Properties

Label 324.3.o.a.65.6
Level $324$
Weight $3$
Character 324.65
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 65.6
Character \(\chi\) \(=\) 324.65
Dual form 324.3.o.a.5.6

$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{31}{54}\right)\)

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 0.314561 0.949237i \(-0.398143\pi\)
−0.819142 + 0.573591i \(0.805550\pi\)
\(6\) 0 0
\(7\) −4.60759 3.03046i −0.658227 0.432922i 0.175966 0.984396i \(-0.443695\pi\)
−0.834192 + 0.551474i \(0.814066\pi\)
\(8\) 0 0
\(9\) −3.93956 + 8.09196i −0.437729 + 0.899107i
\(10\) 0 0
\(11\) 0.644815 + 5.51675i 0.0586196 + 0.501523i 0.990372 + 0.138429i \(0.0442053\pi\)
−0.931753 + 0.363093i \(0.881721\pi\)
\(12\) 0 0
\(13\) 3.12574 10.4407i 0.240441 0.803130i −0.749543 0.661955i \(-0.769727\pi\)
0.989985 0.141175i \(-0.0450879\pi\)
\(14\) 0 0
\(15\) −0.764332 + 9.40485i −0.0509554 + 0.626990i
\(16\) 0 0
\(17\) −9.72857 + 1.71541i −0.572269 + 0.100906i −0.452291 0.891870i \(-0.649393\pi\)
−0.119977 + 0.992777i \(0.538282\pi\)
\(18\) 0 0
\(19\) −5.56429 + 31.5567i −0.292857 + 1.66088i 0.382928 + 0.923778i \(0.374916\pi\)
−0.675785 + 0.737098i \(0.736195\pi\)
\(20\) 0 0
\(21\) −0.379070 + 16.5402i −0.0180510 + 0.787628i
\(22\) 0 0
\(23\) 11.1738 + 16.9889i 0.485817 + 0.738648i 0.992334 0.123581i \(-0.0394380\pi\)
−0.506518 + 0.862229i \(0.669068\pi\)
\(24\) 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 0.938823 0.344401i \(-0.111918\pi\)
−0.289230 + 0.957260i \(0.593399\pi\)
\(30\) 0 0
\(31\) 1.17260 + 20.1327i 0.0378258 + 0.649443i 0.962934 + 0.269739i \(0.0869373\pi\)
−0.925108 + 0.379705i \(0.876026\pi\)
\(32\) 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 −0.468242 0.883601i \(-0.655112\pi\)
−0.926661 + 0.375897i \(0.877335\pi\)
\(38\) 0 0
\(39\) −31.5287 + 8.65710i −0.808428 + 0.221977i
\(40\) 0 0
\(41\) 14.2410 + 60.0876i 0.347342 + 1.46555i 0.813872 + 0.581045i \(0.197356\pi\)
−0.466530 + 0.884506i \(0.654496\pi\)
\(42\) 0 0
\(43\) −8.52424 + 19.7614i −0.198238 + 0.459568i −0.988119 0.153693i \(-0.950883\pi\)
0.789880 + 0.613261i \(0.210143\pi\)
\(44\) 0 0
\(45\) 25.1377 13.0158i 0.558616 0.289241i
\(46\) 0 0
\(47\) −52.0796 3.03329i −1.10808 0.0645381i −0.505669 0.862727i \(-0.668754\pi\)
−0.602407 + 0.798189i \(0.705791\pi\)
\(48\) 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 −0.578546 0.815650i \(-0.696380\pi\)
0.417100 + 0.908860i \(0.363046\pi\)
\(54\) 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 0.669639 + 0.742686i \(0.266449\pi\)
−0.822865 + 0.568238i \(0.807625\pi\)
\(60\) 0 0
\(61\) 19.5983 9.84264i 0.321284 0.161355i −0.280846 0.959753i \(-0.590615\pi\)
0.602130 + 0.798398i \(0.294319\pi\)
\(62\) 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 0.329624 0.944112i \(-0.393078\pi\)
−0.961681 + 0.274171i \(0.911597\pi\)
\(68\) 0 0
\(69\) 25.4388 55.4450i 0.368679 0.803551i
\(70\) 0 0
\(71\) −61.2446 72.9885i −0.862600 1.02801i −0.999301 0.0373940i \(-0.988094\pi\)
0.136701 0.990612i \(-0.456350\pi\)
\(72\) 0 0
\(73\) −46.6879 39.1758i −0.639560 0.536655i 0.264323 0.964434i \(-0.414852\pi\)
−0.903883 + 0.427779i \(0.859296\pi\)
\(74\) 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 0.295423 0.955366i \(-0.404539\pi\)
−0.164768 + 0.986332i \(0.552688\pi\)
\(80\) 0 0
\(81\) −49.9597 63.7576i −0.616786 0.787131i
\(82\) 0 0
\(83\) −18.8178 + 79.3985i −0.226720 + 0.956609i 0.734013 + 0.679136i \(0.237645\pi\)
−0.960733 + 0.277473i \(0.910503\pi\)
\(84\) 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 −0.671996 0.740554i \(-0.734563\pi\)
0.845995 + 0.533191i \(0.179007\pi\)
\(90\) 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 −0.963863 0.266397i \(-0.914167\pi\)
0.0212336 0.999775i \(-0.493241\pi\)
\(98\) 0 0
\(99\) −47.1816 16.5158i −0.476582 0.166826i
\(100\) 0 0
\(101\) 11.9263 + 23.7472i 0.118082 + 0.235121i 0.944907 0.327338i \(-0.106152\pi\)
−0.826825 + 0.562459i \(0.809855\pi\)
\(102\) 0 0
\(103\) 17.8257 + 2.08353i 0.173065 + 0.0202284i 0.202184 0.979348i \(-0.435196\pi\)
−0.0291189 + 0.999576i \(0.509270\pi\)
\(104\) 0 0
\(105\) 32.0227 41.0174i 0.304978 0.390641i
\(106\) 0 0
\(107\) 25.0065 + 14.4375i 0.233706 + 0.134930i 0.612281 0.790641i \(-0.290252\pi\)
−0.378575 + 0.925571i \(0.623586\pi\)
\(108\) 0 0
\(109\) −66.5698 115.302i −0.610732 1.05782i −0.991117 0.132991i \(-0.957542\pi\)
0.380385 0.924828i \(-0.375792\pi\)
\(110\) 0 0
\(111\) 34.3154 + 161.158i 0.309147 + 1.45188i
\(112\) 0 0
\(113\) 102.979 44.4207i 0.911316 0.393104i 0.111788 0.993732i \(-0.464342\pi\)
0.799528 + 0.600629i \(0.205083\pi\)
\(114\) 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 −0.336677 0.941620i \(-0.609303\pi\)
0.347352 + 0.937735i \(0.387081\pi\)
\(128\) 0 0
\(129\) 63.8239 9.75174i 0.494759 0.0755949i
\(130\) 0 0
\(131\) −197.277 + 11.4901i −1.50593 + 0.0877106i −0.791144 0.611630i \(-0.790514\pi\)
−0.714789 + 0.699340i \(0.753477\pi\)
\(132\) 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 −0.565855 0.824505i \(-0.691454\pi\)
−0.0196916 + 0.999806i \(0.506268\pi\)
\(138\) 0 0
\(139\) −100.560 + 66.1390i −0.723450 + 0.475820i −0.857062 0.515213i \(-0.827713\pi\)
0.133612 + 0.991034i \(0.457342\pi\)
\(140\) 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 0.272403 0.962183i \(-0.412182\pi\)
−0.301139 + 0.953580i \(0.597367\pi\)
\(150\) 0 0
\(151\) 7.05223 0.824288i 0.0467035 0.00545886i −0.0927091 0.995693i \(-0.529553\pi\)
0.139413 + 0.990234i \(0.455479\pi\)
\(152\) 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 −0.927446 0.373958i \(-0.878001\pi\)
0.624242 + 0.781231i \(0.285408\pi\)
\(158\) 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 0.987819 + 0.155608i \(0.0497337\pi\)
0.432381 + 0.901691i \(0.357674\pi\)
\(168\) 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 0.767800 + 0.640689i \(0.221351\pi\)
−0.599351 + 0.800486i \(0.704575\pi\)
\(174\) 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 −0.160140 0.987094i \(-0.551194\pi\)
0.187124 + 0.982336i \(0.440083\pi\)
\(180\) 0 0
\(181\) −30.3013 + 171.847i −0.167411 + 0.949434i 0.779133 + 0.626859i \(0.215660\pi\)
−0.946544 + 0.322575i \(0.895452\pi\)
\(182\) 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 0.308218 0.951316i \(-0.400267\pi\)
−0.931785 + 0.363011i \(0.881749\pi\)
\(192\) 0 0
\(193\) 11.8548 + 203.540i 0.0614241 + 1.05461i 0.878396 + 0.477933i \(0.158614\pi\)
−0.816972 + 0.576677i \(0.804349\pi\)
\(194\) 0 0
\(195\) 95.8040 + 37.3772i 0.491302 + 0.191678i
\(196\) 0 0
\(197\) −74.6460 205.088i −0.378914 1.04106i −0.971807 0.235776i \(-0.924237\pi\)
0.592894 0.805281i \(-0.297985\pi\)
\(198\) 0 0
\(199\) −23.0111 8.37537i −0.115634 0.0420873i 0.283555 0.958956i \(-0.408486\pi\)
−0.399189 + 0.916869i \(0.630708\pi\)
\(200\) 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 0.998806 + 0.0488624i \(0.0155596\pi\)
−0.649881 + 0.760036i \(0.725181\pi\)
\(212\) 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 −0.284891 0.958560i \(-0.591957\pi\)
0.598758 + 0.800930i \(0.295661\pi\)
\(224\) 0 0
\(225\) 134.180 + 21.9547i 0.596357 + 0.0975764i
\(226\) 0 0
\(227\) −270.895 + 201.674i −1.19337 + 0.888430i −0.995772 0.0918540i \(-0.970721\pi\)
−0.197596 + 0.980284i \(0.563313\pi\)
\(228\) 0 0
\(229\) 154.888 + 164.172i 0.676367 + 0.716907i 0.971100 0.238673i \(-0.0767123\pi\)
−0.294733 + 0.955579i \(0.595231\pi\)
\(230\) 0 0
\(231\) −91.4925 + 8.57413i −0.396071 + 0.0371175i
\(232\) 0 0
\(233\) −176.360 210.177i −0.756909 0.902049i 0.240740 0.970590i \(-0.422610\pi\)
−0.997648 + 0.0685410i \(0.978166\pi\)
\(234\) 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 −0.371314 0.928508i \(-0.621093\pi\)
0.966511 0.256627i \(-0.0826112\pi\)
\(240\) 0 0
\(241\) −304.379 72.1391i −1.26298 0.299332i −0.456038 0.889960i \(-0.650732\pi\)
−0.806944 + 0.590628i \(0.798880\pi\)
\(242\) 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 −0.650002 0.759933i \(-0.725232\pi\)
0.861259 + 0.508166i \(0.169676\pi\)
\(252\) 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 −0.656581 0.754256i \(-0.727998\pi\)
0.714803 + 0.699326i \(0.246516\pi\)
\(258\) 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 0.997191 + 0.0749012i \(0.0238641\pi\)
−0.535401 + 0.844598i \(0.679840\pi\)
\(264\) 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 0.565858 0.824502i \(-0.308545\pi\)
−0.431111 + 0.902299i \(0.641878\pi\)
\(270\) 0 0
\(271\) 159.519 + 276.295i 0.588631 + 1.01954i 0.994412 + 0.105569i \(0.0336664\pi\)
−0.405781 + 0.913971i \(0.633000\pi\)
\(272\) 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 0.894095 + 0.447877i \(0.147820\pi\)
−0.940045 + 0.341051i \(0.889217\pi\)
\(278\) 0 0
\(279\) −167.533 69.8256i −0.600476 0.250271i
\(280\) 0 0
\(281\) −380.850 164.283i −1.35534 0.584636i −0.410407 0.911902i \(-0.634613\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(282\) 0 0
\(283\) 174.395 41.3323i 0.616236 0.146051i 0.0893695 0.995999i \(-0.471515\pi\)
0.526867 + 0.849948i \(0.323367\pi\)
\(284\) 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 0.397942 0.917411i \(-0.369725\pi\)
0.501756 + 0.865009i \(0.332688\pi\)
\(294\) 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 0.991676 0.128755i \(-0.0410980\pi\)
−0.975908 + 0.218183i \(0.929987\pi\)
\(308\) 0 0
\(309\) −23.0552 48.6553i −0.0746121 0.157460i
\(310\) 0 0
\(311\) 363.335 + 108.775i 1.16828 + 0.349760i 0.811458 0.584411i \(-0.198675\pi\)
0.356824 + 0.934172i \(0.383860\pi\)
\(312\) 0 0
\(313\) 518.083 60.5552i 1.65522 0.193467i 0.763419 0.645903i \(-0.223519\pi\)
0.891797 + 0.452436i \(0.149445\pi\)
\(314\) 0 0
\(315\) −155.268 16.2073i −0.492915 0.0514517i
\(316\) 0 0
\(317\) 20.6710 31.4288i 0.0652083 0.0991444i −0.801412 0.598113i \(-0.795917\pi\)
0.866620 + 0.498969i \(0.166288\pi\)
\(318\) 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 0.462013 0.886873i \(-0.347127\pi\)
−0.631347 + 0.775500i \(0.717498\pi\)
\(332\) 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 −0.522924 0.852379i \(-0.675159\pi\)
0.905287 0.424801i \(-0.139656\pi\)
\(338\) 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 −0.999828 0.0185713i \(-0.994088\pi\)
0.378959 0.925413i \(-0.376282\pi\)
\(348\) 0 0
\(349\) −154.625 516.485i −0.443053 1.47990i −0.829982 0.557790i \(-0.811649\pi\)
0.386929 0.922110i \(-0.373536\pi\)
\(350\) 0 0
\(351\) 54.1565 289.234i 0.154292 0.824029i
\(352\) 0 0
\(353\) −409.040 385.909i −1.15875 1.09323i −0.994276 0.106847i \(-0.965925\pi\)
−0.164478 0.986381i \(-0.552594\pi\)
\(354\) 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 −0.827639 0.561260i \(-0.810317\pi\)
0.273238 0.961947i \(-0.411905\pi\)
\(360\) 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 −0.794276 0.607558i \(-0.792149\pi\)
0.986986 + 0.160804i \(0.0514087\pi\)
\(368\) 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 0.997959 0.0638573i \(-0.0203403\pi\)
−0.731289 + 0.682068i \(0.761081\pi\)
\(374\) 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 −0.249918 0.968267i \(-0.580404\pi\)
0.963503 0.267698i \(-0.0862631\pi\)
\(380\) 0 0
\(381\) −3.41168 2.66354i −0.00895455 0.00699092i
\(382\) 0 0
\(383\) 58.5939 501.303i 0.152987 1.30888i −0.670653 0.741771i \(-0.733986\pi\)
0.823640 0.567113i \(-0.191940\pi\)
\(384\) 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 −0.168619 0.985681i \(-0.553931\pi\)
0.895912 + 0.444232i \(0.146523\pi\)
\(390\) 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 0.374109 0.927385i \(-0.377949\pi\)
−0.848333 + 0.529464i \(0.822393\pi\)
\(398\) 0 0
\(399\) −519.844 103.997i −1.30287 0.260643i
\(400\) 0 0
\(401\) −288.518 + 574.486i −0.719495 + 1.43263i 0.174546 + 0.984649i \(0.444154\pi\)
−0.894042 + 0.447984i \(0.852142\pi\)
\(402\) 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 0.878439 0.477854i \(-0.158585\pi\)
0.141270 + 0.989971i \(0.454881\pi\)
\(410\) 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 0.199559 0.979886i \(-0.436049\pi\)
0.989831 0.142247i \(-0.0454326\pi\)
\(420\) 0 0
\(421\) 108.550 + 145.807i 0.257838 + 0.346336i 0.912127 0.409909i \(-0.134439\pi\)
−0.654289 + 0.756245i \(0.727032\pi\)
\(422\) 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 0.733008 0.680220i \(-0.238116\pi\)
−0.222583 + 0.974914i \(0.571449\pi\)
\(432\) 0 0
\(433\) 115.287 + 199.683i 0.266252 + 0.461161i 0.967891 0.251371i \(-0.0808814\pi\)
−0.701639 + 0.712532i \(0.747548\pi\)
\(434\) 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 0.910156 + 0.414267i \(0.135962\pi\)
−0.952095 + 0.305803i \(0.901075\pi\)
\(440\) 0 0
\(441\) 167.103 + 7.66339i 0.378918 + 0.0173773i
\(442\) 0 0
\(443\) 224.222 + 96.7200i 0.506145 + 0.218330i 0.633812 0.773487i \(-0.281489\pi\)
−0.127667 + 0.991817i \(0.540749\pi\)
\(444\) 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 0.416237 + 0.909256i \(0.363349\pi\)
−0.903315 + 0.428979i \(0.858873\pi\)
\(450\) 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 −0.485379 0.874304i \(-0.661318\pi\)
0.901047 + 0.433722i \(0.142800\pi\)
\(458\) 0 0
\(459\) −256.312 + 73.7935i −0.558415 + 0.160770i
\(460\) 0 0
\(461\) −571.275 + 171.028i −1.23921 + 0.370994i −0.838343 0.545143i \(-0.816475\pi\)
−0.400865 + 0.916137i \(0.631290\pi\)
\(462\) 0 0
\(463\) 491.968 323.572i 1.06257 0.698860i 0.107185 0.994239i \(-0.465816\pi\)
0.955380 + 0.295379i \(0.0954458\pi\)
\(464\) 0 0
\(465\) −190.242 4.35998i −0.409122 0.00937631i
\(466\) 0 0
\(467\) −701.939 123.771i −1.50308 0.265034i −0.639323 0.768939i \(-0.720785\pi\)
−0.863759 + 0.503905i \(0.831896\pi\)
\(468\) 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 0.120149 0.992756i \(-0.461663\pi\)
0.863976 0.503533i \(-0.167967\pi\)
\(480\) 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 0.886940 0.461885i \(-0.152827\pi\)
−0.188104 + 0.982149i \(0.560234\pi\)
\(492\) 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 0.802803 + 0.596245i \(0.203341\pi\)
−0.998374 + 0.0570082i \(0.981844\pi\)
\(500\) 0 0
\(501\) 71.8533 884.131i 0.143420 1.76473i
\(502\) 0 0
\(503\) −599.268 + 105.667i −1.19139 + 0.210074i −0.733972 0.679180i \(-0.762336\pi\)
−0.457415 + 0.889253i \(0.651225\pi\)
\(504\) 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 0.661245 0.750170i \(-0.270028\pi\)
−0.950724 + 0.310039i \(0.899658\pi\)
\(510\) 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 −0.996967 0.0778211i \(-0.975204\pi\)
0.713699 0.700453i \(-0.247019\pi\)
\(522\) 0 0
\(523\) −619.082 225.327i −1.18371 0.430836i −0.326201 0.945300i \(-0.605769\pi\)
−0.857512 + 0.514464i \(0.827991\pi\)
\(524\) 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 −0.950952 0.309338i \(-0.899892\pi\)
0.743371 + 0.668880i \(0.233226\pi\)
\(542\) 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 −0.793160 0.609013i \(-0.791566\pi\)
0.0148606 + 0.999890i \(0.495270\pi\)
\(548\) 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 0.989566 0.144083i \(-0.0460233\pi\)
−0.313730 + 0.949512i \(0.601579\pi\)
\(558\) 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 −0.999992 0.00400743i \(-0.998724\pi\)
0.600368 + 0.799724i \(0.295021\pi\)
\(564\) 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 0.817712 + 0.575627i \(0.195242\pi\)
−0.989075 + 0.147411i \(0.952906\pi\)
\(570\) 0 0
\(571\) −529.303 265.826i −0.926976 0.465545i −0.0797722 0.996813i \(-0.525419\pi\)
−0.847204 + 0.531268i \(0.821716\pi\)
\(572\) 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 −0.897512 0.440990i \(-0.854627\pi\)
0.278439 + 0.960454i \(0.410183\pi\)
\(578\) 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 0.989170 + 0.146771i \(0.0468881\pi\)
−0.472963 + 0.881082i \(0.656816\pi\)
\(588\) 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 0.818840 0.574022i \(-0.194617\pi\)
−0.0876972 + 0.996147i \(0.527951\pi\)
\(594\) 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 −0.719115 0.694892i \(-0.755452\pi\)
0.0119594 + 0.999928i \(0.496193\pi\)
\(600\) 0 0
\(601\) 18.6918 320.925i 0.0311011 0.533986i −0.946392 0.323020i \(-0.895302\pi\)
0.977493 0.210966i \(-0.0676610\pi\)
\(602\) 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 −0.740231 0.672353i \(-0.765284\pi\)
−0.359743 + 0.933052i \(0.617136\pi\)
\(608\) 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 0.387680 0.921794i \(-0.373277\pi\)
0.889498 + 0.456940i \(0.151054\pi\)
\(614\) 0 0
\(615\) −575.999 + 88.0077i −0.936584 + 0.143102i
\(616\) 0 0
\(617\) −818.763 + 47.6875i −1.32701 + 0.0772893i −0.706947 0.707266i \(-0.749928\pi\)
−0.620059 + 0.784555i \(0.712891\pi\)
\(618\) 0 0
\(619\) −692.819 + 734.346i −1.11926 + 1.18634i −0.138652 + 0.990341i \(0.544277\pi\)
−0.980604 + 0.196001i \(0.937205\pi\)
\(620\) 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 −0.760324 0.649543i \(-0.774960\pi\)
0.492314 0.870417i \(-0.336151\pi\)
\(632\) 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 −0.898525 0.438923i \(-0.855360\pi\)
0.758913 + 0.651192i \(0.225731\pi\)
\(642\) 0 0
\(643\) 142.884 191.926i 0.222214 0.298486i −0.677010 0.735974i \(-0.736725\pi\)
0.899224 + 0.437488i \(0.144132\pi\)
\(644\) 0 0
\(645\) −179.338 95.2734i −0.278043 0.147711i
\(646\) 0 0
\(647\) 848.415i 1.31131i 0.755062 + 0.655653i \(0.227607\pi\)
−0.755062 + 0.655653i \(0.772393\pi\)
\(648\) 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 0.958580 0.284824i \(-0.0919352\pi\)
0.00206526 + 0.999998i \(0.499343\pi\)
\(654\) 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 0.997715 0.0675667i \(-0.0215235\pi\)
−0.986403 + 0.164343i \(0.947449\pi\)
\(660\) 0 0
\(661\) 281.575 940.527i 0.425984 1.42289i −0.428564 0.903512i \(-0.640980\pi\)
0.854547 0.519373i \(-0.173835\pi\)
\(662\) 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 −0.743805 0.668396i \(-0.766981\pi\)
0.254150 0.967165i \(-0.418204\pi\)
\(674\) 0 0
\(675\) −157.593 376.221i −0.233471 0.557364i
\(676\) 0 0
\(677\) −637.451 601.404i −0.941582 0.888337i 0.0523167 0.998631i \(-0.483339\pi\)
−0.993899 + 0.110293i \(0.964821\pi\)
\(678\) 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 0.974850 + 0.222864i \(0.0715406\pi\)
−0.603524 + 0.797345i \(0.706237\pi\)
\(684\) 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 −0.877400 0.479759i \(-0.840724\pi\)
0.951073 + 0.308968i \(0.0999835\pi\)
\(692\) 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 0.0944999 0.995525i \(-0.469875\pi\)
0.909400 + 0.415923i \(0.136541\pi\)
\(702\) 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 −0.632382 + 0.774657i \(0.717923\pi\)
−0.999002 + 0.0446555i \(0.985781\pi\)
\(710\) 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 0.983353 0.181705i \(-0.0581615\pi\)
−0.349702 + 0.936861i \(0.613717\pi\)
\(720\) 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 −0.240793 0.970577i \(-0.577407\pi\)
−0.650774 + 0.759271i \(0.725556\pi\)
\(728\) 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 0.975161 0.221498i \(-0.0710947\pi\)
0.404657 + 0.914469i \(0.367391\pi\)
\(734\) 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 −0.913675 0.406446i \(-0.866768\pi\)
0.241613 + 0.970373i \(0.422324\pi\)
\(740\) 0 0
\(741\) −97.7542 1043.11i −0.131922 1.40771i
\(742\) 0 0
\(743\) 403.392 380.581i 0.542923 0.512222i −0.365198 0.930930i \(-0.618999\pi\)
0.908121 + 0.418709i \(0.137517\pi\)
\(744\) 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 −0.853260 0.521486i \(-0.825378\pi\)
−0.950523 + 0.310654i \(0.899452\pi\)
\(752\) 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 0.996934 + 0.0782493i \(0.0249330\pi\)
−0.430701 + 0.902495i \(0.641734\pi\)
\(758\) 0 0
\(759\) 322.280 + 104.588i 0.424611 + 0.137797i
\(760\) 0 0
\(761\) −380.819 + 164.269i −0.500419 + 0.215860i −0.631300 0.775538i \(-0.717478\pi\)
0.130882 + 0.991398i \(0.458219\pi\)
\(762\) 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 0.676043 0.736862i \(-0.263693\pi\)
0.934837 + 0.355076i \(0.115545\pi\)
\(770\) 0 0
\(771\) −59.7092 15.6045i −0.0774438 0.0202393i
\(772\) 0 0
\(773\) 232.607 639.083i 0.300915 0.826757i −0.693427 0.720527i \(-0.743900\pi\)
0.994342 0.106230i \(-0.0338779\pi\)
\(774\) 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 −0.650552 0.759462i \(-0.725462\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(788\) 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