Properties

Label 147.4.e.n.79.2
Level $147$
Weight $4$
Character 147.79
Analytic conductor $8.673$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(0.124036 - 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.n.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.54234 - 2.67141i) q^{10} +(-30.1558 - 52.2313i) q^{11} +(11.9077 - 20.6247i) q^{12} -36.4269 q^{13} +37.3038 q^{15} +(-31.2634 + 54.1498i) q^{16} +(-24.3731 - 42.2154i) q^{17} +(-1.11632 - 1.93353i) q^{18} +(-25.2750 + 43.7776i) q^{19} -98.7116 q^{20} +14.9616 q^{22} +(-69.3962 + 120.198i) q^{23} +(5.93083 + 10.2725i) q^{24} +(-14.8097 - 25.6511i) q^{25} +(4.51824 - 7.82583i) q^{26} +27.0000 q^{27} -61.1345 q^{29} +(-4.62701 + 8.01422i) q^{30} +(-0.584676 - 1.01269i) q^{31} +(-23.5711 - 40.8264i) q^{32} +(-90.4673 + 156.694i) q^{33} +12.0925 q^{34} -71.4461 q^{36} +(-34.7634 + 60.2120i) q^{37} +(-6.27001 - 10.8600i) q^{38} +(54.6403 + 94.6398i) q^{39} +(24.5825 - 42.5781i) q^{40} -308.115 q^{41} +174.443 q^{43} +(239.390 - 414.636i) q^{44} +(-55.9557 - 96.9181i) q^{45} +(-17.2153 - 29.8177i) q^{46} +(194.681 - 337.197i) q^{47} +187.581 q^{48} +7.34774 q^{50} +(-73.1192 + 126.646i) q^{51} +(-144.587 - 250.432i) q^{52} +(-157.467 - 272.742i) q^{53} +(-3.34897 + 5.80059i) q^{54} +749.950 q^{55} +151.650 q^{57} +(7.58287 - 13.1339i) q^{58} +(422.263 + 731.381i) q^{59} +(148.067 + 256.460i) q^{60} +(-169.269 + 293.182i) q^{61} +0.290084 q^{62} -488.520 q^{64} +(226.477 - 392.270i) q^{65} +(-22.4424 - 38.8714i) q^{66} +(485.775 + 841.387i) q^{67} +(193.485 - 335.125i) q^{68} +416.377 q^{69} -98.4698 q^{71} +(17.7925 - 30.8175i) q^{72} +(355.117 + 615.082i) q^{73} +(-8.62383 - 14.9369i) q^{74} +(-44.4291 + 76.9534i) q^{75} -401.289 q^{76} -27.1095 q^{78} +(243.442 - 421.654i) q^{79} +(-388.748 - 673.332i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(38.2174 - 66.1944i) q^{82} -605.688 q^{83} +606.139 q^{85} +(-21.6372 + 37.4767i) q^{86} +(91.7017 + 158.832i) q^{87} +(119.232 + 206.517i) q^{88} +(109.034 - 188.853i) q^{89} +27.7621 q^{90} -1101.80 q^{92} +(-1.75403 + 3.03807i) q^{93} +(48.2949 + 83.6491i) q^{94} +(-314.284 - 544.357i) q^{95} +(-70.7133 + 122.479i) q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} + O(q^{10}) \) \( 6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} - 55q^{10} - 35q^{11} - 75q^{12} - 124q^{13} - 66q^{15} - 241q^{16} + 48q^{17} - 9q^{18} - 202q^{19} - 878q^{20} - 14q^{22} - 216q^{23} - 117q^{24} - 130q^{25} + 274q^{26} + 162q^{27} + 106q^{29} - 165q^{30} - 95q^{31} - 683q^{32} - 105q^{33} + 48q^{34} + 450q^{36} - 262q^{37} - 398q^{38} + 186q^{39} + 21q^{40} - 488q^{41} + 720q^{43} + 905q^{44} + 99q^{45} + 1056q^{46} - 210q^{47} + 1446q^{48} - 2756q^{50} + 144q^{51} + 324q^{52} - 393q^{53} - 27q^{54} + 2062q^{55} + 1212q^{57} + 1249q^{58} + 1143q^{59} + 1317q^{60} - 70q^{61} - 2118q^{62} - 798q^{64} + 472q^{65} + 21q^{66} + 628q^{67} + 1944q^{68} + 1296q^{69} + 636q^{71} - 351q^{72} + 988q^{73} - 1002q^{74} - 390q^{75} + 4680q^{76} - 1644q^{78} - 861q^{79} + 175q^{80} - 243q^{81} + 124q^{82} - 1038q^{83} + 3600q^{85} + 3208q^{86} - 159q^{87} + 891q^{88} + 1766q^{89} + 990q^{90} - 1344q^{92} - 285q^{93} - 3294q^{94} + 736q^{95} - 2049q^{96} - 38q^{97} + 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.124036 + 0.214837i −0.0438533 + 0.0759562i −0.887119 0.461541i \(-0.847297\pi\)
0.843266 + 0.537497i \(0.180630\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 3.96923 + 6.87491i 0.496154 + 0.859364i
\(5\) −6.21730 + 10.7687i −0.556092 + 0.963180i 0.441725 + 0.897150i \(0.354367\pi\)
−0.997818 + 0.0660299i \(0.978967\pi\)
\(6\) 0.744216 0.0506375
\(7\) 0 0
\(8\) −3.95388 −0.174739
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −1.54234 2.67141i −0.0487730 0.0844773i
\(11\) −30.1558 52.2313i −0.826573 1.43167i −0.900711 0.434419i \(-0.856954\pi\)
0.0741379 0.997248i \(-0.476379\pi\)
\(12\) 11.9077 20.6247i 0.286455 0.496154i
\(13\) −36.4269 −0.777154 −0.388577 0.921416i \(-0.627033\pi\)
−0.388577 + 0.921416i \(0.627033\pi\)
\(14\) 0 0
\(15\) 37.3038 0.642120
\(16\) −31.2634 + 54.1498i −0.488491 + 0.846091i
\(17\) −24.3731 42.2154i −0.347726 0.602279i 0.638119 0.769937i \(-0.279713\pi\)
−0.985845 + 0.167659i \(0.946379\pi\)
\(18\) −1.11632 1.93353i −0.0146178 0.0253187i
\(19\) −25.2750 + 43.7776i −0.305183 + 0.528593i −0.977302 0.211851i \(-0.932051\pi\)
0.672119 + 0.740443i \(0.265384\pi\)
\(20\) −98.7116 −1.10363
\(21\) 0 0
\(22\) 14.9616 0.144992
\(23\) −69.3962 + 120.198i −0.629135 + 1.08969i 0.358590 + 0.933495i \(0.383257\pi\)
−0.987726 + 0.156199i \(0.950076\pi\)
\(24\) 5.93083 + 10.2725i 0.0504427 + 0.0873693i
\(25\) −14.8097 25.6511i −0.118478 0.205209i
\(26\) 4.51824 7.82583i 0.0340808 0.0590297i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −61.1345 −0.391462 −0.195731 0.980658i \(-0.562708\pi\)
−0.195731 + 0.980658i \(0.562708\pi\)
\(30\) −4.62701 + 8.01422i −0.0281591 + 0.0487730i
\(31\) −0.584676 1.01269i −0.00338745 0.00586724i 0.864327 0.502931i \(-0.167745\pi\)
−0.867714 + 0.497064i \(0.834412\pi\)
\(32\) −23.5711 40.8264i −0.130213 0.225536i
\(33\) −90.4673 + 156.694i −0.477222 + 0.826573i
\(34\) 12.0925 0.0609957
\(35\) 0 0
\(36\) −71.4461 −0.330769
\(37\) −34.7634 + 60.2120i −0.154461 + 0.267535i −0.932863 0.360232i \(-0.882698\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(38\) −6.27001 10.8600i −0.0267666 0.0463611i
\(39\) 54.6403 + 94.6398i 0.224345 + 0.388577i
\(40\) 24.5825 42.5781i 0.0971708 0.168305i
\(41\) −308.115 −1.17365 −0.586823 0.809715i \(-0.699622\pi\)
−0.586823 + 0.809715i \(0.699622\pi\)
\(42\) 0 0
\(43\) 174.443 0.618657 0.309329 0.950955i \(-0.399896\pi\)
0.309329 + 0.950955i \(0.399896\pi\)
\(44\) 239.390 414.636i 0.820215 1.42065i
\(45\) −55.9557 96.9181i −0.185364 0.321060i
\(46\) −17.2153 29.8177i −0.0551794 0.0955734i
\(47\) 194.681 337.197i 0.604194 1.04649i −0.387984 0.921666i \(-0.626828\pi\)
0.992178 0.124829i \(-0.0398382\pi\)
\(48\) 187.581 0.564061
\(49\) 0 0
\(50\) 7.34774 0.0207825
\(51\) −73.1192 + 126.646i −0.200760 + 0.347726i
\(52\) −144.587 250.432i −0.385588 0.667858i
\(53\) −157.467 272.742i −0.408110 0.706867i 0.586568 0.809900i \(-0.300479\pi\)
−0.994678 + 0.103033i \(0.967145\pi\)
\(54\) −3.34897 + 5.80059i −0.00843958 + 0.0146178i
\(55\) 749.950 1.83860
\(56\) 0 0
\(57\) 151.650 0.352395
\(58\) 7.58287 13.1339i 0.0171669 0.0297339i
\(59\) 422.263 + 731.381i 0.931762 + 1.61386i 0.780308 + 0.625396i \(0.215062\pi\)
0.151455 + 0.988464i \(0.451604\pi\)
\(60\) 148.067 + 256.460i 0.318590 + 0.551815i
\(61\) −169.269 + 293.182i −0.355290 + 0.615380i −0.987167 0.159688i \(-0.948951\pi\)
0.631878 + 0.775068i \(0.282284\pi\)
\(62\) 0.290084 0.000594204
\(63\) 0 0
\(64\) −488.520 −0.954141
\(65\) 226.477 392.270i 0.432169 0.748539i
\(66\) −22.4424 38.8714i −0.0418556 0.0724960i
\(67\) 485.775 + 841.387i 0.885774 + 1.53421i 0.844824 + 0.535044i \(0.179705\pi\)
0.0409498 + 0.999161i \(0.486962\pi\)
\(68\) 193.485 335.125i 0.345051 0.597646i
\(69\) 416.377 0.726463
\(70\) 0 0
\(71\) −98.4698 −0.164595 −0.0822973 0.996608i \(-0.526226\pi\)
−0.0822973 + 0.996608i \(0.526226\pi\)
\(72\) 17.7925 30.8175i 0.0291231 0.0504427i
\(73\) 355.117 + 615.082i 0.569361 + 0.986162i 0.996629 + 0.0820374i \(0.0261427\pi\)
−0.427268 + 0.904125i \(0.640524\pi\)
\(74\) −8.62383 14.9369i −0.0135473 0.0234646i
\(75\) −44.4291 + 76.9534i −0.0684030 + 0.118478i
\(76\) −401.289 −0.605671
\(77\) 0 0
\(78\) −27.1095 −0.0393531
\(79\) 243.442 421.654i 0.346701 0.600504i −0.638960 0.769240i \(-0.720635\pi\)
0.985661 + 0.168736i \(0.0539686\pi\)
\(80\) −388.748 673.332i −0.543292 0.941010i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 38.2174 66.1944i 0.0514683 0.0891458i
\(83\) −605.688 −0.800999 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(84\) 0 0
\(85\) 606.139 0.773470
\(86\) −21.6372 + 37.4767i −0.0271302 + 0.0469908i
\(87\) 91.7017 + 158.832i 0.113005 + 0.195731i
\(88\) 119.232 + 206.517i 0.144434 + 0.250168i
\(89\) 109.034 188.853i 0.129861 0.224925i −0.793762 0.608229i \(-0.791880\pi\)
0.923622 + 0.383303i \(0.125214\pi\)
\(90\) 27.7621 0.0325153
\(91\) 0 0
\(92\) −1101.80 −1.24859
\(93\) −1.75403 + 3.03807i −0.00195575 + 0.00338745i
\(94\) 48.2949 + 83.6491i 0.0529919 + 0.0917846i
\(95\) −314.284 544.357i −0.339420 0.587893i
\(96\) −70.7133 + 122.479i −0.0751787 + 0.130213i
\(97\) 782.288 0.818859 0.409429 0.912342i \(-0.365728\pi\)
0.409429 + 0.912342i \(0.365728\pi\)
\(98\) 0 0
\(99\) 542.804 0.551049
\(100\) 117.566 203.631i 0.117566 0.203631i
\(101\) −155.823 269.893i −0.153514 0.265895i 0.779003 0.627021i \(-0.215726\pi\)
−0.932517 + 0.361126i \(0.882392\pi\)
\(102\) −18.1388 31.4174i −0.0176079 0.0304979i
\(103\) −74.6289 + 129.261i −0.0713922 + 0.123655i −0.899512 0.436897i \(-0.856078\pi\)
0.828119 + 0.560552i \(0.189411\pi\)
\(104\) 144.028 0.135799
\(105\) 0 0
\(106\) 78.1265 0.0715879
\(107\) −425.760 + 737.437i −0.384670 + 0.666269i −0.991723 0.128393i \(-0.959018\pi\)
0.607053 + 0.794661i \(0.292352\pi\)
\(108\) 107.169 + 185.623i 0.0954848 + 0.165385i
\(109\) −680.939 1179.42i −0.598369 1.03640i −0.993062 0.117592i \(-0.962483\pi\)
0.394694 0.918813i \(-0.370851\pi\)
\(110\) −93.0208 + 161.117i −0.0806289 + 0.139653i
\(111\) 208.581 0.178357
\(112\) 0 0
\(113\) 1048.55 0.872917 0.436459 0.899724i \(-0.356233\pi\)
0.436459 + 0.899724i \(0.356233\pi\)
\(114\) −18.8100 + 32.5800i −0.0154537 + 0.0267666i
\(115\) −862.914 1494.61i −0.699715 1.21194i
\(116\) −242.657 420.294i −0.194225 0.336408i
\(117\) 163.921 283.920i 0.129526 0.224345i
\(118\) −209.503 −0.163444
\(119\) 0 0
\(120\) −147.495 −0.112203
\(121\) −1153.24 + 1997.47i −0.866446 + 1.50073i
\(122\) −41.9909 72.7303i −0.0311613 0.0539729i
\(123\) 462.173 + 800.507i 0.338803 + 0.586823i
\(124\) 4.64143 8.03919i 0.00336139 0.00582210i
\(125\) −1186.02 −0.848647
\(126\) 0 0
\(127\) 488.408 0.341254 0.170627 0.985336i \(-0.445421\pi\)
0.170627 + 0.985336i \(0.445421\pi\)
\(128\) 249.163 431.563i 0.172056 0.298009i
\(129\) −261.664 453.215i −0.178591 0.309329i
\(130\) 56.1826 + 97.3111i 0.0379041 + 0.0656519i
\(131\) −927.114 + 1605.81i −0.618338 + 1.07099i 0.371451 + 0.928453i \(0.378861\pi\)
−0.989789 + 0.142541i \(0.954473\pi\)
\(132\) −1436.34 −0.947102
\(133\) 0 0
\(134\) −241.014 −0.155377
\(135\) −167.867 + 290.754i −0.107020 + 0.185364i
\(136\) 96.3683 + 166.915i 0.0607611 + 0.105241i
\(137\) 255.558 + 442.639i 0.159370 + 0.276038i 0.934642 0.355591i \(-0.115720\pi\)
−0.775271 + 0.631628i \(0.782387\pi\)
\(138\) −51.6458 + 89.4531i −0.0318578 + 0.0551794i
\(139\) −2266.10 −1.38279 −0.691397 0.722475i \(-0.743005\pi\)
−0.691397 + 0.722475i \(0.743005\pi\)
\(140\) 0 0
\(141\) −1168.09 −0.697663
\(142\) 12.2138 21.1549i 0.00721802 0.0125020i
\(143\) 1098.48 + 1902.62i 0.642375 + 1.11263i
\(144\) −281.371 487.348i −0.162830 0.282030i
\(145\) 380.091 658.338i 0.217689 0.377048i
\(146\) −176.189 −0.0998735
\(147\) 0 0
\(148\) −551.936 −0.306546
\(149\) −753.950 + 1305.88i −0.414537 + 0.717999i −0.995380 0.0960168i \(-0.969390\pi\)
0.580843 + 0.814016i \(0.302723\pi\)
\(150\) −11.0216 19.0900i −0.00599940 0.0103913i
\(151\) −795.913 1378.56i −0.428943 0.742952i 0.567836 0.823142i \(-0.307781\pi\)
−0.996780 + 0.0801897i \(0.974447\pi\)
\(152\) 99.9344 173.091i 0.0533273 0.0923656i
\(153\) 438.715 0.231817
\(154\) 0 0
\(155\) 14.5404 0.00753494
\(156\) −433.760 + 751.295i −0.222619 + 0.385588i
\(157\) 582.080 + 1008.19i 0.295892 + 0.512500i 0.975192 0.221361i \(-0.0710498\pi\)
−0.679300 + 0.733861i \(0.737717\pi\)
\(158\) 60.3911 + 104.601i 0.0304080 + 0.0526682i
\(159\) −472.402 + 818.225i −0.235622 + 0.408110i
\(160\) 586.195 0.289642
\(161\) 0 0
\(162\) 20.0938 0.00974519
\(163\) 577.940 1001.02i 0.277716 0.481019i −0.693101 0.720841i \(-0.743756\pi\)
0.970817 + 0.239822i \(0.0770892\pi\)
\(164\) −1222.98 2118.26i −0.582309 1.00859i
\(165\) −1124.92 1948.43i −0.530759 0.919302i
\(166\) 75.1271 130.124i 0.0351265 0.0608408i
\(167\) 2890.61 1.33941 0.669707 0.742626i \(-0.266420\pi\)
0.669707 + 0.742626i \(0.266420\pi\)
\(168\) 0 0
\(169\) −870.082 −0.396032
\(170\) −75.1830 + 130.221i −0.0339193 + 0.0587499i
\(171\) −227.475 393.998i −0.101728 0.176198i
\(172\) 692.403 + 1199.28i 0.306949 + 0.531651i
\(173\) 947.468 1641.06i 0.416385 0.721200i −0.579188 0.815194i \(-0.696630\pi\)
0.995573 + 0.0939940i \(0.0299635\pi\)
\(174\) −45.4972 −0.0198226
\(175\) 0 0
\(176\) 3771.09 1.61509
\(177\) 1266.79 2194.14i 0.537953 0.931762i
\(178\) 27.0483 + 46.8491i 0.0113897 + 0.0197275i
\(179\) 2144.25 + 3713.94i 0.895355 + 1.55080i 0.833365 + 0.552723i \(0.186411\pi\)
0.0619893 + 0.998077i \(0.480256\pi\)
\(180\) 444.202 769.381i 0.183938 0.318590i
\(181\) −383.732 −0.157583 −0.0787917 0.996891i \(-0.525106\pi\)
−0.0787917 + 0.996891i \(0.525106\pi\)
\(182\) 0 0
\(183\) 1015.61 0.410253
\(184\) 274.385 475.248i 0.109934 0.190412i
\(185\) −432.269 748.712i −0.171790 0.297548i
\(186\) −0.435125 0.753659i −0.000171532 0.000297102i
\(187\) −1469.98 + 2546.07i −0.574841 + 0.995655i
\(188\) 3090.93 1.19909
\(189\) 0 0
\(190\) 155.930 0.0595388
\(191\) −192.655 + 333.689i −0.0729845 + 0.126413i −0.900208 0.435460i \(-0.856586\pi\)
0.827224 + 0.561873i \(0.189919\pi\)
\(192\) 732.780 + 1269.21i 0.275437 + 0.477070i
\(193\) −315.112 545.790i −0.117525 0.203559i 0.801262 0.598314i \(-0.204163\pi\)
−0.918786 + 0.394756i \(0.870829\pi\)
\(194\) −97.0318 + 168.064i −0.0359097 + 0.0621974i
\(195\) −1358.86 −0.499026
\(196\) 0 0
\(197\) −1250.23 −0.452158 −0.226079 0.974109i \(-0.572591\pi\)
−0.226079 + 0.974109i \(0.572591\pi\)
\(198\) −67.3272 + 116.614i −0.0241653 + 0.0418556i
\(199\) −546.122 945.912i −0.194541 0.336954i 0.752209 0.658924i \(-0.228988\pi\)
−0.946750 + 0.321970i \(0.895655\pi\)
\(200\) 58.5558 + 101.422i 0.0207026 + 0.0358580i
\(201\) 1457.32 2524.16i 0.511402 0.885774i
\(202\) 77.3105 0.0269285
\(203\) 0 0
\(204\) −1160.91 −0.398430
\(205\) 1915.65 3318.00i 0.652656 1.13043i
\(206\) −18.5133 32.0660i −0.00626158 0.0108454i
\(207\) −624.566 1081.78i −0.209712 0.363231i
\(208\) 1138.83 1972.51i 0.379633 0.657543i
\(209\) 3048.75 1.00902
\(210\) 0 0
\(211\) −3620.05 −1.18111 −0.590556 0.806997i \(-0.701091\pi\)
−0.590556 + 0.806997i \(0.701091\pi\)
\(212\) 1250.05 2165.15i 0.404970 0.701429i
\(213\) 147.705 + 255.832i 0.0475143 + 0.0822973i
\(214\) −105.619 182.937i −0.0337382 0.0584362i
\(215\) −1084.56 + 1878.52i −0.344030 + 0.595878i
\(216\) −106.755 −0.0336285
\(217\) 0 0
\(218\) 337.844 0.104962
\(219\) 1065.35 1845.24i 0.328721 0.569361i
\(220\) 2976.72 + 5155.84i 0.912230 + 1.58003i
\(221\) 887.835 + 1537.78i 0.270236 + 0.468063i
\(222\) −25.8715 + 44.8107i −0.00782153 + 0.0135473i
\(223\) 183.844 0.0552069 0.0276034 0.999619i \(-0.491212\pi\)
0.0276034 + 0.999619i \(0.491212\pi\)
\(224\) 0 0
\(225\) 266.574 0.0789850
\(226\) −130.058 + 225.268i −0.0382803 + 0.0663035i
\(227\) 1139.76 + 1974.12i 0.333253 + 0.577211i 0.983148 0.182813i \(-0.0585203\pi\)
−0.649895 + 0.760024i \(0.725187\pi\)
\(228\) 601.933 + 1042.58i 0.174842 + 0.302836i
\(229\) 2706.34 4687.51i 0.780960 1.35266i −0.150424 0.988622i \(-0.548064\pi\)
0.931383 0.364040i \(-0.118603\pi\)
\(230\) 428.130 0.122739
\(231\) 0 0
\(232\) 241.719 0.0684035
\(233\) −569.184 + 985.856i −0.160036 + 0.277191i −0.934882 0.354960i \(-0.884494\pi\)
0.774845 + 0.632151i \(0.217828\pi\)
\(234\) 40.6642 + 70.4325i 0.0113603 + 0.0196766i
\(235\) 2420.78 + 4192.91i 0.671975 + 1.16390i
\(236\) −3352.12 + 5806.04i −0.924595 + 1.60145i
\(237\) −1460.65 −0.400336
\(238\) 0 0
\(239\) −6226.36 −1.68515 −0.842573 0.538583i \(-0.818960\pi\)
−0.842573 + 0.538583i \(0.818960\pi\)
\(240\) −1166.24 + 2020.00i −0.313670 + 0.543292i
\(241\) −1598.10 2767.99i −0.427147 0.739841i 0.569471 0.822012i \(-0.307148\pi\)
−0.996618 + 0.0821704i \(0.973815\pi\)
\(242\) −286.086 495.516i −0.0759931 0.131624i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) −2687.47 −0.705113
\(245\) 0 0
\(246\) −229.304 −0.0594305
\(247\) 920.689 1594.68i 0.237174 0.410798i
\(248\) 2.31174 + 4.00406i 0.000591919 + 0.00102523i
\(249\) 908.532 + 1573.62i 0.231228 + 0.400499i
\(250\) 147.109 254.801i 0.0372160 0.0644600i
\(251\) −239.608 −0.0602546 −0.0301273 0.999546i \(-0.509591\pi\)
−0.0301273 + 0.999546i \(0.509591\pi\)
\(252\) 0 0
\(253\) 8370.78 2.08010
\(254\) −60.5802 + 104.928i −0.0149651 + 0.0259203i
\(255\) −909.208 1574.79i −0.223282 0.386735i
\(256\) −1892.27 3277.51i −0.461980 0.800173i
\(257\) 349.559 605.453i 0.0848439 0.146954i −0.820481 0.571674i \(-0.806294\pi\)
0.905325 + 0.424720i \(0.139628\pi\)
\(258\) 129.823 0.0313272
\(259\) 0 0
\(260\) 3595.76 0.857690
\(261\) 275.105 476.496i 0.0652436 0.113005i
\(262\) −229.991 398.356i −0.0542324 0.0939333i
\(263\) 459.520 + 795.912i 0.107738 + 0.186609i 0.914854 0.403785i \(-0.132306\pi\)
−0.807115 + 0.590394i \(0.798972\pi\)
\(264\) 357.697 619.550i 0.0833892 0.144434i
\(265\) 3916.09 0.907787
\(266\) 0 0
\(267\) −654.206 −0.149950
\(268\) −3856.30 + 6679.32i −0.878960 + 1.52240i
\(269\) −1389.59 2406.84i −0.314961 0.545529i 0.664468 0.747317i \(-0.268658\pi\)
−0.979429 + 0.201788i \(0.935325\pi\)
\(270\) −41.6431 72.1280i −0.00938637 0.0162577i
\(271\) 1113.49 1928.62i 0.249593 0.432308i −0.713820 0.700329i \(-0.753036\pi\)
0.963413 + 0.268021i \(0.0863698\pi\)
\(272\) 3047.94 0.679443
\(273\) 0 0
\(274\) −126.793 −0.0279557
\(275\) −893.195 + 1547.06i −0.195861 + 0.339241i
\(276\) 1652.70 + 2862.56i 0.360437 + 0.624296i
\(277\) −3653.85 6328.65i −0.792557 1.37275i −0.924379 0.381476i \(-0.875416\pi\)
0.131821 0.991273i \(-0.457917\pi\)
\(278\) 281.078 486.842i 0.0606402 0.105032i
\(279\) 10.5242 0.00225830
\(280\) 0 0
\(281\) 2730.61 0.579696 0.289848 0.957073i \(-0.406395\pi\)
0.289848 + 0.957073i \(0.406395\pi\)
\(282\) 144.885 250.947i 0.0305949 0.0529919i
\(283\) −884.926 1532.74i −0.185878 0.321950i 0.757994 0.652261i \(-0.226179\pi\)
−0.943872 + 0.330312i \(0.892846\pi\)
\(284\) −390.849 676.971i −0.0816642 0.141447i
\(285\) −942.853 + 1633.07i −0.195964 + 0.339420i
\(286\) −545.004 −0.112681
\(287\) 0 0
\(288\) 424.280 0.0868088
\(289\) 1268.41 2196.95i 0.258174 0.447170i
\(290\) 94.2900 + 163.315i 0.0190928 + 0.0330696i
\(291\) −1173.43 2032.44i −0.236384 0.409429i
\(292\) −2819.09 + 4882.80i −0.564981 + 0.978576i
\(293\) −8228.81 −1.64072 −0.820362 0.571844i \(-0.806228\pi\)
−0.820362 + 0.571844i \(0.806228\pi\)
\(294\) 0 0
\(295\) −10501.4 −2.07258
\(296\) 137.451 238.071i 0.0269904 0.0467487i
\(297\) −814.206 1410.25i −0.159074 0.275524i
\(298\) −187.034 323.952i −0.0363577 0.0629733i
\(299\) 2527.89 4378.43i 0.488935 0.846860i
\(300\) −705.397 −0.135754
\(301\) 0 0
\(302\) 394.887 0.0752424
\(303\) −467.468 + 809.679i −0.0886316 + 0.153514i
\(304\) −1580.36 2737.27i −0.298158 0.516425i
\(305\) −2104.79 3645.61i −0.395148 0.684416i
\(306\) −54.4165 + 94.2521i −0.0101660 + 0.0176079i
\(307\) −6019.62 −1.11908 −0.559541 0.828803i \(-0.689023\pi\)
−0.559541 + 0.828803i \(0.689023\pi\)
\(308\) 0 0
\(309\) 447.773 0.0824366
\(310\) −1.80354 + 3.12382i −0.000330432 + 0.000572326i
\(311\) 596.857 + 1033.79i 0.108825 + 0.188491i 0.915295 0.402785i \(-0.131958\pi\)
−0.806469 + 0.591276i \(0.798624\pi\)
\(312\) −216.042 374.195i −0.0392018 0.0678994i
\(313\) −4423.02 + 7660.89i −0.798734 + 1.38345i 0.121707 + 0.992566i \(0.461163\pi\)
−0.920441 + 0.390882i \(0.872170\pi\)
\(314\) −288.795 −0.0519034
\(315\) 0 0
\(316\) 3865.11 0.688068
\(317\) −3040.72 + 5266.68i −0.538750 + 0.933142i 0.460222 + 0.887804i \(0.347770\pi\)
−0.998972 + 0.0453380i \(0.985564\pi\)
\(318\) −117.190 202.979i −0.0206656 0.0357940i
\(319\) 1843.56 + 3193.13i 0.323572 + 0.560442i
\(320\) 3037.28 5260.72i 0.530590 0.919009i
\(321\) 2554.56 0.444179
\(322\) 0 0
\(323\) 2464.12 0.424480
\(324\) 321.508 556.868i 0.0551282 0.0954848i
\(325\) 539.471 + 934.391i 0.0920753 + 0.159479i
\(326\) 143.371 + 248.325i 0.0243576 + 0.0421885i
\(327\) −2042.82 + 3538.26i −0.345468 + 0.598369i
\(328\) 1218.25 0.205082
\(329\) 0 0
\(330\) 558.125 0.0931023
\(331\) −1526.65 + 2644.23i −0.253511 + 0.439094i −0.964490 0.264119i \(-0.914919\pi\)
0.710979 + 0.703213i \(0.248252\pi\)
\(332\) −2404.12 4164.05i −0.397419 0.688349i
\(333\) −312.871 541.908i −0.0514871 0.0891783i
\(334\) −358.539 + 621.009i −0.0587377 + 0.101737i
\(335\) −12080.8 −1.97029
\(336\) 0 0
\(337\) 3865.80 0.624877 0.312438 0.949938i \(-0.398854\pi\)
0.312438 + 0.949938i \(0.398854\pi\)
\(338\) 107.921 186.925i 0.0173673 0.0300811i
\(339\) −1572.83 2724.22i −0.251989 0.436459i
\(340\) 2405.90 + 4167.15i 0.383760 + 0.664692i
\(341\) −35.2627 + 61.0768i −0.00559995 + 0.00969940i
\(342\) 112.860 0.0178444
\(343\) 0 0
\(344\) −689.726 −0.108103
\(345\) −2588.74 + 4483.83i −0.403980 + 0.699715i
\(346\) 235.040 + 407.101i 0.0365198 + 0.0632541i
\(347\) 49.7965 + 86.2501i 0.00770380 + 0.0133434i 0.869852 0.493313i \(-0.164214\pi\)
−0.862148 + 0.506657i \(0.830881\pi\)
\(348\) −727.970 + 1260.88i −0.112136 + 0.194225i
\(349\) 3607.34 0.553285 0.276643 0.960973i \(-0.410778\pi\)
0.276643 + 0.960973i \(0.410778\pi\)
\(350\) 0 0
\(351\) −983.526 −0.149563
\(352\) −1421.61 + 2462.30i −0.215262 + 0.372844i
\(353\) 3565.37 + 6175.40i 0.537579 + 0.931114i 0.999034 + 0.0439501i \(0.0139942\pi\)
−0.461455 + 0.887164i \(0.652672\pi\)
\(354\) 314.255 + 544.306i 0.0471821 + 0.0817218i
\(355\) 612.216 1060.39i 0.0915298 0.158534i
\(356\) 1731.13 0.257724
\(357\) 0 0
\(358\) −1063.85 −0.157057
\(359\) 3250.14 5629.41i 0.477816 0.827602i −0.521860 0.853031i \(-0.674762\pi\)
0.999677 + 0.0254289i \(0.00809514\pi\)
\(360\) 221.242 + 383.203i 0.0323903 + 0.0561016i
\(361\) 2151.85 + 3727.11i 0.313727 + 0.543390i
\(362\) 47.5966 82.4398i 0.00691056 0.0119694i
\(363\) 6919.44 1.00049
\(364\) 0 0
\(365\) −8831.49 −1.26647
\(366\) −125.973 + 218.191i −0.0179910 + 0.0311613i
\(367\) 412.443 + 714.372i 0.0586631 + 0.101607i 0.893866 0.448335i \(-0.147983\pi\)
−0.835202 + 0.549943i \(0.814650\pi\)
\(368\) −4339.12 7515.58i −0.614654 1.06461i
\(369\) 1386.52 2401.52i 0.195608 0.338803i
\(370\) 214.468 0.0301342
\(371\) 0 0
\(372\) −27.8486 −0.00388140
\(373\) −666.925 + 1155.15i −0.0925793 + 0.160352i −0.908596 0.417677i \(-0.862845\pi\)
0.816016 + 0.578029i \(0.196178\pi\)
\(374\) −364.660 631.610i −0.0504174 0.0873255i
\(375\) 1779.03 + 3081.37i 0.244983 + 0.424324i
\(376\) −769.746 + 1333.24i −0.105576 + 0.182863i
\(377\) 2226.94 0.304226
\(378\) 0 0
\(379\) −1338.29 −0.181380 −0.0906902 0.995879i \(-0.528907\pi\)
−0.0906902 + 0.995879i \(0.528907\pi\)
\(380\) 2494.93 4321.35i 0.336809 0.583370i
\(381\) −732.612 1268.92i −0.0985114 0.170627i
\(382\) −47.7924 82.7788i −0.00640123 0.0110873i
\(383\) 176.688 306.032i 0.0235727 0.0408290i −0.853998 0.520276i \(-0.825829\pi\)
0.877571 + 0.479447i \(0.159163\pi\)
\(384\) −1494.98 −0.198673
\(385\) 0 0
\(386\) 156.341 0.0206154
\(387\) −784.992 + 1359.65i −0.103110 + 0.178591i
\(388\) 3105.08 + 5378.16i 0.406280 + 0.703697i
\(389\) −5868.59 10164.7i −0.764908 1.32486i −0.940295 0.340360i \(-0.889451\pi\)
0.175387 0.984500i \(-0.443882\pi\)
\(390\) 168.548 291.933i 0.0218840 0.0379041i
\(391\) 6765.59 0.875066
\(392\) 0 0
\(393\) 5562.68 0.713996
\(394\) 155.073 268.595i 0.0198286 0.0343442i
\(395\) 3027.11 + 5243.10i 0.385595 + 0.667871i
\(396\) 2154.51 + 3731.73i 0.273405 + 0.473551i
\(397\) 6640.71 11502.1i 0.839516 1.45408i −0.0507841 0.998710i \(-0.516172\pi\)
0.890300 0.455374i \(-0.150495\pi\)
\(398\) 270.955 0.0341250
\(399\) 0 0
\(400\) 1852.01 0.231501
\(401\) 3741.18 6479.91i 0.465899 0.806961i −0.533343 0.845899i \(-0.679064\pi\)
0.999242 + 0.0389385i \(0.0123976\pi\)
\(402\) 361.521 + 626.173i 0.0448534 + 0.0776883i
\(403\) 21.2979 + 36.8891i 0.00263257 + 0.00455975i
\(404\) 1236.99 2142.54i 0.152333 0.263849i
\(405\) 1007.20 0.123576
\(406\) 0 0
\(407\) 4193.27 0.510694
\(408\) 289.105 500.744i 0.0350805 0.0607611i
\(409\) −6898.30 11948.2i −0.833983 1.44450i −0.894856 0.446355i \(-0.852722\pi\)
0.0608735 0.998145i \(-0.480611\pi\)
\(410\) 475.218 + 823.102i 0.0572423 + 0.0991466i
\(411\) 766.673 1327.92i 0.0920126 0.159370i
\(412\) −1184.88 −0.141686
\(413\) 0 0
\(414\) 309.875 0.0367862
\(415\) 3765.75 6522.46i 0.445429 0.771506i
\(416\) 858.622 + 1487.18i 0.101196 + 0.175276i
\(417\) 3399.16 + 5887.51i 0.399179 + 0.691397i
\(418\) −378.154 + 654.982i −0.0442491 + 0.0766417i
\(419\) −9497.56 −1.10737 −0.553683 0.832728i \(-0.686778\pi\)
−0.553683 + 0.832728i \(0.686778\pi\)
\(420\) 0 0
\(421\) 624.367 0.0722797 0.0361399 0.999347i \(-0.488494\pi\)
0.0361399 + 0.999347i \(0.488494\pi\)
\(422\) 449.016 777.719i 0.0517957 0.0897127i
\(423\) 1752.13 + 3034.77i 0.201398 + 0.348832i
\(424\) 622.608 + 1078.39i 0.0713126 + 0.123517i
\(425\) −721.915 + 1250.39i −0.0823954 + 0.142713i
\(426\) −73.2827 −0.00833465
\(427\) 0 0
\(428\) −6759.75 −0.763423
\(429\) 3295.44 5707.87i 0.370875 0.642375i
\(430\) −269.050 466.007i −0.0301738 0.0522625i
\(431\) 6698.64 + 11602.4i 0.748636 + 1.29668i 0.948476 + 0.316848i \(0.102624\pi\)
−0.199840 + 0.979829i \(0.564042\pi\)
\(432\) −844.112 + 1462.05i −0.0940101 + 0.162830i
\(433\) 14057.3 1.56016 0.780079 0.625681i \(-0.215179\pi\)
0.780079 + 0.625681i \(0.215179\pi\)
\(434\) 0 0
\(435\) −2280.55 −0.251365
\(436\) 5405.61 9362.79i 0.593766 1.02843i
\(437\) −3507.98 6075.99i −0.384003 0.665112i
\(438\) 264.284 + 457.753i 0.0288310 + 0.0499368i
\(439\) −8184.42 + 14175.8i −0.889798 + 1.54117i −0.0496832 + 0.998765i \(0.515821\pi\)
−0.840114 + 0.542409i \(0.817512\pi\)
\(440\) −2965.22 −0.321275
\(441\) 0 0
\(442\) −440.494 −0.0474031
\(443\) 589.354 1020.79i 0.0632078 0.109479i −0.832690 0.553740i \(-0.813200\pi\)
0.895898 + 0.444261i \(0.146534\pi\)
\(444\) 827.904 + 1433.97i 0.0884923 + 0.153273i
\(445\) 1355.80 + 2348.31i 0.144429 + 0.250159i
\(446\) −22.8033 + 39.4965i −0.00242101 + 0.00419331i
\(447\) 4523.70 0.478666
\(448\) 0 0
\(449\) −12400.9 −1.30342 −0.651709 0.758469i \(-0.725948\pi\)
−0.651709 + 0.758469i \(0.725948\pi\)
\(450\) −33.0648 + 57.2699i −0.00346376 + 0.00599940i
\(451\) 9291.45 + 16093.3i 0.970105 + 1.68027i
\(452\) 4161.95 + 7208.71i 0.433101 + 0.750153i
\(453\) −2387.74 + 4135.68i −0.247651 + 0.428943i
\(454\) −565.484 −0.0584570
\(455\) 0 0
\(456\) −599.606 −0.0615771
\(457\) −4962.79 + 8595.81i −0.507986 + 0.879858i 0.491971 + 0.870611i \(0.336277\pi\)
−0.999957 + 0.00924618i \(0.997057\pi\)
\(458\) 671.366 + 1162.84i 0.0684954 + 0.118637i
\(459\) −658.073 1139.82i −0.0669198 0.115909i
\(460\) 6850.21 11864.9i 0.694332 1.20262i
\(461\) 16010.3 1.61751 0.808755 0.588146i \(-0.200142\pi\)
0.808755 + 0.588146i \(0.200142\pi\)
\(462\) 0 0
\(463\) 17372.4 1.74377 0.871883 0.489714i \(-0.162899\pi\)
0.871883 + 0.489714i \(0.162899\pi\)
\(464\) 1911.27 3310.42i 0.191225 0.331212i
\(465\) −21.8107 37.7772i −0.00217515 0.00376747i
\(466\) −141.199 244.563i −0.0140363 0.0243115i
\(467\) 1054.03 1825.64i 0.104443 0.180900i −0.809068 0.587716i \(-0.800027\pi\)
0.913510 + 0.406815i \(0.133361\pi\)
\(468\) 2602.56 0.257059
\(469\) 0 0
\(470\) −1201.05 −0.117873
\(471\) 1746.24 3024.58i 0.170833 0.295892i
\(472\) −1669.58 2891.80i −0.162815 0.282004i
\(473\) −5260.45 9111.37i −0.511365 0.885711i
\(474\) 181.173 313.802i 0.0175561 0.0304080i
\(475\) 1497.26 0.144629
\(476\) 0 0
\(477\) 2834.41 0.272073
\(478\) 772.293 1337.65i 0.0738992 0.127997i
\(479\) −1225.02 2121.80i −0.116853 0.202395i 0.801666 0.597772i \(-0.203947\pi\)
−0.918519 + 0.395377i \(0.870614\pi\)
\(480\) −879.292 1522.98i −0.0836126 0.144821i
\(481\) 1266.32 2193.34i 0.120040 0.207916i
\(482\) 792.887 0.0749274
\(483\) 0 0
\(484\) −18309.9 −1.71956
\(485\) −4863.72 + 8424.21i −0.455361 + 0.788709i
\(486\) −30.1407 52.2053i −0.00281319 0.00487259i
\(487\) −322.618 558.791i −0.0300189 0.0519943i 0.850626 0.525772i \(-0.176223\pi\)
−0.880645 + 0.473778i \(0.842890\pi\)
\(488\) 669.270 1159.21i 0.0620828 0.107531i
\(489\) −3467.64 −0.320679
\(490\) 0 0
\(491\) 11766.1 1.08146 0.540731 0.841196i \(-0.318148\pi\)
0.540731 + 0.841196i \(0.318148\pi\)
\(492\) −3668.94 + 6354.79i −0.336196 + 0.582309i
\(493\) 1490.03 + 2580.81i 0.136121 + 0.235769i
\(494\) 228.397 + 395.595i 0.0208018 + 0.0360297i
\(495\) −3374.77 + 5845.28i −0.306434 + 0.530759i
\(496\) 73.1159 0.00661896
\(497\) 0 0
\(498\) −450.763 −0.0405606
\(499\) 22.0104 38.1232i 0.00197459 0.00342010i −0.865036 0.501709i \(-0.832705\pi\)
0.867011 + 0.498289i \(0.166038\pi\)
\(500\) −4707.59 8153.78i −0.421059 0.729296i
\(501\) −4335.91 7510.02i −0.386655 0.669707i
\(502\) 29.7200 51.4765i 0.00264236 0.00457671i
\(503\) −8290.27 −0.734880 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(504\) 0 0
\(505\) 3875.19 0.341473
\(506\) −1038.28 + 1798.35i −0.0912195 + 0.157997i
\(507\) 1305.12 + 2260.54i 0.114324 + 0.198016i
\(508\) 1938.60 + 3357.76i 0.169314 + 0.293261i
\(509\) 3457.52 5988.60i 0.301084 0.521493i −0.675298 0.737545i \(-0.735985\pi\)
0.976382 + 0.216052i \(0.0693181\pi\)
\(510\) 451.098 0.0391666
\(511\) 0 0
\(512\) 4925.45 0.425148
\(513\) −682.425 + 1181.99i −0.0587325 + 0.101728i
\(514\) 86.7157 + 150.196i 0.00744137 + 0.0128888i
\(515\) −927.980 1607.31i −0.0794014 0.137527i
\(516\) 2077.21 3597.83i 0.177217 0.306949i
\(517\) −23483.0 −1.99764
\(518\) 0 0
\(519\) −5684.81 −0.480800
\(520\) −895.464 + 1550.99i −0.0755167 + 0.130799i
\(521\) 6699.64 + 11604.1i 0.563371 + 0.975788i 0.997199 + 0.0747919i \(0.0238293\pi\)
−0.433828 + 0.900996i \(0.642837\pi\)
\(522\) 68.2458 + 118.205i 0.00572230 + 0.00991131i
\(523\) −4968.50 + 8605.69i −0.415406 + 0.719504i −0.995471 0.0950662i \(-0.969694\pi\)
0.580065 + 0.814570i \(0.303027\pi\)
\(524\) −14719.7 −1.22716
\(525\) 0 0
\(526\) −227.988 −0.0188988
\(527\) −28.5007 + 49.3647i −0.00235581 + 0.00408038i
\(528\) −5656.63 9797.58i −0.466237 0.807547i
\(529\) −3548.17 6145.60i −0.291622 0.505104i
\(530\) −485.736 + 841.320i −0.0398095 + 0.0689521i
\(531\) −7600.74 −0.621175
\(532\) 0 0
\(533\) 11223.7 0.912104
\(534\) 81.1450 140.547i 0.00657582 0.0113897i
\(535\) −5294.15 9169.74i −0.427825 0.741014i
\(536\) −1920.70 3326.75i −0.154779 0.268085i
\(537\) 6432.74 11141.8i 0.516933 0.895355i
\(538\) 689.435 0.0552484
\(539\) 0 0
\(540\) −2665.21 −0.212394
\(541\) −4643.08 + 8042.06i −0.368987 + 0.639103i −0.989407 0.145166i \(-0.953628\pi\)
0.620421 + 0.784269i \(0.286962\pi\)
\(542\) 276.226 + 478.437i 0.0218910 + 0.0379163i
\(543\) 575.599 + 996.966i 0.0454904 + 0.0787917i
\(544\) −1149.00 + 1990.13i −0.0905570 + 0.156849i
\(545\) 16934.4 1.33099
\(546\) 0 0
\(547\) −16821.6 −1.31488 −0.657438 0.753508i \(-0.728360\pi\)
−0.657438 + 0.753508i \(0.728360\pi\)
\(548\) −2028.73 + 3513.87i −0.158144 + 0.273914i
\(549\) −1523.42 2638.64i −0.118430 0.205127i
\(550\) −221.577 383.782i −0.0171783 0.0297537i
\(551\) 1545.17 2676.32i 0.119467 0.206924i
\(552\) −1646.31 −0.126941
\(553\) 0 0
\(554\) 1812.83 0.139025
\(555\) −1296.81 + 2246.14i −0.0991828 + 0.171790i
\(556\) −8994.69 15579.3i −0.686079 1.18832i
\(557\) −902.972 1563.99i −0.0686897 0.118974i 0.829635 0.558306i \(-0.188549\pi\)
−0.898325 + 0.439332i \(0.855215\pi\)
\(558\) −1.30538 + 2.26098i −9.90340e−5 + 0.000171532i
\(559\) −6354.40 −0.480792
\(560\) 0 0
\(561\) 8819.86 0.663770
\(562\) −338.694 + 586.635i −0.0254216 + 0.0440315i
\(563\) 6107.45 + 10578.4i 0.457190 + 0.791877i 0.998811 0.0487460i \(-0.0155225\pi\)
−0.541621 + 0.840623i \(0.682189\pi\)
\(564\) −4636.40 8030.48i −0.346148 0.599546i
\(565\) −6519.17 + 11291.5i −0.485423 + 0.840776i
\(566\) 439.050 0.0326054
\(567\) 0 0
\(568\) 389.338 0.0287610
\(569\) −2141.89 + 3709.86i −0.157808 + 0.273331i −0.934078 0.357070i \(-0.883776\pi\)
0.776270 + 0.630400i \(0.217109\pi\)
\(570\) −233.895 405.119i −0.0171874 0.0297694i
\(571\) −3179.97 5507.87i −0.233060 0.403673i 0.725647 0.688067i \(-0.241541\pi\)
−0.958707 + 0.284395i \(0.908207\pi\)
\(572\) −8720.25 + 15103.9i −0.637433 + 1.10407i
\(573\) 1155.93 0.0842753
\(574\) 0 0
\(575\) 4110.95 0.298153
\(576\) 2198.34 3807.64i 0.159023 0.275437i
\(577\) 7234.36 + 12530.3i 0.521959 + 0.904059i 0.999674 + 0.0255444i \(0.00813192\pi\)
−0.477715 + 0.878515i \(0.658535\pi\)
\(578\) 314.656 + 545.001i 0.0226436 + 0.0392198i
\(579\) −945.335 + 1637.37i −0.0678528 + 0.117525i
\(580\) 6034.68 0.432028
\(581\) 0 0
\(582\) 582.191 0.0414649
\(583\) −9497.10 + 16449.5i −0.674665 + 1.16855i
\(584\) −1404.09 2431.96i −0.0994894 0.172321i
\(585\) 2038.29 + 3530.43i 0.144056 + 0.249513i
\(586\) 1020.67 1767.85i 0.0719513 0.124623i
\(587\) 11132.6 0.782777 0.391388 0.920226i \(-0.371995\pi\)
0.391388 + 0.920226i \(0.371995\pi\)
\(588\) 0 0
\(589\) 59.1108 0.00413517
\(590\) 1302.55 2256.07i 0.0908897 0.157426i
\(591\) 1875.34 + 3248.19i 0.130527 + 0.226079i
\(592\) −2173.65 3764.87i −0.150906 0.261377i
\(593\) −9887.81 + 17126.2i −0.684728 + 1.18598i 0.288794 + 0.957391i \(0.406746\pi\)
−0.973522 + 0.228592i \(0.926588\pi\)
\(594\) 403.963 0.0279037
\(595\) 0 0
\(596\) −11970.4 −0.822696
\(597\) −1638.37 + 2837.73i −0.112318 + 0.194541i
\(598\) 627.098 + 1086.17i 0.0428829 + 0.0742753i
\(599\) 11945.5 + 20690.2i 0.814825 + 1.41132i 0.909453 + 0.415806i \(0.136500\pi\)
−0.0946282 + 0.995513i \(0.530166\pi\)
\(600\) 175.667 304.265i 0.0119527 0.0207026i
\(601\) −19395.5 −1.31641 −0.658204 0.752840i \(-0.728683\pi\)
−0.658204 + 0.752840i \(0.728683\pi\)
\(602\) 0 0
\(603\) −8743.95 −0.590516
\(604\) 6318.32 10943.7i 0.425644 0.737237i
\(605\) −14340.1 24837.8i −0.963648 1.66909i
\(606\) −115.966 200.859i −0.00777358 0.0134642i
\(607\) 7298.36 12641.1i 0.488025 0.845285i −0.511880 0.859057i \(-0.671051\pi\)
0.999905 + 0.0137724i \(0.00438402\pi\)
\(608\) 2383.04 0.158956
\(609\) 0 0
\(610\) 1044.28 0.0693142
\(611\) −7091.62 + 12283.0i −0.469552 + 0.813288i
\(612\) 1741.36 + 3016.13i 0.115017 + 0.199215i
\(613\) −989.898 1714.55i −0.0652229 0.112969i 0.831570 0.555420i \(-0.187442\pi\)
−0.896793 + 0.442451i \(0.854109\pi\)
\(614\) 746.650 1293.24i 0.0490755 0.0850012i
\(615\) −11493.9 −0.753622
\(616\) 0 0
\(617\) 16262.4 1.06110 0.530551 0.847653i \(-0.321985\pi\)
0.530551 + 0.847653i \(0.321985\pi\)
\(618\) −55.5400 + 96.1981i −0.00361512 + 0.00626158i
\(619\) −6010.49 10410.5i −0.390278 0.675981i 0.602208 0.798339i \(-0.294288\pi\)
−0.992486 + 0.122358i \(0.960954\pi\)
\(620\) 57.7143 + 99.9642i 0.00373849 + 0.00647526i
\(621\) −1873.70 + 3245.34i −0.121077 + 0.209712i
\(622\) −296.127 −0.0190894
\(623\) 0 0
\(624\) −6832.97 −0.438362
\(625\) 9225.06 15978.3i 0.590404 1.02261i
\(626\) −1097.23 1900.45i −0.0700543 0.121338i
\(627\) −4573.12 7920.87i −0.291280 0.504512i
\(628\) −4620.82 + 8003.49i −0.293616 + 0.508557i
\(629\) 3389.16 0.214841
\(630\) 0 0
\(631\) 25347.6 1.59916 0.799582 0.600557i \(-0.205055\pi\)
0.799582 + 0.600557i \(0.205055\pi\)
\(632\) −962.542 + 1667.17i −0.0605821 + 0.104931i
\(633\) 5430.07 + 9405.16i 0.340957 + 0.590556i
\(634\) −754.317 1306.51i −0.0472519 0.0818428i
\(635\) −3036.58 + 5259.51i −0.189769 + 0.328689i
\(636\) −7500.29 −0.467620
\(637\) 0 0
\(638\) −914.669 −0.0567588
\(639\) 443.114 767.496i 0.0274324 0.0475143i
\(640\) 3098.24 + 5366.31i 0.191358 + 0.331441i
\(641\) 2555.80 + 4426.78i 0.157485 + 0.272772i 0.933961 0.357374i \(-0.116328\pi\)
−0.776476 + 0.630147i \(0.782995\pi\)
\(642\) −316.857 + 548.812i −0.0194787 + 0.0337382i
\(643\) 10931.3 0.670435 0.335217 0.942141i \(-0.391190\pi\)
0.335217 + 0.942141i \(0.391190\pi\)
\(644\) 0 0
\(645\) 6507.38 0.397252
\(646\) −305.639 + 529.382i −0.0186149 + 0.0322419i
\(647\) −9203.06 15940.2i −0.559211 0.968582i −0.997563 0.0697783i \(-0.977771\pi\)
0.438352 0.898804i \(-0.355563\pi\)
\(648\) 160.132 + 277.357i 0.00970770 + 0.0168142i
\(649\) 25467.3 44110.7i 1.54034 2.66795i
\(650\) −267.655 −0.0161512
\(651\) 0 0
\(652\) 9175.91 0.551160
\(653\) −9960.71 + 17252.5i −0.596926 + 1.03391i 0.396346 + 0.918101i \(0.370278\pi\)
−0.993272 + 0.115805i \(0.963055\pi\)
\(654\) −506.766 877.744i −0.0302999 0.0524809i
\(655\) −11528.3 19967.6i −0.687707 1.19114i
\(656\) 9632.74 16684.4i 0.573316 0.993012i
\(657\) −6392.11 −0.379574
\(658\) 0 0
\(659\) −18858.8 −1.11477 −0.557385 0.830254i \(-0.688195\pi\)
−0.557385 + 0.830254i \(0.688195\pi\)
\(660\) 8930.17 15467.5i 0.526676 0.912230i
\(661\) 12916.0 + 22371.2i 0.760023 + 1.31640i 0.942838 + 0.333251i \(0.108146\pi\)
−0.182815 + 0.983147i \(0.558521\pi\)
\(662\) −378.718 655.960i −0.0222346 0.0385115i
\(663\) 2663.50 4613.33i 0.156021 0.270236i
\(664\) 2394.82 0.139965
\(665\) 0 0
\(666\) 155.229 0.00903153
\(667\) 4242.50 7348.22i 0.246282 0.426573i
\(668\) 11473.5 + 19872.7i 0.664555 + 1.15104i
\(669\) −275.767 477.642i −0.0159369 0.0276034i
\(670\) 1498.46 2595.41i 0.0864037 0.149656i
\(671\) 20417.7 1.17469
\(672\) 0 0
\(673\) −16275.0 −0.932178 −0.466089 0.884738i \(-0.654337\pi\)
−0.466089 + 0.884738i \(0.654337\pi\)
\(674\) −479.498 + 830.515i −0.0274029 + 0.0474633i
\(675\) −399.862 692.581i −0.0228010 0.0394925i
\(676\) −3453.55 5981.73i −0.196493 0.340335i
\(677\) −13135.9 + 22752.0i −0.745720 + 1.29163i 0.204137 + 0.978942i \(0.434561\pi\)
−0.949857 + 0.312683i \(0.898772\pi\)
\(678\) 780.350 0.0442023
\(679\) 0 0
\(680\) −2396.60 −0.135155
\(681\) 3419.28 5922.36i 0.192404 0.333253i
\(682\) −8.74769 15.1514i −0.000491153 0.000850702i
\(683\) 4036.14 + 6990.81i 0.226118 + 0.391648i 0.956654 0.291226i \(-0.0940631\pi\)
−0.730536 + 0.682874i \(0.760730\pi\)
\(684\) 1805.80 3127.74i 0.100945 0.174842i
\(685\) −6355.51 −0.354499
\(686\) 0 0
\(687\) −16238.0 −0.901774
\(688\) −5453.67 + 9446.04i −0.302208 + 0.523440i
\(689\) 5736.05 + 9935.13i 0.317164 + 0.549344i
\(690\) −642.194 1112.31i −0.0354318 0.0613696i
\(691\) −12242.6 + 21204.9i −0.673997 + 1.16740i 0.302763 + 0.953066i \(0.402091\pi\)
−0.976761 + 0.214332i \(0.931243\pi\)
\(692\) 15042.9 0.826364
\(693\) 0 0
\(694\) −24.7062 −0.00135135
\(695\) 14089.1 24403.0i 0.768962 1.33188i
\(696\) −362.578 628.003i −0.0197464 0.0342017i
\(697\) 7509.71 + 13007.2i 0.408107 + 0.706862i
\(698\) −447.440 + 774.989i −0.0242634 + 0.0420254i
\(699\) 3415.10 0.184794
\(700\) 0 0
\(701\) 778.448 0.0419423 0.0209712 0.999780i \(-0.493324\pi\)
0.0209712 + 0.999780i \(0.493324\pi\)
\(702\) 121.993 211.297i 0.00655885 0.0113603i
\(703\) −1757.29 3043.72i −0.0942780 0.163294i
\(704\) 14731.7 + 25516.0i 0.788667 + 1.36601i
\(705\) 7262.34 12578.7i 0.387965 0.671975i
\(706\) −1768.93 −0.0942985
\(707\) 0 0
\(708\) 20112.7 1.06763
\(709\) 12086.0 20933.6i 0.640197 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170322i \(-0.0544806\pi\)
\(710\) 151.874 + 263.053i 0.00802777 + 0.0139045i
\(711\) 2190.98 + 3794.89i 0.115567 + 0.200168i
\(712\) −431.109 + 746.703i −0.0226917 + 0.0393032i
\(713\) 162.297 0.00852466
\(714\) 0 0
\(715\) −27318.3 −1.42888
\(716\) −17022.0 + 29483.0i −0.888467 + 1.53887i
\(717\) 9339.54 + 16176.6i 0.486460 + 0.842573i
\(718\) 806.269 + 1396.50i 0.0419077 + 0.0725862i
\(719\) −40.9418 + 70.9132i −0.00212360 + 0.00367819i −0.867085 0.498160i \(-0.834009\pi\)
0.864962 + 0.501838i \(0.167343\pi\)
\(720\) 6997.47 0.362195
\(721\) 0 0
\(722\) −1067.63 −0.0550318
\(723\) −4794.29 + 8303.96i −0.246614 + 0.427147i
\(724\) −1523.12 2638.13i −0.0781856 0.135421i
\(725\) 905.382 + 1568.17i 0.0463794 + 0.0803315i
\(726\) −858.259 + 1486.55i −0.0438747 + 0.0759931i
\(727\) 32542.9 1.66018 0.830088 0.557632i \(-0.188290\pi\)
0.830088 + 0.557632i \(0.188290\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 1095.42 1897.33i 0.0555389 0.0961962i
\(731\) −4251.70 7364.16i −0.215123 0.372604i
\(732\) 4031.20 + 6982.25i 0.203549 + 0.352557i
\(733\) −2534.47 + 4389.83i −0.127712 + 0.221203i −0.922790 0.385304i \(-0.874097\pi\)
0.795078 + 0.606507i \(0.207430\pi\)
\(734\) −204.631 −0.0102903
\(735\) 0 0
\(736\) 6542.98 0.327687
\(737\) 29297.8 50745.3i 1.46431 2.53627i
\(738\) 343.956 + 595.750i 0.0171561 + 0.0297153i
\(739\) 19214.2 + 33280.0i 0.956437 + 1.65660i 0.731045 + 0.682329i \(0.239033\pi\)
0.225392 + 0.974268i \(0.427634\pi\)
\(740\) 3431.55 5943.62i 0.170468 0.295259i
\(741\) −5524.14 −0.273865
\(742\) 0 0
\(743\) 21592.9 1.06617 0.533086 0.846061i \(-0.321032\pi\)
0.533086 + 0.846061i \(0.321032\pi\)
\(744\) 6.93523 12.0122i 0.000341744 0.000591919i
\(745\) −9375.07 16238.1i −0.461042 0.798548i
\(746\) −165.445 286.560i −0.00811982 0.0140639i
\(747\) 2725.60 4720.87i 0.133500 0.231228i
\(748\) −23338.7 −1.14084
\(749\) 0 0
\(750\) −882.655 −0.0429733
\(751\) −4056.30 + 7025.72i −0.197093 + 0.341374i −0.947585 0.319505i \(-0.896483\pi\)
0.750492 + 0.660880i \(0.229817\pi\)
\(752\) 12172.8 + 21083.9i 0.590287 + 1.02241i
\(753\) 359.411 + 622.519i 0.0173940 + 0.0301273i
\(754\) −276.220 + 478.428i −0.0133413 + 0.0231078i
\(755\) 19793.7 0.954129
\(756\) 0 0
\(757\) 3108.01 0.149224 0.0746120 0.997213i \(-0.476228\pi\)
0.0746120 + 0.997213i \(0.476228\pi\)
\(758\) 165.996 287.513i 0.00795414 0.0137770i
\(759\) −12556.2 21747.9i −0.600475 1.04005i
\(760\) 1242.64 + 2152.32i 0.0593098 + 0.102728i
\(761\) −3605.96 + 6245.71i −0.171769 + 0.297512i −0.939038 0.343812i \(-0.888282\pi\)
0.767269 + 0.641325i \(0.221615\pi\)
\(762\) 363.481 0.0172802
\(763\) 0 0
\(764\) −3058.77 −0.144846
\(765\) −2727.62 + 4724.38i −0.128912 + 0.223282i
\(766\) 43.8313 + 75.9181i 0.00206748 + 0.00358098i
\(767\) −15381.7 26641.9i −0.724123 1.25422i
\(768\) −5676.81 + 9832.52i −0.266724 + 0.461980i
\(769\) 7533.07 0.353250 0.176625 0.984278i \(-0.443482\pi\)
0.176625 + 0.984278i \(0.443482\pi\)
\(770\) 0 0
\(771\) −2097.35 −0.0979693
\(772\) 2501.50 4332.73i 0.116621 0.201993i
\(773\) −12416.3 21505.7i −0.577728 1.00065i −0.995739 0.0922122i \(-0.970606\pi\)
0.418012 0.908442i \(-0.362727\pi\)
\(774\) −194.734 337.290i −0.00904339 0.0156636i
\(775\) −17.3178 + 29.9952i −0.000802674 + 0.00139027i
\(776\) −3093.08 −0.143086
\(777\) 0 0
\(778\) 2911.66 0.134175
\(779\) 7787.61 13488.5i 0.358177 0.620381i