Properties

Label 225.4.e.d.151.5
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.5
Root \(-0.785104 - 1.35984i\) of defining polynomial
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.d.76.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.785104 - 1.35984i) q^{2} +(3.89934 + 3.43441i) q^{3} +(2.76722 + 4.79297i) q^{4} +(7.73164 - 2.60611i) q^{6} +(17.1199 - 29.6525i) q^{7} +21.2519 q^{8} +(3.40971 + 26.7838i) q^{9} +O(q^{10})\) \(q+(0.785104 - 1.35984i) q^{2} +(3.89934 + 3.43441i) q^{3} +(2.76722 + 4.79297i) q^{4} +(7.73164 - 2.60611i) q^{6} +(17.1199 - 29.6525i) q^{7} +21.2519 q^{8} +(3.40971 + 26.7838i) q^{9} +(13.4480 - 23.2926i) q^{11} +(-5.67066 + 28.1932i) q^{12} +(-9.74401 - 16.8771i) q^{13} +(-26.8818 - 46.5607i) q^{14} +(-5.45281 + 9.44454i) q^{16} -29.1232 q^{17} +(39.0987 + 16.3915i) q^{18} +47.1006 q^{19} +(168.595 - 56.8286i) q^{21} +(-21.1162 - 36.5743i) q^{22} +(56.6083 + 98.0485i) q^{23} +(82.8684 + 72.9877i) q^{24} -30.6003 q^{26} +(-78.6910 + 116.150i) q^{27} +189.498 q^{28} +(-40.6219 + 70.3593i) q^{29} +(5.41811 + 9.38445i) q^{31} +(93.5697 + 162.067i) q^{32} +(132.435 - 44.6399i) q^{33} +(-22.8648 + 39.6029i) q^{34} +(-118.939 + 90.4594i) q^{36} -410.002 q^{37} +(36.9789 - 64.0493i) q^{38} +(19.9677 - 99.2746i) q^{39} +(221.755 + 384.091i) q^{41} +(55.0869 - 273.879i) q^{42} +(169.748 - 294.012i) q^{43} +148.854 q^{44} +177.774 q^{46} +(118.121 - 204.591i) q^{47} +(-53.6988 + 18.1003i) q^{48} +(-414.681 - 718.249i) q^{49} +(-113.561 - 100.021i) q^{51} +(53.9277 - 93.4055i) q^{52} -609.634 q^{53} +(96.1643 + 198.197i) q^{54} +(363.830 - 630.173i) q^{56} +(183.661 + 161.763i) q^{57} +(63.7849 + 110.479i) q^{58} +(-7.77272 - 13.4627i) q^{59} +(-30.5255 + 52.8717i) q^{61} +17.0151 q^{62} +(852.582 + 357.430i) q^{63} +206.603 q^{64} +(43.2718 - 215.137i) q^{66} +(108.445 + 187.832i) q^{67} +(-80.5903 - 139.587i) q^{68} +(-116.003 + 576.740i) q^{69} +65.4315 q^{71} +(72.4627 + 569.208i) q^{72} -711.811 q^{73} +(-321.895 + 557.538i) q^{74} +(130.338 + 225.752i) q^{76} +(-460.457 - 797.534i) q^{77} +(-119.321 - 105.094i) q^{78} +(478.876 - 829.438i) q^{79} +(-705.748 + 182.650i) q^{81} +696.404 q^{82} +(-261.220 + 452.446i) q^{83} +(738.918 + 650.814i) q^{84} +(-266.540 - 461.660i) q^{86} +(-400.041 + 134.842i) q^{87} +(285.796 - 495.012i) q^{88} -1602.24 q^{89} -667.266 q^{91} +(-313.296 + 542.644i) q^{92} +(-11.1029 + 55.2011i) q^{93} +(-185.474 - 321.251i) q^{94} +(-191.745 + 953.312i) q^{96} +(400.969 - 694.499i) q^{97} -1302.27 q^{98} +(669.719 + 280.768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.785104 1.35984i 0.277576 0.480776i −0.693206 0.720740i \(-0.743802\pi\)
0.970782 + 0.239964i \(0.0771355\pi\)
\(3\) 3.89934 + 3.43441i 0.750428 + 0.660952i
\(4\) 2.76722 + 4.79297i 0.345903 + 0.599121i
\(5\) 0 0
\(6\) 7.73164 2.60611i 0.526071 0.177324i
\(7\) 17.1199 29.6525i 0.924387 1.60109i 0.131844 0.991271i \(-0.457910\pi\)
0.792544 0.609815i \(-0.208756\pi\)
\(8\) 21.2519 0.939210
\(9\) 3.40971 + 26.7838i 0.126285 + 0.991994i
\(10\) 0 0
\(11\) 13.4480 23.2926i 0.368611 0.638453i −0.620737 0.784019i \(-0.713167\pi\)
0.989349 + 0.145565i \(0.0465000\pi\)
\(12\) −5.67066 + 28.1932i −0.136415 + 0.678223i
\(13\) −9.74401 16.8771i −0.207885 0.360067i 0.743163 0.669110i \(-0.233325\pi\)
−0.951048 + 0.309043i \(0.899991\pi\)
\(14\) −26.8818 46.5607i −0.513176 0.888847i
\(15\) 0 0
\(16\) −5.45281 + 9.44454i −0.0852001 + 0.147571i
\(17\) −29.1232 −0.415495 −0.207747 0.978182i \(-0.566613\pi\)
−0.207747 + 0.978182i \(0.566613\pi\)
\(18\) 39.0987 + 16.3915i 0.511981 + 0.214639i
\(19\) 47.1006 0.568717 0.284358 0.958718i \(-0.408219\pi\)
0.284358 + 0.958718i \(0.408219\pi\)
\(20\) 0 0
\(21\) 168.595 56.8286i 1.75193 0.590525i
\(22\) −21.1162 36.5743i −0.204636 0.354439i
\(23\) 56.6083 + 98.0485i 0.513202 + 0.888892i 0.999883 + 0.0153124i \(0.00487428\pi\)
−0.486680 + 0.873580i \(0.661792\pi\)
\(24\) 82.8684 + 72.9877i 0.704810 + 0.620773i
\(25\) 0 0
\(26\) −30.6003 −0.230816
\(27\) −78.6910 + 116.150i −0.560892 + 0.827889i
\(28\) 189.498 1.27899
\(29\) −40.6219 + 70.3593i −0.260114 + 0.450531i −0.966272 0.257524i \(-0.917093\pi\)
0.706158 + 0.708054i \(0.250427\pi\)
\(30\) 0 0
\(31\) 5.41811 + 9.38445i 0.0313910 + 0.0543708i 0.881294 0.472568i \(-0.156673\pi\)
−0.849903 + 0.526939i \(0.823340\pi\)
\(32\) 93.5697 + 162.067i 0.516904 + 0.895304i
\(33\) 132.435 44.6399i 0.698603 0.235479i
\(34\) −22.8648 + 39.6029i −0.115332 + 0.199760i
\(35\) 0 0
\(36\) −118.939 + 90.4594i −0.550642 + 0.418794i
\(37\) −410.002 −1.82173 −0.910864 0.412706i \(-0.864584\pi\)
−0.910864 + 0.412706i \(0.864584\pi\)
\(38\) 36.9789 64.0493i 0.157862 0.273426i
\(39\) 19.9677 99.2746i 0.0819843 0.407606i
\(40\) 0 0
\(41\) 221.755 + 384.091i 0.844691 + 1.46305i 0.885889 + 0.463897i \(0.153549\pi\)
−0.0411978 + 0.999151i \(0.513117\pi\)
\(42\) 55.0869 273.879i 0.202383 1.00620i
\(43\) 169.748 294.012i 0.602007 1.04271i −0.390510 0.920599i \(-0.627701\pi\)
0.992517 0.122108i \(-0.0389655\pi\)
\(44\) 148.854 0.510015
\(45\) 0 0
\(46\) 177.774 0.569811
\(47\) 118.121 204.591i 0.366589 0.634950i −0.622441 0.782667i \(-0.713859\pi\)
0.989030 + 0.147716i \(0.0471923\pi\)
\(48\) −53.6988 + 18.1003i −0.161474 + 0.0544283i
\(49\) −414.681 718.249i −1.20898 2.09402i
\(50\) 0 0
\(51\) −113.561 100.021i −0.311799 0.274622i
\(52\) 53.9277 93.4055i 0.143816 0.249096i
\(53\) −609.634 −1.57999 −0.789997 0.613111i \(-0.789918\pi\)
−0.789997 + 0.613111i \(0.789918\pi\)
\(54\) 96.1643 + 198.197i 0.242339 + 0.499466i
\(55\) 0 0
\(56\) 363.830 630.173i 0.868194 1.50376i
\(57\) 183.661 + 161.763i 0.426781 + 0.375894i
\(58\) 63.7849 + 110.479i 0.144403 + 0.250113i
\(59\) −7.77272 13.4627i −0.0171512 0.0297068i 0.857322 0.514780i \(-0.172126\pi\)
−0.874474 + 0.485073i \(0.838793\pi\)
\(60\) 0 0
\(61\) −30.5255 + 52.8717i −0.0640719 + 0.110976i −0.896282 0.443485i \(-0.853742\pi\)
0.832210 + 0.554461i \(0.187075\pi\)
\(62\) 17.0151 0.0348536
\(63\) 852.582 + 357.430i 1.70500 + 0.714793i
\(64\) 206.603 0.403521
\(65\) 0 0
\(66\) 43.2718 215.137i 0.0807029 0.401235i
\(67\) 108.445 + 187.832i 0.197741 + 0.342497i 0.947796 0.318879i \(-0.103306\pi\)
−0.750055 + 0.661376i \(0.769973\pi\)
\(68\) −80.5903 139.587i −0.143721 0.248932i
\(69\) −116.003 + 576.740i −0.202394 + 1.00625i
\(70\) 0 0
\(71\) 65.4315 0.109370 0.0546852 0.998504i \(-0.482584\pi\)
0.0546852 + 0.998504i \(0.482584\pi\)
\(72\) 72.4627 + 569.208i 0.118609 + 0.931691i
\(73\) −711.811 −1.14125 −0.570624 0.821211i \(-0.693299\pi\)
−0.570624 + 0.821211i \(0.693299\pi\)
\(74\) −321.895 + 557.538i −0.505669 + 0.875844i
\(75\) 0 0
\(76\) 130.338 + 225.752i 0.196721 + 0.340730i
\(77\) −460.457 797.534i −0.681479 1.18036i
\(78\) −119.321 105.094i −0.173211 0.152558i
\(79\) 478.876 829.438i 0.681997 1.18125i −0.292373 0.956304i \(-0.594445\pi\)
0.974370 0.224949i \(-0.0722217\pi\)
\(80\) 0 0
\(81\) −705.748 + 182.650i −0.968104 + 0.250549i
\(82\) 696.404 0.937865
\(83\) −261.220 + 452.446i −0.345453 + 0.598343i −0.985436 0.170047i \(-0.945608\pi\)
0.639983 + 0.768389i \(0.278942\pi\)
\(84\) 738.918 + 650.814i 0.959792 + 0.845352i
\(85\) 0 0
\(86\) −266.540 461.660i −0.334206 0.578862i
\(87\) −400.041 + 134.842i −0.492976 + 0.166168i
\(88\) 285.796 495.012i 0.346204 0.599642i
\(89\) −1602.24 −1.90828 −0.954141 0.299359i \(-0.903227\pi\)
−0.954141 + 0.299359i \(0.903227\pi\)
\(90\) 0 0
\(91\) −667.266 −0.768664
\(92\) −313.296 + 542.644i −0.355036 + 0.614941i
\(93\) −11.1029 + 55.2011i −0.0123798 + 0.0615494i
\(94\) −185.474 321.251i −0.203513 0.352494i
\(95\) 0 0
\(96\) −191.745 + 953.312i −0.203854 + 1.01351i
\(97\) 400.969 694.499i 0.419714 0.726966i −0.576197 0.817311i \(-0.695464\pi\)
0.995910 + 0.0903455i \(0.0287971\pi\)
\(98\) −1302.27 −1.34234
\(99\) 669.719 + 280.768i 0.679892 + 0.285033i
\(100\) 0 0
\(101\) −293.065 + 507.604i −0.288724 + 0.500084i −0.973505 0.228664i \(-0.926564\pi\)
0.684782 + 0.728748i \(0.259898\pi\)
\(102\) −225.170 + 75.8984i −0.218580 + 0.0736770i
\(103\) −410.337 710.725i −0.392541 0.679901i 0.600243 0.799818i \(-0.295071\pi\)
−0.992784 + 0.119917i \(0.961737\pi\)
\(104\) −207.079 358.671i −0.195248 0.338179i
\(105\) 0 0
\(106\) −478.626 + 829.005i −0.438569 + 0.759623i
\(107\) 1358.33 1.22724 0.613621 0.789600i \(-0.289712\pi\)
0.613621 + 0.789600i \(0.289712\pi\)
\(108\) −774.457 55.7517i −0.690020 0.0496732i
\(109\) 489.495 0.430139 0.215069 0.976599i \(-0.431002\pi\)
0.215069 + 0.976599i \(0.431002\pi\)
\(110\) 0 0
\(111\) −1598.74 1408.11i −1.36708 1.20407i
\(112\) 186.703 + 323.379i 0.157516 + 0.272825i
\(113\) 398.832 + 690.797i 0.332026 + 0.575086i 0.982909 0.184092i \(-0.0589345\pi\)
−0.650883 + 0.759178i \(0.725601\pi\)
\(114\) 364.165 122.750i 0.299185 0.100847i
\(115\) 0 0
\(116\) −449.640 −0.359897
\(117\) 418.810 318.528i 0.330932 0.251692i
\(118\) −24.4096 −0.0190431
\(119\) −498.586 + 863.576i −0.384078 + 0.665243i
\(120\) 0 0
\(121\) 303.803 + 526.202i 0.228251 + 0.395343i
\(122\) 47.9314 + 83.0196i 0.0355697 + 0.0616085i
\(123\) −454.427 + 2259.30i −0.333124 + 1.65621i
\(124\) −29.9862 + 51.9377i −0.0217165 + 0.0376141i
\(125\) 0 0
\(126\) 1155.41 878.756i 0.816924 0.621316i
\(127\) −1728.22 −1.20752 −0.603759 0.797167i \(-0.706331\pi\)
−0.603759 + 0.797167i \(0.706331\pi\)
\(128\) −586.352 + 1015.59i −0.404896 + 0.701301i
\(129\) 1671.66 563.469i 1.14094 0.384579i
\(130\) 0 0
\(131\) −319.551 553.478i −0.213124 0.369142i 0.739566 0.673084i \(-0.235031\pi\)
−0.952691 + 0.303942i \(0.901697\pi\)
\(132\) 580.434 + 511.226i 0.382729 + 0.337095i
\(133\) 806.357 1396.65i 0.525715 0.910564i
\(134\) 340.562 0.219553
\(135\) 0 0
\(136\) −618.923 −0.390237
\(137\) −1417.97 + 2456.00i −0.884274 + 1.53161i −0.0377300 + 0.999288i \(0.512013\pi\)
−0.846544 + 0.532319i \(0.821321\pi\)
\(138\) 693.201 + 610.548i 0.427603 + 0.376618i
\(139\) −87.4981 151.551i −0.0533920 0.0924777i 0.838094 0.545526i \(-0.183670\pi\)
−0.891486 + 0.453048i \(0.850337\pi\)
\(140\) 0 0
\(141\) 1163.24 392.096i 0.694770 0.234187i
\(142\) 51.3706 88.9764i 0.0303586 0.0525827i
\(143\) −524.150 −0.306515
\(144\) −271.554 113.844i −0.157149 0.0658820i
\(145\) 0 0
\(146\) −558.846 + 967.949i −0.316784 + 0.548685i
\(147\) 849.776 4224.88i 0.476791 2.37049i
\(148\) −1134.57 1965.13i −0.630141 1.09144i
\(149\) −511.766 886.405i −0.281379 0.487363i 0.690345 0.723480i \(-0.257459\pi\)
−0.971725 + 0.236117i \(0.924125\pi\)
\(150\) 0 0
\(151\) 436.998 756.902i 0.235512 0.407920i −0.723909 0.689895i \(-0.757656\pi\)
0.959421 + 0.281976i \(0.0909898\pi\)
\(152\) 1000.98 0.534145
\(153\) −99.3015 780.031i −0.0524709 0.412168i
\(154\) −1446.03 −0.756650
\(155\) 0 0
\(156\) 531.075 179.010i 0.272564 0.0918736i
\(157\) 61.7762 + 107.000i 0.0314031 + 0.0543917i 0.881300 0.472558i \(-0.156669\pi\)
−0.849897 + 0.526949i \(0.823336\pi\)
\(158\) −751.936 1302.39i −0.378613 0.655776i
\(159\) −2377.17 2093.73i −1.18567 1.04430i
\(160\) 0 0
\(161\) 3876.51 1.89759
\(162\) −305.711 + 1103.10i −0.148265 + 0.534988i
\(163\) 1410.89 0.677972 0.338986 0.940791i \(-0.389916\pi\)
0.338986 + 0.940791i \(0.389916\pi\)
\(164\) −1227.29 + 2125.73i −0.584362 + 1.01214i
\(165\) 0 0
\(166\) 410.170 + 710.435i 0.191779 + 0.332172i
\(167\) −1013.85 1756.04i −0.469786 0.813692i 0.529618 0.848236i \(-0.322335\pi\)
−0.999403 + 0.0345441i \(0.989002\pi\)
\(168\) 3582.97 1207.72i 1.64543 0.554627i
\(169\) 908.608 1573.76i 0.413568 0.716320i
\(170\) 0 0
\(171\) 160.599 + 1261.53i 0.0718206 + 0.564164i
\(172\) 1878.92 0.832944
\(173\) 1351.99 2341.71i 0.594160 1.02912i −0.399505 0.916731i \(-0.630818\pi\)
0.993665 0.112384i \(-0.0358488\pi\)
\(174\) −130.710 + 649.858i −0.0569487 + 0.283135i
\(175\) 0 0
\(176\) 146.659 + 254.020i 0.0628115 + 0.108793i
\(177\) 15.9281 79.1905i 0.00676399 0.0336289i
\(178\) −1257.93 + 2178.79i −0.529694 + 0.917456i
\(179\) −750.694 −0.313461 −0.156730 0.987641i \(-0.550095\pi\)
−0.156730 + 0.987641i \(0.550095\pi\)
\(180\) 0 0
\(181\) −1134.08 −0.465722 −0.232861 0.972510i \(-0.574809\pi\)
−0.232861 + 0.972510i \(0.574809\pi\)
\(182\) −523.873 + 907.375i −0.213363 + 0.369556i
\(183\) −300.612 + 101.328i −0.121431 + 0.0409309i
\(184\) 1203.03 + 2083.72i 0.482005 + 0.834857i
\(185\) 0 0
\(186\) 66.3478 + 58.4369i 0.0261551 + 0.0230366i
\(187\) −391.649 + 678.355i −0.153156 + 0.265274i
\(188\) 1307.46 0.507216
\(189\) 2096.95 + 4321.85i 0.807040 + 1.66333i
\(190\) 0 0
\(191\) 267.627 463.544i 0.101387 0.175607i −0.810870 0.585227i \(-0.801005\pi\)
0.912256 + 0.409620i \(0.134339\pi\)
\(192\) 805.615 + 709.558i 0.302814 + 0.266708i
\(193\) 1311.77 + 2272.06i 0.489241 + 0.847391i 0.999923 0.0123786i \(-0.00394034\pi\)
−0.510682 + 0.859770i \(0.670607\pi\)
\(194\) −629.605 1090.51i −0.233005 0.403577i
\(195\) 0 0
\(196\) 2295.03 3975.11i 0.836382 1.44866i
\(197\) −2954.08 −1.06837 −0.534186 0.845367i \(-0.679382\pi\)
−0.534186 + 0.845367i \(0.679382\pi\)
\(198\) 907.599 690.279i 0.325759 0.247758i
\(199\) 2639.35 0.940192 0.470096 0.882615i \(-0.344219\pi\)
0.470096 + 0.882615i \(0.344219\pi\)
\(200\) 0 0
\(201\) −222.228 + 1104.86i −0.0779838 + 0.387717i
\(202\) 460.174 + 797.044i 0.160286 + 0.277623i
\(203\) 1390.89 + 2409.09i 0.480892 + 0.832929i
\(204\) 165.148 821.076i 0.0566797 0.281798i
\(205\) 0 0
\(206\) −1288.63 −0.435841
\(207\) −2433.10 + 1850.50i −0.816966 + 0.621348i
\(208\) 212.529 0.0708473
\(209\) 633.409 1097.10i 0.209635 0.363099i
\(210\) 0 0
\(211\) 995.327 + 1723.96i 0.324745 + 0.562474i 0.981461 0.191664i \(-0.0613883\pi\)
−0.656716 + 0.754138i \(0.728055\pi\)
\(212\) −1686.99 2921.96i −0.546524 0.946607i
\(213\) 255.140 + 224.718i 0.0820746 + 0.0722885i
\(214\) 1066.43 1847.12i 0.340654 0.590029i
\(215\) 0 0
\(216\) −1672.33 + 2468.40i −0.526796 + 0.777562i
\(217\) 371.030 0.116070
\(218\) 384.305 665.635i 0.119396 0.206800i
\(219\) −2775.59 2444.65i −0.856425 0.754310i
\(220\) 0 0
\(221\) 283.777 + 491.516i 0.0863751 + 0.149606i
\(222\) −3169.99 + 1068.51i −0.958359 + 0.323035i
\(223\) −337.450 + 584.481i −0.101333 + 0.175515i −0.912234 0.409669i \(-0.865644\pi\)
0.810901 + 0.585184i \(0.198978\pi\)
\(224\) 6407.61 1.91128
\(225\) 0 0
\(226\) 1252.50 0.368650
\(227\) 945.926 1638.39i 0.276579 0.479048i −0.693954 0.720020i \(-0.744133\pi\)
0.970532 + 0.240972i \(0.0774661\pi\)
\(228\) −267.092 + 1327.92i −0.0775815 + 0.385717i
\(229\) −1704.26 2951.86i −0.491792 0.851810i 0.508163 0.861261i \(-0.330325\pi\)
−0.999955 + 0.00945146i \(0.996991\pi\)
\(230\) 0 0
\(231\) 943.580 4691.25i 0.268758 1.33620i
\(232\) −863.294 + 1495.27i −0.244302 + 0.423143i
\(233\) 2841.86 0.799041 0.399521 0.916724i \(-0.369177\pi\)
0.399521 + 0.916724i \(0.369177\pi\)
\(234\) −104.338 819.593i −0.0291486 0.228968i
\(235\) 0 0
\(236\) 43.0177 74.5088i 0.0118653 0.0205513i
\(237\) 4715.93 1589.60i 1.29254 0.435679i
\(238\) 782.884 + 1356.00i 0.213222 + 0.369311i
\(239\) −809.803 1402.62i −0.219171 0.379615i 0.735384 0.677651i \(-0.237002\pi\)
−0.954555 + 0.298036i \(0.903668\pi\)
\(240\) 0 0
\(241\) −13.3504 + 23.1235i −0.00356835 + 0.00618057i −0.867804 0.496907i \(-0.834469\pi\)
0.864236 + 0.503087i \(0.167803\pi\)
\(242\) 954.068 0.253429
\(243\) −3379.24 1711.61i −0.892093 0.451851i
\(244\) −337.883 −0.0886506
\(245\) 0 0
\(246\) 2715.52 + 2391.73i 0.703801 + 0.619884i
\(247\) −458.949 794.923i −0.118228 0.204776i
\(248\) 115.145 + 199.437i 0.0294828 + 0.0510657i
\(249\) −2572.47 + 867.107i −0.654714 + 0.220685i
\(250\) 0 0
\(251\) −427.354 −0.107467 −0.0537337 0.998555i \(-0.517112\pi\)
−0.0537337 + 0.998555i \(0.517112\pi\)
\(252\) 646.133 + 5075.49i 0.161518 + 1.26875i
\(253\) 3045.07 0.756689
\(254\) −1356.83 + 2350.10i −0.335178 + 0.580546i
\(255\) 0 0
\(256\) 1747.11 + 3026.08i 0.426540 + 0.738789i
\(257\) 1920.77 + 3326.88i 0.466204 + 0.807490i 0.999255 0.0385936i \(-0.0122878\pi\)
−0.533051 + 0.846083i \(0.678954\pi\)
\(258\) 546.200 2715.58i 0.131802 0.655288i
\(259\) −7019.19 + 12157.6i −1.68398 + 2.91674i
\(260\) 0 0
\(261\) −2023.00 848.107i −0.479772 0.201136i
\(262\) −1003.52 −0.236633
\(263\) −399.437 + 691.845i −0.0936514 + 0.162209i −0.909045 0.416698i \(-0.863187\pi\)
0.815394 + 0.578907i \(0.196521\pi\)
\(264\) 2814.49 948.684i 0.656135 0.221165i
\(265\) 0 0
\(266\) −1266.15 2193.03i −0.291852 0.505502i
\(267\) −6247.68 5502.74i −1.43203 1.26128i
\(268\) −600.181 + 1039.54i −0.136798 + 0.236941i
\(269\) 7934.42 1.79840 0.899201 0.437536i \(-0.144149\pi\)
0.899201 + 0.437536i \(0.144149\pi\)
\(270\) 0 0
\(271\) −2309.09 −0.517592 −0.258796 0.965932i \(-0.583326\pi\)
−0.258796 + 0.965932i \(0.583326\pi\)
\(272\) 158.803 275.055i 0.0354002 0.0613150i
\(273\) −2601.90 2291.66i −0.576828 0.508050i
\(274\) 2226.51 + 3856.43i 0.490907 + 0.850276i
\(275\) 0 0
\(276\) −3085.31 + 1039.97i −0.672875 + 0.226807i
\(277\) 380.651 659.307i 0.0825672 0.143011i −0.821785 0.569798i \(-0.807021\pi\)
0.904352 + 0.426787i \(0.140355\pi\)
\(278\) −274.781 −0.0592815
\(279\) −232.877 + 177.116i −0.0499713 + 0.0380059i
\(280\) 0 0
\(281\) 643.638 1114.81i 0.136641 0.236670i −0.789582 0.613645i \(-0.789703\pi\)
0.926223 + 0.376975i \(0.123036\pi\)
\(282\) 380.079 1889.66i 0.0802601 0.399034i
\(283\) −1363.25 2361.22i −0.286350 0.495972i 0.686586 0.727049i \(-0.259109\pi\)
−0.972936 + 0.231076i \(0.925775\pi\)
\(284\) 181.064 + 313.611i 0.0378315 + 0.0655261i
\(285\) 0 0
\(286\) −411.512 + 712.760i −0.0850813 + 0.147365i
\(287\) 15185.7 3.12329
\(288\) −4021.74 + 3058.76i −0.822859 + 0.625830i
\(289\) −4064.84 −0.827364
\(290\) 0 0
\(291\) 3948.71 1331.00i 0.795454 0.268125i
\(292\) −1969.74 3411.69i −0.394761 0.683746i
\(293\) −48.1869 83.4622i −0.00960789 0.0166414i 0.861181 0.508298i \(-0.169725\pi\)
−0.870789 + 0.491656i \(0.836392\pi\)
\(294\) −5078.00 4472.53i −1.00733 0.887223i
\(295\) 0 0
\(296\) −8713.33 −1.71099
\(297\) 1647.19 + 3394.90i 0.321817 + 0.663273i
\(298\) −1607.16 −0.312417
\(299\) 1103.18 1910.77i 0.213374 0.369575i
\(300\) 0 0
\(301\) −5812.13 10066.9i −1.11298 1.92773i
\(302\) −686.178 1188.50i −0.130745 0.226458i
\(303\) −2886.08 + 972.815i −0.547198 + 0.184445i
\(304\) −256.831 + 444.844i −0.0484547 + 0.0839261i
\(305\) 0 0
\(306\) −1138.68 477.372i −0.212726 0.0891814i
\(307\) −5258.02 −0.977495 −0.488747 0.872425i \(-0.662546\pi\)
−0.488747 + 0.872425i \(0.662546\pi\)
\(308\) 2548.37 4413.91i 0.471451 0.816577i
\(309\) 840.874 4180.62i 0.154808 0.769668i
\(310\) 0 0
\(311\) 2615.66 + 4530.45i 0.476914 + 0.826039i 0.999650 0.0264555i \(-0.00842202\pi\)
−0.522736 + 0.852495i \(0.675089\pi\)
\(312\) 424.351 2109.77i 0.0770005 0.382828i
\(313\) −1996.33 + 3457.74i −0.360509 + 0.624419i −0.988045 0.154168i \(-0.950730\pi\)
0.627536 + 0.778588i \(0.284064\pi\)
\(314\) 194.003 0.0348670
\(315\) 0 0
\(316\) 5300.63 0.943619
\(317\) −2366.79 + 4099.40i −0.419344 + 0.726325i −0.995874 0.0907509i \(-0.971073\pi\)
0.576529 + 0.817076i \(0.304407\pi\)
\(318\) −4713.47 + 1588.78i −0.831189 + 0.280170i
\(319\) 1092.57 + 1892.38i 0.191762 + 0.332141i
\(320\) 0 0
\(321\) 5296.60 + 4665.07i 0.920958 + 0.811148i
\(322\) 3043.47 5271.44i 0.526726 0.912317i
\(323\) −1371.72 −0.236299
\(324\) −2828.40 2877.19i −0.484979 0.493346i
\(325\) 0 0
\(326\) 1107.70 1918.59i 0.188189 0.325953i
\(327\) 1908.71 + 1681.12i 0.322788 + 0.284301i
\(328\) 4712.72 + 8162.67i 0.793343 + 1.37411i
\(329\) −4044.43 7005.15i −0.677740 1.17388i
\(330\) 0 0
\(331\) −4684.92 + 8114.52i −0.777965 + 1.34747i 0.155148 + 0.987891i \(0.450415\pi\)
−0.933113 + 0.359583i \(0.882919\pi\)
\(332\) −2891.42 −0.477973
\(333\) −1397.99 10981.4i −0.230058 1.80714i
\(334\) −3183.92 −0.521605
\(335\) 0 0
\(336\) −382.597 + 1902.18i −0.0621201 + 0.308846i
\(337\) 2724.41 + 4718.83i 0.440381 + 0.762762i 0.997718 0.0675246i \(-0.0215101\pi\)
−0.557337 + 0.830287i \(0.688177\pi\)
\(338\) −1426.71 2471.13i −0.229593 0.397667i
\(339\) −817.296 + 4063.40i −0.130942 + 0.651014i
\(340\) 0 0
\(341\) 291.451 0.0462843
\(342\) 1841.57 + 772.047i 0.291172 + 0.122069i
\(343\) −16653.0 −2.62150
\(344\) 3607.47 6248.31i 0.565411 0.979321i
\(345\) 0 0
\(346\) −2122.90 3676.98i −0.329850 0.571316i
\(347\) −1948.77 3375.38i −0.301486 0.522189i 0.674987 0.737830i \(-0.264149\pi\)
−0.976473 + 0.215641i \(0.930816\pi\)
\(348\) −1753.30 1544.25i −0.270077 0.237874i
\(349\) 3129.53 5420.51i 0.480000 0.831384i −0.519737 0.854326i \(-0.673970\pi\)
0.999737 + 0.0229422i \(0.00730337\pi\)
\(350\) 0 0
\(351\) 2727.04 + 196.314i 0.414697 + 0.0298532i
\(352\) 5033.30 0.762147
\(353\) 171.433 296.931i 0.0258483 0.0447706i −0.852812 0.522218i \(-0.825105\pi\)
0.878660 + 0.477448i \(0.158438\pi\)
\(354\) −95.1813 83.8324i −0.0142905 0.0125866i
\(355\) 0 0
\(356\) −4433.75 7679.48i −0.660080 1.14329i
\(357\) −4910.03 + 1655.03i −0.727917 + 0.245360i
\(358\) −589.373 + 1020.82i −0.0870093 + 0.150705i
\(359\) 10448.9 1.53613 0.768066 0.640371i \(-0.221219\pi\)
0.768066 + 0.640371i \(0.221219\pi\)
\(360\) 0 0
\(361\) −4640.53 −0.676561
\(362\) −890.373 + 1542.17i −0.129273 + 0.223908i
\(363\) −622.561 + 3095.22i −0.0900164 + 0.447540i
\(364\) −1846.47 3198.18i −0.265883 0.460523i
\(365\) 0 0
\(366\) −98.2222 + 488.337i −0.0140278 + 0.0697426i
\(367\) −2586.87 + 4480.58i −0.367938 + 0.637288i −0.989243 0.146281i \(-0.953270\pi\)
0.621305 + 0.783569i \(0.286603\pi\)
\(368\) −1234.70 −0.174900
\(369\) −9531.32 + 7249.09i −1.34466 + 1.02269i
\(370\) 0 0
\(371\) −10436.9 + 18077.2i −1.46053 + 2.52970i
\(372\) −295.302 + 99.5378i −0.0411577 + 0.0138731i
\(373\) 1050.53 + 1819.58i 0.145830 + 0.252585i 0.929682 0.368362i \(-0.120081\pi\)
−0.783852 + 0.620947i \(0.786748\pi\)
\(374\) 614.970 + 1065.16i 0.0850250 + 0.147268i
\(375\) 0 0
\(376\) 2510.29 4347.95i 0.344304 0.596352i
\(377\) 1583.28 0.216295
\(378\) 7523.36 + 541.593i 1.02370 + 0.0736945i
\(379\) 11242.6 1.52374 0.761868 0.647732i \(-0.224282\pi\)
0.761868 + 0.647732i \(0.224282\pi\)
\(380\) 0 0
\(381\) −6738.92 5935.41i −0.906155 0.798111i
\(382\) −420.231 727.862i −0.0562851 0.0974886i
\(383\) 3397.44 + 5884.53i 0.453266 + 0.785080i 0.998587 0.0531478i \(-0.0169255\pi\)
−0.545321 + 0.838227i \(0.683592\pi\)
\(384\) −5774.34 + 1946.37i −0.767372 + 0.258659i
\(385\) 0 0
\(386\) 4119.52 0.543207
\(387\) 8453.56 + 3544.01i 1.11038 + 0.465509i
\(388\) 4438.28 0.580721
\(389\) −3524.70 + 6104.96i −0.459407 + 0.795717i −0.998930 0.0462544i \(-0.985272\pi\)
0.539522 + 0.841971i \(0.318605\pi\)
\(390\) 0 0
\(391\) −1648.62 2855.49i −0.213233 0.369330i
\(392\) −8812.77 15264.2i −1.13549 1.96673i
\(393\) 654.832 3255.67i 0.0840506 0.417879i
\(394\) −2319.26 + 4017.08i −0.296555 + 0.513648i
\(395\) 0 0
\(396\) 507.550 + 3986.89i 0.0644074 + 0.505931i
\(397\) −3011.36 −0.380694 −0.190347 0.981717i \(-0.560961\pi\)
−0.190347 + 0.981717i \(0.560961\pi\)
\(398\) 2072.16 3589.09i 0.260975 0.452022i
\(399\) 7940.93 2676.66i 0.996350 0.335841i
\(400\) 0 0
\(401\) 2084.07 + 3609.72i 0.259535 + 0.449528i 0.966118 0.258103i \(-0.0830973\pi\)
−0.706582 + 0.707631i \(0.749764\pi\)
\(402\) 1327.97 + 1169.63i 0.164758 + 0.145114i
\(403\) 105.588 182.884i 0.0130514 0.0226058i
\(404\) −3243.91 −0.399481
\(405\) 0 0
\(406\) 4367.96 0.533937
\(407\) −5513.71 + 9550.03i −0.671510 + 1.16309i
\(408\) −2413.39 2125.63i −0.292845 0.257928i
\(409\) 6302.68 + 10916.6i 0.761974 + 1.31978i 0.941832 + 0.336085i \(0.109103\pi\)
−0.179858 + 0.983693i \(0.557564\pi\)
\(410\) 0 0
\(411\) −13964.1 + 4706.88i −1.67590 + 0.564899i
\(412\) 2270.99 3933.47i 0.271562 0.470359i
\(413\) −532.272 −0.0634175
\(414\) 606.156 + 4761.46i 0.0719588 + 0.565249i
\(415\) 0 0
\(416\) 1823.49 3158.37i 0.214913 0.372240i
\(417\) 179.303 891.454i 0.0210564 0.104687i
\(418\) −994.584 1722.67i −0.116380 0.201575i
\(419\) 2572.24 + 4455.24i 0.299909 + 0.519458i 0.976115 0.217255i \(-0.0697102\pi\)
−0.676206 + 0.736713i \(0.736377\pi\)
\(420\) 0 0
\(421\) 1685.03 2918.56i 0.195068 0.337867i −0.751855 0.659329i \(-0.770841\pi\)
0.946923 + 0.321461i \(0.104174\pi\)
\(422\) 3125.74 0.360566
\(423\) 5882.49 + 2466.13i 0.676162 + 0.283469i
\(424\) −12955.9 −1.48395
\(425\) 0 0
\(426\) 505.893 170.522i 0.0575366 0.0193939i
\(427\) 1045.19 + 1810.31i 0.118454 + 0.205169i
\(428\) 3758.81 + 6510.45i 0.424507 + 0.735267i
\(429\) −2043.84 1800.14i −0.230017 0.202592i
\(430\) 0 0
\(431\) 14948.3 1.67061 0.835306 0.549785i \(-0.185290\pi\)
0.835306 + 0.549785i \(0.185290\pi\)
\(432\) −667.893 1376.54i −0.0743843 0.153308i
\(433\) 14011.1 1.55504 0.777520 0.628858i \(-0.216477\pi\)
0.777520 + 0.628858i \(0.216477\pi\)
\(434\) 291.297 504.542i 0.0322182 0.0558036i
\(435\) 0 0
\(436\) 1354.54 + 2346.13i 0.148786 + 0.257705i
\(437\) 2666.29 + 4618.14i 0.291867 + 0.505528i
\(438\) −5503.46 + 1855.06i −0.600378 + 0.202370i
\(439\) 2391.10 4141.50i 0.259956 0.450257i −0.706274 0.707939i \(-0.749625\pi\)
0.966230 + 0.257681i \(0.0829585\pi\)
\(440\) 0 0
\(441\) 17823.5 13555.8i 1.92458 1.46375i
\(442\) 891.178 0.0959027
\(443\) 2387.01 4134.42i 0.256005 0.443413i −0.709163 0.705044i \(-0.750927\pi\)
0.965168 + 0.261631i \(0.0842604\pi\)
\(444\) 2324.99 11559.3i 0.248511 1.23554i
\(445\) 0 0
\(446\) 529.867 + 917.757i 0.0562555 + 0.0974374i
\(447\) 1048.72 5214.01i 0.110969 0.551709i
\(448\) 3537.02 6126.30i 0.373010 0.646072i
\(449\) −855.812 −0.0899516 −0.0449758 0.998988i \(-0.514321\pi\)
−0.0449758 + 0.998988i \(0.514321\pi\)
\(450\) 0 0
\(451\) 11928.7 1.24545
\(452\) −2207.31 + 3823.18i −0.229697 + 0.397848i
\(453\) 4303.51 1450.59i 0.446350 0.150452i
\(454\) −1485.30 2572.62i −0.153543 0.265945i
\(455\) 0 0
\(456\) 3903.15 + 3437.76i 0.400837 + 0.353044i
\(457\) −6708.99 + 11620.3i −0.686725 + 1.18944i 0.286166 + 0.958180i \(0.407619\pi\)
−0.972891 + 0.231263i \(0.925714\pi\)
\(458\) −5352.08 −0.546040
\(459\) 2291.73 3382.65i 0.233048 0.343984i
\(460\) 0 0
\(461\) 7942.99 13757.7i 0.802477 1.38993i −0.115503 0.993307i \(-0.536848\pi\)
0.917981 0.396625i \(-0.129819\pi\)
\(462\) −5638.55 4966.24i −0.567812 0.500109i
\(463\) 3280.69 + 5682.32i 0.329302 + 0.570367i 0.982373 0.186929i \(-0.0598534\pi\)
−0.653072 + 0.757296i \(0.726520\pi\)
\(464\) −443.007 767.311i −0.0443235 0.0767705i
\(465\) 0 0
\(466\) 2231.16 3864.48i 0.221795 0.384160i
\(467\) 6792.37 0.673048 0.336524 0.941675i \(-0.390749\pi\)
0.336524 + 0.941675i \(0.390749\pi\)
\(468\) 2685.64 + 1125.91i 0.265264 + 0.111207i
\(469\) 7426.25 0.731156
\(470\) 0 0
\(471\) −126.593 + 629.392i −0.0123845 + 0.0615730i
\(472\) −165.185 286.109i −0.0161086 0.0279009i
\(473\) −4565.54 7907.74i −0.443813 0.768707i
\(474\) 1540.89 7660.92i 0.149315 0.742358i
\(475\) 0 0
\(476\) −5518.79 −0.531415
\(477\) −2078.67 16328.3i −0.199530 1.56734i
\(478\) −2543.12 −0.243346
\(479\) −8826.24 + 15287.5i −0.841923 + 1.45825i 0.0463438 + 0.998926i \(0.485243\pi\)
−0.888267 + 0.459328i \(0.848090\pi\)
\(480\) 0 0
\(481\) 3995.07 + 6919.66i 0.378710 + 0.655945i
\(482\) 20.9629 + 36.3088i 0.00198098 + 0.00343116i
\(483\) 15115.8 + 13313.5i 1.42401 + 1.25422i
\(484\) −1681.38 + 2912.23i −0.157906 + 0.273501i
\(485\) 0 0
\(486\) −4980.58 + 3251.44i −0.464863 + 0.303474i
\(487\) 5318.16 0.494844 0.247422 0.968908i \(-0.420417\pi\)
0.247422 + 0.968908i \(0.420417\pi\)
\(488\) −648.724 + 1123.62i −0.0601770 + 0.104230i
\(489\) 5501.54 + 4845.57i 0.508769 + 0.448107i
\(490\) 0 0
\(491\) −5434.98 9413.66i −0.499546 0.865239i 0.500454 0.865763i \(-0.333167\pi\)
−1.00000 0.000523887i \(0.999833\pi\)
\(492\) −12086.3 + 4073.93i −1.10750 + 0.373307i
\(493\) 1183.04 2049.09i 0.108076 0.187193i
\(494\) −1441.29 −0.131269
\(495\) 0 0
\(496\) −118.176 −0.0106981
\(497\) 1120.18 1940.21i 0.101101 0.175111i
\(498\) −840.531 + 4178.92i −0.0756328 + 0.376028i
\(499\) −5185.25 8981.12i −0.465178 0.805711i 0.534032 0.845464i \(-0.320676\pi\)
−0.999210 + 0.0397529i \(0.987343\pi\)
\(500\) 0 0
\(501\) 2077.61 10329.4i 0.185271 0.921123i
\(502\) −335.517 + 581.133i −0.0298304 + 0.0516678i
\(503\) 12396.4 1.09886 0.549432 0.835538i \(-0.314844\pi\)
0.549432 + 0.835538i \(0.314844\pi\)
\(504\) 18119.0 + 7596.07i 1.60136 + 0.671341i
\(505\) 0 0
\(506\) 2390.70 4140.82i 0.210039 0.363798i
\(507\) 8947.89 3016.08i 0.783806 0.264199i
\(508\) −4782.37 8283.30i −0.417684 0.723449i
\(509\) −2780.52 4816.00i −0.242130 0.419382i 0.719190 0.694813i \(-0.244513\pi\)
−0.961321 + 0.275431i \(0.911180\pi\)
\(510\) 0 0
\(511\) −12186.1 + 21107.0i −1.05496 + 1.82724i
\(512\) −3894.99 −0.336203
\(513\) −3706.39 + 5470.72i −0.318989 + 0.470834i
\(514\) 6032.03 0.517629
\(515\) 0 0
\(516\) 7326.55 + 6452.98i 0.625065 + 0.550536i
\(517\) −3176.97 5502.68i −0.270258 0.468100i
\(518\) 11021.6 + 19090.0i 0.934868 + 1.61924i
\(519\) 13314.2 4487.85i 1.12607 0.379566i
\(520\) 0 0
\(521\) −2613.39 −0.219760 −0.109880 0.993945i \(-0.535047\pi\)
−0.109880 + 0.993945i \(0.535047\pi\)
\(522\) −2741.56 + 2085.11i −0.229875 + 0.174833i
\(523\) 2927.73 0.244781 0.122391 0.992482i \(-0.460944\pi\)
0.122391 + 0.992482i \(0.460944\pi\)
\(524\) 1768.53 3063.19i 0.147440 0.255374i
\(525\) 0 0
\(526\) 627.199 + 1086.34i 0.0519908 + 0.0900508i
\(527\) −157.793 273.305i −0.0130428 0.0225908i
\(528\) −300.537 + 1494.20i −0.0247712 + 0.123156i
\(529\) −325.506 + 563.793i −0.0267532 + 0.0463379i
\(530\) 0 0
\(531\) 334.081 254.087i 0.0273030 0.0207654i
\(532\) 8925.48 0.727384
\(533\) 4321.57 7485.18i 0.351197 0.608291i
\(534\) −12387.9 + 4175.62i −1.00389 + 0.338383i
\(535\) 0 0
\(536\) 2304.66 + 3991.78i 0.185720 + 0.321677i
\(537\) −2927.21 2578.19i −0.235230 0.207183i
\(538\) 6229.35 10789.5i 0.499194 0.864629i
\(539\) −22306.5 −1.78258
\(540\) 0 0
\(541\) −4023.02 −0.319710 −0.159855 0.987140i \(-0.551103\pi\)
−0.159855 + 0.987140i \(0.551103\pi\)
\(542\) −1812.88 + 3140.00i −0.143671 + 0.248846i
\(543\) −4422.17 3894.90i −0.349491 0.307820i
\(544\) −2725.05 4719.92i −0.214771 0.371994i
\(545\) 0 0
\(546\) −5159.06 + 1738.97i −0.404372 + 0.136302i
\(547\) 1652.77 2862.68i 0.129191 0.223765i −0.794172 0.607692i \(-0.792095\pi\)
0.923363 + 0.383927i \(0.125429\pi\)
\(548\) −15695.4 −1.22349
\(549\) −1520.19 637.312i −0.118179 0.0495443i
\(550\) 0 0
\(551\) −1913.32 + 3313.96i −0.147931 + 0.256224i
\(552\) −2465.29 + 12256.8i −0.190090 + 0.945082i
\(553\) −16396.6 28399.8i −1.26086 2.18387i
\(554\) −597.702 1035.25i −0.0458374 0.0793927i
\(555\) 0 0
\(556\) 484.253 838.752i 0.0369369 0.0639766i
\(557\) −6472.87 −0.492396 −0.246198 0.969220i \(-0.579181\pi\)
−0.246198 + 0.969220i \(0.579181\pi\)
\(558\) 58.0166 + 455.731i 0.00440150 + 0.0345746i
\(559\) −6616.10 −0.500593
\(560\) 0 0
\(561\) −3856.92 + 1300.06i −0.290266 + 0.0978404i
\(562\) −1010.65 1750.49i −0.0758569 0.131388i
\(563\) −10277.6 17801.4i −0.769362 1.33257i −0.937909 0.346881i \(-0.887241\pi\)
0.168547 0.985694i \(-0.446093\pi\)
\(564\) 5098.25 + 4490.37i 0.380629 + 0.335246i
\(565\) 0 0
\(566\) −4281.18 −0.317936
\(567\) −6666.29 + 24054.2i −0.493753 + 1.78162i
\(568\) 1390.54 0.102722
\(569\) −635.311 + 1100.39i −0.0468078 + 0.0810735i −0.888480 0.458915i \(-0.848238\pi\)
0.841672 + 0.539989i \(0.181571\pi\)
\(570\) 0 0
\(571\) 8376.66 + 14508.8i 0.613927 + 1.06335i 0.990572 + 0.136995i \(0.0437444\pi\)
−0.376645 + 0.926358i \(0.622922\pi\)
\(572\) −1450.44 2512.23i −0.106024 0.183639i
\(573\) 2635.57 888.376i 0.192151 0.0647686i
\(574\) 11922.4 20650.1i 0.866951 1.50160i
\(575\) 0 0
\(576\) 704.455 + 5533.62i 0.0509588 + 0.400291i
\(577\) 7800.01 0.562770 0.281385 0.959595i \(-0.409206\pi\)
0.281385 + 0.959595i \(0.409206\pi\)
\(578\) −3191.32 + 5527.53i −0.229657 + 0.397777i
\(579\) −2688.12 + 13364.7i −0.192944 + 0.959271i
\(580\) 0 0
\(581\) 8944.12 + 15491.7i 0.638665 + 1.10620i
\(582\) 1290.20 6414.58i 0.0918912 0.456861i
\(583\) −8198.35 + 14200.0i −0.582403 + 1.00875i
\(584\) −15127.3 −1.07187
\(585\) 0 0
\(586\) −151.327 −0.0106677
\(587\) −1184.62 + 2051.83i −0.0832958 + 0.144273i −0.904664 0.426126i \(-0.859878\pi\)
0.821368 + 0.570399i \(0.193211\pi\)
\(588\) 22601.2 7618.24i 1.58514 0.534304i
\(589\) 255.196 + 442.013i 0.0178526 + 0.0309216i
\(590\) 0 0
\(591\) −11519.0 10145.5i −0.801737 0.706143i
\(592\) 2235.66 3872.28i 0.155212 0.268834i
\(593\) −11974.3 −0.829218 −0.414609 0.910000i \(-0.636082\pi\)
−0.414609 + 0.910000i \(0.636082\pi\)
\(594\) 5909.74 + 425.431i 0.408215 + 0.0293866i
\(595\) 0 0
\(596\) 2832.34 4905.76i 0.194660 0.337160i
\(597\) 10291.7 + 9064.59i 0.705547 + 0.621422i
\(598\) −1732.23 3000.31i −0.118455 0.205170i
\(599\) −11099.7 19225.3i −0.757134 1.31139i −0.944307 0.329067i \(-0.893266\pi\)
0.187173 0.982327i \(-0.440068\pi\)
\(600\) 0 0
\(601\) 5749.47 9958.38i 0.390226 0.675891i −0.602253 0.798305i \(-0.705730\pi\)
0.992479 + 0.122414i \(0.0390635\pi\)
\(602\) −18252.5 −1.23574
\(603\) −4661.09 + 3545.02i −0.314783 + 0.239410i
\(604\) 4837.08 0.325858
\(605\) 0 0
\(606\) −943.000 + 4688.37i −0.0632125 + 0.314277i
\(607\) −7636.51 13226.8i −0.510636 0.884448i −0.999924 0.0123257i \(-0.996077\pi\)
0.489288 0.872122i \(-0.337257\pi\)
\(608\) 4407.19 + 7633.47i 0.293972 + 0.509175i
\(609\) −2850.24 + 14170.7i −0.189651 + 0.942900i
\(610\) 0 0
\(611\) −4603.88 −0.304833
\(612\) 3463.87 2634.47i 0.228789 0.174007i
\(613\) 16440.8 1.08326 0.541630 0.840617i \(-0.317808\pi\)
0.541630 + 0.840617i \(0.317808\pi\)
\(614\) −4128.09 + 7150.07i −0.271329 + 0.469956i
\(615\) 0 0
\(616\) −9785.58 16949.1i −0.640052 1.10860i
\(617\) 4679.57 + 8105.25i 0.305336 + 0.528857i 0.977336 0.211694i \(-0.0678979\pi\)
−0.672000 + 0.740551i \(0.734565\pi\)
\(618\) −5024.81 4425.68i −0.327067 0.288070i
\(619\) 12742.3 22070.3i 0.827392 1.43308i −0.0726861 0.997355i \(-0.523157\pi\)
0.900078 0.435729i \(-0.143510\pi\)
\(620\) 0 0
\(621\) −15842.9 1140.50i −1.02376 0.0736982i
\(622\) 8214.25 0.529520
\(623\) −27430.2 + 47510.4i −1.76399 + 3.05532i
\(624\) 828.723 + 729.911i 0.0531658 + 0.0468266i
\(625\) 0 0
\(626\) 3134.65 + 5429.38i 0.200137 + 0.346648i
\(627\) 6237.75 2102.57i 0.397307 0.133921i
\(628\) −341.897 + 592.183i −0.0217248 + 0.0376285i
\(629\) 11940.6 0.756919
\(630\) 0 0
\(631\) −21733.8 −1.37117 −0.685585 0.727993i \(-0.740454\pi\)
−0.685585 + 0.727993i \(0.740454\pi\)
\(632\) 10177.0 17627.1i 0.640539 1.10945i
\(633\) −2039.65 + 10140.6i −0.128071 + 0.636737i
\(634\) 3716.35 + 6436.91i 0.232800 + 0.403222i
\(635\) 0 0
\(636\) 3457.03 17187.5i 0.215535 1.07159i
\(637\) −8081.32 + 13997.3i −0.502659 + 0.870631i
\(638\) 3431.12 0.212914
\(639\) 223.102 + 1752.51i 0.0138119 + 0.108495i
\(640\) 0 0
\(641\) 10162.4 17601.8i 0.626195 1.08460i −0.362113 0.932134i \(-0.617945\pi\)
0.988308 0.152468i \(-0.0487220\pi\)
\(642\) 10502.1 3539.97i 0.645617 0.217619i
\(643\) 3363.72 + 5826.13i 0.206302 + 0.357325i 0.950547 0.310581i \(-0.100524\pi\)
−0.744245 + 0.667907i \(0.767190\pi\)
\(644\) 10727.2 + 18580.0i 0.656382 + 1.13689i
\(645\) 0 0
\(646\) −1076.94 + 1865.32i −0.0655910 + 0.113607i
\(647\) −6724.69 −0.408616 −0.204308 0.978907i \(-0.565494\pi\)
−0.204308 + 0.978907i \(0.565494\pi\)
\(648\) −14998.5 + 3881.66i −0.909253 + 0.235318i
\(649\) −418.110 −0.0252885
\(650\) 0 0
\(651\) 1446.77 + 1274.27i 0.0871021 + 0.0767166i
\(652\) 3904.25 + 6762.35i 0.234512 + 0.406187i
\(653\) −15398.2 26670.4i −0.922782 1.59831i −0.795089 0.606492i \(-0.792576\pi\)
−0.127693 0.991814i \(-0.540757\pi\)
\(654\) 3784.60 1275.68i 0.226283 0.0762737i
\(655\) 0 0
\(656\) −4836.75 −0.287871
\(657\) −2427.07 19065.0i −0.144123 1.13211i
\(658\) −12701.2 −0.752498
\(659\) −8267.16 + 14319.1i −0.488684 + 0.846426i −0.999915 0.0130174i \(-0.995856\pi\)
0.511231 + 0.859443i \(0.329190\pi\)
\(660\) 0 0
\(661\) −968.527 1677.54i −0.0569914 0.0987121i 0.836122 0.548543i \(-0.184817\pi\)
−0.893114 + 0.449831i \(0.851484\pi\)
\(662\) 7356.30 + 12741.5i 0.431889 + 0.748054i
\(663\) −581.523 + 2891.19i −0.0340641 + 0.169358i
\(664\) −5551.42 + 9615.35i −0.324453 + 0.561970i
\(665\) 0 0
\(666\) −16030.6 6720.53i −0.932691 0.391014i
\(667\) −9198.16 −0.533964
\(668\) 5611.10 9718.72i 0.325000 0.562917i
\(669\) −3323.18 + 1120.15i −0.192050 + 0.0647346i
\(670\) 0 0
\(671\) 821.013 + 1422.04i 0.0472352 + 0.0818138i
\(672\) 24985.5 + 22006.3i 1.43428 + 1.26326i
\(673\) −230.294 + 398.881i −0.0131905 + 0.0228465i −0.872545 0.488533i \(-0.837532\pi\)
0.859355 + 0.511380i \(0.170865\pi\)
\(674\) 8555.80 0.488957
\(675\) 0 0
\(676\) 10057.3 0.572217
\(677\) 14529.8 25166.4i 0.824854 1.42869i −0.0771775 0.997017i \(-0.524591\pi\)
0.902031 0.431671i \(-0.142076\pi\)
\(678\) 4883.92 + 4301.59i 0.276646 + 0.243660i
\(679\) −13729.1 23779.5i −0.775956 1.34400i
\(680\) 0 0
\(681\) 9315.39 3139.95i 0.524180 0.176686i
\(682\) 228.820 396.327i 0.0128474 0.0222524i
\(683\) −14366.9 −0.804881 −0.402440 0.915446i \(-0.631838\pi\)
−0.402440 + 0.915446i \(0.631838\pi\)
\(684\) −5602.08 + 4260.69i −0.313159 + 0.238175i
\(685\) 0 0
\(686\) −13074.3 + 22645.4i −0.727667 + 1.26036i
\(687\) 3492.41 17363.4i 0.193950 0.964273i
\(688\) 1851.21 + 3206.38i 0.102582 + 0.177678i
\(689\) 5940.28 + 10288.9i 0.328457 + 0.568904i
\(690\) 0 0
\(691\) 6353.97 11005.4i 0.349807 0.605883i −0.636408 0.771352i \(-0.719581\pi\)
0.986215 + 0.165469i \(0.0529139\pi\)
\(692\) 14965.0 0.822087
\(693\) 19791.0 15052.1i 1.08485 0.825085i
\(694\) −6119.97 −0.334742
\(695\) 0 0
\(696\) −8501.63 + 2865.66i −0.463008 + 0.156067i
\(697\) −6458.22 11186.0i −0.350965 0.607889i
\(698\) −4914.02 8511.33i −0.266473 0.461545i
\(699\) 11081.4 + 9760.11i 0.599623 + 0.528128i
\(700\) 0 0
\(701\) 5959.06 0.321071 0.160535 0.987030i \(-0.448678\pi\)
0.160535 + 0.987030i \(0.448678\pi\)
\(702\) 2407.97 3554.21i 0.129463 0.191090i
\(703\) −19311.4 −1.03605
\(704\) 2778.40 4812.32i 0.148743 0.257630i
\(705\) 0 0
\(706\) −269.186 466.243i −0.0143498 0.0248545i
\(707\) 10034.5 + 17380.2i 0.533785 + 0.924542i
\(708\) 423.634 142.795i 0.0224875 0.00757989i
\(709\) −225.912 + 391.292i −0.0119666 + 0.0207268i −0.871947 0.489601i \(-0.837143\pi\)
0.859980 + 0.510328i \(0.170476\pi\)
\(710\) 0 0
\(711\) 23848.4 + 9998.00i 1.25792 + 0.527362i
\(712\) −34050.6 −1.79228
\(713\) −613.421 + 1062.48i −0.0322199 + 0.0558065i
\(714\) −1604.31 + 7976.23i −0.0840892 + 0.418071i
\(715\) 0 0
\(716\) −2077.34 3598.05i −0.108427 0.187801i
\(717\) 1659.47 8250.48i 0.0864352 0.429735i
\(718\) 8203.47 14208.8i 0.426394 0.738536i
\(719\) −13488.4 −0.699627 −0.349814 0.936819i \(-0.613755\pi\)
−0.349814 + 0.936819i \(0.613755\pi\)
\(720\) 0 0
\(721\) −28099.7 −1.45144
\(722\) −3643.30 + 6310.39i −0.187797 + 0.325275i
\(723\) −131.473 + 44.3159i −0.00676285 + 0.00227957i
\(724\) −3138.26 5435.62i −0.161094 0.279024i
\(725\) 0 0
\(726\) 3720.23 + 3276.66i 0.190180 + 0.167504i
\(727\) 14591.6 25273.3i 0.744389 1.28932i −0.206090 0.978533i \(-0.566074\pi\)
0.950480 0.310787i \(-0.100593\pi\)
\(728\) −14180.7 −0.721938
\(729\) −7298.46 18279.9i −0.370800 0.928713i
\(730\) 0 0
\(731\) −4943.60 + 8562.57i −0.250131 + 0.433239i
\(732\) −1317.52 1160.43i −0.0665259 0.0585938i
\(733\) 6256.24 + 10836.1i 0.315252 + 0.546032i 0.979491 0.201488i \(-0.0645777\pi\)
−0.664239 + 0.747520i \(0.731244\pi\)
\(734\) 4061.92 + 7035.45i 0.204262 + 0.353792i
\(735\) 0 0
\(736\) −10593.6 + 18348.7i −0.530553 + 0.918945i
\(737\) 5833.46 0.291558
\(738\) 2374.53 + 18652.4i 0.118439 + 0.930357i
\(739\) −32248.2 −1.60524 −0.802619 0.596492i \(-0.796561\pi\)
−0.802619 + 0.596492i \(0.796561\pi\)
\(740\) 0 0
\(741\) 940.490 4675.89i 0.0466259 0.231813i
\(742\) 16388.1 + 28384.9i 0.810815 + 1.40437i
\(743\) 9244.50 + 16011.9i 0.456457 + 0.790607i 0.998771 0.0495691i \(-0.0157848\pi\)
−0.542313 + 0.840176i \(0.682451\pi\)
\(744\) −235.959 + 1173.13i −0.0116272 + 0.0578078i
\(745\) 0 0
\(746\) 3299.12 0.161916
\(747\) −13008.9 5453.77i −0.637178 0.267126i
\(748\) −4335.12 −0.211908
\(749\) 23254.5 40278.0i 1.13445 1.96492i
\(750\) 0 0
\(751\) 1026.10 + 1777.26i 0.0498575 + 0.0863558i 0.889877 0.456200i \(-0.150790\pi\)
−0.840020 + 0.542556i \(0.817457\pi\)
\(752\) 1288.18 + 2231.19i 0.0624668 + 0.108196i
\(753\) −1666.40 1467.71i −0.0806466 0.0710308i
\(754\) 1243.04 2153.01i 0.0600384 0.103990i
\(755\) 0 0
\(756\) −14911.8 + 22010.1i −0.717377 + 1.05886i
\(757\) −10118.9 −0.485834 −0.242917 0.970047i \(-0.578104\pi\)
−0.242917 + 0.970047i \(0.578104\pi\)
\(758\) 8826.65 15288.2i 0.422953 0.732576i
\(759\) 11873.8 + 10458.0i 0.567841 + 0.500135i
\(760\) 0 0
\(761\) −13652.0 23646.0i −0.650309 1.12637i −0.983048 0.183349i \(-0.941306\pi\)
0.332739 0.943019i \(-0.392027\pi\)
\(762\) −13362.0 + 4503.94i −0.635240 + 0.214121i
\(763\) 8380.10 14514.8i 0.397615 0.688689i
\(764\) 2962.34 0.140280
\(765\) 0 0
\(766\) 10669.4 0.503264
\(767\) −151.475 + 262.362i −0.00713096 + 0.0123512i
\(768\) −3580.22 + 17800.0i −0.168216 + 0.836330i
\(769\) 11236.9 + 19462.9i 0.526935 + 0.912679i 0.999507 + 0.0313867i \(0.00999234\pi\)
−0.472572 + 0.881292i \(0.656674\pi\)
\(770\) 0 0
\(771\) −3936.10 + 19569.3i −0.183859 + 0.914102i
\(772\) −7259.94 + 12574.6i −0.338460 + 0.586230i
\(773\) 35405.6 1.64741 0.823707 0.567015i \(-0.191902\pi\)
0.823707 + 0.567015i \(0.191902\pi\)
\(774\) 11456.2 8713.08i 0.532022 0.404632i
\(775\) 0 0
\(776\) 8521.35 14759.4i 0.394200 0.682774i
\(777\) −69124.4 + 23299.9i −3.19154 + 1.07578i
\(778\) 5534.52 + 9586.07i 0.255041 + 0.441744i
\(779\) 10444.8 + 18090.9i 0.480390 + 0.832060i
\(780\) 0 0
\(781\) 879.923 1524.07i 0.0403151 0.0698278i
\(782\) −5177.34 −0.236754
\(783\) −4975.62 10254.9i −0.227093 0.468044i
\(784\) 9044.71 0.412022
\(785\) 0 0
\(786\) −3913.08 3446.50i −0.177576 0.156403i
\(787\) −6090.02 10548.2i −0.275840 0.477769i 0.694507 0.719486i \(-0.255623\pi\)
−0.970347 + 0.241718i \(0.922289\pi\)
\(788\) −8174.59 14158.8i −0.369553 0.640085i
\(789\) −3933.62 + 1325.91i −0.177491 + 0.0598272i
\(790\) 0 0
\(791\) 27311.8 1.22768
\(792\) 14232.8 + 5966.86i 0.638562 + 0.267706i
\(793\) 1189.76 0.0532783
\(794\) −2364.23 + 4094.97i −0.105672 + 0.183029i
\(795\) 0 0
\(796\) 7303.65 + 12650.3i 0.325215 + 0.563289i
\(797\) 1146.54 + 1985.86i 0.0509567 + 0.0882596i 0.890379 0.455221i \(-0.150440\pi\)
−0.839422 + 0.543480i \(0.817106\pi\)
\(798\) 2594.63 12899.9i 0.115099 0.572243i
\(799\) −3440.05 + 5958.35i −0.152316 + 0.263819i
\(800\) 0 0
\(801\) −5463.16 42914.1i −0.240988 1.89300i
\(802\) 6544.86 0.288164
\(803\) −9572.43 + 16579.9i −0.420677 + 0.728634i
\(804\) −5910.53 + 1992.27i −0.259264 + 0.0873905i
\(805\) 0 0
\(806\) −165.796 287.167i −0.00724554 0.0125496i
\(807\) 30939.0 + 27250.0i 1.34957 + 1.18866i
\(808\) −6228.19 + 10787.5i −0.271172 + 0.469684i
\(809\) −25264.0 −1.09794 −0.548972 0.835841i \(-0.684981\pi\)
−0.548972 + 0.835841i \(0.684981\pi\)
\(810\) 0 0
\(811\) 18781.2 0.813190 0.406595 0.913608i \(-0.366716\pi\)
0.406595 + 0.913608i \(0.366716\pi\)
\(812\) −7697.78 + 13333.0i −0.332684 + 0.576225i
\(813\) −9003.94 7930.37i −0.388416 0.342103i
\(814\) 8657.68 + 14995.5i 0.372790 + 0.645692i
\(815\) 0 0
\(816\) 1563.88 527.139i 0.0670916 0.0226147i
\(817\) 7995.23 13848.1i 0.342372 0.593005i
\(818\) 19793.0 0.846023
\(819\) −2275.18 17871.9i −0.0970711 0.762510i
\(820\) 0 0
\(821\) −15787.4 + 27344.6i −0.671114 + 1.16240i 0.306474 + 0.951879i \(0.400851\pi\)
−0.977588 + 0.210525i \(0.932483\pi\)
\(822\) −4562.63 + 22684.3i −0.193601 + 0.962537i
\(823\) −473.129 819.484i −0.0200392 0.0347089i 0.855832 0.517254i \(-0.173046\pi\)
−0.875871 + 0.482545i \(0.839712\pi\)
\(824\) −8720.45 15104.3i −0.368679 0.638570i
\(825\) 0 0
\(826\) −417.889 + 723.806i −0.0176032 + 0.0304896i
\(827\) −35044.7 −1.47355 −0.736774 0.676139i \(-0.763652\pi\)
−0.736774 + 0.676139i \(0.763652\pi\)
\(828\) −15602.3 6541.00i −0.654853 0.274536i
\(829\) 31029.2 1.29999 0.649993 0.759940i \(-0.274772\pi\)
0.649993 + 0.759940i \(0.274772\pi\)
\(830\) 0 0
\(831\) 3748.62 1263.55i 0.156484 0.0527463i
\(832\) −2013.14 3486.86i −0.0838860 0.145295i
\(833\) 12076.8 + 20917.7i 0.502327 + 0.870055i
\(834\) −1071.46 943.708i −0.0444865 0.0391822i
\(835\) 0 0
\(836\) 7011.13 0.290054
\(837\) −1516.36 109.160i −0.0626200 0.00450790i
\(838\) 8077.90 0.332991
\(839\) 10599.9 18359.6i 0.436175 0.755477i −0.561216 0.827669i \(-0.689666\pi\)
0.997391 + 0.0721924i \(0.0229996\pi\)
\(840\) 0 0
\(841\) 8894.22 + 15405.2i 0.364681 + 0.631647i
\(842\) −2645.86 4582.76i −0.108292 0.187568i
\(843\) 6338.49 2136.52i 0.258967 0.0872904i
\(844\) −5508.58 + 9541.14i −0.224660 + 0.389123i
\(845\) 0 0
\(846\) 7971.91 6063.08i 0.323972 0.246398i
\(847\) 20804.3 0.843971
\(848\) 3324.22 5757.71i 0.134616 0.233161i
\(849\) 2793.61 13889.2i 0.112929 0.561455i
\(850\) 0 0
\(851\) −23209.5 40200.1i −0.934915 1.61932i
\(852\) −371.040 + 1844.72i −0.0149197 + 0.0741774i
\(853\) 5489.93 9508.84i 0.220365 0.381684i −0.734554 0.678551i \(-0.762608\pi\)
0.954919 + 0.296867i \(0.0959417\pi\)
\(854\) 3282.32 0.131521
\(855\) 0 0
\(856\) 28867.2 1.15264
\(857\) 22407.2 38810.4i 0.893133 1.54695i 0.0570348 0.998372i \(-0.481835\pi\)
0.836098 0.548580i \(-0.184831\pi\)
\(858\) −4052.54 + 1365.99i −0.161249 + 0.0543523i
\(859\) −18693.1 32377.4i −0.742492 1.28603i −0.951358 0.308089i \(-0.900311\pi\)
0.208866 0.977944i \(-0.433023\pi\)
\(860\) 0 0
\(861\) 59214.2 + 52153.9i 2.34380 + 2.06434i
\(862\) 11736.0 20327.3i 0.463722 0.803191i
\(863\) 30536.3 1.20448 0.602241 0.798314i \(-0.294275\pi\)
0.602241 + 0.798314i \(0.294275\pi\)
\(864\) −26187.2 1885.16i −1.03114 0.0742299i
\(865\) 0 0
\(866\) 11000.2 19052.9i 0.431643 0.747627i
\(867\) −15850.2 13960.3i −0.620877 0.546848i
\(868\) 1026.72 + 1778.34i 0.0401489 + 0.0695399i
\(869\) −12879.8 22308.6i −0.502784 0.870847i
\(870\) 0 0
\(871\) 2113.37 3660.47i 0.0822146 0.142400i
\(872\) 10402.7 0.403991
\(873\) 19968.5 + 8371.45i 0.774149 + 0.324548i
\(874\) 8373.25 0.324061
\(875\) 0 0
\(876\) 4036.44 20068.2i 0.155683 0.774021i
\(877\) 17163.7 + 29728.4i 0.660864 + 1.14465i 0.980389 + 0.197072i \(0.0631434\pi\)
−0.319525 + 0.947578i \(0.603523\pi\)
\(878\) −3754.52 6503.02i −0.144315 0.249962i
\(879\) 98.7460 490.941i 0.00378910 0.0188385i
\(880\) 0 0
\(881\) −18009.6 −0.688718 −0.344359 0.938838i \(-0.611904\pi\)
−0.344359 + 0.938838i \(0.611904\pi\)
\(882\) −4440.37 34879.9i −0.169518 1.33159i
\(883\) 29074.4 1.10808 0.554039 0.832491i \(-0.313086\pi\)
0.554039 + 0.832491i \(0.313086\pi\)
\(884\) −1570.55 + 2720.27i −0.0597548 + 0.103498i
\(885\) 0 0
\(886\) −3748.10 6491.90i −0.142122 0.246162i
\(887\) −16451.3 28494.5i −0.622752 1.07864i −0.988971 0.148109i \(-0.952681\pi\)
0.366220 0.930528i \(-0.380652\pi\)
\(888\) −33976.2 29925.1i −1.28397 1.13088i
\(889\) −29586.9 + 51246.1i −1.11621 + 1.93334i
\(890\) 0 0
\(891\) −5236.50 + 18895.0i −0.196890 + 0.710444i
\(892\) −3735.20 −0.140206
\(893\) 5563.56 9636.36i 0.208485 0.361107i
\(894\) −6266.86 5519.64i −0.234446 0.206493i
\(895\) 0 0
\(896\) 20076.6 + 34773.7i 0.748562 + 1.29655i
\(897\) 10864.1 3661.96i 0.404393 0.136309i
\(898\) −671.902 + 1163.77i −0.0249684 + 0.0432466i
\(899\) −880.377 −0.0326610
\(900\) 0 0
\(901\) 17754.5 0.656479
\(902\) 9365.24 16221.1i 0.345708 0.598783i
\(903\) 11910.4 59215.5i 0.438928 2.18225i
\(904\) 8475.93 + 14680.7i 0.311842 + 0.540127i
\(905\) 0 0
\(906\) 1406.13 6990.96i 0.0515625 0.256357i
\(907\) −407.908 + 706.517i −0.0149331 + 0.0258649i −0.873395 0.487012i \(-0.838087\pi\)
0.858462 + 0.512877i \(0.171420\pi\)
\(908\) 10470.4 0.382677
\(909\) −14594.8 6118.63i −0.532542 0.223259i
\(910\) 0 0
\(911\) −7921.41 + 13720.3i −0.288088 + 0.498983i −0.973353 0.229311i \(-0.926353\pi\)
0.685265 + 0.728293i \(0.259686\pi\)
\(912\) −2529.24 + 852.536i −0.0918329 + 0.0309543i
\(913\) 7025.77 + 12169.0i 0.254676 + 0.441112i
\(914\) 10534.5 + 18246.3i 0.381237 + 0.660322i
\(915\) 0 0
\(916\) 9432.11 16336.9i 0.340225 0.589286i
\(917\) −21882.7 −0.788037
\(918\) −2800.61 5772.12i −0.100691 0.207526i
\(919\) 23848.4 0.856025 0.428013 0.903773i \(-0.359214\pi\)
0.428013 + 0.903773i \(0.359214\pi\)
\(920\) 0 0
\(921\) −20502.8 18058.2i −0.733540 0.646077i
\(922\) −12472.2 21602.4i −0.445498 0.771624i
\(923\) −637.566 1104.30i −0.0227364 0.0393807i
\(924\) 25096.1 8459.19i 0.893508 0.301176i
\(925\) 0 0
\(926\) 10302.7 0.365625
\(927\) 17636.8 13413.8i 0.624886 0.475260i
\(928\) −15203.9 −0.537816
\(929\) 19796.0 34287.7i 0.699123 1.21092i −0.269647 0.962959i \(-0.586907\pi\)
0.968771 0.247958i \(-0.0797595\pi\)
\(930\) 0 0
\(931\) −19531.7 33830.0i −0.687569 1.19090i
\(932\) 7864.07 + 13621.0i 0.276391 + 0.478723i
\(933\) −5360.07 + 26649.0i −0.188082 + 0.935100i
\(934\) 5332.72 9236.54i 0.186822 0.323585i
\(935\) 0 0
\(936\) 8900.51 6769.33i 0.310814 0.236391i
\(937\) −10255.0 −0.357540 −0.178770 0.983891i \(-0.557212\pi\)
−0.178770 + 0.983891i \(0.557212\pi\)
\(938\) 5830.38 10098.5i 0.202952 0.351523i
\(939\) −19659.7 + 6626.71i −0.683247 + 0.230303i
\(940\) 0 0
\(941\) 11947.2 + 20693.1i 0.413886 + 0.716871i 0.995311 0.0967289i \(-0.0308380\pi\)
−0.581425 + 0.813600i \(0.697505\pi\)
\(942\) 756.484 + 666.286i 0.0261652 + 0.0230454i
\(943\) −25106.4 + 43485.5i −0.866995 + 1.50168i
\(944\) 169.533 0.00584514
\(945\) 0 0
\(946\) −14337.7 −0.492768
\(947\) −18128.6 + 31399.7i −0.622072 + 1.07746i 0.367028 + 0.930210i \(0.380375\pi\)
−0.989099 + 0.147250i \(0.952958\pi\)
\(948\) 20668.9 + 18204.5i 0.708118 + 0.623686i
\(949\) 6935.89 + 12013.3i 0.237248 + 0.410926i
\(950\) 0 0
\(951\) −23307.9 + 7856.43i −0.794754 + 0.267889i
\(952\) −10595.9 + 18352.6i −0.360730 + 0.624803i
\(953\) 46736.7 1.58861 0.794307 0.607516i \(-0.207834\pi\)
0.794307 + 0.607516i \(0.207834\pi\)
\(954\) −23835.9 9992.78i −0.808927 0.339128i
\(955\) 0 0
\(956\) 4481.81 7762.72i 0.151623 0.262620i
\(957\) −2238.92 + 11131.4i −0.0756259 + 0.375994i
\(958\) 13859.0 + 24004.6i 0.467396 + 0.809553i
\(959\) 48551.0 + 84092.9i 1.63482 + 2.83160i
\(960\) 0 0
\(961\) 14836.8 25698.1i 0.498029 0.862612i
\(962\) 12546.2 0.420484
\(963\) 4631.51 + 36381.4i 0.154983 + 1.21742i
\(964\) −147.774 −0.00493721
\(965\) 0 0
\(966\) 29971.8 10102.6i 0.998268 0.336488i
\(967\) 22178.5 + 38414.3i 0.737552 + 1.27748i 0.953595 + 0.301094i \(0.0973516\pi\)
−0.216043 + 0.976384i \(0.569315\pi\)
\(968\) 6456.39 + 11182.8i 0.214376 + 0.371310i
\(969\) −5348.80 4711.04i −0.177325 0.156182i
\(970\) 0 0
\(971\) −650.540 −0.0215003 −0.0107502 0.999942i \(-0.503422\pi\)
−0.0107502 + 0.999942i \(0.503422\pi\)
\(972\) −1147.42 20933.0i −0.0378639 0.690769i
\(973\) −5991.83 −0.197420
\(974\) 4175.31 7231.85i 0.137357 0.237909i
\(975\) 0 0
\(976\) −332.899 576.598i −0.0109179 0.0189103i
\(977\) 25837.5 + 44751.9i 0.846075 + 1.46544i 0.884684 + 0.466190i \(0.154374\pi\)
−0.0386096 + 0.999254i \(0.512293\pi\)
\(978\) 10908.5 3676.94i 0.356662 0.120220i
\(979\) −21546.9 + 37320.3i −0.703414 + 1.21835i
\(980\) 0 0
\(981\) 1669.03 + 13110.5i 0.0543202 + 0.426695i
\(982\) −17068.1 −0.554649
\(983\) 11759.5 20368.0i 0.381556 0.660874i −0.609729 0.792610i \(-0.708722\pi\)
0.991285 + 0.131736i \(0.0420551\pi\)
\(984\) −9657.43 + 48014.4i −0.312874 + 1.55553i
\(985\) 0 0
\(986\) −1857.62 3217.49i −0.0599987 0.103921i
\(987\) 8287.95 41205.7i 0.267283 1.32887i
\(988\) 2540.03 4399.46i 0.0817905 0.141665i
\(989\) 38436.6 1.23581
\(990\) 0 0
\(991\) −27732.9 −0.888966 −0.444483 0.895787i \(-0.646613\pi\)
−0.444483 + 0.895787i \(0.646613\pi\)
\(992\) −1013.94 + 1756.20i −0.0324523 + 0.0562090i
\(993\) −46136.6 + 15551.3i −1.47442 + 0.496986i
\(994\) −1758.92 3046.53i −0.0561262 0.0972135i
\(995\) 0 0
\(996\) −11274.6 9930.30i −0.358685 0.315917i
\(997\) −17163.9 + 29728.7i −0.545221 + 0.944351i 0.453372 + 0.891322i \(0.350221\pi\)
−0.998593 + 0.0530293i \(0.983112\pi\)
\(998\) −16283.9 −0.516489
\(999\) 32263.5 47621.6i 1.02179 1.50819i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.4.e.d.151.5 14
5.2 odd 4 225.4.k.d.124.9 28
5.3 odd 4 225.4.k.d.124.6 28
5.4 even 2 45.4.e.c.16.3 14
9.2 odd 6 2025.4.a.ba.1.5 7
9.4 even 3 inner 225.4.e.d.76.5 14
9.7 even 3 2025.4.a.bb.1.3 7
15.14 odd 2 135.4.e.c.46.5 14
45.4 even 6 45.4.e.c.31.3 yes 14
45.13 odd 12 225.4.k.d.49.9 28
45.14 odd 6 135.4.e.c.91.5 14
45.22 odd 12 225.4.k.d.49.6 28
45.29 odd 6 405.4.a.n.1.3 7
45.34 even 6 405.4.a.m.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.3 14 5.4 even 2
45.4.e.c.31.3 yes 14 45.4 even 6
135.4.e.c.46.5 14 15.14 odd 2
135.4.e.c.91.5 14 45.14 odd 6
225.4.e.d.76.5 14 9.4 even 3 inner
225.4.e.d.151.5 14 1.1 even 1 trivial
225.4.k.d.49.6 28 45.22 odd 12
225.4.k.d.49.9 28 45.13 odd 12
225.4.k.d.124.6 28 5.3 odd 4
225.4.k.d.124.9 28 5.2 odd 4
405.4.a.m.1.5 7 45.34 even 6
405.4.a.n.1.3 7 45.29 odd 6
2025.4.a.ba.1.5 7 9.2 odd 6
2025.4.a.bb.1.3 7 9.7 even 3