Properties

Label 43.7.b.b.42.11
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 42.11
Root \(0.567672i\) 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.42.10

$q$-expansion

\(f(q)\) \(=\) \(q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +O(q^{10})\) \(q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +110.969 q^{10} +1184.88 q^{11} +2015.25i q^{12} -15.3814 q^{13} +237.389 q^{14} +6186.48 q^{15} +4034.23 q^{16} -2662.44 q^{17} -154.730i q^{18} -2354.99i q^{19} -12447.8i q^{20} +13234.3 q^{21} +672.625i q^{22} +2891.76 q^{23} -2293.79 q^{24} -22587.6 q^{25} -8.73158i q^{26} +14444.9i q^{27} -26628.7i q^{28} +27723.8i q^{29} +3511.89i q^{30} +50974.7 q^{31} +6928.78i q^{32} +37498.6i q^{33} -1511.40i q^{34} -81745.9 q^{35} -17356.5 q^{36} -64225.2i q^{37} +1336.86 q^{38} -486.783i q^{39} +14168.3 q^{40} -87526.9 q^{41} +7512.77i q^{42} +(-77107.2 - 19386.6i) q^{43} +75450.6 q^{44} +53281.8i q^{45} +1641.57i q^{46} -111128. q^{47} +127674. i q^{48} -57224.7 q^{49} -12822.4i q^{50} -84259.9i q^{51} -979.452 q^{52} +221242. q^{53} -8200.00 q^{54} -231621. i q^{55} +30309.2 q^{56} +74529.6 q^{57} -15738.0 q^{58} -196251. q^{59} +393941. q^{60} +191470. i q^{61} +28936.9i q^{62} +113982. i q^{63} +254258. q^{64} +3006.76i q^{65} -21286.9 q^{66} +180423. q^{67} -169538. q^{68} +91517.0i q^{69} -46404.9i q^{70} -167558. i q^{71} -19755.5i q^{72} +652509. i q^{73} +36458.9 q^{74} -714844. i q^{75} -149960. i q^{76} -495493. i q^{77} +276.333 q^{78} +321108. q^{79} -788614. i q^{80} -655850. q^{81} -49686.6i q^{82} +49368.9 q^{83} +842734. q^{84} +520456. i q^{85} +(11005.3 - 43771.6i) q^{86} -877390. q^{87} +85879.2i q^{88} +1.33745e6i q^{89} -30246.6 q^{90} +6432.17i q^{91} +184140. q^{92} +1.61323e6i q^{93} -63084.1i q^{94} -460354. q^{95} -219279. q^{96} +830874. q^{97} -32484.9i q^{98} -322961. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.567672i 0.0709590i 0.999370 + 0.0354795i \(0.0112959\pi\)
−0.999370 + 0.0354795i \(0.988704\pi\)
\(3\) 31.6476i 1.17213i 0.810263 + 0.586066i \(0.199324\pi\)
−0.810263 + 0.586066i \(0.800676\pi\)
\(4\) 63.6777 0.994965
\(5\) 195.481i 1.56384i −0.623376 0.781922i \(-0.714239\pi\)
0.623376 0.781922i \(-0.285761\pi\)
\(6\) −17.9654 −0.0831734
\(7\) 418.179i 1.21918i −0.792716 0.609591i \(-0.791334\pi\)
0.792716 0.609591i \(-0.208666\pi\)
\(8\) 72.4791i 0.141561i
\(9\) −272.568 −0.373894
\(10\) 110.969 0.110969
\(11\) 1184.88 0.890220 0.445110 0.895476i \(-0.353165\pi\)
0.445110 + 0.895476i \(0.353165\pi\)
\(12\) 2015.25i 1.16623i
\(13\) −15.3814 −0.00700109 −0.00350054 0.999994i \(-0.501114\pi\)
−0.00350054 + 0.999994i \(0.501114\pi\)
\(14\) 237.389 0.0865119
\(15\) 6186.48 1.83303
\(16\) 4034.23 0.984920
\(17\) −2662.44 −0.541918 −0.270959 0.962591i \(-0.587341\pi\)
−0.270959 + 0.962591i \(0.587341\pi\)
\(18\) 154.730i 0.0265311i
\(19\) 2354.99i 0.343343i −0.985154 0.171671i \(-0.945083\pi\)
0.985154 0.171671i \(-0.0549167\pi\)
\(20\) 12447.8i 1.55597i
\(21\) 13234.3 1.42904
\(22\) 672.625i 0.0631691i
\(23\) 2891.76 0.237672 0.118836 0.992914i \(-0.462084\pi\)
0.118836 + 0.992914i \(0.462084\pi\)
\(24\) −2293.79 −0.165928
\(25\) −22587.6 −1.44561
\(26\) 8.73158i 0.000496790i
\(27\) 14444.9i 0.733879i
\(28\) 26628.7i 1.21304i
\(29\) 27723.8i 1.13673i 0.822775 + 0.568367i \(0.192424\pi\)
−0.822775 + 0.568367i \(0.807576\pi\)
\(30\) 3511.89i 0.130070i
\(31\) 50974.7 1.71108 0.855539 0.517738i \(-0.173226\pi\)
0.855539 + 0.517738i \(0.173226\pi\)
\(32\) 6928.78i 0.211450i
\(33\) 37498.6i 1.04345i
\(34\) 1511.40i 0.0384540i
\(35\) −81745.9 −1.90661
\(36\) −17356.5 −0.372011
\(37\) 64225.2i 1.26795i −0.773355 0.633973i \(-0.781423\pi\)
0.773355 0.633973i \(-0.218577\pi\)
\(38\) 1336.86 0.0243633
\(39\) 486.783i 0.00820620i
\(40\) 14168.3 0.221379
\(41\) −87526.9 −1.26996 −0.634980 0.772529i \(-0.718992\pi\)
−0.634980 + 0.772529i \(0.718992\pi\)
\(42\) 7512.77i 0.101403i
\(43\) −77107.2 19386.6i −0.969817 0.243836i
\(44\) 75450.6 0.885737
\(45\) 53281.8i 0.584711i
\(46\) 1641.57i 0.0168650i
\(47\) −111128. −1.07036 −0.535179 0.844739i \(-0.679756\pi\)
−0.535179 + 0.844739i \(0.679756\pi\)
\(48\) 127674.i 1.15446i
\(49\) −57224.7 −0.486402
\(50\) 12822.4i 0.102579i
\(51\) 84259.9i 0.635200i
\(52\) −979.452 −0.00696583
\(53\) 221242. 1.48607 0.743036 0.669251i \(-0.233385\pi\)
0.743036 + 0.669251i \(0.233385\pi\)
\(54\) −8200.00 −0.0520754
\(55\) 231621.i 1.39216i
\(56\) 30309.2 0.172588
\(57\) 74529.6 0.402443
\(58\) −15738.0 −0.0806615
\(59\) −196251. −0.955554 −0.477777 0.878481i \(-0.658557\pi\)
−0.477777 + 0.878481i \(0.658557\pi\)
\(60\) 393941. 1.82380
\(61\) 191470.i 0.843553i 0.906700 + 0.421776i \(0.138593\pi\)
−0.906700 + 0.421776i \(0.861407\pi\)
\(62\) 28936.9i 0.121416i
\(63\) 113982.i 0.455844i
\(64\) 254258. 0.969916
\(65\) 3006.76i 0.0109486i
\(66\) −21286.9 −0.0740425
\(67\) 180423. 0.599883 0.299941 0.953958i \(-0.403033\pi\)
0.299941 + 0.953958i \(0.403033\pi\)
\(68\) −169538. −0.539190
\(69\) 91517.0i 0.278583i
\(70\) 46404.9i 0.135291i
\(71\) 167558.i 0.468156i −0.972218 0.234078i \(-0.924793\pi\)
0.972218 0.234078i \(-0.0752071\pi\)
\(72\) 19755.5i 0.0529287i
\(73\) 652509.i 1.67733i 0.544650 + 0.838664i \(0.316663\pi\)
−0.544650 + 0.838664i \(0.683337\pi\)
\(74\) 36458.9 0.0899722
\(75\) 714844.i 1.69444i
\(76\) 149960.i 0.341614i
\(77\) 495493.i 1.08534i
\(78\) 276.333 0.000582304
\(79\) 321108. 0.651283 0.325641 0.945493i \(-0.394420\pi\)
0.325641 + 0.945493i \(0.394420\pi\)
\(80\) 788614.i 1.54026i
\(81\) −655850. −1.23410
\(82\) 49686.6i 0.0901151i
\(83\) 49368.9 0.0863414 0.0431707 0.999068i \(-0.486254\pi\)
0.0431707 + 0.999068i \(0.486254\pi\)
\(84\) 842734. 1.42185
\(85\) 520456.i 0.847476i
\(86\) 11005.3 43771.6i 0.0173023 0.0688172i
\(87\) −877390. −1.33240
\(88\) 85879.2i 0.126020i
\(89\) 1.33745e6i 1.89718i 0.316511 + 0.948589i \(0.397489\pi\)
−0.316511 + 0.948589i \(0.602511\pi\)
\(90\) −30246.6 −0.0414905
\(91\) 6432.17i 0.00853559i
\(92\) 184140. 0.236475
\(93\) 1.61323e6i 2.00561i
\(94\) 63084.1i 0.0759515i
\(95\) −460354. −0.536935
\(96\) −219279. −0.247847
\(97\) 830874. 0.910374 0.455187 0.890396i \(-0.349572\pi\)
0.455187 + 0.890396i \(0.349572\pi\)
\(98\) 32484.9i 0.0345146i
\(99\) −322961. −0.332847
\(100\) −1.43833e6 −1.43833
\(101\) −392754. −0.381203 −0.190601 0.981668i \(-0.561044\pi\)
−0.190601 + 0.981668i \(0.561044\pi\)
\(102\) 47832.0 0.0450732
\(103\) −1.70809e6 −1.56315 −0.781574 0.623812i \(-0.785583\pi\)
−0.781574 + 0.623812i \(0.785583\pi\)
\(104\) 1114.83i 0.000991079i
\(105\) 2.58706e6i 2.23480i
\(106\) 125593.i 0.105450i
\(107\) −1.45488e6 −1.18762 −0.593808 0.804607i \(-0.702376\pi\)
−0.593808 + 0.804607i \(0.702376\pi\)
\(108\) 919822.i 0.730184i
\(109\) 746414. 0.576369 0.288184 0.957575i \(-0.406948\pi\)
0.288184 + 0.957575i \(0.406948\pi\)
\(110\) 131485. 0.0987867
\(111\) 2.03257e6 1.48620
\(112\) 1.68703e6i 1.20080i
\(113\) 938948.i 0.650738i −0.945587 0.325369i \(-0.894511\pi\)
0.945587 0.325369i \(-0.105489\pi\)
\(114\) 42308.4i 0.0285570i
\(115\) 565282.i 0.371682i
\(116\) 1.76539e6i 1.13101i
\(117\) 4192.48 0.00261766
\(118\) 111406.i 0.0678052i
\(119\) 1.11338e6i 0.660696i
\(120\) 448391.i 0.259485i
\(121\) −367615. −0.207509
\(122\) −108692. −0.0598577
\(123\) 2.77001e6i 1.48856i
\(124\) 3.24596e6 1.70246
\(125\) 1.36106e6i 0.696864i
\(126\) −64704.6 −0.0323462
\(127\) 1.01692e6 0.496451 0.248225 0.968702i \(-0.420153\pi\)
0.248225 + 0.968702i \(0.420153\pi\)
\(128\) 587777.i 0.280274i
\(129\) 613540. 2.44026e6i 0.285807 1.13675i
\(130\) −1706.85 −0.000776903
\(131\) 3.69800e6i 1.64495i 0.568801 + 0.822475i \(0.307407\pi\)
−0.568801 + 0.822475i \(0.692593\pi\)
\(132\) 2.38783e6i 1.03820i
\(133\) −984806. −0.418597
\(134\) 102421.i 0.0425671i
\(135\) 2.82371e6 1.14767
\(136\) 192972.i 0.0767144i
\(137\) 3225.02i 0.00125421i −1.00000 0.000627105i \(-0.999800\pi\)
1.00000 0.000627105i \(-0.000199614\pi\)
\(138\) −51951.7 −0.0197680
\(139\) 2.48038e6 0.923579 0.461790 0.886989i \(-0.347207\pi\)
0.461790 + 0.886989i \(0.347207\pi\)
\(140\) −5.20539e6 −1.89701
\(141\) 3.51692e6i 1.25460i
\(142\) 95118.1 0.0332199
\(143\) −18225.1 −0.00623250
\(144\) −1.09960e6 −0.368255
\(145\) 5.41946e6 1.77767
\(146\) −370411. −0.119022
\(147\) 1.81102e6i 0.570128i
\(148\) 4.08972e6i 1.26156i
\(149\) 4.35151e6i 1.31547i 0.753249 + 0.657736i \(0.228486\pi\)
−0.753249 + 0.657736i \(0.771514\pi\)
\(150\) 405797. 0.120236
\(151\) 5.04923e6i 1.46654i 0.679937 + 0.733271i \(0.262007\pi\)
−0.679937 + 0.733271i \(0.737993\pi\)
\(152\) 170687. 0.0486039
\(153\) 725698. 0.202620
\(154\) 281278. 0.0770146
\(155\) 9.96457e6i 2.67586i
\(156\) 30997.3i 0.00816488i
\(157\) 4.88104e6i 1.26129i −0.776073 0.630643i \(-0.782791\pi\)
0.776073 0.630643i \(-0.217209\pi\)
\(158\) 182284.i 0.0462144i
\(159\) 7.00177e6i 1.74187i
\(160\) 1.35444e6 0.330674
\(161\) 1.20927e6i 0.289765i
\(162\) 372308.i 0.0875703i
\(163\) 3.64275e6i 0.841137i 0.907261 + 0.420569i \(0.138169\pi\)
−0.907261 + 0.420569i \(0.861831\pi\)
\(164\) −5.57352e6 −1.26357
\(165\) 7.33025e6 1.63180
\(166\) 28025.3i 0.00612670i
\(167\) −8.62839e6 −1.85259 −0.926297 0.376793i \(-0.877027\pi\)
−0.926297 + 0.376793i \(0.877027\pi\)
\(168\) 959214.i 0.202296i
\(169\) −4.82657e6 −0.999951
\(170\) −295448. −0.0601361
\(171\) 641895.i 0.128374i
\(172\) −4.91001e6 1.23450e6i −0.964933 0.242608i
\(173\) −2.87792e6 −0.555827 −0.277914 0.960606i \(-0.589643\pi\)
−0.277914 + 0.960606i \(0.589643\pi\)
\(174\) 498070.i 0.0945459i
\(175\) 9.44568e6i 1.76246i
\(176\) 4.78009e6 0.876795
\(177\) 6.21086e6i 1.12004i
\(178\) −759234. −0.134622
\(179\) 2.16118e6i 0.376819i 0.982091 + 0.188409i \(0.0603331\pi\)
−0.982091 + 0.188409i \(0.939667\pi\)
\(180\) 3.39287e6i 0.581767i
\(181\) 7.68800e6 1.29652 0.648258 0.761421i \(-0.275498\pi\)
0.648258 + 0.761421i \(0.275498\pi\)
\(182\) −3651.37 −0.000605677
\(183\) −6.05957e6 −0.988755
\(184\) 209592.i 0.0336450i
\(185\) −1.25548e7 −1.98287
\(186\) −915784. −0.142316
\(187\) −3.15468e6 −0.482426
\(188\) −7.07636e6 −1.06497
\(189\) 6.04058e6 0.894732
\(190\) 261330.i 0.0381004i
\(191\) 9.03078e6i 1.29606i −0.761614 0.648030i \(-0.775593\pi\)
0.761614 0.648030i \(-0.224407\pi\)
\(192\) 8.04663e6i 1.13687i
\(193\) 1.15620e7 1.60827 0.804137 0.594443i \(-0.202628\pi\)
0.804137 + 0.594443i \(0.202628\pi\)
\(194\) 471664.i 0.0645992i
\(195\) −95156.7 −0.0128332
\(196\) −3.64394e6 −0.483953
\(197\) 934269. 0.122201 0.0611003 0.998132i \(-0.480539\pi\)
0.0611003 + 0.998132i \(0.480539\pi\)
\(198\) 183336.i 0.0236185i
\(199\) 3.67317e6i 0.466103i −0.972464 0.233051i \(-0.925129\pi\)
0.972464 0.233051i \(-0.0748711\pi\)
\(200\) 1.63713e6i 0.204642i
\(201\) 5.70994e6i 0.703142i
\(202\) 222955.i 0.0270498i
\(203\) 1.15935e7 1.38588
\(204\) 5.36548e6i 0.632001i
\(205\) 1.71098e7i 1.98602i
\(206\) 969638.i 0.110920i
\(207\) −788201. −0.0888640
\(208\) −62052.1 −0.00689551
\(209\) 2.79038e6i 0.305650i
\(210\) 1.46860e6 0.158579
\(211\) 1.58871e7i 1.69121i −0.533806 0.845607i \(-0.679239\pi\)
0.533806 0.845607i \(-0.320761\pi\)
\(212\) 1.40882e7 1.47859
\(213\) 5.30281e6 0.548741
\(214\) 825896.i 0.0842721i
\(215\) −3.78971e6 + 1.50730e7i −0.381321 + 1.51664i
\(216\) −1.04696e6 −0.103889
\(217\) 2.13166e7i 2.08611i
\(218\) 423719.i 0.0408986i
\(219\) −2.06503e7 −1.96605
\(220\) 1.47491e7i 1.38516i
\(221\) 40952.1 0.00379402
\(222\) 1.15383e6i 0.105459i
\(223\) 14369.2i 0.00129574i −1.00000 0.000647870i \(-0.999794\pi\)
1.00000 0.000647870i \(-0.000206224\pi\)
\(224\) 2.89747e6 0.257795
\(225\) 6.15668e6 0.540504
\(226\) 533015. 0.0461757
\(227\) 1.05446e7i 0.901475i −0.892657 0.450737i \(-0.851161\pi\)
0.892657 0.450737i \(-0.148839\pi\)
\(228\) 4.74588e6 0.400417
\(229\) −2.56800e6 −0.213840 −0.106920 0.994268i \(-0.534099\pi\)
−0.106920 + 0.994268i \(0.534099\pi\)
\(230\) 320895. 0.0263742
\(231\) 1.56811e7 1.27216
\(232\) −2.00940e6 −0.160917
\(233\) 1.82065e7i 1.43933i 0.694323 + 0.719663i \(0.255704\pi\)
−0.694323 + 0.719663i \(0.744296\pi\)
\(234\) 2379.95i 0.000185747i
\(235\) 2.17233e7i 1.67387i
\(236\) −1.24968e7 −0.950743
\(237\) 1.01623e7i 0.763390i
\(238\) −632034. −0.0468824
\(239\) 1.45860e7 1.06842 0.534212 0.845351i \(-0.320608\pi\)
0.534212 + 0.845351i \(0.320608\pi\)
\(240\) 2.49577e7 1.80539
\(241\) 1.31046e7i 0.936210i −0.883673 0.468105i \(-0.844937\pi\)
0.883673 0.468105i \(-0.155063\pi\)
\(242\) 208685.i 0.0147246i
\(243\) 1.02257e7i 0.712645i
\(244\) 1.21924e7i 0.839305i
\(245\) 1.11863e7i 0.760658i
\(246\) 1.57246e6 0.105627
\(247\) 36223.0i 0.00240377i
\(248\) 3.69460e6i 0.242222i
\(249\) 1.56240e6i 0.101203i
\(250\) −772637. −0.0494488
\(251\) 1.75490e6 0.110977 0.0554883 0.998459i \(-0.482328\pi\)
0.0554883 + 0.998459i \(0.482328\pi\)
\(252\) 7.25814e6i 0.453549i
\(253\) 3.42639e6 0.211580
\(254\) 577278.i 0.0352277i
\(255\) −1.64712e7 −0.993354
\(256\) 1.59388e7 0.950028
\(257\) 1.47353e7i 0.868082i −0.900893 0.434041i \(-0.857087\pi\)
0.900893 0.434041i \(-0.142913\pi\)
\(258\) 1.38527e6 + 348289.i 0.0806629 + 0.0202806i
\(259\) −2.68577e7 −1.54585
\(260\) 191464.i 0.0108935i
\(261\) 7.55663e6i 0.425017i
\(262\) −2.09925e6 −0.116724
\(263\) 1.12596e7i 0.618951i −0.950907 0.309475i \(-0.899847\pi\)
0.950907 0.309475i \(-0.100153\pi\)
\(264\) −2.71787e6 −0.147712
\(265\) 4.32485e7i 2.32399i
\(266\) 559047.i 0.0297032i
\(267\) −4.23271e7 −2.22374
\(268\) 1.14889e7 0.596862
\(269\) −1.96066e6 −0.100727 −0.0503634 0.998731i \(-0.516038\pi\)
−0.0503634 + 0.998731i \(0.516038\pi\)
\(270\) 1.60294e6i 0.0814378i
\(271\) 6.70792e6 0.337039 0.168519 0.985698i \(-0.446101\pi\)
0.168519 + 0.985698i \(0.446101\pi\)
\(272\) −1.07409e7 −0.533746
\(273\) −203563. −0.0100048
\(274\) 1830.75 8.89975e−5
\(275\) −2.67637e7 −1.28691
\(276\) 5.82760e6i 0.277180i
\(277\) 2.17631e7i 1.02396i 0.858998 + 0.511979i \(0.171087\pi\)
−0.858998 + 0.511979i \(0.828913\pi\)
\(278\) 1.40804e6i 0.0655363i
\(279\) −1.38941e7 −0.639761
\(280\) 5.92487e6i 0.269901i
\(281\) 2.86481e7 1.29115 0.645575 0.763697i \(-0.276618\pi\)
0.645575 + 0.763697i \(0.276618\pi\)
\(282\) 1.99646e6 0.0890252
\(283\) −3.20199e7 −1.41274 −0.706369 0.707844i \(-0.749668\pi\)
−0.706369 + 0.707844i \(0.749668\pi\)
\(284\) 1.06697e7i 0.465799i
\(285\) 1.45691e7i 0.629358i
\(286\) 10345.9i 0.000442252i
\(287\) 3.66019e7i 1.54831i
\(288\) 1.88857e6i 0.0790597i
\(289\) −1.70490e7 −0.706325
\(290\) 3.07648e6i 0.126142i
\(291\) 2.62951e7i 1.06708i
\(292\) 4.15503e7i 1.66888i
\(293\) 7.53752e6 0.299658 0.149829 0.988712i \(-0.452128\pi\)
0.149829 + 0.988712i \(0.452128\pi\)
\(294\) 1.02807e6 0.0404557
\(295\) 3.83632e7i 1.49434i
\(296\) 4.65499e6 0.179491
\(297\) 1.71156e7i 0.653314i
\(298\) −2.47023e6 −0.0933446
\(299\) −44479.2 −0.00166396
\(300\) 4.55197e7i 1.68591i
\(301\) −8.10708e6 + 3.22446e7i −0.297280 + 1.18238i
\(302\) −2.86631e6 −0.104064
\(303\) 1.24297e7i 0.446820i
\(304\) 9.50056e6i 0.338165i
\(305\) 3.74287e7 1.31919
\(306\) 411959.i 0.0143777i
\(307\) 4.65611e7 1.60919 0.804596 0.593823i \(-0.202382\pi\)
0.804596 + 0.593823i \(0.202382\pi\)
\(308\) 3.15519e7i 1.07987i
\(309\) 5.40570e7i 1.83222i
\(310\) 5.65661e6 0.189876
\(311\) −8.46971e6 −0.281571 −0.140785 0.990040i \(-0.544963\pi\)
−0.140785 + 0.990040i \(0.544963\pi\)
\(312\) 35281.6 0.00116168
\(313\) 4.97624e6i 0.162281i 0.996703 + 0.0811406i \(0.0258563\pi\)
−0.996703 + 0.0811406i \(0.974144\pi\)
\(314\) 2.77083e6 0.0894996
\(315\) 2.22813e7 0.712869
\(316\) 2.04474e7 0.648004
\(317\) −4.15142e7 −1.30322 −0.651611 0.758553i \(-0.725907\pi\)
−0.651611 + 0.758553i \(0.725907\pi\)
\(318\) −3.97471e6 −0.123602
\(319\) 3.28494e7i 1.01194i
\(320\) 4.97024e7i 1.51680i
\(321\) 4.60434e7i 1.39204i
\(322\) 686470. 0.0205615
\(323\) 6.27002e6i 0.186064i
\(324\) −4.17630e7 −1.22788
\(325\) 347429. 0.0101208
\(326\) −2.06789e6 −0.0596863
\(327\) 2.36222e7i 0.675580i
\(328\) 6.34387e6i 0.179777i
\(329\) 4.64713e7i 1.30496i
\(330\) 4.16118e6i 0.115791i
\(331\) 2.14901e7i 0.592589i −0.955097 0.296295i \(-0.904249\pi\)
0.955097 0.296295i \(-0.0957510\pi\)
\(332\) 3.14370e6 0.0859066
\(333\) 1.75058e7i 0.474077i
\(334\) 4.89810e6i 0.131458i
\(335\) 3.52691e7i 0.938124i
\(336\) 5.33904e7 1.40749
\(337\) −5.08482e6 −0.132858 −0.0664288 0.997791i \(-0.521161\pi\)
−0.0664288 + 0.997791i \(0.521161\pi\)
\(338\) 2.73991e6i 0.0709556i
\(339\) 2.97154e7 0.762751
\(340\) 3.31415e7i 0.843209i
\(341\) 6.03991e7 1.52324
\(342\) −364386. −0.00910927
\(343\) 2.52682e7i 0.626169i
\(344\) 1.40513e6 5.58866e6i 0.0345175 0.137288i
\(345\) 1.78898e7 0.435660
\(346\) 1.63371e6i 0.0394410i
\(347\) 3.64450e6i 0.0872267i −0.999048 0.0436134i \(-0.986113\pi\)
0.999048 0.0436134i \(-0.0138870\pi\)
\(348\) −5.58702e7 −1.32569
\(349\) 4.18869e7i 0.985375i −0.870206 0.492687i \(-0.836015\pi\)
0.870206 0.492687i \(-0.163985\pi\)
\(350\) −5.36205e6 −0.125062
\(351\) 222183.i 0.00513795i
\(352\) 8.20979e6i 0.188237i
\(353\) 3.31754e7 0.754209 0.377104 0.926171i \(-0.376920\pi\)
0.377104 + 0.926171i \(0.376920\pi\)
\(354\) 3.52573e6 0.0794766
\(355\) −3.27544e7 −0.732123
\(356\) 8.51659e7i 1.88762i
\(357\) −3.52357e7 −0.774424
\(358\) −1.22684e6 −0.0267387
\(359\) 6.09915e6 0.131821 0.0659107 0.997826i \(-0.479005\pi\)
0.0659107 + 0.997826i \(0.479005\pi\)
\(360\) −3.86182e6 −0.0827722
\(361\) 4.14999e7 0.882116
\(362\) 4.36426e6i 0.0919994i
\(363\) 1.16341e7i 0.243228i
\(364\) 409586.i 0.00849261i
\(365\) 1.27553e8 2.62308
\(366\) 3.43985e6i 0.0701611i
\(367\) −4.06076e7 −0.821502 −0.410751 0.911748i \(-0.634733\pi\)
−0.410751 + 0.911748i \(0.634733\pi\)
\(368\) 1.16660e7 0.234088
\(369\) 2.38571e7 0.474830
\(370\) 7.12700e6i 0.140702i
\(371\) 9.25188e7i 1.81179i
\(372\) 1.02727e8i 1.99551i
\(373\) 2.63198e7i 0.507172i −0.967313 0.253586i \(-0.918390\pi\)
0.967313 0.253586i \(-0.0816101\pi\)
\(374\) 1.79083e6i 0.0342325i
\(375\) −4.30743e7 −0.816816
\(376\) 8.05444e6i 0.151521i
\(377\) 426430.i 0.00795837i
\(378\) 3.42907e6i 0.0634893i
\(379\) −3.23575e7 −0.594370 −0.297185 0.954820i \(-0.596048\pi\)
−0.297185 + 0.954820i \(0.596048\pi\)
\(380\) −2.93143e7 −0.534231
\(381\) 3.21831e7i 0.581906i
\(382\) 5.12653e6 0.0919672
\(383\) 4.85406e7i 0.863991i 0.901876 + 0.431995i \(0.142190\pi\)
−0.901876 + 0.431995i \(0.857810\pi\)
\(384\) −1.86017e7 −0.328518
\(385\) −9.68592e7 −1.69730
\(386\) 6.56341e6i 0.114122i
\(387\) 2.10170e7 + 5.28418e6i 0.362608 + 0.0911685i
\(388\) 5.29082e7 0.905790
\(389\) 1.25283e7i 0.212834i 0.994322 + 0.106417i \(0.0339379\pi\)
−0.994322 + 0.106417i \(0.966062\pi\)
\(390\) 54017.8i 0.000910632i
\(391\) −7.69914e6 −0.128799
\(392\) 4.14760e6i 0.0688555i
\(393\) −1.17033e8 −1.92810
\(394\) 530359.i 0.00867124i
\(395\) 6.27703e7i 1.01851i
\(396\) −2.05655e7 −0.331171
\(397\) −5.82784e7 −0.931399 −0.465700 0.884943i \(-0.654197\pi\)
−0.465700 + 0.884943i \(0.654197\pi\)
\(398\) 2.08516e6 0.0330742
\(399\) 3.11667e7i 0.490651i
\(400\) −9.11238e7 −1.42381
\(401\) 1.27270e8 1.97375 0.986877 0.161474i \(-0.0516249\pi\)
0.986877 + 0.161474i \(0.0516249\pi\)
\(402\) −3.24137e6 −0.0498943
\(403\) −784062. −0.0119794
\(404\) −2.50097e7 −0.379283
\(405\) 1.28206e8i 1.92994i
\(406\) 6.58131e6i 0.0983409i
\(407\) 7.60993e7i 1.12875i
\(408\) 6.10708e6 0.0899194
\(409\) 1.89469e7i 0.276928i −0.990367 0.138464i \(-0.955783\pi\)
0.990367 0.138464i \(-0.0442166\pi\)
\(410\) −9.71276e6 −0.140926
\(411\) 102064. 0.00147010
\(412\) −1.08768e8 −1.55528
\(413\) 8.20680e7i 1.16499i
\(414\) 447440.i 0.00630571i
\(415\) 9.65065e6i 0.135024i
\(416\) 106574.i 0.00148038i
\(417\) 7.84981e7i 1.08256i
\(418\) 1.58402e6 0.0216887
\(419\) 7.41669e7i 1.00825i −0.863631 0.504124i \(-0.831815\pi\)
0.863631 0.504124i \(-0.168185\pi\)
\(420\) 1.64738e8i 2.22355i
\(421\) 7.12823e7i 0.955291i −0.878553 0.477645i \(-0.841490\pi\)
0.878553 0.477645i \(-0.158510\pi\)
\(422\) 9.01869e6 0.120007
\(423\) 3.02899e7 0.400200
\(424\) 1.60354e7i 0.210370i
\(425\) 6.01384e7 0.783402
\(426\) 3.01026e6i 0.0389381i
\(427\) 8.00689e7 1.02844
\(428\) −9.26436e7 −1.18164
\(429\) 576781.i 0.00730532i
\(430\) −8.55650e6 2.15131e6i −0.107619 0.0270582i
\(431\) −6.60708e7 −0.825235 −0.412617 0.910904i \(-0.635385\pi\)
−0.412617 + 0.910904i \(0.635385\pi\)
\(432\) 5.82743e7i 0.722812i
\(433\) 2.98848e7i 0.368118i −0.982915 0.184059i \(-0.941076\pi\)
0.982915 0.184059i \(-0.0589237\pi\)
\(434\) 1.21008e7 0.148029
\(435\) 1.71513e8i 2.08367i
\(436\) 4.75300e7 0.573467
\(437\) 6.81005e6i 0.0816029i
\(438\) 1.17226e7i 0.139509i
\(439\) −4.16010e7 −0.491711 −0.245855 0.969306i \(-0.579069\pi\)
−0.245855 + 0.969306i \(0.579069\pi\)
\(440\) 1.67877e7 0.197076
\(441\) 1.55977e7 0.181863
\(442\) 23247.4i 0.000269220i
\(443\) 1.05065e8 1.20851 0.604253 0.796793i \(-0.293472\pi\)
0.604253 + 0.796793i \(0.293472\pi\)
\(444\) 1.29430e8 1.47872
\(445\) 2.61446e8 2.96689
\(446\) 8157.00 9.19445e−5
\(447\) −1.37715e8 −1.54191
\(448\) 1.06325e8i 1.18250i
\(449\) 1.11616e8i 1.23307i 0.787326 + 0.616537i \(0.211465\pi\)
−0.787326 + 0.616537i \(0.788535\pi\)
\(450\) 3.49498e6i 0.0383536i
\(451\) −1.03709e8 −1.13054
\(452\) 5.97901e7i 0.647462i
\(453\) −1.59796e8 −1.71898
\(454\) 5.98589e6 0.0639678
\(455\) 1.25736e6 0.0133483
\(456\) 5.40184e6i 0.0569701i
\(457\) 9.44586e7i 0.989676i 0.868985 + 0.494838i \(0.164773\pi\)
−0.868985 + 0.494838i \(0.835227\pi\)
\(458\) 1.45778e6i 0.0151739i
\(459\) 3.84589e7i 0.397703i
\(460\) 3.59959e7i 0.369811i
\(461\) −7.58053e7 −0.773743 −0.386871 0.922134i \(-0.626444\pi\)
−0.386871 + 0.922134i \(0.626444\pi\)
\(462\) 8.90175e6i 0.0902713i
\(463\) 1.66599e8i 1.67853i 0.543723 + 0.839265i \(0.317014\pi\)
−0.543723 + 0.839265i \(0.682986\pi\)
\(464\) 1.11844e8i 1.11959i
\(465\) 3.15354e8 3.13646
\(466\) −1.03353e7 −0.102133
\(467\) 1.95492e8i 1.91945i −0.280937 0.959726i \(-0.590645\pi\)
0.280937 0.959726i \(-0.409355\pi\)
\(468\) 266968. 0.00260448
\(469\) 7.54490e7i 0.731366i
\(470\) −1.23317e7 −0.118776
\(471\) 1.54473e8 1.47839
\(472\) 1.42241e7i 0.135269i
\(473\) −9.13630e7 2.29709e7i −0.863350 0.217067i
\(474\) −5.76885e6 −0.0541694
\(475\) 5.31936e7i 0.496339i
\(476\) 7.08974e7i 0.657370i
\(477\) −6.03036e7 −0.555633
\(478\) 8.28009e6i 0.0758143i
\(479\) 1.51297e8 1.37665 0.688326 0.725402i \(-0.258346\pi\)
0.688326 + 0.725402i \(0.258346\pi\)
\(480\) 4.28648e7i 0.387594i
\(481\) 987873.i 0.00887699i
\(482\) 7.43913e6 0.0664326
\(483\) 3.82705e7 0.339643
\(484\) −2.34089e7 −0.206464
\(485\) 1.62420e8i 1.42368i
\(486\) 5.80484e6 0.0505686
\(487\) −4.60012e7 −0.398275 −0.199137 0.979972i \(-0.563814\pi\)
−0.199137 + 0.979972i \(0.563814\pi\)
\(488\) −1.38776e7 −0.119414
\(489\) −1.15284e8 −0.985924
\(490\) −6.35017e6 −0.0539755
\(491\) 1.19775e8i 1.01187i −0.862573 0.505933i \(-0.831148\pi\)
0.862573 0.505933i \(-0.168852\pi\)
\(492\) 1.76388e8i 1.48107i
\(493\) 7.38130e7i 0.616016i
\(494\) −20562.8 −0.000170569
\(495\) 6.31327e7i 0.520521i
\(496\) 2.05644e8 1.68527
\(497\) −7.00693e7 −0.570767
\(498\) −886934. −0.00718130
\(499\) 4.05522e7i 0.326372i 0.986595 + 0.163186i \(0.0521771\pi\)
−0.986595 + 0.163186i \(0.947823\pi\)
\(500\) 8.66693e7i 0.693355i
\(501\) 2.73068e8i 2.17149i
\(502\) 996209.i 0.00787479i
\(503\) 6.33952e7i 0.498141i −0.968485 0.249071i \(-0.919875\pi\)
0.968485 0.249071i \(-0.0801251\pi\)
\(504\) −8.26134e6 −0.0645296
\(505\) 7.67757e7i 0.596142i
\(506\) 1.94507e6i 0.0150135i
\(507\) 1.52749e8i 1.17207i
\(508\) 6.47553e7 0.493951
\(509\) −1.40835e8 −1.06797 −0.533984 0.845494i \(-0.679306\pi\)
−0.533984 + 0.845494i \(0.679306\pi\)
\(510\) 9.35023e6i 0.0704874i
\(511\) 2.72866e8 2.04497
\(512\) 4.66658e7i 0.347687i
\(513\) 3.40177e7 0.251972
\(514\) 8.36484e6 0.0615982
\(515\) 3.33899e8i 2.44452i
\(516\) 3.90688e7 1.55390e8i 0.284368 1.13103i
\(517\) −1.31673e8 −0.952853
\(518\) 1.52463e7i 0.109692i
\(519\) 9.10791e7i 0.651503i
\(520\) −217927. −0.00154989
\(521\) 1.55851e8i 1.10203i 0.834494 + 0.551017i \(0.185760\pi\)
−0.834494 + 0.551017i \(0.814240\pi\)
\(522\) 4.28969e6 0.0301588
\(523\) 1.98296e8i 1.38614i 0.720869 + 0.693071i \(0.243743\pi\)
−0.720869 + 0.693071i \(0.756257\pi\)
\(524\) 2.35480e8i 1.63667i
\(525\) −2.98933e8 −2.06584
\(526\) 6.39177e6 0.0439201
\(527\) −1.35717e8 −0.927264
\(528\) 1.51278e8i 1.02772i
\(529\) −1.39674e8 −0.943512
\(530\) 2.45510e7 0.164908
\(531\) 5.34918e7 0.357276
\(532\) −6.27103e7 −0.416489
\(533\) 1.34629e6 0.00889110
\(534\) 2.40279e7i 0.157795i
\(535\) 2.84401e8i 1.85725i
\(536\) 1.30769e7i 0.0849199i
\(537\) −6.83961e7 −0.441681
\(538\) 1.11301e6i 0.00714747i
\(539\) −6.78046e7 −0.433005
\(540\) 1.79807e8 1.14189
\(541\) −4.07648e7 −0.257450 −0.128725 0.991680i \(-0.541089\pi\)
−0.128725 + 0.991680i \(0.541089\pi\)
\(542\) 3.80790e6i 0.0239159i
\(543\) 2.43306e8i 1.51969i
\(544\) 1.84475e7i 0.114588i
\(545\) 1.45909e8i 0.901351i
\(546\) 115557.i 0.000709934i
\(547\) −1.28177e8 −0.783157 −0.391578 0.920145i \(-0.628071\pi\)
−0.391578 + 0.920145i \(0.628071\pi\)
\(548\) 205362.i 0.00124789i
\(549\) 5.21888e7i 0.315399i
\(550\) 1.51930e7i 0.0913179i
\(551\) 6.52892e7 0.390289
\(552\) −6.63307e6 −0.0394364
\(553\) 1.34281e8i 0.794032i
\(554\) −1.23543e7 −0.0726590
\(555\) 3.97328e8i 2.32418i
\(556\) 1.57945e8 0.918929
\(557\) −6.31632e6 −0.0365509 −0.0182755 0.999833i \(-0.505818\pi\)
−0.0182755 + 0.999833i \(0.505818\pi\)
\(558\) 7.88729e6i 0.0453968i
\(559\) 1.18602e6 + 298193.i 0.00678977 + 0.00170711i
\(560\) −3.29782e8 −1.87786
\(561\) 9.98380e7i 0.565467i
\(562\) 1.62627e7i 0.0916187i
\(563\) −2.95599e8 −1.65645 −0.828224 0.560398i \(-0.810648\pi\)
−0.828224 + 0.560398i \(0.810648\pi\)
\(564\) 2.23950e8i 1.24828i
\(565\) −1.83546e8 −1.01765
\(566\) 1.81768e7i 0.100246i
\(567\) 2.74263e8i 1.50459i
\(568\) 1.21445e7 0.0662725
\(569\) −9.63612e7 −0.523077 −0.261538 0.965193i \(-0.584230\pi\)
−0.261538 + 0.965193i \(0.584230\pi\)
\(570\) 8.27047e6 0.0446586
\(571\) 1.90132e8i 1.02128i −0.859794 0.510641i \(-0.829408\pi\)
0.859794 0.510641i \(-0.170592\pi\)
\(572\) −1.16054e6 −0.00620112
\(573\) 2.85802e8 1.51915
\(574\) −2.07779e7 −0.109867
\(575\) −6.53179e7 −0.343581
\(576\) −6.93026e7 −0.362645
\(577\) 2.43390e8i 1.26699i −0.773745 0.633497i \(-0.781619\pi\)
0.773745 0.633497i \(-0.218381\pi\)
\(578\) 9.67822e6i 0.0501201i
\(579\) 3.65909e8i 1.88511i
\(580\) 3.45099e8 1.76872
\(581\) 2.06450e7i 0.105266i
\(582\) −1.49270e7 −0.0757188
\(583\) 2.62146e8 1.32293
\(584\) −4.72933e7 −0.237444
\(585\) 819548.i 0.00409361i
\(586\) 4.27884e6i 0.0212634i
\(587\) 4.66573e6i 0.0230678i −0.999933 0.0115339i \(-0.996329\pi\)
0.999933 0.0115339i \(-0.00367143\pi\)
\(588\) 1.15322e8i 0.567257i
\(589\) 1.20045e8i 0.587486i
\(590\) −2.17777e7 −0.106037
\(591\) 2.95673e7i 0.143235i
\(592\) 2.59099e8i 1.24882i
\(593\) 4.86626e7i 0.233363i −0.993169 0.116681i \(-0.962774\pi\)
0.993169 0.116681i \(-0.0372256\pi\)
\(594\) −9.71603e6 −0.0463585
\(595\) 2.17644e8 1.03323
\(596\) 2.77094e8i 1.30885i
\(597\) 1.16247e8 0.546334
\(598\) 25249.6i 0.000118073i
\(599\) 2.58627e8 1.20335 0.601677 0.798739i \(-0.294499\pi\)
0.601677 + 0.798739i \(0.294499\pi\)
\(600\) 5.18113e7 0.239867
\(601\) 3.22569e8i 1.48594i 0.669327 + 0.742968i \(0.266582\pi\)
−0.669327 + 0.742968i \(0.733418\pi\)
\(602\) −1.83044e7 4.60217e6i −0.0839007 0.0210947i
\(603\) −4.91775e7 −0.224292
\(604\) 3.21524e8i 1.45916i
\(605\) 7.18616e7i 0.324512i
\(606\) 7.05599e6 0.0317059
\(607\) 8.42013e6i 0.0376489i 0.999823 + 0.0188245i \(0.00599237\pi\)
−0.999823 + 0.0188245i \(0.994008\pi\)
\(608\) 1.63172e7 0.0725997
\(609\) 3.66906e8i 1.62444i
\(610\) 2.12473e7i 0.0936081i
\(611\) 1.70930e6 0.00749366
\(612\) 4.62108e7 0.201600
\(613\) −2.68866e8 −1.16722 −0.583611 0.812033i \(-0.698361\pi\)
−0.583611 + 0.812033i \(0.698361\pi\)
\(614\) 2.64314e7i 0.114187i
\(615\) −5.41484e8 −2.32788
\(616\) 3.59129e7 0.153641
\(617\) 1.31437e8 0.559581 0.279790 0.960061i \(-0.409735\pi\)
0.279790 + 0.960061i \(0.409735\pi\)
\(618\) 3.06867e7 0.130012
\(619\) −1.09866e8 −0.463224 −0.231612 0.972808i \(-0.574400\pi\)
−0.231612 + 0.972808i \(0.574400\pi\)
\(620\) 6.34521e8i 2.66239i
\(621\) 4.17713e7i 0.174423i
\(622\) 4.80802e6i 0.0199800i
\(623\) 5.59294e8 2.31300
\(624\) 1.96380e6i 0.00808245i
\(625\) −8.68709e7 −0.355823
\(626\) −2.82487e6 −0.0115153
\(627\) 8.83088e7 0.358263
\(628\) 3.10814e8i 1.25493i
\(629\) 1.70996e8i 0.687123i
\(630\) 1.26485e7i 0.0505845i
\(631\) 4.55728e8i 1.81392i −0.421220 0.906958i \(-0.638398\pi\)
0.421220 0.906958i \(-0.361602\pi\)
\(632\) 2.32736e7i 0.0921961i
\(633\) 5.02790e8 1.98233
\(634\) 2.35664e7i 0.0924754i
\(635\) 1.98788e8i 0.776372i
\(636\) 4.45857e8i 1.73310i
\(637\) 880196. 0.00340534
\(638\) −1.86477e7 −0.0718064
\(639\) 4.56711e7i 0.175041i
\(640\) 1.14899e8 0.438305
\(641\) 6.65150e7i 0.252549i −0.991995 0.126274i \(-0.959698\pi\)
0.991995 0.126274i \(-0.0403020\pi\)
\(642\) 2.61376e7 0.0987780
\(643\) −7.14740e7 −0.268853 −0.134427 0.990924i \(-0.542919\pi\)
−0.134427 + 0.990924i \(0.542919\pi\)
\(644\) 7.70037e7i 0.288306i
\(645\) −4.77022e8 1.19935e8i −1.77770 0.446958i
\(646\) −3.55932e6 −0.0132029
\(647\) 2.68031e8i 0.989627i −0.868999 0.494813i \(-0.835236\pi\)
0.868999 0.494813i \(-0.164764\pi\)
\(648\) 4.75354e7i 0.174700i
\(649\) −2.32534e8 −0.850653
\(650\) 197226.i 0.000718165i
\(651\) 6.74617e8 2.44520
\(652\) 2.31962e8i 0.836902i
\(653\) 4.14641e8i 1.48913i 0.667549 + 0.744566i \(0.267343\pi\)
−0.667549 + 0.744566i \(0.732657\pi\)
\(654\) −1.34097e7 −0.0479385
\(655\) 7.22887e8 2.57245
\(656\) −3.53104e8 −1.25081
\(657\) 1.77853e8i 0.627142i
\(658\) −2.63805e7 −0.0925987
\(659\) −2.34687e7 −0.0820036 −0.0410018 0.999159i \(-0.513055\pi\)
−0.0410018 + 0.999159i \(0.513055\pi\)
\(660\) 4.66774e8 1.62358
\(661\) −1.37046e8 −0.474527 −0.237264 0.971445i \(-0.576251\pi\)
−0.237264 + 0.971445i \(0.576251\pi\)
\(662\) 1.21993e7 0.0420496
\(663\) 1.29603e6i 0.00444709i
\(664\) 3.57821e6i 0.0122225i
\(665\) 1.92511e8i 0.654620i
\(666\) −9.93754e6 −0.0336400
\(667\) 8.01704e7i 0.270170i
\(668\) −5.49437e8 −1.84327
\(669\) 454750. 0.00151878
\(670\) 2.00213e7 0.0665683
\(671\) 2.26870e8i 0.750947i
\(672\) 9.16980e7i 0.302170i
\(673\) 2.12788e8i 0.698075i −0.937109 0.349037i \(-0.886509\pi\)
0.937109 0.349037i \(-0.113491\pi\)
\(674\) 2.88651e6i 0.00942744i
\(675\) 3.26277e8i 1.06090i
\(676\) −3.07345e8 −0.994916
\(677\) 2.63101e8i 0.847923i 0.905680 + 0.423962i \(0.139361\pi\)
−0.905680 + 0.423962i \(0.860639\pi\)
\(678\) 1.68686e7i 0.0541241i
\(679\) 3.47454e8i 1.10991i
\(680\) −3.77222e7 −0.119969
\(681\) 3.33712e8 1.05665
\(682\) 3.42869e7i 0.108087i
\(683\) −1.47190e8 −0.461972 −0.230986 0.972957i \(-0.574195\pi\)
−0.230986 + 0.972957i \(0.574195\pi\)
\(684\) 4.08744e7i 0.127727i
\(685\) −630428. −0.00196139
\(686\) 1.43440e7 0.0444323
\(687\) 8.12710e7i 0.250649i
\(688\) −3.11068e8 7.82102e7i −0.955192 0.240158i
\(689\) −3.40301e6 −0.0104041
\(690\) 1.01555e7i 0.0309140i
\(691\) 6.71399e7i 0.203492i −0.994810 0.101746i \(-0.967557\pi\)
0.994810 0.101746i \(-0.0324428\pi\)
\(692\) −1.83259e8 −0.553029
\(693\) 1.35056e8i 0.405801i
\(694\) 2.06888e6 0.00618952
\(695\) 4.84866e8i 1.44433i
\(696\) 6.35925e7i 0.188616i
\(697\) 2.33036e8 0.688215
\(698\) 2.37780e7 0.0699213
\(699\) −5.76192e8 −1.68708
\(700\) 6.01480e8i 1.75359i
\(701\) −3.36019e8 −0.975461 −0.487730 0.872994i \(-0.662175\pi\)
−0.487730 + 0.872994i \(0.662175\pi\)
\(702\) 126127. 0.000364584
\(703\) −1.51250e8 −0.435340
\(704\) 3.01265e8 0.863438
\(705\) −6.87490e8 −1.96200
\(706\) 1.88327e7i 0.0535179i
\(707\) 1.64241e8i 0.464755i
\(708\) 3.95494e8i 1.11440i
\(709\) −2.25368e8 −0.632344 −0.316172 0.948702i \(-0.602398\pi\)
−0.316172 + 0.948702i \(0.602398\pi\)
\(710\) 1.85937e7i 0.0519508i
\(711\) −8.75239e7 −0.243510
\(712\) −9.69373e7 −0.268566
\(713\) 1.47406e8 0.406675
\(714\) 2.00023e7i 0.0549523i
\(715\) 3.56266e6i 0.00974667i
\(716\) 1.37619e8i 0.374921i
\(717\) 4.61613e8i 1.25233i
\(718\) 3.46232e6i 0.00935392i
\(719\) −9.20364e7 −0.247613 −0.123806 0.992306i \(-0.539510\pi\)
−0.123806 + 0.992306i \(0.539510\pi\)
\(720\) 2.14951e8i 0.575894i
\(721\) 7.14289e8i 1.90576i
\(722\) 2.35583e7i 0.0625941i
\(723\) 4.14729e8 1.09736
\(724\) 4.89554e8 1.28999
\(725\) 6.26215e8i 1.64327i
\(726\) 6.60437e6 0.0172592
\(727\) 3.95452e8i 1.02918i 0.857437 + 0.514589i \(0.172056\pi\)
−0.857437 + 0.514589i \(0.827944\pi\)
\(728\) −466198. −0.00120830
\(729\) −1.54497e8 −0.398783
\(730\) 7.24082e7i 0.186131i
\(731\) 2.05294e8 + 5.16158e7i 0.525561 + 0.132139i
\(732\) −3.85860e8 −0.983777
\(733\) 1.77578e8i 0.450897i 0.974255 + 0.225448i \(0.0723847\pi\)
−0.974255 + 0.225448i \(0.927615\pi\)
\(734\) 2.30518e7i 0.0582930i
\(735\) −3.54020e8 −0.891591
\(736\) 2.00364e7i 0.0502557i
\(737\) 2.13780e8 0.534028
\(738\) 1.35430e7i 0.0336935i
\(739\) 5.97778e8i 1.48118i −0.671959 0.740588i \(-0.734547\pi\)
0.671959 0.740588i \(-0.265453\pi\)
\(740\) −7.99460e8 −1.97289
\(741\) −1.14637e6 −0.00281754
\(742\) 5.25203e7 0.128563
\(743\) 1.67085e8i 0.407353i −0.979038 0.203676i \(-0.934711\pi\)
0.979038 0.203676i \(-0.0652890\pi\)
\(744\) −1.16925e8 −0.283916
\(745\) 8.50636e8 2.05719
\(746\) 1.49410e7 0.0359884
\(747\) −1.34564e7 −0.0322825
\(748\) −2.00883e8 −0.479997
\(749\) 6.08401e8i 1.44792i
\(750\) 2.44521e7i 0.0579605i
\(751\) 6.80726e8i 1.60714i −0.595213 0.803568i \(-0.702932\pi\)
0.595213 0.803568i \(-0.297068\pi\)
\(752\) −4.48315e8 −1.05422
\(753\) 5.55383e7i 0.130079i
\(754\) 242073. 0.000564718
\(755\) 9.87027e8 2.29344
\(756\) 3.84650e8 0.890227
\(757\) 3.37278e8i 0.777499i 0.921343 + 0.388750i \(0.127093\pi\)
−0.921343 + 0.388750i \(0.872907\pi\)
\(758\) 1.83684e7i 0.0421759i
\(759\) 1.08437e8i 0.248000i
\(760\) 3.33661e7i 0.0760089i
\(761\) 7.23483e7i 0.164163i 0.996626 + 0.0820813i \(0.0261567\pi\)
−0.996626 + 0.0820813i \(0.973843\pi\)
\(762\) −1.82694e7 −0.0412915
\(763\) 3.12135e8i 0.702698i
\(764\) 5.75060e8i 1.28953i
\(765\) 1.41860e8i 0.316866i
\(766\) −2.75552e7 −0.0613079
\(767\) 3.01861e6 0.00668992
\(768\) 5.04425e8i 1.11356i
\(769\) 5.73294e8 1.26066 0.630330 0.776327i \(-0.282919\pi\)
0.630330 + 0.776327i \(0.282919\pi\)
\(770\) 5.49843e7i 0.120439i
\(771\) 4.66337e8 1.01751
\(772\) 7.36241e8 1.60018
\(773\) 2.85371e8i 0.617833i −0.951089 0.308916i \(-0.900034\pi\)
0.951089 0.308916i \(-0.0999663\pi\)
\(774\) −2.99968e6 + 1.19308e7i −0.00646923 + 0.0257303i
\(775\) −1.15140e9 −2.47355
\(776\) 6.02210e7i 0.128873i
\(777\) 8.49979e8i 1.81195i
\(778\) −7.11194e6 −0.0151025
\(779\) 2.06125e8i 0.436031i
\(780\) −6.05936e6 −0.0127686
\(781\) 1.98537e8i 0.416762i
\(782\) 4.37059e6i 0.00913944i