Properties

Label 1050.3.q.c.649.2
Level $1050$
Weight $3$
Character 1050.649
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,3,Mod(199,1050)]
 
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, 3, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.199");
 
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.q (of order \(6\), 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: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.11007531417600000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 649.2
Root \(0.596975 - 0.159959i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.c.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 + 6.51658i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-5.79240 - 10.0327i) q^{11} +(1.73205 - 3.00000i) q^{12} +7.86371 q^{13} +(7.73861 - 6.17364i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(13.8033 + 23.9080i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-27.2149 - 15.7125i) q^{19} +(11.9886 - 1.80922i) q^{21} +16.3834i q^{22} +(15.7263 + 9.07959i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-9.63104 - 5.56049i) q^{26} +5.19615 q^{27} +(-13.8433 + 2.08911i) q^{28} +2.30331 q^{29} +(-4.55860 + 2.63191i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-10.0327 + 17.3772i) q^{33} -39.0416i q^{34} -6.00000 q^{36} +(-1.72017 - 0.993142i) q^{37} +(22.2208 + 38.4876i) q^{38} +(-6.81018 - 11.7956i) q^{39} +22.1905i q^{41} +(-15.9623 - 6.26139i) q^{42} -49.8368i q^{43} +(11.5848 - 20.0655i) q^{44} +(-12.8405 - 22.2404i) q^{46} +(38.3335 - 66.3956i) q^{47} +6.92820 q^{48} +(-35.9317 - 33.3154i) q^{49} +(23.9080 - 41.4099i) q^{51} +(7.86371 + 13.6204i) q^{52} +(-49.4461 + 28.5477i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(18.4317 + 7.23003i) q^{56} +54.4297i q^{57} +(-2.82097 - 1.62869i) q^{58} +(60.9245 - 35.1748i) q^{59} +(-58.5590 - 33.8091i) q^{61} +7.44416 q^{62} +(-13.0963 - 16.4161i) q^{63} -8.00000 q^{64} +(24.5751 - 14.1884i) q^{66} +(85.0131 - 49.0823i) q^{67} +(-27.6066 + 47.8160i) q^{68} -31.4526i q^{69} -34.2597 q^{71} +(7.34847 + 4.24264i) q^{72} +(-9.74573 - 16.8801i) q^{73} +(1.40452 + 2.43269i) q^{74} -62.8501i q^{76} +(80.1856 - 12.1010i) q^{77} +19.2621i q^{78} +(45.2142 - 78.3134i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(15.6911 - 27.1777i) q^{82} -133.803 q^{83} +(15.1223 + 18.9557i) q^{84} +(-35.2400 + 61.0374i) q^{86} +(-1.99472 - 3.45496i) q^{87} +(-28.3768 + 16.3834i) q^{88} +(9.58232 + 5.53235i) q^{89} +(-20.1012 + 51.2445i) q^{91} +36.3184i q^{92} +(7.89573 + 4.55860i) q^{93} +(-93.8975 + 54.2118i) q^{94} +(-8.48528 - 4.89898i) q^{96} -72.3112 q^{97} +(20.4496 + 66.2104i) q^{98} +34.7544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −2.55620 + 6.51658i −0.365172 + 0.930940i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −5.79240 10.0327i −0.526582 0.912066i −0.999520 0.0309707i \(-0.990140\pi\)
0.472939 0.881095i \(-0.343193\pi\)
\(12\) 1.73205 3.00000i 0.144338 0.250000i
\(13\) 7.86371 0.604901 0.302451 0.953165i \(-0.402195\pi\)
0.302451 + 0.953165i \(0.402195\pi\)
\(14\) 7.73861 6.17364i 0.552758 0.440975i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 13.8033 + 23.9080i 0.811959 + 1.40635i 0.911491 + 0.411320i \(0.134932\pi\)
−0.0995321 + 0.995034i \(0.531735\pi\)
\(18\) 3.67423 2.12132i 0.204124 0.117851i
\(19\) −27.2149 15.7125i −1.43236 0.826974i −0.435061 0.900401i \(-0.643273\pi\)
−0.997301 + 0.0734266i \(0.976607\pi\)
\(20\) 0 0
\(21\) 11.9886 1.80922i 0.570886 0.0861535i
\(22\) 16.3834i 0.744699i
\(23\) 15.7263 + 9.07959i 0.683753 + 0.394765i 0.801268 0.598306i \(-0.204159\pi\)
−0.117515 + 0.993071i \(0.537493\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −9.63104 5.56049i −0.370425 0.213865i
\(27\) 5.19615 0.192450
\(28\) −13.8433 + 2.08911i −0.494402 + 0.0746112i
\(29\) 2.30331 0.0794244 0.0397122 0.999211i \(-0.487356\pi\)
0.0397122 + 0.999211i \(0.487356\pi\)
\(30\) 0 0
\(31\) −4.55860 + 2.63191i −0.147052 + 0.0849003i −0.571721 0.820448i \(-0.693724\pi\)
0.424669 + 0.905349i \(0.360391\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) −10.0327 + 17.3772i −0.304022 + 0.526582i
\(34\) 39.0416i 1.14828i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −1.72017 0.993142i −0.0464912 0.0268417i 0.476574 0.879134i \(-0.341878\pi\)
−0.523065 + 0.852293i \(0.675212\pi\)
\(38\) 22.2208 + 38.4876i 0.584759 + 1.01283i
\(39\) −6.81018 11.7956i −0.174620 0.302451i
\(40\) 0 0
\(41\) 22.1905i 0.541233i 0.962687 + 0.270616i \(0.0872275\pi\)
−0.962687 + 0.270616i \(0.912773\pi\)
\(42\) −15.9623 6.26139i −0.380055 0.149081i
\(43\) 49.8368i 1.15900i −0.814974 0.579498i \(-0.803249\pi\)
0.814974 0.579498i \(-0.196751\pi\)
\(44\) 11.5848 20.0655i 0.263291 0.456033i
\(45\) 0 0
\(46\) −12.8405 22.2404i −0.279141 0.483486i
\(47\) 38.3335 66.3956i 0.815606 1.41267i −0.0932854 0.995639i \(-0.529737\pi\)
0.908892 0.417032i \(-0.136930\pi\)
\(48\) 6.92820 0.144338
\(49\) −35.9317 33.3154i −0.733300 0.679906i
\(50\) 0 0
\(51\) 23.9080 41.4099i 0.468785 0.811959i
\(52\) 7.86371 + 13.6204i 0.151225 + 0.261930i
\(53\) −49.4461 + 28.5477i −0.932945 + 0.538636i −0.887742 0.460342i \(-0.847727\pi\)
−0.0452033 + 0.998978i \(0.514394\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 18.4317 + 7.23003i 0.329137 + 0.129108i
\(57\) 54.4297i 0.954908i
\(58\) −2.82097 1.62869i −0.0486373 0.0280808i
\(59\) 60.9245 35.1748i 1.03262 0.596182i 0.114885 0.993379i \(-0.463350\pi\)
0.917734 + 0.397196i \(0.130017\pi\)
\(60\) 0 0
\(61\) −58.5590 33.8091i −0.959984 0.554247i −0.0638160 0.997962i \(-0.520327\pi\)
−0.896168 + 0.443715i \(0.853660\pi\)
\(62\) 7.44416 0.120067
\(63\) −13.0963 16.4161i −0.207877 0.260573i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 24.5751 14.1884i 0.372349 0.214976i
\(67\) 85.0131 49.0823i 1.26885 0.732572i 0.294081 0.955780i \(-0.404986\pi\)
0.974771 + 0.223208i \(0.0716530\pi\)
\(68\) −27.6066 + 47.8160i −0.405979 + 0.703177i
\(69\) 31.4526i 0.455835i
\(70\) 0 0
\(71\) −34.2597 −0.482531 −0.241266 0.970459i \(-0.577563\pi\)
−0.241266 + 0.970459i \(0.577563\pi\)
\(72\) 7.34847 + 4.24264i 0.102062 + 0.0589256i
\(73\) −9.74573 16.8801i −0.133503 0.231234i 0.791521 0.611141i \(-0.209289\pi\)
−0.925025 + 0.379907i \(0.875956\pi\)
\(74\) 1.40452 + 2.43269i 0.0189799 + 0.0328742i
\(75\) 0 0
\(76\) 62.8501i 0.826974i
\(77\) 80.1856 12.1010i 1.04137 0.157155i
\(78\) 19.2621i 0.246950i
\(79\) 45.2142 78.3134i 0.572332 0.991308i −0.423994 0.905665i \(-0.639372\pi\)
0.996326 0.0856432i \(-0.0272945\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 15.6911 27.1777i 0.191355 0.331436i
\(83\) −133.803 −1.61209 −0.806045 0.591854i \(-0.798396\pi\)
−0.806045 + 0.591854i \(0.798396\pi\)
\(84\) 15.1223 + 18.9557i 0.180027 + 0.225663i
\(85\) 0 0
\(86\) −35.2400 + 61.0374i −0.409767 + 0.709737i
\(87\) −1.99472 3.45496i −0.0229279 0.0397122i
\(88\) −28.3768 + 16.3834i −0.322464 + 0.186175i
\(89\) 9.58232 + 5.53235i 0.107666 + 0.0621613i 0.552866 0.833270i \(-0.313534\pi\)
−0.445200 + 0.895431i \(0.646867\pi\)
\(90\) 0 0
\(91\) −20.1012 + 51.2445i −0.220893 + 0.563127i
\(92\) 36.3184i 0.394765i
\(93\) 7.89573 + 4.55860i 0.0849003 + 0.0490172i
\(94\) −93.8975 + 54.2118i −0.998910 + 0.576721i
\(95\) 0 0
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) −72.3112 −0.745476 −0.372738 0.927937i \(-0.621581\pi\)
−0.372738 + 0.927937i \(0.621581\pi\)
\(98\) 20.4496 + 66.2104i 0.208669 + 0.675616i
\(99\) 34.7544 0.351054
\(100\) 0 0
\(101\) 43.8670 25.3266i 0.434327 0.250759i −0.266861 0.963735i \(-0.585987\pi\)
0.701188 + 0.712976i \(0.252653\pi\)
\(102\) −58.5625 + 33.8110i −0.574142 + 0.331481i
\(103\) −98.9823 + 171.442i −0.960993 + 1.66449i −0.240978 + 0.970531i \(0.577468\pi\)
−0.720015 + 0.693958i \(0.755865\pi\)
\(104\) 22.2419i 0.213865i
\(105\) 0 0
\(106\) 80.7451 0.761746
\(107\) −128.116 73.9679i −1.19735 0.691289i −0.237384 0.971416i \(-0.576290\pi\)
−0.959963 + 0.280127i \(0.909623\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) −27.1610 47.0442i −0.249183 0.431598i 0.714116 0.700027i \(-0.246829\pi\)
−0.963299 + 0.268429i \(0.913495\pi\)
\(110\) 0 0
\(111\) 3.44035i 0.0309941i
\(112\) −17.4617 21.8881i −0.155908 0.195429i
\(113\) 47.7883i 0.422906i −0.977388 0.211453i \(-0.932181\pi\)
0.977388 0.211453i \(-0.0678195\pi\)
\(114\) 38.4876 66.6625i 0.337611 0.584759i
\(115\) 0 0
\(116\) 2.30331 + 3.98945i 0.0198561 + 0.0343918i
\(117\) −11.7956 + 20.4305i −0.100817 + 0.174620i
\(118\) −99.4892 −0.843129
\(119\) −191.083 + 28.8367i −1.60574 + 0.242325i
\(120\) 0 0
\(121\) −6.60372 + 11.4380i −0.0545762 + 0.0945288i
\(122\) 47.8132 + 82.8150i 0.391912 + 0.678811i
\(123\) 33.2858 19.2176i 0.270616 0.156240i
\(124\) −9.11720 5.26382i −0.0735258 0.0424501i
\(125\) 0 0
\(126\) 4.43168 + 29.3660i 0.0351720 + 0.233063i
\(127\) 101.973i 0.802940i −0.915872 0.401470i \(-0.868499\pi\)
0.915872 0.401470i \(-0.131501\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) −74.7552 + 43.1600i −0.579498 + 0.334573i
\(130\) 0 0
\(131\) −64.6037 37.2990i −0.493158 0.284725i 0.232726 0.972542i \(-0.425236\pi\)
−0.725884 + 0.687817i \(0.758569\pi\)
\(132\) −40.1309 −0.304022
\(133\) 171.959 137.184i 1.29292 1.03146i
\(134\) −138.826 −1.03601
\(135\) 0 0
\(136\) 67.6221 39.0416i 0.497221 0.287071i
\(137\) −213.821 + 123.449i −1.56074 + 0.901091i −0.563553 + 0.826080i \(0.690566\pi\)
−0.997183 + 0.0750109i \(0.976101\pi\)
\(138\) −22.2404 + 38.5215i −0.161162 + 0.279141i
\(139\) 155.917i 1.12170i −0.827916 0.560852i \(-0.810474\pi\)
0.827916 0.560852i \(-0.189526\pi\)
\(140\) 0 0
\(141\) −132.791 −0.941781
\(142\) 41.9594 + 24.2253i 0.295489 + 0.170601i
\(143\) −45.5498 78.8945i −0.318530 0.551710i
\(144\) −6.00000 10.3923i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 27.5651i 0.188802i
\(147\) −18.8553 + 82.7495i −0.128268 + 0.562922i
\(148\) 3.97257i 0.0268417i
\(149\) 81.5452 141.240i 0.547283 0.947922i −0.451176 0.892435i \(-0.648995\pi\)
0.998459 0.0554872i \(-0.0176712\pi\)
\(150\) 0 0
\(151\) 37.5149 + 64.9778i 0.248443 + 0.430316i 0.963094 0.269165i \(-0.0867477\pi\)
−0.714651 + 0.699481i \(0.753414\pi\)
\(152\) −44.4417 + 76.9753i −0.292380 + 0.506416i
\(153\) −82.8198 −0.541306
\(154\) −106.764 41.8792i −0.693270 0.271943i
\(155\) 0 0
\(156\) 13.6204 23.5911i 0.0873100 0.151225i
\(157\) −112.365 194.622i −0.715702 1.23963i −0.962688 0.270614i \(-0.912773\pi\)
0.246986 0.969019i \(-0.420560\pi\)
\(158\) −110.752 + 63.9426i −0.700961 + 0.404700i
\(159\) 85.6431 + 49.4461i 0.538636 + 0.310982i
\(160\) 0 0
\(161\) −99.3675 + 79.2726i −0.617190 + 0.492376i
\(162\) 12.7279i 0.0785674i
\(163\) −199.288 115.059i −1.22262 0.705882i −0.257147 0.966372i \(-0.582782\pi\)
−0.965476 + 0.260491i \(0.916116\pi\)
\(164\) −38.4351 + 22.1905i −0.234361 + 0.135308i
\(165\) 0 0
\(166\) 163.875 + 94.6133i 0.987199 + 0.569960i
\(167\) 277.788 1.66340 0.831702 0.555223i \(-0.187367\pi\)
0.831702 + 0.555223i \(0.187367\pi\)
\(168\) −5.11726 33.9089i −0.0304599 0.201839i
\(169\) −107.162 −0.634095
\(170\) 0 0
\(171\) 81.6446 47.1375i 0.477454 0.275658i
\(172\) 86.3199 49.8368i 0.501860 0.289749i
\(173\) 63.0327 109.176i 0.364351 0.631074i −0.624321 0.781168i \(-0.714624\pi\)
0.988672 + 0.150094i \(0.0479576\pi\)
\(174\) 5.64193i 0.0324249i
\(175\) 0 0
\(176\) 46.3392 0.263291
\(177\) −105.524 60.9245i −0.596182 0.344206i
\(178\) −7.82393 13.5514i −0.0439547 0.0761317i
\(179\) 38.5535 + 66.7766i 0.215382 + 0.373053i 0.953391 0.301738i \(-0.0975668\pi\)
−0.738008 + 0.674792i \(0.764234\pi\)
\(180\) 0 0
\(181\) 212.012i 1.17134i −0.810551 0.585668i \(-0.800832\pi\)
0.810551 0.585668i \(-0.199168\pi\)
\(182\) 60.8542 48.5478i 0.334364 0.266746i
\(183\) 117.118i 0.639989i
\(184\) 25.6810 44.4807i 0.139570 0.241743i
\(185\) 0 0
\(186\) −6.44683 11.1662i −0.0346604 0.0600336i
\(187\) 159.908 276.969i 0.855125 1.48112i
\(188\) 153.334 0.815606
\(189\) −13.2824 + 33.8612i −0.0702773 + 0.179160i
\(190\) 0 0
\(191\) −82.8480 + 143.497i −0.433759 + 0.751293i −0.997193 0.0748682i \(-0.976146\pi\)
0.563434 + 0.826161i \(0.309480\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) 91.1920 52.6497i 0.472497 0.272796i −0.244787 0.969577i \(-0.578718\pi\)
0.717285 + 0.696780i \(0.245385\pi\)
\(194\) 88.5627 + 51.1317i 0.456509 + 0.263566i
\(195\) 0 0
\(196\) 21.7723 95.5509i 0.111083 0.487504i
\(197\) 244.736i 1.24231i 0.783687 + 0.621156i \(0.213337\pi\)
−0.783687 + 0.621156i \(0.786663\pi\)
\(198\) −42.5653 24.5751i −0.214976 0.124116i
\(199\) −84.8416 + 48.9833i −0.426340 + 0.246147i −0.697786 0.716306i \(-0.745831\pi\)
0.271446 + 0.962454i \(0.412498\pi\)
\(200\) 0 0
\(201\) −147.247 85.0131i −0.732572 0.422951i
\(202\) −71.6346 −0.354627
\(203\) −5.88772 + 15.0097i −0.0290035 + 0.0739394i
\(204\) 95.6321 0.468785
\(205\) 0 0
\(206\) 242.456 139.982i 1.17697 0.679525i
\(207\) −47.1790 + 27.2388i −0.227918 + 0.131588i
\(208\) −15.7274 + 27.2407i −0.0756126 + 0.130965i
\(209\) 364.052i 1.74188i
\(210\) 0 0
\(211\) −388.914 −1.84319 −0.921597 0.388149i \(-0.873114\pi\)
−0.921597 + 0.388149i \(0.873114\pi\)
\(212\) −98.8922 57.0954i −0.466473 0.269318i
\(213\) 29.6698 + 51.3896i 0.139295 + 0.241266i
\(214\) 104.606 + 181.184i 0.488815 + 0.846652i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −5.49835 36.4342i −0.0253380 0.167899i
\(218\) 76.8228i 0.352398i
\(219\) −16.8801 + 29.2372i −0.0770781 + 0.133503i
\(220\) 0 0
\(221\) 108.545 + 188.006i 0.491155 + 0.850705i
\(222\) 2.43269 4.21355i 0.0109581 0.0189799i
\(223\) 251.913 1.12965 0.564827 0.825210i \(-0.308943\pi\)
0.564827 + 0.825210i \(0.308943\pi\)
\(224\) 5.90890 + 39.1546i 0.0263790 + 0.174797i
\(225\) 0 0
\(226\) −33.7915 + 58.5285i −0.149520 + 0.258976i
\(227\) 133.911 + 231.941i 0.589916 + 1.02176i 0.994243 + 0.107150i \(0.0341725\pi\)
−0.404327 + 0.914615i \(0.632494\pi\)
\(228\) −94.2751 + 54.4297i −0.413487 + 0.238727i
\(229\) −299.237 172.765i −1.30671 0.754431i −0.325167 0.945657i \(-0.605420\pi\)
−0.981546 + 0.191226i \(0.938754\pi\)
\(230\) 0 0
\(231\) −87.5942 109.799i −0.379196 0.475319i
\(232\) 6.51474i 0.0280808i
\(233\) −249.471 144.032i −1.07069 0.618164i −0.142321 0.989821i \(-0.545457\pi\)
−0.928370 + 0.371656i \(0.878790\pi\)
\(234\) 28.8931 16.6815i 0.123475 0.0712883i
\(235\) 0 0
\(236\) 121.849 + 70.3495i 0.516309 + 0.298091i
\(237\) −156.627 −0.660872
\(238\) 254.418 + 99.7983i 1.06898 + 0.419320i
\(239\) 188.810 0.789999 0.395000 0.918681i \(-0.370745\pi\)
0.395000 + 0.918681i \(0.370745\pi\)
\(240\) 0 0
\(241\) 84.7389 48.9240i 0.351614 0.203004i −0.313782 0.949495i \(-0.601596\pi\)
0.665396 + 0.746491i \(0.268263\pi\)
\(242\) 16.1758 9.33908i 0.0668420 0.0385912i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 135.236i 0.554247i
\(245\) 0 0
\(246\) −54.3555 −0.220957
\(247\) −214.010 123.559i −0.866437 0.500238i
\(248\) 7.44416 + 12.8937i 0.0300168 + 0.0519906i
\(249\) 115.877 + 200.705i 0.465370 + 0.806045i
\(250\) 0 0
\(251\) 241.345i 0.961533i −0.876849 0.480767i \(-0.840358\pi\)
0.876849 0.480767i \(-0.159642\pi\)
\(252\) 15.3372 39.0995i 0.0608619 0.155157i
\(253\) 210.370i 0.831504i
\(254\) −72.1061 + 124.891i −0.283882 + 0.491698i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 6.28197 10.8807i 0.0244435 0.0423373i −0.853545 0.521019i \(-0.825552\pi\)
0.877988 + 0.478682i \(0.158885\pi\)
\(258\) 122.075 0.473158
\(259\) 10.8690 8.67098i 0.0419653 0.0334787i
\(260\) 0 0
\(261\) −3.45496 + 5.98417i −0.0132374 + 0.0229279i
\(262\) 52.7487 + 91.3635i 0.201331 + 0.348716i
\(263\) 184.014 106.240i 0.699672 0.403956i −0.107554 0.994199i \(-0.534302\pi\)
0.807225 + 0.590244i \(0.200968\pi\)
\(264\) 49.1501 + 28.3768i 0.186175 + 0.107488i
\(265\) 0 0
\(266\) −307.609 + 46.4219i −1.15642 + 0.174518i
\(267\) 19.1646i 0.0717777i
\(268\) 170.026 + 98.1647i 0.634426 + 0.366286i
\(269\) 289.769 167.298i 1.07721 0.621927i 0.147067 0.989127i \(-0.453017\pi\)
0.930142 + 0.367200i \(0.119683\pi\)
\(270\) 0 0
\(271\) −157.920 91.1752i −0.582731 0.336440i 0.179487 0.983760i \(-0.442556\pi\)
−0.762218 + 0.647321i \(0.775889\pi\)
\(272\) −110.426 −0.405979
\(273\) 94.2750 14.2272i 0.345330 0.0521144i
\(274\) 349.168 1.27434
\(275\) 0 0
\(276\) 54.4776 31.4526i 0.197382 0.113959i
\(277\) 144.420 83.3807i 0.521370 0.301013i −0.216125 0.976366i \(-0.569342\pi\)
0.737495 + 0.675353i \(0.236009\pi\)
\(278\) −110.250 + 190.958i −0.396582 + 0.686900i
\(279\) 15.7915i 0.0566002i
\(280\) 0 0
\(281\) 38.3085 0.136329 0.0681647 0.997674i \(-0.478286\pi\)
0.0681647 + 0.997674i \(0.478286\pi\)
\(282\) 162.635 + 93.8975i 0.576721 + 0.332970i
\(283\) 192.748 + 333.849i 0.681088 + 1.17968i 0.974649 + 0.223739i \(0.0718263\pi\)
−0.293561 + 0.955940i \(0.594840\pi\)
\(284\) −34.2597 59.3396i −0.120633 0.208942i
\(285\) 0 0
\(286\) 128.834i 0.450469i
\(287\) −144.606 56.7235i −0.503855 0.197643i
\(288\) 16.9706i 0.0589256i
\(289\) −236.562 + 409.738i −0.818555 + 1.41778i
\(290\) 0 0
\(291\) 62.6233 + 108.467i 0.215200 + 0.372738i
\(292\) 19.4915 33.7602i 0.0667516 0.115617i
\(293\) 90.9844 0.310527 0.155264 0.987873i \(-0.450377\pi\)
0.155264 + 0.987873i \(0.450377\pi\)
\(294\) 81.6057 88.0143i 0.277570 0.299368i
\(295\) 0 0
\(296\) −2.80903 + 4.86538i −0.00948997 + 0.0164371i
\(297\) −30.0982 52.1316i −0.101341 0.175527i
\(298\) −199.744 + 115.322i −0.670282 + 0.386988i
\(299\) 123.667 + 71.3993i 0.413603 + 0.238794i
\(300\) 0 0
\(301\) 324.766 + 127.393i 1.07896 + 0.423232i
\(302\) 106.108i 0.351352i
\(303\) −75.9799 43.8670i −0.250759 0.144776i
\(304\) 108.859 62.8501i 0.358090 0.206744i
\(305\) 0 0
\(306\) 101.433 + 58.5625i 0.331481 + 0.191381i
\(307\) 508.077 1.65497 0.827487 0.561485i \(-0.189770\pi\)
0.827487 + 0.561485i \(0.189770\pi\)
\(308\) 101.145 + 126.785i 0.328393 + 0.411638i
\(309\) 342.885 1.10966
\(310\) 0 0
\(311\) 90.3447 52.1605i 0.290497 0.167719i −0.347669 0.937617i \(-0.613027\pi\)
0.638166 + 0.769899i \(0.279693\pi\)
\(312\) −33.3629 + 19.2621i −0.106932 + 0.0617375i
\(313\) 132.934 230.249i 0.424710 0.735619i −0.571683 0.820474i \(-0.693709\pi\)
0.996393 + 0.0848550i \(0.0270427\pi\)
\(314\) 317.817i 1.01216i
\(315\) 0 0
\(316\) 180.857 0.572332
\(317\) 9.28575 + 5.36113i 0.0292926 + 0.0169121i 0.514575 0.857446i \(-0.327950\pi\)
−0.485282 + 0.874358i \(0.661283\pi\)
\(318\) −69.9273 121.118i −0.219897 0.380873i
\(319\) −13.3417 23.1085i −0.0418234 0.0724403i
\(320\) 0 0
\(321\) 256.232i 0.798231i
\(322\) 177.754 26.8252i 0.552031 0.0833081i
\(323\) 867.538i 2.68588i
\(324\) 9.00000 15.5885i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) 162.718 + 281.835i 0.499134 + 0.864525i
\(327\) −47.0442 + 81.4829i −0.143866 + 0.249183i
\(328\) 62.7643 0.191355
\(329\) 334.684 + 419.524i 1.01728 + 1.27515i
\(330\) 0 0
\(331\) 176.460 305.638i 0.533113 0.923379i −0.466139 0.884711i \(-0.654355\pi\)
0.999252 0.0386675i \(-0.0123113\pi\)
\(332\) −133.803 231.754i −0.403022 0.698055i
\(333\) 5.16052 2.97943i 0.0154971 0.00894723i
\(334\) −340.220 196.426i −1.01862 0.588102i
\(335\) 0 0
\(336\) −17.7099 + 45.1482i −0.0527080 + 0.134370i
\(337\) 220.634i 0.654699i 0.944903 + 0.327349i \(0.106155\pi\)
−0.944903 + 0.327349i \(0.893845\pi\)
\(338\) 131.246 + 75.7750i 0.388302 + 0.224186i
\(339\) −71.6825 + 41.3859i −0.211453 + 0.122082i
\(340\) 0 0
\(341\) 52.8104 + 30.4901i 0.154869 + 0.0894138i
\(342\) −133.325 −0.389839
\(343\) 308.951 148.991i 0.900732 0.434376i
\(344\) −140.960 −0.409767
\(345\) 0 0
\(346\) −154.398 + 89.1417i −0.446237 + 0.257635i
\(347\) −221.710 + 128.004i −0.638933 + 0.368888i −0.784204 0.620504i \(-0.786928\pi\)
0.145270 + 0.989392i \(0.453595\pi\)
\(348\) 3.98945 6.90993i 0.0114639 0.0198561i
\(349\) 407.250i 1.16691i 0.812147 + 0.583453i \(0.198299\pi\)
−0.812147 + 0.583453i \(0.801701\pi\)
\(350\) 0 0
\(351\) 40.8611 0.116413
\(352\) −56.7537 32.7667i −0.161232 0.0930873i
\(353\) 291.619 + 505.099i 0.826116 + 1.43087i 0.901064 + 0.433687i \(0.142788\pi\)
−0.0749482 + 0.997187i \(0.523879\pi\)
\(354\) 86.1602 + 149.234i 0.243390 + 0.421565i
\(355\) 0 0
\(356\) 22.1294i 0.0621613i
\(357\) 208.737 + 261.651i 0.584698 + 0.732915i
\(358\) 109.046i 0.304597i
\(359\) 345.764 598.881i 0.963131 1.66819i 0.248577 0.968612i \(-0.420037\pi\)
0.714554 0.699580i \(-0.246630\pi\)
\(360\) 0 0
\(361\) 313.266 + 542.593i 0.867773 + 1.50303i
\(362\) −149.915 + 259.660i −0.414130 + 0.717294i
\(363\) 22.8760 0.0630192
\(364\) −108.859 + 16.4282i −0.299064 + 0.0451324i
\(365\) 0 0
\(366\) 82.8150 143.440i 0.226270 0.391912i
\(367\) 114.863 + 198.949i 0.312980 + 0.542096i 0.979006 0.203832i \(-0.0653395\pi\)
−0.666026 + 0.745928i \(0.732006\pi\)
\(368\) −62.9053 + 36.3184i −0.170938 + 0.0986912i
\(369\) −57.6527 33.2858i −0.156240 0.0902054i
\(370\) 0 0
\(371\) −59.6394 395.193i −0.160753 1.06521i
\(372\) 18.2344i 0.0490172i
\(373\) −350.401 202.304i −0.939414 0.542371i −0.0496372 0.998767i \(-0.515807\pi\)
−0.889776 + 0.456397i \(0.849140\pi\)
\(374\) −391.694 + 226.145i −1.04731 + 0.604665i
\(375\) 0 0
\(376\) −187.795 108.424i −0.499455 0.288360i
\(377\) 18.1126 0.0480439
\(378\) 40.2110 32.0792i 0.106378 0.0848656i
\(379\) −265.866 −0.701493 −0.350746 0.936471i \(-0.614072\pi\)
−0.350746 + 0.936471i \(0.614072\pi\)
\(380\) 0 0
\(381\) −152.960 + 88.3115i −0.401470 + 0.231789i
\(382\) 202.935 117.165i 0.531244 0.306714i
\(383\) 153.202 265.353i 0.400005 0.692829i −0.593721 0.804671i \(-0.702342\pi\)
0.993726 + 0.111842i \(0.0356751\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −148.916 −0.385792
\(387\) 129.480 + 74.7552i 0.334573 + 0.193166i
\(388\) −72.3112 125.247i −0.186369 0.322801i
\(389\) 53.1772 + 92.1056i 0.136702 + 0.236775i 0.926246 0.376918i \(-0.123016\pi\)
−0.789544 + 0.613694i \(0.789683\pi\)
\(390\) 0 0
\(391\) 501.314i 1.28213i
\(392\) −94.2301 + 101.630i −0.240383 + 0.259261i
\(393\) 129.207i 0.328772i
\(394\) 173.054 299.739i 0.439224 0.760758i
\(395\) 0 0
\(396\) 34.7544 + 60.1964i 0.0877636 + 0.152011i
\(397\) 108.913 188.643i 0.274341 0.475172i −0.695628 0.718402i \(-0.744874\pi\)
0.969969 + 0.243230i \(0.0782070\pi\)
\(398\) 138.546 0.348105
\(399\) −354.696 139.133i −0.888962 0.348705i
\(400\) 0 0
\(401\) −30.9907 + 53.6775i −0.0772836 + 0.133859i −0.902077 0.431575i \(-0.857958\pi\)
0.824793 + 0.565434i \(0.191291\pi\)
\(402\) 120.227 + 208.239i 0.299071 + 0.518007i
\(403\) −35.8475 + 20.6966i −0.0889517 + 0.0513563i
\(404\) 87.7341 + 50.6533i 0.217164 + 0.125379i
\(405\) 0 0
\(406\) 17.8244 14.2198i 0.0439025 0.0350242i
\(407\) 23.0107i 0.0565373i
\(408\) −117.125 67.6221i −0.287071 0.165740i
\(409\) 376.167 217.180i 0.919724 0.531003i 0.0361772 0.999345i \(-0.488482\pi\)
0.883547 + 0.468342i \(0.155149\pi\)
\(410\) 0 0
\(411\) 370.348 + 213.821i 0.901091 + 0.520245i
\(412\) −395.929 −0.960993
\(413\) 73.4840 + 486.933i 0.177927 + 1.17901i
\(414\) 77.0429 0.186094
\(415\) 0 0
\(416\) 38.5242 22.2419i 0.0926062 0.0534662i
\(417\) −233.875 + 135.028i −0.560852 + 0.323808i
\(418\) 257.424 445.871i 0.615847 1.06668i
\(419\) 457.221i 1.09122i −0.838040 0.545609i \(-0.816298\pi\)
0.838040 0.545609i \(-0.183702\pi\)
\(420\) 0 0
\(421\) −653.149 −1.55142 −0.775712 0.631088i \(-0.782609\pi\)
−0.775712 + 0.631088i \(0.782609\pi\)
\(422\) 476.320 + 275.004i 1.12872 + 0.651667i
\(423\) 115.000 + 199.187i 0.271869 + 0.470891i
\(424\) 80.7451 + 139.855i 0.190437 + 0.329846i
\(425\) 0 0
\(426\) 83.9188i 0.196993i
\(427\) 370.008 295.182i 0.866530 0.691293i
\(428\) 295.872i 0.691289i
\(429\) −78.8945 + 136.649i −0.183903 + 0.318530i
\(430\) 0 0
\(431\) 235.128 + 407.253i 0.545540 + 0.944904i 0.998573 + 0.0534095i \(0.0170089\pi\)
−0.453032 + 0.891494i \(0.649658\pi\)
\(432\) −10.3923 + 18.0000i −0.0240563 + 0.0416667i
\(433\) 32.0299 0.0739719 0.0369860 0.999316i \(-0.488224\pi\)
0.0369860 + 0.999316i \(0.488224\pi\)
\(434\) −19.0288 + 48.5105i −0.0438451 + 0.111775i
\(435\) 0 0
\(436\) 54.3219 94.0883i 0.124592 0.215799i
\(437\) −285.326 494.200i −0.652921 1.13089i
\(438\) 41.3476 23.8721i 0.0944010 0.0545024i
\(439\) −331.028 191.119i −0.754051 0.435352i 0.0731046 0.997324i \(-0.476709\pi\)
−0.827156 + 0.561973i \(0.810043\pi\)
\(440\) 0 0
\(441\) 140.453 43.3802i 0.318488 0.0983677i
\(442\) 307.012i 0.694598i
\(443\) 107.163 + 61.8708i 0.241904 + 0.139663i 0.616051 0.787706i \(-0.288731\pi\)
−0.374148 + 0.927369i \(0.622065\pi\)
\(444\) −5.95885 + 3.44035i −0.0134208 + 0.00774853i
\(445\) 0 0
\(446\) −308.529 178.129i −0.691769 0.399393i
\(447\) −282.481 −0.631948
\(448\) 20.4496 52.1327i 0.0456464 0.116368i
\(449\) 266.985 0.594622 0.297311 0.954781i \(-0.403910\pi\)
0.297311 + 0.954781i \(0.403910\pi\)
\(450\) 0 0
\(451\) 222.632 128.536i 0.493640 0.285003i
\(452\) 82.7718 47.7883i 0.183124 0.105726i
\(453\) 64.9778 112.545i 0.143439 0.248443i
\(454\) 378.757i 0.834267i
\(455\) 0 0
\(456\) 153.951 0.337611
\(457\) 389.140 + 224.670i 0.851509 + 0.491619i 0.861160 0.508334i \(-0.169739\pi\)
−0.00965069 + 0.999953i \(0.503072\pi\)
\(458\) 244.326 + 423.185i 0.533463 + 0.923985i
\(459\) 71.7241 + 124.230i 0.156262 + 0.270653i
\(460\) 0 0
\(461\) 105.528i 0.228912i −0.993428 0.114456i \(-0.963487\pi\)
0.993428 0.114456i \(-0.0365125\pi\)
\(462\) 29.6412 + 196.414i 0.0641584 + 0.425138i
\(463\) 588.555i 1.27118i −0.772028 0.635588i \(-0.780758\pi\)
0.772028 0.635588i \(-0.219242\pi\)
\(464\) −4.60662 + 7.97889i −0.00992805 + 0.0171959i
\(465\) 0 0
\(466\) 203.692 + 352.805i 0.437108 + 0.757093i
\(467\) −182.829 + 316.668i −0.391496 + 0.678091i −0.992647 0.121044i \(-0.961376\pi\)
0.601151 + 0.799135i \(0.294709\pi\)
\(468\) −47.1823 −0.100817
\(469\) 102.539 + 679.459i 0.218632 + 1.44874i
\(470\) 0 0
\(471\) −194.622 + 337.096i −0.413211 + 0.715702i
\(472\) −99.4892 172.320i −0.210782 0.365086i
\(473\) −499.999 + 288.675i −1.05708 + 0.610306i
\(474\) 191.828 + 110.752i 0.404700 + 0.233654i
\(475\) 0 0
\(476\) −241.029 302.128i −0.506364 0.634723i
\(477\) 171.286i 0.359091i
\(478\) −231.244 133.509i −0.483774 0.279307i
\(479\) 421.907 243.588i 0.880808 0.508535i 0.00988318 0.999951i \(-0.496854\pi\)
0.870925 + 0.491416i \(0.163521\pi\)
\(480\) 0 0
\(481\) −13.5270 7.80979i −0.0281226 0.0162366i
\(482\) −138.378 −0.287091
\(483\) 204.964 + 80.3992i 0.424355 + 0.166458i
\(484\) −26.4149 −0.0545762
\(485\) 0 0
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) −169.545 + 97.8870i −0.348142 + 0.201000i −0.663867 0.747851i \(-0.731086\pi\)
0.315725 + 0.948851i \(0.397752\pi\)
\(488\) −95.6265 + 165.630i −0.195956 + 0.339406i
\(489\) 398.575i 0.815082i
\(490\) 0 0
\(491\) −349.221 −0.711244 −0.355622 0.934630i \(-0.615731\pi\)
−0.355622 + 0.934630i \(0.615731\pi\)
\(492\) 66.5716 + 38.4351i 0.135308 + 0.0781202i
\(493\) 31.7933 + 55.0675i 0.0644894 + 0.111699i
\(494\) 174.738 + 302.656i 0.353722 + 0.612664i
\(495\) 0 0
\(496\) 21.0553i 0.0424501i
\(497\) 87.5747 223.256i 0.176207 0.449208i
\(498\) 327.750i 0.658133i
\(499\) −167.719 + 290.498i −0.336111 + 0.582161i −0.983698 0.179831i \(-0.942445\pi\)
0.647587 + 0.761992i \(0.275778\pi\)
\(500\) 0 0
\(501\) −240.572 416.683i −0.480183 0.831702i
\(502\) −170.657 + 295.586i −0.339953 + 0.588817i
\(503\) −523.663 −1.04108 −0.520540 0.853837i \(-0.674269\pi\)
−0.520540 + 0.853837i \(0.674269\pi\)
\(504\) −46.4317 + 37.0419i −0.0921263 + 0.0734958i
\(505\) 0 0
\(506\) −148.754 + 257.650i −0.293981 + 0.509190i
\(507\) 92.8050 + 160.743i 0.183047 + 0.317047i
\(508\) 176.623 101.973i 0.347683 0.200735i
\(509\) 417.731 + 241.177i 0.820690 + 0.473825i 0.850654 0.525726i \(-0.176206\pi\)
−0.0299645 + 0.999551i \(0.509539\pi\)
\(510\) 0 0
\(511\) 134.913 20.3599i 0.264017 0.0398433i
\(512\) 22.6274i 0.0441942i
\(513\) −141.413 81.6446i −0.275658 0.159151i
\(514\) −15.3876 + 8.88405i −0.0299370 + 0.0172841i
\(515\) 0 0
\(516\) −149.510 86.3199i −0.289749 0.167287i
\(517\) −888.171 −1.71793
\(518\) −19.4431 + 2.93419i −0.0375349 + 0.00566446i
\(519\) −218.352 −0.420716
\(520\) 0 0
\(521\) −61.7509 + 35.6519i −0.118524 + 0.0684298i −0.558090 0.829780i \(-0.688466\pi\)
0.439566 + 0.898210i \(0.355132\pi\)
\(522\) 8.46290 4.88606i 0.0162124 0.00936026i
\(523\) −301.064 + 521.458i −0.575648 + 0.997052i 0.420323 + 0.907375i \(0.361917\pi\)
−0.995971 + 0.0896773i \(0.971416\pi\)
\(524\) 149.196i 0.284725i
\(525\) 0 0
\(526\) −300.493 −0.571279
\(527\) −125.847 72.6581i −0.238800 0.137871i
\(528\) −40.1309 69.5088i −0.0760055 0.131645i
\(529\) −99.6220 172.550i −0.188321 0.326182i
\(530\) 0 0
\(531\) 211.049i 0.397455i
\(532\) 409.568 + 160.657i 0.769864 + 0.301987i
\(533\) 174.500i 0.327392i
\(534\) −13.5514 + 23.4718i −0.0253772 + 0.0439547i
\(535\) 0 0
\(536\) −138.826 240.453i −0.259003 0.448607i
\(537\) 66.7766 115.660i 0.124351 0.215382i
\(538\) −473.191 −0.879537
\(539\) −126.114 + 553.469i −0.233977 + 1.02684i
\(540\) 0 0
\(541\) 301.657 522.485i 0.557591 0.965776i −0.440106 0.897946i \(-0.645059\pi\)
0.997697 0.0678303i \(-0.0216077\pi\)
\(542\) 128.941 + 223.333i 0.237899 + 0.412053i
\(543\) −318.018 + 183.608i −0.585668 + 0.338136i
\(544\) 135.244 + 78.0833i 0.248611 + 0.143535i
\(545\) 0 0
\(546\) −125.523 49.2378i −0.229896 0.0901791i
\(547\) 879.935i 1.60866i −0.594185 0.804328i \(-0.702525\pi\)
0.594185 0.804328i \(-0.297475\pi\)
\(548\) −427.642 246.899i −0.780368 0.450546i
\(549\) 175.677 101.427i 0.319995 0.184749i
\(550\) 0 0
\(551\) −62.6842 36.1908i −0.113765 0.0656820i
\(552\) −88.9615 −0.161162
\(553\) 394.759 + 494.827i 0.713849 + 0.894805i
\(554\) −235.836 −0.425697
\(555\) 0 0
\(556\) 270.056 155.917i 0.485712 0.280426i
\(557\) −764.533 + 441.404i −1.37259 + 0.792466i −0.991254 0.131970i \(-0.957870\pi\)
−0.381338 + 0.924436i \(0.624536\pi\)
\(558\) −11.1662 + 19.3405i −0.0200112 + 0.0346604i
\(559\) 391.903i 0.701078i
\(560\) 0 0
\(561\) −553.939 −0.987414
\(562\) −46.9182 27.0882i −0.0834843 0.0481997i
\(563\) 260.578 + 451.334i 0.462838 + 0.801659i 0.999101 0.0423920i \(-0.0134978\pi\)
−0.536263 + 0.844051i \(0.680165\pi\)
\(564\) −132.791 230.001i −0.235445 0.407803i
\(565\) 0 0
\(566\) 545.174i 0.963204i
\(567\) 62.2946 9.40101i 0.109867 0.0165803i
\(568\) 96.9011i 0.170601i
\(569\) 122.400 212.004i 0.215115 0.372590i −0.738193 0.674589i \(-0.764321\pi\)
0.953308 + 0.301999i \(0.0976541\pi\)
\(570\) 0 0
\(571\) 208.126 + 360.486i 0.364495 + 0.631323i 0.988695 0.149941i \(-0.0479084\pi\)
−0.624200 + 0.781264i \(0.714575\pi\)
\(572\) 91.0995 157.789i 0.159265 0.275855i
\(573\) 286.994 0.500862
\(574\) 136.996 + 171.724i 0.238670 + 0.299171i
\(575\) 0 0
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 386.784 + 669.929i 0.670336 + 1.16106i 0.977809 + 0.209499i \(0.0671834\pi\)
−0.307473 + 0.951557i \(0.599483\pi\)
\(578\) 579.457 334.550i 1.00252 0.578806i
\(579\) −157.949 91.1920i −0.272796 0.157499i
\(580\) 0 0
\(581\) 342.028 871.941i 0.588689 1.50076i
\(582\) 177.125i 0.304339i
\(583\) 572.823 + 330.719i 0.982543 + 0.567272i
\(584\) −47.7441 + 27.5651i −0.0817537 + 0.0472005i
\(585\) 0 0
\(586\) −111.433 64.3357i −0.190158 0.109788i
\(587\) 633.860 1.07983 0.539915 0.841720i \(-0.318456\pi\)
0.539915 + 0.841720i \(0.318456\pi\)
\(588\) −162.182 + 50.0911i −0.275819 + 0.0851889i
\(589\) 165.416 0.280841
\(590\) 0 0
\(591\) 367.103 211.947i 0.621156 0.358625i
\(592\) 6.88069 3.97257i 0.0116228 0.00671042i
\(593\) 46.4206 80.4028i 0.0782809 0.135587i −0.824227 0.566259i \(-0.808390\pi\)
0.902508 + 0.430672i \(0.141724\pi\)
\(594\) 85.1305i 0.143317i
\(595\) 0 0
\(596\) 326.181 0.547283
\(597\) 146.950 + 84.8416i 0.246147 + 0.142113i
\(598\) −100.974 174.892i −0.168853 0.292461i
\(599\) −307.680 532.918i −0.513657 0.889679i −0.999875 0.0158418i \(-0.994957\pi\)
0.486218 0.873838i \(-0.338376\pi\)
\(600\) 0 0
\(601\) 821.399i 1.36672i 0.730081 + 0.683360i \(0.239482\pi\)
−0.730081 + 0.683360i \(0.760518\pi\)
\(602\) −307.675 385.668i −0.511088 0.640644i
\(603\) 294.494i 0.488381i
\(604\) −75.0299 + 129.956i −0.124222 + 0.215158i
\(605\) 0 0
\(606\) 62.0374 + 107.452i 0.102372 + 0.177313i
\(607\) 502.282 869.979i 0.827483 1.43324i −0.0725231 0.997367i \(-0.523105\pi\)
0.900006 0.435876i \(-0.143562\pi\)
\(608\) −177.767 −0.292380
\(609\) 27.6135 4.16720i 0.0453423 0.00684270i
\(610\) 0 0
\(611\) 301.444 522.116i 0.493361 0.854527i
\(612\) −82.8198 143.448i −0.135326 0.234392i
\(613\) −964.532 + 556.873i −1.57346 + 0.908438i −0.577721 + 0.816234i \(0.696058\pi\)
−0.995740 + 0.0922038i \(0.970609\pi\)
\(614\) −622.264 359.265i −1.01346 0.585121i
\(615\) 0 0
\(616\) −34.2267 226.799i −0.0555628 0.368180i
\(617\) 463.256i 0.750820i −0.926859 0.375410i \(-0.877502\pi\)
0.926859 0.375410i \(-0.122498\pi\)
\(618\) −419.946 242.456i −0.679525 0.392324i
\(619\) −486.109 + 280.655i −0.785314 + 0.453401i −0.838310 0.545193i \(-0.816456\pi\)
0.0529963 + 0.998595i \(0.483123\pi\)
\(620\) 0 0
\(621\) 81.7163 + 47.1790i 0.131588 + 0.0759725i
\(622\) −147.532 −0.237190
\(623\) −60.5464 + 48.3021i −0.0971852 + 0.0775315i
\(624\) 54.4814 0.0873100
\(625\) 0 0
\(626\) −325.621 + 187.997i −0.520161 + 0.300315i
\(627\) 546.079 315.279i 0.870939 0.502837i
\(628\) 224.731 389.245i 0.357851 0.619816i
\(629\) 54.8346i 0.0871774i
\(630\) 0 0
\(631\) 244.533 0.387533 0.193767 0.981048i \(-0.437930\pi\)
0.193767 + 0.981048i \(0.437930\pi\)
\(632\) −221.504 127.885i −0.350480 0.202350i
\(633\) 336.809 + 583.371i 0.532084 + 0.921597i
\(634\) −7.58178 13.1320i −0.0119587 0.0207130i
\(635\) 0 0
\(636\) 197.784i 0.310982i
\(637\) −282.556 261.983i −0.443574 0.411276i
\(638\) 37.7360i 0.0591473i
\(639\) 51.3896 89.0094i 0.0804219 0.139295i
\(640\) 0 0
\(641\) −325.885 564.449i −0.508400 0.880575i −0.999953 0.00972698i \(-0.996904\pi\)
0.491553 0.870848i \(-0.336430\pi\)
\(642\) 181.184 313.819i 0.282217 0.488815i
\(643\) −76.4894 −0.118957 −0.0594786 0.998230i \(-0.518944\pi\)
−0.0594786 + 0.998230i \(0.518944\pi\)
\(644\) −236.672 92.8371i −0.367503 0.144157i
\(645\) 0 0
\(646\) −613.442 + 1062.51i −0.949601 + 1.64476i
\(647\) 81.9453 + 141.933i 0.126654 + 0.219372i 0.922378 0.386288i \(-0.126243\pi\)
−0.795724 + 0.605659i \(0.792909\pi\)
\(648\) −22.0454 + 12.7279i −0.0340207 + 0.0196419i
\(649\) −705.797 407.492i −1.08752 0.627877i
\(650\) 0 0
\(651\) −49.8895 + 39.8004i −0.0766352 + 0.0611374i
\(652\) 460.235i 0.705882i
\(653\) −965.499 557.431i −1.47856 0.853647i −0.478854 0.877895i \(-0.658948\pi\)
−0.999706 + 0.0242480i \(0.992281\pi\)
\(654\) 115.234 66.5305i 0.176199 0.101729i
\(655\) 0 0
\(656\) −76.8703 44.3811i −0.117180 0.0676541i
\(657\) 58.4744 0.0890021
\(658\) −113.254 750.467i −0.172119 1.14053i
\(659\) −1164.66 −1.76732 −0.883660 0.468130i \(-0.844928\pi\)
−0.883660 + 0.468130i \(0.844928\pi\)
\(660\) 0 0
\(661\) 542.087 312.974i 0.820101 0.473485i −0.0303505 0.999539i \(-0.509662\pi\)
0.850451 + 0.526054i \(0.176329\pi\)
\(662\) −432.238 + 249.553i −0.652928 + 0.376968i
\(663\) 188.006 325.636i 0.283568 0.491155i
\(664\) 378.453i 0.569960i
\(665\) 0 0
\(666\) −8.42709 −0.0126533
\(667\) 36.2226 + 20.9131i 0.0543067 + 0.0313540i
\(668\) 277.788 + 481.144i 0.415851 + 0.720275i
\(669\) −218.163 377.869i −0.326103 0.564827i
\(670\) 0 0
\(671\) 783.342i 1.16743i
\(672\) 53.6147 42.7723i 0.0797838 0.0636492i
\(673\) 38.0207i 0.0564943i 0.999601 + 0.0282471i \(0.00899254\pi\)
−0.999601 + 0.0282471i \(0.991007\pi\)
\(674\) 156.011 270.220i 0.231471 0.400920i
\(675\) 0 0
\(676\) −107.162 185.610i −0.158524 0.274571i
\(677\) −390.857 + 676.984i −0.577336 + 0.999976i 0.418447 + 0.908241i \(0.362574\pi\)
−0.995783 + 0.0917347i \(0.970759\pi\)
\(678\) 117.057 0.172651
\(679\) 184.842 471.222i 0.272227 0.693994i
\(680\) 0 0
\(681\) 231.941 401.733i 0.340588 0.589916i
\(682\) −43.1195 74.6852i −0.0632251 0.109509i
\(683\) 116.427 67.2190i 0.170464 0.0984172i −0.412341 0.911030i \(-0.635289\pi\)
0.582804 + 0.812612i \(0.301955\pi\)
\(684\) 163.289 + 94.2751i 0.238727 + 0.137829i
\(685\) 0 0
\(686\) −483.739 35.9855i −0.705158 0.0524570i
\(687\) 598.474i 0.871142i
\(688\) 172.640 + 99.6736i 0.250930 + 0.144874i
\(689\) −388.830 + 224.491i −0.564340 + 0.325822i
\(690\) 0 0
\(691\) −393.253 227.045i −0.569107 0.328574i 0.187686 0.982229i \(-0.439901\pi\)
−0.756792 + 0.653655i \(0.773235\pi\)
\(692\) 252.131 0.364351
\(693\) −88.8392 + 226.480i −0.128195 + 0.326811i
\(694\) 362.051 0.521687
\(695\) 0 0
\(696\) −9.77211 + 5.64193i −0.0140404 + 0.00810622i
\(697\) −530.532 + 306.303i −0.761165 + 0.439459i
\(698\) 287.969 498.778i 0.412564 0.714581i
\(699\) 498.942i 0.713794i
\(700\) 0 0
\(701\) 982.015 1.40088 0.700439 0.713713i \(-0.252988\pi\)
0.700439 + 0.713713i \(0.252988\pi\)
\(702\) −50.0444 28.8931i −0.0712883 0.0411583i
\(703\) 31.2095 + 54.0565i 0.0443948 + 0.0768940i
\(704\) 46.3392 + 80.2618i 0.0658227 + 0.114008i
\(705\) 0 0
\(706\) 824.822i 1.16830i
\(707\) 52.9102 + 350.603i 0.0748376 + 0.495903i
\(708\) 243.698i 0.344206i
\(709\) −166.536 + 288.449i −0.234889 + 0.406839i −0.959240 0.282591i \(-0.908806\pi\)
0.724352 + 0.689431i \(0.242139\pi\)
\(710\) 0 0
\(711\) 135.643 + 234.940i 0.190777 + 0.330436i
\(712\) 15.6479 27.1029i 0.0219773 0.0380658i
\(713\) −95.5866 −0.134063
\(714\) −70.6351 468.055i −0.0989287 0.655539i
\(715\) 0 0
\(716\) −77.1069 + 133.553i −0.107691 + 0.186527i
\(717\) −163.514 283.215i −0.228053 0.395000i
\(718\) −846.946 + 488.984i −1.17959 + 0.681037i
\(719\) −1055.73 609.523i −1.46832 0.847737i −0.468954 0.883223i \(-0.655369\pi\)
−0.999370 + 0.0354852i \(0.988702\pi\)
\(720\) 0 0
\(721\) −864.200 1083.27i −1.19861 1.50245i
\(722\) 886.051i 1.22722i
\(723\) −146.772 84.7389i −0.203004 0.117205i
\(724\) 367.215 212.012i 0.507203 0.292834i
\(725\) 0 0
\(726\) −28.0172 16.1758i −0.0385912 0.0222807i
\(727\) −215.108 −0.295885 −0.147942 0.988996i \(-0.547265\pi\)
−0.147942 + 0.988996i \(0.547265\pi\)
\(728\) 144.941 + 56.8549i 0.199095 + 0.0780974i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1191.50 687.913i 1.62996 0.941057i
\(732\) −202.854 + 117.118i −0.277124 + 0.159997i
\(733\) −374.728 + 649.047i −0.511225 + 0.885467i 0.488691 + 0.872457i \(0.337475\pi\)
−0.999915 + 0.0130099i \(0.995859\pi\)
\(734\) 324.883i 0.442620i
\(735\) 0 0
\(736\) 102.724 0.139570
\(737\) −984.859 568.609i −1.33631 0.771518i
\(738\) 47.0732 + 81.5332i 0.0637849 + 0.110479i
\(739\) −467.102 809.045i −0.632073 1.09478i −0.987127 0.159937i \(-0.948871\pi\)
0.355054 0.934846i \(-0.384462\pi\)
\(740\) 0 0
\(741\) 428.020i 0.577625i
\(742\) −206.401 + 526.182i −0.278168 + 0.709140i
\(743\) 1232.47i 1.65878i −0.558671 0.829389i \(-0.688689\pi\)
0.558671 0.829389i \(-0.311311\pi\)
\(744\) 12.8937 22.3325i 0.0173302 0.0300168i
\(745\) 0 0
\(746\) 286.101 + 495.542i 0.383514 + 0.664266i
\(747\) 200.705 347.632i 0.268682 0.465370i
\(748\) 639.634 0.855125
\(749\) 809.508 645.803i 1.08079 0.862220i
\(750\) 0 0
\(751\) −393.353 + 681.307i −0.523772 + 0.907200i 0.475845 + 0.879529i \(0.342142\pi\)
−0.999617 + 0.0276709i \(0.991191\pi\)
\(752\) 153.334 + 265.582i 0.203902 + 0.353168i
\(753\) −362.017 + 209.011i −0.480767 + 0.277571i
\(754\) −22.1833 12.8075i −0.0294208 0.0169861i
\(755\) 0 0
\(756\) −71.9316 + 10.8553i −0.0951477 + 0.0143589i
\(757\) 1303.18i 1.72151i 0.509023 + 0.860753i \(0.330007\pi\)
−0.509023 + 0.860753i \(0.669993\pi\)
\(758\) 325.618 + 187.995i 0.429575 + 0.248015i
\(759\) −315.556 + 182.186i −0.415752 + 0.240034i
\(760\) 0 0
\(761\) 601.784 + 347.440i 0.790780 + 0.456557i 0.840237 0.542219i \(-0.182416\pi\)
−0.0494571 + 0.998776i \(0.515749\pi\)
\(762\) 249.783 0.327799
\(763\) 375.996 56.7423i 0.492786 0.0743674i
\(764\) −331.392 −0.433759
\(765\) 0 0
\(766\) −375.266 + 216.660i −0.489904 + 0.282846i
\(767\) 479.093 276.604i 0.624632 0.360631i
\(768\) −13.8564 + 24.0000i −0.0180422 + 0.0312500i
\(769\) 263.988i 0.343287i −0.985159 0.171644i \(-0.945092\pi\)
0.985159 0.171644i \(-0.0549077\pi\)
\(770\) 0 0
\(771\) −21.7614 −0.0282249
\(772\) 182.384 + 105.299i 0.236249 + 0.136398i
\(773\) 78.6802 + 136.278i 0.101786 + 0.176298i 0.912420 0.409254i \(-0.134211\pi\)
−0.810635 + 0.585552i \(0.800878\pi\)
\(774\) −105.720 183.112i −0.136589 0.236579i
\(775\) 0 0
\(776\) 204.527i 0.263566i
\(777\) −22.4193 8.79422i −0.0288537 0.0113182i
\(778\) 150.408i 0.193326i
\(779\) 348.669 603.913i 0.447586 0.775241i
\(780\) 0 0
\(781\) 198.446 + 343.718i 0.254092 + 0.440100i
\(782\) 354.482 613.981i 0.453302 0.785142i
\(783\) 11.9683 0.0152852
\(784\) 187.271 57.8402i 0.238866 0.0737758i
\(785\) 0 0
\(786\) 91.3635 158.246i 0.116239 0.201331i
\(787\) 491.129 + 850.660i 0.624052 + 1.08089i 0.988723 + 0.149754i \(0.0478480\pi\)
−0.364671 + 0.931136i \(0.618819\pi\)
\(788\) −423.894 + 244.736i −0.537937 + 0.310578i
\(789\) −318.721 184.014i −0.403956 0.233224i
\(790\) 0 0
\(791\) 311.417 + 122.157i 0.393700 + 0.154433i
\(792\) 98.3002i 0.124116i
\(793\) −460.492 265.865i −0.580695 0.335265i
\(794\) −266.782 + 154.027i −0.335998 + 0.193988i
\(795\) 0 0
\(796\) −169.683 97.9667i −0.213170 0.123074i
\(797\) 946.927 1.18811 0.594057 0.804423i \(-0.297525\pi\)
0.594057 + 0.804423i \(0.297525\pi\)
\(798\) 336.030 + 421.211i 0.421090 + 0.527833i
\(799\) 2116.52 2.64896
\(800\) 0 0
\(801\) −28.7470 + 16.5971i −0.0358888 + 0.0207204i
\(802\) 75.9114 43.8275i 0.0946526 0.0546477i
\(803\) −112.902 + 195.553i −0.140601 + 0.243527i
\(804\) 340.052i 0.422951i
\(805\) 0 0
\(806\) 58.5388 0.0726287
\(807\) −501.895 289.769i −0.621927 0.359070i
\(808\) −71.6346 124.075i −0.0886567 0.153558i
\(809\) 214.568 + 371.642i 0.265226 + 0.459385i 0.967623 0.252401i \(-0.0812201\pi\)
−0.702397 + 0.711786i \(0.747887\pi\)
\(810\) 0 0
\(811\) 948.404i 1.16943i −0.811241 0.584713i \(-0.801207\pi\)
0.811241 0.584713i \(-0.198793\pi\)
\(812\) −31.8853 + 4.81187i −0.0392676 + 0.00592595i
\(813\) 315.840i 0.388487i
\(814\) 16.2710 28.1822i 0.0199890 0.0346219i
\(815\) 0 0
\(816\) 95.6321 + 165.640i 0.117196 + 0.202990i
\(817\) −783.062 + 1356.30i −0.958460 + 1.66010i
\(818\) −614.278 −0.750952
\(819\) −102.985 129.091i −0.125745 0.157621i
\(820\) 0 0
\(821\) 201.884 349.673i 0.245900 0.425911i −0.716484 0.697603i \(-0.754250\pi\)
0.962384 + 0.271692i \(0.0875832\pi\)
\(822\) −302.388 523.752i −0.367869 0.637168i
\(823\) −750.003 + 433.014i −0.911303 + 0.526141i −0.880850 0.473395i \(-0.843028\pi\)
−0.0304530 + 0.999536i \(0.509695\pi\)
\(824\) 484.912 + 279.964i 0.588486 + 0.339762i
\(825\) 0 0
\(826\) 254.314 648.330i 0.307887 0.784903i
\(827\) 363.528i 0.439574i −0.975548 0.219787i \(-0.929464\pi\)
0.975548 0.219787i \(-0.0705363\pi\)
\(828\) −94.3579 54.4776i −0.113959 0.0657942i
\(829\) −208.617 + 120.445i −0.251649 + 0.145290i −0.620519 0.784191i \(-0.713078\pi\)
0.368870 + 0.929481i \(0.379745\pi\)
\(830\) 0 0
\(831\) −250.142 144.420i −0.301013 0.173790i
\(832\) −62.9097 −0.0756126
\(833\) 300.529 1318.92i 0.360779 1.58333i
\(834\) 381.917 0.457934
\(835\) 0 0
\(836\) −630.557 + 364.052i −0.754255 + 0.435469i
\(837\) −23.6872 + 13.6758i −0.0283001 + 0.0163391i
\(838\) −323.304 + 559.979i −0.385804 + 0.668232i
\(839\) 214.638i 0.255826i 0.991785 + 0.127913i \(0.0408278\pi\)
−0.991785 + 0.127913i \(0.959172\pi\)
\(840\) 0 0
\(841\) −835.695 −0.993692
\(842\) 799.941 + 461.846i 0.950049 + 0.548511i
\(843\) −33.1762 57.4628i −0.0393549 0.0681647i
\(844\) −388.914 673.618i −0.460798 0.798126i
\(845\) 0 0
\(846\) 325.271i 0.384481i
\(847\) −57.6561 72.2715i −0.0680710 0.0853264i
\(848\) 228.382i 0.269318i
\(849\) 333.849 578.244i 0.393226 0.681088i
\(850\) 0 0
\(851\) −18.0347 31.2369i −0.0211923 0.0367062i
\(852\) −59.3396 + 102.779i −0.0696474 + 0.120633i
\(853\) −1388.39 −1.62765 −0.813825 0.581110i \(-0.802618\pi\)
−0.813825 + 0.581110i \(0.802618\pi\)
\(854\) −661.891 + 99.8873i −0.775048 + 0.116964i
\(855\) 0 0
\(856\) −209.213 + 362.367i −0.244407 + 0.423326i
\(857\) 548.489 + 950.012i 0.640011 + 1.10853i 0.985430 + 0.170083i \(0.0544036\pi\)
−0.345419 + 0.938449i \(0.612263\pi\)
\(858\) 193.251 111.574i 0.225235 0.130039i
\(859\) 234.305 + 135.276i 0.272764 + 0.157481i 0.630143 0.776479i \(-0.282996\pi\)
−0.357379 + 0.933959i \(0.616330\pi\)
\(860\) 0 0
\(861\) 40.1477 + 266.034i 0.0466291 + 0.308982i
\(862\) 665.042i 0.771511i
\(863\) 232.280 + 134.107i 0.269154 + 0.155396i 0.628503 0.777807i \(-0.283668\pi\)
−0.359349 + 0.933203i \(0.617001\pi\)
\(864\) 25.4558 14.6969i 0.0294628 0.0170103i
\(865\) 0 0
\(866\) −39.2284 22.6485i −0.0452984 0.0261530i
\(867\) 819.476 0.945186
\(868\) 57.6075 45.9576i 0.0663681 0.0529465i
\(869\) −1047.60 −1.20552
\(870\) 0 0
\(871\) 668.519 385.970i 0.767530 0.443134i
\(872\) −133.061 + 76.8228i −0.152593 + 0.0880995i
\(873\) 108.467 187.870i 0.124246 0.215200i
\(874\) 807.025i 0.923370i
\(875\) 0 0
\(876\) −67.5204 −0.0770781
\(877\) −439.430 253.705i −0.501061 0.289288i 0.228091 0.973640i \(-0.426752\pi\)
−0.729152 + 0.684352i \(0.760085\pi\)
\(878\) 270.284 + 468.145i 0.307840 + 0.533195i
\(879\) −78.7948 136.477i −0.0896414 0.155264i
\(880\) 0 0
\(881\) 833.545i 0.946135i 0.881026 + 0.473067i \(0.156853\pi\)
−0.881026 + 0.473067i \(0.843147\pi\)
\(882\) −202.694 46.1859i −0.229812 0.0523650i
\(883\) 1350.99i 1.53000i 0.644028 + 0.765002i \(0.277262\pi\)
−0.644028 + 0.765002i \(0.722738\pi\)
\(884\) −217.090 + 376.012i −0.245577 + 0.425353i
\(885\) 0 0
\(886\) −87.4985 151.552i −0.0987568 0.171052i
\(887\) −187.065 + 324.005i −0.210896 + 0.365282i −0.951995 0.306113i \(-0.900971\pi\)
0.741099 + 0.671395i \(0.234305\pi\)
\(888\) 9.73077 0.0109581
\(889\) 664.518 + 260.664i 0.747489 + 0.293211i
\(890\) 0 0
\(891\) −52.1316 + 90.2945i −0.0585091 + 0.101341i
\(892\) 251.913 + 436.326i 0.282413 + 0.489154i
\(893\) −2086.48 + 1204.63i −2.33649 + 1.34897i
\(894\) 345.967 + 199.744i 0.386988 + 0.223427i
\(895\) 0 0
\(896\) −61.9089 + 49.3891i −0.0690948 + 0.0551218i
\(897\) 247.335i 0.275735i
\(898\) −326.989 188.787i −0.364130 0.210230i
\(899\) −10.4999 + 6.06210i −0.0116795 + 0.00674316i
\(900\) 0 0
\(901\) −1365.04 788.105i −1.51503 0.874701i
\(902\) −363.556 −0.403055
\(903\) −90.1660 597.474i −0.0998516 0.661655i
\(904\) −135.166 −0.149520
\(905\) 0 0
\(906\) −159.162 + 91.8925i −0.175676 + 0.101427i
\(907\) −309.618 + 178.758i −0.341365 + 0.197087i −0.660875 0.750496i \(-0.729815\pi\)
0.319510 + 0.947583i \(0.396482\pi\)
\(908\) −267.822 + 463.881i −0.294958 + 0.510882i
\(909\) 151.960i 0.167173i
\(910\) 0 0
\(911\) −1503.55 −1.65044 −0.825219 0.564813i \(-0.808948\pi\)
−0.825219 + 0.564813i \(0.808948\pi\)
\(912\) −188.550 108.859i −0.206744 0.119363i
\(913\) 775.043 + 1342.41i 0.848897 + 1.47033i
\(914\) −317.731 550.327i −0.347627 0.602108i
\(915\) 0 0
\(916\) 691.059i 0.754431i
\(917\) 408.202 325.652i 0.445149 0.355127i
\(918\) 202.866i 0.220987i
\(919\) −312.499 + 541.265i −0.340043 + 0.588971i −0.984440 0.175719i \(-0.943775\pi\)
0.644398 + 0.764691i \(0.277108\pi\)
\(920\) 0 0
\(921\) −440.007 762.115i −0.477750 0.827487i
\(922\) −74.6199 + 129.245i −0.0809327 + 0.140179i
\(923\) −269.409 −0.291884
\(924\) 102.583 261.516i 0.111020 0.283026i
\(925\) 0 0
\(926\) −416.171 + 720.829i −0.449429 + 0.778433i
\(927\) −296.947 514.327i −0.320331 0.554830i
\(928\) 11.2839 6.51474i 0.0121593 0.00702019i
\(929\) 942.883 + 544.374i 1.01494 + 0.585978i 0.912636 0.408774i \(-0.134044\pi\)
0.102309 + 0.994753i \(0.467377\pi\)
\(930\) 0 0
\(931\) 454.408 + 1471.25i 0.488086 + 1.58029i
\(932\) 576.129i 0.618164i
\(933\) −156.482 90.3447i −0.167719 0.0968325i
\(934\) 447.837 258.559i 0.479483 0.276829i
\(935\) 0 0
\(936\) 57.7863 + 33.3629i 0.0617375 + 0.0356441i
\(937\) −252.836 −0.269835 −0.134918 0.990857i \(-0.543077\pi\)
−0.134918 + 0.990857i \(0.543077\pi\)
\(938\) 354.867 904.670i 0.378323 0.964467i
\(939\) −460.498 −0.490413
\(940\) 0 0
\(941\) −332.262 + 191.832i −0.353095 + 0.203859i −0.666048 0.745909i \(-0.732015\pi\)
0.312953 + 0.949769i \(0.398682\pi\)
\(942\) 476.726 275.238i 0.506078 0.292184i
\(943\) −201.481 + 348.975i −0.213660 + 0.370069i
\(944\) 281.398i 0.298091i
\(945\) 0 0
\(946\) 816.495 0.863103
\(947\) 244.032 + 140.892i 0.257690 + 0.148777i 0.623280 0.781999i \(-0.285800\pi\)
−0.365591 + 0.930776i \(0.619133\pi\)
\(948\) −156.627 271.285i −0.165218 0.286166i
\(949\) −76.6377 132.740i −0.0807562 0.139874i
\(950\) 0 0
\(951\) 18.5715i 0.0195284i
\(952\) 81.5624 + 540.463i 0.0856748 + 0.567713i
\(953\) 332.322i 0.348711i 0.984683 + 0.174356i \(0.0557842\pi\)
−0.984683 + 0.174356i \(0.944216\pi\)
\(954\) −121.118 + 209.782i −0.126958 + 0.219897i
\(955\) 0 0
\(956\) 188.810 + 327.028i 0.197500 + 0.342080i
\(957\) −23.1085 + 40.0250i −0.0241468 + 0.0418234i
\(958\) −688.971 −0.719177
\(959\) −257.900 1708.94i −0.268926 1.78200i
\(960\) 0 0
\(961\) −466.646 + 808.255i −0.485584 + 0.841056i
\(962\) 11.0447 + 19.1300i 0.0114810 + 0.0198857i
\(963\) 384.348 221.904i 0.399116 0.230430i
\(964\) 169.478 + 97.8480i 0.175807 + 0.101502i
\(965\) 0 0
\(966\) −194.177 243.400i −0.201012 0.251967i
\(967\) 1155.53i 1.19496i 0.801882 + 0.597482i \(0.203832\pi\)
−0.801882 + 0.597482i \(0.796168\pi\)
\(968\) 32.3515 + 18.6782i 0.0334210 + 0.0192956i
\(969\) −1301.31 + 751.310i −1.34294 + 0.775346i
\(970\) 0 0
\(971\) −1307.94 755.140i −1.34700 0.777693i −0.359179 0.933269i \(-0.616943\pi\)
−0.987824 + 0.155576i \(0.950277\pi\)
\(972\) −31.1769 −0.0320750
\(973\) 1016.04 + 398.555i 1.04424 + 0.409614i
\(974\) 276.866 0.284257
\(975\) 0 0
\(976\) 234.236 135.236i 0.239996 0.138562i
\(977\) 694.220 400.808i 0.710563 0.410244i −0.100706 0.994916i \(-0.532110\pi\)
0.811269 + 0.584672i \(0.198777\pi\)
\(978\) 281.835 488.153i 0.288175 0.499134i
\(979\) 128.182i 0.130932i
\(980\) 0 0
\(981\) 162.966 0.166122
\(982\) 427.707 + 246.937i 0.435547 + 0.251463i
\(983\) 547.395 + 948.116i 0.556862 + 0.964513i 0.997756 + 0.0669540i \(0.0213281\pi\)
−0.440894 + 0.897559i \(0.645339\pi\)
\(984\) −54.3555 94.1465i −0.0552393 0.0956773i
\(985\) 0 0
\(986\) 89.9249i 0.0912018i
\(987\) 339.441 865.344i 0.343912 0.876742i
\(988\) 494.235i 0.500238i
\(989\) 452.498 783.750i 0.457531 0.792467i
\(990\) 0 0
\(991\) −21.9962 38.0986i −0.0221960 0.0384446i 0.854714 0.519099i \(-0.173732\pi\)
−0.876910 + 0.480655i \(0.840399\pi\)
\(992\) −14.8883 + 25.7873i −0.0150084 + 0.0259953i
\(993\) −611.277 −0.615586
\(994\) −265.123 + 211.507i −0.266723 + 0.212784i
\(995\) 0 0
\(996\) −231.754 + 401.410i −0.232685 + 0.403022i
\(997\) 6.12803 + 10.6141i 0.00614647 + 0.0106460i 0.869082 0.494668i \(-0.164710\pi\)
−0.862936 + 0.505314i \(0.831377\pi\)
\(998\) 410.827 237.191i 0.411650 0.237666i
\(999\) −8.93828 5.16052i −0.00894723 0.00516569i
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.q.c.649.2 16
5.2 odd 4 1050.3.p.b.901.3 8
5.3 odd 4 210.3.o.a.61.2 yes 8
5.4 even 2 inner 1050.3.q.c.649.7 16
7.3 odd 6 inner 1050.3.q.c.199.7 16
15.8 even 4 630.3.v.b.271.3 8
35.3 even 12 210.3.o.a.31.2 8
35.17 even 12 1050.3.p.b.451.3 8
35.23 odd 12 1470.3.f.a.391.7 8
35.24 odd 6 inner 1050.3.q.c.199.2 16
35.33 even 12 1470.3.f.a.391.6 8
105.38 odd 12 630.3.v.b.451.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.o.a.31.2 8 35.3 even 12
210.3.o.a.61.2 yes 8 5.3 odd 4
630.3.v.b.271.3 8 15.8 even 4
630.3.v.b.451.3 8 105.38 odd 12
1050.3.p.b.451.3 8 35.17 even 12
1050.3.p.b.901.3 8 5.2 odd 4
1050.3.q.c.199.2 16 35.24 odd 6 inner
1050.3.q.c.199.7 16 7.3 odd 6 inner
1050.3.q.c.649.2 16 1.1 even 1 trivial
1050.3.q.c.649.7 16 5.4 even 2 inner
1470.3.f.a.391.6 8 35.33 even 12
1470.3.f.a.391.7 8 35.23 odd 12