Properties

Label 15.5.c.a.11.4
Level $15$
Weight $5$
Character 15.11
Analytic conductor $1.551$
Analytic rank $0$
Dimension $6$
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] = [15,5,Mod(11,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.11");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 15.c (of order \(2\), degree \(1\), 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: \(1.55054944626\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 73x^{4} + 1096x^{2} + 180 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.4
Root \(0.407512i\) of defining polynomial
Character \(\chi\) \(=\) 15.11
Dual form 15.5.c.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.407512i q^{2} +(3.21297 - 8.40695i) q^{3} +15.8339 q^{4} +11.1803i q^{5} +(3.42594 + 1.30932i) q^{6} -46.9457 q^{7} +12.9727i q^{8} +(-60.3537 - 54.0225i) q^{9} +O(q^{10})\) \(q+0.407512i q^{2} +(3.21297 - 8.40695i) q^{3} +15.8339 q^{4} +11.1803i q^{5} +(3.42594 + 1.30932i) q^{6} -46.9457 q^{7} +12.9727i q^{8} +(-60.3537 - 54.0225i) q^{9} -4.55613 q^{10} +200.952i q^{11} +(50.8739 - 133.115i) q^{12} -22.3321 q^{13} -19.1309i q^{14} +(93.9926 + 35.9221i) q^{15} +248.056 q^{16} -344.602i q^{17} +(22.0148 - 24.5949i) q^{18} -59.9990 q^{19} +177.029i q^{20} +(-150.835 + 394.670i) q^{21} -81.8903 q^{22} -212.905i q^{23} +(109.061 + 41.6809i) q^{24} -125.000 q^{25} -9.10062i q^{26} +(-648.079 + 333.818i) q^{27} -743.335 q^{28} -578.043i q^{29} +(-14.6387 + 38.3031i) q^{30} +490.110 q^{31} +308.650i q^{32} +(1689.39 + 645.652i) q^{33} +140.429 q^{34} -524.869i q^{35} +(-955.636 - 855.389i) q^{36} +1936.81 q^{37} -24.4503i q^{38} +(-71.7524 + 187.745i) q^{39} -145.039 q^{40} -1638.25i q^{41} +(-160.833 - 61.4671i) q^{42} -2160.31 q^{43} +3181.86i q^{44} +(603.990 - 674.775i) q^{45} +86.7615 q^{46} +2282.28i q^{47} +(796.997 - 2085.40i) q^{48} -197.104 q^{49} -50.9390i q^{50} +(-2897.05 - 1107.19i) q^{51} -353.606 q^{52} +2626.84i q^{53} +(-136.035 - 264.100i) q^{54} -2246.71 q^{55} -609.013i q^{56} +(-192.775 + 504.409i) q^{57} +235.560 q^{58} -4106.06i q^{59} +(1488.27 + 568.788i) q^{60} +4790.63 q^{61} +199.726i q^{62} +(2833.34 + 2536.12i) q^{63} +3843.12 q^{64} -249.681i q^{65} +(-263.111 + 688.448i) q^{66} -1565.70 q^{67} -5456.40i q^{68} +(-1789.88 - 684.058i) q^{69} +213.890 q^{70} +5372.27i q^{71} +(700.819 - 782.951i) q^{72} -4321.67 q^{73} +789.274i q^{74} +(-401.621 + 1050.87i) q^{75} -950.020 q^{76} -9433.82i q^{77} +(-76.5085 - 29.2400i) q^{78} -4801.14 q^{79} +2773.35i q^{80} +(724.132 + 6520.92i) q^{81} +667.606 q^{82} +3384.94i q^{83} +(-2388.31 + 6249.18i) q^{84} +3852.77 q^{85} -880.352i q^{86} +(-4859.58 - 1857.23i) q^{87} -2606.89 q^{88} -3446.38i q^{89} +(274.979 + 246.133i) q^{90} +1048.40 q^{91} -3371.13i q^{92} +(1574.71 - 4120.33i) q^{93} -930.059 q^{94} -670.809i q^{95} +(2594.80 + 991.681i) q^{96} +5447.68 q^{97} -80.3221i q^{98} +(10855.9 - 12128.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 8 q^{3} - 50 q^{4} - 2 q^{6} + 76 q^{7} + 118 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 8 q^{3} - 50 q^{4} - 2 q^{6} + 76 q^{7} + 118 q^{9} + 50 q^{10} - 452 q^{12} - 424 q^{13} + 50 q^{15} + 802 q^{16} + 1160 q^{18} - 244 q^{19} - 876 q^{21} + 340 q^{22} - 786 q^{24} - 750 q^{25} - 352 q^{27} - 3764 q^{28} + 2200 q^{30} + 3772 q^{31} + 4420 q^{33} + 3124 q^{34} - 7606 q^{36} + 1896 q^{37} - 1336 q^{39} - 4650 q^{40} - 1980 q^{42} - 7384 q^{43} + 1900 q^{45} + 8196 q^{46} + 14668 q^{48} - 1318 q^{49} - 8492 q^{51} + 8976 q^{52} - 278 q^{54} - 1300 q^{55} - 11584 q^{57} - 23740 q^{58} + 5050 q^{60} + 6452 q^{61} + 14796 q^{63} + 3174 q^{64} - 12760 q^{66} + 13816 q^{67} + 5472 q^{69} - 2100 q^{70} - 2040 q^{72} + 596 q^{73} - 1000 q^{75} + 21348 q^{76} - 1400 q^{78} - 16124 q^{79} + 5086 q^{81} - 31240 q^{82} - 14736 q^{84} - 3100 q^{85} - 4900 q^{87} + 15660 q^{88} + 7550 q^{90} - 11632 q^{91} - 8184 q^{93} + 34924 q^{94} + 14354 q^{96} + 9756 q^{97} + 9680 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.407512i 0.101878i 0.998702 + 0.0509390i \(0.0162214\pi\)
−0.998702 + 0.0509390i \(0.983779\pi\)
\(3\) 3.21297 8.40695i 0.356996 0.934106i
\(4\) 15.8339 0.989621
\(5\) 11.1803i 0.447214i
\(6\) 3.42594 + 1.30932i 0.0951649 + 0.0363701i
\(7\) −46.9457 −0.958075 −0.479038 0.877794i \(-0.659014\pi\)
−0.479038 + 0.877794i \(0.659014\pi\)
\(8\) 12.9727i 0.202699i
\(9\) −60.3537 54.0225i −0.745107 0.666945i
\(10\) −4.55613 −0.0455613
\(11\) 200.952i 1.66076i 0.557198 + 0.830379i \(0.311876\pi\)
−0.557198 + 0.830379i \(0.688124\pi\)
\(12\) 50.8739 133.115i 0.353291 0.924411i
\(13\) −22.3321 −0.132143 −0.0660714 0.997815i \(-0.521047\pi\)
−0.0660714 + 0.997815i \(0.521047\pi\)
\(14\) 19.1309i 0.0976068i
\(15\) 93.9926 + 35.9221i 0.417745 + 0.159654i
\(16\) 248.056 0.968970
\(17\) 344.602i 1.19239i −0.802838 0.596197i \(-0.796678\pi\)
0.802838 0.596197i \(-0.203322\pi\)
\(18\) 22.0148 24.5949i 0.0679471 0.0759101i
\(19\) −59.9990 −0.166202 −0.0831011 0.996541i \(-0.526482\pi\)
−0.0831011 + 0.996541i \(0.526482\pi\)
\(20\) 177.029i 0.442572i
\(21\) −150.835 + 394.670i −0.342029 + 0.894943i
\(22\) −81.8903 −0.169195
\(23\) 212.905i 0.402467i −0.979543 0.201234i \(-0.935505\pi\)
0.979543 0.201234i \(-0.0644951\pi\)
\(24\) 109.061 + 41.6809i 0.189342 + 0.0723627i
\(25\) −125.000 −0.200000
\(26\) 9.10062i 0.0134625i
\(27\) −648.079 + 333.818i −0.888998 + 0.457912i
\(28\) −743.335 −0.948131
\(29\) 578.043i 0.687328i −0.939093 0.343664i \(-0.888332\pi\)
0.939093 0.343664i \(-0.111668\pi\)
\(30\) −14.6387 + 38.3031i −0.0162652 + 0.0425590i
\(31\) 490.110 0.510000 0.255000 0.966941i \(-0.417925\pi\)
0.255000 + 0.966941i \(0.417925\pi\)
\(32\) 308.650i 0.301416i
\(33\) 1689.39 + 645.652i 1.55132 + 0.592885i
\(34\) 140.429 0.121479
\(35\) 524.869i 0.428464i
\(36\) −955.636 855.389i −0.737374 0.660023i
\(37\) 1936.81 1.41476 0.707382 0.706832i \(-0.249876\pi\)
0.707382 + 0.706832i \(0.249876\pi\)
\(38\) 24.4503i 0.0169324i
\(39\) −71.7524 + 187.745i −0.0471745 + 0.123435i
\(40\) −145.039 −0.0906496
\(41\) 1638.25i 0.974567i −0.873244 0.487284i \(-0.837988\pi\)
0.873244 0.487284i \(-0.162012\pi\)
\(42\) −160.833 61.4671i −0.0911751 0.0348453i
\(43\) −2160.31 −1.16837 −0.584183 0.811622i \(-0.698585\pi\)
−0.584183 + 0.811622i \(0.698585\pi\)
\(44\) 3181.86i 1.64352i
\(45\) 603.990 674.775i 0.298267 0.333222i
\(46\) 86.7615 0.0410026
\(47\) 2282.28i 1.03318i 0.856234 + 0.516588i \(0.172798\pi\)
−0.856234 + 0.516588i \(0.827202\pi\)
\(48\) 796.997 2085.40i 0.345919 0.905121i
\(49\) −197.104 −0.0820923
\(50\) 50.9390i 0.0203756i
\(51\) −2897.05 1107.19i −1.11382 0.425680i
\(52\) −353.606 −0.130771
\(53\) 2626.84i 0.935151i 0.883953 + 0.467575i \(0.154872\pi\)
−0.883953 + 0.467575i \(0.845128\pi\)
\(54\) −136.035 264.100i −0.0466512 0.0905694i
\(55\) −2246.71 −0.742714
\(56\) 609.013i 0.194201i
\(57\) −192.775 + 504.409i −0.0593336 + 0.155250i
\(58\) 235.560 0.0700237
\(59\) 4106.06i 1.17956i −0.807563 0.589782i \(-0.799214\pi\)
0.807563 0.589782i \(-0.200786\pi\)
\(60\) 1488.27 + 568.788i 0.413409 + 0.157997i
\(61\) 4790.63 1.28746 0.643729 0.765254i \(-0.277386\pi\)
0.643729 + 0.765254i \(0.277386\pi\)
\(62\) 199.726i 0.0519578i
\(63\) 2833.34 + 2536.12i 0.713868 + 0.638983i
\(64\) 3843.12 0.938263
\(65\) 249.681i 0.0590961i
\(66\) −263.111 + 688.448i −0.0604020 + 0.158046i
\(67\) −1565.70 −0.348785 −0.174393 0.984676i \(-0.555796\pi\)
−0.174393 + 0.984676i \(0.555796\pi\)
\(68\) 5456.40i 1.18002i
\(69\) −1789.88 684.058i −0.375947 0.143679i
\(70\) 213.890 0.0436511
\(71\) 5372.27i 1.06571i 0.846205 + 0.532857i \(0.178882\pi\)
−0.846205 + 0.532857i \(0.821118\pi\)
\(72\) 700.819 782.951i 0.135189 0.151032i
\(73\) −4321.67 −0.810972 −0.405486 0.914101i \(-0.632898\pi\)
−0.405486 + 0.914101i \(0.632898\pi\)
\(74\) 789.274i 0.144133i
\(75\) −401.621 + 1050.87i −0.0713993 + 0.186821i
\(76\) −950.020 −0.164477
\(77\) 9433.82i 1.59113i
\(78\) −76.5085 29.2400i −0.0125754 0.00480605i
\(79\) −4801.14 −0.769290 −0.384645 0.923065i \(-0.625676\pi\)
−0.384645 + 0.923065i \(0.625676\pi\)
\(80\) 2773.35i 0.433337i
\(81\) 724.132 + 6520.92i 0.110369 + 0.993891i
\(82\) 667.606 0.0992870
\(83\) 3384.94i 0.491354i 0.969352 + 0.245677i \(0.0790103\pi\)
−0.969352 + 0.245677i \(0.920990\pi\)
\(84\) −2388.31 + 6249.18i −0.338479 + 0.885655i
\(85\) 3852.77 0.533255
\(86\) 880.352i 0.119031i
\(87\) −4859.58 1857.23i −0.642037 0.245374i
\(88\) −2606.89 −0.336634
\(89\) 3446.38i 0.435094i −0.976050 0.217547i \(-0.930194\pi\)
0.976050 0.217547i \(-0.0698056\pi\)
\(90\) 274.979 + 246.133i 0.0339480 + 0.0303868i
\(91\) 1048.40 0.126603
\(92\) 3371.13i 0.398290i
\(93\) 1574.71 4120.33i 0.182068 0.476394i
\(94\) −930.059 −0.105258
\(95\) 670.809i 0.0743279i
\(96\) 2594.80 + 991.681i 0.281554 + 0.107604i
\(97\) 5447.68 0.578986 0.289493 0.957180i \(-0.406513\pi\)
0.289493 + 0.957180i \(0.406513\pi\)
\(98\) 80.3221i 0.00836340i
\(99\) 10855.9 12128.2i 1.10763 1.23744i
\(100\) −1979.24 −0.197924
\(101\) 7655.22i 0.750438i 0.926936 + 0.375219i \(0.122433\pi\)
−0.926936 + 0.375219i \(0.877567\pi\)
\(102\) 451.195 1180.58i 0.0433675 0.113474i
\(103\) 16163.7 1.52358 0.761790 0.647824i \(-0.224321\pi\)
0.761790 + 0.647824i \(0.224321\pi\)
\(104\) 289.708i 0.0267852i
\(105\) −4412.55 1686.39i −0.400231 0.152960i
\(106\) −1070.47 −0.0952713
\(107\) 18944.3i 1.65466i 0.561713 + 0.827332i \(0.310143\pi\)
−0.561713 + 0.827332i \(0.689857\pi\)
\(108\) −10261.6 + 5285.65i −0.879771 + 0.453159i
\(109\) −4373.48 −0.368107 −0.184053 0.982916i \(-0.558922\pi\)
−0.184053 + 0.982916i \(0.558922\pi\)
\(110\) 915.562i 0.0756663i
\(111\) 6222.91 16282.7i 0.505065 1.32154i
\(112\) −11645.2 −0.928346
\(113\) 1242.99i 0.0973443i −0.998815 0.0486722i \(-0.984501\pi\)
0.998815 0.0486722i \(-0.0154990\pi\)
\(114\) −205.553 78.5581i −0.0158166 0.00604479i
\(115\) 2380.35 0.179989
\(116\) 9152.69i 0.680194i
\(117\) 1347.83 + 1206.44i 0.0984605 + 0.0881320i
\(118\) 1673.27 0.120172
\(119\) 16177.6i 1.14240i
\(120\) −466.007 + 1219.34i −0.0323616 + 0.0846763i
\(121\) −25740.6 −1.75812
\(122\) 1952.24i 0.131164i
\(123\) −13772.7 5263.64i −0.910349 0.347917i
\(124\) 7760.36 0.504706
\(125\) 1397.54i 0.0894427i
\(126\) −1033.50 + 1154.62i −0.0650984 + 0.0727275i
\(127\) 4143.92 0.256924 0.128462 0.991714i \(-0.458996\pi\)
0.128462 + 0.991714i \(0.458996\pi\)
\(128\) 6504.51i 0.397004i
\(129\) −6941.00 + 18161.6i −0.417102 + 1.09138i
\(130\) 101.748 0.00602059
\(131\) 23414.5i 1.36440i −0.731166 0.682200i \(-0.761023\pi\)
0.731166 0.682200i \(-0.238977\pi\)
\(132\) 26749.7 + 10223.2i 1.53522 + 0.586731i
\(133\) 2816.69 0.159234
\(134\) 638.041i 0.0355336i
\(135\) −3732.20 7245.75i −0.204784 0.397572i
\(136\) 4470.42 0.241697
\(137\) 4168.41i 0.222090i −0.993815 0.111045i \(-0.964580\pi\)
0.993815 0.111045i \(-0.0354198\pi\)
\(138\) 278.762 729.400i 0.0146378 0.0383008i
\(139\) 6702.86 0.346921 0.173460 0.984841i \(-0.444505\pi\)
0.173460 + 0.984841i \(0.444505\pi\)
\(140\) 8310.73i 0.424017i
\(141\) 19187.1 + 7332.91i 0.965095 + 0.368840i
\(142\) −2189.26 −0.108573
\(143\) 4487.68i 0.219457i
\(144\) −14971.1 13400.6i −0.721987 0.646250i
\(145\) 6462.72 0.307382
\(146\) 1761.13i 0.0826203i
\(147\) −633.287 + 1657.04i −0.0293067 + 0.0766829i
\(148\) 30667.3 1.40008
\(149\) 7267.97i 0.327371i −0.986513 0.163686i \(-0.947662\pi\)
0.986513 0.163686i \(-0.0523383\pi\)
\(150\) −428.242 163.665i −0.0190330 0.00727402i
\(151\) −17022.9 −0.746584 −0.373292 0.927714i \(-0.621771\pi\)
−0.373292 + 0.927714i \(0.621771\pi\)
\(152\) 778.350i 0.0336890i
\(153\) −18616.3 + 20798.0i −0.795261 + 0.888461i
\(154\) 3844.40 0.162101
\(155\) 5479.59i 0.228079i
\(156\) −1136.12 + 2972.74i −0.0466849 + 0.122154i
\(157\) −11560.8 −0.469017 −0.234509 0.972114i \(-0.575348\pi\)
−0.234509 + 0.972114i \(0.575348\pi\)
\(158\) 1956.52i 0.0783738i
\(159\) 22083.7 + 8439.95i 0.873530 + 0.333845i
\(160\) −3450.81 −0.134797
\(161\) 9994.98i 0.385594i
\(162\) −2657.35 + 295.093i −0.101256 + 0.0112442i
\(163\) −6066.12 −0.228316 −0.114158 0.993463i \(-0.536417\pi\)
−0.114158 + 0.993463i \(0.536417\pi\)
\(164\) 25939.9i 0.964452i
\(165\) −7218.61 + 18888.0i −0.265146 + 0.693773i
\(166\) −1379.40 −0.0500582
\(167\) 6974.71i 0.250088i −0.992151 0.125044i \(-0.960093\pi\)
0.992151 0.125044i \(-0.0399073\pi\)
\(168\) −5119.94 1956.74i −0.181404 0.0693289i
\(169\) −28062.3 −0.982538
\(170\) 1570.05i 0.0543270i
\(171\) 3621.16 + 3241.30i 0.123838 + 0.110848i
\(172\) −34206.2 −1.15624
\(173\) 27868.0i 0.931135i −0.885012 0.465568i \(-0.845850\pi\)
0.885012 0.465568i \(-0.154150\pi\)
\(174\) 756.845 1980.34i 0.0249982 0.0654095i
\(175\) 5868.21 0.191615
\(176\) 49847.4i 1.60923i
\(177\) −34519.4 13192.6i −1.10184 0.421100i
\(178\) 1404.44 0.0443266
\(179\) 22242.5i 0.694189i 0.937830 + 0.347095i \(0.112832\pi\)
−0.937830 + 0.347095i \(0.887168\pi\)
\(180\) 9563.54 10684.3i 0.295171 0.329763i
\(181\) 33471.7 1.02169 0.510847 0.859672i \(-0.329332\pi\)
0.510847 + 0.859672i \(0.329332\pi\)
\(182\) 427.235i 0.0128980i
\(183\) 15392.1 40274.6i 0.459618 1.20262i
\(184\) 2761.96 0.0815796
\(185\) 21654.2i 0.632701i
\(186\) 1679.08 + 641.712i 0.0485341 + 0.0185487i
\(187\) 69248.4 1.98028
\(188\) 36137.5i 1.02245i
\(189\) 30424.5 15671.3i 0.851726 0.438714i
\(190\) 273.363 0.00757238
\(191\) 602.154i 0.0165060i −0.999966 0.00825298i \(-0.997373\pi\)
0.999966 0.00825298i \(-0.00262704\pi\)
\(192\) 12347.8 32309.0i 0.334956 0.876437i
\(193\) −27201.4 −0.730259 −0.365130 0.930957i \(-0.618975\pi\)
−0.365130 + 0.930957i \(0.618975\pi\)
\(194\) 2220.00i 0.0589860i
\(195\) −2099.05 802.217i −0.0552020 0.0210971i
\(196\) −3120.92 −0.0812402
\(197\) 61640.6i 1.58831i −0.607717 0.794154i \(-0.707915\pi\)
0.607717 0.794154i \(-0.292085\pi\)
\(198\) 4942.38 + 4423.92i 0.126068 + 0.112844i
\(199\) −10712.4 −0.270507 −0.135254 0.990811i \(-0.543185\pi\)
−0.135254 + 0.990811i \(0.543185\pi\)
\(200\) 1621.59i 0.0405397i
\(201\) −5030.53 + 13162.7i −0.124515 + 0.325802i
\(202\) −3119.60 −0.0764532
\(203\) 27136.6i 0.658512i
\(204\) −45871.7 17531.2i −1.10226 0.421262i
\(205\) 18316.2 0.435840
\(206\) 6586.89i 0.155219i
\(207\) −11501.7 + 12849.6i −0.268424 + 0.299881i
\(208\) −5539.63 −0.128042
\(209\) 12056.9i 0.276022i
\(210\) 687.223 1798.17i 0.0155833 0.0407747i
\(211\) 19405.1 0.435865 0.217933 0.975964i \(-0.430069\pi\)
0.217933 + 0.975964i \(0.430069\pi\)
\(212\) 41593.2i 0.925445i
\(213\) 45164.4 + 17260.9i 0.995490 + 0.380456i
\(214\) −7720.02 −0.168574
\(215\) 24153.0i 0.522509i
\(216\) −4330.52 8407.35i −0.0928182 0.180199i
\(217\) −23008.5 −0.488618
\(218\) 1782.25i 0.0375020i
\(219\) −13885.4 + 36332.1i −0.289514 + 0.757534i
\(220\) −35574.3 −0.735005
\(221\) 7695.70i 0.157566i
\(222\) 6635.39 + 2535.91i 0.134636 + 0.0514551i
\(223\) −60220.2 −1.21097 −0.605484 0.795857i \(-0.707021\pi\)
−0.605484 + 0.795857i \(0.707021\pi\)
\(224\) 14489.8i 0.288779i
\(225\) 7544.21 + 6752.82i 0.149021 + 0.133389i
\(226\) 506.534 0.00991725
\(227\) 52638.3i 1.02153i 0.859721 + 0.510764i \(0.170637\pi\)
−0.859721 + 0.510764i \(0.829363\pi\)
\(228\) −3052.38 + 7986.77i −0.0587177 + 0.153639i
\(229\) 54102.0 1.03167 0.515837 0.856687i \(-0.327481\pi\)
0.515837 + 0.856687i \(0.327481\pi\)
\(230\) 970.023i 0.0183369i
\(231\) −79309.7 30310.6i −1.48629 0.568028i
\(232\) 7498.79 0.139321
\(233\) 82178.1i 1.51372i −0.653580 0.756858i \(-0.726734\pi\)
0.653580 0.756858i \(-0.273266\pi\)
\(234\) −491.638 + 549.256i −0.00897871 + 0.0100310i
\(235\) −25516.7 −0.462050
\(236\) 65015.1i 1.16732i
\(237\) −15425.9 + 40362.9i −0.274634 + 0.718598i
\(238\) −6592.56 −0.116386
\(239\) 44047.8i 0.771132i 0.922680 + 0.385566i \(0.125994\pi\)
−0.922680 + 0.385566i \(0.874006\pi\)
\(240\) 23315.5 + 8910.70i 0.404782 + 0.154700i
\(241\) 11775.6 0.202744 0.101372 0.994849i \(-0.467677\pi\)
0.101372 + 0.994849i \(0.467677\pi\)
\(242\) 10489.6i 0.179114i
\(243\) 57147.6 + 14863.8i 0.967800 + 0.251719i
\(244\) 75854.5 1.27410
\(245\) 2203.68i 0.0367128i
\(246\) 2145.00 5612.53i 0.0354451 0.0927446i
\(247\) 1339.91 0.0219624
\(248\) 6358.05i 0.103376i
\(249\) 28457.0 + 10875.7i 0.458977 + 0.175412i
\(250\) 569.516 0.00911225
\(251\) 114693.i 1.82050i −0.414061 0.910249i \(-0.635890\pi\)
0.414061 0.910249i \(-0.364110\pi\)
\(252\) 44863.0 + 40156.8i 0.706459 + 0.632351i
\(253\) 42783.7 0.668401
\(254\) 1688.70i 0.0261749i
\(255\) 12378.8 32390.0i 0.190370 0.498116i
\(256\) 58839.3 0.897817
\(257\) 44360.2i 0.671626i 0.941929 + 0.335813i \(0.109011\pi\)
−0.941929 + 0.335813i \(0.890989\pi\)
\(258\) −7401.08 2828.54i −0.111187 0.0424936i
\(259\) −90924.9 −1.35545
\(260\) 3953.43i 0.0584827i
\(261\) −31227.3 + 34887.0i −0.458410 + 0.512133i
\(262\) 9541.68 0.139002
\(263\) 61162.6i 0.884249i 0.896954 + 0.442124i \(0.145775\pi\)
−0.896954 + 0.442124i \(0.854225\pi\)
\(264\) −8375.86 + 21916.0i −0.120177 + 0.314451i
\(265\) −29368.9 −0.418212
\(266\) 1147.84i 0.0162225i
\(267\) −28973.6 11073.1i −0.406424 0.155327i
\(268\) −24791.1 −0.345165
\(269\) 54930.0i 0.759110i −0.925169 0.379555i \(-0.876077\pi\)
0.925169 0.379555i \(-0.123923\pi\)
\(270\) 2952.73 1520.92i 0.0405038 0.0208630i
\(271\) −48199.5 −0.656302 −0.328151 0.944625i \(-0.606425\pi\)
−0.328151 + 0.944625i \(0.606425\pi\)
\(272\) 85480.7i 1.15539i
\(273\) 3368.47 8813.82i 0.0451967 0.118260i
\(274\) 1698.68 0.0226261
\(275\) 25119.0i 0.332152i
\(276\) −28340.9 10831.3i −0.372045 0.142188i
\(277\) 101493. 1.32275 0.661375 0.750056i \(-0.269973\pi\)
0.661375 + 0.750056i \(0.269973\pi\)
\(278\) 2731.50i 0.0353436i
\(279\) −29579.9 26477.0i −0.380004 0.340142i
\(280\) 6808.97 0.0868491
\(281\) 120902.i 1.53117i 0.643337 + 0.765583i \(0.277549\pi\)
−0.643337 + 0.765583i \(0.722451\pi\)
\(282\) −2988.25 + 7818.96i −0.0375767 + 0.0983220i
\(283\) −111286. −1.38953 −0.694767 0.719235i \(-0.744493\pi\)
−0.694767 + 0.719235i \(0.744493\pi\)
\(284\) 85064.1i 1.05465i
\(285\) −5639.46 2155.29i −0.0694301 0.0265348i
\(286\) 1828.79 0.0223579
\(287\) 76908.6i 0.933708i
\(288\) 16674.0 18628.1i 0.201028 0.224587i
\(289\) −35229.5 −0.421804
\(290\) 2633.64i 0.0313155i
\(291\) 17503.2 45798.4i 0.206696 0.540834i
\(292\) −68429.1 −0.802555
\(293\) 64072.7i 0.746342i 0.927763 + 0.373171i \(0.121730\pi\)
−0.927763 + 0.373171i \(0.878270\pi\)
\(294\) −675.264 258.072i −0.00781230 0.00298570i
\(295\) 45907.1 0.527517
\(296\) 25125.7i 0.286771i
\(297\) −67081.3 130233.i −0.760481 1.47641i
\(298\) 2961.79 0.0333520
\(299\) 4754.63i 0.0531832i
\(300\) −6359.24 + 16639.4i −0.0706582 + 0.184882i
\(301\) 101417. 1.11938
\(302\) 6937.02i 0.0760605i
\(303\) 64357.1 + 24596.0i 0.700989 + 0.267904i
\(304\) −14883.1 −0.161045
\(305\) 53560.9i 0.575769i
\(306\) −8475.44 7586.36i −0.0905147 0.0810197i
\(307\) 33666.4 0.357207 0.178604 0.983921i \(-0.442842\pi\)
0.178604 + 0.983921i \(0.442842\pi\)
\(308\) 149374.i 1.57462i
\(309\) 51933.3 135887.i 0.543913 1.42318i
\(310\) −2233.00 −0.0232362
\(311\) 58424.9i 0.604056i 0.953299 + 0.302028i \(0.0976636\pi\)
−0.953299 + 0.302028i \(0.902336\pi\)
\(312\) −2435.57 930.824i −0.0250202 0.00956221i
\(313\) 40228.4 0.410624 0.205312 0.978697i \(-0.434179\pi\)
0.205312 + 0.978697i \(0.434179\pi\)
\(314\) 4711.17i 0.0477826i
\(315\) −28354.7 + 31677.7i −0.285762 + 0.319252i
\(316\) −76020.9 −0.761305
\(317\) 114181.i 1.13625i −0.822943 0.568124i \(-0.807669\pi\)
0.822943 0.568124i \(-0.192331\pi\)
\(318\) −3439.38 + 8999.38i −0.0340115 + 0.0889935i
\(319\) 116159. 1.14149
\(320\) 42967.4i 0.419604i
\(321\) 159263. + 60867.3i 1.54563 + 0.590709i
\(322\) −4073.08 −0.0392836
\(323\) 20675.8i 0.198178i
\(324\) 11465.9 + 103252.i 0.109224 + 0.983575i
\(325\) 2791.52 0.0264286
\(326\) 2472.02i 0.0232604i
\(327\) −14051.8 + 36767.6i −0.131413 + 0.343851i
\(328\) 21252.5 0.197544
\(329\) 107143.i 0.989860i
\(330\) −7697.08 2941.67i −0.0706803 0.0270126i
\(331\) 479.214 0.00437395 0.00218698 0.999998i \(-0.499304\pi\)
0.00218698 + 0.999998i \(0.499304\pi\)
\(332\) 53596.9i 0.486254i
\(333\) −116894. 104631.i −1.05415 0.943569i
\(334\) 2842.28 0.0254785
\(335\) 17505.0i 0.155981i
\(336\) −37415.6 + 97900.4i −0.331416 + 0.867174i
\(337\) −139642. −1.22958 −0.614790 0.788691i \(-0.710759\pi\)
−0.614790 + 0.788691i \(0.710759\pi\)
\(338\) 11435.7i 0.100099i
\(339\) −10449.8 3993.69i −0.0909299 0.0347516i
\(340\) 61004.4 0.527720
\(341\) 98488.4i 0.846986i
\(342\) −1320.87 + 1475.67i −0.0112929 + 0.0126164i
\(343\) 121970. 1.03673
\(344\) 28025.1i 0.236826i
\(345\) 7648.00 20011.5i 0.0642554 0.168129i
\(346\) 11356.5 0.0948623
\(347\) 131835.i 1.09489i −0.836842 0.547445i \(-0.815600\pi\)
0.836842 0.547445i \(-0.184400\pi\)
\(348\) −76946.3 29407.3i −0.635373 0.242827i
\(349\) −238053. −1.95444 −0.977221 0.212222i \(-0.931930\pi\)
−0.977221 + 0.212222i \(0.931930\pi\)
\(350\) 2391.37i 0.0195214i
\(351\) 14473.0 7454.86i 0.117475 0.0605098i
\(352\) −62023.7 −0.500579
\(353\) 181533.i 1.45682i 0.685142 + 0.728410i \(0.259740\pi\)
−0.685142 + 0.728410i \(0.740260\pi\)
\(354\) 5376.16 14067.1i 0.0429008 0.112253i
\(355\) −60063.8 −0.476602
\(356\) 54569.8i 0.430578i
\(357\) 136004. + 51978.0i 1.06713 + 0.407834i
\(358\) −9064.10 −0.0707227
\(359\) 32567.2i 0.252692i −0.991986 0.126346i \(-0.959675\pi\)
0.991986 0.126346i \(-0.0403249\pi\)
\(360\) 8753.66 + 7835.40i 0.0675437 + 0.0604583i
\(361\) −126721. −0.972377
\(362\) 13640.1i 0.104088i
\(363\) −82703.8 + 216400.i −0.627643 + 1.64227i
\(364\) 16600.2 0.125289
\(365\) 48317.8i 0.362678i
\(366\) 16412.4 + 6272.49i 0.122521 + 0.0468250i
\(367\) 117190. 0.870076 0.435038 0.900412i \(-0.356735\pi\)
0.435038 + 0.900412i \(0.356735\pi\)
\(368\) 52812.5i 0.389979i
\(369\) −88502.3 + 98874.2i −0.649983 + 0.726157i
\(370\) −8824.35 −0.0644584
\(371\) 123319.i 0.895945i
\(372\) 24933.8 65241.0i 0.180178 0.471449i
\(373\) 155803. 1.11984 0.559922 0.828546i \(-0.310831\pi\)
0.559922 + 0.828546i \(0.310831\pi\)
\(374\) 28219.6i 0.201747i
\(375\) −11749.1 4490.26i −0.0835490 0.0319307i
\(376\) −29607.4 −0.209423
\(377\) 12908.9i 0.0908255i
\(378\) 6386.25 + 12398.4i 0.0446953 + 0.0867722i
\(379\) 174237. 1.21301 0.606503 0.795082i \(-0.292572\pi\)
0.606503 + 0.795082i \(0.292572\pi\)
\(380\) 10621.5i 0.0735564i
\(381\) 13314.3 34837.8i 0.0917209 0.239994i
\(382\) 245.385 0.00168160
\(383\) 252899.i 1.72405i −0.506869 0.862023i \(-0.669197\pi\)
0.506869 0.862023i \(-0.330803\pi\)
\(384\) 54683.1 + 20898.8i 0.370844 + 0.141729i
\(385\) 105473. 0.711576
\(386\) 11084.9i 0.0743974i
\(387\) 130383. + 116705.i 0.870558 + 0.779235i
\(388\) 86258.2 0.572977
\(389\) 125454.i 0.829058i 0.910036 + 0.414529i \(0.136054\pi\)
−0.910036 + 0.414529i \(0.863946\pi\)
\(390\) 326.913 855.391i 0.00214933 0.00562387i
\(391\) −73367.5 −0.479900
\(392\) 2556.97i 0.0166400i
\(393\) −196844. 75229.9i −1.27449 0.487086i
\(394\) 25119.3 0.161814
\(395\) 53678.3i 0.344037i
\(396\) 171892. 192037.i 1.09614 1.22460i
\(397\) −225399. −1.43012 −0.715059 0.699064i \(-0.753600\pi\)
−0.715059 + 0.699064i \(0.753600\pi\)
\(398\) 4365.42i 0.0275588i
\(399\) 9049.94 23679.8i 0.0568460 0.148742i
\(400\) −31007.0 −0.193794
\(401\) 128670.i 0.800184i −0.916475 0.400092i \(-0.868978\pi\)
0.916475 0.400092i \(-0.131022\pi\)
\(402\) −5363.98 2050.00i −0.0331921 0.0126854i
\(403\) −10945.2 −0.0673928
\(404\) 121212.i 0.742649i
\(405\) −72906.1 + 8096.04i −0.444481 + 0.0493586i
\(406\) −11058.5 −0.0670879
\(407\) 389206.i 2.34958i
\(408\) 14363.3 37582.6i 0.0862849 0.225770i
\(409\) 105708. 0.631917 0.315958 0.948773i \(-0.397674\pi\)
0.315958 + 0.948773i \(0.397674\pi\)
\(410\) 7464.06i 0.0444025i
\(411\) −35043.6 13393.0i −0.207456 0.0792854i
\(412\) 255934. 1.50777
\(413\) 192762.i 1.13011i
\(414\) −5236.37 4687.08i −0.0305513 0.0273465i
\(415\) −37844.8 −0.219740
\(416\) 6892.80i 0.0398299i
\(417\) 21536.1 56350.6i 0.123850 0.324061i
\(418\) 4913.34 0.0281206
\(419\) 157919.i 0.899512i −0.893151 0.449756i \(-0.851511\pi\)
0.893151 0.449756i \(-0.148489\pi\)
\(420\) −69867.9 26702.1i −0.396077 0.151373i
\(421\) −245033. −1.38248 −0.691242 0.722623i \(-0.742936\pi\)
−0.691242 + 0.722623i \(0.742936\pi\)
\(422\) 7907.84i 0.0444051i
\(423\) 123295. 137744.i 0.689071 0.769826i
\(424\) −34077.2 −0.189554
\(425\) 43075.2i 0.238479i
\(426\) −7034.04 + 18405.0i −0.0387602 + 0.101419i
\(427\) −224899. −1.23348
\(428\) 299962.i 1.63749i
\(429\) −37727.7 14418.8i −0.204996 0.0783455i
\(430\) 9842.64 0.0532322
\(431\) 61385.4i 0.330454i −0.986256 0.165227i \(-0.947164\pi\)
0.986256 0.165227i \(-0.0528356\pi\)
\(432\) −160760. + 82805.6i −0.861412 + 0.443703i
\(433\) 25262.9 0.134743 0.0673716 0.997728i \(-0.478539\pi\)
0.0673716 + 0.997728i \(0.478539\pi\)
\(434\) 9376.26i 0.0497795i
\(435\) 20764.5 54331.7i 0.109734 0.287128i
\(436\) −69249.3 −0.364286
\(437\) 12774.1i 0.0668909i
\(438\) −14805.8 5658.47i −0.0771761 0.0294952i
\(439\) −207087. −1.07455 −0.537273 0.843409i \(-0.680545\pi\)
−0.537273 + 0.843409i \(0.680545\pi\)
\(440\) 29145.9i 0.150547i
\(441\) 11895.9 + 10648.0i 0.0611675 + 0.0547510i
\(442\) −3136.09 −0.0160525
\(443\) 132568.i 0.675508i −0.941234 0.337754i \(-0.890333\pi\)
0.941234 0.337754i \(-0.109667\pi\)
\(444\) 98533.2 257819.i 0.499823 1.30782i
\(445\) 38531.7 0.194580
\(446\) 24540.5i 0.123371i
\(447\) −61101.5 23351.8i −0.305799 0.116870i
\(448\) −180418. −0.898926
\(449\) 200739.i 0.995726i 0.867256 + 0.497863i \(0.165882\pi\)
−0.867256 + 0.497863i \(0.834118\pi\)
\(450\) −2751.86 + 3074.36i −0.0135894 + 0.0151820i
\(451\) 329209. 1.61852
\(452\) 19681.4i 0.0963340i
\(453\) −54693.9 + 143110.i −0.266528 + 0.697388i
\(454\) −21450.8 −0.104071
\(455\) 11721.4i 0.0566185i
\(456\) −6543.55 2500.81i −0.0314691 0.0120268i
\(457\) 396196. 1.89705 0.948523 0.316709i \(-0.102578\pi\)
0.948523 + 0.316709i \(0.102578\pi\)
\(458\) 22047.2i 0.105105i
\(459\) 115034. + 223329.i 0.546011 + 1.06004i
\(460\) 37690.3 0.178121
\(461\) 182217.i 0.857405i 0.903446 + 0.428702i \(0.141029\pi\)
−0.903446 + 0.428702i \(0.858971\pi\)
\(462\) 12351.9 32319.7i 0.0578696 0.151420i
\(463\) 181212. 0.845329 0.422665 0.906286i \(-0.361095\pi\)
0.422665 + 0.906286i \(0.361095\pi\)
\(464\) 143387.i 0.666001i
\(465\) 46066.7 + 17605.8i 0.213050 + 0.0814233i
\(466\) 33488.6 0.154214
\(467\) 370180.i 1.69738i −0.528889 0.848691i \(-0.677391\pi\)
0.528889 0.848691i \(-0.322609\pi\)
\(468\) 21341.4 + 19102.7i 0.0974386 + 0.0872172i
\(469\) 73502.7 0.334162
\(470\) 10398.4i 0.0470728i
\(471\) −37144.5 + 97191.1i −0.167437 + 0.438112i
\(472\) 53266.8 0.239096
\(473\) 434118.i 1.94037i
\(474\) −16448.4 6286.24i −0.0732094 0.0279792i
\(475\) 7499.87 0.0332404
\(476\) 256155.i 1.13055i
\(477\) 141908. 158539.i 0.623694 0.696787i
\(478\) −17950.0 −0.0785615
\(479\) 13652.2i 0.0595020i −0.999557 0.0297510i \(-0.990529\pi\)
0.999557 0.0297510i \(-0.00947143\pi\)
\(480\) −11087.3 + 29010.8i −0.0481221 + 0.125915i
\(481\) −43253.1 −0.186951
\(482\) 4798.68i 0.0206551i
\(483\) 84027.3 + 32113.6i 0.360185 + 0.137656i
\(484\) −407575. −1.73987
\(485\) 60906.9i 0.258931i
\(486\) −6057.16 + 23288.4i −0.0256446 + 0.0985976i
\(487\) −193653. −0.816521 −0.408260 0.912865i \(-0.633864\pi\)
−0.408260 + 0.912865i \(0.633864\pi\)
\(488\) 62147.5i 0.260966i
\(489\) −19490.2 + 50997.6i −0.0815079 + 0.213271i
\(490\) 898.029 0.00374023
\(491\) 26447.9i 0.109705i −0.998494 0.0548527i \(-0.982531\pi\)
0.998494 0.0548527i \(-0.0174689\pi\)
\(492\) −218075. 83344.1i −0.900900 0.344306i
\(493\) −199195. −0.819566
\(494\) 546.028i 0.00223749i
\(495\) 135597. + 121373.i 0.553401 + 0.495349i
\(496\) 121575. 0.494175
\(497\) 252205.i 1.02103i
\(498\) −4431.98 + 11596.6i −0.0178706 + 0.0467597i
\(499\) 365043. 1.46603 0.733015 0.680213i \(-0.238113\pi\)
0.733015 + 0.680213i \(0.238113\pi\)
\(500\) 22128.6i 0.0885144i
\(501\) −58636.1 22409.5i −0.233609 0.0892806i
\(502\) 46738.9 0.185469
\(503\) 85439.2i 0.337693i 0.985642 + 0.168846i \(0.0540041\pi\)
−0.985642 + 0.168846i \(0.945996\pi\)
\(504\) −32900.4 + 36756.2i −0.129521 + 0.144700i
\(505\) −85588.0 −0.335606
\(506\) 17434.9i 0.0680954i
\(507\) −90163.2 + 235918.i −0.350763 + 0.917795i
\(508\) 65614.6 0.254257
\(509\) 28412.1i 0.109665i −0.998496 0.0548325i \(-0.982538\pi\)
0.998496 0.0548325i \(-0.0174625\pi\)
\(510\) 13199.3 + 5044.52i 0.0507471 + 0.0193945i
\(511\) 202884. 0.776972
\(512\) 128050.i 0.488472i
\(513\) 38884.1 20028.7i 0.147753 0.0761059i
\(514\) −18077.3 −0.0684239
\(515\) 180715.i 0.681366i
\(516\) −109903. + 287570.i −0.412773 + 1.08005i
\(517\) −458629. −1.71586
\(518\) 37053.0i 0.138091i
\(519\) −234285. 89538.8i −0.869779 0.332412i
\(520\) 3239.04 0.0119787
\(521\) 2801.47i 0.0103208i −0.999987 0.00516038i \(-0.998357\pi\)
0.999987 0.00516038i \(-0.00164261\pi\)
\(522\) −14216.9 12725.5i −0.0521751 0.0467019i
\(523\) −524249. −1.91661 −0.958306 0.285743i \(-0.907760\pi\)
−0.958306 + 0.285743i \(0.907760\pi\)
\(524\) 370743.i 1.35024i
\(525\) 18854.4 49333.8i 0.0684059 0.178989i
\(526\) −24924.5 −0.0900855
\(527\) 168893.i 0.608121i
\(528\) 419065. + 160158.i 1.50319 + 0.574488i
\(529\) 234512. 0.838020
\(530\) 11968.2i 0.0426066i
\(531\) −221820. + 247816.i −0.786704 + 0.878901i
\(532\) 44599.3 0.157581
\(533\) 36585.6i 0.128782i
\(534\) 4512.43 11807.1i 0.0158244 0.0414057i
\(535\) −211803. −0.739988
\(536\) 20311.3i 0.0706983i
\(537\) 186992. + 71464.5i 0.648446 + 0.247823i
\(538\) 22384.6 0.0773367
\(539\) 39608.3i 0.136335i
\(540\) −59095.3 114729.i −0.202659 0.393445i
\(541\) 300315. 1.02608 0.513042 0.858364i \(-0.328519\pi\)
0.513042 + 0.858364i \(0.328519\pi\)
\(542\) 19641.9i 0.0668628i
\(543\) 107544. 281395.i 0.364741 0.954370i
\(544\) 106361. 0.359406
\(545\) 48897.0i 0.164622i
\(546\) 3591.74 + 1372.69i 0.0120481 + 0.00460455i
\(547\) 255317. 0.853307 0.426653 0.904415i \(-0.359692\pi\)
0.426653 + 0.904415i \(0.359692\pi\)
\(548\) 66002.4i 0.219785i
\(549\) −289132. 258802.i −0.959294 0.858663i
\(550\) 10236.3 0.0338390
\(551\) 34682.0i 0.114235i
\(552\) 8874.09 23219.7i 0.0291236 0.0762040i
\(553\) 225393. 0.737037
\(554\) 41359.7i 0.134759i
\(555\) 182046. + 69574.3i 0.591010 + 0.225872i
\(556\) 106133. 0.343320
\(557\) 517752.i 1.66883i 0.551138 + 0.834414i \(0.314194\pi\)
−0.551138 + 0.834414i \(0.685806\pi\)
\(558\) 10789.7 12054.2i 0.0346530 0.0387141i
\(559\) 48244.3 0.154391
\(560\) 130197.i 0.415169i
\(561\) 222493. 582168.i 0.706953 1.84979i
\(562\) −49269.2 −0.155992
\(563\) 353826.i 1.11628i 0.829747 + 0.558139i \(0.188485\pi\)
−0.829747 + 0.558139i \(0.811515\pi\)
\(564\) 303807. + 116109.i 0.955078 + 0.365012i
\(565\) 13897.1 0.0435337
\(566\) 45350.6i 0.141563i
\(567\) −33994.9 306129.i −0.105742 0.952222i
\(568\) −69692.9 −0.216019
\(569\) 570557.i 1.76228i 0.472857 + 0.881139i \(0.343223\pi\)
−0.472857 + 0.881139i \(0.656777\pi\)
\(570\) 878.306 2298.15i 0.00270331 0.00707340i
\(571\) −108185. −0.331815 −0.165908 0.986141i \(-0.553055\pi\)
−0.165908 + 0.986141i \(0.553055\pi\)
\(572\) 71057.7i 0.217180i
\(573\) −5062.28 1934.70i −0.0154183 0.00589257i
\(574\) −31341.2 −0.0951244
\(575\) 26613.2i 0.0804935i
\(576\) −231947. 207615.i −0.699106 0.625769i
\(577\) 161728. 0.485772 0.242886 0.970055i \(-0.421906\pi\)
0.242886 + 0.970055i \(0.421906\pi\)
\(578\) 14356.4i 0.0429725i
\(579\) −87397.3 + 228681.i −0.260700 + 0.682139i
\(580\) 102330. 0.304192
\(581\) 158908.i 0.470754i
\(582\) 18663.4 + 7132.78i 0.0550992 + 0.0210578i
\(583\) −527868. −1.55306
\(584\) 56063.8i 0.164383i
\(585\) −13488.4 + 15069.2i −0.0394138 + 0.0440329i
\(586\) −26110.4 −0.0760359
\(587\) 61507.6i 0.178506i 0.996009 + 0.0892529i \(0.0284479\pi\)
−0.996009 + 0.0892529i \(0.971552\pi\)
\(588\) −10027.4 + 26237.5i −0.0290025 + 0.0758870i
\(589\) −29406.1 −0.0847630
\(590\) 18707.7i 0.0537424i
\(591\) −518210. 198049.i −1.48365 0.567020i
\(592\) 480438. 1.37086
\(593\) 204770.i 0.582313i −0.956675 0.291157i \(-0.905960\pi\)
0.956675 0.291157i \(-0.0940400\pi\)
\(594\) 53071.4 27336.4i 0.150414 0.0774764i
\(595\) −180871. −0.510898
\(596\) 115081.i 0.323974i
\(597\) −34418.5 + 90058.3i −0.0965702 + 0.252683i
\(598\) −1937.57 −0.00541820
\(599\) 460558.i 1.28360i 0.766871 + 0.641801i \(0.221812\pi\)
−0.766871 + 0.641801i \(0.778188\pi\)
\(600\) −13632.6 5210.12i −0.0378684 0.0144725i
\(601\) −273581. −0.757419 −0.378710 0.925516i \(-0.623632\pi\)
−0.378710 + 0.925516i \(0.623632\pi\)
\(602\) 41328.7i 0.114040i
\(603\) 94495.5 + 84582.9i 0.259882 + 0.232620i
\(604\) −269539. −0.738835
\(605\) 287789.i 0.786255i
\(606\) −10023.2 + 26226.3i −0.0272935 + 0.0714154i
\(607\) 6868.44 0.0186415 0.00932074 0.999957i \(-0.497033\pi\)
0.00932074 + 0.999957i \(0.497033\pi\)
\(608\) 18518.7i 0.0500959i
\(609\) 228136. + 87189.1i 0.615120 + 0.235086i
\(610\) −21826.7 −0.0586582
\(611\) 50968.3i 0.136527i
\(612\) −294769. + 329314.i −0.787007 + 0.879240i
\(613\) 189461. 0.504196 0.252098 0.967702i \(-0.418879\pi\)
0.252098 + 0.967702i \(0.418879\pi\)
\(614\) 13719.5i 0.0363916i
\(615\) 58849.2 153983.i 0.155593 0.407120i
\(616\) 122382. 0.322520
\(617\) 510628.i 1.34132i 0.741763 + 0.670662i \(0.233990\pi\)
−0.741763 + 0.670662i \(0.766010\pi\)
\(618\) 55375.7 + 21163.5i 0.144991 + 0.0554128i
\(619\) −466167. −1.21663 −0.608317 0.793694i \(-0.708155\pi\)
−0.608317 + 0.793694i \(0.708155\pi\)
\(620\) 86763.5i 0.225712i
\(621\) 71071.5 + 137979.i 0.184295 + 0.357793i
\(622\) −23808.9 −0.0615400
\(623\) 161793.i 0.416853i
\(624\) −17798.6 + 46571.4i −0.0457107 + 0.119605i
\(625\) 15625.0 0.0400000
\(626\) 16393.6i 0.0418336i
\(627\) −101362. 38738.4i −0.257833 0.0985388i
\(628\) −183053. −0.464149
\(629\) 667429.i 1.68696i
\(630\) −12909.1 11554.9i −0.0325247 0.0291129i
\(631\) 144471. 0.362847 0.181423 0.983405i \(-0.441930\pi\)
0.181423 + 0.983405i \(0.441930\pi\)
\(632\) 62283.8i 0.155934i
\(633\) 62348.1 163138.i 0.155602 0.407144i
\(634\) 46530.0 0.115759
\(635\) 46330.5i 0.114900i
\(636\) 349672. + 133638.i 0.864463 + 0.330380i
\(637\) 4401.74 0.0108479
\(638\) 47336.1i 0.116292i
\(639\) 290223. 324236.i 0.710773 0.794071i
\(640\) −72722.7 −0.177546
\(641\) 536191.i 1.30498i −0.757798 0.652490i \(-0.773725\pi\)
0.757798 0.652490i \(-0.226275\pi\)
\(642\) −24804.2 + 64901.8i −0.0601803 + 0.157466i
\(643\) 382957. 0.926250 0.463125 0.886293i \(-0.346728\pi\)
0.463125 + 0.886293i \(0.346728\pi\)
\(644\) 158260.i 0.381592i
\(645\) −203053. 77602.7i −0.488079 0.186534i
\(646\) −8425.63 −0.0201900
\(647\) 320474.i 0.765570i −0.923838 0.382785i \(-0.874965\pi\)
0.923838 0.382785i \(-0.125035\pi\)
\(648\) −84594.0 + 9393.96i −0.201460 + 0.0223717i
\(649\) 825120. 1.95897
\(650\) 1137.58i 0.00269249i
\(651\) −73925.7 + 193432.i −0.174435 + 0.456421i
\(652\) −96050.5 −0.225946
\(653\) 227576.i 0.533703i 0.963738 + 0.266851i \(0.0859833\pi\)
−0.963738 + 0.266851i \(0.914017\pi\)
\(654\) −14983.2 5726.30i −0.0350308 0.0133881i
\(655\) 261782. 0.610178
\(656\) 406378.i 0.944327i
\(657\) 260829. + 233468.i 0.604261 + 0.540874i
\(658\) 43662.3 0.100845
\(659\) 531408.i 1.22365i −0.790993 0.611825i \(-0.790436\pi\)
0.790993 0.611825i \(-0.209564\pi\)
\(660\) −114299. + 299071.i −0.262394 + 0.686573i
\(661\) −251100. −0.574704 −0.287352 0.957825i \(-0.592775\pi\)
−0.287352 + 0.957825i \(0.592775\pi\)
\(662\) 195.286i 0.000445610i
\(663\) 64697.3 + 24726.0i 0.147184 + 0.0562506i
\(664\) −43911.9 −0.0995969
\(665\) 31491.6i 0.0712117i
\(666\) 42638.6 47635.6i 0.0961290 0.107395i
\(667\) −123068. −0.276627
\(668\) 110437.i 0.247493i
\(669\) −193486. + 506269.i −0.432311 + 1.13117i
\(670\) 7133.51 0.0158911
\(671\) 962686.i 2.13816i
\(672\) −121815. 46555.1i −0.269750 0.103093i
\(673\) 532133. 1.17487 0.587435 0.809271i \(-0.300138\pi\)
0.587435 + 0.809271i \(0.300138\pi\)
\(674\) 56905.9i 0.125267i
\(675\) 81009.9 41727.2i 0.177800 0.0915824i
\(676\) −444336. −0.972340
\(677\) 73112.8i 0.159520i −0.996814 0.0797602i \(-0.974585\pi\)
0.996814 0.0797602i \(-0.0254154\pi\)
\(678\) 1627.48 4258.40i 0.00354042 0.00926376i
\(679\) −255745. −0.554712
\(680\) 49980.9i 0.108090i
\(681\) 442528. + 169125.i 0.954216 + 0.364682i
\(682\) −40135.2 −0.0862893
\(683\) 674426.i 1.44575i −0.690979 0.722875i \(-0.742820\pi\)
0.690979 0.722875i \(-0.257180\pi\)
\(684\) 57337.2 + 51322.5i 0.122553 + 0.109697i
\(685\) 46604.3 0.0993218
\(686\) 49704.2i 0.105620i
\(687\) 173828. 454833.i 0.368304 0.963692i
\(688\) −535878. −1.13211
\(689\) 58662.9i 0.123573i
\(690\) 8154.94 + 3116.65i 0.0171286 + 0.00654621i
\(691\) 617153. 1.29252 0.646259 0.763118i \(-0.276333\pi\)
0.646259 + 0.763118i \(0.276333\pi\)
\(692\) 441259.i 0.921471i
\(693\) −509639. + 569366.i −1.06120 + 1.18556i
\(694\) 53724.2 0.111545
\(695\) 74940.3i 0.155148i
\(696\) 24093.4 63042.0i 0.0497369 0.130140i
\(697\) −564543. −1.16207
\(698\) 97009.6i 0.199115i
\(699\) −690867. 264036.i −1.41397 0.540391i
\(700\) 92916.8 0.189626
\(701\) 154788.i 0.314993i 0.987520 + 0.157496i \(0.0503422\pi\)
−0.987520 + 0.157496i \(0.949658\pi\)
\(702\) 3037.95 + 5897.92i 0.00616462 + 0.0119681i
\(703\) −116207. −0.235137
\(704\) 772283.i 1.55823i
\(705\) −81984.4 + 214518.i −0.164950 + 0.431604i
\(706\) −73976.9 −0.148418
\(707\) 359379.i 0.718976i
\(708\) −546579. 208891.i −1.09040 0.416729i
\(709\) −480282. −0.955440 −0.477720 0.878512i \(-0.658537\pi\)
−0.477720 + 0.878512i \(0.658537\pi\)
\(710\) 24476.7i 0.0485553i
\(711\) 289766. + 259370.i 0.573203 + 0.513074i
\(712\) 44708.9 0.0881931
\(713\) 104347.i 0.205258i
\(714\) −21181.7 + 55423.3i −0.0415493 + 0.108717i
\(715\) 50173.8 0.0981443
\(716\) 352187.i 0.686984i
\(717\) 370308. + 141524.i 0.720319 + 0.275291i
\(718\) 13271.5 0.0257437
\(719\) 99977.2i 0.193394i 0.995314 + 0.0966971i \(0.0308278\pi\)
−0.995314 + 0.0966971i \(0.969172\pi\)
\(720\) 149824. 167382.i 0.289012 0.322882i
\(721\) −758814. −1.45970
\(722\) 51640.4i 0.0990639i
\(723\) 37834.5 98996.5i 0.0723788 0.189384i
\(724\) 529989. 1.01109
\(725\) 72255.4i 0.137466i
\(726\) −88185.8 33702.8i −0.167311 0.0639430i
\(727\) −182930. −0.346112 −0.173056 0.984912i \(-0.555364\pi\)
−0.173056 + 0.984912i \(0.555364\pi\)
\(728\) 13600.6i 0.0256622i
\(729\) 308572. 432681.i 0.580633 0.814165i
\(730\) 19690.1 0.0369489
\(731\) 744446.i 1.39315i
\(732\) 243718. 637705.i 0.454847 1.19014i
\(733\) 671761. 1.25028 0.625139 0.780513i \(-0.285042\pi\)
0.625139 + 0.780513i \(0.285042\pi\)
\(734\) 47756.2i 0.0886417i
\(735\) −18526.3 7080.37i −0.0342936 0.0131063i
\(736\) 65713.1 0.121310
\(737\) 314630.i 0.579248i
\(738\) −40292.5 36065.8i −0.0739795 0.0662190i
\(739\) −209903. −0.384353 −0.192176 0.981360i \(-0.561555\pi\)
−0.192176 + 0.981360i \(0.561555\pi\)
\(740\) 342871.i 0.626135i
\(741\) 4305.07 11264.5i 0.00784051 0.0205152i
\(742\) 50253.9 0.0912771
\(743\) 980505.i 1.77612i 0.459728 + 0.888060i \(0.347947\pi\)
−0.459728 + 0.888060i \(0.652053\pi\)
\(744\) 53451.9 + 20428.2i 0.0965644 + 0.0369050i
\(745\) 81258.4 0.146405
\(746\) 63491.5i 0.114087i
\(747\) 182863. 204294.i 0.327706 0.366112i
\(748\) 1.09647e6 1.95973
\(749\) 889351.i 1.58529i
\(750\) 1829.84 4787.89i 0.00325304 0.00851181i
\(751\) 642018. 1.13833 0.569164 0.822224i \(-0.307267\pi\)
0.569164 + 0.822224i \(0.307267\pi\)
\(752\) 566135.i 1.00112i
\(753\) −964220. 368506.i −1.70054 0.649911i
\(754\) −5260.55 −0.00925312
\(755\) 190321.i 0.333883i
\(756\) 481740. 248138.i 0.842886 0.434160i
\(757\) −315426. −0.550434 −0.275217 0.961382i \(-0.588750\pi\)
−0.275217 + 0.961382i \(0.588750\pi\)
\(758\) 71003.8i 0.123579i
\(759\) 137463. 359680.i 0.238617 0.624357i
\(760\) 8702.22 0.0150662
\(761\) 843657.i 1.45679i −0.685158 0.728394i \(-0.740267\pi\)
0.685158 0.728394i \(-0.259733\pi\)
\(762\) 14196.8 + 5425.74i 0.0244501 + 0.00934435i
\(763\) 205316. 0.352674
\(764\) 9534.47i 0.0163347i
\(765\) −232529. 208136.i −0.397332 0.355652i
\(766\) 103059. 0.175643
\(767\) 91697.1i 0.155871i
\(768\) 189049. 494659.i 0.320517 0.838656i
\(769\) −326397. −0.551942 −0.275971 0.961166i \(-0.588999\pi\)
−0.275971 + 0.961166i \(0.588999\pi\)
\(770\) 42981.7i 0.0724940i
\(771\) 372934. + 142528.i 0.627369 + 0.239768i
\(772\) −430706. −0.722680
\(773\) 702706.i 1.17602i 0.808853 + 0.588010i \(0.200089\pi\)
−0.808853 + 0.588010i \(0.799911\pi\)
\(774\) −47558.8 + 53132.5i −0.0793870 + 0.0886907i
\(775\) −61263.7 −0.102000
\(776\) 70671.2i 0.117360i
\(777\) −292139. + 764401.i −0.483891 + 1.26613i
\(778\) −51124.0 −0.0844628
\(779\) 98293.2i 0.161975i
\(780\) −33236.3 12702.2i −0.0546290 0.0208781i
\(781\) −1.07957e6 −1.76989
\(782\) 29898.2i 0.0488913i
\(783\) 192961. + 374618.i 0.314736 + 0.611033i
\(784\) −48892.8 −0.0795450
\(785\) 129254.i 0.209751i
\(786\) 30657.1 80216.5i 0.0496234 0.129843i
\(787\) 447743. 0.722902 0.361451 0.932391i \(-0.382282\pi\)
0.361451 + 0.932391i \(0.382282\pi\)
\(788\) 976013.i 1.57182i
\(789\) 514191. + 196513.i 0.825982 + 0.315674i
\(790\) 21874.6 0.0350498
\(791\) 58353.0i 0.0932632i
\(792\) 157335. + 140831.i 0.250828 + 0.224516i
\(793\) −106985. −0.170128
\(794\) 91853.0i 0.145698i
\(795\) −94361.5 + 246903.i −0.149300 + 0.390654i
\(796\) −169619. −0.267700
\(797\) 662789.i 1.04342i 0.853123 + 0.521710i \(0.174706\pi\)
−0.853123 + 0.521710i \(0.825294\pi\)
\(798\) 9649.81 + 3687.96i 0.0151535 + 0.00579136i
\(799\) 786480. 1.23195
\(800\) 38581.2i 0.0602831i
\(801\) −186182. + 208002.i −0.290184 + 0.324192i
\(802\) 52434.7 0.0815212
\(803\) 868448.i 1.34683i
\(804\) −79653.1 + 208418.i −0.123223 + 0.322421i
\(805\) −111747. −0.172443
\(806\) 4460.30i 0.00686585i
\(807\) −461794. 176488.i −0.709089 0.271000i
\(808\) −99309.0 −0.152113
\(809\) 1.20479e6i 1.84084i 0.390936 + 0.920418i \(0.372152\pi\)
−0.390936 + 0.920418i \(0.627848\pi\)
\(810\) −3299.24 29710.1i −0.00502856 0.0452829i
\(811\) −380108. −0.577917 −0.288958 0.957342i \(-0.593309\pi\)
−0.288958 + 0.957342i \(0.593309\pi\)
\(812\) 429679.i 0.651677i
\(813\) −154863. + 405210.i −0.234297 + 0.613055i
\(814\) −158606. −0.239371
\(815\) 67821.3i 0.102106i
\(816\) −718632. 274647.i −1.07926 0.412472i
\(817\) 129616. 0.194185
\(818\) 43077.2i 0.0643785i
\(819\) −63274.6 56637.1i −0.0943326 0.0844370i
\(820\) 290017. 0.431316
\(821\) 1.16909e6i 1.73444i −0.497923 0.867221i \(-0.665904\pi\)
0.497923 0.867221i \(-0.334096\pi\)
\(822\) 5457.80 14280.7i 0.00807745 0.0211352i
\(823\) −1.04796e6 −1.54719 −0.773594 0.633681i \(-0.781543\pi\)
−0.773594 + 0.633681i \(0.781543\pi\)
\(824\) 209687.i 0.308828i
\(825\) −211174. 80706.5i −0.310265 0.118577i
\(826\) −78552.8 −0.115133
\(827\) 9106.01i 0.0133143i 0.999978 + 0.00665713i \(0.00211905\pi\)
−0.999978 + 0.00665713i \(0.997881\pi\)
\(828\) −182117. + 203460.i −0.265638 + 0.296769i
\(829\) −715146. −1.04060 −0.520302 0.853982i \(-0.674181\pi\)
−0.520302 + 0.853982i \(0.674181\pi\)
\(830\) 15422.2i 0.0223867i
\(831\) 326094. 853249.i 0.472217 1.23559i
\(832\) −85825.2 −0.123985
\(833\) 67922.3i 0.0978863i
\(834\) 22963.6 + 8776.22i 0.0330147 + 0.0126176i
\(835\) 77979.7 0.111843
\(836\) 190908.i 0.273157i
\(837\) −317630. + 163607.i −0.453388 + 0.233535i
\(838\) 64354.1 0.0916406
\(839\) 242894.i 0.345059i −0.985004 0.172529i \(-0.944806\pi\)
0.985004 0.172529i \(-0.0551940\pi\)
\(840\) 21877.0 57242.7i 0.0310048 0.0811263i
\(841\) 373147. 0.527580
\(842\) 99853.9i 0.140845i
\(843\) 1.01642e6 + 388456.i 1.43027 + 0.546621i
\(844\) 307260. 0.431341
\(845\) 313746.i 0.439404i
\(846\) 56132.5 + 50244.1i 0.0784284 + 0.0702012i
\(847\) 1.20841e6 1.68441
\(848\) 651604.i 0.906133i
\(849\) −357560. + 935580.i −0.496059 + 1.29797i
\(850\) −17553.7 −0.0242958
\(851\) 412357.i 0.569396i
\(852\) 715130. + 273308.i 0.985158 + 0.376507i
\(853\) 861767. 1.18438 0.592191 0.805797i \(-0.298263\pi\)
0.592191 + 0.805797i \(0.298263\pi\)
\(854\) 91649.3i 0.125665i
\(855\) −36238.8 + 40485.8i −0.0495726 + 0.0553822i
\(856\) −245758. −0.335398
\(857\) 525214.i 0.715113i −0.933891 0.357557i \(-0.883610\pi\)
0.933891 0.357557i \(-0.116390\pi\)
\(858\) 5875.83 15374.5i 0.00798169 0.0208846i
\(859\) 66206.8 0.0897256 0.0448628 0.998993i \(-0.485715\pi\)
0.0448628 + 0.998993i \(0.485715\pi\)
\(860\) 382437.i 0.517086i
\(861\) 646567. + 247105.i 0.872182 + 0.333331i
\(862\) 25015.3 0.0336660
\(863\) 5062.88i 0.00679792i −0.999994 0.00339896i \(-0.998918\pi\)
0.999994 0.00339896i \(-0.00108192\pi\)
\(864\) −103033. 200029.i −0.138022 0.267958i
\(865\) 311573. 0.416416
\(866\) 10294.9i 0.0137274i
\(867\) −113191. + 296172.i −0.150582 + 0.394009i
\(868\) −364316. −0.483546
\(869\) 964797.i 1.27760i
\(870\) 22140.9 + 8461.79i 0.0292520 + 0.0111795i
\(871\) 34965.3 0.0460894
\(872\) 56735.9i 0.0746148i
\(873\) −328788. 294298.i −0.431407 0.386152i
\(874\) −5205.60 −0.00681472
\(875\) 65608.6i 0.0856928i
\(876\) −219860. + 575280.i −0.286509 + 0.749672i
\(877\) 1.24871e6 1.62354 0.811772 0.583975i \(-0.198503\pi\)
0.811772 + 0.583975i \(0.198503\pi\)
\(878\) 84390.7i 0.109473i
\(879\) 538656. + 205864.i 0.697162 + 0.266441i
\(880\) −557311. −0.719668
\(881\) 112260.i 0.144635i 0.997382 + 0.0723173i \(0.0230394\pi\)
−0.997382 + 0.0723173i \(0.976961\pi\)
\(882\) −4339.20 + 4847.73i −0.00557793 + 0.00623163i
\(883\) −329416. −0.422496 −0.211248 0.977432i \(-0.567753\pi\)
−0.211248 + 0.977432i \(0.567753\pi\)
\(884\) 121853.i 0.155931i
\(885\) 147498. 385939.i 0.188322 0.492756i
\(886\) 54023.0 0.0688194
\(887\) 152778.i 0.194185i −0.995275 0.0970923i \(-0.969046\pi\)
0.995275 0.0970923i \(-0.0309542\pi\)
\(888\) 211231. + 80728.1i 0.267874 + 0.102376i
\(889\) −194539. −0.246152
\(890\) 15702.2i 0.0198234i
\(891\) −1.31039e6 + 145516.i −1.65061 + 0.183296i
\(892\) −953523. −1.19840
\(893\) 136935.i 0.171716i
\(894\) 9516.13 24899.6i 0.0119065 0.0311543i
\(895\) −248679. −0.310451
\(896\) 305359.i 0.380360i
\(897\) 39971.9 + 15276.5i 0.0496787 + 0.0189862i
\(898\) −81803.8 −0.101443
\(899\) 283304.i 0.350537i
\(900\) 119455. + 106924.i 0.147475 + 0.132005i
\(901\) 905213. 1.11507
\(902\) 134157.i 0.164892i
\(903\) 325850. 852609.i 0.399615 1.04562i
\(904\) 16125.0 0.0197316
\(905\) 374225.i 0.456916i
\(906\) −58319.2 22288.4i −0.0710486 0.0271533i
\(907\) −1.26534e6 −1.53813 −0.769067 0.639169i \(-0.779279\pi\)
−0.769067 + 0.639169i \(0.779279\pi\)
\(908\) 833472.i 1.01093i
\(909\) 413554. 462021.i 0.500501 0.559157i
\(910\) −4776.63 −0.00576818
\(911\) 702340.i 0.846274i 0.906066 + 0.423137i \(0.139071\pi\)
−0.906066 + 0.423137i \(0.860929\pi\)
\(912\) −47819.0 + 125122.i −0.0574925 + 0.150433i
\(913\) −680210. −0.816021
\(914\) 161455.i 0.193267i
\(915\) 450284. + 172089.i 0.537829 + 0.205547i
\(916\) 856648. 1.02097
\(917\) 1.09921e6i 1.30720i
\(918\) −91009.4 + 46877.9i −0.107994 + 0.0556266i
\(919\) 266756. 0.315851 0.157926 0.987451i \(-0.449519\pi\)
0.157926 + 0.987451i \(0.449519\pi\)
\(920\) 30879.6i 0.0364835i
\(921\) 108169. 283032.i 0.127522 0.333670i
\(922\) −74255.5 −0.0873507
\(923\) 119974.i 0.140827i
\(924\) −1.25578e6 479935.i −1.47086 0.562133i
\(925\) −242101. −0.282953
\(926\) 73846.3i 0.0861205i
\(927\) −975536. 873202.i −1.13523 1.01614i
\(928\) 178413. 0.207171
\(929\) 1.29140e6i 1.49634i 0.663509 + 0.748169i \(0.269067\pi\)
−0.663509 + 0.748169i \(0.730933\pi\)
\(930\) −7174.56 + 18772.7i −0.00829525 + 0.0217051i
\(931\) 11826.0 0.0136439
\(932\) 1.30120e6i 1.49800i
\(933\) 491175. + 187717.i 0.564252 + 0.215646i
\(934\) 150853. 0.172926
\(935\) 774220.i 0.885608i
\(936\) −15650.8 + 17485.0i −0.0178642 + 0.0199578i
\(937\) −399820. −0.455392 −0.227696 0.973732i \(-0.573119\pi\)
−0.227696 + 0.973732i \(0.573119\pi\)
\(938\) 29953.2i 0.0340438i
\(939\) 129253. 338199.i 0.146591 0.383566i
\(940\) −404030. −0.457254
\(941\) 1.22439e6i 1.38274i 0.722499 + 0.691372i \(0.242993\pi\)
−0.722499 + 0.691372i \(0.757007\pi\)
\(942\) −39606.6 15136.8i −0.0446340 0.0170582i
\(943\) −348791. −0.392231
\(944\) 1.01853e6i 1.14296i
\(945\) 175210. + 340156.i 0.196199 + 0.380904i
\(946\) 176908. 0.197682
\(947\) 699832.i 0.780358i 0.920739 + 0.390179i \(0.127587\pi\)
−0.920739 + 0.390179i \(0.872413\pi\)
\(948\) −244253. + 639104.i −0.271783 + 0.711140i
\(949\) 96512.2 0.107164
\(950\) 3056.29i 0.00338647i
\(951\) −959910. 366858.i −1.06138 0.405637i
\(952\) −209867. −0.231564
\(953\) 1.25288e6i 1.37950i −0.724045 0.689752i \(-0.757719\pi\)
0.724045 0.689752i \(-0.242281\pi\)
\(954\) 64606.7 + 57829.4i 0.0709874 + 0.0635407i
\(955\) 6732.29 0.00738169
\(956\) 697451.i 0.763128i
\(957\) 373214. 976541.i 0.407507 1.06627i
\(958\) 5563.43 0.00606194
\(959\) 195689.i 0.212779i
\(960\) 361225. + 138053.i 0.391954 + 0.149797i
\(961\) −683314. −0.739900
\(962\) 17626.2i 0.0190462i
\(963\) 1.02342e6 1.14336e6i 1.10357 1.23290i
\(964\) 186453. 0.200639
\(965\) 304121.i 0.326582i
\(966\) −13086.7 + 34242.2i −0.0140241 + 0.0366950i
\(967\) 580972. 0.621301 0.310651 0.950524i \(-0.399453\pi\)
0.310651 + 0.950524i \(0.399453\pi\)
\(968\) 333926.i 0.356369i
\(969\) 173820. + 66430.6i 0.185120 + 0.0707490i
\(970\) −24820.3 −0.0263793
\(971\) 648131.i 0.687423i 0.939075 + 0.343712i \(0.111684\pi\)
−0.939075 + 0.343712i \(0.888316\pi\)
\(972\) 904872. + 235352.i 0.957755 + 0.249106i
\(973\) −314670. −0.332376
\(974\) 78916.2i 0.0831856i
\(975\) 8969.05 23468.1i 0.00943490 0.0246871i
\(976\) 1.18835e6 1.24751
\(977\) 1.48636e6i 1.55717i −0.627539 0.778585i \(-0.715938\pi\)
0.627539 0.778585i \(-0.284062\pi\)
\(978\) −20782.1 7942.51i −0.0217276 0.00830386i
\(979\) 692557. 0.722587
\(980\) 34893.0i 0.0363317i
\(981\) 263955. + 236266.i 0.274279 + 0.245507i
\(982\) 10777.8 0.0111766
\(983\) 992676.i 1.02731i 0.857998 + 0.513654i \(0.171708\pi\)
−0.857998 + 0.513654i \(0.828292\pi\)
\(984\) 68283.7 178669.i 0.0705223 0.184527i
\(985\) 689163. 0.710313
\(986\) 81174.3i 0.0834958i
\(987\) −900749. 344248.i −0.924634 0.353376i
\(988\) 21216.0 0.0217345
\(989\) 459941.i 0.470229i
\(990\) −49461.0 + 55257.5i −0.0504652 + 0.0563795i
\(991\) 1.60928e6 1.63864 0.819322 0.573334i \(-0.194350\pi\)
0.819322 + 0.573334i \(0.194350\pi\)
\(992\) 151272.i 0.153722i
\(993\) 1539.70 4028.73i 0.00156148 0.00408573i
\(994\) 102777. 0.104021
\(995\) 119768.i 0.120975i
\(996\) 450587. + 172205.i 0.454213 + 0.173591i
\(997\) 375625. 0.377889 0.188945 0.981988i \(-0.439493\pi\)
0.188945 + 0.981988i \(0.439493\pi\)
\(998\) 148759.i 0.149356i
\(999\) −1.25521e6 + 646542.i −1.25772 + 0.647837i
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 15.5.c.a.11.4 yes 6
3.2 odd 2 inner 15.5.c.a.11.3 6
4.3 odd 2 240.5.l.d.161.4 6
5.2 odd 4 75.5.d.d.74.5 12
5.3 odd 4 75.5.d.d.74.8 12
5.4 even 2 75.5.c.i.26.3 6
12.11 even 2 240.5.l.d.161.3 6
15.2 even 4 75.5.d.d.74.7 12
15.8 even 4 75.5.d.d.74.6 12
15.14 odd 2 75.5.c.i.26.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.5.c.a.11.3 6 3.2 odd 2 inner
15.5.c.a.11.4 yes 6 1.1 even 1 trivial
75.5.c.i.26.3 6 5.4 even 2
75.5.c.i.26.4 6 15.14 odd 2
75.5.d.d.74.5 12 5.2 odd 4
75.5.d.d.74.6 12 15.8 even 4
75.5.d.d.74.7 12 15.2 even 4
75.5.d.d.74.8 12 5.3 odd 4
240.5.l.d.161.3 6 12.11 even 2
240.5.l.d.161.4 6 4.3 odd 2