Properties

Label 124.2.j.a.15.2
Level $124$
Weight $2$
Character 124.15
Analytic conductor $0.990$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,2,Mod(15,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.15");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 124.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.990144985064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 15.2
Root \(-0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 124.15
Dual form 124.2.j.a.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.221232 + 1.39680i) q^{2} +(2.48990 + 1.80902i) q^{3} +(-1.90211 - 0.618034i) q^{4} -1.61803 q^{5} +(-3.07768 + 3.07768i) q^{6} +(-0.224514 - 0.0729490i) q^{7} +(1.28408 - 2.52015i) q^{8} +(2.00000 + 6.15537i) q^{9} +O(q^{10})\) \(q+(-0.221232 + 1.39680i) q^{2} +(2.48990 + 1.80902i) q^{3} +(-1.90211 - 0.618034i) q^{4} -1.61803 q^{5} +(-3.07768 + 3.07768i) q^{6} +(-0.224514 - 0.0729490i) q^{7} +(1.28408 - 2.52015i) q^{8} +(2.00000 + 6.15537i) q^{9} +(0.357960 - 2.26007i) q^{10} +(1.90211 - 5.85410i) q^{11} +(-3.61803 - 4.97980i) q^{12} +(-0.263932 + 0.363271i) q^{13} +(0.151565 - 0.297463i) q^{14} +(-4.02874 - 2.92705i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.54508 + 0.502029i) q^{17} +(-9.04029 + 1.43184i) q^{18} +(2.93893 + 4.04508i) q^{19} +(3.07768 + 1.00000i) q^{20} +(-0.427051 - 0.587785i) q^{21} +(7.75621 + 3.95199i) q^{22} +(-0.224514 - 0.690983i) q^{23} +(7.75621 - 3.95199i) q^{24} -2.38197 q^{25} +(-0.449028 - 0.449028i) q^{26} +(-3.30220 + 10.1631i) q^{27} +(0.381966 + 0.277515i) q^{28} +(-4.30902 - 5.93085i) q^{29} +(4.97980 - 4.97980i) q^{30} +(1.76336 - 5.28115i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(15.3262 - 11.1352i) q^{33} +(-0.359413 - 2.26924i) q^{34} +(0.363271 + 0.118034i) q^{35} -12.9443i q^{36} +9.23305i q^{37} +(-6.30037 + 3.21020i) q^{38} +(-1.31433 + 0.427051i) q^{39} +(-2.07768 + 4.07768i) q^{40} +(4.23607 - 3.07768i) q^{41} +(0.915497 - 0.466469i) q^{42} +(2.12663 - 1.54508i) q^{43} +(-7.23607 + 9.95959i) q^{44} +(-3.23607 - 9.95959i) q^{45} +(1.01484 - 0.160734i) q^{46} +(3.30220 - 4.54508i) q^{47} +(3.80423 + 11.7082i) q^{48} +(-5.61803 - 4.08174i) q^{49} +(0.526966 - 3.32714i) q^{50} +(-4.75528 - 1.54508i) q^{51} +(0.726543 - 0.527864i) q^{52} +(-8.78115 + 2.85317i) q^{53} +(-13.4653 - 6.86092i) q^{54} +(-3.07768 + 9.47214i) q^{55} +(-0.472136 + 0.472136i) q^{56} +15.3884i q^{57} +(9.23752 - 4.70675i) q^{58} +(-3.21644 + 4.42705i) q^{59} +(5.85410 + 8.05748i) q^{60} +0.898056i q^{61} +(6.98662 + 3.63142i) q^{62} -1.52786i q^{63} +(-4.70228 - 6.47214i) q^{64} +(0.427051 - 0.587785i) q^{65} +(12.1630 + 23.8712i) q^{66} +5.76393i q^{67} +3.24920 q^{68} +(0.690983 - 2.12663i) q^{69} +(-0.245237 + 0.481305i) q^{70} +(-6.29412 + 2.04508i) q^{71} +(18.0806 + 2.86368i) q^{72} +(-1.80902 - 0.587785i) q^{73} +(-12.8967 - 2.04264i) q^{74} +(-5.93085 - 4.30902i) q^{75} +(-3.09017 - 9.51057i) q^{76} +(-0.854102 + 1.17557i) q^{77} +(-0.305735 - 1.93033i) q^{78} +(-2.07363 - 6.38197i) q^{79} +(-5.23607 - 3.80423i) q^{80} +(-10.8992 + 7.91872i) q^{81} +(3.36176 + 6.59783i) q^{82} +(-5.34307 + 3.88197i) q^{83} +(0.449028 + 1.38197i) q^{84} +(2.50000 - 0.812299i) q^{85} +(1.68770 + 3.31230i) q^{86} -22.5623i q^{87} +(-12.3107 - 12.3107i) q^{88} +(-2.33688 - 0.759299i) q^{89} +(14.6275 - 2.31677i) q^{90} +(0.0857567 - 0.0623059i) q^{91} +1.45309i q^{92} +(13.9443 - 9.95959i) q^{93} +(5.61803 + 5.61803i) q^{94} +(-4.75528 - 6.54508i) q^{95} +(-17.1957 + 2.72353i) q^{96} +(0.454915 - 1.40008i) q^{97} +(6.94427 - 6.94427i) q^{98} +39.8384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.221232 + 1.39680i −0.156434 + 0.987688i
\(3\) 2.48990 + 1.80902i 1.43754 + 1.04444i 0.988549 + 0.150902i \(0.0482178\pi\)
0.448995 + 0.893534i \(0.351782\pi\)
\(4\) −1.90211 0.618034i −0.951057 0.309017i
\(5\) −1.61803 −0.723607 −0.361803 0.932254i \(-0.617839\pi\)
−0.361803 + 0.932254i \(0.617839\pi\)
\(6\) −3.07768 + 3.07768i −1.25646 + 1.25646i
\(7\) −0.224514 0.0729490i −0.0848583 0.0275721i 0.266280 0.963896i \(-0.414205\pi\)
−0.351138 + 0.936324i \(0.614205\pi\)
\(8\) 1.28408 2.52015i 0.453990 0.891007i
\(9\) 2.00000 + 6.15537i 0.666667 + 2.05179i
\(10\) 0.357960 2.26007i 0.113197 0.714698i
\(11\) 1.90211 5.85410i 0.573509 1.76508i −0.0676935 0.997706i \(-0.521564\pi\)
0.641202 0.767372i \(-0.278436\pi\)
\(12\) −3.61803 4.97980i −1.04444 1.43754i
\(13\) −0.263932 + 0.363271i −0.0732016 + 0.100753i −0.844048 0.536268i \(-0.819834\pi\)
0.770846 + 0.637021i \(0.219834\pi\)
\(14\) 0.151565 0.297463i 0.0405074 0.0795003i
\(15\) −4.02874 2.92705i −1.04022 0.755761i
\(16\) 3.23607 + 2.35114i 0.809017 + 0.587785i
\(17\) −1.54508 + 0.502029i −0.374738 + 0.121760i −0.490330 0.871537i \(-0.663124\pi\)
0.115592 + 0.993297i \(0.463124\pi\)
\(18\) −9.04029 + 1.43184i −2.13082 + 0.337488i
\(19\) 2.93893 + 4.04508i 0.674236 + 0.928006i 0.999847 0.0174977i \(-0.00556997\pi\)
−0.325611 + 0.945504i \(0.605570\pi\)
\(20\) 3.07768 + 1.00000i 0.688191 + 0.223607i
\(21\) −0.427051 0.587785i −0.0931902 0.128265i
\(22\) 7.75621 + 3.95199i 1.65363 + 0.842567i
\(23\) −0.224514 0.690983i −0.0468144 0.144080i 0.924917 0.380169i \(-0.124134\pi\)
−0.971731 + 0.236089i \(0.924134\pi\)
\(24\) 7.75621 3.95199i 1.58323 0.806696i
\(25\) −2.38197 −0.476393
\(26\) −0.449028 0.449028i −0.0880616 0.0880616i
\(27\) −3.30220 + 10.1631i −0.635508 + 1.95589i
\(28\) 0.381966 + 0.277515i 0.0721848 + 0.0524453i
\(29\) −4.30902 5.93085i −0.800164 1.10133i −0.992767 0.120055i \(-0.961693\pi\)
0.192603 0.981277i \(-0.438307\pi\)
\(30\) 4.97980 4.97980i 0.909182 0.909182i
\(31\) 1.76336 5.28115i 0.316708 0.948523i
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) 15.3262 11.1352i 2.66796 1.93838i
\(34\) −0.359413 2.26924i −0.0616388 0.389172i
\(35\) 0.363271 + 0.118034i 0.0614041 + 0.0199514i
\(36\) 12.9443i 2.15738i
\(37\) 9.23305i 1.51790i 0.651146 + 0.758952i \(0.274288\pi\)
−0.651146 + 0.758952i \(0.725712\pi\)
\(38\) −6.30037 + 3.21020i −1.02205 + 0.520763i
\(39\) −1.31433 + 0.427051i −0.210461 + 0.0683829i
\(40\) −2.07768 + 4.07768i −0.328511 + 0.644738i
\(41\) 4.23607 3.07768i 0.661563 0.480653i −0.205628 0.978630i \(-0.565924\pi\)
0.867190 + 0.497977i \(0.165924\pi\)
\(42\) 0.915497 0.466469i 0.141264 0.0719777i
\(43\) 2.12663 1.54508i 0.324308 0.235623i −0.413704 0.910412i \(-0.635765\pi\)
0.738011 + 0.674788i \(0.235765\pi\)
\(44\) −7.23607 + 9.95959i −1.09088 + 1.50147i
\(45\) −3.23607 9.95959i −0.482405 1.48469i
\(46\) 1.01484 0.160734i 0.149629 0.0236990i
\(47\) 3.30220 4.54508i 0.481675 0.662969i −0.497151 0.867664i \(-0.665620\pi\)
0.978826 + 0.204695i \(0.0656204\pi\)
\(48\) 3.80423 + 11.7082i 0.549093 + 1.68993i
\(49\) −5.61803 4.08174i −0.802576 0.583106i
\(50\) 0.526966 3.32714i 0.0745243 0.470528i
\(51\) −4.75528 1.54508i −0.665873 0.216355i
\(52\) 0.726543 0.527864i 0.100753 0.0732016i
\(53\) −8.78115 + 2.85317i −1.20618 + 0.391913i −0.842033 0.539427i \(-0.818641\pi\)
−0.364152 + 0.931340i \(0.618641\pi\)
\(54\) −13.4653 6.86092i −1.83240 0.933653i
\(55\) −3.07768 + 9.47214i −0.414995 + 1.27722i
\(56\) −0.472136 + 0.472136i −0.0630918 + 0.0630918i
\(57\) 15.3884i 2.03825i
\(58\) 9.23752 4.70675i 1.21295 0.618027i
\(59\) −3.21644 + 4.42705i −0.418745 + 0.576353i −0.965324 0.261055i \(-0.915930\pi\)
0.546579 + 0.837407i \(0.315930\pi\)
\(60\) 5.85410 + 8.05748i 0.755761 + 1.04022i
\(61\) 0.898056i 0.114984i 0.998346 + 0.0574921i \(0.0183104\pi\)
−0.998346 + 0.0574921i \(0.981690\pi\)
\(62\) 6.98662 + 3.63142i 0.887301 + 0.461191i
\(63\) 1.52786i 0.192493i
\(64\) −4.70228 6.47214i −0.587785 0.809017i
\(65\) 0.427051 0.587785i 0.0529692 0.0729058i
\(66\) 12.1630 + 23.8712i 1.49716 + 2.93834i
\(67\) 5.76393i 0.704176i 0.935967 + 0.352088i \(0.114528\pi\)
−0.935967 + 0.352088i \(0.885472\pi\)
\(68\) 3.24920 0.394023
\(69\) 0.690983 2.12663i 0.0831846 0.256016i
\(70\) −0.245237 + 0.481305i −0.0293115 + 0.0575270i
\(71\) −6.29412 + 2.04508i −0.746975 + 0.242707i −0.657679 0.753298i \(-0.728462\pi\)
−0.0892960 + 0.996005i \(0.528462\pi\)
\(72\) 18.0806 + 2.86368i 2.13082 + 0.337488i
\(73\) −1.80902 0.587785i −0.211729 0.0687951i 0.201232 0.979544i \(-0.435506\pi\)
−0.412961 + 0.910749i \(0.635506\pi\)
\(74\) −12.8967 2.04264i −1.49922 0.237453i
\(75\) −5.93085 4.30902i −0.684836 0.497562i
\(76\) −3.09017 9.51057i −0.354467 1.09094i
\(77\) −0.854102 + 1.17557i −0.0973340 + 0.133969i
\(78\) −0.305735 1.93033i −0.0346176 0.218567i
\(79\) −2.07363 6.38197i −0.233301 0.718027i −0.997342 0.0728596i \(-0.976788\pi\)
0.764041 0.645168i \(-0.223212\pi\)
\(80\) −5.23607 3.80423i −0.585410 0.425325i
\(81\) −10.8992 + 7.91872i −1.21102 + 0.879858i
\(82\) 3.36176 + 6.59783i 0.371245 + 0.728608i
\(83\) −5.34307 + 3.88197i −0.586478 + 0.426101i −0.841054 0.540952i \(-0.818064\pi\)
0.254576 + 0.967053i \(0.418064\pi\)
\(84\) 0.449028 + 1.38197i 0.0489930 + 0.150785i
\(85\) 2.50000 0.812299i 0.271163 0.0881062i
\(86\) 1.68770 + 3.31230i 0.181989 + 0.357174i
\(87\) 22.5623i 2.41893i
\(88\) −12.3107 12.3107i −1.31233 1.31233i
\(89\) −2.33688 0.759299i −0.247709 0.0804855i 0.182531 0.983200i \(-0.441571\pi\)
−0.430240 + 0.902715i \(0.641571\pi\)
\(90\) 14.6275 2.31677i 1.54187 0.244209i
\(91\) 0.0857567 0.0623059i 0.00898975 0.00653143i
\(92\) 1.45309i 0.151495i
\(93\) 13.9443 9.95959i 1.44595 1.03276i
\(94\) 5.61803 + 5.61803i 0.579456 + 0.579456i
\(95\) −4.75528 6.54508i −0.487882 0.671512i
\(96\) −17.1957 + 2.72353i −1.75502 + 0.277969i
\(97\) 0.454915 1.40008i 0.0461896 0.142157i −0.925302 0.379231i \(-0.876188\pi\)
0.971492 + 0.237074i \(0.0761885\pi\)
\(98\) 6.94427 6.94427i 0.701477 0.701477i
\(99\) 39.8384 4.00391
\(100\) 4.53077 + 1.47214i 0.453077 + 0.147214i
\(101\) 2.76393 + 8.50651i 0.275022 + 0.846429i 0.989214 + 0.146480i \(0.0467943\pi\)
−0.714192 + 0.699950i \(0.753206\pi\)
\(102\) 3.21020 6.30037i 0.317857 0.623829i
\(103\) 7.10642 + 9.78115i 0.700217 + 0.963766i 0.999953 + 0.00974339i \(0.00310147\pi\)
−0.299736 + 0.954022i \(0.596899\pi\)
\(104\) 0.576587 + 1.13162i 0.0565390 + 0.110964i
\(105\) 0.690983 + 0.951057i 0.0674330 + 0.0928136i
\(106\) −2.04264 12.8967i −0.198399 1.25264i
\(107\) −6.79615 + 2.20820i −0.657009 + 0.213475i −0.618502 0.785783i \(-0.712260\pi\)
−0.0385069 + 0.999258i \(0.512260\pi\)
\(108\) 12.5623 17.2905i 1.20881 1.66378i
\(109\) 12.2812 + 8.92278i 1.17632 + 0.854647i 0.991752 0.128172i \(-0.0409110\pi\)
0.184569 + 0.982820i \(0.440911\pi\)
\(110\) −12.5498 6.39445i −1.19658 0.609687i
\(111\) −16.7027 + 22.9894i −1.58535 + 2.18205i
\(112\) −0.555029 0.763932i −0.0524453 0.0721848i
\(113\) 2.64590 8.14324i 0.248905 0.766051i −0.746064 0.665874i \(-0.768059\pi\)
0.994970 0.100178i \(-0.0319411\pi\)
\(114\) −21.4946 3.40441i −2.01315 0.318852i
\(115\) 0.363271 + 1.11803i 0.0338752 + 0.104257i
\(116\) 4.53077 + 13.9443i 0.420671 + 1.29469i
\(117\) −2.76393 0.898056i −0.255526 0.0830253i
\(118\) −5.47214 5.47214i −0.503751 0.503751i
\(119\) 0.383516 0.0351568
\(120\) −12.5498 + 6.39445i −1.14564 + 0.583731i
\(121\) −21.7533 15.8047i −1.97757 1.43679i
\(122\) −1.25441 0.198678i −0.113569 0.0179875i
\(123\) 16.1150 1.45304
\(124\) −6.61803 + 8.95554i −0.594317 + 0.804231i
\(125\) 11.9443 1.06833
\(126\) 2.13412 + 0.338012i 0.190123 + 0.0301125i
\(127\) 8.64527 + 6.28115i 0.767143 + 0.557362i 0.901093 0.433626i \(-0.142766\pi\)
−0.133950 + 0.990988i \(0.542766\pi\)
\(128\) 10.0806 5.13632i 0.891007 0.453990i
\(129\) 8.09017 0.712300
\(130\) 0.726543 + 0.726543i 0.0637220 + 0.0637220i
\(131\) 11.5514 + 3.75329i 1.00925 + 0.327926i 0.766557 0.642176i \(-0.221968\pi\)
0.242696 + 0.970102i \(0.421968\pi\)
\(132\) −36.0341 + 11.7082i −3.13637 + 1.01907i
\(133\) −0.364745 1.12257i −0.0316274 0.0973392i
\(134\) −8.05107 1.27516i −0.695507 0.110157i
\(135\) 5.34307 16.4443i 0.459858 1.41530i
\(136\) −0.718826 + 4.53849i −0.0616388 + 0.389172i
\(137\) −5.85410 + 8.05748i −0.500150 + 0.688397i −0.982220 0.187736i \(-0.939885\pi\)
0.482070 + 0.876133i \(0.339885\pi\)
\(138\) 2.81761 + 1.43564i 0.239851 + 0.122210i
\(139\) −4.02874 2.92705i −0.341713 0.248269i 0.403671 0.914904i \(-0.367734\pi\)
−0.745384 + 0.666635i \(0.767734\pi\)
\(140\) −0.618034 0.449028i −0.0522334 0.0379498i
\(141\) 16.4443 5.34307i 1.38486 0.449967i
\(142\) −1.46412 9.24408i −0.122866 0.775746i
\(143\) 1.62460 + 2.23607i 0.135856 + 0.186989i
\(144\) −8.00000 + 24.6215i −0.666667 + 2.05179i
\(145\) 6.97214 + 9.59632i 0.579004 + 0.796931i
\(146\) 1.22123 2.39680i 0.101070 0.198361i
\(147\) −6.60440 20.3262i −0.544721 1.67648i
\(148\) 5.70634 17.5623i 0.469058 1.44361i
\(149\) 4.14590 0.339645 0.169823 0.985475i \(-0.445681\pi\)
0.169823 + 0.985475i \(0.445681\pi\)
\(150\) 7.33094 7.33094i 0.598569 0.598569i
\(151\) 2.66141 8.19098i 0.216583 0.666573i −0.782455 0.622707i \(-0.786033\pi\)
0.999037 0.0438654i \(-0.0139673\pi\)
\(152\) 13.9680 2.21232i 1.13296 0.179443i
\(153\) −6.18034 8.50651i −0.499651 0.687710i
\(154\) −1.45309 1.45309i −0.117093 0.117093i
\(155\) −2.85317 + 8.54508i −0.229172 + 0.686358i
\(156\) 2.76393 0.221292
\(157\) −13.7082 + 9.95959i −1.09403 + 0.794862i −0.980076 0.198624i \(-0.936353\pi\)
−0.113958 + 0.993486i \(0.536353\pi\)
\(158\) 9.37310 1.48455i 0.745684 0.118105i
\(159\) −27.0256 8.78115i −2.14327 0.696391i
\(160\) 6.47214 6.47214i 0.511667 0.511667i
\(161\) 0.171513i 0.0135172i
\(162\) −8.64964 16.9759i −0.679580 1.33375i
\(163\) 1.95511 0.635255i 0.153136 0.0497570i −0.231446 0.972848i \(-0.574346\pi\)
0.384582 + 0.923091i \(0.374346\pi\)
\(164\) −9.95959 + 3.23607i −0.777714 + 0.252694i
\(165\) −24.7984 + 18.0171i −1.93055 + 1.40263i
\(166\) −4.24028 8.32202i −0.329110 0.645914i
\(167\) 16.8415 12.2361i 1.30323 0.946855i 0.303253 0.952910i \(-0.401927\pi\)
0.999982 + 0.00605473i \(0.00192729\pi\)
\(168\) −2.02967 + 0.321469i −0.156593 + 0.0248018i
\(169\) 3.95492 + 12.1720i 0.304224 + 0.936306i
\(170\) 0.581542 + 3.67171i 0.0446022 + 0.281607i
\(171\) −19.0211 + 26.1803i −1.45458 + 2.00206i
\(172\) −5.00000 + 1.62460i −0.381246 + 0.123874i
\(173\) 10.5451 + 7.66145i 0.801728 + 0.582489i 0.911421 0.411476i \(-0.134987\pi\)
−0.109693 + 0.993966i \(0.534987\pi\)
\(174\) 31.5151 + 4.99150i 2.38915 + 0.378405i
\(175\) 0.534785 + 0.173762i 0.0404259 + 0.0131352i
\(176\) 19.9192 14.4721i 1.50147 1.09088i
\(177\) −16.0172 + 5.20431i −1.20393 + 0.391180i
\(178\) 1.57758 3.09618i 0.118245 0.232068i
\(179\) 1.31433 4.04508i 0.0982375 0.302344i −0.889846 0.456260i \(-0.849189\pi\)
0.988084 + 0.153916i \(0.0491886\pi\)
\(180\) 20.9443i 1.56109i
\(181\) 0.726543i 0.0540035i −0.999635 0.0270017i \(-0.991404\pi\)
0.999635 0.0270017i \(-0.00859597\pi\)
\(182\) 0.0680569 + 0.133569i 0.00504471 + 0.00990081i
\(183\) −1.62460 + 2.23607i −0.120094 + 0.165295i
\(184\) −2.02967 0.321469i −0.149629 0.0236990i
\(185\) 14.9394i 1.09837i
\(186\) 10.8267 + 21.6808i 0.793850 + 1.58971i
\(187\) 10.0000i 0.731272i
\(188\) −9.09017 + 6.60440i −0.662969 + 0.481675i
\(189\) 1.48278 2.04087i 0.107856 0.148451i
\(190\) 10.1942 5.19421i 0.739566 0.376828i
\(191\) 0.326238i 0.0236057i −0.999930 0.0118029i \(-0.996243\pi\)
0.999930 0.0118029i \(-0.00375706\pi\)
\(192\) 24.6215i 1.77690i
\(193\) 2.51722 7.74721i 0.181194 0.557656i −0.818669 0.574266i \(-0.805287\pi\)
0.999862 + 0.0166100i \(0.00528738\pi\)
\(194\) 1.85500 + 0.945169i 0.133181 + 0.0678592i
\(195\) 2.12663 0.690983i 0.152291 0.0494823i
\(196\) 8.16348 + 11.2361i 0.583106 + 0.802576i
\(197\) 16.5451 + 5.37582i 1.17879 + 0.383012i 0.831916 0.554901i \(-0.187244\pi\)
0.346872 + 0.937912i \(0.387244\pi\)
\(198\) −8.81351 + 55.6463i −0.626349 + 3.95461i
\(199\) 2.93893 + 2.13525i 0.208335 + 0.151364i 0.687060 0.726601i \(-0.258901\pi\)
−0.478725 + 0.877965i \(0.658901\pi\)
\(200\) −3.05863 + 6.00290i −0.216278 + 0.424469i
\(201\) −10.4271 + 14.3516i −0.735467 + 1.01228i
\(202\) −12.4934 + 1.97876i −0.879031 + 0.139225i
\(203\) 0.534785 + 1.64590i 0.0375345 + 0.115519i
\(204\) 8.09017 + 5.87785i 0.566425 + 0.411532i
\(205\) −6.85410 + 4.97980i −0.478711 + 0.347804i
\(206\) −15.2345 + 7.76237i −1.06144 + 0.540830i
\(207\) 3.80423 2.76393i 0.264412 0.192107i
\(208\) −1.70820 + 0.555029i −0.118443 + 0.0384843i
\(209\) 29.2705 9.51057i 2.02468 0.657860i
\(210\) −1.48131 + 0.754763i −0.102220 + 0.0520836i
\(211\) 5.41641i 0.372881i 0.982466 + 0.186440i \(0.0596951\pi\)
−0.982466 + 0.186440i \(0.940305\pi\)
\(212\) 18.4661 1.26826
\(213\) −19.3713 6.29412i −1.32730 0.431266i
\(214\) −1.58090 9.98141i −0.108068 0.682315i
\(215\) −3.44095 + 2.50000i −0.234671 + 0.170499i
\(216\) 21.3723 + 21.3723i 1.45420 + 1.45420i
\(217\) −0.781153 + 1.05706i −0.0530281 + 0.0717577i
\(218\) −15.1803 + 15.1803i −1.02814 + 1.02814i
\(219\) −3.44095 4.73607i −0.232518 0.320034i
\(220\) 11.7082 16.1150i 0.789367 1.08647i
\(221\) 0.225425 0.693786i 0.0151637 0.0466691i
\(222\) −28.4164 28.4164i −1.90718 1.90718i
\(223\) −2.17963 −0.145959 −0.0729793 0.997333i \(-0.523251\pi\)
−0.0729793 + 0.997333i \(0.523251\pi\)
\(224\) 1.18985 0.606260i 0.0795003 0.0405074i
\(225\) −4.76393 14.6619i −0.317595 0.977458i
\(226\) 10.7891 + 5.49734i 0.717683 + 0.365678i
\(227\) −13.4005 18.4443i −0.889426 1.22419i −0.973720 0.227748i \(-0.926864\pi\)
0.0842944 0.996441i \(-0.473136\pi\)
\(228\) 9.51057 29.2705i 0.629853 1.93849i
\(229\) −6.90983 9.51057i −0.456614 0.628476i 0.517188 0.855872i \(-0.326979\pi\)
−0.973802 + 0.227396i \(0.926979\pi\)
\(230\) −1.64204 + 0.260074i −0.108273 + 0.0171487i
\(231\) −4.25325 + 1.38197i −0.279844 + 0.0909267i
\(232\) −20.4797 + 3.24367i −1.34456 + 0.212958i
\(233\) −1.07295 0.779543i −0.0702912 0.0510696i 0.552085 0.833788i \(-0.313832\pi\)
−0.622376 + 0.782718i \(0.713832\pi\)
\(234\) 1.86588 3.66199i 0.121976 0.239392i
\(235\) −5.34307 + 7.35410i −0.348543 + 0.479729i
\(236\) 8.85410 6.43288i 0.576353 0.418745i
\(237\) 6.38197 19.6417i 0.414553 1.27586i
\(238\) −0.0848458 + 0.535696i −0.00549974 + 0.0347240i
\(239\) 7.95148 + 24.4721i 0.514338 + 1.58297i 0.784482 + 0.620151i \(0.212929\pi\)
−0.270144 + 0.962820i \(0.587071\pi\)
\(240\) −6.15537 18.9443i −0.397327 1.22285i
\(241\) 0.690983 + 0.224514i 0.0445101 + 0.0144622i 0.331187 0.943565i \(-0.392551\pi\)
−0.286677 + 0.958027i \(0.592551\pi\)
\(242\) 26.8885 26.8885i 1.72846 1.72846i
\(243\) −9.40456 −0.603303
\(244\) 0.555029 1.70820i 0.0355321 0.109357i
\(245\) 9.09017 + 6.60440i 0.580750 + 0.421939i
\(246\) −3.56514 + 22.5094i −0.227305 + 1.43515i
\(247\) −2.24514 −0.142855
\(248\) −11.0450 11.2253i −0.701358 0.712809i
\(249\) −20.3262 −1.28812
\(250\) −2.64245 + 16.6838i −0.167123 + 1.05518i
\(251\) 3.07768 + 2.23607i 0.194262 + 0.141139i 0.680664 0.732595i \(-0.261691\pi\)
−0.486403 + 0.873735i \(0.661691\pi\)
\(252\) −0.944272 + 2.90617i −0.0594835 + 0.183072i
\(253\) −4.47214 −0.281161
\(254\) −10.6861 + 10.6861i −0.670508 + 0.670508i
\(255\) 7.69421 + 2.50000i 0.481830 + 0.156556i
\(256\) 4.94427 + 15.2169i 0.309017 + 0.951057i
\(257\) −3.38197 10.4086i −0.210961 0.649272i −0.999416 0.0341788i \(-0.989118\pi\)
0.788454 0.615093i \(-0.210882\pi\)
\(258\) −1.78980 + 11.3004i −0.111428 + 0.703530i
\(259\) 0.673542 2.07295i 0.0418519 0.128807i
\(260\) −1.17557 + 0.854102i −0.0729058 + 0.0529692i
\(261\) 27.8885 38.3853i 1.72626 2.37599i
\(262\) −7.79815 + 15.3047i −0.481771 + 0.945529i
\(263\) −21.3193 15.4894i −1.31460 0.955115i −0.999983 0.00589693i \(-0.998123\pi\)
−0.314620 0.949218i \(-0.601877\pi\)
\(264\) −8.38215 52.9228i −0.515886 3.25717i
\(265\) 14.2082 4.61653i 0.872803 0.283591i
\(266\) 1.64870 0.261129i 0.101088 0.0160108i
\(267\) −4.44501 6.11803i −0.272030 0.374418i
\(268\) 3.56231 10.9637i 0.217602 0.669712i
\(269\) −14.4336 19.8662i −0.880034 1.21126i −0.976412 0.215918i \(-0.930726\pi\)
0.0963776 0.995345i \(-0.469274\pi\)
\(270\) 21.7873 + 11.1012i 1.32594 + 0.675598i
\(271\) −1.81636 5.59017i −0.110336 0.339579i 0.880610 0.473842i \(-0.157133\pi\)
−0.990946 + 0.134263i \(0.957133\pi\)
\(272\) −6.18034 2.00811i −0.374738 0.121760i
\(273\) 0.326238 0.0197448
\(274\) −9.95959 9.95959i −0.601681 0.601681i
\(275\) −4.53077 + 13.9443i −0.273216 + 0.840871i
\(276\) −2.62866 + 3.61803i −0.158226 + 0.217780i
\(277\) −0.263932 0.363271i −0.0158581 0.0218269i 0.801014 0.598645i \(-0.204294\pi\)
−0.816872 + 0.576818i \(0.804294\pi\)
\(278\) 4.97980 4.97980i 0.298668 0.298668i
\(279\) 36.0341 + 0.291796i 2.15731 + 0.0174694i
\(280\) 0.763932 0.763932i 0.0456537 0.0456537i
\(281\) −12.8262 + 9.31881i −0.765149 + 0.555913i −0.900485 0.434886i \(-0.856789\pi\)
0.135336 + 0.990800i \(0.456789\pi\)
\(282\) 3.82521 + 24.1515i 0.227788 + 1.43820i
\(283\) 2.76741 + 0.899187i 0.164506 + 0.0534511i 0.390112 0.920767i \(-0.372436\pi\)
−0.225606 + 0.974219i \(0.572436\pi\)
\(284\) 13.2361 0.785416
\(285\) 24.8990i 1.47489i
\(286\) −3.48276 + 1.77455i −0.205940 + 0.104932i
\(287\) −1.17557 + 0.381966i −0.0693917 + 0.0225467i
\(288\) −32.6215 16.6215i −1.92224 0.979429i
\(289\) −11.6180 + 8.44100i −0.683414 + 0.496529i
\(290\) −14.9466 + 7.61568i −0.877696 + 0.447208i
\(291\) 3.66547 2.66312i 0.214874 0.156115i
\(292\) 3.07768 + 2.23607i 0.180108 + 0.130856i
\(293\) 5.01722 + 15.4414i 0.293109 + 0.902097i 0.983850 + 0.178995i \(0.0572846\pi\)
−0.690741 + 0.723102i \(0.742715\pi\)
\(294\) 29.8528 4.72822i 1.74105 0.275756i
\(295\) 5.20431 7.16312i 0.303007 0.417053i
\(296\) 23.2686 + 11.8560i 1.35246 + 0.689114i
\(297\) 53.2148 + 38.6628i 3.08783 + 2.24344i
\(298\) −0.917204 + 5.79100i −0.0531322 + 0.335464i
\(299\) 0.310271 + 0.100813i 0.0179434 + 0.00583017i
\(300\) 8.61803 + 11.8617i 0.497562 + 0.684836i
\(301\) −0.590170 + 0.191758i −0.0340168 + 0.0110527i
\(302\) 10.8524 + 5.52957i 0.624485 + 0.318191i
\(303\) −8.50651 + 26.1803i −0.488686 + 1.50402i
\(304\) 20.0000i 1.14708i
\(305\) 1.45309i 0.0832034i
\(306\) 13.2492 6.75080i 0.757406 0.385918i
\(307\) 11.8820 16.3541i 0.678139 0.933378i −0.321771 0.946818i \(-0.604278\pi\)
0.999910 + 0.0134396i \(0.00427810\pi\)
\(308\) 2.35114 1.70820i 0.133969 0.0973340i
\(309\) 37.2097i 2.11679i
\(310\) −11.3046 5.87576i −0.642057 0.333721i
\(311\) 17.2361i 0.977368i −0.872461 0.488684i \(-0.837477\pi\)
0.872461 0.488684i \(-0.162523\pi\)
\(312\) −0.611469 + 3.86067i −0.0346176 + 0.218567i
\(313\) 12.2361 16.8415i 0.691623 0.951938i −0.308376 0.951264i \(-0.599786\pi\)
1.00000 0.000673572i \(-0.000214405\pi\)
\(314\) −10.8789 21.3510i −0.613931 1.20491i
\(315\) 2.47214i 0.139289i
\(316\) 13.4208i 0.754979i
\(317\) −5.76393 + 17.7396i −0.323735 + 0.996353i 0.648274 + 0.761407i \(0.275491\pi\)
−0.972009 + 0.234946i \(0.924509\pi\)
\(318\) 18.2445 35.8068i 1.02310 2.00794i
\(319\) −42.9161 + 13.9443i −2.40284 + 0.780729i
\(320\) 7.60845 + 10.4721i 0.425325 + 0.585410i
\(321\) −20.9164 6.79615i −1.16744 0.379324i
\(322\) −0.239570 0.0379442i −0.0133507 0.00211455i
\(323\) −6.57164 4.77458i −0.365656 0.265664i
\(324\) 25.6255 8.32624i 1.42364 0.462569i
\(325\) 0.628677 0.865300i 0.0348727 0.0479982i
\(326\) 0.454792 + 2.87145i 0.0251886 + 0.159035i
\(327\) 14.4374 + 44.4336i 0.798388 + 2.45719i
\(328\) −2.31677 14.6275i −0.127922 0.807669i
\(329\) −1.07295 + 0.779543i −0.0591536 + 0.0429776i
\(330\) −19.6801 38.6244i −1.08335 2.12620i
\(331\) 6.82891 4.96149i 0.375351 0.272708i −0.384075 0.923302i \(-0.625480\pi\)
0.759426 + 0.650593i \(0.225480\pi\)
\(332\) 12.5623 4.08174i 0.689446 0.224015i
\(333\) −56.8328 + 18.4661i −3.11442 + 1.01194i
\(334\) 13.3655 + 26.2313i 0.731327 + 1.43531i
\(335\) 9.32624i 0.509547i
\(336\) 2.90617i 0.158545i
\(337\) 20.5902 + 6.69015i 1.12162 + 0.364436i 0.810385 0.585898i \(-0.199258\pi\)
0.311233 + 0.950334i \(0.399258\pi\)
\(338\) −17.8768 + 2.83141i −0.972370 + 0.154008i
\(339\) 21.3193 15.4894i 1.15790 0.841266i
\(340\) −5.25731 −0.285118
\(341\) −27.5623 20.3682i −1.49258 1.10300i
\(342\) −32.3607 32.3607i −1.74987 1.74987i
\(343\) 1.93487 + 2.66312i 0.104473 + 0.143795i
\(344\) −1.16308 7.34342i −0.0627093 0.395931i
\(345\) −1.11803 + 3.44095i −0.0601929 + 0.185255i
\(346\) −13.0344 + 13.0344i −0.700736 + 0.700736i
\(347\) 10.3431 0.555247 0.277624 0.960690i \(-0.410453\pi\)
0.277624 + 0.960690i \(0.410453\pi\)
\(348\) −13.9443 + 42.9161i −0.747491 + 2.30054i
\(349\) 1.21885 + 3.75123i 0.0652434 + 0.200798i 0.978364 0.206891i \(-0.0663346\pi\)
−0.913121 + 0.407690i \(0.866335\pi\)
\(350\) −0.361023 + 0.708547i −0.0192975 + 0.0378734i
\(351\) −2.82041 3.88197i −0.150543 0.207204i
\(352\) 15.8080 + 31.0249i 0.842567 + 1.65363i
\(353\) 6.64590 + 9.14729i 0.353725 + 0.486861i 0.948387 0.317115i \(-0.102714\pi\)
−0.594662 + 0.803976i \(0.702714\pi\)
\(354\) −3.72587 23.5242i −0.198028 1.25030i
\(355\) 10.1841 3.30902i 0.540516 0.175624i
\(356\) 3.97574 + 2.88854i 0.210714 + 0.153093i
\(357\) 0.954915 + 0.693786i 0.0505395 + 0.0367191i
\(358\) 5.35941 + 2.73076i 0.283254 + 0.144325i
\(359\) 2.82041 3.88197i 0.148856 0.204882i −0.728077 0.685495i \(-0.759586\pi\)
0.876933 + 0.480613i \(0.159586\pi\)
\(360\) −29.2550 4.63354i −1.54187 0.244209i
\(361\) −1.85410 + 5.70634i −0.0975843 + 0.300334i
\(362\) 1.01484 + 0.160734i 0.0533386 + 0.00844801i
\(363\) −25.5725 78.7041i −1.34221 4.13090i
\(364\) −0.201626 + 0.0655123i −0.0105681 + 0.00343378i
\(365\) 2.92705 + 0.951057i 0.153209 + 0.0497806i
\(366\) −2.76393 2.76393i −0.144473 0.144473i
\(367\) −10.4086 −0.543326 −0.271663 0.962392i \(-0.587574\pi\)
−0.271663 + 0.962392i \(0.587574\pi\)
\(368\) 0.898056 2.76393i 0.0468144 0.144080i
\(369\) 27.4164 + 19.9192i 1.42724 + 1.03695i
\(370\) 20.8674 + 3.30507i 1.08484 + 0.171822i
\(371\) 2.17963 0.113161
\(372\) −32.6789 + 10.3262i −1.69432 + 0.535390i
\(373\) 14.4164 0.746453 0.373227 0.927740i \(-0.378251\pi\)
0.373227 + 0.927740i \(0.378251\pi\)
\(374\) −13.9680 2.21232i −0.722269 0.114396i
\(375\) 29.7400 + 21.6074i 1.53577 + 1.11580i
\(376\) −7.21400 14.1583i −0.372034 0.730157i
\(377\) 3.29180 0.169536
\(378\) 2.52265 + 2.52265i 0.129751 + 0.129751i
\(379\) −24.5685 7.98278i −1.26200 0.410048i −0.399792 0.916606i \(-0.630918\pi\)
−0.862206 + 0.506558i \(0.830918\pi\)
\(380\) 5.00000 + 15.3884i 0.256495 + 0.789409i
\(381\) 10.1631 + 31.2789i 0.520672 + 1.60246i
\(382\) 0.455690 + 0.0721742i 0.0233151 + 0.00369275i
\(383\) 0.971301 2.98936i 0.0496312 0.152749i −0.923169 0.384393i \(-0.874411\pi\)
0.972801 + 0.231644i \(0.0744106\pi\)
\(384\) 34.3913 + 5.44705i 1.75502 + 0.277969i
\(385\) 1.38197 1.90211i 0.0704315 0.0969407i
\(386\) 10.2644 + 5.22999i 0.522446 + 0.266199i
\(387\) 13.7638 + 10.0000i 0.699654 + 0.508329i
\(388\) −1.73060 + 2.38197i −0.0878579 + 0.120926i
\(389\) −26.8713 + 8.73102i −1.36243 + 0.442680i −0.896854 0.442327i \(-0.854153\pi\)
−0.465576 + 0.885008i \(0.654153\pi\)
\(390\) 0.494689 + 3.12334i 0.0250496 + 0.158157i
\(391\) 0.693786 + 0.954915i 0.0350863 + 0.0482921i
\(392\) −17.5006 + 8.91699i −0.883913 + 0.450376i
\(393\) 21.9721 + 30.2421i 1.10835 + 1.52551i
\(394\) −11.1693 + 21.9209i −0.562699 + 1.10436i
\(395\) 3.35520 + 10.3262i 0.168818 + 0.519569i
\(396\) −75.7771 24.6215i −3.80794 1.23728i
\(397\) −12.0000 −0.602263 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) −3.63271 + 3.63271i −0.182091 + 0.182091i
\(399\) 1.12257 3.45492i 0.0561988 0.172962i
\(400\) −7.70820 5.60034i −0.385410 0.280017i
\(401\) −5.75329 7.91872i −0.287306 0.395442i 0.640831 0.767682i \(-0.278590\pi\)
−0.928137 + 0.372240i \(0.878590\pi\)
\(402\) −17.7396 17.7396i −0.884769 0.884769i
\(403\) 1.45309 + 2.03444i 0.0723833 + 0.101343i
\(404\) 17.8885i 0.889988i
\(405\) 17.6353 12.8128i 0.876303 0.636671i
\(406\) −2.41731 + 0.382864i −0.119969 + 0.0190012i
\(407\) 54.0512 + 17.5623i 2.67922 + 0.870531i
\(408\) −10.0000 + 10.0000i −0.495074 + 0.495074i
\(409\) 36.0341i 1.78177i −0.454225 0.890887i \(-0.650084\pi\)
0.454225 0.890887i \(-0.349916\pi\)
\(410\) −5.43945 10.6755i −0.268635 0.527226i
\(411\) −29.1522 + 9.47214i −1.43797 + 0.467226i
\(412\) −7.47214 22.9969i −0.368126 1.13297i
\(413\) 1.04508 0.759299i 0.0514253 0.0373626i
\(414\) 3.01905 + 5.92522i 0.148378 + 0.291209i
\(415\) 8.64527 6.28115i 0.424379 0.308330i
\(416\) −0.397357 2.50881i −0.0194820 0.123005i
\(417\) −4.73607 14.5761i −0.231926 0.713796i
\(418\) 6.80881 + 42.9892i 0.333030 + 2.10267i
\(419\) −11.8617 + 16.3262i −0.579482 + 0.797589i −0.993638 0.112617i \(-0.964077\pi\)
0.414156 + 0.910206i \(0.364077\pi\)
\(420\) −0.726543 2.23607i −0.0354516 0.109109i
\(421\) −22.3262 16.2210i −1.08811 0.790561i −0.109034 0.994038i \(-0.534776\pi\)
−0.979080 + 0.203477i \(0.934776\pi\)
\(422\) −7.56565 1.19828i −0.368290 0.0583314i
\(423\) 34.5811 + 11.2361i 1.68139 + 0.546316i
\(424\) −4.08529 + 25.7935i −0.198399 + 1.25264i
\(425\) 3.68034 1.19581i 0.178523 0.0580055i
\(426\) 13.0772 25.6654i 0.633592 1.24349i
\(427\) 0.0655123 0.201626i 0.00317036 0.00975737i
\(428\) 14.2918 0.690820
\(429\) 8.50651i 0.410698i
\(430\) −2.73076 5.35941i −0.131689 0.258454i
\(431\) −7.71445 + 10.6180i −0.371592 + 0.511453i −0.953333 0.301922i \(-0.902372\pi\)
0.581741 + 0.813374i \(0.302372\pi\)
\(432\) −34.5811 + 25.1246i −1.66378 + 1.20881i
\(433\) 28.0827i 1.34957i 0.738016 + 0.674783i \(0.235763\pi\)
−0.738016 + 0.674783i \(0.764237\pi\)
\(434\) −1.30368 1.32497i −0.0625789 0.0636006i
\(435\) 36.5066i 1.75036i
\(436\) −17.8456 24.5623i −0.854647 1.17632i
\(437\) 2.13525 2.93893i 0.102143 0.140588i
\(438\) 7.37660 3.75856i 0.352468 0.179591i
\(439\) 4.52786i 0.216103i 0.994145 + 0.108052i \(0.0344612\pi\)
−0.994145 + 0.108052i \(0.965539\pi\)
\(440\) 19.9192 + 19.9192i 0.949610 + 0.949610i
\(441\) 13.8885 42.7445i 0.661359 2.03545i
\(442\) 0.919211 + 0.468362i 0.0437224 + 0.0222777i
\(443\) 8.67802 2.81966i 0.412305 0.133966i −0.0955174 0.995428i \(-0.530451\pi\)
0.507823 + 0.861462i \(0.330451\pi\)
\(444\) 45.9787 33.4055i 2.18205 1.58535i
\(445\) 3.78115 + 1.22857i 0.179244 + 0.0582399i
\(446\) 0.482203 3.04451i 0.0228330 0.144162i
\(447\) 10.3229 + 7.50000i 0.488255 + 0.354738i
\(448\) 0.583592 + 1.79611i 0.0275721 + 0.0848583i
\(449\) −14.5967 + 20.0907i −0.688863 + 0.948139i −0.999998 0.00222718i \(-0.999291\pi\)
0.311134 + 0.950366i \(0.399291\pi\)
\(450\) 21.5337 3.41060i 1.01511 0.160777i
\(451\) −9.95959 30.6525i −0.468979 1.44337i
\(452\) −10.0656 + 13.8541i −0.473446 + 0.651642i
\(453\) 21.4443 15.5802i 1.00754 0.732021i
\(454\) 28.7276 14.6375i 1.34825 0.686970i
\(455\) −0.138757 + 0.100813i −0.00650504 + 0.00472619i
\(456\) 38.7811 + 19.7599i 1.81609 + 0.925344i
\(457\) 22.8262 7.41669i 1.06777 0.346938i 0.278149 0.960538i \(-0.410279\pi\)
0.789617 + 0.613600i \(0.210279\pi\)
\(458\) 14.8131 7.54763i 0.692168 0.352677i
\(459\) 17.3607i 0.810327i
\(460\) 2.35114i 0.109623i
\(461\) 26.4058 + 8.57975i 1.22984 + 0.399599i 0.850656 0.525723i \(-0.176205\pi\)
0.379183 + 0.925322i \(0.376205\pi\)
\(462\) −0.989378 6.24669i −0.0460301 0.290622i
\(463\) 19.9192 14.4721i 0.925723 0.672577i −0.0192188 0.999815i \(-0.506118\pi\)
0.944942 + 0.327238i \(0.106118\pi\)
\(464\) 29.3238i 1.36132i
\(465\) −22.5623 + 16.1150i −1.04630 + 0.747313i
\(466\) 1.32624 1.32624i 0.0614368 0.0614368i
\(467\) 11.3799 + 15.6631i 0.526600 + 0.724803i 0.986608 0.163112i \(-0.0521533\pi\)
−0.460008 + 0.887915i \(0.652153\pi\)
\(468\) 4.70228 + 3.41641i 0.217363 + 0.157924i
\(469\) 0.420473 1.29408i 0.0194156 0.0597552i
\(470\) −9.09017 9.09017i −0.419298 0.419298i
\(471\) −52.1491 −2.40290
\(472\) 7.02666 + 13.7906i 0.323428 + 0.634763i
\(473\) −5.00000 15.3884i −0.229900 0.707560i
\(474\) 26.0236 + 13.2597i 1.19531 + 0.609038i
\(475\) −7.00042 9.63525i −0.321201 0.442096i
\(476\) −0.729490 0.237026i −0.0334361 0.0108641i
\(477\) −35.1246 48.3449i −1.60825 2.21356i
\(478\) −35.9419 + 5.69263i −1.64394 + 0.260375i
\(479\) 38.2138 12.4164i 1.74603 0.567320i 0.750425 0.660955i \(-0.229849\pi\)
0.995607 + 0.0936351i \(0.0298487\pi\)
\(480\) 27.8232 4.40676i 1.26995 0.201140i
\(481\) −3.35410 2.43690i −0.152934 0.111113i
\(482\) −0.466469 + 0.915497i −0.0212471 + 0.0416997i
\(483\) −0.310271 + 0.427051i −0.0141178 + 0.0194315i
\(484\) 31.6094 + 43.5066i 1.43679 + 1.97757i
\(485\) −0.736068 + 2.26538i −0.0334231 + 0.102866i
\(486\) 2.08059 13.1363i 0.0943774 0.595875i
\(487\) −6.01661 18.5172i −0.272639 0.839095i −0.989835 0.142224i \(-0.954575\pi\)
0.717196 0.696872i \(-0.245425\pi\)
\(488\) 2.26323 + 1.15317i 0.102452 + 0.0522018i
\(489\) 6.01722 + 1.95511i 0.272108 + 0.0884133i
\(490\) −11.2361 + 11.2361i −0.507594 + 0.507594i
\(491\) −11.0697 −0.499566 −0.249783 0.968302i \(-0.580359\pi\)
−0.249783 + 0.968302i \(0.580359\pi\)
\(492\) −30.6525 9.95959i −1.38192 0.449013i
\(493\) 9.63525 + 7.00042i 0.433950 + 0.315283i
\(494\) 0.496696 3.13602i 0.0223474 0.141096i
\(495\) −64.4598 −2.89725
\(496\) 18.1231 12.9443i 0.813750 0.581215i
\(497\) 1.56231 0.0700790
\(498\) 4.49681 28.3917i 0.201507 1.27226i
\(499\) −27.0256 19.6353i −1.20983 0.878995i −0.214617 0.976698i \(-0.568850\pi\)
−0.995216 + 0.0977036i \(0.968850\pi\)
\(500\) −22.7194 7.38197i −1.01604 0.330132i
\(501\) 64.0689 2.86239
\(502\) −3.80423 + 3.80423i −0.169791 + 0.169791i
\(503\) −14.9066 4.84346i −0.664654 0.215959i −0.0427896 0.999084i \(-0.513624\pi\)
−0.621864 + 0.783125i \(0.713624\pi\)
\(504\) −3.85044 1.96190i −0.171512 0.0873899i
\(505\) −4.47214 13.7638i −0.199007 0.612482i
\(506\) 0.989378 6.24669i 0.0439832 0.277699i
\(507\) −12.1720 + 37.4615i −0.540576 + 1.66372i
\(508\) −12.5623 17.2905i −0.557362 0.767143i
\(509\) −16.1180 + 22.1846i −0.714419 + 0.983314i 0.285271 + 0.958447i \(0.407916\pi\)
−0.999691 + 0.0248670i \(0.992084\pi\)
\(510\) −5.19421 + 10.1942i −0.230003 + 0.451407i
\(511\) 0.363271 + 0.263932i 0.0160702 + 0.0116757i
\(512\) −22.3488 + 3.53971i −0.987688 + 0.156434i
\(513\) −50.8156 + 16.5110i −2.24356 + 0.728978i
\(514\) 15.2870 2.42122i 0.674280 0.106795i
\(515\) −11.4984 15.8262i −0.506682 0.697387i
\(516\) −15.3884 5.00000i −0.677437 0.220113i
\(517\) −20.3262 27.9767i −0.893947 1.23041i
\(518\) 2.74649 + 1.39941i 0.120674 + 0.0614864i
\(519\) 12.3965 + 38.1525i 0.544146 + 1.67471i
\(520\) −0.932938 1.83099i −0.0409120 0.0802944i
\(521\) −35.6525 −1.56196 −0.780982 0.624554i \(-0.785281\pi\)
−0.780982 + 0.624554i \(0.785281\pi\)
\(522\) 47.4468 + 47.4468i 2.07669 + 2.07669i
\(523\) 9.62908 29.6353i 0.421050 1.29586i −0.485676 0.874139i \(-0.661426\pi\)
0.906726 0.421720i \(-0.138574\pi\)
\(524\) −19.6525 14.2784i −0.858522 0.623753i
\(525\) 1.01722 + 1.40008i 0.0443952 + 0.0611047i
\(526\) 26.3521 26.3521i 1.14900 1.14900i
\(527\) −0.0732450 + 9.04508i −0.00319060 + 0.394010i
\(528\) 75.7771 3.29777
\(529\) 18.1803 13.2088i 0.790450 0.574295i
\(530\) 3.30507 + 20.8674i 0.143563 + 0.906421i
\(531\) −33.6830 10.9443i −1.46172 0.474941i
\(532\) 2.36068i 0.102348i
\(533\) 2.35114i 0.101839i
\(534\) 9.52906 4.85530i 0.412363 0.210109i
\(535\) 10.9964 3.57295i 0.475416 0.154472i
\(536\) 14.5260 + 7.40134i 0.627426 + 0.319689i
\(537\) 10.5902 7.69421i 0.457000 0.332030i
\(538\) 30.9423 15.7659i 1.33402 0.679716i
\(539\) −34.5811 + 25.1246i −1.48951 + 1.08219i
\(540\) −20.3262 + 27.9767i −0.874702 + 1.20392i
\(541\) 6.38197 + 19.6417i 0.274382 + 0.844461i 0.989382 + 0.145337i \(0.0464266\pi\)
−0.715000 + 0.699124i \(0.753573\pi\)
\(542\) 8.21020 1.30037i 0.352658 0.0558556i
\(543\) 1.31433 1.80902i 0.0564032 0.0776323i
\(544\) 4.17223 8.18845i 0.178883 0.351077i
\(545\) −19.8713 14.4374i −0.851194 0.618429i
\(546\) −0.0721742 + 0.455690i −0.00308877 + 0.0195017i
\(547\) −13.0373 4.23607i −0.557434 0.181121i 0.0167324 0.999860i \(-0.494674\pi\)
−0.574166 + 0.818739i \(0.694674\pi\)
\(548\) 16.1150 11.7082i 0.688397 0.500150i
\(549\) −5.52786 + 1.79611i −0.235923 + 0.0766562i
\(550\) −18.4750 9.41350i −0.787778 0.401393i
\(551\) 11.3269 34.8607i 0.482543 1.48511i
\(552\) −4.47214 4.47214i −0.190347 0.190347i
\(553\) 1.58411i 0.0673632i
\(554\) 0.565808 0.288294i 0.0240389 0.0122484i
\(555\) 27.0256 37.1976i 1.14717 1.57895i
\(556\) 5.85410 + 8.05748i 0.248269 + 0.341713i
\(557\) 31.8869i 1.35109i −0.737318 0.675546i \(-0.763908\pi\)
0.737318 0.675546i \(-0.236092\pi\)
\(558\) −8.37948 + 50.2680i −0.354732 + 2.12802i
\(559\) 1.18034i 0.0499231i
\(560\) 0.898056 + 1.23607i 0.0379498 + 0.0522334i
\(561\) −18.0902 + 24.8990i −0.763768 + 1.05124i
\(562\) −10.1790 19.9773i −0.429374 0.842693i
\(563\) 26.6869i 1.12472i 0.826893 + 0.562360i \(0.190106\pi\)
−0.826893 + 0.562360i \(0.809894\pi\)
\(564\) −34.5811 −1.45613
\(565\) −4.28115 + 13.1760i −0.180109 + 0.554320i
\(566\) −1.86823 + 3.66660i −0.0785274 + 0.154119i
\(567\) 3.02468 0.982779i 0.127025 0.0412728i
\(568\) −2.92824 + 18.4882i −0.122866 + 0.775746i
\(569\) −23.6180 7.67396i −0.990119 0.321709i −0.231209 0.972904i \(-0.574268\pi\)
−0.758911 + 0.651195i \(0.774268\pi\)
\(570\) 34.7790 + 5.50845i 1.45673 + 0.230723i
\(571\) 26.9399 + 19.5729i 1.12740 + 0.819102i 0.985314 0.170752i \(-0.0546198\pi\)
0.142084 + 0.989855i \(0.454620\pi\)
\(572\) −1.70820 5.25731i −0.0714236 0.219819i
\(573\) 0.590170 0.812299i 0.0246547 0.0339343i
\(574\) −0.273457 1.72654i −0.0114139 0.0720645i
\(575\) 0.534785 + 1.64590i 0.0223021 + 0.0686387i
\(576\) 30.4338 41.8885i 1.26808 1.74536i
\(577\) 15.3992 11.1882i 0.641077 0.465769i −0.219143 0.975693i \(-0.570326\pi\)
0.860220 + 0.509923i \(0.170326\pi\)
\(578\) −9.22012 18.0955i −0.383507 0.752674i
\(579\) 20.2825 14.7361i 0.842910 0.612410i
\(580\) −7.33094 22.5623i −0.304401 0.936849i
\(581\) 1.48278 0.481784i 0.0615160 0.0199878i
\(582\) 2.90893 + 5.70910i 0.120579 + 0.236650i
\(583\) 56.8328i 2.35377i
\(584\) −3.80423 + 3.80423i −0.157420 + 0.157420i
\(585\) 4.47214 + 1.45309i 0.184900 + 0.0600777i
\(586\) −22.6786 + 3.59193i −0.936843 + 0.148381i
\(587\) −10.5474 + 7.66312i −0.435337 + 0.316291i −0.783779 0.621039i \(-0.786711\pi\)
0.348442 + 0.937330i \(0.386711\pi\)
\(588\) 42.7445i 1.76276i
\(589\) 26.5451 8.38800i 1.09377 0.345621i
\(590\) 8.85410 + 8.85410i 0.364518 + 0.364518i
\(591\) 31.4706 + 43.3156i 1.29453 + 1.78177i
\(592\) −21.7082 + 29.8788i −0.892202 + 1.22801i
\(593\) −1.85410 + 5.70634i −0.0761388 + 0.234331i −0.981881 0.189497i \(-0.939314\pi\)
0.905742 + 0.423829i \(0.139314\pi\)
\(594\) −65.7771 + 65.7771i −2.69887 + 2.69887i
\(595\) −0.620541 −0.0254397
\(596\) −7.88597 2.56231i −0.323022 0.104956i
\(597\) 3.45492 + 10.6331i 0.141400 + 0.435185i
\(598\) −0.209458 + 0.411084i −0.00856536 + 0.0168105i
\(599\) −21.8415 30.0623i −0.892421 1.22831i −0.972823 0.231550i \(-0.925620\pi\)
0.0804017 0.996763i \(-0.474380\pi\)
\(600\) −18.4750 + 9.41350i −0.754240 + 0.384305i
\(601\) −24.1459 33.2340i −0.984932 1.35564i −0.934130 0.356933i \(-0.883822\pi\)
−0.0508019 0.998709i \(-0.516178\pi\)
\(602\) −0.137283 0.866774i −0.00559526 0.0353271i
\(603\) −35.4791 + 11.5279i −1.44482 + 0.469451i
\(604\) −10.1246 + 13.9353i −0.411965 + 0.567021i
\(605\) 35.1976 + 25.5725i 1.43098 + 1.03967i
\(606\) −34.6868 17.6738i −1.40906 0.717950i
\(607\) −1.45309 + 2.00000i −0.0589789 + 0.0811775i −0.837488 0.546456i \(-0.815976\pi\)
0.778509 + 0.627634i \(0.215976\pi\)
\(608\) −27.9360 4.42463i −1.13296 0.179443i
\(609\) −1.64590 + 5.06555i −0.0666952 + 0.205267i
\(610\) 2.02967 + 0.321469i 0.0821790 + 0.0130159i
\(611\) 0.779543 + 2.39919i 0.0315369 + 0.0970607i
\(612\) 6.49839 + 20.0000i 0.262682 + 0.808452i
\(613\) 36.7082 + 11.9272i 1.48263 + 0.481736i 0.934898 0.354918i \(-0.115491\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(614\) 20.2148 + 20.2148i 0.815802 + 0.815802i
\(615\) −26.0746 −1.05143
\(616\) 1.86588 + 3.66199i 0.0751783 + 0.147546i
\(617\) 7.89919 + 5.73910i 0.318009 + 0.231047i 0.735326 0.677714i \(-0.237029\pi\)
−0.417316 + 0.908761i \(0.637029\pi\)
\(618\) −51.9746 8.23197i −2.09073 0.331138i
\(619\) 43.0876 1.73184 0.865918 0.500186i \(-0.166735\pi\)
0.865918 + 0.500186i \(0.166735\pi\)
\(620\) 10.7082 14.4904i 0.430052 0.581947i
\(621\) 7.76393 0.311556
\(622\) 24.0754 + 3.81317i 0.965335 + 0.152894i
\(623\) 0.469272 + 0.340946i 0.0188010 + 0.0136597i
\(624\) −5.25731 1.70820i −0.210461 0.0683829i
\(625\) −7.41641 −0.296656
\(626\) 20.8172 + 20.8172i 0.832024 + 0.832024i
\(627\) 90.0854 + 29.2705i 3.59766 + 1.16895i
\(628\) 32.2299 10.4721i 1.28611 0.417884i
\(629\) −4.63525 14.2658i −0.184820 0.568817i
\(630\) −3.45309 0.546915i −0.137574 0.0217896i
\(631\) 2.71441 8.35410i 0.108059 0.332572i −0.882377 0.470543i \(-0.844058\pi\)
0.990436 + 0.137971i \(0.0440581\pi\)
\(632\) −18.7462 2.96911i −0.745684 0.118105i
\(633\) −9.79837 + 13.4863i −0.389450 + 0.536032i
\(634\) −23.5035 11.9756i −0.933443 0.475613i
\(635\) −13.9883 10.1631i −0.555110 0.403311i
\(636\) 45.9787 + 33.4055i 1.82317 + 1.32461i
\(637\) 2.96556 0.963568i 0.117500 0.0381780i
\(638\) −9.98300 63.0302i −0.395231 2.49539i
\(639\) −25.1765 34.6525i −0.995967 1.37083i
\(640\) −16.3107 + 8.31073i −0.644738 + 0.328511i
\(641\) 12.9271 + 17.7926i 0.510588 + 0.702764i 0.984018 0.178067i \(-0.0569845\pi\)
−0.473430 + 0.880831i \(0.656984\pi\)
\(642\) 14.1203 27.7126i 0.557282 1.09373i
\(643\) −2.82041 8.68034i −0.111226 0.342319i 0.879915 0.475131i \(-0.157599\pi\)
−0.991141 + 0.132812i \(0.957599\pi\)
\(644\) 0.106001 0.326238i 0.00417703 0.0128556i
\(645\) −13.0902 −0.515425
\(646\) 8.12299 8.12299i 0.319595 0.319595i
\(647\) −1.34708 + 4.14590i −0.0529593 + 0.162992i −0.974038 0.226384i \(-0.927309\pi\)
0.921079 + 0.389376i \(0.127309\pi\)
\(648\) 5.96093 + 37.6358i 0.234167 + 1.47847i
\(649\) 19.7984 + 27.2501i 0.777154 + 1.06966i
\(650\) 1.06957 + 1.06957i 0.0419520 + 0.0419520i
\(651\) −3.85723 + 1.21885i −0.151177 + 0.0477704i
\(652\) −4.11146 −0.161017
\(653\) −29.2254 + 21.2335i −1.14368 + 0.830932i −0.987628 0.156817i \(-0.949877\pi\)
−0.156052 + 0.987749i \(0.549877\pi\)
\(654\) −65.2590 + 10.3360i −2.55183 + 0.404170i
\(655\) −18.6906 6.07295i −0.730303 0.237290i
\(656\) 20.9443 0.817736
\(657\) 12.3107i 0.480287i
\(658\) −0.851497 1.67116i −0.0331948 0.0651485i
\(659\) 6.06961 1.97214i 0.236438 0.0768235i −0.188401 0.982092i \(-0.560331\pi\)
0.424840 + 0.905269i \(0.360331\pi\)
\(660\) 58.3045 18.9443i 2.26950 0.737405i
\(661\) 21.8713 15.8904i 0.850696 0.618067i −0.0746420 0.997210i \(-0.523781\pi\)
0.925338 + 0.379144i \(0.123781\pi\)
\(662\) 5.41945 + 10.6363i 0.210633 + 0.413391i
\(663\) 1.81636 1.31966i 0.0705414 0.0512514i
\(664\) 2.92220 + 18.4501i 0.113403 + 0.716001i
\(665\) 0.590170 + 1.81636i 0.0228858 + 0.0704353i
\(666\) −13.2203 83.4695i −0.512275 3.23438i
\(667\) −3.13068 + 4.30902i −0.121221 + 0.166846i
\(668\) −39.5967 + 12.8658i −1.53204 + 0.497791i
\(669\) −5.42705 3.94298i −0.209822 0.152445i
\(670\) 13.0269 + 2.06326i 0.503273 + 0.0797107i
\(671\) 5.25731 + 1.70820i 0.202956 + 0.0659445i
\(672\) 4.05934 + 0.642937i 0.156593 + 0.0248018i
\(673\) −18.5795 + 6.03685i −0.716188 + 0.232704i −0.644370 0.764714i \(-0.722880\pi\)
−0.0718184 + 0.997418i \(0.522880\pi\)
\(674\) −13.9000 + 27.2803i −0.535409 + 1.05080i
\(675\) 7.86572 24.2082i 0.302752 0.931774i
\(676\) 25.5967i 0.984490i
\(677\) 7.95148i 0.305600i −0.988257 0.152800i \(-0.951171\pi\)
0.988257 0.152800i \(-0.0488291\pi\)
\(678\) 16.9191 + 33.2055i 0.649773 + 1.27525i
\(679\) −0.204270 + 0.281153i −0.00783915 + 0.0107897i
\(680\) 1.16308 7.34342i 0.0446022 0.281607i
\(681\) 70.1662i 2.68877i
\(682\) 34.5480 33.9930i 1.32291 1.30166i
\(683\) 26.1246i 0.999630i 0.866132 + 0.499815i \(0.166599\pi\)
−0.866132 + 0.499815i \(0.833401\pi\)
\(684\) 52.3607 38.0423i 2.00206 1.45458i
\(685\) 9.47214 13.0373i 0.361912 0.498129i
\(686\) −4.14791 + 2.11346i −0.158368 + 0.0806924i
\(687\) 36.1803i 1.38037i
\(688\) 10.5146 0.400866
\(689\) 1.28115 3.94298i 0.0488080 0.150216i
\(690\) −4.55899 2.32292i −0.173558 0.0884321i
\(691\) 34.9116 11.3435i 1.32810 0.431526i 0.442830 0.896605i \(-0.353974\pi\)
0.885269 + 0.465080i \(0.153974\pi\)
\(692\) −15.3229 21.0902i −0.582489 0.801728i
\(693\) −8.94427 2.90617i −0.339765 0.110396i
\(694\) −2.28822 + 14.4473i −0.0868598 + 0.548411i
\(695\) 6.51864 + 4.73607i 0.247266 + 0.179649i
\(696\) −56.8603 28.9718i −2.15529 1.09817i
\(697\) −5.00000 + 6.88191i −0.189389 + 0.260671i
\(698\) −5.50937 + 0.872598i −0.208533 + 0.0330283i
\(699\) −1.26133 3.88197i −0.0477078 0.146829i
\(700\) −0.909830 0.661030i −0.0343883 0.0249846i
\(701\) −21.2533 + 15.4414i −0.802726 + 0.583214i −0.911712 0.410829i \(-0.865239\pi\)
0.108987 + 0.994043i \(0.465239\pi\)
\(702\) 6.04630 3.08075i 0.228203 0.116275i
\(703\) −37.3485 + 27.1353i −1.40862 + 1.02343i
\(704\) −46.8328 + 15.2169i −1.76508 + 0.573509i
\(705\) −26.6074 + 8.64527i −1.00209 + 0.325600i
\(706\) −14.2472 + 7.25933i −0.536202 + 0.273209i
\(707\) 2.11146i 0.0794095i
\(708\) 33.6830 1.26588
\(709\) 38.8050 + 12.6085i 1.45735 + 0.473522i 0.927260 0.374419i \(-0.122158\pi\)
0.530091 + 0.847941i \(0.322158\pi\)
\(710\) 2.36899 + 14.9572i 0.0889068 + 0.561335i
\(711\) 35.1361 25.5279i 1.31771 0.957370i
\(712\) −4.91428 + 4.91428i −0.184171 + 0.184171i
\(713\) −4.04508 0.0327561i −0.151490 0.00122673i
\(714\) −1.18034 + 1.18034i −0.0441731 + 0.0441731i
\(715\) −2.62866 3.61803i −0.0983061 0.135307i
\(716\) −5.00000 + 6.88191i −0.186859 + 0.257189i
\(717\) −24.4721 + 75.3175i −0.913929 + 2.81278i
\(718\) 4.79837 + 4.79837i 0.179074 + 0.179074i
\(719\) 12.5882 0.469462 0.234731 0.972060i \(-0.424579\pi\)
0.234731 + 0.972060i \(0.424579\pi\)
\(720\) 12.9443 39.8384i 0.482405 1.48469i
\(721\) −0.881966 2.71441i −0.0328461 0.101090i
\(722\) −7.56044 3.85224i −0.281370 0.143365i
\(723\) 1.31433 + 1.80902i 0.0488804 + 0.0672781i
\(724\) −0.449028 + 1.38197i −0.0166880 + 0.0513604i
\(725\) 10.2639 + 14.1271i 0.381193 + 0.524667i
\(726\) 115.592 18.3079i 4.29001 0.679470i
\(727\) −22.4948 + 7.30902i −0.834287 + 0.271076i −0.694850 0.719154i \(-0.744529\pi\)
−0.139437 + 0.990231i \(0.544529\pi\)
\(728\) −0.0469016 0.296125i −0.00173829 0.0109751i
\(729\) 9.28115 + 6.74315i 0.343746 + 0.249746i
\(730\) −1.97599 + 3.87811i −0.0731348 + 0.143535i
\(731\) −2.51014 + 3.45492i −0.0928410 + 0.127785i
\(732\) 4.47214 3.24920i 0.165295 0.120094i
\(733\) −6.48936 + 19.9722i −0.239690 + 0.737690i 0.756775 + 0.653676i \(0.226774\pi\)
−0.996465 + 0.0840138i \(0.973226\pi\)
\(734\) 2.30272 14.5388i 0.0849948 0.536636i
\(735\) 10.6861 + 32.8885i 0.394164 + 1.21311i
\(736\) 3.66199 + 1.86588i 0.134983 + 0.0687771i
\(737\) 33.7426 + 10.9637i 1.24293 + 0.403851i
\(738\) −33.8885 + 33.8885i −1.24745 + 1.24745i
\(739\) −26.0746 −0.959168 −0.479584 0.877496i \(-0.659212\pi\)
−0.479584 + 0.877496i \(0.659212\pi\)
\(740\) −9.23305 + 28.4164i −0.339414 + 1.04461i
\(741\) −5.59017 4.06150i −0.205360 0.149203i
\(742\) −0.482203 + 3.04451i −0.0177022 + 0.111767i
\(743\) 6.60440 0.242292 0.121146 0.992635i \(-0.461343\pi\)
0.121146 + 0.992635i \(0.461343\pi\)
\(744\) −7.19409 47.9305i −0.263748 1.75722i
\(745\) −6.70820 −0.245770
\(746\) −3.18937 + 20.1369i −0.116771 + 0.737263i
\(747\) −34.5811 25.1246i −1.26525 0.919261i
\(748\) 6.18034 19.0211i 0.225976 0.695481i
\(749\) 1.68692 0.0616386
\(750\) −36.7607 + 36.7607i −1.34231 + 1.34231i
\(751\) −31.0013 10.0729i −1.13126 0.367567i −0.317202 0.948358i \(-0.602743\pi\)
−0.814053 + 0.580791i \(0.802743\pi\)
\(752\) 21.3723 6.94427i 0.779367 0.253232i
\(753\) 3.61803 + 11.1352i 0.131848 + 0.405788i
\(754\) −0.728250 + 4.59799i −0.0265213 + 0.167449i
\(755\) −4.30625 + 13.2533i −0.156721 + 0.482337i
\(756\) −4.08174 + 2.96556i −0.148451 + 0.107856i
\(757\) −15.5279 + 21.3723i −0.564370 + 0.776788i −0.991874 0.127225i \(-0.959393\pi\)
0.427504 + 0.904013i \(0.359393\pi\)
\(758\) 16.5857 32.5512i 0.602419 1.18231i
\(759\) −11.1352 8.09017i −0.404181 0.293655i
\(760\) −22.6007 + 3.57960i −0.819815 + 0.129846i
\(761\) 25.2254 8.19624i 0.914421 0.297113i 0.186245 0.982503i \(-0.440368\pi\)
0.728176 + 0.685390i \(0.240368\pi\)
\(762\) −45.9388 + 7.27599i −1.66419 + 0.263581i
\(763\) −2.10638 2.89919i −0.0762562 0.104958i
\(764\) −0.201626 + 0.620541i −0.00729458 + 0.0224504i
\(765\) 10.0000 + 13.7638i 0.361551 + 0.497632i
\(766\) 3.96066 + 2.01806i 0.143104 + 0.0729153i
\(767\) −0.759299 2.33688i −0.0274167 0.0843799i
\(768\) −15.2169 + 46.8328i −0.549093 + 1.68993i
\(769\) −11.9098 −0.429479 −0.214740 0.976671i \(-0.568890\pi\)
−0.214740 + 0.976671i \(0.568890\pi\)
\(770\) 2.35114 + 2.35114i 0.0847292 + 0.0847292i
\(771\) 10.4086 32.0344i 0.374857 1.15369i
\(772\) −9.57608 + 13.1803i −0.344651 + 0.474371i
\(773\) −24.2320 33.3525i −0.871565 1.19961i −0.978687 0.205360i \(-0.934164\pi\)
0.107122 0.994246i \(-0.465836\pi\)
\(774\) −17.0130 + 17.0130i −0.611520 + 0.611520i
\(775\) −4.20025 + 12.5795i −0.150878 + 0.451870i
\(776\) −2.94427 2.94427i −0.105693 0.105693i
\(777\) 5.42705 3.94298i 0.194694 0.141454i
\(778\) −6.25072 39.4655i −0.224099 1.41491i
\(779\) 24.8990 + 8.09017i 0.892099 + 0.289860i
\(780\) −4.47214 −0.160128
\(781\) 40.7364i 1.45766i
\(782\) −1.48732 + 0.757825i −0.0531863 + 0.0270998i
\(783\) 74.5052 24.2082i 2.66260 0.865131i
\(784\) −8.58359 26.4176i −0.306557 0.943485i
\(785\) 22.1803 16.1150i 0.791650 0.575168i
\(786\) −47.1031 + 24.0002i −1.68011 + 0.856060i
\(787\) 25.2093 18.3156i 0.898613 0.652880i −0.0394965 0.999220i \(-0.512575\pi\)
0.938109 + 0.346339i \(0.112575\pi\)
\(788\) −28.1482 20.4508i −1.00274 0.728531i
\(789\) −25.0623 77.1338i −0.892242 2.74604i
\(790\) −15.1660 + 2.40206i −0.539582 + 0.0854613i
\(791\) −1.18808 + 1.63525i −0.0422433 + 0.0581430i
\(792\) 51.1556 100.399i 1.81774 3.56751i
\(793\) −0.326238 0.237026i −0.0115850 0.00841703i
\(794\) 2.65478 16.7616i 0.0942146 0.594848i
\(795\) 43.7284 + 14.2082i 1.55088 + 0.503913i
\(796\) −4.27051 5.87785i −0.151364 0.208335i
\(797\) 20.0000 6.49839i 0.708436 0.230185i 0.0674339 0.997724i \(-0.478519\pi\)
0.641002 + 0.767539i \(0.278519\pi\)
\(798\) 4.57748 + 2.33235i 0.162041 + 0.0825641i
\(799\) −2.82041 + 8.68034i −0.0997791 + 0.307088i
\(800\) 9.52786 9.52786i 0.336861 0.336861i
\(801\) 15.9030i 0.561903i
\(802\) 12.3337 6.28433i 0.435518 0.221908i
\(803\) −6.88191 + 9.47214i −0.242857 + 0.334264i
\(804\) 28.7032 20.8541i 1.01228 0.735467i
\(805\) 0.277515i 0.00978110i
\(806\) −3.16318 + 1.57959i −0.111418 + 0.0556387i
\(807\) 75.5755i 2.66038i
\(808\) 24.9868 + 3.95751i 0.879031 + 0.139225i
\(809\) −13.3779 + 18.4131i −0.470342 + 0.647370i −0.976613 0.215004i \(-0.931023\pi\)
0.506271 + 0.862374i \(0.331023\pi\)
\(810\) 13.9954 + 27.4676i 0.491749 + 0.965111i
\(811\) 37.3607i 1.31191i 0.754800 + 0.655955i \(0.227734\pi\)
−0.754800 + 0.655955i \(0.772266\pi\)
\(812\) 3.46120i 0.121464i
\(813\) 5.59017 17.2048i 0.196056 0.603398i
\(814\) −36.4889 + 71.6135i −1.27894 + 2.51005i
\(815\) −3.16344 + 1.02786i −0.110810 + 0.0360045i
\(816\) −11.7557 16.1803i −0.411532 0.566425i
\(817\) 12.5000 + 4.06150i 0.437320 + 0.142094i
\(818\) 50.3326 + 7.97190i 1.75984 + 0.278731i
\(819\) 0.555029 + 0.403252i 0.0193943 + 0.0140908i
\(820\) 16.1150 5.23607i 0.562759 0.182851i
\(821\) 10.4508 14.3844i 0.364737 0.502018i −0.586724 0.809787i \(-0.699583\pi\)
0.951461 + 0.307769i \(0.0995826\pi\)
\(822\) −6.78130 42.8154i −0.236525 1.49336i
\(823\) 9.35156 + 28.7812i 0.325975 + 1.00325i 0.970999 + 0.239085i \(0.0768475\pi\)
−0.645024 + 0.764163i \(0.723152\pi\)
\(824\) 33.7752 5.34946i 1.17661 0.186357i
\(825\) −36.5066 + 26.5236i −1.27100 + 0.923433i
\(826\) 0.829384 + 1.62776i 0.0288580 + 0.0566369i
\(827\) −12.9515 + 9.40983i −0.450368 + 0.327212i −0.789741 0.613440i \(-0.789785\pi\)
0.339373 + 0.940652i \(0.389785\pi\)
\(828\) −8.94427 + 2.90617i −0.310835 + 0.100996i
\(829\) 36.8328 11.9677i 1.27926 0.415656i 0.410938 0.911663i \(-0.365201\pi\)
0.868318 + 0.496007i \(0.165201\pi\)
\(830\) 6.86092 + 13.4653i 0.238146 + 0.467388i
\(831\) 1.38197i 0.0479399i
\(832\) 3.59222 0.124538
\(833\) 10.7295 + 3.48622i 0.371755 + 0.120790i
\(834\) 21.4077 3.39065i 0.741289 0.117409i
\(835\) −27.2501 + 19.7984i −0.943029 + 0.685151i
\(836\) −61.5537 −2.12888
\(837\) 47.8500 + 35.3606i 1.65394 + 1.22224i
\(838\) −20.1803 20.1803i −0.697118 0.697118i
\(839\) 2.93893 + 4.04508i 0.101463 + 0.139652i 0.856730 0.515766i \(-0.172493\pi\)
−0.755267 + 0.655418i \(0.772493\pi\)
\(840\) 3.28408 0.520147i 0.113311 0.0179468i
\(841\) −7.64590 + 23.5317i −0.263652 + 0.811436i
\(842\) 27.5967 27.5967i 0.951047 0.951047i
\(843\) −48.7939 −1.68055
\(844\) 3.34752 10.3026i 0.115227 0.354631i
\(845\) −6.39919 19.6947i −0.220139 0.677517i
\(846\) −23.3450 + 45.8171i −0.802617 + 1.57523i
\(847\) 3.73098 + 5.13525i 0.128198 + 0.176449i
\(848\) −35.1246 11.4127i −1.20618 0.391913i
\(849\) 5.26393 + 7.24518i 0.180658 + 0.248654i
\(850\) 0.856109 + 5.40526i 0.0293643 + 0.185399i
\(851\) 6.37988 2.07295i 0.218700 0.0710598i
\(852\) 32.9565 + 23.9443i 1.12907 + 0.820317i
\(853\) −33.5623 24.3844i −1.14915 0.834907i −0.160784 0.986990i \(-0.551402\pi\)
−0.988368 + 0.152082i \(0.951402\pi\)
\(854\) 0.267138 + 0.136114i 0.00914129 + 0.00465772i
\(855\) 30.7768 42.3607i 1.05255 1.44870i
\(856\) −3.16180 + 19.9628i −0.108068 + 0.682315i
\(857\) 14.0344 43.1936i 0.479407 1.47546i −0.360513 0.932754i \(-0.617398\pi\)
0.839920 0.542710i \(-0.182602\pi\)
\(858\) −11.8819 1.88191i −0.405642 0.0642473i
\(859\) −3.19620 9.83688i −0.109053 0.335630i 0.881607 0.471983i \(-0.156462\pi\)
−0.990660 + 0.136353i \(0.956462\pi\)
\(860\) 8.09017 2.62866i 0.275873 0.0896364i
\(861\) −3.61803 1.17557i −0.123302 0.0400633i
\(862\) −13.1246 13.1246i −0.447026 0.447026i
\(863\) 49.1369 1.67264 0.836320 0.548241i \(-0.184702\pi\)
0.836320 + 0.548241i \(0.184702\pi\)
\(864\) −27.4437 53.8613i −0.933653 1.83240i
\(865\) −17.0623 12.3965i −0.580136 0.421493i
\(866\) −39.2259 6.21278i −1.33295 0.211119i
\(867\) −44.1976 −1.50103
\(868\) 2.13914 1.52786i 0.0726071 0.0518591i
\(869\) −41.3050 −1.40117
\(870\) −50.9925 8.07641i −1.72881 0.273816i
\(871\) −2.09387 1.52129i −0.0709481 0.0515468i
\(872\) 38.2567 19.4928i 1.29553 0.660108i
\(873\) 9.52786 0.322469
\(874\) 3.63271 + 3.63271i 0.122878 + 0.122878i
\(875\) −2.68166 0.871323i −0.0906565 0.0294561i
\(876\) 3.61803 + 11.1352i 0.122242 + 0.376222i
\(877\) −8.52786 26.2461i −0.287966 0.886267i −0.985494 0.169710i \(-0.945717\pi\)
0.697529 0.716557i \(-0.254283\pi\)
\(878\) −6.32453 1.00171i −0.213443 0.0338060i
\(879\) −15.4414 + 47.5238i −0.520826 + 1.60294i
\(880\) −32.2299 + 23.4164i −1.08647 + 0.789367i
\(881\) 3.19098 4.39201i 0.107507 0.147971i −0.751873 0.659308i \(-0.770850\pi\)
0.859380 + 0.511337i \(0.170850\pi\)
\(882\) 56.6331 + 28.8560i 1.90694 + 0.971632i
\(883\) 45.6835 + 33.1910i 1.53737 + 1.11697i 0.951957 + 0.306231i \(0.0990680\pi\)
0.585414 + 0.810735i \(0.300932\pi\)
\(884\) −0.857567 + 1.18034i −0.0288431 + 0.0396991i
\(885\) 25.9164 8.42075i 0.871171 0.283060i
\(886\) 2.01865 + 12.7453i 0.0678180 + 0.428186i
\(887\) −26.3973 36.3328i −0.886336 1.21994i −0.974626 0.223842i \(-0.928140\pi\)
0.0882897 0.996095i \(-0.471860\pi\)
\(888\) 36.4889 + 71.6135i 1.22449 + 2.40319i
\(889\) −1.48278 2.04087i −0.0497308 0.0684486i
\(890\) −2.55258 + 5.00972i −0.0855627 + 0.167926i
\(891\) 25.6255 + 78.8673i 0.858487 + 2.64215i
\(892\) 4.14590 + 1.34708i 0.138815 + 0.0451037i
\(893\) 28.0902 0.940002
\(894\) −12.7598 + 12.7598i −0.426750 + 0.426750i
\(895\) −2.12663 + 6.54508i −0.0710853 + 0.218778i
\(896\) −2.63792 + 0.417806i −0.0881268 + 0.0139579i
\(897\) 0.590170 + 0.812299i 0.0197052 + 0.0271219i
\(898\) −24.8335 24.8335i −0.828704 0.828704i
\(899\) −38.9201 + 12.2984i −1.29806 + 0.410174i
\(900\) 30.8328i 1.02776i
\(901\) 12.1353 8.81678i 0.404284 0.293729i
\(902\) 45.0188 7.13028i 1.49896 0.237412i
\(903\) −1.81636 0.590170i −0.0604446 0.0196396i
\(904\) −17.1246 17.1246i −0.569556 0.569556i
\(905\) 1.17557i 0.0390773i
\(906\) 17.0183 + 33.4002i 0.565394 + 1.10965i
\(907\) −22.2376 + 7.22542i −0.738386 + 0.239916i −0.653977 0.756515i \(-0.726901\pi\)
−0.0844099 + 0.996431i \(0.526901\pi\)
\(908\) 14.0902 + 43.3651i 0.467599 + 1.43912i
\(909\) −46.8328 + 34.0260i −1.55335 + 1.12857i
\(910\) −0.110118 0.216120i −0.00365039 0.00716429i
\(911\) 23.7234 17.2361i 0.785992 0.571056i −0.120780 0.992679i \(-0.538539\pi\)
0.906771 + 0.421623i \(0.138539\pi\)
\(912\) −36.1803 + 49.7980i −1.19805 + 1.64898i
\(913\) 12.5623 + 38.6628i 0.415752 + 1.27955i
\(914\) 5.30977 + 33.5245i 0.175631 + 1.10889i
\(915\) 2.62866 3.61803i 0.0869007 0.119609i
\(916\) 7.26543 + 22.3607i 0.240056 + 0.738818i
\(917\) −2.31966 1.68533i −0.0766019 0.0556546i
\(918\) 24.2494 + 3.84073i 0.800351 + 0.126763i
\(919\) 19.5232 + 6.34346i 0.644010 + 0.209251i 0.612771 0.790261i \(-0.290055\pi\)
0.0312386 + 0.999512i \(0.490055\pi\)
\(920\) 3.28408 + 0.520147i 0.108273 + 0.0171487i
\(921\) 59.1697 19.2254i 1.94971 0.633498i
\(922\) −17.8260 + 34.9855i −0.587068 + 1.15219i
\(923\) 0.918300 2.82624i 0.0302262 0.0930268i
\(924\) 8.94427 0.294245
\(925\) 21.9928i 0.723119i
\(926\) 15.8080 + 31.0249i 0.519482 + 1.01954i
\(927\) −45.9937 + 63.3050i −1.51063 + 2.07921i
\(928\) 40.9595 + 6.48734i 1.34456 + 0.212958i
\(929\) 56.6799i 1.85961i 0.368057 + 0.929803i \(0.380023\pi\)
−0.368057 + 0.929803i \(0.619977\pi\)
\(930\) −17.5179 35.0802i −0.574435 1.15033i
\(931\) 34.7214i 1.13795i
\(932\) 1.55909 + 2.14590i 0.0510696 + 0.0702912i
\(933\) 31.1803 42.9161i 1.02080 1.40501i
\(934\) −24.3959 + 12.4303i −0.798258 + 0.406733i
\(935\) 16.1803i 0.529154i
\(936\) −5.81234 + 5.81234i −0.189982 + 0.189982i
\(937\) −14.3435 + 44.1446i −0.468580 + 1.44214i 0.385843 + 0.922565i \(0.373911\pi\)
−0.854423 + 0.519578i \(0.826089\pi\)
\(938\) 1.71456 + 0.873610i 0.0559823 + 0.0285244i
\(939\) 60.9331 19.7984i 1.98848 0.646096i
\(940\) 14.7082 10.6861i 0.479729 0.348543i
\(941\) 9.14590 + 2.97168i 0.298148 + 0.0968741i 0.454271 0.890863i \(-0.349900\pi\)
−0.156123 + 0.987738i \(0.549900\pi\)
\(942\) 11.5370 72.8420i 0.375897 2.37332i
\(943\) −3.07768 2.23607i −0.100223 0.0728164i
\(944\) −20.8172 + 6.76393i −0.677544 + 0.220147i
\(945\) −2.39919 + 3.30220i −0.0780456 + 0.107420i
\(946\) 22.6007 3.57960i 0.734813 0.116383i
\(947\) −15.2169 46.8328i −0.494483 1.52186i −0.817761 0.575558i \(-0.804785\pi\)
0.323278 0.946304i \(-0.395215\pi\)
\(948\) −24.2784 + 33.4164i −0.788527 + 1.08531i
\(949\) 0.690983 0.502029i 0.0224303 0.0162965i
\(950\) 15.0073 7.64658i 0.486900 0.248088i
\(951\) −46.4428 + 33.7426i −1.50601 + 1.09418i
\(952\) 0.492464 0.966516i 0.0159609 0.0313250i
\(953\) −5.26393 + 1.71036i −0.170515 + 0.0554038i −0.393031 0.919525i \(-0.628573\pi\)
0.222515 + 0.974929i \(0.428573\pi\)
\(954\) 75.2989 38.3667i 2.43789 1.24217i
\(955\) 0.527864i 0.0170813i
\(956\) 51.4631i 1.66443i
\(957\) −132.082 42.9161i −4.26961 1.38728i
\(958\) 8.88917 + 56.1240i 0.287196 + 1.81328i
\(959\) 1.90211 1.38197i 0.0614224 0.0446260i
\(960\) 39.8384i 1.28578i
\(961\) −24.7812 18.6251i −0.799392 0.600810i
\(962\) 4.14590 4.14590i 0.133669 0.133669i
\(963\) −27.1846 37.4164i −0.876012 1.20573i
\(964\) −1.17557 0.854102i −0.0378626 0.0275088i
\(965\) −4.07295 + 12.5352i −0.131113 + 0.403524i
\(966\) −0.527864 0.527864i −0.0169837 0.0169837i
\(967\) −33.5115 −1.07766 −0.538828 0.842416i \(-0.681133\pi\)
−0.538828 + 0.842416i \(0.681133\pi\)
\(968\) −67.7631 + 34.5270i −2.17799 + 1.10974i
\(969\) −7.72542 23.7764i −0.248176 0.763808i
\(970\) −3.00145 1.52932i −0.0963708 0.0491034i
\(971\) 13.1885 + 18.1525i 0.423241 + 0.582541i 0.966385 0.257098i \(-0.0827665\pi\)
−0.543145 + 0.839639i \(0.682766\pi\)
\(972\) 17.8885 + 5.81234i 0.573775 + 0.186431i
\(973\) 0.690983 + 0.951057i 0.0221519 + 0.0304895i
\(974\) 27.1960 4.30742i 0.871415 0.138019i
\(975\) 3.13068 1.01722i 0.100262 0.0325771i
\(976\) −2.11146 + 2.90617i −0.0675861 + 0.0930242i
\(977\) −6.47214 4.70228i −0.207062 0.150439i 0.479421 0.877585i \(-0.340847\pi\)
−0.686483 + 0.727145i \(0.740847\pi\)
\(978\) −4.06211 + 7.97233i −0.129892 + 0.254927i
\(979\) −8.89002 + 12.2361i −0.284126 + 0.391066i
\(980\) −13.2088 18.1803i −0.421939 0.580750i
\(981\) −30.3607 + 93.4406i −0.969342 + 2.98333i
\(982\) 2.44896 15.4621i 0.0781494 0.493416i
\(983\) −0.244758 0.753289i −0.00780658 0.0240262i 0.947077 0.321005i \(-0.104021\pi\)
−0.954884 + 0.296979i \(0.904021\pi\)
\(984\) 20.6929 40.6121i 0.659665 1.29467i
\(985\) −26.7705 8.69827i −0.852979 0.277150i
\(986\) −11.9098 + 11.9098i −0.379286 + 0.379286i
\(987\) −4.08174 −0.129923
\(988\) 4.27051 + 1.38757i 0.135863 + 0.0441446i
\(989\) −1.54508 1.12257i −0.0491308 0.0356956i
\(990\) 14.2606 90.0377i 0.453230 2.86158i
\(991\) 12.9313 0.410776 0.205388 0.978681i \(-0.434154\pi\)
0.205388 + 0.978681i \(0.434154\pi\)
\(992\) 14.0712 + 28.1780i 0.446761 + 0.894654i
\(993\) 25.9787 0.824410
\(994\) −0.345632 + 2.18223i −0.0109628 + 0.0692162i
\(995\) −4.75528 3.45492i −0.150753 0.109528i
\(996\) 38.6628 + 12.5623i 1.22508 + 0.398052i
\(997\) −57.4721 −1.82016 −0.910080 0.414432i \(-0.863980\pi\)
−0.910080 + 0.414432i \(0.863980\pi\)
\(998\) 33.4055 33.4055i 1.05743 1.05743i
\(999\) −93.8366 30.4894i −2.96886 0.964641i
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 124.2.j.a.15.2 yes 8
4.3 odd 2 inner 124.2.j.a.15.1 8
31.29 odd 10 inner 124.2.j.a.91.1 yes 8
124.91 even 10 inner 124.2.j.a.91.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.2.j.a.15.1 8 4.3 odd 2 inner
124.2.j.a.15.2 yes 8 1.1 even 1 trivial
124.2.j.a.91.1 yes 8 31.29 odd 10 inner
124.2.j.a.91.2 yes 8 124.91 even 10 inner