Properties

Label 108.4.h.b.71.1
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 71.1
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +O(q^{10})\) \(q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +(-32.1756 - 33.8118i) q^{10} +(-6.37655 - 11.0445i) q^{11} +(-11.1766 + 19.3584i) q^{13} +(61.1508 - 14.7709i) q^{14} +(26.3558 + 58.3213i) q^{16} +117.295i q^{17} +27.7307i q^{19} +(60.2605 + 117.459i) q^{20} +(8.46941 + 35.0629i) q^{22} +(-17.5836 + 30.4556i) q^{23} +(73.6567 + 127.577i) q^{25} +(45.8008 - 43.5845i) q^{26} +(-177.716 - 8.81837i) q^{28} +(-1.01189 + 0.584217i) q^{29} +(119.361 + 68.9130i) q^{31} +(-24.8745 - 179.302i) q^{32} +(93.7830 - 318.230i) q^{34} -367.033 q^{35} +233.596 q^{37} +(22.1720 - 75.2352i) q^{38} +(-69.5764 - 366.856i) q^{40} +(-13.2561 - 7.65340i) q^{41} +(-361.460 + 208.689i) q^{43} +(5.05631 - 101.900i) q^{44} +(72.0561 - 68.5693i) q^{46} +(116.494 + 201.773i) q^{47} +(75.8499 - 131.376i) q^{49} +(-97.8316 - 405.017i) q^{50} +(-159.109 + 81.6278i) q^{52} -180.951i q^{53} -210.451i q^{55} +(475.105 + 166.017i) q^{56} +(3.21244 - 0.775964i) q^{58} +(313.716 - 543.373i) q^{59} +(-382.110 - 661.834i) q^{61} +(-268.735 - 282.400i) q^{62} +(-75.8742 + 506.347i) q^{64} +(-319.452 + 184.435i) q^{65} +(113.463 + 65.5077i) q^{67} +(-508.879 + 788.395i) q^{68} +(995.785 + 293.460i) q^{70} -22.6910 q^{71} +387.864 q^{73} +(-633.762 - 186.771i) q^{74} +(-120.308 + 186.390i) q^{76} +(245.650 + 141.826i) q^{77} +(486.411 - 280.830i) q^{79} +(-104.553 + 1050.93i) q^{80} +(29.8454 + 31.3630i) q^{82} +(342.111 + 592.554i) q^{83} +(-967.799 + 1676.28i) q^{85} +(1147.52 - 277.183i) q^{86} +(-95.1915 + 272.417i) q^{88} -278.003i q^{89} -497.177i q^{91} +(-250.317 + 128.421i) q^{92} +(-154.728 - 640.565i) q^{94} +(-228.805 + 396.302i) q^{95} +(-264.443 - 458.028i) q^{97} +(-310.827 + 295.786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71307 0.799546i −0.959214 0.282682i
\(3\) 0 0
\(4\) 6.72145 + 4.33844i 0.840181 + 0.542305i
\(5\) 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 −0.919848 0.392276i \(-0.871688\pi\)
−0.120203 + 0.992749i \(0.538355\pi\)
\(8\) −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 0.765304 0.643669i \(-0.222589\pi\)
−0.940086 + 0.340938i \(0.889255\pi\)
\(12\) 0 0
\(13\) −11.1766 + 19.3584i −0.238449 + 0.413005i −0.960269 0.279075i \(-0.909972\pi\)
0.721821 + 0.692080i \(0.243306\pi\)
\(14\) 61.1508 14.7709i 1.16737 0.281978i
\(15\) 0 0
\(16\) 26.3558 + 58.3213i 0.411810 + 0.911270i
\(17\) 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 \(0.0535427\pi\)
−0.985886 + 0.167417i \(0.946457\pi\)
\(20\) 60.2605 + 117.459i 0.673733 + 1.31324i
\(21\) 0 0
\(22\) 8.46941 + 35.0629i 0.0820766 + 0.339792i
\(23\) −17.5836 + 30.4556i −0.159410 + 0.276106i −0.934656 0.355553i \(-0.884292\pi\)
0.775246 + 0.631659i \(0.217626\pi\)
\(24\) 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 0.804190 0.594373i \(-0.202600\pi\)
−0.112647 + 0.993635i \(0.535933\pi\)
\(32\) −24.8745 179.302i −0.137414 0.990514i
\(33\) 0 0
\(34\) 93.7830 318.230i 0.473049 1.60518i
\(35\) −367.033 −1.77257
\(36\) 0 0
\(37\) 233.596 1.03792 0.518959 0.854799i \(-0.326320\pi\)
0.518959 + 0.854799i \(0.326320\pi\)
\(38\) 22.1720 75.2352i 0.0946518 0.321178i
\(39\) 0 0
\(40\) −69.5764 366.856i −0.275025 1.45013i
\(41\) −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 −0.977198 0.212332i \(-0.931894\pi\)
−0.304714 + 0.952444i \(0.598561\pi\)
\(44\) 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 0.988214 0.153076i \(-0.0489180\pi\)
−0.626675 + 0.779281i \(0.715585\pi\)
\(48\) 0 0
\(49\) 75.8499 131.376i 0.221137 0.383020i
\(50\) −97.8316 405.017i −0.276710 1.14556i
\(51\) 0 0
\(52\) −159.109 + 81.6278i −0.424315 + 0.217687i
\(53\) 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
\(56\) 475.105 + 166.017i 1.13372 + 0.396160i
\(57\) 0 0
\(58\) 3.21244 0.775964i 0.00727266 0.00175671i
\(59\) 313.716 543.373i 0.692244 1.19900i −0.278857 0.960333i \(-0.589955\pi\)
0.971101 0.238669i \(-0.0767112\pi\)
\(60\) 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 0.599866 0.800101i \(-0.295221\pi\)
−0.392975 + 0.919549i \(0.628554\pi\)
\(68\) −508.879 + 788.395i −0.907510 + 1.40598i
\(69\) 0 0
\(70\) 995.785 + 293.460i 1.70027 + 0.501074i
\(71\) −22.6910 −0.0379285 −0.0189643 0.999820i \(-0.506037\pi\)
−0.0189643 + 0.999820i \(0.506037\pi\)
\(72\) 0 0
\(73\) 387.864 0.621863 0.310932 0.950432i \(-0.399359\pi\)
0.310932 + 0.950432i \(0.399359\pi\)
\(74\) −633.762 186.771i −0.995586 0.293401i
\(75\) 0 0
\(76\) −120.308 + 186.390i −0.181583 + 0.281322i
\(77\) 245.650 + 141.826i 0.363565 + 0.209904i
\(78\) 0 0
\(79\) 486.411 280.830i 0.692729 0.399947i −0.111905 0.993719i \(-0.535695\pi\)
0.804633 + 0.593772i \(0.202362\pi\)
\(80\) −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 0.998536 0.0540856i \(-0.0172244\pi\)
−0.546108 + 0.837715i \(0.683891\pi\)
\(84\) 0 0
\(85\) −967.799 + 1676.28i −1.23497 + 2.13903i
\(86\) 1147.52 277.183i 1.43884 0.347552i
\(87\) 0 0
\(88\) −95.1915 + 272.417i −0.115312 + 0.329998i
\(89\) 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
\(92\) −250.317 + 128.421i −0.283667 + 0.145530i
\(93\) 0 0
\(94\) −154.728 640.565i −0.169776 0.702865i
\(95\) −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 0.592198 0.805792i \(-0.298260\pi\)
−0.401738 + 0.915755i \(0.631594\pi\)
\(104\) 496.937 94.2469i 0.468545 0.0888622i
\(105\) 0 0
\(106\) −144.679 + 490.932i −0.132570 + 0.449844i
\(107\) 1676.13 1.51437 0.757184 0.653201i \(-0.226574\pi\)
0.757184 + 0.653201i \(0.226574\pi\)
\(108\) 0 0
\(109\) −540.666 −0.475104 −0.237552 0.971375i \(-0.576345\pi\)
−0.237552 + 0.971375i \(0.576345\pi\)
\(110\) −168.265 + 570.967i −0.145850 + 0.494905i
\(111\) 0 0
\(112\) −1156.25 830.284i −0.975496 0.700486i
\(113\) −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
\(122\) 507.523 + 2101.11i 0.376631 + 1.55923i
\(123\) 0 0
\(124\) 503.303 + 981.035i 0.364499 + 0.710480i
\(125\) 368.214i 0.263472i
\(126\) 0 0
\(127\) 2674.79i 1.86889i −0.356109 0.934444i \(-0.615897\pi\)
0.356109 0.934444i \(-0.384103\pi\)
\(128\) 610.699 1313.09i 0.421709 0.906731i
\(129\) 0 0
\(130\) 1014.16 244.969i 0.684212 0.165271i
\(131\) −413.401 + 716.031i −0.275717 + 0.477557i −0.970316 0.241841i \(-0.922249\pi\)
0.694598 + 0.719398i \(0.255582\pi\)
\(132\) 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 0.995505 0.0947110i \(-0.0301927\pi\)
0.415730 + 0.909488i \(0.363526\pi\)
\(140\) −2467.00 1592.35i −1.48928 0.961274i
\(141\) 0 0
\(142\) 61.5622 + 18.1425i 0.0363816 + 0.0107217i
\(143\) 285.073 0.166706
\(144\) 0 0
\(145\) −19.2814 −0.0110430
\(146\) −1052.30 310.115i −0.596500 0.175790i
\(147\) 0 0
\(148\) 1570.11 + 1013.44i 0.872040 + 0.562869i
\(149\) 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 −0.977605 0.210448i \(-0.932508\pi\)
−0.306549 + 0.951855i \(0.599174\pi\)
\(152\) 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 \(0.0711404\pi\)
\(158\) −1544.20 + 373.001i −0.777533 + 0.187812i
\(159\) 0 0
\(160\) 1123.93 2767.66i 0.555341 1.36752i
\(161\) 782.182i 0.382886i
\(162\) 0 0
\(163\) 2930.45i 1.40816i 0.710120 + 0.704081i \(0.248641\pi\)
−0.710120 + 0.704081i \(0.751359\pi\)
\(164\) −55.8963 108.953i −0.0266144 0.0518767i
\(165\) 0 0
\(166\) −454.396 1881.17i −0.212458 0.879562i
\(167\) −435.960 + 755.105i −0.202010 + 0.349891i −0.949176 0.314746i \(-0.898081\pi\)
0.747166 + 0.664637i \(0.231414\pi\)
\(168\) 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
\(176\) 476.071 662.976i 0.203893 0.283941i
\(177\) 0 0
\(178\) −222.276 + 754.239i −0.0935971 + 0.317599i
\(179\) −638.773 −0.266727 −0.133364 0.991067i \(-0.542578\pi\)
−0.133364 + 0.991067i \(0.542578\pi\)
\(180\) 0 0
\(181\) 4031.01 1.65537 0.827686 0.561192i \(-0.189657\pi\)
0.827686 + 0.561192i \(0.189657\pi\)
\(182\) −397.516 + 1348.87i −0.161900 + 0.549369i
\(183\) 0 0
\(184\) 781.805 148.274i 0.313236 0.0594070i
\(185\) 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 \(-0.922550\pi\)
0.276626 0.960978i \(1.58922\pi\)
\(192\) 0 0
\(193\) −708.828 + 1227.73i −0.264366 + 0.457895i −0.967397 0.253264i \(-0.918496\pi\)
0.703032 + 0.711159i \(0.251829\pi\)
\(194\) 351.236 + 1454.10i 0.129986 + 0.538134i
\(195\) 0 0
\(196\) 1079.79 553.966i 0.393509 0.201883i
\(197\) 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 \(0.0852315\pi\)
−0.964365 + 0.264574i \(0.914769\pi\)
\(200\) 1099.57 3146.74i 0.388758 1.11254i
\(201\) 0 0
\(202\) −3942.45 + 952.297i −1.37322 + 0.331700i
\(203\) 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 0.542835 0.839840i \(-0.317351\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(212\) 785.045 1216.25i 0.254326 0.394021i
\(213\) 0 0
\(214\) −4547.45 1340.14i −1.45260 0.428085i
\(215\) −6887.55 −2.18478
\(216\) 0 0
\(217\) −3065.50 −0.958986
\(218\) 1466.86 + 432.287i 0.455727 + 0.134304i
\(219\) 0 0
\(220\) 913.029 1414.53i 0.279802 0.433491i
\(221\) −2270.66 1310.96i −0.691135 0.399027i
\(222\) 0 0
\(223\) 3380.52 1951.74i 1.01514 0.586091i 0.102447 0.994738i \(-0.467333\pi\)
0.912692 + 0.408647i \(0.133999\pi\)
\(224\) 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 0.971871 0.235514i \(-0.0756773\pi\)
−0.689896 + 0.723908i \(0.742344\pi\)
\(228\) 0 0
\(229\) −1148.71 + 1989.62i −0.331479 + 0.574139i −0.982802 0.184662i \(-0.940881\pi\)
0.651323 + 0.758801i \(0.274214\pi\)
\(230\) 1595.52 385.397i 0.457416 0.110488i
\(231\) 0 0
\(232\) 24.9588 + 8.72140i 0.00706303 + 0.00246805i
\(233\) 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
\(236\) 4466.02 2291.21i 1.23184 0.631972i
\(237\) 0 0
\(238\) 1732.56 + 7172.70i 0.471871 + 1.95352i
\(239\) 307.571 532.729i 0.0832432 0.144182i −0.821398 0.570355i \(-0.806805\pi\)
0.904641 + 0.426174i \(0.140139\pi\)
\(240\) 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
\(248\) −581.110 3064.03i −0.148792 0.784540i
\(249\) 0 0
\(250\) 294.404 998.988i 0.0744790 0.252726i
\(251\) 7726.08 1.94289 0.971446 0.237259i \(-0.0762489\pi\)
0.971446 + 0.237259i \(0.0762489\pi\)
\(252\) 0 0
\(253\) 448.490 0.111448
\(254\) −2138.62 + 7256.87i −0.528302 + 1.79266i
\(255\) 0 0
\(256\) −2706.74 + 3074.21i −0.660826 + 0.750539i
\(257\) 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 0.999405 0.0344862i \(-0.0109795\pi\)
−0.529569 + 0.848267i \(0.677646\pi\)
\(264\) 0 0
\(265\) 1493.02 2585.98i 0.346096 0.599456i
\(266\) 409.608 + 1695.75i 0.0944161 + 0.390877i
\(267\) 0 0
\(268\) 478.433 + 932.559i 0.109048 + 0.212556i
\(269\) 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 \(-0.749244\pi\)
0.705426 0.708784i \(-0.250756\pi\)
\(272\) −6840.81 + 3091.41i −1.52495 + 0.689134i
\(273\) 0 0
\(274\) 1780.77 430.144i 0.392629 0.0948393i
\(275\) 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 0.0162801 0.999867i \(-0.494818\pi\)
−0.857771 + 0.514033i \(0.828151\pi\)
\(284\) −152.516 98.4436i −0.0318669 0.0205689i
\(285\) 0 0
\(286\) −773.422 227.929i −0.159907 0.0471249i
\(287\) 340.452 0.0700217
\(288\) 0 0
\(289\) −8845.19 −1.80037
\(290\) 52.3117 + 15.4164i 0.0105926 + 0.00312166i
\(291\) 0 0
\(292\) 2607.01 + 1682.73i 0.522478 + 0.337240i
\(293\) −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
\(302\) 7564.55 1827.21i 1.44136 0.348160i
\(303\) 0 0
\(304\) −1617.29 + 730.865i −0.305125 + 0.137888i
\(305\) 12611.1i 2.36757i
\(306\) 0 0
\(307\) 6609.36i 1.22872i 0.789027 + 0.614359i \(0.210585\pi\)
−0.789027 + 0.614359i \(0.789415\pi\)
\(308\) 1035.82 + 2019.02i 0.191628 + 0.373521i
\(309\) 0 0
\(310\) −1510.44 6253.12i −0.276732 1.14566i
\(311\) 2568.35 4448.51i 0.468288 0.811098i −0.531055 0.847337i \(-0.678204\pi\)
0.999343 + 0.0362387i \(0.0115377\pi\)
\(312\) 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
\(320\) −5262.17 + 6610.21i −0.919264 + 1.15476i
\(321\) 0 0
\(322\) −625.391 + 2122.11i −0.108235 + 0.367269i
\(323\) −3252.68 −0.560322
\(324\) 0 0
\(325\) −3292.93 −0.562027
\(326\) 2343.03 7950.49i 0.398062 1.35073i
\(327\) 0 0
\(328\) 64.5375 + 340.288i 0.0108643 + 0.0572843i
\(329\) −4487.80 2591.03i −0.752038 0.434189i
\(330\) 0 0
\(331\) 3444.37 1988.61i 0.571963 0.330223i −0.185970 0.982555i \(-0.559543\pi\)
0.757933 + 0.652332i \(0.226209\pi\)
\(332\) −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 \(0.136840\pi\)
\(338\) −1127.21 4666.58i −0.181397 0.750971i
\(339\) 0 0
\(340\) −13777.4 + 7068.27i −2.19761 + 1.12744i
\(341\) 1757.71i 0.279136i
\(342\) 0 0
\(343\) 4254.87i 0.669800i
\(344\) 8915.56 + 3115.39i 1.39737 + 0.488286i
\(345\) 0 0
\(346\) 6413.46 1549.17i 0.996502 0.240704i
\(347\) 1241.63 2150.56i 0.192086 0.332703i −0.753855 0.657041i \(-0.771808\pi\)
0.945941 + 0.324337i \(0.105141\pi\)
\(348\) 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
\(356\) 1206.10 1868.58i 0.179559 0.278187i
\(357\) 0 0
\(358\) 1733.03 + 510.729i 0.255848 + 0.0753991i
\(359\) −4218.99 −0.620249 −0.310125 0.950696i \(-0.600371\pi\)
−0.310125 + 0.950696i \(0.600371\pi\)
\(360\) 0 0
\(361\) 6090.01 0.887886
\(362\) −10936.4 3222.98i −1.58785 0.467944i
\(363\) 0 0
\(364\) 2156.97 3341.75i 0.310594 0.481196i
\(365\) 5542.99 + 3200.25i 0.794887 + 0.458928i
\(366\) 0 0
\(367\) −2632.91 + 1520.11i −0.374487 + 0.216210i −0.675417 0.737436i \(-0.736036\pi\)
0.300930 + 0.953646i \(0.402703\pi\)
\(368\) −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 \(0.282259\pi\)
\(374\) −4112.71 + 993.422i −0.568618 + 0.137349i
\(375\) 0 0
\(376\) 1739.06 4976.81i 0.238524 0.682604i
\(377\) 26.1183i 0.00356806i
\(378\) 0 0
\(379\) 2840.61i 0.384993i −0.981298 0.192497i \(-0.938342\pi\)
0.981298 0.192497i \(-0.0616585\pi\)
\(380\) −3257.23 + 1671.06i −0.439717 + 0.225589i
\(381\) 0 0
\(382\) 2432.91 + 10072.1i 0.325860 + 1.34904i
\(383\) −2814.33 + 4874.56i −0.375472 + 0.650336i −0.990397 0.138249i \(-0.955853\pi\)
0.614926 + 0.788585i \(0.289186\pi\)
\(384\) 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
\(392\) −3372.46 + 639.606i −0.434528 + 0.0824106i
\(393\) 0 0
\(394\) 701.135 2379.13i 0.0896515 0.304211i
\(395\) 9268.46 1.18062
\(396\) 0 0
\(397\) −9427.52 −1.19182 −0.595911 0.803050i \(-0.703209\pi\)
−0.595911 + 0.803050i \(0.703209\pi\)
\(398\) 1187.68 4030.12i 0.149581 0.507567i
\(399\) 0 0
\(400\) −5499.18 + 7658.15i −0.687397 + 0.957269i
\(401\) 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 \(0.282022\pi\)
\(410\) 167.748 + 694.465i 0.0202060 + 0.0836516i
\(411\) 0 0
\(412\) 839.514 + 1636.38i 0.100388 + 0.195676i
\(413\) 13955.3i 1.66270i
\(414\) 0 0
\(415\) 11291.0i 1.33555i
\(416\) 3749.02 + 1522.46i 0.441853 + 0.179434i
\(417\) 0 0
\(418\) −972.317 + 234.863i −0.113774 + 0.0274821i
\(419\) −3477.85 + 6023.82i −0.405500 + 0.702346i −0.994379 0.105875i \(-0.966236\pi\)
0.588880 + 0.808221i \(0.299569\pi\)
\(420\) 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
\(428\) 11266.0 + 7271.79i 1.27234 + 0.821250i
\(429\) 0 0
\(430\) 18686.4 + 5506.91i 2.09567 + 0.617597i
\(431\) −7346.03 −0.820988 −0.410494 0.911863i \(-0.634644\pi\)
−0.410494 + 0.911863i \(0.634644\pi\)
\(432\) 0 0
\(433\) 13673.0 1.51751 0.758755 0.651376i \(-0.225808\pi\)
0.758755 + 0.651376i \(0.225808\pi\)
\(434\) 8316.92 + 2451.01i 0.919873 + 0.271088i
\(435\) 0 0
\(436\) −3634.06 2345.65i −0.399174 0.257652i
\(437\) −844.556 487.604i −0.0924498 0.0533759i
\(438\) 0 0
\(439\) −4995.87 + 2884.37i −0.543144 + 0.313584i −0.746352 0.665551i \(-0.768196\pi\)
0.203208 + 0.979135i \(0.434863\pi\)
\(440\) −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 \(-0.993480\pi\)
0.482157 0.876085i \(1.66015\pi\)
\(444\) 0 0
\(445\) 2293.79 3972.96i 0.244351 0.423228i
\(446\) −10732.1 + 2592.33i −1.13941 + 0.275225i
\(447\) 0 0
\(448\) −4169.56 10597.0i −0.439716 1.11755i
\(449\) 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
\(452\) −4683.99 9130.02i −0.487426 0.950088i
\(453\) 0 0
\(454\) −1280.90 5302.86i −0.132413 0.548184i
\(455\) 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 −0.241754 0.970338i \(-0.577723\pi\)
−0.961214 + 0.275804i \(0.911056\pi\)
\(464\) −60.7416 43.6174i −0.00607728 0.00436398i
\(465\) 0 0
\(466\) 2691.75 9133.80i 0.267581 0.907972i
\(467\) 81.1441 0.00804047 0.00402024 0.999992i \(-0.498720\pi\)
0.00402024 + 0.999992i \(0.498720\pi\)
\(468\) 0 0
\(469\) −2914.03 −0.286902
\(470\) 3074.05 10431.0i 0.301692 1.02372i
\(471\) 0 0
\(472\) −13948.5 + 2645.42i −1.36024 + 0.257977i
\(473\) 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 \(-0.914116\pi\)
0.251071 0.967969i \(1.58078\pi\)
\(480\) 0 0
\(481\) −2610.81 + 4522.06i −0.247490 + 0.428666i
\(482\) −2916.45 12073.9i −0.275603 1.14098i
\(483\) 0 0
\(484\) 8316.29 4266.52i 0.781019 0.400688i
\(485\) 8727.63i 0.817116i
\(486\) 0 0
\(487\) 5934.04i 0.552150i −0.961136 0.276075i \(-0.910966\pi\)
0.961136 0.276075i \(-0.0890338\pi\)
\(488\) −5704.27 + 16324.4i −0.529140 + 1.51428i
\(489\) 0 0
\(490\) −6882.57 + 1662.48i −0.634536 + 0.153272i
\(491\) −10032.4 + 17376.6i −0.922110 + 1.59714i −0.125965 + 0.992035i \(0.540203\pi\)
−0.796145 + 0.605106i \(0.793131\pi\)
\(492\) 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 0.0878012 0.996138i \(-0.472016\pi\)
−0.818780 + 0.574107i \(0.805349\pi\)
\(500\) −1597.47 + 2474.93i −0.142882 + 0.221365i
\(501\) 0 0
\(502\) −20961.4 6177.36i −1.86365 0.549221i
\(503\) 12736.4 1.12900 0.564501 0.825432i \(-0.309069\pi\)
0.564501 + 0.825432i \(0.309069\pi\)
\(504\) 0 0
\(505\) 23663.0 2.08513
\(506\) −1216.78 358.589i −0.106902 0.0315044i
\(507\) 0 0
\(508\) 11604.4 17978.4i 1.01351 1.57021i
\(509\) −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
\(518\) 14284.6 3450.43i 1.21164 0.292671i
\(519\) 0 0
\(520\) 7879.40 + 2753.32i 0.664489 + 0.232194i
\(521\) 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 \(0.136811\pi\)
−0.909047 + 0.416694i \(0.863189\pi\)
\(524\) −5885.11 + 3019.25i −0.490634 + 0.251711i
\(525\) 0 0
\(526\) −2661.63 11019.0i −0.220632 0.913404i
\(527\) −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
\(536\) −552.395 2912.62i −0.0445146 0.234713i
\(537\) 0 0
\(538\) 1792.75 6083.25i 0.143663 0.487486i
\(539\) −1934.64 −0.154603
\(540\) 0 0
\(541\) 6050.08 0.480801 0.240400 0.970674i \(-0.422721\pi\)
0.240400 + 0.970674i \(0.422721\pi\)
\(542\) −5056.40 + 17157.7i −0.400721 + 1.35975i
\(543\) 0 0
\(544\) 21031.3 2917.66i 1.65755 0.229952i
\(545\) −7726.70 4461.01i −0.607294 0.350622i
\(546\) 0 0
\(547\) 11232.1 6484.87i 0.877972 0.506898i 0.00798299 0.999968i \(-0.497459\pi\)
0.869989 + 0.493071i \(0.164126\pi\)
\(548\) −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
\(554\) 831.263 + 3441.38i 0.0637491 + 0.263917i
\(555\) 0 0
\(556\) 9751.90 + 19008.4i 0.743836 + 1.44988i
\(557\) 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
\(560\) −9673.46 21405.8i −0.729961 1.61529i
\(561\) 0 0
\(562\) −3778.94 + 912.800i −0.283639 + 0.0685127i
\(563\) 8913.79 15439.1i 0.667267 1.15574i −0.311398 0.950280i \(-0.600797\pi\)
0.978665 0.205461i \(-0.0658695\pi\)
\(564\) 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 0.719735 0.694249i \(-0.244263\pi\)
−0.241370 + 0.970433i \(0.577597\pi\)
\(572\) 1916.10 + 1236.77i 0.140064 + 0.0904057i
\(573\) 0 0
\(574\) −923.668 272.207i −0.0671657 0.0197939i
\(575\) −5180.59 −0.375731
\(576\) 0 0
\(577\) −16888.0 −1.21847 −0.609233 0.792991i \(-0.708523\pi\)
−0.609233 + 0.792991i \(0.708523\pi\)
\(578\) 23997.6 + 7072.14i 1.72693 + 0.508931i
\(579\) 0 0
\(580\) −129.599 83.6513i −0.00927812 0.00598867i
\(581\) −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 \(0.0263182\pi\)
−0.426770 + 0.904360i \(0.640348\pi\)
\(588\) 0 0
\(589\) −1911.00 + 3309.96i −0.133687 + 0.231552i
\(590\) −28466.4 + 6876.05i −1.98635 + 0.479801i
\(591\) 0 0
\(592\) 6156.62 + 13623.6i 0.427425 + 0.945824i
\(593\) 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
\(596\) 380.546 + 741.759i 0.0261540 + 0.0509793i
\(597\) 0 0
\(598\) 522.052 + 2161.27i 0.0356995 + 0.147794i
\(599\) 4883.72 8458.84i 0.333127 0.576993i −0.649996 0.759938i \(-0.725229\pi\)
0.983123 + 0.182944i \(0.0585628\pi\)
\(600\) 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 0.512371 0.858764i \(-0.328767\pi\)
−0.487526 + 0.873108i \(0.662101\pi\)
\(608\) 4972.17 689.787i 0.331658 0.0460108i
\(609\) 0 0
\(610\) −10083.2 + 34214.7i −0.669270 + 2.27101i
\(611\) −5208.01 −0.344834
\(612\) 0 0
\(613\) −4211.54 −0.277492 −0.138746 0.990328i \(-0.544307\pi\)
−0.138746 + 0.990328i \(0.544307\pi\)
\(614\) 5284.49 17931.6i 0.347337 1.17860i
\(615\) 0 0
\(616\) −1195.95 6305.92i −0.0782246 0.412456i
\(617\) 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 −0.746442 0.665450i \(-0.768240\pi\)
0.203075 + 0.979163i \(0.434906\pi\)
\(620\) −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
\(626\) 4119.34 + 17053.8i 0.263006 + 1.08883i
\(627\) 0 0
\(628\) 8278.80 4247.29i 0.526051 0.269881i
\(629\) 27399.8i 1.73688i
\(630\) 0 0
\(631\) 10846.5i 0.684297i 0.939646 + 0.342149i \(0.111155\pi\)
−0.939646 + 0.342149i \(0.888845\pi\)
\(632\) −11997.5 4192.33i −0.755120 0.263864i
\(633\) 0 0
\(634\) 5017.98 1212.09i 0.314337 0.0759279i
\(635\) 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 0.0536706 0.998559i \(-0.482908\pi\)
−0.837942 + 0.545759i \(0.816241\pi\)
\(644\) 3393.45 5257.40i 0.207641 0.321693i
\(645\) 0 0
\(646\) 8824.73 + 2600.67i 0.537468 + 0.158393i
\(647\) 27157.4 1.65018 0.825090 0.565002i \(-0.191125\pi\)
0.825090 + 0.565002i \(0.191125\pi\)
\(648\) 0 0
\(649\) −8001.72 −0.483968
\(650\) 8933.93 + 2632.85i 0.539104 + 0.158875i
\(651\) 0 0
\(652\) −12713.6 + 19696.9i −0.763653 + 1.18311i
\(653\) 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 0.882652 0.470027i \(-0.155756\pi\)
−0.848381 + 0.529386i \(0.822422\pi\)
\(660\) 0 0
\(661\) −8919.74 + 15449.4i −0.524868 + 0.909097i 0.474713 + 0.880141i \(0.342552\pi\)
−0.999581 + 0.0289568i \(0.990781\pi\)
\(662\) −10934.8 + 2641.29i −0.641983 + 0.155071i
\(663\) 0 0
\(664\) 5107.16 14615.6i 0.298488 0.854208i
\(665\) 10178.1i 0.593517i
\(666\) 0 0
\(667\) 41.0905i 0.00238535i
\(668\) −6206.27 + 3184.01i −0.359472 + 0.184421i
\(669\) 0 0
\(670\) −1435.80 5944.13i −0.0827908 0.342749i
\(671\) −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
\(680\) 43030.5 8160.98i 2.42668 0.460234i
\(681\) 0 0
\(682\) −1405.37 + 4768.78i −0.0789068 + 0.267751i
\(683\) −33849.4 −1.89636 −0.948179 0.317738i \(-0.897077\pi\)
−0.948179 + 0.317738i \(0.897077\pi\)
\(684\) 0 0
\(685\) −10688.4 −0.596178
\(686\) −3401.97 + 11543.7i −0.189341 + 0.642481i
\(687\) 0 0
\(688\) −21697.6 15580.7i −1.20234 0.863382i
\(689\) 3502.93 + 2022.42i 0.193688 + 0.111826i
\(690\) 0 0
\(691\) −1786.94 + 1031.69i −0.0983771 + 0.0567980i −0.548381 0.836228i \(-0.684756\pi\)
0.450004 + 0.893026i \(0.351422\pi\)
\(692\) −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
\(698\) −3967.24 16424.1i −0.215132 0.890634i
\(699\) 0 0
\(700\) −11965.0 23322.0i −0.646047 1.25927i
\(701\) 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
\(704\) 6076.17 2390.75i 0.325290 0.127990i
\(705\) 0 0
\(706\) −2835.50 + 684.914i −0.151155 + 0.0365114i
\(707\) −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
\(716\) −4293.48 2771.28i −0.224099 0.144648i
\(717\) 0 0
\(718\) 11446.4 + 3373.27i 0.594952 + 0.175334i
\(719\) 12836.0 0.665788 0.332894 0.942964i \(-0.391975\pi\)
0.332894 + 0.942964i \(0.391975\pi\)
\(720\) 0 0
\(721\) −5113.29 −0.264118
\(722\) −16522.6 4869.24i −0.851672 0.250990i
\(723\) 0 0
\(724\) 27094.2 + 17488.3i 1.39081 + 0.897717i
\(725\) −149.065 86.0630i −0.00763607 0.00440869i
\(726\) 0 0
\(727\) 29745.3 17173.5i 1.51746 0.876106i 0.517670 0.855580i \(-0.326800\pi\)
0.999789 0.0205251i \(-0.00653380\pi\)
\(728\) −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 \(0.240096\pi\)
\(734\) 8358.66 2019.03i 0.420332 0.101531i
\(735\) 0 0
\(736\) 5898.14 + 2395.20i 0.295392 + 0.119957i
\(737\) 1670.85i 0.0835098i
\(738\) 0 0
\(739\) 16863.2i 0.839410i −0.907661 0.419705i \(-0.862134\pi\)
0.907661 0.419705i \(-0.137866\pi\)
\(740\) 14076.6 + 27438.1i 0.699280 + 1.36303i
\(741\) 0 0
\(742\) −2672.81 11065.3i −0.132240 0.547466i
\(743\) 15021.9 26018.6i 0.741721 1.28470i −0.209990 0.977704i \(-0.567343\pi\)
0.951711 0.306995i \(-0.0993235\pi\)
\(744\) 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 0.667032 0.745029i \(-0.267565\pi\)
−0.311698 + 0.950181i \(0.600898\pi\)
\(752\) −8697.37 + 12111.9i −0.421756 + 0.587337i
\(753\) 0 0
\(754\) −20.8828 + 70.8605i −0.00100863 + 0.00342253i
\(755\) −45403.2 −2.18860
\(756\) 0 0
\(757\) 35193.1 1.68971 0.844857 0.534992i \(-0.179685\pi\)
0.844857 + 0.534992i \(0.179685\pi\)
\(758\) −2271.20 + 7706.77i −0.108831 + 0.369291i
\(759\) 0 0
\(760\) 10173.2 1929.40i 0.485553 0.0920878i
\(761\) −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 \(0.00500369\pi\)
\(770\) −3108.55 12869.2i −0.145486 0.602305i
\(771\) 0 0
\(772\) −10090.8 + 5176.89i −0.470434 + 0.241348i
\(773\) 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
\(776\) −3947.70 + 11297.4i −0.182621 + 0.522622i
\(777\) 0 0
\(778\) −9793.13 + 2365.52i −0.451286 + 0.109008i
\(779\) 212.234 367.600i 0.00976133 0.0169071i
\(780\) 0 0