Properties

Label 722.2.c.n.429.2
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
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] = [722,2,Mod(429,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.429");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.2
Root \(0.951057 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.n.653.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.221232 - 0.383185i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.445746 - 0.772054i) q^{5} +(-0.221232 - 0.383185i) q^{6} +2.52015 q^{7} -1.00000 q^{8} +(1.40211 + 2.42853i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.221232 - 0.383185i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.445746 - 0.772054i) q^{5} +(-0.221232 - 0.383185i) q^{6} +2.52015 q^{7} -1.00000 q^{8} +(1.40211 + 2.42853i) q^{9} +(-0.445746 - 0.772054i) q^{10} +1.95199 q^{11} -0.442463 q^{12} +(3.22982 + 5.59422i) q^{13} +(1.26007 - 2.18251i) q^{14} +(-0.197226 - 0.341606i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.71113 - 2.96376i) q^{17} +2.80423 q^{18} -0.891491 q^{20} +(0.557537 - 0.965682i) q^{21} +(0.975994 - 1.69047i) q^{22} +(-4.09252 - 7.08845i) q^{23} +(-0.221232 + 0.383185i) q^{24} +(2.10262 + 3.64185i) q^{25} +6.45965 q^{26} +2.56816 q^{27} +(-1.26007 - 2.18251i) q^{28} +(-2.29032 - 3.96695i) q^{29} -0.394452 q^{30} -8.79360 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.431842 - 0.747972i) q^{33} +(-1.71113 - 2.96376i) q^{34} +(1.12334 - 1.94569i) q^{35} +(1.40211 - 2.42853i) q^{36} -5.97980 q^{37} +2.85816 q^{39} +(-0.445746 + 0.772054i) q^{40} +(1.74466 - 3.02184i) q^{41} +(-0.557537 - 0.965682i) q^{42} +(3.12334 - 5.40979i) q^{43} +(-0.975994 - 1.69047i) q^{44} +2.49994 q^{45} -8.18504 q^{46} +(5.27491 + 9.13641i) q^{47} +(0.221232 + 0.383185i) q^{48} -0.648859 q^{49} +4.20524 q^{50} +(-0.757113 - 1.31136i) q^{51} +(3.22982 - 5.59422i) q^{52} +(-1.88139 - 3.25866i) q^{53} +(1.28408 - 2.22409i) q^{54} +(0.870091 - 1.50704i) q^{55} -2.52015 q^{56} -4.58064 q^{58} +(-1.42081 + 2.46091i) q^{59} +(-0.197226 + 0.341606i) q^{60} +(1.22747 + 2.12605i) q^{61} +(-4.39680 + 7.61548i) q^{62} +(3.53353 + 6.12026i) q^{63} +1.00000 q^{64} +5.75872 q^{65} +(-0.431842 - 0.747972i) q^{66} +(1.33630 + 2.31455i) q^{67} -3.42226 q^{68} -3.62158 q^{69} +(-1.12334 - 1.94569i) q^{70} +(-0.0282202 + 0.0488788i) q^{71} +(-1.40211 - 2.42853i) q^{72} +(3.48459 - 6.03548i) q^{73} +(-2.98990 + 5.17866i) q^{74} +1.86067 q^{75} +4.91930 q^{77} +(1.42908 - 2.47524i) q^{78} +(4.56581 - 7.90821i) q^{79} +(0.445746 + 0.772054i) q^{80} +(-3.63818 + 6.30151i) q^{81} +(-1.74466 - 3.02184i) q^{82} -14.1239 q^{83} -1.11507 q^{84} +(-1.52546 - 2.64217i) q^{85} +(-3.12334 - 5.40979i) q^{86} -2.02677 q^{87} -1.95199 q^{88} +(-0.933870 - 1.61751i) q^{89} +(1.24997 - 2.16501i) q^{90} +(8.13963 + 14.0983i) q^{91} +(-4.09252 + 7.08845i) q^{92} +(-1.94542 + 3.36957i) q^{93} +10.5498 q^{94} +0.442463 q^{96} +(-3.91216 + 6.77606i) q^{97} +(-0.324429 + 0.561928i) q^{98} +(2.73691 + 4.74047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.221232 0.383185i 0.127728 0.221232i −0.795068 0.606520i \(-0.792565\pi\)
0.922796 + 0.385289i \(0.125898\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.445746 0.772054i 0.199344 0.345273i −0.748972 0.662601i \(-0.769452\pi\)
0.948316 + 0.317328i \(0.102786\pi\)
\(6\) −0.221232 0.383185i −0.0903175 0.156434i
\(7\) 2.52015 0.952526 0.476263 0.879303i \(-0.341991\pi\)
0.476263 + 0.879303i \(0.341991\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.40211 + 2.42853i 0.467371 + 0.809510i
\(10\) −0.445746 0.772054i −0.140957 0.244145i
\(11\) 1.95199 0.588547 0.294273 0.955721i \(-0.404922\pi\)
0.294273 + 0.955721i \(0.404922\pi\)
\(12\) −0.442463 −0.127728
\(13\) 3.22982 + 5.59422i 0.895792 + 1.55156i 0.832821 + 0.553542i \(0.186724\pi\)
0.0629711 + 0.998015i \(0.479942\pi\)
\(14\) 1.26007 2.18251i 0.336769 0.583301i
\(15\) −0.197226 0.341606i −0.0509236 0.0882022i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.71113 2.96376i 0.415010 0.718818i −0.580420 0.814318i \(-0.697111\pi\)
0.995430 + 0.0954992i \(0.0304447\pi\)
\(18\) 2.80423 0.660962
\(19\) 0 0
\(20\) −0.891491 −0.199344
\(21\) 0.557537 0.965682i 0.121664 0.210729i
\(22\) 0.975994 1.69047i 0.208083 0.360410i
\(23\) −4.09252 7.08845i −0.853349 1.47804i −0.878168 0.478352i \(-0.841234\pi\)
0.0248186 0.999692i \(-0.492099\pi\)
\(24\) −0.221232 + 0.383185i −0.0451587 + 0.0782172i
\(25\) 2.10262 + 3.64185i 0.420524 + 0.728369i
\(26\) 6.45965 1.26684
\(27\) 2.56816 0.494242
\(28\) −1.26007 2.18251i −0.238132 0.412456i
\(29\) −2.29032 3.96695i −0.425302 0.736645i 0.571146 0.820848i \(-0.306499\pi\)
−0.996449 + 0.0842032i \(0.973166\pi\)
\(30\) −0.394452 −0.0720168
\(31\) −8.79360 −1.57938 −0.789689 0.613507i \(-0.789758\pi\)
−0.789689 + 0.613507i \(0.789758\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.431842 0.747972i 0.0751740 0.130205i
\(34\) −1.71113 2.96376i −0.293456 0.508281i
\(35\) 1.12334 1.94569i 0.189880 0.328882i
\(36\) 1.40211 2.42853i 0.233686 0.404755i
\(37\) −5.97980 −0.983073 −0.491536 0.870857i \(-0.663564\pi\)
−0.491536 + 0.870857i \(0.663564\pi\)
\(38\) 0 0
\(39\) 2.85816 0.457672
\(40\) −0.445746 + 0.772054i −0.0704786 + 0.122072i
\(41\) 1.74466 3.02184i 0.272470 0.471932i −0.697024 0.717048i \(-0.745493\pi\)
0.969494 + 0.245116i \(0.0788260\pi\)
\(42\) −0.557537 0.965682i −0.0860298 0.149008i
\(43\) 3.12334 5.40979i 0.476306 0.824986i −0.523326 0.852133i \(-0.675309\pi\)
0.999631 + 0.0271471i \(0.00864226\pi\)
\(44\) −0.975994 1.69047i −0.147137 0.254848i
\(45\) 2.49994 0.372670
\(46\) −8.18504 −1.20682
\(47\) 5.27491 + 9.13641i 0.769425 + 1.33268i 0.937875 + 0.346973i \(0.112790\pi\)
−0.168451 + 0.985710i \(0.553876\pi\)
\(48\) 0.221232 + 0.383185i 0.0319321 + 0.0553079i
\(49\) −0.648859 −0.0926941
\(50\) 4.20524 0.594711
\(51\) −0.757113 1.31136i −0.106017 0.183627i
\(52\) 3.22982 5.59422i 0.447896 0.775779i
\(53\) −1.88139 3.25866i −0.258429 0.447612i 0.707392 0.706821i \(-0.249871\pi\)
−0.965821 + 0.259209i \(0.916538\pi\)
\(54\) 1.28408 2.22409i 0.174741 0.302660i
\(55\) 0.870091 1.50704i 0.117323 0.203209i
\(56\) −2.52015 −0.336769
\(57\) 0 0
\(58\) −4.58064 −0.601468
\(59\) −1.42081 + 2.46091i −0.184973 + 0.320383i −0.943568 0.331180i \(-0.892553\pi\)
0.758594 + 0.651563i \(0.225887\pi\)
\(60\) −0.197226 + 0.341606i −0.0254618 + 0.0441011i
\(61\) 1.22747 + 2.12605i 0.157162 + 0.272213i 0.933844 0.357680i \(-0.116432\pi\)
−0.776682 + 0.629893i \(0.783099\pi\)
\(62\) −4.39680 + 7.61548i −0.558394 + 0.967168i
\(63\) 3.53353 + 6.12026i 0.445183 + 0.771080i
\(64\) 1.00000 0.125000
\(65\) 5.75872 0.714282
\(66\) −0.431842 0.747972i −0.0531561 0.0920690i
\(67\) 1.33630 + 2.31455i 0.163256 + 0.282767i 0.936034 0.351908i \(-0.114467\pi\)
−0.772779 + 0.634675i \(0.781134\pi\)
\(68\) −3.42226 −0.415010
\(69\) −3.62158 −0.435987
\(70\) −1.12334 1.94569i −0.134265 0.232554i
\(71\) −0.0282202 + 0.0488788i −0.00334912 + 0.00580085i −0.867695 0.497097i \(-0.834399\pi\)
0.864346 + 0.502898i \(0.167733\pi\)
\(72\) −1.40211 2.42853i −0.165241 0.286205i
\(73\) 3.48459 6.03548i 0.407840 0.706400i −0.586807 0.809727i \(-0.699615\pi\)
0.994647 + 0.103327i \(0.0329487\pi\)
\(74\) −2.98990 + 5.17866i −0.347569 + 0.602007i
\(75\) 1.86067 0.214851
\(76\) 0 0
\(77\) 4.91930 0.560606
\(78\) 1.42908 2.47524i 0.161811 0.280266i
\(79\) 4.56581 7.90821i 0.513694 0.889743i −0.486180 0.873859i \(-0.661610\pi\)
0.999874 0.0158848i \(-0.00505650\pi\)
\(80\) 0.445746 + 0.772054i 0.0498359 + 0.0863183i
\(81\) −3.63818 + 6.30151i −0.404242 + 0.700168i
\(82\) −1.74466 3.02184i −0.192666 0.333707i
\(83\) −14.1239 −1.55030 −0.775150 0.631778i \(-0.782326\pi\)
−0.775150 + 0.631778i \(0.782326\pi\)
\(84\) −1.11507 −0.121664
\(85\) −1.52546 2.64217i −0.165459 0.286584i
\(86\) −3.12334 5.40979i −0.336799 0.583353i
\(87\) −2.02677 −0.217292
\(88\) −1.95199 −0.208083
\(89\) −0.933870 1.61751i −0.0989901 0.171456i 0.812277 0.583272i \(-0.198228\pi\)
−0.911267 + 0.411816i \(0.864895\pi\)
\(90\) 1.24997 2.16501i 0.131759 0.228213i
\(91\) 8.13963 + 14.0983i 0.853265 + 1.47790i
\(92\) −4.09252 + 7.08845i −0.426675 + 0.739022i
\(93\) −1.94542 + 3.36957i −0.201731 + 0.349409i
\(94\) 10.5498 1.08813
\(95\) 0 0
\(96\) 0.442463 0.0451587
\(97\) −3.91216 + 6.77606i −0.397219 + 0.688004i −0.993382 0.114860i \(-0.963358\pi\)
0.596162 + 0.802864i \(0.296692\pi\)
\(98\) −0.324429 + 0.561928i −0.0327723 + 0.0567633i
\(99\) 2.73691 + 4.74047i 0.275070 + 0.476435i
\(100\) 2.10262 3.64185i 0.210262 0.364185i
\(101\) 2.69244 + 4.66343i 0.267907 + 0.464029i 0.968321 0.249708i \(-0.0803346\pi\)
−0.700414 + 0.713737i \(0.747001\pi\)
\(102\) −1.51423 −0.149931
\(103\) −4.69468 −0.462580 −0.231290 0.972885i \(-0.574295\pi\)
−0.231290 + 0.972885i \(0.574295\pi\)
\(104\) −3.22982 5.59422i −0.316710 0.548558i
\(105\) −0.497039 0.860897i −0.0485060 0.0840149i
\(106\) −3.76278 −0.365473
\(107\) 16.0373 1.55038 0.775191 0.631727i \(-0.217654\pi\)
0.775191 + 0.631727i \(0.217654\pi\)
\(108\) −1.28408 2.22409i −0.123561 0.214013i
\(109\) −7.05040 + 12.2116i −0.675305 + 1.16966i 0.301074 + 0.953601i \(0.402655\pi\)
−0.976380 + 0.216063i \(0.930678\pi\)
\(110\) −0.870091 1.50704i −0.0829599 0.143691i
\(111\) −1.32292 + 2.29137i −0.125566 + 0.217487i
\(112\) −1.26007 + 2.18251i −0.119066 + 0.206228i
\(113\) −12.7224 −1.19682 −0.598410 0.801190i \(-0.704201\pi\)
−0.598410 + 0.801190i \(0.704201\pi\)
\(114\) 0 0
\(115\) −7.29689 −0.680439
\(116\) −2.29032 + 3.96695i −0.212651 + 0.368322i
\(117\) −9.05716 + 15.6875i −0.837335 + 1.45031i
\(118\) 1.42081 + 2.46091i 0.130796 + 0.226545i
\(119\) 4.31230 7.46912i 0.395308 0.684693i
\(120\) 0.197226 + 0.341606i 0.0180042 + 0.0311842i
\(121\) −7.18974 −0.653613
\(122\) 2.45495 0.222261
\(123\) −0.771949 1.33705i −0.0696043 0.120558i
\(124\) 4.39680 + 7.61548i 0.394844 + 0.683891i
\(125\) 8.20640 0.734002
\(126\) 7.06706 0.629584
\(127\) −3.58721 6.21323i −0.318313 0.551335i 0.661823 0.749660i \(-0.269783\pi\)
−0.980136 + 0.198325i \(0.936450\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.38197 2.39364i −0.121675 0.210748i
\(130\) 2.87936 4.98720i 0.252537 0.437406i
\(131\) 1.76133 3.05071i 0.153888 0.266542i −0.778766 0.627315i \(-0.784154\pi\)
0.932654 + 0.360773i \(0.117487\pi\)
\(132\) −0.863684 −0.0751740
\(133\) 0 0
\(134\) 2.67261 0.230878
\(135\) 1.14475 1.98276i 0.0985240 0.170649i
\(136\) −1.71113 + 2.96376i −0.146728 + 0.254141i
\(137\) 5.50177 + 9.52935i 0.470048 + 0.814147i 0.999413 0.0342466i \(-0.0109032\pi\)
−0.529365 + 0.848394i \(0.677570\pi\)
\(138\) −1.81079 + 3.13638i −0.154145 + 0.266987i
\(139\) −10.8793 18.8435i −0.922771 1.59829i −0.795108 0.606468i \(-0.792586\pi\)
−0.127663 0.991818i \(-0.540747\pi\)
\(140\) −2.24669 −0.189880
\(141\) 4.66791 0.393109
\(142\) 0.0282202 + 0.0488788i 0.00236819 + 0.00410182i
\(143\) 6.30458 + 10.9199i 0.527216 + 0.913164i
\(144\) −2.80423 −0.233686
\(145\) −4.08361 −0.339125
\(146\) −3.48459 6.03548i −0.288387 0.499500i
\(147\) −0.143548 + 0.248633i −0.0118397 + 0.0205069i
\(148\) 2.98990 + 5.17866i 0.245768 + 0.425683i
\(149\) −7.19479 + 12.4617i −0.589420 + 1.02090i 0.404889 + 0.914366i \(0.367310\pi\)
−0.994309 + 0.106539i \(0.966023\pi\)
\(150\) 0.930333 1.61138i 0.0759614 0.131569i
\(151\) 12.4068 1.00965 0.504824 0.863222i \(-0.331557\pi\)
0.504824 + 0.863222i \(0.331557\pi\)
\(152\) 0 0
\(153\) 9.59679 0.775855
\(154\) 2.45965 4.26024i 0.198204 0.343300i
\(155\) −3.91971 + 6.78914i −0.314839 + 0.545317i
\(156\) −1.42908 2.47524i −0.114418 0.198178i
\(157\) 0.225610 0.390768i 0.0180056 0.0311867i −0.856882 0.515512i \(-0.827602\pi\)
0.874888 + 0.484326i \(0.160935\pi\)
\(158\) −4.56581 7.90821i −0.363236 0.629144i
\(159\) −1.66489 −0.132035
\(160\) 0.891491 0.0704786
\(161\) −10.3138 17.8639i −0.812837 1.40788i
\(162\) 3.63818 + 6.30151i 0.285842 + 0.495094i
\(163\) −0.0692542 −0.00542441 −0.00271220 0.999996i \(-0.500863\pi\)
−0.00271220 + 0.999996i \(0.500863\pi\)
\(164\) −3.48932 −0.272470
\(165\) −0.384983 0.666811i −0.0299709 0.0519111i
\(166\) −7.06195 + 12.2317i −0.548114 + 0.949361i
\(167\) −1.08685 1.88248i −0.0841032 0.145671i 0.820906 0.571064i \(-0.193469\pi\)
−0.905009 + 0.425393i \(0.860136\pi\)
\(168\) −0.557537 + 0.965682i −0.0430149 + 0.0745040i
\(169\) −14.3635 + 24.8784i −1.10489 + 1.91372i
\(170\) −3.05092 −0.233995
\(171\) 0 0
\(172\) −6.24669 −0.476306
\(173\) 8.42464 14.5919i 0.640514 1.10940i −0.344804 0.938675i \(-0.612055\pi\)
0.985318 0.170728i \(-0.0546119\pi\)
\(174\) −1.01338 + 1.75523i −0.0768244 + 0.133064i
\(175\) 5.29892 + 9.17799i 0.400560 + 0.693791i
\(176\) −0.975994 + 1.69047i −0.0735684 + 0.127424i
\(177\) 0.628656 + 1.08886i 0.0472526 + 0.0818440i
\(178\) −1.86774 −0.139993
\(179\) 18.9655 1.41755 0.708775 0.705435i \(-0.249248\pi\)
0.708775 + 0.705435i \(0.249248\pi\)
\(180\) −1.24997 2.16501i −0.0931674 0.161371i
\(181\) 0.993436 + 1.72068i 0.0738415 + 0.127897i 0.900582 0.434686i \(-0.143141\pi\)
−0.826740 + 0.562584i \(0.809807\pi\)
\(182\) 16.2793 1.20670
\(183\) 1.08623 0.0802961
\(184\) 4.09252 + 7.08845i 0.301705 + 0.522568i
\(185\) −2.66547 + 4.61673i −0.195969 + 0.339429i
\(186\) 1.94542 + 3.36957i 0.142645 + 0.247069i
\(187\) 3.34011 5.78523i 0.244253 0.423058i
\(188\) 5.27491 9.13641i 0.384712 0.666341i
\(189\) 6.47214 0.470779
\(190\) 0 0
\(191\) −20.9259 −1.51415 −0.757074 0.653329i \(-0.773372\pi\)
−0.757074 + 0.653329i \(0.773372\pi\)
\(192\) 0.221232 0.383185i 0.0159660 0.0276540i
\(193\) −3.89440 + 6.74529i −0.280325 + 0.485537i −0.971465 0.237184i \(-0.923775\pi\)
0.691140 + 0.722721i \(0.257109\pi\)
\(194\) 3.91216 + 6.77606i 0.280877 + 0.486493i
\(195\) 1.27401 2.20665i 0.0912339 0.158022i
\(196\) 0.324429 + 0.561928i 0.0231735 + 0.0401377i
\(197\) 1.82514 0.130036 0.0650180 0.997884i \(-0.479290\pi\)
0.0650180 + 0.997884i \(0.479290\pi\)
\(198\) 5.47382 0.389007
\(199\) −1.17963 2.04317i −0.0836216 0.144837i 0.821181 0.570667i \(-0.193315\pi\)
−0.904803 + 0.425830i \(0.859982\pi\)
\(200\) −2.10262 3.64185i −0.148678 0.257517i
\(201\) 1.18253 0.0834094
\(202\) 5.38487 0.378878
\(203\) −5.77195 9.99731i −0.405111 0.701674i
\(204\) −0.757113 + 1.31136i −0.0530085 + 0.0918134i
\(205\) −1.55535 2.69395i −0.108630 0.188153i
\(206\) −2.34734 + 4.06571i −0.163547 + 0.283271i
\(207\) 11.4764 19.8776i 0.797662 1.38159i
\(208\) −6.45965 −0.447896
\(209\) 0 0
\(210\) −0.994078 −0.0685979
\(211\) 0.180525 0.312679i 0.0124279 0.0215257i −0.859745 0.510724i \(-0.829377\pi\)
0.872172 + 0.489199i \(0.162711\pi\)
\(212\) −1.88139 + 3.25866i −0.129214 + 0.223806i
\(213\) 0.0124864 + 0.0216271i 0.000855554 + 0.00148186i
\(214\) 8.01864 13.8887i 0.548143 0.949411i
\(215\) −2.78444 4.82278i −0.189897 0.328911i
\(216\) −2.56816 −0.174741
\(217\) −22.1612 −1.50440
\(218\) 7.05040 + 12.2116i 0.477513 + 0.827077i
\(219\) −1.54180 2.67048i −0.104185 0.180454i
\(220\) −1.74018 −0.117323
\(221\) 22.1066 1.48705
\(222\) 1.32292 + 2.29137i 0.0887886 + 0.153786i
\(223\) −9.02431 + 15.6306i −0.604312 + 1.04670i 0.387848 + 0.921724i \(0.373219\pi\)
−0.992160 + 0.124976i \(0.960115\pi\)
\(224\) 1.26007 + 2.18251i 0.0841922 + 0.145825i
\(225\) −5.89623 + 10.2126i −0.393082 + 0.680838i
\(226\) −6.36119 + 11.0179i −0.423140 + 0.732900i
\(227\) 12.2845 0.815349 0.407675 0.913127i \(-0.366340\pi\)
0.407675 + 0.913127i \(0.366340\pi\)
\(228\) 0 0
\(229\) 6.79174 0.448811 0.224405 0.974496i \(-0.427956\pi\)
0.224405 + 0.974496i \(0.427956\pi\)
\(230\) −3.64845 + 6.31929i −0.240571 + 0.416682i
\(231\) 1.08831 1.88500i 0.0716052 0.124024i
\(232\) 2.29032 + 3.96695i 0.150367 + 0.260443i
\(233\) −10.7147 + 18.5584i −0.701942 + 1.21580i 0.265842 + 0.964017i \(0.414350\pi\)
−0.967784 + 0.251782i \(0.918983\pi\)
\(234\) 9.05716 + 15.6875i 0.592085 + 1.02552i
\(235\) 9.40507 0.613519
\(236\) 2.84162 0.184973
\(237\) −2.02020 3.49909i −0.131226 0.227291i
\(238\) −4.31230 7.46912i −0.279525 0.484151i
\(239\) −11.8376 −0.765713 −0.382856 0.923808i \(-0.625060\pi\)
−0.382856 + 0.923808i \(0.625060\pi\)
\(240\) 0.394452 0.0254618
\(241\) 10.8732 + 18.8329i 0.700401 + 1.21313i 0.968326 + 0.249691i \(0.0803290\pi\)
−0.267924 + 0.963440i \(0.586338\pi\)
\(242\) −3.59487 + 6.22650i −0.231087 + 0.400254i
\(243\) 5.46200 + 9.46046i 0.350387 + 0.606889i
\(244\) 1.22747 2.12605i 0.0785810 0.136106i
\(245\) −0.289226 + 0.500954i −0.0184780 + 0.0320048i
\(246\) −1.54390 −0.0984353
\(247\) 0 0
\(248\) 8.79360 0.558394
\(249\) −3.12465 + 5.41206i −0.198017 + 0.342975i
\(250\) 4.10320 7.10695i 0.259509 0.449483i
\(251\) −11.8205 20.4737i −0.746104 1.29229i −0.949677 0.313231i \(-0.898589\pi\)
0.203573 0.979060i \(-0.434745\pi\)
\(252\) 3.53353 6.12026i 0.222592 0.385540i
\(253\) −7.98855 13.8366i −0.502236 0.869898i
\(254\) −7.17442 −0.450163
\(255\) −1.34992 −0.0845352
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.461734 + 0.799748i 0.0288022 + 0.0498869i 0.880067 0.474849i \(-0.157497\pi\)
−0.851265 + 0.524736i \(0.824164\pi\)
\(258\) −2.76393 −0.172075
\(259\) −15.0700 −0.936402
\(260\) −2.87936 4.98720i −0.178570 0.309293i
\(261\) 6.42258 11.1242i 0.397548 0.688573i
\(262\) −1.76133 3.05071i −0.108815 0.188473i
\(263\) −2.15984 + 3.74095i −0.133181 + 0.230677i −0.924901 0.380208i \(-0.875853\pi\)
0.791720 + 0.610884i \(0.209186\pi\)
\(264\) −0.431842 + 0.747972i −0.0265780 + 0.0460345i
\(265\) −3.35449 −0.206064
\(266\) 0 0
\(267\) −0.826407 −0.0505753
\(268\) 1.33630 2.31455i 0.0816278 0.141384i
\(269\) 5.39768 9.34905i 0.329102 0.570022i −0.653232 0.757158i \(-0.726587\pi\)
0.982334 + 0.187136i \(0.0599206\pi\)
\(270\) −1.14475 1.98276i −0.0696670 0.120667i
\(271\) −0.403622 + 0.699093i −0.0245183 + 0.0424669i −0.878024 0.478616i \(-0.841139\pi\)
0.853506 + 0.521083i \(0.174472\pi\)
\(272\) 1.71113 + 2.96376i 0.103752 + 0.179705i
\(273\) 7.20298 0.435944
\(274\) 11.0035 0.664749
\(275\) 4.10429 + 7.10885i 0.247498 + 0.428680i
\(276\) 1.81079 + 3.13638i 0.108997 + 0.188788i
\(277\) −9.14869 −0.549691 −0.274846 0.961488i \(-0.588627\pi\)
−0.274846 + 0.961488i \(0.588627\pi\)
\(278\) −21.7586 −1.30499
\(279\) −12.3296 21.3555i −0.738155 1.27852i
\(280\) −1.12334 + 1.94569i −0.0671327 + 0.116277i
\(281\) −10.6079 18.3734i −0.632813 1.09606i −0.986974 0.160880i \(-0.948567\pi\)
0.354161 0.935184i \(-0.384766\pi\)
\(282\) 2.33395 4.04253i 0.138985 0.240729i
\(283\) −2.59493 + 4.49454i −0.154252 + 0.267173i −0.932787 0.360429i \(-0.882630\pi\)
0.778534 + 0.627602i \(0.215964\pi\)
\(284\) 0.0564404 0.00334912
\(285\) 0 0
\(286\) 12.6092 0.745596
\(287\) 4.39680 7.61548i 0.259535 0.449528i
\(288\) −1.40211 + 2.42853i −0.0826203 + 0.143103i
\(289\) 2.64407 + 4.57966i 0.155533 + 0.269392i
\(290\) −2.04180 + 3.53651i −0.119899 + 0.207671i
\(291\) 1.73099 + 2.99816i 0.101472 + 0.175755i
\(292\) −6.96917 −0.407840
\(293\) −17.5660 −1.02621 −0.513107 0.858324i \(-0.671506\pi\)
−0.513107 + 0.858324i \(0.671506\pi\)
\(294\) 0.143548 + 0.248633i 0.00837190 + 0.0145006i
\(295\) 1.26664 + 2.19388i 0.0737465 + 0.127733i
\(296\) 5.97980 0.347569
\(297\) 5.01302 0.290885
\(298\) 7.19479 + 12.4617i 0.416783 + 0.721889i
\(299\) 26.4362 45.7889i 1.52885 2.64804i
\(300\) −0.930333 1.61138i −0.0537128 0.0930333i
\(301\) 7.87129 13.6335i 0.453693 0.785820i
\(302\) 6.20338 10.7446i 0.356964 0.618280i
\(303\) 2.38261 0.136877
\(304\) 0 0
\(305\) 2.18857 0.125317
\(306\) 4.79840 8.31106i 0.274306 0.475112i
\(307\) 10.7842 18.6787i 0.615486 1.06605i −0.374813 0.927100i \(-0.622293\pi\)
0.990299 0.138952i \(-0.0443734\pi\)
\(308\) −2.45965 4.26024i −0.140152 0.242750i
\(309\) −1.03861 + 1.79893i −0.0590846 + 0.102337i
\(310\) 3.91971 + 6.78914i 0.222625 + 0.385597i
\(311\) −2.57368 −0.145940 −0.0729701 0.997334i \(-0.523248\pi\)
−0.0729701 + 0.997334i \(0.523248\pi\)
\(312\) −2.85816 −0.161811
\(313\) 2.59194 + 4.48938i 0.146505 + 0.253755i 0.929934 0.367728i \(-0.119864\pi\)
−0.783428 + 0.621482i \(0.786531\pi\)
\(314\) −0.225610 0.390768i −0.0127319 0.0220523i
\(315\) 6.30023 0.354977
\(316\) −9.13162 −0.513694
\(317\) 10.1281 + 17.5423i 0.568850 + 0.985276i 0.996680 + 0.0814174i \(0.0259447\pi\)
−0.427830 + 0.903859i \(0.640722\pi\)
\(318\) −0.832446 + 1.44184i −0.0466813 + 0.0808543i
\(319\) −4.47068 7.74345i −0.250310 0.433550i
\(320\) 0.445746 0.772054i 0.0249179 0.0431591i
\(321\) 3.54795 6.14524i 0.198028 0.342994i
\(322\) −20.6275 −1.14953
\(323\) 0 0
\(324\) 7.27636 0.404242
\(325\) −13.5822 + 23.5251i −0.753405 + 1.30494i
\(326\) −0.0346271 + 0.0599759i −0.00191782 + 0.00332176i
\(327\) 3.11954 + 5.40321i 0.172511 + 0.298798i
\(328\) −1.74466 + 3.02184i −0.0963328 + 0.166853i
\(329\) 13.2935 + 23.0251i 0.732897 + 1.26941i
\(330\) −0.769967 −0.0423853
\(331\) −21.3280 −1.17229 −0.586146 0.810205i \(-0.699356\pi\)
−0.586146 + 0.810205i \(0.699356\pi\)
\(332\) 7.06195 + 12.2317i 0.387575 + 0.671299i
\(333\) −8.38435 14.5221i −0.459460 0.795807i
\(334\) −2.17371 −0.118940
\(335\) 2.38261 0.130176
\(336\) 0.557537 + 0.965682i 0.0304161 + 0.0526822i
\(337\) 11.3637 19.6826i 0.619022 1.07218i −0.370642 0.928776i \(-0.620862\pi\)
0.989665 0.143402i \(-0.0458042\pi\)
\(338\) 14.3635 + 24.8784i 0.781273 + 1.35321i
\(339\) −2.81459 + 4.87502i −0.152868 + 0.264775i
\(340\) −1.52546 + 2.64217i −0.0827296 + 0.143292i
\(341\) −17.1650 −0.929538
\(342\) 0 0
\(343\) −19.2762 −1.04082
\(344\) −3.12334 + 5.40979i −0.168399 + 0.291676i
\(345\) −1.61430 + 2.79606i −0.0869112 + 0.150535i
\(346\) −8.42464 14.5919i −0.452912 0.784466i
\(347\) 2.46428 4.26825i 0.132289 0.229132i −0.792269 0.610171i \(-0.791101\pi\)
0.924559 + 0.381040i \(0.124434\pi\)
\(348\) 1.01338 + 1.75523i 0.0543231 + 0.0940903i
\(349\) 26.1615 1.40039 0.700197 0.713950i \(-0.253096\pi\)
0.700197 + 0.713950i \(0.253096\pi\)
\(350\) 10.5978 0.566478
\(351\) 8.29470 + 14.3668i 0.442738 + 0.766845i
\(352\) 0.975994 + 1.69047i 0.0520207 + 0.0901025i
\(353\) 2.70813 0.144139 0.0720697 0.997400i \(-0.477040\pi\)
0.0720697 + 0.997400i \(0.477040\pi\)
\(354\) 1.25731 0.0668253
\(355\) 0.0251581 + 0.0435750i 0.00133525 + 0.00231272i
\(356\) −0.933870 + 1.61751i −0.0494950 + 0.0857279i
\(357\) −1.90803 3.30481i −0.100984 0.174909i
\(358\) 9.48276 16.4246i 0.501179 0.868068i
\(359\) 4.65501 8.06272i 0.245682 0.425534i −0.716641 0.697442i \(-0.754321\pi\)
0.962323 + 0.271908i \(0.0876547\pi\)
\(360\) −2.49994 −0.131759
\(361\) 0 0
\(362\) 1.98687 0.104428
\(363\) −1.59060 + 2.75500i −0.0834848 + 0.144600i
\(364\) 8.13963 14.0983i 0.426633 0.738950i
\(365\) −3.10648 5.38058i −0.162601 0.281632i
\(366\) 0.543113 0.940699i 0.0283890 0.0491711i
\(367\) −3.87721 6.71552i −0.202389 0.350548i 0.746909 0.664926i \(-0.231537\pi\)
−0.949298 + 0.314379i \(0.898204\pi\)
\(368\) 8.18504 0.426675
\(369\) 9.78485 0.509379
\(370\) 2.66547 + 4.61673i 0.138571 + 0.240012i
\(371\) −4.74138 8.21231i −0.246160 0.426362i
\(372\) 3.89085 0.201731
\(373\) −25.0124 −1.29509 −0.647546 0.762027i \(-0.724205\pi\)
−0.647546 + 0.762027i \(0.724205\pi\)
\(374\) −3.34011 5.78523i −0.172713 0.299147i
\(375\) 1.81552 3.14456i 0.0937528 0.162385i
\(376\) −5.27491 9.13641i −0.272033 0.471174i
\(377\) 14.7947 25.6251i 0.761965 1.31976i
\(378\) 3.23607 5.60503i 0.166445 0.288292i
\(379\) 19.1802 0.985222 0.492611 0.870250i \(-0.336043\pi\)
0.492611 + 0.870250i \(0.336043\pi\)
\(380\) 0 0
\(381\) −3.17442 −0.162630
\(382\) −10.4630 + 18.1224i −0.535332 + 0.927222i
\(383\) 2.41659 4.18566i 0.123482 0.213877i −0.797656 0.603112i \(-0.793927\pi\)
0.921139 + 0.389235i \(0.127261\pi\)
\(384\) −0.221232 0.383185i −0.0112897 0.0195543i
\(385\) 2.19276 3.79797i 0.111753 0.193562i
\(386\) 3.89440 + 6.74529i 0.198220 + 0.343326i
\(387\) 17.5171 0.890446
\(388\) 7.82432 0.397219
\(389\) −10.8646 18.8180i −0.550855 0.954109i −0.998213 0.0597540i \(-0.980968\pi\)
0.447358 0.894355i \(-0.352365\pi\)
\(390\) −1.27401 2.20665i −0.0645121 0.111738i
\(391\) −28.0113 −1.41659
\(392\) 0.648859 0.0327723
\(393\) −0.779323 1.34983i −0.0393116 0.0680898i
\(394\) 0.912571 1.58062i 0.0459747 0.0796304i
\(395\) −4.07038 7.05010i −0.204803 0.354729i
\(396\) 2.73691 4.74047i 0.137535 0.238217i
\(397\) −5.85701 + 10.1446i −0.293955 + 0.509145i −0.974741 0.223337i \(-0.928305\pi\)
0.680786 + 0.732482i \(0.261638\pi\)
\(398\) −2.35926 −0.118259
\(399\) 0 0
\(400\) −4.20524 −0.210262
\(401\) 5.90617 10.2298i 0.294940 0.510851i −0.680031 0.733183i \(-0.738034\pi\)
0.974971 + 0.222332i \(0.0713670\pi\)
\(402\) 0.591266 1.02410i 0.0294897 0.0510776i
\(403\) −28.4018 49.1934i −1.41479 2.45050i
\(404\) 2.69244 4.66343i 0.133954 0.232015i
\(405\) 3.24341 + 5.61775i 0.161166 + 0.279148i
\(406\) −11.5439 −0.572914
\(407\) −11.6725 −0.578584
\(408\) 0.757113 + 1.31136i 0.0374827 + 0.0649219i
\(409\) −12.6331 21.8812i −0.624668 1.08196i −0.988605 0.150534i \(-0.951901\pi\)
0.363937 0.931424i \(-0.381432\pi\)
\(410\) −3.11070 −0.153627
\(411\) 4.86867 0.240154
\(412\) 2.34734 + 4.06571i 0.115645 + 0.200303i
\(413\) −3.58064 + 6.20186i −0.176192 + 0.305173i
\(414\) −11.4764 19.8776i −0.564032 0.976932i
\(415\) −6.29567 + 10.9044i −0.309042 + 0.535277i
\(416\) −3.22982 + 5.59422i −0.158355 + 0.274279i
\(417\) −9.62739 −0.471455
\(418\) 0 0
\(419\) 31.6143 1.54446 0.772229 0.635344i \(-0.219142\pi\)
0.772229 + 0.635344i \(0.219142\pi\)
\(420\) −0.497039 + 0.860897i −0.0242530 + 0.0420075i
\(421\) 1.09486 1.89635i 0.0533602 0.0924226i −0.838112 0.545499i \(-0.816340\pi\)
0.891472 + 0.453076i \(0.149674\pi\)
\(422\) −0.180525 0.312679i −0.00878783 0.0152210i
\(423\) −14.7920 + 25.6206i −0.719214 + 1.24571i
\(424\) 1.88139 + 3.25866i 0.0913684 + 0.158255i
\(425\) 14.3914 0.698087
\(426\) 0.0249728 0.00120994
\(427\) 3.09342 + 5.35796i 0.149701 + 0.259290i
\(428\) −8.01864 13.8887i −0.387596 0.671335i
\(429\) 5.57909 0.269361
\(430\) −5.56887 −0.268555
\(431\) 0.901858 + 1.56206i 0.0434410 + 0.0752420i 0.886928 0.461907i \(-0.152835\pi\)
−0.843487 + 0.537149i \(0.819501\pi\)
\(432\) −1.28408 + 2.22409i −0.0617803 + 0.107007i
\(433\) 3.28616 + 5.69180i 0.157923 + 0.273531i 0.934120 0.356960i \(-0.116187\pi\)
−0.776197 + 0.630491i \(0.782854\pi\)
\(434\) −11.0806 + 19.1921i −0.531885 + 0.921252i
\(435\) −0.903423 + 1.56477i −0.0433158 + 0.0750252i
\(436\) 14.1008 0.675305
\(437\) 0 0
\(438\) −3.08361 −0.147340
\(439\) 4.56530 7.90733i 0.217890 0.377396i −0.736273 0.676685i \(-0.763416\pi\)
0.954163 + 0.299289i \(0.0967493\pi\)
\(440\) −0.870091 + 1.50704i −0.0414799 + 0.0718454i
\(441\) −0.909774 1.57577i −0.0433226 0.0750369i
\(442\) 11.0533 19.1449i 0.525752 0.910629i
\(443\) 13.7343 + 23.7885i 0.652536 + 1.13023i 0.982505 + 0.186235i \(0.0596284\pi\)
−0.329969 + 0.943992i \(0.607038\pi\)
\(444\) 2.64584 0.125566
\(445\) −1.66508 −0.0789321
\(446\) 9.02431 + 15.6306i 0.427313 + 0.740128i
\(447\) 3.18343 + 5.51386i 0.150571 + 0.260797i
\(448\) 2.52015 0.119066
\(449\) −7.57293 −0.357389 −0.178694 0.983905i \(-0.557187\pi\)
−0.178694 + 0.983905i \(0.557187\pi\)
\(450\) 5.89623 + 10.2126i 0.277951 + 0.481425i
\(451\) 3.40556 5.89860i 0.160362 0.277754i
\(452\) 6.36119 + 11.0179i 0.299205 + 0.518238i
\(453\) 2.74477 4.75408i 0.128960 0.223366i
\(454\) 6.14224 10.6387i 0.288270 0.499297i
\(455\) 14.5128 0.680372
\(456\) 0 0
\(457\) −21.7675 −1.01824 −0.509120 0.860696i \(-0.670029\pi\)
−0.509120 + 0.860696i \(0.670029\pi\)
\(458\) 3.39587 5.88182i 0.158679 0.274839i
\(459\) 4.39445 7.61141i 0.205115 0.355270i
\(460\) 3.64845 + 6.31929i 0.170110 + 0.294639i
\(461\) −5.97219 + 10.3441i −0.278153 + 0.481775i −0.970926 0.239381i \(-0.923055\pi\)
0.692773 + 0.721156i \(0.256389\pi\)
\(462\) −1.08831 1.88500i −0.0506325 0.0876981i
\(463\) −8.75371 −0.406819 −0.203410 0.979094i \(-0.565202\pi\)
−0.203410 + 0.979094i \(0.565202\pi\)
\(464\) 4.58064 0.212651
\(465\) 1.73433 + 3.00395i 0.0804276 + 0.139305i
\(466\) 10.7147 + 18.5584i 0.496348 + 0.859700i
\(467\) 29.3568 1.35847 0.679236 0.733920i \(-0.262311\pi\)
0.679236 + 0.733920i \(0.262311\pi\)
\(468\) 18.1143 0.837335
\(469\) 3.36768 + 5.83300i 0.155505 + 0.269343i
\(470\) 4.70254 8.14503i 0.216912 0.375702i
\(471\) −0.0998242 0.172901i −0.00459966 0.00796684i
\(472\) 1.42081 2.46091i 0.0653980 0.113273i
\(473\) 6.09673 10.5599i 0.280328 0.485543i
\(474\) −4.04041 −0.185582
\(475\) 0 0
\(476\) −8.62460 −0.395308
\(477\) 5.27584 9.13803i 0.241564 0.418401i
\(478\) −5.91881 + 10.2517i −0.270720 + 0.468901i
\(479\) 12.4352 + 21.5385i 0.568180 + 0.984117i 0.996746 + 0.0806064i \(0.0256857\pi\)
−0.428566 + 0.903511i \(0.640981\pi\)
\(480\) 0.197226 0.341606i 0.00900210 0.0155921i
\(481\) −19.3137 33.4523i −0.880629 1.52529i
\(482\) 21.7463 0.990517
\(483\) −9.12692 −0.415289
\(484\) 3.59487 + 6.22650i 0.163403 + 0.283023i
\(485\) 3.48766 + 6.04080i 0.158366 + 0.274298i
\(486\) 10.9240 0.495523
\(487\) −8.53766 −0.386878 −0.193439 0.981112i \(-0.561964\pi\)
−0.193439 + 0.981112i \(0.561964\pi\)
\(488\) −1.22747 2.12605i −0.0555652 0.0962417i
\(489\) −0.0153212 + 0.0265371i −0.000692850 + 0.00120005i
\(490\) 0.289226 + 0.500954i 0.0130659 + 0.0226308i
\(491\) 5.76985 9.99368i 0.260390 0.451008i −0.705956 0.708256i \(-0.749482\pi\)
0.966346 + 0.257248i \(0.0828156\pi\)
\(492\) −0.771949 + 1.33705i −0.0348021 + 0.0602791i
\(493\) −15.6762 −0.706019
\(494\) 0 0
\(495\) 4.87986 0.219333
\(496\) 4.39680 7.61548i 0.197422 0.341945i
\(497\) −0.0711190 + 0.123182i −0.00319013 + 0.00552546i
\(498\) 3.12465 + 5.41206i 0.140019 + 0.242520i
\(499\) 14.8045 25.6422i 0.662742 1.14790i −0.317151 0.948375i \(-0.602726\pi\)
0.979892 0.199527i \(-0.0639406\pi\)
\(500\) −4.10320 7.10695i −0.183501 0.317832i
\(501\) −0.961785 −0.0429694
\(502\) −23.6410 −1.05515
\(503\) −2.93414 5.08207i −0.130827 0.226598i 0.793169 0.609002i \(-0.208430\pi\)
−0.923995 + 0.382403i \(0.875096\pi\)
\(504\) −3.53353 6.12026i −0.157396 0.272618i
\(505\) 4.80057 0.213622
\(506\) −15.9771 −0.710269
\(507\) 6.35534 + 11.0078i 0.282251 + 0.488872i
\(508\) −3.58721 + 6.21323i −0.159157 + 0.275667i
\(509\) −12.7843 22.1431i −0.566656 0.981477i −0.996893 0.0787614i \(-0.974903\pi\)
0.430237 0.902716i \(-0.358430\pi\)
\(510\) −0.674959 + 1.16906i −0.0298877 + 0.0517670i
\(511\) 8.78167 15.2103i 0.388478 0.672864i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 0.923469 0.0407325
\(515\) −2.09263 + 3.62455i −0.0922124 + 0.159717i
\(516\) −1.38197 + 2.39364i −0.0608377 + 0.105374i
\(517\) 10.2966 + 17.8342i 0.452842 + 0.784346i
\(518\) −7.53498 + 13.0510i −0.331068 + 0.573427i
\(519\) −3.72760 6.45639i −0.163623 0.283404i
\(520\) −5.75872 −0.252537
\(521\) 14.0332 0.614807 0.307403 0.951579i \(-0.400540\pi\)
0.307403 + 0.951579i \(0.400540\pi\)
\(522\) −6.42258 11.1242i −0.281109 0.486895i
\(523\) 15.5392 + 26.9147i 0.679482 + 1.17690i 0.975137 + 0.221602i \(0.0711286\pi\)
−0.295655 + 0.955295i \(0.595538\pi\)
\(524\) −3.52265 −0.153888
\(525\) 4.68915 0.204651
\(526\) 2.15984 + 3.74095i 0.0941734 + 0.163113i
\(527\) −15.0470 + 26.0622i −0.655458 + 1.13529i
\(528\) 0.431842 + 0.747972i 0.0187935 + 0.0325513i
\(529\) −21.9974 + 38.1007i −0.956410 + 1.65655i
\(530\) −1.67724 + 2.90507i −0.0728548 + 0.126188i
\(531\) −7.96853 −0.345805
\(532\) 0 0
\(533\) 22.5398 0.976307
\(534\) −0.413204 + 0.715690i −0.0178811 + 0.0309709i
\(535\) 7.14855 12.3816i 0.309059 0.535305i
\(536\) −1.33630 2.31455i −0.0577196 0.0999732i
\(537\) 4.19577 7.26729i 0.181061 0.313607i
\(538\) −5.39768 9.34905i −0.232710 0.403066i
\(539\) −1.26657 −0.0545548
\(540\) −2.28949 −0.0985240
\(541\) −1.44804 2.50808i −0.0622561 0.107831i 0.833217 0.552945i \(-0.186496\pi\)
−0.895474 + 0.445115i \(0.853163\pi\)
\(542\) 0.403622 + 0.699093i 0.0173370 + 0.0300286i
\(543\) 0.879118 0.0377266
\(544\) 3.42226 0.146728
\(545\) 6.28537 + 10.8866i 0.269236 + 0.466330i
\(546\) 3.60149 6.23796i 0.154130 0.266960i
\(547\) 15.1931 + 26.3151i 0.649608 + 1.12515i 0.983217 + 0.182443i \(0.0584004\pi\)
−0.333608 + 0.942712i \(0.608266\pi\)
\(548\) 5.50177 9.52935i 0.235024 0.407074i
\(549\) −3.44212 + 5.96192i −0.146906 + 0.254449i
\(550\) 8.20859 0.350015
\(551\) 0 0
\(552\) 3.62158 0.154145
\(553\) 11.5065 19.9299i 0.489306 0.847504i
\(554\) −4.57434 + 7.92300i −0.194345 + 0.336616i
\(555\) 1.17937 + 2.04273i 0.0500616 + 0.0867092i
\(556\) −10.8793 + 18.8435i −0.461385 + 0.799143i
\(557\) 3.06706 + 5.31231i 0.129956 + 0.225090i 0.923659 0.383215i \(-0.125183\pi\)
−0.793704 + 0.608305i \(0.791850\pi\)
\(558\) −24.6593 −1.04391
\(559\) 40.3514 1.70668
\(560\) 1.12334 + 1.94569i 0.0474700 + 0.0822204i
\(561\) −1.47788 2.55976i −0.0623959 0.108073i
\(562\) −21.2158 −0.894932
\(563\) 28.1917 1.18814 0.594069 0.804414i \(-0.297521\pi\)
0.594069 + 0.804414i \(0.297521\pi\)
\(564\) −2.33395 4.04253i −0.0982772 0.170221i
\(565\) −5.67094 + 9.82236i −0.238578 + 0.413230i
\(566\) 2.59493 + 4.49454i 0.109073 + 0.188920i
\(567\) −9.16875 + 15.8807i −0.385051 + 0.666929i
\(568\) 0.0282202 0.0488788i 0.00118409 0.00205091i
\(569\) 42.1145 1.76553 0.882766 0.469812i \(-0.155678\pi\)
0.882766 + 0.469812i \(0.155678\pi\)
\(570\) 0 0
\(571\) 0.166927 0.00698566 0.00349283 0.999994i \(-0.498888\pi\)
0.00349283 + 0.999994i \(0.498888\pi\)
\(572\) 6.30458 10.9199i 0.263608 0.456582i
\(573\) −4.62948 + 8.01850i −0.193399 + 0.334977i
\(574\) −4.39680 7.61548i −0.183519 0.317864i
\(575\) 17.2100 29.8087i 0.717708 1.24311i
\(576\) 1.40211 + 2.42853i 0.0584214 + 0.101189i
\(577\) −19.9631 −0.831076 −0.415538 0.909576i \(-0.636407\pi\)
−0.415538 + 0.909576i \(0.636407\pi\)
\(578\) 5.28814 0.219957
\(579\) 1.72313 + 2.98455i 0.0716108 + 0.124033i
\(580\) 2.04180 + 3.53651i 0.0847812 + 0.146845i
\(581\) −35.5943 −1.47670
\(582\) 3.46197 0.143503
\(583\) −3.67245 6.36087i −0.152097 0.263440i
\(584\) −3.48459 + 6.03548i −0.144193 + 0.249750i
\(585\) 8.07438 + 13.9852i 0.333835 + 0.578218i
\(586\) −8.78298 + 15.2126i −0.362822 + 0.628426i
\(587\) −5.07202 + 8.78499i −0.209345 + 0.362595i −0.951508 0.307623i \(-0.900466\pi\)
0.742164 + 0.670219i \(0.233800\pi\)
\(588\) 0.287096 0.0118397
\(589\) 0 0
\(590\) 2.53328 0.104293
\(591\) 0.403779 0.699366i 0.0166093 0.0287681i
\(592\) 2.98990 5.17866i 0.122884 0.212841i
\(593\) −3.72658 6.45462i −0.153032 0.265060i 0.779309 0.626640i \(-0.215570\pi\)
−0.932341 + 0.361581i \(0.882237\pi\)
\(594\) 2.50651 4.34140i 0.102843 0.178130i
\(595\) −3.84438 6.65866i −0.157604 0.272978i
\(596\) 14.3896 0.589420
\(597\) −1.04388 −0.0427233
\(598\) −26.4362 45.7889i −1.08106 1.87245i
\(599\) −3.18571 5.51781i −0.130164 0.225451i 0.793575 0.608472i \(-0.208217\pi\)
−0.923740 + 0.383020i \(0.874884\pi\)
\(600\) −1.86067 −0.0759614
\(601\) −1.74631 −0.0712333 −0.0356166 0.999366i \(-0.511340\pi\)
−0.0356166 + 0.999366i \(0.511340\pi\)
\(602\) −7.87129 13.6335i −0.320810 0.555659i
\(603\) −3.74730 + 6.49052i −0.152602 + 0.264314i
\(604\) −6.20338 10.7446i −0.252412 0.437190i
\(605\) −3.20480 + 5.55087i −0.130293 + 0.225675i
\(606\) 1.19130 2.06340i 0.0483934 0.0838199i
\(607\) −32.1612 −1.30538 −0.652691 0.757624i \(-0.726360\pi\)
−0.652691 + 0.757624i \(0.726360\pi\)
\(608\) 0 0
\(609\) −5.10775 −0.206977
\(610\) 1.09428 1.89535i 0.0443062 0.0767407i
\(611\) −34.0741 + 59.0180i −1.37849 + 2.38761i
\(612\) −4.79840 8.31106i −0.193964 0.335955i
\(613\) −6.38223 + 11.0543i −0.257776 + 0.446481i −0.965646 0.259862i \(-0.916323\pi\)
0.707870 + 0.706343i \(0.249656\pi\)
\(614\) −10.7842 18.6787i −0.435214 0.753813i
\(615\) −1.37637 −0.0555007
\(616\) −4.91930 −0.198204
\(617\) 0.841616 + 1.45772i 0.0338822 + 0.0586856i 0.882469 0.470370i \(-0.155880\pi\)
−0.848587 + 0.529056i \(0.822546\pi\)
\(618\) 1.03861 + 1.79893i 0.0417791 + 0.0723635i
\(619\) 31.5285 1.26724 0.633618 0.773646i \(-0.281569\pi\)
0.633618 + 0.773646i \(0.281569\pi\)
\(620\) 7.83942 0.314839
\(621\) −10.5102 18.2043i −0.421761 0.730512i
\(622\) −1.28684 + 2.22887i −0.0515976 + 0.0893697i
\(623\) −2.35349 4.07637i −0.0942906 0.163316i
\(624\) −1.42908 + 2.47524i −0.0572090 + 0.0990888i
\(625\) −6.85514 + 11.8735i −0.274206 + 0.474938i
\(626\) 5.18389 0.207190
\(627\) 0 0
\(628\) −0.451220 −0.0180056
\(629\) −10.2322 + 17.7227i −0.407985 + 0.706651i
\(630\) 3.15011 5.45616i 0.125503 0.217378i
\(631\) 15.8831 + 27.5103i 0.632297 + 1.09517i 0.987081 + 0.160222i \(0.0512209\pi\)
−0.354785 + 0.934948i \(0.615446\pi\)
\(632\) −4.56581 + 7.90821i −0.181618 + 0.314572i
\(633\) −0.0798758 0.138349i −0.00317478 0.00549888i
\(634\) 20.2562 0.804475
\(635\) −6.39593 −0.253815
\(636\) 0.832446 + 1.44184i 0.0330086 + 0.0571726i
\(637\) −2.09570 3.62986i −0.0830347 0.143820i
\(638\) −8.94137 −0.353992
\(639\) −0.158272 −0.00626113
\(640\) −0.445746 0.772054i −0.0176196 0.0305181i
\(641\) −20.2219 + 35.0253i −0.798715 + 1.38342i 0.121738 + 0.992562i \(0.461153\pi\)
−0.920453 + 0.390853i \(0.872180\pi\)
\(642\) −3.54795 6.14524i −0.140027 0.242533i
\(643\) 13.0516 22.6061i 0.514706 0.891497i −0.485148 0.874432i \(-0.661234\pi\)
0.999854 0.0170651i \(-0.00543224\pi\)
\(644\) −10.3138 + 17.8639i −0.406419 + 0.703938i
\(645\) −2.46402 −0.0970208
\(646\) 0 0
\(647\) −48.7713 −1.91740 −0.958699 0.284423i \(-0.908198\pi\)
−0.958699 + 0.284423i \(0.908198\pi\)
\(648\) 3.63818 6.30151i 0.142921 0.247547i
\(649\) −2.77340 + 4.80367i −0.108866 + 0.188561i
\(650\) 13.5822 + 23.5251i 0.532738 + 0.922729i
\(651\) −4.90276 + 8.49182i −0.192154 + 0.332821i
\(652\) 0.0346271 + 0.0599759i 0.00135610 + 0.00234884i
\(653\) −43.1831 −1.68988 −0.844942 0.534858i \(-0.820365\pi\)
−0.844942 + 0.534858i \(0.820365\pi\)
\(654\) 6.23909 0.243968
\(655\) −1.57021 2.71968i −0.0613531 0.106267i
\(656\) 1.74466 + 3.02184i 0.0681176 + 0.117983i
\(657\) 19.5431 0.762451
\(658\) 26.5871 1.03647
\(659\) −7.13844 12.3641i −0.278074 0.481638i 0.692832 0.721099i \(-0.256363\pi\)
−0.970906 + 0.239461i \(0.923029\pi\)
\(660\) −0.384983 + 0.666811i −0.0149855 + 0.0259556i
\(661\) 17.8748 + 30.9601i 0.695251 + 1.20421i 0.970096 + 0.242721i \(0.0780399\pi\)
−0.274846 + 0.961488i \(0.588627\pi\)
\(662\) −10.6640 + 18.4706i −0.414468 + 0.717880i
\(663\) 4.89068 8.47091i 0.189938 0.328983i
\(664\) 14.1239 0.548114
\(665\) 0 0
\(666\) −16.7687 −0.649774
\(667\) −18.7464 + 32.4697i −0.725863 + 1.25723i
\(668\) −1.08685 + 1.88248i −0.0420516 + 0.0728355i
\(669\) 3.99293 + 6.91595i 0.154375 + 0.267386i
\(670\) 1.19130 2.06340i 0.0460241 0.0797161i
\(671\) 2.39602 + 4.15002i 0.0924972 + 0.160210i
\(672\) 1.11507 0.0430149
\(673\) −10.3574 −0.399248 −0.199624 0.979873i \(-0.563972\pi\)
−0.199624 + 0.979873i \(0.563972\pi\)
\(674\) −11.3637 19.6826i −0.437715 0.758144i
\(675\) 5.39986 + 9.35284i 0.207841 + 0.359991i
\(676\) 28.7271 1.10489
\(677\) 10.7171 0.411891 0.205945 0.978564i \(-0.433973\pi\)
0.205945 + 0.978564i \(0.433973\pi\)
\(678\) 2.81459 + 4.87502i 0.108094 + 0.187224i
\(679\) −9.85921 + 17.0767i −0.378362 + 0.655342i
\(680\) 1.52546 + 2.64217i 0.0584986 + 0.101323i
\(681\) 2.71772 4.70722i 0.104143 0.180381i
\(682\) −8.58251 + 14.8653i −0.328641 + 0.569223i
\(683\) −0.122930 −0.00470377 −0.00235188 0.999997i \(-0.500749\pi\)
−0.00235188 + 0.999997i \(0.500749\pi\)
\(684\) 0 0
\(685\) 9.80957 0.374804
\(686\) −9.63812 + 16.6937i −0.367985 + 0.637369i
\(687\) 1.50255 2.60249i 0.0573258 0.0992912i
\(688\) 3.12334 + 5.40979i 0.119076 + 0.206246i
\(689\) 12.1531 21.0498i 0.462997 0.801934i
\(690\) 1.61430 + 2.79606i 0.0614555 + 0.106444i
\(691\) −25.2815 −0.961752 −0.480876 0.876789i \(-0.659681\pi\)
−0.480876 + 0.876789i \(0.659681\pi\)
\(692\) −16.8493 −0.640514
\(693\) 6.89741 + 11.9467i 0.262011 + 0.453816i
\(694\) −2.46428 4.26825i −0.0935427 0.162021i
\(695\) −19.3976 −0.735793
\(696\) 2.02677 0.0768244
\(697\) −5.97068 10.3415i −0.226156 0.391713i
\(698\) 13.0808 22.6565i 0.495114 0.857562i
\(699\) 4.74085 + 8.21140i 0.179316 + 0.310584i
\(700\) 5.29892 9.17799i 0.200280 0.346895i
\(701\) 2.58643 4.47984i 0.0976883 0.169201i −0.813039 0.582209i \(-0.802189\pi\)
0.910727 + 0.413008i \(0.135522\pi\)
\(702\) 16.5894 0.626127
\(703\) 0 0
\(704\) 1.95199 0.0735684
\(705\) 2.08070 3.60388i 0.0783637 0.135730i
\(706\) 1.35407 2.34531i 0.0509610 0.0882670i
\(707\) 6.78533 + 11.7525i 0.255189 + 0.442000i
\(708\) 0.628656 1.08886i 0.0236263 0.0409220i
\(709\) 14.9954 + 25.9727i 0.563162 + 0.975426i 0.997218 + 0.0745396i \(0.0237487\pi\)
−0.434056 + 0.900886i \(0.642918\pi\)
\(710\) 0.0503161 0.00188833
\(711\) 25.6071 0.960342
\(712\) 0.933870 + 1.61751i 0.0349983 + 0.0606188i
\(713\) 35.9880 + 62.3330i 1.34776 + 2.33439i
\(714\) −3.81607 −0.142813
\(715\) 11.2410 0.420388
\(716\) −9.48276 16.4246i −0.354387 0.613817i
\(717\) −2.61886 + 4.53600i −0.0978031 + 0.169400i
\(718\) −4.65501 8.06272i −0.173723 0.300898i
\(719\) 11.3516 19.6616i 0.423344 0.733254i −0.572920 0.819611i \(-0.694189\pi\)
0.996264 + 0.0863576i \(0.0275228\pi\)
\(720\) −1.24997 + 2.16501i −0.0465837 + 0.0806853i
\(721\) −11.8313 −0.440620
\(722\) 0 0
\(723\) 9.62195 0.357844
\(724\) 0.993436 1.72068i 0.0369207 0.0639486i
\(725\) 9.63136 16.6820i 0.357700 0.619554i
\(726\) 1.59060 + 2.75500i 0.0590326 + 0.102248i
\(727\) −18.2969 + 31.6911i −0.678593 + 1.17536i 0.296811 + 0.954936i \(0.404077\pi\)
−0.975405 + 0.220422i \(0.929257\pi\)
\(728\) −8.13963 14.0983i −0.301675 0.522516i
\(729\) −16.9956 −0.629467
\(730\) −6.21296 −0.229952
\(731\) −10.6889 18.5137i −0.395343 0.684754i
\(732\) −0.543113 0.940699i −0.0200740 0.0347692i
\(733\) 21.1522 0.781275 0.390637 0.920545i \(-0.372255\pi\)
0.390637 + 0.920545i \(0.372255\pi\)
\(734\) −7.75442 −0.286221
\(735\) 0.127972 + 0.221654i 0.00472032 + 0.00817583i
\(736\) 4.09252 7.08845i 0.150852 0.261284i
\(737\) 2.60845 + 4.51797i 0.0960836 + 0.166422i
\(738\) 4.89242 8.47393i 0.180093 0.311930i
\(739\) −24.1533 + 41.8348i −0.888494 + 1.53892i −0.0468384 + 0.998902i \(0.514915\pi\)
−0.841656 + 0.540014i \(0.818419\pi\)
\(740\) 5.33094 0.195969
\(741\) 0 0
\(742\) −9.48276 −0.348123
\(743\) 15.9299 27.5914i 0.584412 1.01223i −0.410536 0.911844i \(-0.634659\pi\)
0.994948 0.100387i \(-0.0320082\pi\)
\(744\) 1.94542 3.36957i 0.0713227 0.123535i
\(745\) 6.41409 + 11.1095i 0.234994 + 0.407022i
\(746\) −12.5062 + 21.6614i −0.457884 + 0.793078i
\(747\) −19.8033 34.3003i −0.724565 1.25498i
\(748\) −6.68021 −0.244253
\(749\) 40.4163 1.47678
\(750\) −1.81552 3.14456i −0.0662932 0.114823i
\(751\) −20.4981 35.5038i −0.747987 1.29555i −0.948786 0.315919i \(-0.897687\pi\)
0.200799 0.979632i \(-0.435646\pi\)
\(752\) −10.5498 −0.384712
\(753\) −10.4603 −0.381194
\(754\) −14.7947 25.6251i −0.538790 0.933212i
\(755\) 5.53026 9.57869i 0.201267 0.348604i
\(756\) −3.23607 5.60503i −0.117695 0.203853i
\(757\) 6.41076 11.1038i 0.233003 0.403573i −0.725687 0.688025i \(-0.758478\pi\)
0.958690 + 0.284451i \(0.0918114\pi\)
\(758\) 9.59011 16.6106i 0.348329 0.603323i
\(759\) −7.06929 −0.256599
\(760\) 0 0
\(761\) 35.6382 1.29188 0.645942 0.763386i \(-0.276465\pi\)
0.645942 + 0.763386i \(0.276465\pi\)
\(762\) −1.58721 + 2.74913i −0.0574985 + 0.0995903i
\(763\) −17.7680 + 30.7751i −0.643246 + 1.11413i
\(764\) 10.4630 + 18.1224i 0.378537 + 0.655645i
\(765\) 4.27773 7.40924i 0.154662 0.267882i
\(766\) −2.41659 4.18566i −0.0873151 0.151234i
\(767\) −18.3558 −0.662791
\(768\) −0.442463 −0.0159660
\(769\) 2.78701 + 4.82723i 0.100502 + 0.174075i 0.911892 0.410431i \(-0.134622\pi\)
−0.811390 + 0.584506i \(0.801288\pi\)
\(770\) −2.19276 3.79797i −0.0790215 0.136869i
\(771\) 0.408601 0.0147154
\(772\) 7.78879 0.280325
\(773\) −18.2060 31.5337i −0.654823 1.13419i −0.981938 0.189202i \(-0.939410\pi\)
0.327115 0.944984i \(-0.393923\pi\)
\(774\) 8.75856 15.1703i 0.314820 0.545284i
\(775\) −18.4896 32.0250i −0.664167 1.15037i
\(776\) 3.91216 6.77606i 0.140438 0.243246i
\(777\) −3.33395 + 5.77458i −0.119605 + 0.207162i
\(778\) −21.7291 −0.779027
\(779\) 0 0
\(780\) −2.54802 −0.0912339
\(781\) −0.0550855 + 0.0954109i −0.00197111 + 0.00341407i
\(782\) −14.0057 + 24.2585i −0.500842 + 0.867483i
\(783\) −5.88191 10.1878i −0.210202 0.364081i
\(784\) 0.324429 0.561928i 0.0115868 0.0200689i
\(785\) −0.201129 0.348366i −0.00717862 0.0124337i
\(786\) −1.55865 −0.0555951
\(787\) 31.9046 1.13728 0.568638 0.822588i \(-0.307471\pi\)
0.568638 + 0.822588i \(0.307471\pi\)
\(788\) −0.912571 1.58062i −0.0325090 0.0563072i
\(789\) 0.955649 + 1.65523i 0.0340220 + 0.0589278i
\(790\) −8.14076 −0.289635
\(791\) −32.0622 −1.14000
\(792\) −2.73691 4.74047i −0.0972518 0.168445i
\(793\) −7.92906 + 13.7335i −0.281569 + 0.487692i
\(794\) 5.85701 + 10.1446i 0.207857 + 0.360020i
\(795\) −0.742119 + 1.28539i −0.0263202 + 0.0455880i
\(796\) −1.17963 + 2.04317i −0.0418108 + 0.0724184i
\(797\) −2.09165 −0.0740900 −0.0370450 0.999314i \(-0.511794\pi\)
−0.0370450 + 0.999314i \(0.511794\pi\)
\(798\) 0 0
\(799\) 36.1042 1.27728
\(800\) −2.10262 + 3.64185i −0.0743389 + 0.128759i
\(801\) 2.61878 4.53587i 0.0925302 0.160267i
\(802\) −5.90617 10.2298i −0.208554 0.361226i
\(803\) 6.80188 11.7812i 0.240033 0.415749i
\(804\) −0.591266 1.02410i −0.0208523 0.0361173i
\(805\) −18.3892 −0.648136
\(806\) −56.8036 −2.00082
\(807\) −2.38828 4.13661i −0.0840713 0.145616i
\(808\) −2.69244 4.66343i −0.0947195 0.164059i
\(809\) −30.0719 −1.05727 −0.528636 0.848849i \(-0.677296\pi\)
−0.528636 + 0.848849i \(0.677296\pi\)
\(810\) 6.48681 0.227923
\(811\) −0.411796 0.713252i −0.0144601 0.0250457i 0.858705 0.512471i \(-0.171270\pi\)
−0.873165 + 0.487425i \(0.837936\pi\)
\(812\) −5.77195 + 9.99731i −0.202556 + 0.350837i
\(813\) 0.178588 + 0.309323i 0.00626335 + 0.0108484i
\(814\) −5.83625 + 10.1087i −0.204560 + 0.354309i
\(815\) −0.0308698 + 0.0534680i −0.00108132 + 0.00187290i
\(816\) 1.51423 0.0530085
\(817\) 0 0
\(818\) −25.2663 −0.883414
\(819\) −22.8254 + 39.5347i −0.797583 + 1.38145i
\(820\) −1.55535 + 2.69395i −0.0543152 + 0.0940767i
\(821\) −3.85562 6.67813i −0.134562 0.233068i 0.790868 0.611987i \(-0.209629\pi\)
−0.925430 + 0.378918i \(0.876296\pi\)
\(822\) 2.43433 4.21639i 0.0849071 0.147063i
\(823\) 12.4060 + 21.4879i 0.432447 + 0.749019i 0.997083 0.0763201i \(-0.0243171\pi\)
−0.564637 + 0.825339i \(0.690984\pi\)
\(824\) 4.69468 0.163547
\(825\) 3.63200 0.126450
\(826\) 3.58064 + 6.20186i 0.124587 + 0.215790i
\(827\) −5.31424 9.20453i −0.184794 0.320073i 0.758713 0.651425i \(-0.225828\pi\)
−0.943507 + 0.331352i \(0.892495\pi\)
\(828\) −22.9527 −0.797662
\(829\) 21.4710 0.745718 0.372859 0.927888i \(-0.378377\pi\)
0.372859 + 0.927888i \(0.378377\pi\)
\(830\) 6.29567 + 10.9044i 0.218526 + 0.378498i
\(831\) −2.02398 + 3.50564i −0.0702111 + 0.121609i
\(832\) 3.22982 + 5.59422i 0.111974 + 0.193945i
\(833\) −1.11028 + 1.92307i −0.0384690 + 0.0666303i
\(834\) −4.81370 + 8.33756i −0.166685 + 0.288706i
\(835\) −1.93784 −0.0670617
\(836\) 0 0
\(837\) −22.5834 −0.780595
\(838\) 15.8071 27.3788i 0.546048 0.945783i
\(839\) 24.4119 42.2827i 0.842794 1.45976i −0.0447298 0.998999i \(-0.514243\pi\)
0.887524 0.460762i \(-0.152424\pi\)
\(840\) 0.497039 + 0.860897i 0.0171495 + 0.0297038i
\(841\) 4.00885 6.94353i 0.138236 0.239432i
\(842\) −1.09486 1.89635i −0.0377314 0.0653526i
\(843\) −9.38720 −0.323312
\(844\) −0.361050 −0.0124279
\(845\) 12.8050 + 22.1789i 0.440504 + 0.762976i
\(846\) 14.7920 + 25.6206i 0.508561 + 0.880853i
\(847\) −18.1192 −0.622583
\(848\) 3.76278 0.129214
\(849\) 1.14816 + 1.98867i 0.0394047 + 0.0682510i
\(850\) 7.19572 12.4633i 0.246811 0.427489i
\(851\) 24.4724 + 42.3875i 0.838904 + 1.45302i
\(852\) 0.0124864 0.0216271i 0.000427777 0.000740932i
\(853\) 10.5055 18.1961i 0.359702 0.623022i −0.628209 0.778045i \(-0.716212\pi\)
0.987911 + 0.155022i \(0.0495450\pi\)
\(854\) 6.18683 0.211709
\(855\) 0 0
\(856\) −16.0373 −0.548143
\(857\) −16.1196 + 27.9200i −0.550635 + 0.953727i 0.447594 + 0.894237i \(0.352281\pi\)
−0.998229 + 0.0594906i \(0.981052\pi\)
\(858\) 2.78955 4.83164i 0.0952336 0.164949i
\(859\) 20.6137 + 35.7040i 0.703331 + 1.21820i 0.967291 + 0.253671i \(0.0816380\pi\)
−0.263960 + 0.964534i \(0.585029\pi\)
\(860\) −2.78444 + 4.82278i −0.0949485 + 0.164456i
\(861\) −1.94542 3.36957i −0.0662999 0.114835i
\(862\) 1.80372 0.0614348
\(863\) −42.0649 −1.43191 −0.715953 0.698148i \(-0.754008\pi\)
−0.715953 + 0.698148i \(0.754008\pi\)
\(864\) 1.28408 + 2.22409i 0.0436853 + 0.0756651i
\(865\) −7.51050 13.0086i −0.255365 0.442304i
\(866\) 6.57233 0.223337
\(867\) 2.33981 0.0794640
\(868\) 11.0806 + 19.1921i 0.376100 + 0.651424i
\(869\) 8.91241 15.4367i 0.302333 0.523656i
\(870\) 0.903423 + 1.56477i 0.0306289 + 0.0530508i
\(871\) −8.63206 + 14.9512i −0.292486 + 0.506601i
\(872\) 7.05040 12.2116i 0.238757 0.413538i
\(873\) −21.9412 −0.742596
\(874\) 0 0
\(875\) 20.6813 0.699156
\(876\) −1.54180 + 2.67048i −0.0520927 + 0.0902272i
\(877\) 1.17776 2.03993i 0.0397700 0.0688837i −0.845455 0.534046i \(-0.820671\pi\)
0.885225 + 0.465163i \(0.154004\pi\)
\(878\) −4.56530 7.90733i −0.154071 0.266859i
\(879\) −3.88615 + 6.73101i −0.131077 + 0.227031i
\(880\) 0.870091 + 1.50704i 0.0293308 + 0.0508024i
\(881\) 23.1354 0.779450 0.389725 0.920931i \(-0.372570\pi\)
0.389725 + 0.920931i \(0.372570\pi\)
\(882\) −1.81955 −0.0612673
\(883\) −3.50595 6.07249i −0.117985 0.204356i 0.800984 0.598685i \(-0.204310\pi\)
−0.918969 + 0.394330i \(0.870977\pi\)
\(884\) −11.0533 19.1449i −0.371763 0.643912i
\(885\) 1.12088 0.0376780
\(886\) 27.4686 0.922826
\(887\) 24.4646 + 42.3740i 0.821443 + 1.42278i 0.904608 + 0.426244i \(0.140164\pi\)
−0.0831655 + 0.996536i \(0.526503\pi\)
\(888\) 1.32292 2.29137i 0.0443943 0.0768932i
\(889\) −9.04029 15.6582i −0.303202 0.525161i
\(890\) −0.832538 + 1.44200i −0.0279067 + 0.0483359i
\(891\) −7.10169 + 12.3005i −0.237916 + 0.412082i
\(892\) 18.0486 0.604312
\(893\) 0 0
\(894\) 6.36686 0.212940
\(895\) 8.45380 14.6424i 0.282579 0.489442i
\(896\) 1.26007 2.18251i 0.0420961 0.0729126i
\(897\) −11.6971 20.2599i −0.390554 0.676459i
\(898\) −3.78646 + 6.55835i −0.126356 + 0.218855i
\(899\) 20.1402 + 34.8838i 0.671713 + 1.16344i
\(900\) 11.7925 0.393082
\(901\) −12.8772 −0.429002
\(902\) −3.40556 5.89860i −0.113393 0.196402i
\(903\) −3.48276 6.03231i −0.115899 0.200743i
\(904\) 12.7224 0.423140
\(905\) 1.77128 0.0588793
\(906\) −2.74477 4.75408i −0.0911888 0.157944i
\(907\) −0.596520 + 1.03320i −0.0198071 + 0.0343070i −0.875759 0.482748i \(-0.839639\pi\)
0.855952 + 0.517055i \(0.172972\pi\)
\(908\) −6.14224 10.6387i −0.203837 0.353057i
\(909\) −7.55020 + 13.0773i −0.250424 + 0.433747i
\(910\) 7.25641 12.5685i 0.240548 0.416641i
\(911\) −37.6344 −1.24688 −0.623442 0.781870i \(-0.714266\pi\)
−0.623442 + 0.781870i \(0.714266\pi\)
\(912\) 0 0
\(913\) −27.5697 −0.912424
\(914\) −10.8837 + 18.8512i −0.360002 + 0.623542i
\(915\) 0.484180 0.838625i 0.0160065 0.0277241i
\(916\) −3.39587 5.88182i −0.112203 0.194341i
\(917\) 4.43880 7.68823i 0.146582 0.253888i
\(918\) −4.39445 7.61141i −0.145039 0.251214i
\(919\) 26.9476 0.888921 0.444460 0.895799i \(-0.353395\pi\)
0.444460 + 0.895799i \(0.353395\pi\)
\(920\) 7.29689 0.240571
\(921\) −4.77161 8.26466i −0.157230 0.272330i
\(922\) 5.97219 + 10.3441i 0.196684 + 0.340666i
\(923\) −0.364585 −0.0120005
\(924\) −2.17661 −0.0716052
\(925\) −12.5732 21.7775i −0.413406 0.716040i
\(926\) −4.37685 + 7.58093i −0.143832 + 0.249125i
\(927\) −6.58247 11.4012i −0.216197 0.374464i
\(928\) 2.29032 3.96695i 0.0751835 0.130222i
\(929\) 8.92750 15.4629i 0.292902 0.507321i −0.681593 0.731732i \(-0.738712\pi\)
0.974495 + 0.224411i \(0.0720457\pi\)
\(930\) 3.46866 0.113742
\(931\) 0 0
\(932\) 21.4294 0.701942
\(933\) −0.569380 + 0.986196i −0.0186407 + 0.0322866i
\(934\) 14.6784 25.4238i 0.480293 0.831891i
\(935\) −2.97768 5.15749i −0.0973804 0.168668i
\(936\) 9.05716 15.6875i 0.296042 0.512761i
\(937\) 11.9163 + 20.6396i 0.389288 + 0.674267i 0.992354 0.123425i \(-0.0393878\pi\)
−0.603066 + 0.797691i \(0.706054\pi\)
\(938\) 6.73537 0.219918
\(939\) 2.29368 0.0748514
\(940\) −4.70254 8.14503i −0.153380 0.265662i
\(941\) 10.1825 + 17.6367i 0.331941 + 0.574939i 0.982892 0.184181i \(-0.0589632\pi\)
−0.650951 + 0.759119i \(0.725630\pi\)
\(942\) −0.199648 −0.00650490
\(943\) −28.5602 −0.930049
\(944\) −1.42081 2.46091i −0.0462434 0.0800958i
\(945\) 2.88493 4.99684i 0.0938467 0.162547i
\(946\) −6.09673 10.5599i −0.198222 0.343330i
\(947\) 1.70795 2.95825i 0.0555009 0.0961304i −0.836940 0.547294i \(-0.815658\pi\)
0.892441 + 0.451164i \(0.148991\pi\)
\(948\) −2.02020 + 3.49909i −0.0656132 + 0.113645i
\(949\) 45.0184 1.46136
\(950\) 0 0
\(951\) 8.96261 0.290633
\(952\) −4.31230 + 7.46912i −0.139762 + 0.242076i
\(953\) −8.86967 + 15.3627i −0.287317 + 0.497647i −0.973168 0.230094i \(-0.926097\pi\)
0.685852 + 0.727741i \(0.259430\pi\)
\(954\) −5.27584 9.13803i −0.170812 0.295855i
\(955\) −9.32765 + 16.1560i −0.301836 + 0.522794i
\(956\) 5.91881 + 10.2517i 0.191428 + 0.331563i
\(957\) −3.95623 −0.127887
\(958\) 24.8705 0.803528
\(959\) 13.8653 + 24.0154i 0.447733 + 0.775497i
\(960\) −0.197226 0.341606i −0.00636545 0.0110253i
\(961\) 46.3275 1.49443
\(962\) −38.6274 −1.24540
\(963\) 22.4861 + 38.9470i 0.724604 + 1.25505i
\(964\) 10.8732 18.8329i 0.350201 0.606565i
\(965\) 3.47182 + 6.01337i 0.111762 + 0.193577i
\(966\) −4.56346 + 7.90414i −0.146827 + 0.254312i
\(967\) 21.3776 37.0270i 0.687456 1.19071i −0.285202 0.958467i \(-0.592061\pi\)
0.972658 0.232242i \(-0.0746060\pi\)
\(968\) 7.18974 0.231087
\(969\) 0 0
\(970\) 6.97531 0.223964
\(971\) 26.5243 45.9415i 0.851207 1.47433i −0.0289131 0.999582i \(-0.509205\pi\)
0.880120 0.474751i \(-0.157462\pi\)
\(972\) 5.46200 9.46046i 0.175194 0.303444i
\(973\) −27.4174 47.4884i −0.878963 1.52241i
\(974\) −4.26883 + 7.39383i −0.136782 + 0.236914i
\(975\) 6.00963 + 10.4090i 0.192462 + 0.333354i
\(976\) −2.45495 −0.0785810
\(977\) 12.3264 0.394356 0.197178 0.980368i \(-0.436822\pi\)
0.197178 + 0.980368i \(0.436822\pi\)
\(978\) 0.0153212 + 0.0265371i 0.000489919 + 0.000848564i
\(979\) −1.82290 3.15736i −0.0582603 0.100910i
\(980\) 0.578452 0.0184780
\(981\) −39.5418 −1.26247
\(982\) −5.76985 9.99368i −0.184123 0.318911i
\(983\) −16.1277 + 27.9340i −0.514394 + 0.890956i 0.485467 + 0.874255i \(0.338650\pi\)
−0.999861 + 0.0167010i \(0.994684\pi\)
\(984\) 0.771949 + 1.33705i 0.0246088 + 0.0426237i
\(985\) 0.813549 1.40911i 0.0259218 0.0448979i
\(986\) −7.83808 + 13.5759i −0.249615 + 0.432346i
\(987\) 11.7638 0.374446
\(988\) 0 0
\(989\) −51.1294 −1.62582
\(990\) 2.43993 4.22608i 0.0775461 0.134314i
\(991\) 13.9183 24.1072i 0.442129 0.765790i −0.555718 0.831371i \(-0.687557\pi\)
0.997847 + 0.0655808i \(0.0208900\pi\)
\(992\) −4.39680 7.61548i −0.139599 0.241792i
\(993\) −4.71843 + 8.17256i −0.149735 + 0.259348i
\(994\) 0.0711190 + 0.123182i 0.00225576 + 0.00390709i
\(995\) −2.10326 −0.0666777
\(996\) 6.24931 0.198017
\(997\) 21.6657 + 37.5260i 0.686159 + 1.18846i 0.973071 + 0.230505i \(0.0740377\pi\)
−0.286913 + 0.957957i \(0.592629\pi\)
\(998\) −14.8045 25.6422i −0.468629 0.811689i
\(999\) −15.3571 −0.485876
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 722.2.c.n.429.2 8
19.2 odd 18 722.2.e.r.595.3 24
19.3 odd 18 722.2.e.r.99.2 24
19.4 even 9 722.2.e.s.423.3 24
19.5 even 9 722.2.e.s.389.3 24
19.6 even 9 722.2.e.s.415.2 24
19.7 even 3 inner 722.2.c.n.653.2 8
19.8 odd 6 722.2.a.n.1.2 yes 4
19.9 even 9 722.2.e.s.245.3 24
19.10 odd 18 722.2.e.r.245.2 24
19.11 even 3 722.2.a.m.1.3 4
19.12 odd 6 722.2.c.m.653.3 8
19.13 odd 18 722.2.e.r.415.3 24
19.14 odd 18 722.2.e.r.389.2 24
19.15 odd 18 722.2.e.r.423.2 24
19.16 even 9 722.2.e.s.99.3 24
19.17 even 9 722.2.e.s.595.2 24
19.18 odd 2 722.2.c.m.429.3 8
57.8 even 6 6498.2.a.bx.1.2 4
57.11 odd 6 6498.2.a.ca.1.2 4
76.11 odd 6 5776.2.a.bv.1.2 4
76.27 even 6 5776.2.a.bt.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
722.2.a.m.1.3 4 19.11 even 3
722.2.a.n.1.2 yes 4 19.8 odd 6
722.2.c.m.429.3 8 19.18 odd 2
722.2.c.m.653.3 8 19.12 odd 6
722.2.c.n.429.2 8 1.1 even 1 trivial
722.2.c.n.653.2 8 19.7 even 3 inner
722.2.e.r.99.2 24 19.3 odd 18
722.2.e.r.245.2 24 19.10 odd 18
722.2.e.r.389.2 24 19.14 odd 18
722.2.e.r.415.3 24 19.13 odd 18
722.2.e.r.423.2 24 19.15 odd 18
722.2.e.r.595.3 24 19.2 odd 18
722.2.e.s.99.3 24 19.16 even 9
722.2.e.s.245.3 24 19.9 even 9
722.2.e.s.389.3 24 19.5 even 9
722.2.e.s.415.2 24 19.6 even 9
722.2.e.s.423.3 24 19.4 even 9
722.2.e.s.595.2 24 19.17 even 9
5776.2.a.bt.1.3 4 76.27 even 6
5776.2.a.bv.1.2 4 76.11 odd 6
6498.2.a.bx.1.2 4 57.8 even 6
6498.2.a.ca.1.2 4 57.11 odd 6