Properties

Label 50.2.d.b.11.2
Level $50$
Weight $2$
Character 50.11
Analytic conductor $0.399$
Analytic rank $0$
Dimension $8$
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] = [50,2,Mod(11,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 50.d (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.399252010106\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 11.2
Root \(-0.357358 - 1.86824i\) of defining polynomial
Character \(\chi\) \(=\) 50.11
Dual form 50.2.d.b.41.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.529876 - 1.63079i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +(0.529876 + 1.63079i) q^{6} -2.77447 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.0483405 + 0.0351215i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.529876 - 1.63079i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +(0.529876 + 1.63079i) q^{6} -2.77447 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.0483405 + 0.0351215i) q^{9} +(-2.19625 + 0.420099i) q^{10} +(-2.24459 + 1.63079i) q^{11} +(-1.38723 - 1.00788i) q^{12} +(-4.59343 - 3.33732i) q^{13} +(2.24459 - 1.63079i) q^{14} +(2.62330 - 2.79634i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.59343 + 4.90406i) q^{17} -0.0597522 q^{18} +(0.436451 + 1.34326i) q^{19} +(1.52988 - 1.63079i) q^{20} +(-1.47012 + 4.52458i) q^{21} +(0.857358 - 2.63868i) q^{22} +(0.529876 - 0.384978i) q^{23} +1.71472 q^{24} +(3.19098 + 3.84937i) q^{25} +5.67779 q^{26} +(4.24459 - 3.08388i) q^{27} +(-0.857358 + 2.63868i) q^{28} +(1.26594 - 3.89618i) q^{29} +(-0.478647 + 3.80423i) q^{30} +(-2.20239 - 6.77827i) q^{31} +1.00000 q^{32} +(1.47012 + 4.52458i) q^{33} +(-4.17164 - 3.03088i) q^{34} +(-5.61478 - 2.63868i) q^{35} +(0.0483405 - 0.0351215i) q^{36} +(0.847416 + 0.615684i) q^{37} +(-1.14264 - 0.830178i) q^{38} +(-7.87642 + 5.72255i) q^{39} +(-0.279141 + 2.21858i) q^{40} +(-7.36789 - 5.35309i) q^{41} +(-1.47012 - 4.52458i) q^{42} +9.24660 q^{43} +(0.857358 + 2.63868i) q^{44} +(0.0644258 + 0.117051i) q^{45} +(-0.202395 + 0.622907i) q^{46} +(-0.857358 + 2.63868i) q^{47} +(-1.38723 + 1.00788i) q^{48} +0.697669 q^{49} +(-4.84416 - 1.23859i) q^{50} +8.84181 q^{51} +(-4.59343 + 3.33732i) q^{52} +(-0.162577 + 0.500362i) q^{53} +(-1.62129 + 4.98982i) q^{54} +(-6.09343 + 1.16555i) q^{55} +(-0.857358 - 2.63868i) q^{56} +2.42184 q^{57} +(1.26594 + 3.89618i) q^{58} +(3.05975 + 2.22304i) q^{59} +(-1.84883 - 3.35903i) q^{60} +(8.76365 - 6.36716i) q^{61} +(5.76594 + 4.18920i) q^{62} +(-0.134119 - 0.0974433i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-6.12188 - 11.1224i) q^{65} +(-3.84883 - 2.79634i) q^{66} +(-1.33600 - 4.11180i) q^{67} +5.15643 q^{68} +(-0.347049 - 1.06811i) q^{69} +(6.09343 - 1.16555i) q^{70} +(-4.09343 + 12.5983i) q^{71} +(-0.0184644 + 0.0568277i) q^{72} +(-3.40859 + 2.47648i) q^{73} -1.04746 q^{74} +(7.96834 - 3.16414i) q^{75} +1.41238 q^{76} +(6.22754 - 4.52458i) q^{77} +(3.00852 - 9.25928i) q^{78} +(-3.05975 + 9.41695i) q^{79} +(-1.07822 - 1.95894i) q^{80} +(-2.72466 - 8.38563i) q^{81} +9.10722 q^{82} +(1.44497 + 4.44717i) q^{83} +(3.84883 + 2.79634i) q^{84} +(-1.43937 + 11.4399i) q^{85} +(-7.48066 + 5.43502i) q^{86} +(-5.68305 - 4.12898i) q^{87} +(-2.24459 - 1.63079i) q^{88} +(7.43002 - 5.39823i) q^{89} +(-0.120922 - 0.0568277i) q^{90} +(12.7443 + 9.25928i) q^{91} +(-0.202395 - 0.622907i) q^{92} -12.2209 q^{93} +(-0.857358 - 2.63868i) q^{94} +(-0.394254 + 3.13348i) q^{95} +(0.529876 - 1.63079i) q^{96} +(-0.0278640 + 0.0857567i) q^{97} +(-0.564426 + 0.410079i) q^{98} -0.165781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + q^{11} + 2 q^{12} - 13 q^{13} - q^{14} - 10 q^{15} - 2 q^{16} - 11 q^{17} + 14 q^{18} + 20 q^{19} + 5 q^{20} - 19 q^{21} + q^{22} - 3 q^{23} + 2 q^{24} + 30 q^{25} + 22 q^{26} + 15 q^{27} - q^{28} - 15 q^{29} - 10 q^{30} - 9 q^{31} + 8 q^{32} + 19 q^{33} - q^{34} - 15 q^{35} - q^{36} - 6 q^{37} - 15 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} - 19 q^{42} + 12 q^{43} + q^{44} + 15 q^{45} + 7 q^{46} - q^{47} + 2 q^{48} - 4 q^{49} - 5 q^{50} + 26 q^{51} - 13 q^{52} + 7 q^{53} - 25 q^{54} - 25 q^{55} - q^{56} - 15 q^{58} + 10 q^{59} - 10 q^{60} + 6 q^{61} + 21 q^{62} - 8 q^{63} - 2 q^{64} - 10 q^{65} - 26 q^{66} - 11 q^{67} + 24 q^{68} + 43 q^{69} + 25 q^{70} - 9 q^{71} - 6 q^{72} - 8 q^{73} + 24 q^{74} + 30 q^{75} - 10 q^{76} + 33 q^{77} + 23 q^{78} - 10 q^{79} - 17 q^{81} + 26 q^{82} + 27 q^{83} + 26 q^{84} + 5 q^{85} - 23 q^{86} + q^{88} - 15 q^{89} + 20 q^{90} + q^{91} + 7 q^{92} - 46 q^{93} - q^{94} - 30 q^{95} - 3 q^{96} - 36 q^{97} - 19 q^{98} - 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.529876 1.63079i 0.305924 0.941538i −0.673407 0.739272i \(-0.735170\pi\)
0.979331 0.202265i \(-0.0648303\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 2.02373 + 0.951057i 0.905040 + 0.425325i
\(6\) 0.529876 + 1.63079i 0.216321 + 0.665768i
\(7\) −2.77447 −1.04865 −0.524325 0.851518i \(-0.675682\pi\)
−0.524325 + 0.851518i \(0.675682\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) 0.0483405 + 0.0351215i 0.0161135 + 0.0117072i
\(10\) −2.19625 + 0.420099i −0.694515 + 0.132847i
\(11\) −2.24459 + 1.63079i −0.676770 + 0.491702i −0.872284 0.488999i \(-0.837362\pi\)
0.195515 + 0.980701i \(0.437362\pi\)
\(12\) −1.38723 1.00788i −0.400460 0.290951i
\(13\) −4.59343 3.33732i −1.27399 0.925606i −0.274633 0.961549i \(-0.588556\pi\)
−0.999354 + 0.0359433i \(0.988556\pi\)
\(14\) 2.24459 1.63079i 0.599892 0.435847i
\(15\) 2.62330 2.79634i 0.677334 0.722012i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 1.59343 + 4.90406i 0.386462 + 1.18941i 0.935414 + 0.353555i \(0.115027\pi\)
−0.548951 + 0.835854i \(0.684973\pi\)
\(18\) −0.0597522 −0.0140837
\(19\) 0.436451 + 1.34326i 0.100129 + 0.308164i 0.988556 0.150852i \(-0.0482018\pi\)
−0.888428 + 0.459017i \(0.848202\pi\)
\(20\) 1.52988 1.63079i 0.342091 0.364656i
\(21\) −1.47012 + 4.52458i −0.320807 + 0.987343i
\(22\) 0.857358 2.63868i 0.182789 0.562567i
\(23\) 0.529876 0.384978i 0.110487 0.0802734i −0.531170 0.847265i \(-0.678247\pi\)
0.641657 + 0.766992i \(0.278247\pi\)
\(24\) 1.71472 0.350015
\(25\) 3.19098 + 3.84937i 0.638197 + 0.769873i
\(26\) 5.67779 1.11351
\(27\) 4.24459 3.08388i 0.816872 0.593492i
\(28\) −0.857358 + 2.63868i −0.162025 + 0.498663i
\(29\) 1.26594 3.89618i 0.235080 0.723502i −0.762031 0.647541i \(-0.775798\pi\)
0.997111 0.0759609i \(-0.0242024\pi\)
\(30\) −0.478647 + 3.80423i −0.0873886 + 0.694553i
\(31\) −2.20239 6.77827i −0.395562 1.21741i −0.928523 0.371274i \(-0.878921\pi\)
0.532961 0.846140i \(-0.321079\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.47012 + 4.52458i 0.255916 + 0.787628i
\(34\) −4.17164 3.03088i −0.715431 0.519791i
\(35\) −5.61478 2.63868i −0.949071 0.446018i
\(36\) 0.0483405 0.0351215i 0.00805676 0.00585358i
\(37\) 0.847416 + 0.615684i 0.139314 + 0.101218i 0.655260 0.755404i \(-0.272559\pi\)
−0.515945 + 0.856622i \(0.672559\pi\)
\(38\) −1.14264 0.830178i −0.185361 0.134673i
\(39\) −7.87642 + 5.72255i −1.26124 + 0.916342i
\(40\) −0.279141 + 2.21858i −0.0441361 + 0.350788i
\(41\) −7.36789 5.35309i −1.15067 0.836012i −0.162101 0.986774i \(-0.551827\pi\)
−0.988570 + 0.150762i \(0.951827\pi\)
\(42\) −1.47012 4.52458i −0.226845 0.698157i
\(43\) 9.24660 1.41009 0.705047 0.709161i \(-0.250926\pi\)
0.705047 + 0.709161i \(0.250926\pi\)
\(44\) 0.857358 + 2.63868i 0.129252 + 0.397795i
\(45\) 0.0644258 + 0.117051i 0.00960403 + 0.0174489i
\(46\) −0.202395 + 0.622907i −0.0298415 + 0.0918426i
\(47\) −0.857358 + 2.63868i −0.125058 + 0.384890i −0.993912 0.110179i \(-0.964857\pi\)
0.868853 + 0.495070i \(0.164857\pi\)
\(48\) −1.38723 + 1.00788i −0.200230 + 0.145476i
\(49\) 0.697669 0.0996670
\(50\) −4.84416 1.23859i −0.685068 0.175163i
\(51\) 8.84181 1.23810
\(52\) −4.59343 + 3.33732i −0.636994 + 0.462803i
\(53\) −0.162577 + 0.500362i −0.0223317 + 0.0687299i −0.961601 0.274450i \(-0.911504\pi\)
0.939270 + 0.343180i \(0.111504\pi\)
\(54\) −1.62129 + 4.98982i −0.220630 + 0.679028i
\(55\) −6.09343 + 1.16555i −0.821637 + 0.157163i
\(56\) −0.857358 2.63868i −0.114569 0.352608i
\(57\) 2.42184 0.320780
\(58\) 1.26594 + 3.89618i 0.166227 + 0.511593i
\(59\) 3.05975 + 2.22304i 0.398346 + 0.289415i 0.768867 0.639409i \(-0.220821\pi\)
−0.370521 + 0.928824i \(0.620821\pi\)
\(60\) −1.84883 3.35903i −0.238683 0.433648i
\(61\) 8.76365 6.36716i 1.12207 0.815232i 0.137549 0.990495i \(-0.456078\pi\)
0.984522 + 0.175263i \(0.0560776\pi\)
\(62\) 5.76594 + 4.18920i 0.732276 + 0.532029i
\(63\) −0.134119 0.0974433i −0.0168974 0.0122767i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −6.12188 11.1224i −0.759326 1.37957i
\(66\) −3.84883 2.79634i −0.473759 0.344206i
\(67\) −1.33600 4.11180i −0.163219 0.502336i 0.835682 0.549214i \(-0.185073\pi\)
−0.998901 + 0.0468778i \(0.985073\pi\)
\(68\) 5.15643 0.625309
\(69\) −0.347049 1.06811i −0.0417798 0.128585i
\(70\) 6.09343 1.16555i 0.728304 0.139310i
\(71\) −4.09343 + 12.5983i −0.485800 + 1.49514i 0.345018 + 0.938596i \(0.387873\pi\)
−0.830819 + 0.556543i \(0.812127\pi\)
\(72\) −0.0184644 + 0.0568277i −0.00217606 + 0.00669721i
\(73\) −3.40859 + 2.47648i −0.398945 + 0.289850i −0.769111 0.639115i \(-0.779301\pi\)
0.370166 + 0.928966i \(0.379301\pi\)
\(74\) −1.04746 −0.121765
\(75\) 7.96834 3.16414i 0.920105 0.365363i
\(76\) 1.41238 0.162012
\(77\) 6.22754 4.52458i 0.709695 0.515623i
\(78\) 3.00852 9.25928i 0.340648 1.04841i
\(79\) −3.05975 + 9.41695i −0.344249 + 1.05949i 0.617736 + 0.786386i \(0.288050\pi\)
−0.961985 + 0.273104i \(0.911950\pi\)
\(80\) −1.07822 1.95894i −0.120548 0.219016i
\(81\) −2.72466 8.38563i −0.302740 0.931737i
\(82\) 9.10722 1.00572
\(83\) 1.44497 + 4.44717i 0.158606 + 0.488141i 0.998508 0.0545976i \(-0.0173876\pi\)
−0.839902 + 0.542738i \(0.817388\pi\)
\(84\) 3.84883 + 2.79634i 0.419942 + 0.305106i
\(85\) −1.43937 + 11.4399i −0.156122 + 1.24084i
\(86\) −7.48066 + 5.43502i −0.806660 + 0.586073i
\(87\) −5.68305 4.12898i −0.609287 0.442673i
\(88\) −2.24459 1.63079i −0.239274 0.173843i
\(89\) 7.43002 5.39823i 0.787581 0.572211i −0.119664 0.992814i \(-0.538182\pi\)
0.907245 + 0.420603i \(0.138182\pi\)
\(90\) −0.120922 0.0568277i −0.0127463 0.00599017i
\(91\) 12.7443 + 9.25928i 1.33597 + 0.970637i
\(92\) −0.202395 0.622907i −0.0211011 0.0649425i
\(93\) −12.2209 −1.26725
\(94\) −0.857358 2.63868i −0.0884297 0.272159i
\(95\) −0.394254 + 3.13348i −0.0404496 + 0.321488i
\(96\) 0.529876 1.63079i 0.0540803 0.166442i
\(97\) −0.0278640 + 0.0857567i −0.00282917 + 0.00870727i −0.952461 0.304660i \(-0.901457\pi\)
0.949632 + 0.313367i \(0.101457\pi\)
\(98\) −0.564426 + 0.410079i −0.0570156 + 0.0414243i
\(99\) −0.165781 −0.0166616
\(100\) 4.64703 1.84529i 0.464703 0.184529i
\(101\) −7.90632 −0.786709 −0.393354 0.919387i \(-0.628685\pi\)
−0.393354 + 0.919387i \(0.628685\pi\)
\(102\) −7.15318 + 5.19709i −0.708270 + 0.514588i
\(103\) 2.42091 7.45079i 0.238539 0.734148i −0.758093 0.652146i \(-0.773869\pi\)
0.996632 0.0820014i \(-0.0261312\pi\)
\(104\) 1.75453 5.39990i 0.172046 0.529503i
\(105\) −7.27826 + 7.75836i −0.710286 + 0.757138i
\(106\) −0.162577 0.500362i −0.0157909 0.0485994i
\(107\) −10.2220 −0.988194 −0.494097 0.869407i \(-0.664501\pi\)
−0.494097 + 0.869407i \(0.664501\pi\)
\(108\) −1.62129 4.98982i −0.156009 0.480145i
\(109\) −3.16400 2.29878i −0.303056 0.220183i 0.425855 0.904791i \(-0.359973\pi\)
−0.728911 + 0.684608i \(0.759973\pi\)
\(110\) 4.24459 4.52458i 0.404706 0.431401i
\(111\) 1.45308 1.05572i 0.137920 0.100205i
\(112\) 2.24459 + 1.63079i 0.212094 + 0.154095i
\(113\) 5.15785 + 3.74740i 0.485210 + 0.352526i 0.803339 0.595522i \(-0.203055\pi\)
−0.318129 + 0.948047i \(0.603055\pi\)
\(114\) −1.95931 + 1.42352i −0.183506 + 0.133325i
\(115\) 1.43846 0.275149i 0.134137 0.0256578i
\(116\) −3.31428 2.40797i −0.307724 0.223574i
\(117\) −0.104837 0.322656i −0.00969220 0.0298295i
\(118\) −3.78206 −0.348167
\(119\) −4.42091 13.6062i −0.405264 1.24727i
\(120\) 3.47012 + 1.63079i 0.316778 + 0.148870i
\(121\) −1.02048 + 3.14070i −0.0927706 + 0.285519i
\(122\) −3.34742 + 10.3023i −0.303061 + 0.932725i
\(123\) −12.6338 + 9.17902i −1.13915 + 0.827644i
\(124\) −7.12710 −0.640032
\(125\) 2.79673 + 10.8249i 0.250147 + 0.968208i
\(126\) 0.165781 0.0147689
\(127\) −7.72525 + 5.61272i −0.685505 + 0.498049i −0.875179 0.483798i \(-0.839257\pi\)
0.189674 + 0.981847i \(0.439257\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) 4.89955 15.0793i 0.431382 1.32766i
\(130\) 11.4903 + 5.39990i 1.00777 + 0.473602i
\(131\) 1.73026 + 5.32519i 0.151173 + 0.465264i 0.997753 0.0669981i \(-0.0213421\pi\)
−0.846580 + 0.532262i \(0.821342\pi\)
\(132\) 4.75742 0.414080
\(133\) −1.21092 3.72682i −0.105000 0.323156i
\(134\) 3.49771 + 2.54123i 0.302156 + 0.219529i
\(135\) 11.5229 2.20409i 0.991730 0.189698i
\(136\) −4.17164 + 3.03088i −0.357715 + 0.259895i
\(137\) −6.45931 4.69296i −0.551856 0.400947i 0.276613 0.960981i \(-0.410788\pi\)
−0.828469 + 0.560035i \(0.810788\pi\)
\(138\) 0.908587 + 0.660127i 0.0773440 + 0.0561937i
\(139\) 17.8699 12.9832i 1.51571 1.10122i 0.552140 0.833751i \(-0.313811\pi\)
0.963565 0.267473i \(-0.0861887\pi\)
\(140\) −4.24459 + 4.52458i −0.358733 + 0.382396i
\(141\) 3.84883 + 2.79634i 0.324130 + 0.235494i
\(142\) −4.09343 12.5983i −0.343513 1.05722i
\(143\) 15.7528 1.31732
\(144\) −0.0184644 0.0568277i −0.00153870 0.00473564i
\(145\) 6.26741 6.68083i 0.520480 0.554813i
\(146\) 1.30196 4.00703i 0.107751 0.331624i
\(147\) 0.369678 1.13775i 0.0304905 0.0938402i
\(148\) 0.847416 0.615684i 0.0696572 0.0506089i
\(149\) 4.18401 0.342768 0.171384 0.985204i \(-0.445176\pi\)
0.171384 + 0.985204i \(0.445176\pi\)
\(150\) −4.58669 + 7.24351i −0.374501 + 0.591430i
\(151\) −0.331561 −0.0269821 −0.0134910 0.999909i \(-0.504294\pi\)
−0.0134910 + 0.999909i \(0.504294\pi\)
\(152\) −1.14264 + 0.830178i −0.0926805 + 0.0673364i
\(153\) −0.0952107 + 0.293028i −0.00769733 + 0.0236899i
\(154\) −2.37871 + 7.32092i −0.191682 + 0.589936i
\(155\) 1.98946 15.8120i 0.159798 1.27005i
\(156\) 3.00852 + 9.25928i 0.240875 + 0.741336i
\(157\) 3.60750 0.287910 0.143955 0.989584i \(-0.454018\pi\)
0.143955 + 0.989584i \(0.454018\pi\)
\(158\) −3.05975 9.41695i −0.243421 0.749172i
\(159\) 0.729839 + 0.530259i 0.0578800 + 0.0420523i
\(160\) 2.02373 + 0.951057i 0.159990 + 0.0751876i
\(161\) −1.47012 + 1.06811i −0.115862 + 0.0841787i
\(162\) 7.13324 + 5.18260i 0.560440 + 0.407184i
\(163\) −4.12101 2.99409i −0.322782 0.234515i 0.414580 0.910013i \(-0.363929\pi\)
−0.737362 + 0.675498i \(0.763929\pi\)
\(164\) −7.36789 + 5.35309i −0.575336 + 0.418006i
\(165\) −1.32799 + 10.5547i −0.103384 + 0.821682i
\(166\) −3.78299 2.74850i −0.293617 0.213325i
\(167\) 6.44699 + 19.8418i 0.498883 + 1.53540i 0.810817 + 0.585300i \(0.199023\pi\)
−0.311934 + 0.950104i \(0.600977\pi\)
\(168\) −4.75742 −0.367043
\(169\) 5.94464 + 18.2957i 0.457280 + 1.40736i
\(170\) −5.55975 10.1011i −0.426414 0.774723i
\(171\) −0.0260789 + 0.0802625i −0.00199430 + 0.00613783i
\(172\) 2.85736 8.79404i 0.217871 0.670539i
\(173\) 9.69826 7.04620i 0.737345 0.535713i −0.154533 0.987988i \(-0.549387\pi\)
0.891879 + 0.452275i \(0.149387\pi\)
\(174\) 7.02464 0.532537
\(175\) −8.85328 10.6799i −0.669245 0.807328i
\(176\) 2.77447 0.209133
\(177\) 5.24660 3.81188i 0.394359 0.286518i
\(178\) −2.83802 + 8.73452i −0.212718 + 0.654680i
\(179\) −2.63942 + 8.12330i −0.197279 + 0.607164i 0.802663 + 0.596433i \(0.203416\pi\)
−0.999942 + 0.0107309i \(0.996584\pi\)
\(180\) 0.131231 0.0251018i 0.00978137 0.00187098i
\(181\) 2.41912 + 7.44529i 0.179812 + 0.553404i 0.999820 0.0189471i \(-0.00603140\pi\)
−0.820009 + 0.572351i \(0.806031\pi\)
\(182\) −15.7528 −1.16768
\(183\) −5.73987 17.6655i −0.424303 1.30587i
\(184\) 0.529876 + 0.384978i 0.0390630 + 0.0283809i
\(185\) 1.12939 + 2.05192i 0.0830346 + 0.150860i
\(186\) 9.88695 7.18329i 0.724946 0.526704i
\(187\) −11.5741 8.40906i −0.846381 0.614932i
\(188\) 2.24459 + 1.63079i 0.163704 + 0.118938i
\(189\) −11.7765 + 8.55611i −0.856613 + 0.622366i
\(190\) −1.52286 2.76678i −0.110480 0.200723i
\(191\) −2.72324 1.97855i −0.197047 0.143163i 0.484887 0.874577i \(-0.338861\pi\)
−0.681934 + 0.731414i \(0.738861\pi\)
\(192\) 0.529876 + 1.63079i 0.0382405 + 0.117692i
\(193\) −15.4211 −1.11004 −0.555018 0.831839i \(-0.687288\pi\)
−0.555018 + 0.831839i \(0.687288\pi\)
\(194\) −0.0278640 0.0857567i −0.00200052 0.00615697i
\(195\) −21.3822 + 4.08999i −1.53121 + 0.292891i
\(196\) 0.215591 0.663522i 0.0153994 0.0473945i
\(197\) 2.72086 8.37394i 0.193853 0.596619i −0.806135 0.591732i \(-0.798444\pi\)
0.999988 0.00488692i \(-0.00155556\pi\)
\(198\) 0.134119 0.0974433i 0.00953144 0.00692500i
\(199\) −17.6222 −1.24920 −0.624601 0.780944i \(-0.714738\pi\)
−0.624601 + 0.780944i \(0.714738\pi\)
\(200\) −2.67490 + 4.22433i −0.189144 + 0.298705i
\(201\) −7.41340 −0.522901
\(202\) 6.39635 4.64722i 0.450046 0.326977i
\(203\) −3.51232 + 10.8098i −0.246517 + 0.758700i
\(204\) 2.73227 8.40906i 0.191297 0.588752i
\(205\) −9.81955 17.8405i −0.685827 1.24603i
\(206\) 2.42091 + 7.45079i 0.168673 + 0.519121i
\(207\) 0.0391355 0.00272010
\(208\) 1.75453 + 5.39990i 0.121655 + 0.374415i
\(209\) −3.17022 2.30330i −0.219289 0.159323i
\(210\) 1.32799 10.5547i 0.0916401 0.728344i
\(211\) −4.93617 + 3.58634i −0.339820 + 0.246894i −0.744586 0.667527i \(-0.767353\pi\)
0.404766 + 0.914420i \(0.367353\pi\)
\(212\) 0.425633 + 0.309240i 0.0292326 + 0.0212387i
\(213\) 18.3761 + 13.3510i 1.25911 + 0.914798i
\(214\) 8.26974 6.00832i 0.565308 0.410720i
\(215\) 18.7126 + 8.79404i 1.27619 + 0.599749i
\(216\) 4.24459 + 3.08388i 0.288808 + 0.209831i
\(217\) 6.11047 + 18.8061i 0.414806 + 1.27664i
\(218\) 3.91091 0.264880
\(219\) 2.23250 + 6.87092i 0.150858 + 0.464294i
\(220\) −0.774467 + 6.15537i −0.0522146 + 0.414995i
\(221\) 9.04713 27.8442i 0.608576 1.87300i
\(222\) −0.555026 + 1.70820i −0.0372509 + 0.114647i
\(223\) 4.06828 2.95578i 0.272432 0.197933i −0.443178 0.896434i \(-0.646149\pi\)
0.715610 + 0.698500i \(0.246149\pi\)
\(224\) −2.77447 −0.185377
\(225\) 0.0190585 + 0.298152i 0.00127056 + 0.0198768i
\(226\) −6.37545 −0.424089
\(227\) 14.4314 10.4851i 0.957848 0.695918i 0.00519840 0.999986i \(-0.498345\pi\)
0.952650 + 0.304069i \(0.0983453\pi\)
\(228\) 0.748388 2.30330i 0.0495632 0.152540i
\(229\) −6.66137 + 20.5016i −0.440195 + 1.35478i 0.447472 + 0.894298i \(0.352324\pi\)
−0.887668 + 0.460485i \(0.847676\pi\)
\(230\) −1.00201 + 1.06811i −0.0660707 + 0.0704289i
\(231\) −4.07881 12.5533i −0.268366 0.825946i
\(232\) 4.09668 0.268960
\(233\) 4.54454 + 13.9867i 0.297723 + 0.916297i 0.982293 + 0.187350i \(0.0599899\pi\)
−0.684570 + 0.728947i \(0.740010\pi\)
\(234\) 0.274467 + 0.199412i 0.0179425 + 0.0130360i
\(235\) −4.24459 + 4.52458i −0.276887 + 0.295151i
\(236\) 3.05975 2.22304i 0.199173 0.144708i
\(237\) 13.7358 + 9.97963i 0.892235 + 0.648247i
\(238\) 11.5741 + 8.40906i 0.750236 + 0.545079i
\(239\) −5.61478 + 4.07938i −0.363190 + 0.263873i −0.754381 0.656436i \(-0.772063\pi\)
0.391192 + 0.920309i \(0.372063\pi\)
\(240\) −3.76594 + 0.720350i −0.243091 + 0.0464984i
\(241\) −2.67787 1.94559i −0.172497 0.125326i 0.498187 0.867070i \(-0.333999\pi\)
−0.670684 + 0.741743i \(0.733999\pi\)
\(242\) −1.02048 3.14070i −0.0655987 0.201892i
\(243\) 0.620870 0.0398288
\(244\) −3.34742 10.3023i −0.214296 0.659536i
\(245\) 1.41189 + 0.663522i 0.0902026 + 0.0423909i
\(246\) 4.82570 14.8520i 0.307675 0.946927i
\(247\) 2.47807 7.62672i 0.157676 0.485277i
\(248\) 5.76594 4.18920i 0.366138 0.266015i
\(249\) 8.01806 0.508124
\(250\) −8.62531 7.11365i −0.545513 0.449906i
\(251\) −9.46454 −0.597397 −0.298698 0.954348i \(-0.596552\pi\)
−0.298698 + 0.954348i \(0.596552\pi\)
\(252\) −0.134119 + 0.0974433i −0.00844872 + 0.00613835i
\(253\) −0.561537 + 1.72823i −0.0353036 + 0.108653i
\(254\) 2.95078 9.08158i 0.185149 0.569829i
\(255\) 17.8935 + 8.40906i 1.12053 + 0.526596i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −7.07963 −0.441615 −0.220808 0.975317i \(-0.570869\pi\)
−0.220808 + 0.975317i \(0.570869\pi\)
\(258\) 4.89955 + 15.0793i 0.305033 + 0.938795i
\(259\) −2.35113 1.70820i −0.146092 0.106142i
\(260\) −12.4698 + 2.38523i −0.773347 + 0.147926i
\(261\) 0.198036 0.143881i 0.0122581 0.00890604i
\(262\) −4.52988 3.29115i −0.279857 0.203328i
\(263\) −1.15969 0.842563i −0.0715095 0.0519547i 0.551456 0.834204i \(-0.314072\pi\)
−0.622966 + 0.782249i \(0.714072\pi\)
\(264\) −3.84883 + 2.79634i −0.236879 + 0.172103i
\(265\) −0.804885 + 0.857977i −0.0494437 + 0.0527051i
\(266\) 3.17022 + 2.30330i 0.194379 + 0.141225i
\(267\) −4.86639 14.9772i −0.297818 0.916590i
\(268\) −4.32340 −0.264094
\(269\) −4.41368 13.5839i −0.269107 0.828226i −0.990719 0.135928i \(-0.956598\pi\)
0.721612 0.692298i \(-0.243402\pi\)
\(270\) −8.02665 + 8.55611i −0.488487 + 0.520708i
\(271\) 9.51325 29.2788i 0.577889 1.77856i −0.0482363 0.998836i \(-0.515360\pi\)
0.626125 0.779723i \(-0.284640\pi\)
\(272\) 1.59343 4.90406i 0.0966156 0.297352i
\(273\) 21.8529 15.8770i 1.32260 0.960922i
\(274\) 7.98414 0.482340
\(275\) −13.4400 3.43643i −0.810460 0.207224i
\(276\) −1.12307 −0.0676012
\(277\) −2.58051 + 1.87485i −0.155048 + 0.112649i −0.662604 0.748970i \(-0.730549\pi\)
0.507556 + 0.861619i \(0.330549\pi\)
\(278\) −6.82570 + 21.0073i −0.409378 + 1.25994i
\(279\) 0.131598 0.405017i 0.00787856 0.0242477i
\(280\) 0.774467 6.15537i 0.0462833 0.367854i
\(281\) 6.30053 + 19.3910i 0.375858 + 1.15677i 0.942898 + 0.333081i \(0.108088\pi\)
−0.567040 + 0.823690i \(0.691912\pi\)
\(282\) −4.75742 −0.283300
\(283\) −4.10897 12.6461i −0.244253 0.751733i −0.995758 0.0920063i \(-0.970672\pi\)
0.751506 0.659727i \(-0.229328\pi\)
\(284\) 10.7167 + 7.78616i 0.635921 + 0.462023i
\(285\) 4.90115 + 2.30330i 0.290319 + 0.136436i
\(286\) −12.7443 + 9.25928i −0.753587 + 0.547513i
\(287\) 20.4420 + 14.8520i 1.20665 + 0.876684i
\(288\) 0.0483405 + 0.0351215i 0.00284849 + 0.00206955i
\(289\) −7.75751 + 5.63616i −0.456324 + 0.331539i
\(290\) −1.14355 + 9.08880i −0.0671516 + 0.533713i
\(291\) 0.125087 + 0.0908809i 0.00733272 + 0.00532753i
\(292\) 1.30196 + 4.00703i 0.0761917 + 0.234494i
\(293\) −26.0420 −1.52139 −0.760696 0.649108i \(-0.775142\pi\)
−0.760696 + 0.649108i \(0.775142\pi\)
\(294\) 0.369678 + 1.13775i 0.0215601 + 0.0663550i
\(295\) 4.07788 + 7.40883i 0.237423 + 0.431359i
\(296\) −0.323684 + 0.996198i −0.0188138 + 0.0579028i
\(297\) −4.49821 + 13.8441i −0.261013 + 0.803315i
\(298\) −3.38494 + 2.45930i −0.196084 + 0.142464i
\(299\) −3.71874 −0.215060
\(300\) −0.546923 8.55611i −0.0315766 0.493987i
\(301\) −25.6544 −1.47869
\(302\) 0.268239 0.194887i 0.0154354 0.0112145i
\(303\) −4.18937 + 12.8936i −0.240673 + 0.740716i
\(304\) 0.436451 1.34326i 0.0250322 0.0770411i
\(305\) 23.7908 4.55071i 1.36226 0.260573i
\(306\) −0.0952107 0.293028i −0.00544283 0.0167513i
\(307\) 25.1000 1.43253 0.716267 0.697826i \(-0.245849\pi\)
0.716267 + 0.697826i \(0.245849\pi\)
\(308\) −2.37871 7.32092i −0.135540 0.417148i
\(309\) −10.8679 7.89599i −0.618253 0.449187i
\(310\) 7.68456 + 13.9616i 0.436453 + 0.792964i
\(311\) −0.585185 + 0.425162i −0.0331828 + 0.0241087i −0.604253 0.796792i \(-0.706528\pi\)
0.571070 + 0.820901i \(0.306528\pi\)
\(312\) −7.87642 5.72255i −0.445914 0.323976i
\(313\) −17.4879 12.7057i −0.988477 0.718170i −0.0288898 0.999583i \(-0.509197\pi\)
−0.959587 + 0.281412i \(0.909197\pi\)
\(314\) −2.91853 + 2.12043i −0.164702 + 0.119663i
\(315\) −0.178747 0.324754i −0.0100713 0.0182978i
\(316\) 8.01054 + 5.81999i 0.450628 + 0.327400i
\(317\) −5.81992 17.9119i −0.326879 1.00603i −0.970585 0.240758i \(-0.922604\pi\)
0.643706 0.765273i \(-0.277396\pi\)
\(318\) −0.902131 −0.0505890
\(319\) 3.51232 + 10.8098i 0.196652 + 0.605233i
\(320\) −2.19625 + 0.420099i −0.122774 + 0.0234842i
\(321\) −5.41637 + 16.6699i −0.302312 + 0.930422i
\(322\) 0.561537 1.72823i 0.0312933 0.0963107i
\(323\) −5.89196 + 4.28076i −0.327837 + 0.238188i
\(324\) −8.81717 −0.489843
\(325\) −1.81098 28.3311i −0.100455 1.57153i
\(326\) 5.09385 0.282122
\(327\) −5.42535 + 3.94175i −0.300023 + 0.217979i
\(328\) 2.81428 8.66148i 0.155393 0.478250i
\(329\) 2.37871 7.32092i 0.131143 0.403615i
\(330\) −5.12953 9.31951i −0.282371 0.513022i
\(331\) 5.21494 + 16.0499i 0.286639 + 0.882185i 0.985903 + 0.167320i \(0.0535115\pi\)
−0.699263 + 0.714864i \(0.746489\pi\)
\(332\) 4.67603 0.256631
\(333\) 0.0193408 + 0.0595250i 0.00105987 + 0.00326195i
\(334\) −16.8784 12.2629i −0.923546 0.670996i
\(335\) 1.20684 9.59180i 0.0659366 0.524056i
\(336\) 3.84883 2.79634i 0.209971 0.152553i
\(337\) −15.6562 11.3749i −0.852845 0.619628i 0.0730841 0.997326i \(-0.476716\pi\)
−0.925929 + 0.377698i \(0.876716\pi\)
\(338\) −15.5633 11.3074i −0.846530 0.615040i
\(339\) 8.84425 6.42572i 0.480353 0.348997i
\(340\) 10.4352 + 4.90406i 0.565930 + 0.265960i
\(341\) 15.9974 + 11.6228i 0.866309 + 0.629410i
\(342\) −0.0260789 0.0802625i −0.00141018 0.00434010i
\(343\) 17.4856 0.944134
\(344\) 2.85736 + 8.79404i 0.154058 + 0.474143i
\(345\) 0.313496 2.49163i 0.0168781 0.134145i
\(346\) −3.70441 + 11.4010i −0.199150 + 0.612921i
\(347\) −2.79311 + 8.59630i −0.149942 + 0.461473i −0.997613 0.0690480i \(-0.978004\pi\)
0.847672 + 0.530521i \(0.178004\pi\)
\(348\) −5.68305 + 4.12898i −0.304644 + 0.221337i
\(349\) 36.7305 1.96614 0.983068 0.183240i \(-0.0586584\pi\)
0.983068 + 0.183240i \(0.0586584\pi\)
\(350\) 13.4400 + 3.43643i 0.718396 + 0.183685i
\(351\) −29.7891 −1.59002
\(352\) −2.24459 + 1.63079i −0.119637 + 0.0869214i
\(353\) 5.67779 17.4744i 0.302198 0.930070i −0.678510 0.734591i \(-0.737374\pi\)
0.980708 0.195479i \(-0.0626261\pi\)
\(354\) −2.00402 + 6.16775i −0.106513 + 0.327812i
\(355\) −20.2657 + 21.6024i −1.07559 + 1.14654i
\(356\) −2.83802 8.73452i −0.150415 0.462928i
\(357\) −24.5313 −1.29834
\(358\) −2.63942 8.12330i −0.139498 0.429330i
\(359\) 19.7609 + 14.3572i 1.04294 + 0.757742i 0.970858 0.239657i \(-0.0770348\pi\)
0.0720846 + 0.997399i \(0.477035\pi\)
\(360\) −0.0914135 + 0.0974433i −0.00481791 + 0.00513572i
\(361\) 13.7575 9.99539i 0.724078 0.526073i
\(362\) −6.33334 4.60144i −0.332873 0.241846i
\(363\) 4.58111 + 3.32837i 0.240446 + 0.174694i
\(364\) 12.7443 9.25928i 0.667983 0.485318i
\(365\) −9.25334 + 1.76998i −0.484342 + 0.0926450i
\(366\) 15.0272 + 10.9179i 0.785482 + 0.570686i
\(367\) 4.48768 + 13.8117i 0.234255 + 0.720963i 0.997219 + 0.0745221i \(0.0237431\pi\)
−0.762964 + 0.646441i \(0.776257\pi\)
\(368\) −0.654963 −0.0341423
\(369\) −0.168160 0.517542i −0.00875404 0.0269422i
\(370\) −2.11979 0.996198i −0.110202 0.0517898i
\(371\) 0.451065 1.38824i 0.0234182 0.0720737i
\(372\) −3.77648 + 11.6228i −0.195801 + 0.602615i
\(373\) 18.8410 13.6888i 0.975549 0.708778i 0.0188399 0.999823i \(-0.494003\pi\)
0.956710 + 0.291044i \(0.0940027\pi\)
\(374\) 14.3064 0.739764
\(375\) 19.1351 + 1.17497i 0.988130 + 0.0606753i
\(376\) −2.77447 −0.143082
\(377\) −18.8178 + 13.6719i −0.969166 + 0.704140i
\(378\) 4.49821 13.8441i 0.231363 0.712063i
\(379\) 8.84332 27.2169i 0.454251 1.39804i −0.417762 0.908556i \(-0.637185\pi\)
0.872013 0.489483i \(-0.162815\pi\)
\(380\) 2.85829 + 1.34326i 0.146627 + 0.0689076i
\(381\) 5.05975 + 15.5723i 0.259219 + 0.797794i
\(382\) 3.36611 0.172225
\(383\) −5.13454 15.8025i −0.262363 0.807469i −0.992289 0.123944i \(-0.960446\pi\)
0.729927 0.683526i \(-0.239554\pi\)
\(384\) −1.38723 1.00788i −0.0707920 0.0514334i
\(385\) 16.9060 3.23378i 0.861610 0.164809i
\(386\) 12.4759 9.06430i 0.635008 0.461361i
\(387\) 0.446986 + 0.324754i 0.0227216 + 0.0165082i
\(388\) 0.0729490 + 0.0530006i 0.00370343 + 0.00269070i
\(389\) −21.3392 + 15.5039i −1.08194 + 0.786077i −0.978021 0.208508i \(-0.933139\pi\)
−0.103922 + 0.994585i \(0.533139\pi\)
\(390\) 14.8945 15.8770i 0.754215 0.803965i
\(391\) 2.73227 + 1.98511i 0.138177 + 0.100391i
\(392\) 0.215591 + 0.663522i 0.0108890 + 0.0335129i
\(393\) 9.60109 0.484311
\(394\) 2.72086 + 8.37394i 0.137075 + 0.421873i
\(395\) −15.1482 + 16.1474i −0.762187 + 0.812463i
\(396\) −0.0512290 + 0.157667i −0.00257435 + 0.00792305i
\(397\) −5.53406 + 17.0321i −0.277747 + 0.854816i 0.710733 + 0.703462i \(0.248363\pi\)
−0.988480 + 0.151354i \(0.951637\pi\)
\(398\) 14.2566 10.3580i 0.714620 0.519202i
\(399\) −6.71930 −0.336386
\(400\) −0.318958 4.98982i −0.0159479 0.249491i
\(401\) 32.0164 1.59882 0.799411 0.600785i \(-0.205145\pi\)
0.799411 + 0.600785i \(0.205145\pi\)
\(402\) 5.99757 4.35749i 0.299132 0.217332i
\(403\) −12.5047 + 38.4856i −0.622905 + 1.91710i
\(404\) −2.44319 + 7.51936i −0.121553 + 0.374102i
\(405\) 2.46123 19.5616i 0.122300 0.972022i
\(406\) −3.51232 10.8098i −0.174314 0.536482i
\(407\) −2.90615 −0.144053
\(408\) 2.73227 + 8.40906i 0.135268 + 0.416311i
\(409\) −14.5901 10.6003i −0.721435 0.524153i 0.165407 0.986225i \(-0.447106\pi\)
−0.886842 + 0.462072i \(0.847106\pi\)
\(410\) 18.4306 + 8.66148i 0.910221 + 0.427760i
\(411\) −11.0759 + 8.04709i −0.546332 + 0.396934i
\(412\) −6.33802 4.60484i −0.312252 0.226864i
\(413\) −8.48918 6.16775i −0.417725 0.303495i
\(414\) −0.0316613 + 0.0230033i −0.00155607 + 0.00113055i
\(415\) −1.30527 + 10.3741i −0.0640733 + 0.509246i
\(416\) −4.59343 3.33732i −0.225211 0.163626i
\(417\) −11.7041 36.0216i −0.573153 1.76398i
\(418\) 3.91861 0.191666
\(419\) −6.03511 18.5742i −0.294834 0.907407i −0.983277 0.182116i \(-0.941705\pi\)
0.688443 0.725291i \(-0.258295\pi\)
\(420\) 5.12953 + 9.31951i 0.250295 + 0.454745i
\(421\) −6.04242 + 18.5967i −0.294490 + 0.906346i 0.688903 + 0.724854i \(0.258093\pi\)
−0.983392 + 0.181492i \(0.941907\pi\)
\(422\) 1.88545 5.80281i 0.0917822 0.282477i
\(423\) −0.134119 + 0.0974433i −0.00652110 + 0.00473786i
\(424\) −0.526111 −0.0255502
\(425\) −13.7929 + 21.7825i −0.669055 + 1.05660i
\(426\) −22.7142 −1.10050
\(427\) −24.3145 + 17.6655i −1.17666 + 0.854893i
\(428\) −3.15876 + 9.72166i −0.152684 + 0.469914i
\(429\) 8.34705 25.6896i 0.402999 1.24030i
\(430\) −20.3079 + 3.88449i −0.979332 + 0.187327i
\(431\) −6.55002 20.1589i −0.315503 0.971019i −0.975547 0.219792i \(-0.929462\pi\)
0.660044 0.751227i \(-0.270538\pi\)
\(432\) −5.24660 −0.252427
\(433\) 2.64199 + 8.13122i 0.126966 + 0.390761i 0.994254 0.107045i \(-0.0341389\pi\)
−0.867288 + 0.497807i \(0.834139\pi\)
\(434\) −15.9974 11.6228i −0.767901 0.557913i
\(435\) −7.57408 13.7609i −0.363150 0.659783i
\(436\) −3.16400 + 2.29878i −0.151528 + 0.110091i
\(437\) 0.748388 + 0.543736i 0.0358003 + 0.0260104i
\(438\) −5.84475 4.24646i −0.279273 0.202904i
\(439\) 22.7102 16.4999i 1.08390 0.787499i 0.105541 0.994415i \(-0.466343\pi\)
0.978359 + 0.206916i \(0.0663427\pi\)
\(440\) −2.99148 5.43502i −0.142613 0.259104i
\(441\) 0.0337257 + 0.0245031i 0.00160598 + 0.00116682i
\(442\) 9.04713 + 27.8442i 0.430328 + 1.32441i
\(443\) −33.0546 −1.57047 −0.785236 0.619197i \(-0.787458\pi\)
−0.785236 + 0.619197i \(0.787458\pi\)
\(444\) −0.555026 1.70820i −0.0263404 0.0810673i
\(445\) 20.1704 3.85820i 0.956169 0.182896i
\(446\) −1.55394 + 4.78254i −0.0735813 + 0.226460i
\(447\) 2.21701 6.82325i 0.104861 0.322729i
\(448\) 2.24459 1.63079i 0.106047 0.0770476i
\(449\) −37.1628 −1.75382 −0.876911 0.480652i \(-0.840400\pi\)
−0.876911 + 0.480652i \(0.840400\pi\)
\(450\) −0.190668 0.230008i −0.00898819 0.0108427i
\(451\) 25.2677 1.18981
\(452\) 5.15785 3.74740i 0.242605 0.176263i
\(453\) −0.175686 + 0.540707i −0.00825446 + 0.0254046i
\(454\) −5.51232 + 16.9652i −0.258706 + 0.796215i
\(455\) 16.9850 + 30.8589i 0.796267 + 1.44669i
\(456\) 0.748388 + 2.30330i 0.0350465 + 0.107862i
\(457\) 29.3139 1.37125 0.685624 0.727956i \(-0.259529\pi\)
0.685624 + 0.727956i \(0.259529\pi\)
\(458\) −6.66137 20.5016i −0.311265 0.957976i
\(459\) 21.8870 + 15.9018i 1.02160 + 0.742233i
\(460\) 0.182827 1.45309i 0.00852435 0.0677504i
\(461\) −7.20624 + 5.23564i −0.335628 + 0.243848i −0.742815 0.669497i \(-0.766510\pi\)
0.407187 + 0.913345i \(0.366510\pi\)
\(462\) 10.6785 + 7.75836i 0.496807 + 0.360952i
\(463\) 14.7865 + 10.7430i 0.687187 + 0.499271i 0.875734 0.482793i \(-0.160378\pi\)
−0.188547 + 0.982064i \(0.560378\pi\)
\(464\) −3.31428 + 2.40797i −0.153862 + 0.111787i
\(465\) −24.7319 11.6228i −1.14692 0.538995i
\(466\) −11.8978 8.64424i −0.551154 0.400436i
\(467\) −11.3360 34.8886i −0.524568 1.61445i −0.765169 0.643829i \(-0.777345\pi\)
0.240601 0.970624i \(-0.422655\pi\)
\(468\) −0.339260 −0.0156823
\(469\) 3.70670 + 11.4081i 0.171160 + 0.526775i
\(470\) 0.774467 6.15537i 0.0357235 0.283926i
\(471\) 1.91153 5.88308i 0.0880785 0.271078i
\(472\) −1.16872 + 3.59695i −0.0537948 + 0.165563i
\(473\) −20.7548 + 15.0793i −0.954309 + 0.693346i
\(474\) −16.9784 −0.779842
\(475\) −3.77798 + 5.96637i −0.173346 + 0.273756i
\(476\) −14.3064 −0.655731
\(477\) −0.0254325 + 0.0184778i −0.00116447 + 0.000846040i
\(478\) 2.14465 6.60057i 0.0980942 0.301903i
\(479\) −3.89046 + 11.9736i −0.177760 + 0.547088i −0.999749 0.0224155i \(-0.992864\pi\)
0.821989 + 0.569503i \(0.192864\pi\)
\(480\) 2.62330 2.79634i 0.119737 0.127635i
\(481\) −1.83781 5.65620i −0.0837969 0.257900i
\(482\) 3.31003 0.150768
\(483\) 0.962877 + 2.96343i 0.0438124 + 0.134841i
\(484\) 2.67164 + 1.94106i 0.121438 + 0.0882301i
\(485\) −0.137949 + 0.147048i −0.00626393 + 0.00667712i
\(486\) −0.502294 + 0.364938i −0.0227845 + 0.0165539i
\(487\) 14.8257 + 10.7715i 0.671816 + 0.488103i 0.870633 0.491934i \(-0.163710\pi\)
−0.198816 + 0.980037i \(0.563710\pi\)
\(488\) 8.76365 + 6.36716i 0.396712 + 0.288228i
\(489\) −7.06635 + 5.13401i −0.319552 + 0.232168i
\(490\) −1.53226 + 0.293090i −0.0692202 + 0.0132405i
\(491\) −17.5595 12.7577i −0.792448 0.575747i 0.116241 0.993221i \(-0.462915\pi\)
−0.908689 + 0.417474i \(0.862915\pi\)
\(492\) 4.82570 + 14.8520i 0.217559 + 0.669578i
\(493\) 21.1243 0.951389
\(494\) 2.47807 + 7.62672i 0.111494 + 0.343143i
\(495\) −0.335495 0.157667i −0.0150794 0.00708659i
\(496\) −2.20239 + 6.77827i −0.0988904 + 0.304353i
\(497\) 11.3571 34.9535i 0.509434 1.56788i
\(498\) −6.48675 + 4.71290i −0.290678 + 0.211190i
\(499\) 15.8391 0.709055 0.354527 0.935046i \(-0.384642\pi\)
0.354527 + 0.935046i \(0.384642\pi\)
\(500\) 11.1593 + 0.685229i 0.499060 + 0.0306444i
\(501\) 35.7739 1.59826
\(502\) 7.65697 5.56312i 0.341748 0.248294i
\(503\) 8.51433 26.2044i 0.379635 1.16840i −0.560662 0.828044i \(-0.689453\pi\)
0.940298 0.340353i \(-0.110547\pi\)
\(504\) 0.0512290 0.157667i 0.00228192 0.00702303i
\(505\) −16.0003 7.51936i −0.712003 0.334607i
\(506\) −0.561537 1.72823i −0.0249634 0.0768294i
\(507\) 32.9864 1.46498
\(508\) 2.95078 + 9.08158i 0.130920 + 0.402930i
\(509\) 22.3386 + 16.2300i 0.990142 + 0.719380i 0.959952 0.280164i \(-0.0903889\pi\)
0.0301894 + 0.999544i \(0.490389\pi\)
\(510\) −19.4188 + 3.71444i −0.859881 + 0.164478i
\(511\) 9.45701 6.87092i 0.418354 0.303952i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) 5.99499 + 4.35562i 0.264685 + 0.192305i
\(514\) 5.72754 4.16130i 0.252631 0.183547i
\(515\) 11.9854 12.7760i 0.528139 0.562977i
\(516\) −12.8272 9.31951i −0.564686 0.410268i
\(517\) −2.37871 7.32092i −0.104616 0.321974i
\(518\) 2.90615 0.127689
\(519\) −6.35200 19.5495i −0.278822 0.858126i
\(520\) 8.68631 9.25928i 0.380920 0.406046i
\(521\) 5.28084 16.2527i 0.231358 0.712046i −0.766226 0.642571i \(-0.777868\pi\)
0.997584 0.0694747i \(-0.0221323\pi\)
\(522\) −0.0756429 + 0.232805i −0.00331080 + 0.0101896i
\(523\) −29.3796 + 21.3456i −1.28468 + 0.933376i −0.999684 0.0251516i \(-0.991993\pi\)
−0.284999 + 0.958528i \(0.591993\pi\)
\(524\) 5.59923 0.244604
\(525\) −22.1079 + 8.77880i −0.964868 + 0.383138i
\(526\) 1.43345 0.0625016
\(527\) 29.7317 21.6013i 1.29513 0.940970i
\(528\) 1.47012 4.52458i 0.0639789 0.196907i
\(529\) −6.97483 + 21.4663i −0.303253 + 0.933318i
\(530\) 0.146859 1.16722i 0.00637915 0.0507007i
\(531\) 0.0698337 + 0.214926i 0.00303052 + 0.00932699i
\(532\) −3.91861 −0.169893
\(533\) 15.9789 + 49.1780i 0.692123 + 2.13014i
\(534\) 12.7404 + 9.25642i 0.551330 + 0.400565i
\(535\) −20.6865 9.72166i −0.894356 0.420304i
\(536\) 3.49771 2.54123i 0.151078 0.109764i
\(537\) 11.8488 + 8.60868i 0.511315 + 0.371492i
\(538\) 11.5552 + 8.39532i 0.498178 + 0.361948i
\(539\) −1.56598 + 1.13775i −0.0674516 + 0.0490064i
\(540\) 1.46454 11.6400i 0.0630238 0.500905i
\(541\) −20.1742 14.6574i −0.867355 0.630170i 0.0625209 0.998044i \(-0.480086\pi\)
−0.929876 + 0.367873i \(0.880086\pi\)
\(542\) 9.51325 + 29.2788i 0.408629 + 1.25763i
\(543\) 13.4235 0.576060
\(544\) 1.59343 + 4.90406i 0.0683176 + 0.210260i
\(545\) −4.21681 7.66125i −0.180628 0.328172i
\(546\) −8.34705 + 25.6896i −0.357221 + 1.09941i
\(547\) 2.06176 6.34546i 0.0881547 0.271312i −0.897255 0.441513i \(-0.854442\pi\)
0.985409 + 0.170201i \(0.0544418\pi\)
\(548\) −6.45931 + 4.69296i −0.275928 + 0.200473i
\(549\) 0.647264 0.0276245
\(550\) 12.8930 5.11968i 0.549761 0.218304i
\(551\) 5.78609 0.246496
\(552\) 0.908587 0.660127i 0.0386720 0.0280969i
\(553\) 8.48918 26.1270i 0.360997 1.11103i
\(554\) 0.985668 3.03357i 0.0418770 0.128884i
\(555\) 3.94469 0.754541i 0.167443 0.0320285i
\(556\) −6.82570 21.0073i −0.289474 0.890909i
\(557\) −20.4328 −0.865765 −0.432882 0.901450i \(-0.642503\pi\)
−0.432882 + 0.901450i \(0.642503\pi\)
\(558\) 0.131598 + 0.405017i 0.00557098 + 0.0171457i
\(559\) −42.4736 30.8589i −1.79644 1.30519i
\(560\) 2.99148 + 5.43502i 0.126413 + 0.229671i
\(561\) −19.8463 + 14.4192i −0.837910 + 0.608777i
\(562\) −16.4950 11.9843i −0.695799 0.505528i
\(563\) 0.487680 + 0.354320i 0.0205532 + 0.0149328i 0.598014 0.801485i \(-0.295957\pi\)
−0.577461 + 0.816418i \(0.695957\pi\)
\(564\) 3.84883 2.79634i 0.162065 0.117747i
\(565\) 6.87412 + 12.4891i 0.289196 + 0.525422i
\(566\) 10.7574 + 7.81572i 0.452168 + 0.328519i
\(567\) 7.55947 + 23.2657i 0.317468 + 0.977066i
\(568\) −13.2466 −0.555815
\(569\) 10.4688 + 32.2195i 0.438873 + 1.35071i 0.889065 + 0.457781i \(0.151356\pi\)
−0.450192 + 0.892932i \(0.648644\pi\)
\(570\) −5.31896 + 1.01741i −0.222787 + 0.0426146i
\(571\) −1.92521 + 5.92520i −0.0805677 + 0.247962i −0.983225 0.182399i \(-0.941614\pi\)
0.902657 + 0.430361i \(0.141614\pi\)
\(572\) 4.86789 14.9818i 0.203537 0.626422i
\(573\) −4.66958 + 3.39265i −0.195074 + 0.141730i
\(574\) −25.2677 −1.05465
\(575\) 3.17275 + 0.811231i 0.132313 + 0.0338307i
\(576\) −0.0597522 −0.00248967
\(577\) −3.05893 + 2.22244i −0.127345 + 0.0925214i −0.649634 0.760247i \(-0.725078\pi\)
0.522290 + 0.852768i \(0.325078\pi\)
\(578\) 2.96310 9.11949i 0.123249 0.379321i
\(579\) −8.17127 + 25.1486i −0.339587 + 1.04514i
\(580\) −4.41711 8.02516i −0.183410 0.333226i
\(581\) −4.00903 12.3385i −0.166323 0.511889i
\(582\) −0.154616 −0.00640903
\(583\) −0.451065 1.38824i −0.0186812 0.0574949i
\(584\) −3.40859 2.47648i −0.141048 0.102478i
\(585\) 0.0947014 0.752675i 0.00391542 0.0311193i
\(586\) 21.0684 15.3071i 0.870330 0.632332i
\(587\) −13.2296 9.61184i −0.546042 0.396723i 0.280282 0.959918i \(-0.409572\pi\)
−0.826324 + 0.563195i \(0.809572\pi\)
\(588\) −0.967829 0.703169i −0.0399126 0.0289982i
\(589\) 8.14373 5.91676i 0.335556 0.243796i
\(590\) −7.65388 3.59695i −0.315105 0.148084i
\(591\) −12.2144 8.87430i −0.502435 0.365040i
\(592\) −0.323684 0.996198i −0.0133033 0.0409435i
\(593\) 9.53314 0.391479 0.195740 0.980656i \(-0.437289\pi\)
0.195740 + 0.980656i \(0.437289\pi\)
\(594\) −4.49821 13.8441i −0.184564 0.568030i
\(595\) 3.99349 31.7397i 0.163717 1.30120i
\(596\) 1.29293 3.97923i 0.0529605 0.162996i
\(597\) −9.33756 + 28.7381i −0.382161 + 1.17617i
\(598\) 3.00852 2.18582i 0.123028 0.0893848i
\(599\) −16.0682 −0.656528 −0.328264 0.944586i \(-0.606464\pi\)
−0.328264 + 0.944586i \(0.606464\pi\)
\(600\) 5.47163 + 6.60057i 0.223378 + 0.269467i
\(601\) 15.0380 0.613413 0.306707 0.951804i \(-0.400773\pi\)
0.306707 + 0.951804i \(0.400773\pi\)
\(602\) 20.7548 15.0793i 0.845904 0.614585i
\(603\) 0.0798292 0.245689i 0.00325090 0.0100052i
\(604\) −0.102458 + 0.315333i −0.00416896 + 0.0128307i
\(605\) −5.05216 + 5.38541i −0.205399 + 0.218948i
\(606\) −4.18937 12.8936i −0.170182 0.523765i
\(607\) −44.8348 −1.81979 −0.909894 0.414840i \(-0.863837\pi\)
−0.909894 + 0.414840i \(0.863837\pi\)
\(608\) 0.436451 + 1.34326i 0.0177004 + 0.0544763i
\(609\) 15.7674 + 11.4557i 0.638929 + 0.464209i
\(610\) −16.5723 + 17.6655i −0.670994 + 0.715255i
\(611\) 12.7443 9.25928i 0.515580 0.374590i
\(612\) 0.249265 + 0.181101i 0.0100759 + 0.00732059i
\(613\) 12.5793 + 9.13937i 0.508072 + 0.369136i 0.812092 0.583530i \(-0.198329\pi\)
−0.304020 + 0.952666i \(0.598329\pi\)
\(614\) −20.3064 + 14.7534i −0.819498 + 0.595400i
\(615\) −34.2973 + 6.56038i −1.38300 + 0.264540i
\(616\) 6.22754 + 4.52458i 0.250915 + 0.182300i
\(617\) 5.43852 + 16.7380i 0.218946 + 0.673848i 0.998850 + 0.0479478i \(0.0152681\pi\)
−0.779903 + 0.625900i \(0.784732\pi\)
\(618\) 13.4335 0.540373
\(619\) −11.5229 35.4637i −0.463143 1.42541i −0.861303 0.508091i \(-0.830351\pi\)
0.398161 0.917316i \(-0.369649\pi\)
\(620\) −14.4233 6.77827i −0.579255 0.272222i
\(621\) 1.06188 3.26814i 0.0426120 0.131146i
\(622\) 0.223521 0.687926i 0.00896236 0.0275833i
\(623\) −20.6144 + 14.9772i −0.825897 + 0.600049i
\(624\) 9.73579 0.389743
\(625\) −4.63525 + 24.5665i −0.185410 + 0.982661i
\(626\) 21.6163 0.863960
\(627\) −5.43603 + 3.94951i −0.217094 + 0.157728i
\(628\) 1.11478 3.43094i 0.0444845 0.136909i
\(629\) −1.66906 + 5.13683i −0.0665496 + 0.204819i
\(630\) 0.335495 + 0.157667i 0.0133665 + 0.00628159i
\(631\) 2.64380 + 8.13677i 0.105248 + 0.323920i 0.989789 0.142543i \(-0.0455280\pi\)
−0.884541 + 0.466463i \(0.845528\pi\)
\(632\) −9.90157 −0.393863
\(633\) 3.23301 + 9.95017i 0.128500 + 0.395484i
\(634\) 15.2367 + 11.0701i 0.605129 + 0.439652i
\(635\) −20.9719 + 4.01150i −0.832243 + 0.159191i
\(636\) 0.729839 0.530259i 0.0289400 0.0210261i
\(637\) −3.20469 2.32834i −0.126974 0.0922523i
\(638\) −9.19537 6.68083i −0.364048 0.264497i
\(639\) −0.640348 + 0.465240i −0.0253318 + 0.0184046i
\(640\) 1.52988 1.63079i 0.0604737 0.0644627i
\(641\) 18.4582 + 13.4107i 0.729055 + 0.529690i 0.889264 0.457394i \(-0.151217\pi\)
−0.160209 + 0.987083i \(0.551217\pi\)
\(642\) −5.41637 16.6699i −0.213767 0.657908i
\(643\) 34.7745 1.37137 0.685686 0.727898i \(-0.259503\pi\)
0.685686 + 0.727898i \(0.259503\pi\)
\(644\) 0.561537 + 1.72823i 0.0221277 + 0.0681020i
\(645\) 24.2566 25.8567i 0.955104 1.01811i
\(646\) 2.25053 6.92641i 0.0885459 0.272516i
\(647\) −5.08583 + 15.6526i −0.199945 + 0.615366i 0.799939 + 0.600082i \(0.204865\pi\)
−0.999883 + 0.0152844i \(0.995135\pi\)
\(648\) 7.13324 5.18260i 0.280220 0.203592i
\(649\) −10.4932 −0.411894
\(650\) 18.1177 + 21.8559i 0.710635 + 0.857258i
\(651\) 33.9066 1.32890
\(652\) −4.12101 + 2.99409i −0.161391 + 0.117257i
\(653\) 9.33515 28.7306i 0.365313 1.12432i −0.584473 0.811414i \(-0.698699\pi\)
0.949785 0.312903i \(-0.101301\pi\)
\(654\) 2.07230 6.37788i 0.0810333 0.249395i
\(655\) −1.56298 + 12.4223i −0.0610705 + 0.485381i
\(656\) 2.81428 + 8.66148i 0.109879 + 0.338174i
\(657\) −0.251751 −0.00982173
\(658\) 2.37871 + 7.32092i 0.0927318 + 0.285399i
\(659\) 23.0523 + 16.7485i 0.897991 + 0.652428i 0.937949 0.346773i \(-0.112723\pi\)
−0.0399585 + 0.999201i \(0.512723\pi\)
\(660\) 9.62775 + 4.52458i 0.374759 + 0.176119i
\(661\) −41.0448 + 29.8208i −1.59646 + 1.15990i −0.702562 + 0.711622i \(0.747961\pi\)
−0.893897 + 0.448273i \(0.852039\pi\)
\(662\) −13.6529 9.91941i −0.530635 0.385529i
\(663\) −40.6142 29.5080i −1.57733 1.14599i
\(664\) −3.78299 + 2.74850i −0.146809 + 0.106663i
\(665\) 1.09385 8.69374i 0.0424175 0.337129i
\(666\) −0.0506350 0.0367885i −0.00196207 0.00142552i
\(667\) −0.829146 2.55185i −0.0321047 0.0988080i
\(668\) 20.8629 0.807209
\(669\) −2.66457 8.20070i −0.103018 0.317057i
\(670\) 4.66156 + 8.46929i 0.180092 + 0.327197i
\(671\) −9.28730 + 28.5834i −0.358532 + 1.10345i
\(672\) −1.47012 + 4.52458i −0.0567113 + 0.174539i
\(673\) 16.5401 12.0171i 0.637573 0.463224i −0.221442 0.975173i \(-0.571077\pi\)
0.859016 + 0.511949i \(0.171077\pi\)
\(674\) 19.3521 0.745414
\(675\) 25.4154 + 6.49839i 0.978239 + 0.250123i
\(676\) 19.2373 0.739894
\(677\) −6.90383 + 5.01592i −0.265336 + 0.192778i −0.712496 0.701676i \(-0.752435\pi\)
0.447160 + 0.894454i \(0.352435\pi\)
\(678\) −3.37820 + 10.3970i −0.129739 + 0.399296i
\(679\) 0.0773079 0.237929i 0.00296680 0.00913088i
\(680\) −11.3248 + 2.16621i −0.434287 + 0.0830705i
\(681\) −9.45206 29.0904i −0.362204 1.11475i
\(682\) −19.7739 −0.757182
\(683\) −15.0085 46.1913i −0.574283 1.76746i −0.638608 0.769532i \(-0.720489\pi\)
0.0643246 0.997929i \(-0.479511\pi\)
\(684\) 0.0682754 + 0.0496050i 0.00261058 + 0.00189669i
\(685\) −8.60863 15.6405i −0.328919 0.597591i
\(686\) −14.1462 + 10.2778i −0.540103 + 0.392408i
\(687\) 29.9041 + 21.7266i 1.14091 + 0.828921i
\(688\) −7.48066 5.43502i −0.285197 0.207208i
\(689\) 2.41665 1.75580i 0.0920671 0.0668907i
\(690\) 1.21092 + 2.20004i 0.0460989 + 0.0837540i
\(691\) −36.2501 26.3373i −1.37902 1.00192i −0.996971 0.0777740i \(-0.975219\pi\)
−0.382048 0.924142i \(-0.624781\pi\)
\(692\) −3.70441 11.4010i −0.140820 0.433401i
\(693\) 0.459953 0.0174722
\(694\) −2.79311 8.59630i −0.106025 0.326311i
\(695\) 48.5117 9.27932i 1.84015 0.351985i
\(696\) 2.17073 6.68083i 0.0822814 0.253236i
\(697\) 14.5117 44.6623i 0.549669 1.69171i
\(698\) −29.7156 + 21.5896i −1.12475 + 0.817179i
\(699\) 25.2174 0.953809
\(700\) −12.8930 + 5.11968i −0.487311 + 0.193506i
\(701\) 2.21913 0.0838152 0.0419076 0.999121i \(-0.486656\pi\)
0.0419076 + 0.999121i \(0.486656\pi\)
\(702\) 24.0999 17.5096i 0.909591 0.660857i
\(703\) −0.457166 + 1.40701i −0.0172424 + 0.0530665i
\(704\) 0.857358 2.63868i 0.0323129 0.0994488i
\(705\) 5.12953 + 9.31951i 0.193189 + 0.350993i
\(706\) 5.67779 + 17.4744i 0.213686 + 0.657659i
\(707\) 21.9358 0.824982
\(708\) −2.00402 6.16775i −0.0753158 0.231798i
\(709\) −27.7968 20.1955i −1.04393 0.758459i −0.0728805 0.997341i \(-0.523219\pi\)
−0.971049 + 0.238882i \(0.923219\pi\)
\(710\) 3.69767 29.3886i 0.138771 1.10293i
\(711\) −0.478647 + 0.347757i −0.0179507 + 0.0130419i
\(712\) 7.43002 + 5.39823i 0.278452 + 0.202307i
\(713\) −3.77648 2.74377i −0.141430 0.102755i
\(714\) 19.8463 14.4192i 0.742728 0.539623i
\(715\) 31.8795 + 14.9818i 1.19223 + 0.560289i
\(716\) 6.91009 + 5.02047i 0.258242 + 0.187624i
\(717\) 3.67747 + 11.3181i 0.137338 + 0.422682i
\(718\) −24.4259 −0.911565
\(719\) 3.70511 + 11.4032i 0.138177 + 0.425266i 0.996071 0.0885618i \(-0.0282271\pi\)
−0.857893 + 0.513828i \(0.828227\pi\)
\(720\) 0.0166793 0.132565i 0.000621600 0.00494040i
\(721\) −6.71673 + 20.6720i −0.250144 + 0.769864i
\(722\) −5.25489 + 16.1729i −0.195567 + 0.601892i
\(723\) −4.59179 + 3.33613i −0.170770 + 0.124072i
\(724\) 7.82844 0.290942
\(725\) 19.0374 7.55955i 0.707032 0.280754i
\(726\) −5.66256 −0.210157
\(727\) −34.1265 + 24.7944i −1.26568 + 0.919573i −0.999022 0.0442177i \(-0.985920\pi\)
−0.266661 + 0.963790i \(0.585920\pi\)
\(728\) −4.86789 + 14.9818i −0.180416 + 0.555264i
\(729\) 8.50295 26.1694i 0.314924 0.969237i
\(730\) 6.44574 6.87092i 0.238568 0.254304i
\(731\) 14.7338 + 45.3459i 0.544948 + 1.67718i
\(732\) −18.5746 −0.686537
\(733\) −0.0996219 0.306605i −0.00367962 0.0113247i 0.949200 0.314674i \(-0.101895\pi\)
−0.952879 + 0.303349i \(0.901895\pi\)
\(734\) −11.7489 8.53607i −0.433660 0.315072i
\(735\) 1.83020 1.95092i 0.0675078 0.0719608i
\(736\) 0.529876 0.384978i 0.0195315 0.0141905i
\(737\) 9.70427 + 7.05056i 0.357461 + 0.259711i
\(738\) 0.440248 + 0.319859i 0.0162057 + 0.0117742i
\(739\) 4.44942 3.23269i 0.163674 0.118916i −0.502933 0.864325i \(-0.667746\pi\)
0.666607 + 0.745409i \(0.267746\pi\)
\(740\) 2.30049 0.440039i 0.0845678 0.0161761i
\(741\) −11.1245 8.08244i −0.408670 0.296916i
\(742\) 0.451065 + 1.38824i 0.0165591 + 0.0509638i
\(743\) −6.03812 −0.221517 −0.110759 0.993847i \(-0.535328\pi\)
−0.110759 + 0.993847i \(0.535328\pi\)
\(744\) −3.77648 11.6228i −0.138452 0.426113i
\(745\) 8.46733 + 3.97923i 0.310219 + 0.145788i
\(746\) −7.19662 + 22.1489i −0.263487 + 0.810929i
\(747\) −0.0863404 + 0.265728i −0.00315903 + 0.00972249i
\(748\) −11.5741 + 8.40906i −0.423190 + 0.307466i
\(749\) 28.3605 1.03627
\(750\) −16.1712 + 10.2967i −0.590489 + 0.375984i
\(751\) −13.5719 −0.495244 −0.247622 0.968857i \(-0.579649\pi\)
−0.247622 + 0.968857i \(0.579649\pi\)
\(752\) 2.24459 1.63079i 0.0818518 0.0594688i
\(753\) −5.01503 + 15.4347i −0.182758 + 0.562471i
\(754\) 7.18776 22.1216i 0.261763 0.805623i
\(755\) −0.670991 0.315333i −0.0244199 0.0114762i
\(756\) 4.49821 + 13.8441i 0.163598 + 0.503504i
\(757\) 33.0661 1.20181 0.600904 0.799321i \(-0.294807\pi\)
0.600904 + 0.799321i \(0.294807\pi\)
\(758\) 8.84332 + 27.2169i 0.321204 + 0.988563i
\(759\) 2.52084 + 1.83150i 0.0915008 + 0.0664792i
\(760\) −3.10195 + 0.593341i −0.112520 + 0.0215227i
\(761\) −4.19767 + 3.04978i −0.152165 + 0.110555i −0.661263 0.750154i \(-0.729979\pi\)
0.509098 + 0.860709i \(0.329979\pi\)
\(762\) −13.2466 9.62422i −0.479874 0.348649i
\(763\) 8.77840 + 6.37788i 0.317799 + 0.230895i
\(764\) −2.72324 + 1.97855i −0.0985233 + 0.0715814i
\(765\) −0.471367 + 0.502460i −0.0170423 + 0.0181665i
\(766\) 13.4424 + 9.76647i 0.485694 + 0.352877i
\(767\) −6.63575 20.4227i −0.239603 0.737422i
\(768\) 1.71472 0.0618745
\(769\) 10.2191 + 31.4512i 0.368511 + 1.13416i 0.947753 + 0.319005i \(0.103349\pi\)
−0.579242 + 0.815156i \(0.696651\pi\)
\(770\) −11.7765 + 12.5533i −0.424395 + 0.452389i
\(771\) −3.75133 + 11.5454i −0.135101 + 0.415798i
\(772\) −4.76538 + 14.6663i −0.171510 + 0.527853i
\(773\) 0.914961 0.664758i 0.0329088 0.0239097i −0.571209 0.820804i \(-0.693526\pi\)
0.604118 + 0.796895i \(0.293526\pi\)
\(774\) −0.552505 −0.0198594
\(775\) 19.0643 30.1072i 0.684808 1.08148i
\(776\) −0.0901699 −0.00323691
\(777\) −4.03152 + 2.92907i −0.144630 + 0.105080i
\(778\) 8.15086 25.0858i 0.292223 0.899369i
\(779\) 3.97485 12.2333i 0.142414 0.438305i
\(780\) −2.71766 + 21.5996i −0.0973077 + 0.773389i
\(781\) −11.3571 34.9535i −0.406388 1.25073i
\(782\) −3.37727 −0.120771
\(783\) −6.64191 20.4417i −0.237362 0.730526i
\(784\) −0.564426 0.410079i −0.0201581 0.0146457i
\(785\) 7.30061 + 3.43094i 0.260570 + 0.122455i
\(786\) −7.76745 + 5.64338i −0.277056 + 0.201293i
\(787\) −12.7509 9.26408i −0.454521 0.330229i 0.336857 0.941556i \(-0.390636\pi\)
−0.791378 + 0.611327i \(0.790636\pi\)
\(788\) −7.12330 5.17538i −0.253757 0.184365i
\(789\) −1.98854 + 1.44476i −0.0707938 + 0.0514347i
\(790\) 2.76393 21.9674i 0.0983363 0.781564i
\(791\) −14.3103 10.3970i −0.508815 0.369676i
\(792\) −0.0512290 0.157667i −0.00182034 0.00560244i
\(793\) −61.5044 −2.18409
\(794\) −5.53406 17.0321i −0.196396 0.604446i
\(795\) 0.972693 + 1.76722i 0.0344978 + 0.0626769i
\(796\) −5.44555 + 16.7597i −0.193012 + 0.594031i
\(797\) −7.15055 + 22.0071i −0.253285 + 0.779532i 0.740877 + 0.671640i \(0.234410\pi\)
−0.994163 + 0.107892i \(0.965590\pi\)
\(798\) 5.43603 3.94951i 0.192433 0.139811i
\(799\) −14.3064 −0.506122
\(800\) 3.19098 + 3.84937i 0.112818 + 0.136096i
\(801\) 0.548765 0.0193897
\(802\) −25.9018 + 18.8188i −0.914624 + 0.664513i
\(803\) 3.61226 11.1174i 0.127474 0.392324i
\(804\) −2.29087 + 7.05056i −0.0807927 + 0.248654i
\(805\) −3.99097 + 0.763393i −0.140663 + 0.0269061i
\(806\) −12.5047 38.4856i −0.440460 1.35560i
\(807\) −24.4912 −0.862132
\(808\) −2.44319 7.51936i −0.0859511 0.264530i
\(809\) −27.1345 19.7143i −0.953997 0.693119i −0.00224811 0.999997i \(-0.500716\pi\)
−0.951749 + 0.306878i \(0.900716\pi\)
\(810\) 9.50682 + 17.2723i 0.334036 + 0.606887i
\(811\) 9.67796 7.03145i 0.339839 0.246907i −0.404755 0.914425i \(-0.632643\pi\)
0.744594 + 0.667518i \(0.232643\pi\)
\(812\) 9.19537 + 6.68083i 0.322694 + 0.234451i
\(813\) −42.7067 31.0282i −1.49779 1.08821i
\(814\) 2.35113 1.70820i 0.0824070 0.0598722i
\(815\) −5.49227 9.97854i −0.192386 0.349533i
\(816\) −7.15318 5.19709i −0.250411 0.181934i
\(817\) 4.03569 + 12.4206i 0.141191 + 0.434540i
\(818\) 18.0344 0.630557
\(819\) 0.290867 + 0.895198i 0.0101637 + 0.0312807i
\(820\) −20.0017 + 3.82593i −0.698491 + 0.133607i
\(821\) −3.30466 + 10.1707i −0.115333 + 0.354960i −0.992016 0.126109i \(-0.959751\pi\)
0.876683 + 0.481068i \(0.159751\pi\)
\(822\) 4.23061 13.0205i 0.147559 0.454141i
\(823\) 9.72525 7.06581i 0.339001 0.246299i −0.405239 0.914211i \(-0.632812\pi\)
0.744240 + 0.667912i \(0.232812\pi\)
\(824\) 7.83422 0.272918
\(825\) −12.7256 + 20.0969i −0.443049 + 0.699684i
\(826\) 10.4932 0.365105
\(827\) 3.34912 2.43328i 0.116460 0.0846133i −0.528031 0.849225i \(-0.677069\pi\)
0.644491 + 0.764612i \(0.277069\pi\)
\(828\) 0.0120935 0.0372200i 0.000420279 0.00129349i
\(829\) −6.28859 + 19.3543i −0.218412 + 0.672203i 0.780482 + 0.625178i \(0.214974\pi\)
−0.998894 + 0.0470242i \(0.985026\pi\)
\(830\) −5.04178 9.16007i −0.175003 0.317951i
\(831\) 1.69014 + 5.20171i 0.0586303 + 0.180445i
\(832\) 5.67779 0.196842
\(833\) 1.11168 + 3.42141i 0.0385175 + 0.118545i
\(834\) 30.6418 + 22.2626i 1.06104 + 0.770890i
\(835\) −5.82368 + 46.2859i −0.201537 + 1.60179i
\(836\) −3.17022 + 2.30330i −0.109644 + 0.0796614i
\(837\) −30.2516 21.9791i −1.04565 0.759708i
\(838\) 15.8001 + 11.4795i 0.545806 + 0.396552i
\(839\) −2.53639 + 1.84279i −0.0875658 + 0.0636203i −0.630707 0.776021i \(-0.717235\pi\)
0.543141 + 0.839642i \(0.317235\pi\)
\(840\) −9.62775 4.52458i −0.332189 0.156113i
\(841\) 9.88393 + 7.18109i 0.340825 + 0.247624i
\(842\) −6.04242 18.5967i −0.208236 0.640883i
\(843\) 34.9612 1.20413
\(844\) 1.88545 + 5.80281i 0.0648998 + 0.199741i
\(845\) −5.36990 + 42.6793i −0.184730 + 1.46821i
\(846\) 0.0512290 0.157667i 0.00176129 0.00542069i
\(847\) 2.83128 8.71378i 0.0972839 0.299409i
\(848\) 0.425633 0.309240i 0.0146163 0.0106194i
\(849\) −22.8004 −0.782508
\(850\) −1.64469 25.7297i −0.0564123 0.882520i
\(851\) 0.686050 0.0235175
\(852\) 18.3761 13.3510i 0.629556 0.457399i
\(853\) 7.21464 22.2044i 0.247025 0.760263i −0.748272 0.663392i \(-0.769116\pi\)
0.995297 0.0968717i \(-0.0308837\pi\)
\(854\) 9.28730 28.5834i 0.317805 0.978102i
\(855\) −0.129111 + 0.137627i −0.00441550 + 0.00470676i
\(856\) −3.15876 9.72166i −0.107964 0.332280i
\(857\) 15.3036 0.522762 0.261381 0.965236i \(-0.415822\pi\)
0.261381 + 0.965236i \(0.415822\pi\)
\(858\) 8.34705 + 25.6896i 0.284964 + 0.877028i
\(859\) 2.39576 + 1.74062i 0.0817422 + 0.0593892i 0.627906 0.778289i \(-0.283912\pi\)
−0.546164 + 0.837679i \(0.683912\pi\)
\(860\) 14.1462 15.0793i 0.482380 0.514199i
\(861\) 35.0522 25.4669i 1.19457 0.867909i
\(862\) 17.1482 + 12.4589i 0.584069 + 0.424351i
\(863\) 30.5987 + 22.2312i 1.04159 + 0.756760i 0.970595 0.240717i \(-0.0773824\pi\)
0.0709954 + 0.997477i \(0.477382\pi\)
\(864\) 4.24459 3.08388i 0.144404 0.104916i
\(865\) 26.3280 5.03603i 0.895180 0.171230i
\(866\) −6.91683 5.02537i −0.235043 0.170769i
\(867\) 5.08088 + 15.6373i 0.172556 + 0.531072i
\(868\) 19.7739 0.671170
\(869\) −8.48918 26.1270i −0.287976 0.886298i
\(870\) 14.2160 + 6.68083i 0.481967 + 0.226501i
\(871\) −7.58555 + 23.3459i −0.257027 + 0.791046i
\(872\) 1.20854 3.71950i 0.0409263 0.125958i
\(873\) −0.00435886 + 0.00316690i −0.000147525 + 0.000107183i
\(874\) −0.925059 −0.0312906
\(875\) −7.75943 30.0333i −0.262317 1.01531i
\(876\) 7.22451 0.244094
\(877\) 12.6215 9.17007i 0.426198 0.309651i −0.353929 0.935272i \(-0.615154\pi\)
0.780127 + 0.625621i \(0.215154\pi\)
\(878\) −8.67453 + 26.6975i −0.292751 + 0.900996i
\(879\) −13.7991 + 42.4691i −0.465430 + 1.43245i
\(880\) 5.61478 + 2.63868i 0.189274 + 0.0889497i
\(881\) 0.359812 + 1.10739i 0.0121224 + 0.0373089i 0.956935 0.290303i \(-0.0937561\pi\)
−0.944812 + 0.327612i \(0.893756\pi\)
\(882\) −0.0416872 −0.00140368
\(883\) 15.1063 + 46.4925i 0.508368 + 1.56460i 0.795033 + 0.606566i \(0.207453\pi\)
−0.286665 + 0.958031i \(0.592547\pi\)
\(884\) −23.6857 17.2087i −0.796636 0.578790i
\(885\) 14.2430 2.72441i 0.478774 0.0915800i
\(886\) 26.7417 19.4290i 0.898406 0.652730i
\(887\) −6.98094 5.07195i −0.234397 0.170299i 0.464386 0.885633i \(-0.346275\pi\)
−0.698783 + 0.715333i \(0.746275\pi\)
\(888\) 1.45308 + 1.05572i 0.0487621 + 0.0354277i
\(889\) 21.4335 15.5723i 0.718855 0.522279i
\(890\) −14.0504 + 14.9772i −0.470971 + 0.502037i
\(891\) 19.7909 + 14.3790i 0.663022 + 0.481713i
\(892\) −1.55394 4.78254i −0.0520299 0.160131i
\(893\) −3.91861 −0.131131
\(894\) 2.21701 + 6.82325i 0.0741479 + 0.228204i
\(895\) −13.0672 + 13.9291i −0.436788 + 0.465600i
\(896\) −0.857358 + 2.63868i −0.0286423 + 0.0881520i
\(897\) −1.97047 + 6.06449i −0.0657921 + 0.202487i
\(898\) 30.0654 21.8438i 1.00329 0.728936i
\(899\) −29.1975 −0.973790
\(900\) 0.289449 + 0.0740085i 0.00964831 + 0.00246695i
\(901\) −2.71286 −0.0903784
\(902\) −20.4420 + 14.8520i −0.680643 + 0.494516i
\(903\) −13.5937 + 41.8370i −0.452368 + 1.39225i
\(904\) −1.97012 + 6.06342i −0.0655253 + 0.201666i
\(905\) −2.18524 + 17.3680i −0.0726398 + 0.577332i
\(906\) −0.175686 0.540707i −0.00583679 0.0179638i
\(907\) 29.5085 0.979815 0.489907 0.871774i \(-0.337031\pi\)
0.489907 + 0.871774i \(0.337031\pi\)
\(908\) −5.51232 16.9652i −0.182933 0.563009i
\(909\) −0.382196 0.277682i −0.0126766 0.00921012i
\(910\) −31.8795 14.9818i −1.05680 0.496643i
\(911\) 31.0734 22.5761i 1.02951 0.747981i 0.0612971 0.998120i \(-0.480476\pi\)
0.968210 + 0.250139i \(0.0804763\pi\)
\(912\) −1.95931 1.42352i −0.0648791 0.0471374i
\(913\) −10.4958 7.62563i −0.347360 0.252372i
\(914\) −23.7155 + 17.2303i −0.784438 + 0.569928i
\(915\) 5.18493 41.2092i 0.171408 1.36233i
\(916\) 17.4397 + 12.6707i 0.576223 + 0.418651i
\(917\) −4.80055 14.7746i −0.158528 0.487899i
\(918\) −27.0538 −0.892907
\(919\) 12.8831 + 39.6500i 0.424974 + 1.30793i 0.903020 + 0.429600i \(0.141345\pi\)
−0.478046 + 0.878335i \(0.658655\pi\)
\(920\) 0.706192 + 1.28303i 0.0232825 + 0.0423004i
\(921\) 13.2999 40.9329i 0.438247 1.34879i
\(922\) 2.75254 8.47145i 0.0906501 0.278992i
\(923\) 60.8473 44.2081i 2.00281 1.45513i
\(924\) −13.1993 −0.434225
\(925\) 0.334097 + 5.22665i 0.0109851 + 0.171851i
\(926\) −18.2771 −0.600624
\(927\) 0.378710 0.275149i 0.0124385 0.00903709i
\(928\) 1.26594 3.89618i 0.0415567 0.127898i
\(929\) 8.68484 26.7292i 0.284940 0.876956i −0.701476 0.712693i \(-0.747475\pi\)
0.986417 0.164263i \(-0.0525247\pi\)
\(930\) 26.8403 5.13401i 0.880127 0.168351i
\(931\) 0.304498 + 0.937148i 0.00997952 + 0.0307138i
\(932\) 14.7065 0.481726
\(933\) 0.383274 + 1.17960i 0.0125478 + 0.0386183i
\(934\) 29.6780 + 21.5624i 0.971095 + 0.705542i
\(935\) −15.4254 28.0253i −0.504463 0.916525i
\(936\) 0.274467 0.199412i 0.00897124 0.00651799i
\(937\) 10.4164 + 7.56796i 0.340289 + 0.247234i 0.744784 0.667306i \(-0.232553\pi\)
−0.404495 + 0.914540i \(0.632553\pi\)
\(938\) −9.70427 7.05056i −0.316856 0.230209i
\(939\) −29.9868 + 21.7867i −0.978583 + 0.710982i
\(940\) 2.99148 + 5.43502i 0.0975712 + 0.177271i
\(941\) −8.21234 5.96661i −0.267714 0.194506i 0.445827 0.895119i \(-0.352910\pi\)
−0.713541 + 0.700613i \(0.752910\pi\)
\(942\) 1.91153 + 5.88308i 0.0622809 + 0.191681i
\(943\) −5.96489 −0.194243
\(944\) −1.16872 3.59695i −0.0380386 0.117071i
\(945\) −31.9698 + 6.11518i −1.03998 + 0.198927i
\(946\) 7.92764 24.3988i 0.257750 0.793273i
\(947\) −17.7298 + 54.5669i −0.576143 + 1.77318i 0.0561124 + 0.998424i \(0.482129\pi\)
−0.632255 + 0.774760i \(0.717871\pi\)
\(948\) 13.7358 9.97963i 0.446118 0.324123i
\(949\) 23.9219 0.776538
\(950\) −0.450491 7.04754i −0.0146159 0.228652i
\(951\) −32.2944 −1.04722
\(952\) 11.5741 8.40906i 0.375118 0.272539i
\(953\) 1.59843 4.91947i 0.0517784 0.159357i −0.921824 0.387609i \(-0.873301\pi\)
0.973602 + 0.228252i \(0.0733010\pi\)
\(954\) 0.00971435 0.0298977i 0.000314514 0.000967974i
\(955\) −3.62939 6.59401i −0.117444 0.213377i
\(956\) 2.14465 + 6.60057i 0.0693631 + 0.213478i
\(957\) 19.4896 0.630010
\(958\) −3.89046 11.9736i −0.125695 0.386849i
\(959\) 17.9211 + 13.0205i 0.578704 + 0.420453i
\(960\) −0.478647 + 3.80423i −0.0154483 + 0.122781i
\(961\) −16.0149 + 11.6355i −0.516611 + 0.375340i
\(962\) 4.81145 + 3.49572i 0.155127 + 0.112707i
\(963\) −0.494135 0.359010i −0.0159233 0.0115689i
\(964\) −2.67787 + 1.94559i −0.0862484 + 0.0626631i
\(965\) −31.2082 14.6663i −1.00463 0.472126i
\(966\) −2.52084 1.83150i −0.0811068 0.0589275i
\(967\) −12.7927 39.3718i −0.411384 1.26611i −0.915445 0.402443i \(-0.868161\pi\)
0.504061 0.863668i \(-0.331839\pi\)
\(968\) −3.30233 −0.106141
\(969\) 3.85901 + 11.8768i 0.123969 + 0.381539i
\(970\) 0.0251701 0.200049i 0.000808164 0.00642318i
\(971\) 13.3139 40.9761i 0.427265 1.31499i −0.473544 0.880770i \(-0.657025\pi\)
0.900809 0.434216i \(-0.142975\pi\)
\(972\) 0.191859 0.590483i 0.00615389 0.0189397i
\(973\) −49.5795 + 36.0216i −1.58944 + 1.15480i
\(974\) −18.3256 −0.587189
\(975\) −47.1617 12.0587i −1.51038 0.386186i
\(976\) −10.8325 −0.346739
\(977\) −32.7340 + 23.7826i −1.04725 + 0.760874i −0.971688 0.236267i \(-0.924076\pi\)
−0.0755652 + 0.997141i \(0.524076\pi\)
\(978\) 2.69911 8.30700i 0.0863079 0.265628i
\(979\) −7.87398 + 24.2336i −0.251654 + 0.774510i
\(980\) 1.06735 1.13775i 0.0340951 0.0363441i
\(981\) −0.0722128 0.222248i −0.00230558 0.00709584i
\(982\) 21.7047 0.692625
\(983\) 12.4777 + 38.4023i 0.397976 + 1.22484i 0.926620 + 0.376000i \(0.122701\pi\)
−0.528644 + 0.848844i \(0.677299\pi\)
\(984\) −12.6338 9.17902i −0.402752 0.292616i
\(985\) 13.4704 14.3589i 0.429202 0.457513i
\(986\) −17.0899 + 12.4165i −0.544253 + 0.395423i
\(987\) −10.6785 7.75836i −0.339899 0.246951i
\(988\) −6.48768 4.71358i −0.206401 0.149959i
\(989\) 4.89955 3.55973i 0.155797 0.113193i
\(990\) 0.364096 0.0696442i 0.0115717 0.00221344i
\(991\) 47.0391 + 34.1759i 1.49424 + 1.08563i 0.972604 + 0.232467i \(0.0746798\pi\)
0.521641 + 0.853165i \(0.325320\pi\)
\(992\) −2.20239 6.77827i −0.0699261 0.215210i
\(993\) 28.9374 0.918300
\(994\) 11.3571 + 34.9535i 0.360225 + 1.10866i
\(995\) −35.6625 16.7597i −1.13058 0.531317i
\(996\) 2.47772 7.62563i 0.0785095 0.241627i
\(997\) 12.1434 37.3735i 0.384585 1.18363i −0.552197 0.833714i \(-0.686210\pi\)
0.936781 0.349916i \(-0.113790\pi\)
\(998\) −12.8141 + 9.30998i −0.405623 + 0.294702i
\(999\) 5.49563 0.173874
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 50.2.d.b.11.2 8
3.2 odd 2 450.2.h.e.361.1 8
4.3 odd 2 400.2.u.d.161.1 8
5.2 odd 4 250.2.e.c.199.1 16
5.3 odd 4 250.2.e.c.199.4 16
5.4 even 2 250.2.d.d.51.1 8
25.3 odd 20 1250.2.b.e.1249.3 8
25.4 even 10 1250.2.a.f.1.2 4
25.9 even 10 250.2.d.d.201.1 8
25.12 odd 20 250.2.e.c.49.4 16
25.13 odd 20 250.2.e.c.49.1 16
25.16 even 5 inner 50.2.d.b.41.2 yes 8
25.21 even 5 1250.2.a.l.1.3 4
25.22 odd 20 1250.2.b.e.1249.6 8
75.41 odd 10 450.2.h.e.91.1 8
100.71 odd 10 10000.2.a.t.1.2 4
100.79 odd 10 10000.2.a.x.1.3 4
100.91 odd 10 400.2.u.d.241.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.2.d.b.11.2 8 1.1 even 1 trivial
50.2.d.b.41.2 yes 8 25.16 even 5 inner
250.2.d.d.51.1 8 5.4 even 2
250.2.d.d.201.1 8 25.9 even 10
250.2.e.c.49.1 16 25.13 odd 20
250.2.e.c.49.4 16 25.12 odd 20
250.2.e.c.199.1 16 5.2 odd 4
250.2.e.c.199.4 16 5.3 odd 4
400.2.u.d.161.1 8 4.3 odd 2
400.2.u.d.241.1 8 100.91 odd 10
450.2.h.e.91.1 8 75.41 odd 10
450.2.h.e.361.1 8 3.2 odd 2
1250.2.a.f.1.2 4 25.4 even 10
1250.2.a.l.1.3 4 25.21 even 5
1250.2.b.e.1249.3 8 25.3 odd 20
1250.2.b.e.1249.6 8 25.22 odd 20
10000.2.a.t.1.2 4 100.71 odd 10
10000.2.a.x.1.3 4 100.79 odd 10