Properties

Label 105.3.k.c.62.6
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 16
CM no
Inner twists 8

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 62.6
Root \(0.253395 + 0.611750i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.6

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.353553 0.353553i −0.507877 0.861430i \(-0.669569\pi\)
0.861430 + 0.507877i \(0.169569\pi\)
\(3\) −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 \(0.0375515\pi\)
−0.993049 + 0.117698i \(0.962449\pi\)
\(12\) −8.62705 2.56399i −0.718921 0.213666i
\(13\) 8.94114 + 8.94114i 0.687780 + 0.687780i 0.961741 0.273961i \(-0.0883338\pi\)
−0.273961 + 0.961741i \(0.588334\pi\)
\(14\) −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 \(-0.242301\pi\)
−0.689798 + 0.724002i \(0.742301\pi\)
\(18\) −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 0.986015 + 0.166657i \(0.0532972\pi\)
0.166657 + 0.986015i \(0.446703\pi\)
\(24\) −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 \(-0.834336\pi\)
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
\(35\) 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 −0.991527 0.129902i \(-0.958534\pi\)
−0.129902 0.991527i \(-0.541466\pi\)
\(38\) 11.7233 11.7233i 0.308509 0.308509i
\(39\) −33.3536 + 18.0702i −0.855219 + 0.463339i
\(40\) −12.7081 32.6114i −0.317703 0.815285i
\(41\) −17.1489 −0.418267 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(42\) −18.6760 9.60250i −0.444666 0.228631i
\(43\) −25.1548 + 25.1548i −0.584994 + 0.584994i −0.936272 0.351277i \(-0.885748\pi\)
0.351277 + 0.936272i \(0.385748\pi\)
\(44\) −7.76807 −0.176547
\(45\) 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 \(-0.0116593\pi\)
−0.0366205 + 0.999329i \(0.511659\pi\)
\(48\) 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 0.951665 0.307137i \(-0.0993710\pi\)
−0.307137 + 0.951665i \(0.599371\pi\)
\(54\) 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
\(63\) 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 0.996345 + 0.0854251i \(0.0272248\pi\)
0.0854251 + 0.996345i \(0.472775\pi\)
\(68\) −1.74438 + 1.74438i −0.0256527 + 0.0256527i
\(69\) −98.8969 + 53.5802i −1.43329 + 0.776524i
\(70\) 19.7579 28.8899i 0.282256 0.412712i
\(71\) 49.0193i 0.690413i −0.938527 0.345207i \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(72\) −12.9863 61.6470i −0.180365 0.856209i
\(73\) 26.0359 + 26.0359i 0.356656 + 0.356656i 0.862579 0.505923i \(-0.168848\pi\)
−0.505923 + 0.862579i \(0.668848\pi\)
\(74\) −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 \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(80\) 22.8898 + 10.0527i 0.286123 + 0.125659i
\(81\) 32.6762 + 74.1166i 0.403410 + 0.915019i
\(82\) −12.1261 + 12.1261i −0.147880 + 0.147880i
\(83\) −53.6785 + 53.6785i −0.646729 + 0.646729i −0.952201 0.305472i \(-0.901186\pi\)
0.305472 + 0.952201i \(0.401186\pi\)
\(84\) 59.9877 19.2477i 0.714139 0.229140i
\(85\) −1.49286 3.83095i −0.0175630 0.0450700i
\(86\) 35.5742i 0.413654i
\(87\) 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 \(-0.810618\pi\)
0.560476 + 0.828171i \(0.310618\pi\)
\(98\) −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 0.213362 0.976973i \(-0.431559\pi\)
−0.976973 + 0.213362i \(0.931559\pi\)
\(104\) 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 0.184083 0.982911i \(-0.441069\pi\)
0.982911 0.184083i \(-0.0589315\pi\)
\(108\) 52.4370 + 61.7362i 0.485528 + 0.571632i
\(109\) 72.9857i 0.669594i 0.942290 + 0.334797i \(0.108668\pi\)
−0.942290 + 0.334797i \(0.891332\pi\)
\(110\) −4.70083 12.0632i −0.0427348 0.109666i
\(111\) 154.783 83.8579i 1.39444 0.755477i
\(112\) 28.8991 19.7444i 0.258028 0.176289i
\(113\) −51.8276 51.8276i −0.458651 0.458651i 0.439562 0.898212i \(-0.355134\pi\)
−0.898212 + 0.439562i \(0.855134\pi\)
\(114\) 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 0.787179 0.616725i \(-0.211541\pi\)
−0.616725 + 0.787179i \(0.711541\pi\)
\(128\) −84.1457 84.1457i −0.657388 0.657388i
\(129\) −50.8383 93.8359i −0.394095 0.727410i
\(130\) −57.8869 25.4226i −0.445284 0.195559i
\(131\) 217.662 1.66154 0.830771 0.556614i \(-0.187900\pi\)
0.830771 + 0.556614i \(0.187900\pi\)
\(132\) 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 −0.579890 0.814695i \(-0.696904\pi\)
0.814695 + 0.579890i \(0.196904\pi\)
\(138\) −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 −0.996276 0.0862209i \(-0.972521\pi\)
0.0862209 + 0.996276i \(0.472521\pi\)
\(158\) −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 −0.343215 0.939257i \(-0.611516\pi\)
0.939257 + 0.343215i \(0.111516\pi\)
\(164\) 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 −0.959592 0.281396i \(-0.909203\pi\)
−0.281396 0.959592i \(-0.590797\pi\)
\(168\) 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 −0.289785 0.957092i \(-0.593584\pi\)
0.957092 + 0.289785i \(0.0935837\pi\)
\(174\) −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 \(0.216725\pi\)
−0.777030 + 0.629463i \(0.783275\pi\)
\(182\) −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 \(0.423222\pi\)
−0.238872 + 0.971051i \(0.576778\pi\)
\(192\) −37.3839 11.1106i −0.194708 0.0578678i
\(193\) 81.6333 81.6333i 0.422971 0.422971i −0.463255 0.886225i \(-0.653318\pi\)
0.886225 + 0.463255i \(0.153318\pi\)
\(194\) 36.7220i 0.189289i
\(195\) 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 −0.0725218 0.997367i \(-0.523105\pi\)
0.997367 + 0.0725218i \(0.0231047\pi\)
\(198\) −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 0.504750 0.863266i \(-0.331585\pi\)
−0.863266 + 0.504750i \(0.831585\pi\)
\(224\) 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 \(-0.193400\pi\)
−0.570886 + 0.821029i \(0.693400\pi\)
\(228\) −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 0.806748 0.590895i \(-0.201225\pi\)
−0.590895 + 0.806748i \(0.701225\pi\)
\(234\) −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 \(-0.931430\pi\)
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
\(245\) −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 0.517493 0.855687i \(-0.326865\pi\)
−0.855687 + 0.517493i \(0.826865\pi\)
\(258\) −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 0.867880 0.496774i \(-0.165482\pi\)
−0.496774 + 0.867880i \(0.665482\pi\)
\(264\) −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
\(273\) 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 0.793434 0.608656i \(-0.208291\pi\)
−0.608656 + 0.793434i \(0.708291\pi\)
\(278\) 79.5985 79.5985i 0.286325 0.286325i
\(279\) −151.548 + 232.436i −0.543182 + 0.833104i
\(280\) 202.229 + 138.306i 0.722246 + 0.493949i
\(281\) 6.33365i 0.0225397i 0.999936 + 0.0112698i \(0.00358738\pi\)
−0.999936 + 0.0112698i \(0.996413\pi\)
\(282\) −54.6893 + 184.013i −0.193934 + 0.652529i
\(283\) 242.152 + 242.152i 0.855661 + 0.855661i 0.990823 0.135163i \(-0.0431558\pi\)
−0.135163 + 0.990823i \(0.543156\pi\)
\(284\) 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 −0.148895 + 0.988853i \(0.547572\pi\)
−0.988853 + 0.148895i \(0.952428\pi\)
\(294\) 145.863 18.2483i 0.496132 0.0620689i
\(295\) −95.7464 + 218.013i −0.324564 + 0.739027i
\(296\) 410.758i 1.38770i
\(297\) 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 \(-0.664099\pi\)
0.870030 + 0.492999i \(0.164099\pi\)
\(308\) 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 0.816635 0.577154i \(-0.195837\pi\)
−0.577154 + 0.816635i \(0.695837\pi\)
\(314\) 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 −0.280048 + 0.959986i \(0.590350\pi\)
−0.959986 + 0.280048i \(0.909650\pi\)
\(318\) −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 0.0101086 0.999949i \(-0.496782\pi\)
−0.999949 + 0.0101086i \(0.996782\pi\)
\(338\) −6.44308 6.44308i −0.0190624 0.0190624i
\(339\) 193.335 104.745i 0.570309 0.308981i
\(340\) 11.4929 4.47857i 0.0338025 0.0131723i
\(341\) 79.8317 0.234111
\(342\) −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 −0.953425 0.301629i \(-0.902469\pi\)
0.301629 + 0.953425i \(0.402469\pi\)
\(348\) 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 −0.197281 0.980347i \(-0.563211\pi\)
0.980347 + 0.197281i \(0.0632113\pi\)
\(354\) 125.616 68.0559i 0.354847 0.192248i
\(355\) −98.5552 + 224.409i −0.277620 + 0.632137i
\(356\) 42.1600 0.118427
\(357\) 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 −0.948919 0.315519i \(-0.897821\pi\)
0.315519 + 0.948919i \(0.397821\pi\)
\(368\) −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 −0.918037 0.396494i \(-0.870227\pi\)
0.396494 + 0.918037i \(0.370227\pi\)
\(374\) 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 \(0.150511\pi\)
−0.890276 + 0.455422i \(0.849489\pi\)
\(380\) 100.000 227.698i 0.263158 0.599207i
\(381\) −80.7531 + 43.7503i −0.211950 + 0.114830i
\(382\) 262.295 + 262.295i 0.686637 + 0.686637i
\(383\) −46.7051 + 46.7051i −0.121945 + 0.121945i −0.765446 0.643500i \(-0.777482\pi\)
0.643500 + 0.765446i \(0.277482\pi\)
\(384\) 313.893 170.060i 0.817428 0.442865i
\(385\) 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 −0.176135 0.984366i \(-0.556360\pi\)
0.984366 + 0.176135i \(0.0563597\pi\)
\(398\) 22.0872 22.0872i 0.0554954 0.0554954i
\(399\) −106.371 331.518i −0.266595 0.830873i
\(400\) −84.5774 92.0417i −0.211443 0.230104i
\(401\) 472.603i 1.17856i −0.807928 0.589281i \(-0.799411\pi\)
0.807928 0.589281i \(-0.200589\pi\)
\(402\) −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 \(-0.965321\pi\)
0.994071 0.108731i \(-0.0346788\pi\)
\(420\) −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 \(0.0666545\pi\)
−0.978156 + 0.207874i \(0.933346\pi\)
\(432\) −102.894 + 87.3950i −0.238180 + 0.202303i
\(433\) −234.230 234.230i −0.540947 0.540947i 0.382860 0.923806i \(-0.374939\pi\)
−0.923806 + 0.382860i \(0.874939\pi\)
\(434\) 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 0.432527 0.901621i \(-0.357622\pi\)
−0.901621 + 0.432527i \(0.857622\pi\)
\(444\) 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 0.197440 0.980315i \(-0.436737\pi\)
−0.980315 + 0.197440i \(0.936737\pi\)
\(458\) 108.761 108.761i 0.237470 0.237470i
\(459\) 22.1291 + 1.80237i 0.0482115 + 0.00392674i
\(460\) 524.012 204.198i 1.13916 0.443910i
\(461\) 563.655 1.22268 0.611339 0.791369i \(-0.290631\pi\)
0.611339 + 0.791369i \(0.290631\pi\)
\(462\) 24.8643 48.3588i 0.0538189 0.104673i
\(463\) −26.9857 + 26.9857i −0.0582845 + 0.0582845i −0.735648 0.677364i \(-0.763122\pi\)
0.677364 + 0.735648i \(0.263122\pi\)
\(464\) 57.7639 0.124491
\(465\) −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 \(-0.384867\pi\)
−0.935297 + 0.353864i \(0.884867\pi\)
\(468\) 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
\(483\) 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 0.976019 0.217684i \(-0.0698501\pi\)
−0.217684 + 0.976019i \(0.569850\pi\)
\(488\) −390.998 + 390.998i −0.801226 + 0.801226i
\(489\) 196.352 + 362.421i 0.401537 + 0.741147i
\(490\) −0.115057 + 245.000i −0.000234810 + 0.500000i
\(491\) 421.951i 0.859370i 0.902979 + 0.429685i \(0.141375\pi\)
−0.902979 + 0.429685i \(0.858625\pi\)
\(492\) 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 \(-0.965080\pi\)
0.993988 0.109486i \(-0.0349204\pi\)
\(500\) 354.846 121.283i 0.709691 0.242567i
\(501\) 773.095 418.846i 1.54310 0.836021i
\(502\) 256.959 256.959i 0.511871 0.511871i
\(503\) 134.096 134.096i 0.266592 0.266592i −0.561133 0.827725i \(-0.689635\pi\)
0.827725 + 0.561133i \(0.189635\pi\)
\(504\) 318.495 + 305.028i 0.631934 + 0.605214i
\(505\) 108.463 + 47.6345i 0.214778 + 0.0943258i
\(506\) 97.0824i 0.191862i
\(507\) 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
\(518\) 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 0.903919 0.427704i \(-0.140677\pi\)
−0.427704 + 0.903919i \(0.640677\pi\)
\(524\) 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 0.995405 0.0957494i \(-0.0305247\pi\)
−0.0957494 + 0.995405i \(0.530525\pi\)
\(548\) 96.5049 + 96.5049i 0.176104 + 0.176104i
\(549\) 388.291 595.541i 0.707270 1.08477i
\(550\) −2.73335 + 64.6762i −0.00496972 + 0.117593i
\(551\) −191.537 −0.347617
\(552\) −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 −0.937479 0.348042i \(-0.886847\pi\)
0.348042 + 0.937479i \(0.386847\pi\)
\(558\) 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 −0.996059 0.0886978i \(-0.971729\pi\)
0.0886978 + 0.996059i \(0.471729\pi\)
\(564\) −274.337 506.364i −0.486414 0.897809i
\(565\) 133.063 + 341.466i 0.235510 + 0.604364i
\(566\) 342.455 0.605043
\(567\) −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 −0.381408 0.924407i \(-0.624561\pi\)
0.924407 + 0.381408i \(0.124561\pi\)
\(578\) −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 \(-0.192344\pi\)
−0.568158 + 0.822920i \(0.692344\pi\)
\(588\) −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 −0.854095 0.520118i \(-0.825888\pi\)
0.520118 + 0.854095i \(0.325888\pi\)
\(594\) 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 \(-0.899296\pi\)
0.950371 0.311119i \(-0.100704\pi\)
\(602\) −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 −0.0421025 + 0.999113i \(0.513406\pi\)
−0.999113 + 0.0421025i \(0.986594\pi\)
\(608\) −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 −0.0412636 0.999148i \(-0.513138\pi\)
0.999148 + 0.0412636i \(0.0131383\pi\)
\(614\) 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 −0.611279 0.791415i \(-0.709345\pi\)
0.791415 + 0.611279i \(0.209345\pi\)
\(618\) 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 \(-0.969871\pi\)
0.995524 0.0945120i \(-0.0301291\pi\)
\(642\) 507.818 + 150.925i 0.790994 + 0.235086i
\(643\) 524.336 + 524.336i 0.815453 + 0.815453i 0.985445 0.169993i \(-0.0543744\pi\)
−0.169993 + 0.985445i \(0.554374\pi\)
\(644\) 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 \(-0.141495\pi\)
−0.430025 + 0.902817i \(0.641495\pi\)
\(648\) −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 0.431488 0.902119i \(-0.357989\pi\)
−0.902119 + 0.431488i \(0.857989\pi\)
\(654\) −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 \(-0.658180\pi\)
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
\(665\) 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 −0.490040 0.871700i \(-0.663018\pi\)
0.871700 + 0.490040i \(0.163018\pi\)
\(674\) −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 \(-0.333496\pi\)
−0.866280 + 0.499559i \(0.833496\pi\)
\(678\) 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 0.530952 0.847402i \(-0.321835\pi\)
−0.847402 + 0.530952i \(0.821835\pi\)
\(684\) 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
\(693\) 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 \(-0.858706\pi\)
0.903089 0.429454i \(-0.141294\pi\)
\(702\) 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 \(-0.991506\pi\)
0.999644 0.0266808i \(-0.00849377\pi\)
\(710\) 88.9918 + 228.370i 0.125341 + 0.321648i
\(711\) −372.605 + 571.482i −0.524057 + 0.803772i
\(712\) 69.5605 69.5605i 0.0976973 0.0976973i
\(713\) 817.367 817.367i 1.14638 1.14638i
\(714\) −5.27586 16.4428i −0.00738916 0.0230292i
\(715\) 152.536 59.4405i 0.213337 0.0831336i
\(716\) 710.612i 0.992475i
\(717\) 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 \(-0.527774\pi\)
0.996196 + 0.0871447i \(0.0277742\pi\)
\(728\) −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 0.968325 0.249693i \(-0.0803298\pi\)
−0.249693 + 0.968325i \(0.580330\pi\)
\(734\) 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 \(-0.939993\pi\)
0.982283 0.187402i \(-0.0600069\pi\)
\(740\) −820.127 + 319.589i −1.10828 + 0.431877i
\(741\) −552.979 + 299.592i −0.746261 + 0.404308i
\(742\) −279.221 + 190.768i −0.376308 + 0.257100i
\(743\) −698.839 698.839i −0.940563 0.940563i 0.0577666 0.998330i \(-0.481602\pi\)
−0.998330 + 0.0577666i \(0.981602\pi\)
\(744\) 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 0.506688 0.862129i \(-0.330870\pi\)
−0.862129 + 0.506688i \(0.830870\pi\)
\(758\) 244.100 + 244.100i 0.322032 + 0.322032i
\(759\) −138.738 256.079i −0.182791 0.337390i
\(760\) −210.692 540.675i −0.277226 0.711414i
\(761\) −973.280 −1.27895 −0.639475 0.768812i \(-0.720848\pi\)
−0.639475 + 0.768812i \(0.720848\pi\)
\(762\) −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 \(0.259165\pi\)
\(770\)