Properties

Label 177.5.b.a.119.10
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.10
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.69

$q$-expansion

\(f(q)\) \(=\) \(q-6.42743i q^{2} +(2.05646 + 8.76190i) q^{3} -25.3118 q^{4} -39.0573i q^{5} +(56.3165 - 13.2178i) q^{6} +65.2885 q^{7} +59.8512i q^{8} +(-72.5419 + 36.0371i) q^{9} +O(q^{10})\) \(q-6.42743i q^{2} +(2.05646 + 8.76190i) q^{3} -25.3118 q^{4} -39.0573i q^{5} +(56.3165 - 13.2178i) q^{6} +65.2885 q^{7} +59.8512i q^{8} +(-72.5419 + 36.0371i) q^{9} -251.038 q^{10} +5.09361i q^{11} +(-52.0529 - 221.780i) q^{12} +300.078 q^{13} -419.637i q^{14} +(342.216 - 80.3200i) q^{15} -20.3001 q^{16} -418.344i q^{17} +(231.626 + 466.258i) q^{18} -156.757 q^{19} +988.613i q^{20} +(134.263 + 572.051i) q^{21} +32.7388 q^{22} +238.716i q^{23} +(-524.410 + 123.082i) q^{24} -900.474 q^{25} -1928.73i q^{26} +(-464.933 - 561.496i) q^{27} -1652.57 q^{28} -1294.15i q^{29} +(-516.251 - 2199.57i) q^{30} -398.653 q^{31} +1088.10i q^{32} +(-44.6297 + 10.4748i) q^{33} -2688.88 q^{34} -2549.99i q^{35} +(1836.17 - 912.165i) q^{36} -2417.21 q^{37} +1007.54i q^{38} +(617.099 + 2629.25i) q^{39} +2337.63 q^{40} +3.98886i q^{41} +(3676.82 - 862.968i) q^{42} +159.503 q^{43} -128.929i q^{44} +(1407.51 + 2833.29i) q^{45} +1534.33 q^{46} -1473.68i q^{47} +(-41.7465 - 177.868i) q^{48} +1861.58 q^{49} +5787.73i q^{50} +(3665.49 - 860.309i) q^{51} -7595.52 q^{52} +3452.21i q^{53} +(-3608.98 + 2988.33i) q^{54} +198.943 q^{55} +3907.59i q^{56} +(-322.365 - 1373.49i) q^{57} -8318.04 q^{58} +453.188i q^{59} +(-8662.13 + 2033.05i) q^{60} +3005.69 q^{61} +2562.31i q^{62} +(-4736.15 + 2352.81i) q^{63} +6668.86 q^{64} -11720.2i q^{65} +(67.3262 + 286.854i) q^{66} +8611.05 q^{67} +10589.1i q^{68} +(-2091.60 + 490.910i) q^{69} -16389.9 q^{70} -8909.51i q^{71} +(-2156.86 - 4341.72i) q^{72} -879.765 q^{73} +15536.4i q^{74} +(-1851.79 - 7889.87i) q^{75} +3967.81 q^{76} +332.554i q^{77} +(16899.3 - 3966.36i) q^{78} +3607.80 q^{79} +792.869i q^{80} +(3963.66 - 5228.40i) q^{81} +25.6381 q^{82} +315.278i q^{83} +(-3398.45 - 14479.7i) q^{84} -16339.4 q^{85} -1025.19i q^{86} +(11339.2 - 2661.37i) q^{87} -304.859 q^{88} +12623.1i q^{89} +(18210.8 - 9046.68i) q^{90} +19591.6 q^{91} -6042.33i q^{92} +(-819.815 - 3492.96i) q^{93} -9471.97 q^{94} +6122.50i q^{95} +(-9533.80 + 2237.63i) q^{96} +449.576 q^{97} -11965.2i q^{98} +(-183.559 - 369.500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.42743i 1.60686i −0.595401 0.803429i \(-0.703007\pi\)
0.595401 0.803429i \(-0.296993\pi\)
\(3\) 2.05646 + 8.76190i 0.228496 + 0.973545i
\(4\) −25.3118 −1.58199
\(5\) 39.0573i 1.56229i −0.624348 0.781146i \(-0.714635\pi\)
0.624348 0.781146i \(-0.285365\pi\)
\(6\) 56.3165 13.2178i 1.56435 0.367160i
\(7\) 65.2885 1.33242 0.666209 0.745765i \(-0.267916\pi\)
0.666209 + 0.745765i \(0.267916\pi\)
\(8\) 59.8512i 0.935175i
\(9\) −72.5419 + 36.0371i −0.895579 + 0.444902i
\(10\) −251.038 −2.51038
\(11\) 5.09361i 0.0420960i 0.999778 + 0.0210480i \(0.00670028\pi\)
−0.999778 + 0.0210480i \(0.993300\pi\)
\(12\) −52.0529 221.780i −0.361478 1.54014i
\(13\) 300.078 1.77561 0.887804 0.460222i \(-0.152230\pi\)
0.887804 + 0.460222i \(0.152230\pi\)
\(14\) 419.637i 2.14100i
\(15\) 342.216 80.3200i 1.52096 0.356978i
\(16\) −20.3001 −0.0792974
\(17\) 418.344i 1.44756i −0.690032 0.723779i \(-0.742404\pi\)
0.690032 0.723779i \(-0.257596\pi\)
\(18\) 231.626 + 466.258i 0.714894 + 1.43907i
\(19\) −156.757 −0.434230 −0.217115 0.976146i \(-0.569665\pi\)
−0.217115 + 0.976146i \(0.569665\pi\)
\(20\) 988.613i 2.47153i
\(21\) 134.263 + 572.051i 0.304452 + 1.29717i
\(22\) 32.7388 0.0676422
\(23\) 238.716i 0.451258i 0.974213 + 0.225629i \(0.0724438\pi\)
−0.974213 + 0.225629i \(0.927556\pi\)
\(24\) −524.410 + 123.082i −0.910435 + 0.213684i
\(25\) −900.474 −1.44076
\(26\) 1928.73i 2.85315i
\(27\) −464.933 561.496i −0.637769 0.770228i
\(28\) −1652.57 −2.10787
\(29\) 1294.15i 1.53882i −0.638755 0.769410i \(-0.720550\pi\)
0.638755 0.769410i \(-0.279450\pi\)
\(30\) −516.251 2199.57i −0.573612 2.44397i
\(31\) −398.653 −0.414831 −0.207416 0.978253i \(-0.566505\pi\)
−0.207416 + 0.978253i \(0.566505\pi\)
\(32\) 1088.10i 1.06259i
\(33\) −44.6297 + 10.4748i −0.0409823 + 0.00961876i
\(34\) −2688.88 −2.32602
\(35\) 2549.99i 2.08163i
\(36\) 1836.17 912.165i 1.41680 0.703831i
\(37\) −2417.21 −1.76568 −0.882838 0.469678i \(-0.844370\pi\)
−0.882838 + 0.469678i \(0.844370\pi\)
\(38\) 1007.54i 0.697745i
\(39\) 617.099 + 2629.25i 0.405719 + 1.72863i
\(40\) 2337.63 1.46102
\(41\) 3.98886i 0.00237291i 0.999999 + 0.00118645i \(0.000377660\pi\)
−0.999999 + 0.00118645i \(0.999622\pi\)
\(42\) 3676.82 862.968i 2.08436 0.489211i
\(43\) 159.503 0.0862642 0.0431321 0.999069i \(-0.486266\pi\)
0.0431321 + 0.999069i \(0.486266\pi\)
\(44\) 128.929i 0.0665954i
\(45\) 1407.51 + 2833.29i 0.695067 + 1.39916i
\(46\) 1534.33 0.725108
\(47\) 1473.68i 0.667125i −0.942728 0.333563i \(-0.891749\pi\)
0.942728 0.333563i \(-0.108251\pi\)
\(48\) −41.7465 177.868i −0.0181191 0.0771996i
\(49\) 1861.58 0.775337
\(50\) 5787.73i 2.31509i
\(51\) 3665.49 860.309i 1.40926 0.330761i
\(52\) −7595.52 −2.80899
\(53\) 3452.21i 1.22898i 0.788924 + 0.614491i \(0.210639\pi\)
−0.788924 + 0.614491i \(0.789361\pi\)
\(54\) −3608.98 + 2988.33i −1.23765 + 1.02480i
\(55\) 198.943 0.0657662
\(56\) 3907.59i 1.24604i
\(57\) −322.365 1373.49i −0.0992197 0.422742i
\(58\) −8318.04 −2.47266
\(59\) 453.188i 0.130189i
\(60\) −8662.13 + 2033.05i −2.40615 + 0.564735i
\(61\) 3005.69 0.807763 0.403882 0.914811i \(-0.367661\pi\)
0.403882 + 0.914811i \(0.367661\pi\)
\(62\) 2562.31i 0.666574i
\(63\) −4736.15 + 2352.81i −1.19329 + 0.592796i
\(64\) 6668.86 1.62814
\(65\) 11720.2i 2.77402i
\(66\) 67.3262 + 286.854i 0.0154560 + 0.0658527i
\(67\) 8611.05 1.91825 0.959127 0.282974i \(-0.0913212\pi\)
0.959127 + 0.282974i \(0.0913212\pi\)
\(68\) 10589.1i 2.29002i
\(69\) −2091.60 + 490.910i −0.439320 + 0.103111i
\(70\) −16389.9 −3.34488
\(71\) 8909.51i 1.76741i −0.468045 0.883705i \(-0.655041\pi\)
0.468045 0.883705i \(-0.344959\pi\)
\(72\) −2156.86 4341.72i −0.416061 0.837523i
\(73\) −879.765 −0.165090 −0.0825451 0.996587i \(-0.526305\pi\)
−0.0825451 + 0.996587i \(0.526305\pi\)
\(74\) 15536.4i 2.83719i
\(75\) −1851.79 7889.87i −0.329208 1.40264i
\(76\) 3967.81 0.686947
\(77\) 332.554i 0.0560894i
\(78\) 16899.3 3966.36i 2.77767 0.651933i
\(79\) 3607.80 0.578081 0.289040 0.957317i \(-0.406664\pi\)
0.289040 + 0.957317i \(0.406664\pi\)
\(80\) 792.869i 0.123886i
\(81\) 3963.66 5228.40i 0.604124 0.796890i
\(82\) 25.6381 0.00381293
\(83\) 315.278i 0.0457654i 0.999738 + 0.0228827i \(0.00728442\pi\)
−0.999738 + 0.0228827i \(0.992716\pi\)
\(84\) −3398.45 14479.7i −0.481640 2.05211i
\(85\) −16339.4 −2.26151
\(86\) 1025.19i 0.138614i
\(87\) 11339.2 2661.37i 1.49811 0.351614i
\(88\) −304.859 −0.0393671
\(89\) 12623.1i 1.59363i 0.604225 + 0.796814i \(0.293483\pi\)
−0.604225 + 0.796814i \(0.706517\pi\)
\(90\) 18210.8 9046.68i 2.24825 1.11687i
\(91\) 19591.6 2.36585
\(92\) 6042.33i 0.713886i
\(93\) −819.815 3492.96i −0.0947872 0.403857i
\(94\) −9471.97 −1.07198
\(95\) 6122.50i 0.678394i
\(96\) −9533.80 + 2237.63i −1.03448 + 0.242799i
\(97\) 449.576 0.0477815 0.0238907 0.999715i \(-0.492395\pi\)
0.0238907 + 0.999715i \(0.492395\pi\)
\(98\) 11965.2i 1.24586i
\(99\) −183.559 369.500i −0.0187286 0.0377003i
\(100\) 22792.7 2.27927
\(101\) 4754.47i 0.466079i −0.972467 0.233039i \(-0.925133\pi\)
0.972467 0.233039i \(-0.0748671\pi\)
\(102\) −5529.58 23559.7i −0.531486 2.26448i
\(103\) −10711.2 −1.00963 −0.504816 0.863227i \(-0.668440\pi\)
−0.504816 + 0.863227i \(0.668440\pi\)
\(104\) 17960.0i 1.66050i
\(105\) 22342.8 5243.97i 2.02656 0.475643i
\(106\) 22188.9 1.97480
\(107\) 3010.10i 0.262914i −0.991322 0.131457i \(-0.958034\pi\)
0.991322 0.131457i \(-0.0419656\pi\)
\(108\) 11768.3 + 14212.5i 1.00894 + 1.21849i
\(109\) −450.138 −0.0378872 −0.0189436 0.999821i \(-0.506030\pi\)
−0.0189436 + 0.999821i \(0.506030\pi\)
\(110\) 1278.69i 0.105677i
\(111\) −4970.90 21179.4i −0.403450 1.71896i
\(112\) −1325.36 −0.105657
\(113\) 13280.6i 1.04007i 0.854146 + 0.520034i \(0.174081\pi\)
−0.854146 + 0.520034i \(0.825919\pi\)
\(114\) −8828.00 + 2071.98i −0.679286 + 0.159432i
\(115\) 9323.60 0.704998
\(116\) 32757.3i 2.43440i
\(117\) −21768.2 + 10813.9i −1.59020 + 0.789972i
\(118\) 2912.83 0.209195
\(119\) 27313.0i 1.92875i
\(120\) 4807.25 + 20482.1i 0.333837 + 1.42237i
\(121\) 14615.1 0.998228
\(122\) 19318.8i 1.29796i
\(123\) −34.9500 + 8.20295i −0.00231013 + 0.000542200i
\(124\) 10090.6 0.656259
\(125\) 10759.3i 0.688594i
\(126\) 15122.5 + 30441.3i 0.952538 + 1.91744i
\(127\) 29458.7 1.82644 0.913222 0.407462i \(-0.133586\pi\)
0.913222 + 0.407462i \(0.133586\pi\)
\(128\) 25454.1i 1.55359i
\(129\) 328.011 + 1397.55i 0.0197110 + 0.0839821i
\(130\) −75330.9 −4.45745
\(131\) 4752.97i 0.276963i 0.990365 + 0.138482i \(0.0442222\pi\)
−0.990365 + 0.138482i \(0.955778\pi\)
\(132\) 1129.66 265.137i 0.0648336 0.0152168i
\(133\) −10234.4 −0.578575
\(134\) 55346.9i 3.08236i
\(135\) −21930.5 + 18159.0i −1.20332 + 0.996381i
\(136\) 25038.4 1.35372
\(137\) 9420.01i 0.501892i 0.968001 + 0.250946i \(0.0807417\pi\)
−0.968001 + 0.250946i \(0.919258\pi\)
\(138\) 3155.29 + 13443.6i 0.165684 + 0.705925i
\(139\) 8893.09 0.460281 0.230140 0.973157i \(-0.426081\pi\)
0.230140 + 0.973157i \(0.426081\pi\)
\(140\) 64545.0i 3.29311i
\(141\) 12912.2 3030.57i 0.649476 0.152435i
\(142\) −57265.3 −2.83997
\(143\) 1528.48i 0.0747459i
\(144\) 1472.61 731.557i 0.0710171 0.0352796i
\(145\) −50545.9 −2.40409
\(146\) 5654.63i 0.265276i
\(147\) 3828.28 + 16311.0i 0.177161 + 0.754825i
\(148\) 61184.0 2.79328
\(149\) 698.090i 0.0314441i 0.999876 + 0.0157220i \(0.00500468\pi\)
−0.999876 + 0.0157220i \(0.994995\pi\)
\(150\) −50711.6 + 11902.3i −2.25385 + 0.528990i
\(151\) 11188.7 0.490711 0.245355 0.969433i \(-0.421095\pi\)
0.245355 + 0.969433i \(0.421095\pi\)
\(152\) 9382.09i 0.406081i
\(153\) 15075.9 + 30347.5i 0.644021 + 1.29640i
\(154\) 2137.47 0.0901277
\(155\) 15570.3i 0.648088i
\(156\) −15619.9 66551.2i −0.641844 2.73468i
\(157\) −15221.6 −0.617534 −0.308767 0.951138i \(-0.599916\pi\)
−0.308767 + 0.951138i \(0.599916\pi\)
\(158\) 23188.9i 0.928893i
\(159\) −30248.0 + 7099.35i −1.19647 + 0.280818i
\(160\) 42498.1 1.66008
\(161\) 15585.4i 0.601265i
\(162\) −33605.2 25476.1i −1.28049 0.970741i
\(163\) 15804.3 0.594838 0.297419 0.954747i \(-0.403874\pi\)
0.297419 + 0.954747i \(0.403874\pi\)
\(164\) 100.965i 0.00375392i
\(165\) 409.119 + 1743.12i 0.0150273 + 0.0640264i
\(166\) 2026.43 0.0735384
\(167\) 5741.63i 0.205875i 0.994688 + 0.102937i \(0.0328241\pi\)
−0.994688 + 0.102937i \(0.967176\pi\)
\(168\) −34238.0 + 8035.82i −1.21308 + 0.284716i
\(169\) 61485.6 2.15278
\(170\) 105020.i 3.63392i
\(171\) 11371.4 5649.06i 0.388887 0.193190i
\(172\) −4037.30 −0.136469
\(173\) 55335.1i 1.84888i 0.381331 + 0.924439i \(0.375466\pi\)
−0.381331 + 0.924439i \(0.624534\pi\)
\(174\) −17105.8 72881.9i −0.564994 2.40725i
\(175\) −58790.6 −1.91969
\(176\) 103.401i 0.00333810i
\(177\) −3970.79 + 931.964i −0.126745 + 0.0297476i
\(178\) 81134.2 2.56073
\(179\) 32249.6i 1.00651i −0.864137 0.503256i \(-0.832135\pi\)
0.864137 0.503256i \(-0.167865\pi\)
\(180\) −35626.7 71715.8i −1.09959 2.21345i
\(181\) −12535.0 −0.382621 −0.191310 0.981530i \(-0.561274\pi\)
−0.191310 + 0.981530i \(0.561274\pi\)
\(182\) 125924.i 3.80158i
\(183\) 6181.09 + 26335.5i 0.184571 + 0.786394i
\(184\) −14287.4 −0.422006
\(185\) 94409.7i 2.75850i
\(186\) −22450.7 + 5269.30i −0.648940 + 0.152310i
\(187\) 2130.88 0.0609363
\(188\) 37301.5i 1.05539i
\(189\) −30354.8 36659.2i −0.849774 1.02627i
\(190\) 39352.0 1.09008
\(191\) 35056.0i 0.960939i −0.877012 0.480469i \(-0.840466\pi\)
0.877012 0.480469i \(-0.159534\pi\)
\(192\) 13714.3 + 58431.9i 0.372024 + 1.58507i
\(193\) 17556.0 0.471314 0.235657 0.971836i \(-0.424276\pi\)
0.235657 + 0.971836i \(0.424276\pi\)
\(194\) 2889.62i 0.0767780i
\(195\) 102691. 24102.2i 2.70063 0.633852i
\(196\) −47120.1 −1.22657
\(197\) 30322.4i 0.781323i 0.920534 + 0.390662i \(0.127754\pi\)
−0.920534 + 0.390662i \(0.872246\pi\)
\(198\) −2374.94 + 1179.81i −0.0605789 + 0.0300942i
\(199\) −46440.1 −1.17270 −0.586351 0.810057i \(-0.699436\pi\)
−0.586351 + 0.810057i \(0.699436\pi\)
\(200\) 53894.5i 1.34736i
\(201\) 17708.3 + 75449.2i 0.438314 + 1.86751i
\(202\) −30559.0 −0.748922
\(203\) 84492.9i 2.05035i
\(204\) −92780.3 + 21776.0i −2.22944 + 0.523261i
\(205\) 155.794 0.00370718
\(206\) 68845.4i 1.62234i
\(207\) −8602.62 17316.9i −0.200766 0.404138i
\(208\) −6091.61 −0.140801
\(209\) 798.459i 0.0182793i
\(210\) −33705.2 143607.i −0.764291 3.25639i
\(211\) 55667.4 1.25036 0.625182 0.780479i \(-0.285025\pi\)
0.625182 + 0.780479i \(0.285025\pi\)
\(212\) 87381.9i 1.94424i
\(213\) 78064.3 18322.1i 1.72065 0.403846i
\(214\) −19347.2 −0.422466
\(215\) 6229.74i 0.134770i
\(216\) 33606.2 27826.8i 0.720298 0.596425i
\(217\) −26027.4 −0.552728
\(218\) 2893.23i 0.0608793i
\(219\) −1809.21 7708.42i −0.0377224 0.160723i
\(220\) −5035.61 −0.104041
\(221\) 125536.i 2.57029i
\(222\) −136129. + 31950.1i −2.76213 + 0.648286i
\(223\) −35180.5 −0.707444 −0.353722 0.935351i \(-0.615084\pi\)
−0.353722 + 0.935351i \(0.615084\pi\)
\(224\) 71040.2i 1.41582i
\(225\) 65322.1 32450.5i 1.29031 0.640997i
\(226\) 85360.2 1.67124
\(227\) 22820.8i 0.442874i 0.975175 + 0.221437i \(0.0710747\pi\)
−0.975175 + 0.221437i \(0.928925\pi\)
\(228\) 8159.65 + 34765.5i 0.156965 + 0.668774i
\(229\) 43335.1 0.826359 0.413180 0.910650i \(-0.364418\pi\)
0.413180 + 0.910650i \(0.364418\pi\)
\(230\) 59926.7i 1.13283i
\(231\) −2913.81 + 683.885i −0.0546055 + 0.0128162i
\(232\) 77456.3 1.43907
\(233\) 57288.7i 1.05525i 0.849476 + 0.527627i \(0.176918\pi\)
−0.849476 + 0.527627i \(0.823082\pi\)
\(234\) 69505.7 + 139914.i 1.26937 + 2.55522i
\(235\) −57558.0 −1.04224
\(236\) 11471.0i 0.205958i
\(237\) 7419.31 + 31611.2i 0.132089 + 0.562787i
\(238\) −175553. −3.09923
\(239\) 16376.2i 0.286693i 0.989673 + 0.143346i \(0.0457863\pi\)
−0.989673 + 0.143346i \(0.954214\pi\)
\(240\) −6947.04 + 1630.51i −0.120608 + 0.0283074i
\(241\) −49424.5 −0.850958 −0.425479 0.904968i \(-0.639894\pi\)
−0.425479 + 0.904968i \(0.639894\pi\)
\(242\) 93937.2i 1.60401i
\(243\) 53961.8 + 23977.2i 0.913848 + 0.406056i
\(244\) −76079.5 −1.27787
\(245\) 72708.5i 1.21130i
\(246\) 52.7239 + 224.639i 0.000871239 + 0.00371206i
\(247\) −47039.2 −0.771021
\(248\) 23859.8i 0.387940i
\(249\) −2762.43 + 648.357i −0.0445547 + 0.0104572i
\(250\) 69154.5 1.10647
\(251\) 41797.4i 0.663440i 0.943378 + 0.331720i \(0.107629\pi\)
−0.943378 + 0.331720i \(0.892371\pi\)
\(252\) 119881. 59553.8i 1.88777 0.937797i
\(253\) −1215.93 −0.0189962
\(254\) 189344.i 2.93484i
\(255\) −33601.4 143164.i −0.516746 2.20168i
\(256\) −56902.6 −0.868264
\(257\) 126533.i 1.91574i −0.287207 0.957868i \(-0.592727\pi\)
0.287207 0.957868i \(-0.407273\pi\)
\(258\) 8982.62 2108.27i 0.134947 0.0316728i
\(259\) −157816. −2.35262
\(260\) 296661.i 4.38847i
\(261\) 46637.3 + 93879.9i 0.684624 + 1.37814i
\(262\) 30549.4 0.445041
\(263\) 87556.5i 1.26583i 0.774219 + 0.632917i \(0.218143\pi\)
−0.774219 + 0.632917i \(0.781857\pi\)
\(264\) −626.931 2671.14i −0.00899522 0.0383256i
\(265\) 134834. 1.92003
\(266\) 65781.0i 0.929688i
\(267\) −110603. + 25959.0i −1.55147 + 0.364137i
\(268\) −217961. −3.03466
\(269\) 60072.7i 0.830181i 0.909780 + 0.415091i \(0.136250\pi\)
−0.909780 + 0.415091i \(0.863750\pi\)
\(270\) 116716. + 140957.i 1.60104 + 1.93357i
\(271\) 92136.8 1.25457 0.627285 0.778790i \(-0.284166\pi\)
0.627285 + 0.778790i \(0.284166\pi\)
\(272\) 8492.44i 0.114788i
\(273\) 40289.4 + 171660.i 0.540587 + 2.30326i
\(274\) 60546.5 0.806469
\(275\) 4586.66i 0.0606501i
\(276\) 52942.4 12425.8i 0.695000 0.163120i
\(277\) −8973.13 −0.116946 −0.0584728 0.998289i \(-0.518623\pi\)
−0.0584728 + 0.998289i \(0.518623\pi\)
\(278\) 57159.7i 0.739606i
\(279\) 28919.0 14366.3i 0.371514 0.184559i
\(280\) 152620. 1.94668
\(281\) 3227.90i 0.0408796i 0.999791 + 0.0204398i \(0.00650665\pi\)
−0.999791 + 0.0204398i \(0.993493\pi\)
\(282\) −19478.8 82992.5i −0.244942 1.04362i
\(283\) −61147.6 −0.763496 −0.381748 0.924266i \(-0.624678\pi\)
−0.381748 + 0.924266i \(0.624678\pi\)
\(284\) 225516.i 2.79602i
\(285\) −53644.8 + 12590.7i −0.660447 + 0.155010i
\(286\) 9824.19 0.120106
\(287\) 260.427i 0.00316171i
\(288\) −39211.8 78932.6i −0.472751 0.951638i
\(289\) −91490.7 −1.09542
\(290\) 324880.i 3.86303i
\(291\) 924.537 + 3939.14i 0.0109179 + 0.0465174i
\(292\) 22268.5 0.261171
\(293\) 12342.0i 0.143764i −0.997413 0.0718819i \(-0.977100\pi\)
0.997413 0.0718819i \(-0.0229005\pi\)
\(294\) 104838. 24606.0i 1.21290 0.284673i
\(295\) 17700.3 0.203393
\(296\) 144673.i 1.65122i
\(297\) 2860.04 2368.19i 0.0324235 0.0268475i
\(298\) 4486.92 0.0505261
\(299\) 71633.2i 0.801258i
\(300\) 46872.3 + 199707.i 0.520803 + 2.21897i
\(301\) 10413.7 0.114940
\(302\) 71914.6i 0.788502i
\(303\) 41658.2 9777.40i 0.453749 0.106497i
\(304\) 3182.19 0.0344333
\(305\) 117394.i 1.26196i
\(306\) 195056. 96899.3i 2.08313 1.03485i
\(307\) 159734. 1.69481 0.847404 0.530948i \(-0.178164\pi\)
0.847404 + 0.530948i \(0.178164\pi\)
\(308\) 8417.56i 0.0887329i
\(309\) −22027.2 93850.4i −0.230697 0.982923i
\(310\) 100077. 1.04138
\(311\) 80684.0i 0.834193i −0.908862 0.417096i \(-0.863048\pi\)
0.908862 0.417096i \(-0.136952\pi\)
\(312\) −157364. + 36934.1i −1.61657 + 0.379418i
\(313\) 153894. 1.57085 0.785424 0.618958i \(-0.212445\pi\)
0.785424 + 0.618958i \(0.212445\pi\)
\(314\) 97835.7i 0.992289i
\(315\) 91894.3 + 184981.i 0.926120 + 1.86426i
\(316\) −91320.1 −0.914518
\(317\) 3629.96i 0.0361230i −0.999837 0.0180615i \(-0.994251\pi\)
0.999837 0.0180615i \(-0.00574946\pi\)
\(318\) 45630.6 + 194417.i 0.451234 + 1.92256i
\(319\) 6591.89 0.0647781
\(320\) 260468.i 2.54363i
\(321\) 26374.2 6190.17i 0.255959 0.0600748i
\(322\) 100174. 0.966147
\(323\) 65578.3i 0.628572i
\(324\) −100327. + 132340.i −0.955718 + 1.26067i
\(325\) −270212. −2.55822
\(326\) 101581.i 0.955820i
\(327\) −925.692 3944.06i −0.00865707 0.0368849i
\(328\) −238.738 −0.00221909
\(329\) 96214.3i 0.888889i
\(330\) 11203.8 2629.58i 0.102881 0.0241468i
\(331\) −125930. −1.14941 −0.574703 0.818362i \(-0.694883\pi\)
−0.574703 + 0.818362i \(0.694883\pi\)
\(332\) 7980.26i 0.0724004i
\(333\) 175349. 87109.2i 1.58130 0.785553i
\(334\) 36903.9 0.330811
\(335\) 336324.i 2.99688i
\(336\) −2725.56 11612.7i −0.0241423 0.102862i
\(337\) 32949.8 0.290130 0.145065 0.989422i \(-0.453661\pi\)
0.145065 + 0.989422i \(0.453661\pi\)
\(338\) 395194.i 3.45921i
\(339\) −116364. + 27311.1i −1.01255 + 0.237651i
\(340\) 413580. 3.57768
\(341\) 2030.58i 0.0174627i
\(342\) −36308.9 73089.2i −0.310428 0.624886i
\(343\) −35217.7 −0.299345
\(344\) 9546.42i 0.0806721i
\(345\) 19173.6 + 81692.4i 0.161089 + 0.686347i
\(346\) 355662. 2.97088
\(347\) 156870.i 1.30281i 0.758731 + 0.651404i \(0.225820\pi\)
−0.758731 + 0.651404i \(0.774180\pi\)
\(348\) −287016. + 67364.1i −2.37000 + 0.556250i
\(349\) −179198. −1.47123 −0.735617 0.677397i \(-0.763108\pi\)
−0.735617 + 0.677397i \(0.763108\pi\)
\(350\) 377872.i 3.08467i
\(351\) −139516. 168492.i −1.13243 1.36762i
\(352\) −5542.34 −0.0447309
\(353\) 181513.i 1.45666i −0.685228 0.728329i \(-0.740297\pi\)
0.685228 0.728329i \(-0.259703\pi\)
\(354\) 5990.13 + 25521.9i 0.0478002 + 0.203661i
\(355\) −347982. −2.76121
\(356\) 319514.i 2.52110i
\(357\) 239314. 56168.3i 1.87773 0.440712i
\(358\) −207282. −1.61732
\(359\) 153380.i 1.19009i 0.803691 + 0.595047i \(0.202866\pi\)
−0.803691 + 0.595047i \(0.797134\pi\)
\(360\) −169576. + 84241.3i −1.30846 + 0.650010i
\(361\) −105748. −0.811445
\(362\) 80568.0i 0.614817i
\(363\) 30055.3 + 128056.i 0.228091 + 0.971820i
\(364\) −495900. −3.74275
\(365\) 34361.3i 0.257919i
\(366\) 169270. 39728.5i 1.26362 0.296579i
\(367\) 161326. 1.19776 0.598882 0.800837i \(-0.295612\pi\)
0.598882 + 0.800837i \(0.295612\pi\)
\(368\) 4845.96i 0.0357836i
\(369\) −143.747 289.360i −0.00105571 0.00212513i
\(370\) 606812. 4.43252
\(371\) 225390.i 1.63752i
\(372\) 20751.0 + 88413.2i 0.149952 + 0.638897i
\(373\) −230153. −1.65424 −0.827119 0.562026i \(-0.810022\pi\)
−0.827119 + 0.562026i \(0.810022\pi\)
\(374\) 13696.1i 0.0979160i
\(375\) −94271.7 + 22126.1i −0.670377 + 0.157341i
\(376\) 88201.5 0.623879
\(377\) 388345.i 2.73234i
\(378\) −235625. + 195103.i −1.64906 + 1.36547i
\(379\) 174446. 1.21446 0.607229 0.794527i \(-0.292281\pi\)
0.607229 + 0.794527i \(0.292281\pi\)
\(380\) 154972.i 1.07321i
\(381\) 60580.8 + 258115.i 0.417335 + 1.77813i
\(382\) −225320. −1.54409
\(383\) 60968.8i 0.415633i −0.978168 0.207816i \(-0.933364\pi\)
0.978168 0.207816i \(-0.0666357\pi\)
\(384\) 223026. 52345.4i 1.51249 0.354990i
\(385\) 12988.7 0.0876281
\(386\) 112840.i 0.757334i
\(387\) −11570.6 + 5748.00i −0.0772564 + 0.0383791i
\(388\) −11379.6 −0.0755898
\(389\) 213555.i 1.41127i −0.708576 0.705634i \(-0.750662\pi\)
0.708576 0.705634i \(-0.249338\pi\)
\(390\) −154915. 660042.i −1.01851 4.33953i
\(391\) 99865.3 0.653222
\(392\) 111418.i 0.725075i
\(393\) −41645.0 + 9774.31i −0.269636 + 0.0632850i
\(394\) 194895. 1.25548
\(395\) 140911.i 0.903131i
\(396\) 4646.21 + 9352.73i 0.0296284 + 0.0596414i
\(397\) −63337.5 −0.401864 −0.200932 0.979605i \(-0.564397\pi\)
−0.200932 + 0.979605i \(0.564397\pi\)
\(398\) 298491.i 1.88436i
\(399\) −21046.7 89673.0i −0.132202 0.563269i
\(400\) 18279.7 0.114248
\(401\) 159759.i 0.993519i 0.867888 + 0.496759i \(0.165477\pi\)
−0.867888 + 0.496759i \(0.834523\pi\)
\(402\) 484944. 113819.i 3.00082 0.704307i
\(403\) −119627. −0.736577
\(404\) 120344.i 0.737332i
\(405\) −204207. 154810.i −1.24498 0.943819i
\(406\) −543072. −3.29462
\(407\) 12312.3i 0.0743278i
\(408\) 51490.6 + 219384.i 0.309319 + 1.31791i
\(409\) 61661.2 0.368608 0.184304 0.982869i \(-0.440997\pi\)
0.184304 + 0.982869i \(0.440997\pi\)
\(410\) 1001.36i 0.00595691i
\(411\) −82537.2 + 19371.9i −0.488614 + 0.114680i
\(412\) 271120. 1.59723
\(413\) 29587.9i 0.173466i
\(414\) −111303. + 55292.7i −0.649392 + 0.322602i
\(415\) 12313.9 0.0714989
\(416\) 326514.i 1.88675i
\(417\) 18288.3 + 77920.4i 0.105172 + 0.448104i
\(418\) −5132.04 −0.0293723
\(419\) 272793.i 1.55384i 0.629602 + 0.776918i \(0.283218\pi\)
−0.629602 + 0.776918i \(0.716782\pi\)
\(420\) −565537. + 132734.i −3.20599 + 0.752463i
\(421\) 153748. 0.867451 0.433726 0.901045i \(-0.357199\pi\)
0.433726 + 0.901045i \(0.357199\pi\)
\(422\) 357799.i 2.00916i
\(423\) 53107.1 + 106904.i 0.296806 + 0.597463i
\(424\) −206619. −1.14931
\(425\) 376708.i 2.08558i
\(426\) −117764. 501753.i −0.648923 2.76484i
\(427\) 196237. 1.07628
\(428\) 76191.3i 0.415928i
\(429\) −13392.4 + 3143.26i −0.0727685 + 0.0170791i
\(430\) −40041.2 −0.216556
\(431\) 439.621i 0.00236659i −0.999999 0.00118330i \(-0.999623\pi\)
0.999999 0.00118330i \(-0.000376655\pi\)
\(432\) 9438.21 + 11398.4i 0.0505734 + 0.0610771i
\(433\) 48241.5 0.257303 0.128652 0.991690i \(-0.458935\pi\)
0.128652 + 0.991690i \(0.458935\pi\)
\(434\) 167289.i 0.888155i
\(435\) −103946. 442879.i −0.549324 2.34049i
\(436\) 11393.8 0.0599372
\(437\) 37420.3i 0.195950i
\(438\) −49545.3 + 11628.5i −0.258258 + 0.0606146i
\(439\) 276969. 1.43715 0.718574 0.695450i \(-0.244795\pi\)
0.718574 + 0.695450i \(0.244795\pi\)
\(440\) 11907.0i 0.0615029i
\(441\) −135043. + 67086.0i −0.694375 + 0.344949i
\(442\) −806872. −4.13009
\(443\) 102282.i 0.521186i 0.965449 + 0.260593i \(0.0839181\pi\)
−0.965449 + 0.260593i \(0.916082\pi\)
\(444\) 125823. + 536089.i 0.638254 + 2.71938i
\(445\) 493025. 2.48971
\(446\) 226120.i 1.13676i
\(447\) −6116.59 + 1435.60i −0.0306122 + 0.00718484i
\(448\) 435400. 2.16936
\(449\) 165328.i 0.820074i −0.912069 0.410037i \(-0.865516\pi\)
0.912069 0.410037i \(-0.134484\pi\)
\(450\) −208573. 419853.i −1.02999 2.07335i
\(451\) −20.3177 −9.98899e−5
\(452\) 336157.i 1.64538i
\(453\) 23009.2 + 98034.3i 0.112125 + 0.477729i
\(454\) 146679. 0.711635
\(455\) 765196.i 3.69615i
\(456\) 82205.0 19293.9i 0.395338 0.0927878i
\(457\) 157950. 0.756289 0.378145 0.925747i \(-0.376562\pi\)
0.378145 + 0.925747i \(0.376562\pi\)
\(458\) 278533.i 1.32784i
\(459\) −234899. + 194502.i −1.11495 + 0.923206i
\(460\) −235997. −1.11530
\(461\) 134676.i 0.633708i 0.948474 + 0.316854i \(0.102627\pi\)
−0.948474 + 0.316854i \(0.897373\pi\)
\(462\) 4395.63 + 18728.3i 0.0205938 + 0.0877433i
\(463\) −131341. −0.612688 −0.306344 0.951921i \(-0.599106\pi\)
−0.306344 + 0.951921i \(0.599106\pi\)
\(464\) 26271.4i 0.122024i
\(465\) −136426. + 32019.8i −0.630942 + 0.148085i
\(466\) 368219. 1.69564
\(467\) 181133.i 0.830545i −0.909697 0.415273i \(-0.863686\pi\)
0.909697 0.415273i \(-0.136314\pi\)
\(468\) 550993. 273720.i 2.51568 1.24973i
\(469\) 562202. 2.55592
\(470\) 369950.i 1.67474i
\(471\) −31302.7 133370.i −0.141104 0.601197i
\(472\) −27123.8 −0.121749
\(473\) 812.444i 0.00363137i
\(474\) 203179. 47687.1i 0.904319 0.212248i
\(475\) 141156. 0.625620
\(476\) 691343.i 3.05126i
\(477\) −124408. 250430.i −0.546777 1.10065i
\(478\) 105257. 0.460675
\(479\) 4491.28i 0.0195749i −0.999952 0.00978744i \(-0.996885\pi\)
0.999952 0.00978744i \(-0.00311549\pi\)
\(480\) 87395.9 + 372365.i 0.379323 + 1.61617i
\(481\) −725351. −3.13515
\(482\) 317672.i 1.36737i
\(483\) −136558. + 32050.8i −0.585358 + 0.137387i
\(484\) −369934. −1.57919
\(485\) 17559.2i 0.0746487i
\(486\) 154112. 346836.i 0.652473 1.46842i
\(487\) −195876. −0.825893 −0.412946 0.910755i \(-0.635500\pi\)
−0.412946 + 0.910755i \(0.635500\pi\)
\(488\) 179894.i 0.755400i
\(489\) 32500.9 + 138475.i 0.135918 + 0.579102i
\(490\) −467328. −1.94639
\(491\) 52346.0i 0.217131i 0.994089 + 0.108565i \(0.0346256\pi\)
−0.994089 + 0.108565i \(0.965374\pi\)
\(492\) 884.649 207.632i 0.00365461 0.000857756i
\(493\) −541399. −2.22753
\(494\) 302341.i 1.23892i
\(495\) −14431.7 + 7169.32i −0.0588988 + 0.0292595i
\(496\) 8092.70 0.0328950
\(497\) 581688.i 2.35493i
\(498\) 4167.27 + 17755.3i 0.0168032 + 0.0715930i
\(499\) −182646. −0.733516 −0.366758 0.930316i \(-0.619532\pi\)
−0.366758 + 0.930316i \(0.619532\pi\)
\(500\) 272337.i 1.08935i
\(501\) −50307.6 + 11807.5i −0.200428 + 0.0470415i
\(502\) 268650. 1.06605
\(503\) 111201.i 0.439515i 0.975555 + 0.219757i \(0.0705265\pi\)
−0.975555 + 0.219757i \(0.929473\pi\)
\(504\) −140818. 283464.i −0.554368 1.11593i
\(505\) −185697. −0.728151
\(506\) 7815.27i 0.0305241i
\(507\) 126443. + 538731.i 0.491902 + 2.09583i
\(508\) −745655. −2.88942
\(509\) 161633.i 0.623872i −0.950103 0.311936i \(-0.899023\pi\)
0.950103 0.311936i \(-0.100977\pi\)
\(510\) −920178. + 215970.i −3.53778 + 0.830336i
\(511\) −57438.5 −0.219969
\(512\) 41528.3i 0.158418i
\(513\) 72881.5 + 88018.4i 0.276938 + 0.334456i
\(514\) −813279. −3.07832
\(515\) 418350.i 1.57734i
\(516\) −8302.57 35374.5i −0.0311826 0.132859i
\(517\) 7506.35 0.0280833
\(518\) 1.01435e6i 3.78032i
\(519\) −484840. + 113795.i −1.79997 + 0.422461i
\(520\) 701470. 2.59419
\(521\) 230594.i 0.849517i 0.905307 + 0.424759i \(0.139641\pi\)
−0.905307 + 0.424759i \(0.860359\pi\)
\(522\) 603407. 299758.i 2.21447 1.10009i
\(523\) 451661. 1.65123 0.825617 0.564231i \(-0.190827\pi\)
0.825617 + 0.564231i \(0.190827\pi\)
\(524\) 120306.i 0.438153i
\(525\) −120901. 515117.i −0.438642 1.86891i
\(526\) 562763. 2.03402
\(527\) 166774.i 0.600492i
\(528\) 905.989 212.640i 0.00324979 0.000762742i
\(529\) 222856. 0.796366
\(530\) 866637.i 3.08522i
\(531\) −16331.6 32875.1i −0.0579213 0.116594i
\(532\) 259052. 0.915300
\(533\) 1196.97i 0.00421336i
\(534\) 166850. + 710890.i 0.585117 + 2.49299i
\(535\) −117567. −0.410749
\(536\) 515381.i 1.79390i
\(537\) 282568. 66320.2i 0.979884 0.229984i
\(538\) 386113. 1.33398
\(539\) 9482.18i 0.0326385i
\(540\) 555102. 459639.i 1.90364 1.57627i
\(541\) 218146. 0.745336 0.372668 0.927965i \(-0.378443\pi\)
0.372668 + 0.927965i \(0.378443\pi\)
\(542\) 592203.i 2.01591i
\(543\) −25777.8 109831.i −0.0874273 0.372498i
\(544\) 455199. 1.53817
\(545\) 17581.2i 0.0591909i
\(546\) 1.10333e6 258957.i 3.70101 0.868647i
\(547\) −90378.8 −0.302059 −0.151030 0.988529i \(-0.548259\pi\)
−0.151030 + 0.988529i \(0.548259\pi\)
\(548\) 238438.i 0.793988i
\(549\) −218038. + 108316.i −0.723416 + 0.359376i
\(550\) −29480.5 −0.0974561
\(551\) 202867.i 0.668201i
\(552\) −29381.6 125185.i −0.0964266 0.410841i
\(553\) 235548. 0.770245
\(554\) 57674.1i 0.187915i
\(555\) −827209. + 194150.i −2.68553 + 0.630307i
\(556\) −225100. −0.728160
\(557\) 525332.i 1.69326i 0.532184 + 0.846629i \(0.321372\pi\)
−0.532184 + 0.846629i \(0.678628\pi\)
\(558\) −92338.2 185875.i −0.296560 0.596970i
\(559\) 47863.1 0.153171
\(560\) 51765.2i 0.165068i
\(561\) 4382.08 + 18670.6i 0.0139237 + 0.0593242i
\(562\) 20747.1 0.0656878
\(563\) 531031.i 1.67534i −0.546177 0.837670i \(-0.683917\pi\)
0.546177 0.837670i \(-0.316083\pi\)
\(564\) −326833. + 76709.3i −1.02747 + 0.241151i
\(565\) 518705. 1.62489
\(566\) 393022.i 1.22683i
\(567\) 258781. 341354.i 0.804945 1.06179i
\(568\) 533245. 1.65284
\(569\) 71552.4i 0.221004i 0.993876 + 0.110502i \(0.0352458\pi\)
−0.993876 + 0.110502i \(0.964754\pi\)
\(570\) 80925.9 + 344798.i 0.249079 + 1.06124i
\(571\) −197853. −0.606836 −0.303418 0.952858i \(-0.598128\pi\)
−0.303418 + 0.952858i \(0.598128\pi\)
\(572\) 38688.6i 0.118247i
\(573\) 307157. 72091.4i 0.935517 0.219571i
\(574\) 1673.87 0.00508041
\(575\) 214957.i 0.650154i
\(576\) −483772. + 240326.i −1.45813 + 0.724363i
\(577\) 231477. 0.695273 0.347637 0.937629i \(-0.386984\pi\)
0.347637 + 0.937629i \(0.386984\pi\)
\(578\) 588050.i 1.76019i
\(579\) 36103.2 + 153824.i 0.107693 + 0.458845i
\(580\) 1.27941e6 3.80324
\(581\) 20584.0i 0.0609786i
\(582\) 25318.6 5942.39i 0.0747468 0.0175435i
\(583\) −17584.2 −0.0517352
\(584\) 52655.0i 0.154388i
\(585\) 422363. + 850208.i 1.23417 + 2.48435i
\(586\) −79327.2 −0.231008
\(587\) 540008.i 1.56720i −0.621266 0.783600i \(-0.713381\pi\)
0.621266 0.783600i \(-0.286619\pi\)
\(588\) −96900.8 412862.i −0.280267 1.19413i
\(589\) 62491.6 0.180132
\(590\) 113767.i 0.326824i
\(591\) −265682. + 62356.9i −0.760653 + 0.178529i
\(592\) 49069.7 0.140013
\(593\) 40828.0i 0.116104i −0.998314 0.0580522i \(-0.981511\pi\)
0.998314 0.0580522i \(-0.0184890\pi\)
\(594\) −15221.4 18382.7i −0.0431401 0.0520999i
\(595\) −1.06677e6 −3.01327
\(596\) 17669.9i 0.0497442i
\(597\) −95502.5 406904.i −0.267958 1.14168i
\(598\) 460418. 1.28751
\(599\) 74599.9i 0.207914i −0.994582 0.103957i \(-0.966850\pi\)
0.994582 0.103957i \(-0.0331505\pi\)
\(600\) 472218. 110832.i 1.31172 0.307867i
\(601\) 273202. 0.756370 0.378185 0.925730i \(-0.376548\pi\)
0.378185 + 0.925730i \(0.376548\pi\)
\(602\) 66933.1i 0.184692i
\(603\) −624662. + 310317.i −1.71795 + 0.853436i
\(604\) −283207. −0.776300
\(605\) 570825.i 1.55952i
\(606\) −62843.5 267755.i −0.171126 0.729109i
\(607\) −159647. −0.433296 −0.216648 0.976250i \(-0.569512\pi\)
−0.216648 + 0.976250i \(0.569512\pi\)
\(608\) 170567.i 0.461410i
\(609\) 740319. 173757.i 1.99611 0.468497i
\(610\) −754542. −2.02779
\(611\) 442218.i 1.18455i
\(612\) −381599. 768150.i −1.01884 2.05090i
\(613\) 615909. 1.63906 0.819531 0.573035i \(-0.194234\pi\)
0.819531 + 0.573035i \(0.194234\pi\)
\(614\) 1.02668e6i 2.72332i
\(615\) 320.385 + 1365.05i 0.000847076 + 0.00360911i
\(616\) −19903.8 −0.0524534
\(617\) 695853.i 1.82788i 0.405852 + 0.913939i \(0.366975\pi\)
−0.405852 + 0.913939i \(0.633025\pi\)
\(618\) −603217. + 141578.i −1.57942 + 0.370697i
\(619\) −38457.6 −0.100369 −0.0501847 0.998740i \(-0.515981\pi\)
−0.0501847 + 0.998740i \(0.515981\pi\)
\(620\) 394113.i 1.02527i
\(621\) 134038. 110987.i 0.347572 0.287798i
\(622\) −518591. −1.34043
\(623\) 824144.i 2.12338i
\(624\) −12527.2 53374.1i −0.0321725 0.137076i
\(625\) −142568. −0.364974
\(626\) 989146.i 2.52413i
\(627\) 6996.02 1642.00i 0.0177957 0.00417675i
\(628\) 385287. 0.976933
\(629\) 1.01123e6i 2.55592i
\(630\) 1.18895e6 590644.i 2.99560 1.48814i
\(631\) −647361. −1.62588 −0.812939 0.582349i \(-0.802134\pi\)
−0.812939 + 0.582349i \(0.802134\pi\)
\(632\) 215931.i 0.540606i
\(633\) 114478. + 487753.i 0.285703 + 1.21729i
\(634\) −23331.3 −0.0580445
\(635\) 1.15058e6i 2.85344i
\(636\) 765631. 179698.i 1.89280 0.444251i
\(637\) 558619. 1.37669
\(638\) 42368.9i 0.104089i
\(639\) 321073. + 646313.i 0.786324 + 1.58286i
\(640\) −994169. −2.42717
\(641\) 104411.i 0.254116i −0.991895 0.127058i \(-0.959447\pi\)
0.991895 0.127058i \(-0.0405534\pi\)
\(642\) −39786.9 169519.i −0.0965317 0.411289i
\(643\) 36891.7 0.0892290 0.0446145 0.999004i \(-0.485794\pi\)
0.0446145 + 0.999004i \(0.485794\pi\)
\(644\) 394495.i 0.951195i
\(645\) 54584.4 12811.2i 0.131205 0.0307944i
\(646\) 421500. 1.01003
\(647\) 100450.i 0.239961i 0.992776 + 0.119980i \(0.0382831\pi\)
−0.992776 + 0.119980i \(0.961717\pi\)
\(648\) 312926. + 237230.i 0.745232 + 0.564962i
\(649\) −2308.36 −0.00548043
\(650\) 1.73677e6i 4.11070i
\(651\) −53524.5 228050.i −0.126296 0.538106i
\(652\) −400035. −0.941028
\(653\) 30923.0i 0.0725195i 0.999342 + 0.0362597i \(0.0115444\pi\)
−0.999342 + 0.0362597i \(0.988456\pi\)
\(654\) −25350.2 + 5949.82i −0.0592687 + 0.0139107i
\(655\) 185638. 0.432698
\(656\) 80.9744i 0.000188166i
\(657\) 63819.9 31704.2i 0.147851 0.0734490i
\(658\) −618410. −1.42832
\(659\) 543752.i 1.25208i 0.779793 + 0.626038i \(0.215324\pi\)
−0.779793 + 0.626038i \(0.784676\pi\)
\(660\) −10355.5 44121.5i −0.0237731 0.101289i
\(661\) −653369. −1.49539 −0.747697 0.664040i \(-0.768840\pi\)
−0.747697 + 0.664040i \(0.768840\pi\)
\(662\) 809407.i 1.84693i
\(663\) 1.09993e6 258160.i 2.50230 0.587302i
\(664\) −18869.8 −0.0427986
\(665\) 399729.i 0.903904i
\(666\) −559888. 1.12704e6i −1.26227 2.54093i
\(667\) 308933. 0.694406
\(668\) 145331.i 0.325691i
\(669\) −72347.4 308248.i −0.161648 0.688728i
\(670\) −2.16170e6 −4.81555
\(671\) 15309.8i 0.0340036i
\(672\) −622447. + 146092.i −1.37836 + 0.323509i
\(673\) 554612. 1.22450 0.612251 0.790664i \(-0.290264\pi\)
0.612251 + 0.790664i \(0.290264\pi\)
\(674\) 211782.i 0.466197i
\(675\) 418660. + 505613.i 0.918870 + 1.10971i
\(676\) −1.55631e6 −3.40568
\(677\) 303181.i 0.661492i 0.943720 + 0.330746i \(0.107300\pi\)
−0.943720 + 0.330746i \(0.892700\pi\)
\(678\) 175540. + 747918.i 0.381872 + 1.62703i
\(679\) 29352.1 0.0636649
\(680\) 977932.i 2.11491i
\(681\) −199954. + 46930.2i −0.431157 + 0.101195i
\(682\) −13051.4 −0.0280601
\(683\) 336072.i 0.720428i −0.932870 0.360214i \(-0.882704\pi\)
0.932870 0.360214i \(-0.117296\pi\)
\(684\) −287832. + 142988.i −0.615215 + 0.305624i
\(685\) 367920. 0.784102
\(686\) 226359.i 0.481005i
\(687\) 89117.1 + 379698.i 0.188820 + 0.804498i
\(688\) −3237.92 −0.00684053
\(689\) 1.03593e6i 2.18219i
\(690\) 525072. 123237.i 1.10286 0.258847i
\(691\) 117111. 0.245269 0.122635 0.992452i \(-0.460866\pi\)
0.122635 + 0.992452i \(0.460866\pi\)
\(692\) 1.40063e6i 2.92491i
\(693\) −11984.3 24124.1i −0.0249543 0.0502325i
\(694\) 1.00827e6 2.09343
\(695\) 347340.i 0.719094i
\(696\) 159286. + 678665.i 0.328821 + 1.40100i
\(697\) 1668.72 0.00343492
\(698\) 1.15178e6i 2.36406i
\(699\) −501958. + 117812.i −1.02734 + 0.241121i
\(700\) 1.48810e6 3.03693
\(701\) 148746.i 0.302698i −0.988480 0.151349i \(-0.951638\pi\)
0.988480 0.151349i \(-0.0483618\pi\)
\(702\) −1.08297e6 + 896730.i −2.19757 + 1.81965i
\(703\) 378914. 0.766709
\(704\) 33968.6i 0.0685381i
\(705\) −118366. 504317.i −0.238149 1.01467i
\(706\) −1.16666e6 −2.34064
\(707\) 310412.i 0.621012i
\(708\) 100508. 23589.7i 0.200509 0.0470605i
\(709\) 142329. 0.283141 0.141570 0.989928i \(-0.454785\pi\)
0.141570 + 0.989928i \(0.454785\pi\)
\(710\) 2.23663e6i 4.43687i
\(711\) −261717. + 130015.i −0.517717 + 0.257189i
\(712\) −755509. −1.49032
\(713\) 95164.7i 0.187196i
\(714\) −361018. 1.53818e6i −0.708161 3.01724i
\(715\) 59698.3 0.116775
\(716\) 816298.i 1.59229i
\(717\) −143487. + 33677.0i −0.279108 + 0.0655082i
\(718\) 985842. 1.91231
\(719\) 108893.i 0.210641i 0.994438 + 0.105321i \(0.0335869\pi\)
−0.994438 + 0.105321i \(0.966413\pi\)
\(720\) −28572.7 57516.2i −0.0551170 0.110949i
\(721\) −699317. −1.34525
\(722\) 679689.i 1.30388i
\(723\) −101640. 433052.i −0.194440 0.828445i
\(724\) 317285. 0.605302
\(725\) 1.16535e6i 2.21707i
\(726\) 823069. 193179.i 1.56158 0.366510i
\(727\) 499824. 0.945688 0.472844 0.881146i \(-0.343227\pi\)
0.472844 + 0.881146i \(0.343227\pi\)
\(728\) 1.17258e6i 2.21248i
\(729\) −99115.1 + 522117.i −0.186503 + 0.982454i
\(730\) 220855. 0.414439
\(731\) 66726.9i 0.124872i
\(732\) −156455. 666601.i −0.291989 1.24407i
\(733\) −154763. −0.288044 −0.144022 0.989574i \(-0.546004\pi\)
−0.144022 + 0.989574i \(0.546004\pi\)
\(734\) 1.03691e6i 1.92464i
\(735\) 637064. 149522.i 1.17926 0.276778i
\(736\) −259746. −0.479505
\(737\) 43861.3i 0.0807508i
\(738\) −1859.84 + 923.923i −0.00341478 + 0.00169638i
\(739\) −589.545 −0.00107951 −0.000539757 1.00000i \(-0.500172\pi\)
−0.000539757 1.00000i \(0.500172\pi\)
\(740\) 2.38968e6i 4.36392i
\(741\) −96734.5 412153.i −0.176175 0.750624i
\(742\) 1.44868e6 2.63126
\(743\) 684478.i 1.23989i −0.784647 0.619943i \(-0.787156\pi\)
0.784647 0.619943i \(-0.212844\pi\)
\(744\) 209058. 49066.9i 0.377677 0.0886427i
\(745\) 27265.5 0.0491248
\(746\) 1.47929e6i 2.65813i
\(747\) −11361.7 22870.8i −0.0203611 0.0409865i
\(748\) −53936.5 −0.0964006
\(749\) 196525.i 0.350311i
\(750\) 142214. + 605925.i 0.252824 + 1.07720i
\(751\) −700854. −1.24265 −0.621323 0.783554i \(-0.713405\pi\)
−0.621323 + 0.783554i \(0.713405\pi\)
\(752\) 29915.9i 0.0529013i
\(753\) −366225. + 85954.8i −0.645889 + 0.151593i
\(754\) −2.49606e6 −4.39048
\(755\) 437001.i 0.766634i
\(756\) 768335. + 927913.i 1.34433 + 1.62354i
\(757\) 219518. 0.383070 0.191535 0.981486i \(-0.438653\pi\)
0.191535 + 0.981486i \(0.438653\pi\)
\(758\) 1.12124e6i 1.95146i
\(759\) −2500.51 10653.8i −0.00434055 0.0184936i
\(760\) −366439. −0.634417
\(761\) 480822.i 0.830262i −0.909762 0.415131i \(-0.863736\pi\)
0.909762 0.415131i \(-0.136264\pi\)
\(762\) 1.65901e6 389379.i 2.85719 0.670598i
\(763\) −29388.8 −0.0504816
\(764\) 887332.i 1.52020i
\(765\) 1.18529e6 588824.i 2.02536 1.00615i
\(766\) −391873. −0.667863
\(767\) 135991.i 0.231164i
\(768\) −117018. 498575.i −0.198395 0.845294i
\(769\) −719489. −1.21667 −0.608333 0.793682i \(-0.708162\pi\)
−0.608333 + 0.793682i \(0.708162\pi\)
\(770\) 83483.7i 0.140806i
\(771\) 1.10867e6 260210.i 1.86506 0.437738i
\(772\) −444374. −0.745614
\(773\) 35961.4i 0.0601835i −0.999547 0.0300918i \(-0.990420\pi\)
0.999547 0.0300918i \(-0.00957995\pi\)
\(774\) 36944.9 + 74369.3i 0.0616698 + 0.124140i
\(775\) 358976. 0.597671
\(776\) 26907.7i 0.0446840i
\(777\) −324543. 1.38277e6i −0.537564 2.29038i
\(778\) −1.37261e6 −2.26771
\(779\) 625.282i 0.00103039i
\(780\) −2.59931e6 + 610072.i −4.27237 + 1.00275i
\(781\) 45381.6 0.0744008
\(782\) 641877.i 1.04964i