Properties

Label 572.2.t.a.87.5
Level $572$
Weight $2$
Character 572.87
Analytic conductor $4.567$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(87,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(80\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 87.5
Character \(\chi\) \(=\) 572.87
Dual form 572.2.t.a.263.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39552 + 0.229204i) q^{2} +(2.08234 + 1.20224i) q^{3} +(1.89493 - 0.639716i) q^{4} -2.36335 q^{5} +(-3.18150 - 1.20047i) q^{6} +(-1.42248 - 2.46380i) q^{7} +(-2.49778 + 1.32706i) q^{8} +(1.39077 + 2.40888i) q^{9} +O(q^{10})\) \(q+(-1.39552 + 0.229204i) q^{2} +(2.08234 + 1.20224i) q^{3} +(1.89493 - 0.639716i) q^{4} -2.36335 q^{5} +(-3.18150 - 1.20047i) q^{6} +(-1.42248 - 2.46380i) q^{7} +(-2.49778 + 1.32706i) q^{8} +(1.39077 + 2.40888i) q^{9} +(3.29809 - 0.541689i) q^{10} +(-3.21380 - 0.819455i) q^{11} +(4.71499 + 0.946056i) q^{12} +(-2.34026 - 2.74285i) q^{13} +(2.54980 + 3.11224i) q^{14} +(-4.92130 - 2.84131i) q^{15} +(3.18153 - 2.42444i) q^{16} +(-1.53626 + 0.886961i) q^{17} +(-2.49296 - 3.04286i) q^{18} +(0.0598616 + 0.103683i) q^{19} +(-4.47838 + 1.51187i) q^{20} -6.84064i q^{21} +(4.67273 + 0.406948i) q^{22} +(-5.93594 - 3.42711i) q^{23} +(-6.79668 - 0.239542i) q^{24} +0.585406 q^{25} +(3.89454 + 3.29129i) q^{26} -0.525304i q^{27} +(-4.27163 - 3.75875i) q^{28} +(-2.88768 - 1.66721i) q^{29} +(7.51899 + 2.83712i) q^{30} +6.06160i q^{31} +(-3.88418 + 4.11256i) q^{32} +(-5.70704 - 5.57014i) q^{33} +(1.94058 - 1.58989i) q^{34} +(3.36181 + 5.82282i) q^{35} +(4.17640 + 3.67496i) q^{36} +(2.26363 - 3.92072i) q^{37} +(-0.107303 - 0.130971i) q^{38} +(-1.57565 - 8.52509i) q^{39} +(5.90312 - 3.13630i) q^{40} +(7.34222 + 4.23903i) q^{41} +(1.56790 + 9.54622i) q^{42} +(4.01118 + 6.94756i) q^{43} +(-6.61414 + 0.503106i) q^{44} +(-3.28686 - 5.69301i) q^{45} +(9.06921 + 3.42205i) q^{46} -2.87708i q^{47} +(9.53978 - 1.22354i) q^{48} +(-0.546883 + 0.947228i) q^{49} +(-0.816944 + 0.134177i) q^{50} -4.26536 q^{51} +(-6.18927 - 3.70040i) q^{52} +5.47979 q^{53} +(0.120402 + 0.733071i) q^{54} +(7.59532 + 1.93666i) q^{55} +(6.82265 + 4.26633i) q^{56} +0.287872i q^{57} +(4.41194 + 1.66474i) q^{58} +(-12.7481 + 7.36015i) q^{59} +(-11.1431 - 2.23586i) q^{60} +(1.95850 - 1.13074i) q^{61} +(-1.38934 - 8.45906i) q^{62} +(3.95666 - 6.85314i) q^{63} +(4.47782 - 6.62941i) q^{64} +(5.53083 + 6.48229i) q^{65} +(9.24097 + 6.46515i) q^{66} +(-7.27685 - 4.20129i) q^{67} +(-2.34371 + 2.66350i) q^{68} +(-8.24043 - 14.2729i) q^{69} +(-6.02607 - 7.35530i) q^{70} +(1.24084 - 0.716397i) q^{71} +(-6.67055 - 4.17122i) q^{72} -15.8645i q^{73} +(-2.26029 + 5.99027i) q^{74} +(1.21902 + 0.703799i) q^{75} +(0.179762 + 0.158178i) q^{76} +(2.55258 + 9.08382i) q^{77} +(4.15283 + 11.5358i) q^{78} -13.1522 q^{79} +(-7.51905 + 5.72978i) q^{80} +(4.80384 - 8.32049i) q^{81} +(-11.2178 - 4.23277i) q^{82} +9.19469 q^{83} +(-4.37607 - 12.9625i) q^{84} +(3.63072 - 2.09620i) q^{85} +(-7.19007 - 8.77606i) q^{86} +(-4.00876 - 6.94338i) q^{87} +(9.11483 - 2.21808i) q^{88} +(3.41133 - 5.90860i) q^{89} +(5.89173 + 7.19133i) q^{90} +(-3.42887 + 9.66756i) q^{91} +(-13.4406 - 2.69683i) q^{92} +(-7.28750 + 12.6223i) q^{93} +(0.659439 + 4.01501i) q^{94} +(-0.141474 - 0.245040i) q^{95} +(-13.0325 + 3.89403i) q^{96} +(-0.294457 - 0.510014i) q^{97} +(0.546075 - 1.44722i) q^{98} +(-2.49567 - 8.88131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39552 + 0.229204i −0.986779 + 0.162072i
\(3\) 2.08234 + 1.20224i 1.20224 + 0.694114i 0.961053 0.276364i \(-0.0891297\pi\)
0.241188 + 0.970478i \(0.422463\pi\)
\(4\) 1.89493 0.639716i 0.947466 0.319858i
\(5\) −2.36335 −1.05692 −0.528460 0.848958i \(-0.677230\pi\)
−0.528460 + 0.848958i \(0.677230\pi\)
\(6\) −3.18150 1.20047i −1.29884 0.490088i
\(7\) −1.42248 2.46380i −0.537646 0.931230i −0.999030 0.0440296i \(-0.985980\pi\)
0.461384 0.887200i \(-0.347353\pi\)
\(8\) −2.49778 + 1.32706i −0.883099 + 0.469186i
\(9\) 1.39077 + 2.40888i 0.463589 + 0.802959i
\(10\) 3.29809 0.541689i 1.04295 0.171297i
\(11\) −3.21380 0.819455i −0.968996 0.247075i
\(12\) 4.71499 + 0.946056i 1.36110 + 0.273103i
\(13\) −2.34026 2.74285i −0.649070 0.760729i
\(14\) 2.54980 + 3.11224i 0.681464 + 0.831781i
\(15\) −4.92130 2.84131i −1.27067 0.733623i
\(16\) 3.18153 2.42444i 0.795382 0.606109i
\(17\) −1.53626 + 0.886961i −0.372598 + 0.215120i −0.674593 0.738190i \(-0.735681\pi\)
0.301995 + 0.953310i \(0.402348\pi\)
\(18\) −2.49296 3.04286i −0.587596 0.717208i
\(19\) 0.0598616 + 0.103683i 0.0137332 + 0.0237866i 0.872810 0.488060i \(-0.162295\pi\)
−0.859077 + 0.511846i \(0.828962\pi\)
\(20\) −4.47838 + 1.51187i −1.00140 + 0.338064i
\(21\) 6.84064i 1.49275i
\(22\) 4.67273 + 0.406948i 0.996229 + 0.0867615i
\(23\) −5.93594 3.42711i −1.23773 0.714603i −0.269099 0.963113i \(-0.586726\pi\)
−0.968629 + 0.248510i \(0.920059\pi\)
\(24\) −6.79668 0.239542i −1.38737 0.0488963i
\(25\) 0.585406 0.117081
\(26\) 3.89454 + 3.29129i 0.763781 + 0.645475i
\(27\) 0.525304i 0.101095i
\(28\) −4.27163 3.75875i −0.807262 0.710338i
\(29\) −2.88768 1.66721i −0.536229 0.309592i 0.207320 0.978273i \(-0.433526\pi\)
−0.743549 + 0.668681i \(0.766859\pi\)
\(30\) 7.51899 + 2.83712i 1.37277 + 0.517984i
\(31\) 6.06160i 1.08870i 0.838860 + 0.544348i \(0.183223\pi\)
−0.838860 + 0.544348i \(0.816777\pi\)
\(32\) −3.88418 + 4.11256i −0.686633 + 0.727004i
\(33\) −5.70704 5.57014i −0.993469 0.969638i
\(34\) 1.94058 1.58989i 0.332807 0.272663i
\(35\) 3.36181 + 5.82282i 0.568249 + 0.984236i
\(36\) 4.17640 + 3.67496i 0.696067 + 0.612493i
\(37\) 2.26363 3.92072i 0.372139 0.644563i −0.617756 0.786370i \(-0.711958\pi\)
0.989894 + 0.141807i \(0.0452912\pi\)
\(38\) −0.107303 0.130971i −0.0174068 0.0212464i
\(39\) −1.57565 8.52509i −0.252306 1.36511i
\(40\) 5.90312 3.13630i 0.933366 0.495893i
\(41\) 7.34222 + 4.23903i 1.14666 + 0.662026i 0.948072 0.318057i \(-0.103030\pi\)
0.198591 + 0.980082i \(0.436364\pi\)
\(42\) 1.56790 + 9.54622i 0.241933 + 1.47301i
\(43\) 4.01118 + 6.94756i 0.611699 + 1.05949i 0.990954 + 0.134201i \(0.0428469\pi\)
−0.379255 + 0.925292i \(0.623820\pi\)
\(44\) −6.61414 + 0.503106i −0.997120 + 0.0758461i
\(45\) −3.28686 5.69301i −0.489976 0.848664i
\(46\) 9.06921 + 3.42205i 1.33718 + 0.504554i
\(47\) 2.87708i 0.419665i −0.977737 0.209833i \(-0.932708\pi\)
0.977737 0.209833i \(-0.0672919\pi\)
\(48\) 9.53978 1.22354i 1.37695 0.176603i
\(49\) −0.546883 + 0.947228i −0.0781261 + 0.135318i
\(50\) −0.816944 + 0.134177i −0.115533 + 0.0189756i
\(51\) −4.26536 −0.597271
\(52\) −6.18927 3.70040i −0.858297 0.513154i
\(53\) 5.47979 0.752708 0.376354 0.926476i \(-0.377178\pi\)
0.376354 + 0.926476i \(0.377178\pi\)
\(54\) 0.120402 + 0.733071i 0.0163846 + 0.0997583i
\(55\) 7.59532 + 1.93666i 1.02415 + 0.261139i
\(56\) 6.82265 + 4.26633i 0.911715 + 0.570112i
\(57\) 0.287872i 0.0381296i
\(58\) 4.41194 + 1.66474i 0.579316 + 0.218591i
\(59\) −12.7481 + 7.36015i −1.65967 + 0.958209i −0.686800 + 0.726847i \(0.740985\pi\)
−0.972868 + 0.231362i \(0.925682\pi\)
\(60\) −11.1431 2.23586i −1.43857 0.288648i
\(61\) 1.95850 1.13074i 0.250760 0.144776i −0.369352 0.929290i \(-0.620420\pi\)
0.620112 + 0.784513i \(0.287087\pi\)
\(62\) −1.38934 8.45906i −0.176447 1.07430i
\(63\) 3.95666 6.85314i 0.498493 0.863415i
\(64\) 4.47782 6.62941i 0.559728 0.828676i
\(65\) 5.53083 + 6.48229i 0.686016 + 0.804030i
\(66\) 9.24097 + 6.46515i 1.13748 + 0.795805i
\(67\) −7.27685 4.20129i −0.889009 0.513270i −0.0153908 0.999882i \(-0.504899\pi\)
−0.873618 + 0.486612i \(0.838233\pi\)
\(68\) −2.34371 + 2.66350i −0.284216 + 0.322997i
\(69\) −8.24043 14.2729i −0.992032 1.71825i
\(70\) −6.02607 7.35530i −0.720253 0.879126i
\(71\) 1.24084 0.716397i 0.147260 0.0850206i −0.424560 0.905400i \(-0.639571\pi\)
0.571820 + 0.820379i \(0.306238\pi\)
\(72\) −6.67055 4.17122i −0.786132 0.491583i
\(73\) 15.8645i 1.85680i −0.371576 0.928402i \(-0.621183\pi\)
0.371576 0.928402i \(-0.378817\pi\)
\(74\) −2.26029 + 5.99027i −0.262753 + 0.696355i
\(75\) 1.21902 + 0.703799i 0.140760 + 0.0812677i
\(76\) 0.179762 + 0.158178i 0.0206201 + 0.0181443i
\(77\) 2.55258 + 9.08382i 0.290893 + 1.03520i
\(78\) 4.15283 + 11.5358i 0.470216 + 1.30617i
\(79\) −13.1522 −1.47974 −0.739868 0.672752i \(-0.765112\pi\)
−0.739868 + 0.672752i \(0.765112\pi\)
\(80\) −7.51905 + 5.72978i −0.840655 + 0.640609i
\(81\) 4.80384 8.32049i 0.533760 0.924499i
\(82\) −11.2178 4.23277i −1.23880 0.467432i
\(83\) 9.19469 1.00925 0.504624 0.863339i \(-0.331631\pi\)
0.504624 + 0.863339i \(0.331631\pi\)
\(84\) −4.37607 12.9625i −0.477468 1.41433i
\(85\) 3.63072 2.09620i 0.393807 0.227365i
\(86\) −7.19007 8.77606i −0.775326 0.946347i
\(87\) −4.00876 6.94338i −0.429785 0.744409i
\(88\) 9.11483 2.21808i 0.971644 0.236448i
\(89\) 3.41133 5.90860i 0.361600 0.626310i −0.626624 0.779322i \(-0.715564\pi\)
0.988224 + 0.153011i \(0.0488971\pi\)
\(90\) 5.89173 + 7.19133i 0.621043 + 0.758032i
\(91\) −3.42887 + 9.66756i −0.359443 + 1.01344i
\(92\) −13.4406 2.69683i −1.40128 0.281164i
\(93\) −7.28750 + 12.6223i −0.755679 + 1.30887i
\(94\) 0.659439 + 4.01501i 0.0680159 + 0.414117i
\(95\) −0.141474 0.245040i −0.0145149 0.0251405i
\(96\) −13.0325 + 3.89403i −1.33012 + 0.397433i
\(97\) −0.294457 0.510014i −0.0298976 0.0517841i 0.850689 0.525669i \(-0.176185\pi\)
−0.880587 + 0.473884i \(0.842851\pi\)
\(98\) 0.546075 1.44722i 0.0551619 0.146191i
\(99\) −2.49567 8.88131i −0.250825 0.892605i
\(100\) 1.10930 0.374494i 0.110930 0.0374494i
\(101\) −7.18748 4.14969i −0.715181 0.412910i 0.0977954 0.995207i \(-0.468821\pi\)
−0.812976 + 0.582297i \(0.802154\pi\)
\(102\) 5.95239 0.977639i 0.589374 0.0968007i
\(103\) 0.481129i 0.0474071i 0.999719 + 0.0237035i \(0.00754578\pi\)
−0.999719 + 0.0237035i \(0.992454\pi\)
\(104\) 9.48537 + 3.74537i 0.930117 + 0.367264i
\(105\) 16.1668i 1.57772i
\(106\) −7.64714 + 1.25599i −0.742756 + 0.121993i
\(107\) −1.41158 + 2.44493i −0.136463 + 0.236361i −0.926155 0.377142i \(-0.876907\pi\)
0.789692 + 0.613503i \(0.210240\pi\)
\(108\) −0.336046 0.995416i −0.0323360 0.0957839i
\(109\) 9.26157i 0.887098i 0.896250 + 0.443549i \(0.146281\pi\)
−0.896250 + 0.443549i \(0.853719\pi\)
\(110\) −11.0433 0.961758i −1.05294 0.0917000i
\(111\) 9.42731 5.44286i 0.894801 0.516613i
\(112\) −10.4990 4.38995i −0.992060 0.414811i
\(113\) 4.54653 + 7.87483i 0.427702 + 0.740801i 0.996668 0.0815593i \(-0.0259900\pi\)
−0.568967 + 0.822361i \(0.692657\pi\)
\(114\) −0.0659815 0.401731i −0.00617973 0.0376255i
\(115\) 14.0287 + 8.09946i 1.30818 + 0.755279i
\(116\) −6.53850 1.31194i −0.607084 0.121811i
\(117\) 3.35243 9.45204i 0.309932 0.873842i
\(118\) 16.1033 13.1931i 1.48243 1.21453i
\(119\) 4.37060 + 2.52336i 0.400652 + 0.231316i
\(120\) 16.0629 + 0.566121i 1.46634 + 0.0516796i
\(121\) 9.65699 + 5.26713i 0.877908 + 0.478830i
\(122\) −2.47395 + 2.02686i −0.223981 + 0.183503i
\(123\) 10.1927 + 17.6542i 0.919043 + 1.59183i
\(124\) 3.87770 + 11.4863i 0.348228 + 1.03150i
\(125\) 10.4332 0.933175
\(126\) −3.95082 + 10.4706i −0.351967 + 0.932791i
\(127\) 4.49395 7.78375i 0.398774 0.690697i −0.594801 0.803873i \(-0.702769\pi\)
0.993575 + 0.113176i \(0.0361025\pi\)
\(128\) −4.72939 + 10.2778i −0.418023 + 0.908437i
\(129\) 19.2896i 1.69835i
\(130\) −9.20414 7.77846i −0.807256 0.682216i
\(131\) −20.4382 −1.78570 −0.892849 0.450357i \(-0.851297\pi\)
−0.892849 + 0.450357i \(0.851297\pi\)
\(132\) −14.3778 6.90415i −1.25142 0.600929i
\(133\) 0.170304 0.294974i 0.0147672 0.0255775i
\(134\) 11.1179 + 4.19509i 0.960442 + 0.362400i
\(135\) 1.24148i 0.106849i
\(136\) 2.66020 4.25415i 0.228110 0.364790i
\(137\) 6.69485 + 11.5958i 0.571980 + 0.990698i 0.996363 + 0.0852153i \(0.0271578\pi\)
−0.424383 + 0.905483i \(0.639509\pi\)
\(138\) 14.7711 + 18.0293i 1.25740 + 1.53475i
\(139\) −2.07772 3.59871i −0.176230 0.305239i 0.764356 0.644794i \(-0.223057\pi\)
−0.940586 + 0.339555i \(0.889724\pi\)
\(140\) 10.0953 + 8.88324i 0.853212 + 0.750771i
\(141\) 3.45894 5.99107i 0.291296 0.504539i
\(142\) −1.56740 + 1.28415i −0.131534 + 0.107763i
\(143\) 5.27347 + 10.7327i 0.440990 + 0.897512i
\(144\) 10.2649 + 4.29209i 0.855410 + 0.357674i
\(145\) 6.82460 + 3.94018i 0.566752 + 0.327214i
\(146\) 3.63622 + 22.1392i 0.300936 + 1.83226i
\(147\) −2.27759 + 1.31497i −0.187853 + 0.108457i
\(148\) 1.78128 8.87758i 0.146420 0.729733i
\(149\) 4.85354 2.80219i 0.397617 0.229565i −0.287838 0.957679i \(-0.592936\pi\)
0.685455 + 0.728115i \(0.259603\pi\)
\(150\) −1.86247 0.702760i −0.152070 0.0573801i
\(151\) 8.77335 0.713965 0.356983 0.934111i \(-0.383806\pi\)
0.356983 + 0.934111i \(0.383806\pi\)
\(152\) −0.287115 0.179538i −0.0232881 0.0145625i
\(153\) −4.27316 2.46711i −0.345465 0.199454i
\(154\) −5.64421 12.0916i −0.454824 0.974365i
\(155\) 14.3257i 1.15066i
\(156\) −8.43939 15.1465i −0.675692 1.21269i
\(157\) −19.8613 −1.58510 −0.792551 0.609805i \(-0.791248\pi\)
−0.792551 + 0.609805i \(0.791248\pi\)
\(158\) 18.3541 3.01453i 1.46017 0.239823i
\(159\) 11.4108 + 6.58803i 0.904936 + 0.522465i
\(160\) 9.17967 9.71940i 0.725716 0.768386i
\(161\) 19.5000i 1.53681i
\(162\) −4.79674 + 12.7124i −0.376868 + 0.998784i
\(163\) −4.25844 + 2.45861i −0.333547 + 0.192573i −0.657415 0.753529i \(-0.728350\pi\)
0.323868 + 0.946102i \(0.395017\pi\)
\(164\) 16.6248 + 3.33574i 1.29818 + 0.260478i
\(165\) 13.4877 + 13.1642i 1.05002 + 1.02483i
\(166\) −12.8313 + 2.10746i −0.995905 + 0.163571i
\(167\) 10.4546 18.1078i 0.808998 1.40123i −0.104561 0.994518i \(-0.533344\pi\)
0.913559 0.406707i \(-0.133323\pi\)
\(168\) 9.07794 + 17.0864i 0.700378 + 1.31825i
\(169\) −2.04641 + 12.8379i −0.157416 + 0.987532i
\(170\) −4.58627 + 3.75745i −0.351751 + 0.288183i
\(171\) −0.166507 + 0.288399i −0.0127331 + 0.0220544i
\(172\) 12.0454 + 10.5991i 0.918451 + 0.808177i
\(173\) −1.17223 + 0.676788i −0.0891232 + 0.0514553i −0.543899 0.839151i \(-0.683053\pi\)
0.454776 + 0.890606i \(0.349719\pi\)
\(174\) 7.18575 + 8.77078i 0.544750 + 0.664911i
\(175\) −0.832727 1.44232i −0.0629482 0.109030i
\(176\) −12.2115 + 5.18452i −0.920476 + 0.390798i
\(177\) −35.3947 −2.66043
\(178\) −3.40629 + 9.02744i −0.255313 + 0.676635i
\(179\) −17.6177 10.1716i −1.31681 0.760260i −0.333595 0.942716i \(-0.608262\pi\)
−0.983214 + 0.182456i \(0.941595\pi\)
\(180\) −9.87028 8.68520i −0.735687 0.647357i
\(181\) 13.2029 0.981366 0.490683 0.871338i \(-0.336747\pi\)
0.490683 + 0.871338i \(0.336747\pi\)
\(182\) 2.56920 14.2772i 0.190442 1.05829i
\(183\) 5.43769 0.401965
\(184\) 19.3747 + 0.682840i 1.42832 + 0.0503397i
\(185\) −5.34975 + 9.26603i −0.393321 + 0.681252i
\(186\) 7.27674 19.2850i 0.533556 1.41404i
\(187\) 5.66406 1.59162i 0.414197 0.116391i
\(188\) −1.84051 5.45187i −0.134233 0.397619i
\(189\) −1.29425 + 0.747234i −0.0941426 + 0.0543532i
\(190\) 0.253593 + 0.309531i 0.0183976 + 0.0224557i
\(191\) −17.7425 + 10.2436i −1.28380 + 0.741203i −0.977541 0.210744i \(-0.932411\pi\)
−0.306261 + 0.951948i \(0.599078\pi\)
\(192\) 17.2945 8.42128i 1.24812 0.607753i
\(193\) −4.82031 2.78301i −0.346973 0.200325i 0.316378 0.948633i \(-0.397533\pi\)
−0.663351 + 0.748308i \(0.730867\pi\)
\(194\) 0.527817 + 0.644242i 0.0378950 + 0.0462539i
\(195\) 3.72381 + 20.1477i 0.266668 + 1.44281i
\(196\) −0.430348 + 2.14478i −0.0307391 + 0.153199i
\(197\) −9.88582 5.70758i −0.704336 0.406648i 0.104625 0.994512i \(-0.466636\pi\)
−0.808960 + 0.587863i \(0.799969\pi\)
\(198\) 5.51838 + 11.8220i 0.392174 + 0.840153i
\(199\) −0.905497 + 0.522789i −0.0641890 + 0.0370595i −0.531751 0.846901i \(-0.678466\pi\)
0.467562 + 0.883960i \(0.345132\pi\)
\(200\) −1.46222 + 0.776869i −0.103394 + 0.0549329i
\(201\) −10.1019 17.4971i −0.712535 1.23415i
\(202\) 10.9814 + 4.14357i 0.772647 + 0.291540i
\(203\) 9.48625i 0.665804i
\(204\) −8.08257 + 2.72862i −0.565893 + 0.191042i
\(205\) −17.3522 10.0183i −1.21193 0.699709i
\(206\) −0.110277 0.671424i −0.00768335 0.0467803i
\(207\) 19.0653i 1.32513i
\(208\) −14.0954 3.05264i −0.977343 0.211663i
\(209\) −0.107419 0.382271i −0.00743034 0.0264423i
\(210\) −3.70550 22.5610i −0.255704 1.55686i
\(211\) −12.3290 + 21.3544i −0.848761 + 1.47010i 0.0335534 + 0.999437i \(0.489318\pi\)
−0.882314 + 0.470660i \(0.844016\pi\)
\(212\) 10.3838 3.50551i 0.713165 0.240760i
\(213\) 3.44512 0.236056
\(214\) 1.40950 3.73548i 0.0963513 0.255352i
\(215\) −9.47980 16.4195i −0.646517 1.11980i
\(216\) 0.697110 + 1.31210i 0.0474324 + 0.0892768i
\(217\) 14.9346 8.62249i 1.01383 0.585333i
\(218\) −2.12279 12.9247i −0.143773 0.875369i
\(219\) 19.0730 33.0354i 1.28883 2.23233i
\(220\) 15.6315 1.18901i 1.05388 0.0801634i
\(221\) 6.02805 + 2.13801i 0.405490 + 0.143818i
\(222\) −11.9084 + 9.75638i −0.799242 + 0.654805i
\(223\) 6.34078 + 3.66085i 0.424610 + 0.245149i 0.697048 0.717025i \(-0.254496\pi\)
−0.272438 + 0.962173i \(0.587830\pi\)
\(224\) 15.6577 + 3.71984i 1.04617 + 0.248542i
\(225\) 0.814162 + 1.41017i 0.0542775 + 0.0940114i
\(226\) −8.14970 9.94736i −0.542110 0.661689i
\(227\) 3.13712 + 5.43365i 0.208218 + 0.360644i 0.951153 0.308719i \(-0.0999003\pi\)
−0.742935 + 0.669363i \(0.766567\pi\)
\(228\) 0.184157 + 0.545498i 0.0121961 + 0.0361265i
\(229\) −5.46115 −0.360883 −0.180442 0.983586i \(-0.557753\pi\)
−0.180442 + 0.983586i \(0.557753\pi\)
\(230\) −21.4337 8.08750i −1.41329 0.533274i
\(231\) −5.60560 + 21.9844i −0.368821 + 1.44647i
\(232\) 9.42528 + 0.332185i 0.618800 + 0.0218090i
\(233\) 20.6972i 1.35592i −0.735099 0.677960i \(-0.762864\pi\)
0.735099 0.677960i \(-0.237136\pi\)
\(234\) −2.51192 + 13.9589i −0.164210 + 0.912520i
\(235\) 6.79954i 0.443553i
\(236\) −19.4485 + 22.1022i −1.26599 + 1.43873i
\(237\) −27.3873 15.8121i −1.77900 1.02711i
\(238\) −6.67760 2.51964i −0.432845 0.163324i
\(239\) −0.965907 −0.0624794 −0.0312397 0.999512i \(-0.509946\pi\)
−0.0312397 + 0.999512i \(0.509946\pi\)
\(240\) −22.5458 + 2.89165i −1.45533 + 0.186655i
\(241\) −7.46216 + 4.30828i −0.480680 + 0.277521i −0.720700 0.693247i \(-0.756179\pi\)
0.240020 + 0.970768i \(0.422846\pi\)
\(242\) −14.6837 5.13694i −0.943906 0.330215i
\(243\) 18.6417 10.7628i 1.19587 0.690433i
\(244\) 2.98787 3.39556i 0.191279 0.217378i
\(245\) 1.29247 2.23863i 0.0825731 0.143021i
\(246\) −18.2705 22.3006i −1.16488 1.42183i
\(247\) 0.144296 0.406837i 0.00918133 0.0258864i
\(248\) −8.04410 15.1405i −0.510801 0.961426i
\(249\) 19.1465 + 11.0542i 1.21336 + 0.700533i
\(250\) −14.5597 + 2.39134i −0.920838 + 0.151241i
\(251\) 24.0910 13.9090i 1.52061 0.877925i 0.520907 0.853614i \(-0.325594\pi\)
0.999704 0.0243115i \(-0.00773936\pi\)
\(252\) 3.11354 15.5174i 0.196135 0.977503i
\(253\) 16.2685 + 15.8783i 1.02279 + 0.998259i
\(254\) −4.48732 + 11.8924i −0.281559 + 0.746195i
\(255\) 10.0805 0.631268
\(256\) 4.24423 15.4268i 0.265264 0.964176i
\(257\) 11.4712 19.8688i 0.715556 1.23938i −0.247189 0.968967i \(-0.579507\pi\)
0.962745 0.270412i \(-0.0871598\pi\)
\(258\) −4.42126 26.9190i −0.275255 1.67590i
\(259\) −12.8799 −0.800315
\(260\) 14.6274 + 8.74534i 0.907151 + 0.542363i
\(261\) 9.27477i 0.574094i
\(262\) 28.5219 4.68453i 1.76209 0.289411i
\(263\) 9.18861 15.9151i 0.566594 0.981370i −0.430305 0.902683i \(-0.641594\pi\)
0.996899 0.0786864i \(-0.0250726\pi\)
\(264\) 21.6469 + 6.33942i 1.33227 + 0.390164i
\(265\) −12.9507 −0.795552
\(266\) −0.170052 + 0.450676i −0.0104266 + 0.0276327i
\(267\) 14.2071 8.20248i 0.869462 0.501984i
\(268\) −16.4768 3.30604i −1.00648 0.201949i
\(269\) 8.09997 + 14.0296i 0.493864 + 0.855397i 0.999975 0.00707096i \(-0.00225078\pi\)
−0.506111 + 0.862468i \(0.668917\pi\)
\(270\) −0.284551 1.73250i −0.0173172 0.105437i
\(271\) −0.370870 + 0.642366i −0.0225288 + 0.0390210i −0.877070 0.480363i \(-0.840505\pi\)
0.854541 + 0.519384i \(0.173838\pi\)
\(272\) −2.73728 + 6.54646i −0.165972 + 0.396937i
\(273\) −18.7628 + 16.0088i −1.13558 + 0.968899i
\(274\) −12.0006 14.6477i −0.724982 0.884898i
\(275\) −1.88138 0.479714i −0.113451 0.0289278i
\(276\) −24.7456 21.7745i −1.48951 1.31067i
\(277\) 10.4305 6.02204i 0.626707 0.361830i −0.152769 0.988262i \(-0.548819\pi\)
0.779476 + 0.626432i \(0.215486\pi\)
\(278\) 3.72433 + 4.54584i 0.223370 + 0.272641i
\(279\) −14.6016 + 8.43026i −0.874178 + 0.504707i
\(280\) −16.1243 10.0828i −0.963610 0.602563i
\(281\) 17.8828i 1.06680i −0.845864 0.533399i \(-0.820914\pi\)
0.845864 0.533399i \(-0.179086\pi\)
\(282\) −3.45384 + 9.15344i −0.205673 + 0.545079i
\(283\) −4.44308 + 7.69564i −0.264114 + 0.457459i −0.967331 0.253516i \(-0.918413\pi\)
0.703217 + 0.710975i \(0.251746\pi\)
\(284\) 1.89301 2.15130i 0.112329 0.127656i
\(285\) 0.680342i 0.0403000i
\(286\) −9.81919 13.7689i −0.580621 0.814174i
\(287\) 24.1197i 1.42374i
\(288\) −15.3086 3.63691i −0.902070 0.214307i
\(289\) −6.92660 + 11.9972i −0.407447 + 0.705719i
\(290\) −10.4269 3.93436i −0.612291 0.231034i
\(291\) 1.41603i 0.0830093i
\(292\) −10.1488 30.0622i −0.593914 1.75926i
\(293\) −20.8114 + 12.0155i −1.21582 + 0.701953i −0.964021 0.265827i \(-0.914355\pi\)
−0.251797 + 0.967780i \(0.581022\pi\)
\(294\) 2.87702 2.35709i 0.167791 0.137469i
\(295\) 30.1283 17.3946i 1.75414 1.01275i
\(296\) −0.451021 + 12.7971i −0.0262150 + 0.743816i
\(297\) −0.430463 + 1.68822i −0.0249780 + 0.0979606i
\(298\) −6.13092 + 5.02296i −0.355155 + 0.290972i
\(299\) 4.49156 + 24.3017i 0.259754 + 1.40540i
\(300\) 2.76018 + 0.553827i 0.159359 + 0.0319752i
\(301\) 11.4116 19.7655i 0.657755 1.13926i
\(302\) −12.2434 + 2.01089i −0.704526 + 0.115714i
\(303\) −9.97786 17.2822i −0.573213 0.992834i
\(304\) 0.441825 + 0.184741i 0.0253404 + 0.0105956i
\(305\) −4.62861 + 2.67233i −0.265034 + 0.153017i
\(306\) 6.52874 + 2.46347i 0.373223 + 0.140827i
\(307\) −10.6191 −0.606066 −0.303033 0.952980i \(-0.597999\pi\)
−0.303033 + 0.952980i \(0.597999\pi\)
\(308\) 10.6480 + 15.5803i 0.606727 + 0.887769i
\(309\) −0.578433 + 1.00188i −0.0329059 + 0.0569947i
\(310\) 3.28350 + 19.9917i 0.186490 + 1.13545i
\(311\) 21.7576i 1.23376i 0.787057 + 0.616881i \(0.211604\pi\)
−0.787057 + 0.616881i \(0.788396\pi\)
\(312\) 15.2489 + 19.2028i 0.863301 + 1.08715i
\(313\) 15.5123 0.876807 0.438404 0.898778i \(-0.355544\pi\)
0.438404 + 0.898778i \(0.355544\pi\)
\(314\) 27.7167 4.55229i 1.56415 0.256900i
\(315\) −9.35097 + 16.1964i −0.526867 + 0.912561i
\(316\) −24.9225 + 8.41366i −1.40200 + 0.473305i
\(317\) −24.4399 −1.37268 −0.686341 0.727280i \(-0.740784\pi\)
−0.686341 + 0.727280i \(0.740784\pi\)
\(318\) −17.4340 6.57830i −0.977648 0.368893i
\(319\) 7.91423 + 7.72439i 0.443112 + 0.432483i
\(320\) −10.5827 + 15.6676i −0.591588 + 0.875845i
\(321\) −5.87879 + 3.39412i −0.328122 + 0.189442i
\(322\) −4.46947 27.2125i −0.249074 1.51649i
\(323\) −0.183926 0.106190i −0.0102339 0.00590856i
\(324\) 3.78019 18.8399i 0.210011 1.04666i
\(325\) −1.37000 1.60568i −0.0759939 0.0890670i
\(326\) 5.37920 4.40708i 0.297926 0.244086i
\(327\) −11.1346 + 19.2858i −0.615747 + 1.06651i
\(328\) −23.9647 0.844613i −1.32323 0.0466359i
\(329\) −7.08856 + 4.09258i −0.390805 + 0.225631i
\(330\) −21.8396 15.2794i −1.20223 0.841103i
\(331\) 0.119376 0.0689217i 0.00656149 0.00378828i −0.496716 0.867913i \(-0.665461\pi\)
0.503277 + 0.864125i \(0.332127\pi\)
\(332\) 17.4233 5.88199i 0.956228 0.322816i
\(333\) 12.5927 0.690077
\(334\) −10.4391 + 27.6660i −0.571203 + 1.51382i
\(335\) 17.1977 + 9.92911i 0.939612 + 0.542485i
\(336\) −16.5847 21.7637i −0.904769 1.18731i
\(337\) 20.3914i 1.11079i 0.831586 + 0.555396i \(0.187433\pi\)
−0.831586 + 0.555396i \(0.812567\pi\)
\(338\) −0.0867100 18.3846i −0.00471640 0.999989i
\(339\) 21.8641i 1.18750i
\(340\) 5.53899 6.29478i 0.300394 0.341382i
\(341\) 4.96721 19.4808i 0.268989 1.05494i
\(342\) 0.166261 0.440629i 0.00899037 0.0238265i
\(343\) −16.8030 −0.907275
\(344\) −19.2389 12.0304i −1.03729 0.648637i
\(345\) 19.4750 + 33.7317i 1.04850 + 1.81605i
\(346\) 1.48075 1.21315i 0.0796054 0.0652193i
\(347\) −9.02153 15.6257i −0.484301 0.838834i 0.515536 0.856868i \(-0.327593\pi\)
−0.999837 + 0.0180336i \(0.994259\pi\)
\(348\) −12.0381 10.5928i −0.645311 0.567832i
\(349\) −18.1497 10.4787i −0.971533 0.560915i −0.0718295 0.997417i \(-0.522884\pi\)
−0.899703 + 0.436502i \(0.856217\pi\)
\(350\) 1.49267 + 1.82192i 0.0797866 + 0.0973859i
\(351\) −1.44083 + 1.22935i −0.0769058 + 0.0656177i
\(352\) 15.8530 10.0340i 0.844969 0.534815i
\(353\) 16.7566 29.0234i 0.891866 1.54476i 0.0542310 0.998528i \(-0.482729\pi\)
0.837635 0.546230i \(-0.183937\pi\)
\(354\) 49.3938 8.11260i 2.62525 0.431180i
\(355\) −2.93252 + 1.69309i −0.155642 + 0.0898601i
\(356\) 2.68441 13.3787i 0.142274 0.709068i
\(357\) 6.06738 + 10.5090i 0.321120 + 0.556196i
\(358\) 26.9172 + 10.1566i 1.42262 + 0.536791i
\(359\) 2.43391 0.128457 0.0642284 0.997935i \(-0.479541\pi\)
0.0642284 + 0.997935i \(0.479541\pi\)
\(360\) 15.7648 + 9.85803i 0.830879 + 0.519564i
\(361\) 9.49283 16.4421i 0.499623 0.865372i
\(362\) −18.4249 + 3.02616i −0.968391 + 0.159052i
\(363\) 13.7768 + 22.5780i 0.723094 + 1.18504i
\(364\) −0.312979 + 20.5129i −0.0164045 + 1.07517i
\(365\) 37.4934i 1.96250i
\(366\) −7.58838 + 1.24634i −0.396651 + 0.0651472i
\(367\) −12.6426 7.29918i −0.659936 0.381014i 0.132317 0.991207i \(-0.457758\pi\)
−0.792253 + 0.610193i \(0.791092\pi\)
\(368\) −27.1942 + 3.48784i −1.41759 + 0.181816i
\(369\) 23.5820i 1.22763i
\(370\) 5.34184 14.1571i 0.277709 0.735992i
\(371\) −7.79488 13.5011i −0.404690 0.700944i
\(372\) −5.73461 + 28.5804i −0.297326 + 1.48182i
\(373\) 27.9094 16.1135i 1.44510 0.834327i 0.446913 0.894577i \(-0.352523\pi\)
0.998183 + 0.0602507i \(0.0191900\pi\)
\(374\) −7.53948 + 3.51935i −0.389857 + 0.181981i
\(375\) 21.7255 + 12.5432i 1.12190 + 0.647730i
\(376\) 3.81806 + 7.18632i 0.196901 + 0.370606i
\(377\) 2.18503 + 11.8222i 0.112535 + 0.608872i
\(378\) 1.63487 1.33942i 0.0840888 0.0688925i
\(379\) 6.58561 + 3.80220i 0.338280 + 0.195306i 0.659511 0.751695i \(-0.270763\pi\)
−0.321231 + 0.947001i \(0.604097\pi\)
\(380\) −0.424839 0.373830i −0.0217938 0.0191771i
\(381\) 18.7159 10.8056i 0.958844 0.553589i
\(382\) 22.4121 18.3618i 1.14670 0.939472i
\(383\) −6.32133 + 3.64962i −0.323005 + 0.186487i −0.652731 0.757590i \(-0.726377\pi\)
0.329726 + 0.944077i \(0.393044\pi\)
\(384\) −22.2046 + 15.7160i −1.13312 + 0.802004i
\(385\) −6.03262 21.4682i −0.307451 1.09412i
\(386\) 7.36470 + 2.77890i 0.374853 + 0.141442i
\(387\) −11.1572 + 19.3249i −0.567153 + 0.982338i
\(388\) −0.884239 0.778073i −0.0448905 0.0395007i
\(389\) −8.17082 −0.414277 −0.207139 0.978312i \(-0.566415\pi\)
−0.207139 + 0.978312i \(0.566415\pi\)
\(390\) −9.81458 27.2630i −0.496981 1.38052i
\(391\) 12.1589 0.614901
\(392\) 0.108964 3.09172i 0.00550353 0.156155i
\(393\) −42.5594 24.5717i −2.14684 1.23948i
\(394\) 15.1040 + 5.69915i 0.760930 + 0.287119i
\(395\) 31.0832 1.56396
\(396\) −10.4106 15.2330i −0.523154 0.765485i
\(397\) −11.1737 19.3534i −0.560790 0.971318i −0.997428 0.0716799i \(-0.977164\pi\)
0.436637 0.899638i \(-0.356169\pi\)
\(398\) 1.14381 0.937104i 0.0573341 0.0469728i
\(399\) 0.709261 0.409492i 0.0355074 0.0205002i
\(400\) 1.86249 1.41928i 0.0931243 0.0709639i
\(401\) 11.5234 19.9591i 0.575452 0.996712i −0.420540 0.907274i \(-0.638159\pi\)
0.995992 0.0894383i \(-0.0285072\pi\)
\(402\) 18.1078 + 22.1020i 0.903135 + 1.10235i
\(403\) 16.6260 14.1857i 0.828202 0.706640i
\(404\) −16.2744 3.26544i −0.809682 0.162462i
\(405\) −11.3531 + 19.6642i −0.564142 + 0.977122i
\(406\) −2.17429 13.2382i −0.107908 0.657001i
\(407\) −10.4877 + 10.7455i −0.519857 + 0.532633i
\(408\) 10.6539 5.66039i 0.527449 0.280231i
\(409\) 26.4511 15.2715i 1.30792 0.755129i 0.326172 0.945310i \(-0.394241\pi\)
0.981749 + 0.190182i \(0.0609077\pi\)
\(410\) 26.5115 + 10.0035i 1.30931 + 0.494038i
\(411\) 32.1953i 1.58808i
\(412\) 0.307786 + 0.911707i 0.0151635 + 0.0449166i
\(413\) 36.2679 + 20.9393i 1.78463 + 1.03035i
\(414\) 4.36983 + 26.6059i 0.214766 + 1.30761i
\(415\) −21.7302 −1.06670
\(416\) 20.3701 + 1.02928i 0.998726 + 0.0504645i
\(417\) 9.99167i 0.489294i
\(418\) 0.237523 + 0.508845i 0.0116177 + 0.0248884i
\(419\) −14.4882 8.36475i −0.707794 0.408645i 0.102450 0.994738i \(-0.467332\pi\)
−0.810244 + 0.586093i \(0.800665\pi\)
\(420\) 10.3422 + 30.6350i 0.504646 + 1.49483i
\(421\) 13.2065 0.643646 0.321823 0.946800i \(-0.395704\pi\)
0.321823 + 0.946800i \(0.395704\pi\)
\(422\) 12.3108 32.6263i 0.599278 1.58822i
\(423\) 6.93053 4.00135i 0.336974 0.194552i
\(424\) −13.6873 + 7.27201i −0.664715 + 0.353160i
\(425\) −0.899337 + 0.519233i −0.0436243 + 0.0251865i
\(426\) −4.80773 + 0.789636i −0.232935 + 0.0382580i
\(427\) −5.57184 3.21690i −0.269640 0.155677i
\(428\) −1.11079 + 5.53599i −0.0536920 + 0.267592i
\(429\) −1.92211 + 28.6891i −0.0928002 + 1.38512i
\(430\) 16.9926 + 20.7409i 0.819458 + 1.00021i
\(431\) 17.9496 31.0896i 0.864602 1.49753i −0.00284073 0.999996i \(-0.500904\pi\)
0.867442 0.497538i \(-0.165762\pi\)
\(432\) −1.27357 1.67127i −0.0612745 0.0804090i
\(433\) 3.26905 + 5.66217i 0.157101 + 0.272106i 0.933822 0.357738i \(-0.116452\pi\)
−0.776721 + 0.629844i \(0.783119\pi\)
\(434\) −18.8651 + 15.4559i −0.905556 + 0.741906i
\(435\) 9.47410 + 16.4096i 0.454248 + 0.786781i
\(436\) 5.92478 + 17.5500i 0.283745 + 0.840495i
\(437\) 0.820611i 0.0392551i
\(438\) −19.0448 + 50.4731i −0.909998 + 2.41170i
\(439\) 9.16547 15.8751i 0.437444 0.757675i −0.560048 0.828460i \(-0.689217\pi\)
0.997492 + 0.0707851i \(0.0225505\pi\)
\(440\) −21.5415 + 5.24209i −1.02695 + 0.249907i
\(441\) −3.04234 −0.144873
\(442\) −8.90228 1.60198i −0.423438 0.0761985i
\(443\) 13.3451i 0.634046i −0.948418 0.317023i \(-0.897317\pi\)
0.948418 0.317023i \(-0.102683\pi\)
\(444\) 14.3822 16.3446i 0.682550 0.775683i
\(445\) −8.06216 + 13.9641i −0.382183 + 0.661960i
\(446\) −9.68775 3.65545i −0.458728 0.173090i
\(447\) 13.4756 0.637376
\(448\) −22.7032 1.60229i −1.07262 0.0757011i
\(449\) −4.77171 8.26485i −0.225191 0.390042i 0.731186 0.682178i \(-0.238967\pi\)
−0.956377 + 0.292136i \(0.905634\pi\)
\(450\) −1.45939 1.78131i −0.0687965 0.0839716i
\(451\) −20.1227 19.6400i −0.947542 0.924812i
\(452\) 13.6530 + 12.0138i 0.642184 + 0.565080i
\(453\) 18.2691 + 10.5477i 0.858358 + 0.495573i
\(454\) −5.62332 6.86371i −0.263915 0.322130i
\(455\) 8.10361 22.8478i 0.379903 1.07112i
\(456\) −0.382024 0.719042i −0.0178899 0.0336722i
\(457\) −22.7228 13.1190i −1.06293 0.613681i −0.136686 0.990614i \(-0.543645\pi\)
−0.926240 + 0.376933i \(0.876979\pi\)
\(458\) 7.62113 1.25172i 0.356112 0.0584890i
\(459\) 0.465925 + 0.807005i 0.0217475 + 0.0376678i
\(460\) 31.7647 + 6.37355i 1.48104 + 0.297168i
\(461\) −28.9757 + 16.7291i −1.34953 + 0.779153i −0.988183 0.153278i \(-0.951017\pi\)
−0.361349 + 0.932431i \(0.617684\pi\)
\(462\) 2.78378 31.9645i 0.129513 1.48712i
\(463\) 7.51169i 0.349098i 0.984649 + 0.174549i \(0.0558467\pi\)
−0.984649 + 0.174549i \(0.944153\pi\)
\(464\) −13.2293 + 1.69674i −0.614154 + 0.0787694i
\(465\) 17.2229 29.8309i 0.798692 1.38338i
\(466\) 4.74389 + 28.8833i 0.219756 + 1.33799i
\(467\) 29.5145i 1.36577i −0.730528 0.682883i \(-0.760726\pi\)
0.730528 0.682883i \(-0.239274\pi\)
\(468\) 0.306002 20.0556i 0.0141449 0.927069i
\(469\) 23.9050i 1.10383i
\(470\) −1.55848 9.48887i −0.0718874 0.437689i
\(471\) −41.3580 23.8780i −1.90568 1.10024i
\(472\) 22.0747 35.3016i 1.01607 1.62489i
\(473\) −7.19790 25.6150i −0.330960 1.17778i
\(474\) 41.8437 + 15.7887i 1.92194 + 0.725201i
\(475\) 0.0350434 + 0.0606969i 0.00160790 + 0.00278496i
\(476\) 9.89621 + 1.98566i 0.453592 + 0.0910127i
\(477\) 7.62111 + 13.2001i 0.348947 + 0.604393i
\(478\) 1.34794 0.221390i 0.0616533 0.0101261i
\(479\) −3.86917 + 6.70159i −0.176787 + 0.306204i −0.940778 0.339023i \(-0.889904\pi\)
0.763991 + 0.645226i \(0.223237\pi\)
\(480\) 30.8003 9.20294i 1.40583 0.420055i
\(481\) −16.0514 + 2.96671i −0.731882 + 0.135270i
\(482\) 9.42609 7.72263i 0.429347 0.351756i
\(483\) −23.4437 + 40.6056i −1.06672 + 1.84762i
\(484\) 21.6688 + 3.80311i 0.984945 + 0.172869i
\(485\) 0.695903 + 1.20534i 0.0315993 + 0.0547317i
\(486\) −23.5479 + 19.2924i −1.06815 + 0.875121i
\(487\) 3.37188 1.94676i 0.152795 0.0882160i −0.421653 0.906757i \(-0.638550\pi\)
0.574448 + 0.818541i \(0.305217\pi\)
\(488\) −3.39134 + 5.42339i −0.153519 + 0.245505i
\(489\) −11.8234 −0.534671
\(490\) −1.29056 + 3.42028i −0.0583017 + 0.154513i
\(491\) 6.79853 11.7754i 0.306813 0.531416i −0.670850 0.741593i \(-0.734071\pi\)
0.977663 + 0.210177i \(0.0674039\pi\)
\(492\) 30.6081 + 26.9331i 1.37992 + 1.21424i
\(493\) 5.91499 0.266398
\(494\) −0.108119 + 0.600821i −0.00486449 + 0.0270322i
\(495\) 5.89814 + 20.9896i 0.265102 + 0.943413i
\(496\) 14.6960 + 19.2851i 0.659868 + 0.865928i
\(497\) −3.53012 2.03812i −0.158348 0.0914220i
\(498\) −29.2529 11.0379i −1.31085 0.494620i
\(499\) 3.18132i 0.142415i 0.997462 + 0.0712077i \(0.0226853\pi\)
−0.997462 + 0.0712077i \(0.977315\pi\)
\(500\) 19.7702 6.67429i 0.884151 0.298483i
\(501\) 43.5399 25.1378i 1.94522 1.12307i
\(502\) −30.4314 + 24.9319i −1.35822 + 1.11277i
\(503\) 4.40223 + 7.62489i 0.196286 + 0.339977i 0.947321 0.320285i \(-0.103779\pi\)
−0.751035 + 0.660262i \(0.770445\pi\)
\(504\) −0.788351 + 22.3684i −0.0351160 + 0.996367i
\(505\) 16.9865 + 9.80716i 0.755890 + 0.436413i
\(506\) −26.3424 18.4296i −1.17106 0.819295i
\(507\) −19.6956 + 24.2727i −0.874712 + 1.07799i
\(508\) 3.53634 17.6245i 0.156900 0.781962i
\(509\) −2.33061 + 4.03674i −0.103303 + 0.178925i −0.913043 0.407862i \(-0.866274\pi\)
0.809741 + 0.586788i \(0.199608\pi\)
\(510\) −14.0675 + 2.31050i −0.622922 + 0.102311i
\(511\) −39.0871 + 22.5670i −1.72911 + 0.998303i
\(512\) −2.38700 + 22.5012i −0.105492 + 0.994420i
\(513\) 0.0544653 0.0314456i 0.00240470 0.00138836i
\(514\) −11.4543 + 30.3564i −0.505227 + 1.33896i
\(515\) 1.13708i 0.0501055i
\(516\) 12.3399 + 36.5525i 0.543232 + 1.60913i
\(517\) −2.35764 + 9.24636i −0.103689 + 0.406654i
\(518\) 17.9740 2.95212i 0.789734 0.129709i
\(519\) −3.25465 −0.142863
\(520\) −22.4172 8.85161i −0.983060 0.388169i
\(521\) 0.887537 0.0388837 0.0194419 0.999811i \(-0.493811\pi\)
0.0194419 + 0.999811i \(0.493811\pi\)
\(522\) 2.12581 + 12.9431i 0.0930443 + 0.566504i
\(523\) −0.344696 + 0.597031i −0.0150725 + 0.0261063i −0.873463 0.486890i \(-0.838131\pi\)
0.858391 + 0.512996i \(0.171465\pi\)
\(524\) −38.7291 + 13.0747i −1.69189 + 0.571170i
\(525\) 4.00455i 0.174773i
\(526\) −9.17504 + 24.3159i −0.400051 + 1.06022i
\(527\) −5.37640 9.31221i −0.234200 0.405646i
\(528\) −31.6616 3.88521i −1.37789 0.169082i
\(529\) 11.9902 + 20.7677i 0.521315 + 0.902943i
\(530\) 18.0728 2.96834i 0.785034 0.128937i
\(531\) −35.4594 20.4725i −1.53881 0.888430i
\(532\) 0.134014 0.667902i 0.00581023 0.0289572i
\(533\) −5.55566 30.0590i −0.240642 1.30200i
\(534\) −17.9462 + 14.7030i −0.776609 + 0.636262i
\(535\) 3.33606 5.77822i 0.144230 0.249814i
\(536\) 23.7514 + 0.837093i 1.02590 + 0.0361569i
\(537\) −24.4574 42.3614i −1.05541 1.82803i
\(538\) −14.5193 17.7219i −0.625970 0.764047i
\(539\) 2.53378 2.59605i 0.109138 0.111820i
\(540\) 0.794192 + 2.35251i 0.0341766 + 0.101236i
\(541\) 37.6668i 1.61942i 0.586827 + 0.809712i \(0.300377\pi\)
−0.586827 + 0.809712i \(0.699623\pi\)
\(542\) 0.370323 0.981438i 0.0159067 0.0421564i
\(543\) 27.4930 + 15.8731i 1.17984 + 0.681180i
\(544\) 2.31944 9.76309i 0.0994453 0.418589i
\(545\) 21.8883i 0.937592i
\(546\) 22.5145 26.6411i 0.963533 1.14013i
\(547\) 35.3135 1.50989 0.754947 0.655785i \(-0.227662\pi\)
0.754947 + 0.655785i \(0.227662\pi\)
\(548\) 20.1043 + 17.6905i 0.858814 + 0.755700i
\(549\) 5.44763 + 3.14519i 0.232499 + 0.134233i
\(550\) 2.73544 + 0.238230i 0.116640 + 0.0101581i
\(551\) 0.399206i 0.0170068i
\(552\) 39.5237 + 24.7149i 1.68224 + 1.05194i
\(553\) 18.7087 + 32.4044i 0.795574 + 1.37797i
\(554\) −13.1756 + 10.7946i −0.559779 + 0.458617i
\(555\) −22.2800 + 12.8634i −0.945733 + 0.546019i
\(556\) −6.23929 5.49016i −0.264605 0.232835i
\(557\) 39.8949 + 23.0333i 1.69040 + 0.975954i 0.954189 + 0.299203i \(0.0967209\pi\)
0.736212 + 0.676751i \(0.236612\pi\)
\(558\) 18.4446 15.1113i 0.780821 0.639713i
\(559\) 9.66891 27.2611i 0.408951 1.15302i
\(560\) 24.8127 + 10.3750i 1.04853 + 0.438423i
\(561\) 13.7080 + 3.49528i 0.578753 + 0.147571i
\(562\) 4.09881 + 24.9557i 0.172898 + 1.05269i
\(563\) 0.258018 + 0.446901i 0.0108742 + 0.0188346i 0.871411 0.490553i \(-0.163205\pi\)
−0.860537 + 0.509388i \(0.829872\pi\)
\(564\) 2.72188 13.5654i 0.114612 0.571206i
\(565\) −10.7450 18.6109i −0.452047 0.782968i
\(566\) 4.43652 11.7578i 0.186481 0.494216i
\(567\) −27.3334 −1.14790
\(568\) −2.14863 + 3.43606i −0.0901547 + 0.144174i
\(569\) 32.7473 + 18.9066i 1.37284 + 0.792608i 0.991284 0.131740i \(-0.0420563\pi\)
0.381552 + 0.924347i \(0.375390\pi\)
\(570\) 0.155937 + 0.949428i 0.00653149 + 0.0397672i
\(571\) −4.65834 −0.194945 −0.0974726 0.995238i \(-0.531076\pi\)
−0.0974726 + 0.995238i \(0.531076\pi\)
\(572\) 16.8587 + 16.9642i 0.704899 + 0.709308i
\(573\) −49.2613 −2.05792
\(574\) 5.52834 + 33.6595i 0.230748 + 1.40492i
\(575\) −3.47493 2.00625i −0.144915 0.0836666i
\(576\) 22.1970 + 1.56657i 0.924877 + 0.0652738i
\(577\) −29.2749 −1.21873 −0.609364 0.792890i \(-0.708575\pi\)
−0.609364 + 0.792890i \(0.708575\pi\)
\(578\) 6.91637 18.3299i 0.287683 0.762424i
\(579\) −6.69169 11.5903i −0.278097 0.481678i
\(580\) 15.4527 + 3.10057i 0.641640 + 0.128744i
\(581\) −13.0792 22.6539i −0.542618 0.939842i
\(582\) 0.324560 + 1.97610i 0.0134535 + 0.0819118i
\(583\) −17.6109 4.49045i −0.729371 0.185975i
\(584\) 21.0532 + 39.6262i 0.871188 + 1.63974i
\(585\) −7.92295 + 22.3385i −0.327574 + 0.923581i
\(586\) 26.2887 21.5379i 1.08598 0.889722i
\(587\) −3.28323 1.89557i −0.135513 0.0782386i 0.430711 0.902490i \(-0.358263\pi\)
−0.566224 + 0.824251i \(0.691596\pi\)
\(588\) −3.47468 + 3.94879i −0.143293 + 0.162845i
\(589\) −0.628487 + 0.362857i −0.0258964 + 0.0149513i
\(590\) −38.0576 + 31.1799i −1.56681 + 1.28366i
\(591\) −13.7238 23.7703i −0.564521 0.977778i
\(592\) −2.30374 17.9619i −0.0946830 0.738230i
\(593\) 15.0865i 0.619530i −0.950813 0.309765i \(-0.899750\pi\)
0.950813 0.309765i \(-0.100250\pi\)
\(594\) 0.213771 2.45461i 0.00877115 0.100714i
\(595\) −10.3292 5.96359i −0.423457 0.244483i
\(596\) 7.40452 8.41485i 0.303301 0.344686i
\(597\) −2.51407 −0.102894
\(598\) −11.8381 32.8839i −0.484096 1.34472i
\(599\) 33.5170i 1.36947i −0.728794 0.684733i \(-0.759919\pi\)
0.728794 0.684733i \(-0.240081\pi\)
\(600\) −3.97882 0.140229i −0.162435 0.00572484i
\(601\) 5.37992 + 3.10610i 0.219451 + 0.126700i 0.605696 0.795696i \(-0.292895\pi\)
−0.386245 + 0.922396i \(0.626228\pi\)
\(602\) −11.3948 + 30.1987i −0.464416 + 1.23081i
\(603\) 23.3721i 0.951784i
\(604\) 16.6249 5.61245i 0.676457 0.228367i
\(605\) −22.8228 12.4480i −0.927879 0.506085i
\(606\) 17.8854 + 21.8306i 0.726545 + 0.886806i
\(607\) −13.6690 23.6754i −0.554808 0.960956i −0.997918 0.0644889i \(-0.979458\pi\)
0.443110 0.896467i \(-0.353875\pi\)
\(608\) −0.658917 0.156541i −0.0267226 0.00634857i
\(609\) −11.4048 + 19.7536i −0.462144 + 0.800457i
\(610\) 5.84679 4.79018i 0.236730 0.193949i
\(611\) −7.89139 + 6.73311i −0.319252 + 0.272392i
\(612\) −9.67560 1.94140i −0.391113 0.0784763i
\(613\) −3.54034 2.04402i −0.142993 0.0825570i 0.426797 0.904348i \(-0.359642\pi\)
−0.569790 + 0.821791i \(0.692975\pi\)
\(614\) 14.8192 2.43395i 0.598053 0.0982261i
\(615\) −24.0888 41.7231i −0.971356 1.68244i
\(616\) −18.4306 19.3020i −0.742588 0.777699i
\(617\) −14.1354 24.4832i −0.569068 0.985655i −0.996658 0.0816822i \(-0.973971\pi\)
0.427590 0.903973i \(-0.359363\pi\)
\(618\) 0.577579 1.53071i 0.0232336 0.0615743i
\(619\) 17.8573i 0.717744i −0.933387 0.358872i \(-0.883161\pi\)
0.933387 0.358872i \(-0.116839\pi\)
\(620\) −9.16435 27.1461i −0.368049 1.09021i
\(621\) −1.80028 + 3.11817i −0.0722427 + 0.125128i
\(622\) −4.98693 30.3631i −0.199958 1.21745i
\(623\) −19.4102 −0.777652
\(624\) −25.6815 23.3028i −1.02808 0.932857i
\(625\) −27.5843 −1.10337
\(626\) −21.6477 + 3.55548i −0.865215 + 0.142106i
\(627\) 0.235898 0.925163i 0.00942088 0.0369475i
\(628\) −37.6358 + 12.7056i −1.50183 + 0.507008i
\(629\) 8.03102i 0.320218i
\(630\) 9.33716 24.7456i 0.372001 0.985886i
\(631\) 10.8235 6.24896i 0.430878 0.248767i −0.268843 0.963184i \(-0.586641\pi\)
0.699720 + 0.714417i \(0.253308\pi\)
\(632\) 32.8513 17.4537i 1.30675 0.694272i
\(633\) −51.3462 + 29.6448i −2.04083 + 1.17827i
\(634\) 34.1063 5.60172i 1.35453 0.222473i
\(635\) −10.6208 + 18.3957i −0.421472 + 0.730011i
\(636\) 25.8372 + 5.18419i 1.02451 + 0.205567i
\(637\) 3.87795 0.716742i 0.153650 0.0283984i
\(638\) −12.8149 8.96553i −0.507347 0.354949i
\(639\) 3.45142 + 1.99268i 0.136536 + 0.0788292i
\(640\) 11.1772 24.2900i 0.441817 0.960145i
\(641\) 2.29260 + 3.97090i 0.0905522 + 0.156841i 0.907744 0.419525i \(-0.137803\pi\)
−0.817191 + 0.576366i \(0.804470\pi\)
\(642\) 7.42601 6.08400i 0.293081 0.240116i
\(643\) −31.8153 + 18.3686i −1.25467 + 0.724386i −0.972034 0.234841i \(-0.924543\pi\)
−0.282639 + 0.959226i \(0.591210\pi\)
\(644\) 12.4744 + 36.9511i 0.491562 + 1.45608i
\(645\) 45.5880i 1.79503i
\(646\) 0.281011 + 0.106033i 0.0110562 + 0.00417182i
\(647\) −21.4528 12.3858i −0.843395 0.486935i 0.0150216 0.999887i \(-0.495218\pi\)
−0.858417 + 0.512953i \(0.828552\pi\)
\(648\) −0.957148 + 27.1578i −0.0376003 + 1.06686i
\(649\) 47.0013 13.2075i 1.84496 0.518439i
\(650\) 2.27988 + 1.92674i 0.0894244 + 0.0755730i
\(651\) 41.4652 1.62515
\(652\) −6.49664 + 7.38309i −0.254428 + 0.289144i
\(653\) −10.2499 + 17.7533i −0.401108 + 0.694739i −0.993860 0.110646i \(-0.964708\pi\)
0.592752 + 0.805385i \(0.298041\pi\)
\(654\) 11.1182 29.4657i 0.434756 1.15220i
\(655\) 48.3026 1.88734
\(656\) 33.6367 4.31414i 1.31329 0.168439i
\(657\) 38.2157 22.0639i 1.49094 0.860793i
\(658\) 8.95417 7.33599i 0.349070 0.285987i
\(659\) 21.2486 + 36.8037i 0.827729 + 1.43367i 0.899816 + 0.436270i \(0.143701\pi\)
−0.0720871 + 0.997398i \(0.522966\pi\)
\(660\) 33.9796 + 16.3169i 1.32266 + 0.635135i
\(661\) −15.5819 + 26.9886i −0.606065 + 1.04973i 0.385817 + 0.922575i \(0.373919\pi\)
−0.991882 + 0.127160i \(0.959414\pi\)
\(662\) −0.150794 + 0.123543i −0.00586077 + 0.00480163i
\(663\) 9.98204 + 11.6992i 0.387670 + 0.454361i
\(664\) −22.9663 + 12.2019i −0.891266 + 0.473526i
\(665\) −0.402486 + 0.697127i −0.0156078 + 0.0270334i
\(666\) −17.5733 + 2.88630i −0.680953 + 0.111842i
\(667\) 11.4274 + 19.7929i 0.442471 + 0.766382i
\(668\) 8.22680 41.0010i 0.318304 1.58638i
\(669\) 8.80245 + 15.2463i 0.340323 + 0.589456i
\(670\) −26.2755 9.91445i −1.01511 0.383028i
\(671\) −7.22081 + 2.02907i −0.278756 + 0.0783313i
\(672\) 28.1325 + 26.5703i 1.08524 + 1.02497i
\(673\) −41.6713 24.0589i −1.60631 0.927403i −0.990186 0.139754i \(-0.955369\pi\)
−0.616124 0.787650i \(-0.711298\pi\)
\(674\) −4.67380 28.4566i −0.180028 1.09611i
\(675\) 0.307516i 0.0118363i
\(676\) 4.33482 + 25.6361i 0.166724 + 0.986004i
\(677\) 3.87466i 0.148915i −0.997224 0.0744576i \(-0.976277\pi\)
0.997224 0.0744576i \(-0.0237225\pi\)
\(678\) −5.01134 30.5117i −0.192459 1.17180i
\(679\) −0.837716 + 1.45097i −0.0321486 + 0.0556830i
\(680\) −6.28697 + 10.0540i −0.241094 + 0.385554i
\(681\) 15.0863i 0.578108i
\(682\) −2.46675 + 28.3242i −0.0944569 + 1.08459i
\(683\) 15.6216 9.01915i 0.597745 0.345108i −0.170409 0.985373i \(-0.554509\pi\)
0.768154 + 0.640265i \(0.221176\pi\)
\(684\) −0.131026 + 0.653012i −0.00500991 + 0.0249686i
\(685\) −15.8223 27.4050i −0.604537 1.04709i
\(686\) 23.4488 3.85131i 0.895280 0.147044i
\(687\) −11.3720 6.56562i −0.433868 0.250494i
\(688\) 29.6056 + 12.3790i 1.12870 + 0.471946i
\(689\) −12.8241 15.0302i −0.488560 0.572606i
\(690\) −34.9091 42.6094i −1.32897 1.62211i
\(691\) 44.9224 + 25.9360i 1.70893 + 0.986651i 0.935889 + 0.352294i \(0.114598\pi\)
0.773041 + 0.634357i \(0.218735\pi\)
\(692\) −1.78835 + 2.03236i −0.0679827 + 0.0772588i
\(693\) −18.3318 + 18.7823i −0.696366 + 0.713481i
\(694\) 16.1712 + 19.7382i 0.613849 + 0.749252i
\(695\) 4.91037 + 8.50501i 0.186261 + 0.322613i
\(696\) 19.2273 + 12.0232i 0.728809 + 0.455738i
\(697\) −15.0394 −0.569659
\(698\) 27.7300 + 10.4633i 1.04960 + 0.396041i
\(699\) 24.8830 43.0987i 0.941163 1.63014i
\(700\) −2.50064 2.20040i −0.0945152 0.0831672i
\(701\) 13.1263i 0.495773i 0.968789 + 0.247886i \(0.0797360\pi\)
−0.968789 + 0.247886i \(0.920264\pi\)
\(702\) 1.72893 2.04582i 0.0652542 0.0772144i
\(703\) 0.542019 0.0204426
\(704\) −19.8233 + 17.6362i −0.747120 + 0.664690i
\(705\) −8.17468 + 14.1590i −0.307876 + 0.533258i
\(706\) −16.7319 + 44.3433i −0.629713 + 1.66888i
\(707\) 23.6114i 0.887997i
\(708\) −67.0705 + 22.6425i −2.52066 + 0.850958i
\(709\) −16.0326 27.7693i −0.602117 1.04290i −0.992500 0.122245i \(-0.960991\pi\)
0.390383 0.920653i \(-0.372343\pi\)
\(710\) 3.70432 3.03489i 0.139021 0.113897i
\(711\) −18.2916 31.6820i −0.685989 1.18817i
\(712\) −0.679696 + 19.2854i −0.0254727 + 0.722752i
\(713\) 20.7738 35.9813i 0.777985 1.34751i
\(714\) −10.8758 13.2748i −0.407018 0.496798i
\(715\) −12.4630 25.3651i −0.466091 0.948599i
\(716\) −39.8913 8.00413i −1.49081 0.299128i
\(717\) −2.01135 1.16125i −0.0751152 0.0433678i
\(718\) −3.39656 + 0.557862i −0.126759 + 0.0208192i
\(719\) −7.02705 + 4.05707i −0.262065 + 0.151303i −0.625276 0.780404i \(-0.715014\pi\)
0.363211 + 0.931707i \(0.381680\pi\)
\(720\) −24.2596 10.1437i −0.904101 0.378033i
\(721\) 1.18541 0.684395i 0.0441469 0.0254882i
\(722\) −9.47881 + 25.1210i −0.352765 + 0.934906i
\(723\) −20.7184 −0.770524
\(724\) 25.0186 8.44612i 0.929810 0.313898i
\(725\) −1.69047 0.975992i −0.0627824 0.0362474i
\(726\) −24.4007 28.3502i −0.905595 1.05218i
\(727\) 15.8192i 0.586700i 0.956005 + 0.293350i \(0.0947702\pi\)
−0.956005 + 0.293350i \(0.905230\pi\)
\(728\) −4.26487 28.6978i −0.158066 1.06361i
\(729\) 22.9348 0.849437
\(730\) −8.59364 52.3227i −0.318065 1.93655i
\(731\) −12.3244 7.11552i −0.455836 0.263177i
\(732\) 10.3040 3.47858i 0.380848 0.128572i
\(733\) 19.3043i 0.713022i 0.934291 + 0.356511i \(0.116034\pi\)
−0.934291 + 0.356511i \(0.883966\pi\)
\(734\) 19.3159 + 7.28840i 0.712962 + 0.269020i
\(735\) 5.38274 3.10773i 0.198545 0.114630i
\(736\) 37.1505 11.1003i 1.36938 0.409164i
\(737\) 19.9436 + 19.4652i 0.734630 + 0.717008i
\(738\) −5.40509 32.9091i −0.198964 1.21140i
\(739\) −22.8795 + 39.6284i −0.841634 + 1.45775i 0.0468778 + 0.998901i \(0.485073\pi\)
−0.888512 + 0.458853i \(0.848260\pi\)
\(740\) −4.20977 + 20.9808i −0.154754 + 0.771270i
\(741\) 0.789589 0.673695i 0.0290063 0.0247488i
\(742\) 13.9724 + 17.0544i 0.512943 + 0.626088i
\(743\) −15.4388 + 26.7408i −0.566394 + 0.981023i 0.430524 + 0.902579i \(0.358329\pi\)
−0.996918 + 0.0784444i \(0.975005\pi\)
\(744\) 1.45201 41.1988i 0.0532332 1.51042i
\(745\) −11.4706 + 6.62255i −0.420250 + 0.242631i
\(746\) −35.2548 + 28.8836i −1.29077 + 1.05751i
\(747\) 12.7877 + 22.1489i 0.467876 + 0.810385i
\(748\) 9.71482 6.63939i 0.355209 0.242760i
\(749\) 8.03177 0.293475
\(750\) −33.1933 12.5247i −1.21205 0.457338i
\(751\) 12.5919 + 7.26994i 0.459485 + 0.265284i 0.711828 0.702354i \(-0.247868\pi\)
−0.252343 + 0.967638i \(0.581201\pi\)
\(752\) −6.97530 9.15351i −0.254363 0.333794i
\(753\) 66.8876 2.43752
\(754\) −5.75893 15.9972i −0.209728 0.582584i
\(755\) −20.7345 −0.754605
\(756\) −1.97449 + 2.24391i −0.0718115 + 0.0816101i
\(757\) 13.2309 22.9165i 0.480884 0.832916i −0.518875 0.854850i \(-0.673649\pi\)
0.999759 + 0.0219342i \(0.00698243\pi\)
\(758\) −10.0618 3.79659i −0.365461 0.137898i
\(759\) 14.7871 + 52.6227i 0.536739 + 1.91008i
\(760\) 0.678553 + 0.424312i 0.0246137 + 0.0153914i
\(761\) 43.5122 25.1218i 1.57732 0.910663i 0.582083 0.813129i \(-0.302238\pi\)
0.995232 0.0975339i \(-0.0310955\pi\)
\(762\) −23.6416 + 19.3692i −0.856446 + 0.701672i
\(763\) 22.8187 13.1744i 0.826092 0.476944i
\(764\) −27.0678 + 30.7611i −0.979278 + 1.11290i
\(765\) 10.0990 + 5.83064i 0.365129 + 0.210807i
\(766\) 7.98501 6.54198i 0.288510 0.236371i
\(767\) 50.0217 + 17.7416i 1.80618 + 0.640611i
\(768\) 27.3847 27.0213i 0.988159 0.975048i
\(769\) −3.32733 1.92103i −0.119986 0.0692742i 0.438806 0.898582i \(-0.355402\pi\)
−0.558792 + 0.829308i \(0.688735\pi\)
\(770\) 13.3392 + 28.5765i 0.480712 + 1.02983i
\(771\) 47.7740 27.5824i 1.72054 0.993354i
\(772\) −10.9145 2.18998i −0.392821 0.0788190i
\(773\) 16.3563 + 28.3299i 0.588295 + 1.01896i 0.994456 + 0.105155i \(0.0335340\pi\)
−0.406161 + 0.913802i \(0.633133\pi\)
\(774\) 11.1407 29.5254i 0.400446 1.06127i
\(775\) 3.54850i 0.127466i
\(776\) 1.41231 + 0.883142i 0.0506989 + 0.0317030i
\(777\) −26.8203 15.4847i −0.962172 0.555510i
\(778\) 11.4025 1.87279i 0.408800 0.0671426i
\(779\) 1.01502i 0.0363669i
\(780\) 19.9452 + 35.7964i 0.714153 + 1.28172i
\(781\) −4.57485 + 1.28554i −0.163701 + 0.0460004i
\(782\) −16.9679 + 2.78686i −0.606771 + 0.0996580i
\(783\) −0.875790 + 1.51691i −0.0312982 + 0.0542101i
\(784\) 0.556572 + 4.33951i 0.0198776 + 0.154983i
\(785\) 46.9391 1.67533
\(786\) 65.0243 + 24.5354i 2.31934 + 0.875149i
\(787\) −9.16093 15.8672i −0.326552 0.565605i 0.655273 0.755392i \(-0.272553\pi\)
−0.981825 + 0.189787i \(0.939220\pi\)
\(788\) −22.3842 4.49136i −0.797403 0.159998i
\(789\) 38.2677 22.0939i 1.36237 0.786562i
\(790\) −43.3771 + 7.12439i −1.54329 + 0.253474i
\(791\) 12.9347 22.4035i 0.459904 0.796577i
\(792\) 18.0197 + 18.8717i 0.640301 + 0.670576i
\(793\) −7.68484 2.72564i −0.272897 0.0967903i
\(794\) 20.0289 + 24.4469i 0.710799 + 0.867587i
\(795\) −26.9677 15.5698i −0.956445 0.552204i
\(796\) −1.38142 + 1.56991i −0.0489631 + 0.0556440i
\(797\) −0.786274 1.36187i −0.0278513 0.0482398i 0.851764 0.523926i \(-0.175533\pi\)
−0.879615 + 0.475686i \(0.842200\pi\)
\(798\) −0.895928 + 0.734018i −0.0317155 + 0.0259840i
\(799\) 2.55186 + 4.41995i 0.0902783 + 0.156367i
\(800\) −2.27382 + 2.40752i −0.0803918 + 0.0851185i
\(801\) 18.9775 0.670535
\(802\) −11.5064 + 30.4945i −0.406305 + 1.07680i
\(803\) −13.0003 + 50.9854i −0.458770 + 1.79924i
\(804\) −30.3356 26.6933i −1.06985 0.941402i
\(805\) 46.0852i 1.62429i
\(806\) −19.9505 + 23.6071i −0.702726 + 0.831525i
\(807\) 38.9525i 1.37119i
\(808\) 23.4596 + 0.826812i 0.825307 + 0.0290871i
\(809\) 8.10662 + 4.68036i 0.285014 + 0.164553i 0.635691 0.771944i \(-0.280715\pi\)
−0.350677 + 0.936496i \(0.614049\pi\)
\(810\) 11.3364 30.0439i 0.398319 1.05564i
\(811\) 10.6171 0.372815 0.186408 0.982472i \(-0.440315\pi\)
0.186408 + 0.982472i \(0.440315\pi\)
\(812\) 6.06850 + 17.9758i 0.212963 + 0.630826i
\(813\) −1.54456 + 0.891751i −0.0541700 + 0.0312751i
\(814\) 12.1729 17.3993i 0.426659 0.609845i
\(815\) 10.0642 5.81055i 0.352532 0.203535i
\(816\) −13.5704 + 10.3411i −0.475058 + 0.362011i
\(817\) −0.480231 + 0.831785i −0.0168012 + 0.0291005i
\(818\) −33.4126 + 27.3744i −1.16824 + 0.957122i
\(819\) −28.0567 + 5.18559i −0.980381 + 0.181199i
\(820\) −39.2901 7.88351i −1.37207 0.275304i
\(821\) −32.7687 18.9190i −1.14363 0.660278i −0.196307 0.980543i \(-0.562895\pi\)
−0.947328 + 0.320265i \(0.896228\pi\)
\(822\) −7.37929 44.9291i −0.257382 1.56708i
\(823\) −9.47936 + 5.47291i −0.330430 + 0.190774i −0.656032 0.754733i \(-0.727766\pi\)
0.325602 + 0.945507i \(0.394433\pi\)
\(824\) −0.638487 1.20176i −0.0222428 0.0418651i
\(825\) −3.34094 3.26080i −0.116317 0.113526i
\(826\) −55.4118 20.9084i −1.92802 0.727495i
\(827\) −9.29385 −0.323179 −0.161589 0.986858i \(-0.551662\pi\)
−0.161589 + 0.986858i \(0.551662\pi\)
\(828\) −12.1963 36.1273i −0.423852 1.25551i
\(829\) 3.09454 5.35989i 0.107478 0.186157i −0.807270 0.590182i \(-0.799056\pi\)
0.914748 + 0.404025i \(0.132389\pi\)
\(830\) 30.3249 4.98066i 1.05259 0.172881i
\(831\) 28.9598 1.00460
\(832\) −28.6627 + 3.23253i −0.993701 + 0.112068i
\(833\) 1.94026i 0.0672259i
\(834\) 2.29013 + 13.9435i 0.0793008 + 0.482825i
\(835\) −24.7077 + 42.7951i −0.855046 + 1.48098i
\(836\) −0.448097 0.655660i −0.0154978 0.0226765i
\(837\) 3.18418 0.110062
\(838\) 22.1357 + 8.35240i 0.764666 + 0.288529i
\(839\) 10.3229 5.95994i 0.356387 0.205760i −0.311108 0.950375i \(-0.600700\pi\)
0.667495 + 0.744615i \(0.267367\pi\)
\(840\) −21.4543 40.3811i −0.740244 1.39328i
\(841\) −8.94085 15.4860i −0.308305 0.534000i
\(842\) −18.4299 + 3.02699i −0.635136 + 0.104317i
\(843\) 21.4994 37.2381i 0.740479 1.28255i
\(844\) −9.70179 + 48.3521i −0.333949 + 1.66435i
\(845\) 4.83637 30.3405i 0.166376 1.04374i
\(846\) −8.75455 + 7.17245i −0.300988 + 0.246594i
\(847\) −0.759685 31.2853i −0.0261031 1.07497i
\(848\) 17.4341 13.2854i 0.598690 0.456223i
\(849\) −18.5040 + 10.6833i −0.635057 + 0.366650i
\(850\) 1.13603 0.930729i 0.0389655 0.0319237i
\(851\) −26.8735 + 15.5155i −0.921213 + 0.531863i
\(852\) 6.52827 2.20390i 0.223655 0.0755044i
\(853\) 42.1903i 1.44457i 0.691596 + 0.722284i \(0.256908\pi\)
−0.691596 + 0.722284i \(0.743092\pi\)
\(854\) 8.51292 + 3.21215i 0.291306 + 0.109918i
\(855\) 0.393514 0.681586i 0.0134579 0.0233097i
\(856\) 0.281253 7.98016i 0.00961302 0.272756i
\(857\) 27.4738i 0.938486i −0.883069 0.469243i \(-0.844527\pi\)
0.883069 0.469243i \(-0.155473\pi\)
\(858\) −3.89333 40.4767i −0.132916 1.38185i
\(859\) 16.9290i 0.577611i −0.957388 0.288805i \(-0.906742\pi\)
0.957388 0.288805i \(-0.0932580\pi\)
\(860\) −28.4674 25.0494i −0.970730 0.854179i
\(861\) 28.9977 50.2255i 0.988239 1.71168i
\(862\) −17.9231 + 47.5002i −0.610463 + 1.61786i
\(863\) 9.39194i 0.319705i 0.987141 + 0.159853i \(0.0511019\pi\)
−0.987141 + 0.159853i \(0.948898\pi\)
\(864\) 2.16034 + 2.04038i 0.0734964 + 0.0694151i
\(865\) 2.77039 1.59949i 0.0941961 0.0543841i
\(866\) −5.85981 7.15236i −0.199124 0.243047i
\(867\) −28.8471 + 16.6549i −0.979699 + 0.565629i
\(868\) 22.7841 25.8929i 0.773342 0.878863i
\(869\) 42.2685 + 10.7776i 1.43386 + 0.365606i
\(870\) −16.9824 20.7284i −0.575758 0.702758i
\(871\) 5.50620 + 29.7914i 0.186570 + 1.00944i
\(872\) −12.2907 23.1334i −0.416214 0.783395i
\(873\) 0.819041 1.41862i 0.0277203 0.0480130i
\(874\) 0.188087 + 1.14518i 0.00636215 + 0.0387361i
\(875\) −14.8410 25.7054i −0.501718 0.869001i
\(876\) 15.0087 74.8011i 0.507099 2.52730i
\(877\) −14.5626 + 8.40770i −0.491743 + 0.283908i −0.725297 0.688436i \(-0.758298\pi\)
0.233554 + 0.972344i \(0.424964\pi\)
\(878\) −9.15194 + 24.2547i −0.308863 + 0.818555i
\(879\) −57.7821 −1.94894
\(880\) 28.8600 12.2528i 0.972870 0.413043i
\(881\) −13.8733 + 24.0293i −0.467404 + 0.809567i −0.999306 0.0372383i \(-0.988144\pi\)
0.531902 + 0.846806i \(0.321477\pi\)
\(882\) 4.24564 0.697317i 0.142958 0.0234799i
\(883\) 3.50680i 0.118013i 0.998258 + 0.0590066i \(0.0187933\pi\)
−0.998258 + 0.0590066i \(0.981207\pi\)
\(884\) 12.7905 + 0.195153i 0.430189 + 0.00656369i
\(885\) 83.6499 2.81186
\(886\) 3.05876 + 18.6233i 0.102761 + 0.625663i
\(887\) −24.8404 + 43.0248i −0.834058 + 1.44463i 0.0607365 + 0.998154i \(0.480655\pi\)
−0.894795 + 0.446478i \(0.852678\pi\)
\(888\) −16.3244 + 26.1057i −0.547810 + 0.876049i
\(889\) −25.5702 −0.857596
\(890\) 8.05025 21.3350i 0.269845 0.715150i
\(891\) −22.2568 + 22.8038i −0.745632 + 0.763958i
\(892\) 14.3573 + 2.88076i 0.480716 + 0.0964551i
\(893\) 0.298306 0.172227i 0.00998241 0.00576335i
\(894\) −18.8055 + 3.08867i −0.628949 + 0.103301i
\(895\) 41.6367 + 24.0390i 1.39176 + 0.803534i
\(896\) 32.0499 2.96763i 1.07071 0.0991417i
\(897\) −19.8635 + 56.0044i −0.663223 + 1.86993i
\(898\) 8.55334 + 10.4400i 0.285429 + 0.348388i
\(899\) 10.1059 17.5040i 0.337052 0.583791i
\(900\) 2.44489 + 2.15134i 0.0814963 + 0.0717115i
\(901\) −8.41840 + 4.86037i −0.280458 + 0.161922i
\(902\) 32.5832 + 22.7958i 1.08490 + 0.759016i
\(903\) 47.5258 27.4390i 1.58156 0.913113i
\(904\) −21.8066 13.6361i −0.725277 0.453529i
\(905\) −31.2031 −1.03723
\(906\) −27.9124 10.5321i −0.927328 0.349906i
\(907\) −11.6095 6.70273i −0.385486 0.222560i 0.294716 0.955585i \(-0.404775\pi\)
−0.680202 + 0.733024i \(0.738108\pi\)
\(908\) 9.42062 + 8.28953i 0.312634 + 0.275098i
\(909\) 23.0850i 0.765681i
\(910\) −6.07191 + 33.7419i −0.201282 + 1.11853i
\(911\) 13.4283i 0.444900i 0.974944 + 0.222450i \(0.0714054\pi\)
−0.974944 + 0.222450i \(0.928595\pi\)
\(912\) 0.697928 + 0.915874i 0.0231107 + 0.0303276i
\(913\) −29.5499 7.53463i −0.977958 0.249360i
\(914\) 34.7169 + 13.0996i 1.14833 + 0.433297i
\(915\) −12.8511 −0.424846
\(916\) −10.3485 + 3.49359i −0.341924 + 0.115431i
\(917\) 29.0729 + 50.3558i 0.960073 + 1.66289i
\(918\) −0.835175 1.01940i −0.0275649 0.0336451i
\(919\) 14.0213 + 24.2857i 0.462521 + 0.801110i 0.999086 0.0427490i \(-0.0136116\pi\)
−0.536565 + 0.843859i \(0.680278\pi\)
\(920\) −45.7890 1.61379i −1.50962 0.0532050i
\(921\) −22.1127 12.7668i −0.728637 0.420679i
\(922\) 36.6017 29.9871i 1.20541 0.987573i
\(923\) −4.86884 1.72687i −0.160260 0.0568406i
\(924\) 3.44157 + 45.2450i 0.113219 + 1.48845i
\(925\) 1.32514 2.29522i 0.0435704 0.0754662i
\(926\) −1.72171 10.4827i −0.0565789 0.344482i
\(927\) −1.15898 + 0.669138i −0.0380659 + 0.0219774i
\(928\) 18.0728 5.40004i 0.593268 0.177265i
\(929\) −18.3398 31.7655i −0.601710 1.04219i −0.992562 0.121739i \(-0.961153\pi\)
0.390852 0.920454i \(-0.372180\pi\)
\(930\) −17.1975 + 45.5771i −0.563927 + 1.49453i
\(931\) −0.130949 −0.00429168
\(932\) −13.2403 39.2198i −0.433702 1.28469i
\(933\) −26.1579 + 45.3068i −0.856371 + 1.48328i
\(934\) 6.76483 + 41.1879i 0.221352 + 1.34771i
\(935\) −13.3861 + 3.76154i −0.437774 + 0.123016i
\(936\) 4.16979 + 28.0580i 0.136294 + 0.917105i
\(937\) 11.2157i 0.366401i −0.983076 0.183200i \(-0.941354\pi\)
0.983076 0.183200i \(-0.0586457\pi\)
\(938\) −5.47912 33.3598i −0.178899 1.08924i
\(939\) 32.3019 + 18.6495i 1.05413 + 0.608604i
\(940\) 4.34977 + 12.8847i 0.141874 + 0.420251i
\(941\) 36.8892i 1.20255i −0.799041 0.601277i \(-0.794659\pi\)
0.799041 0.601277i \(-0.205341\pi\)
\(942\) 63.1887 + 23.8428i 2.05880 + 0.776840i
\(943\) −29.0553 50.3253i −0.946171 1.63882i
\(944\) −22.7144 + 54.3236i −0.739290 + 1.76808i
\(945\) 3.05875 1.76597i 0.0995012 0.0574471i
\(946\) 15.9159 + 34.0964i 0.517469 + 1.10857i
\(947\) −6.63580 3.83118i −0.215635 0.124497i 0.388293 0.921536i \(-0.373065\pi\)
−0.603927 + 0.797039i \(0.706398\pi\)
\(948\) −62.0124 12.4427i −2.01407 0.404120i
\(949\) −43.5140 + 37.1271i −1.41252 + 1.20520i
\(950\) −0.0628155 0.0766714i −0.00203801 0.00248755i
\(951\) −50.8922 29.3826i −1.65029 0.952797i
\(952\) −14.2655 0.502771i −0.462346 0.0162949i
\(953\) 30.1089 17.3834i 0.975323 0.563103i 0.0744683 0.997223i \(-0.476274\pi\)
0.900855 + 0.434120i \(0.142941\pi\)
\(954\) −13.6609 16.6742i −0.442288 0.539848i
\(955\) 41.9317 24.2093i 1.35688 0.783393i
\(956\) −1.83033 + 0.617906i −0.0591970 + 0.0199845i
\(957\) 7.19356 + 25.5996i 0.232535 + 0.827518i
\(958\) 3.86345 10.2390i 0.124822 0.330807i
\(959\) 19.0466 32.9896i 0.615045 1.06529i
\(960\) −40.8729 + 19.9024i −1.31917 + 0.642347i
\(961\) −5.74298 −0.185258
\(962\) 21.7200 7.81914i 0.700282 0.252099i
\(963\) −7.85272 −0.253050
\(964\) −11.3842 + 12.9376i −0.366660 + 0.416691i
\(965\) 11.3921 + 6.57721i 0.366723 + 0.211728i
\(966\) 23.4090 62.0392i 0.753173 1.99608i
\(967\) 33.1435 1.06582 0.532912 0.846171i \(-0.321098\pi\)
0.532912 + 0.846171i \(0.321098\pi\)
\(968\) −31.1108 0.340730i −0.999940 0.0109515i
\(969\) −0.255332 0.442247i −0.00820243 0.0142070i
\(970\) −1.24741 1.52257i −0.0400520 0.0488867i
\(971\) 9.34872 5.39749i 0.300015 0.173214i −0.342435 0.939542i \(-0.611252\pi\)
0.642450 + 0.766328i \(0.277918\pi\)
\(972\) 28.4396 32.3201i 0.912200 1.03667i
\(973\) −5.91101 + 10.2382i −0.189498 + 0.328221i
\(974\) −4.25931 + 3.48958i −0.136477 + 0.111813i
\(975\) −0.922396 4.99064i −0.0295403 0.159828i
\(976\) 3.48961 8.34574i 0.111700 0.267140i
\(977\) −8.44509 + 14.6273i −0.270182 + 0.467970i −0.968908 0.247420i \(-0.920417\pi\)
0.698726 + 0.715389i \(0.253751\pi\)
\(978\) 16.4997 2.70996i 0.527602 0.0866551i
\(979\) −15.8052 + 16.1936i −0.505135 + 0.517550i
\(980\) 1.01706 5.06886i 0.0324888 0.161919i
\(981\) −22.3100 + 12.8807i −0.712303 + 0.411248i
\(982\) −6.78849 + 17.9910i −0.216629 + 0.574116i
\(983\) 47.5419i 1.51635i −0.652050 0.758176i \(-0.726091\pi\)
0.652050 0.758176i \(-0.273909\pi\)
\(984\) −48.8873 30.5701i −1.55847 0.974540i
\(985\) 23.3636 + 13.4890i 0.744427 + 0.429795i
\(986\) −8.25446 + 1.35574i −0.262876 + 0.0431755i
\(987\) −19.6811 −0.626456
\(988\) 0.0131710 0.863236i 0.000419025 0.0274632i
\(989\) 54.9871i 1.74849i
\(990\) −13.0419 27.9395i −0.414497 0.887975i
\(991\) 27.0281 + 15.6047i 0.858576 + 0.495699i 0.863535 0.504289i \(-0.168245\pi\)
−0.00495908 + 0.999988i \(0.501579\pi\)
\(992\) −24.9287 23.5444i −0.791486 0.747534i
\(993\) 0.331442 0.0105180
\(994\) 5.39348 + 2.03511i 0.171071 + 0.0645496i
\(995\) 2.14000 1.23553i 0.0678427 0.0391690i
\(996\) 43.3528 + 8.69869i 1.37369 + 0.275629i
\(997\) −9.10162 + 5.25483i −0.288251 + 0.166422i −0.637153 0.770737i \(-0.719888\pi\)
0.348902 + 0.937159i \(0.386555\pi\)
\(998\) −0.729171 4.43958i −0.0230815 0.140533i
\(999\) −2.05957 1.18910i −0.0651620 0.0376213i
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 572.2.t.a.87.5 160
4.3 odd 2 inner 572.2.t.a.87.30 yes 160
11.10 odd 2 inner 572.2.t.a.87.76 yes 160
13.3 even 3 inner 572.2.t.a.263.51 yes 160
44.43 even 2 inner 572.2.t.a.87.51 yes 160
52.3 odd 6 inner 572.2.t.a.263.76 yes 160
143.120 odd 6 inner 572.2.t.a.263.30 yes 160
572.263 even 6 inner 572.2.t.a.263.5 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.t.a.87.5 160 1.1 even 1 trivial
572.2.t.a.87.30 yes 160 4.3 odd 2 inner
572.2.t.a.87.51 yes 160 44.43 even 2 inner
572.2.t.a.87.76 yes 160 11.10 odd 2 inner
572.2.t.a.263.5 yes 160 572.263 even 6 inner
572.2.t.a.263.30 yes 160 143.120 odd 6 inner
572.2.t.a.263.51 yes 160 13.3 even 3 inner
572.2.t.a.263.76 yes 160 52.3 odd 6 inner