Properties

Label 25.3.f.a.8.2
Level $25$
Weight $3$
Character 25.8
Analytic conductor $0.681$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,3,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\), degree \(8\), 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: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 8.2
Character \(\chi\) \(=\) 25.8
Dual form 25.3.f.a.22.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61837 - 0.824603i) q^{2} +(3.42034 + 0.541729i) q^{3} +(-0.411975 - 0.567034i) q^{4} +(4.00059 - 2.99921i) q^{5} +(-5.08868 - 3.69715i) q^{6} +(-8.06323 + 8.06323i) q^{7} +(1.33571 + 8.43332i) q^{8} +(2.84577 + 0.924645i) q^{9} +O(q^{10})\) \(q+(-1.61837 - 0.824603i) q^{2} +(3.42034 + 0.541729i) q^{3} +(-0.411975 - 0.567034i) q^{4} +(4.00059 - 2.99921i) q^{5} +(-5.08868 - 3.69715i) q^{6} +(-8.06323 + 8.06323i) q^{7} +(1.33571 + 8.43332i) q^{8} +(2.84577 + 0.924645i) q^{9} +(-8.94762 + 1.55494i) q^{10} +(-1.43991 - 4.43160i) q^{11} +(-1.10192 - 2.16263i) q^{12} +(-7.37917 + 3.75988i) q^{13} +(19.6983 - 6.40037i) q^{14} +(15.3082 - 8.09108i) q^{15} +(3.92612 - 12.0833i) q^{16} +(16.4746 - 2.60932i) q^{17} +(-3.84305 - 3.84305i) q^{18} +(-2.60721 + 3.58851i) q^{19} +(-3.34880 - 1.03288i) q^{20} +(-31.9471 + 23.2109i) q^{21} +(-1.32399 + 8.35934i) q^{22} +(1.57553 - 3.09215i) q^{23} +29.5684i q^{24} +(7.00952 - 23.9972i) q^{25} +15.0427 q^{26} +(-18.5372 - 9.44519i) q^{27} +(7.89398 + 1.25028i) q^{28} +(-14.6125 - 20.1124i) q^{29} +(-31.4463 + 0.471235i) q^{30} +(39.2975 + 28.5513i) q^{31} +(7.83247 - 7.83247i) q^{32} +(-2.52427 - 15.9376i) q^{33} +(-28.8138 - 9.36216i) q^{34} +(-8.07443 + 56.4410i) q^{35} +(-0.648078 - 1.99458i) q^{36} +(-12.2064 - 23.9564i) q^{37} +(7.17853 - 3.65765i) q^{38} +(-27.2761 + 8.86255i) q^{39} +(30.6369 + 29.7322i) q^{40} +(10.7638 - 33.1275i) q^{41} +(70.8422 - 11.2203i) q^{42} +(-13.5798 - 13.5798i) q^{43} +(-1.91966 + 2.64219i) q^{44} +(14.1580 - 4.83591i) q^{45} +(-5.09959 + 3.70507i) q^{46} +(-8.94405 + 56.4705i) q^{47} +(19.9746 - 39.2023i) q^{48} -81.0315i q^{49} +(-31.1322 + 33.0564i) q^{50} +57.7624 q^{51} +(5.17201 + 2.63527i) q^{52} +(-15.9105 - 2.51997i) q^{53} +(22.2117 + 30.5717i) q^{54} +(-19.0518 - 13.4104i) q^{55} +(-78.7699 - 57.2297i) q^{56} +(-10.8615 + 10.8615i) q^{57} +(7.06378 + 44.5989i) q^{58} +(50.4257 + 16.3843i) q^{59} +(-10.8945 - 5.34694i) q^{60} +(25.1583 + 77.4292i) q^{61} +(-40.0545 - 78.6115i) q^{62} +(-30.4017 + 15.4904i) q^{63} +(-67.4679 + 21.9217i) q^{64} +(-18.2444 + 37.1734i) q^{65} +(-9.05700 + 27.8746i) q^{66} +(3.74472 - 0.593105i) q^{67} +(-8.26671 - 8.26671i) q^{68} +(7.06395 - 9.72269i) q^{69} +(59.6089 - 84.6845i) q^{70} +(-23.0210 + 16.7257i) q^{71} +(-3.99672 + 25.2343i) q^{72} +(-19.4330 + 38.1394i) q^{73} +48.8358i q^{74} +(36.9749 - 78.2815i) q^{75} +3.10891 q^{76} +(47.3434 + 24.1226i) q^{77} +(51.4511 + 8.14905i) q^{78} +(46.6168 + 64.1625i) q^{79} +(-20.5336 - 60.1158i) q^{80} +(-80.0737 - 58.1770i) q^{81} +(-44.7368 + 44.7368i) q^{82} +(-9.69615 - 61.2191i) q^{83} +(26.3228 + 8.55280i) q^{84} +(58.0824 - 59.8497i) q^{85} +(10.7792 + 33.1750i) q^{86} +(-39.0843 - 76.7073i) q^{87} +(35.4498 - 18.0626i) q^{88} +(91.0024 - 29.5685i) q^{89} +(-26.9006 - 3.84838i) q^{90} +(29.1832 - 89.8167i) q^{91} +(-2.40243 + 0.380508i) q^{92} +(118.944 + 118.944i) q^{93} +(61.0406 - 84.0152i) q^{94} +(0.332312 + 22.1757i) q^{95} +(31.0328 - 22.5467i) q^{96} +(-22.8066 + 143.995i) q^{97} +(-66.8188 + 131.139i) q^{98} -13.9427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61837 0.824603i −0.809187 0.412302i −0.000107292 1.00000i \(-0.500034\pi\)
−0.809080 + 0.587698i \(0.800034\pi\)
\(3\) 3.42034 + 0.541729i 1.14011 + 0.180576i 0.697806 0.716287i \(-0.254160\pi\)
0.442308 + 0.896863i \(0.354160\pi\)
\(4\) −0.411975 0.567034i −0.102994 0.141759i
\(5\) 4.00059 2.99921i 0.800119 0.599841i
\(6\) −5.08868 3.69715i −0.848114 0.616191i
\(7\) −8.06323 + 8.06323i −1.15189 + 1.15189i −0.165717 + 0.986173i \(0.552994\pi\)
−0.986173 + 0.165717i \(0.947006\pi\)
\(8\) 1.33571 + 8.43332i 0.166963 + 1.05416i
\(9\) 2.84577 + 0.924645i 0.316196 + 0.102738i
\(10\) −8.94762 + 1.55494i −0.894762 + 0.155494i
\(11\) −1.43991 4.43160i −0.130901 0.402872i 0.864029 0.503442i \(-0.167933\pi\)
−0.994930 + 0.100570i \(0.967933\pi\)
\(12\) −1.10192 2.16263i −0.0918263 0.180219i
\(13\) −7.37917 + 3.75988i −0.567629 + 0.289221i −0.714157 0.699985i \(-0.753190\pi\)
0.146529 + 0.989206i \(0.453190\pi\)
\(14\) 19.6983 6.40037i 1.40702 0.457169i
\(15\) 15.3082 8.09108i 1.02054 0.539405i
\(16\) 3.92612 12.0833i 0.245382 0.755209i
\(17\) 16.4746 2.60932i 0.969096 0.153490i 0.348232 0.937408i \(-0.386782\pi\)
0.620864 + 0.783919i \(0.286782\pi\)
\(18\) −3.84305 3.84305i −0.213503 0.213503i
\(19\) −2.60721 + 3.58851i −0.137221 + 0.188869i −0.872097 0.489333i \(-0.837240\pi\)
0.734876 + 0.678202i \(0.237240\pi\)
\(20\) −3.34880 1.03288i −0.167440 0.0516439i
\(21\) −31.9471 + 23.2109i −1.52129 + 1.10528i
\(22\) −1.32399 + 8.35934i −0.0601813 + 0.379970i
\(23\) 1.57553 3.09215i 0.0685012 0.134441i −0.854217 0.519917i \(-0.825963\pi\)
0.922718 + 0.385476i \(0.125963\pi\)
\(24\) 29.5684i 1.23202i
\(25\) 7.00952 23.9972i 0.280381 0.959889i
\(26\) 15.0427 0.578564
\(27\) −18.5372 9.44519i −0.686564 0.349822i
\(28\) 7.89398 + 1.25028i 0.281928 + 0.0446530i
\(29\) −14.6125 20.1124i −0.503880 0.693531i 0.478992 0.877819i \(-0.341002\pi\)
−0.982872 + 0.184288i \(0.941002\pi\)
\(30\) −31.4463 + 0.471235i −1.04821 + 0.0157078i
\(31\) 39.2975 + 28.5513i 1.26766 + 0.921009i 0.999107 0.0422559i \(-0.0134545\pi\)
0.268553 + 0.963265i \(0.413454\pi\)
\(32\) 7.83247 7.83247i 0.244765 0.244765i
\(33\) −2.52427 15.9376i −0.0764931 0.482958i
\(34\) −28.8138 9.36216i −0.847464 0.275358i
\(35\) −8.07443 + 56.4410i −0.230698 + 1.61260i
\(36\) −0.648078 1.99458i −0.0180022 0.0554049i
\(37\) −12.2064 23.9564i −0.329902 0.647469i 0.665163 0.746699i \(-0.268362\pi\)
−0.995065 + 0.0992294i \(0.968362\pi\)
\(38\) 7.17853 3.65765i 0.188909 0.0962538i
\(39\) −27.2761 + 8.86255i −0.699388 + 0.227245i
\(40\) 30.6369 + 29.7322i 0.765922 + 0.743306i
\(41\) 10.7638 33.1275i 0.262531 0.807987i −0.729721 0.683745i \(-0.760350\pi\)
0.992252 0.124242i \(-0.0396500\pi\)
\(42\) 70.8422 11.2203i 1.68672 0.267150i
\(43\) −13.5798 13.5798i −0.315808 0.315808i 0.531346 0.847155i \(-0.321686\pi\)
−0.847155 + 0.531346i \(0.821686\pi\)
\(44\) −1.91966 + 2.64219i −0.0436286 + 0.0600497i
\(45\) 14.1580 4.83591i 0.314621 0.107465i
\(46\) −5.09959 + 3.70507i −0.110861 + 0.0805449i
\(47\) −8.94405 + 56.4705i −0.190299 + 1.20150i 0.688832 + 0.724921i \(0.258124\pi\)
−0.879131 + 0.476580i \(0.841876\pi\)
\(48\) 19.9746 39.2023i 0.416137 0.816714i
\(49\) 81.0315i 1.65370i
\(50\) −31.1322 + 33.0564i −0.622644 + 0.661129i
\(51\) 57.7624 1.13260
\(52\) 5.17201 + 2.63527i 0.0994617 + 0.0506783i
\(53\) −15.9105 2.51997i −0.300198 0.0475466i 0.00451871 0.999990i \(-0.498562\pi\)
−0.304716 + 0.952443i \(0.598562\pi\)
\(54\) 22.2117 + 30.5717i 0.411327 + 0.566143i
\(55\) −19.0518 13.4104i −0.346396 0.243826i
\(56\) −78.7699 57.2297i −1.40661 1.02196i
\(57\) −10.8615 + 10.8615i −0.190553 + 0.190553i
\(58\) 7.06378 + 44.5989i 0.121789 + 0.768947i
\(59\) 50.4257 + 16.3843i 0.854672 + 0.277700i 0.703402 0.710793i \(-0.251664\pi\)
0.151270 + 0.988492i \(0.451664\pi\)
\(60\) −10.8945 5.34694i −0.181575 0.0891156i
\(61\) 25.1583 + 77.4292i 0.412430 + 1.26933i 0.914529 + 0.404520i \(0.132561\pi\)
−0.502099 + 0.864810i \(0.667439\pi\)
\(62\) −40.0545 78.6115i −0.646041 1.26793i
\(63\) −30.4017 + 15.4904i −0.482567 + 0.245880i
\(64\) −67.4679 + 21.9217i −1.05419 + 0.342526i
\(65\) −18.2444 + 37.1734i −0.280684 + 0.571898i
\(66\) −9.05700 + 27.8746i −0.137227 + 0.422342i
\(67\) 3.74472 0.593105i 0.0558913 0.00885232i −0.128426 0.991719i \(-0.540993\pi\)
0.184318 + 0.982867i \(0.440993\pi\)
\(68\) −8.26671 8.26671i −0.121569 0.121569i
\(69\) 7.06395 9.72269i 0.102376 0.140909i
\(70\) 59.6089 84.6845i 0.851556 1.20978i
\(71\) −23.0210 + 16.7257i −0.324239 + 0.235574i −0.737982 0.674820i \(-0.764221\pi\)
0.413743 + 0.910394i \(0.364221\pi\)
\(72\) −3.99672 + 25.2343i −0.0555100 + 0.350476i
\(73\) −19.4330 + 38.1394i −0.266206 + 0.522458i −0.984955 0.172811i \(-0.944715\pi\)
0.718749 + 0.695269i \(0.244715\pi\)
\(74\) 48.8358i 0.659943i
\(75\) 36.9749 78.2815i 0.492999 1.04375i
\(76\) 3.10891 0.0409067
\(77\) 47.3434 + 24.1226i 0.614849 + 0.313281i
\(78\) 51.4511 + 8.14905i 0.659629 + 0.104475i
\(79\) 46.6168 + 64.1625i 0.590086 + 0.812184i 0.994756 0.102279i \(-0.0326134\pi\)
−0.404669 + 0.914463i \(0.632613\pi\)
\(80\) −20.5336 60.1158i −0.256670 0.751447i
\(81\) −80.0737 58.1770i −0.988565 0.718234i
\(82\) −44.7368 + 44.7368i −0.545571 + 0.545571i
\(83\) −9.69615 61.2191i −0.116821 0.737579i −0.974665 0.223669i \(-0.928197\pi\)
0.857844 0.513910i \(-0.171803\pi\)
\(84\) 26.3228 + 8.55280i 0.313367 + 0.101819i
\(85\) 58.0824 59.8497i 0.683322 0.704114i
\(86\) 10.7792 + 33.1750i 0.125340 + 0.385756i
\(87\) −39.0843 76.7073i −0.449245 0.881693i
\(88\) 35.4498 18.0626i 0.402838 0.205256i
\(89\) 91.0024 29.5685i 1.02250 0.332230i 0.250678 0.968070i \(-0.419346\pi\)
0.771820 + 0.635841i \(0.219346\pi\)
\(90\) −26.9006 3.84838i −0.298895 0.0427598i
\(91\) 29.1832 89.8167i 0.320695 0.986997i
\(92\) −2.40243 + 0.380508i −0.0261134 + 0.00413595i
\(93\) 118.944 + 118.944i 1.27896 + 1.27896i
\(94\) 61.0406 84.0152i 0.649368 0.893778i
\(95\) 0.332312 + 22.1757i 0.00349802 + 0.233429i
\(96\) 31.0328 22.5467i 0.323258 0.234861i
\(97\) −22.8066 + 143.995i −0.235119 + 1.48448i 0.534058 + 0.845448i \(0.320667\pi\)
−0.769177 + 0.639036i \(0.779333\pi\)
\(98\) −66.8188 + 131.139i −0.681824 + 1.33816i
\(99\) 13.9427i 0.140835i
\(100\) −16.4950 + 5.91161i −0.164950 + 0.0591161i
\(101\) −114.662 −1.13526 −0.567632 0.823282i \(-0.692140\pi\)
−0.567632 + 0.823282i \(0.692140\pi\)
\(102\) −93.4812 47.6311i −0.916483 0.466971i
\(103\) −157.550 24.9534i −1.52961 0.242266i −0.665818 0.746114i \(-0.731917\pi\)
−0.863792 + 0.503848i \(0.831917\pi\)
\(104\) −41.5646 57.2088i −0.399660 0.550085i
\(105\) −58.1931 + 188.674i −0.554220 + 1.79689i
\(106\) 23.6711 + 17.1981i 0.223313 + 0.162246i
\(107\) 35.0684 35.0684i 0.327742 0.327742i −0.523985 0.851727i \(-0.675555\pi\)
0.851727 + 0.523985i \(0.175555\pi\)
\(108\) 2.28112 + 14.4024i 0.0211215 + 0.133356i
\(109\) −67.4721 21.9230i −0.619010 0.201129i −0.0173095 0.999850i \(-0.505510\pi\)
−0.601701 + 0.798721i \(0.705510\pi\)
\(110\) 19.7746 + 37.4133i 0.179770 + 0.340121i
\(111\) −28.7721 88.5515i −0.259208 0.797761i
\(112\) 65.7736 + 129.088i 0.587264 + 1.15257i
\(113\) 99.6694 50.7841i 0.882030 0.449417i 0.0465362 0.998917i \(-0.485182\pi\)
0.835494 + 0.549500i \(0.185182\pi\)
\(114\) 26.5345 8.62158i 0.232759 0.0756279i
\(115\) −2.97094 17.0958i −0.0258343 0.148659i
\(116\) −5.38444 + 16.5716i −0.0464176 + 0.142859i
\(117\) −24.4759 + 3.87661i −0.209196 + 0.0331334i
\(118\) −68.0971 68.0971i −0.577094 0.577094i
\(119\) −111.799 + 153.878i −0.939489 + 1.29310i
\(120\) 88.6818 + 118.291i 0.739015 + 0.985761i
\(121\) 80.3254 58.3598i 0.663846 0.482312i
\(122\) 23.1328 146.055i 0.189613 1.19717i
\(123\) 54.7619 107.476i 0.445219 0.873791i
\(124\) 34.0454i 0.274560i
\(125\) −43.9304 117.026i −0.351443 0.936209i
\(126\) 61.9748 0.491864
\(127\) −3.65232 1.86095i −0.0287584 0.0146531i 0.439552 0.898217i \(-0.355137\pi\)
−0.468311 + 0.883564i \(0.655137\pi\)
\(128\) 83.5034 + 13.2256i 0.652370 + 0.103325i
\(129\) −39.0909 53.8040i −0.303030 0.417085i
\(130\) 60.1796 45.1161i 0.462920 0.347047i
\(131\) 72.3111 + 52.5371i 0.551993 + 0.401047i 0.828520 0.559960i \(-0.189183\pi\)
−0.276527 + 0.961006i \(0.589183\pi\)
\(132\) −7.99725 + 7.99725i −0.0605852 + 0.0605852i
\(133\) −7.91249 49.9575i −0.0594924 0.375620i
\(134\) −6.54944 2.12804i −0.0488764 0.0158809i
\(135\) −102.488 + 17.8106i −0.759171 + 0.131930i
\(136\) 44.0105 + 135.450i 0.323607 + 0.995960i
\(137\) 36.3518 + 71.3445i 0.265342 + 0.520763i 0.984783 0.173791i \(-0.0556018\pi\)
−0.719441 + 0.694554i \(0.755602\pi\)
\(138\) −19.4495 + 9.91001i −0.140938 + 0.0718116i
\(139\) −34.6269 + 11.2510i −0.249115 + 0.0809422i −0.430913 0.902394i \(-0.641808\pi\)
0.181798 + 0.983336i \(0.441808\pi\)
\(140\) 35.3305 18.6738i 0.252360 0.133384i
\(141\) −61.1834 + 188.303i −0.433925 + 1.33548i
\(142\) 51.0487 8.08531i 0.359498 0.0569388i
\(143\) 27.2876 + 27.2876i 0.190823 + 0.190823i
\(144\) 22.3456 30.7561i 0.155178 0.213584i
\(145\) −118.780 36.6356i −0.819172 0.252659i
\(146\) 62.8998 45.6994i 0.430820 0.313009i
\(147\) 43.8971 277.155i 0.298620 1.88541i
\(148\) −8.55536 + 16.7908i −0.0578065 + 0.113452i
\(149\) 134.550i 0.903021i 0.892266 + 0.451510i \(0.149115\pi\)
−0.892266 + 0.451510i \(0.850885\pi\)
\(150\) −124.390 + 96.1991i −0.829270 + 0.641327i
\(151\) 4.03813 0.0267426 0.0133713 0.999911i \(-0.495744\pi\)
0.0133713 + 0.999911i \(0.495744\pi\)
\(152\) −33.7455 17.1942i −0.222010 0.113120i
\(153\) 49.2956 + 7.80766i 0.322194 + 0.0510305i
\(154\) −56.7277 78.0790i −0.368362 0.507006i
\(155\) 242.844 3.63912i 1.56674 0.0234782i
\(156\) 16.2624 + 11.8154i 0.104246 + 0.0757395i
\(157\) 110.437 110.437i 0.703420 0.703420i −0.261723 0.965143i \(-0.584291\pi\)
0.965143 + 0.261723i \(0.0842907\pi\)
\(158\) −22.5348 142.279i −0.142626 0.900503i
\(159\) −53.0541 17.2383i −0.333674 0.108417i
\(160\) 7.84334 54.8257i 0.0490209 0.342661i
\(161\) 12.2289 + 37.6365i 0.0759556 + 0.233767i
\(162\) 81.6164 + 160.181i 0.503805 + 0.988773i
\(163\) −159.166 + 81.0992i −0.976480 + 0.497541i −0.868004 0.496558i \(-0.834597\pi\)
−0.108476 + 0.994099i \(0.534597\pi\)
\(164\) −23.2188 + 7.54425i −0.141578 + 0.0460015i
\(165\) −57.8988 56.1892i −0.350902 0.340540i
\(166\) −34.7894 + 107.071i −0.209575 + 0.645005i
\(167\) 31.9422 5.05914i 0.191270 0.0302943i −0.0600642 0.998195i \(-0.519131\pi\)
0.251335 + 0.967900i \(0.419131\pi\)
\(168\) −238.417 238.417i −1.41915 1.41915i
\(169\) −59.0202 + 81.2343i −0.349232 + 0.480677i
\(170\) −143.351 + 48.9643i −0.843243 + 0.288025i
\(171\) −10.7376 + 7.80132i −0.0627930 + 0.0456218i
\(172\) −2.10567 + 13.2947i −0.0122423 + 0.0772948i
\(173\) 71.4907 140.308i 0.413241 0.811031i −0.586758 0.809762i \(-0.699596\pi\)
0.999999 0.00126870i \(-0.000403840\pi\)
\(174\) 156.370i 0.898680i
\(175\) 136.976 + 250.015i 0.782719 + 1.42865i
\(176\) −59.2018 −0.336374
\(177\) 163.597 + 83.3569i 0.924278 + 0.470943i
\(178\) −171.658 27.1880i −0.964372 0.152741i
\(179\) 18.5657 + 25.5534i 0.103719 + 0.142757i 0.857721 0.514115i \(-0.171879\pi\)
−0.754003 + 0.656871i \(0.771879\pi\)
\(180\) −8.57485 6.03578i −0.0476380 0.0335321i
\(181\) −17.5232 12.7314i −0.0968135 0.0703391i 0.538325 0.842737i \(-0.319057\pi\)
−0.635139 + 0.772398i \(0.719057\pi\)
\(182\) −121.293 + 121.293i −0.666443 + 0.666443i
\(183\) 44.1042 + 278.463i 0.241007 + 1.52166i
\(184\) 28.1815 + 9.15673i 0.153160 + 0.0497648i
\(185\) −120.683 59.2303i −0.652340 0.320164i
\(186\) −94.4142 290.577i −0.507603 1.56224i
\(187\) −35.2855 69.2517i −0.188693 0.370330i
\(188\) 35.7054 18.1928i 0.189923 0.0967704i
\(189\) 225.629 73.3113i 1.19380 0.387890i
\(190\) 17.7484 36.1627i 0.0934125 0.190330i
\(191\) 34.1484 105.098i 0.178788 0.550252i −0.820998 0.570930i \(-0.806583\pi\)
0.999786 + 0.0206784i \(0.00658262\pi\)
\(192\) −242.639 + 38.4302i −1.26374 + 0.200158i
\(193\) 202.877 + 202.877i 1.05118 + 1.05118i 0.998618 + 0.0525601i \(0.0167381\pi\)
0.0525601 + 0.998618i \(0.483262\pi\)
\(194\) 155.648 214.231i 0.802311 1.10429i
\(195\) −82.5401 + 117.262i −0.423283 + 0.601345i
\(196\) −45.9476 + 33.3829i −0.234427 + 0.170321i
\(197\) 18.4724 116.630i 0.0937684 0.592030i −0.895402 0.445259i \(-0.853112\pi\)
0.989170 0.146772i \(-0.0468882\pi\)
\(198\) −11.4972 + 22.5645i −0.0580666 + 0.113962i
\(199\) 304.416i 1.52973i −0.644192 0.764864i \(-0.722806\pi\)
0.644192 0.764864i \(-0.277194\pi\)
\(200\) 211.739 + 27.0603i 1.05869 + 0.135301i
\(201\) 13.1295 0.0653210
\(202\) 185.566 + 94.5504i 0.918641 + 0.468071i
\(203\) 279.995 + 44.3469i 1.37929 + 0.218457i
\(204\) −23.7967 32.7533i −0.116650 0.160555i
\(205\) −56.2947 164.812i −0.274608 0.803963i
\(206\) 234.398 + 170.300i 1.13785 + 0.826700i
\(207\) 7.34272 7.34272i 0.0354721 0.0354721i
\(208\) 16.4604 + 103.927i 0.0791364 + 0.499648i
\(209\) 19.6570 + 6.38694i 0.0940526 + 0.0305595i
\(210\) 249.759 257.358i 1.18933 1.22552i
\(211\) −100.154 308.242i −0.474663 1.46086i −0.846411 0.532530i \(-0.821241\pi\)
0.371748 0.928334i \(-0.378759\pi\)
\(212\) 5.12580 + 10.0599i 0.0241783 + 0.0474526i
\(213\) −87.8005 + 44.7366i −0.412209 + 0.210031i
\(214\) −85.6714 + 27.8363i −0.400334 + 0.130076i
\(215\) −95.0556 13.5986i −0.442119 0.0632493i
\(216\) 54.8940 168.946i 0.254139 0.782159i
\(217\) −547.080 + 86.6490i −2.52111 + 0.399304i
\(218\) 91.1174 + 91.1174i 0.417970 + 0.417970i
\(219\) −87.1288 + 119.922i −0.397848 + 0.547591i
\(220\) 0.244678 + 16.3278i 0.00111217 + 0.0742172i
\(221\) −111.758 + 81.1972i −0.505694 + 0.367408i
\(222\) −26.4558 + 167.035i −0.119170 + 0.752410i
\(223\) 17.0342 33.4316i 0.0763868 0.149917i −0.849654 0.527340i \(-0.823189\pi\)
0.926041 + 0.377422i \(0.123189\pi\)
\(224\) 126.310i 0.563884i
\(225\) 42.1364 61.8092i 0.187273 0.274707i
\(226\) −203.179 −0.899023
\(227\) −259.847 132.399i −1.14470 0.583254i −0.224413 0.974494i \(-0.572046\pi\)
−0.920289 + 0.391240i \(0.872046\pi\)
\(228\) 10.6335 + 1.68419i 0.0466384 + 0.00738679i
\(229\) 205.786 + 283.240i 0.898627 + 1.23685i 0.970904 + 0.239469i \(0.0769734\pi\)
−0.0722771 + 0.997385i \(0.523027\pi\)
\(230\) −9.28912 + 30.1172i −0.0403875 + 0.130944i
\(231\) 148.863 + 108.155i 0.644427 + 0.468203i
\(232\) 150.096 150.096i 0.646967 0.646967i
\(233\) −12.3861 78.2025i −0.0531590 0.335633i −0.999907 0.0136566i \(-0.995653\pi\)
0.946748 0.321976i \(-0.104347\pi\)
\(234\) 42.8079 + 13.9091i 0.182940 + 0.0594407i
\(235\) 133.585 + 252.741i 0.568448 + 1.07549i
\(236\) −11.4836 35.3430i −0.0486595 0.149758i
\(237\) 124.687 + 244.712i 0.526105 + 1.03254i
\(238\) 307.822 156.843i 1.29337 0.659004i
\(239\) −375.540 + 122.021i −1.57130 + 0.510546i −0.959797 0.280696i \(-0.909435\pi\)
−0.611503 + 0.791242i \(0.709435\pi\)
\(240\) −37.6656 216.740i −0.156940 0.903084i
\(241\) −9.67765 + 29.7847i −0.0401562 + 0.123588i −0.969125 0.246570i \(-0.920696\pi\)
0.928969 + 0.370158i \(0.120696\pi\)
\(242\) −178.120 + 28.2115i −0.736034 + 0.116576i
\(243\) −109.962 109.962i −0.452520 0.452520i
\(244\) 33.5404 46.1644i 0.137461 0.189199i
\(245\) −243.030 324.174i −0.991960 1.32316i
\(246\) −177.251 + 128.780i −0.720531 + 0.523496i
\(247\) 5.74666 36.2830i 0.0232658 0.146895i
\(248\) −188.292 + 369.544i −0.759243 + 1.49010i
\(249\) 214.643i 0.862020i
\(250\) −25.4043 + 225.617i −0.101617 + 0.902469i
\(251\) −155.694 −0.620295 −0.310147 0.950689i \(-0.600378\pi\)
−0.310147 + 0.950689i \(0.600378\pi\)
\(252\) 21.3083 + 10.8571i 0.0845569 + 0.0430839i
\(253\) −15.9718 2.52968i −0.0631295 0.00999874i
\(254\) 4.37627 + 6.02342i 0.0172294 + 0.0237143i
\(255\) 231.084 173.241i 0.906212 0.679378i
\(256\) 105.333 + 76.5287i 0.411456 + 0.298940i
\(257\) −49.8494 + 49.8494i −0.193967 + 0.193967i −0.797408 0.603441i \(-0.793796\pi\)
0.603441 + 0.797408i \(0.293796\pi\)
\(258\) 18.8968 + 119.309i 0.0732432 + 0.462440i
\(259\) 291.589 + 94.7429i 1.12582 + 0.365803i
\(260\) 28.5948 4.96928i 0.109980 0.0191126i
\(261\) −22.9870 70.7466i −0.0880726 0.271060i
\(262\) −73.7042 144.653i −0.281314 0.552109i
\(263\) −419.056 + 213.520i −1.59337 + 0.811863i −0.593394 + 0.804912i \(0.702212\pi\)
−0.999976 + 0.00695066i \(0.997788\pi\)
\(264\) 131.035 42.5760i 0.496346 0.161273i
\(265\) −71.2093 + 37.6374i −0.268714 + 0.142028i
\(266\) −28.3897 + 87.3747i −0.106728 + 0.328476i
\(267\) 327.277 51.8356i 1.22576 0.194141i
\(268\) −1.87904 1.87904i −0.00701135 0.00701135i
\(269\) 219.028 301.467i 0.814232 1.12069i −0.176425 0.984314i \(-0.556453\pi\)
0.990657 0.136380i \(-0.0435467\pi\)
\(270\) 180.551 + 55.6877i 0.668707 + 0.206251i
\(271\) 269.883 196.082i 0.995878 0.723548i 0.0346779 0.999399i \(-0.488959\pi\)
0.961201 + 0.275850i \(0.0889595\pi\)
\(272\) 33.1519 209.313i 0.121882 0.769533i
\(273\) 148.473 291.395i 0.543857 1.06738i
\(274\) 145.438i 0.530796i
\(275\) −116.439 + 3.49056i −0.423415 + 0.0126929i
\(276\) −8.42327 −0.0305191
\(277\) 255.508 + 130.188i 0.922413 + 0.469993i 0.849644 0.527356i \(-0.176817\pi\)
0.0727686 + 0.997349i \(0.476817\pi\)
\(278\) 65.3169 + 10.3452i 0.234953 + 0.0372129i
\(279\) 85.4316 + 117.586i 0.306206 + 0.421457i
\(280\) −486.770 + 7.29444i −1.73847 + 0.0260516i
\(281\) −162.496 118.060i −0.578278 0.420143i 0.259825 0.965656i \(-0.416335\pi\)
−0.838103 + 0.545512i \(0.816335\pi\)
\(282\) 254.293 254.293i 0.901749 0.901749i
\(283\) −25.4422 160.636i −0.0899019 0.567618i −0.990985 0.133972i \(-0.957227\pi\)
0.901083 0.433646i \(-0.142773\pi\)
\(284\) 18.9681 + 6.16312i 0.0667892 + 0.0217011i
\(285\) −10.8766 + 76.0286i −0.0381636 + 0.266767i
\(286\) −21.6601 66.6630i −0.0757347 0.233088i
\(287\) 180.324 + 353.905i 0.628306 + 1.23312i
\(288\) 29.5316 15.0471i 0.102540 0.0522469i
\(289\) −10.2505 + 3.33060i −0.0354690 + 0.0115246i
\(290\) 162.021 + 157.237i 0.558692 + 0.542195i
\(291\) −156.013 + 480.157i −0.536126 + 1.65002i
\(292\) 29.6323 4.69329i 0.101480 0.0160729i
\(293\) −269.435 269.435i −0.919573 0.919573i 0.0774250 0.996998i \(-0.475330\pi\)
−0.996998 + 0.0774250i \(0.975330\pi\)
\(294\) −299.585 + 412.344i −1.01900 + 1.40253i
\(295\) 250.872 85.6901i 0.850415 0.290475i
\(296\) 185.727 134.939i 0.627458 0.455875i
\(297\) −15.1653 + 95.7498i −0.0510616 + 0.322390i
\(298\) 110.950 217.752i 0.372317 0.730713i
\(299\) 28.7413i 0.0961246i
\(300\) −59.6210 + 11.2839i −0.198737 + 0.0376130i
\(301\) 218.993 0.727553
\(302\) −6.53520 3.32985i −0.0216397 0.0110260i
\(303\) −392.182 62.1156i −1.29433 0.205002i
\(304\) 33.1250 + 45.5927i 0.108964 + 0.149976i
\(305\) 332.874 + 234.308i 1.09139 + 0.768223i
\(306\) −73.3406 53.2850i −0.239675 0.174134i
\(307\) 15.5293 15.5293i 0.0505840 0.0505840i −0.681362 0.731946i \(-0.738612\pi\)
0.731946 + 0.681362i \(0.238612\pi\)
\(308\) −5.82589 36.7832i −0.0189152 0.119426i
\(309\) −525.357 170.699i −1.70018 0.552423i
\(310\) −396.014 194.361i −1.27746 0.626970i
\(311\) 133.569 + 411.082i 0.429481 + 1.32181i 0.898638 + 0.438691i \(0.144558\pi\)
−0.469157 + 0.883115i \(0.655442\pi\)
\(312\) −111.174 218.191i −0.356326 0.699329i
\(313\) 83.8100 42.7034i 0.267764 0.136432i −0.314954 0.949107i \(-0.601989\pi\)
0.582718 + 0.812674i \(0.301989\pi\)
\(314\) −269.795 + 87.6617i −0.859220 + 0.279177i
\(315\) −75.1659 + 153.152i −0.238622 + 0.486197i
\(316\) 17.1774 52.8667i 0.0543589 0.167300i
\(317\) 190.794 30.2188i 0.601874 0.0953274i 0.151940 0.988390i \(-0.451448\pi\)
0.449933 + 0.893062i \(0.351448\pi\)
\(318\) 71.6467 + 71.6467i 0.225304 + 0.225304i
\(319\) −68.0893 + 93.7169i −0.213446 + 0.293783i
\(320\) −204.164 + 290.050i −0.638013 + 0.906406i
\(321\) 138.944 100.948i 0.432846 0.314481i
\(322\) 11.2443 70.9940i 0.0349203 0.220478i
\(323\) −33.5892 + 65.9224i −0.103991 + 0.204094i
\(324\) 69.3720i 0.214111i
\(325\) 38.5021 + 203.435i 0.118468 + 0.625952i
\(326\) 324.465 0.995292
\(327\) −218.902 111.536i −0.669424 0.341088i
\(328\) 293.752 + 46.5257i 0.895585 + 0.141847i
\(329\) −383.217 527.453i −1.16479 1.60320i
\(330\) 47.3682 + 138.679i 0.143540 + 0.420238i
\(331\) −220.979 160.551i −0.667611 0.485048i 0.201613 0.979465i \(-0.435382\pi\)
−0.869225 + 0.494417i \(0.835382\pi\)
\(332\) −30.7187 + 30.7187i −0.0925264 + 0.0925264i
\(333\) −12.5853 79.4608i −0.0377938 0.238621i
\(334\) −55.8662 18.1520i −0.167264 0.0543474i
\(335\) 13.2023 13.6040i 0.0394097 0.0406089i
\(336\) 155.038 + 477.157i 0.461421 + 1.42011i
\(337\) −258.565 507.462i −0.767254 1.50582i −0.860092 0.510140i \(-0.829594\pi\)
0.0928377 0.995681i \(-0.470406\pi\)
\(338\) 162.503 82.7994i 0.480778 0.244969i
\(339\) 368.415 119.705i 1.08677 0.353113i
\(340\) −57.8653 8.27818i −0.170192 0.0243476i
\(341\) 69.9428 215.262i 0.205111 0.631267i
\(342\) 23.8105 3.77121i 0.0696212 0.0110269i
\(343\) 258.277 + 258.277i 0.752995 + 0.752995i
\(344\) 96.3838 132.661i 0.280185 0.385642i
\(345\) −0.900365 60.0828i −0.00260975 0.174153i
\(346\) −231.397 + 168.120i −0.668778 + 0.485896i
\(347\) −52.3196 + 330.333i −0.150777 + 0.951968i 0.790040 + 0.613055i \(0.210059\pi\)
−0.940817 + 0.338914i \(0.889941\pi\)
\(348\) −27.3939 + 53.7636i −0.0787182 + 0.154493i
\(349\) 502.965i 1.44116i 0.693372 + 0.720580i \(0.256124\pi\)
−0.693372 + 0.720580i \(0.743876\pi\)
\(350\) −15.5154 517.568i −0.0443297 1.47877i
\(351\) 172.302 0.490889
\(352\) −45.9884 23.4323i −0.130649 0.0665690i
\(353\) 173.477 + 27.4761i 0.491437 + 0.0778360i 0.397235 0.917717i \(-0.369970\pi\)
0.0942023 + 0.995553i \(0.469970\pi\)
\(354\) −196.025 269.805i −0.553743 0.762162i
\(355\) −41.9337 + 135.958i −0.118123 + 0.382979i
\(356\) −54.2570 39.4200i −0.152407 0.110730i
\(357\) −465.752 + 465.752i −1.30463 + 1.30463i
\(358\) −8.97475 56.6643i −0.0250691 0.158280i
\(359\) −129.730 42.1519i −0.361366 0.117415i 0.122706 0.992443i \(-0.460843\pi\)
−0.484072 + 0.875028i \(0.660843\pi\)
\(360\) 59.6936 + 112.939i 0.165816 + 0.313720i
\(361\) 105.475 + 324.619i 0.292175 + 0.899223i
\(362\) 17.8608 + 35.0539i 0.0493393 + 0.0968339i
\(363\) 306.355 156.096i 0.843954 0.430016i
\(364\) −62.9519 + 20.4543i −0.172945 + 0.0561932i
\(365\) 36.6444 + 210.864i 0.100396 + 0.577710i
\(366\) 158.244 487.026i 0.432362 1.33067i
\(367\) 330.443 52.3370i 0.900389 0.142608i 0.310955 0.950425i \(-0.399351\pi\)
0.589433 + 0.807817i \(0.299351\pi\)
\(368\) −31.1778 31.1778i −0.0847222 0.0847222i
\(369\) 61.2623 84.3204i 0.166023 0.228510i
\(370\) 146.469 + 195.372i 0.395861 + 0.528033i
\(371\) 148.609 107.971i 0.400563 0.291026i
\(372\) 18.4434 116.447i 0.0495790 0.313030i
\(373\) −83.7541 + 164.377i −0.224542 + 0.440688i −0.975602 0.219545i \(-0.929543\pi\)
0.751060 + 0.660233i \(0.229543\pi\)
\(374\) 141.172i 0.377465i
\(375\) −86.8605 424.068i −0.231628 1.13085i
\(376\) −488.180 −1.29835
\(377\) 183.448 + 93.4716i 0.486600 + 0.247935i
\(378\) −425.605 67.4092i −1.12594 0.178331i
\(379\) 143.236 + 197.147i 0.377931 + 0.520178i 0.955035 0.296493i \(-0.0958171\pi\)
−0.577104 + 0.816671i \(0.695817\pi\)
\(380\) 12.4375 9.32427i 0.0327303 0.0245376i
\(381\) −11.4840 8.34365i −0.0301418 0.0218993i
\(382\) −141.929 + 141.929i −0.371542 + 0.371542i
\(383\) −101.123 638.468i −0.264030 1.66702i −0.661912 0.749582i \(-0.730255\pi\)
0.397882 0.917437i \(-0.369745\pi\)
\(384\) 278.445 + 90.4724i 0.725118 + 0.235605i
\(385\) 261.750 45.4876i 0.679871 0.118150i
\(386\) −161.038 495.625i −0.417198 1.28400i
\(387\) −26.0883 51.2012i −0.0674117 0.132303i
\(388\) 91.0458 46.3902i 0.234654 0.119562i
\(389\) 698.667 227.011i 1.79606 0.583575i 0.796288 0.604918i \(-0.206794\pi\)
0.999772 + 0.0213423i \(0.00679398\pi\)
\(390\) 230.276 121.711i 0.590450 0.312080i
\(391\) 17.8878 55.0530i 0.0457489 0.140801i
\(392\) 683.364 108.234i 1.74328 0.276108i
\(393\) 218.868 + 218.868i 0.556916 + 0.556916i
\(394\) −126.069 + 173.519i −0.319971 + 0.440402i
\(395\) 378.932 + 116.875i 0.959321 + 0.295886i
\(396\) −7.90599 + 5.74404i −0.0199646 + 0.0145051i
\(397\) 29.3710 185.441i 0.0739823 0.467106i −0.922687 0.385551i \(-0.874011\pi\)
0.996669 0.0815548i \(-0.0259886\pi\)
\(398\) −251.022 + 492.659i −0.630709 + 1.23784i
\(399\) 175.158i 0.438993i
\(400\) −262.446 178.914i −0.656116 0.447286i
\(401\) 88.3502 0.220325 0.110162 0.993914i \(-0.464863\pi\)
0.110162 + 0.993914i \(0.464863\pi\)
\(402\) −21.2485 10.8267i −0.0528570 0.0269320i
\(403\) −397.332 62.9312i −0.985935 0.156157i
\(404\) 47.2377 + 65.0171i 0.116925 + 0.160933i
\(405\) −494.827 + 7.41518i −1.22180 + 0.0183091i
\(406\) −416.568 302.655i −1.02603 0.745455i
\(407\) −88.5888 + 88.5888i −0.217663 + 0.217663i
\(408\) 77.1536 + 487.129i 0.189102 + 1.19394i
\(409\) −172.391 56.0134i −0.421495 0.136952i 0.0905870 0.995889i \(-0.471126\pi\)
−0.512082 + 0.858936i \(0.671126\pi\)
\(410\) −44.7989 + 313.149i −0.109266 + 0.763778i
\(411\) 85.6864 + 263.715i 0.208483 + 0.641644i
\(412\) 50.7571 + 99.6164i 0.123197 + 0.241787i
\(413\) −538.704 + 274.483i −1.30437 + 0.664609i
\(414\) −17.9381 + 5.82844i −0.0433288 + 0.0140784i
\(415\) −222.399 215.832i −0.535901 0.520077i
\(416\) −28.3480 + 87.2463i −0.0681443 + 0.209727i
\(417\) −124.531 + 19.7238i −0.298635 + 0.0472992i
\(418\) −26.5457 26.5457i −0.0635064 0.0635064i
\(419\) 113.418 156.106i 0.270687 0.372569i −0.651934 0.758275i \(-0.726042\pi\)
0.922622 + 0.385706i \(0.126042\pi\)
\(420\) 130.958 44.7312i 0.311806 0.106503i
\(421\) −659.764 + 479.346i −1.56713 + 1.13859i −0.637298 + 0.770617i \(0.719948\pi\)
−0.929837 + 0.367972i \(0.880052\pi\)
\(422\) −92.0908 + 581.439i −0.218225 + 1.37782i
\(423\) −77.6679 + 152.432i −0.183612 + 0.360359i
\(424\) 137.544i 0.324396i
\(425\) 52.8627 413.635i 0.124383 0.973260i
\(426\) 178.984 0.420150
\(427\) −827.186 421.472i −1.93720 0.987055i
\(428\) −34.3323 5.43771i −0.0802157 0.0127049i
\(429\) 78.5505 + 108.116i 0.183101 + 0.252017i
\(430\) 142.622 + 100.391i 0.331679 + 0.233467i
\(431\) −199.776 145.146i −0.463518 0.336765i 0.331392 0.943493i \(-0.392482\pi\)
−0.794910 + 0.606728i \(0.792482\pi\)
\(432\) −186.909 + 186.909i −0.432659 + 0.432659i
\(433\) 120.729 + 762.250i 0.278819 + 1.76039i 0.587498 + 0.809226i \(0.300113\pi\)
−0.308679 + 0.951166i \(0.599887\pi\)
\(434\) 956.832 + 310.894i 2.20468 + 0.716345i
\(435\) −386.422 189.653i −0.888326 0.435984i
\(436\) 15.3657 + 47.2908i 0.0352424 + 0.108465i
\(437\) 6.98848 + 13.7157i 0.0159919 + 0.0313860i
\(438\) 239.895 122.233i 0.547707 0.279070i
\(439\) −16.9661 + 5.51263i −0.0386472 + 0.0125572i −0.328277 0.944582i \(-0.606468\pi\)
0.289630 + 0.957139i \(0.406468\pi\)
\(440\) 87.6468 178.582i 0.199197 0.405869i
\(441\) 74.9254 230.597i 0.169899 0.522895i
\(442\) 247.822 39.2512i 0.560684 0.0888036i
\(443\) 184.814 + 184.814i 0.417187 + 0.417187i 0.884233 0.467046i \(-0.154682\pi\)
−0.467046 + 0.884233i \(0.654682\pi\)
\(444\) −38.3584 + 52.7958i −0.0863927 + 0.118909i
\(445\) 275.382 391.226i 0.618835 0.879160i
\(446\) −55.1356 + 40.0583i −0.123622 + 0.0898169i
\(447\) −72.8897 + 460.207i −0.163064 + 1.02955i
\(448\) 367.250 720.769i 0.819755 1.60886i
\(449\) 266.342i 0.593189i 0.955004 + 0.296594i \(0.0958509\pi\)
−0.955004 + 0.296594i \(0.904149\pi\)
\(450\) −119.160 + 65.2846i −0.264801 + 0.145077i
\(451\) −162.307 −0.359881
\(452\) −69.8576 35.5942i −0.154552 0.0787483i
\(453\) 13.8118 + 2.18757i 0.0304896 + 0.00482907i
\(454\) 311.354 + 428.542i 0.685801 + 0.943924i
\(455\) −152.629 446.847i −0.335448 0.982081i
\(456\) −106.107 77.0910i −0.232690 0.169059i
\(457\) 473.310 473.310i 1.03569 1.03569i 0.0363511 0.999339i \(-0.488427\pi\)
0.999339 0.0363511i \(-0.0115735\pi\)
\(458\) −99.4779 628.079i −0.217201 1.37135i
\(459\) −330.040 107.236i −0.719041 0.233630i
\(460\) −8.46993 + 8.72764i −0.0184129 + 0.0189731i
\(461\) 14.4681 + 44.5284i 0.0313843 + 0.0965909i 0.965522 0.260323i \(-0.0838290\pi\)
−0.934137 + 0.356914i \(0.883829\pi\)
\(462\) −151.730 297.788i −0.328421 0.644562i
\(463\) 308.662 157.271i 0.666657 0.339679i −0.0876962 0.996147i \(-0.527950\pi\)
0.754354 + 0.656468i \(0.227950\pi\)
\(464\) −300.395 + 97.6044i −0.647404 + 0.210354i
\(465\) 832.583 + 119.109i 1.79050 + 0.256148i
\(466\) −44.4407 + 136.775i −0.0953664 + 0.293508i
\(467\) −106.477 + 16.8643i −0.228002 + 0.0361120i −0.269390 0.963031i \(-0.586822\pi\)
0.0413877 + 0.999143i \(0.486822\pi\)
\(468\) 12.2816 + 12.2816i 0.0262428 + 0.0262428i
\(469\) −25.4122 + 34.9769i −0.0541838 + 0.0745776i
\(470\) −7.78018 519.184i −0.0165536 1.10465i
\(471\) 437.559 317.905i 0.929000 0.674958i
\(472\) −70.8201 + 447.140i −0.150042 + 0.947331i
\(473\) −40.6263 + 79.7337i −0.0858908 + 0.168570i
\(474\) 498.852i 1.05243i
\(475\) 67.8391 + 87.7194i 0.142819 + 0.184673i
\(476\) 133.313 0.280069
\(477\) −42.9474 21.8828i −0.0900365 0.0458759i
\(478\) 708.384 + 112.197i 1.48197 + 0.234722i
\(479\) −214.282 294.934i −0.447353 0.615729i 0.524473 0.851427i \(-0.324262\pi\)
−0.971826 + 0.235698i \(0.924262\pi\)
\(480\) 56.5276 183.274i 0.117766 0.381821i
\(481\) 180.146 + 130.884i 0.374524 + 0.272107i
\(482\) 40.2227 40.2227i 0.0834495 0.0834495i
\(483\) 21.4381 + 135.355i 0.0443852 + 0.280237i
\(484\) −66.1840 21.5045i −0.136744 0.0444308i
\(485\) 340.631 + 644.467i 0.702332 + 1.32880i
\(486\) 87.2850 + 268.636i 0.179599 + 0.552748i
\(487\) −171.861 337.296i −0.352897 0.692599i 0.644508 0.764598i \(-0.277062\pi\)
−0.997405 + 0.0719988i \(0.977062\pi\)
\(488\) −619.381 + 315.590i −1.26922 + 0.646701i
\(489\) −588.337 + 191.162i −1.20314 + 0.390925i
\(490\) 125.999 + 725.039i 0.257141 + 1.47967i
\(491\) −80.8943 + 248.967i −0.164754 + 0.507061i −0.999018 0.0443043i \(-0.985893\pi\)
0.834264 + 0.551365i \(0.185893\pi\)
\(492\) −83.5033 + 13.2256i −0.169722 + 0.0268813i
\(493\) −293.216 293.216i −0.594758 0.594758i
\(494\) −39.2193 + 53.9808i −0.0793914 + 0.109273i
\(495\) −41.8170 55.7791i −0.0844788 0.112685i
\(496\) 499.281 362.749i 1.00662 0.731349i
\(497\) 50.7602 320.487i 0.102133 0.644843i
\(498\) −176.995 + 347.373i −0.355412 + 0.697535i
\(499\) 75.2156i 0.150733i −0.997156 0.0753664i \(-0.975987\pi\)
0.997156 0.0753664i \(-0.0240126\pi\)
\(500\) −48.2597 + 73.1218i −0.0965193 + 0.146244i
\(501\) 111.994 0.223541
\(502\) 251.971 + 128.386i 0.501935 + 0.255748i
\(503\) 778.940 + 123.372i 1.54859 + 0.245272i 0.871413 0.490549i \(-0.163204\pi\)
0.677175 + 0.735822i \(0.263204\pi\)
\(504\) −171.244 235.697i −0.339769 0.467652i
\(505\) −458.715 + 343.894i −0.908346 + 0.680978i
\(506\) 23.7623 + 17.2643i 0.0469611 + 0.0341193i
\(507\) −245.876 + 245.876i −0.484963 + 0.484963i
\(508\) 0.449440 + 2.83765i 0.000884724 + 0.00558593i
\(509\) −193.504 62.8734i −0.380166 0.123523i 0.112699 0.993629i \(-0.464050\pi\)
−0.492865 + 0.870106i \(0.664050\pi\)
\(510\) −516.836 + 89.8169i −1.01340 + 0.176112i
\(511\) −150.834 464.220i −0.295175 0.908454i
\(512\) −260.891 512.028i −0.509553 1.00005i
\(513\) 82.2246 41.8955i 0.160282 0.0816677i
\(514\) 121.781 39.5690i 0.236928 0.0769826i
\(515\) −705.134 + 372.696i −1.36919 + 0.723682i
\(516\) −14.4043 + 44.3317i −0.0279152 + 0.0859142i
\(517\) 263.133 41.6762i 0.508962 0.0806116i
\(518\) −393.774 393.774i −0.760182 0.760182i
\(519\) 320.532 441.174i 0.617595 0.850046i
\(520\) −337.864 104.208i −0.649739 0.200401i
\(521\) −626.036 + 454.842i −1.20160 + 0.873016i −0.994442 0.105290i \(-0.966423\pi\)
−0.207163 + 0.978307i \(0.566423\pi\)
\(522\) −21.1363 + 133.450i −0.0404911 + 0.255651i
\(523\) 328.674 645.059i 0.628440 1.23338i −0.328885 0.944370i \(-0.606673\pi\)
0.957325 0.289013i \(-0.0933271\pi\)
\(524\) 62.6468i 0.119555i
\(525\) 333.064 + 929.339i 0.634408 + 1.77017i
\(526\) 854.259 1.62407
\(527\) 721.911 + 367.832i 1.36985 + 0.697973i
\(528\) −202.490 32.0713i −0.383504 0.0607411i
\(529\) 303.859 + 418.226i 0.574403 + 0.790598i
\(530\) 146.279 2.19205i 0.275998 0.00413595i
\(531\) 128.350 + 93.2517i 0.241714 + 0.175615i
\(532\) −25.0679 + 25.0679i −0.0471201 + 0.0471201i
\(533\) 45.1275 + 284.924i 0.0846670 + 0.534566i
\(534\) −572.401 185.984i −1.07191 0.348286i
\(535\) 35.1171 245.472i 0.0656395 0.458826i
\(536\) 10.0037 + 30.7882i 0.0186636 + 0.0574407i
\(537\) 49.6579 + 97.4590i 0.0924727 + 0.181488i
\(538\) −603.060 + 307.275i −1.12093 + 0.571142i
\(539\) −359.099 + 116.678i −0.666232 + 0.216472i
\(540\) 52.3217 + 50.7767i 0.0968921 + 0.0940310i
\(541\) 283.746 873.280i 0.524484 1.61420i −0.240850 0.970562i \(-0.577426\pi\)
0.765334 0.643633i \(-0.222574\pi\)
\(542\) −598.461 + 94.7870i −1.10417 + 0.174884i
\(543\) −53.0385 53.0385i −0.0976768 0.0976768i
\(544\) 108.600 149.475i 0.199632 0.274769i
\(545\) −335.680 + 114.658i −0.615927 + 0.210381i
\(546\) −480.570 + 349.154i −0.880164 + 0.639477i
\(547\) −55.9587 + 353.309i −0.102301 + 0.645903i 0.882247 + 0.470787i \(0.156030\pi\)
−0.984548 + 0.175116i \(0.943970\pi\)
\(548\) 25.4788 50.0049i 0.0464941 0.0912498i
\(549\) 243.608i 0.443730i
\(550\) 191.320 + 90.3670i 0.347855 + 0.164304i
\(551\) 110.271 0.200130
\(552\) 91.4299 + 46.5859i 0.165634 + 0.0843947i
\(553\) −893.240 141.475i −1.61526 0.255832i
\(554\) −306.155 421.386i −0.552626 0.760625i
\(555\) −380.690 267.965i −0.685928 0.482820i
\(556\) 20.6451 + 14.9995i 0.0371315 + 0.0269776i
\(557\) 404.198 404.198i 0.725670 0.725670i −0.244084 0.969754i \(-0.578487\pi\)
0.969754 + 0.244084i \(0.0784872\pi\)
\(558\) −41.2981 260.746i −0.0740110 0.467287i
\(559\) 151.265 + 49.1491i 0.270600 + 0.0879233i
\(560\) 650.295 + 319.160i 1.16124 + 0.569929i
\(561\) −83.1729 255.980i −0.148258 0.456292i
\(562\) 165.627 + 325.060i 0.294709 + 0.578399i
\(563\) 872.036 444.324i 1.54891 0.789208i 0.549966 0.835187i \(-0.314641\pi\)
0.998942 + 0.0459785i \(0.0146406\pi\)
\(564\) 131.980 42.8830i 0.234008 0.0760338i
\(565\) 246.425 502.096i 0.436150 0.888665i
\(566\) −91.2859 + 280.949i −0.161282 + 0.496376i
\(567\) 1114.75 176.559i 1.96605 0.311391i
\(568\) −171.803 171.803i −0.302469 0.302469i
\(569\) −431.512 + 593.925i −0.758369 + 1.04381i 0.238979 + 0.971025i \(0.423187\pi\)
−0.997348 + 0.0727807i \(0.976813\pi\)
\(570\) 80.2959 114.074i 0.140870 0.200130i
\(571\) −612.726 + 445.171i −1.07308 + 0.779635i −0.976463 0.215687i \(-0.930801\pi\)
−0.0966128 + 0.995322i \(0.530801\pi\)
\(572\) 4.23121 26.7148i 0.00739723 0.0467042i
\(573\) 173.734 340.972i 0.303201 0.595065i
\(574\) 721.447i 1.25688i
\(575\) −63.1592 59.4827i −0.109842 0.103448i
\(576\) −212.268 −0.368520
\(577\) 367.699 + 187.352i 0.637261 + 0.324700i 0.742599 0.669736i \(-0.233593\pi\)
−0.105339 + 0.994436i \(0.533593\pi\)
\(578\) 19.3356 + 3.06246i 0.0334527 + 0.00529838i
\(579\) 584.005 + 803.815i 1.00865 + 1.38828i
\(580\) 28.1607 + 82.4453i 0.0485529 + 0.142147i
\(581\) 571.806 + 415.441i 0.984175 + 0.715045i
\(582\) 648.426 648.426i 1.11413 1.11413i
\(583\) 11.7422 + 74.1373i 0.0201410 + 0.127165i
\(584\) −347.599 112.942i −0.595203 0.193393i
\(585\) −86.2916 + 88.9172i −0.147507 + 0.151995i
\(586\) 213.870 + 658.224i 0.364966 + 1.12325i
\(587\) −199.151 390.856i −0.339269 0.665853i 0.656835 0.754034i \(-0.271895\pi\)
−0.996104 + 0.0881807i \(0.971895\pi\)
\(588\) −175.241 + 89.2898i −0.298029 + 0.151853i
\(589\) −204.913 + 66.5803i −0.347900 + 0.113040i
\(590\) −476.666 68.1916i −0.807908 0.115579i
\(591\) 126.364 388.907i 0.213813 0.658050i
\(592\) −337.397 + 53.4384i −0.569927 + 0.0902675i
\(593\) −279.182 279.182i −0.470796 0.470796i 0.431376 0.902172i \(-0.358028\pi\)
−0.902172 + 0.431376i \(0.858028\pi\)
\(594\) 103.499 142.454i 0.174240 0.239821i
\(595\) 14.2498 + 950.914i 0.0239493 + 1.59817i
\(596\) 76.2945 55.4312i 0.128011 0.0930054i
\(597\) 164.911 1041.21i 0.276233 1.74406i
\(598\) 23.7001 46.5141i 0.0396323 0.0777828i
\(599\) 65.2707i 0.108966i 0.998515 + 0.0544831i \(0.0173511\pi\)
−0.998515 + 0.0544831i \(0.982649\pi\)
\(600\) 709.560 + 207.260i 1.18260 + 0.345434i
\(601\) 192.168 0.319747 0.159873 0.987138i \(-0.448891\pi\)
0.159873 + 0.987138i \(0.448891\pi\)
\(602\) −354.413 180.583i −0.588727 0.299971i
\(603\) 11.2050 + 1.77470i 0.0185821 + 0.00294312i
\(604\) −1.66361 2.28976i −0.00275431 0.00379099i
\(605\) 146.316 474.386i 0.241845 0.784109i
\(606\) 583.477 + 423.921i 0.962833 + 0.699539i
\(607\) −510.986 + 510.986i −0.841822 + 0.841822i −0.989096 0.147274i \(-0.952950\pi\)
0.147274 + 0.989096i \(0.452950\pi\)
\(608\) 7.68605 + 48.5278i 0.0126415 + 0.0798154i
\(609\) 933.655 + 303.363i 1.53310 + 0.498133i
\(610\) −345.504 653.687i −0.566400 1.07162i
\(611\) −146.322 450.334i −0.239480 0.737044i
\(612\) −15.8813 31.1689i −0.0259499 0.0509295i
\(613\) −104.510 + 53.2504i −0.170489 + 0.0868686i −0.537153 0.843485i \(-0.680500\pi\)
0.366663 + 0.930354i \(0.380500\pi\)
\(614\) −37.9377 + 12.3267i −0.0617877 + 0.0200761i
\(615\) −103.263 594.211i −0.167908 0.966197i
\(616\) −140.197 + 431.482i −0.227593 + 0.700458i
\(617\) −667.508 + 105.723i −1.08186 + 0.171350i −0.671818 0.740716i \(-0.734486\pi\)
−0.410043 + 0.912066i \(0.634486\pi\)
\(618\) 709.465 + 709.465i 1.14800 + 1.14800i
\(619\) −239.653 + 329.853i −0.387161 + 0.532881i −0.957464 0.288553i \(-0.906826\pi\)
0.570303 + 0.821434i \(0.306826\pi\)
\(620\) −102.109 136.202i −0.164692 0.219681i
\(621\) −58.4119 + 42.4387i −0.0940610 + 0.0683393i
\(622\) 122.815 775.425i 0.197452 1.24666i
\(623\) −495.356 + 972.191i −0.795114 + 1.56050i
\(624\) 364.382i 0.583946i
\(625\) −526.733 336.418i −0.842773 0.538269i
\(626\) −170.849 −0.272922
\(627\) 63.7736 + 32.4943i 0.101712 + 0.0518250i
\(628\) −108.119 17.1243i −0.172164 0.0272680i
\(629\) −263.605 362.822i −0.419087 0.576823i
\(630\) 247.936 185.875i 0.393549 0.295040i
\(631\) 620.336 + 450.700i 0.983099 + 0.714263i 0.958399 0.285431i \(-0.0921369\pi\)
0.0247001 + 0.999695i \(0.492137\pi\)
\(632\) −478.837 + 478.837i −0.757653 + 0.757653i
\(633\) −175.577 1108.55i −0.277373 1.75126i
\(634\) −333.695 108.424i −0.526332 0.171016i
\(635\) −20.1928 + 3.50915i −0.0317997 + 0.00552622i
\(636\) 12.0822 + 37.1853i 0.0189972 + 0.0584674i
\(637\) 304.668 + 597.945i 0.478286 + 0.938689i
\(638\) 187.473 95.5224i 0.293845 0.149722i
\(639\) −80.9777 + 26.3112i −0.126726 + 0.0411757i
\(640\) 373.730 197.533i 0.583953 0.308646i
\(641\) 8.23463 25.3436i 0.0128465 0.0395376i −0.944428 0.328719i \(-0.893383\pi\)
0.957274 + 0.289181i \(0.0933831\pi\)
\(642\) −308.105 + 48.7991i −0.479915 + 0.0760111i
\(643\) 16.0826 + 16.0826i 0.0250118 + 0.0250118i 0.719502 0.694490i \(-0.244370\pi\)
−0.694490 + 0.719502i \(0.744370\pi\)
\(644\) 16.3032 22.4395i 0.0253156 0.0348439i
\(645\) −317.756 98.0062i −0.492645 0.151948i
\(646\) 108.720 78.9895i 0.168297 0.122275i
\(647\) −79.1197 + 499.542i −0.122287 + 0.772090i 0.847976 + 0.530035i \(0.177821\pi\)
−0.970263 + 0.242054i \(0.922179\pi\)
\(648\) 383.670 752.995i 0.592083 1.16203i
\(649\) 247.058i 0.380675i
\(650\) 105.442 360.982i 0.162218 0.555357i
\(651\) −1918.14 −2.94646
\(652\) 111.558 + 56.8419i 0.171102 + 0.0871808i
\(653\) 1110.46 + 175.880i 1.70055 + 0.269341i 0.929873 0.367881i \(-0.119917\pi\)
0.770680 + 0.637222i \(0.219917\pi\)
\(654\) 262.292 + 361.014i 0.401058 + 0.552009i
\(655\) 446.857 6.69633i 0.682225 0.0102234i
\(656\) −358.031 260.125i −0.545779 0.396531i
\(657\) −90.5672 + 90.5672i −0.137850 + 0.137850i
\(658\) 185.249 + 1169.62i 0.281534 + 1.77754i
\(659\) 837.920 + 272.257i 1.27150 + 0.413136i 0.865580 0.500771i \(-0.166950\pi\)
0.405923 + 0.913907i \(0.366950\pi\)
\(660\) −8.00835 + 55.9791i −0.0121339 + 0.0848169i
\(661\) −406.010 1249.57i −0.614235 1.89042i −0.412401 0.911002i \(-0.635310\pi\)
−0.201834 0.979420i \(-0.564690\pi\)
\(662\) 225.237 + 442.052i 0.340237 + 0.667752i
\(663\) −426.239 + 217.180i −0.642894 + 0.327571i
\(664\) 503.329 163.541i 0.758025 0.246297i
\(665\) −181.488 176.129i −0.272914 0.264855i
\(666\) −45.1558 + 138.975i −0.0678015 + 0.208671i
\(667\) −85.2129 + 13.4964i −0.127756 + 0.0202345i
\(668\) −16.0281 16.0281i −0.0239941 0.0239941i
\(669\) 76.3738 105.120i 0.114161 0.157129i
\(670\) −32.5841 + 11.1297i −0.0486330 + 0.0166115i
\(671\) 306.909 222.983i 0.457391 0.332314i
\(672\) −68.4258 + 432.024i −0.101824 + 0.642893i
\(673\) −533.613 + 1047.27i −0.792887 + 1.55613i 0.0377336 + 0.999288i \(0.487986\pi\)
−0.830620 + 0.556840i \(0.812014\pi\)
\(674\) 1034.48i 1.53483i
\(675\) −356.595 + 378.636i −0.528290 + 0.560942i
\(676\) 70.3775 0.104109
\(677\) −1025.90 522.720i −1.51536 0.772112i −0.518789 0.854902i \(-0.673617\pi\)
−0.996567 + 0.0827899i \(0.973617\pi\)
\(678\) −694.942 110.068i −1.02499 0.162342i
\(679\) −977.170 1344.96i −1.43913 1.98079i
\(680\) 582.312 + 409.886i 0.856342 + 0.602773i
\(681\) −817.042 593.616i −1.19977 0.871683i
\(682\) −290.699 + 290.699i −0.426245 + 0.426245i
\(683\) 99.8898 + 630.679i 0.146252 + 0.923396i 0.946260 + 0.323407i \(0.104828\pi\)
−0.800008 + 0.599989i \(0.795172\pi\)
\(684\) 8.84724 + 2.87464i 0.0129346 + 0.00420269i
\(685\) 359.406 + 176.394i 0.524680 + 0.257509i
\(686\) −205.013 630.965i −0.298853 0.919775i
\(687\) 550.418 + 1080.26i 0.801191 + 1.57243i
\(688\) −217.404 + 110.773i −0.315995 + 0.161007i
\(689\) 126.881 41.2261i 0.184152 0.0598347i
\(690\) −48.0873 + 97.9789i −0.0696918 + 0.141998i
\(691\) −230.779 + 710.264i −0.333978 + 1.02788i 0.633245 + 0.773951i \(0.281723\pi\)
−0.967223 + 0.253928i \(0.918277\pi\)
\(692\) −109.012 + 17.2658i −0.157532 + 0.0249506i
\(693\) 112.423 + 112.423i 0.162227 + 0.162227i
\(694\) 357.066 491.460i 0.514505 0.708155i
\(695\) −104.784 + 148.864i −0.150769 + 0.214193i
\(696\) 594.692 432.069i 0.854443 0.620789i
\(697\) 90.8888 573.849i 0.130400 0.823313i
\(698\) 414.746 813.985i 0.594192 1.16617i
\(699\) 274.189i 0.392259i
\(700\) 85.3363 180.670i 0.121909 0.258100i
\(701\) 1200.51 1.71256 0.856282 0.516508i \(-0.172768\pi\)
0.856282 + 0.516508i \(0.172768\pi\)
\(702\) −278.849 142.081i −0.397222 0.202394i
\(703\) 117.792 + 18.6565i 0.167557 + 0.0265383i
\(704\) 194.296 + 267.425i 0.275988 + 0.379866i
\(705\) 319.990 + 936.827i 0.453887 + 1.32883i
\(706\) −258.094 187.516i −0.365573 0.265604i
\(707\) 924.544 924.544i 1.30770 1.30770i
\(708\) −20.1316 127.106i −0.0284345 0.179528i
\(709\) −428.385 139.191i −0.604210 0.196320i −0.00909262 0.999959i \(-0.502894\pi\)
−0.595117 + 0.803639i \(0.702894\pi\)
\(710\) 179.976 185.452i 0.253487 0.261199i
\(711\) 73.3329 + 225.696i 0.103141 + 0.317434i
\(712\) 370.913 + 727.957i 0.520945 + 1.02241i
\(713\) 150.199 76.5302i 0.210658 0.107335i
\(714\) 1137.82 369.701i 1.59359 0.517788i
\(715\) 191.008 + 27.3255i 0.267144 + 0.0382175i
\(716\) 6.84110 21.0547i 0.00955460 0.0294060i
\(717\) −1350.58 + 213.911i −1.88365 + 0.298341i
\(718\) 175.194 + 175.194i 0.244002 + 0.244002i
\(719\) 571.568 786.696i 0.794949 1.09415i −0.198526 0.980096i \(-0.563615\pi\)
0.993474 0.114057i \(-0.0363847\pi\)
\(720\) −2.84815 190.062i −0.00395576 0.263975i
\(721\) 1471.57 1069.16i 2.04101 1.48288i
\(722\) 96.9837 612.331i 0.134326 0.848104i
\(723\) −49.2361 + 96.6314i −0.0680998 + 0.133653i
\(724\) 15.1813i 0.0209686i
\(725\) −585.068 + 209.682i −0.806991 + 0.289216i
\(726\) −624.515 −0.860214
\(727\) −247.938 126.331i −0.341043 0.173770i 0.275077 0.961422i \(-0.411297\pi\)
−0.616120 + 0.787652i \(0.711297\pi\)
\(728\) 796.433 + 126.143i 1.09400 + 0.173273i
\(729\) 207.054 + 284.985i 0.284024 + 0.390926i
\(730\) 114.575 371.474i 0.156952 0.508869i
\(731\) −259.155 188.287i −0.354522 0.257575i
\(732\) 139.728 139.728i 0.190886 0.190886i
\(733\) 17.0101 + 107.397i 0.0232061 + 0.146518i 0.996571 0.0827448i \(-0.0263686\pi\)
−0.973365 + 0.229262i \(0.926369\pi\)
\(734\) −577.937 187.783i −0.787380 0.255835i
\(735\) −655.632 1240.44i −0.892016 1.68768i
\(736\) −11.8789 36.5594i −0.0161398 0.0496731i
\(737\) −8.02048 15.7411i −0.0108826 0.0213583i
\(738\) −168.676 + 85.9448i −0.228559 + 0.116456i
\(739\) 1097.79 356.694i 1.48551 0.482671i 0.549755 0.835326i \(-0.314721\pi\)
0.935754 + 0.352654i \(0.114721\pi\)
\(740\) 16.1327 + 92.8327i 0.0218009 + 0.125450i
\(741\) 39.3111 120.987i 0.0530515 0.163276i
\(742\) −329.538 + 52.1937i −0.444121 + 0.0703419i
\(743\) −8.69864 8.69864i −0.0117075 0.0117075i 0.701229 0.712936i \(-0.252635\pi\)
−0.712936 + 0.701229i \(0.752635\pi\)
\(744\) −844.216 + 1161.96i −1.13470 + 1.56178i
\(745\) 403.544 + 538.280i 0.541669 + 0.722524i
\(746\) 271.091 196.959i 0.363393 0.264020i
\(747\) 29.0130 183.181i 0.0388393 0.245222i
\(748\) −24.7314 + 48.5380i −0.0330633 + 0.0648904i
\(749\) 565.530i 0.755047i
\(750\) −209.115 + 757.926i −0.278820 + 1.01057i
\(751\) −452.240 −0.602183 −0.301092 0.953595i \(-0.597351\pi\)
−0.301092 + 0.953595i \(0.597351\pi\)
\(752\) 647.237 + 329.784i 0.860688 + 0.438542i
\(753\) −532.527 84.3439i −0.707207 0.112011i
\(754\) −219.811 302.544i −0.291527 0.401252i
\(755\) 16.1549 12.1112i 0.0213972 0.0160413i
\(756\) −134.523 97.7370i −0.177941 0.129282i
\(757\) −706.820 + 706.820i −0.933712 + 0.933712i −0.997936 0.0642239i \(-0.979543\pi\)
0.0642239 + 0.997936i \(0.479543\pi\)
\(758\) −69.2411 437.171i −0.0913471 0.576743i
\(759\) −53.2585 17.3047i −0.0701693 0.0227994i
\(760\) −186.571 + 32.4228i −0.245488 + 0.0426615i
\(761\) 449.482 + 1383.36i 0.590646 + 1.81782i 0.575303 + 0.817941i \(0.304884\pi\)
0.0153439 + 0.999882i \(0.495116\pi\)
\(762\) 11.7053 + 22.9729i 0.0153613 + 0.0301482i
\(763\) 720.814 367.273i 0.944710 0.481354i
\(764\) −73.6625 + 23.9344i −0.0964169 + 0.0313278i
\(765\) 220.629 116.612i 0.288403 0.152435i
\(766\) −362.827 + 1116.67i −0.473665 + 1.45779i
\(767\) −433.702 + 68.6917i −0.565453 + 0.0895590i
\(768\) 318.816 + 318.816i 0.415125 + 0.415125i
\(769\) −181.101 + 249.264i −0.235502 + 0.324141i −0.910368 0.413800i \(-0.864201\pi\)
0.674866 + 0.737940i \(0.264201\pi\)
\(770\) −461.119 142.224i −0.598856 0.184707i
\(771\) −197.507 + 143.497i −0.256170 + 0.186118i
\(772\) 31.4581 198.619i 0.0407489 0.257278i
\(773\) −1.75392 + 3.44225i −0.00226897 + 0.00445311i −0.892138 0.451763i \(-0.850795\pi\)
0.889869 + 0.456216i \(0.150795\pi\)
\(774\) 104.375i 0.134852i
\(775\) 960.608 742.899i 1.23949 0.958580i
\(776\) −1244.82 −1.60415
\(777\) 946.008 + 482.015i 1.21751 + 0.620354i
\(778\) −1317.90 208.735i −1.69396 0.268297i
\(779\) 90.8150 + 124.996i 0.116579 + 0.160457i
\(780\) 100.496 1.50597i 0.128841 0.00193074i
\(781\) 107.270 + 77.9361i 0.137349 + 0.0997902i
\(782\) −74.3461 + 74.3461i −0.0950717 + 0.0950717i
\(783\) 80.9101 + 510.846i 0.103333 + 0.652422i
\(784\) −979.131 318.139i −1.24889 0.405789i
\(785\) 110.590 773.037i 0.140879 0.984760i
\(786\) −173.731 534.689i −0.221032 0.680266i
\(787\) 60.1800 + 118.110i 0.0764676 + 0.150076i 0.926075 0.377340i \(-0.123161\pi\)
−0.849607 + 0.527416i \(0.823161\pi\)
\(788\) −73.7433 + 37.5741i −0.0935829 + 0.0476829i
\(789\) −1548.99 + 503.296i −1.96323 + 0.637891i
\(790\) −516.878 501.616i −0.654276 0.634956i
\(791\) −394.174 + 1213.14i −0.498323 + 1.53368i
\(792\) 117.583 18.6233i 0.148464 0.0235143i
\(793\) −476.771 476.771i −0.601225 0.601225i
\(794\) −200.448 + 275.894i −0.252454 + 0.347473i
\(795\) −263.949 + 90.1567i −0.332012 + 0.113405i
\(796\) −172.614 + 125.412i −0.216852 + 0.157552i
\(797\) 149.295 942.614i 0.187322 1.18270i −0.697435 0.716648i \(-0.745675\pi\)
0.884756 0.466054i \(-0.154325\pi\)
\(798\) −144.436 + 283.472i −0.180998 + 0.355228i
\(799\) 953.669i 1.19358i
\(800\) −133.056 242.859i −0.166320 0.303574i
\(801\) 286.312 0.357443
\(802\) −142.984 72.8539i −0.178284 0.0908402i
\(803\) 197.000 + 31.2018i 0.245331 + 0.0388565i
\(804\) −5.40903 7.44490i −0.00672765 0.00925982i
\(805\) 161.802 + 113.892i 0.200997 + 0.141480i
\(806\) 591.139 + 429.487i 0.733423 + 0.532863i
\(807\) 912.465 912.465i 1.13069 1.13069i
\(808\) −153.154 966.978i −0.189547 1.19676i
\(809\) 1278.62 + 415.449i 1.58049 + 0.513534i 0.962184 0.272400i \(-0.0878175\pi\)
0.618310 + 0.785934i \(0.287818\pi\)
\(810\) 806.931 + 396.036i 0.996211 + 0.488933i
\(811\) 168.798 + 519.506i 0.208135 + 0.640574i 0.999570 + 0.0293206i \(0.00933438\pi\)
−0.791435 + 0.611253i \(0.790666\pi\)
\(812\) −90.2047 177.037i −0.111090 0.218025i
\(813\) 1029.32 524.463i 1.26607 0.645095i
\(814\) 216.421 70.3193i 0.265873 0.0863873i
\(815\) −393.526 + 801.817i −0.482854 + 0.983825i
\(816\) 226.782 697.963i 0.277919 0.855347i
\(817\) 84.1363 13.3259i 0.102982 0.0163108i
\(818\) 232.805 + 232.805i 0.284603 + 0.284603i
\(819\) 166.097 228.613i 0.202805 0.279137i
\(820\) −70.2623 + 99.8195i −0.0856857 + 0.121731i
\(821\) 124.274 90.2905i 0.151369 0.109976i −0.509523 0.860457i \(-0.670178\pi\)
0.660892 + 0.750481i \(0.270178\pi\)
\(822\) 78.7880 497.448i 0.0958491 0.605168i
\(823\) −112.681 + 221.149i −0.136915 + 0.268711i −0.949276 0.314444i \(-0.898182\pi\)
0.812361 + 0.583155i \(0.198182\pi\)
\(824\) 1362.00i 1.65291i
\(825\) −400.153 51.1396i −0.485033 0.0619873i
\(826\) 1098.17 1.32950
\(827\) 8.58569 + 4.37463i 0.0103817 + 0.00528976i 0.459174 0.888347i \(-0.348146\pi\)
−0.448792 + 0.893636i \(0.648146\pi\)
\(828\) −7.18859 1.13856i −0.00868187 0.00137507i
\(829\) −360.443 496.107i −0.434792 0.598440i 0.534253 0.845325i \(-0.320593\pi\)
−0.969045 + 0.246885i \(0.920593\pi\)
\(830\) 181.949 + 532.688i 0.219216 + 0.641793i
\(831\) 803.400 + 583.704i 0.966787 + 0.702412i
\(832\) 415.435 415.435i 0.499320 0.499320i
\(833\) −211.437 1334.96i −0.253826 1.60260i
\(834\) 217.802 + 70.7682i 0.261153 + 0.0848539i
\(835\) 112.614 116.041i 0.134867 0.138971i
\(836\) −4.47656 13.7774i −0.00535474 0.0164802i
\(837\) −458.794 900.434i −0.548141 1.07579i
\(838\) −312.279 + 159.114i −0.372647 + 0.189873i
\(839\) −1114.35 + 362.075i −1.32819 + 0.431555i −0.885300 0.465021i \(-0.846047\pi\)
−0.442890 + 0.896576i \(0.646047\pi\)
\(840\) −1668.87 238.748i −1.98675 0.284224i
\(841\) 68.9002 212.053i 0.0819265 0.252144i
\(842\) 1463.02 231.719i 1.73755 0.275201i
\(843\) −491.835 491.835i −0.583435 0.583435i
\(844\) −133.523 + 183.779i −0.158203 + 0.217747i
\(845\) 7.52266 + 501.999i 0.00890256 + 0.594082i
\(846\) 251.391 182.647i 0.297153 0.215894i
\(847\) −177.114 + 1118.25i −0.209107 + 1.32025i
\(848\) −92.9160 + 182.358i −0.109571 + 0.215045i
\(849\) 563.213i 0.663384i
\(850\) −426.637 + 625.826i −0.501925 + 0.736266i
\(851\) −93.3081 −0.109645
\(852\) 61.5387 + 31.3556i 0.0722286 + 0.0368023i
\(853\) −488.140 77.3137i −0.572262 0.0906374i −0.136405 0.990653i \(-0.543555\pi\)
−0.435857 + 0.900016i \(0.643555\pi\)
\(854\) 991.150 + 1364.20i 1.16060 + 1.59742i
\(855\) −19.5590 + 63.4142i −0.0228760 + 0.0741687i
\(856\) 342.584 + 248.902i 0.400216 + 0.290774i
\(857\) −127.840 + 127.840i −0.149171 + 0.149171i −0.777748 0.628577i \(-0.783638\pi\)
0.628577 + 0.777748i \(0.283638\pi\)
\(858\) −37.9718 239.744i −0.0442562 0.279422i
\(859\) −242.766 78.8793i −0.282614 0.0918269i 0.164280 0.986414i \(-0.447470\pi\)
−0.446894 + 0.894587i \(0.647470\pi\)
\(860\) 31.4496 + 59.5021i 0.0365693 + 0.0691884i
\(861\) 425.048 + 1308.16i 0.493668 + 1.51935i
\(862\) 203.625 + 399.636i 0.236224 + 0.463615i
\(863\) −725.309 + 369.564i −0.840451 + 0.428231i −0.820553 0.571571i \(-0.806334\pi\)
−0.0198983 + 0.999802i \(0.506334\pi\)
\(864\) −219.172 + 71.2132i −0.253671 + 0.0824226i
\(865\) −134.808 775.732i −0.155848 0.896800i
\(866\) 433.170 1333.16i 0.500196 1.53944i
\(867\) −36.8646 + 5.83878i −0.0425198 + 0.00673447i
\(868\) 274.516 + 274.516i 0.316263 + 0.316263i
\(869\) 217.218 298.975i 0.249964 0.344045i
\(870\) 468.987 + 625.574i 0.539065 + 0.719051i
\(871\) −25.4029 + 18.4563i −0.0291652 + 0.0211898i
\(872\) 94.7609 598.297i 0.108671 0.686120i
\(873\) −198.046 + 388.688i −0.226857 + 0.445232i
\(874\) 27.9598i 0.0319906i
\(875\) 1297.83 + 589.388i 1.48323 + 0.673587i
\(876\) 103.895 0.118602
\(877\) 1141.28 + 581.509i 1.30134 + 0.663067i 0.960821 0.277170i \(-0.0893967\pi\)
0.340521 + 0.940237i \(0.389397\pi\)
\(878\) 32.0033 + 5.06882i 0.0364502 + 0.00577315i
\(879\) −775.599 1067.52i −0.882365 1.21447i
\(880\) −236.842 + 177.558i −0.269139 + 0.201771i
\(881\) −1038.70 754.660i −1.17900 0.856595i −0.186943 0.982371i \(-0.559858\pi\)
−0.992059 + 0.125776i \(0.959858\pi\)
\(882\) −311.408 + 311.408i −0.353070 + 0.353070i
\(883\) −101.079 638.190i −0.114473 0.722752i −0.976440 0.215788i \(-0.930768\pi\)
0.861968 0.506963i \(-0.169232\pi\)
\(884\) 92.0832 + 29.9197i 0.104167 + 0.0338458i
\(885\) 904.491 157.184i 1.02202 0.177610i
\(886\) −146.700 451.497i −0.165576 0.509590i
\(887\) 8.37810 + 16.4430i 0.00944544 + 0.0185377i 0.895681 0.444697i \(-0.146689\pi\)
−0.886236 + 0.463235i \(0.846689\pi\)
\(888\) 708.352 360.923i 0.797694 0.406445i
\(889\) 44.4547 14.4442i 0.0500053 0.0162477i
\(890\) −768.277 + 406.070i −0.863233 + 0.456259i
\(891\) −142.518 + 438.624i −0.159953 + 0.492283i
\(892\) −25.9745 + 4.11396i −0.0291194 + 0.00461207i
\(893\) −179.326 179.326i −0.200813 0.200813i
\(894\) 497.451 684.683i 0.556433 0.765865i
\(895\) 150.914 + 46.5467i 0.168619 + 0.0520075i
\(896\) −779.949 + 566.666i −0.870478 + 0.632440i
\(897\) −15.5700 + 98.3050i −0.0173578 + 0.109593i
\(898\) 219.626 431.041i 0.244573 0.480001i
\(899\) 1207.57i 1.34324i
\(900\) −52.4070 + 1.57103i −0.0582300 + 0.00174559i
\(901\) −268.695 −0.298218
\(902\) 262.673 + 133.838i 0.291211 + 0.148380i
\(903\) 749.033 + 118.635i 0.829493 + 0.131379i
\(904\) 561.407 + 772.711i 0.621026 + 0.854769i
\(905\) −108.287 + 1.62273i −0.119655 + 0.00179307i
\(906\) −20.5488 14.9295i −0.0226807 0.0164785i
\(907\) −17.1888 + 17.1888i −0.0189512 + 0.0189512i −0.716519 0.697568i \(-0.754266\pi\)
0.697568 + 0.716519i \(0.254266\pi\)
\(908\) 31.9758 + 201.887i 0.0352156 + 0.222343i
\(909\) −326.300 106.021i −0.358966 0.116635i
\(910\) −121.461 + 849.024i −0.133474 + 0.932993i
\(911\) −541.240 1665.77i −0.594116 1.82850i −0.559077 0.829116i \(-0.688844\pi\)
−0.0350398 0.999386i \(-0.511156\pi\)
\(912\) 88.6000 + 173.887i 0.0971492 + 0.190666i
\(913\) −257.337 + 131.120i −0.281858 + 0.143614i
\(914\) −1156.29 + 375.700i −1.26508 + 0.411051i
\(915\) 1011.61 + 981.741i 1.10559 + 1.07294i
\(916\) 75.8281 233.375i 0.0827818 0.254776i
\(917\) −1006.68 + 159.442i −1.09780 + 0.173874i
\(918\) 445.700 + 445.700i 0.485512 + 0.485512i
\(919\) −374.893 + 515.995i −0.407935 + 0.561475i −0.962713 0.270524i \(-0.912803\pi\)
0.554778 + 0.831998i \(0.312803\pi\)
\(920\) 140.206 47.8898i 0.152397 0.0520541i
\(921\) 61.5281 44.7028i 0.0668058 0.0485372i
\(922\) 13.3034 83.9941i 0.0144288 0.0910999i
\(923\) 106.989 209.978i 0.115915 0.227495i
\(924\) 128.967i 0.139575i
\(925\) −660.447 + 124.997i −0.713997 + 0.135131i
\(926\) −629.218 −0.679501
\(927\) −425.277 216.689i −0.458767 0.233753i
\(928\) −271.982 43.0777i −0.293084 0.0464199i
\(929\) 394.294 + 542.700i 0.424429 + 0.584176i 0.966663 0.256051i \(-0.0824215\pi\)
−0.542234 + 0.840227i \(0.682422\pi\)
\(930\) −1249.21 879.313i −1.34324 0.945498i
\(931\) 290.782 + 211.266i 0.312333 + 0.226923i
\(932\) −39.2408 + 39.2408i −0.0421038 + 0.0421038i
\(933\) 234.155 + 1478.40i 0.250970 + 1.58456i
\(934\) 186.226 + 60.5086i 0.199386 + 0.0647844i
\(935\) −348.863 171.220i −0.373116 0.183122i
\(936\) −65.3853 201.235i −0.0698561 0.214995i
\(937\) 58.1616 + 114.149i 0.0620721 + 0.121823i 0.919958 0.392017i \(-0.128222\pi\)
−0.857886 + 0.513840i \(0.828222\pi\)
\(938\) 69.9685 35.6507i 0.0745933 0.0380072i
\(939\) 309.793 100.658i 0.329918 0.107197i
\(940\) 88.2790 179.870i 0.0939138 0.191351i
\(941\) −46.4634 + 143.000i −0.0493766 + 0.151966i −0.972705 0.232046i \(-0.925458\pi\)
0.923328 + 0.384012i \(0.125458\pi\)
\(942\) −970.280 + 153.677i −1.03002 + 0.163139i
\(943\) −85.4764 85.4764i −0.0906431 0.0906431i
\(944\) 395.954 544.984i 0.419443 0.577313i
\(945\) 682.774 969.996i 0.722512 1.02645i
\(946\) 131.497 95.5383i 0.139003 0.100992i
\(947\) −238.481 + 1505.71i −0.251828 + 1.58998i 0.460191 + 0.887820i \(0.347781\pi\)
−0.712019 + 0.702160i \(0.752219\pi\)
\(948\) 87.3921 171.517i 0.0921858 0.180925i
\(949\) 354.503i 0.373554i
\(950\) −37.4553 197.903i −0.0394266 0.208319i
\(951\) 668.951 0.703419
\(952\) −1447.04 737.302i −1.52000 0.774477i
\(953\) −608.849 96.4322i −0.638876 0.101188i −0.171411 0.985200i \(-0.554833\pi\)
−0.467465 + 0.884012i \(0.654833\pi\)
\(954\) 51.4604 + 70.8291i 0.0539417 + 0.0742443i
\(955\) −178.597 522.873i −0.187012 0.547511i
\(956\) 223.903 + 162.675i 0.234208 + 0.170162i
\(957\) −283.658 + 283.658i −0.296403 + 0.296403i
\(958\) 103.585 + 654.012i 0.108127 + 0.682685i
\(959\) −868.381 282.154i −0.905506 0.294217i
\(960\) −855.440 + 881.468i −0.891083 + 0.918196i
\(961\) 432.150 + 1330.02i 0.449688 + 1.38400i
\(962\) −183.616 360.368i −0.190870 0.374603i
\(963\) 132.222 67.3707i 0.137303 0.0699592i
\(964\) 20.8759 6.78300i 0.0216555 0.00703630i
\(965\) 1420.10 + 203.159i 1.47161 + 0.210527i
\(966\) 76.9190 236.732i 0.0796263 0.245065i
\(967\) −136.090 + 21.5545i −0.140734 + 0.0222901i −0.226404 0.974033i \(-0.572697\pi\)
0.0856700 + 0.996324i \(0.472697\pi\)
\(968\) 599.458 + 599.458i 0.619275 + 0.619275i
\(969\) −150.599 + 207.281i −0.155416 + 0.213912i
\(970\) −19.8388 1323.87i −0.0204524 1.36482i
\(971\) 596.601 433.456i 0.614419 0.446401i −0.236549 0.971620i \(-0.576016\pi\)
0.850968 + 0.525218i \(0.176016\pi\)
\(972\) −17.0507 + 107.654i −0.0175419 + 0.110755i
\(973\) 188.486 369.924i 0.193716 0.380189i
\(974\) 687.587i 0.705942i
\(975\) 21.4841 + 716.674i 0.0220350 + 0.735050i
\(976\) 1034.38 1.05981
\(977\) 443.170 + 225.806i 0.453603 + 0.231122i 0.665838 0.746096i \(-0.268074\pi\)
−0.212235 + 0.977219i \(0.568074\pi\)
\(978\) 1109.78 + 175.772i 1.13475 + 0.179726i
\(979\) −262.071 360.710i −0.267693 0.368447i
\(980\) −83.6956 + 271.358i −0.0854037 + 0.276896i
\(981\) −171.739 124.776i −0.175065 0.127192i
\(982\) 336.216 336.216i 0.342379 0.342379i
\(983\) 117.421 + 741.369i 0.119452 + 0.754190i 0.972594 + 0.232511i \(0.0746942\pi\)
−0.853142 + 0.521679i \(0.825306\pi\)
\(984\) 979.527 + 318.268i 0.995455 + 0.323443i
\(985\) −275.897 521.992i −0.280098 0.529941i
\(986\) 232.746 + 716.319i 0.236051 + 0.726490i
\(987\) −1025.00 2011.67i −1.03850 2.03817i
\(988\) −22.9412 + 11.6891i −0.0232198 + 0.0118311i
\(989\) −63.3859 + 20.5953i −0.0640909 + 0.0208244i
\(990\) 21.6800 + 124.754i 0.0218990 + 0.126014i
\(991\) −40.9055 + 125.894i −0.0412770 + 0.127038i −0.969572 0.244808i \(-0.921275\pi\)
0.928294 + 0.371846i \(0.121275\pi\)
\(992\) 531.423 84.1692i 0.535709 0.0848480i
\(993\) −668.850 668.850i −0.673565 0.673565i
\(994\) −346.424 + 476.811i −0.348515 + 0.479689i
\(995\) −913.006 1217.84i −0.917594 1.22396i
\(996\) −121.710 + 88.4274i −0.122199 + 0.0887825i
\(997\) −78.2443 + 494.015i −0.0784797 + 0.495501i 0.916871 + 0.399184i \(0.130706\pi\)
−0.995351 + 0.0963177i \(0.969294\pi\)
\(998\) −62.0230 + 121.727i −0.0621473 + 0.121971i
\(999\) 559.376i 0.559936i
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 25.3.f.a.8.2 32
3.2 odd 2 225.3.r.a.208.3 32
4.3 odd 2 400.3.bg.c.33.1 32
5.2 odd 4 125.3.f.a.107.3 32
5.3 odd 4 125.3.f.b.107.2 32
5.4 even 2 125.3.f.c.18.3 32
25.3 odd 20 125.3.f.c.7.3 32
25.4 even 10 125.3.f.b.118.2 32
25.21 even 5 125.3.f.a.118.3 32
25.22 odd 20 inner 25.3.f.a.22.2 yes 32
75.47 even 20 225.3.r.a.172.3 32
100.47 even 20 400.3.bg.c.97.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.8.2 32 1.1 even 1 trivial
25.3.f.a.22.2 yes 32 25.22 odd 20 inner
125.3.f.a.107.3 32 5.2 odd 4
125.3.f.a.118.3 32 25.21 even 5
125.3.f.b.107.2 32 5.3 odd 4
125.3.f.b.118.2 32 25.4 even 10
125.3.f.c.7.3 32 25.3 odd 20
125.3.f.c.18.3 32 5.4 even 2
225.3.r.a.172.3 32 75.47 even 20
225.3.r.a.208.3 32 3.2 odd 2
400.3.bg.c.33.1 32 4.3 odd 2
400.3.bg.c.97.1 32 100.47 even 20