Properties

Label 105.3.k.c.83.7
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 83.7
Root \(-0.253395 + 0.611750i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.854662 + 2.87568i) q^{3} -3.00000i q^{4} +(4.57796 - 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(3.94887 + 5.77983i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.854662 + 2.87568i) 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} +(8.62705 - 2.56399i) q^{12} +(-8.94114 + 8.94114i) q^{13} +(-1.29468 + 6.87923i) q^{14} +(9.69428 + 11.4464i) q^{15} -5.00000 q^{16} +(-0.581460 + 0.581460i) q^{17} +(-8.80672 - 1.85519i) q^{18} -16.5793 q^{19} +(-6.03161 - 13.7339i) q^{20} +(-13.2460 + 16.2955i) q^{21} +(1.83095 - 1.83095i) q^{22} +(26.5115 - 26.5115i) q^{23} +(18.4643 + 10.0035i) q^{24} +(16.9155 - 18.4083i) q^{25} -12.6447 q^{26} +(-20.5787 - 17.4790i) q^{27} +(17.3395 - 11.8466i) q^{28} -11.5528 q^{29} +(-1.23896 + 14.9487i) q^{30} -30.8307i q^{31} +(-23.3345 - 23.3345i) q^{32} +(7.44617 - 2.21303i) 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} +(-20.8890 + 2.15633i) q^{42} +(-25.1548 - 25.1548i) q^{43} -7.76807 q^{44} +(-24.6310 + 37.6605i) q^{45} +37.4929 q^{46} +(-45.2473 + 45.2473i) q^{47} +(-4.27331 - 14.3784i) 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} +(-14.1697 - 47.6769i) q^{57} +(-8.16905 - 8.16905i) q^{58} -47.6223i q^{59} +(34.3393 - 29.0828i) q^{60} +78.9936i q^{61} +(21.8006 - 21.8006i) q^{62} +(-58.1816 - 24.1641i) 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} +(-12.9863 + 61.6470i) q^{72} +(-26.0359 + 26.0359i) q^{73} -58.6798 q^{74} +(67.3935 + 32.9106i) q^{75} +49.7380i q^{76} +(14.9660 - 10.2250i) q^{77} +(-10.8069 - 36.3621i) q^{78} +75.8024i q^{79} +(-22.8898 + 10.0527i) q^{80} +(32.6762 - 74.1166i) q^{81} +(12.1261 + 12.1261i) q^{82} +(53.6785 + 53.6785i) q^{83} +(48.8865 + 39.7380i) q^{84} +(-1.49286 + 3.83095i) q^{85} -35.5742i q^{86} +(-9.87373 - 33.2221i) q^{87} +(-12.8167 - 12.8167i) q^{88} -14.0533i q^{89} +(-44.0467 + 9.21327i) q^{90} +(-86.9857 - 16.3708i) q^{91} +(-79.5344 - 79.5344i) q^{92} +(88.6594 - 26.3499i) 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 0.861430 0.507877i \(-0.169569\pi\)
−0.507877 + 0.861430i \(0.669569\pi\)
\(3\) 0.854662 + 2.87568i 0.284887 + 0.958561i
\(4\) 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 \(-0.0375515\pi\)
\(12\) 8.62705 2.56399i 0.718921 0.213666i
\(13\) −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
\(15\) 9.69428 + 11.4464i 0.646285 + 0.763096i
\(16\) −5.00000 −0.312500
\(17\) −0.581460 + 0.581460i −0.0342036 + 0.0342036i −0.724002 0.689798i \(-0.757699\pi\)
0.689798 + 0.724002i \(0.257699\pi\)
\(18\) −8.80672 1.85519i −0.489262 0.103066i
\(19\) −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
\(21\) −13.2460 + 16.2955i −0.630762 + 0.775977i
\(22\) 1.83095 1.83095i 0.0832251 0.0832251i
\(23\) 26.5115 26.5115i 1.15267 1.15267i 0.166657 0.986015i \(-0.446703\pi\)
0.986015 0.166657i \(-0.0532972\pi\)
\(24\) 18.4643 + 10.0035i 0.769344 + 0.416814i
\(25\) 16.9155 18.4083i 0.676619 0.736333i
\(26\) −12.6447 −0.486334
\(27\) −20.5787 17.4790i −0.762176 0.647370i
\(28\) 17.3395 11.8466i 0.619267 0.423094i
\(29\) −11.5528 −0.398372 −0.199186 0.979962i \(-0.563830\pi\)
−0.199186 + 0.979962i \(0.563830\pi\)
\(30\) −1.23896 + 14.9487i −0.0412987 + 0.498291i
\(31\) 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
\(33\) 7.44617 2.21303i 0.225642 0.0670614i
\(34\) −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 \(-0.432936\pi\)
0.209133 + 0.977887i \(0.432936\pi\)
\(42\) −20.8890 + 2.15633i −0.497357 + 0.0513413i
\(43\) −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
\(45\) −24.6310 + 37.6605i −0.547355 + 0.836900i
\(46\) 37.4929 0.815062
\(47\) −45.2473 + 45.2473i −0.962709 + 0.962709i −0.999329 0.0366205i \(-0.988341\pi\)
0.0366205 + 0.999329i \(0.488341\pi\)
\(48\) −4.27331 14.3784i −0.0890273 0.299550i
\(49\) −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 \(-0.599371\pi\)
0.951665 + 0.307137i \(0.0993710\pi\)
\(54\) −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
\(57\) −14.1697 47.6769i −0.248592 0.836436i
\(58\) −8.16905 8.16905i −0.140846 0.140846i
\(59\) 47.6223i 0.807158i −0.914945 0.403579i \(-0.867766\pi\)
0.914945 0.403579i \(-0.132234\pi\)
\(60\) 34.3393 29.0828i 0.572322 0.484714i
\(61\) 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
\(63\) −58.1816 24.1641i −0.923517 0.383557i
\(64\) 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 \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(72\) −12.9863 + 61.6470i −0.180365 + 0.856209i
\(73\) −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
\(75\) 67.3935 + 32.9106i 0.898581 + 0.438808i
\(76\) 49.7380i 0.654447i
\(77\) 14.9660 10.2250i 0.194364 0.132793i
\(78\) −10.8069 36.3621i −0.138550 0.466181i
\(79\) 75.8024i 0.959524i 0.877399 + 0.479762i \(0.159277\pi\)
−0.877399 + 0.479762i \(0.840723\pi\)
\(80\) −22.8898 + 10.0527i −0.286123 + 0.125659i
\(81\) 32.6762 74.1166i 0.403410 0.915019i
\(82\) 12.1261 + 12.1261i 0.147880 + 0.147880i
\(83\) 53.6785 + 53.6785i 0.646729 + 0.646729i 0.952201 0.305472i \(-0.0988143\pi\)
−0.305472 + 0.952201i \(0.598814\pi\)
\(84\) 48.8865 + 39.7380i 0.581983 + 0.473071i
\(85\) −1.49286 + 3.83095i −0.0175630 + 0.0450700i
\(86\) 35.5742i 0.413654i
\(87\) −9.87373 33.2221i −0.113491 0.381864i
\(88\) −12.8167 12.8167i −0.145644 0.145644i
\(89\) 14.0533i 0.157903i −0.996878 0.0789514i \(-0.974843\pi\)
0.996878 0.0789514i \(-0.0251572\pi\)
\(90\) −44.0467 + 9.21327i −0.489408 + 0.102370i
\(91\) −86.9857 16.3708i −0.955887 0.179899i
\(92\) −79.5344 79.5344i −0.864504 0.864504i
\(93\) 88.6594 26.3499i 0.953327 0.283332i
\(94\) −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 \(-0.462580\pi\)
0.117289 + 0.993098i \(0.462580\pi\)
\(102\) −0.702797 2.36470i −0.00689016 0.0231833i
\(103\) 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
\(105\) −27.8769 + 101.232i −0.265494 + 0.964112i
\(106\) 48.3095 0.455750
\(107\) 124.868 + 124.868i 1.16699 + 1.16699i 0.982911 + 0.184083i \(0.0589315\pi\)
0.184083 + 0.982911i \(0.441069\pi\)
\(108\) −52.4370 + 61.7362i −0.485528 + 0.571632i
\(109\) 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 −0.898212 0.439562i \(-0.855134\pi\)
0.439562 + 0.898212i \(0.355134\pi\)
\(114\) 23.6931 43.7321i 0.207834 0.383615i
\(115\) 68.0662 174.671i 0.591880 1.51888i
\(116\) 34.6583i 0.298779i
\(117\) 23.4582 111.358i 0.200498 0.951779i
\(118\) 33.6740 33.6740i 0.285373 0.285373i
\(119\) −5.65685 1.06463i −0.0475366 0.00894644i
\(120\) 104.641 + 8.67273i 0.872010 + 0.0722727i
\(121\) 114.295 0.944589
\(122\) −55.8569 + 55.8569i −0.457843 + 0.457843i
\(123\) 14.6565 + 49.3149i 0.119159 + 0.400934i
\(124\) −92.4922 −0.745905
\(125\) 40.4278 118.282i 0.323422 0.946255i
\(126\) −24.0540 58.2272i −0.190905 0.462121i
\(127\) 21.6476 21.6476i 0.170454 0.170454i −0.616725 0.787179i \(-0.711541\pi\)
0.787179 + 0.616725i \(0.211541\pi\)
\(128\) −84.1457 + 84.1457i −0.657388 + 0.657388i
\(129\) 50.8383 93.8359i 0.394095 0.727410i
\(130\) −57.8869 + 25.4226i −0.445284 + 0.195559i
\(131\) −217.662 −1.66154 −0.830771 0.556614i \(-0.812100\pi\)
−0.830771 + 0.556614i \(0.812100\pi\)
\(132\) −6.63908 22.3385i −0.0502960 0.169231i
\(133\) −65.4696 95.8256i −0.492253 0.720493i
\(134\) 102.500 0.764927
\(135\) −129.351 38.6439i −0.958155 0.286251i
\(136\) 5.75616i 0.0423247i
\(137\) 32.1683 + 32.1683i 0.234805 + 0.234805i 0.814695 0.579890i \(-0.196904\pi\)
−0.579890 + 0.814695i \(0.696904\pi\)
\(138\) 32.0437 + 107.818i 0.232201 + 0.781287i
\(139\) −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
\(147\) −146.492 12.2106i −0.996544 0.0830654i
\(148\) 124.479 + 124.479i 0.841071 + 0.841071i
\(149\) −24.7386 −0.166031 −0.0830155 0.996548i \(-0.526455\pi\)
−0.0830155 + 0.996548i \(0.526455\pi\)
\(150\) 24.3831 + 70.9258i 0.162554 + 0.472838i
\(151\) −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
\(153\) 1.52554 7.24185i 0.00997082 0.0473323i
\(154\) 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
\(162\) 75.5139 29.3028i 0.466135 0.180881i
\(163\) 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
\(165\) 29.6389 25.1020i 0.179630 0.152133i
\(166\) 75.9128i 0.457306i
\(167\) 207.245 207.245i 1.24099 1.24099i 0.281396 0.959592i \(-0.409203\pi\)
0.959592 0.281396i \(-0.0907974\pi\)
\(168\) 15.0943 + 146.223i 0.0898473 + 0.870375i
\(169\) 9.11189i 0.0539165i
\(170\) −3.76450 + 1.65328i −0.0221441 + 0.00972520i
\(171\) 124.993 81.4952i 0.730954 0.476580i
\(172\) −75.4643 + 75.4643i −0.438746 + 0.438746i
\(173\) −115.444 115.444i −0.667307 0.667307i 0.289785 0.957092i \(-0.406416\pi\)
−0.957092 + 0.289785i \(0.906416\pi\)
\(174\) 16.5098 30.4734i 0.0948840 0.175134i
\(175\) 173.194 + 25.0763i 0.989680 + 0.143293i
\(176\) 12.9468i 0.0735613i
\(177\) 136.947 40.7010i 0.773710 0.229949i
\(178\) 9.93722 9.93722i 0.0558271 0.0558271i
\(179\) 236.871 1.32330 0.661650 0.749813i \(-0.269857\pi\)
0.661650 + 0.749813i \(0.269857\pi\)
\(180\) 112.982 + 73.8930i 0.627675 + 0.410516i
\(181\) 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
\(183\) −227.160 + 67.5128i −1.24131 + 0.368923i
\(184\) 262.450i 1.42636i
\(185\) −106.530 + 273.376i −0.575837 + 1.47771i
\(186\) 81.3238 + 44.0595i 0.437225 + 0.236879i
\(187\) 1.50561 + 1.50561i 0.00805138 + 0.00805138i
\(188\) 135.742 + 135.742i 0.722032 + 0.722032i
\(189\) 19.7627 187.964i 0.104565 0.994518i
\(190\) −77.2393 30.0988i −0.406523 0.158415i
\(191\) 370.941i 1.94210i −0.238872 0.971051i \(-0.576778\pi\)
0.238872 0.971051i \(-0.423222\pi\)
\(192\) 37.3839 11.1106i 0.194708 0.0578678i
\(193\) 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
\(195\) −189.022 15.6663i −0.969345 0.0803399i
\(196\) 136.943 + 53.4383i 0.698688 + 0.272645i
\(197\) 182.194 + 182.194i 0.924845 + 0.924845i 0.997367 0.0725218i \(-0.0231047\pi\)
−0.0725218 + 0.997367i \(0.523105\pi\)
\(198\) −4.80374 + 22.8037i −0.0242613 + 0.115170i
\(199\) −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
\(207\) −69.5562 + 330.189i −0.336020 + 1.59512i
\(208\) 44.7057 44.7057i 0.214931 0.214931i
\(209\) 42.9298i 0.205406i
\(210\) −91.2937 + 51.8697i −0.434732 + 0.246999i
\(211\) −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
\(213\) −140.964 + 41.8950i −0.661803 + 0.196690i
\(214\) 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
\(222\) −50.1514 168.744i −0.225907 0.760110i
\(223\) 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
\(225\) −37.0418 + 221.930i −0.164630 + 0.986355i
\(226\) −73.2952 −0.324315
\(227\) −56.7824 + 56.7824i −0.250143 + 0.250143i −0.821029 0.570886i \(-0.806600\pi\)
0.570886 + 0.821029i \(0.306600\pi\)
\(228\) −143.031 + 42.5092i −0.627327 + 0.186444i
\(229\) −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
\(231\) 42.1949 + 34.2986i 0.182662 + 0.148479i
\(232\) −57.1833 + 57.1833i −0.246480 + 0.246480i
\(233\) 50.2938 50.2938i 0.215853 0.215853i −0.590895 0.806748i \(-0.701225\pi\)
0.806748 + 0.590895i \(0.201225\pi\)
\(234\) 95.3296 62.1547i 0.407392 0.265618i
\(235\) −116.169 + 298.112i −0.494336 + 1.26856i
\(236\) −142.867 −0.605368
\(237\) −217.984 + 64.7854i −0.919762 + 0.273356i
\(238\) −3.24720 4.75280i −0.0136437 0.0199698i
\(239\) −131.741 −0.551216 −0.275608 0.961270i \(-0.588879\pi\)
−0.275608 + 0.961270i \(0.588879\pi\)
\(240\) −48.4714 57.2322i −0.201964 0.238467i
\(241\) 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
\(243\) 241.063 + 30.6217i 0.992028 + 0.126015i
\(244\) 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 \(-0.757650\pi\)
−0.723895 + 0.689910i \(0.757650\pi\)
\(252\) −72.4924 + 174.545i −0.287668 + 0.692638i
\(253\) −68.6476 68.6476i −0.271334 0.271334i
\(254\) 30.6144 0.120529
\(255\) −12.2925 1.01881i −0.0482058 0.00399533i
\(256\) −171.000 −0.667969
\(257\) 86.9159 86.9159i 0.338194 0.338194i −0.517493 0.855687i \(-0.673135\pi\)
0.855687 + 0.517493i \(0.173135\pi\)
\(258\) 102.300 30.4039i 0.396512 0.117845i
\(259\) −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 \(-0.665482\pi\)
0.867880 + 0.496774i \(0.165482\pi\)
\(264\) 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
\(267\) 40.4130 12.0109i 0.151359 0.0449845i
\(268\) −217.436 217.436i −0.811327 0.811327i
\(269\) 119.813i 0.445403i −0.974887 0.222701i \(-0.928512\pi\)
0.974887 0.222701i \(-0.0714875\pi\)
\(270\) −64.1395 118.790i −0.237554 0.439964i
\(271\) 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
\(273\) −27.2662 264.135i −0.0998761 0.967527i
\(274\) 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 \(-0.996413\pi\)
0.999936 0.0112698i \(-0.00358738\pi\)
\(282\) −54.6893 184.013i −0.193934 0.652529i
\(283\) −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
\(285\) −160.725 189.774i −0.563946 0.665874i
\(286\) 32.7416i 0.114481i
\(287\) 67.7190 + 99.1178i 0.235955 + 0.345358i
\(288\) 290.622 + 61.2211i 1.00910 + 0.212573i
\(289\) 288.324i 0.997660i
\(290\) −53.8218 20.9734i −0.185592 0.0723221i
\(291\) −52.4786 + 96.8635i −0.180339 + 0.332864i
\(292\) 78.1076 + 78.1076i 0.267492 + 0.267492i
\(293\) 333.360 + 333.360i 1.13775 + 1.13775i 0.988853 + 0.148895i \(0.0475717\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(294\) −94.9513 112.220i −0.322963 0.381700i
\(295\) −95.7464 218.013i −0.324564 0.739027i
\(296\) 410.758i 1.38770i
\(297\) −45.2594 + 53.2857i −0.152388 + 0.179413i
\(298\) −17.4929 17.4929i −0.0587009 0.0587009i
\(299\) 474.085i 1.58557i
\(300\) 98.7319 202.181i 0.329106 0.673935i
\(301\) 46.0572 244.723i 0.153014 0.813034i
\(302\) −82.5025 82.5025i −0.273187 0.273187i
\(303\) 20.2490 + 68.1319i 0.0668285 + 0.224858i
\(304\) 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 \(-0.455074\pi\)
0.140671 + 0.990056i \(0.455074\pi\)
\(312\) −254.535 + 75.6486i −0.815817 + 0.242463i
\(313\) −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
\(315\) −314.936 + 6.35383i −0.999797 + 0.0201709i
\(316\) 227.407 0.719643
\(317\) −393.091 393.091i −1.24003 1.24003i −0.959986 0.280048i \(-0.909650\pi\)
−0.280048 0.959986i \(-0.590350\pi\)
\(318\) 41.2883 + 138.923i 0.129838 + 0.436864i
\(319\) 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
\(327\) 209.884 62.3781i 0.641846 0.190759i
\(328\) 84.8829 84.8829i 0.258789 0.258789i
\(329\) −440.198 82.8456i −1.33799 0.251810i
\(330\) 38.7076 + 3.20811i 0.117296 + 0.00972155i
\(331\) 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
\(333\) 108.862 516.776i 0.326912 1.55188i
\(334\) 293.089 0.877511
\(335\) 186.083 477.525i 0.555472 1.42545i
\(336\) 66.2300 81.4776i 0.197113 0.242493i
\(337\) −333.576 + 333.576i −0.989840 + 0.989840i −0.999949 0.0101086i \(-0.996782\pi\)
0.0101086 + 0.999949i \(0.496782\pi\)
\(338\) −6.44308 + 6.44308i −0.0190624 + 0.0190624i
\(339\) −193.335 104.745i −0.570309 0.308981i
\(340\) 11.4929 + 4.47857i 0.0338025 + 0.0131723i
\(341\) −79.8317 −0.234111
\(342\) 146.009 + 30.7577i 0.426928 + 0.0899348i
\(343\) −334.176 + 77.3019i −0.974273 + 0.225370i
\(344\) −249.019 −0.723894
\(345\) 560.471 + 46.4522i 1.62455 + 0.134644i
\(346\) 163.263i 0.471857i
\(347\) −226.173 226.173i −0.651796 0.651796i 0.301629 0.953425i \(-0.402469\pi\)
−0.953425 + 0.301629i \(0.902469\pi\)
\(348\) −99.6664 + 29.6212i −0.286398 + 0.0851183i
\(349\) 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 \(-0.436789\pi\)
−0.980347 + 0.197281i \(0.936789\pi\)
\(354\) 125.616 + 68.0559i 0.354847 + 0.192248i
\(355\) 98.5552 + 224.409i 0.277620 + 0.632137i
\(356\) −42.1600 −0.118427
\(357\) −1.77317 17.1772i −0.00496687 0.0481154i
\(358\) 167.493 + 167.493i 0.467857 + 0.467857i
\(359\) 392.633 1.09368 0.546842 0.837236i \(-0.315830\pi\)
0.546842 + 0.837236i \(0.315830\pi\)
\(360\) 64.4929 + 308.327i 0.179147 + 0.856464i
\(361\) −86.1262 −0.238577
\(362\) −161.125 + 161.125i −0.445098 + 0.445098i
\(363\) 97.6838 + 328.677i 0.269101 + 0.905446i
\(364\) −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
\(372\) −79.0496 265.978i −0.212499 0.714995i
\(373\) −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
\(375\) 374.693 + 15.1664i 0.999182 + 0.0404437i
\(376\) 447.926i 1.19129i
\(377\) 103.295 103.295i 0.273992 0.273992i
\(378\) 146.885 118.936i 0.388584 0.314646i
\(379\) 345.209i 0.910843i −0.890276 0.455422i \(-0.849489\pi\)
0.890276 0.455422i \(-0.150511\pi\)
\(380\) 100.000 + 227.698i 0.263158 + 0.599207i
\(381\) 80.7531 + 43.7503i 0.211950 + 0.114830i
\(382\) 262.295 262.295i 0.686637 0.686637i
\(383\) 46.7051 + 46.7051i 0.121945 + 0.121945i 0.765446 0.643500i \(-0.222518\pi\)
−0.643500 + 0.765446i \(0.722518\pi\)
\(384\) −313.893 170.060i −0.817428 0.442865i
\(385\) 47.9561 76.8996i 0.124561 0.199739i
\(386\) 115.447i 0.299085i
\(387\) 313.292 + 65.9967i 0.809540 + 0.170534i
\(388\) 77.8991 77.8991i 0.200771 0.200771i
\(389\) −747.341 −1.92119 −0.960593 0.277960i \(-0.910342\pi\)
−0.960593 + 0.277960i \(0.910342\pi\)
\(390\) −122.581 144.737i −0.314311 0.371120i
\(391\) 30.8307i 0.0788509i
\(392\) 137.775 + 314.113i 0.351468 + 0.801309i
\(393\) −186.028 625.927i −0.473353 1.59269i
\(394\) 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
\(399\) 219.610 270.168i 0.550400 0.677114i
\(400\) −84.5774 + 92.0417i −0.211443 + 0.230104i
\(401\) 472.603i 1.17856i 0.807928 + 0.589281i \(0.200589\pi\)
−0.807928 + 0.589281i \(0.799411\pi\)
\(402\) 87.6030 + 294.758i 0.217918 + 0.733229i
\(403\) 275.662 + 275.662i 0.684025 + 0.684025i
\(404\) 71.0773i 0.175934i
\(405\) 0.576206 405.000i 0.00142273 0.999999i
\(406\) 14.9571 79.4742i 0.0368402 0.195749i
\(407\) 107.440 + 107.440i 0.263980 + 0.263980i
\(408\) −16.5529 + 4.91958i −0.0405708 + 0.0120578i
\(409\) −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
\(417\) −96.2087 323.713i −0.230716 0.776291i
\(418\) −30.3559 + 30.3559i −0.0726219 + 0.0726219i
\(419\) 91.1169i 0.217463i −0.994071 0.108731i \(-0.965321\pi\)
0.994071 0.108731i \(-0.0346788\pi\)
\(420\) 303.695 + 83.6308i 0.723084 + 0.199121i
\(421\) 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
\(423\) 118.712 563.536i 0.280643 1.33224i
\(424\) 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 \(-0.0666545\pi\)
\(432\) 102.894 + 87.3950i 0.238180 + 0.202303i
\(433\) 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
\(435\) −111.996 132.238i −0.257462 0.303996i
\(436\) −218.957 −0.502195
\(437\) −439.542 + 439.542i −1.00582 + 1.00582i
\(438\) −31.4689 105.883i −0.0718468 0.241743i
\(439\) 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
\(441\) −90.0873 431.700i −0.204280 0.978913i
\(442\) 7.35238 7.35238i 0.0166344 0.0166344i
\(443\) −207.809 + 207.809i −0.469094 + 0.469094i −0.901621 0.432527i \(-0.857622\pi\)
0.432527 + 0.901621i \(0.357622\pi\)
\(444\) −251.574 + 464.348i −0.566608 + 1.04583i
\(445\) −28.2548 64.3357i −0.0634939 0.144575i
\(446\) 113.065 0.253509
\(447\) −21.1432 71.1405i −0.0473002 0.159151i
\(448\) 75.1377 51.3354i 0.167718 0.114588i
\(449\) −315.151 −0.701895 −0.350947 0.936395i \(-0.614140\pi\)
−0.350947 + 0.936395i \(0.614140\pi\)
\(450\) −183.121 + 130.736i −0.406935 + 0.290524i
\(451\) 44.4047i 0.0984583i
\(452\) 155.483 + 155.483i 0.343988 + 0.343988i
\(453\) −99.7188 335.524i −0.220130 0.740670i
\(454\) −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 \(-0.709369\pi\)
−0.611339 + 0.791369i \(0.709369\pi\)
\(462\) 5.58352 + 54.0891i 0.0120855 + 0.117076i
\(463\) −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
\(465\) 352.902 298.882i 0.758929 0.642756i
\(466\) 71.1262 0.152631
\(467\) 271.529 271.529i 0.581432 0.581432i −0.353864 0.935297i \(-0.615133\pi\)
0.935297 + 0.353864i \(0.115133\pi\)
\(468\) −334.075 70.3747i −0.713835 0.150373i
\(469\) 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
\(477\) −89.6231 + 425.448i −0.187889 + 0.891925i
\(478\) −93.1548 93.1548i −0.194884 0.194884i
\(479\) 517.973i 1.08136i −0.841227 0.540682i \(-0.818166\pi\)
0.841227 0.540682i \(-0.181834\pi\)
\(480\) 40.8857 493.309i 0.0851786 1.02773i
\(481\) 741.987i 1.54259i
\(482\) 72.8542 72.8542i 0.151150 0.151150i
\(483\) 80.8471 + 783.188i 0.167385 + 1.62151i
\(484\) 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 \(-0.858625\pi\)
0.902979 0.429685i \(-0.141375\pi\)
\(492\) 147.945 43.9696i 0.300700 0.0893692i
\(493\) 6.71748 6.71748i 0.0136257 0.0136257i
\(494\) 209.640 0.424373
\(495\) 97.5165 + 63.7784i 0.197003 + 0.128845i
\(496\) 154.154i 0.310794i
\(497\) −283.323 + 193.571i −0.570067 + 0.389479i
\(498\) −218.301 + 64.8798i −0.438356 + 0.130281i
\(499\) 109.267i 0.218971i 0.993988 + 0.109486i \(0.0349204\pi\)
−0.993988 + 0.109486i \(0.965080\pi\)
\(500\) −354.846 121.283i −0.709691 0.242567i
\(501\) 773.095 + 418.846i 1.54310 + 0.836021i
\(502\) −256.959 256.959i −0.511871 0.511871i
\(503\) −134.096 134.096i −0.266592 0.266592i 0.561133 0.827725i \(-0.310365\pi\)
−0.827725 + 0.561133i \(0.810365\pi\)
\(504\) −407.590 + 168.378i −0.808711 + 0.334083i
\(505\) 108.463 47.6345i 0.214778 0.0943258i
\(506\) 97.0824i 0.191862i
\(507\) −26.2029 + 7.78759i −0.0516823 + 0.0153601i
\(508\) −64.9428 64.9428i −0.127840 0.127840i
\(509\) 459.197i 0.902154i −0.892485 0.451077i \(-0.851040\pi\)
0.892485 0.451077i \(-0.148960\pi\)
\(510\) −7.97170 9.41251i −0.0156308 0.0184559i
\(511\) −253.295 47.6704i −0.495685 0.0932885i
\(512\) 215.668 + 215.668i 0.421226 + 0.421226i
\(513\) 341.181 + 289.790i 0.665071 + 0.564893i
\(514\) 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 \(-0.405848\pi\)
0.291491 + 0.956573i \(0.405848\pi\)
\(522\) 101.742 + 21.4325i 0.194908 + 0.0410585i
\(523\) −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
\(525\) 75.9109 + 519.483i 0.144592 + 0.989491i
\(526\) 138.029 0.262412
\(527\) 17.9268 + 17.9268i 0.0340168 + 0.0340168i
\(528\) −37.2308 + 11.0651i −0.0705130 + 0.0209567i
\(529\) 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
\(537\) 202.444 + 681.165i 0.376992 + 1.26846i
\(538\) 84.7209 84.7209i 0.157474 0.157474i
\(539\) 118.198 + 46.1237i 0.219291 + 0.0855726i
\(540\) −115.932 + 388.053i −0.214688 + 0.718616i
\(541\) −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
\(543\) −655.270 + 194.748i −1.20676 + 0.358653i
\(544\) 27.1362 0.0498827
\(545\) −146.741 334.126i −0.269249 0.613075i
\(546\) 167.491 206.052i 0.306761 0.377384i
\(547\) 492.112 492.112i 0.899656 0.899656i −0.0957494 0.995405i \(-0.530525\pi\)
0.995405 + 0.0957494i \(0.0305247\pi\)
\(548\) 96.5049 96.5049i 0.176104 0.176104i
\(549\) −388.291 595.541i −0.707270 1.08477i
\(550\) −2.73335 64.6762i −0.00496972 0.117593i
\(551\) 191.537 0.347617
\(552\) 754.723 224.306i 1.36725 0.406352i
\(553\) −438.125 + 299.334i −0.792269 + 0.541291i
\(554\) 72.3842 0.130657
\(555\) −877.189 72.7019i −1.58052 0.130994i
\(556\) 337.708i 0.607388i
\(557\) −328.316 328.316i −0.589437 0.589437i 0.348042 0.937479i \(-0.386847\pi\)
−0.937479 + 0.348042i \(0.886847\pi\)
\(558\) −57.1967 + 271.517i −0.102503 + 0.486590i
\(559\) 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 \(-0.0282706\pi\)
−0.0886978 + 0.996059i \(0.528271\pi\)
\(564\) −274.337 + 506.364i −0.486414 + 0.897809i
\(565\) −133.063 + 341.466i −0.235510 + 0.604364i
\(566\) −342.455 −0.605043
\(567\) 557.415 103.814i 0.983095 0.183094i
\(568\) 242.633 + 242.633i 0.427171 + 0.427171i
\(569\) 789.111 1.38684 0.693419 0.720534i \(-0.256103\pi\)
0.693419 + 0.720534i \(0.256103\pi\)
\(570\) 20.5411 247.840i 0.0360371 0.434807i
\(571\) −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
\(573\) 1066.71 317.030i 1.86162 0.553280i
\(574\) −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
\(582\) −105.601 + 31.3849i −0.181445 + 0.0539260i
\(583\) −88.4524 88.4524i −0.151719 0.151719i
\(584\) 257.742i 0.441339i
\(585\) −116.499 556.957i −0.199143 0.952064i
\(586\) 471.443i 0.804510i
\(587\) −149.545 + 149.545i −0.254762 + 0.254762i −0.822920 0.568158i \(-0.807656\pi\)
0.568158 + 0.822920i \(0.307656\pi\)
\(588\) −36.6318 + 439.476i −0.0622991 + 0.747408i
\(589\) 511.152i 0.867831i
\(590\) 86.4556 221.861i 0.146535 0.376036i
\(591\) −368.219 + 679.648i −0.623044 + 1.15000i
\(592\) 207.464 207.464i 0.350446 0.350446i
\(593\) 198.048 + 198.048i 0.333977 + 0.333977i 0.854095 0.520118i \(-0.174112\pi\)
−0.520118 + 0.854095i \(0.674112\pi\)
\(594\) −69.6819 + 5.67547i −0.117310 + 0.00955466i
\(595\) −28.0373 + 6.49950i −0.0471216 + 0.0109235i
\(596\) 74.2159i 0.124523i
\(597\) −26.6962 89.8248i −0.0447173 0.150460i
\(598\) −335.229 + 335.229i −0.560584 + 0.560584i
\(599\) 475.156 0.793248 0.396624 0.917981i \(-0.370182\pi\)
0.396624 + 0.917981i \(0.370182\pi\)
\(600\) 496.480 170.682i 0.827467 0.284469i
\(601\) 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
\(603\) −190.157 + 902.690i −0.315351 + 1.49700i
\(604\) 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
\(609\) 153.028 188.258i 0.251278 0.309127i
\(610\) −143.408 + 368.013i −0.235096 + 0.603300i
\(611\) 809.125i 1.32426i
\(612\) −21.7255 4.57661i −0.0354992 0.00747812i
\(613\) 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
\(615\) 166.247 + 196.294i 0.270320 + 0.319177i
\(616\) 23.4667 124.689i 0.0380953 0.202418i
\(617\) 111.144 + 111.144i 0.180136 + 0.180136i 0.791415 0.611279i \(-0.209345\pi\)
−0.611279 + 0.791415i \(0.709345\pi\)
\(618\) 95.0646 + 319.864i 0.153826 + 0.517579i
\(619\) −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
\(627\) −123.452 + 36.6905i −0.196894 + 0.0585175i
\(628\) 428.636 428.636i 0.682541 0.682541i
\(629\) 48.2529i 0.0767137i
\(630\) −227.186 218.200i −0.360613 0.346350i
\(631\) 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
\(633\) −82.5522 277.764i −0.130414 0.438805i
\(634\) 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 \(0.969871\pi\)
\(642\) −507.818 + 150.925i −0.790994 + 0.235086i
\(643\) −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
\(645\) 44.0751 531.790i 0.0683334 0.824480i
\(646\) 13.6333 0.0211042
\(647\) −305.897 + 305.897i −0.472792 + 0.472792i −0.902817 0.430025i \(-0.858505\pi\)
0.430025 + 0.902817i \(0.358505\pi\)
\(648\) −205.119 528.597i −0.316542 0.815736i
\(649\) −123.311 −0.190002
\(650\) −213.891 + 232.768i −0.329063 + 0.358104i
\(651\) 502.402 + 408.384i 0.771739 + 0.627317i
\(652\) 291.464 291.464i 0.447031 0.447031i
\(653\) −307.322 + 307.322i −0.470631 + 0.470631i −0.902119 0.431488i \(-0.857989\pi\)
0.431488 + 0.902119i \(0.357989\pi\)
\(654\) 192.518 + 104.302i 0.294370 + 0.159484i
\(655\) −996.449 + 437.618i −1.52130 + 0.668119i
\(656\) −85.7446 −0.130708
\(657\) 68.3085 324.266i 0.103970 0.493555i
\(658\) −252.686 369.847i −0.384021 0.562078i
\(659\) 903.538 1.37107 0.685537 0.728038i \(-0.259568\pi\)
0.685537 + 0.728038i \(0.259568\pi\)
\(660\) −75.3059 88.9167i −0.114100 0.134722i
\(661\) 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
\(663\) 29.9009 8.88664i 0.0450994 0.0134037i
\(664\) 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
\(672\) 689.337 71.1590i 1.02580 0.105891i
\(673\) 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
\(675\) −669.858 + 83.1546i −0.992383 + 0.123192i
\(676\) 27.3357 0.0404374
\(677\) 248.270 248.270i 0.366721 0.366721i −0.499559 0.866280i \(-0.666504\pi\)
0.866280 + 0.499559i \(0.166504\pi\)
\(678\) −62.6427 210.774i −0.0923933 0.310876i
\(679\) −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 \(-0.821835\pi\)
0.530952 + 0.847402i \(0.321835\pi\)
\(684\) −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
\(687\) −131.457 442.314i −0.191350 0.643835i
\(688\) 125.774 + 125.774i 0.182811 + 0.182811i
\(689\) 610.859i 0.886587i
\(690\) 363.466 + 429.160i 0.526763 + 0.621970i
\(691\) 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
\(693\) −62.5695 + 150.653i −0.0902879 + 0.217392i
\(694\) 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 \(0.858706\pi\)
\(702\) 260.212 + 221.017i 0.370672 + 0.314838i
\(703\) 687.923 687.923i 0.978554 0.978554i
\(704\) −33.6616 −0.0478148
\(705\) −956.561 79.2803i −1.35682 0.112454i
\(706\) 390.920i 0.553711i
\(707\) 93.5584 + 136.938i 0.132332 + 0.193689i
\(708\) −122.103 410.840i −0.172462 0.580282i
\(709\) 37.8334i 0.0533616i 0.999644 + 0.0266808i \(0.00849377\pi\)
−0.999644 + 0.0266808i \(0.991506\pi\)
\(710\) −88.9918 + 228.370i −0.125341 + 0.321648i
\(711\) −372.605 571.482i −0.524057 0.803772i
\(712\) −69.5605 69.5605i −0.0976973 0.0976973i
\(713\) −817.367 817.367i −1.14638 1.14638i
\(714\) 10.8923 13.3999i 0.0152553 0.0187674i
\(715\) 152.536 + 59.4405i 0.213337 + 0.0831336i
\(716\) 710.612i 0.992475i
\(717\) −112.594 378.845i −0.157035 0.528375i
\(718\) 277.633 + 277.633i 0.386676 + 0.386676i
\(719\) 408.265i 0.567824i −0.958850 0.283912i \(-0.908368\pi\)
0.958850 0.283912i \(-0.0916324\pi\)
\(720\) 123.155 188.303i 0.171049 0.261531i
\(721\) 765.181 + 144.008i 1.06128 + 0.199734i
\(722\) −60.9004 60.9004i −0.0843496 0.0843496i
\(723\) 296.286 88.0571i 0.409800 0.121794i
\(724\) 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
\(732\) 202.538 + 681.481i 0.276692 + 0.930985i
\(733\) −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
\(735\) −695.185 + 238.628i −0.945829 + 0.324664i
\(736\) −1237.26 −1.68107
\(737\) −187.673 187.673i −0.254644 0.254644i
\(738\) −151.026 31.8144i −0.204642 0.0431090i
\(739\) 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 −0.998330 0.0577666i \(-0.981602\pi\)
0.0577666 + 0.998330i \(0.481602\pi\)
\(744\) 308.416 569.267i 0.414538 0.765143i
\(745\) −113.253 + 49.7380i −0.152017 + 0.0667624i
\(746\) 275.115i 0.368787i
\(747\) −668.543 140.832i −0.894971 0.188531i
\(748\) 4.51683 4.51683i 0.00603854 0.00603854i
\(749\) −228.628 + 1214.81i −0.305244 + 1.62190i
\(750\) 254.224 + 275.672i 0.338965 + 0.367563i
\(751\) 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
\(753\) −310.580 1045.01i −0.412457 1.38780i
\(754\) 146.081 0.193742
\(755\) −534.139 + 234.582i −0.707469 + 0.310704i
\(756\) −563.892 59.2882i −0.745889 0.0784236i
\(757\) −269.069 + 269.069i −0.355441 + 0.355441i −0.862129 0.506688i \(-0.830870\pi\)
0.506688 + 0.862129i \(0.330870\pi\)
\(758\) 244.100 244.100i 0.322032 0.322032i
\(759\) 138.738 256.079i 0.182791 0.337390i
\(760\) −210.692 + 540.675i −0.277226 + 0.711414i
\(761\) 973.280 1.27895 0.639475 0.768812i \(-0.279152\pi\)
0.639475 + 0.768812i \(0.279152\pi\)
\(762\) 26.1649 + 88.0372i 0.0343372 + 0.115534i
\(763\) 421.845 288.211i 0.552876 0.377734i
\(764\) −1112.82 −1.45658
\(765\) −7.57616 36.2200i −0.00990347 0.0473465i
\(766\) 66.0510i 0.0862285i
\(767\) 425.798 + 425.798i 0.555147 + 0.555147i
\(768\) −146.147 491.742i −0.190296 0.640289i
\(769\) −1055.77 −1.37292 −0.686458 0.727169i \(-0.740835\pi\)
−0.686458 + 0.727169i \(0.740835\pi\)
\(770\) 88.2863 20.4662i