Properties

Label 15.4.e.a.8.1
Level 15
Weight 4
Character 15.8
Analytic conductor 0.885
Analytic rank 0
Dimension 8
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 15.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.885028650086\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.28356903014400.8
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.1
Root \(-2.66260 + 2.66260i\)
Character \(\chi\) = 15.8
Dual form 15.4.e.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +O(q^{10})\) \(q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +(-40.8945 - 10.0000i) q^{10} -34.1375i q^{11} +(17.3301 - 27.0278i) q^{12} +(2.82109 + 2.82109i) q^{13} -49.8323 q^{14} +(-58.0772 - 1.42827i) q^{15} +75.2524 q^{16} +(64.2384 + 64.2384i) q^{17} +(35.3316 - 95.3316i) q^{18} +19.0735i q^{19} +(35.8474 + 59.0536i) q^{20} +(-67.1789 + 14.6869i) q^{21} +(-90.8945 + 90.8945i) q^{22} +(-51.4018 + 51.4018i) q^{23} +(34.8094 - 7.61018i) q^{24} +(57.6836 - 110.895i) q^{25} -15.0229i q^{26} +(19.5337 - 138.930i) q^{27} +(57.8211 + 57.8211i) q^{28} +50.5042 q^{29} +(150.834 + 158.439i) q^{30} -93.3673 q^{31} +(-161.576 - 161.576i) q^{32} +(-95.7458 + 149.324i) q^{33} -342.083i q^{34} +(35.1454 - 143.725i) q^{35} +(-151.610 + 69.6188i) q^{36} +(-161.537 + 161.537i) q^{37} +(50.7850 - 50.7850i) q^{38} +(-4.42765 - 20.2524i) q^{39} +(-18.2109 + 74.4727i) q^{40} +88.7935i q^{41} +(217.976 + 139.765i) q^{42} +(176.399 + 176.399i) q^{43} +210.932 q^{44} +(250.035 + 169.137i) q^{45} +273.725 q^{46} +(38.2843 + 38.2843i) q^{47} +(-329.169 - 211.061i) q^{48} +167.863i q^{49} +(-448.857 + 141.680i) q^{50} +(-100.821 - 461.162i) q^{51} +(-17.4313 + 17.4313i) q^{52} +(344.569 - 344.569i) q^{53} +(-421.925 + 317.904i) q^{54} +(-198.051 - 326.262i) q^{55} +90.7492i q^{56} +(53.4956 - 83.4310i) q^{57} +(-134.473 - 134.473i) q^{58} -421.133 q^{59} +(8.82514 - 358.854i) q^{60} +2.00000 q^{61} +(248.600 + 248.600i) q^{62} +(335.046 + 124.174i) q^{63} +258.409i q^{64} +(43.3287 + 10.5952i) q^{65} +(652.524 - 142.657i) q^{66} +(430.987 - 430.987i) q^{67} +(-396.923 + 396.923i) q^{68} +(369.009 - 80.6742i) q^{69} +(-476.262 + 289.105i) q^{70} +733.866i q^{71} +(-173.607 - 64.3420i) q^{72} +(-348.073 - 348.073i) q^{73} +860.216 q^{74} +(-563.347 + 323.288i) q^{75} -117.853 q^{76} +(-319.452 - 319.452i) q^{77} +(-42.1349 + 65.7131i) q^{78} +588.019i q^{79} +(719.209 - 436.582i) q^{80} +(-475.102 + 552.919i) q^{81} +(236.422 - 236.422i) q^{82} +(-217.997 + 217.997i) q^{83} +(-90.7492 - 415.092i) q^{84} +(986.629 + 241.262i) q^{85} -939.362i q^{86} +(-220.915 - 141.650i) q^{87} +(165.527 + 165.527i) q^{88} -1272.00 q^{89} +(-215.399 - 1116.09i) q^{90} +52.7985 q^{91} +(-317.607 - 317.607i) q^{92} +(408.407 + 261.868i) q^{93} -203.872i q^{94} +(110.656 + 182.291i) q^{95} +(253.591 + 1159.94i) q^{96} +(-432.111 + 432.111i) q^{97} +(446.951 - 446.951i) q^{98} +(837.622 - 384.633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{3} - 12q^{6} - 16q^{7} + O(q^{10}) \) \( 8q - 6q^{3} - 12q^{6} - 16q^{7} - 100q^{10} + 132q^{12} + 68q^{13} + 90q^{15} + 284q^{16} - 240q^{18} - 492q^{21} - 500q^{22} - 220q^{25} + 702q^{27} + 508q^{28} + 660q^{30} + 616q^{31} - 240q^{33} - 804q^{36} - 1156q^{37} - 600q^{40} + 540q^{42} + 548q^{43} + 180q^{45} + 736q^{46} - 1116q^{48} - 852q^{51} + 224q^{52} + 460q^{55} + 684q^{57} + 60q^{58} + 540q^{60} + 16q^{61} + 1428q^{63} + 2040q^{66} + 404q^{67} - 2220q^{70} - 1800q^{72} - 2512q^{73} - 2910q^{75} - 1488q^{76} - 360q^{78} + 288q^{81} + 2800q^{82} + 4940q^{85} - 1680q^{87} + 2460q^{88} + 600q^{90} - 1304q^{91} + 3408q^{93} + 4164q^{96} + 1904q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66260 2.66260i −0.941372 0.941372i 0.0570018 0.998374i \(-0.481846\pi\)
−0.998374 + 0.0570018i \(0.981846\pi\)
\(3\) −4.37420 2.80471i −0.841814 0.539767i
\(4\) 6.17891i 0.772364i
\(5\) 9.55729 5.80157i 0.854830 0.518908i
\(6\) 4.17891 + 19.1146i 0.284339 + 1.30058i
\(7\) 9.35782 9.35782i 0.505275 0.505275i −0.407798 0.913072i \(-0.633703\pi\)
0.913072 + 0.407798i \(0.133703\pi\)
\(8\) −4.84884 + 4.84884i −0.214291 + 0.214291i
\(9\) 11.2672 + 24.5367i 0.417303 + 0.908768i
\(10\) −40.8945 10.0000i −1.29320 0.316228i
\(11\) 34.1375i 0.935712i −0.883805 0.467856i \(-0.845027\pi\)
0.883805 0.467856i \(-0.154973\pi\)
\(12\) 17.3301 27.0278i 0.416897 0.650187i
\(13\) 2.82109 + 2.82109i 0.0601869 + 0.0601869i 0.736560 0.676373i \(-0.236449\pi\)
−0.676373 + 0.736560i \(0.736449\pi\)
\(14\) −49.8323 −0.951303
\(15\) −58.0772 1.42827i −0.999698 0.0245851i
\(16\) 75.2524 1.17582
\(17\) 64.2384 + 64.2384i 0.916477 + 0.916477i 0.996771 0.0802942i \(-0.0255860\pi\)
−0.0802942 + 0.996771i \(0.525586\pi\)
\(18\) 35.3316 95.3316i 0.462652 1.24833i
\(19\) 19.0735i 0.230303i 0.993348 + 0.115151i \(0.0367353\pi\)
−0.993348 + 0.115151i \(0.963265\pi\)
\(20\) 35.8474 + 59.0536i 0.400786 + 0.660240i
\(21\) −67.1789 + 14.6869i −0.698078 + 0.152617i
\(22\) −90.8945 + 90.8945i −0.880854 + 0.880854i
\(23\) −51.4018 + 51.4018i −0.466001 + 0.466001i −0.900616 0.434616i \(-0.856884\pi\)
0.434616 + 0.900616i \(0.356884\pi\)
\(24\) 34.8094 7.61018i 0.296060 0.0647259i
\(25\) 57.6836 110.895i 0.461469 0.887156i
\(26\) 15.0229i 0.113317i
\(27\) 19.5337 138.930i 0.139232 0.990260i
\(28\) 57.8211 + 57.8211i 0.390256 + 0.390256i
\(29\) 50.5042 0.323393 0.161697 0.986841i \(-0.448303\pi\)
0.161697 + 0.986841i \(0.448303\pi\)
\(30\) 150.834 + 158.439i 0.917944 + 0.964232i
\(31\) −93.3673 −0.540944 −0.270472 0.962728i \(-0.587180\pi\)
−0.270472 + 0.962728i \(0.587180\pi\)
\(32\) −161.576 161.576i −0.892592 0.892592i
\(33\) −95.7458 + 149.324i −0.505067 + 0.787696i
\(34\) 342.083i 1.72549i
\(35\) 35.1454 143.725i 0.169733 0.694115i
\(36\) −151.610 + 69.6188i −0.701899 + 0.322309i
\(37\) −161.537 + 161.537i −0.717743 + 0.717743i −0.968142 0.250400i \(-0.919438\pi\)
0.250400 + 0.968142i \(0.419438\pi\)
\(38\) 50.7850 50.7850i 0.216800 0.216800i
\(39\) −4.42765 20.2524i −0.0181793 0.0831531i
\(40\) −18.2109 + 74.4727i −0.0719850 + 0.294379i
\(41\) 88.7935i 0.338225i 0.985597 + 0.169112i \(0.0540901\pi\)
−0.985597 + 0.169112i \(0.945910\pi\)
\(42\) 217.976 + 139.765i 0.800820 + 0.513482i
\(43\) 176.399 + 176.399i 0.625596 + 0.625596i 0.946957 0.321361i \(-0.104140\pi\)
−0.321361 + 0.946957i \(0.604140\pi\)
\(44\) 210.932 0.722710
\(45\) 250.035 + 169.137i 0.828290 + 0.560300i
\(46\) 273.725 0.877360
\(47\) 38.2843 + 38.2843i 0.118816 + 0.118816i 0.764015 0.645199i \(-0.223225\pi\)
−0.645199 + 0.764015i \(0.723225\pi\)
\(48\) −329.169 211.061i −0.989820 0.634668i
\(49\) 167.863i 0.489395i
\(50\) −448.857 + 141.680i −1.26956 + 0.400730i
\(51\) −100.821 461.162i −0.276819 1.26619i
\(52\) −17.4313 + 17.4313i −0.0464862 + 0.0464862i
\(53\) 344.569 344.569i 0.893022 0.893022i −0.101784 0.994806i \(-0.532455\pi\)
0.994806 + 0.101784i \(0.0324551\pi\)
\(54\) −421.925 + 317.904i −1.06327 + 0.801134i
\(55\) −198.051 326.262i −0.485549 0.799875i
\(56\) 90.7492i 0.216551i
\(57\) 53.4956 83.4310i 0.124310 0.193872i
\(58\) −134.473 134.473i −0.304433 0.304433i
\(59\) −421.133 −0.929268 −0.464634 0.885503i \(-0.653814\pi\)
−0.464634 + 0.885503i \(0.653814\pi\)
\(60\) 8.82514 358.854i 0.0189887 0.772130i
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) 248.600 + 248.600i 0.509229 + 0.509229i
\(63\) 335.046 + 124.174i 0.670030 + 0.248325i
\(64\) 258.409i 0.504704i
\(65\) 43.3287 + 10.5952i 0.0826811 + 0.0202181i
\(66\) 652.524 142.657i 1.21697 0.266059i
\(67\) 430.987 430.987i 0.785872 0.785872i −0.194943 0.980815i \(-0.562452\pi\)
0.980815 + 0.194943i \(0.0624521\pi\)
\(68\) −396.923 + 396.923i −0.707853 + 0.707853i
\(69\) 369.009 80.6742i 0.643818 0.140754i
\(70\) −476.262 + 289.105i −0.813202 + 0.493639i
\(71\) 733.866i 1.22667i 0.789822 + 0.613337i \(0.210173\pi\)
−0.789822 + 0.613337i \(0.789827\pi\)
\(72\) −173.607 64.3420i −0.284164 0.105316i
\(73\) −348.073 348.073i −0.558067 0.558067i 0.370690 0.928757i \(-0.379121\pi\)
−0.928757 + 0.370690i \(0.879121\pi\)
\(74\) 860.216 1.35133
\(75\) −563.347 + 323.288i −0.867329 + 0.497735i
\(76\) −117.853 −0.177877
\(77\) −319.452 319.452i −0.472792 0.472792i
\(78\) −42.1349 + 65.7131i −0.0611646 + 0.0953915i
\(79\) 588.019i 0.837434i 0.908117 + 0.418717i \(0.137520\pi\)
−0.908117 + 0.418717i \(0.862480\pi\)
\(80\) 719.209 436.582i 1.00512 0.610141i
\(81\) −475.102 + 552.919i −0.651717 + 0.758462i
\(82\) 236.422 236.422i 0.318395 0.318395i
\(83\) −217.997 + 217.997i −0.288293 + 0.288293i −0.836405 0.548112i \(-0.815347\pi\)
0.548112 + 0.836405i \(0.315347\pi\)
\(84\) −90.7492 415.092i −0.117876 0.539170i
\(85\) 986.629 + 241.262i 1.25900 + 0.307865i
\(86\) 939.362i 1.17784i
\(87\) −220.915 141.650i −0.272237 0.174557i
\(88\) 165.527 + 165.527i 0.200514 + 0.200514i
\(89\) −1272.00 −1.51497 −0.757483 0.652855i \(-0.773571\pi\)
−0.757483 + 0.652855i \(0.773571\pi\)
\(90\) −215.399 1116.09i −0.252278 1.30718i
\(91\) 52.7985 0.0608219
\(92\) −317.607 317.607i −0.359922 0.359922i
\(93\) 408.407 + 261.868i 0.455374 + 0.291984i
\(94\) 203.872i 0.223700i
\(95\) 110.656 + 182.291i 0.119506 + 0.196870i
\(96\) 253.591 + 1159.94i 0.269605 + 1.23319i
\(97\) −432.111 + 432.111i −0.452312 + 0.452312i −0.896121 0.443809i \(-0.853627\pi\)
0.443809 + 0.896121i \(0.353627\pi\)
\(98\) 446.951 446.951i 0.460703 0.460703i
\(99\) 837.622 384.633i 0.850345 0.390475i
\(100\) 685.207 + 356.422i 0.685207 + 0.356422i
\(101\) 1662.30i 1.63767i −0.574029 0.818835i \(-0.694620\pi\)
0.574029 0.818835i \(-0.305380\pi\)
\(102\) −959.444 + 1496.34i −0.931364 + 1.45254i
\(103\) −774.495 774.495i −0.740906 0.740906i 0.231847 0.972752i \(-0.425523\pi\)
−0.972752 + 0.231847i \(0.925523\pi\)
\(104\) −27.3581 −0.0257950
\(105\) −556.841 + 530.110i −0.517544 + 0.492700i
\(106\) −1834.90 −1.68133
\(107\) 1170.26 + 1170.26i 1.05732 + 1.05732i 0.998254 + 0.0590633i \(0.0188114\pi\)
0.0590633 + 0.998254i \(0.481189\pi\)
\(108\) 858.433 + 120.697i 0.764841 + 0.107537i
\(109\) 1264.60i 1.11125i −0.831432 0.555627i \(-0.812478\pi\)
0.831432 0.555627i \(-0.187522\pi\)
\(110\) −341.375 + 1396.04i −0.295898 + 1.21006i
\(111\) 1159.66 253.529i 0.991620 0.216792i
\(112\) 704.198 704.198i 0.594111 0.594111i
\(113\) −381.173 + 381.173i −0.317325 + 0.317325i −0.847739 0.530414i \(-0.822037\pi\)
0.530414 + 0.847739i \(0.322037\pi\)
\(114\) −364.581 + 79.7062i −0.299528 + 0.0654839i
\(115\) −193.051 + 789.473i −0.156540 + 0.640163i
\(116\) 312.061i 0.249777i
\(117\) −37.4346 + 101.006i −0.0295798 + 0.0798121i
\(118\) 1121.31 + 1121.31i 0.874787 + 0.874787i
\(119\) 1202.26 0.926145
\(120\) 288.533 274.682i 0.219494 0.208958i
\(121\) 165.633 0.124442
\(122\) −5.32521 5.32521i −0.00395182 0.00395182i
\(123\) 249.040 388.400i 0.182563 0.284722i
\(124\) 576.908i 0.417805i
\(125\) −92.0630 1394.51i −0.0658749 0.997828i
\(126\) −561.469 1222.72i −0.396981 0.864513i
\(127\) −439.588 + 439.588i −0.307142 + 0.307142i −0.843800 0.536658i \(-0.819687\pi\)
0.536658 + 0.843800i \(0.319687\pi\)
\(128\) −604.571 + 604.571i −0.417477 + 0.417477i
\(129\) −276.856 1266.35i −0.188959 0.864312i
\(130\) −87.1563 143.578i −0.0588009 0.0968664i
\(131\) 1399.28i 0.933247i 0.884456 + 0.466623i \(0.154530\pi\)
−0.884456 + 0.466623i \(0.845470\pi\)
\(132\) −922.659 591.605i −0.608388 0.390095i
\(133\) 178.486 + 178.486i 0.116366 + 0.116366i
\(134\) −2295.09 −1.47960
\(135\) −619.321 1441.12i −0.394834 0.918752i
\(136\) −622.964 −0.392785
\(137\) −1092.28 1092.28i −0.681169 0.681169i 0.279095 0.960264i \(-0.409966\pi\)
−0.960264 + 0.279095i \(0.909966\pi\)
\(138\) −1197.33 767.720i −0.738574 0.473570i
\(139\) 2498.43i 1.52456i 0.647245 + 0.762282i \(0.275921\pi\)
−0.647245 + 0.762282i \(0.724079\pi\)
\(140\) 888.066 + 217.160i 0.536109 + 0.131096i
\(141\) −60.0866 274.840i −0.0358880 0.164154i
\(142\) 1953.99 1953.99i 1.15476 1.15476i
\(143\) 96.3049 96.3049i 0.0563177 0.0563177i
\(144\) 847.881 + 1846.45i 0.490672 + 1.06855i
\(145\) 482.684 293.004i 0.276446 0.167811i
\(146\) 1853.56i 1.05070i
\(147\) 470.806 734.264i 0.264159 0.411980i
\(148\) −998.121 998.121i −0.554358 0.554358i
\(149\) 3570.40 1.96308 0.981538 0.191270i \(-0.0612605\pi\)
0.981538 + 0.191270i \(0.0612605\pi\)
\(150\) 2360.76 + 639.180i 1.28503 + 0.347926i
\(151\) 2687.14 1.44819 0.724094 0.689701i \(-0.242258\pi\)
0.724094 + 0.689701i \(0.242258\pi\)
\(152\) −92.4842 92.4842i −0.0493517 0.0493517i
\(153\) −852.415 + 2299.99i −0.450416 + 1.21531i
\(154\) 1701.15i 0.890146i
\(155\) −892.338 + 541.676i −0.462415 + 0.280700i
\(156\) 125.137 27.3581i 0.0642245 0.0140410i
\(157\) −1810.48 + 1810.48i −0.920333 + 0.920333i −0.997053 0.0767201i \(-0.975555\pi\)
0.0767201 + 0.997053i \(0.475555\pi\)
\(158\) 1565.66 1565.66i 0.788337 0.788337i
\(159\) −2473.63 + 540.795i −1.23378 + 0.269735i
\(160\) −2481.63 606.836i −1.22619 0.299841i
\(161\) 962.017i 0.470916i
\(162\) 2737.21 207.196i 1.32750 0.100487i
\(163\) −2679.06 2679.06i −1.28736 1.28736i −0.936382 0.350982i \(-0.885848\pi\)
−0.350982 0.936382i \(-0.614152\pi\)
\(164\) −548.647 −0.261232
\(165\) −48.7575 + 1982.61i −0.0230046 + 0.935430i
\(166\) 1160.88 0.542782
\(167\) −139.543 139.543i −0.0646597 0.0646597i 0.674037 0.738697i \(-0.264559\pi\)
−0.738697 + 0.674037i \(0.764559\pi\)
\(168\) 254.525 396.955i 0.116887 0.182296i
\(169\) 2181.08i 0.992755i
\(170\) −1984.62 3269.39i −0.895372 1.47500i
\(171\) −468.000 + 214.904i −0.209292 + 0.0961059i
\(172\) −1089.95 + 1089.95i −0.483188 + 0.483188i
\(173\) 881.613 881.613i 0.387444 0.387444i −0.486331 0.873775i \(-0.661665\pi\)
0.873775 + 0.486331i \(0.161665\pi\)
\(174\) 211.053 + 965.367i 0.0919532 + 0.420599i
\(175\) −497.938 1577.52i −0.215089 0.681426i
\(176\) 2568.93i 1.10023i
\(177\) 1842.12 + 1181.16i 0.782271 + 0.501588i
\(178\) 3386.84 + 3386.84i 1.42615 + 1.42615i
\(179\) −2512.87 −1.04928 −0.524638 0.851325i \(-0.675799\pi\)
−0.524638 + 0.851325i \(0.675799\pi\)
\(180\) −1045.08 + 1544.94i −0.432755 + 0.639741i
\(181\) 269.796 0.110795 0.0553973 0.998464i \(-0.482357\pi\)
0.0553973 + 0.998464i \(0.482357\pi\)
\(182\) −140.581 140.581i −0.0572560 0.0572560i
\(183\) −8.74839 5.60943i −0.00353388 0.00226591i
\(184\) 498.478i 0.199719i
\(185\) −606.687 + 2481.02i −0.241106 + 0.985990i
\(186\) −390.173 1784.68i −0.153811 0.703542i
\(187\) 2192.94 2192.94i 0.857559 0.857559i
\(188\) −236.555 + 236.555i −0.0917690 + 0.0917690i
\(189\) −1117.29 1482.87i −0.430003 0.570703i
\(190\) 190.735 780.000i 0.0728281 0.297827i
\(191\) 2420.22i 0.916864i −0.888729 0.458432i \(-0.848411\pi\)
0.888729 0.458432i \(-0.151589\pi\)
\(192\) 724.762 1130.33i 0.272423 0.424867i
\(193\) 1965.28 + 1965.28i 0.732973 + 0.732973i 0.971208 0.238234i \(-0.0765686\pi\)
−0.238234 + 0.971208i \(0.576569\pi\)
\(194\) 2301.08 0.851588
\(195\) −159.812 167.870i −0.0586890 0.0616484i
\(196\) −1037.21 −0.377991
\(197\) 832.602 + 832.602i 0.301119 + 0.301119i 0.841452 0.540333i \(-0.181702\pi\)
−0.540333 + 0.841452i \(0.681702\pi\)
\(198\) −3254.38 1206.13i −1.16807 0.432909i
\(199\) 1540.54i 0.548775i 0.961619 + 0.274387i \(0.0884750\pi\)
−0.961619 + 0.274387i \(0.911525\pi\)
\(200\) 258.011 + 817.409i 0.0912208 + 0.288998i
\(201\) −3094.02 + 676.426i −1.08575 + 0.237370i
\(202\) −4426.04 + 4426.04i −1.54166 + 1.54166i
\(203\) 472.609 472.609i 0.163402 0.163402i
\(204\) 2849.48 622.964i 0.977957 0.213805i
\(205\) 515.142 + 848.625i 0.175508 + 0.289125i
\(206\) 4124.35i 1.39494i
\(207\) −1840.38 682.079i −0.617949 0.229023i
\(208\) 212.294 + 212.294i 0.0707689 + 0.0707689i
\(209\) 651.119 0.215497
\(210\) 2894.12 + 71.1739i 0.951015 + 0.0233879i
\(211\) −10.9380 −0.00356874 −0.00178437 0.999998i \(-0.500568\pi\)
−0.00178437 + 0.999998i \(0.500568\pi\)
\(212\) 2129.06 + 2129.06i 0.689738 + 0.689738i
\(213\) 2058.28 3210.07i 0.662118 1.03263i
\(214\) 6231.86i 1.99066i
\(215\) 2709.29 + 662.507i 0.859405 + 0.210152i
\(216\) 578.932 + 768.364i 0.182367 + 0.242039i
\(217\) −873.714 + 873.714i −0.273325 + 0.273325i
\(218\) −3367.13 + 3367.13i −1.04610 + 1.04610i
\(219\) 546.295 + 2498.79i 0.168563 + 0.771016i
\(220\) 2015.94 1223.74i 0.617794 0.375020i
\(221\) 362.445i 0.110320i
\(222\) −3762.75 2412.66i −1.13757 0.729401i
\(223\) 831.512 + 831.512i 0.249696 + 0.249696i 0.820846 0.571150i \(-0.193503\pi\)
−0.571150 + 0.820846i \(0.693503\pi\)
\(224\) −3024.00 −0.902008
\(225\) 3370.92 + 165.900i 0.998791 + 0.0491554i
\(226\) 2029.83 0.597443
\(227\) −3441.18 3441.18i −1.00616 1.00616i −0.999981 0.00618314i \(-0.998032\pi\)
−0.00618314 0.999981i \(-0.501968\pi\)
\(228\) 515.512 + 330.544i 0.149740 + 0.0960124i
\(229\) 1680.38i 0.484903i −0.970164 0.242451i \(-0.922049\pi\)
0.970164 0.242451i \(-0.0779515\pi\)
\(230\) 2616.07 1588.03i 0.749994 0.455269i
\(231\) 501.375 + 2293.32i 0.142805 + 0.653200i
\(232\) −244.887 + 244.887i −0.0693001 + 0.0693001i
\(233\) −2106.74 + 2106.74i −0.592348 + 0.592348i −0.938265 0.345917i \(-0.887568\pi\)
0.345917 + 0.938265i \(0.387568\pi\)
\(234\) 368.613 169.265i 0.102978 0.0472873i
\(235\) 588.004 + 143.785i 0.163222 + 0.0399129i
\(236\) 2602.14i 0.717733i
\(237\) 1649.22 2572.11i 0.452019 0.704964i
\(238\) −3201.15 3201.15i −0.871847 0.871847i
\(239\) 261.125 0.0706728 0.0353364 0.999375i \(-0.488750\pi\)
0.0353364 + 0.999375i \(0.488750\pi\)
\(240\) −4370.45 107.481i −1.17546 0.0289077i
\(241\) −6001.45 −1.60410 −0.802048 0.597259i \(-0.796256\pi\)
−0.802048 + 0.597259i \(0.796256\pi\)
\(242\) −441.014 441.014i −0.117147 0.117147i
\(243\) 3628.97 1086.05i 0.958018 0.286709i
\(244\) 12.3578i 0.00324233i
\(245\) 973.866 + 1604.31i 0.253951 + 0.418350i
\(246\) −1697.25 + 371.060i −0.439889 + 0.0961704i
\(247\) −53.8080 + 53.8080i −0.0138612 + 0.0138612i
\(248\) 452.723 452.723i 0.115919 0.115919i
\(249\) 1564.98 342.143i 0.398300 0.0870781i
\(250\) −3467.89 + 3958.15i −0.877315 + 1.00134i
\(251\) 3044.59i 0.765630i −0.923825 0.382815i \(-0.874955\pi\)
0.923825 0.382815i \(-0.125045\pi\)
\(252\) −767.260 + 2070.22i −0.191797 + 0.517506i
\(253\) 1754.73 + 1754.73i 0.436042 + 0.436042i
\(254\) 2340.89 0.578271
\(255\) −3639.04 3822.54i −0.893668 0.938732i
\(256\) 5286.74 1.29071
\(257\) 946.317 + 946.317i 0.229687 + 0.229687i 0.812562 0.582875i \(-0.198072\pi\)
−0.582875 + 0.812562i \(0.698072\pi\)
\(258\) −2634.64 + 4108.95i −0.635758 + 0.991521i
\(259\) 3023.26i 0.725314i
\(260\) −65.4670 + 267.724i −0.0156157 + 0.0638598i
\(261\) 569.040 + 1239.21i 0.134953 + 0.293889i
\(262\) 3725.72 3725.72i 0.878532 0.878532i
\(263\) −67.0257 + 67.0257i −0.0157148 + 0.0157148i −0.714921 0.699206i \(-0.753537\pi\)
0.699206 + 0.714921i \(0.253537\pi\)
\(264\) −259.792 1188.31i −0.0605648 0.277027i
\(265\) 1294.11 5292.18i 0.299986 1.22678i
\(266\) 950.474i 0.219088i
\(267\) 5563.99 + 3567.60i 1.27532 + 0.817729i
\(268\) 2663.03 + 2663.03i 0.606979 + 0.606979i
\(269\) −2658.15 −0.602492 −0.301246 0.953546i \(-0.597403\pi\)
−0.301246 + 0.953546i \(0.597403\pi\)
\(270\) −2188.12 + 5486.13i −0.493202 + 1.23657i
\(271\) 145.673 0.0326530 0.0163265 0.999867i \(-0.494803\pi\)
0.0163265 + 0.999867i \(0.494803\pi\)
\(272\) 4834.09 + 4834.09i 1.07761 + 1.07761i
\(273\) −230.951 148.085i −0.0512007 0.0328296i
\(274\) 5816.64i 1.28247i
\(275\) −3785.66 1969.17i −0.830123 0.431802i
\(276\) 498.478 + 2280.07i 0.108713 + 0.497261i
\(277\) −1074.57 + 1074.57i −0.233085 + 0.233085i −0.813979 0.580894i \(-0.802703\pi\)
0.580894 + 0.813979i \(0.302703\pi\)
\(278\) 6652.34 6652.34i 1.43518 1.43518i
\(279\) −1051.98 2290.93i −0.225737 0.491592i
\(280\) 526.488 + 867.316i 0.112370 + 0.185115i
\(281\) 2020.29i 0.428898i −0.976735 0.214449i \(-0.931204\pi\)
0.976735 0.214449i \(-0.0687956\pi\)
\(282\) −571.802 + 891.776i −0.120746 + 0.188314i
\(283\) −2400.34 2400.34i −0.504189 0.504189i 0.408548 0.912737i \(-0.366035\pi\)
−0.912737 + 0.408548i \(0.866035\pi\)
\(284\) −4534.49 −0.947438
\(285\) 27.2420 1107.73i 0.00566202 0.230233i
\(286\) −512.844 −0.106032
\(287\) 830.913 + 830.913i 0.170896 + 0.170896i
\(288\) 2144.05 5785.06i 0.438678 1.18364i
\(289\) 3340.15i 0.679860i
\(290\) −2065.35 505.042i −0.418212 0.102266i
\(291\) 3102.09 678.191i 0.624906 0.136619i
\(292\) 2150.71 2150.71i 0.431031 0.431031i
\(293\) −2533.13 + 2533.13i −0.505075 + 0.505075i −0.913011 0.407936i \(-0.866249\pi\)
0.407936 + 0.913011i \(0.366249\pi\)
\(294\) −3208.62 + 701.482i −0.636499 + 0.139154i
\(295\) −4024.89 + 2443.23i −0.794366 + 0.482204i
\(296\) 1566.53i 0.307611i
\(297\) −4742.71 666.830i −0.926598 0.130281i
\(298\) −9506.54 9506.54i −1.84798 1.84798i
\(299\) −290.018 −0.0560943
\(300\) −1997.57 3480.87i −0.384432 0.669893i
\(301\) 3301.42 0.632196
\(302\) −7154.79 7154.79i −1.36328 1.36328i
\(303\) −4662.27 + 7271.21i −0.883961 + 1.37861i
\(304\) 1435.32i 0.270794i
\(305\) 19.1146 11.6031i 0.00358852 0.00217834i
\(306\) 8393.59 3854.31i 1.56807 0.720052i
\(307\) 3159.93 3159.93i 0.587449 0.587449i −0.349491 0.936940i \(-0.613645\pi\)
0.936940 + 0.349491i \(0.113645\pi\)
\(308\) 1973.87 1973.87i 0.365167 0.365167i
\(309\) 1215.56 + 5560.03i 0.223788 + 1.02362i
\(310\) 3818.21 + 933.673i 0.699548 + 0.171061i
\(311\) 7206.19i 1.31391i 0.753931 + 0.656954i \(0.228155\pi\)
−0.753931 + 0.656954i \(0.771845\pi\)
\(312\) 119.670 + 76.7315i 0.0217146 + 0.0139233i
\(313\) 2029.31 + 2029.31i 0.366464 + 0.366464i 0.866186 0.499722i \(-0.166564\pi\)
−0.499722 + 0.866186i \(0.666564\pi\)
\(314\) 9641.19 1.73275
\(315\) 3922.54 757.026i 0.701619 0.135408i
\(316\) −3633.31 −0.646804
\(317\) 689.223 + 689.223i 0.122116 + 0.122116i 0.765524 0.643408i \(-0.222480\pi\)
−0.643408 + 0.765524i \(0.722480\pi\)
\(318\) 8026.21 + 5146.37i 1.41537 + 0.907528i
\(319\) 1724.09i 0.302603i
\(320\) 1499.18 + 2469.69i 0.261895 + 0.431437i
\(321\) −1836.70 8401.16i −0.319360 1.46077i
\(322\) 2561.47 2561.47i 0.443308 0.443308i
\(323\) −1225.25 + 1225.25i −0.211067 + 0.211067i
\(324\) −3416.44 2935.61i −0.585809 0.503363i
\(325\) 475.574 150.113i 0.0811696 0.0256208i
\(326\) 14266.6i 2.42378i
\(327\) −3546.84 + 5531.60i −0.599818 + 0.935469i
\(328\) −430.546 430.546i −0.0724784 0.0724784i
\(329\) 716.516 0.120069
\(330\) 5408.72 5149.08i 0.902243 0.858932i
\(331\) −8226.53 −1.36608 −0.683038 0.730383i \(-0.739342\pi\)
−0.683038 + 0.730383i \(0.739342\pi\)
\(332\) −1346.99 1346.99i −0.222667 0.222667i
\(333\) −5783.64 2143.52i −0.951777 0.352745i
\(334\) 743.096i 0.121738i
\(335\) 1618.67 6619.47i 0.263992 1.07958i
\(336\) −5055.37 + 1105.23i −0.820813 + 0.179449i
\(337\) 1777.34 1777.34i 0.287294 0.287294i −0.548715 0.836009i \(-0.684883\pi\)
0.836009 + 0.548715i \(0.184883\pi\)
\(338\) −5807.36 + 5807.36i −0.934552 + 0.934552i
\(339\) 2736.41 598.245i 0.438411 0.0958472i
\(340\) −1490.73 + 6096.29i −0.237784 + 0.972405i
\(341\) 3187.32i 0.506168i
\(342\) 1818.30 + 673.895i 0.287493 + 0.106550i
\(343\) 4780.56 + 4780.56i 0.752554 + 0.752554i
\(344\) −1710.66 −0.268119
\(345\) 3058.69 2911.86i 0.477316 0.454403i
\(346\) −4694.77 −0.729458
\(347\) 1715.22 + 1715.22i 0.265354 + 0.265354i 0.827225 0.561871i \(-0.189918\pi\)
−0.561871 + 0.827225i \(0.689918\pi\)
\(348\) 875.242 1365.02i 0.134821 0.210266i
\(349\) 8603.96i 1.31965i −0.751417 0.659827i \(-0.770629\pi\)
0.751417 0.659827i \(-0.229371\pi\)
\(350\) −2874.51 + 5526.13i −0.438997 + 0.843954i
\(351\) 447.039 336.827i 0.0679806 0.0512208i
\(352\) −5515.81 + 5515.81i −0.835209 + 0.835209i
\(353\) 5425.13 5425.13i 0.817990 0.817990i −0.167827 0.985816i \(-0.553675\pi\)
0.985816 + 0.167827i \(0.0536750\pi\)
\(354\) −1759.87 8049.77i −0.264227 1.20859i
\(355\) 4257.57 + 7013.77i 0.636531 + 1.04860i
\(356\) 7859.58i 1.17010i
\(357\) −5258.93 3372.00i −0.779642 0.499903i
\(358\) 6690.76 + 6690.76i 0.987759 + 0.987759i
\(359\) 11418.9 1.67874 0.839370 0.543560i \(-0.182924\pi\)
0.839370 + 0.543560i \(0.182924\pi\)
\(360\) −2032.50 + 392.260i −0.297562 + 0.0574276i
\(361\) 6495.20 0.946961
\(362\) −718.361 718.361i −0.104299 0.104299i
\(363\) −724.510 464.552i −0.104757 0.0671699i
\(364\) 326.237i 0.0469766i
\(365\) −5346.01 1307.27i −0.766638 0.187467i
\(366\) 8.35782 + 38.2292i 0.00119363 + 0.00545976i
\(367\) 6554.73 6554.73i 0.932299 0.932299i −0.0655499 0.997849i \(-0.520880\pi\)
0.997849 + 0.0655499i \(0.0208802\pi\)
\(368\) −3868.11 + 3868.11i −0.547932 + 0.547932i
\(369\) −2178.70 + 1000.45i −0.307368 + 0.141142i
\(370\) 8221.34 4990.60i 1.15515 0.701214i
\(371\) 6448.83i 0.902443i
\(372\) −1618.06 + 2523.51i −0.225518 + 0.351714i
\(373\) −5967.46 5967.46i −0.828374 0.828374i 0.158918 0.987292i \(-0.449199\pi\)
−0.987292 + 0.158918i \(0.949199\pi\)
\(374\) −11677.8 −1.61456
\(375\) −3508.49 + 6358.06i −0.483140 + 0.875543i
\(376\) −371.270 −0.0509222
\(377\) 142.477 + 142.477i 0.0194640 + 0.0194640i
\(378\) −973.408 + 6923.18i −0.132452 + 0.942037i
\(379\) 1680.48i 0.227758i −0.993495 0.113879i \(-0.963672\pi\)
0.993495 0.113879i \(-0.0363276\pi\)
\(380\) −1126.36 + 683.733i −0.152055 + 0.0923020i
\(381\) 3155.76 689.925i 0.424342 0.0927715i
\(382\) −6444.09 + 6444.09i −0.863110 + 0.863110i
\(383\) 7493.42 7493.42i 0.999728 0.999728i −0.000271480 1.00000i \(-0.500086\pi\)
1.00000 0.000271480i \(8.64148e-5\pi\)
\(384\) 4340.16 948.864i 0.576779 0.126098i
\(385\) −4906.42 1199.77i −0.649492 0.158821i
\(386\) 10465.5i 1.38000i
\(387\) −2340.74 + 6315.78i −0.307459 + 0.829584i
\(388\) −2669.98 2669.98i −0.349349 0.349349i
\(389\) −7966.97 −1.03841 −0.519205 0.854650i \(-0.673772\pi\)
−0.519205 + 0.854650i \(0.673772\pi\)
\(390\) −21.4567 + 872.487i −0.00278591 + 0.113282i
\(391\) −6603.94 −0.854158
\(392\) −813.939 813.939i −0.104873 0.104873i
\(393\) 3924.57 6120.71i 0.503736 0.785620i
\(394\) 4433.78i 0.566930i
\(395\) 3411.43 + 5619.87i 0.434551 + 0.715864i
\(396\) 2376.61 + 5175.59i 0.301589 + 0.656776i
\(397\) −8188.88 + 8188.88i −1.03523 + 1.03523i −0.0358786 + 0.999356i \(0.511423\pi\)
−0.999356 + 0.0358786i \(0.988577\pi\)
\(398\) 4101.85 4101.85i 0.516601 0.516601i
\(399\) −280.130 1281.33i −0.0351480 0.160769i
\(400\) 4340.83 8345.08i 0.542604 1.04313i
\(401\) 5167.66i 0.643542i 0.946817 + 0.321771i \(0.104278\pi\)
−0.946817 + 0.321771i \(0.895722\pi\)
\(402\) 10039.2 + 6437.08i 1.24555 + 0.798638i
\(403\) −263.398 263.398i −0.0325577 0.0325577i
\(404\) 10271.2 1.26488
\(405\) −1332.89 + 8040.74i −0.163535 + 0.986537i
\(406\) −2516.74 −0.307645
\(407\) 5514.46 + 5514.46i 0.671601 + 0.671601i
\(408\) 2724.97 + 1747.24i 0.330652 + 0.212012i
\(409\) 8514.82i 1.02941i 0.857366 + 0.514707i \(0.172099\pi\)
−0.857366 + 0.514707i \(0.827901\pi\)
\(410\) 887.935 3631.17i 0.106956 0.437392i
\(411\) 1714.32 + 7841.41i 0.205745 + 0.941090i
\(412\) 4785.54 4785.54i 0.572249 0.572249i
\(413\) −3940.88 + 3940.88i −0.469535 + 0.469535i
\(414\) 3084.11 + 6716.32i 0.366125 + 0.797316i
\(415\) −818.738 + 3348.19i −0.0968440 + 0.396039i
\(416\) 911.644i 0.107445i
\(417\) 7007.39 10928.6i 0.822910 1.28340i
\(418\) −1733.67 1733.67i −0.202863 0.202863i
\(419\) −11939.7 −1.39211 −0.696053 0.717990i \(-0.745062\pi\)
−0.696053 + 0.717990i \(0.745062\pi\)
\(420\) −3275.50 3440.67i −0.380543 0.399732i
\(421\) 10873.3 1.25875 0.629373 0.777103i \(-0.283312\pi\)
0.629373 + 0.777103i \(0.283312\pi\)
\(422\) 29.1236 + 29.1236i 0.00335951 + 0.00335951i
\(423\) −508.016 + 1370.73i −0.0583938 + 0.157558i
\(424\) 3341.52i 0.382733i
\(425\) 10829.2 3418.19i 1.23598 0.390133i
\(426\) −14027.5 + 3066.76i −1.59539 + 0.348791i
\(427\) 18.7156 18.7156i 0.00212111 0.00212111i
\(428\) −7230.91 + 7230.91i −0.816634 + 0.816634i
\(429\) −691.364 + 151.149i −0.0778074 + 0.0170106i
\(430\) −5449.77 8977.76i −0.611189 1.00685i
\(431\) 7603.48i 0.849760i −0.905250 0.424880i \(-0.860316\pi\)
0.905250 0.424880i \(-0.139684\pi\)
\(432\) 1469.95 10454.8i 0.163711 1.16437i
\(433\) 4681.19 + 4681.19i 0.519547 + 0.519547i 0.917434 0.397887i \(-0.130257\pi\)
−0.397887 + 0.917434i \(0.630257\pi\)
\(434\) 4652.70 0.514601
\(435\) −2933.14 72.1336i −0.323295 0.00795067i
\(436\) 7813.84 0.858292
\(437\) −980.409 980.409i −0.107321 0.107321i
\(438\) 5198.71 8107.85i 0.567133 0.884493i
\(439\) 8608.08i 0.935857i −0.883766 0.467929i \(-0.845000\pi\)
0.883766 0.467929i \(-0.155000\pi\)
\(440\) 2542.31 + 621.675i 0.275454 + 0.0673572i
\(441\) −4118.80 + 1891.34i −0.444746 + 0.204226i
\(442\) 965.047 965.047i 0.103852 0.103852i
\(443\) −6466.81 + 6466.81i −0.693561 + 0.693561i −0.963014 0.269453i \(-0.913157\pi\)
0.269453 + 0.963014i \(0.413157\pi\)
\(444\) 1566.53 + 7165.42i 0.167442 + 0.765891i
\(445\) −12156.9 + 7379.61i −1.29504 + 0.786128i
\(446\) 4427.97i 0.470113i
\(447\) −15617.6 10013.9i −1.65254 1.05960i
\(448\) 2418.14 + 2418.14i 0.255014 + 0.255014i
\(449\) −356.370 −0.0374569 −0.0187284 0.999825i \(-0.505962\pi\)
−0.0187284 + 0.999825i \(0.505962\pi\)
\(450\) −8533.70 9417.15i −0.893961 0.986508i
\(451\) 3031.19 0.316481
\(452\) −2355.24 2355.24i −0.245091 0.245091i
\(453\) −11754.1 7536.66i −1.21911 0.781685i
\(454\) 18325.0i 1.89435i
\(455\) 504.611 306.314i 0.0519923 0.0315609i
\(456\) 145.152 + 663.935i 0.0149065 + 0.0681834i
\(457\) 1512.80 1512.80i 0.154849 0.154849i −0.625431 0.780280i \(-0.715077\pi\)
0.780280 + 0.625431i \(0.215077\pi\)
\(458\) −4474.19 + 4474.19i −0.456474 + 0.456474i
\(459\) 10179.4 7669.81i 1.03515 0.779948i
\(460\) −4878.08 1192.84i −0.494438 0.120906i
\(461\) 13307.9i 1.34449i 0.740327 + 0.672246i \(0.234670\pi\)
−0.740327 + 0.672246i \(0.765330\pi\)
\(462\) 4771.23 7441.16i 0.480472 0.749338i
\(463\) −1237.43 1237.43i −0.124208 0.124208i 0.642270 0.766478i \(-0.277993\pi\)
−0.766478 + 0.642270i \(0.777993\pi\)
\(464\) 3800.56 0.380251
\(465\) 5422.51 + 133.353i 0.540780 + 0.0132992i
\(466\) 11218.8 1.11524
\(467\) −8201.87 8201.87i −0.812713 0.812713i 0.172327 0.985040i \(-0.444872\pi\)
−0.985040 + 0.172327i \(0.944872\pi\)
\(468\) −624.107 231.305i −0.0616439 0.0228463i
\(469\) 8066.19i 0.794162i
\(470\) −1182.78 1948.46i −0.116080 0.191225i
\(471\) 12997.3 2841.52i 1.27151 0.277984i
\(472\) 2042.01 2042.01i 0.199133 0.199133i
\(473\) 6021.83 6021.83i 0.585378 0.585378i
\(474\) −11239.7 + 2457.28i −1.08915 + 0.238115i
\(475\) 2115.14 + 1100.23i 0.204314 + 0.106278i
\(476\) 7428.67i 0.715321i
\(477\) 12336.9 + 4572.28i 1.18421 + 0.438889i
\(478\) −695.273 695.273i −0.0665294 0.0665294i
\(479\) −11419.1 −1.08926 −0.544629 0.838677i \(-0.683329\pi\)
−0.544629 + 0.838677i \(0.683329\pi\)
\(480\) 9153.13 + 9614.68i 0.870378 + 0.914267i
\(481\) −911.420 −0.0863974
\(482\) 15979.5 + 15979.5i 1.51005 + 1.51005i
\(483\) 2698.18 4208.05i 0.254185 0.396424i
\(484\) 1023.43i 0.0961147i
\(485\) −1622.89 + 6636.73i −0.151942 + 0.621358i
\(486\) −12554.2 6770.77i −1.17175 0.631952i
\(487\) −6066.93 + 6066.93i −0.564515 + 0.564515i −0.930587 0.366071i \(-0.880703\pi\)
0.366071 + 0.930587i \(0.380703\pi\)
\(488\) −9.69769 + 9.69769i −0.000899577 + 0.000899577i
\(489\) 4204.74 + 19232.7i 0.388845 + 1.77860i
\(490\) 1678.63 6864.66i 0.154760 0.632885i
\(491\) 8978.88i 0.825277i 0.910895 + 0.412639i \(0.135393\pi\)
−0.910895 + 0.412639i \(0.864607\pi\)
\(492\) 2399.89 + 1538.80i 0.219909 + 0.141005i
\(493\) 3244.31 + 3244.31i 0.296382 + 0.296382i
\(494\) 286.538 0.0260971
\(495\) 5773.92 8535.57i 0.524280 0.775041i
\(496\) −7026.11 −0.636051
\(497\) 6867.38 + 6867.38i 0.619807 + 0.619807i
\(498\) −5077.92 3255.94i −0.456922 0.292976i
\(499\) 7674.34i 0.688478i −0.938882 0.344239i \(-0.888137\pi\)
0.938882 0.344239i \(-0.111863\pi\)
\(500\) 8616.53 568.849i 0.770686 0.0508794i
\(501\) 219.010 + 1001.77i 0.0195303 + 0.0893326i
\(502\) −8106.54 + 8106.54i −0.720743 + 0.720743i
\(503\) 4044.23 4044.23i 0.358496 0.358496i −0.504762 0.863258i \(-0.668420\pi\)
0.863258 + 0.504762i \(0.168420\pi\)
\(504\) −2226.69 + 1022.49i −0.196795 + 0.0903674i
\(505\) −9643.93 15887.1i −0.849800 1.39993i
\(506\) 9344.28i 0.820957i
\(507\) −6117.31 + 9540.48i −0.535857 + 0.835715i
\(508\) −2716.17 2716.17i −0.237226 0.237226i
\(509\) 12532.5 1.09134 0.545672 0.837999i \(-0.316275\pi\)
0.545672 + 0.837999i \(0.316275\pi\)
\(510\) −488.586 + 19867.2i −0.0424215 + 1.72497i
\(511\) −6514.42 −0.563955
\(512\) −9239.91 9239.91i −0.797559 0.797559i
\(513\) 2649.87 + 372.574i 0.228059 + 0.0320654i
\(514\) 5039.33i 0.432443i
\(515\) −11895.4 2908.79i −1.01781 0.248887i
\(516\) 7824.69 1710.66i 0.667563 0.145945i
\(517\) 1306.93 1306.93i 0.111177 0.111177i
\(518\) 8049.75 8049.75i 0.682791 0.682791i
\(519\) −6329.02 + 1383.68i −0.535285 + 0.117026i
\(520\) −261.469 + 158.720i −0.0220503 + 0.0133852i
\(521\) 19201.8i 1.61468i −0.590089 0.807338i \(-0.700907\pi\)
0.590089 0.807338i \(-0.299093\pi\)
\(522\) 1784.39 4814.65i 0.149618 0.403700i
\(523\) 5472.69 + 5472.69i 0.457560 + 0.457560i 0.897854 0.440294i \(-0.145126\pi\)
−0.440294 + 0.897854i \(0.645126\pi\)
\(524\) −8646.00 −0.720806
\(525\) −2246.42 + 8296.97i −0.186747 + 0.689732i
\(526\) 356.926 0.0295869
\(527\) −5997.77 5997.77i −0.495762 0.495762i
\(528\) −7205.10 + 11237.0i −0.593867 + 0.926187i
\(529\) 6882.71i 0.565687i
\(530\) −17536.7 + 10645.3i −1.43725 + 0.872457i
\(531\) −4744.97 10333.2i −0.387786 0.844488i
\(532\) −1102.85 + 1102.85i −0.0898769 + 0.0898769i
\(533\) −250.495 + 250.495i −0.0203567 + 0.0203567i
\(534\) −5315.58 24313.8i −0.430763 1.97034i
\(535\) 17973.8 + 4395.16i 1.45248 + 0.355176i
\(536\) 4179.58i 0.336810i
\(537\) 10991.8 + 7047.87i 0.883295 + 0.566365i
\(538\) 7077.60 + 7077.60i 0.567169 + 0.567169i
\(539\) 5730.40 0.457933
\(540\) 8904.53 3826.73i 0.709611 0.304956i
\(541\) 12778.2 1.01548 0.507741 0.861510i \(-0.330481\pi\)
0.507741 + 0.861510i \(0.330481\pi\)
\(542\) −387.868 387.868i −0.0307387 0.0307387i
\(543\) −1180.14 756.702i −0.0932684 0.0598033i
\(544\) 20758.8i 1.63608i
\(545\) −7336.66 12086.1i −0.576638 0.949933i
\(546\) 220.640 + 1009.22i 0.0172940 + 0.0791038i
\(547\) −2414.12 + 2414.12i −0.188702 + 0.188702i −0.795135 0.606433i \(-0.792600\pi\)
0.606433 + 0.795135i \(0.292600\pi\)
\(548\) 6749.12 6749.12i 0.526110 0.526110i
\(549\) 22.5343 + 49.0735i 0.00175181 + 0.00381494i
\(550\) 4836.58 + 15322.8i 0.374968 + 1.18794i
\(551\) 963.290i 0.0744783i
\(552\) −1398.09 + 2180.44i −0.107802 + 0.168126i
\(553\) 5502.57 + 5502.57i 0.423134 + 0.423134i
\(554\) 5722.30 0.438840
\(555\) 9612.32 9150.88i 0.735171 0.699880i
\(556\) −15437.6 −1.17752
\(557\) −5573.05 5573.05i −0.423946 0.423946i 0.462614 0.886560i \(-0.346912\pi\)
−0.886560 + 0.462614i \(0.846912\pi\)
\(558\) −3298.81 + 8900.85i −0.250268 + 0.675274i
\(559\) 995.277i 0.0753054i
\(560\) 2644.77 10815.7i 0.199575 0.816153i
\(561\) −15742.9 + 3441.78i −1.18479 + 0.259023i
\(562\) −5379.23 + 5379.23i −0.403753 + 0.403753i
\(563\) −3488.75 + 3488.75i −0.261160 + 0.261160i −0.825525 0.564365i \(-0.809121\pi\)
0.564365 + 0.825525i \(0.309121\pi\)
\(564\) 1698.21 371.270i 0.126786 0.0277186i
\(565\) −1431.58 + 5854.39i −0.106597 + 0.435922i
\(566\) 12782.3i 0.949260i
\(567\) 728.199 + 9620.03i 0.0539356 + 0.712528i
\(568\) −3558.40 3558.40i −0.262865 0.262865i
\(569\) 4924.15 0.362796 0.181398 0.983410i \(-0.441938\pi\)
0.181398 + 0.983410i \(0.441938\pi\)
\(570\) −3021.99 + 2876.92i −0.222065 + 0.211405i
\(571\) −5642.12 −0.413512 −0.206756 0.978393i \(-0.566291\pi\)
−0.206756 + 0.978393i \(0.566291\pi\)
\(572\) 595.059 + 595.059i 0.0434977 + 0.0434977i
\(573\) −6788.02 + 10586.5i −0.494893 + 0.771829i
\(574\) 4424.78i 0.321754i
\(575\) 2735.14 + 8665.22i 0.198371 + 0.628460i
\(576\) −6340.50 + 2911.53i −0.458659 + 0.210614i
\(577\) 8505.39 8505.39i 0.613663 0.613663i −0.330235 0.943899i \(-0.607128\pi\)
0.943899 + 0.330235i \(0.107128\pi\)
\(578\) 8893.50 8893.50i 0.640002 0.640002i
\(579\) −3084.47 14108.6i −0.221392 1.01266i
\(580\) 1810.44 + 2982.46i 0.129611 + 0.213517i
\(581\) 4079.96i 0.291334i
\(582\) −10065.4 6453.87i −0.716879 0.459659i
\(583\) −11762.7 11762.7i −0.835612 0.835612i
\(584\) 3375.51 0.239177
\(585\) 228.220 + 1182.52i 0.0161295 + 0.0835750i
\(586\) 13489.4 0.950927
\(587\) 1464.72 + 1464.72i 0.102990 + 0.102990i 0.756724 0.653734i \(-0.226798\pi\)
−0.653734 + 0.756724i \(0.726798\pi\)
\(588\) 4536.95 + 2909.07i 0.318198 + 0.204027i
\(589\) 1780.84i 0.124581i
\(590\) 17222.0 + 4211.33i 1.20173 + 0.293860i
\(591\) −1306.75 5977.17i −0.0909521 0.416020i
\(592\) −12156.0 + 12156.0i −0.843935 + 0.843935i
\(593\) −18086.4 + 18086.4i −1.25248 + 1.25248i −0.297871 + 0.954606i \(0.596277\pi\)
−0.954606 + 0.297871i \(0.903723\pi\)
\(594\) 10852.4 + 14403.4i 0.749631 + 0.994917i
\(595\) 11490.4 6975.01i 0.791697 0.480584i
\(596\) 22061.1i 1.51621i
\(597\) 4320.78 6738.63i 0.296211 0.461966i
\(598\) 772.204 + 772.204i 0.0528056 + 0.0528056i
\(599\) 21899.3 1.49379 0.746897 0.664940i \(-0.231543\pi\)
0.746897 + 0.664940i \(0.231543\pi\)
\(600\) 1164.01 4299.16i 0.0792006 0.292520i
\(601\) −12431.8 −0.843766 −0.421883 0.906650i \(-0.638631\pi\)
−0.421883 + 0.906650i \(0.638631\pi\)
\(602\) −8790.38 8790.38i −0.595132 0.595132i
\(603\) 15431.0 + 5719.00i 1.04212 + 0.386229i
\(604\) 16603.6i 1.11853i
\(605\) 1583.00 960.930i 0.106377 0.0645741i
\(606\) 31774.1 6946.59i 2.12993 0.465653i
\(607\) 8237.79 8237.79i 0.550843 0.550843i −0.375841 0.926684i \(-0.622646\pi\)
0.926684 + 0.375841i \(0.122646\pi\)
\(608\) 3081.82 3081.82i 0.205566 0.205566i
\(609\) −3392.82 + 741.752i −0.225754 + 0.0493552i
\(610\) −81.7891 20.0000i −0.00542876 0.00132750i
\(611\) 216.007i 0.0143023i
\(612\) −14211.4 5267.00i −0.938663 0.347885i
\(613\) −8913.02 8913.02i −0.587265 0.587265i 0.349625 0.936890i \(-0.386309\pi\)
−0.936890 + 0.349625i \(0.886309\pi\)
\(614\) −16827.3 −1.10602
\(615\) 126.821 5156.88i 0.00831530 0.338123i
\(616\) 3097.95 0.202630
\(617\) −1378.18 1378.18i −0.0899244 0.0899244i 0.660714 0.750638i \(-0.270254\pi\)
−0.750638 + 0.660714i \(0.770254\pi\)
\(618\) 11567.6 18040.7i 0.752941 1.17428i
\(619\) 18926.2i 1.22893i 0.788945 + 0.614464i \(0.210628\pi\)
−0.788945 + 0.614464i \(0.789372\pi\)
\(620\) −3346.97 5513.67i −0.216802 0.357152i
\(621\) 6137.16 + 8145.29i 0.396580 + 0.526344i
\(622\) 19187.2 19187.2i 1.23688 1.23688i
\(623\) −11903.2 + 11903.2i −0.765474 + 0.765474i
\(624\) −333.191 1524.04i −0.0213755 0.0977730i
\(625\) −8970.20 12793.6i −0.574093 0.818790i
\(626\) 10806.5i 0.689959i
\(627\) −2848.12 1826.20i −0.181408 0.116318i
\(628\) −11186.8 11186.8i −0.710831 0.710831i
\(629\) −20753.7 −1.31559
\(630\) −12459.8 8428.50i −0.787954 0.533015i
\(631\) −26118.8 −1.64782 −0.823909 0.566723i \(-0.808211\pi\)
−0.823909 + 0.566723i \(0.808211\pi\)
\(632\) −2851.21 2851.21i −0.179454 0.179454i
\(633\) 47.8450 + 30.6780i 0.00300421 + 0.00192629i
\(634\) 3670.26i 0.229912i
\(635\) −1650.97 + 6751.56i −0.103176 + 0.421933i
\(636\) −3341.52 15284.3i −0.208333 0.952929i
\(637\) −473.556 + 473.556i −0.0294552 + 0.0294552i
\(638\) −4590.56 + 4590.56i −0.284862 + 0.284862i
\(639\) −18006.7 + 8268.59i −1.11476 + 0.511894i
\(640\) −2270.60 + 9285.53i −0.140240 + 0.573504i
\(641\) 15846.5i 0.976442i −0.872720 0.488221i \(-0.837646\pi\)
0.872720 0.488221i \(-0.162354\pi\)
\(642\) −17478.6 + 27259.4i −1.07449 + 1.67577i
\(643\) 89.9404 + 89.9404i 0.00551618 + 0.00551618i 0.709859 0.704343i \(-0.248758\pi\)
−0.704343 + 0.709859i \(0.748758\pi\)
\(644\) −5944.21 −0.363719
\(645\) −9992.83 10496.7i −0.610027 0.640787i
\(646\) 6524.70 0.397385
\(647\) 20057.0 + 20057.0i 1.21874 + 1.21874i 0.968074 + 0.250665i \(0.0806492\pi\)
0.250665 + 0.968074i \(0.419351\pi\)
\(648\) −377.323 4984.71i −0.0228745 0.302188i
\(649\) 14376.4i 0.869527i
\(650\) −1665.96 866.575i −0.100530 0.0522921i
\(651\) 6272.31 1371.28i 0.377621 0.0825570i
\(652\) 16553.7 16553.7i 0.994313 0.994313i
\(653\) 20478.4 20478.4i 1.22723 1.22723i 0.262225 0.965007i \(-0.415544\pi\)
0.965007 0.262225i \(-0.0844562\pi\)
\(654\) 24172.3 5284.64i 1.44528 0.315972i
\(655\) 8117.99 + 13373.3i 0.484269 + 0.797767i
\(656\) 6681.92i 0.397691i
\(657\) 4618.78 12462.4i 0.274271 0.740036i
\(658\) −1907.80 1907.80i −0.113030 0.113030i
\(659\) −1169.87 −0.0691529 −0.0345765 0.999402i \(-0.511008\pi\)
−0.0345765 + 0.999402i \(0.511008\pi\)
\(660\) −12250.4 301.268i −0.722492 0.0177679i
\(661\) 19622.6 1.15466 0.577329 0.816511i \(-0.304095\pi\)
0.577329 + 0.816511i \(0.304095\pi\)
\(662\) 21904.0 + 21904.0i 1.28599 + 1.28599i
\(663\) 1016.55 1585.41i 0.0595471 0.0928688i
\(664\) 2114.07i 0.123557i
\(665\) 2741.34 + 670.343i 0.159856 + 0.0390899i
\(666\) 9692.20 + 21106.9i 0.563912 + 1.22804i
\(667\) −2596.01 + 2596.01i −0.150701 + 0.150701i
\(668\) 862.224 862.224i 0.0499408 0.0499408i
\(669\) −1305.04 5969.35i −0.0754199 0.344975i
\(670\) −21934.9 + 13315.1i −1.26480 + 0.767774i
\(671\) 68.2750i 0.00392806i
\(672\) 13227.6 + 8481.46i 0.759323 + 0.486874i
\(673\) 15256.3 + 15256.3i 0.873830 + 0.873830i 0.992887 0.119057i \(-0.0379872\pi\)
−0.119057 + 0.992887i \(0.537987\pi\)
\(674\) −9464.72 −0.540901
\(675\) −14279.8 10180.1i −0.814264 0.580495i
\(676\) 13476.7 0.766768
\(677\) 16.1429 + 16.1429i 0.000916428 + 0.000916428i 0.707565 0.706648i \(-0.249794\pi\)
−0.706648 + 0.707565i \(0.749794\pi\)
\(678\) −8878.86 5693.08i −0.502936 0.322480i
\(679\) 8087.23i 0.457083i
\(680\) −5953.85 + 3614.17i −0.335764 + 0.203819i
\(681\) 5400.87 + 24703.9i 0.303909 + 1.39010i
\(682\) 8486.57 8486.57i 0.476492 0.476492i
\(683\) 3894.05 3894.05i 0.218157 0.218157i −0.589564 0.807722i \(-0.700700\pi\)
0.807722 + 0.589564i \(0.200700\pi\)
\(684\) −1327.87 2891.73i −0.0742287 0.161649i
\(685\) −16776.2 4102.32i −0.935747 0.228820i
\(686\) 25457.5i 1.41687i
\(687\) −4712.99 + 7350.31i −0.261735 + 0.408198i
\(688\) 13274.5 + 13274.5i 0.735587 + 0.735587i
\(689\) 1944.12 0.107497
\(690\) −15897.2 390.953i −0.877095 0.0215700i
\(691\) −1041.11 −0.0573163 −0.0286581 0.999589i \(-0.509123\pi\)
−0.0286581 + 0.999589i \(0.509123\pi\)
\(692\) 5447.40 + 5447.40i 0.299247 + 0.299247i
\(693\) 4238.99 11437.6i 0.232361 0.626955i
\(694\) 9133.91i 0.499594i
\(695\) 14494.8 + 23878.3i 0.791108 + 1.30324i
\(696\) 1758.02 384.346i 0.0957438 0.0209319i
\(697\) −5703.96 + 5703.96i −0.309975 + 0.309975i
\(698\) −22908.9 + 22908.9i −1.24229 + 1.24229i
\(699\) 15124.1 3306.49i 0.818378 0.178917i
\(700\) 9747.37 3076.71i 0.526309 0.166127i
\(701\) 29885.3i 1.61020i −0.593138 0.805101i \(-0.702111\pi\)
0.593138 0.805101i \(-0.297889\pi\)
\(702\) −2087.12 293.452i −0.112213 0.0157773i
\(703\) −3081.06 3081.06i −0.165298 0.165298i
\(704\) 8821.42 0.472258
\(705\) −2168.77 2278.13i −0.115859 0.121701i
\(706\) −28889.9 −1.54007
\(707\) −15555.5 15555.5i −0.827473 0.827473i
\(708\) −7298.26 + 11382.3i −0.387409 + 0.604198i
\(709\) 12115.0i 0.641734i 0.947124 + 0.320867i \(0.103974\pi\)
−0.947124 + 0.320867i \(0.896026\pi\)
\(710\) 7338.66 30011.1i 0.387908 1.58633i
\(711\) −14428.1 + 6625.31i −0.761033 + 0.349463i
\(712\) 6167.74 6167.74i 0.324643 0.324643i
\(713\) 4799.24 4799.24i 0.252080 0.252080i
\(714\) 5024.15 + 22980.8i 0.263339 + 1.20453i
\(715\) 361.695 1479.13i 0.0189183 0.0773657i
\(716\) 15526.8i 0.810422i
\(717\) −1142.21 732.381i −0.0594933 0.0381468i
\(718\) −30404.1 30404.1i −1.58032 1.58032i
\(719\) 6371.24 0.330469 0.165234 0.986254i \(-0.447162\pi\)
0.165234 + 0.986254i \(0.447162\pi\)
\(720\) 18815.7 + 12728.0i 0.973918 + 0.658811i
\(721\) −14495.2 −0.748722
\(722\) −17294.1 17294.1i −0.891443 0.891443i
\(723\) 26251.5 + 16832.3i 1.35035 + 0.865839i
\(724\) 1667.05i 0.0855737i
\(725\) 2913.27 5600.64i 0.149236 0.286900i
\(726\) 692.164 + 3166.00i 0.0353838 + 0.161848i
\(727\) 15771.9 15771.9i 0.804604 0.804604i −0.179207 0.983811i \(-0.557353\pi\)
0.983811 + 0.179207i \(0.0573532\pi\)
\(728\) −256.012 + 256.012i −0.0130336 + 0.0130336i
\(729\) −18919.9 5427.61i −0.961229 0.275751i
\(730\) 10753.6 + 17715.0i 0.545216 + 0.898168i
\(731\) 22663.2i 1.14669i
\(732\) 34.6601 54.0555i 0.00175010 0.00272944i
\(733\) −5626.05 5626.05i −0.283496 0.283496i 0.551005 0.834502i \(-0.314244\pi\)
−0.834502 + 0.551005i \(0.814244\pi\)
\(734\) −34905.3 −1.75528
\(735\) 239.753 9748.98i 0.0120319 0.489247i
\(736\) 16610.6 0.831897
\(737\) −14712.8 14712.8i −0.735350 0.735350i
\(738\) 8464.82 + 3137.21i 0.422215 + 0.156480i
\(739\) 30340.1i 1.51026i −0.655577 0.755129i \(-0.727574\pi\)
0.655577 0.755129i \(-0.272426\pi\)
\(740\) −15330.0 3748.66i −0.761543 0.186221i
\(741\) 386.282 84.4506i 0.0191504 0.00418674i
\(742\) −17170.7 + 17170.7i −0.849535 + 0.849535i
\(743\) 2368.77 2368.77i 0.116961 0.116961i −0.646204 0.763165i \(-0.723645\pi\)
0.763165 + 0.646204i \(0.223645\pi\)
\(744\) −3250.06 + 710.541i −0.160152 + 0.0350130i
\(745\) 34123.3 20713.9i 1.67810 1.01866i
\(746\) 31778.0i 1.55962i
\(747\) −7805.16 2892.73i −0.382297 0.141686i
\(748\) 13550.0 + 13550.0i 0.662347 + 0.662347i
\(749\) 21902.1 1.06847
\(750\) 26270.7 7587.26i 1.27903 0.369397i
\(751\) 10606.2 0.515346 0.257673 0.966232i \(-0.417044\pi\)
0.257673 + 0.966232i \(0.417044\pi\)
\(752\) 2880.99 + 2880.99i 0.139706 + 0.139706i
\(753\) −8539.21 + 13317.6i −0.413262 + 0.644518i
\(754\) 758.720i 0.0366458i
\(755\) 25681.8 15589.6i 1.23796 0.751477i
\(756\) 9162.52 6903.60i 0.440790 0.332119i
\(757\) −18470.4 + 18470.4i −0.886812 + 0.886812i −0.994215 0.107404i \(-0.965746\pi\)
0.107404 + 0.994215i \(0.465746\pi\)
\(758\) −4474.44 + 4474.44i −0.214405 + 0.214405i
\(759\) −2754.01 12597.0i −0.131705 0.602428i
\(760\) −1420.45 347.345i −0.0677963 0.0165783i
\(761\) 13568.0i 0.646307i 0.946347 + 0.323153i \(0.104743\pi\)
−0.946347 + 0.323153i \(0.895257\pi\)
\(762\) −10239.5 6565.54i −0.486797 0.312132i
\(763\) −11833.9 11833.9i −0.561488 0.561488i
\(764\) 14954.3 0.708152
\(765\) 5196.74 + 26927.0i 0.245606 + 1.27261i
\(766\) −39904.0 −1.88223
\(767\) −1188.05 1188.05i −0.0559298 0.0559298i
\(768\) −23125.2 14827.8i −1.08654 0.696682i
\(769\) 11029.1i 0.517190i −0.965986 0.258595i \(-0.916741\pi\)
0.965986 0.258595i \(-0.0832594\pi\)
\(770\) 9869.33 + 16258.4i 0.461904 + 0.760924i
\(771\) −1485.23 6793.52i −0.0693764 0.317332i
\(772\) −12143.3 + 12143.3i −0.566122 + 0.566122i
\(773\) 7090.94 7090.94i 0.329940 0.329940i −0.522624 0.852563i \(-0.675047\pi\)
0.852563 + 0.522624i \(0.175047\pi\)
\(774\) 23048.9 10584.0i 1.07038 0.491515i
\(775\) −5385.76 + 10353.9i −0.249629 + 0.479902i
\(776\)