Properties

Label 63.4.e.d.37.2
Level $63$
Weight $4$
Character 63.37
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 37.2
Root \(0.799027 + 1.38396i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.4.e.d.46.2

$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

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

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 −0.972000 0.234983i \(-0.924497\pi\)
0.689501 + 0.724285i \(0.257830\pi\)
\(3\) 0 0
\(4\) 2.72311 + 4.71657i 0.340389 + 0.589571i
\(5\) 9.14584 15.8411i 0.818029 1.41687i −0.0891033 0.996022i \(-0.528400\pi\)
0.907132 0.420846i \(-0.138267\pi\)
\(6\) 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 0.890169 + 0.455630i \(0.150586\pi\)
−0.0504975 + 0.998724i \(0.516081\pi\)
\(12\) 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 −0.995461 0.0951718i \(-0.969660\pi\)
0.415309 0.909680i \(-0.363673\pi\)
\(18\) 0 0
\(19\) 10.4542 18.1072i 0.126230 0.218636i −0.795983 0.605319i \(-0.793046\pi\)
0.922213 + 0.386682i \(0.126379\pi\)
\(20\) 99.6206 1.11379
\(21\) 0 0
\(22\) −97.9084 −0.948825
\(23\) −16.8655 + 29.2119i −0.152900 + 0.264831i −0.932292 0.361705i \(-0.882195\pi\)
0.779392 + 0.626536i \(0.215528\pi\)
\(24\) 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 −0.997342 0.0728626i \(-0.976787\pi\)
0.435570 0.900155i \(-0.356547\pi\)
\(32\) −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 −0.400240 0.916410i \(-0.631073\pi\)
0.993755 0.111587i \(-0.0355935\pi\)
\(38\) 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 −0.991729 0.128346i \(-0.959033\pi\)
0.607016 + 0.794690i \(0.292366\pi\)
\(48\) 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 0.942728 0.333563i \(-0.108251\pi\)
−0.760238 + 0.649645i \(0.774918\pi\)
\(54\) 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 0.717603 0.696453i \(-0.245239\pi\)
−0.961947 + 0.273236i \(0.911906\pi\)
\(60\) 0 0
\(61\) −326.263 + 565.104i −0.684815 + 1.18613i 0.288680 + 0.957426i \(0.406784\pi\)
−0.973495 + 0.228709i \(0.926550\pi\)
\(62\) 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 −0.998195 0.0600592i \(-0.980871\pi\)
0.447085 0.894492i \(-0.352462\pi\)
\(68\) 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 0.666996 0.745061i \(-0.267580\pi\)
−0.978740 + 0.205105i \(0.934246\pi\)
\(74\) 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 −0.744233 0.667920i \(-0.767185\pi\)
0.950552 + 0.310565i \(0.100518\pi\)
\(80\) 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 −0.438152 0.898901i \(-0.644367\pi\)
0.997547 0.0699997i \(-0.0222998\pi\)
\(90\) 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 0.987345 + 0.158587i \(0.0506938\pi\)
−0.356332 + 0.934359i \(0.615973\pi\)
\(102\) 0 0
\(103\) −265.669 + 460.153i −0.254147 + 0.440196i −0.964664 0.263485i \(-0.915128\pi\)
0.710516 + 0.703681i \(0.248461\pi\)
\(104\) −697.198 −0.657364
\(105\) 0 0
\(106\) −225.048 −0.206213
\(107\) 66.6758 115.486i 0.0602411 0.104341i −0.834332 0.551262i \(-0.814146\pi\)
0.894573 + 0.446922i \(0.147480\pi\)
\(108\) 0 0
\(109\) 108.884 + 188.593i 0.0956811 + 0.165725i 0.909893 0.414844i \(-0.136164\pi\)
−0.814212 + 0.580568i \(0.802830\pi\)
\(110\) −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 −0.850322 0.526263i \(-0.823593\pi\)
0.880918 + 0.473268i \(0.156926\pi\)
\(132\) 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 −0.995220 0.0976621i \(-0.968864\pi\)
0.413032 0.910717i \(-0.364470\pi\)
\(138\) 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 0.00747495 + 0.999972i \(0.497621\pi\)
−0.869739 + 0.493513i \(0.835713\pi\)
\(150\) 0 0
\(151\) 1360.68 + 2356.77i 0.733317 + 1.27014i 0.955458 + 0.295128i \(0.0953623\pi\)
−0.222141 + 0.975015i \(0.571304\pi\)
\(152\) −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 −0.956053 0.293193i \(-0.905282\pi\)
0.224114 0.974563i \(-0.428051\pi\)
\(158\) 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 −0.933148 0.359492i \(-0.882950\pi\)
0.777903 + 0.628384i \(0.216283\pi\)
\(164\) −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 −0.492598 0.870257i \(-0.663953\pi\)
0.999964 0.00852600i \(-0.00271394\pi\)
\(174\) 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 0.986854 + 0.161616i \(0.0516705\pi\)
−0.353464 + 0.935448i \(0.614996\pi\)
\(180\) 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 −0.937059 0.349170i \(-0.886464\pi\)
0.770920 + 0.636932i \(0.219797\pi\)
\(192\) 0 0
\(193\) 729.356 + 1263.28i 0.272022 + 0.471155i 0.969379 0.245568i \(-0.0789744\pi\)
−0.697358 + 0.716723i \(0.745641\pi\)
\(194\) −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 −0.993507 0.113774i \(-0.963706\pi\)
0.398222 0.917289i \(-0.369627\pi\)
\(200\) 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 0.996966 0.0778419i \(-0.0248029\pi\)
−0.565896 + 0.824477i \(0.691470\pi\)
\(228\) 0 0
\(229\) 2019.42 3497.74i 0.582739 1.00933i −0.412414 0.910997i \(-0.635314\pi\)
0.995153 0.0983374i \(-0.0313524\pi\)
\(230\) −985.995 −0.282672
\(231\) 0 0
\(232\) 1117.85 0.316339
\(233\) −1497.90 + 2594.44i −0.421162 + 0.729473i −0.996053 0.0887561i \(-0.971711\pi\)
0.574892 + 0.818230i \(0.305044\pi\)
\(234\) 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 0.999999 + 0.00125048i \(0.000398042\pi\)
−0.498917 + 0.866650i \(0.666269\pi\)
\(242\) −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 0.330218 + 0.943905i \(0.392878\pi\)
−0.982554 + 0.185975i \(0.940456\pi\)
\(258\) 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 −0.990376 0.138406i \(-0.955802\pi\)
0.375324 0.926893i \(-0.377531\pi\)
\(264\) 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 0.643214 0.765686i \(-0.277600\pi\)
−0.984711 + 0.174197i \(0.944267\pi\)
\(270\) 0 0
\(271\) −3448.62 + 5973.19i −0.773022 + 1.33891i 0.162877 + 0.986646i \(0.447923\pi\)
−0.935899 + 0.352267i \(0.885411\pi\)
\(272\) 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 0.628027 0.778191i \(-0.283863\pi\)
−0.987947 + 0.154792i \(0.950529\pi\)
\(278\) −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 −0.908391 0.418122i \(-0.862689\pi\)
0.0920914 0.995751i \(-0.470645\pi\)
\(284\) −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 0.974381 + 0.224903i \(0.0722064\pi\)
−0.292419 + 0.956290i \(0.594460\pi\)
\(312\) 0 0
\(313\) −3.12392 + 5.41079i −0.000564135 + 0.000977111i −0.866307 0.499511i \(-0.833513\pi\)
0.865743 + 0.500488i \(0.166846\pi\)
\(314\) 4601.99 0.827088
\(315\) 0 0
\(316\) 1578.00 0.280915
\(317\) 482.902 836.410i 0.0855598 0.148194i −0.820070 0.572263i \(-0.806065\pi\)
0.905630 + 0.424070i \(0.139399\pi\)
\(318\) 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 0.440595 + 0.897706i \(0.354767\pi\)
−0.997734 + 0.0672865i \(0.978566\pi\)
\(332\) 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 0.999080 + 0.0428923i \(0.0136572\pi\)
−0.462394 + 0.886675i \(0.653009\pi\)
\(348\) 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 0.554521 0.832170i \(-0.312902\pi\)
−0.997941 + 0.0641440i \(0.979568\pi\)
\(354\) 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 −0.843555 0.537043i \(-0.819541\pi\)
0.886870 + 0.462019i \(0.152875\pi\)
\(360\) 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 0.964179 0.265254i \(-0.0854558\pi\)
−0.711806 + 0.702376i \(0.752122\pi\)
\(368\) −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 −0.805915 0.592031i \(-0.798326\pi\)
0.915672 + 0.401927i \(0.131660\pi\)
\(374\) 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 0.260678 + 0.965426i \(0.416054\pi\)
−0.966422 + 0.256959i \(0.917280\pi\)
\(384\) 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 0.517964 0.855403i \(-0.326690\pi\)
−0.999782 + 0.0208684i \(0.993357\pi\)
\(390\) 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 −0.916737 0.399492i \(-0.869186\pi\)
0.804339 + 0.594171i \(0.202520\pi\)
\(398\) 5341.04 0.672669
\(399\) 0 0
\(400\) 1934.71 0.241839
\(401\) −73.8031 + 127.831i −0.00919090 + 0.0159191i −0.870584 0.492019i \(-0.836259\pi\)
0.861393 + 0.507938i \(0.169592\pi\)
\(402\) 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 0.923897 0.382641i \(-0.124985\pi\)
−0.793325 + 0.608798i \(0.791652\pi\)
\(410\) −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 −0.999959 0.00910411i \(-0.997102\pi\)
0.492095 0.870542i \(-0.336231\pi\)
\(432\) 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 −0.813513 0.581547i \(-0.802448\pi\)
0.910391 + 0.413749i \(0.135781\pi\)
\(440\) −24081.0 −2.60913
\(441\) 0 0
\(442\) 4216.97 0.453803
\(443\) −6712.36 + 11626.1i −0.719896 + 1.24690i 0.241145 + 0.970489i \(0.422477\pi\)
−0.961041 + 0.276407i \(0.910856\pi\)
\(444\) 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 −0.847328 0.531070i \(-0.821790\pi\)
0.883584 + 0.468273i \(0.155123\pi\)
\(458\) 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 −0.462961 0.886379i \(-0.653213\pi\)
0.999107 0.0422535i \(-0.0134537\pi\)
\(468\) 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 0.602100 0.798420i \(-0.294331\pi\)
−0.992503 + 0.122224i \(0.960997\pi\)
\(480\) 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 0.943994 0.329961i \(-0.107036\pi\)
−0.757752 + 0.652543i \(0.773702\pi\)
\(488\) 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 −0.768968 0.639287i \(-0.779229\pi\)
0.938123 + 0.346302i \(0.112563\pi\)
\(500\) −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 −0.660099 0.751179i \(-0.729485\pi\)
0.980589 + 0.196073i \(0.0628188\pi\)
\(510\) 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 0.995459 + 0.0951930i \(0.0303468\pi\)
−0.415290 + 0.909689i \(0.636320\pi\)
\(522\) 0 0
\(523\) −9423.58 + 16322.1i −0.787886 + 1.36466i 0.139373 + 0.990240i \(0.455491\pi\)
−0.927260 + 0.374419i \(0.877842\pi\)
\(524\) 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 −0.421099 0.907015i \(-0.638356\pi\)
0.996047 0.0888248i \(-0.0283111\pi\)
\(542\) −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 0.950629 0.310330i \(-0.100439\pi\)
−0.744068 + 0.668104i \(0.767106\pi\)
\(558\) 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 −0.823335 0.567556i \(-0.807889\pi\)
−0.0798500 0.996807i \(-0.525444\pi\)
\(564\) 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 −0.314437 0.949278i \(-0.601816\pi\)
0.979318 0.202328i \(-0.0648509\pi\)
\(570\) 0 0
\(571\) 5637.42 + 9764.30i 0.413168 + 0.715628i 0.995234 0.0975136i \(-0.0310889\pi\)
−0.582066 + 0.813141i \(0.697756\pi\)
\(572\) −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 0.862790 + 0.505562i \(0.168715\pi\)
0.00643457 + 0.999979i \(0.497952\pi\)
\(578\) −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 −0.929201 0.369575i \(-0.879503\pi\)
0.784662 + 0.619924i \(0.212837\pi\)
\(594\) 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 0.601841 0.798616i \(-0.294434\pi\)
−0.992542 + 0.121901i \(0.961101\pi\)
\(600\) 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 −0.917058 0.398754i \(-0.869443\pi\)
0.803860 + 0.594818i \(0.202776\pi\)
\(608\) −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 0.787039 0.616903i \(-0.211613\pi\)
−0.927773 + 0.373145i \(0.878279\pi\)
\(614\) −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 0.895131 0.445803i \(-0.147082\pi\)
−0.833642 + 0.552305i \(0.813748\pi\)
\(620\) −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 −0.993906 0.110235i \(-0.964840\pi\)
0.401486 0.915865i \(-0.368494\pi\)
\(642\) 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 0.718040 0.696001i \(-0.245039\pi\)
−0.961775 + 0.273840i \(0.911706\pi\)
\(648\) 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 −0.895126 0.445814i \(-0.852914\pi\)
0.833649 + 0.552295i \(0.186248\pi\)
\(654\) 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 0.856350 0.516397i \(-0.172727\pi\)
−0.875387 + 0.483422i \(0.839394\pi\)
\(662\) −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 0.247377 + 0.968919i \(0.420431\pi\)
−0.962797 + 0.270225i \(0.912902\pi\)
\(678\) 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 0.999646 0.0266151i \(-0.00847285\pi\)
−0.522872 + 0.852411i \(0.675140\pi\)
\(684\) 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 −0.468342 0.883547i \(-0.655149\pi\)
0.999345 0.0361772i \(-0.0115181\pi\)
\(692\) 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 0.193546 + 0.981091i \(0.438001\pi\)
−0.946423 + 0.322930i \(0.895332\pi\)
\(710\) −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 0.432684 + 0.901546i \(0.357567\pi\)
−0.997103 + 0.0760577i \(0.975767\pi\)
\(720\) 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 −0.917731 0.397204i \(-0.869981\pi\)
0.802854 + 0.596176i \(0.203314\pi\)
\(734\) −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 0.810439 + 0.585823i \(0.199228\pi\)
0.102118 + 0.994772i \(0.467438\pi\)
\(740\) 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 −0.335434 0.942064i \(-0.608883\pi\)
0.983568 0.180537i \(-0.0577836\pi\)
\(752\) −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 −0.0126976 0.999919i \(-0.504042\pi\)
0.872304 0.488963i \(-0.162625\pi\)
\(762\) 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 −0.960601 0.277933i \(-0.910351\pi\)
0.239603 0.970871i \(-0.422983\pi\)
\(774\) 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 0.995964 + 0.0897537i \(0.0286080\pi\)
−0.420253 + 0.907407i \(0.638059\pi\)