Properties

Label 300.5.c.c.151.10
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.10
Root \(3.97720 - 0.426493i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.61924 + 3.65760i) q^{2} -5.19615i q^{3} +(-10.7561 + 11.8451i) q^{4} +(19.0055 - 8.41384i) q^{6} -95.1090i q^{7} +(-60.7414 - 20.1614i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(1.61924 + 3.65760i) q^{2} -5.19615i q^{3} +(-10.7561 + 11.8451i) q^{4} +(19.0055 - 8.41384i) q^{6} -95.1090i q^{7} +(-60.7414 - 20.1614i) q^{8} -27.0000 q^{9} +115.814i q^{11} +(61.5490 + 55.8903i) q^{12} -171.055 q^{13} +(347.871 - 154.005i) q^{14} +(-24.6130 - 254.814i) q^{16} +228.789 q^{17} +(-43.7196 - 98.7552i) q^{18} +659.627i q^{19} -494.201 q^{21} +(-423.602 + 187.531i) q^{22} +968.886i q^{23} +(-104.762 + 315.622i) q^{24} +(-276.980 - 625.651i) q^{26} +140.296i q^{27} +(1126.58 + 1023.00i) q^{28} +588.178 q^{29} +515.636i q^{31} +(892.154 - 502.631i) q^{32} +601.788 q^{33} +(370.465 + 836.819i) q^{34} +(290.414 - 319.818i) q^{36} +135.534 q^{37} +(-2412.65 + 1068.10i) q^{38} +888.827i q^{39} -559.656 q^{41} +(-800.232 - 1807.59i) q^{42} -754.185i q^{43} +(-1371.83 - 1245.71i) q^{44} +(-3543.80 + 1568.86i) q^{46} +2164.84i q^{47} +(-1324.05 + 127.893i) q^{48} -6644.72 q^{49} -1188.82i q^{51} +(1839.88 - 2026.16i) q^{52} +1178.44 q^{53} +(-513.147 + 227.174i) q^{54} +(-1917.53 + 5777.06i) q^{56} +3427.52 q^{57} +(952.404 + 2151.32i) q^{58} -183.192i q^{59} -438.111 q^{61} +(-1885.99 + 834.942i) q^{62} +2567.94i q^{63} +(3283.04 + 2449.26i) q^{64} +(974.441 + 2201.10i) q^{66} -709.589i q^{67} +(-2460.87 + 2710.03i) q^{68} +5034.48 q^{69} +8724.78i q^{71} +(1640.02 + 544.357i) q^{72} -5208.61 q^{73} +(219.462 + 495.728i) q^{74} +(-7813.35 - 7095.01i) q^{76} +11015.0 q^{77} +(-3250.98 + 1439.23i) q^{78} -957.643i q^{79} +729.000 q^{81} +(-906.220 - 2047.00i) q^{82} -2603.89i q^{83} +(5315.67 - 5853.86i) q^{84} +(2758.51 - 1221.21i) q^{86} -3056.26i q^{87} +(2334.97 - 7034.71i) q^{88} -10133.8 q^{89} +16268.9i q^{91} +(-11476.6 - 10421.4i) q^{92} +2679.33 q^{93} +(-7918.11 + 3505.40i) q^{94} +(-2611.75 - 4635.77i) q^{96} +8539.24 q^{97} +(-10759.4 - 24303.8i) q^{98} -3126.98i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61924 + 3.65760i 0.404811 + 0.914400i
\(3\) 5.19615i 0.577350i
\(4\) −10.7561 + 11.8451i −0.672256 + 0.740319i
\(5\) 0 0
\(6\) 19.0055 8.41384i 0.527929 0.233718i
\(7\) 95.1090i 1.94100i −0.241101 0.970500i \(-0.577508\pi\)
0.241101 0.970500i \(-0.422492\pi\)
\(8\) −60.7414 20.1614i −0.949085 0.315021i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 115.814i 0.957141i 0.878049 + 0.478571i \(0.158845\pi\)
−0.878049 + 0.478571i \(0.841155\pi\)
\(12\) 61.5490 + 55.8903i 0.427423 + 0.388127i
\(13\) −171.055 −1.01216 −0.506080 0.862487i \(-0.668906\pi\)
−0.506080 + 0.862487i \(0.668906\pi\)
\(14\) 347.871 154.005i 1.77485 0.785739i
\(15\) 0 0
\(16\) −24.6130 254.814i −0.0961444 0.995367i
\(17\) 228.789 0.791657 0.395829 0.918324i \(-0.370457\pi\)
0.395829 + 0.918324i \(0.370457\pi\)
\(18\) −43.7196 98.7552i −0.134937 0.304800i
\(19\) 659.627i 1.82722i 0.406589 + 0.913611i \(0.366718\pi\)
−0.406589 + 0.913611i \(0.633282\pi\)
\(20\) 0 0
\(21\) −494.201 −1.12064
\(22\) −423.602 + 187.531i −0.875210 + 0.387461i
\(23\) 968.886i 1.83154i 0.401700 + 0.915771i \(0.368420\pi\)
−0.401700 + 0.915771i \(0.631580\pi\)
\(24\) −104.762 + 315.622i −0.181878 + 0.547954i
\(25\) 0 0
\(26\) −276.980 625.651i −0.409733 0.925519i
\(27\) 140.296i 0.192450i
\(28\) 1126.58 + 1023.00i 1.43696 + 1.30485i
\(29\) 588.178 0.699379 0.349690 0.936866i \(-0.386287\pi\)
0.349690 + 0.936866i \(0.386287\pi\)
\(30\) 0 0
\(31\) 515.636i 0.536562i 0.963341 + 0.268281i \(0.0864556\pi\)
−0.963341 + 0.268281i \(0.913544\pi\)
\(32\) 892.154 502.631i 0.871244 0.490850i
\(33\) 601.788 0.552606
\(34\) 370.465 + 836.819i 0.320472 + 0.723892i
\(35\) 0 0
\(36\) 290.414 319.818i 0.224085 0.246773i
\(37\) 135.534 0.0990019 0.0495010 0.998774i \(-0.484237\pi\)
0.0495010 + 0.998774i \(0.484237\pi\)
\(38\) −2412.65 + 1068.10i −1.67081 + 0.739680i
\(39\) 888.827i 0.584370i
\(40\) 0 0
\(41\) −559.656 −0.332930 −0.166465 0.986047i \(-0.553235\pi\)
−0.166465 + 0.986047i \(0.553235\pi\)
\(42\) −800.232 1807.59i −0.453646 1.02471i
\(43\) 754.185i 0.407888i −0.978983 0.203944i \(-0.934624\pi\)
0.978983 0.203944i \(-0.0653760\pi\)
\(44\) −1371.83 1245.71i −0.708590 0.643444i
\(45\) 0 0
\(46\) −3543.80 + 1568.86i −1.67476 + 0.741429i
\(47\) 2164.84i 0.980007i 0.871720 + 0.490004i \(0.163005\pi\)
−0.871720 + 0.490004i \(0.836995\pi\)
\(48\) −1324.05 + 127.893i −0.574676 + 0.0555090i
\(49\) −6644.72 −2.76748
\(50\) 0 0
\(51\) 1188.82i 0.457063i
\(52\) 1839.88 2026.16i 0.680430 0.749321i
\(53\) 1178.44 0.419523 0.209762 0.977753i \(-0.432731\pi\)
0.209762 + 0.977753i \(0.432731\pi\)
\(54\) −513.147 + 227.174i −0.175976 + 0.0779060i
\(55\) 0 0
\(56\) −1917.53 + 5777.06i −0.611457 + 1.84217i
\(57\) 3427.52 1.05495
\(58\) 952.404 + 2151.32i 0.283117 + 0.639513i
\(59\) 183.192i 0.0526264i −0.999654 0.0263132i \(-0.991623\pi\)
0.999654 0.0263132i \(-0.00837671\pi\)
\(60\) 0 0
\(61\) −438.111 −0.117740 −0.0588701 0.998266i \(-0.518750\pi\)
−0.0588701 + 0.998266i \(0.518750\pi\)
\(62\) −1885.99 + 834.942i −0.490633 + 0.217206i
\(63\) 2567.94i 0.647000i
\(64\) 3283.04 + 2449.26i 0.801523 + 0.597964i
\(65\) 0 0
\(66\) 974.441 + 2201.10i 0.223701 + 0.505303i
\(67\) 709.589i 0.158073i −0.996872 0.0790365i \(-0.974816\pi\)
0.996872 0.0790365i \(-0.0251844\pi\)
\(68\) −2460.87 + 2710.03i −0.532196 + 0.586079i
\(69\) 5034.48 1.05744
\(70\) 0 0
\(71\) 8724.78i 1.73076i 0.501113 + 0.865382i \(0.332924\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(72\) 1640.02 + 544.357i 0.316362 + 0.105007i
\(73\) −5208.61 −0.977408 −0.488704 0.872450i \(-0.662530\pi\)
−0.488704 + 0.872450i \(0.662530\pi\)
\(74\) 219.462 + 495.728i 0.0400771 + 0.0905274i
\(75\) 0 0
\(76\) −7813.35 7095.01i −1.35273 1.22836i
\(77\) 11015.0 1.85781
\(78\) −3250.98 + 1439.23i −0.534348 + 0.236560i
\(79\) 957.643i 0.153444i −0.997053 0.0767219i \(-0.975555\pi\)
0.997053 0.0767219i \(-0.0244454\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −906.220 2047.00i −0.134774 0.304432i
\(83\) 2603.89i 0.377978i −0.981979 0.188989i \(-0.939479\pi\)
0.981979 0.188989i \(-0.0605211\pi\)
\(84\) 5315.67 5853.86i 0.753355 0.829629i
\(85\) 0 0
\(86\) 2758.51 1221.21i 0.372973 0.165118i
\(87\) 3056.26i 0.403787i
\(88\) 2334.97 7034.71i 0.301520 0.908408i
\(89\) −10133.8 −1.27936 −0.639678 0.768643i \(-0.720932\pi\)
−0.639678 + 0.768643i \(0.720932\pi\)
\(90\) 0 0
\(91\) 16268.9i 1.96460i
\(92\) −11476.6 10421.4i −1.35593 1.23127i
\(93\) 2679.33 0.309784
\(94\) −7918.11 + 3505.40i −0.896119 + 0.396718i
\(95\) 0 0
\(96\) −2611.75 4635.77i −0.283393 0.503013i
\(97\) 8539.24 0.907561 0.453780 0.891114i \(-0.350075\pi\)
0.453780 + 0.891114i \(0.350075\pi\)
\(98\) −10759.4 24303.8i −1.12031 2.53059i
\(99\) 3126.98i 0.319047i
\(100\) 0 0
\(101\) 5132.89 0.503175 0.251588 0.967835i \(-0.419047\pi\)
0.251588 + 0.967835i \(0.419047\pi\)
\(102\) 4348.24 1924.99i 0.417939 0.185024i
\(103\) 9488.29i 0.894363i 0.894443 + 0.447181i \(0.147572\pi\)
−0.894443 + 0.447181i \(0.852428\pi\)
\(104\) 10390.1 + 3448.70i 0.960625 + 0.318852i
\(105\) 0 0
\(106\) 1908.19 + 4310.27i 0.169828 + 0.383612i
\(107\) 10036.7i 0.876645i −0.898818 0.438322i \(-0.855573\pi\)
0.898818 0.438322i \(-0.144427\pi\)
\(108\) −1661.82 1509.04i −0.142474 0.129376i
\(109\) −10512.1 −0.884785 −0.442393 0.896822i \(-0.645870\pi\)
−0.442393 + 0.896822i \(0.645870\pi\)
\(110\) 0 0
\(111\) 704.253i 0.0571588i
\(112\) −24235.1 + 2340.92i −1.93201 + 0.186616i
\(113\) −18605.5 −1.45708 −0.728541 0.685002i \(-0.759801\pi\)
−0.728541 + 0.685002i \(0.759801\pi\)
\(114\) 5550.00 + 12536.5i 0.427054 + 0.964644i
\(115\) 0 0
\(116\) −6326.50 + 6967.03i −0.470162 + 0.517764i
\(117\) 4618.48 0.337386
\(118\) 670.045 296.633i 0.0481216 0.0213037i
\(119\) 21759.9i 1.53661i
\(120\) 0 0
\(121\) 1228.10 0.0838810
\(122\) −709.410 1602.44i −0.0476626 0.107662i
\(123\) 2908.06i 0.192217i
\(124\) −6107.77 5546.23i −0.397227 0.360707i
\(125\) 0 0
\(126\) −9392.51 + 4158.13i −0.591617 + 0.261913i
\(127\) 13799.8i 0.855586i 0.903877 + 0.427793i \(0.140709\pi\)
−0.903877 + 0.427793i \(0.859291\pi\)
\(128\) −3642.37 + 15974.0i −0.222313 + 0.974975i
\(129\) −3918.86 −0.235494
\(130\) 0 0
\(131\) 20145.1i 1.17389i −0.809628 0.586943i \(-0.800331\pi\)
0.809628 0.586943i \(-0.199669\pi\)
\(132\) −6472.88 + 7128.24i −0.371492 + 0.409104i
\(133\) 62736.5 3.54664
\(134\) 2595.40 1149.00i 0.144542 0.0639897i
\(135\) 0 0
\(136\) −13897.0 4612.70i −0.751350 0.249389i
\(137\) 11087.5 0.590734 0.295367 0.955384i \(-0.404558\pi\)
0.295367 + 0.955384i \(0.404558\pi\)
\(138\) 8152.06 + 18414.1i 0.428064 + 0.966925i
\(139\) 9763.23i 0.505317i 0.967556 + 0.252659i \(0.0813049\pi\)
−0.967556 + 0.252659i \(0.918695\pi\)
\(140\) 0 0
\(141\) 11248.8 0.565807
\(142\) −31911.8 + 14127.6i −1.58261 + 0.700633i
\(143\) 19810.6i 0.968779i
\(144\) 664.550 + 6879.98i 0.0320481 + 0.331789i
\(145\) 0 0
\(146\) −8434.01 19051.0i −0.395666 0.893742i
\(147\) 34527.0i 1.59781i
\(148\) −1457.81 + 1605.41i −0.0665546 + 0.0732930i
\(149\) 1558.71 0.0702092 0.0351046 0.999384i \(-0.488824\pi\)
0.0351046 + 0.999384i \(0.488824\pi\)
\(150\) 0 0
\(151\) 32018.5i 1.40426i −0.712049 0.702129i \(-0.752233\pi\)
0.712049 0.702129i \(-0.247767\pi\)
\(152\) 13299.0 40066.7i 0.575614 1.73419i
\(153\) −6177.30 −0.263886
\(154\) 17835.9 + 40288.3i 0.752063 + 1.69878i
\(155\) 0 0
\(156\) −10528.3 9560.31i −0.432621 0.392846i
\(157\) 30661.9 1.24394 0.621971 0.783041i \(-0.286332\pi\)
0.621971 + 0.783041i \(0.286332\pi\)
\(158\) 3502.67 1550.66i 0.140309 0.0621158i
\(159\) 6123.36i 0.242212i
\(160\) 0 0
\(161\) 92149.8 3.55503
\(162\) 1180.43 + 2666.39i 0.0449790 + 0.101600i
\(163\) 36638.2i 1.37898i 0.724293 + 0.689492i \(0.242166\pi\)
−0.724293 + 0.689492i \(0.757834\pi\)
\(164\) 6019.71 6629.18i 0.223814 0.246475i
\(165\) 0 0
\(166\) 9524.01 4216.34i 0.345624 0.153010i
\(167\) 26157.8i 0.937926i 0.883218 + 0.468963i \(0.155372\pi\)
−0.883218 + 0.468963i \(0.844628\pi\)
\(168\) 30018.5 + 9963.77i 1.06358 + 0.353025i
\(169\) 698.786 0.0244664
\(170\) 0 0
\(171\) 17809.9i 0.609074i
\(172\) 8933.40 + 8112.08i 0.301967 + 0.274205i
\(173\) 4778.24 0.159652 0.0798262 0.996809i \(-0.474563\pi\)
0.0798262 + 0.996809i \(0.474563\pi\)
\(174\) 11178.6 4948.84i 0.369223 0.163457i
\(175\) 0 0
\(176\) 29511.1 2850.53i 0.952707 0.0920238i
\(177\) −951.896 −0.0303838
\(178\) −16409.1 37065.3i −0.517898 1.16984i
\(179\) 27576.7i 0.860670i −0.902669 0.430335i \(-0.858395\pi\)
0.902669 0.430335i \(-0.141605\pi\)
\(180\) 0 0
\(181\) −25195.3 −0.769064 −0.384532 0.923112i \(-0.625637\pi\)
−0.384532 + 0.923112i \(0.625637\pi\)
\(182\) −59505.0 + 26343.3i −1.79643 + 0.795293i
\(183\) 2276.49i 0.0679773i
\(184\) 19534.1 58851.5i 0.576975 1.73829i
\(185\) 0 0
\(186\) 4338.48 + 9799.90i 0.125404 + 0.283267i
\(187\) 26497.0i 0.757728i
\(188\) −25642.7 23285.2i −0.725518 0.658815i
\(189\) 13343.4 0.373546
\(190\) 0 0
\(191\) 51407.2i 1.40915i 0.709630 + 0.704574i \(0.248862\pi\)
−0.709630 + 0.704574i \(0.751138\pi\)
\(192\) 12726.7 17059.2i 0.345235 0.462760i
\(193\) −8968.09 −0.240760 −0.120380 0.992728i \(-0.538411\pi\)
−0.120380 + 0.992728i \(0.538411\pi\)
\(194\) 13827.1 + 31233.1i 0.367391 + 0.829874i
\(195\) 0 0
\(196\) 71471.3 78707.4i 1.86046 2.04882i
\(197\) −28331.3 −0.730018 −0.365009 0.931004i \(-0.618934\pi\)
−0.365009 + 0.931004i \(0.618934\pi\)
\(198\) 11437.2 5063.35i 0.291737 0.129154i
\(199\) 25527.9i 0.644629i 0.946633 + 0.322314i \(0.104461\pi\)
−0.946633 + 0.322314i \(0.895539\pi\)
\(200\) 0 0
\(201\) −3687.14 −0.0912635
\(202\) 8311.41 + 18774.1i 0.203691 + 0.460103i
\(203\) 55941.0i 1.35750i
\(204\) 14081.7 + 12787.1i 0.338373 + 0.307264i
\(205\) 0 0
\(206\) −34704.4 + 15363.9i −0.817806 + 0.362048i
\(207\) 26159.9i 0.610514i
\(208\) 4210.17 + 43587.2i 0.0973135 + 1.00747i
\(209\) −76394.1 −1.74891
\(210\) 0 0
\(211\) 56431.4i 1.26752i 0.773528 + 0.633762i \(0.218490\pi\)
−0.773528 + 0.633762i \(0.781510\pi\)
\(212\) −12675.4 + 13958.8i −0.282027 + 0.310581i
\(213\) 45335.3 0.999257
\(214\) 36710.3 16251.9i 0.801604 0.354876i
\(215\) 0 0
\(216\) 2828.56 8521.78i 0.0606259 0.182651i
\(217\) 49041.7 1.04147
\(218\) −17021.7 38449.2i −0.358171 0.809048i
\(219\) 27064.7i 0.564307i
\(220\) 0 0
\(221\) −39135.5 −0.801283
\(222\) 2575.88 1140.36i 0.0522660 0.0231385i
\(223\) 40609.4i 0.816615i 0.912845 + 0.408307i \(0.133881\pi\)
−0.912845 + 0.408307i \(0.866119\pi\)
\(224\) −47804.7 84851.9i −0.952741 1.69108i
\(225\) 0 0
\(226\) −30126.8 68051.5i −0.589843 1.33236i
\(227\) 12054.3i 0.233932i 0.993136 + 0.116966i \(0.0373168\pi\)
−0.993136 + 0.116966i \(0.962683\pi\)
\(228\) −36866.8 + 40599.4i −0.709194 + 0.780997i
\(229\) 60489.3 1.15347 0.576737 0.816930i \(-0.304326\pi\)
0.576737 + 0.816930i \(0.304326\pi\)
\(230\) 0 0
\(231\) 57235.4i 1.07261i
\(232\) −35726.8 11858.5i −0.663770 0.220319i
\(233\) 27750.5 0.511163 0.255582 0.966787i \(-0.417733\pi\)
0.255582 + 0.966787i \(0.417733\pi\)
\(234\) 7478.45 + 16892.6i 0.136578 + 0.308506i
\(235\) 0 0
\(236\) 2169.93 + 1970.43i 0.0389603 + 0.0353784i
\(237\) −4976.06 −0.0885908
\(238\) 79589.0 35234.6i 1.40507 0.622036i
\(239\) 29154.5i 0.510399i 0.966888 + 0.255200i \(0.0821412\pi\)
−0.966888 + 0.255200i \(0.917859\pi\)
\(240\) 0 0
\(241\) 44625.6 0.768334 0.384167 0.923264i \(-0.374489\pi\)
0.384167 + 0.923264i \(0.374489\pi\)
\(242\) 1988.60 + 4491.91i 0.0339560 + 0.0767009i
\(243\) 3788.00i 0.0641500i
\(244\) 4712.37 5189.47i 0.0791515 0.0871653i
\(245\) 0 0
\(246\) −10636.5 + 4708.86i −0.175764 + 0.0778118i
\(247\) 112832.i 1.84944i
\(248\) 10395.9 31320.5i 0.169029 0.509243i
\(249\) −13530.2 −0.218226
\(250\) 0 0
\(251\) 56303.7i 0.893696i −0.894610 0.446848i \(-0.852546\pi\)
0.894610 0.446848i \(-0.147454\pi\)
\(252\) −30417.6 27621.0i −0.478986 0.434950i
\(253\) −112211. −1.75304
\(254\) −50474.0 + 22345.2i −0.782348 + 0.346351i
\(255\) 0 0
\(256\) −64324.4 + 12543.5i −0.981512 + 0.191398i
\(257\) −88714.4 −1.34316 −0.671580 0.740932i \(-0.734384\pi\)
−0.671580 + 0.740932i \(0.734384\pi\)
\(258\) −6345.59 14333.6i −0.0953307 0.215336i
\(259\) 12890.5i 0.192163i
\(260\) 0 0
\(261\) −15880.8 −0.233126
\(262\) 73682.6 32619.8i 1.07340 0.475202i
\(263\) 103470.i 1.49591i −0.663751 0.747953i \(-0.731037\pi\)
0.663751 0.747953i \(-0.268963\pi\)
\(264\) −36553.4 12132.9i −0.524469 0.174083i
\(265\) 0 0
\(266\) 101586. + 229465.i 1.43572 + 3.24305i
\(267\) 52656.7i 0.738637i
\(268\) 8405.16 + 7632.41i 0.117024 + 0.106265i
\(269\) 3553.14 0.0491029 0.0245515 0.999699i \(-0.492184\pi\)
0.0245515 + 0.999699i \(0.492184\pi\)
\(270\) 0 0
\(271\) 99010.4i 1.34816i 0.738657 + 0.674081i \(0.235460\pi\)
−0.738657 + 0.674081i \(0.764540\pi\)
\(272\) −5631.18 58298.6i −0.0761134 0.787990i
\(273\) 84535.5 1.13426
\(274\) 17953.3 + 40553.6i 0.239136 + 0.540167i
\(275\) 0 0
\(276\) −54151.3 + 59633.9i −0.710871 + 0.782844i
\(277\) −100046. −1.30389 −0.651943 0.758268i \(-0.726046\pi\)
−0.651943 + 0.758268i \(0.726046\pi\)
\(278\) −35710.0 + 15809.1i −0.462062 + 0.204558i
\(279\) 13922.2i 0.178854i
\(280\) 0 0
\(281\) −42287.1 −0.535545 −0.267772 0.963482i \(-0.586287\pi\)
−0.267772 + 0.963482i \(0.586287\pi\)
\(282\) 18214.6 + 41143.7i 0.229045 + 0.517374i
\(283\) 81612.9i 1.01903i −0.860463 0.509514i \(-0.829825\pi\)
0.860463 0.509514i \(-0.170175\pi\)
\(284\) −103346. 93844.5i −1.28132 1.16352i
\(285\) 0 0
\(286\) 72459.1 32078.2i 0.885852 0.392173i
\(287\) 53228.3i 0.646218i
\(288\) −24088.2 + 13571.0i −0.290415 + 0.163617i
\(289\) −31176.6 −0.373279
\(290\) 0 0
\(291\) 44371.2i 0.523980i
\(292\) 56024.3 61696.5i 0.657068 0.723594i
\(293\) −138795. −1.61673 −0.808366 0.588680i \(-0.799648\pi\)
−0.808366 + 0.588680i \(0.799648\pi\)
\(294\) −126286. + 55907.7i −1.46103 + 0.646810i
\(295\) 0 0
\(296\) −8232.50 2732.54i −0.0939612 0.0311877i
\(297\) −16248.3 −0.184202
\(298\) 2523.94 + 5701.15i 0.0284215 + 0.0641993i
\(299\) 165733.i 1.85381i
\(300\) 0 0
\(301\) −71729.8 −0.791710
\(302\) 117111. 51845.8i 1.28405 0.568460i
\(303\) 26671.3i 0.290508i
\(304\) 168082. 16235.4i 1.81876 0.175677i
\(305\) 0 0
\(306\) −10002.6 22594.1i −0.106824 0.241297i
\(307\) 123644.i 1.31188i −0.754812 0.655941i \(-0.772272\pi\)
0.754812 0.655941i \(-0.227728\pi\)
\(308\) −118478. + 130473.i −1.24892 + 1.37537i
\(309\) 49302.6 0.516361
\(310\) 0 0
\(311\) 13560.3i 0.140201i −0.997540 0.0701003i \(-0.977668\pi\)
0.997540 0.0701003i \(-0.0223319\pi\)
\(312\) 17920.0 53988.6i 0.184089 0.554617i
\(313\) −97614.2 −0.996378 −0.498189 0.867068i \(-0.666001\pi\)
−0.498189 + 0.867068i \(0.666001\pi\)
\(314\) 49649.1 + 112149.i 0.503561 + 1.13746i
\(315\) 0 0
\(316\) 11343.4 + 10300.5i 0.113597 + 0.103153i
\(317\) 74431.9 0.740697 0.370348 0.928893i \(-0.379238\pi\)
0.370348 + 0.928893i \(0.379238\pi\)
\(318\) 22396.8 9915.22i 0.221479 0.0980501i
\(319\) 68119.3i 0.669405i
\(320\) 0 0
\(321\) −52152.3 −0.506131
\(322\) 149213. + 337047.i 1.43911 + 3.25072i
\(323\) 150915.i 1.44653i
\(324\) −7841.19 + 8635.08i −0.0746951 + 0.0822577i
\(325\) 0 0
\(326\) −134008. + 59326.3i −1.26094 + 0.558228i
\(327\) 54622.6i 0.510831i
\(328\) 33994.3 + 11283.4i 0.315979 + 0.104880i
\(329\) 205895. 1.90219
\(330\) 0 0
\(331\) 76357.2i 0.696937i 0.937320 + 0.348469i \(0.113298\pi\)
−0.937320 + 0.348469i \(0.886702\pi\)
\(332\) 30843.4 + 28007.7i 0.279825 + 0.254098i
\(333\) −3659.41 −0.0330006
\(334\) −95674.9 + 42355.9i −0.857640 + 0.379683i
\(335\) 0 0
\(336\) 12163.8 + 125929.i 0.107743 + 1.11545i
\(337\) 101465. 0.893418 0.446709 0.894679i \(-0.352596\pi\)
0.446709 + 0.894679i \(0.352596\pi\)
\(338\) 1131.50 + 2555.88i 0.00990428 + 0.0223721i
\(339\) 96676.9i 0.841247i
\(340\) 0 0
\(341\) −59718.0 −0.513566
\(342\) 65141.6 28838.6i 0.556937 0.246560i
\(343\) 403616.i 3.43068i
\(344\) −15205.4 + 45810.2i −0.128493 + 0.387120i
\(345\) 0 0
\(346\) 7737.14 + 17476.9i 0.0646291 + 0.145986i
\(347\) 208562.i 1.73212i −0.499944 0.866058i \(-0.666646\pi\)
0.499944 0.866058i \(-0.333354\pi\)
\(348\) 36201.7 + 32873.4i 0.298931 + 0.271448i
\(349\) −3917.08 −0.0321596 −0.0160798 0.999871i \(-0.505119\pi\)
−0.0160798 + 0.999871i \(0.505119\pi\)
\(350\) 0 0
\(351\) 23998.3i 0.194790i
\(352\) 58211.7 + 103324.i 0.469813 + 0.833903i
\(353\) 102995. 0.826548 0.413274 0.910607i \(-0.364385\pi\)
0.413274 + 0.910607i \(0.364385\pi\)
\(354\) −1541.35 3481.65i −0.0122997 0.0277830i
\(355\) 0 0
\(356\) 109000. 120036.i 0.860055 0.947132i
\(357\) −113068. −0.887160
\(358\) 100865. 44653.5i 0.786997 0.348409i
\(359\) 236871.i 1.83790i 0.394371 + 0.918951i \(0.370962\pi\)
−0.394371 + 0.918951i \(0.629038\pi\)
\(360\) 0 0
\(361\) −304787. −2.33874
\(362\) −40797.4 92154.4i −0.311326 0.703233i
\(363\) 6381.41i 0.0484287i
\(364\) −192706. 174989.i −1.45443 1.32071i
\(365\) 0 0
\(366\) −8326.50 + 3686.20i −0.0621585 + 0.0275180i
\(367\) 165846.i 1.23133i −0.788009 0.615664i \(-0.788888\pi\)
0.788009 0.615664i \(-0.211112\pi\)
\(368\) 246886. 23847.2i 1.82306 0.176093i
\(369\) 15110.7 0.110977
\(370\) 0 0
\(371\) 112080.i 0.814295i
\(372\) −28819.1 + 31736.9i −0.208254 + 0.229339i
\(373\) −170798. −1.22762 −0.613812 0.789452i \(-0.710365\pi\)
−0.613812 + 0.789452i \(0.710365\pi\)
\(374\) −96915.4 + 42905.1i −0.692866 + 0.306737i
\(375\) 0 0
\(376\) 43646.1 131495.i 0.308723 0.930110i
\(377\) −100611. −0.707883
\(378\) 21606.3 + 48804.9i 0.151215 + 0.341570i
\(379\) 207834.i 1.44690i 0.690378 + 0.723449i \(0.257444\pi\)
−0.690378 + 0.723449i \(0.742556\pi\)
\(380\) 0 0
\(381\) 71705.6 0.493973
\(382\) −188027. + 83240.8i −1.28853 + 0.570439i
\(383\) 145912.i 0.994706i −0.867548 0.497353i \(-0.834305\pi\)
0.867548 0.497353i \(-0.165695\pi\)
\(384\) 83003.3 + 18926.3i 0.562902 + 0.128352i
\(385\) 0 0
\(386\) −14521.5 32801.7i −0.0974625 0.220151i
\(387\) 20363.0i 0.135963i
\(388\) −91848.8 + 101148.i −0.610113 + 0.671884i
\(389\) −100959. −0.667183 −0.333591 0.942718i \(-0.608261\pi\)
−0.333591 + 0.942718i \(0.608261\pi\)
\(390\) 0 0
\(391\) 221670.i 1.44995i
\(392\) 403610. + 133967.i 2.62657 + 0.871816i
\(393\) −104677. −0.677743
\(394\) −45875.3 103625.i −0.295520 0.667529i
\(395\) 0 0
\(396\) 37039.4 + 33634.1i 0.236197 + 0.214481i
\(397\) −38963.5 −0.247216 −0.123608 0.992331i \(-0.539447\pi\)
−0.123608 + 0.992331i \(0.539447\pi\)
\(398\) −93371.0 + 41336.0i −0.589449 + 0.260953i
\(399\) 325988.i 2.04765i
\(400\) 0 0
\(401\) −63269.6 −0.393465 −0.196732 0.980457i \(-0.563033\pi\)
−0.196732 + 0.980457i \(0.563033\pi\)
\(402\) −5970.37 13486.1i −0.0369445 0.0834513i
\(403\) 88202.2i 0.543087i
\(404\) −55209.8 + 60799.6i −0.338262 + 0.372510i
\(405\) 0 0
\(406\) 204610. 90582.2i 1.24129 0.549529i
\(407\) 15696.7i 0.0947588i
\(408\) −23968.3 + 72210.7i −0.143985 + 0.433792i
\(409\) 188419. 1.12636 0.563181 0.826333i \(-0.309577\pi\)
0.563181 + 0.826333i \(0.309577\pi\)
\(410\) 0 0
\(411\) 57612.2i 0.341060i
\(412\) −112390. 102057.i −0.662114 0.601240i
\(413\) −17423.2 −0.102148
\(414\) 95682.6 42359.3i 0.558254 0.247143i
\(415\) 0 0
\(416\) −152607. + 85977.5i −0.881838 + 0.496819i
\(417\) 50731.2 0.291745
\(418\) −123701. 279419.i −0.707978 1.59920i
\(419\) 31463.3i 0.179216i −0.995977 0.0896080i \(-0.971439\pi\)
0.995977 0.0896080i \(-0.0285614\pi\)
\(420\) 0 0
\(421\) −146901. −0.828822 −0.414411 0.910090i \(-0.636012\pi\)
−0.414411 + 0.910090i \(0.636012\pi\)
\(422\) −206404. + 91376.3i −1.15902 + 0.513108i
\(423\) 58450.6i 0.326669i
\(424\) −71580.2 23759.0i −0.398163 0.132159i
\(425\) 0 0
\(426\) 73408.9 + 165818.i 0.404510 + 0.913721i
\(427\) 41668.3i 0.228534i
\(428\) 118886. + 107956.i 0.648997 + 0.589330i
\(429\) −102939. −0.559325
\(430\) 0 0
\(431\) 184568.i 0.993578i −0.867871 0.496789i \(-0.834512\pi\)
0.867871 0.496789i \(-0.165488\pi\)
\(432\) 35749.4 3453.10i 0.191559 0.0185030i
\(433\) 313272. 1.67088 0.835440 0.549582i \(-0.185213\pi\)
0.835440 + 0.549582i \(0.185213\pi\)
\(434\) 79410.5 + 179375.i 0.421598 + 0.952318i
\(435\) 0 0
\(436\) 113069. 124517.i 0.594802 0.655023i
\(437\) −639104. −3.34664
\(438\) −98991.9 + 43824.4i −0.516002 + 0.228438i
\(439\) 104426.i 0.541851i −0.962600 0.270925i \(-0.912670\pi\)
0.962600 0.270925i \(-0.0873297\pi\)
\(440\) 0 0
\(441\) 179408. 0.922494
\(442\) −63369.9 143142.i −0.324368 0.732694i
\(443\) 23106.0i 0.117738i 0.998266 + 0.0588691i \(0.0187495\pi\)
−0.998266 + 0.0588691i \(0.981251\pi\)
\(444\) 8341.95 + 7575.01i 0.0423157 + 0.0384253i
\(445\) 0 0
\(446\) −148533. + 65756.6i −0.746713 + 0.330575i
\(447\) 8099.32i 0.0405353i
\(448\) 232947. 312247.i 1.16065 1.55576i
\(449\) 63670.0 0.315822 0.157911 0.987453i \(-0.449524\pi\)
0.157911 + 0.987453i \(0.449524\pi\)
\(450\) 0 0
\(451\) 64816.0i 0.318661i
\(452\) 200122. 220384.i 0.979532 1.07871i
\(453\) −166373. −0.810749
\(454\) −44089.7 + 19518.8i −0.213907 + 0.0946982i
\(455\) 0 0
\(456\) −208193. 69103.6i −1.00123 0.332331i
\(457\) −113519. −0.543544 −0.271772 0.962362i \(-0.587610\pi\)
−0.271772 + 0.962362i \(0.587610\pi\)
\(458\) 97947.0 + 221246.i 0.466939 + 1.05474i
\(459\) 32098.2i 0.152354i
\(460\) 0 0
\(461\) 279353. 1.31447 0.657235 0.753685i \(-0.271726\pi\)
0.657235 + 0.753685i \(0.271726\pi\)
\(462\) 209344. 92678.2i 0.980793 0.434204i
\(463\) 47283.9i 0.220572i −0.993900 0.110286i \(-0.964823\pi\)
0.993900 0.110286i \(-0.0351767\pi\)
\(464\) −14476.8 149876.i −0.0672414 0.696139i
\(465\) 0 0
\(466\) 44934.9 + 101500.i 0.206925 + 0.467408i
\(467\) 355616.i 1.63060i 0.579039 + 0.815300i \(0.303428\pi\)
−0.579039 + 0.815300i \(0.696572\pi\)
\(468\) −49676.8 + 54706.4i −0.226810 + 0.249774i
\(469\) −67488.4 −0.306820
\(470\) 0 0
\(471\) 159324.i 0.718190i
\(472\) −3693.41 + 11127.4i −0.0165784 + 0.0499469i
\(473\) 87345.2 0.390406
\(474\) −8057.45 18200.4i −0.0358626 0.0810075i
\(475\) 0 0
\(476\) 257748. + 234051.i 1.13758 + 1.03299i
\(477\) −31817.9 −0.139841
\(478\) −106636. + 47208.3i −0.466709 + 0.206615i
\(479\) 217649.i 0.948605i 0.880362 + 0.474302i \(0.157300\pi\)
−0.880362 + 0.474302i \(0.842700\pi\)
\(480\) 0 0
\(481\) −23183.7 −0.100206
\(482\) 72259.8 + 163223.i 0.311030 + 0.702565i
\(483\) 478824.i 2.05249i
\(484\) −13209.6 + 14547.0i −0.0563895 + 0.0620987i
\(485\) 0 0
\(486\) 13855.0 6133.69i 0.0586588 0.0259687i
\(487\) 26631.0i 0.112287i −0.998423 0.0561435i \(-0.982120\pi\)
0.998423 0.0561435i \(-0.0178804\pi\)
\(488\) 26611.5 + 8832.93i 0.111745 + 0.0370907i
\(489\) 190378. 0.796157
\(490\) 0 0
\(491\) 464401.i 1.92633i −0.268912 0.963165i \(-0.586664\pi\)
0.268912 0.963165i \(-0.413336\pi\)
\(492\) −34446.3 31279.3i −0.142302 0.129219i
\(493\) 134569. 0.553669
\(494\) 412696. 182703.i 1.69113 0.748674i
\(495\) 0 0
\(496\) 131391. 12691.3i 0.534077 0.0515875i
\(497\) 829805. 3.35941
\(498\) −21908.8 49488.2i −0.0883403 0.199546i
\(499\) 94648.3i 0.380112i 0.981773 + 0.190056i \(0.0608670\pi\)
−0.981773 + 0.190056i \(0.939133\pi\)
\(500\) 0 0
\(501\) 135920. 0.541512
\(502\) 205937. 91169.6i 0.817196 0.361778i
\(503\) 276138.i 1.09141i −0.837976 0.545707i \(-0.816261\pi\)
0.837976 0.545707i \(-0.183739\pi\)
\(504\) 51773.3 155981.i 0.203819 0.614058i
\(505\) 0 0
\(506\) −181697. 410422.i −0.709652 1.60298i
\(507\) 3631.00i 0.0141257i
\(508\) −163459. 148431.i −0.633407 0.575173i
\(509\) 423966. 1.63642 0.818212 0.574917i \(-0.194966\pi\)
0.818212 + 0.574917i \(0.194966\pi\)
\(510\) 0 0
\(511\) 495385.i 1.89715i
\(512\) −150036. 214962.i −0.572342 0.820015i
\(513\) −92543.1 −0.351649
\(514\) −143650. 324482.i −0.543726 1.22819i
\(515\) 0 0
\(516\) 42151.6 46419.3i 0.158312 0.174341i
\(517\) −250718. −0.938005
\(518\) 47148.2 20872.8i 0.175714 0.0777896i
\(519\) 24828.5i 0.0921754i
\(520\) 0 0
\(521\) 101217. 0.372889 0.186444 0.982466i \(-0.440304\pi\)
0.186444 + 0.982466i \(0.440304\pi\)
\(522\) −25714.9 58085.6i −0.0943722 0.213171i
\(523\) 161604.i 0.590813i −0.955372 0.295406i \(-0.904545\pi\)
0.955372 0.295406i \(-0.0954550\pi\)
\(524\) 238620. + 216682.i 0.869050 + 0.789152i
\(525\) 0 0
\(526\) 378453. 167544.i 1.36786 0.605560i
\(527\) 117972.i 0.424773i
\(528\) −14811.8 153344.i −0.0531300 0.550046i
\(529\) −658900. −2.35455
\(530\) 0 0
\(531\) 4946.19i 0.0175421i
\(532\) −674799. + 743120.i −2.38425 + 2.62564i
\(533\) 95731.9 0.336979
\(534\) −192597. + 85264.1i −0.675410 + 0.299009i
\(535\) 0 0
\(536\) −14306.3 + 43101.5i −0.0497964 + 0.150025i
\(537\) −143293. −0.496908
\(538\) 5753.40 + 12996.0i 0.0198774 + 0.0448997i
\(539\) 769553.i 2.64887i
\(540\) 0 0
\(541\) 387943. 1.32548 0.662740 0.748850i \(-0.269394\pi\)
0.662740 + 0.748850i \(0.269394\pi\)
\(542\) −362141. + 160322.i −1.23276 + 0.545751i
\(543\) 130919.i 0.444020i
\(544\) 204115. 114996.i 0.689726 0.388585i
\(545\) 0 0
\(546\) 136884. + 309197.i 0.459162 + 1.03717i
\(547\) 27433.2i 0.0916858i −0.998949 0.0458429i \(-0.985403\pi\)
0.998949 0.0458429i \(-0.0145974\pi\)
\(548\) −119258. + 131332.i −0.397124 + 0.437331i
\(549\) 11829.0 0.0392467
\(550\) 0 0
\(551\) 387978.i 1.27792i
\(552\) −305801. 101502.i −1.00360 0.333117i
\(553\) −91080.4 −0.297834
\(554\) −161999. 365928.i −0.527828 1.19227i
\(555\) 0 0
\(556\) −115646. 105014.i −0.374096 0.339702i
\(557\) 313521. 1.01055 0.505273 0.862959i \(-0.331392\pi\)
0.505273 + 0.862959i \(0.331392\pi\)
\(558\) 50921.8 22543.4i 0.163544 0.0724022i
\(559\) 129007.i 0.412847i
\(560\) 0 0
\(561\) 137682. 0.437474
\(562\) −68473.2 154669.i −0.216794 0.489702i
\(563\) 437532.i 1.38036i 0.723637 + 0.690181i \(0.242469\pi\)
−0.723637 + 0.690181i \(0.757531\pi\)
\(564\) −120993. + 133243.i −0.380367 + 0.418878i
\(565\) 0 0
\(566\) 298507. 132151.i 0.931799 0.412514i
\(567\) 69334.5i 0.215667i
\(568\) 175904. 529956.i 0.545228 1.64264i
\(569\) −86379.1 −0.266799 −0.133400 0.991062i \(-0.542589\pi\)
−0.133400 + 0.991062i \(0.542589\pi\)
\(570\) 0 0
\(571\) 204020.i 0.625748i 0.949795 + 0.312874i \(0.101292\pi\)
−0.949795 + 0.312874i \(0.898708\pi\)
\(572\) 234658. + 213084.i 0.717206 + 0.651267i
\(573\) 267119. 0.813572
\(574\) −194688. + 86189.7i −0.590902 + 0.261596i
\(575\) 0 0
\(576\) −88642.0 66130.0i −0.267174 0.199321i
\(577\) 63845.4 0.191769 0.0958844 0.995392i \(-0.469432\pi\)
0.0958844 + 0.995392i \(0.469432\pi\)
\(578\) −50482.6 114032.i −0.151108 0.341326i
\(579\) 46599.5i 0.139003i
\(580\) 0 0
\(581\) −247654. −0.733656
\(582\) 162292. 71847.8i 0.479128 0.212113i
\(583\) 136480.i 0.401543i
\(584\) 316378. + 105013.i 0.927643 + 0.307904i
\(585\) 0 0
\(586\) −224743. 507656.i −0.654471 1.47834i
\(587\) 490014.i 1.42211i 0.703137 + 0.711054i \(0.251782\pi\)
−0.703137 + 0.711054i \(0.748218\pi\)
\(588\) −408976. 371376.i −1.18289 1.07413i
\(589\) −340128. −0.980419
\(590\) 0 0
\(591\) 147214.i 0.421476i
\(592\) −3335.89 34535.9i −0.00951848 0.0985433i
\(593\) 440204. 1.25183 0.625913 0.779893i \(-0.284726\pi\)
0.625913 + 0.779893i \(0.284726\pi\)
\(594\) −26309.9 59429.7i −0.0745670 0.168434i
\(595\) 0 0
\(596\) −16765.7 + 18463.1i −0.0471985 + 0.0519772i
\(597\) 132647. 0.372177
\(598\) 606184. 268362.i 1.69513 0.750444i
\(599\) 363994.i 1.01447i 0.861807 + 0.507236i \(0.169333\pi\)
−0.861807 + 0.507236i \(0.830667\pi\)
\(600\) 0 0
\(601\) 237926. 0.658707 0.329353 0.944207i \(-0.393169\pi\)
0.329353 + 0.944207i \(0.393169\pi\)
\(602\) −116148. 262359.i −0.320493 0.723940i
\(603\) 19158.9i 0.0526910i
\(604\) 379262. + 344394.i 1.03960 + 0.944021i
\(605\) 0 0
\(606\) 97552.9 43187.3i 0.265641 0.117601i
\(607\) 566612.i 1.53783i −0.639351 0.768915i \(-0.720797\pi\)
0.639351 0.768915i \(-0.279203\pi\)
\(608\) 331549. + 588489.i 0.896893 + 1.59196i
\(609\) −290678. −0.783750
\(610\) 0 0
\(611\) 370306.i 0.991923i
\(612\) 66443.6 73170.8i 0.177399 0.195360i
\(613\) −464259. −1.23549 −0.617745 0.786378i \(-0.711954\pi\)
−0.617745 + 0.786378i \(0.711954\pi\)
\(614\) 452239. 200209.i 1.19959 0.531064i
\(615\) 0 0
\(616\) −669064. 222077.i −1.76322 0.585250i
\(617\) −460844. −1.21055 −0.605277 0.796015i \(-0.706938\pi\)
−0.605277 + 0.796015i \(0.706938\pi\)
\(618\) 79833.0 + 180329.i 0.209029 + 0.472160i
\(619\) 38455.6i 0.100364i 0.998740 + 0.0501821i \(0.0159802\pi\)
−0.998740 + 0.0501821i \(0.984020\pi\)
\(620\) 0 0
\(621\) −135931. −0.352481
\(622\) 49598.3 21957.5i 0.128199 0.0567548i
\(623\) 963814.i 2.48323i
\(624\) 226486. 21876.7i 0.581663 0.0561840i
\(625\) 0 0
\(626\) −158061. 357034.i −0.403345 0.911089i
\(627\) 396955.i 1.00973i
\(628\) −329802. + 363194.i −0.836247 + 0.920913i
\(629\) 31008.6 0.0783756
\(630\) 0 0
\(631\) 237480.i 0.596443i −0.954497 0.298221i \(-0.903607\pi\)
0.954497 0.298221i \(-0.0963934\pi\)
\(632\) −19307.4 + 58168.6i −0.0483381 + 0.145631i
\(633\) 293226. 0.731805
\(634\) 120523. + 272242.i 0.299842 + 0.677293i
\(635\) 0 0
\(636\) 72531.8 + 65863.4i 0.179314 + 0.162828i
\(637\) 1.13661e6 2.80113
\(638\) −249153. + 110302.i −0.612104 + 0.270982i
\(639\) 235569.i 0.576921i
\(640\) 0 0
\(641\) −182574. −0.444348 −0.222174 0.975007i \(-0.571315\pi\)
−0.222174 + 0.975007i \(0.571315\pi\)
\(642\) −84447.3 190752.i −0.204888 0.462806i
\(643\) 145787.i 0.352613i −0.984335 0.176306i \(-0.943585\pi\)
0.984335 0.176306i \(-0.0564149\pi\)
\(644\) −991172. + 1.09152e6i −2.38989 + 2.63185i
\(645\) 0 0
\(646\) −551988. + 244369.i −1.32271 + 0.585573i
\(647\) 25742.8i 0.0614959i 0.999527 + 0.0307480i \(0.00978892\pi\)
−0.999527 + 0.0307480i \(0.990211\pi\)
\(648\) −44280.5 14697.6i −0.105454 0.0350024i
\(649\) 21216.3 0.0503709
\(650\) 0 0
\(651\) 254828.i 0.601292i
\(652\) −433984. 394084.i −1.02089 0.927030i
\(653\) 759303. 1.78069 0.890346 0.455285i \(-0.150463\pi\)
0.890346 + 0.455285i \(0.150463\pi\)
\(654\) −199788. + 88447.4i −0.467104 + 0.206790i
\(655\) 0 0
\(656\) 13774.8 + 142608.i 0.0320094 + 0.331388i
\(657\) 140632. 0.325803
\(658\) 333395. + 753083.i 0.770030 + 1.73937i
\(659\) 206499.i 0.475497i 0.971327 + 0.237748i \(0.0764094\pi\)
−0.971327 + 0.237748i \(0.923591\pi\)
\(660\) 0 0
\(661\) −130969. −0.299755 −0.149878 0.988705i \(-0.547888\pi\)
−0.149878 + 0.988705i \(0.547888\pi\)
\(662\) −279284. + 123641.i −0.637280 + 0.282128i
\(663\) 203354.i 0.462621i
\(664\) −52498.1 + 158164.i −0.119071 + 0.358734i
\(665\) 0 0
\(666\) −5925.48 13384.7i −0.0133590 0.0301758i
\(667\) 569877.i 1.28094i
\(668\) −309842. 281356.i −0.694365 0.630526i
\(669\) 211013. 0.471473
\(670\) 0 0
\(671\) 50739.5i 0.112694i
\(672\) −440903. + 248401.i −0.976348 + 0.550065i
\(673\) −703745. −1.55376 −0.776882 0.629647i \(-0.783200\pi\)
−0.776882 + 0.629647i \(0.783200\pi\)
\(674\) 164296. + 371117.i 0.361666 + 0.816942i
\(675\) 0 0
\(676\) −7516.20 + 8277.19i −0.0164477 + 0.0181130i
\(677\) 840675. 1.83422 0.917108 0.398638i \(-0.130517\pi\)
0.917108 + 0.398638i \(0.130517\pi\)
\(678\) −353606. + 156544.i −0.769237 + 0.340546i
\(679\) 812158.i 1.76158i
\(680\) 0 0
\(681\) 62635.8 0.135061
\(682\) −96698.0 218424.i −0.207897 0.469605i
\(683\) 570663.i 1.22332i −0.791123 0.611658i \(-0.790503\pi\)
0.791123 0.611658i \(-0.209497\pi\)
\(684\) 210961. + 191565.i 0.450909 + 0.409453i
\(685\) 0 0
\(686\) −1.47627e6 + 653554.i −3.13702 + 1.38878i
\(687\) 314312.i 0.665958i
\(688\) −192177. + 18562.7i −0.405998 + 0.0392161i
\(689\) −201578. −0.424625
\(690\) 0 0
\(691\) 260946.i 0.546505i 0.961942 + 0.273253i \(0.0880995\pi\)
−0.961942 + 0.273253i \(0.911901\pi\)
\(692\) −51395.2 + 56598.7i −0.107327 + 0.118194i
\(693\) −297404. −0.619270
\(694\) 762838. 337713.i 1.58385 0.701180i
\(695\) 0 0
\(696\) −61618.4 + 185642.i −0.127201 + 0.383228i
\(697\) −128043. −0.263567
\(698\) −6342.71 14327.1i −0.0130186 0.0294068i
\(699\) 144196.i 0.295120i
\(700\) 0 0
\(701\) 655810. 1.33457 0.667286 0.744801i \(-0.267456\pi\)
0.667286 + 0.744801i \(0.267456\pi\)
\(702\) 87776.4 38859.2i 0.178116 0.0788532i
\(703\) 89401.6i 0.180898i
\(704\) −283659. + 380222.i −0.572336 + 0.767171i
\(705\) 0 0
\(706\) 166775. + 376716.i 0.334596 + 0.755796i
\(707\) 488184.i 0.976663i
\(708\) 10238.7 11275.3i 0.0204257 0.0224937i
\(709\) 502376. 0.999393 0.499696 0.866201i \(-0.333445\pi\)
0.499696 + 0.866201i \(0.333445\pi\)
\(710\) 0 0
\(711\) 25856.4i 0.0511479i
\(712\) 615540. + 204311.i 1.21422 + 0.403025i
\(713\) −499593. −0.982737
\(714\) −183084. 413557.i −0.359132 0.811220i
\(715\) 0 0
\(716\) 326649. + 296618.i 0.637170 + 0.578590i
\(717\) 151491. 0.294679
\(718\) −866379. + 383552.i −1.68058 + 0.744004i
\(719\) 666208.i 1.28870i 0.764730 + 0.644350i \(0.222872\pi\)
−0.764730 + 0.644350i \(0.777128\pi\)
\(720\) 0 0
\(721\) 902422. 1.73596
\(722\) −493525. 1.11479e6i −0.946748 2.13854i
\(723\) 231881.i 0.443598i
\(724\) 271003. 298441.i 0.517008 0.569353i
\(725\) 0 0
\(726\) 23340.6 10333.1i 0.0442833 0.0196045i
\(727\) 86784.8i 0.164201i 0.996624 + 0.0821003i \(0.0261628\pi\)
−0.996624 + 0.0821003i \(0.973837\pi\)
\(728\) 328003. 988194.i 0.618891 1.86457i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 172549.i 0.322907i
\(732\) −26965.3 24486.2i −0.0503249 0.0456982i
\(733\) 499460. 0.929592 0.464796 0.885418i \(-0.346128\pi\)
0.464796 + 0.885418i \(0.346128\pi\)
\(734\) 606600. 268546.i 1.12593 0.498456i
\(735\) 0 0
\(736\) 486992. + 864395.i 0.899014 + 1.59572i
\(737\) 82180.4 0.151298
\(738\) 24467.9 + 55269.0i 0.0449247 + 0.101477i
\(739\) 457929.i 0.838512i −0.907868 0.419256i \(-0.862291\pi\)
0.907868 0.419256i \(-0.137709\pi\)
\(740\) 0 0
\(741\) −586295. −1.06777
\(742\) 409945. 181486.i 0.744592 0.329636i
\(743\) 92845.0i 0.168183i 0.996458 + 0.0840913i \(0.0267987\pi\)
−0.996458 + 0.0840913i \(0.973201\pi\)
\(744\) −162746. 54018.9i −0.294012 0.0975887i
\(745\) 0 0
\(746\) −276564. 624711.i −0.496956 1.12254i
\(747\) 70305.1i 0.125993i
\(748\) −313859. 285004.i −0.560960 0.509387i
\(749\) −954581. −1.70157
\(750\) 0 0
\(751\) 415086.i 0.735966i 0.929832 + 0.367983i \(0.119952\pi\)
−0.929832 + 0.367983i \(0.880048\pi\)
\(752\) 551631. 53283.1i 0.975467 0.0942222i
\(753\) −292563. −0.515976
\(754\) −162913. 367994.i −0.286559 0.647289i
\(755\) 0 0
\(756\) −143523. + 158054.i −0.251118 + 0.276543i
\(757\) 144592. 0.252321 0.126161 0.992010i \(-0.459735\pi\)
0.126161 + 0.992010i \(0.459735\pi\)
\(758\) −760173. + 336534.i −1.32304 + 0.585720i
\(759\) 583064.i 1.01212i
\(760\) 0 0
\(761\) −345143. −0.595977 −0.297989 0.954569i \(-0.596316\pi\)
−0.297989 + 0.954569i \(0.596316\pi\)
\(762\) 116109. + 262271.i 0.199966 + 0.451689i
\(763\) 999799.i 1.71737i
\(764\) −608923. 552940.i −1.04322 0.947308i
\(765\) 0 0
\(766\) 533689. 236268.i 0.909559 0.402668i
\(767\) 31336.0i 0.0532663i
\(768\) 65177.8 + 334239.i 0.110504 + 0.566677i
\(769\) −10368.2 −0.0175328 −0.00876641 0.999962i \(-0.502790\pi\)
−0.00876641 + 0.999962i \(0.502790\pi\)
\(770\) 0 0
\(771\) 460973.i 0.775474i
\(772\) 96461.6 106228.i 0.161853 0.178240i
\(773\) 304512. 0.509619 0.254809 0.966991i \(-0.417987\pi\)
0.254809 + 0.966991i \(0.417987\pi\)
\(774\) −74479.7 + 32972.7i −0.124324 + 0.0550392i
\(775\) 0 0
\(776\) −518685. 172163.i −0.861352 0.285901i
\(777\) −66980.8 −0.110945
\(778\) −163477. 369267.i −0.270083 0.610072i
\(779\) 369164.i 0.608338i
\(780\) 0 0
\(781\) −1.01045e6 −1.65659
\(782\) −810782. + 358939.i −1.32584 + 0.586958i
\(783\) 82519.1i 0.134596i