Properties

Label 245.4.e.a.226.1
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, 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("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.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: \(14.4554679514\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.a.116.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 - 19.9186i) q^{9} +(7.50000 + 12.9904i) q^{10} +(22.5000 + 38.9711i) q^{11} +(-1.00000 + 1.73205i) q^{12} -59.0000 q^{13} -10.0000 q^{15} +(35.5000 - 61.4878i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(34.5000 + 59.7558i) q^{18} +(-60.5000 + 104.789i) q^{19} -5.00000 q^{20} -135.000 q^{22} +(-34.5000 + 59.7558i) q^{23} +(21.0000 + 36.3731i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(88.5000 - 153.286i) q^{26} -100.000 q^{27} -162.000 q^{29} +(15.0000 - 25.9808i) q^{30} +(-44.0000 - 76.2102i) q^{31} +(22.5000 + 38.9711i) q^{32} +(45.0000 - 77.9423i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(129.500 - 224.301i) q^{37} +(-181.500 - 314.367i) q^{38} +(59.0000 + 102.191i) q^{39} +(-52.5000 + 90.9327i) q^{40} -195.000 q^{41} -286.000 q^{43} +(22.5000 - 38.9711i) q^{44} +(-57.5000 - 99.5929i) q^{45} +(-103.500 - 179.267i) q^{46} +(22.5000 - 38.9711i) q^{47} -142.000 q^{48} +75.0000 q^{50} +(-54.0000 + 93.5307i) q^{51} +(29.5000 + 51.0955i) q^{52} +(-298.500 - 517.017i) q^{53} +(150.000 - 259.808i) q^{54} +225.000 q^{55} +242.000 q^{57} +(243.000 - 420.888i) q^{58} +(-180.000 - 311.769i) q^{59} +(5.00000 + 8.66025i) q^{60} +(196.000 - 339.482i) q^{61} +264.000 q^{62} +433.000 q^{64} +(-147.500 + 255.477i) q^{65} +(135.000 + 233.827i) q^{66} +(140.000 + 242.487i) q^{67} +(-27.0000 + 46.7654i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-241.500 + 418.290i) q^{72} +(334.000 + 578.505i) q^{73} +(388.500 + 672.902i) q^{74} +(-25.0000 + 43.3013i) q^{75} +121.000 q^{76} -354.000 q^{78} +(-391.000 + 677.232i) q^{79} +(-177.500 - 307.439i) q^{80} +(-210.500 - 364.597i) q^{81} +(292.500 - 506.625i) q^{82} -768.000 q^{83} -270.000 q^{85} +(429.000 - 743.050i) q^{86} +(162.000 + 280.592i) q^{87} +(-472.500 - 818.394i) q^{88} +(-597.000 + 1034.03i) q^{89} +345.000 q^{90} +69.0000 q^{92} +(-88.0000 + 152.420i) q^{93} +(67.5000 + 116.913i) q^{94} +(302.500 + 523.945i) q^{95} +(45.0000 - 77.9423i) q^{96} -902.000 q^{97} +1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9} + 15 q^{10} + 45 q^{11} - 2 q^{12} - 118 q^{13} - 20 q^{15} + 71 q^{16} - 54 q^{17} + 69 q^{18} - 121 q^{19} - 10 q^{20} - 270 q^{22} - 69 q^{23} + 42 q^{24} - 25 q^{25} + 177 q^{26} - 200 q^{27} - 324 q^{29} + 30 q^{30} - 88 q^{31} + 45 q^{32} + 90 q^{33} + 324 q^{34} - 46 q^{36} + 259 q^{37} - 363 q^{38} + 118 q^{39} - 105 q^{40} - 390 q^{41} - 572 q^{43} + 45 q^{44} - 115 q^{45} - 207 q^{46} + 45 q^{47} - 284 q^{48} + 150 q^{50} - 108 q^{51} + 59 q^{52} - 597 q^{53} + 300 q^{54} + 450 q^{55} + 484 q^{57} + 486 q^{58} - 360 q^{59} + 10 q^{60} + 392 q^{61} + 528 q^{62} + 866 q^{64} - 295 q^{65} + 270 q^{66} + 280 q^{67} - 54 q^{68} + 276 q^{69} + 96 q^{71} - 483 q^{72} + 668 q^{73} + 777 q^{74} - 50 q^{75} + 242 q^{76} - 708 q^{78} - 782 q^{79} - 355 q^{80} - 421 q^{81} + 585 q^{82} - 1536 q^{83} - 540 q^{85} + 858 q^{86} + 324 q^{87} - 945 q^{88} - 1194 q^{89} + 690 q^{90} + 138 q^{92} - 176 q^{93} + 135 q^{94} + 605 q^{95} + 90 q^{96} - 1804 q^{97} + 2070 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 2.59808i −0.530330 + 0.918559i 0.469044 + 0.883175i \(0.344599\pi\)
−0.999374 + 0.0353837i \(0.988735\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) −0.500000 0.866025i −0.0625000 0.108253i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) −21.0000 −0.928078
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) 7.50000 + 12.9904i 0.237171 + 0.410792i
\(11\) 22.5000 + 38.9711i 0.616728 + 1.06820i 0.990079 + 0.140514i \(0.0448754\pi\)
−0.373351 + 0.927690i \(0.621791\pi\)
\(12\) −1.00000 + 1.73205i −0.0240563 + 0.0416667i
\(13\) −59.0000 −1.25874 −0.629371 0.777105i \(-0.716688\pi\)
−0.629371 + 0.777105i \(0.716688\pi\)
\(14\) 0 0
\(15\) −10.0000 −0.172133
\(16\) 35.5000 61.4878i 0.554688 0.960747i
\(17\) −27.0000 46.7654i −0.385204 0.667192i 0.606594 0.795012i \(-0.292535\pi\)
−0.991797 + 0.127820i \(0.959202\pi\)
\(18\) 34.5000 + 59.7558i 0.451763 + 0.782476i
\(19\) −60.5000 + 104.789i −0.730508 + 1.26528i 0.226158 + 0.974091i \(0.427383\pi\)
−0.956666 + 0.291186i \(0.905950\pi\)
\(20\) −5.00000 −0.0559017
\(21\) 0 0
\(22\) −135.000 −1.30828
\(23\) −34.5000 + 59.7558i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 21.0000 + 36.3731i 0.178609 + 0.309359i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 88.5000 153.286i 0.667549 1.15623i
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −162.000 −1.03733 −0.518666 0.854977i \(-0.673571\pi\)
−0.518666 + 0.854977i \(0.673571\pi\)
\(30\) 15.0000 25.9808i 0.0912871 0.158114i
\(31\) −44.0000 76.2102i −0.254924 0.441541i 0.709951 0.704251i \(-0.248717\pi\)
−0.964875 + 0.262710i \(0.915384\pi\)
\(32\) 22.5000 + 38.9711i 0.124296 + 0.215287i
\(33\) 45.0000 77.9423i 0.237379 0.411152i
\(34\) 162.000 0.817140
\(35\) 0 0
\(36\) −23.0000 −0.106481
\(37\) 129.500 224.301i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) −181.500 314.367i −0.774821 1.34203i
\(39\) 59.0000 + 102.191i 0.242245 + 0.419581i
\(40\) −52.5000 + 90.9327i −0.207524 + 0.359443i
\(41\) −195.000 −0.742778 −0.371389 0.928477i \(-0.621118\pi\)
−0.371389 + 0.928477i \(0.621118\pi\)
\(42\) 0 0
\(43\) −286.000 −1.01429 −0.507146 0.861860i \(-0.669300\pi\)
−0.507146 + 0.861860i \(0.669300\pi\)
\(44\) 22.5000 38.9711i 0.0770910 0.133525i
\(45\) −57.5000 99.5929i −0.190480 0.329921i
\(46\) −103.500 179.267i −0.331744 0.574598i
\(47\) 22.5000 38.9711i 0.0698290 0.120947i −0.828997 0.559253i \(-0.811088\pi\)
0.898826 + 0.438306i \(0.144421\pi\)
\(48\) −142.000 −0.426999
\(49\) 0 0
\(50\) 75.0000 0.212132
\(51\) −54.0000 + 93.5307i −0.148265 + 0.256802i
\(52\) 29.5000 + 51.0955i 0.0786714 + 0.136263i
\(53\) −298.500 517.017i −0.773625 1.33996i −0.935564 0.353157i \(-0.885108\pi\)
0.161939 0.986801i \(-0.448225\pi\)
\(54\) 150.000 259.808i 0.378008 0.654729i
\(55\) 225.000 0.551618
\(56\) 0 0
\(57\) 242.000 0.562345
\(58\) 243.000 420.888i 0.550129 0.952851i
\(59\) −180.000 311.769i −0.397187 0.687947i 0.596191 0.802843i \(-0.296680\pi\)
−0.993378 + 0.114895i \(0.963347\pi\)
\(60\) 5.00000 + 8.66025i 0.0107583 + 0.0186339i
\(61\) 196.000 339.482i 0.411397 0.712561i −0.583646 0.812009i \(-0.698374\pi\)
0.995043 + 0.0994477i \(0.0317076\pi\)
\(62\) 264.000 0.540775
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) −147.500 + 255.477i −0.281463 + 0.487509i
\(66\) 135.000 + 233.827i 0.251778 + 0.436092i
\(67\) 140.000 + 242.487i 0.255279 + 0.442157i 0.964971 0.262355i \(-0.0844992\pi\)
−0.709692 + 0.704512i \(0.751166\pi\)
\(68\) −27.0000 + 46.7654i −0.0481505 + 0.0833990i
\(69\) 138.000 0.240772
\(70\) 0 0
\(71\) 48.0000 0.0802331 0.0401166 0.999195i \(-0.487227\pi\)
0.0401166 + 0.999195i \(0.487227\pi\)
\(72\) −241.500 + 418.290i −0.395292 + 0.684666i
\(73\) 334.000 + 578.505i 0.535503 + 0.927519i 0.999139 + 0.0414929i \(0.0132114\pi\)
−0.463635 + 0.886026i \(0.653455\pi\)
\(74\) 388.500 + 672.902i 0.610300 + 1.05707i
\(75\) −25.0000 + 43.3013i −0.0384900 + 0.0666667i
\(76\) 121.000 0.182627
\(77\) 0 0
\(78\) −354.000 −0.513880
\(79\) −391.000 + 677.232i −0.556847 + 0.964488i 0.440910 + 0.897551i \(0.354656\pi\)
−0.997757 + 0.0669365i \(0.978678\pi\)
\(80\) −177.500 307.439i −0.248064 0.429659i
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) 292.500 506.625i 0.393917 0.682285i
\(83\) −768.000 −1.01565 −0.507825 0.861460i \(-0.669550\pi\)
−0.507825 + 0.861460i \(0.669550\pi\)
\(84\) 0 0
\(85\) −270.000 −0.344537
\(86\) 429.000 743.050i 0.537910 0.931687i
\(87\) 162.000 + 280.592i 0.199635 + 0.345778i
\(88\) −472.500 818.394i −0.572371 0.991376i
\(89\) −597.000 + 1034.03i −0.711032 + 1.23154i 0.253438 + 0.967352i \(0.418439\pi\)
−0.964470 + 0.264192i \(0.914895\pi\)
\(90\) 345.000 0.404069
\(91\) 0 0
\(92\) 69.0000 0.0781929
\(93\) −88.0000 + 152.420i −0.0981202 + 0.169949i
\(94\) 67.5000 + 116.913i 0.0740648 + 0.128284i
\(95\) 302.500 + 523.945i 0.326693 + 0.565849i
\(96\) 45.0000 77.9423i 0.0478416 0.0828641i
\(97\) −902.000 −0.944167 −0.472084 0.881554i \(-0.656498\pi\)
−0.472084 + 0.881554i \(0.656498\pi\)
\(98\) 0 0
\(99\) 1035.00 1.05072
\(100\) −12.5000 + 21.6506i −0.0125000 + 0.0216506i
\(101\) 342.000 + 592.361i 0.336933 + 0.583586i 0.983854 0.178971i \(-0.0572769\pi\)
−0.646921 + 0.762557i \(0.723944\pi\)
\(102\) −162.000 280.592i −0.157259 0.272380i
\(103\) −758.000 + 1312.89i −0.725126 + 1.25595i 0.233796 + 0.972286i \(0.424885\pi\)
−0.958922 + 0.283669i \(0.908448\pi\)
\(104\) 1239.00 1.16821
\(105\) 0 0
\(106\) 1791.00 1.64111
\(107\) 366.000 633.931i 0.330678 0.572751i −0.651967 0.758247i \(-0.726056\pi\)
0.982645 + 0.185496i \(0.0593892\pi\)
\(108\) 50.0000 + 86.6025i 0.0445486 + 0.0771605i
\(109\) 800.000 + 1385.64i 0.702992 + 1.21762i 0.967411 + 0.253210i \(0.0814863\pi\)
−0.264420 + 0.964408i \(0.585180\pi\)
\(110\) −337.500 + 584.567i −0.292540 + 0.506694i
\(111\) −518.000 −0.442940
\(112\) 0 0
\(113\) −1392.00 −1.15883 −0.579417 0.815031i \(-0.696720\pi\)
−0.579417 + 0.815031i \(0.696720\pi\)
\(114\) −363.000 + 628.734i −0.298229 + 0.516547i
\(115\) 172.500 + 298.779i 0.139876 + 0.242272i
\(116\) 81.0000 + 140.296i 0.0648333 + 0.112295i
\(117\) −678.500 + 1175.20i −0.536131 + 0.928606i
\(118\) 1080.00 0.842560
\(119\) 0 0
\(120\) 210.000 0.159752
\(121\) −347.000 + 601.022i −0.260706 + 0.451556i
\(122\) 588.000 + 1018.45i 0.436353 + 0.755785i
\(123\) 195.000 + 337.750i 0.142948 + 0.247593i
\(124\) −44.0000 + 76.2102i −0.0318655 + 0.0551926i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 803.000 0.561061 0.280530 0.959845i \(-0.409490\pi\)
0.280530 + 0.959845i \(0.409490\pi\)
\(128\) −829.500 + 1436.74i −0.572798 + 0.992115i
\(129\) 286.000 + 495.367i 0.195201 + 0.338098i
\(130\) −442.500 766.432i −0.298537 0.517081i
\(131\) 1009.50 1748.51i 0.673286 1.16617i −0.303681 0.952774i \(-0.598216\pi\)
0.976967 0.213391i \(-0.0684509\pi\)
\(132\) −90.0000 −0.0593447
\(133\) 0 0
\(134\) −840.000 −0.541529
\(135\) −250.000 + 433.013i −0.159382 + 0.276058i
\(136\) 567.000 + 982.073i 0.357499 + 0.619206i
\(137\) −30.0000 51.9615i −0.0187086 0.0324042i 0.856520 0.516115i \(-0.172622\pi\)
−0.875228 + 0.483710i \(0.839289\pi\)
\(138\) −207.000 + 358.535i −0.127688 + 0.221163i
\(139\) 1708.00 1.04224 0.521118 0.853485i \(-0.325515\pi\)
0.521118 + 0.853485i \(0.325515\pi\)
\(140\) 0 0
\(141\) −90.0000 −0.0537544
\(142\) −72.0000 + 124.708i −0.0425500 + 0.0736988i
\(143\) −1327.50 2299.30i −0.776302 1.34459i
\(144\) −816.500 1414.22i −0.472512 0.818414i
\(145\) −405.000 + 701.481i −0.231955 + 0.401757i
\(146\) −2004.00 −1.13597
\(147\) 0 0
\(148\) −259.000 −0.143849
\(149\) 543.000 940.504i 0.298552 0.517108i −0.677253 0.735751i \(-0.736830\pi\)
0.975805 + 0.218643i \(0.0701629\pi\)
\(150\) −75.0000 129.904i −0.0408248 0.0707107i
\(151\) 1433.00 + 2482.03i 0.772291 + 1.33765i 0.936305 + 0.351189i \(0.114222\pi\)
−0.164014 + 0.986458i \(0.552444\pi\)
\(152\) 1270.50 2200.57i 0.677968 1.17428i
\(153\) −1242.00 −0.656273
\(154\) 0 0
\(155\) −440.000 −0.228011
\(156\) 59.0000 102.191i 0.0302806 0.0524476i
\(157\) −114.500 198.320i −0.0582044 0.100813i 0.835455 0.549559i \(-0.185204\pi\)
−0.893659 + 0.448746i \(0.851871\pi\)
\(158\) −1173.00 2031.70i −0.590626 1.02299i
\(159\) −597.000 + 1034.03i −0.297768 + 0.515750i
\(160\) 225.000 0.111174
\(161\) 0 0
\(162\) 1263.00 0.612535
\(163\) 614.000 1063.48i 0.295044 0.511031i −0.679951 0.733258i \(-0.737999\pi\)
0.974995 + 0.222226i \(0.0713323\pi\)
\(164\) 97.5000 + 168.875i 0.0464236 + 0.0804080i
\(165\) −225.000 389.711i −0.106159 0.183873i
\(166\) 1152.00 1995.32i 0.538630 0.932934i
\(167\) 1929.00 0.893835 0.446918 0.894575i \(-0.352522\pi\)
0.446918 + 0.894575i \(0.352522\pi\)
\(168\) 0 0
\(169\) 1284.00 0.584433
\(170\) 405.000 701.481i 0.182718 0.316477i
\(171\) 1391.50 + 2410.15i 0.622285 + 1.07783i
\(172\) 143.000 + 247.683i 0.0633933 + 0.109800i
\(173\) −349.500 + 605.352i −0.153595 + 0.266035i −0.932547 0.361049i \(-0.882419\pi\)
0.778951 + 0.627084i \(0.215752\pi\)
\(174\) −972.000 −0.423489
\(175\) 0 0
\(176\) 3195.00 1.36836
\(177\) −360.000 + 623.538i −0.152877 + 0.264791i
\(178\) −1791.00 3102.10i −0.754164 1.30625i
\(179\) −1558.50 2699.40i −0.650770 1.12717i −0.982936 0.183945i \(-0.941113\pi\)
0.332167 0.943221i \(-0.392220\pi\)
\(180\) −57.5000 + 99.5929i −0.0238100 + 0.0412401i
\(181\) 1798.00 0.738366 0.369183 0.929357i \(-0.379638\pi\)
0.369183 + 0.929357i \(0.379638\pi\)
\(182\) 0 0
\(183\) −784.000 −0.316694
\(184\) 724.500 1254.87i 0.290276 0.502773i
\(185\) −647.500 1121.50i −0.257325 0.445700i
\(186\) −264.000 457.261i −0.104072 0.180258i
\(187\) 1215.00 2104.44i 0.475132 0.822952i
\(188\) −45.0000 −0.0174572
\(189\) 0 0
\(190\) −1815.00 −0.693021
\(191\) 1194.00 2068.07i 0.452329 0.783457i −0.546201 0.837654i \(-0.683927\pi\)
0.998530 + 0.0541974i \(0.0172600\pi\)
\(192\) −433.000 749.978i −0.162756 0.281901i
\(193\) −136.000 235.559i −0.0507228 0.0878544i 0.839549 0.543284i \(-0.182819\pi\)
−0.890272 + 0.455429i \(0.849486\pi\)
\(194\) 1353.00 2343.46i 0.500720 0.867273i
\(195\) 590.000 0.216671
\(196\) 0 0
\(197\) −2109.00 −0.762741 −0.381371 0.924422i \(-0.624548\pi\)
−0.381371 + 0.924422i \(0.624548\pi\)
\(198\) −1552.50 + 2689.01i −0.557229 + 0.965149i
\(199\) 712.000 + 1233.22i 0.253630 + 0.439300i 0.964522 0.264001i \(-0.0850422\pi\)
−0.710893 + 0.703301i \(0.751709\pi\)
\(200\) 262.500 + 454.663i 0.0928078 + 0.160748i
\(201\) 280.000 484.974i 0.0982571 0.170186i
\(202\) −2052.00 −0.714744
\(203\) 0 0
\(204\) 108.000 0.0370662
\(205\) −487.500 + 844.375i −0.166090 + 0.287677i
\(206\) −2274.00 3938.68i −0.769112 1.33214i
\(207\) 793.500 + 1374.38i 0.266435 + 0.461479i
\(208\) −2094.50 + 3627.78i −0.698209 + 1.20933i
\(209\) −5445.00 −1.80210
\(210\) 0 0
\(211\) −3625.00 −1.18273 −0.591363 0.806405i \(-0.701410\pi\)
−0.591363 + 0.806405i \(0.701410\pi\)
\(212\) −298.500 + 517.017i −0.0967031 + 0.167495i
\(213\) −48.0000 83.1384i −0.0154409 0.0267444i
\(214\) 1098.00 + 1901.79i 0.350737 + 0.607494i
\(215\) −715.000 + 1238.42i −0.226803 + 0.392834i
\(216\) 2100.00 0.661513
\(217\) 0 0
\(218\) −4800.00 −1.49127
\(219\) 668.000 1157.01i 0.206115 0.357002i
\(220\) −112.500 194.856i −0.0344761 0.0597144i
\(221\) 1593.00 + 2759.16i 0.484872 + 0.839823i
\(222\) 777.000 1345.80i 0.234905 0.406867i
\(223\) 4960.00 1.48944 0.744722 0.667374i \(-0.232582\pi\)
0.744722 + 0.667374i \(0.232582\pi\)
\(224\) 0 0
\(225\) −575.000 −0.170370
\(226\) 2088.00 3616.52i 0.614565 1.06446i
\(227\) −750.000 1299.04i −0.219292 0.379825i 0.735300 0.677742i \(-0.237041\pi\)
−0.954592 + 0.297917i \(0.903708\pi\)
\(228\) −121.000 209.578i −0.0351466 0.0608757i
\(229\) 3046.00 5275.83i 0.878975 1.52243i 0.0265085 0.999649i \(-0.491561\pi\)
0.852467 0.522781i \(-0.175106\pi\)
\(230\) −1035.00 −0.296721
\(231\) 0 0
\(232\) 3402.00 0.962725
\(233\) −69.0000 + 119.512i −0.0194006 + 0.0336028i −0.875563 0.483104i \(-0.839509\pi\)
0.856162 + 0.516707i \(0.172842\pi\)
\(234\) −2035.50 3525.59i −0.568653 0.984936i
\(235\) −112.500 194.856i −0.0312285 0.0540893i
\(236\) −180.000 + 311.769i −0.0496483 + 0.0859934i
\(237\) 1564.00 0.428661
\(238\) 0 0
\(239\) −5502.00 −1.48910 −0.744550 0.667567i \(-0.767336\pi\)
−0.744550 + 0.667567i \(0.767336\pi\)
\(240\) −355.000 + 614.878i −0.0954798 + 0.165376i
\(241\) 1775.50 + 3075.26i 0.474564 + 0.821970i 0.999576 0.0291256i \(-0.00927228\pi\)
−0.525011 + 0.851095i \(0.675939\pi\)
\(242\) −1041.00 1803.06i −0.276521 0.478948i
\(243\) −1771.00 + 3067.46i −0.467530 + 0.809785i
\(244\) −392.000 −0.102849
\(245\) 0 0
\(246\) −1170.00 −0.303238
\(247\) 3569.50 6182.56i 0.919522 1.59266i
\(248\) 924.000 + 1600.41i 0.236589 + 0.409784i
\(249\) 768.000 + 1330.22i 0.195462 + 0.338550i
\(250\) 187.500 324.760i 0.0474342 0.0821584i
\(251\) −7065.00 −1.77665 −0.888324 0.459216i \(-0.848130\pi\)
−0.888324 + 0.459216i \(0.848130\pi\)
\(252\) 0 0
\(253\) −3105.00 −0.771580
\(254\) −1204.50 + 2086.26i −0.297547 + 0.515367i
\(255\) 270.000 + 467.654i 0.0663061 + 0.114846i
\(256\) −756.500 1310.30i −0.184692 0.319897i
\(257\) −2040.00 + 3533.38i −0.495143 + 0.857613i −0.999984 0.00559954i \(-0.998218\pi\)
0.504842 + 0.863212i \(0.331551\pi\)
\(258\) −1716.00 −0.414083
\(259\) 0 0
\(260\) 295.000 0.0703659
\(261\) −1863.00 + 3226.81i −0.441827 + 0.765267i
\(262\) 3028.50 + 5245.52i 0.714127 + 1.23690i
\(263\) 1644.00 + 2847.49i 0.385450 + 0.667619i 0.991832 0.127555i \(-0.0407128\pi\)
−0.606381 + 0.795174i \(0.707380\pi\)
\(264\) −945.000 + 1636.79i −0.220306 + 0.381581i
\(265\) −2985.00 −0.691951
\(266\) 0 0
\(267\) 2388.00 0.547353
\(268\) 140.000 242.487i 0.0319099 0.0552696i
\(269\) −1632.00 2826.71i −0.369906 0.640697i 0.619644 0.784883i \(-0.287277\pi\)
−0.989551 + 0.144186i \(0.953944\pi\)
\(270\) −750.000 1299.04i −0.169050 0.292803i
\(271\) −1376.00 + 2383.30i −0.308436 + 0.534226i −0.978020 0.208510i \(-0.933139\pi\)
0.669585 + 0.742736i \(0.266472\pi\)
\(272\) −3834.00 −0.854671
\(273\) 0 0
\(274\) 180.000 0.0396869
\(275\) 562.500 974.279i 0.123346 0.213641i
\(276\) −69.0000 119.512i −0.0150482 0.0260643i
\(277\) 2345.00 + 4061.66i 0.508655 + 0.881016i 0.999950 + 0.0100228i \(0.00319040\pi\)
−0.491295 + 0.870993i \(0.663476\pi\)
\(278\) −2562.00 + 4437.51i −0.552729 + 0.957354i
\(279\) −2024.00 −0.434314
\(280\) 0 0
\(281\) 7821.00 1.66036 0.830181 0.557494i \(-0.188237\pi\)
0.830181 + 0.557494i \(0.188237\pi\)
\(282\) 135.000 233.827i 0.0285076 0.0493765i
\(283\) −329.000 569.845i −0.0691061 0.119695i 0.829402 0.558652i \(-0.188681\pi\)
−0.898508 + 0.438957i \(0.855348\pi\)
\(284\) −24.0000 41.5692i −0.00501457 0.00868549i
\(285\) 605.000 1047.89i 0.125744 0.217795i
\(286\) 7965.00 1.64678
\(287\) 0 0
\(288\) 1035.00 0.211764
\(289\) 998.500 1729.45i 0.203236 0.352016i
\(290\) −1215.00 2104.44i −0.246025 0.426128i
\(291\) 902.000 + 1562.31i 0.181705 + 0.314722i
\(292\) 334.000 578.505i 0.0669379 0.115940i
\(293\) 5997.00 1.19573 0.597864 0.801597i \(-0.296016\pi\)
0.597864 + 0.801597i \(0.296016\pi\)
\(294\) 0 0
\(295\) −1800.00 −0.355254
\(296\) −2719.50 + 4710.31i −0.534013 + 0.924937i
\(297\) −2250.00 3897.11i −0.439590 0.761392i
\(298\) 1629.00 + 2821.51i 0.316663 + 0.548476i
\(299\) 2035.50 3525.59i 0.393699 0.681907i
\(300\) 50.0000 0.00962250
\(301\) 0 0
\(302\) −8598.00 −1.63828
\(303\) 684.000 1184.72i 0.129686 0.224622i
\(304\) 4295.50 + 7440.02i 0.810407 + 1.40367i
\(305\) −980.000 1697.41i −0.183982 0.318667i
\(306\) 1863.00 3226.81i 0.348041 0.602825i
\(307\) 6226.00 1.15745 0.578724 0.815523i \(-0.303551\pi\)
0.578724 + 0.815523i \(0.303551\pi\)
\(308\) 0 0
\(309\) 3032.00 0.558202
\(310\) 660.000 1143.15i 0.120921 0.209441i
\(311\) 2340.00 + 4053.00i 0.426653 + 0.738985i 0.996573 0.0827149i \(-0.0263591\pi\)
−0.569920 + 0.821700i \(0.693026\pi\)
\(312\) −1239.00 2146.01i −0.224822 0.389404i
\(313\) 514.000 890.274i 0.0928211 0.160771i −0.815876 0.578227i \(-0.803745\pi\)
0.908697 + 0.417456i \(0.137078\pi\)
\(314\) 687.000 0.123470
\(315\) 0 0
\(316\) 782.000 0.139212
\(317\) −4311.00 + 7466.87i −0.763817 + 1.32297i 0.177053 + 0.984201i \(0.443344\pi\)
−0.940870 + 0.338768i \(0.889990\pi\)
\(318\) −1791.00 3102.10i −0.315831 0.547036i
\(319\) −3645.00 6313.33i −0.639752 1.10808i
\(320\) 1082.50 1874.94i 0.189105 0.327539i
\(321\) −1464.00 −0.254556
\(322\) 0 0
\(323\) 6534.00 1.12558
\(324\) −210.500 + 364.597i −0.0360940 + 0.0625166i
\(325\) 737.500 + 1277.39i 0.125874 + 0.218021i
\(326\) 1842.00 + 3190.44i 0.312942 + 0.542031i
\(327\) 1600.00 2771.28i 0.270582 0.468661i
\(328\) 4095.00 0.689355
\(329\) 0 0
\(330\) 1350.00 0.225197
\(331\) 999.500 1731.18i 0.165974 0.287476i −0.771027 0.636803i \(-0.780256\pi\)
0.937001 + 0.349327i \(0.113590\pi\)
\(332\) 384.000 + 665.108i 0.0634781 + 0.109947i
\(333\) −2978.50 5158.91i −0.490153 0.848969i
\(334\) −2893.50 + 5011.69i −0.474028 + 0.821040i
\(335\) 1400.00 0.228329
\(336\) 0 0
\(337\) 5114.00 0.826639 0.413319 0.910586i \(-0.364369\pi\)
0.413319 + 0.910586i \(0.364369\pi\)
\(338\) −1926.00 + 3335.93i −0.309943 + 0.536836i
\(339\) 1392.00 + 2411.01i 0.223018 + 0.386278i
\(340\) 135.000 + 233.827i 0.0215335 + 0.0372972i
\(341\) 1980.00 3429.46i 0.314437 0.544621i
\(342\) −8349.00 −1.32006
\(343\) 0 0
\(344\) 6006.00 0.941342
\(345\) 345.000 597.558i 0.0538382 0.0932505i
\(346\) −1048.50 1816.06i −0.162912 0.282173i
\(347\) −2160.00 3741.23i −0.334164 0.578789i 0.649160 0.760652i \(-0.275121\pi\)
−0.983324 + 0.181863i \(0.941787\pi\)
\(348\) 162.000 280.592i 0.0249543 0.0432222i
\(349\) −7922.00 −1.21506 −0.607529 0.794298i \(-0.707839\pi\)
−0.607529 + 0.794298i \(0.707839\pi\)
\(350\) 0 0
\(351\) 5900.00 0.897204
\(352\) −1012.50 + 1753.70i −0.153314 + 0.265547i
\(353\) 414.000 + 717.069i 0.0624221 + 0.108118i 0.895548 0.444966i \(-0.146784\pi\)
−0.833125 + 0.553084i \(0.813451\pi\)
\(354\) −1080.00 1870.61i −0.162151 0.280853i
\(355\) 120.000 207.846i 0.0179407 0.0310742i
\(356\) 1194.00 0.177758
\(357\) 0 0
\(358\) 9351.00 1.38049
\(359\) 675.000 1169.13i 0.0992344 0.171879i −0.812134 0.583472i \(-0.801694\pi\)
0.911368 + 0.411593i \(0.135027\pi\)
\(360\) 1207.50 + 2091.45i 0.176780 + 0.306192i
\(361\) −3891.00 6739.41i −0.567284 0.982564i
\(362\) −2697.00 + 4671.34i −0.391578 + 0.678233i
\(363\) 1388.00 0.200692
\(364\) 0 0
\(365\) 3340.00 0.478969
\(366\) 1176.00 2036.89i 0.167952 0.290902i
\(367\) 1400.50 + 2425.74i 0.199198 + 0.345020i 0.948268 0.317470i \(-0.102833\pi\)
−0.749071 + 0.662490i \(0.769500\pi\)
\(368\) 2449.50 + 4242.66i 0.346981 + 0.600989i
\(369\) −2242.50 + 3884.12i −0.316368 + 0.547966i
\(370\) 3885.00 0.545869
\(371\) 0 0
\(372\) 176.000 0.0245300
\(373\) −3301.00 + 5717.50i −0.458229 + 0.793675i −0.998867 0.0475795i \(-0.984849\pi\)
0.540639 + 0.841255i \(0.318183\pi\)
\(374\) 3645.00 + 6313.33i 0.503953 + 0.872872i
\(375\) 125.000 + 216.506i 0.0172133 + 0.0298142i
\(376\) −472.500 + 818.394i −0.0648067 + 0.112249i
\(377\) 9558.00 1.30573
\(378\) 0 0
\(379\) −8305.00 −1.12559 −0.562796 0.826596i \(-0.690274\pi\)
−0.562796 + 0.826596i \(0.690274\pi\)
\(380\) 302.500 523.945i 0.0408366 0.0707311i
\(381\) −803.000 1390.84i −0.107976 0.187020i
\(382\) 3582.00 + 6204.21i 0.479767 + 0.830981i
\(383\) 472.500 818.394i 0.0630382 0.109185i −0.832784 0.553598i \(-0.813254\pi\)
0.895822 + 0.444413i \(0.146588\pi\)
\(384\) 3318.00 0.440940
\(385\) 0 0
\(386\) 816.000 0.107599
\(387\) −3289.00 + 5696.72i −0.432014 + 0.748270i
\(388\) 451.000 + 781.155i 0.0590105 + 0.102209i
\(389\) −6018.00 10423.5i −0.784382 1.35859i −0.929367 0.369156i \(-0.879647\pi\)
0.144985 0.989434i \(-0.453687\pi\)
\(390\) −885.000 + 1532.86i −0.114907 + 0.199025i
\(391\) 3726.00 0.481923
\(392\) 0 0
\(393\) −4038.00 −0.518296
\(394\) 3163.50 5479.34i 0.404505 0.700623i
\(395\) 1955.00 + 3386.16i 0.249030 + 0.431332i
\(396\) −517.500 896.336i −0.0656701 0.113744i
\(397\) −1349.00 + 2336.54i −0.170540 + 0.295384i −0.938609 0.344983i \(-0.887885\pi\)
0.768069 + 0.640367i \(0.221218\pi\)
\(398\) −4272.00 −0.538030
\(399\) 0 0
\(400\) −1775.00 −0.221875
\(401\) −3526.50 + 6108.08i −0.439165 + 0.760655i −0.997625 0.0688756i \(-0.978059\pi\)
0.558461 + 0.829531i \(0.311392\pi\)
\(402\) 840.000 + 1454.92i 0.104217 + 0.180510i
\(403\) 2596.00 + 4496.40i 0.320883 + 0.555786i
\(404\) 342.000 592.361i 0.0421167 0.0729482i
\(405\) −2105.00 −0.258267
\(406\) 0 0
\(407\) 11655.0 1.41945
\(408\) 1134.00 1964.15i 0.137601 0.238333i
\(409\) −5435.00 9413.70i −0.657074 1.13809i −0.981369 0.192130i \(-0.938460\pi\)
0.324295 0.945956i \(-0.394873\pi\)
\(410\) −1462.50 2533.12i −0.176165 0.305127i
\(411\) −60.0000 + 103.923i −0.00720093 + 0.0124724i
\(412\) 1516.00 0.181281
\(413\) 0 0
\(414\) −4761.00 −0.565194
\(415\) −1920.00 + 3325.54i −0.227106 + 0.393360i
\(416\) −1327.50 2299.30i −0.156457 0.270991i
\(417\) −1708.00 2958.34i −0.200578 0.347412i
\(418\) 8167.50 14146.5i 0.955707 1.65533i
\(419\) 9729.00 1.13435 0.567175 0.823597i \(-0.308036\pi\)
0.567175 + 0.823597i \(0.308036\pi\)
\(420\) 0 0
\(421\) −12550.0 −1.45285 −0.726425 0.687246i \(-0.758819\pi\)
−0.726425 + 0.687246i \(0.758819\pi\)
\(422\) 5437.50 9418.03i 0.627235 1.08640i
\(423\) −517.500 896.336i −0.0594840 0.103029i
\(424\) 6268.50 + 10857.4i 0.717984 + 1.24358i
\(425\) −675.000 + 1169.13i −0.0770407 + 0.133438i
\(426\) 288.000 0.0327550
\(427\) 0 0
\(428\) −732.000 −0.0826695
\(429\) −2655.00 + 4598.59i −0.298799 + 0.517534i
\(430\) −2145.00 3715.25i −0.240561 0.416663i
\(431\) −1494.00 2587.68i −0.166969 0.289198i 0.770384 0.637580i \(-0.220065\pi\)
−0.937353 + 0.348382i \(0.886731\pi\)
\(432\) −3550.00 + 6148.78i −0.395369 + 0.684799i
\(433\) −16616.0 −1.84414 −0.922072 0.387019i \(-0.873505\pi\)
−0.922072 + 0.387019i \(0.873505\pi\)
\(434\) 0 0
\(435\) 1620.00 0.178559
\(436\) 800.000 1385.64i 0.0878740 0.152202i
\(437\) −4174.50 7230.45i −0.456964 0.791485i
\(438\) 2004.00 + 3471.03i 0.218618 + 0.378658i
\(439\) 3673.00 6361.82i 0.399323 0.691647i −0.594320 0.804229i \(-0.702579\pi\)
0.993642 + 0.112581i \(0.0359119\pi\)
\(440\) −4725.00 −0.511944
\(441\) 0 0
\(442\) −9558.00 −1.02857
\(443\) −6.00000 + 10.3923i −0.000643496 + 0.00111457i −0.866347 0.499443i \(-0.833538\pi\)
0.865703 + 0.500557i \(0.166871\pi\)
\(444\) 259.000 + 448.601i 0.0276838 + 0.0479497i
\(445\) 2985.00 + 5170.17i 0.317983 + 0.550763i
\(446\) −7440.00 + 12886.5i −0.789897 + 1.36814i
\(447\) −2172.00 −0.229826
\(448\) 0 0
\(449\) 9669.00 1.01628 0.508138 0.861275i \(-0.330334\pi\)
0.508138 + 0.861275i \(0.330334\pi\)
\(450\) 862.500 1493.89i 0.0903525 0.156495i
\(451\) −4387.50 7599.37i −0.458092 0.793438i
\(452\) 696.000 + 1205.51i 0.0724272 + 0.125448i
\(453\) 2866.00 4964.06i 0.297255 0.514860i
\(454\) 4500.00 0.465188
\(455\) 0 0
\(456\) −5082.00 −0.521900
\(457\) 4817.00 8343.29i 0.493063 0.854010i −0.506905 0.862002i \(-0.669211\pi\)
0.999968 + 0.00799181i \(0.00254390\pi\)
\(458\) 9138.00 + 15827.5i 0.932294 + 1.61478i
\(459\) 2700.00 + 4676.54i 0.274565 + 0.475560i
\(460\) 172.500 298.779i 0.0174845 0.0302840i
\(461\) 342.000 0.0345521 0.0172761 0.999851i \(-0.494501\pi\)
0.0172761 + 0.999851i \(0.494501\pi\)
\(462\) 0 0
\(463\) 2411.00 0.242006 0.121003 0.992652i \(-0.461389\pi\)
0.121003 + 0.992652i \(0.461389\pi\)
\(464\) −5751.00 + 9961.02i −0.575395 + 0.996614i
\(465\) 440.000 + 762.102i 0.0438807 + 0.0760035i
\(466\) −207.000 358.535i −0.0205774 0.0356412i
\(467\) −603.000 + 1044.43i −0.0597506 + 0.103491i −0.894353 0.447361i \(-0.852364\pi\)
0.834603 + 0.550852i \(0.185697\pi\)
\(468\) 1357.00 0.134033
\(469\) 0 0
\(470\) 675.000 0.0662456
\(471\) −229.000 + 396.640i −0.0224029 + 0.0388030i
\(472\) 3780.00 + 6547.15i 0.368620 + 0.638468i
\(473\) −6435.00 11145.7i −0.625543 1.08347i
\(474\) −2346.00 + 4063.39i −0.227332 + 0.393751i
\(475\) 3025.00 0.292203
\(476\) 0 0
\(477\) −13731.0 −1.31803
\(478\) 8253.00 14294.6i 0.789714 1.36783i
\(479\) −216.000 374.123i −0.0206039 0.0356871i 0.855540 0.517737i \(-0.173226\pi\)
−0.876144 + 0.482050i \(0.839892\pi\)
\(480\) −225.000 389.711i −0.0213954 0.0370579i
\(481\) −7640.50 + 13233.7i −0.724276 + 1.25448i
\(482\) −10653.0 −1.00670
\(483\) 0 0
\(484\) 694.000 0.0651766
\(485\) −2255.00 + 3905.77i −0.211122 + 0.365674i
\(486\) −5313.00 9202.39i −0.495890 0.858907i
\(487\) 5948.00 + 10302.2i 0.553449 + 0.958602i 0.998022 + 0.0628592i \(0.0200219\pi\)
−0.444574 + 0.895742i \(0.646645\pi\)
\(488\) −4116.00 + 7129.12i −0.381809 + 0.661312i
\(489\) −2456.00 −0.227125
\(490\) 0 0
\(491\) −12276.0 −1.12833 −0.564163 0.825663i \(-0.690801\pi\)
−0.564163 + 0.825663i \(0.690801\pi\)
\(492\) 195.000 337.750i 0.0178685 0.0309491i
\(493\) 4374.00 + 7575.99i 0.399584 + 0.692100i
\(494\) 10708.5 + 18547.7i 0.975300 + 1.68927i
\(495\) 2587.50 4481.68i 0.234948 0.406943i
\(496\) −6248.00 −0.565612
\(497\) 0 0
\(498\) −4608.00 −0.414637
\(499\) 5438.00 9418.89i 0.487852 0.844985i −0.512050 0.858956i \(-0.671114\pi\)
0.999902 + 0.0139706i \(0.00444712\pi\)
\(500\) 62.5000 + 108.253i 0.00559017 + 0.00968246i
\(501\) −1929.00 3341.13i −0.172019 0.297945i
\(502\) 10597.5 18355.4i 0.942210 1.63196i
\(503\) −12000.0 −1.06372 −0.531862 0.846831i \(-0.678508\pi\)
−0.531862 + 0.846831i \(0.678508\pi\)
\(504\) 0 0
\(505\) 3420.00 0.301362
\(506\) 4657.50 8067.03i 0.409192 0.708741i
\(507\) −1284.00 2223.95i −0.112474 0.194811i
\(508\) −401.500 695.418i −0.0350663 0.0607366i
\(509\) −5841.00 + 10116.9i −0.508640 + 0.880990i 0.491310 + 0.870985i \(0.336518\pi\)
−0.999950 + 0.0100055i \(0.996815\pi\)
\(510\) −1620.00 −0.140656
\(511\) 0 0
\(512\) −8733.00 −0.753804
\(513\) 6050.00 10478.9i 0.520690 0.901862i
\(514\) −6120.00 10600.2i −0.525178 0.909635i
\(515\) 3790.00 + 6564.47i 0.324286 + 0.561680i
\(516\) 286.000 495.367i 0.0244001 0.0422622i
\(517\) 2025.00 0.172262
\(518\) 0 0
\(519\) 1398.00 0.118238
\(520\) 3097.50 5365.03i 0.261220 0.452446i
\(521\) 4804.50 + 8321.64i 0.404010 + 0.699765i 0.994206 0.107495i \(-0.0342829\pi\)
−0.590196 + 0.807260i \(0.700950\pi\)
\(522\) −5589.00 9680.43i −0.468628 0.811688i
\(523\) 10594.0 18349.3i 0.885742 1.53415i 0.0408820 0.999164i \(-0.486983\pi\)
0.844860 0.534987i \(-0.179683\pi\)
\(524\) −2019.00 −0.168321
\(525\) 0 0
\(526\) −9864.00 −0.817663
\(527\) −2376.00 + 4115.35i −0.196395 + 0.340166i
\(528\) −3195.00 5533.90i −0.263342 0.456122i
\(529\) 3703.00 + 6413.78i 0.304348 + 0.527146i
\(530\) 4477.50 7755.26i 0.366963 0.635598i
\(531\) −8280.00 −0.676688
\(532\) 0 0
\(533\) 11505.0 0.934966
\(534\) −3582.00 + 6204.21i −0.290278 + 0.502776i
\(535\) −1830.00 3169.65i −0.147884 0.256142i
\(536\) −2940.00 5092.23i −0.236919 0.410356i
\(537\) −3117.00 + 5398.80i −0.250481 + 0.433846i
\(538\) 9792.00 0.784690
\(539\) 0 0
\(540\) 500.000 0.0398455
\(541\) −4036.00 + 6990.56i −0.320742 + 0.555541i −0.980641 0.195813i \(-0.937265\pi\)
0.659900 + 0.751354i \(0.270599\pi\)
\(542\) −4128.00 7149.91i −0.327145 0.566632i
\(543\) −1798.00 3114.23i −0.142099 0.246122i
\(544\) 1215.00 2104.44i 0.0957586 0.165859i
\(545\) 8000.00 0.628775
\(546\) 0 0
\(547\) 344.000 0.0268892 0.0134446 0.999910i \(-0.495720\pi\)
0.0134446 + 0.999910i \(0.495720\pi\)
\(548\) −30.0000 + 51.9615i −0.00233857 + 0.00405052i
\(549\) −4508.00 7808.09i −0.350449 0.606996i
\(550\) 1687.50 + 2922.84i 0.130828 + 0.226600i
\(551\) 9801.00 16975.8i 0.757780 1.31251i
\(552\) −2898.00 −0.223455
\(553\) 0 0
\(554\) −14070.0 −1.07902
\(555\) −1295.00 + 2243.01i −0.0990445 + 0.171550i
\(556\) −854.000 1479.17i −0.0651397 0.112825i
\(557\) −9181.50 15902.8i −0.698443 1.20974i −0.969006 0.247036i \(-0.920543\pi\)
0.270563 0.962702i \(-0.412790\pi\)
\(558\) 3036.00 5258.51i 0.230330 0.398943i
\(559\) 16874.0 1.27673
\(560\) 0 0
\(561\) −4860.00 −0.365756
\(562\) −11731.5 + 20319.6i −0.880540 + 1.52514i
\(563\) −3147.00 5450.76i −0.235578 0.408033i 0.723863 0.689944i \(-0.242365\pi\)
−0.959440 + 0.281912i \(0.909032\pi\)
\(564\) 45.0000 + 77.9423i 0.00335965 + 0.00581908i
\(565\) −3480.00 + 6027.54i −0.259123 + 0.448815i
\(566\) 1974.00 0.146596
\(567\) 0 0
\(568\) −1008.00 −0.0744626
\(569\) −5866.50 + 10161.1i −0.432226 + 0.748637i −0.997065 0.0765642i \(-0.975605\pi\)
0.564839 + 0.825201i \(0.308938\pi\)
\(570\) 1815.00 + 3143.67i 0.133372 + 0.231007i
\(571\) −526.000 911.059i −0.0385506 0.0667717i 0.846106 0.533014i \(-0.178941\pi\)
−0.884657 + 0.466242i \(0.845607\pi\)
\(572\) −1327.50 + 2299.30i −0.0970377 + 0.168074i
\(573\) −4776.00 −0.348203
\(574\) 0 0
\(575\) 1725.00 0.125109
\(576\) 4979.50 8624.75i 0.360207 0.623897i
\(577\) −6578.00 11393.4i −0.474603 0.822036i 0.524974 0.851118i \(-0.324075\pi\)
−0.999577 + 0.0290821i \(0.990742\pi\)
\(578\) 2995.50 + 5188.36i 0.215565 + 0.373369i
\(579\) −272.000 + 471.118i −0.0195232 + 0.0338152i
\(580\) 810.000 0.0579887
\(581\) 0 0
\(582\) −5412.00 −0.385455
\(583\) 13432.5 23265.8i 0.954232 1.65278i
\(584\) −7014.00 12148.6i −0.496989 0.860810i
\(585\) 3392.50 + 5875.98i 0.239765 + 0.415285i
\(586\) −8995.50 + 15580.7i −0.634131 + 1.09835i
\(587\) 13368.0 0.939960 0.469980 0.882677i \(-0.344261\pi\)
0.469980 + 0.882677i \(0.344261\pi\)
\(588\) 0 0
\(589\) 10648.0 0.744895
\(590\) 2700.00 4676.54i 0.188402 0.326322i
\(591\) 2109.00 + 3652.90i 0.146790 + 0.254247i
\(592\) −9194.50 15925.3i −0.638330 1.10562i
\(593\) 13332.0 23091.7i 0.923237 1.59909i 0.128865 0.991662i \(-0.458867\pi\)
0.794372 0.607431i \(-0.207800\pi\)
\(594\) 13500.0 0.932511
\(595\) 0 0
\(596\) −1086.00 −0.0746381
\(597\) 1424.00 2466.44i 0.0976222 0.169087i
\(598\) 6106.50 + 10576.8i 0.417581 + 0.723271i
\(599\) −3807.00 6593.92i −0.259682 0.449783i 0.706474 0.707739i \(-0.250285\pi\)
−0.966157 + 0.257955i \(0.916951\pi\)
\(600\) 525.000 909.327i 0.0357217 0.0618718i
\(601\) −6410.00 −0.435057 −0.217529 0.976054i \(-0.569800\pi\)
−0.217529 + 0.976054i \(0.569800\pi\)
\(602\) 0 0
\(603\) 6440.00 0.434921
\(604\) 1433.00 2482.03i 0.0965363 0.167206i
\(605\) 1735.00 + 3005.11i 0.116591 + 0.201942i
\(606\) 2052.00 + 3554.17i 0.137552 + 0.238248i
\(607\) −10734.5 + 18592.7i −0.717792 + 1.24325i 0.244080 + 0.969755i \(0.421514\pi\)
−0.961873 + 0.273498i \(0.911819\pi\)
\(608\) −5445.00 −0.363197
\(609\) 0 0
\(610\) 5880.00 0.390286
\(611\) −1327.50 + 2299.30i −0.0878967 + 0.152242i
\(612\) 621.000 + 1075.60i 0.0410171 + 0.0710436i
\(613\) −1868.50 3236.34i −0.123113 0.213237i 0.797881 0.602815i \(-0.205954\pi\)
−0.920994 + 0.389578i \(0.872621\pi\)
\(614\) −9339.00 + 16175.6i −0.613830 + 1.06318i
\(615\) 1950.00 0.127856
\(616\) 0 0
\(617\) 18078.0 1.17957 0.589784 0.807561i \(-0.299213\pi\)
0.589784 + 0.807561i \(0.299213\pi\)
\(618\) −4548.00 + 7877.37i −0.296031 + 0.512741i
\(619\) 6143.50 + 10640.9i 0.398915 + 0.690940i 0.993592 0.113024i \(-0.0360537\pi\)
−0.594678 + 0.803964i \(0.702720\pi\)
\(620\) 220.000 + 381.051i 0.0142507 + 0.0246829i
\(621\) 3450.00 5975.58i 0.222937 0.386138i
\(622\) −14040.0 −0.905069
\(623\) 0 0
\(624\) 8378.00 0.537481
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 1542.00 + 2670.82i 0.0984516 + 0.170523i
\(627\) 5445.00 + 9431.02i 0.346814 + 0.600699i
\(628\) −114.500 + 198.320i −0.00727555 + 0.0126016i
\(629\) −13986.0 −0.886579
\(630\) 0 0
\(631\) −9580.00 −0.604396 −0.302198 0.953245i \(-0.597720\pi\)
−0.302198 + 0.953245i \(0.597720\pi\)
\(632\) 8211.00 14221.9i 0.516798 0.895120i
\(633\) 3625.00 + 6278.68i 0.227616 + 0.394242i
\(634\) −12933.0 22400.6i −0.810150 1.40322i
\(635\) 2007.50 3477.09i 0.125457 0.217298i
\(636\) 1194.00 0.0744421
\(637\) 0 0
\(638\) 21870.0 1.35712
\(639\) 552.000 956.092i 0.0341734 0.0591900i
\(640\) 4147.50 + 7183.68i 0.256163 + 0.443687i
\(641\) −5389.50 9334.89i −0.332094 0.575204i 0.650828 0.759225i \(-0.274422\pi\)
−0.982922 + 0.184021i \(0.941089\pi\)
\(642\) 2196.00 3803.58i 0.134999 0.233825i
\(643\) −8882.00 −0.544746 −0.272373 0.962192i \(-0.587809\pi\)
−0.272373 + 0.962192i \(0.587809\pi\)
\(644\) 0 0
\(645\) 2860.00 0.174593
\(646\) −9801.00 + 16975.8i −0.596928 + 1.03391i
\(647\) −5509.50 9542.73i −0.334777 0.579851i 0.648665 0.761074i \(-0.275328\pi\)
−0.983442 + 0.181223i \(0.941994\pi\)
\(648\) 4420.50 + 7656.53i 0.267984 + 0.464162i
\(649\) 8100.00 14029.6i 0.489912 0.848552i
\(650\) −4425.00 −0.267020
\(651\) 0 0
\(652\) −1228.00 −0.0737610
\(653\) −11161.5 + 19332.3i −0.668887 + 1.15855i 0.309329 + 0.950955i \(0.399896\pi\)
−0.978216 + 0.207591i \(0.933438\pi\)
\(654\) 4800.00 + 8313.84i 0.286995 + 0.497090i
\(655\) −5047.50 8742.53i −0.301103 0.521525i
\(656\) −6922.50 + 11990.1i −0.412009 + 0.713621i
\(657\) 15364.0 0.912339
\(658\) 0 0
\(659\) −11856.0 −0.700826 −0.350413 0.936595i \(-0.613959\pi\)
−0.350413 + 0.936595i \(0.613959\pi\)
\(660\) −225.000 + 389.711i −0.0132699 + 0.0229841i
\(661\) −16622.0 28790.1i −0.978095 1.69411i −0.669318 0.742976i \(-0.733414\pi\)
−0.308777 0.951134i \(-0.599920\pi\)
\(662\) 2998.50 + 5193.55i 0.176042 + 0.304914i
\(663\) 3186.00 5518.31i 0.186627 0.323248i
\(664\) 16128.0 0.942602
\(665\) 0 0
\(666\) 17871.0 1.03977
\(667\) 5589.00 9680.43i 0.324448 0.561961i
\(668\) −964.500 1670.56i −0.0558647 0.0967605i
\(669\) −4960.00 8590.97i −0.286644 0.496482i
\(670\) −2100.00 + 3637.31i −0.121090 + 0.209733i
\(671\) 17640.0 1.01488
\(672\) 0 0
\(673\) −12322.0 −0.705763 −0.352881 0.935668i \(-0.614798\pi\)
−0.352881 + 0.935668i \(0.614798\pi\)
\(674\) −7671.00 + 13286.6i −0.438392 + 0.759316i
\(675\) 1250.00 + 2165.06i 0.0712778 + 0.123457i
\(676\) −642.000 1111.98i −0.0365271 0.0632668i
\(677\) −6298.50 + 10909.3i −0.357564 + 0.619320i −0.987553 0.157285i \(-0.949726\pi\)
0.629989 + 0.776604i \(0.283059\pi\)
\(678\) −8352.00 −0.473092
\(679\) 0 0
\(680\) 5670.00 0.319757
\(681\) −1500.00 + 2598.08i −0.0844055 + 0.146195i
\(682\) 5940.00 + 10288.4i 0.333511 + 0.577658i
\(683\) 4170.00 + 7222.65i 0.233617 + 0.404637i 0.958870 0.283846i \(-0.0916104\pi\)
−0.725253 + 0.688483i \(0.758277\pi\)
\(684\) 1391.50 2410.15i 0.0777856 0.134729i
\(685\) −300.000 −0.0167334
\(686\) 0 0
\(687\) −12184.0 −0.676636
\(688\) −10153.0 + 17585.5i −0.562616 + 0.974479i
\(689\) 17611.5 + 30504.0i 0.973795 + 1.68666i
\(690\) 1035.00 + 1792.67i 0.0571040 + 0.0989071i
\(691\) −10100.0 + 17493.7i −0.556038 + 0.963086i 0.441784 + 0.897121i \(0.354346\pi\)
−0.997822 + 0.0659643i \(0.978988\pi\)
\(692\) 699.000 0.0383988
\(693\) 0 0
\(694\) 12960.0 0.708869
\(695\) 4270.00 7395.86i 0.233051 0.403656i
\(696\) −3402.00 5892.44i −0.185277 0.320908i
\(697\) 5265.00 + 9119.25i 0.286121 + 0.495576i
\(698\) 11883.0 20582.0i 0.644381 1.11610i
\(699\) 276.000 0.0149346
\(700\) 0 0
\(701\) 474.000 0.0255388 0.0127694 0.999918i \(-0.495935\pi\)
0.0127694 + 0.999918i \(0.495935\pi\)
\(702\) −8850.00 + 15328.6i −0.475814 + 0.824135i
\(703\) 15669.5 + 27140.4i 0.840663 + 1.45607i
\(704\) 9742.50 + 16874.5i 0.521569 + 0.903383i
\(705\) −225.000 + 389.711i −0.0120198 + 0.0208190i
\(706\) −2484.00 −0.132417
\(707\) 0 0
\(708\) 720.000 0.0382193
\(709\) 12563.0 21759.8i 0.665463 1.15262i −0.313696 0.949523i \(-0.601567\pi\)
0.979160 0.203093i \(-0.0650993\pi\)
\(710\) 360.000 + 623.538i 0.0190290 + 0.0329591i
\(711\) 8993.00 + 15576.3i 0.474351 + 0.821601i
\(712\) 12537.0 21714.7i 0.659893 1.14297i
\(713\) 6072.00 0.318932
\(714\) 0 0
\(715\) −13275.0 −0.694345
\(716\) −1558.50 + 2699.40i −0.0813462 + 0.140896i
\(717\) 5502.00 + 9529.74i 0.286577 + 0.496367i
\(718\) 2025.00 + 3507.40i 0.105254 + 0.182305i
\(719\) −3648.00 + 6318.52i −0.189218 + 0.327734i −0.944990 0.327100i \(-0.893928\pi\)
0.755772 + 0.654835i \(0.227262\pi\)
\(720\) −8165.00 −0.422627
\(721\) 0 0
\(722\) 23346.0 1.20339
\(723\) 3551.00 6150.51i 0.182660 0.316376i
\(724\) −899.000 1557.11i −0.0461479 0.0799305i
\(725\) 2025.00 + 3507.40i 0.103733 + 0.179671i
\(726\) −2082.00 + 3606.13i −0.106433 + 0.184347i
\(727\) 15421.0 0.786703 0.393352 0.919388i \(-0.371316\pi\)
0.393352 + 0.919388i \(0.371316\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) −5010.00 + 8677.57i −0.254012 + 0.439961i
\(731\) 7722.00 + 13374.9i 0.390709 + 0.676728i
\(732\) 392.000 + 678.964i 0.0197934 + 0.0342831i
\(733\) −14583.5 + 25259.4i −0.734862 + 1.27282i 0.219922 + 0.975517i \(0.429420\pi\)
−0.954784 + 0.297301i \(0.903914\pi\)
\(734\) −8403.00 −0.422562
\(735\) 0 0
\(736\) −3105.00 −0.155505
\(737\) −6300.00 + 10911.9i −0.314876 + 0.545381i
\(738\) −6727.50 11652.4i −0.335559 0.581206i
\(739\) 6690.50 + 11588.3i 0.333037 + 0.576836i 0.983106 0.183039i \(-0.0585934\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(740\) −647.500 + 1121.50i −0.0321656 + 0.0557125i
\(741\) −14278.0 −0.707848
\(742\) 0 0
\(743\) 5487.00 0.270927 0.135463 0.990782i \(-0.456748\pi\)
0.135463 + 0.990782i \(0.456748\pi\)
\(744\) 1848.00 3200.83i 0.0910631 0.157726i
\(745\) −2715.00 4702.52i −0.133517 0.231258i
\(746\) −9903.00 17152.5i −0.486025 0.841820i
\(747\) −8832.00 + 15297.5i −0.432592 + 0.749271i
\(748\) −2430.00 −0.118783
\(749\) 0 0
\(750\) −750.000 −0.0365148
\(751\) −3319.00 + 5748.68i −0.161268 + 0.279324i −0.935324 0.353793i \(-0.884892\pi\)
0.774056 + 0.633117i \(0.218225\pi\)
\(752\) −1597.50 2766.95i −0.0774665 0.134176i
\(753\) 7065.00 + 12236.9i 0.341916 + 0.592216i
\(754\) −14337.0 + 24832.4i −0.692470 + 1.19939i
\(755\) 14330.0 0.690758
\(756\) 0 0
\(757\) 14846.0 0.712797 0.356398 0.934334i \(-0.384005\pi\)
0.356398 + 0.934334i \(0.384005\pi\)
\(758\) 12457.5 21577.0i 0.596935 1.03392i
\(759\) 3105.00 + 5378.02i 0.148491 + 0.257193i
\(760\) −6352.50 11002.9i −0.303197 0.525152i
\(761\) −1825.50 + 3161.86i −0.0869571 + 0.150614i −0.906223 0.422799i \(-0.861048\pi\)
0.819266 + 0.573413i \(0.194381\pi\)
\(762\) 4818.00 0.229052
\(763\) 0 0
\(764\) −2388.00 −0.113082
\(765\) −3105.00 + 5378.02i −0.146747 + 0.254173i
\(766\) 1417.50 + 2455.18i 0.0668621 + 0.115809i
\(767\) 10620.0 + 18394.4i 0.499956 + 0.865949i
\(768\) −1513.00 + 2620.59i −0.0710881 + 0.123128i
\(769\) −29855.0 −1.40000 −0.699999 0.714144i \(-0.746816\pi\)
−0.699999 + 0.714144i \(0.746816\pi\)
\(770\) 0 0
\(771\) 8160.00 0.381161
\(772\) −136.000 + 235.559i −0.00634035 + 0.0109818i