Properties

Label 405.4.e.r.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.95327307.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.0280269i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.r.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} +O(q^{10})\) \(q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} -26.0034 q^{10} +(14.4919 + 25.1008i) q^{11} +(32.6960 - 56.6311i) q^{13} +(-63.4517 + 109.902i) q^{14} +(-73.2057 - 126.796i) q^{16} +68.1718 q^{17} +104.424 q^{19} +(47.6174 + 82.4758i) q^{20} +(75.3678 - 130.541i) q^{22} +(77.4033 - 134.067i) q^{23} +(-12.5000 - 21.6506i) q^{25} -340.082 q^{26} +464.772 q^{28} +(102.829 + 178.105i) q^{29} +(9.12485 - 15.8047i) q^{31} +(-150.912 + 261.387i) q^{32} +(-177.269 - 307.040i) q^{34} -122.007 q^{35} -337.613 q^{37} +(-271.538 - 470.317i) q^{38} +(143.629 - 248.773i) q^{40} +(97.9845 - 169.714i) q^{41} +(-167.441 - 290.016i) q^{43} -552.055 q^{44} -805.098 q^{46} +(2.50199 + 4.33358i) q^{47} +(-126.213 + 218.607i) q^{49} +(-65.0084 + 112.598i) q^{50} +(622.759 + 1078.65i) q^{52} -319.965 q^{53} +144.919 q^{55} +(-700.949 - 1214.08i) q^{56} +(534.779 - 926.265i) q^{58} +(-215.305 + 372.920i) q^{59} +(-297.291 - 514.922i) q^{61} -94.9106 q^{62} +398.396 q^{64} +(-163.480 - 283.155i) q^{65} +(-97.9382 + 169.634i) q^{67} +(-649.233 + 1124.50i) q^{68} +(317.258 + 549.508i) q^{70} +425.955 q^{71} +929.193 q^{73} +(877.908 + 1520.58i) q^{74} +(-994.482 + 1722.49i) q^{76} +(353.623 - 612.492i) q^{77} +(-12.2148 - 21.1567i) q^{79} -732.057 q^{80} -1019.17 q^{82} +(272.929 + 472.727i) q^{83} +(170.429 - 295.192i) q^{85} +(-870.805 + 1508.28i) q^{86} +(832.586 + 1442.08i) q^{88} -84.1332 q^{89} -1595.65 q^{91} +(1474.30 + 2553.56i) q^{92} +(13.0120 - 22.5375i) q^{94} +(261.060 - 452.170i) q^{95} +(-413.807 - 716.734i) q^{97} +1312.78 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60034 4.50391i −0.919357 1.59237i −0.800393 0.599475i \(-0.795376\pi\)
−0.118964 0.992899i \(-0.537957\pi\)
\(3\) 0 0
\(4\) −9.52349 + 16.4952i −1.19044 + 2.06190i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) −12.2007 21.1322i −0.658774 1.14103i −0.980933 0.194345i \(-0.937742\pi\)
0.322159 0.946686i \(-0.395591\pi\)
\(8\) 57.4517 2.53903
\(9\) 0 0
\(10\) −26.0034 −0.822298
\(11\) 14.4919 + 25.1008i 0.397226 + 0.688015i 0.993383 0.114853i \(-0.0366397\pi\)
−0.596157 + 0.802868i \(0.703306\pi\)
\(12\) 0 0
\(13\) 32.6960 56.6311i 0.697556 1.20820i −0.271756 0.962366i \(-0.587604\pi\)
0.969311 0.245836i \(-0.0790625\pi\)
\(14\) −63.4517 + 109.902i −1.21130 + 2.09803i
\(15\) 0 0
\(16\) −73.2057 126.796i −1.14384 1.98119i
\(17\) 68.1718 0.972593 0.486296 0.873794i \(-0.338347\pi\)
0.486296 + 0.873794i \(0.338347\pi\)
\(18\) 0 0
\(19\) 104.424 1.26087 0.630435 0.776242i \(-0.282876\pi\)
0.630435 + 0.776242i \(0.282876\pi\)
\(20\) 47.6174 + 82.4758i 0.532379 + 0.922108i
\(21\) 0 0
\(22\) 75.3678 130.541i 0.730385 1.26506i
\(23\) 77.4033 134.067i 0.701727 1.21543i −0.266133 0.963936i \(-0.585746\pi\)
0.967860 0.251490i \(-0.0809205\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −340.082 −2.56521
\(27\) 0 0
\(28\) 464.772 3.13691
\(29\) 102.829 + 178.105i 0.658443 + 1.14046i 0.981019 + 0.193913i \(0.0621179\pi\)
−0.322576 + 0.946544i \(0.604549\pi\)
\(30\) 0 0
\(31\) 9.12485 15.8047i 0.0528668 0.0915680i −0.838381 0.545085i \(-0.816497\pi\)
0.891248 + 0.453517i \(0.149831\pi\)
\(32\) −150.912 + 261.387i −0.833679 + 1.44397i
\(33\) 0 0
\(34\) −177.269 307.040i −0.894160 1.54873i
\(35\) −122.007 −0.589226
\(36\) 0 0
\(37\) −337.613 −1.50009 −0.750044 0.661387i \(-0.769968\pi\)
−0.750044 + 0.661387i \(0.769968\pi\)
\(38\) −271.538 470.317i −1.15919 2.00778i
\(39\) 0 0
\(40\) 143.629 248.773i 0.567744 0.983362i
\(41\) 97.9845 169.714i 0.373234 0.646461i −0.616827 0.787099i \(-0.711582\pi\)
0.990061 + 0.140638i \(0.0449154\pi\)
\(42\) 0 0
\(43\) −167.441 290.016i −0.593826 1.02854i −0.993711 0.111971i \(-0.964284\pi\)
0.399886 0.916565i \(-0.369050\pi\)
\(44\) −552.055 −1.89149
\(45\) 0 0
\(46\) −805.098 −2.58055
\(47\) 2.50199 + 4.33358i 0.00776496 + 0.0134493i 0.869882 0.493260i \(-0.164195\pi\)
−0.862117 + 0.506710i \(0.830862\pi\)
\(48\) 0 0
\(49\) −126.213 + 218.607i −0.367967 + 0.637338i
\(50\) −65.0084 + 112.598i −0.183871 + 0.318475i
\(51\) 0 0
\(52\) 622.759 + 1078.65i 1.66079 + 2.87657i
\(53\) −319.965 −0.829256 −0.414628 0.909991i \(-0.636088\pi\)
−0.414628 + 0.909991i \(0.636088\pi\)
\(54\) 0 0
\(55\) 144.919 0.355289
\(56\) −700.949 1214.08i −1.67265 2.89711i
\(57\) 0 0
\(58\) 534.779 926.265i 1.21069 2.09697i
\(59\) −215.305 + 372.920i −0.475091 + 0.822882i −0.999593 0.0285276i \(-0.990918\pi\)
0.524502 + 0.851409i \(0.324251\pi\)
\(60\) 0 0
\(61\) −297.291 514.922i −0.624002 1.08080i −0.988733 0.149691i \(-0.952172\pi\)
0.364730 0.931113i \(-0.381161\pi\)
\(62\) −94.9106 −0.194414
\(63\) 0 0
\(64\) 398.396 0.778118
\(65\) −163.480 283.155i −0.311956 0.540324i
\(66\) 0 0
\(67\) −97.9382 + 169.634i −0.178583 + 0.309315i −0.941395 0.337305i \(-0.890485\pi\)
0.762812 + 0.646620i \(0.223818\pi\)
\(68\) −649.233 + 1124.50i −1.15781 + 2.00538i
\(69\) 0 0
\(70\) 317.258 + 549.508i 0.541709 + 0.938267i
\(71\) 425.955 0.711994 0.355997 0.934487i \(-0.384141\pi\)
0.355997 + 0.934487i \(0.384141\pi\)
\(72\) 0 0
\(73\) 929.193 1.48978 0.744889 0.667188i \(-0.232502\pi\)
0.744889 + 0.667188i \(0.232502\pi\)
\(74\) 877.908 + 1520.58i 1.37912 + 2.38870i
\(75\) 0 0
\(76\) −994.482 + 1722.49i −1.50099 + 2.59978i
\(77\) 353.623 612.492i 0.523364 0.906493i
\(78\) 0 0
\(79\) −12.2148 21.1567i −0.0173959 0.0301305i 0.857196 0.514990i \(-0.172204\pi\)
−0.874592 + 0.484859i \(0.838871\pi\)
\(80\) −732.057 −1.02308
\(81\) 0 0
\(82\) −1019.17 −1.37254
\(83\) 272.929 + 472.727i 0.360938 + 0.625164i 0.988116 0.153713i \(-0.0491231\pi\)
−0.627177 + 0.778877i \(0.715790\pi\)
\(84\) 0 0
\(85\) 170.429 295.192i 0.217478 0.376684i
\(86\) −870.805 + 1508.28i −1.09188 + 1.89118i
\(87\) 0 0
\(88\) 832.586 + 1442.08i 1.00857 + 1.74689i
\(89\) −84.1332 −0.100203 −0.0501017 0.998744i \(-0.515955\pi\)
−0.0501017 + 0.998744i \(0.515955\pi\)
\(90\) 0 0
\(91\) −1595.65 −1.83813
\(92\) 1474.30 + 2553.56i 1.67072 + 2.89377i
\(93\) 0 0
\(94\) 13.0120 22.5375i 0.0142775 0.0247294i
\(95\) 261.060 452.170i 0.281939 0.488333i
\(96\) 0 0
\(97\) −413.807 716.734i −0.433152 0.750241i 0.563991 0.825781i \(-0.309265\pi\)
−0.997143 + 0.0755403i \(0.975932\pi\)
\(98\) 1312.78 1.35317
\(99\) 0 0
\(100\) 476.174 0.476174
\(101\) −411.788 713.238i −0.405688 0.702671i 0.588714 0.808342i \(-0.299635\pi\)
−0.994401 + 0.105670i \(0.966301\pi\)
\(102\) 0 0
\(103\) −585.595 + 1014.28i −0.560198 + 0.970291i 0.437281 + 0.899325i \(0.355941\pi\)
−0.997479 + 0.0709659i \(0.977392\pi\)
\(104\) 1878.44 3253.55i 1.77111 3.06766i
\(105\) 0 0
\(106\) 832.016 + 1441.09i 0.762383 + 1.32049i
\(107\) 1023.21 0.924460 0.462230 0.886760i \(-0.347049\pi\)
0.462230 + 0.886760i \(0.347049\pi\)
\(108\) 0 0
\(109\) −403.647 −0.354700 −0.177350 0.984148i \(-0.556753\pi\)
−0.177350 + 0.984148i \(0.556753\pi\)
\(110\) −376.839 652.704i −0.326638 0.565754i
\(111\) 0 0
\(112\) −1786.32 + 3093.99i −1.50706 + 2.61031i
\(113\) −541.102 + 937.216i −0.450465 + 0.780229i −0.998415 0.0562825i \(-0.982075\pi\)
0.547950 + 0.836511i \(0.315409\pi\)
\(114\) 0 0
\(115\) −387.017 670.333i −0.313822 0.543555i
\(116\) −3917.16 −3.13534
\(117\) 0 0
\(118\) 2239.46 1.74711
\(119\) −831.741 1440.62i −0.640719 1.10976i
\(120\) 0 0
\(121\) 245.468 425.162i 0.184423 0.319431i
\(122\) −1546.11 + 2677.94i −1.14736 + 1.98729i
\(123\) 0 0
\(124\) 173.801 + 301.032i 0.125869 + 0.218012i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −774.132 −0.540890 −0.270445 0.962735i \(-0.587171\pi\)
−0.270445 + 0.962735i \(0.587171\pi\)
\(128\) 171.332 + 296.756i 0.118311 + 0.204920i
\(129\) 0 0
\(130\) −850.204 + 1472.60i −0.573599 + 0.993503i
\(131\) 607.019 1051.39i 0.404851 0.701222i −0.589453 0.807802i \(-0.700657\pi\)
0.994304 + 0.106580i \(0.0339901\pi\)
\(132\) 0 0
\(133\) −1274.04 2206.71i −0.830629 1.43869i
\(134\) 1018.69 0.656726
\(135\) 0 0
\(136\) 3916.58 2.46944
\(137\) −1150.07 1991.99i −0.717207 1.24224i −0.962102 0.272690i \(-0.912087\pi\)
0.244895 0.969550i \(-0.421247\pi\)
\(138\) 0 0
\(139\) 677.963 1174.27i 0.413698 0.716546i −0.581593 0.813480i \(-0.697570\pi\)
0.995291 + 0.0969339i \(0.0309035\pi\)
\(140\) 1161.93 2012.52i 0.701435 1.21492i
\(141\) 0 0
\(142\) −1107.63 1918.47i −0.654577 1.13376i
\(143\) 1895.31 1.10835
\(144\) 0 0
\(145\) 1028.29 0.588929
\(146\) −2416.21 4185.00i −1.36964 2.37228i
\(147\) 0 0
\(148\) 3215.26 5568.99i 1.78576 3.09303i
\(149\) −129.923 + 225.032i −0.0714340 + 0.123727i −0.899530 0.436859i \(-0.856091\pi\)
0.828096 + 0.560586i \(0.189424\pi\)
\(150\) 0 0
\(151\) 254.152 + 440.204i 0.136971 + 0.237240i 0.926349 0.376667i \(-0.122930\pi\)
−0.789378 + 0.613908i \(0.789597\pi\)
\(152\) 5999.34 3.20139
\(153\) 0 0
\(154\) −3678.15 −1.92463
\(155\) −45.6242 79.0235i −0.0236428 0.0409504i
\(156\) 0 0
\(157\) 11.6526 20.1829i 0.00592342 0.0102597i −0.863049 0.505121i \(-0.831448\pi\)
0.868972 + 0.494861i \(0.164781\pi\)
\(158\) −63.5252 + 110.029i −0.0319860 + 0.0554014i
\(159\) 0 0
\(160\) 754.560 + 1306.94i 0.372833 + 0.645765i
\(161\) −3777.49 −1.84912
\(162\) 0 0
\(163\) −4032.10 −1.93754 −0.968769 0.247964i \(-0.920238\pi\)
−0.968769 + 0.247964i \(0.920238\pi\)
\(164\) 1866.31 + 3232.54i 0.888623 + 1.53914i
\(165\) 0 0
\(166\) 1419.42 2458.50i 0.663663 1.14950i
\(167\) 335.955 581.892i 0.155671 0.269630i −0.777632 0.628719i \(-0.783579\pi\)
0.933303 + 0.359090i \(0.116913\pi\)
\(168\) 0 0
\(169\) −1039.55 1800.56i −0.473169 0.819552i
\(170\) −1772.69 −0.799761
\(171\) 0 0
\(172\) 6378.49 2.82765
\(173\) −816.764 1414.68i −0.358944 0.621710i 0.628840 0.777534i \(-0.283530\pi\)
−0.987785 + 0.155825i \(0.950197\pi\)
\(174\) 0 0
\(175\) −305.017 + 528.305i −0.131755 + 0.228206i
\(176\) 2121.78 3675.04i 0.908725 1.57396i
\(177\) 0 0
\(178\) 218.775 + 378.929i 0.0921227 + 0.159561i
\(179\) 341.260 0.142497 0.0712485 0.997459i \(-0.477302\pi\)
0.0712485 + 0.997459i \(0.477302\pi\)
\(180\) 0 0
\(181\) −1695.92 −0.696447 −0.348223 0.937412i \(-0.613215\pi\)
−0.348223 + 0.937412i \(0.613215\pi\)
\(182\) 4149.23 + 7186.67i 1.68990 + 2.92699i
\(183\) 0 0
\(184\) 4446.95 7702.34i 1.78170 3.08600i
\(185\) −844.033 + 1461.91i −0.335430 + 0.580982i
\(186\) 0 0
\(187\) 987.941 + 1711.16i 0.386339 + 0.669159i
\(188\) −95.3107 −0.0369747
\(189\) 0 0
\(190\) −2715.38 −1.03681
\(191\) 363.226 + 629.125i 0.137603 + 0.238335i 0.926589 0.376076i \(-0.122727\pi\)
−0.788986 + 0.614411i \(0.789394\pi\)
\(192\) 0 0
\(193\) −2123.63 + 3678.24i −0.792032 + 1.37184i 0.132674 + 0.991160i \(0.457644\pi\)
−0.924707 + 0.380681i \(0.875690\pi\)
\(194\) −2152.07 + 3727.50i −0.796442 + 1.37948i
\(195\) 0 0
\(196\) −2403.97 4163.80i −0.876082 1.51742i
\(197\) 2678.52 0.968713 0.484357 0.874871i \(-0.339054\pi\)
0.484357 + 0.874871i \(0.339054\pi\)
\(198\) 0 0
\(199\) 1486.48 0.529517 0.264759 0.964315i \(-0.414708\pi\)
0.264759 + 0.964315i \(0.414708\pi\)
\(200\) −718.146 1243.87i −0.253903 0.439773i
\(201\) 0 0
\(202\) −2141.57 + 3709.31i −0.745944 + 1.29201i
\(203\) 2509.16 4346.00i 0.867530 1.50261i
\(204\) 0 0
\(205\) −489.923 848.571i −0.166915 0.289106i
\(206\) 6090.97 2.06009
\(207\) 0 0
\(208\) −9574.12 −3.19157
\(209\) 1513.31 + 2621.13i 0.500850 + 0.867498i
\(210\) 0 0
\(211\) 2413.71 4180.66i 0.787519 1.36402i −0.139964 0.990157i \(-0.544699\pi\)
0.927483 0.373866i \(-0.121968\pi\)
\(212\) 3047.18 5277.87i 0.987176 1.70984i
\(213\) 0 0
\(214\) −2660.68 4608.44i −0.849909 1.47209i
\(215\) −1674.41 −0.531134
\(216\) 0 0
\(217\) −445.317 −0.139309
\(218\) 1049.62 + 1817.99i 0.326096 + 0.564815i
\(219\) 0 0
\(220\) −1380.14 + 2390.47i −0.422949 + 0.732570i
\(221\) 2228.94 3860.64i 0.678438 1.17509i
\(222\) 0 0
\(223\) −1387.24 2402.77i −0.416576 0.721532i 0.579016 0.815316i \(-0.303437\pi\)
−0.995593 + 0.0937845i \(0.970104\pi\)
\(224\) 7364.91 2.19683
\(225\) 0 0
\(226\) 5628.19 1.65655
\(227\) 2550.67 + 4417.89i 0.745788 + 1.29174i 0.949826 + 0.312779i \(0.101260\pi\)
−0.204038 + 0.978963i \(0.565407\pi\)
\(228\) 0 0
\(229\) 2048.91 3548.82i 0.591249 1.02407i −0.402816 0.915281i \(-0.631968\pi\)
0.994065 0.108792i \(-0.0346983\pi\)
\(230\) −2012.75 + 3486.18i −0.577028 + 0.999443i
\(231\) 0 0
\(232\) 5907.69 + 10232.4i 1.67181 + 2.89565i
\(233\) 357.613 0.100549 0.0502747 0.998735i \(-0.483990\pi\)
0.0502747 + 0.998735i \(0.483990\pi\)
\(234\) 0 0
\(235\) 25.0199 0.00694519
\(236\) −4100.91 7102.99i −1.13113 1.95918i
\(237\) 0 0
\(238\) −4325.61 + 7492.18i −1.17810 + 2.04053i
\(239\) 175.841 304.566i 0.0475909 0.0824298i −0.841249 0.540648i \(-0.818179\pi\)
0.888840 + 0.458219i \(0.151512\pi\)
\(240\) 0 0
\(241\) 3082.76 + 5339.51i 0.823976 + 1.42717i 0.902699 + 0.430273i \(0.141583\pi\)
−0.0787225 + 0.996897i \(0.525084\pi\)
\(242\) −2553.19 −0.678204
\(243\) 0 0
\(244\) 11325.0 2.97134
\(245\) 631.064 + 1093.03i 0.164560 + 0.285026i
\(246\) 0 0
\(247\) 3414.25 5913.65i 0.879528 1.52339i
\(248\) 524.238 908.006i 0.134230 0.232494i
\(249\) 0 0
\(250\) 325.042 + 562.989i 0.0822298 + 0.142426i
\(251\) 3245.53 0.816160 0.408080 0.912946i \(-0.366198\pi\)
0.408080 + 0.912946i \(0.366198\pi\)
\(252\) 0 0
\(253\) 4486.90 1.11498
\(254\) 2013.00 + 3486.62i 0.497271 + 0.861299i
\(255\) 0 0
\(256\) 2484.63 4303.50i 0.606598 1.05066i
\(257\) −1776.10 + 3076.29i −0.431089 + 0.746668i −0.996967 0.0778206i \(-0.975204\pi\)
0.565878 + 0.824489i \(0.308537\pi\)
\(258\) 0 0
\(259\) 4119.11 + 7134.51i 0.988220 + 1.71165i
\(260\) 6227.59 1.48546
\(261\) 0 0
\(262\) −6313.81 −1.48881
\(263\) −2208.29 3824.88i −0.517754 0.896776i −0.999787 0.0206232i \(-0.993435\pi\)
0.482033 0.876153i \(-0.339898\pi\)
\(264\) 0 0
\(265\) −799.913 + 1385.49i −0.185427 + 0.321170i
\(266\) −6625.89 + 11476.4i −1.52729 + 2.64534i
\(267\) 0 0
\(268\) −1865.43 3231.01i −0.425183 0.736439i
\(269\) −3419.93 −0.775155 −0.387578 0.921837i \(-0.626688\pi\)
−0.387578 + 0.921837i \(0.626688\pi\)
\(270\) 0 0
\(271\) 716.407 0.160585 0.0802927 0.996771i \(-0.474415\pi\)
0.0802927 + 0.996771i \(0.474415\pi\)
\(272\) −4990.56 8643.91i −1.11249 1.92689i
\(273\) 0 0
\(274\) −5981.15 + 10359.7i −1.31874 + 2.28412i
\(275\) 362.298 627.519i 0.0794451 0.137603i
\(276\) 0 0
\(277\) −328.764 569.437i −0.0713124 0.123517i 0.828164 0.560485i \(-0.189385\pi\)
−0.899477 + 0.436969i \(0.856052\pi\)
\(278\) −7051.72 −1.52135
\(279\) 0 0
\(280\) −7009.49 −1.49606
\(281\) −756.957 1311.09i −0.160698 0.278338i 0.774421 0.632671i \(-0.218041\pi\)
−0.935119 + 0.354333i \(0.884708\pi\)
\(282\) 0 0
\(283\) −1953.19 + 3383.03i −0.410266 + 0.710601i −0.994919 0.100682i \(-0.967897\pi\)
0.584653 + 0.811284i \(0.301231\pi\)
\(284\) −4056.58 + 7026.20i −0.847584 + 1.46806i
\(285\) 0 0
\(286\) −4928.44 8536.31i −1.01897 1.76491i
\(287\) −4781.91 −0.983509
\(288\) 0 0
\(289\) −265.611 −0.0540629
\(290\) −2673.90 4631.32i −0.541436 0.937795i
\(291\) 0 0
\(292\) −8849.16 + 15327.2i −1.77349 + 3.07177i
\(293\) 4024.38 6970.43i 0.802413 1.38982i −0.115611 0.993295i \(-0.536883\pi\)
0.918024 0.396525i \(-0.129784\pi\)
\(294\) 0 0
\(295\) 1076.53 + 1864.60i 0.212467 + 0.368004i
\(296\) −19396.4 −3.80877
\(297\) 0 0
\(298\) 1351.37 0.262693
\(299\) −5061.55 8766.87i −0.978987 1.69566i
\(300\) 0 0
\(301\) −4085.78 + 7076.78i −0.782394 + 1.35515i
\(302\) 1321.76 2289.35i 0.251850 0.436217i
\(303\) 0 0
\(304\) −7644.44 13240.6i −1.44223 2.49802i
\(305\) −2972.91 −0.558125
\(306\) 0 0
\(307\) 101.564 0.0188814 0.00944068 0.999955i \(-0.496995\pi\)
0.00944068 + 0.999955i \(0.496995\pi\)
\(308\) 6735.44 + 11666.1i 1.24606 + 2.15824i
\(309\) 0 0
\(310\) −237.277 + 410.975i −0.0434723 + 0.0752962i
\(311\) 3842.29 6655.05i 0.700567 1.21342i −0.267700 0.963502i \(-0.586264\pi\)
0.968268 0.249916i \(-0.0804030\pi\)
\(312\) 0 0
\(313\) 672.575 + 1164.93i 0.121457 + 0.210370i 0.920343 0.391113i \(-0.127910\pi\)
−0.798885 + 0.601484i \(0.794577\pi\)
\(314\) −121.202 −0.0217830
\(315\) 0 0
\(316\) 465.310 0.0828346
\(317\) −3811.17 6601.13i −0.675257 1.16958i −0.976394 0.215998i \(-0.930699\pi\)
0.301137 0.953581i \(-0.402634\pi\)
\(318\) 0 0
\(319\) −2980.38 + 5162.17i −0.523101 + 0.906037i
\(320\) 995.991 1725.11i 0.173993 0.301364i
\(321\) 0 0
\(322\) 9822.74 + 17013.5i 1.70000 + 2.94449i
\(323\) 7118.78 1.22631
\(324\) 0 0
\(325\) −1634.80 −0.279022
\(326\) 10484.8 + 18160.2i 1.78129 + 3.08528i
\(327\) 0 0
\(328\) 5629.37 9750.36i 0.947653 1.64138i
\(329\) 61.0519 105.745i 0.0102307 0.0177201i
\(330\) 0 0
\(331\) 3292.54 + 5702.85i 0.546751 + 0.947000i 0.998494 + 0.0548525i \(0.0174689\pi\)
−0.451744 + 0.892148i \(0.649198\pi\)
\(332\) −10397.0 −1.71870
\(333\) 0 0
\(334\) −3494.39 −0.572468
\(335\) 489.691 + 848.170i 0.0798647 + 0.138330i
\(336\) 0 0
\(337\) 1473.47 2552.13i 0.238175 0.412532i −0.722015 0.691877i \(-0.756784\pi\)
0.960191 + 0.279345i \(0.0901174\pi\)
\(338\) −5406.36 + 9364.10i −0.870022 + 1.50692i
\(339\) 0 0
\(340\) 3246.16 + 5622.52i 0.517788 + 0.896835i
\(341\) 528.947 0.0840002
\(342\) 0 0
\(343\) −2210.14 −0.347919
\(344\) −9619.76 16661.9i −1.50774 2.61148i
\(345\) 0 0
\(346\) −4247.72 + 7357.26i −0.659996 + 1.14315i
\(347\) −4246.74 + 7355.57i −0.656994 + 1.13795i 0.324396 + 0.945921i \(0.394839\pi\)
−0.981390 + 0.192025i \(0.938494\pi\)
\(348\) 0 0
\(349\) −2823.27 4890.05i −0.433027 0.750024i 0.564106 0.825703i \(-0.309221\pi\)
−0.997132 + 0.0756785i \(0.975888\pi\)
\(350\) 3172.58 0.484519
\(351\) 0 0
\(352\) −8748.03 −1.32464
\(353\) 610.966 + 1058.22i 0.0921202 + 0.159557i 0.908403 0.418096i \(-0.137302\pi\)
−0.816283 + 0.577652i \(0.803969\pi\)
\(354\) 0 0
\(355\) 1064.89 1844.44i 0.159207 0.275754i
\(356\) 801.242 1387.79i 0.119286 0.206609i
\(357\) 0 0
\(358\) −887.390 1537.00i −0.131006 0.226908i
\(359\) −4151.44 −0.610319 −0.305160 0.952301i \(-0.598710\pi\)
−0.305160 + 0.952301i \(0.598710\pi\)
\(360\) 0 0
\(361\) 4045.41 0.589796
\(362\) 4409.96 + 7638.28i 0.640283 + 1.10900i
\(363\) 0 0
\(364\) 15196.2 26320.5i 2.18817 3.79003i
\(365\) 2322.98 4023.52i 0.333125 0.576989i
\(366\) 0 0
\(367\) 3519.36 + 6095.70i 0.500569 + 0.867011i 1.00000 0.000657484i \(0.000209284\pi\)
−0.499430 + 0.866354i \(0.666457\pi\)
\(368\) −22665.5 −3.21065
\(369\) 0 0
\(370\) 8779.08 1.23352
\(371\) 3903.79 + 6761.56i 0.546293 + 0.946207i
\(372\) 0 0
\(373\) 3559.78 6165.72i 0.494152 0.855896i −0.505826 0.862636i \(-0.668812\pi\)
0.999977 + 0.00674002i \(0.00214543\pi\)
\(374\) 5137.95 8899.20i 0.710367 1.23039i
\(375\) 0 0
\(376\) 143.744 + 248.971i 0.0197154 + 0.0341482i
\(377\) 13448.4 1.83720
\(378\) 0 0
\(379\) 3372.29 0.457053 0.228526 0.973538i \(-0.426609\pi\)
0.228526 + 0.973538i \(0.426609\pi\)
\(380\) 4972.41 + 8612.47i 0.671261 + 1.16266i
\(381\) 0 0
\(382\) 1889.02 3271.87i 0.253012 0.438229i
\(383\) −1979.32 + 3428.28i −0.264069 + 0.457381i −0.967319 0.253562i \(-0.918398\pi\)
0.703250 + 0.710942i \(0.251731\pi\)
\(384\) 0 0
\(385\) −1768.11 3062.46i −0.234056 0.405396i
\(386\) 22088.6 2.91264
\(387\) 0 0
\(388\) 15763.5 2.06256
\(389\) −4827.00 8360.61i −0.629148 1.08972i −0.987723 0.156216i \(-0.950070\pi\)
0.358574 0.933501i \(-0.383263\pi\)
\(390\) 0 0
\(391\) 5276.72 9139.55i 0.682494 1.18211i
\(392\) −7251.13 + 12559.3i −0.934279 + 1.61822i
\(393\) 0 0
\(394\) −6965.04 12063.8i −0.890594 1.54255i
\(395\) −122.148 −0.0155593
\(396\) 0 0
\(397\) 10928.3 1.38155 0.690776 0.723068i \(-0.257269\pi\)
0.690776 + 0.723068i \(0.257269\pi\)
\(398\) −3865.35 6694.99i −0.486816 0.843189i
\(399\) 0 0
\(400\) −1830.14 + 3169.90i −0.228768 + 0.396237i
\(401\) −2042.78 + 3538.21i −0.254393 + 0.440622i −0.964731 0.263239i \(-0.915209\pi\)
0.710337 + 0.703862i \(0.248542\pi\)
\(402\) 0 0
\(403\) −596.691 1033.50i −0.0737551 0.127748i
\(404\) 15686.6 1.93178
\(405\) 0 0
\(406\) −26098.7 −3.19028
\(407\) −4892.67 8474.35i −0.595874 1.03208i
\(408\) 0 0
\(409\) −5078.13 + 8795.57i −0.613930 + 1.06336i 0.376642 + 0.926359i \(0.377079\pi\)
−0.990571 + 0.136998i \(0.956255\pi\)
\(410\) −2547.93 + 4413.14i −0.306910 + 0.531584i
\(411\) 0 0
\(412\) −11153.8 19319.0i −1.33376 2.31014i
\(413\) 10507.5 1.25191
\(414\) 0 0
\(415\) 2729.29 0.322833
\(416\) 9868.43 + 17092.6i 1.16308 + 2.01451i
\(417\) 0 0
\(418\) 7870.22 13631.6i 0.920921 1.59508i
\(419\) −7939.41 + 13751.5i −0.925693 + 1.60335i −0.135250 + 0.990811i \(0.543184\pi\)
−0.790443 + 0.612536i \(0.790149\pi\)
\(420\) 0 0
\(421\) 1139.92 + 1974.40i 0.131963 + 0.228567i 0.924433 0.381344i \(-0.124539\pi\)
−0.792470 + 0.609911i \(0.791205\pi\)
\(422\) −25105.8 −2.89604
\(423\) 0 0
\(424\) −18382.5 −2.10551
\(425\) −852.147 1475.96i −0.0972593 0.168458i
\(426\) 0 0
\(427\) −7254.29 + 12564.8i −0.822154 + 1.42401i
\(428\) −9744.51 + 16878.0i −1.10051 + 1.90614i
\(429\) 0 0
\(430\) 4354.03 + 7541.39i 0.488302 + 0.845763i
\(431\) −1947.38 −0.217638 −0.108819 0.994062i \(-0.534707\pi\)
−0.108819 + 0.994062i \(0.534707\pi\)
\(432\) 0 0
\(433\) 12636.2 1.40244 0.701219 0.712946i \(-0.252639\pi\)
0.701219 + 0.712946i \(0.252639\pi\)
\(434\) 1157.97 + 2005.67i 0.128075 + 0.221832i
\(435\) 0 0
\(436\) 3844.12 6658.22i 0.422248 0.731355i
\(437\) 8082.78 13999.8i 0.884787 1.53250i
\(438\) 0 0
\(439\) 7924.92 + 13726.4i 0.861585 + 1.49231i 0.870399 + 0.492347i \(0.163861\pi\)
−0.00881399 + 0.999961i \(0.502806\pi\)
\(440\) 8325.86 0.902090
\(441\) 0 0
\(442\) −23184.0 −2.49491
\(443\) 8727.78 + 15117.0i 0.936048 + 1.62128i 0.772754 + 0.634706i \(0.218879\pi\)
0.163294 + 0.986577i \(0.447788\pi\)
\(444\) 0 0
\(445\) −210.333 + 364.308i −0.0224062 + 0.0388086i
\(446\) −7214.59 + 12496.0i −0.765965 + 1.32669i
\(447\) 0 0
\(448\) −4860.70 8418.99i −0.512604 0.887857i
\(449\) −16068.1 −1.68887 −0.844435 0.535658i \(-0.820064\pi\)
−0.844435 + 0.535658i \(0.820064\pi\)
\(450\) 0 0
\(451\) 5679.94 0.593033
\(452\) −10306.4 17851.1i −1.07250 1.85762i
\(453\) 0 0
\(454\) 13265.2 22976.0i 1.37129 2.37515i
\(455\) −3989.13 + 6909.37i −0.411018 + 0.711904i
\(456\) 0 0
\(457\) −5945.86 10298.5i −0.608612 1.05415i −0.991469 0.130339i \(-0.958393\pi\)
0.382858 0.923807i \(-0.374940\pi\)
\(458\) −21311.4 −2.17428
\(459\) 0 0
\(460\) 14743.0 1.49434
\(461\) 1401.11 + 2426.80i 0.141554 + 0.245179i 0.928082 0.372376i \(-0.121457\pi\)
−0.786528 + 0.617555i \(0.788123\pi\)
\(462\) 0 0
\(463\) 6466.66 11200.6i 0.649096 1.12427i −0.334244 0.942487i \(-0.608481\pi\)
0.983339 0.181780i \(-0.0581859\pi\)
\(464\) 15055.3 26076.6i 1.50631 2.60900i
\(465\) 0 0
\(466\) −929.915 1610.66i −0.0924409 0.160112i
\(467\) 5748.11 0.569573 0.284787 0.958591i \(-0.408077\pi\)
0.284787 + 0.958591i \(0.408077\pi\)
\(468\) 0 0
\(469\) 4779.65 0.470583
\(470\) −65.0602 112.688i −0.00638511 0.0110593i
\(471\) 0 0
\(472\) −12369.6 + 21424.9i −1.20627 + 2.08932i
\(473\) 4853.09 8405.79i 0.471766 0.817122i
\(474\) 0 0
\(475\) −1305.30 2260.85i −0.126087 0.218389i
\(476\) 31684.3 3.05094
\(477\) 0 0
\(478\) −1828.98 −0.175012
\(479\) 5608.66 + 9714.48i 0.535002 + 0.926651i 0.999163 + 0.0409004i \(0.0130226\pi\)
−0.464161 + 0.885751i \(0.653644\pi\)
\(480\) 0 0
\(481\) −11038.6 + 19119.4i −1.04640 + 1.81241i
\(482\) 16032.4 27769.0i 1.51506 2.62416i
\(483\) 0 0
\(484\) 4675.42 + 8098.06i 0.439089 + 0.760524i
\(485\) −4138.07 −0.387423
\(486\) 0 0
\(487\) −8905.12 −0.828603 −0.414301 0.910140i \(-0.635974\pi\)
−0.414301 + 0.910140i \(0.635974\pi\)
\(488\) −17079.8 29583.1i −1.58436 2.74419i
\(489\) 0 0
\(490\) 3281.95 5684.51i 0.302579 0.524082i
\(491\) 3276.55 5675.15i 0.301158 0.521621i −0.675240 0.737598i \(-0.735960\pi\)
0.976399 + 0.215976i \(0.0692934\pi\)
\(492\) 0 0
\(493\) 7010.03 + 12141.7i 0.640397 + 1.10920i
\(494\) −35512.8 −3.23440
\(495\) 0 0
\(496\) −2671.96 −0.241884
\(497\) −5196.94 9001.37i −0.469044 0.812407i
\(498\) 0 0
\(499\) 2305.04 3992.45i 0.206789 0.358170i −0.743912 0.668278i \(-0.767032\pi\)
0.950701 + 0.310108i \(0.100365\pi\)
\(500\) 1190.44 2061.90i 0.106476 0.184422i
\(501\) 0 0
\(502\) −8439.47 14617.6i −0.750343 1.29963i
\(503\) 13069.1 1.15850 0.579249 0.815151i \(-0.303346\pi\)
0.579249 + 0.815151i \(0.303346\pi\)
\(504\) 0 0
\(505\) −4117.88 −0.362858
\(506\) −11667.4 20208.6i −1.02506 1.77546i
\(507\) 0 0
\(508\) 7372.43 12769.4i 0.643895 1.11526i
\(509\) −7965.40 + 13796.5i −0.693635 + 1.20141i 0.277004 + 0.960869i \(0.410659\pi\)
−0.970639 + 0.240542i \(0.922675\pi\)
\(510\) 0 0
\(511\) −11336.8 19635.9i −0.981428 1.69988i
\(512\) −23102.1 −1.99410
\(513\) 0 0
\(514\) 18473.8 1.58530
\(515\) 2927.97 + 5071.40i 0.250528 + 0.433927i
\(516\) 0 0
\(517\) −72.5174 + 125.604i −0.00616888 + 0.0106848i
\(518\) 21422.1 37104.2i 1.81705 3.14723i
\(519\) 0 0
\(520\) −9392.19 16267.7i −0.792067 1.37190i
\(521\) 3654.38 0.307296 0.153648 0.988126i \(-0.450898\pi\)
0.153648 + 0.988126i \(0.450898\pi\)
\(522\) 0 0
\(523\) −5138.66 −0.429633 −0.214816 0.976654i \(-0.568915\pi\)
−0.214816 + 0.976654i \(0.568915\pi\)
\(524\) 11561.9 + 20025.7i 0.963898 + 1.66952i
\(525\) 0 0
\(526\) −11484.6 + 19891.9i −0.952002 + 1.64892i
\(527\) 622.057 1077.43i 0.0514179 0.0890584i
\(528\) 0 0
\(529\) −5899.05 10217.5i −0.484840 0.839768i
\(530\) 8320.16 0.681896
\(531\) 0 0
\(532\) 48533.4 3.95524
\(533\) −6407.39 11097.9i −0.520704 0.901885i
\(534\) 0 0
\(535\) 2558.02 4430.62i 0.206716 0.358042i
\(536\) −5626.71 + 9745.75i −0.453427 + 0.785359i
\(537\) 0 0
\(538\) 8892.96 + 15403.1i 0.712645 + 1.23434i
\(539\) −7316.27 −0.584664
\(540\) 0 0
\(541\) 6932.06 0.550892 0.275446 0.961317i \(-0.411175\pi\)
0.275446 + 0.961317i \(0.411175\pi\)
\(542\) −1862.90 3226.64i −0.147635 0.255712i
\(543\) 0 0
\(544\) −10287.9 + 17819.2i −0.810831 + 1.40440i
\(545\) −1009.12 + 1747.84i −0.0793134 + 0.137375i
\(546\) 0 0
\(547\) 1711.56 + 2964.50i 0.133786 + 0.231724i 0.925133 0.379643i \(-0.123953\pi\)
−0.791347 + 0.611367i \(0.790620\pi\)
\(548\) 43810.8 3.41516
\(549\) 0 0
\(550\) −3768.39 −0.292154
\(551\) 10737.8 + 18598.4i 0.830211 + 1.43797i
\(552\) 0 0
\(553\) −298.058 + 516.251i −0.0229199 + 0.0396984i
\(554\) −1709.79 + 2961.45i −0.131123 + 0.227112i
\(555\) 0 0
\(556\) 12913.1 + 22366.2i 0.984962 + 1.70600i
\(557\) −24489.2 −1.86291 −0.931455 0.363856i \(-0.881460\pi\)
−0.931455 + 0.363856i \(0.881460\pi\)
\(558\) 0 0
\(559\) −21898.6 −1.65691
\(560\) 8931.59 + 15470.0i 0.673979 + 1.16737i
\(561\) 0 0
\(562\) −3936.68 + 6818.54i −0.295479 + 0.511784i
\(563\) 5026.54 8706.22i 0.376276 0.651729i −0.614241 0.789118i \(-0.710538\pi\)
0.990517 + 0.137389i \(0.0438711\pi\)
\(564\) 0 0
\(565\) 2705.51 + 4686.08i 0.201454 + 0.348929i
\(566\) 20315.8 1.50872
\(567\) 0 0
\(568\) 24471.8 1.80777
\(569\) 3335.23 + 5776.78i 0.245729 + 0.425616i 0.962336 0.271861i \(-0.0876392\pi\)
−0.716607 + 0.697477i \(0.754306\pi\)
\(570\) 0 0
\(571\) −2316.78 + 4012.77i −0.169797 + 0.294097i −0.938348 0.345691i \(-0.887645\pi\)
0.768551 + 0.639788i \(0.220978\pi\)
\(572\) −18050.0 + 31263.5i −1.31942 + 2.28530i
\(573\) 0 0
\(574\) 12434.6 + 21537.3i 0.904196 + 1.56611i
\(575\) −3870.17 −0.280691
\(576\) 0 0
\(577\) 7045.15 0.508307 0.254154 0.967164i \(-0.418203\pi\)
0.254154 + 0.967164i \(0.418203\pi\)
\(578\) 690.677 + 1196.29i 0.0497031 + 0.0860883i
\(579\) 0 0
\(580\) −9792.89 + 16961.8i −0.701082 + 1.21431i
\(581\) 6659.84 11535.2i 0.475554 0.823683i
\(582\) 0 0
\(583\) −4636.91 8031.37i −0.329402 0.570541i
\(584\) 53383.7 3.78259
\(585\) 0 0
\(586\) −41859.0 −2.95082
\(587\) 4000.53 + 6929.12i 0.281294 + 0.487216i 0.971704 0.236203i \(-0.0759030\pi\)
−0.690410 + 0.723419i \(0.742570\pi\)
\(588\) 0 0
\(589\) 952.855 1650.39i 0.0666582 0.115455i
\(590\) 5598.66 9697.16i 0.390666 0.676654i
\(591\) 0 0
\(592\) 24715.2 + 42808.0i 1.71586 + 2.97196i
\(593\) 6747.53 0.467265 0.233632 0.972325i \(-0.424939\pi\)
0.233632 + 0.972325i \(0.424939\pi\)
\(594\) 0 0
\(595\) −8317.41 −0.573077
\(596\) −2474.63 4286.19i −0.170075 0.294579i
\(597\) 0 0
\(598\) −26323.5 + 45593.6i −1.80008 + 3.11783i
\(599\) −10773.6 + 18660.5i −0.734890 + 1.27287i 0.219881 + 0.975527i \(0.429433\pi\)
−0.954771 + 0.297341i \(0.903900\pi\)
\(600\) 0 0
\(601\) 6077.53 + 10526.6i 0.412492 + 0.714456i 0.995162 0.0982525i \(-0.0313253\pi\)
−0.582670 + 0.812709i \(0.697992\pi\)
\(602\) 42497.6 2.87720
\(603\) 0 0
\(604\) −9681.64 −0.652219
\(605\) −1227.34 2125.81i −0.0824767 0.142854i
\(606\) 0 0
\(607\) −8174.47 + 14158.6i −0.546608 + 0.946754i 0.451895 + 0.892071i \(0.350748\pi\)
−0.998504 + 0.0546827i \(0.982585\pi\)
\(608\) −15758.9 + 27295.2i −1.05116 + 1.82067i
\(609\) 0 0
\(610\) 7730.55 + 13389.7i 0.513116 + 0.888743i
\(611\) 327.220 0.0216660
\(612\) 0 0
\(613\) −29955.5 −1.97372 −0.986859 0.161581i \(-0.948341\pi\)
−0.986859 + 0.161581i \(0.948341\pi\)
\(614\) −264.101 457.437i −0.0173587 0.0300662i
\(615\) 0 0
\(616\) 20316.2 35188.7i 1.32884 2.30161i
\(617\) −1079.87 + 1870.39i −0.0704603 + 0.122041i −0.899103 0.437737i \(-0.855780\pi\)
0.828643 + 0.559778i \(0.189113\pi\)
\(618\) 0 0
\(619\) −11050.4 19139.9i −0.717535 1.24281i −0.961974 0.273142i \(-0.911937\pi\)
0.244439 0.969665i \(-0.421396\pi\)
\(620\) 1738.01 0.112581
\(621\) 0 0
\(622\) −39965.0 −2.57629
\(623\) 1026.48 + 1777.92i 0.0660114 + 0.114335i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 3497.84 6058.44i 0.223326 0.386811i
\(627\) 0 0
\(628\) 221.946 + 384.422i 0.0141029 + 0.0244269i
\(629\) −23015.7 −1.45898
\(630\) 0 0
\(631\) 18360.1 1.15833 0.579164 0.815211i \(-0.303379\pi\)
0.579164 + 0.815211i \(0.303379\pi\)
\(632\) −701.761 1215.49i −0.0441686 0.0765023i
\(633\) 0 0
\(634\) −19820.6 + 34330.3i −1.24160 + 2.15052i
\(635\) −1935.33 + 3352.09i −0.120947 + 0.209486i
\(636\) 0 0
\(637\) 8253.29 + 14295.1i 0.513355 + 0.889157i
\(638\) 30999.9 1.92367
\(639\) 0 0
\(640\) 1713.32 0.105820
\(641\) 10532.3 + 18242.4i 0.648985 + 1.12407i 0.983366 + 0.181636i \(0.0581393\pi\)
−0.334381 + 0.942438i \(0.608527\pi\)
\(642\) 0 0
\(643\) 5269.57 9127.16i 0.323190 0.559782i −0.657954 0.753058i \(-0.728578\pi\)
0.981144 + 0.193276i \(0.0619112\pi\)
\(644\) 35974.9 62310.3i 2.20126 3.81269i
\(645\) 0 0
\(646\) −18511.2 32062.4i −1.12742 1.95275i
\(647\) 22553.4 1.37043 0.685213 0.728343i \(-0.259709\pi\)
0.685213 + 0.728343i \(0.259709\pi\)
\(648\) 0 0
\(649\) −12480.8 −0.754873
\(650\) 4251.02 + 7362.99i 0.256521 + 0.444308i
\(651\) 0 0
\(652\) 38399.7 66510.2i 2.30652 3.99500i
\(653\) −11312.0 + 19593.0i −0.677908 + 1.17417i 0.297702 + 0.954659i \(0.403780\pi\)
−0.975610 + 0.219512i \(0.929554\pi\)
\(654\) 0 0
\(655\) −3035.09 5256.94i −0.181055 0.313596i
\(656\) −28692.1 −1.70768
\(657\) 0 0
\(658\) −635.022 −0.0376227
\(659\) −3188.30 5522.29i −0.188465 0.326431i 0.756274 0.654255i \(-0.227018\pi\)
−0.944739 + 0.327824i \(0.893685\pi\)
\(660\) 0 0
\(661\) 11048.8 19137.0i 0.650146 1.12609i −0.332941 0.942948i \(-0.608041\pi\)
0.983087 0.183139i \(-0.0586258\pi\)
\(662\) 17123.4 29658.7i 1.00532 1.74126i
\(663\) 0 0
\(664\) 15680.2 + 27159.0i 0.916433 + 1.58731i
\(665\) −12740.4 −0.742938
\(666\) 0 0
\(667\) 31837.2 1.84819
\(668\) 6398.93 + 11083.3i 0.370632 + 0.641953i
\(669\) 0 0
\(670\) 2546.72 4411.05i 0.146848 0.254349i
\(671\) 8616.63 14924.4i 0.495740 0.858646i
\(672\) 0 0
\(673\) −12016.5 20813.2i −0.688264 1.19211i −0.972399 0.233323i \(-0.925040\pi\)
0.284136 0.958784i \(-0.408293\pi\)
\(674\) −15326.1 −0.875873
\(675\) 0 0
\(676\) 39600.6 2.25311
\(677\) −89.8191 155.571i −0.00509901 0.00883175i 0.863465 0.504409i \(-0.168290\pi\)
−0.868564 + 0.495578i \(0.834956\pi\)
\(678\) 0 0
\(679\) −10097.4 + 17489.3i −0.570698 + 0.988478i
\(680\) 9791.45 16959.3i 0.552184 0.956411i
\(681\) 0 0
\(682\) −1375.44 2382.33i −0.0772262 0.133760i
\(683\) −30434.2 −1.70502 −0.852511 0.522709i \(-0.824921\pi\)
−0.852511 + 0.522709i \(0.824921\pi\)
\(684\) 0 0
\(685\) −11500.7 −0.641490
\(686\) 5747.11 + 9954.28i 0.319862 + 0.554018i
\(687\) 0 0
\(688\) −24515.3 + 42461.7i −1.35848 + 2.35296i
\(689\) −10461.6 + 18120.0i −0.578453 + 1.00191i
\(690\) 0 0
\(691\) −4896.36 8480.75i −0.269561 0.466893i 0.699188 0.714938i \(-0.253545\pi\)
−0.968748 + 0.248045i \(0.920212\pi\)
\(692\) 31113.7 1.70920
\(693\) 0 0
\(694\) 44171.8 2.41605
\(695\) −3389.81 5871.33i −0.185011 0.320449i
\(696\) 0 0
\(697\) 6679.78 11569.7i 0.363005 0.628743i
\(698\) −14682.9 + 25431.5i −0.796212 + 1.37908i
\(699\) 0 0
\(700\) −5809.65 10062.6i −0.313691 0.543329i
\(701\) 8130.47 0.438065 0.219032 0.975718i \(-0.429710\pi\)
0.219032 + 0.975718i \(0.429710\pi\)
\(702\) 0 0
\(703\) −35255.0 −1.89142
\(704\) 5773.54 + 10000.1i 0.309089 + 0.535357i
\(705\) 0 0
\(706\) 3177.43 5503.47i 0.169383 0.293379i
\(707\) −10048.2 + 17404.0i −0.534513 + 0.925804i
\(708\) 0 0
\(709\) 2429.98 + 4208.84i 0.128716 + 0.222943i 0.923179 0.384369i \(-0.125581\pi\)
−0.794463 + 0.607312i \(0.792248\pi\)
\(710\) −11076.3 −0.585472
\(711\) 0 0
\(712\) −4833.59 −0.254419
\(713\) −1412.59 2446.67i −0.0741961 0.128511i
\(714\) 0 0
\(715\) 4738.28 8206.94i 0.247834 0.429262i
\(716\) −3249.98 + 5629.13i −0.169633 + 0.293814i
\(717\) 0 0
\(718\) 10795.1 + 18697.7i 0.561101 + 0.971856i
\(719\) 19463.0 1.00952 0.504762 0.863259i \(-0.331580\pi\)
0.504762 + 0.863259i \(0.331580\pi\)
\(720\) 0 0
\(721\) 28578.6 1.47618
\(722\) −10519.4 18220.2i −0.542233 0.939175i
\(723\) 0 0
\(724\) 16151.1 27974.5i 0.829075 1.43600i
\(725\) 2570.72 4452.62i 0.131689 0.228091i
\(726\) 0 0
\(727\) −1216.33 2106.75i −0.0620512 0.107476i 0.833331 0.552774i \(-0.186431\pi\)
−0.895382 + 0.445299i \(0.853098\pi\)
\(728\) −91672.8 −4.66706
\(729\) 0 0
\(730\) −24162.1 −1.22504
\(731\) −11414.7 19770.9i −0.577551 1.00035i
\(732\) 0 0
\(733\) 8983.79 15560.4i 0.452693 0.784087i −0.545859 0.837877i \(-0.683797\pi\)
0.998552 + 0.0537895i \(0.0171300\pi\)
\(734\) 18303.0 31701.8i 0.920404 1.59419i
\(735\) 0 0
\(736\) 23362.2 + 40464.5i 1.17003 + 2.02655i
\(737\) −5677.26 −0.283751
\(738\) 0 0
\(739\) 23473.0 1.16843 0.584214 0.811599i \(-0.301403\pi\)
0.584214 + 0.811599i \(0.301403\pi\)
\(740\) −16076.3 27844.9i −0.798616 1.38324i
\(741\) 0 0
\(742\) 20302.3 35164.6i 1.00448 1.73980i
\(743\) 16779.6 29063.2i 0.828512 1.43503i −0.0706932 0.997498i \(-0.522521\pi\)
0.899205 0.437527i \(-0.144146\pi\)
\(744\) 0 0
\(745\) 649.613 + 1125.16i 0.0319463 + 0.0553325i
\(746\) −37026.5 −1.81721
\(747\) 0 0
\(748\) −37634.6 −1.83965
\(749\) −12483.8 21622.6i −0.609011 1.05484i
\(750\) 0 0
\(751\) 3891.38 6740.06i 0.189079 0.327495i −0.755864 0.654728i \(-0.772783\pi\)
0.944943 + 0.327234i \(0.106116\pi\)
\(752\) 366.320 634.485i 0.0177637 0.0307677i
\(753\) 0 0
\(754\) −34970.2 60570.2i −1.68905 2.92551i
\(755\) 2541.52 0.122510
\(756\) 0 0
\(757\) −38154.3 −1.83189 −0.915946 0.401300i \(-0.868558\pi\)
−0.915946 + 0.401300i \(0.868558\pi\)
\(758\) −8769.09 15188.5i −0.420195 0.727799i
\(759\) 0 0
\(760\) 14998.4 25977.9i 0.715852 1.23989i
\(761\) −9933.56 + 17205.4i −0.473182 + 0.819575i −0.999529 0.0306951i \(-0.990228\pi\)
0.526347 + 0.850270i \(0.323561\pi\)
\(762\) 0 0
\(763\) 4924.76 + 8529.93i 0.233667 + 0.404724i
\(764\) −13836.7 −0.655228
\(765\) 0 0
\(766\) 20587.5 0.971094
\(767\) 14079.2 + 24385.9i 0.662805 + 1.14801i
\(768\) 0 0
\(769\) 7855.40 13605.9i 0.368365 0.638027i −0.620945 0.783854i \(-0.713251\pi\)
0.989310 + 0.145827i \(0.0465843\pi\)
\(770\) −9195.37 + 15926.9i −0.430361 + 0.745408i
\(771\) 0 0
\(772\) −40448.7 70059.3i −1.88573 3.26618i
\(773\) 25811.9 1.20102 0.600510 0.799617i \(-0.294964\pi\)
0.600510 + 0.799617i \(0.294964\pi\)
\(774\) 0 0
\(775\) −456.242 −0.0211467
\(776\) −23773.9 41177.6i −1.09978 1.90488i
\(777\) 0 0
\(778\) −25103.6 + 43480.8i −1.15682 + 2.00368i
\(779\) 10232.0 17722.3i 0.470600 0.815104i
\(780\) 0 0
\(781\) 6172.92 + 10691.8i 0.282822 + 0.489863i
\(782\) −54885.0 −2.50982
\(783\) 0 0
\(784\) 36958.0 1.68358
\(785\) −58.2629 100.914i