Properties

Label 15.4.e.a.2.1
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 2.1
Root \(-2.66260 - 2.66260i\)
Character \(\chi\) = 15.2
Dual form 15.4.e.a.8.1

$q$-expansion

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

Character Values

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

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

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 −0.998374 0.0570018i \(-0.981846\pi\)
0.0570018 + 0.998374i \(0.481846\pi\)
\(3\) −4.37420 + 2.80471i −0.841814 + 0.539767i
\(4\) 6.17891i 0.772364i
\(5\) 9.55729 + 5.80157i 0.854830 + 0.518908i
\(6\) 4.17891 19.1146i 0.284339 1.30058i
\(7\) 9.35782 + 9.35782i 0.505275 + 0.505275i 0.913072 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 \(0.154973\pi\)
−0.883805 + 0.467856i \(0.845027\pi\)
\(12\) 17.3301 + 27.0278i 0.416897 + 0.650187i
\(13\) 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
\(15\) −58.0772 + 1.42827i −0.999698 + 0.0245851i
\(16\) 75.2524 1.17582
\(17\) 64.2384 64.2384i 0.916477 0.916477i −0.0802942 0.996771i \(-0.525586\pi\)
0.996771 + 0.0802942i \(0.0255860\pi\)
\(18\) 35.3316 + 95.3316i 0.462652 + 1.24833i
\(19\) 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 0.434616 0.900616i \(-0.356884\pi\)
−0.900616 + 0.434616i \(0.856884\pi\)
\(24\) 34.8094 + 7.61018i 0.296060 + 0.0647259i
\(25\) 57.6836 + 110.895i 0.461469 + 0.887156i
\(26\) 15.0229i 0.113317i
\(27\) 19.5337 + 138.930i 0.139232 + 0.990260i
\(28\) 57.8211 57.8211i 0.390256 0.390256i
\(29\) 50.5042 0.323393 0.161697 0.986841i \(-0.448303\pi\)
0.161697 + 0.986841i \(0.448303\pi\)
\(30\) 150.834 158.439i 0.917944 0.964232i
\(31\) −93.3673 −0.540944 −0.270472 0.962728i \(-0.587180\pi\)
−0.270472 + 0.962728i \(0.587180\pi\)
\(32\) −161.576 + 161.576i −0.892592 + 0.892592i
\(33\) −95.7458 149.324i −0.505067 0.787696i
\(34\) 342.083i 1.72549i
\(35\) 35.1454 + 143.725i 0.169733 + 0.694115i
\(36\) −151.610 69.6188i −0.701899 0.322309i
\(37\) −161.537 161.537i −0.717743 0.717743i 0.250400 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 \(-0.945910\pi\)
0.985597 0.169112i \(-0.0540901\pi\)
\(42\) 217.976 139.765i 0.800820 0.513482i
\(43\) 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
\(45\) 250.035 169.137i 0.828290 0.560300i
\(46\) 273.725 0.877360
\(47\) 38.2843 38.2843i 0.118816 0.118816i −0.645199 0.764015i \(-0.723225\pi\)
0.764015 + 0.645199i \(0.223225\pi\)
\(48\) −329.169 + 211.061i −0.989820 + 0.634668i
\(49\) 167.863i 0.489395i
\(50\) −448.857 141.680i −1.26956 0.400730i
\(51\) −100.821 + 461.162i −0.276819 + 1.26619i
\(52\) −17.4313 17.4313i −0.0464862 0.0464862i
\(53\) 344.569 + 344.569i 0.893022 + 0.893022i 0.994806 0.101784i \(-0.0324551\pi\)
−0.101784 + 0.994806i \(0.532455\pi\)
\(54\) −421.925 317.904i −1.06327 0.801134i
\(55\) −198.051 + 326.262i −0.485549 + 0.799875i
\(56\) 90.7492i 0.216551i
\(57\) 53.4956 + 83.4310i 0.124310 + 0.193872i
\(58\) −134.473 + 134.473i −0.304433 + 0.304433i
\(59\) −421.133 −0.929268 −0.464634 0.885503i \(-0.653814\pi\)
−0.464634 + 0.885503i \(0.653814\pi\)
\(60\) 8.82514 + 358.854i 0.0189887 + 0.772130i
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) 248.600 248.600i 0.509229 0.509229i
\(63\) 335.046 124.174i 0.670030 0.248325i
\(64\) 258.409i 0.504704i
\(65\) 43.3287 10.5952i 0.0826811 0.0202181i
\(66\) 652.524 + 142.657i 1.21697 + 0.266059i
\(67\) 430.987 + 430.987i 0.785872 + 0.785872i 0.980815 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 \(-0.789827\pi\)
0.789822 0.613337i \(-0.210173\pi\)
\(72\) −173.607 + 64.3420i −0.284164 + 0.105316i
\(73\) −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
\(75\) −563.347 323.288i −0.867329 0.497735i
\(76\) −117.853 −0.177877
\(77\) −319.452 + 319.452i −0.472792 + 0.472792i
\(78\) −42.1349 65.7131i −0.0611646 0.0953915i
\(79\) 588.019i 0.837434i −0.908117 0.418717i \(-0.862480\pi\)
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 0.548112 0.836405i \(-0.315347\pi\)
−0.836405 + 0.548112i \(0.815347\pi\)
\(84\) −90.7492 + 415.092i −0.117876 + 0.539170i
\(85\) 986.629 241.262i 1.25900 0.307865i
\(86\) 939.362i 1.17784i
\(87\) −220.915 + 141.650i −0.272237 + 0.174557i
\(88\) 165.527 165.527i 0.200514 0.200514i
\(89\) −1272.00 −1.51497 −0.757483 0.652855i \(-0.773571\pi\)
−0.757483 + 0.652855i \(0.773571\pi\)
\(90\) −215.399 + 1116.09i −0.252278 + 1.30718i
\(91\) 52.7985 0.0608219
\(92\) −317.607 + 317.607i −0.359922 + 0.359922i
\(93\) 408.407 261.868i 0.455374 0.291984i
\(94\) 203.872i 0.223700i
\(95\) 110.656 182.291i 0.119506 0.196870i
\(96\) 253.591 1159.94i 0.269605 1.23319i
\(97\) −432.111 432.111i −0.452312 0.452312i 0.443809 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 \(0.305380\pi\)
−0.574029 + 0.818835i \(0.694620\pi\)
\(102\) −959.444 1496.34i −0.931364 1.45254i
\(103\) −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
\(105\) −556.841 530.110i −0.517544 0.492700i
\(106\) −1834.90 −1.68133
\(107\) 1170.26 1170.26i 1.05732 1.05732i 0.0590633 0.998254i \(-0.481189\pi\)
0.998254 0.0590633i \(-0.0188114\pi\)
\(108\) 858.433 120.697i 0.764841 0.107537i
\(109\) 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 0.530414 0.847739i \(-0.322037\pi\)
−0.847739 + 0.530414i \(0.822037\pi\)
\(114\) −364.581 79.7062i −0.299528 0.0654839i
\(115\) −193.051 789.473i −0.156540 0.640163i
\(116\) 312.061i 0.249777i
\(117\) −37.4346 101.006i −0.0295798 0.0798121i
\(118\) 1121.31 1121.31i 0.874787 0.874787i
\(119\) 1202.26 0.926145
\(120\) 288.533 + 274.682i 0.219494 + 0.208958i
\(121\) 165.633 0.124442
\(122\) −5.32521 + 5.32521i −0.00395182 + 0.00395182i
\(123\) 249.040 + 388.400i 0.182563 + 0.284722i
\(124\) 576.908i 0.417805i
\(125\) −92.0630 + 1394.51i −0.0658749 + 0.997828i
\(126\) −561.469 + 1222.72i −0.396981 + 0.864513i
\(127\) −439.588 439.588i −0.307142 0.307142i 0.536658 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 \(-0.845470\pi\)
0.884456 0.466623i \(-0.154530\pi\)
\(132\) −922.659 + 591.605i −0.608388 + 0.390095i
\(133\) 178.486 178.486i 0.116366 0.116366i
\(134\) −2295.09 −1.47960
\(135\) −619.321 + 1441.12i −0.394834 + 0.918752i
\(136\) −622.964 −0.392785
\(137\) −1092.28 + 1092.28i −0.681169 + 0.681169i −0.960264 0.279095i \(-0.909966\pi\)
0.279095 + 0.960264i \(0.409966\pi\)
\(138\) −1197.33 + 767.720i −0.738574 + 0.473570i
\(139\) 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
\(147\) 470.806 + 734.264i 0.264159 + 0.411980i
\(148\) −998.121 + 998.121i −0.554358 + 0.554358i
\(149\) 3570.40 1.96308 0.981538 0.191270i \(-0.0612605\pi\)
0.981538 + 0.191270i \(0.0612605\pi\)
\(150\) 2360.76 639.180i 1.28503 0.347926i
\(151\) 2687.14 1.44819 0.724094 0.689701i \(-0.242258\pi\)
0.724094 + 0.689701i \(0.242258\pi\)
\(152\) −92.4842 + 92.4842i −0.0493517 + 0.0493517i
\(153\) −852.415 2299.99i −0.450416 1.21531i
\(154\) 1701.15i 0.890146i
\(155\) −892.338 541.676i −0.462415 0.280700i
\(156\) 125.137 + 27.3581i 0.0642245 + 0.0140410i
\(157\) −1810.48 1810.48i −0.920333 0.920333i 0.0767201 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
\(162\) 2737.21 + 207.196i 1.32750 + 0.100487i
\(163\) −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
\(165\) −48.7575 1982.61i −0.0230046 0.935430i
\(166\) 1160.88 0.542782
\(167\) −139.543 + 139.543i −0.0646597 + 0.0646597i −0.738697 0.674037i \(-0.764559\pi\)
0.674037 + 0.738697i \(0.264559\pi\)
\(168\) 254.525 + 396.955i 0.116887 + 0.182296i
\(169\) 2181.08i 0.992755i
\(170\) −1984.62 + 3269.39i −0.895372 + 1.47500i
\(171\) −468.000 214.904i −0.209292 0.0961059i
\(172\) −1089.95 1089.95i −0.483188 0.483188i
\(173\) 881.613 + 881.613i 0.387444 + 0.387444i 0.873775 0.486331i \(-0.161665\pi\)
−0.486331 + 0.873775i \(0.661665\pi\)
\(174\) 211.053 965.367i 0.0919532 0.420599i
\(175\) −497.938 + 1577.52i −0.215089 + 0.681426i
\(176\) 2568.93i 1.10023i
\(177\) 1842.12 1181.16i 0.782271 0.501588i
\(178\) 3386.84 3386.84i 1.42615 1.42615i
\(179\) −2512.87 −1.04928 −0.524638 0.851325i \(-0.675799\pi\)
−0.524638 + 0.851325i \(0.675799\pi\)
\(180\) −1045.08 1544.94i −0.432755 0.639741i
\(181\) 269.796 0.110795 0.0553973 0.998464i \(-0.482357\pi\)
0.0553973 + 0.998464i \(0.482357\pi\)
\(182\) −140.581 + 140.581i −0.0572560 + 0.0572560i
\(183\) −8.74839 + 5.60943i −0.00353388 + 0.00226591i
\(184\) 498.478i 0.199719i
\(185\) −606.687 2481.02i −0.241106 0.985990i
\(186\) −390.173 + 1784.68i −0.153811 + 0.703542i
\(187\) 2192.94 + 2192.94i 0.857559 + 0.857559i
\(188\) −236.555 236.555i −0.0917690 0.0917690i
\(189\) −1117.29 + 1482.87i −0.430003 + 0.570703i
\(190\) 190.735 + 780.000i 0.0728281 + 0.297827i
\(191\) 2420.22i 0.916864i 0.888729 + 0.458432i \(0.151589\pi\)
−0.888729 + 0.458432i \(0.848411\pi\)
\(192\) 724.762 + 1130.33i 0.272423 + 0.424867i
\(193\) 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
\(195\) −159.812 + 167.870i −0.0586890 + 0.0616484i
\(196\) −1037.21 −0.377991
\(197\) 832.602 832.602i 0.301119 0.301119i −0.540333 0.841452i \(-0.681702\pi\)
0.841452 + 0.540333i \(0.181702\pi\)
\(198\) −3254.38 + 1206.13i −1.16807 + 0.432909i
\(199\) 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
\(207\) −1840.38 + 682.079i −0.617949 + 0.229023i
\(208\) 212.294 212.294i 0.0707689 0.0707689i
\(209\) 651.119 0.215497
\(210\) 2894.12 71.1739i 0.951015 0.0233879i
\(211\) −10.9380 −0.00356874 −0.00178437 0.999998i \(-0.500568\pi\)
−0.00178437 + 0.999998i \(0.500568\pi\)
\(212\) 2129.06 2129.06i 0.689738 0.689738i
\(213\) 2058.28 + 3210.07i 0.662118 + 1.03263i
\(214\) 6231.86i 1.99066i
\(215\) 2709.29 662.507i 0.859405 0.210152i
\(216\) 578.932 768.364i 0.182367 0.242039i
\(217\) −873.714 873.714i −0.273325 0.273325i
\(218\) −3367.13 3367.13i −1.04610 1.04610i
\(219\) 546.295 2498.79i 0.168563 0.771016i
\(220\) 2015.94 + 1223.74i 0.617794 + 0.375020i
\(221\) 362.445i 0.110320i
\(222\) −3762.75 + 2412.66i −1.13757 + 0.729401i
\(223\) 831.512 831.512i 0.249696 0.249696i −0.571150 0.820846i \(-0.693503\pi\)
0.820846 + 0.571150i \(0.193503\pi\)
\(224\) −3024.00 −0.902008
\(225\) 3370.92 165.900i 0.998791 0.0491554i
\(226\) 2029.83 0.597443
\(227\) −3441.18 + 3441.18i −1.00616 + 1.00616i −0.00618314 + 0.999981i \(0.501968\pi\)
−0.999981 + 0.00618314i \(0.998032\pi\)
\(228\) 515.512 330.544i 0.149740 0.0960124i
\(229\) 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 0.345917 0.938265i \(-0.387568\pi\)
−0.938265 + 0.345917i \(0.887568\pi\)
\(234\) 368.613 + 169.265i 0.102978 + 0.0472873i
\(235\) 588.004 143.785i 0.163222 0.0399129i
\(236\) 2602.14i 0.717733i
\(237\) 1649.22 + 2572.11i 0.452019 + 0.704964i
\(238\) −3201.15 + 3201.15i −0.871847 + 0.871847i
\(239\) 261.125 0.0706728 0.0353364 0.999375i \(-0.488750\pi\)
0.0353364 + 0.999375i \(0.488750\pi\)
\(240\) −4370.45 + 107.481i −1.17546 + 0.0289077i
\(241\) −6001.45 −1.60410 −0.802048 0.597259i \(-0.796256\pi\)
−0.802048 + 0.597259i \(0.796256\pi\)
\(242\) −441.014 + 441.014i −0.117147 + 0.117147i
\(243\) 3628.97 + 1086.05i 0.958018 + 0.286709i
\(244\) 12.3578i 0.00324233i
\(245\) 973.866 1604.31i 0.253951 0.418350i
\(246\) −1697.25 371.060i −0.439889 0.0961704i
\(247\) −53.8080 53.8080i −0.0138612 0.0138612i
\(248\) 452.723 + 452.723i 0.115919 + 0.115919i
\(249\) 1564.98 + 342.143i 0.398300 + 0.0870781i
\(250\) −3467.89 3958.15i −0.877315 1.00134i
\(251\) 3044.59i 0.765630i 0.923825 + 0.382815i \(0.125045\pi\)
−0.923825 + 0.382815i \(0.874955\pi\)
\(252\) −767.260 2070.22i −0.191797 0.517506i
\(253\) 1754.73 1754.73i 0.436042 0.436042i
\(254\) 2340.89 0.578271
\(255\) −3639.04 + 3822.54i −0.893668 + 0.938732i
\(256\) 5286.74 1.29071
\(257\) 946.317 946.317i 0.229687 0.229687i −0.582875 0.812562i \(-0.698072\pi\)
0.812562 + 0.582875i \(0.198072\pi\)
\(258\) −2634.64 4108.95i −0.635758 0.991521i
\(259\) 3023.26i 0.725314i
\(260\) −65.4670 267.724i −0.0156157 0.0638598i
\(261\) 569.040 1239.21i 0.134953 0.293889i
\(262\) 3725.72 + 3725.72i 0.878532 + 0.878532i
\(263\) −67.0257 67.0257i −0.0157148 0.0157148i 0.699206 0.714921i \(-0.253537\pi\)
−0.714921 + 0.699206i \(0.753537\pi\)
\(264\) −259.792 + 1188.31i −0.0605648 + 0.277027i
\(265\) 1294.11 + 5292.18i 0.299986 + 1.22678i
\(266\) 950.474i 0.219088i
\(267\) 5563.99 3567.60i 1.27532 0.817729i
\(268\) 2663.03 2663.03i 0.606979 0.606979i
\(269\) −2658.15 −0.602492 −0.301246 0.953546i \(-0.597403\pi\)
−0.301246 + 0.953546i \(0.597403\pi\)
\(270\) −2188.12 5486.13i −0.493202 1.23657i
\(271\) 145.673 0.0326530 0.0163265 0.999867i \(-0.494803\pi\)
0.0163265 + 0.999867i \(0.494803\pi\)
\(272\) 4834.09 4834.09i 1.07761 1.07761i
\(273\) −230.951 + 148.085i −0.0512007 + 0.0328296i
\(274\) 5816.64i 1.28247i
\(275\) −3785.66 + 1969.17i −0.830123 + 0.431802i
\(276\) 498.478 2280.07i 0.108713 0.497261i
\(277\) −1074.57 1074.57i −0.233085 0.233085i 0.580894 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 \(0.0687956\pi\)
−0.976735 + 0.214449i \(0.931204\pi\)
\(282\) −571.802 891.776i −0.120746 0.188314i
\(283\) −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
\(285\) 27.2420 + 1107.73i 0.00566202 + 0.230233i
\(286\) −512.844 −0.106032
\(287\) 830.913 830.913i 0.170896 0.170896i
\(288\) 2144.05 + 5785.06i 0.438678 + 1.18364i
\(289\) 3340.15i 0.679860i
\(290\) −2065.35 + 505.042i −0.418212 + 0.102266i
\(291\) 3102.09 + 678.191i 0.624906 + 0.136619i
\(292\) 2150.71 + 2150.71i 0.431031 + 0.431031i
\(293\) −2533.13 2533.13i −0.505075 0.505075i 0.407936 0.913011i \(-0.366249\pi\)
−0.913011 + 0.407936i \(0.866249\pi\)
\(294\) −3208.62 701.482i −0.636499 0.139154i
\(295\) −4024.89 2443.23i −0.794366 0.482204i
\(296\) 1566.53i 0.307611i
\(297\) −4742.71 + 666.830i −0.926598 + 0.130281i
\(298\) −9506.54 + 9506.54i −1.84798 + 1.84798i
\(299\) −290.018 −0.0560943
\(300\) −1997.57 + 3480.87i −0.384432 + 0.669893i
\(301\) 3301.42 0.632196
\(302\) −7154.79 + 7154.79i −1.36328 + 1.36328i
\(303\) −4662.27 7271.21i −0.883961 1.37861i
\(304\) 1435.32i 0.270794i
\(305\) 19.1146 + 11.6031i 0.00358852 + 0.00217834i
\(306\) 8393.59 + 3854.31i 1.56807 + 0.720052i
\(307\) 3159.93 + 3159.93i 0.587449 + 0.587449i 0.936940 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 \(-0.771845\pi\)
0.753931 0.656954i \(-0.228155\pi\)
\(312\) 119.670 76.7315i 0.0217146 0.0139233i
\(313\) 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
\(315\) 3922.54 + 757.026i 0.701619 + 0.135408i
\(316\) −3633.31 −0.646804
\(317\) 689.223 689.223i 0.122116 0.122116i −0.643408 0.765524i \(-0.722480\pi\)
0.765524 + 0.643408i \(0.222480\pi\)
\(318\) 8026.21 5146.37i 1.41537 0.907528i
\(319\) 1724.09i 0.302603i
\(320\) 1499.18 2469.69i 0.261895 0.431437i
\(321\) −1836.70 + 8401.16i −0.319360 + 1.46077i
\(322\) 2561.47 + 2561.47i 0.443308 + 0.443308i
\(323\) −1225.25 1225.25i −0.211067 0.211067i
\(324\) −3416.44 + 2935.61i −0.585809 + 0.503363i
\(325\) 475.574 + 150.113i 0.0811696 + 0.0256208i
\(326\) 14266.6i 2.42378i
\(327\) −3546.84 5531.60i −0.599818 0.935469i
\(328\) −430.546 + 430.546i −0.0724784 + 0.0724784i
\(329\) 716.516 0.120069
\(330\) 5408.72 + 5149.08i 0.902243 + 0.858932i
\(331\) −8226.53 −1.36608 −0.683038 0.730383i \(-0.739342\pi\)
−0.683038 + 0.730383i \(0.739342\pi\)
\(332\) −1346.99 + 1346.99i −0.222667 + 0.222667i
\(333\) −5783.64 + 2143.52i −0.951777 + 0.352745i
\(334\) 743.096i 0.121738i
\(335\) 1618.67 + 6619.47i 0.263992 + 1.07958i
\(336\) −5055.37 1105.23i −0.820813 0.179449i
\(337\) 1777.34 + 1777.34i 0.287294 + 0.287294i 0.836009 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
\(342\) 1818.30 673.895i 0.287493 0.106550i
\(343\) 4780.56 4780.56i 0.752554 0.752554i
\(344\) −1710.66 −0.268119
\(345\) 3058.69 + 2911.86i 0.477316 + 0.454403i
\(346\) −4694.77 −0.729458
\(347\) 1715.22 1715.22i 0.265354 0.265354i −0.561871 0.827225i \(-0.689918\pi\)
0.827225 + 0.561871i \(0.189918\pi\)
\(348\) 875.242 + 1365.02i 0.134821 + 0.210266i
\(349\) 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 0.985816 0.167827i \(-0.0536750\pi\)
−0.167827 + 0.985816i \(0.553675\pi\)
\(354\) −1759.87 + 8049.77i −0.264227 + 1.20859i
\(355\) 4257.57 7013.77i 0.636531 1.04860i
\(356\) 7859.58i 1.17010i
\(357\) −5258.93 + 3372.00i −0.779642 + 0.499903i
\(358\) 6690.76 6690.76i 0.987759 0.987759i
\(359\) 11418.9 1.67874 0.839370 0.543560i \(-0.182924\pi\)
0.839370 + 0.543560i \(0.182924\pi\)
\(360\) −2032.50 392.260i −0.297562 0.0574276i
\(361\) 6495.20 0.946961
\(362\) −718.361 + 718.361i −0.104299 + 0.104299i
\(363\) −724.510 + 464.552i −0.104757 + 0.0671699i
\(364\) 326.237i 0.0469766i
\(365\) −5346.01 + 1307.27i −0.766638 + 0.187467i
\(366\) 8.35782 38.2292i 0.00119363 0.00545976i
\(367\) 6554.73 + 6554.73i 0.932299 + 0.932299i 0.997849 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
\(372\) −1618.06 2523.51i −0.225518 0.351714i
\(373\) −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
\(375\) −3508.49 6358.06i −0.483140 0.875543i
\(376\) −371.270 −0.0509222
\(377\) 142.477 142.477i 0.0194640 0.0194640i
\(378\) −973.408 6923.18i −0.132452 0.942037i
\(379\) 1680.48i 0.227758i 0.993495 + 0.113879i \(0.0363276\pi\)
−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 1.00000 0.000271480i \(-8.64148e-5\pi\)
−0.000271480 1.00000i \(0.500086\pi\)
\(384\) 4340.16 + 948.864i 0.576779 + 0.126098i
\(385\) −4906.42 + 1199.77i −0.649492 + 0.158821i
\(386\) 10465.5i 1.38000i
\(387\) −2340.74 6315.78i −0.307459 0.829584i
\(388\) −2669.98 + 2669.98i −0.349349 + 0.349349i
\(389\) −7966.97 −1.03841 −0.519205 0.854650i \(-0.673772\pi\)
−0.519205 + 0.854650i \(0.673772\pi\)
\(390\) −21.4567 872.487i −0.00278591 0.113282i
\(391\) −6603.94 −0.854158
\(392\) −813.939 + 813.939i −0.104873 + 0.104873i
\(393\) 3924.57 + 6120.71i 0.503736 + 0.785620i
\(394\) 4433.78i 0.566930i
\(395\) 3411.43 5619.87i 0.434551 0.715864i
\(396\) 2376.61 5175.59i 0.301589 0.656776i
\(397\) −8188.88 8188.88i −1.03523 1.03523i −0.999356 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 \(-0.895722\pi\)
0.946817 0.321771i \(-0.104278\pi\)
\(402\) 10039.2 6437.08i 1.24555 0.798638i
\(403\) −263.398 + 263.398i −0.0325577 + 0.0325577i
\(404\) 10271.2 1.26488
\(405\) −1332.89 8040.74i −0.163535 0.986537i
\(406\) −2516.74 −0.307645
\(407\) 5514.46 5514.46i 0.671601 0.671601i
\(408\) 2724.97 1747.24i 0.330652 0.212012i
\(409\) 8514.82i 1.02941i −0.857366 0.514707i \(-0.827901\pi\)
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
\(417\) 7007.39 + 10928.6i 0.822910 + 1.28340i
\(418\) −1733.67 + 1733.67i −0.202863 + 0.202863i
\(419\) −11939.7 −1.39211 −0.696053 0.717990i \(-0.745062\pi\)
−0.696053 + 0.717990i \(0.745062\pi\)
\(420\) −3275.50 + 3440.67i −0.380543 + 0.399732i
\(421\) 10873.3 1.25875 0.629373 0.777103i \(-0.283312\pi\)
0.629373 + 0.777103i \(0.283312\pi\)
\(422\) 29.1236 29.1236i 0.00335951 0.00335951i
\(423\) −508.016 1370.73i −0.0583938 0.157558i
\(424\) 3341.52i 0.382733i
\(425\) 10829.2 + 3418.19i 1.23598 + 0.390133i
\(426\) −14027.5 3066.76i −1.59539 0.348791i
\(427\) 18.7156 + 18.7156i 0.00212111 + 0.00212111i
\(428\) −7230.91 7230.91i −0.816634 0.816634i
\(429\) −691.364 151.149i −0.0778074 0.0170106i
\(430\) −5449.77 + 8977.76i −0.611189 + 1.00685i
\(431\) 7603.48i 0.849760i 0.905250 + 0.424880i \(0.139684\pi\)
−0.905250 + 0.424880i \(0.860316\pi\)
\(432\) 1469.95 + 10454.8i 0.163711 + 1.16437i
\(433\) 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
\(435\) −2933.14 + 72.1336i −0.323295 + 0.00795067i
\(436\) 7813.84 0.858292
\(437\) −980.409 + 980.409i −0.107321 + 0.107321i
\(438\) 5198.71 + 8107.85i 0.567133 + 0.884493i
\(439\) 8608.08i 0.935857i 0.883766 + 0.467929i \(0.155000\pi\)
−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 0.269453 0.963014i \(-0.413157\pi\)
−0.963014 + 0.269453i \(0.913157\pi\)
\(444\) 1566.53 7165.42i 0.167442 0.765891i
\(445\) −12156.9 7379.61i −1.29504 0.786128i
\(446\) 4427.97i 0.470113i
\(447\) −15617.6 + 10013.9i −1.65254 + 1.05960i
\(448\) 2418.14 2418.14i 0.255014 0.255014i
\(449\) −356.370 −0.0374569 −0.0187284 0.999825i \(-0.505962\pi\)
−0.0187284 + 0.999825i \(0.505962\pi\)
\(450\) −8533.70 + 9417.15i −0.893961 + 0.986508i
\(451\) 3031.19 0.316481
\(452\) −2355.24 + 2355.24i −0.245091 + 0.245091i
\(453\) −11754.1 + 7536.66i −1.21911 + 0.781685i
\(454\) 18325.0i 1.89435i
\(455\) 504.611 + 306.314i 0.0519923 + 0.0315609i
\(456\) 145.152 663.935i 0.0149065 0.0681834i
\(457\) 1512.80 + 1512.80i 0.154849 + 0.154849i 0.780280 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 \(-0.765330\pi\)
0.740327 0.672246i \(-0.234670\pi\)
\(462\) 4771.23 + 7441.16i 0.480472 + 0.749338i
\(463\) −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
\(465\) 5422.51 133.353i 0.540780 0.0132992i
\(466\) 11218.8 1.11524
\(467\) −8201.87 + 8201.87i −0.812713 + 0.812713i −0.985040 0.172327i \(-0.944872\pi\)
0.172327 + 0.985040i \(0.444872\pi\)
\(468\) −624.107 + 231.305i −0.0616439 + 0.0228463i
\(469\) 8066.19i 0.794162i
\(470\) −1182.78 + 1948.46i −0.116080 + 0.191225i
\(471\) 12997.3 + 2841.52i 1.27151 + 0.277984i
\(472\) 2042.01 + 2042.01i 0.199133 + 0.199133i
\(473\) 6021.83 + 6021.83i 0.585378 + 0.585378i
\(474\) −11239.7 2457.28i −1.08915 0.238115i
\(475\) 2115.14 1100.23i 0.204314 0.106278i
\(476\) 7428.67i 0.715321i
\(477\) 12336.9 4572.28i 1.18421 0.438889i
\(478\) −695.273 + 695.273i −0.0665294 + 0.0665294i
\(479\) −11419.1 −1.08926 −0.544629 0.838677i \(-0.683329\pi\)
−0.544629 + 0.838677i \(0.683329\pi\)
\(480\) 9153.13 9614.68i 0.870378 0.914267i
\(481\) −911.420 −0.0863974
\(482\) 15979.5 15979.5i 1.51005 1.51005i
\(483\) 2698.18 + 4208.05i 0.254185 + 0.396424i
\(484\) 1023.43i 0.0961147i
\(485\) −1622.89 6636.73i −0.151942 0.621358i
\(486\) −12554.2 + 6770.77i −1.17175 + 0.631952i
\(487\) −6066.93 6066.93i −0.564515 0.564515i 0.366071 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 \(-0.864607\pi\)
0.910895 0.412639i \(-0.135393\pi\)
\(492\) 2399.89 1538.80i 0.219909 0.141005i
\(493\) 3244.31 3244.31i 0.296382 0.296382i
\(494\) 286.538 0.0260971
\(495\) 5773.92 + 8535.57i 0.524280 + 0.775041i
\(496\) −7026.11 −0.636051
\(497\) 6867.38 6867.38i 0.619807 0.619807i
\(498\) −5077.92 + 3255.94i −0.456922 + 0.292976i
\(499\) 7674.34i 0.688478i 0.938882 + 0.344239i \(0.111863\pi\)
−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 0.863258 0.504762i \(-0.168420\pi\)
−0.504762 + 0.863258i \(0.668420\pi\)
\(504\) −2226.69 1022.49i −0.196795 0.0903674i
\(505\) −9643.93 + 15887.1i −0.849800 + 1.39993i
\(506\) 9344.28i 0.820957i
\(507\) −6117.31 9540.48i −0.535857 0.835715i
\(508\) −2716.17 + 2716.17i −0.237226 + 0.237226i
\(509\) 12532.5 1.09134 0.545672 0.837999i \(-0.316275\pi\)
0.545672 + 0.837999i \(0.316275\pi\)
\(510\) −488.586 19867.2i −0.0424215 1.72497i
\(511\) −6514.42 −0.563955
\(512\) −9239.91 + 9239.91i −0.797559 + 0.797559i
\(513\) 2649.87 372.574i 0.228059 0.0320654i
\(514\) 5039.33i 0.432443i
\(515\) −11895.4 + 2908.79i −1.01781 + 0.248887i
\(516\) 7824.69 + 1710.66i 0.667563 + 0.145945i
\(517\) 1306.93 + 1306.93i 0.111177 + 0.111177i
\(518\) 8049.75 + 8049.75i 0.682791 + 0.682791i
\(519\) −6329.02 1383.68i −0.535285 0.117026i
\(520\) −261.469 158.720i −0.0220503 0.0133852i
\(521\) 19201.8i 1.61468i 0.590089 + 0.807338i \(0.299093\pi\)
−0.590089 + 0.807338i \(0.700907\pi\)
\(522\) 1784.39 + 4814.65i 0.149618 + 0.403700i
\(523\) 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
\(525\) −2246.42 8296.97i −0.186747 0.689732i
\(526\) 356.926 0.0295869
\(527\) −5997.77 + 5997.77i −0.495762 + 0.495762i
\(528\) −7205.10 11237.0i −0.593867 0.926187i
\(529\) 6882.71i 0.565687i
\(530\) −17536.7 10645.3i −1.43725 0.872457i
\(531\) −4744.97 + 10333.2i −0.387786 + 0.844488i
\(532\) −1102.85 1102.85i −0.0898769 0.0898769i
\(533\) −250.495 250.495i −0.0203567 0.0203567i
\(534\) −5315.58 + 24313.8i −0.430763 + 1.97034i
\(535\) 17973.8 4395.16i 1.45248 0.355176i
\(536\) 4179.58i 0.336810i
\(537\) 10991.8 7047.87i 0.883295 0.566365i
\(538\) 7077.60 7077.60i 0.567169 0.567169i
\(539\) 5730.40 0.457933
\(540\) 8904.53 + 3826.73i 0.709611 + 0.304956i
\(541\) 12778.2 1.01548 0.507741 0.861510i \(-0.330481\pi\)
0.507741 + 0.861510i \(0.330481\pi\)
\(542\) −387.868 + 387.868i −0.0307387 + 0.0307387i
\(543\) −1180.14 + 756.702i −0.0932684 + 0.0598033i
\(544\) 20758.8i 1.63608i
\(545\) −7336.66 + 12086.1i −0.576638 + 0.949933i
\(546\) 220.640 1009.22i 0.0172940 0.0791038i
\(547\) −2414.12 2414.12i −0.188702 0.188702i 0.606433 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
\(552\) −1398.09 2180.44i −0.107802 0.168126i
\(553\) 5502.57 5502.57i 0.423134 0.423134i
\(554\) 5722.30 0.438840
\(555\) 9612.32 + 9150.88i 0.735171 + 0.699880i
\(556\) −15437.6 −1.17752
\(557\) −5573.05 + 5573.05i −0.423946 + 0.423946i −0.886560 0.462614i \(-0.846912\pi\)
0.462614 + 0.886560i \(0.346912\pi\)
\(558\) −3298.81 8900.85i −0.250268 0.675274i
\(559\) 995.277i 0.0753054i
\(560\) 2644.77 + 10815.7i 0.199575 + 0.816153i
\(561\) −15742.9 3441.78i −1.18479 0.259023i
\(562\) −5379.23 5379.23i −0.403753 0.403753i
\(563\) −3488.75 3488.75i −0.261160 0.261160i 0.564365 0.825525i \(-0.309121\pi\)
−0.825525 + 0.564365i \(0.809121\pi\)
\(564\) 1698.21 + 371.270i 0.126786 + 0.0277186i
\(565\) −1431.58 5854.39i −0.106597 0.435922i
\(566\) 12782.3i 0.949260i
\(567\) 728.199 9620.03i 0.0539356 0.712528i
\(568\) −3558.40 + 3558.40i −0.262865 + 0.262865i
\(569\) 4924.15 0.362796 0.181398 0.983410i \(-0.441938\pi\)
0.181398 + 0.983410i \(0.441938\pi\)
\(570\) −3021.99 2876.92i −0.222065 0.211405i
\(571\) −5642.12 −0.413512 −0.206756 0.978393i \(-0.566291\pi\)
−0.206756 + 0.978393i \(0.566291\pi\)
\(572\) 595.059 595.059i 0.0434977 0.0434977i
\(573\) −6788.02 10586.5i −0.494893 0.771829i
\(574\) 4424.78i 0.321754i
\(575\) 2735.14 8665.22i 0.198371 0.628460i
\(576\) −6340.50 2911.53i −0.458659 0.210614i
\(577\) 8505.39 + 8505.39i 0.613663 + 0.613663i 0.943899 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
\(582\) −10065.4 + 6453.87i −0.716879 + 0.459659i
\(583\) −11762.7 + 11762.7i −0.835612 + 0.835612i
\(584\) 3375.51 0.239177
\(585\) 228.220 1182.52i 0.0161295 0.0835750i
\(586\) 13489.4 0.950927
\(587\) 1464.72 1464.72i 0.102990 0.102990i −0.653734 0.756724i \(-0.726798\pi\)
0.756724 + 0.653734i \(0.226798\pi\)
\(588\) 4536.95 2909.07i 0.318198 0.204027i
\(589\) 1780.84i 0.124581i
\(590\) 17222.0 4211.33i 1.20173 0.293860i
\(591\) −1306.75 + 5977.17i −0.0909521 + 0.416020i
\(592\) −12156.0 12156.0i −0.843935 0.843935i
\(593\) −18086.4 18086.4i −1.25248 1.25248i −0.954606 0.297871i \(-0.903723\pi\)
−0.297871 0.954606i \(-0.596277\pi\)
\(594\) 10852.4 14403.4i 0.749631 0.994917i
\(595\) 11490.4 + 6975.01i 0.791697 + 0.480584i
\(596\) 22061.1i 1.51621i
\(597\) 4320.78 + 6738.63i 0.296211 + 0.461966i
\(598\) 772.204 772.204i 0.0528056 0.0528056i
\(599\) 21899.3 1.49379 0.746897 0.664940i \(-0.231543\pi\)
0.746897 + 0.664940i \(0.231543\pi\)
\(600\) 1164.01 + 4299.16i 0.0792006 + 0.292520i
\(601\) −12431.8 −0.843766 −0.421883 0.906650i \(-0.638631\pi\)
−0.421883 + 0.906650i \(0.638631\pi\)
\(602\) −8790.38 + 8790.38i −0.595132 + 0.595132i
\(603\) 15431.0 5719.00i 1.04212 0.386229i
\(604\) 16603.6i 1.11853i
\(605\) 1583.00 + 960.930i 0.106377 + 0.0645741i
\(606\) 31774.1 + 6946.59i 2.12993 + 0.465653i
\(607\) 8237.79 + 8237.79i 0.550843 + 0.550843i 0.926684 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
\(612\) −14211.4 + 5267.00i −0.938663 + 0.347885i
\(613\) −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
\(615\) 126.821 + 5156.88i 0.00831530 + 0.338123i
\(616\) 3097.95 0.202630
\(617\) −1378.18 + 1378.18i −0.0899244 + 0.0899244i −0.750638 0.660714i \(-0.770254\pi\)
0.660714 + 0.750638i \(0.270254\pi\)
\(618\) 11567.6 + 18040.7i 0.752941 + 1.17428i
\(619\) 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
\(627\) −2848.12 + 1826.20i −0.181408 + 0.116318i
\(628\) −11186.8 + 11186.8i −0.710831 + 0.710831i
\(629\) −20753.7 −1.31559
\(630\) −12459.8 + 8428.50i −0.787954 + 0.533015i
\(631\) −26118.8 −1.64782 −0.823909 0.566723i \(-0.808211\pi\)
−0.823909 + 0.566723i \(0.808211\pi\)
\(632\) −2851.21 + 2851.21i −0.179454 + 0.179454i
\(633\) 47.8450 30.6780i 0.00300421 0.00192629i
\(634\) 3670.26i 0.229912i
\(635\) −1650.97 6751.56i −0.103176 0.421933i
\(636\) −3341.52 + 15284.3i −0.208333 + 0.952929i
\(637\) −473.556 473.556i −0.0294552 0.0294552i
\(638\) −4590.56 4590.56i −0.284862 0.284862i
\(639\) −18006.7 8268.59i −1.11476 0.511894i
\(640\) −2270.60 9285.53i −0.140240 0.573504i
\(641\) 15846.5i 0.976442i 0.872720 + 0.488221i \(0.162354\pi\)
−0.872720 + 0.488221i \(0.837646\pi\)
\(642\) −17478.6 27259.4i −1.07449 1.67577i
\(643\) 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
\(645\) −9992.83 + 10496.7i −0.610027 + 0.640787i
\(646\) 6524.70 0.397385
\(647\) 20057.0 20057.0i 1.21874 1.21874i 0.250665 0.968074i \(-0.419351\pi\)
0.968074 0.250665i \(-0.0806492\pi\)
\(648\) −377.323 + 4984.71i −0.0228745 + 0.302188i
\(649\) 14376.4i 0.869527i
\(650\) −1665.96 + 866.575i −0.100530 + 0.0522921i
\(651\) 6272.31 + 1371.28i 0.377621 + 0.0825570i
\(652\) 16553.7 + 16553.7i 0.994313 + 0.994313i
\(653\) 20478.4 + 20478.4i 1.22723 + 1.22723i 0.965007 + 0.262225i \(0.0844562\pi\)
0.262225 + 0.965007i \(0.415544\pi\)
\(654\) 24172.3 + 5284.64i 1.44528 + 0.315972i
\(655\) 8117.99 13373.3i 0.484269 0.797767i
\(656\) 6681.92i 0.397691i
\(657\) 4618.78 + 12462.4i 0.274271 + 0.740036i
\(658\) −1907.80 + 1907.80i −0.113030 + 0.113030i
\(659\) −1169.87 −0.0691529 −0.0345765 0.999402i \(-0.511008\pi\)
−0.0345765 + 0.999402i \(0.511008\pi\)
\(660\) −12250.4 + 301.268i −0.722492 + 0.0177679i
\(661\) 19622.6 1.15466 0.577329 0.816511i \(-0.304095\pi\)
0.577329 + 0.816511i \(0.304095\pi\)
\(662\) 21904.0 21904.0i 1.28599 1.28599i
\(663\) 1016.55 + 1585.41i 0.0595471 + 0.0928688i
\(664\) 2114.07i 0.123557i
\(665\) 2741.34 670.343i 0.159856 0.0390899i
\(666\) 9692.20 21106.9i 0.563912 1.22804i
\(667\) −2596.01 2596.01i −0.150701 0.150701i
\(668\) 862.224 + 862.224i 0.0499408 + 0.0499408i
\(669\) −1305.04 + 5969.35i −0.0754199 + 0.344975i
\(670\) −21934.9 13315.1i −1.26480 0.767774i
\(671\) 68.2750i 0.00392806i
\(672\) 13227.6 8481.46i 0.759323 0.486874i
\(673\) 15256.3 15256.3i 0.873830 0.873830i −0.119057 0.992887i \(-0.537987\pi\)
0.992887 + 0.119057i \(0.0379872\pi\)
\(674\) −9464.72 −0.540901
\(675\) −14279.8 + 10180.1i −0.814264 + 0.580495i
\(676\) 13476.7 0.766768
\(677\) 16.1429 16.1429i 0.000916428 0.000916428i −0.706648 0.707565i \(-0.749794\pi\)
0.707565 + 0.706648i \(0.249794\pi\)
\(678\) −8878.86 + 5693.08i −0.502936 + 0.322480i
\(679\) 8087.23i 0.457083i
\(680\) −5953.85 3614.17i −0.335764 0.203819i
\(681\) 5400.87 24703.9i 0.303909 1.39010i
\(682\) 8486.57 + 8486.57i 0.476492 + 0.476492i
\(683\) 3894.05 + 3894.05i 0.218157 + 0.218157i 0.807722 0.589564i \(-0.200700\pi\)
−0.589564 + 0.807722i \(0.700700\pi\)
\(684\) −1327.87 + 2891.73i −0.0742287 + 0.161649i
\(685\) −16776.2 + 4102.32i −0.935747 + 0.228820i
\(686\) 25457.5i 1.41687i
\(687\) −4712.99 7350.31i −0.261735 0.408198i
\(688\) 13274.5 13274.5i 0.735587 0.735587i
\(689\) 1944.12 0.107497
\(690\) −15897.2 + 390.953i −0.877095 + 0.0215700i
\(691\) −1041.11 −0.0573163 −0.0286581 0.999589i \(-0.509123\pi\)
−0.0286581 + 0.999589i \(0.509123\pi\)
\(692\) 5447.40 5447.40i 0.299247 0.299247i
\(693\) 4238.99 + 11437.6i 0.232361 + 0.626955i
\(694\) 9133.91i 0.499594i
\(695\) 14494.8 23878.3i 0.791108 1.30324i
\(696\) 1758.02 + 384.346i 0.0957438 + 0.0209319i
\(697\) −5703.96 5703.96i −0.309975 0.309975i
\(698\) −22908.9 22908.9i −1.24229 1.24229i
\(699\) 15124.1 + 3306.49i 0.818378 + 0.178917i
\(700\) 9747.37 + 3076.71i 0.526309 + 0.166127i
\(701\) 29885.3i 1.61020i 0.593138 + 0.805101i \(0.297889\pi\)
−0.593138 + 0.805101i \(0.702111\pi\)
\(702\) −2087.12 + 293.452i −0.112213 + 0.0157773i
\(703\) −3081.06 + 3081.06i −0.165298 + 0.165298i
\(704\) 8821.42 0.472258
\(705\) −2168.77 + 2278.13i −0.115859 + 0.121701i
\(706\) −28889.9 −1.54007
\(707\) −15555.5 + 15555.5i −0.827473 + 0.827473i
\(708\) −7298.26 11382.3i −0.387409 0.604198i
\(709\) 12115.0i 0.641734i −0.947124 0.320867i \(-0.896026\pi\)
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
\(717\) −1142.21 + 732.381i −0.0594933 + 0.0381468i
\(718\) −30404.1 + 30404.1i −1.58032 + 1.58032i
\(719\) 6371.24 0.330469 0.165234 0.986254i \(-0.447162\pi\)
0.165234 + 0.986254i \(0.447162\pi\)
\(720\) 18815.7 12728.0i 0.973918 0.658811i
\(721\) −14495.2 −0.748722
\(722\) −17294.1 + 17294.1i −0.891443 + 0.891443i
\(723\) 26251.5 16832.3i 1.35035 0.865839i
\(724\) 1667.05i 0.0855737i
\(725\) 2913.27 + 5600.64i 0.149236 + 0.286900i
\(726\) 692.164 3166.00i 0.0353838 0.161848i
\(727\) 15771.9 + 15771.9i 0.804604 + 0.804604i 0.983811 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
\(732\) 34.6601 + 54.0555i 0.00175010 + 0.00272944i
\(733\) −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
\(735\) 239.753 + 9748.98i 0.0120319 + 0.489247i
\(736\) 16610.6 0.831897
\(737\) −14712.8 + 14712.8i −0.735350 + 0.735350i
\(738\) 8464.82 3137.21i 0.422215 0.156480i
\(739\) 30340.1i 1.51026i 0.655577 + 0.755129i \(0.272426\pi\)
−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 0.763165 0.646204i \(-0.223645\pi\)
−0.646204 + 0.763165i \(0.723645\pi\)
\(744\) −3250.06 710.541i −0.160152 0.0350130i
\(745\) 34123.3 + 20713.9i 1.67810 + 1.01866i
\(746\) 31778.0i 1.55962i
\(747\) −7805.16 + 2892.73i −0.382297 + 0.141686i
\(748\) 13550.0 13550.0i 0.662347 0.662347i
\(749\) 21902.1 1.06847
\(750\) 26270.7 + 7587.26i 1.27903 + 0.369397i
\(751\) 10606.2 0.515346 0.257673 0.966232i \(-0.417044\pi\)
0.257673 + 0.966232i \(0.417044\pi\)
\(752\) 2880.99 2880.99i 0.139706 0.139706i
\(753\) −8539.21 13317.6i −0.413262 0.644518i
\(754\) 758.720i 0.0366458i
\(755\) 25681.8 + 15589.6i 1.23796 + 0.751477i
\(756\) 9162.52 + 6903.60i 0.440790 + 0.332119i
\(757\) −18470.4 18470.4i −0.886812 0.886812i 0.107404 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 \(-0.895257\pi\)
0.946347 0.323153i \(-0.104743\pi\)
\(762\) −10239.5 + 6565.54i −0.486797 + 0.312132i
\(763\) −11833.9 + 11833.9i −0.561488 + 0.561488i
\(764\) 14954.3 0.708152
\(765\) 5196.74 26927.0i 0.245606 1.27261i
\(766\) −39904.0 −1.88223
\(767\) −1188.05 + 1188.05i −0.0559298 + 0.0559298i
\(768\) −23125.2 + 14827.8i −1.08654 + 0.696682i
\(769\) 11029.1i 0.517190i 0.965986 + 0.258595i \(0.0832594\pi\)
−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 0.852563 0.522624i \(-0.175047\pi\)
−0.522624 + 0.852563i \(0.675047\pi\)
\(774\) 23048.9 + 10584.0i 1.07038 + 0.491515i
\(775\) −5385.76 10353.9i −0.249629 0.479902i
\(776\) 4190.48i