Properties

Label 336.7.bh.b.241.1
Level $336$
Weight $7$
Character 336.241
Analytic conductor $77.298$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(77.2981720963\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 212 x^{6} - 787 x^{5} + 38792 x^{4} - 92833 x^{3} + 1563109 x^{2} + 3107772 x + 38787984\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.1
Root \(5.73828 + 9.93899i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.7.bh.b.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\) \(q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +(437.884 - 758.438i) q^{11} -275.049i q^{13} +3156.61 q^{15} +(-3799.10 - 2193.41i) q^{17} +(11697.8 - 6753.75i) q^{19} +(2341.91 + 4806.68i) q^{21} +(-6367.61 - 11029.0i) q^{23} +(12689.9 - 21979.6i) q^{25} -3788.00i q^{27} +6262.53 q^{29} +(17689.7 + 10213.2i) q^{31} +(-11822.9 + 6825.94i) q^{33} +(69285.1 + 4873.70i) q^{35} +(-7862.08 - 13617.5i) q^{37} +(-2143.79 + 3713.16i) q^{39} -69941.8i q^{41} -113322. q^{43} +(-42614.2 - 24603.3i) q^{45} +(40116.2 - 23161.1i) q^{47} +(43981.8 + 109119. i) q^{49} +(34191.9 + 59222.2i) q^{51} +(-64013.2 + 110874. i) q^{53} +177340. i q^{55} -210561. q^{57} +(-242870. - 140221. i) q^{59} +(84759.3 - 48935.8i) q^{61} +(5848.55 - 83143.6i) q^{63} +(27848.2 + 48234.5i) q^{65} +(87278.8 - 151171. i) q^{67} +198522. i q^{69} -345712. q^{71} +(-104589. - 60384.4i) q^{73} +(-342627. + 197816. i) q^{75} +(-270042. + 131570. i) q^{77} +(381933. + 661527. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -859402. i q^{83} +888317. q^{85} +(-84544.2 - 48811.6i) q^{87} +(-155778. + 89938.3i) q^{89} +(-52787.6 + 78190.9i) q^{91} +(-159207. - 275755. i) q^{93} +(-1.36761e6 + 2.36877e6i) q^{95} +340171. i q^{97} +212812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + O(q^{10}) \) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(3\) −13.5000 7.79423i −0.500000 0.288675i
\(4\) 0 0
\(5\) −175.367 + 101.248i −1.40294 + 0.809986i −0.994693 0.102887i \(-0.967192\pi\)
−0.408243 + 0.912873i \(0.633859\pi\)
\(6\) 0 0
\(7\) −284.280 191.921i −0.828806 0.559536i
\(8\) 0 0
\(9\) 121.500 + 210.444i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 437.884 758.438i 0.328989 0.569826i −0.653323 0.757080i \(-0.726625\pi\)
0.982312 + 0.187254i \(0.0599588\pi\)
\(12\) 0 0
\(13\) 275.049i 0.125193i −0.998039 0.0625964i \(-0.980062\pi\)
0.998039 0.0625964i \(-0.0199381\pi\)
\(14\) 0 0
\(15\) 3156.61 0.935291
\(16\) 0 0
\(17\) −3799.10 2193.41i −0.773276 0.446451i 0.0607662 0.998152i \(-0.480646\pi\)
−0.834042 + 0.551701i \(0.813979\pi\)
\(18\) 0 0
\(19\) 11697.8 6753.75i 1.70547 0.984655i 0.765482 0.643458i \(-0.222501\pi\)
0.939992 0.341198i \(-0.110833\pi\)
\(20\) 0 0
\(21\) 2341.91 + 4806.68i 0.252879 + 0.519024i
\(22\) 0 0
\(23\) −6367.61 11029.0i −0.523351 0.906470i −0.999631 0.0271766i \(-0.991348\pi\)
0.476280 0.879294i \(-0.341985\pi\)
\(24\) 0 0
\(25\) 12689.9 21979.6i 0.812154 1.40669i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) 6262.53 0.256777 0.128388 0.991724i \(-0.459020\pi\)
0.128388 + 0.991724i \(0.459020\pi\)
\(30\) 0 0
\(31\) 17689.7 + 10213.2i 0.593793 + 0.342827i 0.766596 0.642130i \(-0.221949\pi\)
−0.172803 + 0.984956i \(0.555282\pi\)
\(32\) 0 0
\(33\) −11822.9 + 6825.94i −0.328989 + 0.189942i
\(34\) 0 0
\(35\) 69285.1 + 4873.70i 1.61598 + 0.113672i
\(36\) 0 0
\(37\) −7862.08 13617.5i −0.155215 0.268840i 0.777923 0.628360i \(-0.216274\pi\)
−0.933137 + 0.359521i \(0.882940\pi\)
\(38\) 0 0
\(39\) −2143.79 + 3713.16i −0.0361400 + 0.0625964i
\(40\) 0 0
\(41\) 69941.8i 1.01481i −0.861707 0.507405i \(-0.830605\pi\)
0.861707 0.507405i \(-0.169395\pi\)
\(42\) 0 0
\(43\) −113322. −1.42530 −0.712652 0.701517i \(-0.752506\pi\)
−0.712652 + 0.701517i \(0.752506\pi\)
\(44\) 0 0
\(45\) −42614.2 24603.3i −0.467645 0.269995i
\(46\) 0 0
\(47\) 40116.2 23161.1i 0.386390 0.223083i −0.294205 0.955742i \(-0.595055\pi\)
0.680595 + 0.732660i \(0.261721\pi\)
\(48\) 0 0
\(49\) 43981.8 + 109119.i 0.373839 + 0.927494i
\(50\) 0 0
\(51\) 34191.9 + 59222.2i 0.257759 + 0.446451i
\(52\) 0 0
\(53\) −64013.2 + 110874.i −0.429973 + 0.744736i −0.996870 0.0790529i \(-0.974810\pi\)
0.566897 + 0.823789i \(0.308144\pi\)
\(54\) 0 0
\(55\) 177340.i 1.06591i
\(56\) 0 0
\(57\) −210561. −1.13698
\(58\) 0 0
\(59\) −242870. 140221.i −1.18254 0.682742i −0.225942 0.974141i \(-0.572546\pi\)
−0.956602 + 0.291398i \(0.905879\pi\)
\(60\) 0 0
\(61\) 84759.3 48935.8i 0.373420 0.215594i −0.301531 0.953456i \(-0.597498\pi\)
0.674952 + 0.737862i \(0.264164\pi\)
\(62\) 0 0
\(63\) 5848.55 83143.6i 0.0233898 0.332512i
\(64\) 0 0
\(65\) 27848.2 + 48234.5i 0.101404 + 0.175638i
\(66\) 0 0
\(67\) 87278.8 151171.i 0.290191 0.502626i −0.683663 0.729797i \(-0.739614\pi\)
0.973855 + 0.227171i \(0.0729477\pi\)
\(68\) 0 0
\(69\) 198522.i 0.604314i
\(70\) 0 0
\(71\) −345712. −0.965915 −0.482957 0.875644i \(-0.660437\pi\)
−0.482957 + 0.875644i \(0.660437\pi\)
\(72\) 0 0
\(73\) −104589. 60384.4i −0.268854 0.155223i 0.359513 0.933140i \(-0.382943\pi\)
−0.628367 + 0.777917i \(0.716276\pi\)
\(74\) 0 0
\(75\) −342627. + 197816.i −0.812154 + 0.468897i
\(76\) 0 0
\(77\) −270042. + 131570.i −0.591506 + 0.288194i
\(78\) 0 0
\(79\) 381933. + 661527.i 0.774650 + 1.34173i 0.934991 + 0.354671i \(0.115407\pi\)
−0.160341 + 0.987062i \(0.551259\pi\)
\(80\) 0 0
\(81\) −29524.5 + 51137.9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 859402.i 1.50301i −0.659727 0.751505i \(-0.729328\pi\)
0.659727 0.751505i \(-0.270672\pi\)
\(84\) 0 0
\(85\) 888317. 1.44648
\(86\) 0 0
\(87\) −84544.2 48811.6i −0.128388 0.0741251i
\(88\) 0 0
\(89\) −155778. + 89938.3i −0.220971 + 0.127578i −0.606400 0.795160i \(-0.707387\pi\)
0.385429 + 0.922738i \(0.374054\pi\)
\(90\) 0 0
\(91\) −52787.6 + 78190.9i −0.0700499 + 0.103761i
\(92\) 0 0
\(93\) −159207. 275755.i −0.197931 0.342827i
\(94\) 0 0
\(95\) −1.36761e6 + 2.36877e6i −1.59511 + 2.76282i
\(96\) 0 0
\(97\) 340171.i 0.372720i 0.982482 + 0.186360i \(0.0596690\pi\)
−0.982482 + 0.186360i \(0.940331\pi\)
\(98\) 0 0
\(99\) 212812. 0.219326
\(100\) 0 0
\(101\) 903587. + 521686.i 0.877013 + 0.506344i 0.869672 0.493630i \(-0.164330\pi\)
0.00734043 + 0.999973i \(0.497663\pi\)
\(102\) 0 0
\(103\) 675522. 390013.i 0.618198 0.356917i −0.157969 0.987444i \(-0.550495\pi\)
0.776167 + 0.630527i \(0.217161\pi\)
\(104\) 0 0
\(105\) −897362. 605819.i −0.775175 0.523329i
\(106\) 0 0
\(107\) −498844. 864024.i −0.407205 0.705301i 0.587370 0.809319i \(-0.300163\pi\)
−0.994575 + 0.104018i \(0.966830\pi\)
\(108\) 0 0
\(109\) −727835. + 1.26065e6i −0.562023 + 0.973452i 0.435297 + 0.900287i \(0.356643\pi\)
−0.997320 + 0.0731648i \(0.976690\pi\)
\(110\) 0 0
\(111\) 245116.i 0.179226i
\(112\) 0 0
\(113\) 177612. 0.123094 0.0615469 0.998104i \(-0.480397\pi\)
0.0615469 + 0.998104i \(0.480397\pi\)
\(114\) 0 0
\(115\) 2.23334e6 + 1.28942e6i 1.46846 + 0.847814i
\(116\) 0 0
\(117\) 57882.4 33418.4i 0.0361400 0.0208655i
\(118\) 0 0
\(119\) 659049. + 1.35267e6i 0.391090 + 0.802697i
\(120\) 0 0
\(121\) 502295. + 870001.i 0.283533 + 0.491093i
\(122\) 0 0
\(123\) −545142. + 944214.i −0.292951 + 0.507405i
\(124\) 0 0
\(125\) 1.97531e6i 1.01136i
\(126\) 0 0
\(127\) −924373. −0.451269 −0.225635 0.974212i \(-0.572446\pi\)
−0.225635 + 0.974212i \(0.572446\pi\)
\(128\) 0 0
\(129\) 1.52984e6 + 883255.i 0.712652 + 0.411450i
\(130\) 0 0
\(131\) −837624. + 483602.i −0.372593 + 0.215117i −0.674591 0.738192i \(-0.735680\pi\)
0.301997 + 0.953309i \(0.402347\pi\)
\(132\) 0 0
\(133\) −4.62165e6 325100.i −1.96446 0.138185i
\(134\) 0 0
\(135\) 383528. + 664290.i 0.155882 + 0.269995i
\(136\) 0 0
\(137\) −2.35006e6 + 4.07043e6i −0.913940 + 1.58299i −0.105493 + 0.994420i \(0.533642\pi\)
−0.808446 + 0.588570i \(0.799691\pi\)
\(138\) 0 0
\(139\) 1.64306e6i 0.611798i −0.952064 0.305899i \(-0.901043\pi\)
0.952064 0.305899i \(-0.0989570\pi\)
\(140\) 0 0
\(141\) −722092. −0.257594
\(142\) 0 0
\(143\) −208607. 120439.i −0.0713381 0.0411870i
\(144\) 0 0
\(145\) −1.09824e6 + 634070.i −0.360242 + 0.207986i
\(146\) 0 0
\(147\) 256742. 1.81591e6i 0.0808249 0.571665i
\(148\) 0 0
\(149\) −2.31369e6 4.00743e6i −0.699433 1.21145i −0.968663 0.248378i \(-0.920103\pi\)
0.269230 0.963076i \(-0.413231\pi\)
\(150\) 0 0
\(151\) −2.24610e6 + 3.89036e6i −0.652377 + 1.12995i 0.330168 + 0.943922i \(0.392895\pi\)
−0.982545 + 0.186028i \(0.940439\pi\)
\(152\) 0 0
\(153\) 1.06600e6i 0.297634i
\(154\) 0 0
\(155\) −4.13625e6 −1.11074
\(156\) 0 0
\(157\) −4.17859e6 2.41251e6i −1.07977 0.623405i −0.148935 0.988847i \(-0.547584\pi\)
−0.930834 + 0.365442i \(0.880918\pi\)
\(158\) 0 0
\(159\) 1.72836e6 997866.i 0.429973 0.248245i
\(160\) 0 0
\(161\) −306513. + 4.35741e6i −0.0734464 + 1.04412i
\(162\) 0 0
\(163\) −1.69763e6 2.94038e6i −0.391994 0.678954i 0.600718 0.799461i \(-0.294881\pi\)
−0.992713 + 0.120507i \(0.961548\pi\)
\(164\) 0 0
\(165\) 1.38223e6 2.39409e6i 0.307700 0.532953i
\(166\) 0 0
\(167\) 2.04579e6i 0.439249i 0.975584 + 0.219625i \(0.0704832\pi\)
−0.975584 + 0.219625i \(0.929517\pi\)
\(168\) 0 0
\(169\) 4.75116e6 0.984327
\(170\) 0 0
\(171\) 2.84258e6 + 1.64116e6i 0.568491 + 0.328218i
\(172\) 0 0
\(173\) −272758. + 157477.i −0.0526792 + 0.0304144i −0.526108 0.850418i \(-0.676349\pi\)
0.473429 + 0.880832i \(0.343016\pi\)
\(174\) 0 0
\(175\) −7.82583e6 + 3.81290e6i −1.46021 + 0.711445i
\(176\) 0 0
\(177\) 2.18583e6 + 3.78596e6i 0.394181 + 0.682742i
\(178\) 0 0
\(179\) −2.01204e6 + 3.48495e6i −0.350814 + 0.607627i −0.986392 0.164409i \(-0.947428\pi\)
0.635579 + 0.772036i \(0.280762\pi\)
\(180\) 0 0
\(181\) 1.53820e6i 0.259405i 0.991553 + 0.129703i \(0.0414022\pi\)
−0.991553 + 0.129703i \(0.958598\pi\)
\(182\) 0 0
\(183\) −1.52567e6 −0.248947
\(184\) 0 0
\(185\) 2.75750e6 + 1.59204e6i 0.435512 + 0.251443i
\(186\) 0 0
\(187\) −3.32714e6 + 1.92092e6i −0.508798 + 0.293755i
\(188\) 0 0
\(189\) −726995. + 1.07685e6i −0.107683 + 0.159504i
\(190\) 0 0
\(191\) 2.13865e6 + 3.70425e6i 0.306931 + 0.531619i 0.977689 0.210056i \(-0.0673647\pi\)
−0.670759 + 0.741676i \(0.734031\pi\)
\(192\) 0 0
\(193\) 3.22312e6 5.58261e6i 0.448337 0.776543i −0.549941 0.835204i \(-0.685350\pi\)
0.998278 + 0.0586609i \(0.0186831\pi\)
\(194\) 0 0
\(195\) 868220.i 0.117092i
\(196\) 0 0
\(197\) −2.73215e6 −0.357359 −0.178680 0.983907i \(-0.557183\pi\)
−0.178680 + 0.983907i \(0.557183\pi\)
\(198\) 0 0
\(199\) −517231. 298623.i −0.0656334 0.0378935i 0.466824 0.884350i \(-0.345398\pi\)
−0.532458 + 0.846457i \(0.678731\pi\)
\(200\) 0 0
\(201\) −2.35653e6 + 1.36054e6i −0.290191 + 0.167542i
\(202\) 0 0
\(203\) −1.78032e6 1.20191e6i −0.212818 0.143676i
\(204\) 0 0
\(205\) 7.08148e6 + 1.22655e7i 0.821982 + 1.42372i
\(206\) 0 0
\(207\) 1.54733e6 2.68005e6i 0.174450 0.302157i
\(208\) 0 0
\(209\) 1.18294e7i 1.29576i
\(210\) 0 0
\(211\) 3.67602e6 0.391319 0.195659 0.980672i \(-0.437315\pi\)
0.195659 + 0.980672i \(0.437315\pi\)
\(212\) 0 0
\(213\) 4.66711e6 + 2.69455e6i 0.482957 + 0.278836i
\(214\) 0 0
\(215\) 1.98729e7 1.14736e7i 1.99961 1.15448i
\(216\) 0 0
\(217\) −3.06872e6 6.29842e6i −0.300316 0.616386i
\(218\) 0 0
\(219\) 941299. + 1.63038e6i 0.0896180 + 0.155223i
\(220\) 0 0
\(221\) −603295. + 1.04494e6i −0.0558924 + 0.0968086i
\(222\) 0 0
\(223\) 1.43225e7i 1.29153i −0.763535 0.645766i \(-0.776538\pi\)
0.763535 0.645766i \(-0.223462\pi\)
\(224\) 0 0
\(225\) 6.16729e6 0.541436
\(226\) 0 0
\(227\) 2.62502e6 + 1.51555e6i 0.224416 + 0.129567i 0.607994 0.793942i \(-0.291975\pi\)
−0.383577 + 0.923509i \(0.625308\pi\)
\(228\) 0 0
\(229\) −5.42194e6 + 3.13036e6i −0.451490 + 0.260668i −0.708459 0.705752i \(-0.750609\pi\)
0.256969 + 0.966420i \(0.417276\pi\)
\(230\) 0 0
\(231\) 4.67105e6 + 328575.i 0.378947 + 0.0266562i
\(232\) 0 0
\(233\) 5.92360e6 + 1.02600e7i 0.468293 + 0.811107i 0.999343 0.0362330i \(-0.0115359\pi\)
−0.531050 + 0.847340i \(0.678203\pi\)
\(234\) 0 0
\(235\) −4.69004e6 + 8.12339e6i −0.361387 + 0.625941i
\(236\) 0 0
\(237\) 1.19075e7i 0.894489i
\(238\) 0 0
\(239\) −4.29229e6 −0.314410 −0.157205 0.987566i \(-0.550248\pi\)
−0.157205 + 0.987566i \(0.550248\pi\)
\(240\) 0 0
\(241\) 1.37366e7 + 7.93085e6i 0.981362 + 0.566589i 0.902681 0.430310i \(-0.141596\pi\)
0.0786807 + 0.996900i \(0.474929\pi\)
\(242\) 0 0
\(243\) 797162. 460241.i 0.0555556 0.0320750i
\(244\) 0 0
\(245\) −1.87610e7 1.46827e7i −1.27573 0.998410i
\(246\) 0 0
\(247\) −1.85761e6 3.21747e6i −0.123272 0.213513i
\(248\) 0 0
\(249\) −6.69838e6 + 1.16019e7i −0.433882 + 0.751505i
\(250\) 0 0
\(251\) 7.11752e6i 0.450099i 0.974347 + 0.225049i \(0.0722543\pi\)
−0.974347 + 0.225049i \(0.927746\pi\)
\(252\) 0 0
\(253\) −1.11531e7 −0.688707
\(254\) 0 0
\(255\) −1.19923e7 6.92374e6i −0.723238 0.417562i
\(256\) 0 0
\(257\) −6.24715e6 + 3.60680e6i −0.368030 + 0.212482i −0.672597 0.740009i \(-0.734821\pi\)
0.304568 + 0.952491i \(0.401488\pi\)
\(258\) 0 0
\(259\) −378451. + 5.38010e6i −0.0217826 + 0.309664i
\(260\) 0 0
\(261\) 760898. + 1.31791e6i 0.0427962 + 0.0741251i
\(262\) 0 0
\(263\) −8.28046e6 + 1.43422e7i −0.455184 + 0.788402i −0.998699 0.0509974i \(-0.983760\pi\)
0.543514 + 0.839400i \(0.317093\pi\)
\(264\) 0 0
\(265\) 2.59249e7i 1.39309i
\(266\) 0 0
\(267\) 2.80400e6 0.147314
\(268\) 0 0
\(269\) 4.73497e6 + 2.73374e6i 0.243254 + 0.140443i 0.616671 0.787221i \(-0.288481\pi\)
−0.373417 + 0.927663i \(0.621814\pi\)
\(270\) 0 0
\(271\) 1.61594e7 9.32961e6i 0.811925 0.468765i −0.0356988 0.999363i \(-0.511366\pi\)
0.847624 + 0.530597i \(0.178032\pi\)
\(272\) 0 0
\(273\) 1.32207e6 644139.i 0.0649780 0.0316586i
\(274\) 0 0
\(275\) −1.11134e7 1.92490e7i −0.534379 0.925572i
\(276\) 0 0
\(277\) 3.81751e6 6.61212e6i 0.179614 0.311101i −0.762134 0.647419i \(-0.775848\pi\)
0.941748 + 0.336318i \(0.109182\pi\)
\(278\) 0 0
\(279\) 4.96359e6i 0.228551i
\(280\) 0 0
\(281\) −2.86272e7 −1.29021 −0.645103 0.764095i \(-0.723186\pi\)
−0.645103 + 0.764095i \(0.723186\pi\)
\(282\) 0 0
\(283\) 1.84385e7 + 1.06455e7i 0.813518 + 0.469685i 0.848176 0.529714i \(-0.177701\pi\)
−0.0346580 + 0.999399i \(0.511034\pi\)
\(284\) 0 0
\(285\) 3.69255e7 2.13189e7i 1.59511 0.920939i
\(286\) 0 0
\(287\) −1.34233e7 + 1.98831e7i −0.567823 + 0.841081i
\(288\) 0 0
\(289\) −2.44666e6 4.23774e6i −0.101363 0.175566i
\(290\) 0 0
\(291\) 2.65137e6 4.59231e6i 0.107595 0.186360i
\(292\) 0 0
\(293\) 1.72102e7i 0.684199i −0.939664 0.342100i \(-0.888862\pi\)
0.939664 0.342100i \(-0.111138\pi\)
\(294\) 0 0
\(295\) 5.67885e7 2.21205
\(296\) 0 0
\(297\) −2.87296e6 1.65870e6i −0.109663 0.0633139i
\(298\) 0 0
\(299\) −3.03352e6 + 1.75140e6i −0.113484 + 0.0655198i
\(300\) 0 0
\(301\) 3.22151e7 + 2.17488e7i 1.18130 + 0.797509i
\(302\) 0 0
\(303\) −8.13228e6 1.40855e7i −0.292338 0.506344i
\(304\) 0 0
\(305\) −9.90933e6 + 1.71635e7i −0.349257 + 0.604930i
\(306\) 0 0
\(307\) 4.11253e7i 1.42133i −0.703533 0.710663i \(-0.748395\pi\)
0.703533 0.710663i \(-0.251605\pi\)
\(308\) 0 0
\(309\) −1.21594e7 −0.412132
\(310\) 0 0
\(311\) −9.88085e6 5.70471e6i −0.328483 0.189650i 0.326684 0.945133i \(-0.394069\pi\)
−0.655167 + 0.755484i \(0.727402\pi\)
\(312\) 0 0
\(313\) −930200. + 537051.i −0.0303350 + 0.0175139i −0.515091 0.857136i \(-0.672242\pi\)
0.484756 + 0.874650i \(0.338908\pi\)
\(314\) 0 0
\(315\) 7.39249e6 + 1.51728e7i 0.236515 + 0.485438i
\(316\) 0 0
\(317\) 9.89978e6 + 1.71469e7i 0.310776 + 0.538280i 0.978531 0.206101i \(-0.0660777\pi\)
−0.667754 + 0.744382i \(0.732744\pi\)
\(318\) 0 0
\(319\) 2.74226e6 4.74974e6i 0.0844768 0.146318i
\(320\) 0 0
\(321\) 1.55524e7i 0.470200i
\(322\) 0 0
\(323\) −5.92551e7 −1.75840
\(324\) 0 0
\(325\) −6.04545e6 3.49034e6i −0.176108 0.101676i
\(326\) 0 0
\(327\) 1.96516e7 1.13458e7i 0.562023 0.324484i
\(328\) 0 0
\(329\) −1.58494e7 1.11489e6i −0.445065 0.0313071i
\(330\) 0 0
\(331\) −9.56610e6 1.65690e7i −0.263785 0.456890i 0.703459 0.710736i \(-0.251638\pi\)
−0.967245 + 0.253846i \(0.918304\pi\)
\(332\) 0 0
\(333\) 1.91049e6 3.30906e6i 0.0517382 0.0896132i
\(334\) 0 0
\(335\) 3.53473e7i 0.940204i
\(336\) 0 0
\(337\) 6.12984e7 1.60162 0.800810 0.598919i \(-0.204403\pi\)
0.800810 + 0.598919i \(0.204403\pi\)
\(338\) 0 0
\(339\) −2.39776e6 1.38435e6i −0.0615469 0.0355341i
\(340\) 0 0
\(341\) 1.54921e7 8.94435e6i 0.390703 0.225572i
\(342\) 0 0
\(343\) 8.43899e6 3.94613e7i 0.209126 0.977889i
\(344\) 0 0
\(345\) −2.01000e7 3.48143e7i −0.489485 0.847814i
\(346\) 0 0
\(347\) 3.87907e7 6.71875e7i 0.928409 1.60805i 0.142424 0.989806i \(-0.454510\pi\)
0.785985 0.618246i \(-0.212156\pi\)
\(348\) 0 0
\(349\) 3.32443e7i 0.782061i −0.920378 0.391031i \(-0.872119\pi\)
0.920378 0.391031i \(-0.127881\pi\)
\(350\) 0 0
\(351\) −1.04188e6 −0.0240934
\(352\) 0 0
\(353\) −1.68383e7 9.72160e6i −0.382802 0.221011i 0.296235 0.955115i \(-0.404269\pi\)
−0.679037 + 0.734104i \(0.737602\pi\)
\(354\) 0 0
\(355\) 6.06264e7 3.50027e7i 1.35512 0.782377i
\(356\) 0 0
\(357\) 1.64587e6 2.33979e7i 0.0361735 0.514246i
\(358\) 0 0
\(359\) 1.27237e7 + 2.20381e7i 0.274999 + 0.476311i 0.970135 0.242567i \(-0.0779893\pi\)
−0.695136 + 0.718878i \(0.744656\pi\)
\(360\) 0 0
\(361\) 6.77034e7 1.17266e8i 1.43909 2.49258i
\(362\) 0 0
\(363\) 1.56600e7i 0.327395i
\(364\) 0 0
\(365\) 2.44552e7 0.502914
\(366\) 0 0
\(367\) 7.02719e6 + 4.05715e6i 0.142162 + 0.0820773i 0.569394 0.822065i \(-0.307178\pi\)
−0.427232 + 0.904142i \(0.640511\pi\)
\(368\) 0 0
\(369\) 1.47188e7 8.49793e6i 0.292951 0.169135i
\(370\) 0 0
\(371\) 3.94767e7 1.92339e7i 0.773071 0.376656i
\(372\) 0 0
\(373\) 3.60324e7 + 6.24099e7i 0.694330 + 1.20262i 0.970406 + 0.241480i \(0.0776327\pi\)
−0.276076 + 0.961136i \(0.589034\pi\)
\(374\) 0 0
\(375\) 1.53960e7 2.66667e7i 0.291955 0.505680i
\(376\) 0 0
\(377\) 1.72250e6i 0.0321466i
\(378\) 0 0
\(379\) −4.53715e7 −0.833423 −0.416711 0.909039i \(-0.636817\pi\)
−0.416711 + 0.909039i \(0.636817\pi\)
\(380\) 0 0
\(381\) 1.24790e7 + 7.20477e6i 0.225635 + 0.130270i
\(382\) 0 0
\(383\) −6.55862e7 + 3.78662e7i −1.16739 + 0.673994i −0.953064 0.302768i \(-0.902089\pi\)
−0.214327 + 0.976762i \(0.568756\pi\)
\(384\) 0 0
\(385\) 3.40352e7 5.04143e7i 0.596412 0.883429i
\(386\) 0 0
\(387\) −1.37686e7 2.38479e7i −0.237551 0.411450i
\(388\) 0 0
\(389\) −4.41471e6 + 7.64649e6i −0.0749986 + 0.129901i −0.901086 0.433641i \(-0.857229\pi\)
0.826087 + 0.563542i \(0.190562\pi\)
\(390\) 0 0
\(391\) 5.58672e7i 0.934602i
\(392\) 0 0
\(393\) 1.50772e7 0.248396
\(394\) 0 0
\(395\) −1.33957e8 7.73400e7i −2.17357 1.25491i
\(396\) 0 0
\(397\) −3.45140e7 + 1.99267e7i −0.551599 + 0.318466i −0.749767 0.661702i \(-0.769834\pi\)
0.198167 + 0.980168i \(0.436501\pi\)
\(398\) 0 0
\(399\) 5.98584e7 + 4.04111e7i 0.942338 + 0.636182i
\(400\) 0 0
\(401\) 1.65566e6 + 2.86769e6i 0.0256767 + 0.0444733i 0.878578 0.477599i \(-0.158493\pi\)
−0.852902 + 0.522072i \(0.825159\pi\)
\(402\) 0 0
\(403\) 2.80911e6 4.86553e6i 0.0429194 0.0743386i
\(404\) 0 0
\(405\) 1.19572e7i 0.179997i
\(406\) 0 0
\(407\) −1.37707e7 −0.204255
\(408\) 0 0
\(409\) −8.98031e7 5.18478e7i −1.31257 0.757811i −0.330046 0.943965i \(-0.607064\pi\)
−0.982521 + 0.186154i \(0.940398\pi\)
\(410\) 0 0
\(411\) 6.34517e7 3.66338e7i 0.913940 0.527663i
\(412\) 0 0
\(413\) 4.21318e7 + 8.64738e7i 0.598081 + 1.22754i
\(414\) 0 0
\(415\) 8.70129e7 + 1.50711e8i 1.21742 + 2.10863i
\(416\) 0 0
\(417\) −1.28064e7 + 2.21813e7i −0.176611 + 0.305899i
\(418\) 0 0
\(419\) 2.42723e7i 0.329965i −0.986296 0.164983i \(-0.947243\pi\)
0.986296 0.164983i \(-0.0527568\pi\)
\(420\) 0 0
\(421\) −8.03195e7 −1.07640 −0.538201 0.842816i \(-0.680896\pi\)
−0.538201 + 0.842816i \(0.680896\pi\)
\(422\) 0 0
\(423\) 9.74824e6 + 5.62815e6i 0.128797 + 0.0743609i
\(424\) 0 0
\(425\) −9.64205e7 + 5.56684e7i −1.25604 + 0.725174i
\(426\) 0 0
\(427\) −3.34872e7 2.35558e6i −0.430126 0.0302562i
\(428\) 0 0
\(429\) 1.87747e6 + 3.25186e6i 0.0237794 + 0.0411870i
\(430\) 0 0
\(431\) −2.93452e7 + 5.08273e7i −0.366526 + 0.634841i −0.989020 0.147783i \(-0.952786\pi\)
0.622494 + 0.782625i \(0.286120\pi\)
\(432\) 0 0
\(433\) 1.51707e8i 1.86871i 0.356344 + 0.934355i \(0.384023\pi\)
−0.356344 + 0.934355i \(0.615977\pi\)
\(434\) 0 0
\(435\) 1.97684e7 0.240161
\(436\) 0 0
\(437\) −1.48975e8 8.60105e7i −1.78512 1.03064i
\(438\) 0 0
\(439\) −1.05336e8 + 6.08155e7i −1.24504 + 0.718821i −0.970115 0.242646i \(-0.921985\pi\)
−0.274920 + 0.961467i \(0.588651\pi\)
\(440\) 0 0
\(441\) −1.76196e7 + 2.25136e7i −0.205438 + 0.262500i
\(442\) 0 0
\(443\) 4.63310e7 + 8.02476e7i 0.532918 + 0.923041i 0.999261 + 0.0384371i \(0.0122379\pi\)
−0.466343 + 0.884604i \(0.654429\pi\)
\(444\) 0 0
\(445\) 1.82122e7 3.15444e7i 0.206672 0.357967i
\(446\) 0 0
\(447\) 7.21337e7i 0.807636i
\(448\) 0 0
\(449\) −2.40772e7 −0.265991 −0.132996 0.991117i \(-0.542460\pi\)
−0.132996 + 0.991117i \(0.542460\pi\)
\(450\) 0 0
\(451\) −5.30465e7 3.06264e7i −0.578265 0.333862i
\(452\) 0 0
\(453\) 6.06447e7 3.50133e7i 0.652377 0.376650i
\(454\) 0 0
\(455\) 1.34051e6 1.90568e7i 0.0142310 0.202309i
\(456\) 0 0
\(457\) 3.25397e7 + 5.63605e7i 0.340930 + 0.590509i 0.984606 0.174790i \(-0.0559247\pi\)
−0.643675 + 0.765299i \(0.722591\pi\)
\(458\) 0 0
\(459\) −8.30864e6 + 1.43910e7i −0.0859195 + 0.148817i
\(460\) 0 0
\(461\) 1.22022e8i 1.24548i 0.782429 + 0.622740i \(0.213980\pi\)
−0.782429 + 0.622740i \(0.786020\pi\)
\(462\) 0 0
\(463\) −2.62985e7 −0.264965 −0.132482 0.991185i \(-0.542295\pi\)
−0.132482 + 0.991185i \(0.542295\pi\)
\(464\) 0 0
\(465\) 5.58394e7 + 3.22389e7i 0.555369 + 0.320643i
\(466\) 0 0
\(467\) −5.31512e7 + 3.06869e7i −0.521870 + 0.301302i −0.737699 0.675129i \(-0.764088\pi\)
0.215829 + 0.976431i \(0.430755\pi\)
\(468\) 0 0
\(469\) −5.38246e7 + 2.62244e7i −0.521750 + 0.254207i
\(470\) 0 0
\(471\) 3.76073e7 + 6.51378e7i 0.359923 + 0.623405i
\(472\) 0 0
\(473\) −4.96218e7 + 8.59475e7i −0.468909 + 0.812175i
\(474\) 0 0
\(475\) 3.42818e8i 3.19877i
\(476\) 0 0
\(477\) −3.11104e7 −0.286649
\(478\) 0 0
\(479\) 1.67375e8 + 9.66342e7i 1.52295 + 0.879274i 0.999632 + 0.0271349i \(0.00863836\pi\)
0.523315 + 0.852139i \(0.324695\pi\)
\(480\) 0 0
\(481\) −3.74548e6 + 2.16246e6i −0.0336568 + 0.0194317i
\(482\) 0 0
\(483\) 3.81006e7 5.64361e7i 0.338135 0.500859i
\(484\) 0 0
\(485\) −3.44417e7 5.96548e7i −0.301898 0.522902i
\(486\) 0 0
\(487\) 741867. 1.28495e6i 0.00642302 0.0111250i −0.862796 0.505552i \(-0.831289\pi\)
0.869219 + 0.494427i \(0.164622\pi\)
\(488\) 0 0
\(489\) 5.29268e7i 0.452636i
\(490\) 0 0
\(491\) −1.33332e8 −1.12639 −0.563195 0.826324i \(-0.690428\pi\)
−0.563195 + 0.826324i \(0.690428\pi\)
\(492\) 0 0
\(493\) −2.37920e7 1.37363e7i −0.198559 0.114638i
\(494\) 0 0
\(495\) −3.73202e7 + 2.15468e7i −0.307700 + 0.177651i
\(496\) 0 0
\(497\) 9.82790e7 + 6.63493e7i 0.800556 + 0.540464i
\(498\) 0 0
\(499\) 7.54918e7 + 1.30756e8i 0.607573 + 1.05235i 0.991639 + 0.129042i \(0.0411901\pi\)
−0.384066 + 0.923306i \(0.625477\pi\)
\(500\) 0 0
\(501\) 1.59453e7 2.76181e7i 0.126800 0.219625i
\(502\) 0 0
\(503\) 9.92575e7i 0.779937i 0.920828 + 0.389968i \(0.127514\pi\)
−0.920828 + 0.389968i \(0.872486\pi\)
\(504\) 0 0
\(505\) −2.11279e8 −1.64052
\(506\) 0 0
\(507\) −6.41406e7 3.70316e7i −0.492163 0.284151i
\(508\) 0 0
\(509\) 1.07059e8 6.18103e7i 0.811835 0.468713i −0.0357576 0.999360i \(-0.511384\pi\)
0.847593 + 0.530647i \(0.178051\pi\)
\(510\) 0 0
\(511\) 1.81435e7 + 3.72389e7i 0.135975 + 0.279083i
\(512\) 0 0
\(513\) −2.55832e7 4.43114e7i −0.189497 0.328218i
\(514\) 0 0
\(515\) −7.89762e7 + 1.36791e8i −0.578195 + 1.00146i
\(516\) 0 0
\(517\) 4.05675e7i 0.293567i
\(518\) 0 0
\(519\) 4.90965e6 0.0351195
\(520\) 0 0
\(521\) 1.41733e8 + 8.18296e7i 1.00221 + 0.578625i 0.908901 0.417012i \(-0.136923\pi\)
0.0933071 + 0.995637i \(0.470256\pi\)
\(522\) 0 0
\(523\) −2.21384e8 + 1.27816e8i −1.54754 + 0.893471i −0.549208 + 0.835686i \(0.685070\pi\)
−0.998329 + 0.0577847i \(0.981596\pi\)
\(524\) 0 0
\(525\) 1.35367e8 + 9.52211e6i 0.935483 + 0.0658044i
\(526\) 0 0
\(527\) −4.48033e7 7.76016e7i −0.306111 0.530199i
\(528\) 0 0
\(529\) −7.07498e6 + 1.22542e7i −0.0477924 + 0.0827788i
\(530\) 0 0
\(531\) 6.81474e7i 0.455161i
\(532\) 0 0
\(533\) −1.92374e7 −0.127047
\(534\) 0 0
\(535\) 1.74962e8 + 1.01014e8i 1.14257 + 0.659661i
\(536\) 0 0
\(537\) 5.43250e7 3.13645e7i 0.350814 0.202542i
\(538\) 0 0
\(539\) 1.02019e8 + 1.44239e7i 0.651498 + 0.0921122i
\(540\) 0 0
\(541\) 1.21035e8 + 2.09639e8i 0.764398 + 1.32398i 0.940564 + 0.339616i \(0.110297\pi\)
−0.176166 + 0.984361i \(0.556369\pi\)
\(542\) 0 0
\(543\) 1.19891e7 2.07658e7i 0.0748838 0.129703i
\(544\) 0 0
\(545\) 2.94768e8i 1.82092i
\(546\) 0 0
\(547\) 3.05715e7 0.186790 0.0933952 0.995629i \(-0.470228\pi\)
0.0933952 + 0.995629i \(0.470228\pi\)
\(548\) 0 0
\(549\) 2.05965e7 + 1.18914e7i 0.124473 + 0.0718648i
\(550\) 0 0
\(551\) 7.32581e7 4.22956e7i 0.437926 0.252837i
\(552\) 0 0
\(553\) 1.83848e7 2.61360e8i 0.108713 1.54548i
\(554\) 0 0
\(555\) −2.48175e7 4.29852e7i −0.145171 0.251443i
\(556\) 0 0
\(557\) −1.16542e8 + 2.01856e8i −0.674396 + 1.16809i 0.302249 + 0.953229i \(0.402263\pi\)
−0.976645 + 0.214860i \(0.931071\pi\)
\(558\) 0 0
\(559\) 3.11690e7i 0.178438i
\(560\) 0 0
\(561\) 5.98884e7 0.339199
\(562\) 0 0
\(563\) −1.95271e8 1.12740e8i −1.09424 0.631758i −0.159536 0.987192i \(-0.551000\pi\)
−0.934702 + 0.355434i \(0.884333\pi\)
\(564\) 0 0
\(565\) −3.11472e7 + 1.79829e7i −0.172693 + 0.0997042i
\(566\) 0 0
\(567\) 1.82077e7 8.87115e6i 0.0998862 0.0486666i
\(568\) 0 0
\(569\) −1.07390e8 1.86004e8i −0.582943 1.00969i −0.995128 0.0985864i \(-0.968568\pi\)
0.412186 0.911100i \(-0.364765\pi\)
\(570\) 0 0
\(571\) 1.71362e8 2.96807e8i 0.920460 1.59428i 0.121757 0.992560i \(-0.461147\pi\)
0.798704 0.601724i \(-0.205519\pi\)
\(572\) 0 0
\(573\) 6.66766e7i 0.354413i
\(574\) 0 0
\(575\) −3.23217e8 −1.70017
\(576\) 0 0
\(577\) 2.42646e8 + 1.40092e8i 1.26312 + 0.729263i 0.973677 0.227931i \(-0.0731962\pi\)
0.289444 + 0.957195i \(0.406530\pi\)
\(578\) 0 0
\(579\) −8.70243e7 + 5.02435e7i −0.448337 + 0.258848i
\(580\) 0 0
\(581\) −1.64937e8 + 2.44311e8i −0.840989 + 1.24570i
\(582\) 0 0
\(583\) 5.60607e7 + 9.71000e7i 0.282913 + 0.490020i
\(584\) 0 0
\(585\) −6.76711e6 + 1.17210e7i −0.0338015 + 0.0585458i
\(586\) 0 0
\(587\) 2.73172e8i 1.35059i 0.737549 + 0.675293i \(0.235983\pi\)
−0.737549 + 0.675293i \(0.764017\pi\)
\(588\) 0 0
\(589\) 2.75908e8 1.35026
\(590\) 0 0
\(591\) 3.68840e7 + 2.12950e7i 0.178680 + 0.103161i
\(592\) 0 0
\(593\) −3.17713e8 + 1.83432e8i −1.52360 + 0.879651i −0.523991 + 0.851724i \(0.675557\pi\)
−0.999610 + 0.0279272i \(0.991109\pi\)
\(594\) 0 0
\(595\) −2.52531e8 1.70487e8i −1.19885 0.809355i
\(596\) 0 0
\(597\) 4.65507e6 + 8.06283e6i 0.0218778 + 0.0378935i
\(598\) 0 0
\(599\) −8.45253e7 + 1.46402e8i −0.393284 + 0.681188i −0.992881 0.119114i \(-0.961994\pi\)
0.599596 + 0.800303i \(0.295328\pi\)
\(600\) 0 0
\(601\) 1.61411e8i 0.743551i 0.928323 + 0.371775i \(0.121251\pi\)
−0.928323 + 0.371775i \(0.878749\pi\)
\(602\) 0 0
\(603\) 4.24175e7 0.193461
\(604\) 0 0
\(605\) −1.76172e8 1.01713e8i −0.795556 0.459315i
\(606\) 0 0
\(607\) −1.67933e8 + 9.69564e7i −0.750881 + 0.433521i −0.826012 0.563652i \(-0.809396\pi\)
0.0751313 + 0.997174i \(0.476062\pi\)
\(608\) 0 0
\(609\) 1.46663e7 + 3.01020e7i 0.0649335 + 0.133273i
\(610\) 0 0
\(611\) −6.37043e6 1.10339e7i −0.0279283 0.0483733i
\(612\) 0 0
\(613\) 5.21774e7 9.03739e7i 0.226517 0.392339i −0.730256 0.683173i \(-0.760599\pi\)
0.956773 + 0.290834i \(0.0939328\pi\)
\(614\) 0 0
\(615\) 2.20779e8i 0.949143i
\(616\) 0 0
\(617\) −3.99769e8 −1.70198 −0.850989 0.525183i \(-0.823997\pi\)
−0.850989 + 0.525183i \(0.823997\pi\)
\(618\) 0 0
\(619\) 2.11757e8 + 1.22258e8i 0.892822 + 0.515471i 0.874865 0.484368i \(-0.160950\pi\)
0.0179577 + 0.999839i \(0.494284\pi\)
\(620\) 0 0
\(621\) −4.17779e7 + 2.41205e7i −0.174450 + 0.100719i
\(622\) 0 0
\(623\) 6.15456e7 + 4.32929e6i 0.254526 + 0.0179041i
\(624\) 0 0
\(625\) −1.71720e6 2.97427e6i −0.00703363 0.0121826i
\(626\) 0 0
\(627\) −9.22014e7 + 1.59698e8i −0.374055 + 0.647881i
\(628\) 0 0
\(629\) 6.89792e7i 0.277183i
\(630\) 0 0
\(631\) 2.46592e8 0.981500 0.490750 0.871301i \(-0.336723\pi\)
0.490750 + 0.871301i \(0.336723\pi\)
\(632\) 0 0
\(633\) −4.96263e7 2.86517e7i −0.195659 0.112964i
\(634\) 0 0
\(635\) 1.62105e8 9.35911e7i 0.633102 0.365522i
\(636\) 0 0
\(637\) 3.00129e7 1.20971e7i 0.116116 0.0468019i
\(638\) 0 0
\(639\) −4.20040e7 7.27530e7i −0.160986 0.278836i
\(640\) 0 0
\(641\) −1.80422e8 + 3.12501e8i −0.685040 + 1.18652i 0.288384 + 0.957515i \(0.406882\pi\)
−0.973424 + 0.229010i \(0.926451\pi\)
\(642\) 0 0
\(643\) 9.49305e7i 0.357086i 0.983932 + 0.178543i \(0.0571384\pi\)
−0.983932 + 0.178543i \(0.942862\pi\)
\(644\) 0 0
\(645\) −3.57712e8 −1.33307
\(646\) 0 0
\(647\) 1.29149e8 + 7.45642e7i 0.476846 + 0.275307i 0.719101 0.694905i \(-0.244554\pi\)
−0.242255 + 0.970213i \(0.577887\pi\)
\(648\) 0 0
\(649\) −2.12698e8 + 1.22801e8i −0.778088 + 0.449229i
\(650\) 0 0
\(651\) −7.66363e6 + 1.08947e8i −0.0277774 + 0.394886i
\(652\) 0 0
\(653\) 2.54667e6 + 4.41096e6i 0.00914604 + 0.0158414i 0.870562 0.492058i \(-0.163755\pi\)
−0.861416 + 0.507900i \(0.830422\pi\)
\(654\) 0 0
\(655\) 9.79278e7 1.69616e8i 0.348483 0.603591i
\(656\) 0 0
\(657\) 2.93468e7i 0.103482i
\(658\) 0 0
\(659\) −5.76822e6 −0.0201551 −0.0100776 0.999949i \(-0.503208\pi\)
−0.0100776 + 0.999949i \(0.503208\pi\)
\(660\) 0 0
\(661\) 1.29229e7 + 7.46102e6i 0.0447460 + 0.0258341i 0.522206 0.852819i \(-0.325109\pi\)
−0.477460 + 0.878653i \(0.658442\pi\)
\(662\) 0 0
\(663\) 1.62890e7 9.40444e6i 0.0558924 0.0322695i
\(664\) 0 0
\(665\) 8.43402e8 4.10922e8i 2.86794 1.39732i
\(666\) 0 0
\(667\) −3.98774e7 6.90696e7i −0.134384 0.232761i
\(668\) 0 0
\(669\) −1.11633e8 + 1.93354e8i −0.372833 + 0.645766i
\(670\) 0 0
\(671\) 8.57129e7i 0.283713i
\(672\) 0 0
\(673\) 2.64968e8 0.869257 0.434629 0.900610i \(-0.356880\pi\)
0.434629 + 0.900610i \(0.356880\pi\)
\(674\) 0 0
\(675\) −8.32584e7 4.80693e7i −0.270718 0.156299i
\(676\) 0 0
\(677\) 2.64867e8 1.52921e8i 0.853615 0.492835i −0.00825369 0.999966i \(-0.502627\pi\)
0.861869 + 0.507131i \(0.169294\pi\)
\(678\) 0 0
\(679\) 6.52860e7 9.67041e7i 0.208550 0.308912i
\(680\) 0 0
\(681\) −2.36252e7 4.09200e7i −0.0748055 0.129567i
\(682\) 0 0
\(683\) 7.48455e7 1.29636e8i 0.234911 0.406878i −0.724336 0.689447i \(-0.757853\pi\)
0.959247 + 0.282570i \(0.0911868\pi\)
\(684\) 0 0
\(685\) 9.51758e8i 2.96111i
\(686\) 0 0
\(687\) 9.75949e7 0.300993
\(688\) 0 0
\(689\) 3.04957e7 + 1.76067e7i 0.0932356 + 0.0538296i
\(690\) 0 0
\(691\) −2.20972e8 + 1.27578e8i −0.669736 + 0.386672i −0.795977 0.605327i \(-0.793042\pi\)
0.126241 + 0.992000i \(0.459709\pi\)
\(692\) 0 0
\(693\) −6.04982e7 4.08430e7i −0.181779 0.122721i
\(694\) 0 0
\(695\) 1.66356e8 + 2.88138e8i 0.495548 + 0.858313i
\(696\) 0 0
\(697\) −1.53411e8 + 2.65716e8i −0.453063 + 0.784729i
\(698\) 0 0
\(699\) 1.84679e8i 0.540738i
\(700\) 0 0
\(701\) −2.47105e8 −0.717343 −0.358672 0.933464i \(-0.616770\pi\)
−0.358672 + 0.933464i \(0.616770\pi\)
\(702\) 0 0
\(703\) −1.83939e8 1.06197e8i −0.529429 0.305666i
\(704\) 0 0
\(705\) 1.26631e8 7.31105e7i 0.361387 0.208647i
\(706\) 0 0
\(707\) −1.56750e8 3.21722e8i −0.443556 0.910381i
\(708\) 0 0
\(709\) 5.21037e7 + 9.02462e7i 0.146194 + 0.253215i 0.929818 0.368020i \(-0.119964\pi\)
−0.783624 + 0.621236i \(0.786631\pi\)
\(710\) 0 0
\(711\) −9.28096e7 + 1.60751e8i −0.258217 + 0.447244i
\(712\) 0 0
\(713\) 2.60133e8i 0.717675i
\(714\) 0 0
\(715\) 4.87771e7 0.133444
\(716\) 0 0
\(717\) 5.79460e7 + 3.34551e7i 0.157205 + 0.0907622i
\(718\) 0 0
\(719\) 4.11126e8 2.37363e8i 1.10608 0.638598i 0.168271 0.985741i \(-0.446182\pi\)
0.937812 + 0.347143i \(0.112848\pi\)
\(720\) 0 0
\(721\) −2.66889e8 1.87737e7i −0.712074 0.0500893i
\(722\) 0 0
\(723\) −1.23630e8 2.14133e8i −0.327121 0.566589i
\(724\) 0 0
\(725\) 7.94709e7 1.37648e8i 0.208542 0.361206i
\(726\) 0 0
\(727\) 1.04048e8i 0.270790i 0.990792 + 0.135395i \(0.0432303\pi\)
−0.990792 + 0.135395i \(0.956770\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) 4.30521e8 + 2.48561e8i 1.10215 + 0.636329i
\(732\) 0 0
\(733\) 5.79355e8 3.34491e8i 1.47107 0.849322i 0.471597 0.881814i \(-0.343678\pi\)
0.999472 + 0.0324917i \(0.0103443\pi\)
\(734\) 0 0
\(735\) 1.38833e8 + 3.44445e8i 0.349648 + 0.867476i
\(736\) 0 0
\(737\) −7.64361e7 1.32391e8i −0.190940 0.330717i
\(738\) 0 0
\(739\) −1.54148e8 + 2.66992e8i −0.381948 + 0.661554i −0.991341 0.131315i \(-0.958080\pi\)
0.609393 + 0.792869i \(0.291413\pi\)
\(740\) 0 0
\(741\) 5.79145e7i 0.142342i
\(742\) 0 0
\(743\) −1.83763e8 −0.448014 −0.224007 0.974588i \(-0.571914\pi\)
−0.224007 + 0.974588i \(0.571914\pi\)
\(744\) 0 0
\(745\) 8.11490e8 + 4.68514e8i 1.96252 + 1.13306i
\(746\) 0 0
\(747\) 1.80856e8 1.04417e8i 0.433882 0.250502i
\(748\) 0 0
\(749\) −2.40125e7 + 3.41364e8i −0.0571467 + 0.812404i
\(750\) 0 0
\(751\) 1.22666e8 + 2.12463e8i 0.289603 + 0.501608i 0.973715 0.227770i \(-0.0731433\pi\)
−0.684112 + 0.729377i \(0.739810\pi\)
\(752\) 0 0
\(753\) 5.54756e7 9.60865e7i 0.129932 0.225049i
\(754\) 0 0
\(755\) 9.09655e8i 2.11366i
\(756\) 0 0
\(757\) −8.44770e8 −1.94738 −0.973690 0.227876i \(-0.926822\pi\)
−0.973690 + 0.227876i \(0.926822\pi\)
\(758\) 0 0
\(759\) 1.50567e8 + 8.69299e7i 0.344353 + 0.198812i
\(760\) 0 0
\(761\) 4.91638e8 2.83847e8i 1.11556 0.644066i 0.175293 0.984516i \(-0.443913\pi\)
0.940263 + 0.340450i \(0.110579\pi\)
\(762\) 0 0
\(763\) 4.48854e8 2.18691e8i 1.01049 0.492331i
\(764\) 0 0
\(765\) 1.07930e8 + 1.86941e8i 0.241079 + 0.417562i
\(766\) 0 0
\(767\) −3.85676e7 + 6.68010e7i −0.0854744 + 0.148046i
\(768\) 0 0
\(769\) 2.83103e6i 0.00622536i 0.999995 + 0.00311268i \(0.000990799\pi\)
−0.999995 + 0.00311268i \(0.999009\pi\)
\(770\) 0 0
\(771\) 1.12449e8 0.245353
\(772\) 0 0
\(773\) 3.83914e8 + 2.21653e8i 0.831181 + 0.479883i 0.854257 0.519851i \(-0.174013\pi\)
−0.0230756 + 0.999734i \(0.507346\pi\)
\(774\) 0 0
\(775\) 4.48961e8 2.59208e8i 0.964503 0.556856i
\(776\) 0 0
\(777\) 4.70428e7 6.96816e7i 0.100284 0.148544i
\(778\) 0 0
\(779\) −4.72369e8 8.18168e8i −0.999239 1.73073i
\(780\) 0 0
\(781\) −1.51382e8 + 2.62201e8i −0.317775 + 0.550403i
\(782\) 0 0
\(783\) 2.37224e7i 0.0494168i
\(784\) 0 0
\(785\) 9.77049e8 2.01980