Properties

Label 108.3.f.c.19.6
Level 108
Weight 3
Character 108.19
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.6
Root \(1.63139 - 1.15696i\) of defining polynomial
Character \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})\) \(q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(15.1205 + 8.72982i) q^{11} +(-0.892255 - 1.54543i) q^{13} +(-1.17622 + 0.110024i) q^{14} +(-12.5001 - 9.98742i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(-24.1656 + 4.56079i) q^{20} +(34.7675 - 3.25214i) q^{22} +(-6.86778 + 3.96511i) q^{23} +(-6.39933 + 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 + 5.49956i) q^{29} +(-27.6558 + 15.9671i) q^{31} +(-31.9476 - 1.83125i) q^{32} +(27.5984 - 19.5725i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(22.5675 + 31.8215i) q^{38} +(-34.1469 + 35.3992i) q^{40} +(2.66948 + 4.62368i) q^{41} +(33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(-9.64117 - 5.56633i) q^{47} +(-24.3255 - 42.1331i) q^{49} +(2.38396 + 25.4861i) q^{50} +(-7.01421 + 1.32380i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-1.14066 + 4.58570i) q^{56} +(1.18285 + 12.6455i) q^{58} +(-20.8974 + 12.0651i) q^{59} +(-37.9460 + 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 + 9.50141i) q^{65} +(31.8200 - 18.3713i) q^{67} +(22.3790 - 63.8607i) q^{68} +(4.20156 + 5.92445i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(95.0830 - 67.4319i) q^{74} +(73.6328 + 25.8035i) q^{76} +(-5.15652 - 8.93136i) q^{77} +(-32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(-66.0281 - 38.1214i) q^{83} +(-52.0037 - 90.0730i) q^{85} +(78.0229 - 7.29823i) q^{86} +(33.7161 - 135.547i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(5.88285 + 31.1706i) q^{92} +(-22.1686 + 2.07364i) q^{94} +(103.856 - 59.9614i) q^{95} +(13.0585 - 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.63139 1.15696i 0.815695 0.578482i
\(3\) 0 0
\(4\) 1.32286 3.77492i 0.330716 0.943730i
\(5\) −3.07403 5.32438i −0.614806 1.06488i −0.990418 0.138099i \(-0.955901\pi\)
0.375612 0.926777i \(-0.377432\pi\)
\(6\) 0 0
\(7\) −0.511543 0.295340i −0.0730776 0.0421914i 0.463016 0.886350i \(-0.346767\pi\)
−0.536094 + 0.844159i \(0.680101\pi\)
\(8\) −2.20934 7.68888i −0.276168 0.961109i
\(9\) 0 0
\(10\) −11.1751 5.12959i −1.11751 0.512959i
\(11\) 15.1205 + 8.72982i 1.37459 + 0.793620i 0.991502 0.130092i \(-0.0415274\pi\)
0.383088 + 0.923712i \(0.374861\pi\)
\(12\) 0 0
\(13\) −0.892255 1.54543i −0.0686350 0.118879i 0.829666 0.558261i \(-0.188531\pi\)
−0.898301 + 0.439381i \(0.855198\pi\)
\(14\) −1.17622 + 0.110024i −0.0840160 + 0.00785882i
\(15\) 0 0
\(16\) −12.5001 9.98742i −0.781254 0.624214i
\(17\) 16.9171 0.995123 0.497562 0.867429i \(-0.334229\pi\)
0.497562 + 0.867429i \(0.334229\pi\)
\(18\) 0 0
\(19\) 19.5058i 1.02662i 0.858203 + 0.513310i \(0.171581\pi\)
−0.858203 + 0.513310i \(0.828419\pi\)
\(20\) −24.1656 + 4.56079i −1.20828 + 0.228040i
\(21\) 0 0
\(22\) 34.7675 3.25214i 1.58034 0.147824i
\(23\) −6.86778 + 3.96511i −0.298599 + 0.172396i −0.641813 0.766861i \(-0.721818\pi\)
0.343214 + 0.939257i \(0.388484\pi\)
\(24\) 0 0
\(25\) −6.39933 + 11.0840i −0.255973 + 0.443359i
\(26\) −3.24362 1.48889i −0.124755 0.0572651i
\(27\) 0 0
\(28\) −1.79159 + 1.54034i −0.0639852 + 0.0550122i
\(29\) −3.17517 + 5.49956i −0.109489 + 0.189640i −0.915563 0.402174i \(-0.868255\pi\)
0.806075 + 0.591814i \(0.201588\pi\)
\(30\) 0 0
\(31\) −27.6558 + 15.9671i −0.892124 + 0.515068i −0.874637 0.484779i \(-0.838900\pi\)
−0.0174873 + 0.999847i \(0.505567\pi\)
\(32\) −31.9476 1.83125i −0.998361 0.0572266i
\(33\) 0 0
\(34\) 27.5984 19.5725i 0.811717 0.575661i
\(35\) 3.63153i 0.103758i
\(36\) 0 0
\(37\) 58.2834 1.57523 0.787614 0.616169i \(-0.211316\pi\)
0.787614 + 0.616169i \(0.211316\pi\)
\(38\) 22.5675 + 31.8215i 0.593881 + 0.837408i
\(39\) 0 0
\(40\) −34.1469 + 35.3992i −0.853672 + 0.884980i
\(41\) 2.66948 + 4.62368i 0.0651093 + 0.112773i 0.896742 0.442553i \(-0.145927\pi\)
−0.831633 + 0.555325i \(0.812594\pi\)
\(42\) 0 0
\(43\) 33.9324 + 19.5909i 0.789126 + 0.455602i 0.839655 0.543121i \(-0.182757\pi\)
−0.0505290 + 0.998723i \(0.516091\pi\)
\(44\) 52.9567 45.5303i 1.20356 1.03478i
\(45\) 0 0
\(46\) −6.61653 + 14.4144i −0.143838 + 0.313357i
\(47\) −9.64117 5.56633i −0.205131 0.118433i 0.393915 0.919147i \(-0.371120\pi\)
−0.599047 + 0.800714i \(0.704454\pi\)
\(48\) 0 0
\(49\) −24.3255 42.1331i −0.496440 0.859859i
\(50\) 2.38396 + 25.4861i 0.0476791 + 0.509721i
\(51\) 0 0
\(52\) −7.01421 + 1.32380i −0.134889 + 0.0254576i
\(53\) −35.8770 −0.676925 −0.338462 0.940980i \(-0.609907\pi\)
−0.338462 + 0.940980i \(0.609907\pi\)
\(54\) 0 0
\(55\) 107.343i 1.95169i
\(56\) −1.14066 + 4.58570i −0.0203689 + 0.0818875i
\(57\) 0 0
\(58\) 1.18285 + 12.6455i 0.0203940 + 0.218026i
\(59\) −20.8974 + 12.0651i −0.354194 + 0.204494i −0.666531 0.745477i \(-0.732222\pi\)
0.312337 + 0.949971i \(0.398888\pi\)
\(60\) 0 0
\(61\) −37.9460 + 65.7244i −0.622066 + 1.07745i 0.367034 + 0.930207i \(0.380373\pi\)
−0.989100 + 0.147243i \(0.952960\pi\)
\(62\) −26.6441 + 58.0454i −0.429743 + 0.936216i
\(63\) 0 0
\(64\) −54.2376 + 33.9747i −0.847463 + 0.530855i
\(65\) −5.48564 + 9.50141i −0.0843944 + 0.146175i
\(66\) 0 0
\(67\) 31.8200 18.3713i 0.474925 0.274198i −0.243374 0.969933i \(-0.578254\pi\)
0.718299 + 0.695734i \(0.244921\pi\)
\(68\) 22.3790 63.8607i 0.329103 0.939128i
\(69\) 0 0
\(70\) 4.20156 + 5.92445i 0.0600222 + 0.0846350i
\(71\) 87.8370i 1.23714i −0.785730 0.618570i \(-0.787712\pi\)
0.785730 0.618570i \(-0.212288\pi\)
\(72\) 0 0
\(73\) −60.0423 −0.822498 −0.411249 0.911523i \(-0.634907\pi\)
−0.411249 + 0.911523i \(0.634907\pi\)
\(74\) 95.0830 67.4319i 1.28490 0.911241i
\(75\) 0 0
\(76\) 73.6328 + 25.8035i 0.968852 + 0.339520i
\(77\) −5.15652 8.93136i −0.0669678 0.115992i
\(78\) 0 0
\(79\) −32.1841 18.5815i −0.407394 0.235209i 0.282275 0.959333i \(-0.408911\pi\)
−0.689669 + 0.724124i \(0.742244\pi\)
\(80\) −14.7512 + 97.2567i −0.184391 + 1.21571i
\(81\) 0 0
\(82\) 9.70439 + 4.45452i 0.118346 + 0.0543234i
\(83\) −66.0281 38.1214i −0.795520 0.459294i 0.0463824 0.998924i \(-0.485231\pi\)
−0.841902 + 0.539630i \(0.818564\pi\)
\(84\) 0 0
\(85\) −52.0037 90.0730i −0.611808 1.05968i
\(86\) 78.0229 7.29823i 0.907243 0.0848632i
\(87\) 0 0
\(88\) 33.7161 135.547i 0.383138 1.54030i
\(89\) 27.5873 0.309969 0.154985 0.987917i \(-0.450467\pi\)
0.154985 + 0.987917i \(0.450467\pi\)
\(90\) 0 0
\(91\) 1.05407i 0.0115832i
\(92\) 5.88285 + 31.1706i 0.0639440 + 0.338811i
\(93\) 0 0
\(94\) −22.1686 + 2.07364i −0.235836 + 0.0220600i
\(95\) 103.856 59.9614i 1.09322 0.631172i
\(96\) 0 0
\(97\) 13.0585 22.6180i 0.134624 0.233176i −0.790830 0.612036i \(-0.790351\pi\)
0.925454 + 0.378861i \(0.123684\pi\)
\(98\) −88.4309 40.5917i −0.902357 0.414201i
\(99\) 0 0
\(100\) 33.3757 + 38.8196i 0.333757 + 0.388196i
\(101\) 12.8831 22.3142i 0.127556 0.220933i −0.795173 0.606382i \(-0.792620\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(102\) 0 0
\(103\) 16.9947 9.81187i 0.164997 0.0952609i −0.415228 0.909717i \(-0.636298\pi\)
0.580225 + 0.814457i \(0.302965\pi\)
\(104\) −9.91133 + 10.2748i −0.0953012 + 0.0987964i
\(105\) 0 0
\(106\) −58.5294 + 41.5085i −0.552164 + 0.391589i
\(107\) 183.200i 1.71215i 0.516850 + 0.856076i \(0.327105\pi\)
−0.516850 + 0.856076i \(0.672895\pi\)
\(108\) 0 0
\(109\) 100.841 0.925147 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(110\) −124.192 175.118i −1.12902 1.59198i
\(111\) 0 0
\(112\) 3.44464 + 8.80076i 0.0307557 + 0.0785782i
\(113\) 9.12484 + 15.8047i 0.0807508 + 0.139865i 0.903573 0.428435i \(-0.140935\pi\)
−0.822822 + 0.568299i \(0.807602\pi\)
\(114\) 0 0
\(115\) 42.2235 + 24.3778i 0.367161 + 0.211981i
\(116\) 16.5601 + 19.2612i 0.142759 + 0.166045i
\(117\) 0 0
\(118\) −20.1329 + 43.8606i −0.170618 + 0.371700i
\(119\) −8.65383 4.99629i −0.0727212 0.0419856i
\(120\) 0 0
\(121\) 91.9194 + 159.209i 0.759664 + 1.31578i
\(122\) 14.1361 + 151.124i 0.115870 + 1.23872i
\(123\) 0 0
\(124\) 23.6896 + 125.521i 0.191045 + 1.01227i
\(125\) −75.0146 −0.600117
\(126\) 0 0
\(127\) 164.386i 1.29438i 0.762331 + 0.647188i \(0.224055\pi\)
−0.762331 + 0.647188i \(0.775945\pi\)
\(128\) −49.1751 + 118.177i −0.384181 + 0.923258i
\(129\) 0 0
\(130\) 2.04358 + 21.8472i 0.0157198 + 0.168055i
\(131\) −123.421 + 71.2570i −0.942143 + 0.543947i −0.890631 0.454726i \(-0.849737\pi\)
−0.0515116 + 0.998672i \(0.516404\pi\)
\(132\) 0 0
\(133\) 5.76083 9.97805i 0.0433145 0.0750229i
\(134\) 30.6559 66.7853i 0.228775 0.498398i
\(135\) 0 0
\(136\) −37.3757 130.073i −0.274821 0.956422i
\(137\) 3.08176 5.33777i 0.0224946 0.0389618i −0.854559 0.519354i \(-0.826172\pi\)
0.877054 + 0.480393i \(0.159506\pi\)
\(138\) 0 0
\(139\) −103.168 + 59.5642i −0.742218 + 0.428519i −0.822875 0.568222i \(-0.807631\pi\)
0.0806575 + 0.996742i \(0.474298\pi\)
\(140\) 13.7088 + 4.80403i 0.0979197 + 0.0343145i
\(141\) 0 0
\(142\) −101.624 143.296i −0.715664 1.00913i
\(143\) 31.1569i 0.217880i
\(144\) 0 0
\(145\) 39.0423 0.269257
\(146\) −97.9524 + 69.4669i −0.670907 + 0.475800i
\(147\) 0 0
\(148\) 77.1011 220.015i 0.520953 1.48659i
\(149\) 103.365 + 179.034i 0.693726 + 1.20157i 0.970608 + 0.240665i \(0.0773657\pi\)
−0.276882 + 0.960904i \(0.589301\pi\)
\(150\) 0 0
\(151\) −127.422 73.5670i −0.843853 0.487199i 0.0147190 0.999892i \(-0.495315\pi\)
−0.858572 + 0.512693i \(0.828648\pi\)
\(152\) 149.977 43.0949i 0.986694 0.283519i
\(153\) 0 0
\(154\) −18.7456 8.60461i −0.121724 0.0558741i
\(155\) 170.030 + 98.1668i 1.09697 + 0.633334i
\(156\) 0 0
\(157\) 31.4395 + 54.4548i 0.200251 + 0.346846i 0.948609 0.316449i \(-0.102491\pi\)
−0.748358 + 0.663295i \(0.769157\pi\)
\(158\) −74.0030 + 6.92221i −0.468373 + 0.0438115i
\(159\) 0 0
\(160\) 88.4575 + 175.730i 0.552859 + 1.09831i
\(161\) 4.68422 0.0290946
\(162\) 0 0
\(163\) 143.325i 0.879292i 0.898171 + 0.439646i \(0.144896\pi\)
−0.898171 + 0.439646i \(0.855104\pi\)
\(164\) 20.9854 3.96058i 0.127960 0.0241499i
\(165\) 0 0
\(166\) −151.823 + 14.2014i −0.914595 + 0.0855508i
\(167\) 150.531 86.9089i 0.901381 0.520413i 0.0237332 0.999718i \(-0.492445\pi\)
0.877648 + 0.479306i \(0.159111\pi\)
\(168\) 0 0
\(169\) 82.9078 143.600i 0.490578 0.849707i
\(170\) −189.050 86.7777i −1.11206 0.510457i
\(171\) 0 0
\(172\) 118.842 102.176i 0.690942 0.594047i
\(173\) 125.806 217.902i 0.727201 1.25955i −0.230861 0.972987i \(-0.574154\pi\)
0.958062 0.286562i \(-0.0925125\pi\)
\(174\) 0 0
\(175\) 6.54707 3.77995i 0.0374118 0.0215997i
\(176\) −101.819 260.138i −0.578515 1.47806i
\(177\) 0 0
\(178\) 45.0056 31.9175i 0.252840 0.179312i
\(179\) 96.0059i 0.536346i 0.963371 + 0.268173i \(0.0864199\pi\)
−0.963371 + 0.268173i \(0.913580\pi\)
\(180\) 0 0
\(181\) −328.757 −1.81634 −0.908170 0.418603i \(-0.862520\pi\)
−0.908170 + 0.418603i \(0.862520\pi\)
\(182\) 1.21953 + 1.71960i 0.00670069 + 0.00944838i
\(183\) 0 0
\(184\) 45.6605 + 44.0452i 0.248155 + 0.239376i
\(185\) −179.165 310.323i −0.968460 1.67742i
\(186\) 0 0
\(187\) 255.795 + 147.683i 1.36789 + 0.789749i
\(188\) −33.7664 + 29.0312i −0.179609 + 0.154421i
\(189\) 0 0
\(190\) 100.057 217.978i 0.526614 1.14725i
\(191\) −0.351914 0.203178i −0.00184248 0.00106376i 0.499078 0.866557i \(-0.333672\pi\)
−0.500921 + 0.865493i \(0.667005\pi\)
\(192\) 0 0
\(193\) −31.2230 54.0798i −0.161777 0.280206i 0.773729 0.633517i \(-0.218389\pi\)
−0.935506 + 0.353311i \(0.885056\pi\)
\(194\) −4.86472 52.0071i −0.0250759 0.268078i
\(195\) 0 0
\(196\) −191.228 + 36.0906i −0.975656 + 0.184136i
\(197\) 207.861 1.05513 0.527566 0.849514i \(-0.323105\pi\)
0.527566 + 0.849514i \(0.323105\pi\)
\(198\) 0 0
\(199\) 299.128i 1.50316i −0.659643 0.751579i \(-0.729293\pi\)
0.659643 0.751579i \(-0.270707\pi\)
\(200\) 99.3616 + 24.7154i 0.496808 + 0.123577i
\(201\) 0 0
\(202\) −4.79938 51.3085i −0.0237593 0.254003i
\(203\) 3.24848 1.87551i 0.0160024 0.00923896i
\(204\) 0 0
\(205\) 16.4121 28.4266i 0.0800592 0.138667i
\(206\) 16.3729 35.6692i 0.0794802 0.173152i
\(207\) 0 0
\(208\) −4.28163 + 28.2293i −0.0205848 + 0.135718i
\(209\) −170.282 + 294.937i −0.814746 + 1.41118i
\(210\) 0 0
\(211\) 141.744 81.8360i 0.671773 0.387848i −0.124975 0.992160i \(-0.539885\pi\)
0.796748 + 0.604311i \(0.206552\pi\)
\(212\) −47.4605 + 135.433i −0.223870 + 0.638835i
\(213\) 0 0
\(214\) 211.956 + 298.871i 0.990450 + 1.39659i
\(215\) 240.892i 1.12043i
\(216\) 0 0
\(217\) 18.8629 0.0869257
\(218\) 164.511 116.669i 0.754637 0.535181i
\(219\) 0 0
\(220\) −405.211 142.000i −1.84187 0.645455i
\(221\) −15.0944 26.1442i −0.0683003 0.118300i
\(222\) 0 0
\(223\) −330.681 190.919i −1.48287 0.856138i −0.483063 0.875586i \(-0.660476\pi\)
−0.999811 + 0.0194478i \(0.993809\pi\)
\(224\) 15.8017 + 10.3721i 0.0705434 + 0.0463042i
\(225\) 0 0
\(226\) 33.1717 + 15.2265i 0.146777 + 0.0673739i
\(227\) −51.5472 29.7608i −0.227080 0.131105i 0.382144 0.924103i \(-0.375186\pi\)
−0.609224 + 0.792998i \(0.708519\pi\)
\(228\) 0 0
\(229\) 64.4366 + 111.608i 0.281383 + 0.487369i 0.971726 0.236113i \(-0.0758736\pi\)
−0.690343 + 0.723482i \(0.742540\pi\)
\(230\) 97.0873 9.08150i 0.422118 0.0394848i
\(231\) 0 0
\(232\) 49.3005 + 12.2631i 0.212502 + 0.0528582i
\(233\) −14.9939 −0.0643513 −0.0321757 0.999482i \(-0.510244\pi\)
−0.0321757 + 0.999482i \(0.510244\pi\)
\(234\) 0 0
\(235\) 68.4443i 0.291252i
\(236\) 17.9005 + 94.8467i 0.0758495 + 0.401893i
\(237\) 0 0
\(238\) −19.8983 + 1.86128i −0.0836063 + 0.00782050i
\(239\) −315.244 + 182.006i −1.31901 + 0.761532i −0.983570 0.180529i \(-0.942219\pi\)
−0.335442 + 0.942061i \(0.608886\pi\)
\(240\) 0 0
\(241\) −40.5235 + 70.1888i −0.168147 + 0.291240i −0.937769 0.347261i \(-0.887112\pi\)
0.769621 + 0.638501i \(0.220445\pi\)
\(242\) 334.156 + 153.385i 1.38081 + 0.633820i
\(243\) 0 0
\(244\) 197.907 + 230.188i 0.811095 + 0.943393i
\(245\) −149.555 + 259.037i −0.610428 + 1.05729i
\(246\) 0 0
\(247\) 30.1448 17.4041i 0.122044 0.0704620i
\(248\) 183.870 + 177.366i 0.741413 + 0.715184i
\(249\) 0 0
\(250\) −122.378 + 86.7892i −0.489512 + 0.347157i
\(251\) 281.883i 1.12304i −0.827463 0.561520i \(-0.810217\pi\)
0.827463 0.561520i \(-0.189783\pi\)
\(252\) 0 0
\(253\) −138.459 −0.547268
\(254\) 190.188 + 268.177i 0.748773 + 1.05582i
\(255\) 0 0
\(256\) 56.5028 + 249.687i 0.220714 + 0.975339i
\(257\) 37.6564 + 65.2227i 0.146523 + 0.253785i 0.929940 0.367711i \(-0.119858\pi\)
−0.783417 + 0.621496i \(0.786525\pi\)
\(258\) 0 0
\(259\) −29.8145 17.2134i −0.115114 0.0664610i
\(260\) 28.6103 + 33.2769i 0.110040 + 0.127988i
\(261\) 0 0
\(262\) −118.905 + 259.041i −0.453838 + 0.988708i
\(263\) −105.914 61.1497i −0.402716 0.232508i 0.284939 0.958546i \(-0.408027\pi\)
−0.687655 + 0.726037i \(0.741360\pi\)
\(264\) 0 0
\(265\) 110.287 + 191.023i 0.416178 + 0.720841i
\(266\) −2.14609 22.9432i −0.00806802 0.0862525i
\(267\) 0 0
\(268\) −27.2566 144.421i −0.101704 0.538883i
\(269\) −280.452 −1.04257 −0.521287 0.853382i \(-0.674548\pi\)
−0.521287 + 0.853382i \(0.674548\pi\)
\(270\) 0 0
\(271\) 81.4468i 0.300542i −0.988645 0.150271i \(-0.951985\pi\)
0.988645 0.150271i \(-0.0480146\pi\)
\(272\) −211.465 168.958i −0.777443 0.621170i
\(273\) 0 0
\(274\) −1.14805 12.2735i −0.00418998 0.0447937i
\(275\) −193.522 + 111.730i −0.703716 + 0.406291i
\(276\) 0 0
\(277\) 224.861 389.471i 0.811774 1.40603i −0.0998479 0.995003i \(-0.531836\pi\)
0.911622 0.411031i \(-0.134831\pi\)
\(278\) −99.3939 + 216.534i −0.357532 + 0.778901i
\(279\) 0 0
\(280\) 27.9224 8.02330i 0.0997229 0.0286546i
\(281\) 37.8649 65.5838i 0.134750 0.233394i −0.790752 0.612137i \(-0.790310\pi\)
0.925502 + 0.378743i \(0.123643\pi\)
\(282\) 0 0
\(283\) 322.061 185.942i 1.13803 0.657039i 0.192084 0.981378i \(-0.438475\pi\)
0.945941 + 0.324339i \(0.105142\pi\)
\(284\) −331.578 116.196i −1.16753 0.409142i
\(285\) 0 0
\(286\) −36.0474 50.8290i −0.126040 0.177724i
\(287\) 3.15361i 0.0109882i
\(288\) 0 0
\(289\) −2.81196 −0.00972996
\(290\) 63.6932 45.1706i 0.219632 0.155761i
\(291\) 0 0
\(292\) −79.4279 + 226.655i −0.272013 + 0.776216i
\(293\) 66.3946 + 114.999i 0.226603 + 0.392488i 0.956799 0.290750i \(-0.0939047\pi\)
−0.730196 + 0.683237i \(0.760571\pi\)
\(294\) 0 0
\(295\) 128.479 + 74.1772i 0.435521 + 0.251448i
\(296\) −128.768 448.134i −0.435027 1.51397i
\(297\) 0 0
\(298\) 375.765 + 172.484i 1.26096 + 0.578806i
\(299\) 12.2556 + 7.07579i 0.0409887 + 0.0236648i
\(300\) 0 0
\(301\) −11.5719 20.0432i −0.0384450 0.0665886i
\(302\) −292.989 + 27.4061i −0.970163 + 0.0907486i
\(303\) 0 0
\(304\) 194.812 243.823i 0.640830 0.802050i
\(305\) 466.589 1.52980
\(306\) 0 0
\(307\) 336.514i 1.09614i 0.836434 + 0.548068i \(0.184637\pi\)
−0.836434 + 0.548068i \(0.815363\pi\)
\(308\) −40.5366 + 7.65048i −0.131612 + 0.0248392i
\(309\) 0 0
\(310\) 390.960 36.5703i 1.26116 0.117969i
\(311\) 304.206 175.634i 0.978156 0.564738i 0.0764428 0.997074i \(-0.475644\pi\)
0.901713 + 0.432336i \(0.142310\pi\)
\(312\) 0 0
\(313\) −95.4299 + 165.289i −0.304888 + 0.528081i −0.977236 0.212154i \(-0.931952\pi\)
0.672349 + 0.740235i \(0.265286\pi\)
\(314\) 114.292 + 52.4626i 0.363988 + 0.167078i
\(315\) 0 0
\(316\) −112.719 + 96.9117i −0.356706 + 0.306683i
\(317\) 202.797 351.255i 0.639738 1.10806i −0.345752 0.938326i \(-0.612376\pi\)
0.985490 0.169733i \(-0.0542906\pi\)
\(318\) 0 0
\(319\) −96.0203 + 55.4374i −0.301004 + 0.173785i
\(320\) 347.622 + 184.342i 1.08632 + 0.576069i
\(321\) 0 0
\(322\) 7.64179 5.41948i 0.0237323 0.0168307i
\(323\) 329.981i 1.02161i
\(324\) 0 0
\(325\) 22.8393 0.0702749
\(326\) 165.821 + 233.818i 0.508655 + 0.717234i
\(327\) 0 0
\(328\) 29.6531 30.7406i 0.0904057 0.0937213i
\(329\) 3.28792 + 5.69484i 0.00999368 + 0.0173096i
\(330\) 0 0
\(331\) −384.104 221.763i −1.16044 0.669978i −0.209027 0.977910i \(-0.567030\pi\)
−0.951408 + 0.307932i \(0.900363\pi\)
\(332\) −231.251 + 198.822i −0.696541 + 0.598860i
\(333\) 0 0
\(334\) 145.024 315.941i 0.434203 0.945931i
\(335\) −195.631 112.948i −0.583974 0.337158i
\(336\) 0 0
\(337\) −254.239 440.356i −0.754420 1.30669i −0.945662 0.325150i \(-0.894585\pi\)
0.191243 0.981543i \(-0.438748\pi\)
\(338\) −30.8858 330.190i −0.0913781 0.976893i
\(339\) 0 0
\(340\) −408.812 + 77.1553i −1.20239 + 0.226927i
\(341\) −557.560 −1.63507
\(342\) 0 0
\(343\) 57.6805i 0.168165i
\(344\) 75.6636 304.185i 0.219952 0.884259i
\(345\) 0 0
\(346\) −46.8667 501.036i −0.135453 1.44808i
\(347\) 492.773 284.503i 1.42010 0.819893i 0.423790 0.905761i \(-0.360700\pi\)
0.996307 + 0.0858678i \(0.0273663\pi\)
\(348\) 0 0
\(349\) −206.901 + 358.363i −0.592840 + 1.02683i 0.401008 + 0.916074i \(0.368660\pi\)
−0.993848 + 0.110754i \(0.964673\pi\)
\(350\) 6.30755 13.7413i 0.0180216 0.0392609i
\(351\) 0 0
\(352\) −467.076 306.586i −1.32692 0.870982i
\(353\) −62.3070 + 107.919i −0.176507 + 0.305719i −0.940682 0.339290i \(-0.889813\pi\)
0.764175 + 0.645009i \(0.223147\pi\)
\(354\) 0 0
\(355\) −467.677 + 270.014i −1.31740 + 0.760602i
\(356\) 36.4942 104.140i 0.102512 0.292527i
\(357\) 0 0
\(358\) 111.076 + 156.623i 0.310267 + 0.437495i
\(359\) 303.196i 0.844557i 0.906466 + 0.422278i \(0.138770\pi\)
−0.906466 + 0.422278i \(0.861230\pi\)
\(360\) 0 0
\(361\) −19.4752 −0.0539480
\(362\) −536.331 + 380.361i −1.48158 + 1.05072i
\(363\) 0 0
\(364\) 3.97904 + 1.39440i 0.0109314 + 0.00383076i
\(365\) 184.572 + 319.688i 0.505677 + 0.875858i
\(366\) 0 0
\(367\) 615.571 + 355.400i 1.67730 + 0.968392i 0.963369 + 0.268181i \(0.0864224\pi\)
0.713936 + 0.700211i \(0.246911\pi\)
\(368\) 125.449 + 19.0273i 0.340894 + 0.0517045i
\(369\) 0 0
\(370\) −651.321 298.970i −1.76033 0.808027i
\(371\) 18.3527 + 10.5959i 0.0494681 + 0.0285604i
\(372\) 0 0
\(373\) 166.740 + 288.803i 0.447025 + 0.774271i 0.998191 0.0601254i \(-0.0191501\pi\)
−0.551166 + 0.834396i \(0.685817\pi\)
\(374\) 588.165 55.0167i 1.57263 0.147103i
\(375\) 0 0
\(376\) −21.4982 + 86.4277i −0.0571761 + 0.229861i
\(377\) 11.3323 0.0300590
\(378\) 0 0
\(379\) 662.686i 1.74851i −0.485465 0.874256i \(-0.661350\pi\)
0.485465 0.874256i \(-0.338650\pi\)
\(380\) −88.9618 471.369i −0.234110 1.24045i
\(381\) 0 0
\(382\) −0.809179 + 0.0756903i −0.00211827 + 0.000198142i
\(383\) −69.9008 + 40.3572i −0.182509 + 0.105371i −0.588471 0.808518i \(-0.700270\pi\)
0.405962 + 0.913890i \(0.366936\pi\)
\(384\) 0 0
\(385\) −31.7026 + 54.9106i −0.0823445 + 0.142625i
\(386\) −113.505 52.1013i −0.294055 0.134977i
\(387\) 0 0
\(388\) −68.1066 79.2155i −0.175533 0.204164i
\(389\) 346.006 599.301i 0.889476 1.54062i 0.0489809 0.998800i \(-0.484403\pi\)
0.840495 0.541819i \(-0.182264\pi\)
\(390\) 0 0
\(391\) −116.183 + 67.0782i −0.297143 + 0.171556i
\(392\) −270.213 + 280.123i −0.689318 + 0.714598i
\(393\) 0 0
\(394\) 339.102 240.488i 0.860665 0.610375i
\(395\) 228.481i 0.578432i
\(396\) 0 0
\(397\) 657.713 1.65671 0.828354 0.560206i \(-0.189278\pi\)
0.828354 + 0.560206i \(0.189278\pi\)
\(398\) −346.081 487.995i −0.869550 1.22612i
\(399\) 0 0
\(400\) 190.692 74.6374i 0.476731 0.186594i
\(401\) −296.433 513.437i −0.739235 1.28039i −0.952840 0.303472i \(-0.901854\pi\)
0.213606 0.976920i \(-0.431479\pi\)
\(402\) 0 0
\(403\) 49.3521 + 28.4935i 0.122462 + 0.0707034i
\(404\) −67.1918 78.1515i −0.166316 0.193444i
\(405\) 0 0
\(406\) 3.12963 6.81806i 0.00770846 0.0167933i
\(407\) 881.274 + 508.804i 2.16529 + 1.25013i
\(408\) 0 0
\(409\) −161.594 279.889i −0.395095 0.684325i 0.598018 0.801483i \(-0.295955\pi\)
−0.993113 + 0.117157i \(0.962622\pi\)
\(410\) −6.11405 65.3632i −0.0149123 0.159422i
\(411\) 0 0
\(412\) −14.5574 77.1333i −0.0353335 0.187217i
\(413\) 14.2533 0.0345115
\(414\) 0 0
\(415\) 468.745i 1.12951i
\(416\) 25.6753 + 51.0067i 0.0617195 + 0.122612i
\(417\) 0 0
\(418\) 63.4354 + 678.167i 0.151759 + 1.62241i
\(419\) −222.744 + 128.601i −0.531608 + 0.306924i −0.741671 0.670764i \(-0.765967\pi\)
0.210063 + 0.977688i \(0.432633\pi\)
\(420\) 0 0
\(421\) 41.9905 72.7297i 0.0997400 0.172755i −0.811837 0.583884i \(-0.801532\pi\)
0.911577 + 0.411129i \(0.134866\pi\)
\(422\) 136.559 297.499i 0.323598 0.704975i
\(423\) 0 0
\(424\) 79.2646 + 275.854i 0.186945 + 0.650599i
\(425\) −108.258 + 187.509i −0.254725 + 0.441197i
\(426\) 0 0
\(427\) 38.8221 22.4139i 0.0909182 0.0524917i
\(428\) 691.567 + 242.349i 1.61581 + 0.566237i
\(429\) 0 0
\(430\) −278.703 392.989i −0.648148 0.913927i
\(431\) 144.348i 0.334914i 0.985879 + 0.167457i \(0.0535555\pi\)
−0.985879 + 0.167457i \(0.946445\pi\)
\(432\) 0 0
\(433\) 395.353 0.913057 0.456528 0.889709i \(-0.349093\pi\)
0.456528 + 0.889709i \(0.349093\pi\)
\(434\) 30.7727 21.8237i 0.0709049 0.0502850i
\(435\) 0 0
\(436\) 133.399 380.667i 0.305961 0.873089i
\(437\) −77.3426 133.961i −0.176985 0.306548i
\(438\) 0 0
\(439\) 194.776 + 112.454i 0.443682 + 0.256160i 0.705158 0.709050i \(-0.250876\pi\)
−0.261476 + 0.965210i \(0.584209\pi\)
\(440\) −825.346 + 237.157i −1.87579 + 0.538994i
\(441\) 0 0
\(442\) −54.8727 25.1877i −0.124146 0.0569858i
\(443\) −369.184 213.148i −0.833373 0.481148i 0.0216335 0.999766i \(-0.493113\pi\)
−0.855006 + 0.518618i \(0.826447\pi\)
\(444\) 0 0
\(445\) −84.8041 146.885i −0.190571 0.330079i
\(446\) −760.356 + 71.1233i −1.70483 + 0.159469i
\(447\) 0 0
\(448\) 37.7790 1.36102i 0.0843281 0.00303799i
\(449\) 406.744 0.905888 0.452944 0.891539i \(-0.350374\pi\)
0.452944 + 0.891539i \(0.350374\pi\)
\(450\) 0 0
\(451\) 93.2163i 0.206688i
\(452\) 71.7324 13.5381i 0.158700 0.0299515i
\(453\) 0 0
\(454\) −118.526 + 11.0869i −0.261070 + 0.0244204i
\(455\) 5.61228 3.24025i 0.0123347 0.00712144i
\(456\) 0 0
\(457\) −159.600 + 276.435i −0.349234 + 0.604891i −0.986114 0.166072i \(-0.946892\pi\)
0.636879 + 0.770963i \(0.280225\pi\)
\(458\) 234.247 + 107.524i 0.511457 + 0.234770i
\(459\) 0 0
\(460\) 147.880 127.142i 0.321479 0.276396i
\(461\) −293.888 + 509.029i −0.637501 + 1.10418i 0.348478 + 0.937317i \(0.386698\pi\)
−0.985979 + 0.166867i \(0.946635\pi\)
\(462\) 0 0
\(463\) −230.088 + 132.841i −0.496950 + 0.286914i −0.727453 0.686157i \(-0.759296\pi\)
0.230503 + 0.973072i \(0.425963\pi\)
\(464\) 94.6163 37.0330i 0.203914 0.0798126i
\(465\) 0 0
\(466\) −24.4608 + 17.3474i −0.0524910 + 0.0372261i
\(467\) 794.598i 1.70149i −0.525575 0.850747i \(-0.676150\pi\)
0.525575 0.850747i \(-0.323850\pi\)
\(468\) 0 0
\(469\) −21.7031 −0.0462752
\(470\) 79.1877 + 111.659i 0.168484 + 0.237573i
\(471\) 0 0
\(472\) 138.937 + 134.022i 0.294358 + 0.283944i
\(473\) 342.050 + 592.447i 0.723149 + 1.25253i
\(474\) 0 0
\(475\) −216.201 124.824i −0.455161 0.262787i
\(476\) −30.3084 + 26.0581i −0.0636732 + 0.0547439i
\(477\) 0 0
\(478\) −303.711 + 661.649i −0.635378 + 1.38420i
\(479\) −572.964 330.801i −1.19617 0.690607i −0.236468 0.971639i \(-0.575990\pi\)
−0.959698 + 0.281033i \(0.909323\pi\)
\(480\) 0 0
\(481\) −52.0037 90.0730i −0.108116 0.187262i
\(482\) 15.0963 + 161.390i 0.0313202 + 0.334833i
\(483\) 0 0
\(484\) 722.599 136.376i 1.49297 0.281769i
\(485\) −160.569 −0.331071
\(486\) 0 0
\(487\) 57.1525i 0.117356i 0.998277 + 0.0586781i \(0.0186886\pi\)
−0.998277 + 0.0586781i \(0.981311\pi\)
\(488\) 589.183 + 146.554i 1.20734 + 0.300317i
\(489\) 0 0
\(490\) 55.7140 + 595.620i 0.113702 + 1.21555i
\(491\) 48.6600 28.0939i 0.0991040 0.0572177i −0.449629 0.893215i \(-0.648444\pi\)
0.548733 + 0.835998i \(0.315110\pi\)
\(492\) 0 0
\(493\) −53.7147 + 93.0366i −0.108955 + 0.188715i
\(494\) 29.0420 63.2694i 0.0587895 0.128076i
\(495\) 0 0
\(496\) 505.170 + 76.6208i 1.01849 + 0.154477i
\(497\) −25.9417 + 44.9324i −0.0521967 + 0.0904073i
\(498\) 0 0
\(499\) −522.225 + 301.507i −1.04654 + 0.604222i −0.921679 0.387952i \(-0.873183\pi\)
−0.124863 + 0.992174i \(0.539849\pi\)
\(500\) −99.2341 + 283.174i −0.198468 + 0.566348i
\(501\) 0 0
\(502\) −326.129 459.861i −0.649659 0.916058i
\(503\) 549.354i 1.09216i 0.837734 + 0.546078i \(0.183880\pi\)
−0.837734 + 0.546078i \(0.816120\pi\)
\(504\) 0 0
\(505\) −158.413 −0.313688
\(506\) −225.880 + 160.192i −0.446404 + 0.316585i
\(507\) 0 0
\(508\) 620.543 + 217.460i 1.22154 + 0.428071i
\(509\) 119.464 + 206.918i 0.234704 + 0.406519i 0.959187 0.282774i \(-0.0912547\pi\)
−0.724483 + 0.689293i \(0.757921\pi\)
\(510\) 0 0
\(511\) 30.7143 + 17.7329i 0.0601062 + 0.0347023i
\(512\) 381.057 + 341.964i 0.744252 + 0.667899i
\(513\) 0 0
\(514\) 136.893 + 62.8366i 0.266328 + 0.122250i
\(515\) −104.484 60.3240i −0.202882 0.117134i
\(516\) 0 0
\(517\) −97.1862 168.331i −0.187981 0.325593i
\(518\) −68.5544 + 6.41255i −0.132344 + 0.0123794i
\(519\) 0 0
\(520\) 85.1748 + 21.1865i 0.163798 + 0.0407433i
\(521\) 567.711 1.08966 0.544828 0.838548i \(-0.316595\pi\)
0.544828 + 0.838548i \(0.316595\pi\)
\(522\) 0 0
\(523\) 941.999i 1.80114i −0.434706 0.900572i \(-0.643148\pi\)
0.434706 0.900572i \(-0.356852\pi\)
\(524\) 105.721 + 560.167i 0.201757 + 1.06902i
\(525\) 0 0
\(526\) −243.536 + 22.7802i −0.462996 + 0.0433084i
\(527\) −467.856 + 270.117i −0.887773 + 0.512556i
\(528\) 0 0
\(529\) −233.056 + 403.664i −0.440559 + 0.763071i
\(530\) 400.928 + 184.034i 0.756468 + 0.347235i
\(531\) 0 0
\(532\) −30.0456 34.9463i −0.0564766 0.0656885i
\(533\) 4.76372 8.25100i 0.00893755 0.0154803i
\(534\) 0 0
\(535\) 975.428 563.163i 1.82323 1.05264i
\(536\) −211.556 204.072i −0.394694 0.380730i
\(537\) 0 0
\(538\) −457.527 + 324.473i −0.850422 + 0.603110i
\(539\) 849.430i 1.57594i
\(540\) 0 0
\(541\) −242.245 −0.447772 −0.223886 0.974615i \(-0.571874\pi\)
−0.223886 + 0.974615i \(0.571874\pi\)
\(542\) −94.2311 132.871i −0.173858 0.245150i
\(543\) 0 0
\(544\) −540.460 30.9794i −0.993492 0.0569475i
\(545\) −309.988 536.915i −0.568786 0.985166i
\(546\) 0 0
\(547\) 170.503 + 98.4402i 0.311706 + 0.179964i 0.647690 0.761904i \(-0.275735\pi\)
−0.335983 + 0.941868i \(0.609069\pi\)
\(548\) −16.0729 18.6945i −0.0293301 0.0341141i
\(549\) 0 0
\(550\) −186.442 + 406.173i −0.338986 + 0.738497i
\(551\) −107.273 61.9342i −0.194688 0.112403i
\(552\) 0 0
\(553\) 10.9757 + 19.0105i 0.0198476 + 0.0343770i
\(554\) −83.7681 895.536i −0.151206 1.61649i
\(555\) 0 0
\(556\) 88.3725 + 468.247i 0.158943 + 0.842171i
\(557\) −958.121 −1.72015 −0.860073 0.510171i \(-0.829582\pi\)
−0.860073 + 0.510171i \(0.829582\pi\)
\(558\) 0 0
\(559\) 69.9202i 0.125081i
\(560\) 36.2697 45.3944i 0.0647672 0.0810614i
\(561\) 0 0
\(562\) −14.1059 150.801i −0.0250994 0.268329i
\(563\) 165.774 95.7097i 0.294448 0.169999i −0.345498 0.938419i \(-0.612290\pi\)
0.639946 + 0.768420i \(0.278957\pi\)
\(564\) 0 0
\(565\) 56.1001 97.1682i 0.0992922 0.171979i
\(566\) 310.279 675.957i 0.548196 1.19427i
\(567\) 0 0
\(568\) −675.368 + 194.062i −1.18903 + 0.341658i
\(569\) −228.215 + 395.280i −0.401081 + 0.694693i −0.993857 0.110675i \(-0.964699\pi\)
0.592775 + 0.805368i \(0.298032\pi\)
\(570\) 0 0
\(571\) 842.764 486.570i 1.47594 0.852136i 0.476312 0.879276i \(-0.341973\pi\)
0.999632 + 0.0271399i \(0.00863995\pi\)
\(572\) −117.615 41.2164i −0.205620 0.0720566i
\(573\) 0 0
\(574\) −3.64862 5.14477i −0.00635648 0.00896302i
\(575\) 101.496i 0.176515i
\(576\) 0 0
\(577\) 138.527 0.240081 0.120040 0.992769i \(-0.461698\pi\)
0.120040 + 0.992769i \(0.461698\pi\)
\(578\) −4.58740 + 3.25334i −0.00793668 + 0.00562861i
\(579\) 0 0
\(580\) 51.6477 147.382i 0.0890478 0.254106i
\(581\) 22.5175 + 39.0015i 0.0387565 + 0.0671282i
\(582\) 0 0
\(583\) −542.478 313.200i −0.930494 0.537221i
\(584\) 132.654 + 461.658i 0.227147 + 0.790510i
\(585\) 0 0
\(586\) 241.365 + 110.792i 0.411886 + 0.189064i
\(587\) 620.808 + 358.424i 1.05759 + 0.610602i 0.924766 0.380537i \(-0.124261\pi\)
0.132829 + 0.991139i \(0.457594\pi\)
\(588\) 0 0
\(589\) −311.451 539.449i −0.528779 0.915872i
\(590\) 295.419 27.6334i 0.500711 0.0468363i
\(591\) 0 0
\(592\) −728.546 582.101i −1.23065 0.983279i
\(593\) −542.129 −0.914214 −0.457107 0.889412i \(-0.651114\pi\)
−0.457107 + 0.889412i \(0.651114\pi\)
\(594\) 0 0
\(595\) 61.4350i 0.103252i
\(596\) 812.577 153.358i 1.36338 0.257312i
\(597\) 0 0
\(598\) 28.1801 2.63596i 0.0471240 0.00440796i
\(599\) −245.527 + 141.755i −0.409895 + 0.236653i −0.690744 0.723099i \(-0.742717\pi\)
0.280850 + 0.959752i \(0.409384\pi\)
\(600\) 0 0
\(601\) 377.424 653.717i 0.627993 1.08772i −0.359961 0.932967i \(-0.617210\pi\)
0.987954 0.154748i \(-0.0494567\pi\)
\(602\) −42.0676 19.3099i −0.0698797 0.0320763i
\(603\) 0 0
\(604\) −446.272 + 383.688i −0.738860 + 0.635245i
\(605\) 565.126 978.827i 0.934093 1.61790i
\(606\) 0 0
\(607\) −77.2227 + 44.5845i −0.127220 + 0.0734506i −0.562260 0.826961i \(-0.690068\pi\)
0.435039 + 0.900411i \(0.356734\pi\)
\(608\) 35.7200 623.162i 0.0587499 1.02494i
\(609\) 0 0
\(610\) 761.189 539.827i 1.24785 0.884962i
\(611\) 19.8664i 0.0325145i
\(612\) 0 0
\(613\) −316.779 −0.516769 −0.258385 0.966042i \(-0.583190\pi\)
−0.258385 + 0.966042i \(0.583190\pi\)
\(614\) 389.335 + 548.985i 0.634096 + 0.894113i
\(615\) 0 0
\(616\) −57.2796 + 59.3803i −0.0929863 + 0.0963966i
\(617\) −534.934 926.533i −0.866992 1.50167i −0.865056 0.501675i \(-0.832717\pi\)
−0.00193565 0.999998i \(-0.500616\pi\)
\(618\) 0 0
\(619\) −578.542 334.021i −0.934640 0.539615i −0.0463638 0.998925i \(-0.514763\pi\)
−0.888276 + 0.459310i \(0.848097\pi\)
\(620\) 595.498 511.988i 0.960481 0.825787i
\(621\) 0 0
\(622\) 293.077 638.483i 0.471185 1.02650i
\(623\) −14.1121 8.14762i −0.0226518 0.0130780i
\(624\) 0 0
\(625\) 390.580 + 676.505i 0.624929 + 1.08241i
\(626\) 35.5507 + 380.060i 0.0567902 + 0.607125i
\(627\) 0 0
\(628\) 247.153 46.6452i 0.393555 0.0742759i
\(629\) 985.986 1.56755
\(630\) 0 0
\(631\) 150.631i 0.238718i 0.992851 + 0.119359i \(0.0380839\pi\)
−0.992851 + 0.119359i \(0.961916\pi\)
\(632\) −71.7652 + 288.513i −0.113553 + 0.456507i
\(633\) 0 0
\(634\) −75.5484 807.662i −0.119162 1.27392i
\(635\) 875.252 505.327i 1.37835 0.795790i
\(636\) 0 0
\(637\) −43.4092 + 75.1869i −0.0681463 + 0.118033i
\(638\) −92.5075 + 201.532i −0.144996 + 0.315881i
\(639\) 0 0
\(640\) 780.385 101.453i 1.21935 0.158520i
\(641\) −351.521 + 608.852i −0.548395 + 0.949847i 0.449990 + 0.893034i \(0.351427\pi\)
−0.998385 + 0.0568139i \(0.981906\pi\)
\(642\) 0 0
\(643\) −742.057 + 428.427i −1.15405 + 0.666293i −0.949872 0.312639i \(-0.898787\pi\)
−0.204182 + 0.978933i \(0.565454\pi\)
\(644\) 6.19659 17.6826i 0.00962204 0.0274574i
\(645\) 0 0
\(646\) 381.776 + 538.328i 0.590985 + 0.833324i
\(647\) 156.257i 0.241510i −0.992682 0.120755i \(-0.961468\pi\)
0.992682 0.120755i \(-0.0385316\pi\)
\(648\) 0 0
\(649\) −421.306 −0.649162
\(650\) 37.2599 26.4243i 0.0573229 0.0406528i
\(651\) 0 0
\(652\) 541.039 + 189.599i 0.829814 + 0.290796i
\(653\) 441.773 + 765.173i 0.676528 + 1.17178i 0.976020 + 0.217682i \(0.0698495\pi\)
−0.299492 + 0.954099i \(0.596817\pi\)
\(654\) 0 0
\(655\) 758.798 + 438.092i 1.15847 + 0.668843i
\(656\) 12.8099 84.4574i 0.0195273 0.128746i
\(657\) 0 0
\(658\) 11.9526 + 5.48650i 0.0181651 + 0.00833815i
\(659\) −379.533 219.123i −0.575922 0.332509i 0.183589 0.983003i \(-0.441228\pi\)
−0.759511 + 0.650494i \(0.774562\pi\)
\(660\) 0 0
\(661\) 233.924 + 405.168i 0.353894 + 0.612963i 0.986928 0.161161i \(-0.0515239\pi\)
−0.633034 + 0.774124i \(0.718191\pi\)
\(662\) −883.195 + 82.6137i −1.33413 + 0.124794i
\(663\) 0 0
\(664\) −147.232 + 591.905i −0.221734 + 0.891424i
\(665\) −70.8359 −0.106520
\(666\) 0 0
\(667\) 50.3597i 0.0755018i
\(668\) −128.943 683.210i −0.193028 1.02277i
\(669\) 0 0
\(670\) −449.827 + 42.0767i −0.671384 + 0.0628010i
\(671\) −1147.52 + 662.524i −1.71017 + 0.987368i
\(672\) 0 0
\(673\) 273.302 473.372i 0.406094 0.703376i −0.588354 0.808604i \(-0.700224\pi\)
0.994448 + 0.105227i \(0.0335571\pi\)
\(674\) −924.240 424.246i −1.37128 0.629444i
\(675\) 0 0
\(676\) −432.405 502.934i −0.639652 0.743986i
\(677\) −227.606 + 394.225i −0.336198 + 0.582312i −0.983714 0.179740i \(-0.942475\pi\)
0.647516 + 0.762052i \(0.275808\pi\)
\(678\) 0 0
\(679\) −13.3600 + 7.71341i −0.0196760 + 0.0113600i
\(680\) −577.666 + 598.852i −0.849509 + 0.880664i
\(681\) 0 0
\(682\) −909.597 + 645.077i −1.33372 + 0.945861i
\(683\) 123.214i 0.180400i −0.995924 0.0902002i \(-0.971249\pi\)
0.995924 0.0902002i \(-0.0287507\pi\)
\(684\) 0 0
\(685\) −37.8937 −0.0553193
\(686\) 66.7343 + 94.0994i 0.0972803 + 0.137171i
\(687\) 0 0
\(688\) −228.495 583.784i −0.332114 0.848524i
\(689\) 32.0115 + 55.4455i 0.0464607 + 0.0804724i
\(690\) 0 0
\(691\) 163.326 + 94.2965i 0.236362 + 0.136464i 0.613504 0.789692i \(-0.289760\pi\)
−0.377141 + 0.926156i \(0.623093\pi\)
\(692\) −656.139 763.162i −0.948177 1.10283i
\(693\) 0 0
\(694\) 474.746 1034.26i 0.684071 1.49028i
\(695\) 634.285 + 366.204i 0.912640 + 0.526913i
\(696\) 0 0
\(697\) 45.1599 + 78.2192i 0.0647918 + 0.112223i
\(698\) 77.0773 + 824.007i 0.110426 + 1.18053i
\(699\) 0 0
\(700\) −5.60814 29.7150i −0.00801162 0.0424501i
\(701\) 810.064 1.15558 0.577792 0.816184i \(-0.303915\pi\)
0.577792 + 0.816184i \(0.303915\pi\)
\(702\) 0 0
\(703\) 1136.86i 1.61716i
\(704\) −1116.69 + 40.2298i −1.58621 + 0.0571447i
\(705\) 0 0
\(706\) 23.2114 + 248.145i 0.0328773 + 0.351480i
\(707\) −13.1806 + 7.60980i −0.0186429 + 0.0107635i
\(708\) 0 0
\(709\) −651.819 + 1128.98i −0.919349 + 1.59236i −0.118944 + 0.992901i \(0.537951\pi\)
−0.800406 + 0.599459i \(0.795382\pi\)
\(710\) −450.568 + 981.583i −0.634602 + 1.38251i
\(711\) 0 0
\(712\) −60.9497 212.115i −0.0856035 0.297914i
\(713\) 126.623 219.317i 0.177592 0.307598i
\(714\) 0 0
\(715\) −165.891 + 95.7772i −0.232015 + 0.133954i
\(716\) 362.415 + 127.003i 0.506166 + 0.177378i
\(717\) 0 0
\(718\) 350.787 + 494.631i 0.488561 + 0.688901i
\(719\) 788.981i 1.09733i 0.836042 + 0.548666i \(0.184864\pi\)
−0.836042 + 0.548666i \(0.815136\pi\)
\(720\) 0 0
\(721\) −11.5913 −0.0160768
\(722\) −31.7717 + 22.5321i −0.0440051 + 0.0312080i
\(723\) 0 0
\(724\) −434.902 + 1241.03i −0.600693 + 1.71413i
\(725\) −40.6380 70.3870i −0.0560524 0.0970856i
\(726\) 0 0
\(727\) 232.676 + 134.335i 0.320049 + 0.184780i 0.651414 0.758722i \(-0.274176\pi\)
−0.331365 + 0.943502i \(0.607509\pi\)
\(728\) 8.10464 2.32881i 0.0111327 0.00319891i
\(729\) 0 0
\(730\) 670.977 + 307.992i 0.919146 + 0.421907i
\(731\) 574.038 + 331.421i 0.785277 + 0.453380i
\(732\) 0 0
\(733\) −36.8343 63.7989i −0.0502514 0.0870380i 0.839806 0.542887i \(-0.182669\pi\)
−0.890057 + 0.455849i \(0.849336\pi\)
\(734\) 1415.42 132.398i 1.92837 0.180379i
\(735\) 0 0
\(736\) 226.670 114.099i 0.307975 0.155026i
\(737\) 641.512 0.870437
\(738\) 0 0
\(739\) 448.249i 0.606562i 0.952901 + 0.303281i \(0.0980820\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(740\) −1408.46 + 265.818i −1.90332 + 0.359214i
\(741\) 0 0
\(742\) 42.1994 3.94732i 0.0568725 0.00531983i
\(743\) 656.602 379.089i 0.883718 0.510215i 0.0118352 0.999930i \(-0.496233\pi\)
0.871882 + 0.489715i \(0.162899\pi\)
\(744\) 0 0
\(745\) 635.496 1100.71i 0.853015 1.47746i
\(746\) 606.153 + 278.237i 0.812538 + 0.372972i
\(747\) 0 0
\(748\) 895.874 770.240i 1.19769 1.02973i
\(749\) 54.1063 93.7149i 0.0722381 0.125120i
\(750\) 0 0
\(751\) −1141.58 + 659.091i −1.52008 + 0.877618i −0.520358 + 0.853948i \(0.674202\pi\)
−0.999720 + 0.0236697i \(0.992465\pi\)
\(752\) 64.9219 + 165.870i 0.0863323 + 0.220572i
\(753\) 0 0
\(754\) 18.4873 13.1110i 0.0245190 0.0173886i
\(755\) 904.589i 1.19813i
\(756\) 0 0
\(757\) 587.874 0.776583 0.388292 0.921537i \(-0.373065\pi\)
0.388292 + 0.921537i \(0.373065\pi\)
\(758\) −766.705 1081.10i −1.01148 1.42625i
\(759\) 0 0
\(760\) −690.489 666.062i −0.908538 0.876397i
\(761\) 188.496 + 326.485i 0.247695 + 0.429021i 0.962886 0.269908i \(-0.0869934\pi\)
−0.715191 + 0.698929i \(0.753660\pi\)
\(762\) 0 0
\(763\) −51.5845 29.7823i −0.0676075 0.0390332i
\(764\) −1.23252 + 1.05967i −0.00161324 + 0.00138701i
\(765\) 0 0
\(766\) −67.3435 + 146.711i −0.0879158 + 0.191529i
\(767\) 37.2917 + 21.5304i 0.0486202 + 0.0280709i
\(768\) 0 0
\(769\) 643.939 + 1115.34i 0.837372 + 1.45037i 0.892084 + 0.451869i \(0.149243\pi\)
−0.0547122 + 0.998502i \(0.517424\pi\)
\(770\) 11.8102 + 126.259i 0.0153380 + 0.163973i
\(771\) 0 0
\(772\) −245.451 + 46.3240i −0.317941 + 0.0600052i
\(773\) −778.578 −1.00722 −0.503608 0.863932i \(-0.667994\pi\)
−0.503608 + 0.863932i \(0.667994\pi\)
\(774\) 0 0
\(775\) 408.715i 0.527375i
\(776\) −202.758 50.4344i −0.261286 0.0649928i
\(777\) 0 0
\(778\) −128.898 1378.01i −0.165679 1.77122i
\(779\) −90.1884 + 52.0703i −0.115775 + 0.0668425i
\(780\) 0 0
\(781\) 766.801 1328.14i 0.981819 1.70056i
\(782\) −111.932 + 243.850i −0.143136 + 0.311829i
\(783\) 0 0