Properties

Label 819.2.ew.a.470.9
Level $819$
Weight $2$
Character 819.470
Analytic conductor $6.540$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(176,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.176");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ew (of order \(12\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 470.9
Character \(\chi\) \(=\) 819.470
Dual form 819.2.ew.a.176.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.63956 - 1.63956i) q^{2} +(1.73159 + 0.0399945i) q^{3} +3.37635i q^{4} +(-1.02893 + 3.84001i) q^{5} +(-2.77348 - 2.90463i) q^{6} +(0.258819 - 0.965926i) q^{7} +(2.25661 - 2.25661i) q^{8} +(2.99680 + 0.138508i) q^{9} +O(q^{10})\) \(q+(-1.63956 - 1.63956i) q^{2} +(1.73159 + 0.0399945i) q^{3} +3.37635i q^{4} +(-1.02893 + 3.84001i) q^{5} +(-2.77348 - 2.90463i) q^{6} +(0.258819 - 0.965926i) q^{7} +(2.25661 - 2.25661i) q^{8} +(2.99680 + 0.138508i) q^{9} +(7.98294 - 4.60895i) q^{10} +(-0.994890 + 0.994890i) q^{11} +(-0.135035 + 5.84644i) q^{12} +(-2.45328 + 2.64224i) q^{13} +(-2.00805 + 1.15935i) q^{14} +(-1.93526 + 6.60817i) q^{15} -0.647021 q^{16} +(-1.81546 + 3.14447i) q^{17} +(-4.68636 - 5.14054i) q^{18} +(-1.52825 - 5.70351i) q^{19} +(-12.9652 - 3.47401i) q^{20} +(0.486800 - 1.66224i) q^{21} +3.26237 q^{22} +(1.33402 - 2.31060i) q^{23} +(3.99777 - 3.81727i) q^{24} +(-9.35685 - 5.40218i) q^{25} +(8.35443 - 0.309823i) q^{26} +(5.18369 + 0.359694i) q^{27} +(3.26130 + 0.873863i) q^{28} +7.46624i q^{29} +(14.0075 - 7.66154i) q^{30} +(-4.03933 - 1.08234i) q^{31} +(-3.45238 - 3.45238i) q^{32} +(-1.76253 + 1.68295i) q^{33} +(8.13214 - 2.17900i) q^{34} +(3.44286 + 1.98774i) q^{35} +(-0.467651 + 10.1182i) q^{36} +(-1.05832 + 3.94969i) q^{37} +(-6.84560 + 11.8569i) q^{38} +(-4.35374 + 4.47716i) q^{39} +(6.34351 + 10.9873i) q^{40} +(-9.93822 + 2.66294i) q^{41} +(-3.52348 + 1.92720i) q^{42} +(-3.32543 + 1.91994i) q^{43} +(-3.35909 - 3.35909i) q^{44} +(-3.61536 + 11.3652i) q^{45} +(-5.97559 + 1.60115i) q^{46} +(1.64013 + 6.12104i) q^{47} +(-1.12037 - 0.0258773i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(6.48394 + 24.1984i) q^{50} +(-3.26940 + 5.37233i) q^{51} +(-8.92112 - 8.28311i) q^{52} +3.56844i q^{53} +(-7.90925 - 9.08873i) q^{54} +(-2.79672 - 4.84406i) q^{55} +(-1.59566 - 2.76377i) q^{56} +(-2.41819 - 9.93725i) q^{57} +(12.2414 - 12.2414i) q^{58} +(3.49703 - 3.49703i) q^{59} +(-22.3115 - 6.53410i) q^{60} +(2.96500 + 5.13554i) q^{61} +(4.84819 + 8.39731i) q^{62} +(0.909418 - 2.85884i) q^{63} +12.6149i q^{64} +(-7.62199 - 12.1393i) q^{65} +(5.64909 + 0.130477i) q^{66} +(1.38415 + 5.16570i) q^{67} +(-10.6168 - 6.12963i) q^{68} +(2.40239 - 3.94765i) q^{69} +(-2.38577 - 8.90381i) q^{70} +(1.51093 - 0.404854i) q^{71} +(7.07517 - 6.45005i) q^{72} +(0.403249 + 0.403249i) q^{73} +(8.21095 - 4.74060i) q^{74} +(-15.9862 - 9.72858i) q^{75} +(19.2570 - 5.15990i) q^{76} +(0.703493 + 1.21849i) q^{77} +(14.4788 - 0.202354i) q^{78} +(3.53774 - 6.12755i) q^{79} +(0.665738 - 2.48457i) q^{80} +(8.96163 + 0.830161i) q^{81} +(20.6604 + 11.9283i) q^{82} +(-12.1945 + 3.26752i) q^{83} +(5.61228 + 1.64360i) q^{84} +(-10.2068 - 10.2068i) q^{85} +(8.60011 + 2.30439i) q^{86} +(-0.298608 + 12.9285i) q^{87} +4.49015i q^{88} +(-1.61701 - 0.433276i) q^{89} +(24.5617 - 12.7064i) q^{90} +(1.91726 + 3.05354i) q^{91} +(7.80137 + 4.50412i) q^{92} +(-6.95118 - 2.03571i) q^{93} +(7.34675 - 12.7249i) q^{94} +23.4740 q^{95} +(-5.84004 - 6.11619i) q^{96} +(17.1380 + 4.59210i) q^{97} +(0.600122 + 2.23969i) q^{98} +(-3.11929 + 2.84369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63956 1.63956i −1.15935 1.15935i −0.984616 0.174731i \(-0.944094\pi\)
−0.174731 0.984616i \(-0.555906\pi\)
\(3\) 1.73159 + 0.0399945i 0.999733 + 0.0230908i
\(4\) 3.37635i 1.68817i
\(5\) −1.02893 + 3.84001i −0.460150 + 1.71730i 0.212338 + 0.977196i \(0.431892\pi\)
−0.672488 + 0.740108i \(0.734774\pi\)
\(6\) −2.77348 2.90463i −1.13227 1.18581i
\(7\) 0.258819 0.965926i 0.0978244 0.365086i
\(8\) 2.25661 2.25661i 0.797832 0.797832i
\(9\) 2.99680 + 0.138508i 0.998934 + 0.0461693i
\(10\) 7.98294 4.60895i 2.52443 1.45748i
\(11\) −0.994890 + 0.994890i −0.299971 + 0.299971i −0.841002 0.541032i \(-0.818034\pi\)
0.541032 + 0.841002i \(0.318034\pi\)
\(12\) −0.135035 + 5.84644i −0.0389813 + 1.68772i
\(13\) −2.45328 + 2.64224i −0.680416 + 0.732826i
\(14\) −2.00805 + 1.15935i −0.536674 + 0.309849i
\(15\) −1.93526 + 6.60817i −0.499682 + 1.70622i
\(16\) −0.647021 −0.161755
\(17\) −1.81546 + 3.14447i −0.440314 + 0.762647i −0.997713 0.0675984i \(-0.978466\pi\)
0.557398 + 0.830245i \(0.311800\pi\)
\(18\) −4.68636 5.14054i −1.10458 1.21164i
\(19\) −1.52825 5.70351i −0.350605 1.30847i −0.885926 0.463826i \(-0.846476\pi\)
0.535322 0.844648i \(-0.320190\pi\)
\(20\) −12.9652 3.47401i −2.89911 0.776813i
\(21\) 0.486800 1.66224i 0.106228 0.362729i
\(22\) 3.26237 0.695540
\(23\) 1.33402 2.31060i 0.278163 0.481792i −0.692765 0.721163i \(-0.743608\pi\)
0.970928 + 0.239371i \(0.0769411\pi\)
\(24\) 3.99777 3.81727i 0.816042 0.779196i
\(25\) −9.35685 5.40218i −1.87137 1.08044i
\(26\) 8.35443 0.309823i 1.63844 0.0607612i
\(27\) 5.18369 + 0.359694i 0.997601 + 0.0692232i
\(28\) 3.26130 + 0.873863i 0.616328 + 0.165145i
\(29\) 7.46624i 1.38645i 0.720723 + 0.693223i \(0.243810\pi\)
−0.720723 + 0.693223i \(0.756190\pi\)
\(30\) 14.0075 7.66154i 2.55741 1.39880i
\(31\) −4.03933 1.08234i −0.725486 0.194393i −0.122868 0.992423i \(-0.539209\pi\)
−0.602618 + 0.798030i \(0.705876\pi\)
\(32\) −3.45238 3.45238i −0.610301 0.610301i
\(33\) −1.76253 + 1.68295i −0.306817 + 0.292964i
\(34\) 8.13214 2.17900i 1.39465 0.373695i
\(35\) 3.44286 + 1.98774i 0.581949 + 0.335989i
\(36\) −0.467651 + 10.1182i −0.0779418 + 1.68637i
\(37\) −1.05832 + 3.94969i −0.173986 + 0.649325i 0.822736 + 0.568424i \(0.192447\pi\)
−0.996722 + 0.0809014i \(0.974220\pi\)
\(38\) −6.84560 + 11.8569i −1.11050 + 1.92345i
\(39\) −4.35374 + 4.47716i −0.697156 + 0.716919i
\(40\) 6.34351 + 10.9873i 1.00300 + 1.73724i
\(41\) −9.93822 + 2.66294i −1.55209 + 0.415881i −0.930149 0.367183i \(-0.880322\pi\)
−0.621941 + 0.783064i \(0.713656\pi\)
\(42\) −3.52348 + 1.92720i −0.543685 + 0.297374i
\(43\) −3.32543 + 1.91994i −0.507123 + 0.292788i −0.731650 0.681680i \(-0.761250\pi\)
0.224527 + 0.974468i \(0.427916\pi\)
\(44\) −3.35909 3.35909i −0.506402 0.506402i
\(45\) −3.61536 + 11.3652i −0.538946 + 1.69423i
\(46\) −5.97559 + 1.60115i −0.881052 + 0.236077i
\(47\) 1.64013 + 6.12104i 0.239237 + 0.892845i 0.976193 + 0.216904i \(0.0695960\pi\)
−0.736956 + 0.675941i \(0.763737\pi\)
\(48\) −1.12037 0.0258773i −0.161712 0.00373506i
\(49\) −0.866025 0.500000i −0.123718 0.0714286i
\(50\) 6.48394 + 24.1984i 0.916968 + 3.42217i
\(51\) −3.26940 + 5.37233i −0.457807 + 0.752276i
\(52\) −8.92112 8.28311i −1.23714 1.14866i
\(53\) 3.56844i 0.490162i 0.969503 + 0.245081i \(0.0788146\pi\)
−0.969503 + 0.245081i \(0.921185\pi\)
\(54\) −7.90925 9.08873i −1.07631 1.23682i
\(55\) −2.79672 4.84406i −0.377109 0.653172i
\(56\) −1.59566 2.76377i −0.213229 0.369324i
\(57\) −2.41819 9.93725i −0.320297 1.31622i
\(58\) 12.2414 12.2414i 1.60737 1.60737i
\(59\) 3.49703 3.49703i 0.455275 0.455275i −0.441826 0.897101i \(-0.645669\pi\)
0.897101 + 0.441826i \(0.145669\pi\)
\(60\) −22.3115 6.53410i −2.88040 0.843549i
\(61\) 2.96500 + 5.13554i 0.379630 + 0.657538i 0.991008 0.133800i \(-0.0427180\pi\)
−0.611379 + 0.791338i \(0.709385\pi\)
\(62\) 4.84819 + 8.39731i 0.615721 + 1.06646i
\(63\) 0.909418 2.85884i 0.114576 0.360180i
\(64\) 12.6149i 1.57686i
\(65\) −7.62199 12.1393i −0.945391 1.50569i
\(66\) 5.64909 + 0.130477i 0.695355 + 0.0160606i
\(67\) 1.38415 + 5.16570i 0.169100 + 0.631091i 0.997482 + 0.0709264i \(0.0225956\pi\)
−0.828381 + 0.560165i \(0.810738\pi\)
\(68\) −10.6168 6.12963i −1.28748 0.743327i
\(69\) 2.40239 3.94765i 0.289214 0.475241i
\(70\) −2.38577 8.90381i −0.285154 1.06421i
\(71\) 1.51093 0.404854i 0.179315 0.0480473i −0.168044 0.985779i \(-0.553745\pi\)
0.347359 + 0.937732i \(0.387078\pi\)
\(72\) 7.07517 6.45005i 0.833816 0.760146i
\(73\) 0.403249 + 0.403249i 0.0471967 + 0.0471967i 0.730311 0.683115i \(-0.239375\pi\)
−0.683115 + 0.730311i \(0.739375\pi\)
\(74\) 8.21095 4.74060i 0.954504 0.551083i
\(75\) −15.9862 9.72858i −1.84592 1.12336i
\(76\) 19.2570 5.15990i 2.20893 0.591881i
\(77\) 0.703493 + 1.21849i 0.0801705 + 0.138859i
\(78\) 14.4788 0.202354i 1.63940 0.0229121i
\(79\) 3.53774 6.12755i 0.398027 0.689403i −0.595456 0.803388i \(-0.703028\pi\)
0.993482 + 0.113986i \(0.0363618\pi\)
\(80\) 0.665738 2.48457i 0.0744317 0.277783i
\(81\) 8.96163 + 0.830161i 0.995737 + 0.0922401i
\(82\) 20.6604 + 11.9283i 2.28156 + 1.31726i
\(83\) −12.1945 + 3.26752i −1.33853 + 0.358657i −0.855887 0.517163i \(-0.826988\pi\)
−0.482638 + 0.875820i \(0.660321\pi\)
\(84\) 5.61228 + 1.64360i 0.612350 + 0.179332i
\(85\) −10.2068 10.2068i −1.10709 1.10709i
\(86\) 8.60011 + 2.30439i 0.927374 + 0.248489i
\(87\) −0.298608 + 12.9285i −0.0320142 + 1.38608i
\(88\) 4.49015i 0.478652i
\(89\) −1.61701 0.433276i −0.171402 0.0459272i 0.172097 0.985080i \(-0.444946\pi\)
−0.343500 + 0.939153i \(0.611612\pi\)
\(90\) 24.5617 12.7064i 2.58903 1.33937i
\(91\) 1.91726 + 3.05354i 0.200983 + 0.320098i
\(92\) 7.80137 + 4.50412i 0.813349 + 0.469587i
\(93\) −6.95118 2.03571i −0.720804 0.211094i
\(94\) 7.34675 12.7249i 0.757759 1.31248i
\(95\) 23.4740 2.40838
\(96\) −5.84004 6.11619i −0.596046 0.624231i
\(97\) 17.1380 + 4.59210i 1.74010 + 0.466258i 0.982469 0.186429i \(-0.0596913\pi\)
0.757628 + 0.652686i \(0.226358\pi\)
\(98\) 0.600122 + 2.23969i 0.0606215 + 0.226243i
\(99\) −3.11929 + 2.84369i −0.313500 + 0.285801i
\(100\) 18.2396 31.5920i 1.82396 3.15920i
\(101\) −13.5033 −1.34363 −0.671813 0.740721i \(-0.734484\pi\)
−0.671813 + 0.740721i \(0.734484\pi\)
\(102\) 14.1687 3.44789i 1.40291 0.341392i
\(103\) 11.5841 6.68807i 1.14141 0.658995i 0.194633 0.980876i \(-0.437648\pi\)
0.946780 + 0.321881i \(0.104315\pi\)
\(104\) 0.426423 + 11.4986i 0.0418142 + 1.12753i
\(105\) 5.88212 + 3.57964i 0.574036 + 0.349337i
\(106\) 5.85068 5.85068i 0.568268 0.568268i
\(107\) 0.446593 0.257841i 0.0431738 0.0249264i −0.478258 0.878220i \(-0.658732\pi\)
0.521432 + 0.853293i \(0.325398\pi\)
\(108\) −1.21445 + 17.5019i −0.116861 + 1.68412i
\(109\) −7.75153 + 7.75153i −0.742462 + 0.742462i −0.973051 0.230589i \(-0.925935\pi\)
0.230589 + 0.973051i \(0.425935\pi\)
\(110\) −3.35674 + 12.5275i −0.320053 + 1.19445i
\(111\) −1.99053 + 6.79691i −0.188933 + 0.645134i
\(112\) −0.167461 + 0.624974i −0.0158236 + 0.0590545i
\(113\) 17.9304i 1.68675i −0.537324 0.843376i \(-0.680565\pi\)
0.537324 0.843376i \(-0.319435\pi\)
\(114\) −12.3280 + 20.2576i −1.15462 + 1.89729i
\(115\) 7.50010 + 7.50010i 0.699387 + 0.699387i
\(116\) −25.2086 −2.34056
\(117\) −7.71795 + 7.57847i −0.713525 + 0.700630i
\(118\) −11.4672 −1.05564
\(119\) 2.56745 + 2.56745i 0.235358 + 0.235358i
\(120\) 10.5449 + 19.2792i 0.962616 + 1.75994i
\(121\) 9.02039i 0.820035i
\(122\) 3.55873 13.2814i 0.322192 1.20244i
\(123\) −17.3154 + 4.21364i −1.56128 + 0.379931i
\(124\) 3.65434 13.6382i 0.328170 1.22475i
\(125\) 16.3165 16.3165i 1.45940 1.45940i
\(126\) −6.17830 + 3.19620i −0.550407 + 0.284740i
\(127\) 16.9216 9.76967i 1.50155 0.866918i 0.501548 0.865130i \(-0.332764\pi\)
0.999998 0.00178875i \(-0.000569378\pi\)
\(128\) 13.7781 13.7781i 1.21782 1.21782i
\(129\) −5.83506 + 3.19154i −0.513748 + 0.281000i
\(130\) −7.40638 + 32.3999i −0.649583 + 2.84166i
\(131\) 1.94130 1.12081i 0.169612 0.0979257i −0.412791 0.910826i \(-0.635446\pi\)
0.582403 + 0.812900i \(0.302113\pi\)
\(132\) −5.68222 5.95091i −0.494574 0.517960i
\(133\) −5.90470 −0.512003
\(134\) 6.20011 10.7389i 0.535608 0.927700i
\(135\) −6.71487 + 19.5353i −0.577924 + 1.68133i
\(136\) 2.99906 + 11.1926i 0.257167 + 0.959761i
\(137\) 9.55061 + 2.55908i 0.815964 + 0.218637i 0.642581 0.766218i \(-0.277864\pi\)
0.173383 + 0.984855i \(0.444530\pi\)
\(138\) −10.4113 + 2.53355i −0.886269 + 0.215670i
\(139\) −11.8512 −1.00521 −0.502604 0.864517i \(-0.667625\pi\)
−0.502604 + 0.864517i \(0.667625\pi\)
\(140\) −6.71128 + 11.6243i −0.567207 + 0.982431i
\(141\) 2.59522 + 10.6647i 0.218557 + 0.898132i
\(142\) −3.14106 1.81349i −0.263592 0.152185i
\(143\) −0.188001 5.06948i −0.0157214 0.423931i
\(144\) −1.93899 0.0896175i −0.161583 0.00746813i
\(145\) −28.6704 7.68222i −2.38095 0.637974i
\(146\) 1.32231i 0.109435i
\(147\) −1.47960 0.900431i −0.122036 0.0742663i
\(148\) −13.3355 3.57324i −1.09617 0.293719i
\(149\) 7.55606 + 7.55606i 0.619016 + 0.619016i 0.945279 0.326263i \(-0.105789\pi\)
−0.326263 + 0.945279i \(0.605789\pi\)
\(150\) 10.2597 + 42.1610i 0.837702 + 3.44243i
\(151\) 0.167710 0.0449379i 0.0136481 0.00365699i −0.251989 0.967730i \(-0.581085\pi\)
0.265637 + 0.964073i \(0.414418\pi\)
\(152\) −16.3192 9.42192i −1.32367 0.764219i
\(153\) −5.87611 + 9.17190i −0.475056 + 0.741505i
\(154\) 0.844364 3.15121i 0.0680408 0.253932i
\(155\) 8.31236 14.3974i 0.667665 1.15643i
\(156\) −15.1164 14.6997i −1.21028 1.17692i
\(157\) 7.21321 + 12.4936i 0.575676 + 0.997101i 0.995968 + 0.0897117i \(0.0285946\pi\)
−0.420291 + 0.907389i \(0.638072\pi\)
\(158\) −15.8469 + 4.24615i −1.26071 + 0.337806i
\(159\) −0.142718 + 6.17906i −0.0113182 + 0.490032i
\(160\) 16.8094 9.70494i 1.32890 0.767243i
\(161\) −1.88659 1.88659i −0.148684 0.148684i
\(162\) −13.3321 16.0543i −1.04747 1.26134i
\(163\) 21.7751 5.83462i 1.70556 0.457003i 0.731230 0.682131i \(-0.238947\pi\)
0.974329 + 0.225128i \(0.0722802\pi\)
\(164\) −8.99100 33.5549i −0.702079 2.62020i
\(165\) −4.64903 8.49977i −0.361926 0.661706i
\(166\) 25.3511 + 14.6364i 1.96762 + 1.13601i
\(167\) −0.631732 2.35765i −0.0488849 0.182441i 0.937166 0.348883i \(-0.113439\pi\)
−0.986051 + 0.166442i \(0.946772\pi\)
\(168\) −2.65250 4.84953i −0.204645 0.374149i
\(169\) −0.962881 12.9643i −0.0740678 0.997253i
\(170\) 33.4695i 2.56699i
\(171\) −3.78988 17.3039i −0.289819 1.32327i
\(172\) −6.48237 11.2278i −0.494276 0.856111i
\(173\) 9.25659 + 16.0329i 0.703766 + 1.21896i 0.967135 + 0.254263i \(0.0818328\pi\)
−0.263369 + 0.964695i \(0.584834\pi\)
\(174\) 21.6866 20.7075i 1.64406 1.56983i
\(175\) −7.63984 + 7.63984i −0.577517 + 0.577517i
\(176\) 0.643715 0.643715i 0.0485218 0.0485218i
\(177\) 6.19529 5.91556i 0.465666 0.444641i
\(178\) 1.94081 + 3.36157i 0.145470 + 0.251961i
\(179\) −3.01792 5.22718i −0.225570 0.390698i 0.730921 0.682463i \(-0.239091\pi\)
−0.956490 + 0.291764i \(0.905758\pi\)
\(180\) −38.3729 12.2067i −2.86015 0.909835i
\(181\) 16.0398i 1.19223i 0.802900 + 0.596114i \(0.203289\pi\)
−0.802900 + 0.596114i \(0.796711\pi\)
\(182\) 1.86302 8.14995i 0.138096 0.604114i
\(183\) 4.92877 + 9.01122i 0.364345 + 0.666129i
\(184\) −2.20374 8.22448i −0.162462 0.606317i
\(185\) −14.0779 8.12789i −1.03503 0.597574i
\(186\) 8.05923 + 14.7346i 0.590931 + 1.08039i
\(187\) −1.32222 4.93459i −0.0966903 0.360853i
\(188\) −20.6667 + 5.53764i −1.50728 + 0.403874i
\(189\) 1.68908 4.91396i 0.122862 0.357438i
\(190\) −38.4871 38.4871i −2.79215 2.79215i
\(191\) 12.6148 7.28314i 0.912773 0.526990i 0.0314504 0.999505i \(-0.489987\pi\)
0.881322 + 0.472516i \(0.156654\pi\)
\(192\) −0.504524 + 21.8438i −0.0364109 + 1.57644i
\(193\) −12.5985 + 3.37577i −0.906862 + 0.242993i −0.681961 0.731389i \(-0.738873\pi\)
−0.224901 + 0.974382i \(0.572206\pi\)
\(194\) −20.5698 35.6279i −1.47682 2.55793i
\(195\) −12.7127 21.3251i −0.910372 1.52712i
\(196\) 1.68817 2.92400i 0.120584 0.208857i
\(197\) 1.81813 6.78536i 0.129537 0.483437i −0.870424 0.492303i \(-0.836155\pi\)
0.999961 + 0.00886559i \(0.00282204\pi\)
\(198\) 9.77668 + 0.451864i 0.694799 + 0.0321126i
\(199\) −21.4802 12.4016i −1.52269 0.879125i −0.999640 0.0268219i \(-0.991461\pi\)
−0.523049 0.852303i \(-0.675205\pi\)
\(200\) −33.3054 + 8.92415i −2.35504 + 0.631032i
\(201\) 2.19017 + 9.00024i 0.154483 + 0.634828i
\(202\) 22.1395 + 22.1395i 1.55773 + 1.55773i
\(203\) 7.21183 + 1.93241i 0.506172 + 0.135628i
\(204\) −18.1388 11.0386i −1.26997 0.772858i
\(205\) 40.9028i 2.85678i
\(206\) −29.9584 8.02732i −2.08730 0.559290i
\(207\) 4.31784 6.73962i 0.300110 0.468436i
\(208\) 1.58732 1.70959i 0.110061 0.118538i
\(209\) 7.19480 + 4.15392i 0.497675 + 0.287333i
\(210\) −3.77507 15.5132i −0.260504 1.07051i
\(211\) −3.65186 + 6.32520i −0.251404 + 0.435445i −0.963913 0.266219i \(-0.914226\pi\)
0.712509 + 0.701663i \(0.247559\pi\)
\(212\) −12.0483 −0.827479
\(213\) 2.63251 0.640611i 0.180377 0.0438940i
\(214\) −1.15497 0.309472i −0.0789518 0.0211551i
\(215\) −3.95095 14.7451i −0.269453 1.00561i
\(216\) 12.5092 10.8859i 0.851146 0.740689i
\(217\) −2.09091 + 3.62157i −0.141940 + 0.245848i
\(218\) 25.4183 1.72154
\(219\) 0.682134 + 0.714390i 0.0460944 + 0.0482740i
\(220\) 16.3552 9.44268i 1.10267 0.636626i
\(221\) −3.85463 12.5111i −0.259290 0.841591i
\(222\) 14.4076 7.88037i 0.966974 0.528896i
\(223\) −4.07179 + 4.07179i −0.272667 + 0.272667i −0.830173 0.557506i \(-0.811758\pi\)
0.557506 + 0.830173i \(0.311758\pi\)
\(224\) −4.22829 + 2.44120i −0.282515 + 0.163110i
\(225\) −27.2924 17.4853i −1.81949 1.16568i
\(226\) −29.3981 + 29.3981i −1.95553 + 1.95553i
\(227\) −0.0393840 + 0.146983i −0.00261401 + 0.00975561i −0.967221 0.253938i \(-0.918274\pi\)
0.964607 + 0.263694i \(0.0849408\pi\)
\(228\) 33.5516 8.16465i 2.22201 0.540717i
\(229\) −5.86816 + 21.9003i −0.387779 + 1.44721i 0.445961 + 0.895052i \(0.352862\pi\)
−0.833740 + 0.552158i \(0.813805\pi\)
\(230\) 24.5938i 1.62167i
\(231\) 1.16943 + 2.13805i 0.0769428 + 0.140674i
\(232\) 16.8484 + 16.8484i 1.10615 + 1.10615i
\(233\) 15.2929 1.00187 0.500935 0.865485i \(-0.332989\pi\)
0.500935 + 0.865485i \(0.332989\pi\)
\(234\) 25.0795 + 0.228678i 1.63950 + 0.0149492i
\(235\) −25.1924 −1.64337
\(236\) 11.8072 + 11.8072i 0.768583 + 0.768583i
\(237\) 6.37098 10.4689i 0.413840 0.680028i
\(238\) 8.41901i 0.545723i
\(239\) 4.31588 16.1071i 0.279171 1.04188i −0.673823 0.738893i \(-0.735349\pi\)
0.952994 0.302988i \(-0.0979842\pi\)
\(240\) 1.25215 4.27562i 0.0808261 0.275990i
\(241\) −6.65807 + 24.8482i −0.428884 + 1.60062i 0.326409 + 0.945229i \(0.394161\pi\)
−0.755293 + 0.655388i \(0.772505\pi\)
\(242\) 14.7895 14.7895i 0.950706 0.950706i
\(243\) 15.4847 + 1.79591i 0.993341 + 0.115208i
\(244\) −17.3393 + 10.0109i −1.11004 + 0.640881i
\(245\) 2.81108 2.81108i 0.179593 0.179593i
\(246\) 35.2983 + 21.4812i 2.25054 + 1.36959i
\(247\) 18.8193 + 9.95427i 1.19744 + 0.633375i
\(248\) −11.5576 + 6.67279i −0.733909 + 0.423722i
\(249\) −21.2466 + 5.17029i −1.34645 + 0.327654i
\(250\) −53.5040 −3.38389
\(251\) −2.41048 + 4.17508i −0.152148 + 0.263529i −0.932017 0.362414i \(-0.881953\pi\)
0.779869 + 0.625943i \(0.215286\pi\)
\(252\) 9.65243 + 3.07051i 0.608046 + 0.193424i
\(253\) 0.971582 + 3.62599i 0.0610828 + 0.227964i
\(254\) −43.7620 11.7260i −2.74587 0.735755i
\(255\) −17.2658 18.0822i −1.08123 1.13235i
\(256\) −19.9505 −1.24691
\(257\) −11.9475 + 20.6937i −0.745267 + 1.29084i 0.204804 + 0.978803i \(0.434344\pi\)
−0.950070 + 0.312036i \(0.898989\pi\)
\(258\) 14.7997 + 4.33422i 0.921389 + 0.269837i
\(259\) 3.54120 + 2.04451i 0.220039 + 0.127040i
\(260\) 40.9864 25.7345i 2.54187 1.59598i
\(261\) −1.03413 + 22.3748i −0.0640112 + 1.38497i
\(262\) −5.02053 1.34525i −0.310169 0.0831096i
\(263\) 11.2773i 0.695389i 0.937608 + 0.347695i \(0.113035\pi\)
−0.937608 + 0.347695i \(0.886965\pi\)
\(264\) −0.179581 + 7.77510i −0.0110525 + 0.478524i
\(265\) −13.7028 3.67166i −0.841758 0.225548i
\(266\) 9.68115 + 9.68115i 0.593589 + 0.593589i
\(267\) −2.78266 0.814927i −0.170296 0.0498727i
\(268\) −17.4412 + 4.67336i −1.06539 + 0.285471i
\(269\) −23.8331 13.7600i −1.45313 0.838964i −0.454470 0.890762i \(-0.650171\pi\)
−0.998658 + 0.0517984i \(0.983505\pi\)
\(270\) 43.0389 21.0199i 2.61926 1.27923i
\(271\) −0.0567513 + 0.211799i −0.00344740 + 0.0128659i −0.967628 0.252380i \(-0.918787\pi\)
0.964181 + 0.265246i \(0.0854532\pi\)
\(272\) 1.17464 2.03454i 0.0712232 0.123362i
\(273\) 3.19777 + 5.36416i 0.193538 + 0.324654i
\(274\) −11.4631 19.8546i −0.692510 1.19946i
\(275\) 14.6836 3.93446i 0.885455 0.237257i
\(276\) 13.3286 + 8.11130i 0.802289 + 0.488243i
\(277\) 23.4200 13.5215i 1.40717 0.812431i 0.412057 0.911158i \(-0.364811\pi\)
0.995115 + 0.0987274i \(0.0314772\pi\)
\(278\) 19.4308 + 19.4308i 1.16538 + 1.16538i
\(279\) −11.9552 3.80303i −0.715737 0.227681i
\(280\) 12.2547 3.28364i 0.732360 0.196235i
\(281\) −1.96670 7.33983i −0.117324 0.437858i 0.882127 0.471012i \(-0.156111\pi\)
−0.999450 + 0.0331547i \(0.989445\pi\)
\(282\) 13.2305 21.7405i 0.787863 1.29463i
\(283\) −12.9060 7.45126i −0.767180 0.442932i 0.0646878 0.997906i \(-0.479395\pi\)
−0.831868 + 0.554974i \(0.812728\pi\)
\(284\) 1.36693 + 5.10144i 0.0811121 + 0.302715i
\(285\) 40.6473 + 0.938829i 2.40774 + 0.0556114i
\(286\) −8.00350 + 8.61998i −0.473257 + 0.509710i
\(287\) 10.2888i 0.607329i
\(288\) −9.86793 10.8243i −0.581473 0.637828i
\(289\) 1.90819 + 3.30508i 0.112247 + 0.194417i
\(290\) 34.4115 + 59.6025i 2.02071 + 3.49998i
\(291\) 29.4923 + 8.63706i 1.72887 + 0.506313i
\(292\) −1.36151 + 1.36151i −0.0796763 + 0.0796763i
\(293\) 13.7280 13.7280i 0.801998 0.801998i −0.181410 0.983408i \(-0.558066\pi\)
0.983408 + 0.181410i \(0.0580660\pi\)
\(294\) 0.949590 + 3.90222i 0.0553812 + 0.227582i
\(295\) 9.83045 + 17.0268i 0.572351 + 0.991340i
\(296\) 6.52470 + 11.3011i 0.379240 + 0.656864i
\(297\) −5.51505 + 4.79934i −0.320016 + 0.278486i
\(298\) 24.7773i 1.43531i
\(299\) 2.83243 + 9.19334i 0.163803 + 0.531664i
\(300\) 32.8471 53.9748i 1.89643 3.11624i
\(301\) 0.993832 + 3.70903i 0.0572835 + 0.213785i
\(302\) −0.348651 0.201294i −0.0200626 0.0115831i
\(303\) −23.3821 0.540056i −1.34327 0.0310254i
\(304\) 0.988810 + 3.69029i 0.0567121 + 0.211653i
\(305\) −22.7713 + 6.10155i −1.30388 + 0.349374i
\(306\) 24.6722 5.40366i 1.41042 0.308907i
\(307\) 5.15172 + 5.15172i 0.294024 + 0.294024i 0.838668 0.544644i \(-0.183335\pi\)
−0.544644 + 0.838668i \(0.683335\pi\)
\(308\) −4.11403 + 2.37524i −0.234419 + 0.135342i
\(309\) 20.3263 11.1177i 1.15633 0.632463i
\(310\) −37.2342 + 9.97687i −2.11476 + 0.566648i
\(311\) 3.54946 + 6.14784i 0.201271 + 0.348612i 0.948938 0.315462i \(-0.102159\pi\)
−0.747667 + 0.664074i \(0.768826\pi\)
\(312\) 0.278510 + 19.9279i 0.0157675 + 1.12819i
\(313\) 13.4840 23.3549i 0.762160 1.32010i −0.179576 0.983744i \(-0.557473\pi\)
0.941735 0.336355i \(-0.109194\pi\)
\(314\) 8.65761 32.3107i 0.488577 1.82340i
\(315\) 10.0422 + 6.43371i 0.565816 + 0.362498i
\(316\) 20.6887 + 11.9446i 1.16383 + 0.671938i
\(317\) 1.09637 0.293771i 0.0615782 0.0164998i −0.227898 0.973685i \(-0.573185\pi\)
0.289477 + 0.957185i \(0.406519\pi\)
\(318\) 10.3650 9.89698i 0.581239 0.554995i
\(319\) −7.42809 7.42809i −0.415893 0.415893i
\(320\) −48.4412 12.9798i −2.70794 0.725591i
\(321\) 0.783628 0.428613i 0.0437379 0.0239228i
\(322\) 6.18638i 0.344754i
\(323\) 20.7090 + 5.54896i 1.15228 + 0.308752i
\(324\) −2.80291 + 30.2576i −0.155717 + 1.68098i
\(325\) 37.2288 11.4700i 2.06508 0.636243i
\(326\) −45.2680 26.1355i −2.50716 1.44751i
\(327\) −13.7325 + 13.1125i −0.759408 + 0.725120i
\(328\) −16.4175 + 28.4359i −0.906503 + 1.57011i
\(329\) 6.33697 0.349368
\(330\) −6.31353 + 21.5583i −0.347549 + 1.18675i
\(331\) 9.15162 + 2.45217i 0.503018 + 0.134783i 0.501400 0.865215i \(-0.332818\pi\)
0.00161785 + 0.999999i \(0.499485\pi\)
\(332\) −11.0323 41.1730i −0.605475 2.25966i
\(333\) −3.71863 + 11.6898i −0.203779 + 0.640600i
\(334\) −2.82976 + 4.90129i −0.154838 + 0.268187i
\(335\) −21.2605 −1.16159
\(336\) −0.314970 + 1.07550i −0.0171830 + 0.0586734i
\(337\) −18.8678 + 10.8933i −1.02779 + 0.593397i −0.916352 0.400374i \(-0.868880\pi\)
−0.111442 + 0.993771i \(0.535547\pi\)
\(338\) −19.6771 + 22.8345i −1.07029 + 1.24203i
\(339\) 0.717117 31.0481i 0.0389485 1.68630i
\(340\) 34.4618 34.4618i 1.86895 1.86895i
\(341\) 5.09550 2.94189i 0.275937 0.159312i
\(342\) −22.1572 + 34.5847i −1.19812 + 1.87013i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) −3.17164 + 11.8367i −0.171004 + 0.638194i
\(345\) 12.6871 + 13.2870i 0.683052 + 0.715350i
\(346\) 11.1102 41.4637i 0.597287 2.22910i
\(347\) 14.9330i 0.801644i 0.916156 + 0.400822i \(0.131275\pi\)
−0.916156 + 0.400822i \(0.868725\pi\)
\(348\) −43.6510 1.00820i −2.33994 0.0540454i
\(349\) 15.9340 + 15.9340i 0.852927 + 0.852927i 0.990493 0.137566i \(-0.0439279\pi\)
−0.137566 + 0.990493i \(0.543928\pi\)
\(350\) 25.0520 1.33909
\(351\) −13.6674 + 12.8141i −0.729512 + 0.683967i
\(352\) 6.86948 0.366145
\(353\) 21.4784 + 21.4784i 1.14318 + 1.14318i 0.987865 + 0.155318i \(0.0496401\pi\)
0.155318 + 0.987865i \(0.450360\pi\)
\(354\) −19.8565 0.458625i −1.05536 0.0243757i
\(355\) 6.21857i 0.330047i
\(356\) 1.46289 5.45958i 0.0775330 0.289357i
\(357\) 4.34309 + 4.54846i 0.229861 + 0.240730i
\(358\) −3.62224 + 13.5184i −0.191441 + 0.714469i
\(359\) 16.1630 16.1630i 0.853051 0.853051i −0.137457 0.990508i \(-0.543893\pi\)
0.990508 + 0.137457i \(0.0438928\pi\)
\(360\) 17.4884 + 33.8053i 0.921720 + 1.78170i
\(361\) −13.7400 + 7.93277i −0.723156 + 0.417514i
\(362\) 26.2983 26.2983i 1.38221 1.38221i
\(363\) −0.360766 + 15.6196i −0.0189353 + 0.819817i
\(364\) −10.3098 + 6.47332i −0.540382 + 0.339294i
\(365\) −1.96339 + 1.13357i −0.102769 + 0.0593336i
\(366\) 6.69344 22.8555i 0.349872 1.19468i
\(367\) 13.2297 0.690583 0.345292 0.938495i \(-0.387780\pi\)
0.345292 + 0.938495i \(0.387780\pi\)
\(368\) −0.863141 + 1.49500i −0.0449943 + 0.0779325i
\(369\) −30.1517 + 6.60377i −1.56964 + 0.343779i
\(370\) 9.75546 + 36.4079i 0.507162 + 1.89275i
\(371\) 3.44684 + 0.923579i 0.178951 + 0.0479498i
\(372\) 6.87327 23.4696i 0.356363 1.21684i
\(373\) 18.7340 0.970011 0.485005 0.874511i \(-0.338818\pi\)
0.485005 + 0.874511i \(0.338818\pi\)
\(374\) −5.92272 + 10.2584i −0.306256 + 0.530452i
\(375\) 28.9061 27.6010i 1.49270 1.42531i
\(376\) 17.5139 + 10.1117i 0.903211 + 0.521469i
\(377\) −19.7276 18.3167i −1.01602 0.943360i
\(378\) −10.8261 + 5.28741i −0.556835 + 0.271955i
\(379\) −17.7073 4.74467i −0.909565 0.243717i −0.226445 0.974024i \(-0.572711\pi\)
−0.683119 + 0.730307i \(0.739377\pi\)
\(380\) 79.2563i 4.06576i
\(381\) 29.6919 16.2403i 1.52116 0.832015i
\(382\) −32.6239 8.74155i −1.66918 0.447257i
\(383\) −5.32746 5.32746i −0.272220 0.272220i 0.557773 0.829993i \(-0.311656\pi\)
−0.829993 + 0.557773i \(0.811656\pi\)
\(384\) 24.4091 23.3070i 1.24562 1.18938i
\(385\) −5.40284 + 1.44769i −0.275354 + 0.0737810i
\(386\) 26.1909 + 15.1213i 1.33308 + 0.769655i
\(387\) −10.2316 + 5.29307i −0.520100 + 0.269062i
\(388\) −15.5045 + 57.8637i −0.787123 + 2.93758i
\(389\) −5.66970 + 9.82020i −0.287465 + 0.497904i −0.973204 0.229944i \(-0.926146\pi\)
0.685739 + 0.727848i \(0.259479\pi\)
\(390\) −14.1206 + 55.8071i −0.715026 + 2.82590i
\(391\) 4.84374 + 8.38960i 0.244958 + 0.424280i
\(392\) −3.08259 + 0.825976i −0.155694 + 0.0417181i
\(393\) 3.40636 1.86314i 0.171828 0.0939831i
\(394\) −14.1060 + 8.14409i −0.710649 + 0.410294i
\(395\) 19.8898 + 19.8898i 1.00076 + 1.00076i
\(396\) −9.60127 10.5318i −0.482482 0.529242i
\(397\) 25.8310 6.92139i 1.29642 0.347375i 0.456324 0.889813i \(-0.349166\pi\)
0.840095 + 0.542439i \(0.182499\pi\)
\(398\) 14.8849 + 55.5513i 0.746114 + 2.78454i
\(399\) −10.2245 0.236155i −0.511866 0.0118226i
\(400\) 6.05408 + 3.49532i 0.302704 + 0.174766i
\(401\) −4.07143 15.1948i −0.203318 0.758791i −0.989956 0.141377i \(-0.954847\pi\)
0.786638 0.617414i \(-0.211820\pi\)
\(402\) 11.1655 18.3474i 0.556887 0.915085i
\(403\) 12.7694 8.01763i 0.636089 0.399387i
\(404\) 45.5917i 2.26827i
\(405\) −12.4087 + 33.5586i −0.616593 + 1.66754i
\(406\) −8.65597 14.9926i −0.429588 0.744069i
\(407\) −2.87660 4.98241i −0.142588 0.246969i
\(408\) 4.74549 + 19.5010i 0.234937 + 0.965443i
\(409\) 16.3728 16.3728i 0.809581 0.809581i −0.174989 0.984570i \(-0.555989\pi\)
0.984570 + 0.174989i \(0.0559890\pi\)
\(410\) −67.0629 + 67.0629i −3.31200 + 3.31200i
\(411\) 16.4354 + 4.81324i 0.810698 + 0.237420i
\(412\) 22.5812 + 39.1118i 1.11250 + 1.92690i
\(413\) −2.47278 4.28297i −0.121677 0.210751i
\(414\) −18.1294 + 3.97067i −0.891012 + 0.195148i
\(415\) 50.1892i 2.46369i
\(416\) 17.5917 0.652384i 0.862503 0.0319858i
\(417\) −20.5214 0.473983i −1.00494 0.0232111i
\(418\) −4.98572 18.6070i −0.243860 0.910096i
\(419\) 12.5426 + 7.24145i 0.612744 + 0.353768i 0.774039 0.633139i \(-0.218234\pi\)
−0.161295 + 0.986906i \(0.551567\pi\)
\(420\) −12.0861 + 19.8601i −0.589741 + 0.969072i
\(421\) −5.80567 21.6671i −0.282951 1.05599i −0.950323 0.311264i \(-0.899248\pi\)
0.667372 0.744724i \(-0.267419\pi\)
\(422\) 16.3580 4.38312i 0.796296 0.213367i
\(423\) 4.06732 + 18.5707i 0.197760 + 0.902939i
\(424\) 8.05256 + 8.05256i 0.391067 + 0.391067i
\(425\) 33.9740 19.6149i 1.64798 0.951463i
\(426\) −5.36649 3.26585i −0.260007 0.158231i
\(427\) 5.72795 1.53480i 0.277195 0.0742741i
\(428\) 0.870560 + 1.50785i 0.0420801 + 0.0728849i
\(429\) −0.122789 8.78577i −0.00592830 0.424181i
\(430\) −17.6978 + 30.6535i −0.853463 + 1.47824i
\(431\) −7.12093 + 26.5757i −0.343003 + 1.28010i 0.551925 + 0.833894i \(0.313894\pi\)
−0.894928 + 0.446211i \(0.852773\pi\)
\(432\) −3.35396 0.232730i −0.161367 0.0111972i
\(433\) 4.28144 + 2.47189i 0.205753 + 0.118792i 0.599336 0.800497i \(-0.295431\pi\)
−0.393583 + 0.919289i \(0.628765\pi\)
\(434\) 9.36598 2.50961i 0.449582 0.120465i
\(435\) −49.3382 14.4491i −2.36558 0.692781i
\(436\) −26.1719 26.1719i −1.25340 1.25340i
\(437\) −15.2172 4.07744i −0.727938 0.195050i
\(438\) 0.0528849 2.28969i 0.00252694 0.109406i
\(439\) 8.07641i 0.385466i −0.981251 0.192733i \(-0.938265\pi\)
0.981251 0.192733i \(-0.0617351\pi\)
\(440\) −17.2422 4.62004i −0.821991 0.220252i
\(441\) −2.52605 1.61835i −0.120288 0.0770644i
\(442\) −14.1929 + 26.8328i −0.675089 + 1.27630i
\(443\) −34.6653 20.0140i −1.64700 0.950894i −0.978257 0.207398i \(-0.933501\pi\)
−0.668740 0.743496i \(-0.733166\pi\)
\(444\) −22.9487 6.72073i −1.08910 0.318952i
\(445\) 3.32757 5.76352i 0.157742 0.273217i
\(446\) 13.3519 0.632232
\(447\) 12.7818 + 13.3862i 0.604558 + 0.633145i
\(448\) 12.1850 + 3.26497i 0.575688 + 0.154255i
\(449\) −4.42512 16.5148i −0.208834 0.779380i −0.988246 0.152869i \(-0.951149\pi\)
0.779412 0.626512i \(-0.215518\pi\)
\(450\) 16.0794 + 73.4158i 0.757991 + 3.46086i
\(451\) 7.23811 12.5368i 0.340829 0.590333i
\(452\) 60.5393 2.84753
\(453\) 0.292203 0.0711064i 0.0137289 0.00334087i
\(454\) 0.305561 0.176416i 0.0143407 0.00827960i
\(455\) −13.6984 + 4.22040i −0.642189 + 0.197855i
\(456\) −27.8814 16.9676i −1.30567 0.794580i
\(457\) 21.0950 21.0950i 0.986782 0.986782i −0.0131317 0.999914i \(-0.504180\pi\)
0.999914 + 0.0131317i \(0.00418007\pi\)
\(458\) 45.5281 26.2857i 2.12739 1.22825i
\(459\) −10.5418 + 15.6470i −0.492051 + 0.730337i
\(460\) −25.3229 + 25.3229i −1.18069 + 1.18069i
\(461\) 1.32518 4.94562i 0.0617196 0.230341i −0.928175 0.372143i \(-0.878623\pi\)
0.989895 + 0.141802i \(0.0452898\pi\)
\(462\) 1.58812 5.42283i 0.0738862 0.252293i
\(463\) −5.34491 + 19.9475i −0.248399 + 0.927037i 0.723246 + 0.690591i \(0.242649\pi\)
−0.971645 + 0.236446i \(0.924017\pi\)
\(464\) 4.83081i 0.224265i
\(465\) 14.9694 24.5980i 0.694190 1.14070i
\(466\) −25.0737 25.0737i −1.16152 1.16152i
\(467\) −10.5443 −0.487932 −0.243966 0.969784i \(-0.578449\pi\)
−0.243966 + 0.969784i \(0.578449\pi\)
\(468\) −25.5876 26.0585i −1.18278 1.20455i
\(469\) 5.34793 0.246945
\(470\) 41.3046 + 41.3046i 1.90524 + 1.90524i
\(471\) 11.9906 + 21.9223i 0.552499 + 1.01013i
\(472\) 15.7829i 0.726465i
\(473\) 1.39831 5.21856i 0.0642943 0.239950i
\(474\) −27.6101 + 6.71881i −1.26817 + 0.308605i
\(475\) −16.5118 + 61.6228i −0.757612 + 2.82745i
\(476\) −8.66861 + 8.66861i −0.397325 + 0.397325i
\(477\) −0.494257 + 10.6939i −0.0226305 + 0.489640i
\(478\) −33.4848 + 19.3324i −1.53156 + 0.884245i
\(479\) 23.3791 23.3791i 1.06822 1.06822i 0.0707238 0.997496i \(-0.477469\pi\)
0.997496 0.0707238i \(-0.0225309\pi\)
\(480\) 29.4952 16.1327i 1.34627 0.736353i
\(481\) −7.83969 12.4860i −0.357459 0.569313i
\(482\) 51.6566 29.8240i 2.35290 1.35845i
\(483\) −3.19135 3.34226i −0.145211 0.152078i
\(484\) −30.4560 −1.38436
\(485\) −35.2674 + 61.0850i −1.60141 + 2.77373i
\(486\) −22.4436 28.3326i −1.01806 1.28519i
\(487\) 3.94924 + 14.7388i 0.178957 + 0.667877i 0.995844 + 0.0910787i \(0.0290315\pi\)
−0.816887 + 0.576798i \(0.804302\pi\)
\(488\) 18.2798 + 4.89804i 0.827485 + 0.221724i
\(489\) 37.9389 9.23229i 1.71566 0.417498i
\(490\) −9.21790 −0.416422
\(491\) −3.92389 + 6.79638i −0.177083 + 0.306717i −0.940880 0.338740i \(-0.889999\pi\)
0.763797 + 0.645456i \(0.223333\pi\)
\(492\) −14.2267 58.4628i −0.641390 2.63571i
\(493\) −23.4774 13.5547i −1.05737 0.610472i
\(494\) −14.5347 47.1761i −0.653949 2.12255i
\(495\) −7.71026 14.9040i −0.346551 0.669887i
\(496\) 2.61353 + 0.700294i 0.117351 + 0.0314441i
\(497\) 1.56423i 0.0701655i
\(498\) 43.3122 + 26.3582i 1.94087 + 1.18114i
\(499\) 0.356915 + 0.0956351i 0.0159777 + 0.00428122i 0.266799 0.963752i \(-0.414034\pi\)
−0.250821 + 0.968033i \(0.580701\pi\)
\(500\) 55.0903 + 55.0903i 2.46371 + 2.46371i
\(501\) −0.999607 4.10776i −0.0446591 0.183521i
\(502\) 10.7975 2.89317i 0.481914 0.129129i
\(503\) 24.7467 + 14.2875i 1.10340 + 0.637049i 0.937112 0.349028i \(-0.113488\pi\)
0.166289 + 0.986077i \(0.446822\pi\)
\(504\) −4.39908 8.50348i −0.195951 0.378775i
\(505\) 13.8939 51.8527i 0.618270 2.30741i
\(506\) 4.35208 7.53802i 0.193474 0.335106i
\(507\) −1.14881 22.4873i −0.0510206 0.998698i
\(508\) 32.9858 + 57.1331i 1.46351 + 2.53487i
\(509\) 35.8540 9.60704i 1.58920 0.425825i 0.647441 0.762116i \(-0.275839\pi\)
0.941758 + 0.336291i \(0.109173\pi\)
\(510\) −1.33859 + 57.9554i −0.0592740 + 2.56631i
\(511\) 0.493877 0.285140i 0.0218478 0.0126139i
\(512\) 5.15391 + 5.15391i 0.227773 + 0.227773i
\(513\) −5.87045 30.1149i −0.259187 1.32961i
\(514\) 53.5175 14.3400i 2.36055 0.632509i
\(515\) 13.7631 + 51.3645i 0.606474 + 2.26339i
\(516\) −10.7757 19.7012i −0.474376 0.867296i
\(517\) −7.72151 4.45801i −0.339591 0.196063i
\(518\) −2.45391 9.15813i −0.107819 0.402385i
\(519\) 15.3874 + 28.1326i 0.675431 + 1.23488i
\(520\) −44.5934 10.1937i −1.95555 0.447025i
\(521\) 11.2240i 0.491732i 0.969304 + 0.245866i \(0.0790723\pi\)
−0.969304 + 0.245866i \(0.920928\pi\)
\(522\) 38.3805 34.9895i 1.67987 1.53145i
\(523\) −11.8559 20.5351i −0.518423 0.897936i −0.999771 0.0214059i \(-0.993186\pi\)
0.481347 0.876530i \(-0.340148\pi\)
\(524\) 3.78424 + 6.55450i 0.165315 + 0.286335i
\(525\) −13.5346 + 12.9235i −0.590699 + 0.564028i
\(526\) 18.4899 18.4899i 0.806198 0.806198i
\(527\) 10.7366 10.7366i 0.467695 0.467695i
\(528\) 1.14039 1.08890i 0.0496293 0.0473885i
\(529\) 7.94077 + 13.7538i 0.345251 + 0.597992i
\(530\) 16.4467 + 28.4866i 0.714401 + 1.23738i
\(531\) 10.9643 9.99554i 0.475809 0.433770i
\(532\) 19.9363i 0.864349i
\(533\) 17.3451 32.7921i 0.751298 1.42038i
\(534\) 3.22623 + 5.89849i 0.139613 + 0.255252i
\(535\) 0.530599 + 1.98022i 0.0229398 + 0.0856125i
\(536\) 14.7805 + 8.53350i 0.638418 + 0.368591i
\(537\) −5.01673 9.17204i −0.216488 0.395803i
\(538\) 16.5154 + 61.6363i 0.712029 + 2.65733i
\(539\) 1.35904 0.364155i 0.0585382 0.0156853i
\(540\) −65.9580 22.6717i −2.83838 0.975635i
\(541\) 2.75010 + 2.75010i 0.118236 + 0.118236i 0.763749 0.645513i \(-0.223356\pi\)
−0.645513 + 0.763749i \(0.723356\pi\)
\(542\) 0.440305 0.254210i 0.0189127 0.0109193i
\(543\) −0.641503 + 27.7743i −0.0275295 + 1.19191i
\(544\) 17.1236 4.58826i 0.734169 0.196720i
\(545\) −21.7902 37.7417i −0.933389 1.61668i
\(546\) 3.55194 14.0379i 0.152009 0.600765i
\(547\) −18.9113 + 32.7553i −0.808587 + 1.40051i 0.105255 + 0.994445i \(0.466434\pi\)
−0.913842 + 0.406069i \(0.866899\pi\)
\(548\) −8.64034 + 32.2462i −0.369097 + 1.37749i
\(549\) 8.17421 + 15.8009i 0.348867 + 0.674364i
\(550\) −30.5255 17.6239i −1.30161 0.751487i
\(551\) 42.5838 11.4103i 1.81413 0.486094i
\(552\) −3.48704 14.3296i −0.148418 0.609906i
\(553\) −5.00312 5.00312i −0.212754 0.212754i
\(554\) −60.5681 16.2292i −2.57329 0.689511i
\(555\) −24.0521 14.6372i −1.02095 0.621315i
\(556\) 40.0138i 1.69696i
\(557\) −1.48344 0.397487i −0.0628554 0.0168421i 0.227254 0.973835i \(-0.427025\pi\)
−0.290110 + 0.956993i \(0.593692\pi\)
\(558\) 13.3660 + 25.8366i 0.565827 + 1.09375i
\(559\) 3.08525 13.4967i 0.130492 0.570850i
\(560\) −2.22760 1.28611i −0.0941333 0.0543479i
\(561\) −2.09218 8.59756i −0.0883321 0.362989i
\(562\) −8.80959 + 15.2587i −0.371610 + 0.643648i
\(563\) −5.31020 −0.223798 −0.111899 0.993720i \(-0.535693\pi\)
−0.111899 + 0.993720i \(0.535693\pi\)
\(564\) −36.0078 + 8.76236i −1.51620 + 0.368962i
\(565\) 68.8530 + 18.4491i 2.89667 + 0.776160i
\(566\) 8.94334 + 33.3770i 0.375917 + 1.40294i
\(567\) 3.12132 8.44141i 0.131083 0.354506i
\(568\) 2.49599 4.32318i 0.104729 0.181397i
\(569\) −22.5499 −0.945340 −0.472670 0.881239i \(-0.656710\pi\)
−0.472670 + 0.881239i \(0.656710\pi\)
\(570\) −65.1046 68.1831i −2.72693 2.85588i
\(571\) 20.5245 11.8498i 0.858924 0.495900i −0.00472807 0.999989i \(-0.501505\pi\)
0.863652 + 0.504089i \(0.168172\pi\)
\(572\) 17.1163 0.634755i 0.715669 0.0265405i
\(573\) 22.1349 12.1069i 0.924698 0.505772i
\(574\) 16.8692 16.8692i 0.704105 0.704105i
\(575\) −24.9645 + 14.4133i −1.04109 + 0.601075i
\(576\) −1.74726 + 37.8042i −0.0728024 + 1.57518i
\(577\) −16.8977 + 16.8977i −0.703460 + 0.703460i −0.965151 0.261692i \(-0.915720\pi\)
0.261692 + 0.965151i \(0.415720\pi\)
\(578\) 2.29030 8.54750i 0.0952638 0.355529i
\(579\) −21.9505 + 5.34157i −0.912231 + 0.221988i
\(580\) 25.9378 96.8013i 1.07701 4.01945i
\(581\) 12.6247i 0.523762i
\(582\) −34.1934 62.5155i −1.41736 2.59135i
\(583\) −3.55020 3.55020i −0.147034 0.147034i
\(584\) 1.81995 0.0753101
\(585\) −21.1602 37.4347i −0.874867 1.54773i
\(586\) −45.0159 −1.85959
\(587\) 11.8271 + 11.8271i 0.488155 + 0.488155i 0.907724 0.419569i \(-0.137819\pi\)
−0.419569 + 0.907724i \(0.637819\pi\)
\(588\) 3.04017 4.99565i 0.125374 0.206017i
\(589\) 24.6925i 1.01743i
\(590\) 11.7989 44.0342i 0.485755 1.81286i
\(591\) 3.41963 11.6767i 0.140665 0.480317i
\(592\) 0.684753 2.55553i 0.0281432 0.105032i
\(593\) 3.57025 3.57025i 0.146613 0.146613i −0.629990 0.776603i \(-0.716941\pi\)
0.776603 + 0.629990i \(0.216941\pi\)
\(594\) 16.9111 + 1.17346i 0.693872 + 0.0481475i
\(595\) −12.5008 + 7.21732i −0.512481 + 0.295881i
\(596\) −25.5119 + 25.5119i −1.04501 + 1.04501i
\(597\) −36.6988 22.3335i −1.50198 0.914051i
\(598\) 10.4291 19.7170i 0.426479 0.806289i
\(599\) −25.3961 + 14.6625i −1.03766 + 0.599092i −0.919169 0.393864i \(-0.871138\pi\)
−0.118488 + 0.992955i \(0.537805\pi\)
\(600\) −58.0281 + 14.1209i −2.36899 + 0.576484i
\(601\) 13.5632 0.553256 0.276628 0.960977i \(-0.410783\pi\)
0.276628 + 0.960977i \(0.410783\pi\)
\(602\) 4.45175 7.71065i 0.181440 0.314263i
\(603\) 3.43252 + 15.6723i 0.139783 + 0.638226i
\(604\) 0.151726 + 0.566248i 0.00617363 + 0.0230403i
\(605\) −34.6384 9.28132i −1.40825 0.377339i
\(606\) 37.4511 + 39.2220i 1.52134 + 1.59328i
\(607\) −40.4469 −1.64169 −0.820845 0.571152i \(-0.806497\pi\)
−0.820845 + 0.571152i \(0.806497\pi\)
\(608\) −14.4146 + 24.9668i −0.584589 + 1.01254i
\(609\) 12.4106 + 3.63456i 0.502905 + 0.147280i
\(610\) 47.3389 + 27.3311i 1.91669 + 1.10660i
\(611\) −20.1970 10.6830i −0.817081 0.432187i
\(612\) −30.9675 19.8398i −1.25179 0.801976i
\(613\) 12.4953 + 3.34810i 0.504679 + 0.135228i 0.502171 0.864768i \(-0.332535\pi\)
0.00250855 + 0.999997i \(0.499202\pi\)
\(614\) 16.8932i 0.681752i
\(615\) 1.63589 70.8269i 0.0659653 2.85602i
\(616\) 4.33716 + 1.16214i 0.174749 + 0.0468239i
\(617\) 2.39107 + 2.39107i 0.0962607 + 0.0962607i 0.753597 0.657337i \(-0.228317\pi\)
−0.657337 + 0.753597i \(0.728317\pi\)
\(618\) −51.5545 15.0982i −2.07383 0.607338i
\(619\) −2.25878 + 0.605237i −0.0907879 + 0.0243265i −0.303927 0.952695i \(-0.598298\pi\)
0.213139 + 0.977022i \(0.431631\pi\)
\(620\) 48.6107 + 28.0654i 1.95225 + 1.12713i
\(621\) 7.74627 11.4976i 0.310847 0.461381i
\(622\) 4.26022 15.8993i 0.170819 0.637506i
\(623\) −0.837025 + 1.44977i −0.0335347 + 0.0580838i
\(624\) 2.81696 2.89682i 0.112769 0.115965i
\(625\) 18.8562 + 32.6599i 0.754249 + 1.30640i
\(626\) −60.3998 + 16.1841i −2.41406 + 0.646846i
\(627\) 12.2923 + 7.48064i 0.490907 + 0.298748i
\(628\) −42.1828 + 24.3543i −1.68328 + 0.971842i
\(629\) −10.4984 10.4984i −0.418597 0.418597i
\(630\) −5.91643 27.0134i −0.235716 1.07624i
\(631\) −4.88894 + 1.30999i −0.194625 + 0.0521497i −0.354815 0.934937i \(-0.615456\pi\)
0.160190 + 0.987086i \(0.448789\pi\)
\(632\) −5.84418 21.8108i −0.232469 0.867586i
\(633\) −6.57649 + 10.8066i −0.261392 + 0.429523i
\(634\) −2.27922 1.31591i −0.0905195 0.0522615i
\(635\) 20.1046 + 75.0313i 0.797826 + 2.97753i
\(636\) −20.8627 0.481864i −0.827258 0.0191072i
\(637\) 3.44572 1.06161i 0.136524 0.0420625i
\(638\) 24.3577i 0.964329i
\(639\) 4.58405 1.00399i 0.181342 0.0397172i
\(640\) 38.7314 + 67.0848i 1.53099 + 2.65176i
\(641\) −14.1521 24.5121i −0.558973 0.968170i −0.997583 0.0694919i \(-0.977862\pi\)
0.438610 0.898678i \(-0.355471\pi\)
\(642\) −1.98755 0.582071i −0.0784423 0.0229725i
\(643\) −9.17658 + 9.17658i −0.361889 + 0.361889i −0.864508 0.502619i \(-0.832370\pi\)
0.502619 + 0.864508i \(0.332370\pi\)
\(644\) 6.36979 6.36979i 0.251005 0.251005i
\(645\) −6.25170 25.6905i −0.246160 1.01156i
\(646\) −24.8559 43.0516i −0.977941 1.69384i
\(647\) −6.04610 10.4721i −0.237697 0.411703i 0.722356 0.691521i \(-0.243059\pi\)
−0.960053 + 0.279818i \(0.909726\pi\)
\(648\) 22.0962 18.3495i 0.868022 0.720838i
\(649\) 6.95832i 0.273138i
\(650\) −79.8449 42.2332i −3.13177 1.65652i
\(651\) −3.76545 + 6.18744i −0.147579 + 0.242505i
\(652\) 19.6997 + 73.5203i 0.771500 + 2.87928i
\(653\) 23.5787 + 13.6132i 0.922707 + 0.532725i 0.884498 0.466545i \(-0.154501\pi\)
0.0382095 + 0.999270i \(0.487835\pi\)
\(654\) 44.0140 + 1.01659i 1.72108 + 0.0397518i
\(655\) 2.30647 + 8.60785i 0.0901211 + 0.336336i
\(656\) 6.43024 1.72298i 0.251059 0.0672710i
\(657\) 1.15260 + 1.26431i 0.0449674 + 0.0493255i
\(658\) −10.3899 10.3899i −0.405039 0.405039i
\(659\) 8.23429 4.75407i 0.320762 0.185192i −0.330970 0.943641i \(-0.607376\pi\)
0.651732 + 0.758449i \(0.274043\pi\)
\(660\) 28.6982 15.6967i 1.11707 0.610994i
\(661\) 19.5470 5.23761i 0.760291 0.203719i 0.142213 0.989836i \(-0.454578\pi\)
0.618078 + 0.786117i \(0.287911\pi\)
\(662\) −10.9842 19.0252i −0.426912 0.739434i
\(663\) −6.17426 21.8183i −0.239788 0.847354i
\(664\) −20.1448 + 34.8918i −0.781770 + 1.35407i
\(665\) 6.07551 22.6741i 0.235598 0.879265i
\(666\) 25.2632 13.0693i 0.978929 0.506427i
\(667\) 17.2515 + 9.96014i 0.667979 + 0.385658i
\(668\) 7.96026 2.13295i 0.307992 0.0825261i
\(669\) −7.21352 + 6.88782i −0.278891 + 0.266298i
\(670\) 34.8580 + 34.8580i 1.34668 + 1.34668i
\(671\) −8.05914 2.15944i −0.311120 0.0833643i
\(672\) −7.41930 + 4.05805i −0.286206 + 0.156543i
\(673\) 7.38770i 0.284775i −0.989811 0.142387i \(-0.954522\pi\)
0.989811 0.142387i \(-0.0454779\pi\)
\(674\) 48.7953 + 13.0747i 1.87952 + 0.503617i
\(675\) −46.5599 31.3688i −1.79209 1.20739i
\(676\) 43.7719 3.25102i 1.68354 0.125039i
\(677\) −33.8395 19.5372i −1.30056 0.750877i −0.320058 0.947398i \(-0.603702\pi\)
−0.980500 + 0.196521i \(0.937036\pi\)
\(678\) −52.0812 + 49.7297i −2.00017 + 1.90986i
\(679\) 8.87126 15.3655i 0.340448 0.589673i
\(680\) −46.0656 −1.76654
\(681\) −0.0740754 + 0.252939i −0.00283858 + 0.00969265i
\(682\) −13.1778 3.53099i −0.504605 0.135208i
\(683\) −11.2595 42.0209i −0.430832 1.60789i −0.750849 0.660474i \(-0.770355\pi\)
0.320017 0.947412i \(-0.396311\pi\)
\(684\) 58.4241 12.7959i 2.23390 0.489265i
\(685\) −19.6538 + 34.0413i −0.750932 + 1.30065i
\(686\) 2.31869 0.0885282
\(687\) −11.0371 + 37.6876i −0.421093 + 1.43787i
\(688\) 2.15162 1.24224i 0.0820298 0.0473599i
\(689\) −9.42867 8.75436i −0.359204 0.333514i
\(690\) 0.983615 42.5863i 0.0374456 1.62123i
\(691\) −22.8659 + 22.8659i −0.869862 + 0.869862i −0.992457 0.122595i \(-0.960878\pi\)
0.122595 + 0.992457i \(0.460878\pi\)
\(692\) −54.1326 + 31.2535i −2.05781 + 1.18808i
\(693\) 1.93946 + 3.74900i 0.0736740 + 0.142413i
\(694\) 24.4836 24.4836i 0.929384 0.929384i
\(695\) 12.1940 45.5088i 0.462547 1.72625i
\(696\) 28.5006 + 29.8483i 1.08031 + 1.13140i
\(697\) 9.66893 36.0849i 0.366237 1.36681i
\(698\) 52.2496i 1.97768i
\(699\) 26.4810 + 0.611631i 1.00160 + 0.0231340i
\(700\) −25.7947 25.7947i −0.974949 0.974949i
\(701\) −19.8464 −0.749589 −0.374795 0.927108i \(-0.622287\pi\)
−0.374795 + 0.927108i \(0.622287\pi\)
\(702\) 43.4182 + 1.39902i 1.63871 + 0.0528025i
\(703\) 24.1445 0.910625
\(704\) −12.5504 12.5504i −0.473011 0.473011i
\(705\) −43.6229 1.00756i −1.64293 0.0379468i
\(706\) 70.4306i 2.65069i
\(707\) −3.49490 + 13.0432i −0.131439 + 0.490539i
\(708\) 19.9730 + 20.9174i 0.750631 + 0.786125i
\(709\) 4.85948 18.1358i 0.182502 0.681105i −0.812650 0.582752i \(-0.801976\pi\)
0.995152 0.0983532i \(-0.0313575\pi\)
\(710\) 10.1957 10.1957i 0.382639 0.382639i
\(711\) 11.4506 17.8730i 0.429432 0.670291i
\(712\) −4.62669 + 2.67122i −0.173392 + 0.100108i
\(713\) −7.88941 + 7.88941i −0.295461 + 0.295461i
\(714\) 0.336714 14.5783i 0.0126012 0.545578i
\(715\) 19.6603 + 4.49420i 0.735253 + 0.168074i
\(716\) 17.6488 10.1895i 0.659566 0.380801i
\(717\) 8.11752 27.7182i 0.303154 1.03516i
\(718\) −53.0006 −1.97797
\(719\) −6.61046 + 11.4497i −0.246529 + 0.427000i −0.962560 0.271068i \(-0.912623\pi\)
0.716032 + 0.698068i \(0.245957\pi\)
\(720\) 2.33922 7.35354i 0.0871774 0.274050i
\(721\) −3.46200 12.9204i −0.128932 0.481179i
\(722\) 35.5338 + 9.52127i 1.32243 + 0.354345i
\(723\) −12.5228 + 42.7607i −0.465729 + 1.59029i
\(724\) −54.1559 −2.01269
\(725\) 40.3340 69.8605i 1.49797 2.59455i
\(726\) 26.2009 25.0179i 0.972405 0.928500i
\(727\) −44.3191 25.5877i −1.64371 0.948994i −0.979500 0.201443i \(-0.935437\pi\)
−0.664205 0.747550i \(-0.731230\pi\)
\(728\) 11.2171 + 2.56416i 0.415735 + 0.0950341i
\(729\) 26.7412 + 3.72908i 0.990416 + 0.138114i
\(730\) 5.07767 + 1.36056i 0.187933 + 0.0503565i
\(731\) 13.9423i 0.515674i
\(732\) −30.4250 + 16.6412i −1.12454 + 0.615078i
\(733\) 15.2728 + 4.09235i 0.564115 + 0.151154i 0.529596 0.848250i \(-0.322343\pi\)
0.0345190 + 0.999404i \(0.489010\pi\)
\(734\) −21.6909 21.6909i −0.800626 0.800626i
\(735\) 4.98007 4.75521i 0.183693 0.175399i
\(736\) −12.5826 + 3.37150i −0.463802 + 0.124275i
\(737\) −6.51638 3.76223i −0.240034 0.138584i
\(738\) 60.2630 + 38.6084i 2.21831 + 1.42119i
\(739\) 2.88591 10.7704i 0.106160 0.396195i −0.892314 0.451415i \(-0.850919\pi\)
0.998474 + 0.0552202i \(0.0175861\pi\)
\(740\) 27.4426 47.5319i 1.00881 1.74731i
\(741\) 32.1891 + 17.9894i 1.18250 + 0.660856i
\(742\) −4.13706 7.16559i −0.151876 0.263057i
\(743\) 0.948264 0.254087i 0.0347884 0.00932154i −0.241383 0.970430i \(-0.577601\pi\)
0.276171 + 0.961108i \(0.410934\pi\)
\(744\) −20.2799 + 11.0923i −0.743497 + 0.406663i
\(745\) −36.7900 + 21.2407i −1.34788 + 0.778199i
\(746\) −30.7156 30.7156i −1.12458 1.12458i
\(747\) −36.9972 + 8.10306i −1.35366 + 0.296476i
\(748\) 16.6609 4.46427i 0.609182 0.163230i
\(749\) −0.133468 0.498110i −0.00487682 0.0182006i
\(750\) −92.6470 2.13986i −3.38299 0.0781368i
\(751\) −11.4294 6.59879i −0.417066 0.240793i 0.276755 0.960940i \(-0.410741\pi\)
−0.693821 + 0.720147i \(0.744074\pi\)
\(752\) −1.06120 3.96044i −0.0386979 0.144422i
\(753\) −4.34095 + 7.13312i −0.158193 + 0.259945i
\(754\) 2.31321 + 62.3762i 0.0842421 + 2.27161i
\(755\) 0.690247i 0.0251207i
\(756\) 16.5912 + 5.70290i 0.603417 + 0.207413i
\(757\) 17.7289 + 30.7074i 0.644369 + 1.11608i 0.984447 + 0.175682i \(0.0562132\pi\)
−0.340078 + 0.940397i \(0.610453\pi\)
\(758\) 21.2531 + 36.8115i 0.771949 + 1.33705i
\(759\) 1.53736 + 6.31759i 0.0558027 + 0.229314i
\(760\) 52.9716 52.9716i 1.92148 1.92148i
\(761\) −5.19502 + 5.19502i −0.188319 + 0.188319i −0.794969 0.606650i \(-0.792513\pi\)
0.606650 + 0.794969i \(0.292513\pi\)
\(762\) −75.3089 22.0549i −2.72815 0.798963i
\(763\) 5.48116 + 9.49365i 0.198431 + 0.343693i
\(764\) 24.5904 + 42.5918i 0.889650 + 1.54092i
\(765\) −29.1741 32.0016i −1.05479 1.15702i
\(766\) 17.4694i 0.631196i
\(767\) 0.660821 + 17.8192i 0.0238609 + 0.643414i
\(768\) −34.5461 0.797909i −1.24657 0.0287921i
\(769\) 8.09220 + 30.2005i 0.291812 + 1.08906i 0.943716 + 0.330757i \(0.107304\pi\)
−0.651904 + 0.758302i \(0.726029\pi\)
\(770\) 11.2319 + 6.48473i 0.404769 + 0.233694i
\(771\) −21.5158 + 35.3552i −0.774874 + 1.27329i
\(772\) −11.3978 42.5370i −0.410214 1.53094i
\(773\) 3.51922 0.942972i 0.126577 0.0339163i −0.194974 0.980808i \(-0.562462\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(774\) 25.4536 + 8.09699i 0.914913 + 0.291040i
\(775\) 31.9485 + 31.9485i 1.14762 + 1.14762i
\(776\) 49.0363 28.3111i 1.76030 1.01631i
\(777\) 6.05013 + 3.68188i 0.217047 + 0.132087i
\(778\) 25.3967 6.80502i 0.910516 0.243972i
\(779\) 30.3762 + 52.6131i 1.08834 + 1.88506i
\(780\) 72.0008 42.9223i 2.57804 1.53687i
\(781\) −1.10043 + 1.90600i −0.0393764 + 0.0682020i
\(782\) 5.81367 21.6969i 0.207896 0.775880i
\(783\) −2.68556 + 38.7027i −0.0959742 + 1.38312i
\(784\) 0.560337 + 0.323511i 0.0200120 + 0.0115539i
\(785\) −55.3976 + 14.8437i −1.97722 + 0.529795i
\(786\) −8.63969 2.53021i −0.308168 0.0902495i
\(787\) 25.4672 + 25.4672i 0.907807 + 0.907807i 0.996095 0.0882881i \(-0.0281396\pi\)
−0.0882881 + 0.996095i \(0.528140\pi\)
\(788\) 22.9097 + 6.13864i 0.816125 + 0.218680i
\(789\) −0.451030 + 19.5277i −0.0160571 + 0.695204i
\(790\) 65.2211i 2.32046i
\(791\) −17.3195 4.64074i −0.615809 0.165006i
\(792\) −0.621922 + 13.4561i −0.0220990 + 0.478142i
\(793\) −20.8433 4.76463i −0.740167 0.169197i
\(794\) −53.6996 31.0035i −1.90573 1.10027i
\(795\) −23.5808 6.90585i −0.836325 0.244925i
\(796\) 41.8720 72.5245i 1.48411 2.57056i
\(797\) 21.3200 0.755194 0.377597 0.925970i \(-0.376750\pi\)
0.377597 + 0.925970i \(0.376750\pi\)
\(798\) 16.3766 + 17.1510i 0.579724 + 0.607137i
\(799\) −22.2250 5.95518i −0.786265 0.210679i
\(800\) 13.6530 + 50.9539i 0.482708 + 1.80149i
\(801\) −4.78584 1.52241i −0.169099 0.0537917i
\(802\) −18.2375 + 31.5882i −0.643987 + 1.11542i
\(803\) −0.802377 −0.0283153
\(804\) −30.3879 + 7.39478i −1.07170 + 0.260794i
\(805\) 9.18570 5.30337i 0.323753 0.186919i
\(806\) −34.0817 7.79083i −1.20048 0.274420i
\(807\) −40.7187 24.7799i −1.43337 0.872294i
\(808\) −30.4716 + 30.4716i −1.07199 + 1.07199i
\(809\) 27.7607 16.0276i 0.976013 0.563501i 0.0749491 0.997187i \(-0.476121\pi\)
0.901064 + 0.433686i \(0.142787\pi\)
\(810\) 75.3663 34.6766i 2.64810 1.21841i
\(811\) 23.0821 23.0821i 0.810523 0.810523i −0.174189 0.984712i \(-0.555730\pi\)
0.984712 + 0.174189i \(0.0557303\pi\)
\(812\) −6.52447 + 24.3496i −0.228964 + 0.854505i
\(813\) −0.106741 + 0.364479i −0.00374356 + 0.0127828i
\(814\) −3.45262 + 12.8854i −0.121014 + 0.451632i
\(815\) 89.6200i 3.13925i
\(816\) 2.11537 3.47601i 0.0740527 0.121685i
\(817\) 16.0325 + 16.0325i 0.560905 + 0.560905i
\(818\) −53.6884 −1.87717
\(819\) 5.32269 + 9.41642i 0.185990 + 0.329036i
\(820\) 138.102 4.82274
\(821\) 4.48288 + 4.48288i 0.156454 + 0.156454i 0.780993 0.624540i \(-0.214713\pi\)
−0.624540 + 0.780993i \(0.714713\pi\)
\(822\) −19.0553 34.8385i −0.664628 1.21513i
\(823\) 46.8335i 1.63251i 0.577690 + 0.816256i \(0.303954\pi\)
−0.577690 + 0.816256i \(0.696046\pi\)
\(824\) 11.0484 41.2331i 0.384888 1.43642i
\(825\) 25.5833 6.22561i 0.890697 0.216748i
\(826\) −2.96794 + 11.0765i −0.103268 + 0.385400i
\(827\) −32.8473 + 32.8473i −1.14221 + 1.14221i −0.154167 + 0.988045i \(0.549269\pi\)
−0.988045 + 0.154167i \(0.950731\pi\)
\(828\) 22.7553 + 14.5785i 0.790801 + 0.506638i
\(829\) 25.0048 14.4365i 0.868452 0.501401i 0.00161835 0.999999i \(-0.499485\pi\)
0.866833 + 0.498598i \(0.166152\pi\)
\(830\) −82.2885 + 82.2885i −2.85627 + 2.85627i
\(831\) 41.0946 22.4771i 1.42556 0.779721i
\(832\) −33.3315 30.9477i −1.15556 1.07292i
\(833\) 3.14447 1.81546i 0.108950 0.0629021i
\(834\) 32.8691 + 34.4234i 1.13816 + 1.19198i
\(835\) 9.70342 0.335801
\(836\) −14.0251 + 24.2921i −0.485067 + 0.840161i
\(837\) −20.5493 7.06342i −0.710289 0.244147i
\(838\) −8.69151 32.4371i −0.300243 1.12052i
\(839\) 9.55752 + 2.56093i 0.329962 + 0.0884131i 0.419997 0.907526i \(-0.362031\pi\)
−0.0900348 + 0.995939i \(0.528698\pi\)
\(840\) 21.3515 5.19580i 0.736696 0.179272i
\(841\) −26.7447 −0.922232
\(842\) −26.0058 + 45.0433i −0.896219 + 1.55230i
\(843\) −3.11197 12.7882i −0.107182 0.440450i
\(844\) −21.3561 12.3299i −0.735106 0.424414i
\(845\) 50.7737 + 9.64184i 1.74667 + 0.331689i
\(846\) 23.7792 37.1165i 0.817547 1.27609i
\(847\) 8.71303 + 2.33465i 0.299383 + 0.0802195i
\(848\) 2.30885i 0.0792863i
\(849\) −22.0498 13.4187i −0.756748 0.460528i
\(850\) −87.8626 23.5427i −3.01366 0.807508i
\(851\) 7.71432 + 7.71432i 0.264443 + 0.264443i
\(852\) 2.16292 + 8.88826i 0.0741006 + 0.304507i
\(853\) −37.2007 + 9.96791i −1.27373 + 0.341295i −0.831459 0.555587i \(-0.812494\pi\)
−0.442271 + 0.896882i \(0.645827\pi\)
\(854\) −11.9077 6.87494i −0.407475 0.235256i
\(855\) 70.3468 + 3.25133i 2.40581 + 0.111193i
\(856\) 0.425941 1.58963i 0.0145584 0.0543325i
\(857\) 6.74964 11.6907i 0.230563 0.399348i −0.727411 0.686202i \(-0.759276\pi\)
0.957974 + 0.286855i \(0.0926097\pi\)
\(858\) −14.2035 + 14.6062i −0.484900 + 0.498646i
\(859\) 6.16401 + 10.6764i 0.210313 + 0.364273i 0.951813 0.306680i \(-0.0992183\pi\)
−0.741499 + 0.670954i \(0.765885\pi\)
\(860\) 49.7847 13.3398i 1.69764 0.454882i
\(861\) −0.411495 + 17.8160i −0.0140237 + 0.607167i
\(862\) 55.2478 31.8973i 1.88175 1.08643i
\(863\) 16.3653 + 16.3653i 0.557081 + 0.557081i 0.928475 0.371394i \(-0.121120\pi\)
−0.371394 + 0.928475i \(0.621120\pi\)
\(864\) −16.6543 19.1379i −0.566590 0.651084i
\(865\) −71.0908 + 19.0487i −2.41716 + 0.647676i
\(866\) −2.96688 11.0725i −0.100819 0.376260i
\(867\) 3.17202 + 5.79936i 0.107727 + 0.196957i
\(868\) −12.2277 7.05965i −0.415034 0.239620i
\(869\) 2.57657 + 9.61589i 0.0874042 + 0.326197i
\(870\) 57.2029 + 104.583i 1.93936 + 3.54571i
\(871\) −17.0447 9.01565i −0.577539 0.305484i
\(872\) 34.9844i 1.18472i
\(873\) 50.7230 + 16.1354i 1.71671 + 0.546099i
\(874\) 18.2644 + 31.6348i 0.617802 + 1.07006i
\(875\) −11.5375 19.9836i −0.390040 0.675569i
\(876\) −2.41203 + 2.30312i −0.0814948 + 0.0778152i
\(877\) 1.74742 1.74742i 0.0590062 0.0590062i −0.676988 0.735994i \(-0.736715\pi\)
0.735994 + 0.676988i \(0.236715\pi\)
\(878\) −13.2418 + 13.2418i −0.446889 + 0.446889i
\(879\) 24.3203 23.2222i 0.820303 0.783265i
\(880\) 1.80953 + 3.13421i 0.0609994 + 0.105654i
\(881\) −3.48296 6.03266i −0.117344 0.203245i 0.801370 0.598168i \(-0.204105\pi\)
−0.918714 + 0.394923i \(0.870771\pi\)
\(882\) 1.48823 + 6.79502i 0.0501114 + 0.228800i
\(883\) 31.9778i 1.07614i −0.842900 0.538070i \(-0.819154\pi\)
0.842900 0.538070i \(-0.180846\pi\)
\(884\) 42.2420 13.0146i 1.42075 0.437727i
\(885\) 16.3413 + 29.8766i 0.549307 + 1.00429i
\(886\) 24.0217 + 89.6502i 0.807025 + 3.01186i
\(887\) 32.0355 + 18.4957i 1.07565 + 0.621025i 0.929719 0.368270i \(-0.120050\pi\)
0.145928 + 0.989295i \(0.453383\pi\)
\(888\) 10.8461 + 19.8298i 0.363972 + 0.665446i
\(889\) −5.05716 18.8736i −0.169612 0.632999i
\(890\) −14.9054 + 3.99390i −0.499631 + 0.133876i
\(891\) −9.74175 + 8.08992i −0.326361 + 0.271022i
\(892\) −13.7478 13.7478i −0.460309 0.460309i
\(893\) 32.4049 18.7090i 1.08439 0.626071i
\(894\) 0.990954 42.9041i 0.0331425 1.43493i
\(895\) 23.1777 6.21043i 0.774744 0.207592i
\(896\) −9.74260 16.8747i −0.325477 0.563743i
\(897\) 4.53692 + 16.0324i 0.151483 + 0.535305i
\(898\) −19.8218 + 34.3323i −0.661461 + 1.14568i
\(899\) 8.08098 30.1586i 0.269516 1.00585i
\(900\) 59.0363 92.1485i 1.96788 3.07162i
\(901\) −11.2209 6.47836i −0.373821 0.215826i
\(902\) −32.4222 + 8.68750i −1.07954 + 0.289262i
\(903\) 1.57257 + 6.46227i 0.0523318 + 0.215051i
\(904\) −40.4620 40.4620i −1.34574 1.34574i
\(905\) −61.5930 16.5038i −2.04742 0.548604i
\(906\) −0.595669 0.362502i −0.0197898 0.0120433i
\(907\) 29.4342i 0.977346i 0.872467 + 0.488673i \(0.162519\pi\)
−0.872467 + 0.488673i \(0.837481\pi\)
\(908\) −0.496266 0.132974i −0.0164692 0.00441290i
\(909\) −40.4666 1.87031i −1.34219 0.0620343i
\(910\) 29.3790 + 15.5397i 0.973903 + 0.515137i
\(911\) 5.00775 + 2.89122i 0.165914 + 0.0957905i 0.580658 0.814148i \(-0.302795\pi\)
−0.414744 + 0.909938i \(0.636129\pi\)
\(912\) 1.56462 + 6.42961i 0.0518098 + 0.212906i
\(913\) 8.88141 15.3831i 0.293932 0.509105i
\(914\) −69.1732 −2.28805
\(915\) −39.6745 + 9.65465i −1.31160 + 0.319173i
\(916\) −73.9429 19.8129i −2.44314 0.654638i
\(917\) −0.580174 2.16524i −0.0191590 0.0715025i
\(918\) 42.9382 8.37017i 1.41717 0.276257i
\(919\) −1.66083 + 2.87665i −0.0547858 + 0.0948919i −0.892118 0.451803i \(-0.850781\pi\)
0.837332 + 0.546695i \(0.184114\pi\)
\(920\) 33.8496 1.11599
\(921\) 8.71462 + 9.12670i 0.287156 + 0.300735i
\(922\) −10.2814 + 5.93596i −0.338599 + 0.195490i
\(923\) −2.63702 + 4.98547i −0.0867985 + 0.164099i
\(924\) −7.21881 + 3.94840i −0.237481 + 0.129893i
\(925\) 31.2394 31.2394i 1.02715 1.02715i
\(926\) 41.4685 23.9418i 1.36274 0.786778i
\(927\) 35.6415 18.4383i 1.17062 0.605594i
\(928\) 25.7763 25.7763i 0.846150 0.846150i
\(929\) −5.73037 + 21.3860i −0.188007 + 0.701653i 0.805959 + 0.591971i \(0.201650\pi\)
−0.993967 + 0.109682i \(0.965017\pi\)
\(930\) −64.8733 + 15.7867i −2.12728 + 0.517666i
\(931\) −1.52825 + 5.70351i −0.0500864 + 0.186925i
\(932\) 51.6341i 1.69133i
\(933\) 5.90032 + 10.7875i 0.193168 + 0.353166i
\(934\) 17.2881 + 17.2881i 0.565683 + 0.565683i
\(935\) 20.3093 0.664186
\(936\) −0.314740 + 34.5180i −0.0102876 + 1.12826i
\(937\) 29.0186 0.947996 0.473998 0.880526i \(-0.342810\pi\)
0.473998 + 0.880526i \(0.342810\pi\)
\(938\) −8.76828 8.76828i −0.286295 0.286295i
\(939\) 24.2828 39.9019i 0.792438 1.30215i
\(940\) 85.0583i 2.77430i
\(941\) −14.1785 + 52.9149i −0.462206 + 1.72498i 0.203783 + 0.979016i \(0.434676\pi\)
−0.665989 + 0.745961i \(0.731990\pi\)
\(942\) 16.2837 55.6025i 0.530551 1.81163i
\(943\) −7.10484 + 26.5156i −0.231365 + 0.863468i
\(944\) −2.26265 + 2.26265i −0.0736431 + 0.0736431i
\(945\) 17.1317 + 11.5422i 0.557295 + 0.375467i
\(946\) −10.8488 + 6.26355i −0.352724 + 0.203645i
\(947\) −4.62509 + 4.62509i −0.150295 + 0.150295i −0.778250 0.627955i \(-0.783892\pi\)
0.627955 + 0.778250i \(0.283892\pi\)
\(948\) 35.3466 + 21.5106i 1.14801 + 0.698633i
\(949\) −2.05476 + 0.0762005i −0.0667004 + 0.00247357i
\(950\) 128.107 73.9624i 4.15633 2.39966i
\(951\) 1.91021 0.464842i 0.0619427 0.0150735i
\(952\) 11.5875 0.375552
\(953\) −3.95346 + 6.84759i −0.128065 + 0.221815i −0.922927 0.384975i \(-0.874210\pi\)
0.794862 + 0.606791i \(0.207543\pi\)
\(954\) 18.3437 16.7230i 0.593899 0.541426i
\(955\) 14.9876 + 55.9347i 0.484989 + 1.81000i
\(956\) 54.3831 + 14.5719i 1.75887 + 0.471289i
\(957\) −12.5653 13.1595i −0.406179 0.425385i
\(958\) −76.6632 −2.47688
\(959\) 4.94376 8.56285i 0.159642 0.276509i
\(960\) −83.3611 24.4130i −2.69047 0.787927i
\(961\) −11.7020 6.75616i −0.377484 0.217941i
\(962\) −7.61793 + 33.3253i −0.245612 + 1.07445i
\(963\) 1.37406 0.710841i 0.0442786 0.0229065i
\(964\) −83.8963 22.4799i −2.70212 0.724030i
\(965\) 51.8519i 1.66917i
\(966\) −0.247421 + 10.7123i −0.00796064 + 0.344662i
\(967\) −12.5881 3.37298i −0.404807 0.108468i 0.0506697 0.998715i \(-0.483864\pi\)
−0.455476 + 0.890248i \(0.650531\pi\)
\(968\) 20.3555 + 20.3555i 0.654250 + 0.654250i
\(969\) 35.6376 + 10.4368i 1.14484 + 0.335277i
\(970\) 157.976 42.3296i 5.07231 1.35912i
\(971\) −42.2941 24.4185i −1.35728 0.783627i −0.368025 0.929816i \(-0.619966\pi\)
−0.989257 + 0.146188i \(0.953299\pi\)
\(972\) −6.06363 + 52.2816i −0.194491 + 1.67693i
\(973\) −3.06732 + 11.4474i −0.0983338 + 0.366987i
\(974\) 17.6901 30.6402i 0.566828 0.981775i
\(975\) 64.9237 18.3724i 2.07922 0.588389i
\(976\) −1.91842 3.32280i −0.0614071 0.106360i
\(977\) 28.2037 7.55717i 0.902318 0.241775i 0.222306 0.974977i \(-0.428642\pi\)
0.680011 + 0.733202i \(0.261975\pi\)
\(978\) −77.3402 47.0664i −2.47307 1.50502i
\(979\) 2.03981 1.17768i 0.0651925 0.0376389i
\(980\) 9.49119 + 9.49119i 0.303185 + 0.303185i
\(981\) −24.3035 + 22.1562i −0.775949 + 0.707392i
\(982\) 17.5766 4.70963i 0.560892 0.150290i
\(983\) 8.14758 + 30.4072i 0.259867 + 0.969838i 0.965318 + 0.261079i \(0.0840782\pi\)
−0.705450 + 0.708759i \(0.749255\pi\)
\(984\) −29.5656 + 48.5827i −0.942516 + 1.54876i
\(985\) 24.1851 + 13.9633i 0.770602 + 0.444907i
\(986\) 16.2689 + 60.7165i 0.518108 + 1.93361i
\(987\) 10.9730 + 0.253444i 0.349275 + 0.00806720i
\(988\) −33.6090 + 63.5403i −1.06925 + 2.02149i
\(989\) 10.2450i 0.325771i
\(990\) −11.7947 + 37.0776i −0.374859 + 1.17840i
\(991\) −13.2580 22.9636i −0.421155 0.729462i 0.574898 0.818225i \(-0.305042\pi\)
−0.996053 + 0.0887633i \(0.971709\pi\)
\(992\) 10.2087 + 17.6820i 0.324126 + 0.561403i
\(993\) 15.7488 + 4.61216i 0.499772 + 0.146363i
\(994\) −2.56466 + 2.56466i −0.0813462 + 0.0813462i
\(995\) 69.7237 69.7237i 2.21039 2.21039i
\(996\) −17.4567 71.7360i −0.553136 2.27304i
\(997\) −18.3648 31.8087i −0.581618 1.00739i −0.995288 0.0969648i \(-0.969087\pi\)
0.413670 0.910427i \(-0.364247\pi\)
\(998\) −0.428386 0.741986i −0.0135603 0.0234871i
\(999\) −6.90666 + 20.0933i −0.218517 + 0.635724i
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 819.2.ew.a.470.9 yes 336
9.5 odd 6 819.2.fy.a.743.9 yes 336
13.7 odd 12 819.2.fy.a.722.9 yes 336
117.59 even 12 inner 819.2.ew.a.176.9 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.176.9 336 117.59 even 12 inner
819.2.ew.a.470.9 yes 336 1.1 even 1 trivial
819.2.fy.a.722.9 yes 336 13.7 odd 12
819.2.fy.a.743.9 yes 336 9.5 odd 6