Properties

Label 475.2.e.f.201.5
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.5
Root \(-0.928369 - 1.60798i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.f.26.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.740597 - 1.28275i) q^{2} +(-1.42837 + 2.47401i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(2.11569 + 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 - 4.46952i) q^{9} +O(q^{10})\) \(q+(0.740597 - 1.28275i) q^{2} +(-1.42837 + 2.47401i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(2.11569 + 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 - 4.46952i) q^{9} -5.59460 q^{11} +0.554026 q^{12} +(2.45326 + 4.24917i) q^{13} +(2.80346 - 4.85574i) q^{14} +(2.17513 - 3.76744i) q^{16} +(-0.875095 + 1.51571i) q^{17} -7.64438 q^{18} +(0.636061 + 4.31224i) q^{19} +(-5.40696 + 9.36514i) q^{21} +(-4.14335 + 7.17648i) q^{22} +(0.290768 + 0.503625i) q^{23} +(-3.82107 + 6.61830i) q^{24} +7.26750 q^{26} +6.17328 q^{27} +(-0.367065 - 0.635775i) q^{28} +(-0.832153 - 1.44133i) q^{29} +7.01680 q^{31} +(-0.546661 - 0.946844i) q^{32} +(7.99116 - 13.8411i) q^{33} +(1.29619 + 2.24506i) q^{34} +(-0.500449 + 0.866803i) q^{36} -2.36322 q^{37} +(6.00260 + 2.37773i) q^{38} -14.0166 q^{39} +(-0.417676 + 0.723435i) q^{41} +(8.00877 + 13.8716i) q^{42} +(-0.535664 + 0.927797i) q^{43} +(0.542499 + 0.939635i) q^{44} +0.861369 q^{46} +(1.93378 + 3.34941i) q^{47} +(6.21378 + 10.7626i) q^{48} +7.32934 q^{49} +(-2.49992 - 4.32999i) q^{51} +(0.475776 - 0.824069i) q^{52} +(-3.39842 - 5.88624i) q^{53} +(4.57192 - 7.91879i) q^{54} +10.1265 q^{56} +(-11.5771 - 4.58585i) q^{57} -2.46516 q^{58} +(0.204282 - 0.353827i) q^{59} +(-6.98016 - 12.0900i) q^{61} +(5.19662 - 9.00081i) q^{62} +(-9.76817 - 16.9190i) q^{63} +7.08110 q^{64} +(-11.8365 - 20.5013i) q^{66} +(0.390703 + 0.676717i) q^{67} +0.339426 q^{68} -1.66130 q^{69} +(-3.18919 + 5.52384i) q^{71} +(-6.90312 - 11.9565i) q^{72} +(1.44458 - 2.50208i) q^{73} +(-1.75019 + 3.03142i) q^{74} +(0.662580 - 0.524980i) q^{76} -21.1779 q^{77} +(-10.3807 + 17.9799i) q^{78} +(6.25135 - 10.8276i) q^{79} +(-1.07630 + 1.86420i) q^{81} +(0.618659 + 1.07155i) q^{82} +10.3903 q^{83} +2.09722 q^{84} +(0.793422 + 1.37425i) q^{86} +4.75449 q^{87} -14.9663 q^{88} +(-8.92106 - 15.4517i) q^{89} +(9.28659 + 16.0848i) q^{91} +(0.0563906 - 0.0976714i) q^{92} +(-10.0226 + 17.3596i) q^{93} +5.72861 q^{94} +3.12333 q^{96} +(5.49995 - 9.52619i) q^{97} +(5.42809 - 9.40172i) q^{98} +(14.4367 + 25.0052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.740597 1.28275i 0.523681 0.907043i −0.475939 0.879478i \(-0.657892\pi\)
0.999620 0.0275641i \(-0.00877505\pi\)
\(3\) −1.42837 + 2.47401i −0.824669 + 1.42837i 0.0775023 + 0.996992i \(0.475305\pi\)
−0.902172 + 0.431377i \(0.858028\pi\)
\(4\) −0.0969683 0.167954i −0.0484841 0.0839770i
\(5\) 0 0
\(6\) 2.11569 + 3.66449i 0.863728 + 1.49602i
\(7\) 3.78541 1.43075 0.715375 0.698740i \(-0.246256\pi\)
0.715375 + 0.698740i \(0.246256\pi\)
\(8\) 2.67513 0.945802
\(9\) −2.58048 4.46952i −0.860159 1.48984i
\(10\) 0 0
\(11\) −5.59460 −1.68684 −0.843418 0.537258i \(-0.819460\pi\)
−0.843418 + 0.537258i \(0.819460\pi\)
\(12\) 0.554026 0.159934
\(13\) 2.45326 + 4.24917i 0.680411 + 1.17851i 0.974855 + 0.222838i \(0.0715322\pi\)
−0.294444 + 0.955669i \(0.595134\pi\)
\(14\) 2.80346 4.85574i 0.749257 1.29775i
\(15\) 0 0
\(16\) 2.17513 3.76744i 0.543783 0.941859i
\(17\) −0.875095 + 1.51571i −0.212242 + 0.367614i −0.952416 0.304802i \(-0.901410\pi\)
0.740174 + 0.672415i \(0.234743\pi\)
\(18\) −7.64438 −1.80180
\(19\) 0.636061 + 4.31224i 0.145922 + 0.989296i
\(20\) 0 0
\(21\) −5.40696 + 9.36514i −1.17990 + 2.04364i
\(22\) −4.14335 + 7.17648i −0.883364 + 1.53003i
\(23\) 0.290768 + 0.503625i 0.0606294 + 0.105013i 0.894747 0.446574i \(-0.147356\pi\)
−0.834118 + 0.551587i \(0.814023\pi\)
\(24\) −3.82107 + 6.61830i −0.779974 + 1.35095i
\(25\) 0 0
\(26\) 7.26750 1.42527
\(27\) 6.17328 1.18805
\(28\) −0.367065 0.635775i −0.0693687 0.120150i
\(29\) −0.832153 1.44133i −0.154527 0.267649i 0.778360 0.627819i \(-0.216052\pi\)
−0.932887 + 0.360170i \(0.882719\pi\)
\(30\) 0 0
\(31\) 7.01680 1.26025 0.630127 0.776492i \(-0.283003\pi\)
0.630127 + 0.776492i \(0.283003\pi\)
\(32\) −0.546661 0.946844i −0.0966369 0.167380i
\(33\) 7.99116 13.8411i 1.39108 2.40942i
\(34\) 1.29619 + 2.24506i 0.222294 + 0.385025i
\(35\) 0 0
\(36\) −0.500449 + 0.866803i −0.0834082 + 0.144467i
\(37\) −2.36322 −0.388510 −0.194255 0.980951i \(-0.562229\pi\)
−0.194255 + 0.980951i \(0.562229\pi\)
\(38\) 6.00260 + 2.37773i 0.973750 + 0.385718i
\(39\) −14.0166 −2.24446
\(40\) 0 0
\(41\) −0.417676 + 0.723435i −0.0652300 + 0.112982i −0.896796 0.442444i \(-0.854111\pi\)
0.831566 + 0.555426i \(0.187445\pi\)
\(42\) 8.00877 + 13.8716i 1.23578 + 2.14043i
\(43\) −0.535664 + 0.927797i −0.0816880 + 0.141488i −0.903975 0.427585i \(-0.859364\pi\)
0.822287 + 0.569073i \(0.192698\pi\)
\(44\) 0.542499 + 0.939635i 0.0817848 + 0.141655i
\(45\) 0 0
\(46\) 0.861369 0.127002
\(47\) 1.93378 + 3.34941i 0.282071 + 0.488561i 0.971895 0.235416i \(-0.0756453\pi\)
−0.689824 + 0.723977i \(0.742312\pi\)
\(48\) 6.21378 + 10.7626i 0.896882 + 1.55345i
\(49\) 7.32934 1.04705
\(50\) 0 0
\(51\) −2.49992 4.32999i −0.350059 0.606319i
\(52\) 0.475776 0.824069i 0.0659783 0.114278i
\(53\) −3.39842 5.88624i −0.466809 0.808537i 0.532472 0.846448i \(-0.321263\pi\)
−0.999281 + 0.0379106i \(0.987930\pi\)
\(54\) 4.57192 7.91879i 0.622159 1.07761i
\(55\) 0 0
\(56\) 10.1265 1.35321
\(57\) −11.5771 4.58585i −1.53342 0.607411i
\(58\) −2.46516 −0.323691
\(59\) 0.204282 0.353827i 0.0265953 0.0460643i −0.852421 0.522855i \(-0.824867\pi\)
0.879017 + 0.476791i \(0.158200\pi\)
\(60\) 0 0
\(61\) −6.98016 12.0900i −0.893718 1.54796i −0.835384 0.549667i \(-0.814754\pi\)
−0.0583341 0.998297i \(-0.518579\pi\)
\(62\) 5.19662 9.00081i 0.659971 1.14310i
\(63\) −9.76817 16.9190i −1.23067 2.13159i
\(64\) 7.08110 0.885138
\(65\) 0 0
\(66\) −11.8365 20.5013i −1.45697 2.52354i
\(67\) 0.390703 + 0.676717i 0.0477319 + 0.0826742i 0.888904 0.458093i \(-0.151467\pi\)
−0.841172 + 0.540767i \(0.818134\pi\)
\(68\) 0.339426 0.0411614
\(69\) −1.66130 −0.199997
\(70\) 0 0
\(71\) −3.18919 + 5.52384i −0.378487 + 0.655559i −0.990842 0.135024i \(-0.956889\pi\)
0.612355 + 0.790583i \(0.290222\pi\)
\(72\) −6.90312 11.9565i −0.813540 1.40909i
\(73\) 1.44458 2.50208i 0.169075 0.292846i −0.769020 0.639225i \(-0.779255\pi\)
0.938095 + 0.346378i \(0.112589\pi\)
\(74\) −1.75019 + 3.03142i −0.203456 + 0.352395i
\(75\) 0 0
\(76\) 0.662580 0.524980i 0.0760032 0.0602193i
\(77\) −21.1779 −2.41344
\(78\) −10.3807 + 17.9799i −1.17538 + 2.03582i
\(79\) 6.25135 10.8276i 0.703331 1.21821i −0.263959 0.964534i \(-0.585028\pi\)
0.967290 0.253672i \(-0.0816383\pi\)
\(80\) 0 0
\(81\) −1.07630 + 1.86420i −0.119589 + 0.207133i
\(82\) 0.618659 + 1.07155i 0.0683194 + 0.118333i
\(83\) 10.3903 1.14048 0.570240 0.821478i \(-0.306850\pi\)
0.570240 + 0.821478i \(0.306850\pi\)
\(84\) 2.09722 0.228825
\(85\) 0 0
\(86\) 0.793422 + 1.37425i 0.0855569 + 0.148189i
\(87\) 4.75449 0.509735
\(88\) −14.9663 −1.59541
\(89\) −8.92106 15.4517i −0.945631 1.63788i −0.754483 0.656320i \(-0.772112\pi\)
−0.191148 0.981561i \(-0.561221\pi\)
\(90\) 0 0
\(91\) 9.28659 + 16.0848i 0.973499 + 1.68615i
\(92\) 0.0563906 0.0976714i 0.00587913 0.0101829i
\(93\) −10.0226 + 17.3596i −1.03929 + 1.80011i
\(94\) 5.72861 0.590861
\(95\) 0 0
\(96\) 3.12333 0.318774
\(97\) 5.49995 9.52619i 0.558435 0.967238i −0.439192 0.898393i \(-0.644735\pi\)
0.997627 0.0688448i \(-0.0219313\pi\)
\(98\) 5.42809 9.40172i 0.548319 0.949717i
\(99\) 14.4367 + 25.0052i 1.45095 + 2.51311i
\(100\) 0 0
\(101\) −2.57944 4.46772i −0.256664 0.444555i 0.708682 0.705528i \(-0.249290\pi\)
−0.965346 + 0.260973i \(0.915957\pi\)
\(102\) −7.40573 −0.733277
\(103\) 7.75851 0.764469 0.382235 0.924065i \(-0.375155\pi\)
0.382235 + 0.924065i \(0.375155\pi\)
\(104\) 6.56279 + 11.3671i 0.643534 + 1.11463i
\(105\) 0 0
\(106\) −10.0674 −0.977837
\(107\) 12.6521 1.22313 0.611564 0.791195i \(-0.290541\pi\)
0.611564 + 0.791195i \(0.290541\pi\)
\(108\) −0.598613 1.03683i −0.0576015 0.0997688i
\(109\) 4.09697 7.09616i 0.392418 0.679689i −0.600350 0.799738i \(-0.704972\pi\)
0.992768 + 0.120049i \(0.0383052\pi\)
\(110\) 0 0
\(111\) 3.37554 5.84661i 0.320392 0.554936i
\(112\) 8.23376 14.2613i 0.778018 1.34757i
\(113\) 12.5551 1.18108 0.590541 0.807007i \(-0.298914\pi\)
0.590541 + 0.807007i \(0.298914\pi\)
\(114\) −14.4564 + 11.4542i −1.35397 + 1.07279i
\(115\) 0 0
\(116\) −0.161385 + 0.279527i −0.0149842 + 0.0259534i
\(117\) 12.6612 21.9298i 1.17052 2.02741i
\(118\) −0.302581 0.524086i −0.0278549 0.0482461i
\(119\) −3.31260 + 5.73758i −0.303665 + 0.525963i
\(120\) 0 0
\(121\) 20.2996 1.84541
\(122\) −20.6779 −1.87209
\(123\) −1.19319 2.06667i −0.107586 0.186345i
\(124\) −0.680407 1.17850i −0.0611023 0.105832i
\(125\) 0 0
\(126\) −28.9371 −2.57792
\(127\) −4.07957 7.06602i −0.362003 0.627007i 0.626287 0.779592i \(-0.284574\pi\)
−0.988290 + 0.152585i \(0.951240\pi\)
\(128\) 6.33757 10.9770i 0.560167 0.970238i
\(129\) −1.53025 2.65047i −0.134731 0.233361i
\(130\) 0 0
\(131\) −9.62491 + 16.6708i −0.840932 + 1.45654i 0.0481757 + 0.998839i \(0.484659\pi\)
−0.889108 + 0.457698i \(0.848674\pi\)
\(132\) −3.09955 −0.269782
\(133\) 2.40775 + 16.3236i 0.208779 + 1.41544i
\(134\) 1.15741 0.0999853
\(135\) 0 0
\(136\) −2.34099 + 4.05472i −0.200739 + 0.347689i
\(137\) −0.785955 1.36131i −0.0671487 0.116305i 0.830496 0.557024i \(-0.188057\pi\)
−0.897645 + 0.440719i \(0.854724\pi\)
\(138\) −1.23035 + 2.13103i −0.104735 + 0.181406i
\(139\) 1.02459 + 1.77464i 0.0869047 + 0.150523i 0.906201 0.422847i \(-0.138969\pi\)
−0.819297 + 0.573370i \(0.805636\pi\)
\(140\) 0 0
\(141\) −11.0486 −0.930461
\(142\) 4.72381 + 8.18188i 0.396413 + 0.686608i
\(143\) −13.7250 23.7724i −1.14774 1.98795i
\(144\) −22.4515 −1.87096
\(145\) 0 0
\(146\) −2.13970 3.70607i −0.177083 0.306716i
\(147\) −10.4690 + 18.1328i −0.863468 + 1.49557i
\(148\) 0.229157 + 0.396911i 0.0188366 + 0.0326259i
\(149\) 0.737839 1.27797i 0.0604461 0.104696i −0.834219 0.551434i \(-0.814081\pi\)
0.894665 + 0.446738i \(0.147414\pi\)
\(150\) 0 0
\(151\) 6.42543 0.522894 0.261447 0.965218i \(-0.415800\pi\)
0.261447 + 0.965218i \(0.415800\pi\)
\(152\) 1.70155 + 11.5358i 0.138014 + 0.935678i
\(153\) 9.03266 0.730247
\(154\) −15.6843 + 27.1659i −1.26387 + 2.18909i
\(155\) 0 0
\(156\) 1.35917 + 2.35415i 0.108821 + 0.188483i
\(157\) −11.1445 + 19.3028i −0.889425 + 1.54053i −0.0488688 + 0.998805i \(0.515562\pi\)
−0.840556 + 0.541724i \(0.817772\pi\)
\(158\) −9.25946 16.0379i −0.736643 1.27590i
\(159\) 19.4168 1.53985
\(160\) 0 0
\(161\) 1.10068 + 1.90643i 0.0867455 + 0.150248i
\(162\) 1.59420 + 2.76124i 0.125253 + 0.216944i
\(163\) −15.0321 −1.17741 −0.588703 0.808350i \(-0.700361\pi\)
−0.588703 + 0.808350i \(0.700361\pi\)
\(164\) 0.162005 0.0126505
\(165\) 0 0
\(166\) 7.69500 13.3281i 0.597248 1.03446i
\(167\) −4.79928 8.31260i −0.371380 0.643249i 0.618398 0.785865i \(-0.287782\pi\)
−0.989778 + 0.142616i \(0.954449\pi\)
\(168\) −14.4643 + 25.0530i −1.11595 + 1.93288i
\(169\) −5.53695 + 9.59028i −0.425919 + 0.737714i
\(170\) 0 0
\(171\) 17.6323 13.9705i 1.34838 1.06835i
\(172\) 0.207770 0.0158423
\(173\) 4.41611 7.64894i 0.335751 0.581538i −0.647878 0.761744i \(-0.724343\pi\)
0.983629 + 0.180207i \(0.0576766\pi\)
\(174\) 3.52116 6.09883i 0.266938 0.462351i
\(175\) 0 0
\(176\) −12.1690 + 21.0773i −0.917272 + 1.58876i
\(177\) 0.583580 + 1.01079i 0.0438646 + 0.0759757i
\(178\) −26.4277 −1.98084
\(179\) 10.8178 0.808564 0.404282 0.914634i \(-0.367522\pi\)
0.404282 + 0.914634i \(0.367522\pi\)
\(180\) 0 0
\(181\) −5.37359 9.30733i −0.399416 0.691808i 0.594238 0.804289i \(-0.297454\pi\)
−0.993654 + 0.112481i \(0.964120\pi\)
\(182\) 27.5105 2.03921
\(183\) 39.8810 2.94809
\(184\) 0.777843 + 1.34726i 0.0573434 + 0.0993216i
\(185\) 0 0
\(186\) 14.8454 + 25.7130i 1.08852 + 1.88537i
\(187\) 4.89581 8.47979i 0.358017 0.620104i
\(188\) 0.375031 0.649573i 0.0273519 0.0473750i
\(189\) 23.3684 1.69980
\(190\) 0 0
\(191\) −6.28362 −0.454667 −0.227334 0.973817i \(-0.573001\pi\)
−0.227334 + 0.973817i \(0.573001\pi\)
\(192\) −10.1144 + 17.5187i −0.729946 + 1.26430i
\(193\) −8.91459 + 15.4405i −0.641686 + 1.11143i 0.343370 + 0.939200i \(0.388431\pi\)
−0.985056 + 0.172233i \(0.944902\pi\)
\(194\) −8.14649 14.1101i −0.584884 1.01305i
\(195\) 0 0
\(196\) −0.710713 1.23099i −0.0507652 0.0879279i
\(197\) −16.9925 −1.21066 −0.605332 0.795973i \(-0.706959\pi\)
−0.605332 + 0.795973i \(0.706959\pi\)
\(198\) 42.7672 3.03934
\(199\) −8.22212 14.2411i −0.582850 1.00953i −0.995140 0.0984735i \(-0.968604\pi\)
0.412289 0.911053i \(-0.364729\pi\)
\(200\) 0 0
\(201\) −2.23227 −0.157452
\(202\) −7.64131 −0.537641
\(203\) −3.15004 5.45603i −0.221090 0.382938i
\(204\) −0.484826 + 0.839743i −0.0339446 + 0.0587937i
\(205\) 0 0
\(206\) 5.74593 9.95225i 0.400338 0.693406i
\(207\) 1.50064 2.59919i 0.104302 0.180656i
\(208\) 21.3446 1.47998
\(209\) −3.55851 24.1253i −0.246147 1.66878i
\(210\) 0 0
\(211\) −7.79632 + 13.5036i −0.536721 + 0.929628i 0.462357 + 0.886694i \(0.347004\pi\)
−0.999078 + 0.0429343i \(0.986329\pi\)
\(212\) −0.659078 + 1.14156i −0.0452657 + 0.0784024i
\(213\) −9.11068 15.7802i −0.624253 1.08124i
\(214\) 9.37013 16.2295i 0.640529 1.10943i
\(215\) 0 0
\(216\) 16.5143 1.12366
\(217\) 26.5615 1.80311
\(218\) −6.06841 10.5108i −0.411004 0.711880i
\(219\) 4.12678 + 7.14779i 0.278862 + 0.483003i
\(220\) 0 0
\(221\) −8.58734 −0.577647
\(222\) −4.99984 8.65997i −0.335567 0.581219i
\(223\) −3.90313 + 6.76042i −0.261373 + 0.452711i −0.966607 0.256263i \(-0.917509\pi\)
0.705234 + 0.708974i \(0.250842\pi\)
\(224\) −2.06933 3.58419i −0.138263 0.239479i
\(225\) 0 0
\(226\) 9.29826 16.1051i 0.618511 1.07129i
\(227\) 16.8511 1.11845 0.559223 0.829017i \(-0.311100\pi\)
0.559223 + 0.829017i \(0.311100\pi\)
\(228\) 0.352394 + 2.38909i 0.0233379 + 0.158222i
\(229\) −0.251385 −0.0166120 −0.00830600 0.999966i \(-0.502644\pi\)
−0.00830600 + 0.999966i \(0.502644\pi\)
\(230\) 0 0
\(231\) 30.2498 52.3942i 1.99029 3.44729i
\(232\) −2.22612 3.85575i −0.146152 0.253142i
\(233\) −11.6014 + 20.0943i −0.760035 + 1.31642i 0.182797 + 0.983151i \(0.441485\pi\)
−0.942832 + 0.333269i \(0.891848\pi\)
\(234\) −18.7536 32.4822i −1.22596 2.12343i
\(235\) 0 0
\(236\) −0.0792355 −0.00515779
\(237\) 17.8585 + 30.9318i 1.16003 + 2.00923i
\(238\) 4.90660 + 8.49848i 0.318047 + 0.550874i
\(239\) −7.58778 −0.490813 −0.245406 0.969420i \(-0.578921\pi\)
−0.245406 + 0.969420i \(0.578921\pi\)
\(240\) 0 0
\(241\) 2.75808 + 4.77714i 0.177664 + 0.307723i 0.941080 0.338184i \(-0.109813\pi\)
−0.763416 + 0.645907i \(0.776479\pi\)
\(242\) 15.0338 26.0393i 0.966409 1.67387i
\(243\) 6.18523 + 10.7131i 0.396783 + 0.687248i
\(244\) −1.35371 + 2.34469i −0.0866623 + 0.150103i
\(245\) 0 0
\(246\) −3.53469 −0.225364
\(247\) −16.7630 + 13.2818i −1.06661 + 0.845099i
\(248\) 18.7708 1.19195
\(249\) −14.8411 + 25.7056i −0.940519 + 1.62903i
\(250\) 0 0
\(251\) 9.32933 + 16.1589i 0.588862 + 1.01994i 0.994382 + 0.105852i \(0.0337571\pi\)
−0.405520 + 0.914086i \(0.632910\pi\)
\(252\) −1.89441 + 3.28121i −0.119336 + 0.206697i
\(253\) −1.62673 2.81758i −0.102272 0.177140i
\(254\) −12.0853 −0.758297
\(255\) 0 0
\(256\) −2.30606 3.99422i −0.144129 0.249639i
\(257\) −0.346352 0.599899i −0.0216048 0.0374207i 0.855021 0.518594i \(-0.173544\pi\)
−0.876626 + 0.481173i \(0.840211\pi\)
\(258\) −4.53320 −0.282225
\(259\) −8.94574 −0.555861
\(260\) 0 0
\(261\) −4.29470 + 7.43865i −0.265836 + 0.460441i
\(262\) 14.2564 + 24.6927i 0.880761 + 1.52552i
\(263\) −5.81338 + 10.0691i −0.358468 + 0.620885i −0.987705 0.156328i \(-0.950034\pi\)
0.629237 + 0.777214i \(0.283368\pi\)
\(264\) 21.3774 37.0267i 1.31569 2.27884i
\(265\) 0 0
\(266\) 22.7223 + 9.00067i 1.39319 + 0.551866i
\(267\) 50.9703 3.11933
\(268\) 0.0757716 0.131240i 0.00462849 0.00801677i
\(269\) 11.8057 20.4481i 0.719809 1.24675i −0.241267 0.970459i \(-0.577563\pi\)
0.961075 0.276286i \(-0.0891038\pi\)
\(270\) 0 0
\(271\) 3.81995 6.61635i 0.232046 0.401915i −0.726364 0.687310i \(-0.758791\pi\)
0.958410 + 0.285395i \(0.0921248\pi\)
\(272\) 3.80689 + 6.59373i 0.230827 + 0.399804i
\(273\) −53.0587 −3.21126
\(274\) −2.32830 −0.140658
\(275\) 0 0
\(276\) 0.161093 + 0.279022i 0.00969667 + 0.0167951i
\(277\) −18.6537 −1.12079 −0.560397 0.828224i \(-0.689352\pi\)
−0.560397 + 0.828224i \(0.689352\pi\)
\(278\) 3.03524 0.182041
\(279\) −18.1067 31.3617i −1.08402 1.87758i
\(280\) 0 0
\(281\) −6.99489 12.1155i −0.417280 0.722750i 0.578385 0.815764i \(-0.303683\pi\)
−0.995665 + 0.0930139i \(0.970350\pi\)
\(282\) −8.18257 + 14.1726i −0.487265 + 0.843968i
\(283\) 12.3334 21.3620i 0.733143 1.26984i −0.222390 0.974958i \(-0.571386\pi\)
0.955533 0.294884i \(-0.0952809\pi\)
\(284\) 1.23700 0.0734025
\(285\) 0 0
\(286\) −40.6588 −2.40420
\(287\) −1.58107 + 2.73850i −0.0933278 + 0.161649i
\(288\) −2.82129 + 4.88662i −0.166246 + 0.287947i
\(289\) 6.96842 + 12.0697i 0.409907 + 0.709979i
\(290\) 0 0
\(291\) 15.7119 + 27.2138i 0.921049 + 1.59530i
\(292\) −0.560312 −0.0327898
\(293\) 10.5784 0.617994 0.308997 0.951063i \(-0.400007\pi\)
0.308997 + 0.951063i \(0.400007\pi\)
\(294\) 15.5066 + 26.8583i 0.904365 + 1.56641i
\(295\) 0 0
\(296\) −6.32191 −0.367454
\(297\) −34.5371 −2.00404
\(298\) −1.09288 1.89293i −0.0633090 0.109654i
\(299\) −1.42666 + 2.47105i −0.0825058 + 0.142904i
\(300\) 0 0
\(301\) −2.02771 + 3.51209i −0.116875 + 0.202434i
\(302\) 4.75866 8.24223i 0.273830 0.474287i
\(303\) 14.7376 0.846652
\(304\) 17.6296 + 6.98337i 1.01113 + 0.400524i
\(305\) 0 0
\(306\) 6.68956 11.5867i 0.382417 0.662365i
\(307\) 6.41222 11.1063i 0.365965 0.633870i −0.622966 0.782249i \(-0.714072\pi\)
0.988931 + 0.148379i \(0.0474057\pi\)
\(308\) 2.05358 + 3.55691i 0.117014 + 0.202674i
\(309\) −11.0820 + 19.1946i −0.630434 + 1.09194i
\(310\) 0 0
\(311\) 3.42706 0.194331 0.0971655 0.995268i \(-0.469022\pi\)
0.0971655 + 0.995268i \(0.469022\pi\)
\(312\) −37.4963 −2.12281
\(313\) −1.42224 2.46339i −0.0803896 0.139239i 0.823028 0.568001i \(-0.192283\pi\)
−0.903417 + 0.428762i \(0.858950\pi\)
\(314\) 16.5071 + 28.5912i 0.931551 + 1.61349i
\(315\) 0 0
\(316\) −2.42473 −0.136402
\(317\) −2.33072 4.03693i −0.130907 0.226737i 0.793120 0.609066i \(-0.208455\pi\)
−0.924026 + 0.382329i \(0.875122\pi\)
\(318\) 14.3800 24.9069i 0.806392 1.39671i
\(319\) 4.65556 + 8.06367i 0.260662 + 0.451479i
\(320\) 0 0
\(321\) −18.0719 + 31.3015i −1.00868 + 1.74708i
\(322\) 3.26063 0.181708
\(323\) −7.09272 2.80954i −0.394649 0.156327i
\(324\) 0.417467 0.0231926
\(325\) 0 0
\(326\) −11.1327 + 19.2825i −0.616585 + 1.06796i
\(327\) 11.7040 + 20.2719i 0.647231 + 1.12104i
\(328\) −1.11734 + 1.93528i −0.0616946 + 0.106858i
\(329\) 7.32016 + 12.6789i 0.403573 + 0.699010i
\(330\) 0 0
\(331\) −7.00260 −0.384898 −0.192449 0.981307i \(-0.561643\pi\)
−0.192449 + 0.981307i \(0.561643\pi\)
\(332\) −1.00753 1.74509i −0.0552952 0.0957741i
\(333\) 6.09822 + 10.5624i 0.334181 + 0.578818i
\(334\) −14.2173 −0.777938
\(335\) 0 0
\(336\) 23.5217 + 40.7408i 1.28321 + 2.22259i
\(337\) −6.76881 + 11.7239i −0.368721 + 0.638643i −0.989366 0.145449i \(-0.953537\pi\)
0.620645 + 0.784092i \(0.286871\pi\)
\(338\) 8.20130 + 14.2051i 0.446092 + 0.772654i
\(339\) −17.9333 + 31.0614i −0.974003 + 1.68702i
\(340\) 0 0
\(341\) −39.2562 −2.12584
\(342\) −4.86229 32.9644i −0.262923 1.78251i
\(343\) 1.24667 0.0673140
\(344\) −1.43297 + 2.48198i −0.0772606 + 0.133819i
\(345\) 0 0
\(346\) −6.54112 11.3296i −0.351653 0.609081i
\(347\) 10.9817 19.0208i 0.589527 1.02109i −0.404768 0.914420i \(-0.632648\pi\)
0.994294 0.106671i \(-0.0340190\pi\)
\(348\) −0.461034 0.798535i −0.0247140 0.0428060i
\(349\) −22.1930 −1.18796 −0.593981 0.804479i \(-0.702445\pi\)
−0.593981 + 0.804479i \(0.702445\pi\)
\(350\) 0 0
\(351\) 15.1447 + 26.2313i 0.808362 + 1.40012i
\(352\) 3.05835 + 5.29721i 0.163010 + 0.282342i
\(353\) 0.679013 0.0361402 0.0180701 0.999837i \(-0.494248\pi\)
0.0180701 + 0.999837i \(0.494248\pi\)
\(354\) 1.72879 0.0918843
\(355\) 0 0
\(356\) −1.73012 + 2.99666i −0.0916962 + 0.158822i
\(357\) −9.46322 16.3908i −0.500847 0.867492i
\(358\) 8.01166 13.8766i 0.423430 0.733402i
\(359\) 12.6627 21.9325i 0.668314 1.15755i −0.310062 0.950716i \(-0.600350\pi\)
0.978375 0.206837i \(-0.0663170\pi\)
\(360\) 0 0
\(361\) −18.1909 + 5.48570i −0.957413 + 0.288721i
\(362\) −15.9187 −0.836666
\(363\) −28.9953 + 50.2213i −1.52186 + 2.63593i
\(364\) 1.80101 3.11944i 0.0943985 0.163503i
\(365\) 0 0
\(366\) 29.5357 51.1574i 1.54386 2.67404i
\(367\) 5.83153 + 10.1005i 0.304404 + 0.527243i 0.977128 0.212650i \(-0.0682095\pi\)
−0.672725 + 0.739893i \(0.734876\pi\)
\(368\) 2.52984 0.131877
\(369\) 4.31121 0.224433
\(370\) 0 0
\(371\) −12.8644 22.2818i −0.667887 1.15681i
\(372\) 3.88749 0.201557
\(373\) 13.0913 0.677843 0.338921 0.940815i \(-0.389938\pi\)
0.338921 + 0.940815i \(0.389938\pi\)
\(374\) −7.25164 12.5602i −0.374974 0.649473i
\(375\) 0 0
\(376\) 5.17312 + 8.96010i 0.266783 + 0.462082i
\(377\) 4.08297 7.07192i 0.210284 0.364222i
\(378\) 17.3066 29.9759i 0.890155 1.54179i
\(379\) −32.7566 −1.68259 −0.841297 0.540573i \(-0.818208\pi\)
−0.841297 + 0.540573i \(0.818208\pi\)
\(380\) 0 0
\(381\) 23.3085 1.19413
\(382\) −4.65363 + 8.06033i −0.238101 + 0.412402i
\(383\) −12.8227 + 22.2096i −0.655211 + 1.13486i 0.326630 + 0.945152i \(0.394087\pi\)
−0.981841 + 0.189707i \(0.939246\pi\)
\(384\) 18.1048 + 31.3584i 0.923905 + 1.60025i
\(385\) 0 0
\(386\) 13.2042 + 22.8704i 0.672078 + 1.16407i
\(387\) 5.52907 0.281059
\(388\) −2.13328 −0.108301
\(389\) 9.27329 + 16.0618i 0.470174 + 0.814366i 0.999418 0.0341039i \(-0.0108577\pi\)
−0.529244 + 0.848470i \(0.677524\pi\)
\(390\) 0 0
\(391\) −1.01780 −0.0514723
\(392\) 19.6069 0.990300
\(393\) −27.4958 47.6242i −1.38698 2.40232i
\(394\) −12.5846 + 21.7971i −0.634002 + 1.09812i
\(395\) 0 0
\(396\) 2.79981 4.84942i 0.140696 0.243692i
\(397\) 7.69806 13.3334i 0.386355 0.669186i −0.605601 0.795768i \(-0.707067\pi\)
0.991956 + 0.126582i \(0.0404007\pi\)
\(398\) −24.3571 −1.22091
\(399\) −43.8239 17.3593i −2.19394 0.869054i
\(400\) 0 0
\(401\) 10.2956 17.8326i 0.514140 0.890517i −0.485725 0.874112i \(-0.661444\pi\)
0.999865 0.0164054i \(-0.00522222\pi\)
\(402\) −1.65321 + 2.86345i −0.0824548 + 0.142816i
\(403\) 17.2140 + 29.8155i 0.857491 + 1.48522i
\(404\) −0.500248 + 0.866455i −0.0248883 + 0.0431078i
\(405\) 0 0
\(406\) −9.33165 −0.463122
\(407\) 13.2212 0.655353
\(408\) −6.68761 11.5833i −0.331086 0.573458i
\(409\) 0.811919 + 1.40629i 0.0401468 + 0.0695363i 0.885401 0.464829i \(-0.153884\pi\)
−0.845254 + 0.534365i \(0.820551\pi\)
\(410\) 0 0
\(411\) 4.49054 0.221502
\(412\) −0.752330 1.30307i −0.0370646 0.0641978i
\(413\) 0.773292 1.33938i 0.0380512 0.0659066i
\(414\) −2.22274 3.84990i −0.109242 0.189212i
\(415\) 0 0
\(416\) 2.68220 4.64570i 0.131506 0.227774i
\(417\) −5.85398 −0.286671
\(418\) −33.5822 13.3024i −1.64256 0.650643i
\(419\) 16.8087 0.821161 0.410580 0.911824i \(-0.365326\pi\)
0.410580 + 0.911824i \(0.365326\pi\)
\(420\) 0 0
\(421\) −10.4718 + 18.1377i −0.510365 + 0.883977i 0.489563 + 0.871968i \(0.337156\pi\)
−0.999928 + 0.0120096i \(0.996177\pi\)
\(422\) 11.5479 + 20.0015i 0.562142 + 0.973658i
\(423\) 9.98016 17.2861i 0.485252 0.840481i
\(424\) −9.09122 15.7465i −0.441509 0.764716i
\(425\) 0 0
\(426\) −26.9894 −1.30764
\(427\) −26.4228 45.7656i −1.27869 2.21475i
\(428\) −1.22686 2.12498i −0.0593023 0.102715i
\(429\) 78.4175 3.78603
\(430\) 0 0
\(431\) −16.8908 29.2557i −0.813600 1.40920i −0.910329 0.413885i \(-0.864171\pi\)
0.0967292 0.995311i \(-0.469162\pi\)
\(432\) 13.4277 23.2575i 0.646041 1.11898i
\(433\) 7.51443 + 13.0154i 0.361120 + 0.625479i 0.988146 0.153520i \(-0.0490610\pi\)
−0.627025 + 0.778999i \(0.715728\pi\)
\(434\) 19.6713 34.0718i 0.944254 1.63550i
\(435\) 0 0
\(436\) −1.58910 −0.0761043
\(437\) −1.98681 + 1.57420i −0.0950419 + 0.0753042i
\(438\) 12.2251 0.584139
\(439\) −18.8607 + 32.6677i −0.900173 + 1.55915i −0.0729045 + 0.997339i \(0.523227\pi\)
−0.827269 + 0.561807i \(0.810106\pi\)
\(440\) 0 0
\(441\) −18.9132 32.7586i −0.900628 1.55993i
\(442\) −6.35976 + 11.0154i −0.302503 + 0.523950i
\(443\) −6.55722 11.3574i −0.311543 0.539608i 0.667154 0.744920i \(-0.267512\pi\)
−0.978697 + 0.205312i \(0.934179\pi\)
\(444\) −1.30928 −0.0621358
\(445\) 0 0
\(446\) 5.78129 + 10.0135i 0.273752 + 0.474153i
\(447\) 2.10781 + 3.65084i 0.0996961 + 0.172679i
\(448\) 26.8049 1.26641
\(449\) 11.6905 0.551711 0.275855 0.961199i \(-0.411039\pi\)
0.275855 + 0.961199i \(0.411039\pi\)
\(450\) 0 0
\(451\) 2.33673 4.04733i 0.110032 0.190581i
\(452\) −1.21744 2.10868i −0.0572638 0.0991838i
\(453\) −9.17789 + 15.8966i −0.431215 + 0.746886i
\(454\) 12.4799 21.6158i 0.585709 1.01448i
\(455\) 0 0
\(456\) −30.9701 12.2678i −1.45031 0.574490i
\(457\) −21.4290 −1.00240 −0.501202 0.865330i \(-0.667109\pi\)
−0.501202 + 0.865330i \(0.667109\pi\)
\(458\) −0.186175 + 0.322465i −0.00869939 + 0.0150678i
\(459\) −5.40221 + 9.35691i −0.252154 + 0.436743i
\(460\) 0 0
\(461\) 4.82920 8.36442i 0.224918 0.389570i −0.731377 0.681974i \(-0.761122\pi\)
0.956295 + 0.292404i \(0.0944551\pi\)
\(462\) −44.8058 77.6060i −2.08456 3.61056i
\(463\) 1.24981 0.0580838 0.0290419 0.999578i \(-0.490754\pi\)
0.0290419 + 0.999578i \(0.490754\pi\)
\(464\) −7.24017 −0.336116
\(465\) 0 0
\(466\) 17.1840 + 29.7635i 0.796032 + 1.37877i
\(467\) −31.3476 −1.45059 −0.725296 0.688437i \(-0.758297\pi\)
−0.725296 + 0.688437i \(0.758297\pi\)
\(468\) −4.91092 −0.227007
\(469\) 1.47897 + 2.56165i 0.0682925 + 0.118286i
\(470\) 0 0
\(471\) −31.8368 55.1430i −1.46696 2.54085i
\(472\) 0.546481 0.946533i 0.0251538 0.0435677i
\(473\) 2.99682 5.19065i 0.137794 0.238666i
\(474\) 52.9037 2.42995
\(475\) 0 0
\(476\) 1.28487 0.0588918
\(477\) −17.5391 + 30.3786i −0.803060 + 1.39094i
\(478\) −5.61949 + 9.73324i −0.257029 + 0.445188i
\(479\) −2.37730 4.11760i −0.108622 0.188138i 0.806591 0.591111i \(-0.201310\pi\)
−0.915212 + 0.402973i \(0.867977\pi\)
\(480\) 0 0
\(481\) −5.79758 10.0417i −0.264347 0.457862i
\(482\) 8.17052 0.372157
\(483\) −6.28870 −0.286146
\(484\) −1.96841 3.40939i −0.0894733 0.154972i
\(485\) 0 0
\(486\) 18.3230 0.831150
\(487\) 17.0491 0.772569 0.386285 0.922380i \(-0.373758\pi\)
0.386285 + 0.922380i \(0.373758\pi\)
\(488\) −18.6728 32.3423i −0.845280 1.46407i
\(489\) 21.4714 37.1896i 0.970970 1.68177i
\(490\) 0 0
\(491\) 2.14031 3.70713i 0.0965910 0.167301i −0.813680 0.581312i \(-0.802539\pi\)
0.910272 + 0.414012i \(0.135873\pi\)
\(492\) −0.231403 + 0.400802i −0.0104325 + 0.0180696i
\(493\) 2.91285 0.131188
\(494\) 4.62258 + 31.3392i 0.207980 + 1.41002i
\(495\) 0 0
\(496\) 15.2624 26.4353i 0.685304 1.18698i
\(497\) −12.0724 + 20.9100i −0.541521 + 0.937942i
\(498\) 21.9826 + 38.0750i 0.985064 + 1.70618i
\(499\) 2.41284 4.17916i 0.108013 0.187085i −0.806952 0.590617i \(-0.798884\pi\)
0.914965 + 0.403532i \(0.132218\pi\)
\(500\) 0 0
\(501\) 27.4206 1.22506
\(502\) 27.6371 1.23350
\(503\) 12.1368 + 21.0215i 0.541153 + 0.937304i 0.998838 + 0.0481900i \(0.0153453\pi\)
−0.457685 + 0.889114i \(0.651321\pi\)
\(504\) −26.1311 45.2604i −1.16397 2.01606i
\(505\) 0 0
\(506\) −4.81901 −0.214231
\(507\) −15.8176 27.3969i −0.702485 1.21674i
\(508\) −0.791177 + 1.37036i −0.0351028 + 0.0607998i
\(509\) 5.05690 + 8.75880i 0.224143 + 0.388227i 0.956062 0.293165i \(-0.0947084\pi\)
−0.731919 + 0.681392i \(0.761375\pi\)
\(510\) 0 0
\(511\) 5.46831 9.47140i 0.241904 0.418990i
\(512\) 18.5188 0.818423
\(513\) 3.92659 + 26.6207i 0.173363 + 1.17533i
\(514\) −1.02603 −0.0452562
\(515\) 0 0
\(516\) −0.296772 + 0.514024i −0.0130646 + 0.0226286i
\(517\) −10.8187 18.7386i −0.475807 0.824123i
\(518\) −6.62519 + 11.4752i −0.291094 + 0.504190i
\(519\) 12.6157 + 21.8510i 0.553767 + 0.959153i
\(520\) 0 0
\(521\) 29.3729 1.28685 0.643426 0.765508i \(-0.277513\pi\)
0.643426 + 0.765508i \(0.277513\pi\)
\(522\) 6.36129 + 11.0181i 0.278426 + 0.482248i
\(523\) 5.59998 + 9.69944i 0.244870 + 0.424127i 0.962095 0.272714i \(-0.0879214\pi\)
−0.717225 + 0.696842i \(0.754588\pi\)
\(524\) 3.73324 0.163087
\(525\) 0 0
\(526\) 8.61074 + 14.9142i 0.375446 + 0.650292i
\(527\) −6.14037 + 10.6354i −0.267479 + 0.463286i
\(528\) −34.7636 60.2124i −1.51289 2.62041i
\(529\) 11.3309 19.6257i 0.492648 0.853292i
\(530\) 0 0
\(531\) −2.10858 −0.0915046
\(532\) 2.50814 1.98726i 0.108742 0.0861588i
\(533\) −4.09866 −0.177533
\(534\) 37.7485 65.3822i 1.63354 2.82937i
\(535\) 0 0
\(536\) 1.04518 + 1.81031i 0.0451450 + 0.0781934i
\(537\) −15.4519 + 26.7634i −0.666798 + 1.15493i
\(538\) −17.4866 30.2877i −0.753901 1.30579i
\(539\) −41.0047 −1.76620
\(540\) 0 0
\(541\) −2.84691 4.93100i −0.122398 0.212000i 0.798315 0.602241i \(-0.205725\pi\)
−0.920713 + 0.390241i \(0.872392\pi\)
\(542\) −5.65809 9.80010i −0.243036 0.420950i
\(543\) 30.7019 1.31754
\(544\) 1.91352 0.0820415
\(545\) 0 0
\(546\) −39.2951 + 68.0612i −1.68168 + 2.91275i
\(547\) −5.99088 10.3765i −0.256151 0.443667i 0.709056 0.705152i \(-0.249121\pi\)
−0.965208 + 0.261485i \(0.915788\pi\)
\(548\) −0.152425 + 0.264009i −0.00651129 + 0.0112779i
\(549\) −36.0243 + 62.3959i −1.53748 + 2.66299i
\(550\) 0 0
\(551\) 5.68607 4.50522i 0.242235 0.191929i
\(552\) −4.44419 −0.189157
\(553\) 23.6639 40.9871i 1.00629 1.74295i
\(554\) −13.8149 + 23.9281i −0.586939 + 1.01661i
\(555\) 0 0
\(556\) 0.198706 0.344168i 0.00842700 0.0145960i
\(557\) 17.2786 + 29.9275i 0.732119 + 1.26807i 0.955976 + 0.293446i \(0.0948019\pi\)
−0.223857 + 0.974622i \(0.571865\pi\)
\(558\) −53.6390 −2.27072
\(559\) −5.25649 −0.222326
\(560\) 0 0
\(561\) 13.9860 + 24.2245i 0.590491 + 1.02276i
\(562\) −20.7216 −0.874087
\(563\) 24.8817 1.04864 0.524318 0.851522i \(-0.324320\pi\)
0.524318 + 0.851522i \(0.324320\pi\)
\(564\) 1.07137 + 1.85566i 0.0451126 + 0.0781374i
\(565\) 0 0
\(566\) −18.2681 31.6413i −0.767867 1.32998i
\(567\) −4.07422 + 7.05676i −0.171101 + 0.296356i
\(568\) −8.53150 + 14.7770i −0.357974 + 0.620029i
\(569\) −38.7345 −1.62384 −0.811918 0.583771i \(-0.801577\pi\)
−0.811918 + 0.583771i \(0.801577\pi\)
\(570\) 0 0
\(571\) −4.53514 −0.189790 −0.0948948 0.995487i \(-0.530251\pi\)
−0.0948948 + 0.995487i \(0.530251\pi\)
\(572\) −2.66178 + 4.61034i −0.111295 + 0.192768i
\(573\) 8.97534 15.5457i 0.374950 0.649433i
\(574\) 2.34188 + 4.05625i 0.0977481 + 0.169305i
\(575\) 0 0
\(576\) −18.2726 31.6491i −0.761359 1.31871i
\(577\) 21.9514 0.913847 0.456923 0.889506i \(-0.348951\pi\)
0.456923 + 0.889506i \(0.348951\pi\)
\(578\) 20.6432 0.858642
\(579\) −25.4666 44.1095i −1.05836 1.83313i
\(580\) 0 0
\(581\) 39.3314 1.63174
\(582\) 46.5448 1.92934
\(583\) 19.0128 + 32.9311i 0.787430 + 1.36387i
\(584\) 3.86443 6.69339i 0.159911 0.276974i
\(585\) 0 0
\(586\) 7.83430 13.5694i 0.323632 0.560547i
\(587\) −20.5232 + 35.5472i −0.847084 + 1.46719i 0.0367158 + 0.999326i \(0.488310\pi\)
−0.883799 + 0.467866i \(0.845023\pi\)
\(588\) 4.06064 0.167458
\(589\) 4.46311 + 30.2581i 0.183899 + 1.24676i
\(590\) 0 0
\(591\) 24.2715 42.0395i 0.998397 1.72927i
\(592\) −5.14030 + 8.90327i −0.211265 + 0.365922i
\(593\) −4.85982 8.41745i −0.199569 0.345663i 0.748820 0.662774i \(-0.230621\pi\)
−0.948389 + 0.317110i \(0.897287\pi\)
\(594\) −25.5780 + 44.3025i −1.04948 + 1.81775i
\(595\) 0 0
\(596\) −0.286188 −0.0117227
\(597\) 46.9769 1.92264
\(598\) 2.11316 + 3.66010i 0.0864135 + 0.149673i
\(599\) 15.2247 + 26.3700i 0.622065 + 1.07745i 0.989101 + 0.147241i \(0.0470392\pi\)
−0.367036 + 0.930207i \(0.619627\pi\)
\(600\) 0 0
\(601\) 24.5483 1.00135 0.500673 0.865637i \(-0.333086\pi\)
0.500673 + 0.865637i \(0.333086\pi\)
\(602\) 3.00343 + 5.20209i 0.122411 + 0.212021i
\(603\) 2.01640 3.49251i 0.0821142 0.142226i
\(604\) −0.623063 1.07918i −0.0253521 0.0439111i
\(605\) 0 0
\(606\) 10.9146 18.9047i 0.443376 0.767949i
\(607\) −39.0162 −1.58362 −0.791810 0.610767i \(-0.790861\pi\)
−0.791810 + 0.610767i \(0.790861\pi\)
\(608\) 3.73531 2.95958i 0.151487 0.120027i
\(609\) 17.9977 0.729303
\(610\) 0 0
\(611\) −9.48813 + 16.4339i −0.383849 + 0.664845i
\(612\) −0.875881 1.51707i −0.0354054 0.0613239i
\(613\) 2.48708 4.30775i 0.100452 0.173988i −0.811419 0.584465i \(-0.801304\pi\)
0.911871 + 0.410477i \(0.134638\pi\)
\(614\) −9.49775 16.4506i −0.383298 0.663891i
\(615\) 0 0
\(616\) −56.6536 −2.28264
\(617\) −19.3210 33.4649i −0.777834 1.34725i −0.933188 0.359389i \(-0.882985\pi\)
0.155354 0.987859i \(-0.450348\pi\)
\(618\) 16.4146 + 28.4310i 0.660293 + 1.14366i
\(619\) −27.9053 −1.12161 −0.560804 0.827949i \(-0.689508\pi\)
−0.560804 + 0.827949i \(0.689508\pi\)
\(620\) 0 0
\(621\) 1.79500 + 3.10902i 0.0720307 + 0.124761i
\(622\) 2.53807 4.39607i 0.101767 0.176266i
\(623\) −33.7699 58.4912i −1.35296 2.34340i
\(624\) −30.4880 + 52.8068i −1.22050 + 2.11396i
\(625\) 0 0
\(626\) −4.21322 −0.168394
\(627\) 64.7690 + 25.6560i 2.58662 + 1.02460i
\(628\) 4.32264 0.172492
\(629\) 2.06804 3.58195i 0.0824581 0.142822i
\(630\) 0 0
\(631\) 6.62012 + 11.4664i 0.263543 + 0.456469i 0.967181 0.254089i \(-0.0817757\pi\)
−0.703638 + 0.710559i \(0.748442\pi\)
\(632\) 16.7232 28.9654i 0.665212 1.15218i
\(633\) −22.2721 38.5763i −0.885235 1.53327i
\(634\) −6.90451 −0.274213
\(635\) 0 0
\(636\) −1.88281 3.26113i −0.0746584 0.129312i
\(637\) 17.9808 + 31.1436i 0.712423 + 1.23395i
\(638\) 13.7916 0.546014
\(639\) 32.9185 1.30224
\(640\) 0 0
\(641\) −18.7555 + 32.4854i −0.740796 + 1.28310i 0.211337 + 0.977413i \(0.432218\pi\)
−0.952133 + 0.305684i \(0.901115\pi\)
\(642\) 26.7680 + 46.3636i 1.05645 + 1.82982i
\(643\) −12.1969 + 21.1257i −0.481000 + 0.833117i −0.999762 0.0218020i \(-0.993060\pi\)
0.518762 + 0.854919i \(0.326393\pi\)
\(644\) 0.213462 0.369726i 0.00841157 0.0145693i
\(645\) 0 0
\(646\) −8.85679 + 7.01746i −0.348466 + 0.276098i
\(647\) −8.05266 −0.316583 −0.158291 0.987392i \(-0.550599\pi\)
−0.158291 + 0.987392i \(0.550599\pi\)
\(648\) −2.87923 + 4.98698i −0.113107 + 0.195907i
\(649\) −1.14288 + 1.97952i −0.0448618 + 0.0777030i
\(650\) 0 0
\(651\) −37.9396 + 65.7133i −1.48697 + 2.57551i
\(652\) 1.45764 + 2.52470i 0.0570855 + 0.0988750i
\(653\) 19.9890 0.782228 0.391114 0.920342i \(-0.372090\pi\)
0.391114 + 0.920342i \(0.372090\pi\)
\(654\) 34.6717 1.35577
\(655\) 0 0
\(656\) 1.81700 + 3.14713i 0.0709419 + 0.122875i
\(657\) −14.9108 −0.581725
\(658\) 21.6852 0.845375
\(659\) 16.2197 + 28.0933i 0.631829 + 1.09436i 0.987178 + 0.159626i \(0.0510287\pi\)
−0.355349 + 0.934734i \(0.615638\pi\)
\(660\) 0 0
\(661\) 17.7771 + 30.7908i 0.691448 + 1.19762i 0.971363 + 0.237599i \(0.0763603\pi\)
−0.279915 + 0.960025i \(0.590306\pi\)
\(662\) −5.18610 + 8.98260i −0.201564 + 0.349118i
\(663\) 12.2659 21.2451i 0.476368 0.825093i
\(664\) 27.7953 1.07867
\(665\) 0 0
\(666\) 18.0653 0.700017
\(667\) 0.483927 0.838187i 0.0187377 0.0324547i
\(668\) −0.930757 + 1.61212i −0.0360121 + 0.0623747i
\(669\) −11.1502 19.3127i −0.431092 0.746674i
\(670\) 0 0
\(671\) 39.0512 + 67.6387i 1.50755 + 2.61116i
\(672\) 11.8231 0.456086
\(673\) −27.5963 −1.06376 −0.531880 0.846820i \(-0.678514\pi\)
−0.531880 + 0.846820i \(0.678514\pi\)
\(674\) 10.0259 + 17.3654i 0.386184 + 0.668891i
\(675\) 0 0
\(676\) 2.14763 0.0826013
\(677\) −21.2114 −0.815221 −0.407610 0.913156i \(-0.633638\pi\)
−0.407610 + 0.913156i \(0.633638\pi\)
\(678\) 26.5627 + 46.0079i 1.02013 + 1.76692i
\(679\) 20.8196 36.0605i 0.798981 1.38388i
\(680\) 0 0
\(681\) −24.0696 + 41.6897i −0.922348 + 1.59755i
\(682\) −29.0730 + 50.3559i −1.11326 + 1.92823i
\(683\) −19.3626 −0.740891 −0.370446 0.928854i \(-0.620795\pi\)
−0.370446 + 0.928854i \(0.620795\pi\)
\(684\) −4.05618 1.60672i −0.155092 0.0614344i
\(685\) 0 0
\(686\) 0.923282 1.59917i 0.0352511 0.0610567i
\(687\) 0.359071 0.621929i 0.0136994 0.0237281i
\(688\) 2.33028 + 4.03616i 0.0888410 + 0.153877i
\(689\) 16.6744 28.8809i 0.635244 1.10028i
\(690\) 0 0
\(691\) −1.28081 −0.0487241 −0.0243621 0.999703i \(-0.507755\pi\)
−0.0243621 + 0.999703i \(0.507755\pi\)
\(692\) −1.71289 −0.0651144
\(693\) 54.6490 + 94.6548i 2.07594 + 3.59564i
\(694\) −16.2660 28.1735i −0.617448 1.06945i
\(695\) 0 0
\(696\) 12.7189 0.482108
\(697\) −0.731012 1.26615i −0.0276891 0.0479588i
\(698\) −16.4361 + 28.4681i −0.622114 + 1.07753i
\(699\) −33.1423 57.4041i −1.25356 2.17122i
\(700\) 0 0
\(701\) 18.5649 32.1553i 0.701185 1.21449i −0.266866 0.963734i \(-0.585988\pi\)
0.968051 0.250754i \(-0.0806787\pi\)
\(702\) 44.8644 1.69330
\(703\) −1.50315 10.1908i −0.0566924 0.384352i
\(704\) −39.6159 −1.49308
\(705\) 0 0
\(706\) 0.502875 0.871005i 0.0189260 0.0327807i
\(707\) −9.76425 16.9122i −0.367222 0.636048i
\(708\) 0.113178 0.196029i 0.00425347 0.00736723i
\(709\) −6.57886 11.3949i −0.247074 0.427945i 0.715638 0.698471i \(-0.246136\pi\)
−0.962713 + 0.270526i \(0.912802\pi\)
\(710\) 0 0
\(711\) −64.5258 −2.41991
\(712\) −23.8650 41.3354i −0.894379 1.54911i
\(713\) 2.04026 + 3.53384i 0.0764084 + 0.132343i
\(714\) −28.0337 −1.04914
\(715\) 0 0
\(716\) −1.04899 1.81690i −0.0392025 0.0679007i
\(717\) 10.8382 18.7722i 0.404758 0.701062i
\(718\) −18.7560 32.4863i −0.699967 1.21238i
\(719\) −7.27853 + 12.6068i −0.271443 + 0.470153i −0.969232 0.246150i \(-0.920834\pi\)
0.697788 + 0.716304i \(0.254168\pi\)
\(720\) 0 0
\(721\) 29.3692 1.09376
\(722\) −6.43530 + 27.3970i −0.239497 + 1.01961i
\(723\) −15.7583 −0.586056
\(724\) −1.04214 + 1.80503i −0.0387306 + 0.0670834i
\(725\) 0 0
\(726\) 42.9476 + 74.3874i 1.59394 + 2.76078i
\(727\) 4.48581 7.76966i 0.166370 0.288161i −0.770771 0.637112i \(-0.780129\pi\)
0.937141 + 0.348951i \(0.113462\pi\)
\(728\) 24.8428 + 43.0291i 0.920737 + 1.59476i
\(729\) −41.7969 −1.54803
\(730\) 0 0
\(731\) −0.937514 1.62382i −0.0346752 0.0600592i
\(732\) −3.86719 6.69817i −0.142935 0.247571i
\(733\) −24.7325 −0.913516 −0.456758 0.889591i \(-0.650990\pi\)
−0.456758 + 0.889591i \(0.650990\pi\)
\(734\) 17.2753 0.637642
\(735\) 0 0
\(736\) 0.317903 0.550624i 0.0117181 0.0202963i
\(737\) −2.18583 3.78596i −0.0805159 0.139458i
\(738\) 3.19287 5.53021i 0.117531 0.203570i
\(739\) 0.784588 1.35895i 0.0288615 0.0499896i −0.851234 0.524787i \(-0.824145\pi\)
0.880095 + 0.474797i \(0.157478\pi\)
\(740\) 0 0
\(741\) −8.91543 60.4431i −0.327517 2.22043i
\(742\) −38.1094 −1.39904
\(743\) −12.1463 + 21.0380i −0.445604 + 0.771808i −0.998094 0.0617109i \(-0.980344\pi\)
0.552490 + 0.833519i \(0.313678\pi\)
\(744\) −26.8117 + 46.4392i −0.982965 + 1.70254i
\(745\) 0 0
\(746\) 9.69539 16.7929i 0.354974 0.614832i
\(747\) −26.8119 46.4395i −0.980994 1.69913i
\(748\) −1.89895 −0.0694326
\(749\) 47.8935 1.74999
\(750\) 0 0
\(751\) −17.4771 30.2712i −0.637748 1.10461i −0.985926 0.167184i \(-0.946533\pi\)
0.348178 0.937429i \(-0.386801\pi\)
\(752\) 16.8249 0.613541
\(753\) −53.3029 −1.94247
\(754\) −6.04768 10.4749i −0.220243 0.381473i
\(755\) 0 0
\(756\) −2.26600 3.92482i −0.0824135 0.142744i
\(757\) −1.61043 + 2.78935i −0.0585321 + 0.101381i −0.893807 0.448452i \(-0.851975\pi\)
0.835275 + 0.549833i \(0.185309\pi\)
\(758\) −24.2595 + 42.0186i −0.881143 + 1.52619i
\(759\) 9.29430 0.337362
\(760\) 0 0
\(761\) 3.72402 0.134996 0.0674979 0.997719i \(-0.478498\pi\)
0.0674979 + 0.997719i \(0.478498\pi\)
\(762\) 17.2622 29.8990i 0.625344 1.08313i
\(763\) 15.5087 26.8619i 0.561453 0.972465i
\(764\) 0.609312 + 1.05536i 0.0220441 + 0.0381816i
\(765\) 0 0
\(766\) 18.9930 + 32.8968i 0.686244 + 1.18861i
\(767\) 2.00463 0.0723829
\(768\) 13.1756 0.475435
\(769\) 16.1032 + 27.8915i 0.580695 + 1.00579i 0.995397 + 0.0958365i \(0.0305526\pi\)
−0.414702 + 0.909957i \(0.636114\pi\)
\(770\) 0 0
\(771\) 1.97887 0.0712674
\(772\) 3.45773 0.124446
\(773\) 10.3416 + 17.9122i 0.371963 + 0.644259i 0.989867 0.141994i \(-0.0453515\pi\)
−0.617904 + 0.786253i \(0.712018\pi\)
\(774\) 4.09482 7.09243i 0.147185 0.254932i
\(775\) 0 0
\(776\) 14.7131 25.4838i 0.528169 0.914815i
\(777\) 12.7778 22.1318i 0.458402 0.793975i
\(778\) 27.4711 0.984886
\(779\) −3.38530 1.34097i −0.121291 0.0480452i
\(780\) 0 0
\(781\) 17.8422 30.9037i 0.638446 1.10582i
\(782\) −0.753780 + 1.30558i −0.0269551 + 0.0466876i
\(783\) −5.13712 8.89775i −0.183586 0.317980i
\(784\) 15.9423 27.6128i 0.569367 0.986172i
\(785\) 0 0
\(786\) −81.4534 −2.90535
\(787\) 46.0227 1.64053 0.820266 0.571982i \(-0.193825\pi\)
0.820266 + 0.571982i \(0.193825\pi\)
\(788\) 1.64773 + 2.85395i 0.0586980 + 0.101668i
\(789\) −16.6073 28.7647i −0.591236 1.02405i
\(790\) 0 0
\(791\) 47.5261 1.68983
\(792\) 38.6202 + 66.8921i 1.37231 + 2.37691i
\(793\) 34.2483 59.3197i 1.21619 2.10651i
\(794\) −11.4023 19.7494i −0.404654 0.700880i
\(795\) 0 0
\(796\) −1.59457 + 2.76187i −0.0565180 + 0.0978920i
\(797\) 25.0847 0.888546 0.444273 0.895891i \(-0.353462\pi\)
0.444273 + 0.895891i \(0.353462\pi\)
\(798\) −54.7236 + 43.3589i −1.93719 + 1.53489i
\(799\) −6.76897 −0.239469
\(800\) 0 0
\(801\) −46.0412 + 79.7457i −1.62679 + 2.81768i
\(802\) −15.2499 26.4135i −0.538491 0.932694i
\(803\) −8.08183 + 13.9981i −0.285201 + 0.493983i
\(804\) 0.216460 + 0.374919i 0.00763394 + 0.0132224i
\(805\) 0 0
\(806\) 50.9946 1.79621
\(807\) 33.7259 + 58.4150i 1.18721 + 2.05631i
\(808\) −6.90034 11.9517i −0.242753 0.420461i
\(809\) 27.6272 0.971319 0.485660 0.874148i \(-0.338579\pi\)
0.485660 + 0.874148i \(0.338579\pi\)
\(810\) 0 0
\(811\) 19.2254 + 33.2993i 0.675094 + 1.16930i 0.976441 + 0.215783i \(0.0692304\pi\)
−0.301347 + 0.953514i \(0.597436\pi\)
\(812\) −0.610908 + 1.05812i −0.0214387 + 0.0371329i
\(813\) 10.9126 + 18.9012i 0.382722 + 0.662893i
\(814\) 9.79162 16.9596i 0.343196 0.594433i
\(815\) 0 0
\(816\) −21.7506 −0.761423
\(817\) −4.34160 1.71978i −0.151893 0.0601674i
\(818\) 2.40522 0.0840966
\(819\) 47.9277 83.0132i 1.67473 2.90071i
\(820\) 0 0
\(821\) −26.3339 45.6117i −0.919060 1.59186i −0.800845 0.598871i \(-0.795616\pi\)
−0.118215 0.992988i \(-0.537717\pi\)
\(822\) 3.32568 5.76024i 0.115996 0.200912i
\(823\) −2.33597 4.04602i −0.0814269 0.141035i 0.822436 0.568857i \(-0.192614\pi\)
−0.903863 + 0.427822i \(0.859281\pi\)
\(824\) 20.7550 0.723036
\(825\) 0 0
\(826\) −1.14540 1.98388i −0.0398534 0.0690281i
\(827\) −13.7124 23.7506i −0.476827 0.825888i 0.522821 0.852443i \(-0.324880\pi\)
−0.999647 + 0.0265546i \(0.991546\pi\)
\(828\) −0.582059 −0.0202279
\(829\) 0.156181 0.00542438 0.00271219 0.999996i \(-0.499137\pi\)
0.00271219 + 0.999996i \(0.499137\pi\)
\(830\) 0 0
\(831\) 26.6444 46.1495i 0.924285 1.60091i
\(832\) 17.3718 + 30.0888i 0.602258 + 1.04314i
\(833\) −6.41387 + 11.1091i −0.222227 + 0.384909i
\(834\) −4.33544 + 7.50920i −0.150124 + 0.260022i
\(835\) 0 0
\(836\) −3.70687 + 2.93705i −0.128205 + 0.101580i
\(837\) 43.3167 1.49724
\(838\) 12.4485 21.5615i 0.430027 0.744828i
\(839\) 14.5946 25.2786i 0.503862 0.872715i −0.496128 0.868249i \(-0.665245\pi\)
0.999990 0.00446519i \(-0.00142132\pi\)
\(840\) 0 0
\(841\) 13.1150 22.7159i 0.452243 0.783308i
\(842\) 15.5108 + 26.8655i 0.534537 + 0.925845i
\(843\) 39.9651 1.37647
\(844\) 3.02398 0.104090
\(845\) 0 0
\(846\) −14.7826 25.6041i −0.508235 0.880288i
\(847\) 76.8421 2.64033
\(848\) −29.5680 −1.01537
\(849\) 35.2332 + 61.0258i 1.20920 + 2.09440i
\(850\) 0 0
\(851\) −0.687148 1.19018i −0.0235551 0.0407987i
\(852\) −1.76689 + 3.06035i −0.0605328 + 0.104846i
\(853\) 22.8832 39.6348i 0.783505 1.35707i −0.146384 0.989228i \(-0.546763\pi\)
0.929888 0.367842i \(-0.119903\pi\)
\(854\) −78.2745 −2.67850
\(855\) 0 0
\(856\) 33.8461 1.15684
\(857\) −7.45807 + 12.9177i −0.254763 + 0.441262i −0.964831 0.262871i \(-0.915331\pi\)
0.710068 + 0.704133i \(0.248664\pi\)
\(858\) 58.0757 100.590i 1.98267 3.43409i
\(859\) −24.6100 42.6258i −0.839682 1.45437i −0.890161 0.455647i \(-0.849408\pi\)
0.0504787 0.998725i \(-0.483925\pi\)
\(860\) 0 0
\(861\) −4.51671 7.82318i −0.153929 0.266613i
\(862\) −50.0370 −1.70427
\(863\) 20.9577 0.713407 0.356704 0.934218i \(-0.383901\pi\)
0.356704 + 0.934218i \(0.383901\pi\)
\(864\) −3.37469 5.84514i −0.114809 0.198856i
\(865\) 0 0
\(866\) 22.2607 0.756448
\(867\) −39.8139 −1.35215
\(868\) −2.57562 4.46110i −0.0874222 0.151420i
\(869\) −34.9738 + 60.5764i −1.18640 + 2.05491i
\(870\) 0 0
\(871\) −1.91699 + 3.32032i −0.0649547 + 0.112505i
\(872\) 10.9599 18.9831i 0.371150 0.642851i
\(873\) −56.7700 −1.92137
\(874\) 0.547883 + 3.71443i 0.0185324 + 0.125642i
\(875\) 0 0
\(876\) 0.800333 1.38622i 0.0270407 0.0468359i
\(877\) 13.1009 22.6914i 0.442385 0.766233i −0.555481 0.831529i \(-0.687466\pi\)
0.997866 + 0.0652963i \(0.0207993\pi\)
\(878\) 27.9364 + 48.3873i 0.942808 + 1.63299i
\(879\) −15.1098 + 26.1709i −0.509641 + 0.882724i
\(880\) 0 0
\(881\) −45.3499 −1.52788 −0.763938 0.645289i \(-0.776737\pi\)
−0.763938 + 0.645289i \(0.776737\pi\)
\(882\) −56.0282 −1.88657
\(883\) 21.6585 + 37.5136i 0.728867 + 1.26243i 0.957362 + 0.288890i \(0.0932861\pi\)
−0.228495 + 0.973545i \(0.573381\pi\)
\(884\) 0.832699 + 1.44228i 0.0280067 + 0.0485090i
\(885\) 0 0
\(886\) −19.4250 −0.652597
\(887\) −19.5073 33.7877i −0.654992 1.13448i −0.981896 0.189422i \(-0.939339\pi\)
0.326904 0.945058i \(-0.393995\pi\)
\(888\) 9.03002 15.6405i 0.303028 0.524859i
\(889\) −15.4428 26.7478i −0.517936 0.897091i
\(890\) 0 0
\(891\) 6.02145 10.4295i 0.201726 0.349400i
\(892\) 1.51392 0.0506898
\(893\) −13.2135 + 10.4694i −0.442171 + 0.350344i
\(894\) 6.24416 0.208836
\(895\) 0 0
\(896\) 23.9903 41.5524i 0.801459 1.38817i
\(897\) −4.07559 7.05913i −0.136080 0.235698i
\(898\) 8.65798 14.9961i 0.288921 0.500425i
\(899\) −5.83905 10.1135i −0.194743 0.337305i
\(900\) 0 0
\(901\) 11.8958 0.396306
\(902\) −3.46115 5.99488i −0.115244 0.199608i
\(903\) −5.79263 10.0331i −0.192767 0.333882i
\(904\) 33.5865 1.11707
\(905\) 0 0
\(906\) 13.5942 + 23.5459i 0.451638 + 0.782260i
\(907\) 25.0804 43.4405i 0.832780 1.44242i −0.0630443 0.998011i \(-0.520081\pi\)
0.895825 0.444407i \(-0.146586\pi\)
\(908\) −1.63402 2.83021i −0.0542269 0.0939237i
\(909\) −13.3124 + 23.0577i −0.441544 + 0.764776i
\(910\) 0 0
\(911\) −50.4028 −1.66992 −0.834959 0.550312i \(-0.814509\pi\)
−0.834959 + 0.550312i \(0.814509\pi\)
\(912\) −42.4585 + 33.6410i −1.40594 + 1.11396i
\(913\) −58.1294 −1.92380
\(914\) −15.8702 + 27.4880i −0.524940 + 0.909223i
\(915\) 0 0
\(916\) 0.0243764 + 0.0422211i 0.000805418 + 0.00139503i
\(917\) −36.4342 + 63.1059i −1.20316 + 2.08394i
\(918\) 8.00173 + 13.8594i 0.264096 + 0.457428i
\(919\) 48.7246 1.60728 0.803638 0.595118i \(-0.202895\pi\)
0.803638 + 0.595118i \(0.202895\pi\)
\(920\) 0 0
\(921\) 18.3180 + 31.7278i 0.603600 + 1.04547i
\(922\) −7.15299 12.3893i −0.235571 0.408021i
\(923\) −31.2956 −1.03011
\(924\) −11.7331 −0.385990
\(925\) 0 0
\(926\) 0.925608 1.60320i 0.0304174 0.0526844i
\(927\) −20.0207 34.6768i −0.657565 1.13894i
\(928\) −0.909811 + 1.57584i −0.0298660 + 0.0517294i
\(929\) −4.01832 + 6.95993i −0.131837 + 0.228348i −0.924385 0.381462i \(-0.875421\pi\)
0.792548 + 0.609810i \(0.208754\pi\)
\(930\) 0 0
\(931\) 4.66191 + 31.6059i 0.152788 + 1.03584i
\(932\) 4.49989 0.147399
\(933\) −4.89511 + 8.47858i −0.160259 + 0.277576i
\(934\) −23.2159 + 40.2111i −0.759648 + 1.31575i
\(935\) 0 0
\(936\) 33.8702 58.6650i 1.10708 1.91752i
\(937\) 12.7713 + 22.1206i 0.417221 + 0.722647i 0.995659 0.0930789i \(-0.0296709\pi\)
−0.578438 + 0.815726i \(0.696338\pi\)
\(938\) 4.38129 0.143054
\(939\) 8.12592 0.265179
\(940\) 0 0
\(941\) −4.30747 7.46075i −0.140419 0.243214i 0.787235 0.616653i \(-0.211512\pi\)
−0.927655 + 0.373439i \(0.878178\pi\)
\(942\) −94.3130 −3.07288
\(943\) −0.485787 −0.0158194
\(944\) −0.888680 1.53924i −0.0289241 0.0500980i
\(945\) 0 0
\(946\) −4.43888 7.68837i −0.144320 0.249970i
\(947\) −19.2138 + 33.2793i −0.624364 + 1.08143i 0.364299 + 0.931282i \(0.381309\pi\)
−0.988663 + 0.150149i \(0.952025\pi\)
\(948\) 3.46341 5.99880i 0.112486 0.194832i
\(949\) 14.1757 0.460162
\(950\) 0 0
\(951\) 13.3165 0.431819
\(952\) −8.86163 + 15.3488i −0.287207 + 0.497457i
\(953\) 4.44520 7.69932i 0.143994 0.249405i −0.785003 0.619492i \(-0.787339\pi\)
0.928997 + 0.370087i \(0.120672\pi\)
\(954\) 25.9788 + 44.9966i 0.841095 + 1.45682i
\(955\) 0 0
\(956\) 0.735774 + 1.27440i 0.0237966 + 0.0412170i
\(957\) −26.5995 −0.859838
\(958\) −7.04248 −0.227532
\(959\) −2.97516 5.15313i −0.0960730 0.166403i
\(960\) 0 0
\(961\) 18.2354 0.588239
\(962\) −17.1747 −0.553734
\(963\) −32.6485 56.5489i −1.05208 1.82226i
\(964\) 0.534893 0.926463i 0.0172278 0.0298394i
\(965\) 0 0
\(966\) −4.65739 + 8.06684i −0.149849 + 0.259546i
\(967\) −30.8149 + 53.3729i −0.990939 + 1.71636i −0.379150 + 0.925335i \(0.623784\pi\)
−0.611789 + 0.791021i \(0.709550\pi\)
\(968\) 54.3040 1.74540
\(969\) 17.0818 13.5344i 0.548748 0.434787i
\(970\) 0 0
\(971\) −2.92998 + 5.07488i −0.0940277 + 0.162861i −0.909202 0.416354i \(-0.863308\pi\)
0.815175 + 0.579215i \(0.196641\pi\)
\(972\) 1.19954 2.07767i 0.0384753 0.0666412i
\(973\) 3.87850 + 6.71776i 0.124339 + 0.215361i
\(974\) 12.6265 21.8698i 0.404580 0.700753i
\(975\) 0 0
\(976\) −60.7310 −1.94395
\(977\) −2.40082 −0.0768089 −0.0384044 0.999262i \(-0.512228\pi\)
−0.0384044 + 0.999262i \(0.512228\pi\)
\(978\) −31.8033 55.0850i −1.01696 1.76142i
\(979\) 49.9098 + 86.4463i 1.59512 + 2.76284i
\(980\) 0 0
\(981\) −42.2885 −1.35017
\(982\) −3.17022 5.49098i −0.101166 0.175224i
\(983\) −9.18425 + 15.9076i −0.292932 + 0.507373i −0.974502 0.224380i \(-0.927964\pi\)
0.681570 + 0.731753i \(0.261298\pi\)
\(984\) −3.19194 5.52860i −0.101755 0.176245i
\(985\) 0 0
\(986\) 2.15725 3.73647i 0.0687009 0.118993i
\(987\) −41.8236 −1.33126
\(988\) 3.85621 + 1.52750i 0.122682 + 0.0485964i
\(989\) −0.623016 −0.0198108
\(990\) 0 0
\(991\) −5.14734 + 8.91546i −0.163511 + 0.283209i −0.936125 0.351666i \(-0.885615\pi\)
0.772615 + 0.634875i \(0.218948\pi\)
\(992\) −3.83581 6.64381i −0.121787 0.210941i
\(993\) 10.0023 17.3245i 0.317413 0.549776i
\(994\) 17.8816 + 30.9718i 0.567169 + 0.982365i
\(995\) 0 0
\(996\) 5.75648 0.182401
\(997\) −1.15115 1.99385i −0.0364573 0.0631459i 0.847221 0.531241i \(-0.178274\pi\)
−0.883678 + 0.468095i \(0.844941\pi\)
\(998\) −3.57388 6.19014i −0.113129 0.195946i
\(999\) −14.5888 −0.461569
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 475.2.e.f.201.5 yes 12
5.2 odd 4 475.2.j.d.49.10 24
5.3 odd 4 475.2.j.d.49.3 24
5.4 even 2 475.2.e.h.201.2 yes 12
19.7 even 3 inner 475.2.e.f.26.5 12
19.8 odd 6 9025.2.a.bs.1.5 6
19.11 even 3 9025.2.a.bz.1.2 6
95.7 odd 12 475.2.j.d.349.3 24
95.49 even 6 9025.2.a.br.1.5 6
95.64 even 6 475.2.e.h.26.2 yes 12
95.83 odd 12 475.2.j.d.349.10 24
95.84 odd 6 9025.2.a.by.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.5 12 19.7 even 3 inner
475.2.e.f.201.5 yes 12 1.1 even 1 trivial
475.2.e.h.26.2 yes 12 95.64 even 6
475.2.e.h.201.2 yes 12 5.4 even 2
475.2.j.d.49.3 24 5.3 odd 4
475.2.j.d.49.10 24 5.2 odd 4
475.2.j.d.349.3 24 95.7 odd 12
475.2.j.d.349.10 24 95.83 odd 12
9025.2.a.br.1.5 6 95.49 even 6
9025.2.a.bs.1.5 6 19.8 odd 6
9025.2.a.by.1.2 6 95.84 odd 6
9025.2.a.bz.1.2 6 19.11 even 3