Properties

Label 105.3.k.c.83.1
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 83.1
Root \(-1.97320 - 0.817327i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-2.87568 - 0.854662i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 + 2.63775i) q^{6} +(3.94887 + 5.77983i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(7.53910 + 4.91548i) q^{9} +O(q^{10})\) \(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} +(3.94887 + 5.77983i) 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} +(-6.41591 - 19.9959i) 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} +(17.3395 - 11.8466i) 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} +(-29.6984 - 18.5205i) 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} +(-9.60250 + 18.6760i) 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} +(1.36038 + 62.9853i) 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} +(7.90396 + 34.0959i) 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} +(-14.9660 + 10.2250i) 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} +(-59.9877 + 19.2477i) 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} +(44.8733 - 19.6822i) 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
\(7\) 3.94887 + 5.77983i 0.564125 + 0.825689i
\(8\) −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 −0.961741 0.273961i \(-0.911666\pi\)
0.273961 + 0.961741i \(0.411666\pi\)
\(14\) 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 \(-0.742301\pi\)
0.724002 + 0.689798i \(0.242301\pi\)
\(18\) −1.85519 8.80672i −0.103066 0.489262i
\(19\) −16.5793 −0.872596 −0.436298 0.899802i \(-0.643711\pi\)
−0.436298 + 0.899802i \(0.643711\pi\)
\(20\) 6.03161 + 13.7339i 0.301581 + 0.686694i
\(21\) −6.41591 19.9959i −0.305520 0.952186i
\(22\) 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
\(28\) 17.3395 11.8466i 0.619267 0.423094i
\(29\) 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
\(35\) −29.6984 18.5205i −0.848524 0.529156i
\(36\) 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 \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(42\) −9.60250 + 18.6760i −0.228631 + 0.444666i
\(43\) −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 −0.0366205 0.999329i \(-0.511659\pi\)
0.999329 + 0.0366205i \(0.0116593\pi\)
\(48\) 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 \(0.132234\pi\)
−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
\(63\) 1.36038 + 62.9853i 0.0215933 + 0.999767i
\(64\) 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
\(70\) 7.90396 + 34.0959i 0.112914 + 0.487084i
\(71\) 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 −0.862579 0.505923i \(-0.831152\pi\)
0.505923 + 0.862579i \(0.331152\pi\)
\(74\) 58.6798 0.792970
\(75\) −64.3765 + 38.4795i −0.858353 + 0.513060i
\(76\) 49.7380i 0.654447i
\(77\) −14.9660 + 10.2250i −0.194364 + 0.132793i
\(78\) −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 0.305472 0.952201i \(-0.401186\pi\)
−0.952201 + 0.305472i \(0.901186\pi\)
\(84\) −59.9877 + 19.2477i −0.714139 + 0.229140i
\(85\) −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 \(-0.189382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(98\) 44.8733 19.6822i 0.457891 0.200839i
\(99\) −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 \(-0.537420\pi\)
−0.117289 + 0.993098i \(0.537420\pi\)
\(102\) 2.36470 + 0.702797i 0.0231833 + 0.00689016i
\(103\) 78.6519 78.6519i 0.763611 0.763611i −0.213362 0.976973i \(-0.568441\pi\)
0.976973 + 0.213362i \(0.0684415\pi\)
\(104\) 88.5128i 0.851085i
\(105\) 69.5743 + 78.6411i 0.662612 + 0.748962i
\(106\) 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
\(112\) −19.7444 28.8991i −0.176289 0.258028i
\(113\) 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
\(126\) 43.5754 45.4993i 0.345837 0.361105i
\(127\) 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 \(-0.187900\pi\)
0.830771 + 0.556614i \(0.187900\pi\)
\(132\) −22.3385 6.63908i −0.169231 0.0502960i
\(133\) −65.4696 95.8256i −0.492253 0.720493i
\(134\) −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 \(-0.632702\pi\)
−0.404925 + 0.914350i \(0.632702\pi\)
\(140\) −55.5614 + 89.0951i −0.396867 + 0.636393i
\(141\) −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
\(147\) 90.2372 116.044i 0.613859 0.789416i
\(148\) 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 \(-0.0274791\pi\)
−0.0862209 + 0.996276i \(0.527479\pi\)
\(158\) 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 \(0.590797\pi\)
−0.959592 + 0.281396i \(0.909203\pi\)
\(168\) 130.732 + 67.2175i 0.778165 + 0.400104i
\(169\) 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 \(-0.0935837\pi\)
−0.289785 + 0.957092i \(0.593584\pi\)
\(174\) 16.5098 + 30.4734i 0.0948840 + 0.175134i
\(175\) 173.194 + 25.0763i 0.989680 + 0.143293i
\(176\) 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 \(0.783275\pi\)
\(182\) 49.9323 + 73.0841i 0.274353 + 0.401561i
\(183\) 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
\(189\) 49.9192 182.288i 0.264123 0.964489i
\(190\) −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 \(-0.525007\pi\)
−0.0784824 + 0.996915i \(0.525007\pi\)
\(200\) 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
\(203\) 45.6205 + 66.7731i 0.224731 + 0.328931i
\(204\) 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
\(210\) 6.41115 104.804i 0.0305293 0.499067i
\(211\) −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
\(217\) 178.196 121.747i 0.821181 0.561044i
\(218\) −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 \(-0.668415\pi\)
0.863266 + 0.504750i \(0.168415\pi\)
\(224\) −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 \(-0.693400\pi\)
0.821029 + 0.570886i \(0.193400\pi\)
\(228\) 42.5092 143.031i 0.186444 0.627327i
\(229\) −153.812 −0.671668 −0.335834 0.941921i \(-0.609018\pi\)
−0.335834 + 0.941921i \(0.609018\pi\)
\(230\) −171.641 + 75.3808i −0.746265 + 0.327743i
\(231\) 51.7765 16.6131i 0.224141 0.0719181i
\(232\) −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
\(238\) −3.24720 4.75280i −0.0136437 0.0199698i
\(239\) 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
\(245\) −10.2300 244.786i −0.0417551 0.999128i
\(246\) −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 \(-0.242350\pi\)
0.723895 + 0.689910i \(0.242350\pi\)
\(252\) 188.956 4.08114i 0.749825 0.0161950i
\(253\) −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 \(-0.826865\pi\)
0.517493 + 0.855687i \(0.326865\pi\)
\(258\) 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 \(0.0714875\pi\)
−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
\(273\) 236.152 + 121.421i 0.865025 + 0.444764i
\(274\) 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
\(280\) 238.671 55.3277i 0.852396 0.197599i
\(281\) 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 −0.990823 0.135163i \(-0.956844\pi\)
0.135163 + 0.990823i \(0.456844\pi\)
\(284\) −147.058 −0.517810
\(285\) −246.752 + 30.9877i −0.865795 + 0.108729i
\(286\) 32.7416i 0.114481i
\(287\) −67.7190 99.1178i −0.235955 0.345358i
\(288\) 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 \(-0.952428\pi\)
−0.148895 0.988853i \(-0.547572\pi\)
\(294\) −145.863 + 18.2483i −0.496132 + 0.0620689i
\(295\) −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 \(-0.335901\pi\)
−0.870030 + 0.492999i \(0.835901\pi\)
\(308\) 30.6751 + 44.8981i 0.0995946 + 0.145773i
\(309\) −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 \(-0.544926\pi\)
−0.140671 + 0.990056i \(0.544926\pi\)
\(312\) −75.6486 + 254.535i −0.242463 + 0.815817i
\(313\) −74.9574 + 74.9574i −0.239481 + 0.239481i −0.816635 0.577154i \(-0.804163\pi\)
0.577154 + 0.816635i \(0.304163\pi\)
\(314\) 202.061i 0.643506i
\(315\) −132.862 285.609i −0.421784 0.906696i
\(316\) 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
\(322\) 148.055 + 216.702i 0.459797 + 0.672988i
\(323\) −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
\(336\) 32.0796 + 99.9795i 0.0954749 + 0.297558i
\(337\) −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
\(343\) −334.176 + 77.3019i −0.974273 + 0.225370i
\(344\) 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 \(-0.384703\pi\)
0.354348 + 0.935114i \(0.384703\pi\)
\(350\) −104.735 140.198i −0.299243 0.400567i
\(351\) 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 \(-0.0632113\pi\)
−0.197281 + 0.980347i \(0.563211\pi\)
\(354\) −125.616 + 68.0559i −0.354847 + 0.192248i
\(355\) 98.5552 + 224.409i 0.277620 + 0.632137i
\(356\) 42.1600 0.118427
\(357\) −15.3574 7.89623i −0.0430180 0.0221183i
\(358\) 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 \(-0.102179\pi\)
−0.315519 + 0.948919i \(0.602179\pi\)
\(368\) 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
\(378\) −164.196 + 93.5992i −0.434380 + 0.247617i
\(379\) 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 0.643500 0.765446i \(-0.277482\pi\)
−0.765446 + 0.643500i \(0.777482\pi\)
\(384\) −313.893 + 170.060i −0.817428 + 0.442865i
\(385\) 47.9561 76.8996i 0.124561 0.199739i
\(386\) 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
\(392\) −137.775 314.113i −0.351468 0.801309i
\(393\) −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 \(-0.443640\pi\)
−0.984366 + 0.176135i \(0.943640\pi\)
\(398\) 22.0872 + 22.0872i 0.0554954 + 0.0554954i
\(399\) 106.371 + 331.518i 0.266595 + 0.830873i
\(400\) −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 \(-0.547575\pi\)
−0.148907 + 0.988851i \(0.547575\pi\)
\(410\) −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
\(413\) −275.249 + 188.054i −0.666462 + 0.455338i
\(414\) 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 \(0.965321\pi\)
\(420\) 235.923 208.723i 0.561722 0.496959i
\(421\) 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
\(427\) −456.569 + 311.936i −1.06925 + 0.730528i
\(428\) −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 −0.382860 0.923806i \(-0.625061\pi\)
0.923806 + 0.382860i \(0.125061\pi\)
\(434\) −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 \(-0.295389\pi\)
0.599443 + 0.800417i \(0.295389\pi\)
\(440\) 84.4426 + 32.9058i 0.191915 + 0.0747859i
\(441\) −358.672 + 256.584i −0.813316 + 0.581823i
\(442\) 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
\(448\) 75.1377 51.3354i 0.167718 0.114588i
\(449\) 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
\(455\) 431.131 99.9431i 0.947542 0.219655i
\(456\) −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 \(-0.290631\pi\)
0.611339 + 0.791369i \(0.290631\pi\)
\(462\) −48.3588 24.8643i −0.104673 0.0538189i
\(463\) −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 −0.935297 0.353864i \(-0.884867\pi\)
0.353864 + 0.935297i \(0.384867\pi\)
\(468\) 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
\(483\) 700.216 + 360.025i 1.44972 + 0.745394i
\(484\) 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
\(490\) −165.856 + 180.324i −0.338482 + 0.368008i
\(491\) 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
\(497\) 283.323 193.571i 0.570067 0.389479i
\(498\) 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 0.827725 0.561133i \(-0.189635\pi\)
−0.561133 + 0.827725i \(0.689635\pi\)
\(504\) −318.495 305.028i −0.631934 0.605214i
\(505\) 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
\(518\) 231.719 + 339.159i 0.447334 + 0.654747i
\(519\) −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 \(-0.594152\pi\)
−0.291491 + 0.956573i \(0.594152\pi\)
\(522\) −21.4325 101.742i −0.0410585 0.194908i
\(523\) −249.060 + 249.060i −0.476215 + 0.476215i −0.903919 0.427704i \(-0.859323\pi\)
0.427704 + 0.903919i \(0.359323\pi\)
\(524\) 652.986i 1.24616i
\(525\) −476.619 220.134i −0.907846 0.419303i
\(526\) 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
\(532\) −287.477 + 196.409i −0.540370 + 0.369190i
\(533\) 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
\(546\) −81.1272 252.842i −0.148585 0.463080i
\(547\) 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
\(553\) −438.125 + 299.334i −0.792269 + 0.541291i
\(554\) −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
\(560\) 148.492 + 92.6023i 0.265164 + 0.165361i
\(561\) −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 \(-0.471729\pi\)
−0.996059 + 0.0886978i \(0.971729\pi\)
\(564\) 274.337 + 506.364i 0.486414 + 0.897809i
\(565\) −133.063 + 341.466i −0.235510 + 0.604364i
\(566\) 342.455 0.605043
\(567\) −299.347 + 481.540i −0.527948 + 0.849276i
\(568\) 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 \(-0.375439\pi\)
−0.924407 + 0.381408i \(0.875439\pi\)
\(578\) 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 \(-0.692344\pi\)
0.822920 + 0.568158i \(0.192344\pi\)
\(588\) −348.132 270.712i −0.592062 0.460394i
\(589\) 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 \(-0.325888\pi\)
−0.854095 + 0.520118i \(0.825888\pi\)
\(594\) −69.6819 5.67547i −0.117310 0.00955466i
\(595\) −28.0373 + 6.49950i −0.0471216 + 0.0109235i
\(596\) 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 \(-0.100704\pi\)
\(602\) −205.613 + 140.478i −0.341549 + 0.233352i
\(603\) 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 \(0.0134056\pi\)
0.0421025 + 0.999113i \(0.486594\pi\)
\(608\) −386.871 386.871i −0.636300 0.636300i
\(609\) −74.1216 231.008i −0.121710 0.379324i
\(610\) −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 \(-0.696448\pi\)
−0.578720 + 0.815526i \(0.696448\pi\)
\(620\) 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
\(623\) −81.2259 + 55.4949i −0.130379 + 0.0890769i
\(624\) −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
\(630\) −108.009 + 295.904i −0.171442 + 0.469689i
\(631\) 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
\(637\) −248.875 567.409i −0.390699 0.890751i
\(638\) 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 −0.985445 0.169993i \(-0.945626\pi\)
0.169993 + 0.985445i \(0.445626\pi\)
\(644\) −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 \(-0.641495\pi\)
0.902817 + 0.430025i \(0.141495\pi\)
\(648\) −528.597 205.119i −0.815736 0.316542i
\(649\) −123.311 −0.190002
\(650\) 213.891 232.768i 0.329063 0.358104i
\(651\) −616.488 + 197.807i −0.946986 + 0.303851i
\(652\) 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
\(658\) −252.686 369.847i −0.384021 0.562078i
\(659\) −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
\(665\) 492.379 + 307.057i 0.740419 + 0.461739i
\(666\) 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
\(672\) 316.883 616.307i 0.471552 0.917124i
\(673\) 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 −0.866280 0.499559i \(-0.833496\pi\)
0.499559 + 0.866280i \(0.333496\pi\)
\(678\) 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 \(-0.961435\pi\)
0.992670 0.120859i \(-0.0385648\pi\)
\(692\) 346.332 346.332i 0.500480 0.500480i
\(693\) −163.091 + 3.52251i −0.235341 + 0.00508298i
\(694\) 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
\(700\) 75.2290 519.582i 0.107470 0.742260i
\(701\) 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
\(707\) −93.5584 136.938i −0.132332 0.193689i
\(708\) −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
\(714\) 5.27586 + 16.4428i 0.00738916 + 0.0230292i
\(715\) 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 \(-0.472226\pi\)
−0.996196 + 0.0871447i \(0.972226\pi\)
\(728\) 511.589 349.526i 0.702732 0.480118i
\(729\) −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 \(-0.919670\pi\)
0.249693 + 0.968325i \(0.419670\pi\)
\(734\) 328.745i 0.447882i
\(735\) −179.791 + 712.671i −0.244614 + 0.969620i
\(736\) −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
\(742\) 190.768 + 279.221i 0.257100 + 0.376308i
\(743\) 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
\(756\) −546.865 149.757i −0.723367 0.198092i
\(757\) −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 \(-0.720848\pi\)
−0.639475 + 0.768812i \(0.720848\pi\)
\(762\) 88.0372 + 26.1649i 0.115534 + 0.0343372i
\(763\) 421.845 288.211i 0.552876 0.377734i
\(764\) 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 \(-0.740835\pi\)
−0.686458 + 0.727169i \(0.740835\pi\)
\(770\) −88.2863 + 20.4662i −0.114658