Properties

Label 15.4.e.a.8.4
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 8.4
Root \(2.66260 - 2.66260i\)
Character \(\chi\) = 15.8
Dual form 15.4.e.a.2.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.66260 + 2.66260i) q^{2} +(-2.80471 - 4.37420i) q^{3} +6.17891i q^{4} +(-9.55729 + 5.80157i) q^{5} +(4.17891 - 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(4.84884 - 4.84884i) q^{8} +(-11.2672 + 24.5367i) q^{9} +O(q^{10})\) \(q+(2.66260 + 2.66260i) q^{2} +(-2.80471 - 4.37420i) 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} +(27.0278 - 17.3301i) q^{12} +(2.82109 + 2.82109i) q^{13} +49.8323 q^{14} +(52.1826 + 25.5337i) q^{15} +75.2524 q^{16} +(-64.2384 - 64.2384i) q^{17} +(-95.3316 + 35.3316i) 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} +(138.930 - 19.5337i) q^{27} +(57.8211 + 57.8211i) q^{28} -50.5042 q^{29} +(70.9555 + 206.928i) q^{30} -93.3673 q^{31} +(161.576 + 161.576i) q^{32} +(149.324 - 95.7458i) 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} +(-139.765 - 217.976i) q^{42} +(176.399 + 176.399i) q^{43} -210.932 q^{44} +(-34.6678 - 299.872i) q^{45} +273.725 q^{46} +(-38.2843 - 38.2843i) q^{47} +(-211.061 - 329.169i) 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} +(83.4310 - 53.4956i) q^{57} +(-134.473 - 134.473i) q^{58} +421.133 q^{59} +(-157.771 + 322.432i) q^{60} +2.00000 q^{61} +(-248.600 - 248.600i) q^{62} +(124.174 + 335.046i) 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} +(64.3420 + 173.607i) q^{72} +(-348.073 - 348.073i) q^{73} -860.216 q^{74} +(-646.860 + 58.7079i) q^{75} -117.853 q^{76} +(319.452 + 319.452i) q^{77} +(65.7131 - 42.1349i) 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} +(141.650 + 220.915i) q^{87} +(165.527 + 165.527i) q^{88} +1272.00 q^{89} +(706.133 - 890.746i) q^{90} +52.7985 q^{91} +(317.607 + 317.607i) q^{92} +(261.868 + 408.407i) 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 0.998374 0.0570018i \(-0.0181541\pi\)
−0.0570018 + 0.998374i \(0.518154\pi\)
\(3\) −2.80471 4.37420i −0.539767 0.841814i
\(4\) 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 \(0.154973\pi\)
−0.883805 + 0.467856i \(0.845027\pi\)
\(12\) 27.0278 17.3301i 0.650187 0.416897i
\(13\) 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
\(15\) 52.1826 + 25.5337i 0.898233 + 0.439519i
\(16\) 75.2524 1.17582
\(17\) −64.2384 64.2384i −0.916477 0.916477i 0.0802942 0.996771i \(-0.474414\pi\)
−0.996771 + 0.0802942i \(0.974414\pi\)
\(18\) −95.3316 + 35.3316i −1.24833 + 0.462652i
\(19\) 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 −0.434616 0.900616i \(-0.643116\pi\)
0.900616 + 0.434616i \(0.143116\pi\)
\(24\) −34.8094 7.61018i −0.296060 0.0647259i
\(25\) 57.6836 110.895i 0.461469 0.887156i
\(26\) 15.0229i 0.113317i
\(27\) 138.930 19.5337i 0.990260 0.139232i
\(28\) 57.8211 + 57.8211i 0.390256 + 0.390256i
\(29\) −50.5042 −0.323393 −0.161697 0.986841i \(-0.551697\pi\)
−0.161697 + 0.986841i \(0.551697\pi\)
\(30\) 70.9555 + 206.928i 0.431821 + 1.25932i
\(31\) −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
\(33\) 149.324 95.7458i 0.787696 0.505067i
\(34\) 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 \(-0.945910\pi\)
0.985597 0.169112i \(-0.0540901\pi\)
\(42\) −139.765 217.976i −0.513482 0.800820i
\(43\) 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
\(45\) −34.6678 299.872i −0.114844 0.993384i
\(46\) 273.725 0.877360
\(47\) −38.2843 38.2843i −0.118816 0.118816i 0.645199 0.764015i \(-0.276775\pi\)
−0.764015 + 0.645199i \(0.776775\pi\)
\(48\) −211.061 329.169i −0.634668 0.989820i
\(49\) 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 −0.994806 0.101784i \(-0.967545\pi\)
0.101784 + 0.994806i \(0.467545\pi\)
\(54\) 421.925 + 317.904i 1.06327 + 0.801134i
\(55\) −198.051 326.262i −0.485549 0.799875i
\(56\) 90.7492i 0.216551i
\(57\) 83.4310 53.4956i 0.193872 0.124310i
\(58\) −134.473 134.473i −0.304433 0.304433i
\(59\) 421.133 0.929268 0.464634 0.885503i \(-0.346186\pi\)
0.464634 + 0.885503i \(0.346186\pi\)
\(60\) −157.771 + 322.432i −0.339468 + 0.693763i
\(61\) 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
\(63\) 124.174 + 335.046i 0.248325 + 0.670030i
\(64\) 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 \(-0.789827\pi\)
0.789822 0.613337i \(-0.210173\pi\)
\(72\) 64.3420 + 173.607i 0.105316 + 0.284164i
\(73\) −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
\(75\) −646.860 + 58.7079i −0.995907 + 0.0903867i
\(76\) −117.853 −0.177877
\(77\) 319.452 + 319.452i 0.472792 + 0.472792i
\(78\) 65.7131 42.1349i 0.0953915 0.0611646i
\(79\) 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 −0.548112 0.836405i \(-0.684653\pi\)
0.836405 + 0.548112i \(0.184653\pi\)
\(84\) 90.7492 415.092i 0.117876 0.539170i
\(85\) 986.629 + 241.262i 1.25900 + 0.307865i
\(86\) 939.362i 1.17784i
\(87\) 141.650 + 220.915i 0.174557 + 0.272237i
\(88\) 165.527 + 165.527i 0.200514 + 0.200514i
\(89\) 1272.00 1.51497 0.757483 0.652855i \(-0.226429\pi\)
0.757483 + 0.652855i \(0.226429\pi\)
\(90\) 706.133 890.746i 0.827033 1.04325i
\(91\) 52.7985 0.0608219
\(92\) 317.607 + 317.607i 0.359922 + 0.359922i
\(93\) 261.868 + 408.407i 0.291984 + 0.455374i
\(94\) 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 \(0.305380\pi\)
−0.574029 + 0.818835i \(0.694620\pi\)
\(102\) −1496.34 + 959.444i −1.45254 + 0.931364i
\(103\) −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
\(105\) 727.256 249.376i 0.675932 0.231777i
\(106\) −1834.90 −1.68133
\(107\) −1170.26 1170.26i −1.05732 1.05732i −0.998254 0.0590633i \(-0.981189\pi\)
−0.0590633 0.998254i \(-0.518811\pi\)
\(108\) 120.697 + 858.433i 0.107537 + 0.764841i
\(109\) 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 −0.530414 0.847739i \(-0.677963\pi\)
0.847739 + 0.530414i \(0.177963\pi\)
\(114\) 364.581 + 79.7062i 0.299528 + 0.0654839i
\(115\) −193.051 + 789.473i −0.156540 + 0.640163i
\(116\) 312.061i 0.249777i
\(117\) −101.006 + 37.4346i −0.0798121 + 0.0295798i
\(118\) 1121.31 + 1121.31i 0.874787 + 0.874787i
\(119\) −1202.26 −0.926145
\(120\) 376.835 129.216i 0.286668 0.0982983i
\(121\) 165.633 0.124442
\(122\) 5.32521 + 5.32521i 0.00395182 + 0.00395182i
\(123\) −388.400 + 249.040i −0.284722 + 0.182563i
\(124\) 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 \(-0.845470\pi\)
0.884456 0.466623i \(-0.154530\pi\)
\(132\) 591.605 + 922.659i 0.390095 + 0.608388i
\(133\) 178.486 + 178.486i 0.116366 + 0.116366i
\(134\) 2295.09 1.47960
\(135\) −1214.46 + 992.698i −0.774255 + 0.632873i
\(136\) −622.964 −0.392785
\(137\) 1092.28 + 1092.28i 0.681169 + 0.681169i 0.960264 0.279095i \(-0.0900344\pi\)
−0.279095 + 0.960264i \(0.590034\pi\)
\(138\) −767.720 1197.33i −0.473570 0.738574i
\(139\) 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
\(147\) 734.264 470.806i 0.411980 0.264159i
\(148\) −998.121 998.121i −0.554358 0.554358i
\(149\) −3570.40 −1.96308 −0.981538 0.191270i \(-0.938739\pi\)
−0.981538 + 0.191270i \(0.938739\pi\)
\(150\) −1878.65 1566.02i −1.02261 0.852431i
\(151\) 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
\(153\) 2299.99 852.415i 1.21531 0.450416i
\(154\) 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
\(162\) 207.196 2737.21i 0.100487 1.32750i
\(163\) −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
\(165\) −871.657 + 1781.38i −0.411263 + 0.840488i
\(166\) 1160.88 0.542782
\(167\) 139.543 + 139.543i 0.0646597 + 0.0646597i 0.738697 0.674037i \(-0.235441\pi\)
−0.674037 + 0.738697i \(0.735441\pi\)
\(168\) −396.955 + 254.525i −0.182296 + 0.116887i
\(169\) 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 −0.873775 0.486331i \(-0.838335\pi\)
0.486331 + 0.873775i \(0.338335\pi\)
\(174\) −211.053 + 965.367i −0.0919532 + 0.420599i
\(175\) −497.938 1577.52i −0.215089 0.681426i
\(176\) 2568.93i 1.10023i
\(177\) −1181.16 1842.12i −0.501588 0.782271i
\(178\) 3386.84 + 3386.84i 1.42615 + 1.42615i
\(179\) 2512.87 1.04928 0.524638 0.851325i \(-0.324201\pi\)
0.524638 + 0.851325i \(0.324201\pi\)
\(180\) 1852.88 214.209i 0.767253 0.0887013i
\(181\) 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
\(183\) −5.60943 8.74839i −0.00226591 0.00353388i
\(184\) 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 \(0.151589\pi\)
−0.888729 + 0.458432i \(0.848411\pi\)
\(192\) 1130.33 724.762i 0.424867 0.272423i
\(193\) 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
\(195\) 75.1791 + 219.245i 0.0276086 + 0.0805152i
\(196\) −1037.21 −0.377991
\(197\) −832.602 832.602i −0.301119 0.301119i 0.540333 0.841452i \(-0.318298\pi\)
−0.841452 + 0.540333i \(0.818298\pi\)
\(198\) −1206.13 3254.38i −0.432909 1.16807i
\(199\) 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
\(207\) 682.079 + 1840.38i 0.229023 + 0.617949i
\(208\) 212.294 + 212.294i 0.0707689 + 0.0707689i
\(209\) −651.119 −0.215497
\(210\) 2600.38 + 1272.40i 0.854492 + 0.418115i
\(211\) −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
\(213\) −3210.07 + 2058.28i −1.03263 + 0.662118i
\(214\) 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
\(222\) 2412.66 + 3762.75i 0.729401 + 1.13757i
\(223\) 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
\(225\) 2071.06 + 2664.83i 0.613647 + 0.789581i
\(226\) 2029.83 0.597443
\(227\) 3441.18 + 3441.18i 1.00616 + 1.00616i 0.999981 + 0.00618314i \(0.00196817\pi\)
0.00618314 + 0.999981i \(0.498032\pi\)
\(228\) 330.544 + 515.512i 0.0960124 + 0.149740i
\(229\) 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 −0.345917 0.938265i \(-0.612432\pi\)
0.938265 + 0.345917i \(0.112432\pi\)
\(234\) −368.613 169.265i −0.102978 0.0472873i
\(235\) 588.004 + 143.785i 0.163222 + 0.0399129i
\(236\) 2602.14i 0.717733i
\(237\) 2572.11 1649.22i 0.704964 0.452019i
\(238\) −3201.15 3201.15i −0.871847 0.871847i
\(239\) −261.125 −0.0706728 −0.0353364 0.999375i \(-0.511250\pi\)
−0.0353364 + 0.999375i \(0.511250\pi\)
\(240\) 3926.87 + 1921.47i 1.05616 + 0.516794i
\(241\) −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
\(243\) −1086.05 + 3628.97i −0.286709 + 0.958018i
\(244\) 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 \(0.125045\pi\)
−0.923825 + 0.382815i \(0.874955\pi\)
\(252\) −2070.22 + 767.260i −0.517506 + 0.191797i
\(253\) 1754.73 + 1754.73i 0.436042 + 0.436042i
\(254\) −2340.89 −0.578271
\(255\) −1711.89 4992.38i −0.420402 1.22602i
\(256\) 5286.74 1.29071
\(257\) −946.317 946.317i −0.229687 0.229687i 0.582875 0.812562i \(-0.301928\pi\)
−0.812562 + 0.582875i \(0.801928\pi\)
\(258\) 4108.95 2634.64i 0.991521 0.635758i
\(259\) 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 −0.699206 0.714921i \(-0.746463\pi\)
0.714921 + 0.699206i \(0.246463\pi\)
\(264\) 259.792 1188.31i 0.0605648 0.277027i
\(265\) 1294.11 5292.18i 0.299986 1.22678i
\(266\) 950.474i 0.219088i
\(267\) −3567.60 5563.99i −0.817729 1.27532i
\(268\) 2663.03 + 2663.03i 0.606979 + 0.606979i
\(269\) 2658.15 0.602492 0.301246 0.953546i \(-0.402597\pi\)
0.301246 + 0.953546i \(0.402597\pi\)
\(270\) −5876.80 590.476i −1.32463 0.133093i
\(271\) 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
\(273\) −148.085 230.951i −0.0328296 0.0512007i
\(274\) 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 \(0.0687956\pi\)
−0.976735 + 0.214449i \(0.931204\pi\)
\(282\) −891.776 + 571.802i −0.188314 + 0.120746i
\(283\) −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
\(285\) −487.016 + 995.303i −0.101222 + 0.206866i
\(286\) −512.844 −0.106032
\(287\) −830.913 830.913i −0.170896 0.170896i
\(288\) −5785.06 + 2144.05i −1.18364 + 0.438678i
\(289\) 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 −0.407936 0.913011i \(-0.633751\pi\)
0.913011 + 0.407936i \(0.133751\pi\)
\(294\) 3208.62 + 701.482i 0.636499 + 0.139154i
\(295\) −4024.89 + 2443.23i −0.794366 + 0.482204i
\(296\) 1566.53i 0.307611i
\(297\) 666.830 + 4742.71i 0.130281 + 0.926598i
\(298\) −9506.54 9506.54i −1.84798 1.84798i
\(299\) 290.018 0.0560943
\(300\) −362.751 3996.89i −0.0698114 0.769202i
\(301\) 3301.42 0.632196
\(302\) 7154.79 + 7154.79i 1.36328 + 1.36328i
\(303\) 7271.21 4662.27i 1.37861 0.883961i
\(304\) 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 \(-0.771845\pi\)
0.753931 0.656954i \(-0.228155\pi\)
\(312\) −76.7315 119.670i −0.0139233 0.0217146i
\(313\) 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
\(315\) −3130.56 2481.73i −0.559959 0.443904i
\(316\) −3633.31 −0.646804
\(317\) −689.223 689.223i −0.122116 0.122116i 0.643408 0.765524i \(-0.277520\pi\)
−0.765524 + 0.643408i \(0.777520\pi\)
\(318\) 5146.37 + 8026.21i 0.907528 + 1.41537i
\(319\) 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
\(327\) −5531.60 + 3546.84i −0.935469 + 0.599818i
\(328\) −430.546 430.546i −0.0724784 0.0724784i
\(329\) −716.516 −0.120069
\(330\) −7063.99 + 2422.24i −1.17836 + 0.404061i
\(331\) −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
\(333\) −2143.52 5783.64i −0.352745 0.951777i
\(334\) 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
\(342\) −673.895 1818.30i −0.106550 0.287493i
\(343\) 4780.56 + 4780.56i 0.752554 + 0.752554i
\(344\) 1710.66 0.268119
\(345\) 3994.76 1369.80i 0.623393 0.213761i
\(346\) −4694.77 −0.729458
\(347\) −1715.22 1715.22i −0.265354 0.265354i 0.561871 0.827225i \(-0.310082\pi\)
−0.827225 + 0.561871i \(0.810082\pi\)
\(348\) −1365.02 + 875.242i −0.210266 + 0.134821i
\(349\) 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 −0.985816 0.167827i \(-0.946325\pi\)
0.167827 + 0.985816i \(0.446325\pi\)
\(354\) 1759.87 8049.77i 0.264227 1.20859i
\(355\) 4257.57 + 7013.77i 0.636531 + 1.04860i
\(356\) 7859.58i 1.17010i
\(357\) 3372.00 + 5258.93i 0.499903 + 0.779642i
\(358\) 6690.76 + 6690.76i 0.987759 + 0.987759i
\(359\) −11418.9 −1.67874 −0.839370 0.543560i \(-0.817076\pi\)
−0.839370 + 0.543560i \(0.817076\pi\)
\(360\) −1622.13 1285.93i −0.237483 0.188263i
\(361\) 6495.20 0.946961
\(362\) 718.361 + 718.361i 0.104299 + 0.104299i
\(363\) −464.552 724.510i −0.0671699 0.104757i
\(364\) 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
\(372\) −2523.51 + 1618.06i −0.351714 + 0.225518i
\(373\) −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
\(375\) 5841.64 4313.89i 0.804429 0.594049i
\(376\) −371.270 −0.0509222
\(377\) −142.477 142.477i −0.0194640 0.0194640i
\(378\) 6923.18 973.408i 0.942037 0.132452i
\(379\) 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 −1.00000 0.000271480i \(-0.999914\pi\)
0.000271480 1.00000i \(0.499914\pi\)
\(384\) −4340.16 948.864i −0.576779 0.126098i
\(385\) −4906.42 1199.77i −0.649492 0.158821i
\(386\) 10465.5i 1.38000i
\(387\) −6315.78 + 2340.74i −0.829584 + 0.307459i
\(388\) −2669.98 2669.98i −0.349349 0.349349i
\(389\) 7966.97 1.03841 0.519205 0.854650i \(-0.326228\pi\)
0.519205 + 0.854650i \(0.326228\pi\)
\(390\) −383.590 + 783.934i −0.0498048 + 0.101785i
\(391\) −6603.94 −0.854158
\(392\) 813.939 + 813.939i 0.104873 + 0.104873i
\(393\) −6120.71 + 3924.57i −0.785620 + 0.503736i
\(394\) 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 \(-0.895722\pi\)
0.946817 0.321771i \(-0.104278\pi\)
\(402\) −6437.08 10039.2i −0.798638 1.24555i
\(403\) −263.398 263.398i −0.0325577 0.0325577i
\(404\) −10271.2 −1.26488
\(405\) 7748.48 + 2528.07i 0.950679 + 0.310175i
\(406\) −2516.74 −0.307645
\(407\) −5514.46 5514.46i −0.671601 0.671601i
\(408\) 1747.24 + 2724.97i 0.212012 + 0.330652i
\(409\) 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
\(417\) 10928.6 7007.39i 1.28340 0.822910i
\(418\) −1733.67 1733.67i −0.202863 0.202863i
\(419\) 11939.7 1.39211 0.696053 0.717990i \(-0.254938\pi\)
0.696053 + 0.717990i \(0.254938\pi\)
\(420\) 1540.87 + 4493.65i 0.179016 + 0.522065i
\(421\) 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
\(423\) 1370.73 508.016i 0.157558 0.0583938i
\(424\) 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 \(0.139684\pi\)
−0.905250 + 0.424880i \(0.860316\pi\)
\(432\) 10454.8 1469.95i 1.16437 0.163711i
\(433\) 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
\(435\) −2635.44 1289.56i −0.290483 0.142137i
\(436\) 7813.84 0.858292
\(437\) 980.409 + 980.409i 0.107321 + 0.107321i
\(438\) −8107.85 + 5198.71i −0.884493 + 0.567133i
\(439\) 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 −0.269453 0.963014i \(-0.586843\pi\)
0.963014 + 0.269453i \(0.0868428\pi\)
\(444\) −1566.53 + 7165.42i −0.167442 + 0.765891i
\(445\) −12156.9 + 7379.61i −1.29504 + 0.786128i
\(446\) 4427.97i 0.470113i
\(447\) 10013.9 + 15617.6i 1.05960 + 1.65254i
\(448\) 2418.14 + 2418.14i 0.255014 + 0.255014i
\(449\) 356.370 0.0374569 0.0187284 0.999825i \(-0.494038\pi\)
0.0187284 + 0.999825i \(0.494038\pi\)
\(450\) −1580.99 + 12609.8i −0.165619 + 1.32096i
\(451\) 3031.19 0.316481
\(452\) 2355.24 + 2355.24i 0.245091 + 0.245091i
\(453\) −7536.66 11754.1i −0.781685 1.21911i
\(454\) 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 \(-0.765330\pi\)
0.740327 0.672246i \(-0.234670\pi\)
\(462\) 7441.16 4771.23i 0.749338 0.480472i
\(463\) −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
\(465\) −4872.15 2384.01i −0.485894 0.237755i
\(466\) 11218.8 1.11524
\(467\) 8201.87 + 8201.87i 0.812713 + 0.812713i 0.985040 0.172327i \(-0.0551285\pi\)
−0.172327 + 0.985040i \(0.555128\pi\)
\(468\) −231.305 624.107i −0.0228463 0.0616439i
\(469\) 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
\(477\) −4572.28 12336.9i −0.438889 1.18421i
\(478\) −695.273 695.273i −0.0665294 0.0665294i
\(479\) 11419.1 1.08926 0.544629 0.838677i \(-0.316671\pi\)
0.544629 + 0.838677i \(0.316671\pi\)
\(480\) 4305.84 + 12557.1i 0.409445 + 1.19407i
\(481\) −911.420 −0.0863974
\(482\) −15979.5 15979.5i −1.51005 1.51005i
\(483\) −4208.05 + 2698.18i −0.396424 + 0.254185i
\(484\) 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 \(-0.864607\pi\)
0.910895 0.412639i \(-0.135393\pi\)
\(492\) −1538.80 2399.89i −0.141005 0.219909i
\(493\) 3244.31 + 3244.31i 0.296382 + 0.296382i
\(494\) −286.538 −0.0260971
\(495\) 10236.9 1183.47i 0.929521 0.107461i
\(496\) −7026.11 −0.636051
\(497\) −6867.38 6867.38i −0.619807 0.619807i
\(498\) −3255.94 5077.92i −0.292976 0.456922i
\(499\) 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 −0.863258 0.504762i \(-0.831580\pi\)
0.504762 + 0.863258i \(0.331580\pi\)
\(504\) 2226.69 + 1022.49i 0.196795 + 0.0903674i
\(505\) −9643.93 15887.1i −0.849800 1.39993i
\(506\) 9344.28i 0.820957i
\(507\) −9540.48 + 6117.31i −0.835715 + 0.535857i
\(508\) −2716.17 2716.17i −0.237226 0.237226i
\(509\) −12532.5 −1.09134 −0.545672 0.837999i \(-0.683725\pi\)
−0.545672 + 0.837999i \(0.683725\pi\)
\(510\) 8734.65 17850.8i 0.758386 1.54989i
\(511\) −6514.42 −0.563955
\(512\) 9239.91 + 9239.91i 0.797559 + 0.797559i
\(513\) 372.574 + 2649.87i 0.0320654 + 0.228059i
\(514\) 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 \(0.299093\pi\)
−0.590089 + 0.807338i \(0.700907\pi\)
\(522\) 4814.65 1784.39i 0.403700 0.149618i
\(523\) 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
\(525\) −5503.82 + 6602.58i −0.457536 + 0.548877i
\(526\) 356.926 0.0295869
\(527\) 5997.77 + 5997.77i 0.495762 + 0.495762i
\(528\) 11237.0 7205.10i 0.926187 0.593867i
\(529\) 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
\(537\) −7047.87 10991.8i −0.566365 0.883295i
\(538\) 7077.60 + 7077.60i 0.567169 + 0.567169i
\(539\) −5730.40 −0.457933
\(540\) −6133.79 7504.07i −0.488808 0.598007i
\(541\) 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
\(543\) −756.702 1180.14i −0.0598033 0.0932684i
\(544\) 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
\(552\) −2180.44 + 1398.09i −0.168126 + 0.107802i
\(553\) 5502.57 + 5502.57i 0.423134 + 0.423134i
\(554\) −5722.30 −0.438840
\(555\) −12554.0 + 4304.78i −0.960162 + 0.329239i
\(556\) −15437.6 −1.17752
\(557\) 5573.05 + 5573.05i 0.423946 + 0.423946i 0.886560 0.462614i \(-0.153088\pi\)
−0.462614 + 0.886560i \(0.653088\pi\)
\(558\) 8900.85 3298.81i 0.675274 0.250268i
\(559\) 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 −0.564365 0.825525i \(-0.690879\pi\)
0.825525 + 0.564365i \(0.190879\pi\)
\(564\) −1698.21 371.270i −0.126786 0.0277186i
\(565\) −1431.58 + 5854.39i −0.106597 + 0.435922i
\(566\) 12782.3i 0.949260i
\(567\) −9620.03 728.199i −0.712528 0.0539356i
\(568\) −3558.40 3558.40i −0.262865 0.262865i
\(569\) −4924.15 −0.362796 −0.181398 0.983410i \(-0.558062\pi\)
−0.181398 + 0.983410i \(0.558062\pi\)
\(570\) −3946.83 + 1353.37i −0.290025 + 0.0994496i
\(571\) −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
\(573\) 10586.5 6788.02i 0.771829 0.494893i
\(574\) 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
\(582\) 6453.87 + 10065.4i 0.459659 + 0.716879i
\(583\) −11762.7 11762.7i −0.835612 0.835612i
\(584\) −3375.51 −0.239177
\(585\) 748.165 943.767i 0.0528766 0.0667008i
\(586\) 13489.4 0.950927
\(587\) −1464.72 1464.72i −0.102990 0.102990i 0.653734 0.756724i \(-0.273202\pi\)
−0.756724 + 0.653734i \(0.773202\pi\)
\(588\) 2909.07 + 4536.95i 0.204027 + 0.318198i
\(589\) 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 \(-0.403723\pi\)
0.954606 0.297871i \(-0.0962766\pi\)
\(594\) −10852.4 + 14403.4i −0.749631 + 0.994917i
\(595\) 11490.4 6975.01i 0.791697 0.480584i
\(596\) 22061.1i 1.51621i
\(597\) 6738.63 4320.78i 0.461966 0.296211i
\(598\) 772.204 + 772.204i 0.0528056 + 0.0528056i
\(599\) −21899.3 −1.49379 −0.746897 0.664940i \(-0.768457\pi\)
−0.746897 + 0.664940i \(0.768457\pi\)
\(600\) −2851.86 + 3421.19i −0.194044 + 0.232783i
\(601\) −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
\(603\) 5719.00 + 15431.0i 0.386229 + 1.04212i
\(604\) 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
\(612\) 5267.00 + 14211.4i 0.347885 + 0.938663i
\(613\) −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
\(615\) 2267.23 4633.48i 0.148656 0.303805i
\(616\) 3097.95 0.202630
\(617\) 1378.18 + 1378.18i 0.0899244 + 0.0899244i 0.750638 0.660714i \(-0.229746\pi\)
−0.660714 + 0.750638i \(0.729746\pi\)
\(618\) −18040.7 + 11567.6i −1.17428 + 0.752941i
\(619\) 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
\(627\) 1826.20 + 2848.12i 0.116318 + 0.181408i
\(628\) −11186.8 11186.8i −0.710831 0.710831i
\(629\) 20753.7 1.31559
\(630\) −1727.58 14943.3i −0.109251 0.945009i
\(631\) −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
\(633\) 30.6780 + 47.8450i 0.00192629 + 0.00300421i
\(634\) 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 \(0.162354\pi\)
−0.872720 + 0.488221i \(0.837646\pi\)
\(642\) −27259.4 + 17478.6i −1.67577 + 1.07449i
\(643\) 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
\(645\) 4700.85 + 13709.1i 0.286970 + 0.836893i
\(646\) 6524.70 0.397385
\(647\) −20057.0 20057.0i −1.21874 1.21874i −0.968074 0.250665i \(-0.919351\pi\)
−0.250665 0.968074i \(-0.580649\pi\)
\(648\) −4984.71 377.323i −0.302188 0.0228745i
\(649\) 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 \(0.584456\pi\)
−0.965007 + 0.262225i \(0.915544\pi\)
\(654\) −24172.3 5284.64i −1.44528 0.315972i
\(655\) 8117.99 + 13373.3i 0.484269 + 0.797767i
\(656\) 6681.92i 0.397691i
\(657\) 12462.4 4618.78i 0.740036 0.274271i
\(658\) −1907.80 1907.80i −0.113030 0.113030i
\(659\) 1169.87 0.0691529 0.0345765 0.999402i \(-0.488992\pi\)
0.0345765 + 0.999402i \(0.488992\pi\)
\(660\) −11007.0 5385.89i −0.649162 0.317645i
\(661\) 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
\(663\) −1585.41 + 1016.55i −0.0928688 + 0.0595471i
\(664\) 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
\(672\) −8481.46 13227.6i −0.486874 0.759323i
\(673\) 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
\(675\) 5847.79 16533.3i 0.333454 0.942766i
\(676\) 13476.7 0.766768
\(677\) −16.1429 16.1429i −0.000916428 0.000916428i 0.706648 0.707565i \(-0.250206\pi\)
−0.707565 + 0.706648i \(0.750206\pi\)
\(678\) −5693.08 8878.86i −0.322480 0.502936i
\(679\) 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 −0.807722 0.589564i \(-0.799300\pi\)
0.589564 + 0.807722i \(0.299300\pi\)
\(684\) 1327.87 2891.73i 0.0742287 0.161649i
\(685\) −16776.2 4102.32i −0.935747 0.228820i
\(686\) 25457.5i 1.41687i
\(687\) −7350.31 + 4712.99i −0.408198 + 0.261735i
\(688\) 13274.5 + 13274.5i 0.735587 + 0.735587i
\(689\) −1944.12 −0.107497
\(690\) 14283.7 + 6989.22i 0.788074 + 0.385616i
\(691\) −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
\(693\) −11437.6 + 4238.99i −0.626955 + 0.232361i
\(694\) 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 \(0.297889\pi\)
−0.593138 + 0.805101i \(0.702111\pi\)
\(702\) 293.452 + 2087.12i 0.0157773 + 0.112213i
\(703\) −3081.06 3081.06i −0.165298 0.165298i
\(704\) −8821.42 −0.472258
\(705\) −1020.24 2975.32i −0.0545026 0.158946i
\(706\) −28889.9 −1.54007
\(707\) 15555.5 + 15555.5i 0.827473 + 0.827473i
\(708\) 11382.3 7298.26i 0.604198 0.387409i
\(709\) 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
\(717\) 732.381 + 1142.21i 0.0381468 + 0.0594933i
\(718\) −30404.1 30404.1i −1.58032 1.58032i
\(719\) −6371.24 −0.330469 −0.165234 0.986254i \(-0.552838\pi\)
−0.165234 + 0.986254i \(0.552838\pi\)
\(720\) −2608.84 22566.1i −0.135036 1.16804i
\(721\) −14495.2 −0.748722
\(722\) 17294.1 + 17294.1i 0.891443 + 0.891443i
\(723\) 16832.3 + 26251.5i 0.865839 + 1.35035i
\(724\) 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
\(732\) 54.0555 34.6601i 0.00272944 0.00175010i
\(733\) −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
\(735\) −4286.16 + 8759.51i −0.215098 + 0.439591i
\(736\) 16610.6 0.831897
\(737\) 14712.8 + 14712.8i 0.735350 + 0.735350i
\(738\) 3137.21 + 8464.82i 0.156480 + 0.422215i
\(739\) 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 −0.763165 0.646204i \(-0.776355\pi\)
0.646204 + 0.763165i \(0.276355\pi\)
\(744\) 3250.06 + 710.541i 0.160152 + 0.0350130i
\(745\) 34123.3 20713.9i 1.67810 1.01866i
\(746\) 31778.0i 1.55962i
\(747\) 2892.73 + 7805.16i 0.141686 + 0.382297i
\(748\) 13550.0 + 13550.0i 0.662347 + 0.662347i
\(749\) −21902.1 −1.06847
\(750\) 27040.1 + 4067.77i 1.31649 + 0.198045i
\(751\) 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
\(753\) 13317.6 8539.21i 0.644518 0.413262i
\(754\) 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 \(-0.895257\pi\)
0.946347 0.323153i \(-0.104743\pi\)
\(762\) 6565.54 + 10239.5i 0.312132 + 0.486797i
\(763\) −11833.9 11833.9i −0.561488 0.561488i
\(764\) −14954.3 −0.708152
\(765\) −17036.3 + 21490.3i −0.805161 + 1.01566i
\(766\) −39904.0 −1.88223
\(767\) 1188.05 + 1188.05i 0.0559298 + 0.0559298i
\(768\) −14827.8 23125.2i −0.696682 1.08654i
\(769\) 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 −0.852563 0.522624i \(-0.824953\pi\)
0.522624 + 0.852563i \(0.324953\pi\)
\(774\) −23048.9 10584.0i −1.07038 0.491515i
\(775\) −5385.76 + 10353.9i −0.249629 + 0.479902i
\(776\) 4190.48i