Properties

Label 418.2.f.g.229.2
Level $418$
Weight $2$
Character 418.229
Analytic conductor $3.338$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} - 2960 x^{7} + 5348 x^{6} - 6872 x^{5} + 8232 x^{4} - 6344 x^{3} + 3984 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 229.2
Root \(0.0560397 - 0.0407152i\) of defining polynomial
Character \(\chi\) \(=\) 418.229
Dual form 418.2.f.g.115.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.0560397 - 0.0407152i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.340306 + 1.04736i) q^{5} +(0.0214053 + 0.0658786i) q^{6} +(-1.61489 - 1.17328i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.925568 + 2.84861i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.0560397 - 0.0407152i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.340306 + 1.04736i) q^{5} +(0.0214053 + 0.0658786i) q^{6} +(-1.61489 - 1.17328i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.925568 + 2.84861i) q^{9} -1.10125 q^{10} +(-2.57744 - 2.08730i) q^{11} -0.0692689 q^{12} +(-1.96288 + 6.04113i) q^{13} +(1.61489 - 1.17328i) q^{14} +(0.0617140 + 0.0448378i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.56097 + 4.80417i) q^{17} +(-2.42317 - 1.76054i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.340306 - 1.04736i) q^{20} -0.138268 q^{21} +(2.78161 - 1.80628i) q^{22} -4.99785 q^{23} +(0.0214053 - 0.0658786i) q^{24} +(3.06394 - 2.22608i) q^{25} +(-5.13889 - 3.73363i) q^{26} +(0.128329 + 0.394956i) q^{27} +(0.616832 + 1.89841i) q^{28} +(-1.32526 - 0.962857i) q^{29} +(-0.0617140 + 0.0448378i) q^{30} +(-1.09630 + 3.37406i) q^{31} -1.00000 q^{32} +(-0.229424 - 0.0120307i) q^{33} -5.05141 q^{34} +(0.679289 - 2.09064i) q^{35} +(2.42317 - 1.76054i) q^{36} +(-0.772437 - 0.561208i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(0.135967 + 0.418463i) q^{39} +(0.890934 + 0.647301i) q^{40} +(-7.31752 + 5.31649i) q^{41} +(0.0427272 - 0.131501i) q^{42} +5.25250 q^{43} +(0.858307 + 3.20364i) q^{44} -3.29848 q^{45} +(1.54442 - 4.75324i) q^{46} +(-0.454281 + 0.330054i) q^{47} +(0.0560397 + 0.0407152i) q^{48} +(-0.931856 - 2.86796i) q^{49} +(1.17032 + 3.60188i) q^{50} +(0.283079 + 0.205669i) q^{51} +(5.13889 - 3.73363i) q^{52} +(2.19428 - 6.75329i) q^{53} -0.415281 q^{54} +(1.30903 - 3.40981i) q^{55} -1.99611 q^{56} +(-0.0214053 + 0.0658786i) q^{57} +(1.32526 - 0.962857i) q^{58} +(2.36038 + 1.71492i) q^{59} +(-0.0235726 - 0.0725492i) q^{60} +(0.413052 + 1.27124i) q^{61} +(-2.87014 - 2.08528i) q^{62} +(4.83691 - 3.51422i) q^{63} +(0.309017 - 0.951057i) q^{64} -6.99520 q^{65} +(0.0823377 - 0.214477i) q^{66} +11.1011 q^{67} +(1.56097 - 4.80417i) q^{68} +(-0.280078 + 0.203489i) q^{69} +(1.77840 + 1.29208i) q^{70} +(2.47414 + 7.61462i) q^{71} +(0.925568 + 2.84861i) q^{72} +(2.03944 + 1.48174i) q^{73} +(0.772437 - 0.561208i) q^{74} +(0.0810668 - 0.249498i) q^{75} +1.00000 q^{76} +(1.71327 + 6.39481i) q^{77} -0.439998 q^{78} +(3.66024 - 11.2651i) q^{79} +(-0.890934 + 0.647301i) q^{80} +(-7.24624 - 5.26470i) q^{81} +(-2.79505 - 8.60227i) q^{82} +(3.01703 + 9.28548i) q^{83} +(0.111861 + 0.0812720i) q^{84} +(-4.50047 + 3.26978i) q^{85} +(-1.62311 + 4.99542i) q^{86} -0.113470 q^{87} +(-3.31207 - 0.173681i) q^{88} +8.93586 q^{89} +(1.01929 - 3.13704i) q^{90} +(10.2578 - 7.45272i) q^{91} +(4.04335 + 2.93766i) q^{92} +(0.0759393 + 0.233717i) q^{93} +(-0.173520 - 0.534039i) q^{94} +(-0.890934 - 0.647301i) q^{95} +(-0.0560397 + 0.0407152i) q^{96} +(0.196662 - 0.605263i) q^{97} +3.01555 q^{98} +(8.33149 - 5.41017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) 0.0560397 0.0407152i 0.0323545 0.0235069i −0.571490 0.820609i \(-0.693635\pi\)
0.603845 + 0.797102i \(0.293635\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.340306 + 1.04736i 0.152190 + 0.468392i 0.997865 0.0653056i \(-0.0208022\pi\)
−0.845676 + 0.533697i \(0.820802\pi\)
\(6\) 0.0214053 + 0.0658786i 0.00873866 + 0.0268948i
\(7\) −1.61489 1.17328i −0.610370 0.443459i 0.239175 0.970977i \(-0.423123\pi\)
−0.849544 + 0.527517i \(0.823123\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) −0.925568 + 2.84861i −0.308523 + 0.949535i
\(10\) −1.10125 −0.348247
\(11\) −2.57744 2.08730i −0.777127 0.629344i
\(12\) −0.0692689 −0.0199962
\(13\) −1.96288 + 6.04113i −0.544406 + 1.67551i 0.177993 + 0.984032i \(0.443040\pi\)
−0.722398 + 0.691477i \(0.756960\pi\)
\(14\) 1.61489 1.17328i 0.431596 0.313573i
\(15\) 0.0617140 + 0.0448378i 0.0159345 + 0.0115771i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 1.56097 + 4.80417i 0.378591 + 1.16518i 0.941024 + 0.338340i \(0.109866\pi\)
−0.562433 + 0.826843i \(0.690134\pi\)
\(18\) −2.42317 1.76054i −0.571146 0.414962i
\(19\) −0.809017 + 0.587785i −0.185601 + 0.134847i
\(20\) 0.340306 1.04736i 0.0760948 0.234196i
\(21\) −0.138268 −0.0301726
\(22\) 2.78161 1.80628i 0.593041 0.385100i
\(23\) −4.99785 −1.04212 −0.521062 0.853519i \(-0.674464\pi\)
−0.521062 + 0.853519i \(0.674464\pi\)
\(24\) 0.0214053 0.0658786i 0.00436933 0.0134474i
\(25\) 3.06394 2.22608i 0.612788 0.445217i
\(26\) −5.13889 3.73363i −1.00782 0.732224i
\(27\) 0.128329 + 0.394956i 0.0246969 + 0.0760093i
\(28\) 0.616832 + 1.89841i 0.116570 + 0.358766i
\(29\) −1.32526 0.962857i −0.246094 0.178798i 0.457900 0.889004i \(-0.348602\pi\)
−0.703994 + 0.710206i \(0.748602\pi\)
\(30\) −0.0617140 + 0.0448378i −0.0112674 + 0.00818623i
\(31\) −1.09630 + 3.37406i −0.196901 + 0.605998i 0.803048 + 0.595914i \(0.203210\pi\)
−0.999949 + 0.0100844i \(0.996790\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.229424 0.0120307i −0.0399375 0.00209427i
\(34\) −5.05141 −0.866309
\(35\) 0.679289 2.09064i 0.114821 0.353382i
\(36\) 2.42317 1.76054i 0.403862 0.293423i
\(37\) −0.772437 0.561208i −0.126988 0.0922621i 0.522478 0.852653i \(-0.325008\pi\)
−0.649466 + 0.760391i \(0.725008\pi\)
\(38\) −0.309017 0.951057i −0.0501292 0.154282i
\(39\) 0.135967 + 0.418463i 0.0217721 + 0.0670076i
\(40\) 0.890934 + 0.647301i 0.140869 + 0.102347i
\(41\) −7.31752 + 5.31649i −1.14281 + 0.830297i −0.987508 0.157571i \(-0.949634\pi\)
−0.155298 + 0.987868i \(0.549634\pi\)
\(42\) 0.0427272 0.131501i 0.00659296 0.0202910i
\(43\) 5.25250 0.800998 0.400499 0.916297i \(-0.368837\pi\)
0.400499 + 0.916297i \(0.368837\pi\)
\(44\) 0.858307 + 3.20364i 0.129395 + 0.482967i
\(45\) −3.29848 −0.491708
\(46\) 1.54442 4.75324i 0.227712 0.700827i
\(47\) −0.454281 + 0.330054i −0.0662637 + 0.0481434i −0.620424 0.784267i \(-0.713039\pi\)
0.554160 + 0.832410i \(0.313039\pi\)
\(48\) 0.0560397 + 0.0407152i 0.00808863 + 0.00587674i
\(49\) −0.931856 2.86796i −0.133122 0.409708i
\(50\) 1.17032 + 3.60188i 0.165508 + 0.509382i
\(51\) 0.283079 + 0.205669i 0.0396390 + 0.0287995i
\(52\) 5.13889 3.73363i 0.712636 0.517761i
\(53\) 2.19428 6.75329i 0.301407 0.927635i −0.679587 0.733595i \(-0.737841\pi\)
0.980994 0.194040i \(-0.0621592\pi\)
\(54\) −0.415281 −0.0565126
\(55\) 1.30903 3.40981i 0.176509 0.459779i
\(56\) −1.99611 −0.266741
\(57\) −0.0214053 + 0.0658786i −0.00283520 + 0.00872584i
\(58\) 1.32526 0.962857i 0.174015 0.126429i
\(59\) 2.36038 + 1.71492i 0.307295 + 0.223263i 0.730735 0.682661i \(-0.239177\pi\)
−0.423440 + 0.905924i \(0.639177\pi\)
\(60\) −0.0235726 0.0725492i −0.00304322 0.00936606i
\(61\) 0.413052 + 1.27124i 0.0528859 + 0.162766i 0.974011 0.226500i \(-0.0727285\pi\)
−0.921125 + 0.389267i \(0.872728\pi\)
\(62\) −2.87014 2.08528i −0.364508 0.264831i
\(63\) 4.83691 3.51422i 0.609393 0.442750i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −6.99520 −0.867647
\(66\) 0.0823377 0.214477i 0.0101351 0.0264003i
\(67\) 11.1011 1.35622 0.678108 0.734962i \(-0.262800\pi\)
0.678108 + 0.734962i \(0.262800\pi\)
\(68\) 1.56097 4.80417i 0.189296 0.582592i
\(69\) −0.280078 + 0.203489i −0.0337174 + 0.0244971i
\(70\) 1.77840 + 1.29208i 0.212560 + 0.154434i
\(71\) 2.47414 + 7.61462i 0.293626 + 0.903689i 0.983679 + 0.179930i \(0.0575872\pi\)
−0.690053 + 0.723759i \(0.742413\pi\)
\(72\) 0.925568 + 2.84861i 0.109079 + 0.335711i
\(73\) 2.03944 + 1.48174i 0.238698 + 0.173424i 0.700703 0.713453i \(-0.252870\pi\)
−0.462005 + 0.886877i \(0.652870\pi\)
\(74\) 0.772437 0.561208i 0.0897940 0.0652391i
\(75\) 0.0810668 0.249498i 0.00936079 0.0288096i
\(76\) 1.00000 0.114708
\(77\) 1.71327 + 6.39481i 0.195246 + 0.728757i
\(78\) −0.439998 −0.0498199
\(79\) 3.66024 11.2651i 0.411809 1.26742i −0.503265 0.864132i \(-0.667868\pi\)
0.915074 0.403286i \(-0.132132\pi\)
\(80\) −0.890934 + 0.647301i −0.0996094 + 0.0723705i
\(81\) −7.24624 5.26470i −0.805137 0.584966i
\(82\) −2.79505 8.60227i −0.308661 0.949961i
\(83\) 3.01703 + 9.28548i 0.331163 + 1.01921i 0.968582 + 0.248696i \(0.0800020\pi\)
−0.637419 + 0.770517i \(0.719998\pi\)
\(84\) 0.111861 + 0.0812720i 0.0122051 + 0.00886751i
\(85\) −4.50047 + 3.26978i −0.488145 + 0.354658i
\(86\) −1.62311 + 4.99542i −0.175025 + 0.538670i
\(87\) −0.113470 −0.0121653
\(88\) −3.31207 0.173681i −0.353068 0.0185144i
\(89\) 8.93586 0.947199 0.473600 0.880740i \(-0.342954\pi\)
0.473600 + 0.880740i \(0.342954\pi\)
\(90\) 1.01929 3.13704i 0.107442 0.330673i
\(91\) 10.2578 7.45272i 1.07531 0.781258i
\(92\) 4.04335 + 2.93766i 0.421548 + 0.306272i
\(93\) 0.0759393 + 0.233717i 0.00787454 + 0.0242353i
\(94\) −0.173520 0.534039i −0.0178972 0.0550819i
\(95\) −0.890934 0.647301i −0.0914079 0.0664117i
\(96\) −0.0560397 + 0.0407152i −0.00571953 + 0.00415548i
\(97\) 0.196662 0.605263i 0.0199680 0.0614552i −0.940576 0.339583i \(-0.889714\pi\)
0.960544 + 0.278128i \(0.0897140\pi\)
\(98\) 3.01555 0.304616
\(99\) 8.33149 5.41017i 0.837346 0.543742i
\(100\) −3.78724 −0.378724
\(101\) −3.13583 + 9.65111i −0.312027 + 0.960321i 0.664934 + 0.746902i \(0.268460\pi\)
−0.976961 + 0.213419i \(0.931540\pi\)
\(102\) −0.283079 + 0.205669i −0.0280290 + 0.0203643i
\(103\) 0.241589 + 0.175525i 0.0238045 + 0.0172949i 0.599624 0.800282i \(-0.295317\pi\)
−0.575819 + 0.817577i \(0.695317\pi\)
\(104\) 1.96288 + 6.04113i 0.192477 + 0.592382i
\(105\) −0.0470536 0.144816i −0.00459196 0.0141326i
\(106\) 5.74469 + 4.17376i 0.557974 + 0.405392i
\(107\) −10.1334 + 7.36236i −0.979634 + 0.711746i −0.957627 0.288012i \(-0.907006\pi\)
−0.0220074 + 0.999758i \(0.507006\pi\)
\(108\) 0.128329 0.394956i 0.0123485 0.0380046i
\(109\) 19.4120 1.85933 0.929666 0.368402i \(-0.120095\pi\)
0.929666 + 0.368402i \(0.120095\pi\)
\(110\) 2.83842 + 2.29865i 0.270632 + 0.219167i
\(111\) −0.0661369 −0.00627743
\(112\) 0.616832 1.89841i 0.0582851 0.179383i
\(113\) 10.0246 7.28326i 0.943031 0.685152i −0.00611771 0.999981i \(-0.501947\pi\)
0.949148 + 0.314829i \(0.101947\pi\)
\(114\) −0.0560397 0.0407152i −0.00524860 0.00381333i
\(115\) −1.70080 5.23453i −0.158600 0.488122i
\(116\) 0.506204 + 1.55794i 0.0469999 + 0.144651i
\(117\) −15.3920 11.1830i −1.42299 1.03387i
\(118\) −2.36038 + 1.71492i −0.217291 + 0.157871i
\(119\) 3.11587 9.58965i 0.285631 0.879082i
\(120\) 0.0762827 0.00696363
\(121\) 2.28637 + 10.7598i 0.207852 + 0.978160i
\(122\) −1.33666 −0.121016
\(123\) −0.193610 + 0.595869i −0.0174572 + 0.0537277i
\(124\) 2.87014 2.08528i 0.257746 0.187264i
\(125\) 7.82885 + 5.68799i 0.700233 + 0.508749i
\(126\) 1.84754 + 5.68613i 0.164592 + 0.506561i
\(127\) 3.41145 + 10.4994i 0.302717 + 0.931667i 0.980519 + 0.196423i \(0.0629325\pi\)
−0.677802 + 0.735244i \(0.737068\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 0.294348 0.213857i 0.0259159 0.0188290i
\(130\) 2.16163 6.65283i 0.189588 0.583492i
\(131\) −15.7061 −1.37225 −0.686126 0.727483i \(-0.740690\pi\)
−0.686126 + 0.727483i \(0.740690\pi\)
\(132\) 0.178536 + 0.144585i 0.0155396 + 0.0125845i
\(133\) 1.99611 0.173085
\(134\) −3.43043 + 10.5578i −0.296344 + 0.912053i
\(135\) −0.369988 + 0.268812i −0.0318435 + 0.0231356i
\(136\) 4.08667 + 2.96914i 0.350429 + 0.254602i
\(137\) 2.25311 + 6.93436i 0.192496 + 0.592442i 0.999997 + 0.00257538i \(0.000819770\pi\)
−0.807501 + 0.589867i \(0.799180\pi\)
\(138\) −0.106980 0.329251i −0.00910677 0.0280277i
\(139\) −2.99863 2.17863i −0.254341 0.184789i 0.453308 0.891354i \(-0.350244\pi\)
−0.707648 + 0.706565i \(0.750244\pi\)
\(140\) −1.77840 + 1.29208i −0.150302 + 0.109201i
\(141\) −0.0120195 + 0.0369923i −0.00101223 + 0.00311531i
\(142\) −8.00649 −0.671889
\(143\) 17.6689 11.4735i 1.47754 0.959464i
\(144\) −2.99520 −0.249600
\(145\) 0.557460 1.71568i 0.0462945 0.142480i
\(146\) −2.03944 + 1.48174i −0.168785 + 0.122629i
\(147\) −0.168991 0.122779i −0.0139381 0.0101266i
\(148\) 0.295045 + 0.908054i 0.0242525 + 0.0746416i
\(149\) 0.488023 + 1.50198i 0.0399804 + 0.123047i 0.969055 0.246846i \(-0.0793943\pi\)
−0.929074 + 0.369893i \(0.879394\pi\)
\(150\) 0.212236 + 0.154198i 0.0173290 + 0.0125902i
\(151\) −17.0001 + 12.3513i −1.38345 + 1.00513i −0.386898 + 0.922123i \(0.626453\pi\)
−0.996549 + 0.0830098i \(0.973547\pi\)
\(152\) −0.309017 + 0.951057i −0.0250646 + 0.0771409i
\(153\) −15.1300 −1.22319
\(154\) −6.61126 0.346685i −0.532751 0.0279367i
\(155\) −3.90691 −0.313811
\(156\) 0.135967 0.418463i 0.0108861 0.0335038i
\(157\) 7.39511 5.37286i 0.590194 0.428801i −0.252191 0.967678i \(-0.581151\pi\)
0.842385 + 0.538876i \(0.181151\pi\)
\(158\) 9.58263 + 6.96219i 0.762353 + 0.553882i
\(159\) −0.151995 0.467793i −0.0120540 0.0370984i
\(160\) −0.340306 1.04736i −0.0269036 0.0828007i
\(161\) 8.07096 + 5.86389i 0.636081 + 0.462140i
\(162\) 7.24624 5.26470i 0.569318 0.413634i
\(163\) 4.44768 13.6886i 0.348369 1.07217i −0.611386 0.791333i \(-0.709388\pi\)
0.959755 0.280838i \(-0.0906123\pi\)
\(164\) 9.04496 0.706292
\(165\) −0.0654740 0.244382i −0.00509714 0.0190251i
\(166\) −9.76333 −0.757781
\(167\) 3.97898 12.2460i 0.307903 0.947627i −0.670675 0.741751i \(-0.733996\pi\)
0.978578 0.205876i \(-0.0660044\pi\)
\(168\) −0.111861 + 0.0812720i −0.00863029 + 0.00627027i
\(169\) −22.1252 16.0749i −1.70194 1.23653i
\(170\) −1.71903 5.29062i −0.131843 0.405772i
\(171\) −0.925568 2.84861i −0.0707800 0.217838i
\(172\) −4.24936 3.08734i −0.324011 0.235407i
\(173\) −10.7254 + 7.79246i −0.815437 + 0.592450i −0.915402 0.402541i \(-0.868127\pi\)
0.0999646 + 0.994991i \(0.468127\pi\)
\(174\) 0.0350642 0.107916i 0.00265821 0.00818113i
\(175\) −7.55974 −0.571463
\(176\) 1.18867 3.09630i 0.0895992 0.233392i
\(177\) 0.202098 0.0151906
\(178\) −2.76133 + 8.49851i −0.206971 + 0.636990i
\(179\) 15.5149 11.2723i 1.15964 0.842528i 0.169908 0.985460i \(-0.445653\pi\)
0.989733 + 0.142932i \(0.0456530\pi\)
\(180\) 2.66853 + 1.93880i 0.198900 + 0.144509i
\(181\) −1.44623 4.45105i −0.107498 0.330844i 0.882811 0.469729i \(-0.155648\pi\)
−0.990309 + 0.138885i \(0.955648\pi\)
\(182\) 3.91813 + 12.0588i 0.290431 + 0.893855i
\(183\) 0.0749063 + 0.0544226i 0.00553723 + 0.00402304i
\(184\) −4.04335 + 2.93766i −0.298079 + 0.216567i
\(185\) 0.324919 0.999999i 0.0238885 0.0735214i
\(186\) −0.245745 −0.0180189
\(187\) 6.00444 15.6407i 0.439088 1.14376i
\(188\) 0.561522 0.0409532
\(189\) 0.256158 0.788374i 0.0186328 0.0573458i
\(190\) 0.890934 0.647301i 0.0646351 0.0469602i
\(191\) −4.29311 3.11913i −0.310638 0.225692i 0.421532 0.906814i \(-0.361493\pi\)
−0.732170 + 0.681122i \(0.761493\pi\)
\(192\) −0.0214053 0.0658786i −0.00154479 0.00475438i
\(193\) 0.0912482 + 0.280833i 0.00656819 + 0.0202148i 0.954287 0.298892i \(-0.0966171\pi\)
−0.947719 + 0.319107i \(0.896617\pi\)
\(194\) 0.514868 + 0.374073i 0.0369653 + 0.0268569i
\(195\) −0.392009 + 0.284811i −0.0280723 + 0.0203957i
\(196\) −0.931856 + 2.86796i −0.0665611 + 0.204854i
\(197\) −24.5980 −1.75253 −0.876267 0.481826i \(-0.839974\pi\)
−0.876267 + 0.481826i \(0.839974\pi\)
\(198\) 2.57080 + 9.59555i 0.182699 + 0.681926i
\(199\) −22.0602 −1.56381 −0.781903 0.623400i \(-0.785751\pi\)
−0.781903 + 0.623400i \(0.785751\pi\)
\(200\) 1.17032 3.60188i 0.0827542 0.254691i
\(201\) 0.622103 0.451984i 0.0438797 0.0318805i
\(202\) −8.20972 5.96471i −0.577634 0.419676i
\(203\) 1.01044 + 3.10981i 0.0709189 + 0.218266i
\(204\) −0.108127 0.332780i −0.00757038 0.0232992i
\(205\) −8.05846 5.85481i −0.562827 0.408918i
\(206\) −0.241589 + 0.175525i −0.0168323 + 0.0122294i
\(207\) 4.62585 14.2369i 0.321519 0.989533i
\(208\) −6.35202 −0.440434
\(209\) 3.31207 + 0.173681i 0.229101 + 0.0120137i
\(210\) 0.152269 0.0105075
\(211\) −0.744593 + 2.29162i −0.0512599 + 0.157762i −0.973410 0.229071i \(-0.926431\pi\)
0.922150 + 0.386833i \(0.126431\pi\)
\(212\) −5.74469 + 4.17376i −0.394547 + 0.286655i
\(213\) 0.448681 + 0.325986i 0.0307431 + 0.0223362i
\(214\) −3.87062 11.9125i −0.264590 0.814325i
\(215\) 1.78746 + 5.50123i 0.121904 + 0.375181i
\(216\) 0.335969 + 0.244096i 0.0228598 + 0.0166086i
\(217\) 5.72912 4.16245i 0.388918 0.282565i
\(218\) −5.99864 + 18.4619i −0.406279 + 1.25040i
\(219\) 0.174619 0.0117996
\(220\) −3.06326 + 1.98917i −0.206525 + 0.134110i
\(221\) −32.0867 −2.15838
\(222\) 0.0204374 0.0628999i 0.00137167 0.00422156i
\(223\) 3.00641 2.18428i 0.201324 0.146270i −0.482556 0.875865i \(-0.660291\pi\)
0.683880 + 0.729595i \(0.260291\pi\)
\(224\) 1.61489 + 1.17328i 0.107899 + 0.0783933i
\(225\) 3.50535 + 10.7883i 0.233690 + 0.719223i
\(226\) 3.82904 + 11.7846i 0.254704 + 0.783898i
\(227\) 9.84384 + 7.15197i 0.653359 + 0.474693i 0.864414 0.502781i \(-0.167690\pi\)
−0.211055 + 0.977474i \(0.567690\pi\)
\(228\) 0.0560397 0.0407152i 0.00371132 0.00269643i
\(229\) −5.51474 + 16.9726i −0.364424 + 1.12158i 0.585917 + 0.810371i \(0.300734\pi\)
−0.950341 + 0.311211i \(0.899266\pi\)
\(230\) 5.50391 0.362917
\(231\) 0.356378 + 0.288607i 0.0234479 + 0.0189890i
\(232\) −1.63811 −0.107547
\(233\) −6.18040 + 19.0213i −0.404892 + 1.24613i 0.516094 + 0.856532i \(0.327386\pi\)
−0.920986 + 0.389597i \(0.872614\pi\)
\(234\) 15.3920 11.1830i 1.00621 0.731053i
\(235\) −0.500279 0.363474i −0.0326346 0.0237104i
\(236\) −0.901585 2.77479i −0.0586882 0.180624i
\(237\) −0.253541 0.780318i −0.0164692 0.0506871i
\(238\) 8.15745 + 5.92673i 0.528769 + 0.384173i
\(239\) −12.6906 + 9.22023i −0.820884 + 0.596407i −0.916965 0.398967i \(-0.869369\pi\)
0.0960818 + 0.995373i \(0.469369\pi\)
\(240\) −0.0235726 + 0.0725492i −0.00152161 + 0.00468303i
\(241\) 4.89755 0.315479 0.157740 0.987481i \(-0.449579\pi\)
0.157740 + 0.987481i \(0.449579\pi\)
\(242\) −10.9397 1.15049i −0.703229 0.0739560i
\(243\) −1.86627 −0.119721
\(244\) 0.413052 1.27124i 0.0264430 0.0813831i
\(245\) 2.68665 1.95197i 0.171644 0.124707i
\(246\) −0.506877 0.368267i −0.0323173 0.0234799i
\(247\) −1.96288 6.04113i −0.124895 0.384388i
\(248\) 1.09630 + 3.37406i 0.0696149 + 0.214253i
\(249\) 0.547134 + 0.397516i 0.0346732 + 0.0251916i
\(250\) −7.82885 + 5.68799i −0.495140 + 0.359740i
\(251\) −7.58959 + 23.3583i −0.479050 + 1.47437i 0.361366 + 0.932424i \(0.382311\pi\)
−0.840416 + 0.541941i \(0.817689\pi\)
\(252\) −5.97875 −0.376626
\(253\) 12.8816 + 10.4320i 0.809862 + 0.655855i
\(254\) −11.0397 −0.692691
\(255\) −0.119075 + 0.366475i −0.00745677 + 0.0229496i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −7.90965 5.74670i −0.493391 0.358469i 0.313096 0.949721i \(-0.398634\pi\)
−0.806487 + 0.591252i \(0.798634\pi\)
\(258\) 0.112431 + 0.346027i 0.00699965 + 0.0215427i
\(259\) 0.588941 + 1.81257i 0.0365950 + 0.112628i
\(260\) 5.65923 + 4.11167i 0.350971 + 0.254995i
\(261\) 3.96942 2.88395i 0.245701 0.178512i
\(262\) 4.85346 14.9374i 0.299848 0.922837i
\(263\) 0.209057 0.0128910 0.00644550 0.999979i \(-0.497948\pi\)
0.00644550 + 0.999979i \(0.497948\pi\)
\(264\) −0.192679 + 0.125119i −0.0118586 + 0.00770053i
\(265\) 7.81982 0.480368
\(266\) −0.616832 + 1.89841i −0.0378204 + 0.116399i
\(267\) 0.500763 0.363826i 0.0306462 0.0222658i
\(268\) −8.98098 6.52507i −0.548601 0.398582i
\(269\) 8.09093 + 24.9013i 0.493313 + 1.51826i 0.819570 + 0.572979i \(0.194213\pi\)
−0.326257 + 0.945281i \(0.605787\pi\)
\(270\) −0.141323 0.434947i −0.00860063 0.0264700i
\(271\) −5.61212 4.07745i −0.340912 0.247687i 0.404134 0.914700i \(-0.367573\pi\)
−0.745047 + 0.667012i \(0.767573\pi\)
\(272\) −4.08667 + 2.96914i −0.247791 + 0.180031i
\(273\) 0.271404 0.835297i 0.0164261 0.0505545i
\(274\) −7.29122 −0.440478
\(275\) −12.5436 0.657770i −0.756408 0.0396650i
\(276\) 0.346195 0.0208385
\(277\) 6.91042 21.2681i 0.415207 1.27787i −0.496859 0.867831i \(-0.665514\pi\)
0.912066 0.410044i \(-0.134486\pi\)
\(278\) 2.99863 2.17863i 0.179846 0.130666i
\(279\) −8.59666 6.24584i −0.514668 0.373928i
\(280\) −0.679289 2.09064i −0.0405953 0.124939i
\(281\) −7.88229 24.2592i −0.470218 1.44718i −0.852299 0.523054i \(-0.824793\pi\)
0.382081 0.924129i \(-0.375207\pi\)
\(282\) −0.0314675 0.0228625i −0.00187386 0.00136144i
\(283\) 22.6224 16.4362i 1.34476 0.977029i 0.345510 0.938415i \(-0.387706\pi\)
0.999254 0.0386137i \(-0.0122942\pi\)
\(284\) 2.47414 7.61462i 0.146813 0.451845i
\(285\) −0.0762827 −0.00451860
\(286\) 5.45199 + 20.3496i 0.322383 + 1.20330i
\(287\) 18.0547 1.06574
\(288\) 0.925568 2.84861i 0.0545396 0.167856i
\(289\) −6.89017 + 5.00600i −0.405304 + 0.294471i
\(290\) 1.45945 + 1.06035i 0.0857018 + 0.0622660i
\(291\) −0.0136226 0.0419259i −0.000798568 0.00245774i
\(292\) −0.778996 2.39750i −0.0455873 0.140303i
\(293\) 7.86544 + 5.71458i 0.459504 + 0.333849i 0.793337 0.608783i \(-0.208342\pi\)
−0.333833 + 0.942632i \(0.608342\pi\)
\(294\) 0.168991 0.122779i 0.00985573 0.00716060i
\(295\) −0.992875 + 3.05575i −0.0578074 + 0.177913i
\(296\) −0.954785 −0.0554957
\(297\) 0.493631 1.28583i 0.0286434 0.0746117i
\(298\) −1.57927 −0.0914849
\(299\) 9.81019 30.1927i 0.567338 1.74609i
\(300\) −0.212236 + 0.154198i −0.0122534 + 0.00890264i
\(301\) −8.48218 6.16267i −0.488905 0.355210i
\(302\) −6.49345 19.9848i −0.373656 1.15000i
\(303\) 0.217216 + 0.668521i 0.0124787 + 0.0384056i
\(304\) −0.809017 0.587785i −0.0464003 0.0337118i
\(305\) −1.19088 + 0.865225i −0.0681896 + 0.0495426i
\(306\) 4.67542 14.3895i 0.267276 0.822591i
\(307\) 34.2676 1.95575 0.977876 0.209183i \(-0.0670805\pi\)
0.977876 + 0.209183i \(0.0670805\pi\)
\(308\) 2.37271 6.18055i 0.135198 0.352170i
\(309\) 0.0206851 0.00117673
\(310\) 1.20730 3.71569i 0.0685702 0.211037i
\(311\) −17.5492 + 12.7502i −0.995121 + 0.722998i −0.961037 0.276421i \(-0.910852\pi\)
−0.0340847 + 0.999419i \(0.510852\pi\)
\(312\) 0.355966 + 0.258624i 0.0201526 + 0.0146417i
\(313\) 4.37523 + 13.4656i 0.247303 + 0.761120i 0.995249 + 0.0973608i \(0.0310401\pi\)
−0.747946 + 0.663759i \(0.768960\pi\)
\(314\) 2.82468 + 8.69347i 0.159406 + 0.490601i
\(315\) 5.32667 + 3.87005i 0.300124 + 0.218053i
\(316\) −9.58263 + 6.96219i −0.539065 + 0.391654i
\(317\) 4.90428 15.0938i 0.275452 0.847753i −0.713648 0.700505i \(-0.752958\pi\)
0.989100 0.147249i \(-0.0470417\pi\)
\(318\) 0.491866 0.0275825
\(319\) 1.40600 + 5.24792i 0.0787210 + 0.293827i
\(320\) 1.10125 0.0615620
\(321\) −0.268114 + 0.825169i −0.0149646 + 0.0460564i
\(322\) −8.07096 + 5.86389i −0.449777 + 0.326782i
\(323\) −4.08667 2.96914i −0.227389 0.165208i
\(324\) 2.76782 + 8.51846i 0.153768 + 0.473248i
\(325\) 7.43391 + 22.8792i 0.412359 + 1.26911i
\(326\) 11.6442 + 8.45999i 0.644912 + 0.468556i
\(327\) 1.08784 0.790364i 0.0601579 0.0437072i
\(328\) −2.79505 + 8.60227i −0.154331 + 0.474981i
\(329\) 1.12086 0.0617949
\(330\) 0.252654 + 0.0132488i 0.0139081 + 0.000729323i
\(331\) 19.4908 1.07131 0.535655 0.844437i \(-0.320065\pi\)
0.535655 + 0.844437i \(0.320065\pi\)
\(332\) 3.01703 9.28548i 0.165581 0.509607i
\(333\) 2.31360 1.68093i 0.126785 0.0921145i
\(334\) 10.4171 + 7.56847i 0.569999 + 0.414128i
\(335\) 3.77778 + 11.6268i 0.206402 + 0.635240i
\(336\) −0.0427272 0.131501i −0.00233096 0.00717396i
\(337\) 23.1845 + 16.8445i 1.26294 + 0.917580i 0.998898 0.0469317i \(-0.0149443\pi\)
0.264042 + 0.964511i \(0.414944\pi\)
\(338\) 22.1252 16.0749i 1.20345 0.874358i
\(339\) 0.265233 0.816304i 0.0144055 0.0443355i
\(340\) 5.56289 0.301690
\(341\) 9.86830 6.40812i 0.534398 0.347019i
\(342\) 2.99520 0.161962
\(343\) −6.17791 + 19.0136i −0.333576 + 1.02664i
\(344\) 4.24936 3.08734i 0.229110 0.166458i
\(345\) −0.308437 0.224093i −0.0166057 0.0120647i
\(346\) −4.09674 12.6085i −0.220242 0.677835i
\(347\) 2.94372 + 9.05982i 0.158027 + 0.486357i 0.998455 0.0555662i \(-0.0176964\pi\)
−0.840428 + 0.541923i \(0.817696\pi\)
\(348\) 0.0917992 + 0.0666961i 0.00492096 + 0.00357528i
\(349\) −19.0824 + 13.8642i −1.02146 + 0.742132i −0.966581 0.256361i \(-0.917476\pi\)
−0.0548760 + 0.998493i \(0.517476\pi\)
\(350\) 2.33609 7.18974i 0.124869 0.384308i
\(351\) −2.63787 −0.140799
\(352\) 2.57744 + 2.08730i 0.137378 + 0.111253i
\(353\) −7.28551 −0.387769 −0.193884 0.981024i \(-0.562109\pi\)
−0.193884 + 0.981024i \(0.562109\pi\)
\(354\) −0.0624518 + 0.192207i −0.00331927 + 0.0102157i
\(355\) −7.13325 + 5.18261i −0.378594 + 0.275064i
\(356\) −7.22926 5.25237i −0.383150 0.278375i
\(357\) −0.215833 0.664265i −0.0114231 0.0351566i
\(358\) 5.92618 + 18.2389i 0.313208 + 0.963956i
\(359\) 1.03661 + 0.753141i 0.0547102 + 0.0397493i 0.614804 0.788680i \(-0.289235\pi\)
−0.560094 + 0.828429i \(0.689235\pi\)
\(360\) −2.66853 + 1.93880i −0.140644 + 0.102184i
\(361\) 0.309017 0.951057i 0.0162641 0.0500556i
\(362\) 4.68011 0.245981
\(363\) 0.566214 + 0.509884i 0.0297185 + 0.0267620i
\(364\) −12.6793 −0.664577
\(365\) −0.857873 + 2.64026i −0.0449031 + 0.138198i
\(366\) −0.0749063 + 0.0544226i −0.00391542 + 0.00284472i
\(367\) −16.9725 12.3312i −0.885957 0.643685i 0.0488641 0.998805i \(-0.484440\pi\)
−0.934821 + 0.355120i \(0.884440\pi\)
\(368\) −1.54442 4.75324i −0.0805085 0.247780i
\(369\) −8.37172 25.7655i −0.435815 1.34130i
\(370\) 0.850650 + 0.618033i 0.0442232 + 0.0321300i
\(371\) −11.4670 + 8.33128i −0.595338 + 0.432539i
\(372\) 0.0759393 0.233717i 0.00393727 0.0121177i
\(373\) 28.1444 1.45726 0.728632 0.684906i \(-0.240157\pi\)
0.728632 + 0.684906i \(0.240157\pi\)
\(374\) 13.0197 + 10.5438i 0.673232 + 0.545207i
\(375\) 0.670314 0.0346149
\(376\) −0.173520 + 0.534039i −0.00894860 + 0.0275410i
\(377\) 8.41808 6.11609i 0.433553 0.314995i
\(378\) 0.670631 + 0.487242i 0.0344936 + 0.0250610i
\(379\) −0.987289 3.03856i −0.0507136 0.156081i 0.922492 0.386015i \(-0.126149\pi\)
−0.973206 + 0.229935i \(0.926149\pi\)
\(380\) 0.340306 + 1.04736i 0.0174574 + 0.0537282i
\(381\) 0.618660 + 0.449483i 0.0316949 + 0.0230277i
\(382\) 4.29311 3.11913i 0.219655 0.159588i
\(383\) −1.43932 + 4.42978i −0.0735460 + 0.226351i −0.981072 0.193645i \(-0.937969\pi\)
0.907526 + 0.419997i \(0.137969\pi\)
\(384\) 0.0692689 0.00353486
\(385\) −6.11461 + 3.97060i −0.311629 + 0.202361i
\(386\) −0.295285 −0.0150296
\(387\) −4.86154 + 14.9623i −0.247126 + 0.760576i
\(388\) −0.514868 + 0.374073i −0.0261384 + 0.0189907i
\(389\) −24.5101 17.8077i −1.24271 0.902884i −0.244938 0.969539i \(-0.578768\pi\)
−0.997776 + 0.0666543i \(0.978768\pi\)
\(390\) −0.149734 0.460834i −0.00758208 0.0233352i
\(391\) −7.80150 24.0105i −0.394539 1.21427i
\(392\) −2.43963 1.77250i −0.123220 0.0895245i
\(393\) −0.880167 + 0.639479i −0.0443986 + 0.0322574i
\(394\) 7.60120 23.3941i 0.382943 1.17858i
\(395\) 13.0441 0.656321
\(396\) −9.92033 0.520208i −0.498515 0.0261414i
\(397\) 27.8353 1.39702 0.698508 0.715602i \(-0.253848\pi\)
0.698508 + 0.715602i \(0.253848\pi\)
\(398\) 6.81698 20.9805i 0.341704 1.05166i
\(399\) 0.111861 0.0812720i 0.00560007 0.00406869i
\(400\) 3.06394 + 2.22608i 0.153197 + 0.111304i
\(401\) 2.52508 + 7.77141i 0.126097 + 0.388086i 0.994099 0.108474i \(-0.0345964\pi\)
−0.868003 + 0.496560i \(0.834596\pi\)
\(402\) 0.237622 + 0.731326i 0.0118515 + 0.0364752i
\(403\) −18.2312 13.2458i −0.908161 0.659818i
\(404\) 8.20972 5.96471i 0.408449 0.296756i
\(405\) 3.04807 9.38100i 0.151460 0.466145i
\(406\) −3.26985 −0.162280
\(407\) 0.819498 + 3.05879i 0.0406210 + 0.151618i
\(408\) 0.349905 0.0173229
\(409\) 5.40164 16.6245i 0.267094 0.822030i −0.724110 0.689685i \(-0.757749\pi\)
0.991204 0.132345i \(-0.0422508\pi\)
\(410\) 8.05846 5.85481i 0.397979 0.289149i
\(411\) 0.408598 + 0.296864i 0.0201546 + 0.0146432i
\(412\) −0.0922787 0.284005i −0.00454625 0.0139919i
\(413\) −1.79966 5.53879i −0.0885556 0.272546i
\(414\) 12.1106 + 8.79889i 0.595205 + 0.432442i
\(415\) −8.69848 + 6.31981i −0.426992 + 0.310228i
\(416\) 1.96288 6.04113i 0.0962383 0.296191i
\(417\) −0.256746 −0.0125729
\(418\) −1.18867 + 3.09630i −0.0581396 + 0.151445i
\(419\) 14.7352 0.719862 0.359931 0.932979i \(-0.382800\pi\)
0.359931 + 0.932979i \(0.382800\pi\)
\(420\) −0.0470536 + 0.144816i −0.00229598 + 0.00706630i
\(421\) −24.4859 + 17.7901i −1.19337 + 0.867035i −0.993616 0.112811i \(-0.964014\pi\)
−0.199755 + 0.979846i \(0.564014\pi\)
\(422\) −1.94937 1.41630i −0.0948939 0.0689444i
\(423\) −0.519727 1.59955i −0.0252700 0.0777730i
\(424\) −2.19428 6.75329i −0.106563 0.327969i
\(425\) 15.4772 + 11.2449i 0.750755 + 0.545455i
\(426\) −0.448681 + 0.325986i −0.0217387 + 0.0157941i
\(427\) 0.824497 2.53754i 0.0399002 0.122800i
\(428\) 12.5256 0.605447
\(429\) 0.523011 1.36236i 0.0252512 0.0657756i
\(430\) −5.78434 −0.278945
\(431\) −10.2401 + 31.5158i −0.493249 + 1.51806i 0.326419 + 0.945225i \(0.394158\pi\)
−0.819668 + 0.572839i \(0.805842\pi\)
\(432\) −0.335969 + 0.244096i −0.0161643 + 0.0117441i
\(433\) −1.00490 0.730106i −0.0482926 0.0350866i 0.563377 0.826200i \(-0.309502\pi\)
−0.611670 + 0.791113i \(0.709502\pi\)
\(434\) 2.18833 + 6.73498i 0.105043 + 0.323289i
\(435\) −0.0386146 0.118844i −0.00185143 0.00569811i
\(436\) −15.7046 11.4101i −0.752116 0.546444i
\(437\) 4.04335 2.93766i 0.193419 0.140527i
\(438\) −0.0539602 + 0.166072i −0.00257832 + 0.00793524i
\(439\) −15.2998 −0.730219 −0.365109 0.930965i \(-0.618968\pi\)
−0.365109 + 0.930965i \(0.618968\pi\)
\(440\) −0.945215 3.52802i −0.0450614 0.168192i
\(441\) 9.03218 0.430104
\(442\) 9.91532 30.5162i 0.471624 1.45151i
\(443\) 22.4067 16.2794i 1.06457 0.773458i 0.0896446 0.995974i \(-0.471427\pi\)
0.974929 + 0.222516i \(0.0714269\pi\)
\(444\) 0.0535058 + 0.0388743i 0.00253928 + 0.00184489i
\(445\) 3.04093 + 9.35902i 0.144154 + 0.443660i
\(446\) 1.14835 + 3.53424i 0.0543757 + 0.167351i
\(447\) 0.0885021 + 0.0643005i 0.00418600 + 0.00304131i
\(448\) −1.61489 + 1.17328i −0.0762962 + 0.0554324i
\(449\) −9.04290 + 27.8312i −0.426761 + 1.31344i 0.474537 + 0.880236i \(0.342616\pi\)
−0.901298 + 0.433200i \(0.857384\pi\)
\(450\) −11.3435 −0.534740
\(451\) 29.9576 + 1.57093i 1.41065 + 0.0739723i
\(452\) −12.3910 −0.582825
\(453\) −0.449794 + 1.38432i −0.0211332 + 0.0650412i
\(454\) −9.84384 + 7.15197i −0.461994 + 0.335659i
\(455\) 11.2964 + 8.20735i 0.529585 + 0.384766i
\(456\) 0.0214053 + 0.0658786i 0.00100239 + 0.00308505i
\(457\) 5.83803 + 17.9676i 0.273092 + 0.840489i 0.989718 + 0.143032i \(0.0456852\pi\)
−0.716626 + 0.697457i \(0.754315\pi\)
\(458\) −14.4378 10.4897i −0.674632 0.490149i
\(459\) −1.69712 + 1.23303i −0.0792147 + 0.0575528i
\(460\) −1.70080 + 5.23453i −0.0793002 + 0.244061i
\(461\) 37.0562 1.72588 0.862940 0.505306i \(-0.168620\pi\)
0.862940 + 0.505306i \(0.168620\pi\)
\(462\) −0.384608 + 0.249751i −0.0178936 + 0.0116195i
\(463\) 16.5823 0.770645 0.385322 0.922782i \(-0.374090\pi\)
0.385322 + 0.922782i \(0.374090\pi\)
\(464\) 0.506204 1.55794i 0.0234999 0.0723254i
\(465\) −0.218942 + 0.159071i −0.0101532 + 0.00737673i
\(466\) −16.1805 11.7558i −0.749548 0.544578i
\(467\) −0.841861 2.59098i −0.0389567 0.119896i 0.929687 0.368351i \(-0.120077\pi\)
−0.968644 + 0.248454i \(0.920077\pi\)
\(468\) 5.87923 + 18.0944i 0.271768 + 0.836415i
\(469\) −17.9270 13.0247i −0.827793 0.601427i
\(470\) 0.500279 0.363474i 0.0230761 0.0167658i
\(471\) 0.195662 0.602187i 0.00901565 0.0277473i
\(472\) 2.91759 0.134293
\(473\) −13.5380 10.9635i −0.622477 0.504104i
\(474\) 0.820475 0.0376857
\(475\) −1.17032 + 3.60188i −0.0536980 + 0.165265i
\(476\) −8.15745 + 5.92673i −0.373896 + 0.271651i
\(477\) 17.2065 + 12.5013i 0.787832 + 0.572393i
\(478\) −4.84736 14.9186i −0.221713 0.682363i
\(479\) −6.14648 18.9169i −0.280840 0.864336i −0.987615 0.156897i \(-0.949851\pi\)
0.706775 0.707438i \(-0.250149\pi\)
\(480\) −0.0617140 0.0448378i −0.00281685 0.00204656i
\(481\) 4.90654 3.56481i 0.223719 0.162541i
\(482\) −1.51343 + 4.65785i −0.0689347 + 0.212159i
\(483\) 0.691044 0.0314436
\(484\) 4.47472 10.0487i 0.203396 0.456760i
\(485\) 0.700851 0.0318240
\(486\) 0.576710 1.77493i 0.0261601 0.0805125i
\(487\) −4.14817 + 3.01382i −0.187971 + 0.136569i −0.677791 0.735255i \(-0.737063\pi\)
0.489820 + 0.871824i \(0.337063\pi\)
\(488\) 1.08138 + 0.785672i 0.0489520 + 0.0355657i
\(489\) −0.308086 0.948191i −0.0139321 0.0428787i
\(490\) 1.02621 + 3.15835i 0.0463595 + 0.142680i
\(491\) 1.06951 + 0.777041i 0.0482661 + 0.0350674i 0.611657 0.791123i \(-0.290503\pi\)
−0.563391 + 0.826191i \(0.690503\pi\)
\(492\) 0.506877 0.368267i 0.0228518 0.0166028i
\(493\) 2.55704 7.86977i 0.115163 0.354437i
\(494\) 6.35202 0.285791
\(495\) 8.50163 + 6.88491i 0.382120 + 0.309454i
\(496\) −3.54769 −0.159296
\(497\) 4.93865 15.1996i 0.221529 0.681796i
\(498\) −0.547134 + 0.397516i −0.0245177 + 0.0178131i
\(499\) 17.7893 + 12.9247i 0.796359 + 0.578589i 0.909844 0.414951i \(-0.136201\pi\)
−0.113485 + 0.993540i \(0.536201\pi\)
\(500\) −2.99035 9.20336i −0.133733 0.411587i
\(501\) −0.275620 0.848270i −0.0123138 0.0378979i
\(502\) −19.8698 14.4362i −0.886832 0.644321i
\(503\) −21.2620 + 15.4478i −0.948027 + 0.688782i −0.950340 0.311215i \(-0.899264\pi\)
0.00231203 + 0.999997i \(0.499264\pi\)
\(504\) 1.84754 5.68613i 0.0822958 0.253280i
\(505\) −11.1753 −0.497294
\(506\) −13.9021 + 9.02750i −0.618023 + 0.401322i
\(507\) −1.89438 −0.0841323
\(508\) 3.41145 10.4994i 0.151358 0.465833i
\(509\) 27.2794 19.8196i 1.20914 0.878489i 0.213984 0.976837i \(-0.431356\pi\)
0.995152 + 0.0983480i \(0.0313558\pi\)
\(510\) −0.311743 0.226494i −0.0138042 0.0100293i
\(511\) −1.55496 4.78567i −0.0687874 0.211706i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −0.335969 0.244096i −0.0148334 0.0107771i
\(514\) 7.90965 5.74670i 0.348880 0.253476i
\(515\) −0.101622 + 0.312761i −0.00447802 + 0.0137819i
\(516\) −0.363835 −0.0160169
\(517\) 1.85980 + 0.0975254i 0.0817940 + 0.00428916i
\(518\) −1.90585 −0.0837384
\(519\) −0.283777 + 0.873375i −0.0124564 + 0.0383369i
\(520\) −5.65923 + 4.11167i −0.248174 + 0.180309i
\(521\) −30.9754 22.5049i −1.35706 0.985960i −0.998626 0.0524035i \(-0.983312\pi\)
−0.358431 0.933556i \(-0.616688\pi\)
\(522\) 1.51618 + 4.66633i 0.0663615 + 0.204240i
\(523\) 0.322839 + 0.993596i 0.0141168 + 0.0434469i 0.957867 0.287213i \(-0.0927287\pi\)
−0.943750 + 0.330660i \(0.892729\pi\)
\(524\) 12.7065 + 9.23183i 0.555087 + 0.403295i
\(525\) −0.423646 + 0.307797i −0.0184894 + 0.0134333i
\(526\) −0.0646022 + 0.198825i −0.00281679 + 0.00866918i
\(527\) −17.9208 −0.780644
\(528\) −0.0594540 0.221913i −0.00258740 0.00965750i
\(529\) 1.97850 0.0860217
\(530\) −2.41646 + 7.43709i −0.104964 + 0.323047i
\(531\) −7.06981 + 5.13652i −0.306804 + 0.222906i
\(532\) −1.61489 1.17328i −0.0700142 0.0508683i
\(533\) −17.7542 54.6418i −0.769019 2.36680i
\(534\) 0.191274 + 0.588682i 0.00827726 + 0.0254748i
\(535\) −11.1595 8.10783i −0.482466 0.350532i
\(536\) 8.98098 6.52507i 0.387919 0.281840i
\(537\) 0.410500 1.26339i 0.0177144 0.0545192i
\(538\) −26.1828 −1.12882
\(539\) −3.58448 + 9.33704i −0.154395 + 0.402175i
\(540\) 0.457330 0.0196804
\(541\) −6.56933 + 20.2183i −0.282438 + 0.869253i 0.704717 + 0.709488i \(0.251074\pi\)
−0.987155 + 0.159765i \(0.948926\pi\)
\(542\) 5.61212 4.07745i 0.241061 0.175141i
\(543\) −0.262272 0.190552i −0.0112552 0.00817735i
\(544\) −1.56097 4.80417i −0.0669261 0.205977i
\(545\) 6.60603 + 20.3313i 0.282971 + 0.870896i
\(546\) 0.710546 + 0.516242i 0.0304086 + 0.0220931i
\(547\) −4.77180 + 3.46691i −0.204027 + 0.148234i −0.685107 0.728442i \(-0.740245\pi\)
0.481080 + 0.876677i \(0.340245\pi\)
\(548\) 2.25311 6.93436i 0.0962481 0.296221i
\(549\) −4.00358 −0.170869
\(550\) 4.50177 11.7264i 0.191956 0.500016i
\(551\) 1.63811 0.0697859
\(552\) −0.106980 + 0.329251i −0.00455338 + 0.0140139i
\(553\) −19.1280 + 13.8973i −0.813404 + 0.590973i
\(554\) 18.0917 + 13.1444i 0.768643 + 0.558452i
\(555\) −0.0225068 0.0692688i −0.000955361 0.00294030i
\(556\) 1.14538 + 3.52510i 0.0485748 + 0.149498i
\(557\) −10.3399 7.51236i −0.438114 0.318309i 0.346771 0.937950i \(-0.387278\pi\)
−0.784885 + 0.619641i \(0.787278\pi\)
\(558\) 8.59666 6.24584i 0.363925 0.264407i
\(559\) −10.3100 + 31.7310i −0.436068 + 1.34208i
\(560\) 2.19822 0.0928919
\(561\) −0.300326 1.12097i −0.0126798 0.0473274i
\(562\) 25.5076 1.07597
\(563\) 3.48196 10.7164i 0.146747 0.451641i −0.850484 0.526000i \(-0.823691\pi\)
0.997232 + 0.0743589i \(0.0236910\pi\)
\(564\) 0.0314675 0.0228625i 0.00132502 0.000962685i
\(565\) 11.0396 + 8.02073i 0.464439 + 0.337435i
\(566\) 8.64100 + 26.5943i 0.363208 + 1.11784i
\(567\) 5.52486 + 17.0038i 0.232022 + 0.714091i
\(568\) 6.47738 + 4.70609i 0.271785 + 0.197463i
\(569\) 1.43659 1.04374i 0.0602249 0.0437560i −0.557265 0.830334i \(-0.688149\pi\)
0.617490 + 0.786578i \(0.288149\pi\)
\(570\) 0.0235726 0.0725492i 0.000987350 0.00303875i
\(571\) −46.3181 −1.93835 −0.969176 0.246371i \(-0.920762\pi\)
−0.969176 + 0.246371i \(0.920762\pi\)
\(572\) −21.0384 1.10322i −0.879659 0.0461281i
\(573\) −0.367580 −0.0153559
\(574\) −5.57921 + 17.1711i −0.232872 + 0.716706i
\(575\) −15.3131 + 11.1256i −0.638601 + 0.463971i
\(576\) 2.42317 + 1.76054i 0.100965 + 0.0733556i
\(577\) 14.2325 + 43.8030i 0.592505 + 1.82354i 0.566771 + 0.823875i \(0.308192\pi\)
0.0257345 + 0.999669i \(0.491808\pi\)
\(578\) −2.63181 8.09988i −0.109469 0.336911i
\(579\) 0.0165477 + 0.0120226i 0.000687699 + 0.000499642i
\(580\) −1.45945 + 1.06035i −0.0606003 + 0.0440287i
\(581\) 6.02233 18.5348i 0.249848 0.768954i
\(582\) 0.0440835 0.00182732
\(583\) −19.7517 + 12.8261i −0.818033 + 0.531201i
\(584\) 2.52088 0.104315
\(585\) 6.47453 19.9266i 0.267689 0.823862i
\(586\) −7.86544 + 5.71458i −0.324918 + 0.236067i
\(587\) 19.2199 + 13.9641i 0.793291 + 0.576360i 0.908938 0.416931i \(-0.136894\pi\)
−0.115647 + 0.993290i \(0.536894\pi\)
\(588\) 0.0645486 + 0.198660i 0.00266194 + 0.00819261i
\(589\) −1.09630 3.37406i −0.0451721 0.139026i
\(590\) −2.59938 1.88856i −0.107015 0.0777508i
\(591\) −1.37846 + 1.00151i −0.0567024 + 0.0411967i
\(592\) 0.295045 0.908054i 0.0121263 0.0373208i
\(593\) −5.15565 −0.211717 −0.105859 0.994381i \(-0.533759\pi\)
−0.105859 + 0.994381i \(0.533759\pi\)
\(594\) 1.07036 + 0.866815i 0.0439174 + 0.0355659i
\(595\) 11.1041 0.455225
\(596\) 0.488023 1.50198i 0.0199902 0.0615235i
\(597\) −1.23625 + 0.898186i −0.0505962 + 0.0367603i
\(598\) 25.6834 + 18.6601i 1.05027 + 0.763068i
\(599\) −9.72625 29.9343i −0.397404 1.22308i −0.927074 0.374879i \(-0.877684\pi\)
0.529670 0.848204i \(-0.322316\pi\)
\(600\) −0.0810668 0.249498i −0.00330954 0.0101857i
\(601\) −7.94983 5.77589i −0.324280 0.235603i 0.413719 0.910404i \(-0.364229\pi\)
−0.738000 + 0.674801i \(0.764229\pi\)
\(602\) 8.48218 6.16267i 0.345708 0.251172i
\(603\) −10.2748 + 31.6227i −0.418423 + 1.28778i
\(604\) 21.0132 0.855017
\(605\) −10.4912 + 6.05626i −0.426529 + 0.246222i
\(606\) −0.702925 −0.0285544
\(607\) 0.206900 0.636773i 0.00839782 0.0258458i −0.946770 0.321911i \(-0.895675\pi\)
0.955168 + 0.296066i \(0.0956747\pi\)
\(608\) 0.809017 0.587785i 0.0328100 0.0238378i
\(609\) 0.183241 + 0.133133i 0.00742531 + 0.00539480i
\(610\) −0.454876 1.39996i −0.0184174 0.0566829i
\(611\) −1.10220 3.39223i −0.0445903 0.137235i
\(612\) 12.2404 + 8.89318i 0.494789 + 0.359486i
\(613\) 5.97114 4.33829i 0.241172 0.175222i −0.460633 0.887591i \(-0.652378\pi\)
0.701805 + 0.712369i \(0.252378\pi\)
\(614\) −10.5893 + 32.5904i −0.427348 + 1.31524i
\(615\) −0.689974 −0.0278224
\(616\) 5.14485 + 4.16648i 0.207292 + 0.167872i
\(617\) 7.03453 0.283200 0.141600 0.989924i \(-0.454775\pi\)
0.141600 + 0.989924i \(0.454775\pi\)
\(618\) −0.00639204 + 0.0196727i −0.000257126 + 0.000791352i
\(619\) −12.1144 + 8.80164i −0.486920 + 0.353768i −0.803998 0.594631i \(-0.797298\pi\)
0.317079 + 0.948399i \(0.397298\pi\)
\(620\) 3.16076 + 2.29643i 0.126939 + 0.0922267i
\(621\) −0.641368 1.97393i −0.0257372 0.0792110i
\(622\) −6.70318 20.6303i −0.268773 0.827198i
\(623\) −14.4304 10.4843i −0.578142 0.420045i
\(624\) −0.355966 + 0.258624i −0.0142500 + 0.0103532i
\(625\) 2.55846 7.87414i 0.102339 0.314966i
\(626\) −14.1586 −0.565890
\(627\) 0.192679 0.125119i 0.00769486 0.00499677i
\(628\) −9.14086 −0.364760
\(629\) 1.49039 4.58695i 0.0594258 0.182894i
\(630\) −5.32667 + 3.87005i −0.212220 + 0.154187i
\(631\) 32.9868 + 23.9663i 1.31318 + 0.954084i 0.999990 + 0.00439533i \(0.00139908\pi\)
0.313194 + 0.949689i \(0.398601\pi\)
\(632\) −3.66024 11.2651i −0.145597 0.448100i
\(633\) 0.0515771 + 0.158738i 0.00205001 + 0.00630927i
\(634\) 12.8396 + 9.32849i 0.509924 + 0.370482i
\(635\) −9.83562 + 7.14599i −0.390315 + 0.283580i
\(636\) −0.151995 + 0.467793i −0.00602700 + 0.0185492i
\(637\) 19.1548 0.758942
\(638\) −5.42554 0.284508i −0.214799 0.0112638i
\(639\) −23.9810 −0.948675
\(640\) −0.340306 + 1.04736i −0.0134518 + 0.0414004i
\(641\) −6.46126 + 4.69438i −0.255205 + 0.185417i −0.708030 0.706182i \(-0.750416\pi\)
0.452826 + 0.891599i \(0.350416\pi\)
\(642\) −0.701930 0.509982i −0.0277030 0.0201274i
\(643\) −11.5188 35.4513i −0.454258 1.39806i −0.872004 0.489498i \(-0.837180\pi\)
0.417747 0.908564i \(-0.362820\pi\)
\(644\) −3.08283 9.48798i −0.121481 0.373879i
\(645\) 0.324153 + 0.235511i 0.0127635 + 0.00927322i
\(646\) 4.08667 2.96914i 0.160788 0.116819i
\(647\) −9.82223 + 30.2297i −0.386152 + 1.18845i 0.549489 + 0.835501i \(0.314822\pi\)
−0.935641 + 0.352953i \(0.885178\pi\)
\(648\) −8.95684 −0.351858
\(649\) −2.50419 9.34691i −0.0982980 0.366898i
\(650\) −24.0566 −0.943578
\(651\) 0.151583 0.466525i 0.00594101 0.0182845i
\(652\) −11.6442 + 8.45999i −0.456021 + 0.331319i
\(653\) −7.36651 5.35208i −0.288274 0.209443i 0.434244 0.900795i \(-0.357015\pi\)
−0.722518 + 0.691352i \(0.757015\pi\)
\(654\) 0.415519 + 1.27884i 0.0162481 + 0.0500065i
\(655\) −5.34490 16.4499i −0.208842 0.642751i
\(656\) −7.31752 5.31649i −0.285701 0.207574i
\(657\) −6.10853 + 4.43810i −0.238316 + 0.173147i
\(658\) −0.346364 + 1.06600i −0.0135027 + 0.0415570i
\(659\) 28.0285 1.09184 0.545918 0.837839i \(-0.316181\pi\)
0.545918 + 0.837839i \(0.316181\pi\)
\(660\) −0.0906747 + 0.236194i −0.00352951 + 0.00919384i
\(661\) 7.83541 0.304762 0.152381 0.988322i \(-0.451306\pi\)
0.152381 + 0.988322i \(0.451306\pi\)
\(662\) −6.02298 + 18.5368i −0.234090 + 0.720454i
\(663\) −1.79813 + 1.30642i −0.0698335 + 0.0507370i
\(664\) 7.89870 + 5.73874i 0.306529 + 0.222706i
\(665\) 0.679289 + 2.09064i 0.0263417 + 0.0810714i
\(666\) 0.883718 + 2.71981i 0.0342434 + 0.105390i
\(667\) 6.62345 + 4.81222i 0.256461 + 0.186330i
\(668\) −10.4171 + 7.56847i −0.403050 + 0.292833i
\(669\) 0.0795446 0.244813i 0.00307537 0.00946502i
\(670\) −12.2251 −0.472299
\(671\) 1.58885 4.13872i 0.0613369 0.159773i
\(672\) 0.138268 0.00533381
\(673\) −6.88209 + 21.1809i −0.265285 + 0.816464i 0.726342 + 0.687333i \(0.241219\pi\)
−0.991628 + 0.129131i \(0.958781\pi\)
\(674\) −23.1845 + 16.8445i −0.893033 + 0.648827i
\(675\) 1.27240 + 0.924450i 0.0489745 + 0.0355821i
\(676\) 8.45106 + 26.0097i 0.325041 + 1.00037i
\(677\) −10.3461 31.8420i −0.397633 1.22379i −0.926892 0.375329i \(-0.877530\pi\)
0.529259 0.848461i \(-0.322470\pi\)
\(678\) 0.694390 + 0.504504i 0.0266679 + 0.0193753i
\(679\) −1.02773 + 0.746691i −0.0394407 + 0.0286554i
\(680\) −1.71903 + 5.29062i −0.0659217 + 0.202886i
\(681\) 0.842840 0.0322977
\(682\) 3.04501 + 11.3655i 0.116599 + 0.435208i
\(683\) 27.8130 1.06424 0.532118 0.846670i \(-0.321396\pi\)
0.532118 + 0.846670i \(0.321396\pi\)
\(684\) −0.925568 + 2.84861i −0.0353900 + 0.108919i
\(685\) −6.49599 + 4.71961i −0.248199 + 0.180327i
\(686\) −16.1740 11.7511i −0.617525 0.448658i
\(687\) 0.382000 + 1.17567i 0.0145742 + 0.0448548i
\(688\) 1.62311 + 4.99542i 0.0618805 + 0.190449i
\(689\) 36.4904 + 26.5118i 1.39017 + 1.01002i
\(690\) 0.308437 0.224093i 0.0117420 0.00853107i
\(691\) −3.15022 + 9.69537i −0.119840 + 0.368829i −0.992926 0.118737i \(-0.962115\pi\)
0.873086 + 0.487567i \(0.162115\pi\)
\(692\) 13.2573 0.503968
\(693\) −19.8021 1.03839i −0.752218 0.0394453i
\(694\) −9.52606 −0.361604
\(695\) 1.26135 3.88204i 0.0478458 0.147254i
\(696\) −0.0917992 + 0.0666961i −0.00347964 + 0.00252811i
\(697\) −36.9638 26.8558i −1.40010 1.01723i
\(698\) −7.28883 22.4327i −0.275886 0.849090i
\(699\) 0.428110 + 1.31759i 0.0161926 + 0.0498357i
\(700\) 6.11596 + 4.44350i 0.231161 + 0.167949i
\(701\) 6.34053 4.60666i 0.239478 0.173991i −0.461572 0.887103i \(-0.652715\pi\)
0.701051 + 0.713111i \(0.252715\pi\)
\(702\) 0.815148 2.50877i 0.0307658 0.0946873i
\(703\) 0.954785 0.0360104
\(704\) −2.78161 + 1.80628i −0.104836 + 0.0680767i
\(705\) −0.0428344 −0.00161324
\(706\) 2.25135 6.92893i 0.0847305 0.260774i
\(707\) 16.3875 11.9062i 0.616315 0.447779i
\(708\) −0.163501 0.118790i −0.00614474 0.00446441i
\(709\) 10.7426 + 33.0624i 0.403448 + 1.24169i 0.922184 + 0.386752i \(0.126403\pi\)
−0.518736 + 0.854935i \(0.673597\pi\)
\(710\) −2.72466 8.38564i −0.102255 0.314707i
\(711\) 28.7019 + 20.8532i 1.07641 + 0.782055i
\(712\) 7.22926 5.25237i 0.270928 0.196841i
\(713\) 5.47913 16.8630i 0.205195 0.631525i
\(714\) 0.698449 0.0261388
\(715\) 18.0297 + 14.6011i 0.674272 + 0.546049i
\(716\) −19.1775 −0.716697
\(717\) −0.335771 + 1.03340i −0.0125396 + 0.0385929i
\(718\) −1.03661 + 0.753141i −0.0386859 + 0.0281070i
\(719\) −16.4459 11.9486i −0.613328 0.445609i 0.237257 0.971447i \(-0.423752\pi\)
−0.850585 + 0.525838i \(0.823752\pi\)
\(720\) −1.01929 3.13704i −0.0379866 0.116911i
\(721\) −0.184198 0.566904i −0.00685991 0.0211126i
\(722\) 0.809017 + 0.587785i 0.0301085 + 0.0218751i
\(723\) 0.274457 0.199405i 0.0102072 0.00741595i
\(724\) −1.44623 + 4.45105i −0.0537488 + 0.165422i
\(725\) −6.20392 −0.230408
\(726\) −0.659898 + 0.380938i −0.0244911 + 0.0141379i
\(727\) −27.7517 −1.02925 −0.514627 0.857414i \(-0.672069\pi\)
−0.514627 + 0.857414i \(0.672069\pi\)
\(728\) 3.91813 12.0588i 0.145216 0.446927i
\(729\) 21.6341 15.7181i 0.801264 0.582152i
\(730\) −2.24594 1.63177i −0.0831260 0.0603945i
\(731\) 8.19899 + 25.2339i 0.303251 + 0.933310i
\(732\) −0.0286117 0.0880577i −0.00105752 0.00325470i
\(733\) −2.47070 1.79507i −0.0912574 0.0663024i 0.541221 0.840880i \(-0.317962\pi\)
−0.632478 + 0.774578i \(0.717962\pi\)
\(734\) 16.9725 12.3312i 0.626466 0.455154i
\(735\) 0.0710845 0.218776i 0.00262199 0.00806966i
\(736\) 4.99785 0.184223
\(737\) −28.6124 23.1713i −1.05395 0.853527i
\(738\) 27.0915 0.997251
\(739\) 9.03723 27.8137i 0.332440 1.02314i −0.635529 0.772077i \(-0.719218\pi\)
0.967969 0.251068i \(-0.0807819\pi\)
\(740\) −0.850650 + 0.618033i −0.0312705 + 0.0227194i
\(741\) −0.355966 0.258624i −0.0130767 0.00950079i
\(742\) −4.38001 13.4803i −0.160795 0.494877i
\(743\) −7.87460 24.2355i −0.288891 0.889115i −0.985205 0.171378i \(-0.945178\pi\)
0.696314 0.717737i \(-0.254822\pi\)
\(744\) 0.198812 + 0.144445i 0.00728879 + 0.00529561i
\(745\) −1.40703 + 1.02227i −0.0515495 + 0.0374529i
\(746\) −8.69711 + 26.7669i −0.318424 + 0.980008i
\(747\) −29.2431 −1.06995
\(748\) −14.0511 + 9.12425i −0.513757 + 0.333615i
\(749\) 25.0024 0.913569
\(750\) −0.207138 + 0.637507i −0.00756363 + 0.0232785i
\(751\) −34.6567 + 25.1796i −1.26464 + 0.918816i −0.998976 0.0452494i \(-0.985592\pi\)
−0.265666 + 0.964065i \(0.585592\pi\)
\(752\) −0.454281 0.330054i −0.0165659 0.0120358i
\(753\) 0.525722 + 1.61801i 0.0191584 + 0.0589634i
\(754\) 3.21542 + 9.89605i 0.117099 + 0.360393i
\(755\) −18.7214 13.6019i −0.681342 0.495024i
\(756\) −0.670631 + 0.487242i −0.0243906 + 0.0177208i
\(757\) 9.74413 29.9893i 0.354156 1.08998i −0.602341 0.798239i \(-0.705765\pi\)
0.956497 0.291742i \(-0.0942349\pi\)
\(758\) 3.19494 0.116045
\(759\) 1.14663 + 0.0601274i 0.0416199 + 0.00218249i
\(760\) −1.10125 −0.0399467
\(761\) 11.1296 34.2534i 0.403448 1.24169i −0.518736 0.854935i \(-0.673597\pi\)
0.922184 0.386752i \(-0.126403\pi\)
\(762\) −0.618660 + 0.449483i −0.0224117 + 0.0162830i
\(763\) −31.3482 22.7758i −1.13488 0.824539i
\(764\) 1.63982 + 5.04685i 0.0593267 + 0.182589i
\(765\) −5.14883 15.8465i −0.186156 0.572930i
\(766\) −3.76820 2.73776i −0.136151 0.0989192i
\(767\) −14.9932 + 10.8932i −0.541373 + 0.393330i
\(768\) −0.0214053 + 0.0658786i −0.000772396 + 0.00237719i
\(769\) 45.0769 1.62552 0.812758 0.582601i \(-0.197965\pi\)
0.812758 + 0.582601i \(0.197965\pi\)
\(770\) −1.88675 7.04232i −0.0679938 0.253788i
\(771\) −0.677233 −0.0243899
\(772\) 0.0912482 0.280833i 0.00328409 0.0101074i
\(773\) −19.9553 + 14.4984i −0.717742 + 0.521470i −0.885662 0.464330i \(-0.846295\pi\)
0.167920 + 0.985801i \(0.446295\pi\)
\(774\) −12.7277 9.24721i −0.457487 0.332384i
\(775\) 4.15194 + 12.7783i 0.149142 + 0.459012i
\(776\) −0.196662 0.605263i −0.00705975 0.0217277i
\(777\) 0.106803 + 0.0775973i 0.00383155 + 0.00278379i
\(778\) 24.5101 17.8077i 0.878731 0.638436i
\(779\) 2.79505 8.60227i 0.100143 0.308208i
\(780\) 0.484549 0.0173497
\(781\) 9.51705 24.7905i 0.340547 0.887073i
\(782\) 25.2462 0.902801
\(783\) 0.210217 0.646981i 0.00751254 0.0231212i
\(784\) 2.43963 1.77250i 0.0871297 0.0633034i
\(785\) 8.14390 + 5.91689i 0.290668 + 0.211183i
\(786\) −0.336194 1.03470i −0.0119916 0.0369065i
\(787\) −5.37646 16.5470i −0.191650 0.589838i −0.999999 0.00113487i \(-0.999639\pi\)
0.808349 0.588703i \(-0.200361\pi\)
\(788\) 19.9002 + 14.4583i 0.708915 + 0.515057i
\(789\) 0.0117155 0.00851180i 0.000417083 0.000303028i
\(790\) −4.03086 + 12.4057i −0.143411 + 0.441375i
\(791\) −24.7338 −0.879434
\(792\) 3.56030 9.27404i 0.126510 0.329539i
\(793\) −8.49053 −0.301507
\(794\) −8.60159 + 26.4730i −0.305259 + 0.939491i
\(795\) 0.438220 0.318386i 0.0155421 0.0112920i
\(796\) 17.8471 + 12.9667i 0.632573 + 0.459591i
\(797\) 0.624283 + 1.92135i 0.0221133 + 0.0680576i 0.961504 0.274790i \(-0.0886084\pi\)
−0.939391 + 0.342848i \(0.888608\pi\)
\(798\) 0.0427272 + 0.131501i 0.00151253 + 0.00465508i
\(799\) −2.29476 1.66724i −0.0811827 0.0589827i
\(800\) −3.06394 + 2.22608i −0.108327 + 0.0787039i
\(801\) −8.27075 + 25.4548i −0.292233 + 0.899399i
\(802\) −8.17135 −0.288540
\(803\) −2.16369 8.07600i −0.0763550 0.284996i
\(804\) −0.768961 −0.0271192
\(805\) −3.39498 + 10.4487i −0.119657 + 0.368268i
\(806\) 18.2312 13.2458i 0.642167 0.466562i
\(807\) 1.46728 + 1.06604i 0.0516506 + 0.0375263i
\(808\) 3.13583 + 9.65111i 0.110318 + 0.339525i
\(809\) −14.9296 45.9485i −0.524896 1.61546i −0.764522 0.644598i \(-0.777025\pi\)
0.239626 0.970865i \(-0.422975\pi\)
\(810\) 7.97995 + 5.79777i 0.280387 + 0.203713i
\(811\) 24.7122 17.9545i 0.867764 0.630468i −0.0622217 0.998062i \(-0.519819\pi\)
0.929986 + 0.367595i \(0.119819\pi\)
\(812\) 1.01044 3.10981i 0.0354594 0.109133i
\(813\) −0.480516 −0.0168524
\(814\) −3.16232 0.165828i −0.110839 0.00581225i
\(815\) 15.8504 0.555214
\(816\) −0.108127 + 0.332780i −0.00378519 + 0.0116496i
\(817\) −4.24936 + 3.08734i −0.148666 + 0.108012i
\(818\) 14.1417 + 10.2745i 0.494452 + 0.359240i
\(819\) 11.7356 + 36.1184i 0.410075 + 1.26208i
\(820\) 3.07806 + 9.47329i 0.107490 + 0.330821i
\(821\) −6.79637 4.93786i −0.237195 0.172332i 0.462838 0.886443i \(-0.346831\pi\)
−0.700033 + 0.714111i \(0.746831\pi\)
\(822\) −0.408598 + 0.296864i −0.0142515 + 0.0103543i
\(823\) 8.22577 25.3163i 0.286732 0.882472i −0.699142 0.714983i \(-0.746434\pi\)
0.985874 0.167488i \(-0.0535657\pi\)
\(824\) 0.298620 0.0104029
\(825\) −0.729722 + 0.473855i −0.0254056 + 0.0164975i
\(826\) 5.82383 0.202637
\(827\) 10.0467 30.9205i 0.349357 1.07521i −0.609852 0.792515i \(-0.708771\pi\)
0.959209 0.282696i \(-0.0912289\pi\)
\(828\) −12.1106 + 8.79889i −0.420874 + 0.305783i
\(829\) 1.84075 + 1.33738i 0.0639318 + 0.0464492i 0.619292 0.785161i \(-0.287420\pi\)
−0.555360 + 0.831610i \(0.687420\pi\)
\(830\) −3.32252 10.2257i −0.115326 0.354938i
\(831\) −0.478677 1.47322i −0.0166051 0.0511053i
\(832\) 5.13889 + 3.73363i 0.178159 + 0.129440i
\(833\) 12.3236 8.95360i 0.426986 0.310224i
\(834\) 0.0793389 0.244180i 0.00274728 0.00845527i
\(835\) 14.1800 0.490720
\(836\) −2.57744 2.08730i −0.0891425 0.0721907i
\(837\) −1.47329 −0.0509243
\(838\) −4.55343 + 14.0140i −0.157296 + 0.484106i
\(839\) 33.0787 24.0331i 1.14200 0.829714i 0.154606 0.987976i \(-0.450589\pi\)
0.987397 + 0.158262i \(0.0505892\pi\)
\(840\) −0.123188 0.0895012i −0.00425038 0.00308809i
\(841\) −8.13227 25.0286i −0.280423 0.863054i
\(842\) −9.35279 28.7849i −0.322318 0.991994i
\(843\) −1.42944 1.03855i −0.0492326 0.0357695i
\(844\) 1.94937 1.41630i 0.0671001 0.0487511i
\(845\) 9.30677 28.6433i 0.320163 0.985359i
\(846\) 1.68187 0.0578239
\(847\) 8.93203 20.0583i 0.306908 0.689213i
\(848\) 7.10083 0.243843
\(849\) 0.598553 1.84216i 0.0205423 0.0632226i
\(850\) −15.4772 + 11.2449i −0.530864 + 0.385695i
\(851\) 3.86052 + 2.80483i 0.132337 + 0.0961485i
\(852\) −0.171381 0.527456i −0.00587141 0.0180704i
\(853\) 16.4963 + 50.7703i 0.564821 + 1.73834i 0.668482 + 0.743729i \(0.266945\pi\)
−0.103660 + 0.994613i \(0.533055\pi\)
\(854\) 2.15856 + 1.56829i 0.0738645 + 0.0536657i
\(855\) 2.66853 1.93880i 0.0912617 0.0663055i
\(856\) −3.87062 + 11.9125i −0.132295 + 0.407162i
\(857\) 29.3716 1.00331 0.501657 0.865067i \(-0.332724\pi\)
0.501657 + 0.865067i \(0.332724\pi\)
\(858\) 1.13407 + 0.918406i 0.0387164 + 0.0313539i
\(859\) 32.9455 1.12409 0.562043 0.827108i \(-0.310016\pi\)
0.562043 + 0.827108i \(0.310016\pi\)
\(860\) 1.78746 5.50123i 0.0609518 0.187590i
\(861\) 1.01178 0.735102i 0.0344814 0.0250522i
\(862\) −26.8090 19.4778i −0.913117 0.663418i
\(863\) 2.63331 + 8.10450i 0.0896389 + 0.275880i 0.985819 0.167809i \(-0.0536693\pi\)
−0.896181 + 0.443690i \(0.853669\pi\)
\(864\) −0.128329 0.394956i −0.00436584 0.0134367i
\(865\) −11.8114 8.58149i −0.401600 0.291779i
\(866\) 1.00490 0.730106i 0.0341480 0.0248100i
\(867\) −0.182303 + 0.561070i −0.00619132 + 0.0190549i
\(868\) −7.08158 −0.240364
\(869\) −32.9476 + 21.3950i −1.11767 + 0.725775i
\(870\) 0.124959 0.00423652
\(871\) −21.7902 + 67.0633i −0.738332 + 2.27235i
\(872\) 15.7046 11.4101i 0.531826 0.386394i
\(873\) 1.54213 + 1.12043i 0.0521933 + 0.0379206i
\(874\) 1.54442 + 4.75324i 0.0522408 + 0.160781i
\(875\) −5.96907 18.3709i −0.201791 0.621050i
\(876\) −0.141270 0.102638i −0.00477305 0.00346783i
\(877\) 37.0899 26.9474i 1.25244 0.909949i 0.254076 0.967184i \(-0.418229\pi\)
0.998361 + 0.0572355i \(0.0182286\pi\)
\(878\) 4.72789 14.5510i 0.159559 0.491071i
\(879\) 0.673447 0.0227148
\(880\) 3.64744 + 0.191267i 0.122955 + 0.00644759i
\(881\) 32.0866 1.08103 0.540513 0.841336i \(-0.318230\pi\)
0.540513 + 0.841336i \(0.318230\pi\)
\(882\) −2.79110 + 8.59011i −0.0939811 + 0.289244i
\(883\) −16.0025 + 11.6265i −0.538526 + 0.391262i −0.823537 0.567262i \(-0.808003\pi\)
0.285011 + 0.958524i \(0.408003\pi\)
\(884\) 25.9587 + 18.8601i 0.873084 + 0.634333i
\(885\) 0.0687753 + 0.211669i 0.00231186 + 0.00711516i
\(886\) 8.55859 + 26.3406i 0.287532 + 0.884931i
\(887\) −2.71459 1.97227i −0.0911472 0.0662223i 0.541278 0.840843i \(-0.317941\pi\)
−0.632425 + 0.774621i \(0.717941\pi\)
\(888\) −0.0535058 + 0.0388743i −0.00179554 + 0.00130454i
\(889\) 6.80962 20.9579i 0.228387 0.702904i
\(890\) −9.84066 −0.329860
\(891\) 7.68772 + 28.6945i 0.257548 + 0.961302i
\(892\) −3.71612 −0.124425
\(893\) 0.173520 0.534039i 0.00580662 0.0178709i
\(894\) −0.0885021 + 0.0643005i −0.00295995 + 0.00215053i
\(895\) 17.0859 + 12.4136i 0.571118 + 0.414942i
\(896\) −0.616832 1.89841i −0.0206069 0.0634215i
\(897\) −0.679541 2.09141i −0.0226892 0.0698302i
\(898\) −23.6746 17.2006i −0.790033 0.573992i
\(899\) 4.70161 3.41592i 0.156808 0.113927i
\(900\) 3.50535 10.7883i 0.116845 0.359612i
\(901\) 35.8692 1.19498
\(902\) −10.7514 + 28.0059i −0.357984 + 0.932494i
\(903\) −0.726253 −0.0241682
\(904\) 3.82904 11.7846i 0.127352 0.391949i
\(905\) 4.16967 3.02944i 0.138604 0.100702i
\(906\) −1.17758 0.855559i −0.0391223 0.0284240i
\(907\) −4.82352 14.8453i −0.160162 0.492929i 0.838485 0.544925i \(-0.183442\pi\)
−0.998647 + 0.0519957i \(0.983442\pi\)
\(908\) −3.76001 11.5721i −0.124780 0.384035i
\(909\) −24.5898 17.8655i −0.815591 0.592562i
\(910\) −11.2964 + 8.20735i −0.374473 + 0.272071i
\(911\) −15.6231 + 48.0829i −0.517616 + 1.59306i 0.260855 + 0.965378i \(0.415996\pi\)
−0.778471 + 0.627680i \(0.784004\pi\)
\(912\) −0.0692689 −0.00229372
\(913\) 11.6053 30.2302i 0.384081 1.00047i
\(914\) −18.8923 −0.624901
\(915\) −0.0315087 + 0.0969739i −0.00104165 + 0.00320586i
\(916\) 14.4378 10.4897i 0.477037 0.346588i
\(917\) 25.3636 + 18.4277i 0.837580 + 0.608538i
\(918\) −0.648241 1.99508i −0.0213952 0.0658475i
\(919\) −6.96159 21.4256i −0.229642 0.706765i −0.997787 0.0664892i \(-0.978820\pi\)
0.768145 0.640275i \(-0.221180\pi\)
\(920\) −4.45275 3.23511i −0.146803 0.106659i
\(921\) 1.92034 1.39521i 0.0632775 0.0459738i
\(922\) −11.4510 + 35.2426i −0.377119 + 1.16065i
\(923\) −50.8574 −1.67399
\(924\) −0.118677 0.442962i −0.00390417 0.0145724i
\(925\) −3.61600 −0.118893
\(926\) −5.12421 + 15.7707i −0.168392 + 0.518258i
\(927\) −0.723607 + 0.525731i −0.0237664 + 0.0172673i
\(928\) 1.32526 + 0.962857i 0.0435038 + 0.0316073i
\(929\) −3.83357 11.7985i −0.125775 0.387097i 0.868266 0.496099i \(-0.165235\pi\)
−0.994042 + 0.109002i \(0.965235\pi\)
\(930\) −0.0836285 0.257382i −0.00274229 0.00843989i
\(931\) 2.43963 + 1.77250i 0.0799557 + 0.0580912i
\(932\) 16.1805 11.7558i 0.530010 0.385075i
\(933\) −0.464322 + 1.42904i −0.0152012 + 0.0467845i
\(934\) 2.72432 0.0891424
\(935\) 18.4247 + 0.966165i 0.602552 + 0.0315970i
\(936\) −19.0256 −0.621871
\(937\) −11.7697 + 36.2235i −0.384501 + 1.18337i 0.552341 + 0.833618i \(0.313735\pi\)
−0.936842 + 0.349753i \(0.886265\pi\)
\(938\) 17.9270 13.0247i 0.585338 0.425273i
\(939\) 0.793441 + 0.576469i 0.0258930 + 0.0188124i
\(940\) 0.191089 + 0.588113i 0.00623265 + 0.0191821i
\(941\) 1.12928 + 3.47556i 0.0368134 + 0.113300i 0.967775 0.251818i \(-0.0810285\pi\)
−0.930961 + 0.365118i \(0.881029\pi\)
\(942\) 0.512251 + 0.372172i 0.0166900 + 0.0121260i
\(943\) 36.5719 26.5710i 1.19094 0.865272i
\(944\) −0.901585 + 2.77479i −0.0293441 + 0.0903118i
\(945\) 0.912881 0.0296960
\(946\) 14.6104 9.48747i 0.475025 0.308464i
\(947\) −3.79469 −0.123311 −0.0616554 0.998097i \(-0.519638\pi\)
−0.0616554 + 0.998097i \(0.519638\pi\)
\(948\) −0.253541 + 0.780318i −0.00823462 + 0.0253436i
\(949\) −12.9546 + 9.41203i −0.420523 + 0.305527i
\(950\) −3.06394 2.22608i −0.0994073 0.0722237i
\(951\) −0.339714 1.04553i −0.0110160 0.0339037i
\(952\) −3.11587 9.58965i −0.100986 0.310802i
\(953\) 32.4632 + 23.5859i 1.05159 + 0.764022i 0.972513 0.232847i \(-0.0748041\pi\)
0.0790727 + 0.996869i \(0.474804\pi\)
\(954\) −17.2065 + 12.5013i −0.557081 + 0.404743i
\(955\) 1.80586 5.55787i 0.0584363 0.179848i
\(956\) 15.6864 0.507334
\(957\) 0.292462 + 0.236846i 0.00945396 + 0.00765614i
\(958\) 19.8904 0.642630
\(959\) 4.49745 13.8417i 0.145230 0.446973i
\(960\) 0.0617140 0.0448378i 0.00199181 0.00144714i
\(961\) 14.8971 + 10.8234i 0.480553 + 0.349142i
\(962\) 1.87413 + 5.76798i 0.0604244 + 0.185967i
\(963\) −11.5933 35.6805i −0.373588 1.14979i
\(964\) −3.96220 2.87871i −0.127614 0.0927170i
\(965\) −0.263080 + 0.191139i −0.00846883 + 0.00615297i
\(966\) −0.213544 + 0.657222i −0.00687067 + 0.0211458i
\(967\) −3.57570 −0.114987 −0.0574934 0.998346i \(-0.518311\pi\)
−0.0574934 + 0.998346i \(0.518311\pi\)
\(968\) 8.17414 + 7.36094i 0.262727 + 0.236590i
\(969\) −0.349905 −0.0112406
\(970\) −0.216575 + 0.666549i −0.00695380 + 0.0214016i
\(971\) 12.7138 9.23708i 0.408004 0.296432i −0.364789 0.931090i \(-0.618859\pi\)
0.772793 + 0.634658i \(0.218859\pi\)
\(972\) 1.50985 + 1.09697i 0.0484284 + 0.0351853i
\(973\) 2.28630 + 7.03649i 0.0732953 + 0.225580i
\(974\) −1.58446 4.87646i −0.0507693 0.156252i
\(975\) 1.34813 + 0.979471i 0.0431746 + 0.0313682i
\(976\) −1.08138 + 0.785672i −0.0346143 + 0.0251487i
\(977\) 9.67894 29.7887i 0.309657 0.953025i −0.668242 0.743944i \(-0.732953\pi\)
0.977898 0.209081i \(-0.0670472\pi\)
\(978\) 0.996987 0.0318801
\(979\) −23.0316 18.6518i −0.736094 0.596115i
\(980\) −3.32089 −0.106082
\(981\) −17.9671 + 55.2972i −0.573646 + 1.76550i
\(982\) −1.06951 + 0.777041i −0.0341293 + 0.0247964i
\(983\) 28.8482 + 20.9594i 0.920113 + 0.668501i 0.943552 0.331224i \(-0.107462\pi\)
−0.0234390 + 0.999725i \(0.507462\pi\)
\(984\) 0.193610 + 0.595869i 0.00617205 + 0.0189956i
\(985\) −8.37085 25.7628i −0.266718 0.820872i
\(986\) 6.69443 + 4.86378i 0.213194 + 0.154894i
\(987\) 0.0628126 0.0456360i 0.00199935 0.00145261i
\(988\) −1.96288 + 6.04113i −0.0624476 + 0.192194i
\(989\) −26.2512 −0.834739
\(990\) −9.17509 + 5.95797i −0.291603 + 0.189357i
\(991\) −16.7562 −0.532278 −0.266139 0.963935i \(-0.585748\pi\)
−0.266139 + 0.963935i \(0.585748\pi\)
\(992\) 1.09630 3.37406i 0.0348075 0.107126i
\(993\) 1.09226 0.793571i 0.0346617 0.0251832i
\(994\) 12.9296 + 9.39388i 0.410101 + 0.297956i
\(995\) −7.50723 23.1049i −0.237995 0.732474i
\(996\) −0.208987 0.643195i −0.00662199 0.0203804i
\(997\) −40.1021 29.1358i −1.27004 0.922741i −0.270840 0.962624i \(-0.587302\pi\)
−0.999204 + 0.0398828i \(0.987302\pi\)
\(998\) −17.7893 + 12.9247i −0.563111 + 0.409124i
\(999\) 0.122526 0.377098i 0.00387656 0.0119308i
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.g.229.2 yes 16
11.4 even 5 4598.2.a.bw.1.5 8
11.5 even 5 inner 418.2.f.g.115.2 16
11.7 odd 10 4598.2.a.bz.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.g.115.2 16 11.5 even 5 inner
418.2.f.g.229.2 yes 16 1.1 even 1 trivial
4598.2.a.bw.1.5 8 11.4 even 5
4598.2.a.bz.1.5 8 11.7 odd 10