Properties

Label 252.4.b.g.55.12
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 55.12
Root \(0.467111 + 0.600106i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.4.b.g.55.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.79845 + 2.18302i) q^{2} +(-1.53113 + 7.85211i) q^{4} +17.7710i q^{5} +(5.15121 + 17.7895i) q^{7} +(-19.8950 + 10.7792i) q^{8} +O(q^{10})\) \(q+(1.79845 + 2.18302i) q^{2} +(-1.53113 + 7.85211i) q^{4} +17.7710i q^{5} +(5.15121 + 17.7895i) q^{7} +(-19.8950 + 10.7792i) q^{8} +(-38.7945 + 31.9604i) q^{10} +10.7792i q^{11} -72.4083i q^{13} +(-29.5705 + 43.2387i) q^{14} +(-59.3113 - 24.0452i) q^{16} -62.7518i q^{17} +98.1938 q^{19} +(-139.540 - 27.2097i) q^{20} +(-23.5311 + 19.3858i) q^{22} +160.312i q^{23} -190.809 q^{25} +(158.069 - 130.223i) q^{26} +(-147.572 + 13.2099i) q^{28} +90.1466 q^{29} -201.859 q^{31} +(-54.1775 - 172.722i) q^{32} +(136.988 - 112.856i) q^{34} +(-316.137 + 91.5424i) q^{35} -139.685 q^{37} +(176.597 + 214.359i) q^{38} +(-191.557 - 353.554i) q^{40} +297.094i q^{41} -22.8078i q^{43} +(-84.6393 - 16.5043i) q^{44} +(-349.963 + 288.313i) q^{46} +484.046 q^{47} +(-289.930 + 183.275i) q^{49} +(-343.162 - 416.540i) q^{50} +(568.558 + 110.866i) q^{52} +502.433 q^{53} -191.557 q^{55} +(-294.239 - 298.395i) q^{56} +(162.125 + 196.792i) q^{58} -148.228 q^{59} +438.958i q^{61} +(-363.035 - 440.663i) q^{62} +(279.619 - 428.903i) q^{64} +1286.77 q^{65} +667.659i q^{67} +(492.734 + 96.0811i) q^{68} +(-768.396 - 525.498i) q^{70} +174.191i q^{71} -1167.55i q^{73} +(-251.217 - 304.934i) q^{74} +(-150.347 + 771.028i) q^{76} +(-191.756 + 55.5258i) q^{77} -680.430i q^{79} +(427.308 - 1054.02i) q^{80} +(-648.562 + 534.310i) q^{82} -780.502 q^{83} +1115.16 q^{85} +(49.7899 - 41.0188i) q^{86} +(-116.191 - 214.451i) q^{88} -27.2097i q^{89} +(1288.10 - 372.990i) q^{91} +(-1258.78 - 245.458i) q^{92} +(870.535 + 1056.68i) q^{94} +1745.00i q^{95} +212.717i q^{97} +(-921.517 - 303.311i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 40q^{4} + O(q^{10}) \) \( 16q + 40q^{4} - 304q^{16} - 312q^{22} - 1376q^{25} - 816q^{28} - 816q^{37} - 2568q^{46} - 640q^{49} + 2336q^{58} + 1120q^{64} - 424q^{70} + 5072q^{85} - 3536q^{88} + O(q^{100}) \)

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 \(0.0471964\pi\)
−0.989028 + 0.147729i \(0.952804\pi\)
\(12\) 0 0
\(13\) 72.4083i 1.54480i −0.635135 0.772402i \(-0.719055\pi\)
0.635135 0.772402i \(-0.280945\pi\)
\(14\) −29.5705 + 43.2387i −0.564503 + 0.825431i
\(15\) 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 \(-0.298014\pi\)
0.592821 + 0.805334i \(0.298014\pi\)
\(20\) −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 \(0.258938\pi\)
−0.686976 + 0.726680i \(0.741062\pi\)
\(24\) 0 0
\(25\) −190.809 −1.52647
\(26\) 158.069 130.223i 1.19230 0.982262i
\(27\) 0 0
\(28\) −147.572 + 13.2099i −0.996017 + 0.0891587i
\(29\) 90.1466 0.577235 0.288617 0.957445i \(-0.406804\pi\)
0.288617 + 0.957445i \(0.406804\pi\)
\(30\) 0 0
\(31\) −201.859 −1.16952 −0.584759 0.811207i \(-0.698811\pi\)
−0.584759 + 0.811207i \(0.698811\pi\)
\(32\) −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 \(-0.274316\pi\)
0.651081 + 0.759009i \(0.274316\pi\)
\(54\) 0 0
\(55\) −191.557 −0.469628
\(56\) −294.239 298.395i −0.702131 0.712048i
\(57\) 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 \(0.152394\pi\)
−0.887567 + 0.460678i \(0.847606\pi\)
\(62\) −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
\(70\) −768.396 525.498i −1.31201 0.897272i
\(71\) 174.191i 0.291165i 0.989346 + 0.145582i \(0.0465056\pi\)
−0.989346 + 0.145582i \(0.953494\pi\)
\(72\) 0 0
\(73\) 1167.55i 1.87193i −0.352088 0.935967i \(-0.614528\pi\)
0.352088 0.935967i \(-0.385472\pi\)
\(74\) −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 \(0.0355112\pi\)
−0.993783 + 0.111331i \(0.964489\pi\)
\(98\) −921.517 303.311i −0.949871 0.312643i
\(99\) 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 \(-0.282559\pi\)
0.631210 + 0.775612i \(0.282559\pi\)
\(104\) 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 \(0.235160\pi\)
−0.739292 + 0.673385i \(0.764840\pi\)
\(108\) 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
\(112\) 122.226 1178.98i 0.103118 0.994669i
\(113\) 75.1011 0.0625214 0.0312607 0.999511i \(-0.490048\pi\)
0.0312607 + 0.999511i \(0.490048\pi\)
\(114\) 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 \(-0.517548\pi\)
−0.0550999 + 0.998481i \(0.517548\pi\)
\(138\) 0 0
\(139\) −370.887 −0.226318 −0.113159 0.993577i \(-0.536097\pi\)
−0.113159 + 0.993577i \(0.536097\pi\)
\(140\) −234.754 2622.51i −0.141717 1.58316i
\(141\) 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 \(-0.285003\pi\)
0.625234 + 0.780437i \(0.285003\pi\)
\(150\) 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
\(154\) −466.078 318.745i −0.243881 0.166787i
\(155\) 3587.25i 1.85893i
\(156\) 0 0
\(157\) 158.340i 0.0804901i −0.999190 0.0402450i \(-0.987186\pi\)
0.999190 0.0402450i \(-0.0128139\pi\)
\(158\) 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 \(-0.855933\pi\)
0.899313 0.437305i \(-0.144067\pi\)
\(180\) 0 0
\(181\) 2968.74i 1.21914i −0.792732 0.609571i \(-0.791342\pi\)
0.792732 0.609571i \(-0.208658\pi\)
\(182\) 3130.84 + 2141.15i 1.27513 + 0.872046i
\(183\) 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 \(-0.849023\pi\)
0.889609 0.456723i \(-0.150977\pi\)
\(192\) 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
\(196\) −995.173 2557.18i −0.362672 0.931917i
\(197\) −2087.70 −0.755039 −0.377520 0.926002i \(-0.623223\pi\)
−0.377520 + 0.926002i \(0.623223\pi\)
\(198\) 0 0
\(199\) 3388.82 1.20717 0.603585 0.797299i \(-0.293738\pi\)
0.603585 + 0.797299i \(0.293738\pi\)
\(200\) 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 \(-0.485900\pi\)
0.0442812 + 0.999019i \(0.485900\pi\)
\(224\) 2793.55 1853.52i 0.833266 0.552872i
\(225\) 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 \(-0.854717\pi\)
0.897635 0.440739i \(-0.145283\pi\)
\(230\) −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 \(-0.652408\pi\)
−0.460717 + 0.887547i \(0.652408\pi\)
\(234\) 0 0
\(235\) 8602.00i 2.38780i
\(236\) 226.955 1163.90i 0.0625997 0.321031i
\(237\) 0 0
\(238\) 2713.31 + 1855.60i 0.738981 + 0.505381i
\(239\) 5776.27i 1.56333i −0.623698 0.781665i \(-0.714371\pi\)
0.623698 0.781665i \(-0.285629\pi\)
\(240\) 0 0
\(241\) 321.470i 0.0859240i −0.999077 0.0429620i \(-0.986321\pi\)
0.999077 0.0429620i \(-0.0136794\pi\)
\(242\) 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 \(0.158893\pi\)
−0.877977 + 0.478703i \(0.841107\pi\)
\(264\) 0 0
\(265\) 8928.76i 2.06977i
\(266\) −2903.64 + 4245.77i −0.669299 + 0.978665i
\(267\) 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 \(-0.781280\pi\)
−0.773070 + 0.634321i \(0.781280\pi\)
\(272\) −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
\(280\) 5302.78 5228.93i 1.13179 1.11603i
\(281\) 6013.55 1.27665 0.638325 0.769767i \(-0.279628\pi\)
0.638325 + 0.769767i \(0.279628\pi\)
\(282\) 0 0
\(283\) 2485.71 0.522121 0.261060 0.965322i \(-0.415928\pi\)
0.261060 + 0.965322i \(0.415928\pi\)
\(284\) −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 \(-0.475142\pi\)
0.0780141 + 0.996952i \(0.475142\pi\)
\(308\) −142.392 1590.70i −0.0263427 0.294282i
\(309\) 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 \(-0.874797\pi\)
0.923636 0.383272i \(-0.125203\pi\)
\(314\) 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 \(-0.611589\pi\)
−0.343431 + 0.939178i \(0.611589\pi\)
\(318\) 0 0
\(319\) 971.706i 0.170549i
\(320\) 7622.04 + 4969.11i 1.33152 + 0.868068i
\(321\) 0 0
\(322\) −6931.67 4740.49i −1.19965 0.820426i
\(323\) 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 \(0.313499\pi\)
−0.552959 + 0.833209i \(0.686501\pi\)
\(348\) 0 0
\(349\) 9281.78i 1.42362i −0.702373 0.711809i \(-0.747876\pi\)
0.702373 0.711809i \(-0.252124\pi\)
\(350\) 5642.33 8250.35i 0.861700 1.26000i
\(351\) 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 \(-0.742822\pi\)
0.690983 0.722871i \(-0.257178\pi\)
\(360\) 0 0
\(361\) 2783.02 0.405747
\(362\) 6480.81 5339.14i 0.940950 0.775190i
\(363\) 0 0
\(364\) 956.509 + 10685.4i 0.137733 + 1.53865i
\(365\) 20748.5 2.97542
\(366\) 0 0
\(367\) 11847.0 1.68504 0.842518 0.538669i \(-0.181073\pi\)
0.842518 + 0.538669i \(0.181073\pi\)
\(368\) 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 \(-0.493478\pi\)
0.0204885 + 0.999790i \(0.493478\pi\)
\(390\) 0 0
\(391\) 10059.8 1.30115
\(392\) 3792.60 6771.45i 0.488661 0.872474i
\(393\) 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 \(-0.957076\pi\)
0.990922 0.134440i \(-0.0429236\pi\)
\(398\) 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 \(-0.367228\pi\)
0.405125 + 0.914261i \(0.367228\pi\)
\(402\) 0 0
\(403\) 14616.3i 1.80667i
\(404\) −7037.82 1372.34i −0.866694 0.169002i
\(405\) 0 0
\(406\) −2665.68 + 3897.82i −0.325851 + 0.476467i
\(407\) 1505.69i 0.183376i
\(408\) 0 0
\(409\) 3280.91i 0.396652i −0.980136 0.198326i \(-0.936450\pi\)
0.980136 0.198326i \(-0.0635505\pi\)
\(410\) −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 \(0.0421088\pi\)
−0.991263 + 0.131903i \(0.957891\pi\)
\(432\) 0 0
\(433\) 4914.75i 0.545468i 0.962089 + 0.272734i \(0.0879279\pi\)
−0.962089 + 0.272734i \(0.912072\pi\)
\(434\) 5969.08 8728.14i 0.660196 0.965355i
\(435\) 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 \(-0.441977\pi\)
0.181276 + 0.983432i \(0.441977\pi\)
\(440\) 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 \(0.0616736\pi\)
−0.981288 + 0.192543i \(0.938326\pi\)
\(444\) 0 0
\(445\) 483.545 0.0515106
\(446\) 530.403 + 643.820i 0.0563124 + 0.0683537i
\(447\) 0 0
\(448\) 9070.32 + 2764.90i 0.956546 + 0.291583i
\(449\) 15166.2 1.59407 0.797037 0.603931i \(-0.206400\pi\)
0.797037 + 0.603931i \(0.206400\pi\)
\(450\) 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
\(476\) 828.947 + 9260.41i 0.0798209 + 0.891702i
\(477\) 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
\(490\) 5390.15 16376.3i 0.496943 1.50981i
\(491\) 7175.25i 0.659500i −0.944068 0.329750i \(-0.893035\pi\)
0.944068 0.329750i \(-0.106965\pi\)
\(492\) 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
\(518\) 4130.55 6039.79i 0.350359 0.512304i
\(519\) 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 \(-0.424152\pi\)
0.236036 + 0.971744i \(0.424152\pi\)
\(524\) 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
\(532\) −14490.7 + 1297.13i −1.18092 + 0.105710i
\(533\) 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 \(-0.779361\pi\)
−0.769231 + 0.638971i \(0.779361\pi\)
\(558\) 0 0
\(559\) −1651.48 −0.124955
\(560\) 20951.6 + 2172.08i 1.58102 + 0.163905i
\(561\) 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 \(-0.517026\pi\)
−0.0534638 + 0.998570i \(0.517026\pi\)
\(570\) 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
\(574\) −12846.0 8785.22i −0.934113 0.638829i
\(575\) 30589.0i 2.21852i
\(576\) 0 0
\(577\) 21396.2i 1.54374i −0.635782 0.771869i \(-0.719322\pi\)
0.635782 0.771869i \(-0.280678\pi\)
\(578\) 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 \(0.0261118\pi\)
−0.996637 + 0.0819407i \(0.973888\pi\)
\(600\) 0 0
\(601\) 15264.1i 1.03600i −0.855382 0.517998i \(-0.826677\pi\)
0.855382 0.517998i \(-0.173323\pi\)
\(602\) 986.181 + 674.439i 0.0667670 + 0.0456612i
\(603\) 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 \(-0.285346\pi\)
0.624395 + 0.781109i \(0.285346\pi\)
\(608\) −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
\(616\) 3216.45 3171.65i 0.210381 0.207451i
\(617\) 3529.67 0.230307 0.115153 0.993348i \(-0.463264\pi\)
0.115153 + 0.993348i \(0.463264\pi\)
\(618\) 0 0
\(619\) −557.614 −0.0362074 −0.0181037 0.999836i \(-0.505763\pi\)
−0.0181037 + 0.999836i \(0.505763\pi\)
\(620\) 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 \(-0.581541\pi\)
−0.253376 + 0.967368i \(0.581541\pi\)
\(642\) 0 0
\(643\) 26162.2 1.60457 0.802283 0.596944i \(-0.203619\pi\)
0.802283 + 0.596944i \(0.203619\pi\)
\(644\) −2117.71 23657.5i −0.129580 1.44757i
\(645\) 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 \(-0.135304\pi\)
0.911009 + 0.412386i \(0.135304\pi\)
\(654\) 0 0
\(655\) 42310.5i 2.52398i
\(656\) 7143.69 17621.0i 0.425174 1.04876i
\(657\) 0 0
\(658\) −14313.5 + 20929.5i −0.848021 + 1.24000i
\(659\) 24719.1i 1.46118i −0.682814 0.730592i \(-0.739244\pi\)
0.682814 0.730592i \(-0.260756\pi\)
\(660\) 0 0
\(661\) 16458.4i 0.968467i −0.874939 0.484233i \(-0.839099\pi\)
0.874939 0.484233i \(-0.160901\pi\)
\(662\) −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 \(0.0519148\pi\)
−0.986729 + 0.162373i \(0.948085\pi\)
\(684\) 0 0
\(685\) 3140.32i 0.175161i
\(686\) 648.810 17955.7i 0.0361103 0.999348i
\(687\) 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 \(-0.685319\pi\)
−0.549861 + 0.835256i \(0.685319\pi\)
\(692\) −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
\(700\) 28158.1 2520.58i 1.52040 0.136099i
\(701\) −35866.0 −1.93244 −0.966219 0.257723i \(-0.917028\pi\)
−0.966219 + 0.257723i \(0.917028\pi\)
\(702\) 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 \(-0.751308\pi\)
−0.710006 + 0.704196i \(0.751308\pi\)
\(728\) −21606.2 + 21305.3i −1.09997 + 1.08465i
\(729\) 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 \(0.237779\pi\)
−0.733727 + 0.679444i \(0.762221\pi\)
\(734\) 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
\(742\) −14857.2 + 21724.6i −0.735074 + 1.07484i
\(743\) 9276.26i 0.458026i −0.973423 0.229013i \(-0.926450\pi\)
0.973423 0.229013i \(-0.0735498\pi\)
\(744\) 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 \(0.0304035\pi\)
−0.995442 + 0.0953702i \(0.969597\pi\)
\(770\) 5664.43 8282.68i 0.265107 0.387646i
\(771\) 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
\(784\) 21603.0 3898.84i 0.984101 0.177607i
\(785\) 2813.87 0.127938
\(786\) 0 0
\(787\) −15197.8 −0.688367 −0.344183 0.938902i \(-0.611844\pi\)
−0.344183 + 0.938902i \(0.611844\pi\)
\(788\) 3196.54