Properties

Label 115.4.e.a.22.15
Level $115$
Weight $4$
Character 115.22
Analytic conductor $6.785$
Analytic rank $0$
Dimension $68$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [115,4,Mod(22,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.78521965066\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.15
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.386420 - 0.386420i) q^{2} +(-0.970983 + 0.970983i) q^{3} -7.70136i q^{4} +(-8.97655 - 6.66495i) q^{5} +0.750415 q^{6} +(-6.23903 + 6.23903i) q^{7} +(-6.06732 + 6.06732i) q^{8} +25.1144i q^{9} +O(q^{10})\) \(q+(-0.386420 - 0.386420i) q^{2} +(-0.970983 + 0.970983i) q^{3} -7.70136i q^{4} +(-8.97655 - 6.66495i) q^{5} +0.750415 q^{6} +(-6.23903 + 6.23903i) q^{7} +(-6.06732 + 6.06732i) q^{8} +25.1144i q^{9} +(0.893251 + 6.04419i) q^{10} +51.7690i q^{11} +(7.47789 + 7.47789i) q^{12} +(30.5538 - 30.5538i) q^{13} +4.82177 q^{14} +(15.1876 - 2.24453i) q^{15} -56.9218 q^{16} +(-58.6549 + 58.6549i) q^{17} +(9.70470 - 9.70470i) q^{18} -111.941 q^{19} +(-51.3291 + 69.1316i) q^{20} -12.1160i q^{21} +(20.0046 - 20.0046i) q^{22} +(81.4693 - 74.3624i) q^{23} -11.7825i q^{24} +(36.1570 + 119.656i) q^{25} -23.6132 q^{26} +(-50.6022 - 50.6022i) q^{27} +(48.0490 + 48.0490i) q^{28} +32.6788i q^{29} +(-6.73614 - 5.00147i) q^{30} -257.276 q^{31} +(70.5343 + 70.5343i) q^{32} +(-50.2668 - 50.2668i) q^{33} +45.3308 q^{34} +(97.5877 - 14.4222i) q^{35} +193.415 q^{36} +(48.0381 - 48.0381i) q^{37} +(43.2561 + 43.2561i) q^{38} +59.3345i q^{39} +(94.9020 - 14.0253i) q^{40} +21.8734 q^{41} +(-4.68186 + 4.68186i) q^{42} +(-100.002 - 100.002i) q^{43} +398.691 q^{44} +(167.386 - 225.441i) q^{45} +(-60.2165 - 2.74624i) q^{46} +(-304.924 - 304.924i) q^{47} +(55.2701 - 55.2701i) q^{48} +265.149i q^{49} +(32.2659 - 60.2095i) q^{50} -113.906i q^{51} +(-235.306 - 235.306i) q^{52} +(-122.425 - 122.425i) q^{53} +39.1074i q^{54} +(345.037 - 464.707i) q^{55} -75.7084i q^{56} +(108.692 - 108.692i) q^{57} +(12.6278 - 12.6278i) q^{58} +638.851i q^{59} +(-17.2859 - 116.965i) q^{60} -593.557i q^{61} +(99.4168 + 99.4168i) q^{62} +(-156.689 - 156.689i) q^{63} +400.863i q^{64} +(-477.907 + 70.6284i) q^{65} +38.8482i q^{66} +(357.935 - 357.935i) q^{67} +(451.722 + 451.722i) q^{68} +(-6.90066 + 151.310i) q^{69} +(-43.2829 - 32.1369i) q^{70} +271.768 q^{71} +(-152.377 - 152.377i) q^{72} +(47.6124 - 47.6124i) q^{73} -37.1258 q^{74} +(-151.292 - 81.0766i) q^{75} +862.094i q^{76} +(-322.988 - 322.988i) q^{77} +(22.9280 - 22.9280i) q^{78} -809.638 q^{79} +(510.962 + 379.381i) q^{80} -579.821 q^{81} +(-8.45233 - 8.45233i) q^{82} +(532.729 + 532.729i) q^{83} -93.3095 q^{84} +(917.450 - 135.587i) q^{85} +77.2853i q^{86} +(-31.7306 - 31.7306i) q^{87} +(-314.099 - 314.099i) q^{88} +1006.82 q^{89} +(-151.796 + 22.4334i) q^{90} +381.252i q^{91} +(-572.691 - 627.424i) q^{92} +(249.811 - 249.811i) q^{93} +235.657i q^{94} +(1004.84 + 746.078i) q^{95} -136.975 q^{96} +(-1293.05 + 1293.05i) q^{97} +(102.459 - 102.459i) q^{98} -1300.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36} + 2248 q^{41} - 96 q^{46} - 1412 q^{47} + 1532 q^{48} - 620 q^{50} + 112 q^{52} + 2688 q^{55} + 2044 q^{58} + 3948 q^{62} - 1836 q^{70} - 2272 q^{71} + 1128 q^{72} + 1100 q^{73} + 2828 q^{75} + 4216 q^{77} - 9180 q^{78} - 3580 q^{81} - 6516 q^{82} - 2684 q^{85} - 6304 q^{87} - 688 q^{92} - 1608 q^{93} - 8616 q^{95} - 544 q^{96} - 3612 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.386420 0.386420i −0.136620 0.136620i 0.635489 0.772110i \(-0.280798\pi\)
−0.772110 + 0.635489i \(0.780798\pi\)
\(3\) −0.970983 + 0.970983i −0.186866 + 0.186866i −0.794340 0.607474i \(-0.792183\pi\)
0.607474 + 0.794340i \(0.292183\pi\)
\(4\) 7.70136i 0.962670i
\(5\) −8.97655 6.66495i −0.802887 0.596131i
\(6\) 0.750415 0.0510592
\(7\) −6.23903 + 6.23903i −0.336876 + 0.336876i −0.855190 0.518314i \(-0.826560\pi\)
0.518314 + 0.855190i \(0.326560\pi\)
\(8\) −6.06732 + 6.06732i −0.268140 + 0.268140i
\(9\) 25.1144i 0.930162i
\(10\) 0.893251 + 6.04419i 0.0282471 + 0.191134i
\(11\) 51.7690i 1.41899i 0.704709 + 0.709497i \(0.251078\pi\)
−0.704709 + 0.709497i \(0.748922\pi\)
\(12\) 7.47789 + 7.47789i 0.179890 + 0.179890i
\(13\) 30.5538 30.5538i 0.651854 0.651854i −0.301585 0.953439i \(-0.597516\pi\)
0.953439 + 0.301585i \(0.0975158\pi\)
\(14\) 4.82177 0.0920481
\(15\) 15.1876 2.24453i 0.261429 0.0386357i
\(16\) −56.9218 −0.889403
\(17\) −58.6549 + 58.6549i −0.836817 + 0.836817i −0.988439 0.151621i \(-0.951551\pi\)
0.151621 + 0.988439i \(0.451551\pi\)
\(18\) 9.70470 9.70470i 0.127079 0.127079i
\(19\) −111.941 −1.35163 −0.675814 0.737073i \(-0.736208\pi\)
−0.675814 + 0.737073i \(0.736208\pi\)
\(20\) −51.3291 + 69.1316i −0.573877 + 0.772915i
\(21\) 12.1160i 0.125901i
\(22\) 20.0046 20.0046i 0.193863 0.193863i
\(23\) 81.4693 74.3624i 0.738588 0.674158i
\(24\) 11.7825i 0.100212i
\(25\) 36.1570 + 119.656i 0.289256 + 0.957252i
\(26\) −23.6132 −0.178113
\(27\) −50.6022 50.6022i −0.360681 0.360681i
\(28\) 48.0490 + 48.0490i 0.324300 + 0.324300i
\(29\) 32.6788i 0.209252i 0.994512 + 0.104626i \(0.0333645\pi\)
−0.994512 + 0.104626i \(0.966635\pi\)
\(30\) −6.73614 5.00147i −0.0409948 0.0304380i
\(31\) −257.276 −1.49059 −0.745294 0.666736i \(-0.767691\pi\)
−0.745294 + 0.666736i \(0.767691\pi\)
\(32\) 70.5343 + 70.5343i 0.389651 + 0.389651i
\(33\) −50.2668 50.2668i −0.265161 0.265161i
\(34\) 45.3308 0.228652
\(35\) 97.5877 14.4222i 0.471295 0.0696512i
\(36\) 193.415 0.895439
\(37\) 48.0381 48.0381i 0.213444 0.213444i −0.592285 0.805729i \(-0.701774\pi\)
0.805729 + 0.592285i \(0.201774\pi\)
\(38\) 43.2561 + 43.2561i 0.184660 + 0.184660i
\(39\) 59.3345i 0.243618i
\(40\) 94.9020 14.0253i 0.375133 0.0554397i
\(41\) 21.8734 0.0833184 0.0416592 0.999132i \(-0.486736\pi\)
0.0416592 + 0.999132i \(0.486736\pi\)
\(42\) −4.68186 + 4.68186i −0.0172006 + 0.0172006i
\(43\) −100.002 100.002i −0.354654 0.354654i 0.507184 0.861838i \(-0.330686\pi\)
−0.861838 + 0.507184i \(0.830686\pi\)
\(44\) 398.691 1.36602
\(45\) 167.386 225.441i 0.554499 0.746815i
\(46\) −60.2165 2.74624i −0.193009 0.00880243i
\(47\) −304.924 304.924i −0.946334 0.946334i 0.0522977 0.998632i \(-0.483346\pi\)
−0.998632 + 0.0522977i \(0.983346\pi\)
\(48\) 55.2701 55.2701i 0.166199 0.166199i
\(49\) 265.149i 0.773029i
\(50\) 32.2659 60.2095i 0.0912617 0.170298i
\(51\) 113.906i 0.312745i
\(52\) −235.306 235.306i −0.627520 0.627520i
\(53\) −122.425 122.425i −0.317291 0.317291i 0.530435 0.847726i \(-0.322029\pi\)
−0.847726 + 0.530435i \(0.822029\pi\)
\(54\) 39.1074i 0.0985526i
\(55\) 345.037 464.707i 0.845906 1.13929i
\(56\) 75.7084i 0.180660i
\(57\) 108.692 108.692i 0.252573 0.252573i
\(58\) 12.6278 12.6278i 0.0285880 0.0285880i
\(59\) 638.851i 1.40968i 0.709364 + 0.704842i \(0.248982\pi\)
−0.709364 + 0.704842i \(0.751018\pi\)
\(60\) −17.2859 116.965i −0.0371934 0.251669i
\(61\) 593.557i 1.24586i −0.782279 0.622928i \(-0.785943\pi\)
0.782279 0.622928i \(-0.214057\pi\)
\(62\) 99.4168 + 99.4168i 0.203644 + 0.203644i
\(63\) −156.689 156.689i −0.313349 0.313349i
\(64\) 400.863i 0.782935i
\(65\) −477.907 + 70.6284i −0.911956 + 0.134775i
\(66\) 38.8482i 0.0724528i
\(67\) 357.935 357.935i 0.652667 0.652667i −0.300967 0.953634i \(-0.597310\pi\)
0.953634 + 0.300967i \(0.0973095\pi\)
\(68\) 451.722 + 451.722i 0.805579 + 0.805579i
\(69\) −6.90066 + 151.310i −0.0120397 + 0.263994i
\(70\) −43.2829 32.1369i −0.0739042 0.0548727i
\(71\) 271.768 0.454266 0.227133 0.973864i \(-0.427065\pi\)
0.227133 + 0.973864i \(0.427065\pi\)
\(72\) −152.377 152.377i −0.249414 0.249414i
\(73\) 47.6124 47.6124i 0.0763372 0.0763372i −0.667907 0.744244i \(-0.732810\pi\)
0.744244 + 0.667907i \(0.232810\pi\)
\(74\) −37.1258 −0.0583215
\(75\) −151.292 81.0766i −0.232930 0.124826i
\(76\) 862.094i 1.30117i
\(77\) −322.988 322.988i −0.478025 0.478025i
\(78\) 22.9280 22.9280i 0.0332832 0.0332832i
\(79\) −809.638 −1.15306 −0.576528 0.817078i \(-0.695593\pi\)
−0.576528 + 0.817078i \(0.695593\pi\)
\(80\) 510.962 + 379.381i 0.714090 + 0.530201i
\(81\) −579.821 −0.795364
\(82\) −8.45233 8.45233i −0.0113830 0.0113830i
\(83\) 532.729 + 532.729i 0.704513 + 0.704513i 0.965376 0.260863i \(-0.0840070\pi\)
−0.260863 + 0.965376i \(0.584007\pi\)
\(84\) −93.3095 −0.121201
\(85\) 917.450 135.587i 1.17072 0.173017i
\(86\) 77.2853i 0.0969056i
\(87\) −31.7306 31.7306i −0.0391020 0.0391020i
\(88\) −314.099 314.099i −0.380489 0.380489i
\(89\) 1006.82 1.19913 0.599565 0.800326i \(-0.295340\pi\)
0.599565 + 0.800326i \(0.295340\pi\)
\(90\) −151.796 + 22.4334i −0.177786 + 0.0262744i
\(91\) 381.252i 0.439188i
\(92\) −572.691 627.424i −0.648991 0.711016i
\(93\) 249.811 249.811i 0.278540 0.278540i
\(94\) 235.657i 0.258577i
\(95\) 1004.84 + 746.078i 1.08520 + 0.805747i
\(96\) −136.975 −0.145625
\(97\) −1293.05 + 1293.05i −1.35350 + 1.35350i −0.471794 + 0.881709i \(0.656393\pi\)
−0.881709 + 0.471794i \(0.843607\pi\)
\(98\) 102.459 102.459i 0.105611 0.105611i
\(99\) −1300.15 −1.31989
\(100\) 921.518 278.458i 0.921518 0.278458i
\(101\) −1250.51 −1.23198 −0.615992 0.787752i \(-0.711245\pi\)
−0.615992 + 0.787752i \(0.711245\pi\)
\(102\) −44.0155 + 44.0155i −0.0427273 + 0.0427273i
\(103\) −1072.36 1072.36i −1.02585 1.02585i −0.999657 0.0261920i \(-0.991662\pi\)
−0.0261920 0.999657i \(-0.508338\pi\)
\(104\) 370.760i 0.349577i
\(105\) −80.7523 + 108.760i −0.0750535 + 0.101084i
\(106\) 94.6151i 0.0866966i
\(107\) −757.558 + 757.558i −0.684447 + 0.684447i −0.960999 0.276552i \(-0.910808\pi\)
0.276552 + 0.960999i \(0.410808\pi\)
\(108\) −389.705 + 389.705i −0.347217 + 0.347217i
\(109\) 855.400 0.751674 0.375837 0.926686i \(-0.377355\pi\)
0.375837 + 0.926686i \(0.377355\pi\)
\(110\) −312.902 + 46.2427i −0.271218 + 0.0400824i
\(111\) 93.2884i 0.0797707i
\(112\) 355.137 355.137i 0.299618 0.299618i
\(113\) 459.308 + 459.308i 0.382372 + 0.382372i 0.871956 0.489584i \(-0.162851\pi\)
−0.489584 + 0.871956i \(0.662851\pi\)
\(114\) −84.0018 −0.0690131
\(115\) −1226.93 + 124.529i −0.994889 + 0.100978i
\(116\) 251.671 0.201441
\(117\) 767.340 + 767.340i 0.606330 + 0.606330i
\(118\) 246.865 246.865i 0.192591 0.192591i
\(119\) 731.899i 0.563807i
\(120\) −78.5299 + 105.766i −0.0597397 + 0.0804593i
\(121\) −1349.03 −1.01354
\(122\) −229.362 + 229.362i −0.170209 + 0.170209i
\(123\) −21.2387 + 21.2387i −0.0155693 + 0.0155693i
\(124\) 1981.38i 1.43494i
\(125\) 472.939 1315.09i 0.338408 0.941000i
\(126\) 121.096i 0.0856196i
\(127\) −473.824 473.824i −0.331063 0.331063i 0.521927 0.852990i \(-0.325213\pi\)
−0.852990 + 0.521927i \(0.825213\pi\)
\(128\) 719.176 719.176i 0.496615 0.496615i
\(129\) 194.200 0.132545
\(130\) 211.965 + 157.381i 0.143004 + 0.106179i
\(131\) −41.9024 −0.0279468 −0.0139734 0.999902i \(-0.504448\pi\)
−0.0139734 + 0.999902i \(0.504448\pi\)
\(132\) −387.123 + 387.123i −0.255263 + 0.255263i
\(133\) 698.400 698.400i 0.455331 0.455331i
\(134\) −276.626 −0.178335
\(135\) 116.972 + 791.494i 0.0745731 + 0.504600i
\(136\) 711.756i 0.448769i
\(137\) 1730.41 1730.41i 1.07911 1.07911i 0.0825249 0.996589i \(-0.473702\pi\)
0.996589 0.0825249i \(-0.0262984\pi\)
\(138\) 61.1357 55.8026i 0.0377117 0.0344220i
\(139\) 138.459i 0.0844889i 0.999107 + 0.0422444i \(0.0134508\pi\)
−0.999107 + 0.0422444i \(0.986549\pi\)
\(140\) −111.070 751.558i −0.0670511 0.453702i
\(141\) 592.151 0.353675
\(142\) −105.016 105.016i −0.0620619 0.0620619i
\(143\) 1581.74 + 1581.74i 0.924977 + 0.924977i
\(144\) 1429.56i 0.827289i
\(145\) 217.803 293.343i 0.124742 0.168006i
\(146\) −36.7968 −0.0208584
\(147\) −257.455 257.455i −0.144453 0.144453i
\(148\) −369.959 369.959i −0.205476 0.205476i
\(149\) 385.809 0.212125 0.106063 0.994359i \(-0.466176\pi\)
0.106063 + 0.994359i \(0.466176\pi\)
\(150\) 27.1327 + 89.7920i 0.0147692 + 0.0488766i
\(151\) −1122.64 −0.605029 −0.302514 0.953145i \(-0.597826\pi\)
−0.302514 + 0.953145i \(0.597826\pi\)
\(152\) 679.179 679.179i 0.362426 0.362426i
\(153\) −1473.08 1473.08i −0.778376 0.778376i
\(154\) 249.618i 0.130616i
\(155\) 2309.46 + 1714.73i 1.19677 + 0.888585i
\(156\) 456.956 0.234524
\(157\) 1567.00 1567.00i 0.796560 0.796560i −0.185992 0.982551i \(-0.559550\pi\)
0.982551 + 0.185992i \(0.0595498\pi\)
\(158\) 312.860 + 312.860i 0.157531 + 0.157531i
\(159\) 237.746 0.118581
\(160\) −163.047 1103.26i −0.0805627 0.545128i
\(161\) −44.3401 + 972.238i −0.0217049 + 0.475920i
\(162\) 224.054 + 224.054i 0.108663 + 0.108663i
\(163\) −1763.65 + 1763.65i −0.847483 + 0.847483i −0.989819 0.142335i \(-0.954539\pi\)
0.142335 + 0.989819i \(0.454539\pi\)
\(164\) 168.455i 0.0802081i
\(165\) 116.197 + 786.248i 0.0548238 + 0.370965i
\(166\) 411.714i 0.192501i
\(167\) 2408.20 + 2408.20i 1.11588 + 1.11588i 0.992339 + 0.123542i \(0.0394253\pi\)
0.123542 + 0.992339i \(0.460575\pi\)
\(168\) 73.5115 + 73.5115i 0.0337592 + 0.0337592i
\(169\) 329.929i 0.150173i
\(170\) −406.915 302.128i −0.183582 0.136307i
\(171\) 2811.32i 1.25723i
\(172\) −770.148 + 770.148i −0.341414 + 0.341414i
\(173\) 1041.07 1041.07i 0.457519 0.457519i −0.440321 0.897840i \(-0.645136\pi\)
0.897840 + 0.440321i \(0.145136\pi\)
\(174\) 24.5227i 0.0106842i
\(175\) −972.124 520.956i −0.419918 0.225032i
\(176\) 2946.78i 1.26206i
\(177\) −620.314 620.314i −0.263422 0.263422i
\(178\) −389.055 389.055i −0.163825 0.163825i
\(179\) 466.508i 0.194796i −0.995246 0.0973979i \(-0.968948\pi\)
0.995246 0.0973979i \(-0.0310519\pi\)
\(180\) −1736.20 1289.10i −0.718937 0.533799i
\(181\) 346.543i 0.142311i −0.997465 0.0711557i \(-0.977331\pi\)
0.997465 0.0711557i \(-0.0226687\pi\)
\(182\) 147.324 147.324i 0.0600019 0.0600019i
\(183\) 576.334 + 576.334i 0.232808 + 0.232808i
\(184\) −43.1198 + 945.481i −0.0172763 + 0.378814i
\(185\) −751.389 + 111.045i −0.298612 + 0.0441309i
\(186\) −193.064 −0.0761083
\(187\) −3036.50 3036.50i −1.18744 1.18744i
\(188\) −2348.33 + 2348.33i −0.911007 + 0.911007i
\(189\) 631.417 0.243010
\(190\) −99.9910 676.590i −0.0381795 0.258342i
\(191\) 4380.19i 1.65937i 0.558234 + 0.829684i \(0.311479\pi\)
−0.558234 + 0.829684i \(0.688521\pi\)
\(192\) −389.231 389.231i −0.146304 0.146304i
\(193\) 3170.58 3170.58i 1.18251 1.18251i 0.203412 0.979093i \(-0.434797\pi\)
0.979093 0.203412i \(-0.0652032\pi\)
\(194\) 999.325 0.369832
\(195\) 395.461 532.619i 0.145228 0.195598i
\(196\) 2042.01 0.744172
\(197\) 1863.77 + 1863.77i 0.674050 + 0.674050i 0.958647 0.284597i \(-0.0918597\pi\)
−0.284597 + 0.958647i \(0.591860\pi\)
\(198\) 502.403 + 502.403i 0.180324 + 0.180324i
\(199\) 1057.56 0.376727 0.188364 0.982099i \(-0.439682\pi\)
0.188364 + 0.982099i \(0.439682\pi\)
\(200\) −945.370 506.618i −0.334239 0.179117i
\(201\) 695.097i 0.243922i
\(202\) 483.222 + 483.222i 0.168314 + 0.168314i
\(203\) −203.884 203.884i −0.0704919 0.0704919i
\(204\) −877.229 −0.301070
\(205\) −196.348 145.785i −0.0668952 0.0496686i
\(206\) 828.760i 0.280303i
\(207\) 1867.57 + 2046.05i 0.627076 + 0.687006i
\(208\) −1739.18 + 1739.18i −0.579761 + 0.579761i
\(209\) 5795.05i 1.91795i
\(210\) 73.2313 10.8226i 0.0240640 0.00355634i
\(211\) 3428.76 1.11870 0.559350 0.828931i \(-0.311051\pi\)
0.559350 + 0.828931i \(0.311051\pi\)
\(212\) −942.841 + 942.841i −0.305446 + 0.305446i
\(213\) −263.882 + 263.882i −0.0848867 + 0.0848867i
\(214\) 585.471 0.187019
\(215\) 231.164 + 1564.17i 0.0733268 + 0.496167i
\(216\) 614.039 0.193426
\(217\) 1605.15 1605.15i 0.502143 0.502143i
\(218\) −330.544 330.544i −0.102694 0.102694i
\(219\) 92.4617i 0.0285296i
\(220\) −3578.87 2657.26i −1.09676 0.814328i
\(221\) 3584.26i 1.09097i
\(222\) 36.0485 36.0485i 0.0108983 0.0108983i
\(223\) −1307.54 + 1307.54i −0.392642 + 0.392642i −0.875628 0.482986i \(-0.839552\pi\)
0.482986 + 0.875628i \(0.339552\pi\)
\(224\) −880.131 −0.262528
\(225\) −3005.10 + 908.060i −0.890400 + 0.269055i
\(226\) 354.972i 0.104479i
\(227\) −3270.11 + 3270.11i −0.956143 + 0.956143i −0.999078 0.0429346i \(-0.986329\pi\)
0.0429346 + 0.999078i \(0.486329\pi\)
\(228\) −837.079 837.079i −0.243144 0.243144i
\(229\) −1156.19 −0.333638 −0.166819 0.985988i \(-0.553350\pi\)
−0.166819 + 0.985988i \(0.553350\pi\)
\(230\) 522.233 + 425.991i 0.149717 + 0.122126i
\(231\) 627.232 0.178653
\(232\) −198.273 198.273i −0.0561089 0.0561089i
\(233\) −4511.16 + 4511.16i −1.26840 + 1.26840i −0.321479 + 0.946917i \(0.604180\pi\)
−0.946917 + 0.321479i \(0.895820\pi\)
\(234\) 593.031i 0.165674i
\(235\) 704.863 + 4769.46i 0.195660 + 1.32394i
\(236\) 4920.02 1.35706
\(237\) 786.144 786.144i 0.215467 0.215467i
\(238\) −282.820 + 282.820i −0.0770274 + 0.0770274i
\(239\) 1758.32i 0.475884i 0.971279 + 0.237942i \(0.0764728\pi\)
−0.971279 + 0.237942i \(0.923527\pi\)
\(240\) −864.507 + 127.763i −0.232515 + 0.0343627i
\(241\) 5809.50i 1.55279i −0.630246 0.776396i \(-0.717046\pi\)
0.630246 0.776396i \(-0.282954\pi\)
\(242\) 521.291 + 521.291i 0.138470 + 0.138470i
\(243\) 1929.25 1929.25i 0.509308 0.509308i
\(244\) −4571.20 −1.19935
\(245\) 1767.20 2380.12i 0.460827 0.620655i
\(246\) 16.4141 0.00425417
\(247\) −3420.21 + 3420.21i −0.881064 + 0.881064i
\(248\) 1560.98 1560.98i 0.399687 0.399687i
\(249\) −1034.54 −0.263299
\(250\) −690.929 + 325.423i −0.174793 + 0.0823262i
\(251\) 1337.99i 0.336466i 0.985747 + 0.168233i \(0.0538060\pi\)
−0.985747 + 0.168233i \(0.946194\pi\)
\(252\) −1206.72 + 1206.72i −0.301652 + 0.301652i
\(253\) 3849.66 + 4217.58i 0.956625 + 1.04805i
\(254\) 366.190i 0.0904599i
\(255\) −759.176 + 1022.48i −0.186437 + 0.251099i
\(256\) 2651.09 0.647240
\(257\) −582.549 582.549i −0.141395 0.141395i 0.632866 0.774261i \(-0.281878\pi\)
−0.774261 + 0.632866i \(0.781878\pi\)
\(258\) −75.0427 75.0427i −0.0181083 0.0181083i
\(259\) 599.423i 0.143808i
\(260\) 543.934 + 3680.54i 0.129744 + 0.877912i
\(261\) −820.709 −0.194638
\(262\) 16.1919 + 16.1919i 0.00381810 + 0.00381810i
\(263\) −3966.74 3966.74i −0.930036 0.930036i 0.0676712 0.997708i \(-0.478443\pi\)
−0.997708 + 0.0676712i \(0.978443\pi\)
\(264\) 609.969 0.142201
\(265\) 282.999 + 1914.91i 0.0656018 + 0.443895i
\(266\) −539.752 −0.124415
\(267\) −977.604 + 977.604i −0.224076 + 0.224076i
\(268\) −2756.58 2756.58i −0.628303 0.628303i
\(269\) 4795.26i 1.08689i −0.839446 0.543443i \(-0.817121\pi\)
0.839446 0.543443i \(-0.182879\pi\)
\(270\) 260.649 351.050i 0.0587503 0.0791267i
\(271\) −2793.44 −0.626161 −0.313080 0.949727i \(-0.601361\pi\)
−0.313080 + 0.949727i \(0.601361\pi\)
\(272\) 3338.74 3338.74i 0.744268 0.744268i
\(273\) −370.189 370.189i −0.0820691 0.0820691i
\(274\) −1337.33 −0.294857
\(275\) −6194.49 + 1871.81i −1.35833 + 0.410452i
\(276\) 1165.29 + 53.1445i 0.254139 + 0.0115903i
\(277\) 3343.20 + 3343.20i 0.725174 + 0.725174i 0.969654 0.244480i \(-0.0786173\pi\)
−0.244480 + 0.969654i \(0.578617\pi\)
\(278\) 53.5034 53.5034i 0.0115429 0.0115429i
\(279\) 6461.34i 1.38649i
\(280\) −504.592 + 679.600i −0.107697 + 0.145050i
\(281\) 4794.50i 1.01785i 0.860811 + 0.508925i \(0.169957\pi\)
−0.860811 + 0.508925i \(0.830043\pi\)
\(282\) −228.819 228.819i −0.0483191 0.0483191i
\(283\) 6064.64 + 6064.64i 1.27387 + 1.27387i 0.944040 + 0.329831i \(0.106992\pi\)
0.329831 + 0.944040i \(0.393008\pi\)
\(284\) 2092.98i 0.437308i
\(285\) −1700.11 + 251.254i −0.353354 + 0.0522210i
\(286\) 1222.43i 0.252741i
\(287\) −136.469 + 136.469i −0.0280679 + 0.0280679i
\(288\) −1771.43 + 1771.43i −0.362438 + 0.362438i
\(289\) 1967.79i 0.400526i
\(290\) −197.517 + 29.1904i −0.0399952 + 0.00591076i
\(291\) 2511.07i 0.505847i
\(292\) −366.680 366.680i −0.0734875 0.0734875i
\(293\) 2809.87 + 2809.87i 0.560253 + 0.560253i 0.929379 0.369126i \(-0.120343\pi\)
−0.369126 + 0.929379i \(0.620343\pi\)
\(294\) 198.972i 0.0394703i
\(295\) 4257.91 5734.68i 0.840356 1.13182i
\(296\) 582.926i 0.114466i
\(297\) 2619.62 2619.62i 0.511804 0.511804i
\(298\) −149.084 149.084i −0.0289806 0.0289806i
\(299\) 217.142 4761.25i 0.0419989 0.920904i
\(300\) −624.400 + 1165.16i −0.120166 + 0.224234i
\(301\) 1247.83 0.238948
\(302\) 433.812 + 433.812i 0.0826592 + 0.0826592i
\(303\) 1214.22 1214.22i 0.230216 0.230216i
\(304\) 6371.86 1.20214
\(305\) −3956.03 + 5328.10i −0.742693 + 1.00028i
\(306\) 1138.46i 0.212684i
\(307\) 3940.94 + 3940.94i 0.732643 + 0.732643i 0.971143 0.238499i \(-0.0766555\pi\)
−0.238499 + 0.971143i \(0.576656\pi\)
\(308\) −2487.45 + 2487.45i −0.460180 + 0.460180i
\(309\) 2082.48 0.383392
\(310\) −229.812 1555.03i −0.0421047 0.284902i
\(311\) −4767.23 −0.869212 −0.434606 0.900621i \(-0.643112\pi\)
−0.434606 + 0.900621i \(0.643112\pi\)
\(312\) −360.001 360.001i −0.0653239 0.0653239i
\(313\) −5442.79 5442.79i −0.982890 0.982890i 0.0169662 0.999856i \(-0.494599\pi\)
−0.999856 + 0.0169662i \(0.994599\pi\)
\(314\) −1211.04 −0.217652
\(315\) 362.204 + 2450.86i 0.0647869 + 0.438381i
\(316\) 6235.31i 1.11001i
\(317\) 3242.64 + 3242.64i 0.574527 + 0.574527i 0.933390 0.358863i \(-0.116836\pi\)
−0.358863 + 0.933390i \(0.616836\pi\)
\(318\) −91.8697 91.8697i −0.0162006 0.0162006i
\(319\) −1691.75 −0.296927
\(320\) 2671.73 3598.36i 0.466732 0.628608i
\(321\) 1471.15i 0.255800i
\(322\) 392.826 358.558i 0.0679855 0.0620549i
\(323\) 6565.86 6565.86i 1.13107 1.13107i
\(324\) 4465.41i 0.765673i
\(325\) 4760.69 + 2551.23i 0.812541 + 0.435436i
\(326\) 1363.02 0.231567
\(327\) −830.578 + 830.578i −0.140462 + 0.140462i
\(328\) −132.713 + 132.713i −0.0223410 + 0.0223410i
\(329\) 3804.85 0.637594
\(330\) 258.921 348.723i 0.0431913 0.0581714i
\(331\) −2475.20 −0.411026 −0.205513 0.978654i \(-0.565886\pi\)
−0.205513 + 0.978654i \(0.565886\pi\)
\(332\) 4102.74 4102.74i 0.678213 0.678213i
\(333\) 1206.45 + 1206.45i 0.198537 + 0.198537i
\(334\) 1861.15i 0.304904i
\(335\) −5598.64 + 827.404i −0.913093 + 0.134943i
\(336\) 689.663i 0.111977i
\(337\) 6425.97 6425.97i 1.03871 1.03871i 0.0394895 0.999220i \(-0.487427\pi\)
0.999220 0.0394895i \(-0.0125732\pi\)
\(338\) 127.491 127.491i 0.0205166 0.0205166i
\(339\) −891.960 −0.142904
\(340\) −1044.20 7065.61i −0.166558 1.12702i
\(341\) 13318.9i 2.11513i
\(342\) −1086.35 + 1086.35i −0.171763 + 0.171763i
\(343\) −3794.26 3794.26i −0.597291 0.597291i
\(344\) 1213.48 0.190194
\(345\) 1070.42 1312.25i 0.167041 0.204780i
\(346\) −804.577 −0.125013
\(347\) −3564.70 3564.70i −0.551479 0.551479i 0.375389 0.926868i \(-0.377509\pi\)
−0.926868 + 0.375389i \(0.877509\pi\)
\(348\) −244.369 + 244.369i −0.0376423 + 0.0376423i
\(349\) 3210.57i 0.492430i −0.969215 0.246215i \(-0.920813\pi\)
0.969215 0.246215i \(-0.0791869\pi\)
\(350\) 174.341 + 576.956i 0.0266254 + 0.0881132i
\(351\) −3092.18 −0.470223
\(352\) −3651.49 + 3651.49i −0.552912 + 0.552912i
\(353\) −1265.66 + 1265.66i −0.190834 + 0.190834i −0.796056 0.605222i \(-0.793084\pi\)
0.605222 + 0.796056i \(0.293084\pi\)
\(354\) 479.403i 0.0719774i
\(355\) −2439.54 1811.32i −0.364724 0.270802i
\(356\) 7753.88i 1.15437i
\(357\) 710.661 + 710.661i 0.105356 + 0.105356i
\(358\) −180.268 + 180.268i −0.0266130 + 0.0266130i
\(359\) 1759.85 0.258722 0.129361 0.991598i \(-0.458707\pi\)
0.129361 + 0.991598i \(0.458707\pi\)
\(360\) 352.236 + 2383.41i 0.0515679 + 0.348935i
\(361\) 5671.68 0.826896
\(362\) −133.911 + 133.911i −0.0194426 + 0.0194426i
\(363\) 1309.88 1309.88i 0.189397 0.189397i
\(364\) 2936.16 0.422793
\(365\) −744.730 + 110.061i −0.106797 + 0.0157832i
\(366\) 445.414i 0.0636125i
\(367\) −1522.15 + 1522.15i −0.216500 + 0.216500i −0.807022 0.590522i \(-0.798922\pi\)
0.590522 + 0.807022i \(0.298922\pi\)
\(368\) −4637.38 + 4232.84i −0.656902 + 0.599598i
\(369\) 549.337i 0.0774996i
\(370\) 333.262 + 247.442i 0.0468256 + 0.0347672i
\(371\) 1527.63 0.213775
\(372\) −1923.88 1923.88i −0.268142 0.268142i
\(373\) 3566.57 + 3566.57i 0.495094 + 0.495094i 0.909907 0.414813i \(-0.136153\pi\)
−0.414813 + 0.909907i \(0.636153\pi\)
\(374\) 2346.73i 0.324456i
\(375\) 817.711 + 1736.14i 0.112604 + 0.239077i
\(376\) 3700.14 0.507500
\(377\) 998.463 + 998.463i 0.136402 + 0.136402i
\(378\) −243.992 243.992i −0.0332000 0.0332000i
\(379\) −2565.25 −0.347673 −0.173837 0.984775i \(-0.555616\pi\)
−0.173837 + 0.984775i \(0.555616\pi\)
\(380\) 5745.81 7738.63i 0.775668 1.04469i
\(381\) 920.149 0.123729
\(382\) 1692.59 1692.59i 0.226703 0.226703i
\(383\) −5086.52 5086.52i −0.678613 0.678613i 0.281073 0.959686i \(-0.409310\pi\)
−0.959686 + 0.281073i \(0.909310\pi\)
\(384\) 1396.61i 0.185601i
\(385\) 746.621 + 5052.02i 0.0988346 + 0.668765i
\(386\) −2450.35 −0.323108
\(387\) 2511.48 2511.48i 0.329885 0.329885i
\(388\) 9958.28 + 9958.28i 1.30298 + 1.30298i
\(389\) −8327.11 −1.08535 −0.542675 0.839943i \(-0.682588\pi\)
−0.542675 + 0.839943i \(0.682588\pi\)
\(390\) −358.629 + 53.0005i −0.0465638 + 0.00688151i
\(391\) −416.853 + 9140.28i −0.0539161 + 1.18221i
\(392\) −1608.74 1608.74i −0.207280 0.207280i
\(393\) 40.6865 40.6865i 0.00522230 0.00522230i
\(394\) 1440.39i 0.184178i
\(395\) 7267.76 + 5396.19i 0.925773 + 0.687372i
\(396\) 10012.9i 1.27062i
\(397\) −7961.32 7961.32i −1.00647 1.00647i −0.999979 0.00648754i \(-0.997935\pi\)
−0.00648754 0.999979i \(-0.502065\pi\)
\(398\) −408.664 408.664i −0.0514685 0.0514685i
\(399\) 1356.27i 0.170171i
\(400\) −2058.12 6811.06i −0.257265 0.851383i
\(401\) 13932.5i 1.73505i −0.497396 0.867524i \(-0.665710\pi\)
0.497396 0.867524i \(-0.334290\pi\)
\(402\) 268.599 268.599i 0.0333247 0.0333247i
\(403\) −7860.78 + 7860.78i −0.971646 + 0.971646i
\(404\) 9630.63i 1.18599i
\(405\) 5204.79 + 3864.47i 0.638588 + 0.474141i
\(406\) 157.570i 0.0192612i
\(407\) 2486.89 + 2486.89i 0.302876 + 0.302876i
\(408\) 691.103 + 691.103i 0.0838595 + 0.0838595i
\(409\) 12233.1i 1.47894i 0.673187 + 0.739472i \(0.264925\pi\)
−0.673187 + 0.739472i \(0.735075\pi\)
\(410\) 19.5384 + 132.207i 0.00235350 + 0.0159250i
\(411\) 3360.39i 0.403299i
\(412\) −8258.60 + 8258.60i −0.987554 + 0.987554i
\(413\) −3985.81 3985.81i −0.474888 0.474888i
\(414\) 68.9702 1512.30i 0.00818769 0.179530i
\(415\) −1231.46 8332.68i −0.145662 0.985627i
\(416\) 4310.18 0.507991
\(417\) −134.441 134.441i −0.0157881 0.0157881i
\(418\) −2239.32 + 2239.32i −0.262031 + 0.262031i
\(419\) −4081.51 −0.475883 −0.237941 0.971280i \(-0.576473\pi\)
−0.237941 + 0.971280i \(0.576473\pi\)
\(420\) 837.597 + 621.903i 0.0973109 + 0.0722518i
\(421\) 8932.02i 1.03401i 0.855981 + 0.517007i \(0.172954\pi\)
−0.855981 + 0.517007i \(0.827046\pi\)
\(422\) −1324.94 1324.94i −0.152837 0.152837i
\(423\) 7657.97 7657.97i 0.880244 0.880244i
\(424\) 1485.59 0.170157
\(425\) −9139.22 4897.65i −1.04310 0.558991i
\(426\) 203.938 0.0231945
\(427\) 3703.22 + 3703.22i 0.419699 + 0.419699i
\(428\) 5834.22 + 5834.22i 0.658897 + 0.658897i
\(429\) −3071.68 −0.345693
\(430\) 515.102 693.755i 0.0577685 0.0778043i
\(431\) 9810.46i 1.09641i 0.836344 + 0.548206i \(0.184689\pi\)
−0.836344 + 0.548206i \(0.815311\pi\)
\(432\) 2880.37 + 2880.37i 0.320791 + 0.320791i
\(433\) −7316.01 7316.01i −0.811975 0.811975i 0.172955 0.984930i \(-0.444668\pi\)
−0.984930 + 0.172955i \(0.944668\pi\)
\(434\) −1240.53 −0.137206
\(435\) 73.3486 + 496.314i 0.00808459 + 0.0547044i
\(436\) 6587.74i 0.723613i
\(437\) −9119.71 + 8324.16i −0.998295 + 0.911210i
\(438\) 35.7291 35.7291i 0.00389772 0.00389772i
\(439\) 7271.64i 0.790561i 0.918560 + 0.395280i \(0.129353\pi\)
−0.918560 + 0.395280i \(0.870647\pi\)
\(440\) 726.073 + 4912.98i 0.0786686 + 0.532312i
\(441\) −6659.06 −0.719043
\(442\) 1385.03 1385.03i 0.149048 0.149048i
\(443\) 6138.23 6138.23i 0.658320 0.658320i −0.296662 0.954982i \(-0.595874\pi\)
0.954982 + 0.296662i \(0.0958735\pi\)
\(444\) 718.448 0.0767928
\(445\) −9037.77 6710.40i −0.962767 0.714839i
\(446\) 1010.52 0.107286
\(447\) −374.614 + 374.614i −0.0396390 + 0.0396390i
\(448\) −2500.99 2500.99i −0.263752 0.263752i
\(449\) 4296.08i 0.451547i −0.974180 0.225774i \(-0.927509\pi\)
0.974180 0.225774i \(-0.0724910\pi\)
\(450\) 1512.12 + 810.338i 0.158405 + 0.0848882i
\(451\) 1132.36i 0.118228i
\(452\) 3537.29 3537.29i 0.368098 0.368098i
\(453\) 1090.07 1090.07i 0.113059 0.113059i
\(454\) 2527.27 0.261257
\(455\) 2541.03 3422.33i 0.261813 0.352618i
\(456\) 1318.94i 0.135450i
\(457\) −3875.44 + 3875.44i −0.396685 + 0.396685i −0.877062 0.480377i \(-0.840500\pi\)
0.480377 + 0.877062i \(0.340500\pi\)
\(458\) 446.775 + 446.775i 0.0455817 + 0.0455817i
\(459\) 5936.13 0.603649
\(460\) 959.046 + 9449.06i 0.0972081 + 0.957749i
\(461\) −15797.0 −1.59597 −0.797984 0.602679i \(-0.794100\pi\)
−0.797984 + 0.602679i \(0.794100\pi\)
\(462\) −242.375 242.375i −0.0244076 0.0244076i
\(463\) −3100.33 + 3100.33i −0.311198 + 0.311198i −0.845373 0.534176i \(-0.820622\pi\)
0.534176 + 0.845373i \(0.320622\pi\)
\(464\) 1860.14i 0.186109i
\(465\) −3907.42 + 577.464i −0.389682 + 0.0575898i
\(466\) 3486.41 0.346577
\(467\) −8385.31 + 8385.31i −0.830891 + 0.830891i −0.987639 0.156748i \(-0.949899\pi\)
0.156748 + 0.987639i \(0.449899\pi\)
\(468\) 5909.56 5909.56i 0.583696 0.583696i
\(469\) 4466.33i 0.439736i
\(470\) 1570.64 2115.39i 0.154145 0.207608i
\(471\) 3043.05i 0.297699i
\(472\) −3876.12 3876.12i −0.377993 0.377993i
\(473\) 5176.98 5176.98i 0.503251 0.503251i
\(474\) −607.564 −0.0588741
\(475\) −4047.43 13394.4i −0.390966 1.29385i
\(476\) −5636.61 −0.542760
\(477\) 3074.63 3074.63i 0.295132 0.295132i
\(478\) 679.450 679.450i 0.0650153 0.0650153i
\(479\) −2280.88 −0.217570 −0.108785 0.994065i \(-0.534696\pi\)
−0.108785 + 0.994065i \(0.534696\pi\)
\(480\) 1229.56 + 912.932i 0.116920 + 0.0868114i
\(481\) 2935.50i 0.278269i
\(482\) −2244.91 + 2244.91i −0.212143 + 0.212143i
\(483\) −900.973 987.080i −0.0848772 0.0929890i
\(484\) 10389.3i 0.975708i
\(485\) 20225.3 2989.03i 1.89358 0.279845i
\(486\) −1491.01 −0.139163
\(487\) −7915.08 7915.08i −0.736482 0.736482i 0.235414 0.971895i \(-0.424356\pi\)
−0.971895 + 0.235414i \(0.924356\pi\)
\(488\) 3601.30 + 3601.30i 0.334064 + 0.334064i
\(489\) 3424.95i 0.316731i
\(490\) −1602.61 + 236.845i −0.147752 + 0.0218358i
\(491\) −12689.1 −1.16630 −0.583150 0.812365i \(-0.698180\pi\)
−0.583150 + 0.812365i \(0.698180\pi\)
\(492\) 163.567 + 163.567i 0.0149881 + 0.0149881i
\(493\) −1916.77 1916.77i −0.175106 0.175106i
\(494\) 2643.28 0.240742
\(495\) 11670.8 + 8665.40i 1.05973 + 0.786830i
\(496\) 14644.6 1.32573
\(497\) −1695.57 + 1695.57i −0.153031 + 0.153031i
\(498\) 399.768 + 399.768i 0.0359719 + 0.0359719i
\(499\) 7978.19i 0.715737i 0.933772 + 0.357868i \(0.116496\pi\)
−0.933772 + 0.357868i \(0.883504\pi\)
\(500\) −10128.0 3642.27i −0.905872 0.325775i
\(501\) −4676.64 −0.417040
\(502\) 517.024 517.024i 0.0459680 0.0459680i
\(503\) −3539.76 3539.76i −0.313778 0.313778i 0.532594 0.846371i \(-0.321217\pi\)
−0.846371 + 0.532594i \(0.821217\pi\)
\(504\) 1901.37 0.168043
\(505\) 11225.3 + 8334.58i 0.989144 + 0.734424i
\(506\) 142.170 3117.35i 0.0124906 0.273879i
\(507\) −320.356 320.356i −0.0280621 0.0280621i
\(508\) −3649.09 + 3649.09i −0.318705 + 0.318705i
\(509\) 10375.1i 0.903470i 0.892152 + 0.451735i \(0.149195\pi\)
−0.892152 + 0.451735i \(0.850805\pi\)
\(510\) 688.468 101.746i 0.0597762 0.00883413i
\(511\) 594.110i 0.0514323i
\(512\) −6777.84 6777.84i −0.585041 0.585041i
\(513\) 5664.43 + 5664.43i 0.487507 + 0.487507i
\(514\) 450.217i 0.0386347i
\(515\) 2478.87 + 16773.3i 0.212101 + 1.43518i
\(516\) 1495.60i 0.127597i
\(517\) 15785.6 15785.6i 1.34284 1.34284i
\(518\) 231.629 231.629i 0.0196471 0.0196471i
\(519\) 2021.71i 0.170989i
\(520\) 2471.09 3328.14i 0.208393 0.280671i
\(521\) 2875.97i 0.241840i −0.992662 0.120920i \(-0.961416\pi\)
0.992662 0.120920i \(-0.0385844\pi\)
\(522\) 317.138 + 317.138i 0.0265915 + 0.0265915i
\(523\) 8691.88 + 8691.88i 0.726710 + 0.726710i 0.969963 0.243253i \(-0.0782144\pi\)
−0.243253 + 0.969963i \(0.578214\pi\)
\(524\) 322.705i 0.0269035i
\(525\) 1449.76 438.077i 0.120519 0.0364176i
\(526\) 3065.66i 0.254123i
\(527\) 15090.5 15090.5i 1.24735 1.24735i
\(528\) 2861.28 + 2861.28i 0.235835 + 0.235835i
\(529\) 1107.48 12116.5i 0.0910231 0.995849i
\(530\) 630.605 849.318i 0.0516825 0.0696076i
\(531\) −16044.4 −1.31124
\(532\) −5378.63 5378.63i −0.438333 0.438333i
\(533\) 668.316 668.316i 0.0543114 0.0543114i
\(534\) 755.532 0.0612267
\(535\) 11849.3 1751.17i 0.957554 0.141514i
\(536\) 4343.41i 0.350013i
\(537\) 452.971 + 452.971i 0.0364007 + 0.0364007i
\(538\) −1852.98 + 1852.98i −0.148490 + 0.148490i
\(539\) −13726.5 −1.09692
\(540\) 6095.58 900.845i 0.485763 0.0717893i
\(541\) 4987.76 0.396378 0.198189 0.980164i \(-0.436494\pi\)
0.198189 + 0.980164i \(0.436494\pi\)
\(542\) 1079.44 + 1079.44i 0.0855462 + 0.0855462i
\(543\) 336.487 + 336.487i 0.0265931 + 0.0265931i
\(544\) −8274.36 −0.652133
\(545\) −7678.54 5701.19i −0.603509 0.448096i
\(546\) 286.097i 0.0224246i
\(547\) −3822.68 3822.68i −0.298804 0.298804i 0.541741 0.840545i \(-0.317765\pi\)
−0.840545 + 0.541741i \(0.817765\pi\)
\(548\) −13326.5 13326.5i −1.03883 1.03883i
\(549\) 14906.8 1.15885
\(550\) 3116.98 + 1670.37i 0.241652 + 0.129500i
\(551\) 3658.09i 0.282831i
\(552\) −876.177 959.914i −0.0675590 0.0740157i
\(553\) 5051.35 5051.35i 0.388437 0.388437i
\(554\) 2583.76i 0.198147i
\(555\) 621.762 837.408i 0.0475538 0.0640469i
\(556\) 1066.32 0.0813349
\(557\) −9922.42 + 9922.42i −0.754805 + 0.754805i −0.975372 0.220567i \(-0.929209\pi\)
0.220567 + 0.975372i \(0.429209\pi\)
\(558\) −2496.79 + 2496.79i −0.189422 + 0.189422i
\(559\) −6110.86 −0.462365
\(560\) −5554.87 + 820.936i −0.419172 + 0.0619480i
\(561\) 5896.78 0.443783
\(562\) 1852.69 1852.69i 0.139059 0.139059i
\(563\) −2571.21 2571.21i −0.192475 0.192475i 0.604289 0.796765i \(-0.293457\pi\)
−0.796765 + 0.604289i \(0.793457\pi\)
\(564\) 4560.37i 0.340472i
\(565\) −1061.74 7184.26i −0.0790578 0.534946i
\(566\) 4687.00i 0.348073i
\(567\) 3617.52 3617.52i 0.267939 0.267939i
\(568\) −1648.90 + 1648.90i −0.121807 + 0.121807i
\(569\) −3251.32 −0.239548 −0.119774 0.992801i \(-0.538217\pi\)
−0.119774 + 0.992801i \(0.538217\pi\)
\(570\) 754.047 + 559.868i 0.0554097 + 0.0411408i
\(571\) 24103.2i 1.76653i −0.468874 0.883265i \(-0.655340\pi\)
0.468874 0.883265i \(-0.344660\pi\)
\(572\) 12181.5 12181.5i 0.890447 0.890447i
\(573\) −4253.09 4253.09i −0.310079 0.310079i
\(574\) 105.469 0.00766929
\(575\) 11843.6 + 7059.61i 0.858979 + 0.512010i
\(576\) −10067.4 −0.728257
\(577\) 7645.52 + 7645.52i 0.551625 + 0.551625i 0.926909 0.375285i \(-0.122455\pi\)
−0.375285 + 0.926909i \(0.622455\pi\)
\(578\) −760.392 + 760.392i −0.0547200 + 0.0547200i
\(579\) 6157.16i 0.441939i
\(580\) −2259.14 1677.38i −0.161734 0.120085i
\(581\) −6647.42 −0.474667
\(582\) −970.327 + 970.327i −0.0691088 + 0.0691088i
\(583\) 6337.83 6337.83i 0.450233 0.450233i
\(584\) 577.760i 0.0409381i
\(585\) −1773.79 12002.4i −0.125363 0.848267i
\(586\) 2171.58i 0.153084i
\(587\) −2779.52 2779.52i −0.195440 0.195440i 0.602602 0.798042i \(-0.294131\pi\)
−0.798042 + 0.602602i \(0.794131\pi\)
\(588\) −1982.75 + 1982.75i −0.139060 + 0.139060i
\(589\) 28799.7 2.01472
\(590\) −3861.34 + 570.655i −0.269439 + 0.0398194i
\(591\) −3619.37 −0.251914
\(592\) −2734.42 + 2734.42i −0.189838 + 0.189838i
\(593\) 15522.3 15522.3i 1.07491 1.07491i 0.0779566 0.996957i \(-0.475160\pi\)
0.996957 0.0779566i \(-0.0248396\pi\)
\(594\) −2024.55 −0.139846
\(595\) −4878.07 + 6569.93i −0.336103 + 0.452673i
\(596\) 2971.25i 0.204207i
\(597\) −1026.88 + 1026.88i −0.0703974 + 0.0703974i
\(598\) −1923.75 + 1755.93i −0.131552 + 0.120076i
\(599\) 10261.7i 0.699966i 0.936756 + 0.349983i \(0.113813\pi\)
−0.936756 + 0.349983i \(0.886187\pi\)
\(600\) 1409.86 426.021i 0.0959286 0.0289870i
\(601\) 24999.8 1.69677 0.848387 0.529376i \(-0.177574\pi\)
0.848387 + 0.529376i \(0.177574\pi\)
\(602\) −482.185 482.185i −0.0326452 0.0326452i
\(603\) 8989.31 + 8989.31i 0.607086 + 0.607086i
\(604\) 8645.87i 0.582443i
\(605\) 12109.6 + 8991.19i 0.813761 + 0.604205i
\(606\) −938.401 −0.0629042
\(607\) −13449.5 13449.5i −0.899341 0.899341i 0.0960364 0.995378i \(-0.469383\pi\)
−0.995378 + 0.0960364i \(0.969383\pi\)
\(608\) −7895.65 7895.65i −0.526662 0.526662i
\(609\) 395.936 0.0263451
\(610\) 3587.57 530.195i 0.238125 0.0351918i
\(611\) −18633.2 −1.23374
\(612\) −11344.7 + 11344.7i −0.749319 + 0.749319i
\(613\) 15051.6 + 15051.6i 0.991728 + 0.991728i 0.999966 0.00823799i \(-0.00262226\pi\)
−0.00823799 + 0.999966i \(0.502622\pi\)
\(614\) 3045.72i 0.200188i
\(615\) 332.205 49.0955i 0.0217818 0.00321906i
\(616\) 3919.34 0.256355
\(617\) −13536.8 + 13536.8i −0.883261 + 0.883261i −0.993865 0.110603i \(-0.964722\pi\)
0.110603 + 0.993865i \(0.464722\pi\)
\(618\) −804.712 804.712i −0.0523791 0.0523791i
\(619\) 23973.2 1.55665 0.778324 0.627862i \(-0.216070\pi\)
0.778324 + 0.627862i \(0.216070\pi\)
\(620\) 13205.8 17785.9i 0.855414 1.15210i
\(621\) −7885.42 359.624i −0.509551 0.0232387i
\(622\) 1842.16 + 1842.16i 0.118752 + 0.118752i
\(623\) −6281.57 + 6281.57i −0.403958 + 0.403958i
\(624\) 3377.42i 0.216675i
\(625\) −13010.3 + 8652.83i −0.832662 + 0.553781i
\(626\) 4206.41i 0.268565i
\(627\) 5626.89 + 5626.89i 0.358399 + 0.358399i
\(628\) −12068.0 12068.0i −0.766824 0.766824i
\(629\) 5635.34i 0.357227i
\(630\) 807.097 1087.02i 0.0510405 0.0687429i
\(631\) 8077.48i 0.509603i 0.966993 + 0.254802i \(0.0820101\pi\)
−0.966993 + 0.254802i \(0.917990\pi\)
\(632\) 4912.33 4912.33i 0.309181 0.309181i
\(633\) −3329.27 + 3329.27i −0.209047 + 0.209047i
\(634\) 2506.05i 0.156984i
\(635\) 1095.29 + 7411.31i 0.0684494 + 0.463164i
\(636\) 1830.96i 0.114155i
\(637\) 8101.31 + 8101.31i 0.503902 + 0.503902i
\(638\) 653.726 + 653.726i 0.0405662 + 0.0405662i
\(639\) 6825.27i 0.422541i
\(640\) −11249.0 + 1662.45i −0.694774 + 0.102678i
\(641\) 18284.9i 1.12669i 0.826220 + 0.563347i \(0.190487\pi\)
−0.826220 + 0.563347i \(0.809513\pi\)
\(642\) −568.482 + 568.482i −0.0349474 + 0.0349474i
\(643\) 1817.65 + 1817.65i 0.111479 + 0.111479i 0.760646 0.649167i \(-0.224882\pi\)
−0.649167 + 0.760646i \(0.724882\pi\)
\(644\) 7487.55 + 341.479i 0.458154 + 0.0208946i
\(645\) −1743.24 1294.33i −0.106419 0.0790143i
\(646\) −5074.36 −0.309053
\(647\) −17679.2 17679.2i −1.07425 1.07425i −0.997013 0.0772374i \(-0.975390\pi\)
−0.0772374 0.997013i \(-0.524610\pi\)
\(648\) 3517.96 3517.96i 0.213269 0.213269i
\(649\) −33072.7 −2.00033
\(650\) −853.782 2825.47i −0.0515202 0.170499i
\(651\) 3117.16i 0.187667i
\(652\) 13582.5 + 13582.5i 0.815847 + 0.815847i
\(653\) −4909.45 + 4909.45i −0.294214 + 0.294214i −0.838742 0.544529i \(-0.816709\pi\)
0.544529 + 0.838742i \(0.316709\pi\)
\(654\) 641.904 0.0383799
\(655\) 376.139 + 279.277i 0.0224381 + 0.0166599i
\(656\) −1245.07 −0.0741036
\(657\) 1195.76 + 1195.76i 0.0710060 + 0.0710060i
\(658\) −1470.27 1470.27i −0.0871082 0.0871082i
\(659\) 14011.8 0.828258 0.414129 0.910218i \(-0.364086\pi\)
0.414129 + 0.910218i \(0.364086\pi\)
\(660\) 6055.18 894.874i 0.357117 0.0527772i
\(661\) 11979.9i 0.704936i 0.935824 + 0.352468i \(0.114657\pi\)
−0.935824 + 0.352468i \(0.885343\pi\)
\(662\) 956.468 + 956.468i 0.0561544 + 0.0561544i
\(663\) −3480.25 3480.25i −0.203864 0.203864i
\(664\) −6464.47 −0.377817
\(665\) −10924.0 + 1614.43i −0.637016 + 0.0941424i
\(666\) 932.392i 0.0542484i
\(667\) 2430.08 + 2662.32i 0.141069 + 0.154551i
\(668\) 18546.4 18546.4i 1.07423 1.07423i
\(669\) 2539.19i 0.146743i
\(670\) 2483.15 + 1843.70i 0.143183 + 0.106311i
\(671\) 30727.8 1.76786
\(672\) 854.592 854.592i 0.0490574 0.0490574i
\(673\) −10297.1 + 10297.1i −0.589785 + 0.589785i −0.937573 0.347788i \(-0.886933\pi\)
0.347788 + 0.937573i \(0.386933\pi\)
\(674\) −4966.25 −0.283817
\(675\) 4225.26 7884.50i 0.240934 0.449592i
\(676\) 2540.90 0.144567
\(677\) −2798.58 + 2798.58i −0.158875 + 0.158875i −0.782068 0.623193i \(-0.785835\pi\)
0.623193 + 0.782068i \(0.285835\pi\)
\(678\) 344.671 + 344.671i 0.0195236 + 0.0195236i
\(679\) 16134.8i 0.911925i
\(680\) −4743.81 + 6389.11i −0.267525 + 0.360311i
\(681\) 6350.43i 0.357341i
\(682\) −5146.71 + 5146.71i −0.288970 + 0.288970i
\(683\) 811.737 811.737i 0.0454762 0.0454762i −0.684003 0.729479i \(-0.739762\pi\)
0.729479 + 0.684003i \(0.239762\pi\)
\(684\) −21651.0 −1.21030
\(685\) −27066.2 + 4000.02i −1.50970 + 0.223114i
\(686\) 2932.36i 0.163204i
\(687\) 1122.64 1122.64i 0.0623456 0.0623456i
\(688\) 5692.27 + 5692.27i 0.315430 + 0.315430i
\(689\) −7481.11 −0.413654
\(690\) −920.709 + 93.4487i −0.0507983 + 0.00515584i
\(691\) 4983.51 0.274359 0.137179 0.990546i \(-0.456196\pi\)
0.137179 + 0.990546i \(0.456196\pi\)
\(692\) −8017.62 8017.62i −0.440439 0.440439i
\(693\) 8111.65 8111.65i 0.444641 0.444641i
\(694\) 2754.94i 0.150686i
\(695\) 922.823 1242.89i 0.0503664 0.0678350i
\(696\) 385.039 0.0209697
\(697\) −1282.98 + 1282.98i −0.0697222 + 0.0697222i
\(698\) −1240.63 + 1240.63i −0.0672759 + 0.0672759i
\(699\) 8760.52i 0.474039i
\(700\) −4012.07 + 7486.68i −0.216631 + 0.404243i
\(701\) 27865.7i 1.50139i 0.660651 + 0.750693i \(0.270280\pi\)
−0.660651 + 0.750693i \(0.729720\pi\)
\(702\) 1194.88 + 1194.88i 0.0642419 + 0.0642419i
\(703\) −5377.42 + 5377.42i −0.288497 + 0.288497i
\(704\) −20752.2 −1.11098
\(705\) −5315.48 3946.66i −0.283961 0.210836i
\(706\) 978.155 0.0521436
\(707\) 7801.97 7801.97i 0.415026 0.415026i
\(708\) −4777.26 + 4777.26i −0.253588 + 0.253588i
\(709\) −4668.78 −0.247306 −0.123653 0.992326i \(-0.539461\pi\)
−0.123653 + 0.992326i \(0.539461\pi\)
\(710\) 242.757 + 1642.61i 0.0128317 + 0.0868257i
\(711\) 20333.6i 1.07253i
\(712\) −6108.70 + 6108.70i −0.321535 + 0.321535i
\(713\) −20960.1 + 19131.7i −1.10093 + 1.00489i
\(714\) 549.227i 0.0287876i
\(715\) −3656.36 24740.8i −0.191245 1.29406i
\(716\) −3592.75 −0.187524
\(717\) −1707.30 1707.30i −0.0889264 0.0889264i
\(718\) −680.041 680.041i −0.0353467 0.0353467i
\(719\) 7376.13i 0.382591i −0.981532 0.191296i \(-0.938731\pi\)
0.981532 0.191296i \(-0.0612689\pi\)
\(720\) −9527.91 + 12832.5i −0.493173 + 0.664220i
\(721\) 13380.9 0.691167
\(722\) −2191.65 2191.65i −0.112971 0.112971i
\(723\) 5640.92 + 5640.92i 0.290163 + 0.290163i
\(724\) −2668.85 −0.136999
\(725\) −3910.23 + 1181.57i −0.200307 + 0.0605273i
\(726\) −1012.33 −0.0517508
\(727\) 5200.64 5200.64i 0.265311 0.265311i −0.561896 0.827208i \(-0.689928\pi\)
0.827208 + 0.561896i \(0.189928\pi\)
\(728\) −2313.18 2313.18i −0.117764 0.117764i
\(729\) 11908.6i 0.605020i
\(730\) 330.308 + 245.249i 0.0167469 + 0.0124343i
\(731\) 11731.2 0.593560
\(732\) 4438.55 4438.55i 0.224117 0.224117i
\(733\) −5286.39 5286.39i −0.266381 0.266381i 0.561259 0.827640i \(-0.310317\pi\)
−0.827640 + 0.561259i \(0.810317\pi\)
\(734\) 1176.38 0.0591564
\(735\) 595.135 + 4026.98i 0.0298665 + 0.202092i
\(736\) 10991.5 + 501.279i 0.550477 + 0.0251052i
\(737\) 18529.9 + 18529.9i 0.926131 + 0.926131i
\(738\) 212.275 212.275i 0.0105880 0.0105880i
\(739\) 15596.2i 0.776338i 0.921588 + 0.388169i \(0.126892\pi\)
−0.921588 + 0.388169i \(0.873108\pi\)
\(740\) 855.199 + 5786.71i 0.0424834 + 0.287465i
\(741\) 6641.93i 0.329281i
\(742\) −590.307 590.307i −0.0292060 0.0292060i
\(743\) 9406.80 + 9406.80i 0.464471 + 0.464471i 0.900118 0.435647i \(-0.143480\pi\)
−0.435647 + 0.900118i \(0.643480\pi\)
\(744\) 3031.37i 0.149375i
\(745\) −3463.23 2571.39i −0.170313 0.126455i
\(746\) 2756.39i 0.135280i
\(747\) −13379.2 + 13379.2i −0.655312 + 0.655312i
\(748\) −23385.2 + 23385.2i −1.14311 + 1.14311i
\(749\) 9452.85i 0.461148i
\(750\) 354.900 986.860i 0.0172788 0.0480467i
\(751\) 10407.4i 0.505687i −0.967507 0.252844i \(-0.918634\pi\)
0.967507 0.252844i \(-0.0813658\pi\)
\(752\) 17356.8 + 17356.8i 0.841672 + 0.841672i
\(753\) −1299.16 1299.16i −0.0628739 0.0628739i
\(754\) 771.652i 0.0372705i
\(755\) 10077.5 + 7482.35i 0.485770 + 0.360676i
\(756\) 4862.77i 0.233938i
\(757\) −11867.4 + 11867.4i −0.569788 + 0.569788i −0.932069 0.362281i \(-0.881998\pi\)
0.362281 + 0.932069i \(0.381998\pi\)
\(758\) 991.265 + 991.265i 0.0474991 + 0.0474991i
\(759\) −7833.15 357.240i −0.374605 0.0170843i
\(760\) −10623.4 + 1569.99i −0.507040 + 0.0749338i
\(761\) 12348.7 0.588227 0.294114 0.955770i \(-0.404976\pi\)
0.294114 + 0.955770i \(0.404976\pi\)
\(762\) −355.564 355.564i −0.0169038 0.0169038i
\(763\) −5336.86 + 5336.86i −0.253221 + 0.253221i
\(764\) 33733.4 1.59742
\(765\) 3405.18 + 23041.2i 0.160934 + 1.08896i
\(766\) 3931.06i 0.185424i
\(767\) 19519.3 + 19519.3i 0.918908 + 0.918908i
\(768\) −2574.17 + 2574.17i −0.120947 + 0.120947i
\(769\) −2448.86 −0.114835 −0.0574176 0.998350i \(-0.518287\pi\)
−0.0574176 + 0.998350i \(0.518287\pi\)
\(770\) 1663.69 2240.71i 0.0778640 0.104870i
\(771\) 1131.29 0.0528436
\(772\) −24417.8 24417.8i −1.13836