Properties

Label 43.6.c.a.6.4
Level $43$
Weight $6$
Character 43.6
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.4
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.4

$q$-expansion

\(f(q)\) \(=\) \(q-8.35737 q^{2} +(-3.42253 + 5.92800i) q^{3} +37.8456 q^{4} +(-28.3920 + 49.1763i) q^{5} +(28.6033 - 49.5425i) q^{6} +(46.8510 + 81.1483i) q^{7} -48.8539 q^{8} +(98.0726 + 169.867i) q^{9} +O(q^{10})\) \(q-8.35737 q^{2} +(-3.42253 + 5.92800i) q^{3} +37.8456 q^{4} +(-28.3920 + 49.1763i) q^{5} +(28.6033 - 49.5425i) q^{6} +(46.8510 + 81.1483i) q^{7} -48.8539 q^{8} +(98.0726 + 169.867i) q^{9} +(237.282 - 410.985i) q^{10} -458.660 q^{11} +(-129.528 + 224.349i) q^{12} +(-575.015 - 995.955i) q^{13} +(-391.551 - 678.186i) q^{14} +(-194.345 - 336.615i) q^{15} -802.769 q^{16} +(130.007 + 225.178i) q^{17} +(-819.629 - 1419.64i) q^{18} +(788.988 - 1366.57i) q^{19} +(-1074.51 + 1861.11i) q^{20} -641.396 q^{21} +3833.19 q^{22} +(-825.957 + 1430.60i) q^{23} +(167.204 - 289.606i) q^{24} +(-49.7075 - 86.0959i) q^{25} +(4805.61 + 8323.56i) q^{26} -3005.98 q^{27} +(1773.10 + 3071.11i) q^{28} +(-2565.15 - 4442.97i) q^{29} +(1624.21 + 2813.22i) q^{30} +(2875.50 - 4980.52i) q^{31} +8272.36 q^{32} +(1569.78 - 2718.93i) q^{33} +(-1086.51 - 1881.90i) q^{34} -5320.77 q^{35} +(3711.62 + 6428.71i) q^{36} +(-4113.59 + 7124.94i) q^{37} +(-6593.87 + 11420.9i) q^{38} +7872.02 q^{39} +(1387.06 - 2402.46i) q^{40} +2696.36 q^{41} +5360.38 q^{42} +(-359.727 - 12119.4i) q^{43} -17358.3 q^{44} -11137.9 q^{45} +(6902.83 - 11956.0i) q^{46} -18376.8 q^{47} +(2747.50 - 4758.81i) q^{48} +(4013.47 - 6951.53i) q^{49} +(415.424 + 719.535i) q^{50} -1779.81 q^{51} +(-21761.8 - 37692.5i) q^{52} +(-8839.64 + 15310.7i) q^{53} +25122.0 q^{54} +(13022.2 - 22555.2i) q^{55} +(-2288.85 - 3964.41i) q^{56} +(5400.67 + 9354.24i) q^{57} +(21437.9 + 37131.5i) q^{58} +10593.6 q^{59} +(-7355.09 - 12739.4i) q^{60} +(-11254.2 - 19492.8i) q^{61} +(-24031.6 + 41624.0i) q^{62} +(-9189.60 + 15916.8i) q^{63} -43446.6 q^{64} +65303.2 q^{65} +(-13119.2 + 22723.1i) q^{66} +(-16289.7 + 28214.6i) q^{67} +(4920.18 + 8522.01i) q^{68} +(-5653.72 - 9792.54i) q^{69} +44467.6 q^{70} +(8577.71 + 14857.0i) q^{71} +(-4791.23 - 8298.65i) q^{72} +(-26423.6 - 45767.1i) q^{73} +(34378.8 - 59545.8i) q^{74} +680.502 q^{75} +(29859.7 - 51718.6i) q^{76} +(-21488.7 - 37219.5i) q^{77} -65789.4 q^{78} +(10680.9 + 18499.9i) q^{79} +(22792.2 - 39477.3i) q^{80} +(-13543.6 + 23458.2i) q^{81} -22534.5 q^{82} +(-54140.1 + 93773.3i) q^{83} -24274.0 q^{84} -14764.6 q^{85} +(3006.37 + 101286. i) q^{86} +35117.2 q^{87} +22407.3 q^{88} +(-3676.02 + 6367.06i) q^{89} +93083.5 q^{90} +(53880.1 - 93323.0i) q^{91} +(-31258.8 + 54141.9i) q^{92} +(19683.0 + 34091.9i) q^{93} +153581. q^{94} +(44801.9 + 77599.1i) q^{95} +(-28312.4 + 49038.5i) q^{96} -2362.34 q^{97} +(-33542.0 + 58096.5i) q^{98} +(-44981.9 - 77911.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} + O(q^{10}) \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} - 317q^{10} + 1326q^{11} - 648q^{12} + 1006q^{13} - 1272q^{14} + 683q^{15} + 3574q^{16} + 200q^{17} + 1861q^{18} + 3361q^{19} + 3825q^{20} - 1320q^{21} - 8768q^{22} + 560q^{23} - 7382q^{24} - 3232q^{25} - 3201q^{26} - 122q^{27} + 13934q^{28} + 8887q^{29} - 19449q^{30} - 6749q^{31} - 19086q^{32} + 7106q^{33} + 8423q^{34} + 31118q^{35} - 14112q^{36} - 4514q^{37} + 7072q^{38} - 5404q^{39} - 18519q^{40} - 28996q^{41} + 58118q^{42} - 14998q^{43} + 71050q^{44} - 92096q^{45} + 20052q^{46} - 10742q^{47} + 32927q^{48} + 7472q^{49} + 20362q^{50} + 20250q^{51} + 59532q^{52} - 50572q^{53} - 230084q^{54} + 38544q^{55} - 40355q^{56} - 18087q^{57} - 33436q^{58} + 112654q^{59} + 134093q^{60} - 20120q^{61} - 31491q^{62} + 188227q^{63} + 125164q^{64} - 36578q^{65} + 8803q^{66} - 73824q^{67} - 128456q^{68} + 8005q^{69} - 141610q^{70} + 142842q^{71} + 98466q^{72} - 91624q^{73} - 99720q^{74} + 298358q^{75} + 258288q^{76} + 68051q^{77} - 201116q^{78} + 99734q^{79} - 31261q^{80} - 28441q^{81} - 147772q^{82} - 47340q^{83} - 624232q^{84} - 71734q^{85} - 115526q^{86} - 215924q^{87} - 720684q^{88} + 60402q^{89} + 676108q^{90} + 164172q^{91} + 78997q^{92} - 40793q^{93} - 341874q^{94} + 123541q^{95} - 442140q^{96} + 318476q^{97} + 217473q^{98} - 134770q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.35737 −1.47739 −0.738694 0.674041i \(-0.764557\pi\)
−0.738694 + 0.674041i \(0.764557\pi\)
\(3\) −3.42253 + 5.92800i −0.219555 + 0.380281i −0.954672 0.297659i \(-0.903794\pi\)
0.735117 + 0.677941i \(0.237127\pi\)
\(4\) 37.8456 1.18268
\(5\) −28.3920 + 49.1763i −0.507891 + 0.879693i 0.492067 + 0.870557i \(0.336241\pi\)
−0.999958 + 0.00913576i \(0.997092\pi\)
\(6\) 28.6033 49.5425i 0.324369 0.561823i
\(7\) 46.8510 + 81.1483i 0.361388 + 0.625943i 0.988190 0.153236i \(-0.0489696\pi\)
−0.626801 + 0.779179i \(0.715636\pi\)
\(8\) −48.8539 −0.269882
\(9\) 98.0726 + 169.867i 0.403591 + 0.699040i
\(10\) 237.282 410.985i 0.750352 1.29965i
\(11\) −458.660 −1.14290 −0.571451 0.820636i \(-0.693619\pi\)
−0.571451 + 0.820636i \(0.693619\pi\)
\(12\) −129.528 + 224.349i −0.259663 + 0.449749i
\(13\) −575.015 995.955i −0.943671 1.63449i −0.758390 0.651801i \(-0.774014\pi\)
−0.185281 0.982686i \(-0.559320\pi\)
\(14\) −391.551 678.186i −0.533910 0.924760i
\(15\) −194.345 336.615i −0.223020 0.386283i
\(16\) −802.769 −0.783954
\(17\) 130.007 + 225.178i 0.109105 + 0.188975i 0.915408 0.402528i \(-0.131868\pi\)
−0.806303 + 0.591503i \(0.798535\pi\)
\(18\) −819.629 1419.64i −0.596260 1.03275i
\(19\) 788.988 1366.57i 0.501403 0.868455i −0.498596 0.866834i \(-0.666151\pi\)
0.999999 0.00162026i \(-0.000515744\pi\)
\(20\) −1074.51 + 1861.11i −0.600670 + 1.04039i
\(21\) −641.396 −0.317379
\(22\) 3833.19 1.68851
\(23\) −825.957 + 1430.60i −0.325565 + 0.563895i −0.981627 0.190812i \(-0.938888\pi\)
0.656062 + 0.754707i \(0.272221\pi\)
\(24\) 167.204 289.606i 0.0592541 0.102631i
\(25\) −49.7075 86.0959i −0.0159064 0.0275507i
\(26\) 4805.61 + 8323.56i 1.39417 + 2.41477i
\(27\) −3005.98 −0.793553
\(28\) 1773.10 + 3071.11i 0.427405 + 0.740287i
\(29\) −2565.15 4442.97i −0.566393 0.981021i −0.996919 0.0784425i \(-0.975005\pi\)
0.430526 0.902578i \(-0.358328\pi\)
\(30\) 1624.21 + 2813.22i 0.329488 + 0.570689i
\(31\) 2875.50 4980.52i 0.537415 0.930829i −0.461628 0.887074i \(-0.652734\pi\)
0.999042 0.0437555i \(-0.0139323\pi\)
\(32\) 8272.36 1.42809
\(33\) 1569.78 2718.93i 0.250930 0.434624i
\(34\) −1086.51 1881.90i −0.161190 0.279189i
\(35\) −5320.77 −0.734183
\(36\) 3711.62 + 6428.71i 0.477317 + 0.826737i
\(37\) −4113.59 + 7124.94i −0.493988 + 0.855613i −0.999976 0.00692807i \(-0.997795\pi\)
0.505988 + 0.862541i \(0.331128\pi\)
\(38\) −6593.87 + 11420.9i −0.740766 + 1.28304i
\(39\) 7872.02 0.828753
\(40\) 1387.06 2402.46i 0.137071 0.237414i
\(41\) 2696.36 0.250506 0.125253 0.992125i \(-0.460026\pi\)
0.125253 + 0.992125i \(0.460026\pi\)
\(42\) 5360.38 0.468892
\(43\) −359.727 12119.4i −0.0296689 0.999560i
\(44\) −17358.3 −1.35168
\(45\) −11137.9 −0.819920
\(46\) 6902.83 11956.0i 0.480986 0.833092i
\(47\) −18376.8 −1.21346 −0.606729 0.794909i \(-0.707518\pi\)
−0.606729 + 0.794909i \(0.707518\pi\)
\(48\) 2747.50 4758.81i 0.172121 0.298123i
\(49\) 4013.47 6951.53i 0.238797 0.413609i
\(50\) 415.424 + 719.535i 0.0234999 + 0.0407031i
\(51\) −1779.81 −0.0958182
\(52\) −21761.8 37692.5i −1.11606 1.93307i
\(53\) −8839.64 + 15310.7i −0.432260 + 0.748696i −0.997068 0.0765266i \(-0.975617\pi\)
0.564808 + 0.825223i \(0.308950\pi\)
\(54\) 25122.0 1.17239
\(55\) 13022.2 22555.2i 0.580469 1.00540i
\(56\) −2288.85 3964.41i −0.0975322 0.168931i
\(57\) 5400.67 + 9354.24i 0.220171 + 0.381348i
\(58\) 21437.9 + 37131.5i 0.836782 + 1.44935i
\(59\) 10593.6 0.396197 0.198099 0.980182i \(-0.436523\pi\)
0.198099 + 0.980182i \(0.436523\pi\)
\(60\) −7355.09 12739.4i −0.263761 0.456847i
\(61\) −11254.2 19492.8i −0.387248 0.670733i 0.604830 0.796354i \(-0.293241\pi\)
−0.992078 + 0.125621i \(0.959908\pi\)
\(62\) −24031.6 + 41624.0i −0.793970 + 1.37520i
\(63\) −9189.60 + 15916.8i −0.291706 + 0.505249i
\(64\) −43446.6 −1.32588
\(65\) 65303.2 1.91713
\(66\) −13119.2 + 22723.1i −0.370721 + 0.642108i
\(67\) −16289.7 + 28214.6i −0.443329 + 0.767869i −0.997934 0.0642450i \(-0.979536\pi\)
0.554605 + 0.832114i \(0.312869\pi\)
\(68\) 4920.18 + 8522.01i 0.129035 + 0.223496i
\(69\) −5653.72 9792.54i −0.142959 0.247612i
\(70\) 44467.6 1.08467
\(71\) 8577.71 + 14857.0i 0.201942 + 0.349773i 0.949154 0.314812i \(-0.101942\pi\)
−0.747212 + 0.664585i \(0.768608\pi\)
\(72\) −4791.23 8298.65i −0.108922 0.188658i
\(73\) −26423.6 45767.1i −0.580344 1.00519i −0.995438 0.0954071i \(-0.969585\pi\)
0.415094 0.909778i \(-0.363749\pi\)
\(74\) 34378.8 59545.8i 0.729812 1.26407i
\(75\) 680.502 0.0139693
\(76\) 29859.7 51718.6i 0.592996 1.02710i
\(77\) −21488.7 37219.5i −0.413031 0.715391i
\(78\) −65789.4 −1.22439
\(79\) 10680.9 + 18499.9i 0.192549 + 0.333505i 0.946094 0.323891i \(-0.104991\pi\)
−0.753545 + 0.657396i \(0.771658\pi\)
\(80\) 22792.2 39477.3i 0.398163 0.689639i
\(81\) −13543.6 + 23458.2i −0.229362 + 0.397267i
\(82\) −22534.5 −0.370095
\(83\) −54140.1 + 93773.3i −0.862628 + 1.49412i 0.00675566 + 0.999977i \(0.497850\pi\)
−0.869383 + 0.494138i \(0.835484\pi\)
\(84\) −24274.0 −0.375356
\(85\) −14764.6 −0.221653
\(86\) 3006.37 + 101286.i 0.0438325 + 1.47674i
\(87\) 35117.2 0.497418
\(88\) 22407.3 0.308449
\(89\) −3676.02 + 6367.06i −0.0491930 + 0.0852048i −0.889573 0.456792i \(-0.848998\pi\)
0.840380 + 0.541997i \(0.182332\pi\)
\(90\) 93083.5 1.21134
\(91\) 53880.1 93323.0i 0.682063 1.18137i
\(92\) −31258.8 + 54141.9i −0.385038 + 0.666905i
\(93\) 19683.0 + 34091.9i 0.235985 + 0.408737i
\(94\) 153581. 1.79275
\(95\) 44801.9 + 77599.1i 0.509316 + 0.882160i
\(96\) −28312.4 + 49038.5i −0.313544 + 0.543075i
\(97\) −2362.34 −0.0254926 −0.0127463 0.999919i \(-0.504057\pi\)
−0.0127463 + 0.999919i \(0.504057\pi\)
\(98\) −33542.0 + 58096.5i −0.352796 + 0.611061i
\(99\) −44981.9 77911.0i −0.461265 0.798934i
\(100\) −1881.21 3258.35i −0.0188121 0.0325835i
\(101\) −83175.6 144064.i −0.811321 1.40525i −0.911940 0.410323i \(-0.865416\pi\)
0.100620 0.994925i \(-0.467918\pi\)
\(102\) 14874.5 0.141561
\(103\) 103656. + 179538.i 0.962727 + 1.66749i 0.715602 + 0.698508i \(0.246152\pi\)
0.247125 + 0.968984i \(0.420514\pi\)
\(104\) 28091.7 + 48656.3i 0.254680 + 0.441119i
\(105\) 18210.5 31541.5i 0.161194 0.279196i
\(106\) 73876.1 127957.i 0.638615 1.10611i
\(107\) 64599.8 0.545471 0.272736 0.962089i \(-0.412072\pi\)
0.272736 + 0.962089i \(0.412072\pi\)
\(108\) −113763. −0.938516
\(109\) −58687.7 + 101650.i −0.473130 + 0.819486i −0.999527 0.0307534i \(-0.990209\pi\)
0.526397 + 0.850239i \(0.323543\pi\)
\(110\) −108832. + 188502.i −0.857578 + 1.48537i
\(111\) −28157.8 48770.7i −0.216916 0.375709i
\(112\) −37610.6 65143.4i −0.283312 0.490710i
\(113\) −71866.8 −0.529459 −0.264729 0.964323i \(-0.585283\pi\)
−0.264729 + 0.964323i \(0.585283\pi\)
\(114\) −45135.4 78176.8i −0.325278 0.563399i
\(115\) −46901.1 81235.0i −0.330703 0.572794i
\(116\) −97079.6 168147.i −0.669858 1.16023i
\(117\) 112786. 195352.i 0.761714 1.31933i
\(118\) −88534.2 −0.585337
\(119\) −12181.9 + 21099.7i −0.0788583 + 0.136587i
\(120\) 9494.50 + 16445.0i 0.0601893 + 0.104251i
\(121\) 49317.6 0.306223
\(122\) 94055.3 + 162909.i 0.572115 + 0.990933i
\(123\) −9228.38 + 15984.0i −0.0550000 + 0.0952628i
\(124\) 108825. 188491.i 0.635587 1.10087i
\(125\) −171805. −0.983467
\(126\) 76800.9 133023.i 0.430963 0.746449i
\(127\) −83291.0 −0.458236 −0.229118 0.973399i \(-0.573584\pi\)
−0.229118 + 0.973399i \(0.573584\pi\)
\(128\) 98383.4 0.530758
\(129\) 73074.7 + 39346.4i 0.386628 + 0.208176i
\(130\) −545763. −2.83234
\(131\) −109663. −0.558321 −0.279160 0.960244i \(-0.590056\pi\)
−0.279160 + 0.960244i \(0.590056\pi\)
\(132\) 59409.1 102900.i 0.296769 0.514019i
\(133\) 147860. 0.724804
\(134\) 136139. 235800.i 0.654969 1.13444i
\(135\) 85345.5 147823.i 0.403038 0.698083i
\(136\) −6351.34 11000.8i −0.0294454 0.0510010i
\(137\) −250271. −1.13922 −0.569611 0.821914i \(-0.692906\pi\)
−0.569611 + 0.821914i \(0.692906\pi\)
\(138\) 47250.3 + 81839.9i 0.211206 + 0.365820i
\(139\) −77739.9 + 134649.i −0.341277 + 0.591109i −0.984670 0.174427i \(-0.944193\pi\)
0.643393 + 0.765536i \(0.277526\pi\)
\(140\) −201368. −0.868300
\(141\) 62895.0 108937.i 0.266421 0.461455i
\(142\) −71687.1 124166.i −0.298346 0.516750i
\(143\) 263736. + 456804.i 1.07852 + 1.86806i
\(144\) −78729.7 136364.i −0.316397 0.548015i
\(145\) 291318. 1.15066
\(146\) 220832. + 382493.i 0.857393 + 1.48505i
\(147\) 27472.4 + 47583.6i 0.104858 + 0.181620i
\(148\) −155681. + 269648.i −0.584228 + 1.01191i
\(149\) 177800. 307958.i 0.656093 1.13639i −0.325525 0.945533i \(-0.605541\pi\)
0.981618 0.190854i \(-0.0611256\pi\)
\(150\) −5687.20 −0.0206381
\(151\) −197297. −0.704172 −0.352086 0.935968i \(-0.614528\pi\)
−0.352086 + 0.935968i \(0.614528\pi\)
\(152\) −38545.2 + 66762.2i −0.135320 + 0.234380i
\(153\) −25500.2 + 44167.6i −0.0880673 + 0.152537i
\(154\) 179589. + 311057.i 0.610207 + 1.05691i
\(155\) 163282. + 282813.i 0.545896 + 0.945519i
\(156\) 297922. 0.980145
\(157\) 255258. + 442120.i 0.826476 + 1.43150i 0.900786 + 0.434263i \(0.142991\pi\)
−0.0743107 + 0.997235i \(0.523676\pi\)
\(158\) −89264.5 154611.i −0.284470 0.492716i
\(159\) −60507.9 104803.i −0.189810 0.328761i
\(160\) −234869. + 406805.i −0.725313 + 1.25628i
\(161\) −154788. −0.470621
\(162\) 113189. 196049.i 0.338857 0.586917i
\(163\) 113749. + 197018.i 0.335334 + 0.580815i 0.983549 0.180642i \(-0.0578177\pi\)
−0.648215 + 0.761457i \(0.724484\pi\)
\(164\) 102045. 0.296267
\(165\) 89138.1 + 154392.i 0.254890 + 0.441483i
\(166\) 452468. 783698.i 1.27444 2.20739i
\(167\) 191803. 332213.i 0.532188 0.921776i −0.467106 0.884201i \(-0.654703\pi\)
0.999294 0.0375748i \(-0.0119632\pi\)
\(168\) 31334.7 0.0856549
\(169\) −475638. + 823829.i −1.28103 + 2.21881i
\(170\) 123393. 0.327468
\(171\) 309512. 0.809446
\(172\) −13614.1 458665.i −0.0350887 1.18215i
\(173\) 125488. 0.318776 0.159388 0.987216i \(-0.449048\pi\)
0.159388 + 0.987216i \(0.449048\pi\)
\(174\) −293487. −0.734880
\(175\) 4657.69 8067.36i 0.0114968 0.0199130i
\(176\) 368198. 0.895983
\(177\) −36256.8 + 62798.6i −0.0869873 + 0.150666i
\(178\) 30721.9 53211.9i 0.0726771 0.125880i
\(179\) 188605. + 326674.i 0.439968 + 0.762047i 0.997686 0.0679829i \(-0.0216563\pi\)
−0.557718 + 0.830030i \(0.688323\pi\)
\(180\) −421520. −0.969700
\(181\) −280458. 485767.i −0.636313 1.10213i −0.986235 0.165348i \(-0.947125\pi\)
0.349922 0.936779i \(-0.386208\pi\)
\(182\) −450295. + 779935.i −1.00767 + 1.74534i
\(183\) 154071. 0.340089
\(184\) 40351.2 69890.4i 0.0878642 0.152185i
\(185\) −233586. 404582.i −0.501784 0.869116i
\(186\) −164498. 284919.i −0.348641 0.603863i
\(187\) −59628.8 103280.i −0.124696 0.215980i
\(188\) −695480. −1.43513
\(189\) −140833. 243930.i −0.286781 0.496719i
\(190\) −374426. 648524.i −0.752457 1.30329i
\(191\) 316299. 547846.i 0.627356 1.08661i −0.360724 0.932673i \(-0.617470\pi\)
0.988080 0.153941i \(-0.0491964\pi\)
\(192\) 148697. 257551.i 0.291105 0.504209i
\(193\) −890110. −1.72009 −0.860043 0.510221i \(-0.829564\pi\)
−0.860043 + 0.510221i \(0.829564\pi\)
\(194\) 19743.0 0.0376624
\(195\) −223502. + 387117.i −0.420916 + 0.729048i
\(196\) 151892. 263085.i 0.282420 0.489165i
\(197\) −454800. 787737.i −0.834940 1.44616i −0.894079 0.447909i \(-0.852169\pi\)
0.0591391 0.998250i \(-0.481164\pi\)
\(198\) 375931. + 651131.i 0.681467 + 1.18033i
\(199\) 767836. 1.37447 0.687235 0.726435i \(-0.258824\pi\)
0.687235 + 0.726435i \(0.258824\pi\)
\(200\) 2428.41 + 4206.12i 0.00429286 + 0.00743544i
\(201\) −111504. 193131.i −0.194671 0.337180i
\(202\) 695129. + 1.20400e6i 1.19864 + 2.07610i
\(203\) 240360. 416315.i 0.409375 0.709058i
\(204\) −67357.9 −0.113322
\(205\) −76555.0 + 132597.i −0.127230 + 0.220368i
\(206\) −866295. 1.50047e6i −1.42232 2.46353i
\(207\) −324015. −0.525580
\(208\) 461604. + 799522.i 0.739795 + 1.28136i
\(209\) −361877. + 626789.i −0.573054 + 0.992558i
\(210\) −152192. + 263604.i −0.238146 + 0.412481i
\(211\) 371398. 0.574293 0.287146 0.957887i \(-0.407293\pi\)
0.287146 + 0.957887i \(0.407293\pi\)
\(212\) −334541. + 579443.i −0.511223 + 0.885464i
\(213\) −117430. −0.177349
\(214\) −539884. −0.805872
\(215\) 606199. + 326403.i 0.894374 + 0.481568i
\(216\) 146854. 0.214166
\(217\) 538881. 0.776861
\(218\) 490475. 849527.i 0.698997 1.21070i
\(219\) 361743. 0.509671
\(220\) 492835. 853615.i 0.686507 1.18906i
\(221\) 149512. 258962.i 0.205918 0.356660i
\(222\) 235325. + 407594.i 0.320468 + 0.555068i
\(223\) −1.38535e6 −1.86551 −0.932756 0.360509i \(-0.882603\pi\)
−0.932756 + 0.360509i \(0.882603\pi\)
\(224\) 387569. + 671289.i 0.516094 + 0.893900i
\(225\) 9749.89 16887.3i 0.0128394 0.0222384i
\(226\) 600617. 0.782216
\(227\) 99294.2 171983.i 0.127897 0.221524i −0.794965 0.606656i \(-0.792511\pi\)
0.922862 + 0.385132i \(0.125844\pi\)
\(228\) 204392. + 354017.i 0.260391 + 0.451011i
\(229\) −342365. 592993.i −0.431420 0.747241i 0.565576 0.824696i \(-0.308654\pi\)
−0.996996 + 0.0774549i \(0.975321\pi\)
\(230\) 391970. + 678911.i 0.488577 + 0.846240i
\(231\) 294182. 0.362733
\(232\) 125318. + 217056.i 0.152859 + 0.264760i
\(233\) −548242. 949584.i −0.661581 1.14589i −0.980200 0.198009i \(-0.936553\pi\)
0.318620 0.947883i \(-0.396781\pi\)
\(234\) −942597. + 1.63263e6i −1.12535 + 1.94916i
\(235\) 521752. 903702.i 0.616304 1.06747i
\(236\) 400920. 0.468573
\(237\) −146223. −0.169101
\(238\) 101809. 176338.i 0.116504 0.201791i
\(239\) −697445. + 1.20801e6i −0.789797 + 1.36797i 0.136295 + 0.990668i \(0.456481\pi\)
−0.926091 + 0.377300i \(0.876853\pi\)
\(240\) 156014. + 270224.i 0.174838 + 0.302828i
\(241\) 162198. + 280934.i 0.179888 + 0.311575i 0.941842 0.336056i \(-0.109093\pi\)
−0.761954 + 0.647631i \(0.775760\pi\)
\(242\) −412165. −0.452411
\(243\) −457933. 793163.i −0.497492 0.861681i
\(244\) −425921. 737717.i −0.457988 0.793259i
\(245\) 227900. + 394735.i 0.242566 + 0.420137i
\(246\) 77124.9 133584.i 0.0812563 0.140740i
\(247\) −1.81472e6 −1.89264
\(248\) −140479. + 243318.i −0.145039 + 0.251214i
\(249\) −370592. 641884.i −0.378789 0.656082i
\(250\) 1.43583e6 1.45296
\(251\) 253707. + 439434.i 0.254184 + 0.440260i 0.964674 0.263448i \(-0.0848597\pi\)
−0.710489 + 0.703708i \(0.751526\pi\)
\(252\) −347786. + 602383.i −0.344993 + 0.597546i
\(253\) 378833. 656158.i 0.372089 0.644477i
\(254\) 696094. 0.676992
\(255\) 50532.3 87524.4i 0.0486652 0.0842906i
\(256\) 568064. 0.541748
\(257\) 1.28760e6 1.21604 0.608020 0.793922i \(-0.291964\pi\)
0.608020 + 0.793922i \(0.291964\pi\)
\(258\) −610713. 328833.i −0.571199 0.307557i
\(259\) −770903. −0.714086
\(260\) 2.47144e6 2.26734
\(261\) 503141. 871467.i 0.457182 0.791862i
\(262\) 916498. 0.824856
\(263\) −730252. + 1.26483e6i −0.651003 + 1.12757i 0.331876 + 0.943323i \(0.392318\pi\)
−0.982880 + 0.184248i \(0.941015\pi\)
\(264\) −76689.7 + 132830.i −0.0677216 + 0.117297i
\(265\) −501949. 869402.i −0.439082 0.760512i
\(266\) −1.23572e6 −1.07082
\(267\) −25162.6 43582.9i −0.0216012 0.0374143i
\(268\) −616494. + 1.06780e6i −0.524315 + 0.908139i
\(269\) −2.06308e6 −1.73834 −0.869172 0.494510i \(-0.835347\pi\)
−0.869172 + 0.494510i \(0.835347\pi\)
\(270\) −713264. + 1.23541e6i −0.595444 + 1.03134i
\(271\) 560182. + 970263.i 0.463346 + 0.802539i 0.999125 0.0418190i \(-0.0133153\pi\)
−0.535779 + 0.844358i \(0.679982\pi\)
\(272\) −104365. 180766.i −0.0855332 0.148148i
\(273\) 368812. + 638802.i 0.299501 + 0.518751i
\(274\) 2.09160e6 1.68307
\(275\) 22798.8 + 39488.7i 0.0181794 + 0.0314877i
\(276\) −213969. 370605.i −0.169074 0.292845i
\(277\) −15759.6 + 27296.4i −0.0123409 + 0.0213750i −0.872130 0.489274i \(-0.837262\pi\)
0.859789 + 0.510649i \(0.170595\pi\)
\(278\) 649701. 1.12532e6i 0.504199 0.873297i
\(279\) 1.12803e6 0.867582
\(280\) 259940. 0.198143
\(281\) 151807. 262937.i 0.114690 0.198649i −0.802966 0.596025i \(-0.796746\pi\)
0.917656 + 0.397376i \(0.130079\pi\)
\(282\) −525637. + 910430.i −0.393607 + 0.681748i
\(283\) 773096. + 1.33904e6i 0.573809 + 0.993866i 0.996170 + 0.0874383i \(0.0278681\pi\)
−0.422361 + 0.906428i \(0.638799\pi\)
\(284\) 324629. + 562273.i 0.238831 + 0.413668i
\(285\) −613343. −0.447292
\(286\) −2.20414e6 3.81768e6i −1.59340 2.75984i
\(287\) 126327. + 218805.i 0.0905299 + 0.156802i
\(288\) 811292. + 1.40520e6i 0.576363 + 0.998290i
\(289\) 676125. 1.17108e6i 0.476192 0.824789i
\(290\) −2.43466e6 −1.69998
\(291\) 8085.20 14004.0i 0.00559704 0.00969435i
\(292\) −1.00002e6 1.73208e6i −0.686359 1.18881i
\(293\) 515354. 0.350701 0.175351 0.984506i \(-0.443894\pi\)
0.175351 + 0.984506i \(0.443894\pi\)
\(294\) −229597. 397674.i −0.154917 0.268324i
\(295\) −300772. + 520952.i −0.201225 + 0.348532i
\(296\) 200965. 348081.i 0.133319 0.230915i
\(297\) 1.37872e6 0.906953
\(298\) −1.48594e6 + 2.57372e6i −0.969305 + 1.67888i
\(299\) 1.89975e6 1.22891
\(300\) 25754.0 0.0165212
\(301\) 966613. 596996.i 0.614945 0.379800i
\(302\) 1.64889e6 1.04034
\(303\) 1.13868e6 0.712519
\(304\) −633376. + 1.09704e6i −0.393077 + 0.680829i
\(305\) 1.27811e6 0.786719
\(306\) 213115. 369125.i 0.130110 0.225357i
\(307\) −1.12118e6 + 1.94195e6i −0.678939 + 1.17596i 0.296362 + 0.955076i \(0.404226\pi\)
−0.975301 + 0.220881i \(0.929107\pi\)
\(308\) −813252. 1.40859e6i −0.488481 0.846075i
\(309\) −1.41907e6 −0.845488
\(310\) −1.36461e6 2.36357e6i −0.806500 1.39690i
\(311\) −496661. + 860242.i −0.291178 + 0.504335i −0.974089 0.226167i \(-0.927381\pi\)
0.682910 + 0.730502i \(0.260714\pi\)
\(312\) −384579. −0.223666
\(313\) −538594. + 932872.i −0.310742 + 0.538221i −0.978523 0.206136i \(-0.933911\pi\)
0.667781 + 0.744358i \(0.267244\pi\)
\(314\) −2.13328e6 3.69496e6i −1.22103 2.11488i
\(315\) −521821. 903821.i −0.296309 0.513223i
\(316\) 404227. + 700141.i 0.227723 + 0.394428i
\(317\) −310312. −0.173441 −0.0867203 0.996233i \(-0.527639\pi\)
−0.0867203 + 0.996233i \(0.527639\pi\)
\(318\) 505687. + 875875.i 0.280423 + 0.485707i
\(319\) 1.17653e6 + 2.03781e6i 0.647331 + 1.12121i
\(320\) 1.23353e6 2.13654e6i 0.673405 1.16637i
\(321\) −221095. + 382947.i −0.119761 + 0.207432i
\(322\) 1.29362e6 0.695290
\(323\) 410295. 0.218822
\(324\) −512566. + 887790.i −0.271261 + 0.469837i
\(325\) −57165.1 + 99012.9i −0.0300208 + 0.0519976i
\(326\) −950639. 1.64655e6i −0.495418 0.858089i
\(327\) −401721. 695801.i −0.207757 0.359845i
\(328\) −131728. −0.0676072
\(329\) −860970. 1.49124e6i −0.438529 0.759554i
\(330\) −744960. 1.29031e6i −0.376572 0.652242i
\(331\) 135030. + 233878.i 0.0677421 + 0.117333i 0.897907 0.440185i \(-0.145087\pi\)
−0.830165 + 0.557518i \(0.811754\pi\)
\(332\) −2.04896e6 + 3.54891e6i −1.02021 + 1.76705i
\(333\) −1.61372e6 −0.797476
\(334\) −1.60297e6 + 2.77643e6i −0.786248 + 1.36182i
\(335\) −924994. 1.60214e6i −0.450326 0.779987i
\(336\) 514893. 0.248811
\(337\) 648277. + 1.12285e6i 0.310946 + 0.538575i 0.978568 0.205926i \(-0.0660207\pi\)
−0.667621 + 0.744501i \(0.732687\pi\)
\(338\) 3.97508e6 6.88504e6i 1.89258 3.27804i
\(339\) 245966. 426026.i 0.116246 0.201343i
\(340\) −558775. −0.262144
\(341\) −1.31888e6 + 2.28436e6i −0.614212 + 1.06385i
\(342\) −2.58671e6 −1.19587
\(343\) 2.32699e6 1.06797
\(344\) 17574.1 + 592078.i 0.00800712 + 0.269763i
\(345\) 642081. 0.290431
\(346\) −1.04875e6 −0.470956
\(347\) 1.78156e6 3.08576e6i 0.794287 1.37575i −0.129004 0.991644i \(-0.541178\pi\)
0.923291 0.384102i \(-0.125489\pi\)
\(348\) 1.32903e6 0.588284
\(349\) 263512. 456416.i 0.115807 0.200584i −0.802295 0.596928i \(-0.796388\pi\)
0.918102 + 0.396344i \(0.129721\pi\)
\(350\) −38926.1 + 67421.9i −0.0169852 + 0.0294192i
\(351\) 1.72848e6 + 2.99382e6i 0.748853 + 1.29705i
\(352\) −3.79420e6 −1.63216
\(353\) −136307. 236090.i −0.0582210 0.100842i 0.835446 0.549573i \(-0.185209\pi\)
−0.893667 + 0.448731i \(0.851876\pi\)
\(354\) 303011. 524831.i 0.128514 0.222593i
\(355\) −974152. −0.410257
\(356\) −139121. + 240965.i −0.0581793 + 0.100770i
\(357\) −83385.8 144428.i −0.0346275 0.0599767i
\(358\) −1.57624e6 2.73014e6i −0.650004 1.12584i
\(359\) −117873. 204162.i −0.0482700 0.0836062i 0.840881 0.541220i \(-0.182037\pi\)
−0.889151 + 0.457614i \(0.848704\pi\)
\(360\) 544130. 0.221282
\(361\) −6955.34 12047.0i −0.00280899 0.00486531i
\(362\) 2.34389e6 + 4.05974e6i 0.940082 + 1.62827i
\(363\) −168791. + 292355.i −0.0672330 + 0.116451i
\(364\) 2.03912e6 3.53187e6i 0.806659 1.39717i
\(365\) 3.00088e6 1.17901
\(366\) −1.28763e6 −0.502444
\(367\) 95690.0 165740.i 0.0370853 0.0642335i −0.846887 0.531773i \(-0.821526\pi\)
0.883972 + 0.467539i \(0.154859\pi\)
\(368\) 663053. 1.14844e6i 0.255228 0.442068i
\(369\) 264439. + 458022.i 0.101102 + 0.175114i
\(370\) 1.95216e6 + 3.38124e6i 0.741330 + 1.28402i
\(371\) −1.65658e6 −0.624854
\(372\) 744915. + 1.29023e6i 0.279093 + 0.483403i
\(373\) 2.13554e6 + 3.69887e6i 0.794761 + 1.37657i 0.922991 + 0.384822i \(0.125737\pi\)
−0.128230 + 0.991744i \(0.540930\pi\)
\(374\) 498340. + 863151.i 0.184224 + 0.319086i
\(375\) 588007. 1.01846e6i 0.215926 0.373994i
\(376\) 897777. 0.327491
\(377\) −2.95000e6 + 5.10955e6i −1.06898 + 1.85152i
\(378\) 1.17699e6 + 2.03861e6i 0.423686 + 0.733846i
\(379\) 1.79297e6 0.641174 0.320587 0.947219i \(-0.396120\pi\)
0.320587 + 0.947219i \(0.396120\pi\)
\(380\) 1.69555e6 + 2.93678e6i 0.602355 + 1.04331i
\(381\) 285066. 493749.i 0.100608 0.174258i
\(382\) −2.64343e6 + 4.57855e6i −0.926849 + 1.60535i
\(383\) −1.84837e6 −0.643860 −0.321930 0.946764i \(-0.604332\pi\)
−0.321930 + 0.946764i \(0.604332\pi\)
\(384\) −336720. + 583216.i −0.116531 + 0.201837i
\(385\) 2.44042e6 0.839099
\(386\) 7.43898e6 2.54124
\(387\) 2.02340e6 1.24968e6i 0.686758 0.424153i
\(388\) −89404.4 −0.0301494
\(389\) −355080. −0.118974 −0.0594870 0.998229i \(-0.518946\pi\)
−0.0594870 + 0.998229i \(0.518946\pi\)
\(390\) 1.86789e6 3.23528e6i 0.621856 1.07709i
\(391\) −429520. −0.142083
\(392\) −196074. + 339609.i −0.0644472 + 0.111626i
\(393\) 375327. 650085.i 0.122582 0.212319i
\(394\) 3.80093e6 + 6.58341e6i 1.23353 + 2.13654i
\(395\) −1.21301e6 −0.391176
\(396\) −1.70237e6 2.94859e6i −0.545526 0.944879i
\(397\) −380957. + 659837.i −0.121311 + 0.210117i −0.920285 0.391249i \(-0.872043\pi\)
0.798974 + 0.601366i \(0.205376\pi\)
\(398\) −6.41708e6 −2.03063
\(399\) −506054. + 876511.i −0.159135 + 0.275629i
\(400\) 39903.7 + 69115.2i 0.0124699 + 0.0215985i
\(401\) 653898. + 1.13258e6i 0.203071 + 0.351730i 0.949517 0.313717i \(-0.101574\pi\)
−0.746445 + 0.665447i \(0.768241\pi\)
\(402\) 931881. + 1.61406e6i 0.287604 + 0.498145i
\(403\) −6.61383e6 −2.02857
\(404\) −3.14783e6 5.45220e6i −0.959529 1.66195i
\(405\) −769058. 1.33205e6i −0.232982 0.403536i
\(406\) −2.00877e6 + 3.47930e6i −0.604806 + 1.04755i
\(407\) 1.88674e6 3.26792e6i 0.564580 0.977881i
\(408\) 86950.6 0.0258596
\(409\) −924961. −0.273411 −0.136705 0.990612i \(-0.543651\pi\)
−0.136705 + 0.990612i \(0.543651\pi\)
\(410\) 639798. 1.10816e6i 0.187968 0.325570i
\(411\) 856559. 1.48360e6i 0.250123 0.433225i
\(412\) 3.92294e6 + 6.79473e6i 1.13859 + 1.97210i
\(413\) 496319. + 859649.i 0.143181 + 0.247997i
\(414\) 2.70791e6 0.776486
\(415\) −3.07429e6 5.32482e6i −0.876242 1.51770i
\(416\) −4.75673e6 8.23890e6i −1.34764 2.33419i
\(417\) −532134. 921684.i −0.149858 0.259562i
\(418\) 3.02434e6 5.23831e6i 0.846623 1.46639i
\(419\) 1.96417e6 0.546569 0.273284 0.961933i \(-0.411890\pi\)
0.273284 + 0.961933i \(0.411890\pi\)
\(420\) 689187. 1.19371e6i 0.190640 0.330198i
\(421\) −2.42480e6 4.19988e6i −0.666762 1.15487i −0.978804 0.204797i \(-0.934346\pi\)
0.312042 0.950068i \(-0.398987\pi\)
\(422\) −3.10391e6 −0.848453
\(423\) −1.80226e6 3.12160e6i −0.489740 0.848255i
\(424\) 431851. 747988.i 0.116659 0.202060i
\(425\) 12924.6 22386.1i 0.00347093 0.00601182i
\(426\) 981405. 0.262014
\(427\) 1.05454e6 1.82651e6i 0.279894 0.484790i
\(428\) 2.44482e6 0.645115
\(429\) −3.61058e6 −0.947182
\(430\) −5.06623e6 2.72787e6i −1.32134 0.711462i
\(431\) −4.86489e6 −1.26148 −0.630740 0.775994i \(-0.717248\pi\)
−0.630740 + 0.775994i \(0.717248\pi\)
\(432\) 2.41310e6 0.622109
\(433\) 2.25579e6 3.90715e6i 0.578202 1.00147i −0.417484 0.908684i \(-0.637088\pi\)
0.995686 0.0927906i \(-0.0295787\pi\)
\(434\) −4.50362e6 −1.14772
\(435\) −997046. + 1.72693e6i −0.252634 + 0.437575i
\(436\) −2.22107e6 + 3.84701e6i −0.559559 + 0.969185i
\(437\) 1.30334e6 + 2.25745e6i 0.326478 + 0.565477i
\(438\) −3.02322e6 −0.752982
\(439\) 137751. + 238592.i 0.0341141 + 0.0590874i 0.882578 0.470165i \(-0.155806\pi\)
−0.848464 + 0.529253i \(0.822472\pi\)
\(440\) −636188. + 1.10191e6i −0.156658 + 0.271340i
\(441\) 1.57444e6 0.385506
\(442\) −1.24952e6 + 2.16424e6i −0.304221 + 0.526926i
\(443\) 156644. + 271315.i 0.0379230 + 0.0656846i 0.884364 0.466798i \(-0.154592\pi\)
−0.846441 + 0.532483i \(0.821259\pi\)
\(444\) −1.06565e6 1.84576e6i −0.256541 0.444341i
\(445\) −208739. 361547.i −0.0499693 0.0865494i
\(446\) 1.15779e7 2.75608
\(447\) 1.21705e6 + 2.10799e6i 0.288098 + 0.499000i
\(448\) −2.03552e6 3.52562e6i −0.479159 0.829927i
\(449\) 1.17180e6 2.02962e6i 0.274308 0.475115i −0.695652 0.718379i \(-0.744885\pi\)
0.969960 + 0.243263i \(0.0782179\pi\)
\(450\) −81483.4 + 141133.i −0.0189687 + 0.0328548i
\(451\) −1.23671e6 −0.286304
\(452\) −2.71984e6 −0.626178
\(453\) 675256. 1.16958e6i 0.154605 0.267784i
\(454\) −829838. + 1.43732e6i −0.188953 + 0.327276i
\(455\) 3.05952e6 + 5.29925e6i 0.692827 + 1.20001i
\(456\) −263844. 456991.i −0.0594203 0.102919i
\(457\) −304510. −0.0682042 −0.0341021 0.999418i \(-0.510857\pi\)
−0.0341021 + 0.999418i \(0.510857\pi\)
\(458\) 2.86127e6 + 4.95586e6i 0.637375 + 1.10397i
\(459\) −390797. 676880.i −0.0865804 0.149962i
\(460\) −1.77500e6 3.07439e6i −0.391114 0.677430i
\(461\) −2.22554e6 + 3.85474e6i −0.487733 + 0.844779i −0.999900 0.0141070i \(-0.995509\pi\)
0.512167 + 0.858886i \(0.328843\pi\)
\(462\) −2.45859e6 −0.535897
\(463\) 2.14765e6 3.71983e6i 0.465597 0.806438i −0.533631 0.845717i \(-0.679173\pi\)
0.999228 + 0.0392792i \(0.0125062\pi\)
\(464\) 2.05922e6 + 3.56668e6i 0.444026 + 0.769076i
\(465\) −2.23535e6 −0.479418
\(466\) 4.58186e6 + 7.93602e6i 0.977411 + 1.69293i
\(467\) 374778. 649134.i 0.0795210 0.137734i −0.823522 0.567284i \(-0.807994\pi\)
0.903043 + 0.429549i \(0.141328\pi\)
\(468\) 4.26847e6 7.39321e6i 0.900860 1.56034i
\(469\) −3.05276e6 −0.640856
\(470\) −4.36048e6 + 7.55257e6i −0.910520 + 1.57707i
\(471\) −3.49451e6 −0.725829
\(472\) −517537. −0.106927
\(473\) 164992. + 5.55866e6i 0.0339087 + 1.14240i
\(474\) 1.22204e6 0.249828
\(475\) −156875. −0.0319020
\(476\) −461031. + 798530.i −0.0932638 + 0.161538i
\(477\) −3.46770e6 −0.697824
\(478\) 5.82881e6 1.00958e7i 1.16684 2.02102i
\(479\) −1.47603e6 + 2.55656e6i −0.293939 + 0.509117i −0.974737 0.223354i \(-0.928300\pi\)
0.680799 + 0.732471i \(0.261633\pi\)
\(480\) −1.60769e6 2.78460e6i −0.318493 0.551645i
\(481\) 9.46150e6 1.86465
\(482\) −1.35554e6 2.34787e6i −0.265764 0.460317i
\(483\) 529765. 917581.i 0.103327 0.178968i
\(484\) 1.86645e6 0.362163
\(485\) 67071.6 116171.i 0.0129475 0.0224256i
\(486\) 3.82711e6 + 6.62875e6i 0.734989 + 1.27304i
\(487\) −4.52006e6 7.82897e6i −0.863617 1.49583i −0.868414 0.495841i \(-0.834860\pi\)
0.00479621 0.999988i \(-0.498473\pi\)
\(488\) 549810. + 952299.i 0.104511 + 0.181019i
\(489\) −1.55723e6 −0.294497
\(490\) −1.90465e6 3.29895e6i −0.358364 0.620705i
\(491\) −965264. 1.67189e6i −0.180693 0.312970i 0.761423 0.648255i \(-0.224501\pi\)
−0.942117 + 0.335285i \(0.891168\pi\)
\(492\) −349254. + 604925.i −0.0650471 + 0.112665i
\(493\) 666973. 1.15523e6i 0.123592 0.214068i
\(494\) 1.51663e7 2.79616
\(495\) 5.10850e6 0.937088
\(496\) −2.30836e6 + 3.99821e6i −0.421309 + 0.729728i
\(497\) −803749. + 1.39213e6i −0.145959 + 0.252808i
\(498\) 3.09717e6 + 5.36446e6i 0.559619 + 0.969288i
\(499\) 4.45984e6 + 7.72466e6i 0.801803 + 1.38876i 0.918428 + 0.395587i \(0.129459\pi\)
−0.116625 + 0.993176i \(0.537208\pi\)
\(500\) −6.50205e6 −1.16312
\(501\) 1.31290e6 + 2.27402e6i 0.233689 + 0.404762i
\(502\) −2.12032e6 3.67251e6i −0.375529 0.650435i
\(503\) −304605. 527591.i −0.0536805 0.0929774i 0.837936 0.545768i \(-0.183762\pi\)
−0.891617 + 0.452790i \(0.850429\pi\)
\(504\) 448948. 777600.i 0.0787262 0.136358i
\(505\) 9.44607e6 1.64825
\(506\) −3.16605e6 + 5.48375e6i −0.549719 + 0.952142i
\(507\) −3.25577e6 5.63916e6i −0.562515 0.974304i
\(508\) −3.15220e6 −0.541944
\(509\) 4.72097e6 + 8.17696e6i 0.807675 + 1.39893i 0.914470 + 0.404654i \(0.132608\pi\)
−0.106795 + 0.994281i \(0.534059\pi\)
\(510\) −422317. + 731474.i −0.0718973 + 0.124530i
\(511\) 2.47595e6 4.28847e6i 0.419459 0.726524i
\(512\) −7.89579e6 −1.33113
\(513\) −2.37168e6 + 4.10787e6i −0.397890 + 0.689165i
\(514\) −1.07609e7 −1.79656
\(515\) −1.17720e7 −1.95584
\(516\) 2.76556e6 + 1.48909e6i 0.457255 + 0.246205i
\(517\) 8.42868e6 1.38686
\(518\) 6.44272e6 1.05498
\(519\) −429485. + 743890.i −0.0699890 + 0.121224i
\(520\) −3.19032e6 −0.517399
\(521\) 2.15292e6 3.72897e6i 0.347483 0.601859i −0.638318 0.769772i \(-0.720370\pi\)
0.985802 + 0.167914i \(0.0537030\pi\)
\(522\) −4.20494e6 + 7.28317e6i −0.675435 + 1.16989i
\(523\) −2.25393e6 3.90392e6i −0.360318 0.624089i 0.627695 0.778459i \(-0.283998\pi\)
−0.988013 + 0.154371i \(0.950665\pi\)
\(524\) −4.15028e6 −0.660312
\(525\) 31882.2 + 55221.6i 0.00504836 + 0.00874401i
\(526\) 6.10298e6 1.05707e7i 0.961785 1.66586i
\(527\) 1.49534e6 0.234538
\(528\) −1.26017e6 + 2.18268e6i −0.196718 + 0.340725i
\(529\) 1.85376e6 + 3.21081e6i 0.288015 + 0.498856i
\(530\) 4.19498e6 + 7.26591e6i 0.648694 + 1.12357i
\(531\) 1.03894e6 + 1.79949e6i 0.159902 + 0.276958i
\(532\) 5.59584e6 0.857207
\(533\) −1.55045e6 2.68545e6i −0.236395 0.409449i
\(534\) 210293. + 364238.i 0.0319133 + 0.0552755i
\(535\) −1.83412e6 + 3.17678e6i −0.277040 + 0.479847i
\(536\) 795816. 1.37839e6i 0.119647 0.207234i
\(537\) −2.58203e6 −0.386390
\(538\) 1.72419e7 2.56821
\(539\) −1.84081e6 + 3.18838e6i −0.272922 + 0.472714i
\(540\) 3.22995e6 5.59444e6i 0.476664 0.825606i
\(541\) −6.30682e6 1.09237e7i −0.926440 1.60464i −0.789229 0.614098i \(-0.789520\pi\)
−0.137210 0.990542i \(-0.543814\pi\)
\(542\) −4.68164e6 8.10885e6i −0.684542 1.18566i
\(543\) 3.83950e6 0.558824
\(544\) 1.07546e6 + 1.86276e6i 0.155811 + 0.269873i
\(545\) −3.33252e6 5.77209e6i −0.480597 0.832419i
\(546\) −3.08230e6 5.33870e6i −0.442480 0.766397i
\(547\) 763367. 1.32219e6i 0.109085 0.188941i −0.806315 0.591487i \(-0.798541\pi\)
0.915400 + 0.402546i \(0.131875\pi\)
\(548\) −9.47165e6 −1.34733
\(549\) 2.20745e6 3.82342e6i 0.312579 0.541403i
\(550\) −190538. 330022.i −0.0268581 0.0465196i
\(551\) −8.09549e6 −1.13596
\(552\) 276207. + 478404.i 0.0385821 + 0.0668262i
\(553\) −1.00083e6 + 1.73348e6i −0.139170 + 0.241049i
\(554\) 131709. 228126.i 0.0182322 0.0315791i
\(555\) 3.19782e6 0.440678
\(556\) −2.94211e6 + 5.09589e6i −0.403620 + 0.699090i
\(557\) 9.01282e6 1.23090 0.615450 0.788176i \(-0.288974\pi\)
0.615450 + 0.788176i \(0.288974\pi\)
\(558\) −9.42737e6 −1.28176
\(559\) −1.18635e7 + 7.32709e6i −1.60577 + 0.991749i
\(560\) 4.27135e6 0.575566
\(561\) 816326. 0.109511
\(562\) −1.26871e6 + 2.19746e6i −0.169442 + 0.293482i
\(563\) 1.21643e6 0.161740 0.0808701 0.996725i \(-0.474230\pi\)
0.0808701 + 0.996725i \(0.474230\pi\)
\(564\) 2.38030e6 4.12280e6i 0.315090 0.545751i
\(565\) 2.04044e6 3.53415e6i 0.268907 0.465761i
\(566\) −6.46105e6 1.11909e7i −0.847738 1.46833i
\(567\) −2.53812e6 −0.331555
\(568\) −419055. 725824.i −0.0545004 0.0943975i
\(569\) −5.37087e6 + 9.30261e6i −0.695447 + 1.20455i 0.274583 + 0.961563i \(0.411460\pi\)
−0.970030 + 0.242985i \(0.921873\pi\)
\(570\) 5.12593e6 0.660824
\(571\) 294182. 509538.i 0.0377595 0.0654013i −0.846528 0.532344i \(-0.821311\pi\)
0.884288 + 0.466943i \(0.154645\pi\)
\(572\) 9.98125e6 + 1.72880e7i 1.27554 + 2.20930i
\(573\) 2.16509e6 + 3.75004e6i 0.275479 + 0.477144i
\(574\) −1.05576e6 1.82864e6i −0.133748 0.231658i
\(575\) 164225. 0.0207143
\(576\) −4.26092e6 7.38013e6i −0.535115 0.926846i
\(577\) 2.68920e6 + 4.65784e6i 0.336267 + 0.582432i 0.983727 0.179668i \(-0.0575022\pi\)
−0.647460 + 0.762099i \(0.724169\pi\)
\(578\) −5.65063e6 + 9.78717e6i −0.703521 + 1.21853i
\(579\) 3.04643e6 5.27657e6i 0.377654 0.654117i
\(580\) 1.10251e7 1.36086
\(581\) −1.01461e7 −1.24697
\(582\) −67571.0 + 117036.i −0.00826899 + 0.0143223i
\(583\) 4.05438e6 7.02240e6i 0.494030 0.855686i
\(584\) 1.29090e6 + 2.23590e6i 0.156625 + 0.271282i
\(585\) 6.40445e6 + 1.10928e7i 0.773735 + 1.34015i
\(586\) −4.30701e6 −0.518121
\(587\) 2.20215e6 + 3.81423e6i 0.263785 + 0.456890i 0.967245 0.253846i \(-0.0816956\pi\)
−0.703459 + 0.710736i \(0.748362\pi\)
\(588\) 1.03971e6 + 1.80083e6i 0.124014 + 0.214798i
\(589\) −4.53747e6 7.85914e6i −0.538922 0.933440i
\(590\) 2.51366e6 4.35379e6i 0.297288 0.514917i
\(591\) 6.22627e6 0.733263
\(592\) 3.30226e6 5.71969e6i 0.387264 0.670761i
\(593\) 7.09043e6 + 1.22810e7i 0.828011 + 1.43416i 0.899596 + 0.436723i \(0.143861\pi\)
−0.0715852 + 0.997434i \(0.522806\pi\)
\(594\) −1.15225e7 −1.33992
\(595\) −691736. 1.19812e6i −0.0801028 0.138742i
\(596\) 6.72894e6 1.16549e7i 0.775946 1.34398i
\(597\) −2.62794e6 + 4.55173e6i −0.301773 + 0.522685i
\(598\) −1.58769e7 −1.81557
\(599\) 7.59442e6 1.31539e7i 0.864824 1.49792i −0.00239863 0.999997i \(-0.500764\pi\)
0.867222 0.497921i \(-0.165903\pi\)
\(600\) −33245.2 −0.00377008
\(601\) 1.34950e7 1.52401 0.762004 0.647573i \(-0.224216\pi\)
0.762004 + 0.647573i \(0.224216\pi\)
\(602\) −8.07834e6 + 4.98931e6i −0.908512 + 0.561112i
\(603\) −6.39030e6 −0.715695
\(604\) −7.46684e6 −0.832807
\(605\) −1.40022e6 + 2.42526e6i −0.155528 + 0.269383i
\(606\) −9.51640e6 −1.05267
\(607\) 4.63617e6 8.03008e6i 0.510726 0.884603i −0.489197 0.872173i \(-0.662710\pi\)
0.999923 0.0124296i \(-0.00395657\pi\)
\(608\) 6.52680e6 1.13047e7i 0.716047 1.24023i
\(609\) 1.64528e6 + 2.84970e6i 0.179761 + 0.311355i
\(610\) −1.06817e7 −1.16229
\(611\) 1.05669e7 + 1.83024e7i 1.14510 + 1.98338i
\(612\) −965070. + 1.67155e6i −0.104155 + 0.180402i
\(613\) −1.76428e7 −1.89634 −0.948170 0.317764i \(-0.897068\pi\)
−0.948170 + 0.317764i \(0.897068\pi\)
\(614\) 9.37014e6 1.62296e7i 1.00306 1.73734i
\(615\) −524024. 907635.i −0.0558680 0.0967662i
\(616\) 1.04981e6 + 1.81832e6i 0.111470 + 0.193071i
\(617\) −3.05802e6 5.29665e6i −0.323391 0.560129i 0.657795 0.753197i \(-0.271489\pi\)
−0.981185 + 0.193068i \(0.938156\pi\)
\(618\) 1.18597e7 1.24911
\(619\) −3.35275e6 5.80713e6i −0.351701 0.609165i 0.634846 0.772639i \(-0.281063\pi\)
−0.986548 + 0.163474i \(0.947730\pi\)
\(620\) 6.17952e6 + 1.07032e7i 0.645618 + 1.11824i
\(621\) 2.48281e6 4.30035e6i 0.258353 0.447481i
\(622\) 4.15078e6 7.18936e6i 0.430183 0.745099i
\(623\) −688901. −0.0711110
\(624\) −6.31942e6 −0.649704
\(625\) 5.03321e6 8.71777e6i 0.515400 0.892700i
\(626\) 4.50123e6 7.79635e6i 0.459087 0.795162i
\(627\) −2.47707e6 4.29041e6i −0.251634 0.435843i
\(628\) 9.66039e6 + 1.67323e7i 0.977452 + 1.69300i
\(629\) −2.13918e6 −0.215586
\(630\) 4.36105e6 + 7.55357e6i 0.437764 + 0.758230i
\(631\) 2.59417e6 + 4.49323e6i 0.259373 + 0.449247i 0.966074 0.258265i \(-0.0831508\pi\)
−0.706701 + 0.707512i \(0.749817\pi\)
\(632\) −521805. 903794.i −0.0519656 0.0900071i
\(633\) −1.27112e6 + 2.20165e6i −0.126089 + 0.218393i
\(634\) 2.59339e6 0.256239
\(635\) 2.36480e6 4.09595e6i 0.232734 0.403107i
\(636\) −2.28996e6 3.96632e6i −0.224484 0.388817i
\(637\) −9.23121e6 −0.901385
\(638\) −9.83269e6 1.70307e7i −0.956359 1.65646i
\(639\) −1.68248e6 + 2.91413e6i −0.163003 + 0.282330i
\(640\) −2.79330e6 + 4.83813e6i −0.269567 + 0.466904i
\(641\) −1.86054e7 −1.78852 −0.894260 0.447548i \(-0.852297\pi\)
−0.894260 + 0.447548i \(0.852297\pi\)
\(642\) 1.84777e6 3.20043e6i 0.176934 0.306458i
\(643\) −1.65511e7 −1.57870 −0.789351 0.613942i \(-0.789583\pi\)
−0.789351 + 0.613942i \(0.789583\pi\)
\(644\) −5.85803e6 −0.556592
\(645\) −4.00965e6 + 2.47642e6i −0.379496 + 0.234383i
\(646\) −3.42899e6 −0.323284
\(647\) −8.62069e6 −0.809620 −0.404810 0.914401i \(-0.632662\pi\)
−0.404810 + 0.914401i \(0.632662\pi\)
\(648\) 661657. 1.14602e6i 0.0619007 0.107215i
\(649\) −4.85884e6 −0.452815
\(650\) 477750. 827487.i 0.0443524 0.0768206i
\(651\) −1.84434e6 + 3.19448e6i −0.170564 + 0.295426i
\(652\) 4.30488e6 + 7.45628e6i 0.396591 + 0.686915i
\(653\) −9.35627e6 −0.858657 −0.429328 0.903148i \(-0.641250\pi\)
−0.429328 + 0.903148i \(0.641250\pi\)
\(654\) 3.35733e6 + 5.81506e6i 0.306937 + 0.531631i
\(655\) 3.11356e6 5.39285e6i 0.283566 0.491151i
\(656\) −2.16456e6 −0.196385
\(657\) 5.18287e6 8.97699e6i 0.468443 0.811367i
\(658\) 7.19544e6 + 1.24629e7i 0.647877 + 1.12216i
\(659\) 2.75315e6 + 4.76859e6i 0.246954 + 0.427737i 0.962679 0.270645i \(-0.0872370\pi\)
−0.715725 + 0.698382i \(0.753904\pi\)
\(660\) 3.37348e6 + 5.84305e6i 0.301453 + 0.522131i
\(661\) 1.49996e7 1.33530 0.667648 0.744478i \(-0.267301\pi\)
0.667648 + 0.744478i \(0.267301\pi\)
\(662\) −1.12849e6 1.95460e6i −0.100081 0.173346i
\(663\) 1.02342e6 + 1.77261e6i 0.0904208 + 0.156613i
\(664\) 2.64495e6 4.58119e6i 0.232808 0.403235i
\(665\) −4.19802e6 + 7.27119e6i −0.368121 + 0.637605i
\(666\) 1.34865e7 1.17818
\(667\) 8.47481e6 0.737590
\(668\) 7.25891e6 1.25728e7i 0.629405 1.09016i
\(669\) 4.74141e6 8.21236e6i 0.409583 0.709419i
\(670\) 7.73052e6 + 1.33896e7i 0.665306 + 1.15234i
\(671\) 5.16183e6 + 8.94056e6i 0.442586 + 0.766582i
\(672\) −5.30586e6 −0.453245
\(673\) 1.08883e7 + 1.88590e7i 0.926660 + 1.60502i 0.788869 + 0.614562i \(0.210667\pi\)
0.137792 + 0.990461i \(0.456000\pi\)
\(674\) −5.41789e6 9.38406e6i −0.459389 0.795684i
\(675\) 149420. + 258802.i 0.0126226 + 0.0218629i
\(676\) −1.80008e7 + 3.11783e7i −1.51504 + 2.62413i
\(677\) 2.24145e7 1.87957 0.939785 0.341767i \(-0.111025\pi\)
0.939785 + 0.341767i \(0.111025\pi\)
\(678\) −2.05563e6 + 3.56046e6i −0.171740 + 0.297462i
\(679\) −110678. 191700.i −0.00921272 0.0159569i
\(680\) 721308. 0.0598203
\(681\) 679675. + 1.17723e6i 0.0561608 + 0.0972734i
\(682\) 1.10223e7 1.90912e7i 0.907429 1.57171i
\(683\) −5.75066e6 + 9.96043e6i −0.471700 + 0.817008i −0.999476 0.0323754i \(-0.989693\pi\)
0.527776 + 0.849384i \(0.323026\pi\)
\(684\) 1.17137e7 0.957312
\(685\) 7.10568e6 1.23074e7i 0.578601 1.00217i
\(686\) −1.94475e7 −1.57781
\(687\) 4.68701e6 0.378882
\(688\) 288778. + 9.72906e6i 0.0232591 + 0.783609i
\(689\) 2.03317e7 1.63164
\(690\) −5.36611e6 −0.429079
\(691\) 5.07027e6 8.78197e6i 0.403958 0.699676i −0.590242 0.807227i \(-0.700968\pi\)
0.994200 + 0.107551i \(0.0343009\pi\)
\(692\) 4.74915e6 0.377008
\(693\) 4.21490e6 7.30042e6i 0.333391 0.577450i
\(694\) −1.48892e7 + 2.57888e7i −1.17347 + 2.03251i
\(695\) −4.41438e6 7.64593e6i −0.346663 0.600438i
\(696\) −1.71561e6 −0.134244
\(697\) 350545. + 607162.i 0.0273314 + 0.0473394i
\(698\) −2.20227e6 + 3.81444e6i −0.171093 + 0.296341i
\(699\) 7.50550e6 0.581014
\(700\) 176273. 305314.i 0.0135969 0.0235506i
\(701\) 609987. + 1.05653e6i 0.0468841 + 0.0812056i 0.888515 0.458847i \(-0.151738\pi\)
−0.841631 + 0.540053i \(0.818404\pi\)
\(702\) −1.44455e7 2.50204e7i −1.10635 1.91625i
\(703\) 6.49115e6 + 1.12430e7i 0.495374 + 0.858013i
\(704\) 1.99272e7 1.51536
\(705\) 3.57143e6 + 6.18589e6i 0.270626 + 0.468737i
\(706\) 1.13916e6 + 1.97309e6i 0.0860151 + 0.148982i
\(707\) 7.79372e6 1.34991e7i 0.586403 1.01568i
\(708\) −1.37216e6 + 2.37665e6i −0.102878 + 0.178189i
\(709\) −1.06325e7 −0.794361 −0.397180 0.917741i \(-0.630011\pi\)
−0.397180 + 0.917741i \(0.630011\pi\)
\(710\) 8.14135e6 0.606109
\(711\) −2.09501e6 + 3.62867e6i −0.155422 + 0.269199i
\(712\) 179588. 311056.i 0.0132763 0.0229953i
\(713\) 4.75008e6 + 8.22738e6i 0.349927 + 0.606091i
\(714\) 696886. + 1.20704e6i 0.0511583 + 0.0886088i
\(715\) −2.99519e7 −2.19109
\(716\) 7.13788e6 + 1.23632e7i 0.520340 + 0.901255i
\(717\) −4.77405e6 8.26890e6i −0.346808 0.600690i
\(718\) 985107. + 1.70626e6i 0.0713136 + 0.123519i
\(719\) −2.70281e6 + 4.68140e6i −0.194981 + 0.337718i −0.946894 0.321545i \(-0.895798\pi\)
0.751913 + 0.659262i \(0.229131\pi\)
\(720\) 8.94116e6 0.642780
\(721\) −9.71281e6 + 1.68231e7i −0.695836 + 1.20522i
\(722\) 58128.3 + 100681.i 0.00414997 + 0.00718796i
\(723\) −2.22050e6 −0.157981
\(724\) −1.06141e7 1.83842e7i −0.752552 1.30346i
\(725\) −255014. + 441698.i −0.0180185 + 0.0312090i
\(726\) 1.41065e6 2.44331e6i 0.0993293 0.172043i
\(727\) 1.11450e7 0.782070 0.391035 0.920376i \(-0.372117\pi\)
0.391035 + 0.920376i \(0.372117\pi\)
\(728\) −2.63225e6 + 4.55919e6i −0.184077 + 0.318830i
\(729\) −313032. −0.0218157
\(730\) −2.50794e7 −1.74185
\(731\) 2.68225e6 1.65660e6i 0.185655 0.114663i
\(732\) 5.83091e6 0.402215
\(733\) −1.95834e7 −1.34625 −0.673127 0.739527i \(-0.735049\pi\)
−0.673127 + 0.739527i \(0.735049\pi\)
\(734\) −799716. + 1.38515e6i −0.0547893 + 0.0948979i
\(735\) −3.11998e6 −0.213027
\(736\) −6.83262e6 + 1.18344e7i −0.464935 + 0.805291i
\(737\) 7.47143e6 1.29409e7i 0.506682 0.877598i
\(738\) −2.21001e6 3.82786e6i −0.149367 0.258711i
\(739\) 1.10845e7 0.746630 0.373315 0.927705i \(-0.378221\pi\)
0.373315 + 0.927705i \(0.378221\pi\)
\(740\) −8.84019e6 1.53117e7i −0.593448 1.02788i
\(741\) 6.21093e6 1.07577e7i 0.415539 0.719734i
\(742\) 1.38447e7 0.923152
\(743\) −7.07390e6 + 1.22524e7i −0.470096 + 0.814231i −0.999415 0.0341923i \(-0.989114\pi\)
0.529319 + 0.848423i \(0.322447\pi\)
\(744\) −961591. 1.66552e6i −0.0636880 0.110311i
\(745\) 1.00962e7 + 1.74871e7i 0.666448 + 1.15432i
\(746\) −1.78475e7 3.09128e7i −1.17417 2.03372i
\(747\) −2.12386e7 −1.39259
\(748\) −2.25669e6 3.90870e6i −0.147475 0.255434i
\(749\) 3.02657e6 + 5.24217e6i 0.197127 + 0.341434i
\(750\) −4.91419e6 + 8.51162e6i −0.319006 + 0.552534i
\(751\) 133556. 231325.i 0.00864096 0.0149666i −0.861673 0.507465i \(-0.830583\pi\)
0.870314 + 0.492498i \(0.163916\pi\)
\(752\) 1.47523e7 0.951295
\(753\) −3.47328e6 −0.223230
\(754\) 2.46542e7 4.27024e7i 1.57929 2.73542i
\(755\) 5.60166e6 9.70236e6i 0.357643 0.619455i
\(756\) −5.32991e6 9.23167e6i −0.339168 0.587457i
\(757\) −6.17733e6 1.06995e7i −0.391797 0.678613i 0.600889 0.799332i \(-0.294813\pi\)
−0.992687 + 0.120720i \(0.961480\pi\)
\(758\) −1.49845e7 −0.947262
\(759\) 2.59313e6 + 4.49144e6i 0.163388 + 0.282997i
\(760\) −2.18875e6 3.79102e6i −0.137455 0.238079i
\(761\) −7069.74 12245.2i −0.000442529 0.000766483i 0.865804 0.500383i \(-0.166808\pi\)
−0.866247 + 0.499617i \(0.833474\pi\)
\(762\) −2.38240e6 + 4.12644e6i −0.148637 + 0.257447i
\(763\) −1.09983e7 −0.683935
\(764\) 1.19705e7 2.07336e7i 0.741959 1.28511i
\(765\) −1.44800e6 2.50801e6i −0.0894572 0.154944i
\(766\) 1.54475e7 0.951231
\(767\) −6.09145e6 1.05507e7i −0.373880 0.647579i
\(768\) −1.94422e6 + 3.36748e6i −0.118944 + 0.206017i
\(769\) 1.56800e6 2.71586e6i 0.0956161 0.165612i −0.814249 0.580515i \(-0.802851\pi\)
0.909866 + 0.414903i \(0.136185\pi\)
\(770\) −2.03955e7 −1.23967
\(771\) −4.40684e6 + 7.63288e6i −0.266988 + 0.462437i
\(772\) −3.36867e7 −2.03430
\(773\)