Properties

Label 147.4.e.n.67.2
Level $147$
Weight $4$
Character 147.67
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 67.2
Root \(0.124036 + 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.n.79.2

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.843266 0.537497i \(-0.180630\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(3\) −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 −0.997818 0.0660299i \(-0.978967\pi\)
0.441725 0.897150i \(-0.354367\pi\)
\(6\) 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 0.0741379 + 0.997248i \(0.476379\pi\)
−0.900711 + 0.434419i \(0.856954\pi\)
\(12\) 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 −0.985845 0.167659i \(-0.946379\pi\)
0.638119 + 0.769937i \(0.279713\pi\)
\(18\) −1.11632 + 1.93353i −0.0146178 + 0.0253187i
\(19\) −25.2750 43.7776i −0.305183 0.528593i 0.672119 0.740443i \(-0.265384\pi\)
−0.977302 + 0.211851i \(0.932051\pi\)
\(20\) −98.7116 −1.10363
\(21\) 0 0
\(22\) 14.9616 0.144992
\(23\) −69.3962 120.198i −0.629135 1.08969i −0.987726 0.156199i \(-0.950076\pi\)
0.358590 0.933495i \(-0.383257\pi\)
\(24\) 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 −0.867714 0.497064i \(-0.834412\pi\)
0.864327 + 0.502931i \(0.167745\pi\)
\(32\) −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 0.778401 0.627767i \(-0.216031\pi\)
−0.932863 + 0.360232i \(0.882698\pi\)
\(38\) −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 0.992178 + 0.124829i \(0.0398382\pi\)
−0.387984 + 0.921666i \(0.626828\pi\)
\(48\) 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 −0.994678 0.103033i \(-0.967145\pi\)
0.586568 + 0.809900i \(0.300479\pi\)
\(54\) −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 0.151455 0.988464i \(-0.451604\pi\)
0.780308 0.625396i \(-0.215062\pi\)
\(60\) 148.067 256.460i 0.318590 0.551815i
\(61\) −169.269 293.182i −0.355290 0.615380i 0.631878 0.775068i \(-0.282284\pi\)
−0.987167 + 0.159688i \(0.948951\pi\)
\(62\) 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 0.0409498 0.999161i \(-0.486962\pi\)
0.844824 0.535044i \(-0.179705\pi\)
\(68\) 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 −0.427268 0.904125i \(-0.640524\pi\)
0.996629 0.0820374i \(-0.0261427\pi\)
\(74\) −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 0.985661 0.168736i \(-0.0539686\pi\)
−0.638960 + 0.769240i \(0.720635\pi\)
\(80\) −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 0.923622 0.383303i \(-0.125214\pi\)
−0.793762 + 0.608229i \(0.791880\pi\)
\(90\) 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 −0.932517 0.361126i \(-0.882392\pi\)
0.779003 + 0.627021i \(0.215726\pi\)
\(102\) −18.1388 + 31.4174i −0.0176079 + 0.0304979i
\(103\) −74.6289 129.261i −0.0713922 0.123655i 0.828119 0.560552i \(-0.189411\pi\)
−0.899512 + 0.436897i \(0.856078\pi\)
\(104\) 144.028 0.135799
\(105\) 0 0
\(106\) 78.1265 0.0715879
\(107\) −425.760 737.437i −0.384670 0.666269i 0.607053 0.794661i \(-0.292352\pi\)
−0.991723 + 0.128393i \(0.959018\pi\)
\(108\) 107.169 185.623i 0.0954848 0.165385i
\(109\) −680.939 + 1179.42i −0.598369 + 1.03640i 0.394694 + 0.918813i \(0.370851\pi\)
−0.993062 + 0.117592i \(0.962483\pi\)
\(110\) −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 −0.989789 0.142541i \(-0.954473\pi\)
0.371451 0.928453i \(-0.378861\pi\)
\(132\) −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 −0.775271 0.631628i \(-0.782387\pi\)
0.934642 + 0.355591i \(0.115720\pi\)
\(138\) −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 0.580843 0.814016i \(-0.302723\pi\)
−0.995380 + 0.0960168i \(0.969390\pi\)
\(150\) −11.0216 + 19.0900i −0.00599940 + 0.0103913i
\(151\) −795.913 + 1378.56i −0.428943 + 0.742952i −0.996780 0.0801897i \(-0.974447\pi\)
0.567836 + 0.823142i \(0.307781\pi\)
\(152\) 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 −0.679300 0.733861i \(-0.737717\pi\)
0.975192 + 0.221361i \(0.0710498\pi\)
\(158\) 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 0.970817 0.239822i \(-0.0770892\pi\)
−0.693101 + 0.720841i \(0.743756\pi\)
\(164\) −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 0.995573 0.0939940i \(-0.0299635\pi\)
−0.579188 + 0.815194i \(0.696630\pi\)
\(174\) −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 0.0619893 0.998077i \(-0.480256\pi\)
0.833365 0.552723i \(-0.186411\pi\)
\(180\) 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 0.827224 0.561873i \(-0.189919\pi\)
−0.900208 + 0.435460i \(0.856586\pi\)
\(192\) 732.780 1269.21i 0.275437 0.477070i
\(193\) −315.112 + 545.790i −0.117525 + 0.203559i −0.918786 0.394756i \(-0.870829\pi\)
0.801262 + 0.598314i \(0.204163\pi\)
\(194\) −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 −0.946750 0.321970i \(-0.895655\pi\)
0.752209 + 0.658924i \(0.228988\pi\)
\(200\) 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 −0.649895 0.760024i \(-0.725187\pi\)
0.983148 + 0.182813i \(0.0585203\pi\)
\(228\) 601.933 1042.58i 0.174842 0.302836i
\(229\) 2706.34 + 4687.51i 0.780960 + 1.35266i 0.931383 + 0.364040i \(0.118603\pi\)
−0.150424 + 0.988622i \(0.548064\pi\)
\(230\) 428.130 0.122739
\(231\) 0 0
\(232\) 241.719 0.0684035
\(233\) −569.184 985.856i −0.160036 0.277191i 0.774845 0.632151i \(-0.217828\pi\)
−0.934882 + 0.354960i \(0.884494\pi\)
\(234\) 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 −0.996618 0.0821704i \(-0.973815\pi\)
0.569471 + 0.822012i \(0.307148\pi\)
\(242\) −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 0.905325 0.424720i \(-0.139628\pi\)
−0.820481 + 0.571674i \(0.806294\pi\)
\(258\) 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 −0.807115 0.590394i \(-0.798972\pi\)
0.914854 + 0.403785i \(0.132306\pi\)
\(264\) 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 −0.979429 0.201788i \(-0.935325\pi\)
0.664468 + 0.747317i \(0.268658\pi\)
\(270\) −41.6431 + 72.1280i −0.00938637 + 0.0162577i
\(271\) 1113.49 + 1928.62i 0.249593 + 0.432308i 0.963413 0.268021i \(-0.0863698\pi\)
−0.713820 + 0.700329i \(0.753036\pi\)
\(272\) 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 0.131821 + 0.991273i \(0.457917\pi\)
−0.924379 + 0.381476i \(0.875416\pi\)
\(278\) 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 −0.943872 0.330312i \(-0.892846\pi\)
0.757994 + 0.652261i \(0.226179\pi\)
\(284\) −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 −0.806469 0.591276i \(-0.798624\pi\)
0.915295 + 0.402785i \(0.131958\pi\)
\(312\) −216.042 + 374.195i −0.0392018 + 0.0678994i
\(313\) −4423.02 7660.89i −0.798734 1.38345i −0.920441 0.390882i \(-0.872170\pi\)
0.121707 0.992566i \(-0.461163\pi\)
\(314\) −288.795 −0.0519034
\(315\) 0 0
\(316\) 3865.11 0.688068
\(317\) −3040.72 5266.68i −0.538750 0.933142i −0.998972 0.0453380i \(-0.985564\pi\)
0.460222 0.887804i \(-0.347770\pi\)
\(318\) −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 0.710979 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264119i \(0.914919\pi\)
\(332\) −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 −0.862148 0.506657i \(-0.830881\pi\)
0.869852 + 0.493313i \(0.164214\pi\)
\(348\) −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 −0.461455 0.887164i \(-0.652672\pi\)
0.999034 0.0439501i \(-0.0139942\pi\)
\(354\) 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 0.999677 0.0254289i \(-0.00809514\pi\)
−0.521860 + 0.853031i \(0.674762\pi\)
\(360\) 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 −0.835202 0.549943i \(-0.814650\pi\)
0.893866 + 0.448335i \(0.147983\pi\)
\(368\) −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 0.816016 0.578029i \(-0.196178\pi\)
−0.908596 + 0.417677i \(0.862845\pi\)
\(374\) −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 0.877571 0.479447i \(-0.159163\pi\)
−0.853998 + 0.520276i \(0.825829\pi\)
\(384\) −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 0.175387 + 0.984500i \(0.443882\pi\)
−0.940295 + 0.340360i \(0.889451\pi\)
\(390\) 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 0.890300 + 0.455374i \(0.150495\pi\)
−0.0507841 + 0.998710i \(0.516172\pi\)
\(398\) 270.955 0.0341250
\(399\) 0 0
\(400\) 1852.01 0.231501
\(401\) 3741.18 + 6479.91i 0.465899 + 0.806961i 0.999242 0.0389385i \(-0.0123976\pi\)
−0.533343 + 0.845899i \(0.679064\pi\)
\(402\) 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 0.0608735 + 0.998145i \(0.480611\pi\)
−0.894856 + 0.446355i \(0.852722\pi\)
\(410\) 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 −0.199840 0.979829i \(-0.564042\pi\)
0.948476 0.316848i \(-0.102624\pi\)
\(432\) −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 −0.840114 0.542409i \(-0.817512\pi\)
−0.0496832 0.998765i \(-0.515821\pi\)
\(440\) −2965.22 −0.321275
\(441\) 0 0
\(442\) −440.494 −0.0474031
\(443\) 589.354 + 1020.79i 0.0632078 + 0.109479i 0.895898 0.444261i \(-0.146534\pi\)
−0.832690 + 0.553740i \(0.813200\pi\)
\(444\) 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 −0.999957 0.00924618i \(-0.997057\pi\)
0.491971 0.870611i \(-0.336277\pi\)
\(458\) 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 0.913510 0.406815i \(-0.133361\pi\)
−0.809068 + 0.587716i \(0.800027\pi\)
\(468\) 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 −0.918519 0.395377i \(-0.870614\pi\)
0.801666 + 0.597772i \(0.203947\pi\)
\(480\) −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 −0.880645 0.473778i \(-0.842890\pi\)
0.850626 + 0.525772i \(0.176223\pi\)
\(488\) 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 0.867011 0.498289i \(-0.166038\pi\)
−0.865036 + 0.501709i \(0.832705\pi\)
\(500\) −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 0.976382 0.216052i \(-0.0693181\pi\)
−0.675298 + 0.737545i \(0.735985\pi\)
\(510\) 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 −0.433828 0.900996i \(-0.642837\pi\)
0.997199 0.0747919i \(-0.0238293\pi\)
\(522\) 68.2458 118.205i 0.00572230 0.00991131i
\(523\) −4968.50 8605.69i −0.415406 0.719504i 0.580065 0.814570i \(-0.303027\pi\)
−0.995471 + 0.0950662i \(0.969694\pi\)
\(524\) −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 0.620421 0.784269i \(-0.286962\pi\)
−0.989407 + 0.145166i \(0.953628\pi\)
\(542\) 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 −0.898325 0.439332i \(-0.855215\pi\)
0.829635 + 0.558306i \(0.188549\pi\)
\(558\) −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 −0.541621 0.840623i \(-0.682189\pi\)
0.998811 + 0.0487460i \(0.0155225\pi\)
\(564\) −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 0.776270 0.630400i \(-0.217109\pi\)
−0.934078 + 0.357070i \(0.883776\pi\)
\(570\) −233.895 + 405.119i −0.0171874 + 0.0297694i
\(571\) −3179.97 + 5507.87i −0.233060 + 0.403673i −0.958707 0.284395i \(-0.908207\pi\)
0.725647 + 0.688067i \(0.241541\pi\)
\(572\) −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 −0.477715 0.878515i \(-0.658535\pi\)
0.999674 0.0255444i \(-0.00813192\pi\)
\(578\) 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 −0.973522 0.228592i \(-0.926588\pi\)
0.288794 0.957391i \(-0.406746\pi\)
\(594\) 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 −0.0946282 0.995513i \(-0.530166\pi\)
0.909453 0.415806i \(-0.136500\pi\)
\(600\) 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 0.999905 0.0137724i \(-0.00438402\pi\)
−0.511880 + 0.859057i \(0.671051\pi\)
\(608\) 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 −0.896793 0.442451i \(-0.854109\pi\)
0.831570 + 0.555420i \(0.187442\pi\)
\(614\) 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 −0.992486 0.122358i \(-0.960954\pi\)
0.602208 + 0.798339i \(0.294288\pi\)
\(620\) 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 −0.776476 0.630147i \(-0.782995\pi\)
0.933961 + 0.357374i \(0.116328\pi\)
\(642\) −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 0.438352 + 0.898804i \(0.355563\pi\)
−0.997563 + 0.0697783i \(0.977771\pi\)
\(648\) 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 −0.993272 0.115805i \(-0.963055\pi\)
0.396346 0.918101i \(-0.370278\pi\)
\(654\) −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 −0.182815 0.983147i \(-0.558521\pi\)
0.942838 0.333251i \(-0.108146\pi\)
\(662\) −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 −0.949857 0.312683i \(-0.898772\pi\)
0.204137 0.978942i \(-0.434561\pi\)
\(678\) 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 −0.730536 0.682874i \(-0.760730\pi\)
0.956654 + 0.291226i \(0.0940631\pi\)
\(684\) 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 −0.976761 0.214332i \(-0.931243\pi\)
0.302763 0.953066i \(-0.402091\pi\)
\(692\) 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 0.985389 + 0.170322i \(0.0544806\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(710\) 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 0.864962 0.501838i \(-0.167343\pi\)
−0.867085 + 0.498160i \(0.834009\pi\)
\(720\) 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 0.795078 0.606507i \(-0.207430\pi\)
−0.922790 + 0.385304i \(0.874097\pi\)
\(734\) −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 0.225392 0.974268i \(-0.427634\pi\)
0.731045 0.682329i \(-0.239033\pi\)
\(740\) 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 0.750492 0.660880i \(-0.229817\pi\)
−0.947585 + 0.319505i \(0.896483\pi\)
\(752\) 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 0.767269 0.641325i \(-0.221615\pi\)
−0.939038 + 0.343812i \(0.888282\pi\)
\(762\) 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 0.418012 + 0.908442i \(0.362727\pi\)
−0.995739 + 0.0922122i \(0.970606\pi\)
\(774\) −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 +