Properties

Label 105.3.k.c.83.4
Level 105
Weight 3
Character 105.83
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 83.4
Root \(1.97320 + 0.817327i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.4

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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 0.507877 0.861430i \(-0.330431\pi\)
−0.861430 + 0.507877i \(0.830431\pi\)
\(3\) 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 \(0.0375515\pi\)
−0.993049 + 0.117698i \(0.962449\pi\)
\(12\) 2.56399 8.62705i 0.213666 0.718921i
\(13\) 8.94114 8.94114i 0.687780 0.687780i −0.273961 0.961741i \(-0.588334\pi\)
0.961741 + 0.273961i \(0.0883338\pi\)
\(14\) 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 −0.724002 0.689798i \(-0.757699\pi\)
0.689798 + 0.724002i \(0.257699\pi\)
\(18\) −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 −0.166657 + 0.986015i \(0.553297\pi\)
−0.986015 + 0.166657i \(0.946703\pi\)
\(24\) −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 \(0.165664\pi\)
−0.867596 + 0.497270i \(0.834336\pi\)
\(32\) 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 −0.129902 + 0.991527i \(0.541466\pi\)
−0.991527 + 0.129902i \(0.958534\pi\)
\(38\) −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 0.351277 0.936272i \(-0.385748\pi\)
−0.936272 + 0.351277i \(0.885748\pi\)
\(44\) 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 −0.999329 0.0366205i \(-0.988341\pi\)
0.0366205 + 0.999329i \(0.488341\pi\)
\(48\) −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 −0.951665 0.307137i \(-0.900629\pi\)
0.307137 + 0.951665i \(0.400629\pi\)
\(54\) 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 \(-0.867766\pi\)
0.914945 0.403579i \(-0.132234\pi\)
\(60\) −5.60717 44.6493i −0.0934529 0.744155i
\(61\) 78.9936i 1.29498i −0.762075 0.647488i \(-0.775819\pi\)
0.762075 0.647488i \(-0.224181\pi\)
\(62\) 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 0.0854251 0.996345i \(-0.472775\pi\)
0.996345 0.0854251i \(-0.0272248\pi\)
\(68\) 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 \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(72\) −61.6470 + 12.9863i −0.856209 + 0.180365i
\(73\) 26.0359 26.0359i 0.356656 0.356656i −0.505923 0.862579i \(-0.668848\pi\)
0.862579 + 0.505923i \(0.168848\pi\)
\(74\) 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 \(0.159277\pi\)
−0.877399 + 0.479762i \(0.840723\pi\)
\(80\) −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 0.952201 0.305472i \(-0.0988143\pi\)
−0.305472 + 0.952201i \(0.598814\pi\)
\(84\) −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 \(-0.974843\pi\)
0.996878 0.0789514i \(-0.0251572\pi\)
\(90\) −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 0.560476 0.828171i \(-0.310618\pi\)
−0.828171 + 0.560476i \(0.810618\pi\)
\(98\) 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 −0.976973 0.213362i \(-0.931559\pi\)
0.213362 + 0.976973i \(0.431559\pi\)
\(104\) 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 −0.982911 0.184083i \(-0.941069\pi\)
−0.184083 0.982911i \(-0.558931\pi\)
\(108\) 61.7362 52.4370i 0.571632 0.485528i
\(109\) 72.9857i 0.669594i −0.942290 0.334797i \(-0.891332\pi\)
0.942290 0.334797i \(-0.108668\pi\)
\(110\) 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 −0.439562 0.898212i \(-0.644866\pi\)
0.898212 + 0.439562i \(0.144866\pi\)
\(114\) −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 −0.616725 0.787179i \(-0.711541\pi\)
0.787179 + 0.616725i \(0.211541\pi\)
\(128\) 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 0.579890 0.814695i \(-0.303096\pi\)
−0.814695 + 0.579890i \(0.803096\pi\)
\(138\) 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 0.0862209 0.996276i \(-0.472521\pi\)
−0.996276 + 0.0862209i \(0.972521\pi\)
\(158\) 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 0.939257 0.343215i \(-0.111516\pi\)
−0.343215 + 0.939257i \(0.611516\pi\)
\(164\) 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 0.281396 0.959592i \(-0.409203\pi\)
0.959592 0.281396i \(-0.0907974\pi\)
\(168\) 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 0.289785 0.957092i \(-0.406416\pi\)
−0.957092 + 0.289785i \(0.906416\pi\)
\(174\) −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 \(-0.783275\pi\)
0.777030 0.629463i \(-0.216725\pi\)
\(182\) 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 \(0.423222\pi\)
−0.238872 + 0.971051i \(0.576778\pi\)
\(192\) 11.1106 37.3839i 0.0578678 0.194708i
\(193\) 81.6333 + 81.6333i 0.422971 + 0.422971i 0.886225 0.463255i \(-0.153318\pi\)
−0.463255 + 0.886225i \(0.653318\pi\)
\(194\) 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 0.0725218 0.997367i \(-0.476895\pi\)
−0.997367 + 0.0725218i \(0.976895\pi\)
\(198\) 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 −0.863266 0.504750i \(-0.831585\pi\)
0.504750 + 0.863266i \(0.331585\pi\)
\(224\) −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 −0.821029 0.570886i \(-0.806600\pi\)
0.570886 + 0.821029i \(0.306600\pi\)
\(228\) 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 −0.806748 0.590895i \(-0.798775\pi\)
0.590895 + 0.806748i \(0.298775\pi\)
\(234\) −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 \(0.0685704\pi\)
−0.976887 + 0.213758i \(0.931430\pi\)
\(242\) −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 −0.517493 0.855687i \(-0.673135\pi\)
0.855687 + 0.517493i \(0.173135\pi\)
\(258\) −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 −0.867880 0.496774i \(-0.834518\pi\)
0.496774 + 0.867880i \(0.334518\pi\)
\(264\) −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 \(-0.928512\pi\)
0.974887 0.222701i \(-0.0714875\pi\)
\(270\) −44.0712 127.604i −0.163227 0.472607i
\(271\) 246.646i 0.910132i 0.890458 + 0.455066i \(0.150384\pi\)
−0.890458 + 0.455066i \(0.849616\pi\)
\(272\) 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 −0.608656 0.793434i \(-0.708291\pi\)
0.793434 + 0.608656i \(0.208291\pi\)
\(278\) −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 \(0.00358738\pi\)
−0.999936 + 0.0112698i \(0.996413\pi\)
\(282\) 184.013 + 54.6893i 0.652529 + 0.193934i
\(283\) 242.152 242.152i 0.855661 0.855661i −0.135163 0.990823i \(-0.543156\pi\)
0.990823 + 0.135163i \(0.0431558\pi\)
\(284\) −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 0.988853 + 0.148895i \(0.0475717\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(294\) 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 0.870030 0.492999i \(-0.164099\pi\)
−0.492999 + 0.870030i \(0.664099\pi\)
\(308\) −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 −0.577154 0.816635i \(-0.695837\pi\)
0.816635 + 0.577154i \(0.195837\pi\)
\(314\) 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 0.959986 + 0.280048i \(0.0903503\pi\)
0.280048 + 0.959986i \(0.409650\pi\)
\(318\) 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 −0.999949 0.0101086i \(-0.996782\pi\)
0.0101086 + 0.999949i \(0.496782\pi\)
\(338\) 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 0.953425 0.301629i \(-0.0975305\pi\)
−0.301629 + 0.953425i \(0.597531\pi\)
\(348\) 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 0.197281 0.980347i \(-0.436789\pi\)
−0.980347 + 0.197281i \(0.936789\pi\)
\(354\) −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 0.315519 0.948919i \(-0.397821\pi\)
−0.948919 + 0.315519i \(0.897821\pi\)
\(368\) 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 0.396494 0.918037i \(-0.370227\pi\)
−0.918037 + 0.396494i \(0.870227\pi\)
\(374\) 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 \(-0.849489\pi\)
0.890276 0.455422i \(-0.150511\pi\)
\(380\) −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 0.765446 0.643500i \(-0.222518\pi\)
−0.643500 + 0.765446i \(0.722518\pi\)
\(384\) 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 0.984366 0.176135i \(-0.0563597\pi\)
−0.176135 + 0.984366i \(0.556360\pi\)
\(398\) −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 \(-0.799411\pi\)
0.807928 0.589281i \(-0.200589\pi\)
\(402\) −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 \(-0.965321\pi\)
0.994071 0.108731i \(-0.0346788\pi\)
\(420\) −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 \(0.0666545\pi\)
−0.978156 + 0.207874i \(0.933346\pi\)
\(432\) −87.3950 102.894i −0.202303 0.238180i
\(433\) −234.230 + 234.230i −0.540947 + 0.540947i −0.923806 0.382860i \(-0.874939\pi\)
0.382860 + 0.923806i \(0.374939\pi\)
\(434\) −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 −0.432527 0.901621i \(-0.642378\pi\)
0.901621 + 0.432527i \(0.142378\pi\)
\(444\) 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 −0.980315 0.197440i \(-0.936737\pi\)
0.197440 + 0.980315i \(0.436737\pi\)
\(458\) −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 0.677364 0.735648i \(-0.263122\pi\)
−0.735648 + 0.677364i \(0.763122\pi\)
\(464\) −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 −0.353864 0.935297i \(-0.615133\pi\)
0.935297 + 0.353864i \(0.115133\pi\)
\(468\) −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 \(-0.818166\pi\)
0.841227 0.540682i \(-0.181834\pi\)
\(480\) 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 −0.217684 0.976019i \(-0.569850\pi\)
0.976019 + 0.217684i \(0.0698501\pi\)
\(488\) 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 \(0.141375\pi\)
−0.902979 + 0.429685i \(0.858625\pi\)
\(492\) 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 \(0.0349204\pi\)
−0.993988 + 0.109486i \(0.965080\pi\)
\(500\) −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 0.561133 0.827725i \(-0.310365\pi\)
−0.827725 + 0.561133i \(0.810365\pi\)
\(504\) 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 \(-0.851040\pi\)
0.892485 0.451077i \(-0.148960\pi\)
\(510\) 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 −0.427704 0.903919i \(-0.640677\pi\)
0.903919 + 0.427704i \(0.140677\pi\)
\(524\) 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 −0.0957494 0.995405i \(-0.530525\pi\)
0.995405 + 0.0957494i \(0.0305247\pi\)
\(548\) −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 0.937479 0.348042i \(-0.113153\pi\)
−0.348042 + 0.937479i \(0.613153\pi\)
\(558\) 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 0.996059 0.0886978i \(-0.0282706\pi\)
−0.0886978 + 0.996059i \(0.528271\pi\)
\(564\) 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 0.924407 0.381408i \(-0.124561\pi\)
−0.381408 + 0.924407i \(0.624561\pi\)
\(578\) 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 −0.822920 0.568158i \(-0.807656\pi\)
0.568158 + 0.822920i \(0.307656\pi\)
\(588\) 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 0.854095 0.520118i \(-0.174112\pi\)
−0.520118 + 0.854095i \(0.674112\pi\)
\(594\) 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 \(0.100704\pi\)
−0.950371 + 0.311119i \(0.899296\pi\)
\(602\) 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 −0.999113 0.0421025i \(-0.986594\pi\)
−0.0421025 0.999113i \(-0.513406\pi\)
\(608\) 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 0.999148 0.0412636i \(-0.0131383\pi\)
−0.0412636 + 0.999148i \(0.513138\pi\)
\(614\) 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 0.611279 0.791415i \(-0.290655\pi\)
−0.791415 + 0.611279i \(0.790655\pi\)
\(618\) 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 \(-0.969871\pi\)
0.995524 0.0945120i \(-0.0301291\pi\)
\(642\) −150.925 + 507.818i −0.235086 + 0.790994i
\(643\) 524.336 524.336i 0.815453 0.815453i −0.169993 0.985445i \(-0.554374\pi\)
0.985445 + 0.169993i \(0.0543744\pi\)
\(644\) −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 −0.902817 0.430025i \(-0.858505\pi\)
0.430025 + 0.902817i \(0.358505\pi\)
\(648\) −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 −0.431488 0.902119i \(-0.642011\pi\)
0.902119 + 0.431488i \(0.142011\pi\)
\(654\) −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 \(0.341820\pi\)
−0.476737 + 0.879046i \(0.658180\pi\)
\(662\) −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 0.871700 0.490040i \(-0.163018\pi\)
−0.490040 + 0.871700i \(0.663018\pi\)
\(674\) 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 −0.499559 0.866280i \(-0.666504\pi\)
0.866280 + 0.499559i \(0.166504\pi\)
\(678\) −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 −0.530952 0.847402i \(-0.678165\pi\)
0.847402 + 0.530952i \(0.178165\pi\)
\(684\) 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 \(0.0385648\pi\)
−0.992670 + 0.120859i \(0.961435\pi\)
\(692\) −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 \(-0.858706\pi\)
0.903089 0.429454i \(-0.141294\pi\)
\(702\) −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 \(0.00849377\pi\)
−0.999644 + 0.0266808i \(0.991506\pi\)
\(710\) −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 \(-0.908368\pi\)
0.958850 0.283912i \(-0.0916324\pi\)
\(720\) −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 0.996196 0.0871447i \(-0.0277742\pi\)
−0.0871447 + 0.996196i \(0.527774\pi\)
\(728\) 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 −0.249693 0.968325i \(-0.580330\pi\)
0.968325 + 0.249693i \(0.0803298\pi\)
\(734\) 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 \(0.0600069\pi\)
−0.982283 + 0.187402i \(0.939993\pi\)
\(740\) 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 −0.0577666 0.998330i \(-0.518398\pi\)
0.998330 + 0.0577666i \(0.0183979\pi\)
\(744\) −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 −0.862129 0.506688i \(-0.830870\pi\)
0.506688 + 0.862129i \(0.330870\pi\)
\(758\) −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