Properties

Label 43.5.b.b.42.5
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 42.5
Root \(-2.75662i\) 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.42.8

$q$-expansion

\(f(q)\) \(=\) \(q-2.75662i q^{2} -12.3317i q^{3} +8.40105 q^{4} -21.9831i q^{5} -33.9937 q^{6} +63.3272i q^{7} -67.2644i q^{8} -71.0696 q^{9} +O(q^{10})\) \(q-2.75662i q^{2} -12.3317i q^{3} +8.40105 q^{4} -21.9831i q^{5} -33.9937 q^{6} +63.3272i q^{7} -67.2644i q^{8} -71.0696 q^{9} -60.5989 q^{10} -1.17035 q^{11} -103.599i q^{12} -173.901 q^{13} +174.569 q^{14} -271.087 q^{15} -51.0054 q^{16} +469.315 q^{17} +195.912i q^{18} +27.8220i q^{19} -184.681i q^{20} +780.929 q^{21} +3.22622i q^{22} +79.3541 q^{23} -829.481 q^{24} +141.745 q^{25} +479.379i q^{26} -122.458i q^{27} +532.015i q^{28} +696.895i q^{29} +747.285i q^{30} +1190.63 q^{31} -935.628i q^{32} +14.4324i q^{33} -1293.72i q^{34} +1392.12 q^{35} -597.060 q^{36} -1535.36i q^{37} +76.6946 q^{38} +2144.49i q^{39} -1478.68 q^{40} -2455.37 q^{41} -2152.72i q^{42} +(-1435.68 + 1165.17i) q^{43} -9.83220 q^{44} +1562.33i q^{45} -218.749i q^{46} +1694.64 q^{47} +628.981i q^{48} -1609.33 q^{49} -390.737i q^{50} -5787.42i q^{51} -1460.95 q^{52} -1990.15 q^{53} -337.569 q^{54} +25.7279i q^{55} +4259.66 q^{56} +343.091 q^{57} +1921.07 q^{58} +3563.55 q^{59} -2277.42 q^{60} +5447.36i q^{61} -3282.13i q^{62} -4500.64i q^{63} -3395.26 q^{64} +3822.88i q^{65} +39.7846 q^{66} +4930.23 q^{67} +3942.74 q^{68} -978.567i q^{69} -3837.56i q^{70} +9660.68i q^{71} +4780.46i q^{72} +5609.18i q^{73} -4232.39 q^{74} -1747.95i q^{75} +233.734i q^{76} -74.1151i q^{77} +5911.54 q^{78} -11423.8 q^{79} +1121.26i q^{80} -7266.75 q^{81} +6768.51i q^{82} +5524.25 q^{83} +6560.62 q^{84} -10317.0i q^{85} +(3211.94 + 3957.62i) q^{86} +8593.86 q^{87} +78.7231i q^{88} +2559.89i q^{89} +4306.74 q^{90} -11012.7i q^{91} +666.658 q^{92} -14682.5i q^{93} -4671.49i q^{94} +611.612 q^{95} -11537.8 q^{96} +3659.79 q^{97} +4436.31i q^{98} +83.1766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.75662i 0.689155i −0.938758 0.344577i \(-0.888022\pi\)
0.938758 0.344577i \(-0.111978\pi\)
\(3\) 12.3317i 1.37018i −0.728457 0.685092i \(-0.759762\pi\)
0.728457 0.685092i \(-0.240238\pi\)
\(4\) 8.40105 0.525066
\(5\) 21.9831i 0.879322i −0.898164 0.439661i \(-0.855099\pi\)
0.898164 0.439661i \(-0.144901\pi\)
\(6\) −33.9937 −0.944268
\(7\) 63.3272i 1.29239i 0.763172 + 0.646196i \(0.223641\pi\)
−0.763172 + 0.646196i \(0.776359\pi\)
\(8\) 67.2644i 1.05101i
\(9\) −71.0696 −0.877403
\(10\) −60.5989 −0.605989
\(11\) −1.17035 −0.00967234 −0.00483617 0.999988i \(-0.501539\pi\)
−0.00483617 + 0.999988i \(0.501539\pi\)
\(12\) 103.599i 0.719437i
\(13\) −173.901 −1.02900 −0.514501 0.857490i \(-0.672023\pi\)
−0.514501 + 0.857490i \(0.672023\pi\)
\(14\) 174.569 0.890657
\(15\) −271.087 −1.20483
\(16\) −51.0054 −0.199240
\(17\) 469.315 1.62393 0.811963 0.583709i \(-0.198399\pi\)
0.811963 + 0.583709i \(0.198399\pi\)
\(18\) 195.912i 0.604666i
\(19\) 27.8220i 0.0770692i 0.999257 + 0.0385346i \(0.0122690\pi\)
−0.999257 + 0.0385346i \(0.987731\pi\)
\(20\) 184.681i 0.461702i
\(21\) 780.929 1.77081
\(22\) 3.22622i 0.00666574i
\(23\) 79.3541 0.150008 0.0750039 0.997183i \(-0.476103\pi\)
0.0750039 + 0.997183i \(0.476103\pi\)
\(24\) −829.481 −1.44007
\(25\) 141.745 0.226792
\(26\) 479.379i 0.709141i
\(27\) 122.458i 0.167980i
\(28\) 532.015i 0.678590i
\(29\) 696.895i 0.828650i 0.910129 + 0.414325i \(0.135982\pi\)
−0.910129 + 0.414325i \(0.864018\pi\)
\(30\) 747.285i 0.830316i
\(31\) 1190.63 1.23895 0.619477 0.785015i \(-0.287345\pi\)
0.619477 + 0.785015i \(0.287345\pi\)
\(32\) 935.628i 0.913699i
\(33\) 14.4324i 0.0132529i
\(34\) 1293.72i 1.11914i
\(35\) 1392.12 1.13643
\(36\) −597.060 −0.460694
\(37\) 1535.36i 1.12152i −0.827980 0.560758i \(-0.810510\pi\)
0.827980 0.560758i \(-0.189490\pi\)
\(38\) 76.6946 0.0531126
\(39\) 2144.49i 1.40992i
\(40\) −1478.68 −0.924173
\(41\) −2455.37 −1.46066 −0.730329 0.683095i \(-0.760633\pi\)
−0.730329 + 0.683095i \(0.760633\pi\)
\(42\) 2152.72i 1.22036i
\(43\) −1435.68 + 1165.17i −0.776463 + 0.630163i
\(44\) −9.83220 −0.00507861
\(45\) 1562.33i 0.771520i
\(46\) 218.749i 0.103379i
\(47\) 1694.64 0.767154 0.383577 0.923509i \(-0.374692\pi\)
0.383577 + 0.923509i \(0.374692\pi\)
\(48\) 628.981i 0.272995i
\(49\) −1609.33 −0.670275
\(50\) 390.737i 0.156295i
\(51\) 5787.42i 2.22508i
\(52\) −1460.95 −0.540294
\(53\) −1990.15 −0.708489 −0.354245 0.935153i \(-0.615262\pi\)
−0.354245 + 0.935153i \(0.615262\pi\)
\(54\) −337.569 −0.115764
\(55\) 25.7279i 0.00850510i
\(56\) 4259.66 1.35831
\(57\) 343.091 0.105599
\(58\) 1921.07 0.571068
\(59\) 3563.55 1.02371 0.511857 0.859071i \(-0.328958\pi\)
0.511857 + 0.859071i \(0.328958\pi\)
\(60\) −2277.42 −0.632617
\(61\) 5447.36i 1.46395i 0.681331 + 0.731975i \(0.261401\pi\)
−0.681331 + 0.731975i \(0.738599\pi\)
\(62\) 3282.13i 0.853831i
\(63\) 4500.64i 1.13395i
\(64\) −3395.26 −0.828920
\(65\) 3822.88i 0.904824i
\(66\) 39.7846 0.00913328
\(67\) 4930.23 1.09829 0.549145 0.835727i \(-0.314953\pi\)
0.549145 + 0.835727i \(0.314953\pi\)
\(68\) 3942.74 0.852668
\(69\) 978.567i 0.205538i
\(70\) 3837.56i 0.783175i
\(71\) 9660.68i 1.91642i 0.286065 + 0.958210i \(0.407653\pi\)
−0.286065 + 0.958210i \(0.592347\pi\)
\(72\) 4780.46i 0.922156i
\(73\) 5609.18i 1.05258i 0.850306 + 0.526288i \(0.176417\pi\)
−0.850306 + 0.526288i \(0.823583\pi\)
\(74\) −4232.39 −0.772898
\(75\) 1747.95i 0.310747i
\(76\) 233.734i 0.0404664i
\(77\) 74.1151i 0.0125004i
\(78\) 5911.54 0.971654
\(79\) −11423.8 −1.83044 −0.915218 0.402959i \(-0.867982\pi\)
−0.915218 + 0.402959i \(0.867982\pi\)
\(80\) 1121.26i 0.175196i
\(81\) −7266.75 −1.10757
\(82\) 6768.51i 1.00662i
\(83\) 5524.25 0.801894 0.400947 0.916101i \(-0.368681\pi\)
0.400947 + 0.916101i \(0.368681\pi\)
\(84\) 6560.62 0.929793
\(85\) 10317.0i 1.42795i
\(86\) 3211.94 + 3957.62i 0.434280 + 0.535103i
\(87\) 8593.86 1.13540
\(88\) 78.7231i 0.0101657i
\(89\) 2559.89i 0.323177i 0.986858 + 0.161589i \(0.0516618\pi\)
−0.986858 + 0.161589i \(0.948338\pi\)
\(90\) 4306.74 0.531697
\(91\) 11012.7i 1.32987i
\(92\) 666.658 0.0787640
\(93\) 14682.5i 1.69759i
\(94\) 4671.49i 0.528688i
\(95\) 611.612 0.0677686
\(96\) −11537.8 −1.25194
\(97\) 3659.79 0.388967 0.194484 0.980906i \(-0.437697\pi\)
0.194484 + 0.980906i \(0.437697\pi\)
\(98\) 4436.31i 0.461923i
\(99\) 83.1766 0.00848654
\(100\) 1190.81 0.119081
\(101\) −10505.1 −1.02981 −0.514907 0.857246i \(-0.672173\pi\)
−0.514907 + 0.857246i \(0.672173\pi\)
\(102\) −15953.7 −1.53342
\(103\) 2014.90 0.189924 0.0949619 0.995481i \(-0.469727\pi\)
0.0949619 + 0.995481i \(0.469727\pi\)
\(104\) 11697.4i 1.08149i
\(105\) 17167.2i 1.55712i
\(106\) 5486.08i 0.488259i
\(107\) 8728.48 0.762379 0.381190 0.924497i \(-0.375514\pi\)
0.381190 + 0.924497i \(0.375514\pi\)
\(108\) 1028.77i 0.0882007i
\(109\) −9286.44 −0.781621 −0.390811 0.920471i \(-0.627805\pi\)
−0.390811 + 0.920471i \(0.627805\pi\)
\(110\) 70.9221 0.00586133
\(111\) −18933.5 −1.53668
\(112\) 3230.03i 0.257496i
\(113\) 16690.4i 1.30711i −0.756881 0.653553i \(-0.773278\pi\)
0.756881 0.653553i \(-0.226722\pi\)
\(114\) 945.771i 0.0727740i
\(115\) 1744.45i 0.131905i
\(116\) 5854.65i 0.435096i
\(117\) 12359.1 0.902849
\(118\) 9823.34i 0.705497i
\(119\) 29720.4i 2.09875i
\(120\) 18234.5i 1.26629i
\(121\) −14639.6 −0.999906
\(122\) 15016.3 1.00889
\(123\) 30278.7i 2.00137i
\(124\) 10002.6 0.650532
\(125\) 16855.4i 1.07875i
\(126\) −12406.5 −0.781466
\(127\) −17016.4 −1.05502 −0.527510 0.849549i \(-0.676874\pi\)
−0.527510 + 0.849549i \(0.676874\pi\)
\(128\) 5610.62i 0.342445i
\(129\) 14368.5 + 17704.3i 0.863440 + 1.06390i
\(130\) 10538.2 0.623564
\(131\) 13378.5i 0.779590i −0.920902 0.389795i \(-0.872546\pi\)
0.920902 0.389795i \(-0.127454\pi\)
\(132\) 121.247i 0.00695863i
\(133\) −1761.89 −0.0996035
\(134\) 13590.8i 0.756892i
\(135\) −2691.99 −0.147709
\(136\) 31568.2i 1.70676i
\(137\) 9129.47i 0.486412i 0.969975 + 0.243206i \(0.0781991\pi\)
−0.969975 + 0.243206i \(0.921801\pi\)
\(138\) −2697.54 −0.141648
\(139\) 28220.0 1.46059 0.730293 0.683134i \(-0.239384\pi\)
0.730293 + 0.683134i \(0.239384\pi\)
\(140\) 11695.3 0.596700
\(141\) 20897.8i 1.05114i
\(142\) 26630.8 1.32071
\(143\) 203.526 0.00995285
\(144\) 3624.94 0.174814
\(145\) 15319.9 0.728651
\(146\) 15462.4 0.725388
\(147\) 19845.7i 0.918400i
\(148\) 12898.6i 0.588870i
\(149\) 11221.8i 0.505464i 0.967536 + 0.252732i \(0.0813291\pi\)
−0.967536 + 0.252732i \(0.918671\pi\)
\(150\) −4818.44 −0.214153
\(151\) 37652.1i 1.65133i 0.564158 + 0.825667i \(0.309201\pi\)
−0.564158 + 0.825667i \(0.690799\pi\)
\(152\) 1871.43 0.0810002
\(153\) −33354.0 −1.42484
\(154\) −204.307 −0.00861474
\(155\) 26173.8i 1.08944i
\(156\) 18016.0i 0.740301i
\(157\) 9904.16i 0.401808i −0.979611 0.200904i \(-0.935612\pi\)
0.979611 0.200904i \(-0.0643879\pi\)
\(158\) 31490.9i 1.26145i
\(159\) 24541.8i 0.970761i
\(160\) −20568.0 −0.803436
\(161\) 5025.27i 0.193869i
\(162\) 20031.6i 0.763285i
\(163\) 20673.8i 0.778117i 0.921213 + 0.389059i \(0.127200\pi\)
−0.921213 + 0.389059i \(0.872800\pi\)
\(164\) −20627.7 −0.766942
\(165\) 317.268 0.0116536
\(166\) 15228.2i 0.552629i
\(167\) −313.151 −0.0112285 −0.00561424 0.999984i \(-0.501787\pi\)
−0.00561424 + 0.999984i \(0.501787\pi\)
\(168\) 52528.7i 1.86114i
\(169\) 1680.65 0.0588441
\(170\) −28439.9 −0.984081
\(171\) 1977.30i 0.0676207i
\(172\) −12061.2 + 9788.67i −0.407694 + 0.330877i
\(173\) −5952.11 −0.198874 −0.0994372 0.995044i \(-0.531704\pi\)
−0.0994372 + 0.995044i \(0.531704\pi\)
\(174\) 23690.0i 0.782468i
\(175\) 8976.32i 0.293104i
\(176\) 59.6944 0.00192712
\(177\) 43944.4i 1.40268i
\(178\) 7056.63 0.222719
\(179\) 39430.1i 1.23062i −0.788287 0.615308i \(-0.789032\pi\)
0.788287 0.615308i \(-0.210968\pi\)
\(180\) 13125.2i 0.405099i
\(181\) 29726.1 0.907361 0.453681 0.891164i \(-0.350111\pi\)
0.453681 + 0.891164i \(0.350111\pi\)
\(182\) −30357.7 −0.916488
\(183\) 67174.9 2.00588
\(184\) 5337.71i 0.157659i
\(185\) −33751.8 −0.986174
\(186\) −40474.0 −1.16991
\(187\) −549.264 −0.0157072
\(188\) 14236.8 0.402806
\(189\) 7754.90 0.217096
\(190\) 1685.98i 0.0467031i
\(191\) 35347.9i 0.968940i −0.874808 0.484470i \(-0.839012\pi\)
0.874808 0.484470i \(-0.160988\pi\)
\(192\) 41869.1i 1.13577i
\(193\) −74147.3 −1.99058 −0.995292 0.0969181i \(-0.969102\pi\)
−0.995292 + 0.0969181i \(0.969102\pi\)
\(194\) 10088.6i 0.268058i
\(195\) 47142.4 1.23978
\(196\) −13520.1 −0.351938
\(197\) 33924.2 0.874133 0.437066 0.899429i \(-0.356017\pi\)
0.437066 + 0.899429i \(0.356017\pi\)
\(198\) 229.286i 0.00584854i
\(199\) 20327.0i 0.513296i 0.966505 + 0.256648i \(0.0826182\pi\)
−0.966505 + 0.256648i \(0.917382\pi\)
\(200\) 9534.40i 0.238360i
\(201\) 60797.9i 1.50486i
\(202\) 28958.6i 0.709701i
\(203\) −44132.4 −1.07094
\(204\) 48620.5i 1.16831i
\(205\) 53976.5i 1.28439i
\(206\) 5554.31i 0.130887i
\(207\) −5639.67 −0.131617
\(208\) 8869.91 0.205018
\(209\) 32.5615i 0.000745439i
\(210\) −47323.4 −1.07309
\(211\) 6957.00i 0.156263i 0.996943 + 0.0781316i \(0.0248954\pi\)
−0.996943 + 0.0781316i \(0.975105\pi\)
\(212\) −16719.3 −0.372004
\(213\) 119132. 2.62585
\(214\) 24061.1i 0.525397i
\(215\) 25614.1 + 31560.6i 0.554117 + 0.682761i
\(216\) −8237.04 −0.176548
\(217\) 75399.5i 1.60121i
\(218\) 25599.2i 0.538658i
\(219\) 69170.4 1.44222
\(220\) 216.142i 0.00446574i
\(221\) −81614.4 −1.67102
\(222\) 52192.3i 1.05901i
\(223\) 2228.35i 0.0448099i 0.999749 + 0.0224050i \(0.00713232\pi\)
−0.999749 + 0.0224050i \(0.992868\pi\)
\(224\) 59250.7 1.18086
\(225\) −10073.8 −0.198988
\(226\) −46009.1 −0.900798
\(227\) 61573.4i 1.19493i −0.801896 0.597464i \(-0.796175\pi\)
0.801896 0.597464i \(-0.203825\pi\)
\(228\) 2882.32 0.0554464
\(229\) −40330.0 −0.769054 −0.384527 0.923114i \(-0.625635\pi\)
−0.384527 + 0.923114i \(0.625635\pi\)
\(230\) −4808.77 −0.0909031
\(231\) −913.962 −0.0171279
\(232\) 46876.2 0.870917
\(233\) 74382.7i 1.37013i −0.728484 0.685063i \(-0.759775\pi\)
0.728484 0.685063i \(-0.240225\pi\)
\(234\) 34069.3i 0.622203i
\(235\) 37253.4i 0.674576i
\(236\) 29937.5 0.537517
\(237\) 140874.i 2.50803i
\(238\) 81927.7 1.44636
\(239\) 11874.5 0.207883 0.103942 0.994583i \(-0.466854\pi\)
0.103942 + 0.994583i \(0.466854\pi\)
\(240\) 13826.9 0.240051
\(241\) 23536.3i 0.405233i −0.979258 0.202616i \(-0.935056\pi\)
0.979258 0.202616i \(-0.0649444\pi\)
\(242\) 40355.9i 0.689090i
\(243\) 79691.9i 1.34959i
\(244\) 45763.6i 0.768670i
\(245\) 35378.0i 0.589388i
\(246\) 83466.9 1.37925
\(247\) 4838.28i 0.0793043i
\(248\) 80087.3i 1.30215i
\(249\) 68123.1i 1.09874i
\(250\) −46463.9 −0.743423
\(251\) −54757.4 −0.869151 −0.434575 0.900635i \(-0.643102\pi\)
−0.434575 + 0.900635i \(0.643102\pi\)
\(252\) 37810.1i 0.595397i
\(253\) −92.8723 −0.00145093
\(254\) 46907.8i 0.727072i
\(255\) −127225. −1.95656
\(256\) −69790.4 −1.06492
\(257\) 57759.9i 0.874501i 0.899340 + 0.437250i \(0.144048\pi\)
−0.899340 + 0.437250i \(0.855952\pi\)
\(258\) 48804.0 39608.5i 0.733189 0.595043i
\(259\) 97229.7 1.44944
\(260\) 32116.2i 0.475092i
\(261\) 49528.1i 0.727060i
\(262\) −36879.5 −0.537258
\(263\) 7567.24i 0.109402i −0.998503 0.0547011i \(-0.982579\pi\)
0.998503 0.0547011i \(-0.0174206\pi\)
\(264\) 970.786 0.0139289
\(265\) 43749.5i 0.622991i
\(266\) 4856.85i 0.0686422i
\(267\) 31567.6 0.442812
\(268\) 41419.1 0.576675
\(269\) −39923.2 −0.551723 −0.275861 0.961197i \(-0.588963\pi\)
−0.275861 + 0.961197i \(0.588963\pi\)
\(270\) 7420.80i 0.101794i
\(271\) 119787. 1.63107 0.815533 0.578710i \(-0.196444\pi\)
0.815533 + 0.578710i \(0.196444\pi\)
\(272\) −23937.6 −0.323551
\(273\) −135804. −1.82217
\(274\) 25166.5 0.335213
\(275\) −165.892 −0.00219361
\(276\) 8221.00i 0.107921i
\(277\) 37526.7i 0.489081i −0.969639 0.244540i \(-0.921363\pi\)
0.969639 0.244540i \(-0.0786371\pi\)
\(278\) 77791.7i 1.00657i
\(279\) −84618.0 −1.08706
\(280\) 93640.4i 1.19439i
\(281\) −29935.1 −0.379113 −0.189556 0.981870i \(-0.560705\pi\)
−0.189556 + 0.981870i \(0.560705\pi\)
\(282\) −57607.1 −0.724399
\(283\) −54918.3 −0.685716 −0.342858 0.939387i \(-0.611395\pi\)
−0.342858 + 0.939387i \(0.611395\pi\)
\(284\) 81159.9i 1.00625i
\(285\) 7542.19i 0.0928555i
\(286\) 561.043i 0.00685905i
\(287\) 155491.i 1.88774i
\(288\) 66494.7i 0.801682i
\(289\) 136735. 1.63713
\(290\) 42231.1i 0.502153i
\(291\) 45131.3i 0.532956i
\(292\) 47123.0i 0.552672i
\(293\) −155740. −1.81412 −0.907060 0.421002i \(-0.861678\pi\)
−0.907060 + 0.421002i \(0.861678\pi\)
\(294\) 54707.0 0.632919
\(295\) 78337.6i 0.900174i
\(296\) −103275. −1.17872
\(297\) 143.319i 0.00162476i
\(298\) 30934.2 0.348343
\(299\) −13799.8 −0.154358
\(300\) 14684.6i 0.163163i
\(301\) −73787.1 90917.5i −0.814418 1.00349i
\(302\) 103792. 1.13802
\(303\) 129546.i 1.41103i
\(304\) 1419.07i 0.0153553i
\(305\) 119750. 1.28728
\(306\) 91944.3i 0.981933i
\(307\) 70887.6 0.752131 0.376065 0.926593i \(-0.377277\pi\)
0.376065 + 0.926593i \(0.377277\pi\)
\(308\) 622.645i 0.00656356i
\(309\) 24847.1i 0.260230i
\(310\) −72151.2 −0.750793
\(311\) −27909.5 −0.288557 −0.144278 0.989537i \(-0.546086\pi\)
−0.144278 + 0.989537i \(0.546086\pi\)
\(312\) 144248. 1.48184
\(313\) 50613.7i 0.516630i 0.966061 + 0.258315i \(0.0831672\pi\)
−0.966061 + 0.258315i \(0.916833\pi\)
\(314\) −27302.0 −0.276908
\(315\) −98937.8 −0.997106
\(316\) −95971.5 −0.961099
\(317\) 111161. 1.10620 0.553099 0.833116i \(-0.313445\pi\)
0.553099 + 0.833116i \(0.313445\pi\)
\(318\) 67652.4 0.669004
\(319\) 815.613i 0.00801498i
\(320\) 74638.1i 0.728888i
\(321\) 107637.i 1.04460i
\(322\) 13852.8 0.133606
\(323\) 13057.3i 0.125155i
\(324\) −61048.3 −0.581546
\(325\) −24649.7 −0.233369
\(326\) 56989.8 0.536243
\(327\) 114517.i 1.07096i
\(328\) 165159.i 1.53516i
\(329\) 107317.i 0.991463i
\(330\) 874.587i 0.00803110i
\(331\) 199722.i 1.82293i −0.411376 0.911466i \(-0.634952\pi\)
0.411376 0.911466i \(-0.365048\pi\)
\(332\) 46409.5 0.421047
\(333\) 109117.i 0.984021i
\(334\) 863.238i 0.00773816i
\(335\) 108381.i 0.965752i
\(336\) −39831.6 −0.352817
\(337\) −19032.7 −0.167588 −0.0837938 0.996483i \(-0.526704\pi\)
−0.0837938 + 0.996483i \(0.526704\pi\)
\(338\) 4632.90i 0.0405527i
\(339\) −205821. −1.79097
\(340\) 86673.4i 0.749770i
\(341\) −1393.46 −0.0119836
\(342\) −5450.66 −0.0466011
\(343\) 50134.2i 0.426134i
\(344\) 78374.6 + 96570.1i 0.662306 + 0.816067i
\(345\) −21511.9 −0.180734
\(346\) 16407.7i 0.137055i
\(347\) 13299.5i 0.110453i −0.998474 0.0552263i \(-0.982412\pi\)
0.998474 0.0552263i \(-0.0175880\pi\)
\(348\) 72197.5 0.596161
\(349\) 207713.i 1.70535i 0.522442 + 0.852675i \(0.325021\pi\)
−0.522442 + 0.852675i \(0.674979\pi\)
\(350\) 24744.3 0.201994
\(351\) 21295.5i 0.172852i
\(352\) 1095.01i 0.00883760i
\(353\) 69576.5 0.558358 0.279179 0.960239i \(-0.409938\pi\)
0.279179 + 0.960239i \(0.409938\pi\)
\(354\) −121138. −0.966660
\(355\) 212371. 1.68515
\(356\) 21505.7i 0.169689i
\(357\) 366501. 2.87567
\(358\) −108694. −0.848084
\(359\) −165095. −1.28099 −0.640495 0.767963i \(-0.721271\pi\)
−0.640495 + 0.767963i \(0.721271\pi\)
\(360\) 105089. 0.810872
\(361\) 129547. 0.994060
\(362\) 81943.4i 0.625312i
\(363\) 180531.i 1.37006i
\(364\) 92518.1i 0.698271i
\(365\) 123307. 0.925554
\(366\) 185176.i 1.38236i
\(367\) −58660.7 −0.435527 −0.217764 0.976002i \(-0.569876\pi\)
−0.217764 + 0.976002i \(0.569876\pi\)
\(368\) −4047.49 −0.0298876
\(369\) 174502. 1.28159
\(370\) 93040.8i 0.679626i
\(371\) 126030.i 0.915645i
\(372\) 123348.i 0.891349i
\(373\) 179031.i 1.28680i −0.765530 0.643401i \(-0.777523\pi\)
0.765530 0.643401i \(-0.222477\pi\)
\(374\) 1514.11i 0.0108247i
\(375\) −207855. −1.47808
\(376\) 113989.i 0.806284i
\(377\) 121191.i 0.852682i
\(378\) 21377.3i 0.149613i
\(379\) −47513.9 −0.330783 −0.165391 0.986228i \(-0.552889\pi\)
−0.165391 + 0.986228i \(0.552889\pi\)
\(380\) 5138.19 0.0355830
\(381\) 209840.i 1.44557i
\(382\) −97440.7 −0.667749
\(383\) 59722.7i 0.407138i 0.979061 + 0.203569i \(0.0652541\pi\)
−0.979061 + 0.203569i \(0.934746\pi\)
\(384\) −69188.2 −0.469212
\(385\) −1629.28 −0.0109919
\(386\) 204396.i 1.37182i
\(387\) 102033. 82808.4i 0.681271 0.552907i
\(388\) 30746.1 0.204233
\(389\) 254851.i 1.68417i −0.539343 0.842086i \(-0.681327\pi\)
0.539343 0.842086i \(-0.318673\pi\)
\(390\) 129954.i 0.854397i
\(391\) 37242.0 0.243601
\(392\) 108251.i 0.704463i
\(393\) −164980. −1.06818
\(394\) 93516.1i 0.602413i
\(395\) 251129.i 1.60954i
\(396\) 698.771 0.00445599
\(397\) −79062.9 −0.501639 −0.250820 0.968034i \(-0.580700\pi\)
−0.250820 + 0.968034i \(0.580700\pi\)
\(398\) 56033.9 0.353741
\(399\) 21727.0i 0.136475i
\(400\) −7229.77 −0.0451861
\(401\) −196389. −1.22132 −0.610658 0.791894i \(-0.709095\pi\)
−0.610658 + 0.791894i \(0.709095\pi\)
\(402\) −167597. −1.03708
\(403\) −207053. −1.27489
\(404\) −88254.1 −0.540720
\(405\) 159745.i 0.973908i
\(406\) 121656.i 0.738043i
\(407\) 1796.91i 0.0108477i
\(408\) −389288. −2.33857
\(409\) 115044.i 0.687729i −0.939019 0.343864i \(-0.888264\pi\)
0.939019 0.343864i \(-0.111736\pi\)
\(410\) 148793. 0.885143
\(411\) 112581. 0.666474
\(412\) 16927.3 0.0997225
\(413\) 225669.i 1.32304i
\(414\) 15546.4i 0.0907047i
\(415\) 121440.i 0.705123i
\(416\) 162707.i 0.940198i
\(417\) 347999.i 2.00127i
\(418\) −89.7597 −0.000513723
\(419\) 281568.i 1.60382i 0.597446 + 0.801909i \(0.296182\pi\)
−0.597446 + 0.801909i \(0.703818\pi\)
\(420\) 144223.i 0.817588i
\(421\) 182603.i 1.03025i 0.857115 + 0.515125i \(0.172255\pi\)
−0.857115 + 0.515125i \(0.827745\pi\)
\(422\) 19177.8 0.107690
\(423\) −120438. −0.673103
\(424\) 133866.i 0.744627i
\(425\) 66523.0 0.368294
\(426\) 328402.i 1.80962i
\(427\) −344966. −1.89200
\(428\) 73328.4 0.400299
\(429\) 2509.81i 0.0136372i
\(430\) 87000.6 70608.2i 0.470528 0.381872i
\(431\) 295412. 1.59028 0.795139 0.606427i \(-0.207398\pi\)
0.795139 + 0.606427i \(0.207398\pi\)
\(432\) 6246.01i 0.0334684i
\(433\) 315628.i 1.68345i −0.539908 0.841724i \(-0.681541\pi\)
0.539908 0.841724i \(-0.318459\pi\)
\(434\) 207848. 1.10348
\(435\) 188919.i 0.998385i
\(436\) −78015.9 −0.410403
\(437\) 2207.79i 0.0115610i
\(438\) 190677.i 0.993915i
\(439\) 289252. 1.50088 0.750442 0.660937i \(-0.229841\pi\)
0.750442 + 0.660937i \(0.229841\pi\)
\(440\) 1730.57 0.00893892
\(441\) 114375. 0.588101
\(442\) 224980.i 1.15159i
\(443\) −13612.9 −0.0693655 −0.0346827 0.999398i \(-0.511042\pi\)
−0.0346827 + 0.999398i \(0.511042\pi\)
\(444\) −159061. −0.806859
\(445\) 56274.1 0.284177
\(446\) 6142.72 0.0308810
\(447\) 138383. 0.692578
\(448\) 215012.i 1.07129i
\(449\) 164810.i 0.817506i 0.912645 + 0.408753i \(0.134036\pi\)
−0.912645 + 0.408753i \(0.865964\pi\)
\(450\) 27769.6i 0.137134i
\(451\) 2873.65 0.0141280
\(452\) 140217.i 0.686316i
\(453\) 464312. 2.26263
\(454\) −169734. −0.823490
\(455\) −242092. −1.16939
\(456\) 23077.8i 0.110985i
\(457\) 157048.i 0.751971i 0.926626 + 0.375985i \(0.122696\pi\)
−0.926626 + 0.375985i \(0.877304\pi\)
\(458\) 111174.i 0.529997i
\(459\) 57471.2i 0.272788i
\(460\) 14655.2i 0.0692589i
\(461\) 332439. 1.56426 0.782131 0.623114i \(-0.214133\pi\)
0.782131 + 0.623114i \(0.214133\pi\)
\(462\) 2519.44i 0.0118038i
\(463\) 197697.i 0.922226i 0.887341 + 0.461113i \(0.152550\pi\)
−0.887341 + 0.461113i \(0.847450\pi\)
\(464\) 35545.4i 0.165100i
\(465\) −322766. −1.49273
\(466\) −205045. −0.944228
\(467\) 121639.i 0.557749i −0.960328 0.278874i \(-0.910039\pi\)
0.960328 0.278874i \(-0.0899613\pi\)
\(468\) 103829. 0.474055
\(469\) 312217.i 1.41942i
\(470\) −102694. −0.464887
\(471\) −122135. −0.550550
\(472\) 239700.i 1.07593i
\(473\) 1680.25 1363.66i 0.00751021 0.00609515i
\(474\) 388335. 1.72842
\(475\) 3943.63i 0.0174787i
\(476\) 249682.i 1.10198i
\(477\) 141439. 0.621631
\(478\) 32733.5i 0.143264i
\(479\) −141700. −0.617586 −0.308793 0.951129i \(-0.599925\pi\)
−0.308793 + 0.951129i \(0.599925\pi\)
\(480\) 253637.i 1.10085i
\(481\) 267000.i 1.15404i
\(482\) −64880.6 −0.279268
\(483\) 61969.9 0.265636
\(484\) −122988. −0.525017
\(485\) 80453.4i 0.342027i
\(486\) 219680. 0.930076
\(487\) 194637. 0.820668 0.410334 0.911935i \(-0.365412\pi\)
0.410334 + 0.911935i \(0.365412\pi\)
\(488\) 366413. 1.53862
\(489\) 254942. 1.06616
\(490\) 97523.6 0.406179
\(491\) 143694.i 0.596040i −0.954560 0.298020i \(-0.903674\pi\)
0.954560 0.298020i \(-0.0963263\pi\)
\(492\) 254373.i 1.05085i
\(493\) 327063.i 1.34567i
\(494\) −13337.3 −0.0546529
\(495\) 1828.48i 0.00746240i
\(496\) −60728.9 −0.246849
\(497\) −611783. −2.47676
\(498\) −187789. −0.757203
\(499\) 328853.i 1.32069i −0.750962 0.660345i \(-0.770410\pi\)
0.750962 0.660345i \(-0.229590\pi\)
\(500\) 141603.i 0.566413i
\(501\) 3861.67i 0.0153851i
\(502\) 150945.i 0.598979i
\(503\) 278129.i 1.09929i −0.835399 0.549643i \(-0.814764\pi\)
0.835399 0.549643i \(-0.185236\pi\)
\(504\) −302733. −1.19179
\(505\) 230935.i 0.905538i
\(506\) 256.014i 0.000999912i
\(507\) 20725.2i 0.0806273i
\(508\) −142956. −0.553955
\(509\) 53485.5 0.206443 0.103222 0.994658i \(-0.467085\pi\)
0.103222 + 0.994658i \(0.467085\pi\)
\(510\) 350712.i 1.34837i
\(511\) −355213. −1.36034
\(512\) 102616.i 0.391448i
\(513\) 3407.01 0.0129461
\(514\) 159222. 0.602666
\(515\) 44293.7i 0.167004i
\(516\) 120711. + 148735.i 0.453363 + 0.558616i
\(517\) −1983.33 −0.00742017
\(518\) 268025.i 0.998886i
\(519\) 73399.4i 0.272494i
\(520\) 257144. 0.950976
\(521\) 43791.8i 0.161331i 0.996741 + 0.0806655i \(0.0257045\pi\)
−0.996741 + 0.0806655i \(0.974295\pi\)
\(522\) −136530. −0.501057
\(523\) 104920.i 0.383578i −0.981436 0.191789i \(-0.938571\pi\)
0.981436 0.191789i \(-0.0614290\pi\)
\(524\) 112394.i 0.409336i
\(525\) 110693. 0.401607
\(526\) −20860.0 −0.0753950
\(527\) 558782. 2.01197
\(528\) 736.130i 0.00264050i
\(529\) −273544. −0.977498
\(530\) 120601. 0.429337
\(531\) −253260. −0.898209
\(532\) −14801.7 −0.0522984
\(533\) 426991. 1.50302
\(534\) 87019.9i 0.305166i
\(535\) 191879.i 0.670377i
\(536\) 331629.i 1.15431i
\(537\) −486239. −1.68617
\(538\) 110053.i 0.380222i
\(539\) 1883.48 0.00648312
\(540\) −22615.6 −0.0775569
\(541\) −60893.0 −0.208052 −0.104026 0.994575i \(-0.533173\pi\)
−0.104026 + 0.994575i \(0.533173\pi\)
\(542\) 330208.i 1.12406i
\(543\) 366571.i 1.24325i
\(544\) 439104.i 1.48378i
\(545\) 204144.i 0.687297i
\(546\) 374361.i 1.25576i
\(547\) 77111.4 0.257717 0.128859 0.991663i \(-0.458869\pi\)
0.128859 + 0.991663i \(0.458869\pi\)
\(548\) 76697.1i 0.255398i
\(549\) 387142.i 1.28447i
\(550\) 457.300i 0.00151174i
\(551\) −19389.0 −0.0638634
\(552\) −65822.7 −0.216022
\(553\) 723434.i 2.36564i
\(554\) −103447. −0.337052
\(555\) 416215.i 1.35124i
\(556\) 237078. 0.766904
\(557\) −496754. −1.60115 −0.800573 0.599235i \(-0.795471\pi\)
−0.800573 + 0.599235i \(0.795471\pi\)
\(558\) 233260.i 0.749154i
\(559\) 249666. 202625.i 0.798981 0.648439i
\(560\) −71006.0 −0.226422
\(561\) 6773.33i 0.0215217i
\(562\) 82519.7i 0.261267i
\(563\) −510115. −1.60935 −0.804676 0.593714i \(-0.797661\pi\)
−0.804676 + 0.593714i \(0.797661\pi\)
\(564\) 175563.i 0.551919i
\(565\) −366907. −1.14937
\(566\) 151389.i 0.472564i
\(567\) 460182.i 1.43141i
\(568\) 649820. 2.01417
\(569\) −18540.2 −0.0572650 −0.0286325 0.999590i \(-0.509115\pi\)
−0.0286325 + 0.999590i \(0.509115\pi\)
\(570\) −20790.9 −0.0639918
\(571\) 145098.i 0.445029i 0.974929 + 0.222515i \(0.0714266\pi\)
−0.974929 + 0.222515i \(0.928573\pi\)
\(572\) 1709.83 0.00522590
\(573\) −435898. −1.32763
\(574\) −428631. −1.30095
\(575\) 11248.1 0.0340206
\(576\) 241300. 0.727297
\(577\) 492406.i 1.47901i 0.673150 + 0.739506i \(0.264941\pi\)
−0.673150 + 0.739506i \(0.735059\pi\)
\(578\) 376927.i 1.12824i
\(579\) 914359.i 2.72747i
\(580\) 128703. 0.382590
\(581\) 349835.i 1.03636i
\(582\) −124410. −0.367289
\(583\) 2329.17 0.00685275
\(584\) 377298. 1.10626
\(585\) 271691.i 0.793895i
\(586\) 429317.i 1.25021i
\(587\) 113204.i 0.328539i 0.986416 + 0.164269i \(0.0525266\pi\)
−0.986416 + 0.164269i \(0.947473\pi\)
\(588\) 166725.i 0.482220i
\(589\) 33125.8i 0.0954852i
\(590\) −215947. −0.620359
\(591\) 418342.i 1.19772i
\(592\) 78311.5i 0.223451i
\(593\) 378754.i 1.07708i −0.842600 0.538540i \(-0.818976\pi\)
0.842600 0.538540i \(-0.181024\pi\)
\(594\) 395.075 0.00111971
\(595\) 653344. 1.84548
\(596\) 94275.0i 0.265402i
\(597\) 250666. 0.703310
\(598\) 38040.7i 0.106377i
\(599\) −70600.5 −0.196768 −0.0983840 0.995149i \(-0.531367\pi\)
−0.0983840 + 0.995149i \(0.531367\pi\)
\(600\) −117575. −0.326597
\(601\) 576111.i 1.59499i −0.603327 0.797494i \(-0.706159\pi\)
0.603327 0.797494i \(-0.293841\pi\)
\(602\) −250625. + 203403.i −0.691562 + 0.561260i
\(603\) −350390. −0.963644
\(604\) 316317.i 0.867059i
\(605\) 321824.i 0.879240i
\(606\) 357108. 0.972420
\(607\) 179183.i 0.486317i −0.969987 0.243159i \(-0.921816\pi\)
0.969987 0.243159i \(-0.0781835\pi\)
\(608\) 26031.0 0.0704180
\(609\) 544225.i 1.46738i
\(610\) 330104.i 0.887138i
\(611\) −294701. −0.789403
\(612\) −280209. −0.748133
\(613\) 527970. 1.40504 0.702519 0.711665i \(-0.252059\pi\)
0.702519 + 0.711665i \(0.252059\pi\)
\(614\) 195410.i 0.518334i
\(615\) 665619. 1.75985
\(616\) −4985.31 −0.0131380
\(617\) 21720.1 0.0570547 0.0285274 0.999593i \(-0.490918\pi\)
0.0285274 + 0.999593i \(0.490918\pi\)
\(618\) −68493.9 −0.179339
\(619\) −64840.3 −0.169225 −0.0846124 0.996414i \(-0.526965\pi\)
−0.0846124 + 0.996414i \(0.526965\pi\)
\(620\) 219887.i 0.572028i
\(621\) 9717.52i 0.0251984i
\(622\) 76935.9i 0.198860i
\(623\) −162110. −0.417671
\(624\) 109381.i 0.280913i
\(625\) −281943. −0.721773
\(626\) 139523. 0.356038
\(627\) −401.537 −0.00102139
\(628\) 83205.4i 0.210976i
\(629\) 720564.i 1.82126i
\(630\) 272734.i 0.687160i
\(631\) 639737.i 1.60673i 0.595488 + 0.803364i \(0.296959\pi\)
−0.595488 + 0.803364i \(0.703041\pi\)
\(632\) 768412.i 1.92380i
\(633\) 85791.3 0.214109
\(634\) 306428.i 0.762341i
\(635\) 374073.i 0.927702i
\(636\) 206177.i 0.509713i
\(637\) 279865. 0.689714
\(638\) −2248.33 −0.00552356
\(639\) 686581.i 1.68147i
\(640\) −123339. −0.301120
\(641\) 92614.4i 0.225404i 0.993629 + 0.112702i \(0.0359506\pi\)
−0.993629 + 0.112702i \(0.964049\pi\)
\(642\) −296713. −0.719891
\(643\) 517514. 1.25170 0.625850 0.779943i \(-0.284752\pi\)
0.625850 + 0.779943i \(0.284752\pi\)
\(644\) 42217.6i 0.101794i
\(645\) 389195. 315864.i 0.935508 0.759242i
\(646\) 35993.9 0.0862509
\(647\) 320760.i 0.766253i −0.923696 0.383126i \(-0.874847\pi\)
0.923696 0.383126i \(-0.125153\pi\)
\(648\) 488793.i 1.16406i
\(649\) −4170.61 −0.00990170
\(650\) 67949.7i 0.160828i
\(651\) 929801. 2.19396
\(652\) 173682.i 0.408563i
\(653\) 271078.i 0.635724i 0.948137 + 0.317862i \(0.102965\pi\)
−0.948137 + 0.317862i \(0.897035\pi\)
\(654\) 315680. 0.738060
\(655\) −294101. −0.685511
\(656\) 125237. 0.291022
\(657\) 398642.i 0.923534i
\(658\) 295832. 0.683271
\(659\) −297067. −0.684044 −0.342022 0.939692i \(-0.611112\pi\)
−0.342022 + 0.939692i \(0.611112\pi\)
\(660\) 2665.38 0.00611888
\(661\) 91628.4 0.209714 0.104857 0.994487i \(-0.466562\pi\)
0.104857 + 0.994487i \(0.466562\pi\)
\(662\) −550558. −1.25628
\(663\) 1.00644e6i 2.28961i
\(664\) 371585.i 0.842796i
\(665\) 38731.7i 0.0875836i
\(666\) 300794. 0.678143
\(667\) 55301.5i 0.124304i
\(668\) −2630.80 −0.00589569
\(669\) 27479.3 0.0613978
\(670\) −298766. −0.665552
\(671\) 6375.33i 0.0141598i
\(672\) 730659.i 1.61799i
\(673\) 601565.i 1.32817i −0.747658 0.664084i \(-0.768822\pi\)
0.747658 0.664084i \(-0.231178\pi\)
\(674\) 52466.0i 0.115494i
\(675\) 17357.8i 0.0380966i
\(676\) 14119.2 0.0308970
\(677\) 211198.i 0.460800i 0.973096 + 0.230400i \(0.0740034\pi\)
−0.973096 + 0.230400i \(0.925997\pi\)
\(678\) 567369.i 1.23426i
\(679\) 231764.i 0.502698i
\(680\) −693965. −1.50079
\(681\) −759302. −1.63727
\(682\) 3841.25i 0.00825854i
\(683\) −260659. −0.558768 −0.279384 0.960179i \(-0.590130\pi\)
−0.279384 + 0.960179i \(0.590130\pi\)
\(684\) 16611.4i 0.0355053i
\(685\) 200694. 0.427713
\(686\) 138201. 0.293672
\(687\) 497335.i 1.05375i
\(688\) 73227.5 59430.1i 0.154702 0.125554i
\(689\) 346089. 0.729037
\(690\) 59300.1i 0.124554i
\(691\) 670752.i 1.40477i 0.711797 + 0.702386i \(0.247882\pi\)
−0.711797 + 0.702386i \(0.752118\pi\)
\(692\) −50004.0 −0.104422
\(693\) 5267.34i 0.0109679i
\(694\) −36661.6 −0.0761190
\(695\) 620361.i 1.28433i
\(696\) 578061.i 1.19332i
\(697\) −1.15234e6 −2.37200
\(698\) 572586. 1.17525
\(699\) −917262. −1.87732
\(700\) 75410.5i 0.153899i
\(701\) 104357. 0.212366 0.106183 0.994347i \(-0.466137\pi\)
0.106183 + 0.994347i \(0.466137\pi\)
\(702\) 58703.7 0.119122
\(703\) 42716.6 0.0864343
\(704\) 3973.65 0.00801759
\(705\) −459396. −0.924293
\(706\) 191796.i 0.384795i
\(707\) 665260.i 1.33092i
\(708\) 369179.i 0.736497i
\(709\) 135186. 0.268930 0.134465 0.990918i \(-0.457068\pi\)
0.134465 + 0.990918i \(0.457068\pi\)
\(710\) 585426.i 1.16133i
\(711\) 811882. 1.60603
\(712\) 172189. 0.339661
\(713\) 94481.8 0.185853
\(714\) 1.01030e6i 1.98178i
\(715\) 4474.12i 0.00875176i
\(716\) 331255.i 0.646154i
\(717\) 146432.i 0.284838i
\(718\) 455105.i 0.882800i
\(719\) 99461.8 0.192397 0.0961985 0.995362i \(-0.469332\pi\)
0.0961985 + 0.995362i \(0.469332\pi\)
\(720\) 79687.3i 0.153718i
\(721\) 127598.i 0.245456i
\(722\) 357112.i 0.685061i
\(723\) −290242. −0.555243
\(724\) 249730. 0.476424
\(725\) 98781.4i 0.187931i
\(726\) 497655. 0.944180
\(727\) 440731.i 0.833882i 0.908933 + 0.416941i \(0.136898\pi\)
−0.908933 + 0.416941i \(0.863102\pi\)
\(728\) −740761. −1.39770
\(729\) 394127. 0.741619
\(730\) 339910.i 0.637850i
\(731\) −673785. + 546832.i −1.26092 + 1.02334i
\(732\) 564340. 1.05322
\(733\) 353122.i 0.657229i −0.944464 0.328615i \(-0.893418\pi\)
0.944464 0.328615i \(-0.106582\pi\)
\(734\) 161705.i 0.300146i
\(735\) 436269. 0.807569
\(736\) 74245.9i 0.137062i
\(737\) −5770.11 −0.0106230
\(738\) 481036.i 0.883211i
\(739\) 511160.i 0.935983i 0.883733 + 0.467992i \(0.155022\pi\)
−0.883733 + 0.467992i \(0.844978\pi\)
\(740\) −283551. −0.517806
\(741\) −59663.9 −0.108661
\(742\) −347418. −0.631021
\(743\) 162933.i 0.295141i −0.989052 0.147571i \(-0.952855\pi\)
0.989052 0.147571i \(-0.0471454\pi\)
\(744\) −987609. −1.78418
\(745\) 246690. 0.444466
\(746\) −493521. −0.886805
\(747\) −392606. −0.703584
\(748\) −4614.39 −0.00824729
\(749\) 552750.i 0.985292i
\(750\) 572977.i 1.01863i
\(751\) 476066.i 0.844087i 0.906576 + 0.422044i \(0.138687\pi\)
−0.906576 + 0.422044i \(0.861313\pi\)
\(752\) −86436.0 −0.152848
\(753\) 675249.i 1.19090i
\(754\) −334077. −0.587630
\(755\) 827708. 1.45205
\(756\) 65149.3 0.113990
\(757\) 513071.i 0.895335i 0.894200 + 0.447667i \(0.147745\pi\)
−0.894200 + 0.447667i \(0.852255\pi\)
\(758\) 130978.i 0.227960i
\(759\) 1145.27i 0.00198803i
\(760\) 41139.7i 0.0712253i
\(761\) 132174.i 0.228233i 0.993467 + 0.114116i \(0.0364036\pi\)
−0.993467 + 0.114116i \(0.963596\pi\)
\(762\) 578450. 0.996222
\(763\) 588084.i 1.01016i
\(764\) 296960.i 0.508757i
\(765\) 733223.i 1.25289i
\(766\) 164633. 0.280581
\(767\) −619705. −1.05340
\(768\) 860631.i 1.45913i
\(769\) −549403. −0.929048 −0.464524 0.885561i \(-0.653775\pi\)
−0.464524 + 0.885561i \(0.653775\pi\)
\(770\) 4491.30i 0.00757513i
\(771\) 712275. 1.19823
\(772\) −622915. −1.04519
\(773\) 357526.i 0.598340i −0.954200 0.299170i \(-0.903290\pi\)
0.954200 0.299170i \(-0.0967098\pi\)
\(774\) −228271. 281267.i −0.381039 0.469501i
\(775\) 168767. 0.280985
\(776\) 246174.i 0.408807i
\(777\) 1.19900e6i 1.98599i
\(778\) −702526. −1.16066
\(779\) 68313.2i 0.112572i
\(780\) 396046. 0.650964
\(781\) 11306.4i 0.0185363i
\(782\) 102662.i 0.167879i
\(783\) 85340.1 0.139197
\(784\) 82084.6 0.133546
\(785\) −217724. −0.353319
\(786\) 454786.i 0.736142i
\(787\) 11905.5 0.0192221 0.00961103 0.999954i \(-0.496941\pi\)
0.00961103 + 0.999954i \(0.496941\pi\)
\(788\) 284999. 0.458977