Properties

Label 287.3.x.a.31.13
Level $287$
Weight $3$
Character 287.31
Analytic conductor $7.820$
Analytic rank $0$
Dimension $432$
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] = [287,3,Mod(31,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 21]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.x (of order \(30\), degree \(8\), 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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(432\)
Relative dimension: \(54\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 31.13
Character \(\chi\) \(=\) 287.31
Dual form 287.3.x.a.250.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.261584 + 2.48881i) q^{2} +(-1.88397 + 3.26313i) q^{3} +(-2.21315 - 0.470420i) q^{4} +(3.91575 + 3.52575i) q^{5} +(-7.62849 - 5.54242i) q^{6} +(5.00297 - 4.89595i) q^{7} +(-1.34357 + 4.13508i) q^{8} +(-2.59868 - 4.50104i) q^{9} +O(q^{10})\) \(q+(-0.261584 + 2.48881i) q^{2} +(-1.88397 + 3.26313i) q^{3} +(-2.21315 - 0.470420i) q^{4} +(3.91575 + 3.52575i) q^{5} +(-7.62849 - 5.54242i) q^{6} +(5.00297 - 4.89595i) q^{7} +(-1.34357 + 4.13508i) q^{8} +(-2.59868 - 4.50104i) q^{9} +(-9.79923 + 8.82326i) q^{10} +(-14.6524 + 13.1931i) q^{11} +(5.70456 - 6.33555i) q^{12} +(-10.6164 - 7.71326i) q^{13} +(10.8764 + 13.7321i) q^{14} +(-18.8821 + 6.13518i) q^{15} +(-18.2079 - 8.10669i) q^{16} +(4.12656 + 4.58301i) q^{17} +(11.8820 - 5.29021i) q^{18} +(14.2830 + 6.35920i) q^{19} +(-7.00756 - 9.64508i) q^{20} +(6.55069 + 25.5491i) q^{21} +(-29.0023 - 39.9182i) q^{22} +(-0.154861 + 1.47340i) q^{23} +(-10.9621 - 12.1746i) q^{24} +(0.288918 + 2.74887i) q^{25} +(21.9739 - 24.4045i) q^{26} -14.3281 q^{27} +(-13.3755 + 8.48200i) q^{28} +(41.6938 - 13.5471i) q^{29} +(-10.3300 - 48.5989i) q^{30} +(1.43861 - 1.29533i) q^{31} +(16.2431 - 28.1339i) q^{32} +(-15.4461 - 72.6683i) q^{33} +(-12.4857 + 9.07139i) q^{34} +(36.8523 - 1.53208i) q^{35} +(3.63389 + 11.1840i) q^{36} +(16.9390 - 18.8127i) q^{37} +(-19.5631 + 33.8842i) q^{38} +(45.1703 - 20.1111i) q^{39} +(-19.8404 + 11.4548i) q^{40} +(-28.3935 + 29.5771i) q^{41} +(-65.3005 + 9.62017i) q^{42} +(33.4478 + 24.3013i) q^{43} +(38.6344 - 22.3056i) q^{44} +(5.69381 - 26.7873i) q^{45} +(-3.62651 - 0.770838i) q^{46} +(-4.31121 + 41.0184i) q^{47} +(60.7563 - 44.1420i) q^{48} +(1.05933 - 48.9885i) q^{49} -6.91700 q^{50} +(-22.7293 + 4.83126i) q^{51} +(19.8672 + 22.0648i) q^{52} +(-4.98655 + 23.4599i) q^{53} +(3.74801 - 35.6599i) q^{54} -103.891 q^{55} +(13.5233 + 27.2657i) q^{56} +(-47.6597 + 34.6268i) q^{57} +(22.8098 + 107.312i) q^{58} +(15.5026 + 34.8195i) q^{59} +(44.6752 - 4.69555i) q^{60} +(-9.13649 + 20.5209i) q^{61} +(2.84751 + 3.91927i) q^{62} +(-35.0380 - 9.79556i) q^{63} +(1.27282 + 0.924758i) q^{64} +(-14.3760 - 67.6340i) q^{65} +(184.898 - 19.4336i) q^{66} +(10.6891 - 50.2880i) q^{67} +(-6.97678 - 12.0841i) q^{68} +(-4.51615 - 3.28118i) q^{69} +(-5.82693 + 92.1190i) q^{70} +(-102.531 - 33.3142i) q^{71} +(22.1037 - 4.69829i) q^{72} +(54.4705 + 31.4486i) q^{73} +(42.3901 + 47.0790i) q^{74} +(-9.51425 - 4.23601i) q^{75} +(-28.6190 - 20.7929i) q^{76} +(-8.71280 + 137.742i) q^{77} +(38.2369 + 117.681i) q^{78} +(65.3729 - 37.7431i) q^{79} +(-42.7154 - 95.9404i) q^{80} +(50.3818 - 87.2639i) q^{81} +(-66.1845 - 78.4030i) q^{82} +32.8272i q^{83} +(-2.47885 - 59.6258i) q^{84} +32.4952i q^{85} +(-69.2306 + 76.8884i) q^{86} +(-34.3437 + 161.575i) q^{87} +(-34.8681 - 78.3149i) q^{88} +(8.18061 + 3.64224i) q^{89} +(65.1790 + 21.1779i) q^{90} +(-90.8772 + 13.3882i) q^{91} +(1.03585 - 3.18802i) q^{92} +(1.51654 + 7.13474i) q^{93} +(-100.959 - 21.4595i) q^{94} +(33.5076 + 75.2594i) q^{95} +(61.2031 + 106.007i) q^{96} +(41.2854 + 127.063i) q^{97} +(121.646 + 15.4511i) q^{98} +(97.4598 + 31.6666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 432 q - 3 q^{2} + 101 q^{4} - 9 q^{5} - 10 q^{7} - 40 q^{8} - 624 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 432 q - 3 q^{2} + 101 q^{4} - 9 q^{5} - 10 q^{7} - 40 q^{8} - 624 q^{9} - 90 q^{10} - 5 q^{11} - 15 q^{12} + 70 q^{15} + 197 q^{16} - 15 q^{17} - 6 q^{18} - 15 q^{19} + 166 q^{21} + 60 q^{22} + 18 q^{23} + 480 q^{24} - 213 q^{25} - 15 q^{26} - 105 q^{28} + 360 q^{29} - 15 q^{30} - 45 q^{31} + 142 q^{32} + 36 q^{33} - 150 q^{35} + 46 q^{36} + 82 q^{37} - 80 q^{39} - 54 q^{40} + 228 q^{42} - 88 q^{43} + 330 q^{45} - 96 q^{46} - 15 q^{47} + 50 q^{49} - 472 q^{50} + 150 q^{51} - 15 q^{52} - 230 q^{53} + 465 q^{54} + 180 q^{56} + 382 q^{57} - 5 q^{58} - 207 q^{59} - 480 q^{60} - 441 q^{61} + 200 q^{63} - 128 q^{64} - 290 q^{65} - 918 q^{66} + 115 q^{67} + 1175 q^{70} - 730 q^{71} - 309 q^{72} - 78 q^{73} + 589 q^{74} + 240 q^{75} + 684 q^{77} - 434 q^{78} - 27 q^{80} - 1936 q^{81} - 309 q^{82} - 173 q^{84} - 439 q^{86} - 1002 q^{87} + 1335 q^{89} - 274 q^{91} - 270 q^{92} + 765 q^{93} + 1515 q^{94} + 715 q^{95} - 454 q^{98} + 480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.261584 + 2.48881i −0.130792 + 1.24440i 0.710451 + 0.703747i \(0.248491\pi\)
−0.841243 + 0.540657i \(0.818176\pi\)
\(3\) −1.88397 + 3.26313i −0.627990 + 1.08771i 0.359965 + 0.932966i \(0.382789\pi\)
−0.987955 + 0.154744i \(0.950545\pi\)
\(4\) −2.21315 0.470420i −0.553288 0.117605i
\(5\) 3.91575 + 3.52575i 0.783149 + 0.705151i 0.960281 0.279036i \(-0.0900150\pi\)
−0.177131 + 0.984187i \(0.556682\pi\)
\(6\) −7.62849 5.54242i −1.27142 0.923737i
\(7\) 5.00297 4.89595i 0.714709 0.699422i
\(8\) −1.34357 + 4.13508i −0.167946 + 0.516885i
\(9\) −2.59868 4.50104i −0.288742 0.500116i
\(10\) −9.79923 + 8.82326i −0.979923 + 0.882326i
\(11\) −14.6524 + 13.1931i −1.33204 + 1.19937i −0.369185 + 0.929356i \(0.620363\pi\)
−0.962855 + 0.270019i \(0.912970\pi\)
\(12\) 5.70456 6.33555i 0.475380 0.527963i
\(13\) −10.6164 7.71326i −0.816646 0.593328i 0.0991039 0.995077i \(-0.468402\pi\)
−0.915750 + 0.401749i \(0.868402\pi\)
\(14\) 10.8764 + 13.7321i 0.776885 + 0.980866i
\(15\) −18.8821 + 6.13518i −1.25881 + 0.409012i
\(16\) −18.2079 8.10669i −1.13799 0.506668i
\(17\) 4.12656 + 4.58301i 0.242739 + 0.269589i 0.852187 0.523237i \(-0.175276\pi\)
−0.609448 + 0.792826i \(0.708609\pi\)
\(18\) 11.8820 5.29021i 0.660112 0.293901i
\(19\) 14.2830 + 6.35920i 0.751737 + 0.334695i 0.746583 0.665292i \(-0.231693\pi\)
0.00515375 + 0.999987i \(0.498360\pi\)
\(20\) −7.00756 9.64508i −0.350378 0.482254i
\(21\) 6.55069 + 25.5491i 0.311938 + 1.21663i
\(22\) −29.0023 39.9182i −1.31829 1.81447i
\(23\) −0.154861 + 1.47340i −0.00673308 + 0.0640610i −0.997373 0.0724437i \(-0.976920\pi\)
0.990639 + 0.136505i \(0.0435869\pi\)
\(24\) −10.9621 12.1746i −0.456753 0.507275i
\(25\) 0.288918 + 2.74887i 0.0115567 + 0.109955i
\(26\) 21.9739 24.4045i 0.845151 0.938635i
\(27\) −14.3281 −0.530671
\(28\) −13.3755 + 8.48200i −0.477696 + 0.302928i
\(29\) 41.6938 13.5471i 1.43772 0.467142i 0.516532 0.856268i \(-0.327223\pi\)
0.921185 + 0.389126i \(0.127223\pi\)
\(30\) −10.3300 48.5989i −0.344334 1.61996i
\(31\) 1.43861 1.29533i 0.0464068 0.0417849i −0.645601 0.763675i \(-0.723393\pi\)
0.692008 + 0.721890i \(0.256726\pi\)
\(32\) 16.2431 28.1339i 0.507598 0.879185i
\(33\) −15.4461 72.6683i −0.468064 2.20207i
\(34\) −12.4857 + 9.07139i −0.367226 + 0.266805i
\(35\) 36.8523 1.53208i 1.05292 0.0437737i
\(36\) 3.63389 + 11.1840i 0.100941 + 0.310666i
\(37\) 16.9390 18.8127i 0.457811 0.508450i −0.469402 0.882984i \(-0.655531\pi\)
0.927213 + 0.374534i \(0.122197\pi\)
\(38\) −19.5631 + 33.8842i −0.514817 + 0.891690i
\(39\) 45.1703 20.1111i 1.15821 0.515670i
\(40\) −19.8404 + 11.4548i −0.496009 + 0.286371i
\(41\) −28.3935 + 29.5771i −0.692525 + 0.721393i
\(42\) −65.3005 + 9.62017i −1.55477 + 0.229052i
\(43\) 33.4478 + 24.3013i 0.777856 + 0.565146i 0.904335 0.426824i \(-0.140367\pi\)
−0.126478 + 0.991969i \(0.540367\pi\)
\(44\) 38.6344 22.3056i 0.878055 0.506945i
\(45\) 5.69381 26.7873i 0.126529 0.595272i
\(46\) −3.62651 0.770838i −0.0788372 0.0167574i
\(47\) −4.31121 + 41.0184i −0.0917278 + 0.872732i 0.847813 + 0.530295i \(0.177919\pi\)
−0.939541 + 0.342437i \(0.888748\pi\)
\(48\) 60.7563 44.1420i 1.26576 0.919626i
\(49\) 1.05933 48.9885i 0.0216189 0.999766i
\(50\) −6.91700 −0.138340
\(51\) −22.7293 + 4.83126i −0.445672 + 0.0947306i
\(52\) 19.8672 + 22.0648i 0.382062 + 0.424323i
\(53\) −4.98655 + 23.4599i −0.0940859 + 0.442640i 0.905737 + 0.423839i \(0.139318\pi\)
−0.999823 + 0.0188001i \(0.994015\pi\)
\(54\) 3.74801 35.6599i 0.0694076 0.660369i
\(55\) −103.891 −1.88893
\(56\) 13.5233 + 27.2657i 0.241488 + 0.486888i
\(57\) −47.6597 + 34.6268i −0.836134 + 0.607487i
\(58\) 22.8098 + 107.312i 0.393272 + 1.85020i
\(59\) 15.5026 + 34.8195i 0.262757 + 0.590161i 0.995955 0.0898538i \(-0.0286400\pi\)
−0.733198 + 0.680015i \(0.761973\pi\)
\(60\) 44.6752 4.69555i 0.744587 0.0782592i
\(61\) −9.13649 + 20.5209i −0.149778 + 0.336408i −0.972816 0.231579i \(-0.925611\pi\)
0.823038 + 0.567987i \(0.192278\pi\)
\(62\) 2.84751 + 3.91927i 0.0459276 + 0.0632140i
\(63\) −35.0380 9.79556i −0.556159 0.155485i
\(64\) 1.27282 + 0.924758i 0.0198878 + 0.0144493i
\(65\) −14.3760 67.6340i −0.221170 1.04052i
\(66\) 184.898 19.4336i 2.80148 0.294448i
\(67\) 10.6891 50.2880i 0.159538 0.750568i −0.823522 0.567284i \(-0.807994\pi\)
0.983060 0.183284i \(-0.0586726\pi\)
\(68\) −6.97678 12.0841i −0.102600 0.177708i
\(69\) −4.51615 3.28118i −0.0654515 0.0475533i
\(70\) −5.82693 + 92.1190i −0.0832418 + 1.31599i
\(71\) −102.531 33.3142i −1.44409 0.469214i −0.520922 0.853604i \(-0.674412\pi\)
−0.923171 + 0.384390i \(0.874412\pi\)
\(72\) 22.1037 4.69829i 0.306996 0.0652540i
\(73\) 54.4705 + 31.4486i 0.746172 + 0.430802i 0.824309 0.566140i \(-0.191564\pi\)
−0.0781374 + 0.996943i \(0.524897\pi\)
\(74\) 42.3901 + 47.0790i 0.572840 + 0.636203i
\(75\) −9.51425 4.23601i −0.126857 0.0564802i
\(76\) −28.6190 20.7929i −0.376566 0.273591i
\(77\) −8.71280 + 137.742i −0.113153 + 1.78886i
\(78\) 38.2369 + 117.681i 0.490217 + 1.50873i
\(79\) 65.3729 37.7431i 0.827505 0.477760i −0.0254925 0.999675i \(-0.508115\pi\)
0.852998 + 0.521915i \(0.174782\pi\)
\(80\) −42.7154 95.9404i −0.533942 1.19925i
\(81\) 50.3818 87.2639i 0.621998 1.07733i
\(82\) −66.1845 78.4030i −0.807128 0.956134i
\(83\) 32.8272i 0.395509i 0.980252 + 0.197754i \(0.0633648\pi\)
−0.980252 + 0.197754i \(0.936635\pi\)
\(84\) −2.47885 59.6258i −0.0295101 0.709831i
\(85\) 32.4952i 0.382296i
\(86\) −69.2306 + 76.8884i −0.805008 + 0.894051i
\(87\) −34.3437 + 161.575i −0.394756 + 1.85718i
\(88\) −34.8681 78.3149i −0.396228 0.889942i
\(89\) 8.18061 + 3.64224i 0.0919169 + 0.0409241i 0.452180 0.891927i \(-0.350646\pi\)
−0.360263 + 0.932851i \(0.617313\pi\)
\(90\) 65.1790 + 21.1779i 0.724211 + 0.235310i
\(91\) −90.8772 + 13.3882i −0.998651 + 0.147123i
\(92\) 1.03585 3.18802i 0.0112592 0.0346524i
\(93\) 1.51654 + 7.13474i 0.0163068 + 0.0767176i
\(94\) −100.959 21.4595i −1.07403 0.228293i
\(95\) 33.5076 + 75.2594i 0.352712 + 0.792204i
\(96\) 61.2031 + 106.007i 0.637532 + 1.10424i
\(97\) 41.2854 + 127.063i 0.425622 + 1.30993i 0.902397 + 0.430905i \(0.141806\pi\)
−0.476775 + 0.879026i \(0.658194\pi\)
\(98\) 121.646 + 15.4511i 1.24129 + 0.157664i
\(99\) 97.4598 + 31.6666i 0.984443 + 0.319865i
\(100\) 0.653706 6.21959i 0.00653706 0.0621959i
\(101\) −6.29159 59.8604i −0.0622929 0.592678i −0.980492 0.196559i \(-0.937023\pi\)
0.918199 0.396119i \(-0.129643\pi\)
\(102\) −6.07846 57.8326i −0.0595927 0.566987i
\(103\) −64.7343 + 145.396i −0.628489 + 1.41161i 0.265760 + 0.964039i \(0.414377\pi\)
−0.894249 + 0.447570i \(0.852290\pi\)
\(104\) 46.1588 33.5364i 0.443835 0.322465i
\(105\) −64.4292 + 123.140i −0.613611 + 1.17276i
\(106\) −57.0828 18.5473i −0.538517 0.174975i
\(107\) 136.468 + 60.7594i 1.27540 + 0.567845i 0.928944 0.370221i \(-0.120718\pi\)
0.346456 + 0.938066i \(0.387385\pi\)
\(108\) 31.7103 + 6.74024i 0.293614 + 0.0624096i
\(109\) −100.170 57.8335i −0.918995 0.530582i −0.0356808 0.999363i \(-0.511360\pi\)
−0.883314 + 0.468781i \(0.844693\pi\)
\(110\) 27.1762 258.565i 0.247057 2.35059i
\(111\) 29.4756 + 90.7166i 0.265546 + 0.817267i
\(112\) −130.783 + 48.5876i −1.16771 + 0.433818i
\(113\) −49.9102 + 153.608i −0.441684 + 1.35936i 0.444397 + 0.895830i \(0.353418\pi\)
−0.886080 + 0.463532i \(0.846582\pi\)
\(114\) −73.7124 127.674i −0.646600 1.11994i
\(115\) −5.80125 + 5.22347i −0.0504457 + 0.0454215i
\(116\) −98.6476 + 10.3683i −0.850410 + 0.0893817i
\(117\) −7.12913 + 67.8292i −0.0609328 + 0.579737i
\(118\) −90.7143 + 29.4749i −0.768766 + 0.249787i
\(119\) 43.0833 + 2.72520i 0.362044 + 0.0229009i
\(120\) 86.3223i 0.719352i
\(121\) 27.9878 266.286i 0.231304 2.20071i
\(122\) −48.6826 28.1069i −0.399038 0.230385i
\(123\) −43.0215 148.374i −0.349768 1.20629i
\(124\) −3.79322 + 2.19001i −0.0305905 + 0.0176614i
\(125\) 68.8678 94.7884i 0.550942 0.758307i
\(126\) 33.5447 84.6405i 0.266228 0.671750i
\(127\) 47.7137 + 146.848i 0.375699 + 1.15628i 0.943006 + 0.332775i \(0.107985\pi\)
−0.567307 + 0.823506i \(0.692015\pi\)
\(128\) 84.3157 93.6421i 0.658717 0.731579i
\(129\) −142.313 + 63.3618i −1.10320 + 0.491177i
\(130\) 172.089 18.0872i 1.32376 0.139133i
\(131\) −7.40503 34.8379i −0.0565270 0.265939i 0.940804 0.338951i \(-0.110072\pi\)
−0.997331 + 0.0730124i \(0.976739\pi\)
\(132\) 168.092i 1.27343i
\(133\) 102.592 38.1140i 0.771367 0.286572i
\(134\) 122.361 + 39.7576i 0.913144 + 0.296698i
\(135\) −56.1053 50.5174i −0.415595 0.374203i
\(136\) −24.4955 + 10.9061i −0.180114 + 0.0801918i
\(137\) −98.5786 56.9144i −0.719552 0.415434i 0.0950358 0.995474i \(-0.469703\pi\)
−0.814588 + 0.580040i \(0.803037\pi\)
\(138\) 9.34758 10.3815i 0.0677361 0.0752285i
\(139\) 95.2738 + 131.133i 0.685423 + 0.943404i 0.999983 0.00583341i \(-0.00185684\pi\)
−0.314560 + 0.949238i \(0.601857\pi\)
\(140\) −82.2804 13.9453i −0.587717 0.0996095i
\(141\) −125.726 91.3454i −0.891675 0.647840i
\(142\) 109.733 246.465i 0.772769 1.73567i
\(143\) 257.318 27.0452i 1.79943 0.189127i
\(144\) 10.8280 + 103.021i 0.0751943 + 0.715426i
\(145\) 211.026 + 93.9549i 1.45535 + 0.647965i
\(146\) −92.5181 + 127.340i −0.633686 + 0.872194i
\(147\) 157.860 + 95.7496i 1.07388 + 0.651358i
\(148\) −46.3385 + 33.6669i −0.313098 + 0.227479i
\(149\) 34.9826 + 31.4985i 0.234782 + 0.211399i 0.778121 0.628115i \(-0.216173\pi\)
−0.543338 + 0.839514i \(0.682840\pi\)
\(150\) 13.0314 22.5711i 0.0868761 0.150474i
\(151\) 42.7109 + 95.9303i 0.282854 + 0.635300i 0.997969 0.0637070i \(-0.0202923\pi\)
−0.715115 + 0.699007i \(0.753626\pi\)
\(152\) −45.4861 + 50.5174i −0.299250 + 0.332351i
\(153\) 9.90473 30.4836i 0.0647368 0.199239i
\(154\) −340.535 57.7157i −2.21127 0.374778i
\(155\) 10.2003 0.0658081
\(156\) −109.430 + 23.2600i −0.701472 + 0.149102i
\(157\) 6.75568 + 64.2760i 0.0430298 + 0.409401i 0.994742 + 0.102410i \(0.0326555\pi\)
−0.951712 + 0.306991i \(0.900678\pi\)
\(158\) 76.8348 + 172.574i 0.486296 + 1.09224i
\(159\) −67.1582 60.4695i −0.422378 0.380311i
\(160\) 162.797 52.8961i 1.01748 0.330600i
\(161\) 6.43894 + 8.12957i 0.0399934 + 0.0504943i
\(162\) 204.004 + 148.218i 1.25928 + 0.914924i
\(163\) 108.969 + 188.739i 0.668519 + 1.15791i 0.978318 + 0.207107i \(0.0664048\pi\)
−0.309799 + 0.950802i \(0.600262\pi\)
\(164\) 76.7530 52.1018i 0.468006 0.317694i
\(165\) 195.727 339.010i 1.18623 2.05460i
\(166\) −81.7007 8.58709i −0.492173 0.0517295i
\(167\) −273.707 −1.63896 −0.819481 0.573107i \(-0.805738\pi\)
−0.819481 + 0.573107i \(0.805738\pi\)
\(168\) −114.449 7.23941i −0.681245 0.0430917i
\(169\) 0.989568 + 3.04558i 0.00585543 + 0.0180212i
\(170\) −80.8743 8.50023i −0.475731 0.0500013i
\(171\) −8.49389 80.8140i −0.0496719 0.472596i
\(172\) −62.5934 69.5170i −0.363915 0.404168i
\(173\) 141.495 81.6922i 0.817890 0.472209i −0.0317980 0.999494i \(-0.510123\pi\)
0.849688 + 0.527285i \(0.176790\pi\)
\(174\) −393.145 127.740i −2.25945 0.734140i
\(175\) 14.9038 + 12.3380i 0.0851646 + 0.0705028i
\(176\) 373.743 121.436i 2.12354 0.689980i
\(177\) −142.827 15.0117i −0.806933 0.0848120i
\(178\) −11.2048 + 19.4072i −0.0629481 + 0.109029i
\(179\) 41.9892 197.543i 0.234576 1.10359i −0.690358 0.723468i \(-0.742547\pi\)
0.924934 0.380127i \(-0.124120\pi\)
\(180\) −25.2025 + 56.6058i −0.140014 + 0.314477i
\(181\) −2.34137 + 7.20600i −0.0129357 + 0.0398121i −0.957316 0.289043i \(-0.906663\pi\)
0.944380 + 0.328855i \(0.106663\pi\)
\(182\) −9.54853 229.678i −0.0524644 1.26197i
\(183\) −49.7495 68.4743i −0.271855 0.374176i
\(184\) −5.88458 2.61998i −0.0319814 0.0142390i
\(185\) 132.658 13.9429i 0.717068 0.0753669i
\(186\) −18.1537 + 1.90803i −0.0976006 + 0.0102582i
\(187\) −120.928 12.7101i −0.646676 0.0679684i
\(188\) 28.8373 88.7520i 0.153390 0.472085i
\(189\) −71.6831 + 70.1498i −0.379276 + 0.371163i
\(190\) −196.071 + 63.7075i −1.03195 + 0.335302i
\(191\) 112.155 64.7526i 0.587198 0.339019i −0.176791 0.984248i \(-0.556572\pi\)
0.763989 + 0.645229i \(0.223238\pi\)
\(192\) −5.41556 + 2.41116i −0.0282060 + 0.0125581i
\(193\) 56.5929 266.249i 0.293228 1.37953i −0.546927 0.837181i \(-0.684202\pi\)
0.840154 0.542347i \(-0.182464\pi\)
\(194\) −327.036 + 69.5136i −1.68575 + 0.358318i
\(195\) 247.783 + 80.5094i 1.27068 + 0.412869i
\(196\) −25.3897 + 107.921i −0.129539 + 0.550617i
\(197\) 46.7085 143.754i 0.237099 0.729715i −0.759737 0.650230i \(-0.774672\pi\)
0.996836 0.0794849i \(-0.0253275\pi\)
\(198\) −104.306 + 234.275i −0.526799 + 1.18321i
\(199\) −319.517 + 142.258i −1.60561 + 0.714864i −0.996911 0.0785365i \(-0.974975\pi\)
−0.608700 + 0.793401i \(0.708309\pi\)
\(200\) −11.7550 2.49860i −0.0587750 0.0124930i
\(201\) 143.959 + 129.621i 0.716212 + 0.644880i
\(202\) 150.627 0.745678
\(203\) 142.266 271.907i 0.700820 1.33944i
\(204\) 52.5761 0.257726
\(205\) −215.464 + 15.7079i −1.05104 + 0.0766240i
\(206\) −344.929 199.145i −1.67441 0.966722i
\(207\) 7.03429 3.13187i 0.0339821 0.0151298i
\(208\) 130.773 + 226.506i 0.628718 + 1.08897i
\(209\) −293.179 + 95.2595i −1.40277 + 0.455787i
\(210\) −289.619 192.563i −1.37914 0.916969i
\(211\) 62.7331 86.3446i 0.297313 0.409216i −0.634059 0.773284i \(-0.718612\pi\)
0.931372 + 0.364068i \(0.118612\pi\)
\(212\) 22.0720 49.5746i 0.104113 0.233842i
\(213\) 301.873 271.808i 1.41725 1.27609i
\(214\) −186.916 + 323.749i −0.873441 + 1.51284i
\(215\) 45.2929 + 213.086i 0.210665 + 0.991100i
\(216\) 19.2508 59.2479i 0.0891242 0.274296i
\(217\) 0.855443 13.5239i 0.00394213 0.0623220i
\(218\) 170.139 234.177i 0.780456 1.07421i
\(219\) −205.242 + 118.496i −0.937176 + 0.541079i
\(220\) 229.927 + 48.8724i 1.04512 + 0.222147i
\(221\) −8.45925 80.4844i −0.0382771 0.364183i
\(222\) −233.487 + 49.6291i −1.05174 + 0.223555i
\(223\) −177.087 + 243.740i −0.794114 + 1.09300i 0.199470 + 0.979904i \(0.436078\pi\)
−0.993584 + 0.113100i \(0.963922\pi\)
\(224\) −56.4785 220.279i −0.252136 0.983387i
\(225\) 11.6220 8.44388i 0.0516533 0.0375283i
\(226\) −369.245 164.399i −1.63383 0.727427i
\(227\) −20.1648 191.855i −0.0888318 0.845178i −0.944689 0.327966i \(-0.893637\pi\)
0.855858 0.517211i \(-0.173030\pi\)
\(228\) 121.767 54.2143i 0.534067 0.237782i
\(229\) 182.196 38.7270i 0.795617 0.169114i 0.207868 0.978157i \(-0.433348\pi\)
0.587749 + 0.809043i \(0.300014\pi\)
\(230\) −11.4827 15.8046i −0.0499248 0.0687156i
\(231\) −433.057 287.933i −1.87470 1.24646i
\(232\) 190.609i 0.821589i
\(233\) −73.6612 7.74210i −0.316142 0.0332279i −0.0548715 0.998493i \(-0.517475\pi\)
−0.261271 + 0.965266i \(0.584142\pi\)
\(234\) −166.949 35.4861i −0.713457 0.151650i
\(235\) −161.502 + 145.417i −0.687244 + 0.618798i
\(236\) −17.9299 84.3537i −0.0759743 0.357431i
\(237\) 284.427i 1.20011i
\(238\) −18.0524 + 106.513i −0.0758505 + 0.447534i
\(239\) 56.3866 + 77.6096i 0.235927 + 0.324726i 0.910521 0.413463i \(-0.135681\pi\)
−0.674593 + 0.738190i \(0.735681\pi\)
\(240\) 393.540 + 41.3628i 1.63975 + 0.172345i
\(241\) 75.7963 356.594i 0.314508 1.47964i −0.482619 0.875830i \(-0.660314\pi\)
0.797127 0.603812i \(-0.206352\pi\)
\(242\) 655.413 + 139.312i 2.70832 + 0.575671i
\(243\) 125.359 + 217.128i 0.515881 + 0.893533i
\(244\) 29.8739 41.1179i 0.122434 0.168516i
\(245\) 176.870 188.092i 0.721917 0.767722i
\(246\) 380.529 68.2599i 1.54687 0.277479i
\(247\) −102.584 177.680i −0.415319 0.719354i
\(248\) 3.42343 + 7.68914i 0.0138041 + 0.0310046i
\(249\) −107.120 61.8455i −0.430199 0.248375i
\(250\) 217.895 + 196.194i 0.871582 + 0.784776i
\(251\) 277.219 90.0739i 1.10446 0.358860i 0.300642 0.953737i \(-0.402799\pi\)
0.803817 + 0.594877i \(0.202799\pi\)
\(252\) 72.9364 + 38.1617i 0.289430 + 0.151435i
\(253\) −17.1697 23.6320i −0.0678644 0.0934073i
\(254\) −377.957 + 80.3373i −1.48802 + 0.316288i
\(255\) −106.036 61.2199i −0.415827 0.240078i
\(256\) 215.213 + 239.018i 0.840674 + 0.933663i
\(257\) 339.137 72.0857i 1.31960 0.280489i 0.506310 0.862351i \(-0.331009\pi\)
0.813287 + 0.581862i \(0.197676\pi\)
\(258\) −120.469 370.764i −0.466932 1.43707i
\(259\) −7.36065 177.052i −0.0284195 0.683597i
\(260\) 156.447i 0.601720i
\(261\) −169.325 152.461i −0.648755 0.584141i
\(262\) 88.6420 9.31665i 0.338328 0.0355597i
\(263\) −320.600 + 288.670i −1.21901 + 1.09760i −0.226684 + 0.973968i \(0.572789\pi\)
−0.992328 + 0.123635i \(0.960545\pi\)
\(264\) 321.242 + 33.7639i 1.21683 + 0.127894i
\(265\) −102.240 + 74.2816i −0.385811 + 0.280308i
\(266\) 68.0221 + 265.301i 0.255722 + 0.997373i
\(267\) −27.2971 + 19.8325i −0.102236 + 0.0742791i
\(268\) −47.3130 + 106.267i −0.176541 + 0.396518i
\(269\) 109.154 + 245.164i 0.405776 + 0.911389i 0.994663 + 0.103173i \(0.0328996\pi\)
−0.588887 + 0.808215i \(0.700434\pi\)
\(270\) 140.404 126.421i 0.520017 0.468225i
\(271\) −88.6507 + 199.113i −0.327124 + 0.734733i −0.999987 0.00503371i \(-0.998398\pi\)
0.672863 + 0.739767i \(0.265064\pi\)
\(272\) −37.9831 116.900i −0.139644 0.429779i
\(273\) 127.523 321.767i 0.467116 1.17863i
\(274\) 167.436 230.455i 0.611079 0.841078i
\(275\) −40.4996 36.4660i −0.147271 0.132604i
\(276\) 8.45141 + 9.38624i 0.0306210 + 0.0340081i
\(277\) 300.029 + 333.216i 1.08314 + 1.20295i 0.978025 + 0.208487i \(0.0668540\pi\)
0.105114 + 0.994460i \(0.466479\pi\)
\(278\) −351.288 + 202.816i −1.26362 + 0.729554i
\(279\) −9.56883 3.10910i −0.0342969 0.0111437i
\(280\) −43.1783 + 154.446i −0.154208 + 0.551591i
\(281\) 165.472 227.753i 0.588868 0.810507i −0.405764 0.913978i \(-0.632995\pi\)
0.994633 + 0.103470i \(0.0329946\pi\)
\(282\) 260.229 289.014i 0.922799 1.02487i
\(283\) −102.740 + 483.355i −0.363040 + 1.70797i 0.295432 + 0.955364i \(0.404536\pi\)
−0.658472 + 0.752605i \(0.728797\pi\)
\(284\) 211.244 + 121.962i 0.743818 + 0.429444i
\(285\) −308.709 32.4466i −1.08319 0.113848i
\(286\) 647.490i 2.26395i
\(287\) 2.75628 + 286.987i 0.00960378 + 0.999954i
\(288\) −168.843 −0.586260
\(289\) 26.2332 249.593i 0.0907725 0.863642i
\(290\) −289.037 + 500.627i −0.996679 + 1.72630i
\(291\) −492.404 104.664i −1.69211 0.359669i
\(292\) −105.758 95.2246i −0.362184 0.326112i
\(293\) −387.621 281.623i −1.32294 0.961170i −0.999891 0.0147873i \(-0.995293\pi\)
−0.323047 0.946383i \(-0.604707\pi\)
\(294\) −279.596 + 367.837i −0.951008 + 1.25115i
\(295\) −62.0606 + 191.003i −0.210375 + 0.647467i
\(296\) 55.0332 + 95.3203i 0.185923 + 0.322028i
\(297\) 209.942 189.033i 0.706875 0.636473i
\(298\) −87.5446 + 78.8255i −0.293774 + 0.264515i
\(299\) 13.0088 14.4477i 0.0435077 0.0483202i
\(300\) 19.0638 + 13.8506i 0.0635459 + 0.0461688i
\(301\) 286.316 42.1805i 0.951216 0.140135i
\(302\) −249.925 + 81.2055i −0.827565 + 0.268892i
\(303\) 207.186 + 92.2449i 0.683781 + 0.304439i
\(304\) −208.512 231.576i −0.685894 0.761762i
\(305\) −108.128 + 48.1416i −0.354517 + 0.157841i
\(306\) 73.2770 + 32.6250i 0.239467 + 0.106618i
\(307\) −20.9393 28.8204i −0.0682061 0.0938776i 0.773551 0.633734i \(-0.218479\pi\)
−0.841757 + 0.539856i \(0.818479\pi\)
\(308\) 84.0796 300.746i 0.272986 0.976449i
\(309\) −352.488 485.158i −1.14074 1.57009i
\(310\) −2.66823 + 25.3865i −0.00860718 + 0.0818919i
\(311\) 170.406 + 189.255i 0.547929 + 0.608536i 0.951965 0.306207i \(-0.0990598\pi\)
−0.404037 + 0.914743i \(0.632393\pi\)
\(312\) 22.4717 + 213.804i 0.0720246 + 0.685269i
\(313\) 316.114 351.080i 1.00995 1.12166i 0.0173948 0.999849i \(-0.494463\pi\)
0.992553 0.121812i \(-0.0388705\pi\)
\(314\) −161.738 −0.515089
\(315\) −102.663 161.892i −0.325915 0.513944i
\(316\) −162.435 + 52.7785i −0.514036 + 0.167020i
\(317\) 47.0704 + 221.449i 0.148487 + 0.698576i 0.987901 + 0.155084i \(0.0495649\pi\)
−0.839414 + 0.543492i \(0.817102\pi\)
\(318\) 168.065 151.326i 0.528505 0.475868i
\(319\) −432.187 + 748.569i −1.35482 + 2.34661i
\(320\) 1.72357 + 8.10877i 0.00538616 + 0.0253399i
\(321\) −455.367 + 330.843i −1.41859 + 1.03066i
\(322\) −21.9173 + 13.8987i −0.0680661 + 0.0431638i
\(323\) 29.7954 + 91.7009i 0.0922459 + 0.283904i
\(324\) −152.553 + 169.428i −0.470844 + 0.522925i
\(325\) 18.1355 31.4116i 0.0558016 0.0966512i
\(326\) −498.240 + 221.831i −1.52834 + 0.680463i
\(327\) 377.436 217.913i 1.15424 0.666400i
\(328\) −84.1552 157.149i −0.256571 0.479112i
\(329\) 179.255 + 226.321i 0.544849 + 0.687906i
\(330\) 792.531 + 575.808i 2.40161 + 1.74487i
\(331\) 441.669 254.998i 1.33435 0.770386i 0.348385 0.937352i \(-0.386730\pi\)
0.985963 + 0.166966i \(0.0533969\pi\)
\(332\) 15.4426 72.6517i 0.0465138 0.218830i
\(333\) −128.696 27.3551i −0.386473 0.0821475i
\(334\) 71.5974 681.203i 0.214363 2.03953i
\(335\) 219.159 159.228i 0.654206 0.475308i
\(336\) 87.8445 518.301i 0.261442 1.54256i
\(337\) −203.681 −0.604395 −0.302198 0.953245i \(-0.597720\pi\)
−0.302198 + 0.953245i \(0.597720\pi\)
\(338\) −7.83872 + 1.66617i −0.0231915 + 0.00492950i
\(339\) −407.213 452.256i −1.20122 1.33409i
\(340\) 15.2864 71.9168i 0.0449600 0.211520i
\(341\) −3.98971 + 37.9595i −0.0117000 + 0.111318i
\(342\) 203.352 0.594598
\(343\) −234.546 250.274i −0.683807 0.729663i
\(344\) −145.427 + 105.659i −0.422754 + 0.307148i
\(345\) −6.11549 28.7711i −0.0177260 0.0833945i
\(346\) 166.303 + 373.524i 0.480646 + 1.07955i
\(347\) 463.524 48.7183i 1.33580 0.140399i 0.590453 0.807072i \(-0.298949\pi\)
0.745350 + 0.666673i \(0.232282\pi\)
\(348\) 152.016 341.433i 0.436827 0.981130i
\(349\) 345.428 + 475.440i 0.989764 + 1.36229i 0.931400 + 0.363998i \(0.118589\pi\)
0.0583647 + 0.998295i \(0.481411\pi\)
\(350\) −34.6055 + 33.8653i −0.0988729 + 0.0967579i
\(351\) 152.113 + 110.517i 0.433370 + 0.314862i
\(352\) 133.173 + 626.528i 0.378332 + 1.77991i
\(353\) 165.740 17.4199i 0.469518 0.0493483i 0.133184 0.991091i \(-0.457480\pi\)
0.336333 + 0.941743i \(0.390813\pi\)
\(354\) 74.7226 351.542i 0.211081 0.993058i
\(355\) −284.026 491.948i −0.800074 1.38577i
\(356\) −16.3916 11.9092i −0.0460437 0.0334527i
\(357\) −90.0602 + 135.452i −0.252270 + 0.379418i
\(358\) 480.664 + 156.177i 1.34264 + 0.436249i
\(359\) 184.043 39.1195i 0.512654 0.108968i 0.0556812 0.998449i \(-0.482267\pi\)
0.456973 + 0.889481i \(0.348934\pi\)
\(360\) 103.117 + 59.5349i 0.286437 + 0.165375i
\(361\) −77.9913 86.6181i −0.216042 0.239939i
\(362\) −17.3219 7.71220i −0.0478505 0.0213044i
\(363\) 816.197 + 593.002i 2.24848 + 1.63361i
\(364\) 207.423 + 13.1204i 0.569844 + 0.0360451i
\(365\) 102.413 + 315.194i 0.280583 + 0.863546i
\(366\) 183.433 105.905i 0.501183 0.289358i
\(367\) −231.047 518.940i −0.629556 1.41401i −0.893321 0.449419i \(-0.851631\pi\)
0.263765 0.964587i \(-0.415036\pi\)
\(368\) 14.7641 25.5722i 0.0401199 0.0694896i
\(369\) 206.914 + 50.9391i 0.560742 + 0.138046i
\(370\) 333.807i 0.902180i
\(371\) 89.9109 + 141.783i 0.242348 + 0.382164i
\(372\) 16.5037i 0.0443647i
\(373\) 421.095 467.673i 1.12894 1.25382i 0.165408 0.986225i \(-0.447106\pi\)
0.963533 0.267591i \(-0.0862275\pi\)
\(374\) 63.2660 297.643i 0.169160 0.795837i
\(375\) 179.562 + 403.303i 0.478832 + 1.07547i
\(376\) −163.822 72.9383i −0.435697 0.193985i
\(377\) −547.130 177.773i −1.45127 0.471547i
\(378\) −155.838 196.756i −0.412270 0.520517i
\(379\) 176.348 542.743i 0.465298 1.43204i −0.393310 0.919406i \(-0.628670\pi\)
0.858608 0.512633i \(-0.171330\pi\)
\(380\) −38.7540 182.323i −0.101984 0.479798i
\(381\) −569.075 120.961i −1.49363 0.317482i
\(382\) 131.819 + 296.070i 0.345076 + 0.775053i
\(383\) −153.911 266.581i −0.401855 0.696033i 0.592095 0.805868i \(-0.298301\pi\)
−0.993950 + 0.109835i \(0.964968\pi\)
\(384\) 146.718 + 451.552i 0.382078 + 1.17592i
\(385\) −519.763 + 508.645i −1.35003 + 1.32116i
\(386\) 647.839 + 210.496i 1.67834 + 0.545325i
\(387\) 22.4609 213.701i 0.0580386 0.552200i
\(388\) −31.5977 300.632i −0.0814374 0.774825i
\(389\) 59.1263 + 562.550i 0.151996 + 1.44614i 0.758817 + 0.651304i \(0.225778\pi\)
−0.606821 + 0.794838i \(0.707556\pi\)
\(390\) −265.189 + 595.623i −0.679971 + 1.52724i
\(391\) −7.39167 + 5.37036i −0.0189045 + 0.0137349i
\(392\) 201.148 + 70.1999i 0.513134 + 0.179081i
\(393\) 127.632 + 41.4700i 0.324762 + 0.105522i
\(394\) 345.558 + 153.852i 0.877050 + 0.390488i
\(395\) 389.057 + 82.6965i 0.984953 + 0.209358i
\(396\) −200.797 115.930i −0.507063 0.292753i
\(397\) 10.3484 98.4581i 0.0260664 0.248005i −0.973728 0.227715i \(-0.926874\pi\)
0.999794 0.0202899i \(-0.00645891\pi\)
\(398\) −270.472 832.428i −0.679579 2.09153i
\(399\) −68.9087 + 406.576i −0.172703 + 1.01899i
\(400\) 17.0237 52.3934i 0.0425591 0.130984i
\(401\) 106.415 + 184.316i 0.265374 + 0.459642i 0.967662 0.252252i \(-0.0811711\pi\)
−0.702287 + 0.711894i \(0.747838\pi\)
\(402\) −360.259 + 324.379i −0.896167 + 0.806912i
\(403\) −25.2641 + 2.65536i −0.0626901 + 0.00658899i
\(404\) −14.2353 + 135.440i −0.0352359 + 0.335248i
\(405\) 504.954 164.069i 1.24680 0.405110i
\(406\) 639.509 + 425.200i 1.57514 + 1.04729i
\(407\) 499.130i 1.22636i
\(408\) 10.5607 100.479i 0.0258841 0.246271i
\(409\) −121.884 70.3699i −0.298005 0.172053i 0.343541 0.939138i \(-0.388374\pi\)
−0.641546 + 0.767084i \(0.721707\pi\)
\(410\) 17.2679 540.357i 0.0421169 1.31794i
\(411\) 371.438 214.450i 0.903742 0.521776i
\(412\) 211.664 291.331i 0.513748 0.707113i
\(413\) 248.034 + 98.3006i 0.600566 + 0.238016i
\(414\) 5.95456 + 18.3262i 0.0143830 + 0.0442663i
\(415\) −115.741 + 128.543i −0.278893 + 0.309742i
\(416\) −389.448 + 173.393i −0.936173 + 0.416811i
\(417\) −607.398 + 63.8401i −1.45659 + 0.153094i
\(418\) −160.392 754.584i −0.383712 1.80523i
\(419\) 494.024i 1.17906i −0.807748 0.589528i \(-0.799314\pi\)
0.807748 0.589528i \(-0.200686\pi\)
\(420\) 200.519 242.219i 0.477427 0.576712i
\(421\) 257.918 + 83.8025i 0.612631 + 0.199056i 0.598866 0.800849i \(-0.295618\pi\)
0.0137652 + 0.999905i \(0.495618\pi\)
\(422\) 198.485 + 178.717i 0.470344 + 0.423500i
\(423\) 195.829 87.1888i 0.462953 0.206120i
\(424\) −90.3088 52.1398i −0.212992 0.122971i
\(425\) −11.4059 + 12.6675i −0.0268374 + 0.0298059i
\(426\) 597.513 + 822.405i 1.40261 + 1.93053i
\(427\) 54.7597 + 147.397i 0.128243 + 0.345192i
\(428\) −273.442 198.667i −0.638883 0.464175i
\(429\) −396.527 + 890.615i −0.924306 + 2.07603i
\(430\) −542.179 + 56.9853i −1.26088 + 0.132524i
\(431\) −63.7189 606.245i −0.147840 1.40660i −0.777086 0.629395i \(-0.783303\pi\)
0.629246 0.777206i \(-0.283364\pi\)
\(432\) 260.885 + 116.154i 0.603901 + 0.268874i
\(433\) 218.209 300.340i 0.503948 0.693625i −0.478936 0.877850i \(-0.658977\pi\)
0.982884 + 0.184225i \(0.0589775\pi\)
\(434\) 33.4345 + 5.66667i 0.0770381 + 0.0130568i
\(435\) −704.154 + 511.598i −1.61874 + 1.17609i
\(436\) 194.487 + 175.117i 0.446070 + 0.401643i
\(437\) −11.5815 + 20.0598i −0.0265024 + 0.0459035i
\(438\) −241.227 541.804i −0.550746 1.23700i
\(439\) −28.0354 + 31.1365i −0.0638620 + 0.0709260i −0.774229 0.632905i \(-0.781862\pi\)
0.710367 + 0.703831i \(0.248529\pi\)
\(440\) 139.585 429.598i 0.317238 0.976358i
\(441\) −223.253 + 122.537i −0.506242 + 0.277863i
\(442\) 202.523 0.458197
\(443\) 690.911 146.858i 1.55962 0.331507i 0.654298 0.756237i \(-0.272964\pi\)
0.905320 + 0.424730i \(0.139631\pi\)
\(444\) −22.5591 214.636i −0.0508088 0.483414i
\(445\) 19.1915 + 43.1049i 0.0431271 + 0.0968650i
\(446\) −560.299 504.495i −1.25627 1.13115i
\(447\) −168.690 + 54.8106i −0.377382 + 0.122619i
\(448\) 10.8954 1.60513i 0.0243202 0.00358288i
\(449\) −673.669 489.450i −1.50038 1.09009i −0.970231 0.242182i \(-0.922137\pi\)
−0.530147 0.847906i \(-0.677863\pi\)
\(450\) 17.9751 + 31.1337i 0.0399446 + 0.0691860i
\(451\) 25.8201 807.977i 0.0572508 1.79152i
\(452\) 182.719 316.479i 0.404246 0.700175i
\(453\) −393.499 41.3584i −0.868651 0.0912989i
\(454\) 482.766 1.06336
\(455\) −403.056 267.986i −0.885836 0.588980i
\(456\) −79.1505 243.600i −0.173576 0.534211i
\(457\) −12.3933 1.30259i −0.0271188 0.00285030i 0.0909593 0.995855i \(-0.471007\pi\)
−0.118078 + 0.993004i \(0.537673\pi\)
\(458\) 48.7245 + 463.582i 0.106385 + 1.01219i
\(459\) −59.1259 65.6660i −0.128815 0.143063i
\(460\) 15.2963 8.83132i 0.0332528 0.0191985i
\(461\) −650.906 211.492i −1.41194 0.458768i −0.498910 0.866654i \(-0.666266\pi\)
−0.913033 + 0.407886i \(0.866266\pi\)
\(462\) 829.892 1002.48i 1.79630 2.16986i
\(463\) −255.442 + 82.9982i −0.551711 + 0.179262i −0.571588 0.820541i \(-0.693672\pi\)
0.0198771 + 0.999802i \(0.493672\pi\)
\(464\) −868.979 91.3334i −1.87280 0.196839i
\(465\) −19.2170 + 33.2848i −0.0413268 + 0.0715801i
\(466\) 38.5372 181.303i 0.0826979 0.389063i
\(467\) −100.521 + 225.773i −0.215248 + 0.483454i −0.988608 0.150512i \(-0.951908\pi\)
0.773360 + 0.633967i \(0.218574\pi\)
\(468\) 47.6861 146.763i 0.101893 0.313596i
\(469\) −192.731 303.922i −0.410940 0.648022i
\(470\) −319.670 439.988i −0.680148 0.936144i
\(471\) −222.469 99.0494i −0.472332 0.210296i
\(472\) −164.810 + 17.3223i −0.349175 + 0.0366997i
\(473\) −810.702 + 85.2082i −1.71396 + 0.180144i
\(474\) −707.885 74.4017i −1.49343 0.156966i
\(475\) −13.3540 + 41.0995i −0.0281137 + 0.0865252i
\(476\) −94.0679 26.2985i −0.197622 0.0552490i
\(477\) 118.552 38.5200i 0.248538 0.0807548i
\(478\) −207.905 + 120.034i −0.434948 + 0.251117i
\(479\) −323.742 + 144.139i −0.675871 + 0.300917i −0.715820 0.698285i \(-0.753947\pi\)
0.0399492 + 0.999202i \(0.487280\pi\)
\(480\) −134.098 + 630.883i −0.279372 + 1.31434i
\(481\) −324.938 + 69.0677i −0.675547 + 0.143592i
\(482\) 867.667 + 281.922i 1.80014 + 0.584900i
\(483\) −38.6586 + 5.69525i −0.0800386 + 0.0117914i
\(484\) −187.207 + 576.165i −0.386792 + 1.19042i
\(485\) −286.331 + 643.110i −0.590373 + 1.32600i
\(486\) −573.183 + 255.198i −1.17939 + 0.525098i
\(487\) 175.081 + 37.2146i 0.359509 + 0.0764161i 0.384126 0.923281i \(-0.374503\pi\)
−0.0246160 + 0.999697i \(0.507836\pi\)
\(488\) −72.5800 65.3514i −0.148730 0.133917i
\(489\) −821.174 −1.67929
\(490\) 421.858 + 489.397i 0.860935 + 0.998769i
\(491\) −880.778 −1.79384 −0.896922 0.442188i \(-0.854202\pi\)
−0.896922 + 0.442188i \(0.854202\pi\)
\(492\) 25.4149 + 348.613i 0.0516563 + 0.708563i
\(493\) 234.139 + 135.180i 0.474926 + 0.274199i
\(494\) 469.047 208.833i 0.949488 0.422739i
\(495\) 269.979 + 467.618i 0.545413 + 0.944683i
\(496\) −36.6949 + 11.9229i −0.0739817 + 0.0240381i
\(497\) −676.062 + 335.315i −1.36029 + 0.674678i
\(498\) 181.942 250.422i 0.365346 0.502856i
\(499\) 158.141 355.190i 0.316915 0.711803i −0.682910 0.730502i \(-0.739286\pi\)
0.999825 + 0.0186996i \(0.00595261\pi\)
\(500\) −197.005 + 177.384i −0.394011 + 0.354769i
\(501\) 515.655 893.140i 1.02925 1.78271i
\(502\) 151.661 + 713.507i 0.302113 + 1.42133i
\(503\) 149.759 460.912i 0.297732 0.916326i −0.684557 0.728959i \(-0.740005\pi\)
0.982290 0.187367i \(-0.0599955\pi\)
\(504\) 87.5815 131.724i 0.173773 0.261357i
\(505\) 186.417 256.581i 0.369142 0.508081i
\(506\) 63.3070 36.5503i 0.125113 0.0722338i
\(507\) −11.8024 2.50868i −0.0232790 0.00494810i
\(508\) −36.5176 347.442i −0.0718851 0.683941i
\(509\) 40.1459 8.53328i 0.0788722 0.0167648i −0.168307 0.985735i \(-0.553830\pi\)
0.247179 + 0.968970i \(0.420497\pi\)
\(510\) 180.102 247.889i 0.353141 0.486057i
\(511\) 426.485 109.349i 0.834608 0.213990i
\(512\) −243.396 + 176.837i −0.475382 + 0.345386i
\(513\) −204.649 91.1154i −0.398925 0.177613i
\(514\) 90.6947 + 862.903i 0.176449 + 1.67880i
\(515\) −766.113 + 341.095i −1.48760 + 0.662321i
\(516\) 344.767 73.2825i 0.668153 0.142020i
\(517\) −477.991 657.898i −0.924547 1.27253i
\(518\) 442.573 + 27.9947i 0.854388 + 0.0540437i
\(519\) 615.622i 1.18617i
\(520\) 298.987 + 31.4248i 0.574976 + 0.0604324i
\(521\) 80.4897 + 17.1086i 0.154491 + 0.0328380i 0.284508 0.958674i \(-0.408170\pi\)
−0.130017 + 0.991512i \(0.541503\pi\)
\(522\) 423.739 381.536i 0.811760 0.730912i
\(523\) 127.504 + 599.857i 0.243793 + 1.14695i 0.914295 + 0.405048i \(0.132745\pi\)
−0.670503 + 0.741907i \(0.733922\pi\)
\(524\) 80.5852i 0.153789i
\(525\) −68.3388 + 25.3886i −0.130169 + 0.0483593i
\(526\) −634.580 873.424i −1.20643 1.66050i
\(527\) 11.8730 + 1.24791i 0.0225295 + 0.00236794i
\(528\) −307.857 + 1448.35i −0.583063 + 2.74310i
\(529\) 515.293 + 109.529i 0.974089 + 0.207049i
\(530\) −158.128 273.887i −0.298356 0.516767i
\(531\) 116.438 160.263i 0.219280 0.301813i
\(532\) −244.981 + 36.0909i −0.460490 + 0.0678401i
\(533\) 529.573 94.9957i 0.993571 0.178228i
\(534\) −42.2189 73.1252i −0.0790615 0.136939i
\(535\) 320.151 + 719.070i 0.598413 + 1.34406i
\(536\) 193.584 + 111.766i 0.361164 + 0.208518i
\(537\) 565.504 + 509.182i 1.05308 + 0.948197i
\(538\) −638.718 + 207.532i −1.18721 + 0.385747i
\(539\) 630.790 + 731.778i 1.17030 + 1.35766i
\(540\) 100.405 + 138.196i 0.185936 + 0.255918i
\(541\) −499.785 + 106.233i −0.923818 + 0.196363i −0.645178 0.764032i \(-0.723217\pi\)
−0.278640 + 0.960396i \(0.589883\pi\)
\(542\) −472.364 272.720i −0.871520 0.503173i
\(543\) −19.1030 21.2161i −0.0351806 0.0390720i
\(544\) 195.967 41.6540i 0.360233 0.0765698i
\(545\) −188.336 579.638i −0.345570 1.06356i
\(546\) 767.459 + 401.549i 1.40560 + 0.735437i
\(547\) 126.159i 0.230638i −0.993329 0.115319i \(-0.963211\pi\)
0.993329 0.115319i \(-0.0367890\pi\)
\(548\) 191.396 + 172.334i 0.349263 + 0.314478i
\(549\) 116.108 12.2035i 0.211490 0.0222285i
\(550\) 101.351 91.2568i 0.184274 0.165921i
\(551\) 681.661 + 71.6455i 1.23714 + 0.130028i
\(552\) 19.6357 14.2662i 0.0355719 0.0258445i
\(553\) 142.270 508.890i 0.257270 0.920235i
\(554\) −907.795 + 659.552i −1.63862 + 1.19053i
\(555\) −204.425 + 459.147i −0.368334 + 0.827292i
\(556\) −149.168 335.037i −0.268288 0.602584i
\(557\) 230.183 207.257i 0.413254 0.372096i −0.436118 0.899889i \(-0.643647\pi\)
0.849373 + 0.527793i \(0.176980\pi\)
\(558\) 10.2410 23.0017i 0.0183531 0.0412217i
\(559\) −167.653 515.984i −0.299916 0.923048i
\(560\) −683.423 270.854i −1.22040 0.483667i
\(561\) 269.300 370.660i 0.480036 0.660713i
\(562\) 523.548 + 471.405i 0.931580 + 0.838798i
\(563\) 61.1917 + 67.9603i 0.108689 + 0.120711i 0.795034 0.606565i \(-0.207453\pi\)
−0.686346 + 0.727276i \(0.740786\pi\)
\(564\) 235.281 + 261.306i 0.417164 + 0.463308i
\(565\) −737.020 + 425.519i −1.30446 + 0.753130i
\(566\) −1176.10 382.139i −2.07792 0.675158i
\(567\) −175.181 683.245i −0.308962 1.20502i
\(568\) 275.514 379.213i 0.485060 0.667628i
\(569\) −6.18727 + 6.87166i −0.0108739 + 0.0120767i −0.748557 0.663070i \(-0.769253\pi\)
0.737683 + 0.675147i \(0.235920\pi\)
\(570\) 161.507 759.829i 0.283345 1.33303i
\(571\) 183.005 + 105.658i 0.320499 + 0.185040i 0.651615 0.758550i \(-0.274092\pi\)
−0.331116 + 0.943590i \(0.607425\pi\)
\(572\) −582.207 61.1924i −1.01784 0.106980i
\(573\) 487.968i 0.851602i
\(574\) −714.976 68.2114i −1.24560 0.118835i
\(575\) −4.09494 −0.00712163
\(576\) 0.854725 8.13217i 0.00148390 0.0141183i
\(577\) 330.736 572.852i 0.573199 0.992810i −0.423035 0.906113i \(-0.639035\pi\)
0.996235 0.0866971i \(-0.0276312\pi\)
\(578\) 614.326 + 130.579i 1.06285 + 0.225915i
\(579\) 762.185 + 686.275i 1.31638 + 1.18528i
\(580\) −422.835 307.208i −0.729026 0.529668i
\(581\) 160.721 + 164.233i 0.276627 + 0.282674i
\(582\) 389.294 1198.12i 0.668889 2.05863i
\(583\) −236.444 409.533i −0.405564 0.702458i
\(584\) −203.227 + 182.987i −0.347992 + 0.313333i
\(585\) −267.065 + 240.466i −0.456521 + 0.411054i
\(586\) 802.301 891.046i 1.36911 1.52056i
\(587\) 775.574 + 563.488i 1.32125 + 0.959945i 0.999916 + 0.0129798i \(0.00413172\pi\)
0.321336 + 0.946965i \(0.395868\pi\)
\(588\) −304.326 286.169i −0.517562 0.486683i
\(589\) 28.7850 9.35280i 0.0488709 0.0158791i
\(590\) −459.135 204.420i −0.778196 0.346475i
\(591\) 381.090 + 423.244i 0.644823 + 0.716148i
\(592\) −460.932 + 205.220i −0.778601 + 0.346656i
\(593\) −195.738 87.1482i −0.330081 0.146961i 0.235004 0.971994i \(-0.424490\pi\)
−0.565085 + 0.825033i \(0.691156\pi\)
\(594\) 415.548 + 571.953i 0.699576 + 0.962884i
\(595\) 159.095 + 162.572i 0.267386 + 0.273231i
\(596\) −62.6043 86.1675i −0.105041 0.144576i
\(597\) 137.753 1310.63i 0.230742 2.19537i
\(598\) 32.5548 + 36.1557i 0.0544394 + 0.0604611i
\(599\) −100.534 956.521i −0.167837 1.59686i −0.676861 0.736111i \(-0.736660\pi\)
0.509024 0.860753i \(-0.330007\pi\)
\(600\) 30.2993 33.6508i 0.0504989 0.0560847i
\(601\) −456.675 −0.759859 −0.379929 0.925016i \(-0.624052\pi\)
−0.379929 + 0.925016i \(0.624052\pi\)
\(602\) 30.0834 + 723.620i 0.0499725 + 1.20203i
\(603\) −254.126 + 82.5706i −0.421436 + 0.136933i
\(604\) −49.3983 232.401i −0.0817852 0.384769i
\(605\) 1048.45 944.029i 1.73298 1.56038i
\(606\) −283.777 + 491.515i −0.468278 + 0.811082i
\(607\) −63.9037 300.643i −0.105278 0.495294i −0.998918 0.0465090i \(-0.985190\pi\)
0.893640 0.448785i \(-0.148143\pi\)
\(608\) 410.910 298.544i 0.675839 0.491026i
\(609\) 619.241 + 976.497i 1.01682 + 1.60344i
\(610\) −91.5307 281.702i −0.150050 0.461807i
\(611\) 362.155 402.214i 0.592726 0.658288i
\(612\) −36.2608 + 62.8056i −0.0592497 + 0.102623i
\(613\) −400.803 + 178.449i −0.653838 + 0.291108i −0.706720 0.707493i \(-0.749826\pi\)
0.0528818 + 0.998601i \(0.483159\pi\)
\(614\) 77.2059 44.5749i 0.125743 0.0725975i
\(615\) 354.670 732.679i 0.576699 1.19135i
\(616\) −557.870 221.095i −0.905633 0.358920i
\(617\) 365.292 + 265.401i 0.592046 + 0.430147i 0.843047 0.537840i \(-0.180760\pi\)
−0.251001 + 0.967987i \(0.580760\pi\)
\(618\) 1299.67 750.365i 2.10303 1.21418i
\(619\) 47.1892 222.008i 0.0762345 0.358655i −0.923451 0.383715i \(-0.874644\pi\)
0.999686 + 0.0250601i \(0.00797773\pi\)
\(620\) −22.5747 4.79841i −0.0364109 0.00773937i
\(621\) 2.21886 21.1111i 0.00357305 0.0339953i
\(622\) −515.594 + 374.601i −0.828930 + 0.602253i
\(623\) 58.7595 21.8298i 0.0943171 0.0350399i
\(624\) −985.492 −1.57931
\(625\) 671.460 142.723i 1.07434 0.228357i
\(626\) 791.080 + 878.584i 1.26371 + 1.40349i
\(627\) 241.495 1136.15i 0.385160 1.81204i
\(628\) 15.2854 145.431i 0.0243398 0.231578i
\(629\) 156.119 0.248201
\(630\) 429.774 213.161i 0.682181 0.338350i
\(631\) 551.369 400.593i 0.873803 0.634855i −0.0578021 0.998328i \(-0.518409\pi\)
0.931605 + 0.363473i \(0.118409\pi\)
\(632\) 68.2376 + 321.033i 0.107971 + 0.507963i
\(633\) 163.567 + 367.377i 0.258399 + 0.580374i
\(634\) −563.456 + 59.2217i −0.888733 + 0.0934096i
\(635\) −330.914 + 743.245i −0.521125 + 1.17047i
\(636\) 120.185 + 165.421i 0.188971 + 0.260096i
\(637\) −389.108 + 511.911i −0.610844 + 0.803628i
\(638\) −1749.99 1271.44i −2.74294 1.99286i
\(639\) 116.495 + 548.068i 0.182309 + 0.857696i
\(640\) 660.318 69.4022i 1.03175 0.108441i
\(641\) −63.1438 + 297.068i −0.0985082 + 0.463445i 0.901050 + 0.433716i \(0.142798\pi\)
−0.999558 + 0.0297290i \(0.990536\pi\)
\(642\) −704.289 1219.86i −1.09702 1.90010i
\(643\) 348.137 + 252.937i 0.541427 + 0.393370i 0.824615 0.565695i \(-0.191392\pi\)
−0.283188 + 0.959064i \(0.591392\pi\)
\(644\) −10.4261 21.0210i −0.0161895 0.0326413i
\(645\) −780.659 253.652i −1.21032 0.393258i
\(646\) −236.020 + 50.1676i −0.365356 + 0.0776588i
\(647\) 5.99223 + 3.45961i 0.00926156 + 0.00534716i 0.504624 0.863339i \(-0.331631\pi\)
−0.495362 + 0.868687i \(0.664965\pi\)
\(648\) 293.152 + 325.578i 0.452395 + 0.502436i
\(649\) −686.529 305.663i −1.05783 0.470975i
\(650\) 73.4336 + 53.3526i 0.112975 + 0.0820810i
\(651\) 42.5185 + 28.2700i 0.0653126 + 0.0434254i
\(652\) −152.378 468.970i −0.233708 0.719279i
\(653\) −765.508 + 441.966i −1.17229 + 0.676824i −0.954219 0.299108i \(-0.903311\pi\)
−0.218075 + 0.975932i \(0.569978\pi\)
\(654\) 443.612 + 996.369i 0.678306 + 1.52350i
\(655\) 93.8338 162.525i 0.143258 0.248130i
\(656\) 756.760 308.360i 1.15360 0.470062i
\(657\) 326.899i 0.497563i
\(658\) −610.160 + 386.930i −0.927296 + 0.588040i
\(659\) 311.382i 0.472507i 0.971691 + 0.236253i \(0.0759196\pi\)
−0.971691 + 0.236253i \(0.924080\pi\)
\(660\) −592.652 + 658.206i −0.897957 + 0.997283i
\(661\) 28.4714 133.947i 0.0430732 0.202644i −0.951349 0.308115i \(-0.900302\pi\)
0.994422 + 0.105471i \(0.0336352\pi\)
\(662\) 519.107 + 1165.93i 0.784149 + 1.76123i
\(663\) 278.568 + 124.026i 0.420163 + 0.187069i
\(664\) −135.743 44.1057i −0.204433 0.0664242i
\(665\) 536.104 + 212.468i 0.806171 + 0.319501i
\(666\) 101.746 313.143i 0.152772 0.470185i
\(667\) 13.5036 + 63.5296i 0.0202453 + 0.0952468i
\(668\) 605.755 + 128.757i 0.906818 + 0.192750i
\(669\) −461.728 1037.06i −0.690176 1.55016i
\(670\) 338.960 + 587.096i 0.505911 + 0.876263i
\(671\) −136.863 421.220i −0.203968 0.627749i
\(672\) 825.202 + 230.701i 1.22798 + 0.343306i
\(673\) 319.099 + 103.682i 0.474144 + 0.154059i 0.536334 0.844006i \(-0.319809\pi\)
−0.0621904 + 0.998064i \(0.519809\pi\)
\(674\) 53.2798 506.924i 0.0790502 0.752112i
\(675\) −4.13965 39.3862i −0.00613282 0.0583499i
\(676\) −0.757365 7.20585i −0.00112036 0.0106595i
\(677\) −191.740 + 430.656i −0.283220 + 0.636124i −0.997999 0.0632271i \(-0.979861\pi\)
0.714779 + 0.699351i \(0.246527\pi\)
\(678\) 1232.10 895.173i 1.81726 1.32031i
\(679\) 828.645 + 433.562i 1.22039 + 0.638530i
\(680\) −134.370 43.6595i −0.197603 0.0642052i
\(681\) 664.039 + 295.649i 0.975094 + 0.434140i
\(682\) −93.4304 19.8592i −0.136995 0.0291191i
\(683\) −858.230 495.499i −1.25656 0.725475i −0.284156 0.958778i \(-0.591713\pi\)
−0.972404 + 0.233303i \(0.925047\pi\)
\(684\) −19.2183 + 182.849i −0.0280969 + 0.267324i
\(685\) −185.343 570.426i −0.270573 0.832739i
\(686\) 684.239 518.272i 0.997433 0.755498i
\(687\) −216.881 + 667.491i −0.315693 + 0.971602i
\(688\) −412.012 713.626i −0.598855 1.03725i
\(689\) 233.892 210.597i 0.339465 0.305656i
\(690\) 73.2055 7.69421i 0.106095 0.0111510i
\(691\) 46.6142 443.505i 0.0674591 0.641831i −0.907592 0.419852i \(-0.862082\pi\)
0.975052 0.221978i \(-0.0712514\pi\)
\(692\) −351.580 + 114.235i −0.508064 + 0.165080i
\(693\) 642.626 318.732i 0.927311 0.459930i
\(694\) 1166.37i 1.68064i
\(695\) −89.2752 + 849.397i −0.128453 + 1.22215i
\(696\) −621.981 359.101i −0.893651 0.515950i
\(697\) −252.720 8.07606i −0.362583 0.0115869i
\(698\) −1273.64 + 735.336i −1.82470 + 1.05349i
\(699\) 164.039 225.780i 0.234676 0.323004i
\(700\) −27.1804 34.3169i −0.0388291 0.0490242i
\(701\) −223.153 686.795i −0.318335 0.979736i −0.974360 0.224996i \(-0.927763\pi\)
0.656024 0.754740i \(-0.272237\pi\)
\(702\) −314.845 + 349.671i −0.448497 + 0.498106i
\(703\) 361.573 160.983i 0.514329 0.228994i
\(704\) −30.8504 + 3.24250i −0.0438215 + 0.00460583i
\(705\) −170.250 800.965i −0.241490 1.13612i
\(706\) 417.051i 0.590724i
\(707\) −324.550 268.676i −0.459053 0.380023i
\(708\) 309.036 + 100.412i 0.436492 + 0.141825i
\(709\) −756.978 681.586i −1.06767 0.961335i −0.0683304 0.997663i \(-0.521767\pi\)
−0.999340 + 0.0363280i \(0.988434\pi\)
\(710\) 1298.66 578.201i 1.82910 0.814368i
\(711\) −339.767 196.164i −0.477871 0.275899i
\(712\) −26.0522 + 28.9339i −0.0365901 + 0.0406375i
\(713\) 1.68576 + 2.32025i 0.00236432 + 0.00325421i
\(714\) −313.556 259.575i −0.439154 0.363550i
\(715\) 1102.95 + 801.338i 1.54258 + 1.12075i
\(716\) −185.857 + 417.441i −0.259577 + 0.583019i
\(717\) −359.481 + 37.7830i −0.501368 + 0.0526959i
\(718\) 49.2183 + 468.281i 0.0685491 + 0.652201i
\(719\) 591.851 + 263.509i 0.823159 + 0.366494i 0.774698 0.632331i \(-0.217902\pi\)
0.0484605 + 0.998825i \(0.484568\pi\)
\(720\) −320.828 + 441.582i −0.445595 + 0.613309i
\(721\) 387.987 + 1044.35i 0.538123 + 1.44847i
\(722\) 235.977 171.448i 0.326838 0.237462i
\(723\) 1020.81 + 919.145i 1.41191 + 1.27129i
\(724\) 8.57166 14.8466i 0.0118393 0.0205063i
\(725\) 49.2854 + 110.697i 0.0679799 + 0.152685i
\(726\) −1689.37 + 1876.24i −2.32696 + 2.58435i
\(727\) −100.788 + 310.193i −0.138635 + 0.426675i −0.996138 0.0878046i \(-0.972015\pi\)
0.857503 + 0.514480i \(0.172015\pi\)
\(728\) 66.7387 393.773i 0.0916741 0.540897i
\(729\) −37.8179 −0.0518765
\(730\) −811.248 + 172.436i −1.11130 + 0.236214i
\(731\) 26.6516 + 253.573i 0.0364590 + 0.346885i
\(732\) 77.8915 + 174.947i 0.106409 + 0.238999i
\(733\) 939.778 + 846.180i 1.28210 + 1.15441i 0.979534 + 0.201278i \(0.0645094\pi\)
0.302564 + 0.953129i \(0.402157\pi\)
\(734\) 1351.98 439.285i 1.84194 0.598481i
\(735\) 280.551 + 931.508i 0.381702 + 1.26736i
\(736\) 38.9372 + 28.2895i 0.0529038 + 0.0384368i
\(737\) 506.835 + 877.865i 0.687701 + 1.19113i
\(738\) −180.903 + 501.644i −0.245126 + 0.679734i
\(739\) 48.9207 84.7331i 0.0661985 0.114659i −0.831027 0.556233i \(-0.812246\pi\)
0.897225 + 0.441574i \(0.145580\pi\)
\(740\) −300.151 31.5471i −0.405609 0.0426312i
\(741\) 773.059 1.04326
\(742\) −376.390 + 186.683i −0.507264 + 0.251594i
\(743\) −239.533 737.206i −0.322386 0.992202i −0.972607 0.232457i \(-0.925324\pi\)
0.650221 0.759745i \(-0.274676\pi\)
\(744\) −31.5403 3.31502i −0.0423929 0.00445567i
\(745\) 25.9271 + 246.680i 0.0348015 + 0.331114i
\(746\) 1053.80 + 1170.36i 1.41260 + 1.56885i
\(747\) 147.757 85.3074i 0.197800 0.114200i
\(748\) 261.654 + 85.0166i 0.349805 + 0.113659i
\(749\) 980.219 364.163i 1.30870 0.486198i
\(750\) −1050.71 + 341.398i −1.40095 + 0.455197i
\(751\) −534.756 56.2051i −0.712059 0.0748404i −0.258429 0.966030i \(-0.583205\pi\)
−0.453630 + 0.891190i \(0.649871\pi\)
\(752\) 411.021 711.910i 0.546571 0.946689i
\(753\) −228.349 + 1074.30i −0.303253 + 1.42669i
\(754\) 585.565 1315.20i 0.776611 1.74430i
\(755\) −170.981 + 526.227i −0.226466 + 0.696989i
\(756\) 191.646 121.531i 0.253499 0.160755i
\(757\) 203.085 + 279.523i 0.268276 + 0.369251i 0.921807 0.387649i \(-0.126713\pi\)
−0.653530 + 0.756900i \(0.726713\pi\)
\(758\) 1304.65 + 580.869i 1.72118 + 0.766318i
\(759\) 109.462 11.5049i 0.144218 0.0151579i
\(760\) −356.224 + 37.4406i −0.468715 + 0.0492640i
\(761\) 356.583 + 37.4784i 0.468572 + 0.0492489i 0.335873 0.941907i \(-0.390969\pi\)
0.132699 + 0.991156i \(0.457635\pi\)
\(762\) 449.909 1384.68i 0.590431 1.81716i
\(763\) −784.299 + 201.091i −1.02792 + 0.263553i
\(764\) −278.677 + 90.5476i −0.364760 + 0.118518i
\(765\) 146.262 84.4445i 0.191192 0.110385i
\(766\) 703.729 313.320i 0.918707 0.409035i
\(767\) 103.990 489.234i 0.135580 0.637853i
\(768\) −1185.40 + 251.965i −1.54349 + 0.328079i
\(769\) −566.435 184.046i −0.736586 0.239331i −0.0833869 0.996517i \(-0.526574\pi\)
−0.653200 + 0.757186i \(0.726574\pi\)
\(770\) −1129.96 1426.64i −1.46748 1.85278i
\(771\) −403.698 + 1242.45i −0.523603 + 1.61148i
\(772\) −250.498 + 562.627i −0.324479 + 0.728792i
\(773\) 796.431 354.594i 1.03031 0.458725i 0.179258 0.983802i \(-0.442630\pi\)
0.851054 + 0.525078i \(0.175964\pi\)
\(774\) 525.986 + 111.802i 0.679569 + 0.144447i
\(775\) 3.97634 + 3.58031i 0.00513076 + 0.00461976i
\(776\) −580.887 −0.748566
\(777\) 591.610 + 309.541i 0.761402 + 0.398380i
\(778\) −1415.54 −1.81947
\(779\) −593.632 + 241.890i −0.762044 + 0.310514i
\(780\) −510.508 294.742i −0.654497 0.377874i
\(781\) 1941.84 864.564i 2.48635 1.10700i
\(782\) −11.4323 19.8013i −0.0146193 0.0253213i
\(783\) −597.393 + 194.105i −0.762954 + 0.247899i
\(784\) −416.423 + 883.392i −0.531152 + 1.12678i
\(785\) −200.168 + 275.508i −0.254991 + 0.350965i
\(786\) −136.597 + 306.803i −0.173788 + 0.390334i
\(787\) 572.484 515.467i 0.727425 0.654977i −0.219800 0.975545i \(-0.570540\pi\)
0.947225 + 0.320568i \(0.103874\pi\)
\(788\) −170.998 + 296.177i −0.217002 + 0.375859i
\(789\) −337.966 1590.00i −0.428347 2.01522i
\(790\) −307.587 + 946.655i −0.389351 + 1.19830i
\(791\) 502.358 + 1012.85i 0.635092 + 1.28047i
\(792\) −261.888 + 360.458i −0.330667 + 0.455124i
\(793\) 255.280 147.386i 0.321916 0.185858i
\(794\) 242.336 + 51.5102i 0.305210 + 0.0648743i
\(795\) −49.7738 473.566i −0.0626086 0.595681i
\(796\) 774.060 164.532i 0.972438 0.206698i
\(797\) −314.526 + 432.908i −0.394638 + 0.543172i −0.959388 0.282090i \(-0.908972\pi\)
0.564750 + 0.825262i \(0.308972\pi\)
\(798\) −993.864 277.854i −1.24544 0.348188i
\(799\) −205.778 + 149.507i −0.257545 + 0.187117i
\(800\) 82.0296 + 36.5219i 0.102537 + 0.0456524i
\(801\) −4.86489 46.2863i −0.00607352 0.0577856i
\(802\) −486.565 + 216.633i −0.606689 + 0.270115i
\(803\) −1213.03 + 257.838i −1.51062 + 0.321093i
\(804\) −257.626 354.592i −0.320431 0.441035i
\(805\) −3.44961 + 54.5355i −0.00428523 + 0.0677460i
\(806\) 63.5721i 0.0788736i
\(807\) −1005.64 105.697i −1.24615 0.130976i
\(808\) 255.981 + 54.4104i 0.316808 + 0.0673397i
\(809\) −730.590 + 657.826i −0.903078 + 0.813135i −0.982988 0.183667i \(-0.941203\pi\)
0.0799108 + 0.996802i \(0.474536\pi\)
\(810\) 276.249 + 1299.65i 0.341049 + 1.60451i
\(811\) 534.912i 0.659571i −0.944056 0.329785i \(-0.893024\pi\)
0.944056 0.329785i \(-0.106976\pi\)
\(812\) −442.768 + 534.846i −0.545281 + 0.658677i
\(813\) −482.716 664.401i −0.593746 0.817222i
\(814\) −1242.24 130.565i −1.52609 0.160399i
\(815\) −238.754 + 1123.25i −0.292950 + 1.37822i
\(816\) 453.018 + 96.2920i 0.555170 + 0.118005i
\(817\) 323.199 + 559.797i 0.395592 + 0.685186i
\(818\) 207.020 284.939i 0.253081 0.348336i
\(819\) 296.422 + 374.251i 0.361931 + 0.456961i
\(820\) 484.243 + 66.5944i 0.590541 + 0.0812127i
\(821\) 421.479 + 730.022i 0.513372 + 0.889187i 0.999880 + 0.0155102i \(0.00493726\pi\)
−0.486508 + 0.873676i \(0.661729\pi\)
\(822\) 436.562 + 980.535i 0.531098 + 1.19287i
\(823\) 174.276 + 100.618i 0.211757 + 0.122258i 0.602128 0.798400i \(-0.294320\pi\)
−0.390371 + 0.920658i \(0.627653\pi\)
\(824\) −514.248 463.031i −0.624088 0.561931i
\(825\) 195.293 63.4546i 0.236719 0.0769147i
\(826\) −309.533 + 591.595i −0.374737 + 0.716216i
\(827\) −160.477 220.877i −0.194047 0.267083i 0.700896 0.713264i \(-0.252784\pi\)
−0.894943 + 0.446181i \(0.852784\pi\)
\(828\) −17.0412 + 3.62223i −0.0205812 + 0.00437467i
\(829\) −791.880 457.192i −0.955224 0.551499i −0.0605239 0.998167i \(-0.519277\pi\)
−0.894700 + 0.446668i \(0.852610\pi\)
\(830\) −289.643 321.681i −0.348968 0.387568i
\(831\) −1652.58 + 351.266i −1.98866 + 0.422702i
\(832\) −6.37986 19.6352i −0.00766810 0.0236000i
\(833\) 228.887 197.299i 0.274774 0.236854i
\(834\) 1528.40i 1.83261i
\(835\) −1071.77 965.022i −1.28355 1.15571i
\(836\) 693.662 72.9068i 0.829739 0.0872090i
\(837\) −20.6126 + 18.5597i −0.0246267 + 0.0221740i
\(838\) 1229.53 + 129.229i 1.46722 + 0.154211i
\(839\) 1068.01 775.951i 1.27295 0.924853i 0.273634 0.961834i \(-0.411774\pi\)
0.999316 + 0.0369812i \(0.0117742\pi\)
\(840\) −422.630 431.867i −0.503130 0.514128i
\(841\) 874.463 635.335i 1.03979 0.755451i
\(842\) −276.036 + 619.986i −0.327833 + 0.736326i
\(843\) 431.442 + 969.035i 0.511794 + 1.14951i
\(844\) −179.456 + 161.583i −0.212626 + 0.191449i
\(845\) −6.86306 + 15.4147i −0.00812197 + 0.0182422i
\(846\) 165.770 + 510.189i 0.195946 + 0.603060i
\(847\) −1163.70 1469.24i −1.37391 1.73465i
\(848\) 280.977 386.731i 0.331340 0.456051i
\(849\) −1383.69 1245.88i −1.62979 1.46747i
\(850\) −28.5434 31.7007i −0.0335805 0.0372949i
\(851\) 25.0954 + 27.8713i 0.0294894 + 0.0327512i
\(852\) −795.956 + 459.545i −0.934220 + 0.539372i
\(853\) 1172.13 + 380.848i 1.37413 + 0.446481i 0.900734 0.434370i \(-0.143029\pi\)
0.473393 + 0.880851i \(0.343029\pi\)
\(854\) −381.167 + 97.7297i −0.446332 + 0.114438i
\(855\) 251.670 346.395i 0.294351 0.405140i
\(856\) −434.599 + 482.671i −0.507709 + 0.563868i
\(857\) −253.555 + 1192.88i −0.295864 + 1.39193i 0.539385 + 0.842059i \(0.318657\pi\)
−0.835249 + 0.549872i \(0.814677\pi\)
\(858\) −2112.85 1219.85i −2.46252 1.42174i
\(859\) −186.498 19.6017i −0.217110 0.0228192i −0.00465111 0.999989i \(-0.501481\pi\)
−0.212459 + 0.977170i \(0.568147\pi\)
\(860\) 492.900i 0.573139i
\(861\) −941.668 531.680i −1.09369 0.617515i
\(862\) 1525.50 1.76972
\(863\) −28.8747 + 274.725i −0.0334585 + 0.318337i 0.964973 + 0.262349i \(0.0844973\pi\)
−0.998431 + 0.0559873i \(0.982169\pi\)
\(864\) −232.733 + 403.106i −0.269367 + 0.466558i
\(865\) 842.085 + 178.991i 0.973509 + 0.206926i
\(866\) 690.408 + 621.646i 0.797237 + 0.717836i
\(867\) 765.031 + 555.827i 0.882388 + 0.641093i
\(868\) −8.25513 + 29.5280i −0.00951052 + 0.0340184i
\(869\) −459.924 + 1415.50i −0.529257 + 1.62888i
\(870\) −1089.07 1886.33i −1.25181 2.16820i
\(871\) −501.364 + 451.430i −0.575619 + 0.518290i
\(872\) 373.732 336.510i 0.428592 0.385906i
\(873\) 464.630 516.024i 0.532222 0.591093i
\(874\) −46.8955 34.0716i −0.0536562 0.0389835i
\(875\) −119.536 811.396i −0.136613 0.927310i
\(876\) 509.974 165.701i 0.582162 0.189156i
\(877\) −865.362 385.284i −0.986729 0.439320i −0.151043 0.988527i \(-0.548263\pi\)
−0.835686 + 0.549207i \(0.814930\pi\)
\(878\) −70.1592 77.9197i −0.0799080 0.0887468i
\(879\) 1649.24 734.288i 1.87627 0.835367i
\(880\) 1891.64 + 842.211i 2.14959 + 0.957058i
\(881\) 283.523 + 390.236i 0.321820 + 0.442947i 0.939022 0.343858i \(-0.111734\pi\)
−0.617202 + 0.786805i \(0.711734\pi\)
\(882\) −246.573 587.687i −0.279561 0.666311i
\(883\) −127.225 175.110i −0.144083 0.198313i 0.730876 0.682510i \(-0.239112\pi\)
−0.874959 + 0.484197i \(0.839112\pi\)
\(884\) −19.1399 + 182.104i −0.0216514 + 0.206000i
\(885\) −506.347 562.355i −0.572143 0.635430i
\(886\) 184.769 + 1757.96i 0.208543 + 1.98415i
\(887\) −768.596 + 853.612i −0.866512 + 0.962359i −0.999587 0.0287473i \(-0.990848\pi\)
0.133075 + 0.991106i \(0.457515\pi\)
\(888\) −414.723 −0.467031
\(889\) 957.670 + 501.070i 1.07724 + 0.563633i
\(890\) −112.300 + 36.4885i −0.126180 + 0.0409983i
\(891\) 413.066 + 1943.32i 0.463598 + 2.18106i
\(892\) 506.582 456.128i 0.567917 0.511354i
\(893\) −322.421 + 558.450i −0.361054 + 0.625364i
\(894\) −92.2865 434.174i −0.103229 0.485653i
\(895\) 860.909 625.487i 0.961909 0.698868i
\(896\) −36.6385 881.294i −0.0408912 0.983587i
\(897\) 22.6367 + 69.6685i 0.0252360 + 0.0776684i
\(898\) 1394.37 1548.60i 1.55275 1.72450i
\(899\) 42.4331 73.4963i 0.0472003 0.0817534i
\(900\) −29.6934 + 13.2204i −0.0329927 + 0.0146893i
\(901\) −128.094 + 73.9553i −0.142169 + 0.0820814i
\(902\) 2004.15 + 275.615i 2.22189 + 0.305560i
\(903\) −401.770 + 1013.75i −0.444928 + 1.12265i
\(904\) −568.124 412.766i −0.628455 0.456599i
\(905\) −34.5748 + 19.9618i −0.0382042 + 0.0220572i
\(906\) 205.866 968.525i 0.227226 1.06901i
\(907\) −914.324 194.346i −1.00807 0.214273i −0.325855 0.945420i \(-0.605652\pi\)
−0.682220 + 0.731147i \(0.738985\pi\)
\(908\) −45.6248 + 434.091i −0.0502476 + 0.478074i
\(909\) −253.085 + 183.877i −0.278421 + 0.202285i
\(910\) 772.399 933.027i 0.848790 1.02530i
\(911\) 618.399 0.678813 0.339407 0.940640i \(-0.389774\pi\)
0.339407 + 0.940640i \(0.389774\pi\)
\(912\) 1148.49 244.119i 1.25931 0.267675i
\(913\) −433.094 480.999i −0.474363 0.526834i
\(914\) 6.48379 30.5038i 0.00709386 0.0333740i
\(915\) 46.6171 443.532i 0.0509477 0.484735i
\(916\) −421.446 −0.460094
\(917\) −207.612 138.038i −0.226404 0.150533i
\(918\) 178.896 129.976i 0.194876 0.141586i
\(919\) −149.654 704.066i −0.162844 0.766122i −0.981443 0.191756i \(-0.938582\pi\)
0.818598 0.574366i \(-0.194751\pi\)
\(920\) −13.8051 31.0068i −0.0150055 0.0337030i
\(921\) 133.494 14.0308i 0.144944 0.0152343i
\(922\) 696.630 1564.66i 0.755564 1.69702i
\(923\) 831.544 + 1144.52i 0.900915 + 1.24000i
\(924\) 822.971 + 840.959i 0.890661 + 0.910129i
\(925\) 56.6076 + 41.1278i 0.0611974 + 0.0444625i
\(926\) −139.747 657.458i −0.150915 0.709998i
\(927\) 822.657 86.4647i 0.887440 0.0932737i
\(928\) 296.104 1393.06i 0.319077 1.50114i
\(929\) 585.679 + 1014.43i 0.630441 + 1.09196i 0.987462 + 0.157859i \(0.0504591\pi\)
−0.357021 + 0.934096i \(0.616208\pi\)
\(930\) −77.8126 56.5341i −0.0836694 0.0607894i
\(931\) 326.659 692.967i 0.350869 0.744326i
\(932\) 159.381 + 51.7862i 0.171010 + 0.0555646i
\(933\) −938.602 + 199.506i −1.00600 + 0.213833i
\(934\) −535.612 309.236i −0.573460 0.331087i
\(935\) −428.713 476.134i −0.458516 0.509234i
\(936\) −270.901 120.613i −0.289424 0.128860i
\(937\) −735.830 534.611i −0.785304 0.570557i 0.121262 0.992620i \(-0.461306\pi\)
−0.906566 + 0.422064i \(0.861306\pi\)
\(938\) 806.820 400.169i 0.860150 0.426619i
\(939\) 550.071 + 1692.94i 0.585805 + 1.80292i
\(940\) 425.837 245.857i 0.453018 0.261550i
\(941\) −367.233 824.818i −0.390258 0.876533i −0.996682 0.0813921i \(-0.974063\pi\)
0.606424 0.795141i \(-0.292603\pi\)
\(942\) 304.709 527.772i 0.323471 0.560268i
\(943\) −39.1820 46.4155i −0.0415504 0.0492211i
\(944\) 759.665i 0.804730i
\(945\) −528.024 + 21.9518i −0.558755 + 0.0232294i
\(946\) 2039.97i 2.15642i
\(947\) 358.888 398.586i 0.378974 0.420893i −0.523238 0.852187i \(-0.675276\pi\)
0.902212 + 0.431294i \(0.141943\pi\)
\(948\) 133.800 629.481i 0.141140 0.664009i
\(949\) −335.710 754.016i −0.353751 0.794537i
\(950\) −98.7955 43.9866i −0.103995 0.0463017i
\(951\) −811.295 263.606i −0.853097 0.277188i
\(952\) −69.1543 + 174.491i −0.0726411 + 0.183289i
\(953\) −263.858 + 812.071i −0.276871 + 0.852121i 0.711847 + 0.702334i \(0.247859\pi\)
−0.988718 + 0.149787i \(0.952141\pi\)
\(954\) 64.8575 + 305.131i 0.0679848 + 0.319844i
\(955\) 667.472 + 141.876i 0.698923 + 0.148561i
\(956\) −88.2832 198.287i −0.0923464 0.207413i
\(957\) −1628.45 2820.56i −1.70162 2.94730i
\(958\) −274.049 843.437i −0.286064 0.880415i
\(959\) −771.835 + 197.895i −0.804834 + 0.206356i
\(960\) −29.7071 9.65243i −0.0309449 0.0100546i
\(961\) −100.060 + 952.009i −0.104121 + 0.990644i
\(962\) −86.8976 826.776i −0.0903302 0.859434i
\(963\) −81.1554 772.142i −0.0842735 0.801809i
\(964\) −335.498 + 753.541i −0.348027 + 0.781681i
\(965\) 1160.33 843.030i 1.20242 0.873607i
\(966\) −4.06189 97.7037i −0.00420485 0.101143i
\(967\) −1304.14 423.742i −1.34865 0.438203i −0.456412 0.889769i \(-0.650866\pi\)
−0.892238 + 0.451566i \(0.850866\pi\)
\(968\) 1063.51 + 473.505i 1.09867 + 0.489158i
\(969\) −355.366 75.5353i −0.366734 0.0779518i
\(970\) −1525.68 880.850i −1.57286 0.908093i
\(971\) −6.51703 + 62.0054i −0.00671167 + 0.0638572i −0.997365 0.0725460i \(-0.976888\pi\)
0.990653 + 0.136403i \(0.0435543\pi\)
\(972\) −175.297 539.510i −0.180347 0.555052i
\(973\) 1118.67 + 189.599i 1.14972 + 0.194860i
\(974\) −138.419 + 426.009i −0.142114 + 0.437381i
\(975\) 68.3335 + 118.357i 0.0700856 + 0.121392i
\(976\) 332.713 299.576i 0.340894 0.306943i
\(977\) 204.227 21.4651i 0.209034 0.0219704i 0.000567614 1.00000i \(-0.499819\pi\)
0.208467 + 0.978029i \(0.433153\pi\)
\(978\) 214.806 2043.75i 0.219638 2.08972i
\(979\) −167.918 + 54.5600i −0.171520 + 0.0557303i
\(980\) −479.922 + 333.073i −0.489716 + 0.339870i
\(981\) 601.162i 0.612806i
\(982\) 230.398 2192.09i 0.234621 2.23227i
\(983\) 157.244 + 90.7849i 0.159963 + 0.0923549i 0.577845 0.816147i \(-0.303894\pi\)
−0.417881 + 0.908502i \(0.637227\pi\)
\(984\) 671.342 + 21.4538i 0.682258 + 0.0218026i
\(985\) 689.739 398.221i 0.700243 0.404285i
\(986\) −397.684 + 547.366i −0.403331 + 0.555137i
\(987\) −1076.23 + 158.551i −1.09040 + 0.160640i
\(988\) 143.449 + 441.492i 0.145192 + 0.446854i
\(989\) −40.9853 + 45.5188i −0.0414412 + 0.0460251i
\(990\) −1234.43 + 549.605i −1.24690 + 0.555157i
\(991\) −1497.34 + 157.377i −1.51094 + 0.158806i −0.823451 0.567388i \(-0.807954\pi\)
−0.687490 + 0.726194i \(0.741287\pi\)
\(992\) −13.0752 61.5140i −0.0131807 0.0620101i
\(993\) 1921.63i 1.93518i
\(994\) −657.688 1770.30i −0.661658 1.78099i
\(995\) −1752.71 569.491i −1.76152 0.572353i
\(996\) 207.979 + 187.265i 0.208814 + 0.188017i
\(997\) −831.526 + 370.219i −0.834028 + 0.371333i −0.778902 0.627146i \(-0.784223\pi\)
−0.0551265 + 0.998479i \(0.517556\pi\)
\(998\) 842.632 + 486.494i 0.844321 + 0.487469i
\(999\) −242.704 + 269.550i −0.242947 + 0.269820i
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 287.3.x.a.31.13 432
7.5 odd 6 inner 287.3.x.a.236.42 yes 432
41.4 even 10 inner 287.3.x.a.45.42 yes 432
287.250 odd 30 inner 287.3.x.a.250.13 yes 432
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.x.a.31.13 432 1.1 even 1 trivial
287.3.x.a.45.42 yes 432 41.4 even 10 inner
287.3.x.a.236.42 yes 432 7.5 odd 6 inner
287.3.x.a.250.13 yes 432 287.250 odd 30 inner