Properties

Label 84.6.i.b.25.1
Level $84$
Weight $6$
Character 84.25
Analytic conductor $13.472$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,6,Mod(25,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.4722408643\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7081})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.1
Root \(-20.7872 - 36.0044i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.6.i.b.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 + 7.79423i) q^{3} +(-32.7872 - 56.7890i) q^{5} +(40.6487 + 123.104i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 + 7.79423i) q^{3} +(-32.7872 - 56.7890i) q^{5} +(40.6487 + 123.104i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(122.787 - 212.674i) q^{11} +434.872 q^{13} +590.169 q^{15} +(551.149 - 954.618i) q^{17} +(1438.65 + 2491.81i) q^{19} +(-1142.42 - 237.145i) q^{21} +(2114.72 + 3662.80i) q^{23} +(-587.497 + 1017.57i) q^{25} +729.000 q^{27} +4969.60 q^{29} +(4391.32 - 7606.00i) q^{31} +(1105.08 + 1914.06i) q^{33} +(5658.22 - 6344.64i) q^{35} +(1220.03 + 2113.15i) q^{37} +(-1956.92 + 3389.49i) q^{39} -3668.55 q^{41} -7198.06 q^{43} +(-2655.76 + 4599.91i) q^{45} +(-1636.66 - 2834.78i) q^{47} +(-13502.4 + 10008.1i) q^{49} +(4960.34 + 8591.56i) q^{51} +(1510.84 - 2616.84i) q^{53} -16103.4 q^{55} -25895.6 q^{57} +(25743.7 - 44589.5i) q^{59} +(6656.65 + 11529.6i) q^{61} +(6989.26 - 7837.15i) q^{63} +(-14258.2 - 24695.9i) q^{65} +(-15447.9 + 26756.5i) q^{67} -38064.9 q^{69} -41882.8 q^{71} +(-17308.7 + 29979.5i) q^{73} +(-5287.47 - 9158.17i) q^{75} +(31172.2 + 6470.74i) q^{77} +(-38771.7 - 67154.6i) q^{79} +(-3280.50 + 5681.99i) q^{81} +100908. q^{83} -72282.4 q^{85} +(-22363.2 + 38734.2i) q^{87} +(-20391.8 - 35319.7i) q^{89} +(17677.0 + 53534.6i) q^{91} +(39521.9 + 68454.0i) q^{93} +(94338.2 - 163399. i) q^{95} +140147. q^{97} -19891.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} - 47 q^{5} - 174 q^{7} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} - 47 q^{5} - 174 q^{7} - 162 q^{9} + 407 q^{11} + 898 q^{13} + 846 q^{15} + 1868 q^{17} + 1463 q^{19} - 783 q^{21} + 44 q^{23} + 1605 q^{25} + 2916 q^{27} + 1534 q^{29} + 11170 q^{31} + 3663 q^{33} + 9674 q^{35} + 3113 q^{37} - 4041 q^{39} - 15684 q^{41} - 25258 q^{43} - 3807 q^{45} - 9576 q^{47} + 4558 q^{49} + 16812 q^{51} - 13395 q^{53} - 26210 q^{55} - 26334 q^{57} + 47521 q^{59} + 63652 q^{61} + 21141 q^{63} - 28254 q^{65} - 44541 q^{67} - 792 q^{69} - 251680 q^{71} - 6039 q^{73} + 14445 q^{75} + 35407 q^{77} - 17588 q^{79} - 13122 q^{81} + 78650 q^{83} - 116120 q^{85} - 6903 q^{87} - 83082 q^{89} + 31747 q^{91} + 100530 q^{93} + 214946 q^{95} + 369570 q^{97} - 65934 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −32.7872 56.7890i −0.586515 1.01587i −0.994685 0.102967i \(-0.967166\pi\)
0.408170 0.912906i \(-0.366167\pi\)
\(6\) 0 0
\(7\) 40.6487 + 123.104i 0.313546 + 0.949573i
\(8\) 0 0
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 0 0
\(11\) 122.787 212.674i 0.305965 0.529946i −0.671511 0.740995i \(-0.734354\pi\)
0.977476 + 0.211048i \(0.0676877\pi\)
\(12\) 0 0
\(13\) 434.872 0.713679 0.356839 0.934166i \(-0.383854\pi\)
0.356839 + 0.934166i \(0.383854\pi\)
\(14\) 0 0
\(15\) 590.169 0.677249
\(16\) 0 0
\(17\) 551.149 954.618i 0.462537 0.801138i −0.536550 0.843869i \(-0.680273\pi\)
0.999087 + 0.0427312i \(0.0136059\pi\)
\(18\) 0 0
\(19\) 1438.65 + 2491.81i 0.914260 + 1.58355i 0.807981 + 0.589209i \(0.200560\pi\)
0.106279 + 0.994336i \(0.466106\pi\)
\(20\) 0 0
\(21\) −1142.42 237.145i −0.565299 0.117345i
\(22\) 0 0
\(23\) 2114.72 + 3662.80i 0.833552 + 1.44375i 0.895204 + 0.445657i \(0.147030\pi\)
−0.0616521 + 0.998098i \(0.519637\pi\)
\(24\) 0 0
\(25\) −587.497 + 1017.57i −0.187999 + 0.325624i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 4969.60 1.09730 0.548652 0.836051i \(-0.315141\pi\)
0.548652 + 0.836051i \(0.315141\pi\)
\(30\) 0 0
\(31\) 4391.32 7606.00i 0.820713 1.42152i −0.0844390 0.996429i \(-0.526910\pi\)
0.905152 0.425088i \(-0.139757\pi\)
\(32\) 0 0
\(33\) 1105.08 + 1914.06i 0.176649 + 0.305965i
\(34\) 0 0
\(35\) 5658.22 6344.64i 0.780746 0.875462i
\(36\) 0 0
\(37\) 1220.03 + 2113.15i 0.146510 + 0.253762i 0.929935 0.367723i \(-0.119863\pi\)
−0.783425 + 0.621486i \(0.786529\pi\)
\(38\) 0 0
\(39\) −1956.92 + 3389.49i −0.206021 + 0.356839i
\(40\) 0 0
\(41\) −3668.55 −0.340828 −0.170414 0.985373i \(-0.554511\pi\)
−0.170414 + 0.985373i \(0.554511\pi\)
\(42\) 0 0
\(43\) −7198.06 −0.593669 −0.296835 0.954929i \(-0.595931\pi\)
−0.296835 + 0.954929i \(0.595931\pi\)
\(44\) 0 0
\(45\) −2655.76 + 4599.91i −0.195505 + 0.338624i
\(46\) 0 0
\(47\) −1636.66 2834.78i −0.108072 0.187187i 0.806917 0.590665i \(-0.201134\pi\)
−0.914989 + 0.403478i \(0.867801\pi\)
\(48\) 0 0
\(49\) −13502.4 + 10008.1i −0.803378 + 0.595470i
\(50\) 0 0
\(51\) 4960.34 + 8591.56i 0.267046 + 0.462537i
\(52\) 0 0
\(53\) 1510.84 2616.84i 0.0738801 0.127964i −0.826719 0.562616i \(-0.809795\pi\)
0.900599 + 0.434651i \(0.143128\pi\)
\(54\) 0 0
\(55\) −16103.4 −0.717811
\(56\) 0 0
\(57\) −25895.6 −1.05570
\(58\) 0 0
\(59\) 25743.7 44589.5i 0.962812 1.66764i 0.247432 0.968905i \(-0.420413\pi\)
0.715381 0.698735i \(-0.246253\pi\)
\(60\) 0 0
\(61\) 6656.65 + 11529.6i 0.229050 + 0.396727i 0.957527 0.288344i \(-0.0931046\pi\)
−0.728477 + 0.685071i \(0.759771\pi\)
\(62\) 0 0
\(63\) 6989.26 7837.15i 0.221860 0.248775i
\(64\) 0 0
\(65\) −14258.2 24695.9i −0.418583 0.725007i
\(66\) 0 0
\(67\) −15447.9 + 26756.5i −0.420418 + 0.728186i −0.995980 0.0895723i \(-0.971450\pi\)
0.575562 + 0.817758i \(0.304783\pi\)
\(68\) 0 0
\(69\) −38064.9 −0.962503
\(70\) 0 0
\(71\) −41882.8 −0.986030 −0.493015 0.870021i \(-0.664105\pi\)
−0.493015 + 0.870021i \(0.664105\pi\)
\(72\) 0 0
\(73\) −17308.7 + 29979.5i −0.380151 + 0.658441i −0.991084 0.133242i \(-0.957461\pi\)
0.610932 + 0.791683i \(0.290795\pi\)
\(74\) 0 0
\(75\) −5287.47 9158.17i −0.108541 0.187999i
\(76\) 0 0
\(77\) 31172.2 + 6470.74i 0.599157 + 0.124373i
\(78\) 0 0
\(79\) −38771.7 67154.6i −0.698952 1.21062i −0.968830 0.247726i \(-0.920317\pi\)
0.269878 0.962895i \(-0.413017\pi\)
\(80\) 0 0
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 100908. 1.60779 0.803897 0.594768i \(-0.202756\pi\)
0.803897 + 0.594768i \(0.202756\pi\)
\(84\) 0 0
\(85\) −72282.4 −1.08514
\(86\) 0 0
\(87\) −22363.2 + 38734.2i −0.316764 + 0.548652i
\(88\) 0 0
\(89\) −20391.8 35319.7i −0.272886 0.472652i 0.696714 0.717349i \(-0.254645\pi\)
−0.969600 + 0.244697i \(0.921312\pi\)
\(90\) 0 0
\(91\) 17677.0 + 53534.6i 0.223771 + 0.677690i
\(92\) 0 0
\(93\) 39521.9 + 68454.0i 0.473839 + 0.820713i
\(94\) 0 0
\(95\) 94338.2 163399.i 1.07245 1.85755i
\(96\) 0 0
\(97\) 140147. 1.51236 0.756178 0.654366i \(-0.227064\pi\)
0.756178 + 0.654366i \(0.227064\pi\)
\(98\) 0 0
\(99\) −19891.5 −0.203976
\(100\) 0 0
\(101\) −4288.23 + 7427.43i −0.0418287 + 0.0724494i −0.886182 0.463338i \(-0.846652\pi\)
0.844353 + 0.535787i \(0.179985\pi\)
\(102\) 0 0
\(103\) 17630.1 + 30536.2i 0.163742 + 0.283610i 0.936208 0.351447i \(-0.114310\pi\)
−0.772466 + 0.635057i \(0.780977\pi\)
\(104\) 0 0
\(105\) 23989.6 + 72652.4i 0.212349 + 0.643097i
\(106\) 0 0
\(107\) 96314.3 + 166821.i 0.813264 + 1.40861i 0.910568 + 0.413360i \(0.135645\pi\)
−0.0973041 + 0.995255i \(0.531022\pi\)
\(108\) 0 0
\(109\) −61646.1 + 106774.i −0.496980 + 0.860795i −0.999994 0.00348322i \(-0.998891\pi\)
0.503014 + 0.864279i \(0.332225\pi\)
\(110\) 0 0
\(111\) −21960.6 −0.169175
\(112\) 0 0
\(113\) 28400.9 0.209236 0.104618 0.994512i \(-0.466638\pi\)
0.104618 + 0.994512i \(0.466638\pi\)
\(114\) 0 0
\(115\) 138671. 240186.i 0.977781 1.69357i
\(116\) 0 0
\(117\) −17612.3 30505.4i −0.118946 0.206021i
\(118\) 0 0
\(119\) 139921. + 29044.9i 0.905765 + 0.188019i
\(120\) 0 0
\(121\) 50372.1 + 87247.1i 0.312771 + 0.541736i
\(122\) 0 0
\(123\) 16508.5 28593.5i 0.0983886 0.170414i
\(124\) 0 0
\(125\) −127870. −0.731973
\(126\) 0 0
\(127\) −47198.8 −0.259670 −0.129835 0.991536i \(-0.541445\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(128\) 0 0
\(129\) 32391.3 56103.3i 0.171377 0.296835i
\(130\) 0 0
\(131\) −39904.7 69116.9i −0.203163 0.351889i 0.746383 0.665517i \(-0.231789\pi\)
−0.949546 + 0.313628i \(0.898456\pi\)
\(132\) 0 0
\(133\) −248273. + 278392.i −1.21703 + 1.36467i
\(134\) 0 0
\(135\) −23901.8 41399.2i −0.112875 0.195505i
\(136\) 0 0
\(137\) 43032.1 74533.9i 0.195881 0.339275i −0.751308 0.659952i \(-0.770577\pi\)
0.947189 + 0.320676i \(0.103910\pi\)
\(138\) 0 0
\(139\) 270587. 1.18787 0.593935 0.804513i \(-0.297573\pi\)
0.593935 + 0.804513i \(0.297573\pi\)
\(140\) 0 0
\(141\) 29459.9 0.124791
\(142\) 0 0
\(143\) 53396.7 92485.7i 0.218360 0.378211i
\(144\) 0 0
\(145\) −162939. 282219.i −0.643585 1.11472i
\(146\) 0 0
\(147\) −17244.4 150277.i −0.0658197 0.573586i
\(148\) 0 0
\(149\) 86273.9 + 149431.i 0.318356 + 0.551410i 0.980145 0.198281i \(-0.0635358\pi\)
−0.661789 + 0.749690i \(0.730202\pi\)
\(150\) 0 0
\(151\) 8949.75 15501.4i 0.0319425 0.0553260i −0.849612 0.527408i \(-0.823164\pi\)
0.881555 + 0.472082i \(0.156497\pi\)
\(152\) 0 0
\(153\) −89286.1 −0.308358
\(154\) 0 0
\(155\) −575916. −1.92544
\(156\) 0 0
\(157\) 89509.3 155035.i 0.289814 0.501972i −0.683951 0.729528i \(-0.739740\pi\)
0.973765 + 0.227555i \(0.0730733\pi\)
\(158\) 0 0
\(159\) 13597.5 + 23551.6i 0.0426547 + 0.0738801i
\(160\) 0 0
\(161\) −364946. + 409219.i −1.10959 + 1.24420i
\(162\) 0 0
\(163\) 118645. + 205498.i 0.349767 + 0.605814i 0.986208 0.165511i \(-0.0529275\pi\)
−0.636441 + 0.771325i \(0.719594\pi\)
\(164\) 0 0
\(165\) 72465.2 125513.i 0.207214 0.358906i
\(166\) 0 0
\(167\) −94040.0 −0.260928 −0.130464 0.991453i \(-0.541647\pi\)
−0.130464 + 0.991453i \(0.541647\pi\)
\(168\) 0 0
\(169\) −182180. −0.490663
\(170\) 0 0
\(171\) 116530. 201836.i 0.304753 0.527848i
\(172\) 0 0
\(173\) −244357. 423238.i −0.620739 1.07515i −0.989348 0.145567i \(-0.953499\pi\)
0.368609 0.929584i \(-0.379834\pi\)
\(174\) 0 0
\(175\) −149149. 30960.4i −0.368150 0.0764207i
\(176\) 0 0
\(177\) 231694. + 401305.i 0.555880 + 0.962812i
\(178\) 0 0
\(179\) −406498. + 704075.i −0.948257 + 1.64243i −0.199161 + 0.979967i \(0.563822\pi\)
−0.749095 + 0.662462i \(0.769512\pi\)
\(180\) 0 0
\(181\) −332961. −0.755434 −0.377717 0.925921i \(-0.623291\pi\)
−0.377717 + 0.925921i \(0.623291\pi\)
\(182\) 0 0
\(183\) −119820. −0.264484
\(184\) 0 0
\(185\) 80002.7 138569.i 0.171860 0.297671i
\(186\) 0 0
\(187\) −135348. 234430.i −0.283040 0.490240i
\(188\) 0 0
\(189\) 29632.9 + 89743.1i 0.0603420 + 0.182745i
\(190\) 0 0
\(191\) 72143.9 + 124957.i 0.143092 + 0.247843i 0.928660 0.370933i \(-0.120962\pi\)
−0.785567 + 0.618776i \(0.787629\pi\)
\(192\) 0 0
\(193\) 447310. 774763.i 0.864400 1.49719i −0.00324119 0.999995i \(-0.501032\pi\)
0.867641 0.497190i \(-0.165635\pi\)
\(194\) 0 0
\(195\) 256648. 0.483338
\(196\) 0 0
\(197\) −599462. −1.10052 −0.550258 0.834995i \(-0.685470\pi\)
−0.550258 + 0.834995i \(0.685470\pi\)
\(198\) 0 0
\(199\) 389129. 673992.i 0.696564 1.20648i −0.273086 0.961990i \(-0.588044\pi\)
0.969651 0.244495i \(-0.0786222\pi\)
\(200\) 0 0
\(201\) −139031. 240808.i −0.242729 0.420418i
\(202\) 0 0
\(203\) 202008. + 611780.i 0.344055 + 1.04197i
\(204\) 0 0
\(205\) 120282. + 208334.i 0.199901 + 0.346238i
\(206\) 0 0
\(207\) 171292. 296687.i 0.277851 0.481251i
\(208\) 0 0
\(209\) 706589. 1.11893
\(210\) 0 0
\(211\) −810532. −1.25333 −0.626663 0.779291i \(-0.715580\pi\)
−0.626663 + 0.779291i \(0.715580\pi\)
\(212\) 0 0
\(213\) 188473. 326444.i 0.284642 0.493015i
\(214\) 0 0
\(215\) 236004. + 408771.i 0.348196 + 0.603093i
\(216\) 0 0
\(217\) 1.11483e6 + 231418.i 1.60717 + 0.333616i
\(218\) 0 0
\(219\) −155778. 269815.i −0.219480 0.380151i
\(220\) 0 0
\(221\) 239679. 415136.i 0.330103 0.571755i
\(222\) 0 0
\(223\) 220486. 0.296905 0.148453 0.988920i \(-0.452571\pi\)
0.148453 + 0.988920i \(0.452571\pi\)
\(224\) 0 0
\(225\) 95174.5 0.125333
\(226\) 0 0
\(227\) −671890. + 1.16375e6i −0.865433 + 1.49897i 0.00118391 + 0.999999i \(0.499623\pi\)
−0.866617 + 0.498974i \(0.833710\pi\)
\(228\) 0 0
\(229\) 521292. + 902904.i 0.656889 + 1.13777i 0.981417 + 0.191889i \(0.0614614\pi\)
−0.324528 + 0.945876i \(0.605205\pi\)
\(230\) 0 0
\(231\) −190709. + 213845.i −0.235148 + 0.263675i
\(232\) 0 0
\(233\) −316256. 547771.i −0.381635 0.661011i 0.609661 0.792662i \(-0.291306\pi\)
−0.991296 + 0.131651i \(0.957972\pi\)
\(234\) 0 0
\(235\) −107323. + 185889.i −0.126772 + 0.219575i
\(236\) 0 0
\(237\) 697891. 0.807081
\(238\) 0 0
\(239\) −684919. −0.775612 −0.387806 0.921741i \(-0.626767\pi\)
−0.387806 + 0.921741i \(0.626767\pi\)
\(240\) 0 0
\(241\) 3866.44 6696.87i 0.00428814 0.00742728i −0.863873 0.503709i \(-0.831968\pi\)
0.868162 + 0.496282i \(0.165302\pi\)
\(242\) 0 0
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 1.01105e6 + 438651.i 1.07611 + 0.466878i
\(246\) 0 0
\(247\) 625626. + 1.08362e6i 0.652488 + 1.13014i
\(248\) 0 0
\(249\) −454086. + 786500.i −0.464130 + 0.803897i
\(250\) 0 0
\(251\) 1.09614e6 1.09820 0.549098 0.835758i \(-0.314971\pi\)
0.549098 + 0.835758i \(0.314971\pi\)
\(252\) 0 0
\(253\) 1.03864e6 1.02015
\(254\) 0 0
\(255\) 325271. 563386.i 0.313253 0.542570i
\(256\) 0 0
\(257\) −357460. 619139.i −0.337594 0.584730i 0.646386 0.763011i \(-0.276280\pi\)
−0.983980 + 0.178281i \(0.942946\pi\)
\(258\) 0 0
\(259\) −210546. + 236088.i −0.195028 + 0.218688i
\(260\) 0 0
\(261\) −201269. 348608.i −0.182884 0.316764i
\(262\) 0 0
\(263\) 298256. 516595.i 0.265889 0.460533i −0.701907 0.712268i \(-0.747668\pi\)
0.967796 + 0.251735i \(0.0810012\pi\)
\(264\) 0 0
\(265\) −198144. −0.173327
\(266\) 0 0
\(267\) 367053. 0.315102
\(268\) 0 0
\(269\) 1.01654e6 1.76070e6i 0.856531 1.48356i −0.0186864 0.999825i \(-0.505948\pi\)
0.875217 0.483730i \(-0.160718\pi\)
\(270\) 0 0
\(271\) −897277. 1.55413e6i −0.742170 1.28548i −0.951505 0.307632i \(-0.900463\pi\)
0.209336 0.977844i \(-0.432870\pi\)
\(272\) 0 0
\(273\) −496807. 103127.i −0.403442 0.0837467i
\(274\) 0 0
\(275\) 144274. + 249890.i 0.115042 + 0.199259i
\(276\) 0 0
\(277\) −211790. + 366831.i −0.165846 + 0.287254i −0.936956 0.349449i \(-0.886369\pi\)
0.771109 + 0.636703i \(0.219702\pi\)
\(278\) 0 0
\(279\) −711395. −0.547142
\(280\) 0 0
\(281\) −1.63799e6 −1.23750 −0.618749 0.785589i \(-0.712360\pi\)
−0.618749 + 0.785589i \(0.712360\pi\)
\(282\) 0 0
\(283\) 147018. 254642.i 0.109120 0.189001i −0.806294 0.591515i \(-0.798530\pi\)
0.915414 + 0.402514i \(0.131863\pi\)
\(284\) 0 0
\(285\) 849044. + 1.47059e6i 0.619182 + 1.07245i
\(286\) 0 0
\(287\) −149122. 451615.i −0.106865 0.323641i
\(288\) 0 0
\(289\) 102399. + 177360.i 0.0721191 + 0.124914i
\(290\) 0 0
\(291\) −630661. + 1.09234e6i −0.436580 + 0.756178i
\(292\) 0 0
\(293\) −356961. −0.242913 −0.121457 0.992597i \(-0.538757\pi\)
−0.121457 + 0.992597i \(0.538757\pi\)
\(294\) 0 0
\(295\) −3.37626e6 −2.25881
\(296\) 0 0
\(297\) 89511.8 155039.i 0.0588829 0.101988i
\(298\) 0 0
\(299\) 919631. + 1.59285e6i 0.594888 + 1.03038i
\(300\) 0 0
\(301\) −292592. 886113.i −0.186143 0.563732i
\(302\) 0 0
\(303\) −38594.0 66846.8i −0.0241498 0.0418287i
\(304\) 0 0
\(305\) 436505. 756049.i 0.268683 0.465372i
\(306\) 0 0
\(307\) −2.04097e6 −1.23592 −0.617960 0.786210i \(-0.712041\pi\)
−0.617960 + 0.786210i \(0.712041\pi\)
\(308\) 0 0
\(309\) −317341. −0.189073
\(310\) 0 0
\(311\) −1.02337e6 + 1.77253e6i −0.599972 + 1.03918i 0.392852 + 0.919602i \(0.371488\pi\)
−0.992824 + 0.119581i \(0.961845\pi\)
\(312\) 0 0
\(313\) −319272. 552996.i −0.184205 0.319052i 0.759104 0.650970i \(-0.225638\pi\)
−0.943308 + 0.331918i \(0.892304\pi\)
\(314\) 0 0
\(315\) −674222. 139955.i −0.382848 0.0794718i
\(316\) 0 0
\(317\) −1.74954e6 3.03030e6i −0.977860 1.69370i −0.670155 0.742221i \(-0.733772\pi\)
−0.307705 0.951482i \(-0.599561\pi\)
\(318\) 0 0
\(319\) 610203. 1.05690e6i 0.335736 0.581512i
\(320\) 0 0
\(321\) −1.73366e6 −0.939076
\(322\) 0 0
\(323\) 3.17163e6 1.69152
\(324\) 0 0
\(325\) −255486. + 442514.i −0.134171 + 0.232391i
\(326\) 0 0
\(327\) −554815. 960967.i −0.286932 0.496980i
\(328\) 0 0
\(329\) 282446. 316710.i 0.143862 0.161314i
\(330\) 0 0
\(331\) 1.47089e6 + 2.54766e6i 0.737923 + 1.27812i 0.953429 + 0.301618i \(0.0975266\pi\)
−0.215506 + 0.976503i \(0.569140\pi\)
\(332\) 0 0
\(333\) 98822.5 171166.i 0.0488366 0.0845874i
\(334\) 0 0
\(335\) 2.02597e6 0.986326
\(336\) 0 0
\(337\) 2.77854e6 1.33273 0.666364 0.745627i \(-0.267850\pi\)
0.666364 + 0.745627i \(0.267850\pi\)
\(338\) 0 0
\(339\) −127804. + 221363.i −0.0604012 + 0.104618i
\(340\) 0 0
\(341\) −1.07840e6 1.86784e6i −0.502218 0.869868i
\(342\) 0 0
\(343\) −1.78089e6 1.25539e6i −0.817338 0.576159i
\(344\) 0 0
\(345\) 1.24804e6 + 2.16167e6i 0.564522 + 0.977781i
\(346\) 0 0
\(347\) 86001.9 148960.i 0.0383429 0.0664118i −0.846217 0.532838i \(-0.821125\pi\)
0.884560 + 0.466426i \(0.154459\pi\)
\(348\) 0 0
\(349\) −3.88321e6 −1.70658 −0.853290 0.521436i \(-0.825397\pi\)
−0.853290 + 0.521436i \(0.825397\pi\)
\(350\) 0 0
\(351\) 317021. 0.137348
\(352\) 0 0
\(353\) 385467. 667649.i 0.164646 0.285175i −0.771884 0.635764i \(-0.780685\pi\)
0.936529 + 0.350589i \(0.114019\pi\)
\(354\) 0 0
\(355\) 1.37322e6 + 2.37849e6i 0.578321 + 1.00168i
\(356\) 0 0
\(357\) −856027. + 959875.i −0.355481 + 0.398606i
\(358\) 0 0
\(359\) −1.57017e6 2.71961e6i −0.642998 1.11370i −0.984760 0.173918i \(-0.944357\pi\)
0.341763 0.939786i \(-0.388976\pi\)
\(360\) 0 0
\(361\) −2.90135e6 + 5.02529e6i −1.17174 + 2.02952i
\(362\) 0 0
\(363\) −906698. −0.361157
\(364\) 0 0
\(365\) 2.27001e6 0.891857
\(366\) 0 0
\(367\) 182842. 316691.i 0.0708615 0.122736i −0.828418 0.560111i \(-0.810758\pi\)
0.899279 + 0.437375i \(0.144092\pi\)
\(368\) 0 0
\(369\) 148576. + 257342.i 0.0568047 + 0.0983886i
\(370\) 0 0
\(371\) 383559. + 79619.2i 0.144676 + 0.0300319i
\(372\) 0 0
\(373\) 77129.9 + 133593.i 0.0287045 + 0.0497177i 0.880021 0.474935i \(-0.157528\pi\)
−0.851316 + 0.524653i \(0.824195\pi\)
\(374\) 0 0
\(375\) 575417. 996651.i 0.211302 0.365986i
\(376\) 0 0
\(377\) 2.16114e6 0.783122
\(378\) 0 0
\(379\) 4.06013e6 1.45192 0.725959 0.687738i \(-0.241396\pi\)
0.725959 + 0.687738i \(0.241396\pi\)
\(380\) 0 0
\(381\) 212395. 367878.i 0.0749602 0.129835i
\(382\) 0 0
\(383\) −1.02152e6 1.76932e6i −0.355834 0.616323i 0.631426 0.775436i \(-0.282470\pi\)
−0.987260 + 0.159113i \(0.949137\pi\)
\(384\) 0 0
\(385\) −654581. 1.98240e6i −0.225067 0.681614i
\(386\) 0 0
\(387\) 291521. + 504930.i 0.0989448 + 0.171377i
\(388\) 0 0
\(389\) 1.06183e6 1.83915e6i 0.355780 0.616229i −0.631471 0.775399i \(-0.717549\pi\)
0.987251 + 0.159170i \(0.0508819\pi\)
\(390\) 0 0
\(391\) 4.66209e6 1.54219
\(392\) 0 0
\(393\) 718284. 0.234593
\(394\) 0 0
\(395\) −2.54243e6 + 4.40362e6i −0.819892 + 1.42009i
\(396\) 0 0
\(397\) 1.83182e6 + 3.17280e6i 0.583319 + 1.01034i 0.995083 + 0.0990473i \(0.0315795\pi\)
−0.411764 + 0.911291i \(0.635087\pi\)
\(398\) 0 0
\(399\) −1.05262e6 3.18786e6i −0.331010 1.00246i
\(400\) 0 0
\(401\) 32044.9 + 55503.3i 0.00995170 + 0.0172369i 0.870958 0.491357i \(-0.163499\pi\)
−0.861007 + 0.508594i \(0.830166\pi\)
\(402\) 0 0
\(403\) 1.90966e6 3.30763e6i 0.585725 1.01451i
\(404\) 0 0
\(405\) 430233. 0.130337
\(406\) 0 0
\(407\) 599216. 0.179307
\(408\) 0 0
\(409\) −1.01287e6 + 1.75434e6i −0.299395 + 0.518568i −0.975998 0.217781i \(-0.930118\pi\)
0.676603 + 0.736348i \(0.263452\pi\)
\(410\) 0 0
\(411\) 387289. + 670805.i 0.113092 + 0.195881i
\(412\) 0 0
\(413\) 6.53561e6 + 1.35666e6i 1.88543 + 0.391379i
\(414\) 0 0
\(415\) −3.30849e6 5.73047e6i −0.942995 1.63332i
\(416\) 0 0
\(417\) −1.21764e6 + 2.10901e6i −0.342909 + 0.593935i
\(418\) 0 0
\(419\) 2.38986e6 0.665025 0.332513 0.943099i \(-0.392104\pi\)
0.332513 + 0.943099i \(0.392104\pi\)
\(420\) 0 0
\(421\) 3.46875e6 0.953822 0.476911 0.878952i \(-0.341756\pi\)
0.476911 + 0.878952i \(0.341756\pi\)
\(422\) 0 0
\(423\) −132570. + 229617.i −0.0360241 + 0.0623956i
\(424\) 0 0
\(425\) 647596. + 1.12167e6i 0.173913 + 0.301226i
\(426\) 0 0
\(427\) −1.14877e6 + 1.28813e6i −0.304903 + 0.341892i
\(428\) 0 0
\(429\) 480570. + 832372.i 0.126070 + 0.218360i
\(430\) 0 0
\(431\) 802201. 1.38945e6i 0.208013 0.360289i −0.743076 0.669207i \(-0.766634\pi\)
0.951088 + 0.308919i \(0.0999671\pi\)
\(432\) 0 0
\(433\) 741661. 0.190102 0.0950508 0.995472i \(-0.469699\pi\)
0.0950508 + 0.995472i \(0.469699\pi\)
\(434\) 0 0
\(435\) 2.93291e6 0.743147
\(436\) 0 0
\(437\) −6.08466e6 + 1.05389e7i −1.52417 + 2.63993i
\(438\) 0 0
\(439\) −1.43394e6 2.48365e6i −0.355115 0.615077i 0.632023 0.774950i \(-0.282225\pi\)
−0.987138 + 0.159873i \(0.948892\pi\)
\(440\) 0 0
\(441\) 1.24889e6 + 541839.i 0.305794 + 0.132670i
\(442\) 0 0
\(443\) 89148.9 + 154410.i 0.0215827 + 0.0373824i 0.876615 0.481192i \(-0.159796\pi\)
−0.855032 + 0.518575i \(0.826463\pi\)
\(444\) 0 0
\(445\) −1.33718e6 + 2.31607e6i −0.320103 + 0.554435i
\(446\) 0 0
\(447\) −1.55293e6 −0.367606
\(448\) 0 0
\(449\) −2.77890e6 −0.650515 −0.325258 0.945625i \(-0.605451\pi\)
−0.325258 + 0.945625i \(0.605451\pi\)
\(450\) 0 0
\(451\) −450451. + 780205.i −0.104281 + 0.180621i
\(452\) 0 0
\(453\) 80547.7 + 139513.i 0.0184420 + 0.0319425i
\(454\) 0 0
\(455\) 2.46060e6 2.75911e6i 0.557202 0.624798i
\(456\) 0 0
\(457\) −3.20669e6 5.55416e6i −0.718236 1.24402i −0.961698 0.274111i \(-0.911617\pi\)
0.243462 0.969910i \(-0.421717\pi\)
\(458\) 0 0
\(459\) 401787. 695916.i 0.0890153 0.154179i
\(460\) 0 0
\(461\) −6.88393e6 −1.50864 −0.754318 0.656510i \(-0.772032\pi\)
−0.754318 + 0.656510i \(0.772032\pi\)
\(462\) 0 0
\(463\) 6.70530e6 1.45367 0.726835 0.686812i \(-0.240991\pi\)
0.726835 + 0.686812i \(0.240991\pi\)
\(464\) 0 0
\(465\) 2.59162e6 4.48882e6i 0.555827 0.962721i
\(466\) 0 0
\(467\) 1.62836e6 + 2.82041e6i 0.345509 + 0.598439i 0.985446 0.169988i \(-0.0543730\pi\)
−0.639937 + 0.768427i \(0.721040\pi\)
\(468\) 0 0
\(469\) −3.92178e6 814084.i −0.823286 0.170898i
\(470\) 0 0
\(471\) 805584. + 1.39531e6i 0.167324 + 0.289814i
\(472\) 0 0
\(473\) −883830. + 1.53084e6i −0.181642 + 0.314613i
\(474\) 0 0
\(475\) −3.38080e6 −0.687520
\(476\) 0 0
\(477\) −244755. −0.0492534
\(478\) 0 0
\(479\) −4.67916e6 + 8.10454e6i −0.931814 + 1.61395i −0.151595 + 0.988443i \(0.548441\pi\)
−0.780219 + 0.625506i \(0.784892\pi\)
\(480\) 0 0
\(481\) 530557. + 918951.i 0.104561 + 0.181105i
\(482\) 0 0
\(483\) −1.54729e6 4.68596e6i −0.301789 0.913967i
\(484\) 0 0
\(485\) −4.59502e6 7.95881e6i −0.887019 1.53636i
\(486\) 0 0
\(487\) 1.31470e6 2.27712e6i 0.251191 0.435075i −0.712663 0.701506i \(-0.752511\pi\)
0.963854 + 0.266431i \(0.0858445\pi\)
\(488\) 0 0
\(489\) −2.13560e6 −0.403876
\(490\) 0 0
\(491\) −4.81856e6 −0.902015 −0.451008 0.892520i \(-0.648935\pi\)
−0.451008 + 0.892520i \(0.648935\pi\)
\(492\) 0 0
\(493\) 2.73899e6 4.74407e6i 0.507543 0.879091i
\(494\) 0 0
\(495\) 652187. + 1.12962e6i 0.119635 + 0.207214i
\(496\) 0 0
\(497\) −1.70248e6 5.15596e6i −0.309166 0.936308i
\(498\) 0 0
\(499\) 2.09549e6 + 3.62949e6i 0.376733 + 0.652521i 0.990585 0.136900i \(-0.0437139\pi\)
−0.613851 + 0.789422i \(0.710381\pi\)
\(500\) 0 0
\(501\) 423180. 732969.i 0.0753236 0.130464i
\(502\) 0 0
\(503\) −1.75338e6 −0.308999 −0.154500 0.987993i \(-0.549377\pi\)
−0.154500 + 0.987993i \(0.549377\pi\)
\(504\) 0 0
\(505\) 562395. 0.0981326
\(506\) 0 0
\(507\) 819808. 1.41995e6i 0.141642 0.245331i
\(508\) 0 0
\(509\) −2.80923e6 4.86573e6i −0.480610 0.832441i 0.519142 0.854688i \(-0.326251\pi\)
−0.999753 + 0.0222464i \(0.992918\pi\)
\(510\) 0 0
\(511\) −4.39418e6 912146.i −0.744433 0.154530i
\(512\) 0 0
\(513\) 1.04877e6 + 1.81653e6i 0.175949 + 0.304753i
\(514\) 0 0
\(515\) 1.15608e6 2.00239e6i 0.192075 0.332683i
\(516\) 0 0
\(517\) −803844. −0.132265
\(518\) 0 0
\(519\) 4.39842e6 0.716768
\(520\) 0 0
\(521\) −5.53589e6 + 9.58845e6i −0.893498 + 1.54758i −0.0578446 + 0.998326i \(0.518423\pi\)
−0.835653 + 0.549258i \(0.814911\pi\)
\(522\) 0 0
\(523\) 3.79894e6 + 6.57996e6i 0.607307 + 1.05189i 0.991682 + 0.128710i \(0.0410836\pi\)
−0.384375 + 0.923177i \(0.625583\pi\)
\(524\) 0 0
\(525\) 912482. 1.02318e6i 0.144486 0.162014i
\(526\) 0 0
\(527\) −4.84055e6 8.38407e6i −0.759220 1.31501i
\(528\) 0 0
\(529\) −5.72588e6 + 9.91752e6i −0.889618 + 1.54086i
\(530\) 0 0
\(531\) −4.17049e6 −0.641875
\(532\) 0 0
\(533\) −1.59535e6 −0.243242
\(534\) 0 0
\(535\) 6.31575e6 1.09392e7i 0.953982 1.65235i
\(536\) 0 0
\(537\) −3.65848e6 6.33668e6i −0.547476 0.948257i
\(538\) 0 0
\(539\) 470532. + 4.10046e6i 0.0697618 + 0.607940i
\(540\) 0 0
\(541\) 1.67539e6 + 2.90187e6i 0.246107 + 0.426270i 0.962442 0.271486i \(-0.0875152\pi\)
−0.716335 + 0.697756i \(0.754182\pi\)
\(542\) 0 0
\(543\) 1.49832e6 2.59517e6i 0.218075 0.377717i
\(544\) 0 0
\(545\) 8.08480e6 1.16595
\(546\) 0 0
\(547\) −1.00856e7 −1.44123 −0.720615 0.693335i \(-0.756140\pi\)
−0.720615 + 0.693335i \(0.756140\pi\)
\(548\) 0 0
\(549\) 539188. 933901.i 0.0763501 0.132242i
\(550\) 0 0
\(551\) 7.14950e6 + 1.23833e7i 1.00322 + 1.73763i
\(552\) 0 0
\(553\) 6.69101e6 7.50272e6i 0.930419 1.04329i
\(554\) 0 0
\(555\) 720024. + 1.24712e6i 0.0992235 + 0.171860i
\(556\) 0 0
\(557\) −6.78337e6 + 1.17491e7i −0.926419 + 1.60460i −0.137155 + 0.990550i \(0.543796\pi\)
−0.789263 + 0.614055i \(0.789537\pi\)
\(558\) 0 0
\(559\) −3.13023e6 −0.423689
\(560\) 0 0
\(561\) 2.43626e6 0.326826
\(562\) 0 0
\(563\) 1.98494e6 3.43802e6i 0.263922 0.457127i −0.703358 0.710835i \(-0.748317\pi\)
0.967281 + 0.253708i \(0.0816504\pi\)
\(564\) 0 0
\(565\) −931185. 1.61286e6i −0.122720 0.212557i
\(566\) 0 0
\(567\) −832826. 172878.i −0.108792 0.0225831i
\(568\) 0 0
\(569\) 2.08724e6 + 3.61521e6i 0.270267 + 0.468116i 0.968930 0.247335i \(-0.0795548\pi\)
−0.698663 + 0.715451i \(0.746221\pi\)
\(570\) 0 0
\(571\) −1.92833e6 + 3.33996e6i −0.247509 + 0.428698i −0.962834 0.270094i \(-0.912945\pi\)
0.715325 + 0.698792i \(0.246279\pi\)
\(572\) 0 0
\(573\) −1.29859e6 −0.165229
\(574\) 0 0
\(575\) −4.96956e6 −0.626828
\(576\) 0 0
\(577\) 1.12288e6 1.94488e6i 0.140408 0.243194i −0.787242 0.616644i \(-0.788492\pi\)
0.927650 + 0.373450i \(0.121825\pi\)
\(578\) 0 0
\(579\) 4.02579e6 + 6.97287e6i 0.499062 + 0.864400i
\(580\) 0 0
\(581\) 4.10178e6 + 1.24222e7i 0.504118 + 1.52672i
\(582\) 0 0
\(583\) −371023. 642630.i −0.0452094 0.0783050i
\(584\) 0 0
\(585\) −1.15492e6 + 2.00037e6i −0.139528 + 0.241669i
\(586\) 0 0
\(587\) 6.40082e6 0.766726 0.383363 0.923598i \(-0.374766\pi\)
0.383363 + 0.923598i \(0.374766\pi\)
\(588\) 0 0
\(589\) 2.52702e7 3.00138
\(590\) 0 0
\(591\) 2.69758e6 4.67234e6i 0.317691 0.550258i
\(592\) 0 0
\(593\) −5.56031e6 9.63074e6i −0.649325 1.12466i −0.983284 0.182077i \(-0.941718\pi\)
0.333959 0.942588i \(-0.391615\pi\)
\(594\) 0 0
\(595\) −2.93818e6 8.89828e6i −0.340241 1.03042i
\(596\) 0 0
\(597\) 3.50216e6 + 6.06592e6i 0.402162 + 0.696564i
\(598\) 0 0
\(599\) 6.56707e6 1.13745e7i 0.747833 1.29528i −0.201027 0.979586i \(-0.564428\pi\)
0.948860 0.315698i \(-0.102239\pi\)
\(600\) 0 0
\(601\) −7.88546e6 −0.890514 −0.445257 0.895403i \(-0.646888\pi\)
−0.445257 + 0.895403i \(0.646888\pi\)
\(602\) 0 0
\(603\) 2.50255e6 0.280279
\(604\) 0 0
\(605\) 3.30312e6 5.72117e6i 0.366890 0.635472i
\(606\) 0 0
\(607\) 3.82967e6 + 6.63319e6i 0.421881 + 0.730719i 0.996123 0.0879660i \(-0.0280367\pi\)
−0.574243 + 0.818685i \(0.694703\pi\)
\(608\) 0 0
\(609\) −5.67739e6 1.17851e6i −0.620305 0.128763i
\(610\) 0 0
\(611\) −711738. 1.23277e6i −0.0771289 0.133591i
\(612\) 0 0
\(613\) 7.62066e6 1.31994e7i 0.819108 1.41874i −0.0872322 0.996188i \(-0.527802\pi\)
0.906340 0.422549i \(-0.138864\pi\)
\(614\) 0 0
\(615\) −2.16507e6 −0.230825
\(616\) 0 0
\(617\) 1.35844e7 1.43657 0.718285 0.695749i \(-0.244927\pi\)
0.718285 + 0.695749i \(0.244927\pi\)
\(618\) 0 0
\(619\) −3.18709e6 + 5.52019e6i −0.334324 + 0.579066i −0.983355 0.181696i \(-0.941841\pi\)
0.649031 + 0.760762i \(0.275175\pi\)
\(620\) 0 0
\(621\) 1.54163e6 + 2.67018e6i 0.160417 + 0.277851i
\(622\) 0 0
\(623\) 3.51911e6 3.94602e6i 0.363256 0.407323i
\(624\) 0 0
\(625\) 6.02844e6 + 1.04416e7i 0.617312 + 1.06922i
\(626\) 0 0
\(627\) −3.17965e6 + 5.50732e6i −0.323006 + 0.559463i
\(628\) 0 0
\(629\) 2.68967e6 0.271065
\(630\) 0 0
\(631\) −1.42736e7 −1.42712 −0.713561 0.700593i \(-0.752919\pi\)
−0.713561 + 0.700593i \(0.752919\pi\)
\(632\) 0 0
\(633\) 3.64739e6 6.31747e6i 0.361804 0.626663i
\(634\) 0 0
\(635\) 1.54751e6 + 2.68037e6i 0.152300 + 0.263792i
\(636\) 0 0
\(637\) −5.87180e6 + 4.35222e6i −0.573354 + 0.424974i
\(638\) 0 0
\(639\) 1.69625e6 + 2.93800e6i 0.164338 + 0.284642i
\(640\) 0 0
\(641\) 4.63480e6 8.02771e6i 0.445539 0.771697i −0.552550 0.833480i \(-0.686345\pi\)
0.998090 + 0.0617828i \(0.0196786\pi\)
\(642\) 0 0
\(643\) 1.17375e7 1.11956 0.559780 0.828641i \(-0.310885\pi\)
0.559780 + 0.828641i \(0.310885\pi\)
\(644\) 0 0
\(645\) −4.24807e6 −0.402062
\(646\) 0 0
\(647\) −5.12724e6 + 8.88063e6i −0.481529 + 0.834033i −0.999775 0.0211984i \(-0.993252\pi\)
0.518246 + 0.855232i \(0.326585\pi\)
\(648\) 0 0
\(649\) −6.32200e6 1.09500e7i −0.589173 1.02048i
\(650\) 0 0
\(651\) −6.82047e6 + 7.64789e6i −0.630757 + 0.707276i
\(652\) 0 0
\(653\) −4.14489e6 7.17915e6i −0.380391 0.658856i 0.610727 0.791841i \(-0.290877\pi\)
−0.991118 + 0.132985i \(0.957544\pi\)
\(654\) 0 0
\(655\) −2.61672e6 + 4.53230e6i −0.238317 + 0.412776i
\(656\) 0 0
\(657\) 2.80400e6 0.253434
\(658\) 0 0
\(659\) −2.06731e7 −1.85435 −0.927174 0.374631i \(-0.877770\pi\)
−0.927174 + 0.374631i \(0.877770\pi\)
\(660\) 0 0
\(661\) −97171.2 + 168305.i −0.00865035 + 0.0149829i −0.870318 0.492490i \(-0.836087\pi\)
0.861668 + 0.507473i \(0.169420\pi\)
\(662\) 0 0
\(663\) 2.15711e6 + 3.73623e6i 0.190585 + 0.330103i
\(664\) 0 0
\(665\) 2.39498e7 + 4.97151e6i 2.10014 + 0.435948i
\(666\) 0 0
\(667\) 1.05093e7 + 1.82026e7i 0.914659 + 1.58424i
\(668\) 0 0
\(669\) −992186. + 1.71852e6i −0.0857092 + 0.148453i
\(670\) 0 0
\(671\) 3.26940e6 0.280325
\(672\) 0 0
\(673\) −1.14437e7 −0.973929 −0.486965 0.873422i \(-0.661896\pi\)
−0.486965 + 0.873422i \(0.661896\pi\)
\(674\) 0 0
\(675\) −428285. + 741812.i −0.0361804 + 0.0626663i
\(676\) 0 0
\(677\) −4.51869e6 7.82660e6i −0.378914 0.656299i 0.611990 0.790865i \(-0.290369\pi\)
−0.990905 + 0.134567i \(0.957036\pi\)
\(678\) 0 0
\(679\) 5.69679e6 + 1.72527e7i 0.474193 + 1.43609i
\(680\) 0 0
\(681\) −6.04701e6 1.04737e7i −0.499658 0.865433i
\(682\) 0 0
\(683\) 5.59212e6 9.68584e6i 0.458696 0.794485i −0.540196 0.841539i \(-0.681650\pi\)
0.998892 + 0.0470541i \(0.0149833\pi\)
\(684\) 0 0
\(685\) −5.64361e6 −0.459548
\(686\) 0 0
\(687\) −9.38325e6 −0.758510
\(688\) 0 0
\(689\) 657020. 1.13799e6i 0.0527267 0.0913253i
\(690\) 0 0
\(691\) −2.83465e6 4.90976e6i −0.225842 0.391170i 0.730730 0.682667i \(-0.239180\pi\)
−0.956572 + 0.291497i \(0.905847\pi\)
\(692\) 0 0
\(693\) −808564. 2.44873e6i −0.0639560 0.193691i
\(694\) 0 0
\(695\) −8.87177e6 1.53664e7i −0.696704 1.20673i
\(696\) 0 0
\(697\) −2.02192e6 + 3.50207e6i −0.157646 + 0.273050i
\(698\) 0 0
\(699\) 5.69260e6 0.440674
\(700\) 0 0
\(701\) −1.31822e6 −0.101320 −0.0506599 0.998716i \(-0.516132\pi\)
−0.0506599 + 0.998716i \(0.516132\pi\)
\(702\) 0 0
\(703\) −3.51038e6 + 6.08016e6i −0.267896 + 0.464009i
\(704\) 0 0
\(705\) −965907. 1.67300e6i −0.0731918 0.126772i
\(706\) 0 0
\(707\) −1.08866e6 225984.i −0.0819112 0.0170032i
\(708\) 0 0
\(709\) −4.13018e6 7.15368e6i −0.308570 0.534458i 0.669480 0.742830i \(-0.266517\pi\)
−0.978050 + 0.208372i \(0.933184\pi\)
\(710\) 0 0
\(711\) −3.14051e6 + 5.43952e6i −0.232984 + 0.403540i
\(712\) 0 0
\(713\) 3.71456e7 2.73643
\(714\) 0 0
\(715\) −7.00290e6 −0.512287
\(716\) 0 0
\(717\) 3.08214e6 5.33842e6i 0.223900 0.387806i
\(718\) 0 0
\(719\) −1.13372e7 1.96365e7i −0.817865 1.41658i −0.907252 0.420587i \(-0.861824\pi\)
0.0893870 0.995997i \(-0.471509\pi\)
\(720\) 0 0
\(721\) −3.04250e6 + 3.41159e6i −0.217968 + 0.244410i
\(722\) 0 0
\(723\) 34798.0 + 60271.9i 0.00247576 + 0.00428814i
\(724\) 0 0
\(725\) −2.91963e6 + 5.05694e6i −0.206292 + 0.357308i
\(726\) 0 0
\(727\) −1.93477e7 −1.35767 −0.678833 0.734293i \(-0.737514\pi\)
−0.678833 + 0.734293i \(0.737514\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −3.96720e6 + 6.87140e6i −0.274594 + 0.475611i
\(732\) 0 0
\(733\) −7.42922e6 1.28678e7i −0.510720 0.884593i −0.999923 0.0124232i \(-0.996045\pi\)
0.489203 0.872170i \(-0.337288\pi\)
\(734\) 0 0
\(735\) −7.96868e6 + 5.90645e6i −0.544087 + 0.403281i
\(736\) 0 0
\(737\) 3.79360e6 + 6.57071e6i 0.257266 + 0.445598i
\(738\) 0 0
\(739\) 8.84089e6 1.53129e7i 0.595504 1.03144i −0.397971 0.917398i \(-0.630286\pi\)
0.993476 0.114045i \(-0.0363810\pi\)
\(740\) 0 0
\(741\) −1.12613e7 −0.753428
\(742\) 0 0
\(743\) −8.28756e6 −0.550750 −0.275375 0.961337i \(-0.588802\pi\)
−0.275375 + 0.961337i \(0.588802\pi\)
\(744\) 0 0
\(745\) 5.65735e6 9.79882e6i 0.373442 0.646820i
\(746\) 0 0
\(747\) −4.08678e6 7.07850e6i −0.267966 0.464130i
\(748\) 0 0
\(749\) −1.66214e7 + 1.86378e7i −1.08259 + 1.21392i
\(750\) 0 0
\(751\) 1.15682e7 + 2.00368e7i 0.748457 + 1.29637i 0.948562 + 0.316592i \(0.102539\pi\)
−0.200104 + 0.979775i \(0.564128\pi\)
\(752\) 0 0
\(753\) −4.93261e6 + 8.54354e6i −0.317022 + 0.549098i
\(754\) 0 0
\(755\) −1.17375e6 −0.0749389
\(756\) 0 0
\(757\) −1.95475e7 −1.23980 −0.619900 0.784681i \(-0.712827\pi\)
−0.619900 + 0.784681i \(0.712827\pi\)
\(758\) 0 0
\(759\) −4.67388e6 + 8.09540e6i −0.294492 + 0.510075i
\(760\) 0 0
\(761\) −3.91233e6 6.77635e6i −0.244891 0.424164i 0.717210 0.696857i \(-0.245419\pi\)
−0.962101 + 0.272693i \(0.912086\pi\)
\(762\) 0 0
\(763\) −1.56502e7 3.24867e6i −0.973214 0.202020i
\(764\) 0 0
\(765\) 2.92744e6 + 5.07047e6i 0.180857 + 0.313253i
\(766\) 0 0
\(767\) 1.11952e7 1.93907e7i 0.687139 1.19016i
\(768\) 0 0
\(769\) −8.27325e6 −0.504499 −0.252250 0.967662i \(-0.581170\pi\)
−0.252250 + 0.967662i \(0.581170\pi\)
\(770\) 0 0
\(771\) 6.43428e6 0.389820
\(772\) 0 0
\(773\) 9.41844e6 1.63132e7i 0.566931 0.981953i −0.429936 0.902859i \(-0.641464\pi\)
0.996867 0.0790941i \(-0.0252028\pi\)
\(774\) 0 0
\(775\) 5.15978e6 + 8.93700e6i 0.308587 + 0.534488i
\(776\) 0 0
\(777\) −892667. 2.70344e6i −0.0530441 0.160644i
\(778\) 0 0
\(779\) −5.27775e6 9.14133e6i −0.311605 0.539717i
\(780\) 0 0
\(781\) −5.14267e6 + 8.90737e6i −0.301690 + 0.522543i
\(782\) 0 0