Properties

Label 32.3.h.a.19.4
Level $32$
Weight $3$
Character 32.19
Analytic conductor $0.872$
Analytic rank $0$
Dimension $28$
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] = [32,3,Mod(3,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.h (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.871936845953\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.4
Character \(\chi\) \(=\) 32.19
Dual form 32.3.h.a.27.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.108191 - 1.99707i) q^{2} +(4.35131 + 1.80237i) q^{3} +(-3.97659 + 0.432130i) q^{4} +(-2.81639 + 1.16659i) q^{5} +(3.12870 - 8.88489i) q^{6} +(-6.23443 - 6.23443i) q^{7} +(1.29322 + 7.89478i) q^{8} +(9.32143 + 9.32143i) q^{9} +O(q^{10})\) \(q+(-0.108191 - 1.99707i) q^{2} +(4.35131 + 1.80237i) q^{3} +(-3.97659 + 0.432130i) q^{4} +(-2.81639 + 1.16659i) q^{5} +(3.12870 - 8.88489i) q^{6} +(-6.23443 - 6.23443i) q^{7} +(1.29322 + 7.89478i) q^{8} +(9.32143 + 9.32143i) q^{9} +(2.63447 + 5.49832i) q^{10} +(-8.06262 + 3.33965i) q^{11} +(-18.0823 - 5.28697i) q^{12} +(13.3208 + 5.51766i) q^{13} +(-11.7761 + 13.1251i) q^{14} -14.3576 q^{15} +(15.6265 - 3.43680i) q^{16} +4.56488i q^{17} +(17.6071 - 19.6241i) q^{18} +(13.4421 - 32.4522i) q^{19} +(10.6955 - 5.85609i) q^{20} +(-15.8912 - 38.3647i) q^{21} +(7.54181 + 15.7403i) q^{22} +(-6.75277 + 6.75277i) q^{23} +(-8.60212 + 36.6836i) q^{24} +(-11.1065 + 11.1065i) q^{25} +(9.57798 - 27.1996i) q^{26} +(7.53841 + 18.1993i) q^{27} +(27.4859 + 22.0977i) q^{28} +(-0.266504 + 0.643399i) q^{29} +(1.55336 + 28.6732i) q^{30} +0.326715i q^{31} +(-8.55419 - 30.8355i) q^{32} -41.1023 q^{33} +(9.11639 - 0.493878i) q^{34} +(24.8316 + 10.2856i) q^{35} +(-41.0956 - 33.0394i) q^{36} +(31.5133 - 13.0532i) q^{37} +(-66.2637 - 23.3339i) q^{38} +(48.0182 + 48.0182i) q^{39} +(-12.8522 - 20.7261i) q^{40} +(15.7509 + 15.7509i) q^{41} +(-74.8979 + 35.8866i) q^{42} +(4.83274 - 2.00179i) q^{43} +(30.6186 - 16.7645i) q^{44} +(-37.1271 - 15.3785i) q^{45} +(14.2164 + 12.7552i) q^{46} -49.7096 q^{47} +(74.1903 + 13.2102i) q^{48} +28.7362i q^{49} +(23.3822 + 20.9789i) q^{50} +(-8.22762 + 19.8632i) q^{51} +(-55.3558 - 16.1852i) q^{52} +(4.45882 + 10.7645i) q^{53} +(35.5298 - 17.0238i) q^{54} +(18.8115 - 18.8115i) q^{55} +(41.1569 - 57.2820i) q^{56} +(116.982 - 116.982i) q^{57} +(1.31375 + 0.462619i) q^{58} +(13.1268 + 31.6909i) q^{59} +(57.0944 - 6.20436i) q^{60} +(-35.4023 + 85.4687i) q^{61} +(0.652473 - 0.0353475i) q^{62} -116.228i q^{63} +(-60.6551 + 20.4194i) q^{64} -43.9535 q^{65} +(4.44689 + 82.0842i) q^{66} +(-41.3348 - 17.1214i) q^{67} +(-1.97262 - 18.1527i) q^{68} +(-41.5545 + 17.2124i) q^{69} +(17.8545 - 50.7033i) q^{70} +(37.6381 + 37.6381i) q^{71} +(-61.5359 + 85.6453i) q^{72} +(-52.2302 - 52.2302i) q^{73} +(-29.4777 - 61.5220i) q^{74} +(-68.3461 + 28.3099i) q^{75} +(-39.4303 + 134.858i) q^{76} +(71.0866 + 29.4450i) q^{77} +(90.7006 - 101.091i) q^{78} +26.9061 q^{79} +(-40.0011 + 27.9091i) q^{80} -25.8643i q^{81} +(29.7516 - 33.1598i) q^{82} +(10.6315 - 25.6667i) q^{83} +(79.7713 + 145.694i) q^{84} +(-5.32533 - 12.8565i) q^{85} +(-4.52057 - 9.43475i) q^{86} +(-2.31929 + 2.31929i) q^{87} +(-36.7926 - 59.3337i) q^{88} +(-103.292 + 103.292i) q^{89} +(-26.6952 + 75.8092i) q^{90} +(-48.6482 - 117.447i) q^{91} +(23.9349 - 29.7711i) q^{92} +(-0.588862 + 1.42164i) q^{93} +(5.37812 + 99.2736i) q^{94} +107.080i q^{95} +(18.3551 - 149.593i) q^{96} +77.9778 q^{97} +(57.3883 - 3.10900i) q^{98} +(-106.285 - 44.0249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.108191 1.99707i −0.0540954 0.998536i
\(3\) 4.35131 + 1.80237i 1.45044 + 0.600791i 0.962304 0.271977i \(-0.0876775\pi\)
0.488135 + 0.872768i \(0.337678\pi\)
\(4\) −3.97659 + 0.432130i −0.994147 + 0.108032i
\(5\) −2.81639 + 1.16659i −0.563278 + 0.233318i −0.646108 0.763246i \(-0.723604\pi\)
0.0828294 + 0.996564i \(0.473604\pi\)
\(6\) 3.12870 8.88489i 0.521449 1.48081i
\(7\) −6.23443 6.23443i −0.890633 0.890633i 0.103950 0.994583i \(-0.466852\pi\)
−0.994583 + 0.103950i \(0.966852\pi\)
\(8\) 1.29322 + 7.89478i 0.161653 + 0.986848i
\(9\) 9.32143 + 9.32143i 1.03571 + 1.03571i
\(10\) 2.63447 + 5.49832i 0.263447 + 0.549832i
\(11\) −8.06262 + 3.33965i −0.732965 + 0.303604i −0.717770 0.696280i \(-0.754837\pi\)
−0.0151955 + 0.999885i \(0.504837\pi\)
\(12\) −18.0823 5.28697i −1.50685 0.440581i
\(13\) 13.3208 + 5.51766i 1.02468 + 0.424436i 0.830789 0.556588i \(-0.187890\pi\)
0.193889 + 0.981023i \(0.437890\pi\)
\(14\) −11.7761 + 13.1251i −0.841150 + 0.937508i
\(15\) −14.3576 −0.957176
\(16\) 15.6265 3.43680i 0.976658 0.214800i
\(17\) 4.56488i 0.268522i 0.990946 + 0.134261i \(0.0428661\pi\)
−0.990946 + 0.134261i \(0.957134\pi\)
\(18\) 17.6071 19.6241i 0.978170 1.09023i
\(19\) 13.4421 32.4522i 0.707481 1.70801i 0.00128016 0.999999i \(-0.499593\pi\)
0.706201 0.708011i \(-0.250407\pi\)
\(20\) 10.6955 5.85609i 0.534776 0.292804i
\(21\) −15.8912 38.3647i −0.756724 1.82689i
\(22\) 7.54181 + 15.7403i 0.342810 + 0.715469i
\(23\) −6.75277 + 6.75277i −0.293599 + 0.293599i −0.838500 0.544901i \(-0.816567\pi\)
0.544901 + 0.838500i \(0.316567\pi\)
\(24\) −8.60212 + 36.6836i −0.358422 + 1.52848i
\(25\) −11.1065 + 11.1065i −0.444261 + 0.444261i
\(26\) 9.57798 27.1996i 0.368384 1.04614i
\(27\) 7.53841 + 18.1993i 0.279200 + 0.674050i
\(28\) 27.4859 + 22.0977i 0.981638 + 0.789203i
\(29\) −0.266504 + 0.643399i −0.00918981 + 0.0221862i −0.928408 0.371563i \(-0.878822\pi\)
0.919218 + 0.393749i \(0.128822\pi\)
\(30\) 1.55336 + 28.6732i 0.0517788 + 0.955774i
\(31\) 0.326715i 0.0105392i 0.999986 + 0.00526959i \(0.00167737\pi\)
−0.999986 + 0.00526959i \(0.998323\pi\)
\(32\) −8.55419 30.8355i −0.267318 0.963608i
\(33\) −41.1023 −1.24552
\(34\) 9.11639 0.493878i 0.268129 0.0145258i
\(35\) 24.8316 + 10.2856i 0.709475 + 0.293874i
\(36\) −41.0956 33.0394i −1.14154 0.917762i
\(37\) 31.5133 13.0532i 0.851710 0.352790i 0.0862502 0.996274i \(-0.472512\pi\)
0.765460 + 0.643484i \(0.222512\pi\)
\(38\) −66.2637 23.3339i −1.74378 0.614050i
\(39\) 48.0182 + 48.0182i 1.23124 + 1.23124i
\(40\) −12.8522 20.7261i −0.321305 0.518153i
\(41\) 15.7509 + 15.7509i 0.384169 + 0.384169i 0.872601 0.488433i \(-0.162431\pi\)
−0.488433 + 0.872601i \(0.662431\pi\)
\(42\) −74.8979 + 35.8866i −1.78328 + 0.854442i
\(43\) 4.83274 2.00179i 0.112389 0.0465531i −0.325780 0.945446i \(-0.605627\pi\)
0.438170 + 0.898892i \(0.355627\pi\)
\(44\) 30.6186 16.7645i 0.695877 0.381011i
\(45\) −37.1271 15.3785i −0.825046 0.341745i
\(46\) 14.2164 + 12.7552i 0.309051 + 0.277287i
\(47\) −49.7096 −1.05765 −0.528825 0.848731i \(-0.677367\pi\)
−0.528825 + 0.848731i \(0.677367\pi\)
\(48\) 74.1903 + 13.2102i 1.54563 + 0.275213i
\(49\) 28.7362i 0.586454i
\(50\) 23.3822 + 20.9789i 0.467643 + 0.419578i
\(51\) −8.22762 + 19.8632i −0.161326 + 0.389475i
\(52\) −55.3558 16.1852i −1.06453 0.311253i
\(53\) 4.45882 + 10.7645i 0.0841286 + 0.203105i 0.960346 0.278812i \(-0.0899407\pi\)
−0.876217 + 0.481917i \(0.839941\pi\)
\(54\) 35.5298 17.0238i 0.657959 0.315255i
\(55\) 18.8115 18.8115i 0.342027 0.342027i
\(56\) 41.1569 57.2820i 0.734946 1.02289i
\(57\) 116.982 116.982i 2.05232 2.05232i
\(58\) 1.31375 + 0.462619i 0.0226508 + 0.00797618i
\(59\) 13.1268 + 31.6909i 0.222488 + 0.537134i 0.995227 0.0975907i \(-0.0311136\pi\)
−0.772739 + 0.634724i \(0.781114\pi\)
\(60\) 57.0944 6.20436i 0.951574 0.103406i
\(61\) −35.4023 + 85.4687i −0.580366 + 1.40113i 0.312116 + 0.950044i \(0.398962\pi\)
−0.892482 + 0.451083i \(0.851038\pi\)
\(62\) 0.652473 0.0353475i 0.0105238 0.000570122i
\(63\) 116.228i 1.84488i
\(64\) −60.6551 + 20.4194i −0.947737 + 0.319054i
\(65\) −43.9535 −0.676207
\(66\) 4.44689 + 82.0842i 0.0673771 + 1.24370i
\(67\) −41.3348 17.1214i −0.616938 0.255544i 0.0522539 0.998634i \(-0.483359\pi\)
−0.669192 + 0.743090i \(0.733359\pi\)
\(68\) −1.97262 18.1527i −0.0290091 0.266951i
\(69\) −41.5545 + 17.2124i −0.602239 + 0.249455i
\(70\) 17.8545 50.7033i 0.255064 0.724333i
\(71\) 37.6381 + 37.6381i 0.530114 + 0.530114i 0.920606 0.390492i \(-0.127695\pi\)
−0.390492 + 0.920606i \(0.627695\pi\)
\(72\) −61.5359 + 85.6453i −0.854666 + 1.18952i
\(73\) −52.2302 52.2302i −0.715482 0.715482i 0.252195 0.967677i \(-0.418848\pi\)
−0.967677 + 0.252195i \(0.918848\pi\)
\(74\) −29.4777 61.5220i −0.398347 0.831379i
\(75\) −68.3461 + 28.3099i −0.911282 + 0.377465i
\(76\) −39.4303 + 134.858i −0.518820 + 1.77445i
\(77\) 71.0866 + 29.4450i 0.923203 + 0.382403i
\(78\) 90.7006 101.091i 1.16283 1.29604i
\(79\) 26.9061 0.340583 0.170292 0.985394i \(-0.445529\pi\)
0.170292 + 0.985394i \(0.445529\pi\)
\(80\) −40.0011 + 27.9091i −0.500014 + 0.348864i
\(81\) 25.8643i 0.319313i
\(82\) 29.7516 33.1598i 0.362824 0.404388i
\(83\) 10.6315 25.6667i 0.128090 0.309237i −0.846804 0.531905i \(-0.821476\pi\)
0.974894 + 0.222667i \(0.0714764\pi\)
\(84\) 79.7713 + 145.694i 0.949658 + 1.73445i
\(85\) −5.32533 12.8565i −0.0626510 0.151253i
\(86\) −4.52057 9.43475i −0.0525647 0.109706i
\(87\) −2.31929 + 2.31929i −0.0266585 + 0.0266585i
\(88\) −36.7926 59.3337i −0.418097 0.674247i
\(89\) −103.292 + 103.292i −1.16058 + 1.16058i −0.176234 + 0.984348i \(0.556391\pi\)
−0.984348 + 0.176234i \(0.943609\pi\)
\(90\) −26.6952 + 75.8092i −0.296614 + 0.842325i
\(91\) −48.6482 117.447i −0.534596 1.29063i
\(92\) 23.9349 29.7711i 0.260162 0.323599i
\(93\) −0.588862 + 1.42164i −0.00633185 + 0.0152864i
\(94\) 5.37812 + 99.2736i 0.0572140 + 1.05610i
\(95\) 107.080i 1.12715i
\(96\) 18.3551 149.593i 0.191198 1.55826i
\(97\) 77.9778 0.803895 0.401948 0.915663i \(-0.368333\pi\)
0.401948 + 0.915663i \(0.368333\pi\)
\(98\) 57.3883 3.10900i 0.585595 0.0317245i
\(99\) −106.285 44.0249i −1.07359 0.444696i
\(100\) 39.3667 48.9656i 0.393667 0.489656i
\(101\) 104.064 43.1046i 1.03033 0.426778i 0.197500 0.980303i \(-0.436718\pi\)
0.832833 + 0.553525i \(0.186718\pi\)
\(102\) 40.5585 + 14.2821i 0.397632 + 0.140021i
\(103\) −76.6571 76.6571i −0.744243 0.744243i 0.229148 0.973392i \(-0.426406\pi\)
−0.973392 + 0.229148i \(0.926406\pi\)
\(104\) −26.3339 + 112.301i −0.253211 + 1.07981i
\(105\) 89.5117 + 89.5117i 0.852492 + 0.852492i
\(106\) 21.0152 10.0692i 0.198256 0.0949925i
\(107\) −40.9728 + 16.9715i −0.382923 + 0.158612i −0.565837 0.824517i \(-0.691447\pi\)
0.182914 + 0.983129i \(0.441447\pi\)
\(108\) −37.8416 69.1137i −0.350386 0.639942i
\(109\) 102.183 + 42.3255i 0.937456 + 0.388307i 0.798502 0.601992i \(-0.205626\pi\)
0.138954 + 0.990299i \(0.455626\pi\)
\(110\) −39.6032 35.5327i −0.360029 0.323024i
\(111\) 160.651 1.44731
\(112\) −118.849 75.9960i −1.06115 0.678536i
\(113\) 123.602i 1.09383i −0.837190 0.546913i \(-0.815803\pi\)
0.837190 0.546913i \(-0.184197\pi\)
\(114\) −246.278 220.965i −2.16033 1.93829i
\(115\) 11.1408 26.8962i 0.0968761 0.233880i
\(116\) 0.781747 2.67370i 0.00673920 0.0230491i
\(117\) 72.7365 + 175.602i 0.621680 + 1.50087i
\(118\) 61.8688 29.6438i 0.524312 0.251219i
\(119\) 28.4594 28.4594i 0.239155 0.239155i
\(120\) −18.5676 113.350i −0.154730 0.944587i
\(121\) −31.7073 + 31.7073i −0.262044 + 0.262044i
\(122\) 174.517 + 61.4540i 1.43047 + 0.503721i
\(123\) 40.1481 + 96.9262i 0.326408 + 0.788018i
\(124\) −0.141183 1.29921i −0.00113857 0.0104775i
\(125\) 47.4883 114.647i 0.379906 0.917175i
\(126\) −232.115 + 12.5748i −1.84218 + 0.0997997i
\(127\) 133.213i 1.04892i 0.851434 + 0.524462i \(0.175734\pi\)
−0.851434 + 0.524462i \(0.824266\pi\)
\(128\) 47.3414 + 118.923i 0.369855 + 0.929090i
\(129\) 24.6367 0.190982
\(130\) 4.75536 + 87.7782i 0.0365797 + 0.675217i
\(131\) 228.056 + 94.4640i 1.74089 + 0.721100i 0.998704 + 0.0509041i \(0.0162103\pi\)
0.742185 + 0.670195i \(0.233790\pi\)
\(132\) 163.447 17.7615i 1.23823 0.134557i
\(133\) −286.125 + 118.517i −2.15132 + 0.891104i
\(134\) −29.7207 + 84.4010i −0.221796 + 0.629858i
\(135\) −42.4622 42.4622i −0.314535 0.314535i
\(136\) −36.0387 + 5.90341i −0.264991 + 0.0434075i
\(137\) −111.817 111.817i −0.816180 0.816180i 0.169372 0.985552i \(-0.445826\pi\)
−0.985552 + 0.169372i \(0.945826\pi\)
\(138\) 38.8702 + 81.1250i 0.281668 + 0.587862i
\(139\) 31.7750 13.1616i 0.228597 0.0946880i −0.265445 0.964126i \(-0.585519\pi\)
0.494042 + 0.869438i \(0.335519\pi\)
\(140\) −103.190 30.1711i −0.737070 0.215508i
\(141\) −216.302 89.5952i −1.53406 0.635427i
\(142\) 71.0939 79.2381i 0.500661 0.558015i
\(143\) −125.828 −0.879914
\(144\) 177.698 + 113.626i 1.23401 + 0.789067i
\(145\) 2.12296i 0.0146411i
\(146\) −98.6566 + 109.958i −0.675730 + 0.753138i
\(147\) −51.7934 + 125.040i −0.352336 + 0.850615i
\(148\) −119.675 + 65.5251i −0.808613 + 0.442737i
\(149\) −108.344 261.565i −0.727140 1.75547i −0.651898 0.758307i \(-0.726027\pi\)
−0.0752422 0.997165i \(-0.523973\pi\)
\(150\) 63.9313 + 133.429i 0.426209 + 0.889528i
\(151\) 51.5292 51.5292i 0.341253 0.341253i −0.515585 0.856838i \(-0.672425\pi\)
0.856838 + 0.515585i \(0.172425\pi\)
\(152\) 273.587 + 64.1548i 1.79991 + 0.422071i
\(153\) −42.5512 + 42.5512i −0.278112 + 0.278112i
\(154\) 51.1129 145.151i 0.331902 0.942538i
\(155\) −0.381142 0.920157i −0.00245898 0.00593650i
\(156\) −211.699 170.199i −1.35704 1.09102i
\(157\) 39.3450 94.9872i 0.250605 0.605014i −0.747648 0.664095i \(-0.768817\pi\)
0.998253 + 0.0590811i \(0.0188171\pi\)
\(158\) −2.91099 53.7334i −0.0184240 0.340085i
\(159\) 54.8764i 0.345134i
\(160\) 60.0642 + 76.8655i 0.375401 + 0.480410i
\(161\) 84.1994 0.522978
\(162\) −51.6529 + 2.79828i −0.318845 + 0.0172734i
\(163\) −4.97467 2.06057i −0.0305194 0.0126416i 0.367372 0.930074i \(-0.380258\pi\)
−0.397891 + 0.917433i \(0.630258\pi\)
\(164\) −69.4413 55.8285i −0.423423 0.340417i
\(165\) 115.760 47.9494i 0.701577 0.290603i
\(166\) −52.4085 18.4550i −0.315714 0.111174i
\(167\) −165.012 165.012i −0.988097 0.988097i 0.0118333 0.999930i \(-0.496233\pi\)
−0.999930 + 0.0118333i \(0.996233\pi\)
\(168\) 282.330 175.072i 1.68054 1.04209i
\(169\) 27.4985 + 27.4985i 0.162713 + 0.162713i
\(170\) −25.0992 + 12.0260i −0.147642 + 0.0707413i
\(171\) 427.801 177.201i 2.50176 1.03626i
\(172\) −18.3528 + 10.0486i −0.106702 + 0.0584224i
\(173\) −115.760 47.9493i −0.669132 0.277163i 0.0221438 0.999755i \(-0.492951\pi\)
−0.691275 + 0.722591i \(0.742951\pi\)
\(174\) 4.88271 + 4.38086i 0.0280616 + 0.0251774i
\(175\) 138.486 0.791348
\(176\) −114.513 + 79.8967i −0.650642 + 0.453959i
\(177\) 161.556i 0.912748i
\(178\) 217.456 + 195.106i 1.22166 + 1.09610i
\(179\) −44.8368 + 108.246i −0.250485 + 0.604724i −0.998243 0.0592467i \(-0.981130\pi\)
0.747758 + 0.663971i \(0.231130\pi\)
\(180\) 154.285 + 45.1104i 0.857137 + 0.250613i
\(181\) 80.3652 + 194.019i 0.444007 + 1.07193i 0.974530 + 0.224256i \(0.0719953\pi\)
−0.530524 + 0.847670i \(0.678005\pi\)
\(182\) −229.287 + 109.861i −1.25982 + 0.603630i
\(183\) −308.093 + 308.093i −1.68357 + 1.68357i
\(184\) −62.0445 44.5788i −0.337198 0.242276i
\(185\) −73.5260 + 73.5260i −0.397438 + 0.397438i
\(186\) 2.90282 + 1.02219i 0.0156066 + 0.00549565i
\(187\) −15.2451 36.8049i −0.0815245 0.196818i
\(188\) 197.675 21.4810i 1.05146 0.114261i
\(189\) 66.4648 160.460i 0.351666 0.848996i
\(190\) 213.846 11.5850i 1.12550 0.0609738i
\(191\) 338.117i 1.77025i −0.465357 0.885123i \(-0.654074\pi\)
0.465357 0.885123i \(-0.345926\pi\)
\(192\) −300.733 20.4718i −1.56632 0.106624i
\(193\) 234.508 1.21507 0.607533 0.794295i \(-0.292159\pi\)
0.607533 + 0.794295i \(0.292159\pi\)
\(194\) −8.43648 155.727i −0.0434870 0.802718i
\(195\) −191.255 79.2206i −0.980797 0.406259i
\(196\) −12.4178 114.272i −0.0633560 0.583022i
\(197\) 237.007 98.1713i 1.20308 0.498332i 0.311086 0.950382i \(-0.399307\pi\)
0.891993 + 0.452050i \(0.149307\pi\)
\(198\) −76.4217 + 217.023i −0.385968 + 1.09607i
\(199\) 39.2172 + 39.2172i 0.197071 + 0.197071i 0.798743 0.601672i \(-0.205499\pi\)
−0.601672 + 0.798743i \(0.705499\pi\)
\(200\) −102.047 73.3204i −0.510234 0.366602i
\(201\) −149.002 149.002i −0.741302 0.741302i
\(202\) −97.3416 203.159i −0.481889 1.00574i
\(203\) 5.67273 2.34972i 0.0279445 0.0115750i
\(204\) 24.1344 82.5433i 0.118306 0.404624i
\(205\) −62.7356 25.9859i −0.306027 0.126761i
\(206\) −144.796 + 161.383i −0.702894 + 0.783414i
\(207\) −125.891 −0.608169
\(208\) 227.121 + 40.4409i 1.09193 + 0.194427i
\(209\) 306.542i 1.46671i
\(210\) 169.077 188.446i 0.805128 0.897360i
\(211\) −79.9026 + 192.902i −0.378685 + 0.914227i 0.613528 + 0.789673i \(0.289750\pi\)
−0.992213 + 0.124554i \(0.960250\pi\)
\(212\) −22.3826 40.8794i −0.105578 0.192827i
\(213\) 95.9373 + 231.613i 0.450410 + 1.08739i
\(214\) 38.3261 + 79.9894i 0.179094 + 0.373782i
\(215\) −11.2756 + 11.2756i −0.0524448 + 0.0524448i
\(216\) −133.931 + 83.0499i −0.620051 + 0.384490i
\(217\) 2.03688 2.03688i 0.00938655 0.00938655i
\(218\) 73.4718 208.645i 0.337026 0.957089i
\(219\) −133.132 321.408i −0.607907 1.46762i
\(220\) −66.6766 + 82.9346i −0.303076 + 0.376976i
\(221\) −25.1875 + 60.8079i −0.113970 + 0.275149i
\(222\) −17.3810 320.831i −0.0782926 1.44519i
\(223\) 344.421i 1.54449i 0.635326 + 0.772244i \(0.280866\pi\)
−0.635326 + 0.772244i \(0.719134\pi\)
\(224\) −138.911 + 245.572i −0.620139 + 1.09630i
\(225\) −207.058 −0.920256
\(226\) −246.843 + 13.3726i −1.09222 + 0.0591709i
\(227\) 68.2639 + 28.2758i 0.300722 + 0.124563i 0.527942 0.849280i \(-0.322964\pi\)
−0.227220 + 0.973843i \(0.572964\pi\)
\(228\) −414.638 + 515.741i −1.81859 + 2.26202i
\(229\) −41.8202 + 17.3225i −0.182621 + 0.0756440i −0.472120 0.881534i \(-0.656511\pi\)
0.289499 + 0.957178i \(0.406511\pi\)
\(230\) −54.9189 19.3390i −0.238778 0.0840824i
\(231\) 256.249 + 256.249i 1.10930 + 1.10930i
\(232\) −5.42414 1.27194i −0.0233799 0.00548248i
\(233\) 203.044 + 203.044i 0.871432 + 0.871432i 0.992629 0.121197i \(-0.0386731\pi\)
−0.121197 + 0.992629i \(0.538673\pi\)
\(234\) 342.819 164.259i 1.46504 0.701960i
\(235\) 140.002 57.9906i 0.595752 0.246768i
\(236\) −65.8944 120.349i −0.279214 0.509954i
\(237\) 117.077 + 48.4948i 0.493995 + 0.204619i
\(238\) −59.9146 53.7565i −0.251742 0.225868i
\(239\) 87.6710 0.366824 0.183412 0.983036i \(-0.441286\pi\)
0.183412 + 0.983036i \(0.441286\pi\)
\(240\) −224.360 + 49.3444i −0.934833 + 0.205602i
\(241\) 15.4754i 0.0642135i 0.999484 + 0.0321067i \(0.0102216\pi\)
−0.999484 + 0.0321067i \(0.989778\pi\)
\(242\) 66.7522 + 59.8913i 0.275836 + 0.247485i
\(243\) 114.463 276.338i 0.471041 1.13719i
\(244\) 103.847 355.172i 0.425602 1.45562i
\(245\) −33.5233 80.9325i −0.136830 0.330337i
\(246\) 189.225 90.6652i 0.769207 0.368558i
\(247\) 358.121 358.121i 1.44988 1.44988i
\(248\) −2.57934 + 0.422516i −0.0104006 + 0.00170369i
\(249\) 92.5220 92.5220i 0.371574 0.371574i
\(250\) −234.096 82.4338i −0.936383 0.329735i
\(251\) 95.9530 + 231.651i 0.382283 + 0.922913i 0.991524 + 0.129927i \(0.0414743\pi\)
−0.609241 + 0.792985i \(0.708526\pi\)
\(252\) 50.2254 + 462.189i 0.199307 + 1.83409i
\(253\) 31.8932 76.9969i 0.126060 0.304336i
\(254\) 266.037 14.4125i 1.04739 0.0567420i
\(255\) 65.5409i 0.257023i
\(256\) 232.377 107.411i 0.907722 0.419573i
\(257\) −131.142 −0.510282 −0.255141 0.966904i \(-0.582122\pi\)
−0.255141 + 0.966904i \(0.582122\pi\)
\(258\) −2.66547 49.2013i −0.0103313 0.190703i
\(259\) −277.847 115.088i −1.07277 0.444355i
\(260\) 174.785 18.9936i 0.672250 0.0730523i
\(261\) −8.48160 + 3.51319i −0.0324965 + 0.0134605i
\(262\) 163.978 465.665i 0.625870 1.77735i
\(263\) −281.350 281.350i −1.06977 1.06977i −0.997376 0.0723955i \(-0.976936\pi\)
−0.0723955 0.997376i \(-0.523064\pi\)
\(264\) −53.1545 324.494i −0.201343 1.22914i
\(265\) −25.1156 25.1156i −0.0947757 0.0947757i
\(266\) 267.643 + 558.590i 1.00618 + 2.09996i
\(267\) −635.626 + 263.285i −2.38062 + 0.986085i
\(268\) 171.770 + 50.2230i 0.640934 + 0.187399i
\(269\) 133.290 + 55.2107i 0.495503 + 0.205244i 0.616419 0.787419i \(-0.288583\pi\)
−0.120915 + 0.992663i \(0.538583\pi\)
\(270\) −80.2061 + 89.3942i −0.297060 + 0.331090i
\(271\) −368.673 −1.36042 −0.680208 0.733019i \(-0.738111\pi\)
−0.680208 + 0.733019i \(0.738111\pi\)
\(272\) 15.6886 + 71.3332i 0.0576787 + 0.262255i
\(273\) 598.732i 2.19316i
\(274\) −211.208 + 235.404i −0.770834 + 0.859137i
\(275\) 52.4559 126.640i 0.190749 0.460508i
\(276\) 157.807 86.4036i 0.571765 0.313057i
\(277\) 21.6001 + 52.1472i 0.0779786 + 0.188257i 0.958061 0.286564i \(-0.0925130\pi\)
−0.880083 + 0.474821i \(0.842513\pi\)
\(278\) −29.7225 62.0329i −0.106915 0.223140i
\(279\) −3.04545 + 3.04545i −0.0109156 + 0.0109156i
\(280\) −49.0896 + 209.342i −0.175320 + 0.747649i
\(281\) 85.0605 85.0605i 0.302706 0.302706i −0.539365 0.842072i \(-0.681336\pi\)
0.842072 + 0.539365i \(0.181336\pi\)
\(282\) −155.526 + 441.664i −0.551511 + 1.56618i
\(283\) 27.0948 + 65.4127i 0.0957414 + 0.231140i 0.964493 0.264107i \(-0.0850773\pi\)
−0.868752 + 0.495248i \(0.835077\pi\)
\(284\) −165.936 133.407i −0.584281 0.469742i
\(285\) −192.997 + 465.937i −0.677184 + 1.63487i
\(286\) 13.6134 + 251.287i 0.0475993 + 0.878626i
\(287\) 196.396i 0.684306i
\(288\) 207.693 367.168i 0.721157 1.27489i
\(289\) 268.162 0.927896
\(290\) −4.23971 + 0.229685i −0.0146197 + 0.000792018i
\(291\) 339.306 + 140.545i 1.16600 + 0.482973i
\(292\) 230.268 + 185.128i 0.788590 + 0.633999i
\(293\) −321.033 + 132.976i −1.09568 + 0.453844i −0.855983 0.517005i \(-0.827047\pi\)
−0.239694 + 0.970849i \(0.577047\pi\)
\(294\) 255.318 + 89.9070i 0.868430 + 0.305806i
\(295\) −73.9404 73.9404i −0.250645 0.250645i
\(296\) 143.806 + 231.910i 0.485831 + 0.783479i
\(297\) −121.559 121.559i −0.409289 0.409289i
\(298\) −510.643 + 244.669i −1.71357 + 0.821039i
\(299\) −127.212 + 52.6929i −0.425458 + 0.176231i
\(300\) 259.551 142.111i 0.865170 0.473704i
\(301\) −42.6094 17.6494i −0.141559 0.0586358i
\(302\) −108.483 97.3326i −0.359214 0.322293i
\(303\) 530.504 1.75084
\(304\) 98.5222 553.313i 0.324086 1.82011i
\(305\) 282.013i 0.924634i
\(306\) 89.5815 + 80.3742i 0.292750 + 0.262661i
\(307\) −92.6973 + 223.791i −0.301946 + 0.728961i 0.697972 + 0.716125i \(0.254086\pi\)
−0.999918 + 0.0128360i \(0.995914\pi\)
\(308\) −295.406 86.3722i −0.959112 0.280429i
\(309\) −195.394 471.724i −0.632344 1.52661i
\(310\) −1.79638 + 0.860719i −0.00579479 + 0.00277651i
\(311\) −44.5768 + 44.5768i −0.143334 + 0.143334i −0.775133 0.631799i \(-0.782317\pi\)
0.631799 + 0.775133i \(0.282317\pi\)
\(312\) −316.995 + 441.191i −1.01601 + 1.41407i
\(313\) −27.9303 + 27.9303i −0.0892343 + 0.0892343i −0.750315 0.661081i \(-0.770098\pi\)
0.661081 + 0.750315i \(0.270098\pi\)
\(314\) −193.953 68.2980i −0.617685 0.217510i
\(315\) 135.590 + 327.342i 0.430443 + 1.03918i
\(316\) −106.994 + 11.6269i −0.338590 + 0.0367940i
\(317\) −125.850 + 303.829i −0.397003 + 0.958450i 0.591370 + 0.806400i \(0.298587\pi\)
−0.988373 + 0.152049i \(0.951413\pi\)
\(318\) 109.592 5.93712i 0.344629 0.0186702i
\(319\) 6.07751i 0.0190518i
\(320\) 147.008 128.269i 0.459399 0.400840i
\(321\) −208.874 −0.650699
\(322\) −9.10960 168.152i −0.0282907 0.522212i
\(323\) 148.140 + 61.3618i 0.458639 + 0.189975i
\(324\) 11.1767 + 102.852i 0.0344961 + 0.317444i
\(325\) −209.230 + 86.6660i −0.643785 + 0.266665i
\(326\) −3.57690 + 10.1577i −0.0109721 + 0.0311586i
\(327\) 368.343 + 368.343i 1.12643 + 1.12643i
\(328\) −103.981 + 144.719i −0.317014 + 0.441218i
\(329\) 309.911 + 309.911i 0.941978 + 0.941978i
\(330\) −108.283 225.994i −0.328129 0.684829i
\(331\) −169.515 + 70.2155i −0.512131 + 0.212131i −0.623756 0.781619i \(-0.714394\pi\)
0.111626 + 0.993750i \(0.464394\pi\)
\(332\) −31.1858 + 106.660i −0.0939330 + 0.321265i
\(333\) 415.423 + 172.074i 1.24752 + 0.516739i
\(334\) −311.688 + 347.394i −0.933198 + 1.04010i
\(335\) 136.389 0.407131
\(336\) −380.176 544.893i −1.13148 1.62170i
\(337\) 67.3116i 0.199738i −0.995001 0.0998689i \(-0.968158\pi\)
0.995001 0.0998689i \(-0.0318423\pi\)
\(338\) 51.9414 57.8916i 0.153673 0.171277i
\(339\) 222.778 537.833i 0.657161 1.58653i
\(340\) 26.7323 + 48.8238i 0.0786245 + 0.143599i
\(341\) −1.09111 2.63418i −0.00319974 0.00772486i
\(342\) −400.167 835.177i −1.17008 2.44204i
\(343\) −126.333 + 126.333i −0.368318 + 0.368318i
\(344\) 22.0535 + 35.5646i 0.0641089 + 0.103386i
\(345\) 96.9538 96.9538i 0.281026 0.281026i
\(346\) −83.2340 + 236.368i −0.240561 + 0.683145i
\(347\) −107.157 258.699i −0.308809 0.745530i −0.999744 0.0226140i \(-0.992801\pi\)
0.690935 0.722916i \(-0.257199\pi\)
\(348\) 8.22063 10.2251i 0.0236225 0.0293825i
\(349\) 165.558 399.692i 0.474378 1.14525i −0.487831 0.872938i \(-0.662212\pi\)
0.962209 0.272311i \(-0.0877881\pi\)
\(350\) −14.9829 276.566i −0.0428083 0.790189i
\(351\) 284.024i 0.809187i
\(352\) 171.949 + 220.047i 0.488491 + 0.625133i
\(353\) −574.524 −1.62755 −0.813773 0.581183i \(-0.802590\pi\)
−0.813773 + 0.581183i \(0.802590\pi\)
\(354\) 322.640 17.4789i 0.911412 0.0493755i
\(355\) −149.912 62.0955i −0.422287 0.174917i
\(356\) 366.114 455.385i 1.02841 1.27917i
\(357\) 175.130 72.5414i 0.490562 0.203197i
\(358\) 221.025 + 77.8311i 0.617389 + 0.217405i
\(359\) 499.243 + 499.243i 1.39065 + 1.39065i 0.823868 + 0.566782i \(0.191812\pi\)
0.566782 + 0.823868i \(0.308188\pi\)
\(360\) 73.3965 312.998i 0.203879 0.869439i
\(361\) −617.189 617.189i −1.70966 1.70966i
\(362\) 378.774 181.486i 1.04634 0.501343i
\(363\) −195.117 + 80.8201i −0.537512 + 0.222645i
\(364\) 244.206 + 446.017i 0.670897 + 1.22532i
\(365\) 208.032 + 86.1696i 0.569950 + 0.236081i
\(366\) 648.617 + 581.951i 1.77218 + 1.59003i
\(367\) 295.566 0.805357 0.402679 0.915341i \(-0.368079\pi\)
0.402679 + 0.915341i \(0.368079\pi\)
\(368\) −82.3144 + 128.730i −0.223681 + 0.349811i
\(369\) 293.642i 0.795778i
\(370\) 154.792 + 138.882i 0.418355 + 0.375356i
\(371\) 39.3126 94.9090i 0.105964 0.255819i
\(372\) 1.72733 5.90774i 0.00464336 0.0158810i
\(373\) −133.878 323.209i −0.358921 0.866512i −0.995452 0.0952612i \(-0.969631\pi\)
0.636531 0.771251i \(-0.280369\pi\)
\(374\) −71.8526 + 34.4275i −0.192119 + 0.0920521i
\(375\) 413.273 413.273i 1.10206 1.10206i
\(376\) −64.2856 392.446i −0.170972 1.04374i
\(377\) −7.10011 + 7.10011i −0.0188332 + 0.0188332i
\(378\) −327.641 115.375i −0.866776 0.305224i
\(379\) 170.642 + 411.967i 0.450244 + 1.08698i 0.972229 + 0.234030i \(0.0751915\pi\)
−0.521986 + 0.852954i \(0.674809\pi\)
\(380\) −46.2722 425.811i −0.121769 1.12056i
\(381\) −240.100 + 579.654i −0.630185 + 1.52140i
\(382\) −675.244 + 36.5812i −1.76765 + 0.0957622i
\(383\) 254.902i 0.665540i −0.943008 0.332770i \(-0.892017\pi\)
0.943008 0.332770i \(-0.107983\pi\)
\(384\) −8.34710 + 602.800i −0.0217372 + 1.56979i
\(385\) −234.558 −0.609242
\(386\) −25.3716 468.328i −0.0657294 1.21329i
\(387\) 63.7075 + 26.3885i 0.164619 + 0.0681874i
\(388\) −310.086 + 33.6965i −0.799190 + 0.0868467i
\(389\) 687.246 284.667i 1.76670 0.731791i 0.771247 0.636536i \(-0.219633\pi\)
0.995453 0.0952550i \(-0.0303666\pi\)
\(390\) −137.517 + 390.522i −0.352608 + 1.00134i
\(391\) −30.8256 30.8256i −0.0788379 0.0788379i
\(392\) −226.866 + 37.1624i −0.578741 + 0.0948020i
\(393\) 822.086 + 822.086i 2.09182 + 2.09182i
\(394\) −221.697 462.698i −0.562683 1.17436i
\(395\) −75.7781 + 31.3883i −0.191843 + 0.0794640i
\(396\) 441.678 + 129.140i 1.11535 + 0.326110i
\(397\) −56.8981 23.5679i −0.143320 0.0593651i 0.309871 0.950779i \(-0.399714\pi\)
−0.453191 + 0.891414i \(0.649714\pi\)
\(398\) 74.0766 82.5625i 0.186122 0.207443i
\(399\) −1458.63 −3.65572
\(400\) −135.386 + 211.728i −0.338464 + 0.529319i
\(401\) 704.010i 1.75564i 0.478994 + 0.877818i \(0.341001\pi\)
−0.478994 + 0.877818i \(0.658999\pi\)
\(402\) −281.446 + 313.687i −0.700115 + 0.780317i
\(403\) −1.80270 + 4.35211i −0.00447321 + 0.0107993i
\(404\) −395.192 + 216.378i −0.978197 + 0.535589i
\(405\) 30.1730 + 72.8441i 0.0745013 + 0.179862i
\(406\) −5.30630 11.0746i −0.0130697 0.0272774i
\(407\) −210.486 + 210.486i −0.517166 + 0.517166i
\(408\) −167.456 39.2677i −0.410431 0.0962442i
\(409\) 528.488 528.488i 1.29215 1.29215i 0.358690 0.933457i \(-0.383224\pi\)
0.933457 0.358690i \(-0.116776\pi\)
\(410\) −45.1083 + 128.099i −0.110020 + 0.312436i
\(411\) −285.014 688.085i −0.693465 1.67417i
\(412\) 337.959 + 271.708i 0.820290 + 0.659485i
\(413\) 115.737 279.413i 0.280234 0.676544i
\(414\) 13.6202 + 251.413i 0.0328991 + 0.607278i
\(415\) 84.6901i 0.204072i
\(416\) 56.1909 457.953i 0.135074 1.10085i
\(417\) 161.985 0.388453
\(418\) 612.186 33.1650i 1.46456 0.0793421i
\(419\) −153.485 63.5754i −0.366312 0.151731i 0.191932 0.981408i \(-0.438525\pi\)
−0.558244 + 0.829677i \(0.688525\pi\)
\(420\) −394.632 317.271i −0.939600 0.755406i
\(421\) −240.175 + 99.4838i −0.570487 + 0.236304i −0.649231 0.760591i \(-0.724909\pi\)
0.0787437 + 0.996895i \(0.474909\pi\)
\(422\) 393.884 + 138.701i 0.933373 + 0.328675i
\(423\) −463.364 463.364i −1.09542 1.09542i
\(424\) −79.2174 + 49.1224i −0.186834 + 0.115855i
\(425\) −50.7000 50.7000i −0.119294 0.119294i
\(426\) 452.168 216.652i 1.06143 0.508573i
\(427\) 753.562 312.136i 1.76478 0.730997i
\(428\) 155.598 85.1941i 0.363547 0.199052i
\(429\) −547.516 226.789i −1.27626 0.528645i
\(430\) 23.7381 + 21.2983i 0.0552050 + 0.0495310i
\(431\) −607.318 −1.40909 −0.704546 0.709659i \(-0.748849\pi\)
−0.704546 + 0.709659i \(0.748849\pi\)
\(432\) 180.347 + 258.484i 0.417469 + 0.598344i
\(433\) 233.380i 0.538984i 0.963003 + 0.269492i \(0.0868557\pi\)
−0.963003 + 0.269492i \(0.913144\pi\)
\(434\) −4.28817 3.84743i −0.00988057 0.00886504i
\(435\) 3.82637 9.23768i 0.00879626 0.0212361i
\(436\) −424.629 124.155i −0.973919 0.284759i
\(437\) 128.371 + 309.914i 0.293754 + 0.709185i
\(438\) −627.472 + 300.647i −1.43258 + 0.686408i
\(439\) −496.850 + 496.850i −1.13178 + 1.13178i −0.141896 + 0.989882i \(0.545320\pi\)
−0.989882 + 0.141896i \(0.954680\pi\)
\(440\) 172.840 + 124.185i 0.392819 + 0.282239i
\(441\) −267.863 + 267.863i −0.607399 + 0.607399i
\(442\) 124.163 + 43.7223i 0.280911 + 0.0989193i
\(443\) 59.8483 + 144.487i 0.135098 + 0.326155i 0.976922 0.213597i \(-0.0685180\pi\)
−0.841824 + 0.539752i \(0.818518\pi\)
\(444\) −638.843 + 69.4220i −1.43884 + 0.156356i
\(445\) 170.411 411.409i 0.382947 0.924515i
\(446\) 687.833 37.2632i 1.54223 0.0835497i
\(447\) 1333.43i 2.98306i
\(448\) 505.454 + 250.847i 1.12825 + 0.559926i
\(449\) −15.4530 −0.0344165 −0.0172082 0.999852i \(-0.505478\pi\)
−0.0172082 + 0.999852i \(0.505478\pi\)
\(450\) 22.4017 + 413.509i 0.0497816 + 0.918908i
\(451\) −179.596 74.3911i −0.398217 0.164947i
\(452\) 53.4122 + 491.516i 0.118169 + 1.08742i
\(453\) 317.095 131.345i 0.699989 0.289945i
\(454\) 49.0833 139.387i 0.108113 0.307020i
\(455\) 274.025 + 274.025i 0.602253 + 0.602253i
\(456\) 1074.83 + 772.263i 2.35709 + 1.69356i
\(457\) −93.8365 93.8365i −0.205332 0.205332i 0.596948 0.802280i \(-0.296380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(458\) 39.1188 + 81.6438i 0.0854122 + 0.178261i
\(459\) −83.0778 + 34.4120i −0.180997 + 0.0749716i
\(460\) −32.6796 + 111.769i −0.0710426 + 0.242977i
\(461\) −574.348 237.903i −1.24588 0.516058i −0.340329 0.940306i \(-0.610538\pi\)
−0.905546 + 0.424248i \(0.860538\pi\)
\(462\) 484.024 539.472i 1.04767 1.16769i
\(463\) 568.089 1.22697 0.613487 0.789705i \(-0.289766\pi\)
0.613487 + 0.789705i \(0.289766\pi\)
\(464\) −1.95330 + 10.9700i −0.00420971 + 0.0236423i
\(465\) 4.69085i 0.0100879i
\(466\) 383.525 427.460i 0.823016 0.917296i
\(467\) −156.459 + 377.726i −0.335030 + 0.808835i 0.663147 + 0.748489i \(0.269220\pi\)
−0.998178 + 0.0603459i \(0.980780\pi\)
\(468\) −365.126 666.864i −0.780184 1.42492i
\(469\) 150.957 + 364.442i 0.321869 + 0.777061i
\(470\) −130.958 273.319i −0.278635 0.581530i
\(471\) 342.405 342.405i 0.726974 0.726974i
\(472\) −233.217 + 144.617i −0.494103 + 0.306391i
\(473\) −32.2793 + 32.2793i −0.0682437 + 0.0682437i
\(474\) 84.1810 239.057i 0.177597 0.504341i
\(475\) 211.136 + 509.727i 0.444497 + 1.07311i
\(476\) −100.873 + 125.470i −0.211919 + 0.263592i
\(477\) −58.7783 + 141.903i −0.123225 + 0.297492i
\(478\) −9.48520 175.085i −0.0198435 0.366287i
\(479\) 327.880i 0.684509i 0.939607 + 0.342254i \(0.111190\pi\)
−0.939607 + 0.342254i \(0.888810\pi\)
\(480\) 122.818 + 442.724i 0.255871 + 0.922342i
\(481\) 491.806 1.02247
\(482\) 30.9056 1.67430i 0.0641194 0.00347365i
\(483\) 366.378 + 151.759i 0.758547 + 0.314200i
\(484\) 112.385 139.789i 0.232201 0.288820i
\(485\) −219.616 + 90.9680i −0.452817 + 0.187563i
\(486\) −564.250 198.693i −1.16101 0.408834i
\(487\) −147.493 147.493i −0.302861 0.302861i 0.539271 0.842132i \(-0.318700\pi\)
−0.842132 + 0.539271i \(0.818700\pi\)
\(488\) −720.540 168.963i −1.47652 0.346236i
\(489\) −17.9324 17.9324i −0.0366716 0.0366716i
\(490\) −158.001 + 75.7047i −0.322451 + 0.154499i
\(491\) 598.802 248.032i 1.21956 0.505157i 0.322288 0.946642i \(-0.395548\pi\)
0.897269 + 0.441485i \(0.145548\pi\)
\(492\) −201.537 368.086i −0.409629 0.748143i
\(493\) −2.93704 1.21656i −0.00595748 0.00246767i
\(494\) −753.938 676.447i −1.52619 1.36933i
\(495\) 350.700 0.708485
\(496\) 1.12285 + 5.10542i 0.00226382 + 0.0102932i
\(497\) 469.304i 0.944274i
\(498\) −194.783 174.763i −0.391131 0.350930i
\(499\) 58.1446 140.373i 0.116522 0.281309i −0.854849 0.518877i \(-0.826350\pi\)
0.971371 + 0.237568i \(0.0763502\pi\)
\(500\) −139.299 + 476.425i −0.278598 + 0.952849i
\(501\) −420.606 1015.43i −0.839533 2.02681i
\(502\) 452.242 216.688i 0.900881 0.431648i
\(503\) −256.204 + 256.204i −0.509351 + 0.509351i −0.914327 0.404976i \(-0.867280\pi\)
0.404976 + 0.914327i \(0.367280\pi\)
\(504\) 917.592 150.308i 1.82062 0.298231i
\(505\) −242.799 + 242.799i −0.480789 + 0.480789i
\(506\) −157.219 55.3626i −0.310709 0.109412i
\(507\) 70.0921 + 169.217i 0.138249 + 0.333762i
\(508\) −57.5655 529.735i −0.113318 1.04279i
\(509\) −229.271 + 553.510i −0.450435 + 1.08745i 0.521722 + 0.853115i \(0.325290\pi\)
−0.972157 + 0.234331i \(0.924710\pi\)
\(510\) −130.890 + 7.09092i −0.256647 + 0.0139038i
\(511\) 651.251i 1.27446i
\(512\) −239.648 452.452i −0.468062 0.883696i
\(513\) 691.941 1.34881
\(514\) 14.1884 + 261.901i 0.0276039 + 0.509534i
\(515\) 305.324 + 126.469i 0.592861 + 0.245571i
\(516\) −97.9702 + 10.6463i −0.189865 + 0.0206323i
\(517\) 400.789 166.012i 0.775221 0.321107i
\(518\) −199.778 + 567.331i −0.385672 + 1.09523i
\(519\) −417.285 417.285i −0.804017 0.804017i
\(520\) −56.8417 347.003i −0.109311 0.667314i
\(521\) 80.7376 + 80.7376i 0.154967 + 0.154967i 0.780332 0.625365i \(-0.215050\pi\)
−0.625365 + 0.780332i \(0.715050\pi\)
\(522\) 7.93373 + 16.5583i 0.0151987 + 0.0317208i
\(523\) 123.197 51.0300i 0.235559 0.0975717i −0.261781 0.965127i \(-0.584310\pi\)
0.497341 + 0.867555i \(0.334310\pi\)
\(524\) −947.707 277.095i −1.80860 0.528807i
\(525\) 602.595 + 249.603i 1.14780 + 0.475435i
\(526\) −531.436 + 592.315i −1.01034 + 1.12607i
\(527\) −1.49141 −0.00283001
\(528\) −642.286 + 141.261i −1.21645 + 0.267539i
\(529\) 437.800i 0.827599i
\(530\) −47.4403 + 52.8748i −0.0895100 + 0.0997639i
\(531\) −173.044 + 417.765i −0.325883 + 0.786751i
\(532\) 1086.59 594.936i 2.04246 1.11830i
\(533\) 122.907 + 296.723i 0.230594 + 0.556704i
\(534\) 594.567 + 1240.90i 1.11342 + 2.32379i
\(535\) 95.5966 95.5966i 0.178685 0.178685i
\(536\) 81.7149 348.471i 0.152453 0.650133i
\(537\) −390.198 + 390.198i −0.726626 + 0.726626i
\(538\) 95.8389 272.164i 0.178139 0.505881i
\(539\) −95.9689 231.689i −0.178050 0.429850i
\(540\) 187.204 + 150.506i 0.346674 + 0.278714i
\(541\) 184.993 446.613i 0.341947 0.825532i −0.655572 0.755132i \(-0.727573\pi\)
0.997519 0.0703996i \(-0.0224275\pi\)
\(542\) 39.8870 + 736.266i 0.0735923 + 1.35842i
\(543\) 989.085i 1.82152i
\(544\) 140.760 39.0489i 0.258750 0.0717810i
\(545\) −337.163 −0.618648
\(546\) −1195.71 + 64.7773i −2.18995 + 0.118640i
\(547\) −570.529 236.321i −1.04302 0.432031i −0.205622 0.978632i \(-0.565922\pi\)
−0.837394 + 0.546600i \(0.815922\pi\)
\(548\) 492.968 + 396.330i 0.899577 + 0.723230i
\(549\) −1126.69 + 466.691i −2.05226 + 0.850074i
\(550\) −258.584 91.0569i −0.470152 0.165558i
\(551\) 17.2973 + 17.2973i 0.0313926 + 0.0313926i
\(552\) −189.628 305.804i −0.343528 0.553992i
\(553\) −167.744 167.744i −0.303335 0.303335i
\(554\) 101.805 48.7787i 0.183763 0.0880482i
\(555\) −452.456 + 187.413i −0.815236 + 0.337682i
\(556\) −120.669 + 66.0693i −0.217030 + 0.118830i
\(557\) 340.362 + 140.983i 0.611063 + 0.253111i 0.666683 0.745341i \(-0.267714\pi\)
−0.0556199 + 0.998452i \(0.517714\pi\)
\(558\) 6.41147 + 5.75249i 0.0114901 + 0.0103091i
\(559\) 75.4212 0.134922
\(560\) 423.381 + 75.3867i 0.756038 + 0.134619i
\(561\) 187.627i 0.334451i
\(562\) −179.075 160.669i −0.318638 0.285888i
\(563\) 241.885 583.963i 0.429637 1.03723i −0.549766 0.835319i \(-0.685283\pi\)
0.979403 0.201916i \(-0.0647168\pi\)
\(564\) 898.861 + 262.813i 1.59373 + 0.465980i
\(565\) 144.193 + 348.113i 0.255209 + 0.616128i
\(566\) 127.702 61.1873i 0.225623 0.108105i
\(567\) −161.249 + 161.249i −0.284390 + 0.284390i
\(568\) −248.470 + 345.819i −0.437447 + 0.608836i
\(569\) 88.6373 88.6373i 0.155777 0.155777i −0.624915 0.780693i \(-0.714866\pi\)
0.780693 + 0.624915i \(0.214866\pi\)
\(570\) 951.390 + 335.019i 1.66910 + 0.587753i
\(571\) −160.453 387.367i −0.281003 0.678401i 0.718857 0.695158i \(-0.244666\pi\)
−0.999860 + 0.0167573i \(0.994666\pi\)
\(572\) 500.365 54.3739i 0.874764 0.0950592i
\(573\) 609.413 1471.25i 1.06355 2.56763i
\(574\) −392.217 + 21.2482i −0.683304 + 0.0370178i
\(575\) 150.000i 0.260869i
\(576\) −755.731 375.054i −1.31203 0.651136i
\(577\) −501.285 −0.868778 −0.434389 0.900725i \(-0.643036\pi\)
−0.434389 + 0.900725i \(0.643036\pi\)
\(578\) −29.0126 535.538i −0.0501949 0.926537i
\(579\) 1020.42 + 422.670i 1.76238 + 0.730000i
\(580\) 0.917395 + 8.44215i 0.00158172 + 0.0145554i
\(581\) −226.299 + 93.7360i −0.389498 + 0.161336i
\(582\) 243.969 692.824i 0.419191 1.19042i
\(583\) −71.8995 71.8995i −0.123327 0.123327i
\(584\) 344.800 479.891i 0.590412 0.821731i
\(585\) −409.709 409.709i −0.700358 0.700358i
\(586\) 300.296 + 626.739i 0.512451 + 1.06952i
\(587\) −805.600 + 333.691i −1.37240 + 0.568468i −0.942439 0.334378i \(-0.891474\pi\)
−0.429964 + 0.902846i \(0.641474\pi\)
\(588\) 151.928 519.616i 0.258380 0.883701i
\(589\) 10.6026 + 4.39175i 0.0180010 + 0.00745628i
\(590\) −139.665 + 155.664i −0.236720 + 0.263837i
\(591\) 1208.23 2.04438
\(592\) 447.582 312.282i 0.756050 0.527503i
\(593\) 1035.33i 1.74591i −0.487798 0.872957i \(-0.662200\pi\)
0.487798 0.872957i \(-0.337800\pi\)
\(594\) −229.610 + 255.913i −0.386549 + 0.430830i
\(595\) −46.9525 + 113.353i −0.0789117 + 0.190510i
\(596\) 543.869 + 993.319i 0.912532 + 1.66664i
\(597\) 99.9623 + 241.330i 0.167441 + 0.404238i
\(598\) 118.995 + 248.351i 0.198988 + 0.415302i
\(599\) 361.938 361.938i 0.604237 0.604237i −0.337197 0.941434i \(-0.609479\pi\)
0.941434 + 0.337197i \(0.109479\pi\)
\(600\) −311.887 502.967i −0.519812 0.838278i
\(601\) −221.839 + 221.839i −0.369116 + 0.369116i −0.867155 0.498039i \(-0.834054\pi\)
0.498039 + 0.867155i \(0.334054\pi\)
\(602\) −30.6371 + 87.0034i −0.0508922 + 0.144524i
\(603\) −225.703 544.896i −0.374301 0.903642i
\(604\) −182.643 + 227.178i −0.302390 + 0.376122i
\(605\) 52.3109 126.290i 0.0864642 0.208743i
\(606\) −57.3957 1059.45i −0.0947123 1.74828i
\(607\) 465.834i 0.767437i 0.923450 + 0.383719i \(0.125357\pi\)
−0.923450 + 0.383719i \(0.874643\pi\)
\(608\) −1115.67 136.892i −1.83498 0.225152i
\(609\) 28.9189 0.0474859
\(610\) −563.201 + 30.5113i −0.923280 + 0.0500185i
\(611\) −662.172 274.281i −1.08375 0.448905i
\(612\) 150.821 187.596i 0.246440 0.306530i
\(613\) 292.579 121.190i 0.477290 0.197700i −0.131051 0.991376i \(-0.541835\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(614\) 456.956 + 160.911i 0.744227 + 0.262070i
\(615\) −226.146 226.146i −0.367717 0.367717i
\(616\) −140.531 + 599.292i −0.228135 + 0.972877i
\(617\) −226.657 226.657i −0.367354 0.367354i 0.499158 0.866511i \(-0.333643\pi\)
−0.866511 + 0.499158i \(0.833643\pi\)
\(618\) −920.926 + 441.253i −1.49017 + 0.714001i
\(619\) 756.530 313.365i 1.22218 0.506244i 0.324078 0.946030i \(-0.394946\pi\)
0.898102 + 0.439787i \(0.144946\pi\)
\(620\) 1.91327 + 3.49438i 0.00308592 + 0.00563610i
\(621\) −173.801 71.9908i −0.279873 0.115927i
\(622\) 93.8459 + 84.2003i 0.150878 + 0.135370i
\(623\) 1287.93 2.06730
\(624\) 915.386 + 585.328i 1.46697 + 0.938026i
\(625\) 14.3854i 0.0230167i
\(626\) 58.8007 + 52.7570i 0.0939308 + 0.0842764i
\(627\) −552.503 + 1333.86i −0.881185 + 2.12737i
\(628\) −115.412 + 394.727i −0.183777 + 0.628546i
\(629\) 59.5864 + 143.854i 0.0947320 + 0.228703i
\(630\) 639.057 306.198i 1.01438 0.486028i
\(631\) 338.810 338.810i 0.536941 0.536941i −0.385688 0.922629i \(-0.626036\pi\)
0.922629 + 0.385688i \(0.126036\pi\)
\(632\) 34.7956 + 212.418i 0.0550563 + 0.336104i
\(633\) −695.363 + 695.363i −1.09852 + 1.09852i
\(634\) 620.383 + 218.460i 0.978522 + 0.344574i
\(635\) −155.405 375.181i −0.244733 0.590837i
\(636\) −23.7137 218.221i −0.0372857 0.343114i
\(637\) −158.557 + 382.790i −0.248912 + 0.600927i
\(638\) −12.1372 + 0.657531i −0.0190239 + 0.00103061i
\(639\) 701.682i 1.09809i
\(640\) −272.067 279.707i −0.425104 0.437042i
\(641\) 729.839 1.13859 0.569297 0.822132i \(-0.307215\pi\)
0.569297 + 0.822132i \(0.307215\pi\)
\(642\) 22.5983 + 417.137i 0.0351998 + 0.649746i
\(643\) −370.578 153.498i −0.576327 0.238722i 0.0754293 0.997151i \(-0.475967\pi\)
−0.651756 + 0.758429i \(0.725967\pi\)
\(644\) −334.826 + 36.3850i −0.519917 + 0.0564985i
\(645\) −69.3867 + 28.7409i −0.107576 + 0.0445595i
\(646\) 106.516 302.486i 0.164886 0.468244i
\(647\) −179.567 179.567i −0.277538 0.277538i 0.554587 0.832126i \(-0.312876\pi\)
−0.832126 + 0.554587i \(0.812876\pi\)
\(648\) 204.193 33.4484i 0.315113 0.0516179i
\(649\) −211.673 211.673i −0.326152 0.326152i
\(650\) 195.715 + 408.471i 0.301100 + 0.628417i
\(651\) 12.5343 5.19189i 0.0192540 0.00797525i
\(652\) 20.6726 + 6.04436i 0.0317065 + 0.00927049i
\(653\) −964.894 399.672i −1.47763 0.612056i −0.509048 0.860738i \(-0.670002\pi\)
−0.968585 + 0.248683i \(0.920002\pi\)
\(654\) 695.756 775.458i 1.06385 1.18572i
\(655\) −752.497 −1.14885
\(656\) 300.265 + 191.999i 0.457721 + 0.292682i
\(657\) 973.720i 1.48207i
\(658\) 585.385 652.444i 0.889642 0.991556i
\(659\) 233.939 564.778i 0.354990 0.857023i −0.640998 0.767542i \(-0.721479\pi\)
0.995989 0.0894804i \(-0.0285206\pi\)
\(660\) −439.610 + 240.699i −0.666076 + 0.364695i
\(661\) 281.181 + 678.831i 0.425387 + 1.02698i 0.980732 + 0.195356i \(0.0625862\pi\)
−0.555345 + 0.831620i \(0.687414\pi\)
\(662\) 158.565 + 330.937i 0.239525 + 0.499905i
\(663\) −219.197 + 219.197i −0.330614 + 0.330614i
\(664\) 216.382 + 50.7405i 0.325876 + 0.0764165i
\(665\) 667.580 667.580i 1.00388 1.00388i
\(666\) 298.699 848.247i 0.448497 1.27364i
\(667\) −2.54508 6.14437i −0.00381571 0.00921195i
\(668\) 727.492 + 584.879i 1.08906 + 0.875567i
\(669\) −620.775 + 1498.68i −0.927915 + 2.24018i
\(670\) −14.7560 272.378i −0.0220239 0.406534i
\(671\) 807.333i 1.20318i
\(672\) −1047.06 + 818.192i −1.55812 + 1.21755i
\(673\) 705.345 1.04806 0.524031 0.851699i \(-0.324428\pi\)
0.524031 + 0.851699i \(0.324428\pi\)
\(674\) −134.426 + 7.28250i −0.199445 + 0.0108049i
\(675\) −285.857 118.406i −0.423492 0.175416i
\(676\) −121.233 97.4673i −0.179339 0.144182i
\(677\) −10.4550 + 4.33061i −0.0154432 + 0.00639676i −0.390392 0.920649i \(-0.627660\pi\)
0.374948 + 0.927046i \(0.377660\pi\)
\(678\) −1098.19 386.714i −1.61975 0.570375i
\(679\) −486.147 486.147i −0.715976 0.715976i
\(680\) 94.6123 58.6687i 0.139136 0.0862775i
\(681\) 246.074 + 246.074i 0.361342 + 0.361342i
\(682\) −5.14259 + 2.46402i −0.00754046 + 0.00361294i
\(683\) −307.101 + 127.205i −0.449635 + 0.186245i −0.595998 0.802986i \(-0.703243\pi\)
0.146363 + 0.989231i \(0.453243\pi\)
\(684\) −1624.61 + 889.521i −2.37517 + 1.30047i
\(685\) 445.364 + 184.476i 0.650166 + 0.269308i
\(686\) 265.964 + 238.628i 0.387703 + 0.347854i
\(687\) −213.194 −0.310327
\(688\) 68.6392 47.8901i 0.0997662 0.0696077i
\(689\) 167.995i 0.243824i
\(690\) −204.113 183.134i −0.295816 0.265412i
\(691\) −243.176 + 587.078i −0.351919 + 0.849607i 0.644465 + 0.764634i \(0.277080\pi\)
−0.996383 + 0.0849727i \(0.972920\pi\)
\(692\) 481.049 + 140.651i 0.695158 + 0.203253i
\(693\) 388.159 + 937.099i 0.560114 + 1.35224i
\(694\) −505.047 + 241.988i −0.727734 + 0.348686i
\(695\) −74.1366 + 74.1366i −0.106671 + 0.106671i
\(696\) −21.3096 15.3109i −0.0306173 0.0219985i
\(697\) −71.9010 + 71.9010i −0.103158 + 0.103158i
\(698\) −816.125 287.388i −1.16923 0.411730i
\(699\) 517.546 + 1249.47i 0.740410 + 1.78751i
\(700\) −550.701 + 59.8438i −0.786716 + 0.0854912i
\(701\) 65.7383 158.706i 0.0937779 0.226400i −0.870029 0.493000i \(-0.835900\pi\)
0.963807 + 0.266600i \(0.0859003\pi\)
\(702\) 567.217 30.7288i 0.808002 0.0437733i
\(703\) 1198.14i 1.70432i
\(704\) 420.846 367.201i 0.597792 0.521592i
\(705\) 713.712 1.01236
\(706\) 62.1582 + 1147.37i 0.0880428 + 1.62516i
\(707\) −917.510 380.045i −1.29775 0.537546i
\(708\) −69.8133 642.444i −0.0986064 0.907406i
\(709\) −1029.00 + 426.228i −1.45135 + 0.601167i −0.962519 0.271214i \(-0.912575\pi\)
−0.488827 + 0.872381i \(0.662575\pi\)
\(710\) −107.790 + 306.103i −0.151817 + 0.431131i
\(711\) 250.803 + 250.803i 0.352747 + 0.352747i
\(712\) −949.046 681.887i −1.33293 0.957706i
\(713\) −2.20623 2.20623i −0.00309429 0.00309429i
\(714\) −163.818 341.900i −0.229437 0.478851i
\(715\) 354.380 146.789i 0.495637 0.205299i
\(716\) 131.521 449.824i 0.183689 0.628245i
\(717\) 381.484 + 158.016i 0.532056 + 0.220385i
\(718\) 943.011 1051.04i 1.31339 1.46384i
\(719\) −439.735 −0.611592 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(720\) −633.020 112.715i −0.879195 0.156548i
\(721\) 955.826i 1.32570i
\(722\) −1165.80 + 1299.34i −1.61468 + 1.79965i
\(723\) −27.8925 + 67.3385i −0.0385789 + 0.0931377i
\(724\) −403.421 736.805i −0.557211 1.01769i
\(725\) −4.18599 10.1059i −0.00577378 0.0139391i
\(726\) 182.513 + 380.919i 0.251396 + 0.524681i
\(727\) 137.308 137.308i 0.188869 0.188869i −0.606338 0.795207i \(-0.707362\pi\)
0.795207 + 0.606338i \(0.207362\pi\)
\(728\) 864.307 535.953i 1.18723 0.736199i
\(729\) 831.529 831.529i 1.14064 1.14064i
\(730\) 149.580 424.777i 0.204904 0.581886i
\(731\) 9.13791 + 22.0609i 0.0125006 + 0.0301790i
\(732\) 1092.02 1358.30i 1.49184 1.85560i
\(733\) 57.7693 139.467i 0.0788121 0.190269i −0.879562 0.475784i \(-0.842164\pi\)
0.958374 + 0.285514i \(0.0921645\pi\)
\(734\) −31.9775 590.267i −0.0435661 0.804178i
\(735\) 412.584i 0.561339i
\(736\) 265.989 + 150.460i 0.361399 + 0.204430i
\(737\) 390.447 0.529778
\(738\) 586.424 31.7694i 0.794613 0.0430479i
\(739\) 536.590 + 222.263i 0.726103 + 0.300762i 0.714950 0.699176i \(-0.246450\pi\)
0.0111538 + 0.999938i \(0.496450\pi\)
\(740\) 260.610 324.155i 0.352176 0.438048i
\(741\) 2203.76 912.828i 2.97404 1.23189i
\(742\) −193.793 68.2418i −0.261177 0.0919700i
\(743\) 907.324 + 907.324i 1.22116 + 1.22116i 0.967219 + 0.253944i \(0.0817279\pi\)
0.253944 + 0.967219i \(0.418272\pi\)
\(744\) −11.9851 2.81044i −0.0161090 0.00377747i
\(745\) 610.278 + 610.278i 0.819165 + 0.819165i
\(746\) −630.987 + 302.331i −0.845827 + 0.405270i
\(747\) 338.351 140.150i 0.452947 0.187617i
\(748\) 76.5279 + 139.770i 0.102310 + 0.186858i
\(749\) 361.249 + 149.634i 0.482309 + 0.199779i
\(750\) −870.048 780.624i −1.16006 1.04083i
\(751\) −662.862 −0.882639 −0.441320 0.897350i \(-0.645489\pi\)
−0.441320 + 0.897350i \(0.645489\pi\)
\(752\) −776.788 + 170.842i −1.03296 + 0.227184i
\(753\) 1180.93i 1.56830i
\(754\) 14.9476 + 13.4113i 0.0198244 + 0.0177868i
\(755\) −85.0132 + 205.240i −0.112600 + 0.271841i
\(756\) −194.964 + 666.806i −0.257888 + 0.882018i
\(757\) 76.1190 + 183.767i 0.100553 + 0.242757i 0.966148 0.257988i \(-0.0830594\pi\)
−0.865595 + 0.500745i \(0.833059\pi\)
\(758\) 804.266 385.356i 1.06104 0.508385i
\(759\) 277.554 277.554i 0.365684 0.365684i
\(760\) −845.370 + 138.478i −1.11233 + 0.182208i
\(761\) 435.811 435.811i 0.572683 0.572683i −0.360195 0.932877i \(-0.617290\pi\)
0.932877 + 0.360195i \(0.117290\pi\)
\(762\) 1183.59 + 416.784i 1.55326 + 0.546961i
\(763\) −373.176 900.926i −0.489090 1.18077i
\(764\) 146.110 + 1344.55i 0.191244 + 1.75989i
\(765\) 70.2012 169.481i 0.0917662 0.221543i
\(766\) −509.057 + 27.5780i −0.664565 + 0.0360026i
\(767\) 494.578i 0.644821i
\(768\) 1204.74 48.5477i 1.56867 0.0632131i
\(769\) −1422.48 −1.84978 −0.924889 0.380237i \(-0.875843\pi\)
−0.924889 + 0.380237i \(0.875843\pi\)
\(770\) 25.3770 + 468.429i 0.0329572 + 0.608350i
\(771\) −570.642 236.368i −0.740132 0.306573i
\(772\) −932.540 + 101.338i −1.20795 + 0.131266i
\(773\) −0.439715 + 0.182136i −0.000568842 + 0.000235622i −0.382968 0.923762i \(-0.625098\pi\)
0.382399 + 0.923997i \(0.375098\pi\)
\(774\) 45.8072 130.083i 0.0591824 0.168067i
\(775\) −3.62867 3.62867i −0.00468215 0.00468215i
\(776\) 100.843 + 615.618i 0.129952 + 0.793322i
\(777\) −1001.57 1001.57i −1.28902 1.28902i
\(778\) −642.854 1341.68i −0.826290 1.72453i
\(779\) 722.878 299.426i 0.927956 0.384372i
\(780\) 794.778 + 232.381i 1.01895 + 0.297924i
\(781\) −429.160 177.764i −0.549500 0.227610i
\(782\) −58.2259 + 64.8960i −0.0744576 + 0.0829872i
\(783\) −13.7184 −0.0175204
\(784\) 98.7608 + 449.048i 0.125970 + 0.572765i
\(785\) 313.420i 0.399262i
\(786\) 1552.82 1730.71i 1.97560 2.20192i
\(787\) 23.0303 55.6002i 0.0292635 0.0706482i −0.908572 0.417728i \(-0.862827\pi\)
0.937836 + 0.347079i \(0.112827\pi\)
\(788\) −900.055 + 492.805i −1.14220 + 0.625386i
\(789\) −717.144 1731.34i −0.908928 2.19435i
\(790\) 70.8832 + 147.938i 0.0897255 + 0.187264i
\(791\) −770.590 + 770.590i −0.974197 + 0.974197i
\(792\) 210.116 896.034i 0.265298 1.13136i
\(793\) −943.175 + 943.175i −1.18938 + 1.18938i
\(794\) −40.9110 + 116.179i −0.0515252 + 0.146322i
\(795\) −64.0181 154.553i −0.0805259 0.194407i
\(796\) −172.898 139.004i −0.217208 0.174628i
\(797\) 49.3444 119.128i 0.0619127 0.149470i −0.889895 0.456165i \(-0.849223\pi\)
0.951808 + 0.306694i \(0.0992229\pi\)
\(798\) 157.811 + 2912.99i 0.197758 + 3.65037i
\(799\) 226.918i 0.284003i
\(800\) 437.482 + 247.468i 0.546853 + 0.309335i
\(801\) −1925.65 −2.40406
\(802\) 1405.96 76.1674i 1.75307 0.0949718i
\(803\) 595.542 + 246.682i 0.741647 + 0.307200i
\(804\) 656.906 + 528.130i 0.817048 + 0.656878i
\(805\) −237.138 + 98.2260i −0.294582 + 0.122020i
\(806\) 8.88651 + 3.12927i 0.0110254 + 0.00388247i
\(807\) 480.478 + 480.478i 0.595388 + 0.595388i
\(808\) 474.879 + 765.816i 0.587721 + 0.947792i
\(809\) 29.6470 + 29.6470i 0.0366465 + 0.0366465i 0.725193 0.688546i \(-0.241751\pi\)
−0.688546 + 0.725193i \(0.741751\pi\)
\(810\) 142.210 68.1387i 0.175568 0.0841219i
\(811\) −755.209 + 312.818i −0.931207 + 0.385719i −0.796136 0.605117i \(-0.793126\pi\)
−0.135071 + 0.990836i \(0.543126\pi\)
\(812\) −21.5427 + 11.7952i −0.0265304 + 0.0145261i
\(813\) −1604.21 664.486i −1.97320 0.817326i
\(814\) 443.129 + 397.584i 0.544385 + 0.488432i
\(815\) 16.4144 0.0201404
\(816\) −60.3031 + 338.670i −0.0739009 + 0.415037i
\(817\) 183.741i 0.224897i
\(818\) −1112.61 998.251i −1.36015 1.22036i
\(819\) 641.305 1548.25i 0.783034 1.89041i
\(820\) 260.703 + 76.2254i 0.317930 + 0.0929578i
\(821\) 120.712 + 291.425i 0.147031 + 0.354964i 0.980187 0.198074i \(-0.0634685\pi\)
−0.833156 + 0.553038i \(0.813469\pi\)
\(822\) −1343.32 + 643.638i −1.63421 + 0.783015i
\(823\) 173.105 173.105i 0.210334 0.210334i −0.594076 0.804409i \(-0.702482\pi\)
0.804409 + 0.594076i \(0.202482\pi\)
\(824\) 506.056 704.326i 0.614146 0.854764i
\(825\) 456.504 456.504i 0.553338 0.553338i
\(826\) −570.529 200.904i −0.690713 0.243225i
\(827\) −59.9551 144.744i −0.0724971 0.175023i 0.883477 0.468475i \(-0.155196\pi\)
−0.955974 + 0.293451i \(0.905196\pi\)
\(828\) 500.617 54.4012i 0.604610 0.0657020i
\(829\) 259.829 627.283i 0.313425 0.756674i −0.686149 0.727461i \(-0.740700\pi\)
0.999573 0.0292124i \(-0.00929993\pi\)
\(830\) 169.132 9.16269i 0.203774 0.0110394i
\(831\) 265.840i 0.319904i
\(832\) −920.644 62.6710i −1.10654 0.0753257i
\(833\) −131.178 −0.157476
\(834\) −17.5253 323.496i −0.0210135 0.387885i
\(835\) 657.240 + 272.238i 0.787114 + 0.326033i
\(836\) −132.466 1218.99i −0.158452 1.45812i
\(837\) −5.94599 + 2.46291i −0.00710394 + 0.00294255i
\(838\) −110.359 + 313.398i −0.131693 + 0.373983i
\(839\) 182.343 + 182.343i 0.217333 + 0.217333i 0.807374 0.590040i \(-0.200888\pi\)
−0.590040 + 0.807374i \(0.700888\pi\)
\(840\) −590.916 + 822.434i −0.703472 + 0.979088i
\(841\) 594.334 + 594.334i 0.706699 + 0.706699i
\(842\) 224.661 + 468.884i 0.266818 + 0.556869i
\(843\) 523.436 216.814i 0.620920 0.257194i
\(844\) 234.381 801.620i 0.277703 0.949787i
\(845\) −109.526 45.3671i −0.129617 0.0536889i
\(846\) −875.240 + 975.503i −1.03456 + 1.15308i
\(847\) 395.354 0.466770
\(848\) 106.671 + 152.888i 0.125792 + 0.180293i
\(849\) 333.466i 0.392775i
\(850\) −95.7663 + 106.737i −0.112666 + 0.125573i
\(851\) −124.657 + 300.947i −0.146482 + 0.353640i
\(852\) −481.590 879.573i −0.565247 1.03236i
\(853\) −300.757 726.092i −0.352588 0.851222i −0.996299 0.0859535i \(-0.972606\pi\)
0.643712 0.765268i \(-0.277394\pi\)
\(854\) −704.886 1471.15i −0.825393 1.72266i
\(855\) −998.134 + 998.134i −1.16741 + 1.16741i
\(856\) −186.973 301.523i −0.218426 0.352247i
\(857\) −545.430 + 545.430i −0.636441 + 0.636441i −0.949676 0.313235i \(-0.898587\pi\)
0.313235 + 0.949676i \(0.398587\pi\)
\(858\) −393.677 + 1117.97i −0.458831 + 1.30299i
\(859\) 230.652 + 556.843i 0.268512 + 0.648246i 0.999414 0.0342370i \(-0.0109001\pi\)
−0.730901 + 0.682483i \(0.760900\pi\)
\(860\) 39.9660 49.7111i 0.0464721 0.0578036i
\(861\) 353.979 854.580i 0.411125 0.992544i
\(862\) 65.7063 + 1212.86i 0.0762254 + 1.40703i
\(863\) 980.846i 1.13655i 0.822837 + 0.568277i \(0.192390\pi\)
−0.822837 + 0.568277i \(0.807610\pi\)
\(864\) 496.700 388.131i 0.574884 0.449226i
\(865\) 381.962 0.441574
\(866\) 466.076 25.2496i 0.538195 0.0291565i
\(867\) 1166.86 + 483.328i 1.34586 + 0.557472i
\(868\) −7.21964 + 8.98004i −0.00831756 + 0.0103457i
\(869\) −216.933 + 89.8568i −0.249636 + 0.103403i
\(870\) −18.8623 6.64211i −0.0216808 0.00763461i
\(871\) −456.143 456.143i −0.523701 0.523701i
\(872\) −202.005 + 861.446i −0.231657 + 0.987897i
\(873\) 726.865 + 726.865i 0.832606 + 0.832606i
\(874\) 605.032 289.895i 0.692256 0.331688i
\(875\) −1010.82 + 418.696i −1.15522 + 0.478509i
\(876\) 668.300 + 1220.58i 0.762899 + 1.39335i
\(877\) 1395.56 + 578.059i 1.59129 + 0.659132i 0.990150 0.140014i \(-0.0447146\pi\)
0.601137 + 0.799146i \(0.294715\pi\)
\(878\) 1046.00 + 938.491i 1.19134 + 1.06890i
\(879\) −1636.59 −1.86188
\(880\) 229.307 358.610i 0.260576 0.407511i
\(881\) 1513.62i 1.71807i −0.511914 0.859037i \(-0.671063\pi\)
0.511914 0.859037i \(-0.328937\pi\)
\(882\) 563.922 + 505.961i 0.639367 + 0.573652i
\(883\) −91.3318 + 220.494i −0.103434 + 0.249711i −0.967121 0.254317i \(-0.918149\pi\)
0.863687 + 0.504028i \(0.168149\pi\)
\(884\) 73.8833 252.692i 0.0835784 0.285851i
\(885\) −188.470 455.006i −0.212960 0.514131i
\(886\) 282.075 135.153i 0.318369 0.152543i
\(887\) 892.828 892.828i 1.00657 1.00657i 0.00659168 0.999978i \(-0.497902\pi\)
0.999978 0.00659168i \(-0.00209821\pi\)
\(888\) 207.758 + 1268.30i 0.233961 + 1.42827i
\(889\) 830.510 830.510i 0.934207 0.934207i
\(890\) −840.050 295.813i −0.943877 0.332374i
\(891\) 86.3777 + 208.534i 0.0969447 + 0.234045i
\(892\) −148.834 1369.62i −0.166855 1.53545i
\(893\) −668.203 + 1613.19i −0.748268 + 1.80648i
\(894\) −2662.95 + 144.265i −2.97870 + 0.161370i
\(895\) 357.168i 0.399071i
\(896\) 446.273 1036.57i 0.498073 1.15688i
\(897\) −648.512 −0.722978
\(898\) 1.67187 + 30.8608i 0.00186177 + 0.0343661i
\(899\) −0.210208 0.0870710i −0.000233824 9.68531e-5i
\(900\) 823.383 89.4757i 0.914870 0.0994174i
\(901\) −49.1388 + 20.3540i −0.0545381 + 0.0225904i
\(902\) −129.134 + 366.715i −0.143164 + 0.406557i
\(903\) −153.596 153.596i −0.170095 0.170095i
\(904\) 975.813 159.845i 1.07944 0.176820i
\(905\) −452.680 452.680i −0.500199 0.500199i
\(906\) −296.612 619.051i −0.327386 0.683279i
\(907\) −469.078 + 194.298i −0.517175 + 0.214221i −0.625976 0.779843i \(-0.715299\pi\)
0.108800 + 0.994064i \(0.465299\pi\)
\(908\) −283.676 82.9425i −0.312419 0.0913464i
\(909\) 1371.82 + 568.226i 1.50915 + 0.625111i
\(910\) 517.600 576.894i 0.568792 0.633950i
\(911\) 469.566 0.515441 0.257720 0.966220i \(-0.417029\pi\)
0.257720 + 0.966220i \(0.417029\pi\)
\(912\) 1425.98 2230.07i 1.56357 2.44525i
\(913\) 242.446i 0.265549i
\(914\) −177.246 + 197.550i −0.193923 + 0.216138i
\(915\) 508.293 1227.13i 0.555512 1.34112i
\(916\) 158.816 86.9562i 0.173380 0.0949303i
\(917\) −832.872 2010.73i −0.908257 2.19273i
\(918\) 77.7114 + 162.189i 0.0846529 + 0.176677i
\(919\) 737.868 737.868i 0.802903 0.802903i −0.180645 0.983548i \(-0.557819\pi\)
0.983548 + 0.180645i \(0.0578186\pi\)
\(920\) 226.747 + 53.1710i 0.246464 + 0.0577946i
\(921\) −806.710 + 806.710i −0.875907 + 0.875907i
\(922\) −412.970 + 1172.75i −0.447907 + 1.27197i
\(923\) 293.696 + 709.045i 0.318197 + 0.768196i
\(924\) −1129.73 908.266i −1.22265 0.982971i
\(925\) −205.027 + 494.979i −0.221651 + 0.535113i
\(926\) −61.4620 1134.51i −0.0663736 1.22518i
\(927\) 1429.11i 1.54165i
\(928\) 22.1192 + 2.71403i 0.0238354 + 0.00292461i
\(929\) 796.539 0.857416 0.428708 0.903443i \(-0.358969\pi\)
0.428708 + 0.903443i \(0.358969\pi\)
\(930\) −9.36797 + 0.507507i −0.0100731 + 0.000545707i
\(931\) 932.554 + 386.277i 1.00167 + 0.414905i
\(932\) −895.162 719.680i −0.960475 0.772189i
\(933\) −274.312 + 113.624i −0.294011 + 0.121783i
\(934\) 771.273 + 271.594i 0.825774 + 0.290786i
\(935\) 85.8723 + 85.8723i 0.0918420 + 0.0918420i
\(936\) −1292.27 + 801.331i −1.38063 + 0.856123i
\(937\) 764.262 + 764.262i 0.815648 + 0.815648i 0.985474 0.169826i \(-0.0543206\pi\)
−0.169826 + 0.985474i \(0.554321\pi\)
\(938\) 711.484 340.900i 0.758511 0.363433i
\(939\) −171.875 + 71.1927i −0.183040 + 0.0758176i
\(940\) −531.670 + 291.104i −0.565606 + 0.309685i
\(941\) 113.549 + 47.0336i 0.120669 + 0.0499826i 0.442201 0.896916i \(-0.354198\pi\)
−0.321532 + 0.946899i \(0.604198\pi\)
\(942\) −720.852 646.762i −0.765235 0.686584i
\(943\) −212.725 −0.225583
\(944\) 314.042 + 450.104i 0.332671 + 0.476805i
\(945\) 529.456i 0.560271i
\(946\) 67.9563 + 60.9717i 0.0718354 + 0.0644521i
\(947\) 396.726 957.782i 0.418930 1.01139i −0.563729 0.825960i \(-0.690634\pi\)
0.982658 0.185425i \(-0.0593663\pi\)
\(948\) −486.522 142.252i −0.513209 0.150054i
\(949\) −407.560 983.937i −0.429463 1.03681i
\(950\) 995.118 476.801i 1.04749 0.501896i
\(951\) −1095.23 + 1095.23i −1.15166 + 1.15166i
\(952\) 261.485 + 187.877i 0.274670 + 0.197349i
\(953\) 391.136 391.136i 0.410426 0.410426i −0.471461 0.881887i \(-0.656273\pi\)
0.881887 + 0.471461i \(0.156273\pi\)
\(954\) 289.751 + 102.032i 0.303722 + 0.106952i
\(955\) 394.443 + 952.270i 0.413030 + 0.997142i
\(956\) −348.632 + 37.8852i −0.364677 + 0.0396289i
\(957\) 10.9539 26.4452i 0.0114461 0.0276334i
\(958\) 654.799 35.4736i 0.683506 0.0370288i
\(959\) 1394.23i 1.45383i
\(960\) 870.864 293.175i 0.907150 0.305391i
\(961\) 960.893 0.999889
\(962\) −53.2089 982.171i −0.0553107 1.02097i
\(963\) −540.123 223.726i −0.560875 0.232322i
\(964\) −6.68740 61.5395i −0.00693713 0.0638377i
\(965\) −660.465 + 273.574i −0.684420 + 0.283496i
\(966\) 263.434 748.102i 0.272706 0.774433i
\(967\) −22.8939 22.8939i −0.0236752 0.0236752i 0.695170 0.718845i \(-0.255329\pi\)
−0.718845 + 0.695170i \(0.755329\pi\)
\(968\) −291.327 209.318i −0.300958 0.216237i
\(969\) 534.009 + 534.009i 0.551093 + 0.551093i
\(970\) 205.430 + 428.747i 0.211784 + 0.442007i
\(971\) −619.006 + 256.401i −0.637493 + 0.264058i −0.677933 0.735124i \(-0.737124\pi\)
0.0404399 + 0.999182i \(0.487124\pi\)
\(972\) −335.758 + 1148.35i −0.345430 + 1.18143i
\(973\) −280.154 116.044i −0.287928 0.119264i
\(974\) −278.597 + 310.512i −0.286034 + 0.318801i
\(975\) −1066.63 −1.09398
\(976\) −259.476 + 1457.25i −0.265856 + 1.49308i
\(977\) 430.856i 0.440999i 0.975387 + 0.220500i \(0.0707688\pi\)
−0.975387 + 0.220500i \(0.929231\pi\)
\(978\) −33.8722 + 37.7524i −0.0346341 + 0.0386017i
\(979\) 487.844 1177.76i 0.498309 1.20302i
\(980\) 168.282 + 307.349i 0.171716 + 0.313621i
\(981\) 557.955 + 1347.02i 0.568762 + 1.37311i
\(982\) −560.123 1169.02i −0.570390 1.19044i
\(983\) 154.209 154.209i 0.156876 0.156876i −0.624305 0.781181i \(-0.714618\pi\)
0.781181 + 0.624305i \(0.214618\pi\)
\(984\) −713.291 + 442.308i −0.724889 + 0.449500i
\(985\) −552.978 + 552.978i −0.561399 + 0.561399i
\(986\) −2.11180 + 5.99710i −0.00214178 + 0.00608225i
\(987\) 789.945 + 1907.09i 0.800349 + 1.93221i
\(988\) −1269.34 + 1578.85i −1.28476 + 1.59803i
\(989\) −19.1168 + 46.1520i −0.0193294 + 0.0466653i
\(990\) −37.9425 700.374i −0.0383258 0.707448i
\(991\) 966.543i 0.975320i −0.873033 0.487660i \(-0.837850\pi\)
0.873033 0.487660i \(-0.162150\pi\)
\(992\) 10.0744 2.79478i 0.0101556 0.00281732i
\(993\) −864.169 −0.870260
\(994\) −937.234 + 50.7744i −0.942891 + 0.0510809i
\(995\) −156.201 64.7007i −0.156986 0.0650258i
\(996\) −327.940 + 407.903i −0.329258 + 0.409542i
\(997\) 732.694 303.492i 0.734899 0.304405i 0.0163357 0.999867i \(-0.494800\pi\)
0.718564 + 0.695461i \(0.244800\pi\)
\(998\) −286.626 100.932i −0.287201 0.101134i
\(999\) 475.120 + 475.120i 0.475596 + 0.475596i
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 32.3.h.a.19.4 28
3.2 odd 2 288.3.u.a.19.4 28
4.3 odd 2 128.3.h.a.111.1 28
8.3 odd 2 256.3.h.a.223.7 28
8.5 even 2 256.3.h.b.223.1 28
32.5 even 8 128.3.h.a.15.1 28
32.11 odd 8 256.3.h.b.31.1 28
32.21 even 8 256.3.h.a.31.7 28
32.27 odd 8 inner 32.3.h.a.27.4 yes 28
96.59 even 8 288.3.u.a.91.4 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.19.4 28 1.1 even 1 trivial
32.3.h.a.27.4 yes 28 32.27 odd 8 inner
128.3.h.a.15.1 28 32.5 even 8
128.3.h.a.111.1 28 4.3 odd 2
256.3.h.a.31.7 28 32.21 even 8
256.3.h.a.223.7 28 8.3 odd 2
256.3.h.b.31.1 28 32.11 odd 8
256.3.h.b.223.1 28 8.5 even 2
288.3.u.a.19.4 28 3.2 odd 2
288.3.u.a.91.4 28 96.59 even 8