Properties

Label 63.4.e.d.46.2
Level $63$
Weight $4$
Character 63.46
Analytic conductor $3.717$
Analytic rank $0$
Dimension $8$
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.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 19 x^{6} + 319 x^{4} + 798 x^{2} + 1764\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.2
Root \(0.799027 - 1.38396i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.4.e.d.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.799027 - 1.38396i) q^{2} +(2.72311 - 4.71657i) q^{4} +(9.14584 + 15.8411i) q^{5} +(12.3924 - 13.7633i) q^{7} -21.4878 q^{8} +O(q^{10})\) \(q+(-0.799027 - 1.38396i) q^{2} +(2.72311 - 4.71657i) q^{4} +(9.14584 + 15.8411i) q^{5} +(12.3924 - 13.7633i) q^{7} -21.4878 q^{8} +(14.6156 - 25.3149i) q^{10} +(30.6336 - 53.0590i) q^{11} +32.4462 q^{13} +(-28.9496 - 6.15337i) q^{14} +(-4.61555 - 7.99438i) q^{16} +(-40.6644 + 70.4329i) q^{17} +(10.4542 + 18.1072i) q^{19} +99.6206 q^{20} -97.9084 q^{22} +(-16.8655 - 29.2119i) q^{23} +(-104.793 + 181.507i) q^{25} +(-25.9254 - 44.9041i) q^{26} +(-31.1693 - 95.9287i) q^{28} -52.0227 q^{29} +(-96.9622 + 167.943i) q^{31} +(-93.3271 + 161.647i) q^{32} +129.968 q^{34} +(331.364 + 70.4329i) q^{35} +(133.578 + 231.363i) q^{37} +(16.7064 - 28.9364i) q^{38} +(-196.524 - 340.390i) q^{40} -203.176 q^{41} -21.9520 q^{43} +(-166.838 - 288.971i) q^{44} +(-26.9520 + 46.6822i) q^{46} +(-123.961 - 214.706i) q^{47} +(-35.8547 - 341.121i) q^{49} +334.929 q^{50} +(88.3547 - 153.035i) q^{52} +(70.4131 - 121.959i) q^{53} +1120.68 q^{55} +(-266.286 + 295.742i) q^{56} +(41.5676 + 71.9971i) q^{58} +(-110.734 + 191.797i) q^{59} +(-326.263 - 565.104i) q^{61} +309.902 q^{62} +224.435 q^{64} +(296.748 + 513.983i) q^{65} +(-302.239 + 523.493i) q^{67} +(221.468 + 383.593i) q^{68} +(-167.293 - 514.871i) q^{70} -716.031 q^{71} +(-194.438 + 336.777i) q^{73} +(213.465 - 369.731i) q^{74} +113.872 q^{76} +(-350.639 - 1079.15i) q^{77} +(144.871 + 250.923i) q^{79} +(84.4263 - 146.231i) q^{80} +(162.343 + 281.186i) q^{82} +115.652 q^{83} -1487.64 q^{85} +(17.5403 + 30.3806i) q^{86} +(-658.249 + 1140.12i) q^{88} +(469.682 + 813.513i) q^{89} +(402.088 - 446.566i) q^{91} -183.707 q^{92} +(-198.096 + 343.112i) q^{94} +(-191.225 + 331.212i) q^{95} +120.394 q^{97} +(-443.447 + 322.186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} - 12q^{7} + O(q^{10}) \) \( 8q - 6q^{4} - 12q^{7} - 22q^{10} + 204q^{13} + 102q^{16} - 222q^{19} - 172q^{22} - 366q^{25} - 166q^{28} - 220q^{31} + 2040q^{34} + 374q^{37} - 822q^{40} - 1676q^{43} - 1716q^{46} + 380q^{49} + 40q^{52} + 5020q^{55} + 1694q^{58} - 1332q^{61} - 1372q^{64} - 1890q^{67} - 866q^{70} - 1750q^{73} + 4912q^{76} - 8q^{79} - 2480q^{82} - 2232q^{85} - 2682q^{88} + 466q^{91} + 1416q^{94} + 6020q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.799027 1.38396i −0.282499 0.489302i 0.689501 0.724285i \(-0.257830\pi\)
−0.972000 + 0.234983i \(0.924497\pi\)
\(3\) 0 0
\(4\) 2.72311 4.71657i 0.340389 0.589571i
\(5\) 9.14584 + 15.8411i 0.818029 + 1.41687i 0.907132 + 0.420846i \(0.138267\pi\)
−0.0891033 + 0.996022i \(0.528400\pi\)
\(6\) 0 0
\(7\) 12.3924 13.7633i 0.669129 0.743146i
\(8\) −21.4878 −0.949635
\(9\) 0 0
\(10\) 14.6156 25.3149i 0.462184 0.800527i
\(11\) 30.6336 53.0590i 0.839672 1.45435i −0.0504975 0.998724i \(-0.516081\pi\)
0.890169 0.455630i \(-0.150586\pi\)
\(12\) 0 0
\(13\) 32.4462 0.692228 0.346114 0.938192i \(-0.387501\pi\)
0.346114 + 0.938192i \(0.387501\pi\)
\(14\) −28.9496 6.15337i −0.552651 0.117468i
\(15\) 0 0
\(16\) −4.61555 7.99438i −0.0721180 0.124912i
\(17\) −40.6644 + 70.4329i −0.580152 + 1.00485i 0.415309 + 0.909680i \(0.363673\pi\)
−0.995461 + 0.0951718i \(0.969660\pi\)
\(18\) 0 0
\(19\) 10.4542 + 18.1072i 0.126230 + 0.218636i 0.922213 0.386682i \(-0.126379\pi\)
−0.795983 + 0.605319i \(0.793046\pi\)
\(20\) 99.6206 1.11379
\(21\) 0 0
\(22\) −97.9084 −0.948825
\(23\) −16.8655 29.2119i −0.152900 0.264831i 0.779392 0.626536i \(-0.215528\pi\)
−0.932292 + 0.361705i \(0.882195\pi\)
\(24\) 0 0
\(25\) −104.793 + 181.507i −0.838343 + 1.45205i
\(26\) −25.9254 44.9041i −0.195554 0.338709i
\(27\) 0 0
\(28\) −31.1693 95.9287i −0.210373 0.647458i
\(29\) −52.0227 −0.333116 −0.166558 0.986032i \(-0.553265\pi\)
−0.166558 + 0.986032i \(0.553265\pi\)
\(30\) 0 0
\(31\) −96.9622 + 167.943i −0.561772 + 0.973017i 0.435570 + 0.900155i \(0.356547\pi\)
−0.997342 + 0.0728626i \(0.976787\pi\)
\(32\) −93.3271 + 161.647i −0.515564 + 0.892983i
\(33\) 0 0
\(34\) 129.968 0.655568
\(35\) 331.364 + 70.4329i 1.60031 + 0.340152i
\(36\) 0 0
\(37\) 133.578 + 231.363i 0.593515 + 1.02800i 0.993755 + 0.111587i \(0.0355935\pi\)
−0.400240 + 0.916410i \(0.631073\pi\)
\(38\) 16.7064 28.9364i 0.0713194 0.123529i
\(39\) 0 0
\(40\) −196.524 340.390i −0.776829 1.34551i
\(41\) −203.176 −0.773921 −0.386960 0.922096i \(-0.626475\pi\)
−0.386960 + 0.922096i \(0.626475\pi\)
\(42\) 0 0
\(43\) −21.9520 −0.0778523 −0.0389262 0.999242i \(-0.512394\pi\)
−0.0389262 + 0.999242i \(0.512394\pi\)
\(44\) −166.838 288.971i −0.571630 0.990092i
\(45\) 0 0
\(46\) −26.9520 + 46.6822i −0.0863882 + 0.149629i
\(47\) −123.961 214.706i −0.384713 0.666343i 0.607016 0.794690i \(-0.292366\pi\)
−0.991729 + 0.128346i \(0.959033\pi\)
\(48\) 0 0
\(49\) −35.8547 341.121i −0.104533 0.994521i
\(50\) 334.929 0.947324
\(51\) 0 0
\(52\) 88.3547 153.035i 0.235627 0.408117i
\(53\) 70.4131 121.959i 0.182490 0.316082i −0.760238 0.649645i \(-0.774918\pi\)
0.942728 + 0.333563i \(0.108251\pi\)
\(54\) 0 0
\(55\) 1120.68 2.74750
\(56\) −266.286 + 295.742i −0.635429 + 0.705718i
\(57\) 0 0
\(58\) 41.5676 + 71.9971i 0.0941050 + 0.162995i
\(59\) −110.734 + 191.797i −0.244344 + 0.423217i −0.961947 0.273236i \(-0.911906\pi\)
0.717603 + 0.696453i \(0.245239\pi\)
\(60\) 0 0
\(61\) −326.263 565.104i −0.684815 1.18613i −0.973495 0.228709i \(-0.926550\pi\)
0.288680 0.957426i \(-0.406784\pi\)
\(62\) 309.902 0.634800
\(63\) 0 0
\(64\) 224.435 0.438349
\(65\) 296.748 + 513.983i 0.566263 + 0.980796i
\(66\) 0 0
\(67\) −302.239 + 523.493i −0.551110 + 0.954551i 0.447085 + 0.894492i \(0.352462\pi\)
−0.998195 + 0.0600592i \(0.980871\pi\)
\(68\) 221.468 + 383.593i 0.394954 + 0.684081i
\(69\) 0 0
\(70\) −167.293 514.871i −0.285647 0.879126i
\(71\) −716.031 −1.19686 −0.598431 0.801174i \(-0.704209\pi\)
−0.598431 + 0.801174i \(0.704209\pi\)
\(72\) 0 0
\(73\) −194.438 + 336.777i −0.311743 + 0.539956i −0.978740 0.205105i \(-0.934246\pi\)
0.666996 + 0.745061i \(0.267580\pi\)
\(74\) 213.465 369.731i 0.335334 0.580816i
\(75\) 0 0
\(76\) 113.872 0.171869
\(77\) −350.639 1079.15i −0.518949 1.59715i
\(78\) 0 0
\(79\) 144.871 + 250.923i 0.206319 + 0.357355i 0.950552 0.310565i \(-0.100518\pi\)
−0.744233 + 0.667920i \(0.767185\pi\)
\(80\) 84.4263 146.231i 0.117989 0.204363i
\(81\) 0 0
\(82\) 162.343 + 281.186i 0.218632 + 0.378681i
\(83\) 115.652 0.152946 0.0764728 0.997072i \(-0.475634\pi\)
0.0764728 + 0.997072i \(0.475634\pi\)
\(84\) 0 0
\(85\) −1487.64 −1.89832
\(86\) 17.5403 + 30.3806i 0.0219932 + 0.0380933i
\(87\) 0 0
\(88\) −658.249 + 1140.12i −0.797382 + 1.38111i
\(89\) 469.682 + 813.513i 0.559395 + 0.968901i 0.997547 + 0.0699997i \(0.0222998\pi\)
−0.438152 + 0.898901i \(0.644367\pi\)
\(90\) 0 0
\(91\) 402.088 446.566i 0.463190 0.514427i
\(92\) −183.707 −0.208182
\(93\) 0 0
\(94\) −198.096 + 343.112i −0.217362 + 0.376482i
\(95\) −191.225 + 331.212i −0.206519 + 0.357701i
\(96\) 0 0
\(97\) 120.394 0.126022 0.0630110 0.998013i \(-0.479930\pi\)
0.0630110 + 0.998013i \(0.479930\pi\)
\(98\) −443.447 + 322.186i −0.457091 + 0.332099i
\(99\) 0 0
\(100\) 570.725 + 988.525i 0.570725 + 0.988525i
\(101\) 640.502 1109.38i 0.631013 1.09295i −0.356332 0.934359i \(-0.615973\pi\)
0.987345 0.158587i \(-0.0506938\pi\)
\(102\) 0 0
\(103\) −265.669 460.153i −0.254147 0.440196i 0.710516 0.703681i \(-0.248461\pi\)
−0.964664 + 0.263485i \(0.915128\pi\)
\(104\) −697.198 −0.657364
\(105\) 0 0
\(106\) −225.048 −0.206213
\(107\) 66.6758 + 115.486i 0.0602411 + 0.104341i 0.894573 0.446922i \(-0.147480\pi\)
−0.834332 + 0.551262i \(0.814146\pi\)
\(108\) 0 0
\(109\) 108.884 188.593i 0.0956811 0.165725i −0.814212 0.580568i \(-0.802830\pi\)
0.909893 + 0.414844i \(0.136164\pi\)
\(110\) −895.455 1550.97i −0.776166 1.34436i
\(111\) 0 0
\(112\) −167.227 35.5448i −0.141084 0.0299881i
\(113\) 2006.09 1.67006 0.835031 0.550204i \(-0.185450\pi\)
0.835031 + 0.550204i \(0.185450\pi\)
\(114\) 0 0
\(115\) 308.499 534.335i 0.250153 0.433278i
\(116\) −141.664 + 245.369i −0.113389 + 0.196396i
\(117\) 0 0
\(118\) 353.917 0.276108
\(119\) 465.454 + 1432.51i 0.358556 + 1.10351i
\(120\) 0 0
\(121\) −1211.34 2098.10i −0.910097 1.57633i
\(122\) −521.386 + 903.067i −0.386919 + 0.670163i
\(123\) 0 0
\(124\) 528.078 + 914.658i 0.382442 + 0.662409i
\(125\) −1547.22 −1.10710
\(126\) 0 0
\(127\) 1638.92 1.14512 0.572562 0.819861i \(-0.305950\pi\)
0.572562 + 0.819861i \(0.305950\pi\)
\(128\) 567.287 + 982.570i 0.391731 + 0.678498i
\(129\) 0 0
\(130\) 474.220 821.372i 0.319937 0.554147i
\(131\) 45.8755 + 79.4587i 0.0305967 + 0.0529950i 0.880918 0.473268i \(-0.156926\pi\)
−0.850322 + 0.526263i \(0.823593\pi\)
\(132\) 0 0
\(133\) 378.768 + 80.5088i 0.246943 + 0.0524887i
\(134\) 965.989 0.622752
\(135\) 0 0
\(136\) 873.789 1513.45i 0.550932 0.954243i
\(137\) −933.564 + 1616.98i −0.582188 + 1.00838i 0.413032 + 0.910717i \(0.364470\pi\)
−0.995220 + 0.0976621i \(0.968864\pi\)
\(138\) 0 0
\(139\) 639.778 0.390397 0.195199 0.980764i \(-0.437465\pi\)
0.195199 + 0.980764i \(0.437465\pi\)
\(140\) 1234.54 1371.10i 0.745271 0.827710i
\(141\) 0 0
\(142\) 572.128 + 990.955i 0.338112 + 0.585627i
\(143\) 993.946 1721.56i 0.581244 1.00674i
\(144\) 0 0
\(145\) −475.792 824.095i −0.272499 0.471982i
\(146\) 621.446 0.352269
\(147\) 0 0
\(148\) 1454.99 0.808103
\(149\) −1568.27 2716.32i −0.862264 1.49348i −0.869739 0.493513i \(-0.835713\pi\)
0.00747495 0.999972i \(-0.497621\pi\)
\(150\) 0 0
\(151\) 1360.68 2356.77i 0.733317 1.27014i −0.222141 0.975015i \(-0.571304\pi\)
0.955458 0.295128i \(-0.0953623\pi\)
\(152\) −224.638 389.085i −0.119872 0.207625i
\(153\) 0 0
\(154\) −1213.32 + 1347.54i −0.634886 + 0.705116i
\(155\) −3547.20 −1.83818
\(156\) 0 0
\(157\) −1439.87 + 2493.93i −0.731939 + 1.26776i 0.224114 + 0.974563i \(0.428051\pi\)
−0.956053 + 0.293193i \(0.905282\pi\)
\(158\) 231.511 400.989i 0.116570 0.201905i
\(159\) 0 0
\(160\) −3414.22 −1.68699
\(161\) −611.056 129.883i −0.299118 0.0635788i
\(162\) 0 0
\(163\) −323.071 559.576i −0.155245 0.268892i 0.777903 0.628384i \(-0.216283\pi\)
−0.933148 + 0.359492i \(0.882950\pi\)
\(164\) −553.271 + 958.293i −0.263434 + 0.456281i
\(165\) 0 0
\(166\) −92.4093 160.058i −0.0432069 0.0748366i
\(167\) 3765.03 1.74459 0.872296 0.488979i \(-0.162630\pi\)
0.872296 + 0.488979i \(0.162630\pi\)
\(168\) 0 0
\(169\) −1144.24 −0.520821
\(170\) 1188.67 + 2058.83i 0.536274 + 0.928854i
\(171\) 0 0
\(172\) −59.7777 + 103.538i −0.0265001 + 0.0458995i
\(173\) 1154.49 + 1999.64i 0.507366 + 0.878783i 0.999964 + 0.00852600i \(0.00271394\pi\)
−0.492598 + 0.870257i \(0.663953\pi\)
\(174\) 0 0
\(175\) 1199.48 + 3691.60i 0.518128 + 1.59462i
\(176\) −565.565 −0.242222
\(177\) 0 0
\(178\) 750.577 1300.04i 0.316057 0.547427i
\(179\) 1516.88 2627.31i 0.633390 1.09706i −0.353464 0.935448i \(-0.614996\pi\)
0.986854 0.161616i \(-0.0516705\pi\)
\(180\) 0 0
\(181\) −4079.71 −1.67537 −0.837686 0.546152i \(-0.816092\pi\)
−0.837686 + 0.546152i \(0.816092\pi\)
\(182\) −939.307 199.654i −0.382561 0.0813149i
\(183\) 0 0
\(184\) 362.403 + 627.700i 0.145199 + 0.251493i
\(185\) −2443.36 + 4232.03i −0.971025 + 1.68186i
\(186\) 0 0
\(187\) 2491.40 + 4315.23i 0.974274 + 1.68749i
\(188\) −1350.24 −0.523809
\(189\) 0 0
\(190\) 611.177 0.233365
\(191\) −438.554 759.599i −0.166140 0.287762i 0.770920 0.636932i \(-0.219797\pi\)
−0.937059 + 0.349170i \(0.886464\pi\)
\(192\) 0 0
\(193\) 729.356 1263.28i 0.272022 0.471155i −0.697358 0.716723i \(-0.745641\pi\)
0.969379 + 0.245568i \(0.0789744\pi\)
\(194\) −96.1979 166.620i −0.0356011 0.0616629i
\(195\) 0 0
\(196\) −1706.56 759.799i −0.621923 0.276895i
\(197\) 952.250 0.344391 0.172195 0.985063i \(-0.444914\pi\)
0.172195 + 0.985063i \(0.444914\pi\)
\(198\) 0 0
\(199\) −1671.11 + 2894.44i −0.595285 + 1.03106i 0.398222 + 0.917289i \(0.369627\pi\)
−0.993507 + 0.113774i \(0.963706\pi\)
\(200\) 2251.77 3900.18i 0.796120 1.37892i
\(201\) 0 0
\(202\) −2047.11 −0.713041
\(203\) −644.689 + 716.002i −0.222898 + 0.247554i
\(204\) 0 0
\(205\) −1858.22 3218.52i −0.633090 1.09654i
\(206\) −424.554 + 735.349i −0.143593 + 0.248710i
\(207\) 0 0
\(208\) −149.757 259.387i −0.0499221 0.0864677i
\(209\) 1281.00 0.423966
\(210\) 0 0
\(211\) 1439.27 0.469589 0.234794 0.972045i \(-0.424558\pi\)
0.234794 + 0.972045i \(0.424558\pi\)
\(212\) −383.485 664.216i −0.124235 0.215182i
\(213\) 0 0
\(214\) 106.552 184.553i 0.0340361 0.0589522i
\(215\) −200.770 347.743i −0.0636855 0.110306i
\(216\) 0 0
\(217\) 1109.85 + 3415.75i 0.347196 + 1.06855i
\(218\) −348.007 −0.108119
\(219\) 0 0
\(220\) 3051.74 5285.77i 0.935220 1.61985i
\(221\) −1319.41 + 2285.28i −0.401597 + 0.695587i
\(222\) 0 0
\(223\) 1009.86 0.303253 0.151626 0.988438i \(-0.451549\pi\)
0.151626 + 0.988438i \(0.451549\pi\)
\(224\) 1068.24 + 3287.69i 0.318638 + 0.980661i
\(225\) 0 0
\(226\) −1602.92 2776.34i −0.471790 0.817165i
\(227\) 1474.30 2553.57i 0.431070 0.746635i −0.565896 0.824477i \(-0.691470\pi\)
0.996966 + 0.0778419i \(0.0248029\pi\)
\(228\) 0 0
\(229\) 2019.42 + 3497.74i 0.582739 + 1.00933i 0.995153 + 0.0983374i \(0.0313524\pi\)
−0.412414 + 0.910997i \(0.635314\pi\)
\(230\) −985.995 −0.282672
\(231\) 0 0
\(232\) 1117.85 0.316339
\(233\) −1497.90 2594.44i −0.421162 0.729473i 0.574892 0.818230i \(-0.305044\pi\)
−0.996053 + 0.0887561i \(0.971711\pi\)
\(234\) 0 0
\(235\) 2267.45 3927.34i 0.629413 1.09018i
\(236\) 603.081 + 1044.57i 0.166344 + 0.288117i
\(237\) 0 0
\(238\) 1610.62 1788.78i 0.438660 0.487183i
\(239\) −1810.28 −0.489948 −0.244974 0.969530i \(-0.578779\pi\)
−0.244974 + 0.969530i \(0.578779\pi\)
\(240\) 0 0
\(241\) 1874.71 3247.10i 0.501083 0.867900i −0.498917 0.866650i \(-0.666269\pi\)
0.999999 0.00125048i \(-0.000398042\pi\)
\(242\) −1935.79 + 3352.88i −0.514203 + 0.890625i
\(243\) 0 0
\(244\) −3553.80 −0.932414
\(245\) 5075.80 3687.81i 1.32359 0.961656i
\(246\) 0 0
\(247\) 339.200 + 587.512i 0.0873797 + 0.151346i
\(248\) 2083.50 3608.74i 0.533478 0.924012i
\(249\) 0 0
\(250\) 1236.27 + 2141.28i 0.312754 + 0.541706i
\(251\) −2706.96 −0.680724 −0.340362 0.940295i \(-0.610550\pi\)
−0.340362 + 0.940295i \(0.610550\pi\)
\(252\) 0 0
\(253\) −2066.61 −0.513544
\(254\) −1309.54 2268.20i −0.323496 0.560312i
\(255\) 0 0
\(256\) 1804.29 3125.13i 0.440502 0.762971i
\(257\) −2687.64 4655.13i −0.652337 1.12988i −0.982554 0.185975i \(-0.940456\pi\)
0.330218 0.943905i \(-0.392878\pi\)
\(258\) 0 0
\(259\) 4839.67 + 1028.69i 1.16109 + 0.246795i
\(260\) 3232.31 0.770998
\(261\) 0 0
\(262\) 73.3116 126.979i 0.0172870 0.0299420i
\(263\) −2623.28 + 4543.66i −0.615051 + 1.06530i 0.375324 + 0.926893i \(0.377531\pi\)
−0.990376 + 0.138406i \(0.955802\pi\)
\(264\) 0 0
\(265\) 2575.95 0.597129
\(266\) −191.225 588.527i −0.0440781 0.135658i
\(267\) 0 0
\(268\) 1646.06 + 2851.06i 0.375184 + 0.649837i
\(269\) −1506.66 + 2609.61i −0.341496 + 0.591489i −0.984711 0.174197i \(-0.944267\pi\)
0.643214 + 0.765686i \(0.277600\pi\)
\(270\) 0 0
\(271\) −3448.62 5973.19i −0.773022 1.33891i −0.935899 0.352267i \(-0.885411\pi\)
0.162877 0.986646i \(-0.447923\pi\)
\(272\) 750.756 0.167358
\(273\) 0 0
\(274\) 2983.77 0.657869
\(275\) 6420.37 + 11120.4i 1.40787 + 2.43850i
\(276\) 0 0
\(277\) −1659.30 + 2874.00i −0.359920 + 0.623400i −0.987947 0.154792i \(-0.950529\pi\)
0.628027 + 0.778191i \(0.283863\pi\)
\(278\) −511.200 885.424i −0.110287 0.191022i
\(279\) 0 0
\(280\) −7120.28 1513.45i −1.51971 0.323021i
\(281\) 6274.14 1.33197 0.665986 0.745964i \(-0.268011\pi\)
0.665986 + 0.745964i \(0.268011\pi\)
\(282\) 0 0
\(283\) −3886.24 + 6731.16i −0.816300 + 1.41387i 0.0920914 + 0.995751i \(0.470645\pi\)
−0.908391 + 0.418122i \(0.862689\pi\)
\(284\) −1949.83 + 3377.21i −0.407399 + 0.705635i
\(285\) 0 0
\(286\) −3176.76 −0.656803
\(287\) −2517.85 + 2796.36i −0.517853 + 0.575136i
\(288\) 0 0
\(289\) −850.695 1473.45i −0.173152 0.299908i
\(290\) −760.341 + 1316.95i −0.153961 + 0.266669i
\(291\) 0 0
\(292\) 1058.95 + 1834.16i 0.212228 + 0.367590i
\(293\) −854.897 −0.170456 −0.0852280 0.996361i \(-0.527162\pi\)
−0.0852280 + 0.996361i \(0.527162\pi\)
\(294\) 0 0
\(295\) −4051.02 −0.799523
\(296\) −2870.29 4971.49i −0.563623 0.976223i
\(297\) 0 0
\(298\) −2506.17 + 4340.82i −0.487177 + 0.843815i
\(299\) −547.222 947.817i −0.105842 0.183323i
\(300\) 0 0
\(301\) −272.039 + 302.131i −0.0520932 + 0.0578557i
\(302\) −4348.89 −0.828645
\(303\) 0 0
\(304\) 96.5041 167.150i 0.0182069 0.0315352i
\(305\) 5967.90 10336.7i 1.12040 1.94058i
\(306\) 0 0
\(307\) 2550.68 0.474185 0.237092 0.971487i \(-0.423806\pi\)
0.237092 + 0.971487i \(0.423806\pi\)
\(308\) −6044.71 1284.83i −1.11828 0.237695i
\(309\) 0 0
\(310\) 2834.31 + 4909.17i 0.519284 + 0.899427i
\(311\) 3740.25 6478.31i 0.681962 1.18119i −0.292419 0.956290i \(-0.594460\pi\)
0.974381 0.224903i \(-0.0722064\pi\)
\(312\) 0 0
\(313\) −3.12392 5.41079i −0.000564135 0.000977111i 0.865743 0.500488i \(-0.166846\pi\)
−0.866307 + 0.499511i \(0.833513\pi\)
\(314\) 4601.99 0.827088
\(315\) 0 0
\(316\) 1578.00 0.280915
\(317\) 482.902 + 836.410i 0.0855598 + 0.148194i 0.905630 0.424070i \(-0.139399\pi\)
−0.820070 + 0.572263i \(0.806065\pi\)
\(318\) 0 0
\(319\) −1593.64 + 2760.27i −0.279708 + 0.484469i
\(320\) 2052.64 + 3555.28i 0.358582 + 0.621083i
\(321\) 0 0
\(322\) 308.499 + 949.455i 0.0533912 + 0.164320i
\(323\) −1700.46 −0.292929
\(324\) 0 0
\(325\) −3400.13 + 5889.20i −0.580324 + 1.00515i
\(326\) −516.285 + 894.232i −0.0877129 + 0.151923i
\(327\) 0 0
\(328\) 4365.80 0.734942
\(329\) −4491.23 954.632i −0.752613 0.159971i
\(330\) 0 0
\(331\) −3355.10 5811.20i −0.557139 0.964992i −0.997734 0.0672865i \(-0.978566\pi\)
0.440595 0.897706i \(-0.354767\pi\)
\(332\) 314.934 545.482i 0.0520610 0.0901723i
\(333\) 0 0
\(334\) −3008.36 5210.64i −0.492845 0.853633i
\(335\) −11056.9 −1.80330
\(336\) 0 0
\(337\) −605.546 −0.0978819 −0.0489409 0.998802i \(-0.515585\pi\)
−0.0489409 + 0.998802i \(0.515585\pi\)
\(338\) 914.281 + 1583.58i 0.147131 + 0.254839i
\(339\) 0 0
\(340\) −4051.02 + 7016.57i −0.646168 + 1.11920i
\(341\) 5940.61 + 10289.4i 0.943408 + 1.63403i
\(342\) 0 0
\(343\) −5139.26 3733.84i −0.809021 0.587780i
\(344\) 471.700 0.0739313
\(345\) 0 0
\(346\) 1844.94 3195.53i 0.286660 0.496510i
\(347\) 3469.08 6008.62i 0.536686 0.929567i −0.462394 0.886675i \(-0.653009\pi\)
0.999080 0.0428923i \(-0.0136572\pi\)
\(348\) 0 0
\(349\) 10368.9 1.59035 0.795176 0.606378i \(-0.207378\pi\)
0.795176 + 0.606378i \(0.207378\pi\)
\(350\) 4150.59 4609.72i 0.633882 0.704000i
\(351\) 0 0
\(352\) 5717.90 + 9903.69i 0.865809 + 1.49963i
\(353\) −2940.88 + 5093.75i −0.443420 + 0.768026i −0.997941 0.0641440i \(-0.979568\pi\)
0.554521 + 0.832170i \(0.312902\pi\)
\(354\) 0 0
\(355\) −6548.70 11342.7i −0.979068 1.69580i
\(356\) 5115.98 0.761647
\(357\) 0 0
\(358\) −4848.11 −0.715728
\(359\) 294.634 + 510.322i 0.0433153 + 0.0750244i 0.886870 0.462019i \(-0.152875\pi\)
−0.843555 + 0.537043i \(0.819541\pi\)
\(360\) 0 0
\(361\) 3210.92 5561.47i 0.468132 0.810829i
\(362\) 3259.80 + 5646.14i 0.473291 + 0.819763i
\(363\) 0 0
\(364\) −1011.33 3112.52i −0.145626 0.448188i
\(365\) −7113.21 −1.02006
\(366\) 0 0
\(367\) 1774.36 3073.28i 0.252373 0.437122i −0.711806 0.702376i \(-0.752122\pi\)
0.964179 + 0.265254i \(0.0854558\pi\)
\(368\) −155.687 + 269.658i −0.0220537 + 0.0381982i
\(369\) 0 0
\(370\) 7809.25 1.09725
\(371\) −805.964 2480.49i −0.112786 0.347117i
\(372\) 0 0
\(373\) 790.667 + 1369.47i 0.109756 + 0.190104i 0.915672 0.401927i \(-0.131660\pi\)
−0.805915 + 0.592031i \(0.798326\pi\)
\(374\) 3981.39 6895.97i 0.550462 0.953429i
\(375\) 0 0
\(376\) 2663.64 + 4613.56i 0.365337 + 0.632783i
\(377\) −1687.94 −0.230592
\(378\) 0 0
\(379\) 3057.01 0.414322 0.207161 0.978307i \(-0.433578\pi\)
0.207161 + 0.978307i \(0.433578\pi\)
\(380\) 1041.46 + 1803.85i 0.140594 + 0.243515i
\(381\) 0 0
\(382\) −700.834 + 1213.88i −0.0938685 + 0.162585i
\(383\) −5289.87 9162.33i −0.705744 1.22238i −0.966422 0.256959i \(-0.917280\pi\)
0.260678 0.965426i \(-0.416054\pi\)
\(384\) 0 0
\(385\) 13888.0 15424.2i 1.83843 2.04180i
\(386\) −2331.10 −0.307383
\(387\) 0 0
\(388\) 327.846 567.845i 0.0428965 0.0742989i
\(389\) −3696.65 + 6402.78i −0.481819 + 0.834534i −0.999782 0.0208684i \(-0.993357\pi\)
0.517964 + 0.855403i \(0.326690\pi\)
\(390\) 0 0
\(391\) 2743.31 0.354821
\(392\) 770.438 + 7329.94i 0.0992678 + 0.944433i
\(393\) 0 0
\(394\) −760.874 1317.87i −0.0972900 0.168511i
\(395\) −2649.93 + 4589.81i −0.337550 + 0.584654i
\(396\) 0 0
\(397\) −889.086 1539.94i −0.112398 0.194679i 0.804339 0.594171i \(-0.202520\pi\)
−0.916737 + 0.399492i \(0.869186\pi\)
\(398\) 5341.04 0.672669
\(399\) 0 0
\(400\) 1934.71 0.241839
\(401\) −73.8031 127.831i −0.00919090 0.0159191i 0.861393 0.507938i \(-0.169592\pi\)
−0.870584 + 0.492019i \(0.836259\pi\)
\(402\) 0 0
\(403\) −3146.06 + 5449.13i −0.388874 + 0.673550i
\(404\) −3488.31 6041.94i −0.429579 0.744053i
\(405\) 0 0
\(406\) 1506.04 + 320.115i 0.184097 + 0.0391307i
\(407\) 16367.9 1.99343
\(408\) 0 0
\(409\) 1080.03 1870.66i 0.130572 0.226157i −0.793325 0.608798i \(-0.791652\pi\)
0.923897 + 0.382641i \(0.124985\pi\)
\(410\) −2969.53 + 5143.37i −0.357694 + 0.619544i
\(411\) 0 0
\(412\) −2893.79 −0.346036
\(413\) 1267.48 + 3900.89i 0.151014 + 0.464770i
\(414\) 0 0
\(415\) 1057.74 + 1832.05i 0.125114 + 0.216704i
\(416\) −3028.11 + 5244.84i −0.356888 + 0.618148i
\(417\) 0 0
\(418\) −1023.56 1772.85i −0.119770 0.207447i
\(419\) 13491.0 1.57298 0.786488 0.617605i \(-0.211897\pi\)
0.786488 + 0.617605i \(0.211897\pi\)
\(420\) 0 0
\(421\) −14146.7 −1.63769 −0.818847 0.574012i \(-0.805386\pi\)
−0.818847 + 0.574012i \(0.805386\pi\)
\(422\) −1150.01 1991.88i −0.132658 0.229771i
\(423\) 0 0
\(424\) −1513.02 + 2620.63i −0.173299 + 0.300163i
\(425\) −8522.69 14761.7i −0.972732 1.68482i
\(426\) 0 0
\(427\) −11820.9 2512.58i −1.33970 0.284759i
\(428\) 726.262 0.0820215
\(429\) 0 0
\(430\) −320.841 + 555.712i −0.0359821 + 0.0623229i
\(431\) −4544.26 + 7870.89i −0.507864 + 0.879646i 0.492095 + 0.870542i \(0.336231\pi\)
−0.999959 + 0.00910411i \(0.997102\pi\)
\(432\) 0 0
\(433\) 15461.2 1.71597 0.857986 0.513673i \(-0.171716\pi\)
0.857986 + 0.513673i \(0.171716\pi\)
\(434\) 3840.44 4265.26i 0.424763 0.471749i
\(435\) 0 0
\(436\) −593.009 1027.12i −0.0651376 0.112822i
\(437\) 352.632 610.776i 0.0386010 0.0668590i
\(438\) 0 0
\(439\) 891.091 + 1543.41i 0.0968780 + 0.167798i 0.910391 0.413749i \(-0.135781\pi\)
−0.813513 + 0.581547i \(0.802448\pi\)
\(440\) −24081.0 −2.60913
\(441\) 0 0
\(442\) 4216.97 0.453803
\(443\) −6712.36 11626.1i −0.719896 1.24690i −0.961041 0.276407i \(-0.910856\pi\)
0.241145 0.970489i \(-0.422477\pi\)
\(444\) 0 0
\(445\) −8591.27 + 14880.5i −0.915203 + 1.58518i
\(446\) −806.907 1397.60i −0.0856685 0.148382i
\(447\) 0 0
\(448\) 2781.29 3088.95i 0.293312 0.325757i
\(449\) 418.639 0.0440018 0.0220009 0.999758i \(-0.492996\pi\)
0.0220009 + 0.999758i \(0.492996\pi\)
\(450\) 0 0
\(451\) −6224.02 + 10780.3i −0.649839 + 1.12555i
\(452\) 5462.80 9461.85i 0.568470 0.984619i
\(453\) 0 0
\(454\) −4712.03 −0.487107
\(455\) 10751.5 + 2285.28i 1.10778 + 0.235463i
\(456\) 0 0
\(457\) 354.205 + 613.501i 0.0362560 + 0.0627973i 0.883584 0.468273i \(-0.155123\pi\)
−0.847328 + 0.531070i \(0.821790\pi\)
\(458\) 3227.15 5589.59i 0.329246 0.570271i
\(459\) 0 0
\(460\) −1680.15 2910.11i −0.170299 0.294966i
\(461\) 8223.97 0.830865 0.415432 0.909624i \(-0.363630\pi\)
0.415432 + 0.909624i \(0.363630\pi\)
\(462\) 0 0
\(463\) −9414.17 −0.944954 −0.472477 0.881343i \(-0.656640\pi\)
−0.472477 + 0.881343i \(0.656640\pi\)
\(464\) 240.114 + 415.889i 0.0240237 + 0.0416103i
\(465\) 0 0
\(466\) −2393.73 + 4146.05i −0.237955 + 0.412151i
\(467\) 5410.76 + 9371.72i 0.536146 + 0.928632i 0.999107 + 0.0422535i \(0.0134537\pi\)
−0.462961 + 0.886379i \(0.653213\pi\)
\(468\) 0 0
\(469\) 3459.50 + 10647.2i 0.340607 + 1.04827i
\(470\) −7247.02 −0.711234
\(471\) 0 0
\(472\) 2379.43 4121.29i 0.232038 0.401902i
\(473\) −672.470 + 1164.75i −0.0653704 + 0.113225i
\(474\) 0 0
\(475\) −4382.11 −0.423295
\(476\) 8024.02 + 1705.54i 0.772648 + 0.164230i
\(477\) 0 0
\(478\) 1446.47 + 2505.35i 0.138410 + 0.239733i
\(479\) −4092.75 + 7088.85i −0.390402 + 0.676196i −0.992503 0.122224i \(-0.960997\pi\)
0.602100 + 0.798420i \(0.294331\pi\)
\(480\) 0 0
\(481\) 4334.09 + 7506.87i 0.410848 + 0.711609i
\(482\) −5991.79 −0.566221
\(483\) 0 0
\(484\) −13194.4 −1.23915
\(485\) 1101.10 + 1907.17i 0.103090 + 0.178557i
\(486\) 0 0
\(487\) 2001.58 3466.83i 0.186242 0.322581i −0.757752 0.652543i \(-0.773702\pi\)
0.943994 + 0.329961i \(0.107036\pi\)
\(488\) 7010.67 + 12142.8i 0.650324 + 1.12639i
\(489\) 0 0
\(490\) −9159.47 4078.01i −0.844455 0.375971i
\(491\) −11180.8 −1.02766 −0.513831 0.857891i \(-0.671774\pi\)
−0.513831 + 0.857891i \(0.671774\pi\)
\(492\) 0 0
\(493\) 2115.47 3664.11i 0.193258 0.334733i
\(494\) 542.060 938.876i 0.0493693 0.0855101i
\(495\) 0 0
\(496\) 1790.14 0.162056
\(497\) −8873.37 + 9854.92i −0.800855 + 0.889443i
\(498\) 0 0
\(499\) 1885.54 + 3265.85i 0.169155 + 0.292985i 0.938123 0.346302i \(-0.112563\pi\)
−0.768968 + 0.639287i \(0.779229\pi\)
\(500\) −4213.24 + 7297.55i −0.376844 + 0.652713i
\(501\) 0 0
\(502\) 2162.93 + 3746.31i 0.192304 + 0.333080i
\(503\) 13597.2 1.20531 0.602654 0.798003i \(-0.294110\pi\)
0.602654 + 0.798003i \(0.294110\pi\)
\(504\) 0 0
\(505\) 23431.7 2.06475
\(506\) 1651.28 + 2860.09i 0.145075 + 0.251278i
\(507\) 0 0
\(508\) 4462.97 7730.08i 0.389788 0.675132i
\(509\) 3680.38 + 6374.60i 0.320491 + 0.555106i 0.980589 0.196073i \(-0.0628188\pi\)
−0.660099 + 0.751179i \(0.729485\pi\)
\(510\) 0 0
\(511\) 2225.58 + 6849.59i 0.192669 + 0.592971i
\(512\) 3309.87 0.285698
\(513\) 0 0
\(514\) −4295.00 + 7439.16i −0.368569 + 0.638380i
\(515\) 4859.54 8416.97i 0.415800 0.720186i
\(516\) 0 0
\(517\) −15189.5 −1.29213
\(518\) −2443.36 7519.84i −0.207249 0.637844i
\(519\) 0 0
\(520\) −6376.46 11044.4i −0.537743 0.931398i
\(521\) 6899.40 11950.1i 0.580169 1.00488i −0.415290 0.909689i \(-0.636320\pi\)
0.995459 0.0951930i \(-0.0303468\pi\)
\(522\) 0 0
\(523\) −9423.58 16322.1i −0.787886 1.36466i −0.927260 0.374419i \(-0.877842\pi\)
0.139373 0.990240i \(-0.455491\pi\)
\(524\) 499.697 0.0416591
\(525\) 0 0
\(526\) 8384.29 0.695005
\(527\) −7885.83 13658.7i −0.651826 1.12900i
\(528\) 0 0
\(529\) 5514.61 9551.58i 0.453243 0.785040i
\(530\) −2058.25 3565.00i −0.168688 0.292177i
\(531\) 0 0
\(532\) 1411.15 1567.25i 0.115002 0.127724i
\(533\) −6592.29 −0.535730
\(534\) 0 0
\(535\) −1219.61 + 2112.43i −0.0985579 + 0.170707i
\(536\) 6494.45 11248.7i 0.523354 0.906475i
\(537\) 0 0
\(538\) 4815.44 0.385889
\(539\) −19197.9 8547.36i −1.53416 0.683044i
\(540\) 0 0
\(541\) 7234.77 + 12531.0i 0.574948 + 0.995839i 0.996047 + 0.0888248i \(0.0283111\pi\)
−0.421099 + 0.907015i \(0.638356\pi\)
\(542\) −5511.09 + 9545.49i −0.436756 + 0.756483i
\(543\) 0 0
\(544\) −7590.19 13146.6i −0.598211 1.03613i
\(545\) 3983.36 0.313080
\(546\) 0 0
\(547\) 5749.63 0.449427 0.224713 0.974425i \(-0.427855\pi\)
0.224713 + 0.974425i \(0.427855\pi\)
\(548\) 5084.39 + 8806.43i 0.396340 + 0.686482i
\(549\) 0 0
\(550\) 10260.1 17771.0i 0.795441 1.37774i
\(551\) −543.857 941.988i −0.0420492 0.0728313i
\(552\) 0 0
\(553\) 5248.82 + 1115.66i 0.403622 + 0.0857916i
\(554\) 5303.31 0.406708
\(555\) 0 0
\(556\) 1742.19 3017.55i 0.132887 0.230167i
\(557\) 2715.39 4703.19i 0.206561 0.357775i −0.744068 0.668104i \(-0.767106\pi\)
0.950629 + 0.310330i \(0.100439\pi\)
\(558\) 0 0
\(559\) −712.260 −0.0538915
\(560\) −966.362 2974.14i −0.0729219 0.224429i
\(561\) 0 0
\(562\) −5013.21 8683.14i −0.376280 0.651737i
\(563\) −12065.3 + 20897.8i −0.903185 + 1.56436i −0.0798500 + 0.996807i \(0.525444\pi\)
−0.823335 + 0.567556i \(0.807889\pi\)
\(564\) 0 0
\(565\) 18347.4 + 31778.6i 1.36616 + 2.36626i
\(566\) 12420.8 0.922415
\(567\) 0 0
\(568\) 15385.9 1.13658
\(569\) 9024.27 + 15630.5i 0.664880 + 1.15161i 0.979318 + 0.202328i \(0.0648509\pi\)
−0.314437 + 0.949278i \(0.601816\pi\)
\(570\) 0 0
\(571\) 5637.42 9764.30i 0.413168 0.715628i −0.582066 0.813141i \(-0.697756\pi\)
0.995234 + 0.0975136i \(0.0310889\pi\)
\(572\) −5413.25 9376.02i −0.395698 0.685369i
\(573\) 0 0
\(574\) 5881.87 + 1250.22i 0.427708 + 0.0909113i
\(575\) 7069.54 0.512731
\(576\) 0 0
\(577\) 12047.5 20866.8i 0.869225 1.50554i 0.00643457 0.999979i \(-0.497952\pi\)
0.862790 0.505562i \(-0.168715\pi\)
\(578\) −1359.46 + 2354.65i −0.0978303 + 0.169447i
\(579\) 0 0
\(580\) −5182.53 −0.371022
\(581\) 1433.21 1591.75i 0.102340 0.113661i
\(582\) 0 0
\(583\) −4314.02 7472.10i −0.306464 0.530811i
\(584\) 4178.05 7236.59i 0.296043 0.512761i
\(585\) 0 0
\(586\) 683.086 + 1183.14i 0.0481536 + 0.0834045i
\(587\) −11438.9 −0.804315 −0.402157 0.915571i \(-0.631740\pi\)
−0.402157 + 0.915571i \(0.631740\pi\)
\(588\) 0 0
\(589\) −4054.66 −0.283649
\(590\) 3236.87 + 5606.43i 0.225864 + 0.391208i
\(591\) 0 0
\(592\) 1233.07 2135.74i 0.0856063 0.148274i
\(593\) −2087.22 3615.17i −0.144539 0.250349i 0.784662 0.619924i \(-0.212837\pi\)
−0.929201 + 0.369575i \(0.879503\pi\)
\(594\) 0 0
\(595\) −18435.5 + 20474.8i −1.27022 + 1.41073i
\(596\) −17082.2 −1.17402
\(597\) 0 0
\(598\) −874.491 + 1514.66i −0.0598003 + 0.103577i
\(599\) −5727.77 + 9920.79i −0.390702 + 0.676715i −0.992542 0.121901i \(-0.961101\pi\)
0.601841 + 0.798616i \(0.294434\pi\)
\(600\) 0 0
\(601\) −17539.2 −1.19042 −0.595208 0.803572i \(-0.702930\pi\)
−0.595208 + 0.803572i \(0.702930\pi\)
\(602\) 635.503 + 135.079i 0.0430252 + 0.00914519i
\(603\) 0 0
\(604\) −7410.59 12835.5i −0.499226 0.864685i
\(605\) 22157.4 38377.8i 1.48897 2.57898i
\(606\) 0 0
\(607\) −1692.86 2932.12i −0.113198 0.196064i 0.803860 0.594818i \(-0.202776\pi\)
−0.917058 + 0.398754i \(0.869443\pi\)
\(608\) −3902.65 −0.260318
\(609\) 0 0
\(610\) −19074.1 −1.26604
\(611\) −4022.06 6966.41i −0.266309 0.461261i
\(612\) 0 0
\(613\) −2135.94 + 3699.56i −0.140734 + 0.243758i −0.927773 0.373145i \(-0.878279\pi\)
0.787039 + 0.616903i \(0.211613\pi\)
\(614\) −2038.06 3530.02i −0.133957 0.232020i
\(615\) 0 0
\(616\) 7534.47 + 23188.5i 0.492812 + 1.51671i
\(617\) 13123.9 0.856321 0.428160 0.903703i \(-0.359162\pi\)
0.428160 + 0.903703i \(0.359162\pi\)
\(618\) 0 0
\(619\) 946.969 1640.20i 0.0614893 0.106503i −0.833642 0.552305i \(-0.813748\pi\)
0.895131 + 0.445803i \(0.147082\pi\)
\(620\) −9659.43 + 16730.6i −0.625697 + 1.08374i
\(621\) 0 0
\(622\) −11954.3 −0.770614
\(623\) 17017.1 + 3617.06i 1.09434 + 0.232607i
\(624\) 0 0
\(625\) −1051.49 1821.23i −0.0672952 0.116559i
\(626\) −4.99219 + 8.64673i −0.000318735 + 0.000552066i
\(627\) 0 0
\(628\) 7841.87 + 13582.5i 0.498288 + 0.863060i
\(629\) −21727.5 −1.37731
\(630\) 0 0
\(631\) 20443.8 1.28979 0.644894 0.764272i \(-0.276902\pi\)
0.644894 + 0.764272i \(0.276902\pi\)
\(632\) −3112.95 5391.79i −0.195928 0.339357i
\(633\) 0 0
\(634\) 771.703 1336.63i 0.0483411 0.0837292i
\(635\) 14989.3 + 25962.3i 0.936745 + 1.62249i
\(636\) 0 0
\(637\) −1163.35 11068.1i −0.0723603 0.688436i
\(638\) 5093.46 0.316069
\(639\) 0 0
\(640\) −10376.6 + 17972.9i −0.640895 + 1.11006i
\(641\) −9614.27 + 16652.4i −0.592419 + 1.02610i 0.401486 + 0.915865i \(0.368494\pi\)
−0.993906 + 0.110235i \(0.964840\pi\)
\(642\) 0 0
\(643\) −18525.1 −1.13617 −0.568087 0.822969i \(-0.692316\pi\)
−0.568087 + 0.822969i \(0.692316\pi\)
\(644\) −2276.57 + 2528.40i −0.139301 + 0.154710i
\(645\) 0 0
\(646\) 1358.71 + 2353.36i 0.0827522 + 0.143331i
\(647\) −4011.20 + 6947.60i −0.243735 + 0.422161i −0.961775 0.273840i \(-0.911706\pi\)
0.718040 + 0.696001i \(0.245039\pi\)
\(648\) 0 0
\(649\) 6784.36 + 11750.9i 0.410338 + 0.710726i
\(650\) 10867.2 0.655764
\(651\) 0 0
\(652\) −3519.03 −0.211374
\(653\) −1025.85 1776.82i −0.0614769 0.106481i 0.833649 0.552295i \(-0.186248\pi\)
−0.895126 + 0.445814i \(0.852914\pi\)
\(654\) 0 0
\(655\) −839.141 + 1453.43i −0.0500579 + 0.0867029i
\(656\) 937.770 + 1624.26i 0.0558136 + 0.0966721i
\(657\) 0 0
\(658\) 2267.45 + 6978.45i 0.134338 + 0.413447i
\(659\) 14765.2 0.872792 0.436396 0.899755i \(-0.356255\pi\)
0.436396 + 0.899755i \(0.356255\pi\)
\(660\) 0 0
\(661\) −323.532 + 560.374i −0.0190377 + 0.0329743i −0.875387 0.483422i \(-0.839394\pi\)
0.856350 + 0.516397i \(0.172727\pi\)
\(662\) −5361.63 + 9286.62i −0.314782 + 0.545218i
\(663\) 0 0
\(664\) −2485.11 −0.145243
\(665\) 2188.81 + 6736.41i 0.127637 + 0.392822i
\(666\) 0 0
\(667\) 877.390 + 1519.68i 0.0509335 + 0.0882195i
\(668\) 10252.6 17758.0i 0.593840 1.02856i
\(669\) 0 0
\(670\) 8834.78 + 15302.3i 0.509429 + 0.882357i
\(671\) −39978.5 −2.30008
\(672\) 0 0
\(673\) −22596.6 −1.29426 −0.647130 0.762380i \(-0.724031\pi\)
−0.647130 + 0.762380i \(0.724031\pi\)
\(674\) 483.848 + 838.049i 0.0276515 + 0.0478938i
\(675\) 0 0
\(676\) −3115.90 + 5396.90i −0.177282 + 0.307061i
\(677\) −12602.1 21827.5i −0.715420 1.23914i −0.962797 0.270225i \(-0.912902\pi\)
0.247377 0.968919i \(-0.420431\pi\)
\(678\) 0 0
\(679\) 1491.97 1657.01i 0.0843250 0.0936528i
\(680\) 31966.2 1.80272
\(681\) 0 0
\(682\) 9493.42 16443.1i 0.533023 0.923223i
\(683\) 8510.27 14740.2i 0.476774 0.825796i −0.522872 0.852411i \(-0.675140\pi\)
0.999646 + 0.0266151i \(0.00847285\pi\)
\(684\) 0 0
\(685\) −34152.9 −1.90499
\(686\) −1061.06 + 10096.0i −0.0590549 + 0.561903i
\(687\) 0 0
\(688\) 101.321 + 175.493i 0.00561456 + 0.00972470i
\(689\) 2284.64 3957.11i 0.126325 0.218801i
\(690\) 0 0
\(691\) 9645.26 + 16706.1i 0.531003 + 0.919724i 0.999345 + 0.0361772i \(0.0115181\pi\)
−0.468342 + 0.883547i \(0.655149\pi\)
\(692\) 12575.2 0.690806
\(693\) 0 0
\(694\) −11087.6 −0.606452
\(695\) 5851.31 + 10134.8i 0.319356 + 0.553142i
\(696\) 0 0
\(697\) 8262.04 14310.3i 0.448991 0.777676i
\(698\) −8285.01 14350.1i −0.449273 0.778163i
\(699\) 0 0
\(700\) 20678.0 + 4395.20i 1.11651 + 0.237319i
\(701\) −28511.4 −1.53618 −0.768088 0.640345i \(-0.778792\pi\)
−0.768088 + 0.640345i \(0.778792\pi\)
\(702\) 0 0
\(703\) −2792.90 + 4837.45i −0.149838 + 0.259528i
\(704\) 6875.25 11908.3i 0.368069 0.637515i
\(705\) 0 0
\(706\) 9399.37 0.501062
\(707\) −7331.32 22563.3i −0.389990 1.20026i
\(708\) 0 0
\(709\) −14213.3 24618.1i −0.752877 1.30402i −0.946423 0.322930i \(-0.895332\pi\)
0.193546 0.981091i \(-0.438001\pi\)
\(710\) −10465.2 + 18126.2i −0.553171 + 0.958120i
\(711\) 0 0
\(712\) −10092.4 17480.6i −0.531221 0.920102i
\(713\) 6541.27 0.343580
\(714\) 0 0
\(715\) 36361.9 1.90190
\(716\) −8261.26 14308.9i −0.431198 0.746857i
\(717\) 0 0
\(718\) 470.842 815.522i 0.0244731 0.0423886i
\(719\) −10881.7 18847.6i −0.564420 0.977603i −0.997103 0.0760577i \(-0.975767\pi\)
0.432684 0.901546i \(-0.357567\pi\)
\(720\) 0 0
\(721\) −9625.49 2045.94i −0.497187 0.105679i
\(722\) −10262.4 −0.528987
\(723\) 0 0
\(724\) −11109.5 + 19242.2i −0.570278 + 0.987750i
\(725\) 5451.61 9442.47i 0.279266 0.483703i
\(726\) 0 0
\(727\) −13422.8 −0.684763 −0.342382 0.939561i \(-0.611234\pi\)
−0.342382 + 0.939561i \(0.611234\pi\)
\(728\) −8639.98 + 9595.71i −0.439861 + 0.488518i
\(729\) 0 0
\(730\) 5683.65 + 9844.36i 0.288166 + 0.499118i
\(731\) 892.666 1546.14i 0.0451661 0.0782301i
\(732\) 0 0
\(733\) −2279.76 3948.66i −0.114877 0.198973i 0.802854 0.596176i \(-0.203314\pi\)
−0.917731 + 0.397204i \(0.869981\pi\)
\(734\) −5671.04 −0.285180
\(735\) 0 0
\(736\) 6296.04 0.315319
\(737\) 18517.4 + 32073.0i 0.925503 + 1.60302i
\(738\) 0 0
\(739\) 18332.7 31753.2i 0.912557 1.58059i 0.102118 0.994772i \(-0.467438\pi\)
0.810439 0.585823i \(-0.199228\pi\)
\(740\) 13307.1 + 23048.6i 0.661052 + 1.14498i
\(741\) 0 0
\(742\) −2788.89 + 3097.39i −0.137983 + 0.153247i
\(743\) 10321.3 0.509625 0.254813 0.966990i \(-0.417986\pi\)
0.254813 + 0.966990i \(0.417986\pi\)
\(744\) 0 0
\(745\) 28686.2 49686.0i 1.41071 2.44343i
\(746\) 1263.53 2188.50i 0.0620121 0.107408i
\(747\) 0 0
\(748\) 27137.4 1.32653
\(749\) 2415.74 + 513.476i 0.117849 + 0.0250494i
\(750\) 0 0
\(751\) 13339.0 + 23103.9i 0.648134 + 1.12260i 0.983568 + 0.180537i \(0.0577836\pi\)
−0.335434 + 0.942064i \(0.608883\pi\)
\(752\) −1144.30 + 1981.98i −0.0554896 + 0.0961107i
\(753\) 0 0
\(754\) 1348.71 + 2336.03i 0.0651421 + 0.112829i
\(755\) 49778.4 2.39950
\(756\) 0 0
\(757\) −11630.8 −0.558425 −0.279212 0.960229i \(-0.590073\pi\)
−0.279212 + 0.960229i \(0.590073\pi\)
\(758\) −2442.63 4230.77i −0.117045 0.202729i
\(759\) 0 0
\(760\) 4109.01 7117.02i 0.196118 0.339686i
\(761\) 18045.8 + 31256.3i 0.859607 + 1.48888i 0.872304 + 0.488963i \(0.162625\pi\)
−0.0126976 + 0.999919i \(0.504042\pi\)
\(762\) 0 0
\(763\) −1246.32 3835.74i −0.0591345 0.181996i
\(764\) −4776.93 −0.226208
\(765\) 0 0
\(766\) −8453.51 + 14641.9i −0.398744 + 0.690644i
\(767\) −3592.89 + 6223.07i −0.169142 + 0.292962i
\(768\) 0 0
\(769\) 33089.3 1.55167 0.775833 0.630938i \(-0.217330\pi\)
0.775833 + 0.630938i \(0.217330\pi\)
\(770\) −32443.3 6895.97i −1.51841 0.322745i
\(771\) 0 0
\(772\) −3972.23 6880.11i −0.185186 0.320752i
\(773\) −15495.4 + 26838.8i −0.720997 + 1.24880i 0.239603 + 0.970871i \(0.422983\pi\)
−0.960601 + 0.277933i \(0.910351\pi\)
\(774\) 0 0
\(775\) −20321.9 35198.6i −0.941915 1.63144i
\(776\) −2587.00 −0.119675
\(777\) 0 0
\(778\) 11814.9 0.544453
\(779\) −2124.05 3678.96i −0.0976917 0.169207i
\(780\) 0 0
\(781\) −21934.6 + 37991.9i −1.00497 + 1.74066i
\(782\) −2191.98 3796.62i −0.100236 0.173615i
\(783\) 0 0
\(784\) −2561.56 + 1861.10i −0.116689 + 0.0847803i
\(785\) −52675.4 −2.39499
\(786\) 0 0
\(787\) 12710.6 22015.4i 0.575711 0.997161i −0.420253 0.907407i \(-0.638059\pi\)
0.995964 0.0897537i \(-0.0286080\pi\)