Properties

Label 15.4.e.a.2.4
Level 15
Weight 4
Character 15.2
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 2.4
Root \(2.66260 + 2.66260i\)
Character \(\chi\) = 15.2
Dual form 15.4.e.a.8.4

$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

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

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 \(-0.518154\pi\)
0.998374 + 0.0570018i \(0.0181541\pi\)
\(3\) −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 0.913072 0.407798i \(-0.133703\pi\)
−0.407798 + 0.913072i \(0.633703\pi\)
\(8\) 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 \(-0.154973\pi\)
\(12\) 27.0278 + 17.3301i 0.650187 + 0.416897i
\(13\) 2.82109 2.82109i 0.0601869 0.0601869i −0.676373 0.736560i \(-0.736449\pi\)
0.736560 + 0.676373i \(0.236449\pi\)
\(14\) 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 −0.996771 0.0802942i \(-0.974414\pi\)
0.0802942 + 0.996771i \(0.474414\pi\)
\(18\) −95.3316 35.3316i −1.24833 0.462652i
\(19\) 19.0735i 0.230303i −0.993348 0.115151i \(-0.963265\pi\)
0.993348 0.115151i \(-0.0367353\pi\)
\(20\) −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 \(-0.143116\pi\)
−0.434616 + 0.900616i \(0.643116\pi\)
\(24\) −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 0.250400 0.968142i \(-0.419438\pi\)
−0.968142 + 0.250400i \(0.919438\pi\)
\(38\) −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 \(0.945910\pi\)
\(42\) −139.765 + 217.976i −0.513482 + 0.800820i
\(43\) 176.399 176.399i 0.625596 0.625596i −0.321361 0.946957i \(-0.604140\pi\)
0.946957 + 0.321361i \(0.104140\pi\)
\(44\) −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 −0.764015 0.645199i \(-0.776775\pi\)
0.645199 + 0.764015i \(0.276775\pi\)
\(48\) −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 0.101784 0.994806i \(-0.467545\pi\)
−0.994806 + 0.101784i \(0.967545\pi\)
\(54\) 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 0.980815 0.194943i \(-0.0624521\pi\)
−0.194943 + 0.980815i \(0.562452\pi\)
\(68\) 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 \(0.789827\pi\)
\(72\) 64.3420 173.607i 0.105316 0.284164i
\(73\) −348.073 + 348.073i −0.558067 + 0.558067i −0.928757 0.370690i \(-0.879121\pi\)
0.370690 + 0.928757i \(0.379121\pi\)
\(74\) −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 \(-0.862480\pi\)
0.908117 0.418717i \(-0.137520\pi\)
\(80\) −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 \(-0.184653\pi\)
−0.548112 + 0.836405i \(0.684653\pi\)
\(84\) 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 0.443809 0.896121i \(-0.353627\pi\)
−0.896121 + 0.443809i \(0.853627\pi\)
\(98\) −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 \(-0.305380\pi\)
\(102\) −1496.34 959.444i −1.45254 0.931364i
\(103\) −774.495 + 774.495i −0.740906 + 0.740906i −0.972752 0.231847i \(-0.925523\pi\)
0.231847 + 0.972752i \(0.425523\pi\)
\(104\) 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 −0.0590633 + 0.998254i \(0.518811\pi\)
−0.998254 + 0.0590633i \(0.981189\pi\)
\(108\) 120.697 858.433i 0.107537 0.764841i
\(109\) 1264.60i 1.11125i 0.831432 + 0.555627i \(0.187522\pi\)
−0.831432 + 0.555627i \(0.812478\pi\)
\(110\) 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 \(-0.177963\pi\)
−0.530414 + 0.847739i \(0.677963\pi\)
\(114\) 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 0.536658 0.843800i \(-0.319687\pi\)
−0.843800 + 0.536658i \(0.819687\pi\)
\(128\) 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 \(0.845470\pi\)
\(132\) 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 −0.279095 0.960264i \(-0.590034\pi\)
0.960264 + 0.279095i \(0.0900344\pi\)
\(138\) −767.720 + 1197.33i −0.473570 + 0.738574i
\(139\) 2498.43i 1.52456i −0.647245 0.762282i \(-0.724079\pi\)
0.647245 0.762282i \(-0.275921\pi\)
\(140\) −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 0.0767201 0.997053i \(-0.475555\pi\)
−0.997053 + 0.0767201i \(0.975555\pi\)
\(158\) −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 −0.350982 + 0.936382i \(0.614152\pi\)
−0.936382 + 0.350982i \(0.885848\pi\)
\(164\) 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 −0.674037 0.738697i \(-0.735441\pi\)
0.738697 + 0.674037i \(0.235441\pi\)
\(168\) −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 0.486331 0.873775i \(-0.338335\pi\)
−0.873775 + 0.486331i \(0.838335\pi\)
\(174\) −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 \(-0.848411\pi\)
0.888729 0.458432i \(-0.151589\pi\)
\(192\) 1130.33 + 724.762i 0.424867 + 0.272423i
\(193\) 1965.28 1965.28i 0.732973 0.732973i −0.238234 0.971208i \(-0.576569\pi\)
0.971208 + 0.238234i \(0.0765686\pi\)
\(194\) −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 −0.841452 0.540333i \(-0.818298\pi\)
0.540333 + 0.841452i \(0.318298\pi\)
\(198\) −1206.13 + 3254.38i −0.432909 + 1.16807i
\(199\) 1540.54i 0.548775i −0.961619 0.274387i \(-0.911525\pi\)
0.961619 0.274387i \(-0.0884750\pi\)
\(200\) −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 −0.571150 0.820846i \(-0.693503\pi\)
0.820846 + 0.571150i \(0.193503\pi\)
\(224\) 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 0.00618314 0.999981i \(-0.498032\pi\)
0.999981 0.00618314i \(-0.00196817\pi\)
\(228\) 330.544 515.512i 0.0960124 0.149740i
\(229\) 1680.38i 0.484903i 0.970164 + 0.242451i \(0.0779515\pi\)
−0.970164 + 0.242451i \(0.922049\pi\)
\(230\) −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 \(-0.112432\pi\)
−0.345917 + 0.938265i \(0.612432\pi\)
\(234\) −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 \(-0.874955\pi\)
0.923825 0.382815i \(-0.125045\pi\)
\(252\) −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 −0.812562 0.582875i \(-0.801928\pi\)
0.582875 + 0.812562i \(0.301928\pi\)
\(258\) 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 0.714921 0.699206i \(-0.246463\pi\)
−0.699206 + 0.714921i \(0.746463\pi\)
\(264\) 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 0.580894 0.813979i \(-0.302703\pi\)
−0.813979 + 0.580894i \(0.802703\pi\)
\(278\) −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 \(-0.0687956\pi\)
\(282\) −891.776 571.802i −0.188314 0.120746i
\(283\) −2400.34 + 2400.34i −0.504189 + 0.504189i −0.912737 0.408548i \(-0.866035\pi\)
0.408548 + 0.912737i \(0.366035\pi\)
\(284\) 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 0.913011 0.407936i \(-0.133751\pi\)
−0.407936 + 0.913011i \(0.633751\pi\)
\(294\) 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 0.936940 0.349491i \(-0.113645\pi\)
−0.349491 + 0.936940i \(0.613645\pi\)
\(308\) −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 \(0.771845\pi\)
\(312\) −76.7315 + 119.670i −0.0139233 + 0.0217146i
\(313\) 2029.31 2029.31i 0.366464 0.366464i −0.499722 0.866186i \(-0.666564\pi\)
0.866186 + 0.499722i \(0.166564\pi\)
\(314\) −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 −0.765524 0.643408i \(-0.777520\pi\)
0.643408 + 0.765524i \(0.277520\pi\)
\(318\) 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 0.836009 0.548715i \(-0.184883\pi\)
−0.548715 + 0.836009i \(0.684883\pi\)
\(338\) 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 −0.827225 0.561871i \(-0.810082\pi\)
0.561871 + 0.827225i \(0.310082\pi\)
\(348\) −1365.02 875.242i −0.210266 0.134821i
\(349\) 8603.96i 1.31965i 0.751417 + 0.659827i \(0.229371\pi\)
−0.751417 + 0.659827i \(0.770629\pi\)
\(350\) 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 \(-0.446325\pi\)
−0.985816 + 0.167827i \(0.946325\pi\)
\(354\) 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 0.997849 0.0655499i \(-0.0208802\pi\)
−0.0655499 + 0.997849i \(0.520880\pi\)
\(368\) 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 −0.987292 0.158918i \(-0.949199\pi\)
0.158918 + 0.987292i \(0.449199\pi\)
\(374\) 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 \(0.0363276\pi\)
−0.993495 + 0.113879i \(0.963672\pi\)
\(380\) 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 \(-0.499914\pi\)
−1.00000 0.000271480i \(0.999914\pi\)
\(384\) −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 −0.999356 0.0358786i \(-0.988577\pi\)
−0.0358786 0.999356i \(-0.511423\pi\)
\(398\) −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 \(0.895722\pi\)
\(402\) −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 \(-0.827901\pi\)
0.857366 0.514707i \(-0.172099\pi\)
\(410\) −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 \(-0.860316\pi\)
0.905250 0.424880i \(-0.139684\pi\)
\(432\) 10454.8 + 1469.95i 1.16437 + 0.163711i
\(433\) 4681.19 4681.19i 0.519547 0.519547i −0.397887 0.917434i \(-0.630257\pi\)
0.917434 + 0.397887i \(0.130257\pi\)
\(434\) −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 \(0.155000\pi\)
−0.883766 + 0.467929i \(0.845000\pi\)
\(440\) −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 \(-0.0868428\pi\)
−0.269453 + 0.963014i \(0.586843\pi\)
\(444\) −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 0.780280 0.625431i \(-0.215077\pi\)
−0.625431 + 0.780280i \(0.715077\pi\)
\(458\) 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 \(0.765330\pi\)
\(462\) 7441.16 + 4771.23i 0.749338 + 0.480472i
\(463\) −1237.43 + 1237.43i −0.124208 + 0.124208i −0.766478 0.642270i \(-0.777993\pi\)
0.642270 + 0.766478i \(0.277993\pi\)
\(464\) −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 −0.172327 0.985040i \(-0.555128\pi\)
0.985040 + 0.172327i \(0.0551285\pi\)
\(468\) −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 0.366071 0.930587i \(-0.380703\pi\)
−0.930587 + 0.366071i \(0.880703\pi\)
\(488\) 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 \(0.864607\pi\)
\(492\) −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 \(0.111863\pi\)
−0.938882 + 0.344239i \(0.888137\pi\)
\(500\) −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 \(-0.331580\pi\)
−0.863258 + 0.504762i \(0.831580\pi\)
\(504\) 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 \(-0.700907\pi\)
0.590089 0.807338i \(-0.299093\pi\)
\(522\) 4814.65 + 1784.39i 0.403700 + 0.149618i
\(523\) 5472.69 5472.69i 0.457560 0.457560i −0.440294 0.897854i \(-0.645126\pi\)
0.897854 + 0.440294i \(0.145126\pi\)
\(524\) 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 0.606433 0.795135i \(-0.292600\pi\)
−0.795135 + 0.606433i \(0.792600\pi\)
\(548\) −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 −0.462614 0.886560i \(-0.653088\pi\)
0.886560 + 0.462614i \(0.153088\pi\)
\(558\) 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 0.825525 0.564365i \(-0.190879\pi\)
−0.564365 + 0.825525i \(0.690879\pi\)
\(564\) −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 0.943899 0.330235i \(-0.107128\pi\)
−0.330235 + 0.943899i \(0.607128\pi\)
\(578\) −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 −0.756724 0.653734i \(-0.773202\pi\)
0.653734 + 0.756724i \(0.273202\pi\)
\(588\) 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 0.954606 + 0.297871i \(0.0962766\pi\)
0.297871 + 0.954606i \(0.403723\pi\)
\(594\) −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 0.926684 0.375841i \(-0.122646\pi\)
−0.375841 + 0.926684i \(0.622646\pi\)
\(608\) −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 −0.936890 0.349625i \(-0.886309\pi\)
0.349625 + 0.936890i \(0.386309\pi\)
\(614\) 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 −0.660714 0.750638i \(-0.729746\pi\)
0.750638 + 0.660714i \(0.229746\pi\)
\(618\) −18040.7 11567.6i −1.17428 0.752941i
\(619\) 18926.2i 1.22893i −0.788945 0.614464i \(-0.789372\pi\)
0.788945 0.614464i \(-0.210628\pi\)
\(620\) 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 \(-0.837646\pi\)
0.872720 0.488221i \(-0.162354\pi\)
\(642\) −27259.4 17478.6i −1.67577 1.07449i
\(643\) 89.9404 89.9404i 0.00551618 0.00551618i −0.704343 0.709859i \(-0.748758\pi\)
0.709859 + 0.704343i \(0.248758\pi\)
\(644\) 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 −0.250665 + 0.968074i \(0.580649\pi\)
−0.968074 + 0.250665i \(0.919351\pi\)
\(648\) −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 −0.965007 0.262225i \(-0.915544\pi\)
−0.262225 0.965007i \(-0.584456\pi\)
\(654\) −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 −0.119057 0.992887i \(-0.537987\pi\)
0.992887 + 0.119057i \(0.0379872\pi\)
\(674\) 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 −0.707565 0.706648i \(-0.750206\pi\)
0.706648 + 0.707565i \(0.250206\pi\)
\(678\) −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 0.589564 0.807722i \(-0.299300\pi\)
−0.807722 + 0.589564i \(0.799300\pi\)
\(684\) 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 \(-0.702111\pi\)
0.593138 0.805101i \(-0.297889\pi\)
\(702\) 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 \(-0.896026\pi\)
0.947124 0.320867i \(-0.103974\pi\)
\(710\) −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 0.983811 0.179207i \(-0.0573532\pi\)
−0.179207 + 0.983811i \(0.557353\pi\)
\(728\) 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 −0.834502 0.551005i \(-0.814244\pi\)
0.551005 + 0.834502i \(0.314244\pi\)
\(734\) 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 \(0.272426\pi\)
−0.655577 + 0.755129i \(0.727574\pi\)
\(740\) 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 \(-0.276355\pi\)
−0.763165 + 0.646204i \(0.776355\pi\)
\(744\) 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 0.107404 0.994215i \(-0.465746\pi\)
−0.994215 + 0.107404i \(0.965746\pi\)
\(758\) 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 \(0.895257\pi\)
\(762\) 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 \(0.0832594\pi\)
−0.965986 + 0.258595i \(0.916741\pi\)
\(770\) −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 \(-0.324953\pi\)
−0.852563 + 0.522624i \(0.824953\pi\)
\(774\) −23048.9 + 10584.0i −1.07038 + 0.491515i
\(775\) −5385.76 10353.9i −0.249629 0.479902i
\(776\) 4190.48i <