Properties

Label 11.5.b.b.10.1
Level 11
Weight 5
Character 11.10
Analytic conductor 1.137
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 11.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.13706959392\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-30}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.1
Root \(-5.47723i\)
Character \(\chi\) = 11.10
Dual form 11.5.b.b.10.2

$q$-expansion

\(f(q)\) \(=\) \(q-5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} +16.4317i q^{6} +54.7723i q^{7} -10.9545i q^{8} -72.0000 q^{9} +O(q^{10})\) \(q-5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} +16.4317i q^{6} +54.7723i q^{7} -10.9545i q^{8} -72.0000 q^{9} -169.794i q^{10} +(11.0000 + 120.499i) q^{11} +42.0000 q^{12} -186.226i q^{13} +300.000 q^{14} -93.0000 q^{15} -284.000 q^{16} +230.043i q^{17} +394.360i q^{18} -98.5901i q^{19} -434.000 q^{20} -164.317i q^{21} +(660.000 - 60.2495i) q^{22} +277.000 q^{23} +32.8634i q^{24} +336.000 q^{25} -1020.00 q^{26} +459.000 q^{27} -766.812i q^{28} -1270.72i q^{29} +509.382i q^{30} -1363.00 q^{31} +1380.26i q^{32} +(-33.0000 - 361.497i) q^{33} +1260.00 q^{34} +1697.94i q^{35} +1008.00 q^{36} +167.000 q^{37} -540.000 q^{38} +558.677i q^{39} -339.588i q^{40} -1062.58i q^{41} -900.000 q^{42} +1204.99i q^{43} +(-154.000 - 1686.99i) q^{44} -2232.00 q^{45} -1517.19i q^{46} +1702.00 q^{47} +852.000 q^{48} -599.000 q^{49} -1840.35i q^{50} -690.130i q^{51} +2607.16i q^{52} +4522.00 q^{53} -2514.05i q^{54} +(341.000 + 3735.47i) q^{55} +600.000 q^{56} +295.770i q^{57} -6960.00 q^{58} -2363.00 q^{59} +1302.00 q^{60} +3965.51i q^{61} +7465.46i q^{62} -3943.60i q^{63} +3016.00 q^{64} -5773.00i q^{65} +(-1980.00 + 180.748i) q^{66} -2803.00 q^{67} -3220.61i q^{68} -831.000 q^{69} +9300.00 q^{70} +3397.00 q^{71} +788.720i q^{72} -3319.20i q^{73} -914.697i q^{74} -1008.00 q^{75} +1380.26i q^{76} +(-6600.00 + 602.495i) q^{77} +3060.00 q^{78} -6090.67i q^{79} -8804.00 q^{80} +4455.00 q^{81} -5820.00 q^{82} +832.538i q^{83} +2300.43i q^{84} +7131.35i q^{85} +6600.00 q^{86} +3812.15i q^{87} +(1320.00 - 120.499i) q^{88} -4673.00 q^{89} +12225.2i q^{90} +10200.0 q^{91} -3878.00 q^{92} +4089.00 q^{93} -9322.24i q^{94} -3056.29i q^{95} -4140.78i q^{96} +4247.00 q^{97} +3280.86i q^{98} +(-792.000 - 8675.93i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 6q^{3} - 28q^{4} + 62q^{5} - 144q^{9} + O(q^{10}) \) \( 2q - 6q^{3} - 28q^{4} + 62q^{5} - 144q^{9} + 22q^{11} + 84q^{12} + 600q^{14} - 186q^{15} - 568q^{16} - 868q^{20} + 1320q^{22} + 554q^{23} + 672q^{25} - 2040q^{26} + 918q^{27} - 2726q^{31} - 66q^{33} + 2520q^{34} + 2016q^{36} + 334q^{37} - 1080q^{38} - 1800q^{42} - 308q^{44} - 4464q^{45} + 3404q^{47} + 1704q^{48} - 1198q^{49} + 9044q^{53} + 682q^{55} + 1200q^{56} - 13920q^{58} - 4726q^{59} + 2604q^{60} + 6032q^{64} - 3960q^{66} - 5606q^{67} - 1662q^{69} + 18600q^{70} + 6794q^{71} - 2016q^{75} - 13200q^{77} + 6120q^{78} - 17608q^{80} + 8910q^{81} - 11640q^{82} + 13200q^{86} + 2640q^{88} - 9346q^{89} + 20400q^{91} - 7756q^{92} + 8178q^{93} + 8494q^{97} - 1584q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.47723i 1.36931i −0.728869 0.684653i \(-0.759954\pi\)
0.728869 0.684653i \(-0.240046\pi\)
\(3\) −3.00000 −0.333333 −0.166667 0.986013i \(-0.553300\pi\)
−0.166667 + 0.986013i \(0.553300\pi\)
\(4\) −14.0000 −0.875000
\(5\) 31.0000 1.24000 0.620000 0.784602i \(-0.287133\pi\)
0.620000 + 0.784602i \(0.287133\pi\)
\(6\) 16.4317i 0.456435i
\(7\) 54.7723i 1.11780i 0.829235 + 0.558901i \(0.188777\pi\)
−0.829235 + 0.558901i \(0.811223\pi\)
\(8\) 10.9545i 0.171163i
\(9\) −72.0000 −0.888889
\(10\) 169.794i 1.69794i
\(11\) 11.0000 + 120.499i 0.0909091 + 0.995859i
\(12\) 42.0000 0.291667
\(13\) 186.226i 1.10193i −0.834529 0.550964i \(-0.814260\pi\)
0.834529 0.550964i \(-0.185740\pi\)
\(14\) 300.000 1.53061
\(15\) −93.0000 −0.413333
\(16\) −284.000 −1.10938
\(17\) 230.043i 0.795998i 0.917386 + 0.397999i \(0.130295\pi\)
−0.917386 + 0.397999i \(0.869705\pi\)
\(18\) 394.360i 1.21716i
\(19\) 98.5901i 0.273103i −0.990633 0.136551i \(-0.956398\pi\)
0.990633 0.136551i \(-0.0436019\pi\)
\(20\) −434.000 −1.08500
\(21\) 164.317i 0.372600i
\(22\) 660.000 60.2495i 1.36364 0.124482i
\(23\) 277.000 0.523629 0.261815 0.965118i \(-0.415679\pi\)
0.261815 + 0.965118i \(0.415679\pi\)
\(24\) 32.8634i 0.0570544i
\(25\) 336.000 0.537600
\(26\) −1020.00 −1.50888
\(27\) 459.000 0.629630
\(28\) 766.812i 0.978076i
\(29\) 1270.72i 1.51096i −0.655172 0.755479i \(-0.727404\pi\)
0.655172 0.755479i \(-0.272596\pi\)
\(30\) 509.382i 0.565980i
\(31\) −1363.00 −1.41831 −0.709157 0.705050i \(-0.750924\pi\)
−0.709157 + 0.705050i \(0.750924\pi\)
\(32\) 1380.26i 1.34791i
\(33\) −33.0000 361.497i −0.0303030 0.331953i
\(34\) 1260.00 1.08997
\(35\) 1697.94i 1.38607i
\(36\) 1008.00 0.777778
\(37\) 167.000 0.121987 0.0609934 0.998138i \(-0.480573\pi\)
0.0609934 + 0.998138i \(0.480573\pi\)
\(38\) −540.000 −0.373961
\(39\) 558.677i 0.367309i
\(40\) 339.588i 0.212242i
\(41\) 1062.58i 0.632113i −0.948740 0.316056i \(-0.897641\pi\)
0.948740 0.316056i \(-0.102359\pi\)
\(42\) −900.000 −0.510204
\(43\) 1204.99i 0.651698i 0.945422 + 0.325849i \(0.105650\pi\)
−0.945422 + 0.325849i \(0.894350\pi\)
\(44\) −154.000 1686.99i −0.0795455 0.871377i
\(45\) −2232.00 −1.10222
\(46\) 1517.19i 0.717009i
\(47\) 1702.00 0.770484 0.385242 0.922816i \(-0.374118\pi\)
0.385242 + 0.922816i \(0.374118\pi\)
\(48\) 852.000 0.369792
\(49\) −599.000 −0.249479
\(50\) 1840.35i 0.736139i
\(51\) 690.130i 0.265333i
\(52\) 2607.16i 0.964186i
\(53\) 4522.00 1.60983 0.804913 0.593393i \(-0.202212\pi\)
0.804913 + 0.593393i \(0.202212\pi\)
\(54\) 2514.05i 0.862156i
\(55\) 341.000 + 3735.47i 0.112727 + 1.23487i
\(56\) 600.000 0.191327
\(57\) 295.770i 0.0910342i
\(58\) −6960.00 −2.06897
\(59\) −2363.00 −0.678828 −0.339414 0.940637i \(-0.610229\pi\)
−0.339414 + 0.940637i \(0.610229\pi\)
\(60\) 1302.00 0.361667
\(61\) 3965.51i 1.06571i 0.846206 + 0.532856i \(0.178881\pi\)
−0.846206 + 0.532856i \(0.821119\pi\)
\(62\) 7465.46i 1.94211i
\(63\) 3943.60i 0.993601i
\(64\) 3016.00 0.736328
\(65\) 5773.00i 1.36639i
\(66\) −1980.00 + 180.748i −0.454545 + 0.0414941i
\(67\) −2803.00 −0.624415 −0.312208 0.950014i \(-0.601068\pi\)
−0.312208 + 0.950014i \(0.601068\pi\)
\(68\) 3220.61i 0.696498i
\(69\) −831.000 −0.174543
\(70\) 9300.00 1.89796
\(71\) 3397.00 0.673874 0.336937 0.941527i \(-0.390609\pi\)
0.336937 + 0.941527i \(0.390609\pi\)
\(72\) 788.720i 0.152145i
\(73\) 3319.20i 0.622856i −0.950270 0.311428i \(-0.899193\pi\)
0.950270 0.311428i \(-0.100807\pi\)
\(74\) 914.697i 0.167037i
\(75\) −1008.00 −0.179200
\(76\) 1380.26i 0.238965i
\(77\) −6600.00 + 602.495i −1.11317 + 0.101618i
\(78\) 3060.00 0.502959
\(79\) 6090.67i 0.975913i −0.872868 0.487957i \(-0.837742\pi\)
0.872868 0.487957i \(-0.162258\pi\)
\(80\) −8804.00 −1.37563
\(81\) 4455.00 0.679012
\(82\) −5820.00 −0.865556
\(83\) 832.538i 0.120850i 0.998173 + 0.0604252i \(0.0192457\pi\)
−0.998173 + 0.0604252i \(0.980754\pi\)
\(84\) 2300.43i 0.326025i
\(85\) 7131.35i 0.987038i
\(86\) 6600.00 0.892374
\(87\) 3812.15i 0.503653i
\(88\) 1320.00 120.499i 0.170455 0.0155603i
\(89\) −4673.00 −0.589951 −0.294975 0.955505i \(-0.595311\pi\)
−0.294975 + 0.955505i \(0.595311\pi\)
\(90\) 12225.2i 1.50928i
\(91\) 10200.0 1.23174
\(92\) −3878.00 −0.458176
\(93\) 4089.00 0.472771
\(94\) 9322.24i 1.05503i
\(95\) 3056.29i 0.338647i
\(96\) 4140.78i 0.449304i
\(97\) 4247.00 0.451376 0.225688 0.974200i \(-0.427537\pi\)
0.225688 + 0.974200i \(0.427537\pi\)
\(98\) 3280.86i 0.341614i
\(99\) −792.000 8675.93i −0.0808081 0.885208i
\(100\) −4704.00 −0.470400
\(101\) 12104.7i 1.18662i 0.804976 + 0.593308i \(0.202178\pi\)
−0.804976 + 0.593308i \(0.797822\pi\)
\(102\) −3780.00 −0.363322
\(103\) −11218.0 −1.05740 −0.528702 0.848807i \(-0.677321\pi\)
−0.528702 + 0.848807i \(0.677321\pi\)
\(104\) −2040.00 −0.188609
\(105\) 5093.82i 0.462024i
\(106\) 24768.0i 2.20434i
\(107\) 4436.55i 0.387506i −0.981050 0.193753i \(-0.937934\pi\)
0.981050 0.193753i \(-0.0620660\pi\)
\(108\) −6426.00 −0.550926
\(109\) 16628.9i 1.39962i 0.714330 + 0.699809i \(0.246731\pi\)
−0.714330 + 0.699809i \(0.753269\pi\)
\(110\) 20460.0 1867.73i 1.69091 0.154358i
\(111\) −501.000 −0.0406623
\(112\) 15555.3i 1.24006i
\(113\) 3847.00 0.301277 0.150638 0.988589i \(-0.451867\pi\)
0.150638 + 0.988589i \(0.451867\pi\)
\(114\) 1620.00 0.124654
\(115\) 8587.00 0.649301
\(116\) 17790.0i 1.32209i
\(117\) 13408.2i 0.979491i
\(118\) 12942.7i 0.929523i
\(119\) −12600.0 −0.889768
\(120\) 1018.76i 0.0707475i
\(121\) −14399.0 + 2650.98i −0.983471 + 0.181065i
\(122\) 21720.0 1.45929
\(123\) 3187.75i 0.210704i
\(124\) 19082.0 1.24102
\(125\) −8959.00 −0.573376
\(126\) −21600.0 −1.36054
\(127\) 13506.8i 0.837426i −0.908119 0.418713i \(-0.862481\pi\)
0.908119 0.418713i \(-0.137519\pi\)
\(128\) 5564.86i 0.339652i
\(129\) 3614.97i 0.217233i
\(130\) −31620.0 −1.87101
\(131\) 21569.3i 1.25688i −0.777858 0.628440i \(-0.783694\pi\)
0.777858 0.628440i \(-0.216306\pi\)
\(132\) 462.000 + 5060.96i 0.0265152 + 0.290459i
\(133\) 5400.00 0.305274
\(134\) 15352.7i 0.855016i
\(135\) 14229.0 0.780741
\(136\) 2520.00 0.136246
\(137\) 11647.0 0.620545 0.310272 0.950648i \(-0.399580\pi\)
0.310272 + 0.950648i \(0.399580\pi\)
\(138\) 4551.57i 0.239003i
\(139\) 17165.6i 0.888444i 0.895917 + 0.444222i \(0.146520\pi\)
−0.895917 + 0.444222i \(0.853480\pi\)
\(140\) 23771.2i 1.21281i
\(141\) −5106.00 −0.256828
\(142\) 18606.1i 0.922740i
\(143\) 22440.0 2048.48i 1.09736 0.100175i
\(144\) 20448.0 0.986111
\(145\) 39392.2i 1.87359i
\(146\) −18180.0 −0.852880
\(147\) 1797.00 0.0831598
\(148\) −2338.00 −0.106738
\(149\) 6517.90i 0.293586i −0.989167 0.146793i \(-0.953105\pi\)
0.989167 0.146793i \(-0.0468951\pi\)
\(150\) 5521.04i 0.245380i
\(151\) 34725.6i 1.52299i 0.648173 + 0.761493i \(0.275533\pi\)
−0.648173 + 0.761493i \(0.724467\pi\)
\(152\) −1080.00 −0.0467452
\(153\) 16563.1i 0.707554i
\(154\) 3300.00 + 36149.7i 0.139147 + 1.52427i
\(155\) −42253.0 −1.75871
\(156\) 7821.48i 0.321395i
\(157\) 23207.0 0.941499 0.470749 0.882267i \(-0.343984\pi\)
0.470749 + 0.882267i \(0.343984\pi\)
\(158\) −33360.0 −1.33632
\(159\) −13566.0 −0.536609
\(160\) 42788.1i 1.67141i
\(161\) 15171.9i 0.585314i
\(162\) 24401.0i 0.929776i
\(163\) 25862.0 0.973390 0.486695 0.873572i \(-0.338202\pi\)
0.486695 + 0.873572i \(0.338202\pi\)
\(164\) 14876.1i 0.553099i
\(165\) −1023.00 11206.4i −0.0375758 0.411622i
\(166\) 4560.00 0.165481
\(167\) 777.766i 0.0278879i 0.999903 + 0.0139440i \(0.00443864\pi\)
−0.999903 + 0.0139440i \(0.995561\pi\)
\(168\) −1800.00 −0.0637755
\(169\) −6119.00 −0.214243
\(170\) 39060.0 1.35156
\(171\) 7098.48i 0.242758i
\(172\) 16869.9i 0.570236i
\(173\) 2388.07i 0.0797912i −0.999204 0.0398956i \(-0.987297\pi\)
0.999204 0.0398956i \(-0.0127025\pi\)
\(174\) 20880.0 0.689655
\(175\) 18403.5i 0.600930i
\(176\) −3124.00 34221.7i −0.100852 1.10478i
\(177\) 7089.00 0.226276
\(178\) 25595.1i 0.807823i
\(179\) −26843.0 −0.837770 −0.418885 0.908039i \(-0.637579\pi\)
−0.418885 + 0.908039i \(0.637579\pi\)
\(180\) 31248.0 0.964444
\(181\) −37633.0 −1.14871 −0.574357 0.818605i \(-0.694748\pi\)
−0.574357 + 0.818605i \(0.694748\pi\)
\(182\) 55867.7i 1.68662i
\(183\) 11896.5i 0.355237i
\(184\) 3034.38i 0.0896262i
\(185\) 5177.00 0.151264
\(186\) 22396.4i 0.647369i
\(187\) −27720.0 + 2530.48i −0.792702 + 0.0723635i
\(188\) −23828.0 −0.674174
\(189\) 25140.5i 0.703801i
\(190\) −16740.0 −0.463712
\(191\) 34597.0 0.948357 0.474178 0.880429i \(-0.342745\pi\)
0.474178 + 0.880429i \(0.342745\pi\)
\(192\) −9048.00 −0.245443
\(193\) 28810.2i 0.773449i −0.922195 0.386725i \(-0.873606\pi\)
0.922195 0.386725i \(-0.126394\pi\)
\(194\) 23261.8i 0.618073i
\(195\) 17319.0i 0.455463i
\(196\) 8386.00 0.218294
\(197\) 53501.5i 1.37859i 0.724483 + 0.689293i \(0.242079\pi\)
−0.724483 + 0.689293i \(0.757921\pi\)
\(198\) −47520.0 + 4337.96i −1.21212 + 0.110651i
\(199\) 8582.00 0.216712 0.108356 0.994112i \(-0.465441\pi\)
0.108356 + 0.994112i \(0.465441\pi\)
\(200\) 3680.70i 0.0920174i
\(201\) 8409.00 0.208138
\(202\) 66300.0 1.62484
\(203\) 69600.0 1.68895
\(204\) 9661.83i 0.232166i
\(205\) 32940.0i 0.783820i
\(206\) 61443.5i 1.44791i
\(207\) −19944.0 −0.465448
\(208\) 52888.1i 1.22245i
\(209\) 11880.0 1084.49i 0.271972 0.0248275i
\(210\) −27900.0 −0.632653
\(211\) 22588.1i 0.507358i 0.967288 + 0.253679i \(0.0816407\pi\)
−0.967288 + 0.253679i \(0.918359\pi\)
\(212\) −63308.0 −1.40860
\(213\) −10191.0 −0.224625
\(214\) −24300.0 −0.530614
\(215\) 37354.7i 0.808106i
\(216\) 5028.09i 0.107769i
\(217\) 74654.6i 1.58539i
\(218\) 91080.0 1.91651
\(219\) 9957.60i 0.207619i
\(220\) −4774.00 52296.5i −0.0986364 1.08051i
\(221\) 42840.0 0.877132
\(222\) 2744.09i 0.0556791i
\(223\) −86683.0 −1.74311 −0.871554 0.490300i \(-0.836887\pi\)
−0.871554 + 0.490300i \(0.836887\pi\)
\(224\) −75600.0 −1.50670
\(225\) −24192.0 −0.477867
\(226\) 21070.9i 0.412540i
\(227\) 8139.16i 0.157953i −0.996876 0.0789765i \(-0.974835\pi\)
0.996876 0.0789765i \(-0.0251652\pi\)
\(228\) 4140.78i 0.0796549i
\(229\) 14807.0 0.282355 0.141178 0.989984i \(-0.454911\pi\)
0.141178 + 0.989984i \(0.454911\pi\)
\(230\) 47032.9i 0.889091i
\(231\) 19800.0 1807.48i 0.371058 0.0338728i
\(232\) −13920.0 −0.258621
\(233\) 9464.65i 0.174338i −0.996194 0.0871691i \(-0.972218\pi\)
0.996194 0.0871691i \(-0.0277820\pi\)
\(234\) 73440.0 1.34122
\(235\) 52762.0 0.955401
\(236\) 33082.0 0.593974
\(237\) 18272.0i 0.325304i
\(238\) 69013.0i 1.21836i
\(239\) 36127.8i 0.632478i −0.948680 0.316239i \(-0.897580\pi\)
0.948680 0.316239i \(-0.102420\pi\)
\(240\) 26412.0 0.458542
\(241\) 101460.i 1.74687i −0.486938 0.873436i \(-0.661886\pi\)
0.486938 0.873436i \(-0.338114\pi\)
\(242\) 14520.0 + 78866.6i 0.247934 + 1.34667i
\(243\) −50544.0 −0.855967
\(244\) 55517.2i 0.932497i
\(245\) −18569.0 −0.309354
\(246\) 17460.0 0.288519
\(247\) −18360.0 −0.300939
\(248\) 14930.9i 0.242763i
\(249\) 2497.61i 0.0402835i
\(250\) 49070.5i 0.785127i
\(251\) −6203.00 −0.0984588 −0.0492294 0.998787i \(-0.515677\pi\)
−0.0492294 + 0.998787i \(0.515677\pi\)
\(252\) 55210.4i 0.869401i
\(253\) 3047.00 + 33378.2i 0.0476027 + 0.521461i
\(254\) −73980.0 −1.14669
\(255\) 21394.0i 0.329013i
\(256\) 78736.0 1.20142
\(257\) −89318.0 −1.35230 −0.676150 0.736764i \(-0.736353\pi\)
−0.676150 + 0.736764i \(0.736353\pi\)
\(258\) −19800.0 −0.297458
\(259\) 9146.97i 0.136357i
\(260\) 80821.9i 1.19559i
\(261\) 91491.6i 1.34307i
\(262\) −118140. −1.72105
\(263\) 62298.0i 0.900663i −0.892861 0.450332i \(-0.851306\pi\)
0.892861 0.450332i \(-0.148694\pi\)
\(264\) −3960.00 + 361.497i −0.0568182 + 0.00518677i
\(265\) 140182. 1.99618
\(266\) 29577.0i 0.418014i
\(267\) 14019.0 0.196650
\(268\) 39242.0 0.546363
\(269\) −38678.0 −0.534514 −0.267257 0.963625i \(-0.586117\pi\)
−0.267257 + 0.963625i \(0.586117\pi\)
\(270\) 77935.4i 1.06907i
\(271\) 16201.6i 0.220607i 0.993898 + 0.110304i \(0.0351824\pi\)
−0.993898 + 0.110304i \(0.964818\pi\)
\(272\) 65332.3i 0.883060i
\(273\) −30600.0 −0.410578
\(274\) 63793.2i 0.849716i
\(275\) 3696.00 + 40487.7i 0.0488727 + 0.535374i
\(276\) 11634.0 0.152725
\(277\) 68377.7i 0.891158i 0.895243 + 0.445579i \(0.147002\pi\)
−0.895243 + 0.445579i \(0.852998\pi\)
\(278\) 94020.0 1.21655
\(279\) 98136.0 1.26072
\(280\) 18600.0 0.237245
\(281\) 123741.i 1.56712i 0.621315 + 0.783561i \(0.286599\pi\)
−0.621315 + 0.783561i \(0.713401\pi\)
\(282\) 27966.7i 0.351676i
\(283\) 126020.i 1.57350i −0.617272 0.786750i \(-0.711762\pi\)
0.617272 0.786750i \(-0.288238\pi\)
\(284\) −47558.0 −0.589640
\(285\) 9168.88i 0.112882i
\(286\) −11220.0 122909.i −0.137171 1.50263i
\(287\) 58200.0 0.706577
\(288\) 99378.8i 1.19814i
\(289\) 30601.0 0.366387
\(290\) −215760. −2.56552
\(291\) −12741.0 −0.150459
\(292\) 46468.8i 0.544999i
\(293\) 90319.4i 1.05207i −0.850462 0.526037i \(-0.823677\pi\)
0.850462 0.526037i \(-0.176323\pi\)
\(294\) 9842.57i 0.113871i
\(295\) −73253.0 −0.841747
\(296\) 1829.39i 0.0208797i
\(297\) 5049.00 + 55309.0i 0.0572391 + 0.627022i
\(298\) −35700.0 −0.402009
\(299\) 51584.5i 0.577001i
\(300\) 14112.0 0.156800
\(301\) −66000.0 −0.728469
\(302\) 190200. 2.08543
\(303\) 36314.0i 0.395539i
\(304\) 27999.6i 0.302973i
\(305\) 122931.i 1.32148i
\(306\) −90720.0 −0.968858
\(307\) 153636.i 1.63011i 0.579384 + 0.815055i \(0.303293\pi\)
−0.579384 + 0.815055i \(0.696707\pi\)
\(308\) 92400.0 8434.93i 0.974026 0.0889160i
\(309\) 33654.0 0.352468
\(310\) 231429.i 2.40821i
\(311\) −90698.0 −0.937728 −0.468864 0.883270i \(-0.655337\pi\)
−0.468864 + 0.883270i \(0.655337\pi\)
\(312\) 6120.00 0.0628698
\(313\) −104953. −1.07129 −0.535644 0.844444i \(-0.679931\pi\)
−0.535644 + 0.844444i \(0.679931\pi\)
\(314\) 127110.i 1.28920i
\(315\) 122252.i 1.23207i
\(316\) 85269.4i 0.853924i
\(317\) 77287.0 0.769109 0.384555 0.923102i \(-0.374355\pi\)
0.384555 + 0.923102i \(0.374355\pi\)
\(318\) 74304.0i 0.734781i
\(319\) 153120. 13977.9i 1.50470 0.137360i
\(320\) 93496.0 0.913047
\(321\) 13309.7i 0.129169i
\(322\) 83100.0 0.801474
\(323\) 22680.0 0.217389
\(324\) −62370.0 −0.594136
\(325\) 62571.8i 0.592396i
\(326\) 141652.i 1.33287i
\(327\) 49886.6i 0.466539i
\(328\) −11640.0 −0.108195
\(329\) 93222.4i 0.861248i
\(330\) −61380.0 + 5603.20i −0.563636 + 0.0514527i
\(331\) −174403. −1.59183 −0.795917 0.605405i \(-0.793011\pi\)
−0.795917 + 0.605405i \(0.793011\pi\)
\(332\) 11655.5i 0.105744i
\(333\) −12024.0 −0.108433
\(334\) 4260.00 0.0381871
\(335\) −86893.0 −0.774275
\(336\) 46666.0i 0.413354i
\(337\) 115493.i 1.01694i 0.861080 + 0.508470i \(0.169789\pi\)
−0.861080 + 0.508470i \(0.830211\pi\)
\(338\) 33515.1i 0.293365i
\(339\) −11541.0 −0.100426
\(340\) 99838.9i 0.863658i
\(341\) −14993.0 164240.i −0.128938 1.41244i
\(342\) 38880.0 0.332410
\(343\) 98699.6i 0.838933i
\(344\) 13200.0 0.111547
\(345\) −25761.0 −0.216434
\(346\) −13080.0 −0.109259
\(347\) 137380.i 1.14094i −0.821317 0.570471i \(-0.806761\pi\)
0.821317 0.570471i \(-0.193239\pi\)
\(348\) 53370.1i 0.440696i
\(349\) 180365.i 1.48082i −0.672157 0.740409i \(-0.734632\pi\)
0.672157 0.740409i \(-0.265368\pi\)
\(350\) 100800. 0.822857
\(351\) 85477.6i 0.693806i
\(352\) −166320. + 15182.9i −1.34233 + 0.122537i
\(353\) 107527. 0.862915 0.431458 0.902133i \(-0.357999\pi\)
0.431458 + 0.902133i \(0.357999\pi\)
\(354\) 38828.1i 0.309841i
\(355\) 105307. 0.835604
\(356\) 65422.0 0.516207
\(357\) 37800.0 0.296589
\(358\) 147025.i 1.14716i
\(359\) 62473.2i 0.484736i 0.970184 + 0.242368i \(0.0779241\pi\)
−0.970184 + 0.242368i \(0.922076\pi\)
\(360\) 24450.3i 0.188660i
\(361\) 120601. 0.925415
\(362\) 206124.i 1.57294i
\(363\) 43197.0 7952.93i 0.327824 0.0603551i
\(364\) −142800. −1.07777
\(365\) 102895.i 0.772341i
\(366\) −65160.0 −0.486428
\(367\) 142397. 1.05723 0.528614 0.848862i \(-0.322712\pi\)
0.528614 + 0.848862i \(0.322712\pi\)
\(368\) −78668.0 −0.580901
\(369\) 76505.9i 0.561878i
\(370\) 28355.6i 0.207126i
\(371\) 247680.i 1.79946i
\(372\) −57246.0 −0.413675
\(373\) 59406.0i 0.426985i −0.976945 0.213492i \(-0.931516\pi\)
0.976945 0.213492i \(-0.0684839\pi\)
\(374\) 13860.0 + 151829.i 0.0990878 + 1.08545i
\(375\) 26877.0 0.191125
\(376\) 18644.5i 0.131879i
\(377\) −236640. −1.66497
\(378\) 137700. 0.963719
\(379\) 123077. 0.856838 0.428419 0.903580i \(-0.359071\pi\)
0.428419 + 0.903580i \(0.359071\pi\)
\(380\) 42788.1i 0.296316i
\(381\) 40520.5i 0.279142i
\(382\) 189496.i 1.29859i
\(383\) −155363. −1.05913 −0.529566 0.848269i \(-0.677645\pi\)
−0.529566 + 0.848269i \(0.677645\pi\)
\(384\) 16694.6i 0.113217i
\(385\) −204600. + 18677.3i −1.38033 + 0.126007i
\(386\) −157800. −1.05909
\(387\) 86759.3i 0.579287i
\(388\) −59458.0 −0.394954
\(389\) −41633.0 −0.275130 −0.137565 0.990493i \(-0.543928\pi\)
−0.137565 + 0.990493i \(0.543928\pi\)
\(390\) 94860.0 0.623669
\(391\) 63722.0i 0.416808i
\(392\) 6561.72i 0.0427017i
\(393\) 64707.9i 0.418960i
\(394\) 293040. 1.88771
\(395\) 188811.i 1.21013i
\(396\) 11088.0 + 121463.i 0.0707071 + 0.774557i
\(397\) 77882.0 0.494147 0.247073 0.968997i \(-0.420531\pi\)
0.247073 + 0.968997i \(0.420531\pi\)
\(398\) 47005.5i 0.296745i
\(399\) −16200.0 −0.101758
\(400\) −95424.0 −0.596400
\(401\) 198922. 1.23707 0.618535 0.785757i \(-0.287727\pi\)
0.618535 + 0.785757i \(0.287727\pi\)
\(402\) 46058.0i 0.285005i
\(403\) 253826.i 1.56288i
\(404\) 169465.i 1.03829i
\(405\) 138105. 0.841975
\(406\) 381215.i 2.31269i
\(407\) 1837.00 + 20123.3i 0.0110897 + 0.121482i
\(408\) −7560.00 −0.0454152
\(409\) 30913.5i 0.184800i −0.995722 0.0923998i \(-0.970546\pi\)
0.995722 0.0923998i \(-0.0294538\pi\)
\(410\) −180420. −1.07329
\(411\) −34941.0 −0.206848
\(412\) 157052. 0.925229
\(413\) 129427.i 0.758795i
\(414\) 109238.i 0.637342i
\(415\) 25808.7i 0.149854i
\(416\) 257040. 1.48530
\(417\) 51496.9i 0.296148i
\(418\) −5940.00 65069.4i −0.0339965 0.372413i
\(419\) −232538. −1.32454 −0.662271 0.749264i \(-0.730407\pi\)
−0.662271 + 0.749264i \(0.730407\pi\)
\(420\) 71313.5i 0.404271i
\(421\) −46918.0 −0.264713 −0.132357 0.991202i \(-0.542254\pi\)
−0.132357 + 0.991202i \(0.542254\pi\)
\(422\) 123720. 0.694728
\(423\) −122544. −0.684875
\(424\) 49536.0i 0.275543i
\(425\) 77294.6i 0.427929i
\(426\) 55818.4i 0.307580i
\(427\) −217200. −1.19125
\(428\) 62111.7i 0.339067i
\(429\) −67320.0 + 6145.45i −0.365788 + 0.0333917i
\(430\) 204600. 1.10654
\(431\) 57412.3i 0.309065i 0.987988 + 0.154533i \(0.0493872\pi\)
−0.987988 + 0.154533i \(0.950613\pi\)
\(432\) −130356. −0.698495
\(433\) 33167.0 0.176901 0.0884505 0.996081i \(-0.471808\pi\)
0.0884505 + 0.996081i \(0.471808\pi\)
\(434\) −408900. −2.17089
\(435\) 118177.i 0.624530i
\(436\) 232804.i 1.22467i
\(437\) 27309.4i 0.143005i
\(438\) 54540.0 0.284293
\(439\) 353303.i 1.83324i 0.399765 + 0.916618i \(0.369092\pi\)
−0.399765 + 0.916618i \(0.630908\pi\)
\(440\) 40920.0 3735.47i 0.211364 0.0192948i
\(441\) 43128.0 0.221759
\(442\) 234644.i 1.20106i
\(443\) 279397. 1.42369 0.711843 0.702339i \(-0.247861\pi\)
0.711843 + 0.702339i \(0.247861\pi\)
\(444\) 7014.00 0.0355795
\(445\) −144863. −0.731539
\(446\) 474782.i 2.38685i
\(447\) 19553.7i 0.0978619i
\(448\) 165193.i 0.823068i
\(449\) 144607. 0.717293 0.358647 0.933473i \(-0.383238\pi\)
0.358647 + 0.933473i \(0.383238\pi\)
\(450\) 132505.i 0.654346i
\(451\) 128040. 11688.4i 0.629495 0.0574648i
\(452\) −53858.0 −0.263617
\(453\) 104177.i 0.507662i
\(454\) −44580.0 −0.216286
\(455\) 316200. 1.52735
\(456\) 3240.00 0.0155817
\(457\) 384282.i 1.84000i −0.391918 0.920000i \(-0.628188\pi\)
0.391918 0.920000i \(-0.371812\pi\)
\(458\) 81101.3i 0.386631i
\(459\) 105590.i 0.501184i
\(460\) −120218. −0.568138
\(461\) 6988.94i 0.0328859i −0.999865 0.0164429i \(-0.994766\pi\)
0.999865 0.0164429i \(-0.00523419\pi\)
\(462\) −9900.00 108449.i −0.0463822 0.508091i
\(463\) −227203. −1.05987 −0.529934 0.848039i \(-0.677783\pi\)
−0.529934 + 0.848039i \(0.677783\pi\)
\(464\) 360883.i 1.67622i
\(465\) 126759. 0.586237
\(466\) −51840.0 −0.238722
\(467\) 328117. 1.50451 0.752255 0.658872i \(-0.228966\pi\)
0.752255 + 0.658872i \(0.228966\pi\)
\(468\) 187715.i 0.857054i
\(469\) 153527.i 0.697972i
\(470\) 288989.i 1.30824i
\(471\) −69621.0 −0.313833
\(472\) 25885.4i 0.116190i
\(473\) −145200. + 13254.9i −0.648999 + 0.0592453i
\(474\) 100080. 0.445441
\(475\) 33126.3i 0.146820i
\(476\) 176400. 0.778547
\(477\) −325584. −1.43096
\(478\) −197880. −0.866056
\(479\) 132560.i 0.577751i −0.957367 0.288876i \(-0.906719\pi\)
0.957367 0.288876i \(-0.0932814\pi\)
\(480\) 128364.i 0.557137i
\(481\) 31099.7i 0.134421i
\(482\) −555720. −2.39200
\(483\) 45515.7i 0.195105i
\(484\) 201586. 37113.7i 0.860537 0.158432i
\(485\) 131657. 0.559707
\(486\) 276841.i 1.17208i
\(487\) −106483. −0.448975 −0.224488 0.974477i \(-0.572071\pi\)
−0.224488 + 0.974477i \(0.572071\pi\)
\(488\) 43440.0 0.182411
\(489\) −77586.0 −0.324463
\(490\) 101707.i 0.423601i
\(491\) 234557.i 0.972937i −0.873698 0.486469i \(-0.838285\pi\)
0.873698 0.486469i \(-0.161715\pi\)
\(492\) 44628.4i 0.184366i
\(493\) 292320. 1.20272
\(494\) 100562.i 0.412078i
\(495\) −24552.0 268954.i −0.100202 1.09766i
\(496\) 387092. 1.57344
\(497\) 186061.i 0.753257i
\(498\) −13680.0 −0.0551604
\(499\) −292378. −1.17420 −0.587102 0.809513i \(-0.699731\pi\)
−0.587102 + 0.809513i \(0.699731\pi\)
\(500\) 125426. 0.501704
\(501\) 2333.30i 0.00929597i
\(502\) 33975.2i 0.134820i
\(503\) 25567.7i 0.101054i 0.998723 + 0.0505272i \(0.0160902\pi\)
−0.998723 + 0.0505272i \(0.983910\pi\)
\(504\) −43200.0 −0.170068
\(505\) 375245.i 1.47140i
\(506\) 182820. 16689.1i 0.714040 0.0651827i
\(507\) 18357.0 0.0714144
\(508\) 189096.i 0.732747i
\(509\) 307447. 1.18668 0.593341 0.804951i \(-0.297808\pi\)
0.593341 + 0.804951i \(0.297808\pi\)
\(510\) −117180. −0.450519
\(511\) 181800. 0.696229
\(512\) 342217.i 1.30545i
\(513\) 45252.8i 0.171954i
\(514\) 489215.i 1.85171i
\(515\) −347758. −1.31118
\(516\) 50609.6i 0.190079i
\(517\) 18722.0 + 205089.i 0.0700440 + 0.767294i
\(518\) 50100.0 0.186715
\(519\) 7164.21i 0.0265971i
\(520\) −63240.0 −0.233876
\(521\) −375593. −1.38370 −0.691850 0.722041i \(-0.743204\pi\)
−0.691850 + 0.722041i \(0.743204\pi\)
\(522\) 501120. 1.83908
\(523\) 272076.i 0.994687i 0.867554 + 0.497343i \(0.165691\pi\)
−0.867554 + 0.497343i \(0.834309\pi\)
\(524\) 301970.i 1.09977i
\(525\) 55210.4i 0.200310i
\(526\) −341220. −1.23328
\(527\) 313549.i 1.12898i
\(528\) 9372.00 + 102665.i 0.0336174 + 0.368260i
\(529\) −203112. −0.725812
\(530\) 767808.i 2.73339i
\(531\) 170136. 0.603403
\(532\) −75600.0 −0.267115
\(533\) −197880. −0.696542
\(534\) 76785.2i 0.269274i
\(535\) 137533.i 0.480507i
\(536\) 30705.3i 0.106877i
\(537\) 80529.0 0.279257
\(538\) 211848.i 0.731914i
\(539\) −6589.00 72178.9i −0.0226799 0.248446i
\(540\) −199206. −0.683148
\(541\) 150810.i 0.515271i −0.966242 0.257635i \(-0.917057\pi\)
0.966242 0.257635i \(-0.0829433\pi\)
\(542\) 88740.0 0.302079
\(543\) 112899. 0.382904
\(544\) −317520. −1.07293
\(545\) 515495.i 1.73553i
\(546\) 167603.i 0.562208i
\(547\) 215430.i 0.719999i −0.932952 0.360000i \(-0.882777\pi\)
0.932952 0.360000i \(-0.117223\pi\)
\(548\) −163058. −0.542976
\(549\) 285517.i 0.947299i
\(550\) 221760. 20243.8i 0.733091 0.0669217i
\(551\) −125280. −0.412647
\(552\) 9103.15i 0.0298754i
\(553\) 333600. 1.09088
\(554\) 374520. 1.22027
\(555\) −15531.0 −0.0504212
\(556\) 240319.i 0.777388i
\(557\) 298892.i 0.963395i 0.876338 + 0.481697i \(0.159980\pi\)
−0.876338 + 0.481697i \(0.840020\pi\)
\(558\) 537513.i 1.72632i
\(559\) 224400. 0.718124
\(560\) 482215.i 1.53768i
\(561\) 83160.0 7591.43i 0.264234 0.0241212i
\(562\) 677760. 2.14587
\(563\) 257079.i 0.811054i 0.914083 + 0.405527i \(0.132912\pi\)
−0.914083 + 0.405527i \(0.867088\pi\)
\(564\) 71484.0 0.224725
\(565\) 119257. 0.373583
\(566\) −690240. −2.15460
\(567\) 244010.i 0.759001i
\(568\) 37212.3i 0.115343i
\(569\) 133250.i 0.411569i −0.978597 0.205784i \(-0.934025\pi\)
0.978597 0.205784i \(-0.0659746\pi\)
\(570\) 50220.0 0.154571
\(571\) 171832.i 0.527024i −0.964656 0.263512i \(-0.915119\pi\)
0.964656 0.263512i \(-0.0848809\pi\)
\(572\) −314160. + 28678.8i −0.960194 + 0.0876533i
\(573\) −103791. −0.316119
\(574\) 318775.i 0.967520i
\(575\) 93072.0 0.281503
\(576\) −217152. −0.654514
\(577\) 41567.0 0.124852 0.0624262 0.998050i \(-0.480116\pi\)
0.0624262 + 0.998050i \(0.480116\pi\)
\(578\) 167609.i 0.501696i
\(579\) 86430.6i 0.257816i
\(580\) 551491.i 1.63939i
\(581\) −45600.0 −0.135087
\(582\) 69785.3i 0.206024i
\(583\) 49742.0 + 544896.i 0.146348 + 1.60316i
\(584\) −36360.0 −0.106610
\(585\) 415656.i 1.21457i
\(586\) −494700. −1.44061
\(587\) 236062. 0.685094 0.342547 0.939501i \(-0.388710\pi\)
0.342547 + 0.939501i \(0.388710\pi\)
\(588\) −25158.0 −0.0727648
\(589\) 134378.i 0.387345i
\(590\) 401223.i 1.15261i
\(591\) 160505.i 0.459529i
\(592\) −47428.0 −0.135329
\(593\) 39764.7i 0.113081i −0.998400 0.0565403i \(-0.981993\pi\)
0.998400 0.0565403i \(-0.0180069\pi\)
\(594\) 302940. 27654.5i 0.858586 0.0783778i
\(595\) −390600. −1.10331
\(596\) 91250.6i 0.256888i
\(597\) −25746.0 −0.0722372
\(598\) −282540. −0.790092
\(599\) −2378.00 −0.00662763 −0.00331381 0.999995i \(-0.501055\pi\)
−0.00331381 + 0.999995i \(0.501055\pi\)
\(600\) 11042.1i 0.0306725i
\(601\) 184309.i 0.510266i −0.966906 0.255133i \(-0.917881\pi\)
0.966906 0.255133i \(-0.0821193\pi\)
\(602\) 361497.i 0.997497i
\(603\) 201816. 0.555036
\(604\) 486159.i 1.33261i
\(605\) −446369. + 82180.3i −1.21950 + 0.224521i
\(606\) −198900. −0.541614
\(607\) 640397.i 1.73809i −0.494734 0.869045i \(-0.664734\pi\)
0.494734 0.869045i \(-0.335266\pi\)
\(608\) 136080. 0.368118
\(609\) −208800. −0.562984
\(610\) 673320. 1.80951
\(611\) 316956.i 0.849018i
\(612\) 231884.i 0.619110i
\(613\) 144139.i 0.383583i 0.981436 + 0.191792i \(0.0614298\pi\)
−0.981436 + 0.191792i \(0.938570\pi\)
\(614\) 841500. 2.23212
\(615\) 98820.1i 0.261273i
\(616\) 6600.00 + 72299.4i 0.0173933 + 0.190534i
\(617\) 707962. 1.85969 0.929843 0.367957i \(-0.119942\pi\)
0.929843 + 0.367957i \(0.119942\pi\)
\(618\) 184331.i 0.482637i
\(619\) −487963. −1.27352 −0.636760 0.771062i \(-0.719726\pi\)
−0.636760 + 0.771062i \(0.719726\pi\)
\(620\) 591542. 1.53887
\(621\) 127143. 0.329693
\(622\) 496773.i 1.28404i
\(623\) 255951.i 0.659448i
\(624\) 158664.i 0.407483i
\(625\) −487729. −1.24859
\(626\) 574851.i 1.46692i
\(627\) −35640.0 + 3253.47i −0.0906573 + 0.00827584i
\(628\) −324898. −0.823811
\(629\) 38417.3i 0.0971013i
\(630\) −669600. −1.68707
\(631\) 274397. 0.689161 0.344580 0.938757i \(-0.388021\pi\)
0.344580 + 0.938757i \(0.388021\pi\)
\(632\) −66720.0 −0.167041
\(633\) 67764.2i 0.169119i
\(634\) 423318.i 1.05315i
\(635\) 418712.i 1.03841i
\(636\) 189924. 0.469532
\(637\) 111549.i 0.274908i
\(638\) −76560.0 838673.i −0.188088 2.06040i
\(639\) −244584. −0.598999
\(640\) 172511.i 0.421169i
\(641\) −99113.0 −0.241221 −0.120610 0.992700i \(-0.538485\pi\)
−0.120610 + 0.992700i \(0.538485\pi\)
\(642\) 72900.0 0.176871
\(643\) 526997. 1.27464 0.637318 0.770601i \(-0.280044\pi\)
0.637318 + 0.770601i \(0.280044\pi\)
\(644\) 212407.i 0.512149i
\(645\) 112064.i 0.269369i
\(646\) 124223.i 0.297672i
\(647\) −140843. −0.336455 −0.168227 0.985748i \(-0.553804\pi\)
−0.168227 + 0.985748i \(0.553804\pi\)
\(648\) 48802.1i 0.116222i
\(649\) −25993.0 284739.i −0.0617116 0.676017i
\(650\) −342720. −0.811172
\(651\) 223964.i 0.528464i
\(652\) −362068. −0.851716
\(653\) −240953. −0.565075 −0.282537 0.959256i \(-0.591176\pi\)
−0.282537 + 0.959256i \(0.591176\pi\)
\(654\) −273240. −0.638835
\(655\) 668649.i 1.55853i
\(656\) 301773.i 0.701250i
\(657\) 238982.i 0.553650i
\(658\) 510600. 1.17931
\(659\) 499830.i 1.15094i 0.817824 + 0.575468i \(0.195180\pi\)
−0.817824 + 0.575468i \(0.804820\pi\)
\(660\) 14322.0 + 156890.i 0.0328788 + 0.360169i
\(661\) 122927. 0.281348 0.140674 0.990056i \(-0.455073\pi\)
0.140674 + 0.990056i \(0.455073\pi\)
\(662\) 955245.i 2.17971i
\(663\) −128520. −0.292377
\(664\) 9120.00 0.0206852
\(665\) 167400. 0.378540
\(666\) 65858.2i 0.148478i
\(667\) 351988.i 0.791183i
\(668\) 10888.7i 0.0244019i
\(669\) 260049. 0.581036
\(670\) 475933.i 1.06022i
\(671\) −477840. + 43620.6i −1.06130 + 0.0968828i
\(672\) 226800. 0.502232
\(673\) 202745.i 0.447631i −0.974632 0.223815i \(-0.928149\pi\)
0.974632 0.223815i \(-0.0718513\pi\)
\(674\) 632580. 1.39250
\(675\) 154224. 0.338489
\(676\) 85666.0 0.187463
\(677\) 776966.i 1.69522i 0.530623 + 0.847608i \(0.321958\pi\)
−0.530623 + 0.847608i \(0.678042\pi\)
\(678\) 63212.7i 0.137513i
\(679\) 232618.i 0.504549i
\(680\) 78120.0 0.168945
\(681\) 24417.5i 0.0526510i
\(682\) −899580. + 82120.0i −1.93406 + 0.176555i
\(683\) 68422.0 0.146674 0.0733372 0.997307i \(-0.476635\pi\)
0.0733372 + 0.997307i \(0.476635\pi\)
\(684\) 99378.8i 0.212413i
\(685\) 361057. 0.769475
\(686\) 540600. 1.14876
\(687\) −44421.0 −0.0941185
\(688\) 342217.i 0.722977i
\(689\) 842112.i 1.77391i
\(690\) 141099.i 0.296364i
\(691\) 662597. 1.38769 0.693846 0.720123i \(-0.255915\pi\)
0.693846 + 0.720123i \(0.255915\pi\)
\(692\) 33433.0i 0.0698173i
\(693\) 475200. 43379.6i 0.989487 0.0903274i
\(694\) −752460. −1.56230
\(695\) 532134.i 1.10167i
\(696\) 41760.0 0.0862069
\(697\) 244440. 0.503161
\(698\) −987900. −2.02769
\(699\) 28393.9i 0.0581127i
\(700\) 257649.i 0.525814i
\(701\) 64247.9i 0.130744i 0.997861 + 0.0653721i \(0.0208234\pi\)
−0.997861 + 0.0653721i \(0.979177\pi\)
\(702\) −468180. −0.950033
\(703\) 16464.5i 0.0333149i
\(704\) 33176.0 + 363425.i 0.0669389 + 0.733279i
\(705\) −158286. −0.318467
\(706\) 588950.i 1.18160i
\(707\) −663000. −1.32640
\(708\) −99246.0 −0.197991
\(709\) −656713. −1.30642 −0.653210 0.757176i \(-0.726578\pi\)
−0.653210 + 0.757176i \(0.726578\pi\)
\(710\) 576790.i 1.14420i
\(711\) 438529.i 0.867478i
\(712\) 51190.2i 0.100978i
\(713\) −377551. −0.742671
\(714\) 207039.i 0.406122i
\(715\) 695640. 63503.0i 1.36073 0.124217i
\(716\) 375802. 0.733049
\(717\) 108383.i 0.210826i
\(718\) 342180. 0.663752
\(719\) 278797. 0.539300 0.269650 0.962958i \(-0.413092\pi\)
0.269650 + 0.962958i \(0.413092\pi\)
\(720\) 633888. 1.22278
\(721\) 614435.i 1.18197i
\(722\) 660559.i 1.26718i
\(723\) 304380.i 0.582291i
\(724\) 526862. 1.00512
\(725\) 426961.i 0.812291i
\(726\) −43560.0 236600.i −0.0826446 0.448891i
\(727\) −384283. −0.727080 −0.363540 0.931579i \(-0.618432\pi\)
−0.363540 + 0.931579i \(0.618432\pi\)
\(728\) 111735.i 0.210828i
\(729\) −209223. −0.393690
\(730\) −563580. −1.05757
\(731\) −277200. −0.518750
\(732\) 166551.i 0.310832i
\(733\) 900303.i 1.67564i 0.545947 + 0.837820i \(0.316170\pi\)
−0.545947 + 0.837820i \(0.683830\pi\)
\(734\) 779940.i 1.44767i
\(735\) 55707.0 0.103118
\(736\) 382332.i 0.705806i
\(737\) −30833.0 337759.i −0.0567650 0.621830i
\(738\) 419040. 0.769383
\(739\) 179237.i 0.328200i 0.986444 + 0.164100i \(0.0524719\pi\)
−0.986444 + 0.164100i \(0.947528\pi\)
\(740\) −72478.0 −0.132356
\(741\) 55080.0 0.100313
\(742\) 1.35660e6 2.46402
\(743\) 815888.i 1.47793i 0.673746 + 0.738963i \(0.264684\pi\)
−0.673746 + 0.738963i \(0.735316\pi\)
\(744\) 44792.8i 0.0809211i
\(745\) 202055.i 0.364046i
\(746\) −325380. −0.584673
\(747\) 59942.8i 0.107423i
\(748\) 388080. 35426.7i 0.693614 0.0633180i
\(749\) 243000. 0.433154
\(750\) 147211.i 0.261709i
\(751\) 463757. 0.822263 0.411131 0.911576i \(-0.365134\pi\)
0.411131 + 0.911576i \(0.365134\pi\)
\(752\) −483368. −0.854756
\(753\) 18609.0 0.0328196
\(754\) 1.29613e6i 2.27985i
\(755\) 1.07649e6i 1.88850i
\(756\) 351967.i 0.615826i
\(757\) −593878. −1.03635 −0.518174 0.855275i \(-0.673388\pi\)
−0.518174 + 0.855275i \(0.673388\pi\)
\(758\) 674120.i 1.17327i
\(759\) −9141.00 100135.i −0.0158676 0.173820i
\(760\) −33480.0 −0.0579640
\(761\) 1.06130e6i 1.83261i −0.400487 0.916303i \(-0.631159\pi\)
0.400487 0.916303i \(-0.368841\pi\)
\(762\) 221940. 0.382231
\(763\) −910800. −1.56449
\(764\) −484358. −0.829812
\(765\) 513457.i 0.877367i
\(766\) 850958.i 1.45028i
\(767\) 440051.i 0.748019i
\(768\) −236208. −0.400472
\(769\) 219188.i 0.370649i −0.982677 0.185325i \(-0.940666\pi\)
0.982677 0.185325i \(-0.0593337\pi\)
\(770\) 102300. + 1.12064e6i 0.172542 + 1.89010i
\(771\) 267954. 0.450766
\(772\) 403343.i 0.676768i
\(773\) −315758. −0.528440 −0.264220 0.964462i \(-0.585114\pi\)
−0.264220 + 0.964462i \(0.585114\pi\)
\(774\) −475200. −0.793222
\(775\) −457968. −0.762486
\(776\) 46523.6i 0.0772591i
\(777\) 27440.9i 0.0454523i
\(778\) 228033.i 0.376738i
\(779\) −104760. −0.172632
\(780\) 242466.i 0.398530i
\(781\) 37367.0 + 409335.i 0.0612613 + 0.671084i
\(782\) 349020. 0.570738
\(783\) 583259.i 0.951344i
\(784\) 170116. 0.276766
\(785\) 719417. 1.16746
\(786\) 354420. 0.573685
\(787\) 15796.3i 0.0255039i −0.999919 0.0127519i \(-0.995941\pi\)
0.999919 0.0127519i \(-0.00405918\pi\)
\(788\) 749022.i 1.20626i
\(789\) 186894.i 0.300221i
\(790\) −1.03416e6 −1.65704
\(791\) 210709.i 0.336767i
\(792\) −95040.0 + 8675.93i −0.151515 + 0.0138314i
\(793\) 738480. 1.17434
\(794\) 426577.i 0.676639i
\(795\) −420546. −0.665395
\(796\) −120148. −0.189623
\(797\) 378607. 0.596035 0.298018 0.954560i \(-0.403675\pi\)
0.298018 + 0.954560i \(0.403675\pi\)