Properties

Label 21.4.e.b.4.2
Level 21
Weight 4
Character 21.4
Analytic conductor 1.239
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 21.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.23904011012\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.2
Root \(0.124036 + 0.214837i\)
Character \(\chi\) = 21.4
Dual form 21.4.e.b.16.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.124036 - 0.214837i) q^{2} +(1.50000 - 2.59808i) q^{3} +(3.96923 - 6.87491i) q^{4} +(6.21730 + 10.7687i) q^{5} -0.744216 q^{6} +(-18.4385 + 1.73873i) q^{7} -3.95388 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(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} +(-18.4385 + 1.73873i) q^{7} -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} +(2.66058 + 3.74559i) q^{14} +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} +(-23.1403 + 50.5126i) q^{21} +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} +(-61.2329 + 133.664i) q^{28} -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} +(-133.361 - 187.748i) q^{35} -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} +(13.7222 - 1.29399i) q^{42} +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} +(336.954 - 64.1190i) q^{49} +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} +(72.9035 - 6.87474i) q^{56} +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} +(96.5251 + 135.889i) q^{63} -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} +(-23.7935 + 51.9384i) q^{70} -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} +(465.210 - 1015.50i) q^{77} -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} +(255.420 + 359.584i) q^{84} +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} +(-671.656 + 63.3365i) q^{91} -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} +(-55.5695 - 64.4369i) q^{98} +542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + O(q^{10}) \) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + 55q^{10} - 35q^{11} + 75q^{12} + 124q^{13} - 326q^{14} - 66q^{15} - 241q^{16} - 48q^{17} - 9q^{18} + 202q^{19} + 878q^{20} + 3q^{21} - 14q^{22} - 216q^{23} + 117q^{24} - 130q^{25} - 274q^{26} - 162q^{27} - 201q^{28} + 106q^{29} - 165q^{30} + 95q^{31} - 683q^{32} + 105q^{33} - 48q^{34} + 56q^{35} + 450q^{36} - 262q^{37} + 398q^{38} + 186q^{39} - 21q^{40} + 488q^{41} - 219q^{42} + 720q^{43} + 905q^{44} - 99q^{45} + 1056q^{46} + 210q^{47} - 1446q^{48} - 303q^{49} - 2756q^{50} + 144q^{51} - 324q^{52} - 393q^{53} + 27q^{54} - 2062q^{55} + 1299q^{56} + 1212q^{57} + 1249q^{58} - 1143q^{59} + 1317q^{60} + 70q^{61} + 2118q^{62} + 126q^{63} - 798q^{64} + 472q^{65} - 21q^{66} + 628q^{67} - 1944q^{68} - 1296q^{69} + 3251q^{70} + 636q^{71} - 351q^{72} - 988q^{73} - 1002q^{74} + 390q^{75} - 4680q^{76} + 1073q^{77} - 1644q^{78} - 861q^{79} - 175q^{80} - 243q^{81} - 124q^{82} + 1038q^{83} + 1620q^{84} + 3600q^{85} + 3208q^{86} + 159q^{87} + 891q^{88} - 1766q^{89} - 990q^{90} - 654q^{91} - 1344q^{92} - 285q^{93} + 3294q^{94} + 736q^{95} + 2049q^{96} + 38q^{97} - 4267q^{98} + 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(0.0210333\pi\)
−0.441725 + 0.897150i \(0.645633\pi\)
\(6\) −0.744216 −0.0506375
\(7\) −18.4385 + 1.73873i −0.995583 + 0.0938826i
\(8\) −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 \(-0.372967\pi\)
0.388577 + 0.921416i \(0.372967\pi\)
\(14\) 2.66058 + 3.74559i 0.0507906 + 0.0715037i
\(15\) 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 \(-0.720287\pi\)
0.985845 + 0.167659i \(0.0536207\pi\)
\(18\) −1.11632 + 1.93353i −0.0146178 + 0.0253187i
\(19\) 25.2750 + 43.7776i 0.305183 + 0.528593i 0.977302 0.211851i \(-0.0679490\pi\)
−0.672119 + 0.740443i \(0.734616\pi\)
\(20\) 98.7116 1.10363
\(21\) −23.1403 + 50.5126i −0.240459 + 0.524893i
\(22\) 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
\(28\) −61.2329 + 133.664i −0.413283 + 0.902148i
\(29\) −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 \(-0.832255\pi\)
0.867714 + 0.497064i \(0.165588\pi\)
\(32\) −23.5711 + 40.8264i −0.130213 + 0.225536i
\(33\) 90.4673 + 156.694i 0.477222 + 0.826573i
\(34\) −12.0925 −0.0609957
\(35\) −133.361 187.748i −0.644062 0.906719i
\(36\) −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 \(-0.300378\pi\)
0.586823 + 0.809715i \(0.300378\pi\)
\(42\) 13.7222 1.29399i 0.0504138 0.00475398i
\(43\) 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 \(-0.960162\pi\)
0.387984 0.921666i \(-0.373172\pi\)
\(48\) −187.581 −0.564061
\(49\) 336.954 64.1190i 0.982372 0.186936i
\(50\) 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
\(56\) 72.9035 6.87474i 0.173967 0.0164049i
\(57\) 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 \(0.548396\pi\)
−0.780308 + 0.625396i \(0.784938\pi\)
\(60\) 148.067 256.460i 0.318590 0.551815i
\(61\) 169.269 + 293.182i 0.355290 + 0.615380i 0.987167 0.159688i \(-0.0510489\pi\)
−0.631878 + 0.775068i \(0.717716\pi\)
\(62\) −0.290084 −0.000594204
\(63\) 96.5251 + 135.889i 0.193032 + 0.271753i
\(64\) −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
\(70\) −23.7935 + 51.9384i −0.0406266 + 0.0886832i
\(71\) −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 \(0.359476\pi\)
−0.996629 + 0.0820374i \(0.973857\pi\)
\(74\) −8.62383 + 14.9369i −0.0135473 + 0.0234646i
\(75\) 44.4291 + 76.9534i 0.0684030 + 0.118478i
\(76\) 401.289 0.605671
\(77\) 465.210 1015.50i 0.688514 1.50294i
\(78\) −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 \(-0.368837\pi\)
0.400499 + 0.916297i \(0.368837\pi\)
\(84\) 255.420 + 359.584i 0.331770 + 0.467069i
\(85\) 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 \(-0.208120\pi\)
−0.923622 + 0.383303i \(0.874786\pi\)
\(90\) −27.7621 −0.0325153
\(91\) −671.656 + 63.3365i −0.773722 + 0.0729612i
\(92\) −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 \(-0.634272\pi\)
−0.409429 + 0.912342i \(0.634272\pi\)
\(98\) −55.5695 64.4369i −0.0572792 0.0664195i
\(99\) 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 \(-0.784274\pi\)
0.932517 + 0.361126i \(0.117608\pi\)
\(102\) −18.1388 + 31.4174i −0.0176079 + 0.0304979i
\(103\) 74.6289 + 129.261i 0.0713922 + 0.123655i 0.899512 0.436897i \(-0.143922\pi\)
−0.828119 + 0.560552i \(0.810589\pi\)
\(104\) −144.028 −0.135799
\(105\) −687.825 + 64.8613i −0.639284 + 0.0602839i
\(106\) 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
\(112\) 670.601 + 944.081i 0.565767 + 0.796493i
\(113\) 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
\(119\) −376.001 + 820.765i −0.289646 + 0.632264i
\(120\) −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
\(126\) 17.2214 37.5923i 0.0121762 0.0265793i
\(127\) 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 \(0.0455272\pi\)
−0.371451 + 0.928453i \(0.621139\pi\)
\(132\) 1436.34 0.947102
\(133\) −542.149 763.244i −0.353461 0.497607i
\(134\) −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 \(-0.256995\pi\)
0.691397 + 0.722475i \(0.256995\pi\)
\(140\) −1820.09 + 171.633i −1.09875 + 0.103612i
\(141\) −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
\(147\) 338.844 971.610i 0.190118 0.545150i
\(148\) −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
\(154\) −275.869 + 26.0142i −0.144352 + 0.0136122i
\(155\) 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 \(-0.928950\pi\)
0.679300 + 0.733861i \(0.262283\pi\)
\(158\) 60.3911 104.601i 0.0304080 0.0526682i
\(159\) 472.402 + 818.225i 0.235622 + 0.408110i
\(160\) −586.195 −0.289642
\(161\) 1488.55 + 2095.60i 0.728660 + 1.02582i
\(162\) 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 \(-0.733580\pi\)
−0.669707 + 0.742626i \(0.733580\pi\)
\(168\) 91.4942 199.721i 0.0420175 0.0917191i
\(169\) −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 \(-0.303370\pi\)
−0.995573 + 0.0939940i \(0.970037\pi\)
\(174\) 45.4972 0.0198226
\(175\) 228.467 498.718i 0.0986887 0.215426i
\(176\) 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 \(-0.474894\pi\)
0.0787917 + 0.996891i \(0.474894\pi\)
\(182\) 96.9165 + 136.440i 0.0394721 + 0.0555694i
\(183\) 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
\(189\) 497.838 46.9457i 0.191600 0.0180677i
\(190\) 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
\(196\) 896.634 2571.03i 0.326762 0.936964i
\(197\) −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 \(-0.771012\pi\)
0.946750 + 0.321970i \(0.104345\pi\)
\(200\) 58.5558 101.422i 0.0207026 0.0358580i
\(201\) −1457.32 2524.16i −0.511402 0.885774i
\(202\) −77.3105 −0.0269285
\(203\) 1127.23 106.296i 0.389733 0.0367514i
\(204\) −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
\(210\) 99.2496 + 139.725i 0.0326137 + 0.0459139i
\(211\) −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
\(217\) −9.01974 + 19.6890i −0.00282166 + 0.00615935i
\(218\) 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 \(-0.508788\pi\)
−0.0276034 + 0.999619i \(0.508788\pi\)
\(224\) 363.629 793.759i 0.108464 0.236765i
\(225\) 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 \(-0.941480\pi\)
0.649895 + 0.760024i \(0.274813\pi\)
\(228\) 601.933 1042.58i 0.174842 0.302836i
\(229\) −2706.34 4687.51i −0.780960 1.35266i −0.931383 0.364040i \(-0.881397\pi\)
0.150424 0.988622i \(-0.451936\pi\)
\(230\) −428.130 −0.122739
\(231\) −1940.53 2731.90i −0.552715 0.778120i
\(232\) 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
\(238\) 222.968 21.0257i 0.0607263 0.00572644i
\(239\) −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 \(-0.692852\pi\)
0.996618 + 0.0821704i \(0.0261852\pi\)
\(242\) −286.086 + 495.516i −0.0759931 + 0.131624i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 2687.47 0.705113
\(245\) 2785.42 + 3229.90i 0.726343 + 0.842248i
\(246\) −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 \(-0.490409\pi\)
0.0301273 + 0.999546i \(0.490409\pi\)
\(252\) 1317.36 124.226i 0.329308 0.0310535i
\(253\) 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 \(-0.193706\pi\)
−0.905325 + 0.424720i \(0.860372\pi\)
\(258\) −129.823 −0.0313272
\(259\) 745.676 + 1049.77i 0.178896 + 0.251852i
\(260\) 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
\(266\) −96.7268 + 211.143i −0.0222959 + 0.0486693i
\(267\) −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 \(-0.731342\pi\)
0.979429 + 0.201788i \(0.0646751\pi\)
\(270\) −41.6431 + 72.1280i −0.00938637 + 0.0162577i
\(271\) −1113.49 1928.62i −0.249593 0.432308i 0.713820 0.700329i \(-0.246964\pi\)
−0.963413 + 0.268021i \(0.913630\pi\)
\(272\) −3047.94 −0.679443
\(273\) −842.931 + 1840.02i −0.186874 + 0.407923i
\(274\) −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
\(280\) 527.295 + 742.333i 0.112543 + 0.158439i
\(281\) 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 \(-0.773821\pi\)
0.943872 + 0.330312i \(0.107154\pi\)
\(284\) −390.849 + 676.971i −0.0816642 + 0.141447i
\(285\) 942.853 + 1633.07i 0.195964 + 0.339420i
\(286\) 545.004 0.112681
\(287\) −5681.17 + 535.729i −1.16846 + 0.110185i
\(288\) 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 \(-0.193772\pi\)
0.820362 + 0.571844i \(0.193772\pi\)
\(294\) −250.766 + 47.7184i −0.0497448 + 0.00946596i
\(295\) −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
\(301\) −3216.45 + 303.309i −0.615925 + 0.0580811i
\(302\) 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 \(-0.310977\pi\)
0.559541 + 0.828803i \(0.310977\pi\)
\(308\) −5134.93 7229.02i −0.949967 1.33738i
\(309\) 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 \(-0.868042\pi\)
0.806469 + 0.591276i \(0.201376\pi\)
\(312\) −216.042 + 374.195i −0.0392018 + 0.0678994i
\(313\) 4423.02 + 7660.89i 0.798734 + 1.38345i 0.920441 + 0.390882i \(0.127830\pi\)
−0.121707 + 0.992566i \(0.538837\pi\)
\(314\) 288.795 0.0519034
\(315\) −863.223 + 1884.31i −0.154403 + 0.337045i
\(316\) 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
\(322\) 265.578 579.725i 0.0459630 0.100332i
\(323\) 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
\(329\) 4175.91 + 5878.90i 0.699773 + 0.985149i
\(330\) 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
\(336\) 3458.70 326.152i 0.561569 0.0529555i
\(337\) 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
\(343\) −6101.42 + 1768.13i −0.960483 + 0.278338i
\(344\) −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 \(-0.589222\pi\)
−0.276643 + 0.960973i \(0.589222\pi\)
\(350\) −135.481 + 12.7757i −0.0206907 + 0.00195112i
\(351\) −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 \(0.347328\pi\)
−0.999034 + 0.0439501i \(0.986006\pi\)
\(354\) 314.255 544.306i 0.0471821 0.0817218i
\(355\) −612.216 1060.39i −0.0915298 0.158534i
\(356\) −1731.13 −0.257724
\(357\) 1568.41 + 2208.03i 0.232518 + 0.327342i
\(358\) −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
\(364\) −2230.52 + 4868.97i −0.321185 + 0.701108i
\(365\) −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 \(-0.852017\pi\)
0.835202 + 0.549943i \(0.185350\pi\)
\(368\) −4339.12 + 7515.58i −0.614654 + 1.06461i
\(369\) −1386.52 2401.52i −0.195608 0.338803i
\(370\) −214.468 −0.0301342
\(371\) 2429.23 5302.73i 0.339945 0.742059i
\(372\) −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
\(378\) −71.8355 101.131i −0.00977466 0.0137609i
\(379\) −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 \(-0.174171\pi\)
−0.877571 + 0.479447i \(0.840837\pi\)
\(384\) 1494.98 0.198673
\(385\) 13827.9 1303.96i 1.83048 0.172613i
\(386\) 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
\(392\) −1332.28 + 253.519i −0.171658 + 0.0326649i
\(393\) 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 \(-0.849505\pi\)
0.0507841 0.998710i \(-0.483828\pi\)
\(398\) −270.955 −0.0341250
\(399\) −2796.19 + 263.678i −0.350839 + 0.0330838i
\(400\) 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
\(406\) −162.653 228.985i −0.0198826 0.0279909i
\(407\) 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 \(-0.519389\pi\)
0.894856 0.446355i \(-0.147278\pi\)
\(410\) 475.218 823.102i 0.0572423 0.0991466i
\(411\) −766.673 1327.92i −0.0920126 0.159370i
\(412\) 1184.88 0.141686
\(413\) 6514.21 14219.7i 0.776134 1.69421i
\(414\) 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 \(-0.313222\pi\)
0.553683 + 0.832728i \(0.313222\pi\)
\(420\) −2284.22 + 4986.18i −0.265377 + 0.579288i
\(421\) 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
\(427\) −3630.82 5111.52i −0.411494 0.579306i
\(428\) −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 \(-0.784821\pi\)
−0.780079 + 0.625681i \(0.784821\pi\)
\(434\) 5.34870 0.504377i 0.000591580 5.57854e-5i
\(435\) −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 \(0.182488\pi\)
0.0496832 + 0.998765i \(0.484179\pi\)
\(440\) 2965.22 0.321275
\(441\) −2016.05 2337.76i −0.217692 0.252430i
\(442\) −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
\(448\) 9007.56 849.404i 0.949926 0.0895772i
\(449\) −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
\(455\) −4857.94 6839.07i −0.500535 0.704660i
\(456\) −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 \(-0.799858\pi\)
−0.808755 + 0.588146i \(0.799858\pi\)
\(462\) −346.216 + 755.749i −0.0348646 + 0.0761053i
\(463\) 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 \(-0.199973\pi\)
−0.913510 + 0.406815i \(0.866639\pi\)
\(468\) −2602.56 −0.257059
\(469\) −7494.00 + 16358.5i −0.737826 + 1.61059i
\(470\) −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
\(476\) 4150.25 + 5842.77i 0.399635 + 0.562612i
\(477\) 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 \(-0.796053\pi\)
0.918519 + 0.395377i \(0.129386\pi\)
\(480\) −879.292 + 1522.98i −0.0836126 + 0.144821i
\(481\) −1266.32 2193.34i −0.120040 0.207916i
\(482\) −792.887 −0.0749274
\(483\) 7677.35 723.967i 0.723254 0.0682022i
\(484\) −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
\(490\) 348.408 999.034i 0.0321214 0.0921056i
\(491\) 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
\(497\) 1815.63 171.212i 0.163868 0.0154526i
\(498\) −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 \(-0.380234\pi\)
0.367440 + 0.930047i \(0.380234\pi\)
\(504\) −381.649 537.291i −0.0337302 0.0474858i
\(505\) 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 \(-0.264015\pi\)
−0.976382 + 0.216052i \(0.930682\pi\)
\(510\) −451.098 −0.0391666
\(511\) 5478.36 11958.6i 0.474263 1.03526i
\(512\) 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
\(518\) 133.039 290.408i 0.0112845 0.0246328i
\(519\) −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 \(0.357163\pi\)
−0.997199 + 0.0747919i \(0.976171\pi\)
\(522\) 68.2458 118.205i 0.00572230 0.00991131i
\(523\) 4968.50 + 8605.69i 0.415406 + 0.719504i 0.995471 0.0950662i \(-0.0303063\pi\)
−0.580065 + 0.814570i \(0.696973\pi\)
\(524\) 14719.7 1.22716
\(525\) −953.005 1341.65i −0.0792239 0.111532i
\(526\) −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
\(532\) −7399.15 + 697.733i −0.602996 + 0.0568620i
\(533\) 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
\(539\) −6812.07 + 19533.1i −0.544373 + 1.56095i
\(540\) −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
\(546\) 499.857 47.1360i 0.0391793 0.00369457i
\(547\) −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
\(553\) −5221.84 7351.37i −0.401546 0.565302i
\(554\) 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
\(560\) −5997.18 + 13091.1i −0.452548 + 0.987859i
\(561\) 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 \(-0.984478\pi\)
0.541621 + 0.840623i \(0.317811\pi\)
\(564\) −4636.40 + 8030.48i −0.346148 + 0.599546i
\(565\) 6519.17 + 11291.5i 0.485423 + 0.840776i
\(566\) −439.050 −0.0326054
\(567\) 624.789 1363.84i 0.0462763 0.101016i
\(568\) 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
\(574\) 819.764 + 1154.07i 0.0596103 + 0.0839201i
\(575\) 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 \(0.341465\pi\)
−0.999674 + 0.0255444i \(0.991868\pi\)
\(578\) 314.656 545.001i 0.0226436 0.0392198i
\(579\) 945.335 + 1637.37i 0.0678528 + 0.117525i
\(580\) −6034.68 −0.432028
\(581\) −11168.0 + 1053.13i −0.797461 + 0.0751998i
\(582\) 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 \(-0.628005\pi\)
−0.391388 + 0.920226i \(0.628005\pi\)
\(588\) −5334.78 6186.07i −0.374154 0.433859i
\(589\) 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 \(0.0734123\pi\)
−0.288794 + 0.957391i \(0.593254\pi\)
\(594\) −403.963 −0.0279037
\(595\) −11176.3 + 1053.91i −0.770054 + 0.0726154i
\(596\) −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 \(-0.271317\pi\)
0.658204 + 0.752840i \(0.271317\pi\)
\(602\) 464.118 + 653.391i 0.0314220 + 0.0442362i
\(603\) −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 \(-0.328949\pi\)
−0.999905 + 0.0137724i \(0.995616\pi\)
\(608\) −2383.04 −0.158956
\(609\) 1414.67 3088.06i 0.0941304 0.205475i
\(610\) 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
\(616\) −1839.39 + 4015.16i −0.120310 + 0.262622i
\(617\) 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 \(-0.705712\pi\)
0.992486 + 0.122358i \(0.0390457\pi\)
\(620\) 57.7143 99.9642i 0.00373849 0.00647526i
\(621\) 1873.70 + 3245.34i 0.121077 + 0.209712i
\(622\) 296.127 0.0190894
\(623\) 2338.79 + 3292.58i 0.150404 + 0.211740i
\(624\) −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
\(630\) 511.890 48.2708i 0.0323717 0.00305262i
\(631\) 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
\(637\) 12274.2 2335.66i 0.763454 0.145278i
\(638\) −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 \(-0.608810\pi\)
−0.335217 + 0.942141i \(0.608810\pi\)
\(644\) 20315.5 1915.73i 1.24308 0.117221i
\(645\) 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 \(-0.644437\pi\)
0.997563 0.0697783i \(-0.0222292\pi\)
\(648\) 160.132 277.357i 0.00970770 0.0168142i
\(649\) −25467.3 44110.7i −1.54034 2.66795i
\(650\) 267.655 0.0161512
\(651\) 37.6240 + 52.9675i 0.00226513 + 0.00318888i
\(652\) 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
\(658\) 745.040 1626.33i 0.0441408 0.0963542i
\(659\) −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 \(0.441479\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(662\) −378.718 + 655.960i −0.0222346 + 0.0385115i
\(663\) −2663.50 4613.33i −0.156021 0.270236i
\(664\) −2394.82 −0.139965
\(665\) 4848.43 10583.6i 0.282728 0.617162i
\(666\) 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
\(672\) −1516.80 2135.37i −0.0870714 0.122580i
\(673\) −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 \(0.101228\pi\)
−0.204137 + 0.978942i \(0.565439\pi\)
\(678\) −780.350 −0.0442023
\(679\) 14424.2 1360.19i 0.815242 0.0768766i
\(680\) −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
\(686\) 1136.65 + 1091.50i 0.0632619 + 0.0607486i
\(687\) −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 \(0.0687575\pi\)
−0.302763 + 0.953066i \(0.597909\pi\)
\(692\) −15042.9 −0.826364
\(693\) −10008.5 + 943.789i −0.548615 + 0.0517339i
\(694\) −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
\(700\) −2521.80 3550.22i −0.136164 0.191694i
\(701\) 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
\(707\) −2403.86 + 5247.35i −0.127873 + 0.279133i
\(708\) 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
\(714\) 279.826 610.826i 0.0146670 0.0320162i
\(715\) −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 \(-0.165991\pi\)
−0.864962 + 0.501838i \(0.832657\pi\)
\(720\) −6997.47 −0.362195
\(721\) −1600.79 2253.61i −0.0826860 0.116406i
\(722\) −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 \(-0.811710\pi\)
−0.830088 + 0.557632i \(0.811710\pi\)
\(728\) 2655.65 250.425i 0.135199 0.0127491i
\(729\) 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 \(-0.125903\pi\)
−0.795078 + 0.606507i \(0.792570\pi\)
\(734\) 204.631 0.0102903
\(735\) 12569.7 2391.88i 0.630801 0.120035i
\(736\) 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
\(742\) −1440.53 + 135.841i −0.0712717 + 0.00672086i
\(743\) 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
\(749\) 9132.55 + 12856.9i 0.445522 + 0.627212i
\(750\) −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
\(756\) 1653.29 3608.93i 0.0795364 0.173618i
\(757\) 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 \(-0.111718\pi\)
−0.767269 + 0.641325i \(0.778385\pi\)
\(762\) −363.481 −0.0172802
\(763\) 10504.8 22930.7i 0.498425 1.08800i
\(764\) −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 \(-0.556518\pi\)
−0.176625 + 0.984278i \(0.556518\pi\)
\(770\) −1995.30 2809.01i −0.0933838 0.131467i
\(771\) −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 \(-0.637273\pi\)
0.995739 0.0922122i \(-0.0293938\pi\)
\(774\) −194.734 + 337.290i −0.00904339 + 0.0156636i
\(775\) 17.3178 + 29.9952i 0.000802674 + 0.00139027i
\(776\) 3093.08 0.143086
\(777\) 3845.90 362.665i 0.177569 0.0167446i
\(778\) 2911.66 0.134175
\(779\)