Properties

Label 43.6.c.a.36.3
Level $43$
Weight $6$
Character 43.36
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 36.3
Character \(\chi\) \(=\) 43.36
Dual form 43.6.c.a.6.3

$q$-expansion

\(f(q)\) \(=\) \(q-8.55067 q^{2} +(-3.32584 - 5.76053i) q^{3} +41.1139 q^{4} +(8.72223 + 15.1073i) q^{5} +(28.4382 + 49.2563i) q^{6} +(-112.908 + 195.562i) q^{7} -77.9301 q^{8} +(99.3776 - 172.127i) q^{9} +O(q^{10})\) \(q-8.55067 q^{2} +(-3.32584 - 5.76053i) q^{3} +41.1139 q^{4} +(8.72223 + 15.1073i) q^{5} +(28.4382 + 49.2563i) q^{6} +(-112.908 + 195.562i) q^{7} -77.9301 q^{8} +(99.3776 - 172.127i) q^{9} +(-74.5809 - 129.178i) q^{10} -94.8489 q^{11} +(-136.738 - 236.838i) q^{12} +(387.984 - 672.008i) q^{13} +(965.438 - 1672.19i) q^{14} +(58.0175 - 100.489i) q^{15} -649.291 q^{16} +(407.492 - 705.798i) q^{17} +(-849.744 + 1471.80i) q^{18} +(-1252.21 - 2168.89i) q^{19} +(358.605 + 621.122i) q^{20} +1502.06 q^{21} +811.021 q^{22} +(1284.33 + 2224.53i) q^{23} +(259.183 + 448.918i) q^{24} +(1410.35 - 2442.79i) q^{25} +(-3317.52 + 5746.12i) q^{26} -2938.41 q^{27} +(-4642.09 + 8040.33i) q^{28} +(1154.17 - 1999.08i) q^{29} +(-496.088 + 859.250i) q^{30} +(-550.205 - 952.983i) q^{31} +8045.64 q^{32} +(315.452 + 546.380i) q^{33} +(-3484.33 + 6035.04i) q^{34} -3939.24 q^{35} +(4085.80 - 7076.81i) q^{36} +(-2898.78 - 5020.83i) q^{37} +(10707.2 + 18545.5i) q^{38} -5161.50 q^{39} +(-679.724 - 1177.32i) q^{40} +4811.95 q^{41} -12843.6 q^{42} +(6825.71 - 10020.9i) q^{43} -3899.61 q^{44} +3467.18 q^{45} +(-10981.9 - 19021.2i) q^{46} +28586.9 q^{47} +(2159.44 + 3740.26i) q^{48} +(-17092.9 - 29605.8i) q^{49} +(-12059.4 + 20887.5i) q^{50} -5421.02 q^{51} +(15951.6 - 27628.9i) q^{52} +(-5552.60 - 9617.39i) q^{53} +25125.4 q^{54} +(-827.294 - 1432.91i) q^{55} +(8798.92 - 15240.2i) q^{56} +(-8329.30 + 14426.8i) q^{57} +(-9868.92 + 17093.5i) q^{58} -12370.0 q^{59} +(2385.33 - 4131.51i) q^{60} +(-18367.6 + 31813.7i) q^{61} +(4704.62 + 8148.64i) q^{62} +(22441.0 + 38869.0i) q^{63} -48018.2 q^{64} +13536.3 q^{65} +(-2697.33 - 4671.91i) q^{66} +(2017.88 + 3495.07i) q^{67} +(16753.6 - 29018.1i) q^{68} +(8542.98 - 14796.9i) q^{69} +33683.1 q^{70} +(18927.8 - 32784.0i) q^{71} +(-7744.50 + 13413.9i) q^{72} +(-18456.1 + 31966.9i) q^{73} +(24786.5 + 42931.4i) q^{74} -18762.3 q^{75} +(-51483.3 - 89171.6i) q^{76} +(10709.2 - 18548.9i) q^{77} +44134.2 q^{78} +(2204.87 - 3818.94i) q^{79} +(-5663.27 - 9809.07i) q^{80} +(-14376.0 - 24900.0i) q^{81} -41145.4 q^{82} +(-5486.28 - 9502.52i) q^{83} +61755.4 q^{84} +14217.0 q^{85} +(-58364.4 + 85685.3i) q^{86} -15354.3 q^{87} +7391.58 q^{88} +(-30160.7 - 52239.8i) q^{89} -29646.7 q^{90} +(87613.0 + 151750. i) q^{91} +(52804.0 + 91459.2i) q^{92} +(-3659.79 + 6338.94i) q^{93} -244437. q^{94} +(21844.1 - 37835.1i) q^{95} +(-26758.5 - 46347.1i) q^{96} +53274.7 q^{97} +(146156. + 253149. i) q^{98} +(-9425.85 + 16326.1i) 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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.55067 −1.51156 −0.755779 0.654826i \(-0.772742\pi\)
−0.755779 + 0.654826i \(0.772742\pi\)
\(3\) −3.32584 5.76053i −0.213353 0.369538i 0.739409 0.673257i \(-0.235105\pi\)
−0.952762 + 0.303719i \(0.901772\pi\)
\(4\) 41.1139 1.28481
\(5\) 8.72223 + 15.1073i 0.156028 + 0.270248i 0.933433 0.358752i \(-0.116798\pi\)
−0.777405 + 0.629000i \(0.783464\pi\)
\(6\) 28.4382 + 49.2563i 0.322495 + 0.558578i
\(7\) −112.908 + 195.562i −0.870922 + 1.50848i −0.00987829 + 0.999951i \(0.503144\pi\)
−0.861044 + 0.508530i \(0.830189\pi\)
\(8\) −77.9301 −0.430507
\(9\) 99.3776 172.127i 0.408961 0.708341i
\(10\) −74.5809 129.178i −0.235845 0.408496i
\(11\) −94.8489 −0.236347 −0.118174 0.992993i \(-0.537704\pi\)
−0.118174 + 0.992993i \(0.537704\pi\)
\(12\) −136.738 236.838i −0.274118 0.474786i
\(13\) 387.984 672.008i 0.636731 1.10285i −0.349415 0.936968i \(-0.613620\pi\)
0.986146 0.165882i \(-0.0530470\pi\)
\(14\) 965.438 1672.19i 1.31645 2.28016i
\(15\) 58.0175 100.489i 0.0665780 0.115317i
\(16\) −649.291 −0.634073
\(17\) 407.492 705.798i 0.341977 0.592322i −0.642823 0.766015i \(-0.722237\pi\)
0.984800 + 0.173693i \(0.0555701\pi\)
\(18\) −849.744 + 1471.80i −0.618169 + 1.07070i
\(19\) −1252.21 2168.89i −0.795780 1.37833i −0.922343 0.386373i \(-0.873728\pi\)
0.126562 0.991959i \(-0.459606\pi\)
\(20\) 358.605 + 621.122i 0.200466 + 0.347218i
\(21\) 1502.06 0.743255
\(22\) 811.021 0.357253
\(23\) 1284.33 + 2224.53i 0.506242 + 0.876837i 0.999974 + 0.00722288i \(0.00229913\pi\)
−0.493732 + 0.869614i \(0.664368\pi\)
\(24\) 259.183 + 448.918i 0.0918499 + 0.159089i
\(25\) 1410.35 2442.79i 0.451311 0.781693i
\(26\) −3317.52 + 5746.12i −0.962456 + 1.66702i
\(27\) −2938.41 −0.775718
\(28\) −4642.09 + 8040.33i −1.11897 + 1.93811i
\(29\) 1154.17 1999.08i 0.254844 0.441403i −0.710009 0.704193i \(-0.751309\pi\)
0.964853 + 0.262790i \(0.0846425\pi\)
\(30\) −496.088 + 859.250i −0.100637 + 0.174308i
\(31\) −550.205 952.983i −0.102830 0.178107i 0.810019 0.586403i \(-0.199456\pi\)
−0.912850 + 0.408296i \(0.866123\pi\)
\(32\) 8045.64 1.38895
\(33\) 315.452 + 546.380i 0.0504254 + 0.0873393i
\(34\) −3484.33 + 6035.04i −0.516919 + 0.895330i
\(35\) −3939.24 −0.543553
\(36\) 4085.80 7076.81i 0.525437 0.910084i
\(37\) −2898.78 5020.83i −0.348105 0.602936i 0.637808 0.770196i \(-0.279841\pi\)
−0.985913 + 0.167260i \(0.946508\pi\)
\(38\) 10707.2 + 18545.5i 1.20287 + 2.08343i
\(39\) −5161.50 −0.543393
\(40\) −679.724 1177.32i −0.0671711 0.116344i
\(41\) 4811.95 0.447055 0.223528 0.974698i \(-0.428243\pi\)
0.223528 + 0.974698i \(0.428243\pi\)
\(42\) −12843.6 −1.12347
\(43\) 6825.71 10020.9i 0.562959 0.826485i
\(44\) −3899.61 −0.303661
\(45\) 3467.18 0.255237
\(46\) −10981.9 19021.2i −0.765215 1.32539i
\(47\) 28586.9 1.88766 0.943828 0.330437i \(-0.107196\pi\)
0.943828 + 0.330437i \(0.107196\pi\)
\(48\) 2159.44 + 3740.26i 0.135281 + 0.234314i
\(49\) −17092.9 29605.8i −1.01701 1.76152i
\(50\) −12059.4 + 20887.5i −0.682182 + 1.18157i
\(51\) −5421.02 −0.291847
\(52\) 15951.6 27628.9i 0.818078 1.41695i
\(53\) −5552.60 9617.39i −0.271523 0.470292i 0.697729 0.716362i \(-0.254194\pi\)
−0.969252 + 0.246070i \(0.920861\pi\)
\(54\) 25125.4 1.17254
\(55\) −827.294 1432.91i −0.0368768 0.0638725i
\(56\) 8798.92 15240.2i 0.374938 0.649412i
\(57\) −8329.30 + 14426.8i −0.339564 + 0.588142i
\(58\) −9868.92 + 17093.5i −0.385212 + 0.667207i
\(59\) −12370.0 −0.462637 −0.231319 0.972878i \(-0.574304\pi\)
−0.231319 + 0.972878i \(0.574304\pi\)
\(60\) 2385.33 4131.51i 0.0855401 0.148160i
\(61\) −18367.6 + 31813.7i −0.632017 + 1.09468i 0.355122 + 0.934820i \(0.384439\pi\)
−0.987139 + 0.159865i \(0.948894\pi\)
\(62\) 4704.62 + 8148.64i 0.155434 + 0.269219i
\(63\) 22441.0 + 38869.0i 0.712347 + 1.23382i
\(64\) −48018.2 −1.46540
\(65\) 13536.3 0.397391
\(66\) −2697.33 4671.91i −0.0762209 0.132018i
\(67\) 2017.88 + 3495.07i 0.0549171 + 0.0951192i 0.892177 0.451686i \(-0.149177\pi\)
−0.837260 + 0.546805i \(0.815844\pi\)
\(68\) 16753.6 29018.1i 0.439376 0.761021i
\(69\) 8542.98 14796.9i 0.216016 0.374151i
\(70\) 33683.1 0.821612
\(71\) 18927.8 32784.0i 0.445610 0.771819i −0.552485 0.833523i \(-0.686320\pi\)
0.998094 + 0.0617042i \(0.0196535\pi\)
\(72\) −7744.50 + 13413.9i −0.176061 + 0.304946i
\(73\) −18456.1 + 31966.9i −0.405353 + 0.702091i −0.994362 0.106034i \(-0.966185\pi\)
0.589010 + 0.808126i \(0.299518\pi\)
\(74\) 24786.5 + 42931.4i 0.526181 + 0.911373i
\(75\) −18762.3 −0.385154
\(76\) −51483.3 89171.6i −1.02243 1.77089i
\(77\) 10709.2 18548.9i 0.205840 0.356526i
\(78\) 44134.2 0.821371
\(79\) 2204.87 3818.94i 0.0397480 0.0688455i −0.845467 0.534028i \(-0.820678\pi\)
0.885215 + 0.465182i \(0.154011\pi\)
\(80\) −5663.27 9809.07i −0.0989332 0.171357i
\(81\) −14376.0 24900.0i −0.243460 0.421684i
\(82\) −41145.4 −0.675750
\(83\) −5486.28 9502.52i −0.0874144 0.151406i 0.819003 0.573789i \(-0.194527\pi\)
−0.906418 + 0.422383i \(0.861194\pi\)
\(84\) 61755.4 0.954941
\(85\) 14217.0 0.213432
\(86\) −58364.4 + 85685.3i −0.850945 + 1.24928i
\(87\) −15354.3 −0.217487
\(88\) 7391.58 0.101749
\(89\) −30160.7 52239.8i −0.403614 0.699080i 0.590545 0.807005i \(-0.298913\pi\)
−0.994159 + 0.107925i \(0.965579\pi\)
\(90\) −29646.7 −0.385806
\(91\) 87613.0 + 151750.i 1.10909 + 1.92099i
\(92\) 52804.0 + 91459.2i 0.650425 + 1.12657i
\(93\) −3659.79 + 6338.94i −0.0438782 + 0.0759993i
\(94\) −244437. −2.85330
\(95\) 21844.1 37835.1i 0.248328 0.430117i
\(96\) −26758.5 46347.1i −0.296336 0.513268i
\(97\) 53274.7 0.574899 0.287449 0.957796i \(-0.407193\pi\)
0.287449 + 0.957796i \(0.407193\pi\)
\(98\) 146156. + 253149.i 1.53727 + 2.66263i
\(99\) −9425.85 + 16326.1i −0.0966569 + 0.167415i
\(100\) 57984.8 100433.i 0.579848 1.00433i
\(101\) −22365.3 + 38737.9i −0.218158 + 0.377861i −0.954245 0.299026i \(-0.903338\pi\)
0.736087 + 0.676887i \(0.236672\pi\)
\(102\) 46353.3 0.441144
\(103\) 57861.6 100219.i 0.537399 0.930803i −0.461644 0.887065i \(-0.652740\pi\)
0.999043 0.0437377i \(-0.0139266\pi\)
\(104\) −30235.6 + 52369.7i −0.274117 + 0.474784i
\(105\) 13101.3 + 22692.1i 0.115969 + 0.200863i
\(106\) 47478.4 + 82235.1i 0.410423 + 0.710874i
\(107\) −182262. −1.53899 −0.769495 0.638653i \(-0.779492\pi\)
−0.769495 + 0.638653i \(0.779492\pi\)
\(108\) −120810. −0.996650
\(109\) −83047.5 143842.i −0.669515 1.15963i −0.978040 0.208417i \(-0.933169\pi\)
0.308525 0.951216i \(-0.400165\pi\)
\(110\) 7073.91 + 12252.4i 0.0557414 + 0.0965470i
\(111\) −19281.7 + 33397.0i −0.148538 + 0.257276i
\(112\) 73310.1 126977.i 0.552229 0.956488i
\(113\) 121707. 0.896645 0.448323 0.893872i \(-0.352022\pi\)
0.448323 + 0.893872i \(0.352022\pi\)
\(114\) 71221.1 123359.i 0.513271 0.889011i
\(115\) −22404.5 + 38805.7i −0.157976 + 0.273622i
\(116\) 47452.4 82190.0i 0.327426 0.567119i
\(117\) −77113.8 133565.i −0.520796 0.902045i
\(118\) 105772. 0.699303
\(119\) 92018.3 + 159380.i 0.595671 + 1.03173i
\(120\) −4521.31 + 7831.13i −0.0286623 + 0.0496445i
\(121\) −152055. −0.944140
\(122\) 157055. 272028.i 0.955330 1.65468i
\(123\) −16003.8 27719.3i −0.0953805 0.165204i
\(124\) −22621.1 39180.9i −0.132117 0.228834i
\(125\) 103719. 0.593724
\(126\) −191886. 332356.i −1.07675 1.86499i
\(127\) −197190. −1.08487 −0.542433 0.840099i \(-0.682497\pi\)
−0.542433 + 0.840099i \(0.682497\pi\)
\(128\) 153128. 0.826092
\(129\) −80426.8 5991.81i −0.425526 0.0317018i
\(130\) −115745. −0.600680
\(131\) −182405. −0.928666 −0.464333 0.885661i \(-0.653706\pi\)
−0.464333 + 0.885661i \(0.653706\pi\)
\(132\) 12969.5 + 22463.8i 0.0647870 + 0.112214i
\(133\) 565538. 2.77225
\(134\) −17254.2 29885.1i −0.0830105 0.143778i
\(135\) −25629.5 44391.6i −0.121034 0.209636i
\(136\) −31755.9 + 55002.9i −0.147224 + 0.254999i
\(137\) 191141. 0.870065 0.435032 0.900415i \(-0.356737\pi\)
0.435032 + 0.900415i \(0.356737\pi\)
\(138\) −73048.2 + 126523.i −0.326521 + 0.565552i
\(139\) 24161.8 + 41849.4i 0.106070 + 0.183718i 0.914175 0.405320i \(-0.132840\pi\)
−0.808105 + 0.589039i \(0.799507\pi\)
\(140\) −161957. −0.698362
\(141\) −95075.6 164676.i −0.402737 0.697561i
\(142\) −161846. + 280325.i −0.673565 + 1.16665i
\(143\) −36799.9 + 63739.3i −0.150490 + 0.260656i
\(144\) −64525.0 + 111761.i −0.259311 + 0.449141i
\(145\) 40267.7 0.159051
\(146\) 157812. 273339.i 0.612714 1.06125i
\(147\) −113697. + 196928.i −0.433964 + 0.751648i
\(148\) −119180. 206426.i −0.447249 0.774658i
\(149\) 261173. + 452364.i 0.963745 + 1.66925i 0.712951 + 0.701214i \(0.247358\pi\)
0.250794 + 0.968041i \(0.419308\pi\)
\(150\) 160431. 0.582182
\(151\) 392778. 1.40186 0.700930 0.713230i \(-0.252768\pi\)
0.700930 + 0.713230i \(0.252768\pi\)
\(152\) 97584.8 + 169022.i 0.342589 + 0.593381i
\(153\) −80991.2 140281.i −0.279711 0.484473i
\(154\) −91570.8 + 158605.i −0.311139 + 0.538909i
\(155\) 9598.03 16624.3i 0.0320888 0.0555793i
\(156\) −212209. −0.698157
\(157\) −104888. + 181672.i −0.339608 + 0.588218i −0.984359 0.176174i \(-0.943628\pi\)
0.644751 + 0.764393i \(0.276961\pi\)
\(158\) −18853.1 + 32654.5i −0.0600814 + 0.104064i
\(159\) −36934.1 + 63971.8i −0.115860 + 0.200676i
\(160\) 70175.9 + 121548.i 0.216714 + 0.375360i
\(161\) −580046. −1.76359
\(162\) 122925. + 212912.i 0.368003 + 0.637401i
\(163\) −284044. + 491978.i −0.837368 + 1.45036i 0.0547203 + 0.998502i \(0.482573\pi\)
−0.892088 + 0.451862i \(0.850760\pi\)
\(164\) 197838. 0.574381
\(165\) −5502.90 + 9531.30i −0.0157355 + 0.0272547i
\(166\) 46911.4 + 81252.9i 0.132132 + 0.228859i
\(167\) 338891. + 586976.i 0.940305 + 1.62866i 0.764890 + 0.644161i \(0.222793\pi\)
0.175414 + 0.984495i \(0.443873\pi\)
\(168\) −117055. −0.319976
\(169\) −115417. 199908.i −0.310852 0.538411i
\(170\) −121565. −0.322615
\(171\) −497766. −1.30177
\(172\) 280632. 411998.i 0.723295 1.06188i
\(173\) −566813. −1.43987 −0.719937 0.694039i \(-0.755829\pi\)
−0.719937 + 0.694039i \(0.755829\pi\)
\(174\) 131290. 0.328744
\(175\) 318478. + 551621.i 0.786113 + 1.36159i
\(176\) 61584.6 0.149862
\(177\) 41140.7 + 71257.8i 0.0987049 + 0.170962i
\(178\) 257894. + 446685.i 0.610086 + 1.05670i
\(179\) 291057. 504125.i 0.678962 1.17600i −0.296332 0.955085i \(-0.595764\pi\)
0.975294 0.220911i \(-0.0709031\pi\)
\(180\) 142549. 0.327932
\(181\) 328534. 569038.i 0.745391 1.29106i −0.204621 0.978841i \(-0.565596\pi\)
0.950012 0.312214i \(-0.101071\pi\)
\(182\) −749150. 1.29757e6i −1.67645 2.90369i
\(183\) 244351. 0.539370
\(184\) −100088. 173358.i −0.217941 0.377484i
\(185\) 50567.6 87585.6i 0.108628 0.188150i
\(186\) 31293.6 54202.2i 0.0663245 0.114877i
\(187\) −38650.2 + 66944.1i −0.0808254 + 0.139994i
\(188\) 1.17532e6 2.42528
\(189\) 331770. 574643.i 0.675590 1.17016i
\(190\) −186782. + 323516.i −0.375362 + 0.650147i
\(191\) −482322. 835406.i −0.956651 1.65697i −0.730543 0.682866i \(-0.760733\pi\)
−0.226108 0.974102i \(-0.572600\pi\)
\(192\) 159701. + 276610.i 0.312647 + 0.541521i
\(193\) 119530. 0.230984 0.115492 0.993308i \(-0.463155\pi\)
0.115492 + 0.993308i \(0.463155\pi\)
\(194\) −455534. −0.868994
\(195\) −45019.7 77976.5i −0.0847845 0.146851i
\(196\) −702756. 1.21721e6i −1.30667 2.26321i
\(197\) −174101. + 301551.i −0.319621 + 0.553599i −0.980409 0.196973i \(-0.936889\pi\)
0.660788 + 0.750572i \(0.270222\pi\)
\(198\) 80597.3 139599.i 0.146103 0.253057i
\(199\) 53982.7 0.0966323 0.0483161 0.998832i \(-0.484615\pi\)
0.0483161 + 0.998832i \(0.484615\pi\)
\(200\) −109908. + 190367.i −0.194292 + 0.336524i
\(201\) 13422.3 23248.1i 0.0234334 0.0405879i
\(202\) 191238. 331235.i 0.329759 0.571159i
\(203\) 260630. + 451424.i 0.443899 + 0.768855i
\(204\) −222879. −0.374968
\(205\) 41970.9 + 72695.7i 0.0697531 + 0.120816i
\(206\) −494755. + 856941.i −0.812311 + 1.40696i
\(207\) 510536. 0.828133
\(208\) −251915. + 436329.i −0.403734 + 0.699288i
\(209\) 118771. + 205717.i 0.188081 + 0.325765i
\(210\) −112025. 194032.i −0.175293 0.303617i
\(211\) −272464. −0.421312 −0.210656 0.977560i \(-0.567560\pi\)
−0.210656 + 0.977560i \(0.567560\pi\)
\(212\) −228289. 395408.i −0.348856 0.604236i
\(213\) −251804. −0.380288
\(214\) 1.55846e6 2.32627
\(215\) 210924. + 15713.9i 0.311194 + 0.0231840i
\(216\) 228991. 0.333952
\(217\) 248490. 0.358228
\(218\) 710111. + 1.22995e6i 1.01201 + 1.75285i
\(219\) 245528. 0.345933
\(220\) −34013.3 58912.7i −0.0473797 0.0820640i
\(221\) −316201. 547677.i −0.435495 0.754299i
\(222\) 164872. 285566.i 0.224525 0.388888i
\(223\) −364985. −0.491488 −0.245744 0.969335i \(-0.579032\pi\)
−0.245744 + 0.969335i \(0.579032\pi\)
\(224\) −908416. + 1.57342e6i −1.20966 + 2.09520i
\(225\) −280313. 485517.i −0.369137 0.639364i
\(226\) −1.04068e6 −1.35533
\(227\) −362710. 628231.i −0.467191 0.809198i 0.532106 0.846677i \(-0.321401\pi\)
−0.999297 + 0.0374790i \(0.988067\pi\)
\(228\) −342450. + 593141.i −0.436275 + 0.755651i
\(229\) 266349. 461331.i 0.335632 0.581331i −0.647974 0.761662i \(-0.724384\pi\)
0.983606 + 0.180331i \(0.0577169\pi\)
\(230\) 191573. 331815.i 0.238790 0.413596i
\(231\) −142468. −0.175666
\(232\) −89944.5 + 155788.i −0.109712 + 0.190027i
\(233\) 352356. 610298.i 0.425199 0.736465i −0.571240 0.820783i \(-0.693538\pi\)
0.996439 + 0.0843173i \(0.0268709\pi\)
\(234\) 659375. + 1.14207e6i 0.787214 + 1.36349i
\(235\) 249342. + 431873.i 0.294527 + 0.510136i
\(236\) −508580. −0.594401
\(237\) −29332.2 −0.0339214
\(238\) −786818. 1.36281e6i −0.900392 1.55952i
\(239\) −46812.7 81081.9i −0.0530113 0.0918183i 0.838302 0.545206i \(-0.183549\pi\)
−0.891313 + 0.453388i \(0.850215\pi\)
\(240\) −37670.3 + 65246.8i −0.0422154 + 0.0731191i
\(241\) 624398. 1.08149e6i 0.692499 1.19944i −0.278518 0.960431i \(-0.589843\pi\)
0.971017 0.239012i \(-0.0768236\pi\)
\(242\) 1.30017e6 1.42712
\(243\) −452642. + 783999.i −0.491744 + 0.851726i
\(244\) −755165. + 1.30798e6i −0.812021 + 1.40646i
\(245\) 298177. 516457.i 0.317364 0.549691i
\(246\) 136843. + 237019.i 0.144173 + 0.249715i
\(247\) −1.94335e6 −2.02679
\(248\) 42877.5 + 74266.0i 0.0442691 + 0.0766763i
\(249\) −36493.0 + 63207.8i −0.0373002 + 0.0646059i
\(250\) −886870. −0.897449
\(251\) 845888. 1.46512e6i 0.847478 1.46787i −0.0359740 0.999353i \(-0.511453\pi\)
0.883452 0.468522i \(-0.155213\pi\)
\(252\) 922639. + 1.59806e6i 0.915230 + 1.58523i
\(253\) −121818. 210994.i −0.119649 0.207238i
\(254\) 1.68611e6 1.63984
\(255\) −47283.4 81897.2i −0.0455363 0.0788712i
\(256\) 227240. 0.216713
\(257\) 455732. 0.430404 0.215202 0.976570i \(-0.430959\pi\)
0.215202 + 0.976570i \(0.430959\pi\)
\(258\) 687703. + 51234.0i 0.643208 + 0.0479191i
\(259\) 1.30918e6 1.21269
\(260\) 556532. 0.510572
\(261\) −229397. 397327.i −0.208443 0.361033i
\(262\) 1.55969e6 1.40373
\(263\) 587760. + 1.01803e6i 0.523975 + 0.907551i 0.999610 + 0.0279088i \(0.00888481\pi\)
−0.475635 + 0.879642i \(0.657782\pi\)
\(264\) −24583.2 42579.4i −0.0217085 0.0376002i
\(265\) 96862.1 167770.i 0.0847304 0.146757i
\(266\) −4.83573e6 −4.19042
\(267\) −200619. + 347483.i −0.172224 + 0.298301i
\(268\) 82962.8 + 143696.i 0.0705581 + 0.122210i
\(269\) −1.08503e6 −0.914238 −0.457119 0.889406i \(-0.651119\pi\)
−0.457119 + 0.889406i \(0.651119\pi\)
\(270\) 219150. + 379578.i 0.182949 + 0.316878i
\(271\) −1.10282e6 + 1.91013e6i −0.912178 + 1.57994i −0.101198 + 0.994866i \(0.532268\pi\)
−0.810981 + 0.585073i \(0.801066\pi\)
\(272\) −264581. + 458268.i −0.216839 + 0.375576i
\(273\) 582774. 1.00939e6i 0.473253 0.819698i
\(274\) −1.63438e6 −1.31515
\(275\) −133770. + 231696.i −0.106666 + 0.184751i
\(276\) 351235. 608358.i 0.277540 0.480713i
\(277\) −306493. 530861.i −0.240005 0.415701i 0.720710 0.693236i \(-0.243816\pi\)
−0.960715 + 0.277535i \(0.910482\pi\)
\(278\) −206599. 357841.i −0.160331 0.277701i
\(279\) −218712. −0.168214
\(280\) 306985. 0.234003
\(281\) 166721. + 288770.i 0.125958 + 0.218166i 0.922107 0.386935i \(-0.126466\pi\)
−0.796149 + 0.605101i \(0.793133\pi\)
\(282\) 812960. + 1.40809e6i 0.608760 + 1.05440i
\(283\) −30457.9 + 52754.6i −0.0226065 + 0.0391557i −0.877107 0.480294i \(-0.840530\pi\)
0.854501 + 0.519450i \(0.173863\pi\)
\(284\) 778197. 1.34788e6i 0.572524 0.991641i
\(285\) −290600. −0.211926
\(286\) 314664. 545013.i 0.227474 0.393996i
\(287\) −543307. + 941036.i −0.389350 + 0.674375i
\(288\) 799556. 1.38487e6i 0.568025 0.983848i
\(289\) 377828. + 654418.i 0.266103 + 0.460904i
\(290\) −344316. −0.240415
\(291\) −177183. 306890.i −0.122656 0.212447i
\(292\) −758803. + 1.31429e6i −0.520801 + 0.902054i
\(293\) 2.26216e6 1.53941 0.769706 0.638399i \(-0.220403\pi\)
0.769706 + 0.638399i \(0.220403\pi\)
\(294\) 972182. 1.68387e6i 0.655963 1.13616i
\(295\) −107894. 186878.i −0.0721843 0.125027i
\(296\) 225902. + 391273.i 0.149862 + 0.259568i
\(297\) 278705. 0.183339
\(298\) −2.23320e6 3.86802e6i −1.45676 2.52318i
\(299\) 1.99320e6 1.28936
\(300\) −771393. −0.494849
\(301\) 1.18903e6 + 2.46629e6i 0.756444 + 1.56902i
\(302\) −3.35851e6 −2.11899
\(303\) 297534. 0.186179
\(304\) 813049. + 1.40824e6i 0.504583 + 0.873964i
\(305\) −640827. −0.394449
\(306\) 692529. + 1.19950e6i 0.422799 + 0.732310i
\(307\) 557789. + 966119.i 0.337772 + 0.585039i 0.984013 0.178095i \(-0.0569933\pi\)
−0.646241 + 0.763133i \(0.723660\pi\)
\(308\) 440297. 762617.i 0.264465 0.458068i
\(309\) −769754. −0.458623
\(310\) −82069.6 + 142149.i −0.0485040 + 0.0840114i
\(311\) −362692. 628202.i −0.212636 0.368297i 0.739902 0.672714i \(-0.234872\pi\)
−0.952539 + 0.304417i \(0.901538\pi\)
\(312\) 402236. 0.233934
\(313\) −453648. 785741.i −0.261733 0.453334i 0.704970 0.709237i \(-0.250961\pi\)
−0.966702 + 0.255903i \(0.917627\pi\)
\(314\) 896865. 1.55342e6i 0.513338 0.889127i
\(315\) −391472. + 678049.i −0.222292 + 0.385021i
\(316\) 90650.8 157012.i 0.0510686 0.0884534i
\(317\) −536132. −0.299656 −0.149828 0.988712i \(-0.547872\pi\)
−0.149828 + 0.988712i \(0.547872\pi\)
\(318\) 315812. 547002.i 0.175130 0.303334i
\(319\) −109472. + 189611.i −0.0602317 + 0.104324i
\(320\) −418826. 725428.i −0.228643 0.396022i
\(321\) 606173. + 1.04992e6i 0.328348 + 0.568715i
\(322\) 4.95978e6 2.66577
\(323\) −2.04106e6 −1.08856
\(324\) −591055. 1.02374e6i −0.312799 0.541784i
\(325\) −1.09438e6 1.89553e6i −0.574726 0.995455i
\(326\) 2.42876e6 4.20674e6i 1.26573 2.19231i
\(327\) −552405. + 956794.i −0.285686 + 0.494822i
\(328\) −374995. −0.192460
\(329\) −3.22769e6 + 5.59053e6i −1.64400 + 2.84749i
\(330\) 47053.4 81498.9i 0.0237852 0.0411971i
\(331\) 15569.8 26967.6i 0.00781110 0.0135292i −0.862093 0.506749i \(-0.830847\pi\)
0.869905 + 0.493220i \(0.164180\pi\)
\(332\) −225563. 390686.i −0.112311 0.194528i
\(333\) −1.15229e6 −0.569446
\(334\) −2.89774e6 5.01904e6i −1.42133 2.46181i
\(335\) −35200.8 + 60969.5i −0.0171372 + 0.0296825i
\(336\) −975272. −0.471278
\(337\) 1.18014e6 2.04407e6i 0.566057 0.980439i −0.430894 0.902403i \(-0.641802\pi\)
0.996951 0.0780365i \(-0.0248651\pi\)
\(338\) 986892. + 1.70935e6i 0.469870 + 0.813839i
\(339\) −404779. 701098.i −0.191302 0.331345i
\(340\) 584515. 0.274220
\(341\) 52186.4 + 90389.4i 0.0243036 + 0.0420951i
\(342\) 4.25623e6 1.96771
\(343\) 3.92441e6 1.80111
\(344\) −531928. + 780928.i −0.242358 + 0.355807i
\(345\) 298055. 0.134818
\(346\) 4.84663e6 2.17645
\(347\) −195452. 338533.i −0.0871398 0.150931i 0.819161 0.573563i \(-0.194439\pi\)
−0.906301 + 0.422633i \(0.861106\pi\)
\(348\) −631277. −0.279429
\(349\) −1.50441e6 2.60571e6i −0.661153 1.14515i −0.980313 0.197450i \(-0.936734\pi\)
0.319160 0.947701i \(-0.396599\pi\)
\(350\) −2.72320e6 4.71673e6i −1.18826 2.05812i
\(351\) −1.14006e6 + 1.97464e6i −0.493923 + 0.855500i
\(352\) −763120. −0.328274
\(353\) 644551. 1.11640e6i 0.275309 0.476850i −0.694904 0.719103i \(-0.744553\pi\)
0.970213 + 0.242253i \(0.0778864\pi\)
\(354\) −351781. 609302.i −0.149198 0.258419i
\(355\) 660371. 0.278110
\(356\) −1.24002e6 2.14778e6i −0.518567 0.898185i
\(357\) 612076. 1.06015e6i 0.254176 0.440246i
\(358\) −2.48873e6 + 4.31061e6i −1.02629 + 1.77759i
\(359\) 461969. 800153.i 0.189181 0.327670i −0.755797 0.654806i \(-0.772750\pi\)
0.944977 + 0.327136i \(0.106084\pi\)
\(360\) −270197. −0.109881
\(361\) −1.89801e6 + 3.28745e6i −0.766532 + 1.32767i
\(362\) −2.80919e6 + 4.86565e6i −1.12670 + 1.95151i
\(363\) 505710. + 875915.i 0.201435 + 0.348896i
\(364\) 3.60211e6 + 6.23904e6i 1.42496 + 2.46811i
\(365\) −643914. −0.252985
\(366\) −2.08937e6 −0.815290
\(367\) 1.75035e6 + 3.03170e6i 0.678360 + 1.17495i 0.975475 + 0.220112i \(0.0706424\pi\)
−0.297114 + 0.954842i \(0.596024\pi\)
\(368\) −833907. 1.44437e6i −0.320995 0.555979i
\(369\) 478200. 828266.i 0.182828 0.316668i
\(370\) −432387. + 748916.i −0.164198 + 0.284399i
\(371\) 2.50773e6 0.945902
\(372\) −150468. + 260619.i −0.0563751 + 0.0976446i
\(373\) −1.78862e6 + 3.09798e6i −0.665651 + 1.15294i 0.313457 + 0.949602i \(0.398513\pi\)
−0.979108 + 0.203339i \(0.934821\pi\)
\(374\) 330485. 572417.i 0.122172 0.211609i
\(375\) −344954. 597478.i −0.126673 0.219404i
\(376\) −2.22778e6 −0.812649
\(377\) −895599. 1.55122e6i −0.324534 0.562110i
\(378\) −2.83686e6 + 4.91358e6i −1.02119 + 1.76876i
\(379\) 330104. 0.118046 0.0590232 0.998257i \(-0.481201\pi\)
0.0590232 + 0.998257i \(0.481201\pi\)
\(380\) 898097. 1.55555e6i 0.319054 0.552618i
\(381\) 655824. + 1.13592e6i 0.231459 + 0.400899i
\(382\) 4.12418e6 + 7.14328e6i 1.44603 + 2.50461i
\(383\) −3.92370e6 −1.36678 −0.683390 0.730054i \(-0.739495\pi\)
−0.683390 + 0.730054i \(0.739495\pi\)
\(384\) −509278. 882096.i −0.176249 0.305272i
\(385\) 373632. 0.128467
\(386\) −1.02206e6 −0.349147
\(387\) −1.04654e6 2.17074e6i −0.355205 0.736767i
\(388\) 2.19033e6 0.738636
\(389\) 3.78830e6 1.26932 0.634659 0.772793i \(-0.281141\pi\)
0.634659 + 0.772793i \(0.281141\pi\)
\(390\) 384949. + 666751.i 0.128157 + 0.221974i
\(391\) 2.09343e6 0.692493
\(392\) 1.33205e6 + 2.30718e6i 0.437830 + 0.758344i
\(393\) 606651. + 1.05075e6i 0.198133 + 0.343177i
\(394\) 1.48868e6 2.57846e6i 0.483125 0.836798i
\(395\) 76925.5 0.0248072
\(396\) −387534. + 671228.i −0.124186 + 0.215096i
\(397\) 1.00789e6 + 1.74572e6i 0.320950 + 0.555903i 0.980684 0.195597i \(-0.0626644\pi\)
−0.659734 + 0.751499i \(0.729331\pi\)
\(398\) −461588. −0.146065
\(399\) −1.88089e6 3.25780e6i −0.591468 1.02445i
\(400\) −915725. + 1.58608e6i −0.286164 + 0.495651i
\(401\) −1.71501e6 + 2.97049e6i −0.532606 + 0.922500i 0.466669 + 0.884432i \(0.345454\pi\)
−0.999275 + 0.0380685i \(0.987879\pi\)
\(402\) −114769. + 198787.i −0.0354210 + 0.0613510i
\(403\) −853884. −0.261900
\(404\) −919526. + 1.59267e6i −0.280292 + 0.485480i
\(405\) 250782. 434368.i 0.0759730 0.131589i
\(406\) −2.22856e6 3.85998e6i −0.670979 1.16217i
\(407\) 274946. + 476220.i 0.0822737 + 0.142502i
\(408\) 422461. 0.125642
\(409\) 927225. 0.274080 0.137040 0.990566i \(-0.456241\pi\)
0.137040 + 0.990566i \(0.456241\pi\)
\(410\) −358879. 621597.i −0.105436 0.182620i
\(411\) −635703. 1.10107e6i −0.185631 0.321522i
\(412\) 2.37892e6 4.12040e6i 0.690456 1.19591i
\(413\) 1.39667e6 2.41911e6i 0.402921 0.697879i
\(414\) −4.36542e6 −1.25177
\(415\) 95705.3 165766.i 0.0272782 0.0472472i
\(416\) 3.12158e6 5.40673e6i 0.884384 1.53180i
\(417\) 160717. 278369.i 0.0452606 0.0783937i
\(418\) −1.01557e6 1.75902e6i −0.284295 0.492413i
\(419\) 226769. 0.0631028 0.0315514 0.999502i \(-0.489955\pi\)
0.0315514 + 0.999502i \(0.489955\pi\)
\(420\) 538645. + 932960.i 0.148998 + 0.258071i
\(421\) 1.25571e6 2.17496e6i 0.345291 0.598061i −0.640116 0.768279i \(-0.721114\pi\)
0.985407 + 0.170217i \(0.0544469\pi\)
\(422\) 2.32975e6 0.636838
\(423\) 2.84090e6 4.92058e6i 0.771978 1.33711i
\(424\) 432715. + 749484.i 0.116893 + 0.202464i
\(425\) −1.14941e6 1.99084e6i −0.308676 0.534642i
\(426\) 2.15309e6 0.574828
\(427\) −4.14770e6 7.18403e6i −1.10087 1.90677i
\(428\) −7.49349e6 −1.97731
\(429\) 489562. 0.128429
\(430\) −1.80354e6 134364.i −0.470387 0.0350439i
\(431\) 4.00047e6 1.03733 0.518667 0.854977i \(-0.326429\pi\)
0.518667 + 0.854977i \(0.326429\pi\)
\(432\) 1.90789e6 0.491862
\(433\) 1.61790e6 + 2.80229e6i 0.414699 + 0.718280i 0.995397 0.0958393i \(-0.0305535\pi\)
−0.580698 + 0.814119i \(0.697220\pi\)
\(434\) −2.12476e6 −0.541483
\(435\) −133924. 231963.i −0.0339340 0.0587755i
\(436\) −3.41441e6 5.91393e6i −0.860199 1.48991i
\(437\) 3.21651e6 5.57116e6i 0.805715 1.39554i
\(438\) −2.09943e6 −0.522897
\(439\) −1.47752e6 + 2.55914e6i −0.365908 + 0.633772i −0.988921 0.148440i \(-0.952575\pi\)
0.623013 + 0.782211i \(0.285908\pi\)
\(440\) 64471.1 + 111667.i 0.0158757 + 0.0274975i
\(441\) −6.79461e6 −1.66367
\(442\) 2.70373e6 + 4.68300e6i 0.658276 + 1.14017i
\(443\) 578945. 1.00276e6i 0.140161 0.242767i −0.787396 0.616448i \(-0.788571\pi\)
0.927557 + 0.373681i \(0.121905\pi\)
\(444\) −792748. + 1.37308e6i −0.190844 + 0.330551i
\(445\) 526137. 911296.i 0.125950 0.218152i
\(446\) 3.12086e6 0.742912
\(447\) 1.73724e6 3.00898e6i 0.411235 0.712280i
\(448\) 5.42164e6 9.39056e6i 1.27625 2.21053i
\(449\) 3.17044e6 + 5.49136e6i 0.742170 + 1.28548i 0.951506 + 0.307632i \(0.0995364\pi\)
−0.209336 + 0.977844i \(0.567130\pi\)
\(450\) 2.39687e6 + 4.15149e6i 0.557972 + 0.966436i
\(451\) −456408. −0.105660
\(452\) 5.00387e6 1.15202
\(453\) −1.30632e6 2.26261e6i −0.299091 0.518041i
\(454\) 3.10141e6 + 5.37180e6i 0.706187 + 1.22315i
\(455\) −1.52836e6 + 2.64720e6i −0.346097 + 0.599457i
\(456\) 649103. 1.12428e6i 0.146185 0.253199i
\(457\) −3.11301e6 −0.697252 −0.348626 0.937262i \(-0.613352\pi\)
−0.348626 + 0.937262i \(0.613352\pi\)
\(458\) −2.27747e6 + 3.94469e6i −0.507327 + 0.878716i
\(459\) −1.19738e6 + 2.07393e6i −0.265278 + 0.459475i
\(460\) −921137. + 1.59546e6i −0.202969 + 0.351553i
\(461\) 2.76471e6 + 4.78861e6i 0.605894 + 1.04944i 0.991910 + 0.126947i \(0.0405178\pi\)
−0.386016 + 0.922492i \(0.626149\pi\)
\(462\) 1.21820e6 0.265530
\(463\) −2.62962e6 4.55464e6i −0.570086 0.987418i −0.996556 0.0829168i \(-0.973576\pi\)
0.426470 0.904502i \(-0.359757\pi\)
\(464\) −749392. + 1.29799e6i −0.161590 + 0.279882i
\(465\) −127686. −0.0273849
\(466\) −3.01288e6 + 5.21846e6i −0.642713 + 1.11321i
\(467\) 497355. + 861444.i 0.105530 + 0.182783i 0.913954 0.405817i \(-0.133013\pi\)
−0.808425 + 0.588599i \(0.799680\pi\)
\(468\) −3.17045e6 5.49138e6i −0.669124 1.15896i
\(469\) −911338. −0.191314
\(470\) −2.13204e6 3.69280e6i −0.445195 0.771101i
\(471\) 1.39537e6 0.289825
\(472\) 963997. 0.199168
\(473\) −647411. + 950470.i −0.133054 + 0.195337i
\(474\) 250810. 0.0512741
\(475\) −7.06419e6 −1.43658
\(476\) 3.78323e6 + 6.55275e6i 0.765324 + 1.32558i
\(477\) −2.20722e6 −0.444170
\(478\) 400280. + 693305.i 0.0801297 + 0.138789i
\(479\) 1.69502e6 + 2.93586e6i 0.337548 + 0.584651i 0.983971 0.178329i \(-0.0570690\pi\)
−0.646423 + 0.762980i \(0.723736\pi\)
\(480\) 466788. 808500.i 0.0924733 0.160168i
\(481\) −4.49872e6 −0.886597
\(482\) −5.33902e6 + 9.24746e6i −1.04675 + 1.81303i
\(483\) 1.92914e6 + 3.34137e6i 0.376267 + 0.651714i
\(484\) −6.25156e6 −1.21304
\(485\) 464674. + 804839.i 0.0897003 + 0.155366i
\(486\) 3.87039e6 6.70372e6i 0.743301 1.28743i
\(487\) 5.03830e6 8.72659e6i 0.962635 1.66733i 0.246796 0.969067i \(-0.420622\pi\)
0.715839 0.698265i \(-0.246044\pi\)
\(488\) 1.43139e6 2.47924e6i 0.272088 0.471269i
\(489\) 3.77874e6 0.714619
\(490\) −2.54961e6 + 4.41605e6i −0.479715 + 0.830891i
\(491\) −290638. + 503401.i −0.0544063 + 0.0942345i −0.891946 0.452142i \(-0.850660\pi\)
0.837540 + 0.546377i \(0.183993\pi\)
\(492\) −657978. 1.13965e6i −0.122546 0.212256i
\(493\) −940631. 1.62922e6i −0.174302 0.301900i
\(494\) 1.66169e7 3.06361
\(495\) −328858. −0.0603247
\(496\) 357243. + 618764.i 0.0652019 + 0.112933i
\(497\) 4.27420e6 + 7.40314e6i 0.776183 + 1.34439i
\(498\) 312040. 540469.i 0.0563815 0.0976556i
\(499\) 2.36539e6 4.09697e6i 0.425257 0.736566i −0.571188 0.820819i \(-0.693517\pi\)
0.996444 + 0.0842535i \(0.0268505\pi\)
\(500\) 4.26431e6 0.762823
\(501\) 2.25419e6 3.90438e6i 0.401233 0.694956i
\(502\) −7.23290e6 + 1.25278e7i −1.28101 + 2.21878i
\(503\) 1.35286e6 2.34322e6i 0.238414 0.412946i −0.721845 0.692055i \(-0.756706\pi\)
0.960259 + 0.279109i \(0.0900390\pi\)
\(504\) −1.74883e6 3.02906e6i −0.306670 0.531168i
\(505\) −780302. −0.136155
\(506\) 1.04162e6 + 1.80414e6i 0.180856 + 0.313253i
\(507\) −767717. + 1.32973e6i −0.132642 + 0.229743i
\(508\) −8.10727e6 −1.39385
\(509\) −834861. + 1.44602e6i −0.142830 + 0.247389i −0.928561 0.371179i \(-0.878954\pi\)
0.785731 + 0.618568i \(0.212287\pi\)
\(510\) 404304. + 700276.i 0.0688308 + 0.119219i
\(511\) −4.16768e6 7.21864e6i −0.706061 1.22293i
\(512\) −6.84314e6 −1.15367
\(513\) 3.67951e6 + 6.37310e6i 0.617301 + 1.06920i
\(514\) −3.89681e6 −0.650581
\(515\) 2.01873e6 0.335397
\(516\) −3.30666e6 246347.i −0.546721 0.0407308i
\(517\) −2.71144e6 −0.446142
\(518\) −1.11944e7 −1.83305
\(519\) 1.88513e6 + 3.26514e6i 0.307201 + 0.532088i
\(520\) −1.05489e6 −0.171080
\(521\) 5.21202e6 + 9.02748e6i 0.841224 + 1.45704i 0.888861 + 0.458178i \(0.151498\pi\)
−0.0476367 + 0.998865i \(0.515169\pi\)
\(522\) 1.96150e6 + 3.39741e6i 0.315073 + 0.545723i
\(523\) −2.38845e6 + 4.13691e6i −0.381822 + 0.661335i −0.991323 0.131450i \(-0.958037\pi\)
0.609501 + 0.792786i \(0.291370\pi\)
\(524\) −7.49940e6 −1.19316
\(525\) 2.11842e6 3.66921e6i 0.335439 0.580997i
\(526\) −5.02574e6 8.70484e6i −0.792019 1.37182i
\(527\) −896818. −0.140662
\(528\) −204820. 354759.i −0.0319734 0.0553795i
\(529\) −80854.8 + 140045.i −0.0125622 + 0.0217584i
\(530\) −828236. + 1.43455e6i −0.128075 + 0.221832i
\(531\) −1.22930e6 + 2.12921e6i −0.189201 + 0.327705i
\(532\) 2.32515e7 3.56182
\(533\) 1.86696e6 3.23367e6i 0.284654 0.493035i
\(534\) 1.71543e6 2.97121e6i 0.260327 0.450900i
\(535\) −1.58973e6 2.75349e6i −0.240125 0.415910i
\(536\) −157253. 272371.i −0.0236422 0.0409495i
\(537\) −3.87204e6 −0.579434
\(538\) 9.27769e6 1.38192
\(539\) 1.62124e6 + 2.80808e6i 0.240368 + 0.416329i
\(540\) −1.05373e6 1.82511e6i −0.155505 0.269343i
\(541\) −485182. + 840361.i −0.0712708 + 0.123445i −0.899459 0.437006i \(-0.856039\pi\)
0.828188 + 0.560451i \(0.189372\pi\)
\(542\) 9.42981e6 1.63329e7i 1.37881 2.38817i
\(543\) −4.37061e6 −0.636125
\(544\) 3.27854e6 5.67859e6i 0.474988 0.822703i
\(545\) 1.44872e6 2.50925e6i 0.208926 0.361871i
\(546\) −4.98311e6 + 8.63099e6i −0.715350 + 1.23902i
\(547\) −3.36621e6 5.83045e6i −0.481031 0.833170i 0.518732 0.854937i \(-0.326404\pi\)
−0.999763 + 0.0217667i \(0.993071\pi\)
\(548\) 7.85854e6 1.11787
\(549\) 3.65066e6 + 6.32313e6i 0.516941 + 0.895367i
\(550\) 1.14382e6 1.98116e6i 0.161232 0.279262i
\(551\) −5.78105e6 −0.811200
\(552\) −665755. + 1.15312e6i −0.0929965 + 0.161075i
\(553\) 497894. + 862378.i 0.0692348 + 0.119918i
\(554\) 2.62072e6 + 4.53921e6i 0.362782 + 0.628357i
\(555\) −672719. −0.0927046
\(556\) 993385. + 1.72059e6i 0.136280 + 0.236043i
\(557\) −1.39802e7 −1.90931 −0.954656 0.297712i \(-0.903777\pi\)
−0.954656 + 0.297712i \(0.903777\pi\)
\(558\) 1.87013e6 0.254266
\(559\) −4.08585e6 8.47488e6i −0.553035 1.14711i
\(560\) 2.55771e6 0.344652
\(561\) 514178. 0.0689773
\(562\) −1.42558e6 2.46918e6i −0.190393 0.329770i
\(563\) −868060. −0.115419 −0.0577097 0.998333i \(-0.518380\pi\)
−0.0577097 + 0.998333i \(0.518380\pi\)
\(564\) −3.90893e6 6.77047e6i −0.517440 0.896233i
\(565\) 1.06156e6 + 1.83867e6i 0.139902 + 0.242317i
\(566\) 260435. 451087.i 0.0341711 0.0591861i
\(567\) 6.49268e6 0.848137
\(568\) −1.47505e6 + 2.55486e6i −0.191838 + 0.332273i
\(569\) 1.24744e6 + 2.16062e6i 0.161524 + 0.279768i 0.935416 0.353550i \(-0.115026\pi\)
−0.773891 + 0.633318i \(0.781692\pi\)
\(570\) 2.48483e6 0.320338
\(571\) 743122. + 1.28712e6i 0.0953827 + 0.165208i 0.909768 0.415116i \(-0.136259\pi\)
−0.814386 + 0.580324i \(0.802926\pi\)
\(572\) −1.51299e6 + 2.62057e6i −0.193350 + 0.334893i
\(573\) −3.20825e6 + 5.55686e6i −0.408209 + 0.707038i
\(574\) 4.64564e6 8.04648e6i 0.588526 1.01936i
\(575\) 7.24542e6 0.913890
\(576\) −4.77193e6 + 8.26523e6i −0.599292 + 1.03800i
\(577\) −33546.6 + 58104.3i −0.00419477 + 0.00726556i −0.868115 0.496363i \(-0.834669\pi\)
0.863920 + 0.503628i \(0.168002\pi\)
\(578\) −3.23068e6 5.59571e6i −0.402230 0.696684i
\(579\) −397537. 688554.i −0.0492812 0.0853575i
\(580\) 1.65556e6 0.204351
\(581\) 2.47778e6 0.304525
\(582\) 1.51503e6 + 2.62412e6i 0.185402 + 0.321126i
\(583\) 526658. + 912199.i 0.0641737 + 0.111152i
\(584\) 1.43829e6 2.49118e6i 0.174507 0.302255i
\(585\) 1.34521e6 2.32997e6i 0.162518 0.281489i
\(586\) −1.93430e7 −2.32691
\(587\) 3.92924e6 6.80564e6i 0.470666 0.815218i −0.528771 0.848765i \(-0.677347\pi\)
0.999437 + 0.0335466i \(0.0106802\pi\)
\(588\) −4.67451e6 + 8.09649e6i −0.557562 + 0.965725i
\(589\) −1.37794e6 + 2.38667e6i −0.163660 + 0.283468i
\(590\) 922567. + 1.59793e6i 0.109111 + 0.188986i
\(591\) 2.31612e6 0.272768
\(592\) 1.88215e6 + 3.25998e6i 0.220724 + 0.382306i
\(593\) 533177. 923489.i 0.0622636 0.107844i −0.833213 0.552952i \(-0.813501\pi\)
0.895477 + 0.445108i \(0.146835\pi\)
\(594\) −2.38312e6 −0.277127
\(595\) −1.60521e6 + 2.78030e6i −0.185883 + 0.321958i
\(596\) 1.07378e7 + 1.85985e7i 1.23823 + 2.14467i
\(597\) −179538. 310969.i −0.0206168 0.0357093i
\(598\) −1.70432e7 −1.94894
\(599\) 5.29841e6 + 9.17711e6i 0.603363 + 1.04505i 0.992308 + 0.123794i \(0.0395061\pi\)
−0.388945 + 0.921261i \(0.627161\pi\)
\(600\) 1.46215e6 0.165811
\(601\) −1.03792e7 −1.17214 −0.586068 0.810262i \(-0.699325\pi\)
−0.586068 + 0.810262i \(0.699325\pi\)
\(602\) −1.01670e7 2.10884e7i −1.14341 2.37166i
\(603\) 802127. 0.0898359
\(604\) 1.61486e7 1.80112
\(605\) −1.32626e6 2.29714e6i −0.147312 0.255152i
\(606\) −2.54411e6 −0.281420
\(607\) 5.88121e6 + 1.01866e7i 0.647880 + 1.12216i 0.983628 + 0.180210i \(0.0576777\pi\)
−0.335748 + 0.941952i \(0.608989\pi\)
\(608\) −1.00748e7 1.74501e7i −1.10530 1.91443i
\(609\) 1.73363e6 3.00273e6i 0.189414 0.328075i
\(610\) 5.47950e6 0.596233
\(611\) 1.10913e7 1.92107e7i 1.20193 2.08180i
\(612\) −3.32987e6 5.76750e6i −0.359375 0.622456i
\(613\) 1.53282e7 1.64756 0.823779 0.566911i \(-0.191862\pi\)
0.823779 + 0.566911i \(0.191862\pi\)
\(614\) −4.76947e6 8.26096e6i −0.510563 0.884320i
\(615\) 279177. 483549.i 0.0297641 0.0515529i
\(616\) −834568. + 1.44551e6i −0.0886156 + 0.153487i
\(617\) −6.79431e6 + 1.17681e7i −0.718509 + 1.24449i 0.243081 + 0.970006i \(0.421842\pi\)
−0.961590 + 0.274489i \(0.911491\pi\)
\(618\) 6.58191e6 0.693235
\(619\) −6.92049e6 + 1.19866e7i −0.725956 + 1.25739i 0.232623 + 0.972567i \(0.425269\pi\)
−0.958579 + 0.284826i \(0.908064\pi\)
\(620\) 394613. 683489.i 0.0412279 0.0714089i
\(621\) −3.77391e6 6.53660e6i −0.392701 0.680178i
\(622\) 3.10126e6 + 5.37154e6i 0.321412 + 0.556702i
\(623\) 1.36215e7 1.40607
\(624\) 3.35131e6 0.344551
\(625\) −3.50267e6 6.06680e6i −0.358673 0.621240i
\(626\) 3.87899e6 + 6.71861e6i 0.395624 + 0.685241i
\(627\) 790025. 1.36836e6i 0.0802550 0.139006i
\(628\) −4.31237e6 + 7.46924e6i −0.436332 + 0.755749i
\(629\) −4.72492e6 −0.476176
\(630\) 3.34734e6 5.79777e6i 0.336007 0.581982i
\(631\) 9.87471e6 1.71035e7i 0.987304 1.71006i 0.356091 0.934451i \(-0.384109\pi\)
0.631213 0.775609i \(-0.282557\pi\)
\(632\) −171826. + 297611.i −0.0171118 + 0.0296385i
\(633\) 906173. + 1.56954e6i 0.0898881 + 0.155691i
\(634\) 4.58429e6 0.452948
\(635\) −1.71994e6 2.97902e6i −0.169270 0.293183i
\(636\) −1.51851e6 + 2.63013e6i −0.148859 + 0.257831i
\(637\) −2.65271e7 −2.59025
\(638\) 936056. 1.62130e6i 0.0910438 0.157692i
\(639\) −3.76200e6 6.51598e6i −0.364474 0.631288i
\(640\) 1.33561e6 + 2.31335e6i 0.128894 + 0.223250i
\(641\) 1.24571e7 1.19749 0.598744 0.800940i \(-0.295667\pi\)
0.598744 + 0.800940i \(0.295667\pi\)
\(642\) −5.18319e6 8.97754e6i −0.496317 0.859646i
\(643\) 8.95524e6 0.854181 0.427090 0.904209i \(-0.359539\pi\)
0.427090 + 0.904209i \(0.359539\pi\)
\(644\) −2.38480e7 −2.26588
\(645\) −610981. 1.26730e6i −0.0578267 0.119944i
\(646\) 1.74525e7 1.64541
\(647\) −1.87092e7 −1.75710 −0.878548 0.477654i \(-0.841487\pi\)
−0.878548 + 0.477654i \(0.841487\pi\)
\(648\) 1.12033e6 + 1.94046e6i 0.104811 + 0.181538i
\(649\) 1.17328e6 0.109343
\(650\) 9.35771e6 + 1.62080e7i 0.868733 + 1.50469i
\(651\) −826439. 1.43143e6i −0.0764290 0.132379i
\(652\) −1.16782e7 + 2.02271e7i −1.07586 + 1.86344i
\(653\) −4.64410e6 −0.426205 −0.213103 0.977030i \(-0.568357\pi\)
−0.213103 + 0.977030i \(0.568357\pi\)
\(654\) 4.72343e6 8.18123e6i 0.431831 0.747953i
\(655\) −1.59098e6 2.75566e6i −0.144898 0.250970i
\(656\) −3.12436e6 −0.283466
\(657\) 3.66825e6 + 6.35359e6i 0.331547 + 0.574256i
\(658\) 2.75989e7 4.78027e7i 2.48501 4.30416i
\(659\) −2.95481e6 + 5.11789e6i −0.265043 + 0.459068i −0.967575 0.252584i \(-0.918720\pi\)
0.702532 + 0.711652i \(0.252053\pi\)
\(660\) −226246. + 391869.i −0.0202172 + 0.0350172i
\(661\) −1.48476e7 −1.32176 −0.660880 0.750492i \(-0.729817\pi\)
−0.660880 + 0.750492i \(0.729817\pi\)
\(662\) −133132. + 230591.i −0.0118069 + 0.0204502i
\(663\) −2.10327e6 + 3.64297e6i −0.185828 + 0.321864i
\(664\) 427547. + 740532.i 0.0376325 + 0.0651814i
\(665\) 4.93275e6 + 8.54377e6i 0.432549 + 0.749196i
\(666\) 9.85288e6 0.860751
\(667\) 5.92936e6 0.516051
\(668\) 1.39331e7 + 2.41329e7i 1.20811 + 2.09251i
\(669\) 1.21388e6 + 2.10250e6i 0.104860 + 0.181623i
\(670\) 300990. 521330.i 0.0259039 0.0448669i
\(671\) 1.74215e6 3.01749e6i 0.149375 0.258726i
\(672\) 1.20850e7 1.03234
\(673\) 1.94361e6 3.36644e6i 0.165414 0.286505i −0.771388 0.636365i \(-0.780437\pi\)
0.936802 + 0.349859i \(0.113771\pi\)
\(674\) −1.00910e7 + 1.74781e7i −0.855628 + 1.48199i
\(675\) −4.14418e6 + 7.17793e6i −0.350090 + 0.606373i
\(676\) −4.74525e6 8.21901e6i −0.399385 0.691755i
\(677\) 9.17886e6 0.769692 0.384846 0.922981i \(-0.374254\pi\)
0.384846 + 0.922981i \(0.374254\pi\)
\(678\) 3.46113e6 + 5.99486e6i 0.289164 + 0.500847i
\(679\) −6.01514e6 + 1.04185e7i −0.500692 + 0.867225i
\(680\) −1.10793e6 −0.0918840
\(681\) −2.41263e6 + 4.17880e6i −0.199353 + 0.345290i
\(682\) −446228. 772890.i −0.0367364 0.0636292i
\(683\) 1.13160e7 + 1.95999e7i 0.928198 + 1.60769i 0.786335 + 0.617801i \(0.211976\pi\)
0.141864 + 0.989886i \(0.454691\pi\)
\(684\) −2.04651e7 −1.67253
\(685\) 1.66717e6 + 2.88763e6i 0.135754 + 0.235134i
\(686\) −3.35564e7 −2.72248
\(687\) −3.54334e6 −0.286432
\(688\) −4.43187e6 + 6.50647e6i −0.356957 + 0.524052i
\(689\) −8.61729e6 −0.691548
\(690\) −2.54857e6 −0.203786
\(691\) 4.38633e6 + 7.59735e6i 0.349467 + 0.605295i 0.986155 0.165827i \(-0.0530292\pi\)
−0.636688 + 0.771122i \(0.719696\pi\)
\(692\) −2.33039e7 −1.84996
\(693\) −2.12851e6 3.68668e6i −0.168361 0.291610i
\(694\) 1.67125e6 + 2.89468e6i 0.131717 + 0.228140i
\(695\) −421489. + 730041.i −0.0330997 + 0.0573304i
\(696\) 1.19656e6 0.0936296
\(697\) 1.96083e6 3.39626e6i 0.152883 0.264801i
\(698\) 1.28637e7 + 2.22806e7i 0.999371 + 1.73096i
\(699\) −4.68752e6 −0.362869
\(700\) 1.30939e7 + 2.26793e7i 1.01001 + 1.74938i
\(701\) 8.14713e6 1.41113e7i 0.626195 1.08460i −0.362113 0.932134i \(-0.617945\pi\)
0.988308 0.152468i \(-0.0487221\pi\)
\(702\) 9.74826e6 1.68845e7i 0.746594 1.29314i
\(703\) −7.25975e6 + 1.25743e7i −0.554030 + 0.959609i
\(704\) 4.55448e6 0.346343
\(705\) 1.65854e6 2.87268e6i 0.125676 0.217678i
\(706\) −5.51134e6 + 9.54593e6i −0.416146 + 0.720786i
\(707\) −5.05044e6 8.74763e6i −0.379998 0.658176i
\(708\) 1.69146e6 + 2.92969e6i 0.126817 + 0.219654i
\(709\) 1.09142e7 0.815407 0.407704 0.913114i \(-0.366330\pi\)
0.407704 + 0.913114i \(0.366330\pi\)
\(710\) −5.64661e6 −0.420380
\(711\) −438229. 759035.i −0.0325108 0.0563103i
\(712\) 2.35042e6 + 4.07105e6i 0.173759 + 0.300959i
\(713\) 1.41329e6 2.44790e6i 0.104114 0.180331i
\(714\) −5.23366e6 + 9.06497e6i −0.384202 + 0.665458i
\(715\) −1.28391e6 −0.0939223
\(716\) 1.19665e7 2.07266e7i 0.872337 1.51093i
\(717\) −311383. + 539331.i −0.0226202 + 0.0391794i
\(718\) −3.95014e6 + 6.84185e6i −0.285958 + 0.495293i
\(719\) 708613. + 1.22735e6i 0.0511195 + 0.0885416i 0.890453 0.455075i \(-0.150388\pi\)
−0.839333 + 0.543617i \(0.817054\pi\)
\(720\) −2.25121e6 −0.161839
\(721\) 1.30661e7 + 2.26311e7i 0.936066 + 1.62131i
\(722\) 1.62293e7 2.81099e7i 1.15866 2.00686i
\(723\) −8.30660e6 −0.590986
\(724\) 1.35073e7 2.33954e7i 0.957686 1.65876i
\(725\) −3.25556e6 5.63879e6i −0.230028 0.398420i
\(726\) −4.32416e6 7.48966e6i −0.304481 0.527376i
\(727\) −2.41036e7 −1.69140 −0.845698 0.533662i \(-0.820815\pi\)
−0.845698 + 0.533662i \(0.820815\pi\)
\(728\) −6.82769e6 1.18259e7i −0.477469 0.827001i
\(729\) −965092. −0.0672589
\(730\) 5.50589e6 0.382402
\(731\) −4.29129e6 8.90100e6i −0.297026 0.616092i
\(732\) 1.00462e7 0.692988
\(733\) 1.52281e7 1.04685 0.523425 0.852072i \(-0.324654\pi\)
0.523425 + 0.852072i \(0.324654\pi\)
\(734\) −1.49667e7 2.59231e7i −1.02538 1.77601i
\(735\) −3.96675e6 −0.270842
\(736\) 1.03333e7 + 1.78978e7i 0.703143 + 1.21788i
\(737\) −191393. 331503.i −0.0129795 0.0224812i
\(738\) −4.08893e6 + 7.08223e6i −0.276356 + 0.478662i
\(739\) −5.93028e6 −0.399452 −0.199726 0.979852i \(-0.564005\pi\)
−0.199726 + 0.979852i \(0.564005\pi\)
\(740\) 2.07903e6 3.60099e6i 0.139567 0.241737i
\(741\) 6.46328e6 + 1.11947e7i 0.432421 + 0.748976i
\(742\) −2.14428e7 −1.42979
\(743\) 7.31882e6 + 1.26766e7i 0.486373 + 0.842422i 0.999877 0.0156648i \(-0.00498647\pi\)
−0.513505 + 0.858087i \(0.671653\pi\)
\(744\) 285208. 493994.i 0.0188899 0.0327182i
\(745\) −4.55601e6 + 7.89125e6i −0.300742 + 0.520901i
\(746\) 1.52939e7 2.64898e7i 1.00617 1.74274i
\(747\) −2.18085e6 −0.142996
\(748\) −1.58906e6 + 2.75234e6i −0.103845 + 0.179865i
\(749\) 2.05788e7 3.56435e7i 1.34034 2.32154i
\(750\) 2.94959e6 + 5.10884e6i 0.191473 + 0.331641i
\(751\) −4.87420e6 8.44236e6i −0.315358 0.546216i 0.664156 0.747594i \(-0.268791\pi\)
−0.979513 + 0.201379i \(0.935458\pi\)
\(752\) −1.85612e7 −1.19691
\(753\) −1.12532e7 −0.723247
\(754\) 7.65797e6 + 1.32640e7i 0.490552 + 0.849662i
\(755\) 3.42590e6 + 5.93383e6i 0.218729 + 0.378850i
\(756\) 1.36404e7 2.36258e7i 0.868005 1.50343i
\(757\) 1.38728e7 2.40284e7i 0.879884 1.52400i 0.0284158 0.999596i \(-0.490954\pi\)
0.851468 0.524407i \(-0.175713\pi\)
\(758\) −2.82261e6 −0.178434
\(759\) −810292. + 1.40347e6i −0.0510549 + 0.0884297i
\(760\) −1.70231e6 + 2.94849e6i −0.106907 + 0.185168i
\(761\) −1.19538e7 + 2.07045e7i −0.748243 + 1.29600i 0.200421 + 0.979710i \(0.435769\pi\)
−0.948664 + 0.316285i \(0.897564\pi\)
\(762\) −5.60773e6 9.71288e6i −0.349864 0.605983i
\(763\) 3.75069e7 2.33238
\(764\) −1.98301e7 3.43468e7i −1.22912 2.12889i
\(765\) 1.41285e6 2.44712e6i 0.0872854 0.151183i
\(766\) 3.35502e7 2.06597
\(767\) −4.79937e6 + 8.31276e6i −0.294575 + 0.510219i
\(768\) −755764. 1.30902e6i −0.0462363 0.0800837i
\(769\) −8.58602e6 1.48714e7i −0.523572 0.906853i −0.999624 0.0274355i \(-0.991266\pi\)
0.476052 0.879417i \(-0.342067\pi\)
\(770\) −3.19480e6 −0.194186
\(771\) −1.51569e6 2.62526e6i −0.0918280 0.159051i
\(772\) 4.91434e6 0.296771
\(773\)