Properties

Label 575.2.k.a.351.1
Level $575$
Weight $2$
Character 575.351
Analytic conductor $4.591$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [575,2,Mod(26,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.k (of order \(11\), degree \(10\), 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: \(4.59139811622\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 351.1
Root \(0.959493 - 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 575.351
Dual form 575.2.k.a.326.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.925839 + 2.02730i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.94306 - 2.24241i) q^{4} +(1.45949 - 1.68434i) q^{6} +(0.0125459 - 0.0872586i) q^{7} +(2.06815 - 0.607265i) q^{8} +(-1.68251 - 1.08128i) q^{9} +(1.01365 + 2.21959i) q^{11} +(1.23259 + 2.69900i) q^{12} +(-0.512546 - 3.56484i) q^{13} +(0.165284 + 0.106222i) q^{14} +(0.160869 - 1.11887i) q^{16} +(2.21537 - 2.55667i) q^{17} +(3.74982 - 2.40986i) q^{18} +(1.87358 + 2.16222i) q^{19} +(-0.0366213 + 0.0801894i) q^{21} -5.43826 q^{22} +(4.28287 + 2.15802i) q^{23} -2.15546 q^{24} +(7.70154 + 2.26138i) q^{26} +(3.27430 + 3.77875i) q^{27} +(-0.220047 + 0.141416i) q^{28} +(4.87604 - 5.62725i) q^{29} +(1.65370 - 0.485571i) q^{31} +(5.74593 + 3.69269i) q^{32} +(-0.347262 - 2.41526i) q^{33} +(3.13208 + 6.85830i) q^{34} +(0.844535 + 5.87387i) q^{36} +(-0.595421 - 0.382654i) q^{37} +(-6.11811 + 1.79644i) q^{38} +(-0.512546 + 3.56484i) q^{39} +(-4.66991 + 3.00117i) q^{41} +(-0.128663 - 0.148485i) q^{42} +(-2.30014 - 0.675383i) q^{43} +(3.00764 - 6.58582i) q^{44} +(-8.34021 + 6.68469i) q^{46} +11.6146 q^{47} +(-0.469574 + 1.02822i) q^{48} +(6.70899 + 1.96994i) q^{49} +(-2.84593 + 1.82897i) q^{51} +(-6.99792 + 8.07603i) q^{52} +(-1.47653 + 10.2695i) q^{53} +(-10.6921 + 3.13950i) q^{54} +(-0.0270422 - 0.188083i) q^{56} +(-1.18852 - 2.60249i) q^{57} +(6.89372 + 15.0951i) q^{58} +(-1.64421 - 11.4357i) q^{59} +(-3.89722 + 1.14433i) q^{61} +(-0.546662 + 3.80211i) q^{62} +(-0.115460 + 0.133248i) q^{63} +(-10.9041 + 7.00766i) q^{64} +(5.21797 + 1.53213i) q^{66} +(5.07177 - 11.1056i) q^{67} -10.0377 q^{68} +(-3.50140 - 3.27723i) q^{69} +(0.787956 - 1.72538i) q^{71} +(-4.13631 - 1.21453i) q^{72} +(-3.61246 - 4.16900i) q^{73} +(1.32702 - 0.852823i) q^{74} +(1.20812 - 8.40266i) q^{76} +(0.206395 - 0.0606031i) q^{77} +(-6.75247 - 4.33955i) q^{78} +(-0.997420 - 6.93721i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-1.76070 - 12.2459i) q^{82} +(-3.51021 - 2.25587i) q^{83} +(0.250975 - 0.0736930i) q^{84} +(3.49877 - 4.03779i) q^{86} +(-6.26391 + 4.02557i) q^{87} +(3.44426 + 3.97489i) q^{88} +(15.3009 + 4.49275i) q^{89} -0.317493 q^{91} +(-3.48270 - 13.7971i) q^{92} -1.72352 q^{93} +(-10.7532 + 23.5463i) q^{94} +(-4.47283 - 5.16192i) q^{96} +(-12.0969 + 7.77424i) q^{97} +(-10.2051 + 11.7773i) q^{98} +(0.694523 - 4.83052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.925839 + 2.02730i −0.654667 + 1.43352i 0.232743 + 0.972538i \(0.425230\pi\)
−0.887410 + 0.460982i \(0.847497\pi\)
\(3\) −0.959493 0.281733i −0.553964 0.162658i −0.00724338 0.999974i \(-0.502306\pi\)
−0.546720 + 0.837315i \(0.684124\pi\)
\(4\) −1.94306 2.24241i −0.971531 1.12121i
\(5\) 0 0
\(6\) 1.45949 1.68434i 0.595836 0.687631i
\(7\) 0.0125459 0.0872586i 0.00474190 0.0329807i −0.987313 0.158785i \(-0.949242\pi\)
0.992055 + 0.125805i \(0.0401513\pi\)
\(8\) 2.06815 0.607265i 0.731203 0.214700i
\(9\) −1.68251 1.08128i −0.560836 0.360427i
\(10\) 0 0
\(11\) 1.01365 + 2.21959i 0.305628 + 0.669231i 0.998664 0.0516714i \(-0.0164549\pi\)
−0.693037 + 0.720902i \(0.743728\pi\)
\(12\) 1.23259 + 2.69900i 0.355819 + 0.779135i
\(13\) −0.512546 3.56484i −0.142155 0.988707i −0.928609 0.371059i \(-0.878995\pi\)
0.786455 0.617648i \(-0.211914\pi\)
\(14\) 0.165284 + 0.106222i 0.0441741 + 0.0283890i
\(15\) 0 0
\(16\) 0.160869 1.11887i 0.0402172 0.279717i
\(17\) 2.21537 2.55667i 0.537306 0.620084i −0.420572 0.907259i \(-0.638171\pi\)
0.957878 + 0.287175i \(0.0927160\pi\)
\(18\) 3.74982 2.40986i 0.883840 0.568010i
\(19\) 1.87358 + 2.16222i 0.429828 + 0.496048i 0.928806 0.370567i \(-0.120837\pi\)
−0.498978 + 0.866615i \(0.666291\pi\)
\(20\) 0 0
\(21\) −0.0366213 + 0.0801894i −0.00799142 + 0.0174988i
\(22\) −5.43826 −1.15944
\(23\) 4.28287 + 2.15802i 0.893039 + 0.449979i
\(24\) −2.15546 −0.439982
\(25\) 0 0
\(26\) 7.70154 + 2.26138i 1.51040 + 0.443492i
\(27\) 3.27430 + 3.77875i 0.630140 + 0.727220i
\(28\) −0.220047 + 0.141416i −0.0415850 + 0.0267251i
\(29\) 4.87604 5.62725i 0.905458 1.04495i −0.0933249 0.995636i \(-0.529750\pi\)
0.998783 0.0493188i \(-0.0157050\pi\)
\(30\) 0 0
\(31\) 1.65370 0.485571i 0.297014 0.0872110i −0.129831 0.991536i \(-0.541443\pi\)
0.426844 + 0.904325i \(0.359625\pi\)
\(32\) 5.74593 + 3.69269i 1.01575 + 0.652781i
\(33\) −0.347262 2.41526i −0.0604505 0.420442i
\(34\) 3.13208 + 6.85830i 0.537147 + 1.17619i
\(35\) 0 0
\(36\) 0.844535 + 5.87387i 0.140756 + 0.978979i
\(37\) −0.595421 0.382654i −0.0978866 0.0629079i 0.490782 0.871283i \(-0.336711\pi\)
−0.588668 + 0.808375i \(0.700348\pi\)
\(38\) −6.11811 + 1.79644i −0.992489 + 0.291421i
\(39\) −0.512546 + 3.56484i −0.0820730 + 0.570830i
\(40\) 0 0
\(41\) −4.66991 + 3.00117i −0.729317 + 0.468704i −0.851867 0.523759i \(-0.824529\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(42\) −0.128663 0.148485i −0.0198531 0.0229117i
\(43\) −2.30014 0.675383i −0.350768 0.102995i 0.101602 0.994825i \(-0.467603\pi\)
−0.452370 + 0.891830i \(0.649421\pi\)
\(44\) 3.00764 6.58582i 0.453419 0.992850i
\(45\) 0 0
\(46\) −8.34021 + 6.68469i −1.22970 + 0.985604i
\(47\) 11.6146 1.69416 0.847079 0.531466i \(-0.178359\pi\)
0.847079 + 0.531466i \(0.178359\pi\)
\(48\) −0.469574 + 1.02822i −0.0677772 + 0.148411i
\(49\) 6.70899 + 1.96994i 0.958428 + 0.281420i
\(50\) 0 0
\(51\) −2.84593 + 1.82897i −0.398510 + 0.256107i
\(52\) −6.99792 + 8.07603i −0.970437 + 1.11994i
\(53\) −1.47653 + 10.2695i −0.202817 + 1.41062i 0.593058 + 0.805160i \(0.297921\pi\)
−0.795874 + 0.605462i \(0.792988\pi\)
\(54\) −10.6921 + 3.13950i −1.45502 + 0.427231i
\(55\) 0 0
\(56\) −0.0270422 0.188083i −0.00361367 0.0251336i
\(57\) −1.18852 2.60249i −0.157423 0.344708i
\(58\) 6.89372 + 15.0951i 0.905190 + 1.98209i
\(59\) −1.64421 11.4357i −0.214058 1.48881i −0.759417 0.650604i \(-0.774516\pi\)
0.545359 0.838203i \(-0.316393\pi\)
\(60\) 0 0
\(61\) −3.89722 + 1.14433i −0.498988 + 0.146516i −0.521535 0.853230i \(-0.674641\pi\)
0.0225474 + 0.999746i \(0.492822\pi\)
\(62\) −0.546662 + 3.80211i −0.0694261 + 0.482869i
\(63\) −0.115460 + 0.133248i −0.0145466 + 0.0167876i
\(64\) −10.9041 + 7.00766i −1.36302 + 0.875958i
\(65\) 0 0
\(66\) 5.21797 + 1.53213i 0.642288 + 0.188593i
\(67\) 5.07177 11.1056i 0.619615 1.35677i −0.296184 0.955131i \(-0.595714\pi\)
0.915799 0.401637i \(-0.131559\pi\)
\(68\) −10.0377 −1.21725
\(69\) −3.50140 3.27723i −0.421518 0.394532i
\(70\) 0 0
\(71\) 0.787956 1.72538i 0.0935131 0.204765i −0.857095 0.515158i \(-0.827733\pi\)
0.950608 + 0.310393i \(0.100461\pi\)
\(72\) −4.13631 1.21453i −0.487468 0.143134i
\(73\) −3.61246 4.16900i −0.422806 0.487944i 0.503884 0.863772i \(-0.331904\pi\)
−0.926690 + 0.375827i \(0.877359\pi\)
\(74\) 1.32702 0.852823i 0.154263 0.0991387i
\(75\) 0 0
\(76\) 1.20812 8.40266i 0.138581 0.963852i
\(77\) 0.206395 0.0606031i 0.0235209 0.00690637i
\(78\) −6.75247 4.33955i −0.764566 0.491357i
\(79\) −0.997420 6.93721i −0.112219 0.780497i −0.965753 0.259461i \(-0.916455\pi\)
0.853535 0.521036i \(-0.174454\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) −1.76070 12.2459i −0.194436 1.35234i
\(83\) −3.51021 2.25587i −0.385295 0.247614i 0.333626 0.942705i \(-0.391728\pi\)
−0.718922 + 0.695091i \(0.755364\pi\)
\(84\) 0.250975 0.0736930i 0.0273836 0.00804056i
\(85\) 0 0
\(86\) 3.49877 4.03779i 0.377282 0.435406i
\(87\) −6.26391 + 4.02557i −0.671561 + 0.431586i
\(88\) 3.44426 + 3.97489i 0.367160 + 0.423725i
\(89\) 15.3009 + 4.49275i 1.62189 + 0.476231i 0.961526 0.274713i \(-0.0885827\pi\)
0.660367 + 0.750943i \(0.270401\pi\)
\(90\) 0 0
\(91\) −0.317493 −0.0332823
\(92\) −3.48270 13.7971i −0.363096 1.43845i
\(93\) −1.72352 −0.178720
\(94\) −10.7532 + 23.5463i −1.10911 + 2.42861i
\(95\) 0 0
\(96\) −4.47283 5.16192i −0.456506 0.526836i
\(97\) −12.0969 + 7.77424i −1.22826 + 0.789354i −0.983619 0.180260i \(-0.942306\pi\)
−0.244640 + 0.969614i \(0.578670\pi\)
\(98\) −10.2051 + 11.7773i −1.03087 + 1.18969i
\(99\) 0.694523 4.83052i 0.0698022 0.485485i
\(100\) 0 0
\(101\) 14.6237 + 9.39808i 1.45511 + 0.935144i 0.998976 + 0.0452346i \(0.0144035\pi\)
0.456137 + 0.889910i \(0.349233\pi\)
\(102\) −1.07300 7.46289i −0.106243 0.738937i
\(103\) −0.483270 1.05821i −0.0476180 0.104269i 0.884328 0.466867i \(-0.154617\pi\)
−0.931946 + 0.362598i \(0.881890\pi\)
\(104\) −3.22482 7.06137i −0.316220 0.692425i
\(105\) 0 0
\(106\) −19.4523 12.5013i −1.88938 1.21423i
\(107\) 16.4556 4.83181i 1.59083 0.467108i 0.637851 0.770160i \(-0.279824\pi\)
0.952974 + 0.303051i \(0.0980053\pi\)
\(108\) 2.11134 14.6847i 0.203164 1.41303i
\(109\) −1.71227 + 1.97606i −0.164006 + 0.189273i −0.831804 0.555070i \(-0.812692\pi\)
0.667798 + 0.744343i \(0.267237\pi\)
\(110\) 0 0
\(111\) 0.463496 + 0.534903i 0.0439931 + 0.0507707i
\(112\) −0.0956126 0.0280744i −0.00903454 0.00265278i
\(113\) 7.44256 16.2969i 0.700137 1.53309i −0.139668 0.990198i \(-0.544604\pi\)
0.839805 0.542888i \(-0.182669\pi\)
\(114\) 6.37640 0.597205
\(115\) 0 0
\(116\) −22.0931 −2.05129
\(117\) −2.99223 + 6.55207i −0.276632 + 0.605739i
\(118\) 24.7060 + 7.25434i 2.27437 + 0.667816i
\(119\) −0.195298 0.225386i −0.0179029 0.0206611i
\(120\) 0 0
\(121\) 3.30439 3.81347i 0.300399 0.346679i
\(122\) 1.28830 8.96031i 0.116637 0.811228i
\(123\) 5.32627 1.56393i 0.480254 0.141015i
\(124\) −4.30209 2.76479i −0.386339 0.248285i
\(125\) 0 0
\(126\) −0.163236 0.357438i −0.0145422 0.0318431i
\(127\) −1.24283 2.72142i −0.110283 0.241487i 0.846441 0.532482i \(-0.178741\pi\)
−0.956724 + 0.290996i \(0.906013\pi\)
\(128\) −2.16711 15.0726i −0.191548 1.33224i
\(129\) 2.01669 + 1.29605i 0.177560 + 0.114111i
\(130\) 0 0
\(131\) 1.91036 13.2869i 0.166909 1.16088i −0.718316 0.695716i \(-0.755087\pi\)
0.885226 0.465162i \(-0.154004\pi\)
\(132\) −4.74125 + 5.47170i −0.412673 + 0.476250i
\(133\) 0.212178 0.136359i 0.0183982 0.0118238i
\(134\) 17.8188 + 20.5640i 1.53931 + 1.77646i
\(135\) 0 0
\(136\) 3.02915 6.63291i 0.259747 0.568767i
\(137\) −19.2932 −1.64833 −0.824165 0.566350i \(-0.808355\pi\)
−0.824165 + 0.566350i \(0.808355\pi\)
\(138\) 9.88567 4.06421i 0.841524 0.345968i
\(139\) 15.4962 1.31437 0.657185 0.753729i \(-0.271747\pi\)
0.657185 + 0.753729i \(0.271747\pi\)
\(140\) 0 0
\(141\) −11.1441 3.27220i −0.938502 0.275569i
\(142\) 2.76835 + 3.19485i 0.232315 + 0.268106i
\(143\) 7.39292 4.75114i 0.618227 0.397310i
\(144\) −1.48047 + 1.70856i −0.123373 + 0.142380i
\(145\) 0 0
\(146\) 11.7964 3.46373i 0.976275 0.286660i
\(147\) −5.88224 3.78028i −0.485159 0.311793i
\(148\) 0.298872 + 2.07870i 0.0245671 + 0.170868i
\(149\) −6.62691 14.5109i −0.542898 1.18878i −0.960020 0.279930i \(-0.909689\pi\)
0.417122 0.908850i \(-0.363039\pi\)
\(150\) 0 0
\(151\) −0.0629411 0.437765i −0.00512208 0.0356248i 0.987100 0.160104i \(-0.0511830\pi\)
−0.992222 + 0.124479i \(0.960274\pi\)
\(152\) 5.18789 + 3.33405i 0.420793 + 0.270427i
\(153\) −6.49186 + 1.90618i −0.524836 + 0.154106i
\(154\) −0.0682278 + 0.474535i −0.00549795 + 0.0382391i
\(155\) 0 0
\(156\) 8.98974 5.77735i 0.719755 0.462559i
\(157\) 4.66176 + 5.37996i 0.372049 + 0.429367i 0.910640 0.413200i \(-0.135589\pi\)
−0.538592 + 0.842567i \(0.681043\pi\)
\(158\) 14.9873 + 4.40066i 1.19232 + 0.350098i
\(159\) 4.30997 9.43751i 0.341803 0.748443i
\(160\) 0 0
\(161\) 0.242038 0.346643i 0.0190753 0.0273193i
\(162\) −2.22871 −0.175104
\(163\) 2.96870 6.50054i 0.232526 0.509162i −0.757017 0.653395i \(-0.773344\pi\)
0.989544 + 0.144233i \(0.0460714\pi\)
\(164\) 15.8038 + 4.64041i 1.23407 + 0.362355i
\(165\) 0 0
\(166\) 7.82322 5.02768i 0.607200 0.390224i
\(167\) 0.872694 1.00714i 0.0675311 0.0779351i −0.720979 0.692957i \(-0.756307\pi\)
0.788510 + 0.615022i \(0.210853\pi\)
\(168\) −0.0270422 + 0.188083i −0.00208635 + 0.0145109i
\(169\) 0.0280633 0.00824014i 0.00215872 0.000633857i
\(170\) 0 0
\(171\) −0.814334 5.66382i −0.0622737 0.433123i
\(172\) 2.95483 + 6.47018i 0.225304 + 0.493346i
\(173\) −1.12194 2.45670i −0.0852992 0.186779i 0.862176 0.506609i \(-0.169101\pi\)
−0.947475 + 0.319830i \(0.896374\pi\)
\(174\) −2.36168 16.4259i −0.179039 1.24524i
\(175\) 0 0
\(176\) 2.64649 0.777080i 0.199487 0.0585746i
\(177\) −1.64421 + 11.4357i −0.123587 + 0.859563i
\(178\) −23.2743 + 26.8600i −1.74449 + 2.01324i
\(179\) −16.6467 + 10.6982i −1.24423 + 0.799620i −0.986046 0.166474i \(-0.946762\pi\)
−0.258188 + 0.966095i \(0.583125\pi\)
\(180\) 0 0
\(181\) −3.82402 1.12283i −0.284237 0.0834596i 0.136506 0.990639i \(-0.456413\pi\)
−0.420744 + 0.907180i \(0.638231\pi\)
\(182\) 0.293947 0.643655i 0.0217888 0.0477109i
\(183\) 4.06175 0.300253
\(184\) 10.1681 + 1.86229i 0.749603 + 0.137290i
\(185\) 0 0
\(186\) 1.59570 3.49409i 0.117002 0.256199i
\(187\) 7.92038 + 2.32563i 0.579195 + 0.170067i
\(188\) −22.5678 26.0447i −1.64593 1.89950i
\(189\) 0.370807 0.238303i 0.0269723 0.0173340i
\(190\) 0 0
\(191\) 0.850935 5.91838i 0.0615715 0.428239i −0.935599 0.353065i \(-0.885140\pi\)
0.997170 0.0751744i \(-0.0239513\pi\)
\(192\) 12.4367 3.65175i 0.897544 0.263543i
\(193\) −8.48523 5.45312i −0.610780 0.392524i 0.198370 0.980127i \(-0.436435\pi\)
−0.809149 + 0.587603i \(0.800072\pi\)
\(194\) −4.56092 31.7219i −0.327455 2.27750i
\(195\) 0 0
\(196\) −8.61857 18.8720i −0.615612 1.34800i
\(197\) −0.728029 5.06355i −0.0518699 0.360763i −0.999182 0.0404498i \(-0.987121\pi\)
0.947312 0.320313i \(-0.103788\pi\)
\(198\) 9.14991 + 5.88029i 0.650255 + 0.417894i
\(199\) −25.5033 + 7.48844i −1.80788 + 0.530842i −0.998413 0.0563229i \(-0.982062\pi\)
−0.809468 + 0.587164i \(0.800244\pi\)
\(200\) 0 0
\(201\) −7.99514 + 9.22689i −0.563934 + 0.650814i
\(202\) −32.5920 + 20.9456i −2.29316 + 1.47373i
\(203\) −0.429852 0.496076i −0.0301697 0.0348177i
\(204\) 9.63112 + 2.82795i 0.674313 + 0.197996i
\(205\) 0 0
\(206\) 2.59275 0.180646
\(207\) −4.87252 8.26187i −0.338664 0.574240i
\(208\) −4.07103 −0.282275
\(209\) −2.90009 + 6.35031i −0.200603 + 0.439260i
\(210\) 0 0
\(211\) 9.65433 + 11.1417i 0.664631 + 0.767026i 0.983526 0.180765i \(-0.0578572\pi\)
−0.318895 + 0.947790i \(0.603312\pi\)
\(212\) 25.8974 16.6432i 1.77864 1.14306i
\(213\) −1.24213 + 1.43350i −0.0851096 + 0.0982217i
\(214\) −5.43971 + 37.8340i −0.371851 + 2.58628i
\(215\) 0 0
\(216\) 9.06646 + 5.82666i 0.616895 + 0.396454i
\(217\) −0.0216231 0.150392i −0.00146787 0.0102092i
\(218\) −2.42080 5.30081i −0.163957 0.359016i
\(219\) 2.29158 + 5.01787i 0.154851 + 0.339076i
\(220\) 0 0
\(221\) −10.2496 6.58702i −0.689463 0.443091i
\(222\) −1.51353 + 0.444413i −0.101582 + 0.0298271i
\(223\) −0.144012 + 1.00163i −0.00964378 + 0.0670740i −0.994075 0.108696i \(-0.965332\pi\)
0.984431 + 0.175770i \(0.0562415\pi\)
\(224\) 0.394306 0.455054i 0.0263457 0.0304046i
\(225\) 0 0
\(226\) 26.1482 + 30.1767i 1.73935 + 2.00732i
\(227\) 4.83803 + 1.42057i 0.321111 + 0.0942867i 0.438316 0.898821i \(-0.355575\pi\)
−0.117205 + 0.993108i \(0.537393\pi\)
\(228\) −3.52649 + 7.72193i −0.233547 + 0.511397i
\(229\) −22.9504 −1.51661 −0.758304 0.651901i \(-0.773972\pi\)
−0.758304 + 0.651901i \(0.773972\pi\)
\(230\) 0 0
\(231\) −0.215109 −0.0141531
\(232\) 6.66717 14.5991i 0.437721 0.958476i
\(233\) 20.6511 + 6.06370i 1.35290 + 0.397246i 0.876254 0.481850i \(-0.160035\pi\)
0.476644 + 0.879097i \(0.341853\pi\)
\(234\) −10.5127 12.1323i −0.687237 0.793114i
\(235\) 0 0
\(236\) −22.4489 + 25.9074i −1.46130 + 1.68643i
\(237\) −0.997420 + 6.93721i −0.0647894 + 0.450620i
\(238\) 0.637740 0.187257i 0.0413386 0.0121381i
\(239\) −7.37760 4.74129i −0.477217 0.306689i 0.279830 0.960050i \(-0.409722\pi\)
−0.757047 + 0.653361i \(0.773358\pi\)
\(240\) 0 0
\(241\) 3.66317 + 8.02123i 0.235966 + 0.516693i 0.990157 0.139962i \(-0.0446980\pi\)
−0.754191 + 0.656655i \(0.771971\pi\)
\(242\) 4.67172 + 10.2296i 0.300310 + 0.657587i
\(243\) −2.27704 15.8371i −0.146072 1.01595i
\(244\) 10.1386 + 6.51568i 0.649057 + 0.417123i
\(245\) 0 0
\(246\) −1.76070 + 12.2459i −0.112258 + 0.780771i
\(247\) 6.74767 7.78723i 0.429344 0.495490i
\(248\) 3.12524 2.00847i 0.198453 0.127538i
\(249\) 2.73247 + 3.15343i 0.173163 + 0.199841i
\(250\) 0 0
\(251\) −2.44763 + 5.35957i −0.154493 + 0.338293i −0.971014 0.239023i \(-0.923173\pi\)
0.816521 + 0.577316i \(0.195900\pi\)
\(252\) 0.523141 0.0329548
\(253\) −0.448583 + 11.6937i −0.0282022 + 0.735175i
\(254\) 6.66780 0.418375
\(255\) 0 0
\(256\) 7.68968 + 2.25789i 0.480605 + 0.141118i
\(257\) −5.05121 5.82941i −0.315086 0.363628i 0.576011 0.817442i \(-0.304609\pi\)
−0.891097 + 0.453814i \(0.850063\pi\)
\(258\) −4.49462 + 2.88852i −0.279823 + 0.179831i
\(259\) −0.0408599 + 0.0471549i −0.00253891 + 0.00293006i
\(260\) 0 0
\(261\) −14.2886 + 4.19552i −0.884443 + 0.259696i
\(262\) 25.1678 + 16.1744i 1.55487 + 0.999256i
\(263\) 3.18652 + 22.1627i 0.196489 + 1.36661i 0.814372 + 0.580343i \(0.197081\pi\)
−0.617883 + 0.786270i \(0.712009\pi\)
\(264\) −2.18489 4.78424i −0.134471 0.294450i
\(265\) 0 0
\(266\) 0.0799977 + 0.556396i 0.00490497 + 0.0341148i
\(267\) −13.4154 8.62153i −0.821007 0.527629i
\(268\) −34.7581 + 10.2059i −2.12319 + 0.623425i
\(269\) −1.31816 + 9.16802i −0.0803698 + 0.558984i 0.909357 + 0.416016i \(0.136574\pi\)
−0.989727 + 0.142968i \(0.954335\pi\)
\(270\) 0 0
\(271\) 18.4727 11.8717i 1.12214 0.721154i 0.158233 0.987402i \(-0.449420\pi\)
0.963905 + 0.266247i \(0.0857838\pi\)
\(272\) −2.50419 2.88999i −0.151839 0.175232i
\(273\) 0.304632 + 0.0894481i 0.0184372 + 0.00541365i
\(274\) 17.8624 39.1132i 1.07911 2.36291i
\(275\) 0 0
\(276\) −0.545473 + 14.2194i −0.0328336 + 0.855909i
\(277\) −12.5089 −0.751589 −0.375795 0.926703i \(-0.622630\pi\)
−0.375795 + 0.926703i \(0.622630\pi\)
\(278\) −14.3470 + 31.4155i −0.860474 + 1.88418i
\(279\) −3.30740 0.971141i −0.198009 0.0581407i
\(280\) 0 0
\(281\) −20.6303 + 13.2583i −1.23070 + 0.790922i −0.984000 0.178171i \(-0.942982\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(282\) 16.9514 19.5629i 1.00944 1.16496i
\(283\) −2.51410 + 17.4860i −0.149448 + 1.03943i 0.767678 + 0.640836i \(0.221412\pi\)
−0.917126 + 0.398597i \(0.869497\pi\)
\(284\) −5.40006 + 1.58560i −0.320435 + 0.0940882i
\(285\) 0 0
\(286\) 2.78736 + 19.3865i 0.164820 + 1.14635i
\(287\) 0.203290 + 0.445142i 0.0119998 + 0.0262759i
\(288\) −5.67474 12.4259i −0.334387 0.732205i
\(289\) 0.790638 + 5.49901i 0.0465081 + 0.323471i
\(290\) 0 0
\(291\) 13.7972 4.05122i 0.808806 0.237487i
\(292\) −2.32939 + 16.2012i −0.136317 + 0.948106i
\(293\) 5.55996 6.41653i 0.324816 0.374858i −0.569731 0.821831i \(-0.692953\pi\)
0.894547 + 0.446973i \(0.147498\pi\)
\(294\) 13.1098 8.42515i 0.764578 0.491365i
\(295\) 0 0
\(296\) −1.46379 0.429809i −0.0850813 0.0249821i
\(297\) −5.06826 + 11.0979i −0.294090 + 0.643968i
\(298\) 35.5535 2.05956
\(299\) 5.49782 16.3738i 0.317947 0.946921i
\(300\) 0 0
\(301\) −0.0877903 + 0.192234i −0.00506015 + 0.0110802i
\(302\) 0.945756 + 0.277699i 0.0544222 + 0.0159798i
\(303\) −11.3836 13.1374i −0.653970 0.754722i
\(304\) 2.72064 1.74845i 0.156039 0.100280i
\(305\) 0 0
\(306\) 2.14600 14.9258i 0.122679 0.853251i
\(307\) −14.0850 + 4.13574i −0.803875 + 0.236039i −0.657759 0.753228i \(-0.728496\pi\)
−0.146116 + 0.989267i \(0.546677\pi\)
\(308\) −0.536936 0.345068i −0.0305948 0.0196621i
\(309\) 0.165561 + 1.15150i 0.00941843 + 0.0655066i
\(310\) 0 0
\(311\) 12.5355 + 27.4490i 0.710826 + 1.55649i 0.826332 + 0.563184i \(0.190424\pi\)
−0.115506 + 0.993307i \(0.536849\pi\)
\(312\) 1.10477 + 7.68388i 0.0625455 + 0.435014i
\(313\) 4.68243 + 3.00922i 0.264667 + 0.170091i 0.666243 0.745734i \(-0.267901\pi\)
−0.401576 + 0.915826i \(0.631538\pi\)
\(314\) −15.2228 + 4.46983i −0.859074 + 0.252247i
\(315\) 0 0
\(316\) −13.6180 + 15.7160i −0.766074 + 0.884097i
\(317\) −2.36484 + 1.51979i −0.132823 + 0.0853600i −0.605365 0.795948i \(-0.706973\pi\)
0.472542 + 0.881308i \(0.343336\pi\)
\(318\) 15.1424 + 17.4752i 0.849142 + 0.979962i
\(319\) 17.4328 + 5.11873i 0.976049 + 0.286594i
\(320\) 0 0
\(321\) −17.1503 −0.957238
\(322\) 0.478662 + 0.811620i 0.0266748 + 0.0452298i
\(323\) 9.67876 0.538541
\(324\) 1.23259 2.69900i 0.0684774 0.149945i
\(325\) 0 0
\(326\) 10.4300 + 12.0369i 0.577667 + 0.666663i
\(327\) 2.19963 1.41362i 0.121640 0.0781732i
\(328\) −7.83558 + 9.04274i −0.432648 + 0.499302i
\(329\) 0.145715 1.01347i 0.00803354 0.0558745i
\(330\) 0 0
\(331\) −11.6540 7.48954i −0.640560 0.411663i 0.179646 0.983731i \(-0.442505\pi\)
−0.820206 + 0.572069i \(0.806141\pi\)
\(332\) 1.76195 + 12.2546i 0.0966995 + 0.672560i
\(333\) 0.588043 + 1.28764i 0.0322246 + 0.0705620i
\(334\) 1.23381 + 2.70167i 0.0675111 + 0.147829i
\(335\) 0 0
\(336\) 0.0838301 + 0.0538744i 0.00457331 + 0.00293909i
\(337\) 20.7059 6.07980i 1.12792 0.331188i 0.336031 0.941851i \(-0.390915\pi\)
0.791890 + 0.610663i \(0.209097\pi\)
\(338\) −0.00927685 + 0.0645219i −0.000504594 + 0.00350953i
\(339\) −11.7325 + 13.5400i −0.637220 + 0.735391i
\(340\) 0 0
\(341\) 2.75404 + 3.17834i 0.149140 + 0.172117i
\(342\) 12.2362 + 3.59288i 0.661659 + 0.194281i
\(343\) 0.512414 1.12203i 0.0276677 0.0605839i
\(344\) −5.16718 −0.278596
\(345\) 0 0
\(346\) 6.01920 0.323594
\(347\) −7.85449 + 17.1989i −0.421651 + 0.923288i 0.572957 + 0.819585i \(0.305796\pi\)
−0.994608 + 0.103702i \(0.966931\pi\)
\(348\) 21.1981 + 6.22434i 1.13634 + 0.333659i
\(349\) −13.7056 15.8171i −0.733643 0.846669i 0.259234 0.965815i \(-0.416530\pi\)
−0.992877 + 0.119146i \(0.961984\pi\)
\(350\) 0 0
\(351\) 11.7924 13.6091i 0.629431 0.726402i
\(352\) −2.37187 + 16.4967i −0.126421 + 0.879277i
\(353\) 1.54672 0.454159i 0.0823238 0.0241724i −0.240311 0.970696i \(-0.577250\pi\)
0.322635 + 0.946523i \(0.395431\pi\)
\(354\) −21.6615 13.9210i −1.15129 0.739891i
\(355\) 0 0
\(356\) −19.6560 43.0406i −1.04177 2.28115i
\(357\) 0.123889 + 0.271278i 0.00655688 + 0.0143576i
\(358\) −6.27632 43.6527i −0.331714 2.30712i
\(359\) 29.2892 + 18.8230i 1.54583 + 0.993442i 0.986362 + 0.164588i \(0.0526294\pi\)
0.559464 + 0.828854i \(0.311007\pi\)
\(360\) 0 0
\(361\) 1.53906 10.7044i 0.0810034 0.563391i
\(362\) 5.81675 6.71289i 0.305722 0.352822i
\(363\) −4.24491 + 2.72804i −0.222800 + 0.143185i
\(364\) 0.616908 + 0.711950i 0.0323348 + 0.0373163i
\(365\) 0 0
\(366\) −3.76052 + 8.23440i −0.196566 + 0.430419i
\(367\) 22.6244 1.18098 0.590491 0.807044i \(-0.298934\pi\)
0.590491 + 0.807044i \(0.298934\pi\)
\(368\) 3.10352 4.44480i 0.161782 0.231701i
\(369\) 11.1023 0.577961
\(370\) 0 0
\(371\) 0.877577 + 0.257680i 0.0455615 + 0.0133781i
\(372\) 3.34890 + 3.86483i 0.173632 + 0.200382i
\(373\) −9.08151 + 5.83633i −0.470223 + 0.302194i −0.754209 0.656635i \(-0.771979\pi\)
0.283986 + 0.958828i \(0.408343\pi\)
\(374\) −12.0478 + 13.9038i −0.622974 + 0.718951i
\(375\) 0 0
\(376\) 24.0207 7.05312i 1.23877 0.363737i
\(377\) −22.5594 14.4981i −1.16187 0.746688i
\(378\) 0.139806 + 0.972370i 0.00719083 + 0.0500133i
\(379\) −1.53173 3.35401i −0.0786795 0.172284i 0.866204 0.499690i \(-0.166553\pi\)
−0.944884 + 0.327406i \(0.893826\pi\)
\(380\) 0 0
\(381\) 0.425774 + 2.96133i 0.0218131 + 0.151713i
\(382\) 11.2105 + 7.20457i 0.573580 + 0.368618i
\(383\) −5.70202 + 1.67426i −0.291360 + 0.0855509i −0.424146 0.905594i \(-0.639426\pi\)
0.132787 + 0.991145i \(0.457608\pi\)
\(384\) −2.16711 + 15.0726i −0.110590 + 0.769171i
\(385\) 0 0
\(386\) 18.9111 12.1534i 0.962549 0.618593i
\(387\) 3.13973 + 3.62344i 0.159601 + 0.184190i
\(388\) 40.9382 + 12.0205i 2.07832 + 0.610250i
\(389\) 2.75929 6.04199i 0.139901 0.306341i −0.826693 0.562654i \(-0.809780\pi\)
0.966594 + 0.256313i \(0.0825077\pi\)
\(390\) 0 0
\(391\) 15.0055 6.16908i 0.758860 0.311984i
\(392\) 15.0715 0.761226
\(393\) −5.57632 + 12.2104i −0.281288 + 0.615935i
\(394\) 10.9394 + 3.21210i 0.551119 + 0.161823i
\(395\) 0 0
\(396\) −12.1815 + 7.82858i −0.612144 + 0.393401i
\(397\) −2.98449 + 3.44429i −0.149787 + 0.172864i −0.825685 0.564132i \(-0.809211\pi\)
0.675897 + 0.736996i \(0.263756\pi\)
\(398\) 8.43058 58.6360i 0.422587 2.93916i
\(399\) −0.242000 + 0.0710577i −0.0121152 + 0.00355733i
\(400\) 0 0
\(401\) 3.97219 + 27.6272i 0.198362 + 1.37964i 0.809038 + 0.587756i \(0.199989\pi\)
−0.610676 + 0.791880i \(0.709102\pi\)
\(402\) −11.3035 24.7512i −0.563767 1.23448i
\(403\) −2.57858 5.64630i −0.128448 0.281262i
\(404\) −7.34038 51.0534i −0.365197 2.54000i
\(405\) 0 0
\(406\) 1.40367 0.412155i 0.0696629 0.0204549i
\(407\) 0.245784 1.70947i 0.0121831 0.0847351i
\(408\) −4.77515 + 5.51082i −0.236405 + 0.272826i
\(409\) 6.83017 4.38949i 0.337730 0.217046i −0.360772 0.932654i \(-0.617487\pi\)
0.698502 + 0.715608i \(0.253850\pi\)
\(410\) 0 0
\(411\) 18.5117 + 5.43552i 0.913115 + 0.268115i
\(412\) −1.43393 + 3.13987i −0.0706446 + 0.154690i
\(413\) −1.01850 −0.0501169
\(414\) 21.2605 2.22893i 1.04490 0.109546i
\(415\) 0 0
\(416\) 10.2188 22.3760i 0.501016 1.09707i
\(417\) −14.8685 4.36578i −0.728113 0.213793i
\(418\) −10.1890 11.7587i −0.498360 0.575138i
\(419\) −23.3315 + 14.9942i −1.13982 + 0.732517i −0.967587 0.252539i \(-0.918734\pi\)
−0.172232 + 0.985056i \(0.555098\pi\)
\(420\) 0 0
\(421\) 4.97445 34.5981i 0.242440 1.68621i −0.397359 0.917663i \(-0.630073\pi\)
0.639799 0.768543i \(-0.279018\pi\)
\(422\) −31.5259 + 9.25685i −1.53466 + 0.450616i
\(423\) −19.5416 12.5586i −0.950145 0.610621i
\(424\) 3.18261 + 22.1355i 0.154561 + 1.07500i
\(425\) 0 0
\(426\) −1.75612 3.84537i −0.0850844 0.186309i
\(427\) 0.0509583 + 0.354423i 0.00246604 + 0.0171517i
\(428\) −42.8092 27.5118i −2.06926 1.32983i
\(429\) −8.43201 + 2.47586i −0.407101 + 0.119536i
\(430\) 0 0
\(431\) 6.06858 7.00351i 0.292313 0.337347i −0.590530 0.807016i \(-0.701081\pi\)
0.882843 + 0.469669i \(0.155627\pi\)
\(432\) 4.75465 3.05563i 0.228758 0.147014i
\(433\) 14.8185 + 17.1014i 0.712129 + 0.821841i 0.990337 0.138680i \(-0.0442859\pi\)
−0.278208 + 0.960521i \(0.589740\pi\)
\(434\) 0.324909 + 0.0954019i 0.0155961 + 0.00457944i
\(435\) 0 0
\(436\) 7.75820 0.371550
\(437\) 3.35816 + 13.3037i 0.160642 + 0.636404i
\(438\) −12.2944 −0.587448
\(439\) −7.68428 + 16.8262i −0.366751 + 0.803072i 0.632835 + 0.774287i \(0.281891\pi\)
−0.999586 + 0.0287853i \(0.990836\pi\)
\(440\) 0 0
\(441\) −9.15787 10.5687i −0.436089 0.503274i
\(442\) 22.8434 14.6805i 1.08655 0.698282i
\(443\) −14.6551 + 16.9129i −0.696284 + 0.803554i −0.988245 0.152876i \(-0.951147\pi\)
0.291962 + 0.956430i \(0.405692\pi\)
\(444\) 0.298872 2.07870i 0.0141838 0.0986507i
\(445\) 0 0
\(446\) −1.89727 1.21930i −0.0898384 0.0577356i
\(447\) 2.27028 + 15.7901i 0.107381 + 0.746848i
\(448\) 0.474677 + 1.03940i 0.0224264 + 0.0491069i
\(449\) 2.04143 + 4.47012i 0.0963412 + 0.210958i 0.951666 0.307134i \(-0.0993699\pi\)
−0.855325 + 0.518092i \(0.826643\pi\)
\(450\) 0 0
\(451\) −11.3950 7.32313i −0.536570 0.344833i
\(452\) −51.0058 + 14.9767i −2.39911 + 0.704442i
\(453\) −0.0629411 + 0.437765i −0.00295723 + 0.0205680i
\(454\) −7.35916 + 8.49293i −0.345383 + 0.398593i
\(455\) 0 0
\(456\) −4.03843 4.66060i −0.189117 0.218252i
\(457\) 11.1134 + 3.26318i 0.519861 + 0.152645i 0.531128 0.847291i \(-0.321768\pi\)
−0.0112669 + 0.999937i \(0.503586\pi\)
\(458\) 21.2484 46.5275i 0.992873 2.17409i
\(459\) 16.9148 0.789516
\(460\) 0 0
\(461\) −15.5495 −0.724210 −0.362105 0.932137i \(-0.617942\pi\)
−0.362105 + 0.932137i \(0.617942\pi\)
\(462\) 0.199156 0.436091i 0.00926558 0.0202888i
\(463\) 9.71687 + 2.85313i 0.451581 + 0.132596i 0.499611 0.866250i \(-0.333476\pi\)
−0.0480300 + 0.998846i \(0.515294\pi\)
\(464\) −5.51175 6.36089i −0.255876 0.295297i
\(465\) 0 0
\(466\) −31.4125 + 36.2520i −1.45516 + 1.67934i
\(467\) 0.0227489 0.158222i 0.00105269 0.00732164i −0.989288 0.145975i \(-0.953368\pi\)
0.990341 + 0.138653i \(0.0442773\pi\)
\(468\) 20.5065 6.02126i 0.947914 0.278333i
\(469\) −0.905432 0.581886i −0.0418089 0.0268690i
\(470\) 0 0
\(471\) −2.95722 6.47540i −0.136261 0.298371i
\(472\) −10.3450 22.6524i −0.476168 1.04266i
\(473\) −0.832472 5.78997i −0.0382771 0.266223i
\(474\) −13.1404 8.44481i −0.603558 0.387883i
\(475\) 0 0
\(476\) −0.125932 + 0.875877i −0.00577209 + 0.0401458i
\(477\) 13.5885 15.6819i 0.622173 0.718026i
\(478\) 16.4425 10.5670i 0.752063 0.483321i
\(479\) −3.84712 4.43982i −0.175779 0.202860i 0.661022 0.750366i \(-0.270123\pi\)
−0.836802 + 0.547506i \(0.815577\pi\)
\(480\) 0 0
\(481\) −1.05892 + 2.31870i −0.0482825 + 0.105724i
\(482\) −19.6530 −0.895169
\(483\) −0.329895 + 0.264411i −0.0150107 + 0.0120311i
\(484\) −14.9720 −0.680545
\(485\) 0 0
\(486\) 34.2149 + 10.0464i 1.55202 + 0.455714i
\(487\) −4.54083 5.24040i −0.205765 0.237465i 0.643482 0.765461i \(-0.277489\pi\)
−0.849247 + 0.527996i \(0.822944\pi\)
\(488\) −7.36514 + 4.73329i −0.333404 + 0.214266i
\(489\) −4.67986 + 5.40085i −0.211631 + 0.244235i
\(490\) 0 0
\(491\) 21.0671 6.18586i 0.950745 0.279164i 0.230648 0.973037i \(-0.425915\pi\)
0.720097 + 0.693873i \(0.244097\pi\)
\(492\) −13.8563 8.90487i −0.624688 0.401463i
\(493\) −3.58481 24.9329i −0.161452 1.12292i
\(494\) 9.53982 + 20.8893i 0.429217 + 0.939854i
\(495\) 0 0
\(496\) −0.277260 1.92839i −0.0124493 0.0865871i
\(497\) −0.140669 0.0904024i −0.00630986 0.00405510i
\(498\) −8.92279 + 2.61997i −0.399840 + 0.117404i
\(499\) 4.04910 28.1621i 0.181263 1.26071i −0.672520 0.740079i \(-0.734788\pi\)
0.853783 0.520630i \(-0.174303\pi\)
\(500\) 0 0
\(501\) −1.12109 + 0.720480i −0.0500866 + 0.0321887i
\(502\) −8.59936 9.92419i −0.383808 0.442938i
\(503\) 32.9609 + 9.67821i 1.46966 + 0.431530i 0.915987 0.401207i \(-0.131409\pi\)
0.553668 + 0.832737i \(0.313227\pi\)
\(504\) −0.157872 + 0.345691i −0.00703217 + 0.0153983i
\(505\) 0 0
\(506\) −23.2913 11.7359i −1.03543 0.521723i
\(507\) −0.0292481 −0.00129895
\(508\) −3.68765 + 8.07482i −0.163613 + 0.358262i
\(509\) 6.60273 + 1.93874i 0.292661 + 0.0859329i 0.424767 0.905303i \(-0.360356\pi\)
−0.132107 + 0.991236i \(0.542174\pi\)
\(510\) 0 0
\(511\) −0.409102 + 0.262914i −0.0180976 + 0.0116306i
\(512\) 8.24708 9.51763i 0.364473 0.420624i
\(513\) −2.03584 + 14.1595i −0.0898843 + 0.625159i
\(514\) 16.4946 4.84325i 0.727545 0.213626i
\(515\) 0 0
\(516\) −1.01228 7.04056i −0.0445631 0.309943i
\(517\) 11.7731 + 25.7796i 0.517782 + 1.13378i
\(518\) −0.0577675 0.126493i −0.00253816 0.00555779i
\(519\) 0.384358 + 2.67327i 0.0168714 + 0.117343i
\(520\) 0 0
\(521\) 5.29187 1.55383i 0.231841 0.0680747i −0.163748 0.986502i \(-0.552358\pi\)
0.395589 + 0.918427i \(0.370540\pi\)
\(522\) 4.72337 32.8517i 0.206736 1.43788i
\(523\) −3.11663 + 3.59678i −0.136281 + 0.157276i −0.819787 0.572668i \(-0.805908\pi\)
0.683507 + 0.729944i \(0.260454\pi\)
\(524\) −33.5066 + 21.5334i −1.46374 + 0.940689i
\(525\) 0 0
\(526\) −47.8808 14.0591i −2.08770 0.613005i
\(527\) 2.42212 5.30369i 0.105509 0.231033i
\(528\) −2.75822 −0.120036
\(529\) 13.6859 + 18.4850i 0.595039 + 0.803697i
\(530\) 0 0
\(531\) −9.59886 + 21.0186i −0.416555 + 0.912129i
\(532\) −0.718048 0.210838i −0.0311313 0.00914098i
\(533\) 13.0922 + 15.1092i 0.567087 + 0.654453i
\(534\) 29.8989 19.2149i 1.29385 0.831508i
\(535\) 0 0
\(536\) 3.74514 26.0480i 0.161766 1.12510i
\(537\) 18.9864 5.57492i 0.819325 0.240576i
\(538\) −17.3660 11.1604i −0.748700 0.481160i
\(539\) 2.42813 + 16.8880i 0.104587 + 0.727419i
\(540\) 0 0
\(541\) −7.02447 15.3814i −0.302006 0.661300i 0.696406 0.717648i \(-0.254782\pi\)
−0.998411 + 0.0563484i \(0.982054\pi\)
\(542\) 6.96478 + 48.4411i 0.299163 + 2.08072i
\(543\) 3.35278 + 2.15470i 0.143882 + 0.0924671i
\(544\) 22.1704 6.50980i 0.950546 0.279106i
\(545\) 0 0
\(546\) −0.463379 + 0.534768i −0.0198308 + 0.0228859i
\(547\) 32.4460 20.8518i 1.38729 0.891557i 0.387746 0.921766i \(-0.373254\pi\)
0.999544 + 0.0302093i \(0.00961739\pi\)
\(548\) 37.4879 + 43.2633i 1.60140 + 1.84812i
\(549\) 7.79444 + 2.28865i 0.332659 + 0.0976774i
\(550\) 0 0
\(551\) 21.3030 0.907539
\(552\) −9.23157 4.65154i −0.392922 0.197983i
\(553\) −0.617845 −0.0262734
\(554\) 11.5813 25.3594i 0.492040 1.07742i
\(555\) 0 0
\(556\) −30.1100 34.7488i −1.27695 1.47368i
\(557\) −35.4471 + 22.7805i −1.50194 + 0.965239i −0.507309 + 0.861764i \(0.669360\pi\)
−0.994632 + 0.103475i \(0.967004\pi\)
\(558\) 5.03092 5.80599i 0.212976 0.245787i
\(559\) −1.22870 + 8.54579i −0.0519685 + 0.361449i
\(560\) 0 0
\(561\) −6.94434 4.46286i −0.293190 0.188422i
\(562\) −7.77824 54.0988i −0.328105 2.28202i
\(563\) 2.50064 + 5.47564i 0.105389 + 0.230771i 0.954979 0.296674i \(-0.0958775\pi\)
−0.849589 + 0.527445i \(0.823150\pi\)
\(564\) 14.3160 + 31.3477i 0.602814 + 1.31998i
\(565\) 0 0
\(566\) −33.1217 21.2860i −1.39221 0.894719i
\(567\) 0.0845850 0.0248364i 0.00355224 0.00104303i
\(568\) 0.581849 4.04685i 0.0244139 0.169802i
\(569\) 11.4512 13.2154i 0.480061 0.554020i −0.463121 0.886295i \(-0.653271\pi\)
0.943183 + 0.332275i \(0.107816\pi\)
\(570\) 0 0
\(571\) −8.64327 9.97487i −0.361710 0.417435i 0.545502 0.838109i \(-0.316339\pi\)
−0.907212 + 0.420674i \(0.861794\pi\)
\(572\) −25.0189 7.34622i −1.04609 0.307161i
\(573\) −2.48387 + 5.43891i −0.103765 + 0.227214i
\(574\) −1.09065 −0.0455229
\(575\) 0 0
\(576\) 25.9235 1.08015
\(577\) 13.4953 29.5506i 0.561818 1.23021i −0.389223 0.921143i \(-0.627257\pi\)
0.951041 0.309065i \(-0.100016\pi\)
\(578\) −11.8802 3.48833i −0.494149 0.145095i
\(579\) 6.60519 + 7.62280i 0.274502 + 0.316793i
\(580\) 0 0
\(581\) −0.240883 + 0.277994i −0.00999351 + 0.0115331i
\(582\) −4.56092 + 31.7219i −0.189056 + 1.31491i
\(583\) −24.2907 + 7.13240i −1.00602 + 0.295394i
\(584\) −10.0028 6.42841i −0.413919 0.266009i
\(585\) 0 0
\(586\) 7.86064 + 17.2124i 0.324720 + 0.711037i
\(587\) 5.47162 + 11.9812i 0.225838 + 0.494516i 0.988301 0.152515i \(-0.0487374\pi\)
−0.762463 + 0.647032i \(0.776010\pi\)
\(588\) 2.95259 + 20.5357i 0.121763 + 0.846879i
\(589\) 4.14825 + 2.66592i 0.170926 + 0.109847i
\(590\) 0 0
\(591\) −0.728029 + 5.06355i −0.0299471 + 0.208287i
\(592\) −0.523923 + 0.604640i −0.0215331 + 0.0248505i
\(593\) −26.5698 + 17.0754i −1.09109 + 0.701202i −0.957094 0.289779i \(-0.906418\pi\)
−0.133999 + 0.990982i \(0.542782\pi\)
\(594\) −17.8065 20.5498i −0.730610 0.843169i
\(595\) 0 0
\(596\) −19.6630 + 43.0559i −0.805426 + 1.76364i
\(597\) 26.5800 1.08785
\(598\) 28.1046 + 26.3053i 1.14928 + 1.07570i
\(599\) −5.38162 −0.219887 −0.109943 0.993938i \(-0.535067\pi\)
−0.109943 + 0.993938i \(0.535067\pi\)
\(600\) 0 0
\(601\) −32.4793 9.53678i −1.32486 0.389013i −0.458614 0.888636i \(-0.651654\pi\)
−0.866243 + 0.499622i \(0.833472\pi\)
\(602\) −0.308437 0.355955i −0.0125710 0.0145077i
\(603\) −20.5416 + 13.2013i −0.836518 + 0.537598i
\(604\) −0.859352 + 0.991745i −0.0349665 + 0.0403535i
\(605\) 0 0
\(606\) 37.1728 10.9149i 1.51004 0.443388i
\(607\) −18.3320 11.7812i −0.744072 0.478186i 0.112863 0.993611i \(-0.463998\pi\)
−0.856935 + 0.515424i \(0.827634\pi\)
\(608\) 2.78103 + 19.3425i 0.112786 + 0.784442i
\(609\) 0.272679 + 0.597084i 0.0110495 + 0.0241951i
\(610\) 0 0
\(611\) −5.95300 41.4040i −0.240833 1.67503i
\(612\) 16.8885 + 10.8536i 0.682678 + 0.438731i
\(613\) −6.50705 + 1.91064i −0.262817 + 0.0771701i −0.410486 0.911867i \(-0.634641\pi\)
0.147669 + 0.989037i \(0.452823\pi\)
\(614\) 4.65607 32.3837i 0.187904 1.30690i
\(615\) 0 0
\(616\) 0.390055 0.250673i 0.0157158 0.0100999i
\(617\) −21.1308 24.3863i −0.850695 0.981755i 0.149280 0.988795i \(-0.452304\pi\)
−0.999975 + 0.00704038i \(0.997759\pi\)
\(618\) −2.48773 0.730462i −0.100071 0.0293835i
\(619\) −14.5801 + 31.9260i −0.586024 + 1.28321i 0.351792 + 0.936078i \(0.385573\pi\)
−0.937815 + 0.347134i \(0.887155\pi\)
\(620\) 0 0
\(621\) 5.86879 + 23.2499i 0.235506 + 0.932986i
\(622\) −67.2534 −2.69661
\(623\) 0.583995 1.27877i 0.0233973 0.0512329i
\(624\) 3.90613 + 1.14694i 0.156370 + 0.0459144i
\(625\) 0 0
\(626\) −10.4358 + 6.70667i −0.417098 + 0.268052i
\(627\) 4.57170 5.27603i 0.182576 0.210704i
\(628\) 3.00600 20.9072i 0.119952 0.834287i
\(629\) −2.29740 + 0.674577i −0.0916033 + 0.0268971i
\(630\) 0 0
\(631\) 1.85675 + 12.9139i 0.0739159 + 0.514096i 0.992820 + 0.119616i \(0.0381663\pi\)
−0.918904 + 0.394480i \(0.870925\pi\)
\(632\) −6.27554 13.7415i −0.249628 0.546608i
\(633\) −6.12428 13.4103i −0.243418 0.533012i
\(634\) −0.891617 6.20133i −0.0354106 0.246286i
\(635\) 0 0
\(636\) −29.5373 + 8.67294i −1.17123 + 0.343904i
\(637\) 3.58384 24.9261i 0.141997 0.987610i
\(638\) −26.5172 + 30.6024i −1.04982 + 1.21156i
\(639\) −3.19136 + 2.05097i −0.126248 + 0.0811349i
\(640\) 0 0
\(641\) 34.6688 + 10.1797i 1.36934 + 0.402073i 0.882044 0.471166i \(-0.156167\pi\)
0.487291 + 0.873239i \(0.337985\pi\)
\(642\) 15.8784 34.7689i 0.626672 1.37222i
\(643\) −31.5510 −1.24425 −0.622126 0.782917i \(-0.713731\pi\)
−0.622126 + 0.782917i \(0.713731\pi\)
\(644\) −1.24761 + 0.130798i −0.0491628 + 0.00515417i
\(645\) 0 0
\(646\) −8.96097 + 19.6218i −0.352565 + 0.772009i
\(647\) −13.3013 3.90562i −0.522929 0.153546i 0.00960580 0.999954i \(-0.496942\pi\)
−0.532535 + 0.846408i \(0.678761\pi\)
\(648\) 1.41153 + 1.62899i 0.0554501 + 0.0639928i
\(649\) 23.7160 15.2413i 0.930934 0.598275i
\(650\) 0 0
\(651\) −0.0216231 + 0.150392i −0.000847474 + 0.00589431i
\(652\) −20.3453 + 5.97391i −0.796782 + 0.233956i
\(653\) 4.75724 + 3.05729i 0.186165 + 0.119641i 0.630404 0.776267i \(-0.282889\pi\)
−0.444239 + 0.895909i \(0.646526\pi\)
\(654\) 0.829328 + 5.76810i 0.0324293 + 0.225551i
\(655\) 0 0
\(656\) 2.60667 + 5.70780i 0.101773 + 0.222852i
\(657\) 1.57012 + 10.9204i 0.0612564 + 0.426047i
\(658\) 1.91971 + 1.23372i 0.0748379 + 0.0480954i
\(659\) −28.0838 + 8.24614i −1.09399 + 0.321224i −0.778461 0.627692i \(-0.784000\pi\)
−0.315527 + 0.948917i \(0.602181\pi\)
\(660\) 0 0
\(661\) −10.5207 + 12.1415i −0.409207 + 0.472250i −0.922519 0.385952i \(-0.873873\pi\)
0.513312 + 0.858202i \(0.328418\pi\)
\(662\) 25.9733 16.6920i 1.00948 0.648753i
\(663\) 7.97864 + 9.20784i 0.309865 + 0.357603i
\(664\) −8.62956 2.53387i −0.334892 0.0983331i
\(665\) 0 0
\(666\) −3.15486 −0.122248
\(667\) 33.0272 13.5782i 1.27882 0.525749i
\(668\) −3.95413 −0.152990
\(669\) 0.420370 0.920482i 0.0162524 0.0355879i
\(670\) 0 0
\(671\) −6.49036 7.49027i −0.250558 0.289159i
\(672\) −0.506538 + 0.325532i −0.0195401 + 0.0125577i
\(673\) 2.50376 2.88949i 0.0965128 0.111382i −0.705438 0.708771i \(-0.749250\pi\)
0.801951 + 0.597389i \(0.203795\pi\)
\(674\) −6.84471 + 47.6060i −0.263649 + 1.83372i
\(675\) 0 0
\(676\) −0.0730065 0.0469185i −0.00280794 0.00180456i
\(677\) 2.33764 + 16.2586i 0.0898428 + 0.624870i 0.984140 + 0.177396i \(0.0567673\pi\)
−0.894297 + 0.447474i \(0.852324\pi\)
\(678\) −16.5873 36.3211i −0.637031 1.39490i
\(679\) 0.526602 + 1.15310i 0.0202091 + 0.0442518i
\(680\) 0 0
\(681\) −4.24183 2.72606i −0.162547 0.104463i
\(682\) −8.99325 + 2.64066i −0.344369 + 0.101116i
\(683\) 1.04764 7.28651i 0.0400869 0.278811i −0.959912 0.280302i \(-0.909566\pi\)
0.999999 + 0.00149105i \(0.000474615\pi\)
\(684\) −11.1183 + 12.8312i −0.425119 + 0.490614i
\(685\) 0 0
\(686\) 1.80028 + 2.07764i 0.0687351 + 0.0793245i
\(687\) 22.0208 + 6.46589i 0.840145 + 0.246689i
\(688\) −1.12569 + 2.46491i −0.0429163 + 0.0939737i
\(689\) 37.3658 1.42352
\(690\) 0 0
\(691\) −9.67502 −0.368055 −0.184028 0.982921i \(-0.558914\pi\)
−0.184028 + 0.982921i \(0.558914\pi\)
\(692\) −3.32894 + 7.28935i −0.126547 + 0.277100i
\(693\) −0.412791 0.121206i −0.0156806 0.00460425i
\(694\) −27.5955 31.8469i −1.04751 1.20889i
\(695\) 0 0
\(696\) −10.5101 + 12.1293i −0.398386 + 0.459762i
\(697\) −2.67257 + 18.5881i −0.101231 + 0.704076i
\(698\) 44.7552 13.1413i 1.69401 0.497406i
\(699\) −18.1062 11.6362i −0.684840 0.440120i
\(700\) 0 0
\(701\) 17.6838 + 38.7221i 0.667908 + 1.46252i 0.874965 + 0.484186i \(0.160884\pi\)
−0.207057 + 0.978329i \(0.566388\pi\)
\(702\) 16.6720 + 36.5066i 0.629244 + 1.37785i
\(703\) −0.288184 2.00436i −0.0108691 0.0755960i
\(704\) −26.6071 17.0994i −1.00279 0.644456i
\(705\) 0 0
\(706\) −0.511298 + 3.55616i −0.0192430 + 0.133838i
\(707\) 1.00353 1.15814i 0.0377417 0.0435562i
\(708\) 28.8385 18.5334i 1.08382 0.696526i
\(709\) −22.9666 26.5049i −0.862529 0.995411i −0.999988 0.00490358i \(-0.998439\pi\)
0.137459 0.990507i \(-0.456106\pi\)
\(710\) 0 0
\(711\) −5.82291 + 12.7504i −0.218376 + 0.478177i
\(712\) 34.3729 1.28818
\(713\) 8.13045 + 1.48909i 0.304488 + 0.0557668i
\(714\) −0.664664 −0.0248744
\(715\) 0 0
\(716\) 56.3353 + 16.5415i 2.10535 + 0.618187i
\(717\) 5.74298 + 6.62775i 0.214475 + 0.247518i
\(718\) −65.2771 + 41.9511i −2.43612 + 1.56560i
\(719\) −14.5394 + 16.7793i −0.542226 + 0.625763i −0.959054 0.283223i \(-0.908596\pi\)
0.416828 + 0.908986i \(0.363142\pi\)
\(720\) 0 0
\(721\) −0.0984013 + 0.0288932i −0.00366466 + 0.00107604i
\(722\) 20.2762 + 13.0307i 0.754602 + 0.484953i
\(723\) −1.25495 8.72835i −0.0466720 0.324611i
\(724\) 4.91245 + 10.7568i 0.182570 + 0.399772i
\(725\) 0 0
\(726\) −1.60046 11.1315i −0.0593987 0.413127i
\(727\) −0.587772 0.377738i −0.0217993 0.0140095i 0.529696 0.848188i \(-0.322306\pi\)
−0.551495 + 0.834178i \(0.685942\pi\)
\(728\) −0.656624 + 0.192802i −0.0243361 + 0.00714573i
\(729\) −1.85009 + 12.8677i −0.0685220 + 0.476581i
\(730\) 0 0
\(731\) −6.82240 + 4.38449i −0.252336 + 0.162166i
\(732\) −7.89223 9.10812i −0.291705 0.336646i
\(733\) −35.7918 10.5094i −1.32200 0.388174i −0.456785 0.889577i \(-0.650999\pi\)
−0.865214 + 0.501403i \(0.832817\pi\)
\(734\) −20.9465 + 45.8664i −0.773149 + 1.69296i
\(735\) 0 0
\(736\) 16.6402 + 28.2151i 0.613364 + 1.04002i
\(737\) 29.7909 1.09736
\(738\) −10.2789 + 22.5077i −0.378372 + 0.828518i
\(739\) 23.5752 + 6.92231i 0.867229 + 0.254641i 0.684936 0.728603i \(-0.259830\pi\)
0.182293 + 0.983244i \(0.441648\pi\)
\(740\) 0 0
\(741\) −8.66826 + 5.57075i −0.318437 + 0.204647i
\(742\) −1.33489 + 1.54054i −0.0490053 + 0.0565552i
\(743\) 5.88612 40.9388i 0.215941 1.50190i −0.536871 0.843665i \(-0.680394\pi\)
0.752811 0.658236i \(-0.228697\pi\)
\(744\) −3.56450 + 1.04663i −0.130681 + 0.0383713i
\(745\) 0 0
\(746\) −3.42400 23.8145i −0.125362 0.871910i
\(747\) 3.46671 + 7.59104i 0.126840 + 0.277742i
\(748\) −10.1748 22.2796i −0.372026 0.814623i
\(749\) −0.215166 1.49651i −0.00786201 0.0546815i
\(750\) 0 0
\(751\) 39.3106 11.5426i 1.43446 0.421197i 0.530091 0.847941i \(-0.322158\pi\)
0.904372 + 0.426744i \(0.140339\pi\)
\(752\) 1.86842 12.9952i 0.0681344 0.473885i
\(753\) 3.85845 4.45289i 0.140610 0.162272i
\(754\) 50.2783 32.3119i 1.83103 1.17673i
\(755\) 0 0
\(756\) −1.25488 0.368465i −0.0456394 0.0134009i
\(757\) −4.14940 + 9.08592i −0.150812 + 0.330233i −0.969927 0.243397i \(-0.921738\pi\)
0.819114 + 0.573630i \(0.194465\pi\)
\(758\) 8.21774 0.298482
\(759\) 3.72490 11.0936i 0.135205 0.402673i
\(760\) 0 0
\(761\) −7.00401 + 15.3366i −0.253895 + 0.555953i −0.993065 0.117566i \(-0.962491\pi\)
0.739170 + 0.673519i \(0.235218\pi\)
\(762\) −6.39771 1.87854i −0.231764 0.0680522i
\(763\) 0.150947 + 0.174202i 0.00546464 + 0.00630653i
\(764\) −14.9249 + 9.59163i −0.539963 + 0.347013i
\(765\) 0 0
\(766\) 1.88491 13.1098i 0.0681045 0.473677i
\(767\) −39.9238 + 11.7227i −1.44157 + 0.423282i
\(768\) −6.74207 4.33287i −0.243283 0.156349i
\(769\) 6.22901 + 43.3237i 0.224624 + 1.56229i 0.720223 + 0.693743i \(0.244039\pi\)
−0.495599 + 0.868551i \(0.665051\pi\)
\(770\) 0 0
\(771\) 3.20427 + 7.01636i 0.115399 + 0.252688i
\(772\) 4.25916 + 29.6231i 0.153291 + 1.06616i
\(773\) −28.2907 18.1814i −1.01755 0.653938i −0.0782114 0.996937i \(-0.524921\pi\)
−0.939336 + 0.342999i \(0.888557\pi\)
\(774\) −10.2527 + 3.01046i −0.368525 + 0.108209i
\(775\) 0 0
\(776\) −20.2973 + 23.4244i −0.728632 + 0.840886i
\(777\) 0.0524899 0.0337332i 0.00188306 0.00121017i
\(778\) 9.69430 + 11.1878i 0.347558 + 0.401103i
\(779\) −15.2386 4.47446i −0.545980 0.160314i
\(780\) 0 0
\(781\) 4.62835 0.165615
\(782\) −1.38607 + 36.1323i −0.0495659 + 1.29209i
\(783\) 37.2296 1.33048
\(784\) 3.28337 7.18957i 0.117263 0.256770i
\(785\) 0 0
\(786\) −19.5915 22.6098i −0.698805 0.806464i
\(787\) −1.05221 + 0.676215i −0.0375073 + 0.0241045i −0.559260 0.828992i \(-0.688915\pi\)
0.521753 + 0.853097i \(0.325278\pi\)
\(788\) −9.93997 + 11.4713i −0.354097 + 0.408649i
\(789\) 3.18652 22.1627i 0.113443 0.789014i
\(790\) 0 0
\(791\) −1.32867 0.853887i −0.0472422 0.0303607i
\(792\) −1.49702 10.4120i −0.0531943 0.369975i
\(793\) 6.07684 + 13.3064i 0.215795 + 0.472525i
\(794\) −4.21946 9.23933i −0.149743 0.327892i
\(795\) 0 0
\(796\) 66.3466 + 42.6384i 2.35159 + 1.51128i
\(797\) −11.7261 + 3.44308i −0.415358 + 0.121960i −0.482733 0.875768i \(-0.660356\pi\)
0.0673749 + 0.997728i \(0.478538\pi\)
\(798\) 0.0799977 0.556396i 0.00283189 0.0196962i
\(799\) 25.7306 29.6947i 0.910282 1.05052i
\(800\) 0 0
\(801\) −20.8860 24.1037i −0.737969 0.851662i
\(802\) −59.6863 17.5255i −2.10760 0.618846i
\(803\) 5.59168 12.2441i 0.197326 0.432084i
\(804\) 36.2255 1.27758
\(805\) 0 0
\(806\) 13.8341 0.487285
\(807\) 3.84770 8.42528i 0.135445 0.296584i
\(808\) 35.9512 + 10.5562i 1.26476 + 0.371367i
\(809\) 17.5520 + 20.2561i 0.617097 + 0.712167i 0.975153 0.221533i \(-0.0711059\pi\)
−0.358056 + 0.933700i \(0.616560\pi\)
\(810\) 0 0
\(811\) 25.9259 29.9201i 0.910381 1.05064i −0.0881316 0.996109i \(-0.528090\pi\)
0.998512 0.0545266i \(-0.0173650\pi\)
\(812\) −0.277177 + 1.92781i −0.00972702 + 0.0676529i
\(813\) −21.0691 + 6.18644i −0.738925 + 0.216968i
\(814\) 3.23805 + 2.08097i 0.113494 + 0.0729379i
\(815\) 0 0
\(816\) 1.58855 + 3.47844i 0.0556104 + 0.121770i
\(817\) −2.84917 6.23880i −0.0996797 0.218268i
\(818\) 2.57518 + 17.9108i 0.0900392 + 0.626236i
\(819\) 0.534184 + 0.343299i 0.0186659 + 0.0119958i
\(820\) 0 0
\(821\) 4.50608 31.3404i 0.157263 1.09379i −0.746385 0.665514i \(-0.768212\pi\)
0.903648 0.428275i \(-0.140879\pi\)
\(822\) −28.1583 + 32.4964i −0.982134 + 1.13344i
\(823\) 39.4672 25.3640i 1.37574 0.884134i 0.376632 0.926363i \(-0.377082\pi\)
0.999108 + 0.0422285i \(0.0134457\pi\)
\(824\) −1.64209 1.89508i −0.0572050 0.0660181i
\(825\) 0 0
\(826\) 0.942962 2.06480i 0.0328099 0.0718436i
\(827\) 24.2676 0.843869 0.421934 0.906626i \(-0.361351\pi\)
0.421934 + 0.906626i \(0.361351\pi\)
\(828\) −9.05891 + 26.9795i −0.314819 + 0.937603i
\(829\) −21.8597 −0.759220 −0.379610 0.925147i \(-0.623942\pi\)
−0.379610 + 0.925147i \(0.623942\pi\)
\(830\) 0 0
\(831\) 12.0022 + 3.52417i 0.416353 + 0.122252i
\(832\) 30.5700 + 35.2797i 1.05983 + 1.22310i
\(833\) 19.8994 12.7886i 0.689473 0.443098i
\(834\) 22.6166 26.1009i 0.783148 0.903801i
\(835\) 0 0
\(836\) 19.8751 5.83585i 0.687393 0.201837i
\(837\) 7.24957 + 4.65902i 0.250582 + 0.161039i
\(838\) −8.79669 61.1823i −0.303876 2.11351i
\(839\) −11.3411 24.8335i −0.391538 0.857348i −0.998059 0.0622806i \(-0.980163\pi\)
0.606521 0.795068i \(-0.292565\pi\)
\(840\) 0 0
\(841\) −3.76305 26.1726i −0.129760 0.902504i
\(842\) 65.5352 + 42.1169i 2.25849 + 1.45145i
\(843\) 23.5299 6.90899i 0.810412 0.237958i
\(844\) 6.22531 43.2980i 0.214284 1.49038i
\(845\) 0 0
\(846\) 43.5525 27.9895i 1.49737 0.962298i
\(847\) −0.291301 0.336180i −0.0100092 0.0115513i
\(848\) 11.2527 + 3.30408i 0.386418 + 0.113463i
\(849\) 7.33863 16.0694i 0.251861 0.551499i
\(850\) 0 0
\(851\) −1.72433 2.92379i −0.0591094 0.100226i
\(852\) 5.62804 0.192813
\(853\) 11.7016 25.6230i 0.400657 0.877316i −0.596547 0.802578i \(-0.703461\pi\)
0.997203 0.0747372i \(-0.0238118\pi\)
\(854\) −0.765701 0.224830i −0.0262018 0.00769353i
\(855\) 0 0
\(856\) 31.0986 19.9858i 1.06293 0.683102i
\(857\) −7.35982 + 8.49369i −0.251407 + 0.290139i −0.867399 0.497613i \(-0.834210\pi\)
0.615992 + 0.787752i \(0.288755\pi\)
\(858\) 2.78736 19.3865i 0.0951588 0.661844i
\(859\) 8.44772 2.48047i 0.288233 0.0846327i −0.134420 0.990924i \(-0.542917\pi\)
0.422653 + 0.906292i \(0.361099\pi\)
\(860\) 0 0
\(861\) −0.0696439 0.484384i −0.00237346 0.0165078i
\(862\) 8.57972 + 18.7870i 0.292226 + 0.639887i
\(863\) 19.8827 + 43.5371i 0.676816 + 1.48202i 0.865982 + 0.500075i \(0.166694\pi\)
−0.189166 + 0.981945i \(0.560579\pi\)
\(864\) 4.86019 + 33.8034i 0.165347 + 1.15001i
\(865\) 0 0
\(866\) −48.3892 + 14.2084i −1.64433 + 0.482820i
\(867\) 0.790638 5.49901i 0.0268515 0.186756i
\(868\) −0.295225 + 0.340708i −0.0100206 + 0.0115644i
\(869\) 14.3867 9.24578i 0.488036 0.313641i
\(870\) 0 0
\(871\) −42.1892 12.3879i −1.42953 0.419747i
\(872\) −2.34124 + 5.12661i −0.0792845 + 0.173609i
\(873\) 28.7593 0.973356
\(874\) −30.0798 5.50910i −1.01746 0.186348i
\(875\) 0 0
\(876\) 6.79944 14.8887i 0.229732 0.503043i
\(877\) −45.2435 13.2847i −1.52776 0.448592i −0.593398 0.804909i \(-0.702214\pi\)
−0.934365 + 0.356317i \(0.884032\pi\)
\(878\) −26.9975 31.1567i −0.911121 1.05149i
\(879\) −7.14248 + 4.59020i −0.240910 + 0.154823i
\(880\) 0 0
\(881\) −5.26169 + 36.5959i −0.177271 + 1.23295i 0.685773 + 0.727816i \(0.259464\pi\)
−0.863043 + 0.505130i \(0.831445\pi\)
\(882\) 29.9048 8.78083i 1.00695 0.295666i
\(883\) 45.8990 + 29.4975i 1.54462 + 0.992670i 0.986658 + 0.162807i \(0.0520548\pi\)
0.557967 + 0.829863i \(0.311582\pi\)
\(884\) 5.14479 + 35.7828i 0.173038 + 1.20351i
\(885\) 0 0
\(886\) −20.7193 45.3689i −0.696077 1.52420i
\(887\) −2.01788 14.0346i −0.0677537 0.471237i −0.995246 0.0973946i \(-0.968949\pi\)
0.927492 0.373843i \(-0.121960\pi\)
\(888\) 1.28341 + 0.824797i 0.0430684 + 0.0276784i
\(889\) −0.253060 + 0.0743050i −0.00848734 + 0.00249211i
\(890\) 0 0
\(891\) −1.59792 + 1.84410i −0.0535324 + 0.0617797i
\(892\) 2.52589 1.62329i 0.0845730 0.0543517i
\(893\) 21.7608 + 25.1133i 0.728197 + 0.840384i
\(894\) −34.1133 10.0166i −1.14092 0.335004i
\(895\) 0 0
\(896\) −1.34240 −0.0448465
\(897\) −9.88816 + 14.1616i −0.330156 + 0.472843i
\(898\) −10.9523 −0.365484
\(899\) 5.33109 11.6735i 0.177802 0.389332i
\(900\) 0 0
\(901\) 22.9847 + 26.5257i 0.765730 + 0.883699i
\(902\) 25.3962 16.3211i 0.845600 0.543434i
\(903\) 0.138393 0.159714i 0.00460542 0.00531494i
\(904\) 5.49580 38.2242i 0.182788 1.27132i
\(905\) 0 0
\(906\) −0.829210 0.532901i −0.0275486 0.0177044i
\(907\) 7.08860 + 49.3023i 0.235373 + 1.63706i 0.674246 + 0.738506i \(0.264469\pi\)
−0.438873 + 0.898549i \(0.644622\pi\)
\(908\) −6.21507 13.6091i −0.206254 0.451634i
\(909\) −14.4425 31.6247i −0.479028 1.04892i
\(910\) 0 0
\(911\) −17.7763 11.4241i −0.588955 0.378498i 0.211959 0.977279i \(-0.432016\pi\)
−0.800913 + 0.598781i \(0.795652\pi\)
\(912\) −3.10303 + 0.911132i −0.102752 + 0.0301706i
\(913\) 1.44898 10.0779i 0.0479543 0.333529i
\(914\) −16.9046 + 19.5090i −0.559156 + 0.645300i
\(915\) 0 0
\(916\) 44.5941 + 51.4644i 1.47343 + 1.70043i
\(917\) −1.13543 0.333391i −0.0374951 0.0110095i
\(918\) −15.6604 + 34.2915i −0.516870 + 1.13179i
\(919\) −1.66022 −0.0547657 −0.0273829 0.999625i \(-0.508717\pi\)
−0.0273829 + 0.999625i \(0.508717\pi\)
\(920\) 0 0
\(921\) 14.6797 0.483711
\(922\) 14.3963 31.5235i 0.474116 1.03817i
\(923\) −6.55457 1.92459i −0.215746 0.0633488i
\(924\) 0.417970 + 0.482363i 0.0137502 + 0.0158686i
\(925\) 0 0
\(926\) −14.7804 + 17.0575i −0.485715 + 0.560545i
\(927\) −0.331122 + 2.30300i −0.0108755 + 0.0756406i
\(928\) 48.7971 14.3281i 1.60184 0.470343i
\(929\) 24.5455 + 15.7744i 0.805311 + 0.517542i 0.877345 0.479860i \(-0.159313\pi\)
−0.0720340 + 0.997402i \(0.522949\pi\)
\(930\) 0 0
\(931\) 8.31037 + 18.1972i 0.272361 + 0.596388i
\(932\) −26.5290 58.0904i −0.868986 1.90281i
\(933\) −4.29449 29.8688i −0.140595 0.977861i
\(934\) 0.299702 + 0.192607i 0.00980656 + 0.00630229i
\(935\) 0 0
\(936\) −2.20955 + 15.3678i −0.0722214 + 0.502311i
\(937\) 12.0573 13.9149i 0.393895 0.454580i −0.523813 0.851833i \(-0.675491\pi\)
0.917709 + 0.397253i \(0.130037\pi\)
\(938\) 2.01794 1.29685i 0.0658881 0.0423437i
\(939\) −3.64497 4.20652i −0.118949 0.137275i
\(940\) 0 0
\(941\) 17.9910 39.3947i 0.586489 1.28423i −0.351052 0.936356i \(-0.614176\pi\)
0.937541 0.347876i \(-0.113097\pi\)
\(942\) 15.8655 0.516926
\(943\) −26.4772 + 2.77584i −0.862215 + 0.0903937i
\(944\) −13.0596 −0.425053
\(945\) 0 0
\(946\) 12.5088 + 3.67290i 0.406695 + 0.119416i
\(947\) −13.8033 15.9299i −0.448548 0.517652i 0.485773 0.874085i \(-0.338538\pi\)
−0.934321 + 0.356433i \(0.883993\pi\)
\(948\) 17.4941 11.2428i 0.568183 0.365149i
\(949\) −13.0102 + 15.0146i −0.422330 + 0.487395i
\(950\) 0 0
\(951\) 2.69722 0.791977i 0.0874635 0.0256816i
\(952\) −0.540775 0.347535i −0.0175266 0.0112637i
\(953\) 2.09831 + 14.5941i 0.0679710 + 0.472749i 0.995169 + 0.0981772i \(0.0313012\pi\)
−0.927198 + 0.374572i \(0.877790\pi\)
\(954\) 19.2113 + 42.0669i 0.621989 + 1.36197i
\(955\) 0 0
\(956\) 3.70319 + 25.7562i 0.119770 + 0.833016i
\(957\) −15.2845 9.82277i −0.494079 0.317525i
\(958\) 12.5627 3.68873i 0.405881 0.119178i
\(959\) −0.242051 + 1.68350i −0.00781622 + 0.0543630i
\(960\) 0 0
\(961\) −23.5799 + 15.1539i −0.760642 + 0.488835i
\(962\) −3.72033 4.29349i −0.119948 0.138428i
\(963\) −32.9113 9.66362i −1.06055 0.311406i
\(964\) 10.8691 23.8001i 0.350071 0.766549i
\(965\) 0 0
\(966\) −0.230613 0.913599i −0.00741984 0.0293946i
\(967\) 25.3720 0.815909 0.407955 0.913002i \(-0.366242\pi\)
0.407955 + 0.913002i \(0.366242\pi\)
\(968\) 4.51820 9.89347i 0.145220 0.317988i
\(969\) −9.28671 2.72682i −0.298332 0.0875982i
\(970\) 0 0
\(971\) −32.9014 + 21.1444i −1.05586 + 0.678557i −0.948858 0.315702i \(-0.897760\pi\)
−0.106997 + 0.994259i \(0.534124\pi\)
\(972\) −31.0890 + 35.8786i −0.997180 + 1.15081i
\(973\) 0.194414 1.35218i 0.00623261 0.0433488i
\(974\) 14.8280 4.35388i 0.475118 0.139507i
\(975\) 0 0
\(976\) 0.653409 + 4.54456i 0.0209151 + 0.145468i
\(977\) 9.66014 + 21.1528i 0.309055 + 0.676736i 0.998884 0.0472363i \(-0.0150414\pi\)
−0.689829 + 0.723973i \(0.742314\pi\)
\(978\) −6.61636 14.4878i −0.211568 0.463269i
\(979\) 5.53774 + 38.5158i 0.176987 + 1.23097i
\(980\) 0 0
\(981\) 5.01759 1.47330i 0.160199 0.0470387i
\(982\) −6.96412 + 48.4365i −0.222234 + 1.54567i
\(983\) 0.430697 0.497051i 0.0137371 0.0158535i −0.748839 0.662751i \(-0.769389\pi\)
0.762577 + 0.646898i \(0.223934\pi\)
\(984\) 10.0658 6.46891i 0.320887 0.206221i
\(985\) 0 0
\(986\) 53.8655 + 15.8163i 1.71543 + 0.503695i
\(987\) −0.425341 + 0.931366i −0.0135387 + 0.0296457i
\(988\) −30.5733 −0.972667
\(989\) −8.39371 7.85633i −0.266905 0.249817i
\(990\) 0 0
\(991\) 1.31140 2.87157i 0.0416581 0.0912185i −0.887659 0.460502i \(-0.847670\pi\)
0.929317 + 0.369283i \(0.120397\pi\)
\(992\) 11.2951 + 3.31654i 0.358620 + 0.105300i
\(993\) 9.07184 + 10.4695i 0.287886 + 0.332238i
\(994\) 0.313510 0.201480i 0.00994392 0.00639057i
\(995\) 0 0
\(996\) 1.76195 12.2546i 0.0558295 0.388303i
\(997\) −8.45136 + 2.48154i −0.267657 + 0.0785913i −0.412807 0.910818i \(-0.635452\pi\)
0.145150 + 0.989410i \(0.453634\pi\)
\(998\) 53.3443 + 34.2823i 1.68858 + 1.08519i
\(999\) −0.503637 3.50287i −0.0159344 0.110826i
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 575.2.k.a.351.1 10
5.2 odd 4 575.2.p.a.374.1 20
5.3 odd 4 575.2.p.a.374.2 20
5.4 even 2 115.2.g.a.6.1 10
23.4 even 11 inner 575.2.k.a.326.1 10
115.4 even 22 115.2.g.a.96.1 yes 10
115.27 odd 44 575.2.p.a.349.2 20
115.44 odd 22 2645.2.a.o.1.5 5
115.73 odd 44 575.2.p.a.349.1 20
115.94 even 22 2645.2.a.n.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.g.a.6.1 10 5.4 even 2
115.2.g.a.96.1 yes 10 115.4 even 22
575.2.k.a.326.1 10 23.4 even 11 inner
575.2.k.a.351.1 10 1.1 even 1 trivial
575.2.p.a.349.1 20 115.73 odd 44
575.2.p.a.349.2 20 115.27 odd 44
575.2.p.a.374.1 20 5.2 odd 4
575.2.p.a.374.2 20 5.3 odd 4
2645.2.a.n.1.5 5 115.94 even 22
2645.2.a.o.1.5 5 115.44 odd 22