Properties

Label 108.5.k.a.29.1
Level 108
Weight 5
Character 108.29
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.1
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.99629 - 0.258464i) q^{3} +(-25.3131 - 30.1670i) q^{5} +(-27.6070 + 10.0481i) q^{7} +(80.8664 + 4.65043i) q^{9} +O(q^{10})\) \(q+(-8.99629 - 0.258464i) q^{3} +(-25.3131 - 30.1670i) q^{5} +(-27.6070 + 10.0481i) q^{7} +(80.8664 + 4.65043i) q^{9} +(15.7890 - 18.8166i) q^{11} +(25.9745 + 147.308i) q^{13} +(219.927 + 277.934i) q^{15} +(172.593 - 99.6466i) q^{17} +(-129.877 + 224.954i) q^{19} +(250.958 - 83.2604i) q^{21} +(-211.930 + 582.273i) q^{23} +(-160.764 + 911.738i) q^{25} +(-726.295 - 62.7377i) q^{27} +(1271.79 + 224.250i) q^{29} +(992.428 + 361.214i) q^{31} +(-146.906 + 165.199i) q^{33} +(1001.94 + 578.471i) q^{35} +(-1125.43 - 1949.31i) q^{37} +(-195.600 - 1331.94i) q^{39} +(-461.110 + 81.3061i) q^{41} +(1135.15 + 952.502i) q^{43} +(-1906.69 - 2557.21i) q^{45} +(829.841 + 2279.97i) q^{47} +(-1178.09 + 988.536i) q^{49} +(-1578.45 + 851.841i) q^{51} -4450.35i q^{53} -967.312 q^{55} +(1226.56 - 1990.19i) q^{57} +(793.356 + 945.485i) q^{59} +(-4790.10 + 1743.45i) q^{61} +(-2279.21 + 684.171i) q^{63} +(3786.36 - 4512.41i) q^{65} +(379.378 + 2151.56i) q^{67} +(2057.08 - 5183.52i) q^{69} +(4243.91 - 2450.22i) q^{71} +(-3145.50 + 5448.16i) q^{73} +(1681.93 - 8160.70i) q^{75} +(-246.816 + 678.121i) q^{77} +(-732.250 + 4152.80i) q^{79} +(6517.75 + 752.128i) q^{81} +(-6036.15 - 1064.34i) q^{83} +(-7374.91 - 2684.25i) q^{85} +(-11383.4 - 2346.13i) q^{87} +(7061.95 + 4077.22i) q^{89} +(-2197.25 - 3805.75i) q^{91} +(-8834.81 - 3506.10i) q^{93} +(10073.8 - 1776.28i) q^{95} +(1708.86 + 1433.90i) q^{97} +(1364.31 - 1448.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −8.99629 0.258464i −0.999588 0.0287182i
\(4\) 0 0
\(5\) −25.3131 30.1670i −1.01253 1.20668i −0.978284 0.207267i \(-0.933543\pi\)
−0.0342406 0.999414i \(-0.510901\pi\)
\(6\) 0 0
\(7\) −27.6070 + 10.0481i −0.563408 + 0.205064i −0.607994 0.793942i \(-0.708025\pi\)
0.0445856 + 0.999006i \(0.485803\pi\)
\(8\) 0 0
\(9\) 80.8664 + 4.65043i 0.998351 + 0.0574128i
\(10\) 0 0
\(11\) 15.7890 18.8166i 0.130488 0.155509i −0.696844 0.717223i \(-0.745413\pi\)
0.827332 + 0.561713i \(0.189858\pi\)
\(12\) 0 0
\(13\) 25.9745 + 147.308i 0.153695 + 0.871648i 0.959969 + 0.280106i \(0.0903695\pi\)
−0.806274 + 0.591542i \(0.798519\pi\)
\(14\) 0 0
\(15\) 219.927 + 277.934i 0.977454 + 1.23526i
\(16\) 0 0
\(17\) 172.593 99.6466i 0.597208 0.344798i −0.170735 0.985317i \(-0.554614\pi\)
0.767942 + 0.640519i \(0.221281\pi\)
\(18\) 0 0
\(19\) −129.877 + 224.954i −0.359771 + 0.623142i −0.987922 0.154949i \(-0.950479\pi\)
0.628151 + 0.778091i \(0.283812\pi\)
\(20\) 0 0
\(21\) 250.958 83.2604i 0.569065 0.188799i
\(22\) 0 0
\(23\) −211.930 + 582.273i −0.400624 + 1.10071i 0.561353 + 0.827576i \(0.310281\pi\)
−0.961977 + 0.273129i \(0.911941\pi\)
\(24\) 0 0
\(25\) −160.764 + 911.738i −0.257222 + 1.45878i
\(26\) 0 0
\(27\) −726.295 62.7377i −0.996290 0.0860599i
\(28\) 0 0
\(29\) 1271.79 + 224.250i 1.51223 + 0.266647i 0.867375 0.497656i \(-0.165806\pi\)
0.644857 + 0.764303i \(0.276917\pi\)
\(30\) 0 0
\(31\) 992.428 + 361.214i 1.03270 + 0.375873i 0.802110 0.597177i \(-0.203711\pi\)
0.230594 + 0.973050i \(0.425933\pi\)
\(32\) 0 0
\(33\) −146.906 + 165.199i −0.134900 + 0.151698i
\(34\) 0 0
\(35\) 1001.94 + 578.471i 0.817911 + 0.472221i
\(36\) 0 0
\(37\) −1125.43 1949.31i −0.822084 1.42389i −0.904128 0.427262i \(-0.859478\pi\)
0.0820437 0.996629i \(-0.473855\pi\)
\(38\) 0 0
\(39\) −195.600 1331.94i −0.128599 0.875702i
\(40\) 0 0
\(41\) −461.110 + 81.3061i −0.274307 + 0.0483677i −0.309109 0.951027i \(-0.600031\pi\)
0.0348026 + 0.999394i \(0.488920\pi\)
\(42\) 0 0
\(43\) 1135.15 + 952.502i 0.613925 + 0.515144i 0.895887 0.444281i \(-0.146541\pi\)
−0.281962 + 0.959425i \(0.590985\pi\)
\(44\) 0 0
\(45\) −1906.69 2557.21i −0.941576 1.26282i
\(46\) 0 0
\(47\) 829.841 + 2279.97i 0.375664 + 1.03213i 0.973135 + 0.230237i \(0.0739502\pi\)
−0.597471 + 0.801891i \(0.703828\pi\)
\(48\) 0 0
\(49\) −1178.09 + 988.536i −0.490667 + 0.411718i
\(50\) 0 0
\(51\) −1578.45 + 851.841i −0.606863 + 0.327505i
\(52\) 0 0
\(53\) 4450.35i 1.58432i −0.610314 0.792160i \(-0.708957\pi\)
0.610314 0.792160i \(-0.291043\pi\)
\(54\) 0 0
\(55\) −967.312 −0.319773
\(56\) 0 0
\(57\) 1226.56 1990.19i 0.377519 0.612553i
\(58\) 0 0
\(59\) 793.356 + 945.485i 0.227910 + 0.271613i 0.867865 0.496799i \(-0.165491\pi\)
−0.639955 + 0.768412i \(0.721047\pi\)
\(60\) 0 0
\(61\) −4790.10 + 1743.45i −1.28732 + 0.468544i −0.892845 0.450364i \(-0.851294\pi\)
−0.394470 + 0.918909i \(0.629072\pi\)
\(62\) 0 0
\(63\) −2279.21 + 684.171i −0.574252 + 0.172379i
\(64\) 0 0
\(65\) 3786.36 4512.41i 0.896180 1.06803i
\(66\) 0 0
\(67\) 379.378 + 2151.56i 0.0845127 + 0.479296i 0.997461 + 0.0712195i \(0.0226891\pi\)
−0.912948 + 0.408076i \(0.866200\pi\)
\(68\) 0 0
\(69\) 2057.08 5183.52i 0.432069 1.08875i
\(70\) 0 0
\(71\) 4243.91 2450.22i 0.841879 0.486059i −0.0160233 0.999872i \(-0.505101\pi\)
0.857903 + 0.513812i \(0.171767\pi\)
\(72\) 0 0
\(73\) −3145.50 + 5448.16i −0.590261 + 1.02236i 0.403936 + 0.914787i \(0.367642\pi\)
−0.994197 + 0.107574i \(0.965692\pi\)
\(74\) 0 0
\(75\) 1681.93 8160.70i 0.299010 1.45079i
\(76\) 0 0
\(77\) −246.816 + 678.121i −0.0416286 + 0.114374i
\(78\) 0 0
\(79\) −732.250 + 4152.80i −0.117329 + 0.665406i 0.868242 + 0.496142i \(0.165250\pi\)
−0.985571 + 0.169264i \(0.945861\pi\)
\(80\) 0 0
\(81\) 6517.75 + 752.128i 0.993408 + 0.114636i
\(82\) 0 0
\(83\) −6036.15 1064.34i −0.876202 0.154498i −0.282581 0.959243i \(-0.591191\pi\)
−0.593620 + 0.804745i \(0.702302\pi\)
\(84\) 0 0
\(85\) −7374.91 2684.25i −1.02075 0.371522i
\(86\) 0 0
\(87\) −11383.4 2346.13i −1.50395 0.309966i
\(88\) 0 0
\(89\) 7061.95 + 4077.22i 0.891548 + 0.514736i 0.874449 0.485118i \(-0.161223\pi\)
0.0170997 + 0.999854i \(0.494557\pi\)
\(90\) 0 0
\(91\) −2197.25 3805.75i −0.265336 0.459576i
\(92\) 0 0
\(93\) −8834.81 3506.10i −1.02148 0.405376i
\(94\) 0 0
\(95\) 10073.8 1776.28i 1.11621 0.196818i
\(96\) 0 0
\(97\) 1708.86 + 1433.90i 0.181619 + 0.152397i 0.729065 0.684445i \(-0.239955\pi\)
−0.547445 + 0.836841i \(0.684400\pi\)
\(98\) 0 0
\(99\) 1364.31 1448.21i 0.139201 0.147761i
\(100\) 0 0
\(101\) −1570.11 4313.84i −0.153917 0.422884i 0.838637 0.544691i \(-0.183353\pi\)
−0.992554 + 0.121807i \(0.961131\pi\)
\(102\) 0 0
\(103\) −9520.09 + 7988.31i −0.897360 + 0.752975i −0.969673 0.244407i \(-0.921407\pi\)
0.0723124 + 0.997382i \(0.476962\pi\)
\(104\) 0 0
\(105\) −8864.24 5463.06i −0.804013 0.495516i
\(106\) 0 0
\(107\) 17618.5i 1.53887i 0.638724 + 0.769436i \(0.279462\pi\)
−0.638724 + 0.769436i \(0.720538\pi\)
\(108\) 0 0
\(109\) 23518.9 1.97953 0.989767 0.142691i \(-0.0455754\pi\)
0.989767 + 0.142691i \(0.0455754\pi\)
\(110\) 0 0
\(111\) 9620.89 + 17827.4i 0.780853 + 1.44691i
\(112\) 0 0
\(113\) 11590.6 + 13813.2i 0.907717 + 1.08177i 0.996320 + 0.0857079i \(0.0273152\pi\)
−0.0886034 + 0.996067i \(0.528240\pi\)
\(114\) 0 0
\(115\) 22930.1 8345.86i 1.73384 0.631067i
\(116\) 0 0
\(117\) 1415.41 + 12033.1i 0.103398 + 0.879034i
\(118\) 0 0
\(119\) −3763.51 + 4485.18i −0.265766 + 0.316728i
\(120\) 0 0
\(121\) 2437.61 + 13824.4i 0.166492 + 0.944224i
\(122\) 0 0
\(123\) 4169.29 612.272i 0.275583 0.0404701i
\(124\) 0 0
\(125\) 10258.7 5922.84i 0.656555 0.379062i
\(126\) 0 0
\(127\) −9957.61 + 17247.1i −0.617373 + 1.06932i 0.372590 + 0.927996i \(0.378470\pi\)
−0.989963 + 0.141325i \(0.954864\pi\)
\(128\) 0 0
\(129\) −9965.93 8862.38i −0.598878 0.532563i
\(130\) 0 0
\(131\) −3024.44 + 8309.58i −0.176239 + 0.484213i −0.996088 0.0883670i \(-0.971835\pi\)
0.819849 + 0.572580i \(0.194057\pi\)
\(132\) 0 0
\(133\) 1325.16 7515.34i 0.0749142 0.424860i
\(134\) 0 0
\(135\) 16492.2 + 23498.2i 0.904922 + 1.28934i
\(136\) 0 0
\(137\) −16794.2 2961.27i −0.894785 0.157775i −0.292698 0.956205i \(-0.594553\pi\)
−0.602087 + 0.798430i \(0.705664\pi\)
\(138\) 0 0
\(139\) −15479.4 5634.06i −0.801172 0.291603i −0.0912000 0.995833i \(-0.529070\pi\)
−0.709972 + 0.704230i \(0.751292\pi\)
\(140\) 0 0
\(141\) −6876.20 20725.8i −0.345868 1.04249i
\(142\) 0 0
\(143\) 3181.96 + 1837.11i 0.155605 + 0.0898385i
\(144\) 0 0
\(145\) −25427.9 44042.5i −1.20941 2.09477i
\(146\) 0 0
\(147\) 10853.9 8588.66i 0.502288 0.397457i
\(148\) 0 0
\(149\) −16943.7 + 2987.63i −0.763194 + 0.134572i −0.541679 0.840585i \(-0.682211\pi\)
−0.221515 + 0.975157i \(0.571100\pi\)
\(150\) 0 0
\(151\) 21558.4 + 18089.6i 0.945502 + 0.793370i 0.978534 0.206084i \(-0.0660721\pi\)
−0.0330327 + 0.999454i \(0.510517\pi\)
\(152\) 0 0
\(153\) 14420.4 7255.43i 0.616019 0.309942i
\(154\) 0 0
\(155\) −14224.7 39082.1i −0.592079 1.62672i
\(156\) 0 0
\(157\) −25228.4 + 21169.1i −1.02350 + 0.858823i −0.990064 0.140618i \(-0.955091\pi\)
−0.0334410 + 0.999441i \(0.510647\pi\)
\(158\) 0 0
\(159\) −1150.26 + 40036.7i −0.0454988 + 1.58367i
\(160\) 0 0
\(161\) 18204.3i 0.702300i
\(162\) 0 0
\(163\) 19799.5 0.745212 0.372606 0.927990i \(-0.378464\pi\)
0.372606 + 0.927990i \(0.378464\pi\)
\(164\) 0 0
\(165\) 8702.22 + 250.015i 0.319641 + 0.00918330i
\(166\) 0 0
\(167\) −27954.3 33314.7i −1.00234 1.19454i −0.980848 0.194776i \(-0.937602\pi\)
−0.0214942 0.999769i \(-0.506842\pi\)
\(168\) 0 0
\(169\) 5813.44 2115.92i 0.203545 0.0740842i
\(170\) 0 0
\(171\) −11548.9 + 17587.3i −0.394954 + 0.601459i
\(172\) 0 0
\(173\) 12197.7 14536.7i 0.407555 0.485706i −0.522753 0.852484i \(-0.675095\pi\)
0.930308 + 0.366779i \(0.119539\pi\)
\(174\) 0 0
\(175\) −4723.05 26785.7i −0.154222 0.874636i
\(176\) 0 0
\(177\) −6892.89 8710.91i −0.220016 0.278046i
\(178\) 0 0
\(179\) 15338.0 8855.40i 0.478699 0.276377i −0.241175 0.970482i \(-0.577533\pi\)
0.719874 + 0.694105i \(0.244199\pi\)
\(180\) 0 0
\(181\) 26541.9 45971.9i 0.810168 1.40325i −0.102579 0.994725i \(-0.532709\pi\)
0.912746 0.408526i \(-0.133957\pi\)
\(182\) 0 0
\(183\) 43543.7 14446.5i 1.30024 0.431382i
\(184\) 0 0
\(185\) −30316.5 + 83294.0i −0.885801 + 2.43372i
\(186\) 0 0
\(187\) 850.063 4820.95i 0.0243090 0.137863i
\(188\) 0 0
\(189\) 20681.2 5565.91i 0.578966 0.155816i
\(190\) 0 0
\(191\) −57550.4 10147.7i −1.57755 0.278164i −0.684802 0.728729i \(-0.740111\pi\)
−0.892744 + 0.450565i \(0.851223\pi\)
\(192\) 0 0
\(193\) 23447.3 + 8534.12i 0.629475 + 0.229110i 0.637003 0.770862i \(-0.280174\pi\)
−0.00752797 + 0.999972i \(0.502396\pi\)
\(194\) 0 0
\(195\) −35229.5 + 39616.3i −0.926483 + 1.04185i
\(196\) 0 0
\(197\) 1584.31 + 914.700i 0.0408232 + 0.0235693i 0.520273 0.854000i \(-0.325830\pi\)
−0.479450 + 0.877569i \(0.659164\pi\)
\(198\) 0 0
\(199\) −37552.8 65043.4i −0.948279 1.64247i −0.749049 0.662515i \(-0.769489\pi\)
−0.199230 0.979953i \(-0.563844\pi\)
\(200\) 0 0
\(201\) −2856.89 19454.1i −0.0707134 0.481525i
\(202\) 0 0
\(203\) −37363.5 + 6588.20i −0.906684 + 0.159873i
\(204\) 0 0
\(205\) 14124.9 + 11852.2i 0.336107 + 0.282027i
\(206\) 0 0
\(207\) −19845.8 + 46100.8i −0.463158 + 1.07589i
\(208\) 0 0
\(209\) 2182.25 + 5995.67i 0.0499587 + 0.137260i
\(210\) 0 0
\(211\) 53061.3 44523.7i 1.19183 1.00006i 0.192000 0.981395i \(-0.438503\pi\)
0.999826 0.0186653i \(-0.00594171\pi\)
\(212\) 0 0
\(213\) −38812.8 + 20946.0i −0.855491 + 0.461681i
\(214\) 0 0
\(215\) 58354.8i 1.26241i
\(216\) 0 0
\(217\) −31027.5 −0.658912
\(218\) 0 0
\(219\) 29706.0 48200.3i 0.619378 1.00499i
\(220\) 0 0
\(221\) 19161.8 + 22836.2i 0.392330 + 0.467561i
\(222\) 0 0
\(223\) 50266.6 18295.5i 1.01081 0.367905i 0.217067 0.976157i \(-0.430351\pi\)
0.793744 + 0.608252i \(0.208129\pi\)
\(224\) 0 0
\(225\) −17240.4 + 72981.3i −0.340551 + 1.44161i
\(226\) 0 0
\(227\) −41479.3 + 49433.0i −0.804969 + 0.959325i −0.999768 0.0215183i \(-0.993150\pi\)
0.194799 + 0.980843i \(0.437594\pi\)
\(228\) 0 0
\(229\) 5176.04 + 29354.8i 0.0987021 + 0.559767i 0.993550 + 0.113396i \(0.0361728\pi\)
−0.894848 + 0.446371i \(0.852716\pi\)
\(230\) 0 0
\(231\) 2395.70 6036.78i 0.0448960 0.113131i
\(232\) 0 0
\(233\) 36745.1 21214.8i 0.676842 0.390775i −0.121822 0.992552i \(-0.538874\pi\)
0.798664 + 0.601777i \(0.205540\pi\)
\(234\) 0 0
\(235\) 47774.0 82747.0i 0.865080 1.49836i
\(236\) 0 0
\(237\) 7660.88 37170.5i 0.136390 0.661762i
\(238\) 0 0
\(239\) −16787.1 + 46122.3i −0.293887 + 0.807449i 0.701602 + 0.712569i \(0.252469\pi\)
−0.995489 + 0.0948791i \(0.969754\pi\)
\(240\) 0 0
\(241\) −12866.3 + 72968.3i −0.221523 + 1.25632i 0.647698 + 0.761897i \(0.275732\pi\)
−0.869221 + 0.494423i \(0.835379\pi\)
\(242\) 0 0
\(243\) −58441.1 8450.96i −0.989706 0.143118i
\(244\) 0 0
\(245\) 59642.3 + 10516.6i 0.993625 + 0.175203i
\(246\) 0 0
\(247\) −36511.2 13289.0i −0.598456 0.217820i
\(248\) 0 0
\(249\) 54027.9 + 11135.2i 0.871403 + 0.179597i
\(250\) 0 0
\(251\) 8436.89 + 4871.04i 0.133917 + 0.0773168i 0.565462 0.824775i \(-0.308698\pi\)
−0.431545 + 0.902091i \(0.642031\pi\)
\(252\) 0 0
\(253\) 7610.25 + 13181.3i 0.118894 + 0.205930i
\(254\) 0 0
\(255\) 65653.0 + 26054.4i 1.00966 + 0.400683i
\(256\) 0 0
\(257\) −6076.74 + 1071.49i −0.0920035 + 0.0162227i −0.219460 0.975621i \(-0.570430\pi\)
0.127457 + 0.991844i \(0.459319\pi\)
\(258\) 0 0
\(259\) 50656.7 + 42506.0i 0.755157 + 0.633652i
\(260\) 0 0
\(261\) 101802. + 24048.7i 1.49443 + 0.353029i
\(262\) 0 0
\(263\) −28561.4 78471.8i −0.412922 1.13449i −0.955629 0.294572i \(-0.904823\pi\)
0.542708 0.839922i \(-0.317399\pi\)
\(264\) 0 0
\(265\) −134254. + 112652.i −1.91177 + 1.60416i
\(266\) 0 0
\(267\) −62477.6 38505.1i −0.876398 0.540127i
\(268\) 0 0
\(269\) 2129.98i 0.0294355i 0.999892 + 0.0147177i \(0.00468497\pi\)
−0.999892 + 0.0147177i \(0.995315\pi\)
\(270\) 0 0
\(271\) −3403.65 −0.0463453 −0.0231727 0.999731i \(-0.507377\pi\)
−0.0231727 + 0.999731i \(0.507377\pi\)
\(272\) 0 0
\(273\) 18783.5 + 34805.5i 0.252029 + 0.467007i
\(274\) 0 0
\(275\) 14617.5 + 17420.5i 0.193290 + 0.230354i
\(276\) 0 0
\(277\) −8558.30 + 3114.97i −0.111539 + 0.0405970i −0.397187 0.917738i \(-0.630014\pi\)
0.285648 + 0.958335i \(0.407791\pi\)
\(278\) 0 0
\(279\) 78574.3 + 33825.3i 1.00942 + 0.434544i
\(280\) 0 0
\(281\) −81.2245 + 96.7995i −0.00102867 + 0.00122592i −0.766559 0.642174i \(-0.778032\pi\)
0.765530 + 0.643400i \(0.222477\pi\)
\(282\) 0 0
\(283\) 9704.17 + 55035.1i 0.121167 + 0.687174i 0.983511 + 0.180850i \(0.0578849\pi\)
−0.862343 + 0.506324i \(0.831004\pi\)
\(284\) 0 0
\(285\) −91086.0 + 13376.2i −1.12140 + 0.164681i
\(286\) 0 0
\(287\) 11912.9 6877.90i 0.144628 0.0835011i
\(288\) 0 0
\(289\) −21901.6 + 37934.7i −0.262229 + 0.454193i
\(290\) 0 0
\(291\) −15002.8 13341.5i −0.177168 0.157550i
\(292\) 0 0
\(293\) −11469.3 + 31511.5i −0.133598 + 0.367058i −0.988395 0.151905i \(-0.951459\pi\)
0.854797 + 0.518962i \(0.173682\pi\)
\(294\) 0 0
\(295\) 8440.13 47866.4i 0.0969851 0.550030i
\(296\) 0 0
\(297\) −12648.0 + 12675.9i −0.143387 + 0.143703i
\(298\) 0 0
\(299\) −91278.6 16094.9i −1.02100 0.180030i
\(300\) 0 0
\(301\) −40908.9 14889.6i −0.451528 0.164343i
\(302\) 0 0
\(303\) 13010.2 + 39214.3i 0.141709 + 0.427130i
\(304\) 0 0
\(305\) 173847. + 100371.i 1.86882 + 1.07896i
\(306\) 0 0
\(307\) 60296.2 + 104436.i 0.639754 + 1.10809i 0.985486 + 0.169754i \(0.0542973\pi\)
−0.345732 + 0.938333i \(0.612369\pi\)
\(308\) 0 0
\(309\) 87710.2 69404.5i 0.918614 0.726893i
\(310\) 0 0
\(311\) 158476. 27943.7i 1.63849 0.288910i 0.722879 0.690974i \(-0.242818\pi\)
0.915612 + 0.402064i \(0.131707\pi\)
\(312\) 0 0
\(313\) 40180.2 + 33715.2i 0.410131 + 0.344141i 0.824394 0.566016i \(-0.191516\pi\)
−0.414263 + 0.910157i \(0.635961\pi\)
\(314\) 0 0
\(315\) 78333.2 + 51438.3i 0.789451 + 0.518401i
\(316\) 0 0
\(317\) −43794.7 120325.i −0.435816 1.19739i −0.942190 0.335080i \(-0.891237\pi\)
0.506374 0.862314i \(-0.330986\pi\)
\(318\) 0 0
\(319\) 24299.9 20390.1i 0.238794 0.200372i
\(320\) 0 0
\(321\) 4553.76 158501.i 0.0441937 1.53824i
\(322\) 0 0
\(323\) 51767.4i 0.496194i
\(324\) 0 0
\(325\) −138482. −1.31108
\(326\) 0 0
\(327\) −211582. 6078.78i −1.97872 0.0568487i
\(328\) 0 0
\(329\) −45818.9 54604.8i −0.423304 0.504474i
\(330\) 0 0
\(331\) 20984.5 7637.74i 0.191533 0.0697122i −0.244473 0.969656i \(-0.578615\pi\)
0.436006 + 0.899944i \(0.356393\pi\)
\(332\) 0 0
\(333\) −81944.6 162867.i −0.738978 1.46874i
\(334\) 0 0
\(335\) 55302.8 65907.4i 0.492785 0.587279i
\(336\) 0 0
\(337\) −105.587 598.812i −0.000929714 0.00527267i 0.984339 0.176284i \(-0.0564077\pi\)
−0.985269 + 0.171011i \(0.945297\pi\)
\(338\) 0 0
\(339\) −100702. 127263.i −0.876276 1.10740i
\(340\) 0 0
\(341\) 22466.3 12970.9i 0.193207 0.111548i
\(342\) 0 0
\(343\) 57859.8 100216.i 0.491800 0.851823i
\(344\) 0 0
\(345\) −208442. + 69155.1i −1.75125 + 0.581014i
\(346\) 0 0
\(347\) −48459.4 + 133141.i −0.402457 + 1.10574i 0.558611 + 0.829430i \(0.311334\pi\)
−0.961068 + 0.276312i \(0.910888\pi\)
\(348\) 0 0
\(349\) 16171.1 91710.8i 0.132767 0.752956i −0.843622 0.536937i \(-0.819581\pi\)
0.976389 0.216020i \(-0.0693075\pi\)
\(350\) 0 0
\(351\) −9623.34 108619.i −0.0781109 0.881641i
\(352\) 0 0
\(353\) 55783.0 + 9836.05i 0.447665 + 0.0789353i 0.392936 0.919566i \(-0.371459\pi\)
0.0547288 + 0.998501i \(0.482571\pi\)
\(354\) 0 0
\(355\) −181343. 66003.3i −1.43894 0.523732i
\(356\) 0 0
\(357\) 35016.9 39377.3i 0.274752 0.308965i
\(358\) 0 0
\(359\) −85755.7 49511.1i −0.665387 0.384161i 0.128940 0.991652i \(-0.458843\pi\)
−0.794326 + 0.607491i \(0.792176\pi\)
\(360\) 0 0
\(361\) 31424.2 + 54428.3i 0.241129 + 0.417648i
\(362\) 0 0
\(363\) −18356.3 124998.i −0.139307 0.948615i
\(364\) 0 0
\(365\) 243977. 43019.8i 1.83132 0.322911i
\(366\) 0 0
\(367\) −71780.1 60230.6i −0.532932 0.447183i 0.336180 0.941798i \(-0.390865\pi\)
−0.869112 + 0.494615i \(0.835309\pi\)
\(368\) 0 0
\(369\) −37666.4 + 4430.57i −0.276631 + 0.0325392i
\(370\) 0 0
\(371\) 44717.7 + 122861.i 0.324887 + 0.892619i
\(372\) 0 0
\(373\) −159172. + 133561.i −1.14406 + 0.959978i −0.999564 0.0295275i \(-0.990600\pi\)
−0.144494 + 0.989506i \(0.546155\pi\)
\(374\) 0 0
\(375\) −93820.8 + 50632.1i −0.667170 + 0.360051i
\(376\) 0 0
\(377\) 193170.i 1.35912i
\(378\) 0 0
\(379\) −49705.2 −0.346038 −0.173019 0.984918i \(-0.555352\pi\)
−0.173019 + 0.984918i \(0.555352\pi\)
\(380\) 0 0
\(381\) 94039.3 152586.i 0.647827 1.05115i
\(382\) 0 0
\(383\) −89094.1 106178.i −0.607367 0.723832i 0.371476 0.928442i \(-0.378852\pi\)
−0.978843 + 0.204610i \(0.934407\pi\)
\(384\) 0 0
\(385\) 26704.6 9719.67i 0.180162 0.0655738i
\(386\) 0 0
\(387\) 87365.7 + 82304.3i 0.583337 + 0.549542i
\(388\) 0 0
\(389\) 43574.8 51930.5i 0.287963 0.343181i −0.602598 0.798045i \(-0.705868\pi\)
0.890561 + 0.454864i \(0.150312\pi\)
\(390\) 0 0
\(391\) 21443.9 + 121614.i 0.140265 + 0.795484i
\(392\) 0 0
\(393\) 29356.5 73973.7i 0.190072 0.478952i
\(394\) 0 0
\(395\) 143813. 83030.5i 0.921731 0.532162i
\(396\) 0 0
\(397\) 15662.5 27128.3i 0.0993757 0.172124i −0.812051 0.583587i \(-0.801649\pi\)
0.911426 + 0.411463i \(0.134982\pi\)
\(398\) 0 0
\(399\) −13863.9 + 67267.7i −0.0870845 + 0.422533i
\(400\) 0 0
\(401\) 17473.9 48009.2i 0.108668 0.298563i −0.873425 0.486958i \(-0.838106\pi\)
0.982093 + 0.188395i \(0.0603286\pi\)
\(402\) 0 0
\(403\) −27432.2 + 155575.i −0.168908 + 0.957924i
\(404\) 0 0
\(405\) −142295. 215660.i −0.867521 1.31480i
\(406\) 0 0
\(407\) −54448.9 9600.81i −0.328701 0.0579588i
\(408\) 0 0
\(409\) 220450. + 80237.1i 1.31784 + 0.479654i 0.902765 0.430133i \(-0.141533\pi\)
0.415074 + 0.909788i \(0.363756\pi\)
\(410\) 0 0
\(411\) 150320. + 30981.2i 0.889885 + 0.183406i
\(412\) 0 0
\(413\) −31402.5 18130.3i −0.184105 0.106293i
\(414\) 0 0
\(415\) 120686. + 209034.i 0.700746 + 1.21373i
\(416\) 0 0
\(417\) 137801. + 54686.5i 0.792467 + 0.314491i
\(418\) 0 0
\(419\) 47825.8 8432.98i 0.272417 0.0480345i −0.0357707 0.999360i \(-0.511389\pi\)
0.308188 + 0.951326i \(0.400278\pi\)
\(420\) 0 0
\(421\) 23690.9 + 19879.0i 0.133665 + 0.112158i 0.707169 0.707045i \(-0.249972\pi\)
−0.573504 + 0.819203i \(0.694416\pi\)
\(422\) 0 0
\(423\) 56503.4 + 188232.i 0.315787 + 1.05199i
\(424\) 0 0
\(425\) 63104.9 + 173379.i 0.349370 + 0.959885i
\(426\) 0 0
\(427\) 114722. 96263.1i 0.629202 0.527963i
\(428\) 0 0
\(429\) −28151.0 17349.6i −0.152961 0.0942701i
\(430\) 0 0
\(431\) 235303.i 1.26670i −0.773866 0.633349i \(-0.781680\pi\)
0.773866 0.633349i \(-0.218320\pi\)
\(432\) 0 0
\(433\) −280559. −1.49640 −0.748201 0.663472i \(-0.769082\pi\)
−0.748201 + 0.663472i \(0.769082\pi\)
\(434\) 0 0
\(435\) 217374. + 402791.i 1.14876 + 2.12864i
\(436\) 0 0
\(437\) −103460. 123299.i −0.541763 0.645648i
\(438\) 0 0
\(439\) −307672. + 111984.i −1.59647 + 0.581066i −0.978700 0.205297i \(-0.934184\pi\)
−0.617765 + 0.786363i \(0.711962\pi\)
\(440\) 0 0
\(441\) −99865.1 + 74460.7i −0.513495 + 0.382869i
\(442\) 0 0
\(443\) 24021.1 28627.2i 0.122401 0.145872i −0.701364 0.712803i \(-0.747425\pi\)
0.823765 + 0.566932i \(0.191870\pi\)
\(444\) 0 0
\(445\) −55762.6 316245.i −0.281594 1.59700i
\(446\) 0 0
\(447\) 153202. 22498.2i 0.766744 0.112599i
\(448\) 0 0
\(449\) −123175. + 71115.4i −0.610987 + 0.352753i −0.773351 0.633978i \(-0.781421\pi\)
0.162365 + 0.986731i \(0.448088\pi\)
\(450\) 0 0
\(451\) −5750.57 + 9960.28i −0.0282721 + 0.0489687i
\(452\) 0 0
\(453\) −189270. 168312.i −0.922327 0.820196i
\(454\) 0 0
\(455\) −59188.8 + 162620.i −0.285902 + 0.785509i
\(456\) 0 0
\(457\) −41844.7 + 237313.i −0.200358 + 1.13629i 0.704220 + 0.709982i \(0.251297\pi\)
−0.904578 + 0.426307i \(0.859814\pi\)
\(458\) 0 0
\(459\) −131605. + 61544.8i −0.624665 + 0.292123i
\(460\) 0 0
\(461\) 111772. + 19708.3i 0.525932 + 0.0927360i 0.430309 0.902682i \(-0.358405\pi\)
0.0956228 + 0.995418i \(0.469516\pi\)
\(462\) 0 0
\(463\) 281207. + 102351.i 1.31179 + 0.477453i 0.900819 0.434195i \(-0.142967\pi\)
0.410972 + 0.911648i \(0.365189\pi\)
\(464\) 0 0
\(465\) 117868. + 355270.i 0.545118 + 1.64306i
\(466\) 0 0
\(467\) −302947. 174907.i −1.38910 0.801996i −0.395884 0.918300i \(-0.629562\pi\)
−0.993214 + 0.116304i \(0.962895\pi\)
\(468\) 0 0
\(469\) −32092.6 55586.0i −0.145901 0.252709i
\(470\) 0 0
\(471\) 232433. 183923.i 1.04775 0.829075i
\(472\) 0 0
\(473\) 35845.8 6320.58i 0.160220 0.0282510i
\(474\) 0 0
\(475\) −184220. 154579.i −0.816487 0.685114i
\(476\) 0 0
\(477\) 20696.1 359884.i 0.0909602 1.58171i
\(478\) 0 0
\(479\) 111988. + 307685.i 0.488092 + 1.34102i 0.902405 + 0.430888i \(0.141800\pi\)
−0.414313 + 0.910134i \(0.635978\pi\)
\(480\) 0 0
\(481\) 257917. 216418.i 1.11478 0.935413i
\(482\) 0 0
\(483\) −4705.16 + 163771.i −0.0201688 + 0.702010i
\(484\) 0 0
\(485\) 87847.6i 0.373462i
\(486\) 0 0
\(487\) 286014. 1.20595 0.602975 0.797760i \(-0.293982\pi\)
0.602975 + 0.797760i \(0.293982\pi\)
\(488\) 0 0
\(489\) −178122. 5117.47i −0.744905 0.0214012i
\(490\) 0 0
\(491\) −81179.6 96746.0i −0.336732 0.401301i 0.570934 0.820996i \(-0.306581\pi\)
−0.907665 + 0.419695i \(0.862137\pi\)
\(492\) 0 0
\(493\) 241847. 88025.3i 0.995056 0.362171i
\(494\) 0 0
\(495\) −78223.0 4498.42i −0.319245 0.0183590i
\(496\) 0 0
\(497\) −92541.5 + 110287.i −0.374648 + 0.446489i
\(498\) 0 0
\(499\) 11759.2 + 66689.8i 0.0472255 + 0.267829i 0.999273 0.0381206i \(-0.0121371\pi\)
−0.952048 + 0.305950i \(0.901026\pi\)
\(500\) 0 0
\(501\) 242874. + 306933.i 0.967623 + 1.22284i
\(502\) 0 0
\(503\) −302234. + 174495.i −1.19456 + 0.689679i −0.959337 0.282262i \(-0.908915\pi\)
−0.235222 + 0.971942i \(0.575582\pi\)
\(504\) 0 0
\(505\) −90391.2 + 156562.i −0.354441 + 0.613909i
\(506\) 0 0
\(507\) −52846.3 + 17532.9i −0.205588 + 0.0682082i
\(508\) 0 0
\(509\) −122685. + 337074.i −0.473539 + 1.30104i 0.441351 + 0.897334i \(0.354499\pi\)
−0.914890 + 0.403703i \(0.867723\pi\)
\(510\) 0 0
\(511\) 32094.0 182014.i 0.122908 0.697048i
\(512\) 0 0
\(513\) 108443. 155235.i 0.412064 0.589869i
\(514\) 0 0
\(515\) 481967. + 84983.7i 1.81720 + 0.320421i
\(516\) 0 0
\(517\) 56003.8 + 20383.7i 0.209525 + 0.0762610i
\(518\) 0 0
\(519\) −113491. + 127623.i −0.421336 + 0.473801i
\(520\) 0 0
\(521\) 299992. + 173200.i 1.10518 + 0.638078i 0.937577 0.347776i \(-0.113063\pi\)
0.167605 + 0.985854i \(0.446397\pi\)
\(522\) 0 0
\(523\) −42058.5 72847.4i −0.153762 0.266324i 0.778845 0.627216i \(-0.215806\pi\)
−0.932608 + 0.360892i \(0.882472\pi\)
\(524\) 0 0
\(525\) 35566.7 + 242193.i 0.129040 + 0.878704i
\(526\) 0 0
\(527\) 207280. 36549.1i 0.746339 0.131600i
\(528\) 0 0
\(529\) −79757.0 66924.1i −0.285008 0.239150i
\(530\) 0 0
\(531\) 59758.9 + 80147.4i 0.211940 + 0.284250i
\(532\) 0 0
\(533\) −23954.1 65813.5i −0.0843192 0.231665i
\(534\) 0 0
\(535\) 531499. 445980.i 1.85693 1.55815i
\(536\) 0 0
\(537\) −140274. + 75701.4i −0.486439 + 0.262516i
\(538\) 0 0
\(539\) 37775.8i 0.130028i
\(540\) 0 0
\(541\) 425335. 1.45324 0.726619 0.687041i \(-0.241091\pi\)
0.726619 + 0.687041i \(0.241091\pi\)
\(542\) 0 0
\(543\) −250661. + 406716.i −0.850132 + 1.37941i
\(544\) 0 0
\(545\) −595336. 709493.i −2.00433 2.38867i
\(546\) 0 0
\(547\) −452072. + 164541.i −1.51089 + 0.549919i −0.958854 0.283900i \(-0.908372\pi\)
−0.552037 + 0.833820i \(0.686149\pi\)
\(548\) 0 0
\(549\) −395466. + 118711.i −1.31209 + 0.393863i
\(550\) 0 0
\(551\) −215623. + 256969.i −0.710217 + 0.846404i
\(552\) 0 0
\(553\) −21512.6 122004.i −0.0703465 0.398955i
\(554\) 0 0
\(555\) 294265. 741501.i 0.955328 2.40728i
\(556\) 0 0
\(557\) −291717. + 168423.i −0.940267 + 0.542863i −0.890044 0.455875i \(-0.849326\pi\)
−0.0502227 + 0.998738i \(0.515993\pi\)
\(558\) 0 0
\(559\) −110827. + 191958.i −0.354667 + 0.614302i
\(560\) 0 0
\(561\) −8893.45 + 43150.9i −0.0282582 + 0.137108i
\(562\) 0 0
\(563\) 60246.4 165526.i 0.190070 0.522214i −0.807653 0.589659i \(-0.799262\pi\)
0.997723 + 0.0674444i \(0.0214845\pi\)
\(564\) 0 0
\(565\) 123307. 699310.i 0.386270 2.19065i
\(566\) 0 0
\(567\) −187493. + 44727.2i −0.583202 + 0.139125i
\(568\) 0 0
\(569\) −486349. 85756.5i −1.50219 0.264876i −0.638781 0.769389i \(-0.720561\pi\)
−0.863404 + 0.504513i \(0.831672\pi\)
\(570\) 0 0
\(571\) −222277. 80902.4i −0.681747 0.248136i −0.0221495 0.999755i \(-0.507051\pi\)
−0.659597 + 0.751619i \(0.729273\pi\)
\(572\) 0 0
\(573\) 515118. + 106166.i 1.56891 + 0.323353i
\(574\) 0 0
\(575\) −496810. 286833.i −1.50264 0.867549i
\(576\) 0 0
\(577\) −220535. 381978.i −0.662409 1.14733i −0.979981 0.199092i \(-0.936201\pi\)
0.317572 0.948234i \(-0.397133\pi\)
\(578\) 0 0
\(579\) −208733. 82835.7i −0.622635 0.247093i
\(580\) 0 0
\(581\) 177335. 31268.9i 0.525341 0.0926318i
\(582\) 0 0
\(583\) −83740.7 70266.8i −0.246377 0.206735i
\(584\) 0 0
\(585\) 327174. 347294.i 0.956020 1.01481i
\(586\) 0 0
\(587\) −4668.67 12827.1i −0.0135493 0.0372264i 0.932734 0.360566i \(-0.117417\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(588\) 0 0
\(589\) −210151. + 176337.i −0.605760 + 0.508293i
\(590\) 0 0
\(591\) −14016.5 8638.40i −0.0401295 0.0247319i
\(592\) 0 0
\(593\) 38180.0i 0.108574i −0.998525 0.0542871i \(-0.982711\pi\)
0.998525 0.0542871i \(-0.0172886\pi\)
\(594\) 0 0
\(595\) 230571. 0.651284
\(596\) 0 0
\(597\) 321024. + 594855.i 0.900719 + 1.66902i
\(598\) 0 0
\(599\) −95924.6 114318.i −0.267348 0.318612i 0.615623 0.788041i \(-0.288904\pi\)
−0.882971 + 0.469428i \(0.844460\pi\)
\(600\) 0 0
\(601\) 227375. 82757.8i 0.629498 0.229119i −0.00751483 0.999972i \(-0.502392\pi\)
0.637013 + 0.770853i \(0.280170\pi\)
\(602\) 0 0
\(603\) 20673.2 + 175753.i 0.0568557 + 0.483357i
\(604\) 0 0
\(605\) 355337. 423474.i 0.970799 1.15695i
\(606\) 0 0
\(607\) −31249.1 177223.i −0.0848126 0.480996i −0.997397 0.0721076i \(-0.977027\pi\)
0.912584 0.408889i \(-0.134084\pi\)
\(608\) 0 0
\(609\) 337836. 49612.2i 0.910901 0.133768i
\(610\) 0 0
\(611\) −314304. + 181464.i −0.841915 + 0.486080i
\(612\) 0 0
\(613\) −208031. + 360320.i −0.553614 + 0.958888i 0.444396 + 0.895831i \(0.353418\pi\)
−0.998010 + 0.0630574i \(0.979915\pi\)
\(614\) 0 0
\(615\) −124008. 110276.i −0.327869 0.291563i
\(616\) 0 0
\(617\) 86694.4 238191.i 0.227730 0.625683i −0.772223 0.635351i \(-0.780855\pi\)
0.999953 + 0.00966797i \(0.00307746\pi\)
\(618\) 0 0
\(619\) 7168.59 40655.1i 0.0187091 0.106105i −0.974023 0.226448i \(-0.927289\pi\)
0.992732 + 0.120344i \(0.0383997\pi\)
\(620\) 0 0
\(621\) 190454. 409606.i 0.493864 1.06214i
\(622\) 0 0
\(623\) −235928. 41600.4i −0.607859 0.107182i
\(624\) 0 0
\(625\) 105378. + 38354.4i 0.269767 + 0.0981873i
\(626\) 0 0
\(627\) −18082.5 54502.8i −0.0459962 0.138639i
\(628\) 0 0
\(629\) −388484. 224291.i −0.981910 0.566906i
\(630\) 0 0
\(631\) 123269. + 213508.i 0.309596 + 0.536236i 0.978274 0.207316i \(-0.0664729\pi\)
−0.668678 + 0.743552i \(0.733140\pi\)
\(632\) 0 0
\(633\) −488862. + 386833.i −1.22005 + 0.965421i
\(634\) 0 0
\(635\) 772351. 136186.i 1.91543 0.337743i
\(636\) 0 0
\(637\) −176220. 147866.i −0.434287 0.364410i
\(638\) 0 0
\(639\) 354585. 178405.i 0.868397 0.436923i
\(640\) 0 0
\(641\) −57343.1 157549.i −0.139561 0.383441i 0.850146 0.526547i \(-0.176513\pi\)
−0.989707 + 0.143105i \(0.954291\pi\)
\(642\) 0 0
\(643\) −10320.7 + 8660.10i −0.0249625 + 0.0209460i −0.655184 0.755470i \(-0.727409\pi\)
0.630221 + 0.776416i \(0.282964\pi\)
\(644\) 0 0
\(645\) −15082.6 + 524977.i −0.0362541 + 1.26189i
\(646\) 0 0
\(647\) 570875.i 1.36374i 0.731472 + 0.681872i \(0.238834\pi\)
−0.731472 + 0.681872i \(0.761166\pi\)
\(648\) 0 0
\(649\) 30317.2 0.0719780
\(650\) 0 0
\(651\) 279132. + 8019.49i 0.658640 + 0.0189228i
\(652\) 0 0
\(653\) −426029. 507721.i −0.999109 1.19069i −0.981620 0.190844i \(-0.938877\pi\)
−0.0174882 0.999847i \(-0.505567\pi\)
\(654\) 0 0
\(655\) 327233. 119103.i 0.762737 0.277614i
\(656\) 0 0
\(657\) −279701. + 425945.i −0.647984 + 0.986787i
\(658\) 0 0
\(659\) −79144.6 + 94320.9i −0.182243 + 0.217189i −0.849430 0.527702i \(-0.823054\pi\)
0.667187 + 0.744890i \(0.267498\pi\)
\(660\) 0 0
\(661\) −4335.49 24587.8i −0.00992282 0.0562751i 0.979444 0.201715i \(-0.0646514\pi\)
−0.989367 + 0.145440i \(0.953540\pi\)
\(662\) 0 0
\(663\) −166483. 210393.i −0.378741 0.478635i
\(664\) 0 0
\(665\) −260259. + 150261.i −0.588522 + 0.339783i
\(666\) 0 0
\(667\) −400105. + 693002.i −0.899337 + 1.55770i
\(668\) 0 0
\(669\) −456942. + 151600.i −1.02096 + 0.338725i
\(670\) 0 0
\(671\) −42825.1 + 117661.i −0.0951160 + 0.261329i
\(672\) 0 0
\(673\) −45851.8 + 260038.i −0.101234 + 0.574126i 0.891424 + 0.453170i \(0.149707\pi\)
−0.992658 + 0.120956i \(0.961404\pi\)
\(674\) 0 0
\(675\) 173962. 652105.i 0.381811 1.43123i
\(676\) 0 0
\(677\) 598424. + 105518.i 1.30566 + 0.230224i 0.782843 0.622219i \(-0.213769\pi\)
0.522821 + 0.852443i \(0.324880\pi\)
\(678\) 0 0
\(679\) −61584.5 22414.9i −0.133577 0.0486180i
\(680\) 0 0
\(681\) 385936. 433993.i 0.832187 0.935812i
\(682\) 0 0
\(683\) 641236. + 370218.i 1.37460 + 0.793626i 0.991503 0.130082i \(-0.0415241\pi\)
0.383097 + 0.923708i \(0.374857\pi\)
\(684\) 0 0
\(685\) 335782. + 581591.i 0.715609 + 1.23947i
\(686\) 0 0
\(687\) −38978.0 265422.i −0.0825858 0.562371i
\(688\) 0 0
\(689\) 655575. 115596.i 1.38097 0.243502i
\(690\) 0 0
\(691\) −564242. 473456.i −1.18171 0.991569i −0.999966 0.00822279i \(-0.997383\pi\)
−0.181740 0.983347i \(-0.558173\pi\)
\(692\) 0 0
\(693\) −23112.7 + 53689.4i −0.0481265 + 0.111795i
\(694\) 0 0
\(695\) 221871. + 609584.i 0.459335 + 1.26201i
\(696\) 0 0
\(697\) −71482.4 + 59980.9i −0.147141 + 0.123466i
\(698\) 0 0
\(699\) −336053. + 181357.i −0.687785 + 0.371176i
\(700\) 0 0
\(701\) 642240.i 1.30696i 0.756945 + 0.653479i \(0.226691\pi\)
−0.756945 + 0.653479i \(0.773309\pi\)
\(702\) 0 0
\(703\) 584674. 1.18305
\(704\) 0 0
\(705\) −451176. + 732068.i −0.907753 + 1.47290i
\(706\) 0 0
\(707\) 86692.0 + 103315.i 0.173436 + 0.206693i
\(708\) 0 0
\(709\) −372966. + 135749.i −0.741954 + 0.270049i −0.685216 0.728340i \(-0.740292\pi\)
−0.0567381 + 0.998389i \(0.518070\pi\)
\(710\) 0 0
\(711\) −78526.8 + 332417.i −0.155338 + 0.657572i
\(712\) 0 0
\(713\) −420651. + 501312.i −0.827452 + 0.986119i
\(714\) 0 0
\(715\) −25125.4 142493.i −0.0491475 0.278729i
\(716\) 0 0
\(717\) 162943. 410590.i 0.316955 0.798676i
\(718\) 0 0
\(719\) 567107. 327419.i 1.09700 0.633354i 0.161569 0.986861i \(-0.448344\pi\)
0.935432 + 0.353507i \(0.115011\pi\)
\(720\) 0 0
\(721\) 182554. 316192.i 0.351172 0.608248i
\(722\) 0 0
\(723\) 134609. 653119.i 0.257511 1.24944i
\(724\) 0 0
\(725\) −408915. + 1.12349e6i −0.777960 + 2.13743i
\(726\) 0 0
\(727\) −12221.8 + 69313.1i −0.0231241 + 0.131143i −0.994184 0.107691i \(-0.965654\pi\)
0.971060 + 0.238835i \(0.0767654\pi\)
\(728\) 0 0
\(729\) 523569. + 91132.2i 0.985187 + 0.171481i
\(730\) 0 0
\(731\) 290832. + 51281.6i 0.544262 + 0.0959680i
\(732\) 0 0
\(733\) 617038. + 224583.i 1.14843 + 0.417994i 0.844950 0.534845i \(-0.179630\pi\)
0.303478 + 0.952839i \(0.401852\pi\)
\(734\) 0 0
\(735\) −533841. 110025.i −0.988184 0.203666i
\(736\) 0 0
\(737\) 46475.1 + 26832.4i 0.0855629 + 0.0493998i
\(738\) 0 0
\(739\) 45948.1 + 79584.4i 0.0841353 + 0.145727i 0.905022 0.425364i \(-0.139854\pi\)
−0.820887 + 0.571091i \(0.806521\pi\)
\(740\) 0 0
\(741\) 325030. + 128988.i 0.591954 + 0.234917i
\(742\) 0 0
\(743\) 842543. 148563.i 1.52621 0.269112i 0.653340 0.757064i \(-0.273367\pi\)
0.872870 + 0.487952i \(0.162256\pi\)
\(744\) 0 0
\(745\) 519025. + 435514.i 0.935138 + 0.784674i
\(746\) 0 0
\(747\) −483172. 114140.i −0.865886 0.204548i
\(748\) 0 0
\(749\) −177033. 486395.i −0.315567 0.867013i
\(750\) 0 0
\(751\) 327108. 274476.i 0.579977 0.486659i −0.304962 0.952364i \(-0.598644\pi\)
0.884940 + 0.465706i \(0.154199\pi\)
\(752\) 0 0
\(753\) −74641.7 46001.9i −0.131641 0.0811308i
\(754\) 0 0
\(755\) 1.10826e6i 1.94423i
\(756\) 0 0
\(757\) 33072.5 0.0577133 0.0288566 0.999584i \(-0.490813\pi\)
0.0288566 + 0.999584i \(0.490813\pi\)
\(758\) 0 0
\(759\) −65057.1 120550.i −0.112931 0.209259i
\(760\) 0 0
\(761\) −46066.4 54899.8i −0.0795454 0.0947985i 0.724804 0.688955i \(-0.241930\pi\)
−0.804349 + 0.594157i \(0.797486\pi\)
\(762\) 0 0
\(763\) −649285. + 236320.i −1.11529 + 0.405931i
\(764\) 0 0
\(765\) −583900. 251362.i −0.997735 0.429513i
\(766\) 0 0
\(767\) −118671. + 141427.i −0.201722 + 0.240403i
\(768\) 0 0
\(769\) 62603.8 + 355044.i 0.105864 + 0.600385i 0.990872 + 0.134808i \(0.0430418\pi\)
−0.885008 + 0.465576i \(0.845847\pi\)
\(770\) 0 0
\(771\) 54945.1 8068.84i 0.0924315 0.0135738i
\(772\) 0 0
\(773\) 226732. 130904.i 0.379449 0.219075i −0.298129 0.954526i \(-0.596363\pi\)
0.677579 + 0.735450i \(0.263029\pi\)
\(774\) 0 0
\(775\) −488880. + 846764.i −0.813951 + 1.40981i
\(776\) 0 0
\(777\) −444736. 395489.i −0.736649 0.655078i
\(778\) 0 0
\(779\) 41597.6 114288.i 0.0685478 0.188333i
\(780\) 0 0