Properties

Label 115.4.e.a.22.16
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 22.16
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.16

$q$-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} +(74.3624 - 81.4693i) 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} +(-627.424 - 572.691i) 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 −0.518314 0.855190i \(-0.673440\pi\)
0.855190 + 0.518314i \(0.173440\pi\)
\(8\) −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 \(-0.748922\pi\)
0.704709 0.709497i \(-0.251078\pi\)
\(12\) 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 −0.151621 0.988439i \(-0.548449\pi\)
0.988439 + 0.151621i \(0.0484494\pi\)
\(18\) 9.70470 9.70470i 0.127079 0.127079i
\(19\) 111.941 1.35163 0.675814 0.737073i \(-0.263792\pi\)
0.675814 + 0.737073i \(0.263792\pi\)
\(20\) 51.3291 69.1316i 0.573877 0.772915i
\(21\) 12.1160i 0.125901i
\(22\) −20.0046 + 20.0046i −0.193863 + 0.193863i
\(23\) 74.3624 81.4693i 0.674158 0.738588i
\(24\) 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 −0.805729 0.592285i \(-0.798226\pi\)
0.592285 + 0.805729i \(0.298226\pi\)
\(38\) −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 0.861838 0.507184i \(-0.169314\pi\)
−0.507184 + 0.861838i \(0.669314\pi\)
\(44\) −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 0.847726 0.530435i \(-0.177971\pi\)
−0.530435 + 0.847726i \(0.677971\pi\)
\(54\) 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 \(0.214057\pi\)
−0.782279 + 0.622928i \(0.785943\pi\)
\(62\) 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 −0.953634 0.300967i \(-0.902690\pi\)
0.300967 + 0.953634i \(0.402690\pi\)
\(68\) −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 \(-0.304407\pi\)
0.576528 + 0.817078i \(0.304407\pi\)
\(80\) −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 0.260863 0.965376i \(-0.415993\pi\)
−0.965376 + 0.260863i \(0.915993\pi\)
\(84\) 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 \(-0.704660\pi\)
−0.599565 + 0.800326i \(0.704660\pi\)
\(90\) 151.796 22.4334i 0.177786 0.0262744i
\(91\) 381.252i 0.439188i
\(92\) −627.424 572.691i −0.711016 0.648991i
\(93\) 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 \(-0.343607\pi\)
0.881709 0.471794i \(-0.156393\pi\)
\(98\) 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 \(0.00833814\pi\)
0.0261920 + 0.999657i \(0.491662\pi\)
\(104\) 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 −0.276552 0.960999i \(-0.589192\pi\)
0.960999 + 0.276552i \(0.0891917\pi\)
\(108\) −389.705 + 389.705i −0.347217 + 0.347217i
\(109\) −855.400 −0.751674 −0.375837 0.926686i \(-0.622645\pi\)
−0.375837 + 0.926686i \(0.622645\pi\)
\(110\) −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 0.489584 0.871956i \(-0.337149\pi\)
−0.871956 + 0.489584i \(0.837149\pi\)
\(114\) 84.0018 0.0690131
\(115\) 1210.51 235.692i 0.981567 0.191116i
\(116\) 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 \(0.526298\pi\)
−0.996589 + 0.0825249i \(0.973702\pi\)
\(138\) 55.8026 61.1357i 0.0344220 0.0377117i
\(139\) 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 \(-0.533824\pi\)
−0.106063 + 0.994359i \(0.533824\pi\)
\(150\) 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 −0.982551 0.185992i \(-0.940450\pi\)
0.185992 + 0.982551i \(0.440450\pi\)
\(158\) −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 \(0.0226687\pi\)
−0.997465 + 0.0711557i \(0.977331\pi\)
\(182\) −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 \(-0.688521\pi\)
0.558234 0.829684i \(-0.311479\pi\)
\(192\) −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 \(-0.560318\pi\)
−0.188364 + 0.982099i \(0.560318\pi\)
\(200\) −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
\(207\) 2046.05 + 1867.57i 0.687006 + 0.627076i
\(208\) −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 −0.0429346 0.999078i \(-0.513671\pi\)
0.999078 + 0.0429346i \(0.0136707\pi\)
\(228\) 837.079 + 837.079i 0.243144 + 0.243144i
\(229\) 1156.19 0.333638 0.166819 0.985988i \(-0.446650\pi\)
0.166819 + 0.985988i \(0.446650\pi\)
\(230\) −558.840 376.688i −0.160212 0.107992i
\(231\) 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 \(0.282954\pi\)
−0.630246 + 0.776396i \(0.717046\pi\)
\(242\) 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 \(-0.946194\pi\)
0.985747 0.168233i \(-0.0538060\pi\)
\(252\) 1206.72 1206.72i 0.301652 0.301652i
\(253\) −4217.58 3849.66i −1.04805 0.956625i
\(254\) 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 0.997708 0.0676712i \(-0.0215569\pi\)
−0.0676712 + 0.997708i \(0.521557\pi\)
\(264\) −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 \(-0.830043\pi\)
0.860811 0.508925i \(-0.169957\pi\)
\(282\) −228.819 228.819i −0.0483191 0.0483191i
\(283\) −6064.64 6064.64i −1.27387 1.27387i −0.944040 0.329831i \(-0.893008\pi\)
−0.329831 0.944040i \(-0.606992\pi\)
\(284\) 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 0.369126 0.929379i \(-0.379657\pi\)
−0.929379 + 0.369126i \(0.879657\pi\)
\(294\) 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 0.999856 0.0169662i \(-0.00540077\pi\)
−0.0169662 + 0.999856i \(0.505401\pi\)
\(314\) 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
\(322\) −358.558 + 392.826i −0.0620549 + 0.0679855i
\(323\) 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 \(0.512573\pi\)
−0.999220 + 0.0394895i \(0.987427\pi\)
\(338\) 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
\(345\) −946.528 + 1404.23i −0.147708 + 0.219134i
\(346\) −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 \(-0.541293\pi\)
−0.129361 + 0.991598i \(0.541293\pi\)
\(360\) −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 −0.590522 0.807022i \(-0.701078\pi\)
0.807022 + 0.590522i \(0.201078\pi\)
\(368\) −4232.84 + 4637.38i −0.599598 + 0.656902i
\(369\) 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 0.414813 0.909907i \(-0.363847\pi\)
−0.909907 + 0.414813i \(0.863847\pi\)
\(374\) 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 \(-0.444384\pi\)
0.173837 + 0.984775i \(0.444384\pi\)
\(380\) 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 0.959686 0.281073i \(-0.0906904\pi\)
−0.281073 + 0.959686i \(0.590690\pi\)
\(384\) 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 \(-0.317412\pi\)
0.542675 + 0.839943i \(0.317412\pi\)
\(390\) 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 \(0.334290\pi\)
−0.497396 + 0.867524i \(0.665710\pi\)
\(402\) −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 \(-0.423527\pi\)
0.237941 + 0.971280i \(0.423527\pi\)
\(420\) 837.597 + 621.903i 0.0973109 + 0.0722518i
\(421\) 8932.02i 1.03401i −0.855981 0.517007i \(-0.827046\pi\)
0.855981 0.517007i \(-0.172954\pi\)
\(422\) −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 \(-0.815311\pi\)
0.836344 0.548206i \(-0.184689\pi\)
\(432\) 2880.37 + 2880.37i 0.320791 + 0.320791i
\(433\) 7316.01 + 7316.01i 0.811975 + 0.811975i 0.984930 0.172955i \(-0.0553315\pi\)
−0.172955 + 0.984930i \(0.555332\pi\)
\(434\) 1240.53 0.137206
\(435\) −73.3486 496.314i −0.00808459 0.0547044i
\(436\) 6587.74i 0.723613i
\(437\) 8324.16 9119.71i 0.911210 0.998295i
\(438\) 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 −0.480377 0.877062i \(-0.659500\pi\)
0.877062 + 0.480377i \(0.159500\pi\)
\(458\) −446.775 446.775i −0.0455817 0.0455817i
\(459\) −5936.13 −0.603649
\(460\) −1815.15 9322.54i −0.183982 0.944925i
\(461\) −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 −0.156748 0.987639i \(-0.550101\pi\)
0.987639 + 0.156748i \(0.0501011\pi\)
\(468\) 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 \(-0.465304\pi\)
0.108785 + 0.994065i \(0.465304\pi\)
\(480\) −1229.56 912.932i −0.116920 0.0868114i
\(481\) 2935.50i 0.278269i
\(482\) 2244.91 2244.91i 0.212143 0.212143i
\(483\) 987.080 + 900.973i 0.0929890 + 0.0848772i
\(484\) 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 0.846371 0.532594i \(-0.178783\pi\)
−0.532594 + 0.846371i \(0.678783\pi\)
\(504\) −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 \(0.0385844\pi\)
−0.992662 + 0.120920i \(0.961416\pi\)
\(522\) 317.138 + 317.138i 0.0265915 + 0.0265915i
\(523\) −8691.88 8691.88i −0.726710 0.726710i 0.243253 0.969963i \(-0.421786\pi\)
−0.969963 + 0.243253i \(0.921786\pi\)
\(524\) 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
\(552\) −959.914 876.177i −0.0740157 0.0675590i
\(553\) 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 −0.220567 0.975372i \(-0.570791\pi\)
0.975372 + 0.220567i \(0.0707908\pi\)
\(558\) −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 0.796765 0.604289i \(-0.206543\pi\)
−0.604289 + 0.796765i \(0.706543\pi\)
\(564\) 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 \(-0.461783\pi\)
0.119774 + 0.992801i \(0.461783\pi\)
\(570\) 754.047 + 559.868i 0.0554097 + 0.0411408i
\(571\) 24103.2i 1.76653i 0.468874 + 0.883265i \(0.344660\pi\)
−0.468874 + 0.883265i \(0.655340\pi\)
\(572\) −12181.5 + 12181.5i −0.890447 + 0.890447i
\(573\) 4253.09 + 4253.09i 0.310079 + 0.310079i
\(574\) −105.469 −0.00766929
\(575\) 12437.0 + 5952.26i 0.902018 + 0.431698i
\(576\) −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
\(598\) −1755.93 + 1923.75i −0.120076 + 0.131552i
\(599\) 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 0.00823799 0.999966i \(-0.497378\pi\)
−0.999966 + 0.00823799i \(0.997378\pi\)
\(614\) 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 −0.110603 0.993865i \(-0.535278\pi\)
0.993865 + 0.110603i \(0.0352783\pi\)
\(618\) 804.712 + 804.712i 0.0523791 + 0.0523791i
\(619\) −23973.2 −1.55665 −0.778324 0.627862i \(-0.783930\pi\)
−0.778324 + 0.627862i \(0.783930\pi\)
\(620\) −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 \(-0.917990\pi\)
0.966993 0.254802i \(-0.0820101\pi\)
\(632\) −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 \(-0.809513\pi\)
0.826220 0.563347i \(-0.190487\pi\)
\(642\) 568.482 568.482i 0.0349474 0.0349474i
\(643\) −1817.65 1817.65i −0.111479 0.111479i 0.649167 0.760646i \(-0.275118\pi\)
−0.760646 + 0.649167i \(0.775118\pi\)
\(644\) −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 \(-0.635914\pi\)
−0.414129 + 0.910218i \(0.635914\pi\)
\(660\) 6055.18 894.874i 0.357117 0.0527772i
\(661\) 11979.9i 0.704936i −0.935824 0.352468i \(-0.885343\pi\)
0.935824 0.352468i \(-0.114657\pi\)
\(662\) 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
\(667\) 2662.32 + 2430.08i 0.154551 + 0.141069i
\(668\) 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 −0.623193 0.782068i \(-0.714165\pi\)
0.782068 + 0.623193i \(0.214165\pi\)
\(678\) −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
\(690\) 908.381 176.867i 0.0501181 0.00975825i
\(691\) 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 \(-0.729720\pi\)
0.660651 0.750693i \(-0.270280\pi\)
\(702\) 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 \(-0.460539\pi\)
0.123653 + 0.992326i \(0.460539\pi\)
\(710\) −242.757 1642.61i −0.0128317 0.0868257i
\(711\) 20333.6i 1.07253i
\(712\) 6108.70 6108.70i 0.321535 0.321535i
\(713\) −19131.7 + 20960.1i −1.00489 + 1.10093i
\(714\) 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 −0.827208 0.561896i \(-0.810072\pi\)
0.561896 + 0.827208i \(0.310072\pi\)
\(728\) 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 0.827640 0.561259i \(-0.189683\pi\)
−0.561259 + 0.827640i \(0.689683\pi\)
\(734\) −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 0.435647 0.900118i \(-0.356520\pi\)
−0.900118 + 0.435647i \(0.856520\pi\)
\(744\) 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 \(0.0813658\pi\)
−0.967507 + 0.252844i \(0.918634\pi\)
\(752\) 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 −0.362281 0.932069i \(-0.618002\pi\)
0.932069 + 0.362281i \(0.118002\pi\)
\(758\) −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 \(-0.481713\pi\)
0.0574176 + 0.998350i \(0.481713\pi\)
\(770\) −1663.69 + 2240.71i −0.0778640 + 0.104870i
\(771\) 1131.29 0.0528436
\(772\) −24417.8 24417.8i