Properties

Label 252.4.b.g.55.6
Level $252$
Weight $4$
Character 252.55
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} - 37785264 x^{9} + 272741368 x^{8} - 1739202044 x^{7} + 9778426658 x^{6} - 39463975388 x^{5} + 101978126949 x^{4} - 176540053420 x^{3} + 219245087130 x^{2} - 139977817400 x + 52705588025\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.6
Root \(4.06402 + 1.75957i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.4.b.g.55.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.79845 - 2.18302i) q^{2} +(-1.53113 + 7.85211i) q^{4} +17.7710i q^{5} +(-5.15121 + 17.7895i) q^{7} +(19.8950 - 10.7792i) q^{8} +O(q^{10})\) \(q+(-1.79845 - 2.18302i) q^{2} +(-1.53113 + 7.85211i) q^{4} +17.7710i q^{5} +(-5.15121 + 17.7895i) q^{7} +(19.8950 - 10.7792i) q^{8} +(38.7945 - 31.9604i) q^{10} -10.7792i q^{11} +72.4083i q^{13} +(48.0989 - 20.7483i) q^{14} +(-59.3113 - 24.0452i) q^{16} -62.7518i q^{17} -98.1938 q^{19} +(-139.540 - 27.2097i) q^{20} +(-23.5311 + 19.3858i) q^{22} -160.312i q^{23} -190.809 q^{25} +(158.069 - 130.223i) q^{26} +(-131.798 - 67.6859i) q^{28} -90.1466 q^{29} +201.859 q^{31} +(54.1775 + 172.722i) q^{32} +(-136.988 + 112.856i) q^{34} +(-316.137 - 91.5424i) q^{35} -139.685 q^{37} +(176.597 + 214.359i) q^{38} +(191.557 + 353.554i) q^{40} +297.094i q^{41} -22.8078i q^{43} +(84.6393 + 16.5043i) q^{44} +(-349.963 + 288.313i) q^{46} +484.046 q^{47} +(-289.930 - 183.275i) q^{49} +(343.162 + 416.540i) q^{50} +(-568.558 - 110.866i) q^{52} -502.433 q^{53} +191.557 q^{55} +(89.2726 + 409.446i) q^{56} +(162.125 + 196.792i) q^{58} -148.228 q^{59} -438.958i q^{61} +(-363.035 - 440.663i) q^{62} +(279.619 - 428.903i) q^{64} -1286.77 q^{65} +667.659i q^{67} +(492.734 + 96.0811i) q^{68} +(368.719 + 854.767i) q^{70} -174.191i q^{71} +1167.55i q^{73} +(251.217 + 304.934i) q^{74} +(150.347 - 771.028i) q^{76} +(191.756 + 55.5258i) q^{77} -680.430i q^{79} +(427.308 - 1054.02i) q^{80} +(648.562 - 534.310i) q^{82} -780.502 q^{83} +1115.16 q^{85} +(-49.7899 + 41.0188i) q^{86} +(-116.191 - 214.451i) q^{88} -27.2097i q^{89} +(-1288.10 - 372.990i) q^{91} +(1258.78 + 245.458i) q^{92} +(-870.535 - 1056.68i) q^{94} -1745.00i q^{95} -212.717i q^{97} +(121.334 + 962.533i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 40 q^{4} + O(q^{10}) \) \( 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79845 2.18302i −0.635849 0.771813i
\(3\) 0 0
\(4\) −1.53113 + 7.85211i −0.191391 + 0.981514i
\(5\) 17.7710i 1.58949i 0.606944 + 0.794744i \(0.292395\pi\)
−0.606944 + 0.794744i \(0.707605\pi\)
\(6\) 0 0
\(7\) −5.15121 + 17.7895i −0.278139 + 0.960541i
\(8\) 19.8950 10.7792i 0.879241 0.476377i
\(9\) 0 0
\(10\) 38.7945 31.9604i 1.22679 1.01068i
\(11\) 10.7792i 0.295459i −0.989028 0.147729i \(-0.952804\pi\)
0.989028 0.147729i \(-0.0471964\pi\)
\(12\) 0 0
\(13\) 72.4083i 1.54480i 0.635135 + 0.772402i \(0.280945\pi\)
−0.635135 + 0.772402i \(0.719055\pi\)
\(14\) 48.0989 20.7483i 0.918213 0.396088i
\(15\) 0 0
\(16\) −59.3113 24.0452i −0.926739 0.375706i
\(17\) 62.7518i 0.895267i −0.894217 0.447634i \(-0.852267\pi\)
0.894217 0.447634i \(-0.147733\pi\)
\(18\) 0 0
\(19\) −98.1938 −1.18564 −0.592821 0.805334i \(-0.701986\pi\)
−0.592821 + 0.805334i \(0.701986\pi\)
\(20\) −139.540 27.2097i −1.56011 0.304214i
\(21\) 0 0
\(22\) −23.5311 + 19.3858i −0.228039 + 0.187867i
\(23\) 160.312i 1.45336i −0.686976 0.726680i \(-0.741062\pi\)
0.686976 0.726680i \(-0.258938\pi\)
\(24\) 0 0
\(25\) −190.809 −1.52647
\(26\) 158.069 130.223i 1.19230 0.982262i
\(27\) 0 0
\(28\) −131.798 67.6859i −0.889551 0.456837i
\(29\) −90.1466 −0.577235 −0.288617 0.957445i \(-0.593196\pi\)
−0.288617 + 0.957445i \(0.593196\pi\)
\(30\) 0 0
\(31\) 201.859 1.16952 0.584759 0.811207i \(-0.301189\pi\)
0.584759 + 0.811207i \(0.301189\pi\)
\(32\) 54.1775 + 172.722i 0.299291 + 0.954162i
\(33\) 0 0
\(34\) −136.988 + 112.856i −0.690979 + 0.569255i
\(35\) −316.137 91.5424i −1.52677 0.442099i
\(36\) 0 0
\(37\) −139.685 −0.620650 −0.310325 0.950631i \(-0.600438\pi\)
−0.310325 + 0.950631i \(0.600438\pi\)
\(38\) 176.597 + 214.359i 0.753890 + 0.915094i
\(39\) 0 0
\(40\) 191.557 + 353.554i 0.757196 + 1.39754i
\(41\) 297.094i 1.13167i 0.824520 + 0.565833i \(0.191445\pi\)
−0.824520 + 0.565833i \(0.808555\pi\)
\(42\) 0 0
\(43\) 22.8078i 0.0808875i −0.999182 0.0404437i \(-0.987123\pi\)
0.999182 0.0404437i \(-0.0128772\pi\)
\(44\) 84.6393 + 16.5043i 0.289997 + 0.0565481i
\(45\) 0 0
\(46\) −349.963 + 288.313i −1.12172 + 0.924118i
\(47\) 484.046 1.50224 0.751122 0.660164i \(-0.229513\pi\)
0.751122 + 0.660164i \(0.229513\pi\)
\(48\) 0 0
\(49\) −289.930 183.275i −0.845277 0.534328i
\(50\) 343.162 + 416.540i 0.970608 + 1.17815i
\(51\) 0 0
\(52\) −568.558 110.866i −1.51625 0.295662i
\(53\) −502.433 −1.30216 −0.651081 0.759009i \(-0.725684\pi\)
−0.651081 + 0.759009i \(0.725684\pi\)
\(54\) 0 0
\(55\) 191.557 0.469628
\(56\) 89.2726 + 409.446i 0.213028 + 0.977046i
\(57\) 0 0
\(58\) 162.125 + 196.792i 0.367034 + 0.445517i
\(59\) −148.228 −0.327078 −0.163539 0.986537i \(-0.552291\pi\)
−0.163539 + 0.986537i \(0.552291\pi\)
\(60\) 0 0
\(61\) 438.958i 0.921357i −0.887567 0.460678i \(-0.847606\pi\)
0.887567 0.460678i \(-0.152394\pi\)
\(62\) −363.035 440.663i −0.743637 0.902649i
\(63\) 0 0
\(64\) 279.619 428.903i 0.546130 0.837700i
\(65\) −1286.77 −2.45545
\(66\) 0 0
\(67\) 667.659i 1.21743i 0.793391 + 0.608713i \(0.208314\pi\)
−0.793391 + 0.608713i \(0.791686\pi\)
\(68\) 492.734 + 96.0811i 0.878717 + 0.171346i
\(69\) 0 0
\(70\) 368.719 + 854.767i 0.629577 + 1.45949i
\(71\) 174.191i 0.291165i −0.989346 0.145582i \(-0.953494\pi\)
0.989346 0.145582i \(-0.0465056\pi\)
\(72\) 0 0
\(73\) 1167.55i 1.87193i 0.352088 + 0.935967i \(0.385472\pi\)
−0.352088 + 0.935967i \(0.614528\pi\)
\(74\) 251.217 + 304.934i 0.394640 + 0.479026i
\(75\) 0 0
\(76\) 150.347 771.028i 0.226921 1.16372i
\(77\) 191.756 + 55.5258i 0.283800 + 0.0821787i
\(78\) 0 0
\(79\) 680.430i 0.969042i −0.874780 0.484521i \(-0.838994\pi\)
0.874780 0.484521i \(-0.161006\pi\)
\(80\) 427.308 1054.02i 0.597181 1.47304i
\(81\) 0 0
\(82\) 648.562 534.310i 0.873435 0.719569i
\(83\) −780.502 −1.03218 −0.516091 0.856534i \(-0.672614\pi\)
−0.516091 + 0.856534i \(0.672614\pi\)
\(84\) 0 0
\(85\) 1115.16 1.42302
\(86\) −49.7899 + 41.0188i −0.0624300 + 0.0514323i
\(87\) 0 0
\(88\) −116.191 214.451i −0.140750 0.259779i
\(89\) 27.2097i 0.0324070i −0.999869 0.0162035i \(-0.994842\pi\)
0.999869 0.0162035i \(-0.00515796\pi\)
\(90\) 0 0
\(91\) −1288.10 372.990i −1.48385 0.429671i
\(92\) 1258.78 + 245.458i 1.42649 + 0.278160i
\(93\) 0 0
\(94\) −870.535 1056.68i −0.955201 1.15945i
\(95\) 1745.00i 1.88456i
\(96\) 0 0
\(97\) 212.717i 0.222661i −0.993783 0.111331i \(-0.964489\pi\)
0.993783 0.111331i \(-0.0355112\pi\)
\(98\) 121.334 + 962.533i 0.125067 + 0.992148i
\(99\) 0 0
\(100\) 292.154 1498.26i 0.292154 1.49826i
\(101\) 896.296i 0.883018i 0.897257 + 0.441509i \(0.145557\pi\)
−0.897257 + 0.441509i \(0.854443\pi\)
\(102\) 0 0
\(103\) −1319.65 −1.26242 −0.631210 0.775612i \(-0.717441\pi\)
−0.631210 + 0.775612i \(0.717441\pi\)
\(104\) 780.502 + 1440.56i 0.735908 + 1.35825i
\(105\) 0 0
\(106\) 903.603 + 1096.82i 0.827978 + 1.00503i
\(107\) 1490.63i 1.34677i −0.739292 0.673385i \(-0.764840\pi\)
0.739292 0.673385i \(-0.235160\pi\)
\(108\) 0 0
\(109\) 555.346 0.488005 0.244002 0.969775i \(-0.421539\pi\)
0.244002 + 0.969775i \(0.421539\pi\)
\(110\) −344.506 418.172i −0.298613 0.362465i
\(111\) 0 0
\(112\) 733.276 931.254i 0.618644 0.785672i
\(113\) −75.1011 −0.0625214 −0.0312607 0.999511i \(-0.509952\pi\)
−0.0312607 + 0.999511i \(0.509952\pi\)
\(114\) 0 0
\(115\) 2848.90 2.31010
\(116\) 138.026 707.841i 0.110478 0.566564i
\(117\) 0 0
\(118\) 266.580 + 323.583i 0.207972 + 0.252443i
\(119\) 1116.32 + 323.248i 0.859941 + 0.249009i
\(120\) 0 0
\(121\) 1214.81 0.912704
\(122\) −958.252 + 789.445i −0.711115 + 0.585844i
\(123\) 0 0
\(124\) −309.073 + 1585.02i −0.223835 + 1.14790i
\(125\) 1169.50i 0.836826i
\(126\) 0 0
\(127\) 14.4669i 0.0101081i 0.999987 + 0.00505404i \(0.00160876\pi\)
−0.999987 + 0.00505404i \(0.998391\pi\)
\(128\) −1439.18 + 160.949i −0.993805 + 0.111141i
\(129\) 0 0
\(130\) 2314.19 + 2809.04i 1.56129 + 1.89515i
\(131\) −2380.87 −1.58792 −0.793960 0.607970i \(-0.791984\pi\)
−0.793960 + 0.607970i \(0.791984\pi\)
\(132\) 0 0
\(133\) 505.817 1746.81i 0.329774 1.13886i
\(134\) 1457.51 1200.75i 0.939625 0.774099i
\(135\) 0 0
\(136\) −676.413 1248.44i −0.426485 0.787156i
\(137\) 176.710 0.110200 0.0550999 0.998481i \(-0.482452\pi\)
0.0550999 + 0.998481i \(0.482452\pi\)
\(138\) 0 0
\(139\) 370.887 0.226318 0.113159 0.993577i \(-0.463903\pi\)
0.113159 + 0.993577i \(0.463903\pi\)
\(140\) 1202.85 2342.18i 0.726137 1.41393i
\(141\) 0 0
\(142\) −380.263 + 313.275i −0.224725 + 0.185137i
\(143\) 780.502 0.456425
\(144\) 0 0
\(145\) 1602.00i 0.917508i
\(146\) 2548.78 2099.78i 1.44478 1.19027i
\(147\) 0 0
\(148\) 213.875 1096.82i 0.118787 0.609176i
\(149\) −2274.32 −1.25047 −0.625234 0.780437i \(-0.714997\pi\)
−0.625234 + 0.780437i \(0.714997\pi\)
\(150\) 0 0
\(151\) 2222.44i 1.19774i 0.800845 + 0.598872i \(0.204384\pi\)
−0.800845 + 0.598872i \(0.795616\pi\)
\(152\) −1953.56 + 1058.45i −1.04247 + 0.564812i
\(153\) 0 0
\(154\) −223.650 518.467i −0.117027 0.271294i
\(155\) 3587.25i 1.85893i
\(156\) 0 0
\(157\) 158.340i 0.0804901i 0.999190 + 0.0402450i \(0.0128139\pi\)
−0.999190 + 0.0402450i \(0.987186\pi\)
\(158\) −1485.39 + 1223.72i −0.747919 + 0.616165i
\(159\) 0 0
\(160\) −3069.44 + 962.791i −1.51663 + 0.475720i
\(161\) 2851.86 + 825.799i 1.39601 + 0.404237i
\(162\) 0 0
\(163\) 1468.12i 0.705470i −0.935723 0.352735i \(-0.885252\pi\)
0.935723 0.352735i \(-0.114748\pi\)
\(164\) −2332.82 454.890i −1.11075 0.216591i
\(165\) 0 0
\(166\) 1403.70 + 1703.85i 0.656313 + 0.796652i
\(167\) 2529.10 1.17190 0.585950 0.810347i \(-0.300721\pi\)
0.585950 + 0.810347i \(0.300721\pi\)
\(168\) 0 0
\(169\) −3045.96 −1.38642
\(170\) −2005.57 2434.42i −0.904825 1.09830i
\(171\) 0 0
\(172\) 179.090 + 34.9217i 0.0793922 + 0.0154811i
\(173\) 834.063i 0.366547i 0.983062 + 0.183273i \(0.0586694\pi\)
−0.983062 + 0.183273i \(0.941331\pi\)
\(174\) 0 0
\(175\) 982.900 3394.40i 0.424573 1.46624i
\(176\) −259.187 + 639.327i −0.111006 + 0.273813i
\(177\) 0 0
\(178\) −59.3993 + 48.9354i −0.0250122 + 0.0206060i
\(179\) 2094.57i 0.874611i 0.899313 + 0.437305i \(0.144067\pi\)
−0.899313 + 0.437305i \(0.855933\pi\)
\(180\) 0 0
\(181\) 2968.74i 1.21914i 0.792732 + 0.609571i \(0.208658\pi\)
−0.792732 + 0.609571i \(0.791342\pi\)
\(182\) 1502.35 + 3482.76i 0.611877 + 1.41846i
\(183\) 0 0
\(184\) −1728.03 3189.39i −0.692347 1.27785i
\(185\) 2482.34i 0.986516i
\(186\) 0 0
\(187\) −676.413 −0.264514
\(188\) −741.138 + 3800.79i −0.287516 + 1.47447i
\(189\) 0 0
\(190\) −3809.37 + 3138.31i −1.45453 + 1.19830i
\(191\) 2411.20i 0.913446i 0.889609 + 0.456723i \(0.150977\pi\)
−0.889609 + 0.456723i \(0.849023\pi\)
\(192\) 0 0
\(193\) 2435.71 0.908426 0.454213 0.890893i \(-0.349921\pi\)
0.454213 + 0.890893i \(0.349921\pi\)
\(194\) −464.365 + 382.561i −0.171853 + 0.141579i
\(195\) 0 0
\(196\) 1883.01 1995.95i 0.686229 0.727385i
\(197\) 2087.70 0.755039 0.377520 0.926002i \(-0.376777\pi\)
0.377520 + 0.926002i \(0.376777\pi\)
\(198\) 0 0
\(199\) −3388.82 −1.20717 −0.603585 0.797299i \(-0.706262\pi\)
−0.603585 + 0.797299i \(0.706262\pi\)
\(200\) −3796.14 + 2056.77i −1.34214 + 0.727177i
\(201\) 0 0
\(202\) 1956.63 1611.95i 0.681525 0.561466i
\(203\) 464.365 1603.66i 0.160552 0.554457i
\(204\) 0 0
\(205\) −5279.67 −1.79877
\(206\) 2373.33 + 2880.83i 0.802709 + 0.974352i
\(207\) 0 0
\(208\) 1741.07 4294.63i 0.580392 1.43163i
\(209\) 1058.45i 0.350308i
\(210\) 0 0
\(211\) 4614.70i 1.50564i 0.658228 + 0.752818i \(0.271306\pi\)
−0.658228 + 0.752818i \(0.728694\pi\)
\(212\) 769.290 3945.16i 0.249222 1.27809i
\(213\) 0 0
\(214\) −3254.06 + 2680.82i −1.03945 + 0.856343i
\(215\) 405.319 0.128570
\(216\) 0 0
\(217\) −1039.82 + 3590.97i −0.325289 + 1.12337i
\(218\) −998.765 1212.33i −0.310298 0.376649i
\(219\) 0 0
\(220\) −293.298 + 1504.13i −0.0898826 + 0.460946i
\(221\) 4543.75 1.38301
\(222\) 0 0
\(223\) −294.922 −0.0885625 −0.0442812 0.999019i \(-0.514100\pi\)
−0.0442812 + 0.999019i \(0.514100\pi\)
\(224\) −3351.71 + 74.0629i −0.999756 + 0.0220917i
\(225\) 0 0
\(226\) 135.066 + 163.947i 0.0397542 + 0.0482548i
\(227\) −2272.00 −0.664310 −0.332155 0.943225i \(-0.607776\pi\)
−0.332155 + 0.943225i \(0.607776\pi\)
\(228\) 0 0
\(229\) 3054.67i 0.881478i 0.897635 + 0.440739i \(0.145283\pi\)
−0.897635 + 0.440739i \(0.854717\pi\)
\(230\) −5123.62 6219.20i −1.46888 1.78297i
\(231\) 0 0
\(232\) −1793.46 + 971.706i −0.507529 + 0.274981i
\(233\) 3277.16 0.921433 0.460717 0.887547i \(-0.347592\pi\)
0.460717 + 0.887547i \(0.347592\pi\)
\(234\) 0 0
\(235\) 8602.00i 2.38780i
\(236\) 226.955 1163.90i 0.0625997 0.321031i
\(237\) 0 0
\(238\) −1302.00 3018.29i −0.354604 0.822046i
\(239\) 5776.27i 1.56333i 0.623698 + 0.781665i \(0.285629\pi\)
−0.623698 + 0.781665i \(0.714371\pi\)
\(240\) 0 0
\(241\) 321.470i 0.0859240i 0.999077 + 0.0429620i \(0.0136794\pi\)
−0.999077 + 0.0429620i \(0.986321\pi\)
\(242\) −2184.78 2651.95i −0.580342 0.704437i
\(243\) 0 0
\(244\) 3446.74 + 672.101i 0.904324 + 0.176339i
\(245\) 3256.98 5152.35i 0.849309 1.34356i
\(246\) 0 0
\(247\) 7110.04i 1.83158i
\(248\) 4015.99 2175.88i 1.02829 0.557131i
\(249\) 0 0
\(250\) −2553.04 + 2103.29i −0.645873 + 0.532095i
\(251\) 1818.09 0.457200 0.228600 0.973520i \(-0.426585\pi\)
0.228600 + 0.973520i \(0.426585\pi\)
\(252\) 0 0
\(253\) −1728.03 −0.429408
\(254\) 31.5814 26.0180i 0.00780155 0.00642722i
\(255\) 0 0
\(256\) 2939.66 + 2852.30i 0.717690 + 0.696363i
\(257\) 2438.33i 0.591824i −0.955215 0.295912i \(-0.904376\pi\)
0.955215 0.295912i \(-0.0956236\pi\)
\(258\) 0 0
\(259\) 719.546 2484.92i 0.172627 0.596159i
\(260\) 1970.21 10103.9i 0.469951 2.41006i
\(261\) 0 0
\(262\) 4281.88 + 5197.48i 1.00968 + 1.22558i
\(263\) 4083.47i 0.957406i −0.877977 0.478703i \(-0.841107\pi\)
0.877977 0.478703i \(-0.158893\pi\)
\(264\) 0 0
\(265\) 8928.76i 2.06977i
\(266\) −4723.01 + 2037.36i −1.08867 + 0.469618i
\(267\) 0 0
\(268\) −5242.53 1022.27i −1.19492 0.233004i
\(269\) 2121.53i 0.480862i 0.970666 + 0.240431i \(0.0772888\pi\)
−0.970666 + 0.240431i \(0.922711\pi\)
\(270\) 0 0
\(271\) 6897.68 1.54614 0.773070 0.634321i \(-0.218720\pi\)
0.773070 + 0.634321i \(0.218720\pi\)
\(272\) −1508.88 + 3721.89i −0.336357 + 0.829679i
\(273\) 0 0
\(274\) −317.805 385.762i −0.0700705 0.0850537i
\(275\) 2056.77i 0.451010i
\(276\) 0 0
\(277\) −1456.63 −0.315957 −0.157979 0.987443i \(-0.550498\pi\)
−0.157979 + 0.987443i \(0.550498\pi\)
\(278\) −667.024 809.654i −0.143904 0.174676i
\(279\) 0 0
\(280\) −7276.28 + 1586.47i −1.55300 + 0.338605i
\(281\) −6013.55 −1.27665 −0.638325 0.769767i \(-0.720372\pi\)
−0.638325 + 0.769767i \(0.720372\pi\)
\(282\) 0 0
\(283\) −2485.71 −0.522121 −0.261060 0.965322i \(-0.584072\pi\)
−0.261060 + 0.965322i \(0.584072\pi\)
\(284\) 1367.77 + 266.709i 0.285782 + 0.0557264i
\(285\) 0 0
\(286\) −1403.70 1703.85i −0.290218 0.352275i
\(287\) −5285.15 1530.40i −1.08701 0.314761i
\(288\) 0 0
\(289\) 975.214 0.198497
\(290\) −3497.19 + 2881.12i −0.708145 + 0.583397i
\(291\) 0 0
\(292\) −9167.72 1787.67i −1.83733 0.358272i
\(293\) 2245.72i 0.447769i 0.974616 + 0.223884i \(0.0718738\pi\)
−0.974616 + 0.223884i \(0.928126\pi\)
\(294\) 0 0
\(295\) 2634.15i 0.519886i
\(296\) −2779.02 + 1505.69i −0.545701 + 0.295663i
\(297\) 0 0
\(298\) 4090.27 + 4964.89i 0.795110 + 0.965128i
\(299\) 11607.9 2.24516
\(300\) 0 0
\(301\) 405.739 + 117.488i 0.0776957 + 0.0224980i
\(302\) 4851.62 3996.95i 0.924435 0.761585i
\(303\) 0 0
\(304\) 5824.00 + 2361.09i 1.09878 + 0.445453i
\(305\) 7800.73 1.46449
\(306\) 0 0
\(307\) −839.287 −0.156028 −0.0780141 0.996952i \(-0.524858\pi\)
−0.0780141 + 0.996952i \(0.524858\pi\)
\(308\) −729.598 + 1420.67i −0.134976 + 0.262825i
\(309\) 0 0
\(310\) 7831.03 6451.50i 1.43475 1.18200i
\(311\) 1155.68 0.210717 0.105358 0.994434i \(-0.466401\pi\)
0.105358 + 0.994434i \(0.466401\pi\)
\(312\) 0 0
\(313\) 4244.76i 0.766543i 0.923636 + 0.383272i \(0.125203\pi\)
−0.923636 + 0.383272i \(0.874797\pi\)
\(314\) 345.660 284.768i 0.0621233 0.0511796i
\(315\) 0 0
\(316\) 5342.81 + 1041.83i 0.951128 + 0.185466i
\(317\) 3876.67 0.686863 0.343431 0.939178i \(-0.388411\pi\)
0.343431 + 0.939178i \(0.388411\pi\)
\(318\) 0 0
\(319\) 971.706i 0.170549i
\(320\) 7622.04 + 4969.11i 1.33152 + 0.868068i
\(321\) 0 0
\(322\) −3326.20 7710.82i −0.575658 1.33449i
\(323\) 6161.83i 1.06147i
\(324\) 0 0
\(325\) 13816.2i 2.35810i
\(326\) −3204.92 + 2640.34i −0.544491 + 0.448573i
\(327\) 0 0
\(328\) 3202.43 + 5910.68i 0.539100 + 0.995008i
\(329\) −2493.43 + 8610.93i −0.417833 + 1.44297i
\(330\) 0 0
\(331\) 475.573i 0.0789724i 0.999220 + 0.0394862i \(0.0125721\pi\)
−0.999220 + 0.0394862i \(0.987428\pi\)
\(332\) 1195.05 6128.58i 0.197551 1.01310i
\(333\) 0 0
\(334\) −4548.46 5521.06i −0.745152 0.904488i
\(335\) −11865.0 −1.93508
\(336\) 0 0
\(337\) 10012.6 1.61847 0.809233 0.587488i \(-0.199883\pi\)
0.809233 + 0.587488i \(0.199883\pi\)
\(338\) 5478.01 + 6649.38i 0.881552 + 1.07005i
\(339\) 0 0
\(340\) −1707.46 + 8756.39i −0.272353 + 1.39671i
\(341\) 2175.88i 0.345544i
\(342\) 0 0
\(343\) 4753.85 4213.61i 0.748349 0.663305i
\(344\) −245.850 453.761i −0.0385329 0.0711196i
\(345\) 0 0
\(346\) 1820.77 1500.02i 0.282906 0.233069i
\(347\) 10771.5i 1.66642i −0.552959 0.833209i \(-0.686501\pi\)
0.552959 0.833209i \(-0.313499\pi\)
\(348\) 0 0
\(349\) 9281.78i 1.42362i 0.702373 + 0.711809i \(0.252124\pi\)
−0.702373 + 0.711809i \(0.747876\pi\)
\(350\) −9177.72 + 3958.98i −1.40163 + 0.604618i
\(351\) 0 0
\(352\) 1861.80 583.989i 0.281915 0.0884282i
\(353\) 4527.91i 0.682709i −0.939935 0.341355i \(-0.889114\pi\)
0.939935 0.341355i \(-0.110886\pi\)
\(354\) 0 0
\(355\) 3095.56 0.462803
\(356\) 213.654 + 41.6616i 0.0318079 + 0.00620242i
\(357\) 0 0
\(358\) 4572.48 3766.98i 0.675036 0.556121i
\(359\) 9834.05i 1.44574i 0.690983 + 0.722871i \(0.257178\pi\)
−0.690983 + 0.722871i \(0.742822\pi\)
\(360\) 0 0
\(361\) 2783.02 0.405747
\(362\) 6480.81 5339.14i 0.940950 0.775190i
\(363\) 0 0
\(364\) 4901.02 9543.24i 0.705723 1.37418i
\(365\) −20748.5 −2.97542
\(366\) 0 0
\(367\) −11847.0 −1.68504 −0.842518 0.538669i \(-0.818927\pi\)
−0.842518 + 0.538669i \(0.818927\pi\)
\(368\) −3854.72 + 9508.29i −0.546036 + 1.34689i
\(369\) 0 0
\(370\) −5419.00 + 4464.38i −0.761406 + 0.627276i
\(371\) 2588.14 8938.02i 0.362182 1.25078i
\(372\) 0 0
\(373\) 10310.6 1.43127 0.715634 0.698475i \(-0.246138\pi\)
0.715634 + 0.698475i \(0.246138\pi\)
\(374\) 1216.50 + 1476.62i 0.168191 + 0.204156i
\(375\) 0 0
\(376\) 9630.08 5217.62i 1.32083 0.715634i
\(377\) 6527.36i 0.891714i
\(378\) 0 0
\(379\) 3861.94i 0.523416i 0.965147 + 0.261708i \(0.0842857\pi\)
−0.965147 + 0.261708i \(0.915714\pi\)
\(380\) 13702.0 + 2671.83i 1.84973 + 0.360689i
\(381\) 0 0
\(382\) 5263.69 4336.43i 0.705010 0.580814i
\(383\) −9178.43 −1.22453 −0.612266 0.790652i \(-0.709742\pi\)
−0.612266 + 0.790652i \(0.709742\pi\)
\(384\) 0 0
\(385\) −986.751 + 3407.70i −0.130622 + 0.451097i
\(386\) −4380.51 5317.19i −0.577622 0.701135i
\(387\) 0 0
\(388\) 1670.28 + 325.697i 0.218545 + 0.0426153i
\(389\) −314.387 −0.0409770 −0.0204885 0.999790i \(-0.506522\pi\)
−0.0204885 + 0.999790i \(0.506522\pi\)
\(390\) 0 0
\(391\) −10059.8 −1.30115
\(392\) −7743.69 521.035i −0.997744 0.0671333i
\(393\) 0 0
\(394\) −3754.64 4557.49i −0.480091 0.582749i
\(395\) 12091.9 1.54028
\(396\) 0 0
\(397\) 2126.89i 0.268880i 0.990922 + 0.134440i \(0.0429236\pi\)
−0.990922 + 0.134440i \(0.957076\pi\)
\(398\) 6094.63 + 7397.85i 0.767579 + 0.931710i
\(399\) 0 0
\(400\) 11317.1 + 4588.05i 1.41464 + 0.573506i
\(401\) −6506.32 −0.810249 −0.405125 0.914261i \(-0.632772\pi\)
−0.405125 + 0.914261i \(0.632772\pi\)
\(402\) 0 0
\(403\) 14616.3i 1.80667i
\(404\) −7037.82 1372.34i −0.866694 0.169002i
\(405\) 0 0
\(406\) −4335.96 + 1870.39i −0.530024 + 0.228635i
\(407\) 1505.69i 0.183376i
\(408\) 0 0
\(409\) 3280.91i 0.396652i 0.980136 + 0.198326i \(0.0635505\pi\)
−0.980136 + 0.198326i \(0.936450\pi\)
\(410\) 9495.24 + 11525.6i 1.14375 + 1.38832i
\(411\) 0 0
\(412\) 2020.56 10362.1i 0.241616 1.23908i
\(413\) 763.552 2636.89i 0.0909732 0.314171i
\(414\) 0 0
\(415\) 13870.3i 1.64064i
\(416\) −12506.5 + 3922.90i −1.47399 + 0.462346i
\(417\) 0 0
\(418\) 2310.61 1903.57i 0.270372 0.222743i
\(419\) 1313.14 0.153105 0.0765526 0.997066i \(-0.475609\pi\)
0.0765526 + 0.997066i \(0.475609\pi\)
\(420\) 0 0
\(421\) 7669.52 0.887861 0.443931 0.896061i \(-0.353584\pi\)
0.443931 + 0.896061i \(0.353584\pi\)
\(422\) 10074.0 8299.33i 1.16207 0.957358i
\(423\) 0 0
\(424\) −9995.89 + 5415.82i −1.14491 + 0.620319i
\(425\) 11973.6i 1.36660i
\(426\) 0 0
\(427\) 7808.82 + 2261.16i 0.885001 + 0.256266i
\(428\) 11704.6 + 2282.34i 1.32187 + 0.257760i
\(429\) 0 0
\(430\) −728.947 884.817i −0.0817510 0.0992318i
\(431\) 2360.49i 0.263807i −0.991263 0.131903i \(-0.957891\pi\)
0.991263 0.131903i \(-0.0421088\pi\)
\(432\) 0 0
\(433\) 4914.75i 0.545468i −0.962089 0.272734i \(-0.912072\pi\)
0.962089 0.272734i \(-0.0879279\pi\)
\(434\) 9709.22 4188.25i 1.07387 0.463231i
\(435\) 0 0
\(436\) −850.307 + 4360.64i −0.0933998 + 0.478984i
\(437\) 15741.6i 1.72316i
\(438\) 0 0
\(439\) −3334.78 −0.362552 −0.181276 0.983432i \(-0.558023\pi\)
−0.181276 + 0.983432i \(0.558023\pi\)
\(440\) 3811.02 2064.83i 0.412916 0.223720i
\(441\) 0 0
\(442\) −8171.72 9919.08i −0.879387 1.06743i
\(443\) 3590.57i 0.385086i −0.981288 0.192543i \(-0.938326\pi\)
0.981288 0.192543i \(-0.0616736\pi\)
\(444\) 0 0
\(445\) 483.545 0.0515106
\(446\) 530.403 + 643.820i 0.0563124 + 0.0683537i
\(447\) 0 0
\(448\) 6189.57 + 7183.64i 0.652745 + 0.757578i
\(449\) −15166.2 −1.59407 −0.797037 0.603931i \(-0.793600\pi\)
−0.797037 + 0.603931i \(0.793600\pi\)
\(450\) 0 0
\(451\) 3202.43 0.334361
\(452\) 114.990 589.702i 0.0119660 0.0613656i
\(453\) 0 0
\(454\) 4086.10 + 4959.83i 0.422401 + 0.512723i
\(455\) 6628.42 22890.9i 0.682957 2.35856i
\(456\) 0 0
\(457\) −15092.8 −1.54489 −0.772443 0.635084i \(-0.780965\pi\)
−0.772443 + 0.635084i \(0.780965\pi\)
\(458\) 6668.40 5493.68i 0.680336 0.560487i
\(459\) 0 0
\(460\) −4362.04 + 22369.9i −0.442133 + 2.26740i
\(461\) 1332.96i 0.134669i 0.997730 + 0.0673344i \(0.0214494\pi\)
−0.997730 + 0.0673344i \(0.978551\pi\)
\(462\) 0 0
\(463\) 10483.5i 1.05229i −0.850394 0.526146i \(-0.823637\pi\)
0.850394 0.526146i \(-0.176363\pi\)
\(464\) 5346.71 + 2167.59i 0.534946 + 0.216871i
\(465\) 0 0
\(466\) −5893.82 7154.10i −0.585893 0.711174i
\(467\) −15964.3 −1.58188 −0.790942 0.611891i \(-0.790409\pi\)
−0.790942 + 0.611891i \(0.790409\pi\)
\(468\) 0 0
\(469\) −11877.3 3439.25i −1.16939 0.338614i
\(470\) 18778.3 15470.3i 1.84293 1.51828i
\(471\) 0 0
\(472\) −2948.98 + 1597.77i −0.287580 + 0.155812i
\(473\) −245.850 −0.0238989
\(474\) 0 0
\(475\) 18736.3 1.80985
\(476\) −4247.41 + 8270.54i −0.408991 + 0.796385i
\(477\) 0 0
\(478\) 12609.7 10388.4i 1.20660 0.994043i
\(479\) −19452.3 −1.85553 −0.927763 0.373170i \(-0.878271\pi\)
−0.927763 + 0.373170i \(0.878271\pi\)
\(480\) 0 0
\(481\) 10114.3i 0.958782i
\(482\) 701.774 578.148i 0.0663172 0.0546347i
\(483\) 0 0
\(484\) −1860.03 + 9538.82i −0.174683 + 0.895832i
\(485\) 3780.20 0.353917
\(486\) 0 0
\(487\) 8465.85i 0.787729i −0.919168 0.393865i \(-0.871138\pi\)
0.919168 0.393865i \(-0.128862\pi\)
\(488\) −4731.60 8733.04i −0.438913 0.810095i
\(489\) 0 0
\(490\) −17105.2 + 2156.23i −1.57701 + 0.198793i
\(491\) 7175.25i 0.659500i 0.944068 + 0.329750i \(0.106965\pi\)
−0.944068 + 0.329750i \(0.893035\pi\)
\(492\) 0 0
\(493\) 5656.86i 0.516779i
\(494\) −15521.3 + 12787.1i −1.41364 + 1.16461i
\(495\) 0 0
\(496\) −11972.5 4853.75i −1.08384 0.439395i
\(497\) 3098.77 + 897.297i 0.279676 + 0.0809844i
\(498\) 0 0
\(499\) 17503.9i 1.57030i 0.619303 + 0.785152i \(0.287415\pi\)
−0.619303 + 0.785152i \(0.712585\pi\)
\(500\) 9183.04 + 1790.65i 0.821356 + 0.160161i
\(501\) 0 0
\(502\) −3269.76 3968.93i −0.290710 0.352873i
\(503\) 16033.8 1.42130 0.710648 0.703548i \(-0.248402\pi\)
0.710648 + 0.703548i \(0.248402\pi\)
\(504\) 0 0
\(505\) −15928.1 −1.40355
\(506\) 3107.78 + 3772.31i 0.273039 + 0.331423i
\(507\) 0 0
\(508\) −113.595 22.1506i −0.00992123 0.00193460i
\(509\) 12929.7i 1.12593i −0.826480 0.562965i \(-0.809660\pi\)
0.826480 0.562965i \(-0.190340\pi\)
\(510\) 0 0
\(511\) −20770.1 6014.29i −1.79807 0.520659i
\(512\) 939.786 11547.1i 0.0811193 0.996704i
\(513\) 0 0
\(514\) −5322.92 + 4385.22i −0.456778 + 0.376311i
\(515\) 23451.6i 2.00660i
\(516\) 0 0
\(517\) 5217.62i 0.443851i
\(518\) −6718.69 + 2898.23i −0.569889 + 0.245832i
\(519\) 0 0
\(520\) −25600.2 + 13870.3i −2.15893 + 1.16972i
\(521\) 19765.0i 1.66204i −0.556245 0.831018i \(-0.687759\pi\)
0.556245 0.831018i \(-0.312241\pi\)
\(522\) 0 0
\(523\) −5646.25 −0.472071 −0.236036 0.971744i \(-0.575848\pi\)
−0.236036 + 0.971744i \(0.575848\pi\)
\(524\) 3645.42 18694.8i 0.303914 1.55856i
\(525\) 0 0
\(526\) −8914.29 + 7343.94i −0.738939 + 0.608766i
\(527\) 12667.0i 1.04703i
\(528\) 0 0
\(529\) −13532.8 −1.11226
\(530\) −19491.6 + 16058.0i −1.59748 + 1.31606i
\(531\) 0 0
\(532\) 12941.7 + 6646.33i 1.05469 + 0.541645i
\(533\) −21512.1 −1.74820
\(534\) 0 0
\(535\) 26490.0 2.14068
\(536\) 7196.81 + 13283.0i 0.579953 + 1.07041i
\(537\) 0 0
\(538\) 4631.33 3815.47i 0.371136 0.305756i
\(539\) −1975.55 + 3125.21i −0.157872 + 0.249744i
\(540\) 0 0
\(541\) 6642.27 0.527862 0.263931 0.964542i \(-0.414981\pi\)
0.263931 + 0.964542i \(0.414981\pi\)
\(542\) −12405.2 15057.7i −0.983112 1.19333i
\(543\) 0 0
\(544\) 10838.6 3399.74i 0.854230 0.267946i
\(545\) 9869.08i 0.775678i
\(546\) 0 0
\(547\) 15445.0i 1.20728i 0.797257 + 0.603640i \(0.206283\pi\)
−0.797257 + 0.603640i \(0.793717\pi\)
\(548\) −270.566 + 1387.55i −0.0210913 + 0.108163i
\(549\) 0 0
\(550\) 4489.96 3699.00i 0.348095 0.286774i
\(551\) 8851.84 0.684394
\(552\) 0 0
\(553\) 12104.5 + 3505.04i 0.930804 + 0.269529i
\(554\) 2619.67 + 3179.84i 0.200901 + 0.243860i
\(555\) 0 0
\(556\) −567.876 + 2912.25i −0.0433153 + 0.222135i
\(557\) 20224.1 1.53846 0.769231 0.638971i \(-0.220639\pi\)
0.769231 + 0.638971i \(0.220639\pi\)
\(558\) 0 0
\(559\) 1651.48 0.124955
\(560\) 16549.3 + 13031.1i 1.24882 + 0.983327i
\(561\) 0 0
\(562\) 10815.1 + 13127.7i 0.811757 + 0.985335i
\(563\) −12972.1 −0.971061 −0.485531 0.874220i \(-0.661374\pi\)
−0.485531 + 0.874220i \(0.661374\pi\)
\(564\) 0 0
\(565\) 1334.62i 0.0993771i
\(566\) 4470.44 + 5426.35i 0.331990 + 0.402980i
\(567\) 0 0
\(568\) −1877.64 3465.53i −0.138704 0.256004i
\(569\) 1451.30 0.106928 0.0534638 0.998570i \(-0.482974\pi\)
0.0534638 + 0.998570i \(0.482974\pi\)
\(570\) 0 0
\(571\) 8530.19i 0.625179i −0.949888 0.312590i \(-0.898804\pi\)
0.949888 0.312590i \(-0.101196\pi\)
\(572\) −1195.05 + 6128.58i −0.0873557 + 0.447988i
\(573\) 0 0
\(574\) 6164.21 + 14289.9i 0.448239 + 1.03911i
\(575\) 30589.0i 2.21852i
\(576\) 0 0
\(577\) 21396.2i 1.54374i 0.635782 + 0.771869i \(0.280678\pi\)
−0.635782 + 0.771869i \(0.719322\pi\)
\(578\) −1753.88 2128.91i −0.126214 0.153202i
\(579\) 0 0
\(580\) 12579.1 + 2452.87i 0.900547 + 0.175603i
\(581\) 4020.53 13884.7i 0.287091 0.991454i
\(582\) 0 0
\(583\) 5415.82i 0.384735i
\(584\) 12585.2 + 23228.3i 0.891746 + 1.64588i
\(585\) 0 0
\(586\) 4902.44 4038.82i 0.345594 0.284714i
\(587\) 7212.11 0.507113 0.253557 0.967321i \(-0.418400\pi\)
0.253557 + 0.967321i \(0.418400\pi\)
\(588\) 0 0
\(589\) −19821.3 −1.38663
\(590\) −5750.41 + 4737.41i −0.401255 + 0.330569i
\(591\) 0 0
\(592\) 8284.89 + 3358.75i 0.575180 + 0.233182i
\(593\) 18362.2i 1.27158i 0.771863 + 0.635789i \(0.219325\pi\)
−0.771863 + 0.635789i \(0.780675\pi\)
\(594\) 0 0
\(595\) −5744.45 + 19838.2i −0.395797 + 1.36687i
\(596\) 3482.28 17858.2i 0.239329 1.22735i
\(597\) 0 0
\(598\) −20876.2 25340.2i −1.42758 1.73284i
\(599\) 2402.54i 0.163881i −0.996637 0.0819407i \(-0.973888\pi\)
0.996637 0.0819407i \(-0.0261118\pi\)
\(600\) 0 0
\(601\) 15264.1i 1.03600i 0.855382 + 0.517998i \(0.173323\pi\)
−0.855382 + 0.517998i \(0.826677\pi\)
\(602\) −473.225 1097.03i −0.0320385 0.0742719i
\(603\) 0 0
\(604\) −17450.8 3402.84i −1.17560 0.229238i
\(605\) 21588.4i 1.45073i
\(606\) 0 0
\(607\) −18675.5 −1.24879 −0.624395 0.781109i \(-0.714654\pi\)
−0.624395 + 0.781109i \(0.714654\pi\)
\(608\) −5319.90 16960.2i −0.354853 1.13129i
\(609\) 0 0
\(610\) −14029.2 17029.1i −0.931193 1.13031i
\(611\) 35049.0i 2.32067i
\(612\) 0 0
\(613\) 6537.07 0.430718 0.215359 0.976535i \(-0.430908\pi\)
0.215359 + 0.976535i \(0.430908\pi\)
\(614\) 1509.42 + 1832.18i 0.0992104 + 0.120425i
\(615\) 0 0
\(616\) 4413.50 962.285i 0.288677 0.0629409i
\(617\) −3529.67 −0.230307 −0.115153 0.993348i \(-0.536736\pi\)
−0.115153 + 0.993348i \(0.536736\pi\)
\(618\) 0 0
\(619\) 557.614 0.0362074 0.0181037 0.999836i \(-0.494237\pi\)
0.0181037 + 0.999836i \(0.494237\pi\)
\(620\) −28167.5 5492.54i −1.82457 0.355783i
\(621\) 0 0
\(622\) −2078.44 2522.88i −0.133984 0.162634i
\(623\) 484.046 + 140.163i 0.0311283 + 0.00901367i
\(624\) 0 0
\(625\) −3067.96 −0.196349
\(626\) 9266.38 7634.00i 0.591628 0.487406i
\(627\) 0 0
\(628\) −1243.31 242.440i −0.0790021 0.0154051i
\(629\) 8765.47i 0.555647i
\(630\) 0 0
\(631\) 14053.9i 0.886650i −0.896361 0.443325i \(-0.853799\pi\)
0.896361 0.443325i \(-0.146201\pi\)
\(632\) −7334.47 13537.1i −0.461629 0.852022i
\(633\) 0 0
\(634\) −6972.01 8462.83i −0.436741 0.530130i
\(635\) −257.091 −0.0160667
\(636\) 0 0
\(637\) 13270.6 20993.3i 0.825432 1.30579i
\(638\) 2121.25 1747.57i 0.131632 0.108443i
\(639\) 0 0
\(640\) −2860.23 25575.8i −0.176657 1.57964i
\(641\) 8223.99 0.506752 0.253376 0.967368i \(-0.418459\pi\)
0.253376 + 0.967368i \(0.418459\pi\)
\(642\) 0 0
\(643\) −26162.2 −1.60457 −0.802283 0.596944i \(-0.796381\pi\)
−0.802283 + 0.596944i \(0.796381\pi\)
\(644\) −10850.8 + 21128.7i −0.663948 + 1.29284i
\(645\) 0 0
\(646\) 13451.4 11081.8i 0.819254 0.674933i
\(647\) 28473.2 1.73014 0.865068 0.501654i \(-0.167275\pi\)
0.865068 + 0.501654i \(0.167275\pi\)
\(648\) 0 0
\(649\) 1597.77i 0.0966379i
\(650\) −30160.9 + 24847.7i −1.82001 + 1.49940i
\(651\) 0 0
\(652\) 11527.8 + 2247.87i 0.692429 + 0.135021i
\(653\) −30403.4 −1.82202 −0.911009 0.412386i \(-0.864696\pi\)
−0.911009 + 0.412386i \(0.864696\pi\)
\(654\) 0 0
\(655\) 42310.5i 2.52398i
\(656\) 7143.69 17621.0i 0.425174 1.04876i
\(657\) 0 0
\(658\) 23282.1 10043.2i 1.37938 0.595020i
\(659\) 24719.1i 1.46118i 0.682814 + 0.730592i \(0.260756\pi\)
−0.682814 + 0.730592i \(0.739244\pi\)
\(660\) 0 0
\(661\) 16458.4i 0.968467i 0.874939 + 0.484233i \(0.160901\pi\)
−0.874939 + 0.484233i \(0.839099\pi\)
\(662\) 1038.18 855.296i 0.0609519 0.0502145i
\(663\) 0 0
\(664\) −15528.0 + 8413.16i −0.907538 + 0.491708i
\(665\) 31042.7 + 8988.89i 1.81020 + 0.524172i
\(666\) 0 0
\(667\) 14451.6i 0.838930i
\(668\) −3872.37 + 19858.7i −0.224291 + 1.15024i
\(669\) 0 0
\(670\) 21338.6 + 25901.5i 1.23042 + 1.49352i
\(671\) −4731.60 −0.272223
\(672\) 0 0
\(673\) 13350.6 0.764676 0.382338 0.924023i \(-0.375119\pi\)
0.382338 + 0.924023i \(0.375119\pi\)
\(674\) −18007.3 21857.8i −1.02910 1.24915i
\(675\) 0 0
\(676\) 4663.75 23917.2i 0.265348 1.36079i
\(677\) 28935.9i 1.64269i −0.570435 0.821343i \(-0.693225\pi\)
0.570435 0.821343i \(-0.306775\pi\)
\(678\) 0 0
\(679\) 3784.12 + 1095.75i 0.213875 + 0.0619308i
\(680\) 22186.1 12020.5i 1.25118 0.677892i
\(681\) 0 0
\(682\) −4749.98 + 3913.22i −0.266695 + 0.219714i
\(683\) 5796.62i 0.324746i −0.986729 0.162373i \(-0.948085\pi\)
0.986729 0.162373i \(-0.0519148\pi\)
\(684\) 0 0
\(685\) 3140.32i 0.175161i
\(686\) −17748.0 2799.75i −0.987785 0.155824i
\(687\) 0 0
\(688\) −548.419 + 1352.76i −0.0303899 + 0.0749616i
\(689\) 36380.3i 2.01158i
\(690\) 0 0
\(691\) 19975.6 1.09972 0.549861 0.835256i \(-0.314681\pi\)
0.549861 + 0.835256i \(0.314681\pi\)
\(692\) −6549.15 1277.06i −0.359771 0.0701538i
\(693\) 0 0
\(694\) −23514.5 + 19372.1i −1.28616 + 1.05959i
\(695\) 6591.05i 0.359731i
\(696\) 0 0
\(697\) 18643.2 1.01314
\(698\) 20262.3 16692.9i 1.09877 0.905206i
\(699\) 0 0
\(700\) 25148.2 + 12915.1i 1.35788 + 0.697350i
\(701\) 35866.0 1.93244 0.966219 0.257723i \(-0.0829721\pi\)
0.966219 + 0.257723i \(0.0829721\pi\)
\(702\) 0 0
\(703\) 13716.2 0.735868
\(704\) −4623.22 3014.06i −0.247506 0.161359i
\(705\) 0 0
\(706\) −9884.51 + 8143.24i −0.526924 + 0.434100i
\(707\) −15944.6 4617.01i −0.848174 0.245602i
\(708\) 0 0
\(709\) −1806.89 −0.0957109 −0.0478555 0.998854i \(-0.515239\pi\)
−0.0478555 + 0.998854i \(0.515239\pi\)
\(710\) −5567.22 6757.66i −0.294273 0.357198i
\(711\) 0 0
\(712\) −293.298 541.336i −0.0154380 0.0284936i
\(713\) 32360.4i 1.69973i
\(714\) 0 0
\(715\) 13870.3i 0.725483i
\(716\) −16446.8 3207.05i −0.858443 0.167393i
\(717\) 0 0
\(718\) 21467.9 17686.1i 1.11584 0.919274i
\(719\) 23227.5 1.20478 0.602391 0.798201i \(-0.294215\pi\)
0.602391 + 0.798201i \(0.294215\pi\)
\(720\) 0 0
\(721\) 6797.81 23475.9i 0.351129 1.21261i
\(722\) −5005.13 6075.37i −0.257994 0.313161i
\(723\) 0 0
\(724\) −23310.9 4545.52i −1.19660 0.233333i
\(725\) 17200.8 0.881134
\(726\) 0 0
\(727\) 27835.1 1.42001 0.710006 0.704196i \(-0.248692\pi\)
0.710006 + 0.704196i \(0.248692\pi\)
\(728\) −29647.3 + 6464.07i −1.50934 + 0.329086i
\(729\) 0 0
\(730\) 37315.3 + 45294.4i 1.89192 + 2.29647i
\(731\) −1431.23 −0.0724159
\(732\) 0 0
\(733\) 26967.4i 1.35889i −0.733727 0.679444i \(-0.762221\pi\)
0.733727 0.679444i \(-0.237779\pi\)
\(734\) 21306.3 + 25862.2i 1.07143 + 1.30053i
\(735\) 0 0
\(736\) 27689.3 8685.29i 1.38674 0.434978i
\(737\) 7196.81 0.359699
\(738\) 0 0
\(739\) 4459.65i 0.221990i 0.993821 + 0.110995i \(0.0354038\pi\)
−0.993821 + 0.110995i \(0.964596\pi\)
\(740\) 19491.6 + 3800.79i 0.968279 + 0.188810i
\(741\) 0 0
\(742\) −24166.5 + 10424.7i −1.19566 + 0.515770i
\(743\) 9276.26i 0.458026i 0.973423 + 0.229013i \(0.0735498\pi\)
−0.973423 + 0.229013i \(0.926450\pi\)
\(744\) 0 0
\(745\) 40417.1i 1.98761i
\(746\) −18543.1 22508.2i −0.910071 1.10467i
\(747\) 0 0
\(748\) 1035.67 5311.27i 0.0506257 0.259625i
\(749\) 26517.5 + 7678.54i 1.29363 + 0.374590i
\(750\) 0 0
\(751\) 6411.40i 0.311525i −0.987795 0.155763i \(-0.950217\pi\)
0.987795 0.155763i \(-0.0497835\pi\)
\(752\) −28709.4 11639.0i −1.39219 0.564402i
\(753\) 0 0
\(754\) −14249.3 + 11739.2i −0.688237 + 0.566996i
\(755\) −39495.0 −1.90380
\(756\) 0 0
\(757\) 18447.3 0.885705 0.442853 0.896594i \(-0.353967\pi\)
0.442853 + 0.896594i \(0.353967\pi\)
\(758\) 8430.68 6945.52i 0.403979 0.332814i
\(759\) 0 0
\(760\) −18809.7 34716.8i −0.897763 1.65699i
\(761\) 31940.7i 1.52149i 0.649054 + 0.760743i \(0.275165\pi\)
−0.649054 + 0.760743i \(0.724835\pi\)
\(762\) 0 0
\(763\) −2860.71 + 9879.31i −0.135733 + 0.468749i
\(764\) −18933.0 3691.86i −0.896560 0.174825i
\(765\) 0 0
\(766\) 16507.0 + 20036.7i 0.778618 + 0.945110i
\(767\) 10732.9i 0.505270i
\(768\) 0 0
\(769\) 4067.55i 0.190740i −0.995442 0.0953702i \(-0.969597\pi\)
0.995442 0.0953702i \(-0.0304035\pi\)
\(770\) 9213.69 3974.49i 0.431218 0.186014i
\(771\) 0 0
\(772\) −3729.38 + 19125.5i −0.173865 + 0.891632i
\(773\) 21053.6i 0.979620i 0.871829 + 0.489810i \(0.162934\pi\)
−0.871829 + 0.489810i \(0.837066\pi\)
\(774\) 0 0
\(775\) −38516.7 −1.78524
\(776\) −2292.91 4231.99i −0.106071 0.195773i
\(777\) 0 0
\(778\) 565.410 + 686.312i 0.0260552 + 0.0316266i
\(779\) 29172.8i 1.34175i
\(780\) 0 0
\(781\) −1877.64 −0.0860272
\(782\) 18092.2 + 21960.8i 0.827333 + 1.00424i
\(783\) 0 0
\(784\) 12789.2 + 17841.7i 0.582601 + 0.812759i
\(785\) −2813.87 −0.127938
\(786\) 0 0
\(787\) 15197.8 0.688367 0.344183 0.938902i \(-0.388156\pi\)
0.344183 + 0.938902i \(0.388156\pi\)
\(788\) −3196.54 +