Properties

Label 529.2.c.o.501.2
Level $529$
Weight $2$
Character 529.501
Analytic conductor $4.224$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $10$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [529,2,Mod(118,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("529.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 529.c (of order \(11\), degree \(10\), 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: \(4.22408626693\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: 20.0.54296067514572573056640625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} - 55 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + \cdots + 1 \) 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 23)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 501.2
Root \(-0.672156 + 1.47182i\) of defining polynomial
Character \(\chi\) \(=\) 529.501
Dual form 529.2.c.o.170.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.55249 + 0.455853i) q^{2} +(-1.46431 + 1.68991i) q^{3} +(0.519923 + 0.334134i) q^{4} +(0.460540 - 3.20313i) q^{5} +(-3.04368 + 1.95606i) q^{6} +(-0.513481 - 1.12437i) q^{7} +(-1.46431 - 1.68991i) q^{8} +(-0.284630 - 1.97964i) q^{9} +O(q^{10})\) \(q+(1.55249 + 0.455853i) q^{2} +(-1.46431 + 1.68991i) q^{3} +(0.519923 + 0.334134i) q^{4} +(0.460540 - 3.20313i) q^{5} +(-3.04368 + 1.95606i) q^{6} +(-0.513481 - 1.12437i) q^{7} +(-1.46431 - 1.68991i) q^{8} +(-0.284630 - 1.97964i) q^{9} +(2.17514 - 4.76289i) q^{10} +(0.732987 - 0.215225i) q^{11} +(-1.32599 + 0.389345i) q^{12} +(1.24625 - 2.72890i) q^{13} +(-0.284630 - 1.97964i) q^{14} +(4.73862 + 5.46866i) q^{15} +(-2.01647 - 4.41545i) q^{16} +(4.40486 - 2.83083i) q^{17} +(0.460540 - 3.20313i) q^{18} +(-1.68251 - 1.08128i) q^{19} +(1.30972 - 1.51150i) q^{20} +(2.65197 + 0.778690i) q^{21} +1.23607 q^{22} +5.00000 q^{24} +(-5.25048 - 1.54168i) q^{25} +(3.17876 - 3.66849i) q^{26} +(-1.88110 - 1.20891i) q^{27} +(0.108719 - 0.756156i) q^{28} +(-2.52376 + 1.62192i) q^{29} +(4.86376 + 10.6502i) q^{30} +(4.39294 + 5.06972i) q^{31} +(-0.481304 - 3.34754i) q^{32} +(-0.709614 + 1.55384i) q^{33} +(8.12895 - 2.38688i) q^{34} +(-3.83797 + 1.12693i) q^{35} +(0.513481 - 1.12437i) q^{36} +(-0.460540 - 3.20313i) q^{37} +(-2.11917 - 2.44566i) q^{38} +(2.78669 + 6.10200i) q^{39} +(-6.08737 + 3.91211i) q^{40} +(-0.778766 + 5.41644i) q^{41} +(3.76220 + 2.41782i) q^{42} +(0.453011 + 0.133016i) q^{44} -6.47214 q^{45} +2.23607 q^{47} +(10.4144 + 3.05795i) q^{48} +(3.58349 - 4.13556i) q^{49} +(-7.44854 - 4.78689i) q^{50} +(-1.66625 + 11.5890i) q^{51} +(1.55977 - 1.00240i) q^{52} +(-3.51945 - 7.70653i) q^{53} +(-2.36931 - 2.73433i) q^{54} +(-0.351822 - 2.44697i) q^{55} +(-1.14818 + 2.51416i) q^{56} +(4.29098 - 1.25995i) q^{57} +(-4.65748 + 1.36756i) q^{58} +(-1.02696 + 2.24873i) q^{59} +(0.636451 + 4.42662i) q^{60} +(-7.16697 - 8.27113i) q^{61} +(4.50896 + 9.87324i) q^{62} +(-2.07969 + 1.33654i) q^{63} +(-0.602855 + 4.19295i) q^{64} +(-8.16706 - 5.24865i) q^{65} +(-1.80999 + 2.08884i) q^{66} +(6.94296 + 2.03864i) q^{67} +3.23607 q^{68} -6.47214 q^{70} +(-7.44944 - 2.18735i) q^{71} +(-2.92863 + 3.37981i) q^{72} +(13.0160 + 8.36487i) q^{73} +(0.745170 - 5.18277i) q^{74} +(10.2936 - 6.61532i) q^{75} +(-0.513481 - 1.12437i) q^{76} +(-0.618367 - 0.713633i) q^{77} +(1.54470 + 10.7436i) q^{78} +(2.88475 - 6.31673i) q^{79} +(-15.0719 + 4.42551i) q^{80} +(10.5544 - 3.09906i) q^{81} +(-3.67813 + 8.05397i) q^{82} +(1.88369 + 13.1013i) q^{83} +(1.11864 + 1.29097i) q^{84} +(-7.03890 - 15.4131i) q^{85} +(0.954677 - 6.63992i) q^{87} +(-1.43703 - 0.923525i) q^{88} +(1.00054 - 1.15468i) q^{89} +(-10.0479 - 2.95034i) q^{90} -3.70820 q^{91} -15.0000 q^{93} +(3.47148 + 1.01932i) q^{94} +(-4.23835 + 4.89131i) q^{95} +(6.36182 + 4.08849i) q^{96} +(-0.610786 + 4.24811i) q^{97} +(7.44854 - 4.78689i) q^{98} +(-0.634698 - 1.38979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} + 6 q^{28} + 6 q^{29} - 10 q^{30} - 9 q^{32} - 10 q^{33} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 10 q^{40} - 2 q^{41} - 8 q^{44} - 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} - 10 q^{51} + 3 q^{52} + 8 q^{53} - 5 q^{54} + 4 q^{55} + 10 q^{56} - 3 q^{58} - 4 q^{59} - 4 q^{61} - 15 q^{62} - 4 q^{63} - 4 q^{64} + 6 q^{65} - 10 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} + 6 q^{74} - 20 q^{75} - 2 q^{76} + 16 q^{77} + 15 q^{78} + 4 q^{79} - 18 q^{80} + 22 q^{81} + 11 q^{82} + 22 q^{83} - 10 q^{84} + 16 q^{85} - 10 q^{88} + 12 q^{89} - 12 q^{90} + 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} - 22 q^{97} - 11 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/529\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{6}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55249 + 0.455853i 1.09778 + 0.322337i 0.779969 0.625818i \(-0.215235\pi\)
0.317809 + 0.948155i \(0.397053\pi\)
\(3\) −1.46431 + 1.68991i −0.845422 + 0.975669i −0.999924 0.0123239i \(-0.996077\pi\)
0.154502 + 0.987992i \(0.450623\pi\)
\(4\) 0.519923 + 0.334134i 0.259962 + 0.167067i
\(5\) 0.460540 3.20313i 0.205960 1.43248i −0.580207 0.814469i \(-0.697028\pi\)
0.786167 0.618014i \(-0.212063\pi\)
\(6\) −3.04368 + 1.95606i −1.24258 + 0.798557i
\(7\) −0.513481 1.12437i −0.194078 0.424971i 0.787427 0.616408i \(-0.211413\pi\)
−0.981505 + 0.191437i \(0.938685\pi\)
\(8\) −1.46431 1.68991i −0.517713 0.597472i
\(9\) −0.284630 1.97964i −0.0948766 0.659881i
\(10\) 2.17514 4.76289i 0.687840 1.50616i
\(11\) 0.732987 0.215225i 0.221004 0.0648926i −0.169356 0.985555i \(-0.554169\pi\)
0.390360 + 0.920662i \(0.372351\pi\)
\(12\) −1.32599 + 0.389345i −0.382779 + 0.112394i
\(13\) 1.24625 2.72890i 0.345646 0.756860i −0.654354 0.756189i \(-0.727059\pi\)
1.00000 0.000670851i \(-0.000213539\pi\)
\(14\) −0.284630 1.97964i −0.0760705 0.529082i
\(15\) 4.73862 + 5.46866i 1.22351 + 1.41200i
\(16\) −2.01647 4.41545i −0.504117 1.10386i
\(17\) 4.40486 2.83083i 1.06834 0.686578i 0.116501 0.993191i \(-0.462832\pi\)
0.951834 + 0.306613i \(0.0991957\pi\)
\(18\) 0.460540 3.20313i 0.108550 0.754985i
\(19\) −1.68251 1.08128i −0.385994 0.248063i 0.333224 0.942848i \(-0.391863\pi\)
−0.719218 + 0.694785i \(0.755500\pi\)
\(20\) 1.30972 1.51150i 0.292863 0.337981i
\(21\) 2.65197 + 0.778690i 0.578708 + 0.169924i
\(22\) 1.23607 0.263531
\(23\) 0 0
\(24\) 5.00000 1.02062
\(25\) −5.25048 1.54168i −1.05010 0.308336i
\(26\) 3.17876 3.66849i 0.623406 0.719449i
\(27\) −1.88110 1.20891i −0.362018 0.232655i
\(28\) 0.108719 0.756156i 0.0205459 0.142900i
\(29\) −2.52376 + 1.62192i −0.468651 + 0.301183i −0.753570 0.657368i \(-0.771670\pi\)
0.284919 + 0.958552i \(0.408033\pi\)
\(30\) 4.86376 + 10.6502i 0.887998 + 1.94444i
\(31\) 4.39294 + 5.06972i 0.788995 + 0.910549i 0.997724 0.0674245i \(-0.0214782\pi\)
−0.208729 + 0.977973i \(0.566933\pi\)
\(32\) −0.481304 3.34754i −0.0850833 0.591767i
\(33\) −0.709614 + 1.55384i −0.123528 + 0.270488i
\(34\) 8.12895 2.38688i 1.39410 0.409346i
\(35\) −3.83797 + 1.12693i −0.648736 + 0.190486i
\(36\) 0.513481 1.12437i 0.0855802 0.187394i
\(37\) −0.460540 3.20313i −0.0757124 0.526591i −0.992017 0.126108i \(-0.959751\pi\)
0.916304 0.400483i \(-0.131158\pi\)
\(38\) −2.11917 2.44566i −0.343775 0.396738i
\(39\) 2.78669 + 6.10200i 0.446227 + 0.977102i
\(40\) −6.08737 + 3.91211i −0.962497 + 0.618559i
\(41\) −0.778766 + 5.41644i −0.121623 + 0.845905i 0.834095 + 0.551621i \(0.185990\pi\)
−0.955718 + 0.294285i \(0.904919\pi\)
\(42\) 3.76220 + 2.41782i 0.580520 + 0.373078i
\(43\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(44\) 0.453011 + 0.133016i 0.0682940 + 0.0200529i
\(45\) −6.47214 −0.964809
\(46\) 0 0
\(47\) 2.23607 0.326164 0.163082 0.986613i \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) 10.4144 + 3.05795i 1.50319 + 0.441378i
\(49\) 3.58349 4.13556i 0.511927 0.590795i
\(50\) −7.44854 4.78689i −1.05338 0.676968i
\(51\) −1.66625 + 11.5890i −0.233322 + 1.62279i
\(52\) 1.55977 1.00240i 0.216301 0.139008i
\(53\) −3.51945 7.70653i −0.483434 1.05857i −0.981505 0.191437i \(-0.938685\pi\)
0.498071 0.867136i \(-0.334042\pi\)
\(54\) −2.36931 2.73433i −0.322422 0.372095i
\(55\) −0.351822 2.44697i −0.0474396 0.329950i
\(56\) −1.14818 + 2.51416i −0.153432 + 0.335969i
\(57\) 4.29098 1.25995i 0.568355 0.166884i
\(58\) −4.65748 + 1.36756i −0.611557 + 0.179569i
\(59\) −1.02696 + 2.24873i −0.133699 + 0.292760i −0.964626 0.263621i \(-0.915083\pi\)
0.830927 + 0.556381i \(0.187811\pi\)
\(60\) 0.636451 + 4.42662i 0.0821655 + 0.571474i
\(61\) −7.16697 8.27113i −0.917637 1.05901i −0.998061 0.0622488i \(-0.980173\pi\)
0.0804237 0.996761i \(-0.474373\pi\)
\(62\) 4.50896 + 9.87324i 0.572638 + 1.25390i
\(63\) −2.07969 + 1.33654i −0.262017 + 0.168388i
\(64\) −0.602855 + 4.19295i −0.0753569 + 0.524119i
\(65\) −8.16706 5.24865i −1.01300 0.651015i
\(66\) −1.80999 + 2.08884i −0.222794 + 0.257118i
\(67\) 6.94296 + 2.03864i 0.848217 + 0.249059i 0.676825 0.736144i \(-0.263355\pi\)
0.171392 + 0.985203i \(0.445174\pi\)
\(68\) 3.23607 0.392431
\(69\) 0 0
\(70\) −6.47214 −0.773568
\(71\) −7.44944 2.18735i −0.884086 0.259591i −0.191990 0.981397i \(-0.561494\pi\)
−0.692096 + 0.721806i \(0.743312\pi\)
\(72\) −2.92863 + 3.37981i −0.345142 + 0.398315i
\(73\) 13.0160 + 8.36487i 1.52341 + 0.979034i 0.991193 + 0.132423i \(0.0422758\pi\)
0.532213 + 0.846610i \(0.321361\pi\)
\(74\) 0.745170 5.18277i 0.0866243 0.602485i
\(75\) 10.2936 6.61532i 1.18861 0.763871i
\(76\) −0.513481 1.12437i −0.0589003 0.128974i
\(77\) −0.618367 0.713633i −0.0704694 0.0813260i
\(78\) 1.54470 + 10.7436i 0.174903 + 1.21648i
\(79\) 2.88475 6.31673i 0.324560 0.710688i −0.675073 0.737751i \(-0.735888\pi\)
0.999634 + 0.0270626i \(0.00861536\pi\)
\(80\) −15.0719 + 4.42551i −1.68509 + 0.494787i
\(81\) 10.5544 3.09906i 1.17271 0.344340i
\(82\) −3.67813 + 8.05397i −0.406181 + 0.889413i
\(83\) 1.88369 + 13.1013i 0.206762 + 1.43806i 0.783633 + 0.621224i \(0.213364\pi\)
−0.576871 + 0.816835i \(0.695727\pi\)
\(84\) 1.11864 + 1.29097i 0.122053 + 0.140857i
\(85\) −7.03890 15.4131i −0.763476 1.67178i
\(86\) 0 0
\(87\) 0.954677 6.63992i 0.102352 0.711875i
\(88\) −1.43703 0.923525i −0.153188 0.0984481i
\(89\) 1.00054 1.15468i 0.106057 0.122396i −0.700239 0.713908i \(-0.746923\pi\)
0.806296 + 0.591512i \(0.201469\pi\)
\(90\) −10.0479 2.95034i −1.05915 0.310993i
\(91\) −3.70820 −0.388725
\(92\) 0 0
\(93\) −15.0000 −1.55543
\(94\) 3.47148 + 1.01932i 0.358056 + 0.105135i
\(95\) −4.23835 + 4.89131i −0.434845 + 0.501838i
\(96\) 6.36182 + 4.08849i 0.649300 + 0.417280i
\(97\) −0.610786 + 4.24811i −0.0620159 + 0.431330i 0.935033 + 0.354561i \(0.115370\pi\)
−0.997049 + 0.0767695i \(0.975539\pi\)
\(98\) 7.44854 4.78689i 0.752417 0.483549i
\(99\) −0.634698 1.38979i −0.0637895 0.139680i
\(100\) −2.21472 2.55592i −0.221472 0.255592i
\(101\) 0.636451 + 4.42662i 0.0633293 + 0.440465i 0.996675 + 0.0814849i \(0.0259662\pi\)
−0.933345 + 0.358980i \(0.883125\pi\)
\(102\) −7.86973 + 17.2323i −0.779220 + 1.70625i
\(103\) −17.4439 + 5.12199i −1.71880 + 0.504685i −0.984685 0.174341i \(-0.944220\pi\)
−0.734114 + 0.679026i \(0.762402\pi\)
\(104\) −6.43647 + 1.88992i −0.631148 + 0.185322i
\(105\) 3.71558 8.13600i 0.362604 0.793992i
\(106\) −1.95088 13.5687i −0.189486 1.31791i
\(107\) 8.78588 + 10.1394i 0.849363 + 0.980217i 0.999965 0.00837738i \(-0.00266663\pi\)
−0.150602 + 0.988594i \(0.548121\pi\)
\(108\) −0.574089 1.25708i −0.0552418 0.120963i
\(109\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(110\) 0.569259 3.95929i 0.0542767 0.377503i
\(111\) 6.08737 + 3.91211i 0.577787 + 0.371321i
\(112\) −3.92916 + 4.53450i −0.371271 + 0.428470i
\(113\) −12.6999 3.72903i −1.19471 0.350798i −0.376880 0.926262i \(-0.623003\pi\)
−0.817827 + 0.575464i \(0.804821\pi\)
\(114\) 7.23607 0.677720
\(115\) 0 0
\(116\) −1.85410 −0.172149
\(117\) −5.75696 1.69040i −0.532231 0.156277i
\(118\) −2.61944 + 3.02300i −0.241139 + 0.278290i
\(119\) −5.44471 3.49910i −0.499115 0.320762i
\(120\) 2.30270 16.0156i 0.210207 1.46202i
\(121\) −8.76284 + 5.63154i −0.796622 + 0.511958i
\(122\) −7.35625 16.1079i −0.666004 1.45835i
\(123\) −8.01292 9.24740i −0.722501 0.833810i
\(124\) 0.590023 + 4.10370i 0.0529856 + 0.368523i
\(125\) −0.634698 + 1.38979i −0.0567691 + 0.124307i
\(126\) −3.83797 + 1.12693i −0.341914 + 0.100395i
\(127\) 19.8694 5.83418i 1.76312 0.517699i 0.770340 0.637633i \(-0.220086\pi\)
0.992782 + 0.119934i \(0.0382682\pi\)
\(128\) −5.65714 + 12.3874i −0.500025 + 1.09490i
\(129\) 0 0
\(130\) −10.2867 11.8715i −0.902202 1.04120i
\(131\) 2.19829 + 4.81359i 0.192066 + 0.420565i 0.981025 0.193880i \(-0.0621072\pi\)
−0.788960 + 0.614445i \(0.789380\pi\)
\(132\) −0.888135 + 0.570770i −0.0773022 + 0.0496791i
\(133\) −0.351822 + 2.44697i −0.0305068 + 0.212179i
\(134\) 9.84957 + 6.32993i 0.850873 + 0.546823i
\(135\) −4.73862 + 5.46866i −0.407835 + 0.470667i
\(136\) −11.2339 3.29858i −0.963302 0.282851i
\(137\) 13.8885 1.18658 0.593289 0.804989i \(-0.297829\pi\)
0.593289 + 0.804989i \(0.297829\pi\)
\(138\) 0 0
\(139\) 2.70820 0.229707 0.114853 0.993382i \(-0.463360\pi\)
0.114853 + 0.993382i \(0.463360\pi\)
\(140\) −2.37200 0.696481i −0.200470 0.0588634i
\(141\) −3.27430 + 3.77875i −0.275746 + 0.318228i
\(142\) −10.5681 6.79170i −0.886854 0.569946i
\(143\) 0.326157 2.26847i 0.0272746 0.189699i
\(144\) −8.16706 + 5.24865i −0.680588 + 0.437388i
\(145\) 4.03293 + 8.83089i 0.334917 + 0.733366i
\(146\) 16.3941 + 18.9198i 1.35678 + 1.56581i
\(147\) 1.74137 + 12.1115i 0.143626 + 0.998942i
\(148\) 0.830830 1.81926i 0.0682938 0.149543i
\(149\) 11.4070 3.34939i 0.934496 0.274393i 0.221178 0.975233i \(-0.429010\pi\)
0.713318 + 0.700841i \(0.247192\pi\)
\(150\) 18.9964 5.57785i 1.55105 0.455429i
\(151\) −0.0980662 + 0.214735i −0.00798051 + 0.0174749i −0.913580 0.406658i \(-0.866694\pi\)
0.905600 + 0.424133i \(0.139421\pi\)
\(152\) 0.636451 + 4.42662i 0.0516230 + 0.359046i
\(153\) −6.85779 7.91431i −0.554420 0.639834i
\(154\) −0.634698 1.38979i −0.0511454 0.111993i
\(155\) 18.2621 11.7363i 1.46685 0.942686i
\(156\) −0.590023 + 4.10370i −0.0472396 + 0.328559i
\(157\) 12.9691 + 8.33474i 1.03505 + 0.665185i 0.943757 0.330640i \(-0.107264\pi\)
0.0912904 + 0.995824i \(0.470901\pi\)
\(158\) 7.35806 8.49165i 0.585376 0.675560i
\(159\) 18.1769 + 5.33722i 1.44152 + 0.423269i
\(160\) −10.9443 −0.865221
\(161\) 0 0
\(162\) 17.7984 1.39837
\(163\) 9.82144 + 2.88383i 0.769274 + 0.225879i 0.642741 0.766083i \(-0.277797\pi\)
0.126533 + 0.991962i \(0.459615\pi\)
\(164\) −2.21472 + 2.55592i −0.172940 + 0.199584i
\(165\) 4.65034 + 2.98859i 0.362028 + 0.232661i
\(166\) −3.04787 + 21.1984i −0.236561 + 1.64532i
\(167\) 8.80972 5.66166i 0.681717 0.438113i −0.153416 0.988162i \(-0.549027\pi\)
0.835132 + 0.550049i \(0.185391\pi\)
\(168\) −2.56741 5.62183i −0.198080 0.433734i
\(169\) 2.61944 + 3.02300i 0.201496 + 0.232538i
\(170\) −3.90176 27.1373i −0.299251 2.08134i
\(171\) −1.66166 + 3.63853i −0.127070 + 0.278245i
\(172\) 0 0
\(173\) −4.85094 + 1.42436i −0.368810 + 0.108292i −0.460885 0.887460i \(-0.652468\pi\)
0.0920755 + 0.995752i \(0.470650\pi\)
\(174\) 4.50896 9.87324i 0.341823 0.748488i
\(175\) 0.962608 + 6.69508i 0.0727663 + 0.506101i
\(176\) −2.42836 2.80247i −0.183044 0.211244i
\(177\) −2.29636 5.02832i −0.172605 0.377952i
\(178\) 2.07969 1.33654i 0.155880 0.100178i
\(179\) 1.80857 12.5789i 0.135179 0.940188i −0.803478 0.595334i \(-0.797020\pi\)
0.938657 0.344853i \(-0.112071\pi\)
\(180\) −3.36501 2.16256i −0.250813 0.161188i
\(181\) 9.59533 11.0736i 0.713215 0.823094i −0.277259 0.960795i \(-0.589426\pi\)
0.990474 + 0.137701i \(0.0439713\pi\)
\(182\) −5.75696 1.69040i −0.426734 0.125300i
\(183\) 24.4721 1.80903
\(184\) 0 0
\(185\) −10.4721 −0.769927
\(186\) −23.2874 6.83779i −1.70751 0.501371i
\(187\) 2.61944 3.02300i 0.191553 0.221064i
\(188\) 1.16258 + 0.747147i 0.0847901 + 0.0544913i
\(189\) −0.393349 + 2.73580i −0.0286119 + 0.199000i
\(190\) −8.80972 + 5.66166i −0.639124 + 0.410740i
\(191\) −1.58674 3.47449i −0.114813 0.251405i 0.843498 0.537132i \(-0.180492\pi\)
−0.958311 + 0.285727i \(0.907765\pi\)
\(192\) −6.20293 7.15856i −0.447658 0.516625i
\(193\) 1.13059 + 7.86341i 0.0813815 + 0.566021i 0.989190 + 0.146637i \(0.0468448\pi\)
−0.907809 + 0.419384i \(0.862246\pi\)
\(194\) −2.88475 + 6.31673i −0.207113 + 0.453515i
\(195\) 20.8289 6.11591i 1.49159 0.437969i
\(196\) 3.24497 0.952810i 0.231784 0.0680579i
\(197\) 3.10404 6.79689i 0.221154 0.484259i −0.766238 0.642557i \(-0.777874\pi\)
0.987391 + 0.158298i \(0.0506008\pi\)
\(198\) −0.351822 2.44697i −0.0250029 0.173899i
\(199\) 16.8353 + 19.4290i 1.19342 + 1.37728i 0.908048 + 0.418867i \(0.137573\pi\)
0.285375 + 0.958416i \(0.407882\pi\)
\(200\) 5.08305 + 11.1303i 0.359426 + 0.787032i
\(201\) −13.6118 + 8.74775i −0.960100 + 0.617019i
\(202\) −1.02980 + 7.16242i −0.0724565 + 0.503946i
\(203\) 3.11954 + 2.00481i 0.218949 + 0.140710i
\(204\) −4.73862 + 5.46866i −0.331770 + 0.382882i
\(205\) 16.9909 + 4.98898i 1.18670 + 0.348445i
\(206\) −29.4164 −2.04954
\(207\) 0 0
\(208\) −14.5623 −1.00971
\(209\) −1.46597 0.430449i −0.101404 0.0297748i
\(210\) 9.47723 10.9373i 0.653991 0.754746i
\(211\) 2.87407 + 1.84705i 0.197859 + 0.127156i 0.635819 0.771838i \(-0.280663\pi\)
−0.437960 + 0.898994i \(0.644299\pi\)
\(212\) 0.745170 5.18277i 0.0511785 0.355954i
\(213\) 14.6047 9.38589i 1.00070 0.643111i
\(214\) 9.01791 + 19.7465i 0.616452 + 1.34984i
\(215\) 0 0
\(216\) 0.711574 + 4.94911i 0.0484165 + 0.336744i
\(217\) 3.44454 7.54248i 0.233830 0.512017i
\(218\) 0 0
\(219\) −33.1953 + 9.74703i −2.24313 + 0.658643i
\(220\) 0.634698 1.38979i 0.0427913 0.0936999i
\(221\) −2.23551 15.5483i −0.150377 1.04589i
\(222\) 7.66724 + 8.84847i 0.514592 + 0.593870i
\(223\) 1.66166 + 3.63853i 0.111273 + 0.243654i 0.957073 0.289846i \(-0.0936039\pi\)
−0.845800 + 0.533499i \(0.820877\pi\)
\(224\) −3.51673 + 2.26006i −0.234971 + 0.151007i
\(225\) −1.55753 + 10.8329i −0.103835 + 0.722192i
\(226\) −18.0166 11.5786i −1.19845 0.770196i
\(227\) −6.66670 + 7.69379i −0.442485 + 0.510655i −0.932555 0.361028i \(-0.882426\pi\)
0.490070 + 0.871683i \(0.336971\pi\)
\(228\) 2.65197 + 0.778690i 0.175631 + 0.0515700i
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 0 0
\(231\) 2.11146 0.138924
\(232\) 6.43647 + 1.88992i 0.422575 + 0.124079i
\(233\) 10.1321 11.6931i 0.663776 0.766038i −0.319614 0.947548i \(-0.603553\pi\)
0.983389 + 0.181510i \(0.0580985\pi\)
\(234\) −8.16706 5.24865i −0.533897 0.343115i
\(235\) 1.02980 7.16242i 0.0671767 0.467224i
\(236\) −1.28532 + 0.826026i −0.0836673 + 0.0537697i
\(237\) 6.45051 + 14.1246i 0.419006 + 0.917494i
\(238\) −6.85779 7.91431i −0.444525 0.513009i
\(239\) −2.59526 18.0505i −0.167874 1.16759i −0.883269 0.468867i \(-0.844662\pi\)
0.715395 0.698720i \(-0.246247\pi\)
\(240\) 14.5913 31.9505i 0.941864 2.06239i
\(241\) −16.4309 + 4.82456i −1.05841 + 0.310777i −0.764211 0.644967i \(-0.776871\pi\)
−0.294200 + 0.955744i \(0.595053\pi\)
\(242\) −16.1714 + 4.74835i −1.03954 + 0.305235i
\(243\) −7.43117 + 16.2720i −0.476710 + 1.04385i
\(244\) −0.962608 6.69508i −0.0616247 0.428609i
\(245\) −11.5964 13.3830i −0.740867 0.855006i
\(246\) −8.22454 18.0092i −0.524378 1.14823i
\(247\) −5.04752 + 3.24384i −0.321166 + 0.206401i
\(248\) 2.13472 14.8473i 0.135555 0.942806i
\(249\) −24.8984 16.0012i −1.57787 1.01404i
\(250\) −1.61890 + 1.86832i −0.102389 + 0.118163i
\(251\) −15.0719 4.42551i −0.951331 0.279336i −0.230990 0.972956i \(-0.574196\pi\)
−0.720341 + 0.693620i \(0.756015\pi\)
\(252\) −1.52786 −0.0962464
\(253\) 0 0
\(254\) 33.5066 2.10239
\(255\) 36.3538 + 10.6744i 2.27656 + 0.668459i
\(256\) −8.88142 + 10.2497i −0.555089 + 0.640607i
\(257\) 1.23844 + 0.795897i 0.0772517 + 0.0496467i 0.578697 0.815543i \(-0.303562\pi\)
−0.501445 + 0.865190i \(0.667198\pi\)
\(258\) 0 0
\(259\) −3.36501 + 2.16256i −0.209092 + 0.134375i
\(260\) −2.49249 5.45779i −0.154578 0.338478i
\(261\) 3.92916 + 4.53450i 0.243209 + 0.280678i
\(262\) 1.21854 + 8.47515i 0.0752818 + 0.523597i
\(263\) −6.20807 + 13.5938i −0.382806 + 0.838229i 0.615922 + 0.787807i \(0.288784\pi\)
−0.998728 + 0.0504215i \(0.983944\pi\)
\(264\) 3.66494 1.07612i 0.225561 0.0662308i
\(265\) −26.3059 + 7.72409i −1.61596 + 0.474487i
\(266\) −1.66166 + 3.63853i −0.101883 + 0.223092i
\(267\) 0.486206 + 3.38163i 0.0297553 + 0.206953i
\(268\) 2.92863 + 3.37981i 0.178894 + 0.206455i
\(269\) 4.13100 + 9.04563i 0.251872 + 0.551522i 0.992761 0.120105i \(-0.0383231\pi\)
−0.740890 + 0.671627i \(0.765596\pi\)
\(270\) −9.84957 + 6.32993i −0.599426 + 0.385227i
\(271\) −1.13852 + 7.91857i −0.0691601 + 0.481019i 0.925577 + 0.378559i \(0.123580\pi\)
−0.994737 + 0.102460i \(0.967329\pi\)
\(272\) −21.3816 13.7411i −1.29645 0.833179i
\(273\) 5.42997 6.26652i 0.328637 0.379267i
\(274\) 21.5619 + 6.33113i 1.30260 + 0.382478i
\(275\) −4.18034 −0.252084
\(276\) 0 0
\(277\) 6.52786 0.392221 0.196111 0.980582i \(-0.437169\pi\)
0.196111 + 0.980582i \(0.437169\pi\)
\(278\) 4.20447 + 1.23454i 0.252167 + 0.0740429i
\(279\) 8.78588 10.1394i 0.525997 0.607033i
\(280\) 7.52440 + 4.83564i 0.449669 + 0.288985i
\(281\) 1.88369 13.1013i 0.112371 0.781561i −0.853230 0.521535i \(-0.825360\pi\)
0.965602 0.260026i \(-0.0837312\pi\)
\(282\) −6.80588 + 4.37388i −0.405284 + 0.260461i
\(283\) 5.93703 + 13.0003i 0.352920 + 0.772786i 0.999947 + 0.0103192i \(0.00328475\pi\)
−0.647027 + 0.762467i \(0.723988\pi\)
\(284\) −3.14227 3.62637i −0.186459 0.215185i
\(285\) −2.05960 14.3248i −0.122000 0.848530i
\(286\) 1.54044 3.37310i 0.0910883 0.199456i
\(287\) 6.48995 1.90562i 0.383089 0.112485i
\(288\) −6.48995 + 1.90562i −0.382424 + 0.112290i
\(289\) 4.32713 9.47510i 0.254537 0.557359i
\(290\) 2.23551 + 15.5483i 0.131274 + 0.913029i
\(291\) −6.28453 7.25274i −0.368406 0.425163i
\(292\) 3.97233 + 8.69818i 0.232463 + 0.509022i
\(293\) −8.80972 + 5.66166i −0.514669 + 0.330758i −0.772060 0.635549i \(-0.780774\pi\)
0.257391 + 0.966307i \(0.417137\pi\)
\(294\) −2.81760 + 19.5969i −0.164326 + 1.14291i
\(295\) 6.73003 + 4.32513i 0.391837 + 0.251819i
\(296\) −4.73862 + 5.46866i −0.275427 + 0.317859i
\(297\) −1.63901 0.481257i −0.0951050 0.0279253i
\(298\) 19.2361 1.11432
\(299\) 0 0
\(300\) 7.56231 0.436610
\(301\) 0 0
\(302\) −0.250135 + 0.288671i −0.0143936 + 0.0166111i
\(303\) −8.41254 5.40641i −0.483288 0.310590i
\(304\) −1.38162 + 9.60939i −0.0792414 + 0.551136i
\(305\) −29.7942 + 19.1476i −1.70601 + 1.09639i
\(306\) −7.03890 15.4131i −0.402387 0.881106i
\(307\) −12.0967 13.9603i −0.690394 0.796757i 0.297027 0.954869i \(-0.404005\pi\)
−0.987421 + 0.158112i \(0.949459\pi\)
\(308\) −0.0830538 0.577652i −0.00473243 0.0329148i
\(309\) 16.8876 36.9788i 0.960705 2.10365i
\(310\) 33.7018 9.89575i 1.91413 0.562041i
\(311\) 8.80847 2.58640i 0.499483 0.146661i −0.0222805 0.999752i \(-0.507093\pi\)
0.521763 + 0.853090i \(0.325275\pi\)
\(312\) 6.23123 13.6445i 0.352774 0.772467i
\(313\) 2.89763 + 20.1534i 0.163784 + 1.13914i 0.891420 + 0.453177i \(0.149710\pi\)
−0.727637 + 0.685962i \(0.759381\pi\)
\(314\) 16.3350 + 18.8516i 0.921839 + 1.06386i
\(315\) 3.32332 + 7.27706i 0.187248 + 0.410016i
\(316\) 3.61049 2.32032i 0.203106 0.130528i
\(317\) 0.201576 1.40199i 0.0113216 0.0787437i −0.983377 0.181574i \(-0.941881\pi\)
0.994699 + 0.102830i \(0.0327899\pi\)
\(318\) 25.7865 + 16.5720i 1.44604 + 0.929310i
\(319\) −1.50081 + 1.73202i −0.0840291 + 0.0969747i
\(320\) 13.1529 + 3.86205i 0.735271 + 0.215895i
\(321\) −30.0000 −1.67444
\(322\) 0 0
\(323\) −10.4721 −0.582685
\(324\) 6.52299 + 1.91532i 0.362388 + 0.106407i
\(325\) −10.7505 + 12.4067i −0.596328 + 0.688200i
\(326\) 13.9331 + 8.95426i 0.771683 + 0.495931i
\(327\) 0 0
\(328\) 10.2936 6.61532i 0.568371 0.365270i
\(329\) −1.14818 2.51416i −0.0633011 0.138610i
\(330\) 5.85725 + 6.75963i 0.322431 + 0.372105i
\(331\) −1.65832 11.5339i −0.0911495 0.633959i −0.983269 0.182159i \(-0.941691\pi\)
0.892120 0.451800i \(-0.149218\pi\)
\(332\) −3.39824 + 7.44110i −0.186502 + 0.408383i
\(333\) −6.20997 + 1.82341i −0.340304 + 0.0999223i
\(334\) 16.2579 4.77375i 0.889593 0.261208i
\(335\) 9.72753 21.3003i 0.531472 1.16376i
\(336\) −1.90935 13.2798i −0.104164 0.724475i
\(337\) 2.23727 + 2.58195i 0.121872 + 0.140648i 0.813407 0.581696i \(-0.197611\pi\)
−0.691535 + 0.722343i \(0.743065\pi\)
\(338\) 2.68862 + 5.88726i 0.146242 + 0.320225i
\(339\) 24.8984 16.0012i 1.35229 0.869066i
\(340\) 1.49034 10.3655i 0.0808251 0.562151i
\(341\) 4.31110 + 2.77057i 0.233459 + 0.150035i
\(342\) −4.23835 + 4.89131i −0.229184 + 0.264492i
\(343\) −14.7919 4.34330i −0.798689 0.234516i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.18034 −0.439778
\(347\) −24.8399 7.29365i −1.33347 0.391543i −0.464137 0.885763i \(-0.653636\pi\)
−0.869337 + 0.494220i \(0.835454\pi\)
\(348\) 2.71499 3.13326i 0.145539 0.167960i
\(349\) −2.03281 1.30641i −0.108814 0.0699305i 0.485102 0.874458i \(-0.338782\pi\)
−0.593916 + 0.804527i \(0.702419\pi\)
\(350\) −1.55753 + 10.8329i −0.0832536 + 0.579042i
\(351\) −5.64330 + 3.62673i −0.301217 + 0.193580i
\(352\) −1.07326 2.35012i −0.0572051 0.125262i
\(353\) 23.1563 + 26.7238i 1.23249 + 1.42237i 0.871932 + 0.489627i \(0.162867\pi\)
0.360555 + 0.932738i \(0.382587\pi\)
\(354\) −1.27290 8.85323i −0.0676540 0.470544i
\(355\) −10.4371 + 22.8542i −0.553946 + 1.21297i
\(356\) 0.906022 0.266032i 0.0480191 0.0140997i
\(357\) 13.8859 4.07727i 0.734920 0.215792i
\(358\) 8.54189 18.7041i 0.451453 0.988544i
\(359\) −2.26118 15.7268i −0.119340 0.830030i −0.958285 0.285814i \(-0.907736\pi\)
0.838945 0.544216i \(-0.183173\pi\)
\(360\) 9.47723 + 10.9373i 0.499494 + 0.576447i
\(361\) −6.23123 13.6445i −0.327959 0.718131i
\(362\) 19.9446 12.8176i 1.04827 0.673679i
\(363\) 3.31477 23.0547i 0.173980 1.21006i
\(364\) −1.92798 1.23904i −0.101054 0.0649433i
\(365\) 32.7881 37.8395i 1.71621 1.98061i
\(366\) 37.9928 + 11.1557i 1.98592 + 0.583117i
\(367\) 18.1803 0.949006 0.474503 0.880254i \(-0.342628\pi\)
0.474503 + 0.880254i \(0.342628\pi\)
\(368\) 0 0
\(369\) 10.9443 0.569736
\(370\) −16.2579 4.77375i −0.845208 0.248176i
\(371\) −6.85779 + 7.91431i −0.356039 + 0.410891i
\(372\) −7.79885 5.01202i −0.404351 0.259861i
\(373\) 0.812362 5.65010i 0.0420625 0.292551i −0.957922 0.287028i \(-0.907333\pi\)
0.999985 0.00552335i \(-0.00175815\pi\)
\(374\) 5.44471 3.49910i 0.281539 0.180934i
\(375\) −1.41923 3.10767i −0.0732886 0.160480i
\(376\) −3.27430 3.77875i −0.168859 0.194874i
\(377\) 1.28083 + 8.90839i 0.0659663 + 0.458806i
\(378\) −1.85779 + 4.06800i −0.0955545 + 0.209235i
\(379\) 19.5359 5.73627i 1.00349 0.294652i 0.261604 0.965175i \(-0.415748\pi\)
0.741889 + 0.670523i \(0.233930\pi\)
\(380\) −3.83797 + 1.12693i −0.196884 + 0.0578103i
\(381\) −19.2358 + 42.1205i −0.985478 + 2.15790i
\(382\) −0.879554 6.11743i −0.0450019 0.312995i
\(383\) −16.3350 18.8516i −0.834681 0.963273i 0.165054 0.986284i \(-0.447220\pi\)
−0.999735 + 0.0230115i \(0.992675\pi\)
\(384\) −12.6497 27.6991i −0.645529 1.41351i
\(385\) −2.57064 + 1.65205i −0.131012 + 0.0841963i
\(386\) −1.82933 + 12.7233i −0.0931104 + 0.647597i
\(387\) 0 0
\(388\) −1.73700 + 2.00461i −0.0881829 + 0.101769i
\(389\) −33.0758 9.71192i −1.67701 0.492414i −0.701554 0.712616i \(-0.747510\pi\)
−0.975454 + 0.220202i \(0.929328\pi\)
\(390\) 35.1246 1.77860
\(391\) 0 0
\(392\) −12.2361 −0.618015
\(393\) −11.3535 3.33369i −0.572708 0.168162i
\(394\) 7.91738 9.13714i 0.398872 0.460323i
\(395\) −18.9048 12.1494i −0.951202 0.611300i
\(396\) 0.134384 0.934661i 0.00675305 0.0469685i
\(397\) 2.03281 1.30641i 0.102024 0.0655668i −0.488634 0.872489i \(-0.662505\pi\)
0.590658 + 0.806922i \(0.298868\pi\)
\(398\) 17.2799 + 37.8377i 0.866164 + 1.89663i
\(399\) −3.61998 4.17768i −0.181226 0.209146i
\(400\) 3.78021 + 26.2919i 0.189011 + 1.31460i
\(401\) 3.39824 7.44110i 0.169700 0.371591i −0.805605 0.592453i \(-0.798160\pi\)
0.975305 + 0.220862i \(0.0708870\pi\)
\(402\) −25.1199 + 7.37585i −1.25286 + 0.367874i
\(403\) 19.3094 5.66976i 0.961871 0.282431i
\(404\) −1.14818 + 2.51416i −0.0571240 + 0.125084i
\(405\) −5.06595 35.2344i −0.251729 1.75081i
\(406\) 3.92916 + 4.53450i 0.195001 + 0.225043i
\(407\) −1.02696 2.24873i −0.0509046 0.111466i
\(408\) 22.0243 14.1542i 1.09037 0.700735i
\(409\) 3.32457 23.1229i 0.164389 1.14335i −0.725847 0.687856i \(-0.758552\pi\)
0.890237 0.455498i \(-0.150539\pi\)
\(410\) 24.1040 + 15.4907i 1.19041 + 0.765031i
\(411\) −20.3372 + 23.4704i −1.00316 + 1.15771i
\(412\) −10.7809 3.16557i −0.531138 0.155956i
\(413\) 3.05573 0.150363
\(414\) 0 0
\(415\) 42.8328 2.10258
\(416\) −9.73492 2.85843i −0.477294 0.140146i
\(417\) −3.96566 + 4.57661i −0.194199 + 0.224118i
\(418\) −2.07969 1.33654i −0.101721 0.0653722i
\(419\) 4.47102 31.0966i 0.218424 1.51917i −0.525435 0.850833i \(-0.676098\pi\)
0.743859 0.668336i \(-0.232993\pi\)
\(420\) 4.65034 2.98859i 0.226913 0.145828i
\(421\) −9.84874 21.5657i −0.479998 1.05105i −0.982464 0.186453i \(-0.940301\pi\)
0.502466 0.864597i \(-0.332426\pi\)
\(422\) 3.61998 + 4.17768i 0.176218 + 0.203366i
\(423\) −0.636451 4.42662i −0.0309453 0.215229i
\(424\) −7.86973 + 17.2323i −0.382188 + 0.836875i
\(425\) −27.4918 + 8.07234i −1.33355 + 0.391566i
\(426\) 26.9523 7.91392i 1.30584 0.383430i
\(427\) −5.61968 + 12.3054i −0.271955 + 0.595499i
\(428\) 1.18005 + 8.20740i 0.0570397 + 0.396720i
\(429\) 3.35591 + 3.87292i 0.162025 + 0.186986i
\(430\) 0 0
\(431\) −22.2698 + 14.3119i −1.07270 + 0.689381i −0.952859 0.303413i \(-0.901874\pi\)
−0.119838 + 0.992793i \(0.538238\pi\)
\(432\) −1.54470 + 10.7436i −0.0743194 + 0.516903i
\(433\) 33.8019 + 21.7231i 1.62441 + 1.04395i 0.953047 + 0.302821i \(0.0979285\pi\)
0.671366 + 0.741126i \(0.265708\pi\)
\(434\) 8.78588 10.1394i 0.421736 0.486709i
\(435\) −20.8289 6.11591i −0.998668 0.293235i
\(436\) 0 0
\(437\) 0 0
\(438\) −55.9787 −2.67477
\(439\) 5.07744 + 1.49087i 0.242333 + 0.0711554i 0.400644 0.916234i \(-0.368787\pi\)
−0.158311 + 0.987389i \(0.550605\pi\)
\(440\) −3.61998 + 4.17768i −0.172576 + 0.199163i
\(441\) −9.20691 5.91692i −0.438424 0.281758i
\(442\) 3.61713 25.1577i 0.172049 1.19663i
\(443\) −1.78734 + 1.14865i −0.0849190 + 0.0545741i −0.582411 0.812894i \(-0.697891\pi\)
0.497492 + 0.867468i \(0.334254\pi\)
\(444\) 1.85779 + 4.06800i 0.0881669 + 0.193059i
\(445\) −3.23781 3.73663i −0.153487 0.177133i
\(446\) 0.921081 + 6.40626i 0.0436144 + 0.303345i
\(447\) −11.0432 + 24.1813i −0.522327 + 1.14374i
\(448\) 5.02397 1.47517i 0.237360 0.0696953i
\(449\) −2.82501 + 0.829497i −0.133320 + 0.0391464i −0.347712 0.937601i \(-0.613041\pi\)
0.214392 + 0.976748i \(0.431223\pi\)
\(450\) −7.35625 + 16.1079i −0.346777 + 0.759336i
\(451\) 0.594924 + 4.13779i 0.0280139 + 0.194841i
\(452\) −5.35698 6.18229i −0.251971 0.290790i
\(453\) −0.219283 0.480162i −0.0103028 0.0225600i
\(454\) −13.8572 + 8.90551i −0.650353 + 0.417956i
\(455\) −1.70778 + 11.8779i −0.0800619 + 0.556843i
\(456\) −8.41254 5.40641i −0.393953 0.253178i
\(457\) −23.0017 + 26.5454i −1.07598 + 1.24174i −0.107086 + 0.994250i \(0.534152\pi\)
−0.968890 + 0.247492i \(0.920394\pi\)
\(458\) −18.6299 5.47023i −0.870518 0.255607i
\(459\) −11.7082 −0.546492
\(460\) 0 0
\(461\) 7.47214 0.348012 0.174006 0.984745i \(-0.444329\pi\)
0.174006 + 0.984745i \(0.444329\pi\)
\(462\) 3.27802 + 0.962513i 0.152507 + 0.0447802i
\(463\) 13.0972 15.1150i 0.608679 0.702453i −0.364837 0.931071i \(-0.618875\pi\)
0.973516 + 0.228618i \(0.0734207\pi\)
\(464\) 12.2506 + 7.87298i 0.568719 + 0.365494i
\(465\) −6.90811 + 48.0469i −0.320356 + 2.22812i
\(466\) 21.0603 13.5346i 0.975600 0.626980i
\(467\) −12.8547 28.1479i −0.594845 1.30253i −0.932470 0.361249i \(-0.882351\pi\)
0.337624 0.941281i \(-0.390377\pi\)
\(468\) −2.42836 2.80247i −0.112251 0.129544i
\(469\) −1.27290 8.85323i −0.0587772 0.408804i
\(470\) 4.86376 10.6502i 0.224349 0.491255i
\(471\) −33.0758 + 9.71192i −1.52405 + 0.447502i
\(472\) 5.30395 1.55738i 0.244134 0.0716842i
\(473\) 0 0
\(474\) 3.57561 + 24.8689i 0.164233 + 1.14227i
\(475\) 7.16697 + 8.27113i 0.328843 + 0.379505i
\(476\) −1.66166 3.63853i −0.0761621 0.166772i
\(477\) −14.2544 + 9.16077i −0.652665 + 0.419443i
\(478\) 4.19922 29.2062i 0.192068 1.33586i
\(479\) −14.8033 9.51352i −0.676381 0.434684i 0.156840 0.987624i \(-0.449869\pi\)
−0.833221 + 0.552940i \(0.813506\pi\)
\(480\) 16.0258 18.4948i 0.731476 0.844169i
\(481\) −9.31495 2.73512i −0.424725 0.124711i
\(482\) −27.7082 −1.26207
\(483\) 0 0
\(484\) −6.43769 −0.292622
\(485\) 13.3260 + 3.91285i 0.605101 + 0.177674i
\(486\) −18.9545 + 21.8746i −0.859792 + 0.992253i
\(487\) −1.08673 0.698398i −0.0492443 0.0316474i 0.515787 0.856717i \(-0.327500\pi\)
−0.565031 + 0.825069i \(0.691136\pi\)
\(488\) −3.48275 + 24.2230i −0.157657 + 1.09653i
\(489\) −19.2551 + 12.3745i −0.870744 + 0.559593i
\(490\) −11.9027 26.0632i −0.537708 1.17742i
\(491\) −25.9668 29.9673i −1.17187 1.35241i −0.923434 0.383758i \(-0.874630\pi\)
−0.248434 0.968649i \(-0.579916\pi\)
\(492\) −1.07623 7.48533i −0.0485201 0.337465i
\(493\) −6.52542 + 14.2887i −0.293890 + 0.643530i
\(494\) −9.31495 + 2.73512i −0.419100 + 0.123059i
\(495\) −4.74399 + 1.39296i −0.213227 + 0.0626090i
\(496\) 13.5269 29.6197i 0.607374 1.32996i
\(497\) 1.36576 + 9.49907i 0.0612627 + 0.426091i
\(498\) −31.3603 36.1917i −1.40529 1.62179i
\(499\) 13.5875 + 29.7524i 0.608259 + 1.33190i 0.923758 + 0.382976i \(0.125101\pi\)
−0.315499 + 0.948926i \(0.602172\pi\)
\(500\) −0.794372 + 0.510512i −0.0355254 + 0.0228308i
\(501\) −3.33250 + 23.1781i −0.148885 + 1.03552i
\(502\) −21.3816 13.7411i −0.954309 0.613297i
\(503\) 5.93024 6.84386i 0.264416 0.305153i −0.607980 0.793953i \(-0.708020\pi\)
0.872396 + 0.488800i \(0.162565\pi\)
\(504\) 5.30395 + 1.55738i 0.236257 + 0.0693712i
\(505\) 14.4721 0.644002
\(506\) 0 0
\(507\) −8.94427 −0.397229
\(508\) 12.2799 + 3.60572i 0.544835 + 0.159978i
\(509\) −22.4650 + 25.9260i −0.995742 + 1.14915i −0.00693079 + 0.999976i \(0.502206\pi\)
−0.988811 + 0.149172i \(0.952339\pi\)
\(510\) 51.5730 + 33.1440i 2.28369 + 1.46764i
\(511\) 2.72172 18.9300i 0.120402 0.837412i
\(512\) 4.45174 2.86096i 0.196741 0.126438i
\(513\) 1.85779 + 4.06800i 0.0820235 + 0.179606i
\(514\) 1.55986 + 1.80017i 0.0688023 + 0.0794021i
\(515\) 8.37278 + 58.2340i 0.368949 + 2.56610i
\(516\) 0 0
\(517\) 1.63901 0.481257i 0.0720836 0.0211656i
\(518\) −6.20997 + 1.82341i −0.272850 + 0.0801161i
\(519\) 4.69625 10.2833i 0.206142 0.451389i
\(520\) 3.08940 + 21.4872i 0.135479 + 0.942278i
\(521\) −3.00161 3.46405i −0.131503 0.151763i 0.686179 0.727433i \(-0.259287\pi\)
−0.817682 + 0.575670i \(0.804741\pi\)
\(522\) 4.03293 + 8.83089i 0.176517 + 0.386518i
\(523\) 0.736423 0.473271i 0.0322015 0.0206947i −0.524441 0.851447i \(-0.675726\pi\)
0.556643 + 0.830752i \(0.312089\pi\)
\(524\) −0.465442 + 3.23722i −0.0203329 + 0.141419i
\(525\) −12.7236 8.17698i −0.555305 0.356873i
\(526\) −15.8348 + 18.2743i −0.690428 + 0.796797i
\(527\) 33.7018 + 9.89575i 1.46807 + 0.431065i
\(528\) 8.29180 0.360854
\(529\) 0 0
\(530\) −44.3607 −1.92690
\(531\) 4.74399 + 1.39296i 0.205872 + 0.0604494i
\(532\) −1.00054 + 1.15468i −0.0433788 + 0.0500618i
\(533\) 13.8104 + 8.87538i 0.598193 + 0.384435i
\(534\) −0.786697 + 5.47160i −0.0340437 + 0.236779i
\(535\) 36.5242 23.4727i 1.57908 1.01481i
\(536\) −6.72156 14.7182i −0.290327 0.635727i
\(537\) 18.6088 + 21.4757i 0.803029 + 0.926744i
\(538\) 2.28987 + 15.9264i 0.0987233 + 0.686636i
\(539\) 1.73658 3.80257i 0.0747996 0.163788i
\(540\) −4.29098 + 1.25995i −0.184655 + 0.0542195i
\(541\) 7.27640 2.13654i 0.312837 0.0918572i −0.121545 0.992586i \(-0.538785\pi\)
0.434382 + 0.900729i \(0.356967\pi\)
\(542\) −5.37724 + 11.7745i −0.230972 + 0.505759i
\(543\) 4.66279 + 32.4304i 0.200100 + 1.39172i
\(544\) −11.5964 13.3830i −0.497192 0.573790i
\(545\) 0 0
\(546\) 11.2866 7.25346i 0.483022 0.310419i
\(547\) −5.34264 + 37.1589i −0.228435 + 1.58880i 0.476270 + 0.879299i \(0.341989\pi\)
−0.704705 + 0.709501i \(0.748920\pi\)
\(548\) 7.22098 + 4.64064i 0.308465 + 0.198238i
\(549\) −14.3339 + 16.5423i −0.611758 + 0.706006i
\(550\) −6.48995 1.90562i −0.276732 0.0812559i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) −8.58359 −0.365011
\(554\) 10.1345 + 2.97575i 0.430572 + 0.126427i
\(555\) 15.3345 17.6969i 0.650913 0.751193i
\(556\) 1.40806 + 0.904904i 0.0597150 + 0.0383765i
\(557\) −2.76324 + 19.2188i −0.117082 + 0.814326i 0.843659 + 0.536880i \(0.180397\pi\)
−0.960741 + 0.277446i \(0.910512\pi\)
\(558\) 18.2621 11.7363i 0.773096 0.496839i
\(559\) 0 0
\(560\) 12.7150 + 14.6739i 0.537309 + 0.620087i
\(561\) 1.27290 + 8.85323i 0.0537420 + 0.373784i
\(562\) 8.89670 19.4810i 0.375285 0.821758i
\(563\) 14.4459 4.24169i 0.608821 0.178766i 0.0372326 0.999307i \(-0.488146\pi\)
0.571588 + 0.820541i \(0.306328\pi\)
\(564\) −2.96500 + 0.870601i −0.124849 + 0.0366589i
\(565\) −17.7934 + 38.9621i −0.748574 + 1.63915i
\(566\) 3.29098 + 22.8892i 0.138330 + 0.962106i
\(567\) −8.90398 10.2757i −0.373932 0.431540i
\(568\) 7.21189 + 15.7918i 0.302604 + 0.662610i
\(569\) 0.151712 0.0974991i 0.00636008 0.00408738i −0.537457 0.843291i \(-0.680615\pi\)
0.543817 + 0.839204i \(0.316979\pi\)
\(570\) 3.33250 23.1781i 0.139583 0.970822i
\(571\) −23.3096 14.9802i −0.975477 0.626901i −0.0472376 0.998884i \(-0.515042\pi\)
−0.928240 + 0.371982i \(0.878678\pi\)
\(572\) 0.927550 1.07045i 0.0387828 0.0447577i
\(573\) 8.19505 + 2.40628i 0.342353 + 0.100524i
\(574\) 10.9443 0.456805
\(575\) 0 0
\(576\) 8.47214 0.353006
\(577\) 12.3665 + 3.63112i 0.514823 + 0.151166i 0.528816 0.848736i \(-0.322636\pi\)
−0.0139932 + 0.999902i \(0.504454\pi\)
\(578\) 11.0371 12.7375i 0.459082 0.529809i
\(579\) −14.9440 9.60391i −0.621050 0.399125i
\(580\) −0.853889 + 5.93893i −0.0354558 + 0.246601i
\(581\) 13.7635 8.84525i 0.571005 0.366963i
\(582\) −6.45051 14.1246i −0.267382 0.585485i
\(583\) −4.23835 4.89131i −0.175534 0.202578i
\(584\) −4.92363 34.2446i −0.203741 1.41705i
\(585\) −8.06587 + 17.6618i −0.333483 + 0.730225i
\(586\) −16.2579 + 4.77375i −0.671608 + 0.197202i
\(587\) 10.8344 3.18127i 0.447184 0.131305i −0.0503845 0.998730i \(-0.516045\pi\)
0.497568 + 0.867425i \(0.334226\pi\)
\(588\) −3.14150 + 6.87892i −0.129553 + 0.283682i
\(589\) −1.90935 13.2798i −0.0786736 0.547187i
\(590\) 8.47670 + 9.78263i 0.348980 + 0.402744i
\(591\) 6.94084 + 15.1983i 0.285508 + 0.625175i
\(592\) −13.2146 + 8.49250i −0.543116 + 0.349039i
\(593\) −2.12679 + 14.7922i −0.0873369 + 0.607441i 0.898404 + 0.439170i \(0.144727\pi\)
−0.985741 + 0.168271i \(0.946182\pi\)
\(594\) −2.32517 1.49429i −0.0954028 0.0613116i
\(595\) −13.7156 + 15.8286i −0.562284 + 0.648910i
\(596\) 7.04990 + 2.07004i 0.288775 + 0.0847920i
\(597\) −57.4853 −2.35272
\(598\) 0 0
\(599\) −1.88854 −0.0771638 −0.0385819 0.999255i \(-0.512284\pi\)
−0.0385819 + 0.999255i \(0.512284\pi\)
\(600\) −26.2524 7.70839i −1.07175 0.314694i
\(601\) −7.27646 + 8.39748i −0.296813 + 0.342540i −0.884493 0.466553i \(-0.845496\pi\)
0.587680 + 0.809093i \(0.300041\pi\)
\(602\) 0 0
\(603\) 2.05960 14.3248i 0.0838734 0.583352i
\(604\) −0.122737 + 0.0788784i −0.00499411 + 0.00320952i
\(605\) 14.0029 + 30.6621i 0.569299 + 1.24659i
\(606\) −10.5959 12.2283i −0.430428 0.496740i
\(607\) −2.49448 17.3495i −0.101248 0.704193i −0.975705 0.219090i \(-0.929691\pi\)
0.874457 0.485103i \(-0.161218\pi\)
\(608\) −2.80984 + 6.15269i −0.113954 + 0.249524i
\(609\) −7.95592 + 2.33607i −0.322390 + 0.0946623i
\(610\) −54.9837 + 16.1447i −2.22622 + 0.653679i
\(611\) 2.78669 6.10200i 0.112737 0.246860i
\(612\) −0.921081 6.40626i −0.0372325 0.258958i
\(613\) 5.04780 + 5.82547i 0.203879 + 0.235289i 0.848476 0.529234i \(-0.177520\pi\)
−0.644597 + 0.764522i \(0.722975\pi\)
\(614\) −12.4161 27.1876i −0.501075 1.09720i
\(615\) −33.3109 + 21.4076i −1.34323 + 0.863238i
\(616\) −0.300492 + 2.08996i −0.0121071 + 0.0842071i
\(617\) −13.8572 8.90551i −0.557872 0.358522i 0.231121 0.972925i \(-0.425761\pi\)
−0.788993 + 0.614403i \(0.789397\pi\)
\(618\) 43.0748 49.7110i 1.73272 1.99967i
\(619\) 7.11599 + 2.08944i 0.286016 + 0.0839818i 0.421594 0.906785i \(-0.361471\pi\)
−0.135578 + 0.990767i \(0.543289\pi\)
\(620\) 13.4164 0.538816
\(621\) 0 0
\(622\) 14.8541 0.595595
\(623\) −1.81204 0.532064i −0.0725980 0.0213167i
\(624\) 21.3238 24.6089i 0.853634 0.985146i
\(625\) −18.8579 12.1192i −0.754315 0.484769i
\(626\) −4.68846 + 32.6089i −0.187388 + 1.30332i
\(627\) 2.87407 1.84705i 0.114779 0.0737641i
\(628\) 3.95802 + 8.66685i 0.157942 + 0.345845i
\(629\) −11.0961 12.8056i −0.442432 0.510594i
\(630\) 1.84216 + 12.8125i 0.0733935 + 0.510463i
\(631\) −13.4431 + 29.4363i −0.535162 + 1.17184i 0.428212 + 0.903678i \(0.359144\pi\)
−0.963374 + 0.268163i \(0.913584\pi\)
\(632\) −14.8989 + 4.37470i −0.592645 + 0.174016i
\(633\) −7.32987 + 2.15225i −0.291336 + 0.0855441i
\(634\) 0.952046 2.08469i 0.0378106 0.0827937i
\(635\) −9.53697 66.3311i −0.378463 2.63227i
\(636\) 7.66724 + 8.84847i 0.304026 + 0.350865i
\(637\) −6.81962 14.9329i −0.270203 0.591663i
\(638\) −3.11954 + 2.00481i −0.123504 + 0.0793710i
\(639\) −2.20985 + 15.3698i −0.0874201 + 0.608020i
\(640\) 37.0731 + 23.8254i 1.46544 + 0.941783i
\(641\) −29.6684 + 34.2392i −1.17183 + 1.35237i −0.248376 + 0.968664i \(0.579897\pi\)
−0.923456 + 0.383703i \(0.874649\pi\)
\(642\) −46.5748 13.6756i −1.83816 0.539732i
\(643\) 19.5967 0.772820 0.386410 0.922327i \(-0.373715\pi\)
0.386410 + 0.922327i \(0.373715\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −16.2579 4.77375i −0.639659 0.187821i
\(647\) 4.39294 5.06972i 0.172704 0.199311i −0.662798 0.748798i \(-0.730631\pi\)
0.835502 + 0.549487i \(0.185177\pi\)
\(648\) −20.6921 13.2980i −0.812862 0.522395i
\(649\) −0.268768 + 1.86932i −0.0105501 + 0.0733773i
\(650\) −22.3456 + 14.3607i −0.876468 + 0.563272i
\(651\) 7.70222 + 16.8655i 0.301874 + 0.661011i
\(652\) 4.14280 + 4.78105i 0.162245 + 0.187240i
\(653\) −3.45896 24.0576i −0.135359 0.941445i −0.938407 0.345531i \(-0.887699\pi\)
0.803048 0.595914i \(-0.203210\pi\)
\(654\) 0 0
\(655\) 16.4309 4.82456i 0.642010 0.188511i
\(656\) 25.4863 7.48347i 0.995075 0.292180i
\(657\) 12.8547 28.1479i 0.501510 1.09815i
\(658\) −0.636451 4.42662i −0.0248115 0.172567i
\(659\) −13.5245 15.6081i −0.526840 0.608005i 0.428490 0.903546i \(-0.359046\pi\)
−0.955330 + 0.295541i \(0.904500\pi\)
\(660\) 1.41923 + 3.10767i 0.0552433 + 0.120966i
\(661\) −4.25315 + 2.73333i −0.165428 + 0.106314i −0.620735 0.784020i \(-0.713166\pi\)
0.455307 + 0.890334i \(0.349529\pi\)
\(662\) 2.68322 18.6622i 0.104286 0.725327i
\(663\) 29.5487 + 18.9898i 1.14758 + 0.737503i
\(664\) 19.3817 22.3677i 0.752158 0.868036i
\(665\) 7.67594 + 2.25386i 0.297660 + 0.0874010i
\(666\) −10.4721 −0.405787
\(667\) 0 0
\(668\) 6.47214 0.250414
\(669\) −8.58197 2.51989i −0.331798 0.0974247i
\(670\) 24.8117 28.6343i 0.958560 1.10624i
\(671\) −7.03345 4.52012i −0.271523 0.174497i
\(672\) 1.33029 9.25238i 0.0513171 0.356918i
\(673\) 2.52376 1.62192i 0.0972838 0.0625205i −0.491094 0.871106i \(-0.663403\pi\)
0.588378 + 0.808586i \(0.299767\pi\)
\(674\) 2.29636 + 5.02832i 0.0884524 + 0.193684i
\(675\) 8.01292 + 9.24740i 0.308417 + 0.355933i
\(676\) 0.351822 + 2.44697i 0.0135316 + 0.0941144i
\(677\) 7.47747 16.3734i 0.287383 0.629280i −0.709791 0.704412i \(-0.751211\pi\)
0.997174 + 0.0751323i \(0.0239379\pi\)
\(678\) 45.9487 13.4918i 1.76465 0.518148i
\(679\) 5.09006 1.49458i 0.195339 0.0573566i
\(680\) −15.7395 + 34.4646i −0.603581 + 1.32166i
\(681\) −3.23965 22.5322i −0.124143 0.863437i
\(682\) 5.42997 + 6.26652i 0.207924 + 0.239958i
\(683\) −9.38703 20.5547i −0.359185 0.786505i −0.999826 0.0186643i \(-0.994059\pi\)
0.640641 0.767840i \(-0.278669\pi\)
\(684\) −2.07969 + 1.33654i −0.0795191 + 0.0511038i
\(685\) 6.39624 44.4868i 0.244388 1.69975i
\(686\) −20.9845 13.4859i −0.801190 0.514894i
\(687\) 17.5718 20.2789i 0.670404 0.773688i
\(688\) 0 0
\(689\) −25.4164 −0.968288
\(690\) 0 0
\(691\) 24.9443 0.948925 0.474462 0.880276i \(-0.342642\pi\)
0.474462 + 0.880276i \(0.342642\pi\)
\(692\) −2.99804 0.880305i −0.113968 0.0334642i
\(693\) −1.23673 + 1.42727i −0.0469796 + 0.0542174i
\(694\) −35.2389 22.6467i −1.33765 0.859655i
\(695\) 1.24724 8.67473i 0.0473104 0.329051i
\(696\) −12.6188 + 8.10961i −0.478314 + 0.307394i
\(697\) 11.9027 + 26.0632i 0.450846 + 0.987214i
\(698\) −2.56039 2.95485i −0.0969123 0.111843i
\(699\) 4.92363 + 34.2446i 0.186229 + 1.29525i
\(700\) −1.73658 + 3.80257i −0.0656364 + 0.143724i
\(701\) 25.1199 7.37585i 0.948764 0.278582i 0.229492 0.973311i \(-0.426294\pi\)
0.719272 + 0.694728i \(0.244475\pi\)
\(702\) −10.4144 + 3.05795i −0.393068 + 0.115415i
\(703\) −2.68862 + 5.88726i −0.101403 + 0.222042i
\(704\) 0.460540 + 3.20313i 0.0173573 + 0.120722i
\(705\) 10.5959 + 12.2283i 0.399064 + 0.460544i
\(706\) 23.7679 + 52.0444i 0.894516 + 1.95872i
\(707\) 4.65034 2.98859i 0.174894 0.112397i
\(708\) 0.486206 3.38163i 0.0182727 0.127090i
\(709\) 13.5180 + 8.68749i 0.507679 + 0.326266i 0.769281 0.638910i \(-0.220614\pi\)
−0.261602 + 0.965176i \(0.584251\pi\)
\(710\) −26.6217 + 30.7231i −0.999095 + 1.15302i
\(711\) −13.3260 3.91285i −0.499763 0.146744i
\(712\) −3.41641 −0.128035
\(713\) 0 0
\(714\) 23.4164 0.876337
\(715\) −7.11599 2.08944i −0.266123 0.0781408i
\(716\) 5.14334 5.93573i 0.192216 0.221829i
\(717\) 34.3039 + 22.0458i 1.28110 + 0.823314i
\(718\) 3.65866 25.4465i 0.136540 0.949656i
\(719\) −17.6194 + 11.3233i −0.657094 + 0.422289i −0.826252 0.563300i \(-0.809532\pi\)
0.169158 + 0.985589i \(0.445895\pi\)
\(720\) 13.0508 + 28.5774i 0.486376 + 1.06502i
\(721\) 14.7161 + 16.9833i 0.548057 + 0.632491i
\(722\) −3.45405 24.0235i −0.128547 0.894061i
\(723\) 15.9070 34.8314i 0.591587 1.29540i
\(724\) 8.68891 2.55129i 0.322921 0.0948181i
\(725\) 15.7514 4.62504i 0.584993 0.171770i
\(726\) 15.6557 34.2812i 0.581038 1.27230i
\(727\) 2.03393 + 14.1463i 0.0754345 + 0.524658i 0.992144 + 0.125103i \(0.0399262\pi\)
−0.916709 + 0.399555i \(0.869165\pi\)
\(728\) 5.42997 + 6.26652i 0.201248 + 0.232253i
\(729\) −2.90791 6.36742i −0.107700 0.235831i
\(730\) 68.1526 43.7990i 2.52244 1.62107i
\(731\) 0 0
\(732\) 12.7236 + 8.17698i 0.470279 + 0.302230i
\(733\) 17.5266 20.2268i 0.647362 0.747095i −0.333297 0.942822i \(-0.608161\pi\)
0.980658 + 0.195727i \(0.0627066\pi\)
\(734\) 28.2248 + 8.28756i 1.04180 + 0.305899i
\(735\) 39.5967 1.46055
\(736\) 0 0
\(737\) 5.52786 0.203621
\(738\) 16.9909 + 4.98898i 0.625444 + 0.183647i
\(739\) −32.2063 + 37.1680i −1.18473 + 1.36725i −0.270159 + 0.962816i \(0.587076\pi\)
−0.914568 + 0.404432i \(0.867469\pi\)
\(740\) −5.44471 3.49910i −0.200151 0.128630i
\(741\) 1.90935 13.2798i 0.0701419 0.487847i
\(742\) −14.2544 + 9.16077i −0.523297 + 0.336302i
\(743\) 0.363649 + 0.796281i 0.0133410 + 0.0292127i 0.916185 0.400755i \(-0.131252\pi\)
−0.902844 + 0.429968i \(0.858525\pi\)
\(744\) 21.9647 + 25.3486i 0.805265 + 0.929325i
\(745\) −5.47516 38.0805i −0.200594 1.39516i
\(746\) 3.83680 8.40142i 0.140475 0.307598i
\(747\) 25.3998 7.45806i 0.929331 0.272876i
\(748\) 2.37200 0.696481i 0.0867288 0.0254659i
\(749\) 6.88907 15.0850i 0.251721 0.551193i
\(750\) −0.786697 5.47160i −0.0287261 0.199795i
\(751\) 29.0501 + 33.5256i 1.06005 + 1.22337i 0.973875 + 0.227085i \(0.0729197\pi\)
0.0861772 + 0.996280i \(0.472535\pi\)
\(752\) −4.50896 9.87324i −0.164425 0.360040i
\(753\) 29.5487 18.9898i 1.07681 0.692027i
\(754\) −2.07243 + 14.4141i −0.0754735 + 0.524930i
\(755\) 0.642661 + 0.413013i 0.0233888 + 0.0150311i
\(756\) −1.11864 + 1.29097i −0.0406844 + 0.0469523i
\(757\) 45.6687 + 13.4096i 1.65986 + 0.487379i 0.971311 0.237813i \(-0.0764304\pi\)
0.688548 + 0.725191i \(0.258249\pi\)
\(758\) 32.9443 1.19659
\(759\) 0 0
\(760\) 14.4721 0.524960
\(761\) 15.6445 + 4.59364i 0.567112 + 0.166519i 0.552705 0.833377i \(-0.313596\pi\)
0.0144073 + 0.999896i \(0.495414\pi\)
\(762\) −49.0641 + 56.6230i −1.77741 + 2.05124i
\(763\) 0 0
\(764\) 0.335960 2.33665i 0.0121546 0.0845371i
\(765\) −28.5089 + 18.3215i −1.03074 + 0.662416i
\(766\) −16.7664 36.7134i −0.605796 1.32651i
\(767\) 4.85671 + 5.60495i 0.175366 + 0.202383i
\(768\) −4.31587 30.0176i −0.155736 1.08317i
\(769\) 7.11382 15.5771i 0.256531 0.561724i −0.736921 0.675979i \(-0.763721\pi\)
0.993451 + 0.114255i \(0.0364481\pi\)
\(770\) −4.74399 + 1.39296i −0.170962 + 0.0501989i
\(771\) −3.15846 + 0.927406i −0.113749 + 0.0333997i
\(772\) −2.03962 + 4.46614i −0.0734074 + 0.160740i
\(773\) 2.05960 + 14.3248i 0.0740787 + 0.515228i 0.992749 + 0.120204i \(0.0383548\pi\)
−0.918671 + 0.395025i \(0.870736\pi\)
\(774\) 0 0
\(775\) −15.2491 33.3910i −0.547765 1.19944i
\(776\) 8.07330 5.18839i 0.289815 0.186252i
\(777\) 1.27290 8.85323i 0.0456651 0.317608i
\(778\) −46.9227 30.1554i −1.68226 1.08112i
\(779\) 7.16697 8.27113i 0.256783 0.296344i
\(780\) 12.8729 + 3.77984i 0.460926 + 0.135340i
\(781\) −5.93112 −0.212232
\(782\) 0 0
\(783\) 6.70820 0.239732
\(784\) −25.4863 7.48347i −0.910227 0.267267i
\(785\) 32.6700 37.7032i 1.16604 1.34569i
\(786\) −16.1066 10.3511i −0.574502 0.369210i
\(787\) −7.31732 + 50.8931i −0.260834 + 1.81414i 0.265776 + 0.964035i \(0.414372\pi\)
−0.526610 + 0.850107i \(0.676537\pi\)
\(788\) 3.88494 2.49670i 0.138395 0.0889412i
\(789\) −13.8817 30.3966i −0.494201 1.08215i
\(790\) −23.8112 27.4796i −0.847164 0.977679i
\(791\) 2.32837 + 16.1942i 0.0827872 + 0.575798i
\(792\) −1.41923 + 3.10767i −0.0504300 + 0.110426i
\(793\) −31.5029 + 9.25007i −1.11870 + 0.328480i
\(794\) 3.75145 1.10153i 0.133134 0.0390917i
\(795\) 25.4670 55.7649i 0.903221 1.97778i
\(796\) 2.26118 + 15.7268i 0.0801452 + 0.557422i
\(797\) −6.78480 7.83008i −0.240330 0.277356i 0.622752 0.782419i \(-0.286015\pi\)
−0.863082 + 0.505064i \(0.831469\pi\)
\(798\) −3.71558 8.13600i −0.131530 0.288011i
\(799\) 9.84957 6.32993i 0.348453 0.223937i
\(800\) −2.63376 + 18.3182i −0.0931175 + 0.647646i
\(801\) −2.57064 1.65205i −0.0908292 0.0583724i
\(802\) 8.66778 10.0032i 0.306070 0.353224i
\(803\) 11.3409 + 3.32998i 0.400211 + 0.117513i
\(804\) −10.0000 −0.352673
\(805\) 0 0
\(806\) 32.5623 1.14696
\(807\) −21.3354 6.26462i −0.751040 0.220525i
\(808\) 6.54861 7.55750i 0.230379 0.265872i
\(809\) 40.2864 + 25.8905i 1.41639 + 0.910262i 0.999999 + 0.00107784i \(0.000343088\pi\)
0.416395 + 0.909184i \(0.363293\pi\)
\(810\) 8.19687 57.0105i 0.288009 2.00314i
\(811\) −46.8178 + 30.0880i −1.64400 + 1.05653i −0.706989 + 0.707225i \(0.749947\pi\)
−0.937008 + 0.349308i \(0.886417\pi\)
\(812\) 0.952046 + 2.08469i 0.0334103 + 0.0731583i
\(813\) −11.7145 13.5193i −0.410846 0.474141i
\(814\) −0.569259 3.95929i −0.0199525 0.138773i
\(815\) 13.7605 30.1312i 0.482008 1.05545i
\(816\) 54.5307 16.0117i 1.90896 0.560520i
\(817\) 0 0
\(818\) 15.7020 34.3826i 0.549008 1.20216i
\(819\) 1.05546 + 7.34092i 0.0368809 + 0.256512i
\(820\) 7.16697 + 8.27113i 0.250282 + 0.288840i
\(821\) −8.74687 19.1530i −0.305268 0.668443i 0.693372 0.720580i \(-0.256124\pi\)
−0.998640 + 0.0521365i \(0.983397\pi\)
\(822\) −42.2723 + 27.1668i −1.47442 + 0.947550i
\(823\) −3.91950 + 27.2607i −0.136625 + 0.950248i 0.800021 + 0.599972i \(0.204821\pi\)
−0.936646 + 0.350276i \(0.886088\pi\)
\(824\) 34.1990 + 21.9784i 1.19138 + 0.765653i
\(825\) 6.12133 7.06439i 0.213117 0.245950i
\(826\) 4.74399 + 1.39296i 0.165065 + 0.0484674i
\(827\) 10.4721 0.364152 0.182076 0.983284i \(-0.441718\pi\)
0.182076 + 0.983284i \(0.441718\pi\)
\(828\) 0 0
\(829\) −40.2492 −1.39791 −0.698957 0.715164i \(-0.746352\pi\)
−0.698957 + 0.715164i \(0.746352\pi\)
\(830\) 66.4976 + 19.5255i 2.30817 + 0.677739i
\(831\) −9.55884 + 11.0315i −0.331592 + 0.382678i
\(832\) 10.6908 + 6.87057i 0.370638 + 0.238194i
\(833\) 4.07767 28.3608i 0.141283 0.982645i
\(834\) −8.24292 + 5.29740i −0.285429 + 0.183434i
\(835\) −14.0778 30.8261i −0.487183 1.06678i
\(836\) −0.618367 0.713633i −0.0213867 0.0246815i
\(837\) −2.13472 14.8473i −0.0737868 0.513199i
\(838\) 21.1167 46.2392i 0.729465 1.59731i
\(839\) 0.839929 0.246625i 0.0289976 0.00851445i −0.267202 0.963641i \(-0.586099\pi\)
0.296199 + 0.955126i \(0.404281\pi\)
\(840\) −19.1899 + 5.63465i −0.662113 + 0.194414i
\(841\) −8.30830 + 18.1926i −0.286493 + 0.627332i
\(842\) −5.45929 37.9702i −0.188140 1.30854i
\(843\) 19.3817 + 22.3677i 0.667543 + 0.770386i
\(844\) 0.877131 + 1.92065i 0.0301921 + 0.0661114i
\(845\) 10.8894 6.99820i 0.374607 0.240745i
\(846\) 1.02980 7.16242i 0.0354052 0.246249i
\(847\) 10.8315 + 6.96096i 0.372174 + 0.239181i
\(848\) −26.9309 + 31.0799i −0.924811 + 1.06729i
\(849\) −30.6629 9.00345i −1.05235 0.308998i
\(850\) −46.3607 −1.59016
\(851\) 0 0
\(852\) 10.7295 0.367586
\(853\) 35.9008 + 10.5414i 1.22922 + 0.360931i 0.830955 0.556339i \(-0.187795\pi\)
0.398264 + 0.917271i \(0.369613\pi\)
\(854\) −14.3339 + 16.5423i −0.490498 + 0.566064i
\(855\) 10.8894 + 6.99820i 0.372410 + 0.239333i
\(856\) 4.26945 29.6946i 0.145927 1.01494i
\(857\) −6.28596 + 4.03974i −0.214724 + 0.137995i −0.643582 0.765377i \(-0.722553\pi\)
0.428858 + 0.903372i \(0.358916\pi\)
\(858\) 3.44454 + 7.54248i 0.117595 + 0.257496i
\(859\) 2.15567 + 2.48777i 0.0735504 + 0.0848817i 0.791332 0.611386i \(-0.209388\pi\)
−0.717782 + 0.696268i \(0.754842\pi\)
\(860\) 0 0
\(861\) −6.28299 + 13.7578i −0.214124 + 0.468866i
\(862\) −41.0978 + 12.0674i −1.39980 + 0.411017i
\(863\) −43.6963 + 12.8304i −1.48744 + 0.436751i −0.921723 0.387849i \(-0.873218\pi\)
−0.565716 + 0.824600i \(0.691400\pi\)
\(864\) −3.14150 + 6.87892i −0.106876 + 0.234025i
\(865\) 2.32837 + 16.1942i 0.0791669 + 0.550618i
\(866\) 42.5746 + 49.1337i 1.44674 + 1.66963i
\(867\) 9.67576 + 21.1870i 0.328606 + 0.719547i
\(868\) 4.31110 2.77057i 0.146328 0.0940394i
\(869\) 0.754973 5.25095i 0.0256107 0.178126i
\(870\) −29.5487 18.9898i −1.00179 0.643814i
\(871\) 14.2159 16.4060i 0.481686 0.555895i
\(872\) 0 0
\(873\) 8.58359 0.290511
\(874\) 0 0
\(875\) 1.88854 0.0638444
\(876\) −20.5158 6.02400i −0.693166 0.203532i
\(877\) 18.0269 20.8042i 0.608726 0.702507i −0.364800 0.931086i \(-0.618863\pi\)
0.973525 + 0.228579i \(0.0734080\pi\)
\(878\) 7.20307 + 4.62913i 0.243092 + 0.156226i
\(879\) 3.33250 23.1781i 0.112403 0.781777i
\(880\) −10.0950 + 6.48769i −0.340304 + 0.218700i
\(881\) 9.06421 + 19.8479i 0.305381 + 0.668691i 0.998648 0.0519899i \(-0.0165564\pi\)
−0.693266 + 0.720681i \(0.743829\pi\)
\(882\) −11.5964 13.3830i −0.390471 0.450628i
\(883\) −0.569259 3.95929i −0.0191571 0.133241i 0.977998 0.208612i \(-0.0668947\pi\)
−0.997155 + 0.0753718i \(0.975986\pi\)
\(884\) 4.03293 8.83089i 0.135642 0.297015i
\(885\) −17.1639 + 5.03979i −0.576959 + 0.169411i
\(886\) −3.29844 + 0.968510i −0.110813 + 0.0325377i
\(887\) −14.5681 + 31.8998i −0.489150 + 1.07109i 0.490695 + 0.871331i \(0.336743\pi\)
−0.979845 + 0.199758i \(0.935984\pi\)
\(888\) −2.30270 16.0156i −0.0772736 0.537450i
\(889\) −16.7623 19.3447i −0.562190 0.648801i
\(890\) −3.32332 7.27706i −0.111398 0.243927i
\(891\) 7.06927 4.54314i 0.236829 0.152201i
\(892\) −0.351822 + 2.44697i −0.0117799 + 0.0819307i
\(893\) −3.76220 2.41782i −0.125897 0.0809092i
\(894\) −28.1676 + 32.5072i −0.942066 + 1.08720i
\(895\) −39.4588 11.5861i −1.31896 0.387282i
\(896\) 16.8328 0.562345
\(897\) 0 0
\(898\) −4.76393 −0.158974
\(899\) −19.3094 5.66976i −0.644005 0.189097i
\(900\) −4.42943 + 5.11184i −0.147648 + 0.170395i
\(901\) −37.3186 23.9832i −1.24326 0.798996i
\(902\) −0.962608 + 6.69508i −0.0320513 + 0.222922i
\(903\) 0 0
\(904\) 12.2949 + 26.9221i 0.408923 + 0.895417i
\(905\) −31.0511 35.8349i −1.03217 1.19119i
\(906\) −0.121551 0.845408i −0.00403827 0.0280868i
\(907\) 16.7201 36.6120i 0.555183 1.21568i −0.399136 0.916892i \(-0.630690\pi\)
0.954319 0.298789i \(-0.0965828\pi\)
\(908\) −6.03693 + 1.77260i −0.200343 + 0.0588259i
\(909\) 8.58197 2.51989i 0.284646 0.0835796i
\(910\) −8.06587 + 17.6618i −0.267381 + 0.585482i
\(911\) 4.45516 + 30.9863i 0.147606 + 1.02662i 0.920123 + 0.391629i \(0.128088\pi\)
−0.772517 + 0.634994i \(0.781003\pi\)
\(912\) −14.2159 16.4060i −0.470734 0.543256i
\(913\) 4.20045 + 9.19770i 0.139015 + 0.304400i
\(914\) −47.8108 + 30.7261i −1.58144 + 1.01633i
\(915\) 11.2704 78.3874i 0.372588 2.59141i
\(916\) −6.23908 4.00961i −0.206145 0.132481i
\(917\) 4.28346 4.94337i 0.141452 0.163245i
\(918\) −18.1769 5.33722i −0.599927 0.176154i
\(919\) 0.875388 0.0288764 0.0144382 0.999896i \(-0.495404\pi\)
0.0144382 + 0.999896i \(0.495404\pi\)
\(920\) 0 0
\(921\) 41.3050 1.36104
\(922\) 11.6004 + 3.40619i 0.382040 + 0.112177i
\(923\) −15.2529 + 17.6028i −0.502055 + 0.579402i
\(924\) 1.09780 + 0.705510i 0.0361148 + 0.0232096i
\(925\) −2.52014 + 17.5280i −0.0828617 + 0.576316i
\(926\) 27.2235 17.4955i 0.894621 0.574938i
\(927\) 15.1048 + 33.0748i 0.496106 + 1.08632i
\(928\) 6.64415 + 7.66776i 0.218105 + 0.251706i
\(929\) 5.96929 + 41.5173i 0.195846 + 1.36214i 0.816178 + 0.577800i \(0.196089\pi\)
−0.620332 + 0.784339i \(0.713002\pi\)
\(930\) −32.6271 + 71.4434i −1.06989 + 2.34272i
\(931\) −10.5010 + 3.08336i −0.344155 + 0.101053i
\(932\) 9.17497 2.69401i 0.300536 0.0882453i
\(933\) −8.52758 + 18.6728i −0.279181 + 0.611320i
\(934\) −7.12555 49.5593i −0.233155 1.62163i
\(935\) −8.47670 9.78263i −0.277218 0.319926i
\(936\) 5.57338 + 12.2040i 0.182172 + 0.398900i
\(937\) 9.94333 6.39019i 0.324834 0.208758i −0.368052 0.929805i \(-0.619975\pi\)
0.692886 + 0.721047i \(0.256339\pi\)
\(938\) 2.05960 14.3248i 0.0672483 0.467722i
\(939\) −38.3005 24.6142i −1.24989 0.803255i
\(940\) 2.92863 3.37981i 0.0955213 0.110237i
\(941\) 23.6539 + 6.94541i 0.771094 + 0.226414i 0.643534 0.765417i \(-0.277467\pi\)
0.127560 + 0.991831i \(0.459285\pi\)
\(942\) −55.7771 −1.81732
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) 8.58197 + 2.51989i 0.279171 + 0.0819721i
\(946\) 0 0
\(947\) −27.9131 17.9386i −0.907053 0.582928i 0.00182090 0.999998i \(-0.499420\pi\)
−0.908874 + 0.417071i \(0.863057\pi\)
\(948\) −1.36576 + 9.49907i −0.0443578 + 0.308515i
\(949\) 39.0480 25.0946i 1.26755 0.814605i
\(950\) 7.35625 + 16.1079i 0.238668 + 0.522611i
\(951\) 2.07406 + 2.39360i 0.0672562 + 0.0776177i
\(952\) 2.05960 + 14.3248i 0.0667520 + 0.464270i
\(953\) 4.78885 10.4861i 0.155126 0.339679i −0.816073 0.577949i \(-0.803853\pi\)
0.971199 + 0.238271i \(0.0765805\pi\)
\(954\) −26.3059 + 7.72409i −0.851683 + 0.250077i
\(955\) −11.8600 + 3.48241i −0.383780 + 0.112688i
\(956\) 4.68194 10.2520i 0.151425 0.331574i
\(957\) −0.729308 5.07245i −0.0235752 0.163969i
\(958\) −18.6453 21.5178i −0.602402 0.695209i
\(959\) −7.13151 15.6158i −0.230288 0.504261i
\(960\) −25.7865 + 16.5720i −0.832256 + 0.534858i
\(961\) −1.99241 + 13.8575i −0.0642712 + 0.447016i
\(962\) −13.2146 8.49250i −0.426055 0.273809i
\(963\) 17.5718 20.2789i 0.566242 0.653478i
\(964\) −10.1549 2.98174i −0.327067 0.0960355i
\(965\) 25.7082 0.827576
\(966\) 0 0
\(967\) −39.5410 −1.27155 −0.635777 0.771873i \(-0.719320\pi\)
−0.635777 + 0.771873i \(0.719320\pi\)
\(968\) 22.3483 + 6.56206i 0.718302 + 0.210913i
\(969\) 15.3345 17.6969i 0.492615 0.568508i
\(970\) 18.9048 + 12.1494i 0.606995 + 0.390092i
\(971\) −1.07133 + 7.45124i −0.0343805 + 0.239122i −0.999764 0.0217120i \(-0.993088\pi\)
0.965384 + 0.260834i \(0.0839974\pi\)
\(972\) −9.30067 + 5.97718i −0.298319 + 0.191718i
\(973\) −1.39061 3.04502i −0.0445810 0.0976187i
\(974\) −1.36877 1.57965i −0.0438582 0.0506151i
\(975\) −5.22412 36.3346i −0.167306 1.16364i
\(976\) −22.0688 + 48.3238i −0.706404 + 1.54681i
\(977\) 52.4387 15.3974i 1.67766 0.492606i 0.702053 0.712124i \(-0.252267\pi\)
0.975608 + 0.219519i \(0.0704487\pi\)
\(978\) −35.5343 + 10.4338i −1.13626 + 0.333636i
\(979\) 0.484866 1.06171i 0.0154964 0.0339323i
\(980\) −1.55753 10.8329i −0.0497535 0.346043i
\(981\) 0 0
\(982\) −26.6526 58.3611i −0.850520 1.86238i
\(983\) −26.5229 + 17.0453i −0.845950 + 0.543659i −0.890309 0.455357i \(-0.849512\pi\)
0.0443591 + 0.999016i \(0.485875\pi\)
\(984\) −3.89383 + 27.0822i −0.124131 + 0.863349i
\(985\) −20.3418 13.0729i −0.648144 0.416537i
\(986\) −16.6442 + 19.2084i −0.530060 + 0.611721i
\(987\) 5.92999 + 1.74120i 0.188754 + 0.0554231i
\(988\) −3.70820 −0.117974
\(989\) 0 0
\(990\) −8.00000 −0.254257
\(991\) −23.0278 6.76158i −0.731503 0.214789i −0.105291 0.994441i \(-0.533577\pi\)
−0.626212 + 0.779653i \(0.715396\pi\)
\(992\) 14.8568 17.1456i 0.471703 0.544374i
\(993\) 21.9195 + 14.0868i 0.695593 + 0.447031i
\(994\) −2.20985 + 15.3698i −0.0700920 + 0.487501i
\(995\) 69.9868 44.9778i 2.21873 1.42589i
\(996\) −7.59869 16.6388i −0.240774 0.527221i
\(997\) 24.1204 + 27.8364i 0.763900 + 0.881587i 0.995838 0.0911434i \(-0.0290522\pi\)
−0.231938 + 0.972731i \(0.574507\pi\)
\(998\) 7.53173 + 52.3843i 0.238413 + 1.65820i
\(999\) −3.00597 + 6.58216i −0.0951047 + 0.208250i
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 529.2.c.o.501.2 20
23.2 even 11 inner 529.2.c.o.118.2 20
23.3 even 11 23.2.a.a.1.1 2
23.4 even 11 inner 529.2.c.o.334.1 20
23.5 odd 22 529.2.c.n.266.2 20
23.6 even 11 inner 529.2.c.o.487.1 20
23.7 odd 22 529.2.c.n.399.2 20
23.8 even 11 inner 529.2.c.o.255.1 20
23.9 even 11 inner 529.2.c.o.170.2 20
23.10 odd 22 529.2.c.n.466.1 20
23.11 odd 22 529.2.c.n.177.2 20
23.12 even 11 inner 529.2.c.o.177.2 20
23.13 even 11 inner 529.2.c.o.466.1 20
23.14 odd 22 529.2.c.n.170.2 20
23.15 odd 22 529.2.c.n.255.1 20
23.16 even 11 inner 529.2.c.o.399.2 20
23.17 odd 22 529.2.c.n.487.1 20
23.18 even 11 inner 529.2.c.o.266.2 20
23.19 odd 22 529.2.c.n.334.1 20
23.20 odd 22 529.2.a.a.1.1 2
23.21 odd 22 529.2.c.n.118.2 20
23.22 odd 2 529.2.c.n.501.2 20
69.20 even 22 4761.2.a.w.1.2 2
69.26 odd 22 207.2.a.d.1.2 2
92.3 odd 22 368.2.a.h.1.1 2
92.43 even 22 8464.2.a.bb.1.1 2
115.3 odd 44 575.2.b.d.24.4 4
115.49 even 22 575.2.a.f.1.2 2
115.72 odd 44 575.2.b.d.24.1 4
161.118 odd 22 1127.2.a.c.1.1 2
184.3 odd 22 1472.2.a.s.1.2 2
184.141 even 22 1472.2.a.t.1.1 2
253.164 odd 22 2783.2.a.c.1.2 2
276.95 even 22 3312.2.a.ba.1.2 2
299.233 even 22 3887.2.a.i.1.2 2
345.164 odd 22 5175.2.a.be.1.1 2
391.118 even 22 6647.2.a.b.1.1 2
437.417 odd 22 8303.2.a.e.1.2 2
460.279 odd 22 9200.2.a.bt.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.2.a.a.1.1 2 23.3 even 11
207.2.a.d.1.2 2 69.26 odd 22
368.2.a.h.1.1 2 92.3 odd 22
529.2.a.a.1.1 2 23.20 odd 22
529.2.c.n.118.2 20 23.21 odd 22
529.2.c.n.170.2 20 23.14 odd 22
529.2.c.n.177.2 20 23.11 odd 22
529.2.c.n.255.1 20 23.15 odd 22
529.2.c.n.266.2 20 23.5 odd 22
529.2.c.n.334.1 20 23.19 odd 22
529.2.c.n.399.2 20 23.7 odd 22
529.2.c.n.466.1 20 23.10 odd 22
529.2.c.n.487.1 20 23.17 odd 22
529.2.c.n.501.2 20 23.22 odd 2
529.2.c.o.118.2 20 23.2 even 11 inner
529.2.c.o.170.2 20 23.9 even 11 inner
529.2.c.o.177.2 20 23.12 even 11 inner
529.2.c.o.255.1 20 23.8 even 11 inner
529.2.c.o.266.2 20 23.18 even 11 inner
529.2.c.o.334.1 20 23.4 even 11 inner
529.2.c.o.399.2 20 23.16 even 11 inner
529.2.c.o.466.1 20 23.13 even 11 inner
529.2.c.o.487.1 20 23.6 even 11 inner
529.2.c.o.501.2 20 1.1 even 1 trivial
575.2.a.f.1.2 2 115.49 even 22
575.2.b.d.24.1 4 115.72 odd 44
575.2.b.d.24.4 4 115.3 odd 44
1127.2.a.c.1.1 2 161.118 odd 22
1472.2.a.s.1.2 2 184.3 odd 22
1472.2.a.t.1.1 2 184.141 even 22
2783.2.a.c.1.2 2 253.164 odd 22
3312.2.a.ba.1.2 2 276.95 even 22
3887.2.a.i.1.2 2 299.233 even 22
4761.2.a.w.1.2 2 69.20 even 22
5175.2.a.be.1.1 2 345.164 odd 22
6647.2.a.b.1.1 2 391.118 even 22
8303.2.a.e.1.2 2 437.417 odd 22
8464.2.a.bb.1.1 2 92.43 even 22
9200.2.a.bt.1.2 2 460.279 odd 22