Properties

Label 198.4.f.d.181.2
Level $198$
Weight $4$
Character 198.181
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 181.2
Root \(2.22300 + 6.84169i\) of defining polynomial
Character \(\chi\) \(=\) 198.181
Dual form 198.4.f.d.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.618034 + 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-1.67119 + 5.14341i) q^{5} +(17.9196 - 13.0193i) q^{7} +(-6.47214 - 4.70228i) q^{8} +O(q^{10})\) \(q+(0.618034 + 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-1.67119 + 5.14341i) q^{5} +(17.9196 - 13.0193i) q^{7} +(-6.47214 - 4.70228i) q^{8} -10.8162 q^{10} +(11.0504 + 34.7691i) q^{11} +(23.7408 + 73.0668i) q^{13} +(35.8392 + 26.0387i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-18.3211 + 56.3866i) q^{17} +(-77.0690 - 55.9939i) q^{19} +(-6.68478 - 20.5736i) q^{20} +(-59.3052 + 42.5075i) q^{22} -142.484 q^{23} +(77.4654 + 56.2819i) q^{25} +(-124.309 + 90.3155i) q^{26} +(-27.3787 + 84.2629i) q^{28} +(-16.5188 + 12.0016i) q^{29} +(65.9146 + 202.864i) q^{31} +32.0000 q^{32} -118.577 q^{34} +(37.0167 + 113.926i) q^{35} +(117.775 - 85.5683i) q^{37} +(58.8755 - 181.200i) q^{38} +(35.0020 - 25.4304i) q^{40} +(67.0130 + 48.6878i) q^{41} -151.373 q^{43} +(-117.507 - 86.5342i) q^{44} +(-88.0599 - 271.020i) q^{46} +(73.1063 + 53.1148i) q^{47} +(45.6154 - 140.390i) q^{49} +(-59.1783 + 182.132i) q^{50} +(-248.617 - 180.631i) q^{52} +(72.5723 + 223.355i) q^{53} +(-197.299 - 1.26939i) q^{55} -177.199 q^{56} +(-33.0375 - 24.0032i) q^{58} +(244.726 - 177.804i) q^{59} +(-46.1299 + 141.973i) q^{61} +(-345.133 + 250.754i) q^{62} +(19.7771 + 60.8676i) q^{64} -415.488 q^{65} +826.236 q^{67} +(-73.2844 - 225.546i) q^{68} +(-193.822 + 140.820i) q^{70} +(277.796 - 854.967i) q^{71} +(111.639 - 81.1105i) q^{73} +(235.549 + 171.137i) q^{74} +381.050 q^{76} +(650.688 + 479.179i) q^{77} +(-94.0829 - 289.557i) q^{79} +(70.0039 + 50.8608i) q^{80} +(-51.1933 + 157.557i) q^{82} +(236.180 - 726.886i) q^{83} +(-259.401 - 188.466i) q^{85} +(-93.5536 - 287.928i) q^{86} +(91.9746 - 276.992i) q^{88} +313.100 q^{89} +(1376.71 + 1000.24i) q^{91} +(461.088 - 335.000i) q^{92} +(-55.8482 + 171.883i) q^{94} +(416.797 - 302.821i) q^{95} +(-180.004 - 553.996i) q^{97} +295.229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(155\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 + 1.90211i 0.218508 + 0.672499i
\(3\) 0 0
\(4\) −3.23607 + 2.35114i −0.404508 + 0.293893i
\(5\) −1.67119 + 5.14341i −0.149476 + 0.460041i −0.997559 0.0698226i \(-0.977757\pi\)
0.848083 + 0.529863i \(0.177757\pi\)
\(6\) 0 0
\(7\) 17.9196 13.0193i 0.967566 0.702978i 0.0126708 0.999920i \(-0.495967\pi\)
0.954896 + 0.296942i \(0.0959667\pi\)
\(8\) −6.47214 4.70228i −0.286031 0.207813i
\(9\) 0 0
\(10\) −10.8162 −0.342038
\(11\) 11.0504 + 34.7691i 0.302892 + 0.953025i
\(12\) 0 0
\(13\) 23.7408 + 73.0668i 0.506502 + 1.55885i 0.798231 + 0.602351i \(0.205769\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(14\) 35.8392 + 26.0387i 0.684173 + 0.497081i
\(15\) 0 0
\(16\) 4.94427 15.2169i 0.0772542 0.237764i
\(17\) −18.3211 + 56.3866i −0.261384 + 0.804456i 0.731121 + 0.682248i \(0.238997\pi\)
−0.992505 + 0.122208i \(0.961003\pi\)
\(18\) 0 0
\(19\) −77.0690 55.9939i −0.930571 0.676099i 0.0155616 0.999879i \(-0.495046\pi\)
−0.946133 + 0.323780i \(0.895046\pi\)
\(20\) −6.68478 20.5736i −0.0747381 0.230020i
\(21\) 0 0
\(22\) −59.3052 + 42.5075i −0.574724 + 0.411938i
\(23\) −142.484 −1.29174 −0.645868 0.763449i \(-0.723505\pi\)
−0.645868 + 0.763449i \(0.723505\pi\)
\(24\) 0 0
\(25\) 77.4654 + 56.2819i 0.619723 + 0.450255i
\(26\) −124.309 + 90.3155i −0.937651 + 0.681243i
\(27\) 0 0
\(28\) −27.3787 + 84.2629i −0.184789 + 0.568721i
\(29\) −16.5188 + 12.0016i −0.105774 + 0.0768496i −0.639415 0.768862i \(-0.720823\pi\)
0.533641 + 0.845711i \(0.320823\pi\)
\(30\) 0 0
\(31\) 65.9146 + 202.864i 0.381891 + 1.17534i 0.938711 + 0.344706i \(0.112021\pi\)
−0.556820 + 0.830633i \(0.687979\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) −118.577 −0.598110
\(35\) 37.0167 + 113.926i 0.178770 + 0.550198i
\(36\) 0 0
\(37\) 117.775 85.5683i 0.523298 0.380199i −0.294547 0.955637i \(-0.595169\pi\)
0.817845 + 0.575439i \(0.195169\pi\)
\(38\) 58.8755 181.200i 0.251339 0.773541i
\(39\) 0 0
\(40\) 35.0020 25.4304i 0.138357 0.100523i
\(41\) 67.0130 + 48.6878i 0.255260 + 0.185457i 0.708055 0.706157i \(-0.249573\pi\)
−0.452795 + 0.891615i \(0.649573\pi\)
\(42\) 0 0
\(43\) −151.373 −0.536841 −0.268420 0.963302i \(-0.586502\pi\)
−0.268420 + 0.963302i \(0.586502\pi\)
\(44\) −117.507 86.5342i −0.402609 0.296489i
\(45\) 0 0
\(46\) −88.0599 271.020i −0.282255 0.868691i
\(47\) 73.1063 + 53.1148i 0.226886 + 0.164842i 0.695421 0.718603i \(-0.255218\pi\)
−0.468535 + 0.883445i \(0.655218\pi\)
\(48\) 0 0
\(49\) 45.6154 140.390i 0.132989 0.409300i
\(50\) −59.1783 + 182.132i −0.167381 + 0.515147i
\(51\) 0 0
\(52\) −248.617 180.631i −0.663019 0.481712i
\(53\) 72.5723 + 223.355i 0.188086 + 0.578870i 0.999988 0.00492438i \(-0.00156749\pi\)
−0.811902 + 0.583794i \(0.801567\pi\)
\(54\) 0 0
\(55\) −197.299 1.26939i −0.483705 0.00311208i
\(56\) −177.199 −0.422842
\(57\) 0 0
\(58\) −33.0375 24.0032i −0.0747937 0.0543408i
\(59\) 244.726 177.804i 0.540009 0.392340i −0.284079 0.958801i \(-0.591688\pi\)
0.824089 + 0.566461i \(0.191688\pi\)
\(60\) 0 0
\(61\) −46.1299 + 141.973i −0.0968250 + 0.297997i −0.987725 0.156203i \(-0.950075\pi\)
0.890900 + 0.454200i \(0.150075\pi\)
\(62\) −345.133 + 250.754i −0.706967 + 0.513642i
\(63\) 0 0
\(64\) 19.7771 + 60.8676i 0.0386271 + 0.118882i
\(65\) −415.488 −0.792845
\(66\) 0 0
\(67\) 826.236 1.50658 0.753290 0.657689i \(-0.228466\pi\)
0.753290 + 0.657689i \(0.228466\pi\)
\(68\) −73.2844 225.546i −0.130692 0.402228i
\(69\) 0 0
\(70\) −193.822 + 140.820i −0.330945 + 0.240445i
\(71\) 277.796 854.967i 0.464342 1.42910i −0.395467 0.918480i \(-0.629417\pi\)
0.859808 0.510617i \(-0.170583\pi\)
\(72\) 0 0
\(73\) 111.639 81.1105i 0.178991 0.130045i −0.494682 0.869074i \(-0.664716\pi\)
0.673673 + 0.739029i \(0.264716\pi\)
\(74\) 235.549 + 171.137i 0.370028 + 0.268841i
\(75\) 0 0
\(76\) 381.050 0.575124
\(77\) 650.688 + 479.179i 0.963024 + 0.709189i
\(78\) 0 0
\(79\) −94.0829 289.557i −0.133989 0.412377i 0.861442 0.507856i \(-0.169562\pi\)
−0.995431 + 0.0954791i \(0.969562\pi\)
\(80\) 70.0039 + 50.8608i 0.0978335 + 0.0710802i
\(81\) 0 0
\(82\) −51.1933 + 157.557i −0.0689434 + 0.212186i
\(83\) 236.180 726.886i 0.312338 0.961279i −0.664498 0.747290i \(-0.731354\pi\)
0.976836 0.213989i \(-0.0686455\pi\)
\(84\) 0 0
\(85\) −259.401 188.466i −0.331012 0.240494i
\(86\) −93.5536 287.928i −0.117304 0.361024i
\(87\) 0 0
\(88\) 91.9746 276.992i 0.111415 0.335539i
\(89\) 313.100 0.372905 0.186452 0.982464i \(-0.440301\pi\)
0.186452 + 0.982464i \(0.440301\pi\)
\(90\) 0 0
\(91\) 1376.71 + 1000.24i 1.58591 + 1.15223i
\(92\) 461.088 335.000i 0.522519 0.379632i
\(93\) 0 0
\(94\) −55.8482 + 171.883i −0.0612798 + 0.188600i
\(95\) 416.797 302.821i 0.450131 0.327040i
\(96\) 0 0
\(97\) −180.004 553.996i −0.188419 0.579894i 0.811571 0.584253i \(-0.198612\pi\)
−0.999990 + 0.00435900i \(0.998612\pi\)
\(98\) 295.229 0.304313
\(99\) 0 0
\(100\) −383.010 −0.383010
\(101\) 43.7427 + 134.626i 0.0430947 + 0.132632i 0.970289 0.241949i \(-0.0777867\pi\)
−0.927194 + 0.374581i \(0.877787\pi\)
\(102\) 0 0
\(103\) −680.691 + 494.551i −0.651169 + 0.473102i −0.863669 0.504059i \(-0.831839\pi\)
0.212500 + 0.977161i \(0.431839\pi\)
\(104\) 189.927 584.534i 0.179075 0.551137i
\(105\) 0 0
\(106\) −379.993 + 276.081i −0.348191 + 0.252975i
\(107\) −52.1265 37.8721i −0.0470959 0.0342172i 0.563988 0.825783i \(-0.309266\pi\)
−0.611084 + 0.791566i \(0.709266\pi\)
\(108\) 0 0
\(109\) 1559.04 1.36999 0.684995 0.728547i \(-0.259804\pi\)
0.684995 + 0.728547i \(0.259804\pi\)
\(110\) −119.523 376.069i −0.103601 0.325971i
\(111\) 0 0
\(112\) −109.515 337.052i −0.0923944 0.284361i
\(113\) −1811.50 1316.13i −1.50807 1.09568i −0.967024 0.254684i \(-0.918029\pi\)
−0.541046 0.840993i \(-0.681971\pi\)
\(114\) 0 0
\(115\) 238.118 732.853i 0.193084 0.594251i
\(116\) 25.2384 77.6758i 0.0202011 0.0621726i
\(117\) 0 0
\(118\) 489.451 + 355.607i 0.381844 + 0.277426i
\(119\) 405.809 + 1248.95i 0.312609 + 0.962111i
\(120\) 0 0
\(121\) −1086.78 + 768.422i −0.816513 + 0.577327i
\(122\) −298.559 −0.221559
\(123\) 0 0
\(124\) −690.267 501.508i −0.499901 0.363200i
\(125\) −965.846 + 701.728i −0.691103 + 0.502116i
\(126\) 0 0
\(127\) 337.896 1039.94i 0.236090 0.726611i −0.760885 0.648887i \(-0.775235\pi\)
0.996975 0.0777237i \(-0.0247652\pi\)
\(128\) −103.554 + 75.2365i −0.0715077 + 0.0519534i
\(129\) 0 0
\(130\) −256.786 790.305i −0.173243 0.533187i
\(131\) 2466.16 1.64481 0.822403 0.568906i \(-0.192633\pi\)
0.822403 + 0.568906i \(0.192633\pi\)
\(132\) 0 0
\(133\) −2110.05 −1.37567
\(134\) 510.642 + 1571.60i 0.329200 + 1.01317i
\(135\) 0 0
\(136\) 383.722 278.790i 0.241940 0.175780i
\(137\) 300.762 925.650i 0.187561 0.577253i −0.812422 0.583069i \(-0.801852\pi\)
0.999983 + 0.00581676i \(0.00185154\pi\)
\(138\) 0 0
\(139\) 1021.82 742.396i 0.623523 0.453016i −0.230627 0.973042i \(-0.574078\pi\)
0.854150 + 0.520026i \(0.174078\pi\)
\(140\) −387.644 281.640i −0.234013 0.170021i
\(141\) 0 0
\(142\) 1797.93 1.06253
\(143\) −2278.12 + 1632.86i −1.33221 + 0.954872i
\(144\) 0 0
\(145\) −34.1230 105.020i −0.0195432 0.0601477i
\(146\) 223.278 + 162.221i 0.126566 + 0.0919555i
\(147\) 0 0
\(148\) −179.944 + 553.810i −0.0999411 + 0.307587i
\(149\) 151.214 465.390i 0.0831407 0.255881i −0.900841 0.434149i \(-0.857049\pi\)
0.983982 + 0.178268i \(0.0570493\pi\)
\(150\) 0 0
\(151\) −1381.62 1003.80i −0.744600 0.540983i 0.149549 0.988754i \(-0.452218\pi\)
−0.894148 + 0.447771i \(0.852218\pi\)
\(152\) 235.502 + 724.801i 0.125669 + 0.386770i
\(153\) 0 0
\(154\) −509.305 + 1533.83i −0.266500 + 0.802595i
\(155\) −1153.57 −0.597787
\(156\) 0 0
\(157\) −2072.48 1505.75i −1.05352 0.765424i −0.0806377 0.996743i \(-0.525696\pi\)
−0.972878 + 0.231320i \(0.925696\pi\)
\(158\) 492.624 357.913i 0.248045 0.180215i
\(159\) 0 0
\(160\) −53.4782 + 164.589i −0.0264239 + 0.0813244i
\(161\) −2553.25 + 1855.05i −1.24984 + 0.908063i
\(162\) 0 0
\(163\) 561.202 + 1727.20i 0.269673 + 0.829969i 0.990580 + 0.136936i \(0.0437256\pi\)
−0.720907 + 0.693032i \(0.756274\pi\)
\(164\) −331.330 −0.157759
\(165\) 0 0
\(166\) 1528.59 0.714707
\(167\) −117.094 360.379i −0.0542576 0.166988i 0.920256 0.391318i \(-0.127981\pi\)
−0.974513 + 0.224330i \(0.927981\pi\)
\(168\) 0 0
\(169\) −2997.71 + 2177.97i −1.36446 + 0.991336i
\(170\) 198.165 609.888i 0.0894032 0.275155i
\(171\) 0 0
\(172\) 489.853 355.899i 0.217157 0.157773i
\(173\) 41.0349 + 29.8136i 0.0180337 + 0.0131022i 0.596766 0.802416i \(-0.296452\pi\)
−0.578732 + 0.815518i \(0.696452\pi\)
\(174\) 0 0
\(175\) 2120.90 0.916142
\(176\) 583.714 + 3.75552i 0.249995 + 0.00160842i
\(177\) 0 0
\(178\) 193.506 + 595.551i 0.0814826 + 0.250778i
\(179\) 16.8824 + 12.2658i 0.00704944 + 0.00512172i 0.591304 0.806448i \(-0.298613\pi\)
−0.584255 + 0.811570i \(0.698613\pi\)
\(180\) 0 0
\(181\) −54.4344 + 167.532i −0.0223540 + 0.0687985i −0.961611 0.274416i \(-0.911516\pi\)
0.939257 + 0.343214i \(0.111516\pi\)
\(182\) −1051.71 + 3236.83i −0.428340 + 1.31830i
\(183\) 0 0
\(184\) 922.175 + 669.999i 0.369476 + 0.268440i
\(185\) 243.288 + 748.765i 0.0966861 + 0.297569i
\(186\) 0 0
\(187\) −2162.96 13.9161i −0.845837 0.00544197i
\(188\) −361.457 −0.140223
\(189\) 0 0
\(190\) 833.594 + 605.642i 0.318291 + 0.231252i
\(191\) −937.829 + 681.372i −0.355282 + 0.258128i −0.751082 0.660209i \(-0.770468\pi\)
0.395799 + 0.918337i \(0.370468\pi\)
\(192\) 0 0
\(193\) −397.068 + 1222.05i −0.148091 + 0.455777i −0.997396 0.0721261i \(-0.977022\pi\)
0.849305 + 0.527903i \(0.177022\pi\)
\(194\) 942.514 684.776i 0.348807 0.253423i
\(195\) 0 0
\(196\) 182.462 + 561.559i 0.0664947 + 0.204650i
\(197\) 2685.06 0.971078 0.485539 0.874215i \(-0.338623\pi\)
0.485539 + 0.874215i \(0.338623\pi\)
\(198\) 0 0
\(199\) −1333.54 −0.475036 −0.237518 0.971383i \(-0.576334\pi\)
−0.237518 + 0.971383i \(0.576334\pi\)
\(200\) −236.713 728.528i −0.0836907 0.257574i
\(201\) 0 0
\(202\) −229.040 + 166.407i −0.0797781 + 0.0579622i
\(203\) −139.757 + 430.126i −0.0483201 + 0.148714i
\(204\) 0 0
\(205\) −362.413 + 263.308i −0.123473 + 0.0897085i
\(206\) −1361.38 989.102i −0.460446 0.334534i
\(207\) 0 0
\(208\) 1229.23 0.409768
\(209\) 1095.22 3298.37i 0.362477 1.09164i
\(210\) 0 0
\(211\) −503.132 1548.48i −0.164156 0.505221i 0.834817 0.550528i \(-0.185574\pi\)
−0.998973 + 0.0453065i \(0.985574\pi\)
\(212\) −759.987 552.163i −0.246208 0.178881i
\(213\) 0 0
\(214\) 39.8211 122.557i 0.0127202 0.0391487i
\(215\) 252.974 778.573i 0.0802449 0.246968i
\(216\) 0 0
\(217\) 3822.32 + 2777.08i 1.19574 + 0.868757i
\(218\) 963.540 + 2965.47i 0.299354 + 0.921317i
\(219\) 0 0
\(220\) 641.457 459.770i 0.196577 0.140899i
\(221\) −4554.94 −1.38642
\(222\) 0 0
\(223\) 2126.25 + 1544.81i 0.638495 + 0.463894i 0.859333 0.511416i \(-0.170879\pi\)
−0.220837 + 0.975311i \(0.570879\pi\)
\(224\) 573.427 416.619i 0.171043 0.124270i
\(225\) 0 0
\(226\) 1383.87 4259.10i 0.407316 1.25359i
\(227\) 1377.40 1000.74i 0.402736 0.292605i −0.367919 0.929858i \(-0.619930\pi\)
0.770654 + 0.637253i \(0.219930\pi\)
\(228\) 0 0
\(229\) 1667.44 + 5131.85i 0.481168 + 1.48088i 0.837455 + 0.546506i \(0.184043\pi\)
−0.356287 + 0.934377i \(0.615957\pi\)
\(230\) 1541.13 0.441823
\(231\) 0 0
\(232\) 163.346 0.0462251
\(233\) 1870.85 + 5757.87i 0.526022 + 1.61893i 0.762286 + 0.647241i \(0.224077\pi\)
−0.236264 + 0.971689i \(0.575923\pi\)
\(234\) 0 0
\(235\) −395.366 + 287.250i −0.109748 + 0.0797368i
\(236\) −373.907 + 1150.77i −0.103133 + 0.317410i
\(237\) 0 0
\(238\) −2124.84 + 1543.79i −0.578711 + 0.420458i
\(239\) 2537.56 + 1843.65i 0.686783 + 0.498977i 0.875601 0.483035i \(-0.160466\pi\)
−0.188818 + 0.982012i \(0.560466\pi\)
\(240\) 0 0
\(241\) −6499.26 −1.73715 −0.868577 0.495555i \(-0.834965\pi\)
−0.868577 + 0.495555i \(0.834965\pi\)
\(242\) −2133.29 1592.27i −0.566666 0.422953i
\(243\) 0 0
\(244\) −184.520 567.893i −0.0484125 0.148998i
\(245\) 645.850 + 469.237i 0.168416 + 0.122361i
\(246\) 0 0
\(247\) 2261.61 6960.53i 0.582603 1.79307i
\(248\) 527.317 1622.91i 0.135019 0.415545i
\(249\) 0 0
\(250\) −1931.69 1403.46i −0.488684 0.355050i
\(251\) −1719.92 5293.38i −0.432512 1.33114i −0.895615 0.444831i \(-0.853264\pi\)
0.463102 0.886305i \(-0.346736\pi\)
\(252\) 0 0
\(253\) −1574.50 4954.04i −0.391256 1.23106i
\(254\) 2186.91 0.540232
\(255\) 0 0
\(256\) −207.108 150.473i −0.0505636 0.0367366i
\(257\) −4883.48 + 3548.05i −1.18530 + 0.861173i −0.992760 0.120116i \(-0.961673\pi\)
−0.192543 + 0.981289i \(0.561673\pi\)
\(258\) 0 0
\(259\) 996.430 3066.70i 0.239055 0.735735i
\(260\) 1344.55 976.870i 0.320712 0.233011i
\(261\) 0 0
\(262\) 1524.17 + 4690.92i 0.359403 + 1.10613i
\(263\) 708.442 0.166100 0.0830502 0.996545i \(-0.473534\pi\)
0.0830502 + 0.996545i \(0.473534\pi\)
\(264\) 0 0
\(265\) −1270.09 −0.294418
\(266\) −1304.08 4013.55i −0.300595 0.925137i
\(267\) 0 0
\(268\) −2673.76 + 1942.60i −0.609424 + 0.442773i
\(269\) 1486.28 4574.30i 0.336878 1.03680i −0.628912 0.777477i \(-0.716499\pi\)
0.965790 0.259327i \(-0.0835006\pi\)
\(270\) 0 0
\(271\) 4239.96 3080.51i 0.950404 0.690509i −0.000498618 1.00000i \(-0.500159\pi\)
0.950902 + 0.309491i \(0.100159\pi\)
\(272\) 767.444 + 557.581i 0.171078 + 0.124295i
\(273\) 0 0
\(274\) 1946.57 0.429185
\(275\) −1100.85 + 3315.34i −0.241395 + 0.726990i
\(276\) 0 0
\(277\) −1650.07 5078.40i −0.357918 1.10156i −0.954298 0.298856i \(-0.903395\pi\)
0.596380 0.802702i \(-0.296605\pi\)
\(278\) 2043.64 + 1484.79i 0.440897 + 0.320331i
\(279\) 0 0
\(280\) 296.133 911.405i 0.0632048 0.194524i
\(281\) 1013.57 3119.44i 0.215175 0.662242i −0.783966 0.620804i \(-0.786806\pi\)
0.999141 0.0414376i \(-0.0131938\pi\)
\(282\) 0 0
\(283\) 3960.54 + 2877.50i 0.831906 + 0.604415i 0.920098 0.391688i \(-0.128109\pi\)
−0.0881920 + 0.996103i \(0.528109\pi\)
\(284\) 1111.18 + 3419.87i 0.232171 + 0.714549i
\(285\) 0 0
\(286\) −4513.84 3324.08i −0.933248 0.687262i
\(287\) 1834.73 0.377354
\(288\) 0 0
\(289\) 1130.92 + 821.661i 0.230189 + 0.167242i
\(290\) 178.670 129.811i 0.0361789 0.0262855i
\(291\) 0 0
\(292\) −170.569 + 524.958i −0.0341843 + 0.105208i
\(293\) 5425.10 3941.57i 1.08170 0.785901i 0.103721 0.994606i \(-0.466925\pi\)
0.977978 + 0.208706i \(0.0669251\pi\)
\(294\) 0 0
\(295\) 505.532 + 1555.87i 0.0997736 + 0.307072i
\(296\) −1164.62 −0.228690
\(297\) 0 0
\(298\) 978.680 0.190246
\(299\) −3382.69 10410.8i −0.654267 2.01363i
\(300\) 0 0
\(301\) −2712.54 + 1970.77i −0.519429 + 0.377387i
\(302\) 1055.46 3248.38i 0.201109 0.618951i
\(303\) 0 0
\(304\) −1233.10 + 895.903i −0.232643 + 0.169025i
\(305\) −653.134 474.530i −0.122618 0.0890869i
\(306\) 0 0
\(307\) 9507.29 1.76746 0.883730 0.467998i \(-0.155025\pi\)
0.883730 + 0.467998i \(0.155025\pi\)
\(308\) −3232.29 20.7960i −0.597977 0.00384728i
\(309\) 0 0
\(310\) −712.946 2194.22i −0.130621 0.402011i
\(311\) 4666.47 + 3390.39i 0.850840 + 0.618171i 0.925378 0.379047i \(-0.123748\pi\)
−0.0745375 + 0.997218i \(0.523748\pi\)
\(312\) 0 0
\(313\) 1847.23 5685.18i 0.333583 1.02666i −0.633833 0.773470i \(-0.718519\pi\)
0.967416 0.253192i \(-0.0814806\pi\)
\(314\) 1583.23 4872.69i 0.284545 0.875739i
\(315\) 0 0
\(316\) 985.249 + 715.825i 0.175394 + 0.127431i
\(317\) −1616.76 4975.87i −0.286455 0.881617i −0.985959 0.166988i \(-0.946596\pi\)
0.699504 0.714628i \(-0.253404\pi\)
\(318\) 0 0
\(319\) −599.822 441.720i −0.105278 0.0775285i
\(320\) −346.118 −0.0604644
\(321\) 0 0
\(322\) −5106.50 3710.09i −0.883771 0.642097i
\(323\) 4569.29 3319.79i 0.787128 0.571882i
\(324\) 0 0
\(325\) −2273.24 + 6996.32i −0.387990 + 1.19411i
\(326\) −2938.49 + 2134.94i −0.499227 + 0.362710i
\(327\) 0 0
\(328\) −204.773 630.228i −0.0344717 0.106093i
\(329\) 2001.55 0.335408
\(330\) 0 0
\(331\) −3963.72 −0.658205 −0.329102 0.944294i \(-0.606746\pi\)
−0.329102 + 0.944294i \(0.606746\pi\)
\(332\) 944.719 + 2907.55i 0.156169 + 0.480639i
\(333\) 0 0
\(334\) 613.114 445.453i 0.100443 0.0729764i
\(335\) −1380.80 + 4249.67i −0.225198 + 0.693088i
\(336\) 0 0
\(337\) −4131.33 + 3001.58i −0.667797 + 0.485183i −0.869287 0.494308i \(-0.835422\pi\)
0.201490 + 0.979491i \(0.435422\pi\)
\(338\) −5995.43 4355.93i −0.964817 0.700981i
\(339\) 0 0
\(340\) 1282.55 0.204576
\(341\) −6325.03 + 4533.51i −1.00446 + 0.719952i
\(342\) 0 0
\(343\) 1337.35 + 4115.94i 0.210525 + 0.647929i
\(344\) 979.706 + 711.798i 0.153553 + 0.111563i
\(345\) 0 0
\(346\) −31.3479 + 96.4789i −0.00487073 + 0.0149906i
\(347\) −2331.77 + 7176.44i −0.360737 + 1.11023i 0.591871 + 0.806033i \(0.298390\pi\)
−0.952608 + 0.304201i \(0.901610\pi\)
\(348\) 0 0
\(349\) 2634.74 + 1914.25i 0.404109 + 0.293603i 0.771213 0.636578i \(-0.219650\pi\)
−0.367103 + 0.930180i \(0.619650\pi\)
\(350\) 1310.79 + 4034.19i 0.200184 + 0.616104i
\(351\) 0 0
\(352\) 353.612 + 1112.61i 0.0535442 + 0.168473i
\(353\) 6506.83 0.981087 0.490543 0.871417i \(-0.336798\pi\)
0.490543 + 0.871417i \(0.336798\pi\)
\(354\) 0 0
\(355\) 3933.19 + 2857.63i 0.588034 + 0.427232i
\(356\) −1013.21 + 736.142i −0.150843 + 0.109594i
\(357\) 0 0
\(358\) −12.8970 + 39.6929i −0.00190399 + 0.00585988i
\(359\) 3289.63 2390.06i 0.483622 0.351372i −0.319105 0.947720i \(-0.603382\pi\)
0.802726 + 0.596348i \(0.203382\pi\)
\(360\) 0 0
\(361\) 684.768 + 2107.50i 0.0998349 + 0.307260i
\(362\) −352.307 −0.0511514
\(363\) 0 0
\(364\) −6806.81 −0.980148
\(365\) 230.614 + 709.756i 0.0330709 + 0.101782i
\(366\) 0 0
\(367\) 1126.37 818.358i 0.160208 0.116398i −0.504793 0.863240i \(-0.668431\pi\)
0.665001 + 0.746843i \(0.268431\pi\)
\(368\) −704.479 + 2168.16i −0.0997922 + 0.307129i
\(369\) 0 0
\(370\) −1273.87 + 925.524i −0.178988 + 0.130042i
\(371\) 4208.39 + 3057.58i 0.588919 + 0.427875i
\(372\) 0 0
\(373\) 9440.30 1.31046 0.655228 0.755431i \(-0.272572\pi\)
0.655228 + 0.755431i \(0.272572\pi\)
\(374\) −1310.32 4122.80i −0.181163 0.570014i
\(375\) 0 0
\(376\) −223.393 687.533i −0.0306399 0.0943000i
\(377\) −1269.09 922.044i −0.173372 0.125962i
\(378\) 0 0
\(379\) 398.740 1227.20i 0.0540420 0.166324i −0.920393 0.390995i \(-0.872131\pi\)
0.974435 + 0.224671i \(0.0721308\pi\)
\(380\) −636.809 + 1959.90i −0.0859674 + 0.264581i
\(381\) 0 0
\(382\) −1875.66 1362.74i −0.251222 0.182524i
\(383\) 1746.84 + 5376.22i 0.233053 + 0.717264i 0.997374 + 0.0724273i \(0.0230745\pi\)
−0.764321 + 0.644836i \(0.776925\pi\)
\(384\) 0 0
\(385\) −3552.04 + 2545.95i −0.470205 + 0.337023i
\(386\) −2569.88 −0.338868
\(387\) 0 0
\(388\) 1885.03 + 1369.55i 0.246644 + 0.179197i
\(389\) −10386.2 + 7545.99i −1.35373 + 0.983539i −0.354909 + 0.934901i \(0.615488\pi\)
−0.998816 + 0.0486380i \(0.984512\pi\)
\(390\) 0 0
\(391\) 2610.46 8034.18i 0.337639 1.03915i
\(392\) −955.381 + 694.125i −0.123097 + 0.0894352i
\(393\) 0 0
\(394\) 1659.46 + 5107.28i 0.212188 + 0.653049i
\(395\) 1646.54 0.209738
\(396\) 0 0
\(397\) 7691.26 0.972326 0.486163 0.873868i \(-0.338396\pi\)
0.486163 + 0.873868i \(0.338396\pi\)
\(398\) −824.173 2536.54i −0.103799 0.319461i
\(399\) 0 0
\(400\) 1239.45 900.510i 0.154931 0.112564i
\(401\) −2406.06 + 7405.09i −0.299633 + 0.922176i 0.681993 + 0.731359i \(0.261114\pi\)
−0.981626 + 0.190817i \(0.938886\pi\)
\(402\) 0 0
\(403\) −13257.8 + 9632.33i −1.63875 + 1.19062i
\(404\) −458.080 332.814i −0.0564117 0.0409855i
\(405\) 0 0
\(406\) −904.523 −0.110568
\(407\) 4276.59 + 3149.36i 0.520842 + 0.383557i
\(408\) 0 0
\(409\) −2737.85 8426.25i −0.330998 1.01871i −0.968660 0.248391i \(-0.920098\pi\)
0.637662 0.770316i \(-0.279902\pi\)
\(410\) −724.826 526.617i −0.0873087 0.0634335i
\(411\) 0 0
\(412\) 1040.00 3200.80i 0.124362 0.382748i
\(413\) 2070.50 6372.33i 0.246689 0.759230i
\(414\) 0 0
\(415\) 3343.97 + 2429.54i 0.395540 + 0.287377i
\(416\) 759.706 + 2338.14i 0.0895377 + 0.275569i
\(417\) 0 0
\(418\) 6950.76 + 44.7200i 0.813332 + 0.00523284i
\(419\) −9469.08 −1.10405 −0.552023 0.833829i \(-0.686144\pi\)
−0.552023 + 0.833829i \(0.686144\pi\)
\(420\) 0 0
\(421\) −4189.04 3043.52i −0.484944 0.352333i 0.318292 0.947993i \(-0.396891\pi\)
−0.803237 + 0.595660i \(0.796891\pi\)
\(422\) 2634.43 1914.03i 0.303891 0.220790i
\(423\) 0 0
\(424\) 580.578 1786.84i 0.0664985 0.204661i
\(425\) −4592.79 + 3336.86i −0.524196 + 0.380850i
\(426\) 0 0
\(427\) 1021.77 + 3144.68i 0.115801 + 0.356398i
\(428\) 257.728 0.0291069
\(429\) 0 0
\(430\) 1637.28 0.183620
\(431\) −3233.42 9951.43i −0.361365 1.11217i −0.952226 0.305393i \(-0.901212\pi\)
0.590862 0.806773i \(-0.298788\pi\)
\(432\) 0 0
\(433\) −12813.4 + 9309.48i −1.42211 + 1.03322i −0.430688 + 0.902501i \(0.641729\pi\)
−0.991419 + 0.130721i \(0.958271\pi\)
\(434\) −2919.99 + 8986.81i −0.322959 + 0.993965i
\(435\) 0 0
\(436\) −5045.16 + 3665.52i −0.554173 + 0.402630i
\(437\) 10981.1 + 7978.23i 1.20205 + 0.873342i
\(438\) 0 0
\(439\) −4824.70 −0.524534 −0.262267 0.964995i \(-0.584470\pi\)
−0.262267 + 0.964995i \(0.584470\pi\)
\(440\) 1270.98 + 935.971i 0.137708 + 0.101411i
\(441\) 0 0
\(442\) −2815.11 8664.01i −0.302944 0.932364i
\(443\) 2899.02 + 2106.26i 0.310918 + 0.225895i 0.732290 0.680993i \(-0.238451\pi\)
−0.421372 + 0.906888i \(0.638451\pi\)
\(444\) 0 0
\(445\) −523.251 + 1610.40i −0.0557404 + 0.171551i
\(446\) −1624.31 + 4999.12i −0.172452 + 0.530752i
\(447\) 0 0
\(448\) 1146.85 + 833.238i 0.120946 + 0.0878723i
\(449\) 2409.09 + 7414.42i 0.253212 + 0.779306i 0.994177 + 0.107762i \(0.0343684\pi\)
−0.740965 + 0.671544i \(0.765632\pi\)
\(450\) 0 0
\(451\) −952.312 + 2868.00i −0.0994293 + 0.299443i
\(452\) 8956.57 0.932039
\(453\) 0 0
\(454\) 2754.79 + 2001.47i 0.284777 + 0.206903i
\(455\) −7445.37 + 5409.38i −0.767130 + 0.557353i
\(456\) 0 0
\(457\) 1034.60 3184.16i 0.105900 0.325927i −0.884041 0.467410i \(-0.845187\pi\)
0.989941 + 0.141483i \(0.0451871\pi\)
\(458\) −8730.83 + 6343.32i −0.890753 + 0.647170i
\(459\) 0 0
\(460\) 952.474 + 2931.41i 0.0965420 + 0.297126i
\(461\) −7171.96 −0.724580 −0.362290 0.932065i \(-0.618005\pi\)
−0.362290 + 0.932065i \(0.618005\pi\)
\(462\) 0 0
\(463\) 4034.74 0.404990 0.202495 0.979283i \(-0.435095\pi\)
0.202495 + 0.979283i \(0.435095\pi\)
\(464\) 100.954 + 310.703i 0.0101006 + 0.0310863i
\(465\) 0 0
\(466\) −9795.87 + 7117.12i −0.973788 + 0.707498i
\(467\) 3653.15 11243.2i 0.361986 1.11408i −0.589860 0.807505i \(-0.700817\pi\)
0.951847 0.306574i \(-0.0991827\pi\)
\(468\) 0 0
\(469\) 14805.8 10757.1i 1.45772 1.05909i
\(470\) −790.732 574.501i −0.0776037 0.0563824i
\(471\) 0 0
\(472\) −2419.98 −0.235993
\(473\) −1672.73 5263.10i −0.162605 0.511622i
\(474\) 0 0
\(475\) −2818.74 8675.18i −0.272279 0.837988i
\(476\) −4249.69 3087.58i −0.409210 0.297309i
\(477\) 0 0
\(478\) −1938.53 + 5966.17i −0.185494 + 0.570891i
\(479\) 2676.07 8236.09i 0.255267 0.785630i −0.738510 0.674242i \(-0.764470\pi\)
0.993777 0.111388i \(-0.0355296\pi\)
\(480\) 0 0
\(481\) 9048.27 + 6573.95i 0.857725 + 0.623173i
\(482\) −4016.76 12362.3i −0.379582 1.16823i
\(483\) 0 0
\(484\) 1710.22 5041.84i 0.160614 0.473501i
\(485\) 3150.25 0.294939
\(486\) 0 0
\(487\) −6009.10 4365.87i −0.559134 0.406235i 0.272008 0.962295i \(-0.412312\pi\)
−0.831142 + 0.556060i \(0.812312\pi\)
\(488\) 966.157 701.954i 0.0896227 0.0651147i
\(489\) 0 0
\(490\) −493.385 + 1518.48i −0.0454875 + 0.139996i
\(491\) −4485.10 + 3258.62i −0.412240 + 0.299510i −0.774508 0.632564i \(-0.782002\pi\)
0.362268 + 0.932074i \(0.382002\pi\)
\(492\) 0 0
\(493\) −374.086 1151.32i −0.0341744 0.105178i
\(494\) 14637.5 1.33314
\(495\) 0 0
\(496\) 3412.87 0.308956
\(497\) −6153.12 18937.4i −0.555342 1.70917i
\(498\) 0 0
\(499\) −16513.7 + 11997.9i −1.48147 + 1.07635i −0.504391 + 0.863476i \(0.668283\pi\)
−0.977079 + 0.212875i \(0.931717\pi\)
\(500\) 1475.68 4541.68i 0.131989 0.406220i
\(501\) 0 0
\(502\) 9005.63 6542.98i 0.800680 0.581728i
\(503\) −147.841 107.413i −0.0131052 0.00952148i 0.581213 0.813751i \(-0.302578\pi\)
−0.594319 + 0.804230i \(0.702578\pi\)
\(504\) 0 0
\(505\) −765.540 −0.0674576
\(506\) 8450.04 6056.64i 0.742392 0.532115i
\(507\) 0 0
\(508\) 1351.58 + 4159.75i 0.118045 + 0.363305i
\(509\) 3847.11 + 2795.09i 0.335010 + 0.243399i 0.742554 0.669787i \(-0.233614\pi\)
−0.407543 + 0.913186i \(0.633614\pi\)
\(510\) 0 0
\(511\) 944.519 2906.93i 0.0817673 0.251654i
\(512\) 158.217 486.941i 0.0136568 0.0420312i
\(513\) 0 0
\(514\) −9766.95 7096.11i −0.838136 0.608941i
\(515\) −1406.11 4327.56i −0.120312 0.370282i
\(516\) 0 0
\(517\) −1038.90 + 3128.78i −0.0883770 + 0.266158i
\(518\) 6449.03 0.547016
\(519\) 0 0
\(520\) 2689.09 + 1953.74i 0.226778 + 0.164764i
\(521\) −9490.70 + 6895.40i −0.798071 + 0.579833i −0.910348 0.413844i \(-0.864186\pi\)
0.112277 + 0.993677i \(0.464186\pi\)
\(522\) 0 0
\(523\) −106.252 + 327.011i −0.00888353 + 0.0273407i −0.955400 0.295315i \(-0.904575\pi\)
0.946517 + 0.322655i \(0.104575\pi\)
\(524\) −7980.67 + 5798.29i −0.665338 + 0.483396i
\(525\) 0 0
\(526\) 437.841 + 1347.54i 0.0362943 + 0.111702i
\(527\) −12646.4 −1.04533
\(528\) 0 0
\(529\) 8134.66 0.668584
\(530\) −784.956 2415.85i −0.0643327 0.197996i
\(531\) 0 0
\(532\) 6828.26 4961.02i 0.556471 0.404300i
\(533\) −1966.51 + 6052.31i −0.159811 + 0.491847i
\(534\) 0 0
\(535\) 281.906 204.816i 0.0227810 0.0165514i
\(536\) −5347.51 3885.20i −0.430928 0.313088i
\(537\) 0 0
\(538\) 9619.41 0.770859
\(539\) 5385.29 + 34.6480i 0.430354 + 0.00276882i
\(540\) 0 0
\(541\) −5328.62 16399.8i −0.423466 1.30329i −0.904455 0.426568i \(-0.859722\pi\)
0.480989 0.876726i \(-0.340278\pi\)
\(542\) 8479.93 + 6161.03i 0.672037 + 0.488263i
\(543\) 0 0
\(544\) −586.275 + 1804.37i −0.0462065 + 0.142209i
\(545\) −2605.46 + 8018.78i −0.204781 + 0.630251i
\(546\) 0 0
\(547\) 6183.49 + 4492.57i 0.483340 + 0.351167i 0.802617 0.596494i \(-0.203440\pi\)
−0.319277 + 0.947661i \(0.603440\pi\)
\(548\) 1203.05 + 3702.60i 0.0937804 + 0.288626i
\(549\) 0 0
\(550\) −6986.50 44.9500i −0.541646 0.00348486i
\(551\) 1945.10 0.150388
\(552\) 0 0
\(553\) −5455.77 3963.85i −0.419535 0.304810i
\(554\) 8639.89 6277.25i 0.662588 0.481399i
\(555\) 0 0
\(556\) −1561.20 + 4804.89i −0.119082 + 0.366498i
\(557\) 21120.3 15344.8i 1.60664 1.16729i 0.733684 0.679491i \(-0.237799\pi\)
0.872955 0.487800i \(-0.162201\pi\)
\(558\) 0 0
\(559\) −3593.72 11060.3i −0.271911 0.836855i
\(560\) 1916.62 0.144628
\(561\) 0 0
\(562\) 6559.94 0.492374
\(563\) 5585.14 + 17189.3i 0.418092 + 1.28675i 0.909456 + 0.415800i \(0.136498\pi\)
−0.491364 + 0.870954i \(0.663502\pi\)
\(564\) 0 0
\(565\) 9796.79 7117.79i 0.729476 0.529996i
\(566\) −3025.58 + 9311.78i −0.224690 + 0.691525i
\(567\) 0 0
\(568\) −5818.23 + 4227.19i −0.429802 + 0.312269i
\(569\) 6314.50 + 4587.76i 0.465233 + 0.338012i 0.795581 0.605848i \(-0.207166\pi\)
−0.330347 + 0.943859i \(0.607166\pi\)
\(570\) 0 0
\(571\) −13039.6 −0.955672 −0.477836 0.878449i \(-0.658579\pi\)
−0.477836 + 0.878449i \(0.658579\pi\)
\(572\) 3533.06 10640.2i 0.258260 0.777780i
\(573\) 0 0
\(574\) 1133.92 + 3489.86i 0.0824548 + 0.253770i
\(575\) −11037.6 8019.26i −0.800519 0.581611i
\(576\) 0 0
\(577\) −2957.12 + 9101.06i −0.213356 + 0.656642i 0.785910 + 0.618340i \(0.212195\pi\)
−0.999266 + 0.0383013i \(0.987805\pi\)
\(578\) −863.946 + 2658.95i −0.0621720 + 0.191346i
\(579\) 0 0
\(580\) 357.340 + 259.623i 0.0255823 + 0.0185866i
\(581\) −5231.34 16100.4i −0.373550 1.14967i
\(582\) 0 0
\(583\) −6963.88 + 4991.42i −0.494708 + 0.354586i
\(584\) −1103.95 −0.0782220
\(585\) 0 0
\(586\) 10850.2 + 7883.14i 0.764877 + 0.555716i
\(587\) 7869.31 5717.39i 0.553324 0.402013i −0.275686 0.961248i \(-0.588905\pi\)
0.829009 + 0.559235i \(0.188905\pi\)
\(588\) 0 0
\(589\) 6279.19 19325.4i 0.439269 1.35193i
\(590\) −2647.00 + 1923.16i −0.184704 + 0.134195i
\(591\) 0 0
\(592\) −719.775 2215.24i −0.0499706 0.153794i
\(593\) −6926.77 −0.479677 −0.239838 0.970813i \(-0.577094\pi\)
−0.239838 + 0.970813i \(0.577094\pi\)
\(594\) 0 0
\(595\) −7102.06 −0.489338
\(596\) 604.858 + 1861.56i 0.0415704 + 0.127940i
\(597\) 0 0
\(598\) 17712.0 12868.5i 1.21120 0.879987i
\(599\) 6793.63 20908.7i 0.463406 1.42622i −0.397570 0.917572i \(-0.630146\pi\)
0.860976 0.508646i \(-0.169854\pi\)
\(600\) 0 0
\(601\) 5957.01 4328.02i 0.404312 0.293750i −0.366983 0.930228i \(-0.619609\pi\)
0.771295 + 0.636478i \(0.219609\pi\)
\(602\) −5425.08 3941.55i −0.367292 0.266853i
\(603\) 0 0
\(604\) 6831.10 0.460188
\(605\) −2136.09 6873.93i −0.143544 0.461926i
\(606\) 0 0
\(607\) 3142.21 + 9670.72i 0.210113 + 0.646660i 0.999465 + 0.0327190i \(0.0104167\pi\)
−0.789352 + 0.613941i \(0.789583\pi\)
\(608\) −2466.21 1791.81i −0.164503 0.119519i
\(609\) 0 0
\(610\) 498.950 1535.61i 0.0331179 0.101926i
\(611\) −2145.32 + 6602.63i −0.142047 + 0.437175i
\(612\) 0 0
\(613\) −20293.8 14744.3i −1.33713 0.971479i −0.999544 0.0301824i \(-0.990391\pi\)
−0.337581 0.941296i \(-0.609609\pi\)
\(614\) 5875.83 + 18083.9i 0.386204 + 1.18861i
\(615\) 0 0
\(616\) −1958.11 6161.03i −0.128075 0.402979i
\(617\) 26335.5 1.71836 0.859178 0.511677i \(-0.170976\pi\)
0.859178 + 0.511677i \(0.170976\pi\)
\(618\) 0 0
\(619\) 19936.7 + 14484.9i 1.29455 + 0.940544i 0.999887 0.0150577i \(-0.00479321\pi\)
0.294661 + 0.955602i \(0.404793\pi\)
\(620\) 3733.03 2712.21i 0.241810 0.175685i
\(621\) 0 0
\(622\) −3564.87 + 10971.5i −0.229804 + 0.707264i
\(623\) 5610.62 4076.35i 0.360810 0.262144i
\(624\) 0 0
\(625\) 1703.48 + 5242.78i 0.109023 + 0.335538i
\(626\) 11955.5 0.763319
\(627\) 0 0
\(628\) 10246.9 0.651108
\(629\) 2667.14 + 8208.62i 0.169071 + 0.520348i
\(630\) 0 0
\(631\) −6031.48 + 4382.13i −0.380522 + 0.276465i −0.761561 0.648094i \(-0.775567\pi\)
0.381039 + 0.924559i \(0.375567\pi\)
\(632\) −752.663 + 2316.46i −0.0473724 + 0.145797i
\(633\) 0 0
\(634\) 8465.45 6150.51i 0.530293 0.385281i
\(635\) 4784.13 + 3475.88i 0.298980 + 0.217222i
\(636\) 0 0
\(637\) 11340.8 0.705397
\(638\) 469.491 1413.93i 0.0291338 0.0877397i
\(639\) 0 0
\(640\) −213.913 658.356i −0.0132120 0.0406622i
\(641\) −2247.99 1633.26i −0.138518 0.100639i 0.516368 0.856367i \(-0.327284\pi\)
−0.654887 + 0.755727i \(0.727284\pi\)
\(642\) 0 0
\(643\) 2335.46 7187.81i 0.143237 0.440839i −0.853543 0.521023i \(-0.825551\pi\)
0.996780 + 0.0801836i \(0.0255507\pi\)
\(644\) 3901.02 12006.1i 0.238698 0.734638i
\(645\) 0 0
\(646\) 9138.59 + 6639.57i 0.556584 + 0.404382i
\(647\) 8476.55 + 26088.1i 0.515066 + 1.58521i 0.783162 + 0.621817i \(0.213605\pi\)
−0.268096 + 0.963392i \(0.586395\pi\)
\(648\) 0 0
\(649\) 8886.37 + 6544.09i 0.537474 + 0.395806i
\(650\) −14712.7 −0.887817
\(651\) 0 0
\(652\) −5876.98 4269.88i −0.353007 0.256474i
\(653\) 230.350 167.359i 0.0138044 0.0100295i −0.580862 0.814002i \(-0.697284\pi\)
0.594666 + 0.803973i \(0.297284\pi\)
\(654\) 0 0
\(655\) −4121.44 + 12684.5i −0.245859 + 0.756677i
\(656\) 1072.21 779.004i 0.0638150 0.0463643i
\(657\) 0 0
\(658\) 1237.03 + 3807.18i 0.0732893 + 0.225561i
\(659\) −20747.0 −1.22639 −0.613193 0.789933i \(-0.710115\pi\)
−0.613193 + 0.789933i \(0.710115\pi\)
\(660\) 0 0
\(661\) −18908.8 −1.11266 −0.556328 0.830963i \(-0.687790\pi\)
−0.556328 + 0.830963i \(0.687790\pi\)
\(662\) −2449.71 7539.44i −0.143823 0.442642i
\(663\) 0 0
\(664\) −4946.61 + 3593.92i −0.289105 + 0.210047i
\(665\) 3526.30 10852.8i 0.205630 0.632865i
\(666\) 0 0
\(667\) 2353.66 1710.03i 0.136633 0.0992694i
\(668\) 1226.23 + 890.906i 0.0710242 + 0.0516021i
\(669\) 0 0
\(670\) −8936.74 −0.515308
\(671\) −5446.03 35.0388i −0.313326 0.00201589i
\(672\) 0 0
\(673\) 9229.07 + 28404.2i 0.528610 + 1.62689i 0.757065 + 0.653340i \(0.226633\pi\)
−0.228455 + 0.973554i \(0.573367\pi\)
\(674\) −8262.65 6003.17i −0.472204 0.343076i
\(675\) 0 0
\(676\) 4580.10 14096.1i 0.260588 0.802008i
\(677\) 5340.04 16435.0i 0.303153 0.933009i −0.677207 0.735793i \(-0.736810\pi\)
0.980360 0.197216i \(-0.0631901\pi\)
\(678\) 0 0
\(679\) −10438.3 7583.84i −0.589961 0.428632i
\(680\) 792.659 + 2439.55i 0.0447016 + 0.137577i
\(681\) 0 0
\(682\) −12532.3 9229.05i −0.703648 0.518180i
\(683\) −25104.0 −1.40641 −0.703204 0.710988i \(-0.748248\pi\)
−0.703204 + 0.710988i \(0.748248\pi\)
\(684\) 0 0
\(685\) 4258.37 + 3093.88i 0.237524 + 0.172571i
\(686\) −7002.45 + 5087.58i −0.389730 + 0.283156i
\(687\) 0 0
\(688\) −748.429 + 2303.43i −0.0414732 + 0.127641i
\(689\) −14596.9 + 10605.2i −0.807106 + 0.586397i
\(690\) 0 0
\(691\) −8085.06 24883.3i −0.445109 1.36990i −0.882364 0.470567i \(-0.844050\pi\)
0.437256 0.899337i \(-0.355950\pi\)
\(692\) −202.888 −0.0111454
\(693\) 0 0
\(694\) −15091.5 −0.825455
\(695\) 2110.79 + 6496.33i 0.115204 + 0.354561i
\(696\) 0 0
\(697\) −3973.09 + 2886.62i −0.215913 + 0.156870i
\(698\) −2012.76 + 6194.64i −0.109146 + 0.335917i
\(699\) 0 0
\(700\) −6863.37 + 4986.53i −0.370587 + 0.269248i
\(701\) −1229.26 893.108i −0.0662317 0.0481201i 0.554177 0.832399i \(-0.313033\pi\)
−0.620408 + 0.784279i \(0.713033\pi\)
\(702\) 0 0
\(703\) −13868.1 −0.744018
\(704\) −1897.77 + 1360.24i −0.101598 + 0.0728210i
\(705\) 0 0
\(706\) 4021.44 + 12376.7i 0.214375 + 0.659779i
\(707\) 2536.59 + 1842.94i 0.134934 + 0.0980354i
\(708\) 0 0
\(709\) −6716.14 + 20670.2i −0.355755 + 1.09490i 0.599816 + 0.800138i \(0.295240\pi\)
−0.955571 + 0.294762i \(0.904760\pi\)
\(710\) −3004.69 + 9247.49i −0.158823 + 0.488806i
\(711\) 0 0
\(712\) −2026.42 1472.28i −0.106662 0.0774946i
\(713\) −9391.77 28904.9i −0.493302 1.51823i
\(714\) 0 0
\(715\) −4591.29 14446.1i −0.240146 0.755601i
\(716\) −83.4712 −0.00435679
\(717\) 0 0
\(718\) 6579.26 + 4780.11i 0.341972 + 0.248457i
\(719\) −11384.4 + 8271.22i −0.590494 + 0.429019i −0.842492 0.538709i \(-0.818912\pi\)
0.251998 + 0.967728i \(0.418912\pi\)
\(720\) 0 0
\(721\) −5758.97 + 17724.3i −0.297469 + 0.915516i
\(722\) −3585.49 + 2605.01i −0.184817 + 0.134278i
\(723\) 0 0
\(724\) −217.737 670.127i −0.0111770 0.0343993i
\(725\) −1955.10 −0.100153
\(726\) 0 0
\(727\) 10409.2 0.531027 0.265513 0.964107i \(-0.414459\pi\)
0.265513 + 0.964107i \(0.414459\pi\)
\(728\) −4206.84 12947.3i −0.214170 0.659148i
\(729\) 0 0
\(730\) −1207.51 + 877.307i −0.0612218 + 0.0444803i
\(731\) 2773.32 8535.39i 0.140321 0.431865i
\(732\) 0 0
\(733\) 15690.8 11400.0i 0.790658 0.574447i −0.117501 0.993073i \(-0.537488\pi\)
0.908159 + 0.418626i \(0.137488\pi\)
\(734\) 2252.75 + 1636.72i 0.113284 + 0.0823056i
\(735\) 0 0
\(736\) −4559.48 −0.228349
\(737\) 9130.21 + 28727.5i 0.456331 + 1.43581i
\(738\) 0 0
\(739\) −2061.83 6345.68i −0.102633 0.315872i 0.886535 0.462662i \(-0.153106\pi\)
−0.989168 + 0.146790i \(0.953106\pi\)
\(740\) −2547.75 1851.05i −0.126564 0.0919539i
\(741\) 0 0
\(742\) −3214.93 + 9894.52i −0.159062 + 0.489541i
\(743\) −2028.75 + 6243.86i −0.100172 + 0.308297i −0.988567 0.150782i \(-0.951821\pi\)
0.888395 + 0.459080i \(0.151821\pi\)
\(744\) 0 0
\(745\) 2140.98 + 1555.52i 0.105288 + 0.0764962i
\(746\) 5834.43 + 17956.5i 0.286345 + 0.881280i
\(747\) 0 0
\(748\) 7032.22 5040.40i 0.343748 0.246384i
\(749\) −1427.16 −0.0696223
\(750\) 0 0
\(751\) −15321.7 11131.9i −0.744470 0.540889i 0.149638 0.988741i \(-0.452189\pi\)
−0.894108 + 0.447852i \(0.852189\pi\)
\(752\) 1169.70 849.837i 0.0567215 0.0412106i
\(753\) 0 0
\(754\) 969.495 2983.80i 0.0468262 0.144116i
\(755\) 7471.93 5428.68i 0.360174 0.261682i
\(756\) 0 0
\(757\) −3386.32 10422.0i −0.162586 0.500389i 0.836264 0.548327i \(-0.184735\pi\)
−0.998850 + 0.0479377i \(0.984735\pi\)
\(758\) 2580.70 0.123661
\(759\) 0 0
\(760\) −4121.52 −0.196715
\(761\) 10952.2 + 33707.5i 0.521706 + 1.60565i 0.770739 + 0.637151i \(0.219887\pi\)
−0.249033 + 0.968495i \(0.580113\pi\)
\(762\) 0 0
\(763\) 27937.4 20297.7i 1.32556 0.963074i
\(764\) 1432.87 4409.93i 0.0678529 0.208830i
\(765\) 0 0
\(766\) −9146.57 + 6645.37i −0.431435 + 0.313456i
\(767\) 18801.5 + 13660.1i 0.885115 + 0.643074i
\(768\) 0 0
\(769\) 4444.21 0.208404 0.104202 0.994556i \(-0.466771\pi\)
0.104202 + 0.994556i \(0.466771\pi\)
\(770\) −7037.98 5182.90i −0.329391 0.242570i
\(771\) 0 0
\(772\) −1588.27 4888.19i −0.0740455 0.227888i
\(773\) 8219.75 + 5972.00i 0.382463 + 0.277876i 0.762360 0.647153i \(-0.224041\pi\)
−0.379897 + 0.925029i \(0.624041\pi\)
\(774\) 0 0
\(775\) −6311.48 + 19424.8i −0.292536 + 0.900333i
\(776\) −1440.03 + 4431.97i −0.0666162 + 0.205024i
\(777\) 0 0
\(778\) −20772.3 15092.0i −0.957228 0.695467i
\(779\) −2438.40 7504.64i −0.112150 0.345162i
\(780\) 0 0
\(781\) 32796.2 + 211.005i 1.50261 + 0.00966754i
\(782\) 16895.3 0.772600
\(783\) 0 0
\(784\) −1910.76 1388.25i −0.0870427 0.0632403i
\(785\) 11208.2 8143.22i 0.509601 0.370247i
\(786\) 0 0
\(787\) −5645.76 + 17375.9i −0.255718 + 0.787018i 0.737970 + 0.674834i \(0.235785\pi\)
−0.993687 + 0.112184i \(0.964215\pi\)
\(788\) −8689.03 + 6312.95i −0.392809 + 0.285393i
\(789\) 0 0
\(790\) 1017.62 + 3131.91i 0.0458295 + 0.141049i
\(791\) −49596.6 −2.22939
\(792\) 0 0
\(793\) −11468.7 −0.513575
\(794\) 4753.46 + 14629.7i 0.212461 + 0.653888i
\(795\) 0 0
\(796\) 4315.42 3135.34i 0.192156 0.139609i
\(797\) −5557.35 + 17103.8i −0.246991 + 0.760159i 0.748312 + 0.663347i \(0.230865\pi\)
−0.995303 + 0.0968123i \(0.969135\pi\)
\(798\) 0 0
\(799\) −4334.35 + 3149.09i −0.191913 + 0.139433i
\(800\) 2478.89 + 1801.02i 0.109553 + 0.0795946i
\(801\) 0 0
\(802\) −15572.3 −0.685634
\(803\) 4053.79 + 2985.29i 0.178151 + 0.131194i
\(804\) 0 0
\(805\) −5274.28 16232.6i −0.230924 0.710711i
\(806\) −26515.5 19264.7i −1.15877 0.841897i
\(807\) 0 0
\(808\) 349.942 1077.01i 0.0152363 0.0468924i
\(809\) −1589.66 + 4892.47i −0.0690846 + 0.212621i −0.979638 0.200770i \(-0.935656\pi\)
0.910554 + 0.413391i \(0.135656\pi\)
\(810\) 0 0
\(811\) 6679.24 + 4852.75i 0.289198 + 0.210115i 0.722919 0.690932i \(-0.242800\pi\)
−0.433721 + 0.901047i \(0.642800\pi\)
\(812\) −559.026 1720.51i −0.0241601 0.0743570i
\(813\) 0 0
\(814\) −3347.36 + 10081.0i −0.144134 + 0.434076i
\(815\) −9821.58 −0.422129
\(816\) 0 0
\(817\) 11666.2 + 8475.96i 0.499568 + 0.362958i
\(818\) 14335.6 10415.4i 0.612753 0.445191i
\(819\) 0 0
\(820\) 553.717 1704.17i 0.0235813 0.0725757i
\(821\) 200.029 145.330i 0.00850314 0.00617789i −0.583526 0.812095i \(-0.698327\pi\)
0.592029 + 0.805917i \(0.298327\pi\)
\(822\) 0 0
\(823\) 3644.80 + 11217.5i 0.154374 + 0.475114i 0.998097 0.0616649i \(-0.0196410\pi\)
−0.843723 + 0.536779i \(0.819641\pi\)
\(824\) 6731.04 0.284571
\(825\) 0 0
\(826\) 13400.5 0.564484
\(827\) 856.491 + 2636.01i 0.0360134 + 0.110838i 0.967447 0.253073i \(-0.0814413\pi\)
−0.931434 + 0.363911i \(0.881441\pi\)
\(828\) 0 0
\(829\) 22084.6 16045.4i 0.925246 0.672231i −0.0195780 0.999808i \(-0.506232\pi\)
0.944824 + 0.327578i \(0.106232\pi\)
\(830\) −2554.57 + 7862.15i −0.106832 + 0.328794i
\(831\) 0 0
\(832\) −3977.87 + 2890.10i −0.165755 + 0.120428i
\(833\) 7080.37 + 5144.19i 0.294502 + 0.213968i
\(834\) 0 0
\(835\) 2049.26 0.0849314
\(836\) 4210.74 + 13248.8i 0.174200 + 0.548108i
\(837\) 0 0
\(838\) −5852.21 18011.3i −0.241243 0.742469i
\(839\) 7082.73 + 5145.91i 0.291446 + 0.211748i 0.723894 0.689911i \(-0.242350\pi\)
−0.432449 + 0.901659i \(0.642350\pi\)
\(840\) 0 0
\(841\) −7407.78 + 22798.8i −0.303735 + 0.934799i
\(842\) 3200.15 9849.03i 0.130979 0.403112i
\(843\) 0 0
\(844\) 5268.86 + 3828.05i 0.214884 + 0.156122i
\(845\) −6192.41 19058.3i −0.252101 0.775887i
\(846\) 0 0
\(847\) −9470.28 + 27918.9i −0.384182 + 1.13259i
\(848\) 3757.58 0.152165
\(849\) 0 0
\(850\) −9185.58 6673.72i −0.370662 0.269302i
\(851\) −16781.0 + 12192.1i −0.675964 + 0.491117i
\(852\) 0 0
\(853\) 12726.6 39168.6i 0.510846 1.57222i −0.279869 0.960038i \(-0.590291\pi\)
0.790715 0.612184i \(-0.209709\pi\)
\(854\) −5350.05 + 3887.04i −0.214373 + 0.155751i
\(855\) 0 0
\(856\) 159.285 + 490.227i 0.00636008 + 0.0195743i
\(857\) 18020.0 0.718265 0.359132 0.933287i \(-0.383073\pi\)
0.359132 + 0.933287i \(0.383073\pi\)
\(858\) 0 0
\(859\) 6159.11 0.244640 0.122320 0.992491i \(-0.460967\pi\)
0.122320 + 0.992491i \(0.460967\pi\)
\(860\) 1011.89 + 3114.29i 0.0401225 + 0.123484i
\(861\) 0 0
\(862\) 16930.4 12300.6i 0.668969 0.486035i
\(863\) −8940.66 + 27516.5i −0.352658 + 1.08537i 0.604697 + 0.796455i \(0.293294\pi\)
−0.957355 + 0.288914i \(0.906706\pi\)
\(864\) 0 0
\(865\) −221.921 + 161.235i −0.00872317 + 0.00633775i
\(866\) −25626.8 18619.0i −1.00558 0.730598i
\(867\) 0 0
\(868\) −18898.6 −0.739009
\(869\) 9027.99 6470.89i 0.352421 0.252601i
\(870\) 0 0
\(871\) 19615.5 + 60370.4i 0.763085 + 2.34853i
\(872\) −10090.3 7331.05i −0.391859 0.284703i
\(873\) 0 0
\(874\) −8388.81 + 25818.1i −0.324663 + 0.999211i
\(875\) −8171.52 + 25149.4i −0.315712 + 0.971661i
\(876\) 0 0
\(877\) 36529.2 + 26540.1i 1.40651 + 1.02189i 0.993819 + 0.111013i \(0.0354094\pi\)
0.412686 + 0.910873i \(0.364591\pi\)
\(878\) −2981.83 9177.13i −0.114615 0.352748i
\(879\) 0 0
\(880\) −994.816 + 2996.00i −0.0381082 + 0.114767i
\(881\) −22263.5 −0.851391 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(882\) 0 0
\(883\) −30917.0 22462.5i −1.17830 0.856086i −0.186322 0.982489i \(-0.559657\pi\)
−0.991979 + 0.126402i \(0.959657\pi\)
\(884\) 14740.1 10709.3i 0.560818 0.407458i
\(885\) 0 0
\(886\) −2214.65 + 6816.00i −0.0839760 + 0.258452i
\(887\) 38962.7 28308.1i 1.47490 1.07158i 0.495750 0.868465i \(-0.334893\pi\)
0.979155 0.203116i \(-0.0651068\pi\)
\(888\) 0 0
\(889\) −7484.34 23034.4i −0.282359 0.869010i
\(890\) −3386.55 −0.127548
\(891\) 0 0
\(892\) −10512.8 −0.394612
\(893\) −2660.12 8187.01i −0.0996838 0.306795i
\(894\) 0 0
\(895\) −91.3017 + 66.3346i −0.00340992 + 0.00247745i
\(896\) −876.118 + 2696.41i −0.0326663 + 0.100537i
\(897\) 0 0
\(898\) −12614.2 + 9164.73i −0.468753 + 0.340569i
\(899\) −3523.52 2559.99i −0.130718 0.0949725i
\(900\) 0 0
\(901\) −13923.8 −0.514838
\(902\) −6043.81 38.8849i −0.223101 0.00143539i
\(903\) 0 0
\(904\) 5535.46 + 17036.4i 0.203658 + 0.626795i
\(905\) −770.714 559.956i −0.0283087 0.0205675i
\(906\) 0 0
\(907\) 2629.70 8093.38i 0.0962709 0.296291i −0.891312 0.453391i \(-0.850214\pi\)
0.987583 + 0.157099i \(0.0502143\pi\)
\(908\) −2104.47 + 6476.90i −0.0769157 + 0.236722i
\(909\) 0 0
\(910\) −14890.7 10818.8i −0.542443 0.394108i
\(911\) −3486.78 10731.2i −0.126808 0.390275i 0.867418 0.497580i \(-0.165778\pi\)
−0.994226 + 0.107305i \(0.965778\pi\)
\(912\) 0 0
\(913\) 27883.0 + 179.395i 1.01073 + 0.00650285i
\(914\) 6696.04 0.242325
\(915\) 0 0
\(916\) −17461.7 12686.6i −0.629857 0.457618i
\(917\) 44192.6 32107.8i 1.59146 1.15626i
\(918\) 0 0
\(919\) 8206.54 25257.1i 0.294569 0.906590i −0.688797 0.724954i \(-0.741861\pi\)
0.983366 0.181635i \(-0.0581391\pi\)
\(920\) −4987.22 + 3623.42i −0.178721 + 0.129849i
\(921\) 0 0
\(922\) −4432.51 13641.9i −0.158327 0.487279i
\(923\) 69064.7 2.46294
\(924\) 0 0
\(925\) 13939.4 0.495486
\(926\) 2493.61 + 7674.54i 0.0884936 + 0.272355i
\(927\) 0 0
\(928\) −528.600 + 384.050i −0.0186984 + 0.0135852i
\(929\) 14806.0 45568.1i 0.522893 1.60930i −0.245551 0.969384i \(-0.578969\pi\)
0.768444 0.639916i \(-0.221031\pi\)
\(930\) 0 0
\(931\) −11376.5 + 8265.52i −0.400483 + 0.290968i
\(932\) −19591.7 14234.2i −0.688572 0.500277i
\(933\) 0 0
\(934\) 23643.7 0.828314
\(935\) 3686.31 11101.8i 0.128936 0.388306i
\(936\) 0 0
\(937\) 1767.25 + 5439.04i 0.0616153 + 0.189633i 0.977126 0.212661i \(-0.0682131\pi\)
−0.915511 + 0.402294i \(0.868213\pi\)
\(938\) 29611.6 + 21514.1i 1.03076 + 0.748892i
\(939\) 0 0
\(940\) 604.066 1859.12i 0.0209601 0.0645084i
\(941\) 3431.82 10562.1i 0.118889 0.365902i −0.873850 0.486196i \(-0.838384\pi\)
0.992738 + 0.120295i \(0.0383840\pi\)
\(942\) 0 0
\(943\) −9548.27 6937.22i −0.329729 0.239562i
\(944\) −1495.63 4603.08i −0.0515663 0.158705i
\(945\) 0 0
\(946\) 8977.20 6434.48i 0.308535 0.221145i
\(947\) −39759.1 −1.36430 −0.682152 0.731210i \(-0.738956\pi\)
−0.682152 + 0.731210i \(0.738956\pi\)
\(948\) 0 0
\(949\) 8576.88 + 6231.47i 0.293380 + 0.213153i
\(950\) 14759.1 10723.1i 0.504051 0.366214i
\(951\) 0 0
\(952\) 3246.47 9991.62i 0.110524 0.340158i
\(953\) −12889.2 + 9364.58i −0.438115 + 0.318309i −0.784885 0.619641i \(-0.787278\pi\)
0.346771 + 0.937950i \(0.387278\pi\)
\(954\) 0 0
\(955\) −1937.28 5962.34i −0.0656429 0.202028i
\(956\) −12546.4 −0.424456
\(957\) 0 0
\(958\) 17319.9 0.584113
\(959\) −6661.82 20503.0i −0.224319 0.690381i
\(960\) 0 0
\(961\) −12707.8 + 9232.73i −0.426564 + 0.309917i
\(962\) −6912.26 + 21273.8i −0.231664 + 0.712987i
\(963\) 0 0
\(964\) 21032.0 15280.7i 0.702693 0.510537i
\(965\) −5621.92 4084.56i −0.187540 0.136256i
\(966\) 0 0
\(967\) 14952.9 0.497264 0.248632 0.968598i \(-0.420019\pi\)
0.248632 + 0.968598i \(0.420019\pi\)
\(968\) 10647.1 + 137.009i 0.353524 + 0.00454922i
\(969\) 0 0
\(970\) 1946.96 + 5992.13i 0.0644465 + 0.198346i
\(971\) 22601.7 + 16421.1i 0.746987 + 0.542718i 0.894892 0.446284i \(-0.147253\pi\)
−0.147904 + 0.989002i \(0.547253\pi\)
\(972\) 0 0
\(973\) 8645.09 26606.9i 0.284840 0.876646i
\(974\) 4590.54 14128.2i 0.151017 0.464782i
\(975\) 0 0
\(976\) 1932.31 + 1403.91i 0.0633728 + 0.0460430i
\(977\) −10308.6 31726.5i −0.337564 1.03892i −0.965445 0.260607i \(-0.916077\pi\)
0.627881 0.778310i \(-0.283923\pi\)
\(978\) 0 0
\(979\) 3459.87 + 10886.2i 0.112950 + 0.355387i
\(980\) −3193.26 −0.104087
\(981\) 0 0
\(982\) −8970.20 6517.23i −0.291498 0.211785i
\(983\) 9991.42 7259.19i 0.324188 0.235536i −0.413772 0.910380i \(-0.635789\pi\)
0.737960 + 0.674844i \(0.235789\pi\)
\(984\) 0 0
\(985\) −4487.25 + 13810.4i −0.145153 + 0.446735i
\(986\) 1958.74 1423.11i 0.0632647 0.0459645i
\(987\) 0 0
\(988\) 9046.45 + 27842.1i 0.291301 + 0.896534i
\(989\) 21568.2 0.693457
\(990\) 0 0
\(991\) −30154.0 −0.966571 −0.483286 0.875463i \(-0.660557\pi\)
−0.483286 + 0.875463i \(0.660557\pi\)
\(992\) 2109.27 + 6491.66i 0.0675094 + 0.207773i
\(993\) 0 0
\(994\) 32218.2 23407.9i 1.02807 0.746934i
\(995\) 2228.60 6858.94i 0.0710065 0.218536i
\(996\) 0 0
\(997\) −1693.35 + 1230.29i −0.0537902 + 0.0390809i −0.614355 0.789029i \(-0.710584\pi\)
0.560565 + 0.828110i \(0.310584\pi\)
\(998\) −33027.3 23995.8i −1.04756 0.761095i
\(999\) 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.181.2 8
3.2 odd 2 22.4.c.b.5.1 8
11.3 even 5 2178.4.a.by.1.3 4
11.8 odd 10 2178.4.a.bt.1.3 4
11.9 even 5 inner 198.4.f.d.163.2 8
12.11 even 2 176.4.m.b.49.2 8
33.2 even 10 242.4.c.q.9.1 8
33.5 odd 10 242.4.c.r.81.2 8
33.8 even 10 242.4.a.o.1.3 4
33.14 odd 10 242.4.a.n.1.3 4
33.17 even 10 242.4.c.n.81.2 8
33.20 odd 10 22.4.c.b.9.1 yes 8
33.26 odd 10 242.4.c.r.3.2 8
33.29 even 10 242.4.c.n.3.2 8
33.32 even 2 242.4.c.q.27.1 8
132.47 even 10 1936.4.a.bn.1.2 4
132.107 odd 10 1936.4.a.bm.1.2 4
132.119 even 10 176.4.m.b.97.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.b.5.1 8 3.2 odd 2
22.4.c.b.9.1 yes 8 33.20 odd 10
176.4.m.b.49.2 8 12.11 even 2
176.4.m.b.97.2 8 132.119 even 10
198.4.f.d.163.2 8 11.9 even 5 inner
198.4.f.d.181.2 8 1.1 even 1 trivial
242.4.a.n.1.3 4 33.14 odd 10
242.4.a.o.1.3 4 33.8 even 10
242.4.c.n.3.2 8 33.29 even 10
242.4.c.n.81.2 8 33.17 even 10
242.4.c.q.9.1 8 33.2 even 10
242.4.c.q.27.1 8 33.32 even 2
242.4.c.r.3.2 8 33.26 odd 10
242.4.c.r.81.2 8 33.5 odd 10
1936.4.a.bm.1.2 4 132.107 odd 10
1936.4.a.bn.1.2 4 132.47 even 10
2178.4.a.bt.1.3 4 11.8 odd 10
2178.4.a.by.1.3 4 11.3 even 5