Properties

Label 108.3.f.c.91.6
Level 108
Weight 3
Character 108.91
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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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: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
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 91.6
Root \(1.63139 + 1.15696i\) of \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Character \(\chi\) \(=\) 108.91
Dual form 108.3.f.c.19.6

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 0.375612 + 0.926777i \(0.377432\pi\)
−0.990418 + 0.138099i \(0.955901\pi\)
\(6\) 0 0
\(7\) −0.511543 + 0.295340i −0.0730776 + 0.0421914i −0.536094 0.844159i \(-0.680101\pi\)
0.463016 + 0.886350i \(0.346767\pi\)
\(8\) −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 0.383088 0.923712i \(-0.374861\pi\)
0.991502 + 0.130092i \(0.0415274\pi\)
\(12\) 0 0
\(13\) −0.892255 + 1.54543i −0.0686350 + 0.118879i −0.898301 0.439381i \(-0.855198\pi\)
0.829666 + 0.558261i \(0.188531\pi\)
\(14\) −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 \(-0.828419\pi\)
0.858203 0.513310i \(-0.171581\pi\)
\(20\) −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 0.343214 0.939257i \(-0.388484\pi\)
−0.641813 + 0.766861i \(0.721818\pi\)
\(24\) 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 0.806075 0.591814i \(-0.201588\pi\)
−0.915563 + 0.402174i \(0.868255\pi\)
\(30\) 0 0
\(31\) −27.6558 15.9671i −0.892124 0.515068i −0.0174873 0.999847i \(-0.505567\pi\)
−0.874637 + 0.484779i \(0.838900\pi\)
\(32\) −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 −0.831633 0.555325i \(-0.812594\pi\)
0.896742 + 0.442553i \(0.145927\pi\)
\(42\) 0 0
\(43\) 33.9324 19.5909i 0.789126 0.455602i −0.0505290 0.998723i \(-0.516091\pi\)
0.839655 + 0.543121i \(0.182757\pi\)
\(44\) 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 −0.599047 0.800714i \(-0.704454\pi\)
0.393915 + 0.919147i \(0.371120\pi\)
\(48\) 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 0.312337 0.949971i \(-0.398888\pi\)
−0.666531 + 0.745477i \(0.732222\pi\)
\(60\) 0 0
\(61\) −37.9460 65.7244i −0.622066 1.07745i −0.989100 0.147243i \(-0.952960\pi\)
0.367034 0.930207i \(-0.380373\pi\)
\(62\) −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 0.718299 0.695734i \(-0.244921\pi\)
−0.243374 + 0.969933i \(0.578254\pi\)
\(68\) 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 \(0.212288\pi\)
−0.785730 + 0.618570i \(0.787712\pi\)
\(72\) 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 −0.689669 0.724124i \(-0.742244\pi\)
0.282275 + 0.959333i \(0.408911\pi\)
\(80\) −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 −0.841902 0.539630i \(-0.818564\pi\)
0.0463824 + 0.998924i \(0.485231\pi\)
\(84\) 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 0.925454 0.378861i \(-0.123684\pi\)
−0.790830 + 0.612036i \(0.790351\pi\)
\(98\) −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 0.922729 0.385449i \(-0.125953\pi\)
−0.795173 + 0.606382i \(0.792620\pi\)
\(102\) 0 0
\(103\) 16.9947 + 9.81187i 0.164997 + 0.0952609i 0.580225 0.814457i \(-0.302965\pi\)
−0.415228 + 0.909717i \(0.636298\pi\)
\(104\) −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 \(-0.672895\pi\)
0.516850 0.856076i \(-0.327105\pi\)
\(108\) 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 −0.822822 0.568299i \(-0.807602\pi\)
0.903573 + 0.428435i \(0.140935\pi\)
\(114\) 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 \(-0.775945\pi\)
0.762331 0.647188i \(-0.224055\pi\)
\(128\) −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 −0.0515116 0.998672i \(-0.516404\pi\)
−0.890631 + 0.454726i \(0.849737\pi\)
\(132\) 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 0.877054 0.480393i \(-0.159506\pi\)
−0.854559 + 0.519354i \(0.826172\pi\)
\(138\) 0 0
\(139\) −103.168 59.5642i −0.742218 0.428519i 0.0806575 0.996742i \(-0.474298\pi\)
−0.822875 + 0.568222i \(0.807631\pi\)
\(140\) 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 −0.276882 0.960904i \(-0.589301\pi\)
0.970608 0.240665i \(-0.0773657\pi\)
\(150\) 0 0
\(151\) −127.422 + 73.5670i −0.843853 + 0.487199i −0.858572 0.512693i \(-0.828648\pi\)
0.0147190 + 0.999892i \(0.495315\pi\)
\(152\) 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 −0.748358 0.663295i \(-0.769157\pi\)
0.948609 + 0.316449i \(0.102491\pi\)
\(158\) −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 \(-0.855104\pi\)
0.898171 0.439646i \(-0.144896\pi\)
\(164\) 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 0.877648 0.479306i \(-0.159111\pi\)
0.0237332 + 0.999718i \(0.492445\pi\)
\(168\) 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 0.958062 + 0.286562i \(0.0925125\pi\)
−0.230861 + 0.972987i \(0.574154\pi\)
\(174\) 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 \(-0.913580\pi\)
0.963371 0.268173i \(-0.0864199\pi\)
\(180\) 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 −0.500921 0.865493i \(-0.667005\pi\)
0.499078 + 0.866557i \(0.333672\pi\)
\(192\) 0 0
\(193\) −31.2230 + 54.0798i −0.161777 + 0.280206i −0.935506 0.353311i \(-0.885056\pi\)
0.773729 + 0.633517i \(0.218389\pi\)
\(194\) −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 \(0.270707\pi\)
−0.659643 + 0.751579i \(0.729293\pi\)
\(200\) 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 0.796748 0.604311i \(-0.206552\pi\)
−0.124975 + 0.992160i \(0.539885\pi\)
\(212\) −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 −0.999811 0.0194478i \(-0.993809\pi\)
−0.483063 + 0.875586i \(0.660476\pi\)
\(224\) 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 −0.609224 0.792998i \(-0.708519\pi\)
0.382144 + 0.924103i \(0.375186\pi\)
\(228\) 0 0
\(229\) 64.4366 111.608i 0.281383 0.487369i −0.690343 0.723482i \(-0.742540\pi\)
0.971726 + 0.236113i \(0.0758736\pi\)
\(230\) 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 −0.335442 0.942061i \(-0.608886\pi\)
−0.983570 + 0.180529i \(0.942219\pi\)
\(240\) 0 0
\(241\) −40.5235 70.1888i −0.168147 0.291240i 0.769621 0.638501i \(-0.220445\pi\)
−0.937769 + 0.347261i \(0.887112\pi\)
\(242\) 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 \(0.189783\pi\)
−0.827463 + 0.561520i \(0.810217\pi\)
\(252\) 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 −0.783417 0.621496i \(-0.786525\pi\)
0.929940 + 0.367711i \(0.119858\pi\)
\(258\) 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 −0.687655 0.726037i \(-0.741360\pi\)
0.284939 + 0.958546i \(0.408027\pi\)
\(264\) 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 \(0.0480146\pi\)
−0.988645 + 0.150271i \(0.951985\pi\)
\(272\) −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 0.911622 + 0.411031i \(0.134831\pi\)
−0.0998479 + 0.995003i \(0.531836\pi\)
\(278\) −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 0.925502 0.378743i \(-0.123643\pi\)
−0.790752 + 0.612137i \(0.790310\pi\)
\(282\) 0 0
\(283\) 322.061 + 185.942i 1.13803 + 0.657039i 0.945941 0.324339i \(-0.105142\pi\)
0.192084 + 0.981378i \(0.438475\pi\)
\(284\) −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 −0.730196 0.683237i \(-0.760571\pi\)
0.956799 + 0.290750i \(0.0939047\pi\)
\(294\) 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 \(-0.815363\pi\)
0.836434 0.548068i \(-0.184637\pi\)
\(308\) −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 0.901713 0.432336i \(-0.142310\pi\)
0.0764428 + 0.997074i \(0.475644\pi\)
\(312\) 0 0
\(313\) −95.4299 165.289i −0.304888 0.528081i 0.672349 0.740235i \(-0.265286\pi\)
−0.977236 + 0.212154i \(0.931952\pi\)
\(314\) 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 0.985490 + 0.169733i \(0.0542906\pi\)
−0.345752 + 0.938326i \(0.612376\pi\)
\(318\) 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 −0.951408 0.307932i \(-0.900363\pi\)
−0.209027 + 0.977910i \(0.567030\pi\)
\(332\) −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 0.191243 + 0.981543i \(0.438748\pi\)
−0.945662 + 0.325150i \(0.894585\pi\)
\(338\) −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 0.996307 0.0858678i \(-0.0273663\pi\)
0.423790 + 0.905761i \(0.360700\pi\)
\(348\) 0 0
\(349\) −206.901 358.363i −0.592840 1.02683i −0.993848 0.110754i \(-0.964673\pi\)
0.401008 0.916074i \(-0.368660\pi\)
\(350\) 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 0.764175 0.645009i \(-0.223147\pi\)
−0.940682 + 0.339290i \(0.889813\pi\)
\(354\) 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 \(-0.861230\pi\)
0.906466 0.422278i \(-0.138770\pi\)
\(360\) 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 0.713936 0.700211i \(-0.246911\pi\)
0.963369 0.268181i \(-0.0864224\pi\)
\(368\) 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 −0.551166 0.834396i \(-0.685817\pi\)
0.998191 + 0.0601254i \(0.0191501\pi\)
\(374\) 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 \(0.338650\pi\)
−0.485465 + 0.874256i \(0.661350\pi\)
\(380\) −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 0.405962 0.913890i \(-0.366936\pi\)
−0.588471 + 0.808518i \(0.700270\pi\)
\(384\) 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 0.840495 + 0.541819i \(0.182264\pi\)
0.0489809 + 0.998800i \(0.484403\pi\)
\(390\) 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 0.213606 + 0.976920i \(0.431479\pi\)
−0.952840 + 0.303472i \(0.901854\pi\)
\(402\) 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 −0.993113 0.117157i \(-0.962622\pi\)
0.598018 + 0.801483i \(0.295955\pi\)
\(410\) −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 0.210063 0.977688i \(-0.432633\pi\)
−0.741671 + 0.670764i \(0.765967\pi\)
\(420\) 0 0
\(421\) 41.9905 + 72.7297i 0.0997400 + 0.172755i 0.911577 0.411129i \(-0.134866\pi\)
−0.811837 + 0.583884i \(0.801532\pi\)
\(422\) 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 \(-0.946445\pi\)
0.985879 0.167457i \(-0.0535555\pi\)
\(432\) 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 −0.261476 0.965210i \(-0.584209\pi\)
0.705158 + 0.709050i \(0.250876\pi\)
\(440\) −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 −0.855006 0.518618i \(-0.826447\pi\)
0.0216335 + 0.999766i \(0.493113\pi\)
\(444\) 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 0.636879 0.770963i \(-0.280225\pi\)
−0.986114 + 0.166072i \(0.946892\pi\)
\(458\) 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 −0.985979 0.166867i \(-0.946635\pi\)
0.348478 0.937317i \(-0.386698\pi\)
\(462\) 0 0
\(463\) −230.088 132.841i −0.496950 0.286914i 0.230503 0.973072i \(-0.425963\pi\)
−0.727453 + 0.686157i \(0.759296\pi\)
\(464\) 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 \(0.323850\pi\)
−0.525575 + 0.850747i \(0.676150\pi\)
\(468\) 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 −0.959698 0.281033i \(-0.909323\pi\)
−0.236468 + 0.971639i \(0.575990\pi\)
\(480\) 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 \(-0.981311\pi\)
0.998277 0.0586781i \(-0.0186886\pi\)
\(488\) 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 0.548733 0.835998i \(-0.315110\pi\)
−0.449629 + 0.893215i \(0.648444\pi\)
\(492\) 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 −0.124863 0.992174i \(-0.539849\pi\)
−0.921679 + 0.387952i \(0.873183\pi\)
\(500\) −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 \(-0.816120\pi\)
0.837734 0.546078i \(-0.183880\pi\)
\(504\) 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 −0.724483 0.689293i \(-0.757921\pi\)
0.959187 + 0.282774i \(0.0912547\pi\)
\(510\) 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 \(0.356852\pi\)
−0.434706 + 0.900572i \(0.643148\pi\)
\(524\) 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 −0.335983 0.941868i \(-0.609069\pi\)
0.647690 + 0.761904i \(0.275735\pi\)
\(548\) −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 0.639946 0.768420i \(-0.278957\pi\)
−0.345498 + 0.938419i \(0.612290\pi\)
\(564\) 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 0.592775 0.805368i \(-0.298032\pi\)
−0.993857 + 0.110675i \(0.964699\pi\)
\(570\) 0 0
\(571\) 842.764 + 486.570i 1.47594 + 0.852136i 0.999632 0.0271399i \(-0.00863995\pi\)
0.476312 + 0.879276i \(0.341973\pi\)
\(572\) −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 0.132829 0.991139i \(-0.457594\pi\)
0.924766 + 0.380537i \(0.124261\pi\)
\(588\) 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 0.280850 0.959752i \(-0.409384\pi\)
−0.690744 + 0.723099i \(0.742717\pi\)
\(600\) 0 0
\(601\) 377.424 + 653.717i 0.627993 + 1.08772i 0.987954 + 0.154748i \(0.0494567\pi\)
−0.359961 + 0.932967i \(0.617210\pi\)
\(602\) −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 0.435039 0.900411i \(-0.356734\pi\)
−0.562260 + 0.826961i \(0.690068\pi\)
\(608\) 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 −0.00193565 + 0.999998i \(0.500616\pi\)
−0.865056 + 0.501675i \(0.832717\pi\)
\(618\) 0 0
\(619\) −578.542 + 334.021i −0.934640 + 0.539615i −0.888276 0.459310i \(-0.848097\pi\)
−0.0463638 + 0.998925i \(0.514763\pi\)
\(620\) 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 \(-0.961916\pi\)
0.992851 0.119359i \(-0.0380839\pi\)
\(632\) −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 −0.998385 0.0568139i \(-0.981906\pi\)
0.449990 0.893034i \(-0.351427\pi\)
\(642\) 0 0
\(643\) −742.057 428.427i −1.15405 0.666293i −0.204182 0.978933i \(-0.565454\pi\)
−0.949872 + 0.312639i \(0.898787\pi\)
\(644\) 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 \(0.0385316\pi\)
−0.992682 + 0.120755i \(0.961468\pi\)
\(648\) 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 −0.299492 0.954099i \(-0.596817\pi\)
0.976020 0.217682i \(-0.0698495\pi\)
\(654\) 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 −0.759511 0.650494i \(-0.774562\pi\)
0.183589 + 0.983003i \(0.441228\pi\)
\(660\) 0 0
\(661\) 233.924 405.168i 0.353894 0.612963i −0.633034 0.774124i \(-0.718191\pi\)
0.986928 + 0.161161i \(0.0515239\pi\)
\(662\) −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 0.994448 0.105227i \(-0.0335571\pi\)
−0.588354 + 0.808604i \(0.700224\pi\)
\(674\) −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 0.647516 0.762052i \(-0.275808\pi\)
−0.983714 + 0.179740i \(0.942475\pi\)
\(678\) 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 \(0.0287507\pi\)
−0.995924 + 0.0902002i \(0.971249\pi\)
\(684\) 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 −0.377141 0.926156i \(-0.623093\pi\)
0.613504 + 0.789692i \(0.289760\pi\)
\(692\) −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 −0.800406 0.599459i \(-0.795382\pi\)
−0.118944 0.992901i \(-0.537951\pi\)
\(710\) −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 \(-0.815136\pi\)
0.836042 0.548666i \(-0.184864\pi\)
\(720\) 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 −0.331365 0.943502i \(-0.607509\pi\)
0.651414 + 0.758722i \(0.274176\pi\)
\(728\) 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 −0.890057 0.455849i \(-0.849336\pi\)
0.839806 + 0.542887i \(0.182669\pi\)
\(734\) 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 \(-0.901918\pi\)
0.952901 0.303281i \(-0.0980820\pi\)
\(740\) −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 0.871882 0.489715i \(-0.162899\pi\)
0.0118352 + 0.999930i \(0.496233\pi\)
\(744\) 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 −0.999720 0.0236697i \(-0.992465\pi\)
−0.520358 0.853948i \(1.32580\pi\)
\(752\) 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 −0.715191 0.698929i \(-0.753660\pi\)
0.962886 + 0.269908i \(0.0869934\pi\)
\(762\) 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 −0.0547122 0.998502i \(-0.517424\pi\)
0.892084 0.451869i \(-0.149243\pi\)
\(770\) 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