28732i
\(346\) 163.263i 0.471857i
\(347\) 226.173 226.173i 0.651796 0.651796i −0.301629 0.953425i \(-0.597531\pi\)
0.953425 + 0.301629i \(0.0975305\pi\)
\(348\) 29.6212 + 99.6664i 0.0851183 + 0.286398i
\(349\) −247.335 −0.708696 −0.354348 0.935114i \(-0.615297\pi\)
−0.354348 + 0.935114i \(0.615297\pi\)
\(350\) 148.535 92.5326i 0.424386 0.264379i
\(351\) 340.280 27.7152i 0.969458 0.0789607i
\(352\) −60.4214 60.4214i −0.171652 0.171652i
\(353\) −276.422 + 276.422i −0.783065 + 0.783065i −0.980347 0.197281i \(-0.936789\pi\)
0.197281 + 0.980347i \(0.436789\pi\)
\(354\) −125.616 68.0559i −0.354847 0.192248i
\(355\) −98.5552 + 224.409i −0.277620 + 0.632137i
\(356\) −42.1600 −0.118427
\(357\) 17.1772 1.77317i 0.0481154 0.00496687i
\(358\) 167.493 167.493i 0.467857 0.467857i
\(359\) −392.633 −1.09368 −0.546842 0.837236i \(-0.684170\pi\)
−0.546842 + 0.837236i \(0.684170\pi\)
\(360\) −256.108 183.394i −0.711412 0.509429i
\(361\) −86.1262 −0.238577
\(362\) −161.125 161.125i −0.445098 0.445098i
\(363\) 328.677 97.6838i 0.905446 0.269101i
\(364\) 49.1124 260.957i 0.134924 0.716915i
\(365\) 66.8451 + 171.537i 0.183137 + 0.469965i
\(366\) −208.365 112.888i −0.569305 0.308437i
\(367\) −232.458 + 232.458i −0.633401 + 0.633401i −0.948919 0.315519i \(-0.897821\pi\)
0.315519 + 0.948919i \(0.397821\pi\)
\(368\) 132.557 + 132.557i 0.360210 + 0.360210i
\(369\) 129.288 84.2951i 0.350373 0.228442i
\(370\) 268.634 + 117.978i 0.726037 + 0.318859i
\(371\) 332.332 + 62.5453i 0.895774 + 0.168586i
\(372\) 265.978 79.0496i 0.714995 0.212499i
\(373\) −194.536 + 194.536i −0.521543 + 0.521543i −0.918037 0.396494i \(-0.870227\pi\)
0.396494 + 0.918037i \(0.370227\pi\)
\(374\) 2.12925i 0.00569319i
\(375\) 217.348 + 305.589i 0.579596 + 0.814904i
\(376\) 447.926i 1.19129i
\(377\) 103.295 + 103.295i 0.273992 + 0.273992i
\(378\) −118.936 146.885i −0.314646 0.388584i
\(379\) 345.209i 0.910843i 0.890276 + 0.455422i \(0.150511\pi\)
−0.890276 + 0.455422i \(0.849489\pi\)
\(380\) −100.000 + 227.698i −0.263158 + 0.599207i
\(381\) 80.7531 + 43.7503i 0.211950 + 0.114830i
\(382\) 262.295 + 262.295i 0.686637 + 0.686637i
\(383\) 46.7051 46.7051i 0.121945 0.121945i −0.643500 0.765446i \(-0.722518\pi\)
0.765446 + 0.643500i \(0.222518\pi\)
\(384\) 313.893 + 170.060i 0.817428 + 0.442865i
\(385\) 16.7201 + 89.0718i 0.0434288 + 0.231355i
\(386\) 115.447i 0.299085i
\(387\) −65.9967 + 313.292i −0.170534 + 0.809540i
\(388\) −77.8991 77.8991i −0.200771 0.200771i
\(389\) 747.341 1.92119 0.960593 0.277960i \(-0.0896582\pi\)
0.960593 + 0.277960i \(0.0896582\pi\)
\(390\) −188.192 23.6336i −0.482544 0.0605991i
\(391\) 30.8307i 0.0788509i
\(392\) −314.113 + 137.775i −0.801309 + 0.351468i
\(393\) −625.927 + 186.028i −1.59269 + 0.473353i
\(394\) 257.662i 0.653964i
\(395\) 152.404 347.020i 0.385832 0.878533i
\(396\) 58.5643 38.1838i 0.147890 0.0964237i
\(397\) 320.867 320.867i 0.808230 0.808230i −0.176135 0.984366i \(-0.556360\pi\)
0.984366 + 0.176135i \(0.0563597\pi\)
\(398\) −22.0872 + 22.0872i −0.0554954 + 0.0554954i
\(399\) −219.610 + 270.168i −0.550400 + 0.677114i
\(400\) −84.5774 92.0417i −0.211443 0.230104i
\(401\) 472.603i 1.17856i 0.807928 + 0.589281i \(0.200589\pi\)
−0.807928 + 0.589281i \(0.799411\pi\)
\(402\) −294.758 + 87.6030i −0.733229 + 0.217918i
\(403\) 275.662 275.662i 0.684025 0.684025i
\(404\) 71.0773i 0.175934i
\(405\) 298.605 273.606i 0.737295 0.675571i
\(406\) 14.9571 79.4742i 0.0368402 0.195749i
\(407\) −107.440 + 107.440i −0.263980 + 0.263980i
\(408\) 4.91958 + 16.5529i 0.0120578 + 0.0405708i
\(409\) 121.806 0.297813 0.148907 0.988851i \(-0.452425\pi\)
0.148907 + 0.988851i \(0.452425\pi\)
\(410\) −79.8930 + 31.1329i −0.194861 + 0.0759339i
\(411\) −65.0128 + 119.999i −0.158182 + 0.291968i
\(412\) 235.956 235.956i 0.572708 0.572708i
\(413\) −188.054 275.249i −0.455338 0.666462i
\(414\) 282.663 184.295i 0.682760 0.445158i
\(415\) 353.661 137.815i 0.852194 0.332085i
\(416\) 417.275 1.00306
\(417\) 323.713 96.2087i 0.776291 0.230716i
\(418\) 30.3559 + 30.3559i 0.0726219 + 0.0726219i
\(419\) 91.1169i 0.217463i 0.994071 + 0.108731i \(0.0346788\pi\)
−0.994071 + 0.108731i \(0.965321\pi\)
\(420\) −143.906 280.207i −0.342633 0.667160i
\(421\) 61.3238 0.145662 0.0728311 0.997344i \(-0.476797\pi\)
0.0728311 + 0.997344i \(0.476797\pi\)
\(422\) 68.2998 68.2998i 0.161848 0.161848i
\(423\) −563.536 118.712i −1.33224 0.280643i
\(424\) 338.167i 0.797563i
\(425\) 0.868036 20.5394i 0.00204244 0.0483280i
\(426\) −129.301 70.0524i −0.303523 0.164442i
\(427\) −311.936 456.569i −0.730528 1.06925i
\(428\) −374.605 374.605i −0.875245 0.875245i
\(429\) 46.7903 86.3643i 0.109068 0.201315i
\(430\) 71.5233 162.857i 0.166333 0.378738i
\(431\) 179.188i 0.415749i −0.978156 0.207874i \(-0.933346\pi\)
0.978156 0.207874i \(-0.0666545\pi\)
\(432\) −87.3950 + 102.894i −0.202303 + 0.238180i
\(433\) −234.230 234.230i −0.540947 0.540947i 0.382860 0.923806i \(-0.374939\pi\)
−0.923806 + 0.382860i \(0.874939\pi\)
\(434\) −212.092 39.9159i −0.488690 0.0919721i
\(435\) 171.941 + 21.5928i 0.395267 + 0.0496386i
\(436\) −218.957 −0.502195
\(437\) −439.542 439.542i −1.00582 1.00582i
\(438\) −105.883 + 31.4689i −0.241743 + 0.0718468i
\(439\) −526.311 −1.19889 −0.599443 0.800417i \(-0.704611\pi\)
−0.599443 + 0.800417i \(0.704611\pi\)
\(440\) −84.4426 + 32.9058i −0.191915 + 0.0747859i
\(441\) −90.0873 431.700i −0.204280 0.978913i
\(442\) 7.35238 + 7.35238i 0.0166344 + 0.0166344i
\(443\) 207.809 + 207.809i 0.469094 + 0.469094i 0.901621 0.432527i \(-0.142378\pi\)
−0.432527 + 0.901621i \(0.642378\pi\)
\(444\) 251.574 464.348i 0.566608 1.04583i
\(445\) −28.2548 + 64.3357i −0.0634939 + 0.144575i
\(446\) 113.065 0.253509
\(447\) 71.1405 21.1432i 0.159151 0.0473002i
\(448\) −51.3354 75.1377i −0.114588 0.167718i
\(449\) 315.151 0.701895 0.350947 0.936395i \(-0.385860\pi\)
0.350947 + 0.936395i \(0.385860\pi\)
\(450\) −193.498 + 114.819i −0.429996 + 0.255153i
\(451\) 44.4047i 0.0984583i
\(452\) −155.483 + 155.483i −0.343988 + 0.343988i
\(453\) −335.524 + 99.7188i −0.740670 + 0.220130i
\(454\) 80.3024 0.176878
\(455\) −365.303 249.833i −0.802864 0.549083i
\(456\) −306.125 165.852i −0.671327 0.363710i
\(457\) −357.774 357.774i −0.782875 0.782875i 0.197440 0.980315i \(-0.436737\pi\)
−0.980315 + 0.197440i \(0.936737\pi\)
\(458\) −108.761 + 108.761i −0.237470 + 0.237470i
\(459\) −22.1291 + 1.80237i −0.0482115 + 0.00392674i
\(460\) 524.012 204.198i 1.13916 0.443910i
\(461\) −563.655 −1.22268 −0.611339 0.791369i \(-0.709369\pi\)
−0.611339 + 0.791369i \(0.709369\pi\)
\(462\) −54.0891 + 5.58352i −0.117076 + 0.0120855i
\(463\) −26.9857 + 26.9857i −0.0582845 + 0.0582845i −0.735648 0.677364i \(-0.763122\pi\)
0.677364 + 0.735648i \(0.263122\pi\)
\(464\) −57.7639 −0.124491
\(465\) 57.6244 458.857i 0.123923 0.986788i
\(466\) 71.1262 0.152631
\(467\) 271.529 + 271.529i 0.581432 + 0.581432i 0.935297 0.353864i \(-0.115133\pi\)
−0.353864 + 0.935297i \(0.615133\pi\)
\(468\) −70.3747 + 334.075i −0.150373 + 0.713835i
\(469\) −705.122 132.705i −1.50346 0.282953i
\(470\) 292.941 + 128.653i 0.623278 + 0.273730i
\(471\) −288.761 + 532.987i −0.613080 + 1.13161i
\(472\) 235.718 235.718i 0.499403 0.499403i
\(473\) 65.1347 + 65.1347i 0.137705 + 0.137705i
\(474\) 199.948 + 108.327i 0.421831 + 0.228539i
\(475\) 280.447 + 305.198i 0.590415 + 0.642521i
\(476\) −3.19388 + 16.9706i −0.00670983 + 0.0356524i
\(477\) −425.448 89.6231i −0.891925 0.187889i
\(478\) −93.1548 + 93.1548i −0.194884 + 0.194884i
\(479\) 517.973i 1.08136i 0.841227 + 0.540682i \(0.181834\pi\)
−0.841227 + 0.540682i \(0.818166\pi\)
\(480\) 390.904 303.676i 0.814382 0.632659i
\(481\) 741.987i 1.54259i
\(482\) 72.8542 + 72.8542i 0.151150 + 0.151150i
\(483\) 783.188 80.8471i 1.62151 0.167385i
\(484\) 342.886i 0.708442i
\(485\) −171.079 + 66.6667i −0.352741 + 0.137457i
\(486\) 148.804 + 192.110i 0.306182 + 0.395288i
\(487\) 369.310 + 369.310i 0.758336 + 0.758336i 0.976019 0.217684i \(-0.0698501\pi\)
−0.217684 + 0.976019i \(0.569850\pi\)
\(488\) 390.998 390.998i 0.801226 0.801226i
\(489\) 196.352 362.421i 0.401537 0.741147i
\(490\) −0.115057 + 245.000i −0.000234810 + 0.500000i
\(491\) 421.951i 0.859370i −0.902979 0.429685i \(-0.858625\pi\)
0.902979 0.429685i \(-0.141375\pi\)
\(492\) 43.9696 + 147.945i 0.0893692 + 0.300700i
\(493\) −6.71748 6.71748i −0.0136257 0.0136257i
\(494\) −209.640 −0.424373
\(495\) −19.0194 114.958i −0.0384230 0.232239i
\(496\) 154.154i 0.310794i
\(497\) −193.571 283.323i −0.389479 0.570067i
\(498\) 64.8798 + 218.301i 0.130281 + 0.438356i
\(499\) 109.267i 0.218971i −0.993988 0.109486i \(-0.965080\pi\)
0.993988 0.109486i \(-0.0349204\pi\)
\(500\) −354.846 + 121.283i −0.709691 + 0.242567i
\(501\) 773.095 + 418.846i 1.54310 + 0.836021i
\(502\) 256.959 256.959i 0.511871 0.511871i
\(503\) −134.096 + 134.096i −0.266592 + 0.266592i −0.827725 0.561133i \(-0.810365\pi\)
0.561133 + 0.827725i \(0.310365\pi\)
\(504\) 407.590 168.378i 0.808711 0.334083i
\(505\) 108.463 + 47.6345i 0.214778 + 0.0943258i
\(506\) 97.0824i 0.191862i
\(507\) −7.78759 26.2029i −0.0153601 0.0516823i
\(508\) −64.9428 + 64.9428i −0.127840 + 0.127840i
\(509\) 459.197i 0.902154i 0.892485 + 0.451077i \(0.148960\pi\)
−0.892485 + 0.451077i \(0.851040\pi\)
\(510\) 12.2385 + 1.53694i 0.0239971 + 0.00301361i
\(511\) −253.295 47.6704i −0.495685 0.0932885i
\(512\) −215.668 + 215.668i −0.421226 + 0.421226i
\(513\) 289.790 341.181i 0.564893 0.665071i
\(514\) −122.918 −0.239139
\(515\) −201.933 518.198i −0.392103 1.00621i
\(516\) −281.508 152.515i −0.545558 0.295571i
\(517\) −117.161 + 117.161i −0.226618 + 0.226618i
\(518\) −339.159 + 231.719i −0.654747 + 0.447334i
\(519\) −233.315 + 430.646i −0.449547 + 0.829762i
\(520\) 177.958 405.208i 0.342228 0.779247i
\(521\) 303.734 0.582983 0.291491 0.956573i \(-0.405848\pi\)
0.291491 + 0.956573i \(0.405848\pi\)
\(522\) −21.4325 + 101.742i −0.0410585 + 0.194908i
\(523\) 249.060 + 249.060i 0.476215 + 0.476215i 0.903919 0.427704i \(-0.140677\pi\)
−0.427704 + 0.903919i \(0.640677\pi\)
\(524\) 652.986i 1.24616i
\(525\) −524.035 + 31.8097i −0.998163 + 0.0605899i
\(526\) 138.029 0.262412
\(527\) −17.9268 + 17.9268i −0.0340168 + 0.0340168i
\(528\) 11.0651 + 37.2308i 0.0209567 + 0.0705130i
\(529\) 876.714i 1.65730i
\(530\) 221.159 + 97.1281i 0.417281 + 0.183261i
\(531\) 234.086 + 359.029i 0.440840 + 0.676138i
\(532\) −196.409 287.477i −0.369190 0.540370i
\(533\) 153.331 + 153.331i 0.287675 + 0.287675i
\(534\) −37.0692 20.0833i −0.0694181 0.0376092i
\(535\) −822.695 + 320.590i −1.53775 + 0.599234i
\(536\) 717.501i 1.33862i
\(537\) −681.165 + 202.444i −1.26846 + 0.376992i
\(538\) −84.7209 84.7209i −0.157474 0.157474i
\(539\) −118.198 46.1237i −0.219291 0.0855726i
\(540\) 177.199 + 364.178i 0.328147 + 0.674403i
\(541\) −198.562 −0.367028 −0.183514 0.983017i \(-0.558747\pi\)
−0.183514 + 0.983017i \(0.558747\pi\)
\(542\) 174.405 + 174.405i 0.321780 + 0.321780i
\(543\) 194.748 + 655.270i 0.358653 + 1.20676i
\(544\) −27.1362 −0.0498827
\(545\) −146.741 + 334.126i −0.269249 + 0.613075i
\(546\) 167.491 206.052i 0.306761 0.377384i
\(547\) 492.112 + 492.112i 0.899656 + 0.899656i 0.995405 0.0957494i \(-0.0305247\pi\)
−0.0957494 + 0.995405i \(0.530525\pi\)
\(548\) −96.5049 96.5049i −0.176104 0.176104i
\(549\) 388.291 + 595.541i 0.707270 + 1.08477i
\(550\) −2.73335 + 64.6762i −0.00496972 + 0.117593i
\(551\) 191.537 0.347617
\(552\) 224.306 + 754.723i 0.406352 + 1.36725i
\(553\) 299.334 + 438.125i 0.541291 + 0.792269i
\(554\) −72.3842 −0.130657
\(555\) −539.990 695.095i −0.972955 1.25242i
\(556\) 337.708i 0.607388i
\(557\) 328.316 328.316i 0.589437 0.589437i −0.348042 0.937479i \(-0.613153\pi\)
0.937479 + 0.348042i \(0.113153\pi\)
\(558\) 271.517 + 57.1967i 0.486590 + 0.102503i
\(559\) −449.825 −0.804695
\(560\) 171.996 32.2862i 0.307136 0.0576539i
\(561\) −3.04287 + 5.61644i −0.00542400 + 0.0100115i
\(562\) 4.47857 + 4.47857i 0.00796898 + 0.00796898i
\(563\) 510.844 510.844i 0.907361 0.907361i −0.0886978 0.996059i \(-0.528271\pi\)
0.996059 + 0.0886978i \(0.0282706\pi\)
\(564\) 274.337 506.364i 0.486414 0.897809i
\(565\) 133.063 + 341.466i 0.235510 + 0.604364i
\(566\) −342.455 −0.605043
\(567\) 103.814 + 557.415i 0.183094 + 0.983095i
\(568\) 242.633 242.633i 0.427171 0.427171i
\(569\) −789.111 −1.38684 −0.693419 0.720534i \(-0.743897\pi\)
−0.693419 + 0.720534i \(0.743897\pi\)
\(570\) −196.391 + 152.568i −0.344546 + 0.267663i
\(571\) −320.476 −0.561254 −0.280627 0.959817i \(-0.590542\pi\)
−0.280627 + 0.959817i \(0.590542\pi\)
\(572\) 69.4554 + 69.4554i 0.121426 + 0.121426i
\(573\) −317.030 1066.71i −0.553280 1.86162i
\(574\) 22.2023 117.971i 0.0386800 0.205525i
\(575\) 39.5778 936.485i 0.0688309 1.62867i
\(576\) 63.9012 + 98.0084i 0.110940 + 0.170153i
\(577\) 313.311 313.311i 0.542999 0.542999i −0.381408 0.924407i \(-0.624561\pi\)
0.924407 + 0.381408i \(0.124561\pi\)
\(578\) 203.876 + 203.876i 0.352726 + 0.352726i
\(579\) 164.983 304.520i 0.284944 0.525942i
\(580\) −69.6819 + 158.665i −0.120141 + 0.273560i
\(581\) −98.2827 + 522.222i −0.169161 + 0.898833i
\(582\) −31.3849 105.601i −0.0539260 0.181445i
\(583\) −88.4524 + 88.4524i −0.151719 + 0.151719i
\(584\) 257.742i 0.441339i
\(585\) 462.630 + 331.281i 0.790820 + 0.566292i
\(586\) 471.443i 0.804510i
\(587\) −149.545 149.545i −0.254762 0.254762i 0.568158 0.822920i \(-0.307656\pi\)
−0.822920 + 0.568158i \(0.807656\pi\)
\(588\) 439.476 + 36.6318i 0.747408 + 0.0622991i
\(589\) 511.152i 0.867831i
\(590\) −86.4556 221.861i −0.146535 0.376036i
\(591\) −368.219 + 679.648i −0.623044 + 1.15000i
\(592\) 207.464 + 207.464i 0.350446 + 0.350446i
\(593\) 198.048 198.048i 0.333977 0.333977i −0.520118 0.854095i \(-0.674112\pi\)
0.854095 + 0.520118i \(0.174112\pi\)
\(594\) 69.6819 5.67547i 0.117310 0.00955466i
\(595\) 23.7564 + 16.2471i 0.0399267 + 0.0273061i
\(596\) 74.2159i 0.124523i
\(597\) 89.8248 26.6962i 0.150460 0.0447173i
\(598\) 335.229 + 335.229i 0.560584 + 0.560584i
\(599\) −475.156 −0.793248 −0.396624 0.917981i \(-0.629818\pi\)
−0.396624 + 0.917981i \(0.629818\pi\)
\(600\) −128.183 509.111i −0.213639 0.848518i
\(601\) 373.965i 0.622237i −0.950371 0.311119i \(-0.899296\pi\)
0.950371 0.311119i \(-0.100704\pi\)
\(602\) 140.478 + 205.613i 0.233352 + 0.341549i
\(603\) 902.690 + 190.157i 1.49700 + 0.315351i
\(604\) 350.029i 0.579518i
\(605\) 523.239 + 229.795i 0.864858 + 0.379826i
\(606\) −33.8583 + 62.4948i −0.0558718 + 0.103127i
\(607\) −632.018 + 632.018i −1.04122 + 1.04122i −0.0421025 + 0.999113i \(0.513406\pi\)
−0.999113 + 0.0421025i \(0.986594\pi\)
\(608\) 386.871 386.871i 0.636300 0.636300i
\(609\) −153.028 + 188.258i −0.251278 + 0.309127i
\(610\) −143.408 368.013i −0.235096 0.603300i
\(611\) 809.125i 1.32426i
\(612\) 4.57661 21.7255i 0.00747812 0.0354992i
\(613\) 587.183 587.183i 0.957885 0.957885i −0.0412636 0.999148i \(-0.513138\pi\)
0.999148 + 0.0412636i \(0.0131383\pi\)
\(614\) 163.693i 0.266601i
\(615\) 255.229 + 32.0523i 0.415007 + 0.0521176i
\(616\) 23.4667 124.689i 0.0380953 0.202418i
\(617\) −111.144 + 111.144i −0.180136 + 0.180136i −0.791415 0.611279i \(-0.790655\pi\)
0.611279 + 0.791415i \(0.290655\pi\)
\(618\) 319.864 95.0646i 0.517579 0.153826i
\(619\) 716.455 1.15744 0.578720 0.815526i \(-0.303552\pi\)
0.578720 + 0.815526i \(0.303552\pi\)
\(620\) 423.426 + 185.959i 0.682945 + 0.299934i
\(621\) −1008.97 + 82.1785i −1.62474 + 0.132333i
\(622\) −61.8700 + 61.8700i −0.0994694 + 0.0994694i
\(623\) −55.4949 81.2259i −0.0890769 0.130379i
\(624\) −166.768 90.3512i −0.267256 0.144794i
\(625\) −52.7333 + 622.771i −0.0843734 + 0.996434i
\(626\) −106.006 −0.169338
\(627\) −36.6905 123.452i −0.0585175 0.196894i
\(628\) −428.636 428.636i −0.682541 0.682541i
\(629\) 48.2529i 0.0767137i
\(630\) 6.94979 314.923i 0.0110314 0.499878i
\(631\) 4.81666 0.00763338 0.00381669 0.999993i \(-0.498785\pi\)
0.00381669 + 0.999993i \(0.498785\pi\)
\(632\) −375.203 + 375.203i −0.593675 + 0.593675i
\(633\) −277.764 + 82.5522i −0.438805 + 0.130414i
\(634\) 555.914i 0.876836i
\(635\) 55.5786 + 142.625i 0.0875254 + 0.224607i
\(636\) 207.114 382.286i 0.325651 0.601078i
\(637\) 567.409 248.875i 0.890751 0.390699i
\(638\) 21.1526 + 21.1526i 0.0331545 + 0.0331545i
\(639\) 240.953 + 369.562i 0.377079 + 0.578344i
\(640\) 216.038 + 554.394i 0.337559 + 0.866241i
\(641\) 121.164i 0.189024i 0.995524 + 0.0945120i \(0.0301291\pi\)
−0.995524 + 0.0945120i \(0.969871\pi\)
\(642\) −150.925 507.818i −0.235086 0.790994i
\(643\) 524.336 + 524.336i 0.815453 + 0.815453i 0.985445 0.169993i \(-0.0543744\pi\)
−0.169993 + 0.985445i \(0.554374\pi\)
\(644\) −145.624 + 773.766i −0.226124 + 1.20150i
\(645\) −421.396 + 327.365i −0.653328 + 0.507543i
\(646\) 13.6333 0.0211042
\(647\) −305.897 305.897i −0.472792 0.472792i 0.430025 0.902817i \(-0.358505\pi\)
−0.902817 + 0.430025i \(0.858505\pi\)
\(648\) −528.597 + 205.119i −0.815736 + 0.316542i
\(649\) 123.311 0.190002
\(650\) −213.891 232.768i −0.329063 0.358104i
\(651\) 502.402 + 408.384i 0.771739 + 0.627317i
\(652\) 291.464 + 291.464i 0.447031 + 0.447031i
\(653\) 307.322 + 307.322i 0.470631 + 0.470631i 0.902119 0.431488i \(-0.142011\pi\)
−0.431488 + 0.902119i \(0.642011\pi\)
\(654\) −192.518 104.302i −0.294370 0.159484i
\(655\) −996.449 437.618i −1.52130 0.668119i
\(656\) −85.7446 −0.130708
\(657\) 324.266 + 68.3085i 0.493555 + 0.103970i
\(658\) −369.847 + 252.686i −0.562078 + 0.384021i
\(659\) −903.538 −1.37107 −0.685537 0.728038i \(-0.740432\pi\)
−0.685537 + 0.728038i \(0.740432\pi\)
\(660\) 115.613 + 14.5190i 0.175171 + 0.0219984i
\(661\) 1162.10i 1.75809i −0.476737 0.879046i \(-0.658180\pi\)
0.476737 0.879046i \(-0.341820\pi\)
\(662\) −173.231 + 173.231i −0.261678 + 0.261678i
\(663\) −8.88664 29.9009i −0.0134037 0.0450994i
\(664\) −531.390 −0.800286
\(665\) −570.315 + 107.057i −0.857617 + 0.160987i
\(666\) 442.393 288.439i 0.664254 0.433092i
\(667\) −306.281 306.281i −0.459192 0.459192i
\(668\) −621.735 + 621.735i −0.930741 + 0.930741i
\(669\) −298.237 161.579i −0.445796 0.241523i
\(670\) −469.242 206.080i −0.700361 0.307583i
\(671\) 204.543 0.304832
\(672\) 71.1590 + 689.337i 0.105891 + 1.02580i
\(673\) 256.857 256.857i 0.381660 0.381660i −0.490040 0.871700i \(-0.663018\pi\)
0.871700 + 0.490040i \(0.163018\pi\)
\(674\) 471.748 0.699923
\(675\) 674.486 26.3399i 0.999238 0.0390221i
\(676\) 27.3357 0.0404374
\(677\) 248.270 + 248.270i 0.366721 + 0.366721i 0.866280 0.499559i \(-0.166504\pi\)
−0.499559 + 0.866280i \(0.666504\pi\)
\(678\) −210.774 + 62.6427i −0.310876 + 0.0923933i
\(679\) 47.5432 252.619i 0.0700194 0.372046i
\(680\) −11.5730 + 26.3515i −0.0170191 + 0.0387522i
\(681\) −211.818 114.758i −0.311039 0.168514i
\(682\) 56.4496 56.4496i 0.0827706 0.0827706i
\(683\) 216.136 + 216.136i 0.316450 + 0.316450i 0.847402 0.530952i \(-0.178165\pi\)
−0.530952 + 0.847402i \(0.678165\pi\)
\(684\) 244.486 + 374.980i 0.357435 + 0.548216i
\(685\) −211.941 + 82.5897i −0.309403 + 0.120569i
\(686\) −290.959 181.637i −0.424138 0.264777i
\(687\) 442.314 131.457i 0.643835 0.191350i
\(688\) 125.774 125.774i 0.182811 0.182811i
\(689\) 610.859i 0.886587i
\(690\) 558.010 + 70.0763i 0.808710 + 0.101560i
\(691\) 167.027i 0.241717i −0.992670 0.120859i \(-0.961435\pi\)
0.992670 0.120859i \(-0.0385648\pi\)
\(692\) −346.332 346.332i −0.500480 0.500480i
\(693\) 150.653 + 62.5695i 0.217392 + 0.0902879i
\(694\) 319.857i 0.460889i
\(695\) 515.338 + 226.325i 0.741493 + 0.325647i
\(696\) −213.314 115.569i −0.306485 0.166047i
\(697\) −9.97142 9.97142i −0.0143062 0.0143062i
\(698\) 174.892 174.892i 0.250562 0.250562i
\(699\) −187.613 101.645i −0.268402 0.145415i
\(700\) 118.800 511.382i 0.169714 0.730546i
\(701\) 602.095i 0.858908i 0.903089 + 0.429454i \(0.141294\pi\)
−0.903089 + 0.429454i \(0.858706\pi\)
\(702\) −221.017 + 260.212i −0.314838 + 0.370672i
\(703\) −687.923 687.923i −0.978554 0.978554i
\(704\) 33.6616 0.0478148
\(705\) −588.850 757.990i −0.835249 1.07516i
\(706\) 390.920i 0.553711i
\(707\) −136.938 + 93.5584i −0.193689 + 0.132332i
\(708\) −410.840 + 122.103i −0.580282 + 0.172462i
\(709\) 37.8334i 0.0533616i −0.999644 0.0266808i \(-0.991506\pi\)
0.999644 0.0266808i \(-0.00849377\pi\)
\(710\) −88.9918 228.370i −0.125341 0.321648i
\(711\) −372.605 571.482i −0.524057 0.803772i
\(712\) 69.5605 69.5605i 0.0976973 0.0976973i
\(713\) −817.367 + 817.367i −1.14638 + 1.14638i
\(714\) −10.8923 + 13.3999i −0.0152553 + 0.0187674i
\(715\) 152.536 59.4405i 0.213337 0.0831336i
\(716\) 710.612i 0.992475i
\(717\) 378.845 112.594i 0.528375 0.157035i
\(718\) 277.633 277.633i 0.386676 0.386676i
\(719\) 408.265i 0.567824i 0.958850 + 0.283912i \(0.0916324\pi\)
−0.958850 + 0.283912i \(0.908368\pi\)
\(720\) −221.982 + 36.7260i −0.308309 + 0.0510084i
\(721\) 765.181 + 144.008i 1.06128 + 0.199734i
\(722\) 60.9004 60.9004i 0.0843496 0.0843496i
\(723\) −88.0571 296.286i −0.121794 0.409800i
\(724\) −683.597 −0.944195
\(725\) 195.421 + 212.667i 0.269546 + 0.293334i
\(726\) −163.337 + 301.483i −0.224982 + 0.415265i
\(727\) 660.880 660.880i 0.909051 0.909051i −0.0871447 0.996196i \(-0.527774\pi\)
0.996196 + 0.0871447i \(0.0277742\pi\)
\(728\) 349.526 + 511.589i 0.480118 + 0.702732i
\(729\) −117.969 719.392i −0.161823 0.986820i
\(730\) −168.562 74.0286i −0.230907 0.101409i
\(731\) 29.2530 0.0400178
\(732\) −681.481 + 202.538i −0.930985 + 0.276692i
\(733\) 526.757 + 526.757i 0.718632 + 0.718632i 0.968325 0.249693i \(-0.0803298\pi\)
−0.249693 + 0.968325i \(0.580330\pi\)
\(734\) 328.745i 0.447882i
\(735\) 350.427 646.085i 0.476772 0.879027i
\(736\) −1237.26 −1.68107
\(737\) 187.673 187.673i 0.254644 0.254644i
\(738\) −31.8144 + 151.026i −0.0431090 + 0.204642i
\(739\) 276.981i 0.374805i −0.982283 0.187402i \(-0.939993\pi\)
0.982283 0.187402i \(-0.0600069\pi\)
\(740\) 820.127 319.589i 1.10828 0.431877i
\(741\) 552.979 + 299.592i 0.746261 + 0.404308i
\(742\) −279.221 + 190.768i −0.376308 + 0.257100i
\(743\) 698.839 + 698.839i 0.940563 + 0.940563i 0.998330 0.0577666i \(-0.0183979\pi\)
−0.0577666 + 0.998330i \(0.518398\pi\)
\(744\) −308.416 + 569.267i −0.414538 + 0.765143i
\(745\) 113.253 + 49.7380i 0.152017 + 0.0667624i
\(746\) 275.115i 0.368787i
\(747\) 140.832 668.543i 0.188531 0.894971i
\(748\) −4.51683 4.51683i −0.00603854 0.00603854i
\(749\) 228.628 1214.81i 0.305244 1.62190i
\(750\) −369.773 62.3955i −0.493030 0.0831940i
\(751\) 488.791 0.650853 0.325426 0.945567i \(-0.394492\pi\)
0.325426 + 0.945567i \(0.394492\pi\)
\(752\) 226.237 + 226.237i 0.300846 + 0.300846i
\(753\) −1045.01 + 310.580i −1.38780 + 0.412457i
\(754\) −146.081 −0.193742
\(755\) −534.139 234.582i −0.707469 0.310704i
\(756\) −563.892 59.2882i −0.745889 0.0784236i
\(757\) −269.069 269.069i −0.355441 0.355441i 0.506688 0.862129i \(-0.330870\pi\)
−0.862129 + 0.506688i \(0.830870\pi\)
\(758\) −244.100 244.100i −0.322032 0.322032i
\(759\) −138.738 + 256.079i −0.182791 + 0.337390i
\(760\) −210.692 540.675i −0.277226 0.711414i
\(761\) 973.280 1.27895 0.639475 0.768812i \(-0.279152\pi\)
0.639475 + 0.768812i \(0.279152\pi\)
\(762\) −88.0372 + 26.1649i −0.115534 + 0.0343372i
\(763\) −288.211 421.845i −0.377734 0.552876i
\(764\) 1112.82 1.45658
\(765\) −30.0857 21.5439i −0.0393278 0.0281619i
\(766\) 66.0510i 0.0862285i
\(767\) −425.798 + 425.798i −0.555147 + 0.555147i
\(768\) −491.742 + 146.147i −0.640289 + 0.190296i
\(769\) 1055.77 1.37292 0.686458 0.727169i \(-0.259165\pi\)
0.686458 + 0.727169i \(0.259165\pi\)
\(770\) −74.8062 51.1604i −0.0971508 0.0664420i