Properties

Label 882.2.e.l.373.2
Level $882$
Weight $2$
Character 882.373
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(373,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.e (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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 882.373
Dual form 882.2.e.l.655.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.500000 + 1.65831i) q^{3} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.500000 + 1.65831i) q^{3} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +(2.18614 + 3.78651i) q^{10} +(0.686141 - 1.18843i) q^{11} +(0.500000 + 1.65831i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(5.18614 - 5.51856i) q^{15} +1.00000 q^{16} +(-0.686141 - 1.18843i) q^{17} +(2.50000 - 1.65831i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(-2.18614 - 3.78651i) q^{20} +(-0.686141 + 1.18843i) q^{22} +(0.813859 + 1.40965i) q^{23} +(-0.500000 - 1.65831i) q^{24} +(-7.05842 + 12.2255i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 - 3.31662i) q^{27} +(4.37228 + 7.57301i) q^{29} +(-5.18614 + 5.51856i) q^{30} +2.00000 q^{31} -1.00000 q^{32} +(2.31386 + 0.543620i) q^{33} +(0.686141 + 1.18843i) q^{34} +(-2.50000 + 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(2.18614 + 3.78651i) q^{40} +(-2.31386 + 4.00772i) q^{41} +(4.05842 + 7.02939i) q^{43} +(0.686141 - 1.18843i) q^{44} +(11.7446 + 5.84096i) q^{45} +(-0.813859 - 1.40965i) q^{46} +(0.500000 + 1.65831i) q^{48} +(7.05842 - 12.2255i) q^{50} +(1.62772 - 1.73205i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(4.37228 + 7.57301i) q^{53} +(4.00000 + 3.31662i) q^{54} -6.00000 q^{55} +(-8.43070 - 1.98072i) q^{57} +(-4.37228 - 7.57301i) q^{58} -10.1168 q^{59} +(5.18614 - 5.51856i) q^{60} +3.11684 q^{61} -2.00000 q^{62} +1.00000 q^{64} +8.74456 q^{65} +(-2.31386 - 0.543620i) q^{66} -2.11684 q^{67} +(-0.686141 - 1.18843i) q^{68} +(-1.93070 + 2.05446i) q^{69} -7.11684 q^{71} +(2.50000 - 1.65831i) q^{72} +(-6.05842 - 10.4935i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-23.8030 - 5.59230i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(3.37228 + 0.792287i) q^{78} -5.11684 q^{79} +(-2.18614 - 3.78651i) q^{80} +(3.50000 - 8.29156i) q^{81} +(2.31386 - 4.00772i) q^{82} +(-8.74456 - 15.1460i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.05842 - 7.02939i) q^{86} +(-10.3723 + 11.0371i) q^{87} +(-0.686141 + 1.18843i) q^{88} +(-7.37228 + 12.7692i) q^{89} +(-11.7446 - 5.84096i) q^{90} +(0.813859 + 1.40965i) q^{92} +(1.00000 + 3.31662i) q^{93} +21.8614 q^{95} +(-0.500000 - 1.65831i) q^{96} +(4.05842 + 7.02939i) q^{97} +(0.255437 + 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9} + 3 q^{10} - 3 q^{11} + 2 q^{12} - 4 q^{13} + 15 q^{15} + 4 q^{16} + 3 q^{17} + 10 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{23} - 2 q^{24} - 11 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 15 q^{30} + 8 q^{31} - 4 q^{32} + 15 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} + 24 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} + 16 q^{54} - 24 q^{55} - 5 q^{57} - 6 q^{58} - 6 q^{59} + 15 q^{60} - 22 q^{61} - 8 q^{62} + 4 q^{64} + 12 q^{65} - 15 q^{66} + 26 q^{67} + 3 q^{68} + 21 q^{69} + 6 q^{71} + 10 q^{72} - 7 q^{73} + 4 q^{74} - 55 q^{75} - 10 q^{76} + 2 q^{78} + 14 q^{79} - 3 q^{80} + 14 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} + q^{86} - 30 q^{87} + 3 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} + 4 q^{93} + 30 q^{95} - 2 q^{96} - q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.500000 + 1.65831i 0.288675 + 0.957427i
\(4\) 1.00000 0.500000
\(5\) −2.18614 3.78651i −0.977672 1.69338i −0.670820 0.741620i \(-0.734058\pi\)
−0.306851 0.951757i \(-0.599275\pi\)
\(6\) −0.500000 1.65831i −0.204124 0.677003i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(10\) 2.18614 + 3.78651i 0.691318 + 1.19740i
\(11\) 0.686141 1.18843i 0.206879 0.358325i −0.743851 0.668346i \(-0.767003\pi\)
0.950730 + 0.310021i \(0.100336\pi\)
\(12\) 0.500000 + 1.65831i 0.144338 + 0.478714i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 5.18614 5.51856i 1.33906 1.42489i
\(16\) 1.00000 0.250000
\(17\) −0.686141 1.18843i −0.166414 0.288237i 0.770743 0.637146i \(-0.219885\pi\)
−0.937156 + 0.348910i \(0.886552\pi\)
\(18\) 2.50000 1.65831i 0.589256 0.390868i
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) −2.18614 3.78651i −0.488836 0.846689i
\(21\) 0 0
\(22\) −0.686141 + 1.18843i −0.146286 + 0.253374i
\(23\) 0.813859 + 1.40965i 0.169701 + 0.293931i 0.938315 0.345782i \(-0.112386\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) −0.500000 1.65831i −0.102062 0.338502i
\(25\) −7.05842 + 12.2255i −1.41168 + 2.44511i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −4.00000 3.31662i −0.769800 0.638285i
\(28\) 0 0
\(29\) 4.37228 + 7.57301i 0.811912 + 1.40627i 0.911524 + 0.411247i \(0.134907\pi\)
−0.0996117 + 0.995026i \(0.531760\pi\)
\(30\) −5.18614 + 5.51856i −0.946855 + 1.00755i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.31386 + 0.543620i 0.402791 + 0.0946322i
\(34\) 0.686141 + 1.18843i 0.117672 + 0.203814i
\(35\) 0 0
\(36\) −2.50000 + 1.65831i −0.416667 + 0.276385i
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 2.50000 4.33013i 0.405554 0.702439i
\(39\) −3.37228 0.792287i −0.539997 0.126867i
\(40\) 2.18614 + 3.78651i 0.345659 + 0.598699i
\(41\) −2.31386 + 4.00772i −0.361364 + 0.625901i −0.988186 0.153262i \(-0.951022\pi\)
0.626821 + 0.779163i \(0.284356\pi\)
\(42\) 0 0
\(43\) 4.05842 + 7.02939i 0.618904 + 1.07197i 0.989686 + 0.143253i \(0.0457562\pi\)
−0.370783 + 0.928720i \(0.620910\pi\)
\(44\) 0.686141 1.18843i 0.103440 0.179163i
\(45\) 11.7446 + 5.84096i 1.75078 + 0.870719i
\(46\) −0.813859 1.40965i −0.119997 0.207841i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0.500000 + 1.65831i 0.0721688 + 0.239357i
\(49\) 0 0
\(50\) 7.05842 12.2255i 0.998212 1.72895i
\(51\) 1.62772 1.73205i 0.227926 0.242536i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 4.37228 + 7.57301i 0.600579 + 1.04023i 0.992733 + 0.120334i \(0.0383965\pi\)
−0.392154 + 0.919899i \(0.628270\pi\)
\(54\) 4.00000 + 3.31662i 0.544331 + 0.451335i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) −8.43070 1.98072i −1.11667 0.262352i
\(58\) −4.37228 7.57301i −0.574109 0.994385i
\(59\) −10.1168 −1.31710 −0.658550 0.752537i \(-0.728830\pi\)
−0.658550 + 0.752537i \(0.728830\pi\)
\(60\) 5.18614 5.51856i 0.669528 0.712443i
\(61\) 3.11684 0.399071 0.199535 0.979891i \(-0.436057\pi\)
0.199535 + 0.979891i \(0.436057\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.74456 1.08463
\(66\) −2.31386 0.543620i −0.284816 0.0669150i
\(67\) −2.11684 −0.258614 −0.129307 0.991605i \(-0.541275\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) −0.686141 1.18843i −0.0832068 0.144118i
\(69\) −1.93070 + 2.05446i −0.232429 + 0.247327i
\(70\) 0 0
\(71\) −7.11684 −0.844614 −0.422307 0.906453i \(-0.638780\pi\)
−0.422307 + 0.906453i \(0.638780\pi\)
\(72\) 2.50000 1.65831i 0.294628 0.195434i
\(73\) −6.05842 10.4935i −0.709085 1.22817i −0.965197 0.261524i \(-0.915775\pi\)
0.256112 0.966647i \(-0.417558\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −23.8030 5.59230i −2.74853 0.645743i
\(76\) −2.50000 + 4.33013i −0.286770 + 0.496700i
\(77\) 0 0
\(78\) 3.37228 + 0.792287i 0.381836 + 0.0897088i
\(79\) −5.11684 −0.575690 −0.287845 0.957677i \(-0.592939\pi\)
−0.287845 + 0.957677i \(0.592939\pi\)
\(80\) −2.18614 3.78651i −0.244418 0.423344i
\(81\) 3.50000 8.29156i 0.388889 0.921285i
\(82\) 2.31386 4.00772i 0.255523 0.442579i
\(83\) −8.74456 15.1460i −0.959840 1.66249i −0.722881 0.690973i \(-0.757182\pi\)
−0.236960 0.971519i \(-0.576151\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) −4.05842 7.02939i −0.437631 0.757999i
\(87\) −10.3723 + 11.0371i −1.11203 + 1.18330i
\(88\) −0.686141 + 1.18843i −0.0731428 + 0.126687i
\(89\) −7.37228 + 12.7692i −0.781460 + 1.35353i 0.149631 + 0.988742i \(0.452192\pi\)
−0.931091 + 0.364787i \(0.881142\pi\)
\(90\) −11.7446 5.84096i −1.23799 0.615692i
\(91\) 0 0
\(92\) 0.813859 + 1.40965i 0.0848507 + 0.146966i
\(93\) 1.00000 + 3.31662i 0.103695 + 0.343918i
\(94\) 0 0
\(95\) 21.8614 2.24293
\(96\) −0.500000 1.65831i −0.0510310 0.169251i
\(97\) 4.05842 + 7.02939i 0.412070 + 0.713727i 0.995116 0.0987127i \(-0.0314725\pi\)
−0.583046 + 0.812439i \(0.698139\pi\)
\(98\) 0 0
\(99\) 0.255437 + 4.10891i 0.0256724 + 0.412961i
\(100\) −7.05842 + 12.2255i −0.705842 + 1.22255i
\(101\) −0.813859 + 1.40965i −0.0809820 + 0.140265i −0.903672 0.428225i \(-0.859139\pi\)
0.822690 + 0.568490i \(0.192472\pi\)
\(102\) −1.62772 + 1.73205i −0.161168 + 0.171499i
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 0 0
\(106\) −4.37228 7.57301i −0.424674 0.735556i
\(107\) 3.68614 6.38458i 0.356353 0.617221i −0.630996 0.775786i \(-0.717354\pi\)
0.987348 + 0.158565i \(0.0506868\pi\)
\(108\) −4.00000 3.31662i −0.384900 0.319142i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 6.00000 0.572078
\(111\) −3.37228 0.792287i −0.320083 0.0752006i
\(112\) 0 0
\(113\) 2.18614 3.78651i 0.205655 0.356205i −0.744686 0.667415i \(-0.767401\pi\)
0.950341 + 0.311210i \(0.100734\pi\)
\(114\) 8.43070 + 1.98072i 0.789608 + 0.185511i
\(115\) 3.55842 6.16337i 0.331825 0.574737i
\(116\) 4.37228 + 7.57301i 0.405956 + 0.703137i
\(117\) −0.372281 5.98844i −0.0344174 0.553631i
\(118\) 10.1168 0.931331
\(119\) 0 0
\(120\) −5.18614 + 5.51856i −0.473428 + 0.503773i
\(121\) 4.55842 + 7.89542i 0.414402 + 0.717765i
\(122\) −3.11684 −0.282186
\(123\) −7.80298 1.83324i −0.703571 0.165298i
\(124\) 2.00000 0.179605
\(125\) 39.8614 3.56531
\(126\) 0 0
\(127\) 3.11684 0.276575 0.138288 0.990392i \(-0.455840\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.62772 + 10.2448i −0.847673 + 0.902007i
\(130\) −8.74456 −0.766949
\(131\) 0.813859 + 1.40965i 0.0711072 + 0.123161i 0.899387 0.437154i \(-0.144013\pi\)
−0.828280 + 0.560315i \(0.810680\pi\)
\(132\) 2.31386 + 0.543620i 0.201396 + 0.0473161i
\(133\) 0 0
\(134\) 2.11684 0.182867
\(135\) −3.81386 + 22.3966i −0.328245 + 1.92760i
\(136\) 0.686141 + 1.18843i 0.0588361 + 0.101907i
\(137\) −5.31386 + 9.20387i −0.453994 + 0.786340i −0.998630 0.0523324i \(-0.983334\pi\)
0.544636 + 0.838672i \(0.316668\pi\)
\(138\) 1.93070 2.05446i 0.164352 0.174887i
\(139\) −6.61684 + 11.4607i −0.561233 + 0.972085i 0.436156 + 0.899871i \(0.356340\pi\)
−0.997389 + 0.0722136i \(0.976994\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.11684 0.597232
\(143\) 1.37228 + 2.37686i 0.114756 + 0.198763i
\(144\) −2.50000 + 1.65831i −0.208333 + 0.138193i
\(145\) 19.1168 33.1113i 1.58757 2.74975i
\(146\) 6.05842 + 10.4935i 0.501399 + 0.868448i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) −1.62772 2.81929i −0.133348 0.230965i 0.791617 0.611017i \(-0.209239\pi\)
−0.924965 + 0.380052i \(0.875906\pi\)
\(150\) 23.8030 + 5.59230i 1.94351 + 0.456609i
\(151\) −4.55842 + 7.89542i −0.370959 + 0.642520i −0.989713 0.143065i \(-0.954304\pi\)
0.618754 + 0.785585i \(0.287638\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) 3.68614 + 1.83324i 0.298007 + 0.148209i
\(154\) 0 0
\(155\) −4.37228 7.57301i −0.351190 0.608279i
\(156\) −3.37228 0.792287i −0.269999 0.0634337i
\(157\) 9.11684 0.727603 0.363802 0.931476i \(-0.381479\pi\)
0.363802 + 0.931476i \(0.381479\pi\)
\(158\) 5.11684 0.407074
\(159\) −10.3723 + 11.0371i −0.822575 + 0.875300i
\(160\) 2.18614 + 3.78651i 0.172830 + 0.299350i
\(161\) 0 0
\(162\) −3.50000 + 8.29156i −0.274986 + 0.651447i
\(163\) 9.11684 15.7908i 0.714086 1.23683i −0.249225 0.968446i \(-0.580176\pi\)
0.963311 0.268388i \(-0.0864909\pi\)
\(164\) −2.31386 + 4.00772i −0.180682 + 0.312951i
\(165\) −3.00000 9.94987i −0.233550 0.774597i
\(166\) 8.74456 + 15.1460i 0.678710 + 1.17556i
\(167\) 2.74456 4.75372i 0.212381 0.367854i −0.740078 0.672521i \(-0.765212\pi\)
0.952459 + 0.304666i \(0.0985450\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) −0.930703 14.9711i −0.0711727 1.14487i
\(172\) 4.05842 + 7.02939i 0.309452 + 0.535986i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 10.3723 11.0371i 0.786321 0.836722i
\(175\) 0 0
\(176\) 0.686141 1.18843i 0.0517198 0.0895813i
\(177\) −5.05842 16.7769i −0.380214 1.26103i
\(178\) 7.37228 12.7692i 0.552576 0.957089i
\(179\) −1.62772 2.81929i −0.121661 0.210724i 0.798762 0.601648i \(-0.205489\pi\)
−0.920423 + 0.390924i \(0.872156\pi\)
\(180\) 11.7446 + 5.84096i 0.875388 + 0.435360i
\(181\) 0.883156 0.0656445 0.0328222 0.999461i \(-0.489550\pi\)
0.0328222 + 0.999461i \(0.489550\pi\)
\(182\) 0 0
\(183\) 1.55842 + 5.16870i 0.115202 + 0.382081i
\(184\) −0.813859 1.40965i −0.0599985 0.103920i
\(185\) 8.74456 0.642913
\(186\) −1.00000 3.31662i −0.0733236 0.243187i
\(187\) −1.88316 −0.137710
\(188\) 0 0
\(189\) 0 0
\(190\) −21.8614 −1.58599
\(191\) −19.1168 −1.38325 −0.691623 0.722259i \(-0.743104\pi\)
−0.691623 + 0.722259i \(0.743104\pi\)
\(192\) 0.500000 + 1.65831i 0.0360844 + 0.119678i
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) −4.05842 7.02939i −0.291378 0.504681i
\(195\) 4.37228 + 14.5012i 0.313106 + 1.03845i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −0.255437 4.10891i −0.0181531 0.292008i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 7.05842 12.2255i 0.499106 0.864477i
\(201\) −1.05842 3.51039i −0.0746553 0.247604i
\(202\) 0.813859 1.40965i 0.0572629 0.0991823i
\(203\) 0 0
\(204\) 1.62772 1.73205i 0.113963 0.121268i
\(205\) 20.2337 1.41318
\(206\) −5.00000 8.66025i −0.348367 0.603388i
\(207\) −4.37228 2.17448i −0.303895 0.151137i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 3.43070 + 5.94215i 0.237307 + 0.411027i
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) 4.37228 + 7.57301i 0.300290 + 0.520117i
\(213\) −3.55842 11.8020i −0.243819 0.808656i
\(214\) −3.68614 + 6.38458i −0.251979 + 0.436441i
\(215\) 17.7446 30.7345i 1.21017 2.09607i
\(216\) 4.00000 + 3.31662i 0.272166 + 0.225668i
\(217\) 0 0
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 14.3723 15.2935i 0.971189 1.03344i
\(220\) −6.00000 −0.404520
\(221\) 2.74456 0.184619
\(222\) 3.37228 + 0.792287i 0.226333 + 0.0531748i
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 0 0
\(225\) −2.62772 42.2689i −0.175181 2.81793i
\(226\) −2.18614 + 3.78651i −0.145420 + 0.251875i
\(227\) 6.12772 10.6135i 0.406711 0.704444i −0.587808 0.809000i \(-0.700009\pi\)
0.994519 + 0.104556i \(0.0333423\pi\)
\(228\) −8.43070 1.98072i −0.558337 0.131176i
\(229\) 1.44158 + 2.49689i 0.0952622 + 0.164999i 0.909718 0.415227i \(-0.136298\pi\)
−0.814456 + 0.580226i \(0.802964\pi\)
\(230\) −3.55842 + 6.16337i −0.234635 + 0.406400i
\(231\) 0 0
\(232\) −4.37228 7.57301i −0.287054 0.497193i
\(233\) 0.127719 0.221215i 0.00836713 0.0144923i −0.861812 0.507229i \(-0.830670\pi\)
0.870179 + 0.492736i \(0.164003\pi\)
\(234\) 0.372281 + 5.98844i 0.0243368 + 0.391477i
\(235\) 0 0
\(236\) −10.1168 −0.658550
\(237\) −2.55842 8.48533i −0.166187 0.551181i
\(238\) 0 0
\(239\) −4.93070 + 8.54023i −0.318941 + 0.552421i −0.980267 0.197677i \(-0.936660\pi\)
0.661327 + 0.750098i \(0.269994\pi\)
\(240\) 5.18614 5.51856i 0.334764 0.356221i
\(241\) −9.05842 + 15.6896i −0.583504 + 1.01066i 0.411556 + 0.911385i \(0.364986\pi\)
−0.995060 + 0.0992745i \(0.968348\pi\)
\(242\) −4.55842 7.89542i −0.293026 0.507537i
\(243\) 15.5000 + 1.65831i 0.994325 + 0.106381i
\(244\) 3.11684 0.199535
\(245\) 0 0
\(246\) 7.80298 + 1.83324i 0.497500 + 0.116883i
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) −2.00000 −0.127000
\(249\) 20.7446 22.0742i 1.31463 1.39890i
\(250\) −39.8614 −2.52106
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) 2.23369 0.140431
\(254\) −3.11684 −0.195568
\(255\) −10.1168 2.37686i −0.633541 0.148845i
\(256\) 1.00000 0.0625000
\(257\) 3.43070 + 5.94215i 0.214001 + 0.370661i 0.952963 0.303086i \(-0.0980170\pi\)
−0.738962 + 0.673747i \(0.764684\pi\)
\(258\) 9.62772 10.2448i 0.599396 0.637815i
\(259\) 0 0
\(260\) 8.74456 0.542315
\(261\) −23.4891 11.6819i −1.45394 0.723093i
\(262\) −0.813859 1.40965i −0.0502804 0.0870882i
\(263\) −3.81386 + 6.60580i −0.235173 + 0.407331i −0.959323 0.282311i \(-0.908899\pi\)
0.724150 + 0.689642i \(0.242232\pi\)
\(264\) −2.31386 0.543620i −0.142408 0.0334575i
\(265\) 19.1168 33.1113i 1.17434 2.03401i
\(266\) 0 0
\(267\) −24.8614 5.84096i −1.52149 0.357461i
\(268\) −2.11684 −0.129307
\(269\) 0.813859 + 1.40965i 0.0496219 + 0.0859476i 0.889769 0.456410i \(-0.150865\pi\)
−0.840148 + 0.542358i \(0.817532\pi\)
\(270\) 3.81386 22.3966i 0.232104 1.36302i
\(271\) −8.11684 + 14.0588i −0.493063 + 0.854010i −0.999968 0.00799154i \(-0.997456\pi\)
0.506905 + 0.862002i \(0.330790\pi\)
\(272\) −0.686141 1.18843i −0.0416034 0.0720592i
\(273\) 0 0
\(274\) 5.31386 9.20387i 0.321022 0.556026i
\(275\) 9.68614 + 16.7769i 0.584096 + 1.01168i
\(276\) −1.93070 + 2.05446i −0.116215 + 0.123664i
\(277\) 6.11684 10.5947i 0.367526 0.636573i −0.621652 0.783293i \(-0.713538\pi\)
0.989178 + 0.146720i \(0.0468717\pi\)
\(278\) 6.61684 11.4607i 0.396852 0.687368i
\(279\) −5.00000 + 3.31662i −0.299342 + 0.198561i
\(280\) 0 0
\(281\) −8.18614 14.1788i −0.488344 0.845837i 0.511566 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134071i \(0.995732\pi\)
\(282\) 0 0
\(283\) 27.1168 1.61193 0.805965 0.591964i \(-0.201647\pi\)
0.805965 + 0.591964i \(0.201647\pi\)
\(284\) −7.11684 −0.422307
\(285\) 10.9307 + 36.2530i 0.647479 + 2.14744i
\(286\) −1.37228 2.37686i −0.0811447 0.140547i
\(287\) 0 0
\(288\) 2.50000 1.65831i 0.147314 0.0977170i
\(289\) 7.55842 13.0916i 0.444613 0.770092i
\(290\) −19.1168 + 33.1113i −1.12258 + 1.94437i
\(291\) −9.62772 + 10.2448i −0.564387 + 0.600562i
\(292\) −6.05842 10.4935i −0.354542 0.614085i
\(293\) 5.18614 8.98266i 0.302978 0.524773i −0.673831 0.738885i \(-0.735353\pi\)
0.976809 + 0.214113i \(0.0686859\pi\)
\(294\) 0 0
\(295\) 22.1168 + 38.3075i 1.28769 + 2.23035i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) −6.68614 + 2.47805i −0.387969 + 0.143791i
\(298\) 1.62772 + 2.81929i 0.0942912 + 0.163317i
\(299\) −3.25544 −0.188267
\(300\) −23.8030 5.59230i −1.37427 0.322871i
\(301\) 0 0
\(302\) 4.55842 7.89542i 0.262308 0.454330i
\(303\) −2.74456 0.644810i −0.157671 0.0370434i
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) −6.81386 11.8020i −0.390160 0.675778i
\(306\) −3.68614 1.83324i −0.210723 0.104799i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) −11.8614 + 12.6217i −0.674772 + 0.718023i
\(310\) 4.37228 + 7.57301i 0.248329 + 0.430118i
\(311\) 8.23369 0.466890 0.233445 0.972370i \(-0.425000\pi\)
0.233445 + 0.972370i \(0.425000\pi\)
\(312\) 3.37228 + 0.792287i 0.190918 + 0.0448544i
\(313\) −20.1168 −1.13707 −0.568536 0.822659i \(-0.692490\pi\)
−0.568536 + 0.822659i \(0.692490\pi\)
\(314\) −9.11684 −0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 10.3723 11.0371i 0.581649 0.618931i
\(319\) 12.0000 0.671871
\(320\) −2.18614 3.78651i −0.122209 0.211672i
\(321\) 12.4307 + 2.92048i 0.693814 + 0.163005i
\(322\) 0 0
\(323\) 6.86141 0.381779
\(324\) 3.50000 8.29156i 0.194444 0.460642i
\(325\) −14.1168 24.4511i −0.783062 1.35630i
\(326\) −9.11684 + 15.7908i −0.504935 + 0.874574i
\(327\) 16.6060 17.6704i 0.918312 0.977173i
\(328\) 2.31386 4.00772i 0.127762 0.221289i
\(329\) 0 0
\(330\) 3.00000 + 9.94987i 0.165145 + 0.547723i
\(331\) 22.2337 1.22207 0.611037 0.791602i \(-0.290753\pi\)
0.611037 + 0.791602i \(0.290753\pi\)
\(332\) −8.74456 15.1460i −0.479920 0.831246i
\(333\) −0.372281 5.98844i −0.0204009 0.328164i
\(334\) −2.74456 + 4.75372i −0.150176 + 0.260112i
\(335\) 4.62772 + 8.01544i 0.252839 + 0.437930i
\(336\) 0 0
\(337\) 4.05842 7.02939i 0.221076 0.382915i −0.734059 0.679086i \(-0.762376\pi\)
0.955135 + 0.296171i \(0.0957097\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 7.37228 + 1.73205i 0.400407 + 0.0940721i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 1.37228 2.37686i 0.0743132 0.128714i
\(342\) 0.930703 + 14.9711i 0.0503267 + 0.809544i
\(343\) 0 0
\(344\) −4.05842 7.02939i −0.218815 0.378999i
\(345\) 12.0000 + 2.81929i 0.646058 + 0.151786i
\(346\) 6.00000 0.322562
\(347\) −10.1168 −0.543101 −0.271550 0.962424i \(-0.587536\pi\)
−0.271550 + 0.962424i \(0.587536\pi\)
\(348\) −10.3723 + 11.0371i −0.556013 + 0.591651i
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) 0 0
\(351\) 9.74456 3.61158i 0.520126 0.192772i
\(352\) −0.686141 + 1.18843i −0.0365714 + 0.0633436i
\(353\) 6.68614 11.5807i 0.355867 0.616380i −0.631399 0.775458i \(-0.717519\pi\)
0.987266 + 0.159078i \(0.0508522\pi\)
\(354\) 5.05842 + 16.7769i 0.268852 + 0.891682i
\(355\) 15.5584 + 26.9480i 0.825755 + 1.43025i
\(356\) −7.37228 + 12.7692i −0.390730 + 0.676764i
\(357\) 0 0
\(358\) 1.62772 + 2.81929i 0.0860276 + 0.149004i
\(359\) −10.9307 + 18.9325i −0.576900 + 0.999221i 0.418932 + 0.908018i \(0.362405\pi\)
−0.995832 + 0.0912032i \(0.970929\pi\)
\(360\) −11.7446 5.84096i −0.618993 0.307846i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −0.883156 −0.0464177
\(363\) −10.8139 + 11.5070i −0.567580 + 0.603961i
\(364\) 0 0
\(365\) −26.4891 + 45.8805i −1.38650 + 2.40150i
\(366\) −1.55842 5.16870i −0.0814600 0.270172i
\(367\) 6.11684 10.5947i 0.319297 0.553038i −0.661045 0.750346i \(-0.729887\pi\)
0.980341 + 0.197308i \(0.0632200\pi\)
\(368\) 0.813859 + 1.40965i 0.0424254 + 0.0734829i
\(369\) −0.861407 13.8564i −0.0448430 0.721336i
\(370\) −8.74456 −0.454608
\(371\) 0 0
\(372\) 1.00000 + 3.31662i 0.0518476 + 0.171959i
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 1.88316 0.0973757
\(375\) 19.9307 + 66.1027i 1.02922 + 3.41353i
\(376\) 0 0
\(377\) −17.4891 −0.900736
\(378\) 0 0
\(379\) −8.11684 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(380\) 21.8614 1.12147
\(381\) 1.55842 + 5.16870i 0.0798404 + 0.264801i
\(382\) 19.1168 0.978103
\(383\) 16.3723 + 28.3576i 0.836584 + 1.44901i 0.892734 + 0.450584i \(0.148784\pi\)
−0.0561493 + 0.998422i \(0.517882\pi\)
\(384\) −0.500000 1.65831i −0.0255155 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) −21.8030 10.8434i −1.10831 0.551199i
\(388\) 4.05842 + 7.02939i 0.206035 + 0.356863i
\(389\) −5.48913 + 9.50744i −0.278310 + 0.482047i −0.970965 0.239222i \(-0.923107\pi\)
0.692655 + 0.721269i \(0.256441\pi\)
\(390\) −4.37228 14.5012i −0.221399 0.734298i
\(391\) 1.11684 1.93443i 0.0564812 0.0978284i
\(392\) 0 0
\(393\) −1.93070 + 2.05446i −0.0973911 + 0.103634i
\(394\) 6.00000 0.302276
\(395\) 11.1861 + 19.3750i 0.562836 + 0.974860i
\(396\) 0.255437 + 4.10891i 0.0128362 + 0.206481i
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) −5.00000 8.66025i −0.250627 0.434099i
\(399\) 0 0
\(400\) −7.05842 + 12.2255i −0.352921 + 0.611277i
\(401\) 5.87228 + 10.1711i 0.293248 + 0.507920i 0.974576 0.224058i \(-0.0719306\pi\)
−0.681328 + 0.731978i \(0.738597\pi\)
\(402\) 1.05842 + 3.51039i 0.0527893 + 0.175082i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) −0.813859 + 1.40965i −0.0404910 + 0.0701325i
\(405\) −39.0475 + 4.87375i −1.94029 + 0.242178i
\(406\) 0 0
\(407\) 1.37228 + 2.37686i 0.0680215 + 0.117817i
\(408\) −1.62772 + 1.73205i −0.0805841 + 0.0857493i
\(409\) −22.3505 −1.10516 −0.552581 0.833459i \(-0.686357\pi\)
−0.552581 + 0.833459i \(0.686357\pi\)
\(410\) −20.2337 −0.999271
\(411\) −17.9198 4.21010i −0.883920 0.207669i
\(412\) 5.00000 + 8.66025i 0.246332 + 0.426660i
\(413\) 0 0
\(414\) 4.37228 + 2.17448i 0.214886 + 0.106870i
\(415\) −38.2337 + 66.2227i −1.87682 + 3.25074i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −22.3139 5.24244i −1.09271 0.256723i
\(418\) −3.43070 5.94215i −0.167801 0.290640i
\(419\) 6.30298 10.9171i 0.307921 0.533335i −0.669986 0.742373i \(-0.733700\pi\)
0.977907 + 0.209039i \(0.0670334\pi\)
\(420\) 0 0
\(421\) −17.1168 29.6472i −0.834224 1.44492i −0.894661 0.446746i \(-0.852583\pi\)
0.0604368 0.998172i \(-0.480751\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 0 0
\(424\) −4.37228 7.57301i −0.212337 0.367778i
\(425\) 19.3723 0.939694
\(426\) 3.55842 + 11.8020i 0.172406 + 0.571806i
\(427\) 0 0
\(428\) 3.68614 6.38458i 0.178176 0.308610i
\(429\) −3.25544 + 3.46410i −0.157174 + 0.167248i
\(430\) −17.7446 + 30.7345i −0.855719 + 1.48215i
\(431\) 3.25544 + 5.63858i 0.156809 + 0.271601i 0.933716 0.358014i \(-0.116546\pi\)
−0.776907 + 0.629615i \(0.783213\pi\)
\(432\) −4.00000 3.31662i −0.192450 0.159571i
\(433\) −20.1168 −0.966754 −0.483377 0.875412i \(-0.660590\pi\)
−0.483377 + 0.875412i \(0.660590\pi\)
\(434\) 0 0
\(435\) 64.4674 + 15.1460i 3.09097 + 0.726196i
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −8.13859 −0.389322
\(438\) −14.3723 + 15.2935i −0.686734 + 0.730752i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) −40.1168 −1.90601 −0.953004 0.302956i \(-0.902026\pi\)
−0.953004 + 0.302956i \(0.902026\pi\)
\(444\) −3.37228 0.792287i −0.160041 0.0376003i
\(445\) 64.4674 3.05605
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) 3.86141 4.10891i 0.182638 0.194345i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 2.62772 + 42.2689i 0.123872 + 1.99258i
\(451\) 3.17527 + 5.49972i 0.149517 + 0.258972i
\(452\) 2.18614 3.78651i 0.102827 0.178102i
\(453\) −15.3723 3.61158i −0.722253 0.169687i
\(454\) −6.12772 + 10.6135i −0.287588 + 0.498117i
\(455\) 0 0
\(456\) 8.43070 + 1.98072i 0.394804 + 0.0927556i
\(457\) −35.4674 −1.65909 −0.829547 0.558437i \(-0.811401\pi\)
−0.829547 + 0.558437i \(0.811401\pi\)
\(458\) −1.44158 2.49689i −0.0673605 0.116672i
\(459\) −1.19702 + 7.02939i −0.0558719 + 0.328104i
\(460\) 3.55842 6.16337i 0.165912 0.287368i
\(461\) −1.06930 1.85208i −0.0498021 0.0862598i 0.840050 0.542509i \(-0.182526\pi\)
−0.889852 + 0.456250i \(0.849192\pi\)
\(462\) 0 0
\(463\) 11.5584 20.0198i 0.537165 0.930398i −0.461890 0.886937i \(-0.652828\pi\)
0.999055 0.0434604i \(-0.0138382\pi\)
\(464\) 4.37228 + 7.57301i 0.202978 + 0.351568i
\(465\) 10.3723 11.0371i 0.481003 0.511834i
\(466\) −0.127719 + 0.221215i −0.00591645 + 0.0102476i
\(467\) −16.5475 + 28.6612i −0.765729 + 1.32628i 0.174131 + 0.984722i \(0.444288\pi\)
−0.939860 + 0.341559i \(0.889045\pi\)
\(468\) −0.372281 5.98844i −0.0172087 0.276816i
\(469\) 0 0
\(470\) 0 0
\(471\) 4.55842 + 15.1186i 0.210041 + 0.696627i
\(472\) 10.1168 0.465665
\(473\) 11.1386 0.512153
\(474\) 2.55842 + 8.48533i 0.117512 + 0.389744i
\(475\) −35.2921 61.1277i −1.61931 2.80473i
\(476\) 0 0
\(477\) −23.4891 11.6819i −1.07549 0.534879i
\(478\) 4.93070 8.54023i 0.225525 0.390621i
\(479\) −16.3723 + 28.3576i −0.748069 + 1.29569i 0.200679 + 0.979657i \(0.435685\pi\)
−0.948747 + 0.316036i \(0.897648\pi\)
\(480\) −5.18614 + 5.51856i −0.236714 + 0.251887i
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) 9.05842 15.6896i 0.412600 0.714644i
\(483\) 0 0
\(484\) 4.55842 + 7.89542i 0.207201 + 0.358883i
\(485\) 17.7446 30.7345i 0.805739 1.39558i
\(486\) −15.5000 1.65831i −0.703094 0.0752226i
\(487\) −17.6753 30.6145i −0.800943 1.38727i −0.918996 0.394266i \(-0.870999\pi\)
0.118053 0.993007i \(-0.462335\pi\)
\(488\) −3.11684 −0.141093
\(489\) 30.7446 + 7.22316i 1.39032 + 0.326642i
\(490\) 0 0
\(491\) 12.6861 21.9730i 0.572518 0.991629i −0.423789 0.905761i \(-0.639300\pi\)
0.996306 0.0858685i \(-0.0273665\pi\)
\(492\) −7.80298 1.83324i −0.351786 0.0826489i
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) 15.0000 9.94987i 0.674200 0.447214i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −20.7446 + 22.0742i −0.929586 + 0.989170i
\(499\) −9.05842 15.6896i −0.405511 0.702365i 0.588870 0.808228i \(-0.299573\pi\)
−0.994381 + 0.105863i \(0.966240\pi\)
\(500\) 39.8614 1.78266
\(501\) 9.25544 + 2.17448i 0.413502 + 0.0971487i
\(502\) 9.00000 0.401690
\(503\) −32.2337 −1.43723 −0.718615 0.695409i \(-0.755223\pi\)
−0.718615 + 0.695409i \(0.755223\pi\)
\(504\) 0 0
\(505\) 7.11684 0.316695
\(506\) −2.23369 −0.0992995
\(507\) −10.6753 + 11.3595i −0.474105 + 0.504494i
\(508\) 3.11684 0.138288
\(509\) 14.4891 + 25.0959i 0.642219 + 1.11236i 0.984936 + 0.172918i \(0.0553194\pi\)
−0.342717 + 0.939439i \(0.611347\pi\)
\(510\) 10.1168 + 2.37686i 0.447981 + 0.105249i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 24.3614 9.02895i 1.07558 0.398638i
\(514\) −3.43070 5.94215i −0.151322 0.262097i
\(515\) 21.8614 37.8651i 0.963329 1.66853i
\(516\) −9.62772 + 10.2448i −0.423837 + 0.451003i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 9.94987i −0.131685 0.436751i
\(520\) −8.74456 −0.383474
\(521\) 12.4307 + 21.5306i 0.544599 + 0.943273i 0.998632 + 0.0522883i \(0.0166515\pi\)
−0.454033 + 0.890985i \(0.650015\pi\)
\(522\) 23.4891 + 11.6819i 1.02809 + 0.511304i
\(523\) 17.5584 30.4121i 0.767776 1.32983i −0.170990 0.985273i \(-0.554697\pi\)
0.938766 0.344555i \(-0.111970\pi\)
\(524\) 0.813859 + 1.40965i 0.0355536 + 0.0615807i
\(525\) 0 0
\(526\) 3.81386 6.60580i 0.166292 0.288026i
\(527\) −1.37228 2.37686i −0.0597775 0.103538i
\(528\) 2.31386 + 0.543620i 0.100698 + 0.0236580i
\(529\) 10.1753 17.6241i 0.442403 0.766264i
\(530\) −19.1168 + 33.1113i −0.830383 + 1.43826i
\(531\) 25.2921 16.7769i 1.09758 0.728055i
\(532\) 0 0
\(533\) −4.62772 8.01544i −0.200449 0.347187i
\(534\) 24.8614 + 5.84096i 1.07586 + 0.252763i
\(535\) −32.2337 −1.39358
\(536\) 2.11684 0.0914337
\(537\) 3.86141 4.10891i 0.166632 0.177313i
\(538\) −0.813859 1.40965i −0.0350880 0.0607741i
\(539\) 0 0
\(540\) −3.81386 + 22.3966i −0.164122 + 0.963798i
\(541\) 3.11684 5.39853i 0.134004 0.232101i −0.791213 0.611541i \(-0.790550\pi\)
0.925216 + 0.379440i \(0.123883\pi\)
\(542\) 8.11684 14.0588i 0.348648 0.603877i
\(543\) 0.441578 + 1.46455i 0.0189499 + 0.0628498i
\(544\) 0.686141 + 1.18843i 0.0294180 + 0.0509535i
\(545\) −30.6060 + 53.0111i −1.31102 + 2.27075i
\(546\) 0 0
\(547\) −9.05842 15.6896i −0.387310 0.670841i 0.604777 0.796395i \(-0.293262\pi\)
−0.992087 + 0.125554i \(0.959929\pi\)
\(548\) −5.31386 + 9.20387i −0.226997 + 0.393170i
\(549\) −7.79211 + 5.16870i −0.332559 + 0.220595i
\(550\) −9.68614 16.7769i −0.413018 0.715369i
\(551\) −43.7228 −1.86265
\(552\) 1.93070 2.05446i 0.0821762 0.0874434i
\(553\) 0 0
\(554\) −6.11684 + 10.5947i −0.259880 + 0.450125i
\(555\) 4.37228 + 14.5012i 0.185593 + 0.615542i
\(556\) −6.61684 + 11.4607i −0.280617 + 0.486042i
\(557\) −14.7446 25.5383i −0.624747 1.08209i −0.988590 0.150633i \(-0.951869\pi\)
0.363843 0.931460i \(-0.381465\pi\)
\(558\) 5.00000 3.31662i 0.211667 0.140404i
\(559\) −16.2337 −0.686612
\(560\) 0 0
\(561\) −0.941578 3.12286i −0.0397535 0.131847i
\(562\) 8.18614 + 14.1788i 0.345312 + 0.598097i
\(563\) 3.00000 0.126435 0.0632175 0.998000i \(-0.479864\pi\)
0.0632175 + 0.998000i \(0.479864\pi\)
\(564\) 0 0
\(565\) −19.1168 −0.804252
\(566\) −27.1168 −1.13981
\(567\) 0 0
\(568\) 7.11684 0.298616
\(569\) 16.1168 0.675653 0.337827 0.941208i \(-0.390308\pi\)
0.337827 + 0.941208i \(0.390308\pi\)
\(570\) −10.9307 36.2530i −0.457837 1.51847i
\(571\) −22.3505 −0.935341 −0.467670 0.883903i \(-0.654907\pi\)
−0.467670 + 0.883903i \(0.654907\pi\)
\(572\) 1.37228 + 2.37686i 0.0573780 + 0.0993815i
\(573\) −9.55842 31.7017i −0.399309 1.32436i
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) −2.50000 + 1.65831i −0.104167 + 0.0690963i
\(577\) −4.94158 8.55906i −0.205721 0.356319i 0.744641 0.667465i \(-0.232620\pi\)
−0.950362 + 0.311146i \(0.899287\pi\)
\(578\) −7.55842 + 13.0916i −0.314389 + 0.544538i
\(579\) −3.50000 11.6082i −0.145455 0.482420i
\(580\) 19.1168 33.1113i 0.793784 1.37487i
\(581\) 0 0
\(582\) 9.62772 10.2448i 0.399082 0.424662i
\(583\) 12.0000 0.496989
\(584\) 6.05842 + 10.4935i 0.250699 + 0.434224i
\(585\) −21.8614 + 14.5012i −0.903858 + 0.599552i
\(586\) −5.18614 + 8.98266i −0.214237 + 0.371070i
\(587\) −7.24456 12.5480i −0.299015 0.517909i 0.676896 0.736079i \(-0.263325\pi\)
−0.975911 + 0.218170i \(0.929991\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) −22.1168 38.3075i −0.910536 1.57709i
\(591\) −3.00000 9.94987i −0.123404 0.409283i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −7.37228 + 12.7692i −0.302743 + 0.524367i −0.976756 0.214353i \(-0.931236\pi\)
0.674013 + 0.738719i \(0.264569\pi\)
\(594\) 6.68614 2.47805i 0.274336 0.101676i
\(595\) 0 0
\(596\) −1.62772 2.81929i −0.0666740 0.115483i
\(597\) −11.8614 + 12.6217i −0.485455 + 0.516571i
\(598\) 3.25544 0.133125
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 23.8030 + 5.59230i 0.971753 + 0.228305i
\(601\) −12.0584 20.8858i −0.491873 0.851950i 0.508083 0.861308i \(-0.330354\pi\)
−0.999956 + 0.00935863i \(0.997021\pi\)
\(602\) 0 0
\(603\) 5.29211 3.51039i 0.215511 0.142954i
\(604\) −4.55842 + 7.89542i −0.185480 + 0.321260i
\(605\) 19.9307 34.5210i 0.810298 1.40348i
\(606\) 2.74456 + 0.644810i 0.111490 + 0.0261936i
\(607\) −11.1168 19.2549i −0.451219 0.781534i 0.547243 0.836974i \(-0.315677\pi\)
−0.998462 + 0.0554398i \(0.982344\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) 0 0
\(610\) 6.81386 + 11.8020i 0.275885 + 0.477847i
\(611\) 0 0
\(612\) 3.68614 + 1.83324i 0.149003 + 0.0741044i
\(613\) 18.1168 + 31.3793i 0.731732 + 1.26740i 0.956142 + 0.292903i \(0.0946213\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(614\) 13.0000 0.524637
\(615\) 10.1168 + 33.5538i 0.407951 + 1.35302i
\(616\) 0 0
\(617\) −9.43070 + 16.3345i −0.379666 + 0.657600i −0.991014 0.133762i \(-0.957294\pi\)
0.611348 + 0.791362i \(0.290628\pi\)
\(618\) 11.8614 12.6217i 0.477136 0.507719i
\(619\) −22.7337 + 39.3759i −0.913744 + 1.58265i −0.105014 + 0.994471i \(0.533489\pi\)
−0.808730 + 0.588180i \(0.799844\pi\)
\(620\) −4.37228 7.57301i −0.175595 0.304140i
\(621\) 1.41983 8.33785i 0.0569758 0.334586i
\(622\) −8.23369 −0.330141
\(623\) 0 0
\(624\) −3.37228 0.792287i −0.134999 0.0317169i
\(625\) −51.8505 89.8078i −2.07402 3.59231i
\(626\) 20.1168 0.804031
\(627\) −8.13859 + 8.66025i −0.325024 + 0.345857i
\(628\) 9.11684 0.363802
\(629\) 2.74456 0.109433
\(630\) 0 0
\(631\) −37.3505 −1.48690 −0.743451 0.668791i \(-0.766812\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(632\) 5.11684 0.203537
\(633\) 26.9783 + 6.33830i 1.07229 + 0.251925i
\(634\) 6.00000 0.238290
\(635\) −6.81386 11.8020i −0.270400 0.468346i
\(636\) −10.3723 + 11.0371i −0.411288 + 0.437650i
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) 17.7921 11.8020i 0.703845 0.466878i
\(640\) 2.18614 + 3.78651i 0.0864148 + 0.149675i
\(641\) −17.1060 + 29.6284i −0.675645 + 1.17025i 0.300635 + 0.953739i \(0.402802\pi\)
−0.976280 + 0.216512i \(0.930532\pi\)
\(642\) −12.4307 2.92048i −0.490601 0.115262i
\(643\) −13.1753 + 22.8202i −0.519582 + 0.899942i 0.480159 + 0.877181i \(0.340579\pi\)
−0.999741 + 0.0227606i \(0.992754\pi\)
\(644\) 0 0
\(645\) 59.8397 + 14.0588i 2.35618 + 0.553564i
\(646\) −6.86141 −0.269958
\(647\) −2.74456 4.75372i −0.107900 0.186888i 0.807019 0.590525i \(-0.201079\pi\)
−0.914919 + 0.403637i \(0.867746\pi\)
\(648\) −3.50000 + 8.29156i −0.137493 + 0.325723i
\(649\) −6.94158 + 12.0232i −0.272481 + 0.471951i
\(650\) 14.1168 + 24.4511i 0.553708 + 0.959051i
\(651\) 0 0
\(652\) 9.11684 15.7908i 0.357043 0.618417i
\(653\) 13.3723 + 23.1615i 0.523298 + 0.906378i 0.999632 + 0.0271143i \(0.00863179\pi\)
−0.476335 + 0.879264i \(0.658035\pi\)
\(654\) −16.6060 + 17.6704i −0.649345 + 0.690966i
\(655\) 3.55842 6.16337i 0.139039 0.240823i
\(656\) −2.31386 + 4.00772i −0.0903410 + 0.156475i
\(657\) 32.5475 + 16.1870i 1.26980 + 0.631514i
\(658\) 0 0
\(659\) 10.3723 + 17.9653i 0.404047 + 0.699829i 0.994210 0.107454i \(-0.0342700\pi\)
−0.590163 + 0.807284i \(0.700937\pi\)
\(660\) −3.00000 9.94987i −0.116775 0.387298i
\(661\) 27.1168 1.05472 0.527361 0.849641i \(-0.323181\pi\)
0.527361 + 0.849641i \(0.323181\pi\)
\(662\) −22.2337 −0.864137
\(663\) 1.37228 + 4.55134i 0.0532950 + 0.176759i
\(664\) 8.74456 + 15.1460i 0.339355 + 0.587780i
\(665\) 0 0
\(666\) 0.372281 + 5.98844i 0.0144256 + 0.232047i
\(667\) −7.11684 + 12.3267i −0.275565 + 0.477293i
\(668\) 2.74456 4.75372i 0.106190 0.183927i
\(669\) −4.74456 + 5.04868i −0.183435 + 0.195193i
\(670\) −4.62772 8.01544i −0.178784 0.309664i
\(671\) 2.13859 3.70415i 0.0825595 0.142997i
\(672\) 0 0
\(673\) 1.44158 + 2.49689i 0.0555687 + 0.0962479i 0.892472 0.451103i \(-0.148969\pi\)
−0.836903 + 0.547351i \(0.815636\pi\)
\(674\) −4.05842 + 7.02939i −0.156325 + 0.270762i
\(675\) 68.7812 25.4920i 2.64739 0.981189i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 34.4674 1.32469 0.662344 0.749199i \(-0.269562\pi\)
0.662344 + 0.749199i \(0.269562\pi\)
\(678\) −7.37228 1.73205i −0.283131 0.0665190i
\(679\) 0 0
\(680\) 3.00000 5.19615i 0.115045 0.199263i
\(681\) 20.6644 + 4.85491i 0.791861 + 0.186041i
\(682\) −1.37228 + 2.37686i −0.0525474 + 0.0910147i
\(683\) −14.9198 25.8419i −0.570891 0.988813i −0.996475 0.0838936i \(-0.973264\pi\)
0.425583 0.904919i \(-0.360069\pi\)
\(684\) −0.930703 14.9711i −0.0355863 0.572434i
\(685\) 46.4674 1.77543
\(686\) 0 0
\(687\) −3.41983 + 3.63903i −0.130475 + 0.138838i
\(688\) 4.05842 + 7.02939i 0.154726 + 0.267993i
\(689\) −17.4891 −0.666283
\(690\) −12.0000 2.81929i −0.456832 0.107329i
\(691\) −23.1168 −0.879406 −0.439703 0.898143i \(-0.644916\pi\)
−0.439703 + 0.898143i \(0.644916\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 10.1168 0.384030
\(695\) 57.8614 2.19481
\(696\) 10.3723 11.0371i 0.393160 0.418361i
\(697\) 6.35053 0.240544
\(698\) −11.0000 19.0526i −0.416356 0.721150i
\(699\) 0.430703 + 0.101190i 0.0162907 + 0.00382735i
\(700\) 0 0
\(701\) −38.2337 −1.44407 −0.722033 0.691858i \(-0.756792\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(702\) −9.74456 + 3.61158i −0.367785 + 0.136310i
\(703\) −5.00000 8.66025i −0.188579 0.326628i
\(704\) 0.686141 1.18843i 0.0258599 0.0447907i
\(705\) 0 0
\(706\) −6.68614 + 11.5807i −0.251636 + 0.435847i
\(707\) 0 0
\(708\) −5.05842 16.7769i −0.190107 0.630514i
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) −15.5584 26.9480i −0.583897 1.01134i
\(711\) 12.7921 8.48533i 0.479742 0.318225i
\(712\) 7.37228 12.7692i 0.276288 0.478545i
\(713\) 1.62772 + 2.81929i 0.0609585 + 0.105583i
\(714\) 0 0
\(715\) 6.00000 10.3923i 0.224387 0.388650i
\(716\) −1.62772 2.81929i −0.0608307 0.105362i
\(717\) −16.6277 3.90653i −0.620974 0.145892i
\(718\) 10.9307 18.9325i 0.407930 0.706556i
\(719\) −1.37228 + 2.37686i −0.0511775 + 0.0886420i −0.890479 0.455024i \(-0.849631\pi\)
0.839302 + 0.543666i \(0.182964\pi\)
\(720\) 11.7446 + 5.84096i 0.437694 + 0.217680i
\(721\) 0 0
\(722\) 3.00000 + 5.19615i 0.111648 + 0.193381i
\(723\) −30.5475 7.17687i −1.13608 0.266911i
\(724\) 0.883156 0.0328222
\(725\) −123.446 −4.58466
\(726\) 10.8139 11.5070i 0.401340 0.427065i
\(727\) 18.1168 + 31.3793i 0.671917 + 1.16379i 0.977360 + 0.211583i \(0.0678620\pi\)
−0.305443 + 0.952210i \(0.598805\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 26.4891 45.8805i 0.980407 1.69811i
\(731\) 5.56930 9.64630i 0.205988 0.356781i
\(732\) 1.55842 + 5.16870i 0.0576009 + 0.191041i
\(733\) 20.5584 + 35.6082i 0.759343 + 1.31522i 0.943186 + 0.332265i \(0.107813\pi\)
−0.183844 + 0.982956i \(0.558854\pi\)
\(734\) −6.11684 + 10.5947i −0.225777 + 0.391057i
\(735\) 0 0
\(736\) −0.813859 1.40965i −0.0299993 0.0519602i
\(737\) −1.45245 + 2.51572i −0.0535018 + 0.0926678i
\(738\) 0.861407 + 13.8564i 0.0317088 + 0.510061i
\(739\) 4.05842 + 7.02939i 0.149291 + 0.258580i 0.930966 0.365106i \(-0.118967\pi\)
−0.781674 + 0.623687i \(0.785634\pi\)
\(740\) 8.74456 0.321457
\(741\) 11.8614 12.6217i 0.435740 0.463669i
\(742\) 0 0
\(743\) 6.86141 11.8843i 0.251721 0.435993i −0.712279 0.701896i \(-0.752337\pi\)
0.964000 + 0.265904i \(0.0856703\pi\)
\(744\) −1.00000 3.31662i −0.0366618 0.121593i
\(745\) −7.11684 + 12.3267i −0.260741 + 0.451617i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 46.9783 + 23.3639i 1.71884 + 0.854839i
\(748\) −1.88316 −0.0688550
\(749\) 0 0
\(750\) −19.9307 66.1027i −0.727766 2.41373i
\(751\) 8.55842 + 14.8236i 0.312301 + 0.540922i 0.978860 0.204531i \(-0.0655668\pi\)
−0.666559 + 0.745452i \(0.732234\pi\)
\(752\) 0 0
\(753\) −4.50000 14.9248i −0.163989 0.543890i
\(754\) 17.4891 0.636916
\(755\) 39.8614 1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) 8.11684 0.294817
\(759\) 1.11684 + 3.70415i 0.0405389 + 0.134452i
\(760\) −21.8614 −0.792997
\(761\) −17.7446 30.7345i −0.643240 1.11412i −0.984705 0.174230i \(-0.944256\pi\)
0.341465 0.939894i \(-0.389077\pi\)
\(762\) −1.55842 5.16870i −0.0564557 0.187242i
\(763\) 0 0
\(764\) −19.1168 −0.691623
\(765\) −1.11684 17.9653i −0.0403796 0.649537i
\(766\) −16.3723 28.3576i −0.591555 1.02460i
\(767\) 10.1168 17.5229i 0.365298 0.632715i
\(768\) 0.500000 + 1.65831i 0.0180422 + 0.0598392i
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) −8.13859 + 8.66025i −0.293104 + 0.311891i
\(772\) −7.00000 −0.251936
\(773\) 19.9307 + 34.5210i 0.716858 + 1.24163i 0.962239 + 0.272207i \(0.0877536\pi\)
−0.245381 + 0.969427i \(0.578913\pi\)
\(774\) 21.8030 + 10.8434i 0.783692 + 0.389756i
\(775\) −14.1168 + 24.4511i −0.507092 + 0.878309i
\(776\) −4.05842 7.02939i −0.145689 0.252341i
\(777\) 0 0
\(778\) 5.48913 9.50744i 0.196795 0.340858i
\(779\) −11.5693 20.0386i −0.414513 0.717958i
\(780\) 4.37228 + 14.5012i 0.156553 + 0.519227i
\(781\) −4.88316 + 8.45787i −0.174733 + 0.302647i
\(782\) −1.11684 + 1.93443i −0.0399383 + 0.0691751i
\(783\) 7.62772 44.7933i 0.272592 1.60078i
\(784\) 0 0
\(785\) −19.9307 34.5210i −0.711357 1.23211i
\(786\) 1.93070 2.05446i 0.0688659 0.0732800i
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) −6.00000 −0.213741
\(789\) −12.8614 3.02167i −0.457878 0.107574i
\(790\) −11.1861 19.3750i −0.397985 0.689330i
\(791\) 0 0
\(792\) −0.255437 4.10891i −0.00907657 0.146004i
\(793\) −3.11684 + 5.39853i −0.110682 + 0.191707i
\(794\) −11.0000 + 19.0526i −0.390375 + 0.676150i
\(795\) 64.4674 + 15.1460i 2.28642 + 0.537174i
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) 4.06930 7.04823i 0.144142 0.249661i −0.784911 0.619609i \(-0.787291\pi\)
0.929052 + 0.369948i \(0.120624\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 7.05842 12.2255i 0.249553 0.432238i
\(801\) −2.74456 44.1485i −0.0969744 1.55991i
\(802\) −5.87228 10.1711i −0.207357 0.359154i
\(803\) −16.6277 −0.586779
\(804\) −1.05842 3.51039i −0.0373277 0.123802i
\(805\) 0 0
\(806\) 2.00000 3.46410i 0.0704470 0.122018i
\(807\) −1.93070 + 2.05446i −0.0679640 + 0.0723203i
\(808\) 0.813859 1.40965i 0.0286315 0.0495912i
\(809\) 3.43070 + 5.94215i 0.120617 + 0.208915i 0.920011 0.391892i \(-0.128179\pi\)
−0.799394 + 0.600807i \(0.794846\pi\)
\(810\) 39.0475 4.87375i 1.37199 0.171246i
\(811\) 42.1168 1.47892 0.739461 0.673199i \(-0.235080\pi\)
0.739461 + 0.673199i \(0.235080\pi\)
\(812\) 0 0
\(813\) −27.3723 6.43087i −0.959988 0.225540i
\(814\) −1.37228 2.37686i −0.0480984 0.0833089i
\(815\) −79.7228 −2.79257
\(816\) 1.62772 1.73205i 0.0569816 0.0606339i
\(817\) −40.5842 −1.41986
\(818\) 22.3505 0.781468
\(819\) 0 0
\(820\) 20.2337 0.706591
\(821\) −3.76631 −0.131445 −0.0657226 0.997838i \(-0.520935\pi\)
−0.0657226 + 0.997838i \(0.520935\pi\)
\(822\) 17.9198 + 4.21010i 0.625026 + 0.146844i
\(823\) −12.2337 −0.426440 −0.213220 0.977004i \(-0.568395\pi\)
−0.213220 + 0.977004i \(0.568395\pi\)
\(824\) −5.00000 8.66025i −0.174183 0.301694i
\(825\) −22.9783 + 24.4511i −0.800000 + 0.851278i
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) −4.37228 2.17448i −0.151947 0.0755684i
\(829\) 6.88316 + 11.9220i 0.239062 + 0.414067i 0.960445 0.278468i \(-0.0898268\pi\)
−0.721383 + 0.692536i \(0.756493\pi\)
\(830\) 38.2337 66.2227i 1.32711 2.29862i
\(831\) 20.6277 + 4.84630i 0.715568 + 0.168116i
\(832\) −1.00000 + 1.73205i −0.0346688 + 0.0600481i
\(833\) 0 0
\(834\) 22.3139 + 5.24244i 0.772666 + 0.181531i
\(835\) −24.0000 −0.830554
\(836\) 3.43070 + 5.94215i 0.118653 + 0.205514i
\(837\) −8.00000 6.63325i −0.276520 0.229279i
\(838\) −6.30298 + 10.9171i −0.217733 + 0.377125i
\(839\) −2.74456 4.75372i −0.0947528 0.164117i 0.814753 0.579809i \(-0.196873\pi\)
−0.909505 + 0.415692i \(0.863539\pi\)
\(840\) 0 0
\(841\) −23.7337 + 41.1080i −0.818403 + 1.41752i
\(842\) 17.1168 + 29.6472i 0.589885 + 1.02171i
\(843\) 19.4198 20.6646i 0.668854 0.711726i
\(844\) 8.00000 13.8564i 0.275371 0.476957i
\(845\) 19.6753 34.0786i 0.676850 1.17234i
\(846\) 0 0
\(847\) 0 0
\(848\) 4.37228 + 7.57301i 0.150145 + 0.260058i
\(849\) 13.5584 + 44.9682i 0.465324 + 1.54330i
\(850\) −19.3723 −0.664464
\(851\) −3.25544 −0.111595
\(852\) −3.55842 11.8020i −0.121910 0.404328i
\(853\) 17.5584 + 30.4121i 0.601189 + 1.04129i 0.992641 + 0.121091i \(0.0386394\pi\)
−0.391452 + 0.920198i \(0.628027\pi\)
\(854\) 0 0
\(855\) −54.6535 + 36.2530i −1.86911 + 1.23983i
\(856\) −3.68614 + 6.38458i −0.125990 + 0.218221i
\(857\) 19.9783 34.6033i 0.682444 1.18203i −0.291789 0.956483i \(-0.594250\pi\)
0.974233 0.225545i \(-0.0724163\pi\)
\(858\) 3.25544 3.46410i 0.111139 0.118262i
\(859\) −16.9416 29.3437i −0.578039 1.00119i −0.995704 0.0925921i \(-0.970485\pi\)
0.417665 0.908601i \(-0.362849\pi\)
\(860\) 17.7446 30.7345i 0.605085 1.04804i
\(861\) 0 0
\(862\) −3.25544 5.63858i −0.110881 0.192051i
\(863\) −4.93070 + 8.54023i −0.167843 + 0.290713i −0.937661 0.347550i \(-0.887014\pi\)
0.769818 + 0.638263i \(0.220347\pi\)
\(864\) 4.00000 + 3.31662i 0.136083 + 0.112834i
\(865\) 13.1168 + 22.7190i 0.445986 + 0.772471i
\(866\) 20.1168 0.683598
\(867\) 25.4891 + 5.98844i 0.865656 + 0.203378i
\(868\) 0 0
\(869\) −3.51087 + 6.08101i −0.119098 + 0.206284i
\(870\) −64.4674 15.1460i −2.18565 0.513498i
\(871\) 2.11684 3.66648i 0.0717265 0.124234i
\(872\) 7.00000 + 12.1244i 0.237050 + 0.410582i
\(873\) −21.8030 10.8434i −0.737919 0.366992i
\(874\) 8.13859 0.275292
\(875\) 0 0
\(876\) 14.3723 15.2935i 0.485594 0.516720i
\(877\) 29.3505 + 50.8366i 0.991097 + 1.71663i 0.610852 + 0.791744i \(0.290827\pi\)
0.380245 + 0.924886i \(0.375840\pi\)
\(878\) −8.00000 −0.269987
\(879\) 17.4891 + 4.10891i 0.589894 + 0.138590i
\(880\) −6.00000 −0.202260
\(881\) −20.2337 −0.681690 −0.340845 0.940119i \(-0.610713\pi\)
−0.340845 + 0.940119i \(0.610713\pi\)
\(882\) 0 0
\(883\) −40.3505 −1.35790 −0.678952 0.734183i \(-0.737565\pi\)
−0.678952 + 0.734183i \(0.737565\pi\)
\(884\) 2.74456 0.0923096
\(885\) −52.4674 + 55.8304i −1.76367 + 1.87672i
\(886\) 40.1168 1.34775
\(887\) −12.8614 22.2766i −0.431844 0.747975i 0.565188 0.824962i \(-0.308803\pi\)
−0.997032 + 0.0769865i \(0.975470\pi\)
\(888\) 3.37228 + 0.792287i 0.113166 + 0.0265874i
\(889\) 0 0
\(890\) −64.4674 −2.16095
\(891\) −7.45245 9.84868i −0.249667 0.329943i
\(892\) 2.00000 + 3.46410i 0.0669650 + 0.115987i
\(893\) 0 0
\(894\) −3.86141 + 4.10891i −0.129145 + 0.137423i
\(895\) −7.11684 + 12.3267i −0.237890 + 0.412037i
\(896\) 0 0
\(897\) −1.62772 5.39853i −0.0543479 0.180252i
\(898\) −33.0000 −1.10122
\(899\) 8.74456 + 15.1460i 0.291647 + 0.505148i
\(900\) −2.62772 42.2689i −0.0875906 1.40896i
\(901\) 6.00000 10.3923i 0.199889 0.346218i
\(902\) −3.17527 5.49972i −0.105725 0.183121i
\(903\) 0 0
\(904\) −2.18614 + 3.78651i −0.0727100 + 0.125937i
\(905\) −1.93070 3.34408i −0.0641787 0.111161i
\(906\) 15.3723 + 3.61158i 0.510710 + 0.119987i
\(907\) 13.0584 22.6179i 0.433598 0.751013i −0.563582 0.826060i \(-0.690577\pi\)
0.997180 + 0.0750466i \(0.0239105\pi\)
\(908\) 6.12772 10.6135i 0.203355 0.352222i
\(909\) −0.302985 4.87375i −0.0100494 0.161652i
\(910\) 0 0
\(911\) 18.8139 + 32.5866i 0.623331 + 1.07964i 0.988861 + 0.148841i \(0.0475544\pi\)
−0.365530 + 0.930800i \(0.619112\pi\)
\(912\) −8.43070 1.98072i −0.279168 0.0655881i
\(913\) −24.0000 −0.794284
\(914\) 35.4674 1.17316
\(915\) 16.1644 17.2005i 0.534378 0.568630i
\(916\) 1.44158 + 2.49689i 0.0476311 + 0.0824994i
\(917\) 0 0
\(918\) 1.19702 7.02939i 0.0395074 0.232005i
\(919\) 23.5584 40.8044i 0.777121 1.34601i −0.156474 0.987682i \(-0.550013\pi\)
0.933595 0.358330i \(-0.116654\pi\)
\(920\) −3.55842 + 6.16337i −0.117318 + 0.203200i
\(921\) −6.50000 21.5581i −0.214182 0.710362i
\(922\) 1.06930 + 1.85208i 0.0352154 + 0.0609949i
\(923\) 7.11684 12.3267i 0.234254 0.405739i
\(924\) 0 0
\(925\) −14.1168 24.4511i −0.464159 0.803947i
\(926\) −11.5584 + 20.0198i −0.379833 + 0.657891i
\(927\) −26.8614 13.3591i −0.882244 0.438770i
\(928\) −4.37228 7.57301i −0.143527 0.248596i
\(929\) 44.2337 1.45126 0.725630 0.688085i \(-0.241548\pi\)
0.725630 + 0.688085i \(0.241548\pi\)
\(930\) −10.3723 + 11.0371i −0.340121 + 0.361921i
\(931\) 0 0
\(932\) 0.127719 0.221215i 0.00418356 0.00724615i
\(933\) 4.11684 + 13.6540i 0.134779 + 0.447013i
\(934\) 16.5475 28.6612i 0.541452 0.937823i
\(935\) 4.11684 + 7.13058i 0.134635 + 0.233195i
\(936\) 0.372281 + 5.98844i 0.0121684 + 0.195738i
\(937\) 30.4674 0.995326 0.497663 0.867371i \(-0.334192\pi\)
0.497663 + 0.867371i \(0.334192\pi\)
\(938\) 0 0
\(939\) −10.0584 33.3600i −0.328244 1.08866i
\(940\) 0 0
\(941\) 19.1168 0.623191 0.311596 0.950215i \(-0.399137\pi\)
0.311596 + 0.950215i \(0.399137\pi\)
\(942\) −4.55842 15.1186i −0.148521 0.492590i
\(943\) −7.53262 −0.245296
\(944\) −10.1168 −0.329275
\(945\) 0 0
\(946\) −11.1386 −0.362147
\(947\) 34.1168 1.10865 0.554324 0.832301i \(-0.312977\pi\)
0.554324 + 0.832301i \(0.312977\pi\)
\(948\) −2.55842 8.48533i −0.0830937 0.275591i
\(949\) 24.2337 0.786659
\(950\) 35.2921 + 61.1277i 1.14503 + 1.98325i
\(951\) −3.00000 9.94987i −0.0972817 0.322647i
\(952\) 0 0
\(953\) 28.1168 0.910794 0.455397 0.890288i \(-0.349497\pi\)
0.455397 + 0.890288i \(0.349497\pi\)
\(954\) 23.4891 + 11.6819i 0.760489 + 0.378216i
\(955\) 41.7921 + 72.3861i 1.35236 + 2.34236i
\(956\) −4.93070 + 8.54023i −0.159470 + 0.276211i
\(957\) 6.00000 + 19.8997i 0.193952 + 0.643268i
\(958\) 16.3723 28.3576i 0.528964 0.916193i
\(959\) 0 0
\(960\) 5.18614 5.51856i 0.167382 0.178111i
\(961\) −27.0000 −0.870968
\(962\) 2.00000 + 3.46410i 0.0644826 + 0.111687i
\(963\) 1.37228 + 22.0742i 0.0442211 + 0.711332i
\(964\) −9.05842 + 15.6896i −0.291752 + 0.505330i
\(965\) 15.3030 + 26.5055i 0.492621 + 0.853244i
\(966\) 0 0
\(967\) −15.4416 + 26.7456i −0.496568 + 0.860080i −0.999992 0.00395879i \(-0.998740\pi\)
0.503424 + 0.864039i \(0.332073\pi\)
\(968\) −4.55842 7.89542i −0.146513 0.253768i
\(969\) 3.43070 + 11.3784i 0.110210 + 0.365525i
\(970\) −17.7446 + 30.7345i −0.569744 + 0.986825i
\(971\) −0.813859 + 1.40965i −0.0261180 + 0.0452377i −0.878789 0.477211i \(-0.841648\pi\)
0.852671 + 0.522448i \(0.174981\pi\)
\(972\) 15.5000 + 1.65831i 0.497163 + 0.0531904i
\(973\) 0 0
\(974\) 17.6753 + 30.6145i 0.566352 + 0.980951i
\(975\) 33.4891 35.6357i 1.07251 1.14126i
\(976\) 3.11684 0.0997677
\(977\) 40.1168 1.28345 0.641726 0.766934i \(-0.278219\pi\)
0.641726 + 0.766934i \(0.278219\pi\)
\(978\) −30.7446 7.22316i −0.983103 0.230971i
\(979\) 10.1168 + 17.5229i 0.323336 + 0.560034i
\(980\) 0 0
\(981\) 37.6060 + 18.7027i 1.20067 + 0.597131i
\(982\) −12.6861 + 21.9730i −0.404831 + 0.701188i
\(983\) 19.6277 33.9962i 0.626027 1.08431i −0.362314 0.932056i \(-0.618013\pi\)
0.988341 0.152255i \(-0.0486534\pi\)
\(984\) 7.80298 + 1.83324i 0.248750 + 0.0584416i
\(985\) 13.1168 + 22.7190i 0.417937 + 0.723889i
\(986\) −6.00000 + 10.3923i −0.191079 + 0.330958i
\(987\) 0 0
\(988\) −5.00000 8.66025i −0.159071 0.275519i
\(989\) −6.60597 + 11.4419i −0.210058 + 0.363830i
\(990\) −15.0000 + 9.94987i −0.476731 + 0.316228i
\(991\) −24.2337 41.9740i −0.769808 1.33335i −0.937667 0.347536i \(-0.887018\pi\)
0.167858 0.985811i \(-0.446315\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 11.1168 + 36.8704i 0.352782 + 1.17005i
\(994\) 0 0
\(995\) 21.8614 37.8651i 0.693053 1.20040i
\(996\) 20.7446 22.0742i 0.657317 0.699449i
\(997\) 2.55842 4.43132i 0.0810260 0.140341i −0.822665 0.568527i \(-0.807514\pi\)
0.903691 + 0.428185i \(0.140847\pi\)
\(998\) 9.05842 + 15.6896i 0.286739 + 0.496647i
\(999\) 9.74456 3.61158i 0.308304 0.114265i
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 882.2.e.l.373.2 4
3.2 odd 2 2646.2.e.n.1549.2 4
7.2 even 3 126.2.f.d.85.1 yes 4
7.3 odd 6 882.2.h.n.67.1 4
7.4 even 3 882.2.h.m.67.2 4
7.5 odd 6 882.2.f.k.589.2 4
7.6 odd 2 882.2.e.k.373.1 4
9.2 odd 6 2646.2.h.k.667.1 4
9.7 even 3 882.2.h.m.79.2 4
21.2 odd 6 378.2.f.c.253.2 4
21.5 even 6 2646.2.f.j.1765.1 4
21.11 odd 6 2646.2.h.k.361.1 4
21.17 even 6 2646.2.h.l.361.2 4
21.20 even 2 2646.2.e.m.1549.1 4
28.23 odd 6 1008.2.r.f.337.2 4
63.2 odd 6 378.2.f.c.127.2 4
63.5 even 6 7938.2.a.bs.1.2 2
63.11 odd 6 2646.2.e.n.2125.2 4
63.16 even 3 126.2.f.d.43.1 4
63.20 even 6 2646.2.h.l.667.2 4
63.23 odd 6 1134.2.a.n.1.1 2
63.25 even 3 inner 882.2.e.l.655.1 4
63.34 odd 6 882.2.h.n.79.1 4
63.38 even 6 2646.2.e.m.2125.1 4
63.40 odd 6 7938.2.a.bh.1.1 2
63.47 even 6 2646.2.f.j.883.1 4
63.52 odd 6 882.2.e.k.655.2 4
63.58 even 3 1134.2.a.k.1.2 2
63.61 odd 6 882.2.f.k.295.2 4
84.23 even 6 3024.2.r.f.1009.2 4
252.23 even 6 9072.2.a.bb.1.1 2
252.79 odd 6 1008.2.r.f.673.2 4
252.191 even 6 3024.2.r.f.2017.2 4
252.247 odd 6 9072.2.a.bm.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.d.43.1 4 63.16 even 3
126.2.f.d.85.1 yes 4 7.2 even 3
378.2.f.c.127.2 4 63.2 odd 6
378.2.f.c.253.2 4 21.2 odd 6
882.2.e.k.373.1 4 7.6 odd 2
882.2.e.k.655.2 4 63.52 odd 6
882.2.e.l.373.2 4 1.1 even 1 trivial
882.2.e.l.655.1 4 63.25 even 3 inner
882.2.f.k.295.2 4 63.61 odd 6
882.2.f.k.589.2 4 7.5 odd 6
882.2.h.m.67.2 4 7.4 even 3
882.2.h.m.79.2 4 9.7 even 3
882.2.h.n.67.1 4 7.3 odd 6
882.2.h.n.79.1 4 63.34 odd 6
1008.2.r.f.337.2 4 28.23 odd 6
1008.2.r.f.673.2 4 252.79 odd 6
1134.2.a.k.1.2 2 63.58 even 3
1134.2.a.n.1.1 2 63.23 odd 6
2646.2.e.m.1549.1 4 21.20 even 2
2646.2.e.m.2125.1 4 63.38 even 6
2646.2.e.n.1549.2 4 3.2 odd 2
2646.2.e.n.2125.2 4 63.11 odd 6
2646.2.f.j.883.1 4 63.47 even 6
2646.2.f.j.1765.1 4 21.5 even 6
2646.2.h.k.361.1 4 21.11 odd 6
2646.2.h.k.667.1 4 9.2 odd 6
2646.2.h.l.361.2 4 21.17 even 6
2646.2.h.l.667.2 4 63.20 even 6
3024.2.r.f.1009.2 4 84.23 even 6
3024.2.r.f.2017.2 4 252.191 even 6
7938.2.a.bh.1.1 2 63.40 odd 6
7938.2.a.bs.1.2 2 63.5 even 6
9072.2.a.bb.1.1 2 252.23 even 6
9072.2.a.bm.1.2 2 252.247 odd 6