Properties

Label 198.4.f.d.37.2
Level $198$
Weight $4$
Character 198.37
Analytic conductor $11.682$
Analytic rank $0$
Dimension $8$
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] = [198,4,Mod(37,198)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(198, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("198.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 198.f (of order \(5\), degree \(4\), 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: \(11.6823781811\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 22)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 37.2
Root \(-4.79501 - 3.48378i\) of defining polynomial
Character \(\chi\) \(=\) 198.37
Dual form 198.4.f.d.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61803 - 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} +(10.3036 - 7.48598i) q^{5} +(7.24988 + 22.3128i) q^{7} +(2.47214 - 7.60845i) q^{8} +O(q^{10})\) \(q+(-1.61803 - 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} +(10.3036 - 7.48598i) q^{5} +(7.24988 + 22.3128i) q^{7} +(2.47214 - 7.60845i) q^{8} -25.4718 q^{10} +(3.69653 + 36.2951i) q^{11} +(-9.27574 - 6.73922i) q^{13} +(14.4998 - 44.6257i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-52.9924 + 38.5012i) q^{17} +(-2.24041 + 6.89528i) q^{19} +(41.2143 + 29.9439i) q^{20} +(36.6864 - 63.0723i) q^{22} +104.072 q^{23} +(11.4965 - 35.3825i) q^{25} +(7.08604 + 21.8086i) q^{26} +(-75.9218 + 55.1604i) q^{28} +(39.3536 + 121.118i) q^{29} +(233.653 + 169.759i) q^{31} +32.0000 q^{32} +131.004 q^{34} +(241.733 + 175.629i) q^{35} +(-26.3908 - 81.2224i) q^{37} +(11.7310 - 8.52303i) q^{38} +(-31.4849 - 96.9006i) q^{40} +(41.8544 - 128.815i) q^{41} +353.691 q^{43} +(-133.506 + 58.9257i) q^{44} +(-168.393 - 122.344i) q^{46} +(41.5948 - 128.016i) q^{47} +(-167.810 + 121.921i) q^{49} +(-60.1964 + 43.7352i) q^{50} +(14.1721 - 43.6171i) q^{52} +(405.666 + 294.734i) q^{53} +(309.792 + 346.297i) q^{55} +187.689 q^{56} +(78.7073 - 242.236i) q^{58} +(-201.373 - 619.763i) q^{59} +(-295.928 + 215.004i) q^{61} +(-178.495 - 549.352i) q^{62} +(-51.7771 - 37.6183i) q^{64} -146.023 q^{65} -294.576 q^{67} +(-211.969 - 154.005i) q^{68} +(-184.668 - 568.349i) q^{70} +(107.151 - 77.8500i) q^{71} +(145.080 + 446.511i) q^{73} +(-52.7815 + 162.445i) q^{74} -29.0005 q^{76} +(-783.048 + 345.616i) q^{77} +(-330.105 - 239.836i) q^{79} +(-62.9698 + 193.801i) q^{80} +(-219.152 + 159.224i) q^{82} +(-1099.89 + 799.119i) q^{83} +(-257.791 + 793.400i) q^{85} +(-572.283 - 415.788i) q^{86} +(285.288 + 61.6016i) q^{88} +260.255 q^{89} +(83.1232 - 255.827i) q^{91} +(128.641 + 395.915i) q^{92} +(-217.793 + 158.236i) q^{94} +(28.5337 + 87.8177i) q^{95} +(-1144.38 - 831.440i) q^{97} +414.848 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8} - 100 q^{10} + 155 q^{11} + 7 q^{13} - 2 q^{14} - 32 q^{16} - 161 q^{17} - 272 q^{19} - 20 q^{20} - 628 q^{23} - 17 q^{25} - 96 q^{26} + 16 q^{28} - 33 q^{29} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} + 49 q^{37} + 576 q^{38} + 240 q^{40} - 361 q^{41} + 1442 q^{43} - 620 q^{44} - 416 q^{46} + 1069 q^{47} - 709 q^{49} + 76 q^{50} - 192 q^{52} + 281 q^{53} - 7 q^{55} - 48 q^{56} - 66 q^{58} + 128 q^{59} - 617 q^{61} - 1044 q^{62} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} + 34 q^{70} - 115 q^{71} - 1487 q^{73} + 98 q^{74} - 128 q^{76} - 553 q^{77} + 71 q^{79} + 480 q^{80} + 658 q^{82} - 1942 q^{83} - 329 q^{85} - 2426 q^{86} + 560 q^{88} + 2202 q^{89} + 4523 q^{91} + 2088 q^{92} - 1332 q^{94} + 793 q^{95} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(155\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 1.17557i −0.572061 0.415627i
\(3\) 0 0
\(4\) 1.23607 + 3.80423i 0.154508 + 0.475528i
\(5\) 10.3036 7.48598i 0.921579 0.669566i −0.0223375 0.999750i \(-0.507111\pi\)
0.943917 + 0.330184i \(0.107111\pi\)
\(6\) 0 0
\(7\) 7.24988 + 22.3128i 0.391457 + 1.20478i 0.931687 + 0.363263i \(0.118337\pi\)
−0.540230 + 0.841518i \(0.681663\pi\)
\(8\) 2.47214 7.60845i 0.109254 0.336249i
\(9\) 0 0
\(10\) −25.4718 −0.805490
\(11\) 3.69653 + 36.2951i 0.101322 + 0.994854i
\(12\) 0 0
\(13\) −9.27574 6.73922i −0.197894 0.143779i 0.484425 0.874833i \(-0.339029\pi\)
−0.682320 + 0.731054i \(0.739029\pi\)
\(14\) 14.4998 44.6257i 0.276802 0.851908i
\(15\) 0 0
\(16\) −12.9443 + 9.40456i −0.202254 + 0.146946i
\(17\) −52.9924 + 38.5012i −0.756032 + 0.549289i −0.897691 0.440626i \(-0.854756\pi\)
0.141659 + 0.989916i \(0.454756\pi\)
\(18\) 0 0
\(19\) −2.24041 + 6.89528i −0.0270519 + 0.0832571i −0.963671 0.267092i \(-0.913937\pi\)
0.936619 + 0.350349i \(0.113937\pi\)
\(20\) 41.2143 + 29.9439i 0.460790 + 0.334783i
\(21\) 0 0
\(22\) 36.6864 63.0723i 0.355525 0.611230i
\(23\) 104.072 0.943504 0.471752 0.881731i \(-0.343622\pi\)
0.471752 + 0.881731i \(0.343622\pi\)
\(24\) 0 0
\(25\) 11.4965 35.3825i 0.0919719 0.283060i
\(26\) 7.08604 + 21.8086i 0.0534495 + 0.164501i
\(27\) 0 0
\(28\) −75.9218 + 55.1604i −0.512424 + 0.372298i
\(29\) 39.3536 + 121.118i 0.251993 + 0.775554i 0.994407 + 0.105613i \(0.0336805\pi\)
−0.742415 + 0.669941i \(0.766319\pi\)
\(30\) 0 0
\(31\) 233.653 + 169.759i 1.35372 + 0.983536i 0.998817 + 0.0486336i \(0.0154867\pi\)
0.354905 + 0.934903i \(0.384513\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) 131.004 0.660796
\(35\) 241.733 + 175.629i 1.16744 + 0.848194i
\(36\) 0 0
\(37\) −26.3908 81.2224i −0.117260 0.360889i 0.875152 0.483849i \(-0.160761\pi\)
−0.992412 + 0.122960i \(0.960761\pi\)
\(38\) 11.7310 8.52303i 0.0500792 0.0363847i
\(39\) 0 0
\(40\) −31.4849 96.9006i −0.124455 0.383033i
\(41\) 41.8544 128.815i 0.159428 0.490670i −0.839154 0.543893i \(-0.816950\pi\)
0.998583 + 0.0532236i \(0.0169496\pi\)
\(42\) 0 0
\(43\) 353.691 1.25436 0.627178 0.778876i \(-0.284210\pi\)
0.627178 + 0.778876i \(0.284210\pi\)
\(44\) −133.506 + 58.9257i −0.457426 + 0.201895i
\(45\) 0 0
\(46\) −168.393 122.344i −0.539742 0.392146i
\(47\) 41.5948 128.016i 0.129090 0.397298i −0.865534 0.500850i \(-0.833021\pi\)
0.994624 + 0.103552i \(0.0330208\pi\)
\(48\) 0 0
\(49\) −167.810 + 121.921i −0.489241 + 0.355454i
\(50\) −60.1964 + 43.7352i −0.170261 + 0.123702i
\(51\) 0 0
\(52\) 14.1721 43.6171i 0.0377945 0.116319i
\(53\) 405.666 + 294.734i 1.05137 + 0.763864i 0.972472 0.233019i \(-0.0748603\pi\)
0.0788966 + 0.996883i \(0.474860\pi\)
\(54\) 0 0
\(55\) 309.792 + 346.297i 0.759497 + 0.848994i
\(56\) 187.689 0.447875
\(57\) 0 0
\(58\) 78.7073 242.236i 0.178186 0.548399i
\(59\) −201.373 619.763i −0.444349 1.36756i −0.883196 0.469003i \(-0.844613\pi\)
0.438848 0.898561i \(-0.355387\pi\)
\(60\) 0 0
\(61\) −295.928 + 215.004i −0.621143 + 0.451287i −0.853320 0.521387i \(-0.825415\pi\)
0.232178 + 0.972673i \(0.425415\pi\)
\(62\) −178.495 549.352i −0.365628 1.12529i
\(63\) 0 0
\(64\) −51.7771 37.6183i −0.101127 0.0734732i
\(65\) −146.023 −0.278645
\(66\) 0 0
\(67\) −294.576 −0.537136 −0.268568 0.963261i \(-0.586550\pi\)
−0.268568 + 0.963261i \(0.586550\pi\)
\(68\) −211.969 154.005i −0.378016 0.274645i
\(69\) 0 0
\(70\) −184.668 568.349i −0.315315 0.970438i
\(71\) 107.151 77.8500i 0.179106 0.130128i −0.494620 0.869109i \(-0.664693\pi\)
0.673726 + 0.738981i \(0.264693\pi\)
\(72\) 0 0
\(73\) 145.080 + 446.511i 0.232607 + 0.715892i 0.997430 + 0.0716507i \(0.0228267\pi\)
−0.764822 + 0.644241i \(0.777173\pi\)
\(74\) −52.7815 + 162.445i −0.0829153 + 0.255187i
\(75\) 0 0
\(76\) −29.0005 −0.0437709
\(77\) −783.048 + 345.616i −1.15892 + 0.511514i
\(78\) 0 0
\(79\) −330.105 239.836i −0.470124 0.341565i 0.327366 0.944898i \(-0.393839\pi\)
−0.797489 + 0.603333i \(0.793839\pi\)
\(80\) −62.9698 + 193.801i −0.0880030 + 0.270845i
\(81\) 0 0
\(82\) −219.152 + 159.224i −0.295138 + 0.214431i
\(83\) −1099.89 + 799.119i −1.45457 + 1.05680i −0.469827 + 0.882758i \(0.655684\pi\)
−0.984738 + 0.174045i \(0.944316\pi\)
\(84\) 0 0
\(85\) −257.791 + 793.400i −0.328957 + 1.01243i
\(86\) −572.283 415.788i −0.717569 0.521344i
\(87\) 0 0
\(88\) 285.288 + 61.6016i 0.345589 + 0.0746222i
\(89\) 260.255 0.309966 0.154983 0.987917i \(-0.450468\pi\)
0.154983 + 0.987917i \(0.450468\pi\)
\(90\) 0 0
\(91\) 83.1232 255.827i 0.0957547 0.294703i
\(92\) 128.641 + 395.915i 0.145779 + 0.448663i
\(93\) 0 0
\(94\) −217.793 + 158.236i −0.238975 + 0.173626i
\(95\) 28.5337 + 87.8177i 0.0308157 + 0.0948411i
\(96\) 0 0
\(97\) −1144.38 831.440i −1.19788 0.870309i −0.203803 0.979012i \(-0.565330\pi\)
−0.994074 + 0.108703i \(0.965330\pi\)
\(98\) 414.848 0.427612
\(99\) 0 0
\(100\) 148.814 0.148814
\(101\) −150.976 109.691i −0.148740 0.108066i 0.510927 0.859624i \(-0.329302\pi\)
−0.659666 + 0.751559i \(0.729302\pi\)
\(102\) 0 0
\(103\) −362.450 1115.51i −0.346731 1.06713i −0.960651 0.277760i \(-0.910408\pi\)
0.613919 0.789369i \(-0.289592\pi\)
\(104\) −74.2059 + 53.9138i −0.0699662 + 0.0508335i
\(105\) 0 0
\(106\) −309.901 953.779i −0.283965 0.873954i
\(107\) 220.241 677.831i 0.198986 0.612415i −0.800921 0.598770i \(-0.795656\pi\)
0.999907 0.0136452i \(-0.00434354\pi\)
\(108\) 0 0
\(109\) 1247.22 1.09598 0.547989 0.836486i \(-0.315394\pi\)
0.547989 + 0.836486i \(0.315394\pi\)
\(110\) −94.1574 924.503i −0.0816141 0.801344i
\(111\) 0 0
\(112\) −303.687 220.642i −0.256212 0.186149i
\(113\) 303.455 933.939i 0.252625 0.777501i −0.741663 0.670773i \(-0.765963\pi\)
0.994288 0.106728i \(-0.0340374\pi\)
\(114\) 0 0
\(115\) 1072.32 779.084i 0.869513 0.631739i
\(116\) −412.117 + 299.420i −0.329863 + 0.239659i
\(117\) 0 0
\(118\) −402.747 + 1239.53i −0.314202 + 0.967014i
\(119\) −1243.26 903.281i −0.957727 0.695829i
\(120\) 0 0
\(121\) −1303.67 + 268.332i −0.979468 + 0.201602i
\(122\) 731.574 0.542899
\(123\) 0 0
\(124\) −356.990 + 1098.70i −0.258538 + 0.795697i
\(125\) 345.533 + 1063.44i 0.247244 + 0.760937i
\(126\) 0 0
\(127\) 1254.52 911.460i 0.876538 0.636842i −0.0557950 0.998442i \(-0.517769\pi\)
0.932333 + 0.361600i \(0.117769\pi\)
\(128\) 39.5542 + 121.735i 0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) 236.270 + 171.660i 0.159402 + 0.115812i
\(131\) −742.114 −0.494953 −0.247476 0.968894i \(-0.579601\pi\)
−0.247476 + 0.968894i \(0.579601\pi\)
\(132\) 0 0
\(133\) −170.096 −0.110896
\(134\) 476.633 + 346.294i 0.307275 + 0.223248i
\(135\) 0 0
\(136\) 161.930 + 498.370i 0.102099 + 0.314227i
\(137\) 417.192 303.108i 0.260169 0.189024i −0.450053 0.893002i \(-0.648595\pi\)
0.710222 + 0.703978i \(0.248595\pi\)
\(138\) 0 0
\(139\) 761.160 + 2342.61i 0.464466 + 1.42948i 0.859653 + 0.510878i \(0.170680\pi\)
−0.395187 + 0.918601i \(0.629320\pi\)
\(140\) −369.335 + 1136.70i −0.222961 + 0.686203i
\(141\) 0 0
\(142\) −264.893 −0.156544
\(143\) 210.313 361.576i 0.122988 0.211444i
\(144\) 0 0
\(145\) 1312.17 + 953.348i 0.751516 + 0.546008i
\(146\) 290.160 893.021i 0.164478 0.506212i
\(147\) 0 0
\(148\) 276.368 200.793i 0.153495 0.111521i
\(149\) −351.726 + 255.544i −0.193386 + 0.140503i −0.680265 0.732966i \(-0.738135\pi\)
0.486879 + 0.873469i \(0.338135\pi\)
\(150\) 0 0
\(151\) −241.340 + 742.768i −0.130066 + 0.400302i −0.994790 0.101945i \(-0.967493\pi\)
0.864724 + 0.502247i \(0.167493\pi\)
\(152\) 46.9238 + 34.0921i 0.0250396 + 0.0181924i
\(153\) 0 0
\(154\) 1673.29 + 361.311i 0.875570 + 0.189060i
\(155\) 3678.27 1.90610
\(156\) 0 0
\(157\) 161.425 496.815i 0.0820580 0.252549i −0.901607 0.432555i \(-0.857612\pi\)
0.983665 + 0.180007i \(0.0576120\pi\)
\(158\) 252.178 + 776.124i 0.126976 + 0.390792i
\(159\) 0 0
\(160\) 329.714 239.551i 0.162914 0.118364i
\(161\) 754.513 + 2322.15i 0.369341 + 1.13672i
\(162\) 0 0
\(163\) −2057.56 1494.91i −0.988716 0.718344i −0.0290761 0.999577i \(-0.509257\pi\)
−0.959639 + 0.281233i \(0.909257\pi\)
\(164\) 541.775 0.257960
\(165\) 0 0
\(166\) 2719.08 1.27134
\(167\) 1120.85 + 814.342i 0.519363 + 0.377339i 0.816364 0.577538i \(-0.195986\pi\)
−0.297001 + 0.954877i \(0.595986\pi\)
\(168\) 0 0
\(169\) −638.288 1964.45i −0.290527 0.894150i
\(170\) 1349.81 980.696i 0.608976 0.442447i
\(171\) 0 0
\(172\) 437.186 + 1345.52i 0.193809 + 0.596482i
\(173\) 137.052 421.804i 0.0602307 0.185371i −0.916414 0.400232i \(-0.868930\pi\)
0.976645 + 0.214861i \(0.0689297\pi\)
\(174\) 0 0
\(175\) 872.833 0.377029
\(176\) −389.189 435.050i −0.166683 0.186324i
\(177\) 0 0
\(178\) −421.101 305.948i −0.177319 0.128830i
\(179\) −116.388 + 358.205i −0.0485991 + 0.149573i −0.972411 0.233274i \(-0.925056\pi\)
0.923812 + 0.382846i \(0.125056\pi\)
\(180\) 0 0
\(181\) −2664.71 + 1936.02i −1.09429 + 0.795047i −0.980118 0.198414i \(-0.936421\pi\)
−0.114170 + 0.993461i \(0.536421\pi\)
\(182\) −435.238 + 316.219i −0.177264 + 0.128790i
\(183\) 0 0
\(184\) 257.281 791.830i 0.103082 0.317252i
\(185\) −879.949 639.320i −0.349703 0.254074i
\(186\) 0 0
\(187\) −1593.29 1781.04i −0.623065 0.696486i
\(188\) 538.415 0.208872
\(189\) 0 0
\(190\) 57.0674 175.635i 0.0217900 0.0670628i
\(191\) −707.730 2178.17i −0.268113 0.825166i −0.990960 0.134158i \(-0.957167\pi\)
0.722847 0.691008i \(-0.242833\pi\)
\(192\) 0 0
\(193\) 1863.49 1353.90i 0.695010 0.504954i −0.183293 0.983058i \(-0.558676\pi\)
0.878303 + 0.478104i \(0.158676\pi\)
\(194\) 874.228 + 2690.60i 0.323536 + 0.995740i
\(195\) 0 0
\(196\) −671.238 487.683i −0.244620 0.177727i
\(197\) 1041.86 0.376801 0.188400 0.982092i \(-0.439670\pi\)
0.188400 + 0.982092i \(0.439670\pi\)
\(198\) 0 0
\(199\) 3463.83 1.23389 0.616946 0.787005i \(-0.288370\pi\)
0.616946 + 0.787005i \(0.288370\pi\)
\(200\) −240.785 174.941i −0.0851305 0.0618509i
\(201\) 0 0
\(202\) 115.336 + 354.966i 0.0401732 + 0.123640i
\(203\) −2417.18 + 1756.18i −0.835728 + 0.607192i
\(204\) 0 0
\(205\) −533.054 1640.57i −0.181610 0.558939i
\(206\) −724.901 + 2231.02i −0.245176 + 0.754574i
\(207\) 0 0
\(208\) 183.447 0.0611527
\(209\) −258.547 55.8274i −0.0855696 0.0184769i
\(210\) 0 0
\(211\) −1692.45 1229.63i −0.552193 0.401192i 0.276400 0.961043i \(-0.410858\pi\)
−0.828593 + 0.559851i \(0.810858\pi\)
\(212\) −619.803 + 1907.56i −0.200794 + 0.617979i
\(213\) 0 0
\(214\) −1153.20 + 837.845i −0.368368 + 0.267635i
\(215\) 3644.28 2647.72i 1.15599 0.839875i
\(216\) 0 0
\(217\) −2093.85 + 6444.20i −0.655022 + 2.01595i
\(218\) −2018.04 1466.19i −0.626967 0.455518i
\(219\) 0 0
\(220\) −934.468 + 1606.57i −0.286372 + 0.492339i
\(221\) 751.012 0.228591
\(222\) 0 0
\(223\) 1144.45 3522.26i 0.343669 1.05770i −0.618623 0.785688i \(-0.712309\pi\)
0.962292 0.272017i \(-0.0876906\pi\)
\(224\) 231.996 + 714.011i 0.0692005 + 0.212977i
\(225\) 0 0
\(226\) −1588.91 + 1154.41i −0.467667 + 0.339780i
\(227\) 1499.81 + 4615.95i 0.438529 + 1.34965i 0.889426 + 0.457079i \(0.151104\pi\)
−0.450897 + 0.892576i \(0.648896\pi\)
\(228\) 0 0
\(229\) 1081.53 + 785.778i 0.312094 + 0.226750i 0.732795 0.680450i \(-0.238216\pi\)
−0.420700 + 0.907200i \(0.638216\pi\)
\(230\) −2650.91 −0.759983
\(231\) 0 0
\(232\) 1018.81 0.288311
\(233\) −4776.36 3470.23i −1.34296 0.975718i −0.999330 0.0366132i \(-0.988343\pi\)
−0.343631 0.939105i \(-0.611657\pi\)
\(234\) 0 0
\(235\) −529.748 1630.40i −0.147051 0.452576i
\(236\) 2108.81 1532.14i 0.581660 0.422601i
\(237\) 0 0
\(238\) 949.766 + 2923.08i 0.258673 + 0.796114i
\(239\) 1025.87 3157.30i 0.277649 0.854515i −0.710858 0.703336i \(-0.751693\pi\)
0.988506 0.151179i \(-0.0483070\pi\)
\(240\) 0 0
\(241\) −5275.95 −1.41018 −0.705091 0.709116i \(-0.749094\pi\)
−0.705091 + 0.709116i \(0.749094\pi\)
\(242\) 2424.83 + 1098.39i 0.644107 + 0.291764i
\(243\) 0 0
\(244\) −1183.71 860.017i −0.310571 0.225643i
\(245\) −816.340 + 2512.44i −0.212874 + 0.655158i
\(246\) 0 0
\(247\) 67.2503 48.8602i 0.0173240 0.0125866i
\(248\) 1869.23 1358.07i 0.478613 0.347733i
\(249\) 0 0
\(250\) 691.067 2126.88i 0.174828 0.538064i
\(251\) −1587.17 1153.15i −0.399129 0.289984i 0.370057 0.929009i \(-0.379338\pi\)
−0.769186 + 0.639025i \(0.779338\pi\)
\(252\) 0 0
\(253\) 384.707 + 3777.32i 0.0955980 + 0.938648i
\(254\) −3101.34 −0.766123
\(255\) 0 0
\(256\) 79.1084 243.470i 0.0193136 0.0594410i
\(257\) −1836.17 5651.15i −0.445669 1.37163i −0.881748 0.471721i \(-0.843633\pi\)
0.436078 0.899909i \(-0.356367\pi\)
\(258\) 0 0
\(259\) 1620.97 1177.71i 0.388890 0.282545i
\(260\) −180.494 555.504i −0.0430530 0.132503i
\(261\) 0 0
\(262\) 1200.77 + 872.408i 0.283143 + 0.205716i
\(263\) 1704.11 0.399544 0.199772 0.979842i \(-0.435980\pi\)
0.199772 + 0.979842i \(0.435980\pi\)
\(264\) 0 0
\(265\) 6386.18 1.48038
\(266\) 275.221 + 199.960i 0.0634395 + 0.0460915i
\(267\) 0 0
\(268\) −364.115 1120.63i −0.0829921 0.255423i
\(269\) −4728.97 + 3435.80i −1.07186 + 0.778752i −0.976246 0.216666i \(-0.930482\pi\)
−0.0956148 + 0.995418i \(0.530482\pi\)
\(270\) 0 0
\(271\) 1825.00 + 5616.79i 0.409082 + 1.25902i 0.917439 + 0.397877i \(0.130253\pi\)
−0.508357 + 0.861146i \(0.669747\pi\)
\(272\) 323.861 996.740i 0.0721946 0.222192i
\(273\) 0 0
\(274\) −1031.36 −0.227396
\(275\) 1326.71 + 286.474i 0.290922 + 0.0628182i
\(276\) 0 0
\(277\) −7186.00 5220.93i −1.55872 1.13247i −0.937051 0.349193i \(-0.886456\pi\)
−0.621667 0.783281i \(-0.713544\pi\)
\(278\) 1522.32 4685.22i 0.328427 1.01079i
\(279\) 0 0
\(280\) 1933.87 1405.04i 0.412752 0.299882i
\(281\) −6594.92 + 4791.49i −1.40007 + 1.01721i −0.405397 + 0.914141i \(0.632867\pi\)
−0.994674 + 0.103070i \(0.967133\pi\)
\(282\) 0 0
\(283\) 1812.06 5576.96i 0.380622 1.17143i −0.558985 0.829178i \(-0.688809\pi\)
0.939607 0.342256i \(-0.111191\pi\)
\(284\) 428.605 + 311.400i 0.0895529 + 0.0650640i
\(285\) 0 0
\(286\) −765.351 + 337.805i −0.158238 + 0.0698420i
\(287\) 3177.66 0.653559
\(288\) 0 0
\(289\) −192.352 + 592.000i −0.0391517 + 0.120497i
\(290\) −1002.41 3085.10i −0.202978 0.624701i
\(291\) 0 0
\(292\) −1519.30 + 1103.83i −0.304487 + 0.221223i
\(293\) −2353.65 7243.79i −0.469289 1.44432i −0.853507 0.521081i \(-0.825529\pi\)
0.384218 0.923242i \(-0.374471\pi\)
\(294\) 0 0
\(295\) −6714.40 4878.30i −1.32518 0.962798i
\(296\) −683.219 −0.134160
\(297\) 0 0
\(298\) 869.515 0.169026
\(299\) −965.348 701.367i −0.186714 0.135656i
\(300\) 0 0
\(301\) 2564.22 + 7891.85i 0.491026 + 1.51122i
\(302\) 1263.67 918.112i 0.240782 0.174938i
\(303\) 0 0
\(304\) −35.8466 110.324i −0.00676297 0.0208143i
\(305\) −1439.60 + 4430.62i −0.270266 + 0.831792i
\(306\) 0 0
\(307\) 4100.68 0.762339 0.381170 0.924505i \(-0.375521\pi\)
0.381170 + 0.924505i \(0.375521\pi\)
\(308\) −2282.70 2551.69i −0.422302 0.472065i
\(309\) 0 0
\(310\) −5951.57 4324.07i −1.09041 0.792228i
\(311\) −449.969 + 1384.86i −0.0820432 + 0.252503i −0.983661 0.180031i \(-0.942380\pi\)
0.901618 + 0.432534i \(0.142380\pi\)
\(312\) 0 0
\(313\) 2800.56 2034.72i 0.505740 0.367442i −0.305465 0.952203i \(-0.598812\pi\)
0.811205 + 0.584761i \(0.198812\pi\)
\(314\) −845.232 + 614.097i −0.151908 + 0.110368i
\(315\) 0 0
\(316\) 504.356 1552.25i 0.0897856 0.276332i
\(317\) 4038.86 + 2934.41i 0.715600 + 0.519914i 0.884975 0.465638i \(-0.154175\pi\)
−0.169375 + 0.985552i \(0.554175\pi\)
\(318\) 0 0
\(319\) −4250.52 + 1876.06i −0.746030 + 0.329277i
\(320\) −815.098 −0.142392
\(321\) 0 0
\(322\) 1509.03 4644.30i 0.261164 0.803779i
\(323\) −146.752 451.656i −0.0252802 0.0778043i
\(324\) 0 0
\(325\) −345.089 + 250.722i −0.0588988 + 0.0427925i
\(326\) 1571.84 + 4837.62i 0.267043 + 0.821874i
\(327\) 0 0
\(328\) −876.610 636.894i −0.147569 0.107215i
\(329\) 3157.95 0.529190
\(330\) 0 0
\(331\) 10199.3 1.69366 0.846832 0.531861i \(-0.178507\pi\)
0.846832 + 0.531861i \(0.178507\pi\)
\(332\) −4399.57 3196.48i −0.727283 0.528402i
\(333\) 0 0
\(334\) −856.250 2635.27i −0.140275 0.431723i
\(335\) −3035.18 + 2205.19i −0.495014 + 0.359648i
\(336\) 0 0
\(337\) −519.376 1598.48i −0.0839532 0.258381i 0.900264 0.435343i \(-0.143373\pi\)
−0.984218 + 0.176962i \(0.943373\pi\)
\(338\) −1276.58 + 3928.90i −0.205434 + 0.632260i
\(339\) 0 0
\(340\) −3336.92 −0.532264
\(341\) −5297.72 + 9107.99i −0.841312 + 1.44641i
\(342\) 0 0
\(343\) 2573.29 + 1869.61i 0.405087 + 0.294313i
\(344\) 874.371 2691.04i 0.137043 0.421776i
\(345\) 0 0
\(346\) −717.616 + 521.378i −0.111501 + 0.0810101i
\(347\) 8515.93 6187.19i 1.31746 0.957192i 0.317501 0.948258i \(-0.397156\pi\)
0.999960 0.00893386i \(-0.00284377\pi\)
\(348\) 0 0
\(349\) −1637.90 + 5040.94i −0.251217 + 0.773168i 0.743334 + 0.668920i \(0.233243\pi\)
−0.994551 + 0.104247i \(0.966757\pi\)
\(350\) −1412.27 1026.08i −0.215683 0.156703i
\(351\) 0 0
\(352\) 118.289 + 1161.44i 0.0179114 + 0.175867i
\(353\) 7438.40 1.12155 0.560773 0.827969i \(-0.310504\pi\)
0.560773 + 0.827969i \(0.310504\pi\)
\(354\) 0 0
\(355\) 521.257 1604.26i 0.0779309 0.239847i
\(356\) 321.693 + 990.068i 0.0478923 + 0.147397i
\(357\) 0 0
\(358\) 609.414 442.765i 0.0899680 0.0653656i
\(359\) −3136.93 9654.47i −0.461172 1.41934i −0.863734 0.503948i \(-0.831880\pi\)
0.402562 0.915393i \(-0.368120\pi\)
\(360\) 0 0
\(361\) 5506.52 + 4000.72i 0.802817 + 0.583281i
\(362\) 6587.52 0.956443
\(363\) 0 0
\(364\) 1075.97 0.154934
\(365\) 4837.41 + 3514.59i 0.693703 + 0.504005i
\(366\) 0 0
\(367\) 147.340 + 453.466i 0.0209567 + 0.0644980i 0.960988 0.276590i \(-0.0892045\pi\)
−0.940031 + 0.341088i \(0.889204\pi\)
\(368\) −1347.14 + 978.755i −0.190828 + 0.138644i
\(369\) 0 0
\(370\) 672.221 + 2068.88i 0.0944516 + 0.290692i
\(371\) −3635.32 + 11188.4i −0.508723 + 1.56569i
\(372\) 0 0
\(373\) −12738.5 −1.76829 −0.884146 0.467210i \(-0.845259\pi\)
−0.884146 + 0.467210i \(0.845259\pi\)
\(374\) 484.262 + 4754.82i 0.0669534 + 0.657395i
\(375\) 0 0
\(376\) −871.173 632.944i −0.119488 0.0868128i
\(377\) 451.207 1388.67i 0.0616402 0.189709i
\(378\) 0 0
\(379\) 1050.66 763.349i 0.142398 0.103458i −0.514306 0.857607i \(-0.671950\pi\)
0.656704 + 0.754149i \(0.271950\pi\)
\(380\) −298.809 + 217.097i −0.0403383 + 0.0293075i
\(381\) 0 0
\(382\) −1415.46 + 4356.34i −0.189584 + 0.583481i
\(383\) −542.501 394.150i −0.0723772 0.0525851i 0.551008 0.834500i \(-0.314243\pi\)
−0.623386 + 0.781915i \(0.714243\pi\)
\(384\) 0 0
\(385\) −5480.92 + 9422.95i −0.725541 + 1.24737i
\(386\) −4606.80 −0.607461
\(387\) 0 0
\(388\) 1748.46 5381.20i 0.228774 0.704095i
\(389\) −1617.98 4979.64i −0.210887 0.649043i −0.999420 0.0340509i \(-0.989159\pi\)
0.788533 0.614992i \(-0.210841\pi\)
\(390\) 0 0
\(391\) −5515.04 + 4006.91i −0.713319 + 0.518256i
\(392\) 512.780 + 1578.18i 0.0660697 + 0.203342i
\(393\) 0 0
\(394\) −1685.77 1224.79i −0.215553 0.156609i
\(395\) −5196.67 −0.661956
\(396\) 0 0
\(397\) 1751.64 0.221442 0.110721 0.993852i \(-0.464684\pi\)
0.110721 + 0.993852i \(0.464684\pi\)
\(398\) −5604.60 4071.98i −0.705862 0.512839i
\(399\) 0 0
\(400\) 183.944 + 566.121i 0.0229930 + 0.0707651i
\(401\) 2922.80 2123.54i 0.363984 0.264450i −0.390728 0.920506i \(-0.627777\pi\)
0.754712 + 0.656056i \(0.227777\pi\)
\(402\) 0 0
\(403\) −1023.26 3149.28i −0.126482 0.389273i
\(404\) 230.671 709.933i 0.0284067 0.0874269i
\(405\) 0 0
\(406\) 5975.60 0.730453
\(407\) 2850.42 1258.10i 0.347151 0.153223i
\(408\) 0 0
\(409\) 9137.83 + 6639.02i 1.10473 + 0.802637i 0.981826 0.189781i \(-0.0607779\pi\)
0.122908 + 0.992418i \(0.460778\pi\)
\(410\) −1066.11 + 3281.14i −0.128418 + 0.395229i
\(411\) 0 0
\(412\) 3795.63 2757.69i 0.453877 0.329761i
\(413\) 12368.8 8986.42i 1.47367 1.07069i
\(414\) 0 0
\(415\) −5350.63 + 16467.5i −0.632897 + 1.94786i
\(416\) −296.824 215.655i −0.0349831 0.0254167i
\(417\) 0 0
\(418\) 352.708 + 394.271i 0.0412716 + 0.0461349i
\(419\) 3680.45 0.429121 0.214560 0.976711i \(-0.431168\pi\)
0.214560 + 0.976711i \(0.431168\pi\)
\(420\) 0 0
\(421\) 2860.31 8803.14i 0.331124 1.01909i −0.637476 0.770470i \(-0.720021\pi\)
0.968600 0.248625i \(-0.0799786\pi\)
\(422\) 1292.91 + 3979.18i 0.149142 + 0.459013i
\(423\) 0 0
\(424\) 3245.33 2357.87i 0.371715 0.270067i
\(425\) 753.045 + 2317.63i 0.0859483 + 0.264522i
\(426\) 0 0
\(427\) −6942.80 5044.24i −0.786852 0.571681i
\(428\) 2850.85 0.321966
\(429\) 0 0
\(430\) −9009.14 −1.01037
\(431\) 2899.55 + 2106.64i 0.324052 + 0.235437i 0.737902 0.674907i \(-0.235816\pi\)
−0.413851 + 0.910345i \(0.635816\pi\)
\(432\) 0 0
\(433\) −2566.94 7900.24i −0.284895 0.876816i −0.986430 0.164181i \(-0.947502\pi\)
0.701535 0.712635i \(-0.252498\pi\)
\(434\) 10963.5 7965.47i 1.21260 0.881002i
\(435\) 0 0
\(436\) 1541.64 + 4744.69i 0.169338 + 0.521168i
\(437\) −233.165 + 717.608i −0.0255236 + 0.0785534i
\(438\) 0 0
\(439\) 11932.4 1.29727 0.648634 0.761101i \(-0.275341\pi\)
0.648634 + 0.761101i \(0.275341\pi\)
\(440\) 3400.63 1500.94i 0.368452 0.162624i
\(441\) 0 0
\(442\) −1215.16 882.867i −0.130768 0.0950084i
\(443\) −333.374 + 1026.02i −0.0357541 + 0.110040i −0.967341 0.253480i \(-0.918425\pi\)
0.931587 + 0.363519i \(0.118425\pi\)
\(444\) 0 0
\(445\) 2681.55 1948.26i 0.285658 0.207543i
\(446\) −5992.43 + 4353.75i −0.636210 + 0.462234i
\(447\) 0 0
\(448\) 463.993 1428.02i 0.0489321 0.150598i
\(449\) 10327.9 + 7503.63i 1.08553 + 0.788682i 0.978638 0.205589i \(-0.0659111\pi\)
0.106889 + 0.994271i \(0.465911\pi\)
\(450\) 0 0
\(451\) 4830.06 + 1042.94i 0.504298 + 0.108892i
\(452\) 3928.01 0.408756
\(453\) 0 0
\(454\) 2999.63 9231.91i 0.310087 0.954350i
\(455\) −1058.65 3258.19i −0.109077 0.335706i
\(456\) 0 0
\(457\) 9082.69 6598.96i 0.929695 0.675463i −0.0162235 0.999868i \(-0.505164\pi\)
0.945918 + 0.324406i \(0.105164\pi\)
\(458\) −826.216 2542.83i −0.0842938 0.259430i
\(459\) 0 0
\(460\) 4289.27 + 3116.33i 0.434757 + 0.315869i
\(461\) 2160.58 0.218283 0.109141 0.994026i \(-0.465190\pi\)
0.109141 + 0.994026i \(0.465190\pi\)
\(462\) 0 0
\(463\) 11469.5 1.15125 0.575627 0.817712i \(-0.304758\pi\)
0.575627 + 0.817712i \(0.304758\pi\)
\(464\) −1648.47 1197.68i −0.164931 0.119830i
\(465\) 0 0
\(466\) 3648.81 + 11229.9i 0.362721 + 1.11634i
\(467\) 1632.91 1186.38i 0.161803 0.117557i −0.503937 0.863740i \(-0.668116\pi\)
0.665741 + 0.746183i \(0.268116\pi\)
\(468\) 0 0
\(469\) −2135.64 6572.82i −0.210266 0.647131i
\(470\) −1059.50 + 3260.79i −0.103981 + 0.320019i
\(471\) 0 0
\(472\) −5213.26 −0.508389
\(473\) 1307.43 + 12837.2i 0.127094 + 1.24790i
\(474\) 0 0
\(475\) 218.216 + 158.543i 0.0210788 + 0.0153146i
\(476\) 1899.53 5846.16i 0.182910 0.562938i
\(477\) 0 0
\(478\) −5371.53 + 3902.64i −0.513991 + 0.373437i
\(479\) −5927.67 + 4306.71i −0.565433 + 0.410811i −0.833443 0.552605i \(-0.813634\pi\)
0.268011 + 0.963416i \(0.413634\pi\)
\(480\) 0 0
\(481\) −302.582 + 931.252i −0.0286831 + 0.0882774i
\(482\) 8536.67 + 6202.26i 0.806711 + 0.586110i
\(483\) 0 0
\(484\) −2632.22 4627.78i −0.247203 0.434615i
\(485\) −18015.3 −1.68667
\(486\) 0 0
\(487\) −1912.75 + 5886.85i −0.177978 + 0.547759i −0.999757 0.0220470i \(-0.992982\pi\)
0.821779 + 0.569806i \(0.192982\pi\)
\(488\) 904.276 + 2783.07i 0.0838824 + 0.258164i
\(489\) 0 0
\(490\) 4274.41 3105.54i 0.394078 0.286315i
\(491\) 3127.54 + 9625.57i 0.287462 + 0.884717i 0.985650 + 0.168802i \(0.0539900\pi\)
−0.698188 + 0.715914i \(0.746010\pi\)
\(492\) 0 0
\(493\) −6748.64 4903.17i −0.616518 0.447926i
\(494\) −166.252 −0.0151418
\(495\) 0 0
\(496\) −4620.98 −0.418323
\(497\) 2513.89 + 1826.45i 0.226888 + 0.164844i
\(498\) 0 0
\(499\) 791.952 + 2437.38i 0.0710474 + 0.218661i 0.980275 0.197638i \(-0.0633269\pi\)
−0.909228 + 0.416299i \(0.863327\pi\)
\(500\) −3618.47 + 2628.97i −0.323646 + 0.235143i
\(501\) 0 0
\(502\) 1212.49 + 3731.66i 0.107801 + 0.331777i
\(503\) −2658.01 + 8180.53i −0.235616 + 0.725152i 0.761423 + 0.648256i \(0.224501\pi\)
−0.997039 + 0.0768967i \(0.975499\pi\)
\(504\) 0 0
\(505\) −2376.74 −0.209432
\(506\) 3818.04 6564.08i 0.335440 0.576698i
\(507\) 0 0
\(508\) 5018.07 + 3645.84i 0.438269 + 0.318421i
\(509\) 4309.27 13262.6i 0.375255 1.15492i −0.568051 0.822993i \(-0.692302\pi\)
0.943306 0.331924i \(-0.107698\pi\)
\(510\) 0 0
\(511\) −8911.11 + 6474.30i −0.771437 + 0.560482i
\(512\) −414.217 + 300.946i −0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −3672.34 + 11302.3i −0.315136 + 0.969889i
\(515\) −12085.2 8780.41i −1.03405 0.751284i
\(516\) 0 0
\(517\) 4800.10 + 1036.47i 0.408333 + 0.0881704i
\(518\) −4007.27 −0.339902
\(519\) 0 0
\(520\) −360.988 + 1111.01i −0.0304431 + 0.0936941i
\(521\) 3736.89 + 11501.0i 0.314234 + 0.967113i 0.976069 + 0.217463i \(0.0697782\pi\)
−0.661834 + 0.749650i \(0.730222\pi\)
\(522\) 0 0
\(523\) 13504.0 9811.21i 1.12904 0.820295i 0.143484 0.989653i \(-0.454169\pi\)
0.985555 + 0.169358i \(0.0541693\pi\)
\(524\) −917.304 2823.17i −0.0764744 0.235364i
\(525\) 0 0
\(526\) −2757.31 2003.30i −0.228564 0.166061i
\(527\) −18917.8 −1.56370
\(528\) 0 0
\(529\) −1335.94 −0.109800
\(530\) −10333.1 7507.41i −0.846867 0.615285i
\(531\) 0 0
\(532\) −210.250 647.084i −0.0171344 0.0527343i
\(533\) −1256.34 + 912.785i −0.102098 + 0.0741784i
\(534\) 0 0
\(535\) −2804.97 8632.79i −0.226671 0.697623i
\(536\) −728.231 + 2241.26i −0.0586843 + 0.180612i
\(537\) 0 0
\(538\) 11690.7 0.936840
\(539\) −5045.44 5639.98i −0.403196 0.450707i
\(540\) 0 0
\(541\) −16725.1 12151.5i −1.32914 0.965679i −0.999769 0.0214796i \(-0.993162\pi\)
−0.329374 0.944200i \(-0.606838\pi\)
\(542\) 3650.01 11233.6i 0.289264 0.890264i
\(543\) 0 0
\(544\) −1695.76 + 1232.04i −0.133649 + 0.0971015i
\(545\) 12850.8 9336.63i 1.01003 0.733830i
\(546\) 0 0
\(547\) 2833.62 8721.00i 0.221494 0.681687i −0.777135 0.629334i \(-0.783328\pi\)
0.998629 0.0523532i \(-0.0166722\pi\)
\(548\) 1668.77 + 1212.43i 0.130084 + 0.0945119i
\(549\) 0 0
\(550\) −1809.89 2023.17i −0.140317 0.156851i
\(551\) −923.311 −0.0713873
\(552\) 0 0
\(553\) 2958.19 9104.37i 0.227477 0.700104i
\(554\) 5489.62 + 16895.3i 0.420995 + 1.29569i
\(555\) 0 0
\(556\) −7970.97 + 5791.25i −0.607994 + 0.441733i
\(557\) −6276.38 19316.7i −0.477449 1.46944i −0.842627 0.538498i \(-0.818992\pi\)
0.365178 0.930938i \(-0.381008\pi\)
\(558\) 0 0
\(559\) −3280.74 2383.60i −0.248230 0.180350i
\(560\) −4780.78 −0.360759
\(561\) 0 0
\(562\) 16303.5 1.22371
\(563\) 4500.68 + 3269.94i 0.336911 + 0.244780i 0.743357 0.668894i \(-0.233232\pi\)
−0.406446 + 0.913675i \(0.633232\pi\)
\(564\) 0 0
\(565\) −3864.78 11894.6i −0.287774 0.885678i
\(566\) −9488.08 + 6893.50i −0.704618 + 0.511935i
\(567\) 0 0
\(568\) −327.425 1007.71i −0.0241874 0.0744412i
\(569\) 7041.09 21670.3i 0.518766 1.59660i −0.257557 0.966263i \(-0.582917\pi\)
0.776323 0.630335i \(-0.217083\pi\)
\(570\) 0 0
\(571\) −11157.6 −0.817743 −0.408871 0.912592i \(-0.634078\pi\)
−0.408871 + 0.912592i \(0.634078\pi\)
\(572\) 1635.48 + 353.145i 0.119550 + 0.0258142i
\(573\) 0 0
\(574\) −5141.56 3735.56i −0.373876 0.271637i
\(575\) 1196.47 3682.34i 0.0867758 0.267068i
\(576\) 0 0
\(577\) −10055.4 + 7305.64i −0.725494 + 0.527102i −0.888135 0.459583i \(-0.847999\pi\)
0.162641 + 0.986685i \(0.447999\pi\)
\(578\) 1007.17 731.752i 0.0724788 0.0526589i
\(579\) 0 0
\(580\) −2004.82 + 6170.20i −0.143527 + 0.441730i
\(581\) −25804.7 18748.2i −1.84262 1.33874i
\(582\) 0 0
\(583\) −9197.84 + 15813.2i −0.653406 + 1.12335i
\(584\) 3755.91 0.266131
\(585\) 0 0
\(586\) −4707.30 + 14487.6i −0.331837 + 1.02129i
\(587\) −1889.62 5815.66i −0.132867 0.408923i 0.862385 0.506253i \(-0.168970\pi\)
−0.995252 + 0.0973299i \(0.968970\pi\)
\(588\) 0 0
\(589\) −1694.02 + 1230.77i −0.118507 + 0.0861005i
\(590\) 5129.35 + 15786.5i 0.357918 + 1.10156i
\(591\) 0 0
\(592\) 1105.47 + 803.172i 0.0767476 + 0.0557604i
\(593\) −7188.32 −0.497789 −0.248894 0.968531i \(-0.580067\pi\)
−0.248894 + 0.968531i \(0.580067\pi\)
\(594\) 0 0
\(595\) −19572.0 −1.34852
\(596\) −1406.90 1022.18i −0.0966930 0.0702516i
\(597\) 0 0
\(598\) 737.461 + 2269.67i 0.0504298 + 0.155207i
\(599\) −818.874 + 594.947i −0.0558569 + 0.0405824i −0.615363 0.788244i \(-0.710991\pi\)
0.559506 + 0.828826i \(0.310991\pi\)
\(600\) 0 0
\(601\) 4134.93 + 12726.0i 0.280644 + 0.863734i 0.987671 + 0.156547i \(0.0500362\pi\)
−0.707026 + 0.707187i \(0.749964\pi\)
\(602\) 5128.43 15783.7i 0.347208 1.06860i
\(603\) 0 0
\(604\) −3123.97 −0.210451
\(605\) −11423.7 + 12524.0i −0.767671 + 0.841611i
\(606\) 0 0
\(607\) −442.493 321.490i −0.0295885 0.0214973i 0.572893 0.819630i \(-0.305821\pi\)
−0.602481 + 0.798133i \(0.705821\pi\)
\(608\) −71.6932 + 220.649i −0.00478214 + 0.0147179i
\(609\) 0 0
\(610\) 7537.83 5476.55i 0.500324 0.363507i
\(611\) −1248.55 + 907.124i −0.0826692 + 0.0600627i
\(612\) 0 0
\(613\) 4247.62 13072.8i 0.279869 0.861349i −0.708020 0.706192i \(-0.750412\pi\)
0.987890 0.155157i \(-0.0495885\pi\)
\(614\) −6635.04 4820.64i −0.436105 0.316849i
\(615\) 0 0
\(616\) 693.798 + 6812.19i 0.0453797 + 0.445570i
\(617\) 3323.39 0.216847 0.108423 0.994105i \(-0.465420\pi\)
0.108423 + 0.994105i \(0.465420\pi\)
\(618\) 0 0
\(619\) −6699.20 + 20618.0i −0.434998 + 1.33879i 0.458091 + 0.888905i \(0.348533\pi\)
−0.893089 + 0.449881i \(0.851467\pi\)
\(620\) 4546.60 + 13993.0i 0.294509 + 0.906406i
\(621\) 0 0
\(622\) 2356.07 1711.79i 0.151881 0.110348i
\(623\) 1886.82 + 5807.03i 0.121338 + 0.373441i
\(624\) 0 0
\(625\) 15283.4 + 11104.0i 0.978138 + 0.710659i
\(626\) −6923.35 −0.442033
\(627\) 0 0
\(628\) 2089.53 0.132773
\(629\) 4525.67 + 3288.09i 0.286885 + 0.208434i
\(630\) 0 0
\(631\) −9236.13 28425.9i −0.582702 1.79337i −0.608311 0.793699i \(-0.708153\pi\)
0.0256092 0.999672i \(-0.491847\pi\)
\(632\) −2640.84 + 1918.68i −0.166214 + 0.120761i
\(633\) 0 0
\(634\) −3085.42 9495.94i −0.193277 0.594845i
\(635\) 6102.83 18782.6i 0.381391 1.17380i
\(636\) 0 0
\(637\) 2378.21 0.147925
\(638\) 9082.93 + 1961.26i 0.563631 + 0.121704i
\(639\) 0 0
\(640\) 1318.86 + 958.205i 0.0814569 + 0.0591819i
\(641\) −8398.45 + 25847.8i −0.517502 + 1.59271i 0.261181 + 0.965290i \(0.415888\pi\)
−0.778683 + 0.627418i \(0.784112\pi\)
\(642\) 0 0
\(643\) −13247.2 + 9624.69i −0.812474 + 0.590297i −0.914547 0.404480i \(-0.867452\pi\)
0.102073 + 0.994777i \(0.467452\pi\)
\(644\) −7901.36 + 5740.67i −0.483474 + 0.351264i
\(645\) 0 0
\(646\) −293.504 + 903.312i −0.0178758 + 0.0550160i
\(647\) 1850.76 + 1344.66i 0.112459 + 0.0817062i 0.642593 0.766207i \(-0.277859\pi\)
−0.530134 + 0.847914i \(0.677859\pi\)
\(648\) 0 0
\(649\) 21750.0 9599.84i 1.31550 0.580627i
\(650\) 853.107 0.0514794
\(651\) 0 0
\(652\) 3143.67 9675.23i 0.188828 0.581152i
\(653\) 354.419 + 1090.79i 0.0212396 + 0.0653689i 0.961115 0.276150i \(-0.0890587\pi\)
−0.939875 + 0.341519i \(0.889059\pi\)
\(654\) 0 0
\(655\) −7646.43 + 5555.45i −0.456138 + 0.331404i
\(656\) 669.670 + 2061.03i 0.0398571 + 0.122667i
\(657\) 0 0
\(658\) −5109.67 3712.40i −0.302729 0.219946i
\(659\) 377.923 0.0223396 0.0111698 0.999938i \(-0.496444\pi\)
0.0111698 + 0.999938i \(0.496444\pi\)
\(660\) 0 0
\(661\) −17500.4 −1.02978 −0.514892 0.857255i \(-0.672168\pi\)
−0.514892 + 0.857255i \(0.672168\pi\)
\(662\) −16502.8 11990.0i −0.968880 0.703932i
\(663\) 0 0
\(664\) 3360.97 + 10344.0i 0.196432 + 0.604556i
\(665\) −1752.60 + 1273.34i −0.102200 + 0.0742524i
\(666\) 0 0
\(667\) 4095.63 + 12605.0i 0.237756 + 0.731738i
\(668\) −1712.50 + 5270.53i −0.0991895 + 0.305274i
\(669\) 0 0
\(670\) 7503.38 0.432658
\(671\) −8897.51 9945.97i −0.511900 0.572221i
\(672\) 0 0
\(673\) 11739.3 + 8529.08i 0.672386 + 0.488517i 0.870823 0.491597i \(-0.163587\pi\)
−0.198437 + 0.980114i \(0.563587\pi\)
\(674\) −1038.75 + 3196.95i −0.0593639 + 0.182703i
\(675\) 0 0
\(676\) 6684.24 4856.38i 0.380305 0.276308i
\(677\) 379.518 275.736i 0.0215451 0.0156534i −0.576961 0.816772i \(-0.695761\pi\)
0.598506 + 0.801119i \(0.295761\pi\)
\(678\) 0 0
\(679\) 10255.2 31562.2i 0.579614 1.78387i
\(680\) 5399.25 + 3922.78i 0.304488 + 0.221223i
\(681\) 0 0
\(682\) 19279.0 8509.20i 1.08245 0.477763i
\(683\) 15892.3 0.890342 0.445171 0.895446i \(-0.353143\pi\)
0.445171 + 0.895446i \(0.353143\pi\)
\(684\) 0 0
\(685\) 2029.51 6246.19i 0.113202 0.348401i
\(686\) −1965.82 6050.17i −0.109410 0.336730i
\(687\) 0 0
\(688\) −4578.27 + 3326.31i −0.253699 + 0.184323i
\(689\) −1776.58 5467.75i −0.0982326 0.302329i
\(690\) 0 0
\(691\) 5020.47 + 3647.58i 0.276393 + 0.200811i 0.717343 0.696721i \(-0.245358\pi\)
−0.440950 + 0.897532i \(0.645358\pi\)
\(692\) 1774.04 0.0974553
\(693\) 0 0
\(694\) −21052.5 −1.15150
\(695\) 25379.4 + 18439.2i 1.38517 + 1.00639i
\(696\) 0 0
\(697\) 2741.55 + 8437.64i 0.148987 + 0.458534i
\(698\) 8576.16 6230.95i 0.465061 0.337887i
\(699\) 0 0
\(700\) 1078.88 + 3320.46i 0.0582541 + 0.179288i
\(701\) −578.646 + 1780.89i −0.0311771 + 0.0959533i −0.965434 0.260647i \(-0.916064\pi\)
0.934257 + 0.356600i \(0.116064\pi\)
\(702\) 0 0
\(703\) 619.178 0.0332187
\(704\) 1173.96 2018.31i 0.0628486 0.108051i
\(705\) 0 0
\(706\) −12035.6 8744.36i −0.641594 0.466145i
\(707\) 1352.95 4163.95i 0.0719702 0.221502i
\(708\) 0 0
\(709\) −4236.02 + 3077.65i −0.224383 + 0.163023i −0.694297 0.719688i \(-0.744285\pi\)
0.469915 + 0.882712i \(0.344285\pi\)
\(710\) −2729.34 + 1982.98i −0.144268 + 0.104817i
\(711\) 0 0
\(712\) 643.385 1980.14i 0.0338650 0.104226i
\(713\) 24316.8 + 17667.2i 1.27724 + 0.927970i
\(714\) 0 0
\(715\) −539.778 5299.92i −0.0282329 0.277211i
\(716\) −1506.56 −0.0786349
\(717\) 0 0
\(718\) −6273.85 + 19308.9i −0.326098 + 1.00363i
\(719\) 5338.20 + 16429.3i 0.276886 + 0.852169i 0.988714 + 0.149814i \(0.0478676\pi\)
−0.711828 + 0.702354i \(0.752132\pi\)
\(720\) 0 0
\(721\) 22262.4 16174.6i 1.14993 0.835470i
\(722\) −4206.61 12946.6i −0.216833 0.667345i
\(723\) 0 0
\(724\) −10658.8 7744.09i −0.547144 0.397523i
\(725\) 4737.89 0.242705
\(726\) 0 0
\(727\) 17292.7 0.882190 0.441095 0.897461i \(-0.354590\pi\)
0.441095 + 0.897461i \(0.354590\pi\)
\(728\) −1740.95 1264.88i −0.0886319 0.0643949i
\(729\) 0 0
\(730\) −3695.45 11373.4i −0.187363 0.576644i
\(731\) −18742.9 + 13617.5i −0.948333 + 0.689004i
\(732\) 0 0
\(733\) −4289.57 13201.9i −0.216151 0.665245i −0.999070 0.0431210i \(-0.986270\pi\)
0.782919 0.622124i \(-0.213730\pi\)
\(734\) 294.680 906.933i 0.0148186 0.0456069i
\(735\) 0 0
\(736\) 3330.32 0.166790
\(737\) −1088.91 10691.7i −0.0544239 0.534372i
\(738\) 0 0
\(739\) −5160.93 3749.64i −0.256898 0.186648i 0.451880 0.892079i \(-0.350753\pi\)
−0.708779 + 0.705431i \(0.750753\pi\)
\(740\) 1344.44 4137.77i 0.0667874 0.205550i
\(741\) 0 0
\(742\) 19034.8 13829.6i 0.941763 0.684231i
\(743\) 18641.9 13544.2i 0.920467 0.668758i −0.0231734 0.999731i \(-0.507377\pi\)
0.943640 + 0.330973i \(0.107377\pi\)
\(744\) 0 0
\(745\) −1711.04 + 5266.03i −0.0841443 + 0.258970i
\(746\) 20611.3 + 14975.0i 1.01157 + 0.734950i
\(747\) 0 0
\(748\) 4806.07 8262.74i 0.234930 0.403898i
\(749\) 16721.1 0.815720
\(750\) 0 0
\(751\) −6429.44 + 19787.8i −0.312401 + 0.961473i 0.664409 + 0.747369i \(0.268683\pi\)
−0.976811 + 0.214104i \(0.931317\pi\)
\(752\) 665.517 + 2048.25i 0.0322725 + 0.0993245i
\(753\) 0 0
\(754\) −2362.55 + 1716.49i −0.114110 + 0.0829059i
\(755\) 3073.68 + 9459.83i 0.148163 + 0.455998i
\(756\) 0 0
\(757\) 17667.1 + 12835.9i 0.848246 + 0.616287i 0.924662 0.380789i \(-0.124348\pi\)
−0.0764161 + 0.997076i \(0.524348\pi\)
\(758\) −2597.38 −0.124460
\(759\) 0 0
\(760\) 738.696 0.0352570
\(761\) −5775.94 4196.47i −0.275135 0.199897i 0.441658 0.897184i \(-0.354391\pi\)
−0.716793 + 0.697286i \(0.754391\pi\)
\(762\) 0 0
\(763\) 9042.17 + 27828.9i 0.429028 + 1.32041i
\(764\) 7411.45 5384.73i 0.350964 0.254990i
\(765\) 0 0
\(766\) 414.434 + 1275.50i 0.0195484 + 0.0601639i
\(767\) −2308.84 + 7105.86i −0.108693 + 0.334521i
\(768\) 0 0
\(769\) 15473.8 0.725618 0.362809 0.931864i \(-0.381818\pi\)
0.362809 + 0.931864i \(0.381818\pi\)
\(770\) 19945.7 8803.46i 0.933496 0.412019i
\(771\) 0 0
\(772\) 7453.96 + 5415.62i 0.347505 + 0.252477i
\(773\) −4709.69 + 14494.9i −0.219141 + 0.674446i 0.779693 + 0.626162i \(0.215375\pi\)
−0.998834 + 0.0482840i \(0.984625\pi\)
\(774\) 0 0
\(775\) 8692.69 6315.61i 0.402904 0.292727i
\(776\) −9155.04 + 6651.52i −0.423514 + 0.307701i
\(777\) 0 0
\(778\) −3235.97 + 9959.28i −0.149120 + 0.458943i
\(779\) 794.442 + 577.196i 0.0365389 + 0.0265471i
\(780\) 0 0
\(781\) 3221.66 + 3601.29i 0.147606 + 0.164999i
\(782\) 13633.9 0.623464
\(783\) 0 0
\(784\) 1025.56 3156.35i 0.0467183 0.143784i
\(785\) −2055.89 6327.39i −0.0934751 0.287687i
\(786\) 0 0
\(787\) −29190.5 + 21208.1i −1.32215 + 0.960595i −0.322243 + 0.946657i \(0.604437\pi\)
−0.999903 + 0.0139380i \(0.995563\pi\)
\(788\) 1287.82 + 3963.49i 0.0582189 + 0.179179i
\(789\) 0 0
\(790\) 8408.39 + 6109.05i 0.378680 + 0.275127i
\(791\) 23038.9 1.03561
\(792\) 0 0
\(793\) 4193.91 0.187806
\(794\) −2834.22 2059.18i −0.126678 0.0920373i
\(795\) 0 0
\(796\) 4281.53 + 13177.2i 0.190647 + 0.586751i
\(797\) 2737.30 1988.76i 0.121656 0.0883885i −0.525293 0.850921i \(-0.676044\pi\)
0.646950 + 0.762533i \(0.276044\pi\)
\(798\) 0 0
\(799\) 2724.55 + 8385.31i 0.120635 + 0.371278i
\(800\) 367.887 1132.24i 0.0162585 0.0500385i
\(801\) 0 0
\(802\) −7225.55 −0.318134
\(803\) −15669.9 + 6916.24i −0.688639 + 0.303946i
\(804\) 0 0
\(805\) 25157.7 + 18278.2i 1.10148 + 0.800274i
\(806\) −2046.53 + 6298.56i −0.0894365 + 0.275257i
\(807\) 0 0
\(808\) −1207.81 + 877.525i −0.0525874 + 0.0382070i
\(809\) 10905.8 7923.49i 0.473950 0.344345i −0.325028 0.945704i \(-0.605374\pi\)
0.798979 + 0.601359i \(0.205374\pi\)
\(810\) 0 0
\(811\) −6620.10 + 20374.6i −0.286638 + 0.882180i 0.699265 + 0.714862i \(0.253511\pi\)
−0.985903 + 0.167318i \(0.946489\pi\)
\(812\) −9668.72 7024.74i −0.417864 0.303596i
\(813\) 0 0
\(814\) −6091.07 1315.23i −0.262275 0.0566324i
\(815\) −32391.1 −1.39216
\(816\) 0 0
\(817\) −792.413 + 2438.80i −0.0339327 + 0.104434i
\(818\) −6980.68 21484.3i −0.298379 0.918315i
\(819\) 0 0
\(820\) 5582.21 4055.71i 0.237731 0.172722i
\(821\) −3295.61 10142.8i −0.140094 0.431166i 0.856253 0.516556i \(-0.172786\pi\)
−0.996348 + 0.0853901i \(0.972786\pi\)
\(822\) 0 0
\(823\) 9705.69 + 7051.60i 0.411080 + 0.298667i 0.774039 0.633138i \(-0.218233\pi\)
−0.362959 + 0.931805i \(0.618233\pi\)
\(824\) −9383.31 −0.396703
\(825\) 0 0
\(826\) −30577.2 −1.28804
\(827\) 33073.2 + 24029.1i 1.39065 + 1.01037i 0.995794 + 0.0916236i \(0.0292057\pi\)
0.394856 + 0.918743i \(0.370794\pi\)
\(828\) 0 0
\(829\) −10270.8 31610.2i −0.430301 1.32433i −0.897826 0.440350i \(-0.854855\pi\)
0.467526 0.883979i \(-0.345145\pi\)
\(830\) 28016.3 20355.0i 1.17164 0.851244i
\(831\) 0 0
\(832\) 226.753 + 697.874i 0.00944862 + 0.0290799i
\(833\) 4198.53 12921.7i 0.174634 0.537469i
\(834\) 0 0
\(835\) 17644.9 0.731288
\(836\) −107.201 1052.58i −0.00443497 0.0435456i
\(837\) 0 0
\(838\) −5955.09 4326.62i −0.245483 0.178354i
\(839\) 1968.00 6056.87i 0.0809806 0.249233i −0.902367 0.430969i \(-0.858172\pi\)
0.983347 + 0.181736i \(0.0581718\pi\)
\(840\) 0 0
\(841\) 6610.24 4802.62i 0.271034 0.196917i
\(842\) −14976.8 + 10881.3i −0.612987 + 0.445361i
\(843\) 0 0
\(844\) 2585.83 7958.36i 0.105460 0.324571i
\(845\) −21282.5 15462.6i −0.866437 0.629503i
\(846\) 0 0
\(847\) −15438.7 27143.2i −0.626305 1.10113i
\(848\) −8022.90 −0.324891
\(849\) 0 0
\(850\) 1506.09 4635.27i 0.0607746 0.187045i
\(851\) −2746.55 8453.01i −0.110635 0.340500i
\(852\) 0 0
\(853\) −2456.51 + 1784.76i −0.0986040 + 0.0716400i −0.635995 0.771693i \(-0.719410\pi\)
0.537391 + 0.843333i \(0.319410\pi\)
\(854\) 5303.83 + 16323.5i 0.212521 + 0.654074i
\(855\) 0 0
\(856\) −4612.78 3351.38i −0.184184 0.133818i
\(857\) 10184.8 0.405959 0.202979 0.979183i \(-0.434938\pi\)
0.202979 + 0.979183i \(0.434938\pi\)
\(858\) 0 0
\(859\) −34929.8 −1.38742 −0.693708 0.720256i \(-0.744024\pi\)
−0.693708 + 0.720256i \(0.744024\pi\)
\(860\) 14577.1 + 10590.9i 0.577994 + 0.419937i
\(861\) 0 0
\(862\) −2215.06 6817.25i −0.0875234 0.269369i
\(863\) −9937.36 + 7219.91i −0.391972 + 0.284784i −0.766263 0.642527i \(-0.777886\pi\)
0.374291 + 0.927311i \(0.377886\pi\)
\(864\) 0 0
\(865\) −1745.49 5372.06i −0.0686108 0.211162i
\(866\) −5133.89 + 15800.5i −0.201451 + 0.620003i
\(867\) 0 0
\(868\) −27103.3 −1.05985
\(869\) 7484.62 12867.8i 0.292173 0.502312i
\(870\) 0 0
\(871\) 2732.41 + 1985.21i 0.106296 + 0.0772288i
\(872\) 3083.29 9489.38i 0.119740 0.368522i
\(873\) 0 0
\(874\) 1220.87 887.012i 0.0472500 0.0343291i
\(875\) −21223.4 + 15419.7i −0.819977 + 0.595748i
\(876\) 0 0
\(877\) 5913.93 18201.2i 0.227707 0.700811i −0.770298 0.637684i \(-0.779893\pi\)
0.998005 0.0631273i \(-0.0201074\pi\)
\(878\) −19307.0 14027.3i −0.742117 0.539179i
\(879\) 0 0
\(880\) −7266.80 1569.10i −0.278368 0.0601074i
\(881\) 16737.0 0.640049 0.320024 0.947409i \(-0.396309\pi\)
0.320024 + 0.947409i \(0.396309\pi\)
\(882\) 0 0
\(883\) −5749.02 + 17693.7i −0.219105 + 0.674336i 0.779731 + 0.626114i \(0.215356\pi\)
−0.998837 + 0.0482222i \(0.984644\pi\)
\(884\) 928.301 + 2857.02i 0.0353192 + 0.108701i
\(885\) 0 0
\(886\) 1745.57 1268.23i 0.0661891 0.0480892i
\(887\) −4917.33 15134.0i −0.186142 0.572886i 0.813824 0.581111i \(-0.197382\pi\)
−0.999966 + 0.00822537i \(0.997382\pi\)
\(888\) 0 0
\(889\) 29432.4 + 21383.9i 1.11038 + 0.806740i
\(890\) −6629.16 −0.249674
\(891\) 0 0
\(892\) 14814.1 0.556068
\(893\) 789.514 + 573.616i 0.0295858 + 0.0214953i
\(894\) 0 0
\(895\) 1482.30 + 4562.06i 0.0553609 + 0.170383i
\(896\) −2429.50 + 1765.13i −0.0905846 + 0.0658135i
\(897\) 0 0
\(898\) −7889.78 24282.3i −0.293191 0.902349i
\(899\) −11365.8 + 34980.3i −0.421657 + 1.29773i
\(900\) 0 0
\(901\) −32844.8 −1.21445
\(902\) −6589.14 7365.59i −0.243231 0.271893i
\(903\) 0 0
\(904\) −6355.65 4617.65i −0.233834 0.169890i
\(905\) −12963.0 + 39895.9i −0.476136 + 1.46540i
\(906\) 0 0
\(907\) 18247.6 13257.7i 0.668029 0.485351i −0.201336 0.979522i \(-0.564528\pi\)
0.869365 + 0.494171i \(0.164528\pi\)
\(908\) −15706.3 + 11411.3i −0.574042 + 0.417066i
\(909\) 0 0
\(910\) −2117.30 + 6516.37i −0.0771294 + 0.237380i
\(911\) 39123.8 + 28425.1i 1.42286 + 1.03377i 0.991291 + 0.131692i \(0.0420410\pi\)
0.431572 + 0.902078i \(0.357959\pi\)
\(912\) 0 0
\(913\) −33069.9 36966.8i −1.19874 1.34000i
\(914\) −22453.6 −0.812583
\(915\) 0 0
\(916\) −1652.43 + 5085.66i −0.0596047 + 0.183444i
\(917\) −5380.24 16558.7i −0.193753 0.596310i
\(918\) 0 0
\(919\) −17000.9 + 12351.9i −0.610238 + 0.443364i −0.849498 0.527592i \(-0.823095\pi\)
0.239260 + 0.970955i \(0.423095\pi\)
\(920\) −3276.71 10084.7i −0.117424 0.361393i
\(921\) 0 0
\(922\) −3495.90 2539.92i −0.124871 0.0907243i
\(923\) −1518.56 −0.0541537
\(924\) 0 0
\(925\) −3177.26 −0.112938
\(926\) −18558.0 13483.2i −0.658588 0.478492i
\(927\) 0 0
\(928\) 1259.32 + 3875.78i 0.0445464 + 0.137100i
\(929\) 3980.09 2891.71i 0.140563 0.102125i −0.515282 0.857021i \(-0.672313\pi\)
0.655844 + 0.754896i \(0.272313\pi\)
\(930\) 0 0
\(931\) −464.715 1430.25i −0.0163592 0.0503485i
\(932\) 7297.63 22459.8i 0.256483 0.789372i
\(933\) 0 0
\(934\) −4036.78 −0.141421
\(935\) −29749.5 6423.74i −1.04055 0.224683i
\(936\) 0 0
\(937\) 13899.1 + 10098.3i 0.484594 + 0.352078i 0.803102 0.595842i \(-0.203182\pi\)
−0.318507 + 0.947920i \(0.603182\pi\)
\(938\) −4271.28 + 13145.6i −0.148680 + 0.457591i
\(939\) 0 0
\(940\) 5547.59 4030.56i 0.192492 0.139854i
\(941\) −41653.8 + 30263.2i −1.44301 + 1.04841i −0.455609 + 0.890180i \(0.650579\pi\)
−0.987402 + 0.158230i \(0.949421\pi\)
\(942\) 0 0
\(943\) 4355.89 13406.0i 0.150421 0.462949i
\(944\) 8435.24 + 6128.56i 0.290830 + 0.211300i
\(945\) 0 0
\(946\) 12975.6 22308.1i 0.445955 0.766700i
\(947\) −45107.8 −1.54784 −0.773920 0.633283i \(-0.781707\pi\)
−0.773920 + 0.633283i \(0.781707\pi\)
\(948\) 0 0
\(949\) 1663.41 5119.44i 0.0568983 0.175115i
\(950\) −166.702 513.056i −0.00569318 0.0175218i
\(951\) 0 0
\(952\) −9946.08 + 7226.25i −0.338608 + 0.246013i
\(953\) −7844.63 24143.3i −0.266645 0.820648i −0.991310 0.131547i \(-0.958006\pi\)
0.724665 0.689101i \(-0.241994\pi\)
\(954\) 0 0
\(955\) −23597.9 17144.9i −0.799591 0.580937i
\(956\) 13279.1 0.449245
\(957\) 0 0
\(958\) 14654.0 0.494206
\(959\) 9787.80 + 7111.25i 0.329577 + 0.239452i
\(960\) 0 0
\(961\) 16569.8 + 50996.6i 0.556201 + 1.71181i
\(962\) 1584.34 1151.09i 0.0530989 0.0385786i
\(963\) 0 0
\(964\) −6521.44 20070.9i −0.217885 0.670582i
\(965\) 9065.29 27900.1i 0.302406 0.930710i
\(966\) 0 0
\(967\) 26837.3 0.892482 0.446241 0.894913i \(-0.352762\pi\)
0.446241 + 0.894913i \(0.352762\pi\)
\(968\) −1181.26 + 10582.3i −0.0392223 + 0.351371i
\(969\) 0 0
\(970\) 29149.4 + 21178.3i 0.964878 + 0.701025i
\(971\) 1684.71 5185.01i 0.0556797 0.171364i −0.919349 0.393443i \(-0.871284\pi\)
0.975029 + 0.222078i \(0.0712840\pi\)
\(972\) 0 0
\(973\) −46752.0 + 33967.3i −1.54039 + 1.11916i
\(974\) 10015.3 7276.55i 0.329478 0.239379i
\(975\) 0 0
\(976\) 1808.55 5566.15i 0.0593138 0.182549i
\(977\) −2919.12 2120.87i −0.0955896 0.0694499i 0.538964 0.842329i \(-0.318816\pi\)
−0.634553 + 0.772879i \(0.718816\pi\)
\(978\) 0 0
\(979\) 962.040 + 9445.98i 0.0314065 + 0.308371i
\(980\) −10566.9 −0.344437
\(981\) 0 0
\(982\) 6255.08 19251.1i 0.203266 0.625589i
\(983\) −17937.1 55204.6i −0.581997 1.79120i −0.611009 0.791624i \(-0.709236\pi\)
0.0290114 0.999579i \(-0.490764\pi\)
\(984\) 0 0
\(985\) 10734.9 7799.38i 0.347252 0.252293i
\(986\) 5155.50 + 15867.0i 0.166516 + 0.512483i
\(987\) 0 0
\(988\) 269.001 + 195.441i 0.00866201 + 0.00629332i
\(989\) 36809.4 1.18349
\(990\) 0 0
\(991\) −18977.5 −0.608315 −0.304157 0.952622i \(-0.598375\pi\)
−0.304157 + 0.952622i \(0.598375\pi\)
\(992\) 7476.90 + 5432.29i 0.239306 + 0.173866i
\(993\) 0 0
\(994\) −1920.44 5910.51i −0.0612803 0.188602i
\(995\) 35689.8 25930.2i 1.13713 0.826173i
\(996\) 0 0
\(997\) −7496.82 23072.8i −0.238141 0.732923i −0.996689 0.0813060i \(-0.974091\pi\)
0.758548 0.651617i \(-0.225909\pi\)
\(998\) 1583.90 4874.76i 0.0502381 0.154617i
\(999\) 0 0
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 198.4.f.d.37.2 8
3.2 odd 2 22.4.c.b.15.2 yes 8
11.3 even 5 inner 198.4.f.d.91.2 8
11.5 even 5 2178.4.a.by.1.2 4
11.6 odd 10 2178.4.a.bt.1.2 4
12.11 even 2 176.4.m.b.81.1 8
33.2 even 10 242.4.c.n.27.1 8
33.5 odd 10 242.4.a.n.1.4 4
33.8 even 10 242.4.c.q.3.2 8
33.14 odd 10 22.4.c.b.3.2 8
33.17 even 10 242.4.a.o.1.4 4
33.20 odd 10 242.4.c.r.27.1 8
33.26 odd 10 242.4.c.r.9.1 8
33.29 even 10 242.4.c.n.9.1 8
33.32 even 2 242.4.c.q.81.2 8
132.47 even 10 176.4.m.b.113.1 8
132.71 even 10 1936.4.a.bn.1.1 4
132.83 odd 10 1936.4.a.bm.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.b.3.2 8 33.14 odd 10
22.4.c.b.15.2 yes 8 3.2 odd 2
176.4.m.b.81.1 8 12.11 even 2
176.4.m.b.113.1 8 132.47 even 10
198.4.f.d.37.2 8 1.1 even 1 trivial
198.4.f.d.91.2 8 11.3 even 5 inner
242.4.a.n.1.4 4 33.5 odd 10
242.4.a.o.1.4 4 33.17 even 10
242.4.c.n.9.1 8 33.29 even 10
242.4.c.n.27.1 8 33.2 even 10
242.4.c.q.3.2 8 33.8 even 10
242.4.c.q.81.2 8 33.32 even 2
242.4.c.r.9.1 8 33.26 odd 10
242.4.c.r.27.1 8 33.20 odd 10
1936.4.a.bm.1.1 4 132.83 odd 10
1936.4.a.bn.1.1 4 132.71 even 10
2178.4.a.bt.1.2 4 11.6 odd 10
2178.4.a.by.1.2 4 11.5 even 5