Properties

Label 63.6.e.e.37.3
Level $63$
Weight $6$
Character 63.37
Analytic conductor $10.104$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (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: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.3
Root \(-0.874091 + 1.51397i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.6.e.e.46.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +O(q^{10})\) \(q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +(-80.2019 - 138.914i) q^{10} +(8.71205 + 15.0897i) q^{11} +889.933 q^{13} +(274.844 + 226.706i) q^{14} +(-178.000 + 308.305i) q^{16} +(513.318 + 889.092i) q^{17} +(869.702 - 1506.37i) q^{19} +1426.93 q^{20} +47.8846 q^{22} +(1968.11 - 3408.87i) q^{23} +(-140.869 - 243.993i) q^{25} +(1222.85 - 2118.04i) q^{26} +(-2969.05 + 1109.04i) q^{28} -5633.53 q^{29} +(1548.27 + 2681.68i) q^{31} +(2971.22 + 5146.31i) q^{32} +2821.38 q^{34} +(5837.27 + 4814.91i) q^{35} +(-2513.43 + 4353.39i) q^{37} +(-2390.10 - 4139.77i) q^{38} +(4527.20 - 7841.34i) q^{40} -18367.0 q^{41} -1630.91 q^{43} +(-212.988 + 368.906i) q^{44} +(-5408.72 - 9368.19i) q^{46} +(-4802.62 + 8318.38i) q^{47} +(-15887.9 - 5481.65i) q^{49} -774.269 q^{50} +(10878.3 + 18841.8i) q^{52} +(-11628.3 - 20140.7i) q^{53} +1017.00 q^{55} +(-3325.41 + 19834.2i) q^{56} +(-7740.98 + 13407.8i) q^{58} +(-1801.62 - 3120.50i) q^{59} +(-11438.3 + 19811.7i) q^{61} +8509.83 q^{62} +4938.92 q^{64} +(25971.5 - 44983.9i) q^{65} +(-23506.4 - 40714.2i) q^{67} +(-12549.3 + 21736.1i) q^{68} +(19480.4 - 7276.56i) q^{70} +1599.63 q^{71} +(-2965.67 - 5136.70i) q^{73} +(6907.36 + 11963.9i) q^{74} +42524.1 q^{76} +(-2116.09 + 790.427i) q^{77} +(44234.4 - 76616.3i) q^{79} +(10389.4 + 17994.9i) q^{80} +(-25237.9 + 43713.3i) q^{82} +95823.9 q^{83} +59921.9 q^{85} +(-2241.02 + 3881.56i) q^{86} +(1351.48 + 2340.84i) q^{88} +(-23253.9 + 40277.0i) q^{89} +(-19077.1 + 113784. i) q^{91} +96230.8 q^{92} +(13198.5 + 22860.4i) q^{94} +(-50762.1 - 87922.5i) q^{95} -75981.8 q^{97} +(-34877.8 + 30281.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37409 2.37999i 0.242907 0.420728i −0.718634 0.695389i \(-0.755232\pi\)
0.961541 + 0.274661i \(0.0885656\pi\)
\(3\) 0 0
\(4\) 12.2237 + 21.1722i 0.381992 + 0.661630i
\(5\) 29.1836 50.5475i 0.522053 0.904222i −0.477618 0.878568i \(-0.658500\pi\)
0.999671 0.0256544i \(-0.00816693\pi\)
\(6\) 0 0
\(7\) −21.4366 + 127.857i −0.165352 + 0.986235i
\(8\) 155.128 0.856969
\(9\) 0 0
\(10\) −80.2019 138.914i −0.253621 0.439284i
\(11\) 8.71205 + 15.0897i 0.0217089 + 0.0376010i 0.876676 0.481082i \(-0.159756\pi\)
−0.854967 + 0.518683i \(0.826423\pi\)
\(12\) 0 0
\(13\) 889.933 1.46049 0.730246 0.683185i \(-0.239406\pi\)
0.730246 + 0.683185i \(0.239406\pi\)
\(14\) 274.844 + 226.706i 0.374771 + 0.309132i
\(15\) 0 0
\(16\) −178.000 + 308.305i −0.173828 + 0.301079i
\(17\) 513.318 + 889.092i 0.430788 + 0.746147i 0.996941 0.0781529i \(-0.0249022\pi\)
−0.566153 + 0.824300i \(0.691569\pi\)
\(18\) 0 0
\(19\) 869.702 1506.37i 0.552696 0.957297i −0.445383 0.895340i \(-0.646932\pi\)
0.998079 0.0619572i \(-0.0197342\pi\)
\(20\) 1426.93 0.797680
\(21\) 0 0
\(22\) 47.8846 0.0210930
\(23\) 1968.11 3408.87i 0.775764 1.34366i −0.158599 0.987343i \(-0.550698\pi\)
0.934364 0.356320i \(-0.115969\pi\)
\(24\) 0 0
\(25\) −140.869 243.993i −0.0450782 0.0780777i
\(26\) 1222.85 2118.04i 0.354764 0.614469i
\(27\) 0 0
\(28\) −2969.05 + 1109.04i −0.715686 + 0.267332i
\(29\) −5633.53 −1.24390 −0.621950 0.783057i \(-0.713659\pi\)
−0.621950 + 0.783057i \(0.713659\pi\)
\(30\) 0 0
\(31\) 1548.27 + 2681.68i 0.289362 + 0.501190i 0.973658 0.228015i \(-0.0732236\pi\)
−0.684296 + 0.729205i \(0.739890\pi\)
\(32\) 2971.22 + 5146.31i 0.512933 + 0.888426i
\(33\) 0 0
\(34\) 2821.38 0.418566
\(35\) 5837.27 + 4814.91i 0.805452 + 0.664382i
\(36\) 0 0
\(37\) −2513.43 + 4353.39i −0.301830 + 0.522785i −0.976551 0.215288i \(-0.930931\pi\)
0.674720 + 0.738073i \(0.264264\pi\)
\(38\) −2390.10 4139.77i −0.268508 0.465069i
\(39\) 0 0
\(40\) 4527.20 7841.34i 0.447383 0.774890i
\(41\) −18367.0 −1.70639 −0.853195 0.521592i \(-0.825338\pi\)
−0.853195 + 0.521592i \(0.825338\pi\)
\(42\) 0 0
\(43\) −1630.91 −0.134511 −0.0672557 0.997736i \(-0.521424\pi\)
−0.0672557 + 0.997736i \(0.521424\pi\)
\(44\) −212.988 + 368.906i −0.0165853 + 0.0287266i
\(45\) 0 0
\(46\) −5408.72 9368.19i −0.376878 0.652771i
\(47\) −4802.62 + 8318.38i −0.317127 + 0.549280i −0.979887 0.199551i \(-0.936051\pi\)
0.662760 + 0.748832i \(0.269385\pi\)
\(48\) 0 0
\(49\) −15887.9 5481.65i −0.945317 0.326153i
\(50\) −774.269 −0.0437992
\(51\) 0 0
\(52\) 10878.3 + 18841.8i 0.557896 + 0.966305i
\(53\) −11628.3 20140.7i −0.568624 0.984886i −0.996702 0.0811440i \(-0.974143\pi\)
0.428078 0.903742i \(-0.359191\pi\)
\(54\) 0 0
\(55\) 1017.00 0.0453328
\(56\) −3325.41 + 19834.2i −0.141702 + 0.845172i
\(57\) 0 0
\(58\) −7740.98 + 13407.8i −0.302152 + 0.523343i
\(59\) −1801.62 3120.50i −0.0673803 0.116706i 0.830367 0.557217i \(-0.188131\pi\)
−0.897747 + 0.440511i \(0.854797\pi\)
\(60\) 0 0
\(61\) −11438.3 + 19811.7i −0.393584 + 0.681707i −0.992919 0.118791i \(-0.962098\pi\)
0.599336 + 0.800498i \(0.295431\pi\)
\(62\) 8509.83 0.281152
\(63\) 0 0
\(64\) 4938.92 0.150724
\(65\) 25971.5 44983.9i 0.762454 1.32061i
\(66\) 0 0
\(67\) −23506.4 40714.2i −0.639733 1.10805i −0.985491 0.169726i \(-0.945712\pi\)
0.345758 0.938324i \(-0.387622\pi\)
\(68\) −12549.3 + 21736.1i −0.329116 + 0.570045i
\(69\) 0 0
\(70\) 19480.4 7276.56i 0.475174 0.177493i
\(71\) 1599.63 0.0376595 0.0188298 0.999823i \(-0.494006\pi\)
0.0188298 + 0.999823i \(0.494006\pi\)
\(72\) 0 0
\(73\) −2965.67 5136.70i −0.0651353 0.112818i 0.831619 0.555347i \(-0.187415\pi\)
−0.896754 + 0.442529i \(0.854081\pi\)
\(74\) 6907.36 + 11963.9i 0.146633 + 0.253976i
\(75\) 0 0
\(76\) 42524.1 0.844502
\(77\) −2116.09 + 790.427i −0.0406730 + 0.0151927i
\(78\) 0 0
\(79\) 44234.4 76616.3i 0.797431 1.38119i −0.123854 0.992300i \(-0.539525\pi\)
0.921284 0.388890i \(-0.127141\pi\)
\(80\) 10389.4 + 17994.9i 0.181495 + 0.314359i
\(81\) 0 0
\(82\) −25237.9 + 43713.3i −0.414495 + 0.717926i
\(83\) 95823.9 1.52679 0.763394 0.645933i \(-0.223531\pi\)
0.763394 + 0.645933i \(0.223531\pi\)
\(84\) 0 0
\(85\) 59921.9 0.899577
\(86\) −2241.02 + 3881.56i −0.0326738 + 0.0565927i
\(87\) 0 0
\(88\) 1351.48 + 2340.84i 0.0186039 + 0.0322229i
\(89\) −23253.9 + 40277.0i −0.311187 + 0.538992i −0.978620 0.205679i \(-0.934060\pi\)
0.667433 + 0.744670i \(0.267393\pi\)
\(90\) 0 0
\(91\) −19077.1 + 113784.i −0.241496 + 1.44039i
\(92\) 96230.8 1.18534
\(93\) 0 0
\(94\) 13198.5 + 22860.4i 0.154065 + 0.266848i
\(95\) −50762.1 87922.5i −0.577073 0.999519i
\(96\) 0 0
\(97\) −75981.8 −0.819937 −0.409968 0.912100i \(-0.634460\pi\)
−0.409968 + 0.912100i \(0.634460\pi\)
\(98\) −34877.8 + 30281.0i −0.366846 + 0.318496i
\(99\) 0 0
\(100\) 3443.90 5965.01i 0.0344390 0.0596501i
\(101\) −23078.7 39973.5i −0.225117 0.389914i 0.731238 0.682123i \(-0.238943\pi\)
−0.956355 + 0.292209i \(0.905610\pi\)
\(102\) 0 0
\(103\) 40986.8 70991.2i 0.380672 0.659343i −0.610487 0.792027i \(-0.709026\pi\)
0.991158 + 0.132683i \(0.0423594\pi\)
\(104\) 138054. 1.25160
\(105\) 0 0
\(106\) −63913.2 −0.552491
\(107\) −1426.84 + 2471.35i −0.0120480 + 0.0208677i −0.871987 0.489530i \(-0.837168\pi\)
0.859939 + 0.510398i \(0.170502\pi\)
\(108\) 0 0
\(109\) 83139.2 + 144001.i 0.670254 + 1.16091i 0.977832 + 0.209391i \(0.0671483\pi\)
−0.307578 + 0.951523i \(0.599518\pi\)
\(110\) 1397.45 2420.45i 0.0110117 0.0190728i
\(111\) 0 0
\(112\) −35603.3 29367.6i −0.268192 0.221220i
\(113\) −260304. −1.91772 −0.958858 0.283886i \(-0.908376\pi\)
−0.958858 + 0.283886i \(0.908376\pi\)
\(114\) 0 0
\(115\) −114873. 198966.i −0.809980 1.40293i
\(116\) −68862.8 119274.i −0.475160 0.823001i
\(117\) 0 0
\(118\) −9902.35 −0.0654687
\(119\) −124681. + 46572.3i −0.807108 + 0.301481i
\(120\) 0 0
\(121\) 80373.7 139211.i 0.499057 0.864393i
\(122\) 31434.5 + 54446.2i 0.191209 + 0.331183i
\(123\) 0 0
\(124\) −37851.2 + 65560.3i −0.221068 + 0.382901i
\(125\) 165953. 0.949973
\(126\) 0 0
\(127\) −233743. −1.28596 −0.642982 0.765882i \(-0.722303\pi\)
−0.642982 + 0.765882i \(0.722303\pi\)
\(128\) −88292.6 + 152927.i −0.476321 + 0.825012i
\(129\) 0 0
\(130\) −71374.4 123624.i −0.370411 0.641571i
\(131\) −78644.9 + 136217.i −0.400398 + 0.693510i −0.993774 0.111415i \(-0.964462\pi\)
0.593376 + 0.804926i \(0.297795\pi\)
\(132\) 0 0
\(133\) 173957. + 143489.i 0.852730 + 0.703379i
\(134\) −129200. −0.621583
\(135\) 0 0
\(136\) 79629.9 + 137923.i 0.369172 + 0.639425i
\(137\) −85773.8 148564.i −0.390439 0.676260i 0.602069 0.798444i \(-0.294343\pi\)
−0.992507 + 0.122185i \(0.961010\pi\)
\(138\) 0 0
\(139\) 210625. 0.924642 0.462321 0.886713i \(-0.347017\pi\)
0.462321 + 0.886713i \(0.347017\pi\)
\(140\) −30588.6 + 182444.i −0.131898 + 0.786700i
\(141\) 0 0
\(142\) 2198.04 3807.12i 0.00914777 0.0158444i
\(143\) 7753.14 + 13428.8i 0.0317057 + 0.0549159i
\(144\) 0 0
\(145\) −164407. + 284761.i −0.649381 + 1.12476i
\(146\) −16300.4 −0.0632873
\(147\) 0 0
\(148\) −122894. −0.461187
\(149\) 119706. 207338.i 0.441725 0.765090i −0.556093 0.831120i \(-0.687700\pi\)
0.997818 + 0.0660304i \(0.0210334\pi\)
\(150\) 0 0
\(151\) −108520. 187962.i −0.387317 0.670852i 0.604771 0.796400i \(-0.293265\pi\)
−0.992088 + 0.125547i \(0.959931\pi\)
\(152\) 134915. 233680.i 0.473643 0.820374i
\(153\) 0 0
\(154\) −1026.48 + 6122.39i −0.00348778 + 0.0208027i
\(155\) 180736. 0.604249
\(156\) 0 0
\(157\) −83452.2 144543.i −0.270202 0.468004i 0.698711 0.715404i \(-0.253757\pi\)
−0.968913 + 0.247400i \(0.920424\pi\)
\(158\) −121564. 210556.i −0.387403 0.671002i
\(159\) 0 0
\(160\) 346844. 1.07111
\(161\) 393659. + 324712.i 1.19689 + 0.987264i
\(162\) 0 0
\(163\) −253086. + 438358.i −0.746104 + 1.29229i 0.203574 + 0.979060i \(0.434744\pi\)
−0.949677 + 0.313230i \(0.898589\pi\)
\(164\) −224514. 388869.i −0.651828 1.12900i
\(165\) 0 0
\(166\) 131671. 228061.i 0.370868 0.642362i
\(167\) 565560. 1.56923 0.784616 0.619982i \(-0.212860\pi\)
0.784616 + 0.619982i \(0.212860\pi\)
\(168\) 0 0
\(169\) 420688. 1.13304
\(170\) 82338.1 142614.i 0.218514 0.378477i
\(171\) 0 0
\(172\) −19935.9 34529.9i −0.0513823 0.0889968i
\(173\) −329718. + 571088.i −0.837581 + 1.45073i 0.0543304 + 0.998523i \(0.482698\pi\)
−0.891911 + 0.452210i \(0.850636\pi\)
\(174\) 0 0
\(175\) 34216.0 12780.8i 0.0844567 0.0315473i
\(176\) −6202.98 −0.0150945
\(177\) 0 0
\(178\) 63906.0 + 110688.i 0.151179 + 0.261850i
\(179\) 82645.0 + 143145.i 0.192790 + 0.333922i 0.946174 0.323659i \(-0.104913\pi\)
−0.753384 + 0.657581i \(0.771580\pi\)
\(180\) 0 0
\(181\) 148492. 0.336904 0.168452 0.985710i \(-0.446123\pi\)
0.168452 + 0.985710i \(0.446123\pi\)
\(182\) 244593. + 201754.i 0.547350 + 0.451484i
\(183\) 0 0
\(184\) 305309. 528811.i 0.664806 1.15148i
\(185\) 146702. + 254095.i 0.315142 + 0.545843i
\(186\) 0 0
\(187\) −8944.10 + 15491.6i −0.0187039 + 0.0323961i
\(188\) −234824. −0.484560
\(189\) 0 0
\(190\) −279007. −0.560701
\(191\) 192955. 334208.i 0.382713 0.662879i −0.608736 0.793373i \(-0.708323\pi\)
0.991449 + 0.130494i \(0.0416564\pi\)
\(192\) 0 0
\(193\) −248148. 429805.i −0.479531 0.830573i 0.520193 0.854049i \(-0.325860\pi\)
−0.999724 + 0.0234760i \(0.992527\pi\)
\(194\) −104406. + 180836.i −0.199169 + 0.344970i
\(195\) 0 0
\(196\) −78152.0 403388.i −0.145312 0.750038i
\(197\) −441439. −0.810411 −0.405206 0.914226i \(-0.632800\pi\)
−0.405206 + 0.914226i \(0.632800\pi\)
\(198\) 0 0
\(199\) 37919.4 + 65678.3i 0.0678779 + 0.117568i 0.897967 0.440063i \(-0.145044\pi\)
−0.830089 + 0.557631i \(0.811710\pi\)
\(200\) −21852.8 37850.1i −0.0386306 0.0669102i
\(201\) 0 0
\(202\) −126849. −0.218730
\(203\) 120764. 720287.i 0.205682 1.22678i
\(204\) 0 0
\(205\) −536016. + 928406.i −0.890826 + 1.54296i
\(206\) −112639. 195097.i −0.184936 0.320318i
\(207\) 0 0
\(208\) −158408. + 274371.i −0.253875 + 0.439724i
\(209\) 30307.5 0.0479938
\(210\) 0 0
\(211\) 778704. 1.20411 0.602055 0.798454i \(-0.294349\pi\)
0.602055 + 0.798454i \(0.294349\pi\)
\(212\) 284282. 492391.i 0.434420 0.752437i
\(213\) 0 0
\(214\) 3921.21 + 6791.73i 0.00585309 + 0.0101379i
\(215\) −47595.9 + 82438.6i −0.0702221 + 0.121628i
\(216\) 0 0
\(217\) −376061. + 140471.i −0.542137 + 0.202506i
\(218\) 456963. 0.651238
\(219\) 0 0
\(220\) 12431.5 + 21532.0i 0.0173168 + 0.0299936i
\(221\) 456818. + 791233.i 0.629163 + 1.08974i
\(222\) 0 0
\(223\) 738085. 0.993903 0.496951 0.867778i \(-0.334453\pi\)
0.496951 + 0.867778i \(0.334453\pi\)
\(224\) −721686. + 269573.i −0.961011 + 0.358969i
\(225\) 0 0
\(226\) −357681. + 619522.i −0.465827 + 0.806836i
\(227\) −272058. 471218.i −0.350426 0.606956i 0.635898 0.771773i \(-0.280630\pi\)
−0.986324 + 0.164817i \(0.947297\pi\)
\(228\) 0 0
\(229\) 116781. 202271.i 0.147158 0.254885i −0.783018 0.621999i \(-0.786321\pi\)
0.930176 + 0.367114i \(0.119654\pi\)
\(230\) −631385. −0.787000
\(231\) 0 0
\(232\) −873917. −1.06598
\(233\) −309050. + 535290.i −0.372940 + 0.645951i −0.990016 0.140952i \(-0.954984\pi\)
0.617077 + 0.786903i \(0.288317\pi\)
\(234\) 0 0
\(235\) 280316. + 485521.i 0.331114 + 0.573506i
\(236\) 44045.1 76288.3i 0.0514775 0.0891617i
\(237\) 0 0
\(238\) −60480.8 + 360734.i −0.0692110 + 0.412805i
\(239\) −937500. −1.06164 −0.530819 0.847485i \(-0.678116\pi\)
−0.530819 + 0.847485i \(0.678116\pi\)
\(240\) 0 0
\(241\) −466018. 807167.i −0.516845 0.895202i −0.999809 0.0195613i \(-0.993773\pi\)
0.482964 0.875640i \(-0.339560\pi\)
\(242\) −220882. 382578.i −0.242449 0.419935i
\(243\) 0 0
\(244\) −559276. −0.601383
\(245\) −740752. + 643122.i −0.788420 + 0.684508i
\(246\) 0 0
\(247\) 773976. 1.34057e6i 0.807208 1.39812i
\(248\) 240179. + 416003.i 0.247974 + 0.429504i
\(249\) 0 0
\(250\) 228035. 394968.i 0.230755 0.399680i
\(251\) −214975. −0.215379 −0.107690 0.994185i \(-0.534345\pi\)
−0.107690 + 0.994185i \(0.534345\pi\)
\(252\) 0 0
\(253\) 68585.1 0.0673641
\(254\) −321184. + 556306.i −0.312370 + 0.541040i
\(255\) 0 0
\(256\) 321667. + 557143.i 0.306765 + 0.531333i
\(257\) 39593.5 68578.0i 0.0373931 0.0647667i −0.846723 0.532034i \(-0.821428\pi\)
0.884116 + 0.467267i \(0.154761\pi\)
\(258\) 0 0
\(259\) −502733. 414682.i −0.465680 0.384119i
\(260\) 1.26988e6 1.16501
\(261\) 0 0
\(262\) 216130. + 374349.i 0.194519 + 0.336917i
\(263\) −216414. 374840.i −0.192928 0.334162i 0.753291 0.657687i \(-0.228465\pi\)
−0.946219 + 0.323526i \(0.895132\pi\)
\(264\) 0 0
\(265\) −1.35742e6 −1.18741
\(266\) 580535. 216849.i 0.503065 0.187911i
\(267\) 0 0
\(268\) 574672. 995361.i 0.488746 0.846533i
\(269\) −2345.93 4063.27i −0.00197667 0.00342369i 0.865035 0.501711i \(-0.167296\pi\)
−0.867012 + 0.498287i \(0.833963\pi\)
\(270\) 0 0
\(271\) −52632.1 + 91161.5i −0.0435339 + 0.0754029i −0.886971 0.461825i \(-0.847195\pi\)
0.843437 + 0.537227i \(0.180528\pi\)
\(272\) −365482. −0.299533
\(273\) 0 0
\(274\) −471444. −0.379362
\(275\) 2454.52 4251.35i 0.00195720 0.00338997i
\(276\) 0 0
\(277\) 381558. + 660879.i 0.298787 + 0.517514i 0.975859 0.218403i \(-0.0700847\pi\)
−0.677072 + 0.735917i \(0.736751\pi\)
\(278\) 289418. 501287.i 0.224602 0.389023i
\(279\) 0 0
\(280\) 905524. + 746927.i 0.690248 + 0.569355i
\(281\) 729540. 0.551167 0.275584 0.961277i \(-0.411129\pi\)
0.275584 + 0.961277i \(0.411129\pi\)
\(282\) 0 0
\(283\) 595214. + 1.03094e6i 0.441781 + 0.765188i 0.997822 0.0659675i \(-0.0210134\pi\)
−0.556040 + 0.831155i \(0.687680\pi\)
\(284\) 19553.5 + 33867.7i 0.0143856 + 0.0249167i
\(285\) 0 0
\(286\) 42614.1 0.0308062
\(287\) 393726. 2.34835e6i 0.282156 1.68290i
\(288\) 0 0
\(289\) 182938. 316859.i 0.128843 0.223162i
\(290\) 451820. + 782575.i 0.315479 + 0.546425i
\(291\) 0 0
\(292\) 72503.3 125579.i 0.0497623 0.0861909i
\(293\) 1.02503e6 0.697537 0.348769 0.937209i \(-0.386600\pi\)
0.348769 + 0.937209i \(0.386600\pi\)
\(294\) 0 0
\(295\) −210311. −0.140704
\(296\) −389903. + 675332.i −0.258659 + 0.448011i
\(297\) 0 0
\(298\) −328975. 569801.i −0.214596 0.371692i
\(299\) 1.75149e6 3.03366e6i 1.13300 1.96241i
\(300\) 0 0
\(301\) 34961.2 208524.i 0.0222418 0.132660i
\(302\) −596464. −0.376328
\(303\) 0 0
\(304\) 309614. + 536267.i 0.192148 + 0.332811i
\(305\) 667623. + 1.15636e6i 0.410943 + 0.711774i
\(306\) 0 0
\(307\) −709845. −0.429850 −0.214925 0.976631i \(-0.568951\pi\)
−0.214925 + 0.976631i \(0.568951\pi\)
\(308\) −42601.5 35140.1i −0.0255887 0.0211070i
\(309\) 0 0
\(310\) 248348. 430151.i 0.146776 0.254224i
\(311\) 783816. + 1.35761e6i 0.459529 + 0.795928i 0.998936 0.0461175i \(-0.0146849\pi\)
−0.539407 + 0.842045i \(0.681352\pi\)
\(312\) 0 0
\(313\) −186476. + 322986.i −0.107588 + 0.186347i −0.914792 0.403924i \(-0.867646\pi\)
0.807205 + 0.590271i \(0.200979\pi\)
\(314\) −458684. −0.262536
\(315\) 0 0
\(316\) 2.16284e6 1.21845
\(317\) −1.51408e6 + 2.62246e6i −0.846253 + 1.46575i 0.0382747 + 0.999267i \(0.487814\pi\)
−0.884528 + 0.466487i \(0.845520\pi\)
\(318\) 0 0
\(319\) −49079.6 85008.3i −0.0270037 0.0467719i
\(320\) 144136. 249650.i 0.0786858 0.136288i
\(321\) 0 0
\(322\) 1.31373e6 490723.i 0.706103 0.263752i
\(323\) 1.78573e6 0.952380
\(324\) 0 0
\(325\) −125364. 217137.i −0.0658363 0.114032i
\(326\) 695526. + 1.20469e6i 0.362468 + 0.627813i
\(327\) 0 0
\(328\) −2.84923e6 −1.46232
\(329\) −960613. 792367.i −0.489281 0.403586i
\(330\) 0 0
\(331\) −533448. + 923959.i −0.267622 + 0.463535i −0.968247 0.249995i \(-0.919571\pi\)
0.700625 + 0.713529i \(0.252905\pi\)
\(332\) 1.17133e6 + 2.02880e6i 0.583221 + 1.01017i
\(333\) 0 0
\(334\) 777130. 1.34603e6i 0.381178 0.660219i
\(335\) −2.74401e6 −1.33590
\(336\) 0 0
\(337\) 1.55734e6 0.746981 0.373490 0.927634i \(-0.378161\pi\)
0.373490 + 0.927634i \(0.378161\pi\)
\(338\) 578064. 1.00124e6i 0.275222 0.476699i
\(339\) 0 0
\(340\) 732470. + 1.26868e6i 0.343631 + 0.595187i
\(341\) −26977.1 + 46725.8i −0.0125635 + 0.0217606i
\(342\) 0 0
\(343\) 1.04145e6 1.91388e6i 0.477973 0.878374i
\(344\) −253000. −0.115272
\(345\) 0 0
\(346\) 906124. + 1.56945e6i 0.406909 + 0.704787i
\(347\) −1.11748e6 1.93553e6i −0.498214 0.862932i 0.501784 0.864993i \(-0.332677\pi\)
−0.999998 + 0.00206105i \(0.999344\pi\)
\(348\) 0 0
\(349\) −1.72982e6 −0.760218 −0.380109 0.924942i \(-0.624114\pi\)
−0.380109 + 0.924942i \(0.624114\pi\)
\(350\) 16597.7 98995.8i 0.00724231 0.0431963i
\(351\) 0 0
\(352\) −51770.9 + 89669.8i −0.0222705 + 0.0385736i
\(353\) −1.18287e6 2.04879e6i −0.505242 0.875105i −0.999982 0.00606386i \(-0.998070\pi\)
0.494739 0.869041i \(-0.335264\pi\)
\(354\) 0 0
\(355\) 46683.1 80857.6i 0.0196603 0.0340526i
\(356\) −1.13700e6 −0.475484
\(357\) 0 0
\(358\) 454247. 0.187320
\(359\) 25514.3 44192.1i 0.0104484 0.0180971i −0.860754 0.509021i \(-0.830007\pi\)
0.871202 + 0.490924i \(0.163341\pi\)
\(360\) 0 0
\(361\) −274712. 475815.i −0.110945 0.192163i
\(362\) 204041. 353410.i 0.0818364 0.141745i
\(363\) 0 0
\(364\) −2.64226e6 + 986968.i −1.04525 + 0.390436i
\(365\) −346197. −0.136016
\(366\) 0 0
\(367\) −1.88411e6 3.26338e6i −0.730200 1.26474i −0.956797 0.290755i \(-0.906093\pi\)
0.226597 0.973989i \(-0.427240\pi\)
\(368\) 700648. + 1.21356e6i 0.269699 + 0.467133i
\(369\) 0 0
\(370\) 806328. 0.306201
\(371\) 2.82441e6 1.05501e6i 1.06535 0.397943i
\(372\) 0 0
\(373\) −2.31720e6 + 4.01351e6i −0.862366 + 1.49366i 0.00727258 + 0.999974i \(0.497685\pi\)
−0.869639 + 0.493689i \(0.835648\pi\)
\(374\) 24580.0 + 42573.8i 0.00908663 + 0.0157385i
\(375\) 0 0
\(376\) −745020. + 1.29041e6i −0.271768 + 0.470716i
\(377\) −5.01346e6 −1.81670
\(378\) 0 0
\(379\) −4.17169e6 −1.49181 −0.745905 0.666052i \(-0.767983\pi\)
−0.745905 + 0.666052i \(0.767983\pi\)
\(380\) 1.24101e6 2.14949e6i 0.440875 0.763617i
\(381\) 0 0
\(382\) −530276. 918465.i −0.185928 0.322036i
\(383\) −2.08586e6 + 3.61281e6i −0.726588 + 1.25849i 0.231730 + 0.972780i \(0.425562\pi\)
−0.958317 + 0.285706i \(0.907772\pi\)
\(384\) 0 0
\(385\) −21800.9 + 130030.i −0.00749590 + 0.0447088i
\(386\) −1.36391e6 −0.465927
\(387\) 0 0
\(388\) −928783. 1.60870e6i −0.313209 0.542495i
\(389\) 1.37697e6 + 2.38498e6i 0.461371 + 0.799119i 0.999030 0.0440442i \(-0.0140242\pi\)
−0.537658 + 0.843163i \(0.680691\pi\)
\(390\) 0 0
\(391\) 4.04106e6 1.33676
\(392\) −2.46466e6 850357.i −0.810108 0.279503i
\(393\) 0 0
\(394\) −606578. + 1.05062e6i −0.196855 + 0.340962i
\(395\) −2.58184e6 4.47189e6i −0.832602 1.44211i
\(396\) 0 0
\(397\) 1.26602e6 2.19281e6i 0.403148 0.698274i −0.590956 0.806704i \(-0.701249\pi\)
0.994104 + 0.108430i \(0.0345825\pi\)
\(398\) 208419. 0.0659522
\(399\) 0 0
\(400\) 100299. 0.0313434
\(401\) −1.07873e6 + 1.86842e6i −0.335007 + 0.580249i −0.983486 0.180983i \(-0.942072\pi\)
0.648479 + 0.761232i \(0.275405\pi\)
\(402\) 0 0
\(403\) 1.37785e6 + 2.38651e6i 0.422611 + 0.731983i
\(404\) 564217. 977252.i 0.171986 0.297888i
\(405\) 0 0
\(406\) −1.54834e6 1.27716e6i −0.466177 0.384529i
\(407\) −87588.5 −0.0262096
\(408\) 0 0
\(409\) 2.16402e6 + 3.74819e6i 0.639665 + 1.10793i 0.985506 + 0.169640i \(0.0542604\pi\)
−0.345841 + 0.938293i \(0.612406\pi\)
\(410\) 1.47307e6 + 2.55143e6i 0.432776 + 0.749590i
\(411\) 0 0
\(412\) 2.00405e6 0.581655
\(413\) 437599. 163457.i 0.126241 0.0471552i
\(414\) 0 0
\(415\) 2.79649e6 4.84366e6i 0.797064 1.38056i
\(416\) 2.64419e6 + 4.57987e6i 0.749134 + 1.29754i
\(417\) 0 0
\(418\) 41645.3 72131.8i 0.0116580 0.0201923i
\(419\) 1.51129e6 0.420544 0.210272 0.977643i \(-0.432565\pi\)
0.210272 + 0.977643i \(0.432565\pi\)
\(420\) 0 0
\(421\) 1.11586e6 0.306835 0.153418 0.988161i \(-0.450972\pi\)
0.153418 + 0.988161i \(0.450972\pi\)
\(422\) 1.07001e6 1.85331e6i 0.292487 0.506603i
\(423\) 0 0
\(424\) −1.80387e6 3.12439e6i −0.487293 0.844016i
\(425\) 144621. 250492.i 0.0388383 0.0672699i
\(426\) 0 0
\(427\) −2.28787e6 1.88717e6i −0.607243 0.500888i
\(428\) −69765.2 −0.0184090
\(429\) 0 0
\(430\) 130802. + 226556.i 0.0341149 + 0.0590887i
\(431\) 3.10672e6 + 5.38100e6i 0.805581 + 1.39531i 0.915898 + 0.401411i \(0.131480\pi\)
−0.110317 + 0.993896i \(0.535187\pi\)
\(432\) 0 0
\(433\) 3.24118e6 0.830775 0.415388 0.909644i \(-0.363646\pi\)
0.415388 + 0.909644i \(0.363646\pi\)
\(434\) −182422. + 1.08804e6i −0.0464892 + 0.277282i
\(435\) 0 0
\(436\) −2.03255e6 + 3.52047e6i −0.512064 + 0.886920i
\(437\) −3.42334e6 5.92939e6i −0.857524 1.48527i
\(438\) 0 0
\(439\) −1.15248e6 + 1.99616e6i −0.285413 + 0.494349i −0.972709 0.232028i \(-0.925464\pi\)
0.687297 + 0.726377i \(0.258797\pi\)
\(440\) 157765. 0.0388488
\(441\) 0 0
\(442\) 2.51084e6 0.611313
\(443\) 766328. 1.32732e6i 0.185526 0.321341i −0.758228 0.651990i \(-0.773934\pi\)
0.943754 + 0.330649i \(0.107268\pi\)
\(444\) 0 0
\(445\) 1.35727e6 + 2.35086e6i 0.324912 + 0.562764i
\(446\) 1.01420e6 1.75664e6i 0.241426 0.418162i
\(447\) 0 0
\(448\) −105874. + 631476.i −0.0249226 + 0.148649i
\(449\) 3.55718e6 0.832702 0.416351 0.909204i \(-0.363309\pi\)
0.416351 + 0.909204i \(0.363309\pi\)
\(450\) 0 0
\(451\) −160014. 277153.i −0.0370439 0.0641620i
\(452\) −3.18189e6 5.51119e6i −0.732553 1.26882i
\(453\) 0 0
\(454\) −1.49533e6 −0.340484
\(455\) 5.19478e6 + 4.28494e6i 1.17636 + 0.970324i
\(456\) 0 0
\(457\) −1.25941e6 + 2.18137e6i −0.282083 + 0.488583i −0.971898 0.235403i \(-0.924359\pi\)
0.689814 + 0.723986i \(0.257692\pi\)
\(458\) −320936. 555877.i −0.0714915 0.123827i
\(459\) 0 0
\(460\) 2.80836e6 4.86423e6i 0.618812 1.07181i
\(461\) 6.63271e6 1.45358 0.726789 0.686861i \(-0.241012\pi\)
0.726789 + 0.686861i \(0.241012\pi\)
\(462\) 0 0
\(463\) −4.40432e6 −0.954830 −0.477415 0.878678i \(-0.658426\pi\)
−0.477415 + 0.878678i \(0.658426\pi\)
\(464\) 1.00277e6 1.73685e6i 0.216225 0.374512i
\(465\) 0 0
\(466\) 849325. + 1.47107e6i 0.181180 + 0.313812i
\(467\) 122922. 212908.i 0.0260819 0.0451751i −0.852690 0.522417i \(-0.825030\pi\)
0.878772 + 0.477242i \(0.158364\pi\)
\(468\) 0 0
\(469\) 5.70951e6 2.13269e6i 1.19858 0.447708i
\(470\) 1.54072e6 0.321720
\(471\) 0 0
\(472\) −279482. 484076.i −0.0577428 0.100014i
\(473\) −14208.6 24610.0i −0.00292010 0.00505776i
\(474\) 0 0
\(475\) −490057. −0.0996581
\(476\) −2.51010e6 2.07047e6i −0.507778 0.418843i
\(477\) 0 0
\(478\) −1.28821e6 + 2.23125e6i −0.257880 + 0.446661i
\(479\) −20175.6 34945.1i −0.00401779 0.00695901i 0.864010 0.503475i \(-0.167946\pi\)
−0.868027 + 0.496516i \(0.834612\pi\)
\(480\) 0 0
\(481\) −2.23678e6 + 3.87422e6i −0.440820 + 0.763523i
\(482\) −2.56140e6 −0.502181
\(483\) 0 0
\(484\) 3.92987e6 0.762544
\(485\) −2.21743e6 + 3.84069e6i −0.428050 + 0.741405i
\(486\) 0 0
\(487\) 1.65484e6 + 2.86627e6i 0.316180 + 0.547639i 0.979688 0.200530i \(-0.0642664\pi\)
−0.663508 + 0.748169i \(0.730933\pi\)
\(488\) −1.77440e6 + 3.07335e6i −0.337289 + 0.584202i
\(489\) 0 0
\(490\) 512768. + 2.64669e6i 0.0964785 + 0.497982i
\(491\) 1.97959e6 0.370570 0.185285 0.982685i \(-0.440679\pi\)
0.185285 + 0.982685i \(0.440679\pi\)
\(492\) 0 0
\(493\) −2.89179e6 5.00872e6i −0.535857 0.928132i
\(494\) −2.12703e6 3.68412e6i −0.392153 0.679229i
\(495\) 0 0
\(496\) −1.10237e6 −0.201197
\(497\) −34290.7 + 204525.i −0.00622709 + 0.0371411i
\(498\) 0 0
\(499\) 1.58498e6 2.74526e6i 0.284952 0.493551i −0.687646 0.726046i \(-0.741356\pi\)
0.972597 + 0.232495i \(0.0746891\pi\)
\(500\) 2.02857e6 + 3.51359e6i 0.362882 + 0.628530i
\(501\) 0 0
\(502\) −295396. + 511640.i −0.0523172 + 0.0906161i
\(503\) 4.01273e6 0.707164 0.353582 0.935403i \(-0.384963\pi\)
0.353582 + 0.935403i \(0.384963\pi\)
\(504\) 0 0
\(505\) −2.69408e6 −0.470092
\(506\) 94242.1 163232.i 0.0163632 0.0283419i
\(507\) 0 0
\(508\) −2.85721e6 4.94884e6i −0.491228 0.850832i
\(509\) 2.05629e6 3.56159e6i 0.351795 0.609326i −0.634769 0.772702i \(-0.718905\pi\)
0.986564 + 0.163375i \(0.0522382\pi\)
\(510\) 0 0
\(511\) 720338. 269070.i 0.122035 0.0455840i
\(512\) −3.88273e6 −0.654580
\(513\) 0 0
\(514\) −108810. 188465.i −0.0181661 0.0314646i
\(515\) −2.39229e6 4.14356e6i −0.397462 0.688424i
\(516\) 0 0
\(517\) −167363. −0.0275380
\(518\) −1.67774e6 + 626691.i −0.274727 + 0.102619i
\(519\) 0 0
\(520\) 4.02890e6 6.97827e6i 0.653399 1.13172i
\(521\) 4.27758e6 + 7.40898e6i 0.690404 + 1.19582i 0.971705 + 0.236196i \(0.0759007\pi\)
−0.281301 + 0.959620i \(0.590766\pi\)
\(522\) 0 0
\(523\) 896820. 1.55334e6i 0.143368 0.248320i −0.785395 0.618995i \(-0.787540\pi\)
0.928763 + 0.370675i \(0.120874\pi\)
\(524\) −3.84534e6 −0.611796
\(525\) 0 0
\(526\) −1.18949e6 −0.187455
\(527\) −1.58950e6 + 2.75310e6i −0.249307 + 0.431813i
\(528\) 0 0
\(529\) −4.52875e6 7.84402e6i −0.703621 1.21871i
\(530\) −1.86522e6 + 3.23065e6i −0.288430 + 0.499575i
\(531\) 0 0
\(532\) −911571. + 5.43701e6i −0.139640 + 0.832877i
\(533\) −1.63454e7 −2.49217
\(534\) 0 0
\(535\) 83280.6 + 144246.i 0.0125794 + 0.0217881i
\(536\) −3.64650e6 6.31592e6i −0.548231 0.949565i
\(537\) 0 0
\(538\) −12894.1 −0.00192059
\(539\) −55700.1 287501.i −0.00825818 0.0426253i
\(540\) 0 0
\(541\) 178780. 309657.i 0.0262619 0.0454870i −0.852596 0.522571i \(-0.824973\pi\)
0.878858 + 0.477084i \(0.158306\pi\)
\(542\) 144643. + 250528.i 0.0211494 + 0.0366318i
\(543\) 0 0
\(544\) −3.05036e6 + 5.28338e6i −0.441931 + 0.765447i
\(545\) 9.70522e6 1.39963
\(546\) 0 0
\(547\) −3.79404e6 −0.542167 −0.271084 0.962556i \(-0.587382\pi\)
−0.271084 + 0.962556i \(0.587382\pi\)
\(548\) 2.09695e6 3.63203e6i 0.298289 0.516652i
\(549\) 0 0
\(550\) −6745.47 11683.5i −0.000950835 0.00164689i
\(551\) −4.89949e6 + 8.48616e6i −0.687498 + 1.19078i
\(552\) 0 0
\(553\) 8.84771e6 + 7.29809e6i 1.23032 + 1.01484i
\(554\) 2.09718e6 0.290310
\(555\) 0 0
\(556\) 2.57463e6 + 4.45939e6i 0.353206 + 0.611771i
\(557\) −2.44799e6 4.24005e6i −0.334328 0.579072i 0.649028 0.760765i \(-0.275176\pi\)
−0.983355 + 0.181692i \(0.941843\pi\)
\(558\) 0 0
\(559\) −1.45140e6 −0.196453
\(560\) −2.52350e6 + 942607.i −0.340042 + 0.127017i
\(561\) 0 0
\(562\) 1.00245e6 1.73630e6i 0.133882 0.231891i
\(563\) −2.16583e6 3.75133e6i −0.287974 0.498786i 0.685352 0.728212i \(-0.259648\pi\)
−0.973326 + 0.229426i \(0.926315\pi\)
\(564\) 0 0
\(565\) −7.59661e6 + 1.31577e7i −1.00115 + 1.73404i
\(566\) 3.27151e6 0.429248
\(567\) 0 0
\(568\) 248148. 0.0322730
\(569\) −1.09848e6 + 1.90262e6i −0.142236 + 0.246361i −0.928338 0.371736i \(-0.878763\pi\)
0.786102 + 0.618097i \(0.212096\pi\)
\(570\) 0 0
\(571\) 3.73846e6 + 6.47520e6i 0.479846 + 0.831118i 0.999733 0.0231172i \(-0.00735908\pi\)
−0.519886 + 0.854235i \(0.674026\pi\)
\(572\) −189545. + 328301.i −0.0242227 + 0.0419549i
\(573\) 0 0
\(574\) −5.04805e6 4.16391e6i −0.639505 0.527500i
\(575\) −1.10899e6 −0.139880
\(576\) 0 0
\(577\) 683110. + 1.18318e6i 0.0854183 + 0.147949i 0.905569 0.424198i \(-0.139444\pi\)
−0.820151 + 0.572147i \(0.806111\pi\)
\(578\) −502748. 870785.i −0.0625937 0.108415i
\(579\) 0 0
\(580\) −8.03867e6 −0.992234
\(581\) −2.05414e6 + 1.22518e7i −0.252458 + 1.50577i
\(582\) 0 0
\(583\) 202612. 350934.i 0.0246884 0.0427616i
\(584\) −460059. 796845.i −0.0558189 0.0966812i
\(585\) 0 0
\(586\) 1.40848e6 2.43956e6i 0.169437 0.293473i
\(587\) 9.27217e6 1.11067 0.555336 0.831626i \(-0.312590\pi\)
0.555336 + 0.831626i \(0.312590\pi\)
\(588\) 0 0
\(589\) 5.38612e6 0.639717
\(590\) −288987. + 500540.i −0.0341781 + 0.0591982i
\(591\) 0 0
\(592\) −894782. 1.54981e6i −0.104933 0.181750i
\(593\) 4.60523e6 7.97649e6i 0.537792 0.931483i −0.461231 0.887280i \(-0.652592\pi\)
0.999023 0.0442028i \(-0.0140748\pi\)
\(594\) 0 0
\(595\) −1.28452e6 + 7.66145e6i −0.148747 + 0.887194i
\(596\) 5.85305e6 0.674942
\(597\) 0 0
\(598\) −4.81340e6 8.33706e6i −0.550426 0.953367i
\(599\) −6.84581e6 1.18573e7i −0.779575 1.35026i −0.932187 0.361977i \(-0.882102\pi\)
0.152612 0.988286i \(-0.451231\pi\)
\(600\) 0 0
\(601\) 1.61113e6 0.181946 0.0909732 0.995853i \(-0.471002\pi\)
0.0909732 + 0.995853i \(0.471002\pi\)
\(602\) −448246. 369738.i −0.0504110 0.0415818i
\(603\) 0 0
\(604\) 2.65304e6 4.59519e6i 0.295904 0.512521i
\(605\) −4.69119e6 8.12539e6i −0.521069 0.902517i
\(606\) 0 0
\(607\) 7.03281e6 1.21812e7i 0.774742 1.34189i −0.160198 0.987085i \(-0.551213\pi\)
0.934940 0.354807i \(-0.115453\pi\)
\(608\) 1.03363e7 1.13398
\(609\) 0 0
\(610\) 3.66950e6 0.399284
\(611\) −4.27401e6 + 7.40280e6i −0.463161 + 0.802219i
\(612\) 0 0
\(613\) −6.79842e6 1.17752e7i −0.730729 1.26566i −0.956572 0.291497i \(-0.905847\pi\)
0.225842 0.974164i \(-0.427487\pi\)
\(614\) −975391. + 1.68943e6i −0.104414 + 0.180850i
\(615\) 0 0
\(616\) −328264. + 122617.i −0.0348555 + 0.0130197i
\(617\) 5.74287e6 0.607318 0.303659 0.952781i \(-0.401792\pi\)
0.303659 + 0.952781i \(0.401792\pi\)
\(618\) 0 0
\(619\) 3.01299e6 + 5.21865e6i 0.316061 + 0.547434i 0.979662 0.200653i \(-0.0643063\pi\)
−0.663602 + 0.748086i \(0.730973\pi\)
\(620\) 2.20927e6 + 3.82657e6i 0.230818 + 0.399789i
\(621\) 0 0
\(622\) 4.30814e6 0.446492
\(623\) −4.65122e6 3.83658e6i −0.480117 0.396027i
\(624\) 0 0
\(625\) 5.28334e6 9.15101e6i 0.541014 0.937064i
\(626\) 512470. + 887625.i 0.0522676 + 0.0905302i
\(627\) 0 0
\(628\) 2.04020e6 3.53373e6i 0.206430 0.357547i
\(629\) −5.16075e6 −0.520099
\(630\) 0 0
\(631\) −6.90670e6 −0.690554 −0.345277 0.938501i \(-0.612215\pi\)
−0.345277 + 0.938501i \(0.612215\pi\)
\(632\) 6.86200e6 1.18853e7i 0.683373 1.18364i
\(633\) 0 0
\(634\) 4.16096e6 + 7.20700e6i 0.411122 + 0.712084i
\(635\) −6.82146e6 + 1.18151e7i −0.671341 + 1.16280i
\(636\) 0 0
\(637\) −1.41392e7 4.87830e6i −1.38063 0.476343i
\(638\) −269759. −0.0262376
\(639\) 0 0
\(640\) 5.15340e6 + 8.92595e6i 0.497329 + 0.861400i
\(641\) 8.24828e6 + 1.42864e7i 0.792900 + 1.37334i 0.924164 + 0.381995i \(0.124763\pi\)
−0.131265 + 0.991347i \(0.541904\pi\)
\(642\) 0 0
\(643\) 1.70171e7 1.62315 0.811576 0.584247i \(-0.198610\pi\)
0.811576 + 0.584247i \(0.198610\pi\)
\(644\) −2.06286e6 + 1.23038e7i −0.195999 + 1.16903i
\(645\) 0 0
\(646\) 2.45376e6 4.25003e6i 0.231340 0.400692i
\(647\) 1.74287e6 + 3.01873e6i 0.163683 + 0.283507i 0.936187 0.351503i \(-0.114329\pi\)
−0.772504 + 0.635010i \(0.780996\pi\)
\(648\) 0 0
\(649\) 31391.6 54371.8i 0.00292551 0.00506713i
\(650\) −689047. −0.0639684
\(651\) 0 0
\(652\) −1.23746e7 −1.14002
\(653\) 7.72245e6 1.33757e7i 0.708716 1.22753i −0.256618 0.966513i \(-0.582608\pi\)
0.965334 0.261019i \(-0.0840586\pi\)
\(654\) 0 0
\(655\) 4.59029e6 + 7.95061e6i 0.418058 + 0.724098i
\(656\) 3.26933e6 5.66264e6i 0.296619 0.513759i
\(657\) 0 0
\(658\) −3.20580e6 + 1.19747e6i −0.288650 + 0.107820i
\(659\) 3.11193e6 0.279136 0.139568 0.990212i \(-0.455429\pi\)
0.139568 + 0.990212i \(0.455429\pi\)
\(660\) 0 0
\(661\) −4.08610e6 7.07733e6i −0.363752 0.630037i 0.624823 0.780766i \(-0.285171\pi\)
−0.988575 + 0.150729i \(0.951838\pi\)
\(662\) 1.46601e6 + 2.53921e6i 0.130015 + 0.225192i
\(663\) 0 0
\(664\) 1.48650e7 1.30841
\(665\) 1.23297e7 4.60554e6i 1.08118 0.403856i
\(666\) 0 0
\(667\) −1.10874e7 + 1.92039e7i −0.964973 + 1.67138i
\(668\) 6.91326e6 + 1.19741e7i 0.599434 + 1.03825i
\(669\) 0 0
\(670\) −3.77051e6 + 6.53072e6i −0.324499 + 0.562049i
\(671\) −398604. −0.0341771
\(672\) 0 0
\(673\) 1.60182e7 1.36325 0.681627 0.731700i \(-0.261273\pi\)
0.681627 + 0.731700i \(0.261273\pi\)
\(674\) 2.13993e6 3.70647e6i 0.181447 0.314276i
\(675\) 0 0
\(676\) 5.14239e6 + 8.90687e6i 0.432811 + 0.749650i
\(677\) 512185. 887131.i 0.0429492 0.0743902i −0.843752 0.536734i \(-0.819658\pi\)
0.886701 + 0.462344i \(0.152991\pi\)
\(678\) 0 0
\(679\) 1.62879e6 9.71483e6i 0.135579 0.808650i
\(680\) 9.29556e6 0.770910
\(681\) 0 0
\(682\) 74138.1 + 128411.i 0.00610352 + 0.0105716i
\(683\) −2.69688e6 4.67114e6i −0.221213 0.383152i 0.733964 0.679189i \(-0.237668\pi\)
−0.955177 + 0.296037i \(0.904335\pi\)
\(684\) 0 0
\(685\) −1.00128e7 −0.815319
\(686\) −3.12398e6 5.10850e6i −0.253453 0.414460i
\(687\) 0 0
\(688\) 290302. 502819.i 0.0233819 0.0404986i
\(689\) −1.03484e7 1.79239e7i −0.830470 1.43842i
\(690\) 0 0
\(691\) 452826. 784318.i 0.0360775 0.0624881i −0.847423 0.530919i \(-0.821847\pi\)
0.883500 + 0.468430i \(0.155180\pi\)
\(692\) −1.61215e7 −1.27980
\(693\) 0 0
\(694\) −6.14207e6 −0.484079
\(695\) 6.14682e6 1.06466e7i 0.482712 0.836082i
\(696\) 0 0
\(697\) −9.42810e6 1.63300e7i −0.735093 1.27322i
\(698\) −2.37693e6 + 4.11697e6i −0.184662 + 0.319845i
\(699\) 0 0
\(700\) 688845. + 568197.i 0.0531344 + 0.0438282i
\(701\) −1.12573e7 −0.865246 −0.432623 0.901575i \(-0.642412\pi\)
−0.432623 + 0.901575i \(0.642412\pi\)
\(702\) 0 0
\(703\) 4.37187e6 + 7.57230e6i 0.333640 + 0.577882i
\(704\) 43028.1 + 74526.9i 0.00327205 + 0.00566736i
\(705\) 0 0
\(706\) −6.50147e6 −0.490908
\(707\) 5.60563e6 2.09388e6i 0.421770 0.157545i
\(708\) 0 0
\(709\) −2.17755e6 + 3.77162e6i −0.162687 + 0.281781i −0.935831 0.352448i \(-0.885349\pi\)
0.773145 + 0.634230i \(0.218683\pi\)
\(710\) −128294. 222211.i −0.00955123 0.0165432i
\(711\) 0 0
\(712\) −3.60733e6 + 6.24809e6i −0.266678 + 0.461899i
\(713\) 1.21886e7 0.897907
\(714\) 0 0
\(715\) 905060. 0.0662082
\(716\) −2.02046e6 + 3.49955e6i −0.147288 + 0.255111i
\(717\) 0 0
\(718\) −70118.0 121448.i −0.00507597 0.00879183i
\(719\) −7.07221e6 + 1.22494e7i −0.510191 + 0.883676i 0.489739 + 0.871869i \(0.337092\pi\)
−0.999930 + 0.0118076i \(0.996241\pi\)
\(720\) 0 0
\(721\) 8.19812e6 + 6.76227e6i 0.587322 + 0.484456i
\(722\) −1.50992e6 −0.107798
\(723\) 0 0
\(724\) 1.81513e6 + 3.14389e6i 0.128695 + 0.222906i
\(725\) 793591. + 1.37454e6i 0.0560727 + 0.0971208i
\(726\) 0 0
\(727\) −6.26406e6 −0.439561 −0.219781 0.975549i \(-0.570534\pi\)
−0.219781 + 0.975549i \(0.570534\pi\)
\(728\) −2.95940e6 + 1.76511e7i −0.206954 + 1.23437i
\(729\) 0 0
\(730\) −475705. + 823946.i −0.0330393 + 0.0572258i
\(731\) −837176. 1.45003e6i −0.0579460 0.100365i
\(732\) 0 0
\(733\) 1.02089e7 1.76823e7i 0.701806 1.21556i −0.266025 0.963966i \(-0.585710\pi\)
0.967832 0.251598i \(-0.0809562\pi\)
\(734\) −1.03558e7 −0.709484
\(735\) 0 0
\(736\) 2.33908e7 1.59166
\(737\) 409577. 709409.i 0.0277758 0.0481092i
\(738\) 0 0
\(739\) −7.42256e6 1.28563e7i −0.499969 0.865971i 0.500031 0.866007i \(-0.333322\pi\)
−1.00000 3.61537e-5i \(0.999988\pi\)
\(740\) −3.58650e6 + 6.21200e6i −0.240764 + 0.417015i
\(741\) 0 0
\(742\) 1.37008e6 8.17176e6i 0.0913558 0.544886i
\(743\) −2.36601e7 −1.57234 −0.786168 0.618013i \(-0.787938\pi\)
−0.786168 + 0.618013i \(0.787938\pi\)
\(744\) 0 0
\(745\) −6.98694e6 1.21017e7i −0.461207 0.798834i
\(746\) 6.36809e6 + 1.10299e7i 0.418950 + 0.725643i
\(747\) 0 0
\(748\) −437322. −0.0285790
\(749\) −285394. 235409.i −0.0185883 0.0153327i
\(750\) 0 0
\(751\) −1.03287e7 + 1.78898e7i −0.668258 + 1.15746i 0.310133 + 0.950693i \(0.399627\pi\)
−0.978391 + 0.206764i \(0.933707\pi\)
\(752\) −1.70973e6 2.96134e6i −0.110251 0.190961i
\(753\) 0 0
\(754\) −6.88895e6 + 1.19320e7i −0.441291 + 0.764338i
\(755\) −1.26680e7 −0.808799
\(756\) 0 0
\(757\) −1.26697e7 −0.803573 −0.401787 0.915733i \(-0.631611\pi\)
−0.401787 + 0.915733i \(0.631611\pi\)
\(758\) −5.73228e6 + 9.92860e6i −0.362372 + 0.627646i
\(759\) 0 0
\(760\) −7.87462e6 1.36392e7i −0.494534 0.856557i
\(761\) 8.13761e6 1.40948e7i 0.509372 0.882259i −0.490569 0.871402i \(-0.663211\pi\)
0.999941 0.0108563i \(-0.00345572\pi\)
\(762\) 0 0
\(763\) −2.01938e7 + 7.54305e6i −1.25576 + 0.469068i
\(764\) 9.43455e6 0.584774
\(765\) 0 0
\(766\) 5.73232e6 + 9.92867e6i 0.352987 + 0.611391i
\(767\) −1.60332e6 2.77703e6i −0.0984084 0.170448i
\(768\) 0 0
\(769\) 1.60471e7 0.978547 0.489273 0.872130i \(-0.337262\pi\)
0.489273 + 0.872130i \(0.337262\pi\)
\(770\) 279515. + 230560.i 0.0169894 + 0.0140138i
\(771\) 0 0
\(772\) 6.06659e6 1.05076e7i 0.366355 0.634545i
\(773\) 1.07839e6 + 1.86782e6i 0.0649121 + 0.112431i 0.896655 0.442730i \(-0.145990\pi\)
−0.831743 + 0.555161i \(0.812657\pi\)
\(774\) 0 0
\(775\) 436206. 755531.i 0.0260878 0.0451854i
\(776\) −1.17869e7 −0.702661
\(777\) 0 0
\(778\) 7.56833e6 0.448282
\(779\) −1.59738e7 + 2.76674e7i −0.943115 + 1.63352i
\(780\) 0 0
\(781\) 13936.1 + 24138.0i 0.000817548 + 0.00141603i
\(782\) 5.55279e6 9.61771e6i 0.324709 0.562412i
\(783\) 0 0
\(784\) 4.51808e6 3.92260e6i 0.262521 0.227921i
\(785\) −9.74175e6 −0.564239
\(786\) 0 0
\(787\) −7.00503e6 1.21331e7i −0.403156 0.698286i 0.590949 0.806709i \(-0.298753\pi\)
−0.994105 + 0.108423i \(0.965420\pi\)
\(788\) −5.39604e6 9.34622e6i −0.309571 0.536192i
\(789\) 0 0
\(790\) −1.41908e7 −0.808980
\(791\) 5.58002e6 3.32817e7i 0.317099 1.89132i
\(792\) 0 0
\(793\) −1.01793e7 + 1.76311e7i −0.574825 + 0.995627i
\(794\) −3.47926e6 6.02625e6i −0.195855 0.339231i
\(795\) 0 0
\(796\) −927034. + 1.60567e6i −0.0518577 + 0.0898202i
\(797\) −4.73289e6 −0.263925 −0.131963 0.991255i \(-0.542128\pi\)
−0.131963 + 0.991255i \(0.542128\pi\)
\(798\) 0 0
\(799\) −9.86107e6 −0.546459
\(800\) 837108. 1.44991e6i 0.0462441 0.0800972i
\(801\) 0 0
\(802\) 2.96456e6 + 5.13477e6i 0.162751 + 0.281893i
\(803\) 51674.2 89502.3i 0.00282804 0.00489830i
\(804\) 0 0
\(805\) 2.79018e7 1.04222e7i 1.51755 0.566853i
\(806\) 7.57318e6 0.410621
\(807\) 0 0
\(808\) −3.58015e6 6.20101e6i −0.192918 0.334144i
\(809\) 4.05446e6 + 7.02253e6i 0.217802 + 0.377244i 0.954136 0.299375i \(-0.0967780\pi\)
−0.736334 + 0.676618i \(0.763445\pi\)
\(810\) 0 0
\(811\) −9.13444e6 −0.487674 −0.243837 0.969816i \(-0.578406\pi\)
−0.243837 + 0.969816i \(0.578406\pi\)
\(812\) 1.67262e7 6.24778e6i 0.890241 0.332534i
\(813\) 0 0
\(814\) −120355. + 208460.i −0.00636651 + 0.0110271i
\(815\) 1.47719e7 + 2.55858e7i 0.779011 + 1.34929i
\(816\) 0 0
\(817\) −1.41841e6 + 2.45675e6i −0.0743439 + 0.128767i
\(818\) 1.18942e7 0.621517
\(819\) 0 0
\(820\) −2.62085e7 −1.36115
\(821\) 850776. 1.47359e6i 0.0440511 0.0762988i −0.843159 0.537664i \(-0.819307\pi\)
0.887210 + 0.461365i \(0.152640\pi\)
\(822\) 0 0
\(823\) 1.24604e7 + 2.15820e7i 0.641256 + 1.11069i 0.985153 + 0.171680i \(0.0549196\pi\)
−0.343897 + 0.939007i \(0.611747\pi\)
\(824\) 6.35820e6 1.10127e7i 0.326224 0.565037i
\(825\) 0 0
\(826\) 212273. 1.26609e6i 0.0108254 0.0645674i
\(827\) 1.91232e7 0.972292 0.486146 0.873878i \(-0.338402\pi\)
0.486146 + 0.873878i \(0.338402\pi\)
\(828\) 0 0
\(829\) 1.10134e7 + 1.90757e7i 0.556588 + 0.964038i 0.997778 + 0.0666248i \(0.0212231\pi\)
−0.441190 + 0.897414i \(0.645444\pi\)
\(830\) −7.68527e6 1.33113e7i −0.387225 0.670694i
\(831\) 0 0
\(832\) 4.39531e6 0.220131
\(833\) −3.28187e6 1.69397e7i −0.163874 0.845849i
\(834\) 0 0
\(835\) 1.65051e7 2.85877e7i 0.819222 1.41893i
\(836\) 370472. + 641676.i 0.0183332 + 0.0317541i
\(837\) 0 0
\(838\) 2.07664e6 3.59685e6i 0.102153 0.176935i
\(839\) −4.28039e6 −0.209932 −0.104966 0.994476i \(-0.533473\pi\)
−0.104966 + 0.994476i \(0.533473\pi\)
\(840\) 0 0
\(841\) 1.12255e7 0.547286
\(842\) 1.53330e6 2.65575e6i 0.0745325 0.129094i
\(843\) 0 0
\(844\) 9.51869e6 + 1.64869e7i 0.459961 + 0.796676i
\(845\) 1.22772e7 2.12648e7i 0.591504 1.02452i
\(846\) 0 0
\(847\) 1.60762e7 + 1.32606e7i 0.769974 + 0.635117i
\(848\) 8.27933e6 0.395372
\(849\) 0 0
\(850\) −397446. 688396.i −0.0188682 0.0326807i
\(851\) 9.89342e6 + 1.71359e7i 0.468298 + 0.811116i
\(852\) 0 0
\(853\) −1.72415e7 −0.811341 −0.405670 0.914019i \(-0.632962\pi\)
−0.405670 + 0.914019i \(0.632962\pi\)
\(854\) −7.63519e6 + 2.85199e6i −0.358241 + 0.133815i
\(855\) 0 0
\(856\) −221342. + 383376.i −0.0103248 + 0.0178830i
\(857\) 1.04170e7 + 1.80427e7i 0.484495 + 0.839171i 0.999841 0.0178115i \(-0.00566989\pi\)
−0.515346 + 0.856982i \(0.672337\pi\)
\(858\) 0 0
\(859\) 7.91782e6 1.37141e7i 0.366119 0.634137i −0.622836 0.782353i \(-0.714020\pi\)
0.988955 + 0.148215i \(0.0473529\pi\)
\(860\) −2.32720e6 −0.107297
\(861\) 0 0
\(862\) 1.70757e7 0.782726
\(863\) −7.96408e6 + 1.37942e7i −0.364006 + 0.630477i −0.988616 0.150460i \(-0.951925\pi\)
0.624610 + 0.780937i \(0.285258\pi\)
\(864\) 0 0
\(865\) 1.92447e7 + 3.33328e7i 0.874523 + 1.51472i
\(866\) 4.45368e6 7.71400e6i 0.201801 0.349530i
\(867\) 0 0
\(868\) −7.57095e6 6.24494e6i −0.341076 0.281338i
\(869\) 1.54149e6 0.0692455
\(870\) 0 0
\(871\) −2.09191e7 3.62330e7i −0.934325 1.61830i
\(872\) 1.28972e7 + 2.23386e7i 0.574387 + 0.994868i
\(873\) 0 0
\(874\) −1.88159e7 −0.833195
\(875\) −3.55747e6 + 2.12183e7i −0.157080 + 0.936896i
\(876\) 0 0
\(877\) −2.60367e6 + 4.50969e6i −0.114311 + 0.197992i −0.917504 0.397727i \(-0.869799\pi\)
0.803193 + 0.595718i \(0.203133\pi\)
\(878\) 3.16723e6 + 5.48581e6i 0.138658 + 0.240162i
\(879\) 0 0
\(880\) −181026. + 313546.i −0.00788013 + 0.0136488i
\(881\) 932829. 0.0404913 0.0202457 0.999795i \(-0.493555\pi\)
0.0202457 + 0.999795i \(0.493555\pi\)
\(882\) 0 0
\(883\) 1.33789e7 0.577457 0.288728 0.957411i \(-0.406768\pi\)
0.288728 + 0.957411i \(0.406768\pi\)
\(884\) −1.11681e7 + 1.93437e7i −0.480670 + 0.832546i
\(885\) 0 0
\(886\) −2.10601e6 3.64771e6i −0.0901313 0.156112i
\(887\) −3.48450e6 + 6.03533e6i −0.148707 + 0.257568i −0.930750 0.365657i \(-0.880844\pi\)
0.782043 + 0.623225i \(0.214178\pi\)
\(888\) 0 0
\(889\) 5.01064e6 2.98857e7i 0.212637 1.26826i
\(890\) 7.46004e6 0.315694
\(891\) 0 0
\(892\) 9.02216e6 + 1.56268e7i 0.379663 + 0.657596i
\(893\) 8.35369e6 + 1.44690e7i 0.350550 + 0.607170i
\(894\) 0 0
\(895\) 9.64753e6 0.402586
\(896\) −1.76602e7 1.45671e7i −0.734894 0.606182i
\(897\) 0 0
\(898\) 4.88788e6 8.46606e6i 0.202269 0.350341i
\(899\) −8.72220e6 1.51073e7i −0.359937 0.623429i
\(900\) 0 0
\(901\) 1.19380e7 2.06772e7i 0.489913 0.848554i
\(902\) −879496. −0.0359929
\(903\) 0 0
\(904\) −4.03804e7 −1.64342
\(905\) 4.33353e6 7.50590e6i 0.175882 0.304636i
\(906\) 0 0
\(907\) 1.88282e7 + 3.26113e7i 0.759959 + 1.31629i 0.942871 + 0.333158i \(0.108114\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(908\) 6.65113e6 1.15201e7i 0.267720 0.463705i
\(909\) 0 0
\(910\) 1.73362e7 6.47565e6i 0.693987 0.259227i
\(911\) 3.09942e7 1.23733 0.618663 0.785657i \(-0.287675\pi\)
0.618663 + 0.785657i \(0.287675\pi\)
\(912\) 0 0
\(913\) 834823. + 1.44596e6i 0.0331450 + 0.0574087i
\(914\) 3.46110e6 + 5.99479e6i 0.137040 + 0.237361i
\(915\) 0 0
\(916\) 5.71002e6 0.224853
\(917\) −1.57304e7 1.29753e7i −0.617757 0.509560i
\(918\) 0 0
\(919\) −358007. + 620086.i −0.0139831 + 0.0242194i −0.872932 0.487841i \(-0.837784\pi\)
0.858949 + 0.512061i \(0.171118\pi\)
\(920\) −1.78201e7 3.08652e7i −0.694128 1.20226i
\(921\) 0 0
\(922\) 9.11394e6 1.57858e7i 0.353085 0.611561i
\(923\) 1.42357e6 0.0550014
\(924\) 0 0
\(925\) 1.41626e6 0.0544238
\(926\) −6.05193e6 + 1.04823e7i −0.231935 + 0.401723i
\(927\) 0 0
\(928\) −1.67385e7 2.89919e7i −0.638037 1.10511i
\(929\) 2.08815e7 3.61678e7i 0.793820 1.37494i −0.129766 0.991545i \(-0.541423\pi\)
0.923586 0.383392i \(-0.125244\pi\)
\(930\) 0 0
\(931\) −2.20751e7 + 1.91657e7i −0.834698 + 0.724686i
\(932\) −1.51110e7 −0.569840
\(933\) 0 0
\(934\) −337813. 585109.i −0.0126709 0.0219467i
\(935\) 522043. + 904204.i 0.0195289 + 0.0338250i
\(936\) 0 0
\(937\) −2.17917e7 −0.810854 −0.405427 0.914127i \(-0.632877\pi\)
−0.405427 + 0.914127i \(0.632877\pi\)
\(938\) 2.76960e6 1.65191e7i 0.102780 0.613027i
\(939\) 0 0
\(940\) −6.85302e6 + 1.18698e7i −0.252966 + 0.438150i
\(941\) −1.07609e6 1.86385e6i −0.0396164 0.0686177i 0.845537 0.533916i \(-0.179280\pi\)
−0.885154 + 0.465299i \(0.845947\pi\)
\(942\) 0 0
\(943\) −3.61483e7 + 6.26106e7i −1.32376 + 2.29281i
\(944\) 1.28275e6 0.0468504
\(945\) 0 0
\(946\) −78095.5 −0.00283725
\(947\) −1.32125e7 + 2.28847e7i −0.478750 + 0.829220i −0.999703 0.0243656i \(-0.992243\pi\)
0.520953 + 0.853585i \(0.325577\pi\)
\(948\) 0 0
\(949\) −2.63925e6 4.57132e6i −0.0951295 0.164769i
\(950\) −673383. + 1.16633e6i −0.0242077 + 0.0419289i
\(951\) 0 0
\(952\) −1.93415e7 + 7.22466e6i −0.691667 + 0.258360i
\(953\) −9.07051e6 −0.323519 −0.161759 0.986830i \(-0.551717\pi\)
−0.161759 + 0.986830i \(0.551717\pi\)
\(954\) 0 0
\(955\) −1.12623e7 1.95068e7i −0.399593 0.692115i
\(956\) −1.14598e7 1.98489e7i −0.405538 0.702412i
\(957\) 0 0
\(958\) −110892. −0.00390380
\(959\) 2.08337e7 7.78208e6i 0.731511 0.273243i
\(960\) 0 0
\(961\) 9.52032e6 1.64897e7i 0.332539 0.575975i
\(962\) 6.14709e6 + 1.06471e7i 0.214157 + 0.370930i
\(963\) 0 0
\(964\) 1.13930e7 1.97332e7i 0.394861 0.683920i
\(965\) −2.89674e7 −1.00136
\(966\) 0 0
\(967\) 1.80108e7 0.619395 0.309698 0.950835i \(-0.399772\pi\)
0.309698 + 0.950835i \(0.399772\pi\)
\(968\) 1.24682e7 2.15956e7i 0.427677 0.740758i
\(969\) 0 0
\(970\) 6.09389e6 + 1.05549e7i 0.207953 + 0.360185i
\(971\) −2.33815e7 + 4.04980e7i −0.795838 + 1.37843i 0.126467 + 0.991971i \(0.459636\pi\)
−0.922305 + 0.386462i \(0.873697\pi\)
\(972\) 0 0
\(973\) −4.51509e6 + 2.69300e7i −0.152892 + 0.911914i
\(974\) 9.09561e6 0.307209
\(975\) 0 0
\(976\) −4.07204e6 7.05298e6i −0.136832 0.237000i
\(977\) 2.16217e6 + 3.74498e6i 0.0724690 + 0.125520i 0.899983 0.435925i \(-0.143579\pi\)
−0.827514 + 0.561445i \(0.810245\pi\)
\(978\) 0 0
\(979\) −810357. −0.0270221
\(980\) −2.26710e7 7.82195e6i −0.754061 0.260165i
\(981\) 0 0
\(982\) 2.72013e6 4.71140e6i 0.0900142 0.155909i
\(983\) 1.04367e7 + 1.80768e7i 0.344491 + 0.596676i 0.985261 0.171057i \(-0.0547181\pi\)
−0.640770 + 0.767733i \(0.721385\pi\)
\(984\) 0 0
\(985\) −1.28828e7 + 2.23137e7i −0.423077 + 0.732792i
\(986\) −1.58943e7 −0.520655
\(987\) 0 0
\(988\) 3.78436e7 1.23339
\(989\) −3.20981e6 + 5.55956e6i −0.104349 + 0.180738i
\(990\) 0 0
\(991\) −2.06104e7 3.56983e7i −0.666658 1.15469i −0.978833 0.204661i \(-0.934391\pi\)
0.312175 0.950025i \(-0.398942\pi\)
\(992\) −9.20049e6 + 1.59357e7i −0.296846 + 0.514153i
\(993\) 0 0
\(994\) 439649. + 362647.i 0.0141137 + 0.0116418i
\(995\) 4.42650e6 0.141743
\(996\) 0 0
\(997\) 2.67307e7 + 4.62990e7i 0.851674 + 1.47514i 0.879697 + 0.475535i \(0.157745\pi\)
−0.0280235 + 0.999607i \(0.508921\pi\)
\(998\) −4.35580e6 7.54447e6i −0.138434 0.239774i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.6.e.e.37.3 8
3.2 odd 2 21.6.e.c.16.2 yes 8
7.2 even 3 441.6.a.w.1.2 4
7.4 even 3 inner 63.6.e.e.46.3 8
7.5 odd 6 441.6.a.v.1.2 4
12.11 even 2 336.6.q.j.289.1 8
21.2 odd 6 147.6.a.m.1.3 4
21.5 even 6 147.6.a.l.1.3 4
21.11 odd 6 21.6.e.c.4.2 8
21.17 even 6 147.6.e.o.67.2 8
21.20 even 2 147.6.e.o.79.2 8
84.11 even 6 336.6.q.j.193.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.e.c.4.2 8 21.11 odd 6
21.6.e.c.16.2 yes 8 3.2 odd 2
63.6.e.e.37.3 8 1.1 even 1 trivial
63.6.e.e.46.3 8 7.4 even 3 inner
147.6.a.l.1.3 4 21.5 even 6
147.6.a.m.1.3 4 21.2 odd 6
147.6.e.o.67.2 8 21.17 even 6
147.6.e.o.79.2 8 21.20 even 2
336.6.q.j.193.1 8 84.11 even 6
336.6.q.j.289.1 8 12.11 even 2
441.6.a.v.1.2 4 7.5 odd 6
441.6.a.w.1.2 4 7.2 even 3