Properties

Label 825.2.bx.h.724.2
Level $825$
Weight $2$
Character 825.724
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(49,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) 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 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 724.2
Root \(1.28932 + 0.418926i\) of defining polynomial
Character \(\chi\) \(=\) 825.724
Dual form 825.2.bx.h.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10527 - 0.359123i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(2.51974 - 3.46813i) q^{7} +(1.80980 + 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-1.10527 - 0.359123i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.525387 - 0.381716i) q^{4} +(0.359123 + 1.10527i) q^{6} +(2.51974 - 3.46813i) q^{7} +(1.80980 + 2.49097i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.15911 - 1.00996i) q^{11} +0.649414i q^{12} +(4.91433 + 1.59676i) q^{13} +(-4.03048 + 2.92831i) q^{14} +(-0.704384 - 2.16787i) q^{16} +(4.75528 - 1.54508i) q^{17} +(0.683093 - 0.940197i) q^{18} +(4.53048 - 3.29158i) q^{19} -4.28684 q^{21} +(3.12896 + 2.25079i) q^{22} -0.219819i q^{23} +(0.951466 - 2.92831i) q^{24} +(-4.85822 - 3.52970i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.64768 + 0.860283i) q^{28} +(5.19262 + 3.77266i) q^{29} +(-0.874813 + 2.69240i) q^{31} -3.50898i q^{32} +(1.03980 + 3.14941i) q^{33} -5.81074 q^{34} +(0.525387 - 0.381716i) q^{36} +(-2.30883 + 3.17784i) q^{37} +(-6.18947 + 2.01108i) q^{38} +(-1.59676 - 4.91433i) q^{39} +(-4.74165 + 3.44501i) q^{41} +(4.73811 + 1.53950i) q^{42} -8.90173i q^{43} +(1.27424 + 1.73650i) q^{44} +(-0.0789420 + 0.242959i) q^{46} +(-0.139821 - 0.192447i) q^{47} +(-1.33982 + 1.84410i) q^{48} +(-3.51569 - 10.8202i) q^{49} +(-4.04508 - 2.93893i) q^{51} +(-1.97242 - 2.71480i) q^{52} +(2.41255 + 0.783885i) q^{53} -1.16215 q^{54} +13.1992 q^{56} +(-5.32589 - 1.73049i) q^{57} +(-4.38439 - 6.03459i) q^{58} +(-6.36725 - 4.62608i) q^{59} +(-1.50123 - 4.62030i) q^{61} +(1.93381 - 2.66165i) q^{62} +(2.51974 + 3.46813i) q^{63} +(-2.66892 + 8.21410i) q^{64} +(-0.0182340 - 3.85436i) q^{66} -12.1280i q^{67} +(-3.08815 - 1.00340i) q^{68} +(-0.177837 + 0.129206i) q^{69} +(-3.08459 - 9.49339i) q^{71} +(-2.92831 + 0.951466i) q^{72} +(8.55964 - 11.7813i) q^{73} +(3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(-11.4628 + 8.41136i) q^{77} +6.00509i q^{78} +(-2.47274 + 7.61030i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(6.47797 - 2.10482i) q^{82} +(-11.9386 + 3.87908i) q^{83} +(2.25225 + 1.63636i) q^{84} +(-3.19682 + 9.83880i) q^{86} -6.41843i q^{87} +(-3.20157 - 9.69707i) q^{88} +2.56545 q^{89} +(17.9206 - 13.0201i) q^{91} +(-0.0839083 + 0.115490i) q^{92} +(2.69240 - 0.874813i) q^{93} +(0.0854274 + 0.262919i) q^{94} +(-2.83882 + 2.06253i) q^{96} +(-1.91351 - 0.621738i) q^{97} +13.2218i q^{98} +(1.93675 - 2.69240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10527 0.359123i −0.781542 0.253938i −0.109044 0.994037i \(-0.534779\pi\)
−0.672499 + 0.740098i \(0.734779\pi\)
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) −0.525387 0.381716i −0.262693 0.190858i
\(5\) 0 0
\(6\) 0.359123 + 1.10527i 0.146611 + 0.451224i
\(7\) 2.51974 3.46813i 0.952373 1.31083i 0.00190785 0.999998i \(-0.499393\pi\)
0.950465 0.310831i \(-0.100607\pi\)
\(8\) 1.80980 + 2.49097i 0.639860 + 0.880691i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) −3.15911 1.00996i −0.952508 0.304514i
\(12\) 0.649414i 0.187470i
\(13\) 4.91433 + 1.59676i 1.36299 + 0.442863i 0.897040 0.441948i \(-0.145713\pi\)
0.465950 + 0.884811i \(0.345713\pi\)
\(14\) −4.03048 + 2.92831i −1.07719 + 0.782624i
\(15\) 0 0
\(16\) −0.704384 2.16787i −0.176096 0.541968i
\(17\) 4.75528 1.54508i 1.15333 0.374738i 0.330930 0.943655i \(-0.392637\pi\)
0.822395 + 0.568917i \(0.192637\pi\)
\(18\) 0.683093 0.940197i 0.161007 0.221607i
\(19\) 4.53048 3.29158i 1.03936 0.755141i 0.0692013 0.997603i \(-0.477955\pi\)
0.970161 + 0.242462i \(0.0779549\pi\)
\(20\) 0 0
\(21\) −4.28684 −0.935466
\(22\) 3.12896 + 2.25079i 0.667097 + 0.479869i
\(23\) 0.219819i 0.0458354i −0.999737 0.0229177i \(-0.992704\pi\)
0.999737 0.0229177i \(-0.00729557\pi\)
\(24\) 0.951466 2.92831i 0.194217 0.597739i
\(25\) 0 0
\(26\) −4.85822 3.52970i −0.952775 0.692232i
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) −2.64768 + 0.860283i −0.500364 + 0.162578i
\(29\) 5.19262 + 3.77266i 0.964246 + 0.700566i 0.954133 0.299383i \(-0.0967809\pi\)
0.0101128 + 0.999949i \(0.496781\pi\)
\(30\) 0 0
\(31\) −0.874813 + 2.69240i −0.157121 + 0.483569i −0.998370 0.0570796i \(-0.981821\pi\)
0.841249 + 0.540649i \(0.181821\pi\)
\(32\) 3.50898i 0.620306i
\(33\) 1.03980 + 3.14941i 0.181007 + 0.548243i
\(34\) −5.81074 −0.996533
\(35\) 0 0
\(36\) 0.525387 0.381716i 0.0875645 0.0636193i
\(37\) −2.30883 + 3.17784i −0.379570 + 0.522433i −0.955471 0.295087i \(-0.904652\pi\)
0.575901 + 0.817520i \(0.304652\pi\)
\(38\) −6.18947 + 2.01108i −1.00406 + 0.326240i
\(39\) −1.59676 4.91433i −0.255687 0.786923i
\(40\) 0 0
\(41\) −4.74165 + 3.44501i −0.740521 + 0.538020i −0.892874 0.450306i \(-0.851315\pi\)
0.152353 + 0.988326i \(0.451315\pi\)
\(42\) 4.73811 + 1.53950i 0.731106 + 0.237551i
\(43\) 8.90173i 1.35750i −0.734369 0.678751i \(-0.762522\pi\)
0.734369 0.678751i \(-0.237478\pi\)
\(44\) 1.27424 + 1.73650i 0.192099 + 0.261788i
\(45\) 0 0
\(46\) −0.0789420 + 0.242959i −0.0116394 + 0.0358223i
\(47\) −0.139821 0.192447i −0.0203950 0.0280713i 0.798698 0.601732i \(-0.205523\pi\)
−0.819093 + 0.573661i \(0.805523\pi\)
\(48\) −1.33982 + 1.84410i −0.193386 + 0.266173i
\(49\) −3.51569 10.8202i −0.502241 1.54574i
\(50\) 0 0
\(51\) −4.04508 2.93893i −0.566425 0.411532i
\(52\) −1.97242 2.71480i −0.273525 0.376475i
\(53\) 2.41255 + 0.783885i 0.331389 + 0.107675i 0.469986 0.882674i \(-0.344259\pi\)
−0.138596 + 0.990349i \(0.544259\pi\)
\(54\) −1.16215 −0.158148
\(55\) 0 0
\(56\) 13.1992 1.76382
\(57\) −5.32589 1.73049i −0.705432 0.229209i
\(58\) −4.38439 6.03459i −0.575698 0.792381i
\(59\) −6.36725 4.62608i −0.828945 0.602264i 0.0903156 0.995913i \(-0.471212\pi\)
−0.919261 + 0.393649i \(0.871212\pi\)
\(60\) 0 0
\(61\) −1.50123 4.62030i −0.192212 0.591569i −0.999998 0.00209225i \(-0.999334\pi\)
0.807785 0.589477i \(-0.200666\pi\)
\(62\) 1.93381 2.66165i 0.245594 0.338031i
\(63\) 2.51974 + 3.46813i 0.317458 + 0.436943i
\(64\) −2.66892 + 8.21410i −0.333615 + 1.02676i
\(65\) 0 0
\(66\) −0.0182340 3.85436i −0.00224445 0.474439i
\(67\) 12.1280i 1.48167i −0.671688 0.740834i \(-0.734431\pi\)
0.671688 0.740834i \(-0.265569\pi\)
\(68\) −3.08815 1.00340i −0.374493 0.121680i
\(69\) −0.177837 + 0.129206i −0.0214091 + 0.0155546i
\(70\) 0 0
\(71\) −3.08459 9.49339i −0.366073 1.12666i −0.949306 0.314353i \(-0.898212\pi\)
0.583233 0.812305i \(-0.301788\pi\)
\(72\) −2.92831 + 0.951466i −0.345105 + 0.112131i
\(73\) 8.55964 11.7813i 1.00183 1.37890i 0.0776335 0.996982i \(-0.475264\pi\)
0.924196 0.381918i \(-0.124736\pi\)
\(74\) 3.69311 2.68320i 0.429316 0.311916i
\(75\) 0 0
\(76\) −3.63670 −0.417158
\(77\) −11.4628 + 8.41136i −1.30631 + 0.958564i
\(78\) 6.00509i 0.679942i
\(79\) −2.47274 + 7.61030i −0.278205 + 0.856226i 0.710149 + 0.704051i \(0.248628\pi\)
−0.988354 + 0.152174i \(0.951372\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 6.47797 2.10482i 0.715373 0.232439i
\(83\) −11.9386 + 3.87908i −1.31043 + 0.425784i −0.879197 0.476458i \(-0.841921\pi\)
−0.431231 + 0.902242i \(0.641921\pi\)
\(84\) 2.25225 + 1.63636i 0.245741 + 0.178541i
\(85\) 0 0
\(86\) −3.19682 + 9.83880i −0.344722 + 1.06094i
\(87\) 6.41843i 0.688128i
\(88\) −3.20157 9.69707i −0.341288 1.03371i
\(89\) 2.56545 0.271937 0.135969 0.990713i \(-0.456585\pi\)
0.135969 + 0.990713i \(0.456585\pi\)
\(90\) 0 0
\(91\) 17.9206 13.0201i 1.87859 1.36488i
\(92\) −0.0839083 + 0.115490i −0.00874805 + 0.0120407i
\(93\) 2.69240 0.874813i 0.279189 0.0907139i
\(94\) 0.0854274 + 0.262919i 0.00881116 + 0.0271180i
\(95\) 0 0
\(96\) −2.83882 + 2.06253i −0.289736 + 0.210506i
\(97\) −1.91351 0.621738i −0.194288 0.0631279i 0.210257 0.977646i \(-0.432570\pi\)
−0.404545 + 0.914518i \(0.632570\pi\)
\(98\) 13.2218i 1.33560i
\(99\) 1.93675 2.69240i 0.194650 0.270596i
\(100\) 0 0
\(101\) −2.34385 + 7.21362i −0.233221 + 0.717782i 0.764131 + 0.645061i \(0.223168\pi\)
−0.997352 + 0.0727205i \(0.976832\pi\)
\(102\) 3.41546 + 4.70098i 0.338181 + 0.465467i
\(103\) −9.91508 + 13.6469i −0.976962 + 1.34467i −0.0385116 + 0.999258i \(0.512262\pi\)
−0.938450 + 0.345414i \(0.887738\pi\)
\(104\) 4.91645 + 15.1313i 0.482098 + 1.48374i
\(105\) 0 0
\(106\) −2.38500 1.73281i −0.231652 0.168305i
\(107\) 4.56216 + 6.27928i 0.441041 + 0.607041i 0.970443 0.241330i \(-0.0775837\pi\)
−0.529402 + 0.848371i \(0.677584\pi\)
\(108\) −0.617629 0.200680i −0.0594314 0.0193104i
\(109\) −4.45671 −0.426876 −0.213438 0.976957i \(-0.568466\pi\)
−0.213438 + 0.976957i \(0.568466\pi\)
\(110\) 0 0
\(111\) 3.92802 0.372831
\(112\) −9.29332 3.01958i −0.878136 0.285324i
\(113\) 4.53327 + 6.23952i 0.426455 + 0.586964i 0.967135 0.254264i \(-0.0818331\pi\)
−0.540680 + 0.841228i \(0.681833\pi\)
\(114\) 5.26508 + 3.82530i 0.493120 + 0.358273i
\(115\) 0 0
\(116\) −1.28805 3.96421i −0.119593 0.368068i
\(117\) −3.03722 + 4.18038i −0.280792 + 0.386476i
\(118\) 5.37618 + 7.39968i 0.494918 + 0.681196i
\(119\) 6.62353 20.3851i 0.607178 1.86870i
\(120\) 0 0
\(121\) 8.95996 + 6.38115i 0.814542 + 0.580105i
\(122\) 5.64579i 0.511146i
\(123\) 5.57414 + 1.81115i 0.502603 + 0.163306i
\(124\) 1.48735 1.08062i 0.133568 0.0970426i
\(125\) 0 0
\(126\) −1.53950 4.73811i −0.137150 0.422104i
\(127\) 1.45620 0.473149i 0.129217 0.0419852i −0.243695 0.969852i \(-0.578359\pi\)
0.372912 + 0.927867i \(0.378359\pi\)
\(128\) 1.77470 2.44266i 0.156863 0.215903i
\(129\) −7.20165 + 5.23231i −0.634070 + 0.460679i
\(130\) 0 0
\(131\) 2.66108 0.232500 0.116250 0.993220i \(-0.462913\pi\)
0.116250 + 0.993220i \(0.462913\pi\)
\(132\) 0.655882 2.05157i 0.0570872 0.178566i
\(133\) 24.0062i 2.08160i
\(134\) −4.35544 + 13.4047i −0.376252 + 1.15799i
\(135\) 0 0
\(136\) 12.4549 + 9.04898i 1.06799 + 0.775944i
\(137\) 9.75352 3.16911i 0.833300 0.270756i 0.138865 0.990311i \(-0.455655\pi\)
0.694435 + 0.719556i \(0.255655\pi\)
\(138\) 0.242959 0.0789420i 0.0206820 0.00671999i
\(139\) −4.28381 3.11237i −0.363348 0.263987i 0.391099 0.920348i \(-0.372095\pi\)
−0.754447 + 0.656361i \(0.772095\pi\)
\(140\) 0 0
\(141\) −0.0735083 + 0.226235i −0.00619051 + 0.0190524i
\(142\) 11.6005i 0.973491i
\(143\) −13.9123 10.0076i −1.16340 0.836880i
\(144\) 2.27943 0.189953
\(145\) 0 0
\(146\) −13.6916 + 9.94756i −1.13313 + 0.823266i
\(147\) −6.68724 + 9.20420i −0.551554 + 0.759149i
\(148\) 2.42606 0.788275i 0.199421 0.0647958i
\(149\) −1.17068 3.60300i −0.0959062 0.295169i 0.891583 0.452858i \(-0.149596\pi\)
−0.987489 + 0.157689i \(0.949596\pi\)
\(150\) 0 0
\(151\) 4.78939 3.47969i 0.389755 0.283173i −0.375600 0.926782i \(-0.622563\pi\)
0.765355 + 0.643608i \(0.222563\pi\)
\(152\) 16.3985 + 5.32819i 1.33009 + 0.432173i
\(153\) 5.00000i 0.404226i
\(154\) 15.6902 5.18024i 1.26435 0.417436i
\(155\) 0 0
\(156\) −1.03696 + 3.19144i −0.0830233 + 0.255519i
\(157\) −4.36671 6.01026i −0.348501 0.479671i 0.598399 0.801198i \(-0.295804\pi\)
−0.946900 + 0.321528i \(0.895804\pi\)
\(158\) 5.46607 7.52340i 0.434857 0.598530i
\(159\) −0.783885 2.41255i −0.0621661 0.191328i
\(160\) 0 0
\(161\) −0.762360 0.553887i −0.0600824 0.0436524i
\(162\) 0.683093 + 0.940197i 0.0536689 + 0.0738688i
\(163\) 5.06044 + 1.64424i 0.396364 + 0.128786i 0.500415 0.865785i \(-0.333181\pi\)
−0.104051 + 0.994572i \(0.533181\pi\)
\(164\) 3.80621 0.297215
\(165\) 0 0
\(166\) 14.5884 1.13228
\(167\) 1.87490 + 0.609193i 0.145084 + 0.0471407i 0.380659 0.924716i \(-0.375697\pi\)
−0.235575 + 0.971856i \(0.575697\pi\)
\(168\) −7.75831 10.6784i −0.598567 0.823856i
\(169\) 11.0838 + 8.05285i 0.852599 + 0.619450i
\(170\) 0 0
\(171\) 1.73049 + 5.32589i 0.132334 + 0.407281i
\(172\) −3.39793 + 4.67685i −0.259090 + 0.356607i
\(173\) 1.16090 + 1.59784i 0.0882617 + 0.121482i 0.850864 0.525385i \(-0.176079\pi\)
−0.762603 + 0.646867i \(0.776079\pi\)
\(174\) −2.30501 + 7.09409i −0.174742 + 0.537801i
\(175\) 0 0
\(176\) 0.0357642 + 7.55994i 0.00269583 + 0.569852i
\(177\) 7.87035i 0.591572i
\(178\) −2.83551 0.921313i −0.212530 0.0690553i
\(179\) −1.63676 + 1.18918i −0.122337 + 0.0888832i −0.647271 0.762260i \(-0.724090\pi\)
0.524934 + 0.851143i \(0.324090\pi\)
\(180\) 0 0
\(181\) 6.22299 + 19.1524i 0.462551 + 1.42359i 0.862036 + 0.506846i \(0.169189\pi\)
−0.399485 + 0.916740i \(0.630811\pi\)
\(182\) −24.4829 + 7.95498i −1.81479 + 0.589662i
\(183\) −2.85550 + 3.93026i −0.211085 + 0.290533i
\(184\) 0.547562 0.397827i 0.0403668 0.0293282i
\(185\) 0 0
\(186\) −3.28999 −0.241234
\(187\) −16.5829 + 0.0784497i −1.21266 + 0.00573681i
\(188\) 0.154481i 0.0112667i
\(189\) 1.32471 4.07703i 0.0963583 0.296560i
\(190\) 0 0
\(191\) −10.2463 7.44439i −0.741398 0.538657i 0.151751 0.988419i \(-0.451509\pi\)
−0.893149 + 0.449762i \(0.851509\pi\)
\(192\) 8.21410 2.66892i 0.592802 0.192613i
\(193\) 13.2502 4.30526i 0.953773 0.309900i 0.209525 0.977803i \(-0.432808\pi\)
0.744248 + 0.667904i \(0.232808\pi\)
\(194\) 1.89166 + 1.37437i 0.135813 + 0.0986743i
\(195\) 0 0
\(196\) −2.28314 + 7.02678i −0.163081 + 0.501913i
\(197\) 14.6060i 1.04064i −0.853972 0.520319i \(-0.825813\pi\)
0.853972 0.520319i \(-0.174187\pi\)
\(198\) −3.10753 + 2.28029i −0.220842 + 0.162053i
\(199\) 11.8748 0.841784 0.420892 0.907111i \(-0.361717\pi\)
0.420892 + 0.907111i \(0.361717\pi\)
\(200\) 0 0
\(201\) −9.81174 + 7.12864i −0.692067 + 0.502816i
\(202\) 5.18115 7.13125i 0.364545 0.501753i
\(203\) 26.1681 8.50254i 1.83664 0.596762i
\(204\) 1.00340 + 3.08815i 0.0702520 + 0.216213i
\(205\) 0 0
\(206\) 15.8597 11.5228i 1.10500 0.802830i
\(207\) 0.209060 + 0.0679277i 0.0145307 + 0.00472130i
\(208\) 11.7784i 0.816683i
\(209\) −17.6366 + 5.82288i −1.21995 + 0.402777i
\(210\) 0 0
\(211\) −6.90710 + 21.2579i −0.475504 + 1.46345i 0.369772 + 0.929122i \(0.379436\pi\)
−0.845277 + 0.534329i \(0.820564\pi\)
\(212\) −0.968301 1.33275i −0.0665032 0.0915338i
\(213\) −5.86724 + 8.07556i −0.402017 + 0.553328i
\(214\) −2.78738 8.57866i −0.190541 0.586425i
\(215\) 0 0
\(216\) 2.49097 + 1.80980i 0.169489 + 0.123141i
\(217\) 7.13328 + 9.81811i 0.484238 + 0.666497i
\(218\) 4.92586 + 1.60051i 0.333621 + 0.108400i
\(219\) −14.5625 −0.984044
\(220\) 0 0
\(221\) 25.8362 1.73793
\(222\) −4.34152 1.41064i −0.291384 0.0946762i
\(223\) 11.2610 + 15.4994i 0.754091 + 1.03792i 0.997683 + 0.0680388i \(0.0216742\pi\)
−0.243592 + 0.969878i \(0.578326\pi\)
\(224\) −12.1696 8.84173i −0.813115 0.590763i
\(225\) 0 0
\(226\) −2.76973 8.52434i −0.184239 0.567031i
\(227\) −9.03772 + 12.4394i −0.599855 + 0.825629i −0.995695 0.0926901i \(-0.970453\pi\)
0.395840 + 0.918319i \(0.370453\pi\)
\(228\) 2.13760 + 2.94215i 0.141566 + 0.194849i
\(229\) −2.75064 + 8.46560i −0.181767 + 0.559422i −0.999878 0.0156388i \(-0.995022\pi\)
0.818110 + 0.575061i \(0.195022\pi\)
\(230\) 0 0
\(231\) 13.5426 + 4.32954i 0.891038 + 0.284863i
\(232\) 19.7624i 1.29747i
\(233\) 21.7185 + 7.05677i 1.42283 + 0.462304i 0.916499 0.400037i \(-0.131003\pi\)
0.506327 + 0.862342i \(0.331003\pi\)
\(234\) 4.85822 3.52970i 0.317592 0.230744i
\(235\) 0 0
\(236\) 1.57942 + 4.86096i 0.102812 + 0.316422i
\(237\) 7.61030 2.47274i 0.494342 0.160621i
\(238\) −14.6416 + 20.1524i −0.949071 + 1.30628i
\(239\) 13.6405 9.91037i 0.882327 0.641048i −0.0515388 0.998671i \(-0.516413\pi\)
0.933866 + 0.357623i \(0.116413\pi\)
\(240\) 0 0
\(241\) −11.9607 −0.770459 −0.385229 0.922821i \(-0.625878\pi\)
−0.385229 + 0.922821i \(0.625878\pi\)
\(242\) −7.61154 10.2706i −0.489288 0.660220i
\(243\) 1.00000i 0.0641500i
\(244\) −0.974917 + 3.00049i −0.0624127 + 0.192087i
\(245\) 0 0
\(246\) −5.51049 4.00361i −0.351336 0.255261i
\(247\) 27.5201 8.94184i 1.75106 0.568955i
\(248\) −8.28992 + 2.69356i −0.526410 + 0.171041i
\(249\) 10.1556 + 7.37844i 0.643582 + 0.467590i
\(250\) 0 0
\(251\) 4.94533 15.2201i 0.312146 0.960687i −0.664767 0.747051i \(-0.731469\pi\)
0.976913 0.213637i \(-0.0685308\pi\)
\(252\) 2.78393i 0.175371i
\(253\) −0.222008 + 0.694432i −0.0139575 + 0.0436586i
\(254\) −1.77941 −0.111650
\(255\) 0 0
\(256\) 11.1359 8.09073i 0.695996 0.505671i
\(257\) −3.21780 + 4.42893i −0.200721 + 0.276269i −0.897498 0.441019i \(-0.854617\pi\)
0.696776 + 0.717288i \(0.254617\pi\)
\(258\) 9.83880 3.19682i 0.612537 0.199025i
\(259\) 5.20348 + 16.0147i 0.323328 + 0.995103i
\(260\) 0 0
\(261\) −5.19262 + 3.77266i −0.321415 + 0.233522i
\(262\) −2.94121 0.955657i −0.181709 0.0590407i
\(263\) 11.9841i 0.738971i 0.929236 + 0.369486i \(0.120466\pi\)
−0.929236 + 0.369486i \(0.879534\pi\)
\(264\) −5.96326 + 8.28992i −0.367014 + 0.510209i
\(265\) 0 0
\(266\) −8.62119 + 26.5333i −0.528599 + 1.62686i
\(267\) −1.50793 2.07549i −0.0922841 0.127018i
\(268\) −4.62944 + 6.37188i −0.282788 + 0.389224i
\(269\) −4.21700 12.9786i −0.257115 0.791318i −0.993406 0.114653i \(-0.963424\pi\)
0.736291 0.676665i \(-0.236576\pi\)
\(270\) 0 0
\(271\) −9.57702 6.95812i −0.581763 0.422675i 0.257596 0.966253i \(-0.417070\pi\)
−0.839359 + 0.543577i \(0.817070\pi\)
\(272\) −6.69909 9.22050i −0.406192 0.559075i
\(273\) −21.0670 6.84507i −1.27503 0.414283i
\(274\) −11.9184 −0.720014
\(275\) 0 0
\(276\) 0.142753 0.00859274
\(277\) −9.76148 3.17170i −0.586511 0.190569i 0.000704561 1.00000i \(-0.499776\pi\)
−0.587215 + 0.809431i \(0.699776\pi\)
\(278\) 3.61703 + 4.97841i 0.216935 + 0.298585i
\(279\) −2.29029 1.66399i −0.137116 0.0996207i
\(280\) 0 0
\(281\) −0.908167 2.79505i −0.0541767 0.166739i 0.920307 0.391197i \(-0.127939\pi\)
−0.974484 + 0.224458i \(0.927939\pi\)
\(282\) 0.162493 0.223652i 0.00967629 0.0133183i
\(283\) −12.8301 17.6592i −0.762673 1.04973i −0.996987 0.0775682i \(-0.975284\pi\)
0.234314 0.972161i \(-0.424716\pi\)
\(284\) −2.00318 + 6.16514i −0.118867 + 0.365834i
\(285\) 0 0
\(286\) 11.7828 + 16.0573i 0.696731 + 0.949490i
\(287\) 25.1252i 1.48309i
\(288\) 3.33724 + 1.08433i 0.196649 + 0.0638950i
\(289\) 6.47214 4.70228i 0.380714 0.276605i
\(290\) 0 0
\(291\) 0.621738 + 1.91351i 0.0364469 + 0.112172i
\(292\) −8.99424 + 2.92241i −0.526348 + 0.171021i
\(293\) −14.5574 + 20.0365i −0.850452 + 1.17055i 0.133311 + 0.991074i \(0.457439\pi\)
−0.983763 + 0.179473i \(0.942561\pi\)
\(294\) 10.6966 7.77156i 0.623840 0.453246i
\(295\) 0 0
\(296\) −12.0944 −0.702974
\(297\) −3.31659 + 0.0156899i −0.192448 + 0.000910423i
\(298\) 4.40269i 0.255041i
\(299\) 0.350999 1.08026i 0.0202988 0.0624732i
\(300\) 0 0
\(301\) −30.8723 22.4301i −1.77945 1.29285i
\(302\) −6.54319 + 2.12601i −0.376518 + 0.122338i
\(303\) 7.21362 2.34385i 0.414411 0.134650i
\(304\) −10.3269 7.50295i −0.592289 0.430323i
\(305\) 0 0
\(306\) 1.79562 5.52634i 0.102649 0.315920i
\(307\) 4.94023i 0.281954i 0.990013 + 0.140977i \(0.0450243\pi\)
−0.990013 + 0.140977i \(0.954976\pi\)
\(308\) 9.23316 0.0436798i 0.526108 0.00248889i
\(309\) 16.8685 0.959618
\(310\) 0 0
\(311\) 11.1722 8.11707i 0.633517 0.460277i −0.224100 0.974566i \(-0.571944\pi\)
0.857617 + 0.514289i \(0.171944\pi\)
\(312\) 9.35164 12.8714i 0.529432 0.728701i
\(313\) 3.87017 1.25750i 0.218755 0.0710779i −0.197589 0.980285i \(-0.563311\pi\)
0.416344 + 0.909207i \(0.363311\pi\)
\(314\) 2.66796 + 8.21113i 0.150562 + 0.463381i
\(315\) 0 0
\(316\) 4.20412 3.05447i 0.236500 0.171827i
\(317\) −24.5562 7.97880i −1.37921 0.448134i −0.476803 0.879010i \(-0.658205\pi\)
−0.902411 + 0.430876i \(0.858205\pi\)
\(318\) 2.94803i 0.165317i
\(319\) −12.5938 17.1626i −0.705119 0.960921i
\(320\) 0 0
\(321\) 2.39847 7.38173i 0.133870 0.412008i
\(322\) 0.643698 + 0.885974i 0.0358719 + 0.0493734i
\(323\) 16.4579 22.6524i 0.915743 1.26041i
\(324\) 0.200680 + 0.617629i 0.0111489 + 0.0343127i
\(325\) 0 0
\(326\) −5.00265 3.63464i −0.277071 0.201304i
\(327\) 2.61959 + 3.60556i 0.144864 + 0.199388i
\(328\) −17.1628 5.57654i −0.947659 0.307913i
\(329\) −1.01974 −0.0562203
\(330\) 0 0
\(331\) −3.35008 −0.184137 −0.0920684 0.995753i \(-0.529348\pi\)
−0.0920684 + 0.995753i \(0.529348\pi\)
\(332\) 7.75307 + 2.51913i 0.425505 + 0.138255i
\(333\) −2.30883 3.17784i −0.126523 0.174144i
\(334\) −1.85349 1.34664i −0.101419 0.0736850i
\(335\) 0 0
\(336\) 3.01958 + 9.29332i 0.164732 + 0.506992i
\(337\) 16.1052 22.1669i 0.877307 1.20751i −0.0998530 0.995002i \(-0.531837\pi\)
0.977160 0.212507i \(-0.0681628\pi\)
\(338\) −9.35859 12.8810i −0.509040 0.700634i
\(339\) 2.38328 7.33499i 0.129442 0.398382i
\(340\) 0 0
\(341\) 5.48285 7.62206i 0.296913 0.412758i
\(342\) 6.50800i 0.351912i
\(343\) −17.8452 5.79826i −0.963550 0.313076i
\(344\) 22.1739 16.1103i 1.19554 0.868610i
\(345\) 0 0
\(346\) −0.709284 2.18295i −0.0381313 0.117356i
\(347\) 15.0519 4.89065i 0.808027 0.262544i 0.124265 0.992249i \(-0.460343\pi\)
0.683762 + 0.729705i \(0.260343\pi\)
\(348\) −2.45002 + 3.37216i −0.131335 + 0.180767i
\(349\) −2.96043 + 2.15088i −0.158468 + 0.115134i −0.664194 0.747561i \(-0.731225\pi\)
0.505725 + 0.862695i \(0.331225\pi\)
\(350\) 0 0
\(351\) 5.16724 0.275807
\(352\) −3.54393 + 11.0853i −0.188892 + 0.590846i
\(353\) 27.4937i 1.46334i −0.681658 0.731671i \(-0.738741\pi\)
0.681658 0.731671i \(-0.261259\pi\)
\(354\) 2.82643 8.69884i 0.150223 0.462338i
\(355\) 0 0
\(356\) −1.34785 0.979273i −0.0714361 0.0519014i
\(357\) −20.3851 + 6.62353i −1.07890 + 0.350555i
\(358\) 2.23612 0.726559i 0.118183 0.0383998i
\(359\) 0.387309 + 0.281397i 0.0204414 + 0.0148515i 0.597959 0.801527i \(-0.295979\pi\)
−0.577518 + 0.816378i \(0.695979\pi\)
\(360\) 0 0
\(361\) 3.81936 11.7548i 0.201019 0.618673i
\(362\) 23.4033i 1.23005i
\(363\) −0.104074 10.9995i −0.00546247 0.577324i
\(364\) −14.3852 −0.753992
\(365\) 0 0
\(366\) 4.56754 3.31851i 0.238749 0.173462i
\(367\) 14.9639 20.5961i 0.781111 1.07511i −0.214047 0.976823i \(-0.568665\pi\)
0.995158 0.0982843i \(-0.0313355\pi\)
\(368\) −0.476539 + 0.154837i −0.0248413 + 0.00807143i
\(369\) −1.81115 5.57414i −0.0942846 0.290178i
\(370\) 0 0
\(371\) 8.79762 6.39184i 0.456750 0.331848i
\(372\) −1.74848 0.568116i −0.0906545 0.0294554i
\(373\) 2.75967i 0.142890i −0.997445 0.0714451i \(-0.977239\pi\)
0.997445 0.0714451i \(-0.0227611\pi\)
\(374\) 18.3568 + 5.86861i 0.949205 + 0.303459i
\(375\) 0 0
\(376\) 0.226333 0.696580i 0.0116722 0.0359234i
\(377\) 19.4942 + 26.8315i 1.00400 + 1.38189i
\(378\) −2.92831 + 4.03048i −0.150616 + 0.207305i
\(379\) 6.69130 + 20.5937i 0.343709 + 1.05783i 0.962271 + 0.272092i \(0.0877156\pi\)
−0.618562 + 0.785736i \(0.712284\pi\)
\(380\) 0 0
\(381\) −1.23872 0.899983i −0.0634616 0.0461075i
\(382\) 8.65148 + 11.9077i 0.442648 + 0.609253i
\(383\) 15.4351 + 5.01518i 0.788699 + 0.256264i 0.675550 0.737314i \(-0.263906\pi\)
0.113149 + 0.993578i \(0.463906\pi\)
\(384\) −3.01930 −0.154078
\(385\) 0 0
\(386\) −16.1912 −0.824109
\(387\) 8.46605 + 2.75079i 0.430353 + 0.139830i
\(388\) 0.768007 + 1.05707i 0.0389897 + 0.0536647i
\(389\) −13.1802 9.57598i −0.668263 0.485522i 0.201180 0.979554i \(-0.435522\pi\)
−0.869443 + 0.494033i \(0.835522\pi\)
\(390\) 0 0
\(391\) −0.339639 1.04530i −0.0171763 0.0528631i
\(392\) 20.5901 28.3398i 1.03996 1.43138i
\(393\) −1.56415 2.15286i −0.0789007 0.108598i
\(394\) −5.24537 + 16.1436i −0.264258 + 0.813302i
\(395\) 0 0
\(396\) −2.04527 + 0.675263i −0.102779 + 0.0339332i
\(397\) 19.9673i 1.00213i 0.865410 + 0.501064i \(0.167058\pi\)
−0.865410 + 0.501064i \(0.832942\pi\)
\(398\) −13.1249 4.26453i −0.657890 0.213761i
\(399\) −19.4214 + 14.1105i −0.972288 + 0.706408i
\(400\) 0 0
\(401\) −8.44448 25.9894i −0.421697 1.29785i −0.906122 0.423017i \(-0.860971\pi\)
0.484425 0.874833i \(-0.339029\pi\)
\(402\) 13.4047 4.35544i 0.668563 0.217229i
\(403\) −8.59825 + 11.8345i −0.428309 + 0.589517i
\(404\) 3.98498 2.89526i 0.198260 0.144044i
\(405\) 0 0
\(406\) −31.9763 −1.58696
\(407\) 10.5034 7.70731i 0.520632 0.382037i
\(408\) 15.3950i 0.762168i
\(409\) −7.70626 + 23.7174i −0.381050 + 1.17275i 0.558255 + 0.829669i \(0.311471\pi\)
−0.939305 + 0.343082i \(0.888529\pi\)
\(410\) 0 0
\(411\) −8.29684 6.02801i −0.409253 0.297340i
\(412\) 10.4185 3.38518i 0.513283 0.166776i
\(413\) −32.0876 + 10.4259i −1.57893 + 0.513025i
\(414\) −0.206673 0.150157i −0.0101574 0.00737980i
\(415\) 0 0
\(416\) 5.60301 17.2443i 0.274710 0.845471i
\(417\) 5.29507i 0.259301i
\(418\) 21.5843 0.102110i 1.05572 0.00499437i
\(419\) −16.8256 −0.821986 −0.410993 0.911639i \(-0.634818\pi\)
−0.410993 + 0.911639i \(0.634818\pi\)
\(420\) 0 0
\(421\) −19.0933 + 13.8721i −0.930551 + 0.676085i −0.946128 0.323793i \(-0.895042\pi\)
0.0155763 + 0.999879i \(0.495042\pi\)
\(422\) 15.2684 21.0151i 0.743253 1.02300i
\(423\) 0.226235 0.0735083i 0.0109999 0.00357409i
\(424\) 2.41359 + 7.42826i 0.117214 + 0.360748i
\(425\) 0 0
\(426\) 9.38499 6.81859i 0.454704 0.330362i
\(427\) −19.8065 6.43552i −0.958504 0.311437i
\(428\) 5.04050i 0.243642i
\(429\) 0.0810736 + 17.1376i 0.00391427 + 0.827411i
\(430\) 0 0
\(431\) −11.6362 + 35.8126i −0.560497 + 1.72503i 0.120469 + 0.992717i \(0.461560\pi\)
−0.680966 + 0.732315i \(0.738440\pi\)
\(432\) −1.33982 1.84410i −0.0644620 0.0887243i
\(433\) −18.2068 + 25.0594i −0.874961 + 1.20428i 0.102831 + 0.994699i \(0.467210\pi\)
−0.977791 + 0.209581i \(0.932790\pi\)
\(434\) −4.35827 13.4134i −0.209204 0.643862i
\(435\) 0 0
\(436\) 2.34150 + 1.70120i 0.112137 + 0.0814726i
\(437\) −0.723552 0.995884i −0.0346122 0.0476396i
\(438\) 16.0955 + 5.22974i 0.769072 + 0.249887i
\(439\) 28.2131 1.34654 0.673268 0.739399i \(-0.264890\pi\)
0.673268 + 0.739399i \(0.264890\pi\)
\(440\) 0 0
\(441\) 11.3770 0.541762
\(442\) −28.5559 9.27837i −1.35827 0.441327i
\(443\) −8.60636 11.8456i −0.408900 0.562803i 0.554050 0.832484i \(-0.313082\pi\)
−0.962950 + 0.269681i \(0.913082\pi\)
\(444\) −2.06373 1.49939i −0.0979404 0.0711578i
\(445\) 0 0
\(446\) −6.88019 21.1751i −0.325787 1.00267i
\(447\) −2.22677 + 3.06489i −0.105323 + 0.144964i
\(448\) 21.7626 + 29.9536i 1.02818 + 1.41517i
\(449\) −3.70749 + 11.4105i −0.174967 + 0.538493i −0.999632 0.0271282i \(-0.991364\pi\)
0.824665 + 0.565622i \(0.191364\pi\)
\(450\) 0 0
\(451\) 18.4587 6.09429i 0.869187 0.286969i
\(452\) 5.00858i 0.235584i
\(453\) −5.63026 1.82938i −0.264533 0.0859519i
\(454\) 14.4564 10.5032i 0.678471 0.492938i
\(455\) 0 0
\(456\) −5.32819 16.3985i −0.249515 0.767929i
\(457\) 9.55211 3.10367i 0.446829 0.145183i −0.0769553 0.997035i \(-0.524520\pi\)
0.523784 + 0.851851i \(0.324520\pi\)
\(458\) 6.08039 8.36893i 0.284118 0.391055i
\(459\) 4.04508 2.93893i 0.188808 0.137177i
\(460\) 0 0
\(461\) −13.4491 −0.626386 −0.313193 0.949689i \(-0.601399\pi\)
−0.313193 + 0.949689i \(0.601399\pi\)
\(462\) −13.4134 9.64876i −0.624046 0.448901i
\(463\) 18.7836i 0.872946i 0.899717 + 0.436473i \(0.143773\pi\)
−0.899717 + 0.436473i \(0.856227\pi\)
\(464\) 4.52104 13.9143i 0.209884 0.645957i
\(465\) 0 0
\(466\) −21.4705 15.5992i −0.994602 0.722620i
\(467\) 25.2515 8.20470i 1.16850 0.379668i 0.340416 0.940275i \(-0.389432\pi\)
0.828082 + 0.560607i \(0.189432\pi\)
\(468\) 3.19144 1.03696i 0.147524 0.0479335i
\(469\) −42.0614 30.5594i −1.94221 1.41110i
\(470\) 0 0
\(471\) −2.29571 + 7.06548i −0.105781 + 0.325560i
\(472\) 24.2329i 1.11541i
\(473\) −8.99039 + 28.1216i −0.413379 + 1.29303i
\(474\) −9.29944 −0.427137
\(475\) 0 0
\(476\) −11.2613 + 8.18178i −0.516159 + 0.375011i
\(477\) −1.49104 + 2.05224i −0.0682699 + 0.0939655i
\(478\) −18.6354 + 6.05501i −0.852363 + 0.276950i
\(479\) −3.33214 10.2553i −0.152249 0.468575i 0.845623 0.533781i \(-0.179229\pi\)
−0.997872 + 0.0652062i \(0.979229\pi\)
\(480\) 0 0
\(481\) −16.4206 + 11.9303i −0.748716 + 0.543974i
\(482\) 13.2198 + 4.29538i 0.602146 + 0.195649i
\(483\) 0.942328i 0.0428774i
\(484\) −2.27166 6.77273i −0.103257 0.307851i
\(485\) 0 0
\(486\) 0.359123 1.10527i 0.0162902 0.0501360i
\(487\) 4.00338 + 5.51018i 0.181410 + 0.249690i 0.890031 0.455899i \(-0.150682\pi\)
−0.708621 + 0.705589i \(0.750682\pi\)
\(488\) 8.79212 12.1013i 0.398001 0.547801i
\(489\) −1.64424 5.06044i −0.0743549 0.228841i
\(490\) 0 0
\(491\) −21.1116 15.3385i −0.952754 0.692216i −0.00129727 0.999999i \(-0.500413\pi\)
−0.951457 + 0.307783i \(0.900413\pi\)
\(492\) −2.23724 3.07929i −0.100862 0.138825i
\(493\) 30.5215 + 9.91703i 1.37462 + 0.446640i
\(494\) −33.6283 −1.51301
\(495\) 0 0
\(496\) 6.45297 0.289747
\(497\) −40.6967 13.2231i −1.82549 0.593139i
\(498\) −8.57484 11.8022i −0.384248 0.528871i
\(499\) 15.6815 + 11.3933i 0.702000 + 0.510033i 0.880583 0.473892i \(-0.157151\pi\)
−0.178583 + 0.983925i \(0.557151\pi\)
\(500\) 0 0
\(501\) −0.609193 1.87490i −0.0272167 0.0837644i
\(502\) −10.9318 + 15.0464i −0.487911 + 0.671552i
\(503\) −11.0752 15.2437i −0.493819 0.679683i 0.487268 0.873253i \(-0.337993\pi\)
−0.981087 + 0.193570i \(0.937993\pi\)
\(504\) −4.07878 + 12.5532i −0.181684 + 0.559164i
\(505\) 0 0
\(506\) 0.494765 0.687805i 0.0219950 0.0305767i
\(507\) 13.7003i 0.608453i
\(508\) −0.945678 0.307270i −0.0419577 0.0136329i
\(509\) −4.16741 + 3.02780i −0.184717 + 0.134205i −0.676301 0.736625i \(-0.736418\pi\)
0.491584 + 0.870830i \(0.336418\pi\)
\(510\) 0 0
\(511\) −19.2911 59.3718i −0.853387 2.62645i
\(512\) −20.9568 + 6.80928i −0.926168 + 0.300930i
\(513\) 3.29158 4.53048i 0.145327 0.200025i
\(514\) 5.14707 3.73956i 0.227027 0.164945i
\(515\) 0 0
\(516\) 5.78091 0.254490
\(517\) 0.247346 + 0.749175i 0.0108783 + 0.0329487i
\(518\) 19.5692i 0.859820i
\(519\) 0.610322 1.87838i 0.0267902 0.0824516i
\(520\) 0 0
\(521\) 33.5759 + 24.3944i 1.47099 + 1.06874i 0.980326 + 0.197387i \(0.0632455\pi\)
0.490663 + 0.871349i \(0.336754\pi\)
\(522\) 7.09409 2.30501i 0.310500 0.100887i
\(523\) 6.58397 2.13926i 0.287897 0.0935434i −0.161508 0.986871i \(-0.551636\pi\)
0.449405 + 0.893328i \(0.351636\pi\)
\(524\) −1.39810 1.01578i −0.0610762 0.0443745i
\(525\) 0 0
\(526\) 4.30377 13.2456i 0.187653 0.577537i
\(527\) 14.1548i 0.616592i
\(528\) 6.09510 4.47256i 0.265255 0.194643i
\(529\) 22.9517 0.997899
\(530\) 0 0
\(531\) 6.36725 4.62608i 0.276315 0.200755i
\(532\) −9.16355 + 12.6125i −0.397290 + 0.546823i
\(533\) −28.8029 + 9.35863i −1.24759 + 0.405367i
\(534\) 0.921313 + 2.83551i 0.0398691 + 0.122704i
\(535\) 0 0
\(536\) 30.2104 21.9492i 1.30489 0.948059i
\(537\) 1.92413 + 0.625187i 0.0830322 + 0.0269788i
\(538\) 15.8592i 0.683740i
\(539\) 0.178505 + 37.7329i 0.00768874 + 1.62527i
\(540\) 0 0
\(541\) −8.78173 + 27.0274i −0.377556 + 1.16200i 0.564182 + 0.825651i \(0.309192\pi\)
−0.941738 + 0.336348i \(0.890808\pi\)
\(542\) 8.08635 + 11.1299i 0.347339 + 0.478071i
\(543\) 11.8368 16.2920i 0.507967 0.699156i
\(544\) −5.42167 16.6862i −0.232452 0.715415i
\(545\) 0 0
\(546\) 20.8264 + 15.1313i 0.891288 + 0.647559i
\(547\) 15.1996 + 20.9205i 0.649889 + 0.894496i 0.999094 0.0425503i \(-0.0135483\pi\)
−0.349205 + 0.937046i \(0.613548\pi\)
\(548\) −6.33407 2.05807i −0.270578 0.0879162i
\(549\) 4.85807 0.207337
\(550\) 0 0
\(551\) 35.9431 1.53123
\(552\) −0.643698 0.209150i −0.0273976 0.00890202i
\(553\) 20.1628 + 27.7518i 0.857411 + 1.18012i
\(554\) 9.65002 + 7.01115i 0.409990 + 0.297875i
\(555\) 0 0
\(556\) 1.06262 + 3.27039i 0.0450649 + 0.138696i
\(557\) 4.73996 6.52399i 0.200838 0.276430i −0.696704 0.717359i \(-0.745351\pi\)
0.897542 + 0.440929i \(0.145351\pi\)
\(558\) 1.93381 + 2.66165i 0.0818645 + 0.112677i
\(559\) 14.2140 43.7461i 0.601186 1.85026i
\(560\) 0 0
\(561\) 9.81067 + 13.3698i 0.414207 + 0.564472i
\(562\) 3.41542i 0.144071i
\(563\) 28.2003 + 9.16284i 1.18850 + 0.386168i 0.835519 0.549462i \(-0.185167\pi\)
0.352983 + 0.935630i \(0.385167\pi\)
\(564\) 0.124978 0.0908017i 0.00526252 0.00382344i
\(565\) 0 0
\(566\) 7.83892 + 24.1257i 0.329494 + 1.01408i
\(567\) −4.07703 + 1.32471i −0.171219 + 0.0556325i
\(568\) 18.0653 24.8647i 0.758002 1.04330i
\(569\) −34.0618 + 24.7473i −1.42794 + 1.03746i −0.437548 + 0.899195i \(0.644153\pi\)
−0.990395 + 0.138266i \(0.955847\pi\)
\(570\) 0 0
\(571\) −26.6823 −1.11662 −0.558311 0.829632i \(-0.688550\pi\)
−0.558311 + 0.829632i \(0.688550\pi\)
\(572\) 3.48924 + 10.5684i 0.145893 + 0.441887i
\(573\) 12.6652i 0.529094i
\(574\) 9.02304 27.7700i 0.376614 1.15910i
\(575\) 0 0
\(576\) −6.98733 5.07659i −0.291139 0.211525i
\(577\) −3.14627 + 1.02228i −0.130981 + 0.0425582i −0.373774 0.927520i \(-0.621936\pi\)
0.242793 + 0.970078i \(0.421936\pi\)
\(578\) −8.84214 + 2.87299i −0.367785 + 0.119500i
\(579\) −11.2713 8.18910i −0.468420 0.340327i
\(580\) 0 0
\(581\) −16.6290 + 51.1788i −0.689887 + 2.12325i
\(582\) 2.33822i 0.0969225i
\(583\) −6.82982 4.91296i −0.282862 0.203474i
\(584\) 44.8381 1.85542
\(585\) 0 0
\(586\) 23.2854 16.9178i 0.961911 0.698869i
\(587\) 5.01246 6.89906i 0.206886 0.284755i −0.692947 0.720989i \(-0.743688\pi\)
0.899833 + 0.436234i \(0.143688\pi\)
\(588\) 7.02678 2.28314i 0.289779 0.0941550i
\(589\) 4.89893 + 15.0774i 0.201857 + 0.621252i
\(590\) 0 0
\(591\) −11.8165 + 8.58522i −0.486068 + 0.353149i
\(592\) 8.51544 + 2.76684i 0.349983 + 0.113716i
\(593\) 23.4343i 0.962333i −0.876629 0.481167i \(-0.840213\pi\)
0.876629 0.481167i \(-0.159787\pi\)
\(594\) 3.67135 + 1.17372i 0.150637 + 0.0481584i
\(595\) 0 0
\(596\) −0.760259 + 2.33984i −0.0311414 + 0.0958434i
\(597\) −6.97985 9.60694i −0.285666 0.393186i
\(598\) −0.775895 + 1.06793i −0.0317287 + 0.0436708i
\(599\) −5.82017 17.9126i −0.237805 0.731890i −0.996737 0.0807194i \(-0.974278\pi\)
0.758931 0.651171i \(-0.225722\pi\)
\(600\) 0 0
\(601\) 30.4664 + 22.1351i 1.24275 + 0.902911i 0.997778 0.0666198i \(-0.0212214\pi\)
0.244971 + 0.969530i \(0.421221\pi\)
\(602\) 26.0670 + 35.8782i 1.06241 + 1.46229i
\(603\) 11.5344 + 3.74775i 0.469717 + 0.152620i
\(604\) −3.84453 −0.156432
\(605\) 0 0
\(606\) −8.81471 −0.358073
\(607\) 27.9306 + 9.07520i 1.13367 + 0.368351i 0.814969 0.579505i \(-0.196754\pi\)
0.318699 + 0.947856i \(0.396754\pi\)
\(608\) −11.5501 15.8973i −0.468418 0.644723i
\(609\) −22.2599 16.1728i −0.902019 0.655355i
\(610\) 0 0
\(611\) −0.379834 1.16901i −0.0153665 0.0472931i
\(612\) 1.90858 2.62693i 0.0771498 0.106188i
\(613\) 7.58894 + 10.4453i 0.306515 + 0.421881i 0.934290 0.356513i \(-0.116035\pi\)
−0.627776 + 0.778394i \(0.716035\pi\)
\(614\) 1.77415 5.46027i 0.0715989 0.220359i
\(615\) 0 0
\(616\) −41.6978 13.3307i −1.68005 0.537109i
\(617\) 41.6041i 1.67492i −0.546500 0.837459i \(-0.684040\pi\)
0.546500 0.837459i \(-0.315960\pi\)
\(618\) −18.6443 6.05789i −0.749982 0.243684i
\(619\) 3.45545 2.51053i 0.138886 0.100907i −0.516173 0.856484i \(-0.672644\pi\)
0.655059 + 0.755578i \(0.272644\pi\)
\(620\) 0 0
\(621\) −0.0679277 0.209060i −0.00272585 0.00838929i
\(622\) −15.2633 + 4.95935i −0.612002 + 0.198852i
\(623\) 6.46427 8.89731i 0.258986 0.356463i
\(624\) −9.52890 + 6.92315i −0.381461 + 0.277148i
\(625\) 0 0
\(626\) −4.72918 −0.189016
\(627\) 15.0774 + 10.8457i 0.602132 + 0.433137i
\(628\) 4.82455i 0.192521i
\(629\) −6.06913 + 18.6789i −0.241992 + 0.744775i
\(630\) 0 0
\(631\) 22.2892 + 16.1941i 0.887319 + 0.644675i 0.935178 0.354179i \(-0.115240\pi\)
−0.0478586 + 0.998854i \(0.515240\pi\)
\(632\) −23.4322 + 7.61358i −0.932082 + 0.302852i
\(633\) 21.2579 6.90710i 0.844924 0.274532i
\(634\) 24.2758 + 17.6374i 0.964116 + 0.700471i
\(635\) 0 0
\(636\) −0.509066 + 1.56674i −0.0201858 + 0.0621254i
\(637\) 58.7877i 2.32925i
\(638\) 7.75607 + 23.4920i 0.307066 + 0.930057i
\(639\) 9.98194 0.394879
\(640\) 0 0
\(641\) −7.41712 + 5.38885i −0.292958 + 0.212847i −0.724550 0.689222i \(-0.757952\pi\)
0.431591 + 0.902069i \(0.357952\pi\)
\(642\) −5.30190 + 7.29744i −0.209249 + 0.288007i
\(643\) 3.24223 1.05346i 0.127861 0.0415446i −0.244387 0.969678i \(-0.578587\pi\)
0.372249 + 0.928133i \(0.378587\pi\)
\(644\) 0.189106 + 0.582010i 0.00745184 + 0.0229344i
\(645\) 0 0
\(646\) −26.3254 + 19.1265i −1.03576 + 0.752523i
\(647\) −21.2663 6.90986i −0.836066 0.271654i −0.140468 0.990085i \(-0.544861\pi\)
−0.695598 + 0.718431i \(0.744861\pi\)
\(648\) 3.07901i 0.120955i
\(649\) 15.4427 + 21.0450i 0.606179 + 0.826087i
\(650\) 0 0
\(651\) 3.75019 11.5419i 0.146981 0.452362i
\(652\) −2.03106 2.79551i −0.0795423 0.109481i
\(653\) −8.69667 + 11.9699i −0.340327 + 0.468420i −0.944537 0.328405i \(-0.893489\pi\)
0.604210 + 0.796825i \(0.293489\pi\)
\(654\) −1.60051 4.92586i −0.0625848 0.192616i
\(655\) 0 0
\(656\) 10.8083 + 7.85267i 0.421992 + 0.306595i
\(657\) 8.55964 + 11.7813i 0.333943 + 0.459633i
\(658\) 1.12709 + 0.366214i 0.0439385 + 0.0142765i
\(659\) 47.4724 1.84926 0.924631 0.380864i \(-0.124373\pi\)
0.924631 + 0.380864i \(0.124373\pi\)
\(660\) 0 0
\(661\) −21.6525 −0.842184 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(662\) 3.70273 + 1.20309i 0.143911 + 0.0467594i
\(663\) −15.1861 20.9019i −0.589780 0.811763i
\(664\) −31.2690 22.7183i −1.21347 0.881641i
\(665\) 0 0
\(666\) 1.41064 + 4.34152i 0.0546614 + 0.168230i
\(667\) 0.829302 1.14144i 0.0321107 0.0441966i
\(668\) −0.752510 1.03574i −0.0291155 0.0400740i
\(669\) 5.92024 18.2206i 0.228890 0.704451i
\(670\) 0 0
\(671\) 0.0762228 + 16.1122i 0.00294255 + 0.622005i
\(672\) 15.0424i 0.580275i
\(673\) −36.5133 11.8639i −1.40748 0.457319i −0.495880 0.868391i \(-0.665154\pi\)
−0.911603 + 0.411072i \(0.865154\pi\)
\(674\) −25.7612 + 18.7166i −0.992285 + 0.720937i
\(675\) 0 0
\(676\) −2.74938 8.46172i −0.105745 0.325451i
\(677\) −21.8108 + 7.08677i −0.838259 + 0.272367i −0.696520 0.717537i \(-0.745269\pi\)
−0.141739 + 0.989904i \(0.545269\pi\)
\(678\) −5.26833 + 7.25124i −0.202329 + 0.278482i
\(679\) −6.97782 + 5.06969i −0.267784 + 0.194557i
\(680\) 0 0
\(681\) 15.3759 0.589206
\(682\) −8.79727 + 6.45540i −0.336865 + 0.247190i
\(683\) 25.9084i 0.991359i 0.868505 + 0.495680i \(0.165081\pi\)
−0.868505 + 0.495680i \(0.834919\pi\)
\(684\) 1.12380 3.45871i 0.0429697 0.132247i
\(685\) 0 0
\(686\) 17.6414 + 12.8173i 0.673553 + 0.489365i
\(687\) 8.46560 2.75064i 0.322983 0.104943i
\(688\) −19.2978 + 6.27024i −0.735722 + 0.239050i
\(689\) 10.6044 + 7.70454i 0.403995 + 0.293520i
\(690\) 0 0
\(691\) 4.57824 14.0904i 0.174165 0.536023i −0.825430 0.564505i \(-0.809067\pi\)
0.999594 + 0.0284814i \(0.00906715\pi\)
\(692\) 1.28262i 0.0487579i
\(693\) −4.45748 13.5010i −0.169325 0.512862i
\(694\) −18.3927 −0.698177
\(695\) 0 0
\(696\) 15.9881 11.6161i 0.606029 0.440305i
\(697\) −17.2250 + 23.7082i −0.652445 + 0.898014i
\(698\) 4.04450 1.31414i 0.153087 0.0497409i
\(699\) −7.05677 21.7185i −0.266911 0.821469i
\(700\) 0 0
\(701\) −4.45471 + 3.23653i −0.168252 + 0.122242i −0.668725 0.743510i \(-0.733160\pi\)
0.500473 + 0.865752i \(0.333160\pi\)
\(702\) −5.71118 1.85567i −0.215555 0.0700379i
\(703\) 21.9968i 0.829626i
\(704\) 16.7273 23.2538i 0.630435 0.876409i
\(705\) 0 0
\(706\) −9.87362 + 30.3879i −0.371599 + 1.14366i
\(707\) 19.1119 + 26.3052i 0.718775 + 0.989309i
\(708\) 3.00424 4.13498i 0.112906 0.155402i
\(709\) 5.53161 + 17.0245i 0.207744 + 0.639370i 0.999590 + 0.0286488i \(0.00912044\pi\)
−0.791846 + 0.610721i \(0.790880\pi\)
\(710\) 0 0
\(711\) −6.47371 4.70342i −0.242783 0.176392i
\(712\) 4.64294 + 6.39046i 0.174002 + 0.239493i
\(713\) 0.591840 + 0.192300i 0.0221646 + 0.00720171i
\(714\) 24.9097 0.932222
\(715\) 0 0
\(716\) 1.31386 0.0491012
\(717\) −16.0353 5.21019i −0.598850 0.194578i
\(718\) −0.327024 0.450110i −0.0122044 0.0167980i
\(719\) 26.3673 + 19.1570i 0.983334 + 0.714434i 0.958451 0.285256i \(-0.0920786\pi\)
0.0248831 + 0.999690i \(0.492079\pi\)
\(720\) 0 0
\(721\) 22.3459 + 68.7735i 0.832204 + 2.56126i
\(722\) −8.44284 + 11.6206i −0.314210 + 0.432473i
\(723\) 7.03035 + 9.67644i 0.261461 + 0.359871i
\(724\) 4.04130 12.4378i 0.150194 0.462248i
\(725\) 0 0
\(726\) −3.83515 + 12.1948i −0.142336 + 0.452591i
\(727\) 43.0199i 1.59552i 0.602976 + 0.797759i \(0.293982\pi\)
−0.602976 + 0.797759i \(0.706018\pi\)
\(728\) 64.8654 + 21.0760i 2.40407 + 0.781130i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) −13.7539 42.3302i −0.508708 1.56564i
\(732\) 3.00049 0.974917i 0.110901 0.0360340i
\(733\) 23.9267 32.9323i 0.883755 1.21638i −0.0916123 0.995795i \(-0.529202\pi\)
0.975367 0.220589i \(-0.0707979\pi\)
\(734\) −23.9357 + 17.3903i −0.883483 + 0.641888i
\(735\) 0 0
\(736\) −0.771340 −0.0284320
\(737\) −12.2488 + 38.3136i −0.451189 + 1.41130i
\(738\) 6.81134i 0.250729i
\(739\) −11.7810 + 36.2581i −0.433370 + 1.33377i 0.461379 + 0.887203i \(0.347355\pi\)
−0.894748 + 0.446571i \(0.852645\pi\)
\(740\) 0 0
\(741\) −23.4100 17.0084i −0.859989 0.624819i
\(742\) −12.0192 + 3.90527i −0.441238 + 0.143367i
\(743\) 17.1553 5.57409i 0.629366 0.204493i 0.0230717 0.999734i \(-0.492655\pi\)
0.606294 + 0.795240i \(0.292655\pi\)
\(744\) 7.05183 + 5.12345i 0.258532 + 0.187835i
\(745\) 0 0
\(746\) −0.991061 + 3.05017i −0.0362853 + 0.111675i
\(747\) 12.5530i 0.459289i
\(748\) 8.74240 + 6.28875i 0.319654 + 0.229940i
\(749\) 33.2728 1.21576
\(750\) 0 0
\(751\) 14.1861 10.3068i 0.517657 0.376100i −0.298064 0.954546i \(-0.596341\pi\)
0.815720 + 0.578446i \(0.196341\pi\)
\(752\) −0.318713 + 0.438670i −0.0116223 + 0.0159967i
\(753\) −15.2201 + 4.94533i −0.554653 + 0.180218i
\(754\) −11.9105 36.6568i −0.433756 1.33496i
\(755\) 0 0
\(756\) −2.25225 + 1.63636i −0.0819136 + 0.0595137i
\(757\) 24.6903 + 8.02236i 0.897383 + 0.291578i 0.721157 0.692772i \(-0.243611\pi\)
0.176227 + 0.984350i \(0.443611\pi\)
\(758\) 25.1646i 0.914019i
\(759\) 0.692300 0.228568i 0.0251289 0.00829651i
\(760\) 0 0
\(761\) 8.65430 26.6352i 0.313718 0.965525i −0.662561 0.749008i \(-0.730530\pi\)
0.976279 0.216517i \(-0.0694697\pi\)
\(762\) 1.04591 + 1.43958i 0.0378894 + 0.0521503i
\(763\) −11.2298 + 15.4564i −0.406545 + 0.559561i
\(764\) 2.54164 + 7.82237i 0.0919534 + 0.283003i
\(765\) 0 0
\(766\) −15.2589 11.0862i −0.551326 0.400562i
\(767\) −23.9040 32.9011i −0.863124 1.18799i
\(768\) −13.0911 4.25355i −0.472384 0.153487i
\(769\) −22.9537 −0.827732 −0.413866 0.910338i \(-0.635822\pi\)
−0.413866 + 0.910338i \(0.635822\pi\)
\(770\) 0 0
\(771\) 5.47446 0.197158
\(772\) −8.60489 2.79590i −0.309697 0.100627i
\(773\) 13.8295 + 19.0347i 0.497414 + 0.684631i 0.981734 0.190259i \(-0.0609329\pi\)
−0.484320 + 0.874891i \(0.660933\pi\)
\(774\) −8.36938 6.08071i −0.300831 0.218567i
\(775\) 0 0
\(776\) −1.91434 5.89172i −0.0687207 0.211500i
\(777\) 9.89761 13.6229i 0.355075 0.488718i
\(778\) 11.1287 + 15.3173i 0.398983 + 0.549153i
\(779\) −10.1424 + 31.2151i −0.363389 + 1.11840i
\(780\) 0 0
\(781\) 0.156616 + 33.1060i 0.00560416 + 1.18463i
\(782\) 1.27731i 0.0456765i
\(783\) 6.10429 + 1.98341i 0.218150 + 0.0708811i
\(784\) −20.9804 + 15.2431i −0.749298 + 0.544397i
\(785\) 0 0
\(786\) 0.955657 + 2.94121i 0.0340872 + 0.104910i
\(787\) −24.0356 + 7.80964i −0.856777 + 0.278384i −0.704282 0.709921i \(-0.748731\pi\)
−0.152495 + 0.988304i \(0.548731\pi\)
\(788\) −5.57536 + 7.67383i −0.198614 + 0.273369i
\(789\) 9.69534 7.04408i 0.345163 0.250776i
\(790\) 0 0
\(791\) 33.0621 1.17555
\(792\) 10.2118 0.0483095i 0.362861 0.00171660i
\(793\) 25.1028i 0.891427i
\(794\) 7.17071 22.0692i 0.254479 0.783205i
\(795\) 0 0
\(796\) −6.23888 4.53281i −0.221131 0.160661i
\(797\) 8.23277 2.67499i 0.291620 0.0947530i −0.159554 0.987189i \(-0.551006\pi\)
0.451173 + 0.892436i \(0.351006\pi\)
\(798\) 26.5333 8.62119i 0.939268 0.305187i
\(799\) −0.962236 0.699105i −0.0340414 0.0247326i
\(800\) 0 0
\(801\) −0.792768 + 2.43989i −0.0280111 + 0.0862092i
\(802\) 31.7579i 1.12141i
\(803\) −38.9395 + 28.5736i −1.37415 + 1.00834i
\(804\) 7.87607 0.277768
\(805\) 0 0
\(806\) 13.7534 9.99243i 0.484443 0.351968i
\(807\) −8.02120 + 11.0402i −0.282360 + 0.388635i
\(808\) −22.2108 + 7.21672i −0.781373 + 0.253883i
\(809\) 3.15582 + 9.71261i 0.110953 + 0.341477i 0.991081 0.133258i \(-0.0425438\pi\)
−0.880129 + 0.474735i \(0.842544\pi\)
\(810\) 0 0
\(811\) 38.5273 27.9917i 1.35288 0.982923i 0.354015 0.935240i \(-0.384816\pi\)
0.998862 0.0476835i \(-0.0151839\pi\)
\(812\) −16.9940 5.52167i −0.596371 0.193773i
\(813\) 11.8379i 0.415172i
\(814\) −14.3769 + 4.74664i −0.503910 + 0.166370i
\(815\) 0 0
\(816\) −3.52192 + 10.8394i −0.123292 + 0.379453i
\(817\) −29.3008 40.3291i −1.02510 1.41094i
\(818\) 17.0350 23.4466i 0.595613 0.819792i
\(819\) 6.84507 + 21.0670i 0.239186 + 0.736139i
\(820\) 0 0
\(821\) 38.4767 + 27.9550i 1.34285 + 0.975635i 0.999334 + 0.0364868i \(0.0116167\pi\)
0.343512 + 0.939148i \(0.388383\pi\)
\(822\) 7.00543 + 9.64215i 0.244343 + 0.336309i
\(823\) −23.5253 7.64384i −0.820041 0.266448i −0.131196 0.991356i \(-0.541882\pi\)
−0.688845 + 0.724909i \(0.741882\pi\)
\(824\) −51.9384 −1.80936
\(825\) 0 0
\(826\) 39.2096 1.36428
\(827\) 1.48523 + 0.482580i 0.0516465 + 0.0167810i 0.334726 0.942315i \(-0.391356\pi\)
−0.283080 + 0.959096i \(0.591356\pi\)
\(828\) −0.0839083 0.115490i −0.00291602 0.00401355i
\(829\) 34.1365 + 24.8016i 1.18561 + 0.861396i 0.992793 0.119839i \(-0.0382377\pi\)
0.192817 + 0.981235i \(0.438238\pi\)
\(830\) 0 0
\(831\) 3.17170 + 9.76148i 0.110025 + 0.338622i
\(832\) −26.2320 + 36.1052i −0.909430 + 1.25172i
\(833\) −33.4362 46.0210i −1.15850 1.59453i
\(834\) 1.90158 5.85247i 0.0658465 0.202655i
\(835\) 0 0
\(836\) 11.4887 + 3.67292i 0.397346 + 0.127031i
\(837\) 2.83095i 0.0978521i
\(838\) 18.5968 + 6.04247i 0.642416 + 0.208734i
\(839\) −5.09236 + 3.69982i −0.175808 + 0.127732i −0.672209 0.740361i \(-0.734654\pi\)
0.496401 + 0.868093i \(0.334654\pi\)
\(840\) 0 0
\(841\) 3.76886 + 11.5994i 0.129961 + 0.399978i
\(842\) 26.0850 8.47554i 0.898949 0.292086i
\(843\) −1.72744 + 2.37761i −0.0594961 + 0.0818893i
\(844\) 11.7434 8.53205i 0.404223 0.293685i
\(845\) 0 0
\(846\) −0.276449 −0.00950451
\(847\) 44.7074 14.9954i 1.53617 0.515249i
\(848\) 5.78225i 0.198563i
\(849\) −6.74521 + 20.7596i −0.231495 + 0.712468i
\(850\) 0 0
\(851\) 0.698548 + 0.507525i 0.0239459 + 0.0173977i
\(852\) 6.16514 2.00318i 0.211214 0.0686276i
\(853\) 6.91532 2.24692i 0.236776 0.0769332i −0.188225 0.982126i \(-0.560274\pi\)
0.425002 + 0.905193i \(0.360274\pi\)
\(854\) 19.5803 + 14.2259i 0.670025 + 0.486802i
\(855\) 0 0
\(856\) −7.38491 + 22.7284i −0.252411 + 0.776841i
\(857\) 39.8590i 1.36156i −0.732489 0.680779i \(-0.761641\pi\)
0.732489 0.680779i \(-0.238359\pi\)
\(858\) 6.06490 18.9707i 0.207052 0.647650i
\(859\) −13.5278 −0.461564 −0.230782 0.973006i \(-0.574128\pi\)
−0.230782 + 0.973006i \(0.574128\pi\)
\(860\) 0 0
\(861\) 20.3267 14.7682i 0.692732 0.503299i
\(862\) 25.7223 35.4037i 0.876104 1.20585i
\(863\) −47.8493 + 15.5472i −1.62881 + 0.529232i −0.973997 0.226560i \(-0.927252\pi\)
−0.654812 + 0.755792i \(0.727252\pi\)
\(864\) −1.08433 3.33724i −0.0368898 0.113535i
\(865\) 0 0
\(866\) 29.1228 21.1589i 0.989632 0.719010i
\(867\) −7.60845 2.47214i −0.258397 0.0839581i
\(868\) 7.88119i 0.267505i
\(869\) 15.4977 21.5444i 0.525725 0.730844i
\(870\) 0 0
\(871\) 19.3655 59.6009i 0.656175 2.01950i
\(872\) −8.06574 11.1015i −0.273140 0.375946i
\(873\) 1.18262 1.62773i 0.0400255 0.0550903i
\(874\) 0.442073 + 1.36056i 0.0149534 + 0.0460217i
\(875\) 0 0
\(876\) 7.65096 + 5.55875i 0.258502 + 0.187813i
\(877\) −0.709667 0.976773i −0.0239638 0.0329833i 0.796867 0.604155i \(-0.206489\pi\)
−0.820831 + 0.571171i \(0.806489\pi\)
\(878\) −31.1830 10.1320i −1.05237 0.341937i
\(879\) 24.7665 0.835354
\(880\) 0 0
\(881\) 1.91816 0.0646245 0.0323123 0.999478i \(-0.489713\pi\)
0.0323123 + 0.999478i \(0.489713\pi\)
\(882\) −12.5746 4.08575i −0.423410 0.137574i
\(883\) −34.1439 46.9950i −1.14903 1.58151i −0.745446 0.666566i \(-0.767763\pi\)
−0.403587 0.914941i \(-0.632237\pi\)
\(884\) −13.5740 9.86208i −0.456543 0.331698i
\(885\) 0 0
\(886\) 5.25828 + 16.1833i 0.176656 + 0.543690i
\(887\) −17.7762 + 24.4668i −0.596866 + 0.821516i −0.995417 0.0956306i \(-0.969513\pi\)
0.398551 + 0.917146i \(0.369513\pi\)
\(888\) 7.10892 + 9.78459i 0.238560 + 0.328349i
\(889\) 2.02832 6.24251i 0.0680275 0.209367i
\(890\) 0 0
\(891\) 1.96213 + 2.67395i 0.0657340 + 0.0895808i
\(892\) 12.4417i 0.416578i
\(893\) −1.26691 0.411644i −0.0423956 0.0137752i
\(894\) 3.56185 2.58784i 0.119126 0.0865503i
\(895\) 0 0
\(896\) −3.99968 12.3098i −0.133620 0.411240i
\(897\) −1.08026 + 0.350999i −0.0360689 + 0.0117195i
\(898\) 8.19553 11.2802i 0.273488 0.376425i
\(899\) −14.7001 + 10.6802i −0.490275 + 0.356206i
\(900\) 0 0
\(901\) 12.6835 0.422550
\(902\) −22.5904 + 0.106870i −0.752179 + 0.00355837i
\(903\) 38.1603i 1.26990i
\(904\) −7.33815 + 22.5845i −0.244063 + 0.751149i
\(905\) 0 0
\(906\) 5.56597 + 4.04391i 0.184917 + 0.134350i
\(907\) −30.4023 + 9.87830i −1.00949 + 0.328004i −0.766652 0.642063i \(-0.778079\pi\)
−0.242839 + 0.970066i \(0.578079\pi\)
\(908\) 9.49660 3.08563i 0.315156 0.102400i
\(909\) −6.13627 4.45826i −0.203527 0.147871i
\(910\) 0 0
\(911\) −16.0211 + 49.3079i −0.530803 + 1.63364i 0.221745 + 0.975105i \(0.428825\pi\)
−0.752547 + 0.658538i \(0.771175\pi\)
\(912\) 12.7648i 0.422684i
\(913\) 41.6330 0.196955i 1.37785 0.00651826i
\(914\) −11.6722 −0.386083
\(915\) 0 0
\(916\) 4.67660 3.39775i 0.154519 0.112265i
\(917\) 6.70525 9.22898i 0.221427 0.304768i
\(918\) −5.52634 + 1.79562i −0.182396 + 0.0592642i
\(919\) 10.5710 + 32.5341i 0.348704 + 1.07320i 0.959571 + 0.281468i \(0.0908212\pi\)
−0.610866 + 0.791734i \(0.709179\pi\)
\(920\) 0 0
\(921\) 3.99673 2.90379i 0.131697 0.0956832i
\(922\) 14.8648 + 4.82988i 0.489547 + 0.159064i
\(923\) 51.5790i 1.69774i
\(924\) −5.46245 7.44411i −0.179702 0.244893i
\(925\) 0 0
\(926\) 6.74561 20.7609i 0.221675 0.682244i
\(927\) −9.91508 13.6469i −0.325654 0.448224i
\(928\) 13.2382 18.2208i 0.434565 0.598127i
\(929\) −5.66990 17.4502i −0.186023 0.572521i 0.813941 0.580947i \(-0.197318\pi\)
−0.999964 + 0.00842624i \(0.997318\pi\)
\(930\) 0 0
\(931\) −51.5433 37.4484i −1.68926 1.22732i
\(932\) −8.71693 11.9978i −0.285533 0.393002i
\(933\) −13.1337 4.26740i −0.429978 0.139708i
\(934\) −30.8561 −1.00964
\(935\) 0 0
\(936\) −15.9100 −0.520033
\(937\) −3.21852 1.04576i −0.105144 0.0341635i 0.255972 0.966684i \(-0.417604\pi\)
−0.361117 + 0.932521i \(0.617604\pi\)
\(938\) 35.5145 + 48.8815i 1.15959 + 1.59604i
\(939\) −3.29217 2.39190i −0.107436 0.0780567i
\(940\) 0 0
\(941\) −10.8465 33.3822i −0.353587 1.08823i −0.956824 0.290668i \(-0.906123\pi\)
0.603237 0.797562i \(-0.293877\pi\)
\(942\) 5.07476 6.98480i 0.165344 0.227577i
\(943\) 0.757278 + 1.04230i 0.0246604 + 0.0339421i
\(944\) −5.54375 + 17.0619i −0.180434 + 0.555318i
\(945\) 0 0
\(946\) 20.0359 27.8532i 0.651423 0.905585i
\(947\) 39.0512i 1.26899i 0.772925 + 0.634497i \(0.218793\pi\)
−0.772925 + 0.634497i \(0.781207\pi\)
\(948\) −4.94223 1.60583i −0.160516 0.0521549i
\(949\) 60.8769 44.2297i 1.97615 1.43576i
\(950\) 0 0
\(951\) 7.97880 + 24.5562i 0.258730 + 0.796290i
\(952\) 62.7660 20.3939i 2.03426 0.660971i
\(953\) 14.5055 19.9652i 0.469881 0.646735i −0.506640 0.862158i \(-0.669113\pi\)
0.976521 + 0.215422i \(0.0691127\pi\)
\(954\) 2.38500 1.73281i 0.0772173 0.0561017i
\(955\) 0 0
\(956\) −10.9495 −0.354131
\(957\) −6.48236 + 20.2765i −0.209545 + 0.655448i
\(958\) 12.5315i 0.404873i
\(959\) 13.5855 41.8118i 0.438698 1.35017i
\(960\) 0 0
\(961\) 18.5958 + 13.5107i 0.599865 + 0.435827i
\(962\) 22.4336 7.28913i 0.723290 0.235011i
\(963\) −7.38173 + 2.39847i −0.237873 + 0.0772896i
\(964\) 6.28401 + 4.56560i 0.202394 + 0.147048i
\(965\) 0 0
\(966\) 0.338412 1.04153i 0.0108882 0.0335105i
\(967\) 1.20724i 0.0388222i −0.999812 0.0194111i \(-0.993821\pi\)
0.999812 0.0194111i \(-0.00617914\pi\)
\(968\) 0.320445 + 33.8676i 0.0102995 + 1.08855i
\(969\) −27.9999 −0.899486
\(970\) 0 0
\(971\) −40.7599 + 29.6138i −1.30805 + 0.950353i −0.999999 0.00101751i \(-0.999676\pi\)
−0.308049 + 0.951370i \(0.599676\pi\)
\(972\) 0.381716 0.525387i 0.0122435 0.0168518i
\(973\) −21.5882 + 7.01442i −0.692085 + 0.224872i
\(974\) −2.44597 7.52793i −0.0783740 0.241210i
\(975\) 0 0
\(976\) −8.95877 + 6.50893i −0.286763 + 0.208346i
\(977\) 5.59535 + 1.81804i 0.179011 + 0.0581642i 0.397151 0.917753i \(-0.369999\pi\)
−0.218140 + 0.975917i \(0.569999\pi\)
\(978\) 6.18362i 0.197730i
\(979\) −8.10454 2.59100i −0.259022 0.0828088i
\(980\) 0 0
\(981\) 1.37720 4.23858i 0.0439706 0.135328i
\(982\) 17.8256 + 24.5348i 0.568837 + 0.782937i
\(983\) 21.4482 29.5210i 0.684093 0.941573i −0.315881 0.948799i \(-0.602300\pi\)
0.999974 + 0.00722580i \(0.00230006\pi\)
\(984\) 5.57654 + 17.1628i 0.177774 + 0.547131i
\(985\) 0 0
\(986\) −30.1730 21.9219i −0.960903 0.698137i
\(987\) 0.599391 + 0.824990i 0.0190788 + 0.0262597i
\(988\) −17.8720 5.80695i −0.568583 0.184744i
\(989\) −1.95677 −0.0622216
\(990\) 0 0
\(991\) −36.8404 −1.17027 −0.585137 0.810934i \(-0.698959\pi\)
−0.585137 + 0.810934i \(0.698959\pi\)
\(992\) 9.44757 + 3.06970i 0.299961 + 0.0974631i
\(993\) 1.96913 + 2.71027i 0.0624883 + 0.0860078i
\(994\) 40.2320 + 29.2302i 1.27608 + 0.927127i
\(995\) 0 0
\(996\) −2.51913 7.75307i −0.0798216 0.245666i
\(997\) −20.4957 + 28.2099i −0.649105 + 0.893417i −0.999060 0.0433498i \(-0.986197\pi\)
0.349955 + 0.936767i \(0.386197\pi\)
\(998\) −13.2406 18.2242i −0.419125 0.576877i
\(999\) −1.21383 + 3.73577i −0.0384037 + 0.118195i
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 825.2.bx.h.724.2 16
5.2 odd 4 165.2.m.a.31.1 yes 8
5.3 odd 4 825.2.n.k.526.2 8
5.4 even 2 inner 825.2.bx.h.724.3 16
11.5 even 5 inner 825.2.bx.h.49.3 16
15.2 even 4 495.2.n.d.361.2 8
55.7 even 20 1815.2.a.o.1.3 4
55.18 even 20 9075.2.a.dj.1.2 4
55.27 odd 20 165.2.m.a.16.1 8
55.37 odd 20 1815.2.a.x.1.2 4
55.38 odd 20 825.2.n.k.676.2 8
55.48 odd 20 9075.2.a.cl.1.3 4
55.49 even 10 inner 825.2.bx.h.49.2 16
165.62 odd 20 5445.2.a.bv.1.2 4
165.92 even 20 5445.2.a.be.1.3 4
165.137 even 20 495.2.n.d.181.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.a.16.1 8 55.27 odd 20
165.2.m.a.31.1 yes 8 5.2 odd 4
495.2.n.d.181.2 8 165.137 even 20
495.2.n.d.361.2 8 15.2 even 4
825.2.n.k.526.2 8 5.3 odd 4
825.2.n.k.676.2 8 55.38 odd 20
825.2.bx.h.49.2 16 55.49 even 10 inner
825.2.bx.h.49.3 16 11.5 even 5 inner
825.2.bx.h.724.2 16 1.1 even 1 trivial
825.2.bx.h.724.3 16 5.4 even 2 inner
1815.2.a.o.1.3 4 55.7 even 20
1815.2.a.x.1.2 4 55.37 odd 20
5445.2.a.be.1.3 4 165.92 even 20
5445.2.a.bv.1.2 4 165.62 odd 20
9075.2.a.cl.1.3 4 55.48 odd 20
9075.2.a.dj.1.2 4 55.18 even 20