Properties

Label 539.2.q.f.324.3
Level $539$
Weight $2$
Character 539.324
Analytic conductor $4.304$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), not 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 324.3
Character \(\chi\) \(=\) 539.324
Dual form 539.2.q.f.361.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37847 + 0.293003i) q^{2} +(-0.226135 + 2.15153i) q^{3} +(-0.0127572 - 0.00567988i) q^{4} +(1.22544 + 1.36099i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(-1.64350 - 0.349337i) q^{9} +O(q^{10})\) \(q+(1.37847 + 0.293003i) q^{2} +(-0.226135 + 2.15153i) q^{3} +(-0.0127572 - 0.00567988i) q^{4} +(1.22544 + 1.36099i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(-1.64350 - 0.349337i) q^{9} +(1.29046 + 2.23514i) q^{10} +(-0.972092 + 3.17097i) q^{11} +(0.0151053 - 0.0261631i) q^{12} +(1.43602 + 4.41961i) q^{13} +(-3.20531 + 2.32880i) q^{15} +(-2.65770 - 2.95168i) q^{16} +(-5.35068 + 1.13732i) q^{17} +(-2.16316 - 0.963102i) q^{18} +(5.29964 - 2.35955i) q^{19} +(-0.00790293 - 0.0243227i) q^{20} +(-2.26911 + 4.08626i) q^{22} +(0.359841 - 0.623263i) q^{23} +(4.10856 - 4.56301i) q^{24} +(0.172056 - 1.63701i) q^{25} +(0.684551 + 6.51307i) q^{26} +(-0.882303 + 2.71545i) q^{27} +(0.948551 - 0.689163i) q^{29} +(-5.10078 + 2.27101i) q^{30} +(0.875133 - 0.971933i) q^{31} +(0.0394969 + 0.0684106i) q^{32} +(-6.60261 - 2.80855i) q^{33} -7.70900 q^{34} +(0.0189823 + 0.0137915i) q^{36} +(-0.218960 - 2.08326i) q^{37} +(7.99676 - 1.69976i) q^{38} +(-9.83366 + 2.09021i) q^{39} +(-0.543325 - 5.16939i) q^{40} +(-0.741582 - 0.538791i) q^{41} +8.02379 q^{43} +(0.0304119 - 0.0349314i) q^{44} +(-1.53856 - 2.66487i) q^{45} +(0.678649 - 0.753716i) q^{46} +(-5.45920 + 2.43059i) q^{47} +(6.95163 - 5.05065i) q^{48} +(0.716823 - 2.20615i) q^{50} +(-1.23701 - 11.7693i) q^{51} +(0.00678326 - 0.0645384i) q^{52} +(6.78828 - 7.53915i) q^{53} +(-2.01186 + 3.48465i) q^{54} +(-5.50688 + 2.56282i) q^{55} +(3.87821 + 11.9359i) q^{57} +(1.50948 - 0.672063i) q^{58} +(7.01677 + 3.12407i) q^{59} +(0.0541182 - 0.0115032i) q^{60} +(4.19955 + 4.66407i) q^{61} +(1.49113 - 1.08337i) q^{62} +(2.48916 + 7.66083i) q^{64} +(-4.25528 + 7.37036i) q^{65} +(-8.27859 - 5.80610i) q^{66} +(7.73363 + 13.3950i) q^{67} +(0.0747196 + 0.0158821i) q^{68} +(1.25960 + 0.915151i) q^{69} +(4.29593 - 13.2215i) q^{71} +(3.19096 + 3.54392i) q^{72} +(-5.49463 - 2.44637i) q^{73} +(0.308573 - 2.93588i) q^{74} +(3.48316 + 0.740369i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(15.2991 + 3.25193i) q^{79} +(0.760344 - 7.23419i) q^{80} +(-10.2477 - 4.56258i) q^{81} +(-0.864382 - 0.959993i) q^{82} +(1.35217 - 4.16157i) q^{83} +(-8.10479 - 5.88848i) q^{85} +(11.0606 + 2.35100i) q^{86} +(1.26825 + 2.19668i) q^{87} +(7.52209 - 5.65936i) q^{88} +(7.67186 - 13.2880i) q^{89} +(-1.34005 - 4.12425i) q^{90} +(-0.00813063 + 0.00590725i) q^{92} +(1.89325 + 2.10266i) q^{93} +(-8.23752 + 1.75094i) q^{94} +(9.70568 + 4.32125i) q^{95} +(-0.156119 + 0.0695087i) q^{96} +(-0.745114 - 2.29323i) q^{97} +(2.70537 - 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37847 + 0.293003i 0.974727 + 0.207185i 0.667630 0.744494i \(-0.267309\pi\)
0.307097 + 0.951678i \(0.400642\pi\)
\(3\) −0.226135 + 2.15153i −0.130559 + 1.24219i 0.711455 + 0.702731i \(0.248036\pi\)
−0.842014 + 0.539455i \(0.818630\pi\)
\(4\) −0.0127572 0.00567988i −0.00637861 0.00283994i
\(5\) 1.22544 + 1.36099i 0.548032 + 0.608651i 0.951991 0.306126i \(-0.0990329\pi\)
−0.403959 + 0.914777i \(0.632366\pi\)
\(6\) −0.942126 + 2.89957i −0.384621 + 1.18374i
\(7\) 0 0
\(8\) −2.29616 1.66826i −0.811817 0.589819i
\(9\) −1.64350 0.349337i −0.547834 0.116446i
\(10\) 1.29046 + 2.23514i 0.408078 + 0.706812i
\(11\) −0.972092 + 3.17097i −0.293097 + 0.956083i
\(12\) 0.0151053 0.0261631i 0.00436052 0.00755264i
\(13\) 1.43602 + 4.41961i 0.398280 + 1.22578i 0.926377 + 0.376596i \(0.122906\pi\)
−0.528097 + 0.849184i \(0.677094\pi\)
\(14\) 0 0
\(15\) −3.20531 + 2.32880i −0.827609 + 0.601293i
\(16\) −2.65770 2.95168i −0.664426 0.737920i
\(17\) −5.35068 + 1.13732i −1.29773 + 0.275841i −0.804445 0.594027i \(-0.797537\pi\)
−0.493285 + 0.869868i \(0.664204\pi\)
\(18\) −2.16316 0.963102i −0.509862 0.227005i
\(19\) 5.29964 2.35955i 1.21582 0.541318i 0.304301 0.952576i \(-0.401577\pi\)
0.911519 + 0.411258i \(0.134910\pi\)
\(20\) −0.00790293 0.0243227i −0.00176715 0.00543873i
\(21\) 0 0
\(22\) −2.26911 + 4.08626i −0.483775 + 0.871194i
\(23\) 0.359841 0.623263i 0.0750321 0.129959i −0.826068 0.563570i \(-0.809427\pi\)
0.901100 + 0.433611i \(0.142761\pi\)
\(24\) 4.10856 4.56301i 0.838656 0.931421i
\(25\) 0.172056 1.63701i 0.0344113 0.327401i
\(26\) 0.684551 + 6.51307i 0.134252 + 1.27732i
\(27\) −0.882303 + 2.71545i −0.169799 + 0.522588i
\(28\) 0 0
\(29\) 0.948551 0.689163i 0.176142 0.127974i −0.496221 0.868196i \(-0.665280\pi\)
0.672363 + 0.740222i \(0.265280\pi\)
\(30\) −5.10078 + 2.27101i −0.931271 + 0.414629i
\(31\) 0.875133 0.971933i 0.157178 0.174564i −0.659412 0.751782i \(-0.729195\pi\)
0.816591 + 0.577217i \(0.195861\pi\)
\(32\) 0.0394969 + 0.0684106i 0.00698213 + 0.0120934i
\(33\) −6.60261 2.80855i −1.14937 0.488906i
\(34\) −7.70900 −1.32208
\(35\) 0 0
\(36\) 0.0189823 + 0.0137915i 0.00316372 + 0.00229858i
\(37\) −0.218960 2.08326i −0.0359968 0.342486i −0.997666 0.0682759i \(-0.978250\pi\)
0.961670 0.274210i \(-0.0884165\pi\)
\(38\) 7.99676 1.69976i 1.29725 0.275738i
\(39\) −9.83366 + 2.09021i −1.57465 + 0.334701i
\(40\) −0.543325 5.16939i −0.0859073 0.817353i
\(41\) −0.741582 0.538791i −0.115816 0.0841449i 0.528370 0.849014i \(-0.322803\pi\)
−0.644185 + 0.764869i \(0.722803\pi\)
\(42\) 0 0
\(43\) 8.02379 1.22362 0.611808 0.791006i \(-0.290442\pi\)
0.611808 + 0.791006i \(0.290442\pi\)
\(44\) 0.0304119 0.0349314i 0.00458477 0.00526610i
\(45\) −1.53856 2.66487i −0.229356 0.397256i
\(46\) 0.678649 0.753716i 0.100061 0.111129i
\(47\) −5.45920 + 2.43059i −0.796306 + 0.354538i −0.764227 0.644947i \(-0.776879\pi\)
−0.0320786 + 0.999485i \(0.510213\pi\)
\(48\) 6.95163 5.05065i 1.00338 0.728999i
\(49\) 0 0
\(50\) 0.716823 2.20615i 0.101374 0.311997i
\(51\) −1.23701 11.7693i −0.173216 1.64804i
\(52\) 0.00678326 0.0645384i 0.000940669 0.00894986i
\(53\) 6.78828 7.53915i 0.932443 1.03558i −0.0668420 0.997764i \(-0.521292\pi\)
0.999285 0.0378188i \(-0.0120410\pi\)
\(54\) −2.01186 + 3.48465i −0.273780 + 0.474201i
\(55\) −5.50688 + 2.56282i −0.742547 + 0.345570i
\(56\) 0 0
\(57\) 3.87821 + 11.9359i 0.513682 + 1.58095i
\(58\) 1.50948 0.672063i 0.198204 0.0882462i
\(59\) 7.01677 + 3.12407i 0.913505 + 0.406719i 0.809002 0.587806i \(-0.200008\pi\)
0.104503 + 0.994525i \(0.466675\pi\)
\(60\) 0.0541182 0.0115032i 0.00698663 0.00148505i
\(61\) 4.19955 + 4.66407i 0.537697 + 0.597173i 0.949371 0.314158i \(-0.101722\pi\)
−0.411674 + 0.911331i \(0.635056\pi\)
\(62\) 1.49113 1.08337i 0.189373 0.137588i
\(63\) 0 0
\(64\) 2.48916 + 7.66083i 0.311144 + 0.957604i
\(65\) −4.25528 + 7.37036i −0.527802 + 0.914180i
\(66\) −8.27859 5.80610i −1.01902 0.714681i
\(67\) 7.73363 + 13.3950i 0.944814 + 1.63647i 0.756124 + 0.654429i \(0.227091\pi\)
0.188690 + 0.982037i \(0.439576\pi\)
\(68\) 0.0747196 + 0.0158821i 0.00906108 + 0.00192599i
\(69\) 1.25960 + 0.915151i 0.151638 + 0.110171i
\(70\) 0 0
\(71\) 4.29593 13.2215i 0.509833 1.56910i −0.282659 0.959221i \(-0.591216\pi\)
0.792491 0.609883i \(-0.208784\pi\)
\(72\) 3.19096 + 3.54392i 0.376059 + 0.417655i
\(73\) −5.49463 2.44637i −0.643098 0.286326i 0.0591596 0.998249i \(-0.481158\pi\)
−0.702258 + 0.711923i \(0.747825\pi\)
\(74\) 0.308573 2.93588i 0.0358709 0.341289i
\(75\) 3.48316 + 0.740369i 0.402201 + 0.0854904i
\(76\) −0.0810106 −0.00929255
\(77\) 0 0
\(78\) −14.1679 −1.60420
\(79\) 15.2991 + 3.25193i 1.72129 + 0.365871i 0.959446 0.281891i \(-0.0909617\pi\)
0.761842 + 0.647762i \(0.224295\pi\)
\(80\) 0.760344 7.23419i 0.0850091 0.808807i
\(81\) −10.2477 4.56258i −1.13864 0.506953i
\(82\) −0.864382 0.959993i −0.0954550 0.106014i
\(83\) 1.35217 4.16157i 0.148420 0.456791i −0.849015 0.528370i \(-0.822804\pi\)
0.997435 + 0.0715783i \(0.0228036\pi\)
\(84\) 0 0
\(85\) −8.10479 5.88848i −0.879088 0.638695i
\(86\) 11.0606 + 2.35100i 1.19269 + 0.253514i
\(87\) 1.26825 + 2.19668i 0.135971 + 0.235509i
\(88\) 7.52209 5.65936i 0.801857 0.603290i
\(89\) 7.67186 13.2880i 0.813215 1.40853i −0.0973874 0.995247i \(-0.531049\pi\)
0.910602 0.413283i \(-0.135618\pi\)
\(90\) −1.34005 4.12425i −0.141254 0.434735i
\(91\) 0 0
\(92\) −0.00813063 + 0.00590725i −0.000847677 + 0.000615873i
\(93\) 1.89325 + 2.10266i 0.196320 + 0.218036i
\(94\) −8.23752 + 1.75094i −0.849635 + 0.180596i
\(95\) 9.70568 + 4.32125i 0.995782 + 0.443351i
\(96\) −0.156119 + 0.0695087i −0.0159338 + 0.00709420i
\(97\) −0.745114 2.29323i −0.0756549 0.232842i 0.906077 0.423114i \(-0.139063\pi\)
−0.981731 + 0.190272i \(0.939063\pi\)
\(98\) 0 0
\(99\) 2.70537 4.87190i 0.271900 0.489645i
\(100\) −0.0114930 + 0.0199064i −0.00114930 + 0.00199064i
\(101\) −7.95989 + 8.84035i −0.792039 + 0.879648i −0.995034 0.0995315i \(-0.968266\pi\)
0.202996 + 0.979180i \(0.434932\pi\)
\(102\) 1.74327 16.5861i 0.172610 1.64227i
\(103\) 0.0414261 + 0.394143i 0.00408183 + 0.0388360i 0.996373 0.0850905i \(-0.0271179\pi\)
−0.992291 + 0.123927i \(0.960451\pi\)
\(104\) 4.07573 12.5438i 0.399658 1.23002i
\(105\) 0 0
\(106\) 11.5665 8.40352i 1.12343 0.816222i
\(107\) −2.98670 + 1.32977i −0.288735 + 0.128553i −0.545993 0.837789i \(-0.683848\pi\)
0.257258 + 0.966343i \(0.417181\pi\)
\(108\) 0.0266791 0.0296302i 0.00256720 0.00285117i
\(109\) 1.42319 + 2.46504i 0.136317 + 0.236108i 0.926100 0.377279i \(-0.123140\pi\)
−0.789783 + 0.613387i \(0.789807\pi\)
\(110\) −8.34199 + 1.91924i −0.795378 + 0.182992i
\(111\) 4.53172 0.430132
\(112\) 0 0
\(113\) −11.7668 8.54906i −1.10692 0.804228i −0.124748 0.992188i \(-0.539812\pi\)
−0.982177 + 0.187961i \(0.939812\pi\)
\(114\) 1.84875 + 17.5896i 0.173151 + 1.64742i
\(115\) 1.28921 0.274031i 0.120220 0.0255535i
\(116\) −0.0160152 + 0.00340414i −0.00148698 + 0.000316067i
\(117\) −0.816165 7.76529i −0.0754545 0.717902i
\(118\) 8.75705 + 6.36237i 0.806152 + 0.585704i
\(119\) 0 0
\(120\) 11.2450 1.02652
\(121\) −9.11007 6.16495i −0.828188 0.560450i
\(122\) 4.42237 + 7.65977i 0.400383 + 0.693483i
\(123\) 1.32692 1.47370i 0.119644 0.132879i
\(124\) −0.0166847 + 0.00742852i −0.00149833 + 0.000667100i
\(125\) 9.84690 7.15419i 0.880734 0.639890i
\(126\) 0 0
\(127\) 1.55524 4.78655i 0.138006 0.424737i −0.858040 0.513583i \(-0.828318\pi\)
0.996045 + 0.0888458i \(0.0283178\pi\)
\(128\) 1.17007 + 11.1324i 0.103420 + 0.983979i
\(129\) −1.81446 + 17.2634i −0.159754 + 1.51996i
\(130\) −8.02532 + 8.91302i −0.703867 + 0.781724i
\(131\) −0.0900265 + 0.155930i −0.00786565 + 0.0136237i −0.869931 0.493173i \(-0.835837\pi\)
0.862066 + 0.506796i \(0.169170\pi\)
\(132\) 0.0682787 + 0.0733313i 0.00594290 + 0.00638267i
\(133\) 0 0
\(134\) 6.73581 + 20.7307i 0.581885 + 1.79086i
\(135\) −4.77689 + 2.12681i −0.411129 + 0.183047i
\(136\) 14.1834 + 6.31485i 1.21621 + 0.541494i
\(137\) −8.14206 + 1.73065i −0.695623 + 0.147859i −0.542135 0.840291i \(-0.682384\pi\)
−0.153488 + 0.988151i \(0.549051\pi\)
\(138\) 1.46818 + 1.63058i 0.124980 + 0.138804i
\(139\) −5.63172 + 4.09169i −0.477677 + 0.347052i −0.800425 0.599432i \(-0.795393\pi\)
0.322749 + 0.946485i \(0.395393\pi\)
\(140\) 0 0
\(141\) −3.99497 12.2953i −0.336438 1.03545i
\(142\) 9.79576 16.9667i 0.822042 1.42382i
\(143\) −15.4104 + 0.257299i −1.28868 + 0.0215164i
\(144\) 3.33681 + 5.77952i 0.278067 + 0.481627i
\(145\) 2.10033 + 0.446439i 0.174423 + 0.0370747i
\(146\) −6.85740 4.98219i −0.567523 0.412329i
\(147\) 0 0
\(148\) −0.00903937 + 0.0278203i −0.000743031 + 0.00228682i
\(149\) −2.15079 2.38870i −0.176200 0.195690i 0.648575 0.761150i \(-0.275365\pi\)
−0.824775 + 0.565461i \(0.808698\pi\)
\(150\) 4.58451 + 2.04115i 0.374324 + 0.166660i
\(151\) −2.32754 + 22.1450i −0.189412 + 1.80214i 0.326185 + 0.945306i \(0.394237\pi\)
−0.515597 + 0.856831i \(0.672430\pi\)
\(152\) −16.1052 3.42326i −1.30630 0.277663i
\(153\) 9.19115 0.743061
\(154\) 0 0
\(155\) 2.39521 0.192388
\(156\) 0.137322 + 0.0291888i 0.0109946 + 0.00233697i
\(157\) 1.38550 13.1822i 0.110575 1.05205i −0.788733 0.614736i \(-0.789263\pi\)
0.899308 0.437316i \(-0.144071\pi\)
\(158\) 20.1366 + 8.96540i 1.60198 + 0.713249i
\(159\) 14.6856 + 16.3101i 1.16465 + 1.29347i
\(160\) −0.0447049 + 0.137588i −0.00353423 + 0.0108773i
\(161\) 0 0
\(162\) −12.7893 9.29200i −1.00483 0.730048i
\(163\) −13.4186 2.85220i −1.05102 0.223402i −0.350154 0.936692i \(-0.613871\pi\)
−0.700869 + 0.713290i \(0.747204\pi\)
\(164\) 0.00640025 + 0.0110856i 0.000499776 + 0.000865637i
\(165\) −4.26868 12.4278i −0.332316 0.967499i
\(166\) 3.08329 5.34041i 0.239310 0.414496i
\(167\) −2.87651 8.85300i −0.222591 0.685066i −0.998527 0.0542539i \(-0.982722\pi\)
0.775936 0.630812i \(-0.217278\pi\)
\(168\) 0 0
\(169\) −6.95361 + 5.05209i −0.534893 + 0.388623i
\(170\) −9.44689 10.4918i −0.724543 0.804687i
\(171\) −9.53424 + 2.02657i −0.729102 + 0.154975i
\(172\) −0.102361 0.0455742i −0.00780497 0.00347500i
\(173\) −9.59742 + 4.27304i −0.729678 + 0.324874i −0.737732 0.675094i \(-0.764103\pi\)
0.00805375 + 0.999968i \(0.497436\pi\)
\(174\) 1.10462 + 3.39966i 0.0837409 + 0.257728i
\(175\) 0 0
\(176\) 11.9432 5.55819i 0.900254 0.418964i
\(177\) −8.30826 + 14.3903i −0.624487 + 1.08164i
\(178\) 14.4689 16.0693i 1.08449 1.20445i
\(179\) 0.870023 8.27771i 0.0650285 0.618705i −0.912671 0.408696i \(-0.865984\pi\)
0.977699 0.210010i \(-0.0673496\pi\)
\(180\) 0.00449165 + 0.0427352i 0.000334788 + 0.00318529i
\(181\) 4.57437 14.0785i 0.340010 1.04644i −0.624191 0.781272i \(-0.714571\pi\)
0.964201 0.265172i \(-0.0854286\pi\)
\(182\) 0 0
\(183\) −10.9845 + 7.98074i −0.812001 + 0.589953i
\(184\) −1.86602 + 0.830806i −0.137565 + 0.0612478i
\(185\) 2.56697 2.85091i 0.188727 0.209603i
\(186\) 1.99370 + 3.45319i 0.146185 + 0.253200i
\(187\) 1.59494 18.0724i 0.116634 1.32159i
\(188\) 0.0834496 0.00608619
\(189\) 0 0
\(190\) 12.1129 + 8.80052i 0.878760 + 0.638457i
\(191\) 1.00418 + 9.55413i 0.0726599 + 0.691313i 0.968851 + 0.247644i \(0.0796565\pi\)
−0.896191 + 0.443668i \(0.853677\pi\)
\(192\) −17.0454 + 3.62311i −1.23015 + 0.261475i
\(193\) 1.45530 0.309333i 0.104755 0.0222663i −0.155236 0.987877i \(-0.549614\pi\)
0.259991 + 0.965611i \(0.416281\pi\)
\(194\) −0.355196 3.37947i −0.0255016 0.242632i
\(195\) −14.8953 10.8221i −1.06667 0.774983i
\(196\) 0 0
\(197\) −14.0434 −1.00055 −0.500274 0.865867i \(-0.666767\pi\)
−0.500274 + 0.865867i \(0.666767\pi\)
\(198\) 5.15676 5.92310i 0.366475 0.420936i
\(199\) −2.14364 3.71290i −0.151959 0.263200i 0.779989 0.625794i \(-0.215225\pi\)
−0.931948 + 0.362593i \(0.881891\pi\)
\(200\) −3.12602 + 3.47180i −0.221043 + 0.245493i
\(201\) −30.5687 + 13.6101i −2.15615 + 0.959979i
\(202\) −13.5627 + 9.85391i −0.954271 + 0.693318i
\(203\) 0 0
\(204\) −0.0510676 + 0.157170i −0.00357545 + 0.0110041i
\(205\) −0.175475 1.66954i −0.0122557 0.116605i
\(206\) −0.0583804 + 0.555453i −0.00406756 + 0.0387002i
\(207\) −0.809128 + 0.898628i −0.0562383 + 0.0624590i
\(208\) 9.22877 15.9847i 0.639900 1.10834i
\(209\) 2.33032 + 19.0987i 0.161192 + 1.32108i
\(210\) 0 0
\(211\) −0.449704 1.38405i −0.0309589 0.0952816i 0.934383 0.356270i \(-0.115952\pi\)
−0.965342 + 0.260988i \(0.915952\pi\)
\(212\) −0.129421 + 0.0576220i −0.00888868 + 0.00395749i
\(213\) 27.4750 + 12.2327i 1.88256 + 0.838168i
\(214\) −4.50671 + 0.957931i −0.308072 + 0.0654828i
\(215\) 9.83265 + 10.9203i 0.670581 + 0.744756i
\(216\) 6.55599 4.76320i 0.446079 0.324095i
\(217\) 0 0
\(218\) 1.23957 + 3.81499i 0.0839540 + 0.258384i
\(219\) 6.50596 11.2687i 0.439632 0.761465i
\(220\) 0.0848089 0.00141601i 0.00571782 9.54673e-5i
\(221\) −12.7102 22.0147i −0.854980 1.48087i
\(222\) 6.24685 + 1.32781i 0.419261 + 0.0891166i
\(223\) −3.92893 2.85453i −0.263101 0.191154i 0.448412 0.893827i \(-0.351990\pi\)
−0.711513 + 0.702673i \(0.751990\pi\)
\(224\) 0 0
\(225\) −0.854642 + 2.63032i −0.0569761 + 0.175354i
\(226\) −13.7153 15.2323i −0.912325 1.01324i
\(227\) −0.362809 0.161533i −0.0240805 0.0107213i 0.394661 0.918827i \(-0.370862\pi\)
−0.418742 + 0.908105i \(0.637529\pi\)
\(228\) 0.0183193 0.174297i 0.00121323 0.0115431i
\(229\) 2.14178 + 0.455250i 0.141533 + 0.0300838i 0.278133 0.960542i \(-0.410284\pi\)
−0.136600 + 0.990626i \(0.543618\pi\)
\(230\) 1.85744 0.122476
\(231\) 0 0
\(232\) −3.32773 −0.218476
\(233\) 1.23262 + 0.262001i 0.0807515 + 0.0171643i 0.248110 0.968732i \(-0.420190\pi\)
−0.167359 + 0.985896i \(0.553524\pi\)
\(234\) 1.15020 10.9434i 0.0751906 0.715391i
\(235\) −9.99790 4.45135i −0.652191 0.290374i
\(236\) −0.0717701 0.0797088i −0.00467184 0.00518860i
\(237\) −10.4563 + 32.1812i −0.679210 + 2.09039i
\(238\) 0 0
\(239\) 9.02997 + 6.56066i 0.584100 + 0.424374i 0.840200 0.542277i \(-0.182438\pi\)
−0.256100 + 0.966650i \(0.582438\pi\)
\(240\) 15.3926 + 3.27181i 0.993591 + 0.211194i
\(241\) −10.7421 18.6059i −0.691962 1.19851i −0.971194 0.238290i \(-0.923413\pi\)
0.279232 0.960224i \(-0.409920\pi\)
\(242\) −10.7516 11.1675i −0.691141 0.717873i
\(243\) 7.85110 13.5985i 0.503648 0.872344i
\(244\) −0.0270832 0.0833535i −0.00173382 0.00533616i
\(245\) 0 0
\(246\) 2.26092 1.64266i 0.144151 0.104732i
\(247\) 18.0387 + 20.0340i 1.14777 + 1.27473i
\(248\) −3.63089 + 0.771769i −0.230562 + 0.0490074i
\(249\) 8.64796 + 3.85032i 0.548042 + 0.244004i
\(250\) 15.6699 6.97668i 0.991050 0.441244i
\(251\) 0.130968 + 0.403077i 0.00826660 + 0.0254420i 0.955105 0.296268i \(-0.0957423\pi\)
−0.946838 + 0.321710i \(0.895742\pi\)
\(252\) 0 0
\(253\) 1.62655 + 1.74691i 0.102260 + 0.109828i
\(254\) 3.54633 6.14243i 0.222517 0.385410i
\(255\) 14.5020 16.1061i 0.908151 1.00860i
\(256\) 0.0350308 0.333296i 0.00218943 0.0208310i
\(257\) 1.82298 + 17.3445i 0.113715 + 1.08192i 0.891384 + 0.453249i \(0.149735\pi\)
−0.777670 + 0.628673i \(0.783598\pi\)
\(258\) −7.55942 + 23.2655i −0.470629 + 1.44845i
\(259\) 0 0
\(260\) 0.0961483 0.0698558i 0.00596286 0.00433227i
\(261\) −1.79970 + 0.801276i −0.111398 + 0.0495977i
\(262\) −0.169787 + 0.188568i −0.0104895 + 0.0116498i
\(263\) −0.757596 1.31219i −0.0467153 0.0809133i 0.841722 0.539911i \(-0.181542\pi\)
−0.888438 + 0.458997i \(0.848209\pi\)
\(264\) 10.4753 + 17.4638i 0.644709 + 1.07482i
\(265\) 18.5793 1.14132
\(266\) 0 0
\(267\) 26.8548 + 19.5111i 1.64348 + 1.19406i
\(268\) −0.0225774 0.214810i −0.00137913 0.0131216i
\(269\) −1.98664 + 0.422274i −0.121128 + 0.0257465i −0.268077 0.963398i \(-0.586388\pi\)
0.146949 + 0.989144i \(0.453055\pi\)
\(270\) −7.20797 + 1.53210i −0.438663 + 0.0932407i
\(271\) 0.794880 + 7.56278i 0.0482855 + 0.459406i 0.991774 + 0.128001i \(0.0408561\pi\)
−0.943489 + 0.331405i \(0.892477\pi\)
\(272\) 17.5775 + 12.7708i 1.06579 + 0.774344i
\(273\) 0 0
\(274\) −11.7307 −0.708676
\(275\) 5.02364 + 2.13691i 0.302937 + 0.128860i
\(276\) −0.0108710 0.0188291i −0.000654358 0.00113338i
\(277\) 9.65342 10.7212i 0.580018 0.644175i −0.379710 0.925105i \(-0.623976\pi\)
0.959728 + 0.280930i \(0.0906430\pi\)
\(278\) −8.96205 + 3.99016i −0.537508 + 0.239314i
\(279\) −1.77781 + 1.29166i −0.106435 + 0.0773295i
\(280\) 0 0
\(281\) 5.48494 16.8809i 0.327204 1.00703i −0.643232 0.765672i \(-0.722407\pi\)
0.970436 0.241359i \(-0.0775933\pi\)
\(282\) −1.90441 18.1192i −0.113406 1.07898i
\(283\) −3.25461 + 30.9656i −0.193467 + 1.84071i 0.280120 + 0.959965i \(0.409626\pi\)
−0.473587 + 0.880747i \(0.657041\pi\)
\(284\) −0.129901 + 0.144269i −0.00770818 + 0.00856080i
\(285\) −11.4921 + 19.9049i −0.680733 + 1.17906i
\(286\) −21.3182 4.16062i −1.26057 0.246022i
\(287\) 0 0
\(288\) −0.0410148 0.126231i −0.00241682 0.00743821i
\(289\) 11.8060 5.25635i 0.694469 0.309197i
\(290\) 2.76444 + 1.23081i 0.162333 + 0.0722755i
\(291\) 5.10244 1.08456i 0.299110 0.0635779i
\(292\) 0.0562012 + 0.0624177i 0.00328892 + 0.00365272i
\(293\) −19.4409 + 14.1247i −1.13575 + 0.825171i −0.986522 0.163632i \(-0.947679\pi\)
−0.149229 + 0.988803i \(0.547679\pi\)
\(294\) 0 0
\(295\) 4.34679 + 13.3781i 0.253080 + 0.778901i
\(296\) −2.97266 + 5.14880i −0.172782 + 0.299268i
\(297\) −7.75292 5.43742i −0.449870 0.315511i
\(298\) −2.26491 3.92295i −0.131203 0.227250i
\(299\) 3.27132 + 0.695341i 0.189185 + 0.0402126i
\(300\) −0.0402302 0.0292290i −0.00232269 0.00168754i
\(301\) 0 0
\(302\) −9.69701 + 29.8443i −0.558000 + 1.71735i
\(303\) −17.2203 19.1251i −0.989279 1.09871i
\(304\) −21.0495 9.37184i −1.20727 0.537512i
\(305\) −1.20145 + 11.4310i −0.0687949 + 0.654540i
\(306\) 12.6697 + 2.69304i 0.724281 + 0.153951i
\(307\) 5.46298 0.311789 0.155894 0.987774i \(-0.450174\pi\)
0.155894 + 0.987774i \(0.450174\pi\)
\(308\) 0 0
\(309\) −0.857378 −0.0487745
\(310\) 3.30172 + 0.701803i 0.187525 + 0.0398597i
\(311\) 1.45174 13.8124i 0.0823204 0.783227i −0.873013 0.487697i \(-0.837837\pi\)
0.955334 0.295530i \(-0.0954962\pi\)
\(312\) 26.0667 + 11.6057i 1.47574 + 0.657041i
\(313\) −18.3667 20.3983i −1.03815 1.15298i −0.988034 0.154234i \(-0.950709\pi\)
−0.0501114 0.998744i \(-0.515958\pi\)
\(314\) 5.77229 17.7653i 0.325749 1.00255i
\(315\) 0 0
\(316\) −0.176704 0.128383i −0.00994038 0.00722211i
\(317\) −7.65469 1.62706i −0.429930 0.0913845i −0.0121365 0.999926i \(-0.503863\pi\)
−0.417794 + 0.908542i \(0.637197\pi\)
\(318\) 15.4648 + 26.7859i 0.867226 + 1.50208i
\(319\) 1.26323 + 3.67776i 0.0707275 + 0.205915i
\(320\) −7.37598 + 12.7756i −0.412330 + 0.714176i
\(321\) −2.18563 6.72669i −0.121990 0.375447i
\(322\) 0 0
\(323\) −25.6731 + 18.6526i −1.42849 + 1.03786i
\(324\) 0.104817 + 0.116412i 0.00582319 + 0.00646731i
\(325\) 7.48201 1.59035i 0.415027 0.0882168i
\(326\) −17.6614 7.86337i −0.978175 0.435512i
\(327\) −5.62544 + 2.50461i −0.311088 + 0.138505i
\(328\) 0.803950 + 2.47430i 0.0443907 + 0.136621i
\(329\) 0 0
\(330\) −2.24288 18.3820i −0.123467 1.01190i
\(331\) 14.0731 24.3753i 0.773527 1.33979i −0.162092 0.986776i \(-0.551824\pi\)
0.935619 0.353012i \(-0.114843\pi\)
\(332\) −0.0408872 + 0.0454098i −0.00224398 + 0.00249219i
\(333\) −0.367900 + 3.50034i −0.0201608 + 0.191817i
\(334\) −1.37124 13.0464i −0.0750307 0.713869i
\(335\) −8.75338 + 26.9401i −0.478248 + 1.47190i
\(336\) 0 0
\(337\) 20.2084 14.6823i 1.10082 0.799793i 0.119628 0.992819i \(-0.461830\pi\)
0.981194 + 0.193025i \(0.0618300\pi\)
\(338\) −11.0656 + 4.92674i −0.601891 + 0.267979i
\(339\) 21.0544 23.3833i 1.14352 1.27001i
\(340\) 0.0699488 + 0.121155i 0.00379350 + 0.00657054i
\(341\) 2.23126 + 3.71983i 0.120829 + 0.201440i
\(342\) −13.7365 −0.742783
\(343\) 0 0
\(344\) −18.4239 13.3858i −0.993352 0.721713i
\(345\) 0.298050 + 2.83575i 0.0160464 + 0.152672i
\(346\) −14.4818 + 3.07820i −0.778545 + 0.165485i
\(347\) −20.1980 + 4.29322i −1.08429 + 0.230472i −0.715197 0.698923i \(-0.753663\pi\)
−0.369088 + 0.929395i \(0.620330\pi\)
\(348\) −0.00370251 0.0352271i −0.000198476 0.00188837i
\(349\) −4.85185 3.52507i −0.259713 0.188693i 0.450307 0.892874i \(-0.351314\pi\)
−0.710021 + 0.704181i \(0.751314\pi\)
\(350\) 0 0
\(351\) −13.2682 −0.708206
\(352\) −0.255322 + 0.0587419i −0.0136087 + 0.00313095i
\(353\) 12.0191 + 20.8177i 0.639712 + 1.10801i 0.985496 + 0.169699i \(0.0542796\pi\)
−0.345784 + 0.938314i \(0.612387\pi\)
\(354\) −15.6691 + 17.4023i −0.832804 + 0.924922i
\(355\) 23.2587 10.3554i 1.23444 0.549609i
\(356\) −0.173346 + 0.125943i −0.00918732 + 0.00667498i
\(357\) 0 0
\(358\) 3.62470 11.1557i 0.191571 0.589596i
\(359\) 1.14460 + 10.8901i 0.0604096 + 0.574759i 0.982301 + 0.187310i \(0.0599770\pi\)
−0.921891 + 0.387449i \(0.873356\pi\)
\(360\) −0.912905 + 8.68571i −0.0481143 + 0.457777i
\(361\) 9.80520 10.8898i 0.516063 0.573146i
\(362\) 10.4307 18.0664i 0.548224 0.949551i
\(363\) 15.3242 18.2065i 0.804311 0.955593i
\(364\) 0 0
\(365\) −3.40385 10.4760i −0.178166 0.548338i
\(366\) −17.4803 + 7.78272i −0.913709 + 0.406809i
\(367\) −9.69981 4.31863i −0.506326 0.225431i 0.137644 0.990482i \(-0.456047\pi\)
−0.643970 + 0.765051i \(0.722714\pi\)
\(368\) −2.79602 + 0.594313i −0.145753 + 0.0309807i
\(369\) 1.03057 + 1.14456i 0.0536494 + 0.0595837i
\(370\) 4.37382 3.17777i 0.227384 0.165204i
\(371\) 0 0
\(372\) −0.0122097 0.0375775i −0.000633042 0.00194830i
\(373\) −18.3018 + 31.6996i −0.947631 + 1.64135i −0.197236 + 0.980356i \(0.563196\pi\)
−0.750395 + 0.660989i \(0.770137\pi\)
\(374\) 7.49386 24.4450i 0.387498 1.26402i
\(375\) 13.1657 + 22.8037i 0.679875 + 1.17758i
\(376\) 16.5901 + 3.52633i 0.855568 + 0.181857i
\(377\) 4.40797 + 3.20258i 0.227022 + 0.164941i
\(378\) 0 0
\(379\) −3.91147 + 12.0383i −0.200919 + 0.618364i 0.798938 + 0.601414i \(0.205396\pi\)
−0.999856 + 0.0169501i \(0.994604\pi\)
\(380\) −0.0992734 0.110254i −0.00509262 0.00565592i
\(381\) 9.94670 + 4.42856i 0.509585 + 0.226882i
\(382\) −1.41516 + 13.4643i −0.0724058 + 0.688895i
\(383\) −15.1299 3.21595i −0.773100 0.164328i −0.195562 0.980691i \(-0.562653\pi\)
−0.577538 + 0.816364i \(0.695987\pi\)
\(384\) −24.2164 −1.23579
\(385\) 0 0
\(386\) 2.09672 0.106720
\(387\) −13.1871 2.80301i −0.670338 0.142485i
\(388\) −0.00351966 + 0.0334873i −0.000178684 + 0.00170006i
\(389\) −11.6139 5.17082i −0.588846 0.262171i 0.0906110 0.995886i \(-0.471118\pi\)
−0.679457 + 0.733715i \(0.737785\pi\)
\(390\) −17.3618 19.2823i −0.879150 0.976395i
\(391\) −1.21654 + 3.74414i −0.0615232 + 0.189349i
\(392\) 0 0
\(393\) −0.315131 0.228956i −0.0158963 0.0115493i
\(394\) −19.3584 4.11475i −0.975261 0.207298i
\(395\) 14.3223 + 24.8070i 0.720633 + 1.24817i
\(396\) −0.0621848 + 0.0467857i −0.00312491 + 0.00235107i
\(397\) −9.47870 + 16.4176i −0.475722 + 0.823975i −0.999613 0.0278101i \(-0.991147\pi\)
0.523891 + 0.851785i \(0.324480\pi\)
\(398\) −1.86706 5.74622i −0.0935873 0.288032i
\(399\) 0 0
\(400\) −5.28919 + 3.84282i −0.264460 + 0.192141i
\(401\) −5.80945 6.45205i −0.290110 0.322200i 0.580418 0.814319i \(-0.302889\pi\)
−0.870528 + 0.492119i \(0.836223\pi\)
\(402\) −46.1259 + 9.80436i −2.30055 + 0.488997i
\(403\) 5.55228 + 2.47203i 0.276579 + 0.123141i
\(404\) 0.151758 0.0675671i 0.00755025 0.00336159i
\(405\) −6.34833 19.5381i −0.315451 0.970858i
\(406\) 0 0
\(407\) 6.81881 + 1.33081i 0.337996 + 0.0659658i
\(408\) −16.7939 + 29.0880i −0.831424 + 1.44007i
\(409\) −3.82345 + 4.24638i −0.189058 + 0.209970i −0.830221 0.557435i \(-0.811786\pi\)
0.641163 + 0.767405i \(0.278452\pi\)
\(410\) 0.247292 2.35282i 0.0122129 0.116198i
\(411\) −1.88234 17.9092i −0.0928488 0.883397i
\(412\) 0.00171020 0.00526346i 8.42556e−5 0.000259312i
\(413\) 0 0
\(414\) −1.37866 + 1.00166i −0.0677575 + 0.0492287i
\(415\) 7.32084 3.25945i 0.359366 0.160000i
\(416\) −0.245630 + 0.272800i −0.0120430 + 0.0133751i
\(417\) −7.52986 13.0421i −0.368739 0.638674i
\(418\) −2.38369 + 27.0098i −0.116590 + 1.32109i
\(419\) 27.1909 1.32836 0.664181 0.747571i \(-0.268780\pi\)
0.664181 + 0.747571i \(0.268780\pi\)
\(420\) 0 0
\(421\) 19.3881 + 14.0863i 0.944921 + 0.686525i 0.949600 0.313464i \(-0.101490\pi\)
−0.00467947 + 0.999989i \(0.501490\pi\)
\(422\) −0.214374 2.03963i −0.0104356 0.0992878i
\(423\) 9.82129 2.08758i 0.477528 0.101502i
\(424\) −28.1643 + 5.98651i −1.36778 + 0.290730i
\(425\) 0.941185 + 8.95478i 0.0456542 + 0.434370i
\(426\) 34.2893 + 24.9126i 1.66132 + 1.20702i
\(427\) 0 0
\(428\) 0.0456549 0.00220681
\(429\) 2.93124 33.2141i 0.141522 1.60359i
\(430\) 10.3544 + 17.9343i 0.499331 + 0.864867i
\(431\) 11.0227 12.2419i 0.530945 0.589674i −0.416683 0.909052i \(-0.636807\pi\)
0.947627 + 0.319378i \(0.103474\pi\)
\(432\) 10.3600 4.61258i 0.498447 0.221923i
\(433\) 16.2539 11.8092i 0.781113 0.567512i −0.124200 0.992257i \(-0.539636\pi\)
0.905313 + 0.424745i \(0.139636\pi\)
\(434\) 0 0
\(435\) −1.43548 + 4.41797i −0.0688262 + 0.211825i
\(436\) −0.00415484 0.0395306i −0.000198981 0.00189317i
\(437\) 0.436407 4.15213i 0.0208762 0.198623i
\(438\) 12.2700 13.6273i 0.586285 0.651136i
\(439\) 13.3841 23.1819i 0.638788 1.10641i −0.346912 0.937898i \(-0.612770\pi\)
0.985699 0.168515i \(-0.0538970\pi\)
\(440\) 16.9201 + 3.30226i 0.806636 + 0.157429i
\(441\) 0 0
\(442\) −11.0703 34.0708i −0.526559 1.62058i
\(443\) 23.9489 10.6627i 1.13785 0.506602i 0.250689 0.968068i \(-0.419343\pi\)
0.887158 + 0.461466i \(0.152676\pi\)
\(444\) −0.0578121 0.0257396i −0.00274364 0.00122155i
\(445\) 27.4862 5.84237i 1.30297 0.276955i
\(446\) −4.57953 5.08609i −0.216847 0.240833i
\(447\) 5.62573 4.08733i 0.266088 0.193324i
\(448\) 0 0
\(449\) 3.01211 + 9.27033i 0.142150 + 0.437494i 0.996634 0.0819851i \(-0.0261260\pi\)
−0.854483 + 0.519479i \(0.826126\pi\)
\(450\) −1.94879 + 3.37541i −0.0918669 + 0.159118i
\(451\) 2.42937 1.82778i 0.114395 0.0860667i
\(452\) 0.101554 + 0.175896i 0.00477668 + 0.00827345i
\(453\) −47.1194 10.0155i −2.21386 0.470571i
\(454\) −0.452792 0.328973i −0.0212506 0.0154395i
\(455\) 0 0
\(456\) 11.0072 33.8767i 0.515459 1.58642i
\(457\) 7.95282 + 8.83250i 0.372017 + 0.413167i 0.899863 0.436173i \(-0.143667\pi\)
−0.527845 + 0.849341i \(0.677000\pi\)
\(458\) 2.81900 + 1.25510i 0.131723 + 0.0586469i
\(459\) 1.63258 15.5329i 0.0762022 0.725016i
\(460\) −0.0180033 0.00382671i −0.000839406 0.000178421i
\(461\) −9.14737 −0.426035 −0.213018 0.977048i \(-0.568329\pi\)
−0.213018 + 0.977048i \(0.568329\pi\)
\(462\) 0 0
\(463\) 38.9342 1.80943 0.904713 0.426021i \(-0.140085\pi\)
0.904713 + 0.426021i \(0.140085\pi\)
\(464\) −4.55516 0.968228i −0.211468 0.0449489i
\(465\) −0.541640 + 5.15336i −0.0251179 + 0.238981i
\(466\) 1.62236 + 0.722322i 0.0751545 + 0.0334609i
\(467\) 13.9068 + 15.4451i 0.643531 + 0.714714i 0.973348 0.229331i \(-0.0736538\pi\)
−0.329817 + 0.944045i \(0.606987\pi\)
\(468\) −0.0336939 + 0.103699i −0.00155750 + 0.00479350i
\(469\) 0 0
\(470\) −12.4776 9.06548i −0.575547 0.418159i
\(471\) 28.0485 + 5.96190i 1.29241 + 0.274710i
\(472\) −10.8999 18.8792i −0.501708 0.868984i
\(473\) −7.79986 + 25.4432i −0.358638 + 1.16988i
\(474\) −23.8429 + 41.2971i −1.09514 + 1.89684i
\(475\) −2.95076 9.08152i −0.135390 0.416689i
\(476\) 0 0
\(477\) −13.7903 + 10.0192i −0.631413 + 0.458748i
\(478\) 10.5253 + 11.6895i 0.481414 + 0.534665i
\(479\) −24.0001 + 5.10138i −1.09659 + 0.233088i −0.720473 0.693483i \(-0.756075\pi\)
−0.376120 + 0.926571i \(0.622742\pi\)
\(480\) −0.285914 0.127297i −0.0130501 0.00581030i
\(481\) 8.89279 3.95932i 0.405476 0.180530i
\(482\) −9.35614 28.7952i −0.426161 1.31159i
\(483\) 0 0
\(484\) 0.0812030 + 0.130392i 0.00369105 + 0.00592690i
\(485\) 2.20796 3.82429i 0.100258 0.173652i
\(486\) 14.8069 16.4448i 0.671656 0.745949i
\(487\) 1.29315 12.3035i 0.0585984 0.557527i −0.925355 0.379102i \(-0.876233\pi\)
0.983953 0.178425i \(-0.0571002\pi\)
\(488\) −1.86196 17.7154i −0.0842872 0.801939i
\(489\) 9.17101 28.2255i 0.414727 1.27640i
\(490\) 0 0
\(491\) −13.3691 + 9.71320i −0.603338 + 0.438350i −0.847062 0.531494i \(-0.821631\pi\)
0.243724 + 0.969845i \(0.421631\pi\)
\(492\) −0.0252982 + 0.0112635i −0.00114053 + 0.000507798i
\(493\) −4.29159 + 4.76630i −0.193284 + 0.214663i
\(494\) 18.9958 + 32.9017i 0.854661 + 1.48032i
\(495\) 9.94585 2.28824i 0.447033 0.102849i
\(496\) −5.19468 −0.233248
\(497\) 0 0
\(498\) 10.7928 + 7.84144i 0.483638 + 0.351383i
\(499\) 1.43632 + 13.6657i 0.0642985 + 0.611760i 0.978464 + 0.206418i \(0.0661807\pi\)
−0.914165 + 0.405342i \(0.867153\pi\)
\(500\) −0.166254 + 0.0353384i −0.00743510 + 0.00158038i
\(501\) 19.6980 4.18693i 0.880041 0.187058i
\(502\) 0.0624323 + 0.594004i 0.00278649 + 0.0265117i
\(503\) −18.2812 13.2820i −0.815117 0.592217i 0.100193 0.994968i \(-0.468054\pi\)
−0.915310 + 0.402751i \(0.868054\pi\)
\(504\) 0 0
\(505\) −21.7859 −0.969461
\(506\) 1.73030 + 2.88466i 0.0769212 + 0.128239i
\(507\) −9.29728 16.1034i −0.412907 0.715175i
\(508\) −0.0470276 + 0.0522294i −0.00208651 + 0.00231731i
\(509\) 19.6080 8.73004i 0.869108 0.386952i 0.0767809 0.997048i \(-0.475536\pi\)
0.792328 + 0.610096i \(0.208869\pi\)
\(510\) 24.7098 17.9527i 1.09417 0.794958i
\(511\) 0 0
\(512\) 7.06408 21.7410i 0.312191 0.960825i
\(513\) 1.73135 + 16.4727i 0.0764411 + 0.727289i
\(514\) −2.56907 + 24.4431i −0.113317 + 1.07814i
\(515\) −0.485657 + 0.539377i −0.0214006 + 0.0237678i
\(516\) 0.121202 0.209927i 0.00533560 0.00924154i
\(517\) −2.40048 19.6737i −0.105573 0.865248i
\(518\) 0 0
\(519\) −7.02327 21.6154i −0.308287 0.948811i
\(520\) 22.0665 9.82464i 0.967680 0.430839i
\(521\) −31.7106 14.1185i −1.38927 0.618541i −0.430462 0.902609i \(-0.641649\pi\)
−0.958804 + 0.284067i \(0.908316\pi\)
\(522\) −2.71561 + 0.577220i −0.118859 + 0.0252642i
\(523\) −13.2007 14.6609i −0.577226 0.641075i 0.381849 0.924225i \(-0.375287\pi\)
−0.959076 + 0.283150i \(0.908621\pi\)
\(524\) 0.00203415 0.00147790i 8.88624e−5 6.45623e-5i
\(525\) 0 0
\(526\) −0.659847 2.03080i −0.0287707 0.0885471i
\(527\) −3.57715 + 6.19581i −0.155823 + 0.269894i
\(528\) 9.25783 + 26.9531i 0.402895 + 1.17298i
\(529\) 11.2410 + 19.4700i 0.488740 + 0.846523i
\(530\) 25.6110 + 5.44379i 1.11247 + 0.236463i
\(531\) −10.4407 7.58562i −0.453088 0.329188i
\(532\) 0 0
\(533\) 1.31632 4.05122i 0.0570162 0.175478i
\(534\) 31.3017 + 34.7641i 1.35456 + 1.50439i
\(535\) −5.46981 2.43531i −0.236480 0.105288i
\(536\) 4.58874 43.6590i 0.198203 1.88578i
\(537\) 17.6130 + 3.74376i 0.760057 + 0.161555i
\(538\) −2.86226 −0.123401
\(539\) 0 0
\(540\) 0.0730199 0.00314227
\(541\) 5.42816 + 1.15379i 0.233375 + 0.0496053i 0.323114 0.946360i \(-0.395270\pi\)
−0.0897397 + 0.995965i \(0.528603\pi\)
\(542\) −1.12020 + 10.6580i −0.0481167 + 0.457800i
\(543\) 29.2558 + 13.0255i 1.25549 + 0.558978i
\(544\) −0.289140 0.321122i −0.0123968 0.0137680i
\(545\) −1.61085 + 4.95770i −0.0690014 + 0.212364i
\(546\) 0 0
\(547\) 6.83353 + 4.96485i 0.292181 + 0.212282i 0.724213 0.689576i \(-0.242203\pi\)
−0.432032 + 0.901858i \(0.642203\pi\)
\(548\) 0.113700 + 0.0241676i 0.00485702 + 0.00103239i
\(549\) −5.27263 9.13246i −0.225030 0.389764i
\(550\) 6.29883 + 4.41761i 0.268583 + 0.188367i
\(551\) 3.40086 5.89047i 0.144882 0.250942i
\(552\) −1.36553 4.20267i −0.0581209 0.178878i
\(553\) 0 0
\(554\) 16.4483 11.9504i 0.698822 0.507724i
\(555\) 5.55333 + 6.16760i 0.235726 + 0.261800i
\(556\) 0.0950854 0.0202110i 0.00403252 0.000857139i
\(557\) −11.1302 4.95547i −0.471600 0.209970i 0.157154 0.987574i \(-0.449768\pi\)
−0.628754 + 0.777604i \(0.716435\pi\)
\(558\) −2.82913 + 1.25961i −0.119766 + 0.0533235i
\(559\) 11.5223 + 35.4620i 0.487342 + 1.49988i
\(560\) 0 0
\(561\) 38.5226 + 7.51837i 1.62643 + 0.317426i
\(562\) 12.5070 21.6628i 0.527576 0.913789i
\(563\) 18.3031 20.3276i 0.771383 0.856707i −0.221579 0.975142i \(-0.571121\pi\)
0.992962 + 0.118435i \(0.0377878\pi\)
\(564\) −0.0188709 + 0.179544i −0.000794607 + 0.00756018i
\(565\) −2.78429 26.4907i −0.117136 1.11447i
\(566\) −13.5594 + 41.7316i −0.569944 + 1.75411i
\(567\) 0 0
\(568\) −31.9211 + 23.1920i −1.33938 + 0.973115i
\(569\) 6.51836 2.90216i 0.273264 0.121665i −0.265530 0.964103i \(-0.585547\pi\)
0.538794 + 0.842438i \(0.318880\pi\)
\(570\) −21.6737 + 24.0711i −0.907812 + 1.00823i
\(571\) −16.2420 28.1319i −0.679705 1.17728i −0.975070 0.221899i \(-0.928775\pi\)
0.295365 0.955385i \(-0.404559\pi\)
\(572\) 0.198055 + 0.0842468i 0.00828110 + 0.00352253i
\(573\) −20.7831 −0.868226
\(574\) 0 0
\(575\) −0.958373 0.696299i −0.0399669 0.0290377i
\(576\) −1.41472 13.4601i −0.0589466 0.560839i
\(577\) 34.0218 7.23156i 1.41635 0.301054i 0.564755 0.825259i \(-0.308971\pi\)
0.851592 + 0.524205i \(0.175637\pi\)
\(578\) 17.8143 3.78655i 0.740978 0.157500i
\(579\) 0.336445 + 3.20106i 0.0139822 + 0.133032i
\(580\) −0.0242587 0.0176249i −0.00100729 0.000731836i
\(581\) 0 0
\(582\) 7.35135 0.304723
\(583\) 17.3076 + 28.8542i 0.716806 + 1.19502i
\(584\) 8.53540 + 14.7837i 0.353197 + 0.611756i
\(585\) 9.56829 10.6267i 0.395600 0.439359i
\(586\) −30.9373 + 13.7742i −1.27801 + 0.569006i
\(587\) −11.7105 + 8.50816i −0.483343 + 0.351169i −0.802618 0.596493i \(-0.796560\pi\)
0.319276 + 0.947662i \(0.396560\pi\)
\(588\) 0 0
\(589\) 2.34456 7.21581i 0.0966059 0.297322i
\(590\) 2.07212 + 19.7149i 0.0853078 + 0.811650i
\(591\) 3.17570 30.2147i 0.130631 1.24287i
\(592\) −5.56720 + 6.18300i −0.228810 + 0.254120i
\(593\) −7.51453 + 13.0155i −0.308585 + 0.534484i −0.978053 0.208356i \(-0.933189\pi\)
0.669468 + 0.742841i \(0.266522\pi\)
\(594\) −9.09400 9.76696i −0.373131 0.400743i
\(595\) 0 0
\(596\) 0.0138706 + 0.0426894i 0.000568163 + 0.00174863i
\(597\) 8.47316 3.77250i 0.346784 0.154398i
\(598\) 4.30569 + 1.91702i 0.176073 + 0.0783926i
\(599\) −1.72198 + 0.366019i −0.0703583 + 0.0149551i −0.242956 0.970037i \(-0.578117\pi\)
0.172598 + 0.984992i \(0.444784\pi\)
\(600\) −6.76278 7.51083i −0.276089 0.306628i
\(601\) 18.9605 13.7756i 0.773415 0.561919i −0.129581 0.991569i \(-0.541363\pi\)
0.902995 + 0.429650i \(0.141363\pi\)
\(602\) 0 0
\(603\) −8.03085 24.7164i −0.327042 1.00653i
\(604\) 0.155474 0.269289i 0.00632615 0.0109572i
\(605\) −2.77342 19.9534i −0.112755 0.811222i
\(606\) −18.1340 31.4089i −0.736642 1.27590i
\(607\) −24.7261 5.25570i −1.00360 0.213322i −0.323334 0.946285i \(-0.604804\pi\)
−0.680269 + 0.732963i \(0.738137\pi\)
\(608\) 0.370738 + 0.269357i 0.0150354 + 0.0109239i
\(609\) 0 0
\(610\) −5.00550 + 15.4053i −0.202667 + 0.623744i
\(611\) −18.5818 20.6372i −0.751739 0.834890i
\(612\) −0.117254 0.0522046i −0.00473969 0.00211025i
\(613\) −0.121352 + 1.15458i −0.00490134 + 0.0466331i −0.996699 0.0811832i \(-0.974130\pi\)
0.991798 + 0.127816i \(0.0407968\pi\)
\(614\) 7.53056 + 1.60067i 0.303909 + 0.0645978i
\(615\) 3.63174 0.146446
\(616\) 0 0
\(617\) 12.9711 0.522197 0.261098 0.965312i \(-0.415915\pi\)
0.261098 + 0.965312i \(0.415915\pi\)
\(618\) −1.18187 0.251214i −0.0475418 0.0101053i
\(619\) 4.78656 45.5411i 0.192388 1.83045i −0.292953 0.956127i \(-0.594638\pi\)
0.485342 0.874325i \(-0.338695\pi\)
\(620\) −0.0305562 0.0136045i −0.00122717 0.000546369i
\(621\) 1.37495 + 1.52704i 0.0551749 + 0.0612779i
\(622\) 6.04824 18.6146i 0.242512 0.746377i
\(623\) 0 0
\(624\) 32.3046 + 23.4707i 1.29322 + 0.939578i
\(625\) 13.7532 + 2.92334i 0.550129 + 0.116934i
\(626\) −19.3412 33.4999i −0.773029 1.33893i
\(627\) −41.6184 + 0.694879i −1.66208 + 0.0277508i
\(628\) −0.0925483 + 0.160298i −0.00369308 + 0.00639660i
\(629\) 3.54092 + 10.8978i 0.141186 + 0.434525i
\(630\) 0 0
\(631\) 10.2103 7.41824i 0.406467 0.295316i −0.365703 0.930732i \(-0.619171\pi\)
0.772170 + 0.635416i \(0.219171\pi\)
\(632\) −29.7043 32.9899i −1.18157 1.31227i
\(633\) 3.07951 0.654570i 0.122400 0.0260168i
\(634\) −10.0750 4.48570i −0.400131 0.178150i
\(635\) 8.42027 3.74895i 0.334148 0.148772i
\(636\) −0.0947088 0.291484i −0.00375545 0.0115581i
\(637\) 0 0
\(638\) 0.663738 + 5.43981i 0.0262776 + 0.215364i
\(639\) −11.6791 + 20.2288i −0.462019 + 0.800240i
\(640\) −13.7173 + 15.2346i −0.542222 + 0.602199i
\(641\) −2.92227 + 27.8036i −0.115423 + 1.09818i 0.771491 + 0.636240i \(0.219511\pi\)
−0.886914 + 0.461935i \(0.847155\pi\)
\(642\) −1.04189 9.91295i −0.0411202 0.391233i
\(643\) 15.3575 47.2657i 0.605642 1.86398i 0.113330 0.993557i \(-0.463848\pi\)
0.492313 0.870418i \(-0.336152\pi\)
\(644\) 0 0
\(645\) −25.7188 + 18.6858i −1.01268 + 0.735752i
\(646\) −40.8549 + 18.1898i −1.60741 + 0.715667i
\(647\) 7.36491 8.17956i 0.289545 0.321572i −0.580770 0.814067i \(-0.697249\pi\)
0.870315 + 0.492496i \(0.163915\pi\)
\(648\) 15.9189 + 27.5723i 0.625352 + 1.08314i
\(649\) −16.7273 + 19.2131i −0.656602 + 0.754178i
\(650\) 10.7797 0.422816
\(651\) 0 0
\(652\) 0.154983 + 0.112602i 0.00606962 + 0.00440984i
\(653\) −3.02468 28.7779i −0.118365 1.12617i −0.878945 0.476922i \(-0.841752\pi\)
0.760581 0.649244i \(-0.224914\pi\)
\(654\) −8.48838 + 1.80426i −0.331922 + 0.0705521i
\(655\) −0.322541 + 0.0685582i −0.0126027 + 0.00267879i
\(656\) 0.380567 + 3.62086i 0.0148587 + 0.141371i
\(657\) 8.17583 + 5.94009i 0.318969 + 0.231745i
\(658\) 0 0
\(659\) 10.8405 0.422288 0.211144 0.977455i \(-0.432281\pi\)
0.211144 + 0.977455i \(0.432281\pi\)
\(660\) −0.0161317 + 0.182789i −0.000627925 + 0.00711506i
\(661\) 10.1722 + 17.6187i 0.395652 + 0.685290i 0.993184 0.116555i \(-0.0371852\pi\)
−0.597532 + 0.801845i \(0.703852\pi\)
\(662\) 26.5414 29.4772i 1.03156 1.14566i
\(663\) 50.2395 22.3681i 1.95114 0.868704i
\(664\) −10.0474 + 7.29986i −0.389915 + 0.283289i
\(665\) 0 0
\(666\) −1.53275 + 4.71732i −0.0593929 + 0.182792i
\(667\) −0.0882020 0.839186i −0.00341520 0.0324934i
\(668\) −0.0135877 + 0.129278i −0.000525722 + 0.00500191i
\(669\) 7.03009 7.80770i 0.271799 0.301863i
\(670\) −19.9598 + 34.5715i −0.771116 + 1.33561i
\(671\) −18.8720 + 8.78272i −0.728544 + 0.339053i
\(672\) 0 0
\(673\) −3.73255 11.4876i −0.143879 0.442815i 0.852986 0.521934i \(-0.174789\pi\)
−0.996865 + 0.0791188i \(0.974789\pi\)
\(674\) 32.1586 14.3180i 1.23870 0.551507i
\(675\) 4.29340 + 1.91155i 0.165253 + 0.0735754i
\(676\) 0.117404 0.0249550i 0.00451554 0.000959807i
\(677\) −2.27257 2.52394i −0.0873418 0.0970029i 0.697890 0.716205i \(-0.254123\pi\)
−0.785231 + 0.619203i \(0.787456\pi\)
\(678\) 35.8743 26.0642i 1.37775 1.00099i
\(679\) 0 0
\(680\) 8.78642 + 27.0418i 0.336944 + 1.03701i
\(681\) 0.429587 0.744066i 0.0164618 0.0285127i
\(682\) 1.98581 + 5.78144i 0.0760405 + 0.221383i
\(683\) 2.37821 + 4.11919i 0.0909999 + 0.157616i 0.907932 0.419117i \(-0.137660\pi\)
−0.816932 + 0.576734i \(0.804327\pi\)
\(684\) 0.133141 + 0.0283000i 0.00509077 + 0.00108208i
\(685\) −12.3330 8.96042i −0.471218 0.342360i
\(686\) 0 0
\(687\) −1.46382 + 4.50516i −0.0558481 + 0.171883i
\(688\) −21.3249 23.6837i −0.813003 0.902931i
\(689\) 43.0683 + 19.1752i 1.64077 + 0.730518i
\(690\) −0.420032 + 3.99633i −0.0159903 + 0.152138i
\(691\) 6.48892 + 1.37926i 0.246850 + 0.0524696i 0.329675 0.944095i \(-0.393061\pi\)
−0.0828248 + 0.996564i \(0.526394\pi\)
\(692\) 0.146707 0.00557695
\(693\) 0 0
\(694\) −29.1003 −1.10463
\(695\) −12.4700 2.65059i −0.473016 0.100543i
\(696\) 0.752517 7.15972i 0.0285241 0.271388i
\(697\) 4.58074 + 2.03948i 0.173508 + 0.0772507i
\(698\) −5.65527 6.28082i −0.214055 0.237733i
\(699\) −0.842441 + 2.59277i −0.0318641 + 0.0980675i
\(700\) 0 0
\(701\) −2.45134 1.78101i −0.0925860 0.0672677i 0.540529 0.841325i \(-0.318224\pi\)
−0.633115 + 0.774058i \(0.718224\pi\)
\(702\) −18.2899 3.88764i −0.690307 0.146729i
\(703\) −6.07597 10.5239i −0.229160 0.396916i
\(704\) −26.7119 + 0.445995i −1.00674 + 0.0168091i
\(705\) 11.8381 20.5042i 0.445848 0.772232i
\(706\) 10.4683 + 32.2182i 0.393981 + 1.21255i
\(707\) 0 0
\(708\) 0.187726 0.136391i 0.00705516 0.00512587i
\(709\) −9.13835 10.1492i −0.343198 0.381160i 0.546693 0.837333i \(-0.315886\pi\)
−0.889891 + 0.456173i \(0.849220\pi\)
\(710\) 35.0956 7.45979i 1.31711 0.279961i
\(711\) −24.0081 10.6891i −0.900376 0.400873i
\(712\) −39.7838 + 17.7129i −1.49096 + 0.663818i
\(713\) −0.290862 0.895180i −0.0108928 0.0335247i
\(714\) 0 0
\(715\) −19.2346 20.6580i −0.719335 0.772566i
\(716\) −0.0581155 + 0.100659i −0.00217188 + 0.00376180i
\(717\) −16.1574 + 17.9447i −0.603411 + 0.670155i
\(718\) −1.61305 + 15.3471i −0.0601984 + 0.572749i
\(719\) −0.198634 1.88988i −0.00740781 0.0704806i 0.990193 0.139703i \(-0.0446148\pi\)
−0.997601 + 0.0692225i \(0.977948\pi\)
\(720\) −3.77680 + 11.6238i −0.140753 + 0.433193i
\(721\) 0 0
\(722\) 16.7069 12.1383i 0.621768 0.451741i
\(723\) 42.4604 18.9046i 1.57912 0.703069i
\(724\) −0.138320 + 0.153620i −0.00514063 + 0.00570924i
\(725\) −0.964960 1.67136i −0.0358377 0.0620727i
\(726\) 26.4585 20.6071i 0.981967 0.764801i
\(727\) 13.8211 0.512595 0.256298 0.966598i \(-0.417497\pi\)
0.256298 + 0.966598i \(0.417497\pi\)
\(728\) 0 0
\(729\) 0.256684 + 0.186492i 0.00950682 + 0.00690711i
\(730\) −1.62262 15.4382i −0.0600558 0.571393i
\(731\) −42.9327 + 9.12563i −1.58792 + 0.337524i
\(732\) 0.185462 0.0394212i 0.00685487 0.00145705i
\(733\) 5.05650 + 48.1094i 0.186766 + 1.77696i 0.540235 + 0.841514i \(0.318335\pi\)
−0.353469 + 0.935446i \(0.614998\pi\)
\(734\) −12.1055 8.79519i −0.446824 0.324636i
\(735\) 0 0
\(736\) 0.0568504 0.00209553
\(737\) −49.9931 + 11.5019i −1.84152 + 0.423677i
\(738\) 1.08525 + 1.87971i 0.0399487 + 0.0691931i
\(739\) 15.5292 17.2470i 0.571253 0.634440i −0.386412 0.922326i \(-0.626286\pi\)
0.957665 + 0.287886i \(0.0929524\pi\)
\(740\) −0.0489402 + 0.0217896i −0.00179908 + 0.000801001i
\(741\) −47.1829 + 34.2804i −1.73331 + 1.25932i
\(742\) 0 0
\(743\) −13.8536 + 42.6369i −0.508238 + 1.56420i 0.287019 + 0.957925i \(0.407336\pi\)
−0.795257 + 0.606272i \(0.792664\pi\)
\(744\) −0.839413 7.98648i −0.0307744 0.292799i
\(745\) 0.615322 5.85440i 0.0225437 0.214489i
\(746\) −34.5166 + 38.3346i −1.26374 + 1.40353i
\(747\) −3.67609 + 6.36717i −0.134501 + 0.232963i
\(748\) −0.122996 + 0.221495i −0.00449718 + 0.00809864i
\(749\) 0 0
\(750\) 11.4670 + 35.2919i 0.418717 + 1.28868i
\(751\) −37.6249 + 16.7517i −1.37295 + 0.611278i −0.954841 0.297118i \(-0.903975\pi\)
−0.418112 + 0.908396i \(0.637308\pi\)
\(752\) 21.6833 + 9.65401i 0.790707 + 0.352045i
\(753\) −0.896848 + 0.190631i −0.0326829 + 0.00694697i
\(754\) 5.13790 + 5.70621i 0.187111 + 0.207808i
\(755\) −32.9913 + 23.9696i −1.20068 + 0.872343i
\(756\) 0 0
\(757\) −6.76401 20.8175i −0.245842 0.756624i −0.995497 0.0947948i \(-0.969781\pi\)
0.749655 0.661829i \(-0.230219\pi\)
\(758\) −8.91910 + 15.4483i −0.323956 + 0.561109i
\(759\) −4.12636 + 3.10453i −0.149777 + 0.112687i
\(760\) −15.0769 26.1139i −0.546896 0.947251i
\(761\) −34.9349 7.42564i −1.26639 0.269179i −0.474724 0.880135i \(-0.657452\pi\)
−0.791665 + 0.610956i \(0.790785\pi\)
\(762\) 12.4137 + 9.01906i 0.449700 + 0.326726i
\(763\) 0 0
\(764\) 0.0414558 0.127588i 0.00149982 0.00461596i
\(765\) 11.2632 + 12.5090i 0.407221 + 0.452265i
\(766\) −19.9138 8.86620i −0.719516 0.320349i
\(767\) −3.73095 + 35.4976i −0.134717 + 1.28174i
\(768\) 0.709175 + 0.150740i 0.0255901 + 0.00543935i
\(769\) −5.30246 −0.191212 −0.0956058 0.995419i \(-0.530479\pi\)
−0.0956058 + 0.995419i \(0.530479\pi\)
\(770\) 0 0
\(771\) −37.7295 −1.35880
\(772\) −0.0203225 0.00431968i −0.000731423 0.000155469i
\(773\) −5.21505 + 49.6179i −0.187572 + 1.78463i 0.345356 + 0.938472i \(0.387758\pi\)
−0.532929 + 0.846160i \(0.678909\pi\)
\(774\) −17.3568 7.72773i −0.623876 0.277768i
\(775\) −1.44049 1.59983i −0.0517439 0.0574674i
\(776\) −2.11479 + 6.50867i −0.0759167 + 0.233648i
\(777\) 0 0
\(778\) −14.4943 10.5307i −0.519646 0.377545i
\(779\) −5.20142 1.10560i −0.186360 0.0396121i
\(780\) 0.128554 + 0.222663i 0.00460298 + 0.00797260i
\(781\) 37.7489 + 26.4748i 1.35076 + 0.947342i
\(782\) −2.77401 + 4.80473i −0.0991986 + 0.171817i
\(783\) 1.03448 + 3.18379i 0.0369692 + 0.113779i
\(784\) 0 0
\(785\) 19.6386 14.2683i 0.700931 0.509256i
\(786\) −0.367314 0.407944i −0.0131017 0.0145509i
\(787\) 35.0734 7.45508i 1.25023 0.265745i 0.465203 0.885204i \(-0.345981\pi\)
0.785029 + 0.619459i \(0.212648\pi\)
\(788\) 0.179154 + 0.0797646i 0.00638211 + 0.00284150i
\(789\) 2.99454 1.33326i 0.106609 0.0474652i
\(790\) 12.4744 + 38.3922i 0.443818 + 1.36593i
\(791\) 0 0
\(792\) −14.3396 + 6.67342i −0.509535 + 0.237130i
\(793\) −14.5828 + 25.2581i −0.517849 + 0.896940i
\(794\) −17.8765 + 19.8539i −0.634414 + 0.704588i
\(795\) −4.20143 + 39.9739i −0.149009 + 1.41773i
\(796\) 0.00625810 + 0.0595419i 0.000221813 + 0.00211041i
\(797\) −4.55530 + 14.0198i −0.161357 + 0.496606i −0.998749 0.0499962i \(-0.984079\pi\)
0.837392 + 0.546602i \(0.184079\pi\)
\(798\) 0 0
\(799\) 26.4460 19.2142i 0.935593 0.679748i
\(800\) 0.118784 0.0528862i 0.00419966 0.00186981i
\(801\) −17.2507 + 19.1589i −0.609524 + 0.676945i
\(802\) −6.11769 10.5962i −0.216023 0.374163i
\(803\) 13.0986 15.0452i 0.462241 0.530934i
\(804\) 0.467275 0.0164795
\(805\) 0 0
\(806\) 6.92934 + 5.03446i 0.244076 + 0.177331i
\(807\) −0.459286 4.36982i −0.0161676 0.153825i
\(808\) 33.0252 7.01973i 1.16182 0.246953i
\(809\) 26.3864 5.60859i 0.927695 0.197188i 0.280800 0.959766i \(-0.409400\pi\)
0.646895 + 0.762579i \(0.276067\pi\)
\(810\) −3.02625 28.7929i −0.106332 1.01168i
\(811\) 1.18472 + 0.860750i 0.0416012 + 0.0302250i 0.608392 0.793637i \(-0.291815\pi\)
−0.566790 + 0.823862i \(0.691815\pi\)
\(812\) 0 0
\(813\) −16.4513 −0.576972
\(814\) 9.00961 + 3.83242i 0.315787 + 0.134326i
\(815\) −12.5618 21.7577i −0.440021 0.762138i
\(816\) −31.4517 + 34.9306i −1.10103 + 1.22282i
\(817\) 42.5232 18.9325i 1.48770 0.662366i
\(818\) −6.51473 + 4.73323i −0.227782 + 0.165493i
\(819\) 0 0
\(820\) −0.00724418 + 0.0222953i −0.000252978 + 0.000778586i
\(821\) −3.20157 30.4609i −0.111736 1.06309i −0.896423 0.443200i \(-0.853843\pi\)
0.784687 0.619892i \(-0.212824\pi\)
\(822\) 2.65272 25.2389i 0.0925241 0.880308i
\(823\) −16.4163 + 18.2322i −0.572237 + 0.635534i −0.957899 0.287107i \(-0.907307\pi\)
0.385661 + 0.922640i \(0.373973\pi\)
\(824\) 0.562412 0.974126i 0.0195925 0.0339353i
\(825\) −5.73364 + 10.3253i −0.199620 + 0.359480i
\(826\) 0 0
\(827\) −2.02927 6.24545i −0.0705646 0.217176i 0.909555 0.415584i \(-0.136423\pi\)
−0.980119 + 0.198408i \(0.936423\pi\)
\(828\) 0.0154263 0.00686824i 0.000536102 0.000238688i
\(829\) 18.1286 + 8.07138i 0.629633 + 0.280331i 0.696639 0.717422i \(-0.254678\pi\)
−0.0670059 + 0.997753i \(0.521345\pi\)
\(830\) 11.0466 2.34803i 0.383433 0.0815012i
\(831\) 20.8840 + 23.1941i 0.724459 + 0.804593i
\(832\) −30.2834 + 22.0022i −1.04989 + 0.762789i
\(833\) 0 0
\(834\) −6.55832 20.1844i −0.227096 0.698930i
\(835\) 8.52382 14.7637i 0.294979 0.510918i
\(836\) 0.0787498 0.256882i 0.00272362 0.00888445i
\(837\) 1.86710 + 3.23392i 0.0645365 + 0.111781i
\(838\) 37.4819 + 7.96702i 1.29479 + 0.275216i
\(839\) −6.44019 4.67907i −0.222340 0.161539i 0.471039 0.882112i \(-0.343879\pi\)
−0.693379 + 0.720573i \(0.743879\pi\)
\(840\) 0 0
\(841\) −8.53669 + 26.2732i −0.294369 + 0.905973i
\(842\) 22.5987 + 25.0984i 0.778802 + 0.864947i
\(843\) 35.0795 + 15.6184i 1.20820 + 0.537926i
\(844\) −0.00212424 + 0.0202108i −7.31195e−5 + 0.000695686i
\(845\) −15.3970 3.27274i −0.529674 0.112586i
\(846\) 14.1500 0.486489
\(847\) 0 0
\(848\) −40.2944 −1.38372
\(849\) −65.8874 14.0048i −2.26125 0.480643i
\(850\) −1.32638 + 12.6197i −0.0454945 + 0.432851i
\(851\) −1.37721 0.613174i −0.0472102 0.0210194i
\(852\) −0.281025 0.312109i −0.00962774 0.0106927i
\(853\) −10.5292 + 32.4055i −0.360513 + 1.10954i 0.592231 + 0.805768i \(0.298247\pi\)
−0.952744 + 0.303776i \(0.901753\pi\)
\(854\) 0 0
\(855\) −14.4417 10.4925i −0.493897 0.358837i
\(856\) 9.07636 + 1.92924i 0.310223 + 0.0659400i
\(857\) 12.4269 + 21.5241i 0.424496 + 0.735249i 0.996373 0.0850904i \(-0.0271179\pi\)
−0.571877 + 0.820339i \(0.693785\pi\)
\(858\) 13.7725 44.9259i 0.470185 1.53374i
\(859\) 1.02827 1.78102i 0.0350841 0.0607675i −0.847950 0.530076i \(-0.822163\pi\)
0.883034 + 0.469308i \(0.155497\pi\)
\(860\) −0.0634115 0.195160i −0.00216231 0.00665491i
\(861\) 0 0
\(862\) 18.7814 13.6455i 0.639697 0.464767i
\(863\) −0.173623 0.192828i −0.00591020 0.00656394i 0.740182 0.672406i \(-0.234739\pi\)
−0.746093 + 0.665842i \(0.768072\pi\)
\(864\) −0.220614 + 0.0468929i −0.00750543 + 0.00159533i
\(865\) −17.5766 7.82560i −0.597621 0.266078i
\(866\) 25.8657 11.5161i 0.878951 0.391334i
\(867\) 8.63946 + 26.5895i 0.293412 + 0.903028i
\(868\) 0 0
\(869\) −25.1840 + 45.3519i −0.854307 + 1.53846i
\(870\) −3.27325 + 5.66944i −0.110974 + 0.192212i
\(871\) −48.0953 + 53.4152i −1.62965 + 1.80991i
\(872\) 0.844449 8.03440i 0.0285967 0.272079i
\(873\) 0.423488 + 4.02921i 0.0143329 + 0.136368i
\(874\) 1.81816 5.59573i 0.0615003 0.189278i
\(875\) 0 0
\(876\) −0.147003 + 0.106804i −0.00496676 + 0.00360856i
\(877\) 16.9855 7.56245i 0.573561 0.255366i −0.0993955 0.995048i \(-0.531691\pi\)
0.672956 + 0.739682i \(0.265024\pi\)
\(878\) 25.2420 28.0340i 0.851875 0.946103i
\(879\) −25.9933 45.0218i −0.876734 1.51855i
\(880\) 22.2003 + 9.44333i 0.748371 + 0.318335i
\(881\) −6.45292 −0.217404 −0.108702 0.994074i \(-0.534670\pi\)
−0.108702 + 0.994074i \(0.534670\pi\)
\(882\) 0 0
\(883\) 0.225301 + 0.163691i 0.00758198 + 0.00550863i 0.591570 0.806254i \(-0.298508\pi\)
−0.583988 + 0.811762i \(0.698508\pi\)
\(884\) 0.0371059 + 0.353039i 0.00124801 + 0.0118740i
\(885\) −29.7663 + 6.32701i −1.00058 + 0.212680i
\(886\) 36.1371 7.68118i 1.21405 0.258054i
\(887\) 3.19407 + 30.3896i 0.107246 + 1.02038i 0.907309 + 0.420465i \(0.138133\pi\)
−0.800062 + 0.599917i \(0.795200\pi\)
\(888\) −10.4056 7.56009i −0.349188 0.253700i
\(889\) 0 0
\(890\) 39.6008 1.32742
\(891\) 24.4295 28.0599i 0.818419 0.940043i
\(892\) 0.0339088 + 0.0587318i 0.00113535 + 0.00196649i
\(893\) −23.1967 + 25.7625i −0.776247 + 0.862109i
\(894\) 8.95251 3.98591i 0.299417 0.133309i
\(895\) 12.3320 8.95972i 0.412213 0.299491i
\(896\) 0 0
\(897\) −2.23581 + 6.88111i −0.0746514 + 0.229753i
\(898\) 1.43588 + 13.6615i 0.0479158 + 0.455889i
\(899\) 0.160288 1.52504i 0.00534590 0.0508628i
\(900\) 0.0258427 0.0287013i 0.000861425 0.000956709i
\(901\) −27.7475 + 48.0600i −0.924402 + 1.60111i
\(902\) 3.88437 1.80773i 0.129335 0.0601907i
\(903\) 0 0
\(904\) 12.7564 + 39.2601i 0.424271 + 1.30577i
\(905\) 24.7662 11.0266i 0.823255 0.366537i
\(906\) −62.0181 27.6122i −2.06041 0.917355i
\(907\) −31.2368 + 6.63959i −1.03720 + 0.220464i −0.694885 0.719121i \(-0.744545\pi\)
−0.342317 + 0.939585i \(0.611212\pi\)
\(908\) 0.00371094 + 0.00412142i 0.000123152 + 0.000136774i
\(909\) 16.1704 11.7484i 0.536337 0.389671i
\(910\) 0 0
\(911\) 0.865378 + 2.66336i 0.0286713 + 0.0882411i 0.964368 0.264564i \(-0.0852280\pi\)
−0.935697 + 0.352805i \(0.885228\pi\)
\(912\) 24.9238 43.1693i 0.825310 1.42948i
\(913\) 11.8818 + 8.33313i 0.393229 + 0.275786i
\(914\) 8.37479 + 14.5056i 0.277013 + 0.479801i
\(915\) −24.3225 5.16992i −0.804078 0.170912i
\(916\) −0.0247374 0.0179728i −0.000817348 0.000593838i
\(917\) 0 0
\(918\) 6.80167 20.9334i 0.224488 0.690904i
\(919\) −10.5949 11.7669i −0.349494 0.388153i 0.542608 0.839986i \(-0.317437\pi\)
−0.892102 + 0.451833i \(0.850770\pi\)
\(920\) −3.41740 1.52153i −0.112668 0.0501632i
\(921\) −1.23537 + 11.7538i −0.0407068 + 0.387300i
\(922\) −12.6094 2.68021i −0.415268 0.0882679i
\(923\) 64.6030 2.12643
\(924\) 0 0
\(925\) −3.44799 −0.113369
\(926\) 53.6697 + 11.4079i 1.76370 + 0.374885i
\(927\) 0.0696048 0.662246i 0.00228612 0.0217510i
\(928\) 0.0846109 + 0.0376712i 0.00277749 + 0.00123662i
\(929\) 18.3900 + 20.4241i 0.603355 + 0.670093i 0.965008 0.262219i \(-0.0844544\pi\)
−0.361654 + 0.932313i \(0.617788\pi\)
\(930\) −2.25659 + 6.94506i −0.0739964 + 0.227737i
\(931\) 0 0
\(932\) −0.0142366 0.0103435i −0.000466337 0.000338814i
\(933\) 29.3894 + 6.24691i 0.962166 + 0.204515i
\(934\) 14.6447 + 25.3654i 0.479189 + 0.829980i
\(935\) 26.5508 19.9759i 0.868303 0.653282i
\(936\) −11.0805 + 19.1920i −0.362177 + 0.627309i
\(937\) 3.80357 + 11.7062i 0.124257 + 0.382425i 0.993765 0.111495i \(-0.0355638\pi\)
−0.869508 + 0.493919i \(0.835564\pi\)
\(938\) 0 0
\(939\) 48.0408 34.9037i 1.56775 1.13904i
\(940\) 0.102262 + 0.113574i 0.00333543 + 0.00370437i
\(941\) 1.42823 0.303580i 0.0465590 0.00989642i −0.184573 0.982819i \(-0.559090\pi\)
0.231132 + 0.972922i \(0.425757\pi\)
\(942\) 36.9172 + 16.4366i 1.20283 + 0.535534i
\(943\) −0.602660 + 0.268322i −0.0196253 + 0.00873775i
\(944\) −9.42725 29.0141i −0.306831 0.944328i
\(945\) 0 0
\(946\) −18.2068 + 32.7873i −0.591955 + 1.06601i
\(947\) −5.53568 + 9.58807i −0.179885 + 0.311571i −0.941841 0.336059i \(-0.890906\pi\)
0.761956 + 0.647629i \(0.224239\pi\)
\(948\) 0.316179 0.351152i 0.0102690 0.0114049i
\(949\) 2.92160 27.7972i 0.0948392 0.902335i
\(950\) −1.40663 13.3832i −0.0456371 0.434208i
\(951\) 5.23165 16.1014i 0.169648 0.522123i
\(952\) 0 0
\(953\) 11.9924 8.71296i 0.388471 0.282240i −0.376358 0.926474i \(-0.622824\pi\)
0.764828 + 0.644234i \(0.222824\pi\)
\(954\) −21.9451 + 9.77061i −0.710500 + 0.316335i
\(955\) −11.7725 + 13.0747i −0.380948 + 0.423086i
\(956\) −0.0779335 0.134985i −0.00252055 0.00436572i
\(957\) −8.19846 + 1.88622i −0.265019 + 0.0609727i
\(958\) −34.5782 −1.11717
\(959\) 0 0
\(960\) −25.8191 18.7586i −0.833306 0.605432i
\(961\) 3.06159 + 29.1290i 0.0987608 + 0.939646i
\(962\) 13.4186 2.85220i 0.432632 0.0919587i
\(963\) 5.37319 1.14211i 0.173148 0.0368038i
\(964\) 0.0313604 + 0.298374i 0.00101005 + 0.00960998i
\(965\) 2.20437 + 1.60157i 0.0709612 + 0.0515563i
\(966\) 0 0
\(967\) 16.5193 0.531224 0.265612 0.964080i \(-0.414426\pi\)
0.265612 + 0.964080i \(0.414426\pi\)
\(968\) 10.6335 + 29.3537i 0.341773 + 0.943464i
\(969\) −34.3260 59.4544i −1.10271 1.90995i
\(970\) 4.16414 4.62474i 0.133702 0.148491i
\(971\) −37.2720 + 16.5946i −1.19612 + 0.532545i −0.905521 0.424301i \(-0.860520\pi\)
−0.290595 + 0.956846i \(0.593853\pi\)
\(972\) −0.177396 + 0.128886i −0.00568998 + 0.00413401i
\(973\) 0 0
\(974\) 5.38755 16.5812i 0.172628 0.531296i
\(975\) 1.72974 + 16.4574i 0.0553961 + 0.527059i
\(976\) 2.60568 24.7914i 0.0834059 0.793554i
\(977\) 32.8640 36.4992i 1.05141 1.16771i 0.0659495 0.997823i \(-0.478992\pi\)
0.985463 0.169889i \(-0.0543410\pi\)
\(978\) 20.9121 36.2209i 0.668696 1.15822i
\(979\) 34.6782 + 37.2444i 1.10832 + 1.19034i
\(980\) 0 0
\(981\) −1.47789 4.54847i −0.0471853 0.145222i
\(982\) −21.2749 + 9.47219i −0.678909 + 0.302270i
\(983\) −1.01110 0.450172i −0.0322492 0.0143583i 0.390549 0.920582i \(-0.372285\pi\)
−0.422798 + 0.906224i \(0.638952\pi\)
\(984\) −5.50534 + 1.17020i −0.175504 + 0.0373045i
\(985\) −17.2093 19.1128i −0.548333 0.608985i
\(986\) −7.31238 + 5.31275i −0.232874 + 0.169193i
\(987\) 0 0
\(988\) −0.116333 0.358036i −0.00370104 0.0113906i
\(989\) 2.88729 5.00093i 0.0918105 0.159020i
\(990\) 14.3805 0.240104i 0.457043 0.00763100i
\(991\) −20.8926 36.1870i −0.663674 1.14952i −0.979643 0.200747i \(-0.935663\pi\)
0.315969 0.948769i \(-0.397670\pi\)
\(992\) 0.101056 + 0.0214800i 0.00320852 + 0.000681991i
\(993\) 49.2618 + 35.7908i 1.56328 + 1.13579i
\(994\) 0 0
\(995\) 2.42630 7.46739i 0.0769189 0.236732i
\(996\) −0.0884546 0.0982387i −0.00280279 0.00311281i
\(997\) −40.3737 17.9755i −1.27865 0.569290i −0.348786 0.937202i \(-0.613406\pi\)
−0.929861 + 0.367912i \(0.880073\pi\)
\(998\) −2.02416 + 19.2586i −0.0640737 + 0.609620i
\(999\) 5.85018 + 1.24349i 0.185092 + 0.0393424i
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 539.2.q.f.324.3 32
7.2 even 3 539.2.f.e.148.2 16
7.3 odd 6 539.2.q.g.214.2 32
7.4 even 3 inner 539.2.q.f.214.2 32
7.5 odd 6 77.2.f.b.71.2 yes 16
7.6 odd 2 539.2.q.g.324.3 32
11.9 even 5 inner 539.2.q.f.471.2 32
21.5 even 6 693.2.m.i.379.3 16
77.5 odd 30 847.2.f.w.323.3 16
77.9 even 15 539.2.f.e.295.2 16
77.19 even 30 847.2.a.o.1.6 8
77.20 odd 10 539.2.q.g.471.2 32
77.26 odd 30 847.2.f.w.729.3 16
77.30 odd 30 5929.2.a.bs.1.6 8
77.31 odd 30 539.2.q.g.361.3 32
77.40 even 30 847.2.f.v.729.2 16
77.47 odd 30 847.2.a.p.1.3 8
77.53 even 15 inner 539.2.q.f.361.3 32
77.54 even 6 847.2.f.x.148.3 16
77.58 even 15 5929.2.a.bt.1.3 8
77.61 even 30 847.2.f.v.323.2 16
77.68 even 30 847.2.f.x.372.3 16
77.75 odd 30 77.2.f.b.64.2 16
231.47 even 30 7623.2.a.ct.1.6 8
231.152 even 30 693.2.m.i.64.3 16
231.173 odd 30 7623.2.a.cw.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.2 16 77.75 odd 30
77.2.f.b.71.2 yes 16 7.5 odd 6
539.2.f.e.148.2 16 7.2 even 3
539.2.f.e.295.2 16 77.9 even 15
539.2.q.f.214.2 32 7.4 even 3 inner
539.2.q.f.324.3 32 1.1 even 1 trivial
539.2.q.f.361.3 32 77.53 even 15 inner
539.2.q.f.471.2 32 11.9 even 5 inner
539.2.q.g.214.2 32 7.3 odd 6
539.2.q.g.324.3 32 7.6 odd 2
539.2.q.g.361.3 32 77.31 odd 30
539.2.q.g.471.2 32 77.20 odd 10
693.2.m.i.64.3 16 231.152 even 30
693.2.m.i.379.3 16 21.5 even 6
847.2.a.o.1.6 8 77.19 even 30
847.2.a.p.1.3 8 77.47 odd 30
847.2.f.v.323.2 16 77.61 even 30
847.2.f.v.729.2 16 77.40 even 30
847.2.f.w.323.3 16 77.5 odd 30
847.2.f.w.729.3 16 77.26 odd 30
847.2.f.x.148.3 16 77.54 even 6
847.2.f.x.372.3 16 77.68 even 30
5929.2.a.bs.1.6 8 77.30 odd 30
5929.2.a.bt.1.3 8 77.58 even 15
7623.2.a.ct.1.6 8 231.47 even 30
7623.2.a.cw.1.3 8 231.173 odd 30