Properties

Label 43.5.b.b.42.1
Level 43
Weight 5
Character 43.42
Analytic conductor 4.445
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.1
Root \(-7.49282i\) of \(x^{12} + 142 x^{10} + 7173 x^{8} + 157368 x^{6} + 1510016 x^{4} + 5098688 x^{2} + 90352\)
Character \(\chi\) \(=\) 43.42
Dual form 43.5.b.b.42.12

$q$-expansion

\(f(q)\) \(=\) \(q-7.49282i q^{2} +14.5182i q^{3} -40.1424 q^{4} +9.40180i q^{5} +108.782 q^{6} +53.5326i q^{7} +180.895i q^{8} -129.777 q^{9} +O(q^{10})\) \(q-7.49282i q^{2} +14.5182i q^{3} -40.1424 q^{4} +9.40180i q^{5} +108.782 q^{6} +53.5326i q^{7} +180.895i q^{8} -129.777 q^{9} +70.4460 q^{10} +151.146 q^{11} -582.793i q^{12} -319.508 q^{13} +401.110 q^{14} -136.497 q^{15} +713.133 q^{16} +32.2585 q^{17} +972.395i q^{18} +304.131i q^{19} -377.411i q^{20} -777.194 q^{21} -1132.51i q^{22} -199.312 q^{23} -2626.26 q^{24} +536.606 q^{25} +2394.02i q^{26} -708.150i q^{27} -2148.92i q^{28} +268.672i q^{29} +1022.75i q^{30} +665.439 q^{31} -2449.06i q^{32} +2194.36i q^{33} -241.707i q^{34} -503.303 q^{35} +5209.55 q^{36} -1176.50i q^{37} +2278.80 q^{38} -4638.66i q^{39} -1700.74 q^{40} +212.488 q^{41} +5823.38i q^{42} +(1352.49 - 1260.78i) q^{43} -6067.35 q^{44} -1220.14i q^{45} +1493.41i q^{46} -3100.78 q^{47} +10353.4i q^{48} -464.736 q^{49} -4020.69i q^{50} +468.334i q^{51} +12825.8 q^{52} +2662.72 q^{53} -5306.04 q^{54} +1421.04i q^{55} -9683.75 q^{56} -4415.43 q^{57} +2013.11 q^{58} +2748.48 q^{59} +5479.31 q^{60} +5880.73i q^{61} -4986.02i q^{62} -6947.29i q^{63} -6940.28 q^{64} -3003.95i q^{65} +16441.9 q^{66} -1093.36 q^{67} -1294.93 q^{68} -2893.64i q^{69} +3771.16i q^{70} +5841.22i q^{71} -23475.9i q^{72} -663.511i q^{73} -8815.31 q^{74} +7790.53i q^{75} -12208.6i q^{76} +8091.21i q^{77} -34756.7 q^{78} +6328.79 q^{79} +6704.74i q^{80} -230.889 q^{81} -1592.13i q^{82} +8356.34 q^{83} +31198.4 q^{84} +303.288i q^{85} +(-9446.83 - 10134.0i) q^{86} -3900.62 q^{87} +27341.4i q^{88} +4257.21i q^{89} -9142.27 q^{90} -17104.1i q^{91} +8000.85 q^{92} +9660.95i q^{93} +23233.6i q^{94} -2859.38 q^{95} +35555.9 q^{96} -3585.40 q^{97} +3482.18i q^{98} -19615.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.49282i 1.87321i −0.350393 0.936603i \(-0.613952\pi\)
0.350393 0.936603i \(-0.386048\pi\)
\(3\) 14.5182i 1.61313i 0.591146 + 0.806564i \(0.298676\pi\)
−0.591146 + 0.806564i \(0.701324\pi\)
\(4\) −40.1424 −2.50890
\(5\) 9.40180i 0.376072i 0.982162 + 0.188036i \(0.0602122\pi\)
−0.982162 + 0.188036i \(0.939788\pi\)
\(6\) 108.782 3.02172
\(7\) 53.5326i 1.09250i 0.837622 + 0.546251i \(0.183945\pi\)
−0.837622 + 0.546251i \(0.816055\pi\)
\(8\) 180.895i 2.82648i
\(9\) −129.777 −1.60218
\(10\) 70.4460 0.704460
\(11\) 151.146 1.24914 0.624569 0.780970i \(-0.285275\pi\)
0.624569 + 0.780970i \(0.285275\pi\)
\(12\) 582.793i 4.04718i
\(13\) −319.508 −1.89058 −0.945289 0.326233i \(-0.894221\pi\)
−0.945289 + 0.326233i \(0.894221\pi\)
\(14\) 401.110 2.04648
\(15\) −136.497 −0.606653
\(16\) 713.133 2.78568
\(17\) 32.2585 0.111621 0.0558106 0.998441i \(-0.482226\pi\)
0.0558106 + 0.998441i \(0.482226\pi\)
\(18\) 972.395i 3.00122i
\(19\) 304.131i 0.842469i 0.906952 + 0.421235i \(0.138403\pi\)
−0.906952 + 0.421235i \(0.861597\pi\)
\(20\) 377.411i 0.943527i
\(21\) −777.194 −1.76235
\(22\) 1132.51i 2.33989i
\(23\) −199.312 −0.376771 −0.188386 0.982095i \(-0.560325\pi\)
−0.188386 + 0.982095i \(0.560325\pi\)
\(24\) −2626.26 −4.55947
\(25\) 536.606 0.858570
\(26\) 2394.02i 3.54144i
\(27\) 708.150i 0.971400i
\(28\) 2148.92i 2.74098i
\(29\) 268.672i 0.319467i 0.987160 + 0.159734i \(0.0510635\pi\)
−0.987160 + 0.159734i \(0.948937\pi\)
\(30\) 1022.75i 1.13639i
\(31\) 665.439 0.692444 0.346222 0.938153i \(-0.387464\pi\)
0.346222 + 0.938153i \(0.387464\pi\)
\(32\) 2449.06i 2.39166i
\(33\) 2194.36i 2.01502i
\(34\) 241.707i 0.209089i
\(35\) −503.303 −0.410859
\(36\) 5209.55 4.01972
\(37\) 1176.50i 0.859387i −0.902975 0.429693i \(-0.858622\pi\)
0.902975 0.429693i \(-0.141378\pi\)
\(38\) 2278.80 1.57812
\(39\) 4638.66i 3.04975i
\(40\) −1700.74 −1.06296
\(41\) 212.488 0.126406 0.0632028 0.998001i \(-0.479868\pi\)
0.0632028 + 0.998001i \(0.479868\pi\)
\(42\) 5823.38i 3.30123i
\(43\) 1352.49 1260.78i 0.731470 0.681873i
\(44\) −6067.35 −3.13396
\(45\) 1220.14i 0.602537i
\(46\) 1493.41i 0.705770i
\(47\) −3100.78 −1.40371 −0.701853 0.712322i \(-0.747643\pi\)
−0.701853 + 0.712322i \(0.747643\pi\)
\(48\) 10353.4i 4.49365i
\(49\) −464.736 −0.193559
\(50\) 4020.69i 1.60828i
\(51\) 468.334i 0.180059i
\(52\) 12825.8 4.74327
\(53\) 2662.72 0.947924 0.473962 0.880545i \(-0.342823\pi\)
0.473962 + 0.880545i \(0.342823\pi\)
\(54\) −5306.04 −1.81963
\(55\) 1421.04i 0.469766i
\(56\) −9683.75 −3.08793
\(57\) −4415.43 −1.35901
\(58\) 2013.11 0.598427
\(59\) 2748.48 0.789565 0.394783 0.918775i \(-0.370820\pi\)
0.394783 + 0.918775i \(0.370820\pi\)
\(60\) 5479.31 1.52203
\(61\) 5880.73i 1.58042i 0.612839 + 0.790208i \(0.290028\pi\)
−0.612839 + 0.790208i \(0.709972\pi\)
\(62\) 4986.02i 1.29709i
\(63\) 6947.29i 1.75039i
\(64\) −6940.28 −1.69440
\(65\) 3003.95i 0.710994i
\(66\) 16441.9 3.77455
\(67\) −1093.36 −0.243565 −0.121782 0.992557i \(-0.538861\pi\)
−0.121782 + 0.992557i \(0.538861\pi\)
\(68\) −1294.93 −0.280046
\(69\) 2893.64i 0.607780i
\(70\) 3771.16i 0.769624i
\(71\) 5841.22i 1.15874i 0.815064 + 0.579371i \(0.196702\pi\)
−0.815064 + 0.579371i \(0.803298\pi\)
\(72\) 23475.9i 4.52854i
\(73\) 663.511i 0.124509i −0.998060 0.0622547i \(-0.980171\pi\)
0.998060 0.0622547i \(-0.0198291\pi\)
\(74\) −8815.31 −1.60981
\(75\) 7790.53i 1.38498i
\(76\) 12208.6i 2.11367i
\(77\) 8091.21i 1.36468i
\(78\) −34756.7 −5.71280
\(79\) 6328.79 1.01407 0.507034 0.861926i \(-0.330742\pi\)
0.507034 + 0.861926i \(0.330742\pi\)
\(80\) 6704.74i 1.04762i
\(81\) −230.889 −0.0351911
\(82\) 1592.13i 0.236784i
\(83\) 8356.34 1.21300 0.606499 0.795084i \(-0.292573\pi\)
0.606499 + 0.795084i \(0.292573\pi\)
\(84\) 31198.4 4.42155
\(85\) 303.288i 0.0419776i
\(86\) −9446.83 10134.0i −1.27729 1.37019i
\(87\) −3900.62 −0.515341
\(88\) 27341.4i 3.53066i
\(89\) 4257.21i 0.537459i 0.963216 + 0.268729i \(0.0866037\pi\)
−0.963216 + 0.268729i \(0.913396\pi\)
\(90\) −9142.27 −1.12868
\(91\) 17104.1i 2.06546i
\(92\) 8000.85 0.945281
\(93\) 9660.95i 1.11700i
\(94\) 23233.6i 2.62943i
\(95\) −2859.38 −0.316829
\(96\) 35555.9 3.85806
\(97\) −3585.40 −0.381061 −0.190530 0.981681i \(-0.561021\pi\)
−0.190530 + 0.981681i \(0.561021\pi\)
\(98\) 3482.18i 0.362576i
\(99\) −19615.2 −2.00135
\(100\) −21540.6 −2.15406
\(101\) 3138.84 0.307699 0.153850 0.988094i \(-0.450833\pi\)
0.153850 + 0.988094i \(0.450833\pi\)
\(102\) 3509.14 0.337288
\(103\) −7225.57 −0.681079 −0.340539 0.940230i \(-0.610610\pi\)
−0.340539 + 0.940230i \(0.610610\pi\)
\(104\) 57797.2i 5.34368i
\(105\) 7307.03i 0.662769i
\(106\) 19951.3i 1.77566i
\(107\) −11372.2 −0.993291 −0.496645 0.867954i \(-0.665435\pi\)
−0.496645 + 0.867954i \(0.665435\pi\)
\(108\) 28426.8i 2.43714i
\(109\) 6830.22 0.574886 0.287443 0.957798i \(-0.407195\pi\)
0.287443 + 0.957798i \(0.407195\pi\)
\(110\) 10647.6 0.879968
\(111\) 17080.6 1.38630
\(112\) 38175.8i 3.04335i
\(113\) 14950.0i 1.17081i 0.810742 + 0.585403i \(0.199064\pi\)
−0.810742 + 0.585403i \(0.800936\pi\)
\(114\) 33084.0i 2.54571i
\(115\) 1873.89i 0.141693i
\(116\) 10785.1i 0.801511i
\(117\) 41464.7 3.02905
\(118\) 20593.8i 1.47902i
\(119\) 1726.88i 0.121946i
\(120\) 24691.5i 1.71469i
\(121\) 8204.00 0.560344
\(122\) 44063.3 2.96044
\(123\) 3084.93i 0.203909i
\(124\) −26712.3 −1.73727
\(125\) 10921.2i 0.698956i
\(126\) −52054.8 −3.27884
\(127\) −11093.6 −0.687806 −0.343903 0.939005i \(-0.611749\pi\)
−0.343903 + 0.939005i \(0.611749\pi\)
\(128\) 12817.2i 0.782303i
\(129\) 18304.3 + 19635.6i 1.09995 + 1.17996i
\(130\) −22508.1 −1.33184
\(131\) 7521.37i 0.438283i 0.975693 + 0.219141i \(0.0703256\pi\)
−0.975693 + 0.219141i \(0.929674\pi\)
\(132\) 88086.7i 5.05548i
\(133\) −16280.9 −0.920399
\(134\) 8192.38i 0.456247i
\(135\) 6657.89 0.365316
\(136\) 5835.39i 0.315495i
\(137\) 15580.8i 0.830137i −0.909790 0.415069i \(-0.863758\pi\)
0.909790 0.415069i \(-0.136242\pi\)
\(138\) −21681.5 −1.13850
\(139\) 9394.31 0.486223 0.243111 0.969998i \(-0.421832\pi\)
0.243111 + 0.969998i \(0.421832\pi\)
\(140\) 20203.8 1.03080
\(141\) 45017.7i 2.26436i
\(142\) 43767.2 2.17056
\(143\) −48292.2 −2.36159
\(144\) −92548.2 −4.46316
\(145\) −2526.00 −0.120143
\(146\) −4971.57 −0.233232
\(147\) 6747.11i 0.312236i
\(148\) 47227.5i 2.15611i
\(149\) 2012.81i 0.0906630i −0.998972 0.0453315i \(-0.985566\pi\)
0.998972 0.0453315i \(-0.0144344\pi\)
\(150\) 58373.1 2.59436
\(151\) 7447.35i 0.326624i 0.986574 + 0.163312i \(0.0522177\pi\)
−0.986574 + 0.163312i \(0.947782\pi\)
\(152\) −55015.7 −2.38122
\(153\) −4186.41 −0.178838
\(154\) 60626.0 2.55633
\(155\) 6256.33i 0.260409i
\(156\) 186207.i 7.65151i
\(157\) 16371.4i 0.664179i −0.943248 0.332090i \(-0.892246\pi\)
0.943248 0.332090i \(-0.107754\pi\)
\(158\) 47420.5i 1.89956i
\(159\) 38657.8i 1.52912i
\(160\) 23025.6 0.899439
\(161\) 10669.7i 0.411623i
\(162\) 1730.01i 0.0659202i
\(163\) 45112.4i 1.69793i −0.528445 0.848967i \(-0.677225\pi\)
0.528445 0.848967i \(-0.322775\pi\)
\(164\) −8529.77 −0.317139
\(165\) −20630.9 −0.757793
\(166\) 62612.6i 2.27219i
\(167\) −24211.5 −0.868139 −0.434069 0.900879i \(-0.642923\pi\)
−0.434069 + 0.900879i \(0.642923\pi\)
\(168\) 140590.i 4.98123i
\(169\) 73524.2 2.57429
\(170\) 2272.48 0.0786327
\(171\) 39469.2i 1.34979i
\(172\) −54292.1 + 50610.9i −1.83518 + 1.71075i
\(173\) 36697.5 1.22615 0.613076 0.790024i \(-0.289932\pi\)
0.613076 + 0.790024i \(0.289932\pi\)
\(174\) 29226.6i 0.965340i
\(175\) 28725.9i 0.937989i
\(176\) 107787. 3.47969
\(177\) 39902.8i 1.27367i
\(178\) 31898.5 1.00677
\(179\) 50619.1i 1.57982i −0.613220 0.789912i \(-0.710126\pi\)
0.613220 0.789912i \(-0.289874\pi\)
\(180\) 48979.2i 1.51170i
\(181\) −31719.0 −0.968194 −0.484097 0.875014i \(-0.660852\pi\)
−0.484097 + 0.875014i \(0.660852\pi\)
\(182\) −128158. −3.86903
\(183\) −85377.3 −2.54941
\(184\) 36054.4i 1.06494i
\(185\) 11061.2 0.323191
\(186\) 72387.8 2.09237
\(187\) 4875.73 0.139430
\(188\) 124473. 3.52175
\(189\) 37909.1 1.06126
\(190\) 21424.9i 0.593486i
\(191\) 49921.7i 1.36843i 0.729280 + 0.684215i \(0.239855\pi\)
−0.729280 + 0.684215i \(0.760145\pi\)
\(192\) 100760.i 2.73329i
\(193\) 541.363 0.0145336 0.00726681 0.999974i \(-0.497687\pi\)
0.00726681 + 0.999974i \(0.497687\pi\)
\(194\) 26864.8i 0.713805i
\(195\) 43611.8 1.14692
\(196\) 18655.6 0.485621
\(197\) −31142.6 −0.802458 −0.401229 0.915978i \(-0.631417\pi\)
−0.401229 + 0.915978i \(0.631417\pi\)
\(198\) 146973.i 3.74894i
\(199\) 59618.5i 1.50548i −0.658319 0.752739i \(-0.728732\pi\)
0.658319 0.752739i \(-0.271268\pi\)
\(200\) 97069.1i 2.42673i
\(201\) 15873.6i 0.392902i
\(202\) 23518.8i 0.576384i
\(203\) −14382.7 −0.349018
\(204\) 18800.0i 0.451750i
\(205\) 1997.77i 0.0475377i
\(206\) 54139.9i 1.27580i
\(207\) 25866.1 0.603656
\(208\) −227852. −5.26654
\(209\) 45968.1i 1.05236i
\(210\) −54750.3 −1.24150
\(211\) 45278.4i 1.01701i −0.861059 0.508506i \(-0.830198\pi\)
0.861059 0.508506i \(-0.169802\pi\)
\(212\) −106888. −2.37825
\(213\) −84803.8 −1.86920
\(214\) 85209.8i 1.86064i
\(215\) 11853.6 + 12715.8i 0.256434 + 0.275086i
\(216\) 128101. 2.74564
\(217\) 35622.7i 0.756496i
\(218\) 51177.7i 1.07688i
\(219\) 9632.95 0.200850
\(220\) 57044.0i 1.17860i
\(221\) −10306.8 −0.211029
\(222\) 127982.i 2.59683i
\(223\) 26029.7i 0.523431i 0.965145 + 0.261716i \(0.0842883\pi\)
−0.965145 + 0.261716i \(0.915712\pi\)
\(224\) 131105. 2.61290
\(225\) −69639.1 −1.37559
\(226\) 112018. 2.19316
\(227\) 57788.9i 1.12148i 0.827991 + 0.560741i \(0.189484\pi\)
−0.827991 + 0.560741i \(0.810516\pi\)
\(228\) 177246. 3.40962
\(229\) −15622.4 −0.297905 −0.148953 0.988844i \(-0.547590\pi\)
−0.148953 + 0.988844i \(0.547590\pi\)
\(230\) −14040.7 −0.265420
\(231\) −117470. −2.20141
\(232\) −48601.3 −0.902967
\(233\) 60252.0i 1.10984i −0.831904 0.554919i \(-0.812749\pi\)
0.831904 0.554919i \(-0.187251\pi\)
\(234\) 310688.i 5.67404i
\(235\) 29153.0i 0.527894i
\(236\) −110330. −1.98094
\(237\) 91882.4i 1.63582i
\(238\) 12939.2 0.228430
\(239\) 91262.4 1.59770 0.798851 0.601528i \(-0.205441\pi\)
0.798851 + 0.601528i \(0.205441\pi\)
\(240\) −97340.4 −1.68994
\(241\) 11694.8i 0.201354i 0.994919 + 0.100677i \(0.0321008\pi\)
−0.994919 + 0.100677i \(0.967899\pi\)
\(242\) 61471.1i 1.04964i
\(243\) 60712.3i 1.02817i
\(244\) 236066.i 3.96510i
\(245\) 4369.36i 0.0727923i
\(246\) 23114.9 0.381963
\(247\) 97172.4i 1.59275i
\(248\) 120374.i 1.95718i
\(249\) 121319.i 1.95672i
\(250\) 81830.6 1.30929
\(251\) 95330.3 1.51316 0.756578 0.653904i \(-0.226870\pi\)
0.756578 + 0.653904i \(0.226870\pi\)
\(252\) 278881.i 4.39155i
\(253\) −30125.1 −0.470639
\(254\) 83122.6i 1.28840i
\(255\) −4403.18 −0.0677153
\(256\) −15007.1 −0.228991
\(257\) 98138.1i 1.48584i 0.669382 + 0.742919i \(0.266559\pi\)
−0.669382 + 0.742919i \(0.733441\pi\)
\(258\) 147126. 137151.i 2.21030 2.06043i
\(259\) 62981.1 0.938881
\(260\) 120586.i 1.78381i
\(261\) 34867.4i 0.511845i
\(262\) 56356.3 0.820994
\(263\) 7996.23i 0.115604i −0.998328 0.0578022i \(-0.981591\pi\)
0.998328 0.0578022i \(-0.0184093\pi\)
\(264\) −396947. −5.69541
\(265\) 25034.4i 0.356488i
\(266\) 121990.i 1.72410i
\(267\) −61806.8 −0.866990
\(268\) 43890.2 0.611080
\(269\) −42975.4 −0.593903 −0.296951 0.954893i \(-0.595970\pi\)
−0.296951 + 0.954893i \(0.595970\pi\)
\(270\) 49886.4i 0.684313i
\(271\) 22222.2 0.302585 0.151293 0.988489i \(-0.451656\pi\)
0.151293 + 0.988489i \(0.451656\pi\)
\(272\) 23004.6 0.310940
\(273\) 248320. 3.33185
\(274\) −116744. −1.55502
\(275\) 81105.7 1.07247
\(276\) 116158.i 1.52486i
\(277\) 67337.1i 0.877596i −0.898586 0.438798i \(-0.855404\pi\)
0.898586 0.438798i \(-0.144596\pi\)
\(278\) 70389.9i 0.910795i
\(279\) −86358.6 −1.10942
\(280\) 91044.7i 1.16129i
\(281\) −14673.1 −0.185828 −0.0929138 0.995674i \(-0.529618\pi\)
−0.0929138 + 0.995674i \(0.529618\pi\)
\(282\) −337309. −4.24161
\(283\) 25223.6 0.314944 0.157472 0.987523i \(-0.449666\pi\)
0.157472 + 0.987523i \(0.449666\pi\)
\(284\) 234481.i 2.90717i
\(285\) 41513.0i 0.511086i
\(286\) 361845.i 4.42375i
\(287\) 11375.0i 0.138098i
\(288\) 317832.i 3.83189i
\(289\) −82480.4 −0.987541
\(290\) 18926.9i 0.225052i
\(291\) 52053.4i 0.614700i
\(292\) 26634.9i 0.312382i
\(293\) 112480. 1.31020 0.655102 0.755540i \(-0.272626\pi\)
0.655102 + 0.755540i \(0.272626\pi\)
\(294\) −50554.9 −0.584882
\(295\) 25840.6i 0.296933i
\(296\) 212823. 2.42904
\(297\) 107034.i 1.21341i
\(298\) −15081.6 −0.169830
\(299\) 63681.7 0.712315
\(300\) 312731.i 3.47478i
\(301\) 67493.0 + 72402.2i 0.744948 + 0.799132i
\(302\) 55801.7 0.611834
\(303\) 45570.2i 0.496359i
\(304\) 216886.i 2.34685i
\(305\) −55289.5 −0.594351
\(306\) 31368.0i 0.334999i
\(307\) 136783. 1.45130 0.725648 0.688067i \(-0.241540\pi\)
0.725648 + 0.688067i \(0.241540\pi\)
\(308\) 324801.i 3.42386i
\(309\) 104902.i 1.09867i
\(310\) 46877.5 0.487800
\(311\) −46529.6 −0.481070 −0.240535 0.970640i \(-0.577323\pi\)
−0.240535 + 0.970640i \(0.577323\pi\)
\(312\) 839109. 8.62004
\(313\) 68823.9i 0.702507i 0.936280 + 0.351253i \(0.114244\pi\)
−0.936280 + 0.351253i \(0.885756\pi\)
\(314\) −122668. −1.24414
\(315\) 65317.1 0.658272
\(316\) −254053. −2.54419
\(317\) −48726.3 −0.484892 −0.242446 0.970165i \(-0.577950\pi\)
−0.242446 + 0.970165i \(0.577950\pi\)
\(318\) 289656. 2.86436
\(319\) 40608.6i 0.399058i
\(320\) 65251.1i 0.637218i
\(321\) 165103.i 1.60231i
\(322\) −79946.0 −0.771054
\(323\) 9810.83i 0.0940374i
\(324\) 9268.43 0.0882910
\(325\) −171450. −1.62319
\(326\) −338019. −3.18058
\(327\) 99162.3i 0.927366i
\(328\) 38437.9i 0.357283i
\(329\) 165993.i 1.53355i
\(330\) 154584.i 1.41950i
\(331\) 61590.4i 0.562156i −0.959685 0.281078i \(-0.909308\pi\)
0.959685 0.281078i \(-0.0906919\pi\)
\(332\) −335444. −3.04329
\(333\) 152683.i 1.37690i
\(334\) 181413.i 1.62620i
\(335\) 10279.6i 0.0915980i
\(336\) −554243. −4.90932
\(337\) 53084.4 0.467420 0.233710 0.972306i \(-0.424913\pi\)
0.233710 + 0.972306i \(0.424913\pi\)
\(338\) 550904.i 4.82217i
\(339\) −217047. −1.88866
\(340\) 12174.7i 0.105318i
\(341\) 100578. 0.864958
\(342\) −295736. −2.52844
\(343\) 103653.i 0.881038i
\(344\) 228069. + 244658.i 1.92730 + 2.06748i
\(345\) 27205.4 0.228569
\(346\) 274968.i 2.29683i
\(347\) 80407.5i 0.667787i 0.942611 + 0.333893i \(0.108363\pi\)
−0.942611 + 0.333893i \(0.891637\pi\)
\(348\) 156580. 1.29294
\(349\) 173808.i 1.42698i −0.700663 0.713492i \(-0.747112\pi\)
0.700663 0.713492i \(-0.252888\pi\)
\(350\) 215238. 1.75705
\(351\) 226260.i 1.83651i
\(352\) 370165.i 2.98752i
\(353\) −80068.2 −0.642556 −0.321278 0.946985i \(-0.604112\pi\)
−0.321278 + 0.946985i \(0.604112\pi\)
\(354\) 298985. 2.38585
\(355\) −54918.0 −0.435771
\(356\) 170895.i 1.34843i
\(357\) −25071.1 −0.196715
\(358\) −379280. −2.95934
\(359\) 83187.2 0.645457 0.322729 0.946492i \(-0.395400\pi\)
0.322729 + 0.946492i \(0.395400\pi\)
\(360\) 220716. 1.70306
\(361\) 37825.1 0.290245
\(362\) 237665.i 1.81363i
\(363\) 119107.i 0.903907i
\(364\) 686598.i 5.18203i
\(365\) 6238.20 0.0468245
\(366\) 639717.i 4.77558i
\(367\) 248797. 1.84719 0.923597 0.383365i \(-0.125235\pi\)
0.923597 + 0.383365i \(0.125235\pi\)
\(368\) −142136. −1.04956
\(369\) −27576.0 −0.202525
\(370\) 82879.8i 0.605404i
\(371\) 142542.i 1.03561i
\(372\) 387813.i 2.80244i
\(373\) 209386.i 1.50498i 0.658603 + 0.752490i \(0.271148\pi\)
−0.658603 + 0.752490i \(0.728852\pi\)
\(374\) 36533.0i 0.261181i
\(375\) −158556. −1.12751
\(376\) 560915.i 3.96754i
\(377\) 85842.7i 0.603978i
\(378\) 284046.i 1.98795i
\(379\) −92058.9 −0.640895 −0.320448 0.947266i \(-0.603833\pi\)
−0.320448 + 0.947266i \(0.603833\pi\)
\(380\) 114783. 0.794893
\(381\) 161059.i 1.10952i
\(382\) 374055. 2.56335
\(383\) 51836.8i 0.353379i −0.984267 0.176690i \(-0.943461\pi\)
0.984267 0.176690i \(-0.0565388\pi\)
\(384\) −186083. −1.26195
\(385\) −76072.0 −0.513220
\(386\) 4056.34i 0.0272245i
\(387\) −175522. + 163621.i −1.17195 + 1.09249i
\(388\) 143926. 0.956043
\(389\) 170164.i 1.12452i 0.826959 + 0.562262i \(0.190069\pi\)
−0.826959 + 0.562262i \(0.809931\pi\)
\(390\) 326776.i 2.14843i
\(391\) −6429.50 −0.0420556
\(392\) 84068.2i 0.547091i
\(393\) −109196. −0.707007
\(394\) 233346.i 1.50317i
\(395\) 59502.1i 0.381362i
\(396\) 787401. 5.02118
\(397\) −201719. −1.27987 −0.639936 0.768428i \(-0.721039\pi\)
−0.639936 + 0.768428i \(0.721039\pi\)
\(398\) −446711. −2.82007
\(399\) 236369.i 1.48472i
\(400\) 382671. 2.39170
\(401\) 38112.2 0.237015 0.118507 0.992953i \(-0.462189\pi\)
0.118507 + 0.992953i \(0.462189\pi\)
\(402\) −118938. −0.735986
\(403\) −212613. −1.30912
\(404\) −126001. −0.771987
\(405\) 2170.77i 0.0132344i
\(406\) 107767.i 0.653783i
\(407\) 177823.i 1.07349i
\(408\) −84719.1 −0.508933
\(409\) 301746.i 1.80383i −0.431918 0.901913i \(-0.642163\pi\)
0.431918 0.901913i \(-0.357837\pi\)
\(410\) 14968.9 0.0890478
\(411\) 226205. 1.33912
\(412\) 290051. 1.70876
\(413\) 147133.i 0.862601i
\(414\) 193810.i 1.13077i
\(415\) 78564.7i 0.456175i
\(416\) 782495.i 4.52163i
\(417\) 136388.i 0.784340i
\(418\) 344431. 1.97129
\(419\) 15464.5i 0.0880859i 0.999030 + 0.0440430i \(0.0140238\pi\)
−0.999030 + 0.0440430i \(0.985976\pi\)
\(420\) 293322.i 1.66282i
\(421\) 218060.i 1.23030i −0.788409 0.615151i \(-0.789095\pi\)
0.788409 0.615151i \(-0.210905\pi\)
\(422\) −339263. −1.90507
\(423\) 402410. 2.24899
\(424\) 481672.i 2.67929i
\(425\) 17310.1 0.0958345
\(426\) 635420.i 3.50140i
\(427\) −314811. −1.72661
\(428\) 456507. 2.49207
\(429\) 701114.i 3.80955i
\(430\) 95277.5 88817.3i 0.515292 0.480353i
\(431\) −173738. −0.935277 −0.467639 0.883920i \(-0.654895\pi\)
−0.467639 + 0.883920i \(0.654895\pi\)
\(432\) 505005.i 2.70600i
\(433\) 252649.i 1.34754i 0.738942 + 0.673769i \(0.235326\pi\)
−0.738942 + 0.673769i \(0.764674\pi\)
\(434\) 266914. 1.41707
\(435\) 36672.9i 0.193806i
\(436\) −274181. −1.44233
\(437\) 60617.0i 0.317418i
\(438\) 72178.0i 0.376233i
\(439\) −197576. −1.02519 −0.512597 0.858630i \(-0.671316\pi\)
−0.512597 + 0.858630i \(0.671316\pi\)
\(440\) −257059. −1.32778
\(441\) 60312.0 0.310118
\(442\) 77227.3i 0.395300i
\(443\) 116118. 0.591685 0.295842 0.955237i \(-0.404400\pi\)
0.295842 + 0.955237i \(0.404400\pi\)
\(444\) −685657. −3.47809
\(445\) −40025.4 −0.202123
\(446\) 195036. 0.980495
\(447\) 29222.3 0.146251
\(448\) 371531.i 1.85114i
\(449\) 221303.i 1.09773i 0.835911 + 0.548864i \(0.184940\pi\)
−0.835911 + 0.548864i \(0.815060\pi\)
\(450\) 521793.i 2.57676i
\(451\) 32116.6 0.157898
\(452\) 600130.i 2.93744i
\(453\) −108122. −0.526886
\(454\) 433002. 2.10077
\(455\) 160809. 0.776762
\(456\) 798727.i 3.84122i
\(457\) 79170.3i 0.379079i −0.981873 0.189540i \(-0.939300\pi\)
0.981873 0.189540i \(-0.0606996\pi\)
\(458\) 117056.i 0.558038i
\(459\) 22843.9i 0.108429i
\(460\) 75222.5i 0.355494i
\(461\) 272584. 1.28262 0.641311 0.767281i \(-0.278391\pi\)
0.641311 + 0.767281i \(0.278391\pi\)
\(462\) 880178.i 4.12370i
\(463\) 324723.i 1.51478i −0.652960 0.757392i \(-0.726473\pi\)
0.652960 0.757392i \(-0.273527\pi\)
\(464\) 191599.i 0.889932i
\(465\) −90830.3 −0.420073
\(466\) −451458. −2.07896
\(467\) 48808.8i 0.223802i −0.993719 0.111901i \(-0.964306\pi\)
0.993719 0.111901i \(-0.0356940\pi\)
\(468\) −1.66449e6 −7.59959
\(469\) 58530.5i 0.266095i
\(470\) −218438. −0.988855
\(471\) 237682. 1.07141
\(472\) 497184.i 2.23169i
\(473\) 204423. 190562.i 0.913707 0.851754i
\(474\) 688459. 3.06423
\(475\) 163199.i 0.723319i
\(476\) 69321.1i 0.305951i
\(477\) −345559. −1.51875
\(478\) 683813.i 2.99283i
\(479\) 383151. 1.66993 0.834966 0.550301i \(-0.185487\pi\)
0.834966 + 0.550301i \(0.185487\pi\)
\(480\) 334290.i 1.45091i
\(481\) 375901.i 1.62474i
\(482\) 87627.3 0.377177
\(483\) 154904. 0.664001
\(484\) −329328. −1.40585
\(485\) 33709.2i 0.143306i
\(486\) −454906. −1.92597
\(487\) 296539. 1.25033 0.625164 0.780494i \(-0.285032\pi\)
0.625164 + 0.780494i \(0.285032\pi\)
\(488\) −1.06379e6 −4.46701
\(489\) 654949. 2.73899
\(490\) −32738.8 −0.136355
\(491\) 234793.i 0.973916i −0.873425 0.486958i \(-0.838106\pi\)
0.873425 0.486958i \(-0.161894\pi\)
\(492\) 123837.i 0.511586i
\(493\) 8666.95i 0.0356593i
\(494\) −728095. −2.98356
\(495\) 184418.i 0.752651i
\(496\) 474546. 1.92893
\(497\) −312696. −1.26593
\(498\) 909019. 3.66534
\(499\) 223696.i 0.898372i −0.893438 0.449186i \(-0.851714\pi\)
0.893438 0.449186i \(-0.148286\pi\)
\(500\) 438403.i 1.75361i
\(501\) 351507.i 1.40042i
\(502\) 714293.i 2.83445i
\(503\) 171252.i 0.676861i −0.940991 0.338430i \(-0.890104\pi\)
0.940991 0.338430i \(-0.109896\pi\)
\(504\) 1.25673e6 4.94743
\(505\) 29510.8i 0.115717i
\(506\) 225722.i 0.881603i
\(507\) 1.06744e6i 4.15266i
\(508\) 445325. 1.72564
\(509\) −489934. −1.89105 −0.945524 0.325554i \(-0.894449\pi\)
−0.945524 + 0.325554i \(0.894449\pi\)
\(510\) 32992.3i 0.126845i
\(511\) 35519.4 0.136027
\(512\) 317522.i 1.21125i
\(513\) 215371. 0.818374
\(514\) 735331. 2.78328
\(515\) 67933.4i 0.256135i
\(516\) −734777. 788221.i −2.75966 2.96039i
\(517\) −468670. −1.75342
\(518\) 471906.i 1.75872i
\(519\) 532780.i 1.97794i
\(520\) 543398. 2.00961
\(521\) 286304.i 1.05476i 0.849630 + 0.527378i \(0.176825\pi\)
−0.849630 + 0.527378i \(0.823175\pi\)
\(522\) −261255. −0.958791
\(523\) 132186.i 0.483263i 0.970368 + 0.241631i \(0.0776825\pi\)
−0.970368 + 0.241631i \(0.922318\pi\)
\(524\) 301926.i 1.09961i
\(525\) −417047. −1.51310
\(526\) −59914.4 −0.216551
\(527\) 21466.1 0.0772914
\(528\) 1.56487e6i 5.61319i
\(529\) −240116. −0.858044
\(530\) 187578. 0.667775
\(531\) −356689. −1.26503
\(532\) 653556. 2.30919
\(533\) −67891.6 −0.238980
\(534\) 463108.i 1.62405i
\(535\) 106919.i 0.373549i
\(536\) 197784.i 0.688431i
\(537\) 734897. 2.54846
\(538\) 322007.i 1.11250i
\(539\) −70242.8 −0.241782
\(540\) −267264. −0.916542
\(541\) 114352. 0.390704 0.195352 0.980733i \(-0.437415\pi\)
0.195352 + 0.980733i \(0.437415\pi\)
\(542\) 166507.i 0.566805i
\(543\) 460501.i 1.56182i
\(544\) 79003.2i 0.266960i
\(545\) 64216.4i 0.216199i
\(546\) 1.86061e6i 6.24124i
\(547\) 48485.5 0.162046 0.0810228 0.996712i \(-0.474181\pi\)
0.0810228 + 0.996712i \(0.474181\pi\)
\(548\) 625452.i 2.08273i
\(549\) 763183.i 2.53212i
\(550\) 607710.i 2.00896i
\(551\) −81711.5 −0.269141
\(552\) 523444. 1.71788
\(553\) 338797.i 1.10787i
\(554\) −504545. −1.64392
\(555\) 160589.i 0.521349i
\(556\) −377110. −1.21988
\(557\) −96856.1 −0.312188 −0.156094 0.987742i \(-0.549890\pi\)
−0.156094 + 0.987742i \(0.549890\pi\)
\(558\) 647070.i 2.07818i
\(559\) −432131. + 402830.i −1.38290 + 1.28914i
\(560\) −358922. −1.14452
\(561\) 70786.6i 0.224919i
\(562\) 109943.i 0.348093i
\(563\) −26855.0 −0.0847244 −0.0423622 0.999102i \(-0.513488\pi\)
−0.0423622 + 0.999102i \(0.513488\pi\)
\(564\) 1.80712e6i 5.68104i
\(565\) −140557. −0.440308
\(566\) 188996.i 0.589955i
\(567\) 12360.1i 0.0384464i
\(568\) −1.05665e6 −3.27516
\(569\) 228140. 0.704654 0.352327 0.935877i \(-0.385390\pi\)
0.352327 + 0.935877i \(0.385390\pi\)
\(570\) −311049. −0.957370
\(571\) 319649.i 0.980396i 0.871611 + 0.490198i \(0.163076\pi\)
−0.871611 + 0.490198i \(0.836924\pi\)
\(572\) 1.93856e6 5.92500
\(573\) −724771. −2.20745
\(574\) 85231.1 0.258687
\(575\) −106952. −0.323484
\(576\) 900688. 2.71475
\(577\) 527850.i 1.58547i 0.609565 + 0.792736i \(0.291344\pi\)
−0.609565 + 0.792736i \(0.708656\pi\)
\(578\) 618011.i 1.84987i
\(579\) 7859.59i 0.0234446i
\(580\) 101400. 0.301426
\(581\) 447336.i 1.32520i
\(582\) −390027. −1.15146
\(583\) 402458. 1.18409
\(584\) 120025. 0.351923
\(585\) 389843.i 1.13914i
\(586\) 842791.i 2.45428i
\(587\) 571037.i 1.65725i −0.559804 0.828625i \(-0.689124\pi\)
0.559804 0.828625i \(-0.310876\pi\)
\(588\) 270845.i 0.783369i
\(589\) 202381.i 0.583363i
\(590\) 193619. 0.556217
\(591\) 452133.i 1.29447i
\(592\) 839001.i 2.39397i
\(593\) 564829.i 1.60623i 0.595824 + 0.803115i \(0.296825\pi\)
−0.595824 + 0.803115i \(0.703175\pi\)
\(594\) −801985. −2.27297
\(595\) −16235.8 −0.0458606
\(596\) 80799.0i 0.227464i
\(597\) 865550. 2.42853
\(598\) 477156.i 1.33431i
\(599\) 323806. 0.902467 0.451233 0.892406i \(-0.350984\pi\)
0.451233 + 0.892406i \(0.350984\pi\)
\(600\) −1.40927e6 −3.91463
\(601\) 239522.i 0.663126i 0.943433 + 0.331563i \(0.107576\pi\)
−0.943433 + 0.331563i \(0.892424\pi\)
\(602\) 542497. 505713.i 1.49694 1.39544i
\(603\) 141893. 0.390236
\(604\) 298954.i 0.819466i
\(605\) 77132.4i 0.210730i
\(606\) 341449. 0.929782
\(607\) 344432.i 0.934816i −0.884042 0.467408i \(-0.845188\pi\)
0.884042 0.467408i \(-0.154812\pi\)
\(608\) 744838. 2.01490
\(609\) 208810.i 0.563011i
\(610\) 414274.i 1.11334i
\(611\) 990725. 2.65382
\(612\) 168052. 0.448685
\(613\) 446348. 1.18783 0.593913 0.804529i \(-0.297582\pi\)
0.593913 + 0.804529i \(0.297582\pi\)
\(614\) 1.02489e6i 2.71857i
\(615\) −29003.9 −0.0766844
\(616\) −1.46366e6 −3.85725
\(617\) −663045. −1.74170 −0.870848 0.491552i \(-0.836430\pi\)
−0.870848 + 0.491552i \(0.836430\pi\)
\(618\) −786011. −2.05803
\(619\) −298590. −0.779281 −0.389641 0.920967i \(-0.627401\pi\)
−0.389641 + 0.920967i \(0.627401\pi\)
\(620\) 251144.i 0.653340i
\(621\) 141143.i 0.365995i
\(622\) 348638.i 0.901143i
\(623\) −227899. −0.587174
\(624\) 3.30798e6i 8.49560i
\(625\) 232700. 0.595712
\(626\) 515685. 1.31594
\(627\) −667373. −1.69759
\(628\) 657185.i 1.66636i
\(629\) 37952.1i 0.0959257i
\(630\) 489409.i 1.23308i
\(631\) 204687.i 0.514082i 0.966400 + 0.257041i \(0.0827475\pi\)
−0.966400 + 0.257041i \(0.917252\pi\)
\(632\) 1.14484e6i 2.86624i
\(633\) 657358. 1.64057
\(634\) 365098.i 0.908303i
\(635\) 104300.i 0.258665i
\(636\) 1.55182e6i 3.83642i
\(637\) 148487. 0.365939
\(638\) 304273. 0.747518
\(639\) 758056.i 1.85652i
\(640\) −120505. −0.294202
\(641\) 293809.i 0.715070i −0.933900 0.357535i \(-0.883617\pi\)
0.933900 0.357535i \(-0.116383\pi\)
\(642\) −1.23709e6 −3.00145
\(643\) −376164. −0.909820 −0.454910 0.890537i \(-0.650329\pi\)
−0.454910 + 0.890537i \(0.650329\pi\)
\(644\) 428306.i 1.03272i
\(645\) −184610. + 172093.i −0.443748 + 0.413660i
\(646\) 73510.8 0.176151
\(647\) 72724.1i 0.173728i 0.996220 + 0.0868640i \(0.0276846\pi\)
−0.996220 + 0.0868640i \(0.972315\pi\)
\(648\) 41766.6i 0.0994669i
\(649\) 415420. 0.986275
\(650\) 1.28464e6i 3.04058i
\(651\) −517175. −1.22033
\(652\) 1.81092e6i 4.25995i
\(653\) 338825.i 0.794602i −0.917688 0.397301i \(-0.869947\pi\)
0.917688 0.397301i \(-0.130053\pi\)
\(654\) 743005. 1.73715
\(655\) −70714.5 −0.164826
\(656\) 151532. 0.352125
\(657\) 86108.3i 0.199487i
\(658\) −1.24376e6 −2.87265
\(659\) 548017. 1.26189 0.630947 0.775826i \(-0.282666\pi\)
0.630947 + 0.775826i \(0.282666\pi\)
\(660\) 828174. 1.90123
\(661\) 487460. 1.11567 0.557836 0.829951i \(-0.311632\pi\)
0.557836 + 0.829951i \(0.311632\pi\)
\(662\) −461486. −1.05303
\(663\) 149636.i 0.340416i
\(664\) 1.51162e6i 3.42851i
\(665\) 153070.i 0.346136i
\(666\) 1.14402e6 2.57921
\(667\) 53549.5i 0.120366i
\(668\) 971908. 2.17807
\(669\) −377904. −0.844362
\(670\) −77023.1 −0.171582
\(671\) 888846.i 1.97416i
\(672\) 1.90340e6i 4.21494i
\(673\) 738888.i 1.63136i −0.578507 0.815678i \(-0.696364\pi\)
0.578507 0.815678i \(-0.303636\pi\)
\(674\) 397752.i 0.875573i
\(675\) 379998.i 0.834014i
\(676\) −2.95144e6 −6.45863
\(677\) 227328.i 0.495994i −0.968761 0.247997i \(-0.920228\pi\)
0.968761 0.247997i \(-0.0797723\pi\)
\(678\) 1.62629e6i 3.53785i
\(679\) 191936.i 0.416309i
\(680\) −54863.2 −0.118649
\(681\) −838988. −1.80910
\(682\) 753615.i 1.62024i
\(683\) 161434. 0.346061 0.173031 0.984916i \(-0.444644\pi\)
0.173031 + 0.984916i \(0.444644\pi\)
\(684\) 1.58439e6i 3.38649i
\(685\) 146488. 0.312191
\(686\) 776655. 1.65036
\(687\) 226809.i 0.480559i
\(688\) 964504. 899107.i 2.03764 1.89948i
\(689\) −850760. −1.79213
\(690\) 203846.i 0.428157i
\(691\) 327344.i 0.685565i −0.939415 0.342783i \(-0.888631\pi\)
0.939415 0.342783i \(-0.111369\pi\)
\(692\) −1.47312e6 −3.07629
\(693\) 1.05005e6i 2.18648i
\(694\) 602479. 1.25090
\(695\) 88323.4i 0.182855i
\(696\) 705601.i 1.45660i
\(697\) 6854.54 0.0141095
\(698\) −1.30231e6 −2.67303
\(699\) 874749. 1.79031
\(700\) 1.15313e6i 2.35332i
\(701\) 436072. 0.887406 0.443703 0.896174i \(-0.353665\pi\)
0.443703 + 0.896174i \(0.353665\pi\)
\(702\) 1.69532e6 3.44016
\(703\) 357811. 0.724007
\(704\) −1.04899e6 −2.11654
\(705\) 423247. 0.851562
\(706\) 599937.i 1.20364i
\(707\) 168030.i 0.336162i
\(708\) 1.60179e6i 3.19551i
\(709\) −453704. −0.902569 −0.451285 0.892380i \(-0.649034\pi\)
−0.451285 + 0.892380i \(0.649034\pi\)
\(710\) 411491.i 0.816289i
\(711\) −821331. −1.62472
\(712\) −770106. −1.51911
\(713\) −132630. −0.260893
\(714\) 187853.i 0.368488i
\(715\) 454034.i 0.888129i
\(716\) 2.03197e6i 3.96362i
\(717\) 1.32496e6i 2.57730i
\(718\) 623307.i 1.20907i
\(719\) −677749. −1.31103 −0.655513 0.755184i \(-0.727547\pi\)
−0.655513 + 0.755184i \(0.727547\pi\)
\(720\) 870120.i 1.67847i
\(721\) 386803.i 0.744080i
\(722\) 283417.i 0.543689i
\(723\) −169787. −0.324810
\(724\) 1.27328e6 2.42910
\(725\) 144171.i 0.274285i
\(726\) 892447. 1.69320
\(727\) 421634.i 0.797751i −0.917005 0.398875i \(-0.869401\pi\)
0.917005 0.398875i \(-0.130599\pi\)
\(728\) 3.09403e6 5.83798
\(729\) 862728. 1.62338
\(730\) 46741.7i 0.0877120i
\(731\) 43629.2 40671.0i 0.0816475 0.0761115i
\(732\) 3.42725e6 6.39622
\(733\) 545085.i 1.01451i 0.861796 + 0.507255i \(0.169340\pi\)
−0.861796 + 0.507255i \(0.830660\pi\)
\(734\) 1.86419e6i 3.46017i
\(735\) 63435.0 0.117423
\(736\) 488128.i 0.901110i
\(737\) −165257. −0.304246
\(738\) 206622.i 0.379371i
\(739\) 308914.i 0.565651i 0.959171 + 0.282826i \(0.0912718\pi\)
−0.959171 + 0.282826i \(0.908728\pi\)
\(740\) −444024. −0.810855
\(741\) 1.41076e6 2.56932
\(742\) 1.06804e6 1.93991
\(743\) 1.03791e6i 1.88011i 0.341026 + 0.940054i \(0.389225\pi\)
−0.341026 + 0.940054i \(0.610775\pi\)
\(744\) −1.74761e6 −3.15718
\(745\) 18924.0 0.0340958
\(746\) 1.56890e6 2.81914
\(747\) −1.08446e6 −1.94345
\(748\) −195724. −0.349816
\(749\) 608782.i 1.08517i
\(750\) 1.18803e6i 2.11205i
\(751\) 162809.i 0.288669i 0.989529 + 0.144334i \(0.0461041\pi\)
−0.989529 + 0.144334i \(0.953896\pi\)
\(752\) −2.21127e6 −3.91027
\(753\) 1.38402e6i 2.44091i
\(754\) −643204. −1.13137
\(755\) −70018.5 −0.122834
\(756\) −1.52176e6 −2.66258
\(757\) 24344.0i 0.0424816i −0.999774 0.0212408i \(-0.993238\pi\)
0.999774 0.0212408i \(-0.00676166\pi\)
\(758\) 689781.i 1.20053i
\(759\) 437361.i 0.759201i
\(760\) 517247.i 0.895511i
\(761\) 935074.i 1.61464i −0.590111 0.807322i \(-0.700916\pi\)
0.590111 0.807322i \(-0.299084\pi\)
\(762\) −1.20679e6 −2.07836
\(763\) 365639.i 0.628064i
\(764\) 2.00398e6i 3.43325i
\(765\) 39359.8i 0.0672558i
\(766\) −388404. −0.661952
\(767\) −878159. −1.49273
\(768\) 217876.i 0.369391i
\(769\) 314204. 0.531323 0.265662 0.964066i \(-0.414410\pi\)
0.265662 + 0.964066i \(0.414410\pi\)
\(770\) 569994.i 0.961366i
\(771\) −1.42478e6 −2.39685
\(772\) −21731.6 −0.0364634
\(773\) 786232.i 1.31581i −0.753103 0.657903i \(-0.771444\pi\)
0.753103 0.657903i \(-0.228556\pi\)
\(774\) 1.22598e6 + 1.31515e6i 2.04645 + 2.19530i
\(775\) 357079. 0.594512
\(776\) 648579.i 1.07706i
\(777\) 914369.i 1.51454i
\(778\) 1.27501e6 2.10646
\(779\) 64624.3i 0.106493i
\(780\) −1.75068e6 −2.87752
\(781\) 882875.i 1.44743i
\(782\) 48175.1i 0.0787788i
\(783\) 190260. 0.310330
\(784\) −331418. −0.539193
\(785\) 153920. 0.249779
\(786\) 818190.i 1.32437i
\(787\) 229414. 0.370400 0.185200 0.982701i \(-0.440707\pi\)
0.185200 + 0.982701i \(0.440707\pi\)
\(788\) 1.25014e6 2.01329
\(789\) 116091.