Properties

Label 1050.3.p.i.451.8
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
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] = [1050,3,Mod(451,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.451");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + \cdots + 101626561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{4}\cdot 7 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.8
Root \(1.92573 - 3.33546i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.i.901.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.578394 + 1.00181i) q^{11} +(-3.00000 + 1.73205i) q^{12} -14.8176i q^{13} +(9.81379 - 1.29982i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.9271 - 6.30878i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(16.7162 - 9.65108i) q^{19} +(9.61312 - 7.38837i) q^{21} -1.63595 q^{22} +(-12.1504 - 21.0450i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(18.1477 - 10.4776i) q^{26} +5.19615i q^{27} +(8.53135 + 11.1003i) q^{28} +49.0382 q^{29} +(-24.9581 - 14.4096i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-1.73518 + 1.00181i) q^{33} -17.8439i q^{34} -6.00000 q^{36} +(-26.6579 - 46.1728i) q^{37} +(23.6402 + 13.6487i) q^{38} +(12.8324 - 22.2264i) q^{39} +38.0398i q^{41} +(15.8464 + 6.54925i) q^{42} +63.5774 q^{43} +(-1.15679 - 2.00362i) q^{44} +(17.1832 - 29.7622i) q^{46} +(-21.8175 + 12.5964i) q^{47} -6.92820i q^{48} +(-34.7024 - 34.5940i) q^{49} +(-10.9271 - 18.9263i) q^{51} +(25.6648 + 14.8176i) q^{52} +(10.4160 - 18.0411i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-7.56243 + 18.2978i) q^{56} +33.4323 q^{57} +(34.6752 + 60.0593i) q^{58} +(21.1419 + 12.2063i) q^{59} +(5.53376 - 3.19492i) q^{61} -40.7564i q^{62} +(20.8182 - 2.75734i) q^{63} +8.00000 q^{64} +(-2.45392 - 1.41677i) q^{66} +(62.2451 - 107.812i) q^{67} +(21.8543 - 12.6176i) q^{68} -42.0901i q^{69} -118.973 q^{71} +(-4.24264 - 7.34847i) q^{72} +(34.2336 + 19.7648i) q^{73} +(37.7000 - 65.2983i) q^{74} +38.6043i q^{76} +(4.93448 + 6.42033i) q^{77} +36.2955 q^{78} +(46.4356 + 80.4288i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.5891 + 26.8982i) q^{82} -5.79665i q^{83} +(3.18391 + 24.0388i) q^{84} +(44.9560 + 77.8661i) q^{86} +(73.5573 + 42.4683i) q^{87} +(1.63595 - 2.83354i) q^{88} +(131.622 - 75.9919i) q^{89} +(-95.8586 - 39.6181i) q^{91} +48.6014 q^{92} +(-24.9581 - 43.2287i) q^{93} +(-30.8546 - 17.8139i) q^{94} +(8.48528 - 4.89898i) q^{96} +144.310i q^{97} +(17.8305 - 66.9632i) q^{98} -3.47036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 2.67372 6.46925i 0.381960 0.924179i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.578394 + 1.00181i −0.0525813 + 0.0910735i −0.891118 0.453772i \(-0.850078\pi\)
0.838537 + 0.544845i \(0.183412\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 14.8176i 1.13981i −0.821710 0.569906i \(-0.806979\pi\)
0.821710 0.569906i \(-0.193021\pi\)
\(14\) 9.81379 1.29982i 0.700985 0.0928446i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −10.9271 6.30878i −0.642772 0.371105i 0.142909 0.989736i \(-0.454354\pi\)
−0.785682 + 0.618631i \(0.787688\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) 16.7162 9.65108i 0.879798 0.507951i 0.00920603 0.999958i \(-0.497070\pi\)
0.870592 + 0.492006i \(0.163736\pi\)
\(20\) 0 0
\(21\) 9.61312 7.38837i 0.457768 0.351827i
\(22\) −1.63595 −0.0743612
\(23\) −12.1504 21.0450i −0.528277 0.915002i −0.999457 0.0329648i \(-0.989505\pi\)
0.471180 0.882037i \(-0.343828\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) 18.1477 10.4776i 0.697990 0.402985i
\(27\) 5.19615i 0.192450i
\(28\) 8.53135 + 11.1003i 0.304691 + 0.396438i
\(29\) 49.0382 1.69097 0.845486 0.533998i \(-0.179311\pi\)
0.845486 + 0.533998i \(0.179311\pi\)
\(30\) 0 0
\(31\) −24.9581 14.4096i −0.805100 0.464825i 0.0401515 0.999194i \(-0.487216\pi\)
−0.845251 + 0.534369i \(0.820549\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) −1.73518 + 1.00181i −0.0525813 + 0.0303578i
\(34\) 17.8439i 0.524822i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −26.6579 46.1728i −0.720484 1.24791i −0.960806 0.277221i \(-0.910586\pi\)
0.240322 0.970693i \(-0.422747\pi\)
\(38\) 23.6402 + 13.6487i 0.622111 + 0.359176i
\(39\) 12.8324 22.2264i 0.329036 0.569906i
\(40\) 0 0
\(41\) 38.0398i 0.927800i 0.885888 + 0.463900i \(0.153550\pi\)
−0.885888 + 0.463900i \(0.846450\pi\)
\(42\) 15.8464 + 6.54925i 0.377294 + 0.155935i
\(43\) 63.5774 1.47854 0.739272 0.673407i \(-0.235170\pi\)
0.739272 + 0.673407i \(0.235170\pi\)
\(44\) −1.15679 2.00362i −0.0262906 0.0455367i
\(45\) 0 0
\(46\) 17.1832 29.7622i 0.373548 0.647004i
\(47\) −21.8175 + 12.5964i −0.464203 + 0.268008i −0.713810 0.700340i \(-0.753032\pi\)
0.249607 + 0.968347i \(0.419699\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −34.7024 34.5940i −0.708213 0.705999i
\(50\) 0 0
\(51\) −10.9271 18.9263i −0.214257 0.371105i
\(52\) 25.6648 + 14.8176i 0.493553 + 0.284953i
\(53\) 10.4160 18.0411i 0.196529 0.340397i −0.750872 0.660448i \(-0.770366\pi\)
0.947401 + 0.320050i \(0.103700\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −7.56243 + 18.2978i −0.135043 + 0.326747i
\(57\) 33.4323 0.586532
\(58\) 34.6752 + 60.0593i 0.597849 + 1.03550i
\(59\) 21.1419 + 12.2063i 0.358337 + 0.206886i 0.668351 0.743846i \(-0.267000\pi\)
−0.310014 + 0.950732i \(0.600334\pi\)
\(60\) 0 0
\(61\) 5.53376 3.19492i 0.0907174 0.0523757i −0.453955 0.891025i \(-0.649987\pi\)
0.544672 + 0.838649i \(0.316654\pi\)
\(62\) 40.7564i 0.657361i
\(63\) 20.8182 2.75734i 0.330447 0.0437674i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −2.45392 1.41677i −0.0371806 0.0214662i
\(67\) 62.2451 107.812i 0.929031 1.60913i 0.144085 0.989565i \(-0.453976\pi\)
0.784946 0.619564i \(-0.212690\pi\)
\(68\) 21.8543 12.6176i 0.321386 0.185552i
\(69\) 42.0901i 0.610001i
\(70\) 0 0
\(71\) −118.973 −1.67567 −0.837835 0.545924i \(-0.816179\pi\)
−0.837835 + 0.545924i \(0.816179\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) 34.2336 + 19.7648i 0.468953 + 0.270750i 0.715801 0.698304i \(-0.246062\pi\)
−0.246848 + 0.969054i \(0.579395\pi\)
\(74\) 37.7000 65.2983i 0.509459 0.882409i
\(75\) 0 0
\(76\) 38.6043i 0.507951i
\(77\) 4.93448 + 6.42033i 0.0640842 + 0.0833809i
\(78\) 36.2955 0.465327
\(79\) 46.4356 + 80.4288i 0.587792 + 1.01809i 0.994521 + 0.104537i \(0.0333360\pi\)
−0.406729 + 0.913549i \(0.633331\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −46.5891 + 26.8982i −0.568159 + 0.328027i
\(83\) 5.79665i 0.0698392i −0.999390 0.0349196i \(-0.988882\pi\)
0.999390 0.0349196i \(-0.0111175\pi\)
\(84\) 3.18391 + 24.0388i 0.0379037 + 0.286176i
\(85\) 0 0
\(86\) 44.9560 + 77.8661i 0.522744 + 0.905420i
\(87\) 73.5573 + 42.4683i 0.845486 + 0.488142i
\(88\) 1.63595 2.83354i 0.0185903 0.0321993i
\(89\) 131.622 75.9919i 1.47890 0.853842i 0.479182 0.877715i \(-0.340933\pi\)
0.999715 + 0.0238738i \(0.00759998\pi\)
\(90\) 0 0
\(91\) −95.8586 39.6181i −1.05339 0.435363i
\(92\) 48.6014 0.528277
\(93\) −24.9581 43.2287i −0.268367 0.464825i
\(94\) −30.8546 17.8139i −0.328241 0.189510i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 144.310i 1.48773i 0.668331 + 0.743864i \(0.267009\pi\)
−0.668331 + 0.743864i \(0.732991\pi\)
\(98\) 17.8305 66.9632i 0.181943 0.683298i
\(99\) −3.47036 −0.0350542
\(100\) 0 0
\(101\) −33.8480 19.5422i −0.335129 0.193487i 0.322987 0.946403i \(-0.395313\pi\)
−0.658116 + 0.752917i \(0.728646\pi\)
\(102\) 15.4533 26.7659i 0.151503 0.262411i
\(103\) −32.7730 + 18.9215i −0.318185 + 0.183704i −0.650583 0.759435i \(-0.725475\pi\)
0.332398 + 0.943139i \(0.392142\pi\)
\(104\) 41.9104i 0.402985i
\(105\) 0 0
\(106\) 29.4609 0.277933
\(107\) 41.5160 + 71.9079i 0.388000 + 0.672036i 0.992180 0.124811i \(-0.0398326\pi\)
−0.604180 + 0.796848i \(0.706499\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 23.8962 41.3894i 0.219231 0.379719i −0.735342 0.677696i \(-0.762978\pi\)
0.954573 + 0.297977i \(0.0963118\pi\)
\(110\) 0 0
\(111\) 92.3457i 0.831943i
\(112\) −27.7576 + 3.67646i −0.247836 + 0.0328255i
\(113\) 16.2283 0.143613 0.0718064 0.997419i \(-0.477124\pi\)
0.0718064 + 0.997419i \(0.477124\pi\)
\(114\) 23.6402 + 40.9461i 0.207370 + 0.359176i
\(115\) 0 0
\(116\) −49.0382 + 84.9366i −0.422743 + 0.732212i
\(117\) 38.4972 22.2264i 0.329036 0.189969i
\(118\) 34.5246i 0.292581i
\(119\) −70.0292 + 53.8224i −0.588481 + 0.452289i
\(120\) 0 0
\(121\) 59.8309 + 103.630i 0.494470 + 0.856448i
\(122\) 7.82592 + 4.51830i 0.0641469 + 0.0370352i
\(123\) −32.9434 + 57.0597i −0.267833 + 0.463900i
\(124\) 49.9162 28.8191i 0.402550 0.232412i
\(125\) 0 0
\(126\) 18.0977 + 23.5472i 0.143633 + 0.186883i
\(127\) −80.5643 −0.634365 −0.317182 0.948365i \(-0.602737\pi\)
−0.317182 + 0.948365i \(0.602737\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 95.3661 + 55.0597i 0.739272 + 0.426819i
\(130\) 0 0
\(131\) 107.981 62.3429i 0.824283 0.475900i −0.0276082 0.999619i \(-0.508789\pi\)
0.851891 + 0.523719i \(0.175456\pi\)
\(132\) 4.00723i 0.0303578i
\(133\) −17.7409 133.945i −0.133390 1.00711i
\(134\) 176.056 1.31385
\(135\) 0 0
\(136\) 30.9066 + 17.8439i 0.227254 + 0.131205i
\(137\) −38.0330 + 65.8750i −0.277613 + 0.480840i −0.970791 0.239927i \(-0.922877\pi\)
0.693178 + 0.720766i \(0.256210\pi\)
\(138\) 51.5496 29.7622i 0.373548 0.215668i
\(139\) 91.7680i 0.660201i −0.943946 0.330101i \(-0.892917\pi\)
0.943946 0.330101i \(-0.107083\pi\)
\(140\) 0 0
\(141\) −43.6350 −0.309468
\(142\) −84.1263 145.711i −0.592439 1.02613i
\(143\) 14.8444 + 8.57039i 0.103807 + 0.0599328i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 55.9032i 0.382898i
\(147\) −22.0944 81.9441i −0.150302 0.557443i
\(148\) 106.632 0.720484
\(149\) 49.4579 + 85.6637i 0.331933 + 0.574924i 0.982891 0.184190i \(-0.0589660\pi\)
−0.650958 + 0.759114i \(0.725633\pi\)
\(150\) 0 0
\(151\) −48.8950 + 84.6886i −0.323808 + 0.560852i −0.981270 0.192635i \(-0.938297\pi\)
0.657462 + 0.753487i \(0.271630\pi\)
\(152\) −47.2804 + 27.2974i −0.311055 + 0.179588i
\(153\) 37.8527i 0.247403i
\(154\) −4.37406 + 10.5833i −0.0284030 + 0.0687230i
\(155\) 0 0
\(156\) 25.6648 + 44.4527i 0.164518 + 0.284953i
\(157\) −115.530 66.7013i −0.735860 0.424849i 0.0847022 0.996406i \(-0.473006\pi\)
−0.820562 + 0.571557i \(0.806339\pi\)
\(158\) −65.6698 + 113.743i −0.415632 + 0.719895i
\(159\) 31.2480 18.0411i 0.196529 0.113466i
\(160\) 0 0
\(161\) −168.632 + 22.3352i −1.04741 + 0.138728i
\(162\) −12.7279 −0.0785674
\(163\) −16.3746 28.3616i −0.100458 0.173998i 0.811416 0.584469i \(-0.198697\pi\)
−0.911873 + 0.410472i \(0.865364\pi\)
\(164\) −65.8869 38.0398i −0.401749 0.231950i
\(165\) 0 0
\(166\) 7.09942 4.09885i 0.0427676 0.0246919i
\(167\) 171.659i 1.02790i 0.857821 + 0.513948i \(0.171818\pi\)
−0.857821 + 0.513948i \(0.828182\pi\)
\(168\) −27.1900 + 20.8975i −0.161845 + 0.124390i
\(169\) −50.5603 −0.299173
\(170\) 0 0
\(171\) 50.1485 + 28.9532i 0.293266 + 0.169317i
\(172\) −63.5774 + 110.119i −0.369636 + 0.640229i
\(173\) −175.336 + 101.230i −1.01350 + 0.585145i −0.912215 0.409712i \(-0.865629\pi\)
−0.101287 + 0.994857i \(0.532296\pi\)
\(174\) 120.119i 0.690336i
\(175\) 0 0
\(176\) 4.62715 0.0262906
\(177\) 21.1419 + 36.6188i 0.119446 + 0.206886i
\(178\) 186.141 + 107.469i 1.04574 + 0.603757i
\(179\) 39.3459 68.1491i 0.219810 0.380721i −0.734940 0.678132i \(-0.762790\pi\)
0.954750 + 0.297411i \(0.0961230\pi\)
\(180\) 0 0
\(181\) 58.1509i 0.321276i −0.987013 0.160638i \(-0.948645\pi\)
0.987013 0.160638i \(-0.0513551\pi\)
\(182\) −19.2602 145.416i −0.105825 0.798992i
\(183\) 11.0675 0.0604783
\(184\) 34.3664 + 59.5244i 0.186774 + 0.323502i
\(185\) 0 0
\(186\) 35.2961 61.1346i 0.189764 0.328681i
\(187\) 12.6404 7.29793i 0.0675956 0.0390263i
\(188\) 50.3854i 0.268008i
\(189\) 33.6152 + 13.8931i 0.177858 + 0.0735083i
\(190\) 0 0
\(191\) −184.204 319.051i −0.964419 1.67042i −0.711168 0.703022i \(-0.751834\pi\)
−0.253251 0.967401i \(-0.581500\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) 140.409 243.196i 0.727510 1.26008i −0.230422 0.973091i \(-0.574011\pi\)
0.957932 0.286994i \(-0.0926559\pi\)
\(194\) −176.742 + 102.042i −0.911044 + 0.525991i
\(195\) 0 0
\(196\) 94.6209 25.5124i 0.482760 0.130165i
\(197\) −7.61779 −0.0386690 −0.0193345 0.999813i \(-0.506155\pi\)
−0.0193345 + 0.999813i \(0.506155\pi\)
\(198\) −2.45392 4.25031i −0.0123935 0.0214662i
\(199\) −174.795 100.918i −0.878366 0.507125i −0.00824641 0.999966i \(-0.502625\pi\)
−0.870119 + 0.492841i \(0.835958\pi\)
\(200\) 0 0
\(201\) 186.735 107.812i 0.929031 0.536376i
\(202\) 55.2736i 0.273632i
\(203\) 131.114 317.240i 0.645884 1.56276i
\(204\) 43.7085 0.214257
\(205\) 0 0
\(206\) −46.3481 26.7591i −0.224991 0.129898i
\(207\) 36.4511 63.1351i 0.176092 0.305001i
\(208\) −51.3296 + 29.6351i −0.246777 + 0.142477i
\(209\) 22.3285i 0.106835i
\(210\) 0 0
\(211\) 30.3818 0.143989 0.0719947 0.997405i \(-0.477064\pi\)
0.0719947 + 0.997405i \(0.477064\pi\)
\(212\) 20.8320 + 36.0821i 0.0982643 + 0.170199i
\(213\) −178.459 103.033i −0.837835 0.483724i
\(214\) −58.7126 + 101.693i −0.274358 + 0.475202i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −159.950 + 122.933i −0.737097 + 0.566512i
\(218\) 67.5886 0.310039
\(219\) 34.2336 + 59.2943i 0.156318 + 0.270750i
\(220\) 0 0
\(221\) −93.4808 + 161.914i −0.422990 + 0.732640i
\(222\) 113.100 65.2983i 0.509459 0.294136i
\(223\) 16.7377i 0.0750569i −0.999296 0.0375284i \(-0.988052\pi\)
0.999296 0.0375284i \(-0.0119485\pi\)
\(224\) −24.1303 31.3963i −0.107725 0.140162i
\(225\) 0 0
\(226\) 11.4751 + 19.8755i 0.0507748 + 0.0879446i
\(227\) 366.738 + 211.736i 1.61558 + 0.932758i 0.988044 + 0.154175i \(0.0492719\pi\)
0.627541 + 0.778583i \(0.284061\pi\)
\(228\) −33.4323 + 57.9065i −0.146633 + 0.253976i
\(229\) −350.596 + 202.417i −1.53099 + 0.883916i −0.531672 + 0.846951i \(0.678436\pi\)
−0.999317 + 0.0369660i \(0.988231\pi\)
\(230\) 0 0
\(231\) 1.84155 + 13.9039i 0.00797209 + 0.0601900i
\(232\) −138.701 −0.597849
\(233\) 138.649 + 240.147i 0.595061 + 1.03068i 0.993538 + 0.113497i \(0.0362053\pi\)
−0.398478 + 0.917178i \(0.630461\pi\)
\(234\) 54.4432 + 31.4328i 0.232663 + 0.134328i
\(235\) 0 0
\(236\) −42.2838 + 24.4125i −0.179169 + 0.103443i
\(237\) 160.858i 0.678724i
\(238\) −115.437 47.7097i −0.485029 0.200461i
\(239\) 290.247 1.21442 0.607211 0.794541i \(-0.292288\pi\)
0.607211 + 0.794541i \(0.292288\pi\)
\(240\) 0 0
\(241\) −350.574 202.404i −1.45466 0.839850i −0.455922 0.890020i \(-0.650690\pi\)
−0.998741 + 0.0501703i \(0.984024\pi\)
\(242\) −84.6137 + 146.555i −0.349643 + 0.605600i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 12.7797i 0.0523757i
\(245\) 0 0
\(246\) −93.1781 −0.378773
\(247\) −143.005 247.693i −0.578970 1.00280i
\(248\) 70.5922 + 40.7564i 0.284646 + 0.164340i
\(249\) 5.02005 8.69498i 0.0201608 0.0349196i
\(250\) 0 0
\(251\) 155.805i 0.620739i 0.950616 + 0.310369i \(0.100453\pi\)
−0.950616 + 0.310369i \(0.899547\pi\)
\(252\) −16.0423 + 38.8155i −0.0636600 + 0.154030i
\(253\) 28.1108 0.111110
\(254\) −56.9676 98.6707i −0.224282 0.388467i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 22.4315 12.9508i 0.0872821 0.0503923i −0.455724 0.890121i \(-0.650619\pi\)
0.543006 + 0.839729i \(0.317286\pi\)
\(258\) 155.732i 0.603613i
\(259\) −369.980 + 49.0033i −1.42849 + 0.189202i
\(260\) 0 0
\(261\) 73.5573 + 127.405i 0.281829 + 0.488142i
\(262\) 152.708 + 88.1662i 0.582856 + 0.336512i
\(263\) −157.902 + 273.495i −0.600389 + 1.03990i 0.392373 + 0.919806i \(0.371654\pi\)
−0.992762 + 0.120098i \(0.961679\pi\)
\(264\) 4.90784 2.83354i 0.0185903 0.0107331i
\(265\) 0 0
\(266\) 151.504 116.442i 0.569564 0.437751i
\(267\) 263.244 0.985931
\(268\) 124.490 + 215.623i 0.464516 + 0.804565i
\(269\) −41.4157 23.9114i −0.153962 0.0888899i 0.421040 0.907042i \(-0.361665\pi\)
−0.575002 + 0.818152i \(0.694999\pi\)
\(270\) 0 0
\(271\) 294.580 170.076i 1.08701 0.627587i 0.154233 0.988035i \(-0.450709\pi\)
0.932779 + 0.360448i \(0.117376\pi\)
\(272\) 50.4703i 0.185552i
\(273\) −109.478 142.443i −0.401017 0.521769i
\(274\) −107.573 −0.392604
\(275\) 0 0
\(276\) 72.9022 + 42.0901i 0.264138 + 0.152500i
\(277\) 105.293 182.374i 0.380121 0.658388i −0.610959 0.791663i \(-0.709216\pi\)
0.991079 + 0.133274i \(0.0425491\pi\)
\(278\) 112.392 64.8898i 0.404289 0.233416i
\(279\) 86.4574i 0.309883i
\(280\) 0 0
\(281\) 471.785 1.67895 0.839476 0.543397i \(-0.182862\pi\)
0.839476 + 0.543397i \(0.182862\pi\)
\(282\) −30.8546 53.4418i −0.109414 0.189510i
\(283\) −405.534 234.135i −1.43298 0.827333i −0.435636 0.900123i \(-0.643476\pi\)
−0.997347 + 0.0727901i \(0.976810\pi\)
\(284\) 118.973 206.067i 0.418917 0.725586i
\(285\) 0 0
\(286\) 24.2407i 0.0847578i
\(287\) 246.089 + 101.708i 0.857453 + 0.354383i
\(288\) 16.9706 0.0589256
\(289\) −64.8985 112.408i −0.224562 0.388953i
\(290\) 0 0
\(291\) −124.976 + 216.464i −0.429470 + 0.743864i
\(292\) −68.4671 + 39.5295i −0.234476 + 0.135375i
\(293\) 63.5067i 0.216746i 0.994110 + 0.108373i \(0.0345642\pi\)
−0.994110 + 0.108373i \(0.965436\pi\)
\(294\) 84.7375 85.0032i 0.288223 0.289127i
\(295\) 0 0
\(296\) 75.3999 + 130.597i 0.254730 + 0.441204i
\(297\) −5.20555 3.00542i −0.0175271 0.0101193i
\(298\) −69.9441 + 121.147i −0.234712 + 0.406533i
\(299\) −311.836 + 180.039i −1.04293 + 0.602136i
\(300\) 0 0
\(301\) 169.988 411.298i 0.564745 1.36644i
\(302\) −138.296 −0.457934
\(303\) −33.8480 58.6265i −0.111710 0.193487i
\(304\) −66.8646 38.6043i −0.219949 0.126988i
\(305\) 0 0
\(306\) 46.3599 26.7659i 0.151503 0.0874703i
\(307\) 211.610i 0.689283i 0.938734 + 0.344642i \(0.112000\pi\)
−0.938734 + 0.344642i \(0.888000\pi\)
\(308\) −16.0548 + 2.12644i −0.0521261 + 0.00690403i
\(309\) −65.5460 −0.212123
\(310\) 0 0
\(311\) 58.3090 + 33.6647i 0.187489 + 0.108247i 0.590806 0.806813i \(-0.298810\pi\)
−0.403318 + 0.915060i \(0.632143\pi\)
\(312\) −36.2955 + 62.8656i −0.116332 + 0.201492i
\(313\) 119.714 69.1168i 0.382472 0.220821i −0.296421 0.955057i \(-0.595793\pi\)
0.678893 + 0.734237i \(0.262460\pi\)
\(314\) 188.660i 0.600827i
\(315\) 0 0
\(316\) −185.742 −0.587792
\(317\) 9.91216 + 17.1684i 0.0312686 + 0.0541589i 0.881236 0.472676i \(-0.156712\pi\)
−0.849968 + 0.526835i \(0.823379\pi\)
\(318\) 44.1914 + 25.5139i 0.138967 + 0.0802325i
\(319\) −28.3634 + 49.1268i −0.0889135 + 0.154003i
\(320\) 0 0
\(321\) 143.816i 0.448024i
\(322\) −146.596 190.738i −0.455267 0.592355i
\(323\) −243.546 −0.754013
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) 23.1572 40.1094i 0.0710342 0.123035i
\(327\) 71.6885 41.3894i 0.219231 0.126573i
\(328\) 107.593i 0.328027i
\(329\) 23.1550 + 174.822i 0.0703799 + 0.531374i
\(330\) 0 0
\(331\) 131.139 + 227.139i 0.396189 + 0.686220i 0.993252 0.115974i \(-0.0369991\pi\)
−0.597063 + 0.802194i \(0.703666\pi\)
\(332\) 10.0401 + 5.79665i 0.0302412 + 0.0174598i
\(333\) 79.9737 138.519i 0.240161 0.415972i
\(334\) −210.238 + 121.381i −0.629455 + 0.363416i
\(335\) 0 0
\(336\) −44.8203 18.5241i −0.133394 0.0551312i
\(337\) −578.125 −1.71550 −0.857752 0.514063i \(-0.828140\pi\)
−0.857752 + 0.514063i \(0.828140\pi\)
\(338\) −35.7515 61.9235i −0.105774 0.183206i
\(339\) 24.3424 + 14.0541i 0.0718064 + 0.0414575i
\(340\) 0 0
\(341\) 28.8712 16.6688i 0.0846664 0.0488822i
\(342\) 81.8921i 0.239451i
\(343\) −316.582 + 132.004i −0.922978 + 0.384852i
\(344\) −179.824 −0.522744
\(345\) 0 0
\(346\) −247.962 143.161i −0.716654 0.413760i
\(347\) 229.861 398.131i 0.662423 1.14735i −0.317554 0.948240i \(-0.602861\pi\)
0.979977 0.199110i \(-0.0638052\pi\)
\(348\) −147.115 + 84.9366i −0.422743 + 0.244071i
\(349\) 389.147i 1.11504i −0.830165 0.557518i \(-0.811754\pi\)
0.830165 0.557518i \(-0.188246\pi\)
\(350\) 0 0
\(351\) 76.9943 0.219357
\(352\) 3.27189 + 5.66708i 0.00929515 + 0.0160997i
\(353\) −559.415 322.978i −1.58475 0.914953i −0.994153 0.107983i \(-0.965561\pi\)
−0.590593 0.806970i \(-0.701106\pi\)
\(354\) −29.8991 + 51.7868i −0.0844608 + 0.146290i
\(355\) 0 0
\(356\) 303.968i 0.853842i
\(357\) −151.655 + 20.0866i −0.424805 + 0.0562649i
\(358\) 111.287 0.310858
\(359\) 33.0206 + 57.1934i 0.0919794 + 0.159313i 0.908344 0.418224i \(-0.137347\pi\)
−0.816365 + 0.577537i \(0.804014\pi\)
\(360\) 0 0
\(361\) 5.78661 10.0227i 0.0160294 0.0277637i
\(362\) 71.2200 41.1189i 0.196740 0.113588i
\(363\) 207.260i 0.570965i
\(364\) 164.479 126.414i 0.451866 0.347291i
\(365\) 0 0
\(366\) 7.82592 + 13.5549i 0.0213823 + 0.0370352i
\(367\) −519.556 299.966i −1.41568 0.817346i −0.419768 0.907631i \(-0.637889\pi\)
−0.995916 + 0.0902858i \(0.971222\pi\)
\(368\) −48.6014 + 84.1802i −0.132069 + 0.228750i
\(369\) −98.8303 + 57.0597i −0.267833 + 0.154633i
\(370\) 0 0
\(371\) −88.8627 115.621i −0.239522 0.311646i
\(372\) 99.8324 0.268367
\(373\) 202.376 + 350.526i 0.542564 + 0.939748i 0.998756 + 0.0498667i \(0.0158796\pi\)
−0.456192 + 0.889881i \(0.650787\pi\)
\(374\) 17.8762 + 10.3208i 0.0477973 + 0.0275958i
\(375\) 0 0
\(376\) 61.7093 35.6279i 0.164120 0.0947550i
\(377\) 726.627i 1.92739i
\(378\) 6.75409 + 50.9939i 0.0178680 + 0.134905i
\(379\) −239.675 −0.632388 −0.316194 0.948695i \(-0.602405\pi\)
−0.316194 + 0.948695i \(0.602405\pi\)
\(380\) 0 0
\(381\) −120.846 69.7707i −0.317182 0.183125i
\(382\) 260.504 451.206i 0.681947 1.18117i
\(383\) −553.486 + 319.555i −1.44513 + 0.834347i −0.998186 0.0602133i \(-0.980822\pi\)
−0.446947 + 0.894561i \(0.647489\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 397.138 1.02885
\(387\) 95.3661 + 165.179i 0.246424 + 0.426819i
\(388\) −249.952 144.310i −0.644205 0.371932i
\(389\) −260.797 + 451.714i −0.670429 + 1.16122i 0.307353 + 0.951596i \(0.400557\pi\)
−0.977782 + 0.209622i \(0.932777\pi\)
\(390\) 0 0
\(391\) 306.616i 0.784184i
\(392\) 98.1533 + 97.8465i 0.250391 + 0.249608i
\(393\) 215.962 0.549522
\(394\) −5.38659 9.32985i −0.0136716 0.0236798i
\(395\) 0 0
\(396\) 3.47036 6.01085i 0.00876355 0.0151789i
\(397\) −125.712 + 72.5800i −0.316656 + 0.182821i −0.649901 0.760019i \(-0.725190\pi\)
0.333245 + 0.942840i \(0.391856\pi\)
\(398\) 285.439i 0.717182i
\(399\) 89.3887 216.282i 0.224032 0.542060i
\(400\) 0 0
\(401\) −107.021 185.366i −0.266886 0.462260i 0.701170 0.712994i \(-0.252661\pi\)
−0.968056 + 0.250734i \(0.919328\pi\)
\(402\) 264.084 + 152.469i 0.656924 + 0.379275i
\(403\) −213.515 + 369.818i −0.529813 + 0.917663i
\(404\) 67.6960 39.0843i 0.167564 0.0967434i
\(405\) 0 0
\(406\) 481.250 63.7410i 1.18535 0.156998i
\(407\) 61.6751 0.151536
\(408\) 30.9066 + 53.5318i 0.0757515 + 0.131205i
\(409\) −479.754 276.986i −1.17299 0.677228i −0.218610 0.975812i \(-0.570152\pi\)
−0.954383 + 0.298585i \(0.903486\pi\)
\(410\) 0 0
\(411\) −114.099 + 65.8750i −0.277613 + 0.160280i
\(412\) 75.6861i 0.183704i
\(413\) 135.493 104.136i 0.328070 0.252145i
\(414\) 103.099 0.249032
\(415\) 0 0
\(416\) −72.5910 41.9104i −0.174497 0.100746i
\(417\) 79.4734 137.652i 0.190584 0.330101i
\(418\) −27.3467 + 15.7886i −0.0654228 + 0.0377719i
\(419\) 268.003i 0.639626i 0.947481 + 0.319813i \(0.103620\pi\)
−0.947481 + 0.319813i \(0.896380\pi\)
\(420\) 0 0
\(421\) −9.12915 −0.0216844 −0.0108422 0.999941i \(-0.503451\pi\)
−0.0108422 + 0.999941i \(0.503451\pi\)
\(422\) 21.4831 + 37.2099i 0.0509079 + 0.0881751i
\(423\) −65.4526 37.7891i −0.154734 0.0893358i
\(424\) −29.4609 + 51.0278i −0.0694833 + 0.120349i
\(425\) 0 0
\(426\) 291.422i 0.684089i
\(427\) −5.87299 44.3416i −0.0137541 0.103845i
\(428\) −166.064 −0.388000
\(429\) 14.8444 + 25.7112i 0.0346022 + 0.0599328i
\(430\) 0 0
\(431\) 134.221 232.478i 0.311419 0.539393i −0.667251 0.744833i \(-0.732529\pi\)
0.978670 + 0.205440i \(0.0658626\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 472.254i 1.09066i 0.838223 + 0.545328i \(0.183595\pi\)
−0.838223 + 0.545328i \(0.816405\pi\)
\(434\) −263.663 108.971i −0.607519 0.251086i
\(435\) 0 0
\(436\) 47.7924 + 82.7788i 0.109616 + 0.189860i
\(437\) −406.215 234.528i −0.929553 0.536678i
\(438\) −48.4136 + 83.8548i −0.110533 + 0.191449i
\(439\) 475.788 274.696i 1.08380 0.625731i 0.151880 0.988399i \(-0.451467\pi\)
0.931919 + 0.362667i \(0.118134\pi\)
\(440\) 0 0
\(441\) 37.8241 142.050i 0.0857689 0.322110i
\(442\) −264.404 −0.598198
\(443\) 235.405 + 407.734i 0.531388 + 0.920392i 0.999329 + 0.0366317i \(0.0116628\pi\)
−0.467940 + 0.883760i \(0.655004\pi\)
\(444\) 159.947 + 92.3457i 0.360242 + 0.207986i
\(445\) 0 0
\(446\) 20.4994 11.8353i 0.0459628 0.0265366i
\(447\) 171.327i 0.383283i
\(448\) 21.3898 51.7540i 0.0477450 0.115522i
\(449\) 559.525 1.24616 0.623079 0.782159i \(-0.285882\pi\)
0.623079 + 0.782159i \(0.285882\pi\)
\(450\) 0 0
\(451\) −38.1086 22.0020i −0.0844980 0.0487849i
\(452\) −16.2283 + 28.1082i −0.0359032 + 0.0621862i
\(453\) −146.685 + 84.6886i −0.323808 + 0.186951i
\(454\) 598.880i 1.31912i
\(455\) 0 0
\(456\) −94.5609 −0.207370
\(457\) 313.689 + 543.325i 0.686409 + 1.18890i 0.972992 + 0.230840i \(0.0741473\pi\)
−0.286583 + 0.958055i \(0.592519\pi\)
\(458\) −495.818 286.261i −1.08257 0.625023i
\(459\) 32.7814 56.7790i 0.0714192 0.123702i
\(460\) 0 0
\(461\) 223.659i 0.485160i 0.970131 + 0.242580i \(0.0779936\pi\)
−0.970131 + 0.242580i \(0.922006\pi\)
\(462\) −15.7265 + 12.0870i −0.0340401 + 0.0261623i
\(463\) 397.204 0.857893 0.428946 0.903330i \(-0.358885\pi\)
0.428946 + 0.903330i \(0.358885\pi\)
\(464\) −98.0764 169.873i −0.211371 0.366106i
\(465\) 0 0
\(466\) −196.079 + 339.620i −0.420771 + 0.728797i
\(467\) 289.014 166.862i 0.618874 0.357307i −0.157557 0.987510i \(-0.550362\pi\)
0.776430 + 0.630203i \(0.217028\pi\)
\(468\) 88.9054i 0.189969i
\(469\) −531.035 690.937i −1.13227 1.47321i
\(470\) 0 0
\(471\) −115.530 200.104i −0.245287 0.424849i
\(472\) −59.7983 34.5246i −0.126691 0.0731452i
\(473\) −36.7728 + 63.6924i −0.0777438 + 0.134656i
\(474\) −197.009 + 113.743i −0.415632 + 0.239965i
\(475\) 0 0
\(476\) −23.1940 175.117i −0.0487268 0.367892i
\(477\) 62.4961 0.131019
\(478\) 205.235 + 355.478i 0.429363 + 0.743678i
\(479\) 527.265 + 304.417i 1.10076 + 0.635526i 0.936421 0.350878i \(-0.114117\pi\)
0.164341 + 0.986404i \(0.447450\pi\)
\(480\) 0 0
\(481\) −684.169 + 395.005i −1.42239 + 0.821217i
\(482\) 572.484i 1.18773i
\(483\) −272.291 112.537i −0.563750 0.232996i
\(484\) −239.324 −0.494470
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −159.238 + 275.809i −0.326978 + 0.566343i −0.981911 0.189344i \(-0.939364\pi\)
0.654932 + 0.755687i \(0.272697\pi\)
\(488\) −15.6518 + 9.03659i −0.0320734 + 0.0185176i
\(489\) 56.7232i 0.115998i
\(490\) 0 0
\(491\) 523.303 1.06579 0.532895 0.846181i \(-0.321104\pi\)
0.532895 + 0.846181i \(0.321104\pi\)
\(492\) −65.8869 114.119i −0.133916 0.231950i
\(493\) −535.847 309.371i −1.08691 0.627528i
\(494\) 202.240 350.290i 0.409393 0.709090i
\(495\) 0 0
\(496\) 115.277i 0.232412i
\(497\) −318.100 + 769.663i −0.640039 + 1.54862i
\(498\) 14.1988 0.0285117
\(499\) 391.909 + 678.806i 0.785388 + 1.36033i 0.928767 + 0.370664i \(0.120870\pi\)
−0.143379 + 0.989668i \(0.545797\pi\)
\(500\) 0 0
\(501\) −148.661 + 257.488i −0.296728 + 0.513948i
\(502\) −190.822 + 110.171i −0.380123 + 0.219464i
\(503\) 58.0772i 0.115462i 0.998332 + 0.0577308i \(0.0183865\pi\)
−0.998332 + 0.0577308i \(0.981613\pi\)
\(504\) −58.8827 + 7.79895i −0.116831 + 0.0154741i
\(505\) 0 0
\(506\) 19.8773 + 34.4286i 0.0392833 + 0.0680406i
\(507\) −75.8404 43.7865i −0.149587 0.0863639i
\(508\) 80.5643 139.541i 0.158591 0.274688i
\(509\) −811.110 + 468.295i −1.59354 + 0.920029i −0.600843 + 0.799367i \(0.705168\pi\)
−0.992694 + 0.120662i \(0.961498\pi\)
\(510\) 0 0
\(511\) 219.394 168.620i 0.429343 0.329981i
\(512\) −22.6274 −0.0441942
\(513\) 50.1485 + 86.8597i 0.0977553 + 0.169317i
\(514\) 31.7229 + 18.3152i 0.0617178 + 0.0356328i
\(515\) 0 0
\(516\) −190.732 + 110.119i −0.369636 + 0.213410i
\(517\) 29.1426i 0.0563687i
\(518\) −321.632 418.480i −0.620910 0.807876i
\(519\) −350.672 −0.675668
\(520\) 0 0
\(521\) −607.133 350.528i −1.16532 0.672799i −0.212749 0.977107i \(-0.568242\pi\)
−0.952574 + 0.304308i \(0.901575\pi\)
\(522\) −104.026 + 180.178i −0.199283 + 0.345168i
\(523\) 594.464 343.214i 1.13664 0.656241i 0.191046 0.981581i \(-0.438812\pi\)
0.945597 + 0.325340i \(0.105479\pi\)
\(524\) 249.372i 0.475900i
\(525\) 0 0
\(526\) −446.615 −0.849078
\(527\) 181.814 + 314.910i 0.344997 + 0.597553i
\(528\) 6.94073 + 4.00723i 0.0131453 + 0.00758945i
\(529\) −30.7626 + 53.2824i −0.0581524 + 0.100723i
\(530\) 0 0
\(531\) 73.2376i 0.137924i
\(532\) 249.741 + 103.217i 0.469438 + 0.194017i
\(533\) 563.657 1.05752
\(534\) 186.141 + 322.406i 0.348579 + 0.603757i
\(535\) 0 0
\(536\) −176.056 + 304.937i −0.328462 + 0.568913i
\(537\) 118.038 68.1491i 0.219810 0.126907i
\(538\) 67.6316i 0.125709i
\(539\) 54.7282 14.7562i 0.101537 0.0273770i
\(540\) 0 0
\(541\) −398.250 689.789i −0.736136 1.27503i −0.954223 0.299096i \(-0.903315\pi\)
0.218087 0.975929i \(-0.430018\pi\)
\(542\) 416.599 + 240.524i 0.768634 + 0.443771i
\(543\) 50.3602 87.2263i 0.0927443 0.160638i
\(544\) −61.8132 + 35.6879i −0.113627 + 0.0656027i
\(545\) 0 0
\(546\) 97.0440 234.805i 0.177736 0.430045i
\(547\) 395.055 0.722221 0.361111 0.932523i \(-0.382398\pi\)
0.361111 + 0.932523i \(0.382398\pi\)
\(548\) −76.0659 131.750i −0.138806 0.240420i
\(549\) 16.6013 + 9.58476i 0.0302391 + 0.0174586i
\(550\) 0 0
\(551\) 819.730 473.271i 1.48771 0.858932i
\(552\) 119.049i 0.215668i
\(553\) 644.470 85.3592i 1.16541 0.154357i
\(554\) 297.815 0.537572
\(555\) 0 0
\(556\) 158.947 + 91.7680i 0.285876 + 0.165050i
\(557\) −20.8443 + 36.1034i −0.0374224 + 0.0648175i −0.884130 0.467241i \(-0.845248\pi\)
0.846708 + 0.532059i \(0.178581\pi\)
\(558\) 105.888 61.1346i 0.189764 0.109560i
\(559\) 942.063i 1.68526i
\(560\) 0 0
\(561\) 25.2808 0.0450637
\(562\) 333.603 + 577.817i 0.593599 + 1.02814i
\(563\) 640.642 + 369.875i 1.13791 + 0.656972i 0.945912 0.324424i \(-0.105170\pi\)
0.191996 + 0.981396i \(0.438504\pi\)
\(564\) 43.6350 75.5781i 0.0773671 0.134004i
\(565\) 0 0
\(566\) 662.234i 1.17003i
\(567\) 38.3911 + 49.9512i 0.0677091 + 0.0880974i
\(568\) 336.505 0.592439
\(569\) −2.38030 4.12281i −0.00418331 0.00724570i 0.863926 0.503618i \(-0.167998\pi\)
−0.868109 + 0.496373i \(0.834665\pi\)
\(570\) 0 0
\(571\) −399.848 + 692.557i −0.700260 + 1.21289i 0.268116 + 0.963387i \(0.413599\pi\)
−0.968375 + 0.249498i \(0.919734\pi\)
\(572\) −29.6887 + 17.1408i −0.0519033 + 0.0299664i
\(573\) 638.101i 1.11362i
\(574\) 49.4451 + 373.315i 0.0861412 + 0.650374i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 148.871 + 85.9510i 0.258009 + 0.148962i 0.623426 0.781882i \(-0.285740\pi\)
−0.365417 + 0.930844i \(0.619074\pi\)
\(578\) 91.7804 158.968i 0.158790 0.275032i
\(579\) 421.228 243.196i 0.727510 0.420028i
\(580\) 0 0
\(581\) −37.5000 15.4986i −0.0645439 0.0266758i
\(582\) −353.485 −0.607362
\(583\) 12.0491 + 20.8697i 0.0206675 + 0.0357971i
\(584\) −96.8271 55.9032i −0.165800 0.0957246i
\(585\) 0 0
\(586\) −77.7795 + 44.9060i −0.132730 + 0.0766314i
\(587\) 724.352i 1.23399i −0.786967 0.616994i \(-0.788350\pi\)
0.786967 0.616994i \(-0.211650\pi\)
\(588\) 164.026 + 43.6755i 0.278955 + 0.0742781i
\(589\) −556.271 −0.944433
\(590\) 0 0
\(591\) −11.4267 6.59720i −0.0193345 0.0111628i
\(592\) −106.632 + 184.691i −0.180121 + 0.311979i
\(593\) 894.293 516.320i 1.50808 0.870692i 0.508127 0.861282i \(-0.330338\pi\)
0.999956 0.00940925i \(-0.00299510\pi\)
\(594\) 8.50062i 0.0143108i
\(595\) 0 0
\(596\) −197.832 −0.331933
\(597\) −174.795 302.753i −0.292789 0.507125i
\(598\) −441.003 254.613i −0.737464 0.425775i
\(599\) 212.436 367.949i 0.354650 0.614272i −0.632408 0.774636i \(-0.717933\pi\)
0.987058 + 0.160363i \(0.0512666\pi\)
\(600\) 0 0
\(601\) 749.418i 1.24695i 0.781843 + 0.623476i \(0.214280\pi\)
−0.781843 + 0.623476i \(0.785720\pi\)
\(602\) 623.935 82.6395i 1.03644 0.137275i
\(603\) 373.471 0.619354
\(604\) −97.7900 169.377i −0.161904 0.280426i
\(605\) 0 0
\(606\) 47.8683 82.9104i 0.0789906 0.136816i
\(607\) 205.133 118.434i 0.337945 0.195113i −0.321418 0.946938i \(-0.604159\pi\)
0.659363 + 0.751825i \(0.270826\pi\)
\(608\) 109.189i 0.179588i
\(609\) 471.410 362.312i 0.774072 0.594929i
\(610\) 0 0
\(611\) 186.647 + 323.283i 0.305478 + 0.529104i
\(612\) 65.5628 + 37.8527i 0.107129 + 0.0618508i
\(613\) −469.189 + 812.659i −0.765398 + 1.32571i 0.174638 + 0.984633i \(0.444124\pi\)
−0.940036 + 0.341075i \(0.889209\pi\)
\(614\) −259.168 + 149.631i −0.422098 + 0.243698i
\(615\) 0 0
\(616\) −13.9568 18.1594i −0.0226572 0.0294796i
\(617\) −225.176 −0.364952 −0.182476 0.983210i \(-0.558411\pi\)
−0.182476 + 0.983210i \(0.558411\pi\)
\(618\) −46.3481 80.2772i −0.0749969 0.129898i
\(619\) 916.115 + 528.919i 1.47999 + 0.854473i 0.999743 0.0226591i \(-0.00721323\pi\)
0.480248 + 0.877133i \(0.340547\pi\)
\(620\) 0 0
\(621\) 109.353 63.1351i 0.176092 0.101667i
\(622\) 95.2182i 0.153084i
\(623\) −139.691 1054.68i −0.224222 1.69290i
\(624\) −102.659 −0.164518
\(625\) 0 0
\(626\) 169.301 + 97.7460i 0.270449 + 0.156144i
\(627\) −19.3371 + 33.4928i −0.0308406 + 0.0534175i
\(628\) 231.060 133.403i 0.367930 0.212424i
\(629\) 672.716i 1.06950i
\(630\) 0 0
\(631\) 877.283 1.39031 0.695153 0.718862i \(-0.255336\pi\)
0.695153 + 0.718862i \(0.255336\pi\)
\(632\) −131.340 227.487i −0.207816 0.359948i
\(633\) 45.5726 + 26.3114i 0.0719947 + 0.0415662i
\(634\) −14.0179 + 24.2797i −0.0221103 + 0.0382961i
\(635\) 0 0
\(636\) 72.1643i 0.113466i
\(637\) −512.598 + 514.205i −0.804707 + 0.807230i
\(638\) −80.2238 −0.125743
\(639\) −178.459 309.100i −0.279278 0.483724i
\(640\) 0 0
\(641\) −26.8684 + 46.5374i −0.0419163 + 0.0726012i −0.886222 0.463260i \(-0.846680\pi\)
0.844306 + 0.535861i \(0.180013\pi\)
\(642\) −176.138 + 101.693i −0.274358 + 0.158401i
\(643\) 99.7799i 0.155179i −0.996985 0.0775893i \(-0.975278\pi\)
0.996985 0.0775893i \(-0.0247223\pi\)
\(644\) 129.947 314.415i 0.201781 0.488222i
\(645\) 0 0
\(646\) −172.213 298.282i −0.266584 0.461737i
\(647\) 657.905 + 379.842i 1.01685 + 0.587081i 0.913191 0.407531i \(-0.133610\pi\)
0.103663 + 0.994612i \(0.466944\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) −24.4567 + 14.1201i −0.0376836 + 0.0217567i
\(650\) 0 0
\(651\) −346.388 + 45.8787i −0.532086 + 0.0704742i
\(652\) 65.4983 0.100458
\(653\) 574.896 + 995.749i 0.880392 + 1.52488i 0.850906 + 0.525318i \(0.176054\pi\)
0.0294854 + 0.999565i \(0.490613\pi\)
\(654\) 101.383 + 58.5334i 0.155020 + 0.0895007i
\(655\) 0 0
\(656\) 131.774 76.0796i 0.200875 0.115975i
\(657\) 118.589i 0.180500i
\(658\) −197.740 + 151.977i −0.300516 + 0.230968i
\(659\) 213.700 0.324280 0.162140 0.986768i \(-0.448160\pi\)
0.162140 + 0.986768i \(0.448160\pi\)
\(660\) 0 0
\(661\) 665.936 + 384.479i 1.00747 + 0.581662i 0.910449 0.413621i \(-0.135736\pi\)
0.0970187 + 0.995283i \(0.469069\pi\)
\(662\) −185.458 + 321.223i −0.280148 + 0.485231i
\(663\) −280.442 + 161.914i −0.422990 + 0.244213i
\(664\) 16.3954i 0.0246919i
\(665\) 0 0
\(666\) 226.200 0.339639
\(667\) −595.832 1032.01i −0.893301 1.54724i
\(668\) −297.322 171.659i −0.445092 0.256974i
\(669\) 14.4953 25.1065i 0.0216671 0.0375284i
\(670\) 0 0
\(671\) 7.39169i 0.0110159i
\(672\) −9.00545 67.9919i −0.0134010 0.101178i
\(673\) 1299.78 1.93133 0.965664 0.259796i \(-0.0836553\pi\)
0.965664 + 0.259796i \(0.0836553\pi\)
\(674\) −408.796 708.056i −0.606523 1.05053i
\(675\) 0 0
\(676\) 50.5603 87.5730i 0.0747933 0.129546i
\(677\) −1073.60 + 619.840i −1.58581 + 0.915569i −0.591826 + 0.806066i \(0.701593\pi\)
−0.993986 + 0.109504i \(0.965074\pi\)
\(678\) 39.7509i 0.0586297i
\(679\) 933.575 + 385.844i 1.37493 + 0.568253i
\(680\) 0 0
\(681\) 366.738 + 635.208i 0.538528 + 0.932758i
\(682\) 40.8301 + 23.5733i 0.0598682 + 0.0345649i
\(683\) −233.043 + 403.643i −0.341205 + 0.590985i −0.984657 0.174502i \(-0.944168\pi\)
0.643452 + 0.765487i \(0.277502\pi\)
\(684\) −100.297 + 57.9065i −0.146633 + 0.0846586i
\(685\) 0 0
\(686\) −385.528 294.391i −0.561995 0.429141i
\(687\) −701.193 −1.02066
\(688\) −127.155 220.239i −0.184818 0.320114i
\(689\) −267.325 154.340i −0.387989 0.224006i
\(690\) 0 0
\(691\) −93.9272 + 54.2289i −0.135929 + 0.0784788i −0.566423 0.824115i \(-0.691673\pi\)
0.430493 + 0.902594i \(0.358340\pi\)
\(692\) 404.921i 0.585145i
\(693\) −9.27879 + 22.4507i −0.0133893 + 0.0323963i
\(694\) 650.145 0.936808
\(695\) 0 0
\(696\) −208.051 120.119i −0.298924 0.172584i
\(697\) 239.985 415.666i 0.344311 0.596364i
\(698\) 476.606 275.169i 0.682817 0.394224i
\(699\) 480.295i 0.687117i
\(700\) 0 0
\(701\) 528.400 0.753780 0.376890 0.926258i \(-0.376993\pi\)
0.376890 + 0.926258i \(0.376993\pi\)
\(702\) 54.4432 + 94.2984i 0.0775544 + 0.134328i
\(703\) −891.235 514.555i −1.26776 0.731942i
\(704\) −4.62715 + 8.01446i −0.00657266 + 0.0113842i
\(705\) 0 0
\(706\) 913.521i 1.29394i
\(707\) −216.923 + 166.721i −0.306822 + 0.235815i
\(708\) −84.5675 −0.119446
\(709\) 466.779 + 808.484i 0.658362 + 1.14032i 0.981040 + 0.193808i \(0.0620837\pi\)
−0.322678 + 0.946509i \(0.604583\pi\)
\(710\) 0 0
\(711\) −139.307 + 241.286i −0.195931 + 0.339362i
\(712\) −372.283 + 214.938i −0.522869 + 0.301879i
\(713\) 700.326i 0.982224i
\(714\) −131.837 171.536i −0.184646 0.240246i
\(715\) 0 0
\(716\) 78.6918 + 136.298i 0.109905 + 0.190361i
\(717\) 435.370 + 251.361i 0.607211 + 0.350573i
\(718\) −46.6982 + 80.8836i −0.0650392 + 0.112651i
\(719\) 557.452 321.845i 0.775316 0.447629i −0.0594517 0.998231i \(-0.518935\pi\)
0.834768 + 0.550602i \(0.185602\pi\)
\(720\) 0 0
\(721\) 34.7821 + 262.608i 0.0482414 + 0.364227i
\(722\) 16.3670 0.0226690
\(723\) −350.574 607.211i −0.484887 0.839850i
\(724\) 100.720 + 58.1509i 0.139116 + 0.0803189i
\(725\) 0 0
\(726\) −253.841 + 146.555i −0.349643 + 0.201867i
\(727\) 317.353i 0.436524i 0.975890 + 0.218262i \(0.0700388\pi\)
−0.975890 + 0.218262i \(0.929961\pi\)
\(728\) 271.129 + 112.057i 0.372430 + 0.153924i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −694.719 401.096i −0.950368 0.548695i
\(732\) −11.0675 + 19.1695i −0.0151196 + 0.0261879i
\(733\) 727.023 419.747i 0.991846 0.572643i 0.0860205 0.996293i \(-0.472585\pi\)
0.905826 + 0.423651i \(0.139252\pi\)
\(734\) 848.431i 1.15590i
\(735\) 0 0
\(736\) −137.466 −0.186774
\(737\) 72.0044 + 124.715i 0.0976993 + 0.169220i
\(738\) −139.767 80.6946i −0.189386 0.109342i
\(739\) 459.403 795.709i 0.621654 1.07674i −0.367523 0.930014i \(-0.619794\pi\)
0.989178 0.146723i \(-0.0468725\pi\)
\(740\) 0 0
\(741\) 495.386i 0.668537i
\(742\) 78.7703 190.590i 0.106160 0.256860i
\(743\) 1034.18 1.39190 0.695952 0.718088i \(-0.254983\pi\)
0.695952 + 0.718088i \(0.254983\pi\)
\(744\) 70.5922 + 122.269i 0.0948819 + 0.164340i
\(745\) 0 0
\(746\) −286.203 + 495.719i −0.383651 + 0.664502i
\(747\) 15.0601 8.69498i 0.0201608 0.0116399i
\(748\) 29.1917i 0.0390263i
\(749\) 576.193 76.3160i 0.769283 0.101891i
\(750\) 0 0
\(751\) 340.948 + 590.540i 0.453992 + 0.786338i 0.998630 0.0523339i \(-0.0166660\pi\)
−0.544637 + 0.838672i \(0.683333\pi\)
\(752\) 87.2701 + 50.3854i 0.116051 + 0.0670019i
\(753\) −134.931 + 233.708i −0.179192 + 0.310369i
\(754\) 889.932 513.803i 1.18028 0.681436i
\(755\) 0 0
\(756\) −57.6787 + 44.3302i −0.0762946 + 0.0586378i
\(757\) −183.172 −0.241971 −0.120985 0.992654i \(-0.538605\pi\)
−0.120985 + 0.992654i \(0.538605\pi\)
\(758\) −169.476 293.541i −0.223583 0.387257i
\(759\) 42.1662 + 24.3447i 0.0555549 + 0.0320747i
\(760\) 0 0
\(761\) −673.743 + 388.985i −0.885338 + 0.511150i −0.872415 0.488766i \(-0.837447\pi\)
−0.0129235 + 0.999916i \(0.504114\pi\)
\(762\) 197.341i 0.258978i
\(763\) −203.867 265.254i −0.267191 0.347646i
\(764\) 736.816 0.964419
\(765\) 0 0
\(766\) −782.747 451.919i −1.02186 0.589973i
\(767\) 180.867 313.271i 0.235811 0.408437i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 302.546i 0.393428i 0.980461 + 0.196714i \(0.0630271\pi\)
−0.980461 + 0.196714i \(0.936973\pi\)
\(770\) 0 0
\(771\) 44.8630 0.0581881
\(772\) 280.819 + 486.393i 0.363755 + 0.630042i
\(773\) 110.995 + 64.0833i 0.143591 + 0.0829020i 0.570074 0.821593i \(-0.306914\pi\)
−0.426484 + 0.904495i \(0.640248\pi\)
\(774\) −134.868 + 233.598i −0.174248 + 0.301807i
\(775\) 0 0
\(776\) 408.169i 0.525991i
\(777\) −597.407 246.907i −0.768864 0.317769i
\(778\) −737.645 −0.948130
\(779\) 367.125 + 635.879i 0.471277 + 0.816277i
\(780\) 0 0
\(781\) 68.8130 119.188i 0.0881089 0.152609i
\(782\) −375.526 + 216.810i −0.480213 + 0.277251i
\(783\) 254.810i 0.325428i
\(784\) −50.4321 + 189.401i −0.0643267 + 0.241582i
\(785\) 0 0
\(786\) 152.708 + 264.499i 0.194285 + 0.336512i
\(787\) 466.311 + 269.225i 0.592518 + 0.342090i 0.766092 0.642731i \(-0.222199\pi\)
−0.173575 + 0.984821i \(0.555532\pi\)
\(788\) 7.61779 13.1944i 0.00966725 0.0167442i
\(789\) −473.707 + 273.495i −0.600389 + 0.346635i
\(790\) 0 0
\(791\) 43.3898 104.985i 0.0548544 0.132724i
\(792\) 9.81567 0.0123935
\(793\) −47.3409 81.9969i −0.0596985 0.103401i
\(794\) −177.784 102.644i −0.223909 0.129274i
\(795\) 0 0
\(796\) 349.589 201.836i 0.439183 0.253562i
\(797\) 207.481i 0.260328i 0.991492 + 0.130164i \(0.0415504\pi\)
−0.991492 + 0.130164i \(0.958450\pi\)
\(798\) 328.098 43.4561i 0.411150 0.0544563i
\(799\) 317.871 0.397836
\(800\) 0 0
\(801\) 394.866 + 227.976i 0.492966 + 0.284614i
\(802\) 151.351 262.148i 0.188717 0.326867i
\(803\) −39.6010 + 22.8636i −0.0493163 + 0.0284728i
\(804\) 431.247i 0.536376i
\(805\) 0 0
\(806\) −603.911 −0.749269
\(807\) −41.4157 71.7341i −0.0513206 0.0888899i
\(808\) 95.7366 + 55.2736i 0.118486 + 0.0684079i
\(809\) −722.858 + 1252.03i −0.893520 + 1.54762i −0.0578954 + 0.998323i \(0.518439\pi\)
−0.835625 + 0.549300i \(0.814894\pi\)
\(810\) 0 0
\(811\) 207.868i 0.256310i 0.991754 + 0.128155i \(0.0409055\pi\)
−0.991754 + 0.128155i \(0.959094\pi\)
\(812\) 418.362 + 544.337i 0.515224 + 0.670366i
\(813\) 589.161 0.724675
\(814\) 43.6109 + 75.5363i 0.0535760 + 0.0927964i
\(815\) 0 0
\(816\) −43.7085 + 75.7054i −0.0535644 + 0.0927762i
\(817\) 1062.77 613.591i 1.30082 0.751029i
\(818\) 783.435i 0.957745i
\(819\) −40.8571 308.475i −0.0498866 0.376648i
\(820\) 0 0
\(821\) −307.642 532.851i −0.374716 0.649027i 0.615568 0.788083i \(-0.288926\pi\)
−0.990285 + 0.139056i \(0.955593\pi\)
\(822\) −161.360 93.1613i −0.196302 0.113335i
\(823\) −167.804 + 290.645i −0.203893 + 0.353153i −0.949779 0.312920i \(-0.898693\pi\)
0.745886 + 0.666073i \(0.232026\pi\)
\(824\) 92.6961 53.5181i 0.112495 0.0649492i
\(825\) 0 0
\(826\) 223.348 + 92.3091i 0.270397 + 0.111754i
\(827\) 1453.38 1.75741 0.878707 0.477362i \(-0.158407\pi\)
0.878707 + 0.477362i \(0.158407\pi\)
\(828\) 72.9022 + 126.270i 0.0880461 + 0.152500i
\(829\) −11.2468 6.49333i −0.0135667 0.00783273i 0.493201 0.869915i \(-0.335827\pi\)
−0.506768 + 0.862082i \(0.669160\pi\)
\(830\) 0 0
\(831\) 315.880 182.374i 0.380121 0.219463i
\(832\) 118.541i 0.142477i
\(833\) 160.952 + 596.943i 0.193220 + 0.716618i
\(834\) 224.785 0.269526
\(835\) 0 0
\(836\) −38.6741 22.3285i −0.0462609 0.0267087i
\(837\) 74.8743 129.686i 0.0894555 0.154942i
\(838\) −328.236 + 189.507i −0.391689 + 0.226142i
\(839\) 940.714i 1.12123i −0.828076 0.560616i \(-0.810564\pi\)
0.828076 0.560616i \(-0.189436\pi\)
\(840\) 0 0
\(841\) 1563.74 1.85939
\(842\) −6.45529 11.1809i −0.00766661 0.0132790i
\(843\) 707.678 + 408.578i 0.839476 + 0.484671i
\(844\) −30.3818 + 52.6228i −0.0359973 + 0.0623492i
\(845\) 0 0
\(846\) 106.884i 0.126340i
\(847\) 830.381 109.983i 0.980379 0.129850i
\(848\) −83.3281 −0.0982643
\(849\) −405.534 702.406i −0.477661 0.827333i
\(850\) 0 0
\(851\) −647.806 + 1122.03i −0.761230 + 1.31849i
\(852\) 356.918 206.067i 0.418917 0.241862i
\(853\) 1176.97i 1.37980i −0.723903 0.689902i \(-0.757654\pi\)
0.723903 0.689902i \(-0.242346\pi\)
\(854\) 50.1543 38.5472i 0.0587287 0.0451372i
\(855\) 0 0
\(856\) −117.425 203.386i −0.137179 0.237601i
\(857\) −415.523 239.902i −0.484858 0.279933i 0.237581 0.971368i \(-0.423645\pi\)
−0.722439 + 0.691435i \(0.756979\pi\)
\(858\) −20.9931 + 36.3611i −0.0244675 + 0.0423789i
\(859\) 1185.54 684.470i 1.38014 0.796821i 0.387960 0.921676i \(-0.373180\pi\)
0.992175 + 0.124855i \(0.0398465\pi\)
\(860\) 0 0
\(861\) 281.052 + 365.681i 0.326425 + 0.424717i
\(862\) 379.635 0.440412
\(863\) 42.7677 + 74.0758i 0.0495570 + 0.0858352i 0.889740 0.456468i \(-0.150886\pi\)
−0.840183 + 0.542303i \(0.817552\pi\)
\(864\) 25.4558 + 14.6969i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) −578.391 + 333.934i −0.667888 + 0.385605i
\(867\) 224.815i 0.259302i
\(868\) −52.9762 399.975i −0.0610324 0.460800i
\(869\) −107.432 −0.123627
\(870\) 0 0
\(871\) −1597.51 922.321i −1.83411 1.05892i
\(872\) −67.5886 + 117.067i −0.0775099 + 0.134251i
\(873\) −374.927 + 216.464i −0.429470 + 0.247955i
\(874\) 663.346i 0.758977i
\(875\) 0 0
\(876\) −136.934 −0.156318
\(877\) −236.635 409.863i −0.269823 0.467347i 0.698993 0.715128i \(-0.253632\pi\)
−0.968816 + 0.247781i \(0.920299\pi\)
\(878\) 672.865 + 388.479i 0.766361 + 0.442459i
\(879\) −54.9984 + 95.2601i −0.0625693 + 0.108373i
\(880\) 0 0
\(881\) 442.658i 0.502449i 0.967929 + 0.251225i \(0.0808333\pi\)
−0.967929 + 0.251225i \(0.919167\pi\)
\(882\) 200.721 54.1200i 0.227575 0.0613605i
\(883\) −432.227 −0.489498 −0.244749 0.969586i \(-0.578706\pi\)
−0.244749 + 0.969586i \(0.578706\pi\)
\(884\) −186.962 323.827i −0.211495 0.366320i
\(885\) 0 0
\(886\) −332.913 + 576.622i −0.375748 + 0.650815i
\(887\) −451.613 + 260.739i −0.509146 + 0.293956i −0.732483 0.680786i \(-0.761638\pi\)
0.223337 + 0.974741i \(0.428305\pi\)
\(888\) 261.193i 0.294136i
\(889\) −215.407 + 521.191i −0.242302 + 0.586266i
\(890\) 0 0
\(891\) −5.20555 9.01627i −0.00584237 0.0101193i
\(892\) 28.9905 + 16.7377i 0.0325006 + 0.0187642i
\(893\) −243.137 + 421.125i −0.272270 + 0.471585i
\(894\) −209.832 + 121.147i −0.234712 + 0.135511i
\(895\) 0 0
\(896\) 78.5103 10.3986i 0.0876231 0.0116056i
\(897\) −623.673 −0.695287
\(898\) 395.644 + 685.275i 0.440583 + 0.763113i
\(899\) −1223.90 706.619i −1.36140 0.786005i
\(900\) 0 0
\(901\) −227.634 + 131.425i −0.252646 + 0.145865i
\(902\) 62.2311i 0.0689923i
\(903\) 611.177 469.733i 0.676830 0.520192i
\(904\) −45.9004 −0.0507748
\(905\) 0 0
\(906\) −207.444 119.768i −0.228967 0.132194i
\(907\) 633.871 1097.90i 0.698865 1.21047i −0.269995 0.962862i \(-0.587022\pi\)
0.968860 0.247608i \(-0.0796446\pi\)
\(908\) −733.475 + 423.472i −0.807792 + 0.466379i
\(909\) 117.253i 0.128991i
\(910\) 0 0
\(911\) 789.834 0.866997 0.433498 0.901154i \(-0.357279\pi\)
0.433498 + 0.901154i \(0.357279\pi\)
\(912\) −66.8646 115.813i −0.0733165 0.126988i
\(913\) 5.80713 + 3.35275i 0.00636049 + 0.00367223i
\(914\) −443.623 + 768.378i −0.485364 + 0.840676i
\(915\) 0 0
\(916\) 809.668i 0.883916i
\(917\) −114.601 865.244i −0.124973 0.943560i
\(918\) 92.7198 0.101002
\(919\) 506.816 + 877.831i 0.551486 + 0.955202i 0.998168 + 0.0605090i \(0.0192724\pi\)
−0.446681 + 0.894693i \(0.647394\pi\)
\(920\) 0 0
\(921\) −183.260 + 317.415i −0.198979 + 0.344642i
\(922\) −273.925 + 158.151i −0.297098 + 0.171530i
\(923\) 1762.88i 1.90995i
\(924\) −25.9238 10.7142i −0.0280561 0.0115955i
\(925\) 0 0
\(926\) 280.866 + 486.474i 0.303311 + 0.525350i
\(927\) −98.3191 56.7645i −0.106062 0.0612347i
\(928\) 138.701 240.237i 0.149462 0.258876i
\(929\) 546.568 315.561i 0.588340 0.339678i −0.176101 0.984372i \(-0.556348\pi\)
0.764441 + 0.644694i \(0.223015\pi\)
\(930\) 0 0
\(931\) −913.960 243.362i −0.981697 0.261399i
\(932\) −554.596 −0.595061
\(933\) 58.3090 + 100.994i 0.0624963 + 0.108247i
\(934\) 408.727 + 235.979i 0.437610 + 0.252654i
\(935\) 0 0
\(936\) −108.886 + 62.8656i −0.116332 + 0.0671641i
\(937\) 867.113i 0.925414i 0.886511 + 0.462707i \(0.153122\pi\)
−0.886511 + 0.462707i \(0.846878\pi\)
\(938\) 470.724 1138.95i 0.501838 1.21423i
\(939\) 239.428 0.254982
\(940\) 0 0
\(941\) −1151.28 664.692i −1.22346 0.706367i −0.257809 0.966196i \(-0.583001\pi\)
−0.965655 + 0.259829i \(0.916334\pi\)
\(942\) 163.384 282.990i 0.173444 0.300414i
\(943\) 800.550 462.197i 0.848939 0.490135i
\(944\) 97.6502i 0.103443i
\(945\) 0 0
\(946\) −104.009 −0.109946
\(947\) −770.741 1334.96i −0.813877 1.40968i −0.910132 0.414319i \(-0.864020\pi\)
0.0962547 0.995357i \(-0.469314\pi\)
\(948\) −278.613 160.858i −0.293896 0.169681i
\(949\) 292.866 507.258i 0.308604 0.534519i
\(950\) 0 0
\(951\) 34.3367i 0.0361059i
\(952\) 198.073 152.233i 0.208059 0.159908i
\(953\) 114.779 0.120439 0.0602196 0.998185i \(-0.480820\pi\)
0.0602196 + 0.998185i \(0.480820\pi\)
\(954\) 44.1914 + 76.5418i 0.0463222 + 0.0802325i
\(955\) 0 0
\(956\) −290.247 + 502.722i −0.303605 + 0.525860i
\(957\) −85.0902 + 49.1268i −0.0889135 + 0.0513342i
\(958\) 861.020i 0.898769i
\(959\) 324.472 + 422.176i 0.338345 + 0.440225i
\(960\) 0 0
\(961\) −65.2290 112.980i −0.0678761 0.117565i
\(962\) −967.561 558.622i −1.00578 0.580688i
\(963\) −124.548 + 215.724i −0.129333 + 0.224012i
\(964\) 701.147 404.808i 0.727331 0.419925i
\(965\) 0 0
\(966\) −54.7097 413.063i −0.0566353 0.427602i
\(967\) 881.904 0.912000 0.456000 0.889980i \(-0.349282\pi\)
0.456000 + 0.889980i \(0.349282\pi\)
\(968\) −169.227 293.110i −0.174822 0.302800i
\(969\) −365.319 210.917i −0.377007 0.217665i
\(970\) 0 0
\(971\) 407.102 235.041i 0.419261 0.242060i −0.275500 0.961301i \(-0.588843\pi\)
0.694761 + 0.719241i \(0.255510\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) −593.670 245.362i −0.610144 0.252171i
\(974\) −450.394 −0.462417
\(975\) 0 0
\(976\) −22.1350 12.7797i −0.0226794 0.0130939i
\(977\) −527.971 + 914.472i −0.540400 + 0.936000i 0.458481 + 0.888704i \(0.348394\pi\)
−0.998881 + 0.0472957i \(0.984940\pi\)
\(978\) 69.4715 40.1094i 0.0710342 0.0410116i
\(979\) 175.813i 0.179584i
\(980\) 0 0
\(981\) 143.377 0.146154
\(982\) 370.031 + 640.913i 0.376814 + 0.652661i
\(983\) 128.137 + 73.9799i 0.130353 + 0.0752593i 0.563758 0.825940i \(-0.309355\pi\)
−0.433406 + 0.901199i \(0.642688\pi\)
\(984\) 93.1781 161.389i 0.0946932 0.164013i
\(985\) 0 0
\(986\) 875.034i 0.887458i
\(987\) −116.668 + 282.286i −0.118205 + 0.286004i
\(988\) 572.022 0.578970
\(989\) −772.489 1337.99i −0.781081 1.35287i
\(990\) 0 0
\(991\) 653.220 1131.41i 0.659153 1.14169i −0.321682 0.946848i \(-0.604248\pi\)
0.980835 0.194839i \(-0.0624183\pi\)
\(992\) −141.184 + 81.5128i −0.142323 + 0.0821702i
\(993\) 454.278i 0.457480i
\(994\) −1167.57 + 154.643i −1.17462 + 0.155577i
\(995\) 0 0
\(996\) 10.0401 + 17.3900i 0.0100804 + 0.0174598i
\(997\) 306.223 + 176.798i 0.307145 + 0.177330i 0.645648 0.763635i \(-0.276587\pi\)
−0.338503 + 0.940965i \(0.609921\pi\)
\(998\) −554.242 + 959.976i −0.555353 + 0.961900i
\(999\) 239.921 138.519i 0.240161 0.138657i
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 1050.3.p.i.451.8 16
5.2 odd 4 1050.3.q.e.199.6 32
5.3 odd 4 1050.3.q.e.199.13 32
5.4 even 2 210.3.o.b.31.3 16
7.5 odd 6 inner 1050.3.p.i.901.8 16
15.14 odd 2 630.3.v.c.451.5 16
35.4 even 6 1470.3.f.d.391.16 16
35.12 even 12 1050.3.q.e.649.14 32
35.19 odd 6 210.3.o.b.61.3 yes 16
35.24 odd 6 1470.3.f.d.391.10 16
35.33 even 12 1050.3.q.e.649.6 32
105.89 even 6 630.3.v.c.271.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.o.b.31.3 16 5.4 even 2
210.3.o.b.61.3 yes 16 35.19 odd 6
630.3.v.c.271.5 16 105.89 even 6
630.3.v.c.451.5 16 15.14 odd 2
1050.3.p.i.451.8 16 1.1 even 1 trivial
1050.3.p.i.901.8 16 7.5 odd 6 inner
1050.3.q.e.199.6 32 5.2 odd 4
1050.3.q.e.199.13 32 5.3 odd 4
1050.3.q.e.649.6 32 35.33 even 12
1050.3.q.e.649.14 32 35.12 even 12
1470.3.f.d.391.10 16 35.24 odd 6
1470.3.f.d.391.16 16 35.4 even 6