Properties

Label 25.3.f.a.8.1
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 8.1
Character \(\chi\) \(=\) 25.8
Dual form 25.3.f.a.22.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.38234 - 1.21387i) q^{2} +(-3.57679 - 0.566508i) q^{3} +(1.85096 + 2.54762i) q^{4} +(-4.45026 - 2.27929i) q^{5} +(7.83348 + 5.69136i) q^{6} +(6.54971 - 6.54971i) q^{7} +(0.355933 + 2.24727i) q^{8} +(3.91299 + 1.27141i) q^{9} +O(q^{10})\) \(q+(-2.38234 - 1.21387i) q^{2} +(-3.57679 - 0.566508i) q^{3} +(1.85096 + 2.54762i) q^{4} +(-4.45026 - 2.27929i) q^{5} +(7.83348 + 5.69136i) q^{6} +(6.54971 - 6.54971i) q^{7} +(0.355933 + 2.24727i) q^{8} +(3.91299 + 1.27141i) q^{9} +(7.83532 + 10.8321i) q^{10} +(-3.18653 - 9.80714i) q^{11} +(-5.17723 - 10.1609i) q^{12} +(-11.3286 + 5.77220i) q^{13} +(-23.5541 + 7.65321i) q^{14} +(14.6264 + 10.6736i) q^{15} +(5.77235 - 17.7655i) q^{16} +(0.578287 - 0.0915916i) q^{17} +(-7.77878 - 7.77878i) q^{18} +(1.57500 - 2.16781i) q^{19} +(-2.43048 - 15.5565i) q^{20} +(-27.1374 + 19.7165i) q^{21} +(-4.31313 + 27.2320i) q^{22} +(16.5548 - 32.4907i) q^{23} -8.23965i q^{24} +(14.6097 + 20.2869i) q^{25} +33.9953 q^{26} +(15.7643 + 8.03233i) q^{27} +(28.8094 + 4.56297i) q^{28} +(9.15785 + 12.6047i) q^{29} +(-21.8888 - 43.1828i) q^{30} +(-15.1042 - 10.9739i) q^{31} +(-28.8811 + 28.8811i) q^{32} +(5.84174 + 36.8833i) q^{33} +(-1.48886 - 0.483759i) q^{34} +(-44.0766 + 14.2193i) q^{35} +(4.00371 + 12.3221i) q^{36} +(-26.1444 - 51.3113i) q^{37} +(-6.38363 + 3.25262i) q^{38} +(43.7900 - 14.2282i) q^{39} +(3.53818 - 10.8122i) q^{40} +(0.808618 - 2.48867i) q^{41} +(88.5838 - 14.0303i) q^{42} +(-7.76543 - 7.76543i) q^{43} +(19.0868 - 26.2707i) q^{44} +(-14.5159 - 14.5769i) q^{45} +(-78.8786 + 57.3086i) q^{46} +(-6.13916 + 38.7611i) q^{47} +(-30.7108 + 60.2733i) q^{48} -36.7975i q^{49} +(-10.1799 - 66.0645i) q^{50} -2.12030 q^{51} +(-35.6741 - 18.1769i) q^{52} +(39.0747 + 6.18882i) q^{53} +(-27.8059 - 38.2716i) q^{54} +(-8.17236 + 50.9074i) q^{55} +(17.0502 + 12.3877i) q^{56} +(-6.86154 + 6.86154i) q^{57} +(-6.51675 - 41.1452i) q^{58} +(0.494461 + 0.160660i) q^{59} +(-0.119521 + 57.0191i) q^{60} +(7.44472 + 22.9125i) q^{61} +(22.6627 + 44.4780i) q^{62} +(33.9563 - 17.3016i) q^{63} +(32.8008 - 10.6576i) q^{64} +(63.5717 + 0.133256i) q^{65} +(30.8543 - 94.9598i) q^{66} +(6.71462 - 1.06349i) q^{67} +(1.30372 + 1.30372i) q^{68} +(-77.6194 + 106.834i) q^{69} +(122.266 + 19.6278i) q^{70} +(80.2586 - 58.3113i) q^{71} +(-1.46444 + 9.24608i) q^{72} +(27.3185 - 53.6155i) q^{73} +153.977i q^{74} +(-40.7632 - 80.8383i) q^{75} +8.43802 q^{76} +(-85.1048 - 43.3631i) q^{77} +(-121.594 - 19.2586i) q^{78} +(2.28841 + 3.14973i) q^{79} +(-66.1811 + 65.9042i) q^{80} +(-81.7927 - 59.4258i) q^{81} +(-4.94732 + 4.94732i) q^{82} +(-10.3587 - 65.4021i) q^{83} +(-100.460 - 32.6415i) q^{84} +(-2.78229 - 0.910474i) q^{85} +(9.07375 + 27.9261i) q^{86} +(-25.6151 - 50.2724i) q^{87} +(20.9051 - 10.6517i) q^{88} +(-49.5405 + 16.0967i) q^{89} +(16.8876 + 52.3477i) q^{90} +(-36.3927 + 112.005i) q^{91} +(113.416 - 17.9634i) q^{92} +(47.8078 + 47.8078i) q^{93} +(61.6764 - 84.8903i) q^{94} +(-11.9502 + 6.05743i) q^{95} +(119.663 - 86.9404i) q^{96} +(0.610311 - 3.85335i) q^{97} +(-44.6672 + 87.6643i) q^{98} -42.4266i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38234 1.21387i −1.19117 0.606933i −0.257924 0.966165i \(-0.583039\pi\)
−0.933248 + 0.359233i \(0.883039\pi\)
\(3\) −3.57679 0.566508i −1.19226 0.188836i −0.471404 0.881917i \(-0.656253\pi\)
−0.720859 + 0.693081i \(0.756253\pi\)
\(4\) 1.85096 + 2.54762i 0.462739 + 0.636906i
\(5\) −4.45026 2.27929i −0.890053 0.455857i
\(6\) 7.83348 + 5.69136i 1.30558 + 0.948560i
\(7\) 6.54971 6.54971i 0.935673 0.935673i −0.0623792 0.998053i \(-0.519869\pi\)
0.998053 + 0.0623792i \(0.0198688\pi\)
\(8\) 0.355933 + 2.24727i 0.0444916 + 0.280909i
\(9\) 3.91299 + 1.27141i 0.434777 + 0.141268i
\(10\) 7.83532 + 10.8321i 0.783532 + 1.08321i
\(11\) −3.18653 9.80714i −0.289685 0.891558i −0.984955 0.172810i \(-0.944715\pi\)
0.695270 0.718748i \(-0.255285\pi\)
\(12\) −5.17723 10.1609i −0.431436 0.846741i
\(13\) −11.3286 + 5.77220i −0.871430 + 0.444016i −0.831720 0.555195i \(-0.812643\pi\)
−0.0397101 + 0.999211i \(0.512643\pi\)
\(14\) −23.5541 + 7.65321i −1.68244 + 0.546658i
\(15\) 14.6264 + 10.6736i 0.975095 + 0.711576i
\(16\) 5.77235 17.7655i 0.360772 1.11034i
\(17\) 0.578287 0.0915916i 0.0340169 0.00538774i −0.139403 0.990236i \(-0.544518\pi\)
0.173420 + 0.984848i \(0.444518\pi\)
\(18\) −7.77878 7.77878i −0.432154 0.432154i
\(19\) 1.57500 2.16781i 0.0828949 0.114095i −0.765556 0.643370i \(-0.777536\pi\)
0.848451 + 0.529275i \(0.177536\pi\)
\(20\) −2.43048 15.5565i −0.121524 0.777823i
\(21\) −27.1374 + 19.7165i −1.29226 + 0.938880i
\(22\) −4.31313 + 27.2320i −0.196051 + 1.23782i
\(23\) 16.5548 32.4907i 0.719775 1.41264i −0.183257 0.983065i \(-0.558664\pi\)
0.903032 0.429573i \(-0.141336\pi\)
\(24\) 8.23965i 0.343319i
\(25\) 14.6097 + 20.2869i 0.584388 + 0.811474i
\(26\) 33.9953 1.30751
\(27\) 15.7643 + 8.03233i 0.583864 + 0.297494i
\(28\) 28.8094 + 4.56297i 1.02891 + 0.162963i
\(29\) 9.15785 + 12.6047i 0.315788 + 0.434645i 0.937175 0.348859i \(-0.113431\pi\)
−0.621387 + 0.783504i \(0.713431\pi\)
\(30\) −21.8888 43.1828i −0.729628 1.43943i
\(31\) −15.1042 10.9739i −0.487233 0.353995i 0.316886 0.948464i \(-0.397363\pi\)
−0.804119 + 0.594468i \(0.797363\pi\)
\(32\) −28.8811 + 28.8811i −0.902536 + 0.902536i
\(33\) 5.84174 + 36.8833i 0.177022 + 1.11767i
\(34\) −1.48886 0.483759i −0.0437900 0.0142282i
\(35\) −44.0766 + 14.2193i −1.25933 + 0.406265i
\(36\) 4.00371 + 12.3221i 0.111214 + 0.342282i
\(37\) −26.1444 51.3113i −0.706606 1.38679i −0.912852 0.408292i \(-0.866125\pi\)
0.206246 0.978500i \(-0.433875\pi\)
\(38\) −6.38363 + 3.25262i −0.167990 + 0.0855953i
\(39\) 43.7900 14.2282i 1.12282 0.364826i
\(40\) 3.53818 10.8122i 0.0884544 0.270305i
\(41\) 0.808618 2.48867i 0.0197224 0.0606993i −0.940711 0.339209i \(-0.889841\pi\)
0.960433 + 0.278510i \(0.0898405\pi\)
\(42\) 88.5838 14.0303i 2.10914 0.334055i
\(43\) −7.76543 7.76543i −0.180591 0.180591i 0.611022 0.791614i \(-0.290759\pi\)
−0.791614 + 0.611022i \(0.790759\pi\)
\(44\) 19.0868 26.2707i 0.433790 0.597061i
\(45\) −14.5159 14.5769i −0.322577 0.323932i
\(46\) −78.8786 + 57.3086i −1.71475 + 1.24584i
\(47\) −6.13916 + 38.7611i −0.130620 + 0.824705i 0.832183 + 0.554501i \(0.187091\pi\)
−0.962803 + 0.270204i \(0.912909\pi\)
\(48\) −30.7108 + 60.2733i −0.639808 + 1.25569i
\(49\) 36.7975i 0.750969i
\(50\) −10.1799 66.0645i −0.203597 1.32129i
\(51\) −2.12030 −0.0415745
\(52\) −35.6741 18.1769i −0.686041 0.349555i
\(53\) 39.0747 + 6.18882i 0.737258 + 0.116770i 0.513760 0.857934i \(-0.328252\pi\)
0.223498 + 0.974704i \(0.428252\pi\)
\(54\) −27.8059 38.2716i −0.514924 0.708733i
\(55\) −8.17236 + 50.9074i −0.148588 + 0.925589i
\(56\) 17.0502 + 12.3877i 0.304468 + 0.221209i
\(57\) −6.86154 + 6.86154i −0.120378 + 0.120378i
\(58\) −6.51675 41.1452i −0.112358 0.709399i
\(59\) 0.494461 + 0.160660i 0.00838070 + 0.00272305i 0.313204 0.949686i \(-0.398598\pi\)
−0.304824 + 0.952409i \(0.598598\pi\)
\(60\) −0.119521 + 57.0191i −0.00199202 + 0.950318i
\(61\) 7.44472 + 22.9125i 0.122045 + 0.375615i 0.993351 0.115125i \(-0.0367267\pi\)
−0.871306 + 0.490739i \(0.836727\pi\)
\(62\) 22.6627 + 44.4780i 0.365527 + 0.717387i
\(63\) 33.9563 17.3016i 0.538989 0.274629i
\(64\) 32.8008 10.6576i 0.512512 0.166525i
\(65\) 63.5717 + 0.133256i 0.978027 + 0.00205010i
\(66\) 30.8543 94.9598i 0.467489 1.43878i
\(67\) 6.71462 1.06349i 0.100218 0.0158730i −0.106124 0.994353i \(-0.533844\pi\)
0.206342 + 0.978480i \(0.433844\pi\)
\(68\) 1.30372 + 1.30372i 0.0191724 + 0.0191724i
\(69\) −77.6194 + 106.834i −1.12492 + 1.54832i
\(70\) 122.266 + 19.6278i 1.74666 + 0.280398i
\(71\) 80.2586 58.3113i 1.13040 0.821286i 0.144650 0.989483i \(-0.453795\pi\)
0.985753 + 0.168197i \(0.0537945\pi\)
\(72\) −1.46444 + 9.24608i −0.0203394 + 0.128418i
\(73\) 27.3185 53.6155i 0.374226 0.734459i −0.624697 0.780867i \(-0.714777\pi\)
0.998923 + 0.0464080i \(0.0147774\pi\)
\(74\) 153.977i 2.08077i
\(75\) −40.7632 80.8383i −0.543510 1.07784i
\(76\) 8.43802 0.111027
\(77\) −85.1048 43.3631i −1.10526 0.563157i
\(78\) −121.594 19.2586i −1.55890 0.246905i
\(79\) 2.28841 + 3.14973i 0.0289672 + 0.0398699i 0.823255 0.567672i \(-0.192156\pi\)
−0.794288 + 0.607542i \(0.792156\pi\)
\(80\) −66.1811 + 65.9042i −0.827263 + 0.823802i
\(81\) −81.7927 59.4258i −1.00979 0.733652i
\(82\) −4.94732 + 4.94732i −0.0603332 + 0.0603332i
\(83\) −10.3587 65.4021i −0.124803 0.787977i −0.968107 0.250539i \(-0.919392\pi\)
0.843303 0.537438i \(-0.180608\pi\)
\(84\) −100.460 32.6415i −1.19596 0.388590i
\(85\) −2.78229 0.910474i −0.0327329 0.0107115i
\(86\) 9.07375 + 27.9261i 0.105509 + 0.324722i
\(87\) −25.6151 50.2724i −0.294426 0.577844i
\(88\) 20.9051 10.6517i 0.237558 0.121042i
\(89\) −49.5405 + 16.0967i −0.556635 + 0.180862i −0.573807 0.818991i \(-0.694534\pi\)
0.0171715 + 0.999853i \(0.494534\pi\)
\(90\) 16.8876 + 52.3477i 0.187640 + 0.581641i
\(91\) −36.3927 + 112.005i −0.399920 + 1.23083i
\(92\) 113.416 17.9634i 1.23278 0.195254i
\(93\) 47.8078 + 47.8078i 0.514063 + 0.514063i
\(94\) 61.6764 84.8903i 0.656132 0.903088i
\(95\) −11.9502 + 6.05743i −0.125792 + 0.0637624i
\(96\) 119.663 86.9404i 1.24649 0.905629i
\(97\) 0.610311 3.85335i 0.00629187 0.0397253i −0.984343 0.176265i \(-0.943598\pi\)
0.990635 + 0.136540i \(0.0435983\pi\)
\(98\) −44.6672 + 87.6643i −0.455788 + 0.894534i
\(99\) 42.4266i 0.428552i
\(100\) −24.6413 + 74.7701i −0.246413 + 0.747701i
\(101\) 76.8760 0.761148 0.380574 0.924750i \(-0.375726\pi\)
0.380574 + 0.924750i \(0.375726\pi\)
\(102\) 5.05128 + 2.57376i 0.0495224 + 0.0252329i
\(103\) −73.6729 11.6686i −0.715270 0.113288i −0.211816 0.977310i \(-0.567938\pi\)
−0.503454 + 0.864022i \(0.667938\pi\)
\(104\) −17.0039 23.4039i −0.163499 0.225037i
\(105\) 165.708 25.8897i 1.57817 0.246568i
\(106\) −85.5769 62.1753i −0.807330 0.586559i
\(107\) 39.5670 39.5670i 0.369785 0.369785i −0.497614 0.867399i \(-0.665790\pi\)
0.867399 + 0.497614i \(0.165790\pi\)
\(108\) 8.71575 + 55.0291i 0.0807014 + 0.509529i
\(109\) 190.485 + 61.8922i 1.74757 + 0.567819i 0.995795 0.0916057i \(-0.0291999\pi\)
0.751771 + 0.659424i \(0.229200\pi\)
\(110\) 81.2641 111.359i 0.738764 1.01235i
\(111\) 64.4448 + 198.341i 0.580584 + 1.78685i
\(112\) −78.5515 154.166i −0.701353 1.37648i
\(113\) −142.279 + 72.4950i −1.25911 + 0.641548i −0.950820 0.309744i \(-0.899757\pi\)
−0.308290 + 0.951293i \(0.599757\pi\)
\(114\) 24.6755 8.01757i 0.216452 0.0703295i
\(115\) −147.729 + 106.859i −1.28460 + 0.929208i
\(116\) −15.1612 + 46.6615i −0.130700 + 0.402254i
\(117\) −51.6675 + 8.18333i −0.441603 + 0.0699430i
\(118\) −0.982957 0.982957i −0.00833015 0.00833015i
\(119\) 3.18771 4.38751i 0.0267875 0.0368699i
\(120\) −18.7805 + 36.6686i −0.156504 + 0.305572i
\(121\) 11.8651 8.62049i 0.0980586 0.0712438i
\(122\) 10.0768 63.6224i 0.0825967 0.521495i
\(123\) −4.30211 + 8.44337i −0.0349765 + 0.0686453i
\(124\) 58.7920i 0.474129i
\(125\) −18.7775 123.582i −0.150220 0.988653i
\(126\) −101.897 −0.808710
\(127\) 215.891 + 110.002i 1.69993 + 0.866157i 0.986164 + 0.165773i \(0.0530119\pi\)
0.713766 + 0.700384i \(0.246988\pi\)
\(128\) 70.2853 + 11.1321i 0.549104 + 0.0869695i
\(129\) 23.3761 + 32.1745i 0.181210 + 0.249415i
\(130\) −151.288 77.4850i −1.16375 0.596038i
\(131\) −43.7237 31.7672i −0.333769 0.242497i 0.408259 0.912866i \(-0.366136\pi\)
−0.742028 + 0.670369i \(0.766136\pi\)
\(132\) −83.1519 + 83.1519i −0.629938 + 0.629938i
\(133\) −3.88269 24.5143i −0.0291932 0.184318i
\(134\) −17.2875 5.61704i −0.129011 0.0419182i
\(135\) −51.8475 71.6774i −0.384056 0.530944i
\(136\) 0.411662 + 1.26697i 0.00302693 + 0.00931593i
\(137\) 69.6488 + 136.693i 0.508385 + 0.997762i 0.992441 + 0.122725i \(0.0391632\pi\)
−0.484056 + 0.875037i \(0.660837\pi\)
\(138\) 314.598 160.296i 2.27970 1.16156i
\(139\) −159.568 + 51.8467i −1.14797 + 0.372998i −0.820378 0.571821i \(-0.806237\pi\)
−0.327592 + 0.944819i \(0.606237\pi\)
\(140\) −117.809 85.9713i −0.841495 0.614081i
\(141\) 43.9170 135.163i 0.311468 0.958600i
\(142\) −261.986 + 41.4945i −1.84497 + 0.292215i
\(143\) 92.7077 + 92.7077i 0.648306 + 0.648306i
\(144\) 45.1743 62.1771i 0.313710 0.431785i
\(145\) −12.0251 76.9676i −0.0829321 0.530811i
\(146\) −130.164 + 94.5697i −0.891535 + 0.647738i
\(147\) −20.8461 + 131.617i −0.141810 + 0.895353i
\(148\) 82.3297 161.581i 0.556282 1.09176i
\(149\) 239.699i 1.60872i −0.594144 0.804359i \(-0.702509\pi\)
0.594144 0.804359i \(-0.297491\pi\)
\(150\) −1.01482 + 242.066i −0.00676547 + 1.61377i
\(151\) −69.4171 −0.459716 −0.229858 0.973224i \(-0.573826\pi\)
−0.229858 + 0.973224i \(0.573826\pi\)
\(152\) 5.43224 + 2.76787i 0.0357384 + 0.0182096i
\(153\) 2.37928 + 0.376841i 0.0155509 + 0.00246301i
\(154\) 150.112 + 206.612i 0.974754 + 1.34163i
\(155\) 42.2052 + 83.2634i 0.272292 + 0.537183i
\(156\) 117.302 + 85.2246i 0.751933 + 0.546311i
\(157\) 14.5029 14.5029i 0.0923752 0.0923752i −0.659409 0.751784i \(-0.729193\pi\)
0.751784 + 0.659409i \(0.229193\pi\)
\(158\) −1.62844 10.2816i −0.0103066 0.0650731i
\(159\) −136.256 44.2722i −0.856955 0.278442i
\(160\) 194.357 62.7003i 1.21473 0.391877i
\(161\) −104.375 321.234i −0.648293 1.99524i
\(162\) 122.723 + 240.858i 0.757551 + 1.48678i
\(163\) −64.6287 + 32.9299i −0.396495 + 0.202024i −0.640858 0.767660i \(-0.721421\pi\)
0.244363 + 0.969684i \(0.421421\pi\)
\(164\) 7.83691 2.54637i 0.0477860 0.0155266i
\(165\) 58.0703 177.455i 0.351941 1.07549i
\(166\) −54.7114 + 168.384i −0.329587 + 1.01436i
\(167\) −29.8337 + 4.72519i −0.178645 + 0.0282945i −0.245116 0.969494i \(-0.578826\pi\)
0.0664711 + 0.997788i \(0.478826\pi\)
\(168\) −53.9674 53.9674i −0.321234 0.321234i
\(169\) −4.31711 + 5.94199i −0.0255450 + 0.0351597i
\(170\) 5.52319 + 5.54639i 0.0324893 + 0.0326258i
\(171\) 8.91914 6.48014i 0.0521587 0.0378955i
\(172\) 5.40992 34.1569i 0.0314530 0.198586i
\(173\) −86.0843 + 168.950i −0.497597 + 0.976589i 0.496494 + 0.868040i \(0.334620\pi\)
−0.994091 + 0.108549i \(0.965380\pi\)
\(174\) 150.859i 0.867008i
\(175\) 228.562 + 37.1836i 1.30607 + 0.212478i
\(176\) −192.622 −1.09444
\(177\) −1.67757 0.854764i −0.00947779 0.00482917i
\(178\) 137.562 + 21.7877i 0.772819 + 0.122403i
\(179\) −160.661 221.131i −0.897547 1.23537i −0.971244 0.238087i \(-0.923480\pi\)
0.0736967 0.997281i \(-0.476520\pi\)
\(180\) 10.2681 63.9624i 0.0570452 0.355347i
\(181\) 226.401 + 164.490i 1.25083 + 0.908784i 0.998270 0.0587961i \(-0.0187262\pi\)
0.252564 + 0.967580i \(0.418726\pi\)
\(182\) 222.659 222.659i 1.22340 1.22340i
\(183\) −13.6481 86.1707i −0.0745798 0.470878i
\(184\) 78.9077 + 25.6387i 0.428846 + 0.139341i
\(185\) −0.603567 + 287.939i −0.00326252 + 1.55643i
\(186\) −55.8625 171.927i −0.300336 0.924339i
\(187\) −2.74098 5.37948i −0.0146577 0.0287673i
\(188\) −110.112 + 56.1049i −0.585703 + 0.298430i
\(189\) 155.861 50.6424i 0.824663 0.267949i
\(190\) 35.8225 + 0.0750896i 0.188539 + 0.000395208i
\(191\) −35.4690 + 109.162i −0.185701 + 0.571530i −0.999960 0.00897264i \(-0.997144\pi\)
0.814258 + 0.580503i \(0.197144\pi\)
\(192\) −123.359 + 19.5382i −0.642495 + 0.101761i
\(193\) −53.7649 53.7649i −0.278575 0.278575i 0.553965 0.832540i \(-0.313114\pi\)
−0.832540 + 0.553965i \(0.813114\pi\)
\(194\) −6.13142 + 8.43918i −0.0316053 + 0.0435009i
\(195\) −227.307 36.4905i −1.16568 0.187131i
\(196\) 93.7461 68.1106i 0.478297 0.347503i
\(197\) 24.8752 157.056i 0.126270 0.797239i −0.840541 0.541748i \(-0.817763\pi\)
0.966811 0.255491i \(-0.0822372\pi\)
\(198\) −51.5002 + 101.075i −0.260102 + 0.510479i
\(199\) 131.741i 0.662017i −0.943628 0.331008i \(-0.892611\pi\)
0.943628 0.331008i \(-0.107389\pi\)
\(200\) −40.3900 + 40.0527i −0.201950 + 0.200264i
\(201\) −24.6193 −0.122484
\(202\) −183.145 93.3171i −0.906659 0.461966i
\(203\) 142.539 + 22.5759i 0.702160 + 0.111211i
\(204\) −3.92458 5.40172i −0.0192381 0.0264790i
\(205\) −9.27096 + 9.23217i −0.0452242 + 0.0450350i
\(206\) 161.350 + 117.228i 0.783252 + 0.569066i
\(207\) 106.088 106.088i 0.512501 0.512501i
\(208\) 37.1533 + 234.577i 0.178622 + 1.12777i
\(209\) −26.2788 8.53849i −0.125736 0.0408540i
\(210\) −426.201 139.469i −2.02953 0.664140i
\(211\) −43.4315 133.668i −0.205836 0.633499i −0.999678 0.0253746i \(-0.991922\pi\)
0.793842 0.608124i \(-0.208078\pi\)
\(212\) 56.5587 + 111.003i 0.266786 + 0.523598i
\(213\) −320.102 + 163.100i −1.50283 + 0.765728i
\(214\) −142.291 + 46.2332i −0.664913 + 0.216043i
\(215\) 16.8586 + 52.2579i 0.0784121 + 0.243060i
\(216\) −12.4398 + 38.2857i −0.0575916 + 0.177249i
\(217\) −170.804 + 27.0527i −0.787115 + 0.124667i
\(218\) −378.671 378.671i −1.73702 1.73702i
\(219\) −128.086 + 176.295i −0.584868 + 0.805002i
\(220\) −144.819 + 73.4072i −0.658270 + 0.333669i
\(221\) −6.02249 + 4.37559i −0.0272511 + 0.0197991i
\(222\) 87.2292 550.743i 0.392924 2.48083i
\(223\) 152.112 298.537i 0.682116 1.33873i −0.247027 0.969009i \(-0.579454\pi\)
0.929143 0.369720i \(-0.120546\pi\)
\(224\) 378.326i 1.68896i
\(225\) 31.3748 + 97.9572i 0.139444 + 0.435365i
\(226\) 426.958 1.88919
\(227\) −11.3192 5.76744i −0.0498645 0.0254072i 0.428880 0.903361i \(-0.358908\pi\)
−0.478745 + 0.877954i \(0.658908\pi\)
\(228\) −30.1810 4.78020i −0.132373 0.0209658i
\(229\) 235.268 + 323.818i 1.02737 + 1.41405i 0.906905 + 0.421335i \(0.138438\pi\)
0.120465 + 0.992718i \(0.461562\pi\)
\(230\) 481.653 75.2518i 2.09415 0.327182i
\(231\) 279.837 + 203.313i 1.21141 + 0.880144i
\(232\) −25.0666 + 25.0666i −0.108046 + 0.108046i
\(233\) 31.0191 + 195.847i 0.133129 + 0.840546i 0.960376 + 0.278707i \(0.0899059\pi\)
−0.827247 + 0.561839i \(0.810094\pi\)
\(234\) 133.023 + 43.2219i 0.568475 + 0.184709i
\(235\) 115.669 158.504i 0.492207 0.674487i
\(236\) 0.505925 + 1.55708i 0.00214375 + 0.00659778i
\(237\) −6.40082 12.5623i −0.0270077 0.0530055i
\(238\) −12.9201 + 6.58311i −0.0542861 + 0.0276601i
\(239\) 403.358 131.059i 1.68769 0.548364i 0.701313 0.712853i \(-0.252598\pi\)
0.986379 + 0.164489i \(0.0525976\pi\)
\(240\) 274.051 198.233i 1.14188 0.825973i
\(241\) 84.5835 260.321i 0.350969 1.08017i −0.607341 0.794441i \(-0.707764\pi\)
0.958310 0.285730i \(-0.0922360\pi\)
\(242\) −38.7309 + 6.13437i −0.160045 + 0.0253486i
\(243\) 146.294 + 146.294i 0.602034 + 0.602034i
\(244\) −44.5926 + 61.3764i −0.182756 + 0.251543i
\(245\) −83.8720 + 163.759i −0.342335 + 0.668402i
\(246\) 20.4982 14.8928i 0.0833261 0.0605399i
\(247\) −5.32955 + 33.6494i −0.0215771 + 0.136233i
\(248\) 19.2851 37.8492i 0.0777626 0.152618i
\(249\) 239.798i 0.963044i
\(250\) −105.277 + 317.207i −0.421107 + 1.26883i
\(251\) 26.5983 0.105969 0.0529847 0.998595i \(-0.483127\pi\)
0.0529847 + 0.998595i \(0.483127\pi\)
\(252\) 106.930 + 54.4834i 0.424324 + 0.216204i
\(253\) −371.393 58.8229i −1.46796 0.232501i
\(254\) −380.799 524.125i −1.49921 2.06349i
\(255\) 9.43589 + 4.83277i 0.0370035 + 0.0189520i
\(256\) −265.539 192.925i −1.03726 0.753615i
\(257\) −337.671 + 337.671i −1.31390 + 1.31390i −0.395376 + 0.918520i \(0.629386\pi\)
−0.918520 + 0.395376i \(0.870614\pi\)
\(258\) −16.6345 105.026i −0.0644749 0.407079i
\(259\) −507.313 164.836i −1.95874 0.636432i
\(260\) 117.329 + 162.203i 0.451265 + 0.623859i
\(261\) 19.8089 + 60.9655i 0.0758961 + 0.233584i
\(262\) 65.6040 + 128.755i 0.250397 + 0.491431i
\(263\) 200.339 102.078i 0.761744 0.388128i −0.0295507 0.999563i \(-0.509408\pi\)
0.791294 + 0.611436i \(0.209408\pi\)
\(264\) −80.8074 + 26.2559i −0.306089 + 0.0994543i
\(265\) −159.787 116.604i −0.602968 0.440016i
\(266\) −20.5072 + 63.1147i −0.0770947 + 0.237273i
\(267\) 186.315 29.5094i 0.697809 0.110522i
\(268\) 15.1378 + 15.1378i 0.0564845 + 0.0564845i
\(269\) −25.7782 + 35.4806i −0.0958297 + 0.131898i −0.854239 0.519880i \(-0.825977\pi\)
0.758410 + 0.651778i \(0.225977\pi\)
\(270\) 36.5119 + 233.696i 0.135229 + 0.865542i
\(271\) −281.141 + 204.261i −1.03742 + 0.753731i −0.969781 0.243979i \(-0.921547\pi\)
−0.0676411 + 0.997710i \(0.521547\pi\)
\(272\) 1.71091 10.8022i 0.00629010 0.0397141i
\(273\) 193.621 380.003i 0.709235 1.39195i
\(274\) 410.195i 1.49706i
\(275\) 152.402 207.924i 0.554188 0.756088i
\(276\) −415.842 −1.50668
\(277\) 184.061 + 93.7837i 0.664480 + 0.338569i 0.753488 0.657461i \(-0.228370\pi\)
−0.0890082 + 0.996031i \(0.528370\pi\)
\(278\) 443.081 + 70.1771i 1.59382 + 0.252436i
\(279\) −45.1504 62.1442i −0.161829 0.222739i
\(280\) −47.6429 93.9910i −0.170153 0.335682i
\(281\) −150.952 109.673i −0.537197 0.390296i 0.285846 0.958276i \(-0.407725\pi\)
−0.823043 + 0.567979i \(0.807725\pi\)
\(282\) −268.695 + 268.695i −0.952818 + 0.952818i
\(283\) 1.96244 + 12.3904i 0.00693443 + 0.0437823i 0.990913 0.134505i \(-0.0429444\pi\)
−0.983978 + 0.178287i \(0.942944\pi\)
\(284\) 297.110 + 96.5370i 1.04616 + 0.339919i
\(285\) 46.1751 14.8963i 0.162018 0.0522676i
\(286\) −108.327 333.396i −0.378766 1.16572i
\(287\) −11.0039 21.5963i −0.0383410 0.0752484i
\(288\) −149.731 + 76.2919i −0.519901 + 0.264903i
\(289\) −274.529 + 89.2000i −0.949928 + 0.308650i
\(290\) −64.7803 + 197.960i −0.223380 + 0.682622i
\(291\) −4.36591 + 13.4369i −0.0150031 + 0.0461749i
\(292\) 187.157 29.6428i 0.640950 0.101517i
\(293\) 253.361 + 253.361i 0.864714 + 0.864714i 0.991881 0.127167i \(-0.0405885\pi\)
−0.127167 + 0.991881i \(0.540589\pi\)
\(294\) 209.428 288.253i 0.712339 0.980451i
\(295\) −1.83429 1.84200i −0.00621794 0.00624406i
\(296\) 106.005 77.0169i 0.358124 0.260192i
\(297\) 28.5406 180.198i 0.0960963 0.606728i
\(298\) −290.962 + 571.045i −0.976383 + 1.91626i
\(299\) 463.631i 1.55061i
\(300\) 130.495 253.478i 0.434982 0.844925i
\(301\) −101.723 −0.337949
\(302\) 165.375 + 84.2630i 0.547601 + 0.279016i
\(303\) −274.969 43.5509i −0.907489 0.143732i
\(304\) −29.4206 40.4940i −0.0967784 0.133204i
\(305\) 19.0932 118.935i 0.0626005 0.389952i
\(306\) −5.21083 3.78589i −0.0170289 0.0123722i
\(307\) 385.809 385.809i 1.25671 1.25671i 0.304053 0.952655i \(-0.401660\pi\)
0.952655 0.304053i \(-0.0983401\pi\)
\(308\) −47.0526 297.078i −0.152768 0.964539i
\(309\) 256.902 + 83.4725i 0.831398 + 0.270138i
\(310\) 0.523187 249.593i 0.00168770 0.805140i
\(311\) 56.4903 + 173.859i 0.181641 + 0.559033i 0.999874 0.0158533i \(-0.00504647\pi\)
−0.818234 + 0.574886i \(0.805046\pi\)
\(312\) 47.5610 + 93.3437i 0.152439 + 0.299178i
\(313\) 432.433 220.336i 1.38158 0.703948i 0.404045 0.914739i \(-0.367604\pi\)
0.977531 + 0.210791i \(0.0676038\pi\)
\(314\) −52.1555 + 16.9464i −0.166100 + 0.0539693i
\(315\) −190.550 0.399423i −0.604921 0.00126801i
\(316\) −3.78857 + 11.6600i −0.0119891 + 0.0368988i
\(317\) −278.457 + 44.1033i −0.878415 + 0.139127i −0.579324 0.815097i \(-0.696683\pi\)
−0.299091 + 0.954225i \(0.596683\pi\)
\(318\) 270.868 + 270.868i 0.851786 + 0.851786i
\(319\) 94.4343 129.978i 0.296032 0.407453i
\(320\) −170.264 27.3331i −0.532075 0.0854160i
\(321\) −163.938 + 119.108i −0.510710 + 0.371053i
\(322\) −141.277 + 891.987i −0.438748 + 2.77015i
\(323\) 0.712251 1.39787i 0.00220511 0.00432777i
\(324\) 318.371i 0.982628i
\(325\) −282.607 145.491i −0.869561 0.447665i
\(326\) 193.940 0.594909
\(327\) −646.262 329.287i −1.97633 1.00699i
\(328\) 5.88053 + 0.931384i 0.0179284 + 0.00283959i
\(329\) 213.665 + 294.084i 0.649436 + 0.893873i
\(330\) −353.750 + 352.270i −1.07197 + 1.06749i
\(331\) 172.973 + 125.672i 0.522576 + 0.379674i 0.817573 0.575824i \(-0.195319\pi\)
−0.294997 + 0.955498i \(0.595319\pi\)
\(332\) 147.446 147.446i 0.444116 0.444116i
\(333\) −37.0653 234.021i −0.111307 0.702765i
\(334\) 76.8098 + 24.9570i 0.229969 + 0.0747216i
\(335\) −32.3058 10.5717i −0.0964353 0.0315574i
\(336\) 193.626 + 595.919i 0.576268 + 1.77357i
\(337\) 38.2515 + 75.0727i 0.113506 + 0.222768i 0.940770 0.339045i \(-0.110104\pi\)
−0.827264 + 0.561813i \(0.810104\pi\)
\(338\) 17.4976 8.91548i 0.0517681 0.0263771i
\(339\) 549.973 178.697i 1.62234 0.527130i
\(340\) −2.83036 8.77348i −0.00832458 0.0258044i
\(341\) −59.4920 + 183.098i −0.174463 + 0.536943i
\(342\) −29.1145 + 4.61128i −0.0851301 + 0.0134833i
\(343\) 79.9229 + 79.9229i 0.233011 + 0.233011i
\(344\) 14.6871 20.2150i 0.0426949 0.0587645i
\(345\) 588.932 298.522i 1.70705 0.865282i
\(346\) 410.165 298.002i 1.18545 0.861278i
\(347\) −22.5157 + 142.159i −0.0648868 + 0.409679i 0.933770 + 0.357873i \(0.116498\pi\)
−0.998657 + 0.0518065i \(0.983502\pi\)
\(348\) 80.6627 158.310i 0.231789 0.454912i
\(349\) 593.244i 1.69984i −0.526913 0.849919i \(-0.676651\pi\)
0.526913 0.849919i \(-0.323349\pi\)
\(350\) −499.379 366.028i −1.42680 1.04580i
\(351\) −224.952 −0.640889
\(352\) 375.272 + 191.211i 1.06611 + 0.543212i
\(353\) 23.8928 + 3.78424i 0.0676849 + 0.0107202i 0.190185 0.981748i \(-0.439091\pi\)
−0.122500 + 0.992468i \(0.539091\pi\)
\(354\) 2.95898 + 4.07268i 0.00835870 + 0.0115048i
\(355\) −490.080 + 76.5684i −1.38051 + 0.215686i
\(356\) −132.706 96.4163i −0.372769 0.270832i
\(357\) −13.8873 + 13.8873i −0.0389001 + 0.0389001i
\(358\) 114.327 + 721.831i 0.319348 + 2.01629i
\(359\) −35.0590 11.3914i −0.0976575 0.0317308i 0.259781 0.965668i \(-0.416350\pi\)
−0.357438 + 0.933937i \(0.616350\pi\)
\(360\) 27.5916 37.8097i 0.0766433 0.105027i
\(361\) 109.336 + 336.503i 0.302871 + 0.932141i
\(362\) −339.696 666.692i −0.938388 1.84169i
\(363\) −47.3225 + 24.1120i −0.130365 + 0.0664243i
\(364\) −352.709 + 114.602i −0.968980 + 0.314841i
\(365\) −243.780 + 176.337i −0.667889 + 0.483114i
\(366\) −72.0852 + 221.855i −0.196954 + 0.606162i
\(367\) 235.695 37.3305i 0.642221 0.101718i 0.173175 0.984891i \(-0.444598\pi\)
0.469047 + 0.883173i \(0.344598\pi\)
\(368\) −481.652 481.652i −1.30884 1.30884i
\(369\) 6.32823 8.71006i 0.0171497 0.0236045i
\(370\) 350.958 685.238i 0.948534 1.85200i
\(371\) 296.463 215.393i 0.799091 0.580574i
\(372\) −33.3061 + 210.287i −0.0895326 + 0.565286i
\(373\) −150.764 + 295.891i −0.404193 + 0.793274i −0.999951 0.00988999i \(-0.996852\pi\)
0.595758 + 0.803164i \(0.296852\pi\)
\(374\) 16.1430i 0.0431630i
\(375\) −2.84659 + 452.663i −0.00759092 + 1.20710i
\(376\) −89.2919 −0.237478
\(377\) −176.503 89.9325i −0.468176 0.238548i
\(378\) −432.789 68.5470i −1.14494 0.181341i
\(379\) 303.312 + 417.473i 0.800296 + 1.10151i 0.992749 + 0.120206i \(0.0383556\pi\)
−0.192453 + 0.981306i \(0.561644\pi\)
\(380\) −37.5514 19.2327i −0.0988195 0.0506122i
\(381\) −709.880 515.758i −1.86320 1.35370i
\(382\) 217.007 217.007i 0.568082 0.568082i
\(383\) −91.6131 578.423i −0.239199 1.51024i −0.756248 0.654286i \(-0.772969\pi\)
0.517049 0.855956i \(-0.327031\pi\)
\(384\) −245.089 79.6344i −0.638254 0.207381i
\(385\) 279.902 + 386.955i 0.727018 + 1.00508i
\(386\) 62.8232 + 193.350i 0.162754 + 0.500907i
\(387\) −20.5130 40.2591i −0.0530053 0.104029i
\(388\) 10.9465 5.57754i 0.0282128 0.0143751i
\(389\) −268.058 + 87.0975i −0.689096 + 0.223901i −0.632573 0.774500i \(-0.718001\pi\)
−0.0565228 + 0.998401i \(0.518001\pi\)
\(390\) 497.230 + 362.853i 1.27495 + 0.930393i
\(391\) 6.59756 20.3052i 0.0168736 0.0519315i
\(392\) 82.6939 13.0974i 0.210954 0.0334118i
\(393\) 138.394 + 138.394i 0.352148 + 0.352148i
\(394\) −249.906 + 343.967i −0.634280 + 0.873012i
\(395\) −3.00490 19.2331i −0.00760735 0.0486913i
\(396\) 108.087 78.5298i 0.272947 0.198308i
\(397\) 91.6244 578.494i 0.230792 1.45716i −0.551460 0.834201i \(-0.685929\pi\)
0.782252 0.622962i \(-0.214071\pi\)
\(398\) −159.916 + 313.853i −0.401800 + 0.788576i
\(399\) 89.8822i 0.225269i
\(400\) 444.738 142.446i 1.11184 0.356114i
\(401\) 209.284 0.521904 0.260952 0.965352i \(-0.415963\pi\)
0.260952 + 0.965352i \(0.415963\pi\)
\(402\) 58.6516 + 29.8845i 0.145899 + 0.0743395i
\(403\) 234.453 + 37.1337i 0.581769 + 0.0921431i
\(404\) 142.294 + 195.851i 0.352213 + 0.484780i
\(405\) 228.550 + 450.890i 0.564322 + 1.11331i
\(406\) −312.172 226.806i −0.768896 0.558636i
\(407\) −419.907 + 419.907i −1.03171 + 1.03171i
\(408\) −0.754683 4.76488i −0.00184971 0.0116786i
\(409\) −389.688 126.617i −0.952782 0.309578i −0.208937 0.977929i \(-0.567000\pi\)
−0.743846 + 0.668351i \(0.767000\pi\)
\(410\) 33.2932 10.7405i 0.0812030 0.0261964i
\(411\) −171.681 528.380i −0.417716 1.28560i
\(412\) −106.638 209.289i −0.258830 0.507983i
\(413\) 4.29086 2.18630i 0.0103895 0.00529371i
\(414\) −381.514 + 123.961i −0.921531 + 0.299424i
\(415\) −102.971 + 314.667i −0.248123 + 0.758234i
\(416\) 160.475 493.890i 0.385757 1.18724i
\(417\) 600.112 95.0485i 1.43912 0.227934i
\(418\) 52.2405 + 52.2405i 0.124977 + 0.124977i
\(419\) 169.332 233.065i 0.404134 0.556242i −0.557642 0.830082i \(-0.688294\pi\)
0.961775 + 0.273840i \(0.0882937\pi\)
\(420\) 372.676 + 374.241i 0.887323 + 0.891051i
\(421\) 266.227 193.425i 0.632368 0.459442i −0.224852 0.974393i \(-0.572190\pi\)
0.857220 + 0.514951i \(0.172190\pi\)
\(422\) −58.7866 + 371.164i −0.139305 + 0.879535i
\(423\) −73.3037 + 143.867i −0.173295 + 0.340110i
\(424\) 90.0142i 0.212298i
\(425\) 10.3067 + 10.3935i 0.0242511 + 0.0244553i
\(426\) 960.575 2.25487
\(427\) 198.831 + 101.310i 0.465647 + 0.237259i
\(428\) 174.039 + 27.5650i 0.406632 + 0.0644042i
\(429\) −279.076 384.116i −0.650528 0.895375i
\(430\) 23.2710 144.960i 0.0541187 0.337117i
\(431\) −264.075 191.862i −0.612703 0.445155i 0.237662 0.971348i \(-0.423619\pi\)
−0.850365 + 0.526193i \(0.823619\pi\)
\(432\) 233.695 233.695i 0.540962 0.540962i
\(433\) −34.0136 214.753i −0.0785532 0.495966i −0.995327 0.0965593i \(-0.969216\pi\)
0.916774 0.399406i \(-0.130784\pi\)
\(434\) 439.752 + 142.884i 1.01325 + 0.329226i
\(435\) −0.591346 + 282.109i −0.00135942 + 0.648527i
\(436\) 194.901 + 599.843i 0.447020 + 1.37579i
\(437\) −44.3596 87.0606i −0.101509 0.199223i
\(438\) 519.144 264.517i 1.18526 0.603920i
\(439\) −221.343 + 71.9188i −0.504199 + 0.163824i −0.550062 0.835124i \(-0.685396\pi\)
0.0458635 + 0.998948i \(0.485396\pi\)
\(440\) −117.311 0.245903i −0.266617 0.000558871i
\(441\) 46.7846 143.988i 0.106088 0.326504i
\(442\) 19.6590 3.11368i 0.0444774 0.00704453i
\(443\) −211.710 211.710i −0.477901 0.477901i 0.426559 0.904460i \(-0.359726\pi\)
−0.904460 + 0.426559i \(0.859726\pi\)
\(444\) −386.013 + 531.301i −0.869398 + 1.19662i
\(445\) 257.157 + 41.2825i 0.577882 + 0.0927696i
\(446\) −724.766 + 526.573i −1.62504 + 1.18066i
\(447\) −135.791 + 857.353i −0.303784 + 1.91802i
\(448\) 145.031 284.640i 0.323731 0.635357i
\(449\) 184.740i 0.411448i 0.978610 + 0.205724i \(0.0659549\pi\)
−0.978610 + 0.205724i \(0.934045\pi\)
\(450\) 44.1612 271.453i 0.0981360 0.603228i
\(451\) −26.9834 −0.0598302
\(452\) −448.043 228.289i −0.991245 0.505065i
\(453\) 248.290 + 39.3253i 0.548102 + 0.0868109i
\(454\) 19.9654 + 27.4800i 0.0439767 + 0.0605287i
\(455\) 417.249 415.504i 0.917032 0.913195i
\(456\) −17.8620 12.9775i −0.0391710 0.0284594i
\(457\) −307.584 + 307.584i −0.673051 + 0.673051i −0.958418 0.285367i \(-0.907884\pi\)
0.285367 + 0.958418i \(0.407884\pi\)
\(458\) −167.417 1057.03i −0.365539 2.30792i
\(459\) 9.85200 + 3.20111i 0.0214641 + 0.00697410i
\(460\) −545.676 178.566i −1.18625 0.388188i
\(461\) 216.873 + 667.468i 0.470441 + 1.44787i 0.852009 + 0.523528i \(0.175384\pi\)
−0.381567 + 0.924341i \(0.624616\pi\)
\(462\) −419.872 824.046i −0.908815 1.78365i
\(463\) −772.932 + 393.828i −1.66940 + 0.850601i −0.675871 + 0.737020i \(0.736232\pi\)
−0.993529 + 0.113581i \(0.963768\pi\)
\(464\) 276.791 89.9348i 0.596532 0.193825i
\(465\) −103.790 321.725i −0.223204 0.691882i
\(466\) 163.834 504.229i 0.351575 1.08204i
\(467\) 428.955 67.9398i 0.918534 0.145481i 0.320773 0.947156i \(-0.396057\pi\)
0.597761 + 0.801675i \(0.296057\pi\)
\(468\) −116.482 116.482i −0.248894 0.248894i
\(469\) 37.0133 50.9444i 0.0789195 0.108623i
\(470\) −467.965 + 237.206i −0.995671 + 0.504694i
\(471\) −60.0899 + 43.6579i −0.127579 + 0.0926919i
\(472\) −0.185052 + 1.16837i −0.000392059 + 0.00247536i
\(473\) −51.4119 + 100.901i −0.108693 + 0.213322i
\(474\) 37.6975i 0.0795306i
\(475\) 66.9883 + 0.280837i 0.141028 + 0.000591237i
\(476\) 17.0780 0.0358782
\(477\) 145.030 + 73.8966i 0.304047 + 0.154920i
\(478\) −1120.03 177.395i −2.34315 0.371119i
\(479\) −47.2284 65.0044i −0.0985980 0.135709i 0.756867 0.653568i \(-0.226729\pi\)
−0.855465 + 0.517860i \(0.826729\pi\)
\(480\) −730.695 + 114.161i −1.52228 + 0.237836i
\(481\) 592.359 + 430.374i 1.23151 + 0.894748i
\(482\) −517.502 + 517.502i −1.07366 + 1.07366i
\(483\) 191.347 + 1208.12i 0.396163 + 2.50127i
\(484\) 43.9235 + 14.2716i 0.0907511 + 0.0294868i
\(485\) −11.4989 + 15.7574i −0.0237091 + 0.0324894i
\(486\) −170.942 526.104i −0.351732 1.08252i
\(487\) −213.899 419.801i −0.439218 0.862014i −0.999433 0.0336667i \(-0.989282\pi\)
0.560215 0.828347i \(-0.310718\pi\)
\(488\) −48.8408 + 24.8856i −0.100084 + 0.0509951i
\(489\) 249.818 81.1709i 0.510876 0.165994i
\(490\) 398.593 288.320i 0.813455 0.588408i
\(491\) 105.330 324.171i 0.214520 0.660226i −0.784667 0.619918i \(-0.787166\pi\)
0.999187 0.0403083i \(-0.0128340\pi\)
\(492\) −29.4735 + 4.66815i −0.0599055 + 0.00948811i
\(493\) 6.45035 + 6.45035i 0.0130839 + 0.0130839i
\(494\) 53.5427 73.6952i 0.108386 0.149181i
\(495\) −96.7024 + 188.810i −0.195358 + 0.381434i
\(496\) −282.142 + 204.989i −0.568836 + 0.413283i
\(497\) 143.749 907.593i 0.289233 1.82614i
\(498\) 291.082 571.281i 0.584503 1.14715i
\(499\) 403.498i 0.808614i 0.914623 + 0.404307i \(0.132487\pi\)
−0.914623 + 0.404307i \(0.867513\pi\)
\(500\) 280.083 276.582i 0.560166 0.553164i
\(501\) 109.386 0.218335
\(502\) −63.3664 32.2868i −0.126228 0.0643163i
\(503\) 217.934 + 34.5173i 0.433268 + 0.0686229i 0.369259 0.929326i \(-0.379611\pi\)
0.0640087 + 0.997949i \(0.479611\pi\)
\(504\) 50.9676 + 70.1508i 0.101126 + 0.139188i
\(505\) −342.119 175.222i −0.677462 0.346975i
\(506\) 813.383 + 590.957i 1.60748 + 1.16790i
\(507\) 18.8076 18.8076i 0.0370958 0.0370958i
\(508\) 119.361 + 753.618i 0.234963 + 1.48350i
\(509\) 207.797 + 67.5173i 0.408245 + 0.132647i 0.505938 0.862570i \(-0.331146\pi\)
−0.0976931 + 0.995217i \(0.531146\pi\)
\(510\) −16.6132 22.9672i −0.0325749 0.0450337i
\(511\) −172.238 530.095i −0.337061 1.03737i
\(512\) 269.194 + 528.322i 0.525769 + 1.03188i
\(513\) 42.2414 21.5231i 0.0823420 0.0419553i
\(514\) 1214.34 394.562i 2.36252 0.767630i
\(515\) 301.268 + 219.850i 0.584986 + 0.426893i
\(516\) −38.7003 + 119.107i −0.0750006 + 0.230828i
\(517\) 399.698 63.3060i 0.773111 0.122449i
\(518\) 1008.51 + 1008.51i 1.94692 + 1.94692i
\(519\) 403.617 555.531i 0.777682 1.07039i
\(520\) 22.3278 + 142.910i 0.0429381 + 0.274827i
\(521\) −554.789 + 403.078i −1.06485 + 0.773662i −0.974980 0.222291i \(-0.928647\pi\)
−0.0898743 + 0.995953i \(0.528647\pi\)
\(522\) 26.8123 169.286i 0.0513645 0.324303i
\(523\) 103.663 203.451i 0.198209 0.389007i −0.770413 0.637545i \(-0.779950\pi\)
0.968622 + 0.248538i \(0.0799501\pi\)
\(524\) 170.191i 0.324792i
\(525\) −796.455 262.481i −1.51706 0.499963i
\(526\) −601.184 −1.14294
\(527\) −9.73968 4.96262i −0.0184814 0.00941673i
\(528\) 688.969 + 109.122i 1.30487 + 0.206670i
\(529\) −470.643 647.784i −0.889684 1.22455i
\(530\) 239.125 + 471.751i 0.451179 + 0.890096i
\(531\) 1.73056 + 1.25732i 0.00325905 + 0.00236784i
\(532\) 55.2666 55.2666i 0.103885 0.103885i
\(533\) 5.20461 + 32.8606i 0.00976475 + 0.0616522i
\(534\) −479.687 155.860i −0.898290 0.291872i
\(535\) −266.268 + 85.8992i −0.497698 + 0.160559i
\(536\) 4.77990 + 14.7110i 0.00891773 + 0.0274460i
\(537\) 449.378 + 881.954i 0.836831 + 1.64237i
\(538\) 104.481 53.2359i 0.194203 0.0989514i
\(539\) −360.878 + 117.256i −0.669533 + 0.217544i
\(540\) 86.6396 264.760i 0.160444 0.490296i
\(541\) −137.435 + 422.980i −0.254038 + 0.781849i 0.739979 + 0.672629i \(0.234835\pi\)
−0.994018 + 0.109220i \(0.965165\pi\)
\(542\) 917.721 145.353i 1.69321 0.268178i
\(543\) −716.604 716.604i −1.31971 1.31971i
\(544\) −14.0563 + 19.3469i −0.0258388 + 0.0355641i
\(545\) −706.637 709.606i −1.29658 1.30203i
\(546\) −922.544 + 670.268i −1.68964 + 1.22760i
\(547\) −64.1848 + 405.247i −0.117340 + 0.740854i 0.856924 + 0.515443i \(0.172373\pi\)
−0.974264 + 0.225411i \(0.927627\pi\)
\(548\) −219.326 + 430.452i −0.400231 + 0.785497i
\(549\) 99.1217i 0.180550i
\(550\) −615.465 + 310.352i −1.11903 + 0.564276i
\(551\) 41.7482 0.0757681
\(552\) −267.712 136.406i −0.484985 0.247112i
\(553\) 35.6182 + 5.64137i 0.0644091 + 0.0102014i
\(554\) −324.656 446.850i −0.586021 0.806589i
\(555\) 165.279 1029.56i 0.297800 1.85506i
\(556\) −427.439 310.553i −0.768775 0.558548i
\(557\) 437.906 437.906i 0.786186 0.786186i −0.194680 0.980867i \(-0.562367\pi\)
0.980867 + 0.194680i \(0.0623670\pi\)
\(558\) 32.1291 + 202.855i 0.0575791 + 0.363540i
\(559\) 132.795 + 43.1477i 0.237558 + 0.0771874i
\(560\) −1.81343 + 865.121i −0.00323827 + 1.54486i
\(561\) 6.75640 + 20.7941i 0.0120435 + 0.0370661i
\(562\) 226.492 + 444.515i 0.403010 + 0.790952i
\(563\) −195.369 + 99.5452i −0.347013 + 0.176812i −0.618806 0.785544i \(-0.712383\pi\)
0.271793 + 0.962356i \(0.412383\pi\)
\(564\) 425.632 138.296i 0.754666 0.245206i
\(565\) 798.418 + 1.67361i 1.41313 + 0.00296214i
\(566\) 10.3650 31.9003i 0.0183128 0.0563610i
\(567\) −924.941 + 146.496i −1.63129 + 0.258371i
\(568\) 159.608 + 159.608i 0.281000 + 0.281000i
\(569\) 297.903 410.029i 0.523556 0.720613i −0.462575 0.886580i \(-0.653074\pi\)
0.986131 + 0.165967i \(0.0530744\pi\)
\(570\) −128.087 20.5623i −0.224714 0.0360742i
\(571\) 152.983 111.149i 0.267921 0.194656i −0.445711 0.895177i \(-0.647049\pi\)
0.713632 + 0.700521i \(0.247049\pi\)
\(572\) −64.5864 + 407.782i −0.112913 + 0.712906i
\(573\) 188.706 370.357i 0.329330 0.646347i
\(574\) 64.8070i 0.112904i
\(575\) 900.995 138.834i 1.56695 0.241451i
\(576\) 141.899 0.246353
\(577\) −334.217 170.292i −0.579233 0.295134i 0.139722 0.990191i \(-0.455379\pi\)
−0.718955 + 0.695057i \(0.755379\pi\)
\(578\) 762.300 + 120.736i 1.31886 + 0.208887i
\(579\) 161.848 + 222.764i 0.279530 + 0.384740i
\(580\) 173.826 173.099i 0.299701 0.298447i
\(581\) −496.211 360.519i −0.854064 0.620514i
\(582\) 26.7117 26.7117i 0.0458963 0.0458963i
\(583\) −63.8181 402.932i −0.109465 0.691135i
\(584\) 130.212 + 42.3085i 0.222966 + 0.0724460i
\(585\) 248.586 + 81.3470i 0.424934 + 0.139055i
\(586\) −296.047 911.140i −0.505200 1.55485i
\(587\) 133.912 + 262.818i 0.228130 + 0.447730i 0.976490 0.215562i \(-0.0691585\pi\)
−0.748360 + 0.663293i \(0.769158\pi\)
\(588\) −373.895 + 190.509i −0.635877 + 0.323995i
\(589\) −47.5784 + 15.4592i −0.0807782 + 0.0262464i
\(590\) 2.13398 + 6.61486i 0.00361691 + 0.0112116i
\(591\) −177.947 + 547.665i −0.301095 + 0.926675i
\(592\) −1062.48 + 168.281i −1.79474 + 0.284258i
\(593\) −482.975 482.975i −0.814460 0.814460i 0.170839 0.985299i \(-0.445352\pi\)
−0.985299 + 0.170839i \(0.945352\pi\)
\(594\) −286.730 + 394.650i −0.482711 + 0.664394i
\(595\) −24.1866 + 12.2599i −0.0406497 + 0.0206048i
\(596\) 610.662 443.672i 1.02460 0.744417i
\(597\) −74.6325 + 471.211i −0.125013 + 0.789299i
\(598\) 562.786 1104.53i 0.941114 1.84704i
\(599\) 549.893i 0.918019i 0.888431 + 0.459010i \(0.151796\pi\)
−0.888431 + 0.459010i \(0.848204\pi\)
\(600\) 167.157 120.379i 0.278594 0.200632i
\(601\) 479.442 0.797740 0.398870 0.917007i \(-0.369402\pi\)
0.398870 + 0.917007i \(0.369402\pi\)
\(602\) 242.339 + 123.478i 0.402556 + 0.205112i
\(603\) 27.6264 + 4.37559i 0.0458149 + 0.00725636i
\(604\) −128.488 176.849i −0.212728 0.292796i
\(605\) −72.4514 + 11.3195i −0.119754 + 0.0187100i
\(606\) 602.207 + 437.529i 0.993741 + 0.721995i
\(607\) −247.960 + 247.960i −0.408502 + 0.408502i −0.881216 0.472714i \(-0.843274\pi\)
0.472714 + 0.881216i \(0.343274\pi\)
\(608\) 17.1208 + 108.097i 0.0281593 + 0.177791i
\(609\) −497.041 161.498i −0.816159 0.265186i
\(610\) −189.858 + 260.168i −0.311243 + 0.426506i
\(611\) −154.189 474.546i −0.252355 0.776670i
\(612\) 3.44390 + 6.75903i 0.00562728 + 0.0110442i
\(613\) 589.854 300.546i 0.962242 0.490287i 0.0990057 0.995087i \(-0.468434\pi\)
0.863236 + 0.504800i \(0.168434\pi\)
\(614\) −1387.45 + 450.810i −2.25969 + 0.734219i
\(615\) 38.3904 27.7695i 0.0624234 0.0451536i
\(616\) 67.1570 206.688i 0.109021 0.335532i
\(617\) −516.552 + 81.8137i −0.837199 + 0.132599i −0.560290 0.828297i \(-0.689310\pi\)
−0.276909 + 0.960896i \(0.589310\pi\)
\(618\) −510.705 510.705i −0.826383 0.826383i
\(619\) −646.583 + 889.945i −1.04456 + 1.43771i −0.151130 + 0.988514i \(0.548291\pi\)
−0.893431 + 0.449201i \(0.851709\pi\)
\(620\) −134.004 + 261.640i −0.216135 + 0.422000i
\(621\) 521.952 379.220i 0.840502 0.610660i
\(622\) 76.4623 482.764i 0.122930 0.776148i
\(623\) −219.048 + 429.905i −0.351601 + 0.690056i
\(624\) 860.080i 1.37833i
\(625\) −198.113 + 592.770i −0.316980 + 0.948432i
\(626\) −1297.66 −2.07294
\(627\) 89.1566 + 45.4275i 0.142195 + 0.0724522i
\(628\) 63.7922 + 10.1037i 0.101580 + 0.0160887i
\(629\) −19.8187 27.2780i −0.0315082 0.0433673i
\(630\) 453.471 + 232.254i 0.719795 + 0.368656i
\(631\) 773.885 + 562.261i 1.22644 + 0.891063i 0.996618 0.0821694i \(-0.0261848\pi\)
0.229824 + 0.973232i \(0.426185\pi\)
\(632\) −6.26377 + 6.26377i −0.00991102 + 0.00991102i
\(633\) 79.6211 + 502.708i 0.125784 + 0.794167i
\(634\) 716.917 + 232.940i 1.13078 + 0.367414i
\(635\) −710.046 981.616i −1.11818 1.54585i
\(636\) −139.415 429.075i −0.219206 0.674646i
\(637\) 212.403 + 416.864i 0.333442 + 0.654417i
\(638\) −382.750 + 195.021i −0.599922 + 0.305676i
\(639\) 388.189 126.130i 0.607494 0.197387i
\(640\) −287.415 209.741i −0.449086 0.327720i
\(641\) −14.7703 + 45.4584i −0.0230426 + 0.0709179i −0.961917 0.273343i \(-0.911871\pi\)
0.938874 + 0.344261i \(0.111871\pi\)
\(642\) 535.138 84.7575i 0.833548 0.132021i
\(643\) 508.705 + 508.705i 0.791143 + 0.791143i 0.981680 0.190537i \(-0.0610230\pi\)
−0.190537 + 0.981680i \(0.561023\pi\)
\(644\) 625.189 860.499i 0.970790 1.33618i
\(645\) −30.6951 196.466i −0.0475894 0.304598i
\(646\) −3.39365 + 2.46563i −0.00525334 + 0.00381677i
\(647\) 23.3935 147.701i 0.0361568 0.228285i −0.962992 0.269529i \(-0.913132\pi\)
0.999149 + 0.0412437i \(0.0131320\pi\)
\(648\) 104.433 204.962i 0.161162 0.316299i
\(649\) 5.36120i 0.00826070i
\(650\) 496.661 + 689.657i 0.764094 + 1.06101i
\(651\) 626.255 0.961990
\(652\) −203.518 103.698i −0.312144 0.159045i
\(653\) 485.576 + 76.9077i 0.743609 + 0.117776i 0.516732 0.856147i \(-0.327148\pi\)
0.226877 + 0.973923i \(0.427148\pi\)
\(654\) 1139.91 + 1568.95i 1.74298 + 2.39900i
\(655\) 122.176 + 241.031i 0.186528 + 0.367986i
\(656\) −39.5448 28.7310i −0.0602817 0.0437972i
\(657\) 175.064 175.064i 0.266460 0.266460i
\(658\) −152.044 959.970i −0.231070 1.45892i
\(659\) −207.038 67.2707i −0.314170 0.102080i 0.147688 0.989034i \(-0.452817\pi\)
−0.461858 + 0.886954i \(0.652817\pi\)
\(660\) 559.575 180.521i 0.847841 0.273517i
\(661\) 315.065 + 969.671i 0.476650 + 1.46698i 0.843720 + 0.536783i \(0.180361\pi\)
−0.367071 + 0.930193i \(0.619639\pi\)
\(662\) −259.532 509.360i −0.392042 0.769425i
\(663\) 24.0200 12.2388i 0.0362292 0.0184597i
\(664\) 143.289 46.5575i 0.215797 0.0701167i
\(665\) −38.5962 + 117.945i −0.0580394 + 0.177361i
\(666\) −195.768 + 602.511i −0.293945 + 0.904670i
\(667\) 561.142 88.8761i 0.841292 0.133248i
\(668\) −67.2588 67.2588i −0.100687 0.100687i
\(669\) −713.196 + 981.630i −1.06606 + 1.46731i
\(670\) 64.1310 + 64.4004i 0.0957179 + 0.0961200i
\(671\) 200.983 146.023i 0.299528 0.217620i
\(672\) 214.325 1353.19i 0.318936 2.01368i
\(673\) −147.992 + 290.450i −0.219898 + 0.431575i −0.974431 0.224688i \(-0.927864\pi\)
0.754532 + 0.656263i \(0.227864\pi\)
\(674\) 225.281i 0.334245i
\(675\) 67.3617 + 437.159i 0.0997951 + 0.647643i
\(676\) −23.1287 −0.0342141
\(677\) 1132.17 + 576.870i 1.67234 + 0.852098i 0.992979 + 0.118290i \(0.0377412\pi\)
0.679357 + 0.733808i \(0.262259\pi\)
\(678\) −1527.14 241.875i −2.25242 0.356748i
\(679\) −21.2410 29.2357i −0.0312828 0.0430570i
\(680\) 1.05577 6.57663i 0.00155261 0.00967152i
\(681\) 37.2192 + 27.0413i 0.0546538 + 0.0397083i
\(682\) 363.986 363.986i 0.533704 0.533704i
\(683\) 114.786 + 724.732i 0.168062 + 1.06110i 0.917124 + 0.398601i \(0.130504\pi\)
−0.749062 + 0.662499i \(0.769496\pi\)
\(684\) 33.0179 + 10.7282i 0.0482718 + 0.0156844i
\(685\) 1.60790 767.071i 0.00234730 1.11981i
\(686\) −93.3883 287.420i −0.136135 0.418979i
\(687\) −658.058 1291.51i −0.957871 1.87993i
\(688\) −182.781 + 93.1318i −0.265671 + 0.135366i
\(689\) −478.384 + 155.436i −0.694317 + 0.225597i
\(690\) −1765.40 3.70057i −2.55856 0.00536314i
\(691\) 214.098 658.927i 0.309838 0.953585i −0.667989 0.744171i \(-0.732845\pi\)
0.977827 0.209413i \(-0.0671554\pi\)
\(692\) −589.759 + 93.4086i −0.852253 + 0.134984i
\(693\) −277.882 277.882i −0.400984 0.400984i
\(694\) 226.202 311.340i 0.325939 0.448617i
\(695\) 828.293 + 132.969i 1.19179 + 0.191322i
\(696\) 103.858 75.4575i 0.149222 0.108416i
\(697\) 0.239672 1.51323i 0.000343862 0.00217106i
\(698\) −720.118 + 1413.31i −1.03169 + 2.02480i
\(699\) 718.077i 1.02729i
\(700\) 328.329 + 651.116i 0.469042 + 0.930166i
\(701\) 367.187 0.523805 0.261902 0.965094i \(-0.415650\pi\)
0.261902 + 0.965094i \(0.415650\pi\)
\(702\) 535.913 + 273.061i 0.763409 + 0.388976i
\(703\) −152.411 24.1395i −0.216800 0.0343378i
\(704\) −209.041 287.721i −0.296934 0.408694i
\(705\) −503.516 + 501.410i −0.714208 + 0.711220i
\(706\) −52.3272 38.0180i −0.0741179 0.0538498i
\(707\) 503.516 503.516i 0.712186 0.712186i
\(708\) −0.927490 5.85594i −0.00131001 0.00827111i
\(709\) −227.327 73.8631i −0.320631 0.104179i 0.144280 0.989537i \(-0.453913\pi\)
−0.464910 + 0.885358i \(0.653913\pi\)
\(710\) 1260.48 + 412.479i 1.77533 + 0.580956i
\(711\) 4.94994 + 15.2343i 0.00696194 + 0.0214267i
\(712\) −53.8067 105.602i −0.0755712 0.148317i
\(713\) −606.595 + 309.076i −0.850765 + 0.433486i
\(714\) 49.9418 16.2271i 0.0699465 0.0227270i
\(715\) −201.266 623.881i −0.281492 0.872561i
\(716\) 265.982 818.607i 0.371483 1.14331i
\(717\) −1516.97 + 240.265i −2.11572 + 0.335098i
\(718\) 69.6951 + 69.6951i 0.0970684 + 0.0970684i
\(719\) 444.920 612.380i 0.618804 0.851711i −0.378461 0.925617i \(-0.623547\pi\)
0.997265 + 0.0739064i \(0.0235466\pi\)
\(720\) −342.757 + 173.739i −0.476051 + 0.241305i
\(721\) −558.962 + 406.110i −0.775260 + 0.563259i
\(722\) 147.992 934.385i 0.204975 1.29416i
\(723\) −450.011 + 883.197i −0.622422 + 1.22157i
\(724\) 881.248i 1.21719i
\(725\) −121.916 + 369.935i −0.168160 + 0.510255i
\(726\) 142.007 0.195602
\(727\) −1151.15 586.543i −1.58343 0.806799i −0.583446 0.812152i \(-0.698296\pi\)
−0.999986 + 0.00535374i \(0.998296\pi\)
\(728\) −264.660 41.9180i −0.363543 0.0575796i
\(729\) 94.4459 + 129.994i 0.129555 + 0.178318i
\(730\) 794.816 124.179i 1.08879 0.170109i
\(731\) −5.20190 3.77940i −0.00711614 0.00517018i
\(732\) 194.268 194.268i 0.265394 0.265394i
\(733\) −132.387 835.857i −0.180609 1.14032i −0.896806 0.442424i \(-0.854119\pi\)
0.716196 0.697899i \(-0.245881\pi\)
\(734\) −606.822 197.168i −0.826732 0.268622i
\(735\) 392.763 538.216i 0.534372 0.732267i
\(736\) 460.245 + 1416.49i 0.625333 + 1.92458i
\(737\) −31.8261 62.4623i −0.0431834 0.0847521i
\(738\) −25.6489 + 13.0688i −0.0347546 + 0.0177083i
\(739\) −213.688 + 69.4313i −0.289158 + 0.0939531i −0.450004 0.893026i \(-0.648578\pi\)
0.160847 + 0.986979i \(0.448578\pi\)
\(740\) −734.678 + 531.426i −0.992808 + 0.718143i
\(741\) 38.1253 117.338i 0.0514512 0.158351i
\(742\) −967.735 + 153.274i −1.30422 + 0.206569i
\(743\) −127.052 127.052i −0.170999 0.170999i 0.616419 0.787418i \(-0.288583\pi\)
−0.787418 + 0.616419i \(0.788583\pi\)
\(744\) −90.4208 + 124.454i −0.121533 + 0.167276i
\(745\) −546.342 + 1066.72i −0.733345 + 1.43184i
\(746\) 718.344 521.908i 0.962928 0.699608i
\(747\) 42.6193 269.088i 0.0570540 0.360225i
\(748\) 8.63145 16.9402i 0.0115394 0.0226473i
\(749\) 518.305i 0.691996i
\(750\) 556.253 1074.94i 0.741671 1.43326i
\(751\) −1293.56 −1.72245 −0.861223 0.508228i \(-0.830301\pi\)
−0.861223 + 0.508228i \(0.830301\pi\)
\(752\) 653.172 + 332.808i 0.868580 + 0.442564i
\(753\) −95.1367 15.0682i −0.126344 0.0200109i
\(754\) 311.324 + 428.501i 0.412896 + 0.568303i
\(755\) 308.924 + 158.221i 0.409171 + 0.209565i
\(756\) 417.510 + 303.339i 0.552262 + 0.401242i
\(757\) −527.385 + 527.385i −0.696678 + 0.696678i −0.963692 0.267015i \(-0.913963\pi\)
0.267015 + 0.963692i \(0.413963\pi\)
\(758\) −215.838 1362.74i −0.284746 1.79782i
\(759\) 1295.07 + 420.794i 1.70629 + 0.554406i
\(760\) −17.8662 24.6994i −0.0235081 0.0324992i
\(761\) −60.6870 186.775i −0.0797463 0.245434i 0.903233 0.429151i \(-0.141187\pi\)
−0.982979 + 0.183717i \(0.941187\pi\)
\(762\) 1065.12 + 2090.41i 1.39779 + 2.74332i
\(763\) 1653.00 842.244i 2.16644 1.10386i
\(764\) −343.756 + 111.693i −0.449942 + 0.146195i
\(765\) −9.72950 7.10011i −0.0127183 0.00928118i
\(766\) −483.873 + 1489.21i −0.631688 + 1.94414i
\(767\) −6.52891 + 1.03408i −0.00851227 + 0.00134821i
\(768\) 840.484 + 840.484i 1.09438 + 1.09438i
\(769\) 668.490 920.097i 0.869297 1.19648i −0.109975 0.993934i \(-0.535077\pi\)
0.979272 0.202551i \(-0.0649230\pi\)
\(770\) −197.112 1261.62i −0.255989 1.63847i
\(771\) 1399.07 1016.49i 1.81462 1.31840i
\(772\) 37.4562 236.489i 0.0485184 0.306333i
\(773\) 267.971 525.923i 0.346664 0.680367i −0.650178 0.759782i \(-0.725305\pi\)
0.996842 + 0.0794158i \(0.0253055\pi\)
\(774\) 120.811i 0.156087i
\(775\) 1.95674 466.742i 0.00252482 0.602247i
\(776\) 8.87675 0.0114391
\(777\) 1721.17 + 876.980i 2.21515 + 1.12867i
\(778\) 744.332 + 117.891i 0.956725 + 0.151530i
\(779\) −4.12138 5.67259i −0.00529060 0.00728189i
\(780\) −327.772 646.636i −0.420220 0.829020i
\(781\) −827.613 601.296i −1.05968 0.769906i
\(782\) −40.3655 + 40.3655i −0.0516182 + 0.0516182i
\(783\) 43.1223 + 272.264i 0.0550732 + 0.347719i
\(784\) −653.725 212.408i −0.833833 0.270929i
\(785\) −97.5981 + 31.4855i −0.124329 + 0.0401089i
\(786\) −161.711 497.695i −0.205739 0.633200i
\(787\) 91.1340 + 178.861i 0.115799 + 0.227269i 0.941630 0.336649i \(-0.109294\pi\)
−0.825831 + 0.563918i \(0.809294\pi\)
\(788\) 446.163 227.331i 0.566196 0.288491i
\(789\) −774.397 + 251.617i −0.981492 + 0.318906i
\(790\) −16.1876 + 49.4673i −0.0204907 + 0.0626168i
\(791\) −457.068 + 1406.71i −0.577836 + 1.77840i
\(792\) 95.3441 15.1010i 0.120384 0.0190669i
\(793\) −216.594 216.594i −0.273132 0.273132i
\(794\) −920.495 + 1266.95i −1.15931 + 1.59566i
\(795\) 505.466 + 507.589i 0.635806 + 0.638477i
\(796\) 335.627 243.848i 0.421642 0.306341i
\(797\) −136.705 + 863.119i −0.171524 + 1.08296i 0.740270 + 0.672310i \(0.234698\pi\)
−0.911793 + 0.410649i \(0.865302\pi\)
\(798\) 109.105 214.130i 0.136723 0.268334i
\(799\) 22.9774i 0.0287576i
\(800\) −1007.85 163.962i −1.25982 0.204953i
\(801\) −214.317 −0.267562
\(802\) −498.586 254.042i −0.621678 0.316761i
\(803\) −612.866 97.0685i −0.763221 0.120882i
\(804\) −45.5692 62.7206i −0.0566781 0.0780107i
\(805\) −267.687 + 1667.48i −0.332530 + 2.07140i
\(806\) −513.472 373.059i −0.637062 0.462853i
\(807\) 112.303 112.303i 0.139161 0.139161i
\(808\) 27.3627 + 172.761i 0.0338647 + 0.213813i
\(809\) 912.596 + 296.520i 1.12805 + 0.366527i 0.812836 0.582492i \(-0.197922\pi\)
0.315218 + 0.949019i \(0.397922\pi\)
\(810\) 2.83318 1351.60i 0.00349775 1.66865i
\(811\) −239.714 737.763i −0.295578 0.909695i −0.983027 0.183462i \(-0.941269\pi\)
0.687449 0.726233i \(-0.258731\pi\)
\(812\) 206.318 + 404.921i 0.254086 + 0.498672i
\(813\) 1121.30 571.330i 1.37921 0.702743i
\(814\) 1510.07 490.653i 1.85513 0.602767i
\(815\) 362.671 + 0.760217i 0.444996 + 0.000932781i
\(816\) −12.2391 + 37.6681i −0.0149989 + 0.0461619i
\(817\) −29.0645 + 4.60337i −0.0355747 + 0.00563448i
\(818\) 774.675 + 774.675i 0.947035 + 0.947035i
\(819\) −284.809 + 392.006i −0.347752 + 0.478639i
\(820\) −40.6802 6.53056i −0.0496100 0.00796409i
\(821\) 242.698 176.330i 0.295613 0.214775i −0.430086 0.902788i \(-0.641517\pi\)
0.725698 + 0.688013i \(0.241517\pi\)
\(822\) −232.379 + 1467.18i −0.282699 + 1.78489i
\(823\) 230.679 452.732i 0.280290 0.550100i −0.707346 0.706868i \(-0.750107\pi\)
0.987635 + 0.156768i \(0.0501075\pi\)
\(824\) 169.716i 0.205966i
\(825\) −662.899 + 657.364i −0.803514 + 0.796805i
\(826\) −12.8762 −0.0155886
\(827\) −1282.57 653.504i −1.55087 0.790210i −0.551832 0.833955i \(-0.686071\pi\)
−0.999043 + 0.0437453i \(0.986071\pi\)
\(828\) 466.635 + 73.9078i 0.563569 + 0.0892606i
\(829\) −410.893 565.546i −0.495649 0.682203i 0.485768 0.874088i \(-0.338540\pi\)
−0.981417 + 0.191885i \(0.938540\pi\)
\(830\) 627.276 624.652i 0.755755 0.752593i
\(831\) −605.218 439.717i −0.728301 0.529142i
\(832\) −310.069 + 310.069i −0.372679 + 0.372679i
\(833\) −3.37034 21.2795i −0.00404603 0.0255456i
\(834\) −1545.05 502.017i −1.85258 0.601939i
\(835\) 143.538 + 46.9711i 0.171902 + 0.0562528i
\(836\) −26.8880 82.7528i −0.0321627 0.0989866i
\(837\) −149.962 294.318i −0.179166 0.351634i
\(838\) −686.317 + 349.696i −0.818994 + 0.417298i
\(839\) −247.248 + 80.3359i −0.294694 + 0.0957519i −0.452633 0.891697i \(-0.649515\pi\)
0.157939 + 0.987449i \(0.449515\pi\)
\(840\) 117.162 + 363.176i 0.139479 + 0.432353i
\(841\) 184.871 568.974i 0.219823 0.676545i
\(842\) −869.036 + 137.642i −1.03211 + 0.163470i
\(843\) 477.794 + 477.794i 0.566778 + 0.566778i
\(844\) 260.147 358.061i 0.308231 0.424243i
\(845\) 32.7558 16.6035i 0.0387642 0.0196491i
\(846\) 349.269 253.759i 0.412848 0.299952i
\(847\) 21.2512 134.175i 0.0250900 0.158412i
\(848\) 335.500 658.456i 0.395637 0.776481i
\(849\) 45.4295i 0.0535095i
\(850\) −11.9378 37.2718i −0.0140445 0.0438492i
\(851\) −2099.95 −2.46763
\(852\) −1008.01 513.608i −1.18311 0.602826i
\(853\) −1173.94 185.933i −1.37624 0.217976i −0.575901 0.817519i \(-0.695349\pi\)
−0.800342 + 0.599544i \(0.795349\pi\)
\(854\) −350.708 482.708i −0.410665 0.565232i
\(855\) −54.4626 + 8.50904i −0.0636990 + 0.00995210i
\(856\) 103.001 + 74.8346i 0.120328 + 0.0874236i
\(857\) 1103.02 1103.02i 1.28707 1.28707i 0.350513 0.936558i \(-0.386007\pi\)
0.936558 0.350513i \(-0.113993\pi\)
\(858\) 198.592 + 1253.86i 0.231459 + 1.46137i
\(859\) 922.654 + 299.788i 1.07410 + 0.348997i 0.792084 0.610412i \(-0.208996\pi\)
0.282018 + 0.959409i \(0.408996\pi\)
\(860\) −101.929 + 139.676i −0.118522 + 0.162414i
\(861\) 27.1240 + 83.4792i 0.0315030 + 0.0969561i
\(862\) 396.223 + 777.632i 0.459656 + 0.902125i
\(863\) −543.074 + 276.710i −0.629286 + 0.320637i −0.739384 0.673284i \(-0.764883\pi\)
0.110099 + 0.993921i \(0.464883\pi\)
\(864\) −687.275 + 223.309i −0.795457 + 0.258460i
\(865\) 768.183 555.661i 0.888073 0.642383i
\(866\) −179.649 + 552.904i −0.207447 + 0.638457i
\(867\) 1032.47 163.527i 1.19085 0.188612i
\(868\) −385.071 385.071i −0.443630 0.443630i
\(869\) 23.5977 32.4795i 0.0271550 0.0373757i
\(870\) 343.852 671.364i 0.395232 0.771683i
\(871\) −69.9285 + 50.8060i −0.0802853 + 0.0583307i
\(872\) −71.2889 + 450.100i −0.0817533 + 0.516170i
\(873\) 7.28732 14.3022i 0.00834745 0.0163828i
\(874\) 261.255i 0.298919i
\(875\) −932.411 686.436i −1.06561 0.784499i
\(876\) −686.216 −0.783352
\(877\) 496.670 + 253.066i 0.566328 + 0.288559i 0.713618 0.700535i \(-0.247055\pi\)
−0.147290 + 0.989093i \(0.547055\pi\)
\(878\) 614.616 + 97.3456i 0.700018 + 0.110872i
\(879\) −762.689 1049.75i −0.867678 1.19426i
\(880\) 857.220 + 439.041i 0.974113 + 0.498910i
\(881\) 571.794 + 415.433i 0.649028 + 0.471547i 0.862940 0.505306i \(-0.168621\pi\)
−0.213912 + 0.976853i \(0.568621\pi\)
\(882\) −286.239 + 286.239i −0.324535 + 0.324535i
\(883\) 63.1426 + 398.666i 0.0715091 + 0.451491i 0.997299 + 0.0734518i \(0.0234015\pi\)
−0.925790 + 0.378039i \(0.876598\pi\)
\(884\) −22.2947 7.24400i −0.0252203 0.00819457i
\(885\) 5.51737 + 7.62758i 0.00623432 + 0.00861874i
\(886\) 247.379 + 761.355i 0.279209 + 0.859317i
\(887\) 675.314 + 1325.38i 0.761346 + 1.49423i 0.866178 + 0.499735i \(0.166569\pi\)
−0.104832 + 0.994490i \(0.533431\pi\)
\(888\) −422.787 + 215.421i −0.476112 + 0.242591i
\(889\) 2134.51 693.543i 2.40102 0.780139i
\(890\) −562.526 410.504i −0.632052 0.461240i
\(891\) −322.162 + 991.514i −0.361574 + 1.11281i
\(892\) 1042.11 165.054i 1.16829 0.185038i
\(893\) 74.3574 + 74.3574i 0.0832670 + 0.0832670i
\(894\) 1364.21 1877.68i 1.52596 2.10031i
\(895\) 210.963 + 1350.28i 0.235713 + 1.50870i
\(896\) 533.261 387.437i 0.595157 0.432407i
\(897\) 262.651 1658.31i 0.292810 1.84873i
\(898\) 224.249 440.114i 0.249721 0.490105i
\(899\) 290.881i 0.323561i
\(900\) −191.485 + 261.246i −0.212761 + 0.290273i
\(901\) 23.1632 0.0257083
\(902\) 64.2838 + 32.7542i 0.0712681 + 0.0363129i
\(903\) 363.841 + 57.6267i 0.402925 + 0.0638170i
\(904\) −213.558 293.937i −0.236236 0.325151i
\(905\) −632.625 1248.06i −0.699033 1.37907i
\(906\) −543.777 395.077i −0.600196 0.436068i
\(907\) −183.343 + 183.343i −0.202142 + 0.202142i −0.800917 0.598775i \(-0.795654\pi\)
0.598775 + 0.800917i \(0.295654\pi\)
\(908\) −6.25815 39.5124i −0.00689224 0.0435159i
\(909\) 300.815 + 97.7407i 0.330930 + 0.107526i
\(910\) −1498.40 + 483.389i −1.64659 + 0.531196i
\(911\) 337.161 + 1037.67i 0.370100 + 1.13905i 0.946726 + 0.322041i \(0.104369\pi\)
−0.576626 + 0.817008i \(0.695631\pi\)
\(912\) 82.2912 + 161.506i 0.0902316 + 0.177090i
\(913\) −608.399 + 309.995i −0.666374 + 0.339534i
\(914\) 1106.14 359.406i 1.21022 0.393223i
\(915\) −135.670 + 414.590i −0.148273 + 0.453104i
\(916\) −389.496 + 1198.75i −0.425214 + 1.30868i
\(917\) −494.444 + 78.3122i −0.539197 + 0.0854004i
\(918\) −19.5852 19.5852i −0.0213346 0.0213346i
\(919\) −355.204 + 488.897i −0.386512 + 0.531988i −0.957295 0.289113i \(-0.906640\pi\)
0.570783 + 0.821101i \(0.306640\pi\)
\(920\) −292.722 293.952i −0.318176 0.319513i
\(921\) −1598.52 + 1161.40i −1.73564 + 1.26102i
\(922\) 293.549 1853.39i 0.318382 2.01019i
\(923\) −572.632 + 1123.85i −0.620403 + 1.21761i
\(924\) 1089.24i 1.17883i
\(925\) 658.982 1280.03i 0.712413 1.38382i
\(926\) 2319.44 2.50480
\(927\) −273.446 139.328i −0.294979 0.150299i
\(928\) −628.528 99.5490i −0.677293 0.107273i
\(929\) 680.551 + 936.698i 0.732563 + 1.00829i 0.999012 + 0.0444375i \(0.0141496\pi\)
−0.266449 + 0.963849i \(0.585850\pi\)
\(930\) −143.268 + 892.447i −0.154052 + 0.959621i
\(931\) −79.7699 57.9562i −0.0856819 0.0622515i
\(932\) −441.530 + 441.530i −0.473744 + 0.473744i
\(933\) −103.561 653.860i −0.110998 0.700814i
\(934\) −1104.39 358.838i −1.18243 0.384195i
\(935\) −0.0632780 + 30.1876i −6.76770e−5 + 0.0322862i
\(936\) −36.7803 113.198i −0.0392952 0.120938i
\(937\) −342.236 671.677i −0.365247 0.716838i 0.633115 0.774058i \(-0.281776\pi\)
−0.998362 + 0.0572205i \(0.981776\pi\)
\(938\) −150.018 + 76.4380i −0.159934 + 0.0814904i
\(939\) −1671.55 + 543.118i −1.78013 + 0.578401i
\(940\) 617.907 + 1.29523i 0.657348 + 0.00137791i
\(941\) 408.472 1257.15i 0.434083 1.33597i −0.459941 0.887949i \(-0.652129\pi\)
0.894024 0.448020i \(-0.147871\pi\)
\(942\) 196.150 31.0670i 0.208227 0.0329799i
\(943\) −67.4720 67.4720i −0.0715504 0.0715504i
\(944\) 5.70841 7.85695i 0.00604704 0.00832304i
\(945\) −809.053 129.880i −0.856141 0.137440i
\(946\) 244.962 177.975i 0.258945 0.188134i
\(947\) −90.9523 + 574.250i −0.0960425 + 0.606389i 0.891979 + 0.452076i \(0.149316\pi\)
−0.988022 + 0.154313i \(0.950684\pi\)
\(948\) 20.1564 39.5592i 0.0212620 0.0417291i
\(949\) 765.076i 0.806192i
\(950\) −159.248 81.9838i −0.167630 0.0862988i
\(951\) 1020.97 1.07357
\(952\) 10.9945 + 5.60200i 0.0115489 + 0.00588445i
\(953\) 1229.45 + 194.726i 1.29008 + 0.204329i 0.763508 0.645798i \(-0.223475\pi\)
0.526577 + 0.850128i \(0.323475\pi\)
\(954\) −255.812 352.095i −0.268146 0.369072i
\(955\) 406.658 404.957i 0.425820 0.424039i
\(956\) 1080.49 + 785.020i 1.13022 + 0.821151i
\(957\) −411.405 + 411.405i −0.429890 + 0.429890i
\(958\) 33.6079 + 212.192i 0.0350813 + 0.221495i
\(959\) 1351.48 + 439.123i 1.40926 + 0.457897i
\(960\) 593.514 + 194.221i 0.618244 + 0.202313i
\(961\) −189.254 582.462i −0.196934 0.606100i
\(962\) −888.787 1744.34i −0.923895 1.81325i
\(963\) 205.131 104.520i 0.213013 0.108535i
\(964\) 819.760 266.356i 0.850374 0.276303i
\(965\) 116.723 + 361.814i 0.120956 + 0.374937i
\(966\) 1010.64 3110.42i 1.04621 3.21989i
\(967\) 606.819 96.1107i 0.627527 0.0993906i 0.165433 0.986221i \(-0.447098\pi\)
0.462095 + 0.886831i \(0.347098\pi\)
\(968\) 23.5958 + 23.5958i 0.0243758 + 0.0243758i
\(969\) −3.33948 + 4.59640i −0.00344631 + 0.00474344i
\(970\) 46.5218 23.5813i 0.0479606 0.0243106i
\(971\) −591.996 + 430.110i −0.609676 + 0.442956i −0.849300 0.527910i \(-0.822976\pi\)
0.239624 + 0.970866i \(0.422976\pi\)
\(972\) −101.918 + 643.486i −0.104854 + 0.662023i
\(973\) −705.543 + 1384.71i −0.725121 + 1.42313i
\(974\) 1259.75i 1.29338i
\(975\) 928.405 + 680.491i 0.952210 + 0.697939i
\(976\) 450.025 0.461091
\(977\) 299.952 + 152.833i 0.307013 + 0.156431i 0.600709 0.799468i \(-0.294885\pi\)
−0.293696 + 0.955899i \(0.594885\pi\)
\(978\) −693.684 109.869i −0.709288 0.112340i
\(979\) 315.725 + 434.558i 0.322497 + 0.443880i
\(980\) −572.439 + 89.4357i −0.584121 + 0.0912610i
\(981\) 666.675 + 484.368i 0.679587 + 0.493749i
\(982\) −644.431 + 644.431i −0.656243 + 0.656243i
\(983\) −178.128 1124.65i −0.181208 1.14410i −0.895765 0.444527i \(-0.853372\pi\)
0.714557 0.699577i \(-0.246628\pi\)
\(984\) −20.5058 6.66273i −0.0208392 0.00677107i
\(985\) −468.677 + 642.243i −0.475814 + 0.652024i
\(986\) −7.53710 23.1968i −0.00764412 0.0235262i
\(987\) −597.633 1172.92i −0.605504 1.18837i
\(988\) −95.5908 + 48.7060i −0.0967519 + 0.0492975i
\(989\) −380.859 + 123.749i −0.385096 + 0.125125i
\(990\) 459.568 332.426i 0.464210 0.335784i
\(991\) 353.468 1087.86i 0.356678 1.09774i −0.598352 0.801233i \(-0.704178\pi\)
0.955030 0.296509i \(-0.0958224\pi\)
\(992\) 753.164 119.290i 0.759238 0.120252i
\(993\) −547.493 547.493i −0.551352 0.551352i
\(994\) −1444.15 + 1987.71i −1.45287 + 1.99971i
\(995\) −300.276 + 586.284i −0.301785 + 0.589230i
\(996\) −610.915 + 443.855i −0.613368 + 0.445638i
\(997\) 181.244 1144.33i 0.181789 1.14777i −0.712962 0.701203i \(-0.752647\pi\)
0.894750 0.446567i \(-0.147353\pi\)
\(998\) 489.793 961.272i 0.490774 0.963198i
\(999\) 1018.89i 1.01991i
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.8.1 32
3.2 odd 2 225.3.r.a.208.4 32
4.3 odd 2 400.3.bg.c.33.3 32
5.2 odd 4 125.3.f.a.107.4 32
5.3 odd 4 125.3.f.b.107.1 32
5.4 even 2 125.3.f.c.18.4 32
25.3 odd 20 125.3.f.c.7.4 32
25.4 even 10 125.3.f.b.118.1 32
25.21 even 5 125.3.f.a.118.4 32
25.22 odd 20 inner 25.3.f.a.22.1 yes 32
75.47 even 20 225.3.r.a.172.4 32
100.47 even 20 400.3.bg.c.97.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.8.1 32 1.1 even 1 trivial
25.3.f.a.22.1 yes 32 25.22 odd 20 inner
125.3.f.a.107.4 32 5.2 odd 4
125.3.f.a.118.4 32 25.21 even 5
125.3.f.b.107.1 32 5.3 odd 4
125.3.f.b.118.1 32 25.4 even 10
125.3.f.c.7.4 32 25.3 odd 20
125.3.f.c.18.4 32 5.4 even 2
225.3.r.a.172.4 32 75.47 even 20
225.3.r.a.208.4 32 3.2 odd 2
400.3.bg.c.33.3 32 4.3 odd 2
400.3.bg.c.97.3 32 100.47 even 20