Properties

Label 76.5.j.a.53.1
Level $76$
Weight $5$
Character 76.53
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 53.1
Character \(\chi\) \(=\) 76.53
Dual form 76.5.j.a.33.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +O(q^{10})\) \(q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +(-106.545 - 184.541i) q^{11} +(67.2882 + 11.8647i) q^{13} +(225.861 - 269.170i) q^{15} +(86.5075 + 31.4861i) q^{17} +(360.844 + 10.5981i) q^{19} +(316.044 - 868.322i) q^{21} +(152.628 + 128.070i) q^{23} +(-38.3938 + 217.742i) q^{25} +(-2175.60 + 1256.08i) q^{27} +(-125.853 - 345.779i) q^{29} +(-715.213 - 412.929i) q^{31} +(2394.78 + 2853.99i) q^{33} +(-184.444 - 1046.03i) q^{35} -2460.86i q^{37} -1194.61 q^{39} +(1695.95 - 299.042i) q^{41} +(-1341.89 + 1125.98i) q^{43} +(-2257.77 + 3910.58i) q^{45} +(1843.05 - 670.816i) q^{47} +(-196.146 - 339.734i) q^{49} +(-1585.10 - 279.496i) q^{51} +(1283.71 - 1529.86i) q^{53} +(4024.24 + 1464.70i) q^{55} +(-6245.28 + 913.057i) q^{57} +(836.628 - 2298.62i) q^{59} +(-1062.83 - 891.820i) q^{61} +(-2062.07 + 11694.6i) q^{63} +(-1189.20 + 686.584i) q^{65} +(415.368 + 1141.22i) q^{67} +(-3016.81 - 1741.76i) q^{69} +(-5933.74 - 7071.56i) q^{71} +(-258.462 - 1465.81i) q^{73} -3865.70i q^{75} +11262.1 q^{77} +(8753.63 - 1543.50i) q^{79} +(19704.9 - 16534.3i) q^{81} +(3718.48 - 6440.60i) q^{83} +(-1738.56 + 632.784i) q^{85} +(3216.77 + 5571.61i) q^{87} +(-4040.87 - 712.515i) q^{89} +(-2321.20 + 2766.30i) q^{91} +(13568.4 + 4938.48i) q^{93} +(-5692.24 + 4498.32i) q^{95} +(-2467.26 + 6778.74i) q^{97} +(-36676.7 - 30775.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −17.2182 + 3.03604i −1.91314 + 0.337338i −0.997854 0.0654748i \(-0.979144\pi\)
−0.915283 + 0.402812i \(0.868033\pi\)
\(4\) 0 0
\(5\) −15.3954 + 12.9183i −0.615815 + 0.516730i −0.896485 0.443074i \(-0.853888\pi\)
0.280670 + 0.959804i \(0.409443\pi\)
\(6\) 0 0
\(7\) −26.4258 + 45.7708i −0.539302 + 0.934099i 0.459640 + 0.888105i \(0.347979\pi\)
−0.998942 + 0.0459931i \(0.985355\pi\)
\(8\) 0 0
\(9\) 211.135 76.8468i 2.60660 0.948726i
\(10\) 0 0
\(11\) −106.545 184.541i −0.880534 1.52513i −0.850748 0.525574i \(-0.823851\pi\)
−0.0297866 0.999556i \(-0.509483\pi\)
\(12\) 0 0
\(13\) 67.2882 + 11.8647i 0.398155 + 0.0702055i 0.369141 0.929373i \(-0.379652\pi\)
0.0290144 + 0.999579i \(0.490763\pi\)
\(14\) 0 0
\(15\) 225.861 269.170i 1.00383 1.19631i
\(16\) 0 0
\(17\) 86.5075 + 31.4861i 0.299334 + 0.108949i 0.487321 0.873223i \(-0.337974\pi\)
−0.187987 + 0.982171i \(0.560196\pi\)
\(18\) 0 0
\(19\) 360.844 + 10.5981i 0.999569 + 0.0293576i
\(20\) 0 0
\(21\) 316.044 868.322i 0.716652 1.96899i
\(22\) 0 0
\(23\) 152.628 + 128.070i 0.288522 + 0.242099i 0.775548 0.631289i \(-0.217474\pi\)
−0.487026 + 0.873388i \(0.661918\pi\)
\(24\) 0 0
\(25\) −38.3938 + 217.742i −0.0614301 + 0.348387i
\(26\) 0 0
\(27\) −2175.60 + 1256.08i −2.98436 + 1.72302i
\(28\) 0 0
\(29\) −125.853 345.779i −0.149647 0.411153i 0.842106 0.539312i \(-0.181315\pi\)
−0.991754 + 0.128159i \(0.959093\pi\)
\(30\) 0 0
\(31\) −715.213 412.929i −0.744238 0.429686i 0.0793699 0.996845i \(-0.474709\pi\)
−0.823608 + 0.567159i \(0.808043\pi\)
\(32\) 0 0
\(33\) 2394.78 + 2853.99i 2.19907 + 2.62075i
\(34\) 0 0
\(35\) −184.444 1046.03i −0.150567 0.853906i
\(36\) 0 0
\(37\) 2460.86i 1.79756i −0.438396 0.898782i \(-0.644453\pi\)
0.438396 0.898782i \(-0.355547\pi\)
\(38\) 0 0
\(39\) −1194.61 −0.785408
\(40\) 0 0
\(41\) 1695.95 299.042i 1.00890 0.177895i 0.355310 0.934748i \(-0.384375\pi\)
0.653585 + 0.756853i \(0.273264\pi\)
\(42\) 0 0
\(43\) −1341.89 + 1125.98i −0.725740 + 0.608968i −0.928967 0.370164i \(-0.879302\pi\)
0.203227 + 0.979132i \(0.434857\pi\)
\(44\) 0 0
\(45\) −2257.77 + 3910.58i −1.11495 + 1.93115i
\(46\) 0 0
\(47\) 1843.05 670.816i 0.834338 0.303674i 0.110700 0.993854i \(-0.464691\pi\)
0.723638 + 0.690180i \(0.242469\pi\)
\(48\) 0 0
\(49\) −196.146 339.734i −0.0816934 0.141497i
\(50\) 0 0
\(51\) −1585.10 279.496i −0.609419 0.107457i
\(52\) 0 0
\(53\) 1283.71 1529.86i 0.456998 0.544629i −0.487510 0.873118i \(-0.662095\pi\)
0.944508 + 0.328488i \(0.106539\pi\)
\(54\) 0 0
\(55\) 4024.24 + 1464.70i 1.33033 + 0.484199i
\(56\) 0 0
\(57\) −6245.28 + 913.057i −1.92222 + 0.281027i
\(58\) 0 0
\(59\) 836.628 2298.62i 0.240341 0.660332i −0.759609 0.650380i \(-0.774610\pi\)
0.999950 0.00995240i \(-0.00316800\pi\)
\(60\) 0 0
\(61\) −1062.83 891.820i −0.285630 0.239672i 0.488703 0.872450i \(-0.337470\pi\)
−0.774333 + 0.632778i \(0.781915\pi\)
\(62\) 0 0
\(63\) −2062.07 + 11694.6i −0.519543 + 2.94647i
\(64\) 0 0
\(65\) −1189.20 + 686.584i −0.281467 + 0.162505i
\(66\) 0 0
\(67\) 415.368 + 1141.22i 0.0925303 + 0.254225i 0.977321 0.211764i \(-0.0679209\pi\)
−0.884791 + 0.465989i \(0.845699\pi\)
\(68\) 0 0
\(69\) −3016.81 1741.76i −0.633651 0.365838i
\(70\) 0 0
\(71\) −5933.74 7071.56i −1.17710 1.40281i −0.896535 0.442972i \(-0.853924\pi\)
−0.280561 0.959836i \(-0.590520\pi\)
\(72\) 0 0
\(73\) −258.462 1465.81i −0.0485010 0.275063i 0.950907 0.309478i \(-0.100154\pi\)
−0.999408 + 0.0344152i \(0.989043\pi\)
\(74\) 0 0
\(75\) 3865.70i 0.687235i
\(76\) 0 0
\(77\) 11262.1 1.89950
\(78\) 0 0
\(79\) 8753.63 1543.50i 1.40260 0.247316i 0.579389 0.815051i \(-0.303291\pi\)
0.823211 + 0.567735i \(0.192180\pi\)
\(80\) 0 0
\(81\) 19704.9 16534.3i 3.00333 2.52009i
\(82\) 0 0
\(83\) 3718.48 6440.60i 0.539771 0.934911i −0.459145 0.888361i \(-0.651844\pi\)
0.998916 0.0465493i \(-0.0148225\pi\)
\(84\) 0 0
\(85\) −1738.56 + 632.784i −0.240631 + 0.0875826i
\(86\) 0 0
\(87\) 3216.77 + 5571.61i 0.424993 + 0.736110i
\(88\) 0 0
\(89\) −4040.87 712.515i −0.510147 0.0899526i −0.0873508 0.996178i \(-0.527840\pi\)
−0.422796 + 0.906225i \(0.638951\pi\)
\(90\) 0 0
\(91\) −2321.20 + 2766.30i −0.280305 + 0.334054i
\(92\) 0 0
\(93\) 13568.4 + 4938.48i 1.56878 + 0.570989i
\(94\) 0 0
\(95\) −5692.24 + 4498.32i −0.630720 + 0.498429i
\(96\) 0 0
\(97\) −2467.26 + 6778.74i −0.262224 + 0.720453i 0.736793 + 0.676118i \(0.236339\pi\)
−0.999017 + 0.0443351i \(0.985883\pi\)
\(98\) 0 0
\(99\) −36676.7 30775.4i −3.74213 3.14002i
\(100\) 0 0
\(101\) −1197.57 + 6791.76i −0.117397 + 0.665794i 0.868138 + 0.496323i \(0.165317\pi\)
−0.985535 + 0.169470i \(0.945794\pi\)
\(102\) 0 0
\(103\) 5231.12 3020.19i 0.493083 0.284682i −0.232770 0.972532i \(-0.574779\pi\)
0.725853 + 0.687850i \(0.241445\pi\)
\(104\) 0 0
\(105\) 6351.60 + 17450.9i 0.576109 + 1.58285i
\(106\) 0 0
\(107\) −3388.86 1956.56i −0.295996 0.170894i 0.344647 0.938733i \(-0.387999\pi\)
−0.640643 + 0.767839i \(0.721332\pi\)
\(108\) 0 0
\(109\) −9566.05 11400.4i −0.805155 0.959547i 0.194617 0.980879i \(-0.437654\pi\)
−0.999772 + 0.0213326i \(0.993209\pi\)
\(110\) 0 0
\(111\) 7471.28 + 42371.7i 0.606386 + 3.43898i
\(112\) 0 0
\(113\) 9372.48i 0.734002i −0.930220 0.367001i \(-0.880384\pi\)
0.930220 0.367001i \(-0.119616\pi\)
\(114\) 0 0
\(115\) −4004.21 −0.302776
\(116\) 0 0
\(117\) 15118.7 2665.83i 1.10444 0.194742i
\(118\) 0 0
\(119\) −3727.18 + 3127.47i −0.263200 + 0.220851i
\(120\) 0 0
\(121\) −15383.0 + 26644.2i −1.05068 + 1.81983i
\(122\) 0 0
\(123\) −28293.4 + 10298.0i −1.87014 + 0.680677i
\(124\) 0 0
\(125\) −8502.15 14726.2i −0.544137 0.942474i
\(126\) 0 0
\(127\) 7087.92 + 1249.79i 0.439452 + 0.0774872i 0.388997 0.921239i \(-0.372822\pi\)
0.0504549 + 0.998726i \(0.483933\pi\)
\(128\) 0 0
\(129\) 19686.5 23461.5i 1.18301 1.40986i
\(130\) 0 0
\(131\) 22572.5 + 8215.72i 1.31534 + 0.478744i 0.901961 0.431817i \(-0.142127\pi\)
0.413376 + 0.910560i \(0.364349\pi\)
\(132\) 0 0
\(133\) −10020.7 + 16236.1i −0.566492 + 0.917863i
\(134\) 0 0
\(135\) 17267.8 47442.8i 0.947478 2.60317i
\(136\) 0 0
\(137\) 5433.87 + 4559.56i 0.289513 + 0.242930i 0.775963 0.630778i \(-0.217264\pi\)
−0.486450 + 0.873708i \(0.661709\pi\)
\(138\) 0 0
\(139\) −3348.80 + 18992.0i −0.173324 + 0.982971i 0.766736 + 0.641962i \(0.221880\pi\)
−0.940060 + 0.341008i \(0.889232\pi\)
\(140\) 0 0
\(141\) −29697.5 + 17145.8i −1.49376 + 0.862423i
\(142\) 0 0
\(143\) −4979.68 13681.5i −0.243517 0.669057i
\(144\) 0 0
\(145\) 6404.43 + 3697.60i 0.304610 + 0.175867i
\(146\) 0 0
\(147\) 4408.73 + 5254.12i 0.204023 + 0.243145i
\(148\) 0 0
\(149\) −4717.58 26754.7i −0.212494 1.20511i −0.885203 0.465205i \(-0.845980\pi\)
0.672709 0.739907i \(-0.265131\pi\)
\(150\) 0 0
\(151\) 5119.66i 0.224537i 0.993678 + 0.112268i \(0.0358116\pi\)
−0.993678 + 0.112268i \(0.964188\pi\)
\(152\) 0 0
\(153\) 20684.3 0.883607
\(154\) 0 0
\(155\) 16345.3 2882.12i 0.680345 0.119963i
\(156\) 0 0
\(157\) −24723.3 + 20745.3i −1.00301 + 0.841628i −0.987399 0.158250i \(-0.949415\pi\)
−0.0156143 + 0.999878i \(0.504970\pi\)
\(158\) 0 0
\(159\) −17458.5 + 30238.9i −0.690576 + 1.19611i
\(160\) 0 0
\(161\) −9895.19 + 3601.56i −0.381744 + 0.138944i
\(162\) 0 0
\(163\) 16504.3 + 28586.3i 0.621186 + 1.07593i 0.989265 + 0.146132i \(0.0466824\pi\)
−0.368079 + 0.929795i \(0.619984\pi\)
\(164\) 0 0
\(165\) −73737.2 13001.9i −2.70844 0.477570i
\(166\) 0 0
\(167\) 28254.6 33672.6i 1.01311 1.20738i 0.0349797 0.999388i \(-0.488863\pi\)
0.978131 0.207990i \(-0.0666922\pi\)
\(168\) 0 0
\(169\) −22451.6 8171.72i −0.786094 0.286115i
\(170\) 0 0
\(171\) 77001.3 25492.1i 2.63333 0.871793i
\(172\) 0 0
\(173\) 5571.00 15306.2i 0.186141 0.511417i −0.811162 0.584822i \(-0.801164\pi\)
0.997302 + 0.0734051i \(0.0233866\pi\)
\(174\) 0 0
\(175\) −8951.65 7511.33i −0.292299 0.245268i
\(176\) 0 0
\(177\) −7426.56 + 42118.1i −0.237051 + 1.34438i
\(178\) 0 0
\(179\) 13361.2 7714.08i 0.417003 0.240757i −0.276792 0.960930i \(-0.589271\pi\)
0.693794 + 0.720173i \(0.255938\pi\)
\(180\) 0 0
\(181\) 2005.49 + 5510.03i 0.0612156 + 0.168189i 0.966530 0.256554i \(-0.0825870\pi\)
−0.905314 + 0.424742i \(0.860365\pi\)
\(182\) 0 0
\(183\) 21007.6 + 12128.8i 0.627300 + 0.362172i
\(184\) 0 0
\(185\) 31790.1 + 37885.9i 0.928855 + 1.10697i
\(186\) 0 0
\(187\) −3406.43 19318.8i −0.0974129 0.552456i
\(188\) 0 0
\(189\) 132772.i 3.71692i
\(190\) 0 0
\(191\) −25118.6 −0.688538 −0.344269 0.938871i \(-0.611873\pi\)
−0.344269 + 0.938871i \(0.611873\pi\)
\(192\) 0 0
\(193\) −14788.4 + 2607.59i −0.397014 + 0.0700043i −0.368591 0.929592i \(-0.620160\pi\)
−0.0284232 + 0.999596i \(0.509049\pi\)
\(194\) 0 0
\(195\) 18391.4 15432.2i 0.483666 0.405844i
\(196\) 0 0
\(197\) −9000.57 + 15589.4i −0.231920 + 0.401697i −0.958373 0.285519i \(-0.907834\pi\)
0.726453 + 0.687216i \(0.241167\pi\)
\(198\) 0 0
\(199\) 31587.8 11497.0i 0.797650 0.290321i 0.0891380 0.996019i \(-0.471589\pi\)
0.708513 + 0.705698i \(0.249367\pi\)
\(200\) 0 0
\(201\) −10616.7 18388.6i −0.262783 0.455153i
\(202\) 0 0
\(203\) 19152.4 + 3377.08i 0.464762 + 0.0819501i
\(204\) 0 0
\(205\) −22246.7 + 26512.6i −0.529369 + 0.630877i
\(206\) 0 0
\(207\) 42066.9 + 15311.1i 0.981747 + 0.357327i
\(208\) 0 0
\(209\) −36490.3 67719.7i −0.835381 1.55032i
\(210\) 0 0
\(211\) 16937.1 46534.2i 0.380428 1.04522i −0.590748 0.806856i \(-0.701167\pi\)
0.971176 0.238362i \(-0.0766106\pi\)
\(212\) 0 0
\(213\) 123638. + 103745.i 2.72517 + 2.28669i
\(214\) 0 0
\(215\) 6113.23 34669.8i 0.132249 0.750023i
\(216\) 0 0
\(217\) 37800.2 21823.9i 0.802739 0.463461i
\(218\) 0 0
\(219\) 8900.51 + 24453.9i 0.185578 + 0.509871i
\(220\) 0 0
\(221\) 5447.36 + 3145.03i 0.111533 + 0.0643933i
\(222\) 0 0
\(223\) −45306.7 53994.4i −0.911071 1.08577i −0.995997 0.0893853i \(-0.971510\pi\)
0.0849257 0.996387i \(-0.472935\pi\)
\(224\) 0 0
\(225\) 8626.51 + 48923.4i 0.170400 + 0.966388i
\(226\) 0 0
\(227\) 35715.4i 0.693112i 0.938029 + 0.346556i \(0.112649\pi\)
−0.938029 + 0.346556i \(0.887351\pi\)
\(228\) 0 0
\(229\) −5528.47 −0.105423 −0.0527113 0.998610i \(-0.516786\pi\)
−0.0527113 + 0.998610i \(0.516786\pi\)
\(230\) 0 0
\(231\) −193914. + 34192.2i −3.63400 + 0.640772i
\(232\) 0 0
\(233\) 32484.7 27257.9i 0.598367 0.502090i −0.292553 0.956249i \(-0.594505\pi\)
0.890920 + 0.454160i \(0.150060\pi\)
\(234\) 0 0
\(235\) −19708.7 + 34136.5i −0.356880 + 0.618134i
\(236\) 0 0
\(237\) −146036. + 53152.7i −2.59994 + 0.946300i
\(238\) 0 0
\(239\) −45449.9 78721.5i −0.795677 1.37815i −0.922408 0.386216i \(-0.873782\pi\)
0.126732 0.991937i \(-0.459551\pi\)
\(240\) 0 0
\(241\) 91025.9 + 16050.3i 1.56722 + 0.276344i 0.888789 0.458318i \(-0.151548\pi\)
0.678434 + 0.734661i \(0.262659\pi\)
\(242\) 0 0
\(243\) −158286. + 188638.i −2.68059 + 3.19460i
\(244\) 0 0
\(245\) 7408.51 + 2696.48i 0.123424 + 0.0449226i
\(246\) 0 0
\(247\) 24154.8 + 4994.45i 0.395923 + 0.0818641i
\(248\) 0 0
\(249\) −44471.8 + 122185.i −0.717275 + 1.97070i
\(250\) 0 0
\(251\) 14358.0 + 12047.8i 0.227901 + 0.191231i 0.749587 0.661906i \(-0.230252\pi\)
−0.521686 + 0.853138i \(0.674697\pi\)
\(252\) 0 0
\(253\) 7372.46 41811.3i 0.115178 0.653209i
\(254\) 0 0
\(255\) 28013.8 16173.8i 0.430816 0.248731i
\(256\) 0 0
\(257\) −33686.6 92553.2i −0.510025 1.40128i −0.881211 0.472723i \(-0.843271\pi\)
0.371187 0.928558i \(-0.378951\pi\)
\(258\) 0 0
\(259\) 112636. + 65030.3i 1.67910 + 0.969430i
\(260\) 0 0
\(261\) −53144.1 63334.6i −0.780142 0.929737i
\(262\) 0 0
\(263\) 11343.4 + 64331.7i 0.163996 + 0.930065i 0.950094 + 0.311964i \(0.100987\pi\)
−0.786098 + 0.618102i \(0.787902\pi\)
\(264\) 0 0
\(265\) 40136.1i 0.571536i
\(266\) 0 0
\(267\) 71739.9 1.00632
\(268\) 0 0
\(269\) 5882.67 1037.27i 0.0812961 0.0143347i −0.132852 0.991136i \(-0.542414\pi\)
0.214148 + 0.976801i \(0.431302\pi\)
\(270\) 0 0
\(271\) 97484.4 81799.1i 1.32738 1.11381i 0.342703 0.939444i \(-0.388658\pi\)
0.984681 0.174364i \(-0.0557868\pi\)
\(272\) 0 0
\(273\) 31568.4 54678.1i 0.423572 0.733649i
\(274\) 0 0
\(275\) 44273.0 16114.0i 0.585428 0.213078i
\(276\) 0 0
\(277\) −12794.5 22160.8i −0.166750 0.288819i 0.770526 0.637409i \(-0.219994\pi\)
−0.937275 + 0.348590i \(0.886661\pi\)
\(278\) 0 0
\(279\) −182739. 32221.8i −2.34759 0.413943i
\(280\) 0 0
\(281\) −34639.1 + 41281.2i −0.438686 + 0.522806i −0.939407 0.342803i \(-0.888624\pi\)
0.500721 + 0.865609i \(0.333068\pi\)
\(282\) 0 0
\(283\) −73639.8 26802.7i −0.919474 0.334661i −0.161445 0.986882i \(-0.551615\pi\)
−0.758029 + 0.652220i \(0.773838\pi\)
\(284\) 0 0
\(285\) 84353.3 94734.9i 1.03851 1.16633i
\(286\) 0 0
\(287\) −31129.5 + 85527.6i −0.377927 + 1.03835i
\(288\) 0 0
\(289\) −57488.6 48238.7i −0.688314 0.577564i
\(290\) 0 0
\(291\) 21901.3 124209.i 0.258633 1.46678i
\(292\) 0 0
\(293\) 7217.48 4167.01i 0.0840718 0.0485389i −0.457375 0.889274i \(-0.651210\pi\)
0.541447 + 0.840735i \(0.317877\pi\)
\(294\) 0 0
\(295\) 16813.9 + 46195.8i 0.193208 + 0.530834i
\(296\) 0 0
\(297\) 463597. + 267658.i 5.25567 + 3.03436i
\(298\) 0 0
\(299\) 8750.55 + 10428.5i 0.0978798 + 0.116649i
\(300\) 0 0
\(301\) −16076.5 91174.5i −0.177443 1.00633i
\(302\) 0 0
\(303\) 120578.i 1.31336i
\(304\) 0 0
\(305\) 27883.4 0.299741
\(306\) 0 0
\(307\) −70590.5 + 12447.0i −0.748979 + 0.132065i −0.535092 0.844793i \(-0.679723\pi\)
−0.213886 + 0.976859i \(0.568612\pi\)
\(308\) 0 0
\(309\) −80901.2 + 67884.1i −0.847301 + 0.710970i
\(310\) 0 0
\(311\) 45054.1 78036.0i 0.465815 0.806815i −0.533423 0.845849i \(-0.679095\pi\)
0.999238 + 0.0390334i \(0.0124279\pi\)
\(312\) 0 0
\(313\) −80691.9 + 29369.4i −0.823647 + 0.299783i −0.719249 0.694752i \(-0.755514\pi\)
−0.104398 + 0.994536i \(0.533292\pi\)
\(314\) 0 0
\(315\) −119327. 206680.i −1.20259 2.08295i
\(316\) 0 0
\(317\) −32268.5 5689.81i −0.321115 0.0566213i 0.0107673 0.999942i \(-0.496573\pi\)
−0.331882 + 0.943321i \(0.607684\pi\)
\(318\) 0 0
\(319\) −50401.4 + 60066.0i −0.495292 + 0.590266i
\(320\) 0 0
\(321\) 64290.4 + 23399.8i 0.623931 + 0.227092i
\(322\) 0 0
\(323\) 30882.0 + 12278.4i 0.296006 + 0.117689i
\(324\) 0 0
\(325\) −5166.90 + 14196.0i −0.0489174 + 0.134400i
\(326\) 0 0
\(327\) 199322. + 167251.i 1.86406 + 1.56413i
\(328\) 0 0
\(329\) −18000.3 + 102085.i −0.166298 + 0.943126i
\(330\) 0 0
\(331\) −39905.3 + 23039.4i −0.364229 + 0.210288i −0.670934 0.741517i \(-0.734107\pi\)
0.306705 + 0.951805i \(0.400773\pi\)
\(332\) 0 0
\(333\) −189110. 519574.i −1.70539 4.68553i
\(334\) 0 0
\(335\) −21137.3 12203.6i −0.188347 0.108742i
\(336\) 0 0
\(337\) −35283.6 42049.4i −0.310680 0.370254i 0.587998 0.808862i \(-0.299916\pi\)
−0.898678 + 0.438608i \(0.855472\pi\)
\(338\) 0 0
\(339\) 28455.2 + 161377.i 0.247607 + 1.40425i
\(340\) 0 0
\(341\) 175981.i 1.51341i
\(342\) 0 0
\(343\) −106163. −0.902374
\(344\) 0 0
\(345\) 68945.4 12156.9i 0.579251 0.102138i
\(346\) 0 0
\(347\) −46603.3 + 39104.8i −0.387041 + 0.324766i −0.815459 0.578814i \(-0.803516\pi\)
0.428418 + 0.903581i \(0.359071\pi\)
\(348\) 0 0
\(349\) −33423.1 + 57890.4i −0.274407 + 0.475287i −0.969985 0.243163i \(-0.921815\pi\)
0.695578 + 0.718450i \(0.255148\pi\)
\(350\) 0 0
\(351\) −161295. + 58706.7i −1.30921 + 0.476512i
\(352\) 0 0
\(353\) −16958.4 29372.8i −0.136093 0.235719i 0.789922 0.613208i \(-0.210121\pi\)
−0.926014 + 0.377488i \(0.876788\pi\)
\(354\) 0 0
\(355\) 182704. + 32215.7i 1.44975 + 0.255630i
\(356\) 0 0
\(357\) 54680.2 65165.4i 0.429036 0.511306i
\(358\) 0 0
\(359\) 188763. + 68704.0i 1.46463 + 0.533081i 0.946636 0.322305i \(-0.104458\pi\)
0.517991 + 0.855386i \(0.326680\pi\)
\(360\) 0 0
\(361\) 130096. + 7648.53i 0.998276 + 0.0586899i
\(362\) 0 0
\(363\) 183976. 505469.i 1.39620 3.83603i
\(364\) 0 0
\(365\) 22914.8 + 19227.8i 0.172001 + 0.144326i
\(366\) 0 0
\(367\) 26055.5 147768.i 0.193450 1.09711i −0.721160 0.692769i \(-0.756391\pi\)
0.914610 0.404338i \(-0.132498\pi\)
\(368\) 0 0
\(369\) 335094. 193467.i 2.46102 1.42087i
\(370\) 0 0
\(371\) 36100.1 + 99184.3i 0.262277 + 0.720601i
\(372\) 0 0
\(373\) −50978.3 29432.3i −0.366410 0.211547i 0.305479 0.952199i \(-0.401183\pi\)
−0.671889 + 0.740652i \(0.734517\pi\)
\(374\) 0 0
\(375\) 191101. + 227745.i 1.35894 + 1.61952i
\(376\) 0 0
\(377\) −4365.87 24760.1i −0.0307177 0.174209i
\(378\) 0 0
\(379\) 177467.i 1.23549i −0.786380 0.617743i \(-0.788047\pi\)
0.786380 0.617743i \(-0.211953\pi\)
\(380\) 0 0
\(381\) −125836. −0.866870
\(382\) 0 0
\(383\) −199006. + 35090.1i −1.35665 + 0.239214i −0.804214 0.594340i \(-0.797413\pi\)
−0.552438 + 0.833554i \(0.686302\pi\)
\(384\) 0 0
\(385\) −173384. + 145487.i −1.16974 + 0.981527i
\(386\) 0 0
\(387\) −196792. + 340854.i −1.31397 + 2.27587i
\(388\) 0 0
\(389\) 55021.1 20026.0i 0.363605 0.132341i −0.153756 0.988109i \(-0.549137\pi\)
0.517361 + 0.855768i \(0.326915\pi\)
\(390\) 0 0
\(391\) 9171.03 + 15884.7i 0.0599880 + 0.103902i
\(392\) 0 0
\(393\) −413602. 72929.2i −2.67792 0.472189i
\(394\) 0 0
\(395\) −114826. + 136844.i −0.735946 + 0.877067i
\(396\) 0 0
\(397\) 120480. + 43851.3i 0.764426 + 0.278228i 0.694663 0.719335i \(-0.255554\pi\)
0.0697628 + 0.997564i \(0.477776\pi\)
\(398\) 0 0
\(399\) 123245. 309980.i 0.774148 1.94710i
\(400\) 0 0
\(401\) −18921.1 + 51985.4i −0.117668 + 0.323290i −0.984519 0.175277i \(-0.943918\pi\)
0.866851 + 0.498567i \(0.166140\pi\)
\(402\) 0 0
\(403\) −43226.1 36271.0i −0.266156 0.223331i
\(404\) 0 0
\(405\) −89768.9 + 509105.i −0.547288 + 3.10382i
\(406\) 0 0
\(407\) −454130. + 262192.i −2.74152 + 1.58282i
\(408\) 0 0
\(409\) 49191.2 + 135152.i 0.294064 + 0.807933i 0.995462 + 0.0951633i \(0.0303373\pi\)
−0.701398 + 0.712770i \(0.747440\pi\)
\(410\) 0 0
\(411\) −107405. 62010.1i −0.635828 0.367095i
\(412\) 0 0
\(413\) 83101.0 + 99035.9i 0.487199 + 0.580621i
\(414\) 0 0
\(415\) 25953.9 + 147192.i 0.150697 + 0.854648i
\(416\) 0 0
\(417\) 337175.i 1.93903i
\(418\) 0 0
\(419\) −317161. −1.80656 −0.903278 0.429055i \(-0.858847\pi\)
−0.903278 + 0.429055i \(0.858847\pi\)
\(420\) 0 0
\(421\) 164298. 28970.2i 0.926976 0.163451i 0.310274 0.950647i \(-0.399579\pi\)
0.616703 + 0.787196i \(0.288468\pi\)
\(422\) 0 0
\(423\) 337582. 283265.i 1.88668 1.58312i
\(424\) 0 0
\(425\) −10177.2 + 17627.4i −0.0563444 + 0.0975914i
\(426\) 0 0
\(427\) 68905.4 25079.5i 0.377918 0.137551i
\(428\) 0 0
\(429\) 127279. + 220454.i 0.691579 + 1.19785i
\(430\) 0 0
\(431\) −134617. 23736.6i −0.724678 0.127780i −0.200872 0.979618i \(-0.564377\pi\)
−0.523806 + 0.851837i \(0.675488\pi\)
\(432\) 0 0
\(433\) −16853.3 + 20085.0i −0.0898895 + 0.107126i −0.809114 0.587651i \(-0.800053\pi\)
0.719225 + 0.694777i \(0.244497\pi\)
\(434\) 0 0
\(435\) −121499. 44222.0i −0.642087 0.233701i
\(436\) 0 0
\(437\) 53717.7 + 47831.0i 0.281290 + 0.250464i
\(438\) 0 0
\(439\) −54851.0 + 150702.i −0.284613 + 0.781969i 0.712183 + 0.701993i \(0.247706\pi\)
−0.996797 + 0.0799755i \(0.974516\pi\)
\(440\) 0 0
\(441\) −67520.7 56656.6i −0.347184 0.291322i
\(442\) 0 0
\(443\) −46580.2 + 264169.i −0.237353 + 1.34609i 0.600250 + 0.799813i \(0.295068\pi\)
−0.837602 + 0.546280i \(0.816043\pi\)
\(444\) 0 0
\(445\) 71415.2 41231.6i 0.360637 0.208214i
\(446\) 0 0
\(447\) 162457. + 446346.i 0.813060 + 2.23386i
\(448\) 0 0
\(449\) −25539.6 14745.3i −0.126684 0.0731409i 0.435319 0.900276i \(-0.356636\pi\)
−0.562003 + 0.827135i \(0.689969\pi\)
\(450\) 0 0
\(451\) −235880. 281111.i −1.15968 1.38205i
\(452\) 0 0
\(453\) −15543.5 88151.5i −0.0757447 0.429570i
\(454\) 0 0
\(455\) 72574.2i 0.350558i
\(456\) 0 0
\(457\) 257900. 1.23486 0.617431 0.786625i \(-0.288174\pi\)
0.617431 + 0.786625i \(0.288174\pi\)
\(458\) 0 0
\(459\) −227755. + 40159.3i −1.08104 + 0.190617i
\(460\) 0 0
\(461\) 54610.5 45823.6i 0.256965 0.215619i −0.505200 0.863003i \(-0.668581\pi\)
0.762165 + 0.647383i \(0.224137\pi\)
\(462\) 0 0
\(463\) 90318.2 156436.i 0.421321 0.729749i −0.574748 0.818331i \(-0.694900\pi\)
0.996069 + 0.0885810i \(0.0282332\pi\)
\(464\) 0 0
\(465\) −272687. + 99249.9i −1.26113 + 0.459012i
\(466\) 0 0
\(467\) 81.5564 + 141.260i 0.000373959 + 0.000647716i 0.866212 0.499676i \(-0.166548\pi\)
−0.865838 + 0.500324i \(0.833214\pi\)
\(468\) 0 0
\(469\) −63210.8 11145.8i −0.287373 0.0506716i
\(470\) 0 0
\(471\) 362708. 432258.i 1.63499 1.94850i
\(472\) 0 0
\(473\) 350761. + 127667.i 1.56779 + 0.570631i
\(474\) 0 0
\(475\) −16161.8 + 78164.1i −0.0716314 + 0.346434i
\(476\) 0 0
\(477\) 153470. 421656.i 0.674509 1.85320i
\(478\) 0 0
\(479\) −8694.79 7295.79i −0.0378955 0.0317981i 0.623643 0.781709i \(-0.285652\pi\)
−0.661539 + 0.749911i \(0.730096\pi\)
\(480\) 0 0
\(481\) 29197.5 165587.i 0.126199 0.715709i
\(482\) 0 0
\(483\) 159443. 92054.6i 0.683458 0.394595i
\(484\) 0 0
\(485\) −49585.1 136234.i −0.210799 0.579165i
\(486\) 0 0
\(487\) −126080. 72792.4i −0.531605 0.306922i 0.210065 0.977687i \(-0.432632\pi\)
−0.741670 + 0.670765i \(0.765966\pi\)
\(488\) 0 0
\(489\) −370964. 442098.i −1.55137 1.84884i
\(490\) 0 0
\(491\) −5635.06 31958.0i −0.0233741 0.132561i 0.970888 0.239535i \(-0.0769950\pi\)
−0.994262 + 0.106974i \(0.965884\pi\)
\(492\) 0 0
\(493\) 33875.1i 0.139376i
\(494\) 0 0
\(495\) 962215. 3.92701
\(496\) 0 0
\(497\) 480475. 84720.7i 1.94517 0.342986i
\(498\) 0 0
\(499\) 371345. 311595.i 1.49134 1.25138i 0.598406 0.801193i \(-0.295801\pi\)
0.892933 0.450189i \(-0.148643\pi\)
\(500\) 0 0
\(501\) −384264. + 665564.i −1.53093 + 2.65164i
\(502\) 0 0
\(503\) −66403.3 + 24168.8i −0.262454 + 0.0955255i −0.469896 0.882722i \(-0.655709\pi\)
0.207442 + 0.978247i \(0.433486\pi\)
\(504\) 0 0
\(505\) −69300.6 120032.i −0.271741 0.470668i
\(506\) 0 0
\(507\) 411387. + 72538.6i 1.60042 + 0.282198i
\(508\) 0 0
\(509\) 16680.1 19878.6i 0.0643818 0.0767272i −0.732892 0.680345i \(-0.761830\pi\)
0.797274 + 0.603617i \(0.206275\pi\)
\(510\) 0 0
\(511\) 73921.3 + 26905.2i 0.283092 + 0.103037i
\(512\) 0 0
\(513\) −798365. + 430193.i −3.03366 + 1.63467i
\(514\) 0 0
\(515\) −41519.5 + 114074.i −0.156544 + 0.430102i
\(516\) 0 0
\(517\) −320160. 268646.i −1.19781 1.00508i
\(518\) 0 0
\(519\) −49452.6 + 280459.i −0.183592 + 1.04120i
\(520\) 0 0
\(521\) −103676. + 59857.4i −0.381947 + 0.220517i −0.678665 0.734448i \(-0.737441\pi\)
0.296718 + 0.954965i \(0.404108\pi\)
\(522\) 0 0
\(523\) 131240. + 360578.i 0.479801 + 1.31824i 0.909663 + 0.415348i \(0.136340\pi\)
−0.429861 + 0.902895i \(0.641438\pi\)
\(524\) 0 0
\(525\) 176936. + 102154.i 0.641946 + 0.370627i
\(526\) 0 0
\(527\) −48869.8 58240.7i −0.175962 0.209703i
\(528\) 0 0
\(529\) −41700.5 236495.i −0.149015 0.845106i
\(530\) 0 0
\(531\) 549610.i 1.94924i
\(532\) 0 0
\(533\) 117666. 0.414186
\(534\) 0 0
\(535\) 77448.2 13656.2i 0.270585 0.0477114i
\(536\) 0 0
\(537\) −206636. + 173388.i −0.716567 + 0.601271i
\(538\) 0 0
\(539\) −41796.6 + 72393.8i −0.143868 + 0.249186i
\(540\) 0 0
\(541\) −420093. + 152901.i −1.43533 + 0.522417i −0.938453 0.345406i \(-0.887741\pi\)
−0.496874 + 0.867823i \(0.665519\pi\)
\(542\) 0 0
\(543\) −51259.6 88784.2i −0.173850 0.301117i
\(544\) 0 0
\(545\) 294546. + 51936.4i 0.991653 + 0.174855i
\(546\) 0 0
\(547\) 220234. 262465.i 0.736055 0.877196i −0.260030 0.965601i \(-0.583732\pi\)
0.996085 + 0.0884048i \(0.0281769\pi\)
\(548\) 0 0
\(549\) −292934. 106619.i −0.971907 0.353745i
\(550\) 0 0
\(551\) −41748.9 126106.i −0.137512 0.415369i
\(552\) 0 0
\(553\) −160674. + 441449.i −0.525407 + 1.44354i
\(554\) 0 0
\(555\) −662392. 555813.i −2.15045 1.80444i
\(556\) 0 0
\(557\) 78672.7 446175.i 0.253579 1.43812i −0.546115 0.837711i \(-0.683894\pi\)
0.799694 0.600408i \(-0.204995\pi\)
\(558\) 0 0
\(559\) −103653. + 59844.1i −0.331710 + 0.191513i
\(560\) 0 0
\(561\) 117305. + 322294.i 0.372728 + 1.02406i
\(562\) 0 0
\(563\) 100361. + 57943.2i 0.316626 + 0.182804i 0.649888 0.760030i \(-0.274816\pi\)
−0.333262 + 0.942834i \(0.608149\pi\)
\(564\) 0 0
\(565\) 121076. + 144293.i 0.379281 + 0.452010i
\(566\) 0 0
\(567\) 236074. + 1.33884e6i 0.734314 + 4.16450i
\(568\) 0 0
\(569\) 329980.i 1.01921i −0.860409 0.509604i \(-0.829792\pi\)
0.860409 0.509604i \(-0.170208\pi\)
\(570\) 0 0
\(571\) 240069. 0.736315 0.368158 0.929763i \(-0.379989\pi\)
0.368158 + 0.929763i \(0.379989\pi\)
\(572\) 0 0
\(573\) 432497. 76260.9i 1.31727 0.232270i
\(574\) 0 0
\(575\) −33746.2 + 28316.5i −0.102068 + 0.0856452i
\(576\) 0 0
\(577\) 132930. 230241.i 0.399273 0.691561i −0.594363 0.804197i \(-0.702596\pi\)
0.993636 + 0.112635i \(0.0359292\pi\)
\(578\) 0 0
\(579\) 246713. 89796.2i 0.735927 0.267856i
\(580\) 0 0
\(581\) 196528. + 340396.i 0.582199 + 1.00840i
\(582\) 0 0
\(583\) −419095. 73897.7i −1.23303 0.217417i
\(584\) 0 0
\(585\) −198320. + 236348.i −0.579501 + 0.690622i
\(586\) 0 0
\(587\) −43133.2 15699.2i −0.125180 0.0455619i 0.278670 0.960387i \(-0.410106\pi\)
−0.403851 + 0.914825i \(0.632328\pi\)
\(588\) 0 0
\(589\) −253704. 156583.i −0.731303 0.451350i
\(590\) 0 0
\(591\) 107644. 295749.i 0.308187 0.846736i
\(592\) 0 0
\(593\) −249153. 209064.i −0.708527 0.594525i 0.215659 0.976469i \(-0.430810\pi\)
−0.924185 + 0.381944i \(0.875255\pi\)
\(594\) 0 0
\(595\) 16979.8 96297.2i 0.0479621 0.272007i
\(596\) 0 0
\(597\) −508980. + 293860.i −1.42808 + 0.824501i
\(598\) 0 0
\(599\) −89235.2 245172.i −0.248704 0.683308i −0.999735 0.0230408i \(-0.992665\pi\)
0.751031 0.660267i \(-0.229557\pi\)
\(600\) 0 0
\(601\) 312353. + 180337.i 0.864763 + 0.499271i 0.865605 0.500728i \(-0.166934\pi\)
−0.000841159 1.00000i \(0.500268\pi\)
\(602\) 0 0
\(603\) 175397. + 209031.i 0.482379 + 0.574877i
\(604\) 0 0
\(605\) −107369. 608919.i −0.293338 1.66360i
\(606\) 0 0
\(607\) 700138.i 1.90023i 0.311898 + 0.950116i \(0.399035\pi\)
−0.311898 + 0.950116i \(0.600965\pi\)
\(608\) 0 0
\(609\) −340023. −0.916799
\(610\) 0 0
\(611\) 131975. 23270.7i 0.353515 0.0623343i
\(612\) 0 0
\(613\) 349037. 292877.i 0.928860 0.779406i −0.0467526 0.998907i \(-0.514887\pi\)
0.975612 + 0.219501i \(0.0704428\pi\)
\(614\) 0 0
\(615\) 302556. 524042.i 0.799937 1.38553i
\(616\) 0 0
\(617\) 262002. 95360.9i 0.688231 0.250496i 0.0258534 0.999666i \(-0.491770\pi\)
0.662378 + 0.749170i \(0.269547\pi\)
\(618\) 0 0
\(619\) 144826. + 250846.i 0.377977 + 0.654675i 0.990768 0.135570i \(-0.0432865\pi\)
−0.612791 + 0.790245i \(0.709953\pi\)
\(620\) 0 0
\(621\) −492924. 86915.9i −1.27819 0.225380i
\(622\) 0 0
\(623\) 139396. 166125.i 0.359148 0.428016i
\(624\) 0 0
\(625\) 191275. + 69618.6i 0.489665 + 0.178224i
\(626\) 0 0
\(627\) 833897. + 1.05523e6i 2.12118 + 2.68418i
\(628\) 0 0
\(629\) 77483.1 212883.i 0.195842 0.538071i
\(630\) 0 0
\(631\) 153557. + 128850.i 0.385666 + 0.323612i 0.814922 0.579571i \(-0.196780\pi\)
−0.429256 + 0.903183i \(0.641224\pi\)
\(632\) 0 0
\(633\) −150347. + 852658.i −0.375220 + 2.12798i
\(634\) 0 0
\(635\) −125266. + 72322.5i −0.310661 + 0.179360i
\(636\) 0 0
\(637\) −9167.45 25187.4i −0.0225928 0.0620731i
\(638\) 0 0
\(639\) −1.79625e6 1.03706e6i −4.39910 2.53982i
\(640\) 0 0
\(641\) 158129. + 188451.i 0.384854 + 0.458651i 0.923340 0.383983i \(-0.125448\pi\)
−0.538486 + 0.842634i \(0.681004\pi\)
\(642\) 0 0
\(643\) 246.266 + 1396.64i 0.000595638 + 0.00337803i 0.985104 0.171959i \(-0.0550096\pi\)
−0.984508 + 0.175337i \(0.943899\pi\)
\(644\) 0 0
\(645\) 615513.i 1.47951i
\(646\) 0 0
\(647\) −740265. −1.76839 −0.884196 0.467116i \(-0.845293\pi\)
−0.884196 + 0.467116i \(0.845293\pi\)
\(648\) 0 0
\(649\) −513327. + 90513.3i −1.21872 + 0.214893i
\(650\) 0 0
\(651\) −584594. + 490532.i −1.37941 + 1.15746i
\(652\) 0 0
\(653\) −232390. + 402512.i −0.544994 + 0.943957i 0.453614 + 0.891199i \(0.350135\pi\)
−0.998607 + 0.0527584i \(0.983199\pi\)
\(654\) 0 0
\(655\) −453645. + 165113.i −1.05739 + 0.384857i
\(656\) 0 0
\(657\) −167213. 289621.i −0.387382 0.670965i
\(658\) 0 0
\(659\) 570323. + 100563.i 1.31326 + 0.231563i 0.786044 0.618170i \(-0.212126\pi\)
0.527213 + 0.849733i \(0.323237\pi\)
\(660\) 0 0
\(661\) 307277. 366198.i 0.703278 0.838134i −0.289616 0.957143i \(-0.593527\pi\)
0.992893 + 0.119010i \(0.0379719\pi\)
\(662\) 0 0
\(663\) −103342. 37613.5i −0.235099 0.0855691i
\(664\) 0 0
\(665\) −55469.6 379410.i −0.125433 0.857958i
\(666\) 0 0
\(667\) 25075.3 68893.7i 0.0563629 0.154856i
\(668\) 0 0
\(669\) 944030. + 792135.i 2.10928 + 1.76989i
\(670\) 0 0
\(671\) −51338.3 + 291154.i −0.114024 + 0.646662i
\(672\) 0 0
\(673\) −174278. + 100620.i −0.384781 + 0.222153i −0.679896 0.733308i \(-0.737975\pi\)
0.295115 + 0.955462i \(0.404642\pi\)
\(674\) 0 0
\(675\) −189973. 521946.i −0.416950 1.14556i
\(676\) 0 0
\(677\) 113461. + 65506.5i 0.247553 + 0.142925i 0.618643 0.785672i \(-0.287683\pi\)
−0.371090 + 0.928597i \(0.621016\pi\)
\(678\) 0 0
\(679\) −245069. 292062.i −0.531557 0.633485i
\(680\) 0 0
\(681\) −108433. 614956.i −0.233813 1.32602i
\(682\) 0 0
\(683\) 322919.i 0.692232i 0.938192 + 0.346116i \(0.112500\pi\)
−0.938192 + 0.346116i \(0.887500\pi\)
\(684\) 0 0
\(685\) −142558. −0.303816
\(686\) 0 0
\(687\) 95190.5 16784.6i 0.201688 0.0355630i
\(688\) 0 0
\(689\) 104530. 87711.0i 0.220192 0.184763i
\(690\) 0 0
\(691\) −210030. + 363782.i −0.439870 + 0.761877i −0.997679 0.0680920i \(-0.978309\pi\)
0.557809 + 0.829969i \(0.311642\pi\)
\(692\) 0 0
\(693\) 2.37782e6 865457.i 4.95123 1.80210i
\(694\) 0 0
\(695\) −193787. 335649.i −0.401195 0.694890i
\(696\) 0 0
\(697\) 156128. + 27529.6i 0.321378 + 0.0566676i
\(698\) 0 0
\(699\) −476574. + 567958.i −0.975384 + 1.16242i
\(700\) 0 0
\(701\) 441203. + 160585.i 0.897847 + 0.326790i 0.749390 0.662129i \(-0.230347\pi\)
0.148457 + 0.988919i \(0.452569\pi\)
\(702\) 0 0
\(703\) 26080.5 887989.i 0.0527722 1.79679i
\(704\) 0 0
\(705\) 235709. 647606.i 0.474240 1.30296i
\(706\) 0 0
\(707\) −279218. 234291.i −0.558604 0.468724i
\(708\) 0 0
\(709\) −17147.2 + 97246.8i −0.0341116 + 0.193456i −0.997102 0.0760804i \(-0.975759\pi\)
0.962990 + 0.269537i \(0.0868706\pi\)
\(710\) 0 0
\(711\) 1.72958e6 998575.i 3.42139 1.97534i
\(712\) 0 0
\(713\) −56277.8 154622.i −0.110703 0.304153i
\(714\) 0 0
\(715\) 253406. + 146304.i 0.495683 + 0.286183i
\(716\) 0 0
\(717\) 1.02157e6 + 1.21746e6i 1.98714 + 2.36818i
\(718\) 0 0
\(719\) −138945. 787996.i −0.268773 1.52429i −0.758073 0.652170i \(-0.773859\pi\)
0.489300 0.872115i \(-0.337252\pi\)
\(720\) 0 0
\(721\) 319243.i 0.614117i
\(722\) 0 0
\(723\) −1.61603e6 −3.09153
\(724\) 0 0
\(725\) 80122.7 14127.8i 0.152433 0.0268781i
\(726\) 0 0
\(727\) −665887. + 558745.i −1.25989 + 1.05717i −0.264193 + 0.964470i \(0.585105\pi\)
−0.995694 + 0.0927005i \(0.970450\pi\)
\(728\) 0 0
\(729\) 1.11092e6 1.92416e6i 2.09038 3.62065i
\(730\) 0 0
\(731\) −151537. + 55154.8i −0.283585 + 0.103216i
\(732\) 0 0
\(733\) 26777.0 + 46379.1i 0.0498372 + 0.0863206i 0.889868 0.456218i \(-0.150796\pi\)
−0.840031 + 0.542539i \(0.817463\pi\)
\(734\) 0 0
\(735\) −135748. 23936.1i −0.251281 0.0443076i
\(736\) 0 0
\(737\) 166345. 198243.i 0.306250 0.364974i
\(738\) 0 0
\(739\) 392557. + 142879.i 0.718809 + 0.261625i 0.675420 0.737433i \(-0.263962\pi\)
0.0433888 + 0.999058i \(0.486185\pi\)
\(740\) 0 0
\(741\) −431067. 12660.6i −0.785070 0.0230577i
\(742\) 0 0
\(743\) −269615. + 740760.i −0.488389 + 1.34184i 0.413750 + 0.910391i \(0.364219\pi\)
−0.902139 + 0.431446i \(0.858003\pi\)
\(744\) 0 0
\(745\) 418253. + 350956.i 0.753575 + 0.632324i
\(746\) 0 0
\(747\) 290162. 1.64559e6i 0.519994 2.94904i
\(748\) 0 0
\(749\) 179107. 103407.i 0.319263 0.184327i
\(750\) 0 0
\(751\) −26385.3 72493.1i −0.0467824 0.128534i 0.914101 0.405486i \(-0.132898\pi\)
−0.960884 + 0.276953i \(0.910676\pi\)
\(752\) 0 0
\(753\) −283797. 163850.i −0.500515 0.288972i
\(754\) 0 0
\(755\) −66137.1 78819.1i −0.116025 0.138273i
\(756\) 0 0
\(757\) 8647.11 + 49040.2i 0.0150897 + 0.0855777i 0.991423 0.130695i \(-0.0417210\pi\)
−0.976333 + 0.216273i \(0.930610\pi\)
\(758\) 0 0
\(759\) 742299.i 1.28853i
\(760\) 0 0
\(761\) −146035. −0.252166 −0.126083 0.992020i \(-0.540241\pi\)
−0.126083 + 0.992020i \(0.540241\pi\)
\(762\) 0 0
\(763\) 774595. 136582.i 1.33053 0.234609i
\(764\) 0 0
\(765\) −318443. + 267206.i −0.544138 + 0.456586i
\(766\) 0 0
\(767\) 83567.7 144743.i 0.142052 0.246041i
\(768\) 0 0
\(769\) −730202. + 265772.i −1.23478 + 0.449424i −0.875233 0.483702i \(-0.839292\pi\)
−0.359549 + 0.933126i \(0.617070\pi\)
\(770\) 0 0
\(771\) 861019. + 1.49133e6i 1.44845 + 2.50879i
\(772\) 0 0
\(773\) 266882. + 47058.4i 0.446642 + 0.0787551i 0.392446 0.919775i \(-0.371629\pi\)
0.0541966 + 0.998530i \(0.482740\pi\)
\(774\) 0 0
\(775\) 117372. 139878.i 0.195416 0.232888i
\(776\) 0 0
\(777\) −2.13682e6 777740.i −3.53938 1.28823i
\(778\) 0 0
\(779\) 615145. 89933.9i 1.01368 0.148200i
\(780\) 0 0
\(781\) −672782. + 1.84845e6i −1.10299 + 3.03045i
\(782\) 0 0
\(783\) 708134. + 594195.i 1.15503 + 0.969183i
\(784\) 0 0
\(785\) 112631. 638763.i 0.182776 1.03657i
\(786\) 0 0
\(787\) −755514. + 436196.i −1.21981 + 0.704259i −0.964878 0.262700i \(-0.915387\pi\)
−0.254934 + 0.966958i \(0.582054\pi\)
\(788\) 0 0
\(789\) −390627. 1.07324e6i −0.627492 1.72402i
\(790\) 0 0
\(791\) 428986. + 247675.i 0.685631 + 0.395849i
\(792\) 0