Properties

Label 63.4.p.a.26.4
Level $63$
Weight $4$
Character 63.26
Analytic conductor $3.717$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.4
Root \(-0.648633 - 0.374489i\) of defining polynomial
Character \(\chi\) \(=\) 63.26
Dual form 63.4.p.a.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(-5.42768 + 9.40102i) q^{5} +(-18.2341 - 3.24321i) q^{7} +11.5635i q^{8} +O(q^{10})\) \(q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(-5.42768 + 9.40102i) q^{5} +(-18.2341 - 3.24321i) q^{7} +11.5635i q^{8} +(7.04115 - 4.06521i) q^{10} +(-44.9131 + 25.9306i) q^{11} -32.1880i q^{13} +(10.6127 + 8.93211i) q^{14} +(-25.4257 + 44.0387i) q^{16} +(-40.7324 - 70.5506i) q^{17} +(-0.0420661 - 0.0242869i) q^{19} +80.7534 q^{20} +38.8428 q^{22} +(77.3322 + 44.6478i) q^{23} +(3.58060 + 6.20178i) q^{25} +(-12.0540 + 20.8782i) q^{26} +(46.9279 + 129.534i) q^{28} -175.246i q^{29} +(186.238 - 107.524i) q^{31} +(113.098 - 65.2972i) q^{32} +61.0153i q^{34} +(129.458 - 153.816i) q^{35} +(-32.2729 + 55.8983i) q^{37} +(0.0181903 + 0.0315065i) q^{38} +(-108.708 - 62.7629i) q^{40} -411.485 q^{41} -234.771 q^{43} +(334.110 + 192.898i) q^{44} +(-33.4402 - 57.9201i) q^{46} +(-316.076 + 547.460i) q^{47} +(321.963 + 118.274i) q^{49} -5.36357i q^{50} +(-207.368 + 119.724i) q^{52} +(-230.049 + 132.819i) q^{53} -562.971i q^{55} +(37.5028 - 210.849i) q^{56} +(-65.6275 + 113.670i) q^{58} +(-175.530 - 304.026i) q^{59} +(-673.827 - 389.034i) q^{61} -161.067 q^{62} +309.000 q^{64} +(302.600 + 174.706i) q^{65} +(98.0043 + 169.748i) q^{67} +(-303.010 + 524.828i) q^{68} +(-141.573 + 51.2894i) q^{70} +142.632i q^{71} +(676.261 - 390.439i) q^{73} +(41.8665 - 24.1716i) q^{74} +0.361341i q^{76} +(903.046 - 327.157i) q^{77} +(-644.525 + 1116.35i) q^{79} +(-276.006 - 478.056i) q^{80} +(266.903 + 154.097i) q^{82} +235.123 q^{83} +884.330 q^{85} +(152.280 + 87.9191i) q^{86} +(-299.848 - 519.351i) q^{88} +(335.390 - 580.913i) q^{89} +(-104.392 + 586.919i) q^{91} -664.273i q^{92} +(410.035 - 236.734i) q^{94} +(0.456642 - 0.263642i) q^{95} +655.891i q^{97} +(-164.544 - 197.288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + 56q^{7} + O(q^{10}) \) \( 16q + 32q^{4} + 56q^{7} - 72q^{10} - 188q^{16} - 612q^{19} + 528q^{22} - 20q^{25} + 1036q^{28} + 1128q^{31} - 1196q^{37} - 3204q^{40} + 328q^{43} - 1392q^{46} + 784q^{49} + 4452q^{52} - 3372q^{58} - 1632q^{61} + 5432q^{64} + 308q^{67} + 3612q^{70} + 4068q^{73} - 2176q^{79} - 10188q^{82} - 4608q^{85} + 708q^{88} + 924q^{91} - 2916q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.648633 0.374489i −0.229326 0.132402i 0.380935 0.924602i \(-0.375602\pi\)
−0.610261 + 0.792200i \(0.708936\pi\)
\(3\) 0 0
\(4\) −3.71952 6.44239i −0.464940 0.805299i
\(5\) −5.42768 + 9.40102i −0.485466 + 0.840852i −0.999861 0.0167014i \(-0.994684\pi\)
0.514394 + 0.857554i \(0.328017\pi\)
\(6\) 0 0
\(7\) −18.2341 3.24321i −0.984548 0.175117i
\(8\) 11.5635i 0.511039i
\(9\) 0 0
\(10\) 7.04115 4.06521i 0.222661 0.128553i
\(11\) −44.9131 + 25.9306i −1.23107 + 0.710760i −0.967254 0.253812i \(-0.918315\pi\)
−0.263819 + 0.964572i \(0.584982\pi\)
\(12\) 0 0
\(13\) 32.1880i 0.686719i −0.939204 0.343360i \(-0.888435\pi\)
0.939204 0.343360i \(-0.111565\pi\)
\(14\) 10.6127 + 8.93211i 0.202597 + 0.170515i
\(15\) 0 0
\(16\) −25.4257 + 44.0387i −0.397277 + 0.688104i
\(17\) −40.7324 70.5506i −0.581121 1.00653i −0.995347 0.0963575i \(-0.969281\pi\)
0.414225 0.910174i \(-0.364053\pi\)
\(18\) 0 0
\(19\) −0.0420661 0.0242869i −0.000507927 0.000293252i 0.499746 0.866172i \(-0.333427\pi\)
−0.500254 + 0.865879i \(0.666760\pi\)
\(20\) 80.7534 0.902850
\(21\) 0 0
\(22\) 38.8428 0.376423
\(23\) 77.3322 + 44.6478i 0.701082 + 0.404770i 0.807750 0.589525i \(-0.200685\pi\)
−0.106668 + 0.994295i \(0.534018\pi\)
\(24\) 0 0
\(25\) 3.58060 + 6.20178i 0.0286448 + 0.0496142i
\(26\) −12.0540 + 20.8782i −0.0909228 + 0.157483i
\(27\) 0 0
\(28\) 46.9279 + 129.534i 0.316734 + 0.874274i
\(29\) 175.246i 1.12215i −0.827766 0.561074i \(-0.810388\pi\)
0.827766 0.561074i \(-0.189612\pi\)
\(30\) 0 0
\(31\) 186.238 107.524i 1.07901 0.622966i 0.148380 0.988930i \(-0.452594\pi\)
0.930629 + 0.365964i \(0.119261\pi\)
\(32\) 113.098 65.2972i 0.624785 0.360720i
\(33\) 0 0
\(34\) 61.0153i 0.307766i
\(35\) 129.458 153.816i 0.625212 0.742846i
\(36\) 0 0
\(37\) −32.2729 + 55.8983i −0.143395 + 0.248368i −0.928773 0.370649i \(-0.879135\pi\)
0.785378 + 0.619017i \(0.212469\pi\)
\(38\) 0.0181903 + 0.0315065i 7.76541e−5 + 0.000134501i
\(39\) 0 0
\(40\) −108.708 62.7629i −0.429708 0.248092i
\(41\) −411.485 −1.56740 −0.783698 0.621142i \(-0.786669\pi\)
−0.783698 + 0.621142i \(0.786669\pi\)
\(42\) 0 0
\(43\) −234.771 −0.832611 −0.416305 0.909225i \(-0.636675\pi\)
−0.416305 + 0.909225i \(0.636675\pi\)
\(44\) 334.110 + 192.898i 1.14475 + 0.660921i
\(45\) 0 0
\(46\) −33.4402 57.9201i −0.107184 0.185649i
\(47\) −316.076 + 547.460i −0.980946 + 1.69905i −0.322219 + 0.946665i \(0.604429\pi\)
−0.658726 + 0.752382i \(0.728905\pi\)
\(48\) 0 0
\(49\) 321.963 + 118.274i 0.938668 + 0.344822i
\(50\) 5.36357i 0.0151705i
\(51\) 0 0
\(52\) −207.368 + 119.724i −0.553014 + 0.319283i
\(53\) −230.049 + 132.819i −0.596220 + 0.344228i −0.767553 0.640985i \(-0.778526\pi\)
0.171333 + 0.985213i \(0.445193\pi\)
\(54\) 0 0
\(55\) 562.971i 1.38020i
\(56\) 37.5028 210.849i 0.0894915 0.503142i
\(57\) 0 0
\(58\) −65.6275 + 113.670i −0.148574 + 0.257338i
\(59\) −175.530 304.026i −0.387322 0.670862i 0.604766 0.796403i \(-0.293267\pi\)
−0.992088 + 0.125541i \(0.959933\pi\)
\(60\) 0 0
\(61\) −673.827 389.034i −1.41434 0.816569i −0.418546 0.908196i \(-0.637460\pi\)
−0.995793 + 0.0916261i \(0.970794\pi\)
\(62\) −161.067 −0.329927
\(63\) 0 0
\(64\) 309.000 0.603515
\(65\) 302.600 + 174.706i 0.577430 + 0.333379i
\(66\) 0 0
\(67\) 98.0043 + 169.748i 0.178703 + 0.309523i 0.941437 0.337190i \(-0.109476\pi\)
−0.762733 + 0.646713i \(0.776143\pi\)
\(68\) −303.010 + 524.828i −0.540373 + 0.935953i
\(69\) 0 0
\(70\) −141.573 + 51.2894i −0.241732 + 0.0875751i
\(71\) 142.632i 0.238412i 0.992870 + 0.119206i \(0.0380349\pi\)
−0.992870 + 0.119206i \(0.961965\pi\)
\(72\) 0 0
\(73\) 676.261 390.439i 1.08425 0.625993i 0.152211 0.988348i \(-0.451361\pi\)
0.932040 + 0.362355i \(0.118027\pi\)
\(74\) 41.8665 24.1716i 0.0657687 0.0379716i
\(75\) 0 0
\(76\) 0.361341i 0.000545378i
\(77\) 903.046 327.157i 1.33652 0.484196i
\(78\) 0 0
\(79\) −644.525 + 1116.35i −0.917908 + 1.58986i −0.115320 + 0.993328i \(0.536789\pi\)
−0.802588 + 0.596534i \(0.796544\pi\)
\(80\) −276.006 478.056i −0.385729 0.668103i
\(81\) 0 0
\(82\) 266.903 + 154.097i 0.359445 + 0.207526i
\(83\) 235.123 0.310940 0.155470 0.987841i \(-0.450311\pi\)
0.155470 + 0.987841i \(0.450311\pi\)
\(84\) 0 0
\(85\) 884.330 1.12846
\(86\) 152.280 + 87.9191i 0.190940 + 0.110239i
\(87\) 0 0
\(88\) −299.848 519.351i −0.363226 0.629125i
\(89\) 335.390 580.913i 0.399453 0.691872i −0.594206 0.804313i \(-0.702534\pi\)
0.993658 + 0.112441i \(0.0358669\pi\)
\(90\) 0 0
\(91\) −104.392 + 586.919i −0.120256 + 0.676108i
\(92\) 664.273i 0.752774i
\(93\) 0 0
\(94\) 410.035 236.734i 0.449914 0.259758i
\(95\) 0.456642 0.263642i 0.000493163 0.000284728i
\(96\) 0 0
\(97\) 655.891i 0.686553i 0.939234 + 0.343276i \(0.111537\pi\)
−0.939234 + 0.343276i \(0.888463\pi\)
\(98\) −164.544 197.288i −0.169606 0.203358i
\(99\) 0 0
\(100\) 26.6362 46.1352i 0.0266362 0.0461352i
\(101\) −581.618 1007.39i −0.573002 0.992468i −0.996256 0.0864572i \(-0.972445\pi\)
0.423254 0.906011i \(-0.360888\pi\)
\(102\) 0 0
\(103\) 22.8802 + 13.2099i 0.0218879 + 0.0126370i 0.510904 0.859638i \(-0.329311\pi\)
−0.489016 + 0.872275i \(0.662644\pi\)
\(104\) 372.206 0.350940
\(105\) 0 0
\(106\) 198.957 0.182305
\(107\) 1270.53 + 733.538i 1.14791 + 0.662746i 0.948377 0.317145i \(-0.102724\pi\)
0.199532 + 0.979891i \(0.436058\pi\)
\(108\) 0 0
\(109\) 67.5343 + 116.973i 0.0593450 + 0.102789i 0.894172 0.447724i \(-0.147765\pi\)
−0.834827 + 0.550513i \(0.814432\pi\)
\(110\) −210.826 + 365.162i −0.182741 + 0.316516i
\(111\) 0 0
\(112\) 606.442 720.544i 0.511637 0.607902i
\(113\) 288.471i 0.240151i 0.992765 + 0.120076i \(0.0383137\pi\)
−0.992765 + 0.120076i \(0.961686\pi\)
\(114\) 0 0
\(115\) −839.469 + 484.668i −0.680703 + 0.393004i
\(116\) −1129.00 + 651.829i −0.903665 + 0.521731i
\(117\) 0 0
\(118\) 262.935i 0.205129i
\(119\) 513.908 + 1418.53i 0.395881 + 1.09274i
\(120\) 0 0
\(121\) 679.288 1176.56i 0.510359 0.883969i
\(122\) 291.378 + 504.681i 0.216230 + 0.374522i
\(123\) 0 0
\(124\) −1385.43 799.877i −1.00335 0.579283i
\(125\) −1434.66 −1.02656
\(126\) 0 0
\(127\) −2269.80 −1.58592 −0.792961 0.609273i \(-0.791461\pi\)
−0.792961 + 0.609273i \(0.791461\pi\)
\(128\) −1105.21 638.095i −0.763187 0.440626i
\(129\) 0 0
\(130\) −130.851 226.641i −0.0882799 0.152905i
\(131\) −194.846 + 337.483i −0.129952 + 0.225084i −0.923658 0.383218i \(-0.874816\pi\)
0.793706 + 0.608302i \(0.208149\pi\)
\(132\) 0 0
\(133\) 0.688269 + 0.579277i 0.000448725 + 0.000377667i
\(134\) 146.806i 0.0946425i
\(135\) 0 0
\(136\) 815.811 471.009i 0.514377 0.296975i
\(137\) 1271.93 734.347i 0.793197 0.457953i −0.0478898 0.998853i \(-0.515250\pi\)
0.841087 + 0.540900i \(0.181916\pi\)
\(138\) 0 0
\(139\) 624.712i 0.381204i −0.981667 0.190602i \(-0.938956\pi\)
0.981667 0.190602i \(-0.0610440\pi\)
\(140\) −1472.46 261.900i −0.888899 0.158104i
\(141\) 0 0
\(142\) 53.4139 92.5156i 0.0315662 0.0546742i
\(143\) 834.654 + 1445.66i 0.488093 + 0.845401i
\(144\) 0 0
\(145\) 1647.49 + 951.177i 0.943561 + 0.544765i
\(146\) −584.860 −0.331530
\(147\) 0 0
\(148\) 480.158 0.266681
\(149\) −1387.25 800.930i −0.762739 0.440367i 0.0675396 0.997717i \(-0.478485\pi\)
−0.830278 + 0.557349i \(0.811818\pi\)
\(150\) 0 0
\(151\) −202.188 350.200i −0.108966 0.188734i 0.806386 0.591390i \(-0.201421\pi\)
−0.915351 + 0.402656i \(0.868087\pi\)
\(152\) 0.280841 0.486430i 0.000149863 0.000259570i
\(153\) 0 0
\(154\) −708.263 125.975i −0.370607 0.0659181i
\(155\) 2334.43i 1.20972i
\(156\) 0 0
\(157\) −2088.91 + 1206.04i −1.06187 + 0.613071i −0.925949 0.377649i \(-0.876733\pi\)
−0.135921 + 0.990720i \(0.543399\pi\)
\(158\) 836.120 482.734i 0.421001 0.243065i
\(159\) 0 0
\(160\) 1417.65i 0.700469i
\(161\) −1265.28 1064.92i −0.619367 0.521287i
\(162\) 0 0
\(163\) 472.684 818.712i 0.227138 0.393414i −0.729821 0.683638i \(-0.760397\pi\)
0.956959 + 0.290224i \(0.0937299\pi\)
\(164\) 1530.53 + 2650.95i 0.728744 + 1.26222i
\(165\) 0 0
\(166\) −152.508 88.0507i −0.0713069 0.0411690i
\(167\) 1271.18 0.589022 0.294511 0.955648i \(-0.404843\pi\)
0.294511 + 0.955648i \(0.404843\pi\)
\(168\) 0 0
\(169\) 1160.93 0.528417
\(170\) −573.606 331.172i −0.258786 0.149410i
\(171\) 0 0
\(172\) 873.235 + 1512.49i 0.387114 + 0.670501i
\(173\) 2217.49 3840.81i 0.974525 1.68793i 0.293032 0.956103i \(-0.405336\pi\)
0.681493 0.731825i \(-0.261331\pi\)
\(174\) 0 0
\(175\) −45.1752 124.696i −0.0195139 0.0538637i
\(176\) 2637.22i 1.12947i
\(177\) 0 0
\(178\) −435.090 + 251.200i −0.183210 + 0.105776i
\(179\) 941.835 543.769i 0.393274 0.227057i −0.290304 0.956935i \(-0.593756\pi\)
0.683578 + 0.729878i \(0.260423\pi\)
\(180\) 0 0
\(181\) 2916.08i 1.19752i −0.800930 0.598758i \(-0.795661\pi\)
0.800930 0.598758i \(-0.204339\pi\)
\(182\) 287.507 341.601i 0.117096 0.139127i
\(183\) 0 0
\(184\) −516.284 + 894.230i −0.206853 + 0.358280i
\(185\) −350.334 606.796i −0.139227 0.241149i
\(186\) 0 0
\(187\) 3658.84 + 2112.43i 1.43081 + 0.826076i
\(188\) 4702.60 1.82432
\(189\) 0 0
\(190\) −0.394924 −0.000150794
\(191\) −3948.97 2279.94i −1.49601 0.863719i −0.496017 0.868313i \(-0.665204\pi\)
−0.999989 + 0.00459364i \(0.998538\pi\)
\(192\) 0 0
\(193\) 1878.60 + 3253.83i 0.700645 + 1.21355i 0.968240 + 0.250022i \(0.0804378\pi\)
−0.267595 + 0.963531i \(0.586229\pi\)
\(194\) 245.624 425.433i 0.0909008 0.157445i
\(195\) 0 0
\(196\) −435.581 2514.13i −0.158739 0.916230i
\(197\) 2014.34i 0.728507i 0.931300 + 0.364253i \(0.118676\pi\)
−0.931300 + 0.364253i \(0.881324\pi\)
\(198\) 0 0
\(199\) 10.8355 6.25590i 0.00385986 0.00222849i −0.498069 0.867137i \(-0.665957\pi\)
0.501929 + 0.864909i \(0.332624\pi\)
\(200\) −71.7141 + 41.4042i −0.0253548 + 0.0146386i
\(201\) 0 0
\(202\) 871.238i 0.303466i
\(203\) −568.358 + 3195.44i −0.196507 + 1.10481i
\(204\) 0 0
\(205\) 2233.41 3868.38i 0.760918 1.31795i
\(206\) −9.89391 17.1367i −0.00334632 0.00579599i
\(207\) 0 0
\(208\) 1417.52 + 818.404i 0.472534 + 0.272818i
\(209\) 2.51909 0.000833727
\(210\) 0 0
\(211\) −2915.84 −0.951349 −0.475675 0.879621i \(-0.657796\pi\)
−0.475675 + 0.879621i \(0.657796\pi\)
\(212\) 1711.34 + 988.044i 0.554413 + 0.320090i
\(213\) 0 0
\(214\) −549.403 951.594i −0.175497 0.303970i
\(215\) 1274.26 2207.09i 0.404205 0.700103i
\(216\) 0 0
\(217\) −3744.60 + 1356.60i −1.17143 + 0.424387i
\(218\) 101.163i 0.0314295i
\(219\) 0 0
\(220\) −3626.88 + 2093.98i −1.11147 + 0.641710i
\(221\) −2270.88 + 1311.10i −0.691205 + 0.399067i
\(222\) 0 0
\(223\) 1097.87i 0.329681i 0.986320 + 0.164841i \(0.0527110\pi\)
−0.986320 + 0.164841i \(0.947289\pi\)
\(224\) −2274.01 + 823.834i −0.678298 + 0.245735i
\(225\) 0 0
\(226\) 108.029 187.112i 0.0317964 0.0550731i
\(227\) 250.297 + 433.527i 0.0731841 + 0.126759i 0.900295 0.435280i \(-0.143351\pi\)
−0.827111 + 0.562039i \(0.810017\pi\)
\(228\) 0 0
\(229\) −981.664 566.764i −0.283276 0.163549i 0.351630 0.936139i \(-0.385628\pi\)
−0.634906 + 0.772590i \(0.718961\pi\)
\(230\) 726.010 0.208138
\(231\) 0 0
\(232\) 2026.45 0.573461
\(233\) −2975.12 1717.68i −0.836508 0.482958i 0.0195676 0.999809i \(-0.493771\pi\)
−0.856076 + 0.516850i \(0.827104\pi\)
\(234\) 0 0
\(235\) −3431.12 5942.87i −0.952432 1.64966i
\(236\) −1305.77 + 2261.66i −0.360163 + 0.623821i
\(237\) 0 0
\(238\) 197.885 1112.56i 0.0538950 0.303010i
\(239\) 2213.97i 0.599203i 0.954064 + 0.299602i \(0.0968537\pi\)
−0.954064 + 0.299602i \(0.903146\pi\)
\(240\) 0 0
\(241\) 5154.55 2975.98i 1.37773 0.795435i 0.385847 0.922563i \(-0.373909\pi\)
0.991886 + 0.127128i \(0.0405760\pi\)
\(242\) −881.218 + 508.772i −0.234078 + 0.135145i
\(243\) 0 0
\(244\) 5788.08i 1.51862i
\(245\) −2859.41 + 2384.83i −0.745636 + 0.621882i
\(246\) 0 0
\(247\) −0.781746 + 1.35402i −0.000201382 + 0.000348803i
\(248\) 1243.36 + 2153.56i 0.318360 + 0.551415i
\(249\) 0 0
\(250\) 930.566 + 537.263i 0.235417 + 0.135918i
\(251\) −4889.86 −1.22966 −0.614831 0.788659i \(-0.710776\pi\)
−0.614831 + 0.788659i \(0.710776\pi\)
\(252\) 0 0
\(253\) −4630.97 −1.15078
\(254\) 1472.27 + 850.013i 0.363694 + 0.209979i
\(255\) 0 0
\(256\) −758.080 1313.03i −0.185078 0.320565i
\(257\) 1598.21 2768.18i 0.387913 0.671884i −0.604256 0.796790i \(-0.706530\pi\)
0.992169 + 0.124906i \(0.0398629\pi\)
\(258\) 0 0
\(259\) 769.756 914.586i 0.184673 0.219419i
\(260\) 2599.29i 0.620005i
\(261\) 0 0
\(262\) 252.767 145.935i 0.0596030 0.0344118i
\(263\) −648.189 + 374.232i −0.151973 + 0.0877419i −0.574058 0.818814i \(-0.694632\pi\)
0.422085 + 0.906556i \(0.361298\pi\)
\(264\) 0 0
\(265\) 2883.59i 0.668444i
\(266\) −0.229501 0.633487i −5.29008e−5 0.000146021i
\(267\) 0 0
\(268\) 729.057 1262.76i 0.166173 0.287819i
\(269\) 649.628 + 1125.19i 0.147244 + 0.255033i 0.930208 0.367033i \(-0.119627\pi\)
−0.782964 + 0.622067i \(0.786293\pi\)
\(270\) 0 0
\(271\) 72.3660 + 41.7806i 0.0162211 + 0.00936527i 0.508089 0.861305i \(-0.330352\pi\)
−0.491868 + 0.870670i \(0.663686\pi\)
\(272\) 4142.61 0.923465
\(273\) 0 0
\(274\) −1100.02 −0.242535
\(275\) −321.631 185.694i −0.0705276 0.0407191i
\(276\) 0 0
\(277\) 2320.93 + 4019.97i 0.503434 + 0.871973i 0.999992 + 0.00396948i \(0.00126353\pi\)
−0.496558 + 0.868003i \(0.665403\pi\)
\(278\) −233.948 + 405.209i −0.0504721 + 0.0874202i
\(279\) 0 0
\(280\) 1778.65 + 1496.99i 0.379623 + 0.319508i
\(281\) 179.289i 0.0380622i −0.999819 0.0190311i \(-0.993942\pi\)
0.999819 0.0190311i \(-0.00605816\pi\)
\(282\) 0 0
\(283\) −3506.14 + 2024.27i −0.736461 + 0.425196i −0.820781 0.571243i \(-0.806461\pi\)
0.0843205 + 0.996439i \(0.473128\pi\)
\(284\) 918.889 530.521i 0.191993 0.110847i
\(285\) 0 0
\(286\) 1250.27i 0.258497i
\(287\) 7503.06 + 1334.53i 1.54318 + 0.274477i
\(288\) 0 0
\(289\) −861.761 + 1492.61i −0.175404 + 0.303809i
\(290\) −712.410 1233.93i −0.144256 0.249858i
\(291\) 0 0
\(292\) −5030.73 2904.49i −1.00822 0.582098i
\(293\) −3389.52 −0.675828 −0.337914 0.941177i \(-0.609721\pi\)
−0.337914 + 0.941177i \(0.609721\pi\)
\(294\) 0 0
\(295\) 3810.88 0.752128
\(296\) −646.379 373.187i −0.126926 0.0732806i
\(297\) 0 0
\(298\) 599.878 + 1039.02i 0.116611 + 0.201976i
\(299\) 1437.12 2489.17i 0.277963 0.481446i
\(300\) 0 0
\(301\) 4280.84 + 761.412i 0.819745 + 0.145804i
\(302\) 302.868i 0.0577089i
\(303\) 0 0
\(304\) 2.13912 1.23502i 0.000403576 0.000233005i
\(305\) 7314.63 4223.11i 1.37323 0.792834i
\(306\) 0 0
\(307\) 2014.64i 0.374534i 0.982309 + 0.187267i \(0.0599629\pi\)
−0.982309 + 0.187267i \(0.940037\pi\)
\(308\) −5466.57 4600.91i −1.01132 0.851173i
\(309\) 0 0
\(310\) 874.218 1514.19i 0.160169 0.277420i
\(311\) −2922.01 5061.07i −0.532772 0.922788i −0.999268 0.0382648i \(-0.987817\pi\)
0.466496 0.884524i \(-0.345516\pi\)
\(312\) 0 0
\(313\) 2121.29 + 1224.73i 0.383074 + 0.221168i 0.679155 0.733995i \(-0.262346\pi\)
−0.296081 + 0.955163i \(0.595680\pi\)
\(314\) 1806.59 0.324686
\(315\) 0 0
\(316\) 9589.28 1.70709
\(317\) 5303.24 + 3061.83i 0.939621 + 0.542490i 0.889842 0.456270i \(-0.150815\pi\)
0.0497796 + 0.998760i \(0.484148\pi\)
\(318\) 0 0
\(319\) 4544.22 + 7870.82i 0.797578 + 1.38145i
\(320\) −1677.15 + 2904.91i −0.292986 + 0.507467i
\(321\) 0 0
\(322\) 421.904 + 1164.57i 0.0730179 + 0.201550i
\(323\) 3.95705i 0.000681660i
\(324\) 0 0
\(325\) 199.623 115.252i 0.0340710 0.0196709i
\(326\) −613.197 + 354.029i −0.104177 + 0.0601468i
\(327\) 0 0
\(328\) 4758.20i 0.801000i
\(329\) 7538.88 8957.33i 1.26332 1.50101i
\(330\) 0 0
\(331\) −3798.52 + 6579.23i −0.630772 + 1.09253i 0.356622 + 0.934249i \(0.383928\pi\)
−0.987394 + 0.158280i \(0.949405\pi\)
\(332\) −874.542 1514.75i −0.144568 0.250400i
\(333\) 0 0
\(334\) −824.528 476.042i −0.135078 0.0779875i
\(335\) −2127.74 −0.347018
\(336\) 0 0
\(337\) −3863.22 −0.624460 −0.312230 0.950007i \(-0.601076\pi\)
−0.312230 + 0.950007i \(0.601076\pi\)
\(338\) −753.019 434.756i −0.121180 0.0699633i
\(339\) 0 0
\(340\) −3289.28 5697.20i −0.524666 0.908747i
\(341\) −5576.34 + 9658.50i −0.885559 + 1.53383i
\(342\) 0 0
\(343\) −5487.11 3200.81i −0.863779 0.503870i
\(344\) 2714.77i 0.425496i
\(345\) 0 0
\(346\) −2876.68 + 1660.85i −0.446969 + 0.258058i
\(347\) −1579.98 + 912.204i −0.244432 + 0.141123i −0.617212 0.786797i \(-0.711738\pi\)
0.372780 + 0.927920i \(0.378405\pi\)
\(348\) 0 0
\(349\) 1537.52i 0.235822i −0.993024 0.117911i \(-0.962380\pi\)
0.993024 0.117911i \(-0.0376197\pi\)
\(350\) −17.3952 + 97.7998i −0.00265660 + 0.0149360i
\(351\) 0 0
\(352\) −3386.39 + 5865.40i −0.512770 + 0.888144i
\(353\) 2963.66 + 5133.22i 0.446855 + 0.773976i 0.998179 0.0603149i \(-0.0192105\pi\)
−0.551324 + 0.834291i \(0.685877\pi\)
\(354\) 0 0
\(355\) −1340.88 774.159i −0.200469 0.115741i
\(356\) −4989.96 −0.742885
\(357\) 0 0
\(358\) −814.541 −0.120251
\(359\) 4191.12 + 2419.74i 0.616153 + 0.355736i 0.775370 0.631508i \(-0.217564\pi\)
−0.159217 + 0.987244i \(0.550897\pi\)
\(360\) 0 0
\(361\) −3429.50 5940.07i −0.500000 0.866025i
\(362\) −1092.04 + 1891.46i −0.158553 + 0.274622i
\(363\) 0 0
\(364\) 4169.45 1510.52i 0.600381 0.217507i
\(365\) 8476.72i 1.21559i
\(366\) 0 0
\(367\) 9967.21 5754.57i 1.41767 0.818491i 0.421575 0.906794i \(-0.361478\pi\)
0.996094 + 0.0883026i \(0.0281442\pi\)
\(368\) −3932.46 + 2270.41i −0.557048 + 0.321612i
\(369\) 0 0
\(370\) 524.784i 0.0737357i
\(371\) 4625.49 1675.73i 0.647287 0.234501i
\(372\) 0 0
\(373\) −93.7487 + 162.378i −0.0130137 + 0.0225405i −0.872459 0.488687i \(-0.837476\pi\)
0.859445 + 0.511228i \(0.170809\pi\)
\(374\) −1582.16 2740.38i −0.218748 0.378882i
\(375\) 0 0
\(376\) −6330.54 3654.94i −0.868279 0.501301i
\(377\) −5640.81 −0.770601
\(378\) 0 0
\(379\) 3515.82 0.476506 0.238253 0.971203i \(-0.423425\pi\)
0.238253 + 0.971203i \(0.423425\pi\)
\(380\) −3.39698 1.96125i −0.000458582 0.000264763i
\(381\) 0 0
\(382\) 1707.62 + 2957.69i 0.228716 + 0.396147i
\(383\) −1014.69 + 1757.49i −0.135374 + 0.234474i −0.925740 0.378160i \(-0.876557\pi\)
0.790366 + 0.612634i \(0.209890\pi\)
\(384\) 0 0
\(385\) −1825.83 + 10265.3i −0.241696 + 1.35887i
\(386\) 2814.06i 0.371067i
\(387\) 0 0
\(388\) 4225.51 2439.60i 0.552880 0.319206i
\(389\) −5577.15 + 3219.97i −0.726923 + 0.419689i −0.817295 0.576219i \(-0.804528\pi\)
0.0903727 + 0.995908i \(0.471194\pi\)
\(390\) 0 0
\(391\) 7274.45i 0.940882i
\(392\) −1367.66 + 3723.02i −0.176217 + 0.479696i
\(393\) 0 0
\(394\) 754.348 1306.57i 0.0964555 0.167066i
\(395\) −6996.55 12118.4i −0.891227 1.54365i
\(396\) 0 0
\(397\) −8369.80 4832.31i −1.05811 0.610898i −0.133199 0.991089i \(-0.542525\pi\)
−0.924908 + 0.380191i \(0.875858\pi\)
\(398\) −9.37106 −0.00118022
\(399\) 0 0
\(400\) −364.157 −0.0455197
\(401\) 10186.9 + 5881.40i 1.26860 + 0.732426i 0.974723 0.223417i \(-0.0717212\pi\)
0.293876 + 0.955843i \(0.405055\pi\)
\(402\) 0 0
\(403\) −3461.00 5994.62i −0.427803 0.740976i
\(404\) −4326.68 + 7494.03i −0.532823 + 0.922876i
\(405\) 0 0
\(406\) 1565.31 1859.83i 0.191343 0.227344i
\(407\) 3347.42i 0.407679i
\(408\) 0 0
\(409\) −4565.71 + 2636.01i −0.551980 + 0.318686i −0.749920 0.661528i \(-0.769908\pi\)
0.197940 + 0.980214i \(0.436575\pi\)
\(410\) −2897.33 + 1672.77i −0.348997 + 0.201494i
\(411\) 0 0
\(412\) 196.538i 0.0235017i
\(413\) 2214.60 + 6112.92i 0.263858 + 0.728322i
\(414\) 0 0
\(415\) −1276.17 + 2210.39i −0.150951 + 0.261455i
\(416\) −2101.79 3640.40i −0.247713 0.429052i
\(417\) 0 0
\(418\) −1.63396 0.943369i −0.000191196 0.000110387i
\(419\) 5103.18 0.595003 0.297502 0.954721i \(-0.403847\pi\)
0.297502 + 0.954721i \(0.403847\pi\)
\(420\) 0 0
\(421\) −8395.31 −0.971882 −0.485941 0.873992i \(-0.661523\pi\)
−0.485941 + 0.873992i \(0.661523\pi\)
\(422\) 1891.31 + 1091.95i 0.218170 + 0.125960i
\(423\) 0 0
\(424\) −1535.85 2660.17i −0.175914 0.304691i
\(425\) 291.693 505.227i 0.0332922 0.0576638i
\(426\) 0 0
\(427\) 11024.9 + 9279.04i 1.24949 + 1.05163i
\(428\) 10913.6i 1.23255i
\(429\) 0 0
\(430\) −1653.06 + 954.394i −0.185390 + 0.107035i
\(431\) −1808.68 + 1044.24i −0.202137 + 0.116704i −0.597652 0.801756i \(-0.703900\pi\)
0.395515 + 0.918460i \(0.370566\pi\)
\(432\) 0 0
\(433\) 11495.3i 1.27582i 0.770111 + 0.637910i \(0.220201\pi\)
−0.770111 + 0.637910i \(0.779799\pi\)
\(434\) 2936.90 + 522.373i 0.324829 + 0.0577758i
\(435\) 0 0
\(436\) 502.390 870.164i 0.0551837 0.0955810i
\(437\) −2.16871 3.75631i −0.000237399 0.000411187i
\(438\) 0 0
\(439\) 3682.95 + 2126.35i 0.400404 + 0.231173i 0.686658 0.726980i \(-0.259077\pi\)
−0.286254 + 0.958154i \(0.592410\pi\)
\(440\) 6509.91 0.705336
\(441\) 0 0
\(442\) 1963.96 0.211349
\(443\) 2862.03 + 1652.40i 0.306951 + 0.177218i 0.645561 0.763708i \(-0.276623\pi\)
−0.338610 + 0.940927i \(0.609957\pi\)
\(444\) 0 0
\(445\) 3640.78 + 6306.02i 0.387842 + 0.671761i
\(446\) 411.140 712.116i 0.0436503 0.0756046i
\(447\) 0 0
\(448\) −5634.32 1002.15i −0.594189 0.105686i
\(449\) 6952.63i 0.730768i −0.930857 0.365384i \(-0.880938\pi\)
0.930857 0.365384i \(-0.119062\pi\)
\(450\) 0 0
\(451\) 18481.1 10670.0i 1.92958 1.11404i
\(452\) 1858.45 1072.97i 0.193394 0.111656i
\(453\) 0 0
\(454\) 374.933i 0.0387588i
\(455\) −4951.02 4167.00i −0.510127 0.429345i
\(456\) 0 0
\(457\) −4870.57 + 8436.08i −0.498546 + 0.863508i −0.999999 0.00167767i \(-0.999466\pi\)
0.501452 + 0.865185i \(0.332799\pi\)
\(458\) 424.493 + 735.244i 0.0433085 + 0.0750124i
\(459\) 0 0
\(460\) 6244.84 + 3605.46i 0.632972 + 0.365447i
\(461\) −5563.15 −0.562043 −0.281021 0.959702i \(-0.590673\pi\)
−0.281021 + 0.959702i \(0.590673\pi\)
\(462\) 0 0
\(463\) 4114.02 0.412948 0.206474 0.978452i \(-0.433801\pi\)
0.206474 + 0.978452i \(0.433801\pi\)
\(464\) 7717.59 + 4455.75i 0.772155 + 0.445804i
\(465\) 0 0
\(466\) 1286.51 + 2228.29i 0.127889 + 0.221510i
\(467\) 3030.79 5249.49i 0.300318 0.520166i −0.675890 0.737002i \(-0.736241\pi\)
0.976208 + 0.216837i \(0.0695739\pi\)
\(468\) 0 0
\(469\) −1236.49 3413.05i −0.121739 0.336034i
\(470\) 5139.66i 0.504415i
\(471\) 0 0
\(472\) 3515.60 2029.73i 0.342836 0.197937i
\(473\) 10544.3 6087.75i 1.02500 0.591787i
\(474\) 0 0
\(475\) 0.347846i 3.36005e-5i
\(476\) 7227.23 8587.04i 0.695924 0.826862i
\(477\) 0 0
\(478\) 829.105 1436.05i 0.0793355 0.137413i
\(479\) −4123.33 7141.82i −0.393319 0.681248i 0.599566 0.800325i \(-0.295340\pi\)
−0.992885 + 0.119077i \(0.962006\pi\)
\(480\) 0 0
\(481\) 1799.25 + 1038.80i 0.170559 + 0.0984724i
\(482\) −4457.88 −0.421268
\(483\) 0 0
\(484\) −10106.5 −0.949145
\(485\) −6166.04 3559.96i −0.577290 0.333298i
\(486\) 0 0
\(487\) −5872.08 10170.7i −0.546385 0.946366i −0.998518 0.0544159i \(-0.982670\pi\)
0.452134 0.891950i \(-0.350663\pi\)
\(488\) 4498.59 7791.79i 0.417298 0.722782i
\(489\) 0 0
\(490\) 2747.80 476.064i 0.253332 0.0438905i
\(491\) 6008.34i 0.552246i −0.961122 0.276123i \(-0.910950\pi\)
0.961122 0.276123i \(-0.0890497\pi\)
\(492\) 0 0
\(493\) −12363.7 + 7138.18i −1.12948 + 0.652104i
\(494\) 1.01413 0.585510i 9.23643e−5 5.33266e-5i
\(495\) 0 0
\(496\) 10935.5i 0.989961i
\(497\) 462.584 2600.76i 0.0417500 0.234728i
\(498\) 0 0
\(499\) 6824.93 11821.1i 0.612276 1.06049i −0.378580 0.925569i \(-0.623587\pi\)
0.990856 0.134925i \(-0.0430792\pi\)
\(500\) 5336.23 + 9242.62i 0.477287 + 0.826685i
\(501\) 0 0
\(502\) 3171.72 + 1831.20i 0.281994 + 0.162809i
\(503\) 4862.69 0.431047 0.215524 0.976499i \(-0.430854\pi\)
0.215524 + 0.976499i \(0.430854\pi\)
\(504\) 0 0
\(505\) 12627.4 1.11269
\(506\) 3003.80 + 1734.25i 0.263904 + 0.152365i
\(507\) 0 0
\(508\) 8442.55 + 14622.9i 0.737358 + 1.27714i
\(509\) −8861.33 + 15348.3i −0.771653 + 1.33654i 0.165003 + 0.986293i \(0.447237\pi\)
−0.936656 + 0.350250i \(0.886097\pi\)
\(510\) 0 0
\(511\) −13597.3 + 4926.05i −1.17712 + 0.426449i
\(512\) 11345.1i 0.979271i
\(513\) 0 0
\(514\) −2073.30 + 1197.02i −0.177917 + 0.102721i
\(515\) −248.373 + 143.398i −0.0212517 + 0.0122697i
\(516\) 0 0
\(517\) 32784.1i 2.78887i
\(518\) −841.791 + 304.966i −0.0714019 + 0.0258676i
\(519\) 0 0
\(520\) −2020.21 + 3499.11i −0.170370 + 0.295089i
\(521\) 6877.95 + 11913.0i 0.578366 + 1.00176i 0.995667 + 0.0929909i \(0.0296427\pi\)
−0.417301 + 0.908768i \(0.637024\pi\)
\(522\) 0 0
\(523\) 1136.17 + 655.971i 0.0949932 + 0.0548443i 0.546744 0.837300i \(-0.315867\pi\)
−0.451751 + 0.892144i \(0.649200\pi\)
\(524\) 2898.93 0.241680
\(525\) 0 0
\(526\) 560.582 0.0464687
\(527\) −15171.8 8759.46i −1.25407 0.724038i
\(528\) 0 0
\(529\) −2096.65 3631.50i −0.172323 0.298472i
\(530\) −1079.87 + 1870.39i −0.0885031 + 0.153292i
\(531\) 0 0
\(532\) 1.17191 6.58873i 9.55048e−5 0.000536950i
\(533\) 13244.9i 1.07636i
\(534\) 0 0
\(535\) −13792.0 + 7962.82i −1.11454 + 0.643482i
\(536\) −1962.88 + 1133.27i −0.158178 + 0.0913243i
\(537\) 0 0
\(538\) 973.114i 0.0779812i
\(539\) −17527.3 + 3036.65i −1.40065 + 0.242667i
\(540\) 0 0
\(541\) −597.954 + 1035.69i −0.0475195 + 0.0823061i −0.888807 0.458282i \(-0.848465\pi\)
0.841287 + 0.540588i \(0.181798\pi\)
\(542\) −31.2927 54.2005i −0.00247996 0.00429541i
\(543\) 0 0
\(544\) −9213.52 5319.43i −0.726152 0.419244i
\(545\) −1466.22 −0.115240
\(546\) 0 0
\(547\) −6178.59 −0.482957 −0.241478 0.970406i \(-0.577632\pi\)
−0.241478 + 0.970406i \(0.577632\pi\)
\(548\) −9461.90 5462.83i −0.737577 0.425841i
\(549\) 0 0
\(550\) 139.080 + 240.894i 0.0107826 + 0.0186759i
\(551\) −4.25617 + 7.37189i −0.000329072 + 0.000569970i
\(552\) 0 0
\(553\) 15372.9 18265.3i 1.18214 1.40455i
\(554\) 3476.65i 0.266622i
\(555\) 0 0
\(556\) −4024.64 + 2323.63i −0.306983 + 0.177237i
\(557\) −2906.56 + 1678.10i −0.221104 + 0.127654i −0.606461 0.795113i \(-0.707411\pi\)
0.385357 + 0.922767i \(0.374078\pi\)
\(558\) 0 0
\(559\) 7556.82i 0.571770i
\(560\) 3482.27 + 9612.05i 0.262773 + 0.725327i
\(561\) 0 0
\(562\) −67.1417 + 116.293i −0.00503950 + 0.00872868i
\(563\) 1792.64 + 3104.94i 0.134193 + 0.232429i 0.925289 0.379263i \(-0.123822\pi\)
−0.791096 + 0.611692i \(0.790489\pi\)
\(564\) 0 0
\(565\) −2711.92 1565.73i −0.201932 0.116585i
\(566\) 3032.26 0.225187
\(567\) 0 0
\(568\) −1649.32 −0.121838
\(569\) −15835.9 9142.84i −1.16674 0.673617i −0.213829 0.976871i \(-0.568593\pi\)
−0.952910 + 0.303254i \(0.901927\pi\)
\(570\) 0 0
\(571\) 8181.51 + 14170.8i 0.599624 + 1.03858i 0.992876 + 0.119149i \(0.0380165\pi\)
−0.393252 + 0.919431i \(0.628650\pi\)
\(572\) 6209.02 10754.3i 0.453867 0.786121i
\(573\) 0 0
\(574\) −4366.96 3675.43i −0.317550 0.267264i
\(575\) 639.463i 0.0463782i
\(576\) 0 0
\(577\) −6678.26 + 3855.69i −0.481836 + 0.278188i −0.721181 0.692746i \(-0.756401\pi\)
0.239345 + 0.970935i \(0.423067\pi\)
\(578\) 1117.93 645.439i 0.0804497 0.0464476i
\(579\) 0 0
\(580\) 14151.7i 1.01313i
\(581\) −4287.24 762.552i −0.306136 0.0544509i
\(582\) 0 0
\(583\) 6888.14 11930.6i 0.489327 0.847539i
\(584\) 4514.84 + 7819.93i 0.319906 + 0.554094i
\(585\) 0 0
\(586\) 2198.55 + 1269.34i 0.154985 + 0.0894808i
\(587\) −4182.21 −0.294069 −0.147034 0.989131i \(-0.546973\pi\)
−0.147034 + 0.989131i \(0.546973\pi\)
\(588\) 0 0
\(589\) −10.4457 −0.000730744
\(590\) −2471.86 1427.13i −0.172483 0.0995830i
\(591\) 0 0
\(592\) −1641.12 2842.51i −0.113935 0.197342i
\(593\) 8094.65 14020.4i 0.560552 0.970905i −0.436896 0.899512i \(-0.643922\pi\)
0.997448 0.0713932i \(-0.0227445\pi\)
\(594\) 0 0
\(595\) −16124.9 2868.07i −1.11102 0.197612i
\(596\) 11916.3i 0.818977i
\(597\) 0 0
\(598\) −1864.33 + 1076.37i −0.127489 + 0.0736056i
\(599\) −11065.5 + 6388.67i −0.754798 + 0.435783i −0.827425 0.561576i \(-0.810195\pi\)
0.0726267 + 0.997359i \(0.476862\pi\)
\(600\) 0 0
\(601\) 24022.7i 1.63046i 0.579137 + 0.815231i \(0.303390\pi\)
−0.579137 + 0.815231i \(0.696610\pi\)
\(602\) −2491.55 2097.00i −0.168685 0.141972i
\(603\) 0 0
\(604\) −1504.08 + 2605.15i −0.101325 + 0.175500i
\(605\) 7373.92 + 12772.0i 0.495525 + 0.858274i
\(606\) 0 0
\(607\) 8371.72 + 4833.42i 0.559798 + 0.323200i 0.753065 0.657947i \(-0.228575\pi\)
−0.193266 + 0.981146i \(0.561908\pi\)
\(608\) −6.34346 −0.000423127
\(609\) 0 0
\(610\) −6326.02 −0.419890
\(611\) 17621.7 + 10173.9i 1.16677 + 0.673634i
\(612\) 0 0
\(613\) −7192.73 12458.2i −0.473918 0.820850i 0.525636 0.850710i \(-0.323827\pi\)
−0.999554 + 0.0298593i \(0.990494\pi\)
\(614\) 754.461 1306.77i 0.0495889 0.0858905i
\(615\) 0 0
\(616\) 3783.08 + 10442.4i 0.247443 + 0.683011i
\(617\) 7712.69i 0.503244i 0.967826 + 0.251622i \(0.0809639\pi\)
−0.967826 + 0.251622i \(0.919036\pi\)
\(618\) 0 0
\(619\) 12398.9 7158.52i 0.805096 0.464822i −0.0401539 0.999194i \(-0.512785\pi\)
0.845250 + 0.534371i \(0.179451\pi\)
\(620\) 15039.3 8682.96i 0.974183 0.562445i
\(621\) 0 0
\(622\) 4377.04i 0.282160i
\(623\) −7999.55 + 9504.67i −0.514439 + 0.611230i
\(624\) 0 0
\(625\) 7339.28 12712.0i 0.469714 0.813569i
\(626\) −917.292 1588.80i −0.0585661 0.101439i
\(627\) 0 0
\(628\) 15539.5 + 8971.73i 0.987410 + 0.570082i
\(629\) 5258.21 0.333320
\(630\) 0 0
\(631\) 4971.96 0.313678 0.156839 0.987624i \(-0.449870\pi\)
0.156839 + 0.987624i \(0.449870\pi\)
\(632\) −12908.9 7452.95i −0.812481 0.469086i
\(633\) 0 0
\(634\) −2293.24 3972.01i −0.143653 0.248815i
\(635\) 12319.7 21338.4i 0.769911 1.33353i
\(636\) 0 0
\(637\) 3807.00 10363.4i 0.236796 0.644601i
\(638\) 6807.03i 0.422403i
\(639\) 0 0
\(640\) 11997.5 6926.75i 0.741003 0.427818i
\(641\) 25481.7 14711.9i 1.57015 0.906529i 0.574004 0.818852i \(-0.305389\pi\)
0.996149 0.0876763i \(-0.0279441\pi\)
\(642\) 0 0
\(643\) 31273.9i 1.91807i 0.283283 + 0.959036i \(0.408576\pi\)
−0.283283 + 0.959036i \(0.591424\pi\)
\(644\) −2154.38 + 12112.4i −0.131823 + 0.741142i
\(645\) 0 0
\(646\) 1.48187 2.56667i 9.02529e−5 0.000156323i
\(647\) −4005.82 6938.29i −0.243408 0.421595i 0.718275 0.695760i \(-0.244932\pi\)
−0.961683 + 0.274164i \(0.911599\pi\)
\(648\) 0 0
\(649\) 15767.2 + 9103.17i 0.953644 + 0.550586i
\(650\) −172.643 −0.0104179
\(651\) 0 0
\(652\) −7032.62 −0.422421
\(653\) −13372.0 7720.32i −0.801357 0.462664i 0.0425886 0.999093i \(-0.486440\pi\)
−0.843945 + 0.536429i \(0.819773\pi\)
\(654\) 0 0
\(655\) −2115.12 3663.50i −0.126175 0.218542i
\(656\) 10462.3 18121.3i 0.622691 1.07853i
\(657\) 0 0
\(658\) −8244.39 + 2986.79i −0.488449 + 0.176956i
\(659\) 31288.9i 1.84953i −0.380537 0.924766i \(-0.624261\pi\)
0.380537 0.924766i \(-0.375739\pi\)
\(660\) 0 0
\(661\) −26263.2 + 15163.1i −1.54541 + 0.892246i −0.546932 + 0.837177i \(0.684205\pi\)
−0.998483 + 0.0550690i \(0.982462\pi\)
\(662\) 4927.69 2845.00i 0.289305 0.167031i
\(663\) 0 0
\(664\) 2718.84i 0.158903i
\(665\) −9.18150 + 3.32629i −0.000535403 + 0.000193967i
\(666\) 0 0
\(667\) 7824.33 13552.1i 0.454212 0.786718i
\(668\) −4728.17 8189.42i −0.273860 0.474339i
\(669\) 0 0
\(670\) 1380.12 + 796.815i 0.0795804 + 0.0459458i
\(671\) 40351.5 2.32154
\(672\) 0 0
\(673\) 12067.9 0.691207 0.345604 0.938381i \(-0.387674\pi\)
0.345604 + 0.938381i \(0.387674\pi\)
\(674\) 2505.81 + 1446.73i 0.143205 + 0.0826795i
\(675\) 0 0
\(676\) −4318.10 7479.18i −0.245682 0.425533i
\(677\) −3272.41 + 5667.98i −0.185774 + 0.321770i −0.943837 0.330411i \(-0.892813\pi\)
0.758063 + 0.652181i \(0.226146\pi\)
\(678\) 0 0
\(679\) 2127.19 11959.6i 0.120227 0.675944i
\(680\) 10225.9i 0.576686i
\(681\) 0 0
\(682\) 7233.99 4176.55i 0.406164 0.234499i
\(683\) −27267.1 + 15742.7i −1.52759 + 0.881956i −0.528130 + 0.849163i \(0.677107\pi\)
−0.999462 + 0.0327927i \(0.989560\pi\)
\(684\) 0 0
\(685\) 15943.2i 0.889282i
\(686\) 2360.46 + 4131.01i 0.131374 + 0.229917i
\(687\) 0 0
\(688\) 5969.23 10339.0i 0.330777 0.572923i
\(689\) 4275.18 + 7404.82i 0.236388 + 0.409436i
\(690\) 0 0
\(691\) −8690.83 5017.66i −0.478459 0.276238i 0.241315 0.970447i \(-0.422421\pi\)
−0.719774 + 0.694209i \(0.755755\pi\)
\(692\) −32992.0 −1.81238
\(693\) 0 0
\(694\) 1366.44 0.0747397
\(695\) 5872.93 + 3390.74i 0.320537 + 0.185062i
\(696\) 0 0
\(697\) 16760.8 + 29030.6i 0.910847 + 1.57763i
\(698\) −575.785 + 997.290i −0.0312232 + 0.0540802i
\(699\) 0 0
\(700\) −635.312 + 754.846i −0.0343036 + 0.0407579i
\(701\) 768.196i 0.0413900i −0.999786 0.0206950i \(-0.993412\pi\)
0.999786 0.0206950i \(-0.00658789\pi\)
\(702\) 0 0
\(703\) 2.71519 1.56761i 0.000145669 8.41019e-5i
\(704\) −13878.1 + 8012.53i −0.742970 + 0.428954i
\(705\) 0 0
\(706\) 4439.43i 0.236658i
\(707\) 7338.09 + 20255.2i 0.390350 + 1.07747i
\(708\) 0 0
\(709\) −6984.30 + 12097.2i −0.369959 + 0.640787i −0.989559 0.144130i \(-0.953962\pi\)
0.619600 + 0.784918i \(0.287295\pi\)
\(710\) 579.827 + 1004.29i 0.0306486 + 0.0530850i
\(711\) 0 0
\(712\) 6717.38 + 3878.28i 0.353573 + 0.204136i
\(713\) 19202.9 1.00863
\(714\) 0 0
\(715\) −18120.9 −0.947810
\(716\) −7006.34 4045.11i −0.365697 0.211135i
\(717\) 0 0
\(718\) −1812.33 3139.05i −0.0942001 0.163159i
\(719\) 5984.78 10365.9i 0.310424 0.537669i −0.668031 0.744134i \(-0.732862\pi\)
0.978454 + 0.206465i \(0.0661958\pi\)
\(720\) 0 0
\(721\) −374.357 315.075i −0.0193367 0.0162746i
\(722\) 5137.23i 0.264803i
\(723\) 0 0
\(724\) −18786.5 + 10846.4i −0.964358 + 0.556772i
\(725\) 1086.83 627.484i 0.0556745 0.0321437i
\(726\) 0 0
\(727\) 12223.3i 0.623575i −0.950152 0.311787i \(-0.899072\pi\)
0.950152 0.311787i \(-0.100928\pi\)
\(728\) −6786.83 1207.14i −0.345517 0.0614555i
\(729\) 0 0
\(730\) 3174.43 5498.28i 0.160947 0.278768i
\(731\) 9562.80 + 16563.3i 0.483848 + 0.838049i
\(732\) 0 0
\(733\) −20598.5 11892.5i −1.03796 0.599264i −0.118702 0.992930i \(-0.537873\pi\)
−0.919253 + 0.393666i \(0.871207\pi\)
\(734\) −8620.09 −0.433478
\(735\) 0 0
\(736\) 11661.5 0.584034
\(737\) −8803.34 5082.61i −0.439994 0.254030i
\(738\) 0 0
\(739\) −5739.04 9940.31i −0.285675 0.494804i 0.687097 0.726565i \(-0.258885\pi\)
−0.972773 + 0.231761i \(0.925551\pi\)
\(740\) −2606.14 + 4513.97i −0.129465 + 0.224239i
\(741\) 0 0
\(742\) −3627.79 645.258i −0.179488 0.0319247i
\(743\) 18604.0i 0.918593i 0.888283 + 0.459297i \(0.151899\pi\)
−0.888283 + 0.459297i \(0.848101\pi\)
\(744\) 0 0
\(745\) 15059.1 8694.38i 0.740568 0.427567i
\(746\) 121.617 70.2157i 0.00596879 0.00344608i
\(747\) 0 0
\(748\) 31428.9i 1.53630i
\(749\) −20787.8 17496.0i −1.01411 0.853523i
\(750\) 0 0
\(751\) −15506.2 + 26857.6i −0.753436 + 1.30499i 0.192713 + 0.981255i \(0.438272\pi\)
−0.946148 + 0.323734i \(0.895062\pi\)
\(752\) −16072.9 27839.1i −0.779415 1.34999i
\(753\) 0 0
\(754\) 3658.82 + 2112.42i 0.176719 + 0.102029i
\(755\) 4389.64 0.211597
\(756\) 0 0
\(757\) −19065.9 −0.915407 −0.457703 0.889105i \(-0.651328\pi\)
−0.457703 + 0.889105i \(0.651328\pi\)
\(758\) −2280.48 1316.63i −0.109275 0.0630901i
\(759\) 0 0
\(760\) 3.04863 + 5.28037i 0.000145507 + 0.000252025i
\(761\) −7339.58 + 12712.5i −0.349618 + 0.605556i −0.986182 0.165668i \(-0.947022\pi\)
0.636563 + 0.771224i \(0.280355\pi\)
\(762\) 0 0
\(763\) −852.058 2351.92i −0.0404280 0.111593i
\(764\) 33921.0i 1.60631i
\(765\) 0 0
\(766\) 1316.32 759.979i 0.0620896 0.0358475i
\(767\) −9786.01 + 5649.95i −0.460694 + 0.265982i
\(768\) 0 0
\(769\) 29972.5i 1.40551i −0.711434 0.702753i \(-0.751954\pi\)
0.711434 0.702753i \(-0.248046\pi\)
\(770\) 5028.52 5974.64i 0.235344 0.279625i
\(771\) 0 0
\(772\) 13975.0 24205.3i 0.651515 1.12846i
\(773\) 11343.9 + 19648.2i 0.527828 + 0.914225i 0.999474 + 0.0324367i \(0.0103267\pi\)
−0.471646 + 0.881788i \(0.656340\pi\)
\(774\) 0 0
\(775\) 1333.68 + 770.003i 0.0618159 + 0.0356894i
\(776\) −7584.38 −0.350855
\(777\) 0 0
\(778\) 4823.37 0.222270
\(779\) 17.3096 + 9.99369i 0.000796123 + 0.000459642i
\(780\) 0 0
\(781\) −3698.52 6406.02i −0.169454 0.293503i
\(782\) −2724.20 + 4718.45i −0.124574 + 0.215769i
\(783\) 0 0
\(784\) −13394.8 + 11171.6i −0.610185 + 0.508912i
\(785\) 26183.9i 1.19050i
\(786\) 0