Properties

Label 294.4.e.k.67.1
Level $294$
Weight $4$
Character 294.67
Analytic conductor $17.347$
Analytic rank $0$
Dimension $4$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not 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: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.4.e.k.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.70711 - 6.42090i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.70711 - 6.42090i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.41421 + 12.8418i) q^{10} +(-5.24264 + 9.08052i) q^{11} +(-6.00000 - 10.3923i) q^{12} +2.78680 q^{13} +22.2426 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-25.2218 + 43.6855i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-62.5269 - 108.300i) q^{19} +29.6569 q^{20} +20.9706 q^{22} +(91.1249 + 157.833i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(35.0147 - 60.6473i) q^{25} +(-2.78680 - 4.82687i) q^{26} +27.0000 q^{27} +156.132 q^{29} +(-22.2426 - 38.5254i) q^{30} +(-69.8162 + 120.925i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-15.7279 - 27.2416i) q^{33} +100.887 q^{34} +36.0000 q^{36} +(197.279 + 341.698i) q^{37} +(-125.054 + 216.600i) q^{38} +(-4.18019 + 7.24031i) q^{39} +(-29.6569 - 51.3672i) q^{40} +197.605 q^{41} +343.294 q^{43} +(-20.9706 - 36.3221i) q^{44} +(-33.3640 + 57.7881i) q^{45} +(182.250 - 315.666i) q^{46} +(305.002 + 528.279i) q^{47} +48.0000 q^{48} -140.059 q^{50} +(-75.6655 - 131.056i) q^{51} +(-5.57359 + 9.65375i) q^{52} +(68.7645 - 119.104i) q^{53} +(-27.0000 - 46.7654i) q^{54} +77.7401 q^{55} +375.161 q^{57} +(-156.132 - 270.429i) q^{58} +(-294.718 + 510.466i) q^{59} +(-44.4853 + 77.0508i) q^{60} +(-123.609 - 214.097i) q^{61} +279.265 q^{62} +64.0000 q^{64} +(-10.3310 - 17.8937i) q^{65} +(-31.4558 + 54.4831i) q^{66} +(197.823 - 342.640i) q^{67} +(-100.887 - 174.742i) q^{68} -546.749 q^{69} +285.661 q^{71} +(-36.0000 - 62.3538i) q^{72} +(498.729 - 863.823i) q^{73} +(394.558 - 683.395i) q^{74} +(105.044 + 181.942i) q^{75} +500.215 q^{76} +16.7208 q^{78} +(424.132 + 734.618i) q^{79} +(-59.3137 + 102.734i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-197.605 - 342.262i) q^{82} -210.863 q^{83} +374.000 q^{85} +(-343.294 - 594.602i) q^{86} +(-234.198 + 405.643i) q^{87} +(-41.9411 + 72.6442i) q^{88} +(276.744 + 479.334i) q^{89} +133.456 q^{90} -728.999 q^{92} +(-209.449 - 362.776i) q^{93} +(610.004 - 1056.56i) q^{94} +(-463.588 + 802.958i) q^{95} +(-48.0000 - 83.1384i) q^{96} -903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 96 q^{13} + 72 q^{15} - 32 q^{16} - 132 q^{17} - 36 q^{18} - 120 q^{19} + 96 q^{20} + 16 q^{22} + 76 q^{23} - 48 q^{24} + 174 q^{25} - 96 q^{26} + 108 q^{27} - 224 q^{29} - 72 q^{30} - 432 q^{31} - 64 q^{32} - 12 q^{33} + 528 q^{34} + 144 q^{36} + 280 q^{37} - 240 q^{38} - 144 q^{39} - 96 q^{40} + 72 q^{41} - 256 q^{43} - 16 q^{44} - 108 q^{45} + 152 q^{46} + 264 q^{47} + 192 q^{48} - 696 q^{50} - 396 q^{51} - 192 q^{52} - 268 q^{53} - 108 q^{54} + 96 q^{55} + 720 q^{57} + 224 q^{58} - 336 q^{59} - 144 q^{60} + 504 q^{61} + 1728 q^{62} + 256 q^{64} - 228 q^{65} - 24 q^{66} + 384 q^{67} - 528 q^{68} - 456 q^{69} - 792 q^{71} - 144 q^{72} + 312 q^{73} + 560 q^{74} + 522 q^{75} + 960 q^{76} + 576 q^{78} + 848 q^{79} - 192 q^{80} - 162 q^{81} - 72 q^{82} - 1296 q^{83} + 1496 q^{85} + 256 q^{86} + 336 q^{87} - 32 q^{88} + 612 q^{89} + 432 q^{90} - 608 q^{92} - 1296 q^{93} + 528 q^{94} - 904 q^{95} - 192 q^{96} - 4368 q^{97} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −3.70711 6.42090i −0.331574 0.574303i 0.651247 0.758866i \(-0.274246\pi\)
−0.982821 + 0.184563i \(0.940913\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −7.41421 + 12.8418i −0.234458 + 0.406093i
\(11\) −5.24264 + 9.08052i −0.143701 + 0.248898i −0.928888 0.370361i \(-0.879234\pi\)
0.785186 + 0.619260i \(0.212567\pi\)
\(12\) −6.00000 10.3923i −0.144338 0.250000i
\(13\) 2.78680 0.0594553 0.0297276 0.999558i \(-0.490536\pi\)
0.0297276 + 0.999558i \(0.490536\pi\)
\(14\) 0 0
\(15\) 22.2426 0.382868
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −25.2218 + 43.6855i −0.359835 + 0.623252i −0.987933 0.154882i \(-0.950500\pi\)
0.628098 + 0.778134i \(0.283834\pi\)
\(18\) −9.00000 + 15.5885i −0.117851 + 0.204124i
\(19\) −62.5269 108.300i −0.754982 1.30767i −0.945383 0.325961i \(-0.894312\pi\)
0.190401 0.981706i \(-0.439021\pi\)
\(20\) 29.6569 0.331574
\(21\) 0 0
\(22\) 20.9706 0.203225
\(23\) 91.1249 + 157.833i 0.826124 + 1.43089i 0.901057 + 0.433700i \(0.142792\pi\)
−0.0749331 + 0.997189i \(0.523874\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) 35.0147 60.6473i 0.280118 0.485178i
\(26\) −2.78680 4.82687i −0.0210206 0.0364088i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 156.132 0.999758 0.499879 0.866095i \(-0.333378\pi\)
0.499879 + 0.866095i \(0.333378\pi\)
\(30\) −22.2426 38.5254i −0.135364 0.234458i
\(31\) −69.8162 + 120.925i −0.404496 + 0.700607i −0.994263 0.106966i \(-0.965886\pi\)
0.589767 + 0.807573i \(0.299220\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) −15.7279 27.2416i −0.0829661 0.143701i
\(34\) 100.887 0.508883
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) 197.279 + 341.698i 0.876554 + 1.51824i 0.855098 + 0.518467i \(0.173497\pi\)
0.0214563 + 0.999770i \(0.493170\pi\)
\(38\) −125.054 + 216.600i −0.533853 + 0.924660i
\(39\) −4.18019 + 7.24031i −0.0171633 + 0.0297276i
\(40\) −29.6569 51.3672i −0.117229 0.203047i
\(41\) 197.605 0.752701 0.376350 0.926477i \(-0.377179\pi\)
0.376350 + 0.926477i \(0.377179\pi\)
\(42\) 0 0
\(43\) 343.294 1.21748 0.608741 0.793369i \(-0.291675\pi\)
0.608741 + 0.793369i \(0.291675\pi\)
\(44\) −20.9706 36.3221i −0.0718507 0.124449i
\(45\) −33.3640 + 57.7881i −0.110525 + 0.191434i
\(46\) 182.250 315.666i 0.584158 1.01179i
\(47\) 305.002 + 528.279i 0.946577 + 1.63952i 0.752562 + 0.658521i \(0.228818\pi\)
0.194015 + 0.980999i \(0.437849\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) −140.059 −0.396146
\(51\) −75.6655 131.056i −0.207751 0.359835i
\(52\) −5.57359 + 9.65375i −0.0148638 + 0.0257449i
\(53\) 68.7645 119.104i 0.178218 0.308682i −0.763053 0.646336i \(-0.776300\pi\)
0.941270 + 0.337655i \(0.109634\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) 77.7401 0.190590
\(56\) 0 0
\(57\) 375.161 0.871778
\(58\) −156.132 270.429i −0.353468 0.612224i
\(59\) −294.718 + 510.466i −0.650322 + 1.12639i 0.332723 + 0.943025i \(0.392033\pi\)
−0.983045 + 0.183366i \(0.941301\pi\)
\(60\) −44.4853 + 77.0508i −0.0957171 + 0.165787i
\(61\) −123.609 214.097i −0.259450 0.449381i 0.706644 0.707569i \(-0.250208\pi\)
−0.966095 + 0.258188i \(0.916875\pi\)
\(62\) 279.265 0.572043
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −10.3310 17.8937i −0.0197138 0.0341453i
\(66\) −31.4558 + 54.4831i −0.0586659 + 0.101612i
\(67\) 197.823 342.640i 0.360716 0.624778i −0.627363 0.778727i \(-0.715866\pi\)
0.988079 + 0.153949i \(0.0491990\pi\)
\(68\) −100.887 174.742i −0.179917 0.311626i
\(69\) −546.749 −0.953926
\(70\) 0 0
\(71\) 285.661 0.477489 0.238745 0.971082i \(-0.423264\pi\)
0.238745 + 0.971082i \(0.423264\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) 498.729 863.823i 0.799613 1.38497i −0.120255 0.992743i \(-0.538371\pi\)
0.919868 0.392228i \(-0.128295\pi\)
\(74\) 394.558 683.395i 0.619817 1.07356i
\(75\) 105.044 + 181.942i 0.161726 + 0.280118i
\(76\) 500.215 0.754982
\(77\) 0 0
\(78\) 16.7208 0.0242725
\(79\) 424.132 + 734.618i 0.604033 + 1.04622i 0.992204 + 0.124628i \(0.0397737\pi\)
−0.388171 + 0.921587i \(0.626893\pi\)
\(80\) −59.3137 + 102.734i −0.0828934 + 0.143576i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −197.605 342.262i −0.266120 0.460933i
\(83\) −210.863 −0.278858 −0.139429 0.990232i \(-0.544527\pi\)
−0.139429 + 0.990232i \(0.544527\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) −343.294 594.602i −0.430445 0.745553i
\(87\) −234.198 + 405.643i −0.288605 + 0.499879i
\(88\) −41.9411 + 72.6442i −0.0508061 + 0.0879988i
\(89\) 276.744 + 479.334i 0.329604 + 0.570891i 0.982433 0.186614i \(-0.0597514\pi\)
−0.652829 + 0.757505i \(0.726418\pi\)
\(90\) 133.456 0.156305
\(91\) 0 0
\(92\) −728.999 −0.826124
\(93\) −209.449 362.776i −0.233536 0.404496i
\(94\) 610.004 1056.56i 0.669331 1.15932i
\(95\) −463.588 + 802.958i −0.500664 + 0.867176i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) −903.910 −0.946166 −0.473083 0.881018i \(-0.656859\pi\)
−0.473083 + 0.881018i \(0.656859\pi\)
\(98\) 0 0
\(99\) 94.3675 0.0958009
\(100\) 140.059 + 242.589i 0.140059 + 0.242589i
\(101\) 156.806 271.595i 0.154482 0.267572i −0.778388 0.627784i \(-0.783962\pi\)
0.932870 + 0.360212i \(0.117296\pi\)
\(102\) −151.331 + 262.113i −0.146902 + 0.254442i
\(103\) −115.487 200.030i −0.110479 0.191355i 0.805485 0.592617i \(-0.201905\pi\)
−0.915963 + 0.401262i \(0.868572\pi\)
\(104\) 22.2944 0.0210206
\(105\) 0 0
\(106\) −275.058 −0.252038
\(107\) −62.7431 108.674i −0.0566879 0.0981863i 0.836289 0.548289i \(-0.184721\pi\)
−0.892977 + 0.450103i \(0.851387\pi\)
\(108\) −54.0000 + 93.5307i −0.0481125 + 0.0833333i
\(109\) −372.764 + 645.646i −0.327562 + 0.567354i −0.982028 0.188738i \(-0.939560\pi\)
0.654465 + 0.756092i \(0.272894\pi\)
\(110\) −77.7401 134.650i −0.0673839 0.116712i
\(111\) −1183.68 −1.01216
\(112\) 0 0
\(113\) −1043.76 −0.868929 −0.434464 0.900689i \(-0.643062\pi\)
−0.434464 + 0.900689i \(0.643062\pi\)
\(114\) −375.161 649.799i −0.308220 0.533853i
\(115\) 675.619 1170.21i 0.547842 0.948890i
\(116\) −312.264 + 540.857i −0.249940 + 0.432908i
\(117\) −12.5406 21.7209i −0.00990921 0.0171633i
\(118\) 1178.87 0.919694
\(119\) 0 0
\(120\) 177.941 0.135364
\(121\) 610.529 + 1057.47i 0.458700 + 0.794491i
\(122\) −247.217 + 428.193i −0.183459 + 0.317760i
\(123\) −296.408 + 513.393i −0.217286 + 0.376350i
\(124\) −279.265 483.701i −0.202248 0.350304i
\(125\) −1445.99 −1.03467
\(126\) 0 0
\(127\) −2080.17 −1.45343 −0.726715 0.686939i \(-0.758954\pi\)
−0.726715 + 0.686939i \(0.758954\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) −514.940 + 891.903i −0.351457 + 0.608741i
\(130\) −20.6619 + 35.7875i −0.0139398 + 0.0241444i
\(131\) 634.764 + 1099.44i 0.423355 + 0.733273i 0.996265 0.0863453i \(-0.0275188\pi\)
−0.572910 + 0.819618i \(0.694186\pi\)
\(132\) 125.823 0.0829661
\(133\) 0 0
\(134\) −791.294 −0.510129
\(135\) −100.092 173.364i −0.0638114 0.110525i
\(136\) −201.775 + 349.484i −0.127221 + 0.220353i
\(137\) −1536.59 + 2661.46i −0.958249 + 1.65974i −0.231497 + 0.972836i \(0.574362\pi\)
−0.726752 + 0.686900i \(0.758971\pi\)
\(138\) 546.749 + 946.998i 0.337264 + 0.584158i
\(139\) 1013.60 0.618504 0.309252 0.950980i \(-0.399921\pi\)
0.309252 + 0.950980i \(0.399921\pi\)
\(140\) 0 0
\(141\) −1830.01 −1.09301
\(142\) −285.661 494.779i −0.168818 0.292401i
\(143\) −14.6102 + 25.3056i −0.00854380 + 0.0147983i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) −578.798 1002.51i −0.331494 0.574164i
\(146\) −1994.91 −1.13082
\(147\) 0 0
\(148\) −1578.23 −0.876554
\(149\) −615.735 1066.48i −0.338544 0.586375i 0.645615 0.763663i \(-0.276601\pi\)
−0.984159 + 0.177288i \(0.943268\pi\)
\(150\) 210.088 363.884i 0.114358 0.198073i
\(151\) 1122.37 1944.00i 0.604881 1.04768i −0.387190 0.922000i \(-0.626554\pi\)
0.992070 0.125684i \(-0.0401125\pi\)
\(152\) −500.215 866.398i −0.266926 0.462330i
\(153\) 453.993 0.239890
\(154\) 0 0
\(155\) 1035.26 0.536481
\(156\) −16.7208 28.9612i −0.00858163 0.0148638i
\(157\) 1893.58 3279.77i 0.962573 1.66723i 0.246575 0.969124i \(-0.420695\pi\)
0.715998 0.698102i \(-0.245972\pi\)
\(158\) 848.264 1469.24i 0.427116 0.739786i
\(159\) 206.294 + 357.311i 0.102894 + 0.178218i
\(160\) 237.255 0.117229
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) 1054.28 + 1826.07i 0.506611 + 0.877476i 0.999971 + 0.00765060i \(0.00243528\pi\)
−0.493360 + 0.869825i \(0.664231\pi\)
\(164\) −395.210 + 684.524i −0.188175 + 0.325929i
\(165\) −116.610 + 201.975i −0.0550187 + 0.0952952i
\(166\) 210.863 + 365.225i 0.0985912 + 0.170765i
\(167\) 1502.41 0.696170 0.348085 0.937463i \(-0.386832\pi\)
0.348085 + 0.937463i \(0.386832\pi\)
\(168\) 0 0
\(169\) −2189.23 −0.996465
\(170\) −374.000 647.787i −0.168732 0.292253i
\(171\) −562.742 + 974.698i −0.251661 + 0.435889i
\(172\) −686.587 + 1189.20i −0.304371 + 0.527186i
\(173\) −235.628 408.120i −0.103552 0.179357i 0.809594 0.586991i \(-0.199687\pi\)
−0.913146 + 0.407634i \(0.866354\pi\)
\(174\) 936.792 0.408150
\(175\) 0 0
\(176\) 167.765 0.0718507
\(177\) −884.153 1531.40i −0.375464 0.650322i
\(178\) 553.487 958.668i 0.233065 0.403681i
\(179\) −666.244 + 1153.97i −0.278198 + 0.481852i −0.970937 0.239336i \(-0.923070\pi\)
0.692739 + 0.721188i \(0.256404\pi\)
\(180\) −133.456 231.152i −0.0552623 0.0957171i
\(181\) −997.727 −0.409726 −0.204863 0.978791i \(-0.565675\pi\)
−0.204863 + 0.978791i \(0.565675\pi\)
\(182\) 0 0
\(183\) 741.652 0.299587
\(184\) 728.999 + 1262.66i 0.292079 + 0.505896i
\(185\) 1462.67 2533.42i 0.581285 1.00681i
\(186\) −418.897 + 725.552i −0.165135 + 0.286022i
\(187\) −264.458 458.055i −0.103418 0.179124i
\(188\) −2440.02 −0.946577
\(189\) 0 0
\(190\) 1854.35 0.708046
\(191\) −613.360 1062.37i −0.232362 0.402463i 0.726141 0.687546i \(-0.241312\pi\)
−0.958503 + 0.285083i \(0.907979\pi\)
\(192\) −96.0000 + 166.277i −0.0360844 + 0.0625000i
\(193\) 1739.65 3013.16i 0.648821 1.12379i −0.334584 0.942366i \(-0.608596\pi\)
0.983405 0.181425i \(-0.0580709\pi\)
\(194\) 903.910 + 1565.62i 0.334520 + 0.579406i
\(195\) 61.9857 0.0227635
\(196\) 0 0
\(197\) 3193.47 1.15495 0.577476 0.816408i \(-0.304038\pi\)
0.577476 + 0.816408i \(0.304038\pi\)
\(198\) −94.3675 163.449i −0.0338708 0.0586659i
\(199\) −532.574 + 922.446i −0.189715 + 0.328595i −0.945155 0.326622i \(-0.894090\pi\)
0.755440 + 0.655217i \(0.227423\pi\)
\(200\) 280.118 485.178i 0.0990366 0.171536i
\(201\) 593.470 + 1027.92i 0.208259 + 0.360716i
\(202\) −627.222 −0.218471
\(203\) 0 0
\(204\) 605.324 0.207751
\(205\) −732.543 1268.80i −0.249576 0.432278i
\(206\) −230.975 + 400.060i −0.0781203 + 0.135308i
\(207\) 820.124 1420.50i 0.275375 0.476963i
\(208\) −22.2944 38.6150i −0.00743191 0.0128724i
\(209\) 1311.22 0.433968
\(210\) 0 0
\(211\) 2057.50 0.671298 0.335649 0.941987i \(-0.391044\pi\)
0.335649 + 0.941987i \(0.391044\pi\)
\(212\) 275.058 + 476.414i 0.0891088 + 0.154341i
\(213\) −428.492 + 742.169i −0.137839 + 0.238745i
\(214\) −125.486 + 217.348i −0.0400844 + 0.0694282i
\(215\) −1272.63 2204.25i −0.403685 0.699204i
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) 1491.05 0.463243
\(219\) 1496.19 + 2591.47i 0.461657 + 0.799613i
\(220\) −155.480 + 269.300i −0.0476476 + 0.0825281i
\(221\) −70.2881 + 121.743i −0.0213941 + 0.0370556i
\(222\) 1183.68 + 2050.19i 0.357852 + 0.619817i
\(223\) 2028.27 0.609071 0.304536 0.952501i \(-0.401499\pi\)
0.304536 + 0.952501i \(0.401499\pi\)
\(224\) 0 0
\(225\) −630.265 −0.186745
\(226\) 1043.76 + 1807.85i 0.307213 + 0.532108i
\(227\) −1211.98 + 2099.21i −0.354369 + 0.613786i −0.987010 0.160660i \(-0.948638\pi\)
0.632640 + 0.774446i \(0.281971\pi\)
\(228\) −750.323 + 1299.60i −0.217945 + 0.377491i
\(229\) 983.584 + 1703.62i 0.283830 + 0.491608i 0.972325 0.233633i \(-0.0750615\pi\)
−0.688495 + 0.725241i \(0.741728\pi\)
\(230\) −2702.48 −0.774766
\(231\) 0 0
\(232\) 1249.06 0.353468
\(233\) −2239.17 3878.35i −0.629582 1.09047i −0.987636 0.156767i \(-0.949893\pi\)
0.358053 0.933701i \(-0.383441\pi\)
\(234\) −25.0812 + 43.4419i −0.00700687 + 0.0121363i
\(235\) 2261.35 3916.77i 0.627720 1.08724i
\(236\) −1178.87 2041.86i −0.325161 0.563195i
\(237\) −2544.79 −0.697477
\(238\) 0 0
\(239\) 6116.92 1.65553 0.827763 0.561078i \(-0.189613\pi\)
0.827763 + 0.561078i \(0.189613\pi\)
\(240\) −177.941 308.203i −0.0478585 0.0828934i
\(241\) −3114.19 + 5393.94i −0.832376 + 1.44172i 0.0637726 + 0.997964i \(0.479687\pi\)
−0.896149 + 0.443754i \(0.853647\pi\)
\(242\) 1221.06 2114.94i 0.324350 0.561790i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 988.870 0.259450
\(245\) 0 0
\(246\) 1185.63 0.307289
\(247\) −174.250 301.809i −0.0448876 0.0777477i
\(248\) −558.530 + 967.402i −0.143011 + 0.247702i
\(249\) 316.294 547.838i 0.0804994 0.139429i
\(250\) 1445.99 + 2504.53i 0.365810 + 0.633601i
\(251\) 5904.42 1.48479 0.742397 0.669960i \(-0.233689\pi\)
0.742397 + 0.669960i \(0.233689\pi\)
\(252\) 0 0
\(253\) −1910.94 −0.474861
\(254\) 2080.17 + 3602.97i 0.513865 + 0.890041i
\(255\) −561.000 + 971.681i −0.137769 + 0.238624i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 204.112 + 353.532i 0.0495414 + 0.0858082i 0.889733 0.456482i \(-0.150891\pi\)
−0.840191 + 0.542290i \(0.817557\pi\)
\(258\) 2059.76 0.497035
\(259\) 0 0
\(260\) 82.6476 0.0197138
\(261\) −702.594 1216.93i −0.166626 0.288605i
\(262\) 1269.53 2198.89i 0.299357 0.518502i
\(263\) 2313.00 4006.24i 0.542304 0.939298i −0.456467 0.889740i \(-0.650885\pi\)
0.998771 0.0495577i \(-0.0157812\pi\)
\(264\) −125.823 217.932i −0.0293329 0.0508061i
\(265\) −1019.67 −0.236369
\(266\) 0 0
\(267\) −1660.46 −0.380594
\(268\) 791.294 + 1370.56i 0.180358 + 0.312389i
\(269\) 435.646 754.562i 0.0987429 0.171028i −0.812422 0.583070i \(-0.801851\pi\)
0.911165 + 0.412043i \(0.135185\pi\)
\(270\) −200.184 + 346.728i −0.0451215 + 0.0781527i
\(271\) −3236.17 5605.22i −0.725401 1.25643i −0.958809 0.284052i \(-0.908321\pi\)
0.233408 0.972379i \(-0.425012\pi\)
\(272\) 807.098 0.179917
\(273\) 0 0
\(274\) 6146.38 1.35517
\(275\) 367.139 + 635.904i 0.0805066 + 0.139442i
\(276\) 1093.50 1894.00i 0.238481 0.413062i
\(277\) −2355.94 + 4080.61i −0.511028 + 0.885126i 0.488890 + 0.872345i \(0.337402\pi\)
−0.999918 + 0.0127811i \(0.995932\pi\)
\(278\) −1013.60 1755.60i −0.218674 0.378755i
\(279\) 1256.69 0.269664
\(280\) 0 0
\(281\) −7165.66 −1.52124 −0.760618 0.649200i \(-0.775104\pi\)
−0.760618 + 0.649200i \(0.775104\pi\)
\(282\) 1830.01 + 3169.67i 0.386439 + 0.669331i
\(283\) −3173.50 + 5496.67i −0.666590 + 1.15457i 0.312261 + 0.949996i \(0.398914\pi\)
−0.978851 + 0.204572i \(0.934420\pi\)
\(284\) −571.322 + 989.559i −0.119372 + 0.206759i
\(285\) −1390.76 2408.87i −0.289059 0.500664i
\(286\) 58.4407 0.0120828
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) 1184.22 + 2051.13i 0.241038 + 0.417490i
\(290\) −1157.60 + 2005.02i −0.234401 + 0.405995i
\(291\) 1355.86 2348.43i 0.273135 0.473083i
\(292\) 1994.91 + 3455.29i 0.399807 + 0.692485i
\(293\) 9233.78 1.84110 0.920552 0.390621i \(-0.127740\pi\)
0.920552 + 0.390621i \(0.127740\pi\)
\(294\) 0 0
\(295\) 4370.20 0.862519
\(296\) 1578.23 + 2733.58i 0.309909 + 0.536778i
\(297\) −141.551 + 245.174i −0.0276554 + 0.0479005i
\(298\) −1231.47 + 2132.97i −0.239386 + 0.414629i
\(299\) 253.947 + 439.848i 0.0491174 + 0.0850739i
\(300\) −840.353 −0.161726
\(301\) 0 0
\(302\) −4489.47 −0.855430
\(303\) 470.417 + 814.785i 0.0891905 + 0.154482i
\(304\) −1000.43 + 1732.80i −0.188745 + 0.326917i
\(305\) −916.461 + 1587.36i −0.172054 + 0.298006i
\(306\) −453.993 786.339i −0.0848139 0.146902i
\(307\) 6786.53 1.26165 0.630827 0.775923i \(-0.282716\pi\)
0.630827 + 0.775923i \(0.282716\pi\)
\(308\) 0 0
\(309\) 692.924 0.127570
\(310\) −1035.26 1793.13i −0.189675 0.328526i
\(311\) −2568.38 + 4448.57i −0.468295 + 0.811111i −0.999343 0.0362307i \(-0.988465\pi\)
0.531048 + 0.847341i \(0.321798\pi\)
\(312\) −33.4416 + 57.9225i −0.00606813 + 0.0105103i
\(313\) 1881.78 + 3259.34i 0.339822 + 0.588590i 0.984399 0.175950i \(-0.0562997\pi\)
−0.644577 + 0.764540i \(0.722966\pi\)
\(314\) −7574.31 −1.36128
\(315\) 0 0
\(316\) −3393.06 −0.604033
\(317\) 517.473 + 896.289i 0.0916851 + 0.158803i 0.908220 0.418492i \(-0.137441\pi\)
−0.816535 + 0.577296i \(0.804108\pi\)
\(318\) 412.587 714.622i 0.0727570 0.126019i
\(319\) −818.544 + 1417.76i −0.143667 + 0.248838i
\(320\) −237.255 410.937i −0.0414467 0.0717878i
\(321\) 376.458 0.0654575
\(322\) 0 0
\(323\) 6308.17 1.08668
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) 97.5789 169.012i 0.0166545 0.0288464i
\(326\) 2108.56 3652.13i 0.358228 0.620469i
\(327\) −1118.29 1936.94i −0.189118 0.327562i
\(328\) 1580.84 0.266120
\(329\) 0 0
\(330\) 466.441 0.0778082
\(331\) −4400.03 7621.08i −0.730657 1.26554i −0.956603 0.291395i \(-0.905880\pi\)
0.225945 0.974140i \(-0.427453\pi\)
\(332\) 421.726 730.451i 0.0697145 0.120749i
\(333\) 1775.51 3075.28i 0.292185 0.506079i
\(334\) −1502.41 2602.26i −0.246133 0.426315i
\(335\) −2933.41 −0.478416
\(336\) 0 0
\(337\) −5859.78 −0.947189 −0.473595 0.880743i \(-0.657044\pi\)
−0.473595 + 0.880743i \(0.657044\pi\)
\(338\) 2189.23 + 3791.86i 0.352304 + 0.610208i
\(339\) 1565.64 2711.78i 0.250838 0.434464i
\(340\) −748.000 + 1295.57i −0.119312 + 0.206654i
\(341\) −732.043 1267.94i −0.116253 0.201356i
\(342\) 2250.97 0.355902
\(343\) 0 0
\(344\) 2746.35 0.430445
\(345\) 2026.86 + 3510.62i 0.316297 + 0.547842i
\(346\) −471.256 + 816.239i −0.0732222 + 0.126825i
\(347\) −3969.27 + 6874.98i −0.614068 + 1.06360i 0.376479 + 0.926425i \(0.377135\pi\)
−0.990547 + 0.137172i \(0.956199\pi\)
\(348\) −936.792 1622.57i −0.144303 0.249940i
\(349\) −9927.75 −1.52269 −0.761347 0.648344i \(-0.775462\pi\)
−0.761347 + 0.648344i \(0.775462\pi\)
\(350\) 0 0
\(351\) 75.2435 0.0114422
\(352\) −167.765 290.577i −0.0254031 0.0439994i
\(353\) 5051.52 8749.49i 0.761658 1.31923i −0.180338 0.983605i \(-0.557719\pi\)
0.941996 0.335625i \(-0.108948\pi\)
\(354\) −1768.31 + 3062.80i −0.265493 + 0.459847i
\(355\) −1058.98 1834.20i −0.158323 0.274223i
\(356\) −2213.95 −0.329604
\(357\) 0 0
\(358\) 2664.97 0.393431
\(359\) 2412.64 + 4178.81i 0.354691 + 0.614343i 0.987065 0.160320i \(-0.0512527\pi\)
−0.632374 + 0.774663i \(0.717919\pi\)
\(360\) −266.912 + 462.305i −0.0390763 + 0.0676822i
\(361\) −4389.73 + 7603.23i −0.639996 + 1.10850i
\(362\) 997.727 + 1728.11i 0.144860 + 0.250905i
\(363\) −3663.18 −0.529661
\(364\) 0 0
\(365\) −7395.36 −1.06052
\(366\) −741.652 1284.58i −0.105920 0.183459i
\(367\) −3467.65 + 6006.15i −0.493215 + 0.854274i −0.999969 0.00781688i \(-0.997512\pi\)
0.506754 + 0.862091i \(0.330845\pi\)
\(368\) 1458.00 2525.33i 0.206531 0.357722i
\(369\) −889.223 1540.18i −0.125450 0.217286i
\(370\) −5850.68 −0.822061
\(371\) 0 0
\(372\) 1675.59 0.233536
\(373\) −7046.55 12205.0i −0.978168 1.69424i −0.669058 0.743210i \(-0.733302\pi\)
−0.309110 0.951026i \(-0.600031\pi\)
\(374\) −528.916 + 916.109i −0.0731272 + 0.126660i
\(375\) 2168.98 3756.79i 0.298682 0.517333i
\(376\) 2440.02 + 4226.23i 0.334666 + 0.579658i
\(377\) 435.108 0.0594409
\(378\) 0 0
\(379\) 5354.17 0.725661 0.362830 0.931855i \(-0.381810\pi\)
0.362830 + 0.931855i \(0.381810\pi\)
\(380\) −1854.35 3211.83i −0.250332 0.433588i
\(381\) 3120.26 5404.45i 0.419569 0.726715i
\(382\) −1226.72 + 2124.74i −0.164305 + 0.284585i
\(383\) 4485.24 + 7768.66i 0.598394 + 1.03645i 0.993058 + 0.117623i \(0.0375276\pi\)
−0.394664 + 0.918825i \(0.629139\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) −6958.58 −0.917571
\(387\) −1544.82 2675.71i −0.202914 0.351457i
\(388\) 1807.82 3131.23i 0.236542 0.409702i
\(389\) 1851.29 3206.53i 0.241296 0.417937i −0.719788 0.694194i \(-0.755761\pi\)
0.961084 + 0.276257i \(0.0890942\pi\)
\(390\) −61.9857 107.362i −0.00804812 0.0139398i
\(391\) −9193.34 −1.18907
\(392\) 0 0
\(393\) −3808.58 −0.488849
\(394\) −3193.47 5531.26i −0.408337 0.707260i
\(395\) 3144.61 5446.62i 0.400563 0.693795i
\(396\) −188.735 + 326.899i −0.0239502 + 0.0414830i
\(397\) 1041.62 + 1804.13i 0.131681 + 0.228078i 0.924325 0.381607i \(-0.124629\pi\)
−0.792644 + 0.609685i \(0.791296\pi\)
\(398\) 2130.30 0.268297
\(399\) 0 0
\(400\) −1120.47 −0.140059
\(401\) 5317.01 + 9209.33i 0.662141 + 1.14686i 0.980052 + 0.198742i \(0.0636855\pi\)
−0.317910 + 0.948121i \(0.602981\pi\)
\(402\) 1186.94 2055.84i 0.147262 0.255065i
\(403\) −194.564 + 336.994i −0.0240494 + 0.0416548i
\(404\) 627.222 + 1086.38i 0.0772412 + 0.133786i
\(405\) 600.551 0.0736830
\(406\) 0 0
\(407\) −4137.06 −0.503848
\(408\) −605.324 1048.45i −0.0734510 0.127221i
\(409\) 3258.18 5643.34i 0.393904 0.682262i −0.599056 0.800707i \(-0.704458\pi\)
0.992961 + 0.118445i \(0.0377908\pi\)
\(410\) −1465.09 + 2537.60i −0.176477 + 0.305667i
\(411\) −4609.78 7984.38i −0.553245 0.958249i
\(412\) 923.899 0.110479
\(413\) 0 0
\(414\) −3280.50 −0.389439
\(415\) 781.691 + 1353.93i 0.0924620 + 0.160149i
\(416\) −44.5887 + 77.2300i −0.00525515 + 0.00910219i
\(417\) −1520.39 + 2633.40i −0.178547 + 0.309252i
\(418\) −1311.22 2271.11i −0.153431 0.265750i
\(419\) 6079.92 0.708887 0.354443 0.935077i \(-0.384670\pi\)
0.354443 + 0.935077i \(0.384670\pi\)
\(420\) 0 0
\(421\) −5631.58 −0.651939 −0.325969 0.945380i \(-0.605691\pi\)
−0.325969 + 0.945380i \(0.605691\pi\)
\(422\) −2057.50 3563.69i −0.237340 0.411084i
\(423\) 2745.02 4754.51i 0.315526 0.546507i
\(424\) 550.116 952.829i 0.0630094 0.109136i
\(425\) 1766.27 + 3059.27i 0.201592 + 0.349168i
\(426\) 1713.97 0.194934
\(427\) 0 0
\(428\) 501.945 0.0566879
\(429\) −43.8305 75.9167i −0.00493277 0.00854380i
\(430\) −2545.25 + 4408.50i −0.285449 + 0.494412i
\(431\) 1868.45 3236.25i 0.208817 0.361681i −0.742525 0.669818i \(-0.766372\pi\)
0.951342 + 0.308137i \(0.0997055\pi\)
\(432\) −216.000 374.123i −0.0240563 0.0416667i
\(433\) −5757.46 −0.638998 −0.319499 0.947587i \(-0.603515\pi\)
−0.319499 + 0.947587i \(0.603515\pi\)
\(434\) 0 0
\(435\) 3472.79 0.382776
\(436\) −1491.05 2582.58i −0.163781 0.283677i
\(437\) 11395.5 19737.6i 1.24742 2.16059i
\(438\) 2992.37 5182.94i 0.326441 0.565412i
\(439\) 4906.38 + 8498.10i 0.533414 + 0.923900i 0.999238 + 0.0390229i \(0.0124245\pi\)
−0.465824 + 0.884877i \(0.654242\pi\)
\(440\) 621.921 0.0673839
\(441\) 0 0
\(442\) 281.152 0.0302558
\(443\) −2915.15 5049.19i −0.312648 0.541522i 0.666287 0.745695i \(-0.267883\pi\)
−0.978935 + 0.204174i \(0.934549\pi\)
\(444\) 2367.35 4100.37i 0.253039 0.438277i
\(445\) 2051.84 3553.89i 0.218576 0.378585i
\(446\) −2028.27 3513.06i −0.215339 0.372978i
\(447\) 3694.41 0.390916
\(448\) 0 0
\(449\) −8674.94 −0.911794 −0.455897 0.890033i \(-0.650681\pi\)
−0.455897 + 0.890033i \(0.650681\pi\)
\(450\) 630.265 + 1091.65i 0.0660244 + 0.114358i
\(451\) −1035.97 + 1794.36i −0.108164 + 0.187346i
\(452\) 2087.53 3615.70i 0.217232 0.376257i
\(453\) 3367.10 + 5831.99i 0.349228 + 0.604881i
\(454\) 4847.91 0.501154
\(455\) 0 0
\(456\) 3001.29 0.308220
\(457\) −4553.41 7886.74i −0.466082 0.807278i 0.533167 0.846010i \(-0.321002\pi\)
−0.999250 + 0.0387315i \(0.987668\pi\)
\(458\) 1967.17 3407.24i 0.200698 0.347619i
\(459\) −680.989 + 1179.51i −0.0692502 + 0.119945i
\(460\) 2702.48 + 4680.83i 0.273921 + 0.474445i
\(461\) −8729.69 −0.881957 −0.440979 0.897518i \(-0.645369\pi\)
−0.440979 + 0.897518i \(0.645369\pi\)
\(462\) 0 0
\(463\) −1795.62 −0.180237 −0.0901184 0.995931i \(-0.528725\pi\)
−0.0901184 + 0.995931i \(0.528725\pi\)
\(464\) −1249.06 2163.43i −0.124970 0.216454i
\(465\) −1552.90 + 2689.70i −0.154869 + 0.268240i
\(466\) −4478.33 + 7756.70i −0.445182 + 0.771078i
\(467\) −65.2797 113.068i −0.00646849 0.0112038i 0.862773 0.505591i \(-0.168726\pi\)
−0.869242 + 0.494388i \(0.835392\pi\)
\(468\) 100.325 0.00990921
\(469\) 0 0
\(470\) −9045.40 −0.887730
\(471\) 5680.74 + 9839.32i 0.555742 + 0.962573i
\(472\) −2357.74 + 4083.73i −0.229924 + 0.398239i
\(473\) −1799.76 + 3117.28i −0.174954 + 0.303029i
\(474\) 2544.79 + 4407.71i 0.246595 + 0.427116i
\(475\) −8757.45 −0.845935
\(476\) 0 0
\(477\) −1237.76 −0.118812
\(478\) −6116.92 10594.8i −0.585317 1.01380i
\(479\) −5922.90 + 10258.8i −0.564978 + 0.978570i 0.432074 + 0.901838i \(0.357782\pi\)
−0.997052 + 0.0767319i \(0.975551\pi\)
\(480\) −355.882 + 616.406i −0.0338411 + 0.0586145i
\(481\) 549.777 + 952.242i 0.0521158 + 0.0902671i
\(482\) 12456.8 1.17716
\(483\) 0 0
\(484\) −4884.24 −0.458700
\(485\) 3350.89 + 5803.91i 0.313724 + 0.543386i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) 2403.61 4163.17i 0.223650 0.387374i −0.732263 0.681022i \(-0.761536\pi\)
0.955914 + 0.293648i \(0.0948693\pi\)
\(488\) −988.870 1712.77i −0.0917296 0.158880i
\(489\) −6325.68 −0.584984
\(490\) 0 0
\(491\) 6068.04 0.557733 0.278866 0.960330i \(-0.410041\pi\)
0.278866 + 0.960330i \(0.410041\pi\)
\(492\) −1185.63 2053.57i −0.108643 0.188175i
\(493\) −3937.93 + 6820.70i −0.359748 + 0.623101i
\(494\) −348.500 + 603.619i −0.0317404 + 0.0549759i
\(495\) −349.831 605.924i −0.0317651 0.0550187i
\(496\) 2234.12 0.202248
\(497\) 0 0
\(498\) −1265.18 −0.113843
\(499\) 7753.21 + 13429.0i 0.695554 + 1.20473i 0.969994 + 0.243130i \(0.0781742\pi\)
−0.274440 + 0.961604i \(0.588492\pi\)
\(500\) 2891.98 5009.06i 0.258667 0.448024i
\(501\) −2253.62 + 3903.39i −0.200967 + 0.348085i
\(502\) −5904.42 10226.7i −0.524954 0.909247i
\(503\) −1496.79 −0.132681 −0.0663405 0.997797i \(-0.521132\pi\)
−0.0663405 + 0.997797i \(0.521132\pi\)
\(504\) 0 0
\(505\) −2325.18 −0.204889
\(506\) 1910.94 + 3309.85i 0.167889 + 0.290792i
\(507\) 3283.85 5687.80i 0.287655 0.498233i
\(508\) 4160.35 7205.94i 0.363358 0.629354i
\(509\) 2526.87 + 4376.66i 0.220042 + 0.381124i 0.954821 0.297183i \(-0.0960472\pi\)
−0.734778 + 0.678307i \(0.762714\pi\)
\(510\) 2244.00 0.194835
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −1688.23 2924.09i −0.145296 0.251661i
\(514\) 408.223 707.063i 0.0350310 0.0606755i
\(515\) −856.248 + 1483.07i −0.0732637 + 0.126896i
\(516\) −2059.76 3567.61i −0.175729 0.304371i
\(517\) −6396.07 −0.544098
\(518\) 0 0
\(519\) 1413.77 0.119571
\(520\) −82.6476 143.150i −0.00696988 0.0120722i
\(521\) −4868.36 + 8432.25i −0.409380 + 0.709067i −0.994820 0.101649i \(-0.967588\pi\)
0.585441 + 0.810715i \(0.300922\pi\)
\(522\) −1405.19 + 2433.86i −0.117823 + 0.204075i
\(523\) 5898.34 + 10216.2i 0.493148 + 0.854157i 0.999969 0.00789446i \(-0.00251291\pi\)
−0.506821 + 0.862051i \(0.669180\pi\)
\(524\) −5078.11 −0.423355
\(525\) 0 0
\(526\) −9252.01 −0.766933
\(527\) −3521.79 6099.91i −0.291103 0.504206i
\(528\) −251.647 + 435.865i −0.0207415 + 0.0359254i
\(529\) −10524.0 + 18228.1i −0.864962 + 1.49816i
\(530\) 1019.67 + 1766.12i 0.0835691 + 0.144746i
\(531\) 5304.92 0.433548
\(532\) 0 0
\(533\) 550.685 0.0447520
\(534\) 1660.46 + 2876.00i 0.134560 + 0.233065i
\(535\) −465.191 + 805.734i −0.0375924 + 0.0651120i
\(536\) 1582.59 2741.12i 0.127532 0.220893i
\(537\) −1998.73 3461.90i −0.160617 0.278198i
\(538\) −1742.59 −0.139644
\(539\) 0 0
\(540\) 800.735 0.0638114
\(541\) 2155.41 + 3733.28i 0.171291 + 0.296684i 0.938871 0.344268i \(-0.111873\pi\)
−0.767581 + 0.640952i \(0.778540\pi\)
\(542\) −6472.35 + 11210.4i −0.512936 + 0.888431i
\(543\) 1496.59 2592.17i 0.118278 0.204863i
\(544\) −807.098 1397.94i −0.0636104 0.110176i
\(545\) 5527.50 0.434444
\(546\) 0 0
\(547\) 17015.9 1.33007 0.665034 0.746813i \(-0.268417\pi\)
0.665034 + 0.746813i \(0.268417\pi\)
\(548\) −6146.38 10645.8i −0.479124 0.829868i
\(549\) −1112.48 + 1926.87i −0.0864835 + 0.149794i
\(550\) 734.278 1271.81i 0.0569268 0.0986001i
\(551\) −9762.45 16909.1i −0.754799 1.30735i
\(552\) −4373.99 −0.337264
\(553\) 0 0
\(554\) 9423.76 0.722703
\(555\) 4388.01 + 7600.26i 0.335605 + 0.581285i
\(556\) −2027.19 + 3511.20i −0.154626 + 0.267820i
\(557\) −870.588 + 1507.90i −0.0662262 + 0.114707i −0.897237 0.441549i \(-0.854429\pi\)
0.831011 + 0.556256i \(0.187763\pi\)
\(558\) −1256.69 2176.65i −0.0953405 0.165135i
\(559\) 956.689 0.0723858
\(560\) 0 0
\(561\) 1586.75 0.119416
\(562\) 7165.66 + 12411.3i 0.537838 + 0.931563i
\(563\) −5673.42 + 9826.66i −0.424700 + 0.735602i −0.996392 0.0848658i \(-0.972954\pi\)
0.571692 + 0.820468i \(0.306287\pi\)
\(564\) 3660.03 6339.35i 0.273253 0.473289i
\(565\) 3869.34 + 6701.89i 0.288114 + 0.499028i
\(566\) 12694.0 0.942701
\(567\) 0 0
\(568\) 2285.29 0.168818
\(569\) 9208.72 + 15950.0i 0.678470 + 1.17514i 0.975442 + 0.220258i \(0.0706900\pi\)
−0.296972 + 0.954886i \(0.595977\pi\)
\(570\) −2781.53 + 4817.75i −0.204395 + 0.354023i
\(571\) −4999.25 + 8658.95i −0.366396 + 0.634616i −0.988999 0.147922i \(-0.952742\pi\)
0.622603 + 0.782538i \(0.286075\pi\)
\(572\) −58.4407 101.222i −0.00427190 0.00739915i
\(573\) 3680.16 0.268309
\(574\) 0 0
\(575\) 12762.8 0.925648
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) 700.855 1213.92i 0.0505667 0.0875840i −0.839634 0.543152i \(-0.817231\pi\)
0.890201 + 0.455568i \(0.150564\pi\)
\(578\) 2368.44 4102.26i 0.170440 0.295210i
\(579\) 5218.94 + 9039.47i 0.374597 + 0.648821i
\(580\) 4630.38 0.331494
\(581\) 0 0
\(582\) −5423.46 −0.386271
\(583\) 721.015 + 1248.83i 0.0512202 + 0.0887160i
\(584\) 3989.83 6910.59i 0.282706 0.489661i
\(585\) −92.9786 + 161.044i −0.00657127 + 0.0113818i
\(586\) −9233.78 15993.4i −0.650928 1.12744i
\(587\) −10851.3 −0.763001 −0.381500 0.924369i \(-0.624593\pi\)
−0.381500 + 0.924369i \(0.624593\pi\)
\(588\) 0 0
\(589\) 17461.6 1.22155
\(590\) −4370.20 7569.41i −0.304946 0.528183i
\(591\) −4790.21 + 8296.88i −0.333406 + 0.577476i
\(592\) 3156.47 5467.16i 0.219139 0.379559i
\(593\) −10231.0 17720.6i −0.708493 1.22715i −0.965416 0.260715i \(-0.916042\pi\)
0.256923 0.966432i \(-0.417291\pi\)
\(594\) 566.205 0.0391106
\(595\) 0 0
\(596\) 4925.88 0.338544
\(597\) −1597.72 2767.34i −0.109532 0.189715i
\(598\) 507.893 879.697i 0.0347313 0.0601563i
\(599\) −4995.21 + 8651.96i −0.340733 + 0.590166i −0.984569 0.174997i \(-0.944008\pi\)
0.643836 + 0.765163i \(0.277342\pi\)
\(600\) 840.353 + 1455.53i 0.0571788 + 0.0990366i
\(601\) 17435.9 1.18341 0.591703 0.806156i \(-0.298456\pi\)
0.591703 + 0.806156i \(0.298456\pi\)
\(602\) 0 0
\(603\) −3560.82 −0.240477
\(604\) 4489.47 + 7775.99i 0.302440 + 0.523842i
\(605\) 4526.60 7840.29i 0.304186 0.526865i
\(606\) 940.833 1629.57i 0.0630672 0.109236i
\(607\) −8350.16 14462.9i −0.558356 0.967102i −0.997634 0.0687503i \(-0.978099\pi\)
0.439277 0.898351i \(-0.355234\pi\)
\(608\) 4001.72 0.266926
\(609\) 0 0
\(610\) 3665.85 0.243321
\(611\) 849.979 + 1472.21i 0.0562790 + 0.0974781i
\(612\) −907.986 + 1572.68i −0.0599725 + 0.103875i
\(613\) 13351.5 23125.4i 0.879707 1.52370i 0.0280452 0.999607i \(-0.491072\pi\)
0.851662 0.524091i \(-0.175595\pi\)
\(614\) −6786.53 11754.6i −0.446062 0.772602i
\(615\) 4395.26 0.288185
\(616\) 0 0
\(617\) 27790.4 1.81329 0.906645 0.421894i \(-0.138635\pi\)
0.906645 + 0.421894i \(0.138635\pi\)
\(618\) −692.924 1200.18i −0.0451028 0.0781203i
\(619\) −868.040 + 1503.49i −0.0563642 + 0.0976257i −0.892831 0.450392i \(-0.851284\pi\)
0.836467 + 0.548018i \(0.184617\pi\)
\(620\) −2070.53 + 3586.26i −0.134120 + 0.232303i
\(621\) 2460.37 + 4261.49i 0.158988 + 0.275375i
\(622\) 10273.5 0.662269
\(623\) 0 0
\(624\) 133.766 0.00858163
\(625\) 983.599 + 1703.64i 0.0629503 + 0.109033i
\(626\) 3763.56 6518.67i 0.240291 0.416196i
\(627\) −1966.84 + 3406.66i −0.125276 + 0.216984i
\(628\) 7574.31 + 13119.1i 0.481287 + 0.833613i
\(629\) −19903.0 −1.26166
\(630\) 0 0
\(631\) −8990.27 −0.567190 −0.283595 0.958944i \(-0.591527\pi\)
−0.283595 + 0.958944i \(0.591527\pi\)
\(632\) 3393.06 + 5876.95i 0.213558 + 0.369893i
\(633\) −3086.24 + 5345.53i −0.193787 + 0.335649i
\(634\) 1034.95 1792.58i 0.0648311 0.112291i
\(635\) 7711.43 + 13356.6i 0.481919 + 0.834709i
\(636\) −1650.35 −0.102894
\(637\) 0 0
\(638\) 3274.18 0.203175
\(639\) −1285.47 2226.51i −0.0795815 0.137839i
\(640\) −474.510 + 821.875i −0.0293073 + 0.0507617i
\(641\) 6884.81 11924.8i 0.424233 0.734794i −0.572115 0.820173i \(-0.693877\pi\)
0.996348 + 0.0853796i \(0.0272103\pi\)
\(642\) −376.458 652.045i −0.0231427 0.0400844i
\(643\) 26969.9 1.65411 0.827053 0.562124i \(-0.190015\pi\)
0.827053 + 0.562124i \(0.190015\pi\)
\(644\) 0 0
\(645\) 7635.75 0.466136
\(646\) −6308.17 10926.1i −0.384198 0.665450i
\(647\) −12200.9 + 21132.5i −0.741368 + 1.28409i 0.210504 + 0.977593i \(0.432490\pi\)
−0.951872 + 0.306495i \(0.900844\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) −3090.20 5352.38i −0.186904 0.323728i
\(650\) −390.316 −0.0235530
\(651\) 0 0
\(652\) −8434.24 −0.506611
\(653\) −7984.79 13830.1i −0.478513 0.828809i 0.521183 0.853445i \(-0.325491\pi\)
−0.999696 + 0.0246357i \(0.992157\pi\)
\(654\) −2236.58 + 3873.87i −0.133727 + 0.231621i
\(655\) 4706.27 8151.50i 0.280747 0.486268i
\(656\) −1580.84 2738.10i −0.0940876 0.162965i
\(657\) −8977.11 −0.533075
\(658\) 0 0
\(659\) −11596.2 −0.685467 −0.342733 0.939433i \(-0.611353\pi\)
−0.342733 + 0.939433i \(0.611353\pi\)
\(660\) −466.441 807.899i −0.0275094 0.0476476i
\(661\) −6301.11 + 10913.8i −0.370779 + 0.642208i −0.989686 0.143257i \(-0.954243\pi\)
0.618907 + 0.785464i \(0.287576\pi\)
\(662\) −8800.06 + 15242.2i −0.516653 + 0.894869i
\(663\) −210.864 365.228i −0.0123519 0.0213941i
\(664\) −1686.90 −0.0985912
\(665\) 0 0
\(666\) −7102.05 −0.413212
\(667\) 14227.5 + 24642.8i 0.825924 + 1.43054i
\(668\) −3004.83 + 5204.52i −0.174042 + 0.301450i
\(669\) −3042.40 + 5269.59i −0.175824 + 0.304536i
\(670\) 2933.41 + 5080.81i 0.169146 + 0.292969i
\(671\) 2592.14 0.149134
\(672\) 0 0
\(673\) 2126.29 0.121787 0.0608934 0.998144i \(-0.480605\pi\)
0.0608934 + 0.998144i \(0.480605\pi\)
\(674\) 5859.78 + 10149.4i 0.334882 + 0.580032i
\(675\) 945.397 1637.48i 0.0539087 0.0933726i
\(676\) 4378.47 7583.73i 0.249116 0.431482i
\(677\) −1309.69 2268.45i −0.0743508 0.128779i 0.826453 0.563006i \(-0.190355\pi\)
−0.900804 + 0.434226i \(0.857022\pi\)
\(678\) −6262.58 −0.354739
\(679\) 0 0
\(680\) 2992.00 0.168732
\(681\) −3635.94 6297.63i −0.204595 0.354369i
\(682\) −1464.09 + 2535.87i −0.0822034 + 0.142381i
\(683\) 14964.9 25919.9i 0.838383 1.45212i −0.0528633 0.998602i \(-0.516835\pi\)
0.891246 0.453520i \(-0.149832\pi\)
\(684\) −2250.97 3898.79i −0.125830 0.217945i
\(685\) 22785.3 1.27092
\(686\) 0 0
\(687\) −5901.51 −0.327739
\(688\) −2746.35 4756.81i −0.152185 0.263593i
\(689\) 191.633 331.918i 0.0105960 0.0183528i
\(690\) 4053.72 7021.24i 0.223656 0.387383i
\(691\) −3380.45 5855.11i −0.186105 0.322343i 0.757844 0.652436i \(-0.226253\pi\)
−0.943948 + 0.330094i \(0.892920\pi\)
\(692\) 1885.02 0.103552
\(693\) 0 0
\(694\) 15877.1 0.868423
\(695\) −3757.51 6508.20i −0.205080 0.355209i
\(696\) −1873.58 + 3245.14i −0.102037 + 0.176734i
\(697\) −4983.96 + 8632.48i −0.270848 + 0.469122i
\(698\) 9927.75 + 17195.4i 0.538354 + 0.932456i
\(699\) 13435.0 0.726979
\(700\) 0 0
\(701\) 467.205 0.0251727 0.0125864 0.999921i \(-0.495994\pi\)
0.0125864 + 0.999921i \(0.495994\pi\)
\(702\) −75.2435 130.326i −0.00404542 0.00700687i
\(703\) 24670.5 42730.6i 1.32357 2.29248i
\(704\) −335.529 + 581.153i −0.0179627 + 0.0311123i
\(705\) 6784.05 + 11750.3i 0.362414 + 0.627720i
\(706\) −20206.1 −1.07715
\(707\) 0 0
\(708\) 7073.23 0.375464
\(709\) −4412.32 7642.36i −0.233721 0.404816i 0.725179 0.688560i \(-0.241757\pi\)
−0.958900 + 0.283744i \(0.908424\pi\)
\(710\) −2117.95 + 3668.40i −0.111951 + 0.193905i
\(711\) 3817.19 6611.56i 0.201344 0.348738i
\(712\) 2213.95 + 3834.67i 0.116533 + 0.201841i
\(713\) −25448.0 −1.33665
\(714\) 0 0
\(715\) 216.646 0.0113316
\(716\) −2664.97 4615.87i −0.139099 0.240926i
\(717\) −9175.38 + 15892.2i −0.477909 + 0.827763i
\(718\) 4825.27 8357.62i 0.250804 0.434406i
\(719\) 10549.4 + 18272.2i 0.547188 + 0.947757i 0.998466 + 0.0553733i \(0.0176349\pi\)
−0.451278 + 0.892383i \(0.649032\pi\)
\(720\) 1067.65 0.0552623
\(721\) 0 0
\(722\) 17558.9 0.905090
\(723\) −9342.57 16181.8i −0.480573 0.832376i
\(724\) 1995.45 3456.23i 0.102432 0.177417i
\(725\) 5466.92 9468.98i 0.280050 0.485061i
\(726\) 3663.18 + 6344.81i 0.187263 + 0.324350i
\(727\) −4616.48 −0.235510 −0.117755 0.993043i \(-0.537570\pi\)
−0.117755 + 0.993043i \(0.537570\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 7395.36 + 12809.1i 0.374951 + 0.649435i
\(731\) −8658.49 + 14996.9i −0.438093 + 0.758799i
\(732\) −1483.30 + 2569.16i −0.0748969 + 0.129725i
\(733\) 5344.03 + 9256.13i 0.269285 + 0.466416i 0.968678 0.248322i \(-0.0798791\pi\)
−0.699392 + 0.714738i \(0.746546\pi\)
\(734\) 13870.6 0.697511
\(735\) 0 0
\(736\) −5831.99 −0.292079
\(737\) 2074.23 + 3592.68i 0.103671 + 0.179563i
\(738\) −1778.45 + 3080.36i −0.0887066 + 0.153644i
\(739\) 7683.78 13308.7i 0.382480 0.662474i −0.608936 0.793219i \(-0.708404\pi\)
0.991416 + 0.130745i \(0.0417369\pi\)
\(740\) 5850.68 + 10133.7i 0.290642 + 0.503407i
\(741\) 1045.50 0.0518318
\(742\) 0 0
\(743\) 6502.58 0.321072 0.160536 0.987030i \(-0.448678\pi\)
0.160536 + 0.987030i \(0.448678\pi\)
\(744\) −1675.59 2902.21i −0.0825673 0.143011i
\(745\) −4565.19 + 7907.14i −0.224504 + 0.388853i
\(746\) −14093.1 + 24410.0i −0.691669 + 1.19801i
\(747\) 948.883 + 1643.51i 0.0464763 + 0.0804994i
\(748\) 2115.66 0.103418
\(749\) 0 0
\(750\) −8675.94 −0.422401
\(751\) 9937.07 + 17211.5i 0.482835 + 0.836295i 0.999806 0.0197085i \(-0.00627380\pi\)
−0.516971 + 0.856003i \(0.672940\pi\)
\(752\) 4880.03 8452.47i 0.236644 0.409880i
\(753\) −8856.62 + 15340.1i −0.428623 + 0.742397i
\(754\) −435.108 753.630i −0.0210155 0.0364000i
\(755\) −16642.9 −0.802250
\(756\) 0 0
\(757\) −15157.8 −0.727765 −0.363883 0.931445i \(-0.618549\pi\)
−0.363883 + 0.931445i \(0.618549\pi\)
\(758\) −5354.17 9273.70i −0.256560 0.444375i
\(759\) 2866.41 4964.77i 0.137081 0.237430i
\(760\) −3708.70 + 6423.66i −0.177012 + 0.306593i
\(761\) −17609.9 30501.3i −0.838842 1.45292i −0.890863 0.454271i \(-0.849900\pi\)
0.0520212 0.998646i \(-0.483434\pi\)
\(762\) −12481.0 −0.593361
\(763\) 0 0
\(764\) 4906.88 0.232362
\(765\) −1683.00 2915.04i −0.0795412 0.137769i
\(766\) 8970.47 15537.3i 0.423128 0.732880i
\(767\) −821.319 + 1422.57i −0.0386651 + 0.0669698i
\(768\) −384.000 665.108i −0.0180422 0.0312500i
\(769\) −2264.35 −0.106183 −0.0530915 0.998590i \(-0.516907\pi\)
−0.0530915 + 0.998590i \(0.516907\pi\)
\(770\) 0 0
\(771\) −1224.67 −0.0572054
\(772\) 6958.58 + 12052.6i 0.324410 + 0.561895i
\(773\) 4766.39 8255.64i 0.221779 0.384133i −0.733569 0.679615i \(-0.762147\pi\)
0.955348 + 0.295482i \(0.0954803\pi\)
\(774\) −3089.64 + 5351.42i −0.143482 + 0.248518i
\(775\) 4889.19 + 8468.33i 0.226613 + 0.392505i
\(776\) −7231.28 −0.334520
\(777\) 0 0
\(778\) −7405.16 −0.341244
\(779\) −12355.6 21400.6i −0.568276 0.984282i
\(780\) −123.971 + 214.725i −0.00569088 + 0.00985690i
\(781\) −1497.62 + 2593.95i −0.0686159 + 0.118846i
\(782\) 9193.34 + 15923.3i 0.420401 + 0.728155i
\(783\) 4215.56 0.192404
\(784\) 0 0
\(785\) −28078.8 −1.27666
\(786\) 3808.58 + 6596.66i 0.172834 + 0.299357i
\(787\) 16606.5 28763.3i 0.752170 1.30280i −0.194599 0.980883i \(-0.562341\pi\)
0.946769 0.321913i \(-0.104326\pi\)
\(788\) −6386.94 + 11062.5i −0.288738 + 0.500109i
\(789\) 6939.01 + 12018.7i 0.313099 + 0.542304i
\(790\) −12578.4 −0.566481
\(791\) 0 0
\(792\) 754.940 0.0338708
\(793\) −344.472 596.643i −0.0154257 0.0267181i
\(794\) 2083.24 3608.27i 0.0931124 0.161275i
\(795\) 1529.50 2649.18i 0.0682339 0.118185i
\(796\) −2130.30 3689.78i −0.0948573 0.164298i
\(797\) 42065.6 1.86956 0.934781 0.355223i \(-0.115595\pi\)
0.934781 + 0.355223i \(0.115595\pi\)
\(798\) 0 0
\(799\) −30770.8 −1.36245
\(800\) 1120.47 + 1940.71i 0.0495183 + 0.0857682i
\(801\) 2490.69 4314.01i 0.109868 0.190297i
\(802\) 10634.0 18418.7i 0.468205 0.810954i
\(803\) 5229.31 + 9057.43i 0.229811 + 0.398044i
\(804\) −4747.76 −0.208259
\(805\) 0 0
\(806\) 778.255 0.0340110
\(807\) 1306.94 + 2263.69i 0.0570092 + 0.0987429i
\(808\) 1254.44 2172.76i 0.0546178 0.0946008i
\(809\) 388.780 673.387i 0.0168959 0.0292646i −0.857454 0.514561i \(-0.827955\pi\)
0.874350 + 0.485296i \(0.161288\pi\)
\(810\) −600.551 1040.19i −0.0260509 0.0451215i
\(811\) 16559.4 0.716991 0.358496 0.933531i \(-0.383290\pi\)
0.358496 + 0.933531i \(0.383290\pi\)
\(812\) 0 0
\(813\) 19417.0 0.837620
\(814\) 4137.06 + 7165.59i 0.178137 + 0.308543i
\(815\) 7816.66 13538.8i 0.335958 0.581896i
\(816\) −1210.65 + 2096.90i −0.0519377 + 0.0899587i
\(817\) −21465.1 37178.6i −0.919178 1.59206i
\(818\) −13032.7 −0.557065
\(819\) 0 0
\(820\) 5860.35 0.249576
\(821\) −115.612 200.246i −0.00491460 0.00851235i 0.863558 0.504250i \(-0.168231\pi\)
−0.868472 + 0.495738i \(0.834898\pi\)
\(822\) −9219.56 + 15968.8i −0.391203 + 0.677584i
\(823\) 2611.43 4523.13i 0.110606 0.191575i −0.805409 0.592720i \(-0.798054\pi\)
0.916015 + 0.401145i \(0.131388\pi\)
\(824\) −923.899 1600.24i −0.0390601 0.0676541i
\(825\) −2202.84 −0.0929611
\(826\) 0 0
\(827\) −46225.5 −1.94367 −0.971836 0.235658i \(-0.924275\pi\)
−0.971836 + 0.235658i \(0.924275\pi\)
\(828\) 3280.50 + 5681.99i 0.137687 + 0.238481i
\(829\) 19797.1 34289.6i 0.829410 1.43658i −0.0690913 0.997610i \(-0.522010\pi\)
0.898502 0.438970i \(-0.144657\pi\)
\(830\) 1563.38 2707.86i 0.0653805 0.113242i
\(831\) −7067.82 12241.8i −0.295042 0.511028i
\(832\) 178.355 0.00743191
\(833\) 0 0
\(834\) 6081.58 0.252503
\(835\) −5569.61 9646.85i −0.230832 0.399812i
\(836\) −2622.45 + 4542.22i −0.108492 + 0.187914i
\(837\) −1885.04 + 3264.98i −0.0778452 + 0.134832i
\(838\) −6079.92 10530.7i −0.250629 0.434103i
\(839\) −45737.6 −1.88205 −0.941023 0.338344i \(-0.890133\pi\)
−0.941023 + 0.338344i \(0.890133\pi\)
\(840\) 0 0
\(841\) −11.7878 −0.000483326
\(842\) 5631.58 + 9754.18i 0.230495 + 0.399229i
\(843\) 10748.5 18616.9i 0.439143 0.760618i
\(844\) −4114.99 + 7127.37i −0.167824 + 0.290680i
\(845\) 8115.72 + 14056.8i 0.330402 + 0.572272i
\(846\) −10980.1 −0.446221
\(847\) 0 0
\(848\) −2200.46 −0.0891088
\(849\) −9520.50 16490.0i −0.384856 0.666590i
\(850\) 3532.54 6118.54i 0.142547 0.246899i
\(851\) −35954.1 + 62274.3i −1.44828 + 2.50850i
\(852\) −1713.97 2968.68i −0.0689196 0.119372i
\(853\) −8795.55 −0.353053 −0.176526 0.984296i \(-0.556486\pi\)
−0.176526 + 0.984296i \(0.556486\pi\)
\(854\) 0 0
\(855\) 8344.58 0.333776
\(856\) −501.945 869.394i −0.0200422 0.0347141i
\(857\) −15127.5 + 26201.6i −0.602969 + 1.04437i 0.389400 + 0.921069i \(0.372683\pi\)
−0.992369 + 0.123305i \(0.960651\pi\)
\(858\) −87.6610 + 151.833i −0.00348799 + 0.00604138i
\(859\) −22496.7 38965.5i −0.893573 1.54771i −0.835561 0.549398i \(-0.814857\pi\)
−0.0580118 0.998316i \(-0.518476\pi\)
\(860\) 10181.0 0.403685
\(861\) 0 0
\(862\) −7473.79 −0.295311
\(863\) −22333.9 38683.5i −0.880946 1.52584i −0.850291 0.526313i \(-0.823574\pi\)
−0.0306555 0.999530i \(-0.509759\pi\)
\(864\) −432.000 + 748.246i −0.0170103 + 0.0294628i
\(865\) −1747.00 + 3025.89i −0.0686701 + 0.118940i
\(866\) 5757.46 + 9972.22i 0.225920 + 0.391305i
\(867\) −7105.31 −0.278327
\(868\) 0 0
\(869\) −8894.29 −0.347201
\(870\) −3472.79 6015.05i −0.135332 0.234401i
\(871\) 551.294 954.868i 0.0214465 0.0371464i
\(872\) −2982.11 + 5165.16i −0.115811 + 0.200590i
\(873\) 4067.59 + 7045.28i 0.157694 + 0.273135i
\(874\) −45582.1 −1.76411
\(875\) 0 0
\(876\) −11969.5 −0.461657
\(877\) −2993.42 5184.76i −0.115257 0.199631i 0.802625 0.596484i \(-0.203436\pi\)
−0.917883 + 0.396852i \(0.870103\pi\)
\(878\) 9812.76 16996.2i 0.377181 0.653296i
\(879\) −13850.7 + 23990.1i −0.531481 + 0.920552i
\(880\) −621.921 1077.20i −0.0238238 0.0412640i
\(881\) 37911.8 1.44981 0.724904 0.688850i \(-0.241884\pi\)
0.724904 + 0.688850i \(0.241884\pi\)
\(882\) 0 0
\(883\) −16293.6 −0.620978 −0.310489 0.950577i \(-0.600493\pi\)
−0.310489 + 0.950577i \(0.600493\pi\)
\(884\) −281.152 486.970i −0.0106970 0.0185278i
\(885\) −6555.30 + 11354.1i −0.248988 + 0.431259i
\(886\) −5830.30 + 10098.4i −0.221075 + 0.382914i
\(887\) −4426.71 7667.28i −0.167570 0.290239i 0.769995 0.638050i \(-0.220259\pi\)
−0.937565 + 0.347811i \(0.886925\pi\)
\(888\) −9469.40 −0.357852
\(889\) 0 0
\(890\) −8207.35 −0.309113
\(891\) −424.654 735.522i −0.0159668 0.0276554i
\(892\) −4056.54 + 7026.12i −0.152268 + 0.263735i
\(893\) 38141.7 66063.3i 1.42930 2.47562i
\(894\) −3694.41 6398.91i −0.138210 0.239386i
\(895\) 9879.34 0.368972
\(896\) 0 0
\(897\) −1523.68 −0.0567159
\(898\) 8674.94 + 15025.4i 0.322368 + 0.558358i
\(899\) −10900.6 + 18880.3i −0.404398 + 0.700438i
\(900\) 1260.53 2183.30i 0.0466863 0.0808630i
\(901\) 3468.73 + 6008.02i 0.128258 + 0.222149i
\(902\) 4143.89 0.152967
\(903\) 0 0
\(904\) −8350.10 −0.307213
\(905\) 3698.68 + 6406.30i 0.135854 + 0.235307i
\(906\) 6734.21 11664.0i 0.246941 0.427715i
\(907\) −8331.23 + 14430.1i −0.304999 + 0.528274i −0.977261 0.212039i \(-0.931989\pi\)
0.672262 + 0.740313i \(0.265323\pi\)
\(908\) −4847.91 8396.83i −0.177185 0.306893i
\(909\) −2822.50 −0.102988
\(910\) 0 0
\(911\) −29071.2 −1.05727 −0.528635 0.848849i \(-0.677296\pi\)
−0.528635 + 0.848849i \(0.677296\pi\)
\(912\) −3001.29 5198.39i −0.108972 0.188745i
\(913\) 1105.48 1914.74i 0.0400723 0.0694072i
\(914\) −9106.82 + 15773.5i −0.329570 + 0.570832i
\(915\) −2749.38 4762.07i −0.0993353 0.172054i
\(916\) −7868.67 −0.283830
\(917\) 0 0
\(918\) 2723.96 0.0979346
\(919\) −3986.70 6905.16i −0.143100 0.247857i 0.785562 0.618782i \(-0.212374\pi\)
−0.928663 + 0.370926i \(0.879040\pi\)
\(920\) 5404.96 9361.66i 0.193691 0.335483i
\(921\) −10179.8 + 17631.9i −0.364208 + 0.630827i
\(922\) 8729.69 + 15120.3i 0.311819 + 0.540086i
\(923\) 796.079 0.0283892
\(924\) 0 0
\(925\) 27630.7 0.982154
\(926\) 1795.62 + 3110.11i 0.0637233 + 0.110372i
\(927\) −1039.39 + 1800.27i −0.0368262 + 0.0637849i
\(928\) −2498.11 + 4326.86i −0.0883670 + 0.153056i
\(929\) −15070.7 26103.3i −0.532244 0.921874i −0.999291 0.0376418i \(-0.988015\pi\)
0.467047 0.884233i \(-0.345318\pi\)
\(930\) 6211.59 0.219017
\(931\) 0 0
\(932\) 17913.3 0.629582
\(933\) −7705.15 13345.7i −0.270370 0.468295i
\(934\) −130.559 + 226.136i −0.00457391 + 0.00792225i
\(935\) −1960.75 + 3396.11i −0.0685811 + 0.118786i
\(936\) −100.325 173.767i −0.00350343 0.00606813i
\(937\) 1126.37 0.0392709 0.0196354 0.999807i \(-0.493749\pi\)
0.0196354 + 0.999807i \(0.493749\pi\)
\(938\) 0 0
\(939\) −11290.7 −0.392393
\(940\) 9045.40 + 15667.1i 0.313860 + 0.543622i
\(941\) 5166.64 8948.89i 0.178988 0.310016i −0.762546 0.646934i \(-0.776051\pi\)
0.941534 + 0.336917i \(0.109384\pi\)
\(942\) 11361.5 19678.6i 0.392969 0.680642i
\(943\) 18006.7 + 31188.6i 0.621824 + 1.07703i
\(944\) 9430.97 0.325161
\(945\) 0 0
\(946\) 7199.06 0.247422
\(947\) −12405.1 21486.3i −0.425673 0.737288i 0.570810 0.821082i \(-0.306629\pi\)
−0.996483 + 0.0837944i \(0.973296\pi\)
\(948\) 5089.58 8815.42i 0.174369 0.302016i
\(949\) 1389.85 2407.30i 0.0475412 0.0823438i
\(950\) 8757.45 + 15168.3i 0.299083 + 0.518028i
\(951\) −3104.84 −0.105869
\(952\) 0 0
\(953\) −15048.6 −0.511513 −0.255757 0.966741i \(-0.582325\pi\)
−0.255757 + 0.966741i \(0.582325\pi\)
\(954\) 1237.76 + 2143.87i 0.0420063 + 0.0727570i
\(955\) −4547.58 + 7876.65i −0.154090 + 0.266893i
\(956\) −12233.8 + 21189.6i −0.413881 + 0.716864i
\(957\) −2455.63 4253.28i −0.0829460 0.143667i
\(958\) 23691.6 0.798999
\(959\) 0 0
\(960\) 1423.53 0.0478585
\(961\) 5146.89 + 8914.67i 0.172767 + 0.299240i
\(962\) 1099.55 1904.48i 0.0368514 0.0638285i
\(963\) −564.688 + 978.068i −0.0188960 + 0.0327288i
\(964\) −12456.8 21575.7i −0.416188 0.720859i
\(965\) −25796.2 −0.860528
\(966\) 0 0
\(967\) −15619.9 −0.519442 −0.259721 0.965684i \(-0.583631\pi\)
−0.259721 + 0.965684i \(0.583631\pi\)
\(968\) 4884.24 + 8459.74i 0.162175 + 0.280895i
\(969\) −9462.26 + 16389.1i −0.313696 + 0.543338i
\(970\) 6701.78 11607.8i 0.221836 0.384232i
\(971\) 12416.5 + 21506.0i 0.410365 + 0.710773i 0.994930 0.100574i \(-0.0320680\pi\)
−0.584565 + 0.811347i \(0.698735\pi\)
\(972\) 972.000 0.0320750
\(973\) 0 0
\(974\) −9614.42 −0.316289
\(975\) 292.737 + 507.035i 0.00961546 + 0.0166545i
\(976\) −1977.74 + 3425.54i −0.0648626 + 0.112345i
\(977\) −19328.4 + 33477.8i −0.632928 + 1.09626i 0.354022 + 0.935237i \(0.384814\pi\)
−0.986950 + 0.161026i \(0.948520\pi\)
\(978\) 6325.68 + 10956.4i 0.206823 + 0.358228i
\(979\) −5803.47 −0.189458
\(980\) 0 0
\(981\) 6709.75 0.218375
\(982\) −6068.04 10510.2i −0.197188 0.341540i
\(983\) −13332.1 + 23091.8i −0.432581 + 0.749252i −0.997095 0.0761716i \(-0.975730\pi\)
0.564514 + 0.825424i \(0.309064\pi\)
\(984\) −2371.26 + 4107.15i −0.0768222 + 0.133060i
\(985\) −11838.5 20505.0i −0.382952 0.663292i
\(986\) 15751.7 0.508760
\(987\) 0 0
\(988\) 1394.00 0.0448876
\(989\) 31282.6 + 54183.0i 1.00579 + 1.74208i
\(990\) −699.661 + 1211.85i −0.0224613 + 0.0389041i
\(991\) −13614.1 + 23580.3i −0.436393 + 0.755855i −0.997408 0.0719507i \(-0.977078\pi\)
0.561015 + 0.827806i \(0.310411\pi\)
\(992\) −2234.12 3869.61i −0.0715054 0.123851i
\(993\) 26400.2 0.843690
\(994\) 0 0
\(995\) 7897.24 0.251617
\(996\) 1265.18 + 2191.35i 0.0402497 + 0.0697145i
\(997\) −2581.46 + 4471.22i −0.0820016 + 0.142031i −0.904110 0.427301i \(-0.859465\pi\)
0.822108 + 0.569332i \(0.192798\pi\)
\(998\) 15506.4 26857.9i 0.491831 0.851876i
\(999\) 5326.54 + 9225.84i 0.168693 + 0.292185i
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 294.4.e.k.67.1 4
3.2 odd 2 882.4.g.bk.361.2 4
7.2 even 3 inner 294.4.e.k.79.1 4
7.3 odd 6 294.4.a.l.1.1 2
7.4 even 3 294.4.a.o.1.2 yes 2
7.5 odd 6 294.4.e.m.79.2 4
7.6 odd 2 294.4.e.m.67.2 4
21.2 odd 6 882.4.g.bk.667.2 4
21.5 even 6 882.4.g.be.667.1 4
21.11 odd 6 882.4.a.t.1.1 2
21.17 even 6 882.4.a.bb.1.2 2
21.20 even 2 882.4.g.be.361.1 4
28.3 even 6 2352.4.a.bw.1.1 2
28.11 odd 6 2352.4.a.bu.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.l.1.1 2 7.3 odd 6
294.4.a.o.1.2 yes 2 7.4 even 3
294.4.e.k.67.1 4 1.1 even 1 trivial
294.4.e.k.79.1 4 7.2 even 3 inner
294.4.e.m.67.2 4 7.6 odd 2
294.4.e.m.79.2 4 7.5 odd 6
882.4.a.t.1.1 2 21.11 odd 6
882.4.a.bb.1.2 2 21.17 even 6
882.4.g.be.361.1 4 21.20 even 2
882.4.g.be.667.1 4 21.5 even 6
882.4.g.bk.361.2 4 3.2 odd 2
882.4.g.bk.667.2 4 21.2 odd 6
2352.4.a.bu.1.2 2 28.11 odd 6
2352.4.a.bw.1.1 2 28.3 even 6