Properties

Label 140.2.o.a.31.13
Level $140$
Weight $2$
Character 140.31
Analytic conductor $1.118$
Analytic rank $0$
Dimension $32$
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] = [140,2,Mod(31,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("140.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.o (of order \(6\), degree \(2\), 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: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.13
Character \(\chi\) \(=\) 140.31
Dual form 140.2.o.a.131.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.05472 + 0.942109i) q^{2} +(0.450639 - 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.21064 - 0.398687i) q^{6} +(2.29962 - 1.30833i) q^{7} +(-1.63511 + 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +O(q^{10})\) \(q+(1.05472 + 0.942109i) q^{2} +(0.450639 - 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.21064 - 0.398687i) q^{6} +(2.29962 - 1.30833i) q^{7} +(-1.63511 + 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(-1.38447 - 0.288532i) q^{10} +(-3.24107 - 1.87123i) q^{11} +(1.65249 + 0.720054i) q^{12} -2.41990i q^{13} +(3.65805 + 0.786573i) q^{14} +0.901278i q^{15} +(-3.89888 + 0.893735i) q^{16} +(-0.505515 - 0.291859i) q^{17} +(-0.631220 + 3.02880i) q^{18} +(-3.07977 - 5.33433i) q^{19} +(-1.18839 - 1.60864i) q^{20} +(0.0151060 - 2.38451i) q^{21} +(-1.65551 - 5.02706i) q^{22} +(-3.73439 + 2.15605i) q^{23} +(1.06454 + 2.31628i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.27981 - 2.55232i) q^{26} +4.67556 q^{27} +(3.11717 + 4.27589i) q^{28} -0.435463 q^{29} +(-0.849103 + 0.950594i) q^{30} +(-1.26933 + 2.19854i) q^{31} +(-4.95421 - 2.73053i) q^{32} +(-2.92110 + 1.68650i) q^{33} +(-0.258212 - 0.784080i) q^{34} +(-1.33736 + 2.28286i) q^{35} +(-3.51922 + 2.59985i) q^{36} +(5.65039 + 9.78676i) q^{37} +(1.77723 - 8.52769i) q^{38} +(-1.88881 - 1.09050i) q^{39} +(0.262094 - 2.81626i) q^{40} -7.35068i q^{41} +(2.26240 - 2.50075i) q^{42} -5.80096i q^{43} +(2.98995 - 6.86180i) q^{44} +(-1.89460 - 1.09385i) q^{45} +(-5.96996 - 1.24418i) q^{46} +(5.78826 + 10.0256i) q^{47} +(-1.05940 + 3.44594i) q^{48} +(3.57652 - 6.01735i) q^{49} +(1.34325 - 0.442358i) q^{50} +(-0.455610 + 0.263046i) q^{51} +(4.80912 - 0.544138i) q^{52} +(1.55746 - 2.69759i) q^{53} +(4.93139 + 4.40489i) q^{54} +3.74246 q^{55} +(-0.740624 + 7.44657i) q^{56} -5.55147 q^{57} +(-0.459290 - 0.410254i) q^{58} +(-1.73534 + 3.00569i) q^{59} +(-1.79113 + 0.202661i) q^{60} +(-8.99597 + 5.19383i) q^{61} +(-3.41004 + 1.12299i) q^{62} +(4.99421 + 2.92575i) q^{63} +(-2.65284 - 7.54735i) q^{64} +(1.20995 + 2.09570i) q^{65} +(-4.66981 - 0.973217i) q^{66} +(8.52602 + 4.92250i) q^{67} +(0.466348 - 1.07025i) q^{68} +3.88640i q^{69} +(-3.56125 + 1.14783i) q^{70} +9.96771i q^{71} +(-6.16112 - 0.573383i) q^{72} +(8.48612 + 4.89946i) q^{73} +(-3.26063 + 15.6456i) q^{74} +(-0.450639 - 0.780530i) q^{75} +(9.90849 - 7.31997i) q^{76} +(-9.90142 - 0.0627260i) q^{77} +(-0.964785 - 2.92964i) q^{78} +(-0.397549 + 0.229525i) q^{79} +(2.92966 - 2.72344i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(6.92515 - 7.75290i) q^{82} -2.59747 q^{83} +(4.74218 - 0.506159i) q^{84} +0.583719 q^{85} +(5.46514 - 6.11837i) q^{86} +(-0.196236 + 0.339892i) q^{87} +(9.61812 - 4.42040i) q^{88} +(-8.55647 + 4.94008i) q^{89} +(-0.967745 - 2.93862i) q^{90} +(-3.16604 - 5.56486i) q^{91} +(-5.12447 - 6.93662i) q^{92} +(1.14402 + 1.98149i) q^{93} +(-3.34020 + 16.0273i) q^{94} +(5.33433 + 3.07977i) q^{95} +(-4.36382 + 2.63643i) q^{96} -4.54044i q^{97} +(9.44122 - 2.97713i) q^{98} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05472 + 0.942109i 0.745798 + 0.666172i
\(3\) 0.450639 0.780530i 0.260177 0.450639i −0.706112 0.708100i \(-0.749553\pi\)
0.966289 + 0.257461i \(0.0828859\pi\)
\(4\) 0.224860 + 1.98732i 0.112430 + 0.993660i
\(5\) −0.866025 + 0.500000i −0.387298 + 0.223607i
\(6\) 1.21064 0.398687i 0.494242 0.162763i
\(7\) 2.29962 1.30833i 0.869175 0.494504i
\(8\) −1.63511 + 2.30790i −0.578098 + 0.815967i
\(9\) 1.09385 + 1.89460i 0.364616 + 0.631534i
\(10\) −1.38447 0.288532i −0.437807 0.0912418i
\(11\) −3.24107 1.87123i −0.977218 0.564197i −0.0757892 0.997124i \(-0.524148\pi\)
−0.901429 + 0.432927i \(0.857481\pi\)
\(12\) 1.65249 + 0.720054i 0.477033 + 0.207862i
\(13\) 2.41990i 0.671161i −0.942012 0.335580i \(-0.891068\pi\)
0.942012 0.335580i \(-0.108932\pi\)
\(14\) 3.65805 + 0.786573i 0.977654 + 0.210220i
\(15\) 0.901278i 0.232709i
\(16\) −3.89888 + 0.893735i −0.974719 + 0.223434i
\(17\) −0.505515 0.291859i −0.122605 0.0707863i 0.437443 0.899246i \(-0.355884\pi\)
−0.560048 + 0.828460i \(0.689218\pi\)
\(18\) −0.631220 + 3.02880i −0.148780 + 0.713894i
\(19\) −3.07977 5.33433i −0.706549 1.22378i −0.966130 0.258057i \(-0.916918\pi\)
0.259581 0.965721i \(-0.416416\pi\)
\(20\) −1.18839 1.60864i −0.265733 0.359703i
\(21\) 0.0151060 2.38451i 0.00329639 0.520343i
\(22\) −1.65551 5.02706i −0.352955 1.07177i
\(23\) −3.73439 + 2.15605i −0.778674 + 0.449568i −0.835960 0.548790i \(-0.815089\pi\)
0.0572861 + 0.998358i \(0.481755\pi\)
\(24\) 1.06454 + 2.31628i 0.217299 + 0.472809i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 2.27981 2.55232i 0.447108 0.500550i
\(27\) 4.67556 0.899812
\(28\) 3.11717 + 4.27589i 0.589090 + 0.808068i
\(29\) −0.435463 −0.0808634 −0.0404317 0.999182i \(-0.512873\pi\)
−0.0404317 + 0.999182i \(0.512873\pi\)
\(30\) −0.849103 + 0.950594i −0.155024 + 0.173554i
\(31\) −1.26933 + 2.19854i −0.227978 + 0.394869i −0.957209 0.289399i \(-0.906545\pi\)
0.729231 + 0.684268i \(0.239878\pi\)
\(32\) −4.95421 2.73053i −0.875789 0.482694i
\(33\) −2.92110 + 1.68650i −0.508499 + 0.293582i
\(34\) −0.258212 0.784080i −0.0442831 0.134469i
\(35\) −1.33736 + 2.28286i −0.226056 + 0.385874i
\(36\) −3.51922 + 2.59985i −0.586536 + 0.433308i
\(37\) 5.65039 + 9.78676i 0.928918 + 1.60893i 0.785136 + 0.619324i \(0.212593\pi\)
0.143782 + 0.989609i \(0.454073\pi\)
\(38\) 1.77723 8.52769i 0.288304 1.38337i
\(39\) −1.88881 1.09050i −0.302451 0.174620i
\(40\) 0.262094 2.81626i 0.0414407 0.445289i
\(41\) 7.35068i 1.14798i −0.818861 0.573992i \(-0.805394\pi\)
0.818861 0.573992i \(-0.194606\pi\)
\(42\) 2.26240 2.50075i 0.349096 0.385875i
\(43\) 5.80096i 0.884637i −0.896858 0.442319i \(-0.854156\pi\)
0.896858 0.442319i \(-0.145844\pi\)
\(44\) 2.98995 6.86180i 0.450752 1.03446i
\(45\) −1.89460 1.09385i −0.282431 0.163061i
\(46\) −5.96996 1.24418i −0.880223 0.183444i
\(47\) 5.78826 + 10.0256i 0.844305 + 1.46238i 0.886223 + 0.463258i \(0.153320\pi\)
−0.0419181 + 0.999121i \(0.513347\pi\)
\(48\) −1.05940 + 3.44594i −0.152911 + 0.497379i
\(49\) 3.57652 6.01735i 0.510932 0.859621i
\(50\) 1.34325 0.442358i 0.189964 0.0625588i
\(51\) −0.455610 + 0.263046i −0.0637981 + 0.0368339i
\(52\) 4.80912 0.544138i 0.666905 0.0754584i
\(53\) 1.55746 2.69759i 0.213933 0.370543i −0.739009 0.673696i \(-0.764706\pi\)
0.952942 + 0.303153i \(0.0980393\pi\)
\(54\) 4.93139 + 4.40489i 0.671078 + 0.599429i
\(55\) 3.74246 0.504633
\(56\) −0.740624 + 7.44657i −0.0989701 + 0.995090i
\(57\) −5.55147 −0.735310
\(58\) −0.459290 0.410254i −0.0603078 0.0538689i
\(59\) −1.73534 + 3.00569i −0.225922 + 0.391308i −0.956596 0.291419i \(-0.905873\pi\)
0.730674 + 0.682727i \(0.239206\pi\)
\(60\) −1.79113 + 0.202661i −0.231234 + 0.0261634i
\(61\) −8.99597 + 5.19383i −1.15182 + 0.665001i −0.949329 0.314284i \(-0.898236\pi\)
−0.202487 + 0.979285i \(0.564902\pi\)
\(62\) −3.41004 + 1.12299i −0.433076 + 0.142620i
\(63\) 4.99421 + 2.92575i 0.629211 + 0.368610i
\(64\) −2.65284 7.54735i −0.331605 0.943418i
\(65\) 1.20995 + 2.09570i 0.150076 + 0.259939i
\(66\) −4.66981 0.973217i −0.574813 0.119795i
\(67\) 8.52602 + 4.92250i 1.04162 + 0.601379i 0.920291 0.391234i \(-0.127952\pi\)
0.121327 + 0.992613i \(0.461285\pi\)
\(68\) 0.466348 1.07025i 0.0565530 0.129787i
\(69\) 3.88640i 0.467868i
\(70\) −3.56125 + 1.14783i −0.425650 + 0.137192i
\(71\) 9.96771i 1.18295i 0.806324 + 0.591475i \(0.201454\pi\)
−0.806324 + 0.591475i \(0.798546\pi\)
\(72\) −6.16112 0.573383i −0.726095 0.0675738i
\(73\) 8.48612 + 4.89946i 0.993225 + 0.573439i 0.906237 0.422771i \(-0.138942\pi\)
0.0869881 + 0.996209i \(0.472276\pi\)
\(74\) −3.26063 + 15.6456i −0.379041 + 1.81876i
\(75\) −0.450639 0.780530i −0.0520353 0.0901278i
\(76\) 9.90849 7.31997i 1.13658 0.839658i
\(77\) −9.90142 0.0627260i −1.12837 0.00714829i
\(78\) −0.964785 2.92964i −0.109240 0.331716i
\(79\) −0.397549 + 0.229525i −0.0447278 + 0.0258236i −0.522197 0.852825i \(-0.674887\pi\)
0.477469 + 0.878648i \(0.341554\pi\)
\(80\) 2.92966 2.72344i 0.327546 0.304489i
\(81\) −1.17456 + 2.03439i −0.130506 + 0.226044i
\(82\) 6.92515 7.75290i 0.764755 0.856164i
\(83\) −2.59747 −0.285109 −0.142554 0.989787i \(-0.545532\pi\)
−0.142554 + 0.989787i \(0.545532\pi\)
\(84\) 4.74218 0.506159i 0.517414 0.0552265i
\(85\) 0.583719 0.0633132
\(86\) 5.46514 6.11837i 0.589321 0.659761i
\(87\) −0.196236 + 0.339892i −0.0210388 + 0.0364402i
\(88\) 9.61812 4.42040i 1.02529 0.471217i
\(89\) −8.55647 + 4.94008i −0.906984 + 0.523648i −0.879460 0.475973i \(-0.842096\pi\)
−0.0275247 + 0.999621i \(0.508763\pi\)
\(90\) −0.967745 2.93862i −0.102009 0.309758i
\(91\) −3.16604 5.56486i −0.331891 0.583356i
\(92\) −5.12447 6.93662i −0.534263 0.723192i
\(93\) 1.14402 + 1.98149i 0.118629 + 0.205471i
\(94\) −3.34020 + 16.0273i −0.344515 + 1.65309i
\(95\) 5.33433 + 3.07977i 0.547290 + 0.315978i
\(96\) −4.36382 + 2.63643i −0.445381 + 0.269079i
\(97\) 4.54044i 0.461011i −0.973071 0.230506i \(-0.925962\pi\)
0.973071 0.230506i \(-0.0740380\pi\)
\(98\) 9.44122 2.97713i 0.953708 0.300735i
\(99\) 8.18738i 0.822862i
\(100\) 1.83350 + 0.798926i 0.183350 + 0.0798926i
\(101\) 7.91930 + 4.57221i 0.787999 + 0.454952i 0.839258 0.543734i \(-0.182990\pi\)
−0.0512584 + 0.998685i \(0.516323\pi\)
\(102\) −0.728358 0.151795i −0.0721182 0.0150299i
\(103\) −5.11597 8.86113i −0.504092 0.873113i −0.999989 0.00473128i \(-0.998494\pi\)
0.495897 0.868381i \(-0.334839\pi\)
\(104\) 5.58490 + 3.95681i 0.547645 + 0.387997i
\(105\) 1.17917 + 2.07260i 0.115075 + 0.202265i
\(106\) 4.18410 1.37790i 0.406396 0.133834i
\(107\) −5.48368 + 3.16601i −0.530128 + 0.306069i −0.741068 0.671430i \(-0.765681\pi\)
0.210941 + 0.977499i \(0.432347\pi\)
\(108\) 1.05134 + 9.29183i 0.101166 + 0.894107i
\(109\) 9.38027 16.2471i 0.898467 1.55619i 0.0690134 0.997616i \(-0.478015\pi\)
0.829454 0.558575i \(-0.188652\pi\)
\(110\) 3.94724 + 3.52581i 0.376355 + 0.336173i
\(111\) 10.1851 0.966731
\(112\) −7.79664 + 7.15629i −0.736713 + 0.676205i
\(113\) 4.17847 0.393077 0.196539 0.980496i \(-0.437030\pi\)
0.196539 + 0.980496i \(0.437030\pi\)
\(114\) −5.85523 5.23009i −0.548393 0.489843i
\(115\) 2.15605 3.73439i 0.201053 0.348234i
\(116\) −0.0979179 0.865403i −0.00909145 0.0803507i
\(117\) 4.58475 2.64701i 0.423861 0.244716i
\(118\) −4.66198 + 1.53528i −0.429170 + 0.141334i
\(119\) −1.54434 0.00978348i −0.141570 0.000896851i
\(120\) −2.08006 1.47369i −0.189883 0.134529i
\(121\) 1.50301 + 2.60329i 0.136637 + 0.236663i
\(122\) −14.3814 2.99717i −1.30203 0.271351i
\(123\) −5.73743 3.31250i −0.517326 0.298678i
\(124\) −4.65461 2.02819i −0.417997 0.182137i
\(125\) 1.00000i 0.0894427i
\(126\) 2.51111 + 7.79093i 0.223707 + 0.694072i
\(127\) 4.91036i 0.435724i −0.975980 0.217862i \(-0.930092\pi\)
0.975980 0.217862i \(-0.0699083\pi\)
\(128\) 4.31243 10.4596i 0.381169 0.924505i
\(129\) −4.52782 2.61414i −0.398652 0.230162i
\(130\) −0.698219 + 3.35028i −0.0612379 + 0.293839i
\(131\) −7.93723 13.7477i −0.693479 1.20114i −0.970691 0.240332i \(-0.922744\pi\)
0.277212 0.960809i \(-0.410590\pi\)
\(132\) −4.00845 5.42594i −0.348891 0.472267i
\(133\) −14.0614 8.23756i −1.21928 0.714287i
\(134\) 4.35501 + 13.2243i 0.376216 + 1.14240i
\(135\) −4.04915 + 2.33778i −0.348496 + 0.201204i
\(136\) 1.50016 0.689459i 0.128637 0.0591206i
\(137\) 3.92110 6.79155i 0.335002 0.580241i −0.648483 0.761229i \(-0.724596\pi\)
0.983485 + 0.180988i \(0.0579295\pi\)
\(138\) −3.66142 + 4.09906i −0.311680 + 0.348935i
\(139\) −17.4044 −1.47623 −0.738113 0.674677i \(-0.764283\pi\)
−0.738113 + 0.674677i \(0.764283\pi\)
\(140\) −4.83749 2.14445i −0.408843 0.181239i
\(141\) 10.4337 0.878674
\(142\) −9.39067 + 10.5131i −0.788048 + 0.882242i
\(143\) −4.52820 + 7.84307i −0.378667 + 0.655871i
\(144\) −5.95805 6.40921i −0.496505 0.534101i
\(145\) 0.377122 0.217731i 0.0313183 0.0180816i
\(146\) 4.33463 + 13.1624i 0.358736 + 1.08933i
\(147\) −3.08500 5.50324i −0.254446 0.453899i
\(148\) −18.1789 + 13.4298i −1.49429 + 1.10392i
\(149\) −0.825776 1.43029i −0.0676502 0.117174i 0.830216 0.557441i \(-0.188217\pi\)
−0.897867 + 0.440268i \(0.854884\pi\)
\(150\) 0.260047 1.24779i 0.0212328 0.101882i
\(151\) 6.37060 + 3.67807i 0.518432 + 0.299317i 0.736293 0.676663i \(-0.236575\pi\)
−0.217861 + 0.975980i \(0.569908\pi\)
\(152\) 17.3469 + 1.61438i 1.40702 + 0.130944i
\(153\) 1.27700i 0.103239i
\(154\) −10.3841 9.39438i −0.836776 0.757021i
\(155\) 2.53865i 0.203909i
\(156\) 1.74246 3.99887i 0.139509 0.320166i
\(157\) −2.66953 1.54125i −0.213052 0.123005i 0.389677 0.920952i \(-0.372587\pi\)
−0.602729 + 0.797946i \(0.705920\pi\)
\(158\) −0.635540 0.132451i −0.0505609 0.0105372i
\(159\) −1.40370 2.43128i −0.111321 0.192813i
\(160\) 5.65574 0.112397i 0.447125 0.00888579i
\(161\) −5.76685 + 9.84393i −0.454491 + 0.775810i
\(162\) −3.15545 + 1.03915i −0.247915 + 0.0816433i
\(163\) 3.91284 2.25908i 0.306477 0.176945i −0.338872 0.940833i \(-0.610045\pi\)
0.645349 + 0.763888i \(0.276712\pi\)
\(164\) 14.6082 1.65287i 1.14071 0.129068i
\(165\) 1.68650 2.92110i 0.131294 0.227408i
\(166\) −2.73959 2.44710i −0.212634 0.189932i
\(167\) −16.9358 −1.31053 −0.655266 0.755398i \(-0.727444\pi\)
−0.655266 + 0.755398i \(0.727444\pi\)
\(168\) 5.47852 + 3.93380i 0.422677 + 0.303499i
\(169\) 7.14406 0.549543
\(170\) 0.615659 + 0.549927i 0.0472189 + 0.0421775i
\(171\) 6.73762 11.6699i 0.515238 0.892419i
\(172\) 11.5284 1.30440i 0.879029 0.0994596i
\(173\) 0.114919 0.0663486i 0.00873715 0.00504439i −0.495625 0.868537i \(-0.665061\pi\)
0.504362 + 0.863492i \(0.331728\pi\)
\(174\) −0.527189 + 0.173613i −0.0399661 + 0.0131616i
\(175\) 0.0167606 2.64570i 0.00126698 0.199996i
\(176\) 14.3089 + 4.39904i 1.07857 + 0.331590i
\(177\) 1.56402 + 2.70897i 0.117559 + 0.203618i
\(178\) −13.6788 2.85074i −1.02527 0.213672i
\(179\) 13.9422 + 8.04953i 1.04209 + 0.601650i 0.920424 0.390921i \(-0.127843\pi\)
0.121664 + 0.992571i \(0.461177\pi\)
\(180\) 1.74781 4.01114i 0.130274 0.298973i
\(181\) 3.99317i 0.296810i −0.988927 0.148405i \(-0.952586\pi\)
0.988927 0.148405i \(-0.0474139\pi\)
\(182\) 1.90343 8.85212i 0.141092 0.656163i
\(183\) 9.36216i 0.692071i
\(184\) 1.13018 12.1440i 0.0833177 0.895267i
\(185\) −9.78676 5.65039i −0.719537 0.415425i
\(186\) −0.660170 + 3.16770i −0.0484060 + 0.232267i
\(187\) 1.09227 + 1.89187i 0.0798749 + 0.138347i
\(188\) −18.6225 + 13.7575i −1.35818 + 1.00337i
\(189\) 10.7520 6.11719i 0.782094 0.444960i
\(190\) 2.72472 + 8.27381i 0.197672 + 0.600245i
\(191\) 17.3638 10.0250i 1.25640 0.725385i 0.284030 0.958815i \(-0.408329\pi\)
0.972373 + 0.233431i \(0.0749953\pi\)
\(192\) −7.08640 1.33051i −0.511417 0.0960214i
\(193\) −9.66959 + 16.7482i −0.696032 + 1.20556i 0.273799 + 0.961787i \(0.411720\pi\)
−0.969832 + 0.243776i \(0.921614\pi\)
\(194\) 4.27759 4.78888i 0.307113 0.343821i
\(195\) 2.18101 0.156185
\(196\) 12.7626 + 5.75464i 0.911615 + 0.411046i
\(197\) −1.63738 −0.116659 −0.0583293 0.998297i \(-0.518577\pi\)
−0.0583293 + 0.998297i \(0.518577\pi\)
\(198\) 7.71340 8.63537i 0.548168 0.613689i
\(199\) 0.391632 0.678326i 0.0277621 0.0480853i −0.851811 0.523850i \(-0.824495\pi\)
0.879573 + 0.475765i \(0.157829\pi\)
\(200\) 1.18115 + 2.57000i 0.0835198 + 0.181726i
\(201\) 7.68431 4.43654i 0.542009 0.312929i
\(202\) 4.04510 + 12.2832i 0.284612 + 0.864245i
\(203\) −1.00140 + 0.569731i −0.0702845 + 0.0399873i
\(204\) −0.625205 0.846294i −0.0437731 0.0592524i
\(205\) 3.67534 + 6.36588i 0.256697 + 0.444612i
\(206\) 2.95224 14.1658i 0.205692 0.986978i
\(207\) −8.16972 4.71679i −0.567835 0.327839i
\(208\) 2.16275 + 9.43491i 0.149960 + 0.654193i
\(209\) 23.0519i 1.59453i
\(210\) −0.708921 + 3.29692i −0.0489202 + 0.227509i
\(211\) 9.22534i 0.635099i 0.948242 + 0.317549i \(0.102860\pi\)
−0.948242 + 0.317549i \(0.897140\pi\)
\(212\) 5.71118 + 2.48858i 0.392246 + 0.170916i
\(213\) 7.78009 + 4.49184i 0.533083 + 0.307776i
\(214\) −8.76646 1.82699i −0.599263 0.124890i
\(215\) 2.90048 + 5.02378i 0.197811 + 0.342619i
\(216\) −7.64505 + 10.7907i −0.520180 + 0.734217i
\(217\) −0.0425494 + 6.71651i −0.00288844 + 0.455946i
\(218\) 25.2001 8.29887i 1.70677 0.562071i
\(219\) 7.64835 4.41578i 0.516828 0.298391i
\(220\) 0.841528 + 7.43747i 0.0567358 + 0.501434i
\(221\) −0.706272 + 1.22330i −0.0475090 + 0.0822880i
\(222\) 10.7425 + 9.59552i 0.720986 + 0.644009i
\(223\) 24.2380 1.62310 0.811550 0.584284i \(-0.198624\pi\)
0.811550 + 0.584284i \(0.198624\pi\)
\(224\) −14.9653 + 0.202576i −0.999908 + 0.0135352i
\(225\) 2.18770 0.145847
\(226\) 4.40710 + 3.93657i 0.293156 + 0.261857i
\(227\) 5.31623 9.20798i 0.352851 0.611155i −0.633897 0.773417i \(-0.718546\pi\)
0.986748 + 0.162262i \(0.0518791\pi\)
\(228\) −1.24830 11.0325i −0.0826707 0.730648i
\(229\) −25.5589 + 14.7564i −1.68898 + 0.975132i −0.733676 + 0.679499i \(0.762197\pi\)
−0.955302 + 0.295633i \(0.904470\pi\)
\(230\) 5.79223 1.90749i 0.381928 0.125776i
\(231\) −4.51093 + 7.70009i −0.296797 + 0.506629i
\(232\) 0.712029 1.00501i 0.0467470 0.0659819i
\(233\) −14.0351 24.3096i −0.919472 1.59257i −0.800218 0.599709i \(-0.795283\pi\)
−0.119254 0.992864i \(-0.538050\pi\)
\(234\) 7.32940 + 1.52749i 0.479138 + 0.0998553i
\(235\) −10.0256 5.78826i −0.653996 0.377585i
\(236\) −6.36348 2.77281i −0.414227 0.180495i
\(237\) 0.413732i 0.0268748i
\(238\) −1.61963 1.46526i −0.104985 0.0949787i
\(239\) 13.6279i 0.881512i 0.897627 + 0.440756i \(0.145290\pi\)
−0.897627 + 0.440756i \(0.854710\pi\)
\(240\) −0.805504 3.51397i −0.0519951 0.226826i
\(241\) −3.64372 2.10370i −0.234713 0.135512i 0.378031 0.925793i \(-0.376601\pi\)
−0.612744 + 0.790281i \(0.709934\pi\)
\(242\) −0.867332 + 4.16174i −0.0557542 + 0.267527i
\(243\) 8.07194 + 13.9810i 0.517815 + 0.896882i
\(244\) −12.3446 16.7100i −0.790283 1.06975i
\(245\) −0.0886870 + 6.99944i −0.00566601 + 0.447178i
\(246\) −2.93062 8.89904i −0.186850 0.567382i
\(247\) −12.9086 + 7.45276i −0.821352 + 0.474208i
\(248\) −2.99852 6.52433i −0.190406 0.414295i
\(249\) −1.17052 + 2.02740i −0.0741787 + 0.128481i
\(250\) −0.942109 + 1.05472i −0.0595842 + 0.0667062i
\(251\) −18.8826 −1.19186 −0.595928 0.803038i \(-0.703216\pi\)
−0.595928 + 0.803038i \(0.703216\pi\)
\(252\) −4.69140 + 10.5830i −0.295531 + 0.666665i
\(253\) 16.1379 1.01458
\(254\) 4.62610 5.17905i 0.290267 0.324962i
\(255\) 0.263046 0.455610i 0.0164726 0.0285314i
\(256\) 14.4025 6.96913i 0.900155 0.435570i
\(257\) 22.3734 12.9173i 1.39561 0.805757i 0.401682 0.915779i \(-0.368426\pi\)
0.993929 + 0.110022i \(0.0350923\pi\)
\(258\) −2.31277 7.02288i −0.143987 0.437225i
\(259\) 25.7981 + 15.1133i 1.60302 + 0.939092i
\(260\) −3.89275 + 2.87580i −0.241418 + 0.178349i
\(261\) −0.476330 0.825028i −0.0294841 0.0510680i
\(262\) 4.58029 21.9777i 0.282971 1.35779i
\(263\) −9.26400 5.34857i −0.571243 0.329807i 0.186403 0.982473i \(-0.440317\pi\)
−0.757645 + 0.652666i \(0.773650\pi\)
\(264\) 0.884043 9.49923i 0.0544091 0.584637i
\(265\) 3.11491i 0.191347i
\(266\) −7.07012 21.9357i −0.433497 1.34496i
\(267\) 8.90478i 0.544963i
\(268\) −7.86542 + 18.0508i −0.480457 + 1.10263i
\(269\) −7.24441 4.18256i −0.441699 0.255015i 0.262619 0.964900i \(-0.415414\pi\)
−0.704318 + 0.709884i \(0.748747\pi\)
\(270\) −6.47316 1.34905i −0.393944 0.0821004i
\(271\) 13.5557 + 23.4791i 0.823448 + 1.42625i 0.903100 + 0.429430i \(0.141286\pi\)
−0.0796525 + 0.996823i \(0.525381\pi\)
\(272\) 2.23179 + 0.686127i 0.135322 + 0.0416025i
\(273\) −5.77028 0.0365550i −0.349234 0.00221241i
\(274\) 10.5340 3.46906i 0.636385 0.209574i
\(275\) −3.24107 + 1.87123i −0.195444 + 0.112839i
\(276\) −7.72352 + 0.873895i −0.464901 + 0.0526023i
\(277\) −1.67991 + 2.90970i −0.100936 + 0.174827i −0.912071 0.410033i \(-0.865517\pi\)
0.811134 + 0.584860i \(0.198850\pi\)
\(278\) −18.3568 16.3969i −1.10097 0.983420i
\(279\) −5.55380 −0.332497
\(280\) −3.08189 6.81924i −0.184178 0.407527i
\(281\) −7.33947 −0.437836 −0.218918 0.975743i \(-0.570253\pi\)
−0.218918 + 0.975743i \(0.570253\pi\)
\(282\) 11.0046 + 9.82966i 0.655313 + 0.585348i
\(283\) −3.60282 + 6.24027i −0.214165 + 0.370945i −0.953014 0.302926i \(-0.902036\pi\)
0.738849 + 0.673871i \(0.235370\pi\)
\(284\) −19.8090 + 2.24133i −1.17545 + 0.132999i
\(285\) 4.80771 2.77573i 0.284784 0.164420i
\(286\) −12.1650 + 4.00617i −0.719332 + 0.236890i
\(287\) −9.61715 16.9038i −0.567682 0.997799i
\(288\) −0.245892 12.3730i −0.0144893 0.729089i
\(289\) −8.32964 14.4274i −0.489979 0.848668i
\(290\) 0.602884 + 0.125645i 0.0354026 + 0.00737812i
\(291\) −3.54395 2.04610i −0.207750 0.119944i
\(292\) −7.82861 + 17.9663i −0.458135 + 1.05140i
\(293\) 8.47879i 0.495336i −0.968845 0.247668i \(-0.920336\pi\)
0.968845 0.247668i \(-0.0796642\pi\)
\(294\) 1.93085 8.71077i 0.112609 0.508022i
\(295\) 3.47068i 0.202071i
\(296\) −31.8259 2.96187i −1.84984 0.172155i
\(297\) −15.1538 8.74905i −0.879312 0.507671i
\(298\) 0.476525 2.28652i 0.0276044 0.132455i
\(299\) 5.21744 + 9.03686i 0.301732 + 0.522615i
\(300\) 1.44983 1.07107i 0.0837060 0.0618384i
\(301\) −7.58959 13.3400i −0.437457 0.768905i
\(302\) 3.25404 + 9.88112i 0.187249 + 0.568595i
\(303\) 7.13749 4.12083i 0.410038 0.236736i
\(304\) 16.7751 + 18.0454i 0.962120 + 1.03497i
\(305\) 5.19383 8.99597i 0.297398 0.515108i
\(306\) 1.20307 1.34687i 0.0687752 0.0769957i
\(307\) 10.4271 0.595104 0.297552 0.954706i \(-0.403830\pi\)
0.297552 + 0.954706i \(0.403830\pi\)
\(308\) −2.10177 19.6914i −0.119760 1.12202i
\(309\) −9.22183 −0.524612
\(310\) 2.39169 2.67756i 0.135839 0.152075i
\(311\) −3.96296 + 6.86404i −0.224719 + 0.389224i −0.956235 0.292600i \(-0.905480\pi\)
0.731516 + 0.681824i \(0.238813\pi\)
\(312\) 5.60518 2.57609i 0.317331 0.145843i
\(313\) 12.5285 7.23333i 0.708152 0.408852i −0.102224 0.994761i \(-0.532596\pi\)
0.810376 + 0.585910i \(0.199263\pi\)
\(314\) −1.36357 4.14058i −0.0769507 0.233666i
\(315\) −5.78799 0.0366672i −0.326116 0.00206596i
\(316\) −0.545533 0.738447i −0.0306886 0.0415409i
\(317\) −1.76853 3.06318i −0.0993305 0.172046i 0.812077 0.583550i \(-0.198337\pi\)
−0.911408 + 0.411504i \(0.865003\pi\)
\(318\) 0.810024 3.88675i 0.0454239 0.217958i
\(319\) 1.41136 + 0.814851i 0.0790212 + 0.0456229i
\(320\) 6.07110 + 5.20978i 0.339385 + 0.291235i
\(321\) 5.70690i 0.318528i
\(322\) −15.3565 + 4.94957i −0.855782 + 0.275829i
\(323\) 3.59544i 0.200056i
\(324\) −4.30710 1.87677i −0.239283 0.104265i
\(325\) −2.09570 1.20995i −0.116248 0.0671161i
\(326\) 6.25524 + 1.30363i 0.346446 + 0.0722015i
\(327\) −8.45423 14.6432i −0.467520 0.809769i
\(328\) 16.9647 + 12.0192i 0.936717 + 0.663648i
\(329\) 26.4276 + 15.4820i 1.45700 + 0.853552i
\(330\) 4.53078 1.49207i 0.249411 0.0821359i
\(331\) −20.3773 + 11.7649i −1.12004 + 0.646655i −0.941411 0.337261i \(-0.890499\pi\)
−0.178629 + 0.983917i \(0.557166\pi\)
\(332\) −0.584065 5.16199i −0.0320547 0.283301i
\(333\) −12.3613 + 21.4105i −0.677397 + 1.17329i
\(334\) −17.8625 15.9554i −0.977393 0.873040i
\(335\) −9.84499 −0.537890
\(336\) 2.07222 + 9.31041i 0.113049 + 0.507924i
\(337\) 5.10057 0.277846 0.138923 0.990303i \(-0.455636\pi\)
0.138923 + 0.990303i \(0.455636\pi\)
\(338\) 7.53497 + 6.73049i 0.409848 + 0.366090i
\(339\) 1.88298 3.26142i 0.102269 0.177136i
\(340\) 0.131255 + 1.16004i 0.00711829 + 0.0629118i
\(341\) 8.22794 4.75040i 0.445568 0.257249i
\(342\) 18.1006 5.96087i 0.978768 0.322327i
\(343\) 0.351954 18.5169i 0.0190037 0.999819i
\(344\) 13.3880 + 9.48520i 0.721835 + 0.511407i
\(345\) −1.94320 3.36572i −0.104618 0.181204i
\(346\) 0.183715 + 0.0382874i 0.00987658 + 0.00205834i
\(347\) −1.44316 0.833209i −0.0774729 0.0447290i 0.460763 0.887523i \(-0.347576\pi\)
−0.538236 + 0.842794i \(0.680909\pi\)
\(348\) −0.719599 0.313557i −0.0385745 0.0168084i
\(349\) 27.6081i 1.47783i 0.673801 + 0.738913i \(0.264661\pi\)
−0.673801 + 0.738913i \(0.735339\pi\)
\(350\) 2.51022 2.77467i 0.134177 0.148313i
\(351\) 11.3144i 0.603918i
\(352\) 10.9475 + 18.1203i 0.583503 + 0.965815i
\(353\) 23.5193 + 13.5789i 1.25180 + 0.722730i 0.971468 0.237172i \(-0.0762205\pi\)
0.280337 + 0.959902i \(0.409554\pi\)
\(354\) −0.902540 + 4.33067i −0.0479695 + 0.230173i
\(355\) −4.98385 8.63229i −0.264516 0.458154i
\(356\) −11.7415 15.8936i −0.622300 0.842360i
\(357\) −0.703578 + 1.20100i −0.0372373 + 0.0635635i
\(358\) 7.12154 + 21.6251i 0.376385 + 1.14292i
\(359\) 14.5102 8.37747i 0.765819 0.442146i −0.0655619 0.997849i \(-0.520884\pi\)
0.831381 + 0.555703i \(0.187551\pi\)
\(360\) 5.62238 2.58400i 0.296325 0.136189i
\(361\) −9.47002 + 16.4026i −0.498422 + 0.863293i
\(362\) 3.76200 4.21166i 0.197726 0.221360i
\(363\) 2.70926 0.142199
\(364\) 10.3472 7.54325i 0.542343 0.395374i
\(365\) −9.79892 −0.512899
\(366\) −8.82018 + 9.87444i −0.461038 + 0.516145i
\(367\) 4.22213 7.31294i 0.220393 0.381732i −0.734534 0.678572i \(-0.762599\pi\)
0.954927 + 0.296839i \(0.0959326\pi\)
\(368\) 12.6330 11.7437i 0.658540 0.612184i
\(369\) 13.9266 8.04054i 0.724991 0.418574i
\(370\) −4.99899 15.1798i −0.259885 0.789158i
\(371\) 0.0522078 8.24111i 0.00271049 0.427857i
\(372\) −3.68062 + 2.71908i −0.190831 + 0.140978i
\(373\) 5.18861 + 8.98694i 0.268656 + 0.465326i 0.968515 0.248955i \(-0.0800871\pi\)
−0.699859 + 0.714281i \(0.746754\pi\)
\(374\) −0.630311 + 3.02443i −0.0325926 + 0.156390i
\(375\) 0.780530 + 0.450639i 0.0403064 + 0.0232709i
\(376\) −32.6025 3.03414i −1.68134 0.156474i
\(377\) 1.05378i 0.0542723i
\(378\) 17.1034 + 3.67767i 0.879704 + 0.189159i
\(379\) 11.7976i 0.606002i 0.952990 + 0.303001i \(0.0979886\pi\)
−0.952990 + 0.303001i \(0.902011\pi\)
\(380\) −4.92102 + 11.2935i −0.252443 + 0.579346i
\(381\) −3.83268 2.21280i −0.196354 0.113365i
\(382\) 27.7586 + 5.78507i 1.42025 + 0.295990i
\(383\) −0.478522 0.828825i −0.0244514 0.0423510i 0.853541 0.521026i \(-0.174451\pi\)
−0.877992 + 0.478675i \(0.841117\pi\)
\(384\) −6.22067 8.07948i −0.317447 0.412304i
\(385\) 8.60625 4.89639i 0.438615 0.249543i
\(386\) −25.9773 + 8.55483i −1.32221 + 0.435430i
\(387\) 10.9905 6.34537i 0.558679 0.322553i
\(388\) 9.02330 1.02096i 0.458088 0.0518314i
\(389\) 15.0820 26.1228i 0.764689 1.32448i −0.175722 0.984440i \(-0.556226\pi\)
0.940411 0.340041i \(-0.110441\pi\)
\(390\) 2.30035 + 2.05475i 0.116483 + 0.104046i
\(391\) 2.51705 0.127293
\(392\) 8.03945 + 18.0933i 0.406054 + 0.913849i
\(393\) −14.3073 −0.721708
\(394\) −1.72697 1.54259i −0.0870037 0.0777147i
\(395\) 0.229525 0.397549i 0.0115487 0.0200029i
\(396\) 16.2709 1.84101i 0.817645 0.0925142i
\(397\) −5.37540 + 3.10349i −0.269783 + 0.155760i −0.628789 0.777576i \(-0.716449\pi\)
0.359006 + 0.933335i \(0.383116\pi\)
\(398\) 1.05212 0.346483i 0.0527380 0.0173676i
\(399\) −12.7663 + 7.26317i −0.639113 + 0.363613i
\(400\) −1.17544 + 3.82339i −0.0587720 + 0.191170i
\(401\) −13.1565 22.7877i −0.657004 1.13796i −0.981387 0.192038i \(-0.938490\pi\)
0.324384 0.945926i \(-0.394843\pi\)
\(402\) 12.2845 + 2.56017i 0.612694 + 0.127689i
\(403\) 5.32025 + 3.07165i 0.265020 + 0.153010i
\(404\) −7.30571 + 16.7663i −0.363473 + 0.834153i
\(405\) 2.34912i 0.116728i
\(406\) −1.59294 0.342523i −0.0790564 0.0169991i
\(407\) 42.2927i 2.09637i
\(408\) 0.137886 1.48161i 0.00682637 0.0733508i
\(409\) −15.9374 9.20148i −0.788055 0.454984i 0.0512223 0.998687i \(-0.483688\pi\)
−0.839277 + 0.543703i \(0.817022\pi\)
\(410\) −2.12091 + 10.1768i −0.104744 + 0.502595i
\(411\) −3.53400 6.12107i −0.174320 0.301930i
\(412\) 16.4595 12.1596i 0.810902 0.599060i
\(413\) −0.0581707 + 9.18236i −0.00286239 + 0.451834i
\(414\) −4.17302 12.6716i −0.205093 0.622777i
\(415\) 2.24947 1.29873i 0.110422 0.0637523i
\(416\) −6.60762 + 11.9887i −0.323965 + 0.587795i
\(417\) −7.84312 + 13.5847i −0.384079 + 0.665245i
\(418\) −21.7174 + 24.3132i −1.06223 + 1.18920i
\(419\) 35.2426 1.72171 0.860856 0.508848i \(-0.169928\pi\)
0.860856 + 0.508848i \(0.169928\pi\)
\(420\) −3.85377 + 2.80944i −0.188045 + 0.137086i
\(421\) −15.6669 −0.763558 −0.381779 0.924254i \(-0.624688\pi\)
−0.381779 + 0.924254i \(0.624688\pi\)
\(422\) −8.69128 + 9.73014i −0.423085 + 0.473656i
\(423\) −12.6630 + 21.9329i −0.615695 + 1.06641i
\(424\) 3.67917 + 8.00531i 0.178676 + 0.388772i
\(425\) −0.505515 + 0.291859i −0.0245211 + 0.0141573i
\(426\) 3.97400 + 12.0673i 0.192541 + 0.584664i
\(427\) −13.8921 + 23.7136i −0.672285 + 1.14758i
\(428\) −7.52492 10.1859i −0.363731 0.492355i
\(429\) 4.08117 + 7.06879i 0.197041 + 0.341284i
\(430\) −1.67376 + 8.03123i −0.0807159 + 0.387300i
\(431\) −1.73673 1.00270i −0.0836555 0.0482985i 0.457589 0.889164i \(-0.348713\pi\)
−0.541244 + 0.840865i \(0.682047\pi\)
\(432\) −18.2294 + 4.17871i −0.877064 + 0.201048i
\(433\) 13.5978i 0.653469i −0.945116 0.326734i \(-0.894052\pi\)
0.945116 0.326734i \(-0.105948\pi\)
\(434\) −6.37256 + 7.04393i −0.305893 + 0.338120i
\(435\) 0.392473i 0.0188176i
\(436\) 34.3974 + 14.9883i 1.64734 + 0.717809i
\(437\) 23.0022 + 13.2803i 1.10034 + 0.635283i
\(438\) 12.2270 + 2.54818i 0.584228 + 0.121757i
\(439\) −14.5247 25.1574i −0.693224 1.20070i −0.970776 0.239989i \(-0.922856\pi\)
0.277552 0.960711i \(-0.410477\pi\)
\(440\) −6.11933 + 8.63724i −0.291728 + 0.411764i
\(441\) 15.3127 + 0.194020i 0.729174 + 0.00923907i
\(442\) −1.89740 + 0.624849i −0.0902500 + 0.0297211i
\(443\) 12.6757 7.31831i 0.602240 0.347703i −0.167683 0.985841i \(-0.553628\pi\)
0.769922 + 0.638138i \(0.220295\pi\)
\(444\) 2.29023 + 20.2411i 0.108689 + 0.960601i
\(445\) 4.94008 8.55647i 0.234182 0.405616i
\(446\) 25.5643 + 22.8349i 1.21050 + 1.08126i
\(447\) −1.48851 −0.0704040
\(448\) −15.9750 13.8853i −0.754747 0.656016i
\(449\) −27.0699 −1.27751 −0.638754 0.769411i \(-0.720550\pi\)
−0.638754 + 0.769411i \(0.720550\pi\)
\(450\) 2.30740 + 2.06105i 0.108772 + 0.0971589i
\(451\) −13.7548 + 23.8241i −0.647689 + 1.12183i
\(452\) 0.939568 + 8.30395i 0.0441936 + 0.390585i
\(453\) 5.74168 3.31496i 0.269768 0.155750i
\(454\) 14.2820 4.70335i 0.670290 0.220739i
\(455\) 5.52431 + 3.23629i 0.258983 + 0.151720i
\(456\) 9.07725 12.8122i 0.425081 0.599989i
\(457\) 3.80306 + 6.58709i 0.177900 + 0.308131i 0.941161 0.337959i \(-0.109736\pi\)
−0.763261 + 0.646090i \(0.776403\pi\)
\(458\) −40.8596 8.51539i −1.90924 0.397898i
\(459\) −2.36357 1.36461i −0.110322 0.0636943i
\(460\) 7.90623 + 3.44505i 0.368630 + 0.160626i
\(461\) 12.7953i 0.595936i −0.954576 0.297968i \(-0.903691\pi\)
0.954576 0.297968i \(-0.0963089\pi\)
\(462\) −12.0121 + 3.87163i −0.558853 + 0.180125i
\(463\) 27.9178i 1.29745i −0.761024 0.648724i \(-0.775303\pi\)
0.761024 0.648724i \(-0.224697\pi\)
\(464\) 1.69782 0.389188i 0.0788191 0.0180676i
\(465\) −1.98149 1.14402i −0.0918895 0.0530524i
\(466\) 8.09917 38.8624i 0.375187 1.80026i
\(467\) 11.3054 + 19.5815i 0.523152 + 0.906126i 0.999637 + 0.0269432i \(0.00857731\pi\)
−0.476485 + 0.879183i \(0.658089\pi\)
\(468\) 6.29138 + 8.51617i 0.290819 + 0.393660i
\(469\) 26.0469 + 0.165008i 1.20273 + 0.00761937i
\(470\) −5.12097 15.5502i −0.236213 0.717276i
\(471\) −2.40599 + 1.38910i −0.110862 + 0.0640062i
\(472\) −4.09938 8.91963i −0.188689 0.410559i
\(473\) −10.8549 + 18.8013i −0.499110 + 0.864484i
\(474\) −0.389781 + 0.436371i −0.0179032 + 0.0200432i
\(475\) −6.15955 −0.282620
\(476\) −0.327817 3.07130i −0.0150255 0.140773i
\(477\) 6.81448 0.312014
\(478\) −12.8389 + 14.3735i −0.587239 + 0.657430i
\(479\) 10.9907 19.0365i 0.502180 0.869801i −0.497817 0.867282i \(-0.665865\pi\)
0.999997 0.00251901i \(-0.000801826\pi\)
\(480\) 2.46097 4.46512i 0.112327 0.203804i
\(481\) 23.6830 13.6734i 1.07985 0.623453i
\(482\) −1.86118 5.65160i −0.0847744 0.257423i
\(483\) 5.08471 + 8.93726i 0.231362 + 0.406659i
\(484\) −4.83560 + 3.57234i −0.219800 + 0.162379i
\(485\) 2.27022 + 3.93213i 0.103085 + 0.178549i
\(486\) −4.65802 + 22.3507i −0.211292 + 1.01385i
\(487\) −21.9822 12.6914i −0.996108 0.575103i −0.0890138 0.996030i \(-0.528372\pi\)
−0.907095 + 0.420927i \(0.861705\pi\)
\(488\) 2.72254 29.2543i 0.123244 1.32428i
\(489\) 4.07212i 0.184147i
\(490\) −6.68778 + 7.29888i −0.302123 + 0.329730i
\(491\) 36.4635i 1.64557i −0.568350 0.822787i \(-0.692418\pi\)
0.568350 0.822787i \(-0.307582\pi\)
\(492\) 5.29289 12.1469i 0.238622 0.547627i
\(493\) 0.220133 + 0.127094i 0.00991429 + 0.00572402i
\(494\) −20.6362 4.30072i −0.928467 0.193498i
\(495\) 4.09369 + 7.09048i 0.183998 + 0.318693i
\(496\) 2.98403 9.70626i 0.133987 0.435824i
\(497\) 13.0411 + 22.9220i 0.584973 + 1.02819i
\(498\) −3.14460 + 1.03558i −0.140913 + 0.0464053i
\(499\) −10.2874 + 5.93945i −0.460528 + 0.265886i −0.712266 0.701909i \(-0.752331\pi\)
0.251738 + 0.967795i \(0.418998\pi\)
\(500\) −1.98732 + 0.224860i −0.0888756 + 0.0100560i
\(501\) −7.63194 + 13.2189i −0.340970 + 0.590577i
\(502\) −19.9158 17.7894i −0.888884 0.793981i
\(503\) −17.3055 −0.771614 −0.385807 0.922580i \(-0.626077\pi\)
−0.385807 + 0.922580i \(0.626077\pi\)
\(504\) −14.9184 + 6.74224i −0.664520 + 0.300323i
\(505\) −9.14442 −0.406921
\(506\) 17.0209 + 15.2036i 0.756672 + 0.675884i
\(507\) 3.21939 5.57615i 0.142978 0.247646i
\(508\) 9.75846 1.10414i 0.432962 0.0489884i
\(509\) −11.8717 + 6.85414i −0.526205 + 0.303805i −0.739470 0.673190i \(-0.764924\pi\)
0.213265 + 0.976994i \(0.431590\pi\)
\(510\) 0.706674 0.232721i 0.0312921 0.0103051i
\(511\) 25.9250 + 0.164236i 1.14685 + 0.00726537i
\(512\) 21.7562 + 6.21824i 0.961498 + 0.274810i
\(513\) −14.3997 24.9410i −0.635761 1.10117i
\(514\) 35.7671 + 7.45408i 1.57762 + 0.328785i
\(515\) 8.86113 + 5.11597i 0.390468 + 0.225437i
\(516\) 4.17700 9.58603i 0.183882 0.422002i
\(517\) 43.3247i 1.90542i
\(518\) 12.9714 + 40.2449i 0.569930 + 1.76826i
\(519\) 0.119597i 0.00524973i
\(520\) −6.81507 0.634243i −0.298861 0.0278134i
\(521\) 31.4817 + 18.1760i 1.37924 + 0.796304i 0.992068 0.125704i \(-0.0401190\pi\)
0.387171 + 0.922008i \(0.373452\pi\)
\(522\) 0.274873 1.31893i 0.0120309 0.0577279i
\(523\) 2.13211 + 3.69292i 0.0932306 + 0.161480i 0.908869 0.417082i \(-0.136947\pi\)
−0.815638 + 0.578562i \(0.803614\pi\)
\(524\) 25.5363 18.8651i 1.11556 0.824126i
\(525\) −2.05749 1.20534i −0.0897964 0.0526052i
\(526\) −4.73196 14.3689i −0.206323 0.626515i
\(527\) 1.28333 0.740929i 0.0559026 0.0322754i
\(528\) 9.88173 9.18614i 0.430047 0.399776i
\(529\) −2.20289 + 3.81552i −0.0957778 + 0.165892i
\(530\) −2.93459 + 3.28535i −0.127470 + 0.142707i
\(531\) −7.59279 −0.329499
\(532\) 13.2088 29.7968i 0.572675 1.29185i
\(533\) −17.7879 −0.770482
\(534\) −8.38927 + 9.39203i −0.363039 + 0.406433i
\(535\) 3.16601 5.48368i 0.136878 0.237080i
\(536\) −25.3016 + 11.6284i −1.09286 + 0.502270i
\(537\) 12.5658 7.25487i 0.542254 0.313071i
\(538\) −3.70038 11.2364i −0.159535 0.484438i
\(539\) −22.8516 + 12.8101i −0.984288 + 0.551771i
\(540\) −5.55640 7.52129i −0.239110 0.323665i
\(541\) 3.34133 + 5.78736i 0.143655 + 0.248818i 0.928870 0.370405i \(-0.120781\pi\)
−0.785215 + 0.619223i \(0.787448\pi\)
\(542\) −7.82248 + 37.5347i −0.336004 + 1.61225i
\(543\) −3.11679 1.79948i −0.133754 0.0772229i
\(544\) 1.70750 + 2.82626i 0.0732084 + 0.121175i
\(545\) 18.7605i 0.803614i
\(546\) −6.05158 5.47479i −0.258984 0.234300i
\(547\) 45.6888i 1.95351i 0.214353 + 0.976756i \(0.431236\pi\)
−0.214353 + 0.976756i \(0.568764\pi\)
\(548\) 14.3787 + 6.26534i 0.614226 + 0.267642i
\(549\) −19.6805 11.3625i −0.839942 0.484941i
\(550\) −5.18132 1.07982i −0.220932 0.0460436i
\(551\) 1.34113 + 2.32290i 0.0571339 + 0.0989589i
\(552\) −8.96944 6.35469i −0.381765 0.270474i
\(553\) −0.613918 + 1.04795i −0.0261064 + 0.0445633i
\(554\) −4.51309 + 1.48625i −0.191743 + 0.0631445i
\(555\) −8.82059 + 5.09257i −0.374413 + 0.216168i
\(556\) −3.91355 34.5882i −0.165972 1.46687i
\(557\) −2.44203 + 4.22972i −0.103472 + 0.179219i −0.913113 0.407707i \(-0.866329\pi\)
0.809641 + 0.586926i \(0.199662\pi\)
\(558\) −5.85769 5.23229i −0.247976 0.221500i
\(559\) −14.0378 −0.593734
\(560\) 3.17394 10.0958i 0.134124 0.426627i
\(561\) 1.96888 0.0831263
\(562\) −7.74107 6.91459i −0.326538 0.291674i
\(563\) 1.36792 2.36931i 0.0576509 0.0998543i −0.835760 0.549096i \(-0.814972\pi\)
0.893410 + 0.449241i \(0.148306\pi\)
\(564\) 2.34611 + 20.7350i 0.0987891 + 0.873103i
\(565\) −3.61866 + 2.08923i −0.152238 + 0.0878947i
\(566\) −9.67897 + 3.18747i −0.406838 + 0.133979i
\(567\) −0.0393726 + 6.21505i −0.00165349 + 0.261008i
\(568\) −23.0045 16.2983i −0.965248 0.683861i
\(569\) −2.29674 3.97807i −0.0962843 0.166769i 0.813860 0.581062i \(-0.197362\pi\)
−0.910144 + 0.414292i \(0.864029\pi\)
\(570\) 7.68582 + 1.60177i 0.321924 + 0.0670910i
\(571\) −4.86573 2.80923i −0.203625 0.117563i 0.394720 0.918801i \(-0.370841\pi\)
−0.598345 + 0.801239i \(0.704175\pi\)
\(572\) −16.6049 7.23539i −0.694286 0.302527i
\(573\) 18.0707i 0.754912i
\(574\) 5.78185 26.8891i 0.241330 1.12233i
\(575\) 4.31210i 0.179827i
\(576\) 11.3974 13.2817i 0.474892 0.553405i
\(577\) −29.7446 17.1731i −1.23828 0.714924i −0.269541 0.962989i \(-0.586872\pi\)
−0.968743 + 0.248065i \(0.920205\pi\)
\(578\) 4.80673 23.0642i 0.199934 0.959345i
\(579\) 8.71499 + 15.0948i 0.362182 + 0.627318i
\(580\) 0.517501 + 0.700502i 0.0214881 + 0.0290868i
\(581\) −5.97319 + 3.39835i −0.247810 + 0.140987i
\(582\) −1.81021 5.49684i −0.0750358 0.227851i
\(583\) −10.0956 + 5.82872i −0.418118 + 0.241401i
\(584\) −25.1832 + 11.5740i −1.04209 + 0.478935i
\(585\) −2.64701 + 4.58475i −0.109440 + 0.189556i
\(586\) 7.98795 8.94273i 0.329979 0.369421i
\(587\) 40.1422 1.65685 0.828423 0.560103i \(-0.189238\pi\)
0.828423 + 0.560103i \(0.189238\pi\)
\(588\) 10.2430 7.36833i 0.422414 0.303865i
\(589\) 15.6369 0.644309
\(590\) 3.26976 3.66058i 0.134614 0.150704i
\(591\) −0.737868 + 1.27802i −0.0303518 + 0.0525709i
\(592\) −30.7769 33.1074i −1.26492 1.36071i
\(593\) 9.46884 5.46684i 0.388839 0.224496i −0.292818 0.956168i \(-0.594593\pi\)
0.681657 + 0.731672i \(0.261260\pi\)
\(594\) −7.74042 23.5043i −0.317593 0.964394i
\(595\) 1.34233 0.763699i 0.0550303 0.0313086i
\(596\) 2.65675 1.96269i 0.108825 0.0803951i
\(597\) −0.352969 0.611361i −0.0144461 0.0250213i
\(598\) −3.01079 + 14.4467i −0.123120 + 0.590771i
\(599\) −4.51466 2.60654i −0.184464 0.106500i 0.404924 0.914350i \(-0.367298\pi\)
−0.589388 + 0.807850i \(0.700631\pi\)
\(600\) 2.53823 + 0.236220i 0.103623 + 0.00964363i
\(601\) 16.1103i 0.657154i 0.944477 + 0.328577i \(0.106569\pi\)
−0.944477 + 0.328577i \(0.893431\pi\)
\(602\) 4.56287 21.2202i 0.185969 0.864869i
\(603\) 21.5379i 0.877090i
\(604\) −5.87700 + 13.4875i −0.239132 + 0.548797i
\(605\) −2.60329 1.50301i −0.105839 0.0611060i
\(606\) 11.4103 + 2.37798i 0.463512 + 0.0965989i
\(607\) −4.82810 8.36252i −0.195967 0.339424i 0.751250 0.660017i \(-0.229451\pi\)
−0.947217 + 0.320593i \(0.896118\pi\)
\(608\) 0.692317 + 34.8368i 0.0280772 + 1.41282i
\(609\) −0.00657809 + 1.03837i −0.000266558 + 0.0420767i
\(610\) 13.9532 4.59506i 0.564949 0.186048i
\(611\) 24.2609 14.0070i 0.981491 0.566664i
\(612\) 2.53781 0.287146i 0.102585 0.0116072i
\(613\) −3.92388 + 6.79635i −0.158484 + 0.274502i −0.934322 0.356430i \(-0.883994\pi\)
0.775838 + 0.630932i \(0.217327\pi\)
\(614\) 10.9976 + 9.82343i 0.443827 + 0.396441i
\(615\) 6.62501 0.267146
\(616\) 16.3347 22.7490i 0.658143 0.916582i
\(617\) −28.8434 −1.16119 −0.580597 0.814191i \(-0.697181\pi\)
−0.580597 + 0.814191i \(0.697181\pi\)
\(618\) −9.72643 8.68797i −0.391254 0.349481i
\(619\) −1.24278 + 2.15256i −0.0499517 + 0.0865189i −0.889920 0.456116i \(-0.849240\pi\)
0.839968 + 0.542635i \(0.182573\pi\)
\(620\) 5.04511 0.570840i 0.202617 0.0229255i
\(621\) −17.4604 + 10.0807i −0.700660 + 0.404526i
\(622\) −10.6465 + 3.50609i −0.426885 + 0.140581i
\(623\) −13.2134 + 22.5550i −0.529383 + 0.903649i
\(624\) 8.33885 + 2.56364i 0.333821 + 0.102628i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 20.0286 + 4.17409i 0.800504 + 0.166830i
\(627\) 17.9927 + 10.3881i 0.718558 + 0.414860i
\(628\) 2.46269 5.65177i 0.0982722 0.225530i
\(629\) 6.59647i 0.263019i
\(630\) −6.07015 5.49159i −0.241841 0.218790i
\(631\) 8.90728i 0.354593i 0.984157 + 0.177297i \(0.0567352\pi\)
−0.984157 + 0.177297i \(0.943265\pi\)
\(632\) 0.120314 1.29280i 0.00478585 0.0514250i
\(633\) 7.20066 + 4.15730i 0.286200 + 0.165238i
\(634\) 1.02055 4.89694i 0.0405314 0.194482i
\(635\) 2.45518 + 4.25250i 0.0974309 + 0.168755i
\(636\) 4.51609 3.33630i 0.179075 0.132293i
\(637\) −14.5614 8.65485i −0.576944 0.342917i
\(638\) 0.720911 + 2.18910i 0.0285412 + 0.0866672i
\(639\) −18.8848 + 10.9032i −0.747073 + 0.431323i
\(640\) 1.49512 + 11.2145i 0.0590996 + 0.443291i
\(641\) −7.31652 + 12.6726i −0.288985 + 0.500537i −0.973568 0.228398i \(-0.926651\pi\)
0.684583 + 0.728935i \(0.259984\pi\)
\(642\) −5.37653 + 6.01917i −0.212195 + 0.237558i
\(643\) −24.2513 −0.956380 −0.478190 0.878256i \(-0.658707\pi\)
−0.478190 + 0.878256i \(0.658707\pi\)
\(644\) −20.8598 9.24707i −0.821990 0.364386i
\(645\) 5.22827 0.205863
\(646\) −3.38730 + 3.79218i −0.133272 + 0.149201i
\(647\) −14.9578 + 25.9077i −0.588053 + 1.01854i 0.406435 + 0.913680i \(0.366772\pi\)
−0.994487 + 0.104857i \(0.966561\pi\)
\(648\) −2.77465 6.03722i −0.108999 0.237164i
\(649\) 11.2487 6.49444i 0.441550 0.254929i
\(650\) −1.07046 3.25054i −0.0419870 0.127496i
\(651\) 5.22326 + 3.05993i 0.204716 + 0.119928i
\(652\) 5.36935 + 7.26808i 0.210280 + 0.284640i
\(653\) 7.78155 + 13.4780i 0.304516 + 0.527436i 0.977153 0.212535i \(-0.0681721\pi\)
−0.672638 + 0.739972i \(0.734839\pi\)
\(654\) 4.87863 23.4092i 0.190770 0.915373i
\(655\) 13.7477 + 7.93723i 0.537167 + 0.310133i
\(656\) 6.56957 + 28.6594i 0.256498 + 1.11896i
\(657\) 21.4371i 0.836340i
\(658\) 13.2879 + 41.2269i 0.518016 + 1.60719i
\(659\) 30.2702i 1.17916i −0.807710 0.589580i \(-0.799293\pi\)
0.807710 0.589580i \(-0.200707\pi\)
\(660\) 6.18439 + 2.69478i 0.240727 + 0.104894i
\(661\) 15.5209 + 8.96099i 0.603693 + 0.348542i 0.770493 0.637449i \(-0.220010\pi\)
−0.166800 + 0.985991i \(0.553344\pi\)
\(662\) −32.5761 6.78907i −1.26611 0.263865i
\(663\) 0.636547 + 1.10253i 0.0247214 + 0.0428188i
\(664\) 4.24714 5.99470i 0.164821 0.232640i
\(665\) 16.2963 + 0.103238i 0.631944 + 0.00400339i
\(666\) −33.2087 + 10.9363i −1.28681 + 0.423772i
\(667\) 1.62619 0.938880i 0.0629662 0.0363536i
\(668\) −3.80818 33.6569i −0.147343 1.30222i
\(669\) 10.9226 18.9185i 0.422292 0.731432i
\(670\) −10.3837 9.27506i −0.401157 0.358327i
\(671\) 38.8754 1.50077
\(672\) −6.58581 + 11.7721i −0.254053 + 0.454119i
\(673\) 21.1876 0.816723 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(674\) 5.37966 + 4.80529i 0.207217 + 0.185093i
\(675\) 2.33778 4.04915i 0.0899812 0.155852i
\(676\) 1.60641 + 14.1975i 0.0617850 + 0.546059i
\(677\) −21.8732 + 12.6285i −0.840657 + 0.485353i −0.857487 0.514505i \(-0.827976\pi\)
0.0168308 + 0.999858i \(0.494642\pi\)
\(678\) 5.05863 1.66590i 0.194275 0.0639786i
\(679\) −5.94041 10.4413i −0.227972 0.400700i
\(680\) −0.954444 + 1.34717i −0.0366012 + 0.0516615i
\(681\) −4.79140 8.29895i −0.183607 0.318016i
\(682\) 13.1536 + 2.74128i 0.503676 + 0.104969i
\(683\) 19.1391 + 11.0499i 0.732336 + 0.422814i 0.819276 0.573399i \(-0.194376\pi\)
−0.0869404 + 0.996214i \(0.527709\pi\)
\(684\) 24.7068 + 10.7657i 0.944689 + 0.411637i
\(685\) 7.84221i 0.299635i
\(686\) 17.8162 19.1985i 0.680225 0.733004i
\(687\) 26.5993i 1.01483i
\(688\) 5.18452 + 22.6172i 0.197658 + 0.862273i
\(689\) −6.52791 3.76889i −0.248694 0.143583i
\(690\) 1.12135 5.38060i 0.0426891 0.204836i
\(691\) 9.05508 + 15.6839i 0.344471 + 0.596642i 0.985258 0.171077i \(-0.0547248\pi\)
−0.640786 + 0.767719i \(0.721391\pi\)
\(692\) 0.157697 + 0.213462i 0.00599473 + 0.00811461i
\(693\) −10.7118 18.8279i −0.406908 0.715212i
\(694\) −0.737153 2.23841i −0.0279819 0.0849691i
\(695\) 15.0727 8.70222i 0.571740 0.330094i
\(696\) −0.463569 1.00865i −0.0175715 0.0382330i
\(697\) −2.14537 + 3.71588i −0.0812615 + 0.140749i
\(698\) −26.0098 + 29.1187i −0.984486 + 1.10216i
\(699\) −25.2991 −0.956901
\(700\) 5.26162 0.561602i 0.198870 0.0212265i
\(701\) 14.4315 0.545070 0.272535 0.962146i \(-0.412138\pi\)
0.272535 + 0.962146i \(0.412138\pi\)
\(702\) 10.6594 11.9335i 0.402313 0.450401i
\(703\) 34.8038 60.2820i 1.31265 2.27358i
\(704\) −5.52481 + 29.4255i −0.208224 + 1.10902i
\(705\) −9.03582 + 5.21684i −0.340309 + 0.196477i
\(706\) 12.0134 + 36.4796i 0.452131 + 1.37293i
\(707\) 24.1934 + 0.153266i 0.909885 + 0.00576416i
\(708\) −5.03189 + 3.71735i −0.189110 + 0.139706i
\(709\) 18.5131 + 32.0657i 0.695275 + 1.20425i 0.970088 + 0.242753i \(0.0780505\pi\)
−0.274814 + 0.961498i \(0.588616\pi\)
\(710\) 2.87600 13.8000i 0.107934 0.517904i
\(711\) −0.869718 0.502132i −0.0326170 0.0188314i
\(712\) 2.58953 27.8251i 0.0970469 1.04279i
\(713\) 10.9469i 0.409965i
\(714\) −1.87355 + 0.603866i −0.0701157 + 0.0225991i
\(715\) 9.05640i 0.338690i
\(716\) −12.8620 + 29.5176i −0.480674 + 1.10312i
\(717\) 10.6369 + 6.14124i 0.397244 + 0.229349i
\(718\) 23.1967 + 4.83433i 0.865692 + 0.180416i
\(719\) −10.0975 17.4894i −0.376573 0.652243i 0.613988 0.789315i \(-0.289564\pi\)
−0.990561 + 0.137072i \(0.956231\pi\)
\(720\) 8.36443 + 2.57151i 0.311724 + 0.0958345i
\(721\) −23.3581 13.6838i −0.869902 0.509613i
\(722\) −25.4412 + 8.37828i −0.946824 + 0.311807i
\(723\) −3.28401 + 1.89602i −0.122134 + 0.0705138i
\(724\) 7.93570 0.897902i 0.294928 0.0333703i
\(725\) −0.217731 + 0.377122i −0.00808634 + 0.0140060i
\(726\) 2.85750 + 2.55242i 0.106052 + 0.0947292i
\(727\) 10.7925 0.400272 0.200136 0.979768i \(-0.435862\pi\)
0.200136 + 0.979768i \(0.435862\pi\)
\(728\) 18.0200 + 1.79224i 0.667865 + 0.0664248i
\(729\) 7.50278 0.277881
\(730\) −10.3351 9.23166i −0.382519 0.341679i
\(731\) −1.69306 + 2.93247i −0.0626202 + 0.108461i
\(732\) −18.6056 + 2.10517i −0.687683 + 0.0778094i
\(733\) 6.26329 3.61611i 0.231340 0.133564i −0.379850 0.925048i \(-0.624024\pi\)
0.611190 + 0.791484i \(0.290691\pi\)
\(734\) 11.3427 3.73538i 0.418668 0.137875i
\(735\) 5.42330 + 3.22344i 0.200042 + 0.118898i
\(736\) 24.3881 0.484669i 0.898958 0.0178651i
\(737\) −18.4223 31.9083i −0.678593 1.17536i
\(738\) 22.2637 + 4.63990i 0.819539 + 0.170797i
\(739\) 1.71927 + 0.992622i 0.0632444 + 0.0365142i 0.531289 0.847191i \(-0.321708\pi\)
−0.468044 + 0.883705i \(0.655041\pi\)
\(740\) 9.02848 20.7200i 0.331893 0.761681i
\(741\) 13.4340i 0.493511i
\(742\) 7.81909 8.64286i 0.287048 0.317289i
\(743\) 19.8225i 0.727216i 0.931552 + 0.363608i \(0.118455\pi\)
−0.931552 + 0.363608i \(0.881545\pi\)
\(744\) −6.44368 0.599680i −0.236237 0.0219853i
\(745\) 1.43029 + 0.825776i 0.0524016 + 0.0302541i
\(746\) −2.99416 + 14.3669i −0.109624 + 0.526011i
\(747\) −2.84124 4.92116i −0.103955 0.180056i
\(748\) −3.51414 + 2.59610i −0.128490 + 0.0949228i
\(749\) −8.46821 + 14.4551i −0.309421 + 0.528178i
\(750\) 0.398687 + 1.21064i 0.0145580 + 0.0442064i
\(751\) −20.8718 + 12.0504i −0.761624 + 0.439724i −0.829879 0.557944i \(-0.811590\pi\)
0.0682545 + 0.997668i \(0.478257\pi\)
\(752\) −31.5279 33.9153i −1.14971 1.23676i
\(753\) −8.50921 + 14.7384i −0.310093 + 0.537097i
\(754\) −0.992774 + 1.11144i −0.0361547 + 0.0404762i
\(755\) −7.35613 −0.267717
\(756\) 14.5745 + 19.9922i 0.530070 + 0.727109i
\(757\) 34.8711 1.26741 0.633706 0.773574i \(-0.281533\pi\)
0.633706 + 0.773574i \(0.281533\pi\)
\(758\) −11.1146 + 12.4431i −0.403702 + 0.451955i
\(759\) 7.27236 12.5961i 0.263970 0.457209i
\(760\) −15.8300 + 7.27534i −0.574215 + 0.263904i
\(761\) 7.76620 4.48382i 0.281524 0.162538i −0.352589 0.935778i \(-0.614699\pi\)
0.634113 + 0.773240i \(0.281365\pi\)
\(762\) −1.95770 5.94469i −0.0709200 0.215353i
\(763\) 0.314438 49.6347i 0.0113834 1.79690i
\(764\) 23.8273 + 32.2533i 0.862043 + 1.16688i
\(765\) 0.638500 + 1.10591i 0.0230850 + 0.0399844i
\(766\) 0.276138 1.32500i 0.00997727 0.0478741i
\(767\) 7.27349 + 4.19935i 0.262631 + 0.151630i
\(768\) 1.05071 14.3821i 0.0379141 0.518970i
\(769\) 0.573577i 0.0206837i 0.999947 + 0.0103419i \(0.00329197\pi\)
−0.999947 + 0.0103419i \(0.996708\pi\)
\(770\) 13.6901 + 2.94372i 0.493357 + 0.106084i
\(771\) 23.2841i 0.838556i
\(772\) −35.4584 15.4506i −1.27617 0.556078i
\(773\) −3.76591 2.17425i −0.135450 0.0782023i 0.430744 0.902474i \(-0.358251\pi\)
−0.566194 + 0.824272i \(0.691585\pi\)
\(774\) 17.5699 + 3.66168i 0.631537 + 0.131616i
\(775\) 1.26933 + 2.19854i 0.0455955 + 0.0789738i
\(776\) 10.4789 + 7.42411i 0.376170 + 0.266510i
\(777\) 23.4220 13.3256i 0.840259 0.478052i
\(778\) 40.5179 13.3433i 1.45264 0.478381i
\(779\) −39.2109 + 22.6384i −1.40488 + 0.811107i
\(780\) 0.490420 + 4.33436i 0.0175599 + 0.155195i
\(781\) 18.6519 32.3060i 0.667417 1.15600i
\(782\) 2.65478 + 2.37134i 0.0949348 + 0.0847990i
\(783\) −2.03603 −0.0727618
\(784\) −8.56651 + 26.6574i −0.305947 + 0.952049i
\(785\) 3.08251 0.110019
\(786\) −15.0902 13.4790i −0.538249 0.480782i
\(787\) −10.5248 + 18.2295i −0.375168 + 0.649811i −0.990352 0.138573i \(-0.955748\pi\)
0.615184 + 0.788384i \(0.289082\pi\)
\(788\) −0.368181 3.25400i −0.0131159 0.115919i
\(789\) −8.34944 + 4.82055i −0.297248 + 0.171616i
\(790\) 0.616619 0.203065i 0.0219383 0.00722471i
\(791\) 9.60890 5.46683i 0.341653 0.194378i
\(792\) 18.8957 + 13.3873i 0.671428 + 0.475695i
\(793\) 12.5686 + 21.7694i 0.446323 + 0.773054i
\(794\) −8.59335 1.79091i −0.304967 0.0635570i
\(795\) 2.43128 + 1.40370i 0.0862286 + 0.0497841i
\(796\) 1.43611 + 0.625770i 0.0509017 + 0.0221798i
\(797\) 14.7349i 0.521938i 0.965347 + 0.260969i \(0.0840420\pi\)
−0.965347 + 0.260969i \(0.915958\pi\)
\(798\) −20.3075 4.36663i −0.718879 0.154577i
\(799\) 6.75744i 0.239061i
\(800\) −4.84181 + 2.92521i −0.171184 + 0.103422i
\(801\) −18.7190 10.8074i −0.661403 0.381861i
\(802\) 7.59213 36.4295i 0.268087 1.28637i
\(803\) −18.3360 31.7590i −0.647065 1.12075i
\(804\) 10.5447 + 14.2736i 0.371883 + 0.503390i
\(805\) 0.0722735 11.4085i 0.00254731 0.402097i
\(806\) 2.71753 + 8.25198i 0.0957210 + 0.290663i
\(807\) −6.52923 + 3.76965i −0.229840 + 0.132698i
\(808\) −23.5011 + 10.8009i −0.826767 + 0.379975i
\(809\) 7.23808 12.5367i 0.254477 0.440768i −0.710276 0.703923i \(-0.751430\pi\)
0.964753 + 0.263156i \(0.0847632\pi\)
\(810\) 2.21312 2.47765i 0.0777613 0.0870559i
\(811\) −18.5825 −0.652521 −0.326260 0.945280i \(-0.605789\pi\)
−0.326260 + 0.945280i \(0.605789\pi\)
\(812\) −1.35741 1.86199i −0.0476358 0.0653431i
\(813\) 24.4348 0.856967
\(814\) 39.8444 44.6069i 1.39654 1.56347i
\(815\) −2.25908 + 3.91284i −0.0791321 + 0.137061i
\(816\) 1.54127 1.43278i 0.0539553 0.0501573i
\(817\) −30.9442 + 17.8656i −1.08260 + 0.625040i
\(818\) −8.14069 24.7198i −0.284633 0.864306i
\(819\) 7.08003 12.0855i 0.247396 0.422302i
\(820\) −11.8246 + 8.73551i −0.412933 + 0.305057i
\(821\) 8.20275 + 14.2076i 0.286278 + 0.495848i 0.972918 0.231149i \(-0.0742486\pi\)
−0.686640 + 0.726997i \(0.740915\pi\)
\(822\) 2.03934 9.78542i 0.0711303 0.341306i
\(823\) −38.0161 21.9486i −1.32516 0.765081i −0.340612 0.940204i \(-0.610634\pi\)
−0.984547 + 0.175123i \(0.943968\pi\)
\(824\) 28.8158 + 2.68173i 1.00385 + 0.0934226i
\(825\) 3.37300i 0.117433i
\(826\) −8.71214 + 9.63000i −0.303134 + 0.335070i
\(827\) 8.10796i 0.281941i −0.990014 0.140971i \(-0.954978\pi\)
0.990014 0.140971i \(-0.0450224\pi\)
\(828\) 7.53673 17.2964i 0.261919 0.601093i
\(829\) −36.5657 21.1112i −1.26998 0.733223i −0.294995 0.955499i \(-0.595318\pi\)
−0.974984 + 0.222276i \(0.928651\pi\)
\(830\) 3.59611 + 0.749452i 0.124823 + 0.0260138i
\(831\) 1.51407 + 2.62245i 0.0525225 + 0.0909716i
\(832\) −18.2639 + 6.41961i −0.633185 + 0.222560i
\(833\) −3.56421 + 1.99802i −0.123492 + 0.0692273i
\(834\) −21.0705 + 6.93893i −0.729613 + 0.240275i
\(835\) 14.6668 8.46791i 0.507567 0.293044i
\(836\) −45.8114 + 5.18343i −1.58442 + 0.179273i
\(837\) −5.93481 + 10.2794i −0.205137 + 0.355308i
\(838\) 37.1710 + 33.2024i 1.28405 + 1.14696i
\(839\) −31.8404 −1.09925 −0.549627 0.835410i \(-0.685230\pi\)
−0.549627 + 0.835410i \(0.685230\pi\)
\(840\) −6.71143 0.667509i −0.231566 0.0230312i
\(841\) −28.8104 −0.993461
\(842\) −16.5242 14.7599i −0.569460 0.508661i
\(843\) −3.30745 + 5.72868i −0.113915 + 0.197306i
\(844\) −18.3337 + 2.07441i −0.631072 + 0.0714040i
\(845\) −6.18694 + 3.57203i −0.212837 + 0.122882i
\(846\) −34.0191 + 11.2031i −1.16960 + 0.385171i
\(847\) 6.86233 + 4.02014i 0.235792 + 0.138134i
\(848\) −3.66139 + 11.9095i −0.125733 + 0.408975i
\(849\) 3.24714 + 5.62422i 0.111442 + 0.193023i
\(850\) −0.808139 0.168421i −0.0277190 0.00577681i
\(851\) −42.2015 24.3650i −1.44665 0.835223i
\(852\) −7.17729 + 16.4716i −0.245890 + 0.564306i
\(853\) 16.2023i 0.554755i −0.960761 0.277378i \(-0.910535\pi\)
0.960761 0.277378i \(-0.0894653\pi\)
\(854\) −36.9930 + 11.9233i −1.26587 + 0.408006i
\(855\) 13.4752i 0.460843i
\(856\) 1.65958 17.8326i 0.0567234 0.609505i
\(857\) 35.4659 + 20.4762i 1.21149 + 0.699455i 0.963084 0.269201i \(-0.0867596\pi\)
0.248407 + 0.968656i \(0.420093\pi\)
\(858\) −2.35509 + 11.3005i −0.0804015 + 0.385792i
\(859\) −6.02640 10.4380i −0.205618 0.356141i 0.744711 0.667387i \(-0.232587\pi\)
−0.950329 + 0.311246i \(0.899254\pi\)
\(860\) −9.33165 + 6.89382i −0.318206 + 0.235077i
\(861\) −17.5278 0.111039i −0.597345 0.00378421i
\(862\) −0.887107 2.69376i −0.0302150 0.0917499i
\(863\) −0.494372 + 0.285426i −0.0168286 + 0.00971602i −0.508391 0.861127i \(-0.669759\pi\)
0.491562 + 0.870843i \(0.336426\pi\)
\(864\) −23.1637 12.7668i −0.788045 0.434334i
\(865\) −0.0663486 + 0.114919i −0.00225592 + 0.00390737i
\(866\) 12.8106 14.3418i 0.435323 0.487356i
\(867\) −15.0146 −0.509924
\(868\) −13.3574 + 1.42571i −0.453380 + 0.0483918i
\(869\) 1.71798 0.0582784
\(870\) 0.369753 0.413948i 0.0125358 0.0140342i
\(871\) 11.9120 20.6321i 0.403622 0.699093i
\(872\) 22.1590 + 48.2146i 0.750398 + 1.63275i
\(873\) 8.60232 4.96655i 0.291144 0.168092i
\(874\) 11.7493 + 35.6775i 0.397426 + 1.20681i
\(875\) 1.30833 + 2.29962i 0.0442298 + 0.0777414i
\(876\) 10.4954 + 14.2068i 0.354605 + 0.480003i
\(877\) −9.47193 16.4059i −0.319844 0.553987i 0.660611 0.750728i \(-0.270297\pi\)
−0.980455 + 0.196742i \(0.936964\pi\)
\(878\) 8.38165 40.2178i 0.282867 1.35729i
\(879\) −6.61794 3.82087i −0.223218 0.128875i
\(880\) −14.5914 + 3.34477i −0.491876 + 0.112752i
\(881\) 35.7695i 1.20511i −0.798079 0.602553i \(-0.794150\pi\)
0.798079 0.602553i \(-0.205850\pi\)
\(882\) 15.9677 + 14.6308i 0.537662 + 0.492646i
\(883\) 25.4594i 0.856776i 0.903595 + 0.428388i \(0.140918\pi\)
−0.903595 + 0.428388i \(0.859082\pi\)
\(884\) −2.58990 1.12852i −0.0871076 0.0379561i
\(885\) −2.70897 1.56402i −0.0910609 0.0525740i
\(886\) 20.2639 + 4.22313i 0.680779 + 0.141879i
\(887\) −5.30243 9.18408i −0.178038 0.308371i 0.763170 0.646197i \(-0.223642\pi\)
−0.941209 + 0.337826i \(0.890308\pi\)
\(888\) −16.6538 + 23.5063i −0.558865 + 0.788821i
\(889\) −6.42439 11.2920i −0.215467 0.378721i
\(890\) 13.2715 4.37057i 0.444863 0.146502i
\(891\) 7.61364 4.39574i 0.255067 0.147263i
\(892\) 5.45015 + 48.1687i 0.182485 + 1.61281i
\(893\) 35.6531 61.7530i 1.19309 2.06648i
\(894\) −1.56996 1.40234i −0.0525072 0.0469012i
\(895\) −16.0991 −0.538132
\(896\) −3.76766 29.6952i −0.125869 0.992047i
\(897\) 9.40472 0.314014
\(898\) −28.5511 25.5028i −0.952763 0.851040i
\(899\) 0.552744 0.957381i 0.0184350 0.0319304i
\(900\) 0.491925 + 4.34765i 0.0163975 + 0.144922i
\(901\) −1.57463 + 0.909116i −0.0524587 + 0.0302870i
\(902\) −36.9523 + 12.1691i −1.23038 + 0.405187i
\(903\) −13.8324 0.0876291i −0.460315 0.00291611i
\(904\) −6.83225 + 9.64350i −0.227237 + 0.320738i
\(905\) 1.99658 + 3.45818i 0.0663687 + 0.114954i
\(906\) 9.17891 + 1.91294i 0.304949 + 0.0635533i
\(907\) 13.3054 + 7.68190i 0.441800 + 0.255073i 0.704361 0.709842i \(-0.251234\pi\)
−0.262561 + 0.964915i \(0.584567\pi\)
\(908\) 19.4946 + 8.49454i 0.646951 + 0.281901i
\(909\) 20.0052i 0.663531i
\(910\) 2.77764 + 8.61788i 0.0920779 + 0.285680i
\(911\) 22.0734i 0.731324i 0.930748 + 0.365662i \(0.119157\pi\)
−0.930748 + 0.365662i \(0.880843\pi\)
\(912\) 21.6445 4.96154i 0.716720 0.164293i
\(913\) 8.41856 + 4.86046i 0.278614 + 0.160858i
\(914\) −2.19461 + 10.5304i −0.0725911 + 0.348315i
\(915\) −4.68108 8.10787i −0.154752 0.268038i
\(916\) −35.0729 47.4755i −1.15884 1.56864i
\(917\) −36.2392 21.2299i −1.19672 0.701074i
\(918\) −1.20729 3.66601i −0.0398464 0.120996i
\(919\) 45.1598 26.0730i 1.48968 0.860069i 0.489753 0.871861i \(-0.337087\pi\)
0.999930 + 0.0117923i \(0.00375369\pi\)
\(920\) 5.09323 + 11.0821i 0.167919 + 0.365366i
\(921\) 4.69884 8.13863i 0.154832 0.268177i
\(922\) 12.0546 13.4954i 0.396996 0.444448i
\(923\) 24.1209 0.793949
\(924\) −16.3169 7.23322i −0.536785 0.237955i
\(925\) 11.3008 0.371567
\(926\) 26.3016 29.4454i 0.864323 0.967634i
\(927\) 11.1922 19.3855i 0.367600 0.636702i
\(928\) 2.15737 + 1.18904i 0.0708193 + 0.0390323i
\(929\) 24.8707 14.3591i 0.815982 0.471107i −0.0330469 0.999454i \(-0.510521\pi\)
0.849029 + 0.528346i \(0.177188\pi\)
\(930\) −1.01213 3.07340i −0.0331890 0.100781i
\(931\) −43.1134 0.546272i −1.41298 0.0179033i
\(932\) 45.1549 33.3585i 1.47910 1.09270i
\(933\) 3.57173 + 6.18641i 0.116933 + 0.202534i
\(934\) −6.52394 + 31.3039i −0.213470 + 1.02430i
\(935\) −1.89187 1.09227i −0.0618708 0.0357211i
\(936\) −1.38753 + 14.9093i −0.0453529 + 0.487326i
\(937\) 44.9045i 1.46697i 0.679707 + 0.733484i \(0.262107\pi\)
−0.679707 + 0.733484i \(0.737893\pi\)
\(938\) 27.3167 + 24.7131i 0.891921 + 0.806910i
\(939\) 13.0385i 0.425495i
\(940\) 9.24879 21.2256i 0.301662 0.692301i
\(941\) 15.3727 + 8.87541i 0.501134 + 0.289330i 0.729182 0.684320i \(-0.239901\pi\)
−0.228048 + 0.973650i \(0.573234\pi\)
\(942\) −3.84632 0.801598i −0.125320 0.0261175i
\(943\) 15.8484 + 27.4503i 0.516096 + 0.893905i
\(944\) 4.07957 13.2698i 0.132779 0.431894i
\(945\) −6.25292 + 10.6737i −0.203408 + 0.347214i
\(946\) −29.1618 + 9.60352i −0.948130 + 0.312237i
\(947\) 32.1100 18.5387i 1.04344 0.602428i 0.122631 0.992452i \(-0.460867\pi\)
0.920804 + 0.390025i \(0.127533\pi\)
\(948\) −0.822218 + 0.0930316i −0.0267044 + 0.00302153i
\(949\) 11.8562 20.5356i 0.384869 0.666613i
\(950\) −6.49659 5.80297i −0.210777 0.188273i
\(951\) −3.18787 −0.103374
\(952\) 2.54775 3.54820i 0.0825730 0.114998i
\(953\) −28.5420 −0.924567 −0.462283 0.886732i \(-0.652970\pi\)
−0.462283 + 0.886732i \(0.652970\pi\)
\(954\) 7.18736 + 6.41999i 0.232699 + 0.207855i
\(955\) −10.0250 + 17.3638i −0.324402 + 0.561881i
\(956\) −27.0829 + 3.06435i −0.875923 + 0.0991082i
\(957\) 1.27203 0.734408i 0.0411189 0.0237400i
\(958\) 29.5266 9.72368i 0.953962 0.314158i
\(959\) 0.131440 20.7481i 0.00424442 0.669991i
\(960\) 6.80226 2.39094i 0.219542 0.0771674i
\(961\) 12.2776 + 21.2655i 0.396052 + 0.685983i
\(962\) 37.8607 + 7.89042i 1.22068 + 0.254397i
\(963\) −11.9966 6.92626i −0.386586 0.223196i
\(964\) 3.36141 7.71428i 0.108264 0.248460i
\(965\) 19.3392i 0.622550i
\(966\) −3.05694 + 14.2166i −0.0983554 + 0.457413i
\(967\) 5.33936i 0.171702i 0.996308 + 0.0858510i \(0.0273609\pi\)
−0.996308 + 0.0858510i \(0.972639\pi\)
\(968\) −8.46573 0.787860i −0.272099 0.0253228i
\(969\) 2.80635 + 1.62025i 0.0901530 + 0.0520498i
\(970\) −1.31006 + 6.28608i −0.0420635 + 0.201834i
\(971\) −5.49906 9.52465i −0.176473 0.305660i 0.764197 0.644983i \(-0.223136\pi\)
−0.940670 + 0.339323i \(0.889802\pi\)
\(972\) −25.9697 + 19.1853i −0.832978 + 0.615368i
\(973\) −40.0236 + 22.7708i −1.28310 + 0.729999i
\(974\) −11.2283 34.0955i −0.359778 1.09249i
\(975\) −1.88881 + 1.09050i −0.0604902 + 0.0349241i
\(976\) 30.4323 28.2901i 0.974113 0.905544i
\(977\) 15.7434 27.2684i 0.503676 0.872392i −0.496315 0.868142i \(-0.665314\pi\)
0.999991 0.00424979i \(-0.00135275\pi\)
\(978\) 3.83638 4.29493i 0.122674 0.137337i
\(979\) 36.9761 1.18176
\(980\) −13.9301 + 1.39764i −0.444979 + 0.0446460i
\(981\) 41.0424 1.31038
\(982\) 34.3526 38.4587i 1.09624 1.22727i
\(983\) −17.2762 + 29.9232i −0.551025 + 0.954402i 0.447176 + 0.894446i \(0.352430\pi\)
−0.998201 + 0.0599567i \(0.980904\pi\)
\(984\) 17.0263 7.82512i 0.542777 0.249456i
\(985\) 1.41801 0.818690i 0.0451817 0.0260856i
\(986\) 0.112442 + 0.341438i 0.00358088 + 0.0108736i
\(987\) 23.9935 13.6507i 0.763722 0.434507i
\(988\) −17.7136 23.9776i −0.563545 0.762829i
\(989\) 12.5072 + 21.6630i 0.397704 + 0.688844i
\(990\) −2.36232 + 11.3352i −0.0750794 + 0.360255i
\(991\) 47.8668 + 27.6359i 1.52054 + 0.877884i 0.999707 + 0.0242247i \(0.00771173\pi\)
0.520833 + 0.853659i \(0.325622\pi\)
\(992\) 12.2917 7.42608i 0.390261 0.235778i
\(993\) 21.2068i 0.672978i
\(994\) −7.84033 + 36.4623i −0.248680 + 1.15652i
\(995\) 0.783264i 0.0248311i
\(996\) −4.29229 1.87032i −0.136007 0.0592632i
\(997\) 13.2344 + 7.64087i 0.419137 + 0.241989i 0.694708 0.719292i \(-0.255534\pi\)
−0.275571 + 0.961281i \(0.588867\pi\)
\(998\) −16.4459 3.42744i −0.520587 0.108494i
\(999\) 26.4187 + 45.7586i 0.835851 + 1.44774i
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 140.2.o.a.31.13 yes 32
4.3 odd 2 inner 140.2.o.a.31.9 32
5.2 odd 4 700.2.t.c.199.6 32
5.3 odd 4 700.2.t.d.199.11 32
5.4 even 2 700.2.p.c.451.4 32
7.2 even 3 980.2.o.f.411.9 32
7.3 odd 6 980.2.g.a.391.8 32
7.4 even 3 980.2.g.a.391.7 32
7.5 odd 6 inner 140.2.o.a.131.9 yes 32
7.6 odd 2 980.2.o.f.31.13 32
20.3 even 4 700.2.t.d.199.16 32
20.7 even 4 700.2.t.c.199.1 32
20.19 odd 2 700.2.p.c.451.8 32
28.3 even 6 980.2.g.a.391.5 32
28.11 odd 6 980.2.g.a.391.6 32
28.19 even 6 inner 140.2.o.a.131.13 yes 32
28.23 odd 6 980.2.o.f.411.13 32
28.27 even 2 980.2.o.f.31.9 32
35.12 even 12 700.2.t.d.299.16 32
35.19 odd 6 700.2.p.c.551.8 32
35.33 even 12 700.2.t.c.299.1 32
140.19 even 6 700.2.p.c.551.4 32
140.47 odd 12 700.2.t.d.299.11 32
140.103 odd 12 700.2.t.c.299.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.9 32 4.3 odd 2 inner
140.2.o.a.31.13 yes 32 1.1 even 1 trivial
140.2.o.a.131.9 yes 32 7.5 odd 6 inner
140.2.o.a.131.13 yes 32 28.19 even 6 inner
700.2.p.c.451.4 32 5.4 even 2
700.2.p.c.451.8 32 20.19 odd 2
700.2.p.c.551.4 32 140.19 even 6
700.2.p.c.551.8 32 35.19 odd 6
700.2.t.c.199.1 32 20.7 even 4
700.2.t.c.199.6 32 5.2 odd 4
700.2.t.c.299.1 32 35.33 even 12
700.2.t.c.299.6 32 140.103 odd 12
700.2.t.d.199.11 32 5.3 odd 4
700.2.t.d.199.16 32 20.3 even 4
700.2.t.d.299.11 32 140.47 odd 12
700.2.t.d.299.16 32 35.12 even 12
980.2.g.a.391.5 32 28.3 even 6
980.2.g.a.391.6 32 28.11 odd 6
980.2.g.a.391.7 32 7.4 even 3
980.2.g.a.391.8 32 7.3 odd 6
980.2.o.f.31.9 32 28.27 even 2
980.2.o.f.31.13 32 7.6 odd 2
980.2.o.f.411.9 32 7.2 even 3
980.2.o.f.411.13 32 28.23 odd 6