Properties

Label 462.2.s.a.125.15
Level $462$
Weight $2$
Character 462.125
Analytic conductor $3.689$
Analytic rank $0$
Dimension $128$
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] = [462,2,Mod(125,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.s (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 125.15
Character \(\chi\) \(=\) 462.125
Dual form 462.2.s.a.377.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{2} +(1.70765 - 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.820027 + 0.595785i) q^{5} +(-0.769325 + 1.55182i) q^{6} +(-0.540692 - 2.58991i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{2} +(1.70765 - 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.820027 + 0.595785i) q^{5} +(-0.769325 + 1.55182i) q^{6} +(-0.540692 - 2.58991i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} -1.01361i q^{10} +(0.0474828 + 3.31628i) q^{11} +(-0.803249 - 1.53453i) q^{12} +(2.98650 - 4.11057i) q^{13} +(2.41309 + 1.08488i) q^{14} +(-1.22769 + 1.25498i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.55268 - 1.12809i) q^{17} +(-0.864112 + 2.87286i) q^{18} +(7.85640 + 2.55270i) q^{19} +(0.820027 + 0.595785i) q^{20} +(-1.67371 - 4.26599i) q^{21} +(-2.71084 - 1.91085i) q^{22} -5.21231i q^{23} +(1.71360 + 0.252133i) q^{24} +(-1.22760 + 3.77816i) q^{25} +(1.57010 + 4.83226i) q^{26} +(4.54952 - 2.51036i) q^{27} +(-2.29607 + 1.31456i) q^{28} +(0.520932 - 0.169261i) q^{29} +(-0.293682 - 1.73088i) q^{30} +(-2.14878 + 2.95754i) q^{31} -1.00000i q^{32} +(1.04194 + 5.64928i) q^{33} +1.91922i q^{34} +(1.98641 + 1.80166i) q^{35} +(-1.81628 - 2.38770i) q^{36} +(-1.56326 - 4.81122i) q^{37} +(-6.68305 + 4.85552i) q^{38} +(3.90889 - 7.88470i) q^{39} +(-0.964000 + 0.313222i) q^{40} +(1.10320 - 3.39530i) q^{41} +(4.43504 + 1.15343i) q^{42} -7.12586 q^{43} +(3.13930 - 1.06995i) q^{44} +(-1.73285 + 2.49877i) q^{45} +(4.21685 + 3.06372i) q^{46} +(2.60985 - 8.03230i) q^{47} +(-1.21121 + 1.23813i) q^{48} +(-6.41530 + 2.80069i) q^{49} +(-2.33503 - 3.21390i) q^{50} +(2.32458 - 2.37625i) q^{51} +(-4.83226 - 1.57010i) q^{52} +(-8.30483 + 11.4306i) q^{53} +(-0.643219 + 5.15619i) q^{54} +(-2.01473 - 2.69115i) q^{55} +(0.286099 - 2.63024i) q^{56} +(14.1556 + 2.08280i) q^{57} +(-0.169261 + 0.520932i) q^{58} +(2.84960 + 8.77015i) q^{59} +(1.57294 + 0.779795i) q^{60} +(5.06513 + 6.97155i) q^{61} +(-1.12968 - 3.47679i) q^{62} +(-4.09412 - 6.79986i) q^{63} +(0.809017 + 0.587785i) q^{64} +5.15009i q^{65} +(-5.18280 - 2.47762i) q^{66} -6.40079 q^{67} +(-1.55268 - 1.12809i) q^{68} +(-1.51021 - 8.90077i) q^{69} +(-2.62516 + 0.548050i) q^{70} +(5.17867 + 7.12783i) q^{71} +(2.99928 - 0.0659423i) q^{72} +(-2.49755 + 0.811503i) q^{73} +(4.81122 + 1.56326i) q^{74} +(-1.00162 + 6.80745i) q^{75} -8.26070i q^{76} +(8.56322 - 1.91606i) q^{77} +(4.08126 + 7.79687i) q^{78} +(-2.10051 - 1.52611i) q^{79} +(0.313222 - 0.964000i) q^{80} +(7.04161 - 5.60497i) q^{81} +(2.09841 + 2.88821i) q^{82} +(10.3171 - 7.49579i) q^{83} +(-3.54000 + 2.91006i) q^{84} +(-0.601143 + 1.85013i) q^{85} +(4.18847 - 5.76494i) q^{86} +(0.840526 - 0.439972i) q^{87} +(-0.979630 + 3.16865i) q^{88} -15.4473 q^{89} +(-1.00301 - 2.87065i) q^{90} +(-12.2608 - 5.51223i) q^{91} +(-4.95720 + 1.61069i) q^{92} +(-2.81243 + 5.67300i) q^{93} +(4.96423 + 6.83268i) q^{94} +(-7.96332 + 2.58744i) q^{95} +(-0.289739 - 1.70765i) q^{96} +(-6.74995 + 9.29051i) q^{97} +(1.50502 - 6.83629i) q^{98} +(3.41608 + 9.34507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.809017i −0.415627 + 0.572061i
\(3\) 1.70765 0.289739i 0.985909 0.167281i
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) −0.820027 + 0.595785i −0.366727 + 0.266443i −0.755853 0.654742i \(-0.772777\pi\)
0.389125 + 0.921185i \(0.372777\pi\)
\(6\) −0.769325 + 1.55182i −0.314076 + 0.633527i
\(7\) −0.540692 2.58991i −0.204362 0.978895i
\(8\) 0.951057 + 0.309017i 0.336249 + 0.109254i
\(9\) 2.83210 0.989542i 0.944034 0.329847i
\(10\) 1.01361i 0.320531i
\(11\) 0.0474828 + 3.31628i 0.0143166 + 0.999898i
\(12\) −0.803249 1.53453i −0.231878 0.442981i
\(13\) 2.98650 4.11057i 0.828307 1.14007i −0.159929 0.987128i \(-0.551127\pi\)
0.988236 0.152938i \(-0.0488734\pi\)
\(14\) 2.41309 + 1.08488i 0.644927 + 0.289947i
\(15\) −1.22769 + 1.25498i −0.316989 + 0.324035i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 1.55268 1.12809i 0.376581 0.273602i −0.383354 0.923602i \(-0.625231\pi\)
0.759934 + 0.650000i \(0.225231\pi\)
\(18\) −0.864112 + 2.87286i −0.203673 + 0.677139i
\(19\) 7.85640 + 2.55270i 1.80238 + 0.585629i 0.999938 0.0111001i \(-0.00353335\pi\)
0.802443 + 0.596729i \(0.203533\pi\)
\(20\) 0.820027 + 0.595785i 0.183364 + 0.133221i
\(21\) −1.67371 4.26599i −0.365233 0.930916i
\(22\) −2.71084 1.91085i −0.577953 0.407394i
\(23\) 5.21231i 1.08684i −0.839461 0.543421i \(-0.817129\pi\)
0.839461 0.543421i \(-0.182871\pi\)
\(24\) 1.71360 + 0.252133i 0.349787 + 0.0514665i
\(25\) −1.22760 + 3.77816i −0.245520 + 0.755633i
\(26\) 1.57010 + 4.83226i 0.307921 + 0.947685i
\(27\) 4.54952 2.51036i 0.875555 0.483118i
\(28\) −2.29607 + 1.31456i −0.433917 + 0.248428i
\(29\) 0.520932 0.169261i 0.0967347 0.0314310i −0.260250 0.965541i \(-0.583805\pi\)
0.356984 + 0.934110i \(0.383805\pi\)
\(30\) −0.293682 1.73088i −0.0536187 0.316015i
\(31\) −2.14878 + 2.95754i −0.385931 + 0.531189i −0.957144 0.289613i \(-0.906473\pi\)
0.571212 + 0.820802i \(0.306473\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.04194 + 5.64928i 0.181378 + 0.983413i
\(34\) 1.91922i 0.329144i
\(35\) 1.98641 + 1.80166i 0.335765 + 0.304537i
\(36\) −1.81628 2.38770i −0.302713 0.397951i
\(37\) −1.56326 4.81122i −0.256998 0.790959i −0.993429 0.114447i \(-0.963491\pi\)
0.736431 0.676512i \(-0.236509\pi\)
\(38\) −6.68305 + 4.85552i −1.08413 + 0.787669i
\(39\) 3.90889 7.88470i 0.625924 1.26256i
\(40\) −0.964000 + 0.313222i −0.152422 + 0.0495248i
\(41\) 1.10320 3.39530i 0.172291 0.530256i −0.827209 0.561895i \(-0.810073\pi\)
0.999499 + 0.0316386i \(0.0100726\pi\)
\(42\) 4.43504 + 1.15343i 0.684342 + 0.177978i
\(43\) −7.12586 −1.08668 −0.543341 0.839512i \(-0.682841\pi\)
−0.543341 + 0.839512i \(0.682841\pi\)
\(44\) 3.13930 1.06995i 0.473267 0.161301i
\(45\) −1.73285 + 2.49877i −0.258318 + 0.372495i
\(46\) 4.21685 + 3.06372i 0.621740 + 0.451721i
\(47\) 2.60985 8.03230i 0.380686 1.17163i −0.558876 0.829252i \(-0.688767\pi\)
0.939562 0.342380i \(-0.111233\pi\)
\(48\) −1.21121 + 1.23813i −0.174823 + 0.178709i
\(49\) −6.41530 + 2.80069i −0.916472 + 0.400099i
\(50\) −2.33503 3.21390i −0.330224 0.454514i
\(51\) 2.32458 2.37625i 0.325506 0.332741i
\(52\) −4.83226 1.57010i −0.670114 0.217733i
\(53\) −8.30483 + 11.4306i −1.14076 + 1.57012i −0.374949 + 0.927045i \(0.622340\pi\)
−0.765807 + 0.643070i \(0.777660\pi\)
\(54\) −0.643219 + 5.15619i −0.0875310 + 0.701668i
\(55\) −2.01473 2.69115i −0.271666 0.362875i
\(56\) 0.286099 2.63024i 0.0382316 0.351480i
\(57\) 14.1556 + 2.08280i 1.87495 + 0.275874i
\(58\) −0.169261 + 0.520932i −0.0222251 + 0.0684018i
\(59\) 2.84960 + 8.77015i 0.370986 + 1.14178i 0.946147 + 0.323737i \(0.104939\pi\)
−0.575162 + 0.818040i \(0.695061\pi\)
\(60\) 1.57294 + 0.779795i 0.203065 + 0.100671i
\(61\) 5.06513 + 6.97155i 0.648523 + 0.892616i 0.999034 0.0439430i \(-0.0139920\pi\)
−0.350511 + 0.936559i \(0.613992\pi\)
\(62\) −1.12968 3.47679i −0.143469 0.441553i
\(63\) −4.09412 6.79986i −0.515811 0.856702i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) 5.15009i 0.638790i
\(66\) −5.18280 2.47762i −0.637959 0.304973i
\(67\) −6.40079 −0.781980 −0.390990 0.920395i \(-0.627867\pi\)
−0.390990 + 0.920395i \(0.627867\pi\)
\(68\) −1.55268 1.12809i −0.188290 0.136801i
\(69\) −1.51021 8.90077i −0.181808 1.07153i
\(70\) −2.62516 + 0.548050i −0.313767 + 0.0655045i
\(71\) 5.17867 + 7.12783i 0.614595 + 0.845918i 0.996946 0.0780994i \(-0.0248852\pi\)
−0.382350 + 0.924018i \(0.624885\pi\)
\(72\) 2.99928 0.0659423i 0.353468 0.00777138i
\(73\) −2.49755 + 0.811503i −0.292316 + 0.0949792i −0.451504 0.892269i \(-0.649112\pi\)
0.159188 + 0.987248i \(0.449112\pi\)
\(74\) 4.81122 + 1.56326i 0.559292 + 0.181725i
\(75\) −1.00162 + 6.80745i −0.115658 + 0.786056i
\(76\) 8.26070i 0.947568i
\(77\) 8.56322 1.91606i 0.975869 0.218356i
\(78\) 4.08126 + 7.79687i 0.462112 + 0.882822i
\(79\) −2.10051 1.52611i −0.236326 0.171701i 0.463319 0.886192i \(-0.346658\pi\)
−0.699645 + 0.714491i \(0.746658\pi\)
\(80\) 0.313222 0.964000i 0.0350193 0.107778i
\(81\) 7.04161 5.60497i 0.782402 0.622774i
\(82\) 2.09841 + 2.88821i 0.231730 + 0.318950i
\(83\) 10.3171 7.49579i 1.13245 0.822770i 0.146396 0.989226i \(-0.453232\pi\)
0.986049 + 0.166456i \(0.0532325\pi\)
\(84\) −3.54000 + 2.91006i −0.386245 + 0.317513i
\(85\) −0.601143 + 1.85013i −0.0652031 + 0.200675i
\(86\) 4.18847 5.76494i 0.451655 0.621649i
\(87\) 0.840526 0.439972i 0.0901138 0.0471700i
\(88\) −0.979630 + 3.16865i −0.104429 + 0.337779i
\(89\) −15.4473 −1.63741 −0.818704 0.574215i \(-0.805307\pi\)
−0.818704 + 0.574215i \(0.805307\pi\)
\(90\) −1.00301 2.87065i −0.105726 0.302593i
\(91\) −12.2608 5.51223i −1.28528 0.577839i
\(92\) −4.95720 + 1.61069i −0.516824 + 0.167926i
\(93\) −2.81243 + 5.67300i −0.291636 + 0.588263i
\(94\) 4.96423 + 6.83268i 0.512022 + 0.704737i
\(95\) −7.96332 + 2.58744i −0.817019 + 0.265466i
\(96\) −0.289739 1.70765i −0.0295713 0.174286i
\(97\) −6.74995 + 9.29051i −0.685354 + 0.943308i −0.999983 0.00590636i \(-0.998120\pi\)
0.314629 + 0.949215i \(0.398120\pi\)
\(98\) 1.50502 6.83629i 0.152030 0.690570i
\(99\) 3.41608 + 9.34507i 0.343329 + 0.939215i
\(100\) 3.97260 0.397260
\(101\) −7.40043 5.37673i −0.736371 0.535005i 0.155202 0.987883i \(-0.450397\pi\)
−0.891572 + 0.452878i \(0.850397\pi\)
\(102\) 0.556073 + 3.27735i 0.0550594 + 0.324506i
\(103\) −8.10663 + 2.63400i −0.798770 + 0.259536i −0.679834 0.733366i \(-0.737948\pi\)
−0.118936 + 0.992902i \(0.537948\pi\)
\(104\) 4.11057 2.98650i 0.403074 0.292851i
\(105\) 3.91410 + 2.50106i 0.381977 + 0.244079i
\(106\) −4.36611 13.4375i −0.424074 1.30516i
\(107\) −1.69523 0.550812i −0.163884 0.0532490i 0.225926 0.974144i \(-0.427459\pi\)
−0.389810 + 0.920895i \(0.627459\pi\)
\(108\) −3.79337 3.55111i −0.365017 0.341705i
\(109\) 10.1884 0.975876 0.487938 0.872878i \(-0.337749\pi\)
0.487938 + 0.872878i \(0.337749\pi\)
\(110\) 3.36142 0.0481290i 0.320499 0.00458892i
\(111\) −4.06349 7.76291i −0.385689 0.736823i
\(112\) 1.95974 + 1.77747i 0.185178 + 0.167955i
\(113\) −7.61373 2.47385i −0.716240 0.232720i −0.0718476 0.997416i \(-0.522890\pi\)
−0.644392 + 0.764695i \(0.722890\pi\)
\(114\) −10.0054 + 10.2278i −0.937096 + 0.957925i
\(115\) 3.10541 + 4.27423i 0.289581 + 0.398574i
\(116\) −0.321954 0.443131i −0.0298927 0.0411437i
\(117\) 4.39050 14.5968i 0.405902 1.34948i
\(118\) −8.77015 2.84960i −0.807358 0.262327i
\(119\) −3.76118 3.41136i −0.344787 0.312719i
\(120\) −1.55542 + 0.814181i −0.141989 + 0.0743242i
\(121\) −10.9955 + 0.314933i −0.999590 + 0.0286303i
\(122\) −8.61731 −0.780175
\(123\) 0.900123 6.11760i 0.0811613 0.551606i
\(124\) 3.47679 + 1.12968i 0.312225 + 0.101448i
\(125\) −2.81042 8.64958i −0.251372 0.773642i
\(126\) 7.90767 + 0.684645i 0.704471 + 0.0609930i
\(127\) 0.806567 0.586005i 0.0715712 0.0519996i −0.551424 0.834225i \(-0.685915\pi\)
0.622996 + 0.782225i \(0.285915\pi\)
\(128\) −0.951057 + 0.309017i −0.0840623 + 0.0273135i
\(129\) −12.1684 + 2.06464i −1.07137 + 0.181781i
\(130\) −4.16651 3.02715i −0.365427 0.265498i
\(131\) −8.06675 −0.704795 −0.352398 0.935850i \(-0.614634\pi\)
−0.352398 + 0.935850i \(0.614634\pi\)
\(132\) 5.05081 2.73667i 0.439616 0.238196i
\(133\) 2.36338 21.7276i 0.204931 1.88402i
\(134\) 3.76229 5.17834i 0.325012 0.447341i
\(135\) −2.23510 + 4.76909i −0.192366 + 0.410458i
\(136\) 1.82529 0.593072i 0.156517 0.0508555i
\(137\) −10.2262 14.0751i −0.873679 1.20252i −0.978132 0.207986i \(-0.933309\pi\)
0.104453 0.994530i \(-0.466691\pi\)
\(138\) 8.08855 + 4.00996i 0.688543 + 0.341350i
\(139\) 0.461104 0.149822i 0.0391103 0.0127077i −0.289396 0.957209i \(-0.593455\pi\)
0.328507 + 0.944502i \(0.393455\pi\)
\(140\) 1.09965 2.44594i 0.0929373 0.206719i
\(141\) 2.12943 14.4725i 0.179331 1.21880i
\(142\) −8.81049 −0.739360
\(143\) 13.7736 + 9.70891i 1.15181 + 0.811900i
\(144\) −1.70958 + 2.46522i −0.142465 + 0.205435i
\(145\) −0.326335 + 0.449162i −0.0271007 + 0.0373009i
\(146\) 0.811503 2.49755i 0.0671604 0.206699i
\(147\) −10.1436 + 6.64135i −0.836630 + 0.547769i
\(148\) −4.09266 + 2.97349i −0.336415 + 0.244420i
\(149\) −3.35397 4.61635i −0.274768 0.378186i 0.649224 0.760597i \(-0.275094\pi\)
−0.923992 + 0.382411i \(0.875094\pi\)
\(150\) −4.91860 4.81165i −0.401602 0.392869i
\(151\) −1.86872 + 5.75134i −0.152075 + 0.468037i −0.997853 0.0654974i \(-0.979137\pi\)
0.845778 + 0.533535i \(0.179137\pi\)
\(152\) 6.68305 + 4.85552i 0.542067 + 0.393835i
\(153\) 3.28106 4.73131i 0.265258 0.382504i
\(154\) −3.48320 + 8.05402i −0.280685 + 0.649012i
\(155\) 3.70547i 0.297630i
\(156\) −8.70671 1.28107i −0.697094 0.102568i
\(157\) 5.65240 + 1.83658i 0.451111 + 0.146575i 0.525756 0.850635i \(-0.323782\pi\)
−0.0746453 + 0.997210i \(0.523782\pi\)
\(158\) 2.46930 0.802325i 0.196447 0.0638295i
\(159\) −10.8698 + 21.9257i −0.862032 + 1.73882i
\(160\) 0.595785 + 0.820027i 0.0471009 + 0.0648288i
\(161\) −13.4994 + 2.81825i −1.06390 + 0.222109i
\(162\) 0.395558 + 8.99130i 0.0310780 + 0.706423i
\(163\) 13.8289 + 10.0473i 1.08316 + 0.786964i 0.978232 0.207516i \(-0.0665379\pi\)
0.104931 + 0.994480i \(0.466538\pi\)
\(164\) −3.57003 −0.278772
\(165\) −4.22017 4.01179i −0.328540 0.312317i
\(166\) 12.7526i 0.989793i
\(167\) 7.95802 + 5.78184i 0.615810 + 0.447412i 0.851455 0.524427i \(-0.175720\pi\)
−0.235645 + 0.971839i \(0.575720\pi\)
\(168\) −0.273526 4.57441i −0.0211030 0.352923i
\(169\) −3.96035 12.1887i −0.304642 0.937592i
\(170\) −1.14344 1.57381i −0.0876980 0.120706i
\(171\) 24.7761 0.544730i 1.89468 0.0416565i
\(172\) 2.20201 + 6.77709i 0.167902 + 0.516748i
\(173\) −6.64471 + 20.4503i −0.505188 + 1.55481i 0.295267 + 0.955415i \(0.404591\pi\)
−0.800455 + 0.599393i \(0.795409\pi\)
\(174\) −0.138104 + 0.938609i −0.0104696 + 0.0711558i
\(175\) 10.4489 + 1.13656i 0.789860 + 0.0859155i
\(176\) −1.98768 2.65502i −0.149827 0.200130i
\(177\) 7.40715 + 14.1507i 0.556755 + 1.06363i
\(178\) 9.07969 12.4971i 0.680551 0.936698i
\(179\) 16.9761 + 5.51588i 1.26886 + 0.412276i 0.864642 0.502389i \(-0.167545\pi\)
0.404213 + 0.914665i \(0.367545\pi\)
\(180\) 2.91196 + 0.875872i 0.217044 + 0.0652837i
\(181\) −4.72552 6.50411i −0.351245 0.483447i 0.596439 0.802659i \(-0.296582\pi\)
−0.947683 + 0.319212i \(0.896582\pi\)
\(182\) 11.6662 6.67918i 0.864756 0.495094i
\(183\) 10.6694 + 10.4374i 0.788703 + 0.771553i
\(184\) 1.61069 4.95720i 0.118742 0.365450i
\(185\) 4.14836 + 3.01396i 0.304994 + 0.221591i
\(186\) −2.93645 5.60981i −0.215311 0.411332i
\(187\) 3.81479 + 5.09557i 0.278965 + 0.372625i
\(188\) −8.44566 −0.615963
\(189\) −8.96149 10.4255i −0.651853 0.758346i
\(190\) 2.58744 7.96332i 0.187713 0.577720i
\(191\) 9.23017 2.99906i 0.667872 0.217005i 0.0445940 0.999005i \(-0.485801\pi\)
0.623278 + 0.782000i \(0.285801\pi\)
\(192\) 1.55182 + 0.769325i 0.111993 + 0.0555212i
\(193\) 2.82361 2.05147i 0.203248 0.147668i −0.481505 0.876443i \(-0.659910\pi\)
0.684754 + 0.728775i \(0.259910\pi\)
\(194\) −3.54866 10.9216i −0.254779 0.784129i
\(195\) 1.49218 + 8.79452i 0.106857 + 0.629789i
\(196\) 4.64605 + 5.23586i 0.331861 + 0.373990i
\(197\) 9.98859i 0.711658i 0.934551 + 0.355829i \(0.115801\pi\)
−0.934551 + 0.355829i \(0.884199\pi\)
\(198\) −9.56824 2.72923i −0.679986 0.193958i
\(199\) 8.94584i 0.634154i 0.948400 + 0.317077i \(0.102701\pi\)
−0.948400 + 0.317077i \(0.897299\pi\)
\(200\) −2.33503 + 3.21390i −0.165112 + 0.227257i
\(201\) −10.9303 + 1.85456i −0.770962 + 0.130810i
\(202\) 8.69973 2.82671i 0.612111 0.198887i
\(203\) −0.720036 1.25765i −0.0505366 0.0882698i
\(204\) −2.97828 1.47650i −0.208521 0.103376i
\(205\) 1.11821 + 3.44150i 0.0780994 + 0.240365i
\(206\) 2.63400 8.10663i 0.183520 0.564816i
\(207\) −5.15780 14.7618i −0.358492 1.02602i
\(208\) 5.08094i 0.352300i
\(209\) −8.09243 + 26.1753i −0.559765 + 1.81058i
\(210\) −4.32405 + 1.69649i −0.298388 + 0.117069i
\(211\) −7.99046 5.80541i −0.550086 0.399661i 0.277731 0.960659i \(-0.410417\pi\)
−0.827817 + 0.560998i \(0.810417\pi\)
\(212\) 13.4375 + 4.36611i 0.922891 + 0.299865i
\(213\) 10.9085 + 10.6713i 0.747441 + 0.731189i
\(214\) 1.44204 1.04771i 0.0985761 0.0716198i
\(215\) 5.84339 4.24547i 0.398516 0.289539i
\(216\) 5.10259 0.981612i 0.347187 0.0667903i
\(217\) 8.82159 + 3.96603i 0.598848 + 0.269231i
\(218\) −5.98861 + 8.24262i −0.405600 + 0.558261i
\(219\) −4.02980 + 2.10940i −0.272309 + 0.142540i
\(220\) −1.93685 + 2.74773i −0.130583 + 0.185252i
\(221\) 9.75145i 0.655953i
\(222\) 8.66878 + 1.27550i 0.581811 + 0.0856056i
\(223\) 1.49979 + 0.487311i 0.100433 + 0.0326327i 0.358803 0.933413i \(-0.383185\pi\)
−0.258369 + 0.966046i \(0.583185\pi\)
\(224\) −2.58991 + 0.540692i −0.173046 + 0.0361265i
\(225\) 0.261962 + 11.9149i 0.0174641 + 0.794327i
\(226\) 6.47663 4.70555i 0.430819 0.313008i
\(227\) −0.469709 1.44562i −0.0311757 0.0959489i 0.934258 0.356598i \(-0.116063\pi\)
−0.965434 + 0.260649i \(0.916063\pi\)
\(228\) −2.39345 14.1064i −0.158510 0.934216i
\(229\) −6.47472 + 8.91168i −0.427861 + 0.588901i −0.967461 0.253021i \(-0.918576\pi\)
0.539599 + 0.841922i \(0.318576\pi\)
\(230\) −5.28324 −0.348367
\(231\) 14.0678 5.75305i 0.925592 0.378523i
\(232\) 0.547741 0.0359609
\(233\) −5.60505 + 7.71469i −0.367199 + 0.505406i −0.952137 0.305672i \(-0.901119\pi\)
0.584938 + 0.811078i \(0.301119\pi\)
\(234\) 9.22840 + 12.1318i 0.603280 + 0.793080i
\(235\) 2.64537 + 8.14161i 0.172565 + 0.531100i
\(236\) 7.46034 5.42025i 0.485627 0.352828i
\(237\) −4.02910 1.99746i −0.261718 0.129749i
\(238\) 4.97062 1.03771i 0.322197 0.0672645i
\(239\) −2.65620 0.863052i −0.171815 0.0558262i 0.221846 0.975082i \(-0.428792\pi\)
−0.393661 + 0.919256i \(0.628792\pi\)
\(240\) 0.255565 1.73692i 0.0164966 0.112118i
\(241\) 21.5649i 1.38912i −0.719437 0.694558i \(-0.755600\pi\)
0.719437 0.694558i \(-0.244400\pi\)
\(242\) 6.20820 9.08065i 0.399078 0.583726i
\(243\) 10.4006 11.6115i 0.667199 0.744880i
\(244\) 5.06513 6.97155i 0.324262 0.446308i
\(245\) 3.59212 6.11878i 0.229492 0.390915i
\(246\) 4.42016 + 4.32405i 0.281819 + 0.275691i
\(247\) 33.9562 24.6706i 2.16058 1.56975i
\(248\) −2.95754 + 2.14878i −0.187804 + 0.136447i
\(249\) 15.4461 15.7894i 0.978855 1.00061i
\(250\) 8.64958 + 2.81042i 0.547047 + 0.177747i
\(251\) 18.9003 + 13.7319i 1.19298 + 0.866748i 0.993576 0.113170i \(-0.0361003\pi\)
0.199401 + 0.979918i \(0.436100\pi\)
\(252\) −5.20190 + 5.99502i −0.327689 + 0.377651i
\(253\) 17.2855 0.247495i 1.08673 0.0155599i
\(254\) 0.996972i 0.0625556i
\(255\) −0.490485 + 3.33354i −0.0307154 + 0.208754i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 8.10825 + 24.9546i 0.505779 + 1.55663i 0.799457 + 0.600723i \(0.205120\pi\)
−0.293679 + 0.955904i \(0.594880\pi\)
\(258\) 5.48210 11.0580i 0.341301 0.688443i
\(259\) −11.6154 + 6.65009i −0.721745 + 0.413216i
\(260\) 4.89803 1.59146i 0.303763 0.0986985i
\(261\) 1.30784 0.994849i 0.0809534 0.0615796i
\(262\) 4.74152 6.52614i 0.292932 0.403186i
\(263\) 12.0306i 0.741836i 0.928666 + 0.370918i \(0.120957\pi\)
−0.928666 + 0.370918i \(0.879043\pi\)
\(264\) −0.754780 + 5.69476i −0.0464535 + 0.350488i
\(265\) 14.3213i 0.879751i
\(266\) 16.1888 + 14.6832i 0.992602 + 0.900284i
\(267\) −26.3785 + 4.47568i −1.61434 + 0.273907i
\(268\) 1.97795 + 6.08751i 0.120823 + 0.371854i
\(269\) −4.61604 + 3.35375i −0.281445 + 0.204482i −0.719547 0.694443i \(-0.755651\pi\)
0.438102 + 0.898925i \(0.355651\pi\)
\(270\) −2.54452 4.61143i −0.154855 0.280643i
\(271\) 28.8487 9.37351i 1.75243 0.569400i 0.756062 0.654500i \(-0.227121\pi\)
0.996372 + 0.0850998i \(0.0271209\pi\)
\(272\) −0.593072 + 1.82529i −0.0359603 + 0.110674i
\(273\) −22.5342 5.86051i −1.36383 0.354694i
\(274\) 17.3978 1.05104
\(275\) −12.5878 3.89167i −0.759070 0.234677i
\(276\) −7.99846 + 4.18678i −0.481451 + 0.252015i
\(277\) −16.9969 12.3489i −1.02124 0.741976i −0.0547053 0.998503i \(-0.517422\pi\)
−0.966537 + 0.256526i \(0.917422\pi\)
\(278\) −0.149822 + 0.461104i −0.00898572 + 0.0276552i
\(279\) −3.15895 + 10.5023i −0.189121 + 0.628759i
\(280\) 1.33245 + 2.32732i 0.0796289 + 0.139084i
\(281\) 7.30532 + 10.0549i 0.435799 + 0.599826i 0.969272 0.245991i \(-0.0791134\pi\)
−0.533473 + 0.845817i \(0.679113\pi\)
\(282\) 10.4568 + 10.2295i 0.622696 + 0.609156i
\(283\) 5.32172 + 1.72913i 0.316343 + 0.102786i 0.462885 0.886418i \(-0.346814\pi\)
−0.146542 + 0.989204i \(0.546814\pi\)
\(284\) 5.17867 7.12783i 0.307298 0.422959i
\(285\) −12.8488 + 6.72571i −0.761099 + 0.398397i
\(286\) −15.9506 + 5.43634i −0.943179 + 0.321457i
\(287\) −9.39002 1.02138i −0.554275 0.0602902i
\(288\) −0.989542 2.83210i −0.0583093 0.166883i
\(289\) −4.11505 + 12.6648i −0.242062 + 0.744990i
\(290\) −0.171565 0.528022i −0.0100746 0.0310065i
\(291\) −8.83470 + 17.8206i −0.517899 + 1.04466i
\(292\) 1.54357 + 2.12454i 0.0903306 + 0.124329i
\(293\) −9.09019 27.9767i −0.531055 1.63442i −0.752023 0.659137i \(-0.770922\pi\)
0.220968 0.975281i \(-0.429078\pi\)
\(294\) 0.589293 12.1100i 0.0343682 0.706271i
\(295\) −7.56187 5.49402i −0.440269 0.319874i
\(296\) 5.05881i 0.294037i
\(297\) 8.54108 + 14.9683i 0.495604 + 0.868549i
\(298\) 5.70612 0.330547
\(299\) −21.4255 15.5666i −1.23907 0.900238i
\(300\) 6.78378 1.15102i 0.391662 0.0664539i
\(301\) 3.85289 + 18.4553i 0.222077 + 1.06375i
\(302\) −3.55452 4.89238i −0.204540 0.281525i
\(303\) −14.1952 7.03735i −0.815491 0.404285i
\(304\) −7.85640 + 2.55270i −0.450595 + 0.146407i
\(305\) −8.30709 2.69914i −0.475662 0.154552i
\(306\) 1.89915 + 5.43543i 0.108567 + 0.310723i
\(307\) 4.31632i 0.246345i −0.992385 0.123173i \(-0.960693\pi\)
0.992385 0.123173i \(-0.0393069\pi\)
\(308\) −4.46847 7.55201i −0.254614 0.430316i
\(309\) −13.0801 + 6.84675i −0.744099 + 0.389498i
\(310\) 2.99779 + 2.17802i 0.170263 + 0.123703i
\(311\) 2.76039 8.49561i 0.156527 0.481742i −0.841785 0.539813i \(-0.818495\pi\)
0.998312 + 0.0580710i \(0.0184950\pi\)
\(312\) 6.15408 6.29088i 0.348406 0.356151i
\(313\) 0.302800 + 0.416768i 0.0171153 + 0.0235571i 0.817489 0.575944i \(-0.195366\pi\)
−0.800374 + 0.599502i \(0.795366\pi\)
\(314\) −4.80822 + 3.49338i −0.271344 + 0.197143i
\(315\) 7.40855 + 3.13686i 0.417424 + 0.176742i
\(316\) −0.802325 + 2.46930i −0.0451343 + 0.138909i
\(317\) 2.45186 3.37469i 0.137710 0.189542i −0.734592 0.678509i \(-0.762626\pi\)
0.872302 + 0.488967i \(0.162626\pi\)
\(318\) −11.3491 21.6814i −0.636427 1.21583i
\(319\) 0.586054 + 1.71952i 0.0328127 + 0.0962748i
\(320\) −1.01361 −0.0566625
\(321\) −3.05443 0.449419i −0.170482 0.0250841i
\(322\) 5.65475 12.5778i 0.315127 0.700933i
\(323\) 15.0782 4.89919i 0.838971 0.272598i
\(324\) −7.50662 4.96494i −0.417034 0.275830i
\(325\) 11.8642 + 16.3296i 0.658106 + 0.905805i
\(326\) −16.2568 + 5.28217i −0.900383 + 0.292552i
\(327\) 17.3982 2.95199i 0.962125 0.163245i
\(328\) 2.09841 2.88821i 0.115865 0.159475i
\(329\) −22.2141 2.41629i −1.22470 0.133215i
\(330\) 5.72616 1.05612i 0.315215 0.0581375i
\(331\) −6.45848 −0.354990 −0.177495 0.984122i \(-0.556799\pi\)
−0.177495 + 0.984122i \(0.556799\pi\)
\(332\) −10.3171 7.49579i −0.566223 0.411385i
\(333\) −9.18821 12.0789i −0.503511 0.661922i
\(334\) −9.35521 + 3.03969i −0.511895 + 0.166325i
\(335\) 5.24882 3.81349i 0.286774 0.208353i
\(336\) 3.86155 + 2.46748i 0.210665 + 0.134612i
\(337\) −8.87266 27.3072i −0.483324 1.48752i −0.834393 0.551170i \(-0.814182\pi\)
0.351069 0.936350i \(-0.385818\pi\)
\(338\) 12.1887 + 3.96035i 0.662978 + 0.215415i
\(339\) −13.7183 2.01847i −0.745077 0.109628i
\(340\) 1.94534 0.105501
\(341\) −9.91006 6.98552i −0.536660 0.378287i
\(342\) −14.1223 + 20.3645i −0.763649 + 1.10119i
\(343\) 10.7222 + 15.1008i 0.578947 + 0.815365i
\(344\) −6.77709 2.20201i −0.365396 0.118724i
\(345\) 6.54135 + 6.39912i 0.352175 + 0.344517i
\(346\) −12.6390 17.3961i −0.679476 0.935219i
\(347\) 12.7665 + 17.5716i 0.685342 + 0.943292i 0.999982 0.00591868i \(-0.00188399\pi\)
−0.314641 + 0.949211i \(0.601884\pi\)
\(348\) −0.678175 0.663429i −0.0363540 0.0355635i
\(349\) −0.0907931 0.0295005i −0.00486004 0.00157912i 0.306586 0.951843i \(-0.400813\pi\)
−0.311446 + 0.950264i \(0.600813\pi\)
\(350\) −7.06118 + 7.78526i −0.377436 + 0.416140i
\(351\) 3.26816 26.1983i 0.174441 1.39836i
\(352\) 3.31628 0.0474828i 0.176759 0.00253084i
\(353\) 24.0019 1.27749 0.638747 0.769416i \(-0.279453\pi\)
0.638747 + 0.769416i \(0.279453\pi\)
\(354\) −15.8019 2.32504i −0.839864 0.123575i
\(355\) −8.49331 2.75964i −0.450778 0.146467i
\(356\) 4.77347 + 14.6912i 0.252994 + 0.778634i
\(357\) −7.41116 4.73564i −0.392240 0.250637i
\(358\) −14.4408 + 10.4918i −0.763218 + 0.554510i
\(359\) −12.8065 + 4.16110i −0.675903 + 0.219614i −0.626801 0.779179i \(-0.715636\pi\)
−0.0491025 + 0.998794i \(0.515636\pi\)
\(360\) −2.42020 + 1.84100i −0.127556 + 0.0970290i
\(361\) 39.8354 + 28.9421i 2.09660 + 1.52327i
\(362\) 8.03953 0.422548
\(363\) −18.6851 + 3.72361i −0.980716 + 0.195439i
\(364\) −1.45365 + 13.3641i −0.0761920 + 0.700468i
\(365\) 1.56458 2.15346i 0.0818937 0.112717i
\(366\) −14.7153 + 2.49677i −0.769181 + 0.130508i
\(367\) −20.0916 + 6.52817i −1.04878 + 0.340768i −0.782188 0.623043i \(-0.785896\pi\)
−0.266588 + 0.963811i \(0.585896\pi\)
\(368\) 3.06372 + 4.21685i 0.159707 + 0.219818i
\(369\) −0.235416 10.7075i −0.0122553 0.557410i
\(370\) −4.87669 + 1.58453i −0.253527 + 0.0823760i
\(371\) 34.0947 + 15.3283i 1.77011 + 0.795808i
\(372\) 6.26444 + 0.921728i 0.324796 + 0.0477894i
\(373\) −13.1476 −0.680755 −0.340377 0.940289i \(-0.610555\pi\)
−0.340377 + 0.940289i \(0.610555\pi\)
\(374\) −6.36468 + 0.0911299i −0.329110 + 0.00471222i
\(375\) −7.30532 13.9561i −0.377245 0.720691i
\(376\) 4.96423 6.83268i 0.256011 0.352369i
\(377\) 0.860006 2.64683i 0.0442926 0.136318i
\(378\) 13.7019 1.12203i 0.704748 0.0577109i
\(379\) 3.99386 2.90171i 0.205151 0.149051i −0.480466 0.877013i \(-0.659533\pi\)
0.685617 + 0.727963i \(0.259533\pi\)
\(380\) 4.92160 + 6.77400i 0.252473 + 0.347499i
\(381\) 1.20754 1.23438i 0.0618642 0.0632393i
\(382\) −2.99906 + 9.23017i −0.153445 + 0.472257i
\(383\) 2.30820 + 1.67701i 0.117944 + 0.0856912i 0.645193 0.764019i \(-0.276777\pi\)
−0.527250 + 0.849710i \(0.676777\pi\)
\(384\) −1.53453 + 0.803249i −0.0783088 + 0.0409906i
\(385\) −5.88051 + 6.67306i −0.299699 + 0.340091i
\(386\) 3.49018i 0.177645i
\(387\) −20.1812 + 7.05133i −1.02587 + 0.358439i
\(388\) 10.9216 + 3.54866i 0.554463 + 0.180156i
\(389\) −13.9784 + 4.54185i −0.708732 + 0.230281i −0.641131 0.767432i \(-0.721534\pi\)
−0.0676008 + 0.997712i \(0.521534\pi\)
\(390\) −7.99200 3.96209i −0.404691 0.200628i
\(391\) −5.87995 8.09306i −0.297362 0.409284i
\(392\) −6.96678 + 0.681177i −0.351875 + 0.0344046i
\(393\) −13.7751 + 2.33725i −0.694864 + 0.117899i
\(394\) −8.08094 5.87115i −0.407112 0.295784i
\(395\) 2.63171 0.132416
\(396\) 7.83207 6.13667i 0.393576 0.308379i
\(397\) 19.0866i 0.957930i −0.877834 0.478965i \(-0.841012\pi\)
0.877834 0.478965i \(-0.158988\pi\)
\(398\) −7.23734 5.25823i −0.362775 0.263571i
\(399\) −2.25952 37.7878i −0.113118 1.89176i
\(400\) −1.22760 3.77816i −0.0613800 0.188908i
\(401\) −14.0631 19.3562i −0.702278 0.966603i −0.999929 0.0119284i \(-0.996203\pi\)
0.297650 0.954675i \(-0.403797\pi\)
\(402\) 4.92428 9.93285i 0.245601 0.495406i
\(403\) 5.73983 + 17.6654i 0.285921 + 0.879975i
\(404\) −2.82671 + 8.69973i −0.140634 + 0.432828i
\(405\) −2.43496 + 8.79151i −0.120994 + 0.436854i
\(406\) 1.44069 + 0.156708i 0.0715001 + 0.00777728i
\(407\) 15.8811 5.41266i 0.787199 0.268296i
\(408\) 2.94511 1.54161i 0.145805 0.0763212i
\(409\) −18.4055 + 25.3331i −0.910095 + 1.25264i 0.0570387 + 0.998372i \(0.481834\pi\)
−0.967134 + 0.254267i \(0.918166\pi\)
\(410\) −3.44150 1.11821i −0.169964 0.0552246i
\(411\) −21.5407 21.0723i −1.06253 1.03942i
\(412\) 5.01017 + 6.89591i 0.246834 + 0.339737i
\(413\) 21.1732 12.1222i 1.04186 0.596492i
\(414\) 14.9742 + 4.50402i 0.735943 + 0.221360i
\(415\) −3.99440 + 12.2935i −0.196077 + 0.603464i
\(416\) −4.11057 2.98650i −0.201537 0.146425i
\(417\) 0.743993 0.389442i 0.0364335 0.0190711i
\(418\) −16.4196 21.9323i −0.803110 1.07275i
\(419\) −3.54560 −0.173214 −0.0866070 0.996243i \(-0.527602\pi\)
−0.0866070 + 0.996243i \(0.527602\pi\)
\(420\) 1.16913 4.49540i 0.0570476 0.219353i
\(421\) 11.2677 34.6785i 0.549155 1.69013i −0.161745 0.986833i \(-0.551712\pi\)
0.710900 0.703293i \(-0.248288\pi\)
\(422\) 9.39334 3.05208i 0.457261 0.148573i
\(423\) −0.556926 25.3309i −0.0270787 1.23163i
\(424\) −11.4306 + 8.30483i −0.555120 + 0.403318i
\(425\) 2.35603 + 7.25113i 0.114284 + 0.351731i
\(426\) −15.0452 + 2.55274i −0.728941 + 0.123681i
\(427\) 15.3170 16.8877i 0.741244 0.817253i
\(428\) 1.78247i 0.0861587i
\(429\) 26.3335 + 12.5886i 1.27139 + 0.607784i
\(430\) 7.22283i 0.348316i
\(431\) −7.26804 + 10.0036i −0.350089 + 0.481856i −0.947354 0.320188i \(-0.896254\pi\)
0.597265 + 0.802044i \(0.296254\pi\)
\(432\) −2.20509 + 4.70506i −0.106092 + 0.226372i
\(433\) 1.43561 0.466458i 0.0689910 0.0224165i −0.274318 0.961639i \(-0.588452\pi\)
0.343309 + 0.939222i \(0.388452\pi\)
\(434\) −8.39378 + 4.80564i −0.402914 + 0.230678i
\(435\) −0.427125 + 0.861562i −0.0204791 + 0.0413087i
\(436\) −3.14840 9.68978i −0.150781 0.464056i
\(437\) 13.3054 40.9500i 0.636486 1.95890i
\(438\) 0.662122 4.50005i 0.0316374 0.215021i
\(439\) 12.8099i 0.611383i 0.952131 + 0.305691i \(0.0988876\pi\)
−0.952131 + 0.305691i \(0.901112\pi\)
\(440\) −1.08451 3.18203i −0.0517019 0.151697i
\(441\) −15.3974 + 14.2801i −0.733210 + 0.680003i
\(442\) 7.88909 + 5.73176i 0.375246 + 0.272632i
\(443\) 19.5796 + 6.36181i 0.930257 + 0.302259i 0.734668 0.678427i \(-0.237338\pi\)
0.195589 + 0.980686i \(0.437338\pi\)
\(444\) −6.12728 + 6.26348i −0.290788 + 0.297251i
\(445\) 12.6672 9.20325i 0.600483 0.436276i
\(446\) −1.27580 + 0.926920i −0.0604107 + 0.0438909i
\(447\) −7.06493 6.91131i −0.334160 0.326894i
\(448\) 1.08488 2.41309i 0.0512560 0.114008i
\(449\) −7.09042 + 9.75912i −0.334617 + 0.460561i −0.942860 0.333190i \(-0.891875\pi\)
0.608242 + 0.793751i \(0.291875\pi\)
\(450\) −9.79334 6.79148i −0.461663 0.320153i
\(451\) 11.3122 + 3.49730i 0.532669 + 0.164682i
\(452\) 8.00555i 0.376549i
\(453\) −1.52473 + 10.3627i −0.0716381 + 0.486881i
\(454\) 1.44562 + 0.469709i 0.0678461 + 0.0220445i
\(455\) 13.3383 2.78461i 0.625308 0.130545i
\(456\) 12.8191 + 6.35517i 0.600310 + 0.297608i
\(457\) 6.52749 4.74250i 0.305343 0.221845i −0.424553 0.905403i \(-0.639569\pi\)
0.729896 + 0.683558i \(0.239569\pi\)
\(458\) −3.40396 10.4763i −0.159057 0.489526i
\(459\) 4.23205 9.03005i 0.197535 0.421487i
\(460\) 3.10541 4.27423i 0.144791 0.199287i
\(461\) −10.6013 −0.493750 −0.246875 0.969047i \(-0.579404\pi\)
−0.246875 + 0.969047i \(0.579404\pi\)
\(462\) −3.61451 + 14.7626i −0.168162 + 0.686820i
\(463\) −3.94527 −0.183352 −0.0916762 0.995789i \(-0.529222\pi\)
−0.0916762 + 0.995789i \(0.529222\pi\)
\(464\) −0.321954 + 0.443131i −0.0149463 + 0.0205719i
\(465\) −1.07362 6.32762i −0.0497878 0.293436i
\(466\) −2.94675 9.06917i −0.136506 0.420121i
\(467\) −0.847134 + 0.615479i −0.0392007 + 0.0284810i −0.607213 0.794539i \(-0.707713\pi\)
0.568012 + 0.823020i \(0.307713\pi\)
\(468\) −15.2391 + 0.335049i −0.704429 + 0.0154876i
\(469\) 3.46085 + 16.5775i 0.159807 + 0.765477i
\(470\) −8.14161 2.64537i −0.375545 0.122022i
\(471\) 10.1844 + 1.49850i 0.469273 + 0.0690473i
\(472\) 9.22148i 0.424453i
\(473\) −0.338355 23.6314i −0.0155576 1.08657i
\(474\) 3.98422 2.08554i 0.183002 0.0957919i
\(475\) −19.2890 + 26.5491i −0.885041 + 1.21815i
\(476\) −2.08213 + 4.63126i −0.0954344 + 0.212274i
\(477\) −12.2091 + 40.5907i −0.559014 + 1.85852i
\(478\) 2.25950 1.64162i 0.103347 0.0750860i
\(479\) 19.8267 14.4050i 0.905907 0.658180i −0.0340695 0.999419i \(-0.510847\pi\)
0.939976 + 0.341240i \(0.110847\pi\)
\(480\) 1.25498 + 1.22769i 0.0572818 + 0.0560363i
\(481\) −24.4455 7.94282i −1.11462 0.362162i
\(482\) 17.4463 + 12.6755i 0.794659 + 0.577354i
\(483\) −22.2357 + 8.72388i −1.01176 + 0.396950i
\(484\) 3.69731 + 10.3600i 0.168060 + 0.470910i
\(485\) 11.6400i 0.528545i
\(486\) 3.28060 + 15.2393i 0.148811 + 0.691271i
\(487\) −5.62488 + 17.3116i −0.254888 + 0.784463i 0.738964 + 0.673745i \(0.235315\pi\)
−0.993852 + 0.110719i \(0.964685\pi\)
\(488\) 2.66290 + 8.19555i 0.120544 + 0.370995i
\(489\) 26.5259 + 13.1504i 1.19954 + 0.594682i
\(490\) 2.83881 + 6.50261i 0.128244 + 0.293758i
\(491\) −20.1057 + 6.53274i −0.907358 + 0.294819i −0.725271 0.688464i \(-0.758285\pi\)
−0.182088 + 0.983282i \(0.558285\pi\)
\(492\) −6.09634 + 1.03437i −0.274844 + 0.0466332i
\(493\) 0.617901 0.850467i 0.0278288 0.0383031i
\(494\) 41.9722i 1.88842i
\(495\) −8.36893 5.62797i −0.376155 0.252958i
\(496\) 3.65572i 0.164146i
\(497\) 15.6604 17.2663i 0.702465 0.774498i
\(498\) 3.69492 + 21.7769i 0.165573 + 0.975847i
\(499\) −3.79351 11.6752i −0.169821 0.522654i 0.829538 0.558450i \(-0.188604\pi\)
−0.999359 + 0.0357953i \(0.988604\pi\)
\(500\) −7.35777 + 5.34573i −0.329050 + 0.239069i
\(501\) 15.2647 + 7.56758i 0.681976 + 0.338095i
\(502\) −22.2186 + 7.21927i −0.991667 + 0.322212i
\(503\) −8.31118 + 25.5792i −0.370577 + 1.14052i 0.575837 + 0.817564i \(0.304676\pi\)
−0.946414 + 0.322955i \(0.895324\pi\)
\(504\) −1.79247 7.73221i −0.0798429 0.344420i
\(505\) 9.27193 0.412595
\(506\) −9.95993 + 14.1297i −0.442773 + 0.628143i
\(507\) −10.2944 19.6665i −0.457191 0.873420i
\(508\) −0.806567 0.586005i −0.0357856 0.0259998i
\(509\) 5.15149 15.8547i 0.228336 0.702746i −0.769600 0.638526i \(-0.779544\pi\)
0.997936 0.0642192i \(-0.0204557\pi\)
\(510\) −2.40859 2.35621i −0.106654 0.104335i
\(511\) 3.45213 + 6.02966i 0.152713 + 0.266737i
\(512\) 0.587785 + 0.809017i 0.0259767 + 0.0357538i
\(513\) 42.1510 8.10881i 1.86101 0.358013i
\(514\) −24.9546 8.10825i −1.10070 0.357640i
\(515\) 5.07836 6.98976i 0.223779 0.308006i
\(516\) 5.72384 + 10.9349i 0.251978 + 0.481380i
\(517\) 26.7613 + 8.27362i 1.17696 + 0.363873i
\(518\) 1.44732 13.3059i 0.0635916 0.584627i
\(519\) −5.42156 + 36.8471i −0.237980 + 1.61741i
\(520\) −1.59146 + 4.89803i −0.0697904 + 0.214793i
\(521\) 3.78190 + 11.6395i 0.165688 + 0.509935i 0.999086 0.0427377i \(-0.0136080\pi\)
−0.833398 + 0.552673i \(0.813608\pi\)
\(522\) 0.0361193 + 1.64282i 0.00158090 + 0.0719045i
\(523\) −16.7754 23.0894i −0.733538 1.00963i −0.998964 0.0454977i \(-0.985513\pi\)
0.265426 0.964131i \(-0.414487\pi\)
\(524\) 2.49276 + 7.67194i 0.108897 + 0.335150i
\(525\) 18.1723 1.08661i 0.793103 0.0474236i
\(526\) −9.73293 7.07139i −0.424376 0.308327i
\(527\) 7.01612i 0.305627i
\(528\) −4.16351 3.95793i −0.181194 0.172247i
\(529\) −4.16816 −0.181224
\(530\) 11.5862 + 8.41785i 0.503271 + 0.365648i
\(531\) 16.7488 + 22.0182i 0.726835 + 0.955508i
\(532\) −21.3945 + 4.46650i −0.927570 + 0.193647i
\(533\) −10.6619 14.6748i −0.461818 0.635638i
\(534\) 11.8840 23.9714i 0.514270 1.03734i
\(535\) 1.71830 0.558308i 0.0742884 0.0241378i
\(536\) −6.08751 1.97795i −0.262940 0.0854345i
\(537\) 30.5874 + 4.50052i 1.31994 + 0.194212i
\(538\) 5.70574i 0.245992i
\(539\) −9.59250 21.1420i −0.413178 0.910650i
\(540\) 5.22636 + 0.651972i 0.224907 + 0.0280564i
\(541\) −17.7621 12.9049i −0.763654 0.554827i 0.136375 0.990657i \(-0.456455\pi\)
−0.900029 + 0.435830i \(0.856455\pi\)
\(542\) −9.37351 + 28.8487i −0.402627 + 1.23916i
\(543\) −9.95400 9.73755i −0.427167 0.417878i
\(544\) −1.12809 1.55268i −0.0483664 0.0665707i
\(545\) −8.35480 + 6.07012i −0.357880 + 0.260015i
\(546\) 17.9865 14.7858i 0.769752 0.632775i
\(547\) 9.94519 30.6081i 0.425226 1.30871i −0.477552 0.878603i \(-0.658476\pi\)
0.902778 0.430107i \(-0.141524\pi\)
\(548\) −10.2262 + 14.0751i −0.436840 + 0.601258i
\(549\) 21.2436 + 14.7320i 0.906655 + 0.628746i
\(550\) 10.5473 7.89624i 0.449740 0.336697i
\(551\) 4.52472 0.192760
\(552\) 1.31420 8.93182i 0.0559359 0.380163i
\(553\) −2.81677 + 6.26530i −0.119781 + 0.266428i
\(554\) 19.9810 6.49222i 0.848912 0.275828i
\(555\) 7.95719 + 3.94484i 0.337764 + 0.167449i
\(556\) −0.284978 0.392239i −0.0120858 0.0166346i
\(557\) −2.55036 + 0.828662i −0.108062 + 0.0351115i −0.362549 0.931965i \(-0.618093\pi\)
0.254487 + 0.967076i \(0.418093\pi\)
\(558\) −6.63980 8.72877i −0.281085 0.369518i
\(559\) −21.2814 + 29.2913i −0.900107 + 1.23889i
\(560\) −2.66603 0.289992i −0.112660 0.0122544i
\(561\) 7.99070 + 7.59613i 0.337367 + 0.320709i
\(562\) −12.4286 −0.524267
\(563\) −12.2852 8.92575i −0.517761 0.376176i 0.297999 0.954566i \(-0.403681\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(564\) −14.4222 + 2.44704i −0.607284 + 0.103039i
\(565\) 7.71735 2.50752i 0.324671 0.105492i
\(566\) −4.52692 + 3.28900i −0.190281 + 0.138247i
\(567\) −18.3237 15.2066i −0.769524 0.638618i
\(568\) 2.72259 + 8.37927i 0.114237 + 0.351586i
\(569\) 7.34653 + 2.38703i 0.307983 + 0.100070i 0.458931 0.888472i \(-0.348233\pi\)
−0.150948 + 0.988542i \(0.548233\pi\)
\(570\) 2.11114 14.3482i 0.0884261 0.600980i
\(571\) −18.4345 −0.771458 −0.385729 0.922612i \(-0.626050\pi\)
−0.385729 + 0.922612i \(0.626050\pi\)
\(572\) 4.97744 16.0997i 0.208117 0.673163i
\(573\) 14.8929 7.79568i 0.622160 0.325669i
\(574\) 6.34563 6.99633i 0.264861 0.292021i
\(575\) 19.6930 + 6.39863i 0.821253 + 0.266841i
\(576\) 2.87286 + 0.864112i 0.119702 + 0.0360047i
\(577\) −8.44416 11.6224i −0.351535 0.483847i 0.596231 0.802813i \(-0.296664\pi\)
−0.947766 + 0.318966i \(0.896664\pi\)
\(578\) −7.82730 10.7733i −0.325573 0.448112i
\(579\) 4.22733 4.32130i 0.175682 0.179587i
\(580\) 0.528022 + 0.171565i 0.0219249 + 0.00712384i
\(581\) −24.9918 22.6674i −1.03683 0.940402i
\(582\) −9.22428 17.6221i −0.382359 0.730460i
\(583\) −38.3015 26.9984i −1.58629 1.11816i
\(584\) −2.62608 −0.108668
\(585\) 5.09623 + 14.5856i 0.210703 + 0.603040i
\(586\) 27.9767 + 9.09019i 1.15571 + 0.375512i
\(587\) −8.32919 25.6346i −0.343782 1.05805i −0.962232 0.272229i \(-0.912239\pi\)
0.618450 0.785824i \(-0.287761\pi\)
\(588\) 9.45084 + 7.59484i 0.389746 + 0.313206i
\(589\) −24.4313 + 17.7504i −1.00668 + 0.731392i
\(590\) 8.88951 2.88838i 0.365975 0.118913i
\(591\) 2.89408 + 17.0570i 0.119047 + 0.701630i
\(592\) 4.09266 + 2.97349i 0.168207 + 0.122210i
\(593\) 20.9730 0.861258 0.430629 0.902529i \(-0.358292\pi\)
0.430629 + 0.902529i \(0.358292\pi\)
\(594\) −17.1299 1.88827i −0.702849 0.0774765i
\(595\) 5.11671 + 0.556559i 0.209764 + 0.0228167i
\(596\) −3.35397 + 4.61635i −0.137384 + 0.189093i
\(597\) 2.59196 + 15.2763i 0.106082 + 0.625218i
\(598\) 25.1872 8.18383i 1.02998 0.334662i
\(599\) −8.93324 12.2955i −0.365002 0.502382i 0.586532 0.809926i \(-0.300493\pi\)
−0.951534 + 0.307544i \(0.900493\pi\)
\(600\) −3.05622 + 6.16475i −0.124770 + 0.251675i
\(601\) 32.2651 10.4836i 1.31612 0.427633i 0.434959 0.900450i \(-0.356763\pi\)
0.881161 + 0.472817i \(0.156763\pi\)
\(602\) −17.1954 7.73073i −0.700831 0.315081i
\(603\) −18.1277 + 6.33385i −0.738216 + 0.257934i
\(604\) 6.04732 0.246062
\(605\) 8.82897 6.80920i 0.358949 0.276833i
\(606\) 14.0370 7.34767i 0.570216 0.298479i
\(607\) 13.2814 18.2803i 0.539076 0.741974i −0.449404 0.893329i \(-0.648364\pi\)
0.988479 + 0.151355i \(0.0483636\pi\)
\(608\) 2.55270 7.85640i 0.103526 0.318619i
\(609\) −1.59396 1.93900i −0.0645903 0.0785722i
\(610\) 7.06643 5.13406i 0.286111 0.207872i
\(611\) −25.2230 34.7165i −1.02041 1.40448i
\(612\) −5.51365 1.65842i −0.222876 0.0670377i
\(613\) −7.72272 + 23.7681i −0.311918 + 0.959984i 0.665087 + 0.746766i \(0.268394\pi\)
−0.977005 + 0.213218i \(0.931606\pi\)
\(614\) 3.49198 + 2.53707i 0.140925 + 0.102388i
\(615\) 2.90665 + 5.55288i 0.117207 + 0.223914i
\(616\) 8.73620 + 0.823894i 0.351992 + 0.0331956i
\(617\) 5.82704i 0.234588i −0.993097 0.117294i \(-0.962578\pi\)
0.993097 0.117294i \(-0.0374219\pi\)
\(618\) 2.14914 14.6064i 0.0864510 0.587556i
\(619\) 21.3983 + 6.95272i 0.860070 + 0.279454i 0.705658 0.708553i \(-0.250652\pi\)
0.154412 + 0.988007i \(0.450652\pi\)
\(620\) −3.52411 + 1.14505i −0.141532 + 0.0459864i
\(621\) −13.0848 23.7135i −0.525073 0.951590i
\(622\) 5.25058 + 7.22680i 0.210529 + 0.289768i
\(623\) 8.35222 + 40.0071i 0.334625 + 1.60285i
\(624\) 1.47215 + 8.67644i 0.0589330 + 0.347336i
\(625\) −8.61158 6.25668i −0.344463 0.250267i
\(626\) −0.515154 −0.0205897
\(627\) −6.23501 + 47.0427i −0.249002 + 1.87871i
\(628\) 5.94329i 0.237163i
\(629\) −7.85473 5.70679i −0.313188 0.227545i
\(630\) −6.89241 + 4.14984i −0.274600 + 0.165334i
\(631\) −1.98371 6.10522i −0.0789701 0.243045i 0.903776 0.428006i \(-0.140784\pi\)
−0.982746 + 0.184962i \(0.940784\pi\)
\(632\) −1.52611 2.10051i −0.0607055 0.0835539i
\(633\) −15.3269 7.59843i −0.609190 0.302010i
\(634\) 1.28902 + 3.96719i 0.0511935 + 0.157557i
\(635\) −0.312274 + 0.961080i −0.0123922 + 0.0381393i
\(636\) 24.2115 + 3.56240i 0.960048 + 0.141258i
\(637\) −7.64689 + 34.7348i −0.302981 + 1.37624i
\(638\) −1.73560 0.536583i −0.0687129 0.0212435i
\(639\) 21.7198 + 15.0622i 0.859223 + 0.595853i
\(640\) 0.595785 0.820027i 0.0235505 0.0324144i
\(641\) 12.0721 + 3.92246i 0.476819 + 0.154928i 0.537560 0.843226i \(-0.319346\pi\)
−0.0607408 + 0.998154i \(0.519346\pi\)
\(642\) 2.15894 2.20693i 0.0852065 0.0871005i
\(643\) 9.65314 + 13.2864i 0.380683 + 0.523965i 0.955765 0.294130i \(-0.0950300\pi\)
−0.575082 + 0.818095i \(0.695030\pi\)
\(644\) 6.85187 + 11.9678i 0.270002 + 0.471599i
\(645\) 8.74837 8.94282i 0.344467 0.352123i
\(646\) −4.89919 + 15.0782i −0.192756 + 0.593242i
\(647\) −28.3351 20.5867i −1.11397 0.809345i −0.130684 0.991424i \(-0.541717\pi\)
−0.983284 + 0.182079i \(0.941717\pi\)
\(648\) 8.42900 3.15466i 0.331123 0.123927i
\(649\) −28.9490 + 9.86650i −1.13635 + 0.387294i
\(650\) −20.1845 −0.791702
\(651\) 16.2133 + 4.21661i 0.635447 + 0.165262i
\(652\) 5.28217 16.2568i 0.206866 0.636667i
\(653\) −16.9538 + 5.50862i −0.663453 + 0.215569i −0.621337 0.783544i \(-0.713410\pi\)
−0.0421165 + 0.999113i \(0.513410\pi\)
\(654\) −7.83822 + 15.8106i −0.306499 + 0.618244i
\(655\) 6.61495 4.80605i 0.258468 0.187788i
\(656\) 1.10320 + 3.39530i 0.0430727 + 0.132564i
\(657\) −6.27030 + 4.76969i −0.244628 + 0.186083i
\(658\) 15.0119 16.5513i 0.585226 0.645237i
\(659\) 19.0631i 0.742592i −0.928514 0.371296i \(-0.878913\pi\)
0.928514 0.371296i \(-0.121087\pi\)
\(660\) −2.51133 + 5.25333i −0.0977536 + 0.204486i
\(661\) 25.6299i 0.996889i −0.866922 0.498445i \(-0.833905\pi\)
0.866922 0.498445i \(-0.166095\pi\)
\(662\) 3.79620 5.22502i 0.147543 0.203076i
\(663\) −2.82537 16.6520i −0.109728 0.646710i
\(664\) 12.1284 3.94077i 0.470675 0.152931i
\(665\) 11.0069 + 19.2253i 0.426831 + 0.745525i
\(666\) 15.1728 0.333590i 0.587933 0.0129263i
\(667\) −0.882241 2.71526i −0.0341605 0.105135i
\(668\) 3.03969 9.35521i 0.117609 0.361964i
\(669\) 2.70230 + 0.397607i 0.104477 + 0.0153724i
\(670\) 6.48790i 0.250649i
\(671\) −22.8791 + 17.1284i −0.883240 + 0.661236i
\(672\) −4.26599 + 1.67371i −0.164564 + 0.0645647i
\(673\) −8.65306 6.28682i −0.333551 0.242339i 0.408385 0.912810i \(-0.366092\pi\)
−0.741936 + 0.670471i \(0.766092\pi\)
\(674\) 27.3072 + 8.87266i 1.05184 + 0.341762i
\(675\) 3.89955 + 20.2705i 0.150094 + 0.780213i
\(676\) −10.3683 + 7.53303i −0.398782 + 0.289732i
\(677\) 0.560407 0.407160i 0.0215382 0.0156484i −0.576964 0.816770i \(-0.695763\pi\)
0.598502 + 0.801121i \(0.295763\pi\)
\(678\) 9.69640 9.91193i 0.372388 0.380665i
\(679\) 27.7113 + 12.4585i 1.06346 + 0.478113i
\(680\) −1.14344 + 1.57381i −0.0438490 + 0.0603530i
\(681\) −1.22095 2.33251i −0.0467868 0.0893818i
\(682\) 11.4764 3.91142i 0.439454 0.149776i
\(683\) 9.64920i 0.369216i −0.982812 0.184608i \(-0.940898\pi\)
0.982812 0.184608i \(-0.0591016\pi\)
\(684\) −8.17431 23.3952i −0.312553 0.894537i
\(685\) 16.7714 + 5.44937i 0.640804 + 0.208210i
\(686\) −18.5192 0.201531i −0.707065 0.00769449i
\(687\) −8.47446 + 17.0940i −0.323321 + 0.652175i
\(688\) 5.76494 4.18847i 0.219786 0.159684i
\(689\) 22.1839 + 68.2751i 0.845140 + 2.60107i
\(690\) −9.02191 + 1.53076i −0.343458 + 0.0582751i
\(691\) 28.3605 39.0349i 1.07889 1.48496i 0.218145 0.975916i \(-0.429999\pi\)
0.860741 0.509043i \(-0.170001\pi\)
\(692\) 21.5027 0.817411
\(693\) 22.3559 13.9002i 0.849230 0.528023i
\(694\) −21.7197 −0.824468
\(695\) −0.288856 + 0.397577i −0.0109569 + 0.0150809i
\(696\) 0.935347 0.158702i 0.0354542 0.00601557i
\(697\) −2.11728 6.51632i −0.0801978 0.246823i
\(698\) 0.0772332 0.0561132i 0.00292332 0.00212392i
\(699\) −7.33619 + 14.7980i −0.277480 + 0.559710i
\(700\) −2.14795 10.2887i −0.0811849 0.388876i
\(701\) −0.932054 0.302843i −0.0352032 0.0114382i 0.291362 0.956613i \(-0.405891\pi\)
−0.326566 + 0.945175i \(0.605891\pi\)
\(702\) 19.2739 + 18.0430i 0.727446 + 0.680988i
\(703\) 41.7893i 1.57612i
\(704\) −1.91085 + 2.71084i −0.0720178 + 0.102169i
\(705\) 6.87630 + 13.1365i 0.258976 + 0.494750i
\(706\) −14.1080 + 19.4180i −0.530961 + 0.730805i
\(707\) −9.92391 + 22.0736i −0.373227 + 0.830165i
\(708\) 11.1692 11.4174i 0.419762 0.429093i
\(709\) −21.4031 + 15.5503i −0.803811 + 0.584003i −0.912030 0.410124i \(-0.865485\pi\)
0.108218 + 0.994127i \(0.465485\pi\)
\(710\) 7.22484 5.24915i 0.271143 0.196997i
\(711\) −7.45902 2.24356i −0.279735 0.0841401i
\(712\) −14.6912 4.77347i −0.550578 0.178893i
\(713\) 15.4156 + 11.2001i 0.577318 + 0.419446i
\(714\) 8.18738 3.21221i 0.306405 0.120214i
\(715\) −17.0792 + 0.244541i −0.638724 + 0.00914530i
\(716\) 17.8498i 0.667077i
\(717\) −4.78591 0.704182i −0.178733 0.0262982i
\(718\) 4.16110 12.8065i 0.155291 0.477936i
\(719\) −15.5196 47.7643i −0.578782 1.78131i −0.622923 0.782283i \(-0.714055\pi\)
0.0441414 0.999025i \(-0.485945\pi\)
\(720\) −0.0668397 3.04009i −0.00249097 0.113298i
\(721\) 11.2050 + 19.5713i 0.417297 + 0.728873i
\(722\) −46.8293 + 15.2158i −1.74281 + 0.566272i
\(723\) −6.24818 36.8251i −0.232372 1.36954i
\(724\) −4.72552 + 6.50411i −0.175622 + 0.241723i
\(725\) 2.17595i 0.0808128i
\(726\) 7.97039 17.3053i 0.295809 0.642259i
\(727\) 14.2750i 0.529430i −0.964327 0.264715i \(-0.914722\pi\)
0.964327 0.264715i \(-0.0852779\pi\)
\(728\) −9.95733 9.03124i −0.369043 0.334720i
\(729\) 14.3962 22.8418i 0.533193 0.845993i
\(730\) 0.822547 + 2.53154i 0.0304438 + 0.0936964i
\(731\) −11.0642 + 8.03860i −0.409224 + 0.297318i
\(732\) 6.62951 13.3725i 0.245034 0.494262i
\(733\) 3.36003 1.09174i 0.124106 0.0403244i −0.246306 0.969192i \(-0.579217\pi\)
0.370411 + 0.928868i \(0.379217\pi\)
\(734\) 6.52817 20.0916i 0.240959 0.741596i
\(735\) 4.36121 11.4895i 0.160866 0.423796i
\(736\) −5.21231 −0.192128
\(737\) −0.303927 21.2268i −0.0111953 0.781900i
\(738\) 8.80092 + 6.10325i 0.323966 + 0.224664i
\(739\) 24.1844 + 17.5710i 0.889637 + 0.646359i 0.935783 0.352575i \(-0.114694\pi\)
−0.0461461 + 0.998935i \(0.514694\pi\)
\(740\) 1.58453 4.87669i 0.0582486 0.179271i
\(741\) 50.8371 51.9671i 1.86755 1.90906i
\(742\) −32.4412 + 18.5734i −1.19096 + 0.681850i
\(743\) 26.6778 + 36.7189i 0.978714 + 1.34708i 0.937519 + 0.347933i \(0.113116\pi\)
0.0411944 + 0.999151i \(0.486884\pi\)
\(744\) −4.42784 + 4.52626i −0.162332 + 0.165941i
\(745\) 5.50070 + 1.78729i 0.201530 + 0.0654811i
\(746\) 7.72794 10.6366i 0.282940 0.389434i
\(747\) 21.8016 31.4380i 0.797679 1.15026i
\(748\) 3.66734 5.20270i 0.134091 0.190230i
\(749\) −0.509961 + 4.68831i −0.0186336 + 0.171307i
\(750\) 15.5847 + 2.29308i 0.569073 + 0.0837314i
\(751\) −10.4682 + 32.2177i −0.381988 + 1.17564i 0.556653 + 0.830745i \(0.312085\pi\)
−0.938642 + 0.344894i \(0.887915\pi\)
\(752\) 2.60985 + 8.03230i 0.0951715 + 0.292908i
\(753\) 36.2537 + 17.9730i 1.32116 + 0.654973i
\(754\) 1.63583 + 2.25152i 0.0595734 + 0.0819957i
\(755\) −1.89416 5.82961i −0.0689354 0.212161i
\(756\) −7.14601 + 11.7446i −0.259898 + 0.427145i
\(757\) 6.29849 + 4.57612i 0.228923 + 0.166322i 0.696334 0.717718i \(-0.254813\pi\)
−0.467411 + 0.884040i \(0.654813\pi\)
\(758\) 4.93668i 0.179308i
\(759\) 29.4458 5.43091i 1.06881 0.197130i
\(760\) −8.37313 −0.303725
\(761\) 25.6965 + 18.6696i 0.931498 + 0.676773i 0.946359 0.323117i \(-0.104731\pi\)
−0.0148614 + 0.999890i \(0.504731\pi\)
\(762\) 0.288861 + 1.70247i 0.0104643 + 0.0616741i
\(763\) −5.50881 26.3872i −0.199432 0.955280i
\(764\) −5.70456 7.85165i −0.206384 0.284063i
\(765\) 0.128280 + 5.83461i 0.00463798 + 0.210951i
\(766\) −2.71346 + 0.881656i −0.0980412 + 0.0318555i
\(767\) 44.5606 + 14.4786i 1.60899 + 0.522793i
\(768\) 0.252133 1.71360i 0.00909808 0.0618343i
\(769\) 46.6841i 1.68347i 0.539889 + 0.841736i \(0.318466\pi\)
−0.539889 + 0.841736i \(0.681534\pi\)
\(770\) −1.94214 8.67976i −0.0699899 0.312797i
\(771\) 21.0763 + 40.2644i 0.759046 + 1.45009i
\(772\) −2.82361 2.05147i −0.101624 0.0738342i
\(773\) −10.8127 + 33.2781i −0.388906 + 1.19693i 0.544701 + 0.838630i \(0.316643\pi\)
−0.933607 + 0.358299i \(0.883357\pi\)
\(774\) 6.15754 20.4716i 0.221328 0.735835i
\(775\) −8.53622 11.7491i −0.306630 0.422040i
\(776\) −9.29051 + 6.74995i −0.333510 + 0.242309i
\(777\) −17.9082 + 14.7214i −0.642452 + 0.528128i
\(778\) 4.54185 13.9784i 0.162833 0.501149i
\(779\) 17.3343 23.8587i 0.621067 0.854825i
\(780\) 7.90298 4.13681i 0.282972 0.148121i
\(781\) −23.3920 + 17.5124i −0.837032 + 0.626643i
\(782\) 10.0036 0.357727
\(783\) 1.94508 2.07778i 0.0695117 0.0742539i
\(784\) 3.54389 6.03663i 0.126567 0.215594i
\(785\) −5.72933 + 1.86157i −0.204488 + 0.0664423i
\(786\) 6.20595 12.5181i 0.221359 0.446507i
\(787\) −25.4599 35.0425i −0.907546 1.24913i −0.967998 0.250959i \(-0.919254\pi\)
0.0604520 0.998171i \(-0.480746\pi\)
\(788\) 9.49972 3.08665i 0.338413 0.109957i
\(789\) 3.48572 + 20.5439i 0.124095 + 0.731383i
\(790\) −1.54688 + 2.12910i −0.0550356 + 0.0757500i
\(791\) −2.29038 + 21.0565i −0.0814365 + 0.748683i
\(792\) 0.361097 + 9.94332i 0.0128310 + 0.353320i
\(793\) 43.7840 1.55482
\(794\) 15.4414 + 11.2188i 0.547995 + 0.398142i
\(795\) −4.14944 24.4557i −0.147165 0.867354i
\(796\) 8.50800 2.76442i 0.301558 0.0979821i
\(797\) 30.9608 22.4943i 1.09669 0.796791i 0.116172 0.993229i \(-0.462938\pi\)
0.980516 + 0.196438i \(0.0629376\pi\)
\(798\) 31.8991 + 20.3831i 1.12922 + 0.721555i
\(799\) −5.00888 15.4158i −0.177202 0.545370i
\(800\) 3.77816 + 1.22760i 0.133578 + 0.0434022i
\(801\) −43.7483 + 15.2857i −1.54577 + 0.540095i
\(802\) 23.9256 0.844842
\(803\) −2.80976 8.24405i −0.0991545 0.290926i
\(804\) 5.14143 + 9.82222i 0.181324 + 0.346403i
\(805\) 9.39083 10.3538i 0.330983 0.364923i
\(806\) −17.6654 5.73983i −0.622236 0.202177i
\(807\) −6.91085 + 7.06446i −0.243273 + 0.248681i
\(808\) −5.37673 7.40043i −0.189153 0.260346i
\(809\) −13.8544 19.0689i −0.487094 0.670427i 0.492755 0.870168i \(-0.335990\pi\)
−0.979849 + 0.199741i \(0.935990\pi\)
\(810\) −5.68125 7.13745i −0.199619 0.250784i
\(811\) 28.0236 + 9.10542i 0.984042 + 0.319735i 0.756471 0.654027i \(-0.226922\pi\)
0.227571 + 0.973762i \(0.426922\pi\)
\(812\) −0.973594 + 1.07343i −0.0341665 + 0.0376700i
\(813\) 46.5475 24.3652i 1.63249 0.854526i
\(814\) −4.95576 + 16.0296i −0.173699 + 0.561837i
\(815\) −17.3261 −0.606906
\(816\) −0.483900 + 3.28878i −0.0169399 + 0.115130i
\(817\) −55.9835 18.1902i −1.95862 0.636393i
\(818\) −9.67637 29.7808i −0.338326 1.04126i
\(819\) −40.1784 3.47864i −1.40395 0.121554i
\(820\) 2.92752 2.12697i 0.102233 0.0742769i
\(821\) −52.4193 + 17.0321i −1.82945 + 0.594423i −0.830126 + 0.557576i \(0.811732\pi\)
−0.999321 + 0.0368475i \(0.988268\pi\)
\(822\) 29.7092 5.04081i 1.03623 0.175818i
\(823\) −26.2208 19.0505i −0.914000 0.664060i 0.0280236 0.999607i \(-0.491079\pi\)
−0.942023 + 0.335548i \(0.891079\pi\)
\(824\) −8.52382 −0.296941
\(825\) −22.6230 2.99843i −0.787631 0.104392i
\(826\) −2.63826 + 24.2547i −0.0917966 + 0.843929i
\(827\) 21.0028 28.9079i 0.730340 1.00523i −0.268777 0.963203i \(-0.586619\pi\)
0.999117 0.0420242i \(-0.0133807\pi\)
\(828\) −12.4455 + 9.46700i −0.432509 + 0.329001i
\(829\) 16.6075 5.39611i 0.576803 0.187415i −0.00606465 0.999982i \(-0.501930\pi\)
0.582868 + 0.812567i \(0.301930\pi\)
\(830\) −7.59780 10.4575i −0.263723 0.362984i
\(831\) −32.6026 16.1630i −1.13097 0.560687i
\(832\) 4.83226 1.57010i 0.167529 0.0544333i
\(833\) −6.80150 + 11.5856i −0.235658 + 0.401418i
\(834\) −0.122243 + 0.830811i −0.00423292 + 0.0287686i
\(835\) −9.97052 −0.345044
\(836\) 27.3948 0.392241i 0.947471 0.0135659i
\(837\) −2.35142 + 18.8496i −0.0812771 + 0.651536i
\(838\) 2.08405 2.86845i 0.0719924 0.0990890i
\(839\) 0.0414202 0.127478i 0.00142998 0.00440104i −0.950339 0.311217i \(-0.899264\pi\)
0.951769 + 0.306816i \(0.0992635\pi\)
\(840\) 2.94966 + 3.58817i 0.101773 + 0.123804i
\(841\) −23.2188 + 16.8694i −0.800647 + 0.581704i
\(842\) 21.4325 + 29.4993i 0.738612 + 1.01661i
\(843\) 15.3882 + 15.0536i 0.529998 + 0.518473i
\(844\) −3.05208 + 9.39334i −0.105057 + 0.323332i
\(845\) 10.5094 + 7.63555i 0.361536 + 0.262671i
\(846\) 20.8204 + 14.4385i 0.715822 + 0.496407i
\(847\) 6.76082 + 28.3071i 0.232305 + 0.972643i
\(848\) 14.1290i 0.485192i
\(849\) 9.58860 + 1.41083i 0.329080 + 0.0484197i
\(850\) −7.25113 2.35603i −0.248712 0.0808113i
\(851\) −25.0775 + 8.14819i −0.859647 + 0.279316i
\(852\) 6.77813 13.6723i 0.232215 0.468404i
\(853\) −16.8800 23.2333i −0.577960 0.795493i 0.415510 0.909589i \(-0.363603\pi\)
−0.993470 + 0.114095i \(0.963603\pi\)
\(854\) 4.65931 + 22.3181i 0.159438 + 0.763709i
\(855\) −19.9926 + 15.2079i −0.683731 + 0.520100i
\(856\) −1.44204 1.04771i −0.0492881 0.0358099i
\(857\) 3.42384 0.116956 0.0584781 0.998289i \(-0.481375\pi\)
0.0584781 + 0.998289i \(0.481375\pi\)
\(858\) −25.6629 + 13.9048i −0.876115 + 0.474704i
\(859\) 34.7965i 1.18724i 0.804745 + 0.593621i \(0.202302\pi\)
−0.804745 + 0.593621i \(0.797698\pi\)
\(860\) −5.84339 4.24547i −0.199258 0.144769i
\(861\) −16.3307 + 0.976497i −0.556550 + 0.0332789i
\(862\) −3.82103 11.7599i −0.130145 0.400545i
\(863\) 23.7530 + 32.6933i 0.808563 + 1.11289i 0.991543 + 0.129775i \(0.0414255\pi\)
−0.182980 + 0.983117i \(0.558574\pi\)
\(864\) −2.51036 4.54952i −0.0854041 0.154778i
\(865\) −6.73514 20.7286i −0.229002 0.704794i
\(866\) −0.466458 + 1.43561i −0.0158509 + 0.0487840i
\(867\) −3.35756 + 22.8193i −0.114029 + 0.774985i
\(868\) 1.04590 9.61540i 0.0355000 0.326368i
\(869\) 4.96128 7.03836i 0.168300 0.238760i
\(870\) −0.445960 0.851965i −0.0151195 0.0288843i
\(871\) −19.1160 + 26.3109i −0.647720 + 0.891510i
\(872\) 9.68978 + 3.14840i 0.328137 + 0.106618i
\(873\) −9.92321 + 32.9910i −0.335850 + 1.11658i
\(874\) 25.3085 + 34.8341i 0.856072 + 1.17828i
\(875\) −20.8821 + 11.9555i −0.705944 + 0.404170i
\(876\) 3.25143 + 3.18073i 0.109856 + 0.107467i
\(877\) 8.31993 25.6061i 0.280944 0.864657i −0.706641 0.707572i \(-0.749790\pi\)
0.987585 0.157085i \(-0.0502096\pi\)
\(878\) −10.3634 7.52947i −0.349749 0.254107i
\(879\) −23.6288 45.1406i −0.796979 1.52255i
\(880\) 3.21177 + 0.992962i 0.108269 + 0.0334727i
\(881\) 23.1397 0.779596 0.389798 0.920900i \(-0.372545\pi\)
0.389798 + 0.920900i \(0.372545\pi\)
\(882\) −2.50244 20.8504i −0.0842616 0.702068i
\(883\) −10.5821 + 32.5683i −0.356115 + 1.09601i 0.599245 + 0.800566i \(0.295468\pi\)
−0.955360 + 0.295444i \(0.904532\pi\)
\(884\) −9.27418 + 3.01336i −0.311924 + 0.101350i
\(885\) −14.5048 7.19087i −0.487574 0.241718i
\(886\) −16.6554 + 12.1009i −0.559550 + 0.406537i
\(887\) −8.12304 25.0002i −0.272745 0.839423i −0.989807 0.142414i \(-0.954514\pi\)
0.717062 0.697009i \(-0.245486\pi\)
\(888\) −1.46573 8.63865i −0.0491868 0.289894i
\(889\) −1.95381 1.77209i −0.0655286 0.0594340i
\(890\) 15.6575i 0.524841i
\(891\) 18.9220 + 23.0859i 0.633912 + 0.773405i
\(892\) 1.57697i 0.0528009i
\(893\) 41.0081 56.4428i 1.37228 1.88879i
\(894\) 9.74403 1.65328i 0.325889 0.0552941i
\(895\) −17.2072 + 5.59094i −0.575172 + 0.186885i
\(896\) 1.31456 + 2.29607i 0.0439162 + 0.0767064i
\(897\) −41.0975 20.3744i −1.37220 0.680280i
\(898\) −3.72765 11.4725i −0.124393 0.382843i
\(899\) −0.618771 + 1.90438i −0.0206372 + 0.0635146i
\(900\) 11.2508 3.93105i 0.375027 0.131035i
\(901\) 27.1167i 0.903388i
\(902\) −9.47850 + 7.09606i −0.315599 + 0.236273i
\(903\) 11.9266 + 30.3989i 0.396892 + 1.01161i
\(904\) −6.47663 4.70555i −0.215409 0.156504i
\(905\) 7.75010 + 2.51816i 0.257622 + 0.0837065i
\(906\) −7.48738 7.32457i −0.248751 0.243342i
\(907\) 10.4744 7.61012i 0.347798 0.252690i −0.400147 0.916451i \(-0.631041\pi\)
0.747945 + 0.663761i \(0.231041\pi\)
\(908\) −1.22971 + 0.893440i −0.0408095 + 0.0296498i
\(909\) −26.2793 7.90441i −0.871629 0.262173i
\(910\) −5.58725 + 12.4277i −0.185216 + 0.411973i
\(911\) −11.9218 + 16.4090i −0.394988 + 0.543655i −0.959477 0.281786i \(-0.909073\pi\)
0.564489 + 0.825441i \(0.309073\pi\)
\(912\) −12.6763 + 6.63540i −0.419755 + 0.219720i
\(913\) 25.3481 + 33.8584i 0.838898 + 1.12055i
\(914\) 8.06842i 0.266880i
\(915\) −14.9676 2.20228i −0.494814 0.0728052i
\(916\) 10.4763 + 3.40396i 0.346147 + 0.112470i
\(917\) 4.36163 + 20.8922i 0.144034 + 0.689921i
\(918\) 4.81793 + 8.73153i 0.159015 + 0.288183i
\(919\) 34.7816 25.2703i 1.14734 0.833591i 0.159215 0.987244i \(-0.449104\pi\)
0.988125 + 0.153653i \(0.0491037\pi\)
\(920\) 1.63261 + 5.02466i 0.0538256 + 0.165658i
\(921\) −1.25060 7.37074i −0.0412088 0.242874i
\(922\) 6.23127 8.57660i 0.205216 0.282455i
\(923\) 44.7656 1.47348
\(924\) −9.81866 11.6015i −0.323010 0.381660i
\(925\) 20.0966 0.660773
\(926\) 2.31897 3.19179i 0.0762062 0.104889i
\(927\) −20.3524 + 15.4816i −0.668459 + 0.508483i
\(928\) −0.169261 0.520932i −0.00555627 0.0171004i
\(929\) −7.71023 + 5.60181i −0.252965 + 0.183790i −0.707040 0.707174i \(-0.749970\pi\)
0.454075 + 0.890963i \(0.349970\pi\)
\(930\) 5.75021 + 2.85071i 0.188557 + 0.0934784i
\(931\) −57.5505 + 5.62700i −1.88614 + 0.184417i
\(932\) 9.06917 + 2.94675i 0.297070 + 0.0965240i
\(933\) 2.25226 15.3073i 0.0737357 0.501138i
\(934\) 1.04712i 0.0342627i
\(935\) −6.16410 1.90571i −0.201587 0.0623235i
\(936\) 8.68628 12.5257i 0.283920 0.409414i
\(937\) 0.370676 0.510192i 0.0121095 0.0166672i −0.802919 0.596088i \(-0.796721\pi\)
0.815029 + 0.579420i \(0.196721\pi\)
\(938\) −15.4457 6.94411i −0.504320 0.226733i
\(939\) 0.637829 + 0.623959i 0.0208148 + 0.0203621i
\(940\) 6.92567 5.03179i 0.225890 0.164119i
\(941\) −12.0898 + 8.78376i −0.394117 + 0.286342i −0.767140 0.641479i \(-0.778321\pi\)
0.373024 + 0.927822i \(0.378321\pi\)
\(942\) −7.19857 + 7.35857i −0.234542 + 0.239755i
\(943\) −17.6973 5.75021i −0.576304 0.187253i
\(944\) −7.46034 5.42025i −0.242813 0.176414i
\(945\) 13.5600 + 3.21010i 0.441108 + 0.104424i
\(946\) 19.3171 + 13.6164i 0.628052 + 0.442708i
\(947\) 21.9105i 0.711996i −0.934487 0.355998i \(-0.884141\pi\)
0.934487 0.355998i \(-0.115859\pi\)
\(948\) −0.654633 + 4.44915i −0.0212615 + 0.144502i
\(949\) −4.12320 + 12.6899i −0.133845 + 0.411931i
\(950\) −10.1408 31.2103i −0.329012 1.01260i
\(951\) 3.20913 6.47318i 0.104063 0.209907i
\(952\) −2.52292 4.40667i −0.0817684 0.142821i
\(953\) 17.6213 5.72551i 0.570810 0.185467i −0.00936930 0.999956i \(-0.502982\pi\)
0.580180 + 0.814489i \(0.302982\pi\)
\(954\) −25.6622 33.7359i −0.830845 1.09224i
\(955\) −5.78219 + 7.95851i −0.187107 + 0.257531i
\(956\) 2.79289i 0.0903287i
\(957\) 1.49898 + 2.76653i 0.0484553 + 0.0894293i
\(958\) 24.5072i 0.791792i
\(959\) −30.9241 + 34.0951i −0.998590 + 1.10099i
\(960\) −1.73088 + 0.293682i −0.0558641 + 0.00947854i
\(961\) 5.44975 + 16.7726i 0.175798 + 0.541051i
\(962\) 20.7946 15.1082i 0.670444 0.487106i
\(963\) −5.34610 + 0.117540i −0.172276 + 0.00378767i
\(964\) −20.5094 + 6.66391i −0.660564 + 0.214630i
\(965\) −1.09320 + 3.36453i −0.0351914 + 0.108308i
\(966\) 6.01203 23.1168i 0.193434 0.743771i
\(967\) −22.7786 −0.732510 −0.366255 0.930515i \(-0.619360\pi\)
−0.366255 + 0.930515i \(0.619360\pi\)
\(968\) −10.5547 3.09827i −0.339239 0.0995823i
\(969\) 24.3287 12.7348i 0.781549 0.409101i
\(970\) 9.41695 + 6.84181i 0.302360 + 0.219677i
\(971\) 5.68625 17.5005i 0.182480 0.561617i −0.817416 0.576048i \(-0.804594\pi\)
0.999896 + 0.0144318i \(0.00459395\pi\)
\(972\) −14.2572 6.30340i −0.457299 0.202182i
\(973\) −0.637341 1.11321i −0.0204322 0.0356880i
\(974\) −10.6992 14.7261i −0.342823 0.471855i
\(975\) 24.9911 + 24.4477i 0.800356 + 0.782953i
\(976\) −8.19555 2.66290i −0.262333 0.0852372i
\(977\) −23.2927 + 32.0596i −0.745198 + 1.02568i 0.253104 + 0.967439i \(0.418548\pi\)
−0.998303 + 0.0582385i \(0.981452\pi\)
\(978\) −26.2305 + 13.7303i −0.838758 + 0.439047i
\(979\) −0.733480 51.2276i −0.0234421 1.63724i
\(980\) −6.92933 1.52550i −0.221349 0.0487302i
\(981\) 28.8547 10.0819i 0.921260 0.321890i
\(982\) 6.53274 20.1057i 0.208468 0.641599i
\(983\) −2.54006 7.81751i −0.0810155 0.249340i 0.902342 0.431020i \(-0.141846\pi\)
−0.983358 + 0.181681i \(0.941846\pi\)
\(984\) 2.74651 5.54003i 0.0875556 0.176610i
\(985\) −5.95105 8.19092i −0.189616 0.260984i
\(986\) 0.324850 + 0.999784i 0.0103453 + 0.0318396i
\(987\) −38.6339 + 2.31011i −1.22973 + 0.0735317i
\(988\) −33.9562 24.6706i −1.08029 0.784877i
\(989\) 37.1422i 1.18105i
\(990\) 9.47225 3.46257i 0.301048 0.110048i
\(991\) −23.5798 −0.749038 −0.374519 0.927219i \(-0.622192\pi\)
−0.374519 + 0.927219i \(0.622192\pi\)
\(992\) 2.95754 + 2.14878i 0.0939019 + 0.0682237i
\(993\) −11.0288 + 1.87127i −0.349988 + 0.0593830i
\(994\) 4.76376 + 22.8184i 0.151097 + 0.723756i
\(995\) −5.32979 7.33583i −0.168966 0.232561i
\(996\) −19.7897 9.81089i −0.627061 0.310870i
\(997\) −29.8354 + 9.69412i −0.944898 + 0.307016i −0.740641 0.671901i \(-0.765478\pi\)
−0.204257 + 0.978917i \(0.565478\pi\)
\(998\) 11.6752 + 3.79351i 0.369572 + 0.120081i
\(999\) −19.1899 17.9644i −0.607143 0.568368i
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 462.2.s.a.125.15 yes 128
3.2 odd 2 inner 462.2.s.a.125.27 yes 128
7.6 odd 2 inner 462.2.s.a.125.2 128
11.3 even 5 inner 462.2.s.a.377.22 yes 128
21.20 even 2 inner 462.2.s.a.125.22 yes 128
33.14 odd 10 inner 462.2.s.a.377.2 yes 128
77.69 odd 10 inner 462.2.s.a.377.27 yes 128
231.146 even 10 inner 462.2.s.a.377.15 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.s.a.125.2 128 7.6 odd 2 inner
462.2.s.a.125.15 yes 128 1.1 even 1 trivial
462.2.s.a.125.22 yes 128 21.20 even 2 inner
462.2.s.a.125.27 yes 128 3.2 odd 2 inner
462.2.s.a.377.2 yes 128 33.14 odd 10 inner
462.2.s.a.377.15 yes 128 231.146 even 10 inner
462.2.s.a.377.22 yes 128 11.3 even 5 inner
462.2.s.a.377.27 yes 128 77.69 odd 10 inner