Properties

Label 405.4.e.o.136.1
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.o.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +O(q^{10})\) \(q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +13.6603 q^{10} +(29.7487 - 51.5263i) q^{11} +(12.5359 + 21.7128i) q^{13} +(-9.46410 - 16.3923i) q^{14} +(29.7128 - 51.4641i) q^{16} +112.995 q^{17} -122.779 q^{19} +(1.33975 - 2.32051i) q^{20} +(81.2750 + 140.772i) q^{22} +(48.7128 + 84.3731i) q^{23} +(-12.5000 + 21.6506i) q^{25} -68.4974 q^{26} -3.71281 q^{28} +(63.2846 - 109.612i) q^{29} +(54.1077 + 93.7173i) q^{31} +(-12.1051 - 20.9667i) q^{32} +(-154.354 + 267.349i) q^{34} +34.6410 q^{35} +294.344 q^{37} +(167.720 - 290.499i) q^{38} +(58.3013 + 100.981i) q^{40} +(102.931 + 178.281i) q^{41} +(40.1000 - 69.4552i) q^{43} +31.8846 q^{44} -266.172 q^{46} +(134.856 - 233.578i) q^{47} +(147.500 + 255.477i) q^{49} +(-34.1506 - 59.1506i) q^{50} +(-6.71797 + 11.6359i) q^{52} -98.7949 q^{53} -297.487 q^{55} +(80.7846 - 139.923i) q^{56} +(172.897 + 299.466i) q^{58} +(152.251 + 263.707i) q^{59} +(-333.277 + 577.252i) q^{61} -295.650 q^{62} +541.549 q^{64} +(62.6795 - 108.564i) q^{65} +(317.967 + 550.734i) q^{67} +(30.2769 + 52.4411i) q^{68} +(-47.3205 + 81.9615i) q^{70} -826.482 q^{71} +751.349 q^{73} +(-402.081 + 696.424i) q^{74} +(-32.8987 - 56.9821i) q^{76} +(206.105 + 356.985i) q^{77} +(-11.9334 + 20.6692i) q^{79} -297.128 q^{80} -562.424 q^{82} +(-408.615 + 707.742i) q^{83} +(-282.487 - 489.282i) q^{85} +(109.555 + 189.755i) q^{86} +(-693.755 + 1201.62i) q^{88} -513.000 q^{89} -173.703 q^{91} +(-26.1051 + 45.2154i) q^{92} +(368.435 + 638.147i) q^{94} +(306.949 + 531.651i) q^{95} +(-214.051 + 370.748i) q^{97} -805.955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + O(q^{10}) \) \( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 2.36603i −0.482963 + 0.836516i −0.999809 0.0195623i \(-0.993773\pi\)
0.516846 + 0.856079i \(0.327106\pi\)
\(3\) 0 0
\(4\) 0.267949 + 0.464102i 0.0334936 + 0.0580127i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 0 0
\(7\) −3.46410 + 6.00000i −0.187044 + 0.323970i −0.944263 0.329191i \(-0.893224\pi\)
0.757219 + 0.653161i \(0.226557\pi\)
\(8\) −23.3205 −1.03063
\(9\) 0 0
\(10\) 13.6603 0.431975
\(11\) 29.7487 51.5263i 0.815416 1.41234i −0.0936131 0.995609i \(-0.529842\pi\)
0.909029 0.416733i \(-0.136825\pi\)
\(12\) 0 0
\(13\) 12.5359 + 21.7128i 0.267449 + 0.463235i 0.968202 0.250169i \(-0.0804861\pi\)
−0.700754 + 0.713403i \(0.747153\pi\)
\(14\) −9.46410 16.3923i −0.180671 0.312931i
\(15\) 0 0
\(16\) 29.7128 51.4641i 0.464263 0.804127i
\(17\) 112.995 1.61208 0.806038 0.591864i \(-0.201608\pi\)
0.806038 + 0.591864i \(0.201608\pi\)
\(18\) 0 0
\(19\) −122.779 −1.48250 −0.741251 0.671228i \(-0.765767\pi\)
−0.741251 + 0.671228i \(0.765767\pi\)
\(20\) 1.33975 2.32051i 0.0149788 0.0259441i
\(21\) 0 0
\(22\) 81.2750 + 140.772i 0.787631 + 1.36422i
\(23\) 48.7128 + 84.3731i 0.441623 + 0.764913i 0.997810 0.0661439i \(-0.0210696\pi\)
−0.556187 + 0.831057i \(0.687736\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −68.4974 −0.516671
\(27\) 0 0
\(28\) −3.71281 −0.0250591
\(29\) 63.2846 109.612i 0.405230 0.701878i −0.589119 0.808047i \(-0.700525\pi\)
0.994348 + 0.106168i \(0.0338583\pi\)
\(30\) 0 0
\(31\) 54.1077 + 93.7173i 0.313485 + 0.542972i 0.979114 0.203311i \(-0.0651702\pi\)
−0.665629 + 0.746282i \(0.731837\pi\)
\(32\) −12.1051 20.9667i −0.0668720 0.115826i
\(33\) 0 0
\(34\) −154.354 + 267.349i −0.778572 + 1.34853i
\(35\) 34.6410 0.167297
\(36\) 0 0
\(37\) 294.344 1.30783 0.653916 0.756567i \(-0.273125\pi\)
0.653916 + 0.756567i \(0.273125\pi\)
\(38\) 167.720 290.499i 0.715994 1.24014i
\(39\) 0 0
\(40\) 58.3013 + 100.981i 0.230456 + 0.399162i
\(41\) 102.931 + 178.281i 0.392075 + 0.679094i 0.992723 0.120419i \(-0.0384239\pi\)
−0.600648 + 0.799514i \(0.705091\pi\)
\(42\) 0 0
\(43\) 40.1000 69.4552i 0.142214 0.246321i −0.786116 0.618079i \(-0.787911\pi\)
0.928330 + 0.371757i \(0.121245\pi\)
\(44\) 31.8846 0.109245
\(45\) 0 0
\(46\) −266.172 −0.853150
\(47\) 134.856 233.578i 0.418528 0.724912i −0.577263 0.816558i \(-0.695879\pi\)
0.995792 + 0.0916458i \(0.0292127\pi\)
\(48\) 0 0
\(49\) 147.500 + 255.477i 0.430029 + 0.744832i
\(50\) −34.1506 59.1506i −0.0965926 0.167303i
\(51\) 0 0
\(52\) −6.71797 + 11.6359i −0.0179157 + 0.0310308i
\(53\) −98.7949 −0.256048 −0.128024 0.991771i \(-0.540863\pi\)
−0.128024 + 0.991771i \(0.540863\pi\)
\(54\) 0 0
\(55\) −297.487 −0.729330
\(56\) 80.7846 139.923i 0.192773 0.333893i
\(57\) 0 0
\(58\) 172.897 + 299.466i 0.391422 + 0.677962i
\(59\) 152.251 + 263.707i 0.335956 + 0.581894i 0.983668 0.179992i \(-0.0576072\pi\)
−0.647712 + 0.761886i \(0.724274\pi\)
\(60\) 0 0
\(61\) −333.277 + 577.252i −0.699537 + 1.21163i 0.269091 + 0.963115i \(0.413277\pi\)
−0.968627 + 0.248518i \(0.920056\pi\)
\(62\) −295.650 −0.605606
\(63\) 0 0
\(64\) 541.549 1.05771
\(65\) 62.6795 108.564i 0.119607 0.207165i
\(66\) 0 0
\(67\) 317.967 + 550.734i 0.579788 + 1.00422i 0.995503 + 0.0947278i \(0.0301981\pi\)
−0.415715 + 0.909495i \(0.636469\pi\)
\(68\) 30.2769 + 52.4411i 0.0539943 + 0.0935208i
\(69\) 0 0
\(70\) −47.3205 + 81.9615i −0.0807983 + 0.139947i
\(71\) −826.482 −1.38148 −0.690742 0.723101i \(-0.742716\pi\)
−0.690742 + 0.723101i \(0.742716\pi\)
\(72\) 0 0
\(73\) 751.349 1.20464 0.602320 0.798255i \(-0.294243\pi\)
0.602320 + 0.798255i \(0.294243\pi\)
\(74\) −402.081 + 696.424i −0.631634 + 1.09402i
\(75\) 0 0
\(76\) −32.8987 56.9821i −0.0496544 0.0860039i
\(77\) 206.105 + 356.985i 0.305037 + 0.528340i
\(78\) 0 0
\(79\) −11.9334 + 20.6692i −0.0169950 + 0.0294363i −0.874398 0.485210i \(-0.838743\pi\)
0.857403 + 0.514646i \(0.172077\pi\)
\(80\) −297.128 −0.415249
\(81\) 0 0
\(82\) −562.424 −0.757431
\(83\) −408.615 + 707.742i −0.540378 + 0.935962i 0.458504 + 0.888692i \(0.348385\pi\)
−0.998882 + 0.0472695i \(0.984948\pi\)
\(84\) 0 0
\(85\) −282.487 489.282i −0.360471 0.624354i
\(86\) 109.555 + 189.755i 0.137368 + 0.237928i
\(87\) 0 0
\(88\) −693.755 + 1201.62i −0.840392 + 1.45560i
\(89\) −513.000 −0.610988 −0.305494 0.952194i \(-0.598822\pi\)
−0.305494 + 0.952194i \(0.598822\pi\)
\(90\) 0 0
\(91\) −173.703 −0.200099
\(92\) −26.1051 + 45.2154i −0.0295831 + 0.0512395i
\(93\) 0 0
\(94\) 368.435 + 638.147i 0.404267 + 0.700211i
\(95\) 306.949 + 531.651i 0.331498 + 0.574171i
\(96\) 0 0
\(97\) −214.051 + 370.748i −0.224058 + 0.388079i −0.956036 0.293248i \(-0.905264\pi\)
0.731979 + 0.681328i \(0.238597\pi\)
\(98\) −805.955 −0.830753
\(99\) 0 0
\(100\) −13.3975 −0.0133975
\(101\) 456.043 789.890i 0.449287 0.778188i −0.549052 0.835788i \(-0.685011\pi\)
0.998340 + 0.0575994i \(0.0183446\pi\)
\(102\) 0 0
\(103\) −139.249 241.186i −0.133210 0.230726i 0.791703 0.610907i \(-0.209195\pi\)
−0.924912 + 0.380181i \(0.875862\pi\)
\(104\) −292.344 506.354i −0.275641 0.477424i
\(105\) 0 0
\(106\) 134.956 233.751i 0.123662 0.214188i
\(107\) 1512.33 1.36638 0.683191 0.730240i \(-0.260592\pi\)
0.683191 + 0.730240i \(0.260592\pi\)
\(108\) 0 0
\(109\) 1991.53 1.75004 0.875020 0.484087i \(-0.160848\pi\)
0.875020 + 0.484087i \(0.160848\pi\)
\(110\) 406.375 703.862i 0.352239 0.610096i
\(111\) 0 0
\(112\) 205.856 + 356.554i 0.173675 + 0.300814i
\(113\) −253.951 439.856i −0.211413 0.366179i 0.740744 0.671788i \(-0.234473\pi\)
−0.952157 + 0.305609i \(0.901140\pi\)
\(114\) 0 0
\(115\) 243.564 421.865i 0.197500 0.342080i
\(116\) 67.8282 0.0542905
\(117\) 0 0
\(118\) −831.917 −0.649018
\(119\) −391.426 + 677.969i −0.301529 + 0.522263i
\(120\) 0 0
\(121\) −1104.47 1913.00i −0.829806 1.43727i
\(122\) −910.529 1577.08i −0.675700 1.17035i
\(123\) 0 0
\(124\) −28.9962 + 50.2229i −0.0209995 + 0.0363722i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1845.91 1.28975 0.644873 0.764290i \(-0.276910\pi\)
0.644873 + 0.764290i \(0.276910\pi\)
\(128\) −642.928 + 1113.58i −0.443964 + 0.768968i
\(129\) 0 0
\(130\) 171.244 + 296.603i 0.115531 + 0.200106i
\(131\) 1282.35 + 2221.10i 0.855265 + 1.48136i 0.876399 + 0.481586i \(0.159939\pi\)
−0.0211333 + 0.999777i \(0.506727\pi\)
\(132\) 0 0
\(133\) 425.321 736.677i 0.277293 0.480286i
\(134\) −1737.40 −1.12006
\(135\) 0 0
\(136\) −2635.10 −1.66145
\(137\) 253.390 438.884i 0.158019 0.273696i −0.776135 0.630566i \(-0.782823\pi\)
0.934154 + 0.356870i \(0.116156\pi\)
\(138\) 0 0
\(139\) −1111.32 1924.87i −0.678138 1.17457i −0.975541 0.219818i \(-0.929454\pi\)
0.297403 0.954752i \(-0.403880\pi\)
\(140\) 9.28203 + 16.0770i 0.00560339 + 0.00970536i
\(141\) 0 0
\(142\) 1129.00 1955.48i 0.667206 1.15563i
\(143\) 1491.71 0.872327
\(144\) 0 0
\(145\) −632.846 −0.362448
\(146\) −1026.36 + 1777.71i −0.581796 + 1.00770i
\(147\) 0 0
\(148\) 78.8691 + 136.605i 0.0438041 + 0.0758709i
\(149\) 255.046 + 441.753i 0.140229 + 0.242884i 0.927583 0.373617i \(-0.121883\pi\)
−0.787354 + 0.616502i \(0.788549\pi\)
\(150\) 0 0
\(151\) −337.631 + 584.793i −0.181960 + 0.315164i −0.942548 0.334071i \(-0.891578\pi\)
0.760588 + 0.649235i \(0.224911\pi\)
\(152\) 2863.28 1.52791
\(153\) 0 0
\(154\) −1126.18 −0.589286
\(155\) 270.538 468.586i 0.140195 0.242824i
\(156\) 0 0
\(157\) 1813.99 + 3141.92i 0.922115 + 1.59715i 0.796136 + 0.605118i \(0.206874\pi\)
0.125979 + 0.992033i \(0.459793\pi\)
\(158\) −32.6025 56.4693i −0.0164159 0.0284332i
\(159\) 0 0
\(160\) −60.5256 + 104.833i −0.0299060 + 0.0517988i
\(161\) −674.985 −0.330411
\(162\) 0 0
\(163\) −119.559 −0.0574514 −0.0287257 0.999587i \(-0.509145\pi\)
−0.0287257 + 0.999587i \(0.509145\pi\)
\(164\) −55.1604 + 95.5407i −0.0262641 + 0.0454907i
\(165\) 0 0
\(166\) −1116.36 1933.59i −0.521965 0.904070i
\(167\) −1534.49 2657.82i −0.711035 1.23155i −0.964469 0.264195i \(-0.914894\pi\)
0.253435 0.967353i \(-0.418440\pi\)
\(168\) 0 0
\(169\) 784.203 1358.28i 0.356942 0.618242i
\(170\) 1543.54 0.696376
\(171\) 0 0
\(172\) 42.9790 0.0190530
\(173\) 1056.30 1829.57i 0.464216 0.804046i −0.534950 0.844884i \(-0.679669\pi\)
0.999166 + 0.0408382i \(0.0130028\pi\)
\(174\) 0 0
\(175\) −86.6025 150.000i −0.0374088 0.0647939i
\(176\) −1767.84 3061.98i −0.757134 1.31140i
\(177\) 0 0
\(178\) 700.771 1213.77i 0.295084 0.511101i
\(179\) 1624.79 0.678449 0.339225 0.940705i \(-0.389835\pi\)
0.339225 + 0.940705i \(0.389835\pi\)
\(180\) 0 0
\(181\) −2545.41 −1.04530 −0.522649 0.852548i \(-0.675056\pi\)
−0.522649 + 0.852548i \(0.675056\pi\)
\(182\) 237.282 410.985i 0.0966402 0.167386i
\(183\) 0 0
\(184\) −1136.01 1967.62i −0.455150 0.788343i
\(185\) −735.859 1274.54i −0.292440 0.506521i
\(186\) 0 0
\(187\) 3361.45 5822.20i 1.31451 2.27680i
\(188\) 144.539 0.0560722
\(189\) 0 0
\(190\) −1677.20 −0.640404
\(191\) 2402.83 4161.82i 0.910274 1.57664i 0.0965970 0.995324i \(-0.469204\pi\)
0.813677 0.581317i \(-0.197462\pi\)
\(192\) 0 0
\(193\) −1788.92 3098.50i −0.667198 1.15562i −0.978684 0.205371i \(-0.934160\pi\)
0.311486 0.950251i \(-0.399173\pi\)
\(194\) −584.799 1012.90i −0.216423 0.374856i
\(195\) 0 0
\(196\) −79.0450 + 136.910i −0.0288065 + 0.0498943i
\(197\) 3788.88 1.37029 0.685144 0.728408i \(-0.259739\pi\)
0.685144 + 0.728408i \(0.259739\pi\)
\(198\) 0 0
\(199\) 2048.31 0.729652 0.364826 0.931076i \(-0.381129\pi\)
0.364826 + 0.931076i \(0.381129\pi\)
\(200\) 291.506 504.904i 0.103063 0.178510i
\(201\) 0 0
\(202\) 1245.93 + 2158.02i 0.433978 + 0.751672i
\(203\) 438.449 + 759.415i 0.151591 + 0.262564i
\(204\) 0 0
\(205\) 514.654 891.407i 0.175341 0.303700i
\(206\) 760.869 0.257341
\(207\) 0 0
\(208\) 1489.91 0.496666
\(209\) −3652.53 + 6326.37i −1.20886 + 2.09380i
\(210\) 0 0
\(211\) −1190.90 2062.69i −0.388553 0.672994i 0.603702 0.797210i \(-0.293692\pi\)
−0.992255 + 0.124216i \(0.960358\pi\)
\(212\) −26.4720 45.8509i −0.00857597 0.0148540i
\(213\) 0 0
\(214\) −2065.89 + 3578.22i −0.659911 + 1.14300i
\(215\) −401.000 −0.127200
\(216\) 0 0
\(217\) −749.738 −0.234542
\(218\) −2720.48 + 4712.02i −0.845204 + 1.46394i
\(219\) 0 0
\(220\) −79.7114 138.064i −0.0244279 0.0423104i
\(221\) 1416.49 + 2453.44i 0.431147 + 0.746769i
\(222\) 0 0
\(223\) 278.577 482.510i 0.0836543 0.144893i −0.821163 0.570694i \(-0.806674\pi\)
0.904817 + 0.425801i \(0.140008\pi\)
\(224\) 167.733 0.0500320
\(225\) 0 0
\(226\) 1387.62 0.408419
\(227\) 2589.04 4484.36i 0.757008 1.31118i −0.187362 0.982291i \(-0.559994\pi\)
0.944370 0.328886i \(-0.106673\pi\)
\(228\) 0 0
\(229\) 459.138 + 795.250i 0.132492 + 0.229483i 0.924637 0.380850i \(-0.124369\pi\)
−0.792145 + 0.610334i \(0.791035\pi\)
\(230\) 665.429 + 1152.56i 0.190770 + 0.330423i
\(231\) 0 0
\(232\) −1475.83 + 2556.21i −0.417642 + 0.723377i
\(233\) −5896.92 −1.65803 −0.829013 0.559230i \(-0.811097\pi\)
−0.829013 + 0.559230i \(0.811097\pi\)
\(234\) 0 0
\(235\) −1348.56 −0.374343
\(236\) −81.5912 + 141.320i −0.0225048 + 0.0389795i
\(237\) 0 0
\(238\) −1069.39 1852.25i −0.291254 0.504468i
\(239\) −263.420 456.257i −0.0712938 0.123485i 0.828175 0.560470i \(-0.189379\pi\)
−0.899469 + 0.436985i \(0.856046\pi\)
\(240\) 0 0
\(241\) 2911.60 5043.03i 0.778226 1.34793i −0.154738 0.987956i \(-0.549453\pi\)
0.932963 0.359971i \(-0.117213\pi\)
\(242\) 6034.95 1.60306
\(243\) 0 0
\(244\) −357.205 −0.0937201
\(245\) 737.500 1277.39i 0.192315 0.333099i
\(246\) 0 0
\(247\) −1539.15 2665.89i −0.396493 0.686746i
\(248\) −1261.82 2185.53i −0.323087 0.559603i
\(249\) 0 0
\(250\) −170.753 + 295.753i −0.0431975 + 0.0748203i
\(251\) −3244.98 −0.816022 −0.408011 0.912977i \(-0.633778\pi\)
−0.408011 + 0.912977i \(0.633778\pi\)
\(252\) 0 0
\(253\) 5796.57 1.44042
\(254\) −2521.56 + 4367.46i −0.622900 + 1.07889i
\(255\) 0 0
\(256\) 409.682 + 709.590i 0.100020 + 0.173240i
\(257\) 630.700 + 1092.40i 0.153082 + 0.265145i 0.932359 0.361534i \(-0.117747\pi\)
−0.779277 + 0.626679i \(0.784414\pi\)
\(258\) 0 0
\(259\) −1019.64 + 1766.06i −0.244622 + 0.423698i
\(260\) 67.1797 0.0160243
\(261\) 0 0
\(262\) −7006.91 −1.65225
\(263\) −962.141 + 1666.48i −0.225582 + 0.390720i −0.956494 0.291752i \(-0.905762\pi\)
0.730912 + 0.682472i \(0.239095\pi\)
\(264\) 0 0
\(265\) 246.987 + 427.795i 0.0572540 + 0.0991668i
\(266\) 1162.00 + 2012.64i 0.267844 + 0.463920i
\(267\) 0 0
\(268\) −170.398 + 295.138i −0.0388384 + 0.0672702i
\(269\) −4762.53 −1.07947 −0.539733 0.841836i \(-0.681475\pi\)
−0.539733 + 0.841836i \(0.681475\pi\)
\(270\) 0 0
\(271\) 1595.10 0.357547 0.178774 0.983890i \(-0.442787\pi\)
0.178774 + 0.983890i \(0.442787\pi\)
\(272\) 3357.39 5815.18i 0.748426 1.29631i
\(273\) 0 0
\(274\) 692.274 + 1199.05i 0.152634 + 0.264370i
\(275\) 743.718 + 1288.16i 0.163083 + 0.282468i
\(276\) 0 0
\(277\) −524.792 + 908.966i −0.113833 + 0.197164i −0.917313 0.398168i \(-0.869646\pi\)
0.803480 + 0.595332i \(0.202979\pi\)
\(278\) 6072.38 1.31006
\(279\) 0 0
\(280\) −807.846 −0.172422
\(281\) −3788.02 + 6561.04i −0.804179 + 1.39288i 0.112665 + 0.993633i \(0.464061\pi\)
−0.916844 + 0.399246i \(0.869272\pi\)
\(282\) 0 0
\(283\) 2926.47 + 5068.79i 0.614701 + 1.06469i 0.990437 + 0.137966i \(0.0440566\pi\)
−0.375736 + 0.926727i \(0.622610\pi\)
\(284\) −221.455 383.572i −0.0462709 0.0801436i
\(285\) 0 0
\(286\) −2037.71 + 3529.42i −0.421302 + 0.729716i
\(287\) −1426.25 −0.293341
\(288\) 0 0
\(289\) 7854.84 1.59879
\(290\) 864.484 1497.33i 0.175049 0.303194i
\(291\) 0 0
\(292\) 201.323 + 348.702i 0.0403478 + 0.0698844i
\(293\) 1769.80 + 3065.38i 0.352876 + 0.611199i 0.986752 0.162235i \(-0.0518704\pi\)
−0.633876 + 0.773435i \(0.718537\pi\)
\(294\) 0 0
\(295\) 761.256 1318.53i 0.150244 0.260231i
\(296\) −6864.24 −1.34789
\(297\) 0 0
\(298\) −1393.60 −0.270902
\(299\) −1221.32 + 2115.38i −0.236223 + 0.409150i
\(300\) 0 0
\(301\) 277.821 + 481.200i 0.0532004 + 0.0921458i
\(302\) −922.424 1597.68i −0.175760 0.304425i
\(303\) 0 0
\(304\) −3648.12 + 6318.73i −0.688270 + 1.19212i
\(305\) 3332.77 0.625685
\(306\) 0 0
\(307\) −293.303 −0.0545267 −0.0272634 0.999628i \(-0.508679\pi\)
−0.0272634 + 0.999628i \(0.508679\pi\)
\(308\) −110.451 + 191.307i −0.0204336 + 0.0353921i
\(309\) 0 0
\(310\) 739.125 + 1280.20i 0.135418 + 0.234550i
\(311\) −2295.95 3976.70i −0.418621 0.725074i 0.577180 0.816617i \(-0.304153\pi\)
−0.995801 + 0.0915436i \(0.970820\pi\)
\(312\) 0 0
\(313\) −3870.53 + 6703.95i −0.698962 + 1.21064i 0.269864 + 0.962898i \(0.413021\pi\)
−0.968827 + 0.247740i \(0.920312\pi\)
\(314\) −9911.82 −1.78139
\(315\) 0 0
\(316\) −12.7901 −0.00227690
\(317\) 958.662 1660.45i 0.169854 0.294196i −0.768514 0.639833i \(-0.779004\pi\)
0.938369 + 0.345636i \(0.112337\pi\)
\(318\) 0 0
\(319\) −3765.27 6521.64i −0.660861 1.14465i
\(320\) −1353.87 2344.97i −0.236512 0.409650i
\(321\) 0 0
\(322\) 922.046 1597.03i 0.159576 0.276395i
\(323\) −13873.4 −2.38990
\(324\) 0 0
\(325\) −626.795 −0.106979
\(326\) 163.321 282.879i 0.0277469 0.0480590i
\(327\) 0 0
\(328\) −2400.40 4157.61i −0.404085 0.699895i
\(329\) 934.313 + 1618.28i 0.156566 + 0.271181i
\(330\) 0 0
\(331\) −4128.27 + 7150.37i −0.685529 + 1.18737i 0.287742 + 0.957708i \(0.407096\pi\)
−0.973270 + 0.229663i \(0.926238\pi\)
\(332\) −437.952 −0.0723969
\(333\) 0 0
\(334\) 8384.63 1.37361
\(335\) 1589.83 2753.67i 0.259289 0.449102i
\(336\) 0 0
\(337\) 4259.34 + 7377.40i 0.688490 + 1.19250i 0.972326 + 0.233627i \(0.0750594\pi\)
−0.283836 + 0.958873i \(0.591607\pi\)
\(338\) 2142.48 + 3710.89i 0.344780 + 0.597176i
\(339\) 0 0
\(340\) 151.384 262.205i 0.0241470 0.0418238i
\(341\) 6438.54 1.02248
\(342\) 0 0
\(343\) −4420.19 −0.695825
\(344\) −935.152 + 1619.73i −0.146570 + 0.253866i
\(345\) 0 0
\(346\) 2885.88 + 4998.49i 0.448398 + 0.776648i
\(347\) 4813.82 + 8337.77i 0.744724 + 1.28990i 0.950324 + 0.311263i \(0.100752\pi\)
−0.205600 + 0.978636i \(0.565915\pi\)
\(348\) 0 0
\(349\) 3795.89 6574.68i 0.582205 1.00841i −0.413013 0.910725i \(-0.635523\pi\)
0.995218 0.0976832i \(-0.0311432\pi\)
\(350\) 473.205 0.0722682
\(351\) 0 0
\(352\) −1440.45 −0.218114
\(353\) 693.613 1201.37i 0.104582 0.181141i −0.808986 0.587828i \(-0.799983\pi\)
0.913567 + 0.406688i \(0.133316\pi\)
\(354\) 0 0
\(355\) 2066.20 + 3578.77i 0.308909 + 0.535046i
\(356\) −137.458 238.084i −0.0204642 0.0354450i
\(357\) 0 0
\(358\) −2219.50 + 3844.29i −0.327666 + 0.567534i
\(359\) −6335.93 −0.931469 −0.465735 0.884924i \(-0.654210\pi\)
−0.465735 + 0.884924i \(0.654210\pi\)
\(360\) 0 0
\(361\) 8215.79 1.19781
\(362\) 3477.09 6022.50i 0.504840 0.874408i
\(363\) 0 0
\(364\) −46.5434 80.6156i −0.00670203 0.0116083i
\(365\) −1878.37 3253.44i −0.269366 0.466555i
\(366\) 0 0
\(367\) 4595.14 7959.01i 0.653581 1.13204i −0.328667 0.944446i \(-0.606599\pi\)
0.982248 0.187589i \(-0.0600674\pi\)
\(368\) 5789.58 0.820116
\(369\) 0 0
\(370\) 4020.81 0.564951
\(371\) 342.236 592.770i 0.0478922 0.0829516i
\(372\) 0 0
\(373\) 6342.70 + 10985.9i 0.880462 + 1.52501i 0.850828 + 0.525444i \(0.176101\pi\)
0.0296342 + 0.999561i \(0.490566\pi\)
\(374\) 9183.66 + 15906.6i 1.26972 + 2.19922i
\(375\) 0 0
\(376\) −3144.92 + 5447.16i −0.431348 + 0.747117i
\(377\) 3173.32 0.433512
\(378\) 0 0
\(379\) −13119.0 −1.77804 −0.889022 0.457865i \(-0.848614\pi\)
−0.889022 + 0.457865i \(0.848614\pi\)
\(380\) −164.493 + 284.911i −0.0222061 + 0.0384621i
\(381\) 0 0
\(382\) 6564.64 + 11370.3i 0.879257 + 1.52292i
\(383\) −867.126 1501.91i −0.115687 0.200376i 0.802367 0.596831i \(-0.203574\pi\)
−0.918054 + 0.396455i \(0.870240\pi\)
\(384\) 0 0
\(385\) 1030.53 1784.92i 0.136417 0.236281i
\(386\) 9774.84 1.28893
\(387\) 0 0
\(388\) −229.419 −0.0300181
\(389\) 4681.99 8109.45i 0.610248 1.05698i −0.380950 0.924596i \(-0.624403\pi\)
0.991198 0.132385i \(-0.0422636\pi\)
\(390\) 0 0
\(391\) 5504.30 + 9533.72i 0.711929 + 1.23310i
\(392\) −3439.77 5957.86i −0.443201 0.767647i
\(393\) 0 0
\(394\) −5175.71 + 8964.59i −0.661798 + 1.14627i
\(395\) 119.334 0.0152008
\(396\) 0 0
\(397\) −7661.94 −0.968619 −0.484309 0.874897i \(-0.660929\pi\)
−0.484309 + 0.874897i \(0.660929\pi\)
\(398\) −2798.04 + 4846.35i −0.352395 + 0.610366i
\(399\) 0 0
\(400\) 742.820 + 1286.60i 0.0928525 + 0.160825i
\(401\) −72.8247 126.136i −0.00906906 0.0157081i 0.861455 0.507833i \(-0.169553\pi\)
−0.870524 + 0.492125i \(0.836220\pi\)
\(402\) 0 0
\(403\) −1356.58 + 2349.66i −0.167682 + 0.290434i
\(404\) 488.786 0.0601931
\(405\) 0 0
\(406\) −2395.73 −0.292852
\(407\) 8756.34 15166.4i 1.06643 1.84711i
\(408\) 0 0
\(409\) −4445.36 7699.59i −0.537430 0.930856i −0.999041 0.0437736i \(-0.986062\pi\)
0.461612 0.887082i \(-0.347271\pi\)
\(410\) 1406.06 + 2435.37i 0.169367 + 0.293352i
\(411\) 0 0
\(412\) 74.6232 129.251i 0.00892335 0.0154557i
\(413\) −2109.66 −0.251354
\(414\) 0 0
\(415\) 4086.15 0.483329
\(416\) 303.497 525.672i 0.0357696 0.0619548i
\(417\) 0 0
\(418\) −9978.90 17284.0i −1.16766 2.02245i
\(419\) −1584.20 2743.91i −0.184709 0.319926i 0.758769 0.651360i \(-0.225801\pi\)
−0.943479 + 0.331434i \(0.892468\pi\)
\(420\) 0 0
\(421\) 4247.51 7356.91i 0.491713 0.851672i −0.508241 0.861215i \(-0.669704\pi\)
0.999954 + 0.00954269i \(0.00303758\pi\)
\(422\) 6507.18 0.750627
\(423\) 0 0
\(424\) 2303.95 0.263891
\(425\) −1412.44 + 2446.41i −0.161208 + 0.279220i
\(426\) 0 0
\(427\) −2309.01 3999.32i −0.261688 0.453257i
\(428\) 405.228 + 701.876i 0.0457651 + 0.0792675i
\(429\) 0 0
\(430\) 547.776 948.775i 0.0614328 0.106405i
\(431\) −2072.30 −0.231599 −0.115799 0.993273i \(-0.536943\pi\)
−0.115799 + 0.993273i \(0.536943\pi\)
\(432\) 0 0
\(433\) 2906.44 0.322574 0.161287 0.986908i \(-0.448435\pi\)
0.161287 + 0.986908i \(0.448435\pi\)
\(434\) 1024.16 1773.90i 0.113275 0.196198i
\(435\) 0 0
\(436\) 533.630 + 924.274i 0.0586152 + 0.101525i
\(437\) −5980.93 10359.3i −0.654707 1.13399i
\(438\) 0 0
\(439\) −965.538 + 1672.36i −0.104972 + 0.181817i −0.913727 0.406329i \(-0.866809\pi\)
0.808755 + 0.588146i \(0.200142\pi\)
\(440\) 6937.55 0.751670
\(441\) 0 0
\(442\) −7739.86 −0.832913
\(443\) −122.312 + 211.851i −0.0131179 + 0.0227209i −0.872510 0.488597i \(-0.837509\pi\)
0.859392 + 0.511317i \(0.170842\pi\)
\(444\) 0 0
\(445\) 1282.50 + 2221.36i 0.136621 + 0.236634i
\(446\) 761.087 + 1318.24i 0.0808038 + 0.139956i
\(447\) 0 0
\(448\) −1875.98 + 3249.29i −0.197839 + 0.342667i
\(449\) −13276.7 −1.39547 −0.697734 0.716357i \(-0.745808\pi\)
−0.697734 + 0.716357i \(0.745808\pi\)
\(450\) 0 0
\(451\) 12248.2 1.27882
\(452\) 136.092 235.718i 0.0141620 0.0245293i
\(453\) 0 0
\(454\) 7073.40 + 12251.5i 0.731214 + 1.26650i
\(455\) 434.256 + 752.154i 0.0447434 + 0.0774978i
\(456\) 0 0
\(457\) −6257.10 + 10837.6i −0.640470 + 1.10933i 0.344859 + 0.938655i \(0.387927\pi\)
−0.985328 + 0.170671i \(0.945406\pi\)
\(458\) −2508.78 −0.255955
\(459\) 0 0
\(460\) 261.051 0.0264599
\(461\) 2245.44 3889.22i 0.226856 0.392926i −0.730019 0.683427i \(-0.760489\pi\)
0.956875 + 0.290501i \(0.0938219\pi\)
\(462\) 0 0
\(463\) 3046.44 + 5276.60i 0.305789 + 0.529642i 0.977437 0.211229i \(-0.0677465\pi\)
−0.671648 + 0.740871i \(0.734413\pi\)
\(464\) −3760.73 6513.77i −0.376266 0.651712i
\(465\) 0 0
\(466\) 8055.34 13952.3i 0.800765 1.38697i
\(467\) 5193.68 0.514635 0.257318 0.966327i \(-0.417161\pi\)
0.257318 + 0.966327i \(0.417161\pi\)
\(468\) 0 0
\(469\) −4405.88 −0.433783
\(470\) 1842.17 3190.74i 0.180794 0.313144i
\(471\) 0 0
\(472\) −3550.58 6149.78i −0.346247 0.599717i
\(473\) −2385.84 4132.40i −0.231927 0.401709i
\(474\) 0 0
\(475\) 1534.74 2658.25i 0.148250 0.256777i
\(476\) −419.529 −0.0403972
\(477\) 0 0
\(478\) 1439.35 0.137729
\(479\) −9441.27 + 16352.8i −0.900590 + 1.55987i −0.0738604 + 0.997269i \(0.523532\pi\)
−0.826730 + 0.562599i \(0.809801\pi\)
\(480\) 0 0
\(481\) 3689.86 + 6391.03i 0.349778 + 0.605833i
\(482\) 7954.63 + 13777.8i 0.751708 + 1.30200i
\(483\) 0 0
\(484\) 591.885 1025.17i 0.0555865 0.0962786i
\(485\) 2140.51 0.200403
\(486\) 0 0
\(487\) −17619.1 −1.63942 −0.819708 0.572781i \(-0.805864\pi\)
−0.819708 + 0.572781i \(0.805864\pi\)
\(488\) 7772.19 13461.8i 0.720964 1.24875i
\(489\) 0 0
\(490\) 2014.89 + 3489.89i 0.185762 + 0.321749i
\(491\) −458.133 793.510i −0.0421085 0.0729341i 0.844203 0.536024i \(-0.180074\pi\)
−0.886312 + 0.463089i \(0.846741\pi\)
\(492\) 0 0
\(493\) 7150.83 12385.6i 0.653260 1.13148i
\(494\) 8410.08 0.765966
\(495\) 0 0
\(496\) 6430.77 0.582157
\(497\) 2863.02 4958.89i 0.258398 0.447559i
\(498\) 0 0
\(499\) −6231.71 10793.6i −0.559058 0.968316i −0.997575 0.0695938i \(-0.977830\pi\)
0.438518 0.898723i \(-0.355504\pi\)
\(500\) 33.4936 + 58.0127i 0.00299576 + 0.00518881i
\(501\) 0 0
\(502\) 4432.73 7677.71i 0.394108 0.682616i
\(503\) −49.4842 −0.00438646 −0.00219323 0.999998i \(-0.500698\pi\)
−0.00219323 + 0.999998i \(0.500698\pi\)
\(504\) 0 0
\(505\) −4560.43 −0.401855
\(506\) −7918.27 + 13714.8i −0.695672 + 1.20494i
\(507\) 0 0
\(508\) 494.609 + 856.689i 0.0431983 + 0.0748217i
\(509\) −3077.51 5330.40i −0.267992 0.464176i 0.700351 0.713799i \(-0.253027\pi\)
−0.968343 + 0.249622i \(0.919694\pi\)
\(510\) 0 0
\(511\) −2602.75 + 4508.09i −0.225321 + 0.390267i
\(512\) −12525.4 −1.08115
\(513\) 0 0
\(514\) −3446.21 −0.295731
\(515\) −696.244 + 1205.93i −0.0595731 + 0.103184i
\(516\) 0 0
\(517\) −8023.61 13897.3i −0.682549 1.18221i
\(518\) −2785.70 4824.97i −0.236287 0.409261i
\(519\) 0 0
\(520\) −1461.72 + 2531.77i −0.123270 + 0.213510i
\(521\) 14718.1 1.23764 0.618821 0.785532i \(-0.287610\pi\)
0.618821 + 0.785532i \(0.287610\pi\)
\(522\) 0 0
\(523\) −8318.46 −0.695489 −0.347744 0.937589i \(-0.613052\pi\)
−0.347744 + 0.937589i \(0.613052\pi\)
\(524\) −687.211 + 1190.28i −0.0572919 + 0.0992325i
\(525\) 0 0
\(526\) −2628.62 4552.90i −0.217896 0.377407i
\(527\) 6113.89 + 10589.6i 0.505361 + 0.875311i
\(528\) 0 0
\(529\) 1337.62 2316.83i 0.109939 0.190419i
\(530\) −1349.56 −0.110606
\(531\) 0 0
\(532\) 455.857 0.0371502
\(533\) −2580.66 + 4469.83i −0.209720 + 0.363246i
\(534\) 0 0
\(535\) −3780.83 6548.59i −0.305532 0.529197i
\(536\) −7415.14 12843.4i −0.597548 1.03498i
\(537\) 0 0
\(538\) 6505.74 11268.3i 0.521342 0.902991i
\(539\) 17551.7 1.40261
\(540\) 0 0
\(541\) 19372.0 1.53949 0.769746 0.638350i \(-0.220383\pi\)
0.769746 + 0.638350i \(0.220383\pi\)
\(542\) −2178.94 + 3774.04i −0.172682 + 0.299094i
\(543\) 0 0
\(544\) −1367.82 2369.13i −0.107803 0.186720i
\(545\) −4978.83 8623.59i −0.391321 0.677787i
\(546\) 0 0
\(547\) 494.864 857.129i 0.0386816 0.0669985i −0.846036 0.533125i \(-0.821018\pi\)
0.884718 + 0.466127i \(0.154351\pi\)
\(548\) 271.582 0.0211705
\(549\) 0 0
\(550\) −4063.75 −0.315052
\(551\) −7770.05 + 13458.1i −0.600754 + 1.04054i
\(552\) 0 0
\(553\) −82.6767 143.200i −0.00635764 0.0110117i
\(554\) −1433.76 2483.34i −0.109954 0.190446i
\(555\) 0 0
\(556\) 595.556 1031.53i 0.0454266 0.0786812i
\(557\) −4616.60 −0.351188 −0.175594 0.984463i \(-0.556185\pi\)
−0.175594 + 0.984463i \(0.556185\pi\)
\(558\) 0 0
\(559\) 2010.76 0.152139
\(560\) 1029.28 1782.77i 0.0776698 0.134528i
\(561\) 0 0
\(562\) −10349.1 17925.1i −0.776777 1.34542i
\(563\) 6754.79 + 11699.6i 0.505649 + 0.875809i 0.999979 + 0.00653505i \(0.00208019\pi\)
−0.494330 + 0.869274i \(0.664586\pi\)
\(564\) 0 0
\(565\) −1269.76 + 2199.28i −0.0945470 + 0.163760i
\(566\) −15990.5 −1.18751
\(567\) 0 0
\(568\) 19274.0 1.42380
\(569\) −5694.04 + 9862.37i −0.419520 + 0.726629i −0.995891 0.0905585i \(-0.971135\pi\)
0.576372 + 0.817188i \(0.304468\pi\)
\(570\) 0 0
\(571\) −4708.69 8155.70i −0.345101 0.597732i 0.640271 0.768149i \(-0.278822\pi\)
−0.985372 + 0.170417i \(0.945489\pi\)
\(572\) 399.702 + 692.304i 0.0292174 + 0.0506061i
\(573\) 0 0
\(574\) 1948.29 3374.55i 0.141673 0.245385i
\(575\) −2435.64 −0.176649
\(576\) 0 0
\(577\) −3751.39 −0.270663 −0.135332 0.990800i \(-0.543210\pi\)
−0.135332 + 0.990800i \(0.543210\pi\)
\(578\) −10729.9 + 18584.7i −0.772154 + 1.33741i
\(579\) 0 0
\(580\) −169.571 293.705i −0.0121397 0.0210266i
\(581\) −2830.97 4903.38i −0.202149 0.350132i
\(582\) 0 0
\(583\) −2939.02 + 5090.53i −0.208785 + 0.361627i
\(584\) −17521.8 −1.24154
\(585\) 0 0
\(586\) −9670.35 −0.681704
\(587\) −4646.77 + 8048.45i −0.326734 + 0.565920i −0.981862 0.189598i \(-0.939281\pi\)
0.655128 + 0.755518i \(0.272615\pi\)
\(588\) 0 0
\(589\) −6643.31 11506.6i −0.464742 0.804957i
\(590\) 2079.79 + 3602.30i 0.145125 + 0.251364i
\(591\) 0 0
\(592\) 8745.77 15148.1i 0.607178 1.05166i
\(593\) −1527.88 −0.105805 −0.0529027 0.998600i \(-0.516847\pi\)
−0.0529027 + 0.998600i \(0.516847\pi\)
\(594\) 0 0
\(595\) 3914.26 0.269696
\(596\) −136.679 + 236.735i −0.00939359 + 0.0162702i
\(597\) 0 0
\(598\) −3336.70 5779.34i −0.228174 0.395209i
\(599\) 835.199 + 1446.61i 0.0569704 + 0.0986757i 0.893104 0.449850i \(-0.148523\pi\)
−0.836134 + 0.548526i \(0.815189\pi\)
\(600\) 0 0
\(601\) −8696.95 + 15063.6i −0.590276 + 1.02239i 0.403919 + 0.914795i \(0.367648\pi\)
−0.994195 + 0.107593i \(0.965686\pi\)
\(602\) −1518.04 −0.102775
\(603\) 0 0
\(604\) −361.871 −0.0243780
\(605\) −5522.36 + 9565.01i −0.371100 + 0.642765i
\(606\) 0 0
\(607\) −2040.68 3534.56i −0.136456 0.236348i 0.789697 0.613497i \(-0.210238\pi\)
−0.926153 + 0.377149i \(0.876904\pi\)
\(608\) 1486.26 + 2574.28i 0.0991378 + 0.171712i
\(609\) 0 0
\(610\) −4552.65 + 7885.42i −0.302182 + 0.523395i
\(611\) 6762.18 0.447739
\(612\) 0 0
\(613\) 2300.45 0.151573 0.0757866 0.997124i \(-0.475853\pi\)
0.0757866 + 0.997124i \(0.475853\pi\)
\(614\) 400.660 693.963i 0.0263344 0.0456125i
\(615\) 0 0
\(616\) −4806.48 8325.06i −0.314381 0.544523i
\(617\) −1452.92 2516.53i −0.0948012 0.164201i 0.814724 0.579848i \(-0.196888\pi\)
−0.909526 + 0.415648i \(0.863555\pi\)
\(618\) 0 0
\(619\) −8927.74 + 15463.3i −0.579703 + 1.00408i 0.415810 + 0.909452i \(0.363498\pi\)
−0.995513 + 0.0946238i \(0.969835\pi\)
\(620\) 289.962 0.0187825
\(621\) 0 0
\(622\) 12545.3 0.808714
\(623\) 1777.08 3078.00i 0.114281 0.197941i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −10574.5 18315.5i −0.675146 1.16939i
\(627\) 0 0
\(628\) −972.114 + 1683.75i −0.0617700 + 0.106989i
\(629\) 33259.3 2.10832
\(630\) 0 0
\(631\) −24250.9 −1.52998 −0.764988 0.644045i \(-0.777255\pi\)
−0.764988 + 0.644045i \(0.777255\pi\)
\(632\) 278.292 482.016i 0.0175156 0.0303379i
\(633\) 0 0
\(634\) 2619.11 + 4536.44i 0.164067 + 0.284172i
\(635\) −4614.77 7993.01i −0.288396 0.499517i
\(636\) 0 0
\(637\) −3698.09 + 6405.28i −0.230021 + 0.398409i
\(638\) 20573.8 1.27669
\(639\) 0 0
\(640\) 6429.28 0.397093
\(641\) 749.919 1298.90i 0.0462091 0.0800364i −0.841996 0.539484i \(-0.818619\pi\)
0.888205 + 0.459448i \(0.151953\pi\)
\(642\) 0 0
\(643\) −11560.1 20022.6i −0.708996 1.22802i −0.965230 0.261402i \(-0.915815\pi\)
0.256234 0.966615i \(-0.417518\pi\)
\(644\) −180.862 313.261i −0.0110667 0.0191681i
\(645\) 0 0
\(646\) 18951.5 32824.9i 1.15424 1.99919i
\(647\) −10703.6 −0.650391 −0.325195 0.945647i \(-0.605430\pi\)
−0.325195 + 0.945647i \(0.605430\pi\)
\(648\) 0 0
\(649\) 18117.1 1.09578
\(650\) 856.218 1483.01i 0.0516671 0.0894901i
\(651\) 0 0
\(652\) −32.0357 55.4875i −0.00192426 0.00333291i
\(653\) −9054.57 15683.0i −0.542623 0.939850i −0.998752 0.0499370i \(-0.984098\pi\)
0.456129 0.889913i \(-0.349235\pi\)
\(654\) 0 0
\(655\) 6411.77 11105.5i 0.382486 0.662486i
\(656\) 12233.5 0.728104
\(657\) 0 0
\(658\) −5105.18 −0.302463
\(659\) 12556.7 21748.8i 0.742244 1.28560i −0.209227 0.977867i \(-0.567095\pi\)
0.951471 0.307737i \(-0.0995718\pi\)
\(660\) 0 0
\(661\) 9296.80 + 16102.5i 0.547055 + 0.947528i 0.998474 + 0.0552157i \(0.0175847\pi\)
−0.451419 + 0.892312i \(0.649082\pi\)
\(662\) −11278.6 19535.2i −0.662170 1.14691i
\(663\) 0 0
\(664\) 9529.12 16504.9i 0.556930 0.964631i
\(665\) −4253.21 −0.248018
\(666\) 0 0
\(667\) 12331.1 0.715834
\(668\) 822.333 1424.32i 0.0476303 0.0824981i
\(669\) 0 0
\(670\) 4343.51 + 7523.17i 0.250454 + 0.433799i
\(671\) 19829.1 + 34345.0i 1.14083 + 1.97597i
\(672\) 0 0
\(673\) −2145.19 + 3715.58i −0.122869 + 0.212816i −0.920898 0.389803i \(-0.872543\pi\)
0.798029 + 0.602619i \(0.205876\pi\)
\(674\) −23273.5 −1.33006
\(675\) 0 0
\(676\) 840.506 0.0478212
\(677\) −13475.3 + 23339.8i −0.764988 + 1.32500i 0.175266 + 0.984521i \(0.443922\pi\)
−0.940253 + 0.340476i \(0.889412\pi\)
\(678\) 0 0
\(679\) −1482.99 2568.61i −0.0838173 0.145176i
\(680\) 6587.74 + 11410.3i 0.371512 + 0.643478i
\(681\) 0 0
\(682\) −8795.20 + 15233.7i −0.493821 + 0.855323i
\(683\) −18870.9 −1.05721 −0.528607 0.848867i \(-0.677285\pi\)
−0.528607 + 0.848867i \(0.677285\pi\)
\(684\) 0 0
\(685\) −2533.90 −0.141336
\(686\) 6038.10 10458.3i 0.336058 0.582069i
\(687\) 0 0
\(688\) −2382.97 4127.42i −0.132049 0.228716i
\(689\) −1238.48 2145.12i −0.0684796 0.118610i
\(690\) 0 0
\(691\) −1848.03 + 3200.88i −0.101740 + 0.176219i −0.912402 0.409296i \(-0.865774\pi\)
0.810662 + 0.585515i \(0.199108\pi\)
\(692\) 1132.14 0.0621931
\(693\) 0 0
\(694\) −26303.2 −1.43870
\(695\) −5556.62 + 9624.34i −0.303273 + 0.525284i
\(696\) 0 0
\(697\) 11630.6 + 20144.9i 0.632055 + 1.09475i
\(698\) 10370.6 + 17962.4i 0.562367 + 0.974048i
\(699\) 0 0
\(700\) 46.4102 80.3848i 0.00250591 0.00434037i
\(701\) 1123.53 0.0605349 0.0302674 0.999542i \(-0.490364\pi\)
0.0302674 + 0.999542i \(0.490364\pi\)
\(702\) 0 0
\(703\) −36139.3 −1.93886
\(704\) 16110.4 27904.0i 0.862475 1.49385i
\(705\) 0 0
\(706\) 1894.99 + 3282.21i 0.101018 + 0.174968i
\(707\) 3159.56 + 5472.52i 0.168073 + 0.291111i
\(708\) 0 0
\(709\) 13233.8 22921.7i 0.700998 1.21416i −0.267118 0.963664i \(-0.586071\pi\)
0.968116 0.250501i \(-0.0805952\pi\)
\(710\) −11290.0 −0.596767
\(711\) 0 0
\(712\) 11963.4 0.629702
\(713\) −5271.48 + 9130.46i −0.276884 + 0.479577i
\(714\) 0 0
\(715\) −3729.27 6459.28i −0.195058 0.337851i
\(716\) 435.361 + 754.067i 0.0227237 + 0.0393587i
\(717\) 0 0
\(718\) 8655.04 14991.0i 0.449865 0.779189i
\(719\) 7882.34 0.408848 0.204424 0.978882i \(-0.434468\pi\)
0.204424 + 0.978882i \(0.434468\pi\)
\(720\) 0 0
\(721\) 1929.49 0.0996641
\(722\) −11223.0 + 19438.8i −0.578499 + 1.00199i
\(723\) 0 0
\(724\) −682.040 1181.33i −0.0350108 0.0606405i
\(725\) 1582.12 + 2740.30i 0.0810459 + 0.140376i
\(726\) 0 0
\(727\) −10004.5 + 17328.2i −0.510379 + 0.884002i 0.489549 + 0.871976i \(0.337161\pi\)
−0.999928 + 0.0120259i \(0.996172\pi\)
\(728\) 4050.83 0.206228
\(729\) 0 0
\(730\) 10263.6 0.520375
\(731\) 4531.09 7848.08i 0.229259 0.397088i
\(732\) 0 0
\(733\) 18146.7 + 31431.1i 0.914414 + 1.58381i 0.807757 + 0.589515i \(0.200681\pi\)
0.106657 + 0.994296i \(0.465985\pi\)
\(734\) 12554.1 + 21744.4i 0.631311 + 1.09346i
\(735\) 0 0
\(736\) 1179.35 2042.69i 0.0590644 0.102302i
\(737\) 37836.4 1.89107
\(738\) 0 0
\(739\) −27475.5 −1.36766 −0.683832 0.729639i \(-0.739688\pi\)
−0.683832 + 0.729639i \(0.739688\pi\)
\(740\) 394.346 683.027i 0.0195898 0.0339305i
\(741\) 0 0
\(742\) 935.005 + 1619.48i 0.0462603 + 0.0801251i
\(743\) −19074.4 33037.9i −0.941822 1.63128i −0.761993 0.647585i \(-0.775779\pi\)
−0.179829 0.983698i \(-0.557554\pi\)
\(744\) 0 0
\(745\) 1275.23 2208.76i 0.0627125 0.108621i
\(746\) −34657.1 −1.70092
\(747\) 0 0
\(748\) 3602.79 0.176111
\(749\) −5238.88 + 9074.00i −0.255573 + 0.442666i
\(750\) 0 0
\(751\) −14111.5 24441.9i −0.685669 1.18761i −0.973226 0.229850i \(-0.926177\pi\)
0.287557 0.957763i \(-0.407157\pi\)
\(752\) −8013.93 13880.5i −0.388614 0.673099i
\(753\) 0 0
\(754\) −4334.83 + 7508.15i −0.209370 + 0.362640i
\(755\) 3376.31 0.162750
\(756\) 0 0
\(757\) 34786.4 1.67019 0.835095 0.550106i \(-0.185413\pi\)
0.835095 + 0.550106i \(0.185413\pi\)
\(758\) 17920.9 31039.9i 0.858729 1.48736i
\(759\) 0 0
\(760\) −7158.20 12398.4i −0.341651 0.591758i
\(761\) −582.982 1009.76i −0.0277702 0.0480993i 0.851806 0.523857i \(-0.175507\pi\)
−0.879576 + 0.475758i \(0.842174\pi\)
\(762\) 0 0
\(763\) −6898.87 + 11949.2i −0.327334 + 0.566959i
\(764\) 2575.34 0.121954
\(765\) 0 0
\(766\) 4738.07 0.223490
\(767\) −3817.21 + 6611.61i −0.179702 + 0.311253i
\(768\) 0 0
\(769\) 13172.7 + 22815.7i 0.617710 + 1.06990i 0.989903 + 0.141749i \(0.0452727\pi\)
−0.372193 + 0.928155i \(0.621394\pi\)
\(770\) 2815.45 + 4876.50i 0.131768 + 0.228230i
\(771\) 0 0
\(772\) 958.679 1660.48i 0.0446938 0.0774120i
\(773\) 25867.0 1.20358 0.601792 0.798653i \(-0.294454\pi\)
0.601792 + 0.798653i \(0.294454\pi\)
\(774\) 0 0
\(775\) −2705.38 −0.125394
\(776\) 4991.78 8646.02i 0.230921 0.399967i
\(777\) 0 0
\(778\) 12791.4 + 22155.4i 0.589454 + 1.02096i
\(779\) −12637.8 21889.3i −0.581252 1.00676i
\(780\) 0 0
\(781\) −24586.8 + 42585.5i −1.12648 + 1.95113i
\(782\) −30076.0 −1.37534
\(783\) 0 0
\(784\) 17530.6 0.798586
\(785\) 9069.95 15709.6i 0.412383 0.714267i
\(786\) 0 0
\(787\) 4035.49 + 6989.67i 0.182782 + 0.316588i 0.942827 0.333283