Properties

Label 224.2.u.b.29.4
Level $224$
Weight $2$
Character 224.29
Analytic conductor $1.789$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(29,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.u (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 29.4
Character \(\chi\) \(=\) 224.29
Dual form 224.2.u.b.85.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.420598 - 1.35022i) q^{2} +(2.28471 + 0.946358i) q^{3} +(-1.64619 + 1.13580i) q^{4} +(0.446012 + 1.07677i) q^{5} +(0.316848 - 3.48290i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.22597 + 1.74501i) q^{8} +(2.20299 + 2.20299i) q^{9} +O(q^{10})\) \(q+(-0.420598 - 1.35022i) q^{2} +(2.28471 + 0.946358i) q^{3} +(-1.64619 + 1.13580i) q^{4} +(0.446012 + 1.07677i) q^{5} +(0.316848 - 3.48290i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.22597 + 1.74501i) q^{8} +(2.20299 + 2.20299i) q^{9} +(1.26628 - 1.05510i) q^{10} +(2.89205 - 1.19792i) q^{11} +(-4.83595 + 1.03709i) q^{12} +(1.10101 - 2.65808i) q^{13} +(1.25216 + 0.657343i) q^{14} +2.88219i q^{15} +(1.41991 - 3.73950i) q^{16} +3.12612i q^{17} +(2.04795 - 3.90110i) q^{18} +(-1.63944 + 3.95797i) q^{19} +(-1.95722 - 1.26599i) q^{20} +(-2.28471 + 0.946358i) q^{21} +(-2.83385 - 3.40106i) q^{22} +(-1.37407 - 1.37407i) q^{23} +(3.43429 + 6.09341i) q^{24} +(2.57503 - 2.57503i) q^{25} +(-4.05208 - 0.368627i) q^{26} +(0.109304 + 0.263882i) q^{27} +(0.360903 - 1.96717i) q^{28} +(-8.15384 - 3.37743i) q^{29} +(3.89159 - 1.21224i) q^{30} -2.07787 q^{31} +(-5.64636 - 0.344370i) q^{32} +7.74116 q^{33} +(4.22095 - 1.31484i) q^{34} +(-1.07677 - 0.446012i) q^{35} +(-6.12871 - 1.12439i) q^{36} +(-2.47273 - 5.96970i) q^{37} +(6.03368 + 0.548898i) q^{38} +(5.03099 - 5.03099i) q^{39} +(-0.886163 + 3.17515i) q^{40} +(-5.68545 - 5.68545i) q^{41} +(2.23874 + 2.68683i) q^{42} +(5.63921 - 2.33584i) q^{43} +(-3.40027 + 5.25681i) q^{44} +(-1.38955 + 3.35467i) q^{45} +(-1.27737 + 2.43323i) q^{46} +8.41845i q^{47} +(6.78300 - 7.19993i) q^{48} -1.00000i q^{49} +(-4.55992 - 2.39381i) q^{50} +(-2.95843 + 7.14227i) q^{51} +(1.20657 + 5.62624i) q^{52} +(-12.4599 + 5.16105i) q^{53} +(0.310327 - 0.258573i) q^{54} +(2.57977 + 2.57977i) q^{55} +(-2.80791 + 0.340089i) q^{56} +(-7.49132 + 7.49132i) q^{57} +(-1.13079 + 12.4300i) q^{58} +(2.20741 + 5.32915i) q^{59} +(-3.27359 - 4.74464i) q^{60} +(4.89845 + 2.02901i) q^{61} +(0.873946 + 2.80558i) q^{62} -3.11550 q^{63} +(1.90987 + 7.76868i) q^{64} +3.35320 q^{65} +(-3.25592 - 10.4523i) q^{66} +(8.29598 + 3.43631i) q^{67} +(-3.55065 - 5.14620i) q^{68} +(-1.83899 - 4.43972i) q^{69} +(-0.149328 + 1.64147i) q^{70} +(6.35827 - 6.35827i) q^{71} +(1.05955 + 8.74803i) q^{72} +(-10.6870 - 10.6870i) q^{73} +(-7.02039 + 5.84958i) q^{74} +(8.32011 - 3.44630i) q^{75} +(-1.79662 - 8.37767i) q^{76} +(-1.19792 + 2.89205i) q^{77} +(-8.90897 - 4.67692i) q^{78} +5.81518i q^{79} +(4.65987 - 0.138945i) q^{80} -8.64016i q^{81} +(-5.28533 + 10.0679i) q^{82} +(-1.91430 + 4.62153i) q^{83} +(2.68620 - 4.15287i) q^{84} +(-3.36610 + 1.39428i) q^{85} +(-5.52574 - 6.63173i) q^{86} +(-15.4329 - 15.4329i) q^{87} +(8.52800 + 2.38011i) q^{88} +(5.79482 - 5.79482i) q^{89} +(5.11399 + 0.465231i) q^{90} +(1.10101 + 2.65808i) q^{91} +(3.82266 + 0.701318i) q^{92} +(-4.74732 - 1.96641i) q^{93} +(11.3668 - 3.54079i) q^{94} -4.99302 q^{95} +(-12.5744 - 6.13027i) q^{96} +13.8362 q^{97} +(-1.35022 + 0.420598i) q^{98} +(9.01017 + 3.73213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9} - 16 q^{10} + 12 q^{11} - 36 q^{12} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 52 q^{22} + 16 q^{23} - 8 q^{24} - 16 q^{25} + 12 q^{26} - 32 q^{27} + 8 q^{28} + 16 q^{29} + 36 q^{30} + 24 q^{31} - 36 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{36} + 16 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 8 q^{41} + 52 q^{43} - 44 q^{44} - 64 q^{45} - 32 q^{46} - 36 q^{48} + 52 q^{50} + 16 q^{51} - 16 q^{52} - 32 q^{54} - 8 q^{55} + 12 q^{56} - 8 q^{57} + 40 q^{58} + 20 q^{59} + 52 q^{60} - 16 q^{61} - 12 q^{62} - 24 q^{63} - 48 q^{64} - 80 q^{65} - 40 q^{66} - 4 q^{67} - 4 q^{68} - 40 q^{69} + 32 q^{70} + 72 q^{72} - 24 q^{73} - 12 q^{74} + 20 q^{75} - 72 q^{76} + 4 q^{77} + 12 q^{78} + 60 q^{80} + 16 q^{82} + 4 q^{83} + 8 q^{84} - 64 q^{85} - 48 q^{86} - 32 q^{87} + 16 q^{88} + 32 q^{89} + 20 q^{90} + 108 q^{92} - 24 q^{93} + 68 q^{94} - 80 q^{95} - 40 q^{96} + 56 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.420598 1.35022i −0.297408 0.954751i
\(3\) 2.28471 + 0.946358i 1.31908 + 0.546380i 0.927520 0.373773i \(-0.121936\pi\)
0.391558 + 0.920153i \(0.371936\pi\)
\(4\) −1.64619 + 1.13580i −0.823097 + 0.567900i
\(5\) 0.446012 + 1.07677i 0.199462 + 0.481545i 0.991685 0.128687i \(-0.0410762\pi\)
−0.792223 + 0.610232i \(0.791076\pi\)
\(6\) 0.316848 3.48290i 0.129353 1.42189i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 2.22597 + 1.74501i 0.786999 + 0.616954i
\(9\) 2.20299 + 2.20299i 0.734330 + 0.734330i
\(10\) 1.26628 1.05510i 0.400434 0.333652i
\(11\) 2.89205 1.19792i 0.871985 0.361188i 0.0986018 0.995127i \(-0.468563\pi\)
0.773383 + 0.633939i \(0.218563\pi\)
\(12\) −4.83595 + 1.03709i −1.39602 + 0.299381i
\(13\) 1.10101 2.65808i 0.305366 0.737218i −0.694478 0.719514i \(-0.744364\pi\)
0.999843 0.0177038i \(-0.00563558\pi\)
\(14\) 1.25216 + 0.657343i 0.334653 + 0.175682i
\(15\) 2.88219i 0.744178i
\(16\) 1.41991 3.73950i 0.354978 0.934875i
\(17\) 3.12612i 0.758195i 0.925357 + 0.379097i \(0.123765\pi\)
−0.925357 + 0.379097i \(0.876235\pi\)
\(18\) 2.04795 3.90110i 0.482707 0.919498i
\(19\) −1.63944 + 3.95797i −0.376114 + 0.908021i 0.616572 + 0.787299i \(0.288521\pi\)
−0.992686 + 0.120722i \(0.961479\pi\)
\(20\) −1.95722 1.26599i −0.437647 0.283084i
\(21\) −2.28471 + 0.946358i −0.498565 + 0.206512i
\(22\) −2.83385 3.40106i −0.604179 0.725108i
\(23\) −1.37407 1.37407i −0.286514 0.286514i 0.549186 0.835700i \(-0.314938\pi\)
−0.835700 + 0.549186i \(0.814938\pi\)
\(24\) 3.43429 + 6.09341i 0.701022 + 1.24381i
\(25\) 2.57503 2.57503i 0.515006 0.515006i
\(26\) −4.05208 0.368627i −0.794678 0.0722937i
\(27\) 0.109304 + 0.263882i 0.0210355 + 0.0507842i
\(28\) 0.360903 1.96717i 0.0682042 0.371760i
\(29\) −8.15384 3.37743i −1.51413 0.627173i −0.537724 0.843121i \(-0.680716\pi\)
−0.976405 + 0.215948i \(0.930716\pi\)
\(30\) 3.89159 1.21224i 0.710504 0.221324i
\(31\) −2.07787 −0.373196 −0.186598 0.982436i \(-0.559746\pi\)
−0.186598 + 0.982436i \(0.559746\pi\)
\(32\) −5.64636 0.344370i −0.998145 0.0608765i
\(33\) 7.74116 1.34756
\(34\) 4.22095 1.31484i 0.723887 0.225493i
\(35\) −1.07677 0.446012i −0.182007 0.0753897i
\(36\) −6.12871 1.12439i −1.02145 0.187399i
\(37\) −2.47273 5.96970i −0.406515 0.981413i −0.986047 0.166464i \(-0.946765\pi\)
0.579533 0.814949i \(-0.303235\pi\)
\(38\) 6.03368 + 0.548898i 0.978793 + 0.0890431i
\(39\) 5.03099 5.03099i 0.805603 0.805603i
\(40\) −0.886163 + 3.17515i −0.140115 + 0.502035i
\(41\) −5.68545 5.68545i −0.887918 0.887918i 0.106405 0.994323i \(-0.466066\pi\)
−0.994323 + 0.106405i \(0.966066\pi\)
\(42\) 2.23874 + 2.68683i 0.345445 + 0.414587i
\(43\) 5.63921 2.33584i 0.859972 0.356212i 0.0912753 0.995826i \(-0.470906\pi\)
0.768697 + 0.639614i \(0.220906\pi\)
\(44\) −3.40027 + 5.25681i −0.512609 + 0.792493i
\(45\) −1.38955 + 3.35467i −0.207142 + 0.500084i
\(46\) −1.27737 + 2.43323i −0.188338 + 0.358761i
\(47\) 8.41845i 1.22796i 0.789322 + 0.613979i \(0.210432\pi\)
−0.789322 + 0.613979i \(0.789568\pi\)
\(48\) 6.78300 7.19993i 0.979041 1.03922i
\(49\) 1.00000i 0.142857i
\(50\) −4.55992 2.39381i −0.644870 0.338536i
\(51\) −2.95843 + 7.14227i −0.414263 + 1.00012i
\(52\) 1.20657 + 5.62624i 0.167321 + 0.780220i
\(53\) −12.4599 + 5.16105i −1.71150 + 0.708925i −0.711517 + 0.702669i \(0.751991\pi\)
−0.999980 + 0.00625642i \(0.998009\pi\)
\(54\) 0.310327 0.258573i 0.0422301 0.0351873i
\(55\) 2.57977 + 2.57977i 0.347857 + 0.347857i
\(56\) −2.80791 + 0.340089i −0.375222 + 0.0454463i
\(57\) −7.49132 + 7.49132i −0.992249 + 0.992249i
\(58\) −1.13079 + 12.4300i −0.148480 + 1.63214i
\(59\) 2.20741 + 5.32915i 0.287380 + 0.693797i 0.999970 0.00778433i \(-0.00247785\pi\)
−0.712590 + 0.701581i \(0.752478\pi\)
\(60\) −3.27359 4.74464i −0.422619 0.612531i
\(61\) 4.89845 + 2.02901i 0.627183 + 0.259788i 0.673556 0.739137i \(-0.264766\pi\)
−0.0463728 + 0.998924i \(0.514766\pi\)
\(62\) 0.873946 + 2.80558i 0.110991 + 0.356309i
\(63\) −3.11550 −0.392516
\(64\) 1.90987 + 7.76868i 0.238734 + 0.971085i
\(65\) 3.35320 0.415913
\(66\) −3.25592 10.4523i −0.400776 1.28659i
\(67\) 8.29598 + 3.43631i 1.01352 + 0.419812i 0.826736 0.562590i \(-0.190195\pi\)
0.186780 + 0.982402i \(0.440195\pi\)
\(68\) −3.55065 5.14620i −0.430579 0.624068i
\(69\) −1.83899 4.43972i −0.221389 0.534480i
\(70\) −0.149328 + 1.64147i −0.0178481 + 0.196193i
\(71\) 6.35827 6.35827i 0.754587 0.754587i −0.220744 0.975332i \(-0.570849\pi\)
0.975332 + 0.220744i \(0.0708486\pi\)
\(72\) 1.05955 + 8.74803i 0.124869 + 1.03097i
\(73\) −10.6870 10.6870i −1.25082 1.25082i −0.955355 0.295460i \(-0.904527\pi\)
−0.295460 0.955355i \(-0.595473\pi\)
\(74\) −7.02039 + 5.84958i −0.816104 + 0.680000i
\(75\) 8.32011 3.44630i 0.960723 0.397945i
\(76\) −1.79662 8.37767i −0.206087 0.960985i
\(77\) −1.19792 + 2.89205i −0.136516 + 0.329579i
\(78\) −8.90897 4.67692i −1.00874 0.529557i
\(79\) 5.81518i 0.654259i 0.944980 + 0.327129i \(0.106081\pi\)
−0.944980 + 0.327129i \(0.893919\pi\)
\(80\) 4.65987 0.138945i 0.520989 0.0155345i
\(81\) 8.64016i 0.960018i
\(82\) −5.28533 + 10.0679i −0.583667 + 1.11181i
\(83\) −1.91430 + 4.62153i −0.210122 + 0.507279i −0.993442 0.114340i \(-0.963525\pi\)
0.783320 + 0.621619i \(0.213525\pi\)
\(84\) 2.68620 4.15287i 0.293089 0.453115i
\(85\) −3.36610 + 1.39428i −0.365105 + 0.151231i
\(86\) −5.52574 6.63173i −0.595856 0.715118i
\(87\) −15.4329 15.4329i −1.65458 1.65458i
\(88\) 8.52800 + 2.38011i 0.909088 + 0.253720i
\(89\) 5.79482 5.79482i 0.614249 0.614249i −0.329801 0.944050i \(-0.606982\pi\)
0.944050 + 0.329801i \(0.106982\pi\)
\(90\) 5.11399 + 0.465231i 0.539061 + 0.0490397i
\(91\) 1.10101 + 2.65808i 0.115417 + 0.278642i
\(92\) 3.82266 + 0.701318i 0.398540 + 0.0731174i
\(93\) −4.74732 1.96641i −0.492274 0.203907i
\(94\) 11.3668 3.54079i 1.17239 0.365204i
\(95\) −4.99302 −0.512274
\(96\) −12.5744 6.13027i −1.28337 0.625668i
\(97\) 13.8362 1.40485 0.702424 0.711759i \(-0.252101\pi\)
0.702424 + 0.711759i \(0.252101\pi\)
\(98\) −1.35022 + 0.420598i −0.136393 + 0.0424868i
\(99\) 9.01017 + 3.73213i 0.905556 + 0.375094i
\(100\) −1.31428 + 7.16373i −0.131428 + 0.716373i
\(101\) 1.30081 + 3.14044i 0.129436 + 0.312486i 0.975290 0.220928i \(-0.0709087\pi\)
−0.845854 + 0.533414i \(0.820909\pi\)
\(102\) 10.8880 + 0.990503i 1.07807 + 0.0980744i
\(103\) 9.32632 9.32632i 0.918950 0.918950i −0.0780034 0.996953i \(-0.524854\pi\)
0.996953 + 0.0780034i \(0.0248545\pi\)
\(104\) 7.08919 3.99552i 0.695153 0.391793i
\(105\) −2.03802 2.03802i −0.198890 0.198890i
\(106\) 12.2092 + 14.6529i 1.18586 + 1.42321i
\(107\) −15.7923 + 6.54138i −1.52670 + 0.632379i −0.978920 0.204245i \(-0.934526\pi\)
−0.547778 + 0.836624i \(0.684526\pi\)
\(108\) −0.479653 0.310255i −0.0461546 0.0298543i
\(109\) 0.154193 0.372256i 0.0147690 0.0356556i −0.916323 0.400440i \(-0.868857\pi\)
0.931092 + 0.364784i \(0.118857\pi\)
\(110\) 2.39822 4.56831i 0.228661 0.435571i
\(111\) 15.9791i 1.51667i
\(112\) 1.64020 + 3.64825i 0.154984 + 0.344728i
\(113\) 3.18758i 0.299863i 0.988696 + 0.149931i \(0.0479053\pi\)
−0.988696 + 0.149931i \(0.952095\pi\)
\(114\) 13.2658 + 6.96410i 1.24245 + 0.652248i
\(115\) 0.866704 2.09241i 0.0808206 0.195118i
\(116\) 17.2589 3.70123i 1.60245 0.343651i
\(117\) 8.28124 3.43020i 0.765601 0.317122i
\(118\) 6.26710 5.22192i 0.576934 0.480717i
\(119\) −2.21050 2.21050i −0.202636 0.202636i
\(120\) −5.02945 + 6.41566i −0.459124 + 0.585667i
\(121\) −0.849266 + 0.849266i −0.0772060 + 0.0772060i
\(122\) 0.679326 7.46739i 0.0615033 0.676066i
\(123\) −7.60914 18.3701i −0.686093 1.65637i
\(124\) 3.42057 2.36004i 0.307176 0.211938i
\(125\) 9.30504 + 3.85427i 0.832268 + 0.344737i
\(126\) 1.31037 + 4.20661i 0.116737 + 0.374755i
\(127\) 12.5601 1.11453 0.557264 0.830335i \(-0.311851\pi\)
0.557264 + 0.830335i \(0.311851\pi\)
\(128\) 9.68615 5.84624i 0.856142 0.516740i
\(129\) 15.0945 1.32900
\(130\) −1.41035 4.52756i −0.123696 0.397093i
\(131\) 2.81182 + 1.16470i 0.245670 + 0.101760i 0.502121 0.864797i \(-0.332553\pi\)
−0.256451 + 0.966557i \(0.582553\pi\)
\(132\) −12.7434 + 8.79241i −1.10917 + 0.765281i
\(133\) −1.63944 3.95797i −0.142158 0.343200i
\(134\) 1.15050 12.6467i 0.0993882 1.09251i
\(135\) −0.235389 + 0.235389i −0.0202591 + 0.0202591i
\(136\) −5.45511 + 6.95864i −0.467772 + 0.596698i
\(137\) −5.08861 5.08861i −0.434750 0.434750i 0.455491 0.890240i \(-0.349464\pi\)
−0.890240 + 0.455491i \(0.849464\pi\)
\(138\) −5.22113 + 4.35039i −0.444452 + 0.370330i
\(139\) −14.5495 + 6.02660i −1.23407 + 0.511170i −0.901857 0.432034i \(-0.857796\pi\)
−0.332216 + 0.943204i \(0.607796\pi\)
\(140\) 2.27915 0.488772i 0.192623 0.0413087i
\(141\) −7.96687 + 19.2337i −0.670932 + 1.61977i
\(142\) −11.2593 5.91079i −0.944863 0.496023i
\(143\) 9.00621i 0.753137i
\(144\) 11.3661 5.11003i 0.947178 0.425836i
\(145\) 10.2862i 0.854219i
\(146\) −9.93485 + 18.9247i −0.822214 + 1.56622i
\(147\) 0.946358 2.28471i 0.0780543 0.188440i
\(148\) 10.8510 + 7.01876i 0.891946 + 0.576939i
\(149\) 5.50184 2.27894i 0.450728 0.186698i −0.145759 0.989320i \(-0.546562\pi\)
0.596488 + 0.802622i \(0.296562\pi\)
\(150\) −8.15269 9.78448i −0.665664 0.798899i
\(151\) 1.49240 + 1.49240i 0.121450 + 0.121450i 0.765219 0.643770i \(-0.222630\pi\)
−0.643770 + 0.765219i \(0.722630\pi\)
\(152\) −10.5561 + 5.94947i −0.856209 + 0.482566i
\(153\) −6.88680 + 6.88680i −0.556765 + 0.556765i
\(154\) 4.40875 + 0.401074i 0.355267 + 0.0323195i
\(155\) −0.926752 2.23738i −0.0744385 0.179711i
\(156\) −2.56778 + 13.9962i −0.205587 + 1.12059i
\(157\) 7.30817 + 3.02714i 0.583256 + 0.241592i 0.654746 0.755849i \(-0.272776\pi\)
−0.0714904 + 0.997441i \(0.522776\pi\)
\(158\) 7.85178 2.44585i 0.624654 0.194582i
\(159\) −33.3515 −2.64494
\(160\) −2.14754 6.23341i −0.169778 0.492794i
\(161\) 1.94323 0.153148
\(162\) −11.6661 + 3.63404i −0.916578 + 0.285517i
\(163\) −15.8361 6.55953i −1.24038 0.513782i −0.336547 0.941667i \(-0.609259\pi\)
−0.903833 + 0.427885i \(0.859259\pi\)
\(164\) 15.8169 + 2.90182i 1.23509 + 0.226594i
\(165\) 3.45265 + 8.33543i 0.268788 + 0.648912i
\(166\) 7.04524 + 0.640922i 0.546817 + 0.0497452i
\(167\) 11.0870 11.0870i 0.857936 0.857936i −0.133159 0.991095i \(-0.542512\pi\)
0.991095 + 0.133159i \(0.0425119\pi\)
\(168\) −6.73710 1.88028i −0.519779 0.145067i
\(169\) 3.33924 + 3.33924i 0.256864 + 0.256864i
\(170\) 3.29837 + 3.95855i 0.252973 + 0.303607i
\(171\) −12.3311 + 5.10769i −0.942979 + 0.390595i
\(172\) −6.63019 + 10.2503i −0.505547 + 0.781576i
\(173\) −5.85781 + 14.1420i −0.445361 + 1.07520i 0.528679 + 0.848822i \(0.322687\pi\)
−0.974040 + 0.226375i \(0.927313\pi\)
\(174\) −14.3468 + 27.3289i −1.08763 + 2.07180i
\(175\) 3.64165i 0.275283i
\(176\) −0.373186 12.5158i −0.0281300 0.943410i
\(177\) 14.2646i 1.07219i
\(178\) −10.2616 5.38700i −0.769137 0.403772i
\(179\) −9.54957 + 23.0547i −0.713768 + 1.72319i −0.0234048 + 0.999726i \(0.507451\pi\)
−0.690363 + 0.723463i \(0.742549\pi\)
\(180\) −1.52277 7.10069i −0.113500 0.529254i
\(181\) 17.0976 7.08206i 1.27086 0.526405i 0.357631 0.933863i \(-0.383585\pi\)
0.913224 + 0.407457i \(0.133585\pi\)
\(182\) 3.12591 2.60459i 0.231708 0.193065i
\(183\) 9.27139 + 9.27139i 0.685361 + 0.685361i
\(184\) −0.660871 5.45641i −0.0487201 0.402252i
\(185\) 5.32512 5.32512i 0.391510 0.391510i
\(186\) −0.658367 + 7.23700i −0.0482738 + 0.530643i
\(187\) 3.74485 + 9.04087i 0.273851 + 0.661134i
\(188\) −9.56169 13.8584i −0.697358 1.01073i
\(189\) −0.263882 0.109304i −0.0191946 0.00795067i
\(190\) 2.10006 + 6.74169i 0.152354 + 0.489093i
\(191\) −4.40429 −0.318683 −0.159342 0.987223i \(-0.550937\pi\)
−0.159342 + 0.987223i \(0.550937\pi\)
\(192\) −2.98844 + 19.5566i −0.215672 + 1.41138i
\(193\) −23.3123 −1.67805 −0.839027 0.544090i \(-0.816875\pi\)
−0.839027 + 0.544090i \(0.816875\pi\)
\(194\) −5.81946 18.6819i −0.417813 1.34128i
\(195\) 7.66108 + 3.17332i 0.548622 + 0.227247i
\(196\) 1.13580 + 1.64619i 0.0811286 + 0.117585i
\(197\) −5.07285 12.2469i −0.361426 0.872559i −0.995092 0.0989524i \(-0.968451\pi\)
0.633667 0.773606i \(-0.281549\pi\)
\(198\) 1.24955 13.7354i 0.0888014 0.976136i
\(199\) −16.2874 + 16.2874i −1.15458 + 1.15458i −0.168961 + 0.985623i \(0.554041\pi\)
−0.985623 + 0.168961i \(0.945959\pi\)
\(200\) 10.2254 1.23848i 0.723045 0.0875739i
\(201\) 15.7019 + 15.7019i 1.10753 + 1.10753i
\(202\) 3.69317 3.07725i 0.259851 0.216515i
\(203\) 8.15384 3.37743i 0.572287 0.237049i
\(204\) −3.24206 15.1178i −0.226989 1.05845i
\(205\) 3.58613 8.65768i 0.250466 0.604679i
\(206\) −16.5152 8.66996i −1.15067 0.604065i
\(207\) 6.05414i 0.420792i
\(208\) −8.37654 7.89147i −0.580808 0.547175i
\(209\) 13.4106i 0.927628i
\(210\) −1.89459 + 3.60896i −0.130739 + 0.249042i
\(211\) 2.78349 6.71993i 0.191623 0.462619i −0.798643 0.601805i \(-0.794448\pi\)
0.990266 + 0.139186i \(0.0444485\pi\)
\(212\) 14.6495 22.6481i 1.00613 1.55547i
\(213\) 20.5440 8.50960i 1.40765 0.583068i
\(214\) 15.4745 + 18.5718i 1.05782 + 1.26954i
\(215\) 5.03031 + 5.03031i 0.343064 + 0.343064i
\(216\) −0.217171 + 0.778130i −0.0147766 + 0.0529451i
\(217\) 1.46927 1.46927i 0.0997407 0.0997407i
\(218\) −0.567481 0.0516251i −0.0384346 0.00349649i
\(219\) −14.3029 34.5303i −0.966503 2.33334i
\(220\) −7.17692 1.31670i −0.483868 0.0887718i
\(221\) 8.30946 + 3.44189i 0.558955 + 0.231527i
\(222\) −21.5754 + 6.72080i −1.44804 + 0.451070i
\(223\) 20.9072 1.40005 0.700026 0.714118i \(-0.253172\pi\)
0.700026 + 0.714118i \(0.253172\pi\)
\(224\) 4.23609 3.74908i 0.283035 0.250496i
\(225\) 11.3455 0.756370
\(226\) 4.30394 1.34069i 0.286294 0.0891815i
\(227\) −0.817212 0.338500i −0.0542403 0.0224670i 0.355398 0.934715i \(-0.384345\pi\)
−0.409639 + 0.912248i \(0.634345\pi\)
\(228\) 3.82352 20.8408i 0.253219 1.38022i
\(229\) 4.36923 + 10.5483i 0.288727 + 0.697049i 0.999983 0.00588476i \(-0.00187319\pi\)
−0.711256 + 0.702933i \(0.751873\pi\)
\(230\) −3.18975 0.290179i −0.210326 0.0191338i
\(231\) −5.47382 + 5.47382i −0.360151 + 0.360151i
\(232\) −12.2565 21.7466i −0.804681 1.42773i
\(233\) 15.1524 + 15.1524i 0.992666 + 0.992666i 0.999973 0.00730773i \(-0.00232614\pi\)
−0.00730773 + 0.999973i \(0.502326\pi\)
\(234\) −8.11460 9.73877i −0.530468 0.636643i
\(235\) −9.06472 + 3.75473i −0.591317 + 0.244931i
\(236\) −9.68668 6.26565i −0.630549 0.407859i
\(237\) −5.50324 + 13.2860i −0.357474 + 0.863019i
\(238\) −2.05493 + 3.91439i −0.133201 + 0.253732i
\(239\) 1.59391i 0.103101i −0.998670 0.0515507i \(-0.983584\pi\)
0.998670 0.0515507i \(-0.0164164\pi\)
\(240\) 10.7779 + 4.09246i 0.695713 + 0.264167i
\(241\) 6.77065i 0.436136i −0.975934 0.218068i \(-0.930025\pi\)
0.975934 0.218068i \(-0.0699755\pi\)
\(242\) 1.50390 + 0.789497i 0.0966741 + 0.0507508i
\(243\) 8.50460 20.5319i 0.545570 1.31712i
\(244\) −10.3684 + 2.22353i −0.663766 + 0.142347i
\(245\) 1.07677 0.446012i 0.0687921 0.0284946i
\(246\) −21.6033 + 18.0004i −1.37738 + 1.14767i
\(247\) 8.71554 + 8.71554i 0.554557 + 0.554557i
\(248\) −4.62526 3.62590i −0.293705 0.230245i
\(249\) −8.74725 + 8.74725i −0.554334 + 0.554334i
\(250\) 1.29044 14.1850i 0.0816146 0.897136i
\(251\) 11.2855 + 27.2456i 0.712335 + 1.71973i 0.694084 + 0.719894i \(0.255810\pi\)
0.0182507 + 0.999833i \(0.494190\pi\)
\(252\) 5.12872 3.53859i 0.323079 0.222910i
\(253\) −5.61992 2.32785i −0.353321 0.146350i
\(254\) −5.28275 16.9589i −0.331470 1.06410i
\(255\) −9.01006 −0.564232
\(256\) −11.9677 10.6195i −0.747981 0.663720i
\(257\) 2.47679 0.154498 0.0772490 0.997012i \(-0.475386\pi\)
0.0772490 + 0.997012i \(0.475386\pi\)
\(258\) −6.34872 20.3809i −0.395254 1.26886i
\(259\) 5.96970 + 2.47273i 0.370939 + 0.153648i
\(260\) −5.52001 + 3.80856i −0.342337 + 0.236197i
\(261\) −10.5224 25.4033i −0.651319 1.57242i
\(262\) 0.389949 4.28645i 0.0240911 0.264818i
\(263\) 3.92237 3.92237i 0.241864 0.241864i −0.575757 0.817621i \(-0.695293\pi\)
0.817621 + 0.575757i \(0.195293\pi\)
\(264\) 17.2316 + 13.5084i 1.06053 + 0.831385i
\(265\) −11.1145 11.1145i −0.682759 0.682759i
\(266\) −4.65459 + 3.87833i −0.285391 + 0.237796i
\(267\) 18.7235 7.75551i 1.14586 0.474629i
\(268\) −17.5598 + 3.76575i −1.07263 + 0.230030i
\(269\) −9.45451 + 22.8252i −0.576452 + 1.39168i 0.319525 + 0.947578i \(0.396477\pi\)
−0.895977 + 0.444100i \(0.853523\pi\)
\(270\) 0.416832 + 0.218823i 0.0253676 + 0.0133172i
\(271\) 16.2549i 0.987416i 0.869628 + 0.493708i \(0.164359\pi\)
−0.869628 + 0.493708i \(0.835641\pi\)
\(272\) 11.6901 + 4.43881i 0.708817 + 0.269142i
\(273\) 7.11489i 0.430613i
\(274\) −4.73049 + 9.01102i −0.285779 + 0.544375i
\(275\) 4.36242 10.5318i 0.263064 0.635092i
\(276\) 8.06999 + 5.21992i 0.485756 + 0.314202i
\(277\) −25.6162 + 10.6106i −1.53913 + 0.637528i −0.981310 0.192434i \(-0.938362\pi\)
−0.557819 + 0.829963i \(0.688362\pi\)
\(278\) 14.2567 + 17.1103i 0.855063 + 1.02621i
\(279\) −4.57752 4.57752i −0.274049 0.274049i
\(280\) −1.61856 2.87178i −0.0967272 0.171622i
\(281\) −7.89840 + 7.89840i −0.471179 + 0.471179i −0.902296 0.431117i \(-0.858120\pi\)
0.431117 + 0.902296i \(0.358120\pi\)
\(282\) 29.3206 + 2.66737i 1.74602 + 0.158840i
\(283\) −6.85592 16.5517i −0.407542 0.983894i −0.985782 0.168027i \(-0.946260\pi\)
0.578240 0.815867i \(-0.303740\pi\)
\(284\) −3.24522 + 17.6887i −0.192568 + 1.04963i
\(285\) −11.4076 4.72519i −0.675729 0.279896i
\(286\) −12.1604 + 3.78800i −0.719058 + 0.223989i
\(287\) 8.04044 0.474612
\(288\) −11.6802 13.1975i −0.688265 0.777672i
\(289\) 7.22740 0.425141
\(290\) −13.8886 + 4.32634i −0.815566 + 0.254051i
\(291\) 31.6116 + 13.0940i 1.85311 + 0.767581i
\(292\) 29.7311 + 5.45456i 1.73988 + 0.319204i
\(293\) −2.86595 6.91901i −0.167431 0.404213i 0.817787 0.575521i \(-0.195201\pi\)
−0.985218 + 0.171308i \(0.945201\pi\)
\(294\) −3.48290 0.316848i −0.203127 0.0184789i
\(295\) −4.75373 + 4.75373i −0.276773 + 0.276773i
\(296\) 4.91297 17.6033i 0.285561 1.02317i
\(297\) 0.632223 + 0.632223i 0.0366853 + 0.0366853i
\(298\) −5.39113 6.47019i −0.312300 0.374808i
\(299\) −5.16526 + 2.13952i −0.298715 + 0.123732i
\(300\) −9.78220 + 15.1233i −0.564776 + 0.873142i
\(301\) −2.33584 + 5.63921i −0.134635 + 0.325039i
\(302\) 1.38737 2.64277i 0.0798342 0.152075i
\(303\) 8.40604i 0.482914i
\(304\) 12.4730 + 11.7507i 0.715373 + 0.673947i
\(305\) 6.17946i 0.353835i
\(306\) 12.1953 + 6.40213i 0.697158 + 0.365986i
\(307\) 3.67610 8.87490i 0.209806 0.506517i −0.783586 0.621283i \(-0.786612\pi\)
0.993393 + 0.114766i \(0.0366118\pi\)
\(308\) −1.31277 6.12148i −0.0748021 0.348803i
\(309\) 30.1340 12.4819i 1.71426 0.710071i
\(310\) −2.63116 + 2.19236i −0.149440 + 0.124518i
\(311\) 11.5111 + 11.5111i 0.652732 + 0.652732i 0.953650 0.300918i \(-0.0972930\pi\)
−0.300918 + 0.953650i \(0.597293\pi\)
\(312\) 19.9780 2.41969i 1.13103 0.136988i
\(313\) 4.54430 4.54430i 0.256859 0.256859i −0.566916 0.823775i \(-0.691864\pi\)
0.823775 + 0.566916i \(0.191864\pi\)
\(314\) 1.01351 11.1409i 0.0571957 0.628715i
\(315\) −1.38955 3.35467i −0.0782922 0.189014i
\(316\) −6.60489 9.57292i −0.371554 0.538519i
\(317\) −1.26017 0.521981i −0.0707784 0.0293174i 0.347013 0.937860i \(-0.387196\pi\)
−0.417792 + 0.908543i \(0.637196\pi\)
\(318\) 14.0276 + 45.0318i 0.786626 + 2.52526i
\(319\) −27.6272 −1.54683
\(320\) −7.51323 + 5.52141i −0.420003 + 0.308656i
\(321\) −42.2713 −2.35935
\(322\) −0.817320 2.62379i −0.0455475 0.146218i
\(323\) −12.3731 5.12510i −0.688456 0.285168i
\(324\) 9.81350 + 14.2234i 0.545195 + 0.790188i
\(325\) −4.00950 9.67978i −0.222407 0.536937i
\(326\) −2.19618 + 24.1412i −0.121635 + 1.33706i
\(327\) 0.704574 0.704574i 0.0389630 0.0389630i
\(328\) −2.73446 22.5768i −0.150985 1.24660i
\(329\) −5.95275 5.95275i −0.328185 0.328185i
\(330\) 9.80249 8.16770i 0.539609 0.449617i
\(331\) 6.90232 2.85903i 0.379386 0.157147i −0.184837 0.982769i \(-0.559176\pi\)
0.564223 + 0.825622i \(0.309176\pi\)
\(332\) −2.09783 9.78220i −0.115133 0.536868i
\(333\) 7.70380 18.5986i 0.422165 1.01920i
\(334\) −19.6330 10.3067i −1.07427 0.563958i
\(335\) 10.4655i 0.571790i
\(336\) 0.294816 + 9.88742i 0.0160835 + 0.539403i
\(337\) 20.8441i 1.13545i −0.823219 0.567724i \(-0.807824\pi\)
0.823219 0.567724i \(-0.192176\pi\)
\(338\) 3.10423 5.91319i 0.168848 0.321635i
\(339\) −3.01660 + 7.28271i −0.163839 + 0.395543i
\(340\) 3.95763 6.11848i 0.214632 0.331821i
\(341\) −6.00928 + 2.48913i −0.325421 + 0.134794i
\(342\) 12.0829 + 14.5014i 0.653370 + 0.784144i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 16.6288 + 4.64098i 0.896563 + 0.250225i
\(345\) 3.96034 3.96034i 0.213217 0.213217i
\(346\) 21.5586 + 1.96124i 1.15900 + 0.105437i
\(347\) −9.06618 21.8877i −0.486698 1.17499i −0.956372 0.292153i \(-0.905628\pi\)
0.469674 0.882840i \(-0.344372\pi\)
\(348\) 42.9343 + 7.87685i 2.30152 + 0.422244i
\(349\) 7.38704 + 3.05981i 0.395419 + 0.163788i 0.571528 0.820583i \(-0.306351\pi\)
−0.176109 + 0.984371i \(0.556351\pi\)
\(350\) 4.91703 1.53167i 0.262826 0.0818712i
\(351\) 0.821765 0.0438626
\(352\) −16.7421 + 5.76799i −0.892355 + 0.307435i
\(353\) 23.8909 1.27158 0.635792 0.771860i \(-0.280673\pi\)
0.635792 + 0.771860i \(0.280673\pi\)
\(354\) 19.2603 5.99965i 1.02368 0.318878i
\(355\) 9.68223 + 4.01051i 0.513880 + 0.212856i
\(356\) −2.95764 + 16.1212i −0.156754 + 0.854419i
\(357\) −2.95843 7.14227i −0.156577 0.378009i
\(358\) 35.1455 + 3.19727i 1.85750 + 0.168981i
\(359\) 5.53219 5.53219i 0.291978 0.291978i −0.545883 0.837861i \(-0.683806\pi\)
0.837861 + 0.545883i \(0.183806\pi\)
\(360\) −8.94702 + 5.04261i −0.471550 + 0.265769i
\(361\) 0.457282 + 0.457282i 0.0240675 + 0.0240675i
\(362\) −16.7536 20.1069i −0.880548 1.05679i
\(363\) −2.74404 + 1.13662i −0.144025 + 0.0596569i
\(364\) −4.83153 3.12518i −0.253241 0.163804i
\(365\) 6.74087 16.2739i 0.352833 0.851815i
\(366\) 8.61889 16.4179i 0.450517 0.858180i
\(367\) 12.6028i 0.657861i 0.944354 + 0.328931i \(0.106688\pi\)
−0.944354 + 0.328931i \(0.893312\pi\)
\(368\) −7.08941 + 3.18728i −0.369561 + 0.166148i
\(369\) 25.0500i 1.30405i
\(370\) −9.42982 4.95035i −0.490233 0.257356i
\(371\) 5.16105 12.4599i 0.267949 0.646885i
\(372\) 10.0485 2.15493i 0.520988 0.111728i
\(373\) −16.1184 + 6.67648i −0.834582 + 0.345695i −0.758715 0.651423i \(-0.774172\pi\)
−0.0758668 + 0.997118i \(0.524172\pi\)
\(374\) 10.6321 8.85895i 0.549773 0.458086i
\(375\) 17.6118 + 17.6118i 0.909470 + 0.909470i
\(376\) −14.6903 + 18.7392i −0.757594 + 0.966401i
\(377\) −17.9549 + 17.9549i −0.924726 + 0.924726i
\(378\) −0.0365957 + 0.402273i −0.00188228 + 0.0206907i
\(379\) 2.44066 + 5.89228i 0.125368 + 0.302666i 0.974085 0.226182i \(-0.0726243\pi\)
−0.848717 + 0.528848i \(0.822624\pi\)
\(380\) 8.21949 5.67108i 0.421651 0.290920i
\(381\) 28.6962 + 11.8864i 1.47015 + 0.608956i
\(382\) 1.85244 + 5.94677i 0.0947789 + 0.304263i
\(383\) −3.22785 −0.164936 −0.0824678 0.996594i \(-0.526280\pi\)
−0.0824678 + 0.996594i \(0.526280\pi\)
\(384\) 27.6627 4.19042i 1.41166 0.213841i
\(385\) −3.64835 −0.185937
\(386\) 9.80510 + 31.4767i 0.499066 + 1.60212i
\(387\) 17.5690 + 7.27730i 0.893081 + 0.369926i
\(388\) −22.7770 + 15.7151i −1.15633 + 0.797814i
\(389\) 2.46724 + 5.95646i 0.125094 + 0.302004i 0.974003 0.226535i \(-0.0727398\pi\)
−0.848909 + 0.528540i \(0.822740\pi\)
\(390\) 1.06245 11.6789i 0.0537994 0.591382i
\(391\) 4.29551 4.29551i 0.217233 0.217233i
\(392\) 1.74501 2.22597i 0.0881364 0.112428i
\(393\) 5.32198 + 5.32198i 0.268459 + 0.268459i
\(394\) −14.4025 + 12.0005i −0.725585 + 0.604577i
\(395\) −6.26160 + 2.59364i −0.315055 + 0.130500i
\(396\) −19.0715 + 4.08994i −0.958376 + 0.205527i
\(397\) 12.4821 30.1346i 0.626461 1.51241i −0.217530 0.976054i \(-0.569800\pi\)
0.843991 0.536357i \(-0.180200\pi\)
\(398\) 28.8420 + 15.1411i 1.44572 + 0.758957i
\(399\) 10.5943i 0.530379i
\(400\) −5.97301 13.2856i −0.298650 0.664282i
\(401\) 28.3687i 1.41667i 0.705879 + 0.708333i \(0.250552\pi\)
−0.705879 + 0.708333i \(0.749448\pi\)
\(402\) 14.5969 27.8053i 0.728027 1.38680i
\(403\) −2.28775 + 5.52313i −0.113961 + 0.275127i
\(404\) −5.70831 3.69231i −0.283999 0.183699i
\(405\) 9.30344 3.85361i 0.462292 0.191488i
\(406\) −7.98976 9.58894i −0.396525 0.475891i
\(407\) −14.3025 14.3025i −0.708949 0.708949i
\(408\) −19.0487 + 10.7360i −0.943052 + 0.531511i
\(409\) 2.09746 2.09746i 0.103713 0.103713i −0.653346 0.757059i \(-0.726635\pi\)
0.757059 + 0.653346i \(0.226635\pi\)
\(410\) −13.1981 1.20066i −0.651808 0.0592965i
\(411\) −6.81036 16.4417i −0.335930 0.811007i
\(412\) −4.76009 + 25.9458i −0.234513 + 1.27826i
\(413\) −5.32915 2.20741i −0.262230 0.108619i
\(414\) −8.17443 + 2.54636i −0.401751 + 0.125147i
\(415\) −5.83012 −0.286189
\(416\) −7.13207 + 14.6293i −0.349679 + 0.717261i
\(417\) −38.9447 −1.90713
\(418\) 18.1072 5.64046i 0.885654 0.275884i
\(419\) −34.2774 14.1982i −1.67456 0.693627i −0.675519 0.737343i \(-0.736080\pi\)
−0.999044 + 0.0437160i \(0.986080\pi\)
\(420\) 5.66975 + 1.04019i 0.276655 + 0.0507561i
\(421\) −3.26832 7.89042i −0.159288 0.384556i 0.824006 0.566582i \(-0.191734\pi\)
−0.983294 + 0.182026i \(0.941734\pi\)
\(422\) −10.2441 0.931933i −0.498676 0.0453658i
\(423\) −18.5458 + 18.5458i −0.901726 + 0.901726i
\(424\) −36.7414 10.2543i −1.78432 0.497993i
\(425\) 8.04985 + 8.04985i 0.390475 + 0.390475i
\(426\) −20.1306 24.1598i −0.975331 1.17055i
\(427\) −4.89845 + 2.02901i −0.237053 + 0.0981905i
\(428\) 18.5675 28.7053i 0.897492 1.38752i
\(429\) 8.52311 20.5766i 0.411499 0.993448i
\(430\) 4.67629 8.90777i 0.225511 0.429571i
\(431\) 8.09042i 0.389702i −0.980833 0.194851i \(-0.937578\pi\)
0.980833 0.194851i \(-0.0624223\pi\)
\(432\) 1.14199 0.0340511i 0.0549440 0.00163828i
\(433\) 0.959859i 0.0461279i 0.999734 + 0.0230639i \(0.00734213\pi\)
−0.999734 + 0.0230639i \(0.992658\pi\)
\(434\) −2.60182 1.36587i −0.124891 0.0655638i
\(435\) 9.73439 23.5009i 0.466728 1.12678i
\(436\) 0.168976 + 0.787938i 0.00809249 + 0.0377354i
\(437\) 7.69125 3.18582i 0.367923 0.152399i
\(438\) −40.6078 + 33.8355i −1.94032 + 1.61672i
\(439\) 1.19473 + 1.19473i 0.0570214 + 0.0570214i 0.735042 0.678021i \(-0.237162\pi\)
−0.678021 + 0.735042i \(0.737162\pi\)
\(440\) 1.24076 + 10.2442i 0.0591510 + 0.488374i
\(441\) 2.20299 2.20299i 0.104904 0.104904i
\(442\) 1.15237 12.6673i 0.0548127 0.602520i
\(443\) −2.88208 6.95795i −0.136932 0.330582i 0.840507 0.541800i \(-0.182257\pi\)
−0.977439 + 0.211218i \(0.932257\pi\)
\(444\) 18.1491 + 26.3048i 0.861319 + 1.24837i
\(445\) 8.82423 + 3.65511i 0.418308 + 0.173269i
\(446\) −8.79354 28.2294i −0.416386 1.33670i
\(447\) 14.7268 0.696554
\(448\) −6.84377 4.14280i −0.323338 0.195729i
\(449\) 10.6484 0.502530 0.251265 0.967918i \(-0.419153\pi\)
0.251265 + 0.967918i \(0.419153\pi\)
\(450\) −4.77191 15.3190i −0.224950 0.722144i
\(451\) −23.2533 9.63184i −1.09496 0.453546i
\(452\) −3.62046 5.24738i −0.170292 0.246816i
\(453\) 1.99736 + 4.82205i 0.0938442 + 0.226560i
\(454\) −0.113332 + 1.24579i −0.00531895 + 0.0584678i
\(455\) −2.37107 + 2.37107i −0.111157 + 0.111157i
\(456\) −29.7479 + 3.60301i −1.39307 + 0.168726i
\(457\) −10.2751 10.2751i −0.480647 0.480647i 0.424691 0.905338i \(-0.360383\pi\)
−0.905338 + 0.424691i \(0.860383\pi\)
\(458\) 12.4048 10.3360i 0.579638 0.482970i
\(459\) −0.824927 + 0.341696i −0.0385043 + 0.0159490i
\(460\) 0.949797 + 4.42892i 0.0442845 + 0.206499i
\(461\) −11.4376 + 27.6129i −0.532704 + 1.28606i 0.397022 + 0.917809i \(0.370044\pi\)
−0.929726 + 0.368252i \(0.879956\pi\)
\(462\) 9.69315 + 5.08859i 0.450966 + 0.236743i
\(463\) 26.3271i 1.22353i 0.791041 + 0.611763i \(0.209539\pi\)
−0.791041 + 0.611763i \(0.790461\pi\)
\(464\) −24.2076 + 25.6956i −1.12381 + 1.19289i
\(465\) 5.98880i 0.277724i
\(466\) 14.0860 26.8321i 0.652522 1.24297i
\(467\) −3.09988 + 7.48378i −0.143446 + 0.346308i −0.979231 0.202748i \(-0.935013\pi\)
0.835785 + 0.549056i \(0.185013\pi\)
\(468\) −9.73650 + 15.0526i −0.450070 + 0.695808i
\(469\) −8.29598 + 3.43631i −0.383073 + 0.158674i
\(470\) 8.88232 + 10.6601i 0.409711 + 0.491716i
\(471\) 13.8323 + 13.8323i 0.637359 + 0.637359i
\(472\) −4.38581 + 15.7145i −0.201873 + 0.723318i
\(473\) 13.5107 13.5107i 0.621223 0.621223i
\(474\) 20.2537 + 1.84253i 0.930283 + 0.0846301i
\(475\) 5.97028 + 14.4135i 0.273935 + 0.661338i
\(476\) 6.14960 + 1.12822i 0.281866 + 0.0517120i
\(477\) −38.8188 16.0793i −1.77739 0.736219i
\(478\) −2.15213 + 0.670395i −0.0984361 + 0.0306632i
\(479\) 15.3471 0.701229 0.350615 0.936520i \(-0.385973\pi\)
0.350615 + 0.936520i \(0.385973\pi\)
\(480\) 0.992538 16.2739i 0.0453030 0.742798i
\(481\) −18.5904 −0.847651
\(482\) −9.14188 + 2.84772i −0.416401 + 0.129710i
\(483\) 4.43972 + 1.83899i 0.202014 + 0.0836771i
\(484\) 0.433460 2.36265i 0.0197027 0.107393i
\(485\) 6.17109 + 14.8983i 0.280215 + 0.676498i
\(486\) −31.2997 2.84740i −1.41978 0.129161i
\(487\) 21.0309 21.0309i 0.953002 0.953002i −0.0459418 0.998944i \(-0.514629\pi\)
0.998944 + 0.0459418i \(0.0146289\pi\)
\(488\) 7.36317 + 13.0644i 0.333315 + 0.591396i
\(489\) −29.9733 29.9733i −1.35544 1.35544i
\(490\) −1.05510 1.26628i −0.0476646 0.0572048i
\(491\) −26.1876 + 10.8473i −1.18183 + 0.489531i −0.885087 0.465426i \(-0.845901\pi\)
−0.296745 + 0.954957i \(0.595901\pi\)
\(492\) 33.3909 + 21.5983i 1.50538 + 0.973725i
\(493\) 10.5582 25.4898i 0.475519 1.14800i
\(494\) 8.10217 15.4337i 0.364534 0.694393i
\(495\) 11.3664i 0.510883i
\(496\) −2.95039 + 7.77017i −0.132476 + 0.348891i
\(497\) 8.99195i 0.403344i
\(498\) 15.4898 + 8.13165i 0.694115 + 0.364388i
\(499\) −3.17109 + 7.65568i −0.141957 + 0.342715i −0.978828 0.204686i \(-0.934383\pi\)
0.836870 + 0.547401i \(0.184383\pi\)
\(500\) −19.6956 + 4.22379i −0.880814 + 0.188894i
\(501\) 35.8228 14.8383i 1.60044 0.662926i
\(502\) 32.0409 26.6974i 1.43006 1.19156i
\(503\) −2.63641 2.63641i −0.117552 0.117552i 0.645884 0.763436i \(-0.276489\pi\)
−0.763436 + 0.645884i \(0.776489\pi\)
\(504\) −6.93500 5.43658i −0.308910 0.242165i
\(505\) −2.80135 + 2.80135i −0.124658 + 0.124658i
\(506\) −0.779380 + 8.56722i −0.0346477 + 0.380859i
\(507\) 4.46908 + 10.7893i 0.198479 + 0.479170i
\(508\) −20.6764 + 14.2658i −0.917365 + 0.632941i
\(509\) −31.7025 13.1316i −1.40519 0.582048i −0.454095 0.890953i \(-0.650037\pi\)
−0.951093 + 0.308906i \(0.900037\pi\)
\(510\) 3.78961 + 12.1656i 0.167807 + 0.538701i
\(511\) 15.1137 0.668589
\(512\) −9.30511 + 20.6256i −0.411232 + 0.911531i
\(513\) −1.22364 −0.0540249
\(514\) −1.04173 3.34422i −0.0459489 0.147507i
\(515\) 14.2019 + 5.88263i 0.625812 + 0.259220i
\(516\) −24.8485 + 17.1444i −1.09389 + 0.754738i
\(517\) 10.0847 + 24.3466i 0.443524 + 1.07076i
\(518\) 0.827889 9.10045i 0.0363754 0.399851i
\(519\) −26.7668 + 26.7668i −1.17493 + 1.17493i
\(520\) 7.46411 + 5.85136i 0.327323 + 0.256599i
\(521\) −0.988325 0.988325i −0.0432993 0.0432993i 0.685126 0.728425i \(-0.259747\pi\)
−0.728425 + 0.685126i \(0.759747\pi\)
\(522\) −29.8743 + 24.8921i −1.30756 + 1.08950i
\(523\) 31.0730 12.8709i 1.35873 0.562804i 0.420019 0.907515i \(-0.362023\pi\)
0.938709 + 0.344712i \(0.112023\pi\)
\(524\) −5.95167 + 1.27636i −0.260000 + 0.0557579i
\(525\) −3.44630 + 8.32011i −0.150409 + 0.363119i
\(526\) −6.94581 3.64633i −0.302852 0.158987i
\(527\) 6.49565i 0.282955i
\(528\) 10.9918 28.9480i 0.478355 1.25980i
\(529\) 19.2238i 0.835819i
\(530\) −10.3323 + 19.6818i −0.448807 + 0.854922i
\(531\) −6.87718 + 16.6030i −0.298444 + 0.720508i
\(532\) 7.19431 + 4.65351i 0.311913 + 0.201755i
\(533\) −21.3721 + 8.85262i −0.925729 + 0.383450i
\(534\) −18.3467 22.0189i −0.793940 0.952849i
\(535\) −14.0871 14.0871i −0.609038 0.609038i
\(536\) 12.4702 + 22.1257i 0.538631 + 0.955685i
\(537\) −43.6360 + 43.6360i −1.88303 + 1.88303i
\(538\) 34.7956 + 3.16544i 1.50015 + 0.136472i
\(539\) −1.19792 2.89205i −0.0515983 0.124569i
\(540\) 0.120141 0.654852i 0.00517005 0.0281803i
\(541\) 37.8714 + 15.6868i 1.62822 + 0.674430i 0.995031 0.0995678i \(-0.0317460\pi\)
0.633188 + 0.773998i \(0.281746\pi\)
\(542\) 21.9477 6.83679i 0.942736 0.293665i
\(543\) 45.7653 1.96398
\(544\) 1.07654 17.6512i 0.0461562 0.756788i
\(545\) 0.469605 0.0201157
\(546\) 9.60668 2.99251i 0.411128 0.128068i
\(547\) −26.3617 10.9194i −1.12714 0.466878i −0.260335 0.965518i \(-0.583833\pi\)
−0.866809 + 0.498640i \(0.833833\pi\)
\(548\) 14.1565 + 2.59720i 0.604736 + 0.110947i
\(549\) 6.32137 + 15.2611i 0.269789 + 0.651329i
\(550\) −16.0551 1.46057i −0.684592 0.0622789i
\(551\) 26.7355 26.7355i 1.13897 1.13897i
\(552\) 3.65382 13.0918i 0.155517 0.557222i
\(553\) −4.11195 4.11195i −0.174858 0.174858i
\(554\) 25.1008 + 30.1248i 1.06643 + 1.27988i
\(555\) 17.2058 7.12688i 0.730346 0.302519i
\(556\) 17.1063 26.4463i 0.725468 1.12157i
\(557\) 8.84578 21.3556i 0.374808 0.904866i −0.618113 0.786089i \(-0.712103\pi\)
0.992921 0.118777i \(-0.0378973\pi\)
\(558\) −4.25537 + 8.10596i −0.180144 + 0.343153i
\(559\) 17.5613i 0.742762i
\(560\) −3.19678 + 3.39327i −0.135088 + 0.143392i
\(561\) 24.1998i 1.02171i
\(562\) 13.9866 + 7.34254i 0.589991 + 0.309726i
\(563\) −9.18532 + 22.1753i −0.387115 + 0.934578i 0.603433 + 0.797413i \(0.293799\pi\)
−0.990548 + 0.137165i \(0.956201\pi\)
\(564\) −8.73067 40.7113i −0.367628 1.71425i
\(565\) −3.43229 + 1.42170i −0.144397 + 0.0598114i
\(566\) −19.4648 + 16.2186i −0.818167 + 0.681719i
\(567\) 6.10952 + 6.10952i 0.256576 + 0.256576i
\(568\) 25.2485 3.05806i 1.05941 0.128313i
\(569\) 28.4584 28.4584i 1.19304 1.19304i 0.216830 0.976209i \(-0.430428\pi\)
0.976209 0.216830i \(-0.0695717\pi\)
\(570\) −1.58203 + 17.3902i −0.0662639 + 0.728396i
\(571\) 9.61551 + 23.2139i 0.402397 + 0.971472i 0.987083 + 0.160212i \(0.0512178\pi\)
−0.584686 + 0.811260i \(0.698782\pi\)
\(572\) 10.2293 + 14.8260i 0.427707 + 0.619905i
\(573\) −10.0625 4.16804i −0.420368 0.174122i
\(574\) −3.38179 10.8564i −0.141153 0.453136i
\(575\) −7.07656 −0.295113
\(576\) −12.9069 + 21.3218i −0.537787 + 0.888407i
\(577\) −37.8988 −1.57775 −0.788875 0.614554i \(-0.789336\pi\)
−0.788875 + 0.614554i \(0.789336\pi\)
\(578\) −3.03983 9.75858i −0.126440 0.405904i
\(579\) −53.2618 22.0618i −2.21349 0.916856i
\(580\) 11.6830 + 16.9330i 0.485111 + 0.703105i
\(581\) −1.91430 4.62153i −0.0794186 0.191733i
\(582\) 4.38396 48.1900i 0.181721 1.99754i
\(583\) −29.8520 + 29.8520i −1.23634 + 1.23634i
\(584\) −5.13998 42.4377i −0.212694 1.75609i
\(585\) 7.38706 + 7.38706i 0.305417 + 0.305417i
\(586\) −8.13679 + 6.77979i −0.336127 + 0.280070i
\(587\) 11.7280 4.85788i 0.484065 0.200506i −0.127286 0.991866i \(-0.540627\pi\)
0.611351 + 0.791360i \(0.290627\pi\)
\(588\) 1.03709 + 4.83595i 0.0427688 + 0.199431i
\(589\) 3.40655 8.22413i 0.140364 0.338869i
\(590\) 8.41800 + 4.41918i 0.346563 + 0.181935i
\(591\) 32.7815i 1.34845i
\(592\) −25.8348 + 0.770323i −1.06180 + 0.0316601i
\(593\) 15.4713i 0.635332i −0.948203 0.317666i \(-0.897101\pi\)
0.948203 0.317666i \(-0.102899\pi\)
\(594\) 0.587729 1.11955i 0.0241148 0.0459358i
\(595\) 1.39428 3.36610i 0.0571601 0.137997i
\(596\) −6.46868 + 10.0006i −0.264968 + 0.409639i
\(597\) −52.6257 + 21.7983i −2.15383 + 0.892145i
\(598\) 5.06133 + 6.07437i 0.206973 + 0.248399i
\(599\) −15.5082 15.5082i −0.633646 0.633646i 0.315334 0.948981i \(-0.397883\pi\)
−0.948981 + 0.315334i \(0.897883\pi\)
\(600\) 24.5341 + 6.84732i 1.00160 + 0.279541i
\(601\) −7.57636 + 7.57636i −0.309046 + 0.309046i −0.844539 0.535493i \(-0.820126\pi\)
0.535493 + 0.844539i \(0.320126\pi\)
\(602\) 8.59663 + 0.782056i 0.350373 + 0.0318742i
\(603\) 10.7058 + 25.8461i 0.435975 + 1.05254i
\(604\) −4.15186 0.761712i −0.168937 0.0309936i
\(605\) −1.29324 0.535679i −0.0525778 0.0217785i
\(606\) 11.3500 3.53556i 0.461063 0.143623i
\(607\) −3.66019 −0.148562 −0.0742812 0.997237i \(-0.523666\pi\)
−0.0742812 + 0.997237i \(0.523666\pi\)
\(608\) 10.6199 21.7836i 0.430694 0.883440i
\(609\) 21.8254 0.884411
\(610\) 8.34363 2.59907i 0.337824 0.105233i
\(611\) 22.3769 + 9.26882i 0.905273 + 0.374976i
\(612\) 3.51498 19.1591i 0.142085 0.774459i
\(613\) 8.44469 + 20.3873i 0.341078 + 0.823434i 0.997607 + 0.0691341i \(0.0220236\pi\)
−0.656530 + 0.754300i \(0.727976\pi\)
\(614\) −13.5292 1.23079i −0.545995 0.0496705i
\(615\) 16.3865 16.3865i 0.660769 0.660769i
\(616\) −7.71320 + 4.34721i −0.310774 + 0.175154i
\(617\) −24.7446 24.7446i −0.996179 0.996179i 0.00381394 0.999993i \(-0.498786\pi\)
−0.999993 + 0.00381394i \(0.998786\pi\)
\(618\) −29.5276 35.4377i −1.18778 1.42551i
\(619\) 4.13930 1.71455i 0.166373 0.0689138i −0.297943 0.954584i \(-0.596300\pi\)
0.464315 + 0.885670i \(0.346300\pi\)
\(620\) 4.06683 + 2.63055i 0.163328 + 0.105646i
\(621\) 0.212402 0.512785i 0.00852342 0.0205773i
\(622\) 10.7009 20.3840i 0.429069 0.817324i
\(623\) 8.19511i 0.328330i
\(624\) −11.6698 25.9569i −0.467166 1.03911i
\(625\) 6.46981i 0.258792i
\(626\) −8.04713 4.22448i −0.321628 0.168844i
\(627\) −12.6912 + 30.6393i −0.506838 + 1.22361i
\(628\) −15.4689 + 3.31736i −0.617277 + 0.132377i
\(629\) 18.6620 7.73005i 0.744102 0.308217i
\(630\) −3.94510 + 3.28717i −0.157177 + 0.130964i
\(631\) 12.1989 + 12.1989i 0.485630 + 0.485630i 0.906924 0.421294i \(-0.138424\pi\)
−0.421294 + 0.906924i \(0.638424\pi\)
\(632\) −10.1476 + 12.9444i −0.403648 + 0.514901i
\(633\) 12.7189 12.7189i 0.505532 0.505532i
\(634\) −0.174763 + 1.92106i −0.00694073 + 0.0762949i
\(635\) 5.60195 + 13.5243i 0.222307 + 0.536696i
\(636\) 54.9030 37.8806i 2.17704 1.50206i
\(637\) −2.65808 1.10101i −0.105317 0.0436237i
\(638\) 11.6199 + 37.3028i 0.460038 + 1.47683i
\(639\) 28.0144 1.10823
\(640\) 10.6152 + 7.82223i 0.419602 + 0.309201i
\(641\) 15.1205 0.597222 0.298611 0.954375i \(-0.403477\pi\)
0.298611 + 0.954375i \(0.403477\pi\)
\(642\) 17.7792 + 57.0756i 0.701690 + 2.25259i
\(643\) −26.5412 10.9937i −1.04668 0.433550i −0.207975 0.978134i \(-0.566687\pi\)
−0.838706 + 0.544584i \(0.816687\pi\)
\(644\) −3.19894 + 2.20713i −0.126056 + 0.0869729i
\(645\) 6.73233 + 16.2533i 0.265085 + 0.639972i
\(646\) −1.71592 + 18.8620i −0.0675120 + 0.742115i
\(647\) 3.63894 3.63894i 0.143061 0.143061i −0.631949 0.775010i \(-0.717745\pi\)
0.775010 + 0.631949i \(0.217745\pi\)
\(648\) 15.0772 19.2327i 0.592287 0.755533i
\(649\) 12.7679 + 12.7679i 0.501182 + 0.501182i
\(650\) −11.3835 + 9.48500i −0.446496 + 0.372032i
\(651\) 4.74732 1.96641i 0.186062 0.0770695i
\(652\) 33.5196 7.18841i 1.31273 0.281520i
\(653\) 4.41810 10.6662i 0.172894 0.417402i −0.813552 0.581493i \(-0.802469\pi\)
0.986445 + 0.164090i \(0.0524689\pi\)
\(654\) −1.24767 0.654988i −0.0487879 0.0256121i
\(655\) 3.54715i 0.138598i
\(656\) −29.3336 + 13.1879i −1.14528 + 0.514901i
\(657\) 47.0866i 1.83702i
\(658\) −5.53381 + 10.5412i −0.215730 + 0.410940i
\(659\) 5.89751 14.2379i 0.229735 0.554628i −0.766410 0.642351i \(-0.777959\pi\)
0.996145 + 0.0877230i \(0.0279590\pi\)
\(660\) −15.1511 9.80021i −0.589756 0.381473i
\(661\) −7.51647 + 3.11342i −0.292357 + 0.121098i −0.524041 0.851693i \(-0.675576\pi\)
0.231685 + 0.972791i \(0.425576\pi\)
\(662\) −6.76343 8.11715i −0.262868 0.315482i
\(663\) 15.7275 + 15.7275i 0.610804 + 0.610804i
\(664\) −12.3258 + 6.94691i −0.478334 + 0.269592i
\(665\) 3.53060 3.53060i 0.136911 0.136911i
\(666\) −28.3524 2.57929i −1.09863 0.0999454i
\(667\) 6.56313 + 15.8448i 0.254125 + 0.613513i
\(668\) −5.65872 + 30.8439i −0.218943 + 1.19339i
\(669\) 47.7670 + 19.7857i 1.84678 + 0.764960i
\(670\) 14.1307 4.40176i 0.545917 0.170055i
\(671\) 16.5972 0.640726
\(672\) 13.2262 4.55670i 0.510212 0.175778i
\(673\) 18.3122 0.705883 0.352942 0.935645i \(-0.385181\pi\)
0.352942 + 0.935645i \(0.385181\pi\)
\(674\) −28.1441 + 8.76697i −1.08407 + 0.337691i
\(675\) 0.960966 + 0.398045i 0.0369876 + 0.0153208i
\(676\) −9.28974 1.70432i −0.357298 0.0655510i
\(677\) 7.06192 + 17.0490i 0.271412 + 0.655246i 0.999544 0.0301906i \(-0.00961144\pi\)
−0.728132 + 0.685436i \(0.759611\pi\)
\(678\) 11.1020 + 1.00998i 0.426371 + 0.0387880i
\(679\) −9.78364 + 9.78364i −0.375462 + 0.375462i
\(680\) −9.92588 2.77025i −0.380640 0.106234i
\(681\) −1.54675 1.54675i −0.0592716 0.0592716i
\(682\) 5.88837 + 7.06694i 0.225477 + 0.270607i
\(683\) 27.6298 11.4446i 1.05722 0.437917i 0.214759 0.976667i \(-0.431103\pi\)
0.842466 + 0.538750i \(0.181103\pi\)
\(684\) 14.4980 22.4139i 0.554345 0.857016i
\(685\) 3.20967 7.74883i 0.122635 0.296068i
\(686\) 0.657343 1.25216i 0.0250975 0.0478076i
\(687\) 28.2346i 1.07722i
\(688\) −0.727677 24.4045i −0.0277424 0.930413i
\(689\) 38.8017i 1.47823i
\(690\) −7.01304 3.68162i −0.266982 0.140157i
\(691\) 12.0259 29.0332i 0.457489 1.10448i −0.511922 0.859032i \(-0.671066\pi\)
0.969411 0.245443i \(-0.0789335\pi\)
\(692\) −6.41941 29.9338i −0.244029 1.13791i
\(693\) −9.01017 + 3.73213i −0.342268 + 0.141772i
\(694\) −25.7400 + 21.4473i −0.977078 + 0.814127i
\(695\) −12.9785 12.9785i −0.492303 0.492303i
\(696\) −7.42258 61.2837i −0.281352 2.32295i
\(697\) 17.7734 17.7734i 0.673215 0.673215i
\(698\) 1.02445 11.2611i 0.0387759 0.426238i
\(699\) 20.2792 + 48.9584i 0.767031 + 1.85178i
\(700\) −4.13618 5.99486i −0.156333 0.226584i
\(701\) 6.59341 + 2.73108i 0.249030 + 0.103151i 0.503707 0.863875i \(-0.331969\pi\)
−0.254677 + 0.967026i \(0.581969\pi\)
\(702\) −0.345633 1.10956i −0.0130451 0.0418778i
\(703\) 27.6818 1.04404
\(704\) 14.8297 + 20.1795i 0.558917 + 0.760543i
\(705\) −24.2636 −0.913819
\(706\) −10.0485 32.2580i −0.378179 1.21405i
\(707\) −3.14044 1.30081i −0.118109 0.0489221i
\(708\) −16.2017 23.4823i −0.608898 0.882518i
\(709\) 2.61002 + 6.30114i 0.0980212 + 0.236644i 0.965282 0.261210i \(-0.0841215\pi\)
−0.867261 + 0.497854i \(0.834122\pi\)
\(710\) 1.34275 14.7600i 0.0503925 0.553932i
\(711\) −12.8108 + 12.8108i −0.480442 + 0.480442i
\(712\) 23.0111 2.78706i 0.862377 0.104450i
\(713\) 2.85514 + 2.85514i 0.106926 + 0.106926i
\(714\) −8.39934 + 6.99856i −0.314337 + 0.261914i
\(715\) 9.69760 4.01688i 0.362670 0.150223i
\(716\) −10.4651 48.7989i −0.391099 1.82370i
\(717\) 1.50841 3.64162i 0.0563326 0.135999i
\(718\) −9.79651 5.14285i −0.365602 0.191930i
\(719\) 2.43833i 0.0909345i −0.998966 0.0454672i \(-0.985522\pi\)
0.998966 0.0454672i \(-0.0144777\pi\)
\(720\) 10.5717 + 9.95955i 0.393985 + 0.371171i
\(721\) 13.1894i 0.491199i
\(722\) 0.425100 0.809764i 0.0158206 0.0301363i
\(723\) 6.40746 15.4690i 0.238296 0.575298i
\(724\) −20.1022 + 31.0779i −0.747091 + 1.15500i
\(725\) −29.6934 + 12.2994i −1.10278 + 0.456788i
\(726\) 2.68882 + 3.22700i 0.0997915 + 0.119765i
\(727\) −29.3111 29.3111i −1.08709 1.08709i −0.995827 0.0912633i \(-0.970910\pi\)
−0.0912633 0.995827i \(-0.529090\pi\)
\(728\) −2.18756 + 7.83808i −0.0810762 + 0.290498i
\(729\) 20.5326 20.5326i 0.760465 0.760465i
\(730\) −24.8086 2.25689i −0.918206 0.0835314i
\(731\) 7.30210 + 17.6288i 0.270078 + 0.652026i
\(732\) −25.7930 4.73205i −0.953335 0.174902i
\(733\) −19.4096 8.03973i −0.716910 0.296954i −0.00574973 0.999983i \(-0.501830\pi\)
−0.711161 + 0.703029i \(0.751830\pi\)
\(734\) 17.0166 5.30072i 0.628093 0.195653i
\(735\) 2.88219 0.106311
\(736\) 7.28532 + 8.23170i 0.268541 + 0.303425i
\(737\) 28.1088 1.03540
\(738\) −33.8230 + 10.5360i −1.24504 + 0.387835i
\(739\) 5.41654 + 2.24361i 0.199251 + 0.0825324i 0.480077 0.877226i \(-0.340609\pi\)
−0.280827 + 0.959759i \(0.590609\pi\)
\(740\) −2.71790 + 14.8144i −0.0999121 + 0.544590i
\(741\) 11.6645 + 28.1605i 0.428505 + 1.03450i
\(742\) −18.9943 1.72796i −0.697304 0.0634354i
\(743\) 13.9385 13.9385i 0.511355 0.511355i −0.403586 0.914942i \(-0.632237\pi\)
0.914942 + 0.403586i \(0.132237\pi\)
\(744\) −7.13599 12.6613i −0.261618 0.464185i
\(745\) 4.90777 + 4.90777i 0.179807 + 0.179807i
\(746\) 15.7941 + 18.9554i 0.578264 + 0.694005i
\(747\) −14.3984 + 5.96400i −0.526809 + 0.218211i
\(748\) −16.4334 10.6296i −0.600864 0.388658i
\(749\) 6.54138 15.7923i 0.239017 0.577038i
\(750\) 16.3723 31.1873i 0.597833 1.13880i
\(751\) 3.64201i 0.132899i −0.997790 0.0664494i \(-0.978833\pi\)
0.997790 0.0664494i \(-0.0211671\pi\)
\(752\) 31.4808 + 11.9535i 1.14799 + 0.435898i
\(753\) 72.9285i 2.65766i
\(754\) 31.7950 + 16.6913i 1.15790 + 0.607862i
\(755\) −0.941341 + 2.27260i −0.0342589 + 0.0827083i
\(756\) 0.558549 0.119783i 0.0203142 0.00435646i
\(757\) −15.5760 + 6.45181i −0.566121 + 0.234495i −0.647340 0.762201i \(-0.724119\pi\)
0.0812192 + 0.996696i \(0.474119\pi\)
\(758\) 6.92935 5.77372i 0.251685 0.209711i
\(759\) −10.6369 10.6369i −0.386095 0.386095i
\(760\) −11.1143 8.71288i −0.403159 0.316049i
\(761\) −6.25525 + 6.25525i −0.226753 + 0.226753i −0.811335 0.584582i \(-0.801259\pi\)
0.584582 + 0.811335i \(0.301259\pi\)
\(762\) 3.97964 43.7456i 0.144167 1.58474i
\(763\) 0.154193 + 0.372256i 0.00558217 + 0.0134766i
\(764\) 7.25032 5.00240i 0.262307 0.180980i
\(765\) −10.4871 4.34389i −0.379161 0.157054i
\(766\) 1.35763 + 4.35831i 0.0490531 + 0.157472i
\(767\) 16.5957 0.599236
\(768\) −17.2929 35.5883i −0.624002 1.28418i
\(769\) −3.13768 −0.113148 −0.0565739 0.998398i \(-0.518018\pi\)
−0.0565739 + 0.998398i \(0.518018\pi\)
\(770\) 1.53449 + 4.92608i 0.0552991 + 0.177524i
\(771\) 5.65875 + 2.34393i 0.203795 + 0.0844147i
\(772\) 38.3765 26.4781i 1.38120 0.952968i
\(773\) −11.0890 26.7712i −0.398844 0.962895i −0.987941 0.154832i \(-0.950516\pi\)
0.589097 0.808062i \(-0.299484\pi\)
\(774\) 2.43650 26.7828i 0.0875780 0.962688i
\(775\) −5.35057 + 5.35057i −0.192198 + 0.192198i
\(776\) 30.7988 + 24.1442i 1.10561 + 0.866728i
\(777\) 11.2990 + 11.2990i 0.405348 + 0.405348i
\(778\) 7.00481 5.83660i 0.251135 0.209252i
\(779\) 31.8238 13.1819i 1.14021 0.472289i
\(780\) −16.2159 + 3.47756i −0.580622 + 0.124517i
\(781\) 10.7717 26.0051i 0.385441 0.930537i
\(782\) −7.60657 3.99321i −0.272011 0.142797i
\(783\) 2.52082i 0.0900867i
\(784\) −3.73950 1.41991i −0.133554 0.0507112i
\(785\) 9.21934i 0.329053i
\(786\) 4.94744 9.42427i 0.176469 0.336153i
\(787\) 1.45934 3.52317i 0.0520200 0.125587i −0.895733 0.444592i \(-0.853349\pi\)
0.947753 + 0.319005i \(0.103349\pi\)
\(788\) 22.2610 + 14.3991i 0.793015 + 0.512947i
\(789\) 12.6735 5.24952i 0.451187 0.186888i
\(790\) 6.13560 + 7.36366i 0.218295 + 0.261987i
\(791\) −2.25396 2.25396i −0.0801417 0.0801417i
\(792\) 13.5437 + 24.0305i 0.481256 + 0.853885i
\(793\) 10.7865 10.7865i 0.383040 0.383040i
\(794\) −45.9383 4.17912i −1.63029 0.148311i
\(795\) −14.8751 35.9118i −0.527567 1.27366i
\(796\) 8.31298 45.3115i 0.294646 1.60602i
\(797\) −13.0235 5.39450i −0.461315 0.191083i 0.139907 0.990165i \(-0.455320\pi\)
−0.601223 + 0.799082i \(0.705320\pi\)
\(798\) −14.3047 + 4.45595i −0.506380 + 0.157739i
\(799\) −26.3171 −0.931031
\(800\) −15.4263 + 13.6528i −0.545403 + 0.482699i
\(801\) 25.5319 0.902124
\(802\) 38.3040 11.9318i 1.35256 0.421327i
\(803\) −43.7094 18.1050i −1.54247 0.638913i
\(804\) −43.6827 8.01417i −1.54057 0.282638i
\(805\) 0.866704 + 2.09241i 0.0305473 + 0.0737477i
\(806\) 8.41967 + 0.765957i 0.296570 + 0.0269797i
\(807\) −43.2017 + 43.2017i −1.52077 + 1.52077i
\(808\) −2.58454 + 9.26046i −0.0909236 + 0.325782i
\(809\) 12.4277 + 12.4277i 0.436933 + 0.436933i 0.890979 0.454045i \(-0.150020\pi\)
−0.454045 + 0.890979i \(0.650020\pi\)
\(810\) −9.11624 10.9409i −0.320312 0.384424i
\(811\) −3.60653 + 1.49387i −0.126642 + 0.0524570i −0.445105 0.895479i \(-0.646834\pi\)
0.318462 + 0.947936i \(0.396834\pi\)
\(812\) −9.58671 + 14.8210i −0.336428 + 0.520117i
\(813\) −15.3830 + 37.1378i −0.539505 + 1.30248i
\(814\) −13.2959 + 25.3272i −0.466023 + 0.887717i
\(815\) 19.9774i 0.699779i
\(816\) 22.5078 + 21.2044i 0.787931 + 0.742304i
\(817\) 26.1493i 0.914849i
\(818\) −3.71423 1.94985i −0.129865 0.0681749i
\(819\) −3.43020 + 8.28124i −0.119861 + 0.289370i
\(820\) 3.92994 + 18.3254i 0.137239 + 0.639949i
\(821\) 6.08026 2.51853i 0.212203 0.0878972i −0.274050 0.961715i \(-0.588363\pi\)
0.486253 + 0.873818i \(0.338363\pi\)
\(822\) −19.3355 + 16.1108i −0.674402 + 0.561930i
\(823\) −16.9010 16.9010i −0.589133 0.589133i 0.348263 0.937397i \(-0.386772\pi\)
−0.937397 + 0.348263i \(0.886772\pi\)
\(824\) 37.0346 4.48557i 1.29016 0.156262i
\(825\) 19.9337 19.9337i 0.694003 0.694003i
\(826\) −0.739057 + 8.12397i −0.0257151 + 0.282669i
\(827\) −9.82853 23.7282i −0.341772 0.825109i −0.997537 0.0701446i \(-0.977654\pi\)
0.655765 0.754965i \(-0.272346\pi\)
\(828\) 6.87630 + 9.96629i 0.238968 + 0.346352i
\(829\) 7.52107 + 3.11533i 0.261217 + 0.108200i 0.509449 0.860501i \(-0.329849\pi\)
−0.248231 + 0.968701i \(0.579849\pi\)
\(830\) 2.45214 + 7.87195i 0.0851149 + 0.273239i
\(831\) −68.5671 −2.37856
\(832\) 22.7525 + 3.47681i 0.788803 + 0.120537i
\(833\) 3.12612 0.108314
\(834\) 16.3801 + 52.5840i 0.567196 + 1.82084i
\(835\) 16.8830 + 6.99318i 0.584261 + 0.242009i
\(836\) −15.2317 22.0764i −0.526801 0.763528i
\(837\) −0.227118 0.548312i −0.00785036 0.0189524i
\(838\) −4.75366 + 52.2539i −0.164212 + 1.80508i
\(839\) 5.31442 5.31442i 0.183474 0.183474i −0.609394 0.792868i \(-0.708587\pi\)
0.792868 + 0.609394i \(0.208587\pi\)
\(840\) −0.980200 8.09292i −0.0338201 0.279232i
\(841\) 34.5719 + 34.5719i 1.19213 + 1.19213i
\(842\) −9.27917 + 7.73165i −0.319781 + 0.266450i
\(843\) −25.5203 + 10.5708i −0.878965 + 0.364079i
\(844\) 3.05035 + 14.2238i 0.104997 + 0.489604i
\(845\) −2.10624 + 5.08492i −0.0724570 + 0.174927i
\(846\) 32.8412 + 17.2406i 1.12910 + 0.592743i
\(847\) 1.20104i 0.0412683i
\(848\) 1.60781 + 53.9220i 0.0552124 + 1.85169i
\(849\) 44.3039i 1.52051i
\(850\) 7.48333 14.2548i 0.256676 0.488937i
\(851\) −4.80509 + 11.6005i −0.164716 + 0.397661i
\(852\) −24.1542 + 37.3424i −0.827509 + 1.27933i
\(853\) 13.4135 5.55607i 0.459271 0.190236i −0.141039 0.990004i \(-0.545044\pi\)
0.600309 + 0.799768i \(0.295044\pi\)
\(854\) 4.79989 + 5.76060i 0.164249 + 0.197124i
\(855\) −10.9996 10.9996i −0.376178 0.376178i
\(856\) −46.5679 12.9968i −1.59166 0.444222i
\(857\) −23.3970 + 23.3970i −0.799226 + 0.799226i −0.982973 0.183748i \(-0.941177\pi\)
0.183748 + 0.982973i \(0.441177\pi\)
\(858\) −31.3678 2.85360i −1.07088 0.0974203i
\(859\) 16.5674 + 39.9974i 0.565274 + 1.36469i 0.905499 + 0.424348i \(0.139497\pi\)
−0.340225 + 0.940344i \(0.610503\pi\)
\(860\) −13.9943 2.56744i −0.477202 0.0875489i
\(861\) 18.3701 + 7.60914i 0.626051 + 0.259319i
\(862\) −10.9239 + 3.40281i −0.372068 + 0.115900i
\(863\) −53.8841 −1.83424 −0.917118 0.398615i \(-0.869491\pi\)
−0.917118 + 0.398615i \(0.869491\pi\)
\(864\) −0.526295 1.52762i −0.0179049 0.0519706i
\(865\) −17.8403 −0.606589
\(866\) 1.29602 0.403715i 0.0440406 0.0137188i
\(867\) 16.5125 + 6.83971i 0.560794 + 0.232289i
\(868\) −0.749907 + 4.08751i −0.0254535 + 0.138739i
\(869\) 6.96615 + 16.8178i 0.236310 + 0.570504i
\(870\) −35.8257 3.25915i −1.21460 0.110495i
\(871\) 18.2680 18.2680i 0.618986 0.618986i
\(872\) 0.992819 0.559560i 0.0336211 0.0189491i
\(873\) 30.4809 + 30.4809i 1.03162 + 1.03162i
\(874\) −7.53649 9.04494i −0.254926 0.305950i
\(875\) −9.30504 + 3.85427i −0.314568 + 0.130298i
\(876\) 62.7650 + 40.5984i 2.12063 + 1.37169i
\(877\) −9.74506 + 23.5266i −0.329067 + 0.794438i 0.669595 + 0.742727i \(0.266468\pi\)
−0.998662 + 0.0517119i \(0.983532\pi\)
\(878\) 1.11065 2.11565i 0.0374826 0.0713998i
\(879\) 18.5202i 0.624670i
\(880\) 13.3101 5.98401i 0.448684 0.201721i
\(881\) 41.2930i 1.39120i −0.718431 0.695598i \(-0.755139\pi\)
0.718431 0.695598i \(-0.244861\pi\)
\(882\) −3.90110 2.04795i −0.131357 0.0689581i
\(883\) 9.58604 23.1427i 0.322596 0.778815i −0.676506 0.736437i \(-0.736507\pi\)
0.999102 0.0423780i \(-0.0134934\pi\)
\(884\) −17.5883 + 3.77187i −0.591558 + 0.126862i
\(885\) −15.3596 + 6.36217i −0.516308 + 0.213862i
\(886\) −8.18258 + 6.81795i −0.274899 + 0.229053i
\(887\) −24.1177 24.1177i −0.809795 0.809795i 0.174808 0.984603i \(-0.444070\pi\)
−0.984603 + 0.174808i \(0.944070\pi\)
\(888\) 27.8838 35.5691i 0.935718 1.19362i
\(889\) −8.88133 + 8.88133i −0.297870 + 0.297870i
\(890\) 1.22376 13.4520i 0.0410205 0.450912i
\(891\) −10.3503 24.9878i −0.346747 0.837121i
\(892\) −34.4174 + 23.7464i −1.15238 + 0.795090i
\(893\) −33.3200 13.8016i −1.11501 0.461853i
\(894\) −6.19407 19.8845i −0.207161 0.665036i
\(895\) −29.0838 −0.972163
\(896\) −2.71522 + 10.9831i −0.0907091 + 0.366918i
\(897\) −13.8259 −0.461633
\(898\) −4.47871 14.3777i −0.149456 0.479791i
\(899\) 16.9426 + 7.01784i 0.565066 + 0.234058i
\(900\) −18.6770 + 12.8863i −0.622566 + 0.429543i
\(901\) −16.1341 38.9511i −0.537503 1.29765i
\(902\) −3.22481 + 35.4483i −0.107375 + 1.18030i
\(903\) −10.6734 + 10.6734i −0.355190 + 0.355190i
\(904\) −5.56237 + 7.09546i −0.185002 + 0.235992i
\(905\) 15.2515 + 15.2515i 0.506976 + 0.506976i
\(906\) 5.67075 4.72503i 0.188398 0.156978i
\(907\) −24.1487 + 10.0027i −0.801845 + 0.332135i −0.745695 0.666287i \(-0.767882\pi\)
−0.0561498 + 0.998422i \(0.517882\pi\)
\(908\) 1.72976 0.370953i 0.0574040 0.0123105i
\(909\) −4.05268 + 9.78405i −0.134419 + 0.324516i
\(910\) 4.19873 + 2.20420i 0.139187 + 0.0730685i
\(911\) 41.8675i 1.38713i −0.720392 0.693567i \(-0.756038\pi\)
0.720392 0.693567i \(-0.243962\pi\)
\(912\) 17.3768 + 38.6508i 0.575402 + 1.27986i
\(913\) 15.6589i 0.518233i
\(914\) −9.55193 + 18.1953i −0.315950 + 0.601846i
\(915\) −5.84798 + 14.1183i −0.193328 + 0.466736i
\(916\) −19.1733 12.4019i −0.633505 0.409771i
\(917\) −2.81182 + 1.16470i −0.0928546 + 0.0384616i
\(918\) 0.808328 + 0.970117i 0.0266788 + 0.0320186i
\(919\) −36.9292 36.9292i −1.21818 1.21818i −0.968268 0.249913i \(-0.919598\pi\)
−0.249913 0.968268i \(-0.580402\pi\)
\(920\) 5.58053 3.14523i 0.183985 0.103695i
\(921\) 16.7977 16.7977i 0.553502 0.553502i
\(922\) 42.0942 + 3.82941i 1.38630 + 0.126115i
\(923\) −9.90024 23.9013i −0.325870 0.786721i
\(924\) 2.79380 15.2282i 0.0919094 0.500970i
\(925\) −21.7395 9.00482i −0.714792 0.296076i
\(926\) 35.5475 11.0731i 1.16816 0.363886i
\(927\) 41.0916 1.34963
\(928\) 44.8764 + 21.8781i 1.47314 + 0.718185i
\(929\) 36.2365 1.18888 0.594441 0.804139i \(-0.297374\pi\)
0.594441 + 0.804139i \(0.297374\pi\)
\(930\) −8.08621 + 2.51888i −0.265157 + 0.0825973i
\(931\) 3.95797 + 1.63944i 0.129717 + 0.0537306i
\(932\) −42.1539 7.73368i −1.38080 0.253325i
\(933\) 15.4059 + 37.1930i 0.504365 + 1.21765i
\(934\) 11.4086 + 1.03786i 0.373300 + 0.0339600i
\(935\) −8.06467 + 8.06467i −0.263743 + 0.263743i
\(936\) 24.4195 + 6.81533i 0.798177 + 0.222766i
\(937\) 32.2352 + 32.2352i 1.05308 + 1.05308i 0.998510 + 0.0545683i \(0.0173783\pi\)
0.0545683 + 0.998510i \(0.482622\pi\)
\(938\) 8.12905 + 9.75611i 0.265423 + 0.318548i
\(939\) 14.6829 6.08187i 0.479160 0.198474i
\(940\) 10.6577 16.4767i 0.347615 0.537412i
\(941\) 15.4697 37.3471i 0.504296 1.21748i −0.442826 0.896607i \(-0.646024\pi\)
0.947123 0.320872i \(-0.103976\pi\)
\(942\) 12.8588 24.4945i 0.418963 0.798074i
\(943\) 15.6244i 0.508802i
\(944\) 23.0627 0.687667i 0.750627 0.0223817i
\(945\) 0.332891i 0.0108289i
\(946\) −23.9250 12.5599i −0.777869 0.408356i
\(947\) −5.36081 + 12.9421i −0.174203 + 0.420563i −0.986732 0.162358i \(-0.948090\pi\)
0.812529 + 0.582921i \(0.198090\pi\)
\(948\) −6.03085 28.1219i −0.195873 0.913358i
\(949\) −40.1733 + 16.6403i −1.30408 + 0.540168i
\(950\) 16.9504 14.1235i 0.549942 0.458227i
\(951\) −2.38515 2.38515i −0.0773438 0.0773438i
\(952\) −1.06316 8.77784i −0.0344571 0.284492i
\(953\) 14.9769 14.9769i 0.485150 0.485150i −0.421622 0.906772i \(-0.638539\pi\)
0.906772 + 0.421622i \(0.138539\pi\)
\(954\) −5.38346 + 59.1768i −0.174296 + 1.91592i
\(955\) −1.96437 4.74240i −0.0635654 0.153460i
\(956\) 1.81036 + 2.62388i 0.0585513 + 0.0848625i
\(957\) −63.1201 26.1452i −2.04038 0.845155i
\(958\) −6.45498 20.7220i −0.208551 0.669499i
\(959\) 7.19639 0.232383
\(960\) −22.3908 + 5.50462i −0.722660 + 0.177661i
\(961\) −26.6825 −0.860725
\(962\) 7.81911 + 25.1012i 0.252098 + 0.809296i
\(963\) −49.2009 20.3797i −1.58548 0.656725i
\(964\) 7.69012 + 11.1458i 0.247682 + 0.358982i
\(965\) −10.3975 25.1019i −0.334709 0.808059i
\(966\) 0.615709 6.76809i 0.0198101 0.217760i
\(967\) −14.9946 + 14.9946i −0.482192 + 0.482192i −0.905831 0.423639i \(-0.860753\pi\)
0.423639 + 0.905831i \(0.360753\pi\)
\(968\) −3.37242 + 0.408461i −0.108394 + 0.0131284i
\(969\) −23.4187 23.4187i −0.752318 0.752318i
\(970\) 17.5205 14.5985i 0.562549 0.468731i
\(971\) −22.5036 + 9.32129i −0.722174 + 0.299134i −0.713332 0.700826i \(-0.752815\pi\)
−0.00884264 + 0.999961i \(0.502815\pi\)
\(972\) 9.31995 + 43.4591i 0.298938 + 1.39395i
\(973\) 6.02660 14.5495i 0.193204 0.466436i
\(974\) −37.2420 19.5508i −1.19331 0.626449i
\(975\) 25.9099i 0.829781i
\(976\) 14.5428 15.4368i 0.465505 0.494118i
\(977\) 51.3075i 1.64147i −0.571307 0.820736i \(-0.693563\pi\)
0.571307 0.820736i \(-0.306437\pi\)
\(978\) −27.8638 + 53.0772i −0.890988 + 1.69722i
\(979\) 9.81712 23.7006i 0.313757 0.757476i
\(980\) −1.26599 + 1.95722i −0.0404405 + 0.0625210i
\(981\) 1.15976 0.480389i 0.0370283 0.0153376i
\(982\) 25.6607 + 30.7968i 0.818865 + 0.982764i
\(983\) 33.2091 + 33.2091i 1.05921 + 1.05921i 0.998133 + 0.0610731i \(0.0194523\pi\)
0.0610731 + 0.998133i \(0.480548\pi\)
\(984\) 15.1183 54.1693i 0.481954 1.72685i
\(985\) 10.9246 10.9246i 0.348085 0.348085i
\(986\) −38.8577 3.53498i −1.23748 0.112577i
\(987\) −7.96687 19.2337i −0.253588 0.612217i
\(988\) −24.2466 4.44836i −0.771387 0.141521i
\(989\) −10.9583 4.53908i −0.348454 0.144334i
\(990\) 15.3472 4.78070i 0.487766 0.151941i
\(991\) 15.3314 0.487018 0.243509 0.969899i \(-0.421701\pi\)
0.243509 + 0.969899i \(0.421701\pi\)
\(992\) 11.7324 + 0.715554i 0.372503 + 0.0227188i
\(993\) 18.4755 0.586301
\(994\) 12.1411 3.78200i 0.385093 0.119958i
\(995\) −24.8021 10.2734i −0.786280 0.325688i
\(996\) 4.46454 24.3348i 0.141464 0.771078i
\(997\) 9.22040 + 22.2600i 0.292013 + 0.704982i 0.999999 0.00124443i \(-0.000396115\pi\)
−0.707986 + 0.706226i \(0.750396\pi\)
\(998\) 11.6706 + 1.06170i 0.369427 + 0.0336076i
\(999\) 1.30502 1.30502i 0.0412890 0.0412890i
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 224.2.u.b.29.4 40
4.3 odd 2 896.2.u.b.337.2 40
32.11 odd 8 896.2.u.b.561.2 40
32.21 even 8 inner 224.2.u.b.85.4 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.u.b.29.4 40 1.1 even 1 trivial
224.2.u.b.85.4 yes 40 32.21 even 8 inner
896.2.u.b.337.2 40 4.3 odd 2
896.2.u.b.561.2 40 32.11 odd 8