Properties

Label 43.7.b.b.42.5
Level 43
Weight 7
Character 43.42
Analytic conductor 9.892
Analytic rank 0
Dimension 20
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.5
Root \(-11.0119i\) of \(x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + 80362197690736 x^{8} + 2545997652841536 x^{6} + 40210452531479040 x^{4} + 212033222410436608 x^{2} + 64236717122519040\)
Character \(\chi\) \(=\) 43.42
Dual form 43.7.b.b.42.16

$q$-expansion

\(f(q)\) \(=\) \(q-11.0119i q^{2} -50.0401i q^{3} -57.2623 q^{4} +30.3065i q^{5} -551.037 q^{6} -75.1486i q^{7} -74.1946i q^{8} -1775.01 q^{9} +O(q^{10})\) \(q-11.0119i q^{2} -50.0401i q^{3} -57.2623 q^{4} +30.3065i q^{5} -551.037 q^{6} -75.1486i q^{7} -74.1946i q^{8} -1775.01 q^{9} +333.733 q^{10} +604.862 q^{11} +2865.41i q^{12} +2635.68 q^{13} -827.530 q^{14} +1516.54 q^{15} -4481.81 q^{16} +4989.55 q^{17} +19546.3i q^{18} -3038.63i q^{19} -1735.42i q^{20} -3760.44 q^{21} -6660.70i q^{22} -12445.5 q^{23} -3712.70 q^{24} +14706.5 q^{25} -29023.9i q^{26} +52342.4i q^{27} +4303.18i q^{28} +4449.10i q^{29} -16700.0i q^{30} -29312.5 q^{31} +44604.9i q^{32} -30267.4i q^{33} -54944.5i q^{34} +2277.49 q^{35} +101641. q^{36} -83027.3i q^{37} -33461.2 q^{38} -131890. i q^{39} +2248.58 q^{40} -33442.2 q^{41} +41409.7i q^{42} +(30046.7 + 73610.9i) q^{43} -34635.8 q^{44} -53794.4i q^{45} +137048. i q^{46} -157085. q^{47} +224270. i q^{48} +112002. q^{49} -161947. i q^{50} -249678. i q^{51} -150925. q^{52} +212620. q^{53} +576391. q^{54} +18331.3i q^{55} -5575.61 q^{56} -152053. q^{57} +48993.1 q^{58} -263304. q^{59} -86840.7 q^{60} +133532. i q^{61} +322787. i q^{62} +133389. i q^{63} +204350. q^{64} +79878.2i q^{65} -333302. q^{66} -157955. q^{67} -285713. q^{68} +622771. i q^{69} -25079.5i q^{70} -485322. i q^{71} +131696. i q^{72} +48573.5i q^{73} -914290. q^{74} -735915. i q^{75} +173999. i q^{76} -45454.5i q^{77} -1.45236e6 q^{78} +762200. q^{79} -135828. i q^{80} +1.32524e6 q^{81} +368262. i q^{82} +268573. q^{83} +215332. q^{84} +151216. i q^{85} +(810597. - 330872. i) q^{86} +222633. q^{87} -44877.5i q^{88} -1.32878e6i q^{89} -592379. q^{90} -198067. i q^{91} +712656. q^{92} +1.46680e6i q^{93} +1.72980e6i q^{94} +92090.4 q^{95} +2.23203e6 q^{96} +1.43066e6 q^{97} -1.23335e6i q^{98} -1.07364e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.0119i 1.37649i −0.725478 0.688245i \(-0.758381\pi\)
0.725478 0.688245i \(-0.241619\pi\)
\(3\) 50.0401i 1.85334i −0.375880 0.926668i \(-0.622660\pi\)
0.375880 0.926668i \(-0.377340\pi\)
\(4\) −57.2623 −0.894724
\(5\) 30.3065i 0.242452i 0.992625 + 0.121226i \(0.0386826\pi\)
−0.992625 + 0.121226i \(0.961317\pi\)
\(6\) −551.037 −2.55110
\(7\) 75.1486i 0.219092i −0.993982 0.109546i \(-0.965060\pi\)
0.993982 0.109546i \(-0.0349397\pi\)
\(8\) 74.1946i 0.144911i
\(9\) −1775.01 −2.43486
\(10\) 333.733 0.333733
\(11\) 604.862 0.454442 0.227221 0.973843i \(-0.427036\pi\)
0.227221 + 0.973843i \(0.427036\pi\)
\(12\) 2865.41i 1.65822i
\(13\) 2635.68 1.19967 0.599836 0.800123i \(-0.295233\pi\)
0.599836 + 0.800123i \(0.295233\pi\)
\(14\) −827.530 −0.301578
\(15\) 1516.54 0.449345
\(16\) −4481.81 −1.09419
\(17\) 4989.55 1.01558 0.507791 0.861481i \(-0.330462\pi\)
0.507791 + 0.861481i \(0.330462\pi\)
\(18\) 19546.3i 3.35155i
\(19\) 3038.63i 0.443014i −0.975159 0.221507i \(-0.928902\pi\)
0.975159 0.221507i \(-0.0710975\pi\)
\(20\) 1735.42i 0.216928i
\(21\) −3760.44 −0.406051
\(22\) 6660.70i 0.625535i
\(23\) −12445.5 −1.02289 −0.511443 0.859317i \(-0.670889\pi\)
−0.511443 + 0.859317i \(0.670889\pi\)
\(24\) −3712.70 −0.268569
\(25\) 14706.5 0.941217
\(26\) 29023.9i 1.65134i
\(27\) 52342.4i 2.65927i
\(28\) 4303.18i 0.196027i
\(29\) 4449.10i 0.182422i 0.995832 + 0.0912111i \(0.0290738\pi\)
−0.995832 + 0.0912111i \(0.970926\pi\)
\(30\) 16700.0i 0.618519i
\(31\) −29312.5 −0.983939 −0.491969 0.870612i \(-0.663723\pi\)
−0.491969 + 0.870612i \(0.663723\pi\)
\(32\) 44604.9i 1.36123i
\(33\) 30267.4i 0.842234i
\(34\) 54944.5i 1.39794i
\(35\) 2277.49 0.0531193
\(36\) 101641. 2.17852
\(37\) 83027.3i 1.63914i −0.572980 0.819570i \(-0.694213\pi\)
0.572980 0.819570i \(-0.305787\pi\)
\(38\) −33461.2 −0.609804
\(39\) 131890.i 2.22339i
\(40\) 2248.58 0.0351340
\(41\) −33442.2 −0.485225 −0.242612 0.970123i \(-0.578004\pi\)
−0.242612 + 0.970123i \(0.578004\pi\)
\(42\) 41409.7i 0.558925i
\(43\) 30046.7 + 73610.9i 0.377912 + 0.925841i
\(44\) −34635.8 −0.406600
\(45\) 53794.4i 0.590336i
\(46\) 137048.i 1.40799i
\(47\) −157085. −1.51301 −0.756503 0.653991i \(-0.773093\pi\)
−0.756503 + 0.653991i \(0.773093\pi\)
\(48\) 224270.i 2.02791i
\(49\) 112002. 0.951999
\(50\) 161947.i 1.29558i
\(51\) 249678.i 1.88221i
\(52\) −150925. −1.07337
\(53\) 212620. 1.42816 0.714078 0.700066i \(-0.246846\pi\)
0.714078 + 0.700066i \(0.246846\pi\)
\(54\) 576391. 3.66046
\(55\) 18331.3i 0.110180i
\(56\) −5575.61 −0.0317489
\(57\) −152053. −0.821054
\(58\) 48993.1 0.251102
\(59\) −263304. −1.28204 −0.641019 0.767525i \(-0.721488\pi\)
−0.641019 + 0.767525i \(0.721488\pi\)
\(60\) −86840.7 −0.402040
\(61\) 133532.i 0.588296i 0.955760 + 0.294148i \(0.0950359\pi\)
−0.955760 + 0.294148i \(0.904964\pi\)
\(62\) 322787.i 1.35438i
\(63\) 133389.i 0.533457i
\(64\) 204350. 0.779532
\(65\) 79878.2i 0.290863i
\(66\) −333302. −1.15933
\(67\) −157955. −0.525182 −0.262591 0.964907i \(-0.584577\pi\)
−0.262591 + 0.964907i \(0.584577\pi\)
\(68\) −285713. −0.908665
\(69\) 622771.i 1.89575i
\(70\) 25079.5i 0.0731182i
\(71\) 485322.i 1.35599i −0.735068 0.677993i \(-0.762850\pi\)
0.735068 0.677993i \(-0.237150\pi\)
\(72\) 131696.i 0.352838i
\(73\) 48573.5i 0.124862i 0.998049 + 0.0624310i \(0.0198853\pi\)
−0.998049 + 0.0624310i \(0.980115\pi\)
\(74\) −914290. −2.25626
\(75\) 735915.i 1.74439i
\(76\) 173999.i 0.396375i
\(77\) 45454.5i 0.0995646i
\(78\) −1.45236e6 −3.06048
\(79\) 762200. 1.54592 0.772961 0.634454i \(-0.218775\pi\)
0.772961 + 0.634454i \(0.218775\pi\)
\(80\) 135828.i 0.265289i
\(81\) 1.32524e6 2.49367
\(82\) 368262.i 0.667907i
\(83\) 268573. 0.469708 0.234854 0.972031i \(-0.424539\pi\)
0.234854 + 0.972031i \(0.424539\pi\)
\(84\) 215332. 0.363304
\(85\) 151216.i 0.246230i
\(86\) 810597. 330872.i 1.27441 0.520192i
\(87\) 222633. 0.338090
\(88\) 44877.5i 0.0658538i
\(89\) 1.32878e6i 1.88488i −0.334381 0.942438i \(-0.608527\pi\)
0.334381 0.942438i \(-0.391473\pi\)
\(90\) −592379. −0.812592
\(91\) 198067.i 0.262838i
\(92\) 712656. 0.915201
\(93\) 1.46680e6i 1.82357i
\(94\) 1.72980e6i 2.08264i
\(95\) 92090.4 0.107410
\(96\) 2.23203e6 2.52282
\(97\) 1.43066e6 1.56755 0.783774 0.621046i \(-0.213292\pi\)
0.783774 + 0.621046i \(0.213292\pi\)
\(98\) 1.23335e6i 1.31042i
\(99\) −1.07364e6 −1.10650
\(100\) −842129. −0.842129
\(101\) 909346. 0.882602 0.441301 0.897359i \(-0.354517\pi\)
0.441301 + 0.897359i \(0.354517\pi\)
\(102\) −2.74943e6 −2.59085
\(103\) 634146. 0.580333 0.290167 0.956976i \(-0.406289\pi\)
0.290167 + 0.956976i \(0.406289\pi\)
\(104\) 195553.i 0.173846i
\(105\) 113966.i 0.0984480i
\(106\) 2.34135e6i 1.96584i
\(107\) −481718. −0.393225 −0.196613 0.980481i \(-0.562994\pi\)
−0.196613 + 0.980481i \(0.562994\pi\)
\(108\) 2.99725e6i 2.37931i
\(109\) 1.74683e6 1.34888 0.674438 0.738332i \(-0.264386\pi\)
0.674438 + 0.738332i \(0.264386\pi\)
\(110\) 201863. 0.151662
\(111\) −4.15469e6 −3.03788
\(112\) 336802.i 0.239729i
\(113\) 1.35156e6i 0.936701i −0.883543 0.468350i \(-0.844849\pi\)
0.883543 0.468350i \(-0.155151\pi\)
\(114\) 1.67440e6i 1.13017i
\(115\) 377178.i 0.248001i
\(116\) 254766.i 0.163218i
\(117\) −4.67835e6 −2.92103
\(118\) 2.89948e6i 1.76471i
\(119\) 374958.i 0.222506i
\(120\) 112519.i 0.0651152i
\(121\) −1.40570e6 −0.793482
\(122\) 1.47044e6 0.809783
\(123\) 1.67345e6i 0.899284i
\(124\) 1.67850e6 0.880354
\(125\) 919243.i 0.470652i
\(126\) 1.46887e6 0.734299
\(127\) −376971. −0.184034 −0.0920168 0.995757i \(-0.529331\pi\)
−0.0920168 + 0.995757i \(0.529331\pi\)
\(128\) 604434.i 0.288216i
\(129\) 3.68349e6 1.50354e6i 1.71590 0.700399i
\(130\) 879613. 0.400370
\(131\) 1.97348e6i 0.877847i 0.898524 + 0.438923i \(0.144640\pi\)
−0.898524 + 0.438923i \(0.855360\pi\)
\(132\) 1.73318e6i 0.753567i
\(133\) −228349. −0.0970608
\(134\) 1.73939e6i 0.722907i
\(135\) −1.58632e6 −0.644746
\(136\) 370197.i 0.147169i
\(137\) 3.58675e6i 1.39489i −0.716638 0.697445i \(-0.754320\pi\)
0.716638 0.697445i \(-0.245680\pi\)
\(138\) 6.85791e6 2.60948
\(139\) −952415. −0.354635 −0.177318 0.984154i \(-0.556742\pi\)
−0.177318 + 0.984154i \(0.556742\pi\)
\(140\) −130414. −0.0475271
\(141\) 7.86053e6i 2.80411i
\(142\) −5.34433e6 −1.86650
\(143\) 1.59422e6 0.545181
\(144\) 7.95527e6 2.66420
\(145\) −134837. −0.0442287
\(146\) 534887. 0.171871
\(147\) 5.60457e6i 1.76437i
\(148\) 4.75434e6i 1.46658i
\(149\) 3.30681e6i 0.999656i 0.866125 + 0.499828i \(0.166604\pi\)
−0.866125 + 0.499828i \(0.833396\pi\)
\(150\) −8.10384e6 −2.40114
\(151\) 5.46323e6i 1.58679i 0.608709 + 0.793393i \(0.291688\pi\)
−0.608709 + 0.793393i \(0.708312\pi\)
\(152\) −225450. −0.0641977
\(153\) −8.85650e6 −2.47279
\(154\) −500542. −0.137050
\(155\) 888361.i 0.238558i
\(156\) 7.55230e6i 1.98932i
\(157\) 833342.i 0.215340i −0.994187 0.107670i \(-0.965661\pi\)
0.994187 0.107670i \(-0.0343390\pi\)
\(158\) 8.39328e6i 2.12795i
\(159\) 1.06395e7i 2.64685i
\(160\) −1.35182e6 −0.330034
\(161\) 935258.i 0.224106i
\(162\) 1.45934e7i 3.43251i
\(163\) 1.39941e6i 0.323134i −0.986862 0.161567i \(-0.948345\pi\)
0.986862 0.161567i \(-0.0516547\pi\)
\(164\) 1.91498e6 0.434142
\(165\) 917299. 0.204202
\(166\) 2.95750e6i 0.646548i
\(167\) 6.41130e6 1.37657 0.688283 0.725442i \(-0.258365\pi\)
0.688283 + 0.725442i \(0.258365\pi\)
\(168\) 279004.i 0.0588414i
\(169\) 2.11999e6 0.439211
\(170\) 1.66518e6 0.338933
\(171\) 5.39360e6i 1.07867i
\(172\) −1.72054e6 4.21513e6i −0.338127 0.828373i
\(173\) −5.06186e6 −0.977624 −0.488812 0.872389i \(-0.662570\pi\)
−0.488812 + 0.872389i \(0.662570\pi\)
\(174\) 2.45162e6i 0.465377i
\(175\) 1.10517e6i 0.206213i
\(176\) −2.71088e6 −0.497247
\(177\) 1.31757e7i 2.37605i
\(178\) −1.46324e7 −2.59451
\(179\) 428340.i 0.0746843i 0.999303 + 0.0373422i \(0.0118891\pi\)
−0.999303 + 0.0373422i \(0.988111\pi\)
\(180\) 3.08039e6i 0.528188i
\(181\) 2.17931e6 0.367522 0.183761 0.982971i \(-0.441173\pi\)
0.183761 + 0.982971i \(0.441173\pi\)
\(182\) −2.18110e6 −0.361794
\(183\) 6.68195e6 1.09031
\(184\) 923385.i 0.148228i
\(185\) 2.51627e6 0.397413
\(186\) 1.61523e7 2.51013
\(187\) 3.01799e6 0.461523
\(188\) 8.99504e6 1.35372
\(189\) 3.93346e6 0.582625
\(190\) 1.01409e6i 0.147848i
\(191\) 4.92816e6i 0.707269i 0.935384 + 0.353635i \(0.115054\pi\)
−0.935384 + 0.353635i \(0.884946\pi\)
\(192\) 1.02257e7i 1.44473i
\(193\) −3.40731e6 −0.473958 −0.236979 0.971515i \(-0.576157\pi\)
−0.236979 + 0.971515i \(0.576157\pi\)
\(194\) 1.57543e7i 2.15772i
\(195\) 3.99711e6 0.539067
\(196\) −6.41348e6 −0.851776
\(197\) −646332. −0.0845390 −0.0422695 0.999106i \(-0.513459\pi\)
−0.0422695 + 0.999106i \(0.513459\pi\)
\(198\) 1.18228e7i 1.52309i
\(199\) 6.52813e6i 0.828379i −0.910191 0.414190i \(-0.864065\pi\)
0.910191 0.414190i \(-0.135935\pi\)
\(200\) 1.09114e6i 0.136393i
\(201\) 7.90409e6i 0.973338i
\(202\) 1.00136e7i 1.21489i
\(203\) 334343. 0.0399673
\(204\) 1.42971e7i 1.68406i
\(205\) 1.01352e6i 0.117644i
\(206\) 6.98316e6i 0.798823i
\(207\) 2.20908e7 2.49058
\(208\) −1.18126e7 −1.31267
\(209\) 1.83795e6i 0.201324i
\(210\) −1.25498e6 −0.135513
\(211\) 2.63536e6i 0.280539i 0.990113 + 0.140269i \(0.0447968\pi\)
−0.990113 + 0.140269i \(0.955203\pi\)
\(212\) −1.21751e7 −1.27781
\(213\) −2.42856e7 −2.51310
\(214\) 5.30464e6i 0.541271i
\(215\) −2.23089e6 + 910610.i −0.224472 + 0.0916257i
\(216\) 3.88352e6 0.385358
\(217\) 2.20279e6i 0.215573i
\(218\) 1.92360e7i 1.85671i
\(219\) 2.43062e6 0.231411
\(220\) 1.04969e6i 0.0985811i
\(221\) 1.31508e7 1.21836
\(222\) 4.57512e7i 4.18161i
\(223\) 1.69760e7i 1.53081i 0.643551 + 0.765403i \(0.277460\pi\)
−0.643551 + 0.765403i \(0.722540\pi\)
\(224\) 3.35200e6 0.298235
\(225\) −2.61042e7 −2.29173
\(226\) −1.48833e7 −1.28936
\(227\) 1.01092e7i 0.864247i −0.901814 0.432124i \(-0.857764\pi\)
0.901814 0.432124i \(-0.142236\pi\)
\(228\) 8.70693e6 0.734616
\(229\) 7.19101e6 0.598802 0.299401 0.954127i \(-0.403213\pi\)
0.299401 + 0.954127i \(0.403213\pi\)
\(230\) −4.15346e6 −0.341371
\(231\) −2.27455e6 −0.184527
\(232\) 330099. 0.0264350
\(233\) 1.30168e7i 1.02905i −0.857475 0.514526i \(-0.827968\pi\)
0.857475 0.514526i \(-0.172032\pi\)
\(234\) 5.15177e7i 4.02076i
\(235\) 4.76069e6i 0.366831i
\(236\) 1.50774e7 1.14707
\(237\) 3.81405e7i 2.86511i
\(238\) −4.12900e6 −0.306277
\(239\) −5.98455e6 −0.438367 −0.219183 0.975684i \(-0.570339\pi\)
−0.219183 + 0.975684i \(0.570339\pi\)
\(240\) −6.79686e6 −0.491671
\(241\) 1.94706e7i 1.39101i 0.718523 + 0.695503i \(0.244818\pi\)
−0.718523 + 0.695503i \(0.755182\pi\)
\(242\) 1.54795e7i 1.09222i
\(243\) 2.81574e7i 1.96233i
\(244\) 7.64636e6i 0.526363i
\(245\) 3.39438e6i 0.230814i
\(246\) 1.84279e7 1.23786
\(247\) 8.00885e6i 0.531471i
\(248\) 2.17483e6i 0.142584i
\(249\) 1.34394e7i 0.870527i
\(250\) 1.01226e7 0.647848
\(251\) −6.05694e6 −0.383029 −0.191515 0.981490i \(-0.561340\pi\)
−0.191515 + 0.981490i \(0.561340\pi\)
\(252\) 7.63819e6i 0.477297i
\(253\) −7.52779e6 −0.464842
\(254\) 4.15118e6i 0.253320i
\(255\) 7.56686e6 0.456347
\(256\) 1.97343e7 1.17626
\(257\) 1.73952e7i 1.02478i 0.858754 + 0.512388i \(0.171239\pi\)
−0.858754 + 0.512388i \(0.828761\pi\)
\(258\) −1.65568e7 4.05623e7i −0.964092 2.36191i
\(259\) −6.23938e6 −0.359122
\(260\) 4.57402e6i 0.260242i
\(261\) 7.89719e6i 0.444172i
\(262\) 2.17318e7 1.20835
\(263\) 2.18225e7i 1.19960i 0.800149 + 0.599801i \(0.204754\pi\)
−0.800149 + 0.599801i \(0.795246\pi\)
\(264\) −2.24567e6 −0.122049
\(265\) 6.44376e6i 0.346259i
\(266\) 2.51456e6i 0.133603i
\(267\) −6.64922e7 −3.49331
\(268\) 9.04488e6 0.469893
\(269\) 759715. 0.0390296 0.0195148 0.999810i \(-0.493788\pi\)
0.0195148 + 0.999810i \(0.493788\pi\)
\(270\) 1.74684e7i 0.887486i
\(271\) 3.82518e7 1.92196 0.960978 0.276624i \(-0.0892155\pi\)
0.960978 + 0.276624i \(0.0892155\pi\)
\(272\) −2.23622e7 −1.11124
\(273\) −9.91131e6 −0.487128
\(274\) −3.94970e7 −1.92005
\(275\) 8.89542e6 0.427729
\(276\) 3.56614e7i 1.69617i
\(277\) 2.70372e7i 1.27210i 0.771647 + 0.636052i \(0.219433\pi\)
−0.771647 + 0.636052i \(0.780567\pi\)
\(278\) 1.04879e7i 0.488152i
\(279\) 5.20300e7 2.39575
\(280\) 168977.i 0.00769759i
\(281\) −1.84904e7 −0.833352 −0.416676 0.909055i \(-0.636805\pi\)
−0.416676 + 0.909055i \(0.636805\pi\)
\(282\) 8.65595e7 3.85983
\(283\) 3.01118e7 1.32855 0.664274 0.747489i \(-0.268741\pi\)
0.664274 + 0.747489i \(0.268741\pi\)
\(284\) 2.77907e7i 1.21323i
\(285\) 4.60821e6i 0.199066i
\(286\) 1.75555e7i 0.750436i
\(287\) 2.51313e6i 0.106309i
\(288\) 7.91742e7i 3.31441i
\(289\) 758046. 0.0314052
\(290\) 1.48481e6i 0.0608803i
\(291\) 7.15903e7i 2.90520i
\(292\) 2.78143e6i 0.111717i
\(293\) 1.61065e6 0.0640324 0.0320162 0.999487i \(-0.489807\pi\)
0.0320162 + 0.999487i \(0.489807\pi\)
\(294\) −6.17171e7 −2.42864
\(295\) 7.97982e6i 0.310833i
\(296\) −6.16018e6 −0.237530
\(297\) 3.16600e7i 1.20848i
\(298\) 3.64143e7 1.37602
\(299\) −3.28022e7 −1.22713
\(300\) 4.21402e7i 1.56075i
\(301\) 5.53175e6 2.25796e6i 0.202844 0.0827976i
\(302\) 6.01606e7 2.18420
\(303\) 4.55037e7i 1.63576i
\(304\) 1.36186e7i 0.484743i
\(305\) −4.04689e6 −0.142634
\(306\) 9.75271e7i 3.40378i
\(307\) 3.91736e7 1.35388 0.676938 0.736040i \(-0.263307\pi\)
0.676938 + 0.736040i \(0.263307\pi\)
\(308\) 2.60283e6i 0.0890829i
\(309\) 3.17327e7i 1.07555i
\(310\) −9.78256e6 −0.328373
\(311\) −2.65437e7 −0.882429 −0.441215 0.897402i \(-0.645452\pi\)
−0.441215 + 0.897402i \(0.645452\pi\)
\(312\) −9.78549e6 −0.322195
\(313\) 3.65208e7i 1.19099i 0.803359 + 0.595495i \(0.203044\pi\)
−0.803359 + 0.595495i \(0.796956\pi\)
\(314\) −9.17669e6 −0.296413
\(315\) −4.04257e6 −0.129338
\(316\) −4.36453e7 −1.38317
\(317\) 3.58851e7 1.12651 0.563257 0.826282i \(-0.309548\pi\)
0.563257 + 0.826282i \(0.309548\pi\)
\(318\) −1.17161e8 −3.64337
\(319\) 2.69109e6i 0.0829004i
\(320\) 6.19313e6i 0.188999i
\(321\) 2.41052e7i 0.728779i
\(322\) 1.02990e7 0.308480
\(323\) 1.51614e7i 0.449916i
\(324\) −7.58862e7 −2.23114
\(325\) 3.87616e7 1.12915
\(326\) −1.54102e7 −0.444790
\(327\) 8.74117e7i 2.49992i
\(328\) 2.48123e6i 0.0703145i
\(329\) 1.18047e7i 0.331487i
\(330\) 1.01012e7i 0.281081i
\(331\) 4.13224e7i 1.13947i −0.821829 0.569734i \(-0.807046\pi\)
0.821829 0.569734i \(-0.192954\pi\)
\(332\) −1.53791e7 −0.420259
\(333\) 1.47374e8i 3.99107i
\(334\) 7.06008e7i 1.89483i
\(335\) 4.78707e6i 0.127331i
\(336\) 1.68536e7 0.444298
\(337\) 5.37649e7 1.40478 0.702392 0.711790i \(-0.252115\pi\)
0.702392 + 0.711790i \(0.252115\pi\)
\(338\) 2.33452e7i 0.604570i
\(339\) −6.76323e7 −1.73602
\(340\) 8.65898e6i 0.220308i
\(341\) −1.77300e7 −0.447143
\(342\) 5.93939e7 1.48478
\(343\) 1.72579e7i 0.427667i
\(344\) 5.46153e6 2.22930e6i 0.134165 0.0547637i
\(345\) −1.88740e7 −0.459629
\(346\) 5.57408e7i 1.34569i
\(347\) 7.03541e7i 1.68384i 0.539603 + 0.841920i \(0.318574\pi\)
−0.539603 + 0.841920i \(0.681426\pi\)
\(348\) −1.27485e7 −0.302497
\(349\) 5.74051e7i 1.35044i −0.737618 0.675218i \(-0.764049\pi\)
0.737618 0.675218i \(-0.235951\pi\)
\(350\) −1.21701e7 −0.283850
\(351\) 1.37958e8i 3.19025i
\(352\) 2.69798e7i 0.618602i
\(353\) −6.11985e7 −1.39129 −0.695644 0.718387i \(-0.744881\pi\)
−0.695644 + 0.718387i \(0.744881\pi\)
\(354\) 1.45090e8 3.27061
\(355\) 1.47084e7 0.328762
\(356\) 7.60890e7i 1.68644i
\(357\) −1.87629e7 −0.412378
\(358\) 4.71684e6 0.102802
\(359\) 1.65832e7 0.358414 0.179207 0.983811i \(-0.442647\pi\)
0.179207 + 0.983811i \(0.442647\pi\)
\(360\) −3.99125e6 −0.0855464
\(361\) 3.78126e7 0.803739
\(362\) 2.39984e7i 0.505891i
\(363\) 7.03415e7i 1.47059i
\(364\) 1.13418e7i 0.235168i
\(365\) −1.47209e6 −0.0302731
\(366\) 7.35811e7i 1.50080i
\(367\) −7.49850e6 −0.151697 −0.0758484 0.997119i \(-0.524166\pi\)
−0.0758484 + 0.997119i \(0.524166\pi\)
\(368\) 5.57782e7 1.11923
\(369\) 5.93602e7 1.18145
\(370\) 2.77090e7i 0.547035i
\(371\) 1.59780e7i 0.312897i
\(372\) 8.39925e7i 1.63159i
\(373\) 2.28773e7i 0.440837i −0.975405 0.220419i \(-0.929258\pi\)
0.975405 0.220419i \(-0.0707423\pi\)
\(374\) 3.32339e7i 0.635282i
\(375\) 4.59990e7 0.872277
\(376\) 1.16548e7i 0.219251i
\(377\) 1.17264e7i 0.218847i
\(378\) 4.33149e7i 0.801977i
\(379\) −3.49753e7 −0.642457 −0.321228 0.947002i \(-0.604096\pi\)
−0.321228 + 0.947002i \(0.604096\pi\)
\(380\) −5.27331e6 −0.0961020
\(381\) 1.88637e7i 0.341076i
\(382\) 5.42685e7 0.973549
\(383\) 3.06385e7i 0.545345i 0.962107 + 0.272672i \(0.0879075\pi\)
−0.962107 + 0.272672i \(0.912093\pi\)
\(384\) 3.02459e7 0.534162
\(385\) 1.37757e6 0.0241397
\(386\) 3.75210e7i 0.652398i
\(387\) −5.33332e7 1.30660e8i −0.920162 2.25429i
\(388\) −8.19229e7 −1.40252
\(389\) 8.00209e6i 0.135942i −0.997687 0.0679711i \(-0.978347\pi\)
0.997687 0.0679711i \(-0.0216526\pi\)
\(390\) 4.40159e7i 0.742020i
\(391\) −6.20972e7 −1.03882
\(392\) 8.30992e6i 0.137955i
\(393\) 9.87531e7 1.62695
\(394\) 7.11736e6i 0.116367i
\(395\) 2.30996e7i 0.374812i
\(396\) 6.14790e7 0.990013
\(397\) −7.52627e7 −1.20284 −0.601421 0.798932i \(-0.705399\pi\)
−0.601421 + 0.798932i \(0.705399\pi\)
\(398\) −7.18872e7 −1.14026
\(399\) 1.14266e7i 0.179886i
\(400\) −6.59119e7 −1.02987
\(401\) −3.64743e7 −0.565658 −0.282829 0.959170i \(-0.591273\pi\)
−0.282829 + 0.959170i \(0.591273\pi\)
\(402\) 8.70392e7 1.33979
\(403\) −7.72584e7 −1.18040
\(404\) −5.20713e7 −0.789685
\(405\) 4.01633e7i 0.604595i
\(406\) 3.68176e6i 0.0550145i
\(407\) 5.02201e7i 0.744894i
\(408\) −1.85247e7 −0.272754
\(409\) 1.19043e8i 1.73993i −0.493111 0.869966i \(-0.664140\pi\)
0.493111 0.869966i \(-0.335860\pi\)
\(410\) −1.11608e7 −0.161935
\(411\) −1.79481e8 −2.58520
\(412\) −3.63127e7 −0.519238
\(413\) 1.97869e7i 0.280884i
\(414\) 2.43262e8i 3.42826i
\(415\) 8.13951e6i 0.113882i
\(416\) 1.17564e8i 1.63303i
\(417\) 4.76589e7i 0.657258i
\(418\) −2.02394e7 −0.277121
\(419\) 1.30796e8i 1.77809i −0.457824 0.889043i \(-0.651371\pi\)
0.457824 0.889043i \(-0.348629\pi\)
\(420\) 6.52595e6i 0.0880838i
\(421\) 1.08991e8i 1.46064i 0.683105 + 0.730320i \(0.260629\pi\)
−0.683105 + 0.730320i \(0.739371\pi\)
\(422\) 2.90204e7 0.386159
\(423\) 2.78827e8 3.68395
\(424\) 1.57752e7i 0.206956i
\(425\) 7.33789e7 0.955882
\(426\) 2.67431e8i 3.45925i
\(427\) 1.00347e7 0.128891
\(428\) 2.75843e7 0.351828
\(429\) 7.97750e7i 1.01040i
\(430\) 1.00276e7 + 2.45664e7i 0.126122 + 0.308984i
\(431\) −2.84336e7 −0.355141 −0.177570 0.984108i \(-0.556824\pi\)
−0.177570 + 0.984108i \(0.556824\pi\)
\(432\) 2.34589e8i 2.90976i
\(433\) 1.31732e7i 0.162266i 0.996703 + 0.0811330i \(0.0258539\pi\)
−0.996703 + 0.0811330i \(0.974146\pi\)
\(434\) 2.42570e7 0.296734
\(435\) 6.74724e6i 0.0819706i
\(436\) −1.00028e8 −1.20687
\(437\) 3.78171e7i 0.453153i
\(438\) 2.67658e7i 0.318535i
\(439\) 9.21820e7 1.08956 0.544782 0.838578i \(-0.316612\pi\)
0.544782 + 0.838578i \(0.316612\pi\)
\(440\) 1.36008e6 0.0159664
\(441\) −1.98804e8 −2.31798
\(442\) 1.44816e8i 1.67707i
\(443\) −1.32293e8 −1.52169 −0.760843 0.648935i \(-0.775214\pi\)
−0.760843 + 0.648935i \(0.775214\pi\)
\(444\) 2.37908e8 2.71806
\(445\) 4.02707e7 0.456992
\(446\) 1.86938e8 2.10714
\(447\) 1.65473e8 1.85270
\(448\) 1.53566e7i 0.170789i
\(449\) 8.50172e7i 0.939221i 0.882874 + 0.469610i \(0.155606\pi\)
−0.882874 + 0.469610i \(0.844394\pi\)
\(450\) 2.87457e8i 3.15454i
\(451\) −2.02279e7 −0.220506
\(452\) 7.73936e7i 0.838089i
\(453\) 2.73380e8 2.94085
\(454\) −1.11321e8 −1.18963
\(455\) 6.00273e6 0.0637257
\(456\) 1.12815e7i 0.118980i
\(457\) 923905.i 0.00968008i −0.999988 0.00484004i \(-0.998459\pi\)
0.999988 0.00484004i \(-0.00154064\pi\)
\(458\) 7.91868e7i 0.824245i
\(459\) 2.61165e8i 2.70071i
\(460\) 2.15981e7i 0.221892i
\(461\) −6.17034e7 −0.629806 −0.314903 0.949124i \(-0.601972\pi\)
−0.314903 + 0.949124i \(0.601972\pi\)
\(462\) 2.50471e7i 0.253999i
\(463\) 1.17785e8i 1.18672i 0.804938 + 0.593358i \(0.202198\pi\)
−0.804938 + 0.593358i \(0.797802\pi\)
\(464\) 1.99400e7i 0.199605i
\(465\) −4.44536e7 −0.442129
\(466\) −1.43340e8 −1.41648
\(467\) 2.00013e6i 0.0196385i −0.999952 0.00981923i \(-0.996874\pi\)
0.999952 0.00981923i \(-0.00312561\pi\)
\(468\) 2.67894e8 2.61351
\(469\) 1.18701e7i 0.115063i
\(470\) −5.24243e7 −0.504940
\(471\) −4.17005e7 −0.399097
\(472\) 1.95357e7i 0.185782i
\(473\) 1.81741e7 + 4.45245e7i 0.171739 + 0.420741i
\(474\) −4.20001e8 −3.94380
\(475\) 4.46877e7i 0.416972i
\(476\) 2.14709e7i 0.199081i
\(477\) −3.77402e8 −3.47735
\(478\) 6.59014e7i 0.603408i
\(479\) 5.60261e7 0.509781 0.254890 0.966970i \(-0.417961\pi\)
0.254890 + 0.966970i \(0.417961\pi\)
\(480\) 6.76452e7i 0.611664i
\(481\) 2.18833e8i 1.96643i
\(482\) 2.14409e8 1.91471
\(483\) 4.68004e7 0.415344
\(484\) 8.04938e7 0.709948
\(485\) 4.33583e7i 0.380056i
\(486\) −3.10066e8 −2.70113
\(487\) −8.02252e7 −0.694582 −0.347291 0.937757i \(-0.612898\pi\)
−0.347291 + 0.937757i \(0.612898\pi\)
\(488\) 9.90735e6 0.0852507
\(489\) −7.00266e7 −0.598875
\(490\) 3.73787e7 0.317713
\(491\) 4.73660e7i 0.400149i 0.979781 + 0.200075i \(0.0641185\pi\)
−0.979781 + 0.200075i \(0.935882\pi\)
\(492\) 9.58256e7i 0.804611i
\(493\) 2.21990e7i 0.185265i
\(494\) −8.81928e7 −0.731564
\(495\) 3.25382e7i 0.268274i
\(496\) 1.31373e8 1.07662
\(497\) −3.64713e7 −0.297086
\(498\) −1.47994e8 −1.19827
\(499\) 1.29386e8i 1.04132i −0.853763 0.520662i \(-0.825685\pi\)
0.853763 0.520662i \(-0.174315\pi\)
\(500\) 5.26380e7i 0.421104i
\(501\) 3.20822e8i 2.55124i
\(502\) 6.66985e7i 0.527236i
\(503\) 4.95506e7i 0.389355i −0.980867 0.194677i \(-0.937634\pi\)
0.980867 0.194677i \(-0.0623660\pi\)
\(504\) 9.89677e6 0.0773040
\(505\) 2.75591e7i 0.213989i
\(506\) 8.28954e7i 0.639851i
\(507\) 1.06084e8i 0.814007i
\(508\) 2.15863e7 0.164659
\(509\) 1.13027e8 0.857098 0.428549 0.903519i \(-0.359025\pi\)
0.428549 + 0.903519i \(0.359025\pi\)
\(510\) 8.33256e7i 0.628157i
\(511\) 3.65022e6 0.0273563
\(512\) 1.78629e8i 1.33089i
\(513\) 1.59049e8 1.17809
\(514\) 1.91554e8 1.41059
\(515\) 1.92188e7i 0.140703i
\(516\) −2.10925e8 + 8.60961e7i −1.53525 + 0.626664i
\(517\) −9.50147e7 −0.687573
\(518\) 6.87076e7i 0.494328i
\(519\) 2.53296e8i 1.81187i
\(520\) 5.92653e6 0.0421493
\(521\) 3.09027e7i 0.218516i −0.994013 0.109258i \(-0.965152\pi\)
0.994013 0.109258i \(-0.0348475\pi\)
\(522\) −8.69632e7 −0.611398
\(523\) 1.39183e8i 0.972932i −0.873699 0.486466i \(-0.838286\pi\)
0.873699 0.486466i \(-0.161714\pi\)
\(524\) 1.13006e8i 0.785431i
\(525\) −5.53030e7 −0.382182
\(526\) 2.40308e8 1.65124
\(527\) −1.46256e8 −0.999270
\(528\) 1.35653e8i 0.921567i
\(529\) 6.85340e6 0.0462955
\(530\) 7.09581e7 0.476623
\(531\) 4.67367e8 3.12158
\(532\) 1.30758e7 0.0868426
\(533\) −8.81428e7 −0.582110
\(534\) 7.32207e8i 4.80850i
\(535\) 1.45992e7i 0.0953383i
\(536\) 1.17194e7i 0.0761047i
\(537\) 2.14342e7 0.138415
\(538\) 8.36591e6i 0.0537238i
\(539\) 6.77456e7 0.432628
\(540\) 9.08362e7 0.576870
\(541\) 6.32657e7 0.399555 0.199777 0.979841i \(-0.435978\pi\)
0.199777 + 0.979841i \(0.435978\pi\)
\(542\) 4.21225e8i 2.64555i
\(543\) 1.09053e8i 0.681143i
\(544\) 2.22558e8i 1.38244i
\(545\) 5.29405e7i 0.327038i
\(546\) 1.09143e8i 0.670527i
\(547\) −1.95485e8 −1.19441 −0.597203 0.802090i \(-0.703721\pi\)
−0.597203 + 0.802090i \(0.703721\pi\)
\(548\) 2.05386e8i 1.24804i
\(549\) 2.37021e8i 1.43242i
\(550\) 9.79556e7i 0.588764i
\(551\) 1.35192e7 0.0808156
\(552\) 4.62063e7 0.274716
\(553\) 5.72782e7i 0.338699i
\(554\) 2.97731e8 1.75104
\(555\) 1.25914e8i 0.736540i
\(556\) 5.45375e7 0.317301
\(557\) 3.96240e7 0.229294 0.114647 0.993406i \(-0.463426\pi\)
0.114647 + 0.993406i \(0.463426\pi\)
\(558\) 5.72950e8i 3.29772i
\(559\) 7.91934e7 + 1.94015e8i 0.453371 + 1.11071i
\(560\) −1.02073e7 −0.0581228
\(561\) 1.51021e8i 0.855357i
\(562\) 2.03615e8i 1.14710i
\(563\) 2.83973e8 1.59130 0.795649 0.605758i \(-0.207130\pi\)
0.795649 + 0.605758i \(0.207130\pi\)
\(564\) 4.50112e8i 2.50890i
\(565\) 4.09612e7 0.227105
\(566\) 3.31589e8i 1.82873i
\(567\) 9.95897e7i 0.546343i
\(568\) −3.60083e7 −0.196498
\(569\) −1.60879e8 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(570\) −5.07452e7 −0.274013
\(571\) 2.43494e8i 1.30792i 0.756530 + 0.653959i \(0.226893\pi\)
−0.756530 + 0.653959i \(0.773107\pi\)
\(572\) −9.12889e7 −0.487787
\(573\) 2.46606e8 1.31081
\(574\) 2.76744e7 0.146333
\(575\) −1.83029e8 −0.962758
\(576\) −3.62723e8 −1.89805
\(577\) 2.31171e8i 1.20339i −0.798727 0.601693i \(-0.794493\pi\)
0.798727 0.601693i \(-0.205507\pi\)
\(578\) 8.34754e6i 0.0432290i
\(579\) 1.70502e8i 0.878403i
\(580\) 7.72106e6 0.0395725
\(581\) 2.01829e7i 0.102909i
\(582\) −7.88347e8 −3.99897
\(583\) 1.28606e8 0.649014
\(584\) 3.60389e6 0.0180939
\(585\) 1.41785e8i 0.708209i
\(586\) 1.77364e7i 0.0881399i
\(587\) 2.10877e8i 1.04259i 0.853375 + 0.521297i \(0.174552\pi\)
−0.853375 + 0.521297i \(0.825448\pi\)
\(588\) 3.20931e8i 1.57863i
\(589\) 8.90700e7i 0.435898i
\(590\) −8.78732e7 −0.427859
\(591\) 3.23425e7i 0.156679i
\(592\) 3.72113e8i 1.79353i
\(593\) 2.60310e8i 1.24832i 0.781295 + 0.624162i \(0.214560\pi\)
−0.781295 + 0.624162i \(0.785440\pi\)
\(594\) 3.48637e8 1.66347
\(595\) 1.13637e7 0.0539470
\(596\) 1.89356e8i 0.894417i
\(597\) −3.26668e8 −1.53527
\(598\) 3.61215e8i 1.68913i
\(599\) 1.98069e8 0.921587 0.460794 0.887507i \(-0.347565\pi\)
0.460794 + 0.887507i \(0.347565\pi\)
\(600\) −5.46009e7 −0.252782
\(601\) 2.10475e8i 0.969565i 0.874635 + 0.484783i \(0.161101\pi\)
−0.874635 + 0.484783i \(0.838899\pi\)
\(602\) −2.48645e7 6.09152e7i −0.113970 0.279213i
\(603\) 2.80372e8 1.27874
\(604\) 3.12837e8i 1.41974i
\(605\) 4.26020e7i 0.192382i
\(606\) −5.01083e8 −2.25160
\(607\) 6.23544e7i 0.278805i 0.990236 + 0.139403i \(0.0445182\pi\)
−0.990236 + 0.139403i \(0.955482\pi\)
\(608\) 1.35538e8 0.603045
\(609\) 1.67306e7i 0.0740728i
\(610\) 4.45640e7i 0.196334i
\(611\) −4.14025e8 −1.81511
\(612\) 5.07144e8 2.21247
\(613\) −3.02341e7 −0.131255 −0.0656276 0.997844i \(-0.520905\pi\)
−0.0656276 + 0.997844i \(0.520905\pi\)
\(614\) 4.31377e8i 1.86360i
\(615\) −5.07164e7 −0.218033
\(616\) −3.37248e6 −0.0144280
\(617\) 5.23405e7 0.222834 0.111417 0.993774i \(-0.464461\pi\)
0.111417 + 0.993774i \(0.464461\pi\)
\(618\) −3.49438e8 −1.48049
\(619\) −6.04729e7 −0.254970 −0.127485 0.991841i \(-0.540690\pi\)
−0.127485 + 0.991841i \(0.540690\pi\)
\(620\) 5.08696e7i 0.213444i
\(621\) 6.51425e8i 2.72013i
\(622\) 2.92297e8i 1.21465i
\(623\) −9.98558e7 −0.412961
\(624\) 5.91104e8i 2.43282i
\(625\) 2.01930e8 0.827106
\(626\) 4.02165e8 1.63938
\(627\) −9.19714e7 −0.373121
\(628\) 4.77191e7i 0.192670i
\(629\) 4.14269e8i 1.66468i
\(630\) 4.45165e7i 0.178032i
\(631\) 5.68881e7i 0.226430i 0.993571 + 0.113215i \(0.0361149\pi\)
−0.993571 + 0.113215i \(0.963885\pi\)
\(632\) 5.65511e7i 0.224021i
\(633\) 1.31874e8 0.519933
\(634\) 3.95164e8i 1.55064i
\(635\) 1.14247e7i 0.0446194i
\(636\) 6.09243e8i 2.36820i
\(637\) 2.95200e8 1.14209
\(638\) 2.96341e7 0.114111
\(639\) 8.61452e8i 3.30163i
\(640\) −1.83183e7 −0.0698787
\(641\) 5.01358e8i 1.90359i 0.306734 + 0.951795i \(0.400764\pi\)
−0.306734 + 0.951795i \(0.599236\pi\)
\(642\) 2.65445e8 1.00316
\(643\) −2.03232e8 −0.764468 −0.382234 0.924065i \(-0.624845\pi\)
−0.382234 + 0.924065i \(0.624845\pi\)
\(644\) 5.35550e7i 0.200513i
\(645\) 4.55670e7 + 1.11634e8i 0.169813 + 0.416023i
\(646\) −1.66956e8 −0.619305
\(647\) 1.76979e8i 0.653443i 0.945121 + 0.326722i \(0.105944\pi\)
−0.945121 + 0.326722i \(0.894056\pi\)
\(648\) 9.83254e7i 0.361361i
\(649\) −1.59263e8 −0.582612
\(650\) 4.26840e8i 1.55426i
\(651\) 1.10228e8 0.399530
\(652\) 8.01335e7i 0.289115i
\(653\) 7.16442e7i 0.257301i 0.991690 + 0.128651i \(0.0410646\pi\)
−0.991690 + 0.128651i \(0.958935\pi\)
\(654\) −9.62570e8 −3.44112
\(655\) −5.98093e7 −0.212836
\(656\) 1.49882e8 0.530929
\(657\) 8.62184e7i 0.304021i
\(658\) 1.29992e8 0.456289
\(659\) −4.47258e8 −1.56279 −0.781397 0.624035i \(-0.785492\pi\)
−0.781397 + 0.624035i \(0.785492\pi\)
\(660\) −5.25267e7 −0.182704
\(661\) −1.23912e8 −0.429049 −0.214525 0.976719i \(-0.568820\pi\)
−0.214525 + 0.976719i \(0.568820\pi\)
\(662\) −4.55039e8 −1.56847
\(663\) 6.58070e8i 2.25804i
\(664\) 1.99266e7i 0.0680659i
\(665\) 6.92046e6i 0.0235326i
\(666\) 1.62287e9 5.49366
\(667\) 5.53710e7i 0.186597i
\(668\) −3.67126e8 −1.23165
\(669\) 8.49480e8 2.83710
\(670\) −5.27148e7 −0.175270
\(671\) 8.07685e7i 0.267346i
\(672\) 1.67734e8i 0.552731i
\(673\) 1.92398e7i 0.0631185i −0.999502 0.0315592i \(-0.989953\pi\)
0.999502 0.0315592i \(-0.0100473\pi\)
\(674\) 5.92055e8i 1.93367i
\(675\) 7.69775e8i 2.50295i
\(676\) −1.21396e8 −0.392973
\(677\) 4.42129e8i 1.42490i −0.701725 0.712448i \(-0.747586\pi\)
0.701725 0.712448i \(-0.252414\pi\)
\(678\) 7.44761e8i 2.38962i
\(679\) 1.07512e8i 0.343437i
\(680\) 1.12194e7 0.0356815
\(681\) −5.05864e8 −1.60174
\(682\) 1.95242e8i 0.615488i
\(683\) 9.46019e6 0.0296919 0.0148459 0.999890i \(-0.495274\pi\)
0.0148459 + 0.999890i \(0.495274\pi\)
\(684\) 3.08850e8i 0.965116i
\(685\) 1.08702e8 0.338194
\(686\) −1.90043e8 −0.588680
\(687\) 3.59839e8i 1.10978i
\(688\) −1.34664e8 3.29910e8i −0.413509 1.01305i
\(689\) 5.60397e8 1.71332
\(690\) 2.07839e8i 0.632675i
\(691\) 4.38108e8i 1.32784i −0.747802 0.663922i \(-0.768891\pi\)
0.747802 0.663922i \(-0.231109\pi\)
\(692\) 2.89854e8 0.874703
\(693\) 8.06823e7i 0.242426i
\(694\) 7.74733e8 2.31779
\(695\) 2.88644e7i 0.0859821i
\(696\) 1.65182e7i 0.0489930i
\(697\) −1.66861e8 −0.492785
\(698\) −6.32140e8 −1.85886
\(699\) −6.51363e8 −1.90718
\(700\) 6.32848e7i 0.184504i
\(701\) 1.11880e8 0.324786 0.162393 0.986726i \(-0.448079\pi\)
0.162393 + 0.986726i \(0.448079\pi\)
\(702\) 1.51918e9 4.39135
\(703\) −2.52289e8 −0.726161
\(704\) 1.23603e8 0.354252
\(705\) −2.38225e8 −0.679862
\(706\) 6.73913e8i 1.91509i
\(707\) 6.83360e7i 0.193371i
\(708\) 7.54474e8i 2.12591i
\(709\) −1.44384e8 −0.405117 −0.202559 0.979270i \(-0.564926\pi\)
−0.202559 + 0.979270i \(0.564926\pi\)
\(710\) 1.61968e8i 0.452537i
\(711\) −1.35291e9 −3.76410
\(712\) −9.85882e7 −0.273140
\(713\) 3.64808e8 1.00646
\(714\) 2.06616e8i 0.567634i
\(715\) 4.83154e7i 0.132180i
\(716\) 2.45277e7i 0.0668219i
\(717\) 2.99467e8i 0.812441i
\(718\) 1.82613e8i 0.493353i
\(719\) 1.65815e8 0.446105 0.223052 0.974806i \(-0.428398\pi\)
0.223052 + 0.974806i \(0.428398\pi\)
\(720\) 2.41096e8i 0.645942i
\(721\) 4.76551e7i 0.127146i
\(722\) 4.16389e8i 1.10634i
\(723\) 9.74312e8 2.57800
\(724\) −1.24793e8 −0.328831
\(725\) 6.54307e7i 0.171699i
\(726\) 7.74594e8 2.02425
\(727\) 6.29238e8i 1.63761i −0.574069 0.818807i \(-0.694636\pi\)
0.574069 0.818807i \(-0.305364\pi\)
\(728\) −1.46955e7 −0.0380882
\(729\) −4.42898e8 −1.14320
\(730\) 1.62106e7i 0.0416706i
\(731\) 1.49919e8 + 3.67285e8i 0.383801 + 0.940267i
\(732\) −3.82624e8 −0.975527
\(733\) 5.55695e8i 1.41099i 0.708714 + 0.705495i \(0.249275\pi\)
−0.708714 + 0.705495i \(0.750725\pi\)
\(734\) 8.25729e7i 0.208809i
\(735\) 1.69855e8 0.427776
\(736\) 5.55128e8i 1.39239i
\(737\) −9.55412e7 −0.238665
\(738\) 6.53669e8i 1.62626i
\(739\) 1.18378e8i 0.293318i 0.989187 + 0.146659i \(0.0468519\pi\)
−0.989187 + 0.146659i \(0.953148\pi\)
\(740\) −1.44087e8 −0.355575
\(741\) −4.00764e8 −0.984994
\(742\) −1.75949e8 −0.430700
\(743\) 2.35083e8i 0.573132i 0.958060 + 0.286566i \(0.0925138\pi\)
−0.958060 + 0.286566i \(0.907486\pi\)
\(744\) 1.08829e8 0.264256
\(745\) −1.00218e8 −0.242369
\(746\) −2.51923e8 −0.606808
\(747\) −4.76719e8 −1.14367
\(748\) −1.72817e8 −0.412936
\(749\) 3.62004e7i 0.0861525i
\(750\) 5.06537e8i 1.20068i
\(751\) 2.67999e8i 0.632722i −0.948639 0.316361i \(-0.897539\pi\)
0.948639 0.316361i \(-0.102461\pi\)
\(752\) 7.04025e8 1.65552
\(753\) 3.03090e8i 0.709882i
\(754\) 1.29130e8 0.301240
\(755\) −1.65571e8 −0.384720
\(756\) −2.25239e8 −0.521289
\(757\) 3.48844e8i 0.804162i −0.915604 0.402081i \(-0.868287\pi\)
0.915604 0.402081i \(-0.131713\pi\)
\(758\) 3.85145e8i 0.884335i
\(759\) 3.76691e8i 0.861509i
\(760\) 6.83260e6i 0.0155649i
\(761\) 3.74723e8i 0.850269i 0.905130 + 0.425135i \(0.139773\pi\)
−0.905130 + 0.425135i \(0.860227\pi\)
\(762\) 2.07725e8 0.469488
\(763\) 1.31272e8i 0.295528i
\(764\) 2.82198e8i 0.632811i
\(765\) 2.68410e8i 0.599534i
\(766\) 3.37389e8 0.750661
\(767\) −6.93984e8 −1.53803
\(768\) 9.87508e8i 2.18000i
\(769\) 1.68131e8 0.369716 0.184858 0.982765i \(-0.440817\pi\)
0.184858 + 0.982765i \(0.440817\pi\)
\(770\) 1.51697e7i 0.0332280i
\(771\) 8.70456e8 1.89926
\(772\) 1.95111e8 0.424061
\(773\) 1.56150e8i 0.338068i 0.985610 + 0.169034i \(0.0540647\pi\)
−0.985610 + 0.169034i \(0.945935\pi\)
\(774\) −1.43882e9 + 5.87300e8i −3.10301 + 1.26659i
\(775\) −4.31085e8 −0.926100
\(776\) 1.06147e8i 0.227155i
\(777\) 3.12219e8i 0.665574i
\(778\) −8.81183e7 −0.187123
\(779\) 1.01618e8i 0.214961i
\(780\) −2.28884e8 −0.482316
\(781\) 2.93553e8i 0.616217i
\(782\) 6.83809e8i 1.42993i
\(783\) −2.32877e8 −0.485110