Properties

Label 336.7.bh.b.145.2
Level $336$
Weight $7$
Character 336.145
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 145.2
Root \(-7.08935 + 12.2791i\) of defining polynomial
Character \(\chi\) \(=\) 336.145
Dual form 336.7.bh.b.241.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\) \(q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +(411.119 + 712.080i) q^{11} +2429.15i q^{13} +1240.32 q^{15} +(6751.11 - 3897.76i) q^{17} +(-5786.98 - 3341.12i) q^{19} +(5333.59 + 376.196i) q^{21} +(9416.30 - 16309.5i) q^{23} +(-4647.06 - 8048.94i) q^{25} +3788.00i q^{27} +13888.2 q^{29} +(24131.1 - 13932.1i) q^{31} +(-11100.2 - 6408.72i) q^{33} +(11949.0 + 24536.6i) q^{35} +(-39837.6 + 69000.8i) q^{37} +(-18933.3 - 32793.5i) q^{39} +59196.1i q^{41} +91825.9 q^{43} +(-16744.4 + 9667.37i) q^{45} +(4347.44 + 2509.99i) q^{47} +(43940.4 + 109135. i) q^{49} +(-60760.0 + 105239. i) q^{51} +(-93194.8 - 161418. i) q^{53} -65422.9i q^{55} +104166. q^{57} +(-195032. + 112602. i) q^{59} +(-125018. - 72179.1i) q^{61} +(-74935.6 + 36492.6i) q^{63} +(96639.7 - 167385. i) q^{65} +(-117740. - 203932. i) q^{67} +293571. i q^{69} -96269.3 q^{71} +(238634. - 137775. i) q^{73} +(125471. + 72440.5i) q^{75} +(19843.1 - 281329. i) q^{77} +(-340667. + 590052. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +128019. i q^{83} -620264. q^{85} +(-187491. + 108248. i) q^{87} +(-322756. - 186343. i) q^{89} +(466335. - 690470. i) q^{91} +(-217180. + 376167. i) q^{93} +(265842. + 460452. i) q^{95} +620049. i q^{97} +199804. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + O(q^{10}) \) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) −68.9069 39.7834i −0.551255 0.318267i 0.198373 0.980127i \(-0.436434\pi\)
−0.749628 + 0.661859i \(0.769768\pi\)
\(6\) 0 0
\(7\) −284.244 191.975i −0.828700 0.559693i
\(8\) 0 0
\(9\) 121.500 210.444i 0.166667 0.288675i
\(10\) 0 0
\(11\) 411.119 + 712.080i 0.308880 + 0.534996i 0.978118 0.208052i \(-0.0667125\pi\)
−0.669238 + 0.743049i \(0.733379\pi\)
\(12\) 0 0
\(13\) 2429.15i 1.10567i 0.833292 + 0.552833i \(0.186453\pi\)
−0.833292 + 0.552833i \(0.813547\pi\)
\(14\) 0 0
\(15\) 1240.32 0.367503
\(16\) 0 0
\(17\) 6751.11 3897.76i 1.37413 0.793355i 0.382687 0.923878i \(-0.374999\pi\)
0.991445 + 0.130523i \(0.0416656\pi\)
\(18\) 0 0
\(19\) −5786.98 3341.12i −0.843706 0.487114i 0.0148160 0.999890i \(-0.495284\pi\)
−0.858522 + 0.512776i \(0.828617\pi\)
\(20\) 0 0
\(21\) 5333.59 + 376.196i 0.575919 + 0.0406215i
\(22\) 0 0
\(23\) 9416.30 16309.5i 0.773921 1.34047i −0.161478 0.986876i \(-0.551626\pi\)
0.935399 0.353594i \(-0.115041\pi\)
\(24\) 0 0
\(25\) −4647.06 8048.94i −0.297412 0.515132i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) 13888.2 0.569446 0.284723 0.958610i \(-0.408098\pi\)
0.284723 + 0.958610i \(0.408098\pi\)
\(30\) 0 0
\(31\) 24131.1 13932.1i 0.810014 0.467662i −0.0369467 0.999317i \(-0.511763\pi\)
0.846961 + 0.531655i \(0.178430\pi\)
\(32\) 0 0
\(33\) −11100.2 6408.72i −0.308880 0.178332i
\(34\) 0 0
\(35\) 11949.0 + 24536.6i 0.278693 + 0.572282i
\(36\) 0 0
\(37\) −39837.6 + 69000.8i −0.786481 + 1.36223i 0.141629 + 0.989920i \(0.454766\pi\)
−0.928110 + 0.372305i \(0.878567\pi\)
\(38\) 0 0
\(39\) −18933.3 32793.5i −0.319178 0.552833i
\(40\) 0 0
\(41\) 59196.1i 0.858898i 0.903091 + 0.429449i \(0.141292\pi\)
−0.903091 + 0.429449i \(0.858708\pi\)
\(42\) 0 0
\(43\) 91825.9 1.15494 0.577471 0.816411i \(-0.304040\pi\)
0.577471 + 0.816411i \(0.304040\pi\)
\(44\) 0 0
\(45\) −16744.4 + 9667.37i −0.183752 + 0.106089i
\(46\) 0 0
\(47\) 4347.44 + 2509.99i 0.0418735 + 0.0241757i 0.520791 0.853684i \(-0.325637\pi\)
−0.478917 + 0.877860i \(0.658971\pi\)
\(48\) 0 0
\(49\) 43940.4 + 109135.i 0.373487 + 0.927635i
\(50\) 0 0
\(51\) −60760.0 + 105239.i −0.458044 + 0.793355i
\(52\) 0 0
\(53\) −93194.8 161418.i −0.625985 1.08424i −0.988350 0.152201i \(-0.951364\pi\)
0.362365 0.932036i \(-0.381970\pi\)
\(54\) 0 0
\(55\) 65422.9i 0.393226i
\(56\) 0 0
\(57\) 104166. 0.562471
\(58\) 0 0
\(59\) −195032. + 112602.i −0.949618 + 0.548262i −0.892962 0.450132i \(-0.851377\pi\)
−0.0566558 + 0.998394i \(0.518044\pi\)
\(60\) 0 0
\(61\) −125018. 72179.1i −0.550786 0.317996i 0.198653 0.980070i \(-0.436343\pi\)
−0.749439 + 0.662074i \(0.769677\pi\)
\(62\) 0 0
\(63\) −74935.6 + 36492.6i −0.299686 + 0.145943i
\(64\) 0 0
\(65\) 96639.7 167385.i 0.351897 0.609504i
\(66\) 0 0
\(67\) −117740. 203932.i −0.391471 0.678048i 0.601173 0.799119i \(-0.294700\pi\)
−0.992644 + 0.121071i \(0.961367\pi\)
\(68\) 0 0
\(69\) 293571.i 0.893647i
\(70\) 0 0
\(71\) −96269.3 −0.268975 −0.134488 0.990915i \(-0.542939\pi\)
−0.134488 + 0.990915i \(0.542939\pi\)
\(72\) 0 0
\(73\) 238634. 137775.i 0.613428 0.354163i −0.160878 0.986974i \(-0.551433\pi\)
0.774306 + 0.632812i \(0.218099\pi\)
\(74\) 0 0
\(75\) 125471. + 72440.5i 0.297412 + 0.171711i
\(76\) 0 0
\(77\) 19843.1 281329.i 0.0434647 0.616229i
\(78\) 0 0
\(79\) −340667. + 590052.i −0.690953 + 1.19677i 0.280573 + 0.959833i \(0.409476\pi\)
−0.971526 + 0.236933i \(0.923858\pi\)
\(80\) 0 0
\(81\) −29524.5 51137.9i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 128019.i 0.223893i 0.993714 + 0.111946i \(0.0357085\pi\)
−0.993714 + 0.111946i \(0.964291\pi\)
\(84\) 0 0
\(85\) −620264. −1.01000
\(86\) 0 0
\(87\) −187491. + 108248.i −0.284723 + 0.164385i
\(88\) 0 0
\(89\) −322756. 186343.i −0.457829 0.264328i 0.253302 0.967387i \(-0.418483\pi\)
−0.711131 + 0.703059i \(0.751817\pi\)
\(90\) 0 0
\(91\) 466335. 690470.i 0.618833 0.916265i
\(92\) 0 0
\(93\) −217180. + 376167.i −0.270005 + 0.467662i
\(94\) 0 0
\(95\) 265842. + 460452.i 0.310065 + 0.537048i
\(96\) 0 0
\(97\) 620049.i 0.679377i 0.940538 + 0.339688i \(0.110322\pi\)
−0.940538 + 0.339688i \(0.889678\pi\)
\(98\) 0 0
\(99\) 199804. 0.205920
\(100\) 0 0
\(101\) −578698. + 334111.i −0.561678 + 0.324285i −0.753819 0.657082i \(-0.771790\pi\)
0.192141 + 0.981367i \(0.438457\pi\)
\(102\) 0 0
\(103\) −1.34180e6 774691.i −1.22794 0.708952i −0.261342 0.965246i \(-0.584165\pi\)
−0.966599 + 0.256294i \(0.917498\pi\)
\(104\) 0 0
\(105\) −352555. 238111.i −0.304550 0.205689i
\(106\) 0 0
\(107\) −477948. + 827829.i −0.390148 + 0.675755i −0.992469 0.122498i \(-0.960909\pi\)
0.602321 + 0.798254i \(0.294243\pi\)
\(108\) 0 0
\(109\) −785863. 1.36115e6i −0.606830 1.05106i −0.991759 0.128115i \(-0.959107\pi\)
0.384929 0.922946i \(-0.374226\pi\)
\(110\) 0 0
\(111\) 1.24201e6i 0.908150i
\(112\) 0 0
\(113\) −2.47576e6 −1.71582 −0.857912 0.513797i \(-0.828238\pi\)
−0.857912 + 0.513797i \(0.828238\pi\)
\(114\) 0 0
\(115\) −1.29770e6 + 749225.i −0.853256 + 0.492628i
\(116\) 0 0
\(117\) 511200. + 295141.i 0.319178 + 0.184278i
\(118\) 0 0
\(119\) −2.66723e6 188129.i −1.58278 0.111639i
\(120\) 0 0
\(121\) 547742. 948717.i 0.309186 0.535526i
\(122\) 0 0
\(123\) −461388. 799148.i −0.247943 0.429449i
\(124\) 0 0
\(125\) 1.98274e6i 1.01516i
\(126\) 0 0
\(127\) −292592. −0.142840 −0.0714202 0.997446i \(-0.522753\pi\)
−0.0714202 + 0.997446i \(0.522753\pi\)
\(128\) 0 0
\(129\) −1.23965e6 + 715712.i −0.577471 + 0.333403i
\(130\) 0 0
\(131\) 2.36324e6 + 1.36442e6i 1.05122 + 0.606924i 0.922991 0.384820i \(-0.125737\pi\)
0.128231 + 0.991744i \(0.459070\pi\)
\(132\) 0 0
\(133\) 1.00351e6 + 2.06065e6i 0.426545 + 0.875888i
\(134\) 0 0
\(135\) 150699. 261019.i 0.0612506 0.106089i
\(136\) 0 0
\(137\) 453922. + 786216.i 0.176530 + 0.305760i 0.940690 0.339268i \(-0.110179\pi\)
−0.764159 + 0.645027i \(0.776846\pi\)
\(138\) 0 0
\(139\) 4640.07i 0.00172775i 1.00000 0.000863874i \(0.000274980\pi\)
−1.00000 0.000863874i \(0.999725\pi\)
\(140\) 0 0
\(141\) −78253.8 −0.0279157
\(142\) 0 0
\(143\) −1.72975e6 + 998669.i −0.591526 + 0.341518i
\(144\) 0 0
\(145\) −956994. 552521.i −0.313910 0.181236i
\(146\) 0 0
\(147\) −1.44382e6 1.13085e6i −0.454529 0.356001i
\(148\) 0 0
\(149\) 823601. 1.42652e6i 0.248976 0.431240i −0.714266 0.699875i \(-0.753239\pi\)
0.963242 + 0.268635i \(0.0865725\pi\)
\(150\) 0 0
\(151\) −1.22295e6 2.11820e6i −0.355203 0.615229i 0.631950 0.775009i \(-0.282255\pi\)
−0.987153 + 0.159780i \(0.948921\pi\)
\(152\) 0 0
\(153\) 1.89431e6i 0.528904i
\(154\) 0 0
\(155\) −2.21707e6 −0.595366
\(156\) 0 0
\(157\) −2.43822e6 + 1.40771e6i −0.630049 + 0.363759i −0.780771 0.624817i \(-0.785174\pi\)
0.150722 + 0.988576i \(0.451840\pi\)
\(158\) 0 0
\(159\) 2.51626e6 + 1.45276e6i 0.625985 + 0.361413i
\(160\) 0 0
\(161\) −5.80754e6 + 2.82819e6i −1.39160 + 0.677690i
\(162\) 0 0
\(163\) −781407. + 1.35344e6i −0.180432 + 0.312518i −0.942028 0.335535i \(-0.891083\pi\)
0.761596 + 0.648053i \(0.224416\pi\)
\(164\) 0 0
\(165\) 509921. + 883210.i 0.113515 + 0.196613i
\(166\) 0 0
\(167\) 1.15538e6i 0.248070i −0.992278 0.124035i \(-0.960416\pi\)
0.992278 0.124035i \(-0.0395835\pi\)
\(168\) 0 0
\(169\) −1.07394e6 −0.222495
\(170\) 0 0
\(171\) −1.40624e6 + 811891.i −0.281235 + 0.162371i
\(172\) 0 0
\(173\) −4.98920e6 2.88052e6i −0.963591 0.556330i −0.0663149 0.997799i \(-0.521124\pi\)
−0.897277 + 0.441469i \(0.854458\pi\)
\(174\) 0 0
\(175\) −224295. + 3.17998e6i −0.0418509 + 0.593350i
\(176\) 0 0
\(177\) 1.75528e6 3.04024e6i 0.316539 0.548262i
\(178\) 0 0
\(179\) −597801. 1.03542e6i −0.104231 0.180534i 0.809193 0.587543i \(-0.199905\pi\)
−0.913424 + 0.407010i \(0.866571\pi\)
\(180\) 0 0
\(181\) 1.00030e7i 1.68692i 0.537191 + 0.843461i \(0.319486\pi\)
−0.537191 + 0.843461i \(0.680514\pi\)
\(182\) 0 0
\(183\) 2.25032e6 0.367190
\(184\) 0 0
\(185\) 5.49017e6 3.16975e6i 0.867104 0.500622i
\(186\) 0 0
\(187\) 5.55102e6 + 3.20489e6i 0.848884 + 0.490103i
\(188\) 0 0
\(189\) 727199. 1.07672e6i 0.107713 0.159483i
\(190\) 0 0
\(191\) −3.79135e6 + 6.56682e6i −0.544120 + 0.942443i 0.454542 + 0.890725i \(0.349803\pi\)
−0.998662 + 0.0517175i \(0.983530\pi\)
\(192\) 0 0
\(193\) −3.54806e6 6.14542e6i −0.493537 0.854830i 0.506436 0.862278i \(-0.330963\pi\)
−0.999972 + 0.00744730i \(0.997629\pi\)
\(194\) 0 0
\(195\) 3.01293e6i 0.406336i
\(196\) 0 0
\(197\) 2.00096e6 0.261722 0.130861 0.991401i \(-0.458226\pi\)
0.130861 + 0.991401i \(0.458226\pi\)
\(198\) 0 0
\(199\) 3.76381e6 2.17304e6i 0.477605 0.275745i −0.241813 0.970323i \(-0.577742\pi\)
0.719418 + 0.694578i \(0.244409\pi\)
\(200\) 0 0
\(201\) 3.17898e6 + 1.83539e6i 0.391471 + 0.226016i
\(202\) 0 0
\(203\) −3.94764e6 2.66619e6i −0.471900 0.318715i
\(204\) 0 0
\(205\) 2.35502e6 4.07902e6i 0.273359 0.473472i
\(206\) 0 0
\(207\) −2.28816e6 3.96321e6i −0.257974 0.446824i
\(208\) 0 0
\(209\) 5.49439e6i 0.601839i
\(210\) 0 0
\(211\) −1.03642e7 −1.10328 −0.551641 0.834082i \(-0.685998\pi\)
−0.551641 + 0.834082i \(0.685998\pi\)
\(212\) 0 0
\(213\) 1.29964e6 750345.i 0.134488 0.0776465i
\(214\) 0 0
\(215\) −6.32744e6 3.65315e6i −0.636667 0.367580i
\(216\) 0 0
\(217\) −9.53375e6 672446.i −0.933006 0.0658079i
\(218\) 0 0
\(219\) −2.14770e6 + 3.71993e6i −0.204476 + 0.354163i
\(220\) 0 0
\(221\) 9.46822e6 + 1.63994e7i 0.877185 + 1.51933i
\(222\) 0 0
\(223\) 4.84791e6i 0.437159i 0.975819 + 0.218580i \(0.0701424\pi\)
−0.975819 + 0.218580i \(0.929858\pi\)
\(224\) 0 0
\(225\) −2.25847e6 −0.198275
\(226\) 0 0
\(227\) 1.30838e7 7.55396e6i 1.11856 0.645798i 0.177524 0.984117i \(-0.443191\pi\)
0.941032 + 0.338318i \(0.109858\pi\)
\(228\) 0 0
\(229\) −3.68382e6 2.12685e6i −0.306755 0.177105i 0.338718 0.940888i \(-0.390007\pi\)
−0.645474 + 0.763783i \(0.723340\pi\)
\(230\) 0 0
\(231\) 1.92486e6 + 3.95260e6i 0.156158 + 0.320662i
\(232\) 0 0
\(233\) −6.29087e6 + 1.08961e7i −0.497328 + 0.861397i −0.999995 0.00308269i \(-0.999019\pi\)
0.502667 + 0.864480i \(0.332352\pi\)
\(234\) 0 0
\(235\) −199712. 345912.i −0.0153887 0.0266540i
\(236\) 0 0
\(237\) 1.06209e7i 0.797844i
\(238\) 0 0
\(239\) −7.54342e6 −0.552554 −0.276277 0.961078i \(-0.589101\pi\)
−0.276277 + 0.961078i \(0.589101\pi\)
\(240\) 0 0
\(241\) 1.69553e7 9.78914e6i 1.21131 0.699348i 0.248262 0.968693i \(-0.420140\pi\)
0.963044 + 0.269345i \(0.0868071\pi\)
\(242\) 0 0
\(243\) 797162. + 460241.i 0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 1.31398e6 9.26828e6i 0.0893492 0.630233i
\(246\) 0 0
\(247\) 8.11606e6 1.40574e7i 0.538585 0.932857i
\(248\) 0 0
\(249\) −997810. 1.72826e6i −0.0646323 0.111946i
\(250\) 0 0
\(251\) 1.39590e7i 0.882743i 0.897324 + 0.441372i \(0.145508\pi\)
−0.897324 + 0.441372i \(0.854492\pi\)
\(252\) 0 0
\(253\) 1.54849e7 0.956195
\(254\) 0 0
\(255\) 8.37356e6 4.83448e6i 0.504998 0.291561i
\(256\) 0 0
\(257\) −567649. 327732.i −0.0334411 0.0193072i 0.483186 0.875518i \(-0.339479\pi\)
−0.516627 + 0.856210i \(0.672813\pi\)
\(258\) 0 0
\(259\) 2.45700e7 1.19652e7i 1.41418 0.688688i
\(260\) 0 0
\(261\) 1.68742e6 2.92269e6i 0.0949076 0.164385i
\(262\) 0 0
\(263\) −7.46998e6 1.29384e7i −0.410632 0.711235i 0.584327 0.811518i \(-0.301358\pi\)
−0.994959 + 0.100283i \(0.968025\pi\)
\(264\) 0 0
\(265\) 1.48304e7i 0.796922i
\(266\) 0 0
\(267\) 5.80960e6 0.305220
\(268\) 0 0
\(269\) −2.72017e7 + 1.57049e7i −1.39746 + 0.806825i −0.994126 0.108227i \(-0.965483\pi\)
−0.403335 + 0.915052i \(0.632149\pi\)
\(270\) 0 0
\(271\) 1.29500e6 + 747670.i 0.0650673 + 0.0375666i 0.532181 0.846631i \(-0.321373\pi\)
−0.467113 + 0.884197i \(0.654706\pi\)
\(272\) 0 0
\(273\) −913834. + 1.29561e7i −0.0449138 + 0.636774i
\(274\) 0 0
\(275\) 3.82099e6 6.61815e6i 0.183729 0.318228i
\(276\) 0 0
\(277\) 991747. + 1.71776e6i 0.0466618 + 0.0808207i 0.888413 0.459045i \(-0.151808\pi\)
−0.841751 + 0.539866i \(0.818475\pi\)
\(278\) 0 0
\(279\) 6.77101e6i 0.311775i
\(280\) 0 0
\(281\) −3.50353e6 −0.157902 −0.0789508 0.996879i \(-0.525157\pi\)
−0.0789508 + 0.996879i \(0.525157\pi\)
\(282\) 0 0
\(283\) −2.82715e7 + 1.63226e7i −1.24736 + 0.720161i −0.970581 0.240774i \(-0.922599\pi\)
−0.276774 + 0.960935i \(0.589265\pi\)
\(284\) 0 0
\(285\) −7.17773e6 4.14407e6i −0.310065 0.179016i
\(286\) 0 0
\(287\) 1.13642e7 1.68261e7i 0.480719 0.711769i
\(288\) 0 0
\(289\) 1.83162e7 3.17246e7i 0.758826 1.31432i
\(290\) 0 0
\(291\) −4.83280e6 8.37066e6i −0.196119 0.339688i
\(292\) 0 0
\(293\) 2.57653e7i 1.02431i 0.858892 + 0.512156i \(0.171153\pi\)
−0.858892 + 0.512156i \(0.828847\pi\)
\(294\) 0 0
\(295\) 1.79187e7 0.697976
\(296\) 0 0
\(297\) −2.69735e6 + 1.55732e6i −0.102960 + 0.0594440i
\(298\) 0 0
\(299\) 3.96182e7 + 2.28736e7i 1.48211 + 0.855698i
\(300\) 0 0
\(301\) −2.61010e7 1.76283e7i −0.957100 0.646413i
\(302\) 0 0
\(303\) 5.20828e6 9.02100e6i 0.187226 0.324285i
\(304\) 0 0
\(305\) 5.74306e6 + 9.94727e6i 0.202416 + 0.350594i
\(306\) 0 0
\(307\) 1.89894e7i 0.656289i 0.944628 + 0.328145i \(0.106423\pi\)
−0.944628 + 0.328145i \(0.893577\pi\)
\(308\) 0 0
\(309\) 2.41525e7 0.818627
\(310\) 0 0
\(311\) −2.80365e7 + 1.61869e7i −0.932057 + 0.538124i −0.887462 0.460881i \(-0.847533\pi\)
−0.0445958 + 0.999005i \(0.514200\pi\)
\(312\) 0 0
\(313\) 2.81397e7 + 1.62465e7i 0.917671 + 0.529818i 0.882891 0.469577i \(-0.155594\pi\)
0.0347798 + 0.999395i \(0.488927\pi\)
\(314\) 0 0
\(315\) 6.61538e6 + 466604.i 0.211652 + 0.0149285i
\(316\) 0 0
\(317\) 8.17142e6 1.41533e7i 0.256519 0.444304i −0.708788 0.705422i \(-0.750758\pi\)
0.965307 + 0.261118i \(0.0840910\pi\)
\(318\) 0 0
\(319\) 5.70972e6 + 9.88952e6i 0.175891 + 0.304651i
\(320\) 0 0
\(321\) 1.49009e7i 0.450504i
\(322\) 0 0
\(323\) −5.20914e7 −1.54582
\(324\) 0 0
\(325\) 1.95521e7 1.12884e7i 0.569564 0.328838i
\(326\) 0 0
\(327\) 2.12183e7 + 1.22504e7i 0.606830 + 0.350354i
\(328\) 0 0
\(329\) −753878. 1.54805e6i −0.0211696 0.0434707i
\(330\) 0 0
\(331\) 2.58785e7 4.48229e7i 0.713601 1.23599i −0.249896 0.968273i \(-0.580396\pi\)
0.963497 0.267720i \(-0.0862702\pi\)
\(332\) 0 0
\(333\) 9.68054e6 + 1.67672e7i 0.262160 + 0.454075i
\(334\) 0 0
\(335\) 1.87364e7i 0.498370i
\(336\) 0 0
\(337\) 6.13986e7 1.60424 0.802119 0.597164i \(-0.203706\pi\)
0.802119 + 0.597164i \(0.203706\pi\)
\(338\) 0 0
\(339\) 3.34227e7 1.92966e7i 0.857912 0.495316i
\(340\) 0 0
\(341\) 1.98416e7 + 1.14555e7i 0.500395 + 0.288903i
\(342\) 0 0
\(343\) 8.46143e6 3.94565e7i 0.209682 0.977770i
\(344\) 0 0
\(345\) 1.16793e7 2.02291e7i 0.284419 0.492628i
\(346\) 0 0
\(347\) 1.77833e7 + 3.08017e7i 0.425623 + 0.737200i 0.996478 0.0838501i \(-0.0267217\pi\)
−0.570855 + 0.821051i \(0.693388\pi\)
\(348\) 0 0
\(349\) 5.17156e7i 1.21659i −0.793710 0.608297i \(-0.791853\pi\)
0.793710 0.608297i \(-0.208147\pi\)
\(350\) 0 0
\(351\) −9.20159e6 −0.212785
\(352\) 0 0
\(353\) −669058. + 386281.i −0.0152104 + 0.00878171i −0.507586 0.861601i \(-0.669462\pi\)
0.492376 + 0.870383i \(0.336129\pi\)
\(354\) 0 0
\(355\) 6.63362e6 + 3.82992e6i 0.148274 + 0.0856061i
\(356\) 0 0
\(357\) 3.74740e7 1.82493e7i 0.823617 0.401090i
\(358\) 0 0
\(359\) −2.08340e7 + 3.60856e7i −0.450287 + 0.779920i −0.998404 0.0564819i \(-0.982012\pi\)
0.548117 + 0.836402i \(0.315345\pi\)
\(360\) 0 0
\(361\) −1.19684e6 2.07298e6i −0.0254398 0.0440630i
\(362\) 0 0
\(363\) 1.70769e7i 0.357017i
\(364\) 0 0
\(365\) −2.19247e7 −0.450874
\(366\) 0 0
\(367\) −5.71734e6 + 3.30091e6i −0.115663 + 0.0667783i −0.556716 0.830703i \(-0.687939\pi\)
0.441052 + 0.897481i \(0.354605\pi\)
\(368\) 0 0
\(369\) 1.24575e7 + 7.19233e6i 0.247943 + 0.143150i
\(370\) 0 0
\(371\) −4.49813e6 + 6.37732e7i −0.0880867 + 1.24887i
\(372\) 0 0
\(373\) 2.47581e6 4.28823e6i 0.0477080 0.0826326i −0.841185 0.540747i \(-0.818142\pi\)
0.888893 + 0.458114i \(0.151475\pi\)
\(374\) 0 0
\(375\) −1.54539e7 2.67669e7i −0.293052 0.507580i
\(376\) 0 0
\(377\) 3.37365e7i 0.629616i
\(378\) 0 0
\(379\) 1.05876e8 1.94482 0.972409 0.233282i \(-0.0749466\pi\)
0.972409 + 0.233282i \(0.0749466\pi\)
\(380\) 0 0
\(381\) 3.94999e6 2.28053e6i 0.0714202 0.0412345i
\(382\) 0 0
\(383\) 4.26092e7 + 2.46004e7i 0.758414 + 0.437871i 0.828726 0.559654i \(-0.189066\pi\)
−0.0703117 + 0.997525i \(0.522399\pi\)
\(384\) 0 0
\(385\) −1.25596e7 + 1.85961e7i −0.220086 + 0.325866i
\(386\) 0 0
\(387\) 1.11568e7 1.93242e7i 0.192490 0.333403i
\(388\) 0 0
\(389\) −3.33099e7 5.76945e7i −0.565880 0.980134i −0.996967 0.0778231i \(-0.975203\pi\)
0.431087 0.902310i \(-0.358130\pi\)
\(390\) 0 0
\(391\) 1.46810e8i 2.45598i
\(392\) 0 0
\(393\) −4.25384e7 −0.700815
\(394\) 0 0
\(395\) 4.69486e7 2.71058e7i 0.761783 0.439816i
\(396\) 0 0
\(397\) 4.16040e7 + 2.40201e7i 0.664911 + 0.383887i 0.794146 0.607727i \(-0.207919\pi\)
−0.129234 + 0.991614i \(0.541252\pi\)
\(398\) 0 0
\(399\) −2.96085e7 1.99972e7i −0.466120 0.314811i
\(400\) 0 0
\(401\) −6.97156e6 + 1.20751e7i −0.108118 + 0.187265i −0.915008 0.403436i \(-0.867816\pi\)
0.806890 + 0.590702i \(0.201149\pi\)
\(402\) 0 0
\(403\) 3.38431e7 + 5.86180e7i 0.517077 + 0.895604i
\(404\) 0 0
\(405\) 4.69834e6i 0.0707261i
\(406\) 0 0
\(407\) −6.55121e7 −0.971713
\(408\) 0 0
\(409\) 1.93849e7 1.11919e7i 0.283331 0.163581i −0.351599 0.936151i \(-0.614362\pi\)
0.634931 + 0.772569i \(0.281029\pi\)
\(410\) 0 0
\(411\) −1.22559e7 7.07594e6i −0.176530 0.101920i
\(412\) 0 0
\(413\) 7.70532e7 + 5.43482e6i 1.09381 + 0.0771498i
\(414\) 0 0
\(415\) 5.09304e6 8.82140e6i 0.0712578 0.123422i
\(416\) 0 0
\(417\) −36165.8 62641.0i −0.000498758 0.000863874i
\(418\) 0 0
\(419\) 5.41233e7i 0.735770i 0.929871 + 0.367885i \(0.119918\pi\)
−0.929871 + 0.367885i \(0.880082\pi\)
\(420\) 0 0
\(421\) −1.30034e8 −1.74265 −0.871323 0.490709i \(-0.836738\pi\)
−0.871323 + 0.490709i \(0.836738\pi\)
\(422\) 0 0
\(423\) 1.05643e6 609928.i 0.0139578 0.00805856i
\(424\) 0 0
\(425\) −6.27456e7 3.62262e7i −0.817366 0.471907i
\(426\) 0 0
\(427\) 2.16790e7 + 4.45167e7i 0.278456 + 0.571794i
\(428\) 0 0
\(429\) 1.55677e7 2.69641e7i 0.197175 0.341518i
\(430\) 0 0
\(431\) −5.99710e7 1.03873e8i −0.749047 1.29739i −0.948280 0.317436i \(-0.897178\pi\)
0.199233 0.979952i \(-0.436155\pi\)
\(432\) 0 0
\(433\) 1.11549e8i 1.37404i 0.726636 + 0.687022i \(0.241083\pi\)
−0.726636 + 0.687022i \(0.758917\pi\)
\(434\) 0 0
\(435\) 1.72259e7 0.209273
\(436\) 0 0
\(437\) −1.08984e8 + 6.29219e7i −1.30592 + 0.753976i
\(438\) 0 0
\(439\) −1.06743e8 6.16284e7i −1.26168 0.728429i −0.288277 0.957547i \(-0.593082\pi\)
−0.973399 + 0.229118i \(0.926416\pi\)
\(440\) 0 0
\(441\) 2.83057e7 + 4.01295e6i 0.330033 + 0.0467894i
\(442\) 0 0
\(443\) −3.55708e7 + 6.16104e7i −0.409150 + 0.708669i −0.994795 0.101899i \(-0.967508\pi\)
0.585645 + 0.810568i \(0.300841\pi\)
\(444\) 0 0
\(445\) 1.48267e7 + 2.56806e7i 0.168254 + 0.291424i
\(446\) 0 0
\(447\) 2.56773e7i 0.287493i
\(448\) 0 0
\(449\) −1.07566e8 −1.18833 −0.594165 0.804343i \(-0.702517\pi\)
−0.594165 + 0.804343i \(0.702517\pi\)
\(450\) 0 0
\(451\) −4.21524e7 + 2.43367e7i −0.459507 + 0.265297i
\(452\) 0 0
\(453\) 3.30195e7 + 1.90638e7i 0.355203 + 0.205076i
\(454\) 0 0
\(455\) −5.96030e7 + 2.90258e7i −0.632752 + 0.308141i
\(456\) 0 0
\(457\) −6.43381e6 + 1.11437e7i −0.0674093 + 0.116756i −0.897760 0.440485i \(-0.854807\pi\)
0.830351 + 0.557241i \(0.188140\pi\)
\(458\) 0 0
\(459\) 1.47647e7 + 2.55732e7i 0.152681 + 0.264452i
\(460\) 0 0
\(461\) 7.08717e6i 0.0723386i −0.999346 0.0361693i \(-0.988484\pi\)
0.999346 0.0361693i \(-0.0115156\pi\)
\(462\) 0 0
\(463\) −1.44698e8 −1.45788 −0.728938 0.684580i \(-0.759986\pi\)
−0.728938 + 0.684580i \(0.759986\pi\)
\(464\) 0 0
\(465\) 2.99304e7 1.72803e7i 0.297683 0.171867i
\(466\) 0 0
\(467\) −7.34759e7 4.24214e7i −0.721431 0.416518i 0.0938485 0.995586i \(-0.470083\pi\)
−0.815279 + 0.579068i \(0.803416\pi\)
\(468\) 0 0
\(469\) −5.68283e6 + 8.05695e7i −0.0550866 + 0.781002i
\(470\) 0 0
\(471\) 2.19440e7 3.80082e7i 0.210016 0.363759i
\(472\) 0 0
\(473\) 3.77514e7 + 6.53874e7i 0.356738 + 0.617889i
\(474\) 0 0
\(475\) 6.21054e7i 0.579494i
\(476\) 0 0
\(477\) −4.52927e7 −0.417323
\(478\) 0 0
\(479\) −1.38250e8 + 7.98185e7i −1.25793 + 0.726268i −0.972672 0.232182i \(-0.925414\pi\)
−0.285261 + 0.958450i \(0.592080\pi\)
\(480\) 0 0
\(481\) −1.67613e8 9.67714e7i −1.50616 0.869585i
\(482\) 0 0
\(483\) 5.63582e7 8.34459e7i 0.500168 0.740565i
\(484\) 0 0
\(485\) 2.46677e7 4.27256e7i 0.216223 0.374510i
\(486\) 0 0
\(487\) 6.90017e7 + 1.19515e8i 0.597411 + 1.03475i 0.993202 + 0.116405i \(0.0371372\pi\)
−0.395791 + 0.918341i \(0.629529\pi\)
\(488\) 0 0
\(489\) 2.43619e7i 0.208345i
\(490\) 0 0
\(491\) 3.91824e7 0.331014 0.165507 0.986209i \(-0.447074\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(492\) 0 0
\(493\) 9.37609e7 5.41329e7i 0.782494 0.451773i
\(494\) 0 0
\(495\) −1.37679e7 7.94889e6i −0.113515 0.0655376i
\(496\) 0 0
\(497\) 2.73640e7 + 1.84813e7i 0.222900 + 0.150544i
\(498\) 0 0
\(499\) 1.14482e7 1.98288e7i 0.0921370 0.159586i −0.816273 0.577666i \(-0.803964\pi\)
0.908410 + 0.418080i \(0.137297\pi\)
\(500\) 0 0
\(501\) 9.00527e6 + 1.55976e7i 0.0716116 + 0.124035i
\(502\) 0 0
\(503\) 1.38751e8i 1.09027i −0.838349 0.545133i \(-0.816479\pi\)
0.838349 0.545133i \(-0.183521\pi\)
\(504\) 0 0
\(505\) 5.31683e7 0.412837
\(506\) 0 0
\(507\) 1.44982e7 8.37055e6i 0.111248 0.0642289i
\(508\) 0 0
\(509\) −5.07588e7 2.93056e7i −0.384909 0.222227i 0.295043 0.955484i \(-0.404666\pi\)
−0.679952 + 0.733257i \(0.737999\pi\)
\(510\) 0 0
\(511\) −9.42796e7 6.64985e6i −0.706570 0.0498367i
\(512\) 0 0
\(513\) 1.26561e7 2.19211e7i 0.0937451 0.162371i
\(514\) 0 0
\(515\) 6.16397e7 + 1.06763e8i 0.451272 + 0.781627i
\(516\) 0 0
\(517\) 4.12763e6i 0.0298696i
\(518\) 0 0
\(519\) 8.98057e7 0.642394
\(520\) 0 0
\(521\) −1.88084e8 + 1.08590e8i −1.32996 + 0.767853i −0.985293 0.170872i \(-0.945342\pi\)
−0.344668 + 0.938725i \(0.612008\pi\)
\(522\) 0 0
\(523\) −1.64929e7 9.52217e6i −0.115290 0.0665627i 0.441246 0.897386i \(-0.354537\pi\)
−0.556536 + 0.830823i \(0.687870\pi\)
\(524\) 0 0
\(525\) −2.17575e7 4.46780e7i −0.150360 0.308756i
\(526\) 0 0
\(527\) 1.08608e8 1.88114e8i 0.742044 1.28526i
\(528\) 0 0
\(529\) −1.03315e8 1.78948e8i −0.697908 1.20881i
\(530\) 0 0
\(531\) 5.47244e7i 0.365508i
\(532\) 0 0
\(533\) −1.43796e8 −0.949654
\(534\) 0 0
\(535\) 6.58678e7 3.80288e7i 0.430142 0.248342i
\(536\) 0 0
\(537\) 1.61406e7 + 9.31879e6i 0.104231 + 0.0601778i
\(538\) 0 0
\(539\) −5.96483e7 + 7.61567e7i −0.380918 + 0.486342i
\(540\) 0 0
\(541\) 5.05360e7 8.75310e7i 0.319161 0.552803i −0.661152 0.750252i \(-0.729932\pi\)
0.980313 + 0.197449i \(0.0632657\pi\)
\(542\) 0 0
\(543\) −7.79657e7 1.35041e8i −0.486972 0.843461i
\(544\) 0 0
\(545\) 1.25057e8i 0.772537i
\(546\) 0 0
\(547\) 2.29198e7 0.140039 0.0700196 0.997546i \(-0.477694\pi\)
0.0700196 + 0.997546i \(0.477694\pi\)
\(548\) 0 0
\(549\) −3.03793e7 + 1.75395e7i −0.183595 + 0.105999i
\(550\) 0 0
\(551\) −8.03708e7 4.64021e7i −0.480445 0.277385i
\(552\) 0 0
\(553\) 2.10108e8 1.02319e8i 1.24241 0.605038i
\(554\) 0 0
\(555\) −4.94116e7 + 8.55834e7i −0.289035 + 0.500622i
\(556\) 0 0
\(557\) −6.91655e7 1.19798e8i −0.400243 0.693242i 0.593512 0.804825i \(-0.297741\pi\)
−0.993755 + 0.111584i \(0.964408\pi\)
\(558\) 0 0
\(559\) 2.23059e8i 1.27698i
\(560\) 0 0
\(561\) −9.99184e7 −0.565923
\(562\) 0 0
\(563\) −1.95097e8 + 1.12639e8i −1.09326 + 0.631195i −0.934443 0.356112i \(-0.884102\pi\)
−0.158819 + 0.987308i \(0.550769\pi\)
\(564\) 0 0
\(565\) 1.70597e8 + 9.84941e7i 0.945857 + 0.546091i
\(566\) 0 0
\(567\) −1.42503e6 + 2.02036e7i −0.00781761 + 0.110836i
\(568\) 0 0
\(569\) −1.10276e8 + 1.91003e8i −0.598609 + 1.03682i 0.394417 + 0.918931i \(0.370946\pi\)
−0.993027 + 0.117890i \(0.962387\pi\)
\(570\) 0 0
\(571\) −3.36594e7 5.82999e7i −0.180800 0.313155i 0.761353 0.648337i \(-0.224535\pi\)
−0.942153 + 0.335182i \(0.891202\pi\)
\(572\) 0 0
\(573\) 1.18203e8i 0.628295i
\(574\) 0 0
\(575\) −1.75032e8 −0.920693
\(576\) 0 0
\(577\) −9.29650e6 + 5.36734e6i −0.0483941 + 0.0279403i −0.524002 0.851717i \(-0.675562\pi\)
0.475608 + 0.879657i \(0.342228\pi\)
\(578\) 0 0
\(579\) 9.57977e7 + 5.53088e7i 0.493537 + 0.284943i
\(580\) 0 0
\(581\) 2.45764e7 3.63887e7i 0.125311 0.185540i
\(582\) 0 0
\(583\) 7.66284e7 1.32724e8i 0.386709 0.669799i
\(584\) 0 0
\(585\) −2.34835e7 4.06745e7i −0.117299 0.203168i
\(586\) 0 0
\(587\) 2.34143e8i 1.15762i 0.815461 + 0.578812i \(0.196484\pi\)
−0.815461 + 0.578812i \(0.803516\pi\)
\(588\) 0 0
\(589\) −1.86195e8 −0.911219
\(590\) 0 0
\(591\) −2.70130e7 + 1.55960e7i −0.130861 + 0.0755527i
\(592\) 0 0
\(593\) 1.45328e8 + 8.39054e7i 0.696926 + 0.402370i 0.806202 0.591641i \(-0.201520\pi\)
−0.109275 + 0.994012i \(0.534853\pi\)
\(594\) 0 0
\(595\) 1.76306e8 + 1.19075e8i 0.836984 + 0.565288i
\(596\) 0 0
\(597\) −3.38743e7 + 5.86720e7i −0.159202 + 0.275745i
\(598\) 0 0
\(599\) 2.72137e7 + 4.71356e7i 0.126622 + 0.219315i 0.922366 0.386318i \(-0.126253\pi\)
−0.795744 + 0.605633i \(0.792920\pi\)
\(600\) 0 0
\(601\) 1.02729e7i 0.0473226i −0.999720 0.0236613i \(-0.992468\pi\)
0.999720 0.0236613i \(-0.00753233\pi\)
\(602\) 0 0
\(603\) −5.72217e7 −0.260981
\(604\) 0 0
\(605\) −7.54864e7 + 4.35821e7i −0.340881 + 0.196808i
\(606\) 0 0
\(607\) −3.20092e8 1.84805e8i −1.43123 0.826319i −0.434012 0.900907i \(-0.642902\pi\)
−0.997214 + 0.0745880i \(0.976236\pi\)
\(608\) 0 0
\(609\) 7.40740e7 + 5.22468e6i 0.327955 + 0.0231317i
\(610\) 0 0
\(611\) −6.09714e6 + 1.05606e7i −0.0267302 + 0.0462981i
\(612\) 0 0
\(613\) −2.33412e7 4.04282e7i −0.101331 0.175510i 0.810902 0.585182i \(-0.198977\pi\)
−0.912233 + 0.409671i \(0.865643\pi\)
\(614\) 0 0
\(615\) 7.34224e7i 0.315648i
\(616\) 0 0
\(617\) 4.39158e8 1.86967 0.934836 0.355080i \(-0.115546\pi\)
0.934836 + 0.355080i \(0.115546\pi\)
\(618\) 0 0
\(619\) 1.84752e8 1.06666e8i 0.778962 0.449734i −0.0571005 0.998368i \(-0.518186\pi\)
0.836062 + 0.548635i \(0.184852\pi\)
\(620\) 0 0
\(621\) 6.17803e7 + 3.56689e7i 0.257974 + 0.148941i
\(622\) 0 0
\(623\) 5.59682e7 + 1.14928e8i 0.231461 + 0.475292i
\(624\) 0 0
\(625\) 6.26968e6 1.08594e7i 0.0256806 0.0444801i
\(626\) 0 0
\(627\) 4.28245e7 + 7.41743e7i 0.173736 + 0.300920i
\(628\) 0 0
\(629\) 6.21109e8i 2.49584i
\(630\) 0 0
\(631\) −2.58817e8 −1.03016 −0.515080 0.857142i \(-0.672238\pi\)
−0.515080 + 0.857142i \(0.672238\pi\)
\(632\) 0 0
\(633\) 1.39916e8 8.07806e7i 0.551641 0.318490i
\(634\) 0 0
\(635\) 2.01616e7 + 1.16403e7i 0.0787415 + 0.0454614i
\(636\) 0 0
\(637\) −2.65106e8 + 1.06738e8i −1.02565 + 0.412952i
\(638\) 0 0
\(639\) −1.16967e7 + 2.02593e7i −0.0448292 + 0.0776465i
\(640\) 0 0
\(641\) −6.64356e7 1.15070e8i −0.252247 0.436905i 0.711897 0.702284i \(-0.247836\pi\)
−0.964144 + 0.265379i \(0.914503\pi\)
\(642\) 0 0
\(643\) 1.84168e8i 0.692757i 0.938095 + 0.346378i \(0.112589\pi\)
−0.938095 + 0.346378i \(0.887411\pi\)
\(644\) 0 0
\(645\) 1.13894e8 0.424445
\(646\) 0 0
\(647\) 2.88189e8 1.66386e8i 1.06405 0.614332i 0.137504 0.990501i \(-0.456092\pi\)
0.926551 + 0.376169i \(0.122759\pi\)
\(648\) 0 0
\(649\) −1.60363e8 9.25854e7i −0.586636 0.338695i
\(650\) 0 0
\(651\) 1.33947e8 6.52302e7i 0.485500 0.236432i
\(652\) 0 0
\(653\) −1.28291e8 + 2.22206e8i −0.460741 + 0.798026i −0.998998 0.0447544i \(-0.985749\pi\)
0.538257 + 0.842780i \(0.319083\pi\)
\(654\) 0 0
\(655\) −1.08563e8 1.88036e8i −0.386328 0.669140i
\(656\) 0 0
\(657\) 6.69588e7i 0.236108i
\(658\) 0 0
\(659\) −1.84717e8 −0.645431 −0.322715 0.946496i \(-0.604596\pi\)
−0.322715 + 0.946496i \(0.604596\pi\)
\(660\) 0 0
\(661\) 1.74480e8 1.00736e8i 0.604144 0.348803i −0.166526 0.986037i \(-0.553255\pi\)
0.770670 + 0.637234i \(0.219922\pi\)
\(662\) 0 0
\(663\) −2.55642e8 1.47595e8i −0.877185 0.506443i
\(664\) 0 0
\(665\) 1.28311e7 1.81916e8i 0.0436314 0.618593i
\(666\) 0 0
\(667\) 1.30776e8 2.26510e8i 0.440706 0.763326i
\(668\) 0 0
\(669\) −3.77857e7 6.54468e7i −0.126197 0.218580i
\(670\) 0 0
\(671\) 1.18697e8i 0.392891i
\(672\) 0 0
\(673\) −4.93893e8 −1.62027 −0.810135 0.586243i \(-0.800606\pi\)
−0.810135 + 0.586243i \(0.800606\pi\)
\(674\) 0 0
\(675\) 3.04894e7 1.76030e7i 0.0991373 0.0572369i
\(676\) 0 0
\(677\) −2.71512e8 1.56758e8i −0.875030 0.505199i −0.00601364 0.999982i \(-0.501914\pi\)
−0.869017 + 0.494783i \(0.835248\pi\)
\(678\) 0 0
\(679\) 1.19034e8 1.76245e8i 0.380243 0.563000i
\(680\) 0 0
\(681\) −1.17755e8 + 2.03957e8i −0.372852 + 0.645798i
\(682\) 0 0
\(683\) −7.42502e7 1.28605e8i −0.233043 0.403642i 0.725659 0.688054i \(-0.241535\pi\)
−0.958702 + 0.284412i \(0.908202\pi\)
\(684\) 0 0
\(685\) 7.22343e7i 0.224735i
\(686\) 0 0
\(687\) 6.63087e7 0.204503
\(688\) 0 0
\(689\) 3.92108e8 2.26384e8i 1.19880 0.692130i
\(690\) 0 0
\(691\) 3.35862e8 + 1.93910e8i 1.01795 + 0.587714i 0.913510 0.406817i \(-0.133361\pi\)
0.104441 + 0.994531i \(0.466695\pi\)
\(692\) 0 0
\(693\) −5.67931e7 3.83573e7i −0.170646 0.115252i
\(694\) 0 0
\(695\) 184598. 319733.i 0.000549886 0.000952430i
\(696\) 0 0
\(697\) 2.30732e8 + 3.99640e8i 0.681412 + 1.18024i
\(698\) 0 0
\(699\) 1.96130e8i 0.574265i
\(700\) 0 0
\(701\) 4.86782e7 0.141312 0.0706562 0.997501i \(-0.477491\pi\)
0.0706562 + 0.997501i \(0.477491\pi\)
\(702\) 0 0
\(703\) 4.61079e8 2.66204e8i 1.32712 0.766212i
\(704\) 0 0
\(705\) 5.39223e6 + 3.11320e6i 0.0153887 + 0.00888465i
\(706\) 0 0
\(707\) 2.28632e8 + 1.61262e7i 0.646963 + 0.0456324i
\(708\) 0 0
\(709\) 1.58977e8 2.75357e8i 0.446064 0.772605i −0.552062 0.833803i \(-0.686159\pi\)
0.998126 + 0.0611981i \(0.0194921\pi\)
\(710\) 0 0
\(711\) 8.27820e7 + 1.43383e8i 0.230318 + 0.398922i
\(712\) 0 0
\(713\) 5.24756e8i 1.44773i
\(714\) 0 0
\(715\) 1.58922e8 0.434776
\(716\) 0 0
\(717\) 1.01836e8 5.87951e7i 0.276277 0.159509i
\(718\) 0 0
\(719\) 1.50536e8 + 8.69119e7i 0.404998 + 0.233826i 0.688638 0.725105i \(-0.258209\pi\)
−0.283640 + 0.958931i \(0.591542\pi\)
\(720\) 0 0
\(721\) 2.32679e8 + 4.77794e8i 0.620799 + 1.27478i
\(722\) 0 0
\(723\) −1.52598e8 + 2.64307e8i −0.403769 + 0.699348i
\(724\) 0 0
\(725\) −6.45394e7 1.11785e8i −0.169360 0.293340i
\(726\) 0 0
\(727\) 4.58803e8i 1.19405i 0.802222 + 0.597026i \(0.203651\pi\)
−0.802222 + 0.597026i \(0.796349\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) 6.19927e8 3.57915e8i 1.58704 0.916279i
\(732\) 0 0
\(733\) 5.55746e8 + 3.20860e8i 1.41112 + 0.814711i 0.995494 0.0948235i \(-0.0302287\pi\)
0.415627 + 0.909535i \(0.363562\pi\)
\(734\) 0 0
\(735\) 5.45003e7 + 1.35363e8i 0.137258 + 0.340909i
\(736\) 0 0
\(737\) 9.68105e7 1.67681e8i 0.241835 0.418871i
\(738\) 0 0
\(739\) −1.70001e8 2.94450e8i −0.421229 0.729590i 0.574831 0.818272i \(-0.305068\pi\)
−0.996060 + 0.0886823i \(0.971734\pi\)
\(740\) 0 0
\(741\) 2.53034e8i 0.621904i
\(742\) 0 0
\(743\) −6.08554e8 −1.48365 −0.741827 0.670591i \(-0.766040\pi\)
−0.741827 + 0.670591i \(0.766040\pi\)
\(744\) 0 0
\(745\) −1.13504e8 + 6.55313e7i −0.274499 + 0.158482i
\(746\) 0 0
\(747\) 2.69409e7 + 1.55543e7i 0.0646323 + 0.0373155i
\(748\) 0 0
\(749\) 2.94776e8 1.43552e8i 0.701531 0.341636i
\(750\) 0 0
\(751\) 8.06132e7 1.39626e8i 0.190321 0.329645i −0.755036 0.655684i \(-0.772381\pi\)
0.945357 + 0.326038i \(0.105714\pi\)
\(752\) 0 0
\(753\) −1.08800e8 1.88447e8i −0.254826 0.441372i
\(754\) 0 0
\(755\) 1.94612e8i 0.452198i
\(756\) 0 0
\(757\) 1.60953e8 0.371031 0.185516 0.982641i \(-0.440604\pi\)
0.185516 + 0.982641i \(0.440604\pi\)
\(758\) 0 0
\(759\) −2.09046e8 + 1.20693e8i −0.478098 + 0.276030i
\(760\) 0 0
\(761\) −3.75605e8 2.16856e8i −0.852271 0.492059i 0.00914540 0.999958i \(-0.497089\pi\)
−0.861416 + 0.507899i \(0.830422\pi\)
\(762\) 0 0
\(763\) −3.79304e7 + 5.37766e8i −0.0853913 + 1.21065i
\(764\) 0 0
\(765\) −7.53621e7 + 1.30531e8i −0.168333 + 0.291561i
\(766\) 0 0
\(767\) −2.73526e8 4.73760e8i −0.606194 1.04996i
\(768\) 0 0
\(769\) 3.73405e8i 0.821110i −0.911836 0.410555i \(-0.865335\pi\)
0.911836 0.410555i \(-0.134665\pi\)
\(770\) 0 0
\(771\) 1.02177e7 0.0222941
\(772\) 0 0
\(773\) 5.92885e8 3.42302e8i 1.28361 0.741090i 0.306100 0.951999i \(-0.400976\pi\)
0.977506 + 0.210909i \(0.0676423\pi\)
\(774\) 0 0
\(775\) −2.24278e8 1.29487e8i −0.481816 0.278176i
\(776\) 0 0
\(777\) −2.38435e8 + 3.53035e8i −0.508285 + 0.752584i
\(778\) 0 0
\(779\) 1.97781e8 3.42567e8i 0.418381 0.724658i
\(780\) 0 0
\(781\) −3.95782e7 6.85514e7i −0.0830812 0.143901i
\(782\) 0 0
\(783\) 5.26085e7i 0.109590i
\(784\) 0 0
\(785\) 2.24014e8 0.463091