Properties

Label 105.3.k.c.62.1
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 16
CM no
Inner twists 8

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 62.1
Root \(-1.97320 + 0.817327i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.1

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.353553 + 0.353553i −0.861430 0.507877i \(-0.830431\pi\)
0.507877 + 0.861430i \(0.330431\pi\)
\(3\) −2.87568 + 0.854662i −0.958561 + 0.284887i
\(4\) 3.00000i 0.750000i
\(5\) −4.57796 2.01054i −0.915592 0.402108i
\(6\) 1.42908 2.63775i 0.238180 0.439625i
\(7\) 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 \(-0.962449\pi\)
0.993049 0.117698i \(-0.0375515\pi\)
\(12\) −2.56399 8.62705i −0.213666 0.718921i
\(13\) −8.94114 8.94114i −0.687780 0.687780i 0.273961 0.961741i \(-0.411666\pi\)
−0.961741 + 0.273961i \(0.911666\pi\)
\(14\) 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 \(-0.242301\pi\)
−0.689798 + 0.724002i \(0.742301\pi\)
\(18\) −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 −0.986015 0.166657i \(-0.946703\pi\)
−0.166657 0.986015i \(-0.553297\pi\)
\(24\) 18.4643 + 10.0035i 0.769344 + 0.416814i
\(25\) 16.9155 + 18.4083i 0.676619 + 0.736333i
\(26\) 12.6447 0.486334
\(27\) −17.4790 + 20.5787i −0.647370 + 0.762176i
\(28\) 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 \(0.165664\pi\)
−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
\(35\) −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 −0.991527 0.129902i \(-0.958534\pi\)
−0.129902 0.991527i \(-0.541466\pi\)
\(38\) 11.7233 11.7233i 0.308509 0.308509i
\(39\) 33.3536 + 18.0702i 0.855219 + 0.463339i
\(40\) 12.7081 + 32.6114i 0.317703 + 0.815285i
\(41\) −17.1489 −0.418267 −0.209133 0.977887i \(-0.567064\pi\)
−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 −0.936272 0.351277i \(-0.885748\pi\)
0.351277 + 0.936272i \(0.385748\pi\)
\(44\) 7.76807 0.176547
\(45\) −44.3965 + 7.34521i −0.986589 + 0.163227i
\(46\) 37.4929 0.815062
\(47\) 45.2473 + 45.2473i 0.962709 + 0.962709i 0.999329 0.0366205i \(-0.0116593\pi\)
−0.0366205 + 0.999329i \(0.511659\pi\)
\(48\) 14.3784 4.27331i 0.299550 0.0890273i
\(49\) −17.8128 45.6476i −0.363526 0.931584i
\(50\) −24.9777 1.05561i −0.499554 0.0211122i
\(51\) −2.16905 1.17514i −0.0425304 0.0230420i
\(52\) 26.8234 26.8234i 0.515835 0.515835i
\(53\) −34.1600 34.1600i −0.644528 0.644528i 0.307137 0.951665i \(-0.400629\pi\)
−0.951665 + 0.307137i \(0.900629\pi\)
\(54\) −2.19185 26.9109i −0.0405897 0.498350i
\(55\) −5.20600 + 11.8540i −0.0946545 + 0.215527i
\(56\) −48.1546 + 9.06275i −0.859904 + 0.161835i
\(57\) 47.6769 14.1697i 0.836436 0.248592i
\(58\) −8.16905 + 8.16905i −0.140846 + 0.140846i
\(59\) 47.6223i 0.807158i −0.914945 0.403579i \(-0.867766\pi\)
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
\(63\) 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 0.996345 + 0.0854251i \(0.0272248\pi\)
0.0854251 + 0.996345i \(0.472775\pi\)
\(68\) −1.74438 + 1.74438i −0.0256527 + 0.0256527i
\(69\) 98.8969 + 53.5802i 1.43329 + 0.776524i
\(70\) 7.90396 34.0959i 0.112914 0.487084i
\(71\) 49.0193i 0.690413i 0.938527 + 0.345207i \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(72\) −61.6470 12.9863i −0.856209 0.180365i
\(73\) −26.0359 26.0359i −0.356656 0.356656i 0.505923 0.862579i \(-0.331152\pi\)
−0.862579 + 0.505923i \(0.831152\pi\)
\(74\) 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 \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(80\) 22.8898 + 10.0527i 0.286123 + 0.125659i
\(81\) 32.6762 74.1166i 0.403410 0.915019i
\(82\) 12.1261 12.1261i 0.147880 0.147880i
\(83\) −53.6785 + 53.6785i −0.646729 + 0.646729i −0.952201 0.305472i \(-0.901186\pi\)
0.305472 + 0.952201i \(0.401186\pi\)
\(84\) −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 \(-0.974843\pi\)
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 \(-0.689382\pi\)
0.828171 + 0.560476i \(0.189382\pi\)
\(98\) 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 0.976973 0.213362i \(-0.0684415\pi\)
−0.213362 + 0.976973i \(0.568441\pi\)
\(104\) 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 −0.184083 + 0.982911i \(0.558931\pi\)
−0.982911 + 0.184083i \(0.941069\pi\)
\(108\) −61.7362 52.4370i −0.571632 0.485528i
\(109\) 72.9857i 0.669594i 0.942290 + 0.334797i \(0.108668\pi\)
−0.942290 + 0.334797i \(0.891332\pi\)
\(110\) −4.70083 12.0632i −0.0427348 0.109666i
\(111\) 154.783 + 83.8579i 1.39444 + 0.755477i
\(112\) −19.7444 + 28.8991i −0.176289 + 0.258028i
\(113\) 51.8276 + 51.8276i 0.458651 + 0.458651i 0.898212 0.439562i \(-0.144866\pi\)
−0.439562 + 0.898212i \(0.644866\pi\)
\(114\) −23.6931 + 43.7321i −0.207834 + 0.383615i
\(115\) 68.0662 + 174.671i 0.591880 + 1.51888i
\(116\) 34.6583i 0.298779i
\(117\) −111.358 23.4582i −0.951779 0.200498i
\(118\) 33.6740 + 33.6740i 0.285373 + 0.285373i
\(119\) 5.65685 1.06463i 0.0475366 0.00894644i
\(120\) −64.4162 82.9189i −0.536802 0.690991i
\(121\) 114.295 0.944589
\(122\) 55.8569 + 55.8569i 0.457843 + 0.457843i
\(123\) 49.3149 14.6565i 0.400934 0.119159i
\(124\) −92.4922 −0.745905
\(125\) −40.4278 118.282i −0.323422 0.946255i
\(126\) 43.5754 + 45.4993i 0.345837 + 0.361105i
\(127\) 21.6476 + 21.6476i 0.170454 + 0.170454i 0.787179 0.616725i \(-0.211541\pi\)
−0.616725 + 0.787179i \(0.711541\pi\)
\(128\) 84.1457 + 84.1457i 0.657388 + 0.657388i
\(129\) 50.8383 93.8359i 0.394095 0.727410i
\(130\) −57.8869 25.4226i −0.445284 0.195559i
\(131\) 217.662 1.66154 0.830771 0.556614i \(-0.187900\pi\)
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 −0.814695 0.579890i \(-0.803096\pi\)
0.579890 + 0.814695i \(0.303096\pi\)
\(138\) −107.818 + 32.0437i −0.781287 + 0.232201i
\(139\) −112.569 −0.809851 −0.404925 0.914350i \(-0.632702\pi\)
−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 −0.0862209 0.996276i \(-0.527479\pi\)
0.996276 + 0.0862209i \(0.0274791\pi\)
\(158\) 53.6004 + 53.6004i 0.339243 + 0.339243i
\(159\) 127.429 + 69.0380i 0.801437 + 0.434202i
\(160\) −153.740 + 59.9096i −0.960872 + 0.374435i
\(161\) −257.922 + 48.5412i −1.60200 + 0.301498i
\(162\) 29.3028 + 75.5139i 0.180881 + 0.466135i
\(163\) 97.1548 97.1548i 0.596041 0.596041i −0.343215 0.939257i \(-0.611516\pi\)
0.939257 + 0.343215i \(0.111516\pi\)
\(164\) 51.4468i 0.313700i
\(165\) 4.83966 38.5377i 0.0293312 0.233562i
\(166\) 75.9128i 0.457306i
\(167\) −207.245 207.245i −1.24099 1.24099i −0.959592 0.281396i \(-0.909203\pi\)
−0.281396 0.959592i \(-0.590797\pi\)
\(168\) 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 −0.289785 0.957092i \(-0.593584\pi\)
0.957092 + 0.289785i \(0.0935837\pi\)
\(174\) 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 \(-0.783275\pi\)
0.777030 0.629463i \(-0.216725\pi\)
\(182\) 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 \(-0.576778\pi\)
0.238872 0.971051i \(-0.423222\pi\)
\(192\) −11.1106 37.3839i −0.0578678 0.194708i
\(193\) 81.6333 81.6333i 0.422971 0.422971i −0.463255 0.886225i \(-0.653318\pi\)
0.886225 + 0.463255i \(0.153318\pi\)
\(194\) 36.7220i 0.189289i
\(195\) −116.360 149.783i −0.596720 0.768120i
\(196\) 136.943 53.4383i 0.698688 0.272645i
\(197\) −182.194 + 182.194i −0.924845 + 0.924845i −0.997367 0.0725218i \(-0.976895\pi\)
0.0725218 + 0.997367i \(0.476895\pi\)
\(198\) 22.8037 + 4.80374i 0.115170 + 0.0242613i
\(199\) −31.2360 −0.156965 −0.0784824 0.996915i \(-0.525007\pi\)
−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 0.863266 0.504750i \(-0.168415\pi\)
−0.504750 + 0.863266i \(0.668415\pi\)
\(224\) −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 \(-0.193400\pi\)
−0.570886 + 0.821029i \(0.693400\pi\)
\(228\) 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 0.590895 0.806748i \(-0.298775\pi\)
−0.806748 + 0.590895i \(0.798775\pi\)
\(234\) 95.3296 62.1547i 0.407392 0.265618i
\(235\) −116.169 298.112i −0.494336 1.26856i
\(236\) 142.867 0.605368
\(237\) 64.7854 + 217.984i 0.273356 + 0.919762i
\(238\) −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 \(0.0685704\pi\)
−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
\(245\) −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 0.517493 0.855687i \(-0.326865\pi\)
−0.855687 + 0.517493i \(0.826865\pi\)
\(258\) 30.4039 + 102.300i 0.117845 + 0.396512i
\(259\) −403.672 + 75.9714i −1.55858 + 0.293326i
\(260\) −176.726 + 68.8671i −0.679716 + 0.264874i
\(261\) 87.0976 56.7874i 0.333707 0.217576i
\(262\) −153.910 + 153.910i −0.587444 + 0.587444i
\(263\) −97.6009 97.6009i −0.371106 0.371106i 0.496774 0.867880i \(-0.334518\pi\)
−0.867880 + 0.496774i \(0.834518\pi\)
\(264\) 25.9027 47.8106i 0.0981164 0.181101i
\(265\) 87.7032 + 225.063i 0.330955 + 0.849295i
\(266\) −21.4649 114.053i −0.0806951 0.428770i
\(267\) 12.0109 + 40.4130i 0.0449845 + 0.151359i
\(268\) −217.436 + 217.436i −0.811327 + 0.811327i
\(269\) 119.813i 0.445403i −0.974887 0.222701i \(-0.928512\pi\)
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
\(273\) 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 0.793434 0.608656i \(-0.208291\pi\)
−0.608656 + 0.793434i \(0.708291\pi\)
\(278\) 79.5985 79.5985i 0.286325 0.286325i
\(279\) 151.548 + 232.436i 0.543182 + 0.833104i
\(280\) 238.671 + 55.3277i 0.852396 + 0.197599i
\(281\) 6.33365i 0.0225397i −0.999936 0.0112698i \(-0.996413\pi\)
0.999936 0.0112698i \(-0.00358738\pi\)
\(282\) 184.013 54.6893i 0.652529 0.193934i
\(283\) −242.152 242.152i −0.855661 0.855661i 0.135163 0.990823i \(-0.456844\pi\)
−0.990823 + 0.135163i \(0.956844\pi\)
\(284\) −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 −0.148895 + 0.988853i \(0.547572\pi\)
−0.988853 + 0.148895i \(0.952428\pi\)
\(294\) −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 −0.870030 0.492999i \(-0.835901\pi\)
0.492999 + 0.870030i \(0.335901\pi\)
\(308\) 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 0.577154 0.816635i \(-0.304163\pi\)
−0.816635 + 0.577154i \(0.804163\pi\)
\(314\) 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 0.280048 0.959986i \(-0.409650\pi\)
0.959986 0.280048i \(-0.0903503\pi\)
\(318\) −138.923 + 41.2883i −0.436864 + 0.129838i
\(319\) 29.9143i 0.0937751i
\(320\) 26.1370 59.5135i 0.0816781 0.185980i
\(321\) 252.361 465.802i 0.786173 1.45110i
\(322\) 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 0.0101086 0.999949i \(-0.496782\pi\)
−0.999949 + 0.0101086i \(0.996782\pi\)
\(338\) 6.44308 + 6.44308i 0.0190624 + 0.0190624i
\(339\) −193.335 104.745i −0.570309 0.308981i
\(340\) 11.4929 4.47857i 0.0338025 0.0131723i
\(341\) 79.8317 0.234111
\(342\) 30.7577 146.009i 0.0899348 0.426928i
\(343\) −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 −0.301629 0.953425i \(-0.597531\pi\)
0.953425 + 0.301629i \(0.0975305\pi\)
\(348\) −29.6212 99.6664i −0.0851183 0.286398i
\(349\) 247.335 0.708696 0.354348 0.935114i \(-0.384703\pi\)
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 −0.197281 0.980347i \(-0.563211\pi\)
0.980347 + 0.197281i \(0.0632113\pi\)
\(354\) −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 −0.315519 0.948919i \(-0.602179\pi\)
0.948919 + 0.315519i \(0.102179\pi\)
\(368\) 132.557 + 132.557i 0.360210 + 0.360210i
\(369\) −129.288 + 84.2951i −0.350373 + 0.228442i
\(370\) −268.634 117.978i −0.726037 0.318859i
\(371\) −332.332 + 62.5453i −0.895774 + 0.168586i
\(372\) 265.978 79.0496i 0.714995 0.212499i
\(373\) −194.536 + 194.536i −0.521543 + 0.521543i −0.918037 0.396494i \(-0.870227\pi\)
0.396494 + 0.918037i \(0.370227\pi\)
\(374\) 2.12925i 0.00569319i
\(375\) 217.348 + 305.589i 0.579596 + 0.814904i
\(376\) 447.926i 1.19129i
\(377\) −103.295 103.295i −0.273992 0.273992i
\(378\) −164.196 93.5992i −0.434380 0.247617i
\(379\) 345.209i 0.910843i 0.890276 + 0.455422i \(0.150511\pi\)
−0.890276 + 0.455422i \(0.849489\pi\)
\(380\) −100.000 + 227.698i −0.263158 + 0.599207i
\(381\) −80.7531 43.7503i −0.211950 0.114830i
\(382\) 262.295 + 262.295i 0.686637 + 0.686637i
\(383\) −46.7051 + 46.7051i −0.121945 + 0.121945i −0.765446 0.643500i \(-0.777482\pi\)
0.643500 + 0.765446i \(0.277482\pi\)
\(384\) −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 −0.984366 0.176135i \(-0.943640\pi\)
0.176135 + 0.984366i \(0.443640\pi\)
\(398\) 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 \(0.200589\pi\)
−0.807928 + 0.589281i \(0.799411\pi\)
\(402\) 294.758 87.6030i 0.733229 0.217918i
\(403\) 275.662 275.662i 0.684025 0.684025i
\(404\) 71.0773i 0.175934i
\(405\) −298.605 + 273.606i −0.737295 + 0.675571i
\(406\) 14.9571 + 79.4742i 0.0368402 + 0.195749i
\(407\) −107.440 + 107.440i −0.263980 + 0.263980i
\(408\) 4.91958 + 16.5529i 0.0120578 + 0.0405708i
\(409\) −121.806 −0.297813 −0.148907 0.988851i \(-0.547575\pi\)
−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 \(-0.965321\pi\)
0.994071 0.108731i \(-0.0346788\pi\)
\(420\) 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 \(-0.933346\pi\)
0.978156 0.207874i \(-0.0666545\pi\)
\(432\) 87.3950 102.894i 0.202303 0.238180i
\(433\) 234.230 + 234.230i 0.540947 + 0.540947i 0.923806 0.382860i \(-0.125061\pi\)
−0.382860 + 0.923806i \(0.625061\pi\)
\(434\) −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 0.901621 0.432527i \(-0.142378\pi\)
−0.432527 + 0.901621i \(0.642378\pi\)
\(444\) −251.574 + 464.348i −0.566608 + 1.04583i
\(445\) −28.2548 + 64.3357i −0.0634939 + 0.144575i
\(446\) −113.065 −0.253509
\(447\) −71.1405 + 21.1432i −0.159151 + 0.0473002i
\(448\) 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 0.197440 0.980315i \(-0.436737\pi\)
−0.980315 + 0.197440i \(0.936737\pi\)
\(458\) 108.761 108.761i 0.237470 0.237470i
\(459\) −22.1291 + 1.80237i −0.0482115 + 0.00392674i
\(460\) −524.012 + 204.198i −1.13916 + 0.443910i
\(461\) 563.655 1.22268 0.611339 0.791369i \(-0.290631\pi\)
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 −0.735648 0.677364i \(-0.763122\pi\)
0.677364 + 0.735648i \(0.263122\pi\)
\(464\) −57.7639 −0.124491
\(465\) −57.6244 + 458.857i −0.123923 + 0.986788i
\(466\) 71.1262 0.152631
\(467\) −271.529 271.529i −0.581432 0.581432i 0.353864 0.935297i \(-0.384867\pi\)
−0.935297 + 0.353864i \(0.884867\pi\)
\(468\) 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
\(483\) 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 0.976019 0.217684i \(-0.0698501\pi\)
−0.217684 + 0.976019i \(0.569850\pi\)
\(488\) −390.998 + 390.998i −0.801226 + 0.801226i
\(489\) −196.352 + 362.421i −0.401537 + 0.741147i
\(490\) −165.856 180.324i −0.338482 0.368008i
\(491\) 421.951i 0.859370i −0.902979 0.429685i \(-0.858625\pi\)
0.902979 0.429685i \(-0.141375\pi\)
\(492\) 43.9696 + 147.945i 0.0893692 + 0.300700i
\(493\) 6.71748 + 6.71748i 0.0136257 + 0.0136257i
\(494\) −209.640 −0.424373
\(495\) 19.0194 + 114.958i 0.0384230 + 0.232239i
\(496\) 154.154i 0.310794i
\(497\) 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 \(-0.965080\pi\)
0.993988 0.109486i \(-0.0349204\pi\)
\(500\) 354.846 121.283i 0.709691 0.242567i
\(501\) 773.095 + 418.846i 1.54310 + 0.836021i
\(502\) −256.959 + 256.959i −0.511871 + 0.511871i
\(503\) 134.096 134.096i 0.266592 0.266592i −0.561133 0.827725i \(-0.689635\pi\)
0.827725 + 0.561133i \(0.189635\pi\)
\(504\) −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 \(-0.851040\pi\)
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
\(518\) 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 0.427704 0.903919i \(-0.359323\pi\)
−0.903919 + 0.427704i \(0.859323\pi\)
\(524\) 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 0.995405 0.0957494i \(-0.0305247\pi\)
−0.0957494 + 0.995405i \(0.530525\pi\)
\(548\) −96.5049 96.5049i −0.176104 0.176104i
\(549\) −388.291 595.541i −0.707270 1.08477i
\(550\) −2.73335 + 64.6762i −0.00496972 + 0.117593i
\(551\) −191.537 −0.347617
\(552\) −224.306 754.723i −0.406352 1.36725i
\(553\) −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 −0.348042 0.937479i \(-0.613153\pi\)
0.937479 + 0.348042i \(0.113153\pi\)
\(558\) −271.517 57.1967i −0.486590 0.102503i
\(559\) 449.825 0.804695
\(560\) 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 −0.996059 0.0886978i \(-0.971729\pi\)
0.0886978 + 0.996059i \(0.471729\pi\)
\(564\) 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 −0.924407 0.381408i \(-0.875439\pi\)
0.381408 + 0.924407i \(0.375439\pi\)
\(578\) 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 \(-0.192344\pi\)
−0.568158 + 0.822920i \(0.692344\pi\)
\(588\) −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 −0.854095 0.520118i \(-0.825888\pi\)
0.520118 + 0.854095i \(0.325888\pi\)
\(594\) −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 \(0.100704\pi\)
−0.950371 + 0.311119i \(0.899296\pi\)
\(602\) −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 0.0421025 0.999113i \(-0.486594\pi\)
0.999113 0.0421025i \(-0.0134056\pi\)
\(608\) −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 −0.0412636 0.999148i \(-0.513138\pi\)
0.999148 + 0.0412636i \(0.0131383\pi\)
\(614\) 163.693i 0.266601i
\(615\) −255.229 32.0523i −0.415007 0.0521176i
\(616\) 23.4667 + 124.689i 0.0380953 + 0.202418i
\(617\) −111.144 + 111.144i −0.180136 + 0.180136i −0.791415 0.611279i \(-0.790655\pi\)
0.611279 + 0.791415i \(0.290655\pi\)
\(618\) 319.864 95.0646i 0.517579 0.153826i
\(619\) −716.455 −1.15744 −0.578720 0.815526i \(-0.696448\pi\)
−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 \(0.0301291\pi\)
−0.995524 + 0.0945120i \(0.969871\pi\)
\(642\) 150.925 + 507.818i 0.235086 + 0.790994i
\(643\) −524.336 524.336i −0.815453 0.815453i 0.169993 0.985445i \(-0.445626\pi\)
−0.985445 + 0.169993i \(0.945626\pi\)
\(644\) −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 \(-0.141495\pi\)
−0.430025 + 0.902817i \(0.641495\pi\)
\(648\) −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 0.902119 0.431488i \(-0.142011\pi\)
−0.431488 + 0.902119i \(0.642011\pi\)
\(654\) 192.518 + 104.302i 0.294370 + 0.159484i
\(655\) −996.449 437.618i −1.52130 0.668119i
\(656\) 85.7446 0.130708
\(657\) −324.266 68.3085i −0.493555 0.103970i
\(658\) −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 \(0.341820\pi\)
−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
\(665\) 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 −0.490040 0.871700i \(-0.663018\pi\)
0.871700 + 0.490040i \(0.163018\pi\)
\(674\) 471.748 0.699923
\(675\) −674.486 + 26.3399i −0.999238 + 0.0390221i
\(676\) 27.3357 0.0404374
\(677\) −248.270 248.270i −0.366721 0.366721i 0.499559 0.866280i \(-0.333496\pi\)
−0.866280 + 0.499559i \(0.833496\pi\)
\(678\) 210.774 62.6427i 0.310876 0.0923933i
\(679\) −47.5432 252.619i −0.0700194 0.372046i
\(680\) −11.5730 + 26.3515i −0.0170191 + 0.0387522i
\(681\) −211.818 114.758i −0.311039 0.168514i
\(682\) −56.4496 + 56.4496i −0.0827706 + 0.0827706i
\(683\) 216.136 + 216.136i 0.316450 + 0.316450i 0.847402 0.530952i \(-0.178165\pi\)
−0.530952 + 0.847402i \(0.678165\pi\)
\(684\) −244.486 374.980i −0.357435 0.548216i
\(685\) 211.941 82.5897i 0.309403 0.120569i
\(686\) 290.959 181.637i 0.424138 0.264777i
\(687\) 442.314 131.457i 0.643835 0.191350i
\(688\) 125.774 125.774i 0.182811 0.182811i
\(689\) 610.859i 0.886587i
\(690\) 558.010 + 70.0763i 0.808710 + 0.101560i
\(691\) 167.027i 0.241717i 0.992670 + 0.120859i \(0.0385648\pi\)
−0.992670 + 0.120859i \(0.961435\pi\)
\(692\) 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 \(0.141294\pi\)
−0.903089 + 0.429454i \(0.858706\pi\)
\(702\) −221.017 + 260.212i −0.314838 + 0.370672i
\(703\) 687.923 + 687.923i 0.978554 + 0.978554i
\(704\) 33.6616 0.0478148
\(705\) 588.850 + 757.990i 0.835249 + 1.07516i
\(706\) 390.920i 0.553711i
\(707\) −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 \(-0.991506\pi\)
0.999644 0.0266808i \(-0.00849377\pi\)
\(710\) 88.9918 + 228.370i 0.125341 + 0.321648i
\(711\) −372.605 571.482i −0.524057 0.803772i
\(712\) −69.5605 + 69.5605i −0.0976973 + 0.0976973i
\(713\) 817.367 817.367i 1.14638 1.14638i
\(714\) 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 \(-0.908368\pi\)
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 \(-0.972226\pi\)
0.0871447 + 0.996196i \(0.472226\pi\)
\(728\) 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 0.249693 0.968325i \(-0.419670\pi\)
−0.968325 + 0.249693i \(0.919670\pi\)
\(734\) 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 \(-0.939993\pi\)
0.982283 0.187402i \(-0.0600069\pi\)
\(740\) −820.127 + 319.589i −1.10828 + 0.431877i
\(741\) −552.979 299.592i −0.746261 0.404308i
\(742\) 190.768 279.221i 0.257100 0.376308i
\(743\) 698.839 + 698.839i 0.940563 + 0.940563i 0.998330 0.0577666i \(-0.0183979\pi\)
−0.0577666 + 0.998330i \(0.518398\pi\)
\(744\) −308.416 + 569.267i −0.414538 + 0.765143i
\(745\) −113.253 49.7380i −0.152017 0.0667624i
\(746\) 275.115i 0.368787i
\(747\) −140.832 + 668.543i −0.188531 + 0.894971i
\(748\) 4.51683 + 4.51683i 0.00603854 + 0.00603854i
\(749\) 228.628 + 1214.81i 0.305244 + 1.62190i
\(750\) −369.773 62.3955i −0.493030 0.0831940i
\(751\) 488.791 0.650853 0.325426 0.945567i \(-0.394492\pi\)
0.325426 + 0.945567i \(0.394492\pi\)
\(752\) −226.237 226.237i −0.300846 0.300846i
\(753\) −1045.01 + 310.580i −1.38780 + 0.412457i
\(754\) 146.081 0.193742
\(755\) 534.139 + 234.582i 0.707469 + 0.310704i
\(756\) −546.865 + 149.757i −0.723367 + 0.198092i
\(757\) −269.069 269.069i −0.355441 0.355441i 0.506688 0.862129i \(-0.330870\pi\)
−0.862129 + 0.506688i \(0.830870\pi\)
\(758\) −244.100 244.100i −0.322032 0.322032i
\(759\) 138.738 256.079i 0.182791 0.337390i
\(760\) −210.692 540.675i −0.277226 0.711414i
\(761\) −973.280 −1.27895 −0.639475 0.768812i \(-0.720848\pi\)
−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