Properties

Label 39.3.l.b.19.3
Level $39$
Weight $3$
Character 39.19
Analytic conductor $1.063$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,3,Mod(7,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 39.l (of order \(12\), degree \(4\), 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: \(1.06267303101\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} - 22128 x^{3} + 28800 x^{2} - 17280 x + 5184 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 19.3
Root \(2.74087 - 2.74087i\) of defining polynomial
Character \(\chi\) \(=\) 39.19
Dual form 39.3.l.b.37.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00323 + 3.74409i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-9.54767 + 5.51235i) q^{4} +(3.30327 - 3.30327i) q^{5} +(6.48496 + 1.73764i) q^{6} +(0.235277 - 0.878067i) q^{7} +(-19.2537 - 19.2537i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.00323 + 3.74409i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-9.54767 + 5.51235i) q^{4} +(3.30327 - 3.30327i) q^{5} +(6.48496 + 1.73764i) q^{6} +(0.235277 - 0.878067i) q^{7} +(-19.2537 - 19.2537i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(15.6817 + 9.05381i) q^{10} +(5.60803 - 1.50267i) q^{11} +19.0953i q^{12} +(-3.44589 + 12.5350i) q^{13} +3.52360 q^{14} +(-2.09419 - 7.81561i) q^{15} +(30.7226 - 53.2130i) q^{16} +(6.85933 - 3.96024i) q^{17} +(8.22260 - 8.22260i) q^{18} +(-27.7306 - 7.43040i) q^{19} +(-13.3297 + 49.7472i) q^{20} +(-1.11334 - 1.11334i) q^{21} +(11.2522 + 19.4895i) q^{22} +(-9.29823 - 5.36834i) q^{23} +(-45.5549 + 12.2064i) q^{24} +3.17685i q^{25} +(-50.3892 - 0.326284i) q^{26} -5.19615 q^{27} +(2.59386 + 9.68042i) q^{28} +(7.56721 - 13.1068i) q^{29} +(27.1614 - 15.6817i) q^{30} +(-13.6593 + 13.6593i) q^{31} +(124.852 + 33.4539i) q^{32} +(2.60270 - 9.71339i) q^{33} +(21.7090 + 21.7090i) q^{34} +(-2.12331 - 3.67768i) q^{35} +(28.6430 + 16.5370i) q^{36} +(-2.46101 + 0.659427i) q^{37} -111.280i q^{38} +(15.8183 + 16.0244i) q^{39} -127.201 q^{40} +(11.4567 + 42.7572i) q^{41} +(3.05153 - 5.28540i) q^{42} +(-3.74071 + 2.15970i) q^{43} +(-45.2604 + 45.2604i) q^{44} +(-13.5370 - 3.62724i) q^{45} +(10.7713 - 40.1991i) q^{46} +(18.4764 + 18.4764i) q^{47} +(-53.2130 - 92.1677i) q^{48} +(41.7196 + 24.0868i) q^{49} +(-11.8944 + 3.18710i) q^{50} -13.7187i q^{51} +(-36.1970 - 138.675i) q^{52} +81.0078 q^{53} +(-5.21292 - 19.4549i) q^{54} +(13.5611 - 23.4885i) q^{55} +(-21.4361 + 12.3761i) q^{56} +(-35.1610 + 35.1610i) q^{57} +(56.6647 + 15.1832i) q^{58} +(3.85460 - 14.3856i) q^{59} +(63.0770 + 63.0770i) q^{60} +(17.7204 + 30.6926i) q^{61} +(-64.8452 - 37.4384i) q^{62} +(-2.63420 + 0.705832i) q^{63} +255.238i q^{64} +(30.0237 + 52.7891i) q^{65} +38.9789 q^{66} +(-24.9466 - 93.1019i) q^{67} +(-43.6604 + 75.6220i) q^{68} +(-16.1050 + 9.29823i) q^{69} +(11.6394 - 11.6394i) q^{70} +(-94.0489 - 25.2003i) q^{71} +(-21.1421 + 78.9033i) q^{72} +(3.74695 + 3.74695i) q^{73} +(-4.93791 - 8.55271i) q^{74} +(4.76528 + 2.75123i) q^{75} +(305.722 - 81.9179i) q^{76} -5.27777i q^{77} +(-44.1277 + 75.3012i) q^{78} +43.6772 q^{79} +(-74.2920 - 277.262i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-148.593 + 85.7902i) q^{82} +(-29.7042 + 29.7042i) q^{83} +(16.7670 + 4.49270i) q^{84} +(9.57649 - 35.7399i) q^{85} +(-11.8389 - 11.8389i) q^{86} +(-13.1068 - 22.7016i) q^{87} +(-136.908 - 79.0436i) q^{88} +(-27.1548 + 7.27610i) q^{89} -54.3229i q^{90} +(10.1958 + 5.97492i) q^{91} +118.369 q^{92} +(8.65967 + 32.3183i) q^{93} +(-50.6414 + 87.7135i) q^{94} +(-116.146 + 67.0571i) q^{95} +(158.306 - 158.306i) q^{96} +(-129.936 - 34.8163i) q^{97} +(-48.3291 + 180.367i) q^{98} +(-12.3161 - 12.3161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22} - 18 q^{23} - 54 q^{24} - 44 q^{26} - 78 q^{28} + 128 q^{29} + 6 q^{30} - 66 q^{31} + 358 q^{32} - 6 q^{33} + 336 q^{34} + 14 q^{35} + 36 q^{36} - 36 q^{37} - 18 q^{39} - 12 q^{40} - 326 q^{41} - 6 q^{42} + 60 q^{43} - 236 q^{44} - 24 q^{45} - 138 q^{46} + 40 q^{47} - 144 q^{48} + 78 q^{49} - 40 q^{50} - 392 q^{52} + 80 q^{53} - 18 q^{54} + 166 q^{55} - 102 q^{56} + 250 q^{58} - 164 q^{59} + 396 q^{60} - 98 q^{61} + 228 q^{62} + 66 q^{63} + 514 q^{65} + 60 q^{66} - 230 q^{67} + 78 q^{68} - 54 q^{69} - 92 q^{70} + 70 q^{71} - 18 q^{72} + 106 q^{73} - 16 q^{74} - 150 q^{75} + 534 q^{76} - 456 q^{78} + 16 q^{79} + 124 q^{80} - 54 q^{81} - 156 q^{82} - 176 q^{83} - 30 q^{84} + 90 q^{85} - 612 q^{86} + 48 q^{87} - 318 q^{88} - 476 q^{89} + 106 q^{91} + 228 q^{92} + 66 q^{93} - 374 q^{94} - 234 q^{95} + 384 q^{96} - 306 q^{97} - 350 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00323 + 3.74409i 0.501613 + 1.87205i 0.489288 + 0.872122i \(0.337257\pi\)
0.0123254 + 0.999924i \(0.496077\pi\)
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) −9.54767 + 5.51235i −2.38692 + 1.37809i
\(5\) 3.30327 3.30327i 0.660653 0.660653i −0.294881 0.955534i \(-0.595280\pi\)
0.955534 + 0.294881i \(0.0952799\pi\)
\(6\) 6.48496 + 1.73764i 1.08083 + 0.289607i
\(7\) 0.235277 0.878067i 0.0336111 0.125438i −0.947082 0.320992i \(-0.895984\pi\)
0.980693 + 0.195554i \(0.0626504\pi\)
\(8\) −19.2537 19.2537i −2.40672 2.40672i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 15.6817 + 9.05381i 1.56817 + 0.905381i
\(11\) 5.60803 1.50267i 0.509821 0.136606i 0.00526673 0.999986i \(-0.498324\pi\)
0.504554 + 0.863380i \(0.331657\pi\)
\(12\) 19.0953i 1.59128i
\(13\) −3.44589 + 12.5350i −0.265068 + 0.964230i
\(14\) 3.52360 0.251686
\(15\) −2.09419 7.81561i −0.139613 0.521041i
\(16\) 30.7226 53.2130i 1.92016 3.32581i
\(17\) 6.85933 3.96024i 0.403490 0.232955i −0.284499 0.958676i \(-0.591827\pi\)
0.687989 + 0.725721i \(0.258494\pi\)
\(18\) 8.22260 8.22260i 0.456811 0.456811i
\(19\) −27.7306 7.43040i −1.45951 0.391074i −0.560188 0.828366i \(-0.689271\pi\)
−0.899320 + 0.437292i \(0.855938\pi\)
\(20\) −13.3297 + 49.7472i −0.666487 + 2.48736i
\(21\) −1.11334 1.11334i −0.0530164 0.0530164i
\(22\) 11.2522 + 19.4895i 0.511466 + 0.885885i
\(23\) −9.29823 5.36834i −0.404271 0.233406i 0.284054 0.958808i \(-0.408320\pi\)
−0.688325 + 0.725402i \(0.741654\pi\)
\(24\) −45.5549 + 12.2064i −1.89812 + 0.508599i
\(25\) 3.17685i 0.127074i
\(26\) −50.3892 0.326284i −1.93804 0.0125494i
\(27\) −5.19615 −0.192450
\(28\) 2.59386 + 9.68042i 0.0926379 + 0.345729i
\(29\) 7.56721 13.1068i 0.260938 0.451958i −0.705553 0.708657i \(-0.749301\pi\)
0.966491 + 0.256699i \(0.0826348\pi\)
\(30\) 27.1614 15.6817i 0.905381 0.522722i
\(31\) −13.6593 + 13.6593i −0.440624 + 0.440624i −0.892222 0.451598i \(-0.850854\pi\)
0.451598 + 0.892222i \(0.350854\pi\)
\(32\) 124.852 + 33.4539i 3.90162 + 1.04544i
\(33\) 2.60270 9.71339i 0.0788696 0.294345i
\(34\) 21.7090 + 21.7090i 0.638499 + 0.638499i
\(35\) −2.12331 3.67768i −0.0606659 0.105076i
\(36\) 28.6430 + 16.5370i 0.795639 + 0.459362i
\(37\) −2.46101 + 0.659427i −0.0665139 + 0.0178223i −0.291923 0.956442i \(-0.594295\pi\)
0.225409 + 0.974264i \(0.427628\pi\)
\(38\) 111.280i 2.92843i
\(39\) 15.8183 + 16.0244i 0.405596 + 0.410883i
\(40\) −127.201 −3.18001
\(41\) 11.4567 + 42.7572i 0.279433 + 1.04286i 0.952812 + 0.303560i \(0.0981754\pi\)
−0.673379 + 0.739297i \(0.735158\pi\)
\(42\) 3.05153 5.28540i 0.0726554 0.125843i
\(43\) −3.74071 + 2.15970i −0.0869932 + 0.0502255i −0.542866 0.839820i \(-0.682661\pi\)
0.455872 + 0.890045i \(0.349327\pi\)
\(44\) −45.2604 + 45.2604i −1.02864 + 1.02864i
\(45\) −13.5370 3.62724i −0.300823 0.0806053i
\(46\) 10.7713 40.1991i 0.234159 0.873893i
\(47\) 18.4764 + 18.4764i 0.393115 + 0.393115i 0.875796 0.482681i \(-0.160337\pi\)
−0.482681 + 0.875796i \(0.660337\pi\)
\(48\) −53.2130 92.1677i −1.10860 1.92016i
\(49\) 41.7196 + 24.0868i 0.851420 + 0.491568i
\(50\) −11.8944 + 3.18710i −0.237888 + 0.0637420i
\(51\) 13.7187i 0.268993i
\(52\) −36.1970 138.675i −0.696097 2.66682i
\(53\) 81.0078 1.52845 0.764224 0.644951i \(-0.223122\pi\)
0.764224 + 0.644951i \(0.223122\pi\)
\(54\) −5.21292 19.4549i −0.0965355 0.360275i
\(55\) 13.5611 23.4885i 0.246566 0.427064i
\(56\) −21.4361 + 12.3761i −0.382787 + 0.221002i
\(57\) −35.1610 + 35.1610i −0.616861 + 0.616861i
\(58\) 56.6647 + 15.1832i 0.976977 + 0.261780i
\(59\) 3.85460 14.3856i 0.0653322 0.243823i −0.925536 0.378661i \(-0.876385\pi\)
0.990868 + 0.134838i \(0.0430514\pi\)
\(60\) 63.0770 + 63.0770i 1.05128 + 1.05128i
\(61\) 17.7204 + 30.6926i 0.290498 + 0.503158i 0.973928 0.226859i \(-0.0728456\pi\)
−0.683429 + 0.730017i \(0.739512\pi\)
\(62\) −64.8452 37.4384i −1.04589 0.603845i
\(63\) −2.63420 + 0.705832i −0.0418127 + 0.0112037i
\(64\) 255.238i 3.98809i
\(65\) 30.0237 + 52.7891i 0.461903 + 0.812140i
\(66\) 38.9789 0.590590
\(67\) −24.9466 93.1019i −0.372337 1.38958i −0.857197 0.514989i \(-0.827796\pi\)
0.484860 0.874592i \(-0.338871\pi\)
\(68\) −43.6604 + 75.6220i −0.642065 + 1.11209i
\(69\) −16.1050 + 9.29823i −0.233406 + 0.134757i
\(70\) 11.6394 11.6394i 0.166277 0.166277i
\(71\) −94.0489 25.2003i −1.32463 0.354934i −0.473921 0.880567i \(-0.657162\pi\)
−0.850711 + 0.525633i \(0.823828\pi\)
\(72\) −21.1421 + 78.9033i −0.293640 + 1.09588i
\(73\) 3.74695 + 3.74695i 0.0513281 + 0.0513281i 0.732305 0.680977i \(-0.238445\pi\)
−0.680977 + 0.732305i \(0.738445\pi\)
\(74\) −4.93791 8.55271i −0.0667285 0.115577i
\(75\) 4.76528 + 2.75123i 0.0635370 + 0.0366831i
\(76\) 305.722 81.9179i 4.02266 1.07787i
\(77\) 5.27777i 0.0685425i
\(78\) −44.1277 + 75.3012i −0.565740 + 0.965399i
\(79\) 43.6772 0.552876 0.276438 0.961032i \(-0.410846\pi\)
0.276438 + 0.961032i \(0.410846\pi\)
\(80\) −74.2920 277.262i −0.928650 3.46577i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −148.593 + 85.7902i −1.81211 + 1.04622i
\(83\) −29.7042 + 29.7042i −0.357882 + 0.357882i −0.863032 0.505150i \(-0.831437\pi\)
0.505150 + 0.863032i \(0.331437\pi\)
\(84\) 16.7670 + 4.49270i 0.199607 + 0.0534845i
\(85\) 9.57649 35.7399i 0.112665 0.420470i
\(86\) −11.8389 11.8389i −0.137661 0.137661i
\(87\) −13.1068 22.7016i −0.150653 0.260938i
\(88\) −136.908 79.0436i −1.55577 0.898223i
\(89\) −27.1548 + 7.27610i −0.305110 + 0.0817540i −0.408126 0.912926i \(-0.633817\pi\)
0.103016 + 0.994680i \(0.467151\pi\)
\(90\) 54.3229i 0.603588i
\(91\) 10.1958 + 5.97492i 0.112042 + 0.0656584i
\(92\) 118.369 1.28661
\(93\) 8.65967 + 32.3183i 0.0931148 + 0.347509i
\(94\) −50.6414 + 87.7135i −0.538738 + 0.933122i
\(95\) −116.146 + 67.0571i −1.22259 + 0.705864i
\(96\) 158.306 158.306i 1.64902 1.64902i
\(97\) −129.936 34.8163i −1.33955 0.358930i −0.483281 0.875465i \(-0.660555\pi\)
−0.856266 + 0.516535i \(0.827222\pi\)
\(98\) −48.3291 + 180.367i −0.493154 + 1.84048i
\(99\) −12.3161 12.3161i −0.124405 0.124405i
\(100\) −17.5119 30.3315i −0.175119 0.303315i
\(101\) 85.7700 + 49.5193i 0.849208 + 0.490290i 0.860383 0.509647i \(-0.170224\pi\)
−0.0111758 + 0.999938i \(0.503557\pi\)
\(102\) 51.3640 13.7629i 0.503568 0.134931i
\(103\) 132.264i 1.28412i −0.766655 0.642059i \(-0.778080\pi\)
0.766655 0.642059i \(-0.221920\pi\)
\(104\) 307.692 174.999i 2.95857 1.68268i
\(105\) −7.35535 −0.0700510
\(106\) 81.2692 + 303.301i 0.766690 + 2.86133i
\(107\) 69.0289 119.561i 0.645130 1.11740i −0.339142 0.940735i \(-0.610137\pi\)
0.984272 0.176662i \(-0.0565299\pi\)
\(108\) 49.6111 28.6430i 0.459362 0.265213i
\(109\) 26.2463 26.2463i 0.240792 0.240792i −0.576386 0.817178i \(-0.695538\pi\)
0.817178 + 0.576386i \(0.195538\pi\)
\(110\) 101.548 + 27.2097i 0.923165 + 0.247361i
\(111\) −1.14216 + 4.26260i −0.0102897 + 0.0384018i
\(112\) −39.4963 39.4963i −0.352645 0.352645i
\(113\) −90.5319 156.806i −0.801167 1.38766i −0.918848 0.394611i \(-0.870879\pi\)
0.117681 0.993051i \(-0.462454\pi\)
\(114\) −166.921 96.3717i −1.46422 0.845366i
\(115\) −48.4476 + 12.9815i −0.421283 + 0.112883i
\(116\) 166.852i 1.43838i
\(117\) 37.7357 9.84980i 0.322527 0.0841864i
\(118\) 57.7279 0.489219
\(119\) −1.86351 6.95471i −0.0156597 0.0584429i
\(120\) −110.159 + 190.801i −0.917991 + 1.59001i
\(121\) −75.5971 + 43.6460i −0.624769 + 0.360711i
\(122\) −97.1385 + 97.1385i −0.796217 + 0.796217i
\(123\) 74.0576 + 19.8437i 0.602094 + 0.161331i
\(124\) 55.1198 205.710i 0.444514 1.65895i
\(125\) 93.0757 + 93.0757i 0.744605 + 0.744605i
\(126\) −5.28540 9.15459i −0.0419476 0.0726554i
\(127\) 188.451 + 108.802i 1.48387 + 0.856710i 0.999832 0.0183386i \(-0.00583769\pi\)
0.484034 + 0.875049i \(0.339171\pi\)
\(128\) −456.228 + 122.246i −3.56428 + 0.955045i
\(129\) 7.48141i 0.0579954i
\(130\) −167.527 + 165.371i −1.28867 + 1.27208i
\(131\) −158.787 −1.21212 −0.606058 0.795421i \(-0.707250\pi\)
−0.606058 + 0.795421i \(0.707250\pi\)
\(132\) 28.6939 + 107.087i 0.217378 + 0.811267i
\(133\) −13.0488 + 22.6012i −0.0981112 + 0.169934i
\(134\) 323.555 186.805i 2.41459 1.39406i
\(135\) −17.1643 + 17.1643i −0.127143 + 0.127143i
\(136\) −208.317 55.8184i −1.53174 0.410430i
\(137\) 62.8465 234.546i 0.458733 1.71202i −0.218141 0.975917i \(-0.569999\pi\)
0.676874 0.736098i \(-0.263334\pi\)
\(138\) −50.9704 50.9704i −0.369351 0.369351i
\(139\) 39.8702 + 69.0573i 0.286836 + 0.496815i 0.973053 0.230582i \(-0.0740631\pi\)
−0.686217 + 0.727397i \(0.740730\pi\)
\(140\) 40.5452 + 23.4088i 0.289609 + 0.167206i
\(141\) 43.7157 11.7136i 0.310040 0.0830751i
\(142\) 377.409i 2.65781i
\(143\) −0.488720 + 75.4746i −0.00341762 + 0.527794i
\(144\) −184.335 −1.28011
\(145\) −18.2987 68.2917i −0.126198 0.470978i
\(146\) −10.2699 + 17.7880i −0.0703418 + 0.121836i
\(147\) 72.2605 41.7196i 0.491568 0.283807i
\(148\) 19.8619 19.8619i 0.134202 0.134202i
\(149\) −46.6353 12.4959i −0.312988 0.0838650i 0.0989054 0.995097i \(-0.468466\pi\)
−0.411894 + 0.911232i \(0.635133\pi\)
\(150\) −5.52022 + 20.6017i −0.0368015 + 0.137345i
\(151\) 181.386 + 181.386i 1.20123 + 1.20123i 0.973793 + 0.227437i \(0.0730346\pi\)
0.227437 + 0.973793i \(0.426965\pi\)
\(152\) 390.856 + 676.982i 2.57142 + 4.45383i
\(153\) −20.5780 11.8807i −0.134497 0.0776517i
\(154\) 19.7605 5.29480i 0.128315 0.0343818i
\(155\) 90.2409i 0.582199i
\(156\) −239.360 65.8003i −1.53436 0.421797i
\(157\) 80.3793 0.511970 0.255985 0.966681i \(-0.417600\pi\)
0.255985 + 0.966681i \(0.417600\pi\)
\(158\) 43.8181 + 163.531i 0.277330 + 1.03501i
\(159\) 70.1548 121.512i 0.441225 0.764224i
\(160\) 522.926 301.911i 3.26829 1.88695i
\(161\) −6.90142 + 6.90142i −0.0428660 + 0.0428660i
\(162\) −33.6968 9.02904i −0.208005 0.0557348i
\(163\) −45.5771 + 170.096i −0.279614 + 1.04353i 0.673072 + 0.739577i \(0.264974\pi\)
−0.952686 + 0.303956i \(0.901692\pi\)
\(164\) −345.077 345.077i −2.10413 2.10413i
\(165\) −23.4885 40.6833i −0.142355 0.246566i
\(166\) −141.015 81.4153i −0.849490 0.490453i
\(167\) −140.594 + 37.6720i −0.841880 + 0.225581i −0.653890 0.756590i \(-0.726864\pi\)
−0.187990 + 0.982171i \(0.560197\pi\)
\(168\) 42.8721i 0.255191i
\(169\) −145.252 86.3883i −0.859478 0.511173i
\(170\) 143.421 0.843653
\(171\) 22.2912 + 83.1919i 0.130358 + 0.486503i
\(172\) 23.8100 41.2401i 0.138430 0.239768i
\(173\) 136.733 78.9429i 0.790364 0.456317i −0.0497264 0.998763i \(-0.515835\pi\)
0.840091 + 0.542446i \(0.182502\pi\)
\(174\) 71.8479 71.8479i 0.412919 0.412919i
\(175\) 2.78949 + 0.747441i 0.0159399 + 0.00427109i
\(176\) 92.3315 344.586i 0.524611 1.95787i
\(177\) −18.2402 18.2402i −0.103052 0.103052i
\(178\) −54.4848 94.3705i −0.306094 0.530171i
\(179\) −82.5165 47.6409i −0.460986 0.266150i 0.251473 0.967864i \(-0.419085\pi\)
−0.712459 + 0.701714i \(0.752418\pi\)
\(180\) 149.242 39.9892i 0.829121 0.222162i
\(181\) 169.256i 0.935116i 0.883962 + 0.467558i \(0.154866\pi\)
−0.883962 + 0.467558i \(0.845134\pi\)
\(182\) −12.1419 + 44.1683i −0.0667139 + 0.242683i
\(183\) 61.3853 0.335439
\(184\) 75.6652 + 282.386i 0.411224 + 1.53471i
\(185\) −5.95112 + 10.3076i −0.0321682 + 0.0557170i
\(186\) −112.315 + 64.8452i −0.603845 + 0.348630i
\(187\) 32.5164 32.5164i 0.173885 0.173885i
\(188\) −278.255 74.5582i −1.48008 0.396586i
\(189\) −1.22254 + 4.56257i −0.00646845 + 0.0241406i
\(190\) −367.589 367.589i −1.93468 1.93468i
\(191\) 46.3432 + 80.2688i 0.242635 + 0.420256i 0.961464 0.274931i \(-0.0886550\pi\)
−0.718829 + 0.695187i \(0.755322\pi\)
\(192\) 382.857 + 221.043i 1.99405 + 1.15126i
\(193\) −310.573 + 83.2179i −1.60919 + 0.431181i −0.947801 0.318863i \(-0.896699\pi\)
−0.661388 + 0.750044i \(0.730032\pi\)
\(194\) 521.421i 2.68774i
\(195\) 105.185 + 0.681103i 0.539410 + 0.00349283i
\(196\) −531.100 −2.70969
\(197\) −29.0041 108.245i −0.147229 0.549466i −0.999646 0.0266038i \(-0.991531\pi\)
0.852417 0.522863i \(-0.175136\pi\)
\(198\) 33.7567 58.4684i 0.170489 0.295295i
\(199\) −59.4497 + 34.3233i −0.298742 + 0.172479i −0.641878 0.766807i \(-0.721844\pi\)
0.343136 + 0.939286i \(0.388511\pi\)
\(200\) 61.1663 61.1663i 0.305831 0.305831i
\(201\) −161.257 43.2087i −0.802275 0.214969i
\(202\) −99.3582 + 370.810i −0.491872 + 1.83569i
\(203\) −9.72825 9.72825i −0.0479224 0.0479224i
\(204\) 75.6220 + 130.981i 0.370696 + 0.642065i
\(205\) 179.083 + 103.394i 0.873576 + 0.504359i
\(206\) 495.209 132.691i 2.40393 0.644131i
\(207\) 32.2100i 0.155604i
\(208\) 561.158 + 568.473i 2.69788 + 2.73304i
\(209\) −166.680 −0.797511
\(210\) −7.37908 27.5391i −0.0351385 0.131139i
\(211\) −22.2146 + 38.4768i −0.105282 + 0.182355i −0.913854 0.406044i \(-0.866908\pi\)
0.808571 + 0.588398i \(0.200241\pi\)
\(212\) −773.435 + 446.543i −3.64828 + 2.10633i
\(213\) −119.249 + 119.249i −0.559856 + 0.559856i
\(214\) 516.901 + 138.503i 2.41542 + 0.647211i
\(215\) −5.22249 + 19.4906i −0.0242907 + 0.0906540i
\(216\) 100.045 + 100.045i 0.463173 + 0.463173i
\(217\) 8.78009 + 15.2076i 0.0404612 + 0.0700809i
\(218\) 124.599 + 71.9375i 0.571557 + 0.329989i
\(219\) 8.86539 2.37547i 0.0404812 0.0108469i
\(220\) 299.014i 1.35916i
\(221\) 26.0050 + 99.6282i 0.117670 + 0.450806i
\(222\) −17.1054 −0.0770514
\(223\) −78.3280 292.324i −0.351247 1.31087i −0.885142 0.465320i \(-0.845939\pi\)
0.533896 0.845550i \(-0.320727\pi\)
\(224\) 58.7496 101.757i 0.262275 0.454274i
\(225\) 8.25370 4.76528i 0.0366831 0.0211790i
\(226\) 496.272 496.272i 2.19589 2.19589i
\(227\) 302.517 + 81.0591i 1.33267 + 0.357088i 0.853711 0.520747i \(-0.174347\pi\)
0.478962 + 0.877836i \(0.341013\pi\)
\(228\) 141.886 529.526i 0.622307 2.32248i
\(229\) −113.873 113.873i −0.497260 0.497260i 0.413324 0.910584i \(-0.364368\pi\)
−0.910584 + 0.413324i \(0.864368\pi\)
\(230\) −97.2078 168.369i −0.422643 0.732039i
\(231\) −7.91666 4.57068i −0.0342712 0.0197865i
\(232\) −398.052 + 106.658i −1.71574 + 0.459731i
\(233\) 191.488i 0.821838i 0.911672 + 0.410919i \(0.134792\pi\)
−0.911672 + 0.410919i \(0.865208\pi\)
\(234\) 74.7360 + 131.404i 0.319385 + 0.561557i
\(235\) 122.065 0.519426
\(236\) 42.4958 + 158.596i 0.180067 + 0.672018i
\(237\) 37.8255 65.5158i 0.159601 0.276438i
\(238\) 24.1696 13.9543i 0.101553 0.0586315i
\(239\) −173.094 + 173.094i −0.724244 + 0.724244i −0.969467 0.245223i \(-0.921139\pi\)
0.245223 + 0.969467i \(0.421139\pi\)
\(240\) −480.231 128.678i −2.00096 0.536157i
\(241\) 15.1870 56.6788i 0.0630167 0.235182i −0.927233 0.374485i \(-0.877820\pi\)
0.990250 + 0.139303i \(0.0444863\pi\)
\(242\) −239.256 239.256i −0.988660 0.988660i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) −338.377 195.362i −1.38679 0.800664i
\(245\) 217.376 58.2458i 0.887250 0.237738i
\(246\) 297.186i 1.20807i
\(247\) 188.697 321.999i 0.763954 1.30364i
\(248\) 525.987 2.12091
\(249\) 18.8317 + 70.2809i 0.0756294 + 0.282253i
\(250\) −255.108 + 441.860i −1.02043 + 1.76744i
\(251\) 98.6857 56.9762i 0.393170 0.226997i −0.290363 0.956917i \(-0.593776\pi\)
0.683533 + 0.729920i \(0.260443\pi\)
\(252\) 21.2597 21.2597i 0.0843638 0.0843638i
\(253\) −60.2116 16.1336i −0.237990 0.0637693i
\(254\) −218.307 + 814.731i −0.859475 + 3.20760i
\(255\) −45.3164 45.3164i −0.177711 0.177711i
\(256\) −404.923 701.348i −1.58173 2.73964i
\(257\) −324.407 187.297i −1.26229 0.728781i −0.288769 0.957399i \(-0.593246\pi\)
−0.973516 + 0.228618i \(0.926579\pi\)
\(258\) −28.0111 + 7.50555i −0.108570 + 0.0290913i
\(259\) 2.31608i 0.00894241i
\(260\) −577.648 338.511i −2.22172 1.30197i
\(261\) −45.4033 −0.173959
\(262\) −159.300 594.514i −0.608013 2.26914i
\(263\) 57.8742 100.241i 0.220054 0.381145i −0.734770 0.678316i \(-0.762710\pi\)
0.954824 + 0.297171i \(0.0960433\pi\)
\(264\) −237.131 + 136.908i −0.898223 + 0.518589i
\(265\) 267.590 267.590i 1.00977 1.00977i
\(266\) −97.7118 26.1818i −0.367337 0.0984278i
\(267\) −12.6026 + 47.0335i −0.0472007 + 0.176155i
\(268\) 751.392 + 751.392i 2.80370 + 2.80370i
\(269\) 51.2997 + 88.8537i 0.190705 + 0.330311i 0.945484 0.325668i \(-0.105589\pi\)
−0.754779 + 0.655979i \(0.772256\pi\)
\(270\) −81.4843 47.0450i −0.301794 0.174241i
\(271\) −89.8030 + 24.0626i −0.331376 + 0.0887920i −0.420671 0.907213i \(-0.638205\pi\)
0.0892948 + 0.996005i \(0.471539\pi\)
\(272\) 486.674i 1.78924i
\(273\) 17.7922 10.1193i 0.0651730 0.0370670i
\(274\) 941.212 3.43508
\(275\) 4.77375 + 17.8159i 0.0173591 + 0.0647850i
\(276\) 102.510 177.553i 0.371414 0.643307i
\(277\) 366.341 211.507i 1.32253 0.763563i 0.338398 0.941003i \(-0.390115\pi\)
0.984132 + 0.177441i \(0.0567818\pi\)
\(278\) −218.558 + 218.558i −0.786179 + 0.786179i
\(279\) 55.9770 + 14.9990i 0.200634 + 0.0537598i
\(280\) −29.9274 + 111.691i −0.106884 + 0.398895i
\(281\) 6.57627 + 6.57627i 0.0234031 + 0.0234031i 0.718712 0.695308i \(-0.244732\pi\)
−0.695308 + 0.718712i \(0.744732\pi\)
\(282\) 87.7135 + 151.924i 0.311041 + 0.538738i
\(283\) 48.9456 + 28.2588i 0.172953 + 0.0998543i 0.583977 0.811770i \(-0.301496\pi\)
−0.411025 + 0.911624i \(0.634829\pi\)
\(284\) 1036.86 277.826i 3.65092 0.978260i
\(285\) 232.293i 0.815062i
\(286\) −283.074 + 73.8883i −0.989770 + 0.258351i
\(287\) 40.2392 0.140206
\(288\) −100.362 374.555i −0.348478 1.30054i
\(289\) −113.133 + 195.952i −0.391464 + 0.678035i
\(290\) 237.333 137.024i 0.818389 0.472497i
\(291\) −164.752 + 164.752i −0.566159 + 0.566159i
\(292\) −56.4292 15.1202i −0.193251 0.0517813i
\(293\) 53.0538 197.999i 0.181071 0.675766i −0.814367 0.580351i \(-0.802916\pi\)
0.995438 0.0954150i \(-0.0304178\pi\)
\(294\) 228.696 + 228.696i 0.777876 + 0.777876i
\(295\) −34.7866 60.2521i −0.117921 0.204244i
\(296\) 60.0802 + 34.6873i 0.202973 + 0.117187i
\(297\) −29.1402 + 7.80809i −0.0981151 + 0.0262899i
\(298\) 187.143i 0.627997i
\(299\) 99.3326 98.0545i 0.332216 0.327942i
\(300\) −60.6630 −0.202210
\(301\) 1.01626 + 3.79272i 0.00337627 + 0.0126004i
\(302\) −497.154 + 861.096i −1.64621 + 2.85131i
\(303\) 148.558 85.7700i 0.490290 0.283069i
\(304\) −1247.35 + 1247.35i −4.10313 + 4.10313i
\(305\) 159.921 + 42.8507i 0.524332 + 0.140494i
\(306\) 23.8381 88.9650i 0.0779023 0.290735i
\(307\) −21.2456 21.2456i −0.0692039 0.0692039i 0.671658 0.740862i \(-0.265583\pi\)
−0.740862 + 0.671658i \(0.765583\pi\)
\(308\) 29.0929 + 50.3904i 0.0944575 + 0.163605i
\(309\) −198.396 114.544i −0.642059 0.370693i
\(310\) −337.870 + 90.5321i −1.08990 + 0.292039i
\(311\) 328.015i 1.05471i 0.849645 + 0.527355i \(0.176816\pi\)
−0.849645 + 0.527355i \(0.823184\pi\)
\(312\) 3.96994 613.091i 0.0127242 1.96504i
\(313\) −572.183 −1.82806 −0.914030 0.405647i \(-0.867046\pi\)
−0.914030 + 0.405647i \(0.867046\pi\)
\(314\) 80.6387 + 300.948i 0.256811 + 0.958432i
\(315\) −6.36992 + 11.0330i −0.0202220 + 0.0350255i
\(316\) −417.015 + 240.764i −1.31967 + 0.761911i
\(317\) 263.833 263.833i 0.832280 0.832280i −0.155548 0.987828i \(-0.549714\pi\)
0.987828 + 0.155548i \(0.0497143\pi\)
\(318\) 525.332 + 140.762i 1.65199 + 0.442649i
\(319\) 22.7420 84.8743i 0.0712915 0.266064i
\(320\) 843.119 + 843.119i 2.63475 + 2.63475i
\(321\) −119.561 207.087i −0.372466 0.645130i
\(322\) −32.7633 18.9159i −0.101749 0.0587450i
\(323\) −219.640 + 58.8523i −0.680000 + 0.182205i
\(324\) 99.2222i 0.306241i
\(325\) −39.8218 10.9471i −0.122529 0.0336833i
\(326\) −682.579 −2.09380
\(327\) −16.6395 62.0994i −0.0508852 0.189906i
\(328\) 602.650 1043.82i 1.83735 3.18238i
\(329\) 20.5706 11.8765i 0.0625247 0.0360987i
\(330\) 128.758 128.758i 0.390175 0.390175i
\(331\) 82.4800 + 22.1005i 0.249184 + 0.0667688i 0.381249 0.924472i \(-0.375494\pi\)
−0.132065 + 0.991241i \(0.542161\pi\)
\(332\) 119.866 447.346i 0.361042 1.34743i
\(333\) 5.40476 + 5.40476i 0.0162305 + 0.0162305i
\(334\) −282.095 488.603i −0.844596 1.46288i
\(335\) −389.946 225.135i −1.16402 0.672046i
\(336\) −93.4492 + 25.0396i −0.278123 + 0.0745228i
\(337\) 151.474i 0.449476i −0.974419 0.224738i \(-0.927847\pi\)
0.974419 0.224738i \(-0.0721527\pi\)
\(338\) 177.725 630.503i 0.525814 1.86539i
\(339\) −313.612 −0.925108
\(340\) 105.578 + 394.022i 0.310523 + 1.15889i
\(341\) −56.0765 + 97.1274i −0.164447 + 0.284831i
\(342\) −289.115 + 166.921i −0.845366 + 0.488072i
\(343\) 62.4622 62.4622i 0.182106 0.182106i
\(344\) 113.605 + 30.4403i 0.330247 + 0.0884893i
\(345\) −22.4846 + 83.9137i −0.0651728 + 0.243228i
\(346\) 432.744 + 432.744i 1.25070 + 1.25070i
\(347\) 68.0738 + 117.907i 0.196178 + 0.339790i 0.947286 0.320389i \(-0.103814\pi\)
−0.751108 + 0.660179i \(0.770480\pi\)
\(348\) 250.278 + 144.498i 0.719191 + 0.415225i
\(349\) −162.066 + 43.4254i −0.464371 + 0.124428i −0.483416 0.875391i \(-0.660604\pi\)
0.0190447 + 0.999819i \(0.493938\pi\)
\(350\) 11.1940i 0.0319827i
\(351\) 17.9053 65.1337i 0.0510124 0.185566i
\(352\) 750.442 2.13194
\(353\) 82.1005 + 306.403i 0.232579 + 0.867998i 0.979225 + 0.202776i \(0.0649963\pi\)
−0.746646 + 0.665222i \(0.768337\pi\)
\(354\) 49.9938 86.5918i 0.141225 0.244610i
\(355\) −393.912 + 227.425i −1.10961 + 0.640634i
\(356\) 219.156 219.156i 0.615608 0.615608i
\(357\) −12.0459 3.22769i −0.0337421 0.00904116i
\(358\) 95.5892 356.744i 0.267009 0.996491i
\(359\) −61.9541 61.9541i −0.172574 0.172574i 0.615535 0.788109i \(-0.288940\pi\)
−0.788109 + 0.615535i \(0.788940\pi\)
\(360\) 190.801 + 330.477i 0.530002 + 0.917991i
\(361\) 401.143 + 231.600i 1.11120 + 0.641551i
\(362\) −633.710 + 169.802i −1.75058 + 0.469067i
\(363\) 151.194i 0.416513i
\(364\) −130.282 0.843614i −0.357918 0.00231762i
\(365\) 24.7544 0.0678202
\(366\) 61.5833 + 229.832i 0.168260 + 0.627956i
\(367\) −232.100 + 402.010i −0.632426 + 1.09539i 0.354628 + 0.935007i \(0.384607\pi\)
−0.987054 + 0.160387i \(0.948726\pi\)
\(368\) −571.331 + 329.858i −1.55253 + 0.896353i
\(369\) 93.9012 93.9012i 0.254475 0.254475i
\(370\) −44.5631 11.9406i −0.120441 0.0322720i
\(371\) 19.0593 71.1303i 0.0513728 0.191726i
\(372\) −260.830 260.830i −0.701155 0.701155i
\(373\) 28.9854 + 50.2042i 0.0777088 + 0.134596i 0.902261 0.431190i \(-0.141906\pi\)
−0.824552 + 0.565786i \(0.808573\pi\)
\(374\) 154.366 + 89.1232i 0.412743 + 0.238297i
\(375\) 220.219 59.0076i 0.587252 0.157354i
\(376\) 711.481i 1.89224i
\(377\) 138.218 + 140.019i 0.366625 + 0.371404i
\(378\) −18.3092 −0.0484370
\(379\) −18.1969 67.9119i −0.0480130 0.179187i 0.937755 0.347297i \(-0.112900\pi\)
−0.985768 + 0.168110i \(0.946234\pi\)
\(380\) 739.284 1280.48i 1.94548 3.36968i
\(381\) 326.407 188.451i 0.856710 0.494622i
\(382\) −254.041 + 254.041i −0.665029 + 0.665029i
\(383\) 201.339 + 53.9485i 0.525688 + 0.140858i 0.511896 0.859047i \(-0.328943\pi\)
0.0137918 + 0.999905i \(0.495610\pi\)
\(384\) −211.736 + 790.209i −0.551396 + 2.05784i
\(385\) −17.4339 17.4339i −0.0452828 0.0452828i
\(386\) −623.151 1079.33i −1.61438 2.79619i
\(387\) 11.2221 + 6.47909i 0.0289977 + 0.0167418i
\(388\) 1432.51 383.839i 3.69202 0.989275i
\(389\) 459.988i 1.18249i 0.806492 + 0.591245i \(0.201363\pi\)
−0.806492 + 0.591245i \(0.798637\pi\)
\(390\) 102.974 + 394.505i 0.264036 + 1.01155i
\(391\) −85.0395 −0.217492
\(392\) −339.497 1267.02i −0.866064 3.23219i
\(393\) −137.514 + 238.181i −0.349908 + 0.606058i
\(394\) 376.181 217.188i 0.954775 0.551239i
\(395\) 144.277 144.277i 0.365259 0.365259i
\(396\) 185.480 + 49.6993i 0.468385 + 0.125503i
\(397\) −149.364 + 557.434i −0.376232 + 1.40412i 0.475305 + 0.879821i \(0.342338\pi\)
−0.851537 + 0.524295i \(0.824329\pi\)
\(398\) −188.151 188.151i −0.472741 0.472741i
\(399\) 22.6012 + 39.1464i 0.0566445 + 0.0981112i
\(400\) 169.050 + 97.6010i 0.422625 + 0.244002i
\(401\) 141.512 37.9181i 0.352898 0.0945588i −0.0780149 0.996952i \(-0.524858\pi\)
0.430913 + 0.902393i \(0.358192\pi\)
\(402\) 647.110i 1.60973i
\(403\) −124.151 218.288i −0.308067 0.541658i
\(404\) −1091.87 −2.70265
\(405\) 10.8817 + 40.6111i 0.0268684 + 0.100274i
\(406\) 26.6638 46.1831i 0.0656745 0.113752i
\(407\) −12.8105 + 7.39617i −0.0314755 + 0.0181724i
\(408\) −264.136 + 264.136i −0.647391 + 0.647391i
\(409\) 220.136 + 58.9852i 0.538230 + 0.144218i 0.517686 0.855571i \(-0.326794\pi\)
0.0205438 + 0.999789i \(0.493460\pi\)
\(410\) −207.454 + 774.231i −0.505986 + 1.88837i
\(411\) −297.393 297.393i −0.723583 0.723583i
\(412\) 729.086 + 1262.81i 1.76963 + 3.06508i
\(413\) −11.7246 6.76919i −0.0283888 0.0163903i
\(414\) −120.597 + 32.3139i −0.291298 + 0.0780530i
\(415\) 196.242i 0.472872i
\(416\) −849.569 + 1449.74i −2.04223 + 3.48494i
\(417\) 138.115 0.331210
\(418\) −167.218 624.064i −0.400042 1.49298i
\(419\) 206.102 356.979i 0.491889 0.851977i −0.508067 0.861318i \(-0.669640\pi\)
0.999956 + 0.00934013i \(0.00297310\pi\)
\(420\) 70.2264 40.5452i 0.167206 0.0965363i
\(421\) 516.646 516.646i 1.22719 1.22719i 0.262163 0.965024i \(-0.415564\pi\)
0.965024 0.262163i \(-0.0844358\pi\)
\(422\) −166.347 44.5725i −0.394187 0.105622i
\(423\) 20.2885 75.7178i 0.0479634 0.179002i
\(424\) −1559.70 1559.70i −3.67855 3.67855i
\(425\) 12.5811 + 21.7911i 0.0296026 + 0.0512731i
\(426\) −566.114 326.846i −1.32891 0.767245i
\(427\) 31.1194 8.33842i 0.0728792 0.0195279i
\(428\) 1522.04i 3.55618i
\(429\) 112.789 + 66.0960i 0.262911 + 0.154070i
\(430\) −78.2140 −0.181893
\(431\) −22.6165 84.4059i −0.0524745 0.195837i 0.934713 0.355404i \(-0.115657\pi\)
−0.987187 + 0.159567i \(0.948990\pi\)
\(432\) −159.639 + 276.503i −0.369535 + 0.640053i
\(433\) −270.622 + 156.244i −0.624994 + 0.360840i −0.778811 0.627259i \(-0.784177\pi\)
0.153817 + 0.988099i \(0.450843\pi\)
\(434\) −48.1301 + 48.1301i −0.110899 + 0.110899i
\(435\) −118.285 31.6943i −0.271919 0.0728605i
\(436\) −105.912 + 395.269i −0.242918 + 0.906581i
\(437\) 217.957 + 217.957i 0.498757 + 0.498757i
\(438\) 17.7880 + 30.8097i 0.0406118 + 0.0703418i
\(439\) 114.773 + 66.2644i 0.261443 + 0.150944i 0.624992 0.780631i \(-0.285102\pi\)
−0.363550 + 0.931575i \(0.618435\pi\)
\(440\) −713.344 + 191.140i −1.62124 + 0.434409i
\(441\) 144.521i 0.327712i
\(442\) −346.928 + 197.315i −0.784905 + 0.446414i
\(443\) 762.677 1.72162 0.860809 0.508928i \(-0.169958\pi\)
0.860809 + 0.508928i \(0.169958\pi\)
\(444\) −12.5920 46.9939i −0.0283603 0.105842i
\(445\) −65.6646 + 113.734i −0.147561 + 0.255583i
\(446\) 1015.91 586.535i 2.27782 1.31510i
\(447\) −59.1312 + 59.1312i −0.132284 + 0.132284i
\(448\) 224.116 + 60.0517i 0.500259 + 0.134044i
\(449\) 71.2323 265.843i 0.158647 0.592077i −0.840119 0.542402i \(-0.817515\pi\)
0.998765 0.0496748i \(-0.0158185\pi\)
\(450\) 26.1220 + 26.1220i 0.0580488 + 0.0580488i
\(451\) 128.500 + 222.568i 0.284921 + 0.493498i
\(452\) 1728.74 + 998.086i 3.82464 + 2.20816i
\(453\) 429.163 114.994i 0.947380 0.253850i
\(454\) 1213.97i 2.67394i
\(455\) 53.4163 13.9428i 0.117398 0.0306435i
\(456\) 1353.96 2.96922
\(457\) 147.457 + 550.316i 0.322662 + 1.20419i 0.916641 + 0.399711i \(0.130890\pi\)
−0.593979 + 0.804481i \(0.702444\pi\)
\(458\) 312.110 540.590i 0.681462 1.18033i
\(459\) −35.6421 + 20.5780i −0.0776517 + 0.0448322i
\(460\) 391.003 391.003i 0.850006 0.850006i
\(461\) −131.737 35.2989i −0.285764 0.0765704i 0.113090 0.993585i \(-0.463925\pi\)
−0.398854 + 0.917014i \(0.630592\pi\)
\(462\) 9.17086 34.2261i 0.0198504 0.0740825i
\(463\) −555.943 555.943i −1.20074 1.20074i −0.973942 0.226798i \(-0.927174\pi\)
−0.226798 0.973942i \(-0.572826\pi\)
\(464\) −464.968 805.348i −1.00209 1.73566i
\(465\) 135.361 + 78.1509i 0.291100 + 0.168066i
\(466\) −716.950 + 192.106i −1.53852 + 0.412245i
\(467\) 684.656i 1.46607i −0.680189 0.733037i \(-0.738102\pi\)
0.680189 0.733037i \(-0.261898\pi\)
\(468\) −305.992 + 302.055i −0.653829 + 0.645416i
\(469\) −87.6191 −0.186821
\(470\) 122.459 + 457.023i 0.260551 + 0.972390i
\(471\) 69.6105 120.569i 0.147793 0.255985i
\(472\) −351.191 + 202.760i −0.744049 + 0.429577i
\(473\) −17.7327 + 17.7327i −0.0374898 + 0.0374898i
\(474\) 283.245 + 75.8952i 0.597563 + 0.160116i
\(475\) 23.6053 88.0961i 0.0496953 0.185466i
\(476\) 56.1289 + 56.1289i 0.117918 + 0.117918i
\(477\) −121.512 210.464i −0.254741 0.441225i
\(478\) −821.733 474.428i −1.71911 0.992527i
\(479\) −808.391 + 216.608i −1.68766 + 0.452208i −0.969785 0.243960i \(-0.921554\pi\)
−0.717879 + 0.696168i \(0.754887\pi\)
\(480\) 1045.85i 2.17886i
\(481\) 0.214468 33.1211i 0.000445880 0.0688588i
\(482\) 227.447 0.471881
\(483\) 4.37533 + 16.3289i 0.00905865 + 0.0338073i
\(484\) 481.184 833.435i 0.994181 1.72197i
\(485\) −544.221 + 314.206i −1.12210 + 0.647848i
\(486\) −42.7259 + 42.7259i −0.0879133 + 0.0879133i
\(487\) 421.775 + 113.014i 0.866068 + 0.232062i 0.664387 0.747389i \(-0.268693\pi\)
0.201681 + 0.979451i \(0.435359\pi\)
\(488\) 249.764 932.132i 0.511812 1.91011i
\(489\) 215.673 + 215.673i 0.441049 + 0.441049i
\(490\) 436.155 + 755.443i 0.890113 + 1.54172i
\(491\) −384.073 221.744i −0.782226 0.451618i 0.0549929 0.998487i \(-0.482486\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(492\) −816.462 + 218.770i −1.65948 + 0.444655i
\(493\) 119.872i 0.243148i
\(494\) 1394.90 + 383.460i 2.82368 + 0.776234i
\(495\) −81.3667 −0.164377
\(496\) 307.205 + 1146.50i 0.619365 + 2.31150i
\(497\) −44.2552 + 76.6522i −0.0890446 + 0.154230i
\(498\) −244.246 + 141.015i −0.490453 + 0.283163i
\(499\) −453.730 + 453.730i −0.909279 + 0.909279i −0.996214 0.0869354i \(-0.972293\pi\)
0.0869354 + 0.996214i \(0.472293\pi\)
\(500\) −1401.72 375.590i −2.80344 0.751180i
\(501\) −65.2499 + 243.516i −0.130239 + 0.486059i
\(502\) 312.328 + 312.328i 0.622168 + 0.622168i
\(503\) 163.827 + 283.757i 0.325700 + 0.564129i 0.981654 0.190672i \(-0.0610666\pi\)
−0.655954 + 0.754801i \(0.727733\pi\)
\(504\) 64.3082 + 37.1283i 0.127596 + 0.0736673i
\(505\) 446.897 119.746i 0.884944 0.237120i
\(506\) 241.623i 0.477517i
\(507\) −255.374 + 143.063i −0.503696 + 0.282176i
\(508\) −2399.02 −4.72249
\(509\) −97.4223 363.585i −0.191399 0.714312i −0.993170 0.116680i \(-0.962775\pi\)
0.801770 0.597632i \(-0.203892\pi\)
\(510\) 124.206 215.132i 0.243542 0.421827i
\(511\) 4.17165 2.40850i 0.00816370 0.00471332i
\(512\) 883.754 883.754i 1.72608 1.72608i
\(513\) 144.093 + 38.6095i 0.280882 + 0.0752622i
\(514\) 375.802 1402.51i 0.731132 2.72862i
\(515\) −436.904 436.904i −0.848357 0.848357i
\(516\) −41.2401 71.4300i −0.0799228 0.138430i
\(517\) 131.380 + 75.8524i 0.254120 + 0.146716i
\(518\) −8.67163 + 2.32356i −0.0167406 + 0.00448563i
\(519\) 273.466i 0.526910i
\(520\) 438.319 1594.46i 0.842920 3.06626i
\(521\) −615.884 −1.18212 −0.591060 0.806628i \(-0.701290\pi\)
−0.591060 + 0.806628i \(0.701290\pi\)
\(522\) −45.5497 169.994i −0.0872601 0.325659i
\(523\) −122.231 + 211.711i −0.233712 + 0.404801i −0.958898 0.283752i \(-0.908421\pi\)
0.725185 + 0.688554i \(0.241754\pi\)
\(524\) 1516.05 875.290i 2.89322 1.67040i
\(525\) 3.53693 3.53693i 0.00673701 0.00673701i
\(526\) 433.373 + 116.122i 0.823903 + 0.220764i
\(527\) −39.5997 + 147.788i −0.0751418 + 0.280433i
\(528\) −436.918 436.918i −0.827495 0.827495i
\(529\) −206.862 358.295i −0.391043 0.677307i
\(530\) 1270.34 + 733.429i 2.39686 + 1.38383i
\(531\) −43.1567 + 11.5638i −0.0812743 + 0.0217774i
\(532\) 287.718i 0.540823i
\(533\) −575.439 3.72613i −1.07962 0.00699087i
\(534\) −188.741 −0.353447
\(535\) −166.923 622.964i −0.312005 1.16442i
\(536\) −1312.25 + 2272.88i −2.44822 + 4.24044i
\(537\) −142.923 + 82.5165i −0.266150 + 0.153662i
\(538\) −281.211 + 281.211i −0.522698 + 0.522698i
\(539\) 270.159 + 72.3889i 0.501223 + 0.134302i
\(540\) 69.2633 258.494i 0.128265 0.478693i
\(541\) 264.659 + 264.659i 0.489204 + 0.489204i 0.908055 0.418851i \(-0.137567\pi\)
−0.418851 + 0.908055i \(0.637567\pi\)
\(542\) −180.185 312.090i −0.332446 0.575813i
\(543\) 253.884 + 146.580i 0.467558 + 0.269945i
\(544\) 988.885 264.971i 1.81780 0.487079i
\(545\) 173.397i 0.318160i
\(546\) 55.7372 + 56.4638i 0.102083 + 0.103413i
\(547\) 439.360 0.803218 0.401609 0.915811i \(-0.368451\pi\)
0.401609 + 0.915811i \(0.368451\pi\)
\(548\) 692.863 + 2585.80i 1.26435 + 4.71861i
\(549\) 53.1612 92.0779i 0.0968328 0.167719i
\(550\) −61.9151 + 35.7467i −0.112573 + 0.0649940i
\(551\) −307.232 + 307.232i −0.557590 + 0.557590i
\(552\) 489.107 + 131.056i 0.886064 + 0.237420i
\(553\) 10.2763 38.3515i 0.0185827 0.0693517i
\(554\) 1159.42 + 1159.42i 2.09282 + 2.09282i
\(555\) 10.3076 + 17.8534i 0.0185723 + 0.0321682i
\(556\) −761.335 439.557i −1.36931 0.790570i
\(557\) 81.7290 21.8992i 0.146731 0.0393164i −0.184706 0.982794i \(-0.559133\pi\)
0.331437 + 0.943477i \(0.392467\pi\)
\(558\) 224.631i 0.402564i
\(559\) −14.1817 54.3318i −0.0253698 0.0971946i
\(560\) −260.934 −0.465953
\(561\) −20.6146 76.9347i −0.0367461 0.137138i
\(562\) −18.0247 + 31.2197i −0.0320724 + 0.0555510i
\(563\) 131.716 76.0461i 0.233953 0.135073i −0.378441 0.925625i \(-0.623540\pi\)
0.612394 + 0.790552i \(0.290206\pi\)
\(564\) −352.813 + 352.813i −0.625556 + 0.625556i
\(565\) −817.023 218.921i −1.44606 0.387470i
\(566\) −56.6999 + 211.607i −0.100176 + 0.373864i
\(567\) 5.78511 + 5.78511i 0.0102030 + 0.0102030i
\(568\) 1325.59 + 2295.99i 2.33379 + 4.04224i
\(569\) −634.451 366.300i −1.11503 0.643761i −0.174901 0.984586i \(-0.555960\pi\)
−0.940127 + 0.340825i \(0.889294\pi\)
\(570\) −869.725 + 233.042i −1.52583 + 0.408846i
\(571\) 965.471i 1.69084i −0.534100 0.845421i \(-0.679349\pi\)
0.534100 0.845421i \(-0.320651\pi\)
\(572\) −411.376 723.300i −0.719189 1.26451i
\(573\) 160.538 0.280170
\(574\) 40.3690 + 150.659i 0.0703293 + 0.262472i
\(575\) 17.0544 29.5391i 0.0296598 0.0513723i
\(576\) 663.128 382.857i 1.15126 0.664682i
\(577\) 232.745 232.745i 0.403371 0.403371i −0.476048 0.879419i \(-0.657931\pi\)
0.879419 + 0.476048i \(0.157931\pi\)
\(578\) −847.161 226.996i −1.46568 0.392727i
\(579\) −144.138 + 537.929i −0.248942 + 0.929065i
\(580\) 551.158 + 551.158i 0.950272 + 0.950272i
\(581\) 19.0936 + 33.0710i 0.0328633 + 0.0569209i
\(582\) −782.132 451.564i −1.34387 0.775883i
\(583\) 454.294 121.728i 0.779235 0.208795i
\(584\) 144.286i 0.247065i
\(585\) 92.1145 157.188i 0.157461 0.268697i
\(586\) 794.553 1.35589
\(587\) −34.0511 127.081i −0.0580087 0.216492i 0.930837 0.365435i \(-0.119080\pi\)
−0.988846 + 0.148943i \(0.952413\pi\)
\(588\) −459.946 + 796.649i −0.782221 + 1.35485i
\(589\) 480.277 277.288i 0.815410 0.470777i
\(590\) 190.691 190.691i 0.323204 0.323204i
\(591\) −187.486 50.2366i −0.317235 0.0850028i
\(592\) −40.5185 + 151.217i −0.0684435 + 0.255434i
\(593\) 310.017 + 310.017i 0.522794 + 0.522794i 0.918414 0.395620i \(-0.129470\pi\)
−0.395620 + 0.918414i \(0.629470\pi\)
\(594\) −58.4684 101.270i −0.0984317 0.170489i
\(595\) −29.1289 16.8176i −0.0489562 0.0282649i
\(596\) 514.140 137.763i 0.862650 0.231146i
\(597\) 118.899i 0.199161i
\(598\) 466.778 + 273.540i 0.780566 + 0.457424i
\(599\) 934.777 1.56056 0.780281 0.625429i \(-0.215076\pi\)
0.780281 + 0.625429i \(0.215076\pi\)
\(600\) −38.7779 144.721i −0.0646298 0.241202i
\(601\) 479.955 831.307i 0.798595 1.38321i −0.121937 0.992538i \(-0.538910\pi\)
0.920531 0.390669i \(-0.127756\pi\)
\(602\) −13.1808 + 7.60992i −0.0218950 + 0.0126411i
\(603\) −204.466 + 204.466i −0.339081 + 0.339081i
\(604\) −2731.67 731.949i −4.52263 1.21184i
\(605\) −105.543 + 393.892i −0.174451 + 0.651061i
\(606\) 470.168 + 470.168i 0.775855 + 0.775855i
\(607\) 137.053 + 237.384i 0.225788 + 0.391077i 0.956556 0.291550i \(-0.0941709\pi\)
−0.730767 + 0.682627i \(0.760838\pi\)
\(608\) −3213.64 1855.40i −5.28560 3.05164i
\(609\) −23.0173 + 6.16746i −0.0377952 + 0.0101272i
\(610\) 641.749i 1.05205i
\(611\) −295.269 + 167.934i −0.483256 + 0.274851i
\(612\) 261.962 0.428043
\(613\) 97.1779 + 362.673i 0.158528 + 0.591636i 0.998777 + 0.0494352i \(0.0157421\pi\)
−0.840249 + 0.542201i \(0.817591\pi\)
\(614\) 58.2314 100.860i 0.0948394 0.164267i
\(615\) 310.181 179.083i 0.504359 0.291192i
\(616\) −101.617 + 101.617i −0.164962 + 0.164962i
\(617\) 236.820 + 63.4556i 0.383824 + 0.102845i 0.445571 0.895246i \(-0.353001\pi\)
−0.0617470 + 0.998092i \(0.519667\pi\)
\(618\) 229.828 857.728i 0.371889 1.38791i
\(619\) 334.351 + 334.351i 0.540147 + 0.540147i 0.923572 0.383425i \(-0.125256\pi\)
−0.383425 + 0.923572i \(0.625256\pi\)
\(620\) −497.439 861.590i −0.802321 1.38966i
\(621\) 48.3150 + 27.8947i 0.0778020 + 0.0449190i
\(622\) −1228.12 + 329.073i −1.97446 + 0.529056i
\(623\) 25.5556i 0.0410203i
\(624\) 1338.69 349.425i 2.14533 0.559976i
\(625\) 535.486 0.856778
\(626\) −574.029 2142.30i −0.916979 3.42221i
\(627\) −144.349 + 250.020i −0.230221 + 0.398755i
\(628\) −767.435 + 443.079i −1.22203 + 0.705539i
\(629\) −14.2694 + 14.2694i −0.0226859 + 0.0226859i
\(630\) −47.6991 12.7809i −0.0757129 0.0202872i
\(631\) −16.9296 + 63.1822i −0.0268298 + 0.100130i −0.978042 0.208406i \(-0.933172\pi\)
0.951213 + 0.308536i \(0.0998391\pi\)
\(632\) −840.949 840.949i −1.33062 1.33062i
\(633\) 38.4768 + 66.6438i 0.0607848 + 0.105282i
\(634\) 1252.50 + 723.131i 1.97555 + 1.14058i
\(635\) 981.907 263.101i 1.54631 0.414332i
\(636\) 1546.87i 2.43219i
\(637\) −445.689 + 439.954i −0.699669 + 0.690666i
\(638\) 340.592 0.533844
\(639\) 75.6010 + 282.147i 0.118311 + 0.441544i
\(640\) −1103.23 + 1910.85i −1.72380 + 2.98571i
\(641\) −404.577 + 233.583i −0.631166 + 0.364404i −0.781204 0.624276i \(-0.785394\pi\)
0.150037 + 0.988680i \(0.452061\pi\)
\(642\) 655.404 655.404i 1.02088 1.02088i
\(643\) −535.165 143.397i −0.832294 0.223012i −0.182580 0.983191i \(-0.558445\pi\)
−0.649714 + 0.760179i \(0.725111\pi\)
\(644\) 27.8494 103.936i 0.0432445 0.161391i
\(645\) 24.7131 + 24.7131i 0.0383149 + 0.0383149i
\(646\) −440.697 763.310i −0.682194 1.18159i
\(647\) 365.279 + 210.894i 0.564573 + 0.325956i 0.754979 0.655749i \(-0.227647\pi\)
−0.190406 + 0.981705i \(0.560980\pi\)
\(648\) 236.710 63.4262i 0.365293 0.0978800i
\(649\) 86.4668i 0.133231i
\(650\) 1.03656 160.079i 0.00159470 0.246275i
\(651\) 30.4151 0.0467206
\(652\) −502.473 1875.26i −0.770665 2.87616i
\(653\) −182.251 + 315.668i −0.279098 + 0.483412i −0.971161 0.238425i \(-0.923369\pi\)
0.692063 + 0.721837i \(0.256702\pi\)
\(654\) 215.813 124.599i 0.329989 0.190519i
\(655\) −524.516 + 524.516i −0.800788 + 0.800788i
\(656\) 2627.22 + 703.961i 4.00490 + 1.07311i
\(657\) 4.11444 15.3553i 0.00626247 0.0233718i
\(658\) 65.1036 + 65.1036i 0.0989416 + 0.0989416i
\(659\) 286.379 + 496.022i 0.434565 + 0.752689i 0.997260 0.0739756i \(-0.0235687\pi\)
−0.562695 + 0.826665i \(0.690235\pi\)
\(660\) 448.521 + 258.954i 0.679578 + 0.392354i
\(661\) 849.859 227.719i 1.28572 0.344507i 0.449685 0.893187i \(-0.351536\pi\)
0.836032 + 0.548681i \(0.184870\pi\)
\(662\) 330.985i 0.499977i
\(663\) 171.963 + 47.2730i 0.259371 + 0.0713016i
\(664\) 1143.83 1.72264
\(665\) 31.5541 + 117.761i 0.0474497 + 0.177085i
\(666\) −14.8137 + 25.6581i −0.0222428 + 0.0385257i
\(667\) −140.723 + 81.2466i −0.210979 + 0.121809i
\(668\) 1134.68 1134.68i 1.69863 1.69863i
\(669\) −506.320 135.668i −0.756831 0.202792i
\(670\) 451.723 1685.85i 0.674214 2.51620i
\(671\) 145.497 + 145.497i 0.216837 + 0.216837i
\(672\) −101.757 176.249i −0.151425 0.262275i
\(673\) 44.2409 + 25.5425i 0.0657369 + 0.0379532i 0.532508 0.846425i \(-0.321250\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(674\) 567.131 151.962i 0.841441 0.225463i
\(675\) 16.5074i 0.0244554i
\(676\) 1863.02 + 24.1282i 2.75594 + 0.0356925i
\(677\) −1045.92 −1.54494 −0.772469 0.635053i \(-0.780978\pi\)
−0.772469 + 0.635053i \(0.780978\pi\)
\(678\) −314.624 1174.19i −0.464047 1.73185i
\(679\) −61.1420 + 105.901i −0.0900472 + 0.155966i
\(680\) −872.511 + 503.744i −1.28310 + 0.740801i
\(681\) 383.576 383.576i 0.563254 0.563254i
\(682\) −419.912 112.515i −0.615706 0.164978i
\(683\) 161.532 602.846i 0.236504 0.882644i −0.740962 0.671547i \(-0.765630\pi\)
0.977465 0.211096i \(-0.0677034\pi\)
\(684\) −671.412 671.412i −0.981596 0.981596i
\(685\) −567.170 982.367i −0.827985 1.43411i
\(686\) 296.528 + 171.201i 0.432257 + 0.249564i
\(687\) −269.426 + 72.1923i −0.392177 + 0.105083i
\(688\) 265.406i 0.385764i
\(689\) −279.144 + 1015.43i −0.405143 + 1.47378i
\(690\) −336.738 −0.488026
\(691\) 138.390 + 516.478i 0.200275 + 0.747436i 0.990838 + 0.135055i \(0.0431213\pi\)
−0.790563 + 0.612380i \(0.790212\pi\)
\(692\) −870.321 + 1507.44i −1.25769 + 2.17838i
\(693\) −13.7121 + 7.91666i −0.0197865 + 0.0114237i
\(694\) −373.162 + 373.162i −0.537698 + 0.537698i
\(695\) 359.817 + 96.4126i 0.517722 + 0.138723i
\(696\) −184.737 + 689.446i −0.265426 + 0.990583i
\(697\) 247.914 + 247.914i 0.355687 + 0.355687i
\(698\) −325.177 563.223i −0.465870 0.806910i
\(699\) 287.232 + 165.834i 0.410919 + 0.237244i
\(700\) −30.7533 + 8.24031i −0.0439332 + 0.0117719i
\(701\) 1086.67i 1.55017i −0.631854 0.775087i \(-0.717706\pi\)
0.631854 0.775087i \(-0.282294\pi\)
\(702\) 261.830 + 1.69542i 0.372977 + 0.00241513i
\(703\) 73.1453 0.104047
\(704\) 383.538 + 1431.38i 0.544798 + 2.03321i
\(705\) 105.712 183.098i 0.149945 0.259713i
\(706\) −1064.84 + 614.784i −1.50827 + 0.870798i
\(707\) 63.6610 63.6610i 0.0900439 0.0900439i
\(708\) 274.697 + 73.6048i 0.387990 + 0.103962i
\(709\) −115.524 + 431.140i −0.162939 + 0.608096i 0.835355 + 0.549710i \(0.185262\pi\)
−0.998294 + 0.0583855i \(0.981405\pi\)
\(710\) −1246.68 1246.68i −1.75589 1.75589i
\(711\) −65.5158 113.477i −0.0921460 0.159601i
\(712\) 662.924 + 382.739i 0.931073 + 0.537555i
\(713\) 200.336 53.6798i 0.280976 0.0752872i
\(714\) 48.3391i 0.0677018i
\(715\) 247.698 + 250.927i 0.346431 + 0.350947i
\(716\) 1050.45 1.46711
\(717\) 109.737 + 409.545i 0.153051 + 0.571193i
\(718\) 169.808 294.116i 0.236501 0.409632i
\(719\) −905.624 + 522.862i −1.25956 + 0.727207i −0.972989 0.230851i \(-0.925849\pi\)
−0.286571 + 0.958059i \(0.592516\pi\)
\(720\) −608.909 + 608.909i −0.845707 + 0.845707i
\(721\) −116.137 31.1188i −0.161077 0.0431606i
\(722\) −464.694 + 1734.26i −0.643621 + 2.40203i
\(723\) −71.8658 71.8658i −0.0993994 0.0993994i
\(724\) −932.998 1616.00i −1.28867 2.23204i
\(725\) 41.6383 + 24.0399i 0.0574322 + 0.0331585i
\(726\) −566.085 + 151.682i −0.779731 + 0.208928i
\(727\) 346.434i 0.476525i 0.971201 + 0.238263i \(0.0765779\pi\)
−0.971201 + 0.238263i \(0.923422\pi\)
\(728\) −81.2682 311.347i −0.111632 0.427675i
\(729\) 27.0000 0.0370370
\(730\) 24.8343 + 92.6827i 0.0340195 + 0.126963i
\(731\) −17.1058 + 29.6282i −0.0234006 + 0.0405310i
\(732\) −586.086 + 338.377i −0.800664 + 0.462263i
\(733\) −632.247 + 632.247i −0.862547 + 0.862547i −0.991633 0.129087i \(-0.958796\pi\)
0.129087 + 0.991633i \(0.458796\pi\)
\(734\) −1738.01 465.698i −2.36786 0.634467i
\(735\) 100.885 376.507i 0.137258 0.512254i
\(736\) −981.308 981.308i −1.33330 1.33330i
\(737\) −279.802 484.632i −0.379650 0.657574i
\(738\) 445.779 + 257.371i 0.604037 + 0.348741i
\(739\) 31.2351 8.36942i 0.0422667 0.0113253i −0.237624 0.971357i \(-0.576369\pi\)
0.279890 + 0.960032i \(0.409702\pi\)
\(740\) 131.219i 0.177322i
\(741\) −319.582 561.904i −0.431285 0.758305i
\(742\) 285.439 0.384689
\(743\) 192.884 + 719.854i 0.259602 + 0.968847i 0.965472 + 0.260506i \(0.0838895\pi\)
−0.705870 + 0.708341i \(0.749444\pi\)
\(744\) 455.518 788.980i 0.612255 1.06046i
\(745\) −195.326 + 112.772i −0.262183 + 0.151371i
\(746\) −158.890 + 158.890i −0.212989 + 0.212989i
\(747\) 121.730 + 32.6175i 0.162959 + 0.0436646i
\(748\) −131.214 + 489.698i −0.175420 + 0.654676i
\(749\) −88.7421 88.7421i −0.118481 0.118481i
\(750\) 441.860 + 765.324i 0.589147 + 1.02043i
\(751\) −894.943 516.695i −1.19167 0.688010i −0.232983 0.972481i \(-0.574849\pi\)
−0.958685 + 0.284471i \(0.908182\pi\)
\(752\) 1550.83 415.543i 2.06227 0.552584i
\(753\) 197.371i 0.262114i
\(754\) −385.582 + 657.971i −0.511382 + 0.872641i
\(755\) 1198.33 1.58719
\(756\) −13.4781 50.3010i −0.0178282 0.0665357i
\(757\) 378.681 655.895i 0.500240 0.866440i −0.499760 0.866164i \(-0.666579\pi\)
1.00000 0.000276678i \(-8.80693e-5\pi\)
\(758\) 236.013 136.262i 0.311362 0.179765i
\(759\) −76.3452 + 76.3452i −0.100587 + 0.100587i
\(760\) 3527.35 + 945.151i 4.64125 + 1.24362i
\(761\) 215.400 803.884i 0.283049 1.05635i −0.667205 0.744874i \(-0.732509\pi\)
0.950253 0.311478i \(-0.100824\pi\)
\(762\) 1033.04 + 1033.04i 1.35569 + 1.35569i
\(763\) −16.8708 29.2212i −0.0221112 0.0382977i
\(764\) −884.939 510.920i −1.15830 0.668743i
\(765\) −107.220 + 28.7295i −0.140157 + 0.0375548i
\(766\) 807.953i 1.05477i
\(767\) 167.040 + 97.8883i 0.217784 + 0.127625i
\(768\) −1402.70 −1.82643
\(769\) 251.358 + 938.081i 0.326864 + 1.21987i 0.912425 + 0.409243i \(0.134207\pi\)
−0.585562 + 0.810628i \(0.699126\pi\)
\(770\) 47.7840 82.7642i 0.0620571 0.107486i
\(771\) −561.890 + 324.407i −0.728781 + 0.420762i
\(772\) 2506.52 2506.52i 3.24679 3.24679i
\(773\) −657.402 176.150i −0.850456 0.227879i −0.192838 0.981231i \(-0.561769\pi\)
−0.657618 + 0.753352i \(0.728436\pi\)
\(774\) −13.0000 + 48.5167i −0.0167959 + 0.0626830i
\(775\) −43.3937 43.3937i −0.0559919 0.0559919i
\(776\) 1831.41 + 3172.10i 2.36007 + 4.08776i
\(777\) 3.47413 + 2.00579i 0.00447120 + 0.00258145i
\(778\) −1722.24 + 461.473i −2.21367 + 0.593152i
\(779\) 1270.81i 1.63134i
\(780\) −1008.03 + 573.313i −1.29234 + 0.735017i
\(781\) −565.297 −0.723811
\(782\) −85.3139 318.396i −0.109097 0.407156i
\(783\) −39.3204 + 68.1049i −0.0502176 + 0.0869794i
\(784\) 2563.46 1480.02i 3.26973 1.88778i
\(785\) 265.514 265.514i 0.338235 0.338235i
\(786\) −1029.73 275.915i −1.31009 0.351037i
\(787\) −193.341 + 721.557i −0.245668 + 0.916845i 0.727379 + 0.686236i \(0.240738\pi\)
−0.973047 + 0.230609i \(0.925928\pi\)
\(788\) 873.605 + 873.605i 1.10864 + 1.10864i
\(789\) −100.241 173.623i −0.127048 0.220054i
\(790\) 684.931 + 395.445i 0.867001 + 0.500563i
\(791\) −158.986 + 42.6002i −0.200994 + 0.0538562i
\(792\) 474.262i 0.598815i
\(793\) −445.794 + 116.362i −0.562162 + 0.146736i
\(794\) −2236.93 −2.81729
\(795\) −169.645 633.126i −0.213391 0.796384i
\(796\) 378.404 655.415i 0.475382 0.823385i
\(797\) 431.093 248.892i 0.540895 0.312286i −0.204547 0.978857i \(-0.565572\pi\)
0.745442 + 0.666571i \(0.232239\pi\)
\(798\) −123.894 + 123.894i −0.155255 + 0.155255i
\(799\) 199.907 + 53.5649i 0.250196 + 0.0670399i
\(800\) −106.278 + 396.635i −0.132848 + 0.495794i
\(801\) 59.6361 + 59.6361i 0.0744520 + 0.0744520i
\(802\) 283.938 + 491.794i 0.354037 + 0.613210i
\(803\) 26.6435 + 15.3826i 0.0331799 + 0.0191564i
\(804\) 1777.81 476.363i 2.21121 0.592492i
\(805\) 45.5945i 0.0566391i
\(806\) 692.739 683.826i 0.859478 0.848419i
\(807\) 177.707 0.220208
\(808\) −697.961 2604.83i −0.863813 3.22379i
\(809\) 26.3804 45.6922i 0.0326087 0.0564799i −0.849261 0.527974i \(-0.822952\pi\)
0.881869 + 0.471494i \(0.156285\pi\)
\(810\) −141.135 + 81.4843i −0.174241 + 0.100598i
\(811\) −883.046 + 883.046i −1.08884 + 1.08884i −0.0931873 + 0.995649i \(0.529706\pi\)
−0.995649 + 0.0931873i \(0.970294\pi\)
\(812\) 146.508 + 39.2566i 0.180428 + 0.0483455i
\(813\) −41.6777 + 155.543i −0.0512641 + 0.191320i
\(814\) −40.5438 40.5438i −0.0498081 0.0498081i
\(815\) 411.319 + 712.426i 0.504686 + 0.874142i
\(816\) −730.012 421.472i −0.894622 0.516510i
\(817\) 119.780 32.0949i 0.146609 0.0392838i
\(818\) 883.385i 1.07993i
\(819\) 0.229561 35.4519i 0.000280295 0.0432868i
\(820\) −2279.77 −2.78020
\(821\) −150.881 563.097i −0.183778 0.685867i −0.994889 0.100976i \(-0.967804\pi\)
0.811111 0.584892i \(-0.198863\pi\)
\(822\) 815.113 1411.82i 0.991622 1.71754i
\(823\) 1096.00 632.773i 1.33171 0.768862i 0.346147 0.938180i \(-0.387490\pi\)
0.985561 + 0.169319i \(0.0541567\pi\)
\(824\) −2546.58 + 2546.58i −3.09051 + 3.09051i
\(825\) 30.8580 + 8.26838i 0.0374036 + 0.0100223i
\(826\) 13.5821 50.6890i 0.0164432 0.0613668i
\(827\) 513.651 + 513.651i 0.621102 + 0.621102i 0.945813 0.324712i \(-0.105267\pi\)
−0.324712 + 0.945813i \(0.605267\pi\)
\(828\) −177.553 307.530i −0.214436 0.371414i
\(829\) −759.340 438.405i −0.915972 0.528836i −0.0336239 0.999435i \(-0.510705\pi\)
−0.882348 + 0.470598i \(0.844038\pi\)
\(830\) −734.748 + 196.875i −0.885238 + 0.237199i
\(831\) 732.681i 0.881686i
\(832\) −3199.40 879.521i −3.84544 1.05712i
\(833\) 381.558 0.458053
\(834\) 138.560 + 517.114i 0.166139 + 0.620040i
\(835\) −339.978 + 588.860i −0.407160 + 0.705222i
\(836\) 1591.40 918.796i 1.90359 1.09904i
\(837\) 70.9760 70.9760i 0.0847981 0.0847981i
\(838\) 1543.33 + 413.533i 1.84168 + 0.493477i
\(839\) 122.684 457.864i 0.146227 0.545726i −0.853471 0.521140i \(-0.825507\pi\)
0.999698 0.0245853i \(-0.00782652\pi\)
\(840\) 141.618 + 141.618i 0.168593 + 0.168593i
\(841\) 305.975 + 529.964i 0.363822 + 0.630159i
\(842\) 2452.68 + 1416.06i 2.91292 + 1.68178i
\(843\) 15.5596 4.16919i 0.0184574 0.00494566i
\(844\) 489.818i 0.580353i
\(845\) −765.169 + 194.442i −0.905525 + 0.230109i
\(846\) 303.848 0.359159
\(847\) 20.5378 + 76.6482i 0.0242477 + 0.0904938i
\(848\) 2488.77 4310.67i 2.93486 5.08334i
\(849\) 84.7763 48.9456i 0.0998543 0.0576509i
\(850\) −68.9661 + 68.9661i −0.0811366 + 0.0811366i
\(851\) 26.4231 + 7.08005i 0.0310495 + 0.00831968i
\(852\) 481.209 1795.89i 0.564799 2.10786i
\(853\) −703.767 703.767i −0.825049 0.825049i 0.161778 0.986827i \(-0.448277\pi\)
−0.986827 + 0.161778i \(0.948277\pi\)
\(854\) 62.4396 + 108.149i 0.0731143 + 0.126638i
\(855\) 348.439 + 201.171i 0.407531 + 0.235288i
\(856\) −3631.07 + 972.942i −4.24190 + 1.13661i
\(857\) 12.6753i 0.0147903i 0.999973 + 0.00739514i \(0.00235397\pi\)
−0.999973 + 0.00739514i \(0.997646\pi\)
\(858\) −134.317 + 488.600i −0.156547 + 0.569464i
\(859\) 317.200 0.369266 0.184633 0.982808i \(-0.440890\pi\)
0.184633 + 0.982808i \(0.440890\pi\)
\(860\) −57.5764 214.878i −0.0669493 0.249858i
\(861\) 34.8481 60.3588i 0.0404740 0.0701031i
\(862\) 293.334 169.357i 0.340295 0.196469i
\(863\) −26.7486 + 26.7486i −0.0309949 + 0.0309949i −0.722434 0.691439i \(-0.756977\pi\)
0.691439 + 0.722434i \(0.256977\pi\)
\(864\) −648.749 173.832i −0.750866 0.201194i
\(865\) 190.896 712.435i 0.220690 0.823625i
\(866\) −856.487 856.487i −0.989015 0.989015i
\(867\) 195.952 + 339.399i 0.226012 + 0.391464i
\(868\) −167.659 96.7978i −0.193155 0.111518i
\(869\) 244.943 65.6323i 0.281868 0.0755262i
\(870\) 474.666i 0.545593i
\(871\) 1252.99 + 8.11350i 1.43857 + 0.00931515i
\(872\) −1010.68 −1.15903
\(873\) 104.449 + 389.808i 0.119643 + 0.446516i
\(874\) −597.391 + 1034.71i −0.683514 + 1.18388i
\(875\) 103.625 59.8281i 0.118429 0.0683750i
\(876\) −71.5493 + 71.5493i −0.0816773 + 0.0816773i
\(877\) −445.096 119.263i −0.507521 0.135990i −0.00403275 0.999992i \(-0.501284\pi\)
−0.503488 + 0.864002i \(0.667950\pi\)
\(878\) −132.956 + 496.200i −0.151431 + 0.565148i
\(879\) −251.053 251.053i −0.285612 0.285612i
\(880\) −833.264 1443.26i −0.946891 1.64006i
\(881\) 1118.08 + 645.522i 1.26910 + 0.732715i 0.974818 0.223003i \(-0.0715860\pi\)
0.294283 + 0.955718i \(0.404919\pi\)
\(882\) 541.100 144.987i 0.613492 0.164385i
\(883\) 721.384i 0.816970i −0.912765 0.408485i \(-0.866057\pi\)
0.912765 0.408485i \(-0.133943\pi\)
\(884\) −797.473 807.868i −0.902118 0.913877i
\(885\) −120.504 −0.136163
\(886\) 765.138 + 2855.53i 0.863587 + 3.22295i
\(887\) 300.489 520.463i 0.338770 0.586767i −0.645431 0.763818i \(-0.723322\pi\)
0.984202 + 0.177051i \(0.0566557\pi\)
\(888\) 104.062 60.0802i 0.117187 0.0676578i
\(889\) 139.874 139.874i 0.157339 0.157339i
\(890\) −491.709 131.753i −0.552482 0.148037i
\(891\) −13.5240 + 50.4723i −0.0151785 + 0.0566468i
\(892\) 2359.24 + 2359.24i 2.64489 + 2.64489i
\(893\) −375.076 649.650i −0.420018 0.727492i
\(894\) −280.715 162.071i −0.313998 0.181287i
\(895\) −429.945 + 115.203i −0.480385 + 0.128719i
\(896\) 429.360i 0.479197i
\(897\) −61.0572 233.917i −0.0680682 0.260777i
\(898\) 1066.80 1.18798
\(899\) 75.6670 + 282.393i 0.0841680 + 0.314119i
\(900\) −52.5357 + 90.9945i −0.0583730 + 0.101105i
\(901\) 555.659 320.810i 0.616714 0.356060i
\(902\) −704.400 + 704.400i −0.780931 + 0.780931i
\(903\) 6.56918 + 1.76021i 0.00727484 + 0.00194929i
\(904\) −1276.02 + 4762.18i −1.41153 + 5.26790i
\(905\) 559.098 + 559.098i 0.617788 + 0.617788i
\(906\) 861.096 + 1491.46i 0.950437 + 1.64621i
\(907\) −281.007 162.240i −0.309820 0.178875i 0.337026 0.941495i \(-0.390579\pi\)
−0.646846 + 0.762621i \(0.723912\pi\)
\(908\) −3335.15 + 893.652i −3.67308 + 0.984198i
\(909\) 297.116i 0.326860i
\(910\) 105.792 + 186.008i 0.116255 + 0.204404i
\(911\) −894.435 −0.981817 −0.490908 0.871211i \(-0.663335\pi\)
−0.490908 + 0.871211i \(0.663335\pi\)
\(912\) 790.788 + 2951.26i 0.867093 + 3.23603i
\(913\) −121.947 + 211.218i −0.133567 + 0.231345i
\(914\) −1912.50 + 1104.18i −2.09245 + 1.20808i
\(915\) 202.772 202.772i 0.221609 0.221609i
\(916\) 1714.92 + 459.512i 1.87219 + 0.501651i
\(917\) −37.3590 + 139.426i −0.0407405 + 0.152046i
\(918\) −112.803 112.803i −0.122879 0.122879i
\(919\) 160.850 + 278.600i 0.175027 + 0.303155i 0.940171 0.340704i \(-0.110665\pi\)
−0.765144 + 0.643860i \(0.777332\pi\)
\(920\) 1182.74 + 682.855i 1.28559 + 0.742234i
\(921\) −50.2676 + 13.4692i −0.0545794 + 0.0146245i
\(922\) 528.650i 0.573373i
\(923\) 639.968 1092.06i 0.693356 1.18317i
\(924\) 100.781 0.109070
\(925\) −2.09490 7.81827i −0.00226476 0.00845219i
\(926\) 1523.76 2639.24i 1.64553 2.85015i
\(927\) −343.632 + 198.396i −0.370693 + 0.214020i
\(928\) 1383.25 1383.25i 1.49057 1.49057i
\(929\) 1606.59 + 430.484i 1.72937 + 0.463384i 0.980039 0.198806i \(-0.0637064\pi\)
0.749336 + 0.662190i \(0.230373\pi\)
\(930\) −156.806 + 585.209i −0.168609 + 0.629256i
\(931\) −977.937 977.937i −1.05042 1.05042i
\(932\) −1055.55 1828.27i −1.13256 1.96166i
\(933\) 492.022 + 284.069i 0.527355 + 0.304468i
\(934\) 2563.42 686.865i 2.74456 0.735402i
\(935\) 214.821i 0.229755i
\(936\) −916.199 536.907i −0.978845 0.573619i
\(937\) 34.1401 0.0364355 0.0182178 0.999834i \(-0.494201\pi\)
0.0182178 + 0.999834i \(0.494201\pi\)
\(938\) −87.9018 328.054i −0.0937120 0.349738i
\(939\) −495.525 + 858.274i −0.527715 + 0.914030i
\(940\) −1165.44 + 672.865i −1.23983 + 0.715814i
\(941\) 135.813 135.813i 0.144328 0.144328i −0.631251 0.775579i \(-0.717458\pi\)
0.775579 + 0.631251i \(0.217458\pi\)
\(942\) 521.257 + 139.670i 0.553351 + 0.148270i
\(943\) 123.007 459.069i 0.130443 0.486818i
\(944\) −647.076 647.076i −0.685462 0.685462i
\(945\) 11.0330 + 19.1098i 0.0116752 + 0.0202220i
\(946\) −84.1827 48.6029i −0.0889881 0.0513773i
\(947\) −1083.44 + 290.306i −1.14407 + 0.306554i −0.780588 0.625046i \(-0.785080\pi\)
−0.363486 + 0.931600i \(0.618414\pi\)
\(948\) 834.030i 0.879779i
\(949\) −59.8796 + 34.0564i −0.0630976 + 0.0358867i
\(950\) 353.522 0.372128
\(951\) −167.263 624.235i −0.175882 0.656399i
\(952\) −98.0247 + 169.784i −0.102967 + 0.178344i
\(953\) −310.812 + 179.447i −0.326140 + 0.188297i −0.654126 0.756385i \(-0.726963\pi\)
0.327986 + 0.944683i \(0.393630\pi\)
\(954\) 666.094 666.094i 0.698212 0.698212i
\(955\) 418.233 + 112.065i 0.437941 + 0.117346i
\(956\) 698.490 2606.80i 0.730638 2.72678i
\(957\) −107.616 107.616i −0.112452 0.112452i
\(958\) −1622.00 2809.38i −1.69311 2.93255i
\(959\) −191.161 110.367i −0.199334 0.115085i
\(960\) 1994.84 534.516i 2.07796 0.556788i
\(961\) 587.845i 0.611701i
\(962\) 124.224 32.4250i 0.129130 0.0337058i
\(963\) −414.173 −0.430086
\(964\) 167.432 + 624.866i 0.173685 + 0.648201i
\(965\) −751.016 + 1300.80i −0.778255 + 1.34798i
\(966\) −56.7476 + 32.7633i −0.0587450 + 0.0339164i
\(967\) 139.945 139.945i 0.144721 0.144721i −0.631034 0.775755i \(-0.717369\pi\)
0.775755 + 0.631034i \(0.217369\pi\)
\(968\) 2295.88 + 615.178i 2.37177 + 0.635515i
\(969\) −101.935 + 380.427i −0.105196 + 0.392598i
\(970\) −1722.39 1722.39i −1.77566 1.77566i
\(971\) 711.780 + 1232.84i 0.733038 + 1.26966i 0.955579 + 0.294736i \(0.0952316\pi\)
−0.222541 + 0.974923i \(0.571435\pi\)
\(972\) −148.833 85.9290i −0.153121 0.0884043i
\(973\) 70.0175 18.7611i 0.0719604 0.0192817i
\(974\) 1692.54i 1.73773i
\(975\) −50.9073 + 50.2522i −0.0522126 + 0.0515408i
\(976\) 2177.66 2.23121
\(977\) −8.38753 31.3027i −0.00858499 0.0320396i 0.961500 0.274803i \(-0.0886127\pi\)
−0.970085 + 0.242764i \(0.921946\pi\)
\(978\) −591.131 + 1023.87i −0.604428 + 1.04690i
\(979\) −141.351 + 81.6092i −0.144383 + 0.0833598i
\(980\) −1754.36 + 1754.36i −1.79017 + 1.79017i
\(981\) −107.559 28.8204i −0.109642 0.0293786i
\(982\) 444.920 1660.46i 0.453075 1.69090i
\(983\) −370.965 370.965i −0.377381 0.377381i 0.492776 0.870156i \(-0.335982\pi\)
−0.870156 + 0.492776i \(0.835982\pi\)
\(984\) −1043.82 1807.95i −1.06079 1.83735i
\(985\) −453.370 261.753i −0.460274 0.265739i
\(986\) 448.811 120.259i 0.455184 0.121966i
\(987\) 41.1413i 0.0416831i
\(988\) −26.6426 + 4114.50i −0.0269662 + 4.16447i
\(989\) 46.3759 0.0468917
\(990\) −81.6292 304.644i −0.0824537 0.307722i
\(991\) 600.773 1040.57i 0.606229 1.05002i −0.385627 0.922655i \(-0.626015\pi\)
0.991856 0.127365i \(-0.0406518\pi\)
\(992\) −2162.35 + 1248.43i −2.17979 + 1.25850i
\(993\) 104.580 104.580i 0.105318 0.105318i
\(994\) −331.391 88.7959i −0.333391 0.0893319i
\(995\) −82.9992 + 309.757i −0.0834163 + 0.311314i
\(996\) −567.212 567.212i −0.569490 0.569490i
\(997\) −523.573 906.855i −0.525148 0.909584i −0.999571 0.0292865i \(-0.990676\pi\)
0.474423 0.880297i \(-0.342657\pi\)
\(998\) −2154.00 1243.61i −2.15832 1.24611i
\(999\) 12.7878 3.42648i 0.0128006 0.00342991i
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 39.3.l.b.19.3 12
3.2 odd 2 117.3.bd.d.19.1 12
13.11 odd 12 inner 39.3.l.b.37.3 yes 12
39.11 even 12 117.3.bd.d.37.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.3.l.b.19.3 12 1.1 even 1 trivial
39.3.l.b.37.3 yes 12 13.11 odd 12 inner
117.3.bd.d.19.1 12 3.2 odd 2
117.3.bd.d.37.1 12 39.11 even 12