Properties

Label 32.3.h.a.3.2
Level $32$
Weight $3$
Character 32.3
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 3.2
Character \(\chi\) \(=\) 32.3
Dual form 32.3.h.a.11.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.46783 + 1.35848i) q^{2} +(2.10187 - 5.07436i) q^{3} +(0.309042 - 3.98804i) q^{4} +(1.74699 + 4.21761i) q^{5} +(3.80826 + 10.3037i) q^{6} +(-0.392379 - 0.392379i) q^{7} +(4.96407 + 6.27359i) q^{8} +(-14.9674 - 14.9674i) q^{9} +O(q^{10})\) \(q+(-1.46783 + 1.35848i) q^{2} +(2.10187 - 5.07436i) q^{3} +(0.309042 - 3.98804i) q^{4} +(1.74699 + 4.21761i) q^{5} +(3.80826 + 10.3037i) q^{6} +(-0.392379 - 0.392379i) q^{7} +(4.96407 + 6.27359i) q^{8} +(-14.9674 - 14.9674i) q^{9} +(-8.29385 - 3.81747i) q^{10} +(2.90924 + 7.02353i) q^{11} +(-19.5872 - 9.95055i) q^{12} +(-4.50555 + 10.8774i) q^{13} +(1.10898 + 0.0429045i) q^{14} +25.0737 q^{15} +(-15.8090 - 2.46495i) q^{16} +10.5402i q^{17} +(42.3024 + 1.63660i) q^{18} +(-1.88707 - 0.781651i) q^{19} +(17.3599 - 5.66366i) q^{20} +(-2.81580 + 1.16634i) q^{21} +(-13.8116 - 6.35718i) q^{22} +(-0.445453 + 0.445453i) q^{23} +(42.2683 - 12.0032i) q^{24} +(2.94139 - 2.94139i) q^{25} +(-8.16334 - 22.0868i) q^{26} +(-61.7400 + 25.5735i) q^{27} +(-1.68608 + 1.44356i) q^{28} +(0.741814 + 0.307270i) q^{29} +(-36.8038 + 34.0622i) q^{30} -47.6947i q^{31} +(26.5535 - 17.8581i) q^{32} +41.7548 q^{33} +(-14.3187 - 15.4712i) q^{34} +(0.969419 - 2.34038i) q^{35} +(-64.3160 + 55.0649i) q^{36} +(14.5080 + 35.0255i) q^{37} +(3.83176 - 1.41623i) q^{38} +(45.7256 + 45.7256i) q^{39} +(-17.7874 + 31.8965i) q^{40} +(-11.3365 - 11.3365i) q^{41} +(2.54866 - 5.53721i) q^{42} +(-14.6421 - 35.3493i) q^{43} +(28.9092 - 9.43161i) q^{44} +(36.9787 - 89.2744i) q^{45} +(0.0487080 - 1.25899i) q^{46} -80.5164 q^{47} +(-45.7365 + 75.0396i) q^{48} -48.6921i q^{49} +(-0.321625 + 8.31328i) q^{50} +(53.4849 + 22.1542i) q^{51} +(41.9870 + 21.3299i) q^{52} +(-66.6128 + 27.5919i) q^{53} +(55.8825 - 121.410i) q^{54} +(-24.5401 + 24.5401i) q^{55} +(0.513828 - 4.40942i) q^{56} +(-7.93277 + 7.93277i) q^{57} +(-1.50628 + 0.556724i) q^{58} +(65.0706 - 26.9531i) q^{59} +(7.74883 - 99.9949i) q^{60} +(87.4322 + 36.2156i) q^{61} +(64.7925 + 70.0077i) q^{62} +11.7457i q^{63} +(-14.7160 + 62.2852i) q^{64} -53.7476 q^{65} +(-61.2889 + 56.7232i) q^{66} +(-7.12379 + 17.1984i) q^{67} +(42.0348 + 3.25737i) q^{68} +(1.32411 + 3.19668i) q^{69} +(1.75643 + 4.75222i) q^{70} +(-14.8103 - 14.8103i) q^{71} +(19.6001 - 168.198i) q^{72} +(18.6720 + 18.6720i) q^{73} +(-68.8769 - 31.7025i) q^{74} +(-8.74326 - 21.1081i) q^{75} +(-3.70044 + 7.28417i) q^{76} +(1.61436 - 3.89741i) q^{77} +(-129.235 - 4.99985i) q^{78} -36.2398 q^{79} +(-17.2220 - 70.9824i) q^{80} +176.540i q^{81} +(32.0406 + 1.23959i) q^{82} +(27.0868 + 11.2197i) q^{83} +(3.78122 + 11.5900i) q^{84} +(-44.4545 + 18.4137i) q^{85} +(69.5135 + 31.9955i) q^{86} +(3.11840 - 3.11840i) q^{87} +(-29.6211 + 53.1167i) q^{88} +(-56.4944 + 56.4944i) q^{89} +(66.9995 + 181.274i) q^{90} +(6.03592 - 2.50016i) q^{91} +(1.63882 + 1.91415i) q^{92} +(-242.020 - 100.248i) q^{93} +(118.184 - 109.380i) q^{94} -9.32448i q^{95} +(-34.8067 - 172.278i) q^{96} +158.579 q^{97} +(66.1474 + 71.4716i) q^{98} +(61.5800 - 148.667i) 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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.46783 + 1.35848i −0.733914 + 0.679242i
\(3\) 2.10187 5.07436i 0.700624 1.69145i −0.0215732 0.999767i \(-0.506867\pi\)
0.722197 0.691688i \(-0.243133\pi\)
\(4\) 0.309042 3.98804i 0.0772606 0.997011i
\(5\) 1.74699 + 4.21761i 0.349399 + 0.843523i 0.996691 + 0.0812812i \(0.0259012\pi\)
−0.647293 + 0.762242i \(0.724099\pi\)
\(6\) 3.80826 + 10.3037i 0.634710 + 1.71728i
\(7\) −0.392379 0.392379i −0.0560541 0.0560541i 0.678524 0.734578i \(-0.262620\pi\)
−0.734578 + 0.678524i \(0.762620\pi\)
\(8\) 4.96407 + 6.27359i 0.620509 + 0.784199i
\(9\) −14.9674 14.9674i −1.66304 1.66304i
\(10\) −8.29385 3.81747i −0.829385 0.381747i
\(11\) 2.90924 + 7.02353i 0.264477 + 0.638503i 0.999205 0.0398581i \(-0.0126906\pi\)
−0.734729 + 0.678361i \(0.762691\pi\)
\(12\) −19.5872 9.95055i −1.63227 0.829212i
\(13\) −4.50555 + 10.8774i −0.346581 + 0.836720i 0.650438 + 0.759559i \(0.274585\pi\)
−0.997019 + 0.0771604i \(0.975415\pi\)
\(14\) 1.10898 + 0.0429045i 0.0792132 + 0.00306461i
\(15\) 25.0737 1.67158
\(16\) −15.8090 2.46495i −0.988062 0.154059i
\(17\) 10.5402i 0.620012i 0.950735 + 0.310006i \(0.100331\pi\)
−0.950735 + 0.310006i \(0.899669\pi\)
\(18\) 42.3024 + 1.63660i 2.35014 + 0.0909223i
\(19\) −1.88707 0.781651i −0.0993196 0.0411395i 0.332470 0.943114i \(-0.392118\pi\)
−0.431790 + 0.901974i \(0.642118\pi\)
\(20\) 17.3599 5.66366i 0.867996 0.283183i
\(21\) −2.81580 + 1.16634i −0.134086 + 0.0555401i
\(22\) −13.8116 6.35718i −0.627801 0.288963i
\(23\) −0.445453 + 0.445453i −0.0193675 + 0.0193675i −0.716724 0.697357i \(-0.754359\pi\)
0.697357 + 0.716724i \(0.254359\pi\)
\(24\) 42.2683 12.0032i 1.76118 0.500135i
\(25\) 2.94139 2.94139i 0.117656 0.117656i
\(26\) −8.16334 22.0868i −0.313975 0.849493i
\(27\) −61.7400 + 25.5735i −2.28667 + 0.947168i
\(28\) −1.68608 + 1.44356i −0.0602173 + 0.0515558i
\(29\) 0.741814 + 0.307270i 0.0255798 + 0.0105955i 0.395437 0.918493i \(-0.370593\pi\)
−0.369857 + 0.929089i \(0.620593\pi\)
\(30\) −36.8038 + 34.0622i −1.22679 + 1.13541i
\(31\) 47.6947i 1.53854i −0.638924 0.769270i \(-0.720620\pi\)
0.638924 0.769270i \(-0.279380\pi\)
\(32\) 26.5535 17.8581i 0.829796 0.558067i
\(33\) 41.7548 1.26530
\(34\) −14.3187 15.4712i −0.421138 0.455036i
\(35\) 0.969419 2.34038i 0.0276977 0.0668681i
\(36\) −64.3160 + 55.0649i −1.78656 + 1.52958i
\(37\) 14.5080 + 35.0255i 0.392109 + 0.946635i 0.989480 + 0.144670i \(0.0462120\pi\)
−0.597371 + 0.801965i \(0.703788\pi\)
\(38\) 3.83176 1.41623i 0.100836 0.0372692i
\(39\) 45.7256 + 45.7256i 1.17245 + 1.17245i
\(40\) −17.7874 + 31.8965i −0.444685 + 0.797412i
\(41\) −11.3365 11.3365i −0.276501 0.276501i 0.555209 0.831711i \(-0.312638\pi\)
−0.831711 + 0.555209i \(0.812638\pi\)
\(42\) 2.54866 5.53721i 0.0606823 0.131838i
\(43\) −14.6421 35.3493i −0.340515 0.822076i −0.997664 0.0683149i \(-0.978238\pi\)
0.657149 0.753761i \(-0.271762\pi\)
\(44\) 28.9092 9.43161i 0.657028 0.214355i
\(45\) 36.9787 89.2744i 0.821748 1.98388i
\(46\) 0.0487080 1.25899i 0.00105887 0.0273694i
\(47\) −80.5164 −1.71312 −0.856558 0.516051i \(-0.827402\pi\)
−0.856558 + 0.516051i \(0.827402\pi\)
\(48\) −45.7365 + 75.0396i −0.952844 + 1.56332i
\(49\) 48.6921i 0.993716i
\(50\) −0.321625 + 8.31328i −0.00643251 + 0.166266i
\(51\) 53.4849 + 22.1542i 1.04872 + 0.434395i
\(52\) 41.9870 + 21.3299i 0.807442 + 0.410190i
\(53\) −66.6128 + 27.5919i −1.25685 + 0.520602i −0.908940 0.416927i \(-0.863107\pi\)
−0.347905 + 0.937530i \(0.613107\pi\)
\(54\) 55.8825 121.410i 1.03486 2.24834i
\(55\) −24.5401 + 24.5401i −0.446184 + 0.446184i
\(56\) 0.513828 4.40942i 0.00917551 0.0787396i
\(57\) −7.93277 + 7.93277i −0.139171 + 0.139171i
\(58\) −1.50628 + 0.556724i −0.0259703 + 0.00959869i
\(59\) 65.0706 26.9531i 1.10289 0.456833i 0.244408 0.969673i \(-0.421406\pi\)
0.858484 + 0.512840i \(0.171406\pi\)
\(60\) 7.74883 99.9949i 0.129147 1.66658i
\(61\) 87.4322 + 36.2156i 1.43331 + 0.593698i 0.958168 0.286208i \(-0.0923948\pi\)
0.475147 + 0.879906i \(0.342395\pi\)
\(62\) 64.7925 + 70.0077i 1.04504 + 1.12916i
\(63\) 11.7457i 0.186440i
\(64\) −14.7160 + 62.2852i −0.229937 + 0.973205i
\(65\) −53.7476 −0.826887
\(66\) −61.2889 + 56.7232i −0.928620 + 0.859443i
\(67\) −7.12379 + 17.1984i −0.106325 + 0.256692i −0.968084 0.250627i \(-0.919363\pi\)
0.861759 + 0.507319i \(0.169363\pi\)
\(68\) 42.0348 + 3.25737i 0.618159 + 0.0479025i
\(69\) 1.32411 + 3.19668i 0.0191900 + 0.0463287i
\(70\) 1.75643 + 4.75222i 0.0250919 + 0.0678889i
\(71\) −14.8103 14.8103i −0.208596 0.208596i 0.595074 0.803671i \(-0.297123\pi\)
−0.803671 + 0.595074i \(0.797123\pi\)
\(72\) 19.6001 168.198i 0.272223 2.33609i
\(73\) 18.6720 + 18.6720i 0.255781 + 0.255781i 0.823336 0.567555i \(-0.192110\pi\)
−0.567555 + 0.823336i \(0.692110\pi\)
\(74\) −68.8769 31.7025i −0.930769 0.428412i
\(75\) −8.74326 21.1081i −0.116577 0.281441i
\(76\) −3.70044 + 7.28417i −0.0486901 + 0.0958443i
\(77\) 1.61436 3.89741i 0.0209657 0.0506157i
\(78\) −129.235 4.99985i −1.65686 0.0641007i
\(79\) −36.2398 −0.458732 −0.229366 0.973340i \(-0.573665\pi\)
−0.229366 + 0.973340i \(0.573665\pi\)
\(80\) −17.2220 70.9824i −0.215275 0.887281i
\(81\) 176.540i 2.17951i
\(82\) 32.0406 + 1.23959i 0.390739 + 0.0151170i
\(83\) 27.0868 + 11.2197i 0.326347 + 0.135177i 0.539841 0.841767i \(-0.318484\pi\)
−0.213494 + 0.976944i \(0.568484\pi\)
\(84\) 3.78122 + 11.5900i 0.0450146 + 0.137976i
\(85\) −44.4545 + 18.4137i −0.522994 + 0.216631i
\(86\) 69.5135 + 31.9955i 0.808297 + 0.372041i
\(87\) 3.11840 3.11840i 0.0358436 0.0358436i
\(88\) −29.6211 + 53.1167i −0.336603 + 0.603599i
\(89\) −56.4944 + 56.4944i −0.634769 + 0.634769i −0.949260 0.314491i \(-0.898166\pi\)
0.314491 + 0.949260i \(0.398166\pi\)
\(90\) 66.9995 + 181.274i 0.744439 + 2.01416i
\(91\) 6.03592 2.50016i 0.0663288 0.0274743i
\(92\) 1.63882 + 1.91415i 0.0178133 + 0.0208060i
\(93\) −242.020 100.248i −2.60237 1.07794i
\(94\) 118.184 109.380i 1.25728 1.16362i
\(95\) 9.32448i 0.0981525i
\(96\) −34.8067 172.278i −0.362570 1.79456i
\(97\) 158.579 1.63484 0.817419 0.576043i \(-0.195404\pi\)
0.817419 + 0.576043i \(0.195404\pi\)
\(98\) 66.1474 + 71.4716i 0.674974 + 0.729302i
\(99\) 61.5800 148.667i 0.622021 1.50169i
\(100\) −10.8214 12.6394i −0.108214 0.126394i
\(101\) −53.8420 129.986i −0.533089 1.28699i −0.929468 0.368903i \(-0.879733\pi\)
0.396379 0.918087i \(-0.370267\pi\)
\(102\) −108.603 + 40.1398i −1.06473 + 0.393528i
\(103\) 9.94607 + 9.94607i 0.0965638 + 0.0965638i 0.753738 0.657175i \(-0.228249\pi\)
−0.657175 + 0.753738i \(0.728249\pi\)
\(104\) −90.6060 + 25.7300i −0.871211 + 0.247404i
\(105\) −9.83837 9.83837i −0.0936987 0.0936987i
\(106\) 60.2930 130.993i 0.568802 1.23578i
\(107\) 68.8129 + 166.129i 0.643111 + 1.55261i 0.822461 + 0.568822i \(0.192601\pi\)
−0.179350 + 0.983785i \(0.557399\pi\)
\(108\) 82.9081 + 254.125i 0.767668 + 2.35301i
\(109\) 3.61301 8.72257i 0.0331469 0.0800236i −0.906439 0.422336i \(-0.861210\pi\)
0.939586 + 0.342313i \(0.111210\pi\)
\(110\) 2.68333 69.3580i 0.0243939 0.630528i
\(111\) 208.226 1.87591
\(112\) 5.23591 + 7.17030i 0.0467492 + 0.0640205i
\(113\) 85.8345i 0.759598i −0.925069 0.379799i \(-0.875993\pi\)
0.925069 0.379799i \(-0.124007\pi\)
\(114\) 0.867406 22.4205i 0.00760883 0.196671i
\(115\) −2.65695 1.10055i −0.0231039 0.00956997i
\(116\) 1.45466 2.86343i 0.0125401 0.0246847i
\(117\) 230.241 95.3691i 1.96788 0.815121i
\(118\) −58.8971 + 127.960i −0.499128 + 1.08441i
\(119\) 4.13575 4.13575i 0.0347542 0.0347542i
\(120\) 124.467 + 157.302i 1.03723 + 1.31085i
\(121\) 44.6936 44.6936i 0.369369 0.369369i
\(122\) −177.534 + 65.6169i −1.45520 + 0.537844i
\(123\) −81.3537 + 33.6978i −0.661412 + 0.273966i
\(124\) −190.209 14.7397i −1.53394 0.118869i
\(125\) 122.985 + 50.9419i 0.983877 + 0.407535i
\(126\) −15.9564 17.2407i −0.126638 0.136831i
\(127\) 17.2873i 0.136120i −0.997681 0.0680601i \(-0.978319\pi\)
0.997681 0.0680601i \(-0.0216810\pi\)
\(128\) −63.0128 111.415i −0.492288 0.870432i
\(129\) −210.151 −1.62908
\(130\) 78.8923 73.0153i 0.606864 0.561656i
\(131\) −40.2223 + 97.1053i −0.307041 + 0.741262i 0.692758 + 0.721171i \(0.256396\pi\)
−0.999798 + 0.0200911i \(0.993604\pi\)
\(132\) 12.9040 166.520i 0.0977576 1.26152i
\(133\) 0.433744 + 1.04715i 0.00326123 + 0.00787331i
\(134\) −12.9072 34.9218i −0.0963223 0.260610i
\(135\) −215.719 215.719i −1.59792 1.59792i
\(136\) −66.1250 + 52.3224i −0.486213 + 0.384723i
\(137\) 25.5351 + 25.5351i 0.186387 + 0.186387i 0.794132 0.607745i \(-0.207926\pi\)
−0.607745 + 0.794132i \(0.707926\pi\)
\(138\) −6.28620 2.89340i −0.0455522 0.0209666i
\(139\) −52.2202 126.071i −0.375685 0.906984i −0.992764 0.120083i \(-0.961684\pi\)
0.617079 0.786901i \(-0.288316\pi\)
\(140\) −9.03396 4.58936i −0.0645283 0.0327812i
\(141\) −169.235 + 408.570i −1.20025 + 2.89766i
\(142\) 41.8587 + 1.61943i 0.294779 + 0.0114045i
\(143\) −89.5052 −0.625910
\(144\) 199.725 + 273.513i 1.38698 + 1.89939i
\(145\) 3.66548i 0.0252792i
\(146\) −52.7730 2.04169i −0.361459 0.0139842i
\(147\) −247.081 102.344i −1.68083 0.696221i
\(148\) 144.167 47.0343i 0.974100 0.317799i
\(149\) 151.298 62.6697i 1.01542 0.420602i 0.187993 0.982170i \(-0.439802\pi\)
0.827430 + 0.561569i \(0.189802\pi\)
\(150\) 41.5086 + 19.1055i 0.276724 + 0.127370i
\(151\) −123.292 + 123.292i −0.816505 + 0.816505i −0.985600 0.169095i \(-0.945916\pi\)
0.169095 + 0.985600i \(0.445916\pi\)
\(152\) −4.46380 15.7189i −0.0293671 0.103414i
\(153\) 157.759 157.759i 1.03111 1.03111i
\(154\) 2.92496 + 7.91381i 0.0189933 + 0.0513883i
\(155\) 201.158 83.3223i 1.29779 0.537563i
\(156\) 196.487 168.225i 1.25953 1.07836i
\(157\) 107.069 + 44.3494i 0.681968 + 0.282480i 0.696649 0.717412i \(-0.254673\pi\)
−0.0146813 + 0.999892i \(0.504673\pi\)
\(158\) 53.1939 49.2312i 0.336670 0.311590i
\(159\) 396.012i 2.49064i
\(160\) 121.707 + 80.7943i 0.760671 + 0.504964i
\(161\) 0.349573 0.00217126
\(162\) −239.827 259.131i −1.48041 1.59957i
\(163\) −48.6441 + 117.437i −0.298430 + 0.720474i 0.701539 + 0.712631i \(0.252497\pi\)
−0.999969 + 0.00784306i \(0.997503\pi\)
\(164\) −48.7141 + 41.7072i −0.297037 + 0.254312i
\(165\) 72.9453 + 176.106i 0.442093 + 1.06731i
\(166\) −55.0006 + 20.3284i −0.331329 + 0.122460i
\(167\) 88.6392 + 88.6392i 0.530774 + 0.530774i 0.920803 0.390029i \(-0.127535\pi\)
−0.390029 + 0.920803i \(0.627535\pi\)
\(168\) −21.2950 11.8754i −0.126756 0.0706868i
\(169\) 21.4841 + 21.4841i 0.127125 + 0.127125i
\(170\) 40.2370 87.4189i 0.236688 0.514229i
\(171\) 16.5452 + 39.9437i 0.0967558 + 0.233589i
\(172\) −145.499 + 47.4691i −0.845927 + 0.275983i
\(173\) 87.2836 210.721i 0.504530 1.21804i −0.442463 0.896787i \(-0.645895\pi\)
0.946993 0.321255i \(-0.104105\pi\)
\(174\) −0.340980 + 8.81356i −0.00195966 + 0.0506527i
\(175\) −2.30827 −0.0131901
\(176\) −28.6795 118.206i −0.162952 0.671625i
\(177\) 386.844i 2.18556i
\(178\) 6.17737 159.671i 0.0347043 0.897028i
\(179\) −5.53118 2.29109i −0.0309005 0.0127994i 0.367180 0.930150i \(-0.380323\pi\)
−0.398080 + 0.917351i \(0.630323\pi\)
\(180\) −344.602 175.062i −1.91446 0.972567i
\(181\) −273.836 + 113.427i −1.51291 + 0.626666i −0.976155 0.217075i \(-0.930348\pi\)
−0.536751 + 0.843741i \(0.680348\pi\)
\(182\) −5.46327 + 11.8695i −0.0300180 + 0.0652171i
\(183\) 367.542 367.542i 2.00843 2.00843i
\(184\) −5.00586 0.583331i −0.0272057 0.00317028i
\(185\) −122.379 + 122.379i −0.661506 + 0.661506i
\(186\) 491.430 181.634i 2.64210 0.976526i
\(187\) −74.0295 + 30.6640i −0.395880 + 0.163979i
\(188\) −24.8830 + 321.103i −0.132356 + 1.70800i
\(189\) 34.2600 + 14.1909i 0.181270 + 0.0750843i
\(190\) 12.6672 + 13.6867i 0.0666693 + 0.0720355i
\(191\) 140.503i 0.735620i −0.929901 0.367810i \(-0.880108\pi\)
0.929901 0.367810i \(-0.119892\pi\)
\(192\) 285.126 + 205.590i 1.48503 + 1.07078i
\(193\) −159.719 −0.827560 −0.413780 0.910377i \(-0.635792\pi\)
−0.413780 + 0.910377i \(0.635792\pi\)
\(194\) −232.767 + 215.427i −1.19983 + 1.11045i
\(195\) −112.971 + 272.735i −0.579336 + 1.39864i
\(196\) −194.186 15.0479i −0.990746 0.0767751i
\(197\) −23.3511 56.3745i −0.118533 0.286165i 0.853466 0.521149i \(-0.174496\pi\)
−0.971999 + 0.234984i \(0.924496\pi\)
\(198\) 111.573 + 301.874i 0.563501 + 1.52461i
\(199\) 138.741 + 138.741i 0.697191 + 0.697191i 0.963804 0.266613i \(-0.0859044\pi\)
−0.266613 + 0.963804i \(0.585904\pi\)
\(200\) 33.0543 + 3.85181i 0.165272 + 0.0192591i
\(201\) 72.2974 + 72.2974i 0.359689 + 0.359689i
\(202\) 255.615 + 117.654i 1.26542 + 0.582444i
\(203\) −0.170506 0.411638i −0.000839931 0.00202777i
\(204\) 104.881 206.453i 0.514122 1.01203i
\(205\) 28.0083 67.6180i 0.136626 0.329844i
\(206\) −28.1107 1.08755i −0.136460 0.00527937i
\(207\) 13.3345 0.0644180
\(208\) 98.0403 160.854i 0.471348 0.773337i
\(209\) 15.5279i 0.0742963i
\(210\) 27.8063 + 1.07577i 0.132411 + 0.00512273i
\(211\) −194.276 80.4718i −0.920740 0.381383i −0.128582 0.991699i \(-0.541043\pi\)
−0.792158 + 0.610316i \(0.791043\pi\)
\(212\) 89.4516 + 274.182i 0.421942 + 1.29331i
\(213\) −106.283 + 44.0237i −0.498979 + 0.206684i
\(214\) −326.689 150.368i −1.52658 0.702653i
\(215\) 123.510 123.510i 0.574464 0.574464i
\(216\) −466.920 260.383i −2.16167 1.20548i
\(217\) −18.7144 + 18.7144i −0.0862414 + 0.0862414i
\(218\) 6.54620 + 17.7115i 0.0300284 + 0.0812452i
\(219\) 133.995 55.5025i 0.611849 0.253436i
\(220\) 90.2831 + 105.451i 0.410378 + 0.479323i
\(221\) −114.650 47.4894i −0.518776 0.214884i
\(222\) −305.640 + 282.872i −1.37676 + 1.27420i
\(223\) 285.957i 1.28232i −0.767408 0.641160i \(-0.778454\pi\)
0.767408 0.641160i \(-0.221546\pi\)
\(224\) −17.4262 3.41187i −0.0777954 0.0152316i
\(225\) −88.0496 −0.391332
\(226\) 116.605 + 125.990i 0.515951 + 0.557480i
\(227\) 8.02885 19.3834i 0.0353694 0.0853893i −0.905208 0.424969i \(-0.860285\pi\)
0.940577 + 0.339580i \(0.110285\pi\)
\(228\) 29.1847 + 34.0878i 0.128003 + 0.149508i
\(229\) −66.9028 161.518i −0.292152 0.705317i 0.707848 0.706365i \(-0.249666\pi\)
−0.999999 + 0.00104819i \(0.999666\pi\)
\(230\) 5.39503 1.99402i 0.0234566 0.00866963i
\(231\) −16.3837 16.3837i −0.0709251 0.0709251i
\(232\) 1.75474 + 6.17915i 0.00756352 + 0.0266343i
\(233\) 282.286 + 282.286i 1.21153 + 1.21153i 0.970525 + 0.241001i \(0.0774758\pi\)
0.241001 + 0.970525i \(0.422524\pi\)
\(234\) −208.398 + 452.765i −0.890588 + 1.93489i
\(235\) −140.662 339.587i −0.598560 1.44505i
\(236\) −87.3807 267.834i −0.370257 1.13489i
\(237\) −76.1714 + 183.894i −0.321398 + 0.775925i
\(238\) −0.452223 + 11.6889i −0.00190010 + 0.0491131i
\(239\) 13.1618 0.0550704 0.0275352 0.999621i \(-0.491234\pi\)
0.0275352 + 0.999621i \(0.491234\pi\)
\(240\) −396.389 61.8053i −1.65162 0.257522i
\(241\) 231.745i 0.961599i 0.876830 + 0.480800i \(0.159654\pi\)
−0.876830 + 0.480800i \(0.840346\pi\)
\(242\) −4.88701 + 126.318i −0.0201943 + 0.521976i
\(243\) 340.169 + 140.903i 1.39987 + 0.579847i
\(244\) 171.450 337.491i 0.702663 1.38316i
\(245\) 205.364 85.0647i 0.838222 0.347203i
\(246\) 73.6354 159.980i 0.299331 0.650327i
\(247\) 17.0046 17.0046i 0.0688445 0.0688445i
\(248\) 299.217 236.760i 1.20652 0.954678i
\(249\) 113.866 113.866i 0.457293 0.457293i
\(250\) −249.724 + 92.2986i −0.998896 + 0.369194i
\(251\) 131.701 54.5521i 0.524703 0.217339i −0.104578 0.994517i \(-0.533349\pi\)
0.629281 + 0.777177i \(0.283349\pi\)
\(252\) 46.8425 + 3.62993i 0.185883 + 0.0144045i
\(253\) −4.42459 1.83272i −0.0174885 0.00724397i
\(254\) 23.4845 + 25.3748i 0.0924586 + 0.0999006i
\(255\) 264.282i 1.03640i
\(256\) 243.848 + 77.9367i 0.952531 + 0.304440i
\(257\) −70.0955 −0.272745 −0.136373 0.990658i \(-0.543544\pi\)
−0.136373 + 0.990658i \(0.543544\pi\)
\(258\) 308.466 285.487i 1.19560 1.10654i
\(259\) 8.05061 19.4359i 0.0310834 0.0750420i
\(260\) −16.6103 + 214.348i −0.0638858 + 0.824415i
\(261\) −6.50399 15.7020i −0.0249195 0.0601610i
\(262\) −72.8765 197.175i −0.278155 0.752577i
\(263\) −245.883 245.883i −0.934916 0.934916i 0.0630921 0.998008i \(-0.479904\pi\)
−0.998008 + 0.0630921i \(0.979904\pi\)
\(264\) 207.274 + 261.953i 0.785128 + 0.992245i
\(265\) −232.744 232.744i −0.878280 0.878280i
\(266\) −2.05920 0.947803i −0.00774135 0.00356317i
\(267\) 167.929 + 405.417i 0.628949 + 1.51842i
\(268\) 66.3862 + 33.7250i 0.247710 + 0.125840i
\(269\) 7.33716 17.7135i 0.0272757 0.0658493i −0.909655 0.415365i \(-0.863654\pi\)
0.936931 + 0.349516i \(0.113654\pi\)
\(270\) 609.688 + 23.5877i 2.25811 + 0.0873619i
\(271\) 327.600 1.20886 0.604429 0.796659i \(-0.293401\pi\)
0.604429 + 0.796659i \(0.293401\pi\)
\(272\) 25.9811 166.630i 0.0955187 0.612610i
\(273\) 35.8835i 0.131441i
\(274\) −72.1701 2.79213i −0.263394 0.0101902i
\(275\) 29.2161 + 12.1017i 0.106240 + 0.0440063i
\(276\) 13.1577 4.29269i 0.0476728 0.0155532i
\(277\) −31.9345 + 13.2277i −0.115287 + 0.0477535i −0.439581 0.898203i \(-0.644873\pi\)
0.324294 + 0.945956i \(0.394873\pi\)
\(278\) 247.916 + 114.110i 0.891783 + 0.410468i
\(279\) −713.864 + 713.864i −2.55865 + 2.55865i
\(280\) 19.4949 5.53609i 0.0696246 0.0197718i
\(281\) −263.413 + 263.413i −0.937413 + 0.937413i −0.998154 0.0607409i \(-0.980654\pi\)
0.0607409 + 0.998154i \(0.480654\pi\)
\(282\) −306.627 829.614i −1.08733 2.94189i
\(283\) −268.113 + 111.056i −0.947397 + 0.392425i −0.802252 0.596986i \(-0.796365\pi\)
−0.145145 + 0.989410i \(0.546365\pi\)
\(284\) −63.6413 + 54.4873i −0.224089 + 0.191857i
\(285\) −47.3158 19.5989i −0.166020 0.0687679i
\(286\) 131.378 121.591i 0.459365 0.425145i
\(287\) 8.89644i 0.0309980i
\(288\) −664.724 130.146i −2.30807 0.451897i
\(289\) 177.904 0.615585
\(290\) −4.97950 5.38030i −0.0171707 0.0185528i
\(291\) 333.313 804.689i 1.14541 2.76526i
\(292\) 80.2353 68.6944i 0.274778 0.235255i
\(293\) 44.7772 + 108.102i 0.152823 + 0.368948i 0.981687 0.190503i \(-0.0610120\pi\)
−0.828863 + 0.559451i \(0.811012\pi\)
\(294\) 501.706 185.432i 1.70648 0.630721i
\(295\) 227.356 + 227.356i 0.770698 + 0.770698i
\(296\) −147.717 + 264.887i −0.499043 + 0.894887i
\(297\) −359.233 359.233i −1.20954 1.20954i
\(298\) −136.944 + 297.524i −0.459543 + 0.998404i
\(299\) −2.83834 6.85237i −0.00949279 0.0229176i
\(300\) −86.8820 + 28.3452i −0.289607 + 0.0944840i
\(301\) −8.12503 + 19.6155i −0.0269934 + 0.0651679i
\(302\) 13.4814 348.462i 0.0446403 1.15385i
\(303\) −772.765 −2.55038
\(304\) 27.9060 + 17.0087i 0.0917960 + 0.0559495i
\(305\) 432.024i 1.41647i
\(306\) −17.2501 + 445.876i −0.0563730 + 1.45711i
\(307\) 430.497 + 178.318i 1.40227 + 0.580839i 0.950340 0.311215i \(-0.100736\pi\)
0.451930 + 0.892054i \(0.350736\pi\)
\(308\) −15.0441 7.64260i −0.0488446 0.0248136i
\(309\) 71.3754 29.5646i 0.230988 0.0956784i
\(310\) −182.073 + 395.573i −0.587333 + 1.27604i
\(311\) −61.3250 + 61.3250i −0.197187 + 0.197187i −0.798793 0.601606i \(-0.794528\pi\)
0.601606 + 0.798793i \(0.294528\pi\)
\(312\) −59.8787 + 513.849i −0.191919 + 1.64695i
\(313\) 129.308 129.308i 0.413124 0.413124i −0.469701 0.882826i \(-0.655638\pi\)
0.882826 + 0.469701i \(0.155638\pi\)
\(314\) −217.407 + 80.3541i −0.692379 + 0.255905i
\(315\) −49.5390 + 20.5197i −0.157267 + 0.0651420i
\(316\) −11.1996 + 144.526i −0.0354419 + 0.457361i
\(317\) −286.711 118.760i −0.904452 0.374636i −0.118522 0.992951i \(-0.537816\pi\)
−0.785930 + 0.618315i \(0.787816\pi\)
\(318\) −537.976 581.278i −1.69175 1.82792i
\(319\) 6.10408i 0.0191350i
\(320\) −288.403 + 46.7454i −0.901261 + 0.146079i
\(321\) 987.635 3.07674
\(322\) −0.513113 + 0.474889i −0.00159352 + 0.00147481i
\(323\) 8.23877 19.8901i 0.0255070 0.0615794i
\(324\) 704.050 + 54.5584i 2.17299 + 0.168390i
\(325\) 18.7420 + 45.2471i 0.0576676 + 0.139222i
\(326\) −88.1354 238.460i −0.270354 0.731472i
\(327\) −36.6674 36.6674i −0.112133 0.112133i
\(328\) 14.8455 127.396i 0.0452606 0.388403i
\(329\) 31.5929 + 31.5929i 0.0960271 + 0.0960271i
\(330\) −346.308 159.398i −1.04942 0.483024i
\(331\) 123.164 + 297.345i 0.372098 + 0.898324i 0.993395 + 0.114748i \(0.0366061\pi\)
−0.621297 + 0.783575i \(0.713394\pi\)
\(332\) 53.1158 104.556i 0.159987 0.314928i
\(333\) 307.092 741.386i 0.922198 2.22638i
\(334\) −250.522 9.69223i −0.750066 0.0290187i
\(335\) −84.9812 −0.253675
\(336\) 47.3899 11.4979i 0.141041 0.0342199i
\(337\) 263.653i 0.782354i 0.920315 + 0.391177i \(0.127932\pi\)
−0.920315 + 0.391177i \(0.872068\pi\)
\(338\) −60.7209 2.34918i −0.179648 0.00695023i
\(339\) −435.556 180.413i −1.28483 0.532192i
\(340\) 59.6962 + 182.977i 0.175577 + 0.538168i
\(341\) 334.985 138.755i 0.982362 0.406908i
\(342\) −78.5485 36.1541i −0.229674 0.105714i
\(343\) −38.3323 + 38.3323i −0.111756 + 0.111756i
\(344\) 149.082 267.335i 0.433379 0.777137i
\(345\) −11.1691 + 11.1691i −0.0323743 + 0.0323743i
\(346\) 158.144 + 427.876i 0.457064 + 1.23664i
\(347\) −388.417 + 160.888i −1.11936 + 0.463653i −0.864151 0.503233i \(-0.832144\pi\)
−0.255208 + 0.966886i \(0.582144\pi\)
\(348\) −11.4726 13.4000i −0.0329672 0.0385058i
\(349\) 448.277 + 185.683i 1.28446 + 0.532042i 0.917330 0.398127i \(-0.130340\pi\)
0.367132 + 0.930169i \(0.380340\pi\)
\(350\) 3.38815 3.13575i 0.00968044 0.00895930i
\(351\) 786.791i 2.24157i
\(352\) 202.678 + 134.546i 0.575789 + 0.382232i
\(353\) −106.951 −0.302976 −0.151488 0.988459i \(-0.548407\pi\)
−0.151488 + 0.988459i \(0.548407\pi\)
\(354\) 525.522 + 567.821i 1.48452 + 1.60401i
\(355\) 36.5908 88.3379i 0.103073 0.248839i
\(356\) 207.843 + 242.761i 0.583829 + 0.681914i
\(357\) −12.2935 29.6791i −0.0344356 0.0831348i
\(358\) 11.2312 4.15109i 0.0313722 0.0115952i
\(359\) −208.761 208.761i −0.581508 0.581508i 0.353810 0.935317i \(-0.384886\pi\)
−0.935317 + 0.353810i \(0.884886\pi\)
\(360\) 743.636 211.175i 2.06566 0.586598i
\(361\) −252.315 252.315i −0.698935 0.698935i
\(362\) 247.856 538.492i 0.684685 1.48755i
\(363\) −132.852 320.732i −0.365982 0.883559i
\(364\) −8.10539 24.8442i −0.0222676 0.0682532i
\(365\) −46.1315 + 111.371i −0.126388 + 0.305127i
\(366\) −40.1888 + 1038.79i −0.109806 + 2.83822i
\(367\) 711.002 1.93734 0.968668 0.248361i \(-0.0798919\pi\)
0.968668 + 0.248361i \(0.0798919\pi\)
\(368\) 8.14019 5.94415i 0.0221201 0.0161526i
\(369\) 339.356i 0.919665i
\(370\) 13.3815 345.880i 0.0361661 0.934811i
\(371\) 36.9639 + 15.3110i 0.0996332 + 0.0412694i
\(372\) −474.589 + 934.207i −1.27578 + 2.51131i
\(373\) −587.430 + 243.321i −1.57488 + 0.652336i −0.987592 0.157043i \(-0.949804\pi\)
−0.587287 + 0.809379i \(0.699804\pi\)
\(374\) 67.0060 145.577i 0.179160 0.389244i
\(375\) 516.995 516.995i 1.37865 1.37865i
\(376\) −399.689 505.128i −1.06300 1.34342i
\(377\) −6.68456 + 6.68456i −0.0177309 + 0.0177309i
\(378\) −69.5659 + 25.7117i −0.184037 + 0.0680205i
\(379\) −34.5203 + 14.2988i −0.0910825 + 0.0377276i −0.427759 0.903893i \(-0.640697\pi\)
0.336677 + 0.941620i \(0.390697\pi\)
\(380\) −37.1864 2.88166i −0.0978591 0.00758332i
\(381\) −87.7220 36.3356i −0.230241 0.0953691i
\(382\) 190.872 + 206.235i 0.499664 + 0.539882i
\(383\) 347.623i 0.907631i 0.891096 + 0.453815i \(0.149937\pi\)
−0.891096 + 0.453815i \(0.850063\pi\)
\(384\) −697.807 + 85.5695i −1.81721 + 0.222837i
\(385\) 19.2580 0.0500209
\(386\) 234.440 216.976i 0.607359 0.562114i
\(387\) −309.931 + 748.239i −0.800855 + 1.93343i
\(388\) 49.0077 632.421i 0.126309 1.62995i
\(389\) −60.7529 146.670i −0.156177 0.377045i 0.826352 0.563154i \(-0.190412\pi\)
−0.982529 + 0.186109i \(0.940412\pi\)
\(390\) −204.685 553.797i −0.524833 1.41999i
\(391\) −4.69517 4.69517i −0.0120081 0.0120081i
\(392\) 305.474 241.711i 0.779271 0.616610i
\(393\) 408.205 + 408.205i 1.03869 + 1.03869i
\(394\) 110.859 + 51.0260i 0.281368 + 0.129508i
\(395\) −63.3107 152.846i −0.160280 0.386951i
\(396\) −573.861 291.528i −1.44914 0.736183i
\(397\) 179.460 433.255i 0.452041 1.09132i −0.519505 0.854468i \(-0.673883\pi\)
0.971545 0.236855i \(-0.0761165\pi\)
\(398\) −392.126 15.1706i −0.985240 0.0381171i
\(399\) 6.22529 0.0156022
\(400\) −53.7507 + 39.2500i −0.134377 + 0.0981250i
\(401\) 680.550i 1.69713i −0.529089 0.848566i \(-0.677466\pi\)
0.529089 0.848566i \(-0.322534\pi\)
\(402\) −204.335 7.90535i −0.508297 0.0196650i
\(403\) 518.792 + 214.891i 1.28733 + 0.533228i
\(404\) −535.029 + 174.553i −1.32433 + 0.432062i
\(405\) −744.578 + 308.414i −1.83847 + 0.761517i
\(406\) 0.809477 + 0.372584i 0.00199379 + 0.000917696i
\(407\) −203.795 + 203.795i −0.500725 + 0.500725i
\(408\) 126.517 + 445.517i 0.310090 + 1.09195i
\(409\) 239.915 239.915i 0.586589 0.586589i −0.350117 0.936706i \(-0.613858\pi\)
0.936706 + 0.350117i \(0.113858\pi\)
\(410\) 50.7466 + 137.301i 0.123772 + 0.334879i
\(411\) 183.246 75.9028i 0.445853 0.184678i
\(412\) 42.7391 36.5916i 0.103736 0.0888146i
\(413\) −36.1082 14.9565i −0.0874289 0.0362143i
\(414\) −19.5728 + 18.1147i −0.0472773 + 0.0437554i
\(415\) 133.843i 0.322512i
\(416\) 74.6112 + 369.292i 0.179354 + 0.887722i
\(417\) −749.489 −1.79734
\(418\) 21.0944 + 22.7923i 0.0504652 + 0.0545271i
\(419\) 33.5102 80.9009i 0.0799767 0.193081i −0.878833 0.477129i \(-0.841678\pi\)
0.958810 + 0.284048i \(0.0916775\pi\)
\(420\) −42.2763 + 36.1954i −0.100658 + 0.0861794i
\(421\) 37.2975 + 90.0441i 0.0885926 + 0.213882i 0.961966 0.273170i \(-0.0880723\pi\)
−0.873373 + 0.487052i \(0.838072\pi\)
\(422\) 394.484 145.802i 0.934796 0.345503i
\(423\) 1205.12 + 1205.12i 2.84898 + 2.84898i
\(424\) −503.771 280.933i −1.18814 0.662579i
\(425\) 31.0028 + 31.0028i 0.0729479 + 0.0729479i
\(426\) 96.1991 209.002i 0.225820 0.490616i
\(427\) −20.0963 48.5167i −0.0470639 0.113622i
\(428\) 683.796 223.088i 1.59765 0.521233i
\(429\) −188.128 + 454.182i −0.438527 + 1.05870i
\(430\) −13.5051 + 349.077i −0.0314073 + 0.811808i
\(431\) −509.094 −1.18119 −0.590596 0.806967i \(-0.701107\pi\)
−0.590596 + 0.806967i \(0.701107\pi\)
\(432\) 1039.08 252.106i 2.40529 0.583578i
\(433\) 66.0083i 0.152444i 0.997091 + 0.0762220i \(0.0242858\pi\)
−0.997091 + 0.0762220i \(0.975714\pi\)
\(434\) 2.04632 52.8927i 0.00471502 0.121873i
\(435\) 18.6000 + 7.70438i 0.0427586 + 0.0177112i
\(436\) −33.6694 17.1045i −0.0772235 0.0392305i
\(437\) 1.18879 0.492414i 0.00272035 0.00112681i
\(438\) −121.282 + 263.498i −0.276900 + 0.601593i
\(439\) −39.8501 + 39.8501i −0.0907747 + 0.0907747i −0.751036 0.660261i \(-0.770446\pi\)
0.660261 + 0.751036i \(0.270446\pi\)
\(440\) −275.774 32.1358i −0.626758 0.0730360i
\(441\) −728.792 + 728.792i −1.65259 + 1.65259i
\(442\) 232.800 86.0433i 0.526696 0.194668i
\(443\) −193.778 + 80.2656i −0.437423 + 0.181187i −0.590517 0.807025i \(-0.701076\pi\)
0.153094 + 0.988212i \(0.451076\pi\)
\(444\) 64.3507 830.415i 0.144934 1.87030i
\(445\) −336.967 139.576i −0.757229 0.313655i
\(446\) 388.468 + 419.736i 0.871005 + 0.941113i
\(447\) 899.465i 2.01223i
\(448\) 30.2136 18.6651i 0.0674410 0.0416632i
\(449\) 124.217 0.276652 0.138326 0.990387i \(-0.455828\pi\)
0.138326 + 0.990387i \(0.455828\pi\)
\(450\) 129.242 119.614i 0.287204 0.265809i
\(451\) 46.6418 112.603i 0.103419 0.249675i
\(452\) −342.312 26.5265i −0.757327 0.0586870i
\(453\) 366.485 + 884.774i 0.809019 + 1.95314i
\(454\) 14.5470 + 39.3585i 0.0320419 + 0.0866928i
\(455\) 21.0894 + 21.0894i 0.0463504 + 0.0463504i
\(456\) −89.1458 10.3881i −0.195495 0.0227810i
\(457\) −573.100 573.100i −1.25405 1.25405i −0.953889 0.300159i \(-0.902960\pi\)
−0.300159 0.953889i \(-0.597040\pi\)
\(458\) 317.621 + 146.194i 0.693495 + 0.319200i
\(459\) −269.550 650.752i −0.587256 1.41776i
\(460\) −5.21014 + 10.2559i −0.0113264 + 0.0222955i
\(461\) −86.0707 + 207.793i −0.186704 + 0.450744i −0.989321 0.145750i \(-0.953440\pi\)
0.802617 + 0.596495i \(0.203440\pi\)
\(462\) 46.3054 + 1.79147i 0.100228 + 0.00387764i
\(463\) −555.587 −1.19997 −0.599986 0.800010i \(-0.704827\pi\)
−0.599986 + 0.800010i \(0.704827\pi\)
\(464\) −10.9699 6.68616i −0.0236421 0.0144098i
\(465\) 1195.88i 2.57179i
\(466\) −797.827 30.8664i −1.71208 0.0662370i
\(467\) −319.806 132.468i −0.684809 0.283657i 0.0130269 0.999915i \(-0.495853\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(468\) −309.182 947.686i −0.660645 2.02497i
\(469\) 9.54349 3.95304i 0.0203486 0.00842866i
\(470\) 667.791 + 307.369i 1.42083 + 0.653977i
\(471\) 450.090 450.090i 0.955606 0.955606i
\(472\) 492.108 + 274.429i 1.04260 + 0.581418i
\(473\) 205.679 205.679i 0.434839 0.434839i
\(474\) −138.011 373.403i −0.291162 0.787769i
\(475\) −7.84975 + 3.25147i −0.0165258 + 0.00684521i
\(476\) −15.2154 17.7717i −0.0319652 0.0373355i
\(477\) 1410.00 + 584.039i 2.95597 + 1.22440i
\(478\) −19.3193 + 17.8801i −0.0404170 + 0.0374061i
\(479\) 239.576i 0.500159i 0.968225 + 0.250079i \(0.0804567\pi\)
−0.968225 + 0.250079i \(0.919543\pi\)
\(480\) 665.793 447.769i 1.38707 0.932852i
\(481\) −446.351 −0.927965
\(482\) −314.822 340.163i −0.653159 0.705732i
\(483\) 0.734757 1.77386i 0.00152124 0.00367259i
\(484\) −164.428 192.052i −0.339727 0.396802i
\(485\) 277.037 + 668.826i 0.571210 + 1.37902i
\(486\) −690.725 + 255.294i −1.42124 + 0.525295i
\(487\) −269.525 269.525i −0.553439 0.553439i 0.373992 0.927432i \(-0.377989\pi\)
−0.927432 + 0.373992i \(0.877989\pi\)
\(488\) 206.818 + 728.291i 0.423807 + 1.49240i
\(489\) 493.676 + 493.676i 1.00956 + 1.00956i
\(490\) −185.881 + 403.845i −0.379348 + 0.824173i
\(491\) 285.394 + 689.002i 0.581250 + 1.40326i 0.891680 + 0.452666i \(0.149527\pi\)
−0.310430 + 0.950596i \(0.600473\pi\)
\(492\) 109.247 + 334.856i 0.222046 + 0.680602i
\(493\) −3.23869 + 7.81888i −0.00656934 + 0.0158598i
\(494\) −1.85936 + 48.0603i −0.00376389 + 0.0972881i
\(495\) 734.601 1.48404
\(496\) −117.565 + 754.005i −0.237026 + 1.52017i
\(497\) 11.6225i 0.0233854i
\(498\) −12.4507 + 321.821i −0.0250013 + 0.646227i
\(499\) 581.267 + 240.769i 1.16486 + 0.482503i 0.879492 0.475914i \(-0.157883\pi\)
0.285373 + 0.958417i \(0.407883\pi\)
\(500\) 241.166 474.725i 0.482332 0.949449i
\(501\) 636.096 263.479i 1.26965 0.525907i
\(502\) −119.206 + 258.986i −0.237461 + 0.515909i
\(503\) 204.189 204.189i 0.405942 0.405942i −0.474379 0.880321i \(-0.657327\pi\)
0.880321 + 0.474379i \(0.157327\pi\)
\(504\) −73.6880 + 58.3067i −0.146206 + 0.115688i
\(505\) 454.169 454.169i 0.899345 0.899345i
\(506\) 8.98426 3.32061i 0.0177555 0.00656246i
\(507\) 154.175 63.8615i 0.304093 0.125960i
\(508\) −68.9424 5.34250i −0.135713 0.0105167i
\(509\) −397.562 164.676i −0.781066 0.323528i −0.0437202 0.999044i \(-0.513921\pi\)
−0.737345 + 0.675516i \(0.763921\pi\)
\(510\) −359.022 387.920i −0.703965 0.760628i
\(511\) 14.6530i 0.0286751i
\(512\) −463.803 + 216.866i −0.905865 + 0.423566i
\(513\) 136.497 0.266077
\(514\) 102.888 95.2236i 0.200172 0.185260i
\(515\) −24.5730 + 59.3244i −0.0477145 + 0.115193i
\(516\) −64.9456 + 838.091i −0.125863 + 1.62421i
\(517\) −234.242 565.510i −0.453079 1.09383i
\(518\) 14.5864 + 39.4652i 0.0281591 + 0.0761876i
\(519\) −885.818 885.818i −1.70678 1.70678i
\(520\) −266.807 337.191i −0.513091 0.648444i
\(521\) −333.835 333.835i −0.640759 0.640759i 0.309983 0.950742i \(-0.399676\pi\)
−0.950742 + 0.309983i \(0.899676\pi\)
\(522\) 30.8777 + 14.2123i 0.0591526 + 0.0272266i
\(523\) −211.672 511.022i −0.404727 0.977097i −0.986502 0.163748i \(-0.947642\pi\)
0.581775 0.813350i \(-0.302358\pi\)
\(524\) 374.830 + 190.418i 0.715324 + 0.363393i
\(525\) −4.85170 + 11.7130i −0.00924132 + 0.0223105i
\(526\) 694.942 + 26.8860i 1.32118 + 0.0511141i
\(527\) 502.712 0.953913
\(528\) −660.101 102.924i −1.25019 0.194931i
\(529\) 528.603i 0.999250i
\(530\) 657.808 + 25.4494i 1.24115 + 0.0480177i
\(531\) −1377.35 570.518i −2.59388 1.07442i
\(532\) 4.31013 1.40618i 0.00810174 0.00264319i
\(533\) 174.389 72.2343i 0.327184 0.135524i
\(534\) −797.245 366.954i −1.49297 0.687180i
\(535\) −580.452 + 580.452i −1.08496 + 1.08496i
\(536\) −143.259 + 40.6821i −0.267273 + 0.0758994i
\(537\) −23.2517 + 23.2517i −0.0432992 + 0.0432992i
\(538\) 13.2938 + 35.9677i 0.0247096 + 0.0668545i
\(539\) 341.990 141.657i 0.634490 0.262815i
\(540\) −926.962 + 793.629i −1.71660 + 1.46968i
\(541\) −529.582 219.360i −0.978896 0.405472i −0.164879 0.986314i \(-0.552723\pi\)
−0.814016 + 0.580842i \(0.802723\pi\)
\(542\) −480.861 + 445.040i −0.887198 + 0.821107i
\(543\) 1627.95i 2.99807i
\(544\) 188.228 + 279.879i 0.346008 + 0.514484i
\(545\) 43.1003 0.0790832
\(546\) 48.7471 + 52.6708i 0.0892805 + 0.0964667i
\(547\) −68.4960 + 165.364i −0.125221 + 0.302311i −0.974041 0.226371i \(-0.927314\pi\)
0.848820 + 0.528682i \(0.177314\pi\)
\(548\) 109.726 93.9435i 0.200231 0.171430i
\(549\) −766.577 1850.68i −1.39632 3.37100i
\(550\) −59.3243 + 21.9264i −0.107862 + 0.0398662i
\(551\) −1.15968 1.15968i −0.00210468 0.00210468i
\(552\) −13.4817 + 24.1755i −0.0244234 + 0.0437961i
\(553\) 14.2197 + 14.2197i 0.0257138 + 0.0257138i
\(554\) 28.9048 62.7986i 0.0521747 0.113355i
\(555\) 363.770 + 878.217i 0.655441 + 1.58237i
\(556\) −518.914 + 169.295i −0.933299 + 0.304488i
\(557\) −308.610 + 745.049i −0.554057 + 1.33761i 0.360351 + 0.932817i \(0.382657\pi\)
−0.914408 + 0.404794i \(0.867343\pi\)
\(558\) 78.0573 2017.60i 0.139888 3.61578i
\(559\) 450.477 0.805863
\(560\) −21.0945 + 34.6095i −0.0376687 + 0.0618027i
\(561\) 440.104i 0.784500i
\(562\) 28.8028 744.487i 0.0512506 1.32471i
\(563\) −347.195 143.813i −0.616687 0.255440i 0.0523978 0.998626i \(-0.483314\pi\)
−0.669085 + 0.743186i \(0.733314\pi\)
\(564\) 1577.09 + 801.183i 2.79626 + 1.42054i
\(565\) 362.017 149.952i 0.640738 0.265402i
\(566\) 242.676 527.239i 0.428757 0.931518i
\(567\) 69.2706 69.2706i 0.122170 0.122170i
\(568\) 19.3945 166.434i 0.0341452 0.293017i
\(569\) 717.322 717.322i 1.26067 1.26067i 0.309903 0.950768i \(-0.399703\pi\)
0.950768 0.309903i \(-0.100297\pi\)
\(570\) 96.0763 35.5100i 0.168555 0.0622983i
\(571\) −327.041 + 135.465i −0.572751 + 0.237241i −0.650210 0.759754i \(-0.725319\pi\)
0.0774591 + 0.996996i \(0.475319\pi\)
\(572\) −27.6609 + 356.951i −0.0483582 + 0.624039i
\(573\) −712.966 295.320i −1.24427 0.515393i
\(574\) −12.0857 13.0584i −0.0210552 0.0227499i
\(575\) 2.62050i 0.00455740i
\(576\) 1152.50 711.985i 2.00087 1.23608i
\(577\) 531.710 0.921507 0.460754 0.887528i \(-0.347579\pi\)
0.460754 + 0.887528i \(0.347579\pi\)
\(578\) −261.133 + 241.680i −0.451787 + 0.418131i
\(579\) −335.709 + 810.473i −0.579808 + 1.39978i
\(580\) 14.6181 + 1.13279i 0.0252036 + 0.00195309i
\(581\) −6.22591 15.0307i −0.0107158 0.0258703i
\(582\) 603.911 + 1633.95i 1.03765 + 2.80747i
\(583\) −387.585 387.585i −0.664812 0.664812i
\(584\) −24.4514 + 209.830i −0.0418689 + 0.359298i
\(585\) 804.460 + 804.460i 1.37515 + 1.37515i
\(586\) −212.580 97.8456i −0.362764 0.166972i
\(587\) 105.581 + 254.894i 0.179865 + 0.434232i 0.987938 0.154850i \(-0.0494895\pi\)
−0.808073 + 0.589082i \(0.799490\pi\)
\(588\) −484.513 + 953.743i −0.824001 + 1.62201i
\(589\) −37.2806 + 90.0034i −0.0632948 + 0.152807i
\(590\) −642.579 24.8602i −1.08912 0.0421359i
\(591\) −335.145 −0.567082
\(592\) −143.021 589.479i −0.241590 0.995742i
\(593\) 405.861i 0.684419i 0.939624 + 0.342210i \(0.111175\pi\)
−0.939624 + 0.342210i \(0.888825\pi\)
\(594\) 1015.31 + 39.2803i 1.70927 + 0.0661284i
\(595\) 24.6681 + 10.2179i 0.0414590 + 0.0171729i
\(596\) −203.172 622.751i −0.340892 1.04488i
\(597\) 995.638 412.407i 1.66774 0.690799i
\(598\) 13.4750 + 6.20226i 0.0225335 + 0.0103717i
\(599\) 561.484 561.484i 0.937370 0.937370i −0.0607815 0.998151i \(-0.519359\pi\)
0.998151 + 0.0607815i \(0.0193593\pi\)
\(600\) 89.0215 159.634i 0.148369 0.266056i
\(601\) −358.762 + 358.762i −0.596941 + 0.596941i −0.939497 0.342556i \(-0.888707\pi\)
0.342556 + 0.939497i \(0.388707\pi\)
\(602\) −14.7213 39.8300i −0.0244539 0.0661628i
\(603\) 364.038 150.790i 0.603712 0.250066i
\(604\) 453.592 + 529.797i 0.750981 + 0.877148i
\(605\) 266.580 + 110.421i 0.440628 + 0.182514i
\(606\) 1134.29 1049.79i 1.87176 1.73233i
\(607\) 571.923i 0.942213i −0.882076 0.471107i \(-0.843855\pi\)
0.882076 0.471107i \(-0.156145\pi\)
\(608\) −64.0672 + 12.9440i −0.105374 + 0.0212895i
\(609\) −2.44718 −0.00401836
\(610\) −586.897 634.137i −0.962126 1.03957i
\(611\) 362.771 875.806i 0.593733 1.43340i
\(612\) −580.396 677.904i −0.948359 1.10769i
\(613\) 401.254 + 968.712i 0.654574 + 1.58028i 0.806068 + 0.591823i \(0.201591\pi\)
−0.151494 + 0.988458i \(0.548409\pi\)
\(614\) −874.137 + 323.083i −1.42368 + 0.526194i
\(615\) −284.249 284.249i −0.462193 0.462193i
\(616\) 32.4645 9.21918i 0.0527022 0.0149662i
\(617\) −151.870 151.870i −0.246143 0.246143i 0.573242 0.819386i \(-0.305685\pi\)
−0.819386 + 0.573242i \(0.805685\pi\)
\(618\) −64.6037 + 140.358i −0.104537 + 0.227117i
\(619\) 146.518 + 353.725i 0.236701 + 0.571446i 0.996938 0.0781999i \(-0.0249173\pi\)
−0.760237 + 0.649646i \(0.774917\pi\)
\(620\) −270.127 827.977i −0.435688 1.33545i
\(621\) 16.1105 38.8941i 0.0259428 0.0626314i
\(622\) 6.70557 173.324i 0.0107807 0.278656i
\(623\) 44.3344 0.0711628
\(624\) −610.164 835.587i −0.977827 1.33908i
\(625\) 503.703i 0.805924i
\(626\) −14.1391 + 365.465i −0.0225865 + 0.583809i
\(627\) −78.7944 32.6377i −0.125669 0.0520537i
\(628\) 209.956 413.290i 0.334325 0.658105i
\(629\) −369.176 + 152.918i −0.586925 + 0.243112i
\(630\) 44.8390 97.4174i 0.0711731 0.154631i
\(631\) −682.535 + 682.535i −1.08167 + 1.08167i −0.0853189 + 0.996354i \(0.527191\pi\)
−0.996354 + 0.0853189i \(0.972809\pi\)
\(632\) −179.897 227.354i −0.284647 0.359737i
\(633\) −816.687 + 816.687i −1.29018 + 1.29018i
\(634\) 582.176 215.174i 0.918259 0.339391i
\(635\) 72.9111 30.2007i 0.114821 0.0475602i
\(636\) 1579.31 + 122.385i 2.48320 + 0.192429i
\(637\) 529.641 + 219.385i 0.831462 + 0.344403i
\(638\) −8.29229 8.95974i −0.0129973 0.0140435i
\(639\) 443.344i 0.693808i
\(640\) 359.824 460.406i 0.562225 0.719384i
\(641\) 38.9310 0.0607348 0.0303674 0.999539i \(-0.490332\pi\)
0.0303674 + 0.999539i \(0.490332\pi\)
\(642\) −1449.68 + 1341.69i −2.25807 + 2.08985i
\(643\) 318.631 769.243i 0.495538 1.19633i −0.456326 0.889813i \(-0.650835\pi\)
0.951864 0.306522i \(-0.0991652\pi\)
\(644\) 0.108033 1.39411i 0.000167753 0.00216477i
\(645\) −367.132 886.335i −0.569197 1.37416i
\(646\) 14.9273 + 40.3876i 0.0231073 + 0.0625194i
\(647\) −157.445 157.445i −0.243346 0.243346i 0.574887 0.818233i \(-0.305046\pi\)
−0.818233 + 0.574887i \(0.805046\pi\)
\(648\) −1107.54 + 876.358i −1.70917 + 1.35240i
\(649\) 378.612 + 378.612i 0.583378 + 0.583378i
\(650\) −88.9774 40.9543i −0.136888 0.0630067i
\(651\) 55.6284 + 134.299i 0.0854507 + 0.206296i
\(652\) 453.312 + 230.288i 0.695264 + 0.353202i
\(653\) −15.6861 + 37.8696i −0.0240216 + 0.0579933i −0.935435 0.353498i \(-0.884992\pi\)
0.911414 + 0.411492i \(0.134992\pi\)
\(654\) 103.634 + 4.00939i 0.158461 + 0.00613057i
\(655\) −479.821 −0.732551
\(656\) 151.275 + 207.163i 0.230603 + 0.315798i
\(657\) 558.942i 0.850748i
\(658\) −89.2915 3.45452i −0.135701 0.00525003i
\(659\) 187.169 + 77.5281i 0.284020 + 0.117645i 0.520146 0.854078i \(-0.325878\pi\)
−0.236125 + 0.971723i \(0.575878\pi\)
\(660\) 724.860 236.485i 1.09827 0.358311i
\(661\) 30.1818 12.5017i 0.0456608 0.0189133i −0.359736 0.933054i \(-0.617133\pi\)
0.405397 + 0.914141i \(0.367133\pi\)
\(662\) −584.723 269.135i −0.883267 0.406548i
\(663\) −481.957 + 481.957i −0.726934 + 0.726934i
\(664\) 64.0729 + 225.627i 0.0964954 + 0.339800i
\(665\) −3.65873 + 3.65873i −0.00550184 + 0.00550184i
\(666\) 556.402 + 1505.41i 0.835439 + 2.26037i
\(667\) −0.467318 + 0.193569i −0.000700627 + 0.000290209i
\(668\) 380.890 326.104i 0.570195 0.488179i
\(669\) −1451.05 601.045i −2.16899 0.898423i
\(670\) 124.738 115.446i 0.186176 0.172307i
\(671\) 719.443i 1.07219i
\(672\) −53.9406 + 81.2554i −0.0802688 + 0.120916i
\(673\) −327.878 −0.487189 −0.243595 0.969877i \(-0.578327\pi\)
−0.243595 + 0.969877i \(0.578327\pi\)
\(674\) −358.169 386.998i −0.531408 0.574181i
\(675\) −106.380 + 256.823i −0.157599 + 0.380479i
\(676\) 92.3192 79.0402i 0.136567 0.116923i
\(677\) 117.661 + 284.058i 0.173797 + 0.419583i 0.986643 0.162895i \(-0.0520832\pi\)
−0.812846 + 0.582478i \(0.802083\pi\)
\(678\) 884.410 326.880i 1.30444 0.482124i
\(679\) −62.2231 62.2231i −0.0916393 0.0916393i
\(680\) −336.195 187.483i −0.494405 0.275710i
\(681\) −81.4826 81.4826i −0.119651 0.119651i
\(682\) −303.204 + 658.741i −0.444581 + 0.965897i
\(683\) −324.811 784.162i −0.475564 1.14811i −0.961669 0.274213i \(-0.911583\pi\)
0.486104 0.873901i \(-0.338417\pi\)
\(684\) 164.411 53.6388i 0.240366 0.0784193i
\(685\) −63.0875 + 152.307i −0.0920985 + 0.222345i
\(686\) 4.19143 108.339i 0.00610996 0.157929i
\(687\) −960.220 −1.39770
\(688\) 144.343 + 594.928i 0.209801 + 0.864721i
\(689\) 848.888i 1.23206i
\(690\) 1.22129 31.5675i 0.00176998 0.0457500i
\(691\) 826.286 + 342.259i 1.19578 + 0.495309i 0.889634 0.456674i \(-0.150959\pi\)
0.306149 + 0.951984i \(0.400959\pi\)
\(692\) −813.391 413.213i −1.17542 0.597128i
\(693\) −82.4966 + 34.1712i −0.119043 + 0.0493091i
\(694\) 351.567 763.815i 0.506580 1.10060i
\(695\) 440.490 440.490i 0.633798 0.633798i
\(696\) 35.0435 + 4.08361i 0.0503499 + 0.00586726i
\(697\) 119.490 119.490i 0.171434 0.171434i
\(698\) −910.241 + 336.427i −1.30407 + 0.481988i
\(699\) 2025.75 839.092i 2.89807 1.20042i
\(700\) −0.713355 + 9.20550i −0.00101908 + 0.0131507i
\(701\) 430.597 + 178.359i 0.614260 + 0.254435i 0.668049 0.744117i \(-0.267130\pi\)
−0.0537885 + 0.998552i \(0.517130\pi\)
\(702\) 1068.84 + 1154.87i 1.52257 + 1.64512i
\(703\) 77.4359i 0.110151i
\(704\) −480.274 + 77.8444i −0.682207 + 0.110574i
\(705\) −2018.84 −2.86361
\(706\) 156.985 145.291i 0.222359 0.205794i
\(707\) −29.8773 + 72.1301i −0.0422592 + 0.102023i
\(708\) −1542.75 119.551i −2.17903 0.168858i
\(709\) −77.1066 186.152i −0.108754 0.262555i 0.860128 0.510078i \(-0.170384\pi\)
−0.968882 + 0.247523i \(0.920384\pi\)
\(710\) 66.2967 + 179.373i 0.0933756 + 0.252638i
\(711\) 542.414 + 542.414i 0.762889 + 0.762889i
\(712\) −634.866 73.9807i −0.891665 0.103906i
\(713\) 21.2458 + 21.2458i 0.0297977 + 0.0297977i
\(714\) 58.3634 + 26.8634i 0.0817414 + 0.0376238i
\(715\) −156.365 377.498i −0.218692 0.527970i
\(716\) −10.8463 + 21.3506i −0.0151485 + 0.0298192i
\(717\) 27.6645 66.7879i 0.0385836 0.0931491i
\(718\) 590.025 + 22.8270i 0.821762 + 0.0317924i
\(719\) 809.898 1.12642 0.563212 0.826313i \(-0.309566\pi\)
0.563212 + 0.826313i \(0.309566\pi\)
\(720\) −804.652 + 1320.19i −1.11757 + 1.83359i
\(721\) 7.80525i 0.0108256i
\(722\) 713.122 + 27.5894i 0.987704 + 0.0382124i
\(723\) 1175.96 + 487.099i 1.62650 + 0.673719i
\(724\) 367.723 + 1127.12i 0.507905 + 1.55680i
\(725\) 3.08576 1.27817i 0.00425623 0.00176299i
\(726\) 630.713 + 290.303i 0.868750 + 0.399866i
\(727\) 542.456 542.456i 0.746156 0.746156i −0.227599 0.973755i \(-0.573087\pi\)
0.973755 + 0.227599i \(0.0730875\pi\)
\(728\) 45.6477 + 25.4559i 0.0627029 + 0.0349670i
\(729\) 306.489 306.489i 0.420424 0.420424i
\(730\) −83.5830 226.143i −0.114497 0.309785i
\(731\) 372.588 154.331i 0.509697 0.211123i
\(732\) −1352.19 1579.36i −1.84725 2.15760i
\(733\) 562.276 + 232.903i 0.767089 + 0.317739i 0.731693 0.681635i \(-0.238731\pi\)
0.0353965 + 0.999373i \(0.488731\pi\)
\(734\) −1043.63 + 965.885i −1.42184 + 1.31592i
\(735\) 1220.89i 1.66107i
\(736\) −3.87337 + 19.7833i −0.00526273 + 0.0268795i
\(737\) −141.518 −0.192019
\(738\) −461.010 498.117i −0.624675 0.674955i
\(739\) −305.819 + 738.312i −0.413828 + 0.999070i 0.570272 + 0.821456i \(0.306838\pi\)
−0.984100 + 0.177614i \(0.943162\pi\)
\(740\) 450.231 + 525.871i 0.608420 + 0.710637i
\(741\) −50.5461 122.029i −0.0682133 0.164681i
\(742\) −75.0564 + 27.7410i −0.101154 + 0.0373868i
\(743\) 581.334 + 581.334i 0.782414 + 0.782414i 0.980238 0.197823i \(-0.0633873\pi\)
−0.197823 + 0.980238i \(0.563387\pi\)
\(744\) −572.491 2015.98i −0.769477 2.70965i
\(745\) 528.633 + 528.633i 0.709574 + 0.709574i
\(746\) 531.698 1155.17i 0.712732 1.54848i
\(747\) −237.488 573.348i −0.317923 0.767534i
\(748\) 99.4112 + 304.709i 0.132903 + 0.407365i
\(749\) 38.1847 92.1861i 0.0509810 0.123079i
\(750\) −56.5307 + 1461.19i −0.0753743 + 1.94825i
\(751\) −187.901 −0.250201 −0.125100 0.992144i \(-0.539925\pi\)
−0.125100 + 0.992144i \(0.539925\pi\)
\(752\) 1272.88 + 198.469i 1.69266 + 0.263922i
\(753\) 782.958i 1.03978i
\(754\) 0.730922 18.8927i 0.000969392 0.0250566i
\(755\) −735.390 304.608i −0.974026 0.403455i
\(756\) 67.1819 132.245i 0.0888649 0.174927i
\(757\) −168.645 + 69.8549i −0.222780 + 0.0922786i −0.491282 0.871001i \(-0.663472\pi\)
0.268502 + 0.963279i \(0.413472\pi\)
\(758\) 31.2452 67.8833i 0.0412206 0.0895559i
\(759\) −18.5998 + 18.5998i −0.0245057 + 0.0245057i
\(760\) 58.4980 46.2874i 0.0769711 0.0609045i
\(761\) 391.406 391.406i 0.514331 0.514331i −0.401520 0.915850i \(-0.631518\pi\)
0.915850 + 0.401520i \(0.131518\pi\)
\(762\) 178.122 65.8344i 0.233756 0.0863968i
\(763\) −4.84022 + 2.00488i −0.00634367 + 0.00262763i
\(764\) −560.334 43.4215i −0.733421 0.0568345i
\(765\) 940.971 + 389.763i 1.23003 + 0.509494i
\(766\) −472.240 510.250i −0.616501 0.666123i
\(767\) 829.235i 1.08114i
\(768\) 908.016 1073.56i 1.18231 1.39787i
\(769\) 184.433 0.239835 0.119918 0.992784i \(-0.461737\pi\)
0.119918 + 0.992784i \(0.461737\pi\)
\(770\) −28.2675 + 26.1617i −0.0367110 + 0.0339763i
\(771\) −147.332 + 355.690i −0.191092 + 0.461336i
\(772\) −49.3600 + 636.967i −0.0639378 + 0.825087i
\(773\) −140.532 339.275i −0.181801 0.438907i 0.806537 0.591184i \(-0.201339\pi\)
−0.988338 + 0.152277i \(0.951339\pi\)
\(774\) −561.545 1519.32i −0.725511 1.96295i
\(775\) −140.289 140.289i −0.181018 0.181018i
\(776\) 787.199 + 994.862i 1.01443 + 1.28204i
\(777\) −81.7035 81.7035i −0.105152 0.105152i
\(778\) 288.424 + 132.755i 0.370725 + 0.170637i
\(779\) 12.5317 + 30.2541i 0.0160869 + 0.0388371i
\(780\) 1052.77 + 534.818i 1.34970 + 0.685665i
\(781\) 60.9340 147.108i 0.0780206 0.188358i
\(782\) 13.2700 + 0.513392i 0.0169693 + 0.000656512i
\(783\) −53.6576 −0.0685282
\(784\) −120.024 + 769.772i −0.153091 + 0.981852i
\(785\) 529.054i 0.673954i
\(786\) −1153.72 44.6351i −1.46783 0.0567877i
\(787\) −926.743 383.870i −1.17756 0.487763i −0.293878 0.955843i \(-0.594946\pi\)
−0.883686 + 0.468080i \(0.844946\pi\)
\(788\) −232.040 + 75.7030i −0.294467 + 0.0960697i
\(789\) −1764.51 + 730.885i −2.23639 + 0.926344i
\(790\) 300.568 + 138.345i 0.380465 + 0.175120i
\(791\) −33.6796 + 33.6796i −0.0425785 + 0.0425785i
\(792\) 1238.37 351.667i 1.56359 0.444024i
\(793\) −787.860 + 787.860i −0.993518 + 0.993518i
\(794\) 325.153 + 879.738i 0.409513 + 1.10798i
\(795\) −1670.23 + 691.831i −2.10091 + 0.870227i
\(796\) 596.182 510.428i 0.748973 0.641242i
\(797\) −871.860 361.136i −1.09393 0.453119i −0.238553 0.971130i \(-0.576673\pi\)
−0.855374 + 0.518010i \(0.826673\pi\)
\(798\) −9.13767 + 8.45696i −0.0114507 + 0.0105977i
\(799\) 848.660i 1.06215i
\(800\) 25.5764 130.632i 0.0319705 0.163290i
\(801\) 1691.14 2.11129
\(802\) 924.516 + 998.931i 1.15276 + 1.24555i
\(803\) −76.8221 + 185.465i −0.0956689 + 0.230965i
\(804\) 310.668 265.982i 0.386403 0.330824i
\(805\) 0.610701 + 1.47436i 0.000758635 + 0.00183151i
\(806\) −1053.42 + 389.348i −1.30698 + 0.483062i
\(807\) −74.4628 74.4628i −0.0922711 0.0922711i
\(808\) 548.204 983.042i 0.678470 1.21664i
\(809\) 744.003 + 744.003i 0.919658 + 0.919658i 0.997004 0.0773465i \(-0.0246448\pi\)
−0.0773465 + 0.997004i \(0.524645\pi\)
\(810\) 673.937 1464.20i 0.832021 1.80765i
\(811\) −307.315 741.925i −0.378934 0.914827i −0.992166 0.124924i \(-0.960131\pi\)
0.613233 0.789902i \(-0.289869\pi\)
\(812\) −1.69432 + 0.552772i −0.00208661 + 0.000680754i
\(813\) 688.574 1662.36i 0.846954 2.04473i
\(814\) 22.2839 575.989i 0.0273758 0.707603i
\(815\) −580.286 −0.712007
\(816\) −790.933 482.072i −0.969280 0.590775i
\(817\) 78.1517i 0.0956569i
\(818\) −26.2335 + 678.075i −0.0320702 + 0.828943i
\(819\) −127.763 52.9210i −0.155998 0.0646166i
\(820\) −261.008 132.595i −0.318302 0.161701i
\(821\) −948.269 + 392.786i −1.15502 + 0.478424i −0.876213 0.481924i \(-0.839938\pi\)
−0.278804 + 0.960348i \(0.589938\pi\)
\(822\) −165.860 + 360.349i −0.201777 + 0.438380i
\(823\) 492.275 492.275i 0.598147 0.598147i −0.341672 0.939819i \(-0.610993\pi\)
0.939819 + 0.341672i \(0.110993\pi\)
\(824\) −13.0246 + 111.771i −0.0158066 + 0.135644i
\(825\) 122.817 122.817i 0.148869 0.148869i
\(826\) 73.3187 27.0988i 0.0887636 0.0328072i
\(827\) −1350.77 + 559.506i −1.63333 + 0.676549i −0.995600 0.0937082i \(-0.970128\pi\)
−0.637734 + 0.770257i \(0.720128\pi\)
\(828\) 4.12093 53.1786i 0.00497697 0.0642254i
\(829\) 441.547 + 182.895i 0.532627 + 0.220621i 0.632753 0.774354i \(-0.281925\pi\)
−0.100127 + 0.994975i \(0.531925\pi\)
\(830\) −181.823 196.458i −0.219064 0.236696i
\(831\) 189.850i 0.228460i
\(832\) −611.194 440.700i −0.734608 0.529687i
\(833\) 513.225 0.616116
\(834\) 1100.12 1018.17i 1.31909 1.22083i
\(835\) −218.994 + 528.698i −0.262268 + 0.633171i
\(836\) −61.9260 4.79879i −0.0740742 0.00574018i
\(837\) 1219.72 + 2944.67i 1.45726 + 3.51813i
\(838\) 60.7152 + 164.272i 0.0724526 + 0.196028i
\(839\) 849.569 + 849.569i 1.01260 + 1.01260i 0.999920 + 0.0126775i \(0.00403549\pi\)
0.0126775 + 0.999920i \(0.495965\pi\)
\(840\) 12.8836 110.560i 0.0153376 0.131619i
\(841\) −594.221 594.221i −0.706565 0.706565i
\(842\) −177.070 81.5013i −0.210297 0.0967949i
\(843\) 782.994 + 1890.31i 0.928818 + 2.24236i
\(844\) −380.965 + 749.913i −0.451380 + 0.888522i
\(845\) −53.0792 + 128.144i −0.0628156 + 0.151650i
\(846\) −3406.04 131.773i −4.02605 0.155760i
\(847\) −35.0736 −0.0414093
\(848\) 1121.09 272.003i 1.32204 0.320758i
\(849\) 1593.93i 1.87742i
\(850\) −87.6237 3.39000i −0.103087 0.00398823i
\(851\) −22.0649 9.13957i −0.0259282 0.0107398i
\(852\) 142.723 + 437.465i 0.167515 + 0.513456i
\(853\) 773.493 320.391i 0.906791 0.375605i 0.119964 0.992778i \(-0.461722\pi\)
0.786827 + 0.617173i \(0.211722\pi\)
\(854\) 95.4071 + 43.9138i 0.111718 + 0.0514213i
\(855\) −139.563 + 139.563i −0.163231 + 0.163231i
\(856\) −700.634 + 1256.38i −0.818497 + 1.46773i
\(857\) −259.040 + 259.040i −0.302264 + 0.302264i −0.841899 0.539635i \(-0.818562\pi\)
0.539635 + 0.841899i \(0.318562\pi\)
\(858\) −340.859 922.230i −0.397271 1.07486i
\(859\) −762.123 + 315.682i −0.887221 + 0.367499i −0.779293 0.626660i \(-0.784422\pi\)
−0.107928 + 0.994159i \(0.534422\pi\)
\(860\) −454.393 530.732i −0.528364 0.617130i
\(861\) 45.1438 + 18.6992i 0.0524318 + 0.0217180i
\(862\) 747.263 691.596i 0.866894 0.802316i
\(863\) 1078.25i 1.24942i −0.780855 0.624712i \(-0.785216\pi\)
0.780855 0.624712i \(-0.214784\pi\)
\(864\) −1182.72 + 1781.63i −1.36888 + 2.06207i
\(865\) 1041.22 1.20373
\(866\) −89.6712 96.8888i −0.103546 0.111881i
\(867\) 373.931 902.750i 0.431293 1.04123i
\(868\) 68.8502 + 80.4173i 0.0793206 + 0.0926467i
\(869\) −105.430 254.532i −0.121324 0.292902i
\(870\) −37.7679 + 13.9591i −0.0434114 + 0.0160450i
\(871\) −154.976 154.976i −0.177929 0.177929i
\(872\) 72.6571 20.6329i 0.0833224 0.0236616i
\(873\) −2373.51 2373.51i −2.71880 2.71880i
\(874\) −1.07601 + 2.33773i −0.00123113 + 0.00267475i
\(875\) −28.2680 68.2450i −0.0323063 0.0779943i
\(876\) −179.936 551.530i −0.205407 0.629600i
\(877\) 387.984 936.676i 0.442399 1.06805i −0.532706 0.846301i \(-0.678825\pi\)
0.975105 0.221745i \(-0.0711753\pi\)
\(878\) 4.35740 112.629i 0.00496287 0.128279i
\(879\) 642.663 0.731130
\(880\) 448.444 327.464i 0.509596 0.372118i
\(881\) 1281.50i 1.45460i −0.686318 0.727301i \(-0.740774\pi\)
0.686318 0.727301i \(-0.259226\pi\)
\(882\) 79.6896 2059.79i 0.0903510 2.33537i
\(883\) −1014.19 420.092i −1.14857 0.475755i −0.274519 0.961582i \(-0.588519\pi\)
−0.874055 + 0.485826i \(0.838519\pi\)
\(884\) −224.821 + 442.551i −0.254323 + 0.500624i
\(885\) 1631.56 675.814i 1.84357 0.763632i
\(886\) 175.394 381.061i 0.197961 0.430091i
\(887\) −57.0987 + 57.0987i −0.0643728 + 0.0643728i −0.738560 0.674187i \(-0.764494\pi\)
0.674187 + 0.738560i \(0.264494\pi\)
\(888\) 1033.65 + 1306.33i 1.16402 + 1.47109i
\(889\) −6.78316 + 6.78316i −0.00763010 + 0.00763010i
\(890\) 684.222 252.890i 0.768789 0.284146i
\(891\) −1239.94 + 513.598i −1.39162 + 0.576429i
\(892\) −1140.41 88.3729i −1.27849 0.0990728i
\(893\) 151.940 + 62.9358i 0.170146 + 0.0704768i
\(894\) 1221.91 + 1320.26i 1.36679 + 1.47680i
\(895\) 27.3309i 0.0305373i
\(896\) −18.9921 + 68.4419i −0.0211965 + 0.0763860i
\(897\) −40.7372 −0.0454150
\(898\) −182.329 + 168.747i −0.203039 + 0.187914i
\(899\) 14.6551 35.3806i 0.0163016 0.0393555i
\(900\) −27.2111 + 351.146i −0.0302345 + 0.390162i
\(901\) −290.825 702.113i −0.322780 0.779260i
\(902\) 84.5076 + 228.645i 0.0936892 + 0.253486i
\(903\) 82.4587 + 82.4587i 0.0913164 + 0.0913164i
\(904\) 538.491 426.089i 0.595676 0.471337i
\(905\) −956.779 956.779i −1.05721 1.05721i
\(906\) −1739.89 800.832i −1.92041 0.883921i
\(907\) 312.323 + 754.015i 0.344348 + 0.831329i 0.997266 + 0.0739002i \(0.0235446\pi\)
−0.652918 + 0.757429i \(0.726455\pi\)
\(908\) −74.8204 38.0097i −0.0824014 0.0418609i
\(909\) −1139.67 + 2751.42i −1.25377 + 3.02686i
\(910\) −59.6053 2.30602i −0.0655003 0.00253409i
\(911\) 1374.15 1.50840 0.754201 0.656644i \(-0.228024\pi\)
0.754201 + 0.656644i \(0.228024\pi\)
\(912\) 144.963 105.855i 0.158951 0.116069i
\(913\) 222.886i 0.244125i
\(914\) 1619.76 + 62.6655i 1.77217 + 0.0685618i
\(915\) 2192.25 + 908.058i 2.39590 + 0.992413i
\(916\) −664.815 + 216.895i −0.725781 + 0.236785i
\(917\) 53.8844 22.3196i 0.0587616 0.0243399i
\(918\) 1279.69 + 589.013i 1.39400 + 0.641627i
\(919\) −317.523 + 317.523i −0.345510 + 0.345510i −0.858434 0.512924i \(-0.828562\pi\)
0.512924 + 0.858434i \(0.328562\pi\)
\(920\) −6.28493 22.1318i −0.00683145 0.0240564i
\(921\) 1809.70 1809.70i 1.96493 1.96493i
\(922\) −155.947 421.930i −0.169139 0.457625i
\(923\) 227.826 94.3687i 0.246832 0.102241i
\(924\) −70.4021 + 60.2756i −0.0761928 + 0.0652333i
\(925\) 145.697 + 60.3498i 0.157511 + 0.0652430i
\(926\) 815.507 754.756i 0.880677 0.815071i
\(927\) 297.733i 0.321179i
\(928\) 25.1850 5.08834i 0.0271390 0.00548313i
\(929\) −46.9926 −0.0505841 −0.0252920 0.999680i \(-0.508052\pi\)
−0.0252920 + 0.999680i \(0.508052\pi\)
\(930\) 1624.59 + 1755.35i 1.74687 + 1.88747i
\(931\) −38.0602 + 91.8855i −0.0408810 + 0.0986955i
\(932\) 1213.01 1038.53i 1.30151 1.11430i
\(933\) 182.288 + 440.083i 0.195379 + 0.471686i
\(934\) 649.375 240.011i 0.695263 0.256971i
\(935\) −258.658 258.658i −0.276640 0.276640i
\(936\) 1741.24 + 971.022i 1.86030 + 1.03742i
\(937\) 381.311 + 381.311i 0.406949 + 0.406949i 0.880673 0.473724i \(-0.157091\pi\)
−0.473724 + 0.880673i \(0.657091\pi\)
\(938\) −8.63806 + 18.7671i −0.00920902 + 0.0200075i
\(939\) −384.367 927.944i −0.409337 0.988226i
\(940\) −1397.76 + 456.018i −1.48698 + 0.485125i
\(941\) 319.284 770.819i 0.339303 0.819149i −0.658480 0.752598i \(-0.728800\pi\)
0.997783 0.0665513i \(-0.0211996\pi\)
\(942\) −49.2150 + 1272.10i −0.0522452 + 1.35042i
\(943\) 10.0998 0.0107103
\(944\) −1095.14 + 265.706i −1.16010 + 0.281468i
\(945\) 169.287i 0.179139i
\(946\) −22.4899 + 581.313i −0.0237737 + 0.614496i
\(947\) −46.3711 19.2075i −0.0489663 0.0202825i 0.358066 0.933696i \(-0.383436\pi\)
−0.407032 + 0.913414i \(0.633436\pi\)
\(948\) 709.838 + 360.606i 0.748774 + 0.380386i
\(949\) −287.230 + 118.975i −0.302666 + 0.125368i
\(950\) 7.10502 15.4364i 0.00747897 0.0162488i
\(951\) −1205.26 + 1205.26i −1.26736 + 1.26736i
\(952\) 46.4762 + 5.41586i 0.0488195 + 0.00568893i
\(953\) −456.351 + 456.351i −0.478858 + 0.478858i −0.904766 0.425909i \(-0.859955\pi\)
0.425909 + 0.904766i \(0.359955\pi\)
\(954\) −2863.04 + 1058.19i −3.00109 + 1.10921i
\(955\) 592.589 245.459i 0.620512 0.257025i
\(956\) 4.06756 52.4899i 0.00425477 0.0549058i
\(957\) 30.9743 + 12.8300i 0.0323661 + 0.0134065i
\(958\) −325.460 351.657i −0.339729 0.367074i
\(959\) 20.0388i 0.0208955i
\(960\) −368.983 + 1561.72i −0.384358 + 1.62679i
\(961\) −1313.79 −1.36710
\(962\) 655.167 606.361i 0.681047 0.630313i
\(963\) 1456.56 3516.46i 1.51253 3.65157i
\(964\) 924.211 + 71.6192i 0.958725 + 0.0742938i
\(965\) −279.028 673.634i −0.289148 0.698066i
\(966\) 1.33126 + 3.60188i 0.00137812 + 0.00372865i
\(967\) 476.069 + 476.069i 0.492316 + 0.492316i 0.909035 0.416719i \(-0.136820\pi\)
−0.416719 + 0.909035i \(0.636820\pi\)
\(968\) 502.252 + 58.5273i 0.518855 + 0.0604621i
\(969\) −83.6130 83.6130i −0.0862879 0.0862879i
\(970\) −1315.23 605.372i −1.35591 0.624095i
\(971\) −502.303 1212.67i −0.517305 1.24888i −0.939553 0.342404i \(-0.888759\pi\)
0.422248 0.906480i \(-0.361241\pi\)
\(972\) 667.053 1313.07i 0.686269 1.35089i
\(973\) −28.9774 + 69.9576i −0.0297815 + 0.0718988i
\(974\) 761.762 + 29.4711i 0.782096 + 0.0302579i
\(975\) 268.993 0.275891
\(976\) −1292.94 788.048i −1.32474 0.807426i
\(977\) 1.17535i 0.00120302i 1.00000 0.000601512i \(0.000191467\pi\)
−1.00000 0.000601512i \(0.999809\pi\)
\(978\) −1395.28 53.9809i −1.42667 0.0551952i
\(979\) −561.146 232.434i −0.573183 0.237420i
\(980\) −275.775 845.291i −0.281404 0.862542i
\(981\) −184.631 + 76.4767i −0.188207 + 0.0779579i
\(982\) −1354.91 623.634i −1.37974 0.635065i
\(983\) −1006.98 + 1006.98i −1.02439 + 1.02439i −0.0246998 + 0.999695i \(0.507863\pi\)
−0.999695 + 0.0246998i \(0.992137\pi\)
\(984\) −615.252 343.102i −0.625256 0.348681i
\(985\) 196.972 196.972i 0.199971 0.199971i
\(986\) −5.86799 15.8765i −0.00595130 0.0161019i
\(987\) 226.718 93.9098i 0.229704 0.0951467i
\(988\) −62.5599 73.0702i −0.0633198 0.0739577i
\(989\) 22.2688 + 9.22405i 0.0225165 + 0.00932665i
\(990\) −1078.27 + 997.944i −1.08916 + 1.00802i
\(991\) 1294.48i 1.30624i 0.757256 + 0.653118i \(0.226539\pi\)
−0.757256 + 0.653118i \(0.773461\pi\)
\(992\) −851.739 1266.46i −0.858607 1.27667i
\(993\) 1767.71 1.78017
\(994\) −15.7890 17.0599i −0.0158843 0.0171629i
\(995\) −342.777 + 827.536i −0.344499 + 0.831694i
\(996\) −418.913 489.292i −0.420596 0.491257i
\(997\) 82.2498 + 198.568i 0.0824973 + 0.199166i 0.959746 0.280871i \(-0.0906233\pi\)
−0.877248 + 0.480037i \(0.840623\pi\)
\(998\) −1180.28 + 436.235i −1.18265 + 0.437109i
\(999\) −1791.45 1791.45i −1.79325 1.79325i
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.3.2 28
3.2 odd 2 288.3.u.a.163.6 28
4.3 odd 2 128.3.h.a.47.1 28
8.3 odd 2 256.3.h.a.95.7 28
8.5 even 2 256.3.h.b.95.1 28
32.5 even 8 256.3.h.a.159.7 28
32.11 odd 8 inner 32.3.h.a.11.2 yes 28
32.21 even 8 128.3.h.a.79.1 28
32.27 odd 8 256.3.h.b.159.1 28
96.11 even 8 288.3.u.a.235.6 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.3.2 28 1.1 even 1 trivial
32.3.h.a.11.2 yes 28 32.11 odd 8 inner
128.3.h.a.47.1 28 4.3 odd 2
128.3.h.a.79.1 28 32.21 even 8
256.3.h.a.95.7 28 8.3 odd 2
256.3.h.a.159.7 28 32.5 even 8
256.3.h.b.95.1 28 8.5 even 2
256.3.h.b.159.1 28 32.27 odd 8
288.3.u.a.163.6 28 3.2 odd 2
288.3.u.a.235.6 28 96.11 even 8