Properties

Label 117.4.g.b.100.1
Level $117$
Weight $4$
Character 117.100
Analytic conductor $6.903$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.100
Dual form 117.4.g.b.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +21.0000 q^{8} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +21.0000 q^{8} +(13.5000 - 23.3827i) q^{10} +(15.0000 - 25.9808i) q^{11} +(32.5000 + 33.7750i) q^{13} -6.00000 q^{14} +(35.5000 - 61.4878i) q^{16} +(-55.5000 - 96.1288i) q^{17} +(23.0000 + 39.8372i) q^{19} +(-4.50000 - 7.79423i) q^{20} +(-45.0000 - 77.9423i) q^{22} +(-3.00000 + 5.19615i) q^{23} -44.0000 q^{25} +(136.500 - 33.7750i) q^{26} +(-1.00000 + 1.73205i) q^{28} +(-52.5000 + 90.9327i) q^{29} -100.000 q^{31} +(-22.5000 - 38.9711i) q^{32} -333.000 q^{34} +(-9.00000 - 15.5885i) q^{35} +(-8.50000 + 14.7224i) q^{37} +138.000 q^{38} +189.000 q^{40} +(-115.500 + 200.052i) q^{41} +(257.000 + 445.137i) q^{43} -30.0000 q^{44} +(9.00000 + 15.5885i) q^{46} +162.000 q^{47} +(169.500 - 293.583i) q^{49} +(-66.0000 + 114.315i) q^{50} +(13.0000 - 45.0333i) q^{52} -639.000 q^{53} +(135.000 - 233.827i) q^{55} +(-21.0000 - 36.3731i) q^{56} +(157.500 + 272.798i) q^{58} +(300.000 + 519.615i) q^{59} +(-116.500 - 201.784i) q^{61} +(-150.000 + 259.808i) q^{62} +433.000 q^{64} +(292.500 + 303.975i) q^{65} +(-463.000 + 801.940i) q^{67} +(-55.5000 + 96.1288i) q^{68} -54.0000 q^{70} +(-465.000 - 805.404i) q^{71} -253.000 q^{73} +(25.5000 + 44.1673i) q^{74} +(23.0000 - 39.8372i) q^{76} -60.0000 q^{77} -1324.00 q^{79} +(319.500 - 553.390i) q^{80} +(346.500 + 600.156i) q^{82} -810.000 q^{83} +(-499.500 - 865.159i) q^{85} +1542.00 q^{86} +(315.000 - 545.596i) q^{88} +(249.000 - 431.281i) q^{89} +(26.0000 - 90.0666i) q^{91} +6.00000 q^{92} +(243.000 - 420.888i) q^{94} +(207.000 + 358.535i) q^{95} +(-679.000 - 1176.06i) q^{97} +(-508.500 - 880.748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8} + 27 q^{10} + 30 q^{11} + 65 q^{13} - 12 q^{14} + 71 q^{16} - 111 q^{17} + 46 q^{19} - 9 q^{20} - 90 q^{22} - 6 q^{23} - 88 q^{25} + 273 q^{26} - 2 q^{28} - 105 q^{29} - 200 q^{31} - 45 q^{32} - 666 q^{34} - 18 q^{35} - 17 q^{37} + 276 q^{38} + 378 q^{40} - 231 q^{41} + 514 q^{43} - 60 q^{44} + 18 q^{46} + 324 q^{47} + 339 q^{49} - 132 q^{50} + 26 q^{52} - 1278 q^{53} + 270 q^{55} - 42 q^{56} + 315 q^{58} + 600 q^{59} - 233 q^{61} - 300 q^{62} + 866 q^{64} + 585 q^{65} - 926 q^{67} - 111 q^{68} - 108 q^{70} - 930 q^{71} - 506 q^{73} + 51 q^{74} + 46 q^{76} - 120 q^{77} - 2648 q^{79} + 639 q^{80} + 693 q^{82} - 1620 q^{83} - 999 q^{85} + 3084 q^{86} + 630 q^{88} + 498 q^{89} + 52 q^{91} + 12 q^{92} + 486 q^{94} + 414 q^{95} - 1358 q^{97} - 1017 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 2.59808i 0.530330 0.918559i −0.469044 0.883175i \(-0.655401\pi\)
0.999374 0.0353837i \(-0.0112653\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.0625000 0.108253i
\(5\) 9.00000 0.804984 0.402492 0.915423i \(-0.368144\pi\)
0.402492 + 0.915423i \(0.368144\pi\)
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.0539949 0.0935220i 0.837765 0.546032i \(-0.183862\pi\)
−0.891760 + 0.452510i \(0.850529\pi\)
\(8\) 21.0000 0.928078
\(9\) 0 0
\(10\) 13.5000 23.3827i 0.426907 0.739425i
\(11\) 15.0000 25.9808i 0.411152 0.712136i −0.583864 0.811851i \(-0.698460\pi\)
0.995016 + 0.0997155i \(0.0317933\pi\)
\(12\) 0 0
\(13\) 32.5000 + 33.7750i 0.693375 + 0.720577i
\(14\) −6.00000 −0.114541
\(15\) 0 0
\(16\) 35.5000 61.4878i 0.554688 0.960747i
\(17\) −55.5000 96.1288i −0.791807 1.37145i −0.924847 0.380340i \(-0.875807\pi\)
0.133039 0.991111i \(-0.457526\pi\)
\(18\) 0 0
\(19\) 23.0000 + 39.8372i 0.277714 + 0.481014i 0.970816 0.239825i \(-0.0770900\pi\)
−0.693102 + 0.720839i \(0.743757\pi\)
\(20\) −4.50000 7.79423i −0.0503115 0.0871421i
\(21\) 0 0
\(22\) −45.0000 77.9423i −0.436092 0.755334i
\(23\) −3.00000 + 5.19615i −0.0271975 + 0.0471075i −0.879304 0.476261i \(-0.841992\pi\)
0.852106 + 0.523369i \(0.175325\pi\)
\(24\) 0 0
\(25\) −44.0000 −0.352000
\(26\) 136.500 33.7750i 1.02961 0.254762i
\(27\) 0 0
\(28\) −1.00000 + 1.73205i −0.00674937 + 0.0116902i
\(29\) −52.5000 + 90.9327i −0.336173 + 0.582268i −0.983709 0.179766i \(-0.942466\pi\)
0.647537 + 0.762034i \(0.275799\pi\)
\(30\) 0 0
\(31\) −100.000 −0.579372 −0.289686 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(32\) −22.5000 38.9711i −0.124296 0.215287i
\(33\) 0 0
\(34\) −333.000 −1.67968
\(35\) −9.00000 15.5885i −0.0434651 0.0752837i
\(36\) 0 0
\(37\) −8.50000 + 14.7224i −0.0377673 + 0.0654149i −0.884291 0.466936i \(-0.845358\pi\)
0.846524 + 0.532351i \(0.178691\pi\)
\(38\) 138.000 0.589120
\(39\) 0 0
\(40\) 189.000 0.747088
\(41\) −115.500 + 200.052i −0.439953 + 0.762021i −0.997685 0.0680000i \(-0.978338\pi\)
0.557732 + 0.830021i \(0.311672\pi\)
\(42\) 0 0
\(43\) 257.000 + 445.137i 0.911445 + 1.57867i 0.812024 + 0.583623i \(0.198366\pi\)
0.0994205 + 0.995046i \(0.468301\pi\)
\(44\) −30.0000 −0.102788
\(45\) 0 0
\(46\) 9.00000 + 15.5885i 0.0288473 + 0.0499651i
\(47\) 162.000 0.502769 0.251384 0.967887i \(-0.419114\pi\)
0.251384 + 0.967887i \(0.419114\pi\)
\(48\) 0 0
\(49\) 169.500 293.583i 0.494169 0.855926i
\(50\) −66.0000 + 114.315i −0.186676 + 0.323333i
\(51\) 0 0
\(52\) 13.0000 45.0333i 0.0346688 0.120096i
\(53\) −639.000 −1.65610 −0.828051 0.560653i \(-0.810550\pi\)
−0.828051 + 0.560653i \(0.810550\pi\)
\(54\) 0 0
\(55\) 135.000 233.827i 0.330971 0.573258i
\(56\) −21.0000 36.3731i −0.0501115 0.0867956i
\(57\) 0 0
\(58\) 157.500 + 272.798i 0.356565 + 0.617588i
\(59\) 300.000 + 519.615i 0.661978 + 1.14658i 0.980095 + 0.198527i \(0.0636159\pi\)
−0.318118 + 0.948051i \(0.603051\pi\)
\(60\) 0 0
\(61\) −116.500 201.784i −0.244529 0.423537i 0.717470 0.696590i \(-0.245300\pi\)
−0.961999 + 0.273052i \(0.911967\pi\)
\(62\) −150.000 + 259.808i −0.307258 + 0.532187i
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 292.500 + 303.975i 0.558156 + 0.580053i
\(66\) 0 0
\(67\) −463.000 + 801.940i −0.844246 + 1.46228i 0.0420292 + 0.999116i \(0.486618\pi\)
−0.886275 + 0.463160i \(0.846716\pi\)
\(68\) −55.5000 + 96.1288i −0.0989759 + 0.171431i
\(69\) 0 0
\(70\) −54.0000 −0.0922033
\(71\) −465.000 805.404i −0.777258 1.34625i −0.933516 0.358535i \(-0.883276\pi\)
0.156258 0.987716i \(-0.450057\pi\)
\(72\) 0 0
\(73\) −253.000 −0.405636 −0.202818 0.979216i \(-0.565010\pi\)
−0.202818 + 0.979216i \(0.565010\pi\)
\(74\) 25.5000 + 44.1673i 0.0400583 + 0.0693830i
\(75\) 0 0
\(76\) 23.0000 39.8372i 0.0347142 0.0601268i
\(77\) −60.0000 −0.0888004
\(78\) 0 0
\(79\) −1324.00 −1.88559 −0.942795 0.333373i \(-0.891813\pi\)
−0.942795 + 0.333373i \(0.891813\pi\)
\(80\) 319.500 553.390i 0.446515 0.773386i
\(81\) 0 0
\(82\) 346.500 + 600.156i 0.466641 + 0.808245i
\(83\) −810.000 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(84\) 0 0
\(85\) −499.500 865.159i −0.637393 1.10400i
\(86\) 1542.00 1.93347
\(87\) 0 0
\(88\) 315.000 545.596i 0.381581 0.660917i
\(89\) 249.000 431.281i 0.296561 0.513659i −0.678786 0.734336i \(-0.737493\pi\)
0.975347 + 0.220677i \(0.0708268\pi\)
\(90\) 0 0
\(91\) 26.0000 90.0666i 0.0299510 0.103753i
\(92\) 6.00000 0.00679938
\(93\) 0 0
\(94\) 243.000 420.888i 0.266633 0.461823i
\(95\) 207.000 + 358.535i 0.223555 + 0.387209i
\(96\) 0 0
\(97\) −679.000 1176.06i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) −508.500 880.748i −0.524145 0.907847i
\(99\) 0 0
\(100\) 22.0000 + 38.1051i 0.0220000 + 0.0381051i
\(101\) −178.500 + 309.171i −0.175856 + 0.304591i −0.940457 0.339913i \(-0.889603\pi\)
0.764601 + 0.644503i \(0.222936\pi\)
\(102\) 0 0
\(103\) 1118.00 1.06951 0.534756 0.845006i \(-0.320403\pi\)
0.534756 + 0.845006i \(0.320403\pi\)
\(104\) 682.500 + 709.275i 0.643506 + 0.668751i
\(105\) 0 0
\(106\) −958.500 + 1660.17i −0.878281 + 1.52123i
\(107\) 357.000 618.342i 0.322547 0.558667i −0.658466 0.752610i \(-0.728794\pi\)
0.981013 + 0.193943i \(0.0621277\pi\)
\(108\) 0 0
\(109\) 2006.00 1.76275 0.881376 0.472416i \(-0.156618\pi\)
0.881376 + 0.472416i \(0.156618\pi\)
\(110\) −405.000 701.481i −0.351048 0.608032i
\(111\) 0 0
\(112\) −142.000 −0.119801
\(113\) −559.500 969.082i −0.465782 0.806758i 0.533455 0.845829i \(-0.320893\pi\)
−0.999236 + 0.0390710i \(0.987560\pi\)
\(114\) 0 0
\(115\) −27.0000 + 46.7654i −0.0218936 + 0.0379208i
\(116\) 105.000 0.0840431
\(117\) 0 0
\(118\) 1800.00 1.40427
\(119\) −111.000 + 192.258i −0.0855072 + 0.148103i
\(120\) 0 0
\(121\) 215.500 + 373.257i 0.161908 + 0.280433i
\(122\) −699.000 −0.518725
\(123\) 0 0
\(124\) 50.0000 + 86.6025i 0.0362107 + 0.0627189i
\(125\) −1521.00 −1.08834
\(126\) 0 0
\(127\) 302.000 523.079i 0.211009 0.365479i −0.741021 0.671481i \(-0.765658\pi\)
0.952031 + 0.306003i \(0.0989917\pi\)
\(128\) 829.500 1436.74i 0.572798 0.992115i
\(129\) 0 0
\(130\) 1228.50 303.975i 0.828820 0.205080i
\(131\) 1584.00 1.05645 0.528224 0.849105i \(-0.322858\pi\)
0.528224 + 0.849105i \(0.322858\pi\)
\(132\) 0 0
\(133\) 46.0000 79.6743i 0.0299903 0.0519447i
\(134\) 1389.00 + 2405.82i 0.895458 + 1.55098i
\(135\) 0 0
\(136\) −1165.50 2018.71i −0.734859 1.27281i
\(137\) 358.500 + 620.940i 0.223567 + 0.387230i 0.955889 0.293729i \(-0.0948964\pi\)
−0.732321 + 0.680959i \(0.761563\pi\)
\(138\) 0 0
\(139\) 410.000 + 710.141i 0.250185 + 0.433334i 0.963577 0.267432i \(-0.0861751\pi\)
−0.713391 + 0.700766i \(0.752842\pi\)
\(140\) −9.00000 + 15.5885i −0.00543313 + 0.00941046i
\(141\) 0 0
\(142\) −2790.00 −1.64881
\(143\) 1365.00 337.750i 0.798231 0.197511i
\(144\) 0 0
\(145\) −472.500 + 818.394i −0.270614 + 0.468717i
\(146\) −379.500 + 657.313i −0.215121 + 0.372600i
\(147\) 0 0
\(148\) 17.0000 0.00944183
\(149\) −874.500 1514.68i −0.480818 0.832801i 0.518940 0.854811i \(-0.326327\pi\)
−0.999758 + 0.0220100i \(0.992993\pi\)
\(150\) 0 0
\(151\) −370.000 −0.199405 −0.0997026 0.995017i \(-0.531789\pi\)
−0.0997026 + 0.995017i \(0.531789\pi\)
\(152\) 483.000 + 836.581i 0.257740 + 0.446419i
\(153\) 0 0
\(154\) −90.0000 + 155.885i −0.0470935 + 0.0815684i
\(155\) −900.000 −0.466385
\(156\) 0 0
\(157\) −2611.00 −1.32726 −0.663632 0.748059i \(-0.730986\pi\)
−0.663632 + 0.748059i \(0.730986\pi\)
\(158\) −1986.00 + 3439.85i −0.999985 + 1.73203i
\(159\) 0 0
\(160\) −202.500 350.740i −0.100056 0.173303i
\(161\) 12.0000 0.00587411
\(162\) 0 0
\(163\) 818.000 + 1416.82i 0.393072 + 0.680820i 0.992853 0.119344i \(-0.0380790\pi\)
−0.599781 + 0.800164i \(0.704746\pi\)
\(164\) 231.000 0.109988
\(165\) 0 0
\(166\) −1215.00 + 2104.44i −0.568086 + 0.983954i
\(167\) 132.000 228.631i 0.0611645 0.105940i −0.833822 0.552034i \(-0.813852\pi\)
0.894986 + 0.446094i \(0.147185\pi\)
\(168\) 0 0
\(169\) −84.5000 + 2195.37i −0.0384615 + 0.999260i
\(170\) −2997.00 −1.35211
\(171\) 0 0
\(172\) 257.000 445.137i 0.113931 0.197334i
\(173\) 705.000 + 1221.10i 0.309827 + 0.536637i 0.978324 0.207078i \(-0.0663954\pi\)
−0.668497 + 0.743715i \(0.733062\pi\)
\(174\) 0 0
\(175\) 44.0000 + 76.2102i 0.0190062 + 0.0329197i
\(176\) −1065.00 1844.63i −0.456122 0.790026i
\(177\) 0 0
\(178\) −747.000 1293.84i −0.314551 0.544818i
\(179\) −237.000 + 410.496i −0.0989621 + 0.171407i −0.911255 0.411842i \(-0.864886\pi\)
0.812293 + 0.583249i \(0.198219\pi\)
\(180\) 0 0
\(181\) 2249.00 0.923574 0.461787 0.886991i \(-0.347208\pi\)
0.461787 + 0.886991i \(0.347208\pi\)
\(182\) −195.000 202.650i −0.0794196 0.0825352i
\(183\) 0 0
\(184\) −63.0000 + 109.119i −0.0252414 + 0.0437194i
\(185\) −76.5000 + 132.502i −0.0304021 + 0.0526580i
\(186\) 0 0
\(187\) −3330.00 −1.30221
\(188\) −81.0000 140.296i −0.0314230 0.0544263i
\(189\) 0 0
\(190\) 1242.00 0.474232
\(191\) 1722.00 + 2982.59i 0.652354 + 1.12991i 0.982550 + 0.185997i \(0.0595516\pi\)
−0.330197 + 0.943912i \(0.607115\pi\)
\(192\) 0 0
\(193\) 2136.50 3700.53i 0.796832 1.38015i −0.124837 0.992177i \(-0.539841\pi\)
0.921669 0.387977i \(-0.126826\pi\)
\(194\) −4074.00 −1.50771
\(195\) 0 0
\(196\) −339.000 −0.123542
\(197\) −993.000 + 1719.93i −0.359129 + 0.622029i −0.987815 0.155630i \(-0.950259\pi\)
0.628687 + 0.777658i \(0.283593\pi\)
\(198\) 0 0
\(199\) 1193.00 + 2066.34i 0.424973 + 0.736074i 0.996418 0.0845661i \(-0.0269504\pi\)
−0.571445 + 0.820640i \(0.693617\pi\)
\(200\) −924.000 −0.326683
\(201\) 0 0
\(202\) 535.500 + 927.513i 0.186523 + 0.323067i
\(203\) 210.000 0.0726065
\(204\) 0 0
\(205\) −1039.50 + 1800.47i −0.354155 + 0.613415i
\(206\) 1677.00 2904.65i 0.567195 0.982410i
\(207\) 0 0
\(208\) 3230.50 799.341i 1.07690 0.266463i
\(209\) 1380.00 0.456730
\(210\) 0 0
\(211\) 800.000 1385.64i 0.261016 0.452092i −0.705497 0.708713i \(-0.749276\pi\)
0.966512 + 0.256621i \(0.0826093\pi\)
\(212\) 319.500 + 553.390i 0.103506 + 0.179278i
\(213\) 0 0
\(214\) −1071.00 1855.03i −0.342112 0.592556i
\(215\) 2313.00 + 4006.23i 0.733699 + 1.27080i
\(216\) 0 0
\(217\) 100.000 + 173.205i 0.0312831 + 0.0541840i
\(218\) 3009.00 5211.74i 0.934840 1.61919i
\(219\) 0 0
\(220\) −270.000 −0.0827427
\(221\) 1443.00 4998.70i 0.439216 1.52149i
\(222\) 0 0
\(223\) 1916.00 3318.61i 0.575358 0.996549i −0.420645 0.907226i \(-0.638196\pi\)
0.996003 0.0893239i \(-0.0284706\pi\)
\(224\) −45.0000 + 77.9423i −0.0134227 + 0.0232488i
\(225\) 0 0
\(226\) −3357.00 −0.988072
\(227\) −699.000 1210.70i −0.204380 0.353997i 0.745555 0.666444i \(-0.232184\pi\)
−0.949935 + 0.312448i \(0.898851\pi\)
\(228\) 0 0
\(229\) 4466.00 1.28874 0.644370 0.764714i \(-0.277120\pi\)
0.644370 + 0.764714i \(0.277120\pi\)
\(230\) 81.0000 + 140.296i 0.0232217 + 0.0402211i
\(231\) 0 0
\(232\) −1102.50 + 1909.59i −0.311994 + 0.540390i
\(233\) 1638.00 0.460553 0.230277 0.973125i \(-0.426037\pi\)
0.230277 + 0.973125i \(0.426037\pi\)
\(234\) 0 0
\(235\) 1458.00 0.404721
\(236\) 300.000 519.615i 0.0827472 0.143322i
\(237\) 0 0
\(238\) 333.000 + 576.773i 0.0906941 + 0.157087i
\(239\) 594.000 0.160764 0.0803821 0.996764i \(-0.474386\pi\)
0.0803821 + 0.996764i \(0.474386\pi\)
\(240\) 0 0
\(241\) −1151.50 1994.46i −0.307779 0.533088i 0.670098 0.742273i \(-0.266252\pi\)
−0.977876 + 0.209185i \(0.932919\pi\)
\(242\) 1293.00 0.343459
\(243\) 0 0
\(244\) −116.500 + 201.784i −0.0305662 + 0.0529422i
\(245\) 1525.50 2642.24i 0.397798 0.689007i
\(246\) 0 0
\(247\) −598.000 + 2071.53i −0.154048 + 0.533638i
\(248\) −2100.00 −0.537702
\(249\) 0 0
\(250\) −2281.50 + 3951.67i −0.577179 + 0.999703i
\(251\) 3162.00 + 5476.74i 0.795154 + 1.37725i 0.922741 + 0.385420i \(0.125943\pi\)
−0.127587 + 0.991827i \(0.540723\pi\)
\(252\) 0 0
\(253\) 90.0000 + 155.885i 0.0223646 + 0.0387367i
\(254\) −906.000 1569.24i −0.223809 0.387649i
\(255\) 0 0
\(256\) −756.500 1310.30i −0.184692 0.319897i
\(257\) 3916.50 6783.58i 0.950601 1.64649i 0.206474 0.978452i \(-0.433801\pi\)
0.744127 0.668038i \(-0.232866\pi\)
\(258\) 0 0
\(259\) 34.0000 0.00815698
\(260\) 117.000 405.300i 0.0279078 0.0966755i
\(261\) 0 0
\(262\) 2376.00 4115.35i 0.560266 0.970410i
\(263\) −1515.00 + 2624.06i −0.355205 + 0.615233i −0.987153 0.159778i \(-0.948922\pi\)
0.631948 + 0.775011i \(0.282256\pi\)
\(264\) 0 0
\(265\) −5751.00 −1.33314
\(266\) −138.000 239.023i −0.0318095 0.0550956i
\(267\) 0 0
\(268\) 926.000 0.211061
\(269\) −267.000 462.458i −0.0605178 0.104820i 0.834179 0.551493i \(-0.185942\pi\)
−0.894697 + 0.446674i \(0.852609\pi\)
\(270\) 0 0
\(271\) 1844.00 3193.90i 0.413340 0.715925i −0.581913 0.813251i \(-0.697696\pi\)
0.995253 + 0.0973259i \(0.0310289\pi\)
\(272\) −7881.00 −1.75682
\(273\) 0 0
\(274\) 2151.00 0.474258
\(275\) −660.000 + 1143.15i −0.144725 + 0.250672i
\(276\) 0 0
\(277\) −932.500 1615.14i −0.202269 0.350340i 0.746990 0.664835i \(-0.231498\pi\)
−0.949259 + 0.314495i \(0.898165\pi\)
\(278\) 2460.00 0.530723
\(279\) 0 0
\(280\) −189.000 327.358i −0.0403390 0.0698691i
\(281\) −2997.00 −0.636249 −0.318125 0.948049i \(-0.603053\pi\)
−0.318125 + 0.948049i \(0.603053\pi\)
\(282\) 0 0
\(283\) 2057.00 3562.83i 0.432071 0.748368i −0.564981 0.825104i \(-0.691116\pi\)
0.997051 + 0.0767359i \(0.0244498\pi\)
\(284\) −465.000 + 805.404i −0.0971573 + 0.168281i
\(285\) 0 0
\(286\) 1170.00 4053.00i 0.241901 0.837968i
\(287\) 462.000 0.0950209
\(288\) 0 0
\(289\) −3704.00 + 6415.52i −0.753918 + 1.30582i
\(290\) 1417.50 + 2455.18i 0.287029 + 0.497149i
\(291\) 0 0
\(292\) 126.500 + 219.104i 0.0253522 + 0.0439114i
\(293\) −2332.50 4040.01i −0.465072 0.805528i 0.534133 0.845401i \(-0.320638\pi\)
−0.999205 + 0.0398722i \(0.987305\pi\)
\(294\) 0 0
\(295\) 2700.00 + 4676.54i 0.532882 + 0.922978i
\(296\) −178.500 + 309.171i −0.0350510 + 0.0607101i
\(297\) 0 0
\(298\) −5247.00 −1.01997
\(299\) −273.000 + 67.5500i −0.0528027 + 0.0130653i
\(300\) 0 0
\(301\) 514.000 890.274i 0.0984268 0.170480i
\(302\) −555.000 + 961.288i −0.105751 + 0.183165i
\(303\) 0 0
\(304\) 3266.00 0.616177
\(305\) −1048.50 1816.06i −0.196842 0.340941i
\(306\) 0 0
\(307\) 1502.00 0.279230 0.139615 0.990206i \(-0.455413\pi\)
0.139615 + 0.990206i \(0.455413\pi\)
\(308\) 30.0000 + 51.9615i 0.00555003 + 0.00961293i
\(309\) 0 0
\(310\) −1350.00 + 2338.27i −0.247338 + 0.428402i
\(311\) −2106.00 −0.383988 −0.191994 0.981396i \(-0.561495\pi\)
−0.191994 + 0.981396i \(0.561495\pi\)
\(312\) 0 0
\(313\) −3898.00 −0.703923 −0.351962 0.936014i \(-0.614485\pi\)
−0.351962 + 0.936014i \(0.614485\pi\)
\(314\) −3916.50 + 6783.58i −0.703888 + 1.21917i
\(315\) 0 0
\(316\) 662.000 + 1146.62i 0.117849 + 0.204121i
\(317\) −9351.00 −1.65680 −0.828398 0.560140i \(-0.810747\pi\)
−0.828398 + 0.560140i \(0.810747\pi\)
\(318\) 0 0
\(319\) 1575.00 + 2727.98i 0.276436 + 0.478801i
\(320\) 3897.00 0.680778
\(321\) 0 0
\(322\) 18.0000 31.1769i 0.00311522 0.00539572i
\(323\) 2553.00 4421.93i 0.439792 0.761742i
\(324\) 0 0
\(325\) −1430.00 1486.10i −0.244068 0.253643i
\(326\) 4908.00 0.833831
\(327\) 0 0
\(328\) −2425.50 + 4201.09i −0.408310 + 0.707214i
\(329\) −162.000 280.592i −0.0271470 0.0470199i
\(330\) 0 0
\(331\) 4586.00 + 7943.19i 0.761539 + 1.31902i 0.942057 + 0.335452i \(0.108889\pi\)
−0.180518 + 0.983572i \(0.557778\pi\)
\(332\) 405.000 + 701.481i 0.0669496 + 0.115960i
\(333\) 0 0
\(334\) −396.000 685.892i −0.0648747 0.112366i
\(335\) −4167.00 + 7217.46i −0.679605 + 1.17711i
\(336\) 0 0
\(337\) −11089.0 −1.79245 −0.896226 0.443598i \(-0.853702\pi\)
−0.896226 + 0.443598i \(0.853702\pi\)
\(338\) 5577.00 + 3512.60i 0.897482 + 0.565267i
\(339\) 0 0
\(340\) −499.500 + 865.159i −0.0796741 + 0.138000i
\(341\) −1500.00 + 2598.08i −0.238210 + 0.412592i
\(342\) 0 0
\(343\) −1364.00 −0.214720
\(344\) 5397.00 + 9347.88i 0.845892 + 1.46513i
\(345\) 0 0
\(346\) 4230.00 0.657243
\(347\) 4881.00 + 8454.14i 0.755118 + 1.30790i 0.945316 + 0.326156i \(0.105754\pi\)
−0.190198 + 0.981746i \(0.560913\pi\)
\(348\) 0 0
\(349\) 4145.00 7179.35i 0.635750 1.10115i −0.350606 0.936523i \(-0.614024\pi\)
0.986356 0.164628i \(-0.0526424\pi\)
\(350\) 264.000 0.0403183
\(351\) 0 0
\(352\) −1350.00 −0.204418
\(353\) 6202.50 10743.0i 0.935200 1.61981i 0.160924 0.986967i \(-0.448552\pi\)
0.774276 0.632848i \(-0.218114\pi\)
\(354\) 0 0
\(355\) −4185.00 7248.63i −0.625681 1.08371i
\(356\) −498.000 −0.0741403
\(357\) 0 0
\(358\) 711.000 + 1231.49i 0.104965 + 0.181805i
\(359\) 1098.00 0.161421 0.0807106 0.996738i \(-0.474281\pi\)
0.0807106 + 0.996738i \(0.474281\pi\)
\(360\) 0 0
\(361\) 2371.50 4107.56i 0.345750 0.598857i
\(362\) 3373.50 5843.07i 0.489799 0.848357i
\(363\) 0 0
\(364\) −91.0000 + 22.5167i −0.0131036 + 0.00324229i
\(365\) −2277.00 −0.326530
\(366\) 0 0
\(367\) 2867.00 4965.79i 0.407783 0.706300i −0.586858 0.809690i \(-0.699635\pi\)
0.994641 + 0.103390i \(0.0329688\pi\)
\(368\) 213.000 + 368.927i 0.0301723 + 0.0522599i
\(369\) 0 0
\(370\) 229.500 + 397.506i 0.0322463 + 0.0558523i
\(371\) 639.000 + 1106.78i 0.0894211 + 0.154882i
\(372\) 0 0
\(373\) 4485.50 + 7769.11i 0.622655 + 1.07847i 0.988989 + 0.147987i \(0.0472794\pi\)
−0.366334 + 0.930483i \(0.619387\pi\)
\(374\) −4995.00 + 8651.59i −0.690602 + 1.19616i
\(375\) 0 0
\(376\) 3402.00 0.466608
\(377\) −4777.50 + 1182.12i −0.652663 + 0.161492i
\(378\) 0 0
\(379\) −3622.00 + 6273.49i −0.490896 + 0.850257i −0.999945 0.0104805i \(-0.996664\pi\)
0.509049 + 0.860738i \(0.329997\pi\)
\(380\) 207.000 358.535i 0.0279444 0.0484011i
\(381\) 0 0
\(382\) 10332.0 1.38385
\(383\) −3156.00 5466.35i −0.421055 0.729289i 0.574988 0.818162i \(-0.305007\pi\)
−0.996043 + 0.0888732i \(0.971673\pi\)
\(384\) 0 0
\(385\) −540.000 −0.0714830
\(386\) −6409.50 11101.6i −0.845168 1.46387i
\(387\) 0 0
\(388\) −679.000 + 1176.06i −0.0888428 + 0.153880i
\(389\) −3627.00 −0.472741 −0.236370 0.971663i \(-0.575958\pi\)
−0.236370 + 0.971663i \(0.575958\pi\)
\(390\) 0 0
\(391\) 666.000 0.0861408
\(392\) 3559.50 6165.23i 0.458627 0.794366i
\(393\) 0 0
\(394\) 2979.00 + 5159.78i 0.380913 + 0.659761i
\(395\) −11916.0 −1.51787
\(396\) 0 0
\(397\) 1949.00 + 3375.77i 0.246392 + 0.426763i 0.962522 0.271204i \(-0.0874217\pi\)
−0.716130 + 0.697967i \(0.754088\pi\)
\(398\) 7158.00 0.901503
\(399\) 0 0
\(400\) −1562.00 + 2705.46i −0.195250 + 0.338183i
\(401\) −2851.50 + 4938.94i −0.355105 + 0.615060i −0.987136 0.159883i \(-0.948888\pi\)
0.632031 + 0.774943i \(0.282222\pi\)
\(402\) 0 0
\(403\) −3250.00 3377.50i −0.401722 0.417482i
\(404\) 357.000 0.0439639
\(405\) 0 0
\(406\) 315.000 545.596i 0.0385054 0.0666933i
\(407\) 255.000 + 441.673i 0.0310562 + 0.0537909i
\(408\) 0 0
\(409\) −3155.50 5465.49i −0.381490 0.660760i 0.609785 0.792567i \(-0.291256\pi\)
−0.991275 + 0.131806i \(0.957922\pi\)
\(410\) 3118.50 + 5401.40i 0.375638 + 0.650625i
\(411\) 0 0
\(412\) −559.000 968.216i −0.0668445 0.115778i
\(413\) 600.000 1039.23i 0.0714869 0.123819i
\(414\) 0 0
\(415\) −7290.00 −0.862294
\(416\) 585.000 2026.50i 0.0689471 0.238840i
\(417\) 0 0
\(418\) 2070.00 3585.35i 0.242218 0.419533i
\(419\) −1164.00 + 2016.11i −0.135716 + 0.235067i −0.925871 0.377840i \(-0.876667\pi\)
0.790155 + 0.612908i \(0.210000\pi\)
\(420\) 0 0
\(421\) 2045.00 0.236739 0.118370 0.992970i \(-0.462233\pi\)
0.118370 + 0.992970i \(0.462233\pi\)
\(422\) −2400.00 4156.92i −0.276849 0.479516i
\(423\) 0 0
\(424\) −13419.0 −1.53699
\(425\) 2442.00 + 4229.67i 0.278716 + 0.482751i
\(426\) 0 0
\(427\) −233.000 + 403.568i −0.0264067 + 0.0457377i
\(428\) −714.000 −0.0806367
\(429\) 0 0
\(430\) 13878.0 1.55641
\(431\) 2517.00 4359.57i 0.281298 0.487223i −0.690406 0.723422i \(-0.742568\pi\)
0.971705 + 0.236199i \(0.0759016\pi\)
\(432\) 0 0
\(433\) −2141.50 3709.19i −0.237676 0.411668i 0.722371 0.691506i \(-0.243052\pi\)
−0.960047 + 0.279838i \(0.909719\pi\)
\(434\) 600.000 0.0663616
\(435\) 0 0
\(436\) −1003.00 1737.25i −0.110172 0.190823i
\(437\) −276.000 −0.0302125
\(438\) 0 0
\(439\) 653.000 1131.03i 0.0709931 0.122964i −0.828344 0.560220i \(-0.810716\pi\)
0.899337 + 0.437257i \(0.144050\pi\)
\(440\) 2835.00 4910.36i 0.307167 0.532028i
\(441\) 0 0
\(442\) −10822.5 11247.1i −1.16465 1.21034i
\(443\) 5796.00 0.621617 0.310808 0.950473i \(-0.399400\pi\)
0.310808 + 0.950473i \(0.399400\pi\)
\(444\) 0 0
\(445\) 2241.00 3881.53i 0.238727 0.413488i
\(446\) −5748.00 9955.83i −0.610259 1.05700i
\(447\) 0 0
\(448\) −433.000 749.978i −0.0456637 0.0790918i
\(449\) 1353.00 + 2343.46i 0.142209 + 0.246314i 0.928328 0.371761i \(-0.121246\pi\)
−0.786119 + 0.618075i \(0.787913\pi\)
\(450\) 0 0
\(451\) 3465.00 + 6001.56i 0.361775 + 0.626612i
\(452\) −559.500 + 969.082i −0.0582227 + 0.100845i
\(453\) 0 0
\(454\) −4194.00 −0.433555
\(455\) 234.000 810.600i 0.0241101 0.0835198i
\(456\) 0 0
\(457\) 414.500 717.935i 0.0424278 0.0734871i −0.844032 0.536293i \(-0.819824\pi\)
0.886459 + 0.462806i \(0.153157\pi\)
\(458\) 6699.00 11603.0i 0.683458 1.18378i
\(459\) 0 0
\(460\) 54.0000 0.00547340
\(461\) −2746.50 4757.08i −0.277478 0.480606i 0.693279 0.720669i \(-0.256165\pi\)
−0.970757 + 0.240063i \(0.922832\pi\)
\(462\) 0 0
\(463\) −15346.0 −1.54037 −0.770183 0.637823i \(-0.779835\pi\)
−0.770183 + 0.637823i \(0.779835\pi\)
\(464\) 3727.50 + 6456.22i 0.372941 + 0.645954i
\(465\) 0 0
\(466\) 2457.00 4255.65i 0.244245 0.423045i
\(467\) 9594.00 0.950658 0.475329 0.879808i \(-0.342329\pi\)
0.475329 + 0.879808i \(0.342329\pi\)
\(468\) 0 0
\(469\) 1852.00 0.182340
\(470\) 2187.00 3788.00i 0.214636 0.371760i
\(471\) 0 0
\(472\) 6300.00 + 10911.9i 0.614367 + 1.06411i
\(473\) 15420.0 1.49897
\(474\) 0 0
\(475\) −1012.00 1752.84i −0.0977553 0.169317i
\(476\) 222.000 0.0213768
\(477\) 0 0
\(478\) 891.000 1543.26i 0.0852581 0.147671i
\(479\) −6420.00 + 11119.8i −0.612395 + 1.06070i 0.378440 + 0.925626i \(0.376461\pi\)
−0.990836 + 0.135074i \(0.956873\pi\)
\(480\) 0 0
\(481\) −773.500 + 191.392i −0.0733234 + 0.0181428i
\(482\) −6909.00 −0.652897
\(483\) 0 0
\(484\) 215.500 373.257i 0.0202385 0.0350542i
\(485\) −6111.00 10584.6i −0.572137 0.990970i
\(486\) 0 0
\(487\) 7043.00 + 12198.8i 0.655336 + 1.13508i 0.981809 + 0.189869i \(0.0608064\pi\)
−0.326473 + 0.945207i \(0.605860\pi\)
\(488\) −2446.50 4237.46i −0.226942 0.393076i
\(489\) 0 0
\(490\) −4576.50 7926.73i −0.421929 0.730802i
\(491\) 5847.00 10127.3i 0.537416 0.930832i −0.461626 0.887075i \(-0.652734\pi\)
0.999042 0.0437577i \(-0.0139329\pi\)
\(492\) 0 0
\(493\) 11655.0 1.06474
\(494\) 4485.00 + 4660.95i 0.408481 + 0.424506i
\(495\) 0 0
\(496\) −3550.00 + 6148.78i −0.321370 + 0.556630i
\(497\) −930.000 + 1610.81i −0.0839360 + 0.145381i
\(498\) 0 0
\(499\) −3688.00 −0.330857 −0.165428 0.986222i \(-0.552901\pi\)
−0.165428 + 0.986222i \(0.552901\pi\)
\(500\) 760.500 + 1317.22i 0.0680212 + 0.117816i
\(501\) 0 0
\(502\) 18972.0 1.68678
\(503\) −2373.00 4110.16i −0.210352 0.364340i 0.741473 0.670983i \(-0.234128\pi\)
−0.951825 + 0.306643i \(0.900794\pi\)
\(504\) 0 0
\(505\) −1606.50 + 2782.54i −0.141561 + 0.245191i
\(506\) 540.000 0.0474425
\(507\) 0 0
\(508\) −604.000 −0.0527523
\(509\) −7252.50 + 12561.7i −0.631555 + 1.09389i 0.355679 + 0.934608i \(0.384250\pi\)
−0.987234 + 0.159277i \(0.949084\pi\)
\(510\) 0 0
\(511\) 253.000 + 438.209i 0.0219023 + 0.0379358i
\(512\) 8733.00 0.753804
\(513\) 0 0
\(514\) −11749.5 20350.7i −1.00827 1.74637i
\(515\) 10062.0 0.860941
\(516\) 0 0
\(517\) 2430.00 4208.88i 0.206714 0.358040i
\(518\) 51.0000 88.3346i 0.00432589 0.00749266i
\(519\) 0 0
\(520\) 6142.50 + 6383.47i 0.518012 + 0.538334i
\(521\) −5085.00 −0.427597 −0.213798 0.976878i \(-0.568584\pi\)
−0.213798 + 0.976878i \(0.568584\pi\)
\(522\) 0 0
\(523\) 5441.00 9424.09i 0.454911 0.787929i −0.543772 0.839233i \(-0.683004\pi\)
0.998683 + 0.0513043i \(0.0163378\pi\)
\(524\) −792.000 1371.78i −0.0660280 0.114364i
\(525\) 0 0
\(526\) 4545.00 + 7872.17i 0.376752 + 0.652553i
\(527\) 5550.00 + 9612.88i 0.458751 + 0.794580i
\(528\) 0 0
\(529\) 6065.50 + 10505.8i 0.498521 + 0.863463i
\(530\) −8626.50 + 14941.5i −0.707002 + 1.22456i
\(531\) 0 0
\(532\) −92.0000 −0.00749757
\(533\) −10510.5 + 2600.67i −0.854147 + 0.211347i
\(534\) 0 0
\(535\) 3213.00 5565.08i 0.259645 0.449718i
\(536\) −9723.00 + 16840.7i −0.783525 + 1.35711i
\(537\) 0 0
\(538\) −1602.00 −0.128378
\(539\) −5085.00 8807.48i −0.406357 0.703831i
\(540\) 0 0
\(541\) −4699.00 −0.373430 −0.186715 0.982414i \(-0.559784\pi\)
−0.186715 + 0.982414i \(0.559784\pi\)
\(542\) −5532.00 9581.71i −0.438413 0.759353i
\(543\) 0 0
\(544\) −2497.50 + 4325.80i −0.196837 + 0.340932i
\(545\) 18054.0 1.41899
\(546\) 0 0
\(547\) 8270.00 0.646434 0.323217 0.946325i \(-0.395236\pi\)
0.323217 + 0.946325i \(0.395236\pi\)
\(548\) 358.500 620.940i 0.0279459 0.0484037i
\(549\) 0 0
\(550\) 1980.00 + 3429.46i 0.153505 + 0.265878i
\(551\) −4830.00 −0.373439
\(552\) 0 0
\(553\) 1324.00 + 2293.24i 0.101812 + 0.176344i
\(554\) −5595.00 −0.429077
\(555\) 0 0
\(556\) 410.000 710.141i 0.0312732 0.0541667i
\(557\) −11392.5 + 19732.4i −0.866635 + 1.50106i −0.00122056 + 0.999999i \(0.500389\pi\)
−0.865414 + 0.501057i \(0.832945\pi\)
\(558\) 0 0
\(559\) −6682.00 + 23147.1i −0.505579 + 1.75138i
\(560\) −1278.00 −0.0964381
\(561\) 0 0
\(562\) −4495.50 + 7786.43i −0.337422 + 0.584432i
\(563\) −5964.00 10330.0i −0.446452 0.773278i 0.551700 0.834043i \(-0.313979\pi\)
−0.998152 + 0.0607647i \(0.980646\pi\)
\(564\) 0 0
\(565\) −5035.50 8721.74i −0.374947 0.649427i
\(566\) −6171.00 10688.5i −0.458280 0.793764i
\(567\) 0 0
\(568\) −9765.00 16913.5i −0.721356 1.24943i
\(569\) −3981.00 + 6895.29i −0.293308 + 0.508024i −0.974590 0.223997i \(-0.928089\pi\)
0.681282 + 0.732021i \(0.261423\pi\)
\(570\) 0 0
\(571\) 20618.0 1.51110 0.755549 0.655093i \(-0.227370\pi\)
0.755549 + 0.655093i \(0.227370\pi\)
\(572\) −975.000 1013.25i −0.0712706 0.0740666i
\(573\) 0 0
\(574\) 693.000 1200.31i 0.0503924 0.0872823i
\(575\) 132.000 228.631i 0.00957353 0.0165818i
\(576\) 0 0
\(577\) −3493.00 −0.252020 −0.126010 0.992029i \(-0.540217\pi\)
−0.126010 + 0.992029i \(0.540217\pi\)
\(578\) 11112.0 + 19246.5i 0.799651 + 1.38504i
\(579\) 0 0
\(580\) 945.000 0.0676534
\(581\) 810.000 + 1402.96i 0.0578390 + 0.100180i
\(582\) 0 0
\(583\) −9585.00 + 16601.7i −0.680909 + 1.17937i
\(584\) −5313.00 −0.376461
\(585\) 0 0
\(586\) −13995.0 −0.986567
\(587\) 5208.00 9020.52i 0.366196 0.634270i −0.622771 0.782404i \(-0.713993\pi\)
0.988967 + 0.148134i \(0.0473266\pi\)
\(588\) 0 0
\(589\) −2300.00 3983.72i −0.160900 0.278686i
\(590\) 16200.0 1.13041
\(591\) 0 0
\(592\) 603.500 + 1045.29i 0.0418981 + 0.0725697i
\(593\) −2061.00 −0.142724 −0.0713618 0.997450i \(-0.522734\pi\)
−0.0713618 + 0.997450i \(0.522734\pi\)
\(594\) 0 0
\(595\) −999.000 + 1730.32i −0.0688319 + 0.119220i
\(596\) −874.500 + 1514.68i −0.0601022 + 0.104100i
\(597\) 0 0
\(598\) −234.000 + 810.600i −0.0160016 + 0.0554313i
\(599\) −12456.0 −0.849647 −0.424823 0.905276i \(-0.639664\pi\)
−0.424823 + 0.905276i \(0.639664\pi\)
\(600\) 0 0
\(601\) 390.500 676.366i 0.0265039 0.0459061i −0.852469 0.522777i \(-0.824896\pi\)
0.878973 + 0.476871i \(0.158229\pi\)
\(602\) −1542.00 2670.82i −0.104397 0.180822i
\(603\) 0 0
\(604\) 185.000 + 320.429i 0.0124628 + 0.0215862i
\(605\) 1939.50 + 3359.31i 0.130334 + 0.225745i
\(606\) 0 0
\(607\) −9652.00 16717.8i −0.645408 1.11788i −0.984207 0.177021i \(-0.943354\pi\)
0.338799 0.940859i \(-0.389979\pi\)
\(608\) 1035.00 1792.67i 0.0690375 0.119576i
\(609\) 0 0
\(610\) −6291.00 −0.417566
\(611\) 5265.00 + 5471.55i 0.348607 + 0.362283i
\(612\) 0 0
\(613\) −6020.50 + 10427.8i −0.396681 + 0.687072i −0.993314 0.115442i \(-0.963172\pi\)
0.596633 + 0.802514i \(0.296505\pi\)
\(614\) 2253.00 3902.31i 0.148084 0.256489i
\(615\) 0 0
\(616\) −1260.00 −0.0824137
\(617\) 4858.50 + 8415.17i 0.317011 + 0.549079i 0.979863 0.199671i \(-0.0639874\pi\)
−0.662852 + 0.748751i \(0.730654\pi\)
\(618\) 0 0
\(619\) −21040.0 −1.36619 −0.683093 0.730332i \(-0.739366\pi\)
−0.683093 + 0.730332i \(0.739366\pi\)
\(620\) 450.000 + 779.423i 0.0291491 + 0.0504877i
\(621\) 0 0
\(622\) −3159.00 + 5471.55i −0.203640 + 0.352716i
\(623\) −996.000 −0.0640512
\(624\) 0 0
\(625\) −8189.00 −0.524096
\(626\) −5847.00 + 10127.3i −0.373312 + 0.646595i
\(627\) 0 0
\(628\) 1305.50 + 2261.19i 0.0829540 + 0.143681i
\(629\) 1887.00 0.119618
\(630\) 0 0
\(631\) 2534.00 + 4389.02i 0.159868 + 0.276900i 0.934821 0.355119i \(-0.115560\pi\)
−0.774953 + 0.632019i \(0.782226\pi\)
\(632\) −27804.0 −1.74997
\(633\) 0 0
\(634\) −14026.5 + 24294.6i −0.878649 + 1.52186i
\(635\) 2718.00 4707.71i 0.169859 0.294205i
\(636\) 0 0
\(637\) 15424.5 3816.57i 0.959405 0.237391i
\(638\) 9450.00 0.586409
\(639\) 0 0
\(640\) 7465.50 12930.6i 0.461093 0.798637i
\(641\) 5092.50 + 8820.47i 0.313794 + 0.543506i 0.979180 0.202992i \(-0.0650667\pi\)
−0.665387 + 0.746499i \(0.731733\pi\)
\(642\) 0 0
\(643\) −12964.0 22454.3i −0.795101 1.37716i −0.922775 0.385340i \(-0.874084\pi\)
0.127673 0.991816i \(-0.459249\pi\)
\(644\) −6.00000 10.3923i −0.000367132 0.000635892i
\(645\) 0 0
\(646\) −7659.00 13265.8i −0.466470 0.807949i
\(647\) 11580.0 20057.1i 0.703643 1.21874i −0.263537 0.964649i \(-0.584889\pi\)
0.967179 0.254095i \(-0.0817777\pi\)
\(648\) 0 0
\(649\) 18000.0 1.08869
\(650\) −6006.00 + 1486.10i −0.362423 + 0.0896763i
\(651\) 0 0
\(652\) 818.000 1416.82i 0.0491340 0.0851025i
\(653\) 8313.00 14398.5i 0.498182 0.862876i −0.501816 0.864974i \(-0.667334\pi\)
0.999998 + 0.00209801i \(0.000667816\pi\)
\(654\) 0 0
\(655\) 14256.0 0.850424
\(656\) 8200.50 + 14203.7i 0.488073 + 0.845367i
\(657\) 0 0
\(658\) −972.000 −0.0575874
\(659\) −7404.00 12824.1i −0.437661 0.758052i 0.559847 0.828596i \(-0.310860\pi\)
−0.997509 + 0.0705440i \(0.977526\pi\)
\(660\) 0 0
\(661\) −2426.50 + 4202.82i −0.142784 + 0.247308i −0.928544 0.371223i \(-0.878939\pi\)
0.785760 + 0.618531i \(0.212272\pi\)
\(662\) 27516.0 1.61547
\(663\) 0 0
\(664\) −17010.0 −0.994151
\(665\) 414.000 717.069i 0.0241417 0.0418147i
\(666\) 0 0
\(667\) −315.000 545.596i −0.0182861 0.0316725i
\(668\) −264.000 −0.0152911
\(669\) 0 0
\(670\) 12501.0 + 21652.4i 0.720829 + 1.24851i
\(671\) −6990.00 −0.402155
\(672\) 0 0
\(673\) 8082.50 13999.3i 0.462938 0.801833i −0.536168 0.844112i \(-0.680128\pi\)
0.999106 + 0.0422789i \(0.0134618\pi\)
\(674\) −16633.5 + 28810.1i −0.950591 + 1.64647i
\(675\) 0 0
\(676\) 1943.50 1024.51i 0.110577 0.0582902i
\(677\) 25686.0 1.45819 0.729094 0.684414i \(-0.239942\pi\)
0.729094 + 0.684414i \(0.239942\pi\)
\(678\) 0 0
\(679\) −1358.00 + 2352.12i −0.0767530 + 0.132940i
\(680\) −10489.5 18168.3i −0.591550 1.02459i
\(681\) 0 0
\(682\) 4500.00 + 7794.23i 0.252660 + 0.437619i
\(683\) −9528.00 16503.0i −0.533790 0.924552i −0.999221 0.0394675i \(-0.987434\pi\)
0.465431 0.885084i \(-0.345900\pi\)
\(684\) 0 0
\(685\) 3226.50 + 5588.46i 0.179968 + 0.311714i
\(686\) −2046.00 + 3543.78i −0.113873 + 0.197233i
\(687\) 0 0
\(688\) 36494.0 2.02227
\(689\) −20767.5 21582.2i −1.14830 1.19335i
\(690\) 0 0
\(691\) 8195.00 14194.2i 0.451161 0.781434i −0.547297 0.836938i \(-0.684343\pi\)
0.998458 + 0.0555040i \(0.0176766\pi\)
\(692\) 705.000 1221.10i 0.0387284 0.0670796i
\(693\) 0 0
\(694\) 29286.0 1.60185
\(695\) 3690.00 + 6391.27i 0.201395 + 0.348827i
\(696\) 0 0
\(697\) 25641.0 1.39343
\(698\) −12435.0 21538.1i −0.674315 1.16795i
\(699\) 0 0
\(700\) 44.0000 76.2102i 0.00237578 0.00411497i
\(701\) 27846.0 1.50033 0.750163 0.661253i \(-0.229975\pi\)
0.750163 + 0.661253i \(0.229975\pi\)
\(702\) 0 0
\(703\) −782.000 −0.0419540
\(704\) 6495.00 11249.7i 0.347712 0.602256i
\(705\) 0 0
\(706\) −18607.5 32229.1i −0.991930 1.71807i
\(707\) 714.000 0.0379812
\(708\) 0 0
\(709\) 6141.50 + 10637.4i 0.325316 + 0.563463i 0.981576 0.191071i \(-0.0611961\pi\)
−0.656260 + 0.754534i \(0.727863\pi\)
\(710\) −25110.0 −1.32727
\(711\) 0 0
\(712\) 5229.00 9056.89i 0.275232 0.476716i
\(713\) 300.000 519.615i 0.0157575 0.0272928i
\(714\) 0 0
\(715\) 12285.0 3039.75i 0.642564 0.158993i
\(716\) 474.000 0.0247405
\(717\) 0 0
\(718\) 1647.00 2852.69i 0.0856065 0.148275i
\(719\) 12756.0 + 22094.0i 0.661639 + 1.14599i 0.980185 + 0.198085i \(0.0634722\pi\)
−0.318546 + 0.947908i \(0.603194\pi\)
\(720\) 0 0
\(721\) −1118.00 1936.43i −0.0577483 0.100023i
\(722\) −7114.50 12322.7i −0.366723 0.635184i
\(723\) 0 0
\(724\) −1124.50 1947.69i −0.0577234 0.0999798i
\(725\) 2310.00 4001.04i 0.118333 0.204958i
\(726\) 0 0
\(727\) 6110.00 0.311702 0.155851 0.987781i \(-0.450188\pi\)
0.155851 + 0.987781i \(0.450188\pi\)
\(728\) 546.000 1891.40i 0.0277968 0.0962911i
\(729\) 0 0
\(730\) −3415.50 + 5915.82i −0.173169 + 0.299937i
\(731\) 28527.0 49410.2i 1.44338 2.50000i
\(732\) 0 0
\(733\) −27127.0 −1.36693 −0.683464 0.729984i \(-0.739527\pi\)
−0.683464 + 0.729984i \(0.739527\pi\)
\(734\) −8601.00 14897.4i −0.432519 0.749144i
\(735\) 0 0
\(736\) 270.000 0.0135222
\(737\) 13890.0 + 24058.2i 0.694226 + 1.20244i
\(738\) 0 0
\(739\) 440.000 762.102i 0.0219021 0.0379356i −0.854867 0.518848i \(-0.826361\pi\)
0.876769 + 0.480912i \(0.159694\pi\)
\(740\) 153.000 0.00760053
\(741\) 0 0
\(742\) 3834.00 0.189691
\(743\) −10938.0 + 18945.2i −0.540076 + 0.935439i 0.458823 + 0.888528i \(0.348271\pi\)
−0.998899 + 0.0469111i \(0.985062\pi\)
\(744\) 0 0
\(745\) −7870.50 13632.1i −0.387051 0.670392i
\(746\) 26913.0 1.32085
\(747\) 0 0
\(748\) 1665.00 + 2883.86i 0.0813883 + 0.140969i
\(749\) −1428.00 −0.0696635
\(750\) 0 0
\(751\) −5899.00 + 10217.4i −0.286628 + 0.496454i −0.973003 0.230794i \(-0.925868\pi\)
0.686375 + 0.727248i \(0.259201\pi\)
\(752\) 5751.00 9961.02i 0.278880 0.483033i
\(753\) 0 0
\(754\) −4095.00 + 14185.5i −0.197787 + 0.685153i
\(755\) −3330.00 −0.160518
\(756\) 0 0
\(757\) 4037.00 6992.29i 0.193827 0.335719i −0.752688 0.658377i \(-0.771243\pi\)
0.946515 + 0.322658i \(0.104577\pi\)
\(758\) 10866.0 + 18820.5i 0.520674 + 0.901834i
\(759\) 0 0
\(760\) 4347.00 + 7529.22i 0.207477 + 0.359360i
\(761\) 9777.00 + 16934.3i 0.465724 + 0.806658i 0.999234 0.0391362i \(-0.0124606\pi\)
−0.533510 + 0.845794i \(0.679127\pi\)
\(762\) 0 0
\(763\) −2006.00 3474.49i −0.0951797 0.164856i
\(764\) 1722.00 2982.59i 0.0815442 0.141239i
\(765\) 0 0
\(766\) −18936.0 −0.893193
\(767\) −7800.00 + 27020.0i −0.367199 + 1.27201i
\(768\) 0 0
\(769\) −7015.00 + 12150.3i −0.328956 + 0.569769i −0.982305 0.187288i \(-0.940030\pi\)
0.653349 + 0.757057i \(0.273364\pi\)
\(770\) −810.000 + 1402.96i −0.0379096 + 0.0656613i
\(771\) 0 0
\(772\) −4273.00 −0.199208
\(773\) 18021.0 + 31213.3i 0.838513 + 1.45235i 0.891138 + 0.453732i \(0.149908\pi\)
−0.0526253 + 0.998614i \(0.516759\pi\)
\(774\) 0 0
\(775\) 4400.00 0.203939
\(776\) −14259.0 24697.3i −0.659624 1.14250i
\(777\) 0 0
\(778\) −5440.50 + 9423.22i −0.250709 + 0.434240i
\(779\) −10626.0 −0.488724
\(780\) 0 0
\(781\) −27900.0 −1.27828
\(782\) 999.000 1730.32i 0.0456831 0.0791254i
\(783\) 0 0
\(784\) −12034.5 20844.4i −0.548219