Properties

Label 418.2.f.c.191.1
Level $418$
Weight $2$
Character 418.191
Analytic conductor $3.338$
Analytic rank $0$
Dimension $4$
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] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 191.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 418.191
Dual form 418.2.f.c.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.190983 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.190983 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.61803 + 1.17557i) q^{9} -0.381966 q^{10} +(-2.19098 + 2.48990i) q^{11} -1.00000 q^{12} +(1.50000 + 1.08981i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(0.118034 + 0.363271i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.42705 - 2.48990i) q^{17} +(-0.618034 - 1.90211i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(0.309017 + 0.224514i) q^{20} +0.618034 q^{21} +(3.23607 - 0.726543i) q^{22} -1.00000 q^{23} +(0.809017 + 0.587785i) q^{24} +(-1.50000 + 4.61653i) q^{25} +(-0.572949 - 1.76336i) q^{26} +(-4.04508 + 2.93893i) q^{27} +(0.500000 - 0.363271i) q^{28} +(2.76393 + 8.50651i) q^{29} +(0.118034 - 0.363271i) q^{30} +(3.80902 + 2.76741i) q^{31} +1.00000 q^{32} +(-1.69098 - 2.85317i) q^{33} -4.23607 q^{34} +(-0.190983 - 0.138757i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(3.59017 + 11.0494i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(-0.118034 - 0.363271i) q^{40} +(1.57295 - 4.84104i) q^{41} +(-0.500000 - 0.363271i) q^{42} +5.70820 q^{43} +(-3.04508 - 1.31433i) q^{44} +0.763932 q^{45} +(0.809017 + 0.587785i) q^{46} +(1.45492 - 4.47777i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(5.35410 - 3.88998i) q^{49} +(3.92705 - 2.85317i) q^{50} +(1.30902 + 4.02874i) q^{51} +(-0.572949 + 1.76336i) q^{52} +(-10.8992 - 7.91872i) q^{53} +5.00000 q^{54} +(-0.118034 + 1.26133i) q^{55} -0.618034 q^{56} +(-0.809017 - 0.587785i) q^{57} +(2.76393 - 8.50651i) q^{58} +(0.263932 + 0.812299i) q^{59} +(-0.309017 + 0.224514i) q^{60} +(4.50000 - 3.26944i) q^{61} +(-1.45492 - 4.47777i) q^{62} +(0.381966 - 1.17557i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.708204 q^{65} +(-0.309017 + 3.30220i) q^{66} -3.38197 q^{67} +(3.42705 + 2.48990i) q^{68} +(0.309017 - 0.951057i) q^{69} +(0.0729490 + 0.224514i) q^{70} +(-11.5172 + 8.36775i) q^{71} +(1.61803 - 1.17557i) q^{72} +(0.809017 + 2.48990i) q^{73} +(3.59017 - 11.0494i) q^{74} +(-3.92705 - 2.85317i) q^{75} -1.00000 q^{76} +(1.88197 + 0.812299i) q^{77} +1.85410 q^{78} +(-12.1353 - 8.81678i) q^{79} +(-0.118034 + 0.363271i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-4.11803 + 2.99193i) q^{82} +(12.7812 - 9.28605i) q^{83} +(0.190983 + 0.587785i) q^{84} +(0.500000 - 1.53884i) q^{85} +(-4.61803 - 3.35520i) q^{86} -8.94427 q^{87} +(1.69098 + 2.85317i) q^{88} -8.41641 q^{89} +(-0.618034 - 0.449028i) q^{90} +(0.354102 - 1.08981i) q^{91} +(-0.309017 - 0.951057i) q^{92} +(-3.80902 + 2.76741i) q^{93} +(-3.80902 + 2.76741i) q^{94} +(0.118034 + 0.363271i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(10.6631 + 7.74721i) q^{97} -6.61803 q^{98} +(-6.47214 + 1.45309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9} - 6 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + q^{19} - q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} + 2 q^{28} + 20 q^{29} - 4 q^{30} + 13 q^{31} + 4 q^{32} - 9 q^{33} - 8 q^{34} - 3 q^{35} + 2 q^{36} - 8 q^{37} + q^{38} - 6 q^{39} + 4 q^{40} + 13 q^{41} - 2 q^{42} - 4 q^{43} - q^{44} + 12 q^{45} + q^{46} + 17 q^{47} + q^{48} + 8 q^{49} + 9 q^{50} + 3 q^{51} - 9 q^{52} - 19 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{56} - q^{57} + 20 q^{58} + 10 q^{59} + q^{60} + 18 q^{61} - 17 q^{62} + 6 q^{63} - q^{64} - 24 q^{65} + q^{66} - 18 q^{67} + 7 q^{68} - q^{69} + 7 q^{70} - 17 q^{71} + 2 q^{72} + q^{73} - 8 q^{74} - 9 q^{75} - 4 q^{76} + 12 q^{77} - 6 q^{78} - 15 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 31 q^{83} + 3 q^{84} + 2 q^{85} - 14 q^{86} + 9 q^{88} + 20 q^{89} + 2 q^{90} - 12 q^{91} + q^{92} - 13 q^{93} - 13 q^{94} - 4 q^{95} + q^{96} + 27 q^{97} - 22 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 0.587785i −0.572061 0.415627i
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i −0.999773 0.0213149i \(-0.993215\pi\)
0.821362 + 0.570408i \(0.193215\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 0.309017 0.224514i 0.138197 0.100406i −0.516539 0.856264i \(-0.672780\pi\)
0.654736 + 0.755858i \(0.272780\pi\)
\(6\) 0.809017 0.587785i 0.330280 0.239962i
\(7\) −0.190983 0.587785i −0.0721848 0.222162i 0.908455 0.417983i \(-0.137263\pi\)
−0.980640 + 0.195821i \(0.937263\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 1.61803 + 1.17557i 0.539345 + 0.391857i
\(10\) −0.381966 −0.120788
\(11\) −2.19098 + 2.48990i −0.660606 + 0.750733i
\(12\) −1.00000 −0.288675
\(13\) 1.50000 + 1.08981i 0.416025 + 0.302260i 0.776037 0.630688i \(-0.217227\pi\)
−0.360011 + 0.932948i \(0.617227\pi\)
\(14\) −0.190983 + 0.587785i −0.0510424 + 0.157092i
\(15\) 0.118034 + 0.363271i 0.0304762 + 0.0937962i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 3.42705 2.48990i 0.831182 0.603889i −0.0887115 0.996057i \(-0.528275\pi\)
0.919893 + 0.392168i \(0.128275\pi\)
\(18\) −0.618034 1.90211i −0.145672 0.448332i
\(19\) −0.309017 + 0.951057i −0.0708934 + 0.218187i
\(20\) 0.309017 + 0.224514i 0.0690983 + 0.0502029i
\(21\) 0.618034 0.134866
\(22\) 3.23607 0.726543i 0.689932 0.154899i
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0.809017 + 0.587785i 0.165140 + 0.119981i
\(25\) −1.50000 + 4.61653i −0.300000 + 0.923305i
\(26\) −0.572949 1.76336i −0.112365 0.345823i
\(27\) −4.04508 + 2.93893i −0.778477 + 0.565597i
\(28\) 0.500000 0.363271i 0.0944911 0.0686518i
\(29\) 2.76393 + 8.50651i 0.513249 + 1.57962i 0.786445 + 0.617660i \(0.211919\pi\)
−0.273196 + 0.961958i \(0.588081\pi\)
\(30\) 0.118034 0.363271i 0.0215500 0.0663240i
\(31\) 3.80902 + 2.76741i 0.684120 + 0.497042i 0.874722 0.484625i \(-0.161044\pi\)
−0.190602 + 0.981667i \(0.561044\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.69098 2.85317i −0.294362 0.496673i
\(34\) −4.23607 −0.726480
\(35\) −0.190983 0.138757i −0.0322820 0.0234543i
\(36\) −0.618034 + 1.90211i −0.103006 + 0.317019i
\(37\) 3.59017 + 11.0494i 0.590220 + 1.81651i 0.577210 + 0.816596i \(0.304142\pi\)
0.0130106 + 0.999915i \(0.495858\pi\)
\(38\) 0.809017 0.587785i 0.131240 0.0953514i
\(39\) −1.50000 + 1.08981i −0.240192 + 0.174510i
\(40\) −0.118034 0.363271i −0.0186628 0.0574382i
\(41\) 1.57295 4.84104i 0.245653 0.756043i −0.749875 0.661580i \(-0.769886\pi\)
0.995528 0.0944637i \(-0.0301136\pi\)
\(42\) −0.500000 0.363271i −0.0771517 0.0560540i
\(43\) 5.70820 0.870493 0.435246 0.900311i \(-0.356661\pi\)
0.435246 + 0.900311i \(0.356661\pi\)
\(44\) −3.04508 1.31433i −0.459064 0.198142i
\(45\) 0.763932 0.113880
\(46\) 0.809017 + 0.587785i 0.119283 + 0.0866642i
\(47\) 1.45492 4.47777i 0.212221 0.653150i −0.787118 0.616802i \(-0.788428\pi\)
0.999339 0.0363472i \(-0.0115722\pi\)
\(48\) −0.309017 0.951057i −0.0446028 0.137273i
\(49\) 5.35410 3.88998i 0.764872 0.555712i
\(50\) 3.92705 2.85317i 0.555369 0.403499i
\(51\) 1.30902 + 4.02874i 0.183299 + 0.564136i
\(52\) −0.572949 + 1.76336i −0.0794537 + 0.244533i
\(53\) −10.8992 7.91872i −1.49712 1.08772i −0.971511 0.236993i \(-0.923838\pi\)
−0.525607 0.850727i \(-0.676162\pi\)
\(54\) 5.00000 0.680414
\(55\) −0.118034 + 1.26133i −0.0159157 + 0.170077i
\(56\) −0.618034 −0.0825883
\(57\) −0.809017 0.587785i −0.107157 0.0778541i
\(58\) 2.76393 8.50651i 0.362922 1.11696i
\(59\) 0.263932 + 0.812299i 0.0343610 + 0.105752i 0.966766 0.255663i \(-0.0822937\pi\)
−0.932405 + 0.361415i \(0.882294\pi\)
\(60\) −0.309017 + 0.224514i −0.0398939 + 0.0289846i
\(61\) 4.50000 3.26944i 0.576166 0.418609i −0.261174 0.965292i \(-0.584110\pi\)
0.837340 + 0.546683i \(0.184110\pi\)
\(62\) −1.45492 4.47777i −0.184774 0.568677i
\(63\) 0.381966 1.17557i 0.0481232 0.148108i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 0.708204 0.0878419
\(66\) −0.309017 + 3.30220i −0.0380374 + 0.406472i
\(67\) −3.38197 −0.413173 −0.206586 0.978428i \(-0.566235\pi\)
−0.206586 + 0.978428i \(0.566235\pi\)
\(68\) 3.42705 + 2.48990i 0.415591 + 0.301945i
\(69\) 0.309017 0.951057i 0.0372013 0.114494i
\(70\) 0.0729490 + 0.224514i 0.00871908 + 0.0268346i
\(71\) −11.5172 + 8.36775i −1.36684 + 0.993069i −0.368866 + 0.929482i \(0.620254\pi\)
−0.997976 + 0.0635869i \(0.979746\pi\)
\(72\) 1.61803 1.17557i 0.190687 0.138542i
\(73\) 0.809017 + 2.48990i 0.0946883 + 0.291421i 0.987172 0.159658i \(-0.0510393\pi\)
−0.892484 + 0.451079i \(0.851039\pi\)
\(74\) 3.59017 11.0494i 0.417349 1.28447i
\(75\) −3.92705 2.85317i −0.453457 0.329456i
\(76\) −1.00000 −0.114708
\(77\) 1.88197 + 0.812299i 0.214470 + 0.0925701i
\(78\) 1.85410 0.209936
\(79\) −12.1353 8.81678i −1.36532 0.991965i −0.998086 0.0618376i \(-0.980304\pi\)
−0.367237 0.930128i \(-0.619696\pi\)
\(80\) −0.118034 + 0.363271i −0.0131966 + 0.0406150i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −4.11803 + 2.99193i −0.454761 + 0.330403i
\(83\) 12.7812 9.28605i 1.40291 1.01928i 0.408608 0.912710i \(-0.366014\pi\)
0.994306 0.106567i \(-0.0339858\pi\)
\(84\) 0.190983 + 0.587785i 0.0208380 + 0.0641326i
\(85\) 0.500000 1.53884i 0.0542326 0.166911i
\(86\) −4.61803 3.35520i −0.497975 0.361800i
\(87\) −8.94427 −0.958927
\(88\) 1.69098 + 2.85317i 0.180259 + 0.304149i
\(89\) −8.41641 −0.892137 −0.446069 0.894999i \(-0.647176\pi\)
−0.446069 + 0.894999i \(0.647176\pi\)
\(90\) −0.618034 0.449028i −0.0651465 0.0473317i
\(91\) 0.354102 1.08981i 0.0371200 0.114244i
\(92\) −0.309017 0.951057i −0.0322172 0.0991545i
\(93\) −3.80902 + 2.76741i −0.394977 + 0.286967i
\(94\) −3.80902 + 2.76741i −0.392870 + 0.285437i
\(95\) 0.118034 + 0.363271i 0.0121100 + 0.0372708i
\(96\) −0.309017 + 0.951057i −0.0315389 + 0.0970668i
\(97\) 10.6631 + 7.74721i 1.08268 + 0.786610i 0.978148 0.207912i \(-0.0666668\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(98\) −6.61803 −0.668522
\(99\) −6.47214 + 1.45309i −0.650474 + 0.146041i
\(100\) −4.85410 −0.485410
\(101\) −10.6631 7.74721i −1.06102 0.770876i −0.0867432 0.996231i \(-0.527646\pi\)
−0.974277 + 0.225355i \(0.927646\pi\)
\(102\) 1.30902 4.02874i 0.129612 0.398905i
\(103\) −1.95492 6.01661i −0.192624 0.592834i −0.999996 0.00279224i \(-0.999111\pi\)
0.807373 0.590042i \(-0.200889\pi\)
\(104\) 1.50000 1.08981i 0.147087 0.106865i
\(105\) 0.190983 0.138757i 0.0186380 0.0135413i
\(106\) 4.16312 + 12.8128i 0.404358 + 1.24449i
\(107\) 3.16312 9.73508i 0.305790 0.941126i −0.673591 0.739104i \(-0.735249\pi\)
0.979381 0.202021i \(-0.0647510\pi\)
\(108\) −4.04508 2.93893i −0.389238 0.282798i
\(109\) 1.90983 0.182929 0.0914643 0.995808i \(-0.470845\pi\)
0.0914643 + 0.995808i \(0.470845\pi\)
\(110\) 0.836881 0.951057i 0.0797935 0.0906797i
\(111\) −11.6180 −1.10273
\(112\) 0.500000 + 0.363271i 0.0472456 + 0.0343259i
\(113\) 4.69098 14.4374i 0.441291 1.35815i −0.445210 0.895426i \(-0.646871\pi\)
0.886501 0.462727i \(-0.153129\pi\)
\(114\) 0.309017 + 0.951057i 0.0289421 + 0.0890746i
\(115\) −0.309017 + 0.224514i −0.0288160 + 0.0209360i
\(116\) −7.23607 + 5.25731i −0.671852 + 0.488129i
\(117\) 1.14590 + 3.52671i 0.105938 + 0.326045i
\(118\) 0.263932 0.812299i 0.0242969 0.0747782i
\(119\) −2.11803 1.53884i −0.194160 0.141065i
\(120\) 0.381966 0.0348686
\(121\) −1.39919 10.9106i −0.127199 0.991877i
\(122\) −5.56231 −0.503588
\(123\) 4.11803 + 2.99193i 0.371311 + 0.269773i
\(124\) −1.45492 + 4.47777i −0.130655 + 0.402115i
\(125\) 1.16312 + 3.57971i 0.104033 + 0.320179i
\(126\) −1.00000 + 0.726543i −0.0890871 + 0.0647256i
\(127\) −1.04508 + 0.759299i −0.0927363 + 0.0673769i −0.633187 0.773999i \(-0.718254\pi\)
0.540451 + 0.841376i \(0.318254\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) −1.76393 + 5.42882i −0.155306 + 0.477981i
\(130\) −0.572949 0.416272i −0.0502510 0.0365095i
\(131\) −15.2361 −1.33118 −0.665591 0.746317i \(-0.731820\pi\)
−0.665591 + 0.746317i \(0.731820\pi\)
\(132\) 2.19098 2.48990i 0.190701 0.216718i
\(133\) 0.618034 0.0535903
\(134\) 2.73607 + 1.98787i 0.236360 + 0.171726i
\(135\) −0.590170 + 1.81636i −0.0507937 + 0.156327i
\(136\) −1.30902 4.02874i −0.112247 0.345462i
\(137\) 9.28115 6.74315i 0.792942 0.576106i −0.115893 0.993262i \(-0.536973\pi\)
0.908835 + 0.417155i \(0.136973\pi\)
\(138\) −0.809017 + 0.587785i −0.0688681 + 0.0500356i
\(139\) 5.42705 + 16.7027i 0.460316 + 1.41671i 0.864778 + 0.502154i \(0.167459\pi\)
−0.404462 + 0.914555i \(0.632541\pi\)
\(140\) 0.0729490 0.224514i 0.00616532 0.0189749i
\(141\) 3.80902 + 2.76741i 0.320777 + 0.233058i
\(142\) 14.2361 1.19466
\(143\) −6.00000 + 1.34708i −0.501745 + 0.112649i
\(144\) −2.00000 −0.166667
\(145\) 2.76393 + 2.00811i 0.229532 + 0.166765i
\(146\) 0.809017 2.48990i 0.0669547 0.206065i
\(147\) 2.04508 + 6.29412i 0.168676 + 0.519131i
\(148\) −9.39919 + 6.82891i −0.772608 + 0.561333i
\(149\) 11.2812 8.19624i 0.924188 0.671462i −0.0203749 0.999792i \(-0.506486\pi\)
0.944563 + 0.328330i \(0.106486\pi\)
\(150\) 1.50000 + 4.61653i 0.122474 + 0.376938i
\(151\) 1.47214 4.53077i 0.119801 0.368709i −0.873117 0.487510i \(-0.837905\pi\)
0.992918 + 0.118801i \(0.0379052\pi\)
\(152\) 0.809017 + 0.587785i 0.0656199 + 0.0476757i
\(153\) 8.47214 0.684932
\(154\) −1.04508 1.76336i −0.0842153 0.142095i
\(155\) 1.79837 0.144449
\(156\) −1.50000 1.08981i −0.120096 0.0872549i
\(157\) 0.236068 0.726543i 0.0188403 0.0579844i −0.941194 0.337866i \(-0.890295\pi\)
0.960035 + 0.279881i \(0.0902951\pi\)
\(158\) 4.63525 + 14.2658i 0.368761 + 1.13493i
\(159\) 10.8992 7.91872i 0.864362 0.627996i
\(160\) 0.309017 0.224514i 0.0244299 0.0177494i
\(161\) 0.190983 + 0.587785i 0.0150516 + 0.0463240i
\(162\) 0.309017 0.951057i 0.0242787 0.0747221i
\(163\) −3.50000 2.54290i −0.274141 0.199175i 0.442217 0.896908i \(-0.354192\pi\)
−0.716358 + 0.697733i \(0.754192\pi\)
\(164\) 5.09017 0.397475
\(165\) −1.16312 0.502029i −0.0905487 0.0390829i
\(166\) −15.7984 −1.22619
\(167\) −3.11803 2.26538i −0.241281 0.175301i 0.460573 0.887622i \(-0.347644\pi\)
−0.701854 + 0.712321i \(0.747644\pi\)
\(168\) 0.190983 0.587785i 0.0147347 0.0453486i
\(169\) −2.95492 9.09429i −0.227301 0.699561i
\(170\) −1.30902 + 0.951057i −0.100397 + 0.0729427i
\(171\) −1.61803 + 1.17557i −0.123734 + 0.0898981i
\(172\) 1.76393 + 5.42882i 0.134499 + 0.413944i
\(173\) 4.59017 14.1271i 0.348984 1.07406i −0.610432 0.792069i \(-0.709004\pi\)
0.959416 0.281994i \(-0.0909959\pi\)
\(174\) 7.23607 + 5.25731i 0.548565 + 0.398556i
\(175\) 3.00000 0.226779
\(176\) 0.309017 3.30220i 0.0232930 0.248913i
\(177\) −0.854102 −0.0641982
\(178\) 6.80902 + 4.94704i 0.510357 + 0.370796i
\(179\) −0.527864 + 1.62460i −0.0394544 + 0.121428i −0.968844 0.247673i \(-0.920334\pi\)
0.929389 + 0.369101i \(0.120334\pi\)
\(180\) 0.236068 + 0.726543i 0.0175955 + 0.0541533i
\(181\) −20.1353 + 14.6291i −1.49664 + 1.08737i −0.524947 + 0.851135i \(0.675915\pi\)
−0.971695 + 0.236239i \(0.924085\pi\)
\(182\) −0.927051 + 0.673542i −0.0687176 + 0.0499263i
\(183\) 1.71885 + 5.29007i 0.127061 + 0.391053i
\(184\) −0.309017 + 0.951057i −0.0227810 + 0.0701128i
\(185\) 3.59017 + 2.60841i 0.263955 + 0.191774i
\(186\) 4.70820 0.345222
\(187\) −1.30902 + 13.9883i −0.0957248 + 1.02293i
\(188\) 4.70820 0.343381
\(189\) 2.50000 + 1.81636i 0.181848 + 0.132120i
\(190\) 0.118034 0.363271i 0.00856309 0.0263545i
\(191\) −1.45492 4.47777i −0.105274 0.324000i 0.884521 0.466501i \(-0.154486\pi\)
−0.989795 + 0.142501i \(0.954486\pi\)
\(192\) 0.809017 0.587785i 0.0583858 0.0424197i
\(193\) 5.54508 4.02874i 0.399144 0.289995i −0.370048 0.929013i \(-0.620659\pi\)
0.769192 + 0.639017i \(0.220659\pi\)
\(194\) −4.07295 12.5352i −0.292421 0.899978i
\(195\) −0.218847 + 0.673542i −0.0156720 + 0.0482333i
\(196\) 5.35410 + 3.88998i 0.382436 + 0.277856i
\(197\) 23.0000 1.63868 0.819341 0.573306i \(-0.194340\pi\)
0.819341 + 0.573306i \(0.194340\pi\)
\(198\) 6.09017 + 2.62866i 0.432810 + 0.186810i
\(199\) 23.4164 1.65995 0.829973 0.557804i \(-0.188356\pi\)
0.829973 + 0.557804i \(0.188356\pi\)
\(200\) 3.92705 + 2.85317i 0.277684 + 0.201750i
\(201\) 1.04508 3.21644i 0.0737146 0.226870i
\(202\) 4.07295 + 12.5352i 0.286572 + 0.881977i
\(203\) 4.47214 3.24920i 0.313882 0.228049i
\(204\) −3.42705 + 2.48990i −0.239942 + 0.174328i
\(205\) −0.600813 1.84911i −0.0419626 0.129148i
\(206\) −1.95492 + 6.01661i −0.136205 + 0.419197i
\(207\) −1.61803 1.17557i −0.112461 0.0817078i
\(208\) −1.85410 −0.128559
\(209\) −1.69098 2.85317i −0.116968 0.197358i
\(210\) −0.236068 −0.0162902
\(211\) −2.57295 1.86936i −0.177129 0.128692i 0.495688 0.868501i \(-0.334916\pi\)
−0.672817 + 0.739809i \(0.734916\pi\)
\(212\) 4.16312 12.8128i 0.285924 0.879984i
\(213\) −4.39919 13.5393i −0.301427 0.927698i
\(214\) −8.28115 + 6.01661i −0.566088 + 0.411287i
\(215\) 1.76393 1.28157i 0.120299 0.0874025i
\(216\) 1.54508 + 4.75528i 0.105130 + 0.323556i
\(217\) 0.899187 2.76741i 0.0610408 0.187864i
\(218\) −1.54508 1.12257i −0.104646 0.0760300i
\(219\) −2.61803 −0.176910
\(220\) −1.23607 + 0.277515i −0.0833357 + 0.0187100i
\(221\) 7.85410 0.528324
\(222\) 9.39919 + 6.82891i 0.630832 + 0.458326i
\(223\) −1.52786 + 4.70228i −0.102313 + 0.314888i −0.989091 0.147309i \(-0.952939\pi\)
0.886777 + 0.462197i \(0.152939\pi\)
\(224\) −0.190983 0.587785i −0.0127606 0.0392731i
\(225\) −7.85410 + 5.70634i −0.523607 + 0.380423i
\(226\) −12.2812 + 8.92278i −0.816930 + 0.593534i
\(227\) 7.37132 + 22.6866i 0.489252 + 1.50576i 0.825727 + 0.564070i \(0.190765\pi\)
−0.336475 + 0.941692i \(0.609235\pi\)
\(228\) 0.309017 0.951057i 0.0204652 0.0629853i
\(229\) 2.07295 + 1.50609i 0.136984 + 0.0995249i 0.654167 0.756350i \(-0.273019\pi\)
−0.517183 + 0.855875i \(0.673019\pi\)
\(230\) 0.381966 0.0251861
\(231\) −1.35410 + 1.53884i −0.0890934 + 0.101248i
\(232\) 8.94427 0.587220
\(233\) 10.2812 + 7.46969i 0.673541 + 0.489356i 0.871209 0.490913i \(-0.163337\pi\)
−0.197668 + 0.980269i \(0.563337\pi\)
\(234\) 1.14590 3.52671i 0.0749097 0.230548i
\(235\) −0.555728 1.71036i −0.0362517 0.111571i
\(236\) −0.690983 + 0.502029i −0.0449792 + 0.0326793i
\(237\) 12.1353 8.81678i 0.788270 0.572711i
\(238\) 0.809017 + 2.48990i 0.0524408 + 0.161396i
\(239\) −3.19098 + 9.82084i −0.206408 + 0.635257i 0.793245 + 0.608902i \(0.208390\pi\)
−0.999653 + 0.0263546i \(0.991610\pi\)
\(240\) −0.309017 0.224514i −0.0199470 0.0144923i
\(241\) 5.09017 0.327887 0.163943 0.986470i \(-0.447579\pi\)
0.163943 + 0.986470i \(0.447579\pi\)
\(242\) −5.28115 + 9.64932i −0.339485 + 0.620282i
\(243\) −16.0000 −1.02640
\(244\) 4.50000 + 3.26944i 0.288083 + 0.209305i
\(245\) 0.781153 2.40414i 0.0499060 0.153595i
\(246\) −1.57295 4.84104i −0.100288 0.308653i
\(247\) −1.50000 + 1.08981i −0.0954427 + 0.0693432i
\(248\) 3.80902 2.76741i 0.241873 0.175731i
\(249\) 4.88197 + 15.0251i 0.309382 + 0.952180i
\(250\) 1.16312 3.57971i 0.0735621 0.226401i
\(251\) 9.23607 + 6.71040i 0.582975 + 0.423556i 0.839796 0.542903i \(-0.182675\pi\)
−0.256820 + 0.966459i \(0.582675\pi\)
\(252\) 1.23607 0.0778650
\(253\) 2.19098 2.48990i 0.137746 0.156539i
\(254\) 1.29180 0.0810545
\(255\) 1.30902 + 0.951057i 0.0819738 + 0.0595575i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −5.02786 15.4742i −0.313630 0.965252i −0.976315 0.216355i \(-0.930583\pi\)
0.662685 0.748898i \(-0.269417\pi\)
\(258\) 4.61803 3.35520i 0.287506 0.208886i
\(259\) 5.80902 4.22050i 0.360955 0.262249i
\(260\) 0.218847 + 0.673542i 0.0135723 + 0.0417713i
\(261\) −5.52786 + 17.0130i −0.342166 + 1.05308i
\(262\) 12.3262 + 8.95554i 0.761518 + 0.553275i
\(263\) −14.6180 −0.901387 −0.450693 0.892679i \(-0.648823\pi\)
−0.450693 + 0.892679i \(0.648823\pi\)
\(264\) −3.23607 + 0.726543i −0.199166 + 0.0447156i
\(265\) −5.14590 −0.316110
\(266\) −0.500000 0.363271i −0.0306570 0.0222736i
\(267\) 2.60081 8.00448i 0.159167 0.489866i
\(268\) −1.04508 3.21644i −0.0638387 0.196475i
\(269\) −8.51722 + 6.18812i −0.519304 + 0.377297i −0.816342 0.577569i \(-0.804001\pi\)
0.297038 + 0.954866i \(0.404001\pi\)
\(270\) 1.54508 1.12257i 0.0940309 0.0683174i
\(271\) 2.52786 + 7.77997i 0.153557 + 0.472599i 0.998012 0.0630273i \(-0.0200755\pi\)
−0.844455 + 0.535627i \(0.820076\pi\)
\(272\) −1.30902 + 4.02874i −0.0793708 + 0.244278i
\(273\) 0.927051 + 0.673542i 0.0561077 + 0.0407646i
\(274\) −11.4721 −0.693057
\(275\) −8.20820 13.8496i −0.494973 0.835161i
\(276\) 1.00000 0.0601929
\(277\) −19.2984 14.0211i −1.15953 0.842446i −0.169809 0.985477i \(-0.554315\pi\)
−0.989718 + 0.143031i \(0.954315\pi\)
\(278\) 5.42705 16.7027i 0.325493 1.00176i
\(279\) 2.90983 + 8.95554i 0.174207 + 0.536154i
\(280\) −0.190983 + 0.138757i −0.0114134 + 0.00829233i
\(281\) −22.5344 + 16.3722i −1.34429 + 0.976685i −0.345018 + 0.938596i \(0.612127\pi\)
−0.999274 + 0.0380892i \(0.987873\pi\)
\(282\) −1.45492 4.47777i −0.0866389 0.266647i
\(283\) 1.60081 4.92680i 0.0951585 0.292868i −0.892136 0.451766i \(-0.850794\pi\)
0.987295 + 0.158898i \(0.0507942\pi\)
\(284\) −11.5172 8.36775i −0.683421 0.496535i
\(285\) −0.381966 −0.0226257
\(286\) 5.64590 + 2.43690i 0.333849 + 0.144097i
\(287\) −3.14590 −0.185696
\(288\) 1.61803 + 1.17557i 0.0953436 + 0.0692712i
\(289\) 0.291796 0.898056i 0.0171645 0.0528268i
\(290\) −1.05573 3.24920i −0.0619945 0.190799i
\(291\) −10.6631 + 7.74721i −0.625083 + 0.454149i
\(292\) −2.11803 + 1.53884i −0.123949 + 0.0900539i
\(293\) 0.746711 + 2.29814i 0.0436233 + 0.134259i 0.970496 0.241117i \(-0.0775137\pi\)
−0.926873 + 0.375376i \(0.877514\pi\)
\(294\) 2.04508 6.29412i 0.119272 0.367081i
\(295\) 0.263932 + 0.191758i 0.0153667 + 0.0111646i
\(296\) 11.6180 0.675285
\(297\) 1.54508 16.5110i 0.0896549 0.958065i
\(298\) −13.9443 −0.807770
\(299\) −1.50000 1.08981i −0.0867472 0.0630256i
\(300\) 1.50000 4.61653i 0.0866025 0.266535i
\(301\) −1.09017 3.35520i −0.0628364 0.193390i
\(302\) −3.85410 + 2.80017i −0.221779 + 0.161132i
\(303\) 10.6631 7.74721i 0.612580 0.445066i
\(304\) −0.309017 0.951057i −0.0177233 0.0545468i
\(305\) 0.656541 2.02063i 0.0375934 0.115701i
\(306\) −6.85410 4.97980i −0.391823 0.284676i
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) −0.190983 + 2.04087i −0.0108823 + 0.116289i
\(309\) 6.32624 0.359887
\(310\) −1.45492 1.05706i −0.0826336 0.0600368i
\(311\) 0.618034 1.90211i 0.0350455 0.107859i −0.932004 0.362449i \(-0.881941\pi\)
0.967049 + 0.254590i \(0.0819406\pi\)
\(312\) 0.572949 + 1.76336i 0.0324369 + 0.0998304i
\(313\) 1.66312 1.20833i 0.0940050 0.0682987i −0.539790 0.841800i \(-0.681496\pi\)
0.633795 + 0.773501i \(0.281496\pi\)
\(314\) −0.618034 + 0.449028i −0.0348777 + 0.0253401i
\(315\) −0.145898 0.449028i −0.00822042 0.0252999i
\(316\) 4.63525 14.2658i 0.260753 0.802517i
\(317\) 13.7533 + 9.99235i 0.772462 + 0.561226i 0.902707 0.430256i \(-0.141577\pi\)
−0.130245 + 0.991482i \(0.541577\pi\)
\(318\) −13.4721 −0.755480
\(319\) −27.2361 11.7557i −1.52493 0.658193i
\(320\) −0.381966 −0.0213525
\(321\) 8.28115 + 6.01661i 0.462209 + 0.335814i
\(322\) 0.190983 0.587785i 0.0106431 0.0327560i
\(323\) 1.30902 + 4.02874i 0.0728357 + 0.224165i
\(324\) −0.809017 + 0.587785i −0.0449454 + 0.0326547i
\(325\) −7.28115 + 5.29007i −0.403886 + 0.293440i
\(326\) 1.33688 + 4.11450i 0.0740430 + 0.227881i
\(327\) −0.590170 + 1.81636i −0.0326365 + 0.100445i
\(328\) −4.11803 2.99193i −0.227380 0.165202i
\(329\) −2.90983 −0.160424
\(330\) 0.645898 + 1.08981i 0.0355555 + 0.0599923i
\(331\) −1.81966 −0.100018 −0.0500088 0.998749i \(-0.515925\pi\)
−0.0500088 + 0.998749i \(0.515925\pi\)
\(332\) 12.7812 + 9.28605i 0.701457 + 0.509638i
\(333\) −7.18034 + 22.0988i −0.393480 + 1.21101i
\(334\) 1.19098 + 3.66547i 0.0651677 + 0.200566i
\(335\) −1.04508 + 0.759299i −0.0570991 + 0.0414849i
\(336\) −0.500000 + 0.363271i −0.0272772 + 0.0198181i
\(337\) −2.16312 6.65740i −0.117833 0.362651i 0.874695 0.484674i \(-0.161062\pi\)
−0.992527 + 0.122023i \(0.961062\pi\)
\(338\) −2.95492 + 9.09429i −0.160726 + 0.494664i
\(339\) 12.2812 + 8.92278i 0.667021 + 0.484619i
\(340\) 1.61803 0.0877502
\(341\) −15.2361 + 3.42071i −0.825079 + 0.185242i
\(342\) 2.00000 0.108148
\(343\) −6.80902 4.94704i −0.367652 0.267115i
\(344\) 1.76393 5.42882i 0.0951048 0.292703i
\(345\) −0.118034 0.363271i −0.00635474 0.0195579i
\(346\) −12.0172 + 8.73102i −0.646050 + 0.469383i
\(347\) −15.0902 + 10.9637i −0.810083 + 0.588560i −0.913855 0.406042i \(-0.866909\pi\)
0.103772 + 0.994601i \(0.466909\pi\)
\(348\) −2.76393 8.50651i −0.148162 0.455997i
\(349\) 9.57295 29.4625i 0.512428 1.57709i −0.275485 0.961305i \(-0.588838\pi\)
0.787913 0.615786i \(-0.211162\pi\)
\(350\) −2.42705 1.76336i −0.129731 0.0942553i
\(351\) −9.27051 −0.494823
\(352\) −2.19098 + 2.48990i −0.116780 + 0.132712i
\(353\) −26.0000 −1.38384 −0.691920 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0.690983 + 0.502029i 0.0367253 + 0.0266825i
\(355\) −1.68034 + 5.17155i −0.0891832 + 0.274478i
\(356\) −2.60081 8.00448i −0.137843 0.424237i
\(357\) 2.11803 1.53884i 0.112098 0.0814441i
\(358\) 1.38197 1.00406i 0.0730392 0.0530661i
\(359\) −3.55573 10.9434i −0.187664 0.577571i 0.812320 0.583212i \(-0.198204\pi\)
−0.999984 + 0.00564120i \(0.998204\pi\)
\(360\) 0.236068 0.726543i 0.0124419 0.0382922i
\(361\) −0.809017 0.587785i −0.0425798 0.0309361i
\(362\) 24.8885 1.30811
\(363\) 10.8090 + 2.04087i 0.567326 + 0.107118i
\(364\) 1.14590 0.0600614
\(365\) 0.809017 + 0.587785i 0.0423459 + 0.0307661i
\(366\) 1.71885 5.29007i 0.0898456 0.276516i
\(367\) −7.75329 23.8622i −0.404718 1.24560i −0.921130 0.389255i \(-0.872733\pi\)
0.516412 0.856340i \(-0.327267\pi\)
\(368\) 0.809017 0.587785i 0.0421729 0.0306404i
\(369\) 8.23607 5.98385i 0.428753 0.311507i
\(370\) −1.37132 4.22050i −0.0712917 0.219413i
\(371\) −2.57295 + 7.91872i −0.133581 + 0.411120i
\(372\) −3.80902 2.76741i −0.197488 0.143484i
\(373\) 16.7639 0.868003 0.434002 0.900912i \(-0.357101\pi\)
0.434002 + 0.900912i \(0.357101\pi\)
\(374\) 9.28115 10.5474i 0.479917 0.545392i
\(375\) −3.76393 −0.194369
\(376\) −3.80902 2.76741i −0.196435 0.142718i
\(377\) −5.12461 + 15.7719i −0.263931 + 0.812296i
\(378\) −0.954915 2.93893i −0.0491155 0.151162i
\(379\) 24.6353 17.8986i 1.26543 0.919387i 0.266417 0.963858i \(-0.414160\pi\)
0.999011 + 0.0444705i \(0.0141601\pi\)
\(380\) −0.309017 + 0.224514i −0.0158522 + 0.0115173i
\(381\) −0.399187 1.22857i −0.0204510 0.0629416i
\(382\) −1.45492 + 4.47777i −0.0744399 + 0.229103i
\(383\) 1.07295 + 0.779543i 0.0548251 + 0.0398328i 0.614860 0.788636i \(-0.289212\pi\)
−0.560035 + 0.828469i \(0.689212\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0.763932 0.171513i 0.0389336 0.00874113i
\(386\) −6.85410 −0.348865
\(387\) 9.23607 + 6.71040i 0.469496 + 0.341109i
\(388\) −4.07295 + 12.5352i −0.206773 + 0.636381i
\(389\) −1.18034 3.63271i −0.0598456 0.184186i 0.916664 0.399658i \(-0.130871\pi\)
−0.976510 + 0.215472i \(0.930871\pi\)
\(390\) 0.572949 0.416272i 0.0290124 0.0210787i
\(391\) −3.42705 + 2.48990i −0.173313 + 0.125920i
\(392\) −2.04508 6.29412i −0.103292 0.317901i
\(393\) 4.70820 14.4904i 0.237497 0.730942i
\(394\) −18.6074 13.5191i −0.937427 0.681080i
\(395\) −5.72949 −0.288282
\(396\) −3.38197 5.70634i −0.169950 0.286754i
\(397\) −33.1803 −1.66527 −0.832637 0.553819i \(-0.813170\pi\)
−0.832637 + 0.553819i \(0.813170\pi\)
\(398\) −18.9443 13.7638i −0.949591 0.689918i
\(399\) −0.190983 + 0.587785i −0.00956111 + 0.0294261i
\(400\) −1.50000 4.61653i −0.0750000 0.230826i
\(401\) 26.3713 19.1599i 1.31692 0.956799i 0.316956 0.948440i \(-0.397339\pi\)
0.999965 0.00835887i \(-0.00266074\pi\)
\(402\) −2.73607 + 1.98787i −0.136463 + 0.0991459i
\(403\) 2.69756 + 8.30224i 0.134375 + 0.413564i
\(404\) 4.07295 12.5352i 0.202637 0.623652i
\(405\) 0.309017 + 0.224514i 0.0153552 + 0.0111562i
\(406\) −5.52786 −0.274343
\(407\) −35.3779 15.2699i −1.75362 0.756901i
\(408\) 4.23607 0.209717
\(409\) −13.5172 9.82084i −0.668384 0.485609i 0.201100 0.979571i \(-0.435548\pi\)
−0.869484 + 0.493962i \(0.835548\pi\)
\(410\) −0.600813 + 1.84911i −0.0296720 + 0.0913212i
\(411\) 3.54508 + 10.9106i 0.174866 + 0.538183i
\(412\) 5.11803 3.71847i 0.252147 0.183196i
\(413\) 0.427051 0.310271i 0.0210138 0.0152674i
\(414\) 0.618034 + 1.90211i 0.0303747 + 0.0934838i
\(415\) 1.86475 5.73910i 0.0915367 0.281721i
\(416\) 1.50000 + 1.08981i 0.0735436 + 0.0534325i
\(417\) −17.5623 −0.860030
\(418\) −0.309017 + 3.30220i −0.0151145 + 0.161516i
\(419\) 34.4721 1.68407 0.842037 0.539420i \(-0.181356\pi\)
0.842037 + 0.539420i \(0.181356\pi\)
\(420\) 0.190983 + 0.138757i 0.00931902 + 0.00677066i
\(421\) −3.36475 + 10.3556i −0.163988 + 0.504702i −0.998960 0.0455894i \(-0.985483\pi\)
0.834973 + 0.550291i \(0.185483\pi\)
\(422\) 0.982779 + 3.02468i 0.0478409 + 0.147239i
\(423\) 7.61803 5.53483i 0.370401 0.269112i
\(424\) −10.8992 + 7.91872i −0.529311 + 0.384567i
\(425\) 6.35410 + 19.5559i 0.308219 + 0.948601i
\(426\) −4.39919 + 13.5393i −0.213141 + 0.655981i
\(427\) −2.78115 2.02063i −0.134589 0.0977849i
\(428\) 10.2361 0.494779
\(429\) 0.572949 6.12261i 0.0276622 0.295602i
\(430\) −2.18034 −0.105145
\(431\) −17.5344 12.7395i −0.844604 0.613641i 0.0790487 0.996871i \(-0.474812\pi\)
−0.923653 + 0.383230i \(0.874812\pi\)
\(432\) 1.54508 4.75528i 0.0743379 0.228789i
\(433\) 3.67376 + 11.3067i 0.176550 + 0.543364i 0.999701 0.0244581i \(-0.00778604\pi\)
−0.823151 + 0.567822i \(0.807786\pi\)
\(434\) −2.35410 + 1.71036i −0.113001 + 0.0820997i
\(435\) −2.76393 + 2.00811i −0.132520 + 0.0962817i
\(436\) 0.590170 + 1.81636i 0.0282640 + 0.0869877i
\(437\) 0.309017 0.951057i 0.0147823 0.0454952i
\(438\) 2.11803 + 1.53884i 0.101204 + 0.0735287i
\(439\) 4.14590 0.197873 0.0989365 0.995094i \(-0.468456\pi\)
0.0989365 + 0.995094i \(0.468456\pi\)
\(440\) 1.16312 + 0.502029i 0.0554495 + 0.0239333i
\(441\) 13.2361 0.630289
\(442\) −6.35410 4.61653i −0.302234 0.219586i
\(443\) 4.26393 13.1230i 0.202586 0.623494i −0.797218 0.603691i \(-0.793696\pi\)
0.999804 0.0198031i \(-0.00630393\pi\)
\(444\) −3.59017 11.0494i −0.170382 0.524382i
\(445\) −2.60081 + 1.88960i −0.123290 + 0.0895757i
\(446\) 4.00000 2.90617i 0.189405 0.137611i
\(447\) 4.30902 + 13.2618i 0.203810 + 0.627261i
\(448\) −0.190983 + 0.587785i −0.00902310 + 0.0277702i
\(449\) 18.5172 + 13.4535i 0.873882 + 0.634912i 0.931626 0.363419i \(-0.118391\pi\)
−0.0577440 + 0.998331i \(0.518391\pi\)
\(450\) 9.70820 0.457649
\(451\) 8.60739 + 14.5231i 0.405306 + 0.683867i
\(452\) 15.1803 0.714023
\(453\) 3.85410 + 2.80017i 0.181082 + 0.131563i
\(454\) 7.37132 22.6866i 0.345953 1.06473i
\(455\) −0.135255 0.416272i −0.00634085 0.0195151i
\(456\) −0.809017 + 0.587785i −0.0378857 + 0.0275256i
\(457\) 12.8992 9.37181i 0.603399 0.438395i −0.243685 0.969854i \(-0.578356\pi\)
0.847084 + 0.531460i \(0.178356\pi\)
\(458\) −0.791796 2.43690i −0.0369982 0.113869i
\(459\) −6.54508 + 20.1437i −0.305498 + 0.940227i
\(460\) −0.309017 0.224514i −0.0144080 0.0104680i
\(461\) −15.7639 −0.734200 −0.367100 0.930182i \(-0.619649\pi\)
−0.367100 + 0.930182i \(0.619649\pi\)
\(462\) 2.00000 0.449028i 0.0930484 0.0208907i
\(463\) 23.1459 1.07568 0.537841 0.843047i \(-0.319240\pi\)
0.537841 + 0.843047i \(0.319240\pi\)
\(464\) −7.23607 5.25731i −0.335926 0.244065i
\(465\) −0.555728 + 1.71036i −0.0257713 + 0.0793158i
\(466\) −3.92705 12.0862i −0.181917 0.559883i
\(467\) −10.7812 + 7.83297i −0.498892 + 0.362466i −0.808594 0.588367i \(-0.799771\pi\)
0.309701 + 0.950834i \(0.399771\pi\)
\(468\) −3.00000 + 2.17963i −0.138675 + 0.100753i
\(469\) 0.645898 + 1.98787i 0.0298248 + 0.0917913i
\(470\) −0.555728 + 1.71036i −0.0256338 + 0.0788928i
\(471\) 0.618034 + 0.449028i 0.0284775 + 0.0206901i
\(472\) 0.854102 0.0393132
\(473\) −12.5066 + 14.2128i −0.575053 + 0.653507i
\(474\) −15.0000 −0.688973
\(475\) −3.92705 2.85317i −0.180185 0.130912i
\(476\) 0.809017 2.48990i 0.0370812 0.114124i
\(477\) −8.32624 25.6255i −0.381232 1.17331i
\(478\) 8.35410 6.06961i 0.382108 0.277618i
\(479\) 6.80902 4.94704i 0.311112 0.226036i −0.421262 0.906939i \(-0.638413\pi\)
0.732373 + 0.680903i \(0.238413\pi\)
\(480\) 0.118034 + 0.363271i 0.00538749 + 0.0165810i
\(481\) −6.65654 + 20.4867i −0.303512 + 0.934114i
\(482\) −4.11803 2.99193i −0.187571 0.136279i
\(483\) −0.618034 −0.0281215
\(484\) 9.94427 4.70228i 0.452012 0.213740i
\(485\) 5.03444 0.228602
\(486\) 12.9443 + 9.40456i 0.587164 + 0.426600i
\(487\) 7.51064 23.1154i 0.340340 1.04746i −0.623692 0.781670i \(-0.714368\pi\)
0.964032 0.265788i \(-0.0856320\pi\)
\(488\) −1.71885 5.29007i −0.0778086 0.239470i
\(489\) 3.50000 2.54290i 0.158275 0.114994i
\(490\) −2.04508 + 1.48584i −0.0923875 + 0.0671235i
\(491\) −4.28115 13.1760i −0.193206 0.594626i −0.999993 0.00378385i \(-0.998796\pi\)
0.806787 0.590842i \(-0.201204\pi\)
\(492\) −1.57295 + 4.84104i −0.0709140 + 0.218251i
\(493\) 30.6525 + 22.2703i 1.38052 + 1.00301i
\(494\) 1.85410 0.0834200
\(495\) −1.67376 + 1.90211i −0.0752300 + 0.0854936i
\(496\) −4.70820 −0.211405
\(497\) 7.11803 + 5.17155i 0.319287 + 0.231976i
\(498\) 4.88197 15.0251i 0.218766 0.673293i
\(499\) 0.892609 + 2.74717i 0.0399587 + 0.122980i 0.969046 0.246880i \(-0.0794055\pi\)
−0.929087 + 0.369861i \(0.879405\pi\)
\(500\) −3.04508 + 2.21238i −0.136180 + 0.0989408i
\(501\) 3.11803 2.26538i 0.139303 0.101210i
\(502\) −3.52786 10.8576i −0.157456 0.484601i
\(503\) 6.17376 19.0009i 0.275274 0.847208i −0.713872 0.700276i \(-0.753060\pi\)
0.989147 0.146932i \(-0.0469397\pi\)
\(504\) −1.00000 0.726543i −0.0445435 0.0323628i
\(505\) −5.03444 −0.224030
\(506\) −3.23607 + 0.726543i −0.143861 + 0.0322988i
\(507\) 9.56231 0.424677
\(508\) −1.04508 0.759299i −0.0463681 0.0336884i
\(509\) −11.0172 + 33.9075i −0.488330 + 1.50292i 0.338770 + 0.940869i \(0.389989\pi\)
−0.827100 + 0.562055i \(0.810011\pi\)
\(510\) −0.500000 1.53884i −0.0221404 0.0681411i
\(511\) 1.30902 0.951057i 0.0579075 0.0420723i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) −1.54508 4.75528i −0.0682172 0.209951i
\(514\) −5.02786 + 15.4742i −0.221770 + 0.682537i
\(515\) −1.95492 1.42033i −0.0861438 0.0625872i
\(516\) −5.70820 −0.251290
\(517\) 7.96149 + 13.4333i 0.350146 + 0.590796i
\(518\) −7.18034 −0.315486
\(519\) 12.0172 + 8.73102i 0.527497 + 0.383249i
\(520\) 0.218847 0.673542i 0.00959708 0.0295368i
\(521\) 11.6353 + 35.8096i 0.509750 + 1.56885i 0.792636 + 0.609695i \(0.208708\pi\)
−0.282886 + 0.959153i \(0.591292\pi\)
\(522\) 14.4721 10.5146i 0.633428 0.460213i
\(523\) −28.7254 + 20.8702i −1.25608 + 0.912592i −0.998558 0.0536818i \(-0.982904\pi\)
−0.257517 + 0.966274i \(0.582904\pi\)
\(524\) −4.70820 14.4904i −0.205679 0.633014i
\(525\) −0.927051 + 2.85317i −0.0404598 + 0.124523i
\(526\) 11.8262 + 8.59226i 0.515648 + 0.374641i
\(527\) 19.9443 0.868786
\(528\) 3.04508 + 1.31433i 0.132520 + 0.0571988i
\(529\) −22.0000 −0.956522
\(530\) 4.16312 + 3.02468i 0.180834 + 0.131384i
\(531\) −0.527864 + 1.62460i −0.0229073 + 0.0705016i
\(532\) 0.190983 + 0.587785i 0.00828016 + 0.0254837i
\(533\) 7.63525 5.54734i 0.330720 0.240282i
\(534\) −6.80902 + 4.94704i −0.294655 + 0.214079i
\(535\) −1.20820 3.71847i −0.0522352 0.160763i
\(536\) −1.04508 + 3.21644i −0.0451408 + 0.138929i
\(537\) −1.38197 1.00406i −0.0596362 0.0433283i
\(538\) 10.5279 0.453888
\(539\) −2.04508 + 21.8541i −0.0880880 + 0.941321i
\(540\) −1.90983 −0.0821860
\(541\) −15.7254 11.4252i −0.676089 0.491207i 0.195969 0.980610i \(-0.437215\pi\)
−0.872058 + 0.489403i \(0.837215\pi\)
\(542\) 2.52786 7.77997i 0.108581 0.334178i
\(543\) −7.69098 23.6704i −0.330052 1.01579i
\(544\) 3.42705 2.48990i 0.146934 0.106754i
\(545\) 0.590170 0.428784i 0.0252801 0.0183671i
\(546\) −0.354102 1.08981i −0.0151542 0.0466397i
\(547\) 4.11803 12.6740i 0.176074 0.541901i −0.823606 0.567162i \(-0.808041\pi\)
0.999681 + 0.0252603i \(0.00804147\pi\)
\(548\) 9.28115 + 6.74315i 0.396471 + 0.288053i
\(549\) 11.1246 0.474787
\(550\) −1.50000 + 16.0292i −0.0639602 + 0.683488i
\(551\) −8.94427 −0.381039
\(552\) −0.809017 0.587785i −0.0344340 0.0250178i
\(553\) −2.86475 + 8.81678i −0.121821 + 0.374928i
\(554\) 7.37132 + 22.6866i 0.313178 + 0.963861i
\(555\) −3.59017 + 2.60841i −0.152394 + 0.110721i
\(556\) −14.2082 + 10.3229i −0.602562 + 0.437787i
\(557\) −6.14590 18.9151i −0.260410 0.801460i −0.992715 0.120483i \(-0.961556\pi\)
0.732305 0.680976i \(-0.238444\pi\)
\(558\) 2.90983 8.95554i 0.123183 0.379118i
\(559\) 8.56231 + 6.22088i 0.362147 + 0.263115i
\(560\) 0.236068 0.00997569
\(561\) −12.8992 5.56758i −0.544604 0.235063i
\(562\) 27.8541 1.17495
\(563\) −1.95492 1.42033i −0.0823898 0.0598597i 0.545828 0.837897i \(-0.316215\pi\)
−0.628218 + 0.778038i \(0.716215\pi\)
\(564\) −1.45492 + 4.47777i −0.0612630 + 0.188548i
\(565\) −1.79180 5.51458i −0.0753814 0.232000i
\(566\) −4.19098 + 3.04493i −0.176160 + 0.127988i
\(567\) 0.500000 0.363271i 0.0209980 0.0152560i
\(568\) 4.39919 + 13.5393i 0.184586 + 0.568097i
\(569\) −6.18034 + 19.0211i −0.259093 + 0.797407i 0.733902 + 0.679255i \(0.237697\pi\)
−0.992996 + 0.118152i \(0.962303\pi\)
\(570\) 0.309017 + 0.224514i 0.0129433 + 0.00940386i
\(571\) −25.3607 −1.06131 −0.530656 0.847587i \(-0.678054\pi\)
−0.530656 + 0.847587i \(0.678054\pi\)
\(572\) −3.13525 5.29007i −0.131092 0.221189i
\(573\) 4.70820 0.196688
\(574\) 2.54508 + 1.84911i 0.106230 + 0.0771805i
\(575\) 1.50000 4.61653i 0.0625543 0.192522i
\(576\) −0.618034 1.90211i −0.0257514 0.0792547i
\(577\) 2.30902 1.67760i 0.0961256 0.0698394i −0.538684 0.842508i \(-0.681078\pi\)
0.634810 + 0.772668i \(0.281078\pi\)
\(578\) −0.763932 + 0.555029i −0.0317754 + 0.0230862i
\(579\) 2.11803 + 6.51864i 0.0880225 + 0.270905i
\(580\) −1.05573 + 3.24920i −0.0438367 + 0.134916i
\(581\) −7.89919 5.73910i −0.327713 0.238098i
\(582\) 13.1803 0.546343
\(583\) 43.5967 9.78808i 1.80559 0.405381i
\(584\) 2.61803 0.108335
\(585\) 1.14590 + 0.832544i 0.0473771 + 0.0344214i
\(586\) 0.746711 2.29814i 0.0308464 0.0949353i
\(587\) 12.6353 + 38.8873i 0.521513 + 1.60505i 0.771110 + 0.636702i \(0.219702\pi\)
−0.249597 + 0.968350i \(0.580298\pi\)
\(588\) −5.35410 + 3.88998i −0.220799 + 0.160420i
\(589\) −3.80902 + 2.76741i −0.156948 + 0.114029i
\(590\) −0.100813 0.310271i −0.00415041 0.0127736i
\(591\) −7.10739 + 21.8743i −0.292359 + 0.899788i
\(592\) −9.39919 6.82891i −0.386304 0.280666i
\(593\) −2.05573 −0.0844186 −0.0422093 0.999109i \(-0.513440\pi\)
−0.0422093 + 0.999109i \(0.513440\pi\)
\(594\) −10.9549 + 12.4495i −0.449486 + 0.510809i
\(595\) −1.00000 −0.0409960
\(596\) 11.2812 + 8.19624i 0.462094 + 0.335731i
\(597\) −7.23607 + 22.2703i −0.296153 + 0.911464i
\(598\) 0.572949 + 1.76336i 0.0234296 + 0.0721090i
\(599\) 15.5902 11.3269i 0.636997 0.462805i −0.221820 0.975088i \(-0.571200\pi\)
0.858817 + 0.512282i \(0.171200\pi\)
\(600\) −3.92705 + 2.85317i −0.160321 + 0.116480i
\(601\) −12.4098 38.1935i −0.506208 1.55795i −0.798731 0.601688i \(-0.794495\pi\)
0.292524 0.956258i \(-0.405505\pi\)
\(602\) −1.09017 + 3.35520i −0.0444320 + 0.136748i
\(603\) −5.47214 3.97574i −0.222843 0.161905i
\(604\) 4.76393 0.193842
\(605\) −2.88197 3.05744i −0.117169 0.124303i
\(606\) −13.1803 −0.535415
\(607\) −31.3713 22.7926i −1.27332 0.925123i −0.273993 0.961732i \(-0.588345\pi\)
−0.999330 + 0.0366086i \(0.988345\pi\)
\(608\) −0.309017 + 0.951057i −0.0125323 + 0.0385704i
\(609\) 1.70820 + 5.25731i 0.0692199 + 0.213037i
\(610\) −1.71885 + 1.24882i −0.0695941 + 0.0505631i
\(611\) 7.06231 5.13107i 0.285710 0.207581i
\(612\) 2.61803 + 8.05748i 0.105828 + 0.325704i
\(613\) −2.38197 + 7.33094i −0.0962067 + 0.296094i −0.987566 0.157203i \(-0.949752\pi\)
0.891360 + 0.453297i \(0.149752\pi\)
\(614\) −18.6074 13.5191i −0.750933 0.545585i
\(615\) 1.94427 0.0784006
\(616\) 1.35410 1.53884i 0.0545583 0.0620017i
\(617\) −11.2705 −0.453734 −0.226867 0.973926i \(-0.572848\pi\)
−0.226867 + 0.973926i \(0.572848\pi\)
\(618\) −5.11803 3.71847i −0.205878 0.149579i
\(619\) 0.791796 2.43690i 0.0318250 0.0979472i −0.933882 0.357581i \(-0.883602\pi\)
0.965707 + 0.259633i \(0.0836017\pi\)
\(620\) 0.555728 + 1.71036i 0.0223186 + 0.0686895i
\(621\) 4.04508 2.93893i 0.162324 0.117935i
\(622\) −1.61803 + 1.17557i −0.0648773 + 0.0471361i
\(623\) 1.60739 + 4.94704i 0.0643988 + 0.198199i
\(624\) 0.572949 1.76336i 0.0229363 0.0705907i
\(625\) −18.4721 13.4208i −0.738885 0.536832i
\(626\) −2.05573 −0.0821634
\(627\) 3.23607 0.726543i 0.129236 0.0290153i
\(628\) 0.763932 0.0304842
\(629\) 39.8156 + 28.9277i 1.58755 + 1.15342i
\(630\) −0.145898 + 0.449028i −0.00581272 + 0.0178897i
\(631\) 9.29837 + 28.6175i 0.370162 + 1.13924i 0.946685 + 0.322161i \(0.104409\pi\)
−0.576522 + 0.817081i \(0.695591\pi\)
\(632\) −12.1353 + 8.81678i −0.482715 + 0.350713i
\(633\) 2.57295 1.86936i 0.102266 0.0743003i
\(634\) −5.25329 16.1680i −0.208635 0.642112i
\(635\) −0.152476 + 0.469272i −0.00605082 + 0.0186225i
\(636\) 10.8992 + 7.91872i 0.432181 + 0.313998i
\(637\) 12.2705 0.486175
\(638\) 15.1246 + 25.5195i 0.598789 + 1.01033i
\(639\) −28.4721 −1.12634
\(640\) 0.309017 + 0.224514i 0.0122150 + 0.00887469i
\(641\) −2.67376 + 8.22899i −0.105607 + 0.325026i −0.989872 0.141959i \(-0.954660\pi\)
0.884265 + 0.466985i \(0.154660\pi\)
\(642\) −3.16312 9.73508i −0.124838 0.384213i
\(643\) 28.2705 20.5397i 1.11488 0.810008i 0.131455 0.991322i \(-0.458035\pi\)
0.983425 + 0.181314i \(0.0580352\pi\)
\(644\) −0.500000 + 0.363271i −0.0197028 + 0.0143149i
\(645\) 0.673762 + 2.07363i 0.0265294 + 0.0816490i
\(646\) 1.30902 4.02874i 0.0515026 0.158509i
\(647\) −13.8713 10.0781i −0.545338 0.396211i 0.280726 0.959788i \(-0.409425\pi\)
−0.826064 + 0.563577i \(0.809425\pi\)
\(648\) 1.00000 0.0392837
\(649\) −2.60081 1.12257i −0.102091 0.0440647i
\(650\) 9.00000 0.353009
\(651\) 2.35410 + 1.71036i 0.0922645 + 0.0670341i
\(652\) 1.33688 4.11450i 0.0523563 0.161136i
\(653\) 6.70163 + 20.6255i 0.262255 + 0.807138i 0.992313 + 0.123753i \(0.0394929\pi\)
−0.730058 + 0.683385i \(0.760507\pi\)
\(654\) 1.54508 1.12257i 0.0604176 0.0438960i
\(655\) −4.70820 + 3.42071i −0.183965 + 0.133658i
\(656\) 1.57295 + 4.84104i 0.0614133 + 0.189011i
\(657\) −1.61803 + 4.97980i −0.0631255 + 0.194280i
\(658\) 2.35410 + 1.71036i 0.0917724 + 0.0666766i
\(659\) 15.6525 0.609734 0.304867 0.952395i \(-0.401388\pi\)
0.304867 + 0.952395i \(0.401388\pi\)
\(660\) 0.118034 1.26133i 0.00459447 0.0490971i
\(661\) −17.1459 −0.666898 −0.333449 0.942768i \(-0.608213\pi\)
−0.333449 + 0.942768i \(0.608213\pi\)
\(662\) 1.47214 + 1.06957i 0.0572162 + 0.0415700i
\(663\) −2.42705 + 7.46969i −0.0942588 + 0.290099i
\(664\) −4.88197 15.0251i −0.189457 0.583089i
\(665\) 0.190983 0.138757i 0.00740600 0.00538078i
\(666\) 18.7984 13.6578i 0.728422 0.529230i
\(667\) −2.76393 8.50651i −0.107020 0.329373i
\(668\) 1.19098 3.66547i 0.0460805 0.141821i
\(669\) −4.00000 2.90617i −0.154649 0.112359i
\(670\) 1.29180 0.0499064
\(671\) −1.71885 + 18.3678i −0.0663554 + 0.709082i
\(672\) 0.618034 0.0238412
\(673\) 1.07295 + 0.779543i 0.0413591 + 0.0300492i 0.608273 0.793728i \(-0.291863\pi\)
−0.566914 + 0.823777i \(0.691863\pi\)
\(674\) −2.16312 + 6.65740i −0.0833202 + 0.256433i
\(675\) −7.50000 23.0826i −0.288675 0.888451i
\(676\) 7.73607 5.62058i 0.297541 0.216176i
\(677\) −9.66312 + 7.02067i −0.371384 + 0.269826i −0.757785 0.652505i \(-0.773718\pi\)
0.386401 + 0.922331i \(0.373718\pi\)
\(678\) −4.69098 14.4374i −0.180156 0.554464i
\(679\) 2.51722 7.74721i 0.0966021 0.297311i
\(680\) −1.30902 0.951057i −0.0501985 0.0364714i
\(681\) −23.8541 −0.914091
\(682\) 14.3369 + 6.18812i 0.548988 + 0.236955i
\(683\) 44.9787 1.72106 0.860531 0.509398i \(-0.170132\pi\)
0.860531 + 0.509398i \(0.170132\pi\)
\(684\) −1.61803 1.17557i −0.0618671 0.0449491i
\(685\) 1.35410 4.16750i 0.0517376 0.159232i
\(686\) 2.60081 + 8.00448i 0.0992995 + 0.305612i
\(687\) −2.07295 + 1.50609i −0.0790879 + 0.0574608i
\(688\) −4.61803 + 3.35520i −0.176061 + 0.127916i
\(689\) −7.71885 23.7562i −0.294065 0.905038i
\(690\) −0.118034 + 0.363271i −0.00449348 + 0.0138295i
\(691\) 30.4164 + 22.0988i 1.15709 + 0.840678i 0.989408 0.145162i \(-0.0463703\pi\)
0.167687 + 0.985840i \(0.446370\pi\)
\(692\) 14.8541 0.564668
\(693\) 2.09017 + 3.52671i 0.0793990 + 0.133969i
\(694\) 18.6525 0.708038
\(695\) 5.42705 + 3.94298i 0.205860 + 0.149566i
\(696\) −2.76393 + 8.50651i −0.104767 + 0.322438i
\(697\) −6.66312 20.5070i −0.252384 0.776757i
\(698\) −25.0623 + 18.2088i −0.948622 + 0.689214i
\(699\) −10.2812 + 7.46969i −0.388869 + 0.282530i
\(700\) 0.927051 + 2.85317i 0.0350392 + 0.107840i
\(701\) −2.24671 + 6.91467i −0.0848571 + 0.261163i −0.984478 0.175509i \(-0.943843\pi\)
0.899621 + 0.436672i \(0.143843\pi\)
\(702\) 7.50000 + 5.44907i 0.283069 + 0.205662i
\(703\) −11.6180 −0.438182
\(704\) 3.23607 0.726543i 0.121964 0.0273826i
\(705\) 1.79837 0.0677307
\(706\) 21.0344 + 15.2824i 0.791642 + 0.575161i
\(707\) −2.51722 + 7.74721i −0.0946698 + 0.291364i
\(708\) −0.263932 0.812299i −0.00991917 0.0305281i
\(709\) 17.4615 12.6865i 0.655780 0.476452i −0.209455 0.977818i \(-0.567169\pi\)
0.865235 + 0.501366i \(0.167169\pi\)
\(710\) 4.39919 3.19620i 0.165099 0.119951i
\(711\) −9.27051 28.5317i −0.347671 1.07002i
\(712\) −2.60081 + 8.00448i −0.0974696 + 0.299981i
\(713\) −3.80902 2.76741i −0.142649 0.103640i
\(714\) −2.61803 −0.0979775
\(715\) −1.55166 + 1.76336i −0.0580289 + 0.0659458i
\(716\) −1.70820 −0.0638386
\(717\) −8.35410 6.06961i −0.311990 0.226674i
\(718\) −3.55573 + 10.9434i −0.132699 + 0.408404i
\(719\) −3.51722 10.8249i −0.131170 0.403700i 0.863804 0.503827i \(-0.168075\pi\)
−0.994975 + 0.100127i \(0.968075\pi\)
\(720\) −0.618034 + 0.449028i −0.0230328 + 0.0167343i
\(721\) −3.16312 + 2.29814i −0.117801 + 0.0855872i
\(722\) 0.309017 + 0.951057i 0.0115004 + 0.0353947i
\(723\) −1.57295 + 4.84104i −0.0584986 + 0.180040i
\(724\) −20.1353 14.6291i −0.748321 0.543687i
\(725\) −43.4164 −1.61244
\(726\) −7.54508 8.00448i −0.280024 0.297074i
\(727\) 44.7082 1.65814 0.829068 0.559148i \(-0.188872\pi\)
0.829068 + 0.559148i \(0.188872\pi\)
\(728\) −0.927051 0.673542i −0.0343588 0.0249631i
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) −0.309017 0.951057i −0.0114372 0.0352002i
\(731\) 19.5623 14.2128i 0.723538 0.525681i
\(732\) −4.50000 + 3.26944i −0.166325 + 0.120842i
\(733\) 3.37132 + 10.3759i 0.124523 + 0.383241i 0.993814 0.111059i \(-0.0354243\pi\)
−0.869291 + 0.494300i \(0.835424\pi\)
\(734\) −7.75329 + 23.8622i −0.286179 + 0.880769i
\(735\) 2.04508 + 1.48584i 0.0754341 + 0.0548061i
\(736\) −1.00000 −0.0368605
\(737\) 7.40983 8.42075i 0.272945 0.310182i
\(738\) −10.1803 −0.374743
\(739\) 14.7984 + 10.7516i 0.544367 + 0.395506i 0.825704 0.564103i \(-0.190778\pi\)
−0.281337 + 0.959609i \(0.590778\pi\)
\(740\) −1.37132 + 4.22050i −0.0504108 + 0.155149i
\(741\) −0.572949 1.76336i −0.0210478 0.0647785i
\(742\) 6.73607 4.89404i 0.247289 0.179666i
\(743\) 13.4721 9.78808i 0.494245 0.359090i −0.312570 0.949895i \(-0.601190\pi\)
0.806814 + 0.590805i \(0.201190\pi\)
\(744\) 1.45492 + 4.47777i 0.0533398 + 0.164163i
\(745\) 1.64590 5.06555i 0.0603010 0.185588i
\(746\) −13.5623 9.85359i −0.496551 0.360766i
\(747\) 31.5967 1.15606
\(748\) −13.7082 + 3.07768i −0.501222 + 0.112531i
\(749\) −6.32624 −0.231156
\(750\) 3.04508 + 2.21238i 0.111191 + 0.0807848i
\(751\) 0.781153 2.40414i 0.0285047 0.0877284i −0.935792 0.352552i \(-0.885314\pi\)
0.964297 + 0.264824i \(0.0853138\pi\)
\(752\) 1.45492 + 4.47777i 0.0530553 + 0.163287i
\(753\) −9.23607 + 6.71040i −0.336581 + 0.244540i
\(754\) 13.4164 9.74759i 0.488597 0.354986i
\(755\) −0.562306 1.73060i −0.0204644 0.0629830i
\(756\) −0.954915 + 2.93893i −0.0347299 + 0.106888i
\(757\) 8.48936 + 6.16788i 0.308551 + 0.224175i 0.731274 0.682083i \(-0.238926\pi\)
−0.422724 + 0.906259i \(0.638926\pi\)
\(758\) −30.4508 −1.10602
\(759\) 1.69098 + 2.85317i 0.0613788 + 0.103563i
\(760\) 0.381966 0.0138554
\(761\) 12.2254 + 8.88229i 0.443171 + 0.321983i 0.786894 0.617088i \(-0.211688\pi\)
−0.343722 + 0.939071i \(0.611688\pi\)
\(762\) −0.399187 + 1.22857i −0.0144610 + 0.0445064i
\(763\) −0.364745 1.12257i −0.0132047 0.0406398i
\(764\) 3.80902 2.76741i 0.137805 0.100121i
\(765\) 2.61803 1.90211i 0.0946552 0.0687710i
\(766\) −0.409830 1.26133i −0.0148078 0.0455736i
\(767\) −0.489357 + 1.50609i −0.0176697 + 0.0543816i
\(768\) 0.809017 + 0.587785i 0.0291929 + 0.0212099i
\(769\) 16.7082 0.602513 0.301257 0.953543i \(-0.402594\pi\)
0.301257 + 0.953543i \(0.402594\pi\)
\(770\) −0.718847 0.310271i −0.0259054 0.0111814i
\(771\) 16.2705 0.585968
\(772\) 5.54508 + 4.02874i 0.199572 + 0.144998i
\(773\) −11.9164 + 36.6749i −0.428603 + 1.31911i 0.470898 + 0.882188i \(0.343930\pi\)
−0.899501 + 0.436918i \(0.856070\pi\)
\(774\) −3.52786 10.8576i −0.126806 0.390270i
\(775\) −18.4894 + 13.4333i −0.664157 + 0.482539i
\(776\) 10.6631 7.74721i 0.382784 0.278109i
\(777\) 2.21885 + 6.82891i 0.0796007 + 0.244986i
\(778\) −1.18034 + 3.63271i −0.0423172 + 0.130239i
\(779\) 4.11803 + 2.99193i 0.147544 + 0.107197i
\(780\) −0.708204 −0.0253578
\(781\) 4.39919 47.0103i 0.157415 1.68216i
\(782\) 4.23607 0.151481
\(783\) −36.1803 26.2866i −1.29298 0.939405i
\(784\) −2.04508 + 6.29412i −0.0730387 + 0.224790i
\(785\) −0.0901699 0.277515i −0.00321830 0.00990492i
\(786\) −12.3262 + 8.95554i −0.439662 + 0.319433i
\(787\) 40.0344 29.0867i 1.42707 1.03683i 0.436521 0.899694i \(-0.356210\pi\)
0.990552 0.137136i \(-0.0437897\pi\)
\(788\) 7.10739 + 21.8743i 0.253190 + 0.779240i
\(789\) 4.51722 13.9026i 0.160817 0.494945i
\(790\) 4.63525 + 3.36771i 0.164915 + 0.119818i
\(791\) −9.38197 −0.333584
\(792\) −0.618034 + 6.60440i −0.0219609 + 0.234677i
\(793\) 10.3131 0.366228
\(794\) 26.8435 + 19.5029i 0.952639 + 0.692133i
\(795\) 1.59017 4.89404i 0.0563975 0.173574i
\(796\) 7.23607 + 22.2703i 0.256476 + 0.789351i
\(797\) −4.50000 + 3.26944i −0.159398 + 0.115810i −0.664625 0.747177i \(-0.731409\pi\)
0.505227 + 0.862986i \(0.331409\pi\)
\(798\) 0.500000 0.363271i 0.0176998 0.0128597i
\(799\) −6.16312 18.9681i −0.218035 0.671044i
\(800\) −1.50000 + 4.61653i −0.0530330 + 0.163219i
\(801\) −13.6180 9.89408i −0.481170 0.349590i
\(802\) −32.5967 −1.15103
\(803\) −7.97214 3.44095i −0.281331 0.121429i
\(804\) 3.38197 0.119273
\(805\) 0.190983 + 0.138757i 0.00673127 + 0.00489055i
\(806\) 2.69756 8.30224i 0.0950175 0.292434i
\(807\) −3.25329 10.0126i −0.114521 0.352460i
\(808\) −10.6631 + 7.74721i −0.375127 + 0.272546i
\(809\) −14.4721 + 10.5146i −0.508813 + 0.369674i −0.812373 0.583138i \(-0.801825\pi\)
0.303560 + 0.952812i \(0.401825\pi\)
\(810\) −0.118034 0.363271i −0.00414729 0.0127641i
\(811\) 5.41641 16.6700i 0.190196 0.585362i −0.809803 0.586701i \(-0.800426\pi\)
0.999999 + 0.00133898i \(0.000426209\pi\)
\(812\) 4.47214 + 3.24920i 0.156941 + 0.114024i
\(813\) −8.18034 −0.286897
\(814\) 19.6459 + 33.1482i 0.688588 + 1.16184i
\(815\) −1.65248 −0.0578837
\(816\) −3.42705 2.48990i −0.119971 0.0871639i
\(817\) −1.76393 + 5.42882i −0.0617122 + 0.189931i
\(818\) 5.16312 + 15.8904i 0.180524 + 0.555596i
\(819\) 1.85410 1.34708i 0.0647876 0.0470709i
\(820\) 1.57295 1.14281i 0.0549298 0.0399088i
\(821\) −2.20820 6.79615i −0.0770668 0.237187i 0.905100 0.425199i \(-0.139796\pi\)
−0.982167 + 0.188011i \(0.939796\pi\)
\(822\) 3.54508 10.9106i 0.123649 0.380553i
\(823\) 6.23607 + 4.53077i 0.217376 + 0.157933i 0.691145 0.722717i \(-0.257107\pi\)
−0.473769 + 0.880649i \(0.657107\pi\)
\(824\) −6.32624 −0.220385
\(825\) 15.7082 3.52671i 0.546889 0.122784i
\(826\) −0.527864 −0.0183667
\(827\) −15.6803 11.3924i −0.545259 0.396154i 0.280776 0.959773i \(-0.409408\pi\)
−0.826034 + 0.563620i \(0.809408\pi\)
\(828\) 0.618034 1.90211i 0.0214782 0.0661030i
\(829\) −5.12461 15.7719i −0.177985 0.547782i 0.821772 0.569816i \(-0.192986\pi\)
−0.999757 + 0.0220344i \(0.992986\pi\)
\(830\) −4.88197 + 3.54696i −0.169456 + 0.123117i
\(831\) 19.2984 14.0211i 0.669453 0.486386i
\(832\) −0.572949 1.76336i −0.0198634 0.0611334i
\(833\) 8.66312 26.6623i 0.300159 0.923795i
\(834\) 14.2082 + 10.3229i 0.491990 + 0.357452i
\(835\) −1.47214 −0.0509454
\(836\) 2.19098 2.48990i 0.0757767 0.0861149i
\(837\) −23.5410 −0.813697
\(838\) −27.8885 20.2622i −0.963394 0.699947i
\(839\) −0.263932 + 0.812299i −0.00911195 + 0.0280437i −0.955509 0.294962i \(-0.904693\pi\)
0.946397 + 0.323005i \(0.104693\pi\)
\(840\) −0.0729490 0.224514i −0.00251698 0.00774647i
\(841\) −41.2599 + 29.9770i −1.42275 + 1.03369i
\(842\) 8.80902 6.40013i 0.303579 0.220563i
\(843\) −8.60739 26.4908i −0.296454 0.912392i
\(844\) 0.982779 3.02468i 0.0338287 0.104114i
\(845\) −2.95492 2.14687i −0.101652 0.0738546i
\(846\) −9.41641 −0.323743
\(847\) −6.14590 + 2.90617i −0.211176 + 0.0998572i
\(848\) 13.4721 0.462635
\(849\) 4.19098 + 3.04493i 0.143834 + 0.104502i
\(850\) 6.35410 19.5559i 0.217944 0.670762i
\(851\) −3.59017 11.0494i −0.123069 0.378769i
\(852\) 11.5172 8.36775i 0.394573 0.286674i
\(853\) −24.1525 + 17.5478i −0.826965 + 0.600825i −0.918699 0.394958i \(-0.870759\pi\)
0.0917340 + 0.995784i \(0.470759\pi\)
\(854\) 1.06231 + 3.26944i 0.0363514 + 0.111878i
\(855\) −0.236068 + 0.726543i −0.00807335 + 0.0248472i
\(856\) −8.28115 6.01661i −0.283044 0.205643i
\(857\) 27.1459 0.927286 0.463643 0.886022i \(-0.346542\pi\)
0.463643 + 0.886022i \(0.346542\pi\)
\(858\) −4.06231 + 4.61653i −0.138685 + 0.157606i
\(859\) 46.3050 1.57990 0.789952 0.613168i \(-0.210105\pi\)
0.789952 + 0.613168i \(0.210105\pi\)
\(860\) 1.76393 + 1.28157i 0.0601496 + 0.0437012i
\(861\) 0.972136 2.99193i 0.0331303 0.101965i
\(862\) 6.69756 + 20.6130i 0.228120 + 0.702081i
\(863\) 2.61803 1.90211i 0.0891189 0.0647487i −0.542334 0.840163i \(-0.682459\pi\)
0.631452 + 0.775415i \(0.282459\pi\)
\(864\) −4.04508 + 2.93893i −0.137617 + 0.0999843i
\(865\) −1.75329 5.39607i −0.0596136 0.183472i
\(866\) 3.67376 11.3067i 0.124840 0.384217i
\(867\) 0.763932 + 0.555029i 0.0259445 + 0.0188498i
\(868\) 2.90983 0.0987661
\(869\) 48.5410 10.8981i 1.64664 0.369694i
\(870\) 3.41641 0.115827
\(871\) −5.07295 3.68571i −0.171890 0.124886i
\(872\) 0.590170 1.81636i 0.0199857 0.0615096i
\(873\) 8.14590 + 25.0705i 0.275697 + 0.848508i
\(874\) −0.809017 + 0.587785i −0.0273654 + 0.0198821i
\(875\) 1.88197 1.36733i 0.0636221 0.0462241i
\(876\) −0.809017 2.48990i −0.0273342 0.0841259i
\(877\) 8.26393 25.4338i 0.279053 0.858837i −0.709065 0.705143i \(-0.750883\pi\)
0.988118 0.153694i \(-0.0491171\pi\)
\(878\) −3.35410 2.43690i −0.113195 0.0822413i
\(879\) −2.41641 −0.0815034
\(880\) −0.645898 1.08981i −0.0217732 0.0367376i
\(881\) −4.58359 −0.154425 −0.0772126 0.997015i \(-0.524602\pi\)
−0.0772126 + 0.997015i \(0.524602\pi\)
\(882\) −10.7082 7.77997i −0.360564 0.261965i
\(883\) −4.49342 + 13.8293i −0.151216 + 0.465394i −0.997758 0.0669277i \(-0.978680\pi\)
0.846542 + 0.532322i \(0.178680\pi\)
\(884\) 2.42705 + 7.46969i 0.0816306 + 0.251233i
\(885\) −0.263932 + 0.191758i −0.00887198 + 0.00644587i
\(886\) −11.1631 + 8.11048i −0.375032 + 0.272477i
\(887\) −10.9828 33.8015i −0.368766 1.13494i −0.947589 0.319491i \(-0.896488\pi\)
0.578824 0.815453i \(-0.303512\pi\)
\(888\) −3.59017 + 11.0494i −0.120478 + 0.370794i
\(889\) 0.645898 + 0.469272i 0.0216627 + 0.0157389i
\(890\) 3.21478 0.107760
\(891\) −3.04508 1.31433i −0.102014 0.0440316i
\(892\) −4.94427 −0.165546
\(893\) 3.80902 + 2.76741i 0.127464 + 0.0926079i
\(894\) 4.30902 13.2618i 0.144115 0.443541i
\(895\) 0.201626 + 0.620541i 0.00673962 + 0.0207424i
\(896\) 0.500000 0.363271i 0.0167038 0.0121360i
\(897\) 1.50000 1.08981i 0.0500835 0.0363878i
\(898\) −7.07295 21.7683i −0.236027 0.726418i
\(899\) −13.0132 + 40.0504i −0.434013 + 1.33575i
\(900\) −7.85410 5.70634i −0.261803 0.190211i
\(901\) −57.0689 −1.90124
\(902\) 1.57295 16.8087i 0.0523735 0.559670i
\(903\) 3.52786 0.117400
\(904\) −12.2812 8.92278i −0.408465 0.296767i
\(905\) −2.93769 + 9.04129i −0.0976523 + 0.300543i
\(906\) −1.47214 4.53077i −0.0489084 0.150525i
\(907\) 0.826238 0.600297i 0.0274348 0.0199325i −0.573983 0.818867i \(-0.694603\pi\)
0.601418 + 0.798934i \(0.294603\pi\)
\(908\) −19.2984 + 14.0211i −0.640439 + 0.465306i
\(909\) −8.14590 25.0705i −0.270182 0.831536i
\(910\) −0.135255 + 0.416272i −0.00448366 + 0.0137993i
\(911\) −25.8885 18.8091i −0.857726 0.623174i 0.0695396 0.997579i \(-0.477847\pi\)
−0.927265 + 0.374405i \(0.877847\pi\)
\(912\) 1.00000 0.0331133
\(913\) −4.88197 + 52.1694i −0.161569 + 1.72655i
\(914\) −15.9443 −0.527390
\(915\) 1.71885 + 1.24882i 0.0568233 + 0.0412846i
\(916\) −0.791796 + 2.43690i −0.0261617 + 0.0805174i
\(917\) 2.90983 + 8.95554i 0.0960911 + 0.295738i
\(918\) 17.1353 12.4495i 0.565548 0.410894i
\(919\) −41.4058 + 30.0830i −1.36585 + 0.992348i −0.367802 + 0.929904i \(0.619889\pi\)
−0.998048 + 0.0624440i \(0.980111\pi\)
\(920\) 0.118034 + 0.363271i 0.00389147 + 0.0119767i
\(921\) −7.10739 + 21.8743i −0.234196 + 0.720783i
\(922\) 12.7533 + 9.26581i 0.420007 + 0.305153i
\(923\) −26.3951 −0.868806
\(924\) −1.88197 0.812299i −0.0619121 0.0267227i
\(925\) −56.3951 −1.85426
\(926\) −18.7254 13.6048i −0.615356 0.447082i
\(927\) 3.90983 12.0332i 0.128416 0.395223i
\(928\) 2.76393 + 8.50651i 0.0907305 + 0.279240i
\(929\) 24.8992 18.0903i 0.816916 0.593524i −0.0989116 0.995096i \(-0.531536\pi\)
0.915827 + 0.401572i \(0.131536\pi\)
\(930\) 1.45492 1.05706i 0.0477085 0.0346623i
\(931\) 2.04508 + 6.29412i 0.0670250 + 0.206282i
\(932\) −3.92705 + 12.0862i −0.128635 + 0.395897i
\(933\) 1.61803 + 1.17557i 0.0529721 + 0.0384865i
\(934\) 13.3262 0.436048
\(935\) 2.73607 + 4.61653i 0.0894790 + 0.150977i
\(936\) 3.70820 0.121206
\(937\) −32.3262 23.4864i −1.05605 0.767267i −0.0826982 0.996575i \(-0.526354\pi\)
−0.973354 + 0.229308i \(0.926354\pi\)
\(938\) 0.645898 1.98787i 0.0210893 0.0649062i
\(939\) 0.635255 + 1.95511i 0.0207308 + 0.0638027i
\(940\) 1.45492 1.05706i 0.0474541 0.0344774i
\(941\) 44.7877 32.5402i 1.46004 1.06078i 0.476685 0.879074i \(-0.341838\pi\)
0.983353 0.181706i \(-0.0581619\pi\)
\(942\) −0.236068 0.726543i −0.00769151 0.0236720i
\(943\) −1.57295 + 4.84104i −0.0512223 + 0.157646i
\(944\) −0.690983 0.502029i −0.0224896 0.0163396i
\(945\) 1.18034 0.0383965
\(946\) 18.4721 4.14725i 0.600581 0.134839i
\(947\) −14.8885 −0.483813 −0.241906 0.970300i \(-0.577773\pi\)
−0.241906 + 0.970300i \(0.577773\pi\)
\(948\) 12.1353 + 8.81678i 0.394135 + 0.286356i
\(949\) −1.50000 + 4.61653i −0.0486921 + 0.149859i
\(950\) 1.50000 + 4.61653i 0.0486664 + 0.149780i
\(951\) −13.7533 + 9.99235i −0.445981 + 0.324024i
\(952\) −2.11803 + 1.53884i −0.0686459 + 0.0498741i
\(953\) −6.85410 21.0948i −0.222026 0.683326i −0.998580 0.0532752i \(-0.983034\pi\)
0.776554 0.630051i \(-0.216966\pi\)
\(954\) −8.32624 + 25.6255i −0.269572 + 0.829657i
\(955\) −1.45492 1.05706i −0.0470799 0.0342056i
\(956\) −10.3262 −0.333974
\(957\) 19.5967 22.2703i 0.633473 0.719897i
\(958\) −8.41641 −0.271922
\(959\) −5.73607 4.16750i −0.185227 0.134576i
\(960\) 0.118034 0.363271i 0.00380953 0.0117245i
\(961\) −2.72949 8.40051i −0.0880481 0.270984i
\(962\) 17.4271 12.6615i 0.561871 0.408223i
\(963\) 16.5623 12.0332i 0.533713 0.387765i
\(964\) 1.57295 + 4.84104i 0.0506613 + 0.155919i
\(965\) 0.809017 2.48990i 0.0260432 0.0801527i
\(966\) 0.500000 + 0.363271i 0.0160872 + 0.0116881i
\(967\) −30.7426 −0.988617 −0.494308 0.869287i \(-0.664579\pi\)
−0.494308 + 0.869287i \(0.664579\pi\)
\(968\) −10.8090 2.04087i −0.347415 0.0655961i
\(969\) −4.23607 −0.136082
\(970\) −4.07295 2.95917i −0.130775 0.0950132i
\(971\) −17.7361 + 54.5860i −0.569178 + 1.75175i 0.0860229 + 0.996293i \(0.472584\pi\)
−0.655200 + 0.755455i \(0.727416\pi\)
\(972\) −4.94427 15.2169i −0.158588 0.488082i
\(973\) 8.78115 6.37988i 0.281511 0.204530i
\(974\) −19.6631 + 14.2861i −0.630047 + 0.457756i
\(975\) −2.78115 8.55951i −0.0890682 0.274124i
\(976\) −1.71885 + 5.29007i −0.0550190 + 0.169331i
\(977\) −0.618034 0.449028i −0.0197727 0.0143657i 0.577855 0.816139i \(-0.303890\pi\)
−0.597628 + 0.801774i \(0.703890\pi\)
\(978\) −4.32624 −0.138338
\(979\) 18.4402 20.9560i 0.589352 0.669757i
\(980\) 2.52786 0.0807497
\(981\) 3.09017 + 2.24514i 0.0986615 + 0.0716818i
\(982\) −4.28115 + 13.1760i −0.136617 + 0.420464i
\(983\) 7.94427 + 24.4500i 0.253383 + 0.779832i 0.994144 + 0.108064i \(0.0344651\pi\)
−0.740761 + 0.671769i \(0.765535\pi\)
\(984\) 4.11803 2.99193i 0.131278 0.0953791i
\(985\) 7.10739 5.16382i 0.226460 0.164533i
\(986\) −11.7082 36.0341i −0.372865 1.14756i
\(987\) 0.899187 2.76741i 0.0286214 0.0880877i
\(988\) −1.50000 1.08981i −0.0477214 0.0346716i
\(989\) −5.70820 −0.181510
\(990\) 2.47214 0.555029i 0.0785696 0.0176400i
\(991\) 47.0000 1.49300 0.746502 0.665383i \(-0.231732\pi\)
0.746502 + 0.665383i \(0.231732\pi\)
\(992\) 3.80902 + 2.76741i 0.120936 + 0.0878654i
\(993\) 0.562306 1.73060i 0.0178442 0.0549189i
\(994\) −2.71885 8.36775i −0.0862366 0.265409i
\(995\) 7.23607 5.25731i 0.229399 0.166668i
\(996\) −12.7812 + 9.28605i −0.404986 + 0.294240i
\(997\) −1.63525 5.03280i −0.0517890 0.159390i 0.921817 0.387625i \(-0.126705\pi\)
−0.973606 + 0.228235i \(0.926705\pi\)
\(998\) 0.892609 2.74717i 0.0282550 0.0869601i
\(999\) −46.9959 34.1445i −1.48689 1.08029i
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 418.2.f.c.191.1 4
11.3 even 5 inner 418.2.f.c.267.1 yes 4
11.5 even 5 4598.2.a.bd.1.2 2
11.6 odd 10 4598.2.a.u.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.c.191.1 4 1.1 even 1 trivial
418.2.f.c.267.1 yes 4 11.3 even 5 inner
4598.2.a.u.1.2 2 11.6 odd 10
4598.2.a.bd.1.2 2 11.5 even 5