Properties

Label 210.3.h.a.139.4
Level $210$
Weight $3$
Character 210.139
Analytic conductor $5.722$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + 362298 x^{8} - 722060 x^{7} + 1208164 x^{6} - 1570812 x^{5} + \cdots + 33750 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.4
Root \(0.500000 - 4.10071i\) of defining polynomial
Character \(\chi\) \(=\) 210.139
Dual form 210.3.h.a.139.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +2.44949i q^{6} +(6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +2.44949i q^{6} +(6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +(-2.77894 - 6.50212i) q^{10} -8.15965 q^{11} +3.46410 q^{12} +14.6064 q^{13} +(2.23278 - 9.64441i) q^{14} +(-7.96343 + 3.40349i) q^{15} +4.00000 q^{16} +5.81421 q^{17} -4.24264i q^{18} -33.7736i q^{19} +(-9.19538 + 3.93001i) q^{20} +(-11.8119 - 2.73459i) q^{21} +11.5395i q^{22} -37.2576i q^{23} -4.89898i q^{24} +(17.2775 - 18.0690i) q^{25} -20.6566i q^{26} -5.19615 q^{27} +(-13.6393 - 3.15763i) q^{28} -9.25305 q^{29} +(4.81326 + 11.2620i) q^{30} +19.2558i q^{31} -5.65685i q^{32} +14.1329 q^{33} -8.22253i q^{34} +(34.4569 - 6.14171i) q^{35} -6.00000 q^{36} +63.4350i q^{37} -47.7631 q^{38} -25.2990 q^{39} +(5.55788 + 13.0042i) q^{40} -8.25880i q^{41} +(-3.86729 + 16.7046i) q^{42} +42.0893i q^{43} +16.3193 q^{44} +(13.7931 - 5.89502i) q^{45} -52.6901 q^{46} +23.3380 q^{47} -6.92820 q^{48} +(44.0147 + 21.5339i) q^{49} +(-25.5534 - 24.4341i) q^{50} -10.0705 q^{51} -29.2128 q^{52} -71.3497i q^{53} +7.34847i q^{54} +(-37.5155 + 16.0337i) q^{55} +(-4.46556 + 19.2888i) q^{56} +58.4976i q^{57} +13.0858i q^{58} +42.9350i q^{59} +(15.9269 - 6.80698i) q^{60} +34.2864i q^{61} +27.2318 q^{62} +(20.4589 + 4.73644i) q^{63} -8.00000 q^{64} +(67.1557 - 28.7017i) q^{65} -19.9870i q^{66} +4.99889i q^{67} -11.6284 q^{68} +64.5320i q^{69} +(-8.68569 - 48.7294i) q^{70} -38.8120 q^{71} +8.48528i q^{72} +124.629 q^{73} +89.7107 q^{74} +(-29.9255 + 31.2964i) q^{75} +67.5472i q^{76} +(-55.6458 - 12.8826i) q^{77} +35.7782i q^{78} -56.1842 q^{79} +(18.3908 - 7.86002i) q^{80} +9.00000 q^{81} -11.6797 q^{82} -90.3980 q^{83} +(23.6239 + 5.46917i) q^{84} +(26.7319 - 11.4249i) q^{85} +59.5233 q^{86} +16.0267 q^{87} -23.0790i q^{88} -16.2289i q^{89} +(-8.33681 - 19.5063i) q^{90} +(99.6102 + 23.0608i) q^{91} +74.5151i q^{92} -33.3520i q^{93} -33.0048i q^{94} +(-66.3653 - 155.280i) q^{95} +9.79796i q^{96} +82.7605 q^{97} +(30.4535 - 62.2462i) q^{98} -24.4789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −1.73205 −0.577350
\(4\) −2.00000 −0.500000
\(5\) 4.59769 1.96501i 0.919538 0.393001i
\(6\) 2.44949i 0.408248i
\(7\) 6.81963 + 1.57881i 0.974233 + 0.225545i
\(8\) 2.82843i 0.353553i
\(9\) 3.00000 0.333333
\(10\) −2.77894 6.50212i −0.277894 0.650212i
\(11\) −8.15965 −0.741786 −0.370893 0.928676i \(-0.620948\pi\)
−0.370893 + 0.928676i \(0.620948\pi\)
\(12\) 3.46410 0.288675
\(13\) 14.6064 1.12357 0.561785 0.827284i \(-0.310115\pi\)
0.561785 + 0.827284i \(0.310115\pi\)
\(14\) 2.23278 9.64441i 0.159484 0.688887i
\(15\) −7.96343 + 3.40349i −0.530896 + 0.226899i
\(16\) 4.00000 0.250000
\(17\) 5.81421 0.342012 0.171006 0.985270i \(-0.445298\pi\)
0.171006 + 0.985270i \(0.445298\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 33.7736i 1.77756i −0.458337 0.888778i \(-0.651555\pi\)
0.458337 0.888778i \(-0.348445\pi\)
\(20\) −9.19538 + 3.93001i −0.459769 + 0.196501i
\(21\) −11.8119 2.73459i −0.562474 0.130218i
\(22\) 11.5395i 0.524522i
\(23\) 37.2576i 1.61989i −0.586503 0.809947i \(-0.699496\pi\)
0.586503 0.809947i \(-0.300504\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 17.2775 18.0690i 0.691100 0.722759i
\(26\) 20.6566i 0.794483i
\(27\) −5.19615 −0.192450
\(28\) −13.6393 3.15763i −0.487116 0.112772i
\(29\) −9.25305 −0.319071 −0.159535 0.987192i \(-0.551000\pi\)
−0.159535 + 0.987192i \(0.551000\pi\)
\(30\) 4.81326 + 11.2620i 0.160442 + 0.375400i
\(31\) 19.2558i 0.621154i 0.950548 + 0.310577i \(0.100522\pi\)
−0.950548 + 0.310577i \(0.899478\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 14.1329 0.428270
\(34\) 8.22253i 0.241839i
\(35\) 34.4569 6.14171i 0.984483 0.175478i
\(36\) −6.00000 −0.166667
\(37\) 63.4350i 1.71446i 0.514933 + 0.857230i \(0.327817\pi\)
−0.514933 + 0.857230i \(0.672183\pi\)
\(38\) −47.7631 −1.25692
\(39\) −25.2990 −0.648693
\(40\) 5.55788 + 13.0042i 0.138947 + 0.325106i
\(41\) 8.25880i 0.201434i −0.994915 0.100717i \(-0.967886\pi\)
0.994915 0.100717i \(-0.0321137\pi\)
\(42\) −3.86729 + 16.7046i −0.0920783 + 0.397729i
\(43\) 42.0893i 0.978822i 0.872053 + 0.489411i \(0.162788\pi\)
−0.872053 + 0.489411i \(0.837212\pi\)
\(44\) 16.3193 0.370893
\(45\) 13.7931 5.89502i 0.306513 0.131000i
\(46\) −52.6901 −1.14544
\(47\) 23.3380 0.496552 0.248276 0.968689i \(-0.420136\pi\)
0.248276 + 0.968689i \(0.420136\pi\)
\(48\) −6.92820 −0.144338
\(49\) 44.0147 + 21.5339i 0.898259 + 0.439466i
\(50\) −25.5534 24.4341i −0.511068 0.488682i
\(51\) −10.0705 −0.197461
\(52\) −29.2128 −0.561785
\(53\) 71.3497i 1.34622i −0.739542 0.673110i \(-0.764958\pi\)
0.739542 0.673110i \(-0.235042\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −37.5155 + 16.0337i −0.682100 + 0.291523i
\(56\) −4.46556 + 19.2888i −0.0797422 + 0.344443i
\(57\) 58.4976i 1.02627i
\(58\) 13.0858i 0.225617i
\(59\) 42.9350i 0.727712i 0.931455 + 0.363856i \(0.118540\pi\)
−0.931455 + 0.363856i \(0.881460\pi\)
\(60\) 15.9269 6.80698i 0.265448 0.113450i
\(61\) 34.2864i 0.562072i 0.959697 + 0.281036i \(0.0906781\pi\)
−0.959697 + 0.281036i \(0.909322\pi\)
\(62\) 27.2318 0.439222
\(63\) 20.4589 + 4.73644i 0.324744 + 0.0751816i
\(64\) −8.00000 −0.125000
\(65\) 67.1557 28.7017i 1.03316 0.441564i
\(66\) 19.9870i 0.302833i
\(67\) 4.99889i 0.0746102i 0.999304 + 0.0373051i \(0.0118773\pi\)
−0.999304 + 0.0373051i \(0.988123\pi\)
\(68\) −11.6284 −0.171006
\(69\) 64.5320i 0.935246i
\(70\) −8.68569 48.7294i −0.124081 0.696135i
\(71\) −38.8120 −0.546648 −0.273324 0.961922i \(-0.588123\pi\)
−0.273324 + 0.961922i \(0.588123\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 124.629 1.70725 0.853626 0.520886i \(-0.174398\pi\)
0.853626 + 0.520886i \(0.174398\pi\)
\(74\) 89.7107 1.21231
\(75\) −29.9255 + 31.2964i −0.399007 + 0.417285i
\(76\) 67.5472i 0.888778i
\(77\) −55.6458 12.8826i −0.722672 0.167306i
\(78\) 35.7782i 0.458695i
\(79\) −56.1842 −0.711192 −0.355596 0.934640i \(-0.615722\pi\)
−0.355596 + 0.934640i \(0.615722\pi\)
\(80\) 18.3908 7.86002i 0.229884 0.0982503i
\(81\) 9.00000 0.111111
\(82\) −11.6797 −0.142435
\(83\) −90.3980 −1.08913 −0.544566 0.838718i \(-0.683306\pi\)
−0.544566 + 0.838718i \(0.683306\pi\)
\(84\) 23.6239 + 5.46917i 0.281237 + 0.0651092i
\(85\) 26.7319 11.4249i 0.314493 0.134411i
\(86\) 59.5233 0.692131
\(87\) 16.0267 0.184215
\(88\) 23.0790i 0.262261i
\(89\) 16.2289i 0.182347i −0.995835 0.0911736i \(-0.970938\pi\)
0.995835 0.0911736i \(-0.0290618\pi\)
\(90\) −8.33681 19.5063i −0.0926313 0.216737i
\(91\) 99.6102 + 23.0608i 1.09462 + 0.253415i
\(92\) 74.5151i 0.809947i
\(93\) 33.3520i 0.358624i
\(94\) 33.0048i 0.351115i
\(95\) −66.3653 155.280i −0.698582 1.63453i
\(96\) 9.79796i 0.102062i
\(97\) 82.7605 0.853201 0.426601 0.904440i \(-0.359711\pi\)
0.426601 + 0.904440i \(0.359711\pi\)
\(98\) 30.4535 62.2462i 0.310750 0.635165i
\(99\) −24.4789 −0.247262
\(100\) −34.5550 + 36.1379i −0.345550 + 0.361379i
\(101\) 87.2055i 0.863420i 0.902012 + 0.431710i \(0.142090\pi\)
−0.902012 + 0.431710i \(0.857910\pi\)
\(102\) 14.2418i 0.139626i
\(103\) −187.567 −1.82104 −0.910521 0.413462i \(-0.864319\pi\)
−0.910521 + 0.413462i \(0.864319\pi\)
\(104\) 41.3131i 0.397242i
\(105\) −59.6811 + 10.6378i −0.568392 + 0.101312i
\(106\) −100.904 −0.951922
\(107\) 157.858i 1.47531i 0.675180 + 0.737653i \(0.264066\pi\)
−0.675180 + 0.737653i \(0.735934\pi\)
\(108\) 10.3923 0.0962250
\(109\) −112.073 −1.02819 −0.514097 0.857732i \(-0.671873\pi\)
−0.514097 + 0.857732i \(0.671873\pi\)
\(110\) 22.6751 + 53.0550i 0.206138 + 0.482318i
\(111\) 109.873i 0.989844i
\(112\) 27.2785 + 6.31526i 0.243558 + 0.0563862i
\(113\) 141.987i 1.25653i 0.778001 + 0.628263i \(0.216234\pi\)
−0.778001 + 0.628263i \(0.783766\pi\)
\(114\) 82.7280 0.725684
\(115\) −73.2113 171.299i −0.636620 1.48955i
\(116\) 18.5061 0.159535
\(117\) 43.8192 0.374523
\(118\) 60.7192 0.514570
\(119\) 39.6507 + 9.17955i 0.333199 + 0.0771391i
\(120\) −9.62652 22.5240i −0.0802210 0.187700i
\(121\) −54.4202 −0.449754
\(122\) 48.4883 0.397445
\(123\) 14.3047i 0.116298i
\(124\) 38.5116i 0.310577i
\(125\) 43.9310 117.026i 0.351448 0.936207i
\(126\) 6.69834 28.9332i 0.0531614 0.229629i
\(127\) 202.414i 1.59381i 0.604104 + 0.796905i \(0.293531\pi\)
−0.604104 + 0.796905i \(0.706469\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 72.9008i 0.565123i
\(130\) −40.5903 94.9725i −0.312233 0.730558i
\(131\) 141.260i 1.07832i −0.842203 0.539160i \(-0.818742\pi\)
0.842203 0.539160i \(-0.181258\pi\)
\(132\) −28.2658 −0.214135
\(133\) 53.3222 230.323i 0.400919 1.73175i
\(134\) 7.06949 0.0527574
\(135\) −23.8903 + 10.2105i −0.176965 + 0.0756331i
\(136\) 16.4451i 0.120920i
\(137\) 50.6430i 0.369657i −0.982771 0.184829i \(-0.940827\pi\)
0.982771 0.184829i \(-0.0591730\pi\)
\(138\) 91.2620 0.661319
\(139\) 74.0256i 0.532559i −0.963896 0.266279i \(-0.914206\pi\)
0.963896 0.266279i \(-0.0857943\pi\)
\(140\) −68.9138 + 12.2834i −0.492242 + 0.0877388i
\(141\) −40.4225 −0.286685
\(142\) 54.8885i 0.386538i
\(143\) −119.183 −0.833448
\(144\) 12.0000 0.0833333
\(145\) −42.5426 + 18.1823i −0.293397 + 0.125395i
\(146\) 176.253i 1.20721i
\(147\) −76.2357 37.2977i −0.518610 0.253726i
\(148\) 126.870i 0.857230i
\(149\) −226.979 −1.52335 −0.761676 0.647958i \(-0.775623\pi\)
−0.761676 + 0.647958i \(0.775623\pi\)
\(150\) 44.2598 + 42.3211i 0.295065 + 0.282140i
\(151\) 294.426 1.94984 0.974920 0.222558i \(-0.0714406\pi\)
0.974920 + 0.222558i \(0.0714406\pi\)
\(152\) 95.5261 0.628461
\(153\) 17.4426 0.114004
\(154\) −18.2187 + 78.6950i −0.118303 + 0.511006i
\(155\) 37.8377 + 88.5321i 0.244114 + 0.571175i
\(156\) 50.5981 0.324346
\(157\) −65.8596 −0.419488 −0.209744 0.977756i \(-0.567263\pi\)
−0.209744 + 0.977756i \(0.567263\pi\)
\(158\) 79.4564i 0.502889i
\(159\) 123.581i 0.777241i
\(160\) −11.1158 26.0085i −0.0694734 0.162553i
\(161\) 58.8227 254.083i 0.365359 1.57815i
\(162\) 12.7279i 0.0785674i
\(163\) 28.2075i 0.173052i 0.996250 + 0.0865260i \(0.0275766\pi\)
−0.996250 + 0.0865260i \(0.972423\pi\)
\(164\) 16.5176i 0.100717i
\(165\) 64.9788 27.7713i 0.393811 0.168311i
\(166\) 127.842i 0.770133i
\(167\) 128.461 0.769227 0.384614 0.923078i \(-0.374335\pi\)
0.384614 + 0.923078i \(0.374335\pi\)
\(168\) 7.73458 33.4092i 0.0460392 0.198864i
\(169\) 44.3469 0.262408
\(170\) −16.1573 37.8046i −0.0950431 0.222380i
\(171\) 101.321i 0.592519i
\(172\) 84.1786i 0.489411i
\(173\) 112.446 0.649976 0.324988 0.945718i \(-0.394640\pi\)
0.324988 + 0.945718i \(0.394640\pi\)
\(174\) 22.6652i 0.130260i
\(175\) 146.354 95.9457i 0.836307 0.548261i
\(176\) −32.6386 −0.185446
\(177\) 74.3656i 0.420144i
\(178\) −22.9511 −0.128939
\(179\) −68.9019 −0.384927 −0.192464 0.981304i \(-0.561648\pi\)
−0.192464 + 0.981304i \(0.561648\pi\)
\(180\) −27.5861 + 11.7900i −0.153256 + 0.0655002i
\(181\) 166.537i 0.920094i 0.887895 + 0.460047i \(0.152167\pi\)
−0.887895 + 0.460047i \(0.847833\pi\)
\(182\) 32.6129 140.870i 0.179192 0.774012i
\(183\) 59.3858i 0.324513i
\(184\) 105.380 0.572719
\(185\) 124.650 + 291.655i 0.673785 + 1.57651i
\(186\) −47.1668 −0.253585
\(187\) −47.4419 −0.253700
\(188\) −46.6759 −0.248276
\(189\) −35.4358 8.20376i −0.187491 0.0434061i
\(190\) −219.600 + 93.8547i −1.15579 + 0.493972i
\(191\) −148.289 −0.776382 −0.388191 0.921579i \(-0.626900\pi\)
−0.388191 + 0.921579i \(0.626900\pi\)
\(192\) 13.8564 0.0721688
\(193\) 35.1886i 0.182324i −0.995836 0.0911622i \(-0.970942\pi\)
0.995836 0.0911622i \(-0.0290582\pi\)
\(194\) 117.041i 0.603304i
\(195\) −116.317 + 49.7127i −0.596498 + 0.254937i
\(196\) −88.0294 43.0677i −0.449130 0.219733i
\(197\) 193.634i 0.982915i 0.870902 + 0.491457i \(0.163536\pi\)
−0.870902 + 0.491457i \(0.836464\pi\)
\(198\) 34.6184i 0.174841i
\(199\) 181.838i 0.913759i −0.889529 0.456880i \(-0.848967\pi\)
0.889529 0.456880i \(-0.151033\pi\)
\(200\) 51.1068 + 48.8682i 0.255534 + 0.244341i
\(201\) 8.65832i 0.0430762i
\(202\) 123.327 0.610530
\(203\) −63.1023 14.6088i −0.310849 0.0719647i
\(204\) 20.1410 0.0987304
\(205\) −16.2286 37.9714i −0.0791638 0.185226i
\(206\) 265.260i 1.28767i
\(207\) 111.773i 0.539965i
\(208\) 58.4256 0.280892
\(209\) 275.580i 1.31857i
\(210\) 15.0441 + 84.4019i 0.0716384 + 0.401914i
\(211\) 175.914 0.833717 0.416859 0.908971i \(-0.363131\pi\)
0.416859 + 0.908971i \(0.363131\pi\)
\(212\) 142.699i 0.673110i
\(213\) 67.2244 0.315607
\(214\) 223.244 1.04320
\(215\) 82.7058 + 193.514i 0.384678 + 0.900064i
\(216\) 14.6969i 0.0680414i
\(217\) −30.4013 + 131.317i −0.140098 + 0.605149i
\(218\) 158.495i 0.727042i
\(219\) −215.864 −0.985683
\(220\) 75.0310 32.0675i 0.341050 0.145761i
\(221\) 84.9246 0.384274
\(222\) −155.384 −0.699926
\(223\) 20.5675 0.0922308 0.0461154 0.998936i \(-0.485316\pi\)
0.0461154 + 0.998936i \(0.485316\pi\)
\(224\) 8.93112 38.5776i 0.0398711 0.172222i
\(225\) 51.8325 54.2069i 0.230367 0.240920i
\(226\) 200.801 0.888498
\(227\) −414.087 −1.82417 −0.912085 0.410001i \(-0.865528\pi\)
−0.912085 + 0.410001i \(0.865528\pi\)
\(228\) 116.995i 0.513136i
\(229\) 195.520i 0.853799i −0.904299 0.426899i \(-0.859606\pi\)
0.904299 0.426899i \(-0.140394\pi\)
\(230\) −242.253 + 103.536i −1.05327 + 0.450158i
\(231\) 96.3813 + 22.3133i 0.417235 + 0.0965942i
\(232\) 26.1716i 0.112808i
\(233\) 81.3006i 0.348930i −0.984663 0.174465i \(-0.944180\pi\)
0.984663 0.174465i \(-0.0558195\pi\)
\(234\) 61.9697i 0.264828i
\(235\) 107.301 45.8592i 0.456599 0.195146i
\(236\) 85.8700i 0.363856i
\(237\) 97.3138 0.410607
\(238\) 12.9818 56.0746i 0.0545456 0.235608i
\(239\) −249.265 −1.04295 −0.521475 0.853267i \(-0.674618\pi\)
−0.521475 + 0.853267i \(0.674618\pi\)
\(240\) −31.8537 + 13.6140i −0.132724 + 0.0567248i
\(241\) 262.343i 1.08856i 0.838904 + 0.544280i \(0.183197\pi\)
−0.838904 + 0.544280i \(0.816803\pi\)
\(242\) 76.9618i 0.318024i
\(243\) −15.5885 −0.0641500
\(244\) 68.5728i 0.281036i
\(245\) 244.680 + 12.5169i 0.998694 + 0.0510892i
\(246\) 20.2298 0.0822351
\(247\) 493.310i 1.99721i
\(248\) −54.4636 −0.219611
\(249\) 156.574 0.628811
\(250\) −165.500 62.1278i −0.661999 0.248511i
\(251\) 141.917i 0.565406i 0.959208 + 0.282703i \(0.0912310\pi\)
−0.959208 + 0.282703i \(0.908769\pi\)
\(252\) −40.9178 9.47288i −0.162372 0.0375908i
\(253\) 304.008i 1.20161i
\(254\) 286.257 1.12699
\(255\) −46.3010 + 19.7886i −0.181573 + 0.0776023i
\(256\) 16.0000 0.0625000
\(257\) 170.843 0.664757 0.332379 0.943146i \(-0.392149\pi\)
0.332379 + 0.943146i \(0.392149\pi\)
\(258\) −103.097 −0.399602
\(259\) −100.152 + 432.604i −0.386688 + 1.67028i
\(260\) −134.311 + 57.4033i −0.516582 + 0.220782i
\(261\) −27.7591 −0.106357
\(262\) −199.772 −0.762488
\(263\) 383.417i 1.45786i 0.684588 + 0.728930i \(0.259982\pi\)
−0.684588 + 0.728930i \(0.740018\pi\)
\(264\) 39.9739i 0.151416i
\(265\) −140.203 328.044i −0.529066 1.23790i
\(266\) −325.726 75.4090i −1.22454 0.283492i
\(267\) 28.1093i 0.105278i
\(268\) 9.99777i 0.0373051i
\(269\) 154.512i 0.574393i 0.957872 + 0.287196i \(0.0927232\pi\)
−0.957872 + 0.287196i \(0.907277\pi\)
\(270\) 14.4398 + 33.7860i 0.0534807 + 0.125133i
\(271\) 320.328i 1.18202i 0.806664 + 0.591010i \(0.201271\pi\)
−0.806664 + 0.591010i \(0.798729\pi\)
\(272\) 23.2568 0.0855030
\(273\) −172.530 39.9425i −0.631978 0.146309i
\(274\) −71.6200 −0.261387
\(275\) −140.978 + 147.436i −0.512648 + 0.536132i
\(276\) 129.064i 0.467623i
\(277\) 222.854i 0.804526i −0.915524 0.402263i \(-0.868224\pi\)
0.915524 0.402263i \(-0.131776\pi\)
\(278\) −104.688 −0.376576
\(279\) 57.7673i 0.207051i
\(280\) 17.3714 + 97.4589i 0.0620407 + 0.348067i
\(281\) 218.973 0.779263 0.389631 0.920971i \(-0.372602\pi\)
0.389631 + 0.920971i \(0.372602\pi\)
\(282\) 57.1661i 0.202717i
\(283\) 36.3957 0.128607 0.0643034 0.997930i \(-0.479517\pi\)
0.0643034 + 0.997930i \(0.479517\pi\)
\(284\) 77.6240 0.273324
\(285\) 114.948 + 268.954i 0.403326 + 0.943697i
\(286\) 168.550i 0.589337i
\(287\) 13.0391 56.3219i 0.0454324 0.196244i
\(288\) 16.9706i 0.0589256i
\(289\) −255.195 −0.883028
\(290\) 25.7136 + 60.1644i 0.0886677 + 0.207463i
\(291\) −143.345 −0.492596
\(292\) −249.259 −0.853626
\(293\) −168.440 −0.574882 −0.287441 0.957798i \(-0.592805\pi\)
−0.287441 + 0.957798i \(0.592805\pi\)
\(294\) −52.7470 + 107.814i −0.179411 + 0.366713i
\(295\) 84.3675 + 197.402i 0.285991 + 0.669158i
\(296\) −179.421 −0.606153
\(297\) 42.3988 0.142757
\(298\) 320.997i 1.07717i
\(299\) 544.199i 1.82006i
\(300\) 59.8510 62.5928i 0.199503 0.208643i
\(301\) −66.4512 + 287.034i −0.220768 + 0.953600i
\(302\) 416.381i 1.37874i
\(303\) 151.044i 0.498496i
\(304\) 135.094i 0.444389i
\(305\) 67.3730 + 157.638i 0.220895 + 0.516847i
\(306\) 24.6676i 0.0806130i
\(307\) 223.400 0.727688 0.363844 0.931460i \(-0.381464\pi\)
0.363844 + 0.931460i \(0.381464\pi\)
\(308\) 111.292 + 25.7651i 0.361336 + 0.0836530i
\(309\) 324.876 1.05138
\(310\) 125.203 53.5106i 0.403882 0.172615i
\(311\) 46.0396i 0.148037i −0.997257 0.0740186i \(-0.976418\pi\)
0.997257 0.0740186i \(-0.0235824\pi\)
\(312\) 71.5565i 0.229348i
\(313\) −80.0375 −0.255711 −0.127855 0.991793i \(-0.540809\pi\)
−0.127855 + 0.991793i \(0.540809\pi\)
\(314\) 93.1395i 0.296623i
\(315\) 103.371 18.4251i 0.328161 0.0584925i
\(316\) 112.368 0.355596
\(317\) 185.237i 0.584343i −0.956366 0.292171i \(-0.905622\pi\)
0.956366 0.292171i \(-0.0943777\pi\)
\(318\) 174.770 0.549592
\(319\) 75.5016 0.236682
\(320\) −36.7815 + 15.7200i −0.114942 + 0.0491251i
\(321\) 273.418i 0.851768i
\(322\) −359.327 83.1879i −1.11592 0.258348i
\(323\) 196.367i 0.607946i
\(324\) −18.0000 −0.0555556
\(325\) 252.362 263.923i 0.776499 0.812070i
\(326\) 39.8914 0.122366
\(327\) 194.116 0.593628
\(328\) 23.3594 0.0712177
\(329\) 159.156 + 36.8463i 0.483757 + 0.111995i
\(330\) −39.2745 91.8939i −0.119014 0.278466i
\(331\) 61.4686 0.185706 0.0928529 0.995680i \(-0.470401\pi\)
0.0928529 + 0.995680i \(0.470401\pi\)
\(332\) 180.796 0.544566
\(333\) 190.305i 0.571487i
\(334\) 181.671i 0.543926i
\(335\) 9.82284 + 22.9833i 0.0293219 + 0.0686069i
\(336\) −47.2478 10.9383i −0.140618 0.0325546i
\(337\) 656.501i 1.94807i −0.226387 0.974037i \(-0.572691\pi\)
0.226387 0.974037i \(-0.427309\pi\)
\(338\) 62.7160i 0.185550i
\(339\) 245.929i 0.725456i
\(340\) −53.4638 + 22.8499i −0.157247 + 0.0672056i
\(341\) 157.120i 0.460764i
\(342\) −143.289 −0.418974
\(343\) 266.166 + 216.344i 0.775994 + 0.630740i
\(344\) −119.047 −0.346066
\(345\) 126.806 + 296.698i 0.367553 + 0.859994i
\(346\) 159.022i 0.459603i
\(347\) 321.323i 0.926002i −0.886358 0.463001i \(-0.846773\pi\)
0.886358 0.463001i \(-0.153227\pi\)
\(348\) −32.0535 −0.0921077
\(349\) 185.135i 0.530474i 0.964183 + 0.265237i \(0.0854501\pi\)
−0.964183 + 0.265237i \(0.914550\pi\)
\(350\) −135.688 206.975i −0.387679 0.591358i
\(351\) −75.8971 −0.216231
\(352\) 46.1579i 0.131130i
\(353\) 597.338 1.69218 0.846088 0.533043i \(-0.178952\pi\)
0.846088 + 0.533043i \(0.178952\pi\)
\(354\) −105.169 −0.297087
\(355\) −178.446 + 76.2658i −0.502664 + 0.214833i
\(356\) 32.4578i 0.0911736i
\(357\) −68.6771 15.8995i −0.192373 0.0445363i
\(358\) 97.4421i 0.272185i
\(359\) 239.446 0.666982 0.333491 0.942753i \(-0.391773\pi\)
0.333491 + 0.942753i \(0.391773\pi\)
\(360\) 16.6736 + 39.0127i 0.0463156 + 0.108369i
\(361\) −779.655 −2.15971
\(362\) 235.519 0.650604
\(363\) 94.2585 0.259665
\(364\) −199.220 46.1216i −0.547309 0.126708i
\(365\) 573.007 244.898i 1.56988 0.670952i
\(366\) −83.9842 −0.229465
\(367\) 398.743 1.08649 0.543246 0.839573i \(-0.317195\pi\)
0.543246 + 0.839573i \(0.317195\pi\)
\(368\) 149.030i 0.404973i
\(369\) 24.7764i 0.0671447i
\(370\) 412.462 176.282i 1.11476 0.476438i
\(371\) 112.648 486.578i 0.303633 1.31153i
\(372\) 66.7040i 0.179312i
\(373\) 34.7064i 0.0930466i −0.998917 0.0465233i \(-0.985186\pi\)
0.998917 0.0465233i \(-0.0148142\pi\)
\(374\) 67.0929i 0.179393i
\(375\) −76.0907 + 202.695i −0.202908 + 0.540520i
\(376\) 66.0097i 0.175558i
\(377\) −135.154 −0.358498
\(378\) −11.6019 + 50.1138i −0.0306928 + 0.132576i
\(379\) −109.217 −0.288172 −0.144086 0.989565i \(-0.546024\pi\)
−0.144086 + 0.989565i \(0.546024\pi\)
\(380\) 132.731 + 310.561i 0.349291 + 0.817265i
\(381\) 350.591i 0.920187i
\(382\) 209.712i 0.548985i
\(383\) 336.420 0.878381 0.439191 0.898394i \(-0.355265\pi\)
0.439191 + 0.898394i \(0.355265\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −281.156 + 50.1142i −0.730276 + 0.130167i
\(386\) −49.7642 −0.128923
\(387\) 126.268i 0.326274i
\(388\) −165.521 −0.426601
\(389\) −311.173 −0.799930 −0.399965 0.916530i \(-0.630978\pi\)
−0.399965 + 0.916530i \(0.630978\pi\)
\(390\) 70.3044 + 164.497i 0.180268 + 0.421788i
\(391\) 216.623i 0.554023i
\(392\) −60.9069 + 124.492i −0.155375 + 0.317583i
\(393\) 244.669i 0.622568i
\(394\) 273.840 0.695026
\(395\) −258.317 + 110.402i −0.653968 + 0.279499i
\(396\) 48.9579 0.123631
\(397\) −41.2679 −0.103949 −0.0519747 0.998648i \(-0.516552\pi\)
−0.0519747 + 0.998648i \(0.516552\pi\)
\(398\) −257.158 −0.646125
\(399\) −92.3568 + 398.932i −0.231471 + 0.999829i
\(400\) 69.1100 72.2759i 0.172775 0.180690i
\(401\) −495.642 −1.23601 −0.618007 0.786173i \(-0.712060\pi\)
−0.618007 + 0.786173i \(0.712060\pi\)
\(402\) −12.2447 −0.0304595
\(403\) 281.258i 0.697910i
\(404\) 174.411i 0.431710i
\(405\) 41.3792 17.6851i 0.102171 0.0436668i
\(406\) −20.6600 + 89.2402i −0.0508867 + 0.219803i
\(407\) 517.608i 1.27176i
\(408\) 28.4837i 0.0698129i
\(409\) 359.920i 0.880001i −0.897998 0.440000i \(-0.854978\pi\)
0.897998 0.440000i \(-0.145022\pi\)
\(410\) −53.6997 + 22.9507i −0.130975 + 0.0559773i
\(411\) 87.7163i 0.213422i
\(412\) 375.135 0.910521
\(413\) −67.7863 + 292.801i −0.164132 + 0.708960i
\(414\) −158.070 −0.381813
\(415\) −415.622 + 177.633i −1.00150 + 0.428030i
\(416\) 82.6263i 0.198621i
\(417\) 128.216i 0.307473i
\(418\) 389.730 0.932367
\(419\) 482.910i 1.15253i 0.817263 + 0.576265i \(0.195490\pi\)
−0.817263 + 0.576265i \(0.804510\pi\)
\(420\) 119.362 21.2755i 0.284196 0.0506560i
\(421\) −523.520 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(422\) 248.780i 0.589527i
\(423\) 70.0139 0.165517
\(424\) 201.807 0.475961
\(425\) 100.455 105.057i 0.236365 0.247192i
\(426\) 95.0696i 0.223168i
\(427\) −54.1319 + 233.821i −0.126773 + 0.547589i
\(428\) 315.715i 0.737653i
\(429\) 206.431 0.481191
\(430\) 273.670 116.964i 0.636441 0.272008i
\(431\) 517.027 1.19960 0.599799 0.800150i \(-0.295247\pi\)
0.599799 + 0.800150i \(0.295247\pi\)
\(432\) −20.7846 −0.0481125
\(433\) −567.712 −1.31111 −0.655557 0.755146i \(-0.727566\pi\)
−0.655557 + 0.755146i \(0.727566\pi\)
\(434\) 185.711 + 42.9939i 0.427905 + 0.0990644i
\(435\) 73.6860 31.4926i 0.169393 0.0723969i
\(436\) 224.146 0.514097
\(437\) −1258.32 −2.87945
\(438\) 305.279i 0.696983i
\(439\) 622.875i 1.41885i −0.704781 0.709425i \(-0.748955\pi\)
0.704781 0.709425i \(-0.251045\pi\)
\(440\) −45.3503 106.110i −0.103069 0.241159i
\(441\) 132.044 + 64.6016i 0.299420 + 0.146489i
\(442\) 120.102i 0.271723i
\(443\) 476.699i 1.07607i −0.842923 0.538035i \(-0.819167\pi\)
0.842923 0.538035i \(-0.180833\pi\)
\(444\) 219.745i 0.494922i
\(445\) −31.8899 74.6154i −0.0716626 0.167675i
\(446\) 29.0868i 0.0652170i
\(447\) 393.140 0.879507
\(448\) −54.5570 12.6305i −0.121779 0.0281931i
\(449\) 861.931 1.91967 0.959834 0.280570i \(-0.0905233\pi\)
0.959834 + 0.280570i \(0.0905233\pi\)
\(450\) −76.6602 73.3022i −0.170356 0.162894i
\(451\) 67.3889i 0.149421i
\(452\) 283.975i 0.628263i
\(453\) −509.960 −1.12574
\(454\) 585.607i 1.28988i
\(455\) 503.292 89.7083i 1.10614 0.197161i
\(456\) −165.456 −0.362842
\(457\) 27.5401i 0.0602629i 0.999546 + 0.0301314i \(0.00959258\pi\)
−0.999546 + 0.0301314i \(0.990407\pi\)
\(458\) −276.507 −0.603727
\(459\) −30.2115 −0.0658203
\(460\) 146.423 + 342.597i 0.318310 + 0.744777i
\(461\) 378.183i 0.820353i −0.912006 0.410176i \(-0.865467\pi\)
0.912006 0.410176i \(-0.134533\pi\)
\(462\) 31.5557 136.304i 0.0683024 0.295030i
\(463\) 724.994i 1.56586i −0.622108 0.782931i \(-0.713724\pi\)
0.622108 0.782931i \(-0.286276\pi\)
\(464\) −37.0122 −0.0797676
\(465\) −65.5369 153.342i −0.140939 0.329768i
\(466\) −114.976 −0.246731
\(467\) −371.451 −0.795398 −0.397699 0.917516i \(-0.630191\pi\)
−0.397699 + 0.917516i \(0.630191\pi\)
\(468\) −87.6384 −0.187262
\(469\) −7.89231 + 34.0905i −0.0168280 + 0.0726877i
\(470\) −64.8547 151.746i −0.137989 0.322864i
\(471\) 114.072 0.242191
\(472\) −121.438 −0.257285
\(473\) 343.434i 0.726076i
\(474\) 137.623i 0.290343i
\(475\) −610.254 583.523i −1.28475 1.22847i
\(476\) −79.3015 18.3591i −0.166600 0.0385695i
\(477\) 214.049i 0.448740i
\(478\) 352.514i 0.737477i
\(479\) 860.650i 1.79677i 0.439214 + 0.898383i \(0.355257\pi\)
−0.439214 + 0.898383i \(0.644743\pi\)
\(480\) 19.2530 + 45.0480i 0.0401105 + 0.0938500i
\(481\) 926.558i 1.92632i
\(482\) 371.009 0.769728
\(483\) −101.884 + 440.084i −0.210940 + 0.911147i
\(484\) 108.840 0.224877
\(485\) 380.507 162.625i 0.784551 0.335309i
\(486\) 22.0454i 0.0453609i
\(487\) 887.173i 1.82171i 0.412726 + 0.910855i \(0.364577\pi\)
−0.412726 + 0.910855i \(0.635423\pi\)
\(488\) −96.9766 −0.198723
\(489\) 48.8568i 0.0999116i
\(490\) 17.7015 346.030i 0.0361255 0.706183i
\(491\) −50.1823 −0.102204 −0.0511021 0.998693i \(-0.516273\pi\)
−0.0511021 + 0.998693i \(0.516273\pi\)
\(492\) 28.6093i 0.0581490i
\(493\) −53.7991 −0.109126
\(494\) −697.646 −1.41224
\(495\) −112.547 + 48.1012i −0.227367 + 0.0971742i
\(496\) 77.0231i 0.155289i
\(497\) −264.683 61.2769i −0.532562 0.123294i
\(498\) 221.429i 0.444636i
\(499\) 160.443 0.321529 0.160765 0.986993i \(-0.448604\pi\)
0.160765 + 0.986993i \(0.448604\pi\)
\(500\) −87.8620 + 234.052i −0.175724 + 0.468104i
\(501\) −222.501 −0.444113
\(502\) 200.701 0.399802
\(503\) 742.042 1.47523 0.737616 0.675220i \(-0.235951\pi\)
0.737616 + 0.675220i \(0.235951\pi\)
\(504\) −13.3967 + 57.8665i −0.0265807 + 0.114814i
\(505\) 171.359 + 400.944i 0.339325 + 0.793948i
\(506\) 429.933 0.849670
\(507\) −76.8111 −0.151501
\(508\) 404.828i 0.796905i
\(509\) 978.447i 1.92229i −0.276038 0.961147i \(-0.589021\pi\)
0.276038 0.961147i \(-0.410979\pi\)
\(510\) 27.9853 + 65.4796i 0.0548731 + 0.128391i
\(511\) 849.927 + 196.767i 1.66326 + 0.385062i
\(512\) 22.6274i 0.0441942i
\(513\) 175.493i 0.342091i
\(514\) 241.608i 0.470054i
\(515\) −862.377 + 368.571i −1.67452 + 0.715672i
\(516\) 145.802i 0.282561i
\(517\) −190.429 −0.368335
\(518\) 611.794 + 141.637i 1.18107 + 0.273430i
\(519\) −194.762 −0.375264
\(520\) 81.1805 + 189.945i 0.156116 + 0.365279i
\(521\) 575.650i 1.10489i 0.833548 + 0.552447i \(0.186306\pi\)
−0.833548 + 0.552447i \(0.813694\pi\)
\(522\) 39.2573i 0.0752056i
\(523\) −339.090 −0.648355 −0.324178 0.945996i \(-0.605088\pi\)
−0.324178 + 0.945996i \(0.605088\pi\)
\(524\) 282.520i 0.539160i
\(525\) −253.492 + 166.183i −0.482842 + 0.316539i
\(526\) 542.234 1.03086
\(527\) 111.957i 0.212442i
\(528\) 56.5317 0.107068
\(529\) −859.125 −1.62406
\(530\) −463.924 + 198.276i −0.875328 + 0.374106i
\(531\) 128.805i 0.242571i
\(532\) −106.644 + 460.647i −0.200459 + 0.865877i
\(533\) 120.631i 0.226325i
\(534\) 39.7525 0.0744429
\(535\) 310.191 + 725.781i 0.579797 + 1.35660i
\(536\) −14.1390 −0.0263787
\(537\) 119.342 0.222238
\(538\) 218.512 0.406157
\(539\) −359.144 175.709i −0.666316 0.325990i
\(540\) 47.7806 20.4209i 0.0884826 0.0378166i
\(541\) 35.8638 0.0662916 0.0331458 0.999451i \(-0.489447\pi\)
0.0331458 + 0.999451i \(0.489447\pi\)
\(542\) 453.012 0.835815
\(543\) 288.450i 0.531216i
\(544\) 32.8901i 0.0604598i
\(545\) −515.277 + 220.224i −0.945463 + 0.404081i
\(546\) −56.4872 + 243.994i −0.103456 + 0.446876i
\(547\) 700.845i 1.28125i −0.767853 0.640626i \(-0.778675\pi\)
0.767853 0.640626i \(-0.221325\pi\)
\(548\) 101.286i 0.184829i
\(549\) 102.859i 0.187357i
\(550\) 208.507 + 199.373i 0.379103 + 0.362497i
\(551\) 312.508i 0.567166i
\(552\) −182.524 −0.330659
\(553\) −383.155 88.7044i −0.692867 0.160406i
\(554\) −315.163 −0.568886
\(555\) −215.901 505.161i −0.389010 0.910200i
\(556\) 148.051i 0.266279i
\(557\) 639.349i 1.14784i 0.818910 + 0.573922i \(0.194579\pi\)
−0.818910 + 0.573922i \(0.805421\pi\)
\(558\) 81.6954 0.146407
\(559\) 614.773i 1.09977i
\(560\) 137.828 24.5669i 0.246121 0.0438694i
\(561\) 82.1717 0.146474
\(562\) 309.674i 0.551022i
\(563\) −227.519 −0.404120 −0.202060 0.979373i \(-0.564764\pi\)
−0.202060 + 0.979373i \(0.564764\pi\)
\(564\) 80.8450 0.143342
\(565\) 279.006 + 652.814i 0.493816 + 1.15542i
\(566\) 51.4713i 0.0909387i
\(567\) 61.3767 + 14.2093i 0.108248 + 0.0250605i
\(568\) 109.777i 0.193269i
\(569\) 613.901 1.07891 0.539456 0.842014i \(-0.318630\pi\)
0.539456 + 0.842014i \(0.318630\pi\)
\(570\) 380.358 162.561i 0.667294 0.285195i
\(571\) 366.674 0.642161 0.321081 0.947052i \(-0.395954\pi\)
0.321081 + 0.947052i \(0.395954\pi\)
\(572\) 238.366 0.416724
\(573\) 256.844 0.448244
\(574\) −79.6513 18.4401i −0.138765 0.0321256i
\(575\) −673.206 643.718i −1.17079 1.11951i
\(576\) −24.0000 −0.0416667
\(577\) −62.1951 −0.107790 −0.0538952 0.998547i \(-0.517164\pi\)
−0.0538952 + 0.998547i \(0.517164\pi\)
\(578\) 360.900i 0.624395i
\(579\) 60.9485i 0.105265i
\(580\) 85.0853 36.3646i 0.146699 0.0626975i
\(581\) −616.481 142.722i −1.06107 0.245648i
\(582\) 202.721i 0.348318i
\(583\) 582.188i 0.998607i
\(584\) 352.505i 0.603605i
\(585\) 201.467 86.1050i 0.344388 0.147188i
\(586\) 238.211i 0.406503i
\(587\) −176.872 −0.301315 −0.150658 0.988586i \(-0.548139\pi\)
−0.150658 + 0.988586i \(0.548139\pi\)
\(588\) 152.471 + 74.5955i 0.259305 + 0.126863i
\(589\) 650.337 1.10414
\(590\) 279.168 119.314i 0.473166 0.202226i
\(591\) 335.384i 0.567486i
\(592\) 253.740i 0.428615i
\(593\) 154.878 0.261176 0.130588 0.991437i \(-0.458313\pi\)
0.130588 + 0.991437i \(0.458313\pi\)
\(594\) 59.9609i 0.100944i
\(595\) 200.340 35.7092i 0.336705 0.0600154i
\(596\) 453.959 0.761676
\(597\) 314.953i 0.527559i
\(598\) −769.613 −1.28698
\(599\) 900.825 1.50388 0.751940 0.659231i \(-0.229118\pi\)
0.751940 + 0.659231i \(0.229118\pi\)
\(600\) −88.5195 84.6421i −0.147533 0.141070i
\(601\) 682.387i 1.13542i −0.823229 0.567710i \(-0.807830\pi\)
0.823229 0.567710i \(-0.192170\pi\)
\(602\) 405.927 + 93.9762i 0.674297 + 0.156107i
\(603\) 14.9967i 0.0248701i
\(604\) −588.851 −0.974920
\(605\) −250.207 + 106.936i −0.413566 + 0.176754i
\(606\) −213.609 −0.352490
\(607\) 367.814 0.605954 0.302977 0.952998i \(-0.402019\pi\)
0.302977 + 0.952998i \(0.402019\pi\)
\(608\) −191.052 −0.314231
\(609\) 109.296 + 25.3032i 0.179469 + 0.0415488i
\(610\) 222.934 95.2798i 0.365466 0.156196i
\(611\) 340.883 0.557911
\(612\) −34.8852 −0.0570020
\(613\) 117.271i 0.191306i 0.995415 + 0.0956532i \(0.0304940\pi\)
−0.995415 + 0.0956532i \(0.969506\pi\)
\(614\) 315.936i 0.514553i
\(615\) 28.1087 + 65.7684i 0.0457053 + 0.106940i
\(616\) 36.4374 157.390i 0.0591516 0.255503i
\(617\) 1070.18i 1.73449i 0.497881 + 0.867245i \(0.334112\pi\)
−0.497881 + 0.867245i \(0.665888\pi\)
\(618\) 459.444i 0.743438i
\(619\) 532.192i 0.859761i −0.902886 0.429880i \(-0.858556\pi\)
0.902886 0.429880i \(-0.141444\pi\)
\(620\) −75.6754 177.064i −0.122057 0.285587i
\(621\) 193.596i 0.311749i
\(622\) −65.1098 −0.104678
\(623\) 25.6224 110.675i 0.0411275 0.177649i
\(624\) −101.196 −0.162173
\(625\) −27.9756 624.374i −0.0447610 0.998998i
\(626\) 113.190i 0.180815i
\(627\) 477.319i 0.761275i
\(628\) 131.719 0.209744
\(629\) 368.825i 0.586366i
\(630\) −26.0571 146.188i −0.0413604 0.232045i
\(631\) 472.933 0.749498 0.374749 0.927126i \(-0.377729\pi\)
0.374749 + 0.927126i \(0.377729\pi\)
\(632\) 158.913i 0.251444i
\(633\) −304.693 −0.481347
\(634\) −261.964 −0.413193
\(635\) 397.745 + 930.636i 0.626369 + 1.46557i
\(636\) 247.163i 0.388620i
\(637\) 642.896 + 314.532i 1.00926 + 0.493771i
\(638\) 106.775i 0.167359i
\(639\) −116.436 −0.182216
\(640\) 22.2315 + 52.0169i 0.0347367 + 0.0812764i
\(641\) −486.990 −0.759734 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(642\) −386.671 −0.602291
\(643\) −111.425 −0.173289 −0.0866447 0.996239i \(-0.527614\pi\)
−0.0866447 + 0.996239i \(0.527614\pi\)
\(644\) −117.645 + 508.165i −0.182679 + 0.789077i
\(645\) −143.251 335.176i −0.222094 0.519652i
\(646\) −277.704 −0.429883
\(647\) 737.696 1.14018 0.570090 0.821583i \(-0.306908\pi\)
0.570090 + 0.821583i \(0.306908\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 350.334i 0.539806i
\(650\) −373.243 356.894i −0.574220 0.549068i
\(651\) 52.6566 227.448i 0.0808857 0.349383i
\(652\) 56.4149i 0.0865260i
\(653\) 193.734i 0.296682i 0.988936 + 0.148341i \(0.0473934\pi\)
−0.988936 + 0.148341i \(0.952607\pi\)
\(654\) 274.522i 0.419758i
\(655\) −277.577 649.469i −0.423781 0.991556i
\(656\) 33.0352i 0.0503585i
\(657\) 373.888 0.569084
\(658\) 52.1085 225.081i 0.0791923 0.342068i
\(659\) −823.339 −1.24938 −0.624688 0.780874i \(-0.714774\pi\)
−0.624688 + 0.780874i \(0.714774\pi\)
\(660\) −129.958 + 55.5425i −0.196905 + 0.0841554i
\(661\) 657.833i 0.995208i −0.867404 0.497604i \(-0.834213\pi\)
0.867404 0.497604i \(-0.165787\pi\)
\(662\) 86.9298i 0.131314i
\(663\) −147.094 −0.221861
\(664\) 255.684i 0.385066i
\(665\) −207.428 1163.73i −0.311921 1.74998i
\(666\) 269.132 0.404102
\(667\) 344.746i 0.516860i
\(668\) −256.922 −0.384614
\(669\) −35.6239 −0.0532495
\(670\) 32.5033 13.8916i 0.0485124 0.0207337i
\(671\) 279.765i 0.416937i
\(672\) −15.4692 + 66.8184i −0.0230196 + 0.0994322i
\(673\) 727.300i 1.08068i −0.841446 0.540342i \(-0.818295\pi\)
0.841446 0.540342i \(-0.181705\pi\)
\(674\) −928.433 −1.37750
\(675\) −89.7766 + 93.8891i −0.133002 + 0.139095i
\(676\) −88.6938 −0.131204
\(677\) −385.964 −0.570110 −0.285055 0.958511i \(-0.592012\pi\)
−0.285055 + 0.958511i \(0.592012\pi\)
\(678\) −347.797 −0.512975
\(679\) 564.396 + 130.663i 0.831217 + 0.192435i
\(680\) 32.3146 + 75.6093i 0.0475215 + 0.111190i
\(681\) 717.219 1.05319
\(682\) −222.202 −0.325809
\(683\) 236.488i 0.346249i 0.984900 + 0.173124i \(0.0553863\pi\)
−0.984900 + 0.173124i \(0.944614\pi\)
\(684\) 202.641i 0.296259i
\(685\) −99.5138 232.841i −0.145276 0.339914i
\(686\) 305.957 376.415i 0.446001 0.548711i
\(687\) 338.650i 0.492941i
\(688\) 168.357i 0.244705i
\(689\) 1042.16i 1.51257i
\(690\) 419.594 179.330i 0.608108 0.259899i
\(691\) 337.426i 0.488316i −0.969735 0.244158i \(-0.921488\pi\)
0.969735 0.244158i \(-0.0785116\pi\)
\(692\) −224.892 −0.324988
\(693\) −166.937 38.6477i −0.240891 0.0557687i
\(694\) −454.419 −0.654782
\(695\) −145.461 340.347i −0.209296 0.489708i
\(696\) 45.3305i 0.0651300i
\(697\) 48.0184i 0.0688929i
\(698\) 261.821 0.375101
\(699\) 140.817i 0.201455i
\(700\) −292.707 + 191.891i −0.418154 + 0.274131i
\(701\) 89.2192 0.127274 0.0636371 0.997973i \(-0.479730\pi\)
0.0636371 + 0.997973i \(0.479730\pi\)
\(702\) 107.335i 0.152898i
\(703\) 2142.43 3.04755
\(704\) 65.2772 0.0927232
\(705\) −185.850 + 79.4305i −0.263617 + 0.112667i
\(706\) 844.764i 1.19655i
\(707\) −137.681 + 594.709i −0.194740 + 0.841172i
\(708\) 148.731i 0.210072i
\(709\) 569.646 0.803450 0.401725 0.915760i \(-0.368411\pi\)
0.401725 + 0.915760i \(0.368411\pi\)
\(710\) 107.856 + 252.360i 0.151910 + 0.355437i
\(711\) −168.552 −0.237064
\(712\) 45.9023 0.0644695
\(713\) 717.423 1.00620
\(714\) −22.4852 + 97.1241i −0.0314919 + 0.136028i
\(715\) −547.967 + 234.195i −0.766387 + 0.327546i
\(716\) 137.804 0.192464
\(717\) 431.740 0.602147
\(718\) 338.628i 0.471627i
\(719\) 1261.33i 1.75428i −0.480233 0.877141i \(-0.659448\pi\)
0.480233 0.877141i \(-0.340552\pi\)
\(720\) 55.1723 23.5801i 0.0766282 0.0327501i
\(721\) −1279.14 296.134i −1.77412 0.410727i
\(722\) 1102.60i 1.52714i
\(723\) 454.391i 0.628481i
\(724\) 333.074i 0.460047i
\(725\) −159.870 + 167.193i −0.220510 + 0.230611i
\(726\) 133.302i 0.183611i
\(727\) −307.746 −0.423310 −0.211655 0.977344i \(-0.567885\pi\)
−0.211655 + 0.977344i \(0.567885\pi\)
\(728\) −65.2258 + 281.740i −0.0895958 + 0.387006i
\(729\) 27.0000 0.0370370
\(730\) −346.337 810.355i −0.474435 1.11008i
\(731\) 244.716i 0.334769i
\(732\) 118.772i 0.162256i
\(733\) −633.490 −0.864243 −0.432121 0.901815i \(-0.642235\pi\)
−0.432121 + 0.901815i \(0.642235\pi\)
\(734\) 563.908i 0.768266i
\(735\) −423.798 21.6798i −0.576596 0.0294964i
\(736\) −210.761 −0.286359
\(737\) 40.7891i 0.0553448i
\(738\) −35.0391 −0.0474785
\(739\) 749.557 1.01428 0.507142 0.861862i \(-0.330702\pi\)
0.507142 + 0.861862i \(0.330702\pi\)
\(740\) −249.300 583.309i −0.336893 0.788256i
\(741\) 854.439i 1.15309i
\(742\) −688.126 159.308i −0.927393 0.214701i
\(743\) 145.699i 0.196095i −0.995182 0.0980476i \(-0.968740\pi\)
0.995182 0.0980476i \(-0.0312597\pi\)
\(744\) 94.3337 0.126793
\(745\) −1043.58 + 446.016i −1.40078 + 0.598679i
\(746\) −49.0822 −0.0657939
\(747\) −271.194 −0.363044
\(748\) 94.8837 0.126850
\(749\) −249.228 + 1076.53i −0.332748 + 1.43729i
\(750\) 286.654 + 107.608i 0.382205 + 0.143478i
\(751\) 156.811 0.208803 0.104402 0.994535i \(-0.466707\pi\)
0.104402 + 0.994535i \(0.466707\pi\)
\(752\) 93.3518 0.124138
\(753\) 245.807i 0.326437i
\(754\) 191.136i 0.253496i
\(755\) 1353.68 578.548i 1.79295 0.766289i
\(756\) 70.8717 + 16.4075i 0.0937456 + 0.0217031i
\(757\) 296.377i 0.391515i 0.980652 + 0.195758i \(0.0627166\pi\)
−0.980652 + 0.195758i \(0.937283\pi\)
\(758\) 154.457i 0.203769i
\(759\) 526.558i 0.693752i
\(760\) 439.199 187.709i 0.577894 0.246986i
\(761\) 312.747i 0.410968i 0.978660 + 0.205484i \(0.0658769\pi\)
−0.978660 + 0.205484i \(0.934123\pi\)
\(762\) −495.811 −0.650670
\(763\) −764.297 176.942i −1.00170 0.231904i
\(764\) 296.578 0.388191
\(765\) 80.1958 34.2748i 0.104831 0.0448037i
\(766\) 475.770i 0.621109i
\(767\) 627.125i 0.817634i
\(768\) −27.7128 −0.0360844
\(769\) 91.1460i 0.118525i 0.998242 + 0.0592627i \(0.0188750\pi\)
−0.998242 + 0.0592627i \(0.981125\pi\)
\(770\) 70.8722 + 397.615i 0.0920418 + 0.516383i
\(771\) −295.908 −0.383798
\(772\) 70.3772i 0.0911622i
\(773\) 417.539 0.540154 0.270077 0.962839i \(-0.412951\pi\)
0.270077 + 0.962839i \(0.412951\pi\)
\(774\) 178.570 0.230710
\(775\) 347.932 + 332.692i 0.448945 + 0.429280i
\(776\) 234.082i 0.301652i
\(777\) 173.469 749.291i 0.223254 0.964339i
\(778\) 440.065i 0.565636i
\(779\) −278.929 −0.358061
\(780\) 232.634 99.4255i 0.298249 0.127469i
\(781\) 316.692 0.405496