Properties

Label 324.3.o.a.5.6
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.6
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +O(q^{10})\) \(q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +(0.644815 - 5.51675i) q^{11} +(3.12574 + 10.4407i) q^{13} +(-0.764332 - 9.40485i) q^{15} +(-9.72857 - 1.71541i) q^{17} +(-5.56429 - 31.5567i) q^{19} +(-0.379070 - 16.5402i) q^{21} +(11.1738 - 16.9889i) q^{23} +(-4.33279 + 14.4725i) q^{25} +(26.8491 + 2.85102i) q^{27} +(18.8382 - 17.7729i) q^{29} +(1.17260 - 20.1327i) q^{31} +(13.0066 + 10.4154i) q^{33} +(5.93260 - 16.2997i) q^{35} +(-51.6114 + 18.7850i) q^{37} +(-31.5287 - 8.65710i) q^{39} +(14.2410 - 60.0876i) q^{41} +(-8.52424 - 19.7614i) q^{43} +(25.1377 + 13.0158i) q^{45} +(-52.0796 + 3.03329i) q^{47} +(-7.36173 + 17.0664i) q^{49} +(19.8382 - 22.0167i) q^{51} +(-8.55662 - 4.94017i) q^{53} +(8.73493 + 15.1293i) q^{55} +(89.1177 + 36.0429i) q^{57} +(-9.04028 - 77.3445i) q^{59} +(19.5983 + 9.84264i) q^{61} +(42.6742 + 25.3457i) q^{63} +(-27.4960 - 20.4700i) q^{65} +(-42.3478 + 44.8861i) q^{67} +(25.4388 + 55.4450i) q^{69} +(-61.2446 + 72.9885i) q^{71} +(-46.6879 + 39.1758i) q^{73} +(-29.9200 - 34.0417i) q^{75} +(13.7472 + 27.3730i) q^{77} +(10.3218 - 2.44630i) q^{79} +(-49.9597 + 63.7576i) q^{81} +(-18.8178 - 79.3985i) q^{83} +(27.7662 - 13.9447i) q^{85} +(15.2415 + 76.1871i) q^{87} +(15.4859 + 18.4553i) q^{89} +(-46.0422 - 38.6340i) q^{91} +(49.3440 + 35.0071i) q^{93} +(73.3089 + 69.1634i) q^{95} +(-91.4351 + 122.819i) q^{97} +(-47.1816 + 16.5158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q+O(q^{10}) \) Copy content Toggle raw display \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.59067 + 2.54358i −0.530222 + 0.847859i
\(4\) 0 0
\(5\) −2.52291 + 1.87823i −0.504581 + 0.375647i −0.819142 0.573591i \(-0.805550\pi\)
0.314561 + 0.949237i \(0.398143\pi\)
\(6\) 0 0
\(7\) −4.60759 + 3.03046i −0.658227 + 0.432922i −0.834192 0.551474i \(-0.814066\pi\)
0.175966 + 0.984396i \(0.443695\pi\)
\(8\) 0 0
\(9\) −3.93956 8.09196i −0.437729 0.899107i
\(10\) 0 0
\(11\) 0.644815 5.51675i 0.0586196 0.501523i −0.931753 0.363093i \(-0.881721\pi\)
0.990372 0.138429i \(-0.0442053\pi\)
\(12\) 0 0
\(13\) 3.12574 + 10.4407i 0.240441 + 0.803130i 0.989985 + 0.141175i \(0.0450879\pi\)
−0.749543 + 0.661955i \(0.769727\pi\)
\(14\) 0 0
\(15\) −0.764332 9.40485i −0.0509554 0.626990i
\(16\) 0 0
\(17\) −9.72857 1.71541i −0.572269 0.100906i −0.119977 0.992777i \(-0.538282\pi\)
−0.452291 + 0.891870i \(0.649393\pi\)
\(18\) 0 0
\(19\) −5.56429 31.5567i −0.292857 1.66088i −0.675785 0.737098i \(-0.736195\pi\)
0.382928 0.923778i \(-0.374916\pi\)
\(20\) 0 0
\(21\) −0.379070 16.5402i −0.0180510 0.787628i
\(22\) 0 0
\(23\) 11.1738 16.9889i 0.485817 0.738648i −0.506518 0.862229i \(-0.669068\pi\)
0.992334 + 0.123581i \(0.0394380\pi\)
\(24\) 0 0
\(25\) −4.33279 + 14.4725i −0.173312 + 0.578901i
\(26\) 0 0
\(27\) 26.8491 + 2.85102i 0.994409 + 0.105593i
\(28\) 0 0
\(29\) 18.8382 17.7729i 0.649593 0.612859i −0.289230 0.957260i \(-0.593399\pi\)
0.938823 + 0.344401i \(0.111918\pi\)
\(30\) 0 0
\(31\) 1.17260 20.1327i 0.0378258 0.649443i −0.925108 0.379705i \(-0.876026\pi\)
0.962934 0.269739i \(-0.0869373\pi\)
\(32\) 0 0
\(33\) 13.0066 + 10.4154i 0.394139 + 0.315619i
\(34\) 0 0
\(35\) 5.93260 16.2997i 0.169503 0.465705i
\(36\) 0 0
\(37\) −51.6114 + 18.7850i −1.39490 + 0.507703i −0.926661 0.375897i \(-0.877335\pi\)
−0.468242 + 0.883601i \(0.655112\pi\)
\(38\) 0 0
\(39\) −31.5287 8.65710i −0.808428 0.221977i
\(40\) 0 0
\(41\) 14.2410 60.0876i 0.347342 1.46555i −0.466530 0.884506i \(-0.654496\pi\)
0.813872 0.581045i \(-0.197356\pi\)
\(42\) 0 0
\(43\) −8.52424 19.7614i −0.198238 0.459568i 0.789880 0.613261i \(-0.210143\pi\)
−0.988119 + 0.153693i \(0.950883\pi\)
\(44\) 0 0
\(45\) 25.1377 + 13.0158i 0.558616 + 0.289241i
\(46\) 0 0
\(47\) −52.0796 + 3.03329i −1.10808 + 0.0645381i −0.602407 0.798189i \(-0.705791\pi\)
−0.505669 + 0.862727i \(0.668754\pi\)
\(48\) 0 0
\(49\) −7.36173 + 17.0664i −0.150239 + 0.348294i
\(50\) 0 0
\(51\) 19.8382 22.0167i 0.388984 0.431700i
\(52\) 0 0
\(53\) −8.55662 4.94017i −0.161446 0.0932107i 0.417100 0.908860i \(-0.363046\pi\)
−0.578546 + 0.815650i \(0.696380\pi\)
\(54\) 0 0
\(55\) 8.73493 + 15.1293i 0.158817 + 0.275079i
\(56\) 0 0
\(57\) 89.1177 + 36.0429i 1.56347 + 0.632331i
\(58\) 0 0
\(59\) −9.04028 77.3445i −0.153225 1.31092i −0.822865 0.568238i \(-0.807625\pi\)
0.669639 0.742686i \(-0.266449\pi\)
\(60\) 0 0
\(61\) 19.5983 + 9.84264i 0.321284 + 0.161355i 0.602130 0.798398i \(-0.294319\pi\)
−0.280846 + 0.959753i \(0.590615\pi\)
\(62\) 0 0
\(63\) 42.6742 + 25.3457i 0.677369 + 0.402313i
\(64\) 0 0
\(65\) −27.4960 20.4700i −0.423015 0.314923i
\(66\) 0 0
\(67\) −42.3478 + 44.8861i −0.632057 + 0.669941i −0.961681 0.274171i \(-0.911597\pi\)
0.329624 + 0.944112i \(0.393078\pi\)
\(68\) 0 0
\(69\) 25.4388 + 55.4450i 0.368679 + 0.803551i
\(70\) 0 0
\(71\) −61.2446 + 72.9885i −0.862600 + 1.02801i 0.136701 + 0.990612i \(0.456350\pi\)
−0.999301 + 0.0373940i \(0.988094\pi\)
\(72\) 0 0
\(73\) −46.6879 + 39.1758i −0.639560 + 0.536655i −0.903883 0.427779i \(-0.859296\pi\)
0.264323 + 0.964434i \(0.414852\pi\)
\(74\) 0 0
\(75\) −29.9200 34.0417i −0.398933 0.453890i
\(76\) 0 0
\(77\) 13.7472 + 27.3730i 0.178535 + 0.355493i
\(78\) 0 0
\(79\) 10.3218 2.44630i 0.130655 0.0309659i −0.164768 0.986332i \(-0.552688\pi\)
0.295423 + 0.955366i \(0.404539\pi\)
\(80\) 0 0
\(81\) −49.9597 + 63.7576i −0.616786 + 0.787131i
\(82\) 0 0
\(83\) −18.8178 79.3985i −0.226720 0.956609i −0.960733 0.277473i \(-0.910503\pi\)
0.734013 0.679136i \(-0.237645\pi\)
\(84\) 0 0
\(85\) 27.7662 13.9447i 0.326661 0.164055i
\(86\) 0 0
\(87\) 15.2415 + 76.1871i 0.175190 + 0.875714i
\(88\) 0 0
\(89\) 15.4859 + 18.4553i 0.173998 + 0.207363i 0.845995 0.533191i \(-0.179007\pi\)
−0.671996 + 0.740554i \(0.734563\pi\)
\(90\) 0 0
\(91\) −46.0422 38.6340i −0.505958 0.424549i
\(92\) 0 0
\(93\) 49.3440 + 35.0071i 0.530580 + 0.376420i
\(94\) 0 0
\(95\) 73.3089 + 69.1634i 0.771673 + 0.728036i
\(96\) 0 0
\(97\) −91.4351 + 122.819i −0.942630 + 1.26617i 0.0212336 + 0.999775i \(0.493241\pi\)
−0.963863 + 0.266397i \(0.914167\pi\)
\(98\) 0 0
\(99\) −47.1816 + 16.5158i −0.476582 + 0.166826i
\(100\) 0 0
\(101\) 11.9263 23.7472i 0.118082 0.235121i −0.826825 0.562459i \(-0.809855\pi\)
0.944907 + 0.327338i \(0.106152\pi\)
\(102\) 0 0
\(103\) 17.8257 2.08353i 0.173065 0.0202284i −0.0291189 0.999576i \(-0.509270\pi\)
0.202184 + 0.979348i \(0.435196\pi\)
\(104\) 0 0
\(105\) 32.0227 + 41.0174i 0.304978 + 0.390641i
\(106\) 0 0
\(107\) 25.0065 14.4375i 0.233706 0.134930i −0.378575 0.925571i \(-0.623586\pi\)
0.612281 + 0.790641i \(0.290252\pi\)
\(108\) 0 0
\(109\) −66.5698 + 115.302i −0.610732 + 1.05782i 0.380385 + 0.924828i \(0.375792\pi\)
−0.991117 + 0.132991i \(0.957542\pi\)
\(110\) 0 0
\(111\) 34.3154 161.158i 0.309147 1.45188i
\(112\) 0 0
\(113\) 102.979 + 44.4207i 0.911316 + 0.393104i 0.799528 0.600629i \(-0.205083\pi\)
0.111788 + 0.993732i \(0.464342\pi\)
\(114\) 0 0
\(115\) 3.71874 + 63.8484i 0.0323369 + 0.555203i
\(116\) 0 0
\(117\) 72.1716 66.4251i 0.616851 0.567736i
\(118\) 0 0
\(119\) 50.0237 21.5781i 0.420367 0.181329i
\(120\) 0 0
\(121\) 87.7197 + 20.7900i 0.724956 + 0.171818i
\(122\) 0 0
\(123\) 130.185 + 131.802i 1.05841 + 1.07156i
\(124\) 0 0
\(125\) −43.1453 118.541i −0.345163 0.948327i
\(126\) 0 0
\(127\) 1.35575 + 0.493453i 0.0106752 + 0.00388546i 0.347352 0.937735i \(-0.387081\pi\)
−0.336677 + 0.941620i \(0.609303\pi\)
\(128\) 0 0
\(129\) 63.8239 + 9.75174i 0.494759 + 0.0755949i
\(130\) 0 0
\(131\) −197.277 11.4901i −1.50593 0.0877106i −0.714789 0.699340i \(-0.753477\pi\)
−0.791144 + 0.611630i \(0.790514\pi\)
\(132\) 0 0
\(133\) 121.269 + 128.538i 0.911797 + 0.966448i
\(134\) 0 0
\(135\) −73.0925 + 43.2359i −0.541426 + 0.320266i
\(136\) 0 0
\(137\) −80.2198 24.0162i −0.585546 0.175301i −0.0196916 0.999806i \(-0.506268\pi\)
−0.565855 + 0.824505i \(0.691454\pi\)
\(138\) 0 0
\(139\) −100.560 66.1390i −0.723450 0.475820i 0.133612 0.991034i \(-0.457342\pi\)
−0.857062 + 0.515213i \(0.827713\pi\)
\(140\) 0 0
\(141\) 75.1258 137.293i 0.532807 0.973712i
\(142\) 0 0
\(143\) 59.6142 10.5116i 0.416882 0.0735076i
\(144\) 0 0
\(145\) −14.1453 + 80.2219i −0.0975537 + 0.553254i
\(146\) 0 0
\(147\) −31.6997 45.8721i −0.215644 0.312055i
\(148\) 0 0
\(149\) −4.28158 + 1.28182i −0.0287354 + 0.00860282i −0.301139 0.953580i \(-0.597367\pi\)
0.272403 + 0.962183i \(0.412182\pi\)
\(150\) 0 0
\(151\) 7.05223 + 0.824288i 0.0467035 + 0.00545886i 0.139413 0.990234i \(-0.455479\pi\)
−0.0927091 + 0.995693i \(0.529553\pi\)
\(152\) 0 0
\(153\) 24.4453 + 85.4812i 0.159773 + 0.558701i
\(154\) 0 0
\(155\) 34.8556 + 52.9954i 0.224875 + 0.341906i
\(156\) 0 0
\(157\) −47.6030 63.9420i −0.303204 0.407274i 0.624242 0.781231i \(-0.285408\pi\)
−0.927446 + 0.373958i \(0.878001\pi\)
\(158\) 0 0
\(159\) 26.1764 13.9063i 0.164631 0.0874608i
\(160\) 0 0
\(161\) 112.140i 0.696519i
\(162\) 0 0
\(163\) −220.718 −1.35410 −0.677050 0.735937i \(-0.736742\pi\)
−0.677050 + 0.735937i \(0.736742\pi\)
\(164\) 0 0
\(165\) −52.3770 1.84776i −0.317436 0.0111986i
\(166\) 0 0
\(167\) 237.173 176.569i 1.42020 1.05730i 0.432381 0.901691i \(-0.357674\pi\)
0.987819 0.155608i \(-0.0497337\pi\)
\(168\) 0 0
\(169\) 41.9597 27.5973i 0.248282 0.163298i
\(170\) 0 0
\(171\) −233.434 + 169.346i −1.36511 + 0.990325i
\(172\) 0 0
\(173\) 29.1417 249.323i 0.168449 1.44118i −0.599351 0.800486i \(-0.704575\pi\)
0.767800 0.640689i \(-0.221351\pi\)
\(174\) 0 0
\(175\) −23.8947 79.8137i −0.136541 0.456079i
\(176\) 0 0
\(177\) 211.112 + 100.035i 1.19272 + 0.565167i
\(178\) 0 0
\(179\) 4.83021 + 0.851697i 0.0269844 + 0.00475808i 0.187124 0.982336i \(-0.440083\pi\)
−0.160140 + 0.987094i \(0.551194\pi\)
\(180\) 0 0
\(181\) −30.3013 171.847i −0.167411 0.949434i −0.946544 0.322575i \(-0.895452\pi\)
0.779133 0.626859i \(-0.215660\pi\)
\(182\) 0 0
\(183\) −56.2099 + 34.1934i −0.307158 + 0.186849i
\(184\) 0 0
\(185\) 94.9280 144.331i 0.513125 0.780168i
\(186\) 0 0
\(187\) −15.7366 + 52.5639i −0.0841530 + 0.281091i
\(188\) 0 0
\(189\) −132.349 + 68.2286i −0.700260 + 0.360998i
\(190\) 0 0
\(191\) −119.101 + 112.366i −0.623567 + 0.588305i −0.931785 0.363011i \(-0.881749\pi\)
0.308218 + 0.951316i \(0.400267\pi\)
\(192\) 0 0
\(193\) 11.8548 203.540i 0.0614241 1.05461i −0.816972 0.576677i \(-0.804349\pi\)
0.878396 0.477933i \(-0.158614\pi\)
\(194\) 0 0
\(195\) 95.8040 37.3772i 0.491302 0.191678i
\(196\) 0 0
\(197\) −74.6460 + 205.088i −0.378914 + 1.04106i 0.592894 + 0.805281i \(0.297985\pi\)
−0.971807 + 0.235776i \(0.924237\pi\)
\(198\) 0 0
\(199\) −23.0111 + 8.37537i −0.115634 + 0.0420873i −0.399189 0.916869i \(-0.630708\pi\)
0.283555 + 0.958956i \(0.408486\pi\)
\(200\) 0 0
\(201\) −46.8099 179.114i −0.232885 0.891112i
\(202\) 0 0
\(203\) −32.9385 + 138.979i −0.162259 + 0.684623i
\(204\) 0 0
\(205\) 76.9297 + 178.343i 0.375267 + 0.869967i
\(206\) 0 0
\(207\) −181.493 23.4889i −0.876780 0.113473i
\(208\) 0 0
\(209\) −177.678 + 10.3486i −0.850134 + 0.0495147i
\(210\) 0 0
\(211\) 73.6231 170.678i 0.348925 0.808899i −0.649881 0.760036i \(-0.725181\pi\)
0.998806 0.0488624i \(-0.0155596\pi\)
\(212\) 0 0
\(213\) −88.2321 271.881i −0.414235 1.27643i
\(214\) 0 0
\(215\) 58.6224 + 33.8457i 0.272662 + 0.157422i
\(216\) 0 0
\(217\) 55.6086 + 96.3168i 0.256261 + 0.443856i
\(218\) 0 0
\(219\) −25.3818 181.070i −0.115899 0.826803i
\(220\) 0 0
\(221\) −12.4989 106.935i −0.0565561 0.483868i
\(222\) 0 0
\(223\) 69.9923 + 35.1515i 0.313867 + 0.157630i 0.598758 0.800930i \(-0.295661\pi\)
−0.284891 + 0.958560i \(0.591957\pi\)
\(224\) 0 0
\(225\) 134.180 21.9547i 0.596357 0.0975764i
\(226\) 0 0
\(227\) −270.895 201.674i −1.19337 0.888430i −0.197596 0.980284i \(-0.563313\pi\)
−0.995772 + 0.0918540i \(0.970721\pi\)
\(228\) 0 0
\(229\) 154.888 164.172i 0.676367 0.716907i −0.294733 0.955579i \(-0.595231\pi\)
0.971100 + 0.238673i \(0.0767123\pi\)
\(230\) 0 0
\(231\) −91.4925 8.57413i −0.396071 0.0371175i
\(232\) 0 0
\(233\) −176.360 + 210.177i −0.756909 + 0.902049i −0.997648 0.0685410i \(-0.978166\pi\)
0.240740 + 0.970590i \(0.422610\pi\)
\(234\) 0 0
\(235\) 125.695 105.470i 0.534871 0.448810i
\(236\) 0 0
\(237\) −10.1961 + 30.1455i −0.0430216 + 0.127196i
\(238\) 0 0
\(239\) 142.252 + 283.247i 0.595197 + 1.18513i 0.966511 + 0.256627i \(0.0826112\pi\)
−0.371314 + 0.928508i \(0.621093\pi\)
\(240\) 0 0
\(241\) −304.379 + 72.1391i −1.26298 + 0.299332i −0.806944 0.590628i \(-0.798880\pi\)
−0.456038 + 0.889960i \(0.650732\pi\)
\(242\) 0 0
\(243\) −82.7033 228.493i −0.340343 0.940302i
\(244\) 0 0
\(245\) −13.4818 56.8840i −0.0550276 0.232180i
\(246\) 0 0
\(247\) 312.081 156.733i 1.26348 0.634546i
\(248\) 0 0
\(249\) 231.889 + 78.4320i 0.931282 + 0.314988i
\(250\) 0 0
\(251\) 53.0256 + 63.1935i 0.211257 + 0.251767i 0.861259 0.508166i \(-0.169676\pi\)
−0.650002 + 0.759933i \(0.725232\pi\)
\(252\) 0 0
\(253\) −86.5185 72.5976i −0.341970 0.286947i
\(254\) 0 0
\(255\) −8.69731 + 92.8068i −0.0341071 + 0.363948i
\(256\) 0 0
\(257\) 14.9632 + 14.1170i 0.0582225 + 0.0549301i 0.714803 0.699326i \(-0.246516\pi\)
−0.656581 + 0.754256i \(0.727998\pi\)
\(258\) 0 0
\(259\) 180.877 242.960i 0.698366 0.938068i
\(260\) 0 0
\(261\) −218.032 82.4203i −0.835371 0.315787i
\(262\) 0 0
\(263\) 121.451 241.828i 0.461790 0.919499i −0.535401 0.844598i \(-0.679840\pi\)
0.997191 0.0749012i \(-0.0238641\pi\)
\(264\) 0 0
\(265\) 30.8663 3.60776i 0.116477 0.0136142i
\(266\) 0 0
\(267\) −71.5754 + 10.0332i −0.268073 + 0.0375776i
\(268\) 0 0
\(269\) 36.2471 20.9273i 0.134748 0.0777966i −0.431111 0.902299i \(-0.641878\pi\)
0.565858 + 0.824502i \(0.308545\pi\)
\(270\) 0 0
\(271\) 159.519 276.295i 0.588631 1.01954i −0.405781 0.913971i \(-0.633000\pi\)
0.994412 0.105569i \(-0.0336664\pi\)
\(272\) 0 0
\(273\) 171.506 55.6581i 0.628228 0.203876i
\(274\) 0 0
\(275\) 77.0474 + 33.2350i 0.280172 + 0.120855i
\(276\) 0 0
\(277\) −12.7281 218.533i −0.0459498 0.788928i −0.940045 0.341051i \(-0.889217\pi\)
0.894095 0.447877i \(-0.147820\pi\)
\(278\) 0 0
\(279\) −167.533 + 69.8256i −0.600476 + 0.250271i
\(280\) 0 0
\(281\) −380.850 + 164.283i −1.35534 + 0.584636i −0.944932 0.327266i \(-0.893873\pi\)
−0.410407 + 0.911902i \(0.634613\pi\)
\(282\) 0 0
\(283\) 174.395 + 41.3323i 0.616236 + 0.146051i 0.526867 0.849948i \(-0.323367\pi\)
0.0893695 + 0.995999i \(0.471515\pi\)
\(284\) 0 0
\(285\) −292.532 + 76.4510i −1.02643 + 0.268249i
\(286\) 0 0
\(287\) 116.476 + 320.015i 0.405840 + 1.11504i
\(288\) 0 0
\(289\) −179.869 65.4669i −0.622383 0.226529i
\(290\) 0 0
\(291\) −166.956 427.936i −0.573732 1.47057i
\(292\) 0 0
\(293\) 263.611 + 15.3536i 0.899698 + 0.0524014i 0.501756 0.865009i \(-0.332688\pi\)
0.397942 + 0.917411i \(0.369725\pi\)
\(294\) 0 0
\(295\) 168.079 + 178.153i 0.569759 + 0.603909i
\(296\) 0 0
\(297\) 33.0410 146.281i 0.111249 0.492529i
\(298\) 0 0
\(299\) 212.302 + 63.5591i 0.710041 + 0.212572i
\(300\) 0 0
\(301\) 99.1623 + 65.2201i 0.329443 + 0.216678i
\(302\) 0 0
\(303\) 41.4321 + 68.1094i 0.136740 + 0.224784i
\(304\) 0 0
\(305\) −67.9314 + 11.9781i −0.222726 + 0.0392726i
\(306\) 0 0
\(307\) 4.84099 27.4546i 0.0157687 0.0894287i −0.975908 0.218183i \(-0.929987\pi\)
0.991676 + 0.128755i \(0.0410980\pi\)
\(308\) 0 0
\(309\) −23.0552 + 48.6553i −0.0746121 + 0.157460i
\(310\) 0 0
\(311\) 363.335 108.775i 1.16828 0.349760i 0.356824 0.934172i \(-0.383860\pi\)
0.811458 + 0.584411i \(0.198675\pi\)
\(312\) 0 0
\(313\) 518.083 + 60.5552i 1.65522 + 0.193467i 0.891797 0.452436i \(-0.149445\pi\)
0.763419 + 0.645903i \(0.223519\pi\)
\(314\) 0 0
\(315\) −155.268 + 16.2073i −0.492915 + 0.0514517i
\(316\) 0 0
\(317\) 20.6710 + 31.4288i 0.0652083 + 0.0991444i 0.866620 0.498969i \(-0.166288\pi\)
−0.801412 + 0.598113i \(0.795917\pi\)
\(318\) 0 0
\(319\) −85.9015 115.386i −0.269284 0.361711i
\(320\) 0 0
\(321\) −3.05408 + 86.5713i −0.00951425 + 0.269693i
\(322\) 0 0
\(323\) 316.546i 0.980019i
\(324\) 0 0
\(325\) −164.646 −0.506604
\(326\) 0 0
\(327\) −187.390 352.733i −0.573058 1.07869i
\(328\) 0 0
\(329\) 230.769 171.801i 0.701425 0.522192i
\(330\) 0 0
\(331\) −56.0498 + 36.8645i −0.169335 + 0.111373i −0.631347 0.775500i \(-0.717498\pi\)
0.462013 + 0.886873i \(0.347127\pi\)
\(332\) 0 0
\(333\) 355.334 + 343.633i 1.06707 + 1.03193i
\(334\) 0 0
\(335\) 22.5330 192.782i 0.0672628 0.575470i
\(336\) 0 0
\(337\) 128.856 + 430.410i 0.382363 + 1.27718i 0.905287 + 0.424801i \(0.139656\pi\)
−0.522924 + 0.852379i \(0.675159\pi\)
\(338\) 0 0
\(339\) −276.792 + 191.276i −0.816496 + 0.564236i
\(340\) 0 0
\(341\) −110.311 19.4508i −0.323493 0.0570406i
\(342\) 0 0
\(343\) −64.7237 367.066i −0.188699 1.07016i
\(344\) 0 0
\(345\) −168.319 92.1025i −0.487880 0.266964i
\(346\) 0 0
\(347\) −215.441 + 327.563i −0.620869 + 0.943985i 0.378959 + 0.925413i \(0.376282\pi\)
−0.999828 + 0.0185713i \(0.994088\pi\)
\(348\) 0 0
\(349\) −154.625 + 516.485i −0.443053 + 1.47990i 0.386929 + 0.922110i \(0.373536\pi\)
−0.829982 + 0.557790i \(0.811649\pi\)
\(350\) 0 0
\(351\) 54.1565 + 289.234i 0.154292 + 0.824029i
\(352\) 0 0
\(353\) −409.040 + 385.909i −1.15875 + 1.09323i −0.164478 + 0.986381i \(0.552594\pi\)
−0.994276 + 0.106847i \(0.965925\pi\)
\(354\) 0 0
\(355\) 17.4249 299.175i 0.0490843 0.842745i
\(356\) 0 0
\(357\) −24.6854 + 161.563i −0.0691467 + 0.452557i
\(358\) 0 0
\(359\) −199.030 + 546.831i −0.554402 + 1.52321i 0.273238 + 0.961947i \(0.411905\pi\)
−0.827639 + 0.561260i \(0.810317\pi\)
\(360\) 0 0
\(361\) −625.632 + 227.711i −1.73305 + 0.630780i
\(362\) 0 0
\(363\) −192.414 + 190.052i −0.530065 + 0.523559i
\(364\) 0 0
\(365\) 44.2079 186.528i 0.121117 0.511035i
\(366\) 0 0
\(367\) 70.7248 + 163.959i 0.192711 + 0.446754i 0.986986 0.160804i \(-0.0514087\pi\)
−0.794276 + 0.607558i \(0.792149\pi\)
\(368\) 0 0
\(369\) −542.330 + 121.481i −1.46973 + 0.329217i
\(370\) 0 0
\(371\) 54.3963 3.16822i 0.146621 0.00853969i
\(372\) 0 0
\(373\) 99.4679 230.592i 0.266670 0.618210i −0.731289 0.682068i \(-0.761081\pi\)
0.997959 + 0.0638573i \(0.0203403\pi\)
\(374\) 0 0
\(375\) 370.147 + 78.8154i 0.987060 + 0.210174i
\(376\) 0 0
\(377\) 244.445 + 141.130i 0.648394 + 0.374351i
\(378\) 0 0
\(379\) 270.449 + 468.431i 0.713585 + 1.23597i 0.963503 + 0.267698i \(0.0862631\pi\)
−0.249918 + 0.968267i \(0.580404\pi\)
\(380\) 0 0
\(381\) −3.41168 + 2.66354i −0.00895455 + 0.00699092i
\(382\) 0 0
\(383\) 58.5939 + 501.303i 0.152987 + 1.30888i 0.823640 + 0.567113i \(0.191940\pi\)
−0.670653 + 0.741771i \(0.733986\pi\)
\(384\) 0 0
\(385\) −86.0958 43.2389i −0.223625 0.112309i
\(386\) 0 0
\(387\) −126.327 + 146.829i −0.326426 + 0.379404i
\(388\) 0 0
\(389\) 282.917 + 210.624i 0.727293 + 0.541449i 0.895912 0.444232i \(-0.146523\pi\)
−0.168619 + 0.985681i \(0.553931\pi\)
\(390\) 0 0
\(391\) −137.848 + 146.110i −0.352552 + 0.373683i
\(392\) 0 0
\(393\) 343.028 483.513i 0.872845 1.23031i
\(394\) 0 0
\(395\) −21.4461 + 25.5585i −0.0542940 + 0.0647050i
\(396\) 0 0
\(397\) −188.267 + 157.975i −0.474224 + 0.397921i −0.848333 0.529464i \(-0.822393\pi\)
0.374109 + 0.927385i \(0.377949\pi\)
\(398\) 0 0
\(399\) −519.844 + 103.997i −1.30287 + 0.260643i
\(400\) 0 0
\(401\) −288.518 574.486i −0.719495 1.43263i −0.894042 0.447984i \(-0.852142\pi\)
0.174546 0.984649i \(-0.444154\pi\)
\(402\) 0 0
\(403\) 213.865 50.6869i 0.530682 0.125774i
\(404\) 0 0
\(405\) 6.29182 254.690i 0.0155353 0.628865i
\(406\) 0 0
\(407\) 70.3524 + 296.840i 0.172856 + 0.729337i
\(408\) 0 0
\(409\) 417.061 209.456i 1.01971 0.512117i 0.141270 0.989971i \(-0.454881\pi\)
0.878439 + 0.477854i \(0.158585\pi\)
\(410\) 0 0
\(411\) 188.690 165.843i 0.459100 0.403512i
\(412\) 0 0
\(413\) 276.043 + 328.975i 0.668385 + 0.796550i
\(414\) 0 0
\(415\) 196.605 + 164.971i 0.473746 + 0.397520i
\(416\) 0 0
\(417\) 328.186 150.576i 0.787017 0.361093i
\(418\) 0 0
\(419\) 498.355 + 470.173i 1.18939 + 1.12213i 0.989831 + 0.142247i \(0.0454326\pi\)
0.199559 + 0.979886i \(0.436049\pi\)
\(420\) 0 0
\(421\) 108.550 145.807i 0.257838 0.346336i −0.654289 0.756245i \(-0.727032\pi\)
0.912127 + 0.409909i \(0.134439\pi\)
\(422\) 0 0
\(423\) 229.716 + 409.476i 0.543064 + 0.968029i
\(424\) 0 0
\(425\) 66.9782 133.364i 0.157596 0.313799i
\(426\) 0 0
\(427\) −120.129 + 14.0410i −0.281331 + 0.0328829i
\(428\) 0 0
\(429\) −68.0892 + 168.354i −0.158716 + 0.392433i
\(430\) 0 0
\(431\) 219.993 127.013i 0.510425 0.294694i −0.222583 0.974914i \(-0.571449\pi\)
0.733008 + 0.680220i \(0.238116\pi\)
\(432\) 0 0
\(433\) 115.287 199.683i 0.266252 0.461161i −0.701639 0.712532i \(-0.747548\pi\)
0.967891 + 0.251371i \(0.0808814\pi\)
\(434\) 0 0
\(435\) −181.550 163.586i −0.417357 0.376059i
\(436\) 0 0
\(437\) −598.287 258.076i −1.36908 0.590563i
\(438\) 0 0
\(439\) −18.4113 316.111i −0.0419393 0.720069i −0.952095 0.305803i \(-0.901075\pi\)
0.910156 0.414267i \(-0.135962\pi\)
\(440\) 0 0
\(441\) 167.103 7.66339i 0.378918 0.0173773i
\(442\) 0 0
\(443\) 224.222 96.7200i 0.506145 0.218330i −0.127667 0.991817i \(-0.540749\pi\)
0.633812 + 0.773487i \(0.281489\pi\)
\(444\) 0 0
\(445\) −73.7328 17.4750i −0.165692 0.0392696i
\(446\) 0 0
\(447\) 3.55015 12.9295i 0.00794217 0.0289250i
\(448\) 0 0
\(449\) −218.698 600.868i −0.487078 1.33824i −0.903315 0.428979i \(-0.858873\pi\)
0.416237 0.909256i \(-0.363349\pi\)
\(450\) 0 0
\(451\) −322.305 117.309i −0.714645 0.260110i
\(452\) 0 0
\(453\) −13.3144 + 16.6267i −0.0293916 + 0.0367036i
\(454\) 0 0
\(455\) 188.724 + 10.9919i 0.414777 + 0.0241580i
\(456\) 0 0
\(457\) 189.960 + 201.346i 0.415668 + 0.440582i 0.901047 0.433722i \(-0.142800\pi\)
−0.485379 + 0.874304i \(0.661318\pi\)
\(458\) 0 0
\(459\) −256.312 73.7935i −0.558415 0.160770i
\(460\) 0 0
\(461\) −571.275 171.028i −1.23921 0.370994i −0.400865 0.916137i \(-0.631290\pi\)
−0.838343 + 0.545143i \(0.816475\pi\)
\(462\) 0 0
\(463\) 491.968 + 323.572i 1.06257 + 0.698860i 0.955380 0.295379i \(-0.0954458\pi\)
0.107185 + 0.994239i \(0.465816\pi\)
\(464\) 0 0
\(465\) −190.242 + 4.35998i −0.409122 + 0.00937631i
\(466\) 0 0
\(467\) −701.939 + 123.771i −1.50308 + 0.265034i −0.863759 0.503905i \(-0.831896\pi\)
−0.639323 + 0.768939i \(0.720785\pi\)
\(468\) 0 0
\(469\) 59.0959 335.150i 0.126004 0.714605i
\(470\) 0 0
\(471\) 238.362 19.3717i 0.506076 0.0411288i
\(472\) 0 0
\(473\) −114.515 + 34.2836i −0.242104 + 0.0724812i
\(474\) 0 0
\(475\) 480.813 + 56.1990i 1.01224 + 0.118314i
\(476\) 0 0
\(477\) −6.26627 + 88.7019i −0.0131368 + 0.185958i
\(478\) 0 0
\(479\) 471.396 + 716.722i 0.984125 + 1.49629i 0.863976 + 0.503533i \(0.167967\pi\)
0.120149 + 0.992756i \(0.461663\pi\)
\(480\) 0 0
\(481\) −357.452 480.142i −0.743144 0.998216i
\(482\) 0 0
\(483\) −285.235 178.376i −0.590550 0.369309i
\(484\) 0 0
\(485\) 481.596i 0.992982i
\(486\) 0 0
\(487\) 627.663 1.28884 0.644418 0.764674i \(-0.277100\pi\)
0.644418 + 0.764674i \(0.277100\pi\)
\(488\) 0 0
\(489\) 351.089 561.414i 0.717974 1.14809i
\(490\) 0 0
\(491\) 343.128 255.449i 0.698835 0.520264i −0.188104 0.982149i \(-0.560234\pi\)
0.886940 + 0.461885i \(0.152827\pi\)
\(492\) 0 0
\(493\) −213.756 + 140.590i −0.433583 + 0.285172i
\(494\) 0 0
\(495\) 88.0142 130.286i 0.177807 0.263204i
\(496\) 0 0
\(497\) 61.0013 521.900i 0.122739 1.05010i
\(498\) 0 0
\(499\) −97.5900 325.973i −0.195571 0.653253i −0.998374 0.0570082i \(-0.981844\pi\)
0.802803 0.596245i \(-0.203341\pi\)
\(500\) 0 0
\(501\) 71.8533 + 884.131i 0.143420 + 1.76473i
\(502\) 0 0
\(503\) −599.268 105.667i −1.19139 0.210074i −0.457415 0.889253i \(-0.651225\pi\)
−0.733972 + 0.679180i \(0.762336\pi\)
\(504\) 0 0
\(505\) 14.5139 + 82.3124i 0.0287404 + 0.162995i
\(506\) 0 0
\(507\) 3.45206 + 150.626i 0.00680880 + 0.297092i
\(508\) 0 0
\(509\) −147.345 + 224.027i −0.289479 + 0.440131i −0.950724 0.310039i \(-0.899658\pi\)
0.661245 + 0.750170i \(0.270028\pi\)
\(510\) 0 0
\(511\) 96.3979 321.991i 0.188646 0.630120i
\(512\) 0 0
\(513\) −59.4273 863.130i −0.115843 1.68252i
\(514\) 0 0
\(515\) −41.0593 + 38.7374i −0.0797267 + 0.0752183i
\(516\) 0 0
\(517\) −16.8478 + 289.266i −0.0325877 + 0.559508i
\(518\) 0 0
\(519\) 587.818 + 470.714i 1.13260 + 0.906964i
\(520\) 0 0
\(521\) −147.583 + 405.481i −0.283268 + 0.778274i 0.713699 + 0.700453i \(0.247019\pi\)
−0.996967 + 0.0778211i \(0.975204\pi\)
\(522\) 0 0
\(523\) −619.082 + 225.327i −1.18371 + 0.430836i −0.857512 0.514464i \(-0.827991\pi\)
−0.326201 + 0.945300i \(0.605769\pi\)
\(524\) 0 0
\(525\) 241.021 + 66.1791i 0.459087 + 0.126055i
\(526\) 0 0
\(527\) −45.9436 + 193.851i −0.0871795 + 0.367839i
\(528\) 0 0
\(529\) 45.7566 + 106.076i 0.0864964 + 0.200521i
\(530\) 0 0
\(531\) −590.254 + 377.857i −1.11159 + 0.711596i
\(532\) 0 0
\(533\) 671.869 39.1319i 1.26054 0.0734183i
\(534\) 0 0
\(535\) −35.9721 + 83.3926i −0.0672375 + 0.155874i
\(536\) 0 0
\(537\) −9.84961 + 10.9312i −0.0183419 + 0.0203561i
\(538\) 0 0
\(539\) 89.4041 + 51.6175i 0.165870 + 0.0957653i
\(540\) 0 0
\(541\) −112.301 194.512i −0.207581 0.359541i 0.743371 0.668880i \(-0.233226\pi\)
−0.950952 + 0.309338i \(0.899892\pi\)
\(542\) 0 0
\(543\) 485.307 + 196.278i 0.893751 + 0.361470i
\(544\) 0 0
\(545\) −48.6153 415.931i −0.0892024 0.763175i
\(546\) 0 0
\(547\) −425.730 213.810i −0.778300 0.390877i 0.0148606 0.999890i \(-0.495270\pi\)
−0.793160 + 0.609013i \(0.791566\pi\)
\(548\) 0 0
\(549\) 2.43745 197.364i 0.00443980 0.359498i
\(550\) 0 0
\(551\) −665.675 495.577i −1.20812 0.899413i
\(552\) 0 0
\(553\) −40.1450 + 42.5512i −0.0725950 + 0.0769462i
\(554\) 0 0
\(555\) 216.118 + 471.039i 0.389403 + 0.848719i
\(556\) 0 0
\(557\) 376.440 448.624i 0.675835 0.805429i −0.313730 0.949512i \(-0.601579\pi\)
0.989566 + 0.144083i \(0.0460233\pi\)
\(558\) 0 0
\(559\) 179.678 150.768i 0.321428 0.269710i
\(560\) 0 0
\(561\) −108.669 123.639i −0.193705 0.220390i
\(562\) 0 0
\(563\) −224.988 447.988i −0.399624 0.795716i 0.600368 0.799724i \(-0.295021\pi\)
−0.999992 + 0.00400743i \(0.998724\pi\)
\(564\) 0 0
\(565\) −343.238 + 81.3489i −0.607501 + 0.143980i
\(566\) 0 0
\(567\) 36.9787 445.169i 0.0652182 0.785131i
\(568\) 0 0
\(569\) −97.5056 411.409i −0.171363 0.723038i −0.989075 0.147411i \(-0.952906\pi\)
0.817712 0.575627i \(-0.195242\pi\)
\(570\) 0 0
\(571\) −529.303 + 265.826i −0.926976 + 0.465545i −0.847204 0.531268i \(-0.821716\pi\)
−0.0797722 + 0.996813i \(0.525419\pi\)
\(572\) 0 0
\(573\) −96.3619 481.681i −0.168171 0.840629i
\(574\) 0 0
\(575\) 197.459 + 235.322i 0.343407 + 0.409256i
\(576\) 0 0
\(577\) −357.205 299.730i −0.619073 0.519464i 0.278439 0.960454i \(-0.410183\pi\)
−0.897512 + 0.440990i \(0.854627\pi\)
\(578\) 0 0
\(579\) 498.862 + 353.917i 0.861592 + 0.611256i
\(580\) 0 0
\(581\) 327.318 + 308.809i 0.563371 + 0.531513i
\(582\) 0 0
\(583\) −32.7711 + 44.0192i −0.0562111 + 0.0755046i
\(584\) 0 0
\(585\) −57.3203 + 303.139i −0.0979833 + 0.518187i
\(586\) 0 0
\(587\) 303.014 603.350i 0.516207 1.02785i −0.472963 0.881082i \(-0.656816\pi\)
0.989170 0.146771i \(-0.0468881\pi\)
\(588\) 0 0
\(589\) −641.847 + 75.0211i −1.08972 + 0.127370i
\(590\) 0 0
\(591\) −402.921 516.095i −0.681761 0.873257i
\(592\) 0 0
\(593\) 433.568 250.320i 0.731143 0.422126i −0.0876972 0.996147i \(-0.527951\pi\)
0.818840 + 0.574022i \(0.194617\pi\)
\(594\) 0 0
\(595\) −85.6763 + 148.396i −0.143994 + 0.249405i
\(596\) 0 0
\(597\) 15.2996 71.8530i 0.0256275 0.120357i
\(598\) 0 0
\(599\) −423.586 182.717i −0.707155 0.305037i 0.0119594 0.999928i \(-0.496193\pi\)
−0.719115 + 0.694892i \(0.755452\pi\)
\(600\) 0 0
\(601\) 18.6918 + 320.925i 0.0311011 + 0.533986i 0.977493 + 0.210966i \(0.0676610\pi\)
−0.946392 + 0.323020i \(0.895302\pi\)
\(602\) 0 0
\(603\) 530.048 + 165.845i 0.879018 + 0.275034i
\(604\) 0 0
\(605\) −260.357 + 112.307i −0.430342 + 0.185631i
\(606\) 0 0
\(607\) −667.684 158.244i −1.09997 0.260699i −0.359743 0.933052i \(-0.617136\pi\)
−0.740231 + 0.672353i \(0.765284\pi\)
\(608\) 0 0
\(609\) −301.108 304.850i −0.494431 0.500575i
\(610\) 0 0
\(611\) −194.457 534.266i −0.318260 0.874412i
\(612\) 0 0
\(613\) 782.910 + 284.956i 1.27718 + 0.464855i 0.889498 0.456940i \(-0.151054\pi\)
0.387680 + 0.921794i \(0.373277\pi\)
\(614\) 0 0
\(615\) −575.999 88.0077i −0.936584 0.143102i
\(616\) 0 0
\(617\) −818.763 47.6875i −1.32701 0.0772893i −0.620059 0.784555i \(-0.712891\pi\)
−0.706947 + 0.707266i \(0.749928\pi\)
\(618\) 0 0
\(619\) −692.819 734.346i −1.11926 1.18634i −0.980604 0.196001i \(-0.937205\pi\)
−0.138652 0.990341i \(-0.544277\pi\)
\(620\) 0 0
\(621\) 348.441 424.279i 0.561097 0.683220i
\(622\) 0 0
\(623\) −127.280 38.1053i −0.204303 0.0611642i
\(624\) 0 0
\(625\) 15.9522 + 10.4919i 0.0255234 + 0.0167870i
\(626\) 0 0
\(627\) 256.304 468.399i 0.408778 0.747048i
\(628\) 0 0
\(629\) 534.329 94.2167i 0.849490 0.149788i
\(630\) 0 0
\(631\) −169.114 + 959.095i −0.268010 + 1.51996i 0.492314 + 0.870417i \(0.336151\pi\)
−0.760324 + 0.649543i \(0.774960\pi\)
\(632\) 0 0
\(633\) 317.022 + 458.757i 0.500824 + 0.724735i
\(634\) 0 0
\(635\) −4.34725 + 1.30148i −0.00684607 + 0.00204958i
\(636\) 0 0
\(637\) −201.196 23.5164i −0.315849 0.0369175i
\(638\) 0 0
\(639\) 831.897 + 208.046i 1.30187 + 0.325581i
\(640\) 0 0
\(641\) −89.4910 136.064i −0.139612 0.212269i 0.758913 0.651192i \(-0.225731\pi\)
−0.898525 + 0.438923i \(0.855360\pi\)
\(642\) 0 0
\(643\) 142.884 + 191.926i 0.222214 + 0.298486i 0.899224 0.437488i \(-0.144132\pi\)
−0.677010 + 0.735974i \(0.736725\pi\)
\(644\) 0 0
\(645\) −179.338 + 95.2734i −0.278043 + 0.147711i
\(646\) 0 0
\(647\) 848.415i 1.31131i −0.755062 0.655653i \(-0.772393\pi\)
0.755062 0.655653i \(-0.227607\pi\)
\(648\) 0 0
\(649\) −432.519 −0.666440
\(650\) 0 0
\(651\) −333.444 11.7633i −0.512203 0.0180696i
\(652\) 0 0
\(653\) 627.301 467.008i 0.960645 0.715174i 0.00206526 0.999998i \(-0.499343\pi\)
0.958580 + 0.284824i \(0.0919352\pi\)
\(654\) 0 0
\(655\) 519.293 341.544i 0.792814 0.521442i
\(656\) 0 0
\(657\) 500.939 + 223.461i 0.762464 + 0.340123i
\(658\) 0 0
\(659\) 7.45433 63.7759i 0.0113116 0.0967768i −0.986403 0.164343i \(-0.947449\pi\)
0.997715 + 0.0675667i \(0.0215235\pi\)
\(660\) 0 0
\(661\) 281.575 + 940.527i 0.425984 + 1.42289i 0.854547 + 0.519373i \(0.173835\pi\)
−0.428564 + 0.903512i \(0.640980\pi\)
\(662\) 0 0
\(663\) 291.879 + 138.306i 0.440239 + 0.208606i
\(664\) 0 0
\(665\) −547.374 96.5168i −0.823119 0.145138i
\(666\) 0 0
\(667\) −91.4486 518.631i −0.137104 0.777557i
\(668\) 0 0
\(669\) −200.745 + 122.117i −0.300067 + 0.182536i
\(670\) 0 0
\(671\) 66.9366 101.772i 0.0997565 0.151672i
\(672\) 0 0
\(673\) −329.538 + 1100.73i −0.489655 + 1.63556i 0.254150 + 0.967165i \(0.418204\pi\)
−0.743805 + 0.668396i \(0.766981\pi\)
\(674\) 0 0
\(675\) −157.593 + 376.221i −0.233471 + 0.557364i
\(676\) 0 0
\(677\) −637.451 + 601.404i −0.941582 + 0.888337i −0.993899 0.110293i \(-0.964821\pi\)
0.0523167 + 0.998631i \(0.483339\pi\)
\(678\) 0 0
\(679\) 49.0984 842.987i 0.0723099 1.24151i
\(680\) 0 0
\(681\) 943.875 368.246i 1.38601 0.540743i
\(682\) 0 0
\(683\) 253.615 696.803i 0.371326 1.02021i −0.603524 0.797345i \(-0.706237\pi\)
0.974850 0.222864i \(-0.0715406\pi\)
\(684\) 0 0
\(685\) 247.495 90.0809i 0.361307 0.131505i
\(686\) 0 0
\(687\) 171.208 + 655.112i 0.249211 + 0.953583i
\(688\) 0 0
\(689\) 24.8330 104.779i 0.0360421 0.152074i
\(690\) 0 0
\(691\) 50.9074 + 118.017i 0.0736721 + 0.170791i 0.951073 0.308968i \(-0.0999835\pi\)
−0.877400 + 0.479759i \(0.840724\pi\)
\(692\) 0 0
\(693\) 167.343 219.080i 0.241476 0.316132i
\(694\) 0 0
\(695\) 377.927 22.0117i 0.543779 0.0316715i
\(696\) 0 0
\(697\) −241.620 + 560.137i −0.346656 + 0.803640i
\(698\) 0 0
\(699\) −254.073 782.906i −0.363480 1.12004i
\(700\) 0 0
\(701\) 703.734 + 406.301i 1.00390 + 0.579602i 0.909400 0.415923i \(-0.136541\pi\)
0.0944999 + 0.995525i \(0.469875\pi\)
\(702\) 0 0
\(703\) 879.973 + 1524.16i 1.25174 + 2.16808i
\(704\) 0 0
\(705\) 68.3337 + 487.482i 0.0969272 + 0.691464i
\(706\) 0 0
\(707\) 17.0135 + 145.560i 0.0240643 + 0.205883i
\(708\) 0 0
\(709\) −1156.65 580.892i −1.63138 0.819312i −0.999002 0.0446555i \(-0.985781\pi\)
−0.632382 0.774657i \(-0.717923\pi\)
\(710\) 0 0
\(711\) −60.4587 73.8860i −0.0850333 0.103918i
\(712\) 0 0
\(713\) −328.931 244.880i −0.461334 0.343450i
\(714\) 0 0
\(715\) −130.658 + 138.489i −0.182738 + 0.193691i
\(716\) 0 0
\(717\) −946.736 88.7225i −1.32041 0.123741i
\(718\) 0 0
\(719\) 455.595 542.957i 0.633651 0.755156i −0.349702 0.936861i \(-0.613717\pi\)
0.983353 + 0.181705i \(0.0581615\pi\)
\(720\) 0 0
\(721\) −75.8195 + 63.6201i −0.105159 + 0.0882387i
\(722\) 0 0
\(723\) 300.674 888.960i 0.415869 1.22954i
\(724\) 0 0
\(725\) 175.597 + 349.642i 0.242203 + 0.482265i
\(726\) 0 0
\(727\) −648.169 + 153.619i −0.891567 + 0.211305i −0.650774 0.759271i \(-0.725556\pi\)
−0.240793 + 0.970577i \(0.577407\pi\)
\(728\) 0 0
\(729\) 712.743 + 153.094i 0.977700 + 0.210006i
\(730\) 0 0
\(731\) 49.0298 + 206.873i 0.0670722 + 0.283000i
\(732\) 0 0
\(733\) 1011.41 507.947i 1.37982 0.692970i 0.404657 0.914469i \(-0.367391\pi\)
0.975161 + 0.221498i \(0.0710947\pi\)
\(734\) 0 0
\(735\) 166.134 + 56.1915i 0.226032 + 0.0764511i
\(736\) 0 0
\(737\) 220.319 + 262.565i 0.298940 + 0.356262i
\(738\) 0 0
\(739\) −496.654 416.742i −0.672062 0.563927i 0.241613 0.970373i \(-0.422324\pi\)
−0.913675 + 0.406446i \(0.866768\pi\)
\(740\) 0 0
\(741\) −97.7542 + 1043.11i −0.131922 + 1.40771i
\(742\) 0 0
\(743\) 403.392 + 380.581i 0.542923 + 0.512222i 0.908121 0.418709i \(-0.137517\pi\)
−0.365198 + 0.930930i \(0.618999\pi\)
\(744\) 0 0
\(745\) 8.39446 11.2757i 0.0112677 0.0151352i
\(746\) 0 0
\(747\) −568.356 + 465.069i −0.760851 + 0.622582i
\(748\) 0 0
\(749\) −71.4674 + 142.303i −0.0954172 + 0.189991i
\(750\) 0 0
\(751\) −1354.64 + 158.335i −1.80378 + 0.210832i −0.950523 0.310654i \(-0.899452\pi\)
−0.853260 + 0.521486i \(0.825378\pi\)
\(752\) 0 0
\(753\) −245.083 + 34.3550i −0.325476 + 0.0456242i
\(754\) 0 0
\(755\) −19.3403 + 11.1661i −0.0256163 + 0.0147896i
\(756\) 0 0
\(757\) 428.638 742.423i 0.566233 0.980744i −0.430701 0.902495i \(-0.641734\pi\)
0.996934 0.0782493i \(-0.0249330\pi\)
\(758\) 0 0
\(759\) 322.280 104.588i 0.424611 0.137797i
\(760\) 0 0
\(761\) −380.819 164.269i −0.500419 0.215860i 0.130882 0.991398i \(-0.458219\pi\)
−0.631300 + 0.775538i \(0.717478\pi\)
\(762\) 0 0
\(763\) −42.6925 733.002i −0.0559535 0.960684i
\(764\) 0 0
\(765\) −222.227 169.747i −0.290493 0.221891i
\(766\) 0 0
\(767\) 779.273 336.145i 1.01600 0.438260i
\(768\) 0 0
\(769\) 1238.77 + 293.593i 1.61088 + 0.381786i 0.934837 0.355076i \(-0.115545\pi\)
0.676043 + 0.736862i \(0.263693\pi\)
\(770\) 0 0
\(771\) −59.7092 + 15.6045i −0.0774438 + 0.0202393i
\(772\) 0 0
\(773\) 232.607 + 639.083i 0.300915 + 0.826757i 0.994342 + 0.106230i \(0.0338779\pi\)
−0.693427 + 0.720527i \(0.743900\pi\)
\(774\) 0 0
\(775\) 286.291 + 104.201i 0.369408 + 0.134453i
\(776\) 0 0
\(777\) 330.272 + 846.542i 0.425061 + 1.08950i
\(778\) 0 0
\(779\) −1975.40 115.054i −2.53582 0.147695i
\(780\) 0 0
\(781\) 363.167 + 384.935i 0.465003 + 0.492875i
\(782\) 0 0
\(783\) 556.458 423.478i 0.710675 0.540840i
\(784\) 0 0
\(785\) 240.196 + 71.9099i 0.305982 + 0.0916050i
\(786\) 0 0
\(787\) −165.957 109.152i −0.210873 0.138693i 0.439679 0.898155i \(-0.355092\pi\)
−0.650552 + 0.759462i \(0.725462\pi\)
\(788\) 0 0
\(789\) 421.921 + 693.587i 0.534754 + 0.879071i
\(790\) 0 0
\(791\) −609.098 + 107.400i −0.770036 + 0.135778i
\(792\) 0 0
\(793\) −41.5048 + 235.385i −0.0523389 + 0.296829i
\(794\) 0 0
\(795\)