Properties

Label 245.4.e.p.226.5
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $12$
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] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not 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: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.5
Root \(2.14754 + 3.71965i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.p.116.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.44043 - 2.49490i) q^{2} +(1.44526 + 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(2.50000 - 4.33013i) q^{5} +8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +O(q^{10})\) \(q+(1.44043 - 2.49490i) q^{2} +(1.44526 + 2.50327i) q^{3} +(-0.149696 - 0.259281i) q^{4} +(2.50000 - 4.33013i) q^{5} +8.32721 q^{6} +22.1844 q^{8} +(9.32244 - 16.1469i) q^{9} +(-7.20217 - 12.4745i) q^{10} +(23.2440 + 40.2598i) q^{11} +(0.432700 - 0.749459i) q^{12} -31.0537 q^{13} +14.4526 q^{15} +(33.1528 - 57.4223i) q^{16} +(30.9258 + 53.5651i) q^{17} +(-26.8567 - 46.5172i) q^{18} +(-12.3107 + 21.3227i) q^{19} -1.49696 q^{20} +133.926 q^{22} +(77.4708 - 134.183i) q^{23} +(32.0623 + 55.5335i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-44.7308 + 77.4760i) q^{26} +131.938 q^{27} +200.436 q^{29} +(20.8180 - 36.0579i) q^{30} +(-64.6273 - 111.938i) q^{31} +(-6.77096 - 11.7277i) q^{32} +(-67.1874 + 116.372i) q^{33} +178.186 q^{34} -5.58213 q^{36} +(38.9831 - 67.5207i) q^{37} +(35.4654 + 61.4279i) q^{38} +(-44.8808 - 77.7357i) q^{39} +(55.4611 - 96.0614i) q^{40} +235.479 q^{41} -278.388 q^{43} +(6.95909 - 12.0535i) q^{44} +(-46.6122 - 80.7347i) q^{45} +(-223.183 - 386.565i) q^{46} +(-184.042 + 318.771i) q^{47} +191.658 q^{48} -72.0217 q^{50} +(-89.3918 + 154.831i) q^{51} +(4.64862 + 8.05165i) q^{52} +(84.7920 + 146.864i) q^{53} +(190.047 - 329.172i) q^{54} +232.440 q^{55} -71.1686 q^{57} +(288.714 - 500.068i) q^{58} +(-345.745 - 598.847i) q^{59} +(-2.16350 - 3.74730i) q^{60} +(-348.286 + 603.249i) q^{61} -372.365 q^{62} +491.432 q^{64} +(-77.6343 + 134.467i) q^{65} +(193.558 + 335.252i) q^{66} +(-1.16656 - 2.02054i) q^{67} +(9.25895 - 16.0370i) q^{68} +447.863 q^{69} -866.599 q^{71} +(206.813 - 358.210i) q^{72} +(-376.222 - 651.635i) q^{73} +(-112.305 - 194.518i) q^{74} +(36.1315 - 62.5817i) q^{75} +7.37145 q^{76} -258.591 q^{78} +(-421.391 + 729.871i) q^{79} +(-165.764 - 287.111i) q^{80} +(-61.0215 - 105.692i) q^{81} +(339.192 - 587.497i) q^{82} -1443.44 q^{83} +309.258 q^{85} +(-400.999 + 694.550i) q^{86} +(289.682 + 501.744i) q^{87} +(515.655 + 893.141i) q^{88} +(719.031 - 1245.40i) q^{89} -268.567 q^{90} -46.3884 q^{92} +(186.807 - 323.559i) q^{93} +(530.201 + 918.335i) q^{94} +(61.5534 + 106.614i) q^{95} +(19.5716 - 33.8990i) q^{96} +23.4509 q^{97} +866.764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9} - 10 q^{10} + 16 q^{11} - 160 q^{12} + 336 q^{13} - 160 q^{15} - 298 q^{16} + 4 q^{17} - 354 q^{18} - 308 q^{19} - 140 q^{20} - 472 q^{22} + 336 q^{23} + 92 q^{24} - 150 q^{25} - 56 q^{26} + 1928 q^{27} + 352 q^{29} + 120 q^{30} - 392 q^{31} + 770 q^{32} - 188 q^{33} + 1624 q^{34} + 460 q^{36} + 140 q^{37} - 20 q^{38} - 140 q^{39} - 330 q^{40} + 1312 q^{41} - 776 q^{43} + 160 q^{44} + 350 q^{45} + 388 q^{46} - 628 q^{47} + 2792 q^{48} - 100 q^{50} - 744 q^{51} - 1520 q^{52} + 676 q^{53} - 2284 q^{54} + 160 q^{55} + 2936 q^{57} + 2012 q^{58} - 996 q^{59} + 800 q^{60} - 740 q^{61} - 728 q^{62} + 2852 q^{64} + 840 q^{65} + 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 2096 q^{69} - 448 q^{71} - 2858 q^{72} - 2640 q^{73} - 928 q^{74} - 400 q^{75} - 2680 q^{76} + 16 q^{78} - 1636 q^{79} + 1490 q^{80} - 4442 q^{81} + 1756 q^{82} + 280 q^{83} + 40 q^{85} - 1180 q^{86} - 1940 q^{87} + 5652 q^{88} + 1904 q^{89} - 3540 q^{90} - 3904 q^{92} + 1592 q^{93} + 3332 q^{94} + 1540 q^{95} + 6460 q^{96} + 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.44043 2.49490i 0.509270 0.882082i −0.490672 0.871344i \(-0.663249\pi\)
0.999942 0.0107374i \(-0.00341790\pi\)
\(3\) 1.44526 + 2.50327i 0.278141 + 0.481754i 0.970923 0.239393i \(-0.0769485\pi\)
−0.692782 + 0.721147i \(0.743615\pi\)
\(4\) −0.149696 0.259281i −0.0187120 0.0324102i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 8.32721 0.566595
\(7\) 0 0
\(8\) 22.1844 0.980422
\(9\) 9.32244 16.1469i 0.345275 0.598035i
\(10\) −7.20217 12.4745i −0.227753 0.394479i
\(11\) 23.2440 + 40.2598i 0.637122 + 1.10353i 0.986061 + 0.166382i \(0.0532085\pi\)
−0.348940 + 0.937145i \(0.613458\pi\)
\(12\) 0.432700 0.749459i 0.0104092 0.0180292i
\(13\) −31.0537 −0.662519 −0.331260 0.943540i \(-0.607474\pi\)
−0.331260 + 0.943540i \(0.607474\pi\)
\(14\) 0 0
\(15\) 14.4526 0.248777
\(16\) 33.1528 57.4223i 0.518012 0.897223i
\(17\) 30.9258 + 53.5651i 0.441212 + 0.764202i 0.997780 0.0666002i \(-0.0212152\pi\)
−0.556567 + 0.830803i \(0.687882\pi\)
\(18\) −26.8567 46.5172i −0.351677 0.609122i
\(19\) −12.3107 + 21.3227i −0.148645 + 0.257461i −0.930727 0.365715i \(-0.880825\pi\)
0.782082 + 0.623176i \(0.214158\pi\)
\(20\) −1.49696 −0.0167365
\(21\) 0 0
\(22\) 133.926 1.29787
\(23\) 77.4708 134.183i 0.702339 1.21649i −0.265305 0.964165i \(-0.585473\pi\)
0.967643 0.252322i \(-0.0811941\pi\)
\(24\) 32.0623 + 55.5335i 0.272695 + 0.472322i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −44.7308 + 77.4760i −0.337401 + 0.584396i
\(27\) 131.938 0.940422
\(28\) 0 0
\(29\) 200.436 1.28345 0.641724 0.766936i \(-0.278219\pi\)
0.641724 + 0.766936i \(0.278219\pi\)
\(30\) 20.8180 36.0579i 0.126694 0.219441i
\(31\) −64.6273 111.938i −0.374432 0.648536i 0.615810 0.787895i \(-0.288829\pi\)
−0.990242 + 0.139359i \(0.955496\pi\)
\(32\) −6.77096 11.7277i −0.0374046 0.0647867i
\(33\) −67.1874 + 116.372i −0.354419 + 0.613872i
\(34\) 178.186 0.898785
\(35\) 0 0
\(36\) −5.58213 −0.0258432
\(37\) 38.9831 67.5207i 0.173210 0.300009i −0.766330 0.642447i \(-0.777919\pi\)
0.939540 + 0.342438i \(0.111253\pi\)
\(38\) 35.4654 + 61.4279i 0.151401 + 0.262235i
\(39\) −44.8808 77.7357i −0.184274 0.319171i
\(40\) 55.4611 96.0614i 0.219229 0.379716i
\(41\) 235.479 0.896967 0.448483 0.893791i \(-0.351964\pi\)
0.448483 + 0.893791i \(0.351964\pi\)
\(42\) 0 0
\(43\) −278.388 −0.987296 −0.493648 0.869662i \(-0.664337\pi\)
−0.493648 + 0.869662i \(0.664337\pi\)
\(44\) 6.95909 12.0535i 0.0238437 0.0412985i
\(45\) −46.6122 80.7347i −0.154412 0.267449i
\(46\) −223.183 386.565i −0.715360 1.23904i
\(47\) −184.042 + 318.771i −0.571177 + 0.989308i 0.425268 + 0.905067i \(0.360180\pi\)
−0.996445 + 0.0842404i \(0.973154\pi\)
\(48\) 191.658 0.576321
\(49\) 0 0
\(50\) −72.0217 −0.203708
\(51\) −89.3918 + 154.831i −0.245438 + 0.425112i
\(52\) 4.64862 + 8.05165i 0.0123971 + 0.0214724i
\(53\) 84.7920 + 146.864i 0.219756 + 0.380629i 0.954733 0.297463i \(-0.0961405\pi\)
−0.734977 + 0.678092i \(0.762807\pi\)
\(54\) 190.047 329.172i 0.478929 0.829529i
\(55\) 232.440 0.569859
\(56\) 0 0
\(57\) −71.1686 −0.165377
\(58\) 288.714 500.068i 0.653622 1.13211i
\(59\) −345.745 598.847i −0.762918 1.32141i −0.941341 0.337458i \(-0.890433\pi\)
0.178423 0.983954i \(-0.442900\pi\)
\(60\) −2.16350 3.74730i −0.00465511 0.00806290i
\(61\) −348.286 + 603.249i −0.731041 + 1.26620i 0.225398 + 0.974267i \(0.427632\pi\)
−0.956439 + 0.291933i \(0.905702\pi\)
\(62\) −372.365 −0.762749
\(63\) 0 0
\(64\) 491.432 0.959827
\(65\) −77.6343 + 134.467i −0.148144 + 0.256593i
\(66\) 193.558 + 335.252i 0.360990 + 0.625253i
\(67\) −1.16656 2.02054i −0.00212713 0.00368430i 0.864960 0.501841i \(-0.167344\pi\)
−0.867087 + 0.498157i \(0.834010\pi\)
\(68\) 9.25895 16.0370i 0.0165120 0.0285995i
\(69\) 447.863 0.781396
\(70\) 0 0
\(71\) −866.599 −1.44854 −0.724270 0.689516i \(-0.757823\pi\)
−0.724270 + 0.689516i \(0.757823\pi\)
\(72\) 206.813 358.210i 0.338516 0.586326i
\(73\) −376.222 651.635i −0.603197 1.04477i −0.992334 0.123588i \(-0.960560\pi\)
0.389136 0.921180i \(-0.372774\pi\)
\(74\) −112.305 194.518i −0.176422 0.305571i
\(75\) 36.1315 62.5817i 0.0556281 0.0963508i
\(76\) 7.37145 0.0111258
\(77\) 0 0
\(78\) −258.591 −0.375380
\(79\) −421.391 + 729.871i −0.600130 + 1.03945i 0.392671 + 0.919679i \(0.371551\pi\)
−0.992801 + 0.119776i \(0.961782\pi\)
\(80\) −165.764 287.111i −0.231662 0.401250i
\(81\) −61.0215 105.692i −0.0837058 0.144983i
\(82\) 339.192 587.497i 0.456798 0.791198i
\(83\) −1443.44 −1.90890 −0.954450 0.298372i \(-0.903556\pi\)
−0.954450 + 0.298372i \(0.903556\pi\)
\(84\) 0 0
\(85\) 309.258 0.394632
\(86\) −400.999 + 694.550i −0.502800 + 0.870875i
\(87\) 289.682 + 501.744i 0.356979 + 0.618306i
\(88\) 515.655 + 893.141i 0.624648 + 1.08192i
\(89\) 719.031 1245.40i 0.856372 1.48328i −0.0189949 0.999820i \(-0.506047\pi\)
0.875367 0.483460i \(-0.160620\pi\)
\(90\) −268.567 −0.314549
\(91\) 0 0
\(92\) −46.3884 −0.0525687
\(93\) 186.807 323.559i 0.208290 0.360768i
\(94\) 530.201 + 918.335i 0.581767 + 1.00765i
\(95\) 61.5534 + 106.614i 0.0664763 + 0.115140i
\(96\) 19.5716 33.8990i 0.0208075 0.0360397i
\(97\) 23.4509 0.0245472 0.0122736 0.999925i \(-0.496093\pi\)
0.0122736 + 0.999925i \(0.496093\pi\)
\(98\) 0 0
\(99\) 866.764 0.879930
\(100\) −3.74241 + 6.48204i −0.00374241 + 0.00648204i
\(101\) 738.207 + 1278.61i 0.727271 + 1.25967i 0.958032 + 0.286660i \(0.0925450\pi\)
−0.230761 + 0.973010i \(0.574122\pi\)
\(102\) 257.526 + 446.048i 0.249989 + 0.432993i
\(103\) −504.721 + 874.202i −0.482831 + 0.836289i −0.999806 0.0197124i \(-0.993725\pi\)
0.516974 + 0.856001i \(0.327058\pi\)
\(104\) −688.909 −0.649549
\(105\) 0 0
\(106\) 488.549 0.447661
\(107\) −709.253 + 1228.46i −0.640805 + 1.10991i 0.344449 + 0.938805i \(0.388066\pi\)
−0.985253 + 0.171101i \(0.945267\pi\)
\(108\) −19.7506 34.2090i −0.0175972 0.0304793i
\(109\) 438.930 + 760.249i 0.385705 + 0.668061i 0.991867 0.127281i \(-0.0406249\pi\)
−0.606162 + 0.795341i \(0.707292\pi\)
\(110\) 334.815 579.916i 0.290212 0.502662i
\(111\) 225.363 0.192707
\(112\) 0 0
\(113\) −1500.11 −1.24884 −0.624419 0.781090i \(-0.714664\pi\)
−0.624419 + 0.781090i \(0.714664\pi\)
\(114\) −102.514 + 177.559i −0.0842218 + 0.145876i
\(115\) −387.354 670.917i −0.314095 0.544029i
\(116\) −30.0045 51.9693i −0.0240159 0.0415968i
\(117\) −289.496 + 501.422i −0.228752 + 0.396210i
\(118\) −1992.09 −1.55412
\(119\) 0 0
\(120\) 320.623 0.243906
\(121\) −415.070 + 718.922i −0.311848 + 0.540137i
\(122\) 1003.37 + 1737.88i 0.744594 + 1.28968i
\(123\) 340.329 + 589.467i 0.249483 + 0.432117i
\(124\) −19.3489 + 33.5133i −0.0140128 + 0.0242708i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 416.639 0.291108 0.145554 0.989350i \(-0.453503\pi\)
0.145554 + 0.989350i \(0.453503\pi\)
\(128\) 762.042 1319.90i 0.526216 0.911433i
\(129\) −402.343 696.878i −0.274607 0.475634i
\(130\) 223.654 + 387.380i 0.150890 + 0.261350i
\(131\) 205.248 355.500i 0.136890 0.237101i −0.789428 0.613843i \(-0.789623\pi\)
0.926318 + 0.376743i \(0.122956\pi\)
\(132\) 40.2308 0.0265276
\(133\) 0 0
\(134\) −6.72139 −0.00433313
\(135\) 329.844 571.306i 0.210285 0.364224i
\(136\) 686.071 + 1188.31i 0.432574 + 0.749241i
\(137\) −880.987 1525.91i −0.549400 0.951589i −0.998316 0.0580146i \(-0.981523\pi\)
0.448916 0.893574i \(-0.351810\pi\)
\(138\) 645.116 1117.37i 0.397942 0.689255i
\(139\) 865.719 0.528268 0.264134 0.964486i \(-0.414914\pi\)
0.264134 + 0.964486i \(0.414914\pi\)
\(140\) 0 0
\(141\) −1063.96 −0.635470
\(142\) −1248.28 + 2162.08i −0.737698 + 1.27773i
\(143\) −721.814 1250.22i −0.422106 0.731108i
\(144\) −618.129 1070.63i −0.357713 0.619578i
\(145\) 501.089 867.912i 0.286988 0.497077i
\(146\) −2167.69 −1.22876
\(147\) 0 0
\(148\) −23.3425 −0.0129645
\(149\) −1509.62 + 2614.73i −0.830018 + 1.43763i 0.0680059 + 0.997685i \(0.478336\pi\)
−0.898023 + 0.439948i \(0.854997\pi\)
\(150\) −104.090 180.289i −0.0566595 0.0981371i
\(151\) −270.948 469.296i −0.146023 0.252919i 0.783731 0.621100i \(-0.213314\pi\)
−0.929754 + 0.368181i \(0.879981\pi\)
\(152\) −273.105 + 473.032i −0.145735 + 0.252421i
\(153\) 1153.22 0.609359
\(154\) 0 0
\(155\) −646.273 −0.334902
\(156\) −13.4370 + 23.2735i −0.00689627 + 0.0119447i
\(157\) −1293.04 2239.62i −0.657300 1.13848i −0.981312 0.192424i \(-0.938365\pi\)
0.324012 0.946053i \(-0.394968\pi\)
\(158\) 1213.97 + 2102.66i 0.611256 + 1.05873i
\(159\) −245.093 + 424.514i −0.122246 + 0.211737i
\(160\) −67.7096 −0.0334557
\(161\) 0 0
\(162\) −351.590 −0.170515
\(163\) 1233.07 2135.74i 0.592525 1.02628i −0.401366 0.915918i \(-0.631464\pi\)
0.993891 0.110366i \(-0.0352024\pi\)
\(164\) −35.2503 61.0553i −0.0167841 0.0290709i
\(165\) 335.937 + 581.860i 0.158501 + 0.274532i
\(166\) −2079.19 + 3601.26i −0.972145 + 1.68381i
\(167\) 459.020 0.212695 0.106347 0.994329i \(-0.466084\pi\)
0.106347 + 0.994329i \(0.466084\pi\)
\(168\) 0 0
\(169\) −1232.67 −0.561068
\(170\) 445.466 771.569i 0.200974 0.348098i
\(171\) 229.531 + 397.560i 0.102647 + 0.177790i
\(172\) 41.6736 + 72.1807i 0.0184743 + 0.0319984i
\(173\) 2250.73 3898.38i 0.989132 1.71323i 0.367233 0.930129i \(-0.380305\pi\)
0.621899 0.783097i \(-0.286361\pi\)
\(174\) 1669.07 0.727195
\(175\) 0 0
\(176\) 3082.41 1.32015
\(177\) 999.383 1730.98i 0.424397 0.735077i
\(178\) −2071.43 3587.82i −0.872249 1.51078i
\(179\) −980.055 1697.51i −0.409233 0.708813i 0.585571 0.810621i \(-0.300870\pi\)
−0.994804 + 0.101808i \(0.967537\pi\)
\(180\) −13.9553 + 24.1714i −0.00577872 + 0.0100090i
\(181\) 3645.47 1.49705 0.748524 0.663108i \(-0.230763\pi\)
0.748524 + 0.663108i \(0.230763\pi\)
\(182\) 0 0
\(183\) −2013.46 −0.813329
\(184\) 1718.65 2976.78i 0.688588 1.19267i
\(185\) −194.915 337.604i −0.0774620 0.134168i
\(186\) −538.165 932.129i −0.212151 0.367457i
\(187\) −1437.68 + 2490.14i −0.562212 + 0.973780i
\(188\) 110.202 0.0427515
\(189\) 0 0
\(190\) 354.654 0.135417
\(191\) −1257.22 + 2177.57i −0.476280 + 0.824941i −0.999631 0.0271763i \(-0.991348\pi\)
0.523351 + 0.852117i \(0.324682\pi\)
\(192\) 710.247 + 1230.18i 0.266967 + 0.462400i
\(193\) −1094.68 1896.05i −0.408274 0.707152i 0.586422 0.810006i \(-0.300536\pi\)
−0.994697 + 0.102854i \(0.967203\pi\)
\(194\) 33.7795 58.5078i 0.0125012 0.0216526i
\(195\) −448.808 −0.164819
\(196\) 0 0
\(197\) −3886.50 −1.40559 −0.702795 0.711392i \(-0.748065\pi\)
−0.702795 + 0.711392i \(0.748065\pi\)
\(198\) 1248.52 2162.49i 0.448122 0.776170i
\(199\) −484.680 839.491i −0.172654 0.299045i 0.766693 0.642014i \(-0.221901\pi\)
−0.939347 + 0.342969i \(0.888567\pi\)
\(200\) −277.305 480.307i −0.0980422 0.169814i
\(201\) 3.37196 5.84041i 0.00118328 0.00204951i
\(202\) 4253.35 1.48151
\(203\) 0 0
\(204\) 53.5264 0.0183706
\(205\) 588.697 1019.65i 0.200568 0.347394i
\(206\) 1454.03 + 2518.46i 0.491783 + 0.851794i
\(207\) −1444.43 2501.83i −0.485001 0.840046i
\(208\) −1029.52 + 1783.17i −0.343193 + 0.594427i
\(209\) −1144.60 −0.378821
\(210\) 0 0
\(211\) 3079.69 1.00481 0.502404 0.864633i \(-0.332449\pi\)
0.502404 + 0.864633i \(0.332449\pi\)
\(212\) 25.3861 43.9700i 0.00822417 0.0142447i
\(213\) −1252.46 2169.33i −0.402898 0.697840i
\(214\) 2043.26 + 3539.04i 0.652685 + 1.13048i
\(215\) −695.969 + 1205.45i −0.220766 + 0.382378i
\(216\) 2926.96 0.922011
\(217\) 0 0
\(218\) 2529.00 0.785712
\(219\) 1087.48 1883.57i 0.335547 0.581185i
\(220\) −34.7954 60.2675i −0.0106632 0.0184692i
\(221\) −960.362 1663.40i −0.292312 0.506299i
\(222\) 324.621 562.259i 0.0981401 0.169984i
\(223\) −162.003 −0.0486480 −0.0243240 0.999704i \(-0.507743\pi\)
−0.0243240 + 0.999704i \(0.507743\pi\)
\(224\) 0 0
\(225\) −466.122 −0.138110
\(226\) −2160.81 + 3742.63i −0.635995 + 1.10158i
\(227\) 189.976 + 329.048i 0.0555470 + 0.0962101i 0.892462 0.451123i \(-0.148976\pi\)
−0.836915 + 0.547333i \(0.815643\pi\)
\(228\) 10.6537 + 18.4527i 0.00309455 + 0.00535991i
\(229\) −2390.75 + 4140.90i −0.689892 + 1.19493i 0.281980 + 0.959420i \(0.409009\pi\)
−0.971872 + 0.235508i \(0.924325\pi\)
\(230\) −2231.83 −0.639838
\(231\) 0 0
\(232\) 4446.55 1.25832
\(233\) 1262.27 2186.31i 0.354910 0.614722i −0.632193 0.774811i \(-0.717845\pi\)
0.987103 + 0.160090i \(0.0511783\pi\)
\(234\) 834.000 + 1444.53i 0.232993 + 0.403555i
\(235\) 920.211 + 1593.85i 0.255438 + 0.442432i
\(236\) −103.513 + 179.290i −0.0285515 + 0.0494526i
\(237\) −2436.08 −0.667682
\(238\) 0 0
\(239\) 113.452 0.0307053 0.0153527 0.999882i \(-0.495113\pi\)
0.0153527 + 0.999882i \(0.495113\pi\)
\(240\) 479.144 829.902i 0.128869 0.223208i
\(241\) 3362.67 + 5824.32i 0.898791 + 1.55675i 0.829041 + 0.559187i \(0.188887\pi\)
0.0697499 + 0.997565i \(0.477780\pi\)
\(242\) 1195.76 + 2071.12i 0.317630 + 0.550151i
\(243\) 1957.54 3390.56i 0.516775 0.895081i
\(244\) 208.549 0.0547170
\(245\) 0 0
\(246\) 1960.88 0.508217
\(247\) 382.292 662.150i 0.0984805 0.170573i
\(248\) −1433.72 2483.27i −0.367102 0.635839i
\(249\) −2086.16 3613.33i −0.530943 0.919620i
\(250\) −180.054 + 311.863i −0.0455505 + 0.0788958i
\(251\) 3815.00 0.959366 0.479683 0.877442i \(-0.340752\pi\)
0.479683 + 0.877442i \(0.340752\pi\)
\(252\) 0 0
\(253\) 7202.94 1.78990
\(254\) 600.141 1039.48i 0.148253 0.256781i
\(255\) 446.959 + 774.156i 0.109763 + 0.190116i
\(256\) −229.615 397.705i −0.0560584 0.0970961i
\(257\) 1100.95 1906.90i 0.267220 0.462838i −0.700923 0.713237i \(-0.747228\pi\)
0.968143 + 0.250399i \(0.0805617\pi\)
\(258\) −2318.19 −0.559397
\(259\) 0 0
\(260\) 46.4862 0.0110883
\(261\) 1868.55 3236.42i 0.443143 0.767546i
\(262\) −591.292 1024.15i −0.139428 0.241496i
\(263\) 602.090 + 1042.85i 0.141165 + 0.244505i 0.927936 0.372740i \(-0.121582\pi\)
−0.786770 + 0.617246i \(0.788248\pi\)
\(264\) −1490.51 + 2581.65i −0.347480 + 0.601853i
\(265\) 847.920 0.196556
\(266\) 0 0
\(267\) 4156.75 0.952767
\(268\) −0.349258 + 0.604933i −7.96058e−5 + 0.000137881i
\(269\) 2564.49 + 4441.83i 0.581263 + 1.00678i 0.995330 + 0.0965307i \(0.0307746\pi\)
−0.414067 + 0.910246i \(0.635892\pi\)
\(270\) −950.236 1645.86i −0.214183 0.370977i
\(271\) 404.196 700.087i 0.0906020 0.156927i −0.817163 0.576407i \(-0.804454\pi\)
0.907765 + 0.419480i \(0.137788\pi\)
\(272\) 4101.10 0.914213
\(273\) 0 0
\(274\) −5076.01 −1.11917
\(275\) 581.101 1006.50i 0.127424 0.220705i
\(276\) −67.0433 116.122i −0.0146215 0.0253252i
\(277\) −90.1326 156.114i −0.0195507 0.0338628i 0.856085 0.516836i \(-0.172890\pi\)
−0.875635 + 0.482973i \(0.839557\pi\)
\(278\) 1247.01 2159.88i 0.269031 0.465976i
\(279\) −2409.93 −0.517129
\(280\) 0 0
\(281\) −3068.29 −0.651384 −0.325692 0.945476i \(-0.605597\pi\)
−0.325692 + 0.945476i \(0.605597\pi\)
\(282\) −1532.56 + 2654.47i −0.323626 + 0.560537i
\(283\) −1934.09 3349.94i −0.406253 0.703651i 0.588214 0.808706i \(-0.299831\pi\)
−0.994466 + 0.105055i \(0.966498\pi\)
\(284\) 129.727 + 224.693i 0.0271051 + 0.0469475i
\(285\) −177.922 + 308.169i −0.0369795 + 0.0640504i
\(286\) −4158.90 −0.859863
\(287\) 0 0
\(288\) −252.488 −0.0516596
\(289\) 543.688 941.696i 0.110663 0.191674i
\(290\) −1443.57 2500.34i −0.292308 0.506293i
\(291\) 33.8927 + 58.7039i 0.00682758 + 0.0118257i
\(292\) −112.638 + 195.095i −0.0225741 + 0.0390995i
\(293\) 1967.79 0.392353 0.196176 0.980569i \(-0.437147\pi\)
0.196176 + 0.980569i \(0.437147\pi\)
\(294\) 0 0
\(295\) −3457.45 −0.682374
\(296\) 864.817 1497.91i 0.169819 0.294136i
\(297\) 3066.76 + 5311.79i 0.599163 + 1.03778i
\(298\) 4349.00 + 7532.70i 0.845406 + 1.46429i
\(299\) −2405.76 + 4166.90i −0.465313 + 0.805946i
\(300\) −21.6350 −0.00416366
\(301\) 0 0
\(302\) −1561.13 −0.297460
\(303\) −2133.81 + 3695.86i −0.404567 + 0.700731i
\(304\) 816.266 + 1413.81i 0.154000 + 0.266736i
\(305\) 1741.43 + 3016.25i 0.326931 + 0.566262i
\(306\) 1661.13 2877.16i 0.310328 0.537505i
\(307\) −5487.54 −1.02016 −0.510082 0.860126i \(-0.670385\pi\)
−0.510082 + 0.860126i \(0.670385\pi\)
\(308\) 0 0
\(309\) −2917.82 −0.537180
\(310\) −930.913 + 1612.39i −0.170556 + 0.295411i
\(311\) −2586.40 4479.77i −0.471579 0.816799i 0.527892 0.849312i \(-0.322983\pi\)
−0.999471 + 0.0325121i \(0.989649\pi\)
\(312\) −995.654 1724.52i −0.180666 0.312923i
\(313\) 2881.46 4990.83i 0.520351 0.901274i −0.479370 0.877613i \(-0.659135\pi\)
0.999720 0.0236604i \(-0.00753204\pi\)
\(314\) −7450.17 −1.33897
\(315\) 0 0
\(316\) 252.323 0.0449186
\(317\) −1590.44 + 2754.72i −0.281792 + 0.488077i −0.971826 0.235699i \(-0.924262\pi\)
0.690035 + 0.723776i \(0.257595\pi\)
\(318\) 706.081 + 1222.97i 0.124513 + 0.215662i
\(319\) 4658.94 + 8069.51i 0.817713 + 1.41632i
\(320\) 1228.58 2127.96i 0.214624 0.371739i
\(321\) −4100.23 −0.712936
\(322\) 0 0
\(323\) −1522.87 −0.262337
\(324\) −18.2694 + 31.6435i −0.00313261 + 0.00542584i
\(325\) 388.172 + 672.333i 0.0662519 + 0.114752i
\(326\) −3552.32 6152.79i −0.603511 1.04531i
\(327\) −1268.74 + 2197.52i −0.214561 + 0.371630i
\(328\) 5223.97 0.879406
\(329\) 0 0
\(330\) 1935.58 0.322879
\(331\) −4616.51 + 7996.03i −0.766606 + 1.32780i 0.172788 + 0.984959i \(0.444722\pi\)
−0.939394 + 0.342841i \(0.888611\pi\)
\(332\) 216.078 + 374.258i 0.0357194 + 0.0618678i
\(333\) −726.835 1258.92i −0.119611 0.207172i
\(334\) 661.188 1145.21i 0.108319 0.187614i
\(335\) −11.6656 −0.00190256
\(336\) 0 0
\(337\) −3259.50 −0.526874 −0.263437 0.964677i \(-0.584856\pi\)
−0.263437 + 0.964677i \(0.584856\pi\)
\(338\) −1775.57 + 3075.38i −0.285735 + 0.494908i
\(339\) −2168.05 3755.18i −0.347353 0.601632i
\(340\) −46.2948 80.1849i −0.00738437 0.0127901i
\(341\) 3004.40 5203.77i 0.477118 0.826392i
\(342\) 1322.50 0.209101
\(343\) 0 0
\(344\) −6175.87 −0.967967
\(345\) 1119.66 1939.30i 0.174725 0.302633i
\(346\) −6484.05 11230.7i −1.00747 1.74499i
\(347\) −925.566 1603.13i −0.143190 0.248013i 0.785506 0.618854i \(-0.212403\pi\)
−0.928696 + 0.370841i \(0.879069\pi\)
\(348\) 86.7286 150.218i 0.0133596 0.0231395i
\(349\) −1102.14 −0.169043 −0.0845216 0.996422i \(-0.526936\pi\)
−0.0845216 + 0.996422i \(0.526936\pi\)
\(350\) 0 0
\(351\) −4097.15 −0.623048
\(352\) 314.769 545.196i 0.0476626 0.0825541i
\(353\) 1335.12 + 2312.50i 0.201307 + 0.348674i 0.948950 0.315427i \(-0.102148\pi\)
−0.747643 + 0.664101i \(0.768814\pi\)
\(354\) −2879.09 4986.73i −0.432265 0.748705i
\(355\) −2166.50 + 3752.48i −0.323904 + 0.561017i
\(356\) −430.545 −0.0640978
\(357\) 0 0
\(358\) −5646.82 −0.833641
\(359\) −217.726 + 377.113i −0.0320088 + 0.0554409i −0.881586 0.472023i \(-0.843524\pi\)
0.849577 + 0.527464i \(0.176857\pi\)
\(360\) −1034.06 1791.05i −0.151389 0.262213i
\(361\) 3126.39 + 5415.07i 0.455809 + 0.789484i
\(362\) 5251.06 9095.10i 0.762402 1.32052i
\(363\) −2399.54 −0.346951
\(364\) 0 0
\(365\) −3762.22 −0.539516
\(366\) −2900.25 + 5023.39i −0.414204 + 0.717422i
\(367\) −1237.33 2143.11i −0.175989 0.304822i 0.764514 0.644607i \(-0.222979\pi\)
−0.940503 + 0.339785i \(0.889646\pi\)
\(368\) −5136.74 8897.10i −0.727639 1.26031i
\(369\) 2195.24 3802.26i 0.309701 0.536417i
\(370\) −1123.05 −0.157796
\(371\) 0 0
\(372\) −111.857 −0.0155901
\(373\) −2719.09 + 4709.61i −0.377451 + 0.653764i −0.990691 0.136133i \(-0.956533\pi\)
0.613240 + 0.789897i \(0.289866\pi\)
\(374\) 4141.77 + 7173.75i 0.572636 + 0.991834i
\(375\) −180.658 312.908i −0.0248777 0.0430894i
\(376\) −4082.87 + 7071.74i −0.559995 + 0.969939i
\(377\) −6224.28 −0.850309
\(378\) 0 0
\(379\) 10597.1 1.43624 0.718122 0.695917i \(-0.245002\pi\)
0.718122 + 0.695917i \(0.245002\pi\)
\(380\) 18.4286 31.9193i 0.00248781 0.00430902i
\(381\) 602.153 + 1042.96i 0.0809691 + 0.140243i
\(382\) 3621.89 + 6273.30i 0.485110 + 0.840236i
\(383\) −2335.68 + 4045.52i −0.311613 + 0.539729i −0.978712 0.205240i \(-0.934203\pi\)
0.667099 + 0.744969i \(0.267536\pi\)
\(384\) 4405.40 0.585448
\(385\) 0 0
\(386\) −6307.27 −0.831688
\(387\) −2595.25 + 4495.11i −0.340889 + 0.590437i
\(388\) −3.51051 6.08039i −0.000459328 0.000795580i
\(389\) −1778.84 3081.05i −0.231853 0.401582i 0.726500 0.687166i \(-0.241146\pi\)
−0.958354 + 0.285585i \(0.907812\pi\)
\(390\) −646.477 + 1119.73i −0.0839376 + 0.145384i
\(391\) 9583.40 1.23952
\(392\) 0 0
\(393\) 1186.55 0.152299
\(394\) −5598.24 + 9696.43i −0.715825 + 1.23985i
\(395\) 2106.96 + 3649.36i 0.268386 + 0.464858i
\(396\) −129.751 224.736i −0.0164653 0.0285187i
\(397\) −4592.28 + 7954.07i −0.580554 + 1.00555i 0.414859 + 0.909886i \(0.363831\pi\)
−0.995414 + 0.0956642i \(0.969503\pi\)
\(398\) −2792.60 −0.351709
\(399\) 0 0
\(400\) −1657.64 −0.207205
\(401\) 4603.26 7973.08i 0.573256 0.992909i −0.422972 0.906143i \(-0.639013\pi\)
0.996229 0.0867664i \(-0.0276534\pi\)
\(402\) −9.71417 16.8254i −0.00120522 0.00208750i
\(403\) 2006.92 + 3476.08i 0.248069 + 0.429668i
\(404\) 221.014 382.807i 0.0272174 0.0471420i
\(405\) −610.215 −0.0748687
\(406\) 0 0
\(407\) 3624.50 0.441424
\(408\) −1983.11 + 3434.84i −0.240633 + 0.416789i
\(409\) −3826.83 6628.26i −0.462652 0.801336i 0.536441 0.843938i \(-0.319769\pi\)
−0.999092 + 0.0426020i \(0.986435\pi\)
\(410\) −1695.96 2937.49i −0.204286 0.353834i
\(411\) 2546.51 4410.69i 0.305621 0.529351i
\(412\) 302.219 0.0361390
\(413\) 0 0
\(414\) −8322.44 −0.987985
\(415\) −3608.61 + 6250.30i −0.426843 + 0.739314i
\(416\) 210.264 + 364.187i 0.0247813 + 0.0429225i
\(417\) 1251.19 + 2167.12i 0.146933 + 0.254495i
\(418\) −1648.72 + 2855.66i −0.192922 + 0.334151i
\(419\) 370.864 0.0432408 0.0216204 0.999766i \(-0.493117\pi\)
0.0216204 + 0.999766i \(0.493117\pi\)
\(420\) 0 0
\(421\) 1221.96 0.141460 0.0707302 0.997495i \(-0.477467\pi\)
0.0707302 + 0.997495i \(0.477467\pi\)
\(422\) 4436.09 7683.53i 0.511719 0.886323i
\(423\) 3431.44 + 5943.44i 0.394427 + 0.683167i
\(424\) 1881.06 + 3258.09i 0.215454 + 0.373177i
\(425\) 773.145 1339.13i 0.0882425 0.152840i
\(426\) −7216.35 −0.820736
\(427\) 0 0
\(428\) 424.690 0.0479630
\(429\) 2086.42 3613.78i 0.234809 0.406702i
\(430\) 2004.99 + 3472.75i 0.224859 + 0.389467i
\(431\) 7464.46 + 12928.8i 0.834224 + 1.44492i 0.894661 + 0.446746i \(0.147417\pi\)
−0.0604373 + 0.998172i \(0.519250\pi\)
\(432\) 4374.09 7576.15i 0.487150 0.843768i
\(433\) −4544.42 −0.504367 −0.252184 0.967679i \(-0.581149\pi\)
−0.252184 + 0.967679i \(0.581149\pi\)
\(434\) 0 0
\(435\) 2896.82 0.319292
\(436\) 131.412 227.613i 0.0144346 0.0250015i
\(437\) 1907.44 + 3303.78i 0.208799 + 0.361650i
\(438\) −3132.88 5426.30i −0.341769 0.591961i
\(439\) 4715.94 8168.25i 0.512710 0.888040i −0.487181 0.873301i \(-0.661975\pi\)
0.999891 0.0147389i \(-0.00469170\pi\)
\(440\) 5156.55 0.558702
\(441\) 0 0
\(442\) −5533.35 −0.595463
\(443\) 2771.30 4800.04i 0.297220 0.514801i −0.678279 0.734805i \(-0.737274\pi\)
0.975499 + 0.220004i \(0.0706071\pi\)
\(444\) −33.7360 58.4325i −0.00360595 0.00624568i
\(445\) −3595.15 6226.99i −0.382981 0.663343i
\(446\) −233.354 + 404.181i −0.0247750 + 0.0429115i
\(447\) −8727.16 −0.923447
\(448\) 0 0
\(449\) 16311.6 1.71446 0.857229 0.514936i \(-0.172184\pi\)
0.857229 + 0.514936i \(0.172184\pi\)
\(450\) −671.417 + 1162.93i −0.0703354 + 0.121824i
\(451\) 5473.48 + 9480.35i 0.571477 + 0.989827i
\(452\) 224.561 + 388.951i 0.0233683 + 0.0404750i
\(453\) 783.181 1356.51i 0.0812297 0.140694i
\(454\) 1094.59 0.113154
\(455\) 0 0
\(456\) −1578.83 −0.162140
\(457\) 7115.54 12324.5i 0.728339 1.26152i −0.229246 0.973368i \(-0.573626\pi\)
0.957585 0.288151i \(-0.0930405\pi\)
\(458\) 6887.44 + 11929.4i 0.702683 + 1.21708i
\(459\) 4080.28 + 7067.25i 0.414926 + 0.718673i
\(460\) −115.971 + 200.868i −0.0117547 + 0.0203598i
\(461\) 4960.94 0.501202 0.250601 0.968090i \(-0.419372\pi\)
0.250601 + 0.968090i \(0.419372\pi\)
\(462\) 0 0
\(463\) 15479.5 1.55377 0.776885 0.629642i \(-0.216799\pi\)
0.776885 + 0.629642i \(0.216799\pi\)
\(464\) 6645.00 11509.5i 0.664841 1.15154i
\(465\) −934.033 1617.79i −0.0931500 0.161341i
\(466\) −3636.43 6298.48i −0.361490 0.626119i
\(467\) −7407.82 + 12830.7i −0.734033 + 1.27138i 0.221114 + 0.975248i \(0.429031\pi\)
−0.955146 + 0.296134i \(0.904303\pi\)
\(468\) 173.346 0.0171216
\(469\) 0 0
\(470\) 5302.01 0.520348
\(471\) 3737.57 6473.67i 0.365644 0.633314i
\(472\) −7670.15 13285.1i −0.747981 1.29554i
\(473\) −6470.85 11207.8i −0.629027 1.08951i
\(474\) −3509.02 + 6077.79i −0.340030 + 0.588950i
\(475\) 615.534 0.0594582
\(476\) 0 0
\(477\) 3161.87 0.303506
\(478\) 163.419 283.051i 0.0156373 0.0270846i
\(479\) −4549.48 7879.93i −0.433969 0.751656i 0.563242 0.826292i \(-0.309554\pi\)
−0.997211 + 0.0746358i \(0.976221\pi\)
\(480\) −97.8581 169.495i −0.00930540 0.0161174i
\(481\) −1210.57 + 2096.77i −0.114755 + 0.198762i
\(482\) 19374.8 1.83091
\(483\) 0 0
\(484\) 248.538 0.0233412
\(485\) 58.6273 101.545i 0.00548892 0.00950710i
\(486\) −5639.42 9767.75i −0.526356 0.911676i
\(487\) 7495.72 + 12983.0i 0.697461 + 1.20804i 0.969344 + 0.245707i \(0.0790202\pi\)
−0.271883 + 0.962330i \(0.587646\pi\)
\(488\) −7726.53 + 13382.7i −0.716729 + 1.24141i
\(489\) 7128.45 0.659222
\(490\) 0 0
\(491\) 8243.61 0.757697 0.378848 0.925459i \(-0.376320\pi\)
0.378848 + 0.925459i \(0.376320\pi\)
\(492\) 101.892 176.482i 0.00933667 0.0161716i
\(493\) 6198.64 + 10736.4i 0.566273 + 0.980814i
\(494\) −1101.33 1907.57i −0.100306 0.173736i
\(495\) 2166.91 3753.20i 0.196758 0.340795i
\(496\) −8570.29 −0.775841
\(497\) 0 0
\(498\) −12019.9 −1.08157
\(499\) −4613.74 + 7991.24i −0.413907 + 0.716908i −0.995313 0.0967057i \(-0.969169\pi\)
0.581406 + 0.813614i \(0.302503\pi\)
\(500\) 18.7120 + 32.4102i 0.00167365 + 0.00289885i
\(501\) 663.405 + 1149.05i 0.0591591 + 0.102467i
\(502\) 5495.26 9518.06i 0.488576 0.846239i
\(503\) 13750.9 1.21893 0.609465 0.792813i \(-0.291384\pi\)
0.609465 + 0.792813i \(0.291384\pi\)
\(504\) 0 0
\(505\) 7382.07 0.650491
\(506\) 10375.4 17970.6i 0.911543 1.57884i
\(507\) −1781.53 3085.69i −0.156056 0.270297i
\(508\) −62.3693 108.027i −0.00544723 0.00943488i
\(509\) 7771.98 13461.5i 0.676792 1.17224i −0.299150 0.954206i \(-0.596703\pi\)
0.975942 0.218032i \(-0.0699637\pi\)
\(510\) 2575.26 0.223597
\(511\) 0 0
\(512\) 10869.7 0.938236
\(513\) −1624.24 + 2813.27i −0.139789 + 0.242122i
\(514\) −3171.69 5493.53i −0.272174 0.471419i
\(515\) 2523.61 + 4371.01i 0.215929 + 0.374000i
\(516\) −120.458 + 208.640i −0.0102769 + 0.0178001i
\(517\) −17111.5 −1.45564
\(518\) 0 0
\(519\) 13011.6 1.10047
\(520\) −1722.27 + 2983.06i −0.145244 + 0.251569i
\(521\) −7623.86 13204.9i −0.641089 1.11040i −0.985190 0.171466i \(-0.945150\pi\)
0.344101 0.938933i \(-0.388184\pi\)
\(522\) −5383.04 9323.71i −0.451359 0.781777i
\(523\) −11108.1 + 19239.8i −0.928723 + 1.60860i −0.143263 + 0.989685i \(0.545759\pi\)
−0.785461 + 0.618912i \(0.787574\pi\)
\(524\) −122.899 −0.0102460
\(525\) 0 0
\(526\) 3469.08 0.287565
\(527\) 3997.30 6923.53i 0.330408 0.572284i
\(528\) 4454.89 + 7716.10i 0.367186 + 0.635985i
\(529\) −5919.96 10253.7i −0.486559 0.842745i
\(530\) 1221.37 2115.48i 0.100100 0.173378i
\(531\) −12892.7 −1.05367
\(532\) 0 0
\(533\) −7312.50 −0.594258
\(534\) 5987.52 10370.7i 0.485216 0.840419i
\(535\) 3546.27 + 6142.31i 0.286577 + 0.496365i
\(536\) −25.8794 44.8244i −0.00208548 0.00361217i
\(537\) 2832.87 4906.68i 0.227649 0.394299i
\(538\) 14775.9 1.18408
\(539\) 0 0
\(540\) −197.506 −0.0157394
\(541\) 6492.65 11245.6i 0.515972 0.893690i −0.483856 0.875148i \(-0.660764\pi\)
0.999828 0.0185424i \(-0.00590258\pi\)
\(542\) −1164.43 2016.86i −0.0922818 0.159837i
\(543\) 5268.66 + 9125.58i 0.416390 + 0.721208i
\(544\) 418.795 725.374i 0.0330068 0.0571694i
\(545\) 4389.30 0.344985
\(546\) 0 0
\(547\) −8226.94 −0.643069 −0.321534 0.946898i \(-0.604199\pi\)
−0.321534 + 0.946898i \(0.604199\pi\)
\(548\) −263.761 + 456.847i −0.0205608 + 0.0356123i
\(549\) 6493.75 + 11247.5i 0.504821 + 0.874375i
\(550\) −1674.07 2899.58i −0.129787 0.224797i
\(551\) −2467.50 + 4273.84i −0.190779 + 0.330438i
\(552\) 9935.57 0.766098
\(553\) 0 0
\(554\) −519.320 −0.0398263
\(555\) 563.408 975.851i 0.0430907 0.0746352i
\(556\) −129.595 224.465i −0.00988497 0.0171213i
\(557\) −8920.63 15451.0i −0.678599 1.17537i −0.975403 0.220429i \(-0.929254\pi\)
0.296804 0.954938i \(-0.404079\pi\)
\(558\) −3471.35 + 6012.56i −0.263358 + 0.456150i
\(559\) 8644.97 0.654103
\(560\) 0 0
\(561\) −8311.30 −0.625496
\(562\) −4419.67 + 7655.09i −0.331731 + 0.574574i
\(563\) 539.199 + 933.919i 0.0403633 + 0.0699112i 0.885501 0.464637i \(-0.153815\pi\)
−0.845138 + 0.534548i \(0.820482\pi\)
\(564\) 159.270 + 275.864i 0.0118909 + 0.0205957i
\(565\) −3750.28 + 6495.67i −0.279248 + 0.483673i
\(566\) −11143.7 −0.827570
\(567\) 0 0
\(568\) −19225.0 −1.42018
\(569\) −8493.24 + 14710.7i −0.625756 + 1.08384i 0.362638 + 0.931930i \(0.381876\pi\)
−0.988394 + 0.151911i \(0.951457\pi\)
\(570\) 512.568 + 887.794i 0.0376651 + 0.0652379i
\(571\) 6131.49 + 10620.1i 0.449378 + 0.778346i 0.998346 0.0574980i \(-0.0183123\pi\)
−0.548968 + 0.835844i \(0.684979\pi\)
\(572\) −216.106 + 374.306i −0.0157969 + 0.0273610i
\(573\) −7268.07 −0.529891
\(574\) 0 0
\(575\) −3873.54 −0.280935
\(576\) 4581.34 7935.11i 0.331405 0.574010i
\(577\) −3525.25 6105.92i −0.254347 0.440542i 0.710371 0.703827i \(-0.248527\pi\)
−0.964718 + 0.263286i \(0.915194\pi\)
\(578\) −1566.29 2712.90i −0.112715 0.195228i
\(579\) 3164.21 5480.56i 0.227116 0.393376i
\(580\) −300.045 −0.0214805
\(581\) 0 0
\(582\) 195.281 0.0139083
\(583\) −3941.82 + 6827.42i −0.280023 + 0.485014i
\(584\) −8346.26 14456.1i −0.591388 1.02431i
\(585\) 1447.48 + 2507.11i 0.102301 + 0.177190i
\(586\) 2834.47 4909.44i 0.199814 0.346087i
\(587\) 20085.3 1.41228 0.706141 0.708071i \(-0.250434\pi\)
0.706141 + 0.708071i \(0.250434\pi\)
\(588\) 0 0
\(589\) 3182.42 0.222631
\(590\) −4980.22 + 8626.00i −0.347513 + 0.601910i
\(591\) −5617.00 9728.94i −0.390952 0.677149i
\(592\) −2584.79 4476.99i −0.179450 0.310816i
\(593\) −9487.17 + 16432.3i −0.656984 + 1.13793i 0.324409 + 0.945917i \(0.394835\pi\)
−0.981392 + 0.192013i \(0.938499\pi\)
\(594\) 17669.9 1.22054
\(595\) 0 0
\(596\) 903.936 0.0621252
\(597\) 1400.98 2426.57i 0.0960440 0.166353i
\(598\) 6930.67 + 12004.3i 0.473940 + 0.820888i
\(599\) −8397.87 14545.5i −0.572834 0.992178i −0.996273 0.0862537i \(-0.972510\pi\)
0.423439 0.905925i \(-0.360823\pi\)
\(600\) 801.557 1388.34i 0.0545391 0.0944644i
\(601\) 13624.3 0.924702 0.462351 0.886697i \(-0.347006\pi\)
0.462351 + 0.886697i \(0.347006\pi\)
\(602\) 0 0
\(603\) −43.5006 −0.00293778
\(604\) −81.1198 + 140.504i −0.00546476 + 0.00946525i
\(605\) 2075.35 + 3594.61i 0.139463 + 0.241556i
\(606\) 6147.21 + 10647.3i 0.412068 + 0.713723i
\(607\) −4199.75 + 7274.19i −0.280828 + 0.486409i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(608\) 333.421 0.0222401
\(609\) 0 0
\(610\) 10033.7 0.665985
\(611\) 5715.20 9899.01i 0.378416 0.655436i
\(612\) −172.632 299.007i −0.0114023 0.0197494i
\(613\) −7760.21 13441.1i −0.511308 0.885612i −0.999914 0.0131070i \(-0.995828\pi\)
0.488606 0.872505i \(-0.337506\pi\)
\(614\) −7904.43 + 13690.9i −0.519539 + 0.899868i
\(615\) 3403.29 0.223144
\(616\) 0 0
\(617\) −26665.1 −1.73987 −0.869933 0.493169i \(-0.835838\pi\)
−0.869933 + 0.493169i \(0.835838\pi\)
\(618\) −4202.92 + 7279.67i −0.273570 + 0.473837i
\(619\) −6115.78 10592.8i −0.397114 0.687822i 0.596254 0.802796i \(-0.296655\pi\)
−0.993369 + 0.114973i \(0.963322\pi\)
\(620\) 96.7446 + 167.567i 0.00626670 + 0.0108542i
\(621\) 10221.3 17703.8i 0.660495 1.14401i
\(622\) −14902.1 −0.960645
\(623\) 0 0
\(624\) −5951.68 −0.381824
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −8301.10 14377.9i −0.529998 0.917983i
\(627\) −1654.25 2865.24i −0.105366 0.182498i
\(628\) −387.128 + 670.525i −0.0245988 + 0.0426064i
\(629\) 4822.34 0.305690
\(630\) 0 0
\(631\) −7237.27 −0.456595 −0.228297 0.973591i \(-0.573316\pi\)
−0.228297 + 0.973591i \(0.573316\pi\)
\(632\) −9348.33 + 16191.8i −0.588380 + 1.01910i
\(633\) 4450.96 + 7709.29i 0.279478 + 0.484071i
\(634\) 4581.84 + 7935.98i 0.287016 + 0.497126i
\(635\) 1041.60 1804.10i 0.0650938 0.112746i
\(636\) 146.758 0.00914990
\(637\) 0 0
\(638\) 26843.5 1.66575
\(639\) −8078.82 + 13992.9i −0.500146 + 0.866278i
\(640\) −3810.21 6599.48i −0.235331 0.407605i
\(641\) −2452.42 4247.71i −0.151115 0.261739i 0.780523 0.625127i \(-0.214953\pi\)
−0.931638 + 0.363389i \(0.881620\pi\)
\(642\) −5906.10 + 10229.7i −0.363077 + 0.628867i
\(643\) 8394.46 0.514845 0.257422 0.966299i \(-0.417127\pi\)
0.257422 + 0.966299i \(0.417127\pi\)
\(644\) 0 0
\(645\) −4023.43 −0.245616
\(646\) −2193.59 + 3799.42i −0.133600 + 0.231403i
\(647\) 4763.22 + 8250.15i 0.289431 + 0.501309i 0.973674 0.227945i \(-0.0732007\pi\)
−0.684243 + 0.729254i \(0.739867\pi\)
\(648\) −1353.73 2344.72i −0.0820670 0.142144i
\(649\) 16073.0 27839.3i 0.972143 1.68380i
\(650\) 2236.54 0.134961
\(651\) 0 0
\(652\) −738.345 −0.0443494
\(653\) −7975.03 + 13813.2i −0.477928 + 0.827796i −0.999680 0.0253017i \(-0.991945\pi\)
0.521752 + 0.853097i \(0.325279\pi\)
\(654\) 3655.06 + 6330.75i 0.218539 + 0.378520i
\(655\) −1026.24 1777.50i −0.0612191 0.106035i
\(656\) 7806.78 13521.7i 0.464639 0.804779i
\(657\) −14029.2 −0.833077
\(658\) 0 0
\(659\) −3370.65 −0.199244 −0.0996221 0.995025i \(-0.531763\pi\)
−0.0996221 + 0.995025i \(0.531763\pi\)
\(660\) 100.577 174.204i 0.00593175 0.0102741i
\(661\) 12127.0 + 21004.6i 0.713594 + 1.23598i 0.963499 + 0.267710i \(0.0862671\pi\)
−0.249906 + 0.968270i \(0.580400\pi\)
\(662\) 13299.6 + 23035.5i 0.780819 + 1.35242i
\(663\) 2775.95 4808.08i 0.162608 0.281645i
\(664\) −32022.0 −1.87153
\(665\) 0 0
\(666\) −4187.83 −0.243656
\(667\) 15527.9 26895.2i 0.901415 1.56130i
\(668\) −68.7136 119.015i −0.00397995 0.00689348i
\(669\) −234.136 405.536i −0.0135310 0.0234364i
\(670\) −16.8035 + 29.1045i −0.000968918 + 0.00167821i
\(671\) −32382.3 −1.86305
\(672\) 0 0
\(673\) −3510.41 −0.201064 −0.100532 0.994934i \(-0.532055\pi\)
−0.100532 + 0.994934i \(0.532055\pi\)
\(674\) −4695.10 + 8132.15i −0.268321 + 0.464746i
\(675\) −1649.22 2856.53i −0.0940422 0.162886i
\(676\) 184.525 + 319.607i 0.0104987 + 0.0181843i
\(677\) 4525.59 7838.56i 0.256917 0.444993i −0.708498 0.705713i \(-0.750627\pi\)
0.965414 + 0.260720i \(0.0839600\pi\)
\(678\) −12491.7 −0.707585
\(679\) 0 0
\(680\) 6860.71 0.386906
\(681\) −549.130 + 951.122i −0.0308997 + 0.0535199i
\(682\) −8655.27 14991.4i −0.485964 0.841714i
\(683\) −3552.86 6153.74i −0.199043 0.344753i 0.749175 0.662372i \(-0.230450\pi\)
−0.948219 + 0.317619i \(0.897117\pi\)
\(684\) 68.7199 119.026i 0.00384148 0.00665363i
\(685\) −8809.87 −0.491398
\(686\) 0 0
\(687\) −13821.0 −0.767548
\(688\) −9229.32 + 15985.6i −0.511431 + 0.885824i
\(689\) −2633.11 4560.68i −0.145593 0.252174i
\(690\) −3225.58 5586.87i −0.177965 0.308244i
\(691\) −6314.70 + 10937.4i −0.347645 + 0.602138i −0.985831 0.167744i \(-0.946352\pi\)
0.638186 + 0.769882i \(0.279685\pi\)
\(692\) −1347.70 −0.0740346
\(693\) 0 0
\(694\) −5332.86 −0.291690
\(695\) 2164.30 3748.67i 0.118124 0.204597i
\(696\) 6426.43 + 11130.9i 0.349990 + 0.606201i
\(697\) 7282.38 + 12613.5i 0.395753 + 0.685464i
\(698\) −1587.56 + 2749.73i −0.0860887 + 0.149110i
\(699\) 7297.23 0.394859
\(700\) 0 0
\(701\) −912.952 −0.0491893 −0.0245947 0.999698i \(-0.507830\pi\)
−0.0245947 + 0.999698i \(0.507830\pi\)
\(702\) −5901.68 + 10222.0i −0.317300 + 0.549579i
\(703\) 959.817 + 1662.45i 0.0514939 + 0.0891900i
\(704\) 11422.8 + 19785.0i 0.611527 + 1.05920i
\(705\) −2659.89 + 4607.07i −0.142096 + 0.246117i
\(706\) 7692.63 0.410079
\(707\) 0 0
\(708\) −598.416 −0.0317653
\(709\) 10355.2 17935.8i 0.548518 0.950061i −0.449858 0.893100i \(-0.648525\pi\)
0.998376 0.0569613i \(-0.0181412\pi\)
\(710\) 6241.39 + 10810.4i 0.329909 + 0.571419i
\(711\) 7856.79 + 13608.4i 0.414420 + 0.717797i
\(712\) 15951.3 27628.4i 0.839606 1.45424i
\(713\) −20026.9 −1.05191
\(714\) 0 0
\(715\) −7218.14 −0.377543
\(716\) −293.421 + 508.220i −0.0153152 + 0.0265266i
\(717\) 163.967 + 283.999i 0.00854040 + 0.0147924i
\(718\) 627.241 + 1086.41i 0.0326023 + 0.0564688i
\(719\) 1234.88 2138.88i 0.0640518 0.110941i −0.832221 0.554444i \(-0.812931\pi\)
0.896273 + 0.443503i \(0.146264\pi\)
\(720\) −6181.29 −0.319949
\(721\) 0 0
\(722\) 18013.4 0.928520
\(723\) −9719.88 + 16835.3i −0.499981 + 0.865992i
\(724\) −545.713 945.203i −0.0280128 0.0485196i
\(725\) −2505.45 4339.56i −0.128345 0.222300i
\(726\) −3456.37 + 5986.62i −0.176692 + 0.306039i
\(727\) −10893.4 −0.555729 −0.277865 0.960620i \(-0.589627\pi\)
−0.277865 + 0.960620i \(0.589627\pi\)
\(728\) 0 0
\(729\) 8021.48 0.407533
\(730\) −5419.22 + 9386.37i −0.274759 + 0.475897i
\(731\) −8609.36 14911.9i −0.435607 0.754494i
\(732\) 301.407 + 522.053i 0.0152190 + 0.0263601i
\(733\) 13130.0 22741.8i 0.661619 1.14596i −0.318571 0.947899i \(-0.603203\pi\)
0.980190 0.198059i \(-0.0634636\pi\)
\(734\) −7129.14 −0.358503
\(735\) 0 0
\(736\) −2098.21 −0.105083
\(737\) 54.2310 93.9308i 0.00271048 0.00469469i
\(738\) −6324.19 10953.8i −0.315443 0.546363i
\(739\) 920.414 + 1594.20i 0.0458160 + 0.0793556i 0.888024 0.459797i \(-0.152078\pi\)
−0.842208 + 0.539153i \(0.818745\pi\)
\(740\) −58.3562 + 101.076i −0.00289894 + 0.00502112i
\(741\) 2210.05 0.109566
\(742\) 0 0
\(743\) 4022.25 0.198603 0.0993015 0.995057i \(-0.468339\pi\)
0.0993015 + 0.995057i \(0.468339\pi\)
\(744\) 4144.20 7177.96i 0.204212 0.353705i
\(745\) 7548.08 + 13073.7i 0.371195 + 0.642929i
\(746\) 7833.34 + 13567.7i 0.384449 + 0.665885i
\(747\) −13456.4 + 23307.2i −0.659096 + 1.14159i
\(748\) 860.862 0.0420805
\(749\) 0 0
\(750\) −1040.90 −0.0506778
\(751\) −12862.6 + 22278.7i −0.624986 + 1.08251i 0.363558 + 0.931572i \(0.381562\pi\)
−0.988544 + 0.150936i \(0.951771\pi\)
\(752\) 12203.0 + 21136.2i 0.591753 + 1.02495i
\(753\) 5513.68 + 9549.97i 0.266839 + 0.462178i
\(754\) −8965.66 + 15529.0i −0.433037 + 0.750042i
\(755\) −2709.48 −0.130607
\(756\) 0 0
\(757\) 11359.2 0.545385 0.272692 0.962101i \(-0.412086\pi\)
0.272692 + 0.962101i \(0.412086\pi\)
\(758\) 15264.4 26438.7i 0.731436 1.26688i
\(759\) 10410.1 + 18030.9i 0.497844 + 0.862292i
\(760\) 1365.53 + 2365.16i 0.0651748 + 0.112886i
\(761\) 3921.69 6792.56i 0.186808 0.323561i −0.757376 0.652979i \(-0.773519\pi\)
0.944184 + 0.329418i \(0.106852\pi\)
\(762\) 3469.45 0.164941
\(763\) 0 0
\(764\) 752.806 0.0356487
\(765\) 2883.04 4993.57i 0.136257 0.236004i
\(766\) 6728.79 + 11654.6i 0.317390 + 0.549736i
\(767\) 10736.7 + 18596.4i 0.505448 + 0.875461i
\(768\) 663.709 1149.58i 0.0311843 0.0540127i
\(769\) −29007.8 −1.36027 −0.680136 0.733086i \(-0.738079\pi\)
−0.680136 + 0.733086i \(0.738079\pi\)
\(770\) 0 0
\(771\) 6364.65 0.297299
\(772\) −327.740 + 567.662i −0.0152793 + 0.0264645i
\(773\) −339.580 588.170i −0.0158006 0.0273674i 0.858017 0.513621i \(-0.171696\pi\)
−0.873818 + 0.486254i \(0.838363\pi\)
\(774\) 7476.57 + 12949.8i 0.347209 + 0.601384i
\(775\) −1615.68 + 2798.44i −0.0748865 + 0.129707i
\(776\) 520.245 0.0240666
\(777\) 0 0
\(778\) −10249.2 −0.472304
\(779\) −2898.91 + 5021.05i −0.133330 + 0.230934i
\(780\) 67.1848 + 116.367i 0.00308410 + 0.00534183i
\(781\) −20143.3 34889.1i −0.922897 1.59850i
\(782\) 13804.2 23909.6i 0.631252 1.09336i
\(783\) 26445.0 1.20698
\(784\) 0 0
\(785\) −12930.4 −0.587907
\(786\) 1709.14 2960.32i 0.0775612 0.134340i
\(787\) −12164.5 21069.6i −0.550976 0.954318i −0.998204 0.0598987i \(-0.980922\pi\)
0.447228 0.894420i \(-0.352411\pi\)
\(788\) 581.794 + 1007.70i 0.0263015 + 0.0455554i
\(789\) −1740.35 + 3014.38i −0.0785276 + 0.136014i
\(790\) 12139.7 0.546724
\(791\) 0 0
\(792\) 19228.7 0.862703
\(793\) 10815.6 18733.1i 0.484329 0.838882i
\(794\) 13229.8 + 22914.6i 0.591318 + 1.02419i
\(795\) 1225.47 + 2122.57i 0.0546702 + 0.0946916i
\(796\) −145.110 + 251.337i −0.00646140 + 0.0111915i
\(797\) −2791.24 −0.124054 −0.0620269 0.998074i \(-0.519756\pi\)
−0.0620269 + 0.998074i \(0.519756\pi\)
\(798\) 0 0
\(799\) −22766.6 −1.00804
\(800\) −169.274 + 293.191i −0.00748093 + 0.0129573i
\(801\) −13406.2 23220.3i −0.591368 1.02428i
\(802\) −13261.4 22969.4i −0.583885 1.01132i
\(803\) 17489.8 30293.2i 0.768620 1.33129i
\(804\) −2.01908 −8.85664e−5
\(805\) 0 0
\(806\) 11563.3 0.505336
\(807\) −7412.72 + 12839.2i −0.323346 + 0.560051i
\(808\) 16376.7 + 28365.3i 0.713033 + 1.23501i
\(809\) −7847.97 13593.1i −0.341063 0.590739i 0.643567 0.765390i \(-0.277454\pi\)
−0.984630 + 0.174651i \(0.944120\pi\)
\(810\) −878.974 + 1522.43i −0.0381284 + 0.0660403i
\(811\) 9580.84 0.414832 0.207416 0.978253i \(-0.433495\pi\)
0.207416 + 0.978253i \(0.433495\pi\)
\(812\) 0 0
\(813\) 2336.67 0.100800
\(814\) 5220.85 9042.77i 0.224804 0.389372i
\(815\) −6165.36 10678.7i −0.264985 0.458968i
\(816\) 5927.17 + 10266.2i 0.254280 + 0.440426i
\(817\) 3427.14 5935.98i 0.146757 0.254191i
\(818\) −22049.2 −0.942458
\(819\) 0 0
\(820\) −352.503 −0.0150121
\(821\) −13770.5 + 23851.2i −0.585376 + 1.01390i 0.409452 + 0.912332i \(0.365720\pi\)
−0.994828 + 0.101570i \(0.967614\pi\)
\(822\) −7336.16 12706.6i −0.311287 0.539165i
\(823\) 5873.23 + 10172.7i 0.248758 + 0.430862i 0.963182 0.268852i \(-0.0866442\pi\)
−0.714423 + 0.699714i \(0.753311\pi\)
\(824\) −11196.9 + 19393.7i −0.473379 + 0.819916i
\(825\) 3359.37 0.141768
\(826\) 0 0
\(827\) −20831.7 −0.875924 −0.437962 0.898994i \(-0.644300\pi\)
−0.437962 + 0.898994i \(0.644300\pi\)
\(828\) −432.453 + 749.030i −0.0181507 + 0.0314379i
\(829\) −1795.00 3109.03i −0.0752027 0.130255i 0.825972 0.563712i \(-0.190627\pi\)
−0.901174 + 0.433457i \(0.857294\pi\)
\(830\) 10395.9 + 18006.3i 0.434757 + 0.753021i
\(831\) 260.530 451.252i 0.0108757 0.0188372i
\(832\) −15260.8 −0.635904
\(833\) 0 0
\(834\) 7209.02 0.299314
\(835\) 1147.55 1987.62i 0.0475600 0.0823764i
\(836\) 171.342 + 296.773i 0.00708851 + 0.0122777i
\(837\) −8526.77 14768.8i −0.352124 0.609897i
\(838\) 534.205 925.271i 0.0220213 0.0381419i
\(839\) −10917.2 −0.449229 −0.224614 0.974448i \(-0.572112\pi\)
−0.224614 + 0.974448i \(0.572112\pi\)
\(840\) 0 0
\(841\) 15785.5 0.647239
\(842\) 1760.16 3048.68i 0.0720416 0.124780i
\(843\) −4434.49 7680.75i −0.181177 0.313807i
\(844\) −461.018 798.507i −0.0188020 0.0325660i
\(845\) −3081.67 + 5337.60i −0.125459 + 0.217301i
\(846\) 19771.1 0.803479
\(847\) 0 0
\(848\) 11244.4 0.455345
\(849\) 5590.52 9683.07i 0.225991 0.391428i
\(850\) −2227.33 3857.85i −0.0898785 0.155674i
\(851\) −6040.11 10461.8i −0.243305 0.421416i
\(852\) −374.978 + 649.481i −0.0150781 + 0.0261160i
\(853\) 35912.9 1.44154 0.720770 0.693175i \(-0.243789\pi\)
0.720770 + 0.693175i \(0.243789\pi\)
\(854\) 0 0
\(855\) 2295.31 0.0918105
\(856\) −15734.4 + 27252.7i −0.628259 + 1.08818i
\(857\) 19676.6 + 34080.9i 0.784295 + 1.35844i 0.929419 + 0.369025i \(0.120308\pi\)
−0.145124 + 0.989413i \(0.546358\pi\)
\(858\) −6010.70 10410.8i −0.239163 0.414242i
\(859\) −16117.4 + 27916.1i −0.640183 + 1.10883i 0.345208 + 0.938526i \(0.387808\pi\)
−0.985392 + 0.170304i \(0.945525\pi\)
\(860\) 416.736 0.0165239
\(861\) 0 0
\(862\) 43008.2 1.69938
\(863\) −21905.7 + 37941.7i −0.864053 + 1.49658i 0.00393116 + 0.999992i \(0.498749\pi\)
−0.867984 + 0.496592i \(0.834585\pi\)
\(864\) −893.344 1547.32i −0.0351761 0.0609269i
\(865\) −11253.6 19491.9i −0.442353 0.766178i
\(866\) −6545.94 + 11337.9i −0.256859 + 0.444893i
\(867\) 3143.09 0.123120
\(868\) 0 0
\(869\) −39179.3 −1.52942
\(870\) 4172.68 7227.29i 0.162606 0.281641i
\(871\) 36.2259 + 62.7452i 0.00140926 + 0.00244092i
\(872\) 9737.41 + 16865.7i 0.378154 + 0.654982i
\(873\) 218.620 378.660i 0.00847555 0.0146801i
\(874\) 10990.1 0.425340
\(875\) 0 0
\(876\) −651.165 −0.0251151
\(877\) 4570.34 7916.06i 0.175974 0.304796i −0.764524 0.644596i \(-0.777026\pi\)
0.940498 + 0.339799i \(0.110359\pi\)
\(878\) −13586.0 23531.6i −0.522216 0.904504i
\(879\) 2843.97 + 4925.90i 0.109129 + 0.189017i
\(880\) 7706.04 13347.2i 0.295194 0.511290i
\(881\) 23013.1 0.880058 0.440029 0.897984i \(-0.354968\pi\)
0.440029 + 0.897984i \(0.354968\pi\)
\(882\) 0 0
\(883\) 7448.15 0.283862 0.141931 0.989877i \(-0.454669\pi\)
0.141931 + 0.989877i \(0.454669\pi\)
\(884\) −287.525 + 498.008i −0.0109395 + 0.0189478i
\(885\) −4996.92 8654.91i −0.189796 0.328736i
\(886\) −7983.76 13828.3i −0.302731 0.524345i
\(887\) −23030.5 + 39890.0i −0.871803 + 1.51001i −0.0116736 + 0.999932i \(0.503716\pi\)
−0.860130 + 0.510076i \(0.829617\pi\)
\(888\) 4999.55 0.188935
\(889\) 0 0
\(890\) −20714.3 −0.780163
\(891\) 2836.77 4913.43i 0.106662 0.184743i
\(892\) 24.2512 + 42.0043i 0.000910303 + 0.00157669i
\(893\) −4531.37 7848.56i −0.169806 0.294112i
\(894\) −12570.9 + 21773.4i −0.470284 + 0.814555i
\(895\) −9800.55 −0.366029
\(896\) 0 0
\(897\) −13907.8 −0.517690
\(898\) 23495.8 40695.8i 0.873122 1.51229i
\(899\) −12953.6 22436.3i −0.480564 0.832362i
\(900\) 69.7767 + 120.857i 0.00258432 + 0.00447618i
\(901\) −5244.52 + 9083.78i −0.193918 + 0.335876i
\(902\) 31536.7 1.16414
\(903\) 0 0
\(904\) −33279.1 −1.22439
\(905\) 9113.67 15785.3i 0.334750 0.579804i
\(906\) −2256.24 3907.92i −0.0827358 0.143303i
\(907\) −19248.0 33338.6i −0.704653 1.22050i −0.966817 0.255472i \(-0.917769\pi\)
0.262163 0.965024i \(-0.415564\pi\)
\(908\) 56.8774 98.5146i 0.00207879 0.00360057i
\(909\) 27527.6 1.00444
\(910\) 0 0
\(911\) −18329.1 −0.666596 −0.333298 0.942822i \(-0.608162\pi\)
−0.333298 + 0.942822i \(0.608162\pi\)
\(912\) −2359.44 + 4086.66i −0.0856674 + 0.148380i
\(913\) −33551.5 58112.9i −1.21620 2.10652i
\(914\) −20498.9 35505.2i −0.741842 1.28491i
\(915\) −5033.65 + 8718.53i −0.181866 + 0.315001i
\(916\) 1431.55 0.0516371
\(917\) 0 0
\(918\) 23509.5 0.845237
\(919\) 18724.2 32431.3i 0.672094 1.16410i −0.305216 0.952283i \(-0.598729\pi\)
0.977309 0.211817i \(-0.0679381\pi\)
\(920\) −8593.23 14883.9i −0.307946 0.533378i
\(921\) −7930.93 13736.8i −0.283749 0.491468i
\(922\) 7145.91 12377.1i 0.255247 0.442101i
\(923\) 26911.1 0.959686
\(924\) 0 0
\(925\) −1949.15 −0.0692841
\(926\) 22297.3 38620.0i 0.791289 1.37055i
\(927\) 9410.46 + 16299.4i 0.333420 + 0.577500i
\(928\) −1357.14 2350.64i −0.0480069 0.0831504i
\(929\) 1473.17 2551.61i 0.0520271 0.0901136i −0.838839 0.544380i \(-0.816765\pi\)
0.890866 + 0.454266i \(0.150098\pi\)
\(930\) −5381.65 −0.189754
\(931\) 0 0
\(932\) −755.827 −0.0265643
\(933\) 7476.04 12948.9i 0.262331 0.454370i
\(934\) 21341.0 + 36963.6i 0.747642 + 1.29495i
\(935\) 7188.41 + 12450.7i 0.251429 + 0.435488i
\(936\) −6422.31 + 11123.8i −0.224273 + 0.388453i
\(937\) 48870.0 1.70386 0.851928 0.523659i \(-0.175434\pi\)
0.851928 + 0.523659i \(0.175434\pi\)
\(938\) 0 0
\(939\) 16657.9 0.578923
\(940\) 275.504 477.187i 0.00955953 0.0165576i
\(941\) −10330.5 17892.9i −0.357879 0.619864i 0.629727 0.776816i \(-0.283167\pi\)
−0.987606 + 0.156952i \(0.949833\pi\)
\(942\) −10767.5 18649.8i −0.372423 0.645056i
\(943\) 18242.8 31597.4i 0.629974 1.09115i
\(944\) −45849.6 −1.58080
\(945\) 0 0
\(946\) −37283.3 −1.28138
\(947\) −6565.16 + 11371.2i −0.225279 + 0.390194i −0.956403 0.292050i \(-0.905663\pi\)
0.731124 + 0.682244i \(0.238996\pi\)
\(948\) 364.672 + 631.631i 0.0124937 + 0.0216397i
\(949\) 11683.1 + 20235.7i 0.399630 + 0.692179i
\(950\) 886.636 1535.70i 0.0302803 0.0524470i
\(951\) −9194.40 −0.313511
\(952\) 0 0
\(953\) 16098.9 0.547214 0.273607 0.961842i \(-0.411783\pi\)
0.273607 + 0.961842i \(0.411783\pi\)
\(954\) 4554.47 7888.57i 0.154566 0.267717i
\(955\) 6286.12 + 10887.9i 0.212999 + 0.368925i
\(956\) −16.9833 29.4159i −0.000574559 0.000995165i
\(957\) −13466.8 + 23325.1i −0.454878 + 0.787872i
\(958\) −26212.9 −0.884030
\(959\) 0 0
\(960\) 7102.47 0.238783
\(961\) 6542.13 11331.3i 0.219601 0.380360i
\(962\) 3487.49 + 6040.51i 0.116883 + 0.202447i
\(963\) 13223.9 + 22904.5i 0.442508 + 0.766447i
\(964\) 1006.76 1743.76i 0.0336364 0.0582600i
\(965\) −10946.8 −0.365172
\(966\) 0 0
\(967\) 15916.9 0.529320 0.264660 0.964342i \(-0.414740\pi\)
0.264660 + 0.964342i \(0.414740\pi\)
\(968\) −9208.08 + 15948.9i −0.305743 + 0.529562i
\(969\) −2200.95 3812.15i −0.0729666 0.126382i
\(970\) −168.897 292.539i −0.00559069 0.00968336i
\(971\) 337.954 585.354i 0.0111694 0.0193459i −0.860387 0.509642i \(-0.829778\pi\)
0.871556 + 0.490296i \(0.163111\pi\)
\(972\) −1172.15 −0.0386796
\(973\) 0 0
\(974\) 43188.3 1.42078
\(975\) −1122.02 + 1943.39i −0.0368547 + 0.0638343i
\(976\) 23093.3 + 39998.8i 0.757375 + 1.31181i
\(977\) 23084.7 + 39983.8i 0.755931 + 1.30931i 0.944910 + 0.327329i \(0.106149\pi\)
−0.188980 + 0.981981i \(0.560518\pi\)
\(978\) 10268.1 17784.8i 0.335722 0.581487i
\(979\) 66852.7 2.18245
\(980\) 0 0
\(981\) 16367.6 0.532698
\(982\) 11874.4 20567.0i 0.385872 0.668350i
\(983\) −25168.1 43592.4i −0.816620 1.41443i −0.908159 0.418626i \(-0.862512\pi\)
0.0915383 0.995802i \(-0.470822\pi\)
\(984\) 7550.00 + 13077.0i 0.244599 + 0.423657i
\(985\) −9716.24 + 16829.0i −0.314300 + 0.544383i
\(986\) 35714.9 1.15354
\(987\) 0 0
\(988\) −228.911 −0.00737108
\(989\) −21566.9 + 37355.0i −0.693416 + 1.20103i
\(990\) −6242.58 10812.5i −0.200406 0.347114i
\(991\) −20093.5 34802.9i −0.644087 1.11559i −0.984512 0.175319i \(-0.943904\pi\)
0.340425 0.940272i \(-0.389429\pi\)
\(992\) −875.178 + 1515.85i −0.0280110 + 0.0485165i
\(993\) −26688.3 −0.852897
\(994\) 0 0
\(995\) −4846.80 −0.154426
\(996\) −624.579 + 1081.80i −0.0198700 + 0.0344159i
\(997\) 8875.10 + 15372.1i 0.281923 + 0.488305i 0.971858 0.235566i \(-0.0756944\pi\)
−0.689935 + 0.723871i \(0.742361\pi\)
\(998\) 13291.6 + 23021.7i 0.421581 + 0.730199i
\(999\) 5143.34 8908.52i 0.162891 0.282135i
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 245.4.e.p.226.5 12
7.2 even 3 245.4.a.p.1.2 yes 6
7.3 odd 6 245.4.e.q.116.5 12
7.4 even 3 inner 245.4.e.p.116.5 12
7.5 odd 6 245.4.a.o.1.2 6
7.6 odd 2 245.4.e.q.226.5 12
21.2 odd 6 2205.4.a.ca.1.5 6
21.5 even 6 2205.4.a.bz.1.5 6
35.9 even 6 1225.4.a.bi.1.5 6
35.19 odd 6 1225.4.a.bj.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.2 6 7.5 odd 6
245.4.a.p.1.2 yes 6 7.2 even 3
245.4.e.p.116.5 12 7.4 even 3 inner
245.4.e.p.226.5 12 1.1 even 1 trivial
245.4.e.q.116.5 12 7.3 odd 6
245.4.e.q.226.5 12 7.6 odd 2
1225.4.a.bi.1.5 6 35.9 even 6
1225.4.a.bj.1.5 6 35.19 odd 6
2205.4.a.bz.1.5 6 21.5 even 6
2205.4.a.ca.1.5 6 21.2 odd 6