Properties

Label 63.4.e.c.46.3
Level $63$
Weight $4$
Character 63.46
Analytic conductor $3.717$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.3
Root \(2.65415 + 4.59712i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.4.e.c.37.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +O(q^{10})\) \(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +(-14.7608 + 25.5664i) q^{10} +(-6.95869 + 12.0528i) q^{11} +38.6718 q^{13} +(98.2771 + 2.58082i) q^{14} +(-90.8636 - 157.380i) q^{16} +(21.7394 - 37.6537i) q^{17} +(54.5139 + 94.4208i) q^{19} -112.218 q^{20} -73.8775 q^{22} +(-37.4389 - 64.8461i) q^{23} +(47.0354 - 81.4677i) q^{25} +(102.641 + 177.779i) q^{26} +(178.290 + 328.429i) q^{28} +72.3589 q^{29} +(-32.0215 + 55.4629i) q^{31} +(223.754 - 387.553i) q^{32} +230.798 q^{34} +(102.963 + 2.70387i) q^{35} +(-94.3636 - 163.443i) q^{37} +(-289.376 + 501.213i) q^{38} +(-179.756 - 311.347i) q^{40} +24.7923 q^{41} -243.881 q^{43} +(-140.412 - 243.201i) q^{44} +(198.737 - 344.222i) q^{46} +(-310.274 - 537.411i) q^{47} +(-155.673 - 305.638i) q^{49} +499.356 q^{50} +(-390.159 + 675.776i) q^{52} +(-143.919 + 249.276i) q^{53} -77.4001 q^{55} +(-625.627 + 1020.76i) q^{56} +(192.051 + 332.642i) q^{58} +(262.526 - 454.708i) q^{59} +(191.718 + 332.065i) q^{61} -339.960 q^{62} +921.681 q^{64} +(107.535 + 186.255i) q^{65} +(-99.0583 + 171.574i) q^{67} +(438.657 + 759.776i) q^{68} +(260.849 + 480.510i) q^{70} -785.432 q^{71} +(165.570 - 286.776i) q^{73} +(500.910 - 867.602i) q^{74} -2199.96 q^{76} +(122.972 + 226.527i) q^{77} +(-218.823 - 379.013i) q^{79} +(505.329 - 875.255i) q^{80} +(65.8024 + 113.973i) q^{82} -241.241 q^{83} +241.803 q^{85} +(-647.297 - 1121.15i) q^{86} +(449.840 - 779.145i) q^{88} +(792.772 + 1373.12i) q^{89} +(374.265 - 610.643i) q^{91} +1510.88 q^{92} +(1647.03 - 2852.73i) q^{94} +(-303.173 + 525.112i) q^{95} +79.2754 q^{97} +(991.877 - 1526.86i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} + 11q^{5} - 13q^{7} - 78q^{8} + 55q^{10} + 35q^{11} + 124q^{13} + 326q^{14} - 241q^{16} + 48q^{17} + 202q^{19} - 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} + 274q^{26} - 201q^{28} - 106q^{29} + 95q^{31} + 683q^{32} - 48q^{34} - 56q^{35} - 262q^{37} - 398q^{38} - 21q^{40} - 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} - 210q^{47} - 303q^{49} + 2756q^{50} - 324q^{52} + 393q^{53} - 2062q^{55} - 1299q^{56} + 1249q^{58} + 1143q^{59} + 70q^{61} - 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} + 1944q^{68} + 3251q^{70} - 636q^{71} - 988q^{73} + 1002q^{74} - 4680q^{76} - 1073q^{77} - 861q^{79} + 175q^{80} - 124q^{82} - 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} + 1766q^{89} - 654q^{91} + 1344q^{92} + 3294q^{94} - 736q^{95} + 38q^{97} + 4267q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.65415 + 4.59712i 0.938383 + 1.62533i 0.768488 + 0.639864i \(0.221009\pi\)
0.169895 + 0.985462i \(0.445657\pi\)
\(3\) 0 0
\(4\) −10.0890 + 17.4746i −1.26112 + 2.18433i
\(5\) 2.78070 + 4.81631i 0.248713 + 0.430784i 0.963169 0.268897i \(-0.0866590\pi\)
−0.714456 + 0.699681i \(0.753326\pi\)
\(6\) 0 0
\(7\) 9.67799 15.7904i 0.522562 0.852601i
\(8\) −64.6443 −2.85690
\(9\) 0 0
\(10\) −14.7608 + 25.5664i −0.466777 + 0.808481i
\(11\) −6.95869 + 12.0528i −0.190738 + 0.330369i −0.945495 0.325636i \(-0.894422\pi\)
0.754757 + 0.656005i \(0.227755\pi\)
\(12\) 0 0
\(13\) 38.6718 0.825048 0.412524 0.910947i \(-0.364647\pi\)
0.412524 + 0.910947i \(0.364647\pi\)
\(14\) 98.2771 + 2.58082i 1.87612 + 0.0492680i
\(15\) 0 0
\(16\) −90.8636 157.380i −1.41974 2.45907i
\(17\) 21.7394 37.6537i 0.310152 0.537198i −0.668243 0.743943i \(-0.732954\pi\)
0.978395 + 0.206744i \(0.0662869\pi\)
\(18\) 0 0
\(19\) 54.5139 + 94.4208i 0.658228 + 1.14009i 0.981074 + 0.193633i \(0.0620273\pi\)
−0.322845 + 0.946452i \(0.604639\pi\)
\(20\) −112.218 −1.25463
\(21\) 0 0
\(22\) −73.8775 −0.715943
\(23\) −37.4389 64.8461i −0.339415 0.587885i 0.644907 0.764261i \(-0.276896\pi\)
−0.984323 + 0.176376i \(0.943563\pi\)
\(24\) 0 0
\(25\) 47.0354 81.4677i 0.376283 0.651742i
\(26\) 102.641 + 177.779i 0.774211 + 1.34097i
\(27\) 0 0
\(28\) 178.290 + 328.429i 1.20335 + 2.21668i
\(29\) 72.3589 0.463335 0.231667 0.972795i \(-0.425582\pi\)
0.231667 + 0.972795i \(0.425582\pi\)
\(30\) 0 0
\(31\) −32.0215 + 55.4629i −0.185524 + 0.321337i −0.943753 0.330652i \(-0.892732\pi\)
0.758229 + 0.651988i \(0.226065\pi\)
\(32\) 223.754 387.553i 1.23608 2.14095i
\(33\) 0 0
\(34\) 230.798 1.16416
\(35\) 102.963 + 2.70387i 0.497255 + 0.0130582i
\(36\) 0 0
\(37\) −94.3636 163.443i −0.419278 0.726211i 0.576589 0.817034i \(-0.304383\pi\)
−0.995867 + 0.0908235i \(0.971050\pi\)
\(38\) −289.376 + 501.213i −1.23534 + 2.13967i
\(39\) 0 0
\(40\) −179.756 311.347i −0.710550 1.23071i
\(41\) 24.7923 0.0944367 0.0472184 0.998885i \(-0.484964\pi\)
0.0472184 + 0.998885i \(0.484964\pi\)
\(42\) 0 0
\(43\) −243.881 −0.864920 −0.432460 0.901653i \(-0.642354\pi\)
−0.432460 + 0.901653i \(0.642354\pi\)
\(44\) −140.412 243.201i −0.481090 0.833272i
\(45\) 0 0
\(46\) 198.737 344.222i 0.637003 1.10332i
\(47\) −310.274 537.411i −0.962940 1.66786i −0.715052 0.699071i \(-0.753597\pi\)
−0.247888 0.968789i \(-0.579736\pi\)
\(48\) 0 0
\(49\) −155.673 305.638i −0.453857 0.891074i
\(50\) 499.356 1.41239
\(51\) 0 0
\(52\) −390.159 + 675.776i −1.04049 + 1.80218i
\(53\) −143.919 + 249.276i −0.372997 + 0.646050i −0.990025 0.140891i \(-0.955003\pi\)
0.617028 + 0.786941i \(0.288337\pi\)
\(54\) 0 0
\(55\) −77.4001 −0.189757
\(56\) −625.627 + 1020.76i −1.49291 + 2.43580i
\(57\) 0 0
\(58\) 192.051 + 332.642i 0.434785 + 0.753070i
\(59\) 262.526 454.708i 0.579287 1.00335i −0.416275 0.909239i \(-0.636664\pi\)
0.995561 0.0941152i \(-0.0300022\pi\)
\(60\) 0 0
\(61\) 191.718 + 332.065i 0.402409 + 0.696993i 0.994016 0.109234i \(-0.0348397\pi\)
−0.591607 + 0.806226i \(0.701506\pi\)
\(62\) −339.960 −0.696369
\(63\) 0 0
\(64\) 921.681 1.80016
\(65\) 107.535 + 186.255i 0.205200 + 0.355417i
\(66\) 0 0
\(67\) −99.0583 + 171.574i −0.180625 + 0.312852i −0.942094 0.335350i \(-0.891145\pi\)
0.761468 + 0.648202i \(0.224479\pi\)
\(68\) 438.657 + 759.776i 0.782279 + 1.35495i
\(69\) 0 0
\(70\) 260.849 + 480.510i 0.445392 + 0.820456i
\(71\) −785.432 −1.31287 −0.656434 0.754384i \(-0.727936\pi\)
−0.656434 + 0.754384i \(0.727936\pi\)
\(72\) 0 0
\(73\) 165.570 286.776i 0.265459 0.459789i −0.702224 0.711956i \(-0.747810\pi\)
0.967684 + 0.252166i \(0.0811430\pi\)
\(74\) 500.910 867.602i 0.786887 1.36293i
\(75\) 0 0
\(76\) −2199.96 −3.32043
\(77\) 122.972 + 226.527i 0.182000 + 0.335262i
\(78\) 0 0
\(79\) −218.823 379.013i −0.311640 0.539776i 0.667078 0.744988i \(-0.267545\pi\)
−0.978718 + 0.205212i \(0.934212\pi\)
\(80\) 505.329 875.255i 0.706219 1.22321i
\(81\) 0 0
\(82\) 65.8024 + 113.973i 0.0886178 + 0.153491i
\(83\) −241.241 −0.319032 −0.159516 0.987195i \(-0.550993\pi\)
−0.159516 + 0.987195i \(0.550993\pi\)
\(84\) 0 0
\(85\) 241.803 0.308555
\(86\) −647.297 1121.15i −0.811626 1.40578i
\(87\) 0 0
\(88\) 449.840 779.145i 0.544921 0.943831i
\(89\) 792.772 + 1373.12i 0.944198 + 1.63540i 0.757349 + 0.653010i \(0.226494\pi\)
0.186849 + 0.982389i \(0.440172\pi\)
\(90\) 0 0
\(91\) 374.265 610.643i 0.431139 0.703437i
\(92\) 1510.88 1.71218
\(93\) 0 0
\(94\) 1647.03 2852.73i 1.80721 3.13018i
\(95\) −303.173 + 525.112i −0.327420 + 0.567109i
\(96\) 0 0
\(97\) 79.2754 0.0829814 0.0414907 0.999139i \(-0.486789\pi\)
0.0414907 + 0.999139i \(0.486789\pi\)
\(98\) 991.877 1526.86i 1.02239 1.57384i
\(99\) 0 0
\(100\) 949.080 + 1643.85i 0.949080 + 1.64385i
\(101\) 577.487 1000.24i 0.568931 0.985418i −0.427741 0.903902i \(-0.640690\pi\)
0.996672 0.0815165i \(-0.0259763\pi\)
\(102\) 0 0
\(103\) 722.430 + 1251.28i 0.691098 + 1.19702i 0.971478 + 0.237128i \(0.0762061\pi\)
−0.280380 + 0.959889i \(0.590461\pi\)
\(104\) −2499.91 −2.35708
\(105\) 0 0
\(106\) −1527.93 −1.40006
\(107\) 495.480 + 858.197i 0.447662 + 0.775374i 0.998233 0.0594143i \(-0.0189233\pi\)
−0.550571 + 0.834788i \(0.685590\pi\)
\(108\) 0 0
\(109\) −976.585 + 1691.49i −0.858164 + 1.48638i 0.0155145 + 0.999880i \(0.495061\pi\)
−0.873678 + 0.486504i \(0.838272\pi\)
\(110\) −205.431 355.817i −0.178064 0.308417i
\(111\) 0 0
\(112\) −3364.48 88.3533i −2.83851 0.0745410i
\(113\) −672.882 −0.560172 −0.280086 0.959975i \(-0.590363\pi\)
−0.280086 + 0.959975i \(0.590363\pi\)
\(114\) 0 0
\(115\) 208.213 360.635i 0.168834 0.292430i
\(116\) −730.028 + 1264.45i −0.584323 + 1.01208i
\(117\) 0 0
\(118\) 2787.13 2.17437
\(119\) −384.174 707.686i −0.295942 0.545155i
\(120\) 0 0
\(121\) 568.653 + 984.936i 0.427238 + 0.739997i
\(122\) −1017.69 + 1762.70i −0.755227 + 1.30809i
\(123\) 0 0
\(124\) −646.130 1119.13i −0.467937 0.810491i
\(125\) 1218.34 0.871773
\(126\) 0 0
\(127\) 175.815 0.122843 0.0614216 0.998112i \(-0.480437\pi\)
0.0614216 + 0.998112i \(0.480437\pi\)
\(128\) 656.249 + 1136.66i 0.453163 + 0.784900i
\(129\) 0 0
\(130\) −570.825 + 988.698i −0.385113 + 0.667035i
\(131\) 562.965 + 975.085i 0.375470 + 0.650332i 0.990397 0.138251i \(-0.0441481\pi\)
−0.614928 + 0.788584i \(0.710815\pi\)
\(132\) 0 0
\(133\) 2018.53 + 53.0078i 1.31600 + 0.0345591i
\(134\) −1051.66 −0.677983
\(135\) 0 0
\(136\) −1405.33 + 2434.10i −0.886073 + 1.53472i
\(137\) 934.350 1618.34i 0.582678 1.00923i −0.412483 0.910966i \(-0.635338\pi\)
0.995161 0.0982624i \(-0.0313285\pi\)
\(138\) 0 0
\(139\) −2817.19 −1.71907 −0.859537 0.511074i \(-0.829248\pi\)
−0.859537 + 0.511074i \(0.829248\pi\)
\(140\) −1086.04 + 1771.96i −0.655624 + 1.06970i
\(141\) 0 0
\(142\) −2084.65 3610.72i −1.23197 2.13384i
\(143\) −269.105 + 466.103i −0.157368 + 0.272570i
\(144\) 0 0
\(145\) 201.208 + 348.503i 0.115238 + 0.199597i
\(146\) 1757.79 0.996410
\(147\) 0 0
\(148\) 3808.14 2.11505
\(149\) 900.163 + 1559.13i 0.494928 + 0.857240i 0.999983 0.00584714i \(-0.00186121\pi\)
−0.505055 + 0.863087i \(0.668528\pi\)
\(150\) 0 0
\(151\) 226.492 392.296i 0.122064 0.211421i −0.798517 0.601972i \(-0.794382\pi\)
0.920581 + 0.390551i \(0.127715\pi\)
\(152\) −3524.01 6103.77i −1.88050 3.25711i
\(153\) 0 0
\(154\) −714.986 + 1166.56i −0.374125 + 0.610414i
\(155\) −356.169 −0.184569
\(156\) 0 0
\(157\) 931.829 1613.98i 0.473682 0.820441i −0.525864 0.850569i \(-0.676258\pi\)
0.999546 + 0.0301273i \(0.00959128\pi\)
\(158\) 1161.58 2011.91i 0.584875 1.01303i
\(159\) 0 0
\(160\) 2488.77 1.22971
\(161\) −1386.28 36.4046i −0.678597 0.0178204i
\(162\) 0 0
\(163\) −1160.57 2010.16i −0.557686 0.965940i −0.997689 0.0679437i \(-0.978356\pi\)
0.440004 0.897996i \(-0.354977\pi\)
\(164\) −250.129 + 433.237i −0.119096 + 0.206281i
\(165\) 0 0
\(166\) −640.290 1109.01i −0.299374 0.518531i
\(167\) −3211.62 −1.48816 −0.744079 0.668092i \(-0.767111\pi\)
−0.744079 + 0.668092i \(0.767111\pi\)
\(168\) 0 0
\(169\) −701.494 −0.319296
\(170\) 641.780 + 1111.60i 0.289543 + 0.501503i
\(171\) 0 0
\(172\) 2460.52 4261.74i 1.09077 1.88927i
\(173\) 107.139 + 185.569i 0.0470844 + 0.0815525i 0.888607 0.458669i \(-0.151674\pi\)
−0.841523 + 0.540222i \(0.818340\pi\)
\(174\) 0 0
\(175\) −831.199 1531.15i −0.359044 0.661395i
\(176\) 2529.17 1.08320
\(177\) 0 0
\(178\) −4208.27 + 7288.93i −1.77204 + 3.06926i
\(179\) −1218.61 + 2110.70i −0.508845 + 0.881345i 0.491102 + 0.871102i \(0.336594\pi\)
−0.999948 + 0.0102437i \(0.996739\pi\)
\(180\) 0 0
\(181\) −248.631 −0.102103 −0.0510514 0.998696i \(-0.516257\pi\)
−0.0510514 + 0.998696i \(0.516257\pi\)
\(182\) 3800.55 + 99.8048i 1.54789 + 0.0406485i
\(183\) 0 0
\(184\) 2420.21 + 4191.93i 0.969677 + 1.67953i
\(185\) 524.794 908.970i 0.208560 0.361237i
\(186\) 0 0
\(187\) 302.555 + 524.041i 0.118316 + 0.204929i
\(188\) 12521.4 4.85755
\(189\) 0 0
\(190\) −3218.67 −1.22898
\(191\) −2156.54 3735.24i −0.816972 1.41504i −0.907903 0.419180i \(-0.862317\pi\)
0.0909306 0.995857i \(-0.471016\pi\)
\(192\) 0 0
\(193\) −1030.43 + 1784.75i −0.384309 + 0.665643i −0.991673 0.128781i \(-0.958894\pi\)
0.607364 + 0.794424i \(0.292227\pi\)
\(194\) 210.409 + 364.438i 0.0778683 + 0.134872i
\(195\) 0 0
\(196\) 6911.51 + 363.252i 2.51877 + 0.132380i
\(197\) 1666.09 0.602557 0.301279 0.953536i \(-0.402587\pi\)
0.301279 + 0.953536i \(0.402587\pi\)
\(198\) 0 0
\(199\) 543.767 941.832i 0.193702 0.335501i −0.752773 0.658281i \(-0.771284\pi\)
0.946474 + 0.322780i \(0.104617\pi\)
\(200\) −3040.57 + 5266.43i −1.07501 + 1.86196i
\(201\) 0 0
\(202\) 6130.94 2.13550
\(203\) 700.288 1142.58i 0.242121 0.395040i
\(204\) 0 0
\(205\) 68.9399 + 119.407i 0.0234877 + 0.0406818i
\(206\) −3834.87 + 6642.19i −1.29703 + 2.24652i
\(207\) 0 0
\(208\) −3513.86 6086.18i −1.17136 2.02885i
\(209\) −1517.38 −0.502198
\(210\) 0 0
\(211\) −4676.47 −1.52579 −0.762895 0.646522i \(-0.776223\pi\)
−0.762895 + 0.646522i \(0.776223\pi\)
\(212\) −2904.01 5029.88i −0.940792 1.62950i
\(213\) 0 0
\(214\) −2630.15 + 4555.56i −0.840157 + 1.45520i
\(215\) −678.161 1174.61i −0.215117 0.372594i
\(216\) 0 0
\(217\) 565.878 + 1042.40i 0.177024 + 0.326096i
\(218\) −10368.0 −3.22114
\(219\) 0 0
\(220\) 780.889 1352.54i 0.239307 0.414492i
\(221\) 840.701 1456.14i 0.255890 0.443214i
\(222\) 0 0
\(223\) 3246.03 0.974754 0.487377 0.873192i \(-0.337954\pi\)
0.487377 + 0.873192i \(0.337954\pi\)
\(224\) −3954.12 7283.89i −1.17945 2.17266i
\(225\) 0 0
\(226\) −1785.93 3093.32i −0.525656 0.910463i
\(227\) 2569.08 4449.77i 0.751171 1.30107i −0.196085 0.980587i \(-0.562823\pi\)
0.947256 0.320479i \(-0.103844\pi\)
\(228\) 0 0
\(229\) −307.403 532.438i −0.0887064 0.153644i 0.818258 0.574851i \(-0.194940\pi\)
−0.906965 + 0.421207i \(0.861607\pi\)
\(230\) 2210.51 0.633725
\(231\) 0 0
\(232\) −4677.59 −1.32370
\(233\) 1413.71 + 2448.61i 0.397490 + 0.688472i 0.993415 0.114567i \(-0.0365482\pi\)
−0.595926 + 0.803039i \(0.703215\pi\)
\(234\) 0 0
\(235\) 1725.56 2988.76i 0.478992 0.829638i
\(236\) 5297.24 + 9175.09i 1.46111 + 2.53071i
\(237\) 0 0
\(238\) 2233.66 3644.39i 0.608348 0.992567i
\(239\) 3432.45 0.928983 0.464491 0.885578i \(-0.346237\pi\)
0.464491 + 0.885578i \(0.346237\pi\)
\(240\) 0 0
\(241\) 1318.06 2282.94i 0.352296 0.610195i −0.634355 0.773042i \(-0.718734\pi\)
0.986651 + 0.162847i \(0.0520675\pi\)
\(242\) −3018.58 + 5228.33i −0.801825 + 1.38880i
\(243\) 0 0
\(244\) −7736.96 −2.02995
\(245\) 1039.17 1599.66i 0.270980 0.417137i
\(246\) 0 0
\(247\) 2108.15 + 3651.42i 0.543070 + 0.940625i
\(248\) 2070.01 3585.37i 0.530024 0.918028i
\(249\) 0 0
\(250\) 3233.65 + 5600.85i 0.818057 + 1.41692i
\(251\) −2057.57 −0.517422 −0.258711 0.965955i \(-0.583298\pi\)
−0.258711 + 0.965955i \(0.583298\pi\)
\(252\) 0 0
\(253\) 1042.10 0.258958
\(254\) 466.639 + 808.243i 0.115274 + 0.199660i
\(255\) 0 0
\(256\) 203.161 351.885i 0.0495998 0.0859093i
\(257\) 1075.10 + 1862.13i 0.260946 + 0.451972i 0.966494 0.256691i \(-0.0826322\pi\)
−0.705548 + 0.708663i \(0.749299\pi\)
\(258\) 0 0
\(259\) −3494.07 91.7566i −0.838267 0.0220134i
\(260\) −4339.66 −1.03513
\(261\) 0 0
\(262\) −2988.39 + 5176.04i −0.704668 + 1.22052i
\(263\) −2295.08 + 3975.19i −0.538100 + 0.932017i 0.460906 + 0.887449i \(0.347525\pi\)
−0.999006 + 0.0445683i \(0.985809\pi\)
\(264\) 0 0
\(265\) −1600.79 −0.371078
\(266\) 5113.78 + 9420.09i 1.17874 + 2.17136i
\(267\) 0 0
\(268\) −1998.80 3462.02i −0.455582 0.789091i
\(269\) −189.689 + 328.551i −0.0429945 + 0.0744687i −0.886722 0.462303i \(-0.847023\pi\)
0.843727 + 0.536772i \(0.180356\pi\)
\(270\) 0 0
\(271\) 2684.42 + 4649.55i 0.601723 + 1.04221i 0.992560 + 0.121755i \(0.0388521\pi\)
−0.390837 + 0.920460i \(0.627815\pi\)
\(272\) −7901.28 −1.76134
\(273\) 0 0
\(274\) 9919.61 2.18710
\(275\) 654.610 + 1133.82i 0.143543 + 0.248624i
\(276\) 0 0
\(277\) 2390.80 4140.99i 0.518590 0.898224i −0.481177 0.876624i \(-0.659791\pi\)
0.999767 0.0216003i \(-0.00687613\pi\)
\(278\) −7477.25 12951.0i −1.61315 2.79406i
\(279\) 0 0
\(280\) −6655.98 174.790i −1.42061 0.0373061i
\(281\) 2076.57 0.440845 0.220423 0.975404i \(-0.429256\pi\)
0.220423 + 0.975404i \(0.429256\pi\)
\(282\) 0 0
\(283\) −1278.81 + 2214.96i −0.268612 + 0.465250i −0.968504 0.248999i \(-0.919898\pi\)
0.699892 + 0.714249i \(0.253232\pi\)
\(284\) 7924.21 13725.1i 1.65569 2.86774i
\(285\) 0 0
\(286\) −2856.97 −0.590687
\(287\) 239.940 391.480i 0.0493491 0.0805169i
\(288\) 0 0
\(289\) 1511.30 + 2617.65i 0.307612 + 0.532800i
\(290\) −1068.07 + 1849.96i −0.216274 + 0.374597i
\(291\) 0 0
\(292\) 3340.88 + 5786.57i 0.669555 + 1.15970i
\(293\) −560.049 −0.111667 −0.0558335 0.998440i \(-0.517782\pi\)
−0.0558335 + 0.998440i \(0.517782\pi\)
\(294\) 0 0
\(295\) 2920.02 0.576305
\(296\) 6100.08 + 10565.6i 1.19784 + 2.07471i
\(297\) 0 0
\(298\) −4778.33 + 8276.31i −0.928863 + 1.60884i
\(299\) −1447.83 2507.71i −0.280034 0.485033i
\(300\) 0 0
\(301\) −2360.28 + 3850.98i −0.451975 + 0.737432i
\(302\) 2404.57 0.458171
\(303\) 0 0
\(304\) 9906.66 17158.8i 1.86903 3.23726i
\(305\) −1066.22 + 1846.75i −0.200169 + 0.346703i
\(306\) 0 0
\(307\) 3653.02 0.679117 0.339558 0.940585i \(-0.389722\pi\)
0.339558 + 0.940585i \(0.389722\pi\)
\(308\) −5199.15 136.533i −0.961848 0.0252587i
\(309\) 0 0
\(310\) −945.325 1637.35i −0.173196 0.299985i
\(311\) 1746.13 3024.39i 0.318374 0.551439i −0.661775 0.749702i \(-0.730197\pi\)
0.980149 + 0.198263i \(0.0635300\pi\)
\(312\) 0 0
\(313\) −4356.05 7544.90i −0.786640 1.36250i −0.928014 0.372544i \(-0.878485\pi\)
0.141374 0.989956i \(-0.454848\pi\)
\(314\) 9892.85 1.77798
\(315\) 0 0
\(316\) 8830.83 1.57207
\(317\) 970.165 + 1680.37i 0.171892 + 0.297726i 0.939081 0.343695i \(-0.111679\pi\)
−0.767189 + 0.641421i \(0.778345\pi\)
\(318\) 0 0
\(319\) −503.523 + 872.127i −0.0883758 + 0.153071i
\(320\) 2562.92 + 4439.11i 0.447724 + 0.775480i
\(321\) 0 0
\(322\) −3512.03 6469.51i −0.607820 1.11966i
\(323\) 4740.39 0.816602
\(324\) 0 0
\(325\) 1818.94 3150.50i 0.310452 0.537718i
\(326\) 6160.64 10670.5i 1.04665 1.81284i
\(327\) 0 0
\(328\) −1602.68 −0.269797
\(329\) −11488.8 301.702i −1.92522 0.0505574i
\(330\) 0 0
\(331\) 2865.75 + 4963.63i 0.475879 + 0.824247i 0.999618 0.0276315i \(-0.00879650\pi\)
−0.523739 + 0.851879i \(0.675463\pi\)
\(332\) 2433.88 4215.61i 0.402339 0.696872i
\(333\) 0 0
\(334\) −8524.10 14764.2i −1.39646 2.41874i
\(335\) −1101.81 −0.179696
\(336\) 0 0
\(337\) 2403.74 0.388547 0.194273 0.980947i \(-0.437765\pi\)
0.194273 + 0.980947i \(0.437765\pi\)
\(338\) −1861.87 3224.85i −0.299622 0.518960i
\(339\) 0 0
\(340\) −2439.55 + 4225.42i −0.389127 + 0.673987i
\(341\) −445.656 771.898i −0.0707731 0.122583i
\(342\) 0 0
\(343\) −6332.75 499.826i −0.996900 0.0786824i
\(344\) 15765.6 2.47099
\(345\) 0 0
\(346\) −568.723 + 985.057i −0.0883663 + 0.153055i
\(347\) −1668.22 + 2889.45i −0.258083 + 0.447013i −0.965728 0.259555i \(-0.916424\pi\)
0.707645 + 0.706568i \(0.249758\pi\)
\(348\) 0 0
\(349\) −2424.54 −0.371870 −0.185935 0.982562i \(-0.559531\pi\)
−0.185935 + 0.982562i \(0.559531\pi\)
\(350\) 4832.76 7885.02i 0.738062 1.20421i
\(351\) 0 0
\(352\) 3114.06 + 5393.71i 0.471534 + 0.816721i
\(353\) −6201.56 + 10741.4i −0.935059 + 1.61957i −0.160531 + 0.987031i \(0.551321\pi\)
−0.774528 + 0.632540i \(0.782013\pi\)
\(354\) 0 0
\(355\) −2184.05 3782.88i −0.326528 0.565562i
\(356\) −31993.1 −4.76300
\(357\) 0 0
\(358\) −12937.5 −1.90997
\(359\) 676.921 + 1172.46i 0.0995168 + 0.172368i 0.911485 0.411334i \(-0.134937\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(360\) 0 0
\(361\) −2514.03 + 4354.42i −0.366529 + 0.634848i
\(362\) −659.903 1142.99i −0.0958114 0.165950i
\(363\) 0 0
\(364\) 6894.81 + 12700.9i 0.992819 + 1.82887i
\(365\) 1841.61 0.264093
\(366\) 0 0
\(367\) 689.031 1193.44i 0.0980031 0.169746i −0.812855 0.582466i \(-0.802088\pi\)
0.910858 + 0.412720i \(0.135421\pi\)
\(368\) −6803.67 + 11784.3i −0.963766 + 1.66929i
\(369\) 0 0
\(370\) 5571.52 0.782837
\(371\) 2543.31 + 4685.03i 0.355909 + 0.655619i
\(372\) 0 0
\(373\) −2728.46 4725.83i −0.378752 0.656017i 0.612129 0.790758i \(-0.290313\pi\)
−0.990881 + 0.134741i \(0.956980\pi\)
\(374\) −1606.05 + 2781.76i −0.222051 + 0.384603i
\(375\) 0 0
\(376\) 20057.5 + 34740.6i 2.75103 + 4.76492i
\(377\) 2798.25 0.382273
\(378\) 0 0
\(379\) 554.675 0.0751761 0.0375881 0.999293i \(-0.488033\pi\)
0.0375881 + 0.999293i \(0.488033\pi\)
\(380\) −6117.43 10595.7i −0.825836 1.43039i
\(381\) 0 0
\(382\) 11447.5 19827.7i 1.53327 2.65569i
\(383\) 2930.33 + 5075.48i 0.390948 + 0.677141i 0.992575 0.121636i \(-0.0388140\pi\)
−0.601627 + 0.798777i \(0.705481\pi\)
\(384\) 0 0
\(385\) −749.077 + 1222.18i −0.0991597 + 0.161787i
\(386\) −10939.6 −1.44252
\(387\) 0 0
\(388\) −799.809 + 1385.31i −0.104650 + 0.181259i
\(389\) 3889.43 6736.69i 0.506946 0.878056i −0.493022 0.870017i \(-0.664108\pi\)
0.999968 0.00803932i \(-0.00255902\pi\)
\(390\) 0 0
\(391\) −3255.60 −0.421081
\(392\) 10063.4 + 19757.8i 1.29663 + 2.54571i
\(393\) 0 0
\(394\) 4422.04 + 7659.20i 0.565429 + 0.979352i
\(395\) 1216.96 2107.84i 0.155018 0.268499i
\(396\) 0 0
\(397\) −4013.94 6952.35i −0.507440 0.878912i −0.999963 0.00861270i \(-0.997258\pi\)
0.492523 0.870300i \(-0.336075\pi\)
\(398\) 5772.95 0.727065
\(399\) 0 0
\(400\) −17095.2 −2.13690
\(401\) 389.990 + 675.482i 0.0485665 + 0.0841196i 0.889287 0.457350i \(-0.151201\pi\)
−0.840720 + 0.541470i \(0.817868\pi\)
\(402\) 0 0
\(403\) −1238.33 + 2144.85i −0.153066 + 0.265118i
\(404\) 11652.5 + 20182.8i 1.43499 + 2.48547i
\(405\) 0 0
\(406\) 7111.22 + 186.745i 0.869271 + 0.0228276i
\(407\) 2626.59 0.319890
\(408\) 0 0
\(409\) −7346.25 + 12724.1i −0.888139 + 1.53830i −0.0460654 + 0.998938i \(0.514668\pi\)
−0.842073 + 0.539363i \(0.818665\pi\)
\(410\) −365.953 + 633.850i −0.0440809 + 0.0763503i
\(411\) 0 0
\(412\) −29154.4 −3.48624
\(413\) −4639.29 8546.04i −0.552748 1.01822i
\(414\) 0 0
\(415\) −670.820 1161.89i −0.0793476 0.137434i
\(416\) 8652.95 14987.3i 1.01982 1.76638i
\(417\) 0 0
\(418\) −4027.35 6975.57i −0.471254 0.816236i
\(419\) −3370.31 −0.392960 −0.196480 0.980508i \(-0.562951\pi\)
−0.196480 + 0.980508i \(0.562951\pi\)
\(420\) 0 0
\(421\) 15651.0 1.81184 0.905919 0.423450i \(-0.139181\pi\)
0.905919 + 0.423450i \(0.139181\pi\)
\(422\) −12412.0 21498.3i −1.43178 2.47991i
\(423\) 0 0
\(424\) 9303.58 16114.3i 1.06562 1.84570i
\(425\) −2045.04 3542.12i −0.233410 0.404277i
\(426\) 0 0
\(427\) 7098.88 + 186.421i 0.804541 + 0.0211277i
\(428\) −19995.6 −2.25823
\(429\) 0 0
\(430\) 3599.88 6235.17i 0.403724 0.699271i
\(431\) 2444.06 4233.24i 0.273147 0.473104i −0.696519 0.717538i \(-0.745269\pi\)
0.969666 + 0.244434i \(0.0786022\pi\)
\(432\) 0 0
\(433\) −5255.73 −0.583313 −0.291656 0.956523i \(-0.594206\pi\)
−0.291656 + 0.956523i \(0.594206\pi\)
\(434\) −3290.12 + 5368.10i −0.363896 + 0.593725i
\(435\) 0 0
\(436\) −19705.5 34131.0i −2.16450 3.74903i
\(437\) 4081.88 7070.03i 0.446826 0.773925i
\(438\) 0 0
\(439\) 412.488 + 714.451i 0.0448451 + 0.0776740i 0.887577 0.460660i \(-0.152387\pi\)
−0.842732 + 0.538334i \(0.819054\pi\)
\(440\) 5003.48 0.542117
\(441\) 0 0
\(442\) 8925.37 0.960490
\(443\) 6513.64 + 11281.9i 0.698583 + 1.20998i 0.968958 + 0.247226i \(0.0795190\pi\)
−0.270375 + 0.962755i \(0.587148\pi\)
\(444\) 0 0
\(445\) −4408.92 + 7636.47i −0.469669 + 0.813491i
\(446\) 8615.44 + 14922.4i 0.914693 + 1.58429i
\(447\) 0 0
\(448\) 8920.02 14553.7i 0.940695 1.53482i
\(449\) −16526.1 −1.73700 −0.868500 0.495689i \(-0.834916\pi\)
−0.868500 + 0.495689i \(0.834916\pi\)
\(450\) 0 0
\(451\) −172.522 + 298.817i −0.0180127 + 0.0311989i
\(452\) 6788.71 11758.4i 0.706447 1.22360i
\(453\) 0 0
\(454\) 27274.9 2.81954
\(455\) 3981.76 + 104.564i 0.410259 + 0.0107737i
\(456\) 0 0
\(457\) 1855.41 + 3213.67i 0.189918 + 0.328947i 0.945223 0.326426i \(-0.105844\pi\)
−0.755305 + 0.655374i \(0.772511\pi\)
\(458\) 1631.79 2826.34i 0.166481 0.288354i
\(459\) 0 0
\(460\) 4201.31 + 7276.89i 0.425842 + 0.737580i
\(461\) 9714.00 0.981401 0.490701 0.871328i \(-0.336741\pi\)
0.490701 + 0.871328i \(0.336741\pi\)
\(462\) 0 0
\(463\) −43.2780 −0.00434406 −0.00217203 0.999998i \(-0.500691\pi\)
−0.00217203 + 0.999998i \(0.500691\pi\)
\(464\) −6574.79 11387.9i −0.657817 1.13937i
\(465\) 0 0
\(466\) −7504.38 + 12998.0i −0.745995 + 1.29210i
\(467\) −766.618 1327.82i −0.0759633 0.131572i 0.825541 0.564341i \(-0.190870\pi\)
−0.901505 + 0.432769i \(0.857537\pi\)
\(468\) 0 0
\(469\) 1750.54 + 3224.66i 0.172350 + 0.317486i
\(470\) 18319.6 1.79791
\(471\) 0 0
\(472\) −16970.8 + 29394.3i −1.65497 + 2.86649i
\(473\) 1697.09 2939.45i 0.164974 0.285743i
\(474\) 0 0
\(475\) 10256.3 0.990722
\(476\) 16242.5 + 426.538i 1.56402 + 0.0410721i
\(477\) 0 0
\(478\) 9110.23 + 15779.4i 0.871741 + 1.50990i
\(479\) −3517.69 + 6092.81i −0.335547 + 0.581185i −0.983590 0.180419i \(-0.942255\pi\)
0.648042 + 0.761604i \(0.275588\pi\)
\(480\) 0 0
\(481\) −3649.21 6320.62i −0.345924 0.599159i
\(482\) 13993.3 1.32236
\(483\) 0 0
\(484\) −22948.6 −2.15520
\(485\) 220.441 + 381.815i 0.0206386 + 0.0357471i
\(486\) 0 0
\(487\) 7685.64 13311.9i 0.715132 1.23865i −0.247776 0.968817i \(-0.579700\pi\)
0.962908 0.269828i \(-0.0869669\pi\)
\(488\) −12393.5 21466.1i −1.14964 1.99124i
\(489\) 0 0
\(490\) 10111.9 + 531.458i 0.932266 + 0.0489976i
\(491\) 2393.35 0.219980 0.109990 0.993933i \(-0.464918\pi\)
0.109990 + 0.993933i \(0.464918\pi\)
\(492\) 0 0
\(493\) 1573.04 2724.58i 0.143704 0.248903i
\(494\) −11190.7 + 19382.8i −1.01921 + 1.76533i
\(495\) 0 0
\(496\) 11638.4 1.05359
\(497\) −7601.40 + 12402.3i −0.686055 + 1.11935i
\(498\) 0 0
\(499\) −346.760 600.606i −0.0311084 0.0538814i 0.850052 0.526699i \(-0.176570\pi\)
−0.881160 + 0.472817i \(0.843237\pi\)
\(500\) −12291.8 + 21290.1i −1.09941 + 1.90424i
\(501\) 0 0
\(502\) −5461.10 9458.91i −0.485540 0.840979i
\(503\) 8646.95 0.766498 0.383249 0.923645i \(-0.374805\pi\)
0.383249 + 0.923645i \(0.374805\pi\)
\(504\) 0 0
\(505\) 6423.27 0.566003
\(506\) 2765.89 + 4790.67i 0.243002 + 0.420892i
\(507\) 0 0
\(508\) −1773.80 + 3072.31i −0.154920 + 0.268330i
\(509\) −7750.44 13424.1i −0.674916 1.16899i −0.976494 0.215546i \(-0.930847\pi\)
0.301578 0.953441i \(-0.402487\pi\)
\(510\) 0 0
\(511\) −2925.92 5389.84i −0.253298 0.466600i
\(512\) 12656.9 1.09250
\(513\) 0 0
\(514\) −5706.96 + 9884.75i −0.489734 + 0.848245i
\(515\) −4017.72 + 6958.89i −0.343771 + 0.595428i
\(516\) 0 0
\(517\) 8636.41 0.734678
\(518\) −8851.97 16306.2i −0.750836 1.38311i
\(519\) 0 0
\(520\) −6951.50 12040.4i −0.586238 1.01539i
\(521\) 432.354 748.858i 0.0363565 0.0629714i −0.847275 0.531155i \(-0.821758\pi\)
0.883631 + 0.468184i \(0.155091\pi\)
\(522\) 0 0
\(523\) 3127.81 + 5417.52i 0.261509 + 0.452947i 0.966643 0.256127i \(-0.0824465\pi\)
−0.705134 + 0.709074i \(0.749113\pi\)
\(524\) −22719.0 −1.89406
\(525\) 0 0
\(526\) −24365.9 −2.01978
\(527\) 1392.26 + 2411.46i 0.115081 + 0.199326i
\(528\) 0 0
\(529\) 3280.15 5681.39i 0.269594 0.466951i
\(530\) −4248.72 7359.01i −0.348213 0.603122i
\(531\) 0 0
\(532\) −21291.2 + 34738.2i −1.73513 + 2.83100i
\(533\) 958.762 0.0779148
\(534\) 0 0
\(535\) −2755.56 + 4772.78i −0.222679 + 0.385692i
\(536\) 6403.56 11091.3i 0.516029 0.893789i
\(537\) 0 0
\(538\) −2013.85 −0.161381
\(539\) 4767.08 + 250.546i 0.380951 + 0.0200218i
\(540\) 0 0
\(541\) −71.9353 124.596i −0.00571671 0.00990164i 0.863153 0.504943i \(-0.168486\pi\)
−0.868870 + 0.495041i \(0.835153\pi\)
\(542\) −14249.7 + 24681.2i −1.12929 + 1.95599i
\(543\) 0 0
\(544\) −9728.53 16850.3i −0.766741 1.32804i
\(545\) −10862.4 −0.853747
\(546\) 0 0
\(547\) 5455.65 0.426448 0.213224 0.977003i \(-0.431604\pi\)
0.213224 + 0.977003i \(0.431604\pi\)
\(548\) 18853.3 + 32654.9i 1.46966 + 2.54552i
\(549\) 0 0
\(550\) −3474.86 + 6018.63i −0.269397 + 0.466610i
\(551\) 3944.56 + 6832.18i 0.304980 + 0.528241i
\(552\) 0 0
\(553\) −8102.54 212.778i −0.623065 0.0163621i
\(554\) 25382.2 1.94654
\(555\) 0 0
\(556\) 28422.7 49229.5i 2.16797 3.75503i
\(557\) 12404.9 21486.0i 0.943652 1.63445i 0.185223 0.982696i \(-0.440699\pi\)
0.758428 0.651756i \(-0.225968\pi\)
\(558\) 0 0
\(559\) −9431.33 −0.713600
\(560\) −8930.06 16450.1i −0.673864 1.24132i
\(561\) 0 0
\(562\) 5511.51 + 9546.22i 0.413682 + 0.716517i
\(563\) 8184.91 14176.7i 0.612705 1.06124i −0.378077 0.925774i \(-0.623415\pi\)
0.990782 0.135462i \(-0.0432520\pi\)
\(564\) 0 0
\(565\) −1871.08 3240.81i −0.139322 0.241313i
\(566\) −13576.6 −1.00824
\(567\) 0 0
\(568\) 50773.7 3.75074
\(569\) −9225.29 15978.7i −0.679691 1.17726i −0.975074 0.221881i \(-0.928781\pi\)
0.295383 0.955379i \(-0.404553\pi\)
\(570\) 0 0
\(571\) 3554.34 6156.30i 0.260499 0.451197i −0.705876 0.708335i \(-0.749446\pi\)
0.966374 + 0.257139i \(0.0827797\pi\)
\(572\) −5429.99 9405.02i −0.396922 0.687489i
\(573\) 0 0
\(574\) 2436.52 + 63.9844i 0.177175 + 0.00465271i
\(575\) −7043.82 −0.510865
\(576\) 0 0
\(577\) −3797.09 + 6576.75i −0.273960 + 0.474512i −0.969872 0.243615i \(-0.921667\pi\)
0.695912 + 0.718127i \(0.255000\pi\)
\(578\) −8022.42 + 13895.2i −0.577316 + 0.999940i
\(579\) 0 0
\(580\) −8119.96 −0.581315
\(581\) −2334.73 + 3809.30i −0.166714 + 0.272007i
\(582\) 0 0
\(583\) −2002.98 3469.26i −0.142290 0.246453i
\(584\) −10703.2 + 18538.5i −0.758392 + 1.31357i
\(585\) 0 0
\(586\) −1486.45 2574.61i −0.104786 0.181495i
\(587\) 1763.34 0.123988 0.0619939 0.998077i \(-0.480254\pi\)
0.0619939 + 0.998077i \(0.480254\pi\)
\(588\) 0 0
\(589\) −6982.47 −0.488468
\(590\) 7750.16 + 13423.7i 0.540795 + 0.936684i
\(591\) 0 0
\(592\) −17148.4 + 29702.0i −1.19054 + 2.06207i
\(593\) −6158.07 10666.1i −0.426445 0.738624i 0.570109 0.821569i \(-0.306901\pi\)
−0.996554 + 0.0829448i \(0.973567\pi\)
\(594\) 0 0
\(595\) 2340.16 3818.16i 0.161239 0.263075i
\(596\) −36327.0 −2.49666
\(597\) 0 0
\(598\) 7685.50 13311.7i 0.525558 0.910293i
\(599\) −4451.70 + 7710.57i −0.303659 + 0.525952i −0.976962 0.213414i \(-0.931542\pi\)
0.673303 + 0.739367i \(0.264875\pi\)
\(600\) 0 0
\(601\) −19157.1 −1.30022 −0.650112 0.759838i \(-0.725278\pi\)
−0.650112 + 0.759838i \(0.725278\pi\)
\(602\) −23968.0 629.413i −1.62269 0.0426129i
\(603\) 0 0
\(604\) 4570.15 + 7915.74i 0.307876 + 0.533256i
\(605\) −3162.51 + 5477.62i −0.212519 + 0.368094i
\(606\) 0 0
\(607\) 3784.96 + 6555.75i 0.253092 + 0.438369i 0.964376 0.264537i \(-0.0852191\pi\)
−0.711283 + 0.702905i \(0.751886\pi\)
\(608\) 48790.7 3.25448
\(609\) 0 0
\(610\) −11319.6 −0.751340
\(611\) −11998.9 20782.6i −0.794471 1.37606i
\(612\) 0 0
\(613\) −1453.56 + 2517.65i −0.0957730 + 0.165884i −0.909931 0.414760i \(-0.863866\pi\)
0.814158 + 0.580643i \(0.197199\pi\)
\(614\) 9695.65 + 16793.4i 0.637272 + 1.10379i
\(615\) 0 0
\(616\) −7949.47 14643.7i −0.519956 0.957811i
\(617\) 12510.9 0.816320 0.408160 0.912910i \(-0.366171\pi\)
0.408160 + 0.912910i \(0.366171\pi\)
\(618\) 0 0
\(619\) −5032.78 + 8717.03i −0.326792 + 0.566021i −0.981873 0.189538i \(-0.939301\pi\)
0.655081 + 0.755558i \(0.272634\pi\)
\(620\) 3593.39 6223.93i 0.232764 0.403160i
\(621\) 0 0
\(622\) 18538.0 1.19503
\(623\) 29354.6 + 770.869i 1.88775 + 0.0495734i
\(624\) 0 0
\(625\) −2491.59 4315.56i −0.159462 0.276196i
\(626\) 23123.2 40050.5i 1.47634 2.55709i
\(627\) 0 0
\(628\) 18802.4 + 32566.8i 1.19474 + 2.06936i
\(629\) −8205.63 −0.520159
\(630\) 0 0
\(631\) −25146.6 −1.58648 −0.793242 0.608907i \(-0.791608\pi\)
−0.793242 + 0.608907i \(0.791608\pi\)
\(632\) 14145.7 + 24501.1i 0.890325 + 1.54209i
\(633\) 0 0
\(634\) −5149.92 + 8919.92i −0.322602 + 0.558762i
\(635\) 488.889 + 846.781i 0.0305527 + 0.0529189i
\(636\) 0 0
\(637\) −6020.16 11819.6i −0.374454 0.735179i
\(638\) −5345.70 −0.331721
\(639\) 0 0
\(640\) −3649.66 + 6321.41i −0.225415 + 0.390430i
\(641\) −14479.5 + 25079.1i −0.892206 + 1.54535i −0.0549809 + 0.998487i \(0.517510\pi\)
−0.837225 + 0.546859i \(0.815824\pi\)
\(642\) 0 0
\(643\) 7341.90 0.450290 0.225145 0.974325i \(-0.427714\pi\)
0.225145 + 0.974325i \(0.427714\pi\)
\(644\) 14622.3 23857.5i 0.894721 1.45981i
\(645\) 0 0
\(646\) 12581.7 + 21792.1i 0.766285 + 1.32725i
\(647\) 3035.99 5258.49i 0.184478 0.319525i −0.758923 0.651181i \(-0.774274\pi\)
0.943400 + 0.331656i \(0.107607\pi\)
\(648\) 0 0
\(649\) 3653.67 + 6328.34i 0.220985 + 0.382756i
\(650\) 19311.0 1.16529
\(651\) 0 0
\(652\) 46835.9 2.81324
\(653\) 13131.1 + 22743.7i 0.786920 + 1.36298i 0.927846 + 0.372965i \(0.121659\pi\)
−0.140926 + 0.990020i \(0.545008\pi\)
\(654\) 0 0
\(655\) −3130.88 + 5422.84i −0.186769 + 0.323493i
\(656\) −2252.72 3901.82i −0.134076 0.232226i
\(657\) 0 0
\(658\) −29105.9 53615.9i −1.72442 3.17655i
\(659\) −26130.1 −1.54459 −0.772296 0.635263i \(-0.780892\pi\)
−0.772296 + 0.635263i \(0.780892\pi\)
\(660\) 0 0
\(661\) 5962.75 10327.8i 0.350868 0.607722i −0.635533 0.772073i \(-0.719220\pi\)
0.986402 + 0.164351i \(0.0525531\pi\)
\(662\) −15212.3 + 26348.4i −0.893114 + 1.54692i
\(663\) 0 0
\(664\) 15594.9 0.911444
\(665\) 5357.61 + 9869.25i 0.312420 + 0.575509i
\(666\) 0 0
\(667\) −2709.04 4692.19i −0.157263 0.272387i
\(668\) 32402.0 56121.9i 1.87675 3.25063i
\(669\) 0 0
\(670\) −2924.35 5065.13i −0.168623 0.292064i
\(671\) −5336.42 −0.307019
\(672\) 0 0
\(673\) −6359.85 −0.364271 −0.182135 0.983273i \(-0.558301\pi\)
−0.182135 + 0.983273i \(0.558301\pi\)
\(674\) 6379.89 + 11050.3i 0.364606 + 0.631516i
\(675\) 0 0
\(676\) 7077.36 12258.4i 0.402672 0.697449i
\(677\) 4280.81 + 7414.57i 0.243020 + 0.420924i 0.961573 0.274549i \(-0.0885285\pi\)
−0.718553 + 0.695472i \(0.755195\pi\)
\(678\) 0 0
\(679\) 767.226 1251.79i 0.0433629 0.0707500i
\(680\) −15631.2 −0.881513
\(681\) 0 0
\(682\) 2365.67 4097.46i 0.132824 0.230059i
\(683\) −3352.94 + 5807.47i −0.187843 + 0.325354i −0.944531 0.328423i \(-0.893483\pi\)
0.756688 + 0.653776i \(0.226816\pi\)
\(684\) 0 0
\(685\) 10392.6 0.579679
\(686\) −14510.3 30439.0i −0.807589 1.69412i
\(687\) 0 0
\(688\) 22160.0 + 38382.2i 1.22797 + 2.12690i
\(689\) −5565.62 + 9639.94i −0.307741 + 0.533022i
\(690\) 0 0
\(691\) 12665.3 + 21937.0i 0.697267 + 1.20770i 0.969410 + 0.245445i \(0.0789342\pi\)
−0.272143 + 0.962257i \(0.587732\pi\)
\(692\) −4323.68 −0.237517
\(693\) 0 0
\(694\) −17710.8 −0.968723
\(695\) −7833.77 13568.5i −0.427557 0.740550i
\(696\) 0 0
\(697\) 538.969 933.522i 0.0292897 0.0507312i
\(698\) −6435.08 11145.9i −0.348956 0.604410i
\(699\) 0 0
\(700\) 35142.3 + 922.859i 1.89751 + 0.0498297i
\(701\) 27184.1 1.46467 0.732333 0.680947i \(-0.238432\pi\)
0.732333 + 0.680947i \(0.238432\pi\)
\(702\) 0 0
\(703\) 10288.3 17819.8i 0.551961 0.956025i
\(704\) −6413.69 + 11108.8i −0.343360 + 0.594716i
\(705\) 0 0
\(706\) −65839.5 −3.50977
\(707\) −10205.2 18799.0i −0.542867 1.00001i
\(708\) 0 0
\(709\) −8072.75 13982.4i −0.427614 0.740649i 0.569047 0.822305i \(-0.307312\pi\)
−0.996661 + 0.0816561i \(0.973979\pi\)
\(710\) 11593.6 20080.7i 0.612816 1.06143i
\(711\) 0 0
\(712\) −51248.2 88764.5i −2.69748 4.67218i
\(713\) 4795.41 0.251879
\(714\) 0 0
\(715\) −2993.20 −0.156558
\(716\) −24589.1 42589.6i −1.28343 2.22297i
\(717\) 0 0
\(718\) −3593.30 + 6223.77i −0.186770 + 0.323494i
\(719\) 8648.74 + 14980.0i 0.448600 + 0.776998i 0.998295 0.0583673i \(-0.0185895\pi\)
−0.549695 + 0.835365i \(0.685256\pi\)
\(720\) 0 0
\(721\) 26749.9 + 702.470i 1.38172 + 0.0362848i
\(722\) −26690.4 −1.37578
\(723\) 0 0
\(724\) 2508.44 4344.74i 0.128764 0.223026i
\(725\) 3403.43 5894.91i 0.174345 0.301975i
\(726\) 0 0
\(727\) 3514.71 0.179303 0.0896516 0.995973i \(-0.471425\pi\)
0.0896516 + 0.995973i \(0.471425\pi\)
\(728\) −24194.1 + 39474.6i −1.23172 + 2.00965i
\(729\) 0 0
\(730\) 4887.89 + 8466.08i 0.247821 + 0.429238i
\(731\) −5301.83 + 9183.04i −0.268256 + 0.464633i
\(732\) 0 0
\(733\) 13755.6 + 23825.4i 0.693144 + 1.20056i 0.970802 + 0.239881i \(0.0771083\pi\)
−0.277658 + 0.960680i \(0.589558\pi\)
\(734\) 7315.16 0.367858
\(735\) 0 0
\(736\) −33508.4 −1.67817
\(737\) −1378.63 2387.86i −0.0689044 0.119346i
\(738\) 0 0
\(739\) −8050.80 + 13944.4i −0.400749 + 0.694117i −0.993816 0.111035i \(-0.964583\pi\)
0.593068 + 0.805153i \(0.297917\pi\)
\(740\) 10589.3 + 18341.2i 0.526040 + 0.911129i
\(741\) 0 0
\(742\) −14787.3 + 24126.7i −0.731617 + 1.19369i
\(743\) −14682.4 −0.724961 −0.362480 0.931991i \(-0.618070\pi\)
−0.362480 + 0.931991i \(0.618070\pi\)
\(744\) 0 0
\(745\) −5006.17 + 8670.93i −0.246190 + 0.426414i
\(746\) 14483.5 25086.1i 0.710828 1.23119i
\(747\) 0 0
\(748\) −12209.9 −0.596843
\(749\) 18346.5 + 481.791i 0.895016 + 0.0235037i
\(750\) 0 0
\(751\) 3636.53 + 6298.66i 0.176696 + 0.306047i 0.940747 0.339109i \(-0.110126\pi\)
−0.764051 + 0.645156i \(0.776792\pi\)
\(752\) −56385.3 + 97662.2i −2.73426 + 4.73587i
\(753\) 0 0
\(754\) 7426.96 + 12863.9i 0.358719 + 0.621319i
\(755\) 2519.23 0.121436
\(756\) 0 0
\(757\) 8505.93 0.408393 0.204196 0.978930i \(-0.434542\pi\)
0.204196 + 0.978930i \(0.434542\pi\)
\(758\) 1472.19 + 2549.91i 0.0705440 + 0.122186i
\(759\) 0 0
\(760\) 19598.4 33945.5i 0.935408 1.62017i
\(761\) 7108.86 + 12312.9i 0.338628 + 0.586521i 0.984175 0.177200i \(-0.0567038\pi\)
−0.645547 + 0.763721i \(0.723370\pi\)
\(762\) 0 0
\(763\) 17258.0 + 31790.9i 0.818848 + 1.50840i
\(764\) 87029.3 4.12121
\(765\) 0 0
\(766\) −15555.1 + 26942.2i −0.733717 + 1.27084i
\(767\) 10152.3 17584.4i 0.477939 0.827815i
\(768\) 0 0
\(769\) 16379.1 0.768068 0.384034 0.923319i \(-0.374534\pi\)
0.384034 + 0.923319i \(0.374534\pi\)
\(770\) −7606.66 199.756i −0.356006 0.00934895i
\(771\) 0 0
\(772\) −20791.9 36012.6i −0.969323 1.67892i
\(773\) −19948.3 + 34551.6i −0.928192 + 1.60768i −0.141846 + 0.989889i \(0.545304\pi\)
−0.786346 + 0.617787i \(0.788030\pi\)
\(774\) 0 0
\(775\) 3012.29 + 5217.45i 0.139619 + 0.241827i
\(776\) −5124.70 −0.237070
\(777\) 0 0
\(778\) 41292.5 1.90284
\(779\) 1351.52 + 2340.91i 0.0621609 + 0.107666i
\(780\) 0 0
\(781\) 5465.57 9466.65i 0.250414 0.433730i
\(782\) −8640.83 14966.4i −0.395135 0.684394i
\(783\) 0 0
\(784\) −33956.5 + 52271.3i −1.54685 + 2.38116i
\(785\) 10364.5 0.471244
\(786\) 0