Properties

Label 105.3.k.c.83.6
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 83.6
Root \(0.253395 - 0.611750i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +(-4.65877 - 1.81544i) q^{10} -2.58936i q^{11} +(-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} +(-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} +(20.5787 + 17.4790i) q^{27} +(-11.8466 + 17.3395i) 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} +(34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 + 41.4929i) q^{37} +(11.7233 + 11.7233i) q^{38} +(-33.3536 - 18.0702i) q^{39} +(-12.7081 + 32.6114i) q^{40} -17.1489 q^{41} +(-18.6760 + 9.60250i) 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} +(62.9853 + 1.36038i) q^{63} -13.0000i q^{64} +(-22.9557 + 58.9087i) q^{65} +(-6.83008 - 3.70039i) q^{66} +(72.4786 - 72.4786i) q^{67} +(-1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 + 28.8899i) q^{70} +49.0193i q^{71} +(-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} +(-10.2250 + 14.9660i) 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} +(59.9877 + 19.2477i) 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} +(-19.6822 + 44.8733i) q^{98} +(12.7279 + 19.5214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.353553 + 0.353553i 0.861430 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
\(7\) −5.77983 3.94887i −0.825689 0.564125i
\(8\) 4.94975 4.94975i 0.618718 0.618718i
\(9\) −7.53910 + 4.91548i −0.837678 + 0.546164i
\(10\) −4.65877 1.81544i −0.465877 0.181544i
\(11\) 2.58936i 0.235396i −0.993049 0.117698i \(-0.962449\pi\)
0.993049 0.117698i \(-0.0375515\pi\)
\(12\) −8.62705 + 2.56399i −0.718921 + 0.213666i
\(13\) 8.94114 8.94114i 0.687780 0.687780i −0.273961 0.961741i \(-0.588334\pi\)
0.961741 + 0.273961i \(0.0883338\pi\)
\(14\) −1.29468 6.87923i −0.0924770 0.491374i
\(15\) 9.69428 + 11.4464i 0.646285 + 0.763096i
\(16\) −5.00000 −0.312500
\(17\) 0.581460 0.581460i 0.0342036 0.0342036i −0.689798 0.724002i \(-0.742301\pi\)
0.724002 + 0.689798i \(0.242301\pi\)
\(18\) −8.80672 1.85519i −0.489262 0.103066i
\(19\) 16.5793 0.872596 0.436298 0.899802i \(-0.356289\pi\)
0.436298 + 0.899802i \(0.356289\pi\)
\(20\) 6.03161 + 13.7339i 0.301581 + 0.686694i
\(21\) −6.41591 + 19.9959i −0.305520 + 0.952186i
\(22\) 1.83095 1.83095i 0.0832251 0.0832251i
\(23\) 26.5115 26.5115i 1.15267 1.15267i 0.166657 0.986015i \(-0.446703\pi\)
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
\(28\) −11.8466 + 17.3395i −0.423094 + 0.619267i
\(29\) −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 \(0.165664\pi\)
−0.867596 + 0.497270i \(0.834336\pi\)
\(32\) −23.3345 23.3345i −0.729204 0.729204i
\(33\) −7.44617 + 2.21303i −0.225642 + 0.0670614i
\(34\) 0.822309 0.0241856
\(35\) 34.3992 + 6.45724i 0.982834 + 0.184493i
\(36\) 14.7464 + 22.6173i 0.409623 + 0.628259i
\(37\) −41.4929 + 41.4929i −1.12143 + 1.12143i −0.129902 + 0.991527i \(0.541466\pi\)
−0.991527 + 0.129902i \(0.958534\pi\)
\(38\) 11.7233 + 11.7233i 0.308509 + 0.308509i
\(39\) −33.3536 18.0702i −0.855219 0.463339i
\(40\) −12.7081 + 32.6114i −0.317703 + 0.815285i
\(41\) −17.1489 −0.418267 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(42\) −18.6760 + 9.60250i −0.444666 + 0.228631i
\(43\) −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 −0.0366205 0.999329i \(-0.511659\pi\)
0.999329 + 0.0366205i \(0.0116593\pi\)
\(48\) 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 \(0.132234\pi\)
−0.914945 + 0.403579i \(0.867766\pi\)
\(60\) 34.3393 29.0828i 0.572322 0.484714i
\(61\) 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
\(63\) 62.9853 + 1.36038i 0.999767 + 0.0215933i
\(64\) 13.0000i 0.203125i
\(65\) −22.9557 + 58.9087i −0.353165 + 0.906288i
\(66\) −6.83008 3.70039i −0.103486 0.0560665i
\(67\) 72.4786 72.4786i 1.08177 1.08177i 0.0854251 0.996345i \(-0.472775\pi\)
0.996345 0.0854251i \(-0.0272248\pi\)
\(68\) −1.74438 1.74438i −0.0256527 0.0256527i
\(69\) −98.8969 53.5802i −1.43329 0.776524i
\(70\) 19.7579 + 28.8899i 0.282256 + 0.412712i
\(71\) 49.0193i 0.690413i 0.938527 + 0.345207i \(0.112191\pi\)
−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 −0.505923 0.862579i \(-0.668848\pi\)
0.862579 + 0.505923i \(0.168848\pi\)
\(74\) −58.6798 −0.792970
\(75\) −67.3935 32.9106i −0.898581 0.438808i
\(76\) 49.7380i 0.654447i
\(77\) −10.2250 + 14.9660i −0.132793 + 0.194364i
\(78\) −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 0.305472 0.952201i \(-0.401186\pi\)
−0.952201 + 0.305472i \(0.901186\pi\)
\(84\) 59.9877 + 19.2477i 0.714139 + 0.229140i
\(85\) −1.49286 + 3.83095i −0.0175630 + 0.0450700i
\(86\) 35.5742i 0.413654i
\(87\) 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 \(0.0251572\pi\)
−0.996878 + 0.0789514i \(0.974843\pi\)
\(90\) 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 0.560476 0.828171i \(-0.310618\pi\)
−0.828171 + 0.560476i \(0.810618\pi\)
\(98\) −19.6822 + 44.8733i −0.200839 + 0.457891i
\(99\) 12.7279 + 19.5214i 0.128565 + 0.197186i
\(100\) −55.2250 50.7464i −0.552250 0.507464i
\(101\) −23.6924 −0.234579 −0.117289 0.993098i \(-0.537420\pi\)
−0.117289 + 0.993098i \(0.537420\pi\)
\(102\) −0.702797 2.36470i −0.00689016 0.0231833i
\(103\) −78.6519 + 78.6519i −0.763611 + 0.763611i −0.976973 0.213362i \(-0.931559\pi\)
0.213362 + 0.976973i \(0.431559\pi\)
\(104\) 88.5128i 0.851085i
\(105\) −10.8307 104.440i −0.103150 0.994666i
\(106\) 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
\(112\) 28.8991 + 19.7444i 0.258028 + 0.176289i
\(113\) −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
\(126\) 43.5754 + 45.4993i 0.345837 + 0.361105i
\(127\) 21.6476 21.6476i 0.170454 0.170454i −0.616725 0.787179i \(-0.711541\pi\)
0.787179 + 0.616725i \(0.211541\pi\)
\(128\) −84.1457 + 84.1457i −0.657388 + 0.657388i
\(129\) −50.8383 + 93.8359i −0.394095 + 0.727410i
\(130\) −57.8869 + 25.4226i −0.445284 + 0.195559i
\(131\) 217.662 1.66154 0.830771 0.556614i \(-0.187900\pi\)
0.830771 + 0.556614i \(0.187900\pi\)
\(132\) 6.63908 + 22.3385i 0.0502960 + 0.169231i
\(133\) −95.8256 65.4696i −0.720493 0.492253i
\(134\) 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 \(-0.367298\pi\)
0.404925 + 0.914350i \(0.367298\pi\)
\(140\) 19.3717 103.198i 0.138369 0.737125i
\(141\) −168.788 91.4457i −1.19708 0.648551i
\(142\) −34.6619 + 34.6619i −0.244098 + 0.244098i
\(143\) −23.1518 23.1518i −0.161901 0.161901i
\(144\) 37.6955 24.5774i 0.261774 0.170676i
\(145\) 52.8882 23.2273i 0.364746 0.160188i
\(146\) 36.8203 0.252194
\(147\) 116.044 90.2372i 0.789416 0.613859i
\(148\) 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 0.0862209 0.996276i \(-0.472521\pi\)
−0.996276 + 0.0862209i \(0.972521\pi\)
\(158\) −53.6004 + 53.6004i −0.339243 + 0.339243i
\(159\) −127.429 69.0380i −0.801437 0.434202i
\(160\) 153.740 + 59.9096i 0.960872 + 0.374435i
\(161\) −257.922 + 48.5412i −1.60200 + 0.301498i
\(162\) 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 \(0.590797\pi\)
−0.959592 + 0.281396i \(0.909203\pi\)
\(168\) 67.2175 + 130.732i 0.400104 + 0.778165i
\(169\) 9.11189i 0.0539165i
\(170\) −3.76450 + 1.65328i −0.0221441 + 0.00972520i
\(171\) −124.993 + 81.4952i −0.730954 + 0.476580i
\(172\) −75.4643 + 75.4643i −0.438746 + 0.438746i
\(173\) 115.444 + 115.444i 0.667307 + 0.667307i 0.957092 0.289785i \(-0.0935837\pi\)
−0.289785 + 0.957092i \(0.593584\pi\)
\(174\) −16.5098 + 30.4734i −0.0948840 + 0.175134i
\(175\) −170.461 + 39.5999i −0.974061 + 0.226285i
\(176\) 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 \(-0.783275\pi\)
0.777030 0.629463i \(-0.216725\pi\)
\(182\) −73.0841 49.9323i −0.401561 0.274353i
\(183\) −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
\(189\) −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 \(-0.423222\pi\)
\(192\) −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 \(-0.474993\pi\)
0.0784824 + 0.996915i \(0.474993\pi\)
\(200\) −7.38926 174.844i −0.0369463 0.874220i
\(201\) −270.370 146.481i −1.34512 0.728760i
\(202\) −16.7531 16.7531i −0.0829360 0.0829360i
\(203\) 66.7731 + 45.6205i 0.328931 + 0.224731i
\(204\) −3.52543 + 6.50714i −0.0172815 + 0.0318978i
\(205\) 78.5071 34.4786i 0.382962 0.168188i
\(206\) −111.231 −0.539954
\(207\) −69.5562 + 330.189i −0.336020 + 1.59512i
\(208\) −44.7057 + 44.7057i −0.214931 + 0.214931i
\(209\) 42.9298i 0.205406i
\(210\) 66.1917 81.5086i 0.315199 0.388136i
\(211\) −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
\(217\) 121.747 178.196i 0.561044 0.821181i
\(218\) 51.6087 51.6087i 0.236737 0.236737i
\(219\) −97.1228 52.6190i −0.443483 0.240270i
\(220\) 35.5619 15.6180i 0.161645 0.0709909i
\(221\) 10.3978i 0.0470491i
\(222\) 50.1514 + 168.744i 0.225907 + 0.760110i
\(223\) −79.9490 + 79.9490i −0.358516 + 0.358516i −0.863266 0.504750i \(-0.831585\pi\)
0.504750 + 0.863266i \(0.331585\pi\)
\(224\) 42.7244 + 227.015i 0.190734 + 1.01346i
\(225\) −37.0418 + 221.930i −0.164630 + 0.986355i
\(226\) −73.2952 −0.324315
\(227\) 56.7824 56.7824i 0.250143 0.250143i −0.570886 0.821029i \(-0.693400\pi\)
0.821029 + 0.570886i \(0.193400\pi\)
\(228\) −143.031 + 42.5092i −0.627327 + 0.186444i
\(229\) 153.812 0.671668 0.335834 0.941921i \(-0.390982\pi\)
0.335834 + 0.941921i \(0.390982\pi\)
\(230\) −171.641 + 75.3808i −0.746265 + 0.327743i
\(231\) 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 \(-0.701225\pi\)
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
\(238\) −4.75280 3.24720i −0.0199698 0.0136437i
\(239\) −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 \(0.0685704\pi\)
−0.976887 + 0.213758i \(0.931430\pi\)
\(242\) 80.8189 + 80.8189i 0.333963 + 0.333963i
\(243\) −241.063 30.6217i −0.992028 0.126015i
\(244\) −236.981 −0.971232
\(245\) −173.322 173.160i −0.707439 0.706775i
\(246\) −24.5071 + 45.2346i −0.0996225 + 0.183881i
\(247\) 148.238 148.238i 0.600154 0.600154i
\(248\) 152.604 + 152.604i 0.615340 + 0.615340i
\(249\) −108.485 + 200.239i −0.435684 + 0.804174i
\(250\) −112.225 + 55.0512i −0.448899 + 0.220205i
\(251\) 363.395 1.44779 0.723895 0.689910i \(-0.242350\pi\)
0.723895 + 0.689910i \(0.242350\pi\)
\(252\) 4.08114 188.956i 0.0161950 0.749825i
\(253\) −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 −0.855687 0.517493i \(-0.826865\pi\)
0.517493 + 0.855687i \(0.326865\pi\)
\(258\) −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 \(0.0714875\pi\)
−0.974887 + 0.222701i \(0.928512\pi\)
\(270\) −64.1395 118.790i −0.237554 0.439964i
\(271\) 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
\(273\) 121.421 + 236.152i 0.444764 + 0.865025i
\(274\) 45.4929i 0.166032i
\(275\) −47.6657 43.8002i −0.173330 0.159273i
\(276\) −160.741 + 296.691i −0.582393 + 1.07497i
\(277\) 51.1833 51.1833i 0.184777 0.184777i −0.608656 0.793434i \(-0.708291\pi\)
0.793434 + 0.608656i \(0.208291\pi\)
\(278\) 79.5985 + 79.5985i 0.286325 + 0.286325i
\(279\) −151.548 232.436i −0.543182 0.833104i
\(280\) 202.229 138.306i 0.722246 0.493949i
\(281\) 6.33365i 0.0225397i −0.999936 0.0112698i \(-0.996413\pi\)
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 −0.135163 0.990823i \(-0.543156\pi\)
0.990823 + 0.135163i \(0.0431558\pi\)
\(284\) 147.058 0.517810
\(285\) 160.725 + 189.774i 0.563946 + 0.665874i
\(286\) 32.7416i 0.114481i
\(287\) 99.1178 + 67.7190i 0.345358 + 0.235955i
\(288\) 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 \(-0.952428\pi\)
−0.148895 0.988853i \(-0.547572\pi\)
\(294\) 145.863 + 18.2483i 0.496132 + 0.0620689i
\(295\) −95.7464 218.013i −0.324564 0.739027i
\(296\) 410.758i 1.38770i
\(297\) 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 0.870030 0.492999i \(-0.164099\pi\)
−0.492999 + 0.870030i \(0.664099\pi\)
\(308\) 44.8981 + 30.6751i 0.145773 + 0.0995946i
\(309\) 293.399 + 158.957i 0.949511 + 0.514424i
\(310\) 55.9714 143.633i 0.180553 0.463333i
\(311\) −87.4973 −0.281342 −0.140671 0.990056i \(-0.544926\pi\)
−0.140671 + 0.990056i \(0.544926\pi\)
\(312\) −254.535 + 75.6486i −0.815817 + 0.242463i
\(313\) 74.9574 74.9574i 0.239481 0.239481i −0.577154 0.816635i \(-0.695837\pi\)
0.816635 + 0.577154i \(0.195837\pi\)
\(314\) 202.061i 0.643506i
\(315\) −291.079 + 120.407i −0.924062 + 0.382243i
\(316\) 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
\(322\) −216.702 148.055i −0.672988 0.459797i
\(323\) 9.64022 9.64022i 0.0298459 0.0298459i
\(324\) −222.350 98.0286i −0.686265 0.302557i
\(325\) −13.3478 315.835i −0.0410703 0.971801i
\(326\) 137.398i 0.421465i
\(327\) −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
\(336\) 32.0796 99.9795i 0.0954749 0.297558i
\(337\) −333.576 + 333.576i −0.989840 + 0.989840i −0.999949 0.0101086i \(-0.996782\pi\)
0.0101086 + 0.999949i \(0.496782\pi\)
\(338\) −6.44308 + 6.44308i −0.0190624 + 0.0190624i
\(339\) 193.335 + 104.745i 0.570309 + 0.308981i
\(340\) 11.4929 + 4.47857i 0.0338025 + 0.0131723i
\(341\) 79.8317 0.234111
\(342\) −146.009 30.7577i −0.426928 0.0899348i
\(343\) 77.3019 334.176i 0.225370 0.974273i
\(344\) −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 \(-0.615297\pi\)
−0.354348 + 0.935114i \(0.615297\pi\)
\(350\) −148.535 92.5326i −0.424386 0.264379i
\(351\) 340.280 27.7152i 0.969458 0.0789607i
\(352\) −60.4214 + 60.4214i −0.171652 + 0.171652i
\(353\) 276.422 + 276.422i 0.783065 + 0.783065i 0.980347 0.197281i \(-0.0632113\pi\)
−0.197281 + 0.980347i \(0.563211\pi\)
\(354\) 125.616 + 68.0559i 0.354847 + 0.192248i
\(355\) −98.5552 224.409i −0.277620 0.632137i
\(356\) 42.1600 0.118427
\(357\) 7.89623 + 15.3574i 0.0221183 + 0.0430180i
\(358\) 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 0.315519 0.948919i \(-0.397821\pi\)
−0.948919 + 0.315519i \(0.897821\pi\)
\(368\) −132.557 + 132.557i −0.360210 + 0.360210i
\(369\) 129.288 84.2951i 0.350373 0.228442i
\(370\) 268.634 117.978i 0.726037 0.318859i
\(371\) −332.332 + 62.5453i −0.895774 + 0.168586i
\(372\) −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
\(378\) 93.5992 164.196i 0.247617 0.434380i
\(379\) 345.209i 0.910843i −0.890276 0.455422i \(-0.849489\pi\)
0.890276 0.455422i \(-0.150511\pi\)
\(380\) 100.000 + 227.698i 0.263158 + 0.599207i
\(381\) −80.7531 43.7503i −0.211950 0.114830i
\(382\) 262.295 262.295i 0.686637 0.686637i
\(383\) −46.7051 46.7051i −0.121945 0.121945i 0.643500 0.765446i \(-0.277482\pi\)
−0.765446 + 0.643500i \(0.777482\pi\)
\(384\) 313.893 + 170.060i 0.817428 + 0.442865i
\(385\) 16.7201 89.0718i 0.0434288 0.231355i
\(386\) 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
\(392\) 314.113 + 137.775i 0.801309 + 0.351468i
\(393\) −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 0.984366 0.176135i \(-0.0563597\pi\)
−0.176135 + 0.984366i \(0.556360\pi\)
\(398\) 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 \(0.799411\pi\)
\(402\) −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 \(-0.452425\pi\)
0.148907 + 0.988851i \(0.452425\pi\)
\(410\) 79.8930 + 31.1329i 0.194861 + 0.0759339i
\(411\) 65.0128 119.999i 0.158182 0.291968i
\(412\) 235.956 + 235.956i 0.572708 + 0.572708i
\(413\) 188.054 275.249i 0.455338 0.666462i
\(414\) −282.663 + 184.295i −0.682760 + 0.445158i
\(415\) 353.661 + 137.815i 0.852194 + 0.332085i
\(416\) −417.275 −1.00306
\(417\) −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 \(0.0346788\pi\)
−0.994071 + 0.108731i \(0.965321\pi\)
\(420\) −313.320 + 32.4922i −0.745999 + 0.0773623i
\(421\) 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
\(427\) −311.936 + 456.569i −0.730528 + 1.06925i
\(428\) 374.605 374.605i 0.875245 0.875245i
\(429\) −46.7903 + 86.3643i −0.109068 + 0.201315i
\(430\) 71.5233 + 162.857i 0.166333 + 0.378738i
\(431\) 179.188i 0.415749i −0.978156 0.207874i \(-0.933346\pi\)
0.978156 0.207874i \(-0.0666545\pi\)
\(432\) −102.894 87.3950i −0.238180 0.202303i
\(433\) −234.230 + 234.230i −0.540947 + 0.540947i −0.923806 0.382860i \(-0.874939\pi\)
0.382860 + 0.923806i \(0.374939\pi\)
\(434\) 212.092 39.9159i 0.488690 0.0919721i
\(435\) −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 \(-0.704611\pi\)
−0.599443 + 0.800417i \(0.704611\pi\)
\(440\) 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 \(-0.857622\pi\)
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
\(448\) −51.3354 + 75.1377i −0.114588 + 0.167718i
\(449\) −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
\(455\) 365.303 249.833i 0.802864 0.549083i
\(456\) −306.125 165.852i −0.671327 0.363710i
\(457\) −357.774 + 357.774i −0.782875 + 0.782875i −0.980315 0.197440i \(-0.936737\pi\)
0.197440 + 0.980315i \(0.436737\pi\)
\(458\) 108.761 + 108.761i 0.237470 + 0.237470i
\(459\) 22.1291 1.80237i 0.0482115 0.00392674i
\(460\) 524.012 + 204.198i 1.13916 + 0.443910i
\(461\) 563.655 1.22268 0.611339 0.791369i \(-0.290631\pi\)
0.611339 + 0.791369i \(0.290631\pi\)
\(462\) 24.8643 + 48.3588i 0.0538189 + 0.104673i
\(463\) −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 −0.935297 0.353864i \(-0.884867\pi\)
0.353864 + 0.935297i \(0.384867\pi\)
\(468\) 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 \(0.181834\pi\)
−0.841227 + 0.540682i \(0.818166\pi\)
\(480\) 40.8857 493.309i 0.0851786 1.02773i
\(481\) 741.987i 1.54259i
\(482\) −72.8542 + 72.8542i −0.151150 + 0.151150i
\(483\) 360.025 + 700.216i 0.745394 + 1.44972i
\(484\) 342.886i 0.708442i
\(485\) 171.079 + 66.6667i 0.352741 + 0.137457i
\(486\) −148.804 192.110i −0.306182 0.395288i
\(487\) 369.310 369.310i 0.758336 0.758336i −0.217684 0.976019i \(-0.569850\pi\)
0.976019 + 0.217684i \(0.0698501\pi\)
\(488\) −390.998 390.998i −0.801226 0.801226i
\(489\) 196.352 362.421i 0.401537 0.741147i
\(490\) −0.115057 245.000i −0.000234810 0.500000i
\(491\) 421.951i 0.859370i −0.902979 0.429685i \(-0.858625\pi\)
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
\(497\) 193.571 283.323i 0.389479 0.570067i
\(498\) −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 0.827725 0.561133i \(-0.189635\pi\)
−0.561133 + 0.827725i \(0.689635\pi\)
\(504\) 318.495 305.028i 0.631934 0.605214i
\(505\) 108.463 47.6345i 0.214778 0.0943258i
\(506\) 97.0824i 0.191862i
\(507\) 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 \(0.148960\pi\)
−0.892485 + 0.451077i \(0.851040\pi\)
\(510\) 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
\(518\) 339.159 + 231.719i 0.654747 + 0.447334i
\(519\) 233.315 430.646i 0.449547 0.829762i
\(520\) 177.958 + 405.208i 0.342228 + 0.779247i
\(521\) −303.734 −0.582983 −0.291491 0.956573i \(-0.594152\pi\)
−0.291491 + 0.956573i \(0.594152\pi\)
\(522\) 101.742 + 21.4325i 0.194908 + 0.0410585i
\(523\) 249.060 249.060i 0.476215 0.476215i −0.427704 0.903919i \(-0.640677\pi\)
0.903919 + 0.427704i \(0.140677\pi\)
\(524\) 652.986i 1.24616i
\(525\) 259.563 + 456.346i 0.494406 + 0.869231i
\(526\) 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
\(532\) −196.409 + 287.477i −0.369190 + 0.540370i
\(533\) −153.331 + 153.331i −0.287675 + 0.287675i
\(534\) 37.0692 + 20.0833i 0.0694181 + 0.0376092i
\(535\) −822.695 320.590i −1.53775 0.599234i
\(536\) 717.501i 1.33862i
\(537\) −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
\(546\) −81.1272 + 252.842i −0.148585 + 0.463080i
\(547\) 492.112 492.112i 0.899656 0.899656i −0.0957494 0.995405i \(-0.530525\pi\)
0.995405 + 0.0957494i \(0.0305247\pi\)
\(548\) 96.5049 96.5049i 0.176104 0.176104i
\(549\) 388.291 + 595.541i 0.707270 + 1.08477i
\(550\) −2.73335 64.6762i −0.00496972 0.117593i
\(551\) −191.537 −0.347617
\(552\) −754.723 + 224.306i −1.36725 + 0.406352i
\(553\) 299.334 438.125i 0.541291 0.792269i
\(554\) 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
\(560\) −171.996 32.2862i −0.307136 0.0576539i
\(561\) −3.04287 + 5.61644i −0.00542400 + 0.0100115i
\(562\) 4.47857 4.47857i 0.00796898 0.00796898i
\(563\) −510.844 510.844i −0.907361 0.907361i 0.0886978 0.996059i \(-0.471729\pi\)
−0.996059 + 0.0886978i \(0.971729\pi\)
\(564\) −274.337 + 506.364i −0.486414 + 0.897809i
\(565\) 133.063 341.466i 0.235510 0.604364i
\(566\) 342.455 0.605043
\(567\) −481.540 + 299.347i −0.849276 + 0.527948i
\(568\) 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 0.924407 0.381408i \(-0.124561\pi\)
−0.381408 + 0.924407i \(0.624561\pi\)
\(578\) −203.876 + 203.876i −0.352726 + 0.352726i
\(579\) 164.983 304.520i 0.284944 0.525942i
\(580\) −69.6819 158.665i −0.120141 0.273560i
\(581\) 98.2827 + 522.222i 0.169161 + 0.898833i
\(582\) −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 −0.568158 0.822920i \(-0.692344\pi\)
0.822920 + 0.568158i \(0.192344\pi\)
\(588\) −270.712 348.132i −0.460394 0.592062i
\(589\) 511.152i 0.867831i
\(590\) 86.4556 221.861i 0.146535 0.376036i
\(591\) 368.219 679.648i 0.623044 1.15000i
\(592\) 207.464 207.464i 0.350446 0.350446i
\(593\) −198.048 198.048i −0.333977 0.333977i 0.520118 0.854095i \(-0.325888\pi\)
−0.854095 + 0.520118i \(0.825888\pi\)
\(594\) 69.6819 5.67547i 0.117310 0.00955466i
\(595\) 23.7564 16.2471i 0.0399267 0.0273061i
\(596\) 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 \(0.100704\pi\)
−0.950371 + 0.311119i \(0.899296\pi\)
\(602\) −140.478 + 205.613i −0.233352 + 0.341549i
\(603\) −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 \(-0.986594\pi\)
−0.0421025 0.999113i \(-0.513406\pi\)
\(608\) −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
\(612\) 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 \(-0.303552\pi\)
0.578720 + 0.815526i \(0.303552\pi\)
\(620\) −423.426 + 185.959i −0.682945 + 0.299934i
\(621\) 1008.97 82.1785i 1.62474 0.132333i
\(622\) −61.8700 61.8700i −0.0994694 0.0994694i
\(623\) 55.4949 81.2259i 0.0890769 0.130379i
\(624\) 166.768 + 90.3512i 0.267256 + 0.144794i
\(625\) −52.7333 622.771i −0.0843734 0.996434i
\(626\) 106.006 0.169338
\(627\) −123.452 + 36.6905i −0.196894 + 0.0585175i
\(628\) −428.636 + 428.636i −0.682541 + 0.682541i
\(629\) 48.2529i 0.0767137i
\(630\) −290.965 120.684i −0.461849 0.191562i
\(631\) 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
\(637\) 567.409 + 248.875i 0.890751 + 0.390699i
\(638\) −21.1526 + 21.1526i −0.0331545 + 0.0331545i
\(639\) −240.953 369.562i −0.377079 0.578344i
\(640\) 216.038 554.394i 0.337559 0.866241i
\(641\) 121.164i 0.189024i 0.995524 + 0.0945120i \(0.0301291\pi\)
−0.995524 + 0.0945120i \(0.969871\pi\)
\(642\) 507.818 150.925i 0.790994 0.235086i
\(643\) 524.336 524.336i 0.815453 0.815453i −0.169993 0.985445i \(-0.554374\pi\)
0.985445 + 0.169993i \(0.0543744\pi\)
\(644\) 145.624 + 773.766i 0.226124 + 1.20150i
\(645\) 44.0751 531.790i 0.0683334 0.824480i
\(646\) 13.6333 0.0211042
\(647\) 305.897 305.897i 0.472792 0.472792i −0.430025 0.902817i \(-0.641495\pi\)
0.902817 + 0.430025i \(0.141495\pi\)
\(648\) −205.119 528.597i −0.316542 0.815736i
\(649\) 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 \(-0.857989\pi\)
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
\(658\) −369.847 252.686i −0.562078 0.384021i
\(659\) 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 \(0.341820\pi\)
−0.476737 + 0.879046i \(0.658180\pi\)
\(662\) 173.231 + 173.231i 0.261678 + 0.261678i
\(663\) −29.9009 + 8.88664i −0.0450994 + 0.0134037i
\(664\) −531.390 −0.800286
\(665\) 570.315 + 107.057i 0.857617 + 0.160987i
\(666\) 442.393 288.439i 0.664254 0.433092i
\(667\) −306.281 + 306.281i −0.459192 + 0.459192i
\(668\) 621.735 + 621.735i 0.930741 + 0.930741i
\(669\) 298.237 + 161.579i 0.445796 + 0.241523i
\(670\) −469.242 + 206.080i −0.700361 + 0.307583i
\(671\) −204.543 −0.304832
\(672\) 616.307 316.883i 0.917124 0.471552i
\(673\) 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 −0.866280 0.499559i \(-0.833496\pi\)
0.499559 + 0.866280i \(0.333496\pi\)
\(678\) 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 \(0.0385648\pi\)
−0.992670 + 0.120859i \(0.961435\pi\)
\(692\) 346.332 346.332i 0.500480 0.500480i
\(693\) 3.52251 163.091i 0.00508298 0.235341i
\(694\) 319.857i 0.460889i
\(695\) −515.338 + 226.325i −0.741493 + 0.325647i
\(696\) 213.314 + 115.569i 0.306485 + 0.166047i
\(697\) −9.97142 + 9.97142i −0.0143062 + 0.0143062i
\(698\) −174.892 174.892i −0.250562 0.250562i
\(699\) −187.613 101.645i −0.268402 0.145415i
\(700\) 118.800 + 511.382i 0.169714 + 0.730546i
\(701\) 602.095i 0.858908i 0.903089 + 0.429454i \(0.141294\pi\)
−0.903089 + 0.429454i \(0.858706\pi\)
\(702\) 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
\(707\) 136.938 + 93.5584i 0.193689 + 0.132332i
\(708\) −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
\(714\) −5.27586 + 16.4428i −0.00738916 + 0.0230292i
\(715\) 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 \(0.0916324\pi\)
−0.958850 + 0.283912i \(0.908368\pi\)
\(720\) −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 0.996196 0.0871447i \(-0.0277742\pi\)
−0.0871447 + 0.996196i \(0.527774\pi\)
\(728\) −349.526 + 511.589i −0.480118 + 0.702732i
\(729\) 117.969 + 719.392i 0.161823 + 0.986820i
\(730\) −168.562 + 74.0286i −0.230907 + 0.101409i
\(731\) −29.2530 −0.0400178
\(732\) 202.538 + 681.481i 0.276692 + 0.930985i
\(733\) 526.757 526.757i 0.718632 0.718632i −0.249693 0.968325i \(-0.580330\pi\)
0.968325 + 0.249693i \(0.0803298\pi\)
\(734\) 328.745i 0.447882i
\(735\) −349.820 + 646.414i −0.475946 + 0.879474i
\(736\) −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
\(742\) −279.221 190.768i −0.376308 0.257100i
\(743\) −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
\(756\) −546.865 + 149.757i −0.723367 + 0.198092i
\(757\) −269.069 + 269.069i −0.355441 + 0.355441i −0.862129 0.506688i \(-0.830870\pi\)
0.506688 + 0.862129i \(0.330870\pi\)
\(758\) 244.100 244.100i 0.322032 0.322032i
\(759\) −138.738 + 256.079i −0.182791 + 0.337390i
\(760\) −210.692 + 540.675i −0.277226 + 0.711414i
\(761\) −973.280 −1.27895 −0.639475 0.768812i \(-0.720848\pi\)
−0.639475 + 0.768812i \(0.720848\pi\)
\(762\) −26.1649 88.0372i −0.0343372 0.115534i
\(763\) −288.211 + 421.845i −0.377734 + 0.552876i
\(764\) −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 \(-0.259165\pi\)
0.686458 + 0.727169i \(0.259165\pi\)
\(770\) 74.8062 51.1604i 0.0971508 0.0664420i