Properties

Label 108.4.h.b.71.6
Level 108
Weight 4
Character 108.71
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.6
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.664105 + 2.74936i) q^{2} +(-7.11793 - 3.65173i) q^{4} +(14.2911 + 8.25096i) q^{5} +(19.2620 - 11.1209i) q^{7} +(14.7670 - 17.1446i) q^{8} +O(q^{10})\) \(q+(-0.664105 + 2.74936i) q^{2} +(-7.11793 - 3.65173i) q^{4} +(14.2911 + 8.25096i) q^{5} +(19.2620 - 11.1209i) q^{7} +(14.7670 - 17.1446i) q^{8} +(-32.1756 + 33.8118i) q^{10} +(6.37655 + 11.0445i) q^{11} +(-11.1766 + 19.3584i) q^{13} +(17.7834 + 60.3436i) q^{14} +(37.3298 + 51.9854i) q^{16} +117.295i q^{17} -27.7307i q^{19} +(-71.5926 - 110.917i) q^{20} +(-34.6000 + 10.1967i) q^{22} +(17.5836 - 30.4556i) q^{23} +(73.6567 + 127.577i) q^{25} +(-45.8008 - 43.5845i) q^{26} +(-177.716 + 8.81837i) q^{28} +(-1.01189 + 0.584217i) q^{29} +(-119.361 - 68.9130i) q^{31} +(-167.717 + 68.1091i) q^{32} +(-322.487 - 77.8965i) q^{34} +367.033 q^{35} +233.596 q^{37} +(76.2416 + 18.4161i) q^{38} +(352.495 - 123.173i) q^{40} +(-13.2561 - 7.65340i) q^{41} +(361.460 - 208.689i) q^{43} +(-5.05631 - 101.900i) q^{44} +(72.0561 + 68.5693i) q^{46} +(-116.494 - 201.773i) q^{47} +(75.8499 - 131.376i) q^{49} +(-399.671 + 117.784i) q^{50} +(150.246 - 96.9781i) q^{52} -180.951i q^{53} +210.451i q^{55} +(93.7774 - 494.461i) q^{56} +(-0.934217 - 3.17004i) q^{58} +(-313.716 + 543.373i) q^{59} +(-382.110 - 661.834i) q^{61} +(268.735 - 282.400i) q^{62} +(-75.8742 - 506.347i) q^{64} +(-319.452 + 184.435i) q^{65} +(-113.463 - 65.5077i) q^{67} +(428.330 - 834.900i) q^{68} +(-243.749 + 1009.11i) q^{70} +22.6910 q^{71} +387.864 q^{73} +(-155.133 + 642.240i) q^{74} +(-101.265 + 197.385i) q^{76} +(245.650 + 141.826i) q^{77} +(-486.411 + 280.830i) q^{79} +(104.553 + 1050.93i) q^{80} +(29.8454 - 31.3630i) q^{82} +(-342.111 - 592.554i) q^{83} +(-967.799 + 1676.28i) q^{85} +(333.713 + 1132.38i) q^{86} +(283.516 + 53.7704i) q^{88} -278.003i q^{89} +497.177i q^{91} +(-236.374 + 152.571i) q^{92} +(632.110 - 186.284i) q^{94} +(228.805 - 396.302i) q^{95} +(-264.443 - 458.028i) q^{97} +(310.827 + 295.786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.664105 + 2.74936i −0.234797 + 0.972044i
\(3\) 0 0
\(4\) −7.11793 3.65173i −0.889741 0.456466i
\(5\) 14.2911 + 8.25096i 1.27823 + 0.737988i 0.976523 0.215411i \(-0.0691093\pi\)
0.301710 + 0.953400i \(0.402443\pi\)
\(6\) 0 0
\(7\) 19.2620 11.1209i 1.04005 0.600473i 0.120203 0.992749i \(-0.461645\pi\)
0.919848 + 0.392276i \(0.128312\pi\)
\(8\) 14.7670 17.1446i 0.652613 0.757691i
\(9\) 0 0
\(10\) −32.1756 + 33.8118i −1.01748 + 1.06922i
\(11\) 6.37655 + 11.0445i 0.174782 + 0.302732i 0.940086 0.340938i \(-0.110745\pi\)
−0.765304 + 0.643669i \(0.777411\pi\)
\(12\) 0 0
\(13\) −11.1766 + 19.3584i −0.238449 + 0.413005i −0.960269 0.279075i \(-0.909972\pi\)
0.721821 + 0.692080i \(0.243306\pi\)
\(14\) 17.7834 + 60.3436i 0.339486 + 1.15196i
\(15\) 0 0
\(16\) 37.3298 + 51.9854i 0.583278 + 0.812273i
\(17\) 117.295i 1.67343i 0.547639 + 0.836715i \(0.315527\pi\)
−0.547639 + 0.836715i \(0.684473\pi\)
\(18\) 0 0
\(19\) 27.7307i 0.334835i −0.985886 0.167417i \(-0.946457\pi\)
0.985886 0.167417i \(-0.0535427\pi\)
\(20\) −71.5926 110.917i −0.800430 1.24009i
\(21\) 0 0
\(22\) −34.6000 + 10.1967i −0.335307 + 0.0988156i
\(23\) 17.5836 30.4556i 0.159410 0.276106i −0.775246 0.631659i \(-0.782374\pi\)
0.934656 + 0.355553i \(0.115708\pi\)
\(24\) 0 0
\(25\) 73.6567 + 127.577i 0.589254 + 1.02062i
\(26\) −45.8008 43.5845i −0.345472 0.328755i
\(27\) 0 0
\(28\) −177.716 + 8.81837i −1.19947 + 0.0595184i
\(29\) −1.01189 + 0.584217i −0.00647945 + 0.00374091i −0.503236 0.864149i \(-0.667857\pi\)
0.496757 + 0.867890i \(0.334524\pi\)
\(30\) 0 0
\(31\) −119.361 68.9130i −0.691543 0.399263i 0.112647 0.993635i \(-0.464067\pi\)
−0.804190 + 0.594373i \(0.797400\pi\)
\(32\) −167.717 + 68.1091i −0.926517 + 0.376253i
\(33\) 0 0
\(34\) −322.487 77.8965i −1.62665 0.392916i
\(35\) 367.033 1.77257
\(36\) 0 0
\(37\) 233.596 1.03792 0.518959 0.854799i \(-0.326320\pi\)
0.518959 + 0.854799i \(0.326320\pi\)
\(38\) 76.2416 + 18.4161i 0.325474 + 0.0786180i
\(39\) 0 0
\(40\) 352.495 123.173i 1.39336 0.486885i
\(41\) −13.2561 7.65340i −0.0504940 0.0291527i 0.474541 0.880234i \(-0.342614\pi\)
−0.525034 + 0.851081i \(0.675948\pi\)
\(42\) 0 0
\(43\) 361.460 208.689i 1.28191 0.740112i 0.304714 0.952444i \(-0.401439\pi\)
0.977198 + 0.212332i \(0.0681059\pi\)
\(44\) −5.05631 101.900i −0.0173243 0.349135i
\(45\) 0 0
\(46\) 72.0561 + 68.5693i 0.230958 + 0.219782i
\(47\) −116.494 201.773i −0.361539 0.626204i 0.626675 0.779281i \(-0.284415\pi\)
−0.988214 + 0.153076i \(0.951082\pi\)
\(48\) 0 0
\(49\) 75.8499 131.376i 0.221137 0.383020i
\(50\) −399.671 + 117.784i −1.13044 + 0.333143i
\(51\) 0 0
\(52\) 150.246 96.9781i 0.400680 0.258624i
\(53\) 180.951i 0.468972i −0.972120 0.234486i \(-0.924659\pi\)
0.972120 0.234486i \(-0.0753407\pi\)
\(54\) 0 0
\(55\) 210.451i 0.515949i
\(56\) 93.7774 494.461i 0.223777 1.17991i
\(57\) 0 0
\(58\) −0.934217 3.17004i −0.00211498 0.00717666i
\(59\) −313.716 + 543.373i −0.692244 + 1.19900i 0.278857 + 0.960333i \(0.410045\pi\)
−0.971101 + 0.238669i \(0.923289\pi\)
\(60\) 0 0
\(61\) −382.110 661.834i −0.802035 1.38917i −0.918274 0.395945i \(-0.870417\pi\)
0.116239 0.993221i \(-0.462916\pi\)
\(62\) 268.735 282.400i 0.550473 0.578465i
\(63\) 0 0
\(64\) −75.8742 506.347i −0.148192 0.988959i
\(65\) −319.452 + 184.435i −0.609586 + 0.351945i
\(66\) 0 0
\(67\) −113.463 65.5077i −0.206891 0.119448i 0.392975 0.919549i \(-0.371446\pi\)
−0.599866 + 0.800101i \(0.704779\pi\)
\(68\) 428.330 834.900i 0.763863 1.48892i
\(69\) 0 0
\(70\) −243.749 + 1009.11i −0.416194 + 1.72302i
\(71\) 22.6910 0.0379285 0.0189643 0.999820i \(-0.493963\pi\)
0.0189643 + 0.999820i \(0.493963\pi\)
\(72\) 0 0
\(73\) 387.864 0.621863 0.310932 0.950432i \(-0.399359\pi\)
0.310932 + 0.950432i \(0.399359\pi\)
\(74\) −155.133 + 642.240i −0.243700 + 1.00890i
\(75\) 0 0
\(76\) −101.265 + 197.385i −0.152840 + 0.297916i
\(77\) 245.650 + 141.826i 0.363565 + 0.209904i
\(78\) 0 0
\(79\) −486.411 + 280.830i −0.692729 + 0.399947i −0.804633 0.593772i \(-0.797638\pi\)
0.111905 + 0.993719i \(0.464305\pi\)
\(80\) 104.553 + 1050.93i 0.146118 + 1.46873i
\(81\) 0 0
\(82\) 29.8454 31.3630i 0.0401935 0.0422374i
\(83\) −342.111 592.554i −0.452429 0.783629i 0.546108 0.837715i \(-0.316109\pi\)
−0.998536 + 0.0540856i \(0.982776\pi\)
\(84\) 0 0
\(85\) −967.799 + 1676.28i −1.23497 + 2.13903i
\(86\) 333.713 + 1132.38i 0.418433 + 1.41985i
\(87\) 0 0
\(88\) 283.516 + 53.7704i 0.343442 + 0.0651357i
\(89\) 278.003i 0.331103i −0.986201 0.165552i \(-0.947060\pi\)
0.986201 0.165552i \(-0.0529405\pi\)
\(90\) 0 0
\(91\) 497.177i 0.572728i
\(92\) −236.374 + 152.571i −0.267866 + 0.172898i
\(93\) 0 0
\(94\) 632.110 186.284i 0.693587 0.204402i
\(95\) 228.805 396.302i 0.247104 0.427997i
\(96\) 0 0
\(97\) −264.443 458.028i −0.276805 0.479440i 0.693784 0.720183i \(-0.255942\pi\)
−0.970589 + 0.240743i \(0.922609\pi\)
\(98\) 310.827 + 295.786i 0.320390 + 0.304887i
\(99\) 0 0
\(100\) −58.4063 1177.06i −0.0584063 1.17706i
\(101\) 1241.84 716.977i 1.22344 0.706355i 0.257793 0.966200i \(-0.417005\pi\)
0.965650 + 0.259845i \(0.0836714\pi\)
\(102\) 0 0
\(103\) −199.095 114.948i −0.190460 0.109962i 0.401738 0.915755i \(-0.368406\pi\)
−0.592198 + 0.805792i \(0.701740\pi\)
\(104\) 166.848 + 477.484i 0.157316 + 0.450203i
\(105\) 0 0
\(106\) 497.498 + 120.170i 0.455862 + 0.110113i
\(107\) −1676.13 −1.51437 −0.757184 0.653201i \(-0.773426\pi\)
−0.757184 + 0.653201i \(0.773426\pi\)
\(108\) 0 0
\(109\) −540.666 −0.475104 −0.237552 0.971375i \(-0.576345\pi\)
−0.237552 + 0.971375i \(0.576345\pi\)
\(110\) −578.604 139.762i −0.501525 0.121143i
\(111\) 0 0
\(112\) 1297.17 + 586.202i 1.09439 + 0.494562i
\(113\) −1110.83 641.340i −0.924764 0.533913i −0.0396123 0.999215i \(-0.512612\pi\)
−0.885152 + 0.465302i \(0.845946\pi\)
\(114\) 0 0
\(115\) 502.576 290.163i 0.407526 0.235285i
\(116\) 9.33599 0.463257i 0.00747263 0.000370796i
\(117\) 0 0
\(118\) −1285.59 1223.38i −1.00295 0.954414i
\(119\) 1304.43 + 2259.34i 1.00485 + 1.74045i
\(120\) 0 0
\(121\) 584.179 1011.83i 0.438902 0.760201i
\(122\) 2073.38 611.029i 1.53865 0.453442i
\(123\) 0 0
\(124\) 597.950 + 926.391i 0.433044 + 0.670906i
\(125\) 368.214i 0.263472i
\(126\) 0 0
\(127\) 2674.79i 1.86889i 0.356109 + 0.934444i \(0.384103\pi\)
−0.356109 + 0.934444i \(0.615897\pi\)
\(128\) 1442.52 + 127.662i 0.996107 + 0.0881552i
\(129\) 0 0
\(130\) −294.929 1000.77i −0.198977 0.675180i
\(131\) 413.401 716.031i 0.275717 0.477557i −0.694598 0.719398i \(-0.744418\pi\)
0.970316 + 0.241841i \(0.0777513\pi\)
\(132\) 0 0
\(133\) −308.391 534.149i −0.201059 0.348245i
\(134\) 255.455 268.446i 0.164686 0.173061i
\(135\) 0 0
\(136\) 2010.98 + 1732.09i 1.26794 + 1.09210i
\(137\) −560.929 + 323.852i −0.349806 + 0.201960i −0.664600 0.747200i \(-0.731398\pi\)
0.314794 + 0.949160i \(0.398065\pi\)
\(138\) 0 0
\(139\) −2312.71 1335.24i −1.41124 0.814777i −0.415730 0.909488i \(-0.636474\pi\)
−0.995505 + 0.0947110i \(0.969807\pi\)
\(140\) −2612.52 1340.30i −1.57713 0.809117i
\(141\) 0 0
\(142\) −15.0692 + 62.3857i −0.00890550 + 0.0368682i
\(143\) −285.073 −0.166706
\(144\) 0 0
\(145\) −19.2814 −0.0110430
\(146\) −257.583 + 1066.38i −0.146012 + 0.604479i
\(147\) 0 0
\(148\) −1662.72 853.030i −0.923479 0.473774i
\(149\) 90.2485 + 52.1050i 0.0496204 + 0.0286484i 0.524605 0.851346i \(-0.324213\pi\)
−0.474985 + 0.879994i \(0.657546\pi\)
\(150\) 0 0
\(151\) 2382.77 1375.69i 1.28415 0.741407i 0.306549 0.951855i \(-0.400826\pi\)
0.977605 + 0.210448i \(0.0674924\pi\)
\(152\) −475.431 409.498i −0.253701 0.218517i
\(153\) 0 0
\(154\) −553.069 + 581.193i −0.289400 + 0.304116i
\(155\) −1137.20 1969.68i −0.589302 1.02070i
\(156\) 0 0
\(157\) 581.545 1007.27i 0.295620 0.512029i −0.679509 0.733667i \(-0.737807\pi\)
0.975129 + 0.221638i \(0.0711404\pi\)
\(158\) −449.073 1523.82i −0.226116 0.767269i
\(159\) 0 0
\(160\) −2958.83 410.477i −1.46198 0.202819i
\(161\) 782.182i 0.382886i
\(162\) 0 0
\(163\) 2930.45i 1.40816i −0.710120 0.704081i \(-0.751359\pi\)
0.710120 0.704081i \(-0.248641\pi\)
\(164\) 66.4077 + 102.884i 0.0316193 + 0.0489871i
\(165\) 0 0
\(166\) 1856.34 547.067i 0.867951 0.255787i
\(167\) 435.960 755.105i 0.202010 0.349891i −0.747166 0.664637i \(-0.768586\pi\)
0.949176 + 0.314746i \(0.101919\pi\)
\(168\) 0 0
\(169\) 848.667 + 1469.93i 0.386284 + 0.669064i
\(170\) −3965.96 3774.05i −1.78927 1.70268i
\(171\) 0 0
\(172\) −3334.92 + 165.481i −1.47840 + 0.0733592i
\(173\) −2020.19 + 1166.36i −0.887816 + 0.512581i −0.873227 0.487313i \(-0.837977\pi\)
−0.0145882 + 0.999894i \(0.504644\pi\)
\(174\) 0 0
\(175\) 2837.55 + 1638.26i 1.22571 + 0.707662i
\(176\) −336.119 + 743.778i −0.143954 + 0.318547i
\(177\) 0 0
\(178\) 764.328 + 184.623i 0.321847 + 0.0777420i
\(179\) 638.773 0.266727 0.133364 0.991067i \(-0.457422\pi\)
0.133364 + 0.991067i \(0.457422\pi\)
\(180\) 0 0
\(181\) 4031.01 1.65537 0.827686 0.561192i \(-0.189657\pi\)
0.827686 + 0.561192i \(0.189657\pi\)
\(182\) −1366.92 330.178i −0.556717 0.134475i
\(183\) 0 0
\(184\) −262.494 751.200i −0.105170 0.300974i
\(185\) 3338.34 + 1927.39i 1.32670 + 0.765972i
\(186\) 0 0
\(187\) −1295.47 + 747.940i −0.506600 + 0.292486i
\(188\) 92.3740 + 1861.61i 0.0358355 + 0.722190i
\(189\) 0 0
\(190\) 937.624 + 892.252i 0.358013 + 0.340688i
\(191\) 1831.72 + 3172.63i 0.693918 + 1.20190i 0.970544 + 0.240924i \(0.0774505\pi\)
−0.276626 + 0.960978i \(0.589216\pi\)
\(192\) 0 0
\(193\) −708.828 + 1227.73i −0.264366 + 0.457895i −0.967397 0.253264i \(-0.918496\pi\)
0.703032 + 0.711159i \(0.251829\pi\)
\(194\) 1434.90 422.868i 0.531030 0.156496i
\(195\) 0 0
\(196\) −1019.64 + 658.141i −0.371590 + 0.239847i
\(197\) 876.917i 0.317146i 0.987347 + 0.158573i \(0.0506893\pi\)
−0.987347 + 0.158573i \(0.949311\pi\)
\(198\) 0 0
\(199\) 1485.45i 0.529149i −0.964365 0.264574i \(-0.914769\pi\)
0.964365 0.264574i \(-0.0852315\pi\)
\(200\) 3274.94 + 621.111i 1.15787 + 0.219596i
\(201\) 0 0
\(202\) 1146.51 + 3890.41i 0.399348 + 1.35509i
\(203\) −12.9941 + 22.5064i −0.00449263 + 0.00778147i
\(204\) 0 0
\(205\) −126.296 218.751i −0.0430287 0.0745279i
\(206\) 448.252 471.046i 0.151608 0.159317i
\(207\) 0 0
\(208\) −1423.58 + 141.626i −0.474555 + 0.0472116i
\(209\) 306.272 176.826i 0.101365 0.0585231i
\(210\) 0 0
\(211\) −266.434 153.826i −0.0869294 0.0501887i 0.455905 0.890028i \(-0.349316\pi\)
−0.542835 + 0.839840i \(0.682649\pi\)
\(212\) −660.783 + 1288.00i −0.214070 + 0.417264i
\(213\) 0 0
\(214\) 1113.13 4608.28i 0.355569 1.47203i
\(215\) 6887.55 2.18478
\(216\) 0 0
\(217\) −3065.50 −0.958986
\(218\) 359.059 1486.48i 0.111553 0.461823i
\(219\) 0 0
\(220\) 768.509 1497.97i 0.235513 0.459061i
\(221\) −2270.66 1310.96i −0.691135 0.399027i
\(222\) 0 0
\(223\) −3380.52 + 1951.74i −1.01514 + 0.586091i −0.912692 0.408647i \(-0.866001\pi\)
−0.102447 + 0.994738i \(0.532667\pi\)
\(224\) −2473.14 + 3177.09i −0.737694 + 0.947671i
\(225\) 0 0
\(226\) 2500.98 2628.16i 0.736119 0.773551i
\(227\) −964.382 1670.36i −0.281975 0.488394i 0.689896 0.723908i \(-0.257656\pi\)
−0.971871 + 0.235514i \(0.924323\pi\)
\(228\) 0 0
\(229\) −1148.71 + 1989.62i −0.331479 + 0.574139i −0.982802 0.184662i \(-0.940881\pi\)
0.651323 + 0.758801i \(0.274214\pi\)
\(230\) 463.997 + 1574.46i 0.133022 + 0.451378i
\(231\) 0 0
\(232\) −4.92642 + 25.9756i −0.00139412 + 0.00735079i
\(233\) 3366.60i 0.946580i 0.880907 + 0.473290i \(0.156934\pi\)
−0.880907 + 0.473290i \(0.843066\pi\)
\(234\) 0 0
\(235\) 3844.74i 1.06725i
\(236\) 4217.26 2722.08i 1.16322 0.750816i
\(237\) 0 0
\(238\) −7078.02 + 2085.91i −1.92773 + 0.568106i
\(239\) −307.571 + 532.729i −0.0832432 + 0.144182i −0.904641 0.426174i \(-0.859861\pi\)
0.821398 + 0.570355i \(0.193195\pi\)
\(240\) 0 0
\(241\) 2195.78 + 3803.20i 0.586898 + 1.01654i 0.994636 + 0.103438i \(0.0329844\pi\)
−0.407738 + 0.913099i \(0.633682\pi\)
\(242\) 2393.92 + 2278.08i 0.635897 + 0.605125i
\(243\) 0 0
\(244\) 302.995 + 6106.25i 0.0794971 + 1.60210i
\(245\) 2167.95 1251.67i 0.565329 0.326393i
\(246\) 0 0
\(247\) 536.823 + 309.935i 0.138288 + 0.0798408i
\(248\) −2944.08 + 1028.76i −0.753828 + 0.263412i
\(249\) 0 0
\(250\) −1012.35 244.533i −0.256107 0.0618624i
\(251\) −7726.08 −1.94289 −0.971446 0.237259i \(-0.923751\pi\)
−0.971446 + 0.237259i \(0.923751\pi\)
\(252\) 0 0
\(253\) 448.490 0.111448
\(254\) −7353.94 1776.34i −1.81664 0.438809i
\(255\) 0 0
\(256\) −1308.97 + 3881.21i −0.319573 + 0.947562i
\(257\) 2222.83 + 1283.35i 0.539518 + 0.311491i 0.744884 0.667194i \(-0.232505\pi\)
−0.205365 + 0.978685i \(0.565838\pi\)
\(258\) 0 0
\(259\) 4499.53 2597.81i 1.07949 0.623243i
\(260\) 2947.34 146.249i 0.703024 0.0348844i
\(261\) 0 0
\(262\) 1694.08 + 1612.11i 0.399469 + 0.380138i
\(263\) −2003.92 3470.89i −0.469837 0.813781i 0.529569 0.848267i \(-0.322354\pi\)
−0.999405 + 0.0344862i \(0.989021\pi\)
\(264\) 0 0
\(265\) 1493.02 2585.98i 0.346096 0.599456i
\(266\) 1673.37 493.146i 0.385717 0.113672i
\(267\) 0 0
\(268\) 568.403 + 880.614i 0.129555 + 0.200717i
\(269\) 2242.21i 0.508214i 0.967176 + 0.254107i \(0.0817816\pi\)
−0.967176 + 0.254107i \(0.918218\pi\)
\(270\) 0 0
\(271\) 6324.08i 1.41757i 0.705426 + 0.708784i \(0.250756\pi\)
−0.705426 + 0.708784i \(0.749244\pi\)
\(272\) −6097.65 + 4378.61i −1.35928 + 0.976075i
\(273\) 0 0
\(274\) −517.870 1757.27i −0.114181 0.387446i
\(275\) −939.352 + 1627.01i −0.205982 + 0.356771i
\(276\) 0 0
\(277\) −625.852 1084.01i −0.135754 0.235132i 0.790131 0.612938i \(-0.210012\pi\)
−0.925885 + 0.377805i \(0.876679\pi\)
\(278\) 5206.95 5471.73i 1.12335 1.18048i
\(279\) 0 0
\(280\) 5419.96 6292.64i 1.15680 1.34306i
\(281\) 1190.34 687.240i 0.252703 0.145898i −0.368298 0.929708i \(-0.620060\pi\)
0.621001 + 0.783810i \(0.286726\pi\)
\(282\) 0 0
\(283\) 4006.16 + 2312.96i 0.841490 + 0.485835i 0.857771 0.514033i \(-0.171849\pi\)
−0.0162801 + 0.999867i \(0.505182\pi\)
\(284\) −161.513 82.8613i −0.0337466 0.0173131i
\(285\) 0 0
\(286\) 189.318 783.767i 0.0391421 0.162046i
\(287\) −340.452 −0.0700217
\(288\) 0 0
\(289\) −8845.19 −1.80037
\(290\) 12.8049 53.0115i 0.00259286 0.0107343i
\(291\) 0 0
\(292\) −2760.79 1416.37i −0.553297 0.283859i
\(293\) −5522.68 3188.52i −1.10116 0.635752i −0.164631 0.986355i \(-0.552643\pi\)
−0.936524 + 0.350603i \(0.885977\pi\)
\(294\) 0 0
\(295\) −8966.70 + 5176.92i −1.76970 + 1.02174i
\(296\) 3449.51 4004.91i 0.677360 0.786422i
\(297\) 0 0
\(298\) −203.190 + 213.522i −0.0394982 + 0.0415067i
\(299\) 393.049 + 680.781i 0.0760221 + 0.131674i
\(300\) 0 0
\(301\) 4641.63 8039.54i 0.888835 1.53951i
\(302\) 2199.86 + 7464.70i 0.419165 + 1.42233i
\(303\) 0 0
\(304\) 1441.59 1035.18i 0.271977 0.195302i
\(305\) 12611.1i 2.36757i
\(306\) 0 0
\(307\) 6609.36i 1.22872i −0.789027 0.614359i \(-0.789415\pi\)
0.789027 0.614359i \(-0.210585\pi\)
\(308\) −1230.61 1906.56i −0.227664 0.352715i
\(309\) 0 0
\(310\) 6170.58 1818.48i 1.13053 0.333171i
\(311\) −2568.35 + 4448.51i −0.468288 + 0.811098i −0.999343 0.0362387i \(-0.988462\pi\)
0.531055 + 0.847337i \(0.321796\pi\)
\(312\) 0 0
\(313\) −3101.42 5371.82i −0.560072 0.970074i −0.997489 0.0708150i \(-0.977440\pi\)
0.437417 0.899259i \(-0.355893\pi\)
\(314\) 2383.13 + 2267.81i 0.428305 + 0.407579i
\(315\) 0 0
\(316\) 4487.75 222.685i 0.798911 0.0396424i
\(317\) −1580.62 + 912.574i −0.280053 + 0.161689i −0.633447 0.773786i \(-0.718361\pi\)
0.353395 + 0.935474i \(0.385027\pi\)
\(318\) 0 0
\(319\) −12.9048 7.45058i −0.00226498 0.00130769i
\(320\) 3093.52 7862.28i 0.540416 1.37348i
\(321\) 0 0
\(322\) 2150.50 + 519.451i 0.372182 + 0.0899003i
\(323\) 3252.68 0.560322
\(324\) 0 0
\(325\) −3292.93 −0.562027
\(326\) 8056.84 + 1946.13i 1.36880 + 0.330632i
\(327\) 0 0
\(328\) −326.966 + 114.253i −0.0550418 + 0.0192334i
\(329\) −4487.80 2591.03i −0.752038 0.434189i
\(330\) 0 0
\(331\) −3444.37 + 1988.61i −0.571963 + 0.330223i −0.757933 0.652332i \(-0.773791\pi\)
0.185970 + 0.982555i \(0.440457\pi\)
\(332\) 271.278 + 5467.05i 0.0448443 + 0.903745i
\(333\) 0 0
\(334\) 1786.53 + 1700.08i 0.292678 + 0.278516i
\(335\) −1081.00 1872.35i −0.176303 0.305366i
\(336\) 0 0
\(337\) 578.847 1002.59i 0.0935662 0.162061i −0.815443 0.578837i \(-0.803507\pi\)
0.909009 + 0.416776i \(0.136840\pi\)
\(338\) −4604.98 + 1357.10i −0.741059 + 0.218392i
\(339\) 0 0
\(340\) 13010.0 8397.48i 2.07520 1.33946i
\(341\) 1757.71i 0.279136i
\(342\) 0 0
\(343\) 4254.87i 0.669800i
\(344\) 1759.78 9278.79i 0.275816 1.45430i
\(345\) 0 0
\(346\) −1865.11 6328.80i −0.289795 0.983348i
\(347\) −1241.63 + 2150.56i −0.192086 + 0.332703i −0.945941 0.324337i \(-0.894859\pi\)
0.753855 + 0.657041i \(0.228192\pi\)
\(348\) 0 0
\(349\) 2986.90 + 5173.47i 0.458124 + 0.793494i 0.998862 0.0476973i \(-0.0151883\pi\)
−0.540738 + 0.841191i \(0.681855\pi\)
\(350\) −6388.60 + 6713.46i −0.975671 + 1.02528i
\(351\) 0 0
\(352\) −1821.69 1418.06i −0.275842 0.214724i
\(353\) 893.160 515.666i 0.134669 0.0777511i −0.431152 0.902279i \(-0.641893\pi\)
0.565821 + 0.824528i \(0.308559\pi\)
\(354\) 0 0
\(355\) 324.279 + 187.223i 0.0484815 + 0.0279908i
\(356\) −1015.19 + 1978.80i −0.151137 + 0.294596i
\(357\) 0 0
\(358\) −424.213 + 1756.22i −0.0626267 + 0.259271i
\(359\) 4218.99 0.620249 0.310125 0.950696i \(-0.399629\pi\)
0.310125 + 0.950696i \(0.399629\pi\)
\(360\) 0 0
\(361\) 6090.01 0.887886
\(362\) −2677.01 + 11082.7i −0.388676 + 1.60909i
\(363\) 0 0
\(364\) 1815.55 3538.87i 0.261431 0.509580i
\(365\) 5542.99 + 3200.25i 0.794887 + 0.458928i
\(366\) 0 0
\(367\) 2632.91 1520.11i 0.374487 0.216210i −0.300930 0.953646i \(-0.597297\pi\)
0.675417 + 0.737436i \(0.263964\pi\)
\(368\) 2239.64 222.813i 0.317254 0.0315623i
\(369\) 0 0
\(370\) −7516.11 + 7898.31i −1.05606 + 1.10977i
\(371\) −2012.34 3485.48i −0.281605 0.487754i
\(372\) 0 0
\(373\) −2558.92 + 4432.17i −0.355216 + 0.615253i −0.987155 0.159766i \(-0.948926\pi\)
0.631939 + 0.775018i \(0.282259\pi\)
\(374\) −1196.03 4058.42i −0.165361 0.561112i
\(375\) 0 0
\(376\) −5179.57 982.335i −0.710415 0.134734i
\(377\) 26.1183i 0.00356806i
\(378\) 0 0
\(379\) 2840.61i 0.384993i 0.981298 + 0.192497i \(0.0616585\pi\)
−0.981298 + 0.192497i \(0.938342\pi\)
\(380\) −3075.80 + 1985.31i −0.415224 + 0.268012i
\(381\) 0 0
\(382\) −9939.14 + 2929.09i −1.33123 + 0.392317i
\(383\) 2814.33 4874.56i 0.375472 0.650336i −0.614926 0.788585i \(-0.710814\pi\)
0.990397 + 0.138249i \(0.0441474\pi\)
\(384\) 0 0
\(385\) 2340.41 + 4053.70i 0.309814 + 0.536613i
\(386\) −2904.72 2764.16i −0.383022 0.364487i
\(387\) 0 0
\(388\) 209.691 + 4225.88i 0.0274367 + 0.552930i
\(389\) 3084.76 1780.99i 0.402065 0.232132i −0.285309 0.958435i \(-0.592096\pi\)
0.687375 + 0.726303i \(0.258763\pi\)
\(390\) 0 0
\(391\) 3572.30 + 2062.47i 0.462044 + 0.266761i
\(392\) −1132.31 3240.44i −0.145894 0.417517i
\(393\) 0 0
\(394\) −2410.96 582.365i −0.308280 0.0744648i
\(395\) −9268.46 −1.18062
\(396\) 0 0
\(397\) −9427.52 −1.19182 −0.595911 0.803050i \(-0.703209\pi\)
−0.595911 + 0.803050i \(0.703209\pi\)
\(398\) 4084.03 + 986.494i 0.514356 + 0.124242i
\(399\) 0 0
\(400\) −3882.56 + 8591.50i −0.485321 + 1.07394i
\(401\) 7475.17 + 4315.79i 0.930903 + 0.537457i 0.887097 0.461583i \(-0.152718\pi\)
0.0438059 + 0.999040i \(0.486052\pi\)
\(402\) 0 0
\(403\) 2668.10 1540.43i 0.329795 0.190407i
\(404\) −11457.5 + 568.529i −1.41097 + 0.0700133i
\(405\) 0 0
\(406\) −53.2487 50.6719i −0.00650908 0.00619410i
\(407\) 1489.54 + 2579.96i 0.181410 + 0.314211i
\(408\) 0 0
\(409\) −2932.40 + 5079.07i −0.354518 + 0.614044i −0.987035 0.160503i \(-0.948688\pi\)
0.632517 + 0.774546i \(0.282022\pi\)
\(410\) 685.298 201.959i 0.0825474 0.0243269i
\(411\) 0 0
\(412\) 997.387 + 1545.23i 0.119266 + 0.184777i
\(413\) 13955.3i 1.66270i
\(414\) 0 0
\(415\) 11291.0i 1.33555i
\(416\) 556.025 4007.98i 0.0655321 0.472373i
\(417\) 0 0
\(418\) 282.762 + 959.482i 0.0330869 + 0.112272i
\(419\) 3477.85 6023.82i 0.405500 0.702346i −0.588880 0.808221i \(-0.700431\pi\)
0.994379 + 0.105875i \(0.0337642\pi\)
\(420\) 0 0
\(421\) 4697.89 + 8136.99i 0.543851 + 0.941978i 0.998678 + 0.0513981i \(0.0163677\pi\)
−0.454827 + 0.890580i \(0.650299\pi\)
\(422\) 599.863 630.366i 0.0691964 0.0727151i
\(423\) 0 0
\(424\) −3102.33 2672.09i −0.355336 0.306057i
\(425\) −14964.2 + 8639.59i −1.70793 + 0.986074i
\(426\) 0 0
\(427\) −14720.4 8498.83i −1.66831 0.963202i
\(428\) 11930.6 + 6120.76i 1.34740 + 0.691258i
\(429\) 0 0
\(430\) −4574.06 + 18936.3i −0.512978 + 2.12370i
\(431\) 7346.03 0.820988 0.410494 0.911863i \(-0.365356\pi\)
0.410494 + 0.911863i \(0.365356\pi\)
\(432\) 0 0
\(433\) 13673.0 1.51751 0.758755 0.651376i \(-0.225808\pi\)
0.758755 + 0.651376i \(0.225808\pi\)
\(434\) 2035.82 8428.17i 0.225167 0.932177i
\(435\) 0 0
\(436\) 3848.42 + 1974.36i 0.422720 + 0.216869i
\(437\) −844.556 487.604i −0.0924498 0.0533759i
\(438\) 0 0
\(439\) 4995.87 2884.37i 0.543144 0.313584i −0.203208 0.979135i \(-0.565137\pi\)
0.746352 + 0.665551i \(0.231804\pi\)
\(440\) 3608.09 + 3107.72i 0.390930 + 0.336715i
\(441\) 0 0
\(442\) 5112.26 5372.22i 0.550148 0.578124i
\(443\) 4826.45 + 8359.66i 0.517634 + 0.896568i 0.999790 + 0.0204826i \(0.00652029\pi\)
−0.482157 + 0.876085i \(0.660146\pi\)
\(444\) 0 0
\(445\) 2293.79 3972.96i 0.244351 0.423228i
\(446\) −3121.02 10590.4i −0.331355 1.12437i
\(447\) 0 0
\(448\) −7092.53 8909.46i −0.747970 0.939582i
\(449\) 11492.2i 1.20791i 0.797018 + 0.603955i \(0.206410\pi\)
−0.797018 + 0.603955i \(0.793590\pi\)
\(450\) 0 0
\(451\) 195.209i 0.0203815i
\(452\) 5564.83 + 8621.46i 0.579088 + 0.897167i
\(453\) 0 0
\(454\) 5232.86 1542.14i 0.540948 0.159419i
\(455\) −4102.19 + 7105.19i −0.422667 + 0.732080i
\(456\) 0 0
\(457\) −8821.06 15278.5i −0.902914 1.56389i −0.823693 0.567036i \(-0.808090\pi\)
−0.0792214 0.996857i \(-0.525243\pi\)
\(458\) −4707.31 4479.53i −0.480258 0.457018i
\(459\) 0 0
\(460\) −4636.90 + 230.085i −0.469992 + 0.0233213i
\(461\) 11142.2 6432.95i 1.12569 0.649918i 0.182843 0.983142i \(-0.441470\pi\)
0.942848 + 0.333224i \(0.108137\pi\)
\(462\) 0 0
\(463\) 11984.7 + 6919.34i 1.20297 + 0.694534i 0.961214 0.275804i \(-0.0889440\pi\)
0.241754 + 0.970338i \(0.422277\pi\)
\(464\) −68.1446 30.7950i −0.00681796 0.00308109i
\(465\) 0 0
\(466\) −9255.98 2235.78i −0.920118 0.222254i
\(467\) −81.1441 −0.00804047 −0.00402024 0.999992i \(-0.501280\pi\)
−0.00402024 + 0.999992i \(0.501280\pi\)
\(468\) 0 0
\(469\) −2914.03 −0.286902
\(470\) 10570.6 + 2553.31i 1.03741 + 0.250586i
\(471\) 0 0
\(472\) 4683.27 + 13402.5i 0.456706 + 1.30699i
\(473\) 4609.74 + 2661.44i 0.448110 + 0.258717i
\(474\) 0 0
\(475\) 3537.80 2042.55i 0.341738 0.197302i
\(476\) −1034.35 20845.3i −0.0995998 2.00723i
\(477\) 0 0
\(478\) −1260.40 1199.41i −0.120606 0.114769i
\(479\) 7472.06 + 12942.0i 0.712750 + 1.23452i 0.963821 + 0.266550i \(0.0858838\pi\)
−0.251071 + 0.967969i \(0.580783\pi\)
\(480\) 0 0
\(481\) −2610.81 + 4522.06i −0.247490 + 0.428666i
\(482\) −11914.6 + 3511.25i −1.12592 + 0.331811i
\(483\) 0 0
\(484\) −7853.06 + 5068.86i −0.737515 + 0.476038i
\(485\) 8727.63i 0.817116i
\(486\) 0 0
\(487\) 5934.04i 0.552150i 0.961136 + 0.276075i \(0.0890338\pi\)
−0.961136 + 0.276075i \(0.910966\pi\)
\(488\) −16989.5 3222.15i −1.57598 0.298893i
\(489\) 0 0
\(490\) 2001.53 + 6791.72i 0.184531 + 0.626160i
\(491\) 10032.4 17376.6i 0.922110 1.59714i 0.125965 0.992035i \(-0.459797\pi\)
0.796145 0.605106i \(-0.206869\pi\)
\(492\) 0 0
\(493\) −68.5259 118.690i −0.00626015 0.0108429i
\(494\) −1208.63 + 1270.09i −0.110079 + 0.115676i
\(495\) 0 0
\(496\) −873.242 8777.53i −0.0790519 0.794602i
\(497\) 437.074 252.345i 0.0394476 0.0227751i
\(498\) 0 0
\(499\) 8148.09 + 4704.30i 0.730979 + 0.422031i 0.818780 0.574107i \(-0.194651\pi\)
−0.0878012 + 0.996138i \(0.527984\pi\)
\(500\) 1344.62 2620.92i 0.120266 0.234422i
\(501\) 0 0
\(502\) 5130.93 21241.8i 0.456185 1.88858i
\(503\) −12736.4 −1.12900 −0.564501 0.825432i \(-0.690931\pi\)
−0.564501 + 0.825432i \(0.690931\pi\)
\(504\) 0 0
\(505\) 23663.0 2.08513
\(506\) −297.845 + 1233.06i −0.0261676 + 0.108332i
\(507\) 0 0
\(508\) 9767.58 19038.9i 0.853084 1.66283i
\(509\) −7921.59 4573.53i −0.689820 0.398268i 0.113724 0.993512i \(-0.463722\pi\)
−0.803545 + 0.595244i \(0.797055\pi\)
\(510\) 0 0
\(511\) 7471.04 4313.40i 0.646769 0.373412i
\(512\) −9801.54 6176.37i −0.846037 0.533124i
\(513\) 0 0
\(514\) −5004.58 + 5259.07i −0.429460 + 0.451299i
\(515\) −1896.86 3285.45i −0.162302 0.281115i
\(516\) 0 0
\(517\) 1485.66 2573.23i 0.126381 0.218899i
\(518\) 4154.13 + 14096.0i 0.352359 + 1.19565i
\(519\) 0 0
\(520\) −1555.26 + 8200.42i −0.131159 + 0.691562i
\(521\) 7691.78i 0.646801i −0.946262 0.323400i \(-0.895174\pi\)
0.946262 0.323400i \(-0.104826\pi\)
\(522\) 0 0
\(523\) 9967.82i 0.833389i −0.909047 0.416694i \(-0.863189\pi\)
0.909047 0.416694i \(-0.136811\pi\)
\(524\) −5557.30 + 3587.03i −0.463305 + 0.299046i
\(525\) 0 0
\(526\) 10873.5 3204.45i 0.901347 0.265629i
\(527\) 8083.17 14000.5i 0.668138 1.15725i
\(528\) 0 0
\(529\) 5465.14 + 9465.89i 0.449177 + 0.777997i
\(530\) 6118.27 + 5822.21i 0.501435 + 0.477171i
\(531\) 0 0
\(532\) 244.539 + 4928.19i 0.0199288 + 0.401624i
\(533\) 296.316 171.078i 0.0240804 0.0139028i
\(534\) 0 0
\(535\) −23953.7 13829.7i −1.93572 1.11759i
\(536\) −2798.60 + 977.923i −0.225525 + 0.0788057i
\(537\) 0 0
\(538\) −6164.62 1489.06i −0.494007 0.119327i
\(539\) 1934.64 0.154603
\(540\) 0 0
\(541\) 6050.08 0.480801 0.240400 0.970674i \(-0.422721\pi\)
0.240400 + 0.970674i \(0.422721\pi\)
\(542\) −17387.2 4199.86i −1.37794 0.332840i
\(543\) 0 0
\(544\) −7988.88 19672.5i −0.629633 1.55046i
\(545\) −7726.70 4461.01i −0.607294 0.350622i
\(546\) 0 0
\(547\) −11232.1 + 6484.87i −0.877972 + 0.506898i −0.869989 0.493071i \(-0.835874\pi\)
−0.00798299 + 0.999968i \(0.502541\pi\)
\(548\) 5175.27 256.800i 0.403425 0.0200181i
\(549\) 0 0
\(550\) −3849.39 3663.12i −0.298434 0.283992i
\(551\) 16.2007 + 28.0605i 0.00125259 + 0.00216954i
\(552\) 0 0
\(553\) −6246.17 + 10818.7i −0.480315 + 0.831930i
\(554\) 3395.95 1000.80i 0.260434 0.0767504i
\(555\) 0 0
\(556\) 11585.8 + 17949.6i 0.883716 + 1.36912i
\(557\) 2223.88i 0.169172i 0.996416 + 0.0845859i \(0.0269567\pi\)
−0.996416 + 0.0845859i \(0.973043\pi\)
\(558\) 0 0
\(559\) 9329.75i 0.705915i
\(560\) 13701.3 + 19080.4i 1.03390 + 1.43981i
\(561\) 0 0
\(562\) 1098.96 + 3729.06i 0.0824855 + 0.279895i
\(563\) −8913.79 + 15439.1i −0.667267 + 1.15574i 0.311398 + 0.950280i \(0.399203\pi\)
−0.978665 + 0.205461i \(0.934131\pi\)
\(564\) 0 0
\(565\) −10583.3 18330.9i −0.788043 1.36493i
\(566\) −9019.67 + 9478.33i −0.669832 + 0.703894i
\(567\) 0 0
\(568\) 335.077 389.028i 0.0247527 0.0287381i
\(569\) −9765.76 + 5638.26i −0.719511 + 0.415410i −0.814573 0.580061i \(-0.803029\pi\)
0.0950615 + 0.995471i \(0.469695\pi\)
\(570\) 0 0
\(571\) −6527.00 3768.37i −0.478365 0.276184i 0.241370 0.970433i \(-0.422403\pi\)
−0.719735 + 0.694249i \(0.755737\pi\)
\(572\) 2029.13 + 1041.01i 0.148325 + 0.0760957i
\(573\) 0 0
\(574\) 226.096 936.023i 0.0164409 0.0680642i
\(575\) 5180.59 0.375731
\(576\) 0 0
\(577\) −16888.0 −1.21847 −0.609233 0.792991i \(-0.708523\pi\)
−0.609233 + 0.792991i \(0.708523\pi\)
\(578\) 5874.14 24318.6i 0.422720 1.75004i
\(579\) 0 0
\(580\) 137.244 + 70.4104i 0.00982540 + 0.00504075i
\(581\) −13179.5 7609.18i −0.941097 0.543343i
\(582\) 0 0
\(583\) 1998.51 1153.84i 0.141973 0.0819679i
\(584\) 5727.57 6649.77i 0.405836 0.471180i
\(585\) 0 0
\(586\) 12434.0 13066.3i 0.876527 0.921099i
\(587\) −8103.83 14036.3i −0.569814 0.986947i −0.996584 0.0825870i \(-0.973682\pi\)
0.426770 0.904360i \(1.64035\pi\)
\(588\) 0 0
\(589\) −1911.00 + 3309.96i −0.133687 + 0.231552i
\(590\) −8278.38 28090.7i −0.577654 1.96013i
\(591\) 0 0
\(592\) 8720.10 + 12143.6i 0.605395 + 0.843073i
\(593\) 22320.8i 1.54571i −0.634583 0.772855i \(-0.718828\pi\)
0.634583 0.772855i \(-0.281172\pi\)
\(594\) 0 0
\(595\) 43051.3i 2.96627i
\(596\) −452.109 700.442i −0.0310723 0.0481397i
\(597\) 0 0
\(598\) −2132.74 + 628.522i −0.145843 + 0.0429802i
\(599\) −4883.72 + 8458.84i −0.333127 + 0.576993i −0.983123 0.182944i \(-0.941437\pi\)
0.649996 + 0.759938i \(0.274771\pi\)
\(600\) 0 0
\(601\) −9316.81 16137.2i −0.632347 1.09526i −0.987071 0.160286i \(-0.948758\pi\)
0.354724 0.934971i \(-0.384575\pi\)
\(602\) 19021.0 + 18100.6i 1.28777 + 1.22546i
\(603\) 0 0
\(604\) −21984.1 + 1090.86i −1.48099 + 0.0734876i
\(605\) 16697.1 9640.08i 1.12204 0.647810i
\(606\) 0 0
\(607\) −371.545 214.512i −0.0248444 0.0143439i 0.487526 0.873108i \(-0.337899\pi\)
−0.512371 + 0.858764i \(0.671233\pi\)
\(608\) 1888.71 + 4650.92i 0.125983 + 0.310230i
\(609\) 0 0
\(610\) 34672.4 + 8375.10i 2.30138 + 0.555898i
\(611\) 5208.01 0.344834
\(612\) 0 0
\(613\) −4211.54 −0.277492 −0.138746 0.990328i \(-0.544307\pi\)
−0.138746 + 0.990328i \(0.544307\pi\)
\(614\) 18171.5 + 4389.31i 1.19437 + 0.288499i
\(615\) 0 0
\(616\) 6059.06 2117.23i 0.396309 0.138483i
\(617\) 23419.6 + 13521.3i 1.52810 + 0.882248i 0.999442 + 0.0334113i \(0.0106371\pi\)
0.528656 + 0.848836i \(0.322696\pi\)
\(618\) 0 0
\(619\) 8368.15 4831.35i 0.543367 0.313713i −0.203075 0.979163i \(-0.565094\pi\)
0.746442 + 0.665450i \(0.231760\pi\)
\(620\) 901.744 + 18172.8i 0.0584111 + 1.17716i
\(621\) 0 0
\(622\) −10524.9 10015.6i −0.678471 0.645640i
\(623\) −3091.65 5354.89i −0.198819 0.344364i
\(624\) 0 0
\(625\) 6168.97 10685.0i 0.394814 0.683838i
\(626\) 16828.7 4959.46i 1.07446 0.316645i
\(627\) 0 0
\(628\) −7817.66 + 5046.00i −0.496749 + 0.320633i
\(629\) 27399.8i 1.73688i
\(630\) 0 0
\(631\) 10846.5i 0.684297i −0.939646 0.342149i \(-0.888845\pi\)
0.939646 0.342149i \(-0.111155\pi\)
\(632\) −2368.10 + 12486.3i −0.149048 + 0.785885i
\(633\) 0 0
\(634\) −1459.29 4951.75i −0.0914130 0.310188i
\(635\) −22069.6 + 38225.6i −1.37922 + 2.38888i
\(636\) 0 0
\(637\) 1695.49 + 2936.67i 0.105459 + 0.182661i
\(638\) 29.0545 30.5319i 0.00180294 0.00189462i
\(639\) 0 0
\(640\) 19561.8 + 13726.6i 1.20820 + 0.847798i
\(641\) −12772.5 + 7374.18i −0.787023 + 0.454388i −0.838914 0.544265i \(-0.816809\pi\)
0.0518903 + 0.998653i \(0.483475\pi\)
\(642\) 0 0
\(643\) 12787.4 + 7382.82i 0.784271 + 0.452799i 0.837942 0.545759i \(-0.183759\pi\)
−0.0536706 + 0.998559i \(0.517092\pi\)
\(644\) −2856.31 + 5567.52i −0.174774 + 0.340669i
\(645\) 0 0
\(646\) −2160.12 + 8942.78i −0.131562 + 0.544658i
\(647\) −27157.4 −1.65018 −0.825090 0.565002i \(-0.808875\pi\)
−0.825090 + 0.565002i \(0.808875\pi\)
\(648\) 0 0
\(649\) −8001.72 −0.483968
\(650\) 2186.85 9053.43i 0.131962 0.546315i
\(651\) 0 0
\(652\) −10701.2 + 20858.7i −0.642777 + 1.25290i
\(653\) 2658.60 + 1534.94i 0.159325 + 0.0919861i 0.577542 0.816361i \(-0.304012\pi\)
−0.418218 + 0.908347i \(0.637345\pi\)
\(654\) 0 0
\(655\) 11815.9 6821.90i 0.704862 0.406952i
\(656\) −96.9813 974.823i −0.00577208 0.0580190i
\(657\) 0 0
\(658\) 10104.1 10617.9i 0.598628 0.629068i
\(659\) −579.767 1004.19i −0.0342709 0.0593589i 0.848381 0.529386i \(-0.177578\pi\)
−0.882652 + 0.470027i \(0.844244\pi\)
\(660\) 0 0
\(661\) −8919.74 + 15449.4i −0.524868 + 0.909097i 0.474713 + 0.880141i \(0.342552\pi\)
−0.999581 + 0.0289568i \(0.990781\pi\)
\(662\) −3179.97 10790.5i −0.186697 0.633509i
\(663\) 0 0
\(664\) −15211.0 2884.86i −0.889010 0.168606i
\(665\) 10178.1i 0.593517i
\(666\) 0 0
\(667\) 41.0905i 0.00238535i
\(668\) −5860.57 + 3782.78i −0.339449 + 0.219102i
\(669\) 0 0
\(670\) 5865.67 1728.62i 0.338225 0.0996755i
\(671\) 4873.09 8440.44i 0.280363 0.485603i
\(672\) 0 0
\(673\) 6058.30 + 10493.3i 0.346999 + 0.601020i 0.985715 0.168423i \(-0.0538673\pi\)
−0.638716 + 0.769443i \(0.720534\pi\)
\(674\) 2372.07 + 2257.28i 0.135562 + 0.129002i
\(675\) 0 0
\(676\) −672.953 13562.0i −0.0382882 0.771620i
\(677\) 18626.5 10754.0i 1.05742 0.610504i 0.132705 0.991156i \(-0.457634\pi\)
0.924718 + 0.380652i \(0.124300\pi\)
\(678\) 0 0
\(679\) −10187.4 5881.70i −0.575783 0.332428i
\(680\) 14447.6 + 41346.0i 0.814768 + 2.33169i
\(681\) 0 0
\(682\) 4832.57 + 1167.30i 0.271332 + 0.0655402i
\(683\) 33849.4 1.89636 0.948179 0.317738i \(-0.102923\pi\)
0.948179 + 0.317738i \(0.102923\pi\)
\(684\) 0 0
\(685\) −10688.4 −0.596178
\(686\) −11698.2 2825.68i −0.651075 0.157267i
\(687\) 0 0
\(688\) 24342.0 + 11000.3i 1.34888 + 0.609570i
\(689\) 3502.93 + 2022.42i 0.193688 + 0.111826i
\(690\) 0 0
\(691\) 1786.94 1031.69i 0.0983771 0.0567980i −0.450004 0.893026i \(-0.648578\pi\)
0.548381 + 0.836228i \(0.315244\pi\)
\(692\) 18638.8 924.866i 1.02390 0.0508065i
\(693\) 0 0
\(694\) −5088.08 4841.87i −0.278301 0.264834i
\(695\) −22034.1 38164.2i −1.20259 2.08295i
\(696\) 0 0
\(697\) 897.708 1554.88i 0.0487850 0.0844981i
\(698\) −16207.3 + 4776.33i −0.878877 + 0.259007i
\(699\) 0 0
\(700\) −14215.0 22023.0i −0.767538 1.18913i
\(701\) 19641.7i 1.05828i −0.848534 0.529141i \(-0.822514\pi\)
0.848534 0.529141i \(-0.177486\pi\)
\(702\) 0 0
\(703\) 6477.79i 0.347531i
\(704\) 5108.54 4066.74i 0.273488 0.217715i
\(705\) 0 0
\(706\) 824.598 + 2798.07i 0.0439577 + 0.149160i
\(707\) 15946.9 27620.8i 0.848295 1.46929i
\(708\) 0 0
\(709\) 2685.98 + 4652.26i 0.142277 + 0.246431i 0.928354 0.371698i \(-0.121224\pi\)
−0.786077 + 0.618129i \(0.787891\pi\)
\(710\) −730.097 + 767.223i −0.0385916 + 0.0405540i
\(711\) 0 0
\(712\) −4766.24 4105.25i −0.250874 0.216083i
\(713\) −4197.58 + 2423.47i −0.220478 + 0.127293i
\(714\) 0 0
\(715\) −4074.00 2352.13i −0.213090 0.123027i
\(716\) −4546.74 2332.63i −0.237318 0.121752i
\(717\) 0 0
\(718\) −2801.85 + 11599.5i −0.145633 + 0.602910i
\(719\) −12836.0 −0.665788 −0.332894 0.942964i \(-0.608025\pi\)
−0.332894 + 0.942964i \(0.608025\pi\)
\(720\) 0 0
\(721\) −5113.29 −0.264118
\(722\) −4044.41 + 16743.6i −0.208473 + 0.863065i
\(723\) 0 0
\(724\) −28692.4 14720.1i −1.47285 0.755620i
\(725\) −149.065 86.0630i −0.00763607 0.00440869i
\(726\) 0 0
\(727\) −29745.3 + 17173.5i −1.51746 + 0.876106i −0.517670 + 0.855580i \(0.673200\pi\)
−0.999789 + 0.0205251i \(0.993466\pi\)
\(728\) 8523.89 + 7341.78i 0.433951 + 0.373770i
\(729\) 0 0
\(730\) −12479.8 + 13114.4i −0.632735 + 0.664910i
\(731\) 24478.3 + 42397.6i 1.23852 + 2.14519i
\(732\) 0 0
\(733\) −4537.51 + 7859.19i −0.228645 + 0.396024i −0.957407 0.288743i \(-0.906763\pi\)
0.728762 + 0.684767i \(0.240096\pi\)
\(734\) 2430.80 + 8248.33i 0.122238 + 0.414784i
\(735\) 0 0
\(736\) −874.765 + 6305.54i −0.0438101 + 0.315795i
\(737\) 1670.85i 0.0835098i
\(738\) 0 0
\(739\) 16863.2i 0.839410i 0.907661 + 0.419705i \(0.137866\pi\)
−0.907661 + 0.419705i \(0.862134\pi\)
\(740\) −16723.8 25909.8i −0.830781 1.28711i
\(741\) 0 0
\(742\) 10919.2 3217.92i 0.540239 0.159210i
\(743\) −15021.9 + 26018.6i −0.741721 + 1.28470i 0.209990 + 0.977704i \(0.432657\pi\)
−0.951711 + 0.306995i \(0.900677\pi\)
\(744\) 0 0
\(745\) 859.832 + 1489.27i 0.0422843 + 0.0732386i
\(746\) −10486.2 9978.81i −0.514649 0.489745i
\(747\) 0 0
\(748\) 11952.3 593.081i 0.584252 0.0289909i
\(749\) −32285.6 + 18640.1i −1.57502 + 0.909338i
\(750\) 0 0
\(751\) −7313.00 4222.17i −0.355333 0.205152i 0.311698 0.950181i \(-0.399102\pi\)
−0.667032 + 0.745029i \(0.732435\pi\)
\(752\) 6140.57 13588.1i 0.297771 0.658920i
\(753\) 0 0
\(754\) 71.8084 + 17.3453i 0.00346831 + 0.000837769i
\(755\) 45403.2 2.18860
\(756\) 0 0
\(757\) 35193.1 1.68971 0.844857 0.534992i \(-0.179685\pi\)
0.844857 + 0.534992i \(0.179685\pi\)
\(758\) −7809.86 1886.47i −0.374231 0.0903952i
\(759\) 0 0
\(760\) −3415.68 9774.93i −0.163026 0.466545i
\(761\) −13659.8 7886.50i −0.650681 0.375671i 0.138036 0.990427i \(-0.455921\pi\)
−0.788717 + 0.614756i \(0.789254\pi\)
\(762\) 0 0
\(763\) −10414.3 + 6012.70i −0.494133 + 0.285288i
\(764\) −1452.47 29271.5i −0.0687806 1.38613i
\(765\) 0 0
\(766\) 11532.9 + 10974.8i 0.543996 + 0.517672i
\(767\) −7012.57 12146.1i −0.330129 0.571801i
\(768\) 0 0
\(769\) 10370.9 17962.9i 0.486325 0.842340i −0.513551 0.858059i \(-0.671670\pi\)
0.999876 + 0.0157189i \(0.00500369\pi\)
\(770\) −12699.4 + 3742.53i −0.594355 + 0.175158i
\(771\) 0 0
\(772\) 9528.70 6150.42i 0.444230 0.286734i
\(773\) 35223.1i 1.63892i 0.573133 + 0.819462i \(0.305728\pi\)
−0.573133 + 0.819462i \(0.694272\pi\)
\(774\) 0 0
\(775\) 20303.6i 0.941067i
\(776\) −11757.7 2229.92i −0.543915 0.103156i
\(777\) 0 0
\(778\) 2847.96 + 9663.86i 0.131239 + 0.445329i
\(779\) −212.234 + 367.600i −0.00976133 + 0.0169071i
\(780\) 0 0