Properties

Label 300.3.c.f.151.6
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.6080256576.2
Defining polynomial: \(x^{8} - 3 x^{7} + 7 x^{6} - 12 x^{5} + 12 x^{4} - 48 x^{3} + 112 x^{2} - 192 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.6
Root \(1.96705 + 0.361553i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.f.151.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +15.7955i q^{11} +(-6.83966 - 1.10411i) q^{12} +5.18655 q^{13} +(1.27492 - 1.08561i) q^{14} +(-15.1873 - 5.03449i) q^{16} -27.3586 q^{17} +(-3.88991 - 4.56821i) q^{18} +17.9667i q^{19} +1.45017 q^{21} +(-24.0524 + 20.4811i) q^{22} -19.1101i q^{23} +(-7.18729 - 11.8466i) q^{24} +(6.72508 + 7.89776i) q^{26} -5.19615i q^{27} +(3.30621 + 0.533714i) q^{28} +45.6495 q^{29} -13.6243i q^{31} +(-12.0262 - 29.6542i) q^{32} -27.3586 q^{33} +(-35.4743 - 41.6600i) q^{34} +(1.91238 - 11.8466i) q^{36} +15.5597 q^{37} +(-27.3586 + 23.2964i) q^{38} +8.98337i q^{39} +13.2990 q^{41} +(1.88034 + 2.20822i) q^{42} +27.9430i q^{43} +(-62.3746 - 10.0690i) q^{44} +(29.0997 - 24.7789i) q^{46} +55.6558i q^{47} +(8.72000 - 26.3052i) q^{48} +48.2990 q^{49} -47.3865i q^{51} +(-3.30621 + 20.4811i) q^{52} -15.5597 q^{53} +(7.91238 - 6.73753i) q^{54} +(3.47425 + 5.72653i) q^{56} -31.1193 q^{57} +(59.1909 + 69.5122i) q^{58} +87.6625i q^{59} +38.0000 q^{61} +(20.7462 - 17.6658i) q^{62} +2.51176i q^{63} +(29.5619 - 56.7635i) q^{64} +(-35.4743 - 41.6600i) q^{66} -92.2015i q^{67} +(17.4400 - 108.036i) q^{68} +33.0997 q^{69} +130.707i q^{71} +(20.5190 - 12.4488i) q^{72} +54.7173 q^{73} +(20.1752 + 23.6933i) q^{74} +(-70.9485 - 11.4531i) q^{76} +13.2249 q^{77} +(-13.6793 + 11.6482i) q^{78} -13.6243i q^{79} +9.00000 q^{81} +(17.2440 + 20.2509i) q^{82} +59.0048i q^{83} +(-0.924421 + 5.72653i) q^{84} +(-42.5498 + 36.2319i) q^{86} +79.0673i q^{87} +(-65.5448 - 108.036i) q^{88} -39.8007 q^{89} -4.34246i q^{91} +(75.4635 + 12.1819i) q^{92} +23.5980 q^{93} +(-84.7492 + 72.1654i) q^{94} +(51.3625 - 20.8300i) q^{96} +168.821 q^{97} +(62.6263 + 73.5467i) q^{98} -47.3865i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 10q^{4} - 6q^{6} - 24q^{9} + O(q^{10}) \) \( 8q + 10q^{4} - 6q^{6} - 24q^{9} - 20q^{14} - 46q^{16} + 72q^{21} + 18q^{24} + 84q^{26} + 184q^{29} - 12q^{34} - 30q^{36} - 256q^{41} - 348q^{44} + 112q^{46} + 24q^{49} + 18q^{54} - 244q^{56} + 304q^{61} + 10q^{64} - 12q^{66} + 144q^{69} + 252q^{74} - 24q^{76} + 72q^{81} + 204q^{84} - 280q^{86} - 560q^{89} - 376q^{94} + 426q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29664 + 1.52274i 0.648319 + 0.761369i
\(3\) 1.73205i 0.577350i
\(4\) −0.637459 + 3.94888i −0.159365 + 0.987220i
\(5\) 0 0
\(6\) −2.63746 + 2.24584i −0.439576 + 0.374307i
\(7\) 0.837253i 0.119608i −0.998210 0.0598038i \(-0.980952\pi\)
0.998210 0.0598038i \(-0.0190475\pi\)
\(8\) −6.83966 + 4.14959i −0.854957 + 0.518698i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 15.7955i 1.43596i 0.696066 + 0.717978i \(0.254932\pi\)
−0.696066 + 0.717978i \(0.745068\pi\)
\(12\) −6.83966 1.10411i −0.569972 0.0920092i
\(13\) 5.18655 0.398966 0.199483 0.979901i \(-0.436074\pi\)
0.199483 + 0.979901i \(0.436074\pi\)
\(14\) 1.27492 1.08561i 0.0910655 0.0775439i
\(15\) 0 0
\(16\) −15.1873 5.03449i −0.949206 0.314656i
\(17\) −27.3586 −1.60933 −0.804666 0.593728i \(-0.797656\pi\)
−0.804666 + 0.593728i \(0.797656\pi\)
\(18\) −3.88991 4.56821i −0.216106 0.253790i
\(19\) 17.9667i 0.945618i 0.881165 + 0.472809i \(0.156760\pi\)
−0.881165 + 0.472809i \(0.843240\pi\)
\(20\) 0 0
\(21\) 1.45017 0.0690555
\(22\) −24.0524 + 20.4811i −1.09329 + 0.930958i
\(23\) 19.1101i 0.830874i −0.909622 0.415437i \(-0.863629\pi\)
0.909622 0.415437i \(-0.136371\pi\)
\(24\) −7.18729 11.8466i −0.299471 0.493610i
\(25\) 0 0
\(26\) 6.72508 + 7.89776i 0.258657 + 0.303760i
\(27\) 5.19615i 0.192450i
\(28\) 3.30621 + 0.533714i 0.118079 + 0.0190612i
\(29\) 45.6495 1.57412 0.787060 0.616876i \(-0.211602\pi\)
0.787060 + 0.616876i \(0.211602\pi\)
\(30\) 0 0
\(31\) 13.6243i 0.439493i −0.975557 0.219747i \(-0.929477\pi\)
0.975557 0.219747i \(-0.0705230\pi\)
\(32\) −12.0262 29.6542i −0.375819 0.926693i
\(33\) −27.3586 −0.829050
\(34\) −35.4743 41.6600i −1.04336 1.22529i
\(35\) 0 0
\(36\) 1.91238 11.8466i 0.0531216 0.329073i
\(37\) 15.5597 0.420531 0.210266 0.977644i \(-0.432567\pi\)
0.210266 + 0.977644i \(0.432567\pi\)
\(38\) −27.3586 + 23.2964i −0.719964 + 0.613062i
\(39\) 8.98337i 0.230343i
\(40\) 0 0
\(41\) 13.2990 0.324366 0.162183 0.986761i \(-0.448147\pi\)
0.162183 + 0.986761i \(0.448147\pi\)
\(42\) 1.88034 + 2.20822i 0.0447700 + 0.0525767i
\(43\) 27.9430i 0.649837i 0.945742 + 0.324918i \(0.105337\pi\)
−0.945742 + 0.324918i \(0.894663\pi\)
\(44\) −62.3746 10.0690i −1.41760 0.228841i
\(45\) 0 0
\(46\) 29.0997 24.7789i 0.632601 0.538672i
\(47\) 55.6558i 1.18417i 0.805877 + 0.592083i \(0.201694\pi\)
−0.805877 + 0.592083i \(0.798306\pi\)
\(48\) 8.72000 26.3052i 0.181667 0.548024i
\(49\) 48.2990 0.985694
\(50\) 0 0
\(51\) 47.3865i 0.929148i
\(52\) −3.30621 + 20.4811i −0.0635810 + 0.393867i
\(53\) −15.5597 −0.293578 −0.146789 0.989168i \(-0.546894\pi\)
−0.146789 + 0.989168i \(0.546894\pi\)
\(54\) 7.91238 6.73753i 0.146525 0.124769i
\(55\) 0 0
\(56\) 3.47425 + 5.72653i 0.0620403 + 0.102259i
\(57\) −31.1193 −0.545953
\(58\) 59.1909 + 69.5122i 1.02053 + 1.19849i
\(59\) 87.6625i 1.48581i 0.669400 + 0.742903i \(0.266551\pi\)
−0.669400 + 0.742903i \(0.733449\pi\)
\(60\) 0 0
\(61\) 38.0000 0.622951 0.311475 0.950254i \(-0.399177\pi\)
0.311475 + 0.950254i \(0.399177\pi\)
\(62\) 20.7462 17.6658i 0.334616 0.284932i
\(63\) 2.51176i 0.0398692i
\(64\) 29.5619 56.7635i 0.461904 0.886930i
\(65\) 0 0
\(66\) −35.4743 41.6600i −0.537489 0.631212i
\(67\) 92.2015i 1.37614i −0.725643 0.688071i \(-0.758458\pi\)
0.725643 0.688071i \(-0.241542\pi\)
\(68\) 17.4400 108.036i 0.256471 1.58876i
\(69\) 33.0997 0.479705
\(70\) 0 0
\(71\) 130.707i 1.84094i 0.390816 + 0.920469i \(0.372193\pi\)
−0.390816 + 0.920469i \(0.627807\pi\)
\(72\) 20.5190 12.4488i 0.284986 0.172899i
\(73\) 54.7173 0.749552 0.374776 0.927115i \(-0.377720\pi\)
0.374776 + 0.927115i \(0.377720\pi\)
\(74\) 20.1752 + 23.6933i 0.272638 + 0.320179i
\(75\) 0 0
\(76\) −70.9485 11.4531i −0.933533 0.150698i
\(77\) 13.2249 0.171751
\(78\) −13.6793 + 11.6482i −0.175376 + 0.149336i
\(79\) 13.6243i 0.172459i −0.996275 0.0862297i \(-0.972518\pi\)
0.996275 0.0862297i \(-0.0274819\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 17.2440 + 20.2509i 0.210293 + 0.246962i
\(83\) 59.0048i 0.710901i 0.934695 + 0.355451i \(0.115673\pi\)
−0.934695 + 0.355451i \(0.884327\pi\)
\(84\) −0.924421 + 5.72653i −0.0110050 + 0.0681730i
\(85\) 0 0
\(86\) −42.5498 + 36.2319i −0.494766 + 0.421302i
\(87\) 79.0673i 0.908819i
\(88\) −65.5448 108.036i −0.744828 1.22768i
\(89\) −39.8007 −0.447198 −0.223599 0.974681i \(-0.571781\pi\)
−0.223599 + 0.974681i \(0.571781\pi\)
\(90\) 0 0
\(91\) 4.34246i 0.0477193i
\(92\) 75.4635 + 12.1819i 0.820255 + 0.132412i
\(93\) 23.5980 0.253741
\(94\) −84.7492 + 72.1654i −0.901587 + 0.767717i
\(95\) 0 0
\(96\) 51.3625 20.8300i 0.535026 0.216979i
\(97\) 168.821 1.74043 0.870214 0.492675i \(-0.163981\pi\)
0.870214 + 0.492675i \(0.163981\pi\)
\(98\) 62.6263 + 73.5467i 0.639044 + 0.750477i
\(99\) 47.3865i 0.478652i
\(100\) 0 0
\(101\) 44.5498 0.441087 0.220544 0.975377i \(-0.429217\pi\)
0.220544 + 0.975377i \(0.429217\pi\)
\(102\) 72.1573 61.4432i 0.707424 0.602384i
\(103\) 126.466i 1.22782i −0.789375 0.613911i \(-0.789595\pi\)
0.789375 0.613911i \(-0.210405\pi\)
\(104\) −35.4743 + 21.5220i −0.341099 + 0.206943i
\(105\) 0 0
\(106\) −20.1752 23.6933i −0.190333 0.223521i
\(107\) 104.383i 0.975546i −0.872971 0.487773i \(-0.837809\pi\)
0.872971 0.487773i \(-0.162191\pi\)
\(108\) 20.5190 + 3.31233i 0.189991 + 0.0306697i
\(109\) 0.501656 0.00460235 0.00230117 0.999997i \(-0.499268\pi\)
0.00230117 + 0.999997i \(0.499268\pi\)
\(110\) 0 0
\(111\) 26.9501i 0.242794i
\(112\) −4.21515 + 12.7156i −0.0376352 + 0.113532i
\(113\) −16.9855 −0.150314 −0.0751572 0.997172i \(-0.523946\pi\)
−0.0751572 + 0.997172i \(0.523946\pi\)
\(114\) −40.3505 47.3865i −0.353952 0.415671i
\(115\) 0 0
\(116\) −29.0997 + 180.264i −0.250859 + 1.55400i
\(117\) −15.5597 −0.132989
\(118\) −133.487 + 113.667i −1.13125 + 0.963276i
\(119\) 22.9061i 0.192488i
\(120\) 0 0
\(121\) −128.498 −1.06197
\(122\) 49.2723 + 57.8640i 0.403871 + 0.474295i
\(123\) 23.0346i 0.187273i
\(124\) 53.8007 + 8.68492i 0.433876 + 0.0700397i
\(125\) 0 0
\(126\) −3.82475 + 3.25684i −0.0303552 + 0.0258480i
\(127\) 8.45598i 0.0665825i −0.999446 0.0332913i \(-0.989401\pi\)
0.999446 0.0332913i \(-0.0105989\pi\)
\(128\) 124.767 28.5867i 0.974742 0.223334i
\(129\) −48.3987 −0.375184
\(130\) 0 0
\(131\) 51.7290i 0.394878i −0.980315 0.197439i \(-0.936738\pi\)
0.980315 0.197439i \(-0.0632624\pi\)
\(132\) 17.4400 108.036i 0.132121 0.818454i
\(133\) 15.0427 0.113103
\(134\) 140.399 119.552i 1.04775 0.892179i
\(135\) 0 0
\(136\) 187.124 113.527i 1.37591 0.834757i
\(137\) 53.8083 0.392762 0.196381 0.980528i \(-0.437081\pi\)
0.196381 + 0.980528i \(0.437081\pi\)
\(138\) 42.9183 + 50.4021i 0.311002 + 0.365233i
\(139\) 13.6243i 0.0980165i 0.998798 + 0.0490082i \(0.0156061\pi\)
−0.998798 + 0.0490082i \(0.984394\pi\)
\(140\) 0 0
\(141\) −96.3987 −0.683679
\(142\) −199.032 + 169.479i −1.40163 + 1.19352i
\(143\) 81.9243i 0.572897i
\(144\) 45.5619 + 15.1035i 0.316402 + 0.104885i
\(145\) 0 0
\(146\) 70.9485 + 83.3200i 0.485949 + 0.570685i
\(147\) 83.6563i 0.569091i
\(148\) −9.91864 + 61.4432i −0.0670178 + 0.415157i
\(149\) 33.6495 0.225836 0.112918 0.993604i \(-0.463980\pi\)
0.112918 + 0.993604i \(0.463980\pi\)
\(150\) 0 0
\(151\) 139.988i 0.927076i −0.886077 0.463538i \(-0.846580\pi\)
0.886077 0.463538i \(-0.153420\pi\)
\(152\) −74.5546 122.886i −0.490490 0.808463i
\(153\) 82.0759 0.536444
\(154\) 17.1478 + 20.1380i 0.111350 + 0.130766i
\(155\) 0 0
\(156\) −35.4743 5.72653i −0.227399 0.0367085i
\(157\) −21.2631 −0.135434 −0.0677170 0.997705i \(-0.521572\pi\)
−0.0677170 + 0.997705i \(0.521572\pi\)
\(158\) 20.7462 17.6658i 0.131305 0.111809i
\(159\) 26.9501i 0.169498i
\(160\) 0 0
\(161\) −16.0000 −0.0993789
\(162\) 11.6697 + 13.7046i 0.0720355 + 0.0845965i
\(163\) 210.211i 1.28964i −0.764335 0.644819i \(-0.776933\pi\)
0.764335 0.644819i \(-0.223067\pi\)
\(164\) −8.47757 + 52.5162i −0.0516925 + 0.320221i
\(165\) 0 0
\(166\) −89.8488 + 76.5079i −0.541258 + 0.460891i
\(167\) 238.384i 1.42745i 0.700426 + 0.713725i \(0.252994\pi\)
−0.700426 + 0.713725i \(0.747006\pi\)
\(168\) −9.91864 + 6.01759i −0.0590395 + 0.0358190i
\(169\) −142.100 −0.840826
\(170\) 0 0
\(171\) 53.9002i 0.315206i
\(172\) −110.343 17.8125i −0.641532 0.103561i
\(173\) −2.33481 −0.0134960 −0.00674800 0.999977i \(-0.502148\pi\)
−0.00674800 + 0.999977i \(0.502148\pi\)
\(174\) −120.399 + 102.522i −0.691946 + 0.589205i
\(175\) 0 0
\(176\) 79.5224 239.891i 0.451832 1.36302i
\(177\) −151.836 −0.857830
\(178\) −51.6071 60.6060i −0.289927 0.340483i
\(179\) 227.054i 1.26846i −0.773145 0.634229i \(-0.781318\pi\)
0.773145 0.634229i \(-0.218682\pi\)
\(180\) 0 0
\(181\) 114.096 0.630367 0.315183 0.949031i \(-0.397934\pi\)
0.315183 + 0.949031i \(0.397934\pi\)
\(182\) 6.61243 5.63060i 0.0363320 0.0309374i
\(183\) 65.8179i 0.359661i
\(184\) 79.2990 + 130.707i 0.430973 + 0.710362i
\(185\) 0 0
\(186\) 30.5980 + 35.9335i 0.164505 + 0.193191i
\(187\) 432.144i 2.31093i
\(188\) −219.778 35.4783i −1.16903 0.188714i
\(189\) −4.35050 −0.0230185
\(190\) 0 0
\(191\) 139.392i 0.729798i −0.931047 0.364899i \(-0.881103\pi\)
0.931047 0.364899i \(-0.118897\pi\)
\(192\) 98.3173 + 51.2027i 0.512069 + 0.266681i
\(193\) −182.046 −0.943245 −0.471623 0.881801i \(-0.656331\pi\)
−0.471623 + 0.881801i \(0.656331\pi\)
\(194\) 218.900 + 257.071i 1.12835 + 1.32511i
\(195\) 0 0
\(196\) −30.7886 + 190.727i −0.157085 + 0.973097i
\(197\) −258.027 −1.30978 −0.654890 0.755724i \(-0.727285\pi\)
−0.654890 + 0.755724i \(0.727285\pi\)
\(198\) 72.1573 61.4432i 0.364431 0.310319i
\(199\) 256.474i 1.28881i −0.764683 0.644407i \(-0.777104\pi\)
0.764683 0.644407i \(-0.222896\pi\)
\(200\) 0 0
\(201\) 159.698 0.794516
\(202\) 57.7650 + 67.8377i 0.285965 + 0.335830i
\(203\) 38.2202i 0.188277i
\(204\) 187.124 + 30.2070i 0.917273 + 0.148073i
\(205\) 0 0
\(206\) 192.574 163.980i 0.934825 0.796020i
\(207\) 57.3303i 0.276958i
\(208\) −78.7697 26.1117i −0.378700 0.125537i
\(209\) −283.794 −1.35787
\(210\) 0 0
\(211\) 211.855i 1.00405i 0.864852 + 0.502027i \(0.167412\pi\)
−0.864852 + 0.502027i \(0.832588\pi\)
\(212\) 9.91864 61.4432i 0.0467860 0.289826i
\(213\) −226.390 −1.06287
\(214\) 158.949 135.348i 0.742750 0.632465i
\(215\) 0 0
\(216\) 21.5619 + 35.5399i 0.0998235 + 0.164537i
\(217\) −11.4070 −0.0525667
\(218\) 0.650466 + 0.763890i 0.00298379 + 0.00350408i
\(219\) 94.7731i 0.432754i
\(220\) 0 0
\(221\) −141.897 −0.642068
\(222\) −41.0380 + 34.9446i −0.184856 + 0.157408i
\(223\) 349.843i 1.56880i 0.620255 + 0.784401i \(0.287029\pi\)
−0.620255 + 0.784401i \(0.712971\pi\)
\(224\) −24.8281 + 10.0690i −0.110840 + 0.0449508i
\(225\) 0 0
\(226\) −22.0241 25.8645i −0.0974517 0.114445i
\(227\) 185.554i 0.817418i 0.912665 + 0.408709i \(0.134021\pi\)
−0.912665 + 0.408709i \(0.865979\pi\)
\(228\) 19.8373 122.886i 0.0870056 0.538976i
\(229\) −263.897 −1.15239 −0.576194 0.817313i \(-0.695463\pi\)
−0.576194 + 0.817313i \(0.695463\pi\)
\(230\) 0 0
\(231\) 22.9061i 0.0991607i
\(232\) −312.227 + 189.427i −1.34581 + 0.816494i
\(233\) 58.4780 0.250978 0.125489 0.992095i \(-0.459950\pi\)
0.125489 + 0.992095i \(0.459950\pi\)
\(234\) −20.1752 23.6933i −0.0862190 0.101253i
\(235\) 0 0
\(236\) −346.169 55.8812i −1.46682 0.236785i
\(237\) 23.5980 0.0995694
\(238\) −34.8800 + 29.7009i −0.146555 + 0.124794i
\(239\) 113.337i 0.474212i −0.971484 0.237106i \(-0.923801\pi\)
0.971484 0.237106i \(-0.0761989\pi\)
\(240\) 0 0
\(241\) −77.7940 −0.322797 −0.161398 0.986889i \(-0.551600\pi\)
−0.161398 + 0.986889i \(0.551600\pi\)
\(242\) −166.616 195.669i −0.688495 0.808551i
\(243\) 15.5885i 0.0641500i
\(244\) −24.2234 + 150.057i −0.0992763 + 0.614989i
\(245\) 0 0
\(246\) −35.0756 + 29.8675i −0.142584 + 0.121413i
\(247\) 93.1855i 0.377269i
\(248\) 56.5351 + 93.1855i 0.227964 + 0.375748i
\(249\) −102.199 −0.410439
\(250\) 0 0
\(251\) 106.226i 0.423212i −0.977355 0.211606i \(-0.932131\pi\)
0.977355 0.211606i \(-0.0678693\pi\)
\(252\) −9.91864 1.60114i −0.0393597 0.00635374i
\(253\) 301.854 1.19310
\(254\) 12.8762 10.9644i 0.0506939 0.0431667i
\(255\) 0 0
\(256\) 205.308 + 152.921i 0.801983 + 0.597346i
\(257\) −381.078 −1.48279 −0.741397 0.671067i \(-0.765836\pi\)
−0.741397 + 0.671067i \(0.765836\pi\)
\(258\) −62.7556 73.6985i −0.243239 0.285653i
\(259\) 13.0274i 0.0502988i
\(260\) 0 0
\(261\) −136.949 −0.524707
\(262\) 78.7697 67.0738i 0.300648 0.256007i
\(263\) 11.4914i 0.0436934i −0.999761 0.0218467i \(-0.993045\pi\)
0.999761 0.0218467i \(-0.00695458\pi\)
\(264\) 187.124 113.527i 0.708802 0.430027i
\(265\) 0 0
\(266\) 19.5050 + 22.9061i 0.0733269 + 0.0861132i
\(267\) 68.9368i 0.258190i
\(268\) 364.093 + 58.7746i 1.35855 + 0.219308i
\(269\) 77.9518 0.289784 0.144892 0.989447i \(-0.453717\pi\)
0.144892 + 0.989447i \(0.453717\pi\)
\(270\) 0 0
\(271\) 86.6851i 0.319871i 0.987127 + 0.159936i \(0.0511287\pi\)
−0.987127 + 0.159936i \(0.948871\pi\)
\(272\) 415.504 + 137.737i 1.52759 + 0.506386i
\(273\) 7.52136 0.0275508
\(274\) 69.7700 + 81.9360i 0.254635 + 0.299036i
\(275\) 0 0
\(276\) −21.0997 + 130.707i −0.0764481 + 0.473575i
\(277\) 287.328 1.03729 0.518643 0.854991i \(-0.326437\pi\)
0.518643 + 0.854991i \(0.326437\pi\)
\(278\) −20.7462 + 17.6658i −0.0746267 + 0.0635459i
\(279\) 40.8729i 0.146498i
\(280\) 0 0
\(281\) −224.598 −0.799281 −0.399641 0.916672i \(-0.630865\pi\)
−0.399641 + 0.916672i \(0.630865\pi\)
\(282\) −124.994 146.790i −0.443242 0.520531i
\(283\) 84.1224i 0.297252i −0.988893 0.148626i \(-0.952515\pi\)
0.988893 0.148626i \(-0.0474851\pi\)
\(284\) −516.145 83.3200i −1.81741 0.293380i
\(285\) 0 0
\(286\) −124.749 + 106.226i −0.436186 + 0.371420i
\(287\) 11.1346i 0.0387967i
\(288\) 36.0786 + 88.9625i 0.125273 + 0.308898i
\(289\) 459.495 1.58995
\(290\) 0 0
\(291\) 292.407i 1.00484i
\(292\) −34.8800 + 216.072i −0.119452 + 0.739972i
\(293\) −246.620 −0.841706 −0.420853 0.907129i \(-0.638269\pi\)
−0.420853 + 0.907129i \(0.638269\pi\)
\(294\) −127.387 + 108.472i −0.433288 + 0.368952i
\(295\) 0 0
\(296\) −106.423 + 64.5661i −0.359536 + 0.218129i
\(297\) 82.0759 0.276350
\(298\) 43.6312 + 51.2394i 0.146414 + 0.171944i
\(299\) 99.1156i 0.331490i
\(300\) 0 0
\(301\) 23.3954 0.0777255
\(302\) 213.166 181.514i 0.705846 0.601041i
\(303\) 77.1626i 0.254662i
\(304\) 90.4535 272.866i 0.297544 0.897586i
\(305\) 0 0
\(306\) 106.423 + 124.980i 0.347787 + 0.408432i
\(307\) 115.811i 0.377236i 0.982051 + 0.188618i \(0.0604008\pi\)
−0.982051 + 0.188618i \(0.939599\pi\)
\(308\) −8.43030 + 52.2233i −0.0273711 + 0.169556i
\(309\) 219.045 0.708883
\(310\) 0 0
\(311\) 203.767i 0.655201i −0.944816 0.327600i \(-0.893760\pi\)
0.944816 0.327600i \(-0.106240\pi\)
\(312\) −37.2773 61.4432i −0.119478 0.196933i
\(313\) −99.0614 −0.316490 −0.158245 0.987400i \(-0.550584\pi\)
−0.158245 + 0.987400i \(0.550584\pi\)
\(314\) −27.5706 32.3782i −0.0878045 0.103115i
\(315\) 0 0
\(316\) 53.8007 + 8.68492i 0.170255 + 0.0274839i
\(317\) 471.192 1.48641 0.743206 0.669063i \(-0.233304\pi\)
0.743206 + 0.669063i \(0.233304\pi\)
\(318\) 41.0380 34.9446i 0.129050 0.109889i
\(319\) 721.057i 2.26037i
\(320\) 0 0
\(321\) 180.797 0.563232
\(322\) −20.7462 24.3638i −0.0644292 0.0756640i
\(323\) 491.546i 1.52181i
\(324\) −5.73713 + 35.5399i −0.0177072 + 0.109691i
\(325\) 0 0
\(326\) 320.096 272.568i 0.981891 0.836098i
\(327\) 0.868893i 0.00265717i
\(328\) −90.9607 + 55.1854i −0.277319 + 0.168248i
\(329\) 46.5980 0.141635
\(330\) 0 0
\(331\) 270.695i 0.817810i −0.912577 0.408905i \(-0.865911\pi\)
0.912577 0.408905i \(-0.134089\pi\)
\(332\) −233.003 37.6131i −0.701816 0.113293i
\(333\) −46.6790 −0.140177
\(334\) −362.997 + 309.098i −1.08682 + 0.925444i
\(335\) 0 0
\(336\) −22.0241 7.30085i −0.0655479 0.0217287i
\(337\) 377.317 1.11964 0.559818 0.828615i \(-0.310871\pi\)
0.559818 + 0.828615i \(0.310871\pi\)
\(338\) −184.252 216.380i −0.545124 0.640179i
\(339\) 29.4198i 0.0867841i
\(340\) 0 0
\(341\) 215.203 0.631093
\(342\) 82.0759 69.8891i 0.239988 0.204354i
\(343\) 81.4639i 0.237504i
\(344\) −115.952 191.121i −0.337069 0.555583i
\(345\) 0 0
\(346\) −3.02740 3.55530i −0.00874971 0.0102754i
\(347\) 462.222i 1.33205i −0.745929 0.666025i \(-0.767994\pi\)
0.745929 0.666025i \(-0.232006\pi\)
\(348\) −312.227 50.4021i −0.897204 0.144834i
\(349\) −200.598 −0.574779 −0.287390 0.957814i \(-0.592787\pi\)
−0.287390 + 0.957814i \(0.592787\pi\)
\(350\) 0 0
\(351\) 26.9501i 0.0767810i
\(352\) 468.403 189.960i 1.33069 0.539660i
\(353\) 250.897 0.710757 0.355379 0.934722i \(-0.384352\pi\)
0.355379 + 0.934722i \(0.384352\pi\)
\(354\) −196.876 231.206i −0.556148 0.653125i
\(355\) 0 0
\(356\) 25.3713 157.168i 0.0712676 0.441483i
\(357\) −39.6746 −0.111133
\(358\) 345.744 294.407i 0.965764 0.822366i
\(359\) 215.601i 0.600560i 0.953851 + 0.300280i \(0.0970801\pi\)
−0.953851 + 0.300280i \(0.902920\pi\)
\(360\) 0 0
\(361\) 38.1960 0.105806
\(362\) 147.942 + 173.739i 0.408679 + 0.479941i
\(363\) 222.566i 0.613129i
\(364\) 17.1478 + 2.76814i 0.0471095 + 0.00760478i
\(365\) 0 0
\(366\) −100.223 + 85.3420i −0.273835 + 0.233175i
\(367\) 67.0637i 0.182735i 0.995817 + 0.0913675i \(0.0291238\pi\)
−0.995817 + 0.0913675i \(0.970876\pi\)
\(368\) −96.2097 + 290.231i −0.261439 + 0.788670i
\(369\) −39.8970 −0.108122
\(370\) 0 0
\(371\) 13.0274i 0.0351142i
\(372\) −15.0427 + 93.1855i −0.0404374 + 0.250499i
\(373\) 567.402 1.52119 0.760593 0.649230i \(-0.224909\pi\)
0.760593 + 0.649230i \(0.224909\pi\)
\(374\) 658.042 560.334i 1.75947 1.49822i
\(375\) 0 0
\(376\) −230.949 380.667i −0.614225 1.01241i
\(377\) 236.764 0.628020
\(378\) −5.64102 6.62466i −0.0149233 0.0175256i
\(379\) 240.298i 0.634031i −0.948420 0.317016i \(-0.897319\pi\)
0.948420 0.317016i \(-0.102681\pi\)
\(380\) 0 0
\(381\) 14.6462 0.0384414
\(382\) 212.257 180.740i 0.555646 0.473142i
\(383\) 670.068i 1.74952i 0.484553 + 0.874762i \(0.338982\pi\)
−0.484553 + 0.874762i \(0.661018\pi\)
\(384\) 49.5137 + 216.103i 0.128942 + 0.562768i
\(385\) 0 0
\(386\) −236.048 277.209i −0.611524 0.718157i
\(387\) 83.8290i 0.216612i
\(388\) −107.617 + 666.655i −0.277363 + 1.71818i
\(389\) 474.640 1.22015 0.610077 0.792342i \(-0.291139\pi\)
0.610077 + 0.792342i \(0.291139\pi\)
\(390\) 0 0
\(391\) 522.826i 1.33715i
\(392\) −330.349 + 200.421i −0.842726 + 0.511278i
\(393\) 89.5973 0.227983
\(394\) −334.567 392.907i −0.849156 0.997226i
\(395\) 0 0
\(396\) 187.124 + 30.2070i 0.472535 + 0.0762802i
\(397\) −499.460 −1.25809 −0.629043 0.777371i \(-0.716553\pi\)
−0.629043 + 0.777371i \(0.716553\pi\)
\(398\) 390.542 332.554i 0.981262 0.835562i
\(399\) 26.0548i 0.0653001i
\(400\) 0 0
\(401\) 344.694 0.859587 0.429793 0.902927i \(-0.358586\pi\)
0.429793 + 0.902927i \(0.358586\pi\)
\(402\) 207.070 + 243.178i 0.515100 + 0.604920i
\(403\) 70.6631i 0.175343i
\(404\) −28.3987 + 175.922i −0.0702938 + 0.435450i
\(405\) 0 0
\(406\) 58.1993 49.5578i 0.143348 0.122063i
\(407\) 245.773i 0.603864i
\(408\) 196.635 + 324.108i 0.481947 + 0.794382i
\(409\) 501.890 1.22712 0.613558 0.789650i \(-0.289738\pi\)
0.613558 + 0.789650i \(0.289738\pi\)
\(410\) 0 0
\(411\) 93.1988i 0.226761i
\(412\) 499.397 + 80.6166i 1.21213 + 0.195671i
\(413\) 73.3957 0.177714
\(414\) −87.2990 + 74.3367i −0.210867 + 0.179557i
\(415\) 0 0
\(416\) −62.3746 153.803i −0.149939 0.369719i
\(417\) −23.5980 −0.0565898
\(418\) −367.978 432.144i −0.880331 1.03384i
\(419\) 218.369i 0.521167i 0.965451 + 0.260584i \(0.0839150\pi\)
−0.965451 + 0.260584i \(0.916085\pi\)
\(420\) 0 0
\(421\) 281.698 0.669116 0.334558 0.942375i \(-0.391413\pi\)
0.334558 + 0.942375i \(0.391413\pi\)
\(422\) −322.600 + 274.700i −0.764455 + 0.650947i
\(423\) 166.967i 0.394722i
\(424\) 106.423 64.5661i 0.250997 0.152279i
\(425\) 0 0
\(426\) −293.547 344.733i −0.689076 0.809233i
\(427\) 31.8156i 0.0745097i
\(428\) 412.197 + 66.5401i 0.963078 + 0.155468i
\(429\) −141.897 −0.330762
\(430\) 0 0
\(431\) 441.081i 1.02339i −0.859167 0.511694i \(-0.829018\pi\)
0.859167 0.511694i \(-0.170982\pi\)
\(432\) −26.1600 + 78.9155i −0.0605556 + 0.182675i
\(433\) −123.443 −0.285089 −0.142544 0.989788i \(-0.545528\pi\)
−0.142544 + 0.989788i \(0.545528\pi\)
\(434\) −14.7907 17.3698i −0.0340800 0.0400227i
\(435\) 0 0
\(436\) −0.319785 + 1.98098i −0.000733451 + 0.00454353i
\(437\) 343.346 0.785690
\(438\) −144.315 + 122.886i −0.329485 + 0.280563i
\(439\) 330.728i 0.753368i −0.926342 0.376684i \(-0.877064\pi\)
0.926342 0.376684i \(-0.122936\pi\)
\(440\) 0 0
\(441\) −144.897 −0.328565
\(442\) −183.989 216.072i −0.416265 0.488850i
\(443\) 154.952i 0.349780i 0.984588 + 0.174890i \(0.0559569\pi\)
−0.984588 + 0.174890i \(0.944043\pi\)
\(444\) −106.423 17.1796i −0.239691 0.0386928i
\(445\) 0 0
\(446\) −532.718 + 453.619i −1.19444 + 1.01708i
\(447\) 58.2826i 0.130386i
\(448\) −47.5254 24.7508i −0.106084 0.0552473i
\(449\) 95.8970 0.213579 0.106790 0.994282i \(-0.465943\pi\)
0.106790 + 0.994282i \(0.465943\pi\)
\(450\) 0 0
\(451\) 210.065i 0.465775i
\(452\) 10.8276 67.0738i 0.0239548 0.148393i
\(453\) 242.467 0.535247
\(454\) −282.550 + 240.596i −0.622356 + 0.529948i
\(455\) 0 0
\(456\) 212.846 129.132i 0.466767 0.283185i
\(457\) −485.718 −1.06284 −0.531420 0.847108i \(-0.678341\pi\)
−0.531420 + 0.847108i \(0.678341\pi\)
\(458\) −342.179 401.846i −0.747116 0.877393i
\(459\) 142.160i 0.309716i
\(460\) 0 0
\(461\) 353.650 0.767136 0.383568 0.923513i \(-0.374695\pi\)
0.383568 + 0.923513i \(0.374695\pi\)
\(462\) −34.8800 + 29.7009i −0.0754978 + 0.0642878i
\(463\) 421.720i 0.910842i 0.890276 + 0.455421i \(0.150511\pi\)
−0.890276 + 0.455421i \(0.849489\pi\)
\(464\) −693.292 229.822i −1.49416 0.495306i
\(465\) 0 0
\(466\) 75.8248 + 89.0466i 0.162714 + 0.191087i
\(467\) 640.974i 1.37254i −0.727349 0.686268i \(-0.759248\pi\)
0.727349 0.686268i \(-0.240752\pi\)
\(468\) 9.91864 61.4432i 0.0211937 0.131289i
\(469\) −77.1960 −0.164597
\(470\) 0 0
\(471\) 36.8289i 0.0781929i
\(472\) −363.763 599.582i −0.770684 1.27030i
\(473\) −441.374 −0.933137
\(474\) 30.5980 + 35.9335i 0.0645528 + 0.0758091i
\(475\) 0 0
\(476\) −90.4535 14.6017i −0.190028 0.0306758i
\(477\) 46.6790 0.0978595
\(478\) 172.582 146.957i 0.361050 0.307441i
\(479\) 221.137i 0.461664i 0.972994 + 0.230832i \(0.0741448\pi\)
−0.972994 + 0.230832i \(0.925855\pi\)
\(480\) 0 0
\(481\) 80.7010 0.167778
\(482\) −100.871 118.460i −0.209275 0.245767i
\(483\) 27.7128i 0.0573764i
\(484\) 81.9124 507.424i 0.169240 1.04840i
\(485\) 0 0
\(486\) −23.7371 + 20.2126i −0.0488418 + 0.0415897i
\(487\) 889.949i 1.82741i 0.406377 + 0.913705i \(0.366792\pi\)
−0.406377 + 0.913705i \(0.633208\pi\)
\(488\) −259.907 + 157.684i −0.532596 + 0.323123i
\(489\) 364.096 0.744573
\(490\) 0 0
\(491\) 552.843i 1.12595i 0.826473 + 0.562977i \(0.190344\pi\)
−0.826473 + 0.562977i \(0.809656\pi\)
\(492\) −90.9607 14.6836i −0.184879 0.0298447i
\(493\) −1248.91 −2.53328
\(494\) −141.897 + 120.828i −0.287241 + 0.244591i
\(495\) 0 0
\(496\) −68.5914 + 206.916i −0.138289 + 0.417169i
\(497\) 109.435 0.220190
\(498\) −132.516 155.623i −0.266096 0.312495i
\(499\) 533.302i 1.06874i 0.845250 + 0.534371i \(0.179451\pi\)
−0.845250 + 0.534371i \(0.820549\pi\)
\(500\) 0 0
\(501\) −412.894 −0.824139
\(502\) 161.755 137.737i 0.322220 0.274376i
\(503\) 574.914i 1.14297i −0.820612 0.571485i \(-0.806367\pi\)
0.820612 0.571485i \(-0.193633\pi\)
\(504\) −10.4228 17.1796i −0.0206801 0.0340865i
\(505\) 0 0
\(506\) 391.395 + 459.644i 0.773509 + 0.908388i
\(507\) 246.124i 0.485451i
\(508\) 33.3917 + 5.39034i 0.0657316 + 0.0106109i
\(509\) −207.547 −0.407753 −0.203877 0.978997i \(-0.565354\pi\)
−0.203877 + 0.978997i \(0.565354\pi\)
\(510\) 0 0
\(511\) 45.8122i 0.0896521i
\(512\) 33.3518 + 510.913i 0.0651403 + 0.997876i
\(513\) 93.3580 0.181984
\(514\) −494.120 580.282i −0.961324 1.12895i
\(515\) 0 0
\(516\) 30.8522 191.121i 0.0597910 0.370389i
\(517\) −879.112 −1.70041
\(518\) 19.8373 16.8918i 0.0382959 0.0326096i
\(519\) 4.04401i 0.00779192i
\(520\) 0 0
\(521\) −712.900 −1.36833 −0.684165 0.729327i \(-0.739833\pi\)
−0.684165 + 0.729327i \(0.739833\pi\)
\(522\) −177.573 208.537i −0.340178 0.399495i
\(523\) 139.548i 0.266822i −0.991061 0.133411i \(-0.957407\pi\)
0.991061 0.133411i \(-0.0425931\pi\)
\(524\) 204.272 + 32.9751i 0.389831 + 0.0629296i
\(525\) 0 0
\(526\) 17.4983 14.9002i 0.0332668 0.0283273i
\(527\) 372.742i 0.707290i
\(528\) 415.504 + 137.737i 0.786939 + 0.260865i
\(529\) 163.804 0.309648
\(530\) 0 0
\(531\) 262.988i 0.495268i
\(532\) −9.58911 + 59.4019i −0.0180246 + 0.111658i
\(533\) 68.9760 0.129411
\(534\) 104.973 89.3861i 0.196578 0.167390i
\(535\) 0 0
\(536\) 382.598 + 630.627i 0.713802 + 1.17654i
\(537\) 393.269 0.732345
\(538\) 101.075 + 118.700i 0.187872 + 0.220632i
\(539\) 762.908i 1.41541i
\(540\) 0 0
\(541\) −946.688 −1.74988 −0.874942 0.484227i \(-0.839101\pi\)
−0.874942 + 0.484227i \(0.839101\pi\)
\(542\) −131.999 + 112.399i −0.243540 + 0.207379i
\(543\) 197.621i 0.363942i
\(544\) 329.021 + 811.298i 0.604818 + 1.49136i
\(545\) 0 0
\(546\) 9.75248 + 11.4531i 0.0178617 + 0.0209763i
\(547\) 50.3388i 0.0920271i 0.998941 + 0.0460136i \(0.0146517\pi\)
−0.998941 + 0.0460136i \(0.985348\pi\)
\(548\) −34.3006 + 212.483i −0.0625923 + 0.387742i
\(549\) −114.000 −0.207650
\(550\) 0 0
\(551\) 820.173i 1.48852i
\(552\) −226.390 + 137.350i −0.410128 + 0.248822i
\(553\) −11.4070 −0.0206275
\(554\) 372.561 + 437.525i 0.672492 + 0.789757i
\(555\) 0 0
\(556\) −53.8007 8.68492i −0.0967638 0.0156204i
\(557\) −790.157 −1.41859 −0.709297 0.704910i \(-0.750987\pi\)
−0.709297 + 0.704910i \(0.750987\pi\)
\(558\) −62.2386 + 52.9973i −0.111539 + 0.0949773i
\(559\) 144.928i 0.259263i
\(560\) 0 0
\(561\) 748.495 1.33422
\(562\) −291.222 342.004i −0.518189 0.608548i
\(563\) 354.133i 0.629010i 0.949256 + 0.314505i \(0.101838\pi\)
−0.949256 + 0.314505i \(0.898162\pi\)
\(564\) 61.4502 380.667i 0.108954 0.674941i
\(565\) 0 0
\(566\) 128.096 109.076i 0.226319 0.192714i
\(567\) 7.53528i 0.0132897i
\(568\) −542.378 893.989i −0.954891 1.57392i
\(569\) −55.4983 −0.0975366 −0.0487683 0.998810i \(-0.515530\pi\)
−0.0487683 + 0.998810i \(0.515530\pi\)
\(570\) 0 0
\(571\) 791.134i 1.38552i −0.721167 0.692762i \(-0.756394\pi\)
0.721167 0.692762i \(-0.243606\pi\)
\(572\) −323.509 52.2233i −0.565575 0.0912995i
\(573\) 241.433 0.421349
\(574\) 16.9551 14.4376i 0.0295386 0.0251526i
\(575\) 0 0
\(576\) −88.6856 + 170.291i −0.153968 + 0.295643i
\(577\) −201.759 −0.349668 −0.174834 0.984598i \(-0.555939\pi\)
−0.174834 + 0.984598i \(0.555939\pi\)
\(578\) 595.799 + 699.690i 1.03079 + 1.21054i
\(579\) 315.313i 0.544583i
\(580\) 0 0
\(581\) 49.4020 0.0850292
\(582\) −445.260 + 379.146i −0.765051 + 0.651454i
\(583\) 245.773i 0.421566i
\(584\) −374.248 + 227.054i −0.640835 + 0.388791i
\(585\) 0 0
\(586\) −319.777 375.537i −0.545694 0.640848i
\(587\) 444.556i 0.757335i −0.925533 0.378668i \(-0.876382\pi\)
0.925533 0.378668i \(-0.123618\pi\)
\(588\) −330.349 53.3274i −0.561818 0.0906929i
\(589\) 244.784 0.415593
\(590\) 0 0
\(591\) 446.915i 0.756202i
\(592\) −236.309 78.3350i −0.399171 0.132323i
\(593\) 563.908 0.950942 0.475471 0.879731i \(-0.342278\pi\)
0.475471 + 0.879731i \(0.342278\pi\)
\(594\) 106.423 + 124.980i 0.179163 + 0.210404i
\(595\) 0 0
\(596\) −21.4502 + 132.878i −0.0359902 + 0.222949i
\(597\) 444.226 0.744097
\(598\) 150.927 128.517i 0.252386 0.214911i
\(599\) 845.034i 1.41074i −0.708839 0.705371i \(-0.750781\pi\)
0.708839 0.705371i \(-0.249219\pi\)
\(600\) 0 0
\(601\) 672.296 1.11863 0.559314 0.828956i \(-0.311065\pi\)
0.559314 + 0.828956i \(0.311065\pi\)
\(602\) 30.3353 + 35.6250i 0.0503909 + 0.0591777i
\(603\) 276.604i 0.458714i
\(604\) 552.797 + 89.2368i 0.915227 + 0.147743i
\(605\) 0 0
\(606\) −117.498 + 100.052i −0.193892 + 0.165102i
\(607\) 882.664i 1.45414i 0.686562 + 0.727071i \(0.259119\pi\)
−0.686562 + 0.727071i \(0.740881\pi\)
\(608\) 532.789 216.072i 0.876298 0.355381i
\(609\) 66.1993 0.108702
\(610\) 0 0
\(611\) 288.662i 0.472442i
\(612\) −52.3200 + 324.108i −0.0854902 + 0.529588i
\(613\) −469.374 −0.765701 −0.382850 0.923810i \(-0.625057\pi\)
−0.382850 + 0.923810i \(0.625057\pi\)
\(614\) −176.350 + 150.166i −0.287216 + 0.244569i
\(615\) 0 0
\(616\) −90.4535 + 54.8777i −0.146840 + 0.0890871i
\(617\) −218.994 −0.354934 −0.177467 0.984127i \(-0.556790\pi\)
−0.177467 + 0.984127i \(0.556790\pi\)
\(618\) 284.022 + 333.548i 0.459582 + 0.539721i
\(619\) 879.610i 1.42102i −0.703689 0.710509i \(-0.748465\pi\)
0.703689 0.710509i \(-0.251535\pi\)
\(620\) 0 0
\(621\) −99.2990 −0.159902
\(622\) 310.284 264.213i 0.498849 0.424779i
\(623\) 33.3232i 0.0534884i
\(624\) 45.2267 136.433i 0.0724787 0.218643i
\(625\) 0 0
\(626\) −128.447 150.845i −0.205187 0.240966i
\(627\) 491.546i 0.783964i
\(628\) 13.5544 83.9656i 0.0215834 0.133703i
\(629\) −425.691 −0.676774
\(630\) 0 0
\(631\) 635.566i 1.00724i −0.863926 0.503618i \(-0.832002\pi\)
0.863926 0.503618i \(-0.167998\pi\)
\(632\) 56.5351 + 93.1855i 0.0894543 + 0.147445i
\(633\) −366.944 −0.579691
\(634\) 610.966 + 717.502i 0.963669 + 1.13171i
\(635\) 0 0
\(636\) 106.423 + 17.1796i 0.167331 + 0.0270119i
\(637\) 250.505 0.393258
\(638\) −1097.98 + 934.951i −1.72097 + 1.46544i
\(639\) 392.120i 0.613646i
\(640\) 0 0
\(641\) −296.309 −0.462260 −0.231130 0.972923i \(-0.574242\pi\)
−0.231130 + 0.972923i \(0.574242\pi\)
\(642\) 234.429 + 275.307i 0.365154 + 0.428827i
\(643\) 591.032i 0.919179i 0.888131 + 0.459590i \(0.152003\pi\)
−0.888131 + 0.459590i \(0.847997\pi\)
\(644\) 10.1993 63.1821i 0.0158375 0.0981088i
\(645\) 0 0
\(646\) 748.495 637.357i 1.15866 0.986621i
\(647\) 166.507i 0.257352i 0.991687 + 0.128676i \(0.0410728\pi\)
−0.991687 + 0.128676i \(0.958927\pi\)
\(648\) −61.5569 + 37.3463i −0.0949953 + 0.0576331i
\(649\) −1384.67 −2.13355
\(650\) 0 0
\(651\) 19.7575i 0.0303494i
\(652\) 830.098 + 134.001i 1.27316 + 0.205523i
\(653\) 621.335 0.951509 0.475754 0.879578i \(-0.342175\pi\)
0.475754 + 0.879578i \(0.342175\pi\)
\(654\) −1.32310 + 1.12664i −0.00202308 + 0.00172269i
\(655\) 0 0
\(656\) −201.976 66.9538i −0.307890 0.102064i
\(657\) −164.152 −0.249851
\(658\) 60.4208 + 70.9565i 0.0918249 + 0.107837i
\(659\) 702.113i 1.06542i −0.846297 0.532711i \(-0.821173\pi\)
0.846297 0.532711i \(-0.178827\pi\)
\(660\) 0 0
\(661\) 358.193 0.541895 0.270948 0.962594i \(-0.412663\pi\)
0.270948 + 0.962594i \(0.412663\pi\)
\(662\) 412.197 350.994i 0.622655 0.530202i
\(663\) 245.773i 0.370698i
\(664\) −244.846 403.573i −0.368743 0.607790i
\(665\) 0 0
\(666\) −60.5257 71.0798i −0.0908795 0.106726i
\(667\) 872.367i 1.30790i
\(668\) −941.351 151.960i −1.40921 0.227485i
\(669\) −605.945 −0.905748
\(670\) 0 0
\(671\) 600.230i 0.894530i
\(672\) −17.4400 43.0035i −0.0259524 0.0639933i
\(673\) 714.176 1.06118 0.530592 0.847628i \(-0.321970\pi\)
0.530592 + 0.847628i \(0.321970\pi\)
\(674\) 489.244 + 574.555i 0.725882 + 0.852456i
\(675\) 0 0
\(676\) 90.5827 561.134i 0.133998 0.830081i
\(677\) 509.833 0.753077 0.376538 0.926401i \(-0.377114\pi\)
0.376538 + 0.926401i \(0.377114\pi\)
\(678\) 44.7986 38.1468i 0.0660747 0.0562638i
\(679\) 141.346i 0.208168i
\(680\) 0 0
\(681\) −321.389 −0.471936
\(682\) 279.040 + 327.697i 0.409150 + 0.480494i
\(683\) 1263.93i 1.85055i −0.379298 0.925275i \(-0.623834\pi\)
0.379298 0.925275i \(-0.376166\pi\)
\(684\) 212.846 + 34.3592i 0.311178 + 0.0502327i
\(685\) 0 0
\(686\) 124.048 105.629i 0.180828 0.153978i
\(687\) 457.083i 0.665332i
\(688\) 140.679 424.378i 0.204475 0.616829i
\(689\) −80.7010 −0.117128
\(690\) 0 0
\(691\) 512.351i 0.741463i −0.928740 0.370731i \(-0.879107\pi\)
0.928740 0.370731i \(-0.120893\pi\)
\(692\) 1.48834 9.21987i 0.00215078 0.0133235i
\(693\) −39.6746 −0.0572504
\(694\) 703.842 599.334i 1.01418 0.863594i
\(695\) 0 0
\(696\) −328.096 540.793i −0.471403 0.777002i
\(697\) −363.843 −0.522012
\(698\) −260.103 305.458i −0.372640 0.437619i
\(699\) 101.287i 0.144902i
\(700\) 0 0
\(701\) 1092.03 1.55781 0.778907 0.627139i \(-0.215774\pi\)
0.778907 + 0.627139i \(0.215774\pi\)
\(702\) 41.0380 34.9446i 0.0584586 0.0497786i
\(703\) 279.556i 0.397662i
\(704\) 896.609 + 466.945i 1.27359 + 0.663274i
\(705\) 0 0
\(706\) 325.323 + 382.051i 0.460798 + 0.541148i
\(707\) 37.2995i 0.0527574i
\(708\) 96.7891 599.582i 0.136708 0.846867i
\(709\) −416.887 −0.587993 −0.293997 0.955806i \(-0.594985\pi\)
−0.293997 + 0.955806i \(0.594985\pi\)
\(710\) 0 0
\(711\) 40.8729i 0.0574864i
\(712\) 272.223 165.156i 0.382336 0.231961i
\(713\) −260.362 −0.365163
\(714\) −51.4435 60.4139i −0.0720498 0.0846133i
\(715\) 0 0
\(716\) 896.609 + 144.738i 1.25225 + 0.202147i
\(717\) 196.305 0.273787
\(718\) −328.304 + 279.556i −0.457247 + 0.389354i
\(719\) 395.268i 0.549747i −0.961480 0.274874i \(-0.911364\pi\)
0.961480 0.274874i \(-0.0886361\pi\)
\(720\) 0 0
\(721\) −105.884 −0.146857
\(722\) 49.5264 + 58.1625i 0.0685962 + 0.0805575i
\(723\) 134.743i 0.186367i
\(724\) −72.7317 + 450.553i −0.100458 + 0.622310i
\(725\) 0 0
\(726\) 338.909 288.587i 0.466817 0.397503i
\(727\) 597.583i 0.821985i 0.911639 + 0.410993i \(0.134818\pi\)
−0.911639 + 0.410993i \(0.865182\pi\)
\(728\) 18.0194 + 29.7009i 0.0247519 + 0.0407980i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 764.482i 1.04580i
\(732\) −259.907 41.9562i −0.355064 0.0573172i
\(733\) −23.8650 −0.0325580 −0.0162790 0.999867i \(-0.505182\pi\)
−0.0162790 + 0.999867i \(0.505182\pi\)
\(734\) −102.120 + 86.9574i −0.139129 + 0.118471i
\(735\) 0 0
\(736\) −566.694 + 229.822i −0.769965 + 0.312258i
\(737\) 1456.37 1.97608
\(738\) −51.7320 60.7527i −0.0700976 0.0823207i
\(739\) 125.767i 0.170186i 0.996373 + 0.0850928i \(0.0271187\pi\)
−0.996373 + 0.0850928i \(0.972881\pi\)
\(740\) 0 0
\(741\) −161.402 −0.217816
\(742\) −19.8373 + 16.8918i −0.0267349 + 0.0227652i
\(743\) 148.841i 0.200325i −0.994971 0.100162i \(-0.968064\pi\)
0.994971 0.100162i \(-0.0319362\pi\)
\(744\) −161.402 + 97.9217i −0.216938 + 0.131615i
\(745\) 0 0
\(746\) 735.715 + 864.004i 0.986213 + 1.15818i
\(747\) 177.014i 0.236967i
\(748\) 1706.48 + 275.474i 2.28140 + 0.368280i
\(749\) −87.3954 −0.116683
\(750\) 0 0
\(751\) 463.390i 0.617030i 0.951219 + 0.308515i \(0.0998321\pi\)
−0.951219 + 0.308515i \(0.900168\pi\)
\(752\) 280.199 845.261i 0.372605 1.12402i
\(753\) 183.989 0.244341
\(754\) 306.997 + 360.529i 0.407157 + 0.478155i
\(755\) 0 0
\(756\) 2.77326 17.1796i 0.00366834 0.0227243i
\(757\) 719.363 0.950281 0.475141 0.879910i \(-0.342397\pi\)
0.475141 + 0.879910i \(0.342397\pi\)
\(758\) 365.910 311.579i 0.482731 0.411054i
\(759\) 522.826i 0.688836i
\(760\) 0 0
\(761\) −1107.49 −1.45530 −0.727651 0.685947i \(-0.759388\pi\)
−0.727651 + 0.685947i \(0.759388\pi\)
\(762\) 18.9908 + 22.3023i 0.0249223 + 0.0292681i
\(763\) 0.420013i 0.000550476i
\(764\) 550.440 + 88.8563i 0.720472 + 0.116304i
\(765\) 0 0
\(766\) −1020.34 + 868.835i −1.33203 + 1.13425i
\(767\) 454.666i 0.592785i
\(768\) −264.866 + 355.603i −0.344878 + 0.463025i
\(769\) 231.691 0.301289 0.150644 0.988588i \(-0.451865\pi\)
0.150644 + 0.988588i \(0.451865\pi\)
\(770\) 0 0
\(771\) 660.047i 0.856092i
\(772\) 116.047 718.879i 0.150320 0.931190i
\(773\) 519.956 0.672647 0.336324 0.941746i \(-0.390816\pi\)
0.336324 + 0.941746i \(0.390816\pi\)
\(774\) 127.650 108.696i 0.164922 0.140434i
\(775\) 0 0
\(776\) −1154.68 + 700.539i −1.48799 + 0.902756i
\(777\) 22.5641 0.0290400
\(778\) 615.436 + 722.751i 0.791049 + 0.928986i
\(779\) 238.940i 0.306726i
\(780\) 0 0
\(781\) −2064.58 −2.64351
\(782\) −796.127 + 677.917i −1.01807 + 0.866901i
\(783\) 237.202i 0.302940i
\(784\) −733.531 243.161i −0.935626 0.310154i
\(785\) 0 0
\(786\) 116.175 + 136.433i 0.147806 + 0.173579i
\(787\) 46.0288i 0.0584864i 0.999572 + 0.0292432i