Properties

Label 69.7.d.a.22.14
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.14
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.13

$q$-expansion

\(f(q)\) \(=\) \(q-0.368531 q^{2} +15.5885 q^{3} -63.8642 q^{4} +113.928i q^{5} -5.74483 q^{6} -569.901i q^{7} +47.1219 q^{8} +243.000 q^{9} +O(q^{10})\) \(q-0.368531 q^{2} +15.5885 q^{3} -63.8642 q^{4} +113.928i q^{5} -5.74483 q^{6} -569.901i q^{7} +47.1219 q^{8} +243.000 q^{9} -41.9859i q^{10} +814.298i q^{11} -995.544 q^{12} +3513.83 q^{13} +210.026i q^{14} +1775.96i q^{15} +4069.94 q^{16} +7484.26i q^{17} -89.5530 q^{18} -4283.93i q^{19} -7275.90i q^{20} -8883.88i q^{21} -300.094i q^{22} +(12048.1 - 1696.83i) q^{23} +734.558 q^{24} +2645.50 q^{25} -1294.96 q^{26} +3788.00 q^{27} +36396.3i q^{28} -3314.46 q^{29} -654.495i q^{30} +34401.9 q^{31} -4515.70 q^{32} +12693.6i q^{33} -2758.18i q^{34} +64927.5 q^{35} -15519.0 q^{36} +7160.07i q^{37} +1578.76i q^{38} +54775.2 q^{39} +5368.49i q^{40} +77969.3 q^{41} +3273.99i q^{42} -113275. i q^{43} -52004.5i q^{44} +27684.4i q^{45} +(-4440.10 + 625.334i) q^{46} -62809.9 q^{47} +63444.1 q^{48} -207138. q^{49} -974.947 q^{50} +116668. i q^{51} -224408. q^{52} +135215. i q^{53} -1395.99 q^{54} -92771.0 q^{55} -26854.8i q^{56} -66779.9i q^{57} +1221.48 q^{58} -101668. q^{59} -113420. i q^{60} +38234.1i q^{61} -12678.2 q^{62} -138486. i q^{63} -258812. q^{64} +400322. i q^{65} -4678.00i q^{66} -229273. i q^{67} -477976. i q^{68} +(187811. - 26451.0i) q^{69} -23927.8 q^{70} -64522.4 q^{71} +11450.6 q^{72} -53631.6 q^{73} -2638.71i q^{74} +41239.2 q^{75} +273590. i q^{76} +464069. q^{77} -20186.4 q^{78} +458737. i q^{79} +463679. i q^{80} +59049.0 q^{81} -28734.1 q^{82} -1.13063e6i q^{83} +567362. i q^{84} -852664. q^{85} +41745.4i q^{86} -51667.4 q^{87} +38371.3i q^{88} +829443. i q^{89} -10202.6i q^{90} -2.00254e6i q^{91} +(-769442. + 108367. i) q^{92} +536273. q^{93} +23147.4 q^{94} +488058. q^{95} -70392.8 q^{96} +525418. i q^{97} +76337.0 q^{98} +197874. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{2} + 816 q^{4} - 324 q^{6} - 940 q^{8} + 5832 q^{9} + O(q^{10}) \) \( 24 q - 20 q^{2} + 816 q^{4} - 324 q^{6} - 940 q^{8} + 5832 q^{9} + 384 q^{13} + 29544 q^{16} - 4860 q^{18} + 29336 q^{23} - 39204 q^{24} - 61272 q^{25} + 10088 q^{26} + 64672 q^{29} + 9696 q^{31} - 319620 q^{32} - 225744 q^{35} + 198288 q^{36} - 11664 q^{39} + 135280 q^{41} + 233232 q^{46} - 74336 q^{47} + 552096 q^{48} - 722136 q^{49} + 619324 q^{50} + 1059720 q^{52} - 78732 q^{54} - 1019328 q^{55} - 694344 q^{58} + 1057648 q^{59} - 488776 q^{62} - 273888 q^{64} - 23328 q^{69} + 2785512 q^{70} - 255392 q^{71} - 228420 q^{72} - 322560 q^{73} - 365472 q^{75} - 1002960 q^{77} - 171072 q^{78} + 1417176 q^{81} - 5732712 q^{82} - 2704704 q^{85} + 611712 q^{87} - 1611444 q^{92} + 2484432 q^{93} - 147720 q^{94} - 1672656 q^{95} - 1818612 q^{96} + 9104212 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.368531 −0.0460664 −0.0230332 0.999735i \(-0.507332\pi\)
−0.0230332 + 0.999735i \(0.507332\pi\)
\(3\) 15.5885 0.577350
\(4\) −63.8642 −0.997878
\(5\) 113.928i 0.911421i 0.890128 + 0.455711i \(0.150615\pi\)
−0.890128 + 0.455711i \(0.849385\pi\)
\(6\) −5.74483 −0.0265964
\(7\) 569.901i 1.66152i −0.556631 0.830760i \(-0.687906\pi\)
0.556631 0.830760i \(-0.312094\pi\)
\(8\) 47.1219 0.0920350
\(9\) 243.000 0.333333
\(10\) 41.9859i 0.0419859i
\(11\) 814.298i 0.611794i 0.952065 + 0.305897i \(0.0989563\pi\)
−0.952065 + 0.305897i \(0.901044\pi\)
\(12\) −995.544 −0.576125
\(13\) 3513.83 1.59938 0.799689 0.600415i \(-0.204998\pi\)
0.799689 + 0.600415i \(0.204998\pi\)
\(14\) 210.026i 0.0765402i
\(15\) 1775.96i 0.526209i
\(16\) 4069.94 0.993638
\(17\) 7484.26i 1.52336i 0.647954 + 0.761679i \(0.275625\pi\)
−0.647954 + 0.761679i \(0.724375\pi\)
\(18\) −89.5530 −0.0153555
\(19\) 4283.93i 0.624571i −0.949988 0.312285i \(-0.898905\pi\)
0.949988 0.312285i \(-0.101095\pi\)
\(20\) 7275.90i 0.909487i
\(21\) 8883.88i 0.959279i
\(22\) 300.094i 0.0281831i
\(23\) 12048.1 1696.83i 0.990227 0.139462i
\(24\) 734.558 0.0531364
\(25\) 2645.50 0.169312
\(26\) −1294.96 −0.0736775
\(27\) 3788.00 0.192450
\(28\) 36396.3i 1.65799i
\(29\) −3314.46 −0.135900 −0.0679500 0.997689i \(-0.521646\pi\)
−0.0679500 + 0.997689i \(0.521646\pi\)
\(30\) 654.495i 0.0242405i
\(31\) 34401.9 1.15478 0.577388 0.816470i \(-0.304072\pi\)
0.577388 + 0.816470i \(0.304072\pi\)
\(32\) −4515.70 −0.137808
\(33\) 12693.6i 0.353219i
\(34\) 2758.18i 0.0701756i
\(35\) 64927.5 1.51434
\(36\) −15519.0 −0.332626
\(37\) 7160.07i 0.141355i 0.997499 + 0.0706776i \(0.0225162\pi\)
−0.997499 + 0.0706776i \(0.977484\pi\)
\(38\) 1578.76i 0.0287717i
\(39\) 54775.2 0.923401
\(40\) 5368.49i 0.0838826i
\(41\) 77969.3 1.13129 0.565643 0.824650i \(-0.308628\pi\)
0.565643 + 0.824650i \(0.308628\pi\)
\(42\) 3273.99i 0.0441905i
\(43\) 113275.i 1.42472i −0.701815 0.712359i \(-0.747627\pi\)
0.701815 0.712359i \(-0.252373\pi\)
\(44\) 52004.5i 0.610496i
\(45\) 27684.4i 0.303807i
\(46\) −4440.10 + 625.334i −0.0456162 + 0.00642449i
\(47\) −62809.9 −0.604971 −0.302485 0.953154i \(-0.597816\pi\)
−0.302485 + 0.953154i \(0.597816\pi\)
\(48\) 63444.1 0.573677
\(49\) −207138. −1.76065
\(50\) −974.947 −0.00779958
\(51\) 116668.i 0.879511i
\(52\) −224408. −1.59598
\(53\) 135215.i 0.908235i 0.890942 + 0.454118i \(0.150045\pi\)
−0.890942 + 0.454118i \(0.849955\pi\)
\(54\) −1395.99 −0.00886548
\(55\) −92771.0 −0.557602
\(56\) 26854.8i 0.152918i
\(57\) 66779.9i 0.360596i
\(58\) 1221.48 0.00626042
\(59\) −101668. −0.495025 −0.247513 0.968885i \(-0.579613\pi\)
−0.247513 + 0.968885i \(0.579613\pi\)
\(60\) 113420.i 0.525093i
\(61\) 38234.1i 0.168446i 0.996447 + 0.0842231i \(0.0268409\pi\)
−0.996447 + 0.0842231i \(0.973159\pi\)
\(62\) −12678.2 −0.0531963
\(63\) 138486.i 0.553840i
\(64\) −258812. −0.987290
\(65\) 400322.i 1.45771i
\(66\) 4678.00i 0.0162715i
\(67\) 229273.i 0.762306i −0.924512 0.381153i \(-0.875527\pi\)
0.924512 0.381153i \(-0.124473\pi\)
\(68\) 477976.i 1.52013i
\(69\) 187811. 26451.0i 0.571708 0.0805182i
\(70\) −23927.8 −0.0697603
\(71\) −64522.4 −0.180275 −0.0901375 0.995929i \(-0.528731\pi\)
−0.0901375 + 0.995929i \(0.528731\pi\)
\(72\) 11450.6 0.0306783
\(73\) −53631.6 −0.137864 −0.0689322 0.997621i \(-0.521959\pi\)
−0.0689322 + 0.997621i \(0.521959\pi\)
\(74\) 2638.71i 0.00651172i
\(75\) 41239.2 0.0977522
\(76\) 273590.i 0.623245i
\(77\) 464069. 1.01651
\(78\) −20186.4 −0.0425377
\(79\) 458737.i 0.930427i 0.885199 + 0.465213i \(0.154022\pi\)
−0.885199 + 0.465213i \(0.845978\pi\)
\(80\) 463679.i 0.905623i
\(81\) 59049.0 0.111111
\(82\) −28734.1 −0.0521142
\(83\) 1.13063e6i 1.97736i −0.150055 0.988678i \(-0.547945\pi\)
0.150055 0.988678i \(-0.452055\pi\)
\(84\) 567362.i 0.957243i
\(85\) −852664. −1.38842
\(86\) 41745.4i 0.0656316i
\(87\) −51667.4 −0.0784619
\(88\) 38371.3i 0.0563065i
\(89\) 829443.i 1.17657i 0.808655 + 0.588284i \(0.200196\pi\)
−0.808655 + 0.588284i \(0.799804\pi\)
\(90\) 10202.6i 0.0139953i
\(91\) 2.00254e6i 2.65740i
\(92\) −769442. + 108367.i −0.988126 + 0.139166i
\(93\) 536273. 0.666710
\(94\) 23147.4 0.0278688
\(95\) 488058. 0.569247
\(96\) −70392.8 −0.0795637
\(97\) 525418.i 0.575691i 0.957677 + 0.287846i \(0.0929390\pi\)
−0.957677 + 0.287846i \(0.907061\pi\)
\(98\) 76337.0 0.0811067
\(99\) 197874.i 0.203931i
\(100\) −168952. −0.168952
\(101\) 1.66810e6 1.61904 0.809521 0.587090i \(-0.199727\pi\)
0.809521 + 0.587090i \(0.199727\pi\)
\(102\) 42995.8i 0.0405159i
\(103\) 226535.i 0.207311i 0.994613 + 0.103656i \(0.0330540\pi\)
−0.994613 + 0.103656i \(0.966946\pi\)
\(104\) 165578. 0.147199
\(105\) 1.01212e6 0.874307
\(106\) 49831.0i 0.0418391i
\(107\) 742387.i 0.606009i 0.952989 + 0.303004i \(0.0979897\pi\)
−0.952989 + 0.303004i \(0.902010\pi\)
\(108\) −241917. −0.192042
\(109\) 2.09107e6i 1.61469i 0.590080 + 0.807344i \(0.299096\pi\)
−0.590080 + 0.807344i \(0.700904\pi\)
\(110\) 34189.0 0.0256867
\(111\) 111614.i 0.0816115i
\(112\) 2.31947e6i 1.65095i
\(113\) 2.20924e6i 1.53111i −0.643368 0.765557i \(-0.722464\pi\)
0.643368 0.765557i \(-0.277536\pi\)
\(114\) 24610.5i 0.0166114i
\(115\) 193316. + 1.37261e6i 0.127108 + 0.902514i
\(116\) 211676. 0.135612
\(117\) 853861. 0.533126
\(118\) 37467.7 0.0228040
\(119\) 4.26529e6 2.53109
\(120\) 83686.4i 0.0484297i
\(121\) 1.10848e6 0.625708
\(122\) 14090.5i 0.00775971i
\(123\) 1.21542e6 0.653148
\(124\) −2.19705e6 −1.15232
\(125\) 2.08151e6i 1.06574i
\(126\) 51036.4i 0.0255134i
\(127\) −723004. −0.352963 −0.176482 0.984304i \(-0.556472\pi\)
−0.176482 + 0.984304i \(0.556472\pi\)
\(128\) 384385. 0.183289
\(129\) 1.76578e6i 0.822561i
\(130\) 147531.i 0.0671512i
\(131\) −3.35181e6 −1.49096 −0.745479 0.666529i \(-0.767779\pi\)
−0.745479 + 0.666529i \(0.767779\pi\)
\(132\) 810669.i 0.352470i
\(133\) −2.44142e6 −1.03774
\(134\) 84494.3i 0.0351167i
\(135\) 431557.i 0.175403i
\(136\) 352673.i 0.140202i
\(137\) 546016.i 0.212346i 0.994348 + 0.106173i \(0.0338597\pi\)
−0.994348 + 0.106173i \(0.966140\pi\)
\(138\) −69214.3 + 9748.00i −0.0263365 + 0.00370918i
\(139\) 1.07985e6 0.402086 0.201043 0.979582i \(-0.435567\pi\)
0.201043 + 0.979582i \(0.435567\pi\)
\(140\) −4.14654e6 −1.51113
\(141\) −979109. −0.349280
\(142\) 23778.5 0.00830461
\(143\) 2.86131e6i 0.978489i
\(144\) 988996. 0.331213
\(145\) 377609.i 0.123862i
\(146\) 19764.9 0.00635091
\(147\) −3.22897e6 −1.01651
\(148\) 457272.i 0.141055i
\(149\) 4.51099e6i 1.36368i −0.731501 0.681840i \(-0.761180\pi\)
0.731501 0.681840i \(-0.238820\pi\)
\(150\) −15197.9 −0.00450309
\(151\) 3.08008e6 0.894605 0.447302 0.894383i \(-0.352385\pi\)
0.447302 + 0.894383i \(0.352385\pi\)
\(152\) 201867.i 0.0574824i
\(153\) 1.81868e6i 0.507786i
\(154\) −171024. −0.0468268
\(155\) 3.91933e6i 1.05249i
\(156\) −3.49817e6 −0.921441
\(157\) 5.92399e6i 1.53079i −0.643562 0.765394i \(-0.722544\pi\)
0.643562 0.765394i \(-0.277456\pi\)
\(158\) 169059.i 0.0428614i
\(159\) 2.10780e6i 0.524370i
\(160\) 514463.i 0.125601i
\(161\) −967025. 6.86623e6i −0.231718 1.64528i
\(162\) −21761.4 −0.00511849
\(163\) 917099. 0.211765 0.105882 0.994379i \(-0.466233\pi\)
0.105882 + 0.994379i \(0.466233\pi\)
\(164\) −4.97945e6 −1.12888
\(165\) −1.44616e6 −0.321932
\(166\) 416671.i 0.0910896i
\(167\) −7.58083e6 −1.62767 −0.813837 0.581094i \(-0.802625\pi\)
−0.813837 + 0.581094i \(0.802625\pi\)
\(168\) 418626.i 0.0882872i
\(169\) 7.52020e6 1.55801
\(170\) 314233. 0.0639595
\(171\) 1.04100e6i 0.208190i
\(172\) 7.23422e6i 1.42169i
\(173\) 5.62249e6 1.08590 0.542951 0.839765i \(-0.317307\pi\)
0.542951 + 0.839765i \(0.317307\pi\)
\(174\) 19041.0 0.00361445
\(175\) 1.50767e6i 0.281315i
\(176\) 3.31414e6i 0.607902i
\(177\) −1.58484e6 −0.285803
\(178\) 305676.i 0.0542002i
\(179\) 656490. 0.114464 0.0572320 0.998361i \(-0.481773\pi\)
0.0572320 + 0.998361i \(0.481773\pi\)
\(180\) 1.76804e6i 0.303162i
\(181\) 9.20126e6i 1.55171i 0.630909 + 0.775857i \(0.282682\pi\)
−0.630909 + 0.775857i \(0.717318\pi\)
\(182\) 737997.i 0.122417i
\(183\) 596011.i 0.0972525i
\(184\) 567729. 79957.9i 0.0911356 0.0128353i
\(185\) −815730. −0.128834
\(186\) −197633. −0.0307129
\(187\) −6.09442e6 −0.931982
\(188\) 4.01130e6 0.603687
\(189\) 2.15878e6i 0.319760i
\(190\) −179865. −0.0262231
\(191\) 9.24960e6i 1.32746i −0.747971 0.663732i \(-0.768972\pi\)
0.747971 0.663732i \(-0.231028\pi\)
\(192\) −4.03448e6 −0.570012
\(193\) −1.56196e6 −0.217269 −0.108634 0.994082i \(-0.534648\pi\)
−0.108634 + 0.994082i \(0.534648\pi\)
\(194\) 193633.i 0.0265200i
\(195\) 6.24041e6i 0.841607i
\(196\) 1.32287e7 1.75691
\(197\) −1.12002e7 −1.46496 −0.732482 0.680786i \(-0.761638\pi\)
−0.732482 + 0.680786i \(0.761638\pi\)
\(198\) 72922.8i 0.00939438i
\(199\) 4.87456e6i 0.618552i −0.950972 0.309276i \(-0.899913\pi\)
0.950972 0.309276i \(-0.100087\pi\)
\(200\) 124661. 0.0155826
\(201\) 3.57402e6i 0.440117i
\(202\) −614747. −0.0745834
\(203\) 1.88892e6i 0.225800i
\(204\) 7.45091e6i 0.877645i
\(205\) 8.88286e6i 1.03108i
\(206\) 83485.1i 0.00955008i
\(207\) 2.92769e6 412330.i 0.330076 0.0464872i
\(208\) 1.43011e7 1.58920
\(209\) 3.48840e6 0.382109
\(210\) −372997. −0.0402762
\(211\) 1.01176e7 1.07704 0.538518 0.842614i \(-0.318984\pi\)
0.538518 + 0.842614i \(0.318984\pi\)
\(212\) 8.63542e6i 0.906308i
\(213\) −1.00580e6 −0.104082
\(214\) 273593.i 0.0279166i
\(215\) 1.29052e7 1.29852
\(216\) 178498. 0.0177121
\(217\) 1.96057e7i 1.91868i
\(218\) 770624.i 0.0743829i
\(219\) −836034. −0.0795960
\(220\) 5.92475e6 0.556419
\(221\) 2.62984e7i 2.43642i
\(222\) 41133.4i 0.00375955i
\(223\) −1.27139e7 −1.14647 −0.573236 0.819390i \(-0.694312\pi\)
−0.573236 + 0.819390i \(0.694312\pi\)
\(224\) 2.57350e6i 0.228971i
\(225\) 642855. 0.0564372
\(226\) 814173.i 0.0705328i
\(227\) 1.69641e7i 1.45028i 0.688599 + 0.725142i \(0.258226\pi\)
−0.688599 + 0.725142i \(0.741774\pi\)
\(228\) 4.26484e6i 0.359831i
\(229\) 1.22935e7i 1.02369i 0.859077 + 0.511847i \(0.171038\pi\)
−0.859077 + 0.511847i \(0.828962\pi\)
\(230\) −71242.8 505850.i −0.00585542 0.0415756i
\(231\) 7.23413e6 0.586881
\(232\) −156184. −0.0125075
\(233\) −171237. −0.0135372 −0.00676861 0.999977i \(-0.502155\pi\)
−0.00676861 + 0.999977i \(0.502155\pi\)
\(234\) −314674. −0.0245592
\(235\) 7.15578e6i 0.551383i
\(236\) 6.49293e6 0.493975
\(237\) 7.15100e6i 0.537182i
\(238\) −1.57189e6 −0.116598
\(239\) −543012. −0.0397755 −0.0198877 0.999802i \(-0.506331\pi\)
−0.0198877 + 0.999802i \(0.506331\pi\)
\(240\) 7.22804e6i 0.522862i
\(241\) 3.84804e6i 0.274909i 0.990508 + 0.137455i \(0.0438921\pi\)
−0.990508 + 0.137455i \(0.956108\pi\)
\(242\) −408509. −0.0288241
\(243\) 920483. 0.0641500
\(244\) 2.44179e6i 0.168089i
\(245\) 2.35988e7i 1.60469i
\(246\) −447920. −0.0300882
\(247\) 1.50530e7i 0.998924i
\(248\) 1.62108e6 0.106280
\(249\) 1.76247e7i 1.14163i
\(250\) 767103.i 0.0490946i
\(251\) 1.18733e7i 0.750845i −0.926854 0.375422i \(-0.877498\pi\)
0.926854 0.375422i \(-0.122502\pi\)
\(252\) 8.84430e6i 0.552665i
\(253\) 1.38172e6 + 9.81074e6i 0.0853218 + 0.605815i
\(254\) 266449. 0.0162597
\(255\) −1.32917e7 −0.801605
\(256\) 1.64223e7 0.978846
\(257\) −1.02407e7 −0.603296 −0.301648 0.953419i \(-0.597537\pi\)
−0.301648 + 0.953419i \(0.597537\pi\)
\(258\) 650746.i 0.0378924i
\(259\) 4.08053e6 0.234865
\(260\) 2.55663e7i 1.45461i
\(261\) −805415. −0.0453000
\(262\) 1.23525e6 0.0686831
\(263\) 2.04038e6i 0.112162i −0.998426 0.0560809i \(-0.982140\pi\)
0.998426 0.0560809i \(-0.0178605\pi\)
\(264\) 598149.i 0.0325085i
\(265\) −1.54048e7 −0.827785
\(266\) 899738. 0.0478048
\(267\) 1.29297e7i 0.679291i
\(268\) 1.46424e7i 0.760688i
\(269\) −3.09947e7 −1.59232 −0.796161 0.605085i \(-0.793139\pi\)
−0.796161 + 0.605085i \(0.793139\pi\)
\(270\) 159042.i 0.00808018i
\(271\) −4.55560e6 −0.228896 −0.114448 0.993429i \(-0.536510\pi\)
−0.114448 + 0.993429i \(0.536510\pi\)
\(272\) 3.04605e7i 1.51367i
\(273\) 3.12165e7i 1.53425i
\(274\) 201224.i 0.00978200i
\(275\) 2.15422e6i 0.103584i
\(276\) −1.19944e7 + 1.68927e6i −0.570495 + 0.0803473i
\(277\) −1.18273e7 −0.556475 −0.278237 0.960512i \(-0.589750\pi\)
−0.278237 + 0.960512i \(0.589750\pi\)
\(278\) −397958. −0.0185226
\(279\) 8.35966e6 0.384925
\(280\) 3.05951e6 0.139373
\(281\) 1.70316e7i 0.767601i 0.923416 + 0.383801i \(0.125385\pi\)
−0.923416 + 0.383801i \(0.874615\pi\)
\(282\) 360832. 0.0160901
\(283\) 3.65196e7i 1.61126i 0.592418 + 0.805631i \(0.298174\pi\)
−0.592418 + 0.805631i \(0.701826\pi\)
\(284\) 4.12067e6 0.179892
\(285\) 7.60807e6 0.328655
\(286\) 1.05448e6i 0.0450755i
\(287\) 4.44348e7i 1.87965i
\(288\) −1.09732e6 −0.0459361
\(289\) −3.18766e7 −1.32062
\(290\) 139161.i 0.00570588i
\(291\) 8.19045e6i 0.332375i
\(292\) 3.42514e6 0.137572
\(293\) 1.85690e7i 0.738220i 0.929386 + 0.369110i \(0.120337\pi\)
−0.929386 + 0.369110i \(0.879663\pi\)
\(294\) 1.18998e6 0.0468270
\(295\) 1.15828e7i 0.451177i
\(296\) 337396.i 0.0130096i
\(297\) 3.08456e6i 0.117740i
\(298\) 1.66244e6i 0.0628198i
\(299\) 4.23350e7 5.96237e6i 1.58375 0.223052i
\(300\) −2.63371e6 −0.0975447
\(301\) −6.45556e7 −2.36720
\(302\) −1.13511e6 −0.0412112
\(303\) 2.60031e7 0.934755
\(304\) 1.74354e7i 0.620597i
\(305\) −4.35592e6 −0.153525
\(306\) 670238.i 0.0233919i
\(307\) −3.39160e7 −1.17217 −0.586084 0.810250i \(-0.699331\pi\)
−0.586084 + 0.810250i \(0.699331\pi\)
\(308\) −2.96374e7 −1.01435
\(309\) 3.53133e6i 0.119691i
\(310\) 1.44439e6i 0.0484842i
\(311\) −3.91451e7 −1.30136 −0.650679 0.759353i \(-0.725516\pi\)
−0.650679 + 0.759353i \(0.725516\pi\)
\(312\) 2.58111e6 0.0849852
\(313\) 4.03448e7i 1.31569i −0.753152 0.657847i \(-0.771467\pi\)
0.753152 0.657847i \(-0.228533\pi\)
\(314\) 2.18317e6i 0.0705179i
\(315\) 1.57774e7 0.504781
\(316\) 2.92968e7i 0.928452i
\(317\) 3.59652e7 1.12903 0.564514 0.825423i \(-0.309063\pi\)
0.564514 + 0.825423i \(0.309063\pi\)
\(318\) 776789.i 0.0241558i
\(319\) 2.69896e6i 0.0831428i
\(320\) 2.94858e7i 0.899837i
\(321\) 1.15727e7i 0.349879i
\(322\) 356379. + 2.53042e6i 0.0106744 + 0.0757922i
\(323\) 3.20621e7 0.951445
\(324\) −3.77112e6 −0.110875
\(325\) 9.29583e6 0.270793
\(326\) −337979. −0.00975523
\(327\) 3.25965e7i 0.932241i
\(328\) 3.67406e6 0.104118
\(329\) 3.57954e7i 1.00517i
\(330\) 532954. 0.0148302
\(331\) −2.80276e7 −0.772863 −0.386431 0.922318i \(-0.626292\pi\)
−0.386431 + 0.922318i \(0.626292\pi\)
\(332\) 7.22065e7i 1.97316i
\(333\) 1.73990e6i 0.0471184i
\(334\) 2.79377e6 0.0749810
\(335\) 2.61206e7 0.694781
\(336\) 3.61569e7i 0.953176i
\(337\) 3.06197e7i 0.800038i −0.916507 0.400019i \(-0.869003\pi\)
0.916507 0.400019i \(-0.130997\pi\)
\(338\) −2.77143e6 −0.0717717
\(339\) 3.44386e7i 0.883989i
\(340\) 5.44547e7 1.38547
\(341\) 2.80134e7i 0.706485i
\(342\) 383639.i 0.00959057i
\(343\) 5.10002e7i 1.26383i
\(344\) 5.33774e6i 0.131124i
\(345\) 3.01349e6 + 2.13969e7i 0.0733860 + 0.521067i
\(346\) −2.07206e6 −0.0500235
\(347\) 7.04261e7 1.68556 0.842782 0.538255i \(-0.180916\pi\)
0.842782 + 0.538255i \(0.180916\pi\)
\(348\) 3.29969e6 0.0782954
\(349\) −6.68006e7 −1.57146 −0.785731 0.618568i \(-0.787713\pi\)
−0.785731 + 0.618568i \(0.787713\pi\)
\(350\) 555624.i 0.0129592i
\(351\) 1.33104e7 0.307800
\(352\) 3.67713e6i 0.0843103i
\(353\) −7.85575e6 −0.178593 −0.0892963 0.996005i \(-0.528462\pi\)
−0.0892963 + 0.996005i \(0.528462\pi\)
\(354\) 584064. 0.0131659
\(355\) 7.35088e6i 0.164306i
\(356\) 5.29717e7i 1.17407i
\(357\) 6.64893e7 1.46133
\(358\) −241937. −0.00527294
\(359\) 8.88485e6i 0.192029i 0.995380 + 0.0960145i \(0.0306095\pi\)
−0.995380 + 0.0960145i \(0.969390\pi\)
\(360\) 1.30454e6i 0.0279609i
\(361\) 2.86938e7 0.609911
\(362\) 3.39095e6i 0.0714818i
\(363\) 1.72795e7 0.361253
\(364\) 1.27890e8i 2.65176i
\(365\) 6.11012e6i 0.125652i
\(366\) 219648.i 0.00448007i
\(367\) 8.43071e7i 1.70556i −0.522274 0.852778i \(-0.674916\pi\)
0.522274 0.852778i \(-0.325084\pi\)
\(368\) 4.90351e7 6.90600e6i 0.983928 0.138574i
\(369\) 1.89465e7 0.377095
\(370\) 300622. 0.00593492
\(371\) 7.70594e7 1.50905
\(372\) −3.42486e7 −0.665295
\(373\) 6.67702e7i 1.28664i −0.765599 0.643318i \(-0.777557\pi\)
0.765599 0.643318i \(-0.222443\pi\)
\(374\) 2.24598e6 0.0429330
\(375\) 3.24476e7i 0.615303i
\(376\) −2.95972e6 −0.0556785
\(377\) −1.16465e7 −0.217355
\(378\) 795579.i 0.0147302i
\(379\) 5.19954e7i 0.955097i 0.878605 + 0.477549i \(0.158475\pi\)
−0.878605 + 0.477549i \(0.841525\pi\)
\(380\) −3.11694e7 −0.568039
\(381\) −1.12705e7 −0.203783
\(382\) 3.40876e6i 0.0611514i
\(383\) 3.43487e7i 0.611384i −0.952130 0.305692i \(-0.901112\pi\)
0.952130 0.305692i \(-0.0988878\pi\)
\(384\) 5.99197e6 0.105822
\(385\) 5.28703e7i 0.926467i
\(386\) 575629. 0.0100088
\(387\) 2.75258e7i 0.474906i
\(388\) 3.35554e7i 0.574470i
\(389\) 7.76864e7i 1.31976i −0.751369 0.659882i \(-0.770606\pi\)
0.751369 0.659882i \(-0.229394\pi\)
\(390\) 2.29978e6i 0.0387698i
\(391\) 1.26995e7 + 9.01711e7i 0.212450 + 1.50847i
\(392\) −9.76076e6 −0.162041
\(393\) −5.22496e7 −0.860805
\(394\) 4.12762e6 0.0674856
\(395\) −5.22628e7 −0.848011
\(396\) 1.26371e7i 0.203499i
\(397\) −9.93649e7 −1.58804 −0.794020 0.607892i \(-0.792015\pi\)
−0.794020 + 0.607892i \(0.792015\pi\)
\(398\) 1.79643e6i 0.0284945i
\(399\) −3.80579e7 −0.599138
\(400\) 1.07670e7 0.168235
\(401\) 3.38580e7i 0.525083i −0.964921 0.262542i \(-0.915439\pi\)
0.964921 0.262542i \(-0.0845607\pi\)
\(402\) 1.31714e6i 0.0202746i
\(403\) 1.20883e8 1.84692
\(404\) −1.06532e8 −1.61561
\(405\) 6.72731e6i 0.101269i
\(406\) 696124.i 0.0104018i
\(407\) −5.83043e6 −0.0864803
\(408\) 5.49762e6i 0.0809458i
\(409\) 4.05687e7 0.592955 0.296477 0.955040i \(-0.404188\pi\)
0.296477 + 0.955040i \(0.404188\pi\)
\(410\) 3.27361e6i 0.0474980i
\(411\) 8.51155e6i 0.122598i
\(412\) 1.44675e7i 0.206871i
\(413\) 5.79406e7i 0.822494i
\(414\) −1.07894e6 + 151956.i −0.0152054 + 0.00214150i
\(415\) 1.28810e8 1.80220
\(416\) −1.58674e7 −0.220407
\(417\) 1.68332e7 0.232144
\(418\) −1.28558e6 −0.0176024
\(419\) 8.70221e7i 1.18301i 0.806302 + 0.591504i \(0.201466\pi\)
−0.806302 + 0.591504i \(0.798534\pi\)
\(420\) −6.46382e7 −0.872452
\(421\) 6.05889e7i 0.811983i −0.913877 0.405991i \(-0.866926\pi\)
0.913877 0.405991i \(-0.133074\pi\)
\(422\) −3.72865e6 −0.0496152
\(423\) −1.52628e7 −0.201657
\(424\) 6.37161e6i 0.0835894i
\(425\) 1.97996e7i 0.257922i
\(426\) 370670. 0.00479467
\(427\) 2.17897e7 0.279877
\(428\) 4.74119e7i 0.604723i
\(429\) 4.46033e7i 0.564931i
\(430\) −4.75595e6 −0.0598180
\(431\) 5.02127e7i 0.627165i 0.949561 + 0.313583i \(0.101529\pi\)
−0.949561 + 0.313583i \(0.898471\pi\)
\(432\) 1.54169e7 0.191226
\(433\) 1.09950e8i 1.35435i −0.735820 0.677177i \(-0.763203\pi\)
0.735820 0.677177i \(-0.236797\pi\)
\(434\) 7.22531e6i 0.0883867i
\(435\) 5.88634e6i 0.0715118i
\(436\) 1.33544e8i 1.61126i
\(437\) −7.26910e6 5.16132e7i −0.0871037 0.618467i
\(438\) 308104. 0.00366670
\(439\) −3.55005e7 −0.419606 −0.209803 0.977744i \(-0.567282\pi\)
−0.209803 + 0.977744i \(0.567282\pi\)
\(440\) −4.37155e6 −0.0513189
\(441\) −5.03347e7 −0.586883
\(442\) 9.69179e6i 0.112237i
\(443\) −9.78683e7 −1.12572 −0.562861 0.826552i \(-0.690299\pi\)
−0.562861 + 0.826552i \(0.690299\pi\)
\(444\) 7.12816e6i 0.0814383i
\(445\) −9.44965e7 −1.07235
\(446\) 4.68546e6 0.0528138
\(447\) 7.03193e7i 0.787322i
\(448\) 1.47497e8i 1.64040i
\(449\) −8.49424e7 −0.938394 −0.469197 0.883093i \(-0.655457\pi\)
−0.469197 + 0.883093i \(0.655457\pi\)
\(450\) −236912. −0.00259986
\(451\) 6.34903e7i 0.692114i
\(452\) 1.41091e8i 1.52786i
\(453\) 4.80137e7 0.516500
\(454\) 6.25180e6i 0.0668093i
\(455\) 2.28144e8 2.42201
\(456\) 3.14680e6i 0.0331875i
\(457\) 8.16735e7i 0.855722i 0.903844 + 0.427861i \(0.140733\pi\)
−0.903844 + 0.427861i \(0.859267\pi\)
\(458\) 4.53055e6i 0.0471579i
\(459\) 2.83503e7i 0.293170i
\(460\) −1.23460e7 8.76607e7i −0.126839 0.900599i
\(461\) −1.10947e8 −1.13243 −0.566215 0.824258i \(-0.691593\pi\)
−0.566215 + 0.824258i \(0.691593\pi\)
\(462\) −2.66600e6 −0.0270355
\(463\) 1.53700e8 1.54857 0.774287 0.632835i \(-0.218109\pi\)
0.774287 + 0.632835i \(0.218109\pi\)
\(464\) −1.34897e7 −0.135035
\(465\) 6.10963e7i 0.607653i
\(466\) 63106.1 0.000623611
\(467\) 2.80988e7i 0.275890i −0.990440 0.137945i \(-0.955950\pi\)
0.990440 0.137945i \(-0.0440498\pi\)
\(468\) −5.45311e7 −0.531994
\(469\) −1.30663e8 −1.26659
\(470\) 2.63713e6i 0.0254002i
\(471\) 9.23458e7i 0.883801i
\(472\) −4.79078e6 −0.0455597
\(473\) 9.22396e7 0.871634
\(474\) 2.63536e6i 0.0247460i
\(475\) 1.13331e7i 0.105747i
\(476\) −2.72399e8 −2.52572
\(477\) 3.28573e7i 0.302745i
\(478\) 200117. 0.00183231
\(479\) 2.05854e8i 1.87307i −0.350578 0.936534i \(-0.614015\pi\)
0.350578 0.936534i \(-0.385985\pi\)
\(480\) 8.01969e6i 0.0725160i
\(481\) 2.51593e7i 0.226080i
\(482\) 1.41812e6i 0.0126641i
\(483\) −1.50744e7 1.07034e8i −0.133783 0.949904i
\(484\) −7.07922e7 −0.624380
\(485\) −5.98596e7 −0.524697
\(486\) −339226. −0.00295516
\(487\) 7.83541e7 0.678383 0.339191 0.940717i \(-0.389847\pi\)
0.339191 + 0.940717i \(0.389847\pi\)
\(488\) 1.80166e6i 0.0155029i
\(489\) 1.42962e7 0.122262
\(490\) 8.69689e6i 0.0739223i
\(491\) −9.63485e7 −0.813955 −0.406978 0.913438i \(-0.633417\pi\)
−0.406978 + 0.913438i \(0.633417\pi\)
\(492\) −7.76219e7 −0.651762
\(493\) 2.48063e7i 0.207024i
\(494\) 5.54750e6i 0.0460168i
\(495\) −2.25434e7 −0.185867
\(496\) 1.40014e8 1.14743
\(497\) 3.67714e7i 0.299530i
\(498\) 6.49525e6i 0.0525906i
\(499\) −3.11543e7 −0.250736 −0.125368 0.992110i \(-0.540011\pi\)
−0.125368 + 0.992110i \(0.540011\pi\)
\(500\) 1.32934e8i 1.06347i
\(501\) −1.18173e8 −0.939738
\(502\) 4.37568e6i 0.0345887i
\(503\) 5.43218e7i 0.426845i 0.976960 + 0.213423i \(0.0684611\pi\)
−0.976960 + 0.213423i \(0.931539\pi\)
\(504\) 6.52573e6i 0.0509727i
\(505\) 1.90043e8i 1.47563i
\(506\) −509208. 3.61556e6i −0.00393047 0.0279077i
\(507\) 1.17228e8 0.899516
\(508\) 4.61740e7 0.352214
\(509\) 2.23459e8 1.69451 0.847255 0.531187i \(-0.178254\pi\)
0.847255 + 0.531187i \(0.178254\pi\)
\(510\) 4.89841e6 0.0369270
\(511\) 3.05647e7i 0.229064i
\(512\) −3.06528e7 −0.228381
\(513\) 1.62275e7i 0.120199i
\(514\) 3.77402e6 0.0277917
\(515\) −2.58086e7 −0.188948
\(516\) 1.12770e8i 0.820816i
\(517\) 5.11459e7i 0.370117i
\(518\) −1.50380e6 −0.0108194
\(519\) 8.76459e7 0.626945
\(520\) 1.88640e7i 0.134160i
\(521\) 1.32853e7i 0.0939415i −0.998896 0.0469707i \(-0.985043\pi\)
0.998896 0.0469707i \(-0.0149568\pi\)
\(522\) 296820. 0.00208681
\(523\) 9.24267e7i 0.646089i 0.946384 + 0.323044i \(0.104706\pi\)
−0.946384 + 0.323044i \(0.895294\pi\)
\(524\) 2.14061e8 1.48779
\(525\) 2.35023e7i 0.162417i
\(526\) 751945.i 0.00516689i
\(527\) 2.57473e8i 1.75914i
\(528\) 5.16624e7i 0.350972i
\(529\) 1.42277e8 4.08871e7i 0.961101 0.276197i
\(530\) 5.67713e6 0.0381330
\(531\) −2.47053e7 −0.165008
\(532\) 1.55919e8 1.03553
\(533\) 2.73971e8 1.80935
\(534\) 4.76501e6i 0.0312925i
\(535\) −8.45784e7 −0.552329
\(536\) 1.08038e7i 0.0701588i
\(537\) 1.02337e7 0.0660859
\(538\) 1.14225e7 0.0733525
\(539\) 1.68672e8i 1.07715i
\(540\) 2.75611e7i 0.175031i
\(541\) 5.01668e7 0.316829 0.158414 0.987373i \(-0.449362\pi\)
0.158414 + 0.987373i \(0.449362\pi\)
\(542\) 1.67888e6 0.0105444
\(543\) 1.43433e8i 0.895883i
\(544\) 3.37967e7i 0.209931i
\(545\) −2.38231e8 −1.47166
\(546\) 1.15042e7i 0.0706773i
\(547\) 8.48201e7 0.518247 0.259124 0.965844i \(-0.416566\pi\)
0.259124 + 0.965844i \(0.416566\pi\)
\(548\) 3.48709e7i 0.211895i
\(549\) 9.29089e6i 0.0561488i
\(550\) 793897.i 0.00477173i
\(551\) 1.41989e7i 0.0848791i
\(552\) 8.85003e6 1.24642e6i 0.0526171 0.00741049i
\(553\) 2.61435e8 1.54592
\(554\) 4.35872e6 0.0256348
\(555\) −1.27160e7 −0.0743824
\(556\) −6.89637e7 −0.401233
\(557\) 1.80275e8i 1.04321i −0.853189 0.521603i \(-0.825334\pi\)
0.853189 0.521603i \(-0.174666\pi\)
\(558\) −3.08080e6 −0.0177321
\(559\) 3.98029e8i 2.27866i
\(560\) 2.64251e8 1.50471
\(561\) −9.50026e7 −0.538080
\(562\) 6.27666e6i 0.0353606i
\(563\) 3.03781e8i 1.70230i 0.524925 + 0.851149i \(0.324093\pi\)
−0.524925 + 0.851149i \(0.675907\pi\)
\(564\) 6.25300e7 0.348539
\(565\) 2.51693e8 1.39549
\(566\) 1.34586e7i 0.0742250i
\(567\) 3.36521e7i 0.184613i
\(568\) −3.04042e6 −0.0165916
\(569\) 1.02127e8i 0.554376i 0.960816 + 0.277188i \(0.0894025\pi\)
−0.960816 + 0.277188i \(0.910598\pi\)
\(570\) −2.80381e6 −0.0151399
\(571\) 2.29011e7i 0.123012i 0.998107 + 0.0615059i \(0.0195903\pi\)
−0.998107 + 0.0615059i \(0.980410\pi\)
\(572\) 1.82735e8i 0.976413i
\(573\) 1.44187e8i 0.766411i
\(574\) 1.63756e7i 0.0865888i
\(575\) 3.18732e7 4.48895e6i 0.167657 0.0236125i
\(576\) −6.28913e7 −0.329097
\(577\) −2.38699e8 −1.24257 −0.621287 0.783583i \(-0.713390\pi\)
−0.621287 + 0.783583i \(0.713390\pi\)
\(578\) 1.17475e7 0.0608362
\(579\) −2.43485e7 −0.125440
\(580\) 2.41157e7i 0.123599i
\(581\) −6.44345e8 −3.28541
\(582\) 3.01844e6i 0.0153113i
\(583\) −1.10106e8 −0.555653
\(584\) −2.52722e6 −0.0126883
\(585\) 9.72784e7i 0.485902i
\(586\) 6.84325e6i 0.0340071i
\(587\) 1.94478e8 0.961514 0.480757 0.876854i \(-0.340362\pi\)
0.480757 + 0.876854i \(0.340362\pi\)
\(588\) 2.06215e8 1.01435
\(589\) 1.47375e8i 0.721239i
\(590\) 4.26861e6i 0.0207841i
\(591\) −1.74594e8 −0.845798
\(592\) 2.91411e7i 0.140456i
\(593\) 1.04386e8 0.500586 0.250293 0.968170i \(-0.419473\pi\)
0.250293 + 0.968170i \(0.419473\pi\)
\(594\) 1.13675e6i 0.00542385i
\(595\) 4.85934e8i 2.30689i
\(596\) 2.88091e8i 1.36079i
\(597\) 7.59869e7i 0.357121i
\(598\) −1.56018e7 + 2.19732e6i −0.0729575 + 0.0102752i
\(599\) −8.10305e7 −0.377023 −0.188512 0.982071i \(-0.560366\pi\)
−0.188512 + 0.982071i \(0.560366\pi\)
\(600\) 1.94327e6 0.00899662
\(601\) −2.22644e7 −0.102562 −0.0512812 0.998684i \(-0.516330\pi\)
−0.0512812 + 0.998684i \(0.516330\pi\)
\(602\) 2.37907e7 0.109048
\(603\) 5.57134e7i 0.254102i
\(604\) −1.96707e8 −0.892707
\(605\) 1.26286e8i 0.570283i
\(606\) −9.58296e6 −0.0430608
\(607\) −3.25433e8 −1.45511 −0.727554 0.686050i \(-0.759343\pi\)
−0.727554 + 0.686050i \(0.759343\pi\)
\(608\) 1.93450e7i 0.0860710i
\(609\) 2.94453e7i 0.130366i
\(610\) 1.60529e6 0.00707236
\(611\) −2.20703e8 −0.967576
\(612\) 1.16148e8i 0.506709i
\(613\) 5.64281e7i 0.244971i −0.992470 0.122485i \(-0.960914\pi\)
0.992470 0.122485i \(-0.0390864\pi\)
\(614\) 1.24991e7 0.0539975
\(615\) 1.38470e8i 0.595293i
\(616\) 2.18678e7 0.0935543
\(617\) 1.30168e8i 0.554176i −0.960845 0.277088i \(-0.910631\pi\)
0.960845 0.277088i \(-0.0893694\pi\)
\(618\) 1.30140e6i 0.00551374i
\(619\) 9.93172e7i 0.418748i −0.977836 0.209374i \(-0.932857\pi\)
0.977836 0.209374i \(-0.0671426\pi\)
\(620\) 2.50305e8i 1.05025i
\(621\) 4.56381e7 6.42758e6i 0.190569 0.0268394i
\(622\) 1.44262e7 0.0599488
\(623\) 4.72701e8 1.95489
\(624\) 2.22932e8 0.917526
\(625\) −1.95806e8 −0.802022
\(626\) 1.48683e7i 0.0606092i
\(627\) 5.43787e7 0.220611
\(628\) 3.78331e8i 1.52754i
\(629\) −5.35878e7 −0.215335
\(630\) −5.81445e6 −0.0232534
\(631\) 2.00601e8i 0.798444i −0.916854 0.399222i \(-0.869280\pi\)
0.916854 0.399222i \(-0.130720\pi\)
\(632\) 2.16166e7i 0.0856318i
\(633\) 1.57718e8 0.621828
\(634\) −1.32543e7 −0.0520103
\(635\) 8.23701e7i 0.321698i
\(636\) 1.34613e8i 0.523257i
\(637\) −7.27850e8 −2.81594
\(638\) 994651.i 0.00383009i
\(639\) −1.56789e7 −0.0600916
\(640\) 4.37921e7i 0.167054i
\(641\) 4.64796e8i 1.76477i −0.470528 0.882385i \(-0.655937\pi\)
0.470528 0.882385i \(-0.344063\pi\)
\(642\) 4.26489e6i 0.0161177i
\(643\) 8.47536e7i 0.318805i −0.987214 0.159402i \(-0.949043\pi\)
0.987214 0.159402i \(-0.0509568\pi\)
\(644\) 6.17583e7 + 4.38506e8i 0.231227 + 1.64179i
\(645\) 2.01172e8 0.749700
\(646\) −1.18159e7 −0.0438296
\(647\) −1.91959e8 −0.708752 −0.354376 0.935103i \(-0.615307\pi\)
−0.354376 + 0.935103i \(0.615307\pi\)
\(648\) 2.78250e6 0.0102261
\(649\) 8.27879e7i 0.302854i
\(650\) −3.42580e6 −0.0124745
\(651\) 3.05623e8i 1.10775i
\(652\) −5.85698e7 −0.211315
\(653\) −1.15990e8 −0.416564 −0.208282 0.978069i \(-0.566787\pi\)
−0.208282 + 0.978069i \(0.566787\pi\)
\(654\) 1.20128e7i 0.0429450i
\(655\) 3.81864e8i 1.35889i
\(656\) 3.17331e8 1.12409
\(657\) −1.30325e7 −0.0459548
\(658\) 1.31917e7i 0.0463046i
\(659\) 1.84207e8i 0.643649i 0.946799 + 0.321824i \(0.104296\pi\)
−0.946799 + 0.321824i \(0.895704\pi\)
\(660\) 9.23576e7 0.321248
\(661\) 8.44401e6i 0.0292378i −0.999893 0.0146189i \(-0.995346\pi\)
0.999893 0.0146189i \(-0.00465350\pi\)
\(662\) 1.03291e7 0.0356030
\(663\) 4.09952e8i 1.40667i
\(664\) 5.32773e7i 0.181986i
\(665\) 2.78145e8i 0.945815i
\(666\) 641206.i 0.00217057i
\(667\) −3.99330e7 + 5.62408e6i −0.134572 + 0.0189528i
\(668\) 4.84143e8 1.62422
\(669\) −1.98190e8 −0.661916
\(670\) −9.62624e6 −0.0320061
\(671\) −3.11339e7 −0.103054
\(672\) 4.01170e7i 0.132197i
\(673\) −4.84325e8 −1.58888 −0.794441 0.607341i \(-0.792236\pi\)
−0.794441 + 0.607341i \(0.792236\pi\)
\(674\) 1.12843e7i 0.0368549i
\(675\) 1.00211e7 0.0325841
\(676\) −4.80272e8 −1.55470
\(677\) 2.68560e8i 0.865517i 0.901510 + 0.432759i \(0.142460\pi\)
−0.901510 + 0.432759i \(0.857540\pi\)
\(678\) 1.26917e7i 0.0407222i
\(679\) 2.99436e8 0.956522
\(680\) −4.01792e7 −0.127783
\(681\) 2.64444e8i 0.837322i
\(682\) 1.03238e7i 0.0325452i
\(683\) −4.25685e8 −1.33606 −0.668030 0.744134i \(-0.732862\pi\)
−0.668030 + 0.744134i \(0.732862\pi\)
\(684\) 6.64823e7i 0.207748i
\(685\) −6.22063e7 −0.193536
\(686\) 1.87951e7i 0.0582201i
\(687\) 1.91637e8i 0.591030i
\(688\) 4.61023e8i 1.41565i
\(689\) 4.75124e8i 1.45261i
\(690\) −1.11057e6 7.88542e6i −0.00338063 0.0240037i
\(691\) 1.62850e8 0.493577 0.246788 0.969069i \(-0.420625\pi\)
0.246788 + 0.969069i \(0.420625\pi\)
\(692\) −3.59076e8 −1.08360
\(693\) 1.12769e8 0.338836
\(694\) −2.59542e7 −0.0776478
\(695\) 1.23025e8i 0.366470i
\(696\) −2.43467e6 −0.00722124
\(697\) 5.83543e8i 1.72335i
\(698\) 2.46181e7 0.0723916
\(699\) −2.66932e6 −0.00781572
\(700\) 9.62862e7i 0.280718i
\(701\) 2.15840e7i 0.0626581i −0.999509 0.0313291i \(-0.990026\pi\)
0.999509 0.0313291i \(-0.00997398\pi\)
\(702\) −4.90529e6 −0.0141792
\(703\) 3.06732e7 0.0882864
\(704\) 2.10750e8i 0.604018i
\(705\) 1.11548e8i 0.318341i
\(706\) 2.89509e6 0.00822711
\(707\) 9.50653e8i 2.69007i
\(708\) 1.01215e8 0.285197
\(709\) 4.64513e8i 1.30334i 0.758501 + 0.651672i \(0.225932\pi\)
−0.758501 + 0.651672i \(0.774068\pi\)
\(710\) 2.70903e6i 0.00756900i
\(711\) 1.11473e8i 0.310142i
\(712\) 3.90850e7i 0.108285i
\(713\) 4.14478e8 5.83742e7i 1.14349 0.161047i
\(714\) −2.45034e7 −0.0673180
\(715\) −3.25982e8 −0.891816
\(716\) −4.19262e7 −0.114221
\(717\) −8.46471e6 −0.0229644
\(718\) 3.27434e6i 0.00884608i
\(719\) −3.55461e8 −0.956324 −0.478162 0.878272i \(-0.658697\pi\)
−0.478162 + 0.878272i \(0.658697\pi\)
\(720\) 1.12674e8i 0.301874i
\(721\) 1.29102e8 0.344452
\(722\) −1.05746e7 −0.0280964
\(723\) 5.99851e7i 0.158719i
\(724\) 5.87631e8i 1.54842i
\(725\) −8.76840e6 −0.0230094
\(726\) −6.36803e6 −0.0166416
\(727\) 9.14852e7i 0.238094i 0.992889 + 0.119047i \(0.0379839\pi\)
−0.992889 + 0.119047i \(0.962016\pi\)
\(728\) 9.43634e7i 0.244573i
\(729\) 1.43489e7 0.0370370
\(730\) 2.25177e6i 0.00578835i
\(731\) 8.47780e8 2.17036
\(732\) 3.80637e7i 0.0970461i
\(733\) 5.88821e8i 1.49510i −0.664203 0.747552i \(-0.731229\pi\)
0.664203 0.747552i \(-0.268771\pi\)
\(734\) 3.10698e7i 0.0785688i
\(735\) 3.67869e8i 0.926469i
\(736\) −5.44056e7 + 7.66238e6i −0.136462 + 0.0192190i
\(737\) 1.86697e8 0.466374
\(738\) −6.98239e6 −0.0173714
\(739\) 5.03241e8 1.24693 0.623466 0.781850i \(-0.285724\pi\)
0.623466 + 0.781850i \(0.285724\pi\)
\(740\) 5.20959e7 0.128561
\(741\) 2.34653e8i 0.576729i
\(742\) −2.83988e7 −0.0695165
\(743\) 5.26147e8i 1.28275i 0.767230 + 0.641373i \(0.221635\pi\)
−0.767230 + 0.641373i \(0.778365\pi\)
\(744\) 2.52702e7 0.0613606
\(745\) 5.13926e8 1.24289
\(746\) 2.46069e7i 0.0592707i
\(747\) 2.74742e8i 0.659118i
\(748\) 3.89215e8 0.930004
\(749\) 4.23087e8 1.00690
\(750\) 1.19579e7i 0.0283448i
\(751\) 2.74856e8i 0.648911i 0.945901 + 0.324456i \(0.105181\pi\)
−0.945901 + 0.324456i \(0.894819\pi\)
\(752\) −2.55632e8 −0.601122
\(753\) 1.85086e8i 0.433500i
\(754\) 4.29208e6 0.0100128
\(755\) 3.50906e8i 0.815362i
\(756\) 1.37869e8i 0.319081i
\(757\) 2.98024e8i 0.687010i 0.939151 + 0.343505i \(0.111614\pi\)
−0.939151 + 0.343505i \(0.888386\pi\)
\(758\) 1.91619e7i 0.0439979i
\(759\) 2.15390e7 + 1.52934e8i 0.0492606 + 0.349768i
\(760\) 2.29982e7 0.0523906
\(761\) −1.44743e8 −0.328431 −0.164216 0.986424i \(-0.552509\pi\)
−0.164216 + 0.986424i \(0.552509\pi\)
\(762\) 4.15353e6 0.00938756
\(763\) 1.19170e9 2.68284
\(764\) 5.90718e8i 1.32465i
\(765\) −2.07197e8 −0.462807
\(766\) 1.26586e7i 0.0281642i
\(767\) −3.57244e8 −0.791732
\(768\) 2.55999e8 0.565137
\(769\) 4.15230e8i 0.913082i 0.889702 + 0.456541i \(0.150912\pi\)
−0.889702 + 0.456541i \(0.849088\pi\)
\(770\) 1.94844e7i 0.0426790i
\(771\) −1.59637e8 −0.348313
\(772\) 9.97530e7 0.216807
\(773\) 3.40961e7i 0.0738187i −0.999319 0.0369094i \(-0.988249\pi\)
0.999319 0.0369094i \(-0.0117513\pi\)
\(774\) 1.01441e7i 0.0218772i
\(775\) 9.10101e7 0.195517
\(776\) 2.47587e7i 0.0529837i
\(777\) 6.36092e7 0.135599
\(778\) 2.86299e7i 0.0607968i
\(779\) 3.34015e8i 0.706568i
\(780\) 3.98539e8i 0.839821i
\(781\) 5.25404e7i 0.110291i
\(782\) −4.68016e6 3.32308e7i −0.00978680 0.0694898i
\(783\) −1.25552e7 −0.0261540