Properties

Label 75.2.g.b.46.1
Level $75$
Weight $2$
Character 75.46
Analytic conductor $0.599$
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] = [75,2,Mod(16,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 75.g (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: \(0.598878015160\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) 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 46.1
Root \(1.40799 - 0.132563i\) of defining polynomial
Character \(\chi\) \(=\) 75.46
Dual form 75.2.g.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.346820 + 1.06740i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.598970 + 0.435177i) q^{4} +(0.407987 + 2.19853i) q^{5} +(0.907987 - 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 + 1.80780i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.346820 + 1.06740i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.598970 + 0.435177i) q^{4} +(0.407987 + 2.19853i) q^{5} +(0.907987 - 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 + 1.80780i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.48822 - 0.327009i) q^{10} +(1.13412 - 3.49045i) q^{11} +(-0.228786 - 0.704131i) q^{12} +(-1.25215 - 3.85372i) q^{13} +(-0.386266 + 1.18880i) q^{14} +(0.962197 - 2.01846i) q^{15} +(-0.609110 - 1.87465i) q^{16} +(-1.71700 + 1.24748i) q^{17} -1.12233 q^{18} +(3.28513 - 2.38678i) q^{19} +(-0.712379 + 1.49440i) q^{20} +(-0.901030 - 0.654637i) q^{21} +(3.33238 + 2.42112i) q^{22} +(1.90799 - 5.87218i) q^{23} +3.07561 q^{24} +(-4.66709 + 1.79395i) q^{25} +4.54774 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.667093 + 0.484672i) q^{28} +(1.82808 + 1.32818i) q^{29} +(1.82080 + 1.72709i) q^{30} +(-8.13227 + 5.90844i) q^{31} -3.93896 q^{32} +(-2.96915 + 2.15722i) q^{33} +(-0.736068 - 2.26538i) q^{34} +(0.454389 + 2.44858i) q^{35} +(-0.228786 + 0.704131i) q^{36} +(2.27817 + 7.01149i) q^{37} +(1.40831 + 4.33434i) q^{38} +(-1.25215 + 3.85372i) q^{39} +(-4.98966 - 4.73287i) q^{40} +(-2.30902 - 7.10642i) q^{41} +(1.01126 - 0.734721i) q^{42} +9.24998 q^{43} +(2.19826 - 1.59713i) q^{44} +(-1.96485 + 1.06740i) q^{45} +(5.60625 + 4.07318i) q^{46} +(2.53032 + 1.83839i) q^{47} +(-0.609110 + 1.87465i) q^{48} -5.75960 q^{49} +(-0.296220 - 5.60384i) q^{50} +2.12233 q^{51} +(0.927051 - 2.85317i) q^{52} +(2.83934 + 2.06290i) q^{53} +(0.907987 + 0.659691i) q^{54} +(8.13657 + 1.06933i) q^{55} +(-2.77121 + 2.01340i) q^{56} -4.06064 q^{57} +(-2.05172 + 1.49066i) q^{58} +(-2.03760 - 6.27109i) q^{59} +(1.45471 - 0.790270i) q^{60} +(-2.81332 + 8.65850i) q^{61} +(-3.48625 - 10.7296i) q^{62} +(0.344163 + 1.05922i) q^{63} +(2.58433 - 7.95375i) q^{64} +(7.96167 - 4.32516i) q^{65} +(-1.27286 - 3.91745i) q^{66} +(-2.12499 + 1.54390i) q^{67} -1.57131 q^{68} +(-4.99517 + 3.62921i) q^{69} +(-2.77121 - 0.364201i) q^{70} +(-0.534620 - 0.388424i) q^{71} +(-2.48822 - 1.80780i) q^{72} +(2.31003 - 7.10955i) q^{73} -8.27420 q^{74} +(4.83021 + 1.29192i) q^{75} +3.00637 q^{76} +(1.26310 - 3.88743i) q^{77} +(-3.67920 - 2.67310i) q^{78} +(-6.90667 - 5.01799i) q^{79} +(3.87297 - 2.10398i) q^{80} +(-0.809017 + 0.587785i) q^{81} +8.38623 q^{82} +(-9.92170 + 7.20854i) q^{83} +(-0.254807 - 0.784215i) q^{84} +(-3.44313 - 3.26594i) q^{85} +(-3.20808 + 9.87345i) q^{86} +(-0.698265 - 2.14904i) q^{87} +(3.48809 + 10.7352i) q^{88} +(-4.72429 + 14.5399i) q^{89} +(-0.457897 - 2.46749i) q^{90} +(-1.39456 - 4.29202i) q^{91} +(3.69826 - 2.68695i) q^{92} +10.0520 q^{93} +(-2.83986 + 2.06328i) q^{94} +(6.58771 + 6.24868i) q^{95} +(3.18668 + 2.31526i) q^{96} +(-10.9217 - 7.93508i) q^{97} +(1.99754 - 6.14781i) q^{98} +3.67008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.346820 + 1.06740i −0.245239 + 0.754768i 0.750358 + 0.661031i \(0.229881\pi\)
−0.995597 + 0.0937362i \(0.970119\pi\)
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) 0.598970 + 0.435177i 0.299485 + 0.217589i
\(5\) 0.407987 + 2.19853i 0.182457 + 0.983214i
\(6\) 0.907987 0.659691i 0.370684 0.269318i
\(7\) 1.11373 0.420952 0.210476 0.977599i \(-0.432499\pi\)
0.210476 + 0.977599i \(0.432499\pi\)
\(8\) −2.48822 + 1.80780i −0.879718 + 0.639152i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) −2.48822 0.327009i −0.786844 0.103409i
\(11\) 1.13412 3.49045i 0.341949 1.05241i −0.621248 0.783614i \(-0.713374\pi\)
0.963197 0.268796i \(-0.0866258\pi\)
\(12\) −0.228786 0.704131i −0.0660449 0.203265i
\(13\) −1.25215 3.85372i −0.347284 1.06883i −0.960350 0.278798i \(-0.910064\pi\)
0.613066 0.790032i \(-0.289936\pi\)
\(14\) −0.386266 + 1.18880i −0.103234 + 0.317721i
\(15\) 0.962197 2.01846i 0.248438 0.521164i
\(16\) −0.609110 1.87465i −0.152277 0.468662i
\(17\) −1.71700 + 1.24748i −0.416435 + 0.302557i −0.776202 0.630485i \(-0.782856\pi\)
0.359767 + 0.933042i \(0.382856\pi\)
\(18\) −1.12233 −0.264537
\(19\) 3.28513 2.38678i 0.753660 0.547566i −0.143299 0.989679i \(-0.545771\pi\)
0.896959 + 0.442113i \(0.145771\pi\)
\(20\) −0.712379 + 1.49440i −0.159293 + 0.334158i
\(21\) −0.901030 0.654637i −0.196621 0.142853i
\(22\) 3.33238 + 2.42112i 0.710466 + 0.516184i
\(23\) 1.90799 5.87218i 0.397843 1.22443i −0.528883 0.848695i \(-0.677389\pi\)
0.926725 0.375739i \(-0.122611\pi\)
\(24\) 3.07561 0.627806
\(25\) −4.66709 + 1.79395i −0.933419 + 0.358789i
\(26\) 4.54774 0.891886
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 0.667093 + 0.484672i 0.126069 + 0.0915943i
\(29\) 1.82808 + 1.32818i 0.339466 + 0.246637i 0.744437 0.667693i \(-0.232718\pi\)
−0.404970 + 0.914330i \(0.632718\pi\)
\(30\) 1.82080 + 1.72709i 0.332431 + 0.315323i
\(31\) −8.13227 + 5.90844i −1.46060 + 1.06119i −0.477393 + 0.878690i \(0.658418\pi\)
−0.983206 + 0.182498i \(0.941582\pi\)
\(32\) −3.93896 −0.696316
\(33\) −2.96915 + 2.15722i −0.516863 + 0.375523i
\(34\) −0.736068 2.26538i −0.126235 0.388510i
\(35\) 0.454389 + 2.44858i 0.0768058 + 0.413886i
\(36\) −0.228786 + 0.704131i −0.0381310 + 0.117355i
\(37\) 2.27817 + 7.01149i 0.374529 + 1.15268i 0.943796 + 0.330529i \(0.107227\pi\)
−0.569267 + 0.822153i \(0.692773\pi\)
\(38\) 1.40831 + 4.33434i 0.228458 + 0.703123i
\(39\) −1.25215 + 3.85372i −0.200504 + 0.617089i
\(40\) −4.98966 4.73287i −0.788934 0.748333i
\(41\) −2.30902 7.10642i −0.360608 1.10984i −0.952686 0.303956i \(-0.901692\pi\)
0.592078 0.805881i \(-0.298308\pi\)
\(42\) 1.01126 0.734721i 0.156040 0.113370i
\(43\) 9.24998 1.41061 0.705304 0.708905i \(-0.250810\pi\)
0.705304 + 0.708905i \(0.250810\pi\)
\(44\) 2.19826 1.59713i 0.331401 0.240777i
\(45\) −1.96485 + 1.06740i −0.292903 + 0.159119i
\(46\) 5.60625 + 4.07318i 0.826597 + 0.600558i
\(47\) 2.53032 + 1.83839i 0.369085 + 0.268156i 0.756831 0.653610i \(-0.226746\pi\)
−0.387746 + 0.921766i \(0.626746\pi\)
\(48\) −0.609110 + 1.87465i −0.0879174 + 0.270582i
\(49\) −5.75960 −0.822799
\(50\) −0.296220 5.60384i −0.0418918 0.792503i
\(51\) 2.12233 0.297186
\(52\) 0.927051 2.85317i 0.128559 0.395663i
\(53\) 2.83934 + 2.06290i 0.390013 + 0.283361i 0.765461 0.643483i \(-0.222511\pi\)
−0.375448 + 0.926844i \(0.622511\pi\)
\(54\) 0.907987 + 0.659691i 0.123561 + 0.0897726i
\(55\) 8.13657 + 1.06933i 1.09714 + 0.144189i
\(56\) −2.77121 + 2.01340i −0.370319 + 0.269053i
\(57\) −4.06064 −0.537845
\(58\) −2.05172 + 1.49066i −0.269404 + 0.195733i
\(59\) −2.03760 6.27109i −0.265273 0.816427i −0.991630 0.129110i \(-0.958788\pi\)
0.726357 0.687317i \(-0.241212\pi\)
\(60\) 1.45471 0.790270i 0.187803 0.102023i
\(61\) −2.81332 + 8.65850i −0.360208 + 1.10861i 0.592719 + 0.805409i \(0.298054\pi\)
−0.952928 + 0.303198i \(0.901946\pi\)
\(62\) −3.48625 10.7296i −0.442754 1.36266i
\(63\) 0.344163 + 1.05922i 0.0433604 + 0.133450i
\(64\) 2.58433 7.95375i 0.323041 0.994219i
\(65\) 7.96167 4.32516i 0.987524 0.536470i
\(66\) −1.27286 3.91745i −0.156678 0.482205i
\(67\) −2.12499 + 1.54390i −0.259609 + 0.188617i −0.709975 0.704227i \(-0.751294\pi\)
0.450366 + 0.892844i \(0.351294\pi\)
\(68\) −1.57131 −0.190549
\(69\) −4.99517 + 3.62921i −0.601348 + 0.436905i
\(70\) −2.77121 0.364201i −0.331223 0.0435304i
\(71\) −0.534620 0.388424i −0.0634477 0.0460975i 0.555609 0.831443i \(-0.312485\pi\)
−0.619057 + 0.785346i \(0.712485\pi\)
\(72\) −2.48822 1.80780i −0.293239 0.213051i
\(73\) 2.31003 7.10955i 0.270369 0.832110i −0.720039 0.693934i \(-0.755876\pi\)
0.990408 0.138176i \(-0.0441239\pi\)
\(74\) −8.27420 −0.961856
\(75\) 4.83021 + 1.29192i 0.557745 + 0.149178i
\(76\) 3.00637 0.344854
\(77\) 1.26310 3.88743i 0.143944 0.443014i
\(78\) −3.67920 2.67310i −0.416587 0.302668i
\(79\) −6.90667 5.01799i −0.777061 0.564568i 0.127034 0.991898i \(-0.459454\pi\)
−0.904096 + 0.427330i \(0.859454\pi\)
\(80\) 3.87297 2.10398i 0.433011 0.235232i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 8.38623 0.926104
\(83\) −9.92170 + 7.20854i −1.08905 + 0.791240i −0.979238 0.202713i \(-0.935024\pi\)
−0.109810 + 0.993953i \(0.535024\pi\)
\(84\) −0.254807 0.784215i −0.0278017 0.0855649i
\(85\) −3.44313 3.26594i −0.373460 0.354240i
\(86\) −3.20808 + 9.87345i −0.345936 + 1.06468i
\(87\) −0.698265 2.14904i −0.0748618 0.230401i
\(88\) 3.48809 + 10.7352i 0.371832 + 1.14438i
\(89\) −4.72429 + 14.5399i −0.500773 + 1.54122i 0.306989 + 0.951713i \(0.400679\pi\)
−0.807762 + 0.589509i \(0.799321\pi\)
\(90\) −0.457897 2.46749i −0.0482666 0.260096i
\(91\) −1.39456 4.29202i −0.146190 0.449926i
\(92\) 3.69826 2.68695i 0.385571 0.280134i
\(93\) 10.0520 1.04235
\(94\) −2.83986 + 2.06328i −0.292910 + 0.212811i
\(95\) 6.58771 + 6.24868i 0.675885 + 0.641101i
\(96\) 3.18668 + 2.31526i 0.325240 + 0.236300i
\(97\) −10.9217 7.93508i −1.10893 0.805685i −0.126436 0.991975i \(-0.540354\pi\)
−0.982495 + 0.186290i \(0.940354\pi\)
\(98\) 1.99754 6.14781i 0.201782 0.621022i
\(99\) 3.67008 0.368856
\(100\) −3.57613 0.956493i −0.357613 0.0956493i
\(101\) 7.22642 0.719055 0.359528 0.933134i \(-0.382938\pi\)
0.359528 + 0.933134i \(0.382938\pi\)
\(102\) −0.736068 + 2.26538i −0.0728816 + 0.224306i
\(103\) −4.26957 3.10203i −0.420693 0.305652i 0.357223 0.934019i \(-0.383723\pi\)
−0.777917 + 0.628367i \(0.783723\pi\)
\(104\) 10.0824 + 7.32526i 0.988657 + 0.718301i
\(105\) 1.07163 2.24803i 0.104581 0.219385i
\(106\) −3.18668 + 2.31526i −0.309518 + 0.224878i
\(107\) 5.46682 0.528498 0.264249 0.964455i \(-0.414876\pi\)
0.264249 + 0.964455i \(0.414876\pi\)
\(108\) 0.598970 0.435177i 0.0576359 0.0418749i
\(109\) 3.50410 + 10.7845i 0.335632 + 1.03297i 0.966410 + 0.257005i \(0.0827358\pi\)
−0.630778 + 0.775963i \(0.717264\pi\)
\(110\) −3.96334 + 8.31413i −0.377889 + 0.792721i
\(111\) 2.27817 7.01149i 0.216234 0.665501i
\(112\) −0.678387 2.08786i −0.0641015 0.197284i
\(113\) 1.49416 + 4.59855i 0.140559 + 0.432595i 0.996413 0.0846215i \(-0.0269681\pi\)
−0.855854 + 0.517217i \(0.826968\pi\)
\(114\) 1.40831 4.33434i 0.131900 0.405948i
\(115\) 13.6886 + 1.79900i 1.27647 + 0.167758i
\(116\) 0.516973 + 1.59108i 0.0479997 + 0.147728i
\(117\) 3.27817 2.38173i 0.303067 0.220191i
\(118\) 7.40046 0.681268
\(119\) −1.91229 + 1.38936i −0.175299 + 0.127362i
\(120\) 1.25481 + 6.76182i 0.114548 + 0.617267i
\(121\) −1.99783 1.45151i −0.181621 0.131955i
\(122\) −8.26639 6.00588i −0.748404 0.543747i
\(123\) −2.30902 + 7.10642i −0.208197 + 0.640765i
\(124\) −7.44220 −0.668330
\(125\) −5.84816 9.52885i −0.523075 0.852286i
\(126\) −1.24998 −0.111357
\(127\) 0.234728 0.722418i 0.0208287 0.0641043i −0.940102 0.340894i \(-0.889270\pi\)
0.960931 + 0.276789i \(0.0892704\pi\)
\(128\) 1.22019 + 0.886518i 0.107850 + 0.0783578i
\(129\) −7.48339 5.43700i −0.658876 0.478701i
\(130\) 1.85542 + 9.99836i 0.162731 + 0.876914i
\(131\) −11.8562 + 8.61406i −1.03588 + 0.752614i −0.969478 0.245179i \(-0.921153\pi\)
−0.0664061 + 0.997793i \(0.521153\pi\)
\(132\) −2.71720 −0.236502
\(133\) 3.65876 2.65824i 0.317255 0.230499i
\(134\) −0.910969 2.80367i −0.0786958 0.242201i
\(135\) 2.21700 + 0.291365i 0.190809 + 0.0250767i
\(136\) 2.01710 6.20799i 0.172965 0.532330i
\(137\) 3.79825 + 11.6898i 0.324506 + 0.998728i 0.971663 + 0.236371i \(0.0759580\pi\)
−0.647157 + 0.762357i \(0.724042\pi\)
\(138\) −2.14140 6.59054i −0.182288 0.561024i
\(139\) 4.55306 14.0129i 0.386185 1.18856i −0.549432 0.835539i \(-0.685156\pi\)
0.935617 0.353017i \(-0.114844\pi\)
\(140\) −0.793401 + 1.66437i −0.0670547 + 0.140665i
\(141\) −0.966496 2.97457i −0.0813937 0.250504i
\(142\) 0.600022 0.435941i 0.0503527 0.0365834i
\(143\) −14.8713 −1.24360
\(144\) 1.59467 1.15860i 0.132889 0.0965497i
\(145\) −2.17421 + 4.56098i −0.180558 + 0.378768i
\(146\) 6.78758 + 4.93147i 0.561744 + 0.408131i
\(147\) 4.65961 + 3.38541i 0.384318 + 0.279224i
\(148\) −1.68668 + 5.19108i −0.138645 + 0.426704i
\(149\) 15.6498 1.28208 0.641041 0.767507i \(-0.278503\pi\)
0.641041 + 0.767507i \(0.278503\pi\)
\(150\) −3.05421 + 4.70772i −0.249375 + 0.384384i
\(151\) 3.95819 0.322113 0.161056 0.986945i \(-0.448510\pi\)
0.161056 + 0.986945i \(0.448510\pi\)
\(152\) −3.85929 + 11.8777i −0.313030 + 0.963407i
\(153\) −1.71700 1.24748i −0.138812 0.100852i
\(154\) 3.71139 + 2.69648i 0.299072 + 0.217289i
\(155\) −16.3078 15.4685i −1.30987 1.24246i
\(156\) −2.42705 + 1.76336i −0.194320 + 0.141181i
\(157\) −4.50061 −0.359188 −0.179594 0.983741i \(-0.557478\pi\)
−0.179594 + 0.983741i \(0.557478\pi\)
\(158\) 7.75159 5.63186i 0.616683 0.448047i
\(159\) −1.08453 3.33784i −0.0860089 0.264708i
\(160\) −1.60704 8.65993i −0.127048 0.684627i
\(161\) 2.12499 6.54005i 0.167473 0.515428i
\(162\) −0.346820 1.06740i −0.0272488 0.0838631i
\(163\) −0.758292 2.33378i −0.0593940 0.182796i 0.916958 0.398985i \(-0.130637\pi\)
−0.976352 + 0.216189i \(0.930637\pi\)
\(164\) 1.70952 5.26137i 0.133491 0.410844i
\(165\) −5.95409 5.64767i −0.463525 0.439670i
\(166\) −4.25337 13.0905i −0.330125 1.01602i
\(167\) 2.47824 1.80055i 0.191772 0.139331i −0.487756 0.872980i \(-0.662184\pi\)
0.679528 + 0.733649i \(0.262184\pi\)
\(168\) 3.42541 0.264276
\(169\) −2.76606 + 2.00966i −0.212774 + 0.154589i
\(170\) 4.68022 2.54252i 0.358956 0.195002i
\(171\) 3.28513 + 2.38678i 0.251220 + 0.182522i
\(172\) 5.54046 + 4.02538i 0.422456 + 0.306932i
\(173\) 3.47942 10.7085i 0.264535 0.814156i −0.727265 0.686357i \(-0.759209\pi\)
0.991800 0.127799i \(-0.0407912\pi\)
\(174\) 2.53606 0.192258
\(175\) −5.19790 + 1.99798i −0.392925 + 0.151033i
\(176\) −7.23416 −0.545296
\(177\) −2.03760 + 6.27109i −0.153156 + 0.471364i
\(178\) −13.8814 10.0854i −1.04046 0.755935i
\(179\) −8.13657 5.91157i −0.608156 0.441851i 0.240609 0.970622i \(-0.422653\pi\)
−0.848764 + 0.528771i \(0.822653\pi\)
\(180\) −1.64140 0.215717i −0.122343 0.0160786i
\(181\) 15.7503 11.4433i 1.17071 0.850571i 0.179617 0.983737i \(-0.442514\pi\)
0.991094 + 0.133165i \(0.0425141\pi\)
\(182\) 5.06498 0.375441
\(183\) 7.36536 5.35125i 0.544463 0.395575i
\(184\) 5.86822 + 18.0605i 0.432611 + 1.33144i
\(185\) −14.4855 + 7.86923i −1.06500 + 0.578557i
\(186\) −3.48625 + 10.7296i −0.255624 + 0.786731i
\(187\) 2.40697 + 7.40790i 0.176015 + 0.541719i
\(188\) 0.715563 + 2.20227i 0.0521878 + 0.160617i
\(189\) 0.344163 1.05922i 0.0250342 0.0770472i
\(190\) −8.95461 + 4.86457i −0.649636 + 0.352913i
\(191\) −3.58739 11.0408i −0.259574 0.798888i −0.992894 0.119003i \(-0.962030\pi\)
0.733320 0.679884i \(-0.237970\pi\)
\(192\) −6.76586 + 4.91569i −0.488284 + 0.354759i
\(193\) −3.38156 −0.243410 −0.121705 0.992566i \(-0.538836\pi\)
−0.121705 + 0.992566i \(0.538836\pi\)
\(194\) 12.2578 8.90581i 0.880058 0.639400i
\(195\) −8.98339 1.18062i −0.643314 0.0845463i
\(196\) −3.44982 2.50644i −0.246416 0.179032i
\(197\) 14.2291 + 10.3380i 1.01378 + 0.736554i 0.964998 0.262256i \(-0.0844663\pi\)
0.0487811 + 0.998809i \(0.484466\pi\)
\(198\) −1.27286 + 3.91745i −0.0904579 + 0.278401i
\(199\) 20.0102 1.41849 0.709244 0.704963i \(-0.249037\pi\)
0.709244 + 0.704963i \(0.249037\pi\)
\(200\) 8.36966 12.9009i 0.591824 0.912230i
\(201\) 2.62663 0.185268
\(202\) −2.50627 + 7.71350i −0.176340 + 0.542720i
\(203\) 2.03600 + 1.47924i 0.142899 + 0.103822i
\(204\) 1.27121 + 0.923591i 0.0890028 + 0.0646643i
\(205\) 14.6817 7.97578i 1.02541 0.557052i
\(206\) 4.79188 3.48151i 0.333866 0.242568i
\(207\) 6.17438 0.429149
\(208\) −6.46167 + 4.69468i −0.448036 + 0.325517i
\(209\) −4.60524 14.1735i −0.318551 0.980399i
\(210\) 2.02789 + 1.92352i 0.139937 + 0.132736i
\(211\) 0.754807 2.32306i 0.0519631 0.159926i −0.921707 0.387886i \(-0.873206\pi\)
0.973671 + 0.227960i \(0.0732055\pi\)
\(212\) 0.802951 + 2.47123i 0.0551469 + 0.169725i
\(213\) 0.204207 + 0.628483i 0.0139920 + 0.0430630i
\(214\) −1.89600 + 5.83530i −0.129608 + 0.398893i
\(215\) 3.77387 + 20.3364i 0.257376 + 1.38693i
\(216\) 0.950415 + 2.92508i 0.0646675 + 0.199026i
\(217\) −9.05719 + 6.58044i −0.614842 + 0.446709i
\(218\) −12.7267 −0.861961
\(219\) −6.04774 + 4.39394i −0.408669 + 0.296915i
\(220\) 4.40821 + 4.18135i 0.297202 + 0.281906i
\(221\) 6.95737 + 5.05483i 0.468003 + 0.340024i
\(222\) 6.69397 + 4.86345i 0.449270 + 0.326413i
\(223\) −7.92223 + 24.3821i −0.530511 + 1.63275i 0.222641 + 0.974900i \(0.428532\pi\)
−0.753153 + 0.657846i \(0.771468\pi\)
\(224\) −4.38695 −0.293116
\(225\) −3.14835 3.88431i −0.209890 0.258954i
\(226\) −5.42671 −0.360979
\(227\) 2.02819 6.24212i 0.134616 0.414304i −0.860914 0.508750i \(-0.830108\pi\)
0.995530 + 0.0944455i \(0.0301078\pi\)
\(228\) −2.43220 1.76710i −0.161076 0.117029i
\(229\) 6.44293 + 4.68106i 0.425761 + 0.309333i 0.779952 0.625840i \(-0.215244\pi\)
−0.354191 + 0.935173i \(0.615244\pi\)
\(230\) −6.66774 + 13.9873i −0.439658 + 0.922297i
\(231\) −3.30685 + 2.40257i −0.217575 + 0.158077i
\(232\) −6.94974 −0.456273
\(233\) 7.62181 5.53757i 0.499321 0.362778i −0.309436 0.950920i \(-0.600140\pi\)
0.808758 + 0.588142i \(0.200140\pi\)
\(234\) 1.40533 + 4.32516i 0.0918693 + 0.282745i
\(235\) −3.00941 + 6.31303i −0.196312 + 0.411817i
\(236\) 1.50857 4.64291i 0.0981998 0.302228i
\(237\) 2.63811 + 8.11928i 0.171364 + 0.527404i
\(238\) −0.819784 2.52304i −0.0531387 0.163544i
\(239\) −3.46814 + 10.6738i −0.224335 + 0.690433i 0.774023 + 0.633157i \(0.218241\pi\)
−0.998358 + 0.0572756i \(0.981759\pi\)
\(240\) −4.36998 0.574317i −0.282081 0.0370720i
\(241\) 7.00879 + 21.5708i 0.451476 + 1.38950i 0.875223 + 0.483719i \(0.160714\pi\)
−0.423748 + 0.905780i \(0.639286\pi\)
\(242\) 2.24223 1.62908i 0.144136 0.104721i
\(243\) 1.00000 0.0641500
\(244\) −5.45307 + 3.96189i −0.349097 + 0.253634i
\(245\) −2.34984 12.6627i −0.150126 0.808988i
\(246\) −6.78460 4.92930i −0.432570 0.314281i
\(247\) −13.3115 9.67135i −0.846989 0.615373i
\(248\) 9.55361 29.4030i 0.606655 1.86709i
\(249\) 12.2639 0.777193
\(250\) 12.1994 2.93754i 0.771557 0.185787i
\(251\) −6.76819 −0.427205 −0.213602 0.976921i \(-0.568520\pi\)
−0.213602 + 0.976921i \(0.568520\pi\)
\(252\) −0.254807 + 0.784215i −0.0160513 + 0.0494009i
\(253\) −18.3327 13.3195i −1.15257 0.837387i
\(254\) 0.689703 + 0.501098i 0.0432758 + 0.0314417i
\(255\) 0.865884 + 4.66602i 0.0542238 + 0.292198i
\(256\) 12.1623 8.83640i 0.760142 0.552275i
\(257\) −14.7934 −0.922786 −0.461393 0.887196i \(-0.652650\pi\)
−0.461393 + 0.887196i \(0.652650\pi\)
\(258\) 8.39886 6.10213i 0.522890 0.379902i
\(259\) 2.53728 + 7.80894i 0.157659 + 0.485224i
\(260\) 6.65101 + 0.874096i 0.412478 + 0.0542092i
\(261\) −0.698265 + 2.14904i −0.0432215 + 0.133022i
\(262\) −5.08269 15.6429i −0.314009 0.966422i
\(263\) 6.17070 + 18.9915i 0.380502 + 1.17106i 0.939691 + 0.342024i \(0.111113\pi\)
−0.559189 + 0.829040i \(0.688887\pi\)
\(264\) 3.48809 10.7352i 0.214677 0.660709i
\(265\) −3.37694 + 7.08401i −0.207444 + 0.435167i
\(266\) 1.56849 + 4.82730i 0.0961700 + 0.295981i
\(267\) 12.3683 8.98613i 0.756930 0.549942i
\(268\) −1.94467 −0.118790
\(269\) 8.28280 6.01780i 0.505011 0.366912i −0.305917 0.952058i \(-0.598963\pi\)
0.810928 + 0.585146i \(0.198963\pi\)
\(270\) −1.07991 + 2.26538i −0.0657210 + 0.137867i
\(271\) −9.95701 7.23419i −0.604845 0.439446i 0.242750 0.970089i \(-0.421950\pi\)
−0.847595 + 0.530643i \(0.821950\pi\)
\(272\) 3.38442 + 2.45893i 0.205211 + 0.149094i
\(273\) −1.39456 + 4.29202i −0.0844028 + 0.259765i
\(274\) −13.7950 −0.833389
\(275\) 0.968651 + 18.3248i 0.0584118 + 1.10503i
\(276\) −4.57131 −0.275160
\(277\) 9.75011 30.0077i 0.585827 1.80299i −0.0100963 0.999949i \(-0.503214\pi\)
0.595923 0.803041i \(-0.296786\pi\)
\(278\) 13.3783 + 9.71989i 0.802376 + 0.582960i
\(279\) −8.13227 5.90844i −0.486866 0.353729i
\(280\) −5.55716 5.27116i −0.332104 0.315012i
\(281\) 17.2417 12.5268i 1.02855 0.747288i 0.0605353 0.998166i \(-0.480719\pi\)
0.968019 + 0.250878i \(0.0807192\pi\)
\(282\) 3.51026 0.209033
\(283\) 0.699317 0.508083i 0.0415701 0.0302024i −0.566806 0.823851i \(-0.691821\pi\)
0.608376 + 0.793649i \(0.291821\pi\)
\(284\) −0.151188 0.465309i −0.00897135 0.0276110i
\(285\) −1.65669 8.92745i −0.0981337 0.528817i
\(286\) 5.15767 15.8737i 0.304979 0.938629i
\(287\) −2.57163 7.91467i −0.151799 0.467188i
\(288\) −1.21720 3.74617i −0.0717245 0.220745i
\(289\) −3.86138 + 11.8841i −0.227140 + 0.699066i
\(290\) −4.11434 3.90260i −0.241602 0.229168i
\(291\) 4.17172 + 12.8392i 0.244550 + 0.752649i
\(292\) 4.47755 3.25313i 0.262029 0.190375i
\(293\) 3.17701 0.185603 0.0928014 0.995685i \(-0.470418\pi\)
0.0928014 + 0.995685i \(0.470418\pi\)
\(294\) −5.22964 + 3.79955i −0.304999 + 0.221594i
\(295\) 12.9559 7.03826i 0.754321 0.409783i
\(296\) −18.3439 13.3276i −1.06622 0.774653i
\(297\) −2.96915 2.15722i −0.172288 0.125174i
\(298\) −5.42766 + 16.7046i −0.314416 + 0.967673i
\(299\) −25.0188 −1.44688
\(300\) 2.33094 + 2.87582i 0.134577 + 0.166035i
\(301\) 10.3020 0.593799
\(302\) −1.37278 + 4.22498i −0.0789945 + 0.243120i
\(303\) −5.84629 4.24758i −0.335861 0.244017i
\(304\) −6.47538 4.70464i −0.371389 0.269830i
\(305\) −20.1838 2.65262i −1.15572 0.151888i
\(306\) 1.92705 1.40008i 0.110162 0.0800375i
\(307\) −0.507986 −0.0289923 −0.0144961 0.999895i \(-0.504614\pi\)
−0.0144961 + 0.999895i \(0.504614\pi\)
\(308\) 2.44828 1.77878i 0.139504 0.101356i
\(309\) 1.63083 + 5.01918i 0.0927747 + 0.285531i
\(310\) 22.1670 12.0422i 1.25900 0.683949i
\(311\) −4.52519 + 13.9271i −0.256600 + 0.789734i 0.736910 + 0.675991i \(0.236284\pi\)
−0.993510 + 0.113743i \(0.963716\pi\)
\(312\) −3.85112 11.8525i −0.218027 0.671017i
\(313\) −4.62171 14.2241i −0.261234 0.803996i −0.992537 0.121943i \(-0.961087\pi\)
0.731303 0.682053i \(-0.238913\pi\)
\(314\) 1.56090 4.80397i 0.0880869 0.271103i
\(315\) −2.18833 + 1.18880i −0.123298 + 0.0669815i
\(316\) −1.95317 6.01125i −0.109875 0.338159i
\(317\) −14.6586 + 10.6501i −0.823310 + 0.598170i −0.917659 0.397369i \(-0.869923\pi\)
0.0943487 + 0.995539i \(0.469923\pi\)
\(318\) 3.93896 0.220886
\(319\) 6.70920 4.87452i 0.375643 0.272921i
\(320\) 18.5409 + 2.43671i 1.03647 + 0.136216i
\(321\) −4.42275 3.21332i −0.246854 0.179350i
\(322\) 6.24388 + 4.53644i 0.347958 + 0.252806i
\(323\) −2.66312 + 8.19624i −0.148180 + 0.456051i
\(324\) −0.740367 −0.0411315
\(325\) 12.7573 + 15.7394i 0.707646 + 0.873064i
\(326\) 2.75408 0.152534
\(327\) 3.50410 10.7845i 0.193777 0.596385i
\(328\) 18.5923 + 13.5081i 1.02659 + 0.745860i
\(329\) 2.81811 + 2.04747i 0.155367 + 0.112881i
\(330\) 8.09333 4.39668i 0.445523 0.242029i
\(331\) −21.3188 + 15.4890i −1.17178 + 0.851351i −0.991221 0.132212i \(-0.957792\pi\)
−0.180563 + 0.983563i \(0.557792\pi\)
\(332\) −9.07979 −0.498318
\(333\) −5.96433 + 4.33334i −0.326843 + 0.237465i
\(334\) 1.06241 + 3.26975i 0.0581322 + 0.178913i
\(335\) −4.26127 4.04197i −0.232818 0.220837i
\(336\) −0.678387 + 2.08786i −0.0370090 + 0.113902i
\(337\) −3.30488 10.1714i −0.180028 0.554070i 0.819799 0.572651i \(-0.194085\pi\)
−0.999827 + 0.0185811i \(0.994085\pi\)
\(338\) −1.18579 3.64949i −0.0644986 0.198506i
\(339\) 1.49416 4.59855i 0.0811516 0.249759i
\(340\) −0.641073 3.45457i −0.0347670 0.187350i
\(341\) 11.4002 + 35.0861i 0.617354 + 1.90002i
\(342\) −3.68701 + 2.67877i −0.199371 + 0.144851i
\(343\) −14.2108 −0.767311
\(344\) −23.0160 + 16.7221i −1.24094 + 0.901594i
\(345\) −10.0169 9.50139i −0.539292 0.511537i
\(346\) 10.2236 + 7.42788i 0.549624 + 0.399325i
\(347\) −13.0850 9.50682i −0.702441 0.510353i 0.178286 0.983979i \(-0.442945\pi\)
−0.880726 + 0.473626i \(0.842945\pi\)
\(348\) 0.516973 1.59108i 0.0277126 0.0852907i
\(349\) 15.2383 0.815688 0.407844 0.913052i \(-0.366281\pi\)
0.407844 + 0.913052i \(0.366281\pi\)
\(350\) −0.329910 6.24119i −0.0176344 0.333606i
\(351\) −4.05204 −0.216282
\(352\) −4.46723 + 13.7487i −0.238104 + 0.732810i
\(353\) 23.8970 + 17.3622i 1.27191 + 0.924097i 0.999277 0.0380214i \(-0.0121055\pi\)
0.272633 + 0.962118i \(0.412106\pi\)
\(354\) −5.98710 4.34988i −0.318211 0.231194i
\(355\) 0.635845 1.33385i 0.0337472 0.0707935i
\(356\) −9.15712 + 6.65304i −0.485326 + 0.352610i
\(357\) 2.36372 0.125101
\(358\) 9.13195 6.63475i 0.482638 0.350657i
\(359\) −4.06875 12.5223i −0.214740 0.660903i −0.999172 0.0406876i \(-0.987045\pi\)
0.784431 0.620216i \(-0.212955\pi\)
\(360\) 2.95934 6.20799i 0.155971 0.327190i
\(361\) −0.776002 + 2.38829i −0.0408422 + 0.125699i
\(362\) 6.75205 + 20.7807i 0.354880 + 1.09221i
\(363\) 0.763104 + 2.34859i 0.0400526 + 0.123269i
\(364\) 1.03249 3.17767i 0.0541171 0.166555i
\(365\) 16.5730 + 2.17808i 0.867472 + 0.114006i
\(366\) 3.15748 + 9.71772i 0.165044 + 0.507953i
\(367\) 3.14622 2.28586i 0.164232 0.119321i −0.502634 0.864499i \(-0.667636\pi\)
0.666865 + 0.745178i \(0.267636\pi\)
\(368\) −12.1704 −0.634428
\(369\) 6.04508 4.39201i 0.314695 0.228639i
\(370\) −3.37576 18.1911i −0.175498 0.945710i
\(371\) 3.16227 + 2.29752i 0.164177 + 0.119281i
\(372\) 6.02087 + 4.37442i 0.312168 + 0.226803i
\(373\) −2.51641 + 7.74470i −0.130295 + 0.401006i −0.994829 0.101569i \(-0.967614\pi\)
0.864534 + 0.502575i \(0.167614\pi\)
\(374\) −8.74200 −0.452038
\(375\) −0.869658 + 11.1465i −0.0449089 + 0.575601i
\(376\) −9.61941 −0.496083
\(377\) 2.82940 8.70799i 0.145721 0.448484i
\(378\) 1.01126 + 0.734721i 0.0520134 + 0.0377900i
\(379\) −8.01509 5.82330i −0.411708 0.299123i 0.362585 0.931951i \(-0.381894\pi\)
−0.774293 + 0.632828i \(0.781894\pi\)
\(380\) 1.22656 + 6.60960i 0.0629211 + 0.339065i
\(381\) −0.614526 + 0.446479i −0.0314831 + 0.0228738i
\(382\) 13.0292 0.666632
\(383\) 4.22481 3.06951i 0.215878 0.156844i −0.474591 0.880206i \(-0.657404\pi\)
0.690469 + 0.723362i \(0.257404\pi\)
\(384\) −0.466070 1.43442i −0.0237840 0.0731997i
\(385\) 9.06198 + 1.19095i 0.461841 + 0.0606966i
\(386\) 1.17279 3.60949i 0.0596937 0.183718i
\(387\) 2.85840 + 8.79726i 0.145301 + 0.447190i
\(388\) −3.08860 9.50575i −0.156800 0.482581i
\(389\) −1.15255 + 3.54719i −0.0584367 + 0.179850i −0.976014 0.217708i \(-0.930142\pi\)
0.917577 + 0.397557i \(0.130142\pi\)
\(390\) 4.37582 9.17943i 0.221578 0.464819i
\(391\) 4.04938 + 12.4627i 0.204786 + 0.630267i
\(392\) 14.3311 10.4122i 0.723831 0.525894i
\(393\) 14.6551 0.739253
\(394\) −15.9698 + 11.6027i −0.804545 + 0.584536i
\(395\) 8.21438 17.2318i 0.413310 0.867027i
\(396\) 2.19826 + 1.59713i 0.110467 + 0.0802589i
\(397\) −3.24870 2.36032i −0.163048 0.118461i 0.503270 0.864130i \(-0.332130\pi\)
−0.666317 + 0.745668i \(0.732130\pi\)
\(398\) −6.93995 + 21.3590i −0.347868 + 1.07063i
\(399\) −4.52248 −0.226407
\(400\) 6.20579 + 7.65645i 0.310289 + 0.382822i
\(401\) −24.9890 −1.24789 −0.623945 0.781468i \(-0.714471\pi\)
−0.623945 + 0.781468i \(0.714471\pi\)
\(402\) −0.910969 + 2.80367i −0.0454350 + 0.139835i
\(403\) 32.9523 + 23.9413i 1.64147 + 1.19260i
\(404\) 4.32841 + 3.14477i 0.215346 + 0.156458i
\(405\) −1.62233 1.53884i −0.0806144 0.0764657i
\(406\) −2.28507 + 1.66020i −0.113406 + 0.0823943i
\(407\) 27.0570 1.34116
\(408\) −5.28083 + 3.83675i −0.261440 + 0.189947i
\(409\) −7.84186 24.1348i −0.387755 1.19339i −0.934462 0.356063i \(-0.884119\pi\)
0.546707 0.837324i \(-0.315881\pi\)
\(410\) 3.42147 + 18.4374i 0.168974 + 0.910558i
\(411\) 3.79825 11.6898i 0.187354 0.576616i
\(412\) −1.20741 3.71604i −0.0594850 0.183076i
\(413\) −2.26935 6.98433i −0.111667 0.343677i
\(414\) −2.14140 + 6.59054i −0.105244 + 0.323908i
\(415\) −19.8961 18.8722i −0.976663 0.926400i
\(416\) 4.93216 + 15.1796i 0.241819 + 0.744243i
\(417\) −11.9201 + 8.66043i −0.583728 + 0.424103i
\(418\) 16.7260 0.818094
\(419\) 24.9354 18.1166i 1.21817 0.885056i 0.222227 0.974995i \(-0.428667\pi\)
0.995947 + 0.0899392i \(0.0286673\pi\)
\(420\) 1.62017 0.880151i 0.0790560 0.0429470i
\(421\) −6.91425 5.02350i −0.336980 0.244830i 0.406406 0.913692i \(-0.366782\pi\)
−0.743387 + 0.668862i \(0.766782\pi\)
\(422\) 2.21785 + 1.61137i 0.107963 + 0.0784401i
\(423\) −0.966496 + 2.97457i −0.0469927 + 0.144629i
\(424\) −10.7942 −0.524212
\(425\) 5.77551 8.90230i 0.280154 0.431825i
\(426\) −0.741668 −0.0359339
\(427\) −3.13329 + 9.64327i −0.151630 + 0.466670i
\(428\) 3.27446 + 2.37904i 0.158277 + 0.114995i
\(429\) 12.0311 + 8.74113i 0.580869 + 0.422026i
\(430\) −23.0160 3.02483i −1.10993 0.145870i
\(431\) 21.3431 15.5067i 1.02806 0.746929i 0.0601403 0.998190i \(-0.480845\pi\)
0.967919 + 0.251261i \(0.0808452\pi\)
\(432\) −1.97112 −0.0948356
\(433\) 7.58269 5.50914i 0.364401 0.264753i −0.390485 0.920609i \(-0.627693\pi\)
0.754885 + 0.655857i \(0.227693\pi\)
\(434\) −3.88276 11.9499i −0.186378 0.573613i
\(435\) 4.43985 2.41194i 0.212874 0.115644i
\(436\) −2.59432 + 7.98450i −0.124245 + 0.382388i
\(437\) −7.74765 23.8448i −0.370620 1.14065i
\(438\) −2.59263 7.97928i −0.123880 0.381265i
\(439\) −0.159447 + 0.490727i −0.00760998 + 0.0234211i −0.954789 0.297283i \(-0.903920\pi\)
0.947179 + 0.320704i \(0.103920\pi\)
\(440\) −22.1787 + 12.0485i −1.05733 + 0.574391i
\(441\) −1.77981 5.47770i −0.0847530 0.260843i
\(442\) −7.80849 + 5.67320i −0.371412 + 0.269847i
\(443\) −17.8348 −0.847357 −0.423678 0.905813i \(-0.639261\pi\)
−0.423678 + 0.905813i \(0.639261\pi\)
\(444\) 4.41579 3.20826i 0.209564 0.152257i
\(445\) −33.8938 4.45443i −1.60672 0.211160i
\(446\) −23.2779 16.9124i −1.10224 0.800826i
\(447\) −12.6610 9.19872i −0.598842 0.435084i
\(448\) 2.87826 8.85836i 0.135985 0.418518i
\(449\) −4.16533 −0.196574 −0.0982870 0.995158i \(-0.531336\pi\)
−0.0982870 + 0.995158i \(0.531336\pi\)
\(450\) 5.23804 2.01340i 0.246923 0.0949128i
\(451\) −27.4233 −1.29131
\(452\) −1.10623 + 3.40462i −0.0520325 + 0.160140i
\(453\) −3.20224 2.32656i −0.150454 0.109311i
\(454\) 5.95944 + 4.32979i 0.279691 + 0.203207i
\(455\) 8.86719 4.81708i 0.415700 0.225828i
\(456\) 10.1038 7.34081i 0.473152 0.343765i
\(457\) −17.6734 −0.826725 −0.413362 0.910567i \(-0.635646\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(458\) −7.23112 + 5.25371i −0.337888 + 0.245490i
\(459\) 0.655837 + 2.01846i 0.0306119 + 0.0942136i
\(460\) 7.41618 + 7.03452i 0.345781 + 0.327986i
\(461\) −0.0633350 + 0.194925i −0.00294981 + 0.00907857i −0.952521 0.304474i \(-0.901519\pi\)
0.949571 + 0.313553i \(0.101519\pi\)
\(462\) −1.41762 4.36300i −0.0659538 0.202985i
\(463\) −3.96084 12.1902i −0.184076 0.566528i 0.815855 0.578256i \(-0.196267\pi\)
−0.999931 + 0.0117286i \(0.996267\pi\)
\(464\) 1.37636 4.23601i 0.0638961 0.196652i
\(465\) 4.10110 + 22.0997i 0.190184 + 1.02485i
\(466\) 3.26742 + 10.0561i 0.151360 + 0.465839i
\(467\) −0.901030 + 0.654637i −0.0416947 + 0.0302930i −0.608437 0.793602i \(-0.708203\pi\)
0.566743 + 0.823895i \(0.308203\pi\)
\(468\) 3.00000 0.138675
\(469\) −2.36668 + 1.71949i −0.109283 + 0.0793987i
\(470\) −5.69482 5.40174i −0.262682 0.249164i
\(471\) 3.64107 + 2.64539i 0.167772 + 0.121893i
\(472\) 16.4069 + 11.9203i 0.755187 + 0.548675i
\(473\) 10.4905 32.2866i 0.482356 1.48454i
\(474\) −9.58149 −0.440092
\(475\) −11.0502 + 17.0327i −0.507020 + 0.781513i
\(476\) −1.75002 −0.0802120
\(477\) −1.08453 + 3.33784i −0.0496572 + 0.152829i
\(478\) −10.1905 7.40380i −0.466101 0.338642i
\(479\) 20.3670 + 14.7975i 0.930590 + 0.676113i 0.946137 0.323766i \(-0.104949\pi\)
−0.0155470 + 0.999879i \(0.504949\pi\)
\(480\) −3.79005 + 7.95062i −0.172991 + 0.362895i
\(481\) 24.1677 17.5589i 1.10195 0.800615i
\(482\) −25.4555 −1.15947
\(483\) −5.56330 + 4.04197i −0.253139 + 0.183916i
\(484\) −0.564977 1.73882i −0.0256808 0.0790373i
\(485\) 12.9896 27.2491i 0.589828 1.23732i
\(486\) −0.346820 + 1.06740i −0.0157321 + 0.0484184i
\(487\) 3.20135 + 9.85274i 0.145067 + 0.446470i 0.997020 0.0771487i \(-0.0245816\pi\)
−0.851953 + 0.523619i \(0.824582\pi\)
\(488\) −8.65265 26.6301i −0.391687 1.20549i
\(489\) −0.758292 + 2.33378i −0.0342912 + 0.105537i
\(490\) 14.3311 + 1.88344i 0.647414 + 0.0850852i
\(491\) −4.83831 14.8908i −0.218350 0.672012i −0.998899 0.0469170i \(-0.985060\pi\)
0.780549 0.625095i \(-0.214940\pi\)
\(492\) −4.47558 + 3.25170i −0.201775 + 0.146598i
\(493\) −4.79569 −0.215987
\(494\) 14.9399 10.8545i 0.672178 0.488366i
\(495\) 1.49734 + 8.06878i 0.0673006 + 0.362665i
\(496\) 16.0297 + 11.6463i 0.719754 + 0.522932i
\(497\) −0.595425 0.432601i −0.0267084 0.0194048i
\(498\) −4.25337 + 13.0905i −0.190598 + 0.586600i
\(499\) 35.7864 1.60202 0.801010 0.598651i \(-0.204296\pi\)
0.801010 + 0.598651i \(0.204296\pi\)
\(500\) 0.643866 8.25248i 0.0287946 0.369062i
\(501\) −3.06328 −0.136857
\(502\) 2.34735 7.22439i 0.104767 0.322440i
\(503\) 9.52947 + 6.92356i 0.424898 + 0.308706i 0.779606 0.626271i \(-0.215420\pi\)
−0.354708 + 0.934977i \(0.615420\pi\)
\(504\) −2.77121 2.01340i −0.123440 0.0896842i
\(505\) 2.94828 + 15.8875i 0.131197 + 0.706985i
\(506\) 20.5754 14.9489i 0.914687 0.664559i
\(507\) 3.41904 0.151845
\(508\) 0.454975 0.330559i 0.0201862 0.0146662i
\(509\) 10.3986 + 32.0037i 0.460912 + 1.41854i 0.864052 + 0.503402i \(0.167918\pi\)
−0.403141 + 0.915138i \(0.632082\pi\)
\(510\) −5.28083 0.694023i −0.233839 0.0307318i
\(511\) 2.57276 7.91815i 0.113812 0.350278i
\(512\) 6.14602 + 18.9155i 0.271618 + 0.835955i
\(513\) −1.25481 3.86190i −0.0554011 0.170507i
\(514\) 5.13064 15.7905i 0.226303 0.696489i
\(515\) 5.07798 10.6524i 0.223762 0.469400i
\(516\) −2.11627 6.51320i −0.0931635 0.286728i
\(517\) 9.28647 6.74701i 0.408418 0.296733i
\(518\) −9.21526 −0.404895
\(519\) −9.10923 + 6.61825i −0.399851 + 0.290509i
\(520\) −11.9914 + 25.1550i −0.525856 + 1.10312i
\(521\) 9.58263 + 6.96219i 0.419823 + 0.305019i 0.777566 0.628801i \(-0.216454\pi\)
−0.357744 + 0.933820i \(0.616454\pi\)
\(522\) −2.05172 1.49066i −0.0898012 0.0652444i
\(523\) 1.26602 3.89642i 0.0553593 0.170379i −0.919554 0.392964i \(-0.871450\pi\)
0.974913 + 0.222586i \(0.0714497\pi\)
\(524\) −10.8502 −0.473992
\(525\) 5.37957 + 1.43885i 0.234784 + 0.0627967i
\(526\) −22.4117 −0.977195
\(527\) 6.59250 20.2896i 0.287174 0.883830i
\(528\) 5.85256 + 4.25213i 0.254700 + 0.185050i
\(529\) −12.2347 8.88902i −0.531943 0.386479i
\(530\) −6.39030 6.06143i −0.277577 0.263292i
\(531\) 5.33451 3.87575i 0.231498 0.168193i
\(532\) 3.34829 0.145167
\(533\) −24.4949 + 17.7966i −1.06099 + 0.770857i
\(534\) 5.30222 + 16.3186i 0.229450 + 0.706174i
\(535\) 2.23039 + 12.0190i 0.0964282 + 0.519626i
\(536\) 2.49639 7.68310i 0.107828 0.331859i
\(537\) 3.10789 + 9.56511i 0.134116 + 0.412765i
\(538\) 3.55078 + 10.9282i 0.153085 + 0.471147i
\(539\) −6.53205 + 20.1036i −0.281355 + 0.865922i
\(540\) 1.20112 + 1.13931i 0.0516881 + 0.0490280i
\(541\) 4.31332 + 13.2750i 0.185444 + 0.570738i 0.999956 0.00940920i \(-0.00299509\pi\)
−0.814512 + 0.580147i \(0.802995\pi\)
\(542\) 11.1751 8.11917i 0.480011 0.348748i
\(543\) −19.4684 −0.835471
\(544\) 6.76321 4.91376i 0.289970 0.210676i
\(545\) −22.2805 + 12.1038i −0.954390 + 0.518470i
\(546\) −4.09765 2.97712i −0.175363 0.127409i
\(547\) 21.4426 + 15.5789i 0.916818 + 0.666107i 0.942730 0.333557i \(-0.108249\pi\)
−0.0259119 + 0.999664i \(0.508249\pi\)
\(548\) −2.81210 + 8.65476i −0.120127 + 0.369713i
\(549\) −9.10408 −0.388553
\(550\) −19.8959 5.32147i −0.848363 0.226908i
\(551\) 9.17556 0.390892
\(552\) 5.86822 18.0605i 0.249768 0.768706i
\(553\) −7.69220 5.58871i −0.327105 0.237656i
\(554\) 28.6488 + 20.8146i 1.21717 + 0.884327i
\(555\) 16.3445 + 2.14804i 0.693783 + 0.0911791i
\(556\) 8.82522 6.41190i 0.374273 0.271925i
\(557\) 10.6860 0.452781 0.226391 0.974037i \(-0.427307\pi\)
0.226391 + 0.974037i \(0.427307\pi\)
\(558\) 9.12712 6.63124i 0.386382 0.280723i
\(559\) −11.5824 35.6468i −0.489882 1.50770i
\(560\) 4.31345 2.34327i 0.182277 0.0990214i
\(561\) 2.40697 7.40790i 0.101622 0.312762i
\(562\) 7.39140 + 22.7484i 0.311788 + 0.959583i
\(563\) −7.90310 24.3232i −0.333076 1.02510i −0.967662 0.252250i \(-0.918829\pi\)
0.634586 0.772852i \(-0.281171\pi\)
\(564\) 0.715563 2.20227i 0.0301306 0.0927325i
\(565\) −9.50047 + 5.16111i −0.399688 + 0.217129i
\(566\) 0.299792 + 0.922666i 0.0126012 + 0.0387825i
\(567\) −0.901030 + 0.654637i −0.0378397 + 0.0274922i
\(568\) 2.03244 0.0852794
\(569\) −4.93670 + 3.58672i −0.206957 + 0.150363i −0.686436 0.727190i \(-0.740826\pi\)
0.479479 + 0.877554i \(0.340826\pi\)
\(570\) 10.1038 + 1.32787i 0.423200 + 0.0556182i
\(571\) −19.2058 13.9538i −0.803737 0.583949i 0.108271 0.994121i \(-0.465468\pi\)
−0.912008 + 0.410173i \(0.865468\pi\)
\(572\) −8.90746 6.47165i −0.372440 0.270593i
\(573\) −3.58739 + 11.0408i −0.149865 + 0.461238i
\(574\) 9.34003 0.389845
\(575\) 1.62962 + 30.8288i 0.0679597 + 1.28565i
\(576\) 8.36307 0.348461
\(577\) −13.6474 + 42.0024i −0.568149 + 1.74858i 0.0902565 + 0.995919i \(0.471231\pi\)
−0.658405 + 0.752664i \(0.728769\pi\)
\(578\) −11.3459 8.24330i −0.471929 0.342876i
\(579\) 2.73574 + 1.98763i 0.113694 + 0.0826032i
\(580\) −3.28712 + 1.78572i −0.136490 + 0.0741480i
\(581\) −11.0501 + 8.02840i −0.458437 + 0.333074i
\(582\) −15.1515 −0.628048
\(583\) 10.4206 7.57100i 0.431576 0.313559i
\(584\) 7.10475 + 21.8662i 0.293997 + 0.904828i
\(585\) 6.57376 + 6.23545i 0.271792 + 0.257804i
\(586\) −1.10185 + 3.39115i −0.0455170 + 0.140087i
\(587\) 0.158206 + 0.486909i 0.00652987 + 0.0200969i 0.954268 0.298951i \(-0.0966368\pi\)
−0.947738 + 0.319048i \(0.896637\pi\)
\(588\) 1.31772 + 4.05551i 0.0543417 + 0.167246i
\(589\) −12.6134 + 38.8200i −0.519725 + 1.59955i
\(590\) 3.01929 + 16.2702i 0.124302 + 0.669832i
\(591\) −5.43502 16.7273i −0.223567 0.688068i
\(592\) 11.7564 8.54153i 0.483186 0.351055i
\(593\) −18.8405 −0.773687 −0.386844 0.922145i \(-0.626435\pi\)
−0.386844 + 0.922145i \(0.626435\pi\)
\(594\) 3.33238 2.42112i 0.136729 0.0993396i
\(595\) −3.83474 3.63738i −0.157209 0.149118i
\(596\) 9.37376 + 6.81043i 0.383964 + 0.278966i
\(597\) −16.1886 11.7617i −0.662556 0.481375i
\(598\) 8.67703 26.7052i 0.354830 1.09206i
\(599\) 6.20712 0.253616 0.126808 0.991927i \(-0.459527\pi\)
0.126808 + 0.991927i \(0.459527\pi\)
\(600\) −14.3541 + 5.51747i −0.586005 + 0.225250i
\(601\) 34.0303 1.38813 0.694063 0.719915i \(-0.255819\pi\)
0.694063 + 0.719915i \(0.255819\pi\)
\(602\) −3.57295 + 10.9964i −0.145623 + 0.448180i
\(603\) −2.12499 1.54390i −0.0865363 0.0628723i
\(604\) 2.37083 + 1.72251i 0.0964679 + 0.0700880i
\(605\) 2.37610 4.98450i 0.0966023 0.202649i
\(606\) 6.56149 4.76720i 0.266542 0.193654i
\(607\) 16.2488 0.659518 0.329759 0.944065i \(-0.393032\pi\)
0.329759 + 0.944065i \(0.393032\pi\)
\(608\) −12.9400 + 9.40144i −0.524785 + 0.381279i
\(609\) −0.777682 2.39346i −0.0315132 0.0969878i
\(610\) 9.83155 20.6242i 0.398068 0.835051i
\(611\) 3.91628 12.0531i 0.158436 0.487615i
\(612\) −0.485560 1.49440i −0.0196276 0.0604076i
\(613\) −0.0210086 0.0646578i −0.000848529 0.00261150i 0.950631 0.310322i \(-0.100437\pi\)
−0.951480 + 0.307711i \(0.900437\pi\)
\(614\) 0.176180 0.542225i 0.00711004 0.0218824i
\(615\) −16.5658 2.17712i −0.667996 0.0877900i
\(616\) 3.88481 + 11.9562i 0.156523 + 0.481730i
\(617\) −26.5445 + 19.2857i −1.06864 + 0.776413i −0.975667 0.219256i \(-0.929637\pi\)
−0.0929733 + 0.995669i \(0.529637\pi\)
\(618\) −5.92309 −0.238262
\(619\) 5.48280 3.98349i 0.220372 0.160110i −0.472122 0.881533i \(-0.656512\pi\)
0.692494 + 0.721423i \(0.256512\pi\)
\(620\) −3.03632 16.3619i −0.121942 0.657111i
\(621\) −4.99517 3.62921i −0.200449 0.145635i
\(622\) −13.2964 9.66040i −0.533137 0.387347i
\(623\) −5.26160 + 16.1935i −0.210802 + 0.648780i
\(624\) 7.98706 0.319738
\(625\) 18.5635 16.7450i 0.742541 0.669801i
\(626\) 16.7858 0.670895
\(627\) −4.60524 + 14.1735i −0.183915 + 0.566034i
\(628\) −2.69573 1.95856i −0.107571 0.0781552i
\(629\) −12.6583 9.19679i −0.504719 0.366700i
\(630\) −0.509976 2.74813i −0.0203179 0.109488i
\(631\) 6.20352 4.50712i 0.246958 0.179426i −0.457419 0.889251i \(-0.651226\pi\)
0.704378 + 0.709825i \(0.251226\pi\)
\(632\) 26.2568 1.04444
\(633\) −1.97611 + 1.43573i −0.0785433 + 0.0570651i
\(634\) −6.28405 19.3403i −0.249572 0.768102i
\(635\) 1.68403 + 0.221320i 0.0668285 + 0.00878281i
\(636\) 0.802951 2.47123i 0.0318391 0.0979906i
\(637\) 7.21188 + 22.1959i 0.285745 + 0.879432i
\(638\) 2.87619 + 8.85199i 0.113869 + 0.350454i
\(639\) 0.204207 0.628483i 0.00807829 0.0248624i
\(640\) −1.45122 + 3.04431i −0.0573644 + 0.120337i
\(641\) −7.32096 22.5316i −0.289161 0.889945i −0.985121 0.171864i \(-0.945021\pi\)
0.695960 0.718081i \(-0.254979\pi\)
\(642\) 4.96380 3.60641i 0.195906 0.142334i
\(643\) 2.16861 0.0855218 0.0427609 0.999085i \(-0.486385\pi\)
0.0427609 + 0.999085i \(0.486385\pi\)
\(644\) 4.11889 2.99255i 0.162307 0.117923i
\(645\) 8.90030 18.6707i 0.350449 0.735158i
\(646\) −7.82506 5.68524i −0.307873 0.223683i
\(647\) −2.06737 1.50203i −0.0812767 0.0590510i 0.546405 0.837521i \(-0.315996\pi\)
−0.627682 + 0.778470i \(0.715996\pi\)
\(648\) 0.950415 2.92508i 0.0373358 0.114908i
\(649\) −24.1998 −0.949926
\(650\) −21.2247 + 8.15840i −0.832503 + 0.319999i
\(651\) 11.1953 0.438779
\(652\) 0.561415 1.72786i 0.0219867 0.0676681i
\(653\) −26.2233 19.0523i −1.02620 0.745575i −0.0586517 0.998279i \(-0.518680\pi\)
−0.967544 + 0.252704i \(0.918680\pi\)
\(654\) 10.2961 + 7.48057i 0.402610 + 0.292513i
\(655\) −23.7755 22.5519i −0.928985 0.881175i
\(656\) −11.9156 + 8.65719i −0.465226 + 0.338006i
\(657\) 7.47542 0.291644
\(658\) −3.16285 + 2.29795i −0.123301 + 0.0895833i
\(659\) 0.139043 + 0.427929i 0.00541633 + 0.0166697i 0.953728 0.300670i \(-0.0972104\pi\)
−0.948312 + 0.317340i \(0.897210\pi\)
\(660\) −1.10858 5.97386i −0.0431516 0.232532i
\(661\) −8.33812 + 25.6621i −0.324315 + 0.998140i 0.647433 + 0.762122i \(0.275842\pi\)
−0.971749 + 0.236018i \(0.924158\pi\)
\(662\) −9.13921 28.1276i −0.355205 1.09321i
\(663\) −2.65748 8.17888i −0.103208 0.317641i
\(664\) 11.6558 35.8728i 0.452332 1.39214i
\(665\) 7.33696 + 6.95937i 0.284515 + 0.269873i
\(666\) −2.55687 7.86923i −0.0990766 0.304926i
\(667\) 11.2873 8.20067i 0.437044 0.317531i
\(668\) 2.26795 0.0877496
\(669\) 20.7407 15.0690i 0.801880 0.582600i
\(670\) 5.79231 3.14666i 0.223776 0.121566i
\(671\) 27.0314 + 19.6395i 1.04354 + 0.758174i
\(672\) 3.54912 + 2.57859i 0.136910 + 0.0994711i
\(673\) 5.44561 16.7599i 0.209913 0.646046i −0.789563 0.613670i \(-0.789693\pi\)
0.999476 0.0323758i \(-0.0103073\pi\)
\(674\) 12.0032 0.462344
\(675\) 0.263932 + 4.99303i 0.0101587 + 0.192182i
\(676\) −2.53135 −0.0973595
\(677\) −5.97899 + 18.4014i −0.229791 + 0.707225i 0.767978 + 0.640476i \(0.221263\pi\)
−0.997770 + 0.0667494i \(0.978737\pi\)
\(678\) 4.39030 + 3.18974i 0.168608 + 0.122501i
\(679\) −12.1639 8.83757i −0.466807 0.339155i
\(680\) 14.4714 + 1.90188i 0.554953 + 0.0729336i
\(681\) −5.30987 + 3.85784i −0.203475 + 0.147833i
\(682\) −41.4049 −1.58547
\(683\) 24.2268 17.6018i 0.927015 0.673515i −0.0182455 0.999834i \(-0.505808\pi\)
0.945260 + 0.326318i \(0.105808\pi\)
\(684\) 0.929018 + 2.85922i 0.0355219 + 0.109325i
\(685\) −24.1508 + 13.1199i −0.922755 + 0.501284i
\(686\) 4.92859 15.1686i 0.188175 0.579142i
\(687\) −2.46098 7.57412i −0.0938923 0.288971i
\(688\) −5.63426 17.3405i −0.214804 0.661099i
\(689\) 4.39456 13.5251i 0.167419 0.515264i
\(690\) 13.6159 7.39679i 0.518347 0.281591i
\(691\) −6.16024 18.9593i −0.234346 0.721244i −0.997207 0.0746817i \(-0.976206\pi\)
0.762861 0.646563i \(-0.223794\pi\)
\(692\) 6.74418 4.89993i 0.256375 0.186268i
\(693\) 4.08749 0.155271
\(694\) 14.6858 10.6698i 0.557464 0.405021i
\(695\) 32.6653 + 4.29298i 1.23907 + 0.162842i
\(696\) 5.62246 + 4.08495i 0.213119 + 0.154840i
\(697\) 12.8297 + 9.32131i 0.485959 + 0.353070i
\(698\) −5.28495 + 16.2654i −0.200038 + 0.615655i
\(699\) −9.42107 −0.356338
\(700\) −3.98286 1.06528i −0.150538 0.0402638i
\(701\) −49.0150 −1.85127 −0.925636 0.378415i \(-0.876469\pi\)
−0.925636 + 0.378415i \(0.876469\pi\)
\(702\) 1.40533 4.32516i 0.0530407 0.163243i
\(703\) 24.2190 + 17.5961i 0.913437 + 0.663651i
\(704\) −24.8312 18.0409i −0.935862 0.679944i
\(705\) 6.14537 3.33846i 0.231448 0.125734i
\(706\) −26.8204 + 19.4862i −1.00940 + 0.733372i
\(707\) 8.04831 0.302688
\(708\) −3.94950 + 2.86948i −0.148431 + 0.107842i
\(709\) −1.48744 4.57788i −0.0558621 0.171926i 0.919233 0.393715i \(-0.128810\pi\)
−0.975095 + 0.221789i \(0.928810\pi\)
\(710\) 1.20323 + 1.14131i 0.0451565 + 0.0428326i
\(711\) 2.63811 8.11928i 0.0989370 0.304497i
\(712\) −14.5300 44.7189i −0.544536 1.67591i
\(713\) 19.1792 + 59.0274i 0.718265 + 2.21059i
\(714\) −0.819784 + 2.52304i −0.0306797 + 0.0944223i
\(715\) −6.06730 32.6950i −0.226904 1.22273i
\(716\) −2.30098 7.08170i −0.0859918 0.264656i
\(717\) 9.07970 6.59679i 0.339088 0.246362i
\(718\) 14.7775 0.551491
\(719\) −26.0917 + 18.9568i −0.973058 + 0.706968i −0.956146 0.292889i \(-0.905383\pi\)
−0.0169113 + 0.999857i \(0.505383\pi\)
\(720\) 3.19782 + 3.03324i 0.119176 + 0.113042i
\(721\) −4.75517 3.45483i −0.177092 0.128665i
\(722\) −2.28013 1.65661i −0.0848578 0.0616528i
\(723\) 7.00879 21.5708i 0.260660 0.802228i
\(724\) 14.4138 0.535685
\(725\) −10.9145 2.91926i −0.405355 0.108418i
\(726\) −2.77155 −0.102862
\(727\) −9.01548 + 27.7468i −0.334366 + 1.02907i 0.632668 + 0.774423i \(0.281960\pi\)
−0.967034 + 0.254648i \(0.918040\pi\)
\(728\) 11.2291 + 8.15840i 0.416177 + 0.302370i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) −8.07275 + 16.9347i −0.298786 + 0.626781i
\(731\) −15.8823 + 11.5391i −0.587426 + 0.426790i
\(732\) 6.74037 0.249131
\(733\) −4.20771 + 3.05708i −0.155415 + 0.112916i −0.662775 0.748818i \(-0.730622\pi\)
0.507360 + 0.861734i \(0.330622\pi\)
\(734\) 1.34876 + 4.15107i 0.0497838 + 0.153219i
\(735\) −5.54186 + 11.6255i −0.204415 + 0.428813i
\(736\) −7.51548 + 23.1303i −0.277024 + 0.852593i
\(737\) 2.97891 + 9.16813i 0.109729 + 0.337712i
\(738\) 2.59149 + 7.97578i 0.0953940 + 0.293592i
\(739\) −5.04334 + 15.5218i −0.185522 + 0.570979i −0.999957 0.00927620i \(-0.997047\pi\)
0.814435 + 0.580255i \(0.197047\pi\)
\(740\) −12.1009 1.59034i −0.444838 0.0584620i
\(741\) 5.08453 + 15.6486i 0.186785 + 0.574865i
\(742\) −3.54912 + 2.57859i −0.130292 + 0.0946629i
\(743\) 53.4487 1.96084 0.980421 0.196914i \(-0.0630919\pi\)
0.980421 + 0.196914i \(0.0630919\pi\)
\(744\) −25.0117 + 18.1720i −0.916972 + 0.666219i
\(745\) 6.38491 + 34.4066i 0.233925 + 1.26056i
\(746\) −7.39398 5.37204i −0.270713 0.196684i
\(747\) −9.92170 7.20854i −0.363016 0.263747i
\(748\) −1.78204 + 5.48457i −0.0651580 + 0.200536i
\(749\) 6.08859 0.222472
\(750\) −11.5962 4.79409i −0.423432 0.175056i
\(751\) −0.566970 −0.0206890 −0.0103445 0.999946i \(-0.503293\pi\)
−0.0103445 + 0.999946i \(0.503293\pi\)
\(752\) 1.90508 5.86324i 0.0694712 0.213810i
\(753\) 5.47558 + 3.97824i 0.199541 + 0.144975i
\(754\) 8.31364 + 6.04021i 0.302765 + 0.219972i
\(755\) 1.61489 + 8.70220i 0.0587718 + 0.316706i
\(756\) 0.667093 0.484672i 0.0242620 0.0176273i
\(757\) 53.0708 1.92889 0.964445 0.264282i \(-0.0851350\pi\)
0.964445 + 0.264282i \(0.0851350\pi\)
\(758\) 8.99560 6.53569i 0.326735 0.237387i
\(759\) 7.00246 + 21.5513i 0.254173 + 0.782264i
\(760\) −27.6880 3.63884i −1.00435 0.131995i
\(761\) −8.49970 + 26.1594i −0.308114 + 0.948277i 0.670383 + 0.742015i \(0.266130\pi\)
−0.978497 + 0.206262i \(0.933870\pi\)
\(762\) −0.263443 0.810794i −0.00954353 0.0293720i
\(763\) 3.90264 + 12.0111i 0.141285 + 0.434830i
\(764\) 2.65599 8.17428i 0.0960902 0.295735i
\(765\) 2.04210 4.28384i 0.0738324 0.154883i
\(766\) 1.81115 + 5.57414i 0.0654394 + 0.201402i
\(767\) −21.6157 + 15.7047i −0.780496 + 0.567064i
\(768\) −15.0334 −0.542471
\(769\) −12.1123 + 8.80007i −0.436779 + 0.317339i −0.784354 0.620314i \(-0.787005\pi\)
0.347575 + 0.937652i \(0.387005\pi\)
\(770\) −4.41410 + 9.25974i −0.159073 + 0.333698i
\(771\) 11.9681 + 8.69533i 0.431021 + 0.313155i
\(772\) −2.02546 1.47158i −0.0728977 0.0529633i
\(773\) −0.634806 + 1.95373i −0.0228324 + 0.0702708i −0.961823 0.273671i \(-0.911762\pi\)
0.938991 + 0.343941i \(0.111762\pi\)
\(774\) −10.3816 −0.373158
\(775\) 27.3547 42.1641i 0.982608 1.51458i
\(776\) 41.5206 1.49050
\(777\) 2.53728 7.80894i 0.0910243 0.280144i
\(778\) −3.38655 2.46048i −0.121414 0.0882123i
\(779\) −24.5469 17.8344i −0.879485 0.638983i
\(780\) −4.86700 4.61653i −0.174267 0.165298i
\(781\) −1.96210 + 1.42555i −0.0702093 + 0.0510100i
\(782\) −14.7072 −0.525927
\(783\) 1.82808 1.32818i 0.0653303 0.0474652i
\(784\) 3.50823 + 10.7972i 0.125294 + 0.385615i
\(785\) −1.83619 9.89475i −0.0655365 0.353159i
\(786\) −5.08269 + 15.6429i −0.181293 + 0.557964i
\(787\) −5.19981 16.0034i −0.185353 0.570458i 0.814601 0.580022i \(-0.196956\pi\)
−0.999954 + 0.00956327i \(0.996956\pi\)
\(788\) 4.02391 + 12.3843i 0.143346 + 0.441174i
\(789\) 6.17070 18.9915i 0.219683 0.676114i
\(790\) 15.5444 + 14.7444i 0.553044 + 0.524582i
\(791\) 1.66410 + 5.12156i 0.0591685 + 0.182102i
\(792\) −9.13195 + 6.63475i −0.324490 + 0.235756i
\(793\) 36.8901 1.31001
\(794\) 3.64613 2.64907i 0.129396 0.0940118i
\(795\) 6.89588 3.74617i 0.244572 0.132863i
\(796\) 11.9855 + 8.70799i 0.424816 + 0.308647i
\(797\) 0.168996 + 0.122783i 0.00598616 + 0.00434920i 0.590774 0.806837i \(-0.298822\pi\)
−0.584788 + 0.811186i \(0.698822\pi\)
\(798\) 1.56849 4.82730i 0.0555238 0.170885i
\(799\) −6.63791 −0.234832
\(800\) 18.3835 7.06627i 0.649954 0.249830i
\(801\) −15.2881 −0.540179
\(802\) 8.66668 26.6733i 0.306031 0.941867i
\(803\) −22.1957 16.1261i −0.783268 0.569078i
\(804\) 1.57327 + 1.14305i 0.0554851 + 0.0403123i
\(805\) 15.2455 + 2.00361i 0.537333 + 0.0706179i
\(806\) −36.9835 + 26.8701i −1.30269 + 0.946458i
\(807\) −10.2381 −0.360398
\(808\) −17.9809 + 13.0639i −0.632566 + 0.459586i
\(809\) −5.24264 16.1352i −0.184321 0.567283i 0.815615 0.578595i \(-0.196399\pi\)
−0.999936 + 0.0113128i \(0.996399\pi\)
\(810\) 2.20522 1.19798i 0.0774836 0.0420928i
\(811\) −6.32508 + 19.4666i −0.222103 + 0.683564i 0.776469 + 0.630155i \(0.217009\pi\)
−0.998573 + 0.0534090i \(0.982991\pi\)
\(812\) 0.575770 + 1.77204i 0.0202056 + 0.0621864i
\(813\) 3.80324 + 11.7052i 0.133385 + 0.410518i
\(814\) −9.38390 + 28.8807i −0.328905 + 1.01227i
\(815\) 4.82153 2.61928i 0.168891 0.0917495i
\(816\) −1.29273 3.97863i −0.0452548 0.139280i
\(817\) 30.3874 22.0777i 1.06312 0.772401i
\(818\) 28.4812 0.995822
\(819\) 3.65101 2.65262i 0.127577 0.0926899i
\(820\) 12.2647 + 1.61187i 0.428304 + 0.0562890i
\(821\) −31.0368 22.5496i −1.08319 0.786985i −0.104955 0.994477i \(-0.533470\pi\)
−0.978237 + 0.207492i \(0.933470\pi\)
\(822\) 11.1604 + 8.10852i 0.389265 + 0.282817i
\(823\) −8.96451 + 27.5899i −0.312483 + 0.961725i 0.664295 + 0.747471i \(0.268732\pi\)
−0.976778 + 0.214254i \(0.931268\pi\)
\(824\) 16.2315 0.565449
\(825\) 9.98739 15.3944i 0.347716 0.535965i
\(826\) 8.24215 0.286781
\(827\) 4.43648 13.6541i 0.154271 0.474799i −0.843815 0.536634i \(-0.819695\pi\)
0.998086 + 0.0618356i \(0.0196955\pi\)
\(828\) 3.69826 + 2.68695i 0.128524 + 0.0933779i
\(829\) −3.75031 2.72476i −0.130254 0.0946347i 0.520751 0.853709i \(-0.325652\pi\)
−0.651004 + 0.759074i \(0.725652\pi\)
\(830\) 27.0446 14.6919i 0.938732 0.509964i
\(831\) −25.5261 + 18.5458i −0.885491 + 0.643347i
\(832\) −33.8875 −1.17484
\(833\) 9.88925 7.18496i 0.342642 0.248944i
\(834\) −5.11005 15.7271i −0.176946 0.544585i
\(835\) 4.96965 + 4.71390i 0.171982 + 0.163131i
\(836\) 3.40957 10.4936i 0.117922 0.362928i
\(837\) 3.10625 + 9.56006i 0.107368 + 0.330444i
\(838\) 10.6896 + 32.8993i 0.369268 + 1.13649i
\(839\) 1.52235 4.68531i 0.0525573 0.161755i −0.921333 0.388775i \(-0.872898\pi\)
0.973890 + 0.227020i \(0.0728983\pi\)
\(840\) 1.39752 + 7.53087i 0.0482191 + 0.259840i
\(841\) −7.38367 22.7246i −0.254609 0.783607i
\(842\) 7.76010 5.63804i 0.267431 0.194300i
\(843\) −21.3119 −0.734022
\(844\) 1.46305 1.06297i 0.0503602 0.0365888i
\(845\) −5.54683 5.26137i −0.190817 0.180996i
\(846\) −2.83986 2.06328i −0.0976365 0.0709371i
\(847\) −2.22505 1.61660i −0.0764538 0.0555469i
\(848\) 2.13774 6.57929i 0.0734103 0.225934i
\(849\) −0.864403 −0.0296662
\(850\) 7.49927 + 9.25229i 0.257223 + 0.317351i
\(851\) 45.5194 1.56039
\(852\) −0.151188 + 0.465309i −0.00517961 + 0.0159412i
\(853\) −43.4018 31.5333i −1.48605 1.07968i −0.975544 0.219805i \(-0.929458\pi\)
−0.510507 0.859874i \(-0.670542\pi\)
\(854\) −9.20656 6.68896i −0.315042 0.228891i
\(855\) −3.90714 + 8.19624i −0.133621 + 0.280305i
\(856\) −13.6026 + 9.88290i −0.464929 + 0.337790i
\(857\) −27.1144 −0.926210 −0.463105 0.886303i \(-0.653265\pi\)
−0.463105 + 0.886303i \(0.653265\pi\)
\(858\) −13.5029 + 9.81046i −0.460983 + 0.334924i
\(859\) 3.21966 + 9.90910i 0.109853 + 0.338094i 0.990839 0.135049i \(-0.0431193\pi\)
−0.880985 + 0.473143i \(0.843119\pi\)
\(860\) −6.58950 + 13.8232i −0.224700 + 0.471367i
\(861\) −2.57163 + 7.91467i −0.0876410 + 0.269731i
\(862\) 9.14963 + 28.1597i 0.311638 + 0.959122i
\(863\) −13.4865 41.5072i −0.459086 1.41292i −0.866271 0.499575i \(-0.833490\pi\)
0.407185 0.913346i \(-0.366510\pi\)
\(864\) −1.21720 + 3.74617i −0.0414101 + 0.127447i
\(865\) 24.9626 + 3.28067i 0.848756 + 0.111546i
\(866\) 3.25065 + 10.0045i 0.110461 + 0.339965i
\(867\) 10.1092 7.34479i 0.343328 0.249442i
\(868\) −8.28864 −0.281335
\(869\) −25.3480 + 18.4164i −0.859872 + 0.624734i
\(870\) 1.03468 + 5.57561i 0.0350789 + 0.189031i
\(871\) 8.61055 + 6.25593i 0.291757 + 0.211974i
\(872\) −28.2151 20.4995i −0.955485 0.694201i
\(873\) 4.17172 12.8392i 0.141191 0.434542i
\(874\) 28.1391 0.951818
\(875\) −6.51330 10.6126i −0.220190 0.358772i
\(876\) −5.53456 −0.186995
\(877\) 16.5767 51.0180i 0.559757 1.72275i −0.123281 0.992372i \(-0.539342\pi\)
0.683038 0.730383i \(-0.260658\pi\)
\(878\) −0.468503 0.340388i −0.0158112 0.0114875i
\(879\) −2.57025 1.86740i −0.0866925 0.0629858i
\(880\) −2.95144 15.9045i −0.0994931 0.536142i
\(881\) 44.4110 32.2665i 1.49625 1.08709i 0.524398 0.851473i \(-0.324290\pi\)
0.971847 0.235613i \(-0.0757097\pi\)
\(882\) 6.46419 0.217661
\(883\) 15.4483 11.2239i 0.519877 0.377713i −0.296681 0.954977i \(-0.595880\pi\)
0.816558 + 0.577264i \(0.195880\pi\)
\(884\) 1.96751 + 6.05538i 0.0661746 + 0.203664i
\(885\) −14.6185 1.92121i −0.491396 0.0645808i
\(886\) 6.18547 19.0369i 0.207805 0.639558i
\(887\) −3.46598 10.6672i −0.116376 0.358170i 0.875855 0.482574i \(-0.160298\pi\)
−0.992232 + 0.124404i \(0.960298\pi\)
\(888\) 7.00676 + 21.5646i 0.235131 + 0.723660i
\(889\) 0.261425 0.804582i 0.00876790 0.0269848i
\(890\) 16.5097 34.6334i 0.553407 1.16092i
\(891\) 1.13412 + 3.49045i 0.0379943 + 0.116934i
\(892\) −15.3557 + 11.1566i −0.514147 + 0.373550i
\(893\) 12.7003 0.424998
\(894\) 14.2098 10.3240i 0.475247 0.345287i
\(895\) 9.67716 20.3004i 0.323472 0.678566i
\(896\) 1.35896 + 0.987345i 0.0453998 + 0.0329849i
\(897\) 20.2407 + 14.7057i 0.675816 + 0.491009i
\(898\) 1.44462 4.44608i 0.0482076 0.148368i
\(899\) −22.7139 −0.757552
\(900\) −0.195407 3.69668i −0.00651356 0.123223i
\(901\) −7.44857 −0.248148
\(902\) 9.51095 29.2717i 0.316680 0.974641i
\(903\) −8.33451 6.05538i −0.277355 0.201510i
\(904\) −12.0310 8.74106i −0.400146 0.290723i
\(905\) 31.5843 + 29.9589i 1.04990 + 0.995866i
\(906\) 3.59398 2.61118i 0.119402 0.0867506i
\(907\) −36.4513 −1.21034 −0.605172 0.796095i \(-0.706896\pi\)
−0.605172 + 0.796095i \(0.706896\pi\)
\(908\) 3.93125 2.85622i 0.130463 0.0947871i
\(909\) 2.23309 + 6.87273i 0.0740668 + 0.227954i
\(910\) 2.06644 + 11.1355i 0.0685020 + 0.369139i
\(911\) 0.360106 1.10829i 0.0119309 0.0367194i −0.944914 0.327319i \(-0.893855\pi\)
0.956845 + 0.290600i \(0.0938548\pi\)
\(912\) 2.47338 + 7.61227i 0.0819017 + 0.252067i
\(913\) 13.9087 + 42.8065i 0.460310 + 1.41669i
\(914\) 6.12948 18.8646i 0.202745 0.623985i
\(915\) 14.7699 + 14.0097i 0.488276 + 0.463148i
\(916\) 1.82203 + 5.60763i 0.0602016 + 0.185281i
\(917\) −13.2047 + 9.59377i −0.436057 + 0.316814i
\(918\) −2.38197 −0.0786166
\(919\) −35.5543 + 25.8317i −1.17283 + 0.852109i −0.991345 0.131286i \(-0.958089\pi\)
−0.181482 + 0.983394i \(0.558089\pi\)
\(920\) −37.3125 + 20.2699i −1.23016 + 0.668279i
\(921\) 0.410969 + 0.298587i 0.0135419 + 0.00983876i
\(922\) −0.186098 0.135208i −0.00612880 0.00445283i
\(923\) −0.827454 + 2.54664i −0.0272360 + 0.0838237i
\(924\) −3.02624 −0.0995561
\(925\) −23.2107 28.6364i −0.763162 0.941558i
\(926\) 14.3856 0.472739
\(927\) 1.63083 5.01918i 0.0535635 0.164852i
\(928\) −7.20073 5.23164i −0.236376 0.171737i
\(929\) −25.2512 18.3460i −0.828464 0.601914i 0.0906606 0.995882i \(-0.471102\pi\)
−0.919124 + 0.393968i \(0.871102\pi\)
\(930\) −25.0117 3.28711i −0.820165 0.107789i
\(931\) −18.9210 + 13.7469i −0.620111 + 0.450537i
\(932\) 6.97506 0.228476
\(933\) 11.8471 8.60743i 0.387857 0.281795i
\(934\) −0.386266 1.18880i −0.0126390 0.0388988i
\(935\) −15.3045 + 8.31413i −0.500510 + 0.271901i
\(936\) −3.85112 + 11.8525i −0.125878 + 0.387412i
\(937\) −13.9385 42.8983i −0.455351 1.40143i −0.870722 0.491775i \(-0.836348\pi\)
0.415371 0.909652i \(-0.363652\pi\)
\(938\) −1.01458 3.12255i −0.0331271 0.101955i
\(939\) −4.62171 + 14.2241i −0.150824 + 0.464188i
\(940\) −4.54983 + 2.47169i −0.148399 + 0.0806175i
\(941\) −12.0931 37.2187i −0.394224 1.21330i −0.929565 0.368659i \(-0.879817\pi\)
0.535341 0.844636i \(-0.320183\pi\)
\(942\) −4.08650 + 2.96901i −0.133145 + 0.0967357i
\(943\) −46.1358 −1.50239
\(944\) −10.5150 + 7.63957i −0.342233 + 0.248647i
\(945\) 2.46915 + 0.324504i 0.0803216 + 0.0105561i
\(946\) 30.8245 + 22.3953i 1.00219 + 0.728133i
\(947\) 39.5235 + 28.7155i 1.28434 + 0.933128i 0.999675 0.0254991i \(-0.00811748\pi\)
0.284665 + 0.958627i \(0.408117\pi\)
\(948\) −1.95317 + 6.01125i −0.0634361 + 0.195236i
\(949\) −30.2907 −0.983278
\(950\) −14.3483 17.7023i −0.465520 0.574339i
\(951\) 18.1190 0.587550
\(952\) 2.24651 6.91405i 0.0728098 0.224086i
\(953\) −18.4314 13.3912i −0.597051 0.433783i 0.247780 0.968816i \(-0.420299\pi\)
−0.844831 + 0.535034i \(0.820299\pi\)
\(954\) −3.18668 2.31526i −0.103173 0.0749593i
\(955\) 22.8101 12.3915i 0.738116 0.400980i
\(956\) −6.72232 + 4.88405i −0.217415 + 0.157961i
\(957\) −8.29302 −0.268075
\(958\) −22.8585 + 16.6077i −0.738525 + 0.536570i
\(959\) 4.23024 + 13.0193i 0.136602 + 0.420417i
\(960\) −13.5677 12.8694i −0.437895 0.415359i
\(961\) 21.6446 66.6154i 0.698214 2.14888i
\(962\) 10.3605 + 31.8864i 0.334037 + 1.02806i
\(963\) 1.68934 + 5.19926i 0.0544382 + 0.167544i
\(964\) −5.18908 + 15.9703i −0.167129 + 0.514370i
\(965\) −1.37963 7.43448i −0.0444120 0.239324i
\(966\) −2.38495 7.34012i −0.0767345 0.236164i
\(967\) −34.9436 + 25.3880i −1.12371 + 0.816425i −0.984768 0.173876i \(-0.944371\pi\)
−0.138944 + 0.990300i \(0.544371\pi\)
\(968\) 7.59507 0.244115
\(969\) 6.97214 5.06555i 0.223977 0.162729i
\(970\) 24.5807 + 23.3157i 0.789239 + 0.748622i
\(971\) 25.9089 + 18.8239i 0.831457 + 0.604089i 0.919971 0.391986i \(-0.128212\pi\)
−0.0885142 + 0.996075i \(0.528212\pi\)
\(972\) 0.598970 + 0.435177i 0.0192120 + 0.0139583i
\(973\) 5.07090 15.6066i 0.162565 0.500325i
\(974\) −11.6271 −0.372557
\(975\) −1.06946 20.2320i −0.0342502 0.647941i
\(976\) 17.9452 0.574413
\(977\) −2.24659 + 6.91428i −0.0718747 + 0.221208i −0.980541 0.196316i \(-0.937102\pi\)
0.908666 + 0.417524i \(0.137102\pi\)
\(978\) −2.22810 1.61881i −0.0712467 0.0517637i
\(979\) 45.3927 + 32.9798i 1.45076 + 1.05404i
\(980\) 4.10302 8.60715i 0.131066 0.274945i
\(981\) −9.17385 + 6.66519i −0.292898 + 0.212803i
\(982\) 17.5725 0.560760
\(983\) 4.11915 2.99274i 0.131380 0.0954535i −0.520154 0.854072i \(-0.674126\pi\)
0.651535 + 0.758619i \(0.274126\pi\)
\(984\) −7.10163 21.8566i −0.226392 0.696762i
\(985\) −16.9232 + 35.5009i −0.539219 + 1.13115i
\(986\) 1.66324 5.11894i 0.0529685 0.163020i
\(987\) −1.07642 3.31288i −0.0342628 0.105450i
\(988\) −3.76442 11.5857i −0.119762 0.368590i
\(989\) 17.6488 54.3176i 0.561201 1.72720i
\(990\) −9.13195 1.20015i −0.290232 0.0381432i
\(991\) −19.1826 59.0380i −0.609356 1.87540i −0.463497 0.886098i \(-0.653406\pi\)
−0.145859 0.989305i \(-0.546594\pi\)
\(992\) 32.0327 23.2731i 1.01704 0.738922i
\(993\) 26.3514 0.836237
\(994\) 0.668265 0.485523i 0.0211961 0.0153999i
\(995\) 8.16391 + 43.9931i 0.258813 + 1.39468i
\(996\) 7.34570 + 5.33697i 0.232758 + 0.169108i
\(997\) −2.07832 1.50999i −0.0658212 0.0478219i 0.554388 0.832258i \(-0.312952\pi\)
−0.620209 + 0.784436i \(0.712952\pi\)
\(998\) −12.4114 + 38.1985i −0.392878 + 1.20915i
\(999\) 7.37232 0.233250
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 75.2.g.b.46.1 yes 8
3.2 odd 2 225.2.h.c.46.2 8
5.2 odd 4 375.2.i.b.274.2 16
5.3 odd 4 375.2.i.b.274.3 16
5.4 even 2 375.2.g.b.226.2 8
25.6 even 5 inner 75.2.g.b.31.1 8
25.8 odd 20 375.2.i.b.349.2 16
25.9 even 10 1875.2.a.e.1.3 4
25.12 odd 20 1875.2.b.c.1249.4 8
25.13 odd 20 1875.2.b.c.1249.5 8
25.16 even 5 1875.2.a.h.1.2 4
25.17 odd 20 375.2.i.b.349.3 16
25.19 even 10 375.2.g.b.151.2 8
75.41 odd 10 5625.2.a.i.1.3 4
75.56 odd 10 225.2.h.c.181.2 8
75.59 odd 10 5625.2.a.n.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.b.31.1 8 25.6 even 5 inner
75.2.g.b.46.1 yes 8 1.1 even 1 trivial
225.2.h.c.46.2 8 3.2 odd 2
225.2.h.c.181.2 8 75.56 odd 10
375.2.g.b.151.2 8 25.19 even 10
375.2.g.b.226.2 8 5.4 even 2
375.2.i.b.274.2 16 5.2 odd 4
375.2.i.b.274.3 16 5.3 odd 4
375.2.i.b.349.2 16 25.8 odd 20
375.2.i.b.349.3 16 25.17 odd 20
1875.2.a.e.1.3 4 25.9 even 10
1875.2.a.h.1.2 4 25.16 even 5
1875.2.b.c.1249.4 8 25.12 odd 20
1875.2.b.c.1249.5 8 25.13 odd 20
5625.2.a.i.1.3 4 75.41 odd 10
5625.2.a.n.1.2 4 75.59 odd 10