Properties

Label 84.6.i.b.37.1
Level $84$
Weight $6$
Character 84.37
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 37.1
Root \(-20.7872 + 36.0044i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.6.i.b.25.1

$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

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

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 0.408170 + 0.912906i \(0.366167\pi\)
−0.994685 + 0.102967i \(0.967166\pi\)
\(6\) 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 0.977476 0.211048i \(-0.0676877\pi\)
−0.671511 + 0.740995i \(0.734354\pi\)
\(12\) 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 0.999087 0.0427312i \(-0.0136059\pi\)
−0.536550 + 0.843869i \(0.680273\pi\)
\(18\) 0 0
\(19\) 1438.65 2491.81i 0.914260 1.58355i 0.106279 0.994336i \(-0.466106\pi\)
0.807981 0.589209i \(-0.200560\pi\)
\(20\) 0 0
\(21\) −1142.42 + 237.145i −0.565299 + 0.117345i
\(22\) 0 0
\(23\) 2114.72 3662.80i 0.833552 1.44375i −0.0616521 0.998098i \(-0.519637\pi\)
0.895204 0.445657i \(-0.147030\pi\)
\(24\) 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 0.905152 + 0.425088i \(0.139757\pi\)
−0.0844390 + 0.996429i \(0.526910\pi\)
\(32\) 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 −0.783425 0.621486i \(-0.786529\pi\)
0.929935 + 0.367723i \(0.119863\pi\)
\(38\) 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 −0.914989 0.403478i \(-0.867801\pi\)
0.806917 + 0.590665i \(0.201134\pi\)
\(48\) 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 0.900599 0.434651i \(-0.143128\pi\)
−0.826719 + 0.562616i \(0.809795\pi\)
\(54\) 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 0.715381 + 0.698735i \(0.246253\pi\)
0.247432 + 0.968905i \(0.420413\pi\)
\(60\) 0 0
\(61\) 6656.65 11529.6i 0.229050 0.396727i −0.728477 0.685071i \(-0.759771\pi\)
0.957527 + 0.288344i \(0.0931046\pi\)
\(62\) 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 0.575562 0.817758i \(-0.304783\pi\)
−0.995980 + 0.0895723i \(0.971450\pi\)
\(68\) 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 0.610932 0.791683i \(-0.290795\pi\)
−0.991084 + 0.133242i \(0.957461\pi\)
\(74\) 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 0.269878 + 0.962895i \(0.413017\pi\)
−0.968830 + 0.247726i \(0.920317\pi\)
\(80\) 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 −0.969600 0.244697i \(-0.921312\pi\)
0.696714 + 0.717349i \(0.254645\pi\)
\(90\) 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 0.844353 0.535787i \(-0.179985\pi\)
−0.886182 + 0.463338i \(0.846652\pi\)
\(102\) 0 0
\(103\) 17630.1 30536.2i 0.163742 0.283610i −0.772466 0.635057i \(-0.780977\pi\)
0.936208 + 0.351447i \(0.114310\pi\)
\(104\) 0 0
\(105\) 23989.6 72652.4i 0.212349 0.643097i
\(106\) 0 0
\(107\) 96314.3 166821.i 0.813264 1.40861i −0.0973041 0.995255i \(-0.531022\pi\)
0.910568 0.413360i \(-0.135645\pi\)
\(108\) 0 0
\(109\) −61646.1 106774.i −0.496980 0.860795i 0.503014 0.864279i \(-0.332225\pi\)
−0.999994 + 0.00348322i \(0.998891\pi\)
\(110\) 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 −0.949546 0.313628i \(-0.898456\pi\)
0.746383 + 0.665517i \(0.231789\pi\)
\(132\) 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 0.947189 0.320676i \(-0.103910\pi\)
−0.751308 + 0.659952i \(0.770577\pi\)
\(138\) 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 −0.661789 0.749690i \(-0.730202\pi\)
0.980145 + 0.198281i \(0.0635358\pi\)
\(150\) 0 0
\(151\) 8949.75 + 15501.4i 0.0319425 + 0.0553260i 0.881555 0.472082i \(-0.156497\pi\)
−0.849612 + 0.527408i \(0.823164\pi\)
\(152\) 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 0.973765 0.227555i \(-0.0730733\pi\)
−0.683951 + 0.729528i \(0.739740\pi\)
\(158\) 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 −0.636441 0.771325i \(-0.719594\pi\)
0.986208 + 0.165511i \(0.0529275\pi\)
\(164\) 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 0.368609 + 0.929584i \(0.379834\pi\)
−0.989348 + 0.145567i \(0.953499\pi\)
\(174\) 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 −0.749095 0.662462i \(-0.769512\pi\)
−0.199161 0.979967i \(-0.563822\pi\)
\(180\) 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 −0.785567 0.618776i \(-0.787629\pi\)
0.928660 + 0.370933i \(0.120962\pi\)
\(192\) 0 0
\(193\) 447310. + 774763.i 0.864400 + 1.49719i 0.867641 + 0.497190i \(0.165635\pi\)
−0.00324119 + 0.999995i \(0.501032\pi\)
\(194\) 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 0.969651 + 0.244495i \(0.0786222\pi\)
−0.273086 + 0.961990i \(0.588044\pi\)
\(200\) 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 −0.866617 0.498974i \(-0.833710\pi\)
0.00118391 0.999999i \(-0.499623\pi\)
\(228\) 0 0
\(229\) 521292. 902904.i 0.656889 1.13777i −0.324528 0.945876i \(-0.605205\pi\)
0.981417 0.191889i \(-0.0614614\pi\)
\(230\) 0 0
\(231\) −190709. 213845.i −0.235148 0.263675i
\(232\) 0 0
\(233\) −316256. + 547771.i −0.381635 + 0.661011i −0.991296 0.131651i \(-0.957972\pi\)
0.609661 + 0.792662i \(0.291306\pi\)
\(234\) 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 0.868162 0.496282i \(-0.165302\pi\)
−0.863873 + 0.503709i \(0.831968\pi\)
\(242\) 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 −0.983980 0.178281i \(-0.942946\pi\)
0.646386 + 0.763011i \(0.276280\pi\)
\(258\) 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 0.967796 0.251735i \(-0.0810012\pi\)
−0.701907 + 0.712268i \(0.747668\pi\)
\(264\) 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 0.875217 + 0.483730i \(0.160718\pi\)
−0.0186864 + 0.999825i \(0.505948\pi\)
\(270\) 0 0
\(271\) −897277. + 1.55413e6i −0.742170 + 1.28548i 0.209336 + 0.977844i \(0.432870\pi\)
−0.951505 + 0.307632i \(0.900463\pi\)
\(272\) 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 0.771109 0.636703i \(-0.219702\pi\)
−0.936956 + 0.349449i \(0.886369\pi\)
\(278\) 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 0.915414 0.402514i \(-0.131863\pi\)
−0.806294 + 0.591515i \(0.798530\pi\)
\(284\) 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 −0.992824 0.119581i \(-0.961845\pi\)
0.392852 0.919602i \(-0.371488\pi\)
\(312\) 0 0
\(313\) −319272. + 552996.i −0.184205 + 0.319052i −0.943308 0.331918i \(-0.892304\pi\)
0.759104 + 0.650970i \(0.225638\pi\)
\(314\) 0 0
\(315\) −674222. + 139955.i −0.382848 + 0.0794718i
\(316\) 0 0
\(317\) −1.74954e6 + 3.03030e6i −0.977860 + 1.69370i −0.307705 + 0.951482i \(0.599561\pi\)
−0.670155 + 0.742221i \(0.733772\pi\)
\(318\) 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 −0.215506 0.976503i \(-0.569140\pi\)
0.953429 0.301618i \(-0.0975266\pi\)
\(332\) 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 0.884560 0.466426i \(-0.154459\pi\)
−0.846217 + 0.532838i \(0.821125\pi\)
\(348\) 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 0.936529 0.350589i \(-0.114019\pi\)
−0.771884 + 0.635764i \(0.780685\pi\)
\(354\) 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 0.341763 + 0.939786i \(0.388976\pi\)
−0.984760 + 0.173918i \(0.944357\pi\)
\(360\) 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 0.899279 0.437375i \(-0.144092\pi\)
−0.828418 + 0.560111i \(0.810758\pi\)
\(368\) 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 −0.851316 0.524653i \(-0.824195\pi\)
0.880021 + 0.474935i \(0.157528\pi\)
\(374\) 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 −0.987260 0.159113i \(-0.949137\pi\)
0.631426 + 0.775436i \(0.282470\pi\)
\(384\) 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 0.987251 0.159170i \(-0.0508819\pi\)
−0.631471 + 0.775399i \(0.717549\pi\)
\(390\) 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 −0.411764 0.911291i \(-0.635087\pi\)
0.995083 0.0990473i \(-0.0315795\pi\)
\(398\) 0 0
\(399\) −1.05262e6 + 3.18786e6i −0.331010 + 1.00246i
\(400\) 0 0
\(401\) 32044.9 55503.3i 0.00995170 0.0172369i −0.861007 0.508594i \(-0.830166\pi\)
0.870958 + 0.491357i \(0.163499\pi\)
\(402\) 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 0.676603 0.736348i \(-0.263452\pi\)
−0.975998 + 0.217781i \(0.930118\pi\)
\(410\) 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 0.951088 0.308919i \(-0.0999671\pi\)
−0.743076 + 0.669207i \(0.766634\pi\)
\(432\) 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 −0.987138 0.159873i \(-0.948892\pi\)
0.632023 + 0.774950i \(0.282225\pi\)
\(440\) 0 0
\(441\) 1.24889e6 541839.i 0.305794 0.132670i
\(442\) 0 0
\(443\) 89148.9 154410.i 0.0215827 0.0373824i −0.855032 0.518575i \(-0.826463\pi\)
0.876615 + 0.481192i \(0.159796\pi\)
\(444\) 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 0.243462 + 0.969910i \(0.421717\pi\)
−0.961698 + 0.274111i \(0.911617\pi\)
\(458\) 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 −0.639937 0.768427i \(-0.721040\pi\)
0.985446 + 0.169988i \(0.0543730\pi\)
\(468\) 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 −0.780219 0.625506i \(-0.784892\pi\)
−0.151595 0.988443i \(-0.548441\pi\)
\(480\) 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 0.963854 0.266431i \(-0.0858445\pi\)
−0.712663 + 0.701506i \(0.752511\pi\)
\(488\) 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 −0.613851 0.789422i \(-0.710381\pi\)
0.990585 + 0.136900i \(0.0437139\pi\)
\(500\) 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 −0.999753 0.0222464i \(-0.992918\pi\)
0.519142 + 0.854688i \(0.326251\pi\)
\(510\) 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 −0.835653 0.549258i \(-0.814911\pi\)
−0.0578446 0.998326i \(-0.518423\pi\)
\(522\) 0 0
\(523\) 3.79894e6 6.57996e6i 0.607307 1.05189i −0.384375 0.923177i \(-0.625583\pi\)
0.991682 0.128710i \(-0.0410836\pi\)
\(524\) 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 −0.716335 0.697756i \(-0.754182\pi\)
0.962442 + 0.271486i \(0.0875152\pi\)
\(542\) 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 −0.789263 0.614055i \(-0.789537\pi\)
−0.137155 0.990550i \(-0.543796\pi\)
\(558\) 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 0.967281 0.253708i \(-0.0816504\pi\)
−0.703358 + 0.710835i \(0.748317\pi\)
\(564\) 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 −0.698663 0.715451i \(-0.746221\pi\)
0.968930 + 0.247335i \(0.0795548\pi\)
\(570\) 0 0
\(571\) −1.92833e6 3.33996e6i −0.247509 0.428698i 0.715325 0.698792i \(-0.246279\pi\)
−0.962834 + 0.270094i \(0.912945\pi\)
\(572\) 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 0.927650 0.373450i \(-0.121825\pi\)
−0.787242 + 0.616644i \(0.788492\pi\)
\(578\) 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 0.333959 + 0.942588i \(0.391615\pi\)
−0.983284 + 0.182077i \(0.941718\pi\)
\(594\) 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 0.948860 + 0.315698i \(0.102239\pi\)
−0.201027 + 0.979586i \(0.564428\pi\)
\(600\) 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 −0.574243 0.818685i \(-0.694703\pi\)
0.996123 + 0.0879660i \(0.0280367\pi\)
\(608\) 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 0.906340 + 0.422549i \(0.138864\pi\)
−0.0872322 + 0.996188i \(0.527802\pi\)
\(614\) 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 0.649031 0.760762i \(-0.275175\pi\)
−0.983355 + 0.181696i \(0.941841\pi\)
\(620\) 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 0.998090 0.0617828i \(-0.0196786\pi\)
−0.552550 + 0.833480i \(0.686345\pi\)
\(642\) 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 0.518246 0.855232i \(-0.326585\pi\)
−0.999775 + 0.0211984i \(0.993252\pi\)
\(648\) 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 −0.991118 0.132985i \(-0.957544\pi\)
0.610727 + 0.791841i \(0.290877\pi\)
\(654\) 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 0.861668 0.507473i \(-0.169420\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(662\) 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 −0.990905 0.134567i \(-0.957036\pi\)
0.611990 + 0.790865i \(0.290369\pi\)
\(678\) 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 0.998892 0.0470541i \(-0.0149833\pi\)
−0.540196 + 0.841539i \(0.681650\pi\)
\(684\) 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 −0.956572 0.291497i \(-0.905847\pi\)
0.730730 + 0.682667i \(0.239180\pi\)
\(692\) 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 −0.978050 0.208372i \(-0.933184\pi\)
0.669480 + 0.742830i \(0.266517\pi\)
\(710\) 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 0.0893870 + 0.995997i \(0.471509\pi\)
−0.907252 + 0.420587i \(0.861824\pi\)
\(720\) 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 0.489203 + 0.872170i \(0.337288\pi\)
−0.999923 + 0.0124232i \(0.996045\pi\)
\(734\) 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 0.993476 + 0.114045i \(0.0363810\pi\)
−0.397971 + 0.917398i \(0.630286\pi\)
\(740\) 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 −0.200104 0.979775i \(-0.564128\pi\)
0.948562 0.316592i \(-0.102539\pi\)
\(752\) 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 −0.962101 0.272693i \(-0.912086\pi\)
0.717210 + 0.696857i \(0.245419\pi\)
\(762\) 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 0.996867 + 0.0790941i \(0.0252028\pi\)
−0.429936 + 0.902859i \(0.641464\pi\)
\(774\) 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