Properties

Label 75.2.i.a.19.1
Level $75$
Weight $2$
Character 75.19
Analytic conductor $0.599$
Analytic rank $0$
Dimension $16$
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(4,75)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 75.i (of order \(10\), 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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.1
Root \(-2.35083i\) of defining polynomial
Character \(\chi\) \(=\) 75.19
Dual form 75.2.i.a.4.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.23577 + 0.726446i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(0.725498 + 2.11510i) q^{5} +(1.90186 + 1.38178i) q^{6} +3.48189i q^{7} +(-2.10915 + 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-2.23577 + 0.726446i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(0.725498 + 2.11510i) q^{5} +(1.90186 + 1.38178i) q^{6} +3.48189i q^{7} +(-2.10915 + 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.15856 - 4.20185i) q^{10} +(0.905762 + 2.78765i) q^{11} +(-3.35381 - 1.08972i) q^{12} +(1.78394 + 0.579638i) q^{13} +(-2.52940 - 7.78470i) q^{14} +(1.28472 - 1.83017i) q^{15} +(0.427277 - 1.31502i) q^{16} +(3.98851 - 5.48972i) q^{17} -2.35083i q^{18} +(-2.38620 - 1.73367i) q^{19} +(6.45390 + 4.53042i) q^{20} +(2.81691 - 2.04660i) q^{21} +(-4.05015 - 5.57456i) q^{22} +(-5.22149 + 1.69656i) q^{23} +3.58831 q^{24} +(-3.94730 + 3.06900i) q^{25} -4.40956 q^{26} +(0.951057 - 0.309017i) q^{27} +(7.21714 + 9.93354i) q^{28} +(2.06779 - 1.50234i) q^{29} +(-1.54281 + 5.02511i) q^{30} +(-0.338237 - 0.245744i) q^{31} -3.92613i q^{32} +(1.72286 - 2.37132i) q^{33} +(-4.92942 + 15.1712i) q^{34} +(-7.36454 + 2.52610i) q^{35} +(1.08972 + 3.35381i) q^{36} +(4.98314 + 1.61912i) q^{37} +(6.59441 + 2.14265i) q^{38} +(-0.579638 - 1.78394i) q^{39} +(-7.67033 - 2.35495i) q^{40} +(0.518744 - 1.59653i) q^{41} +(-4.81121 + 6.62206i) q^{42} -10.9233i q^{43} +(8.36221 + 6.07550i) q^{44} +(-2.23577 + 0.0363878i) q^{45} +(10.4416 - 7.58626i) q^{46} +(4.40356 + 6.06098i) q^{47} +(-1.31502 + 0.427277i) q^{48} -5.12353 q^{49} +(6.59580 - 9.72910i) q^{50} -6.78566 q^{51} +(6.29089 - 2.04403i) q^{52} +(2.18041 + 3.00107i) q^{53} +(-1.90186 + 1.38178i) q^{54} +(-5.23903 + 3.93821i) q^{55} +(-10.1079 - 7.34383i) q^{56} +2.94950i q^{57} +(-3.53175 + 4.86103i) q^{58} +(2.19666 - 6.76062i) q^{59} +(-0.128318 - 7.88423i) q^{60} +(-1.98917 - 6.12204i) q^{61} +(0.934741 + 0.303716i) q^{62} +(-3.31147 - 1.07596i) q^{63} +(3.70667 + 11.4080i) q^{64} +(0.0682544 + 4.19374i) q^{65} +(-2.12929 + 6.55329i) q^{66} +(5.90225 - 8.12376i) q^{67} -23.9290i q^{68} +(4.44166 + 3.22706i) q^{69} +(14.6304 - 10.9977i) q^{70} +(-0.589451 + 0.428261i) q^{71} +(-2.10915 - 2.90300i) q^{72} +(-3.41685 + 1.11020i) q^{73} -12.3174 q^{74} +(4.80304 + 1.38952i) q^{75} -10.4011 q^{76} +(-9.70628 + 3.15376i) q^{77} +(2.59188 + 3.56741i) q^{78} +(2.48583 - 1.80606i) q^{79} +(3.09140 - 0.0503134i) q^{80} +(-0.809017 - 0.587785i) q^{81} +3.94632i q^{82} +(-5.94559 + 8.18340i) q^{83} +(3.79427 - 11.6776i) q^{84} +(14.5050 + 4.45333i) q^{85} +(7.93517 + 24.4219i) q^{86} +(-2.43084 - 0.789827i) q^{87} +(-10.0029 - 3.25015i) q^{88} +(-0.0888461 - 0.273440i) q^{89} +(4.97224 - 1.70552i) q^{90} +(-2.01823 + 6.21148i) q^{91} +(-11.3799 + 15.6631i) q^{92} +0.418084i q^{93} +(-14.2483 - 10.3520i) q^{94} +(1.93571 - 6.30482i) q^{95} +(-3.17630 + 2.30772i) q^{96} +(6.11828 + 8.42109i) q^{97} +(11.4551 - 3.72197i) q^{98} -2.93111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23577 + 0.726446i −1.58093 + 0.513675i −0.962296 0.272005i \(-0.912313\pi\)
−0.618634 + 0.785680i \(0.712313\pi\)
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) 2.85292 2.07277i 1.42646 1.03638i
\(5\) 0.725498 + 2.11510i 0.324453 + 0.945902i
\(6\) 1.90186 + 1.38178i 0.776432 + 0.564111i
\(7\) 3.48189i 1.31603i 0.753005 + 0.658015i \(0.228604\pi\)
−0.753005 + 0.658015i \(0.771396\pi\)
\(8\) −2.10915 + 2.90300i −0.745698 + 1.02637i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) −3.15856 4.20185i −0.998823 1.32874i
\(11\) 0.905762 + 2.78765i 0.273097 + 0.840508i 0.989717 + 0.143043i \(0.0456887\pi\)
−0.716619 + 0.697465i \(0.754311\pi\)
\(12\) −3.35381 1.08972i −0.968160 0.314574i
\(13\) 1.78394 + 0.579638i 0.494776 + 0.160763i 0.545768 0.837937i \(-0.316238\pi\)
−0.0509914 + 0.998699i \(0.516238\pi\)
\(14\) −2.52940 7.78470i −0.676012 2.08055i
\(15\) 1.28472 1.83017i 0.331712 0.472547i
\(16\) 0.427277 1.31502i 0.106819 0.328756i
\(17\) 3.98851 5.48972i 0.967356 1.33145i 0.0239850 0.999712i \(-0.492365\pi\)
0.943371 0.331739i \(-0.107635\pi\)
\(18\) 2.35083i 0.554096i
\(19\) −2.38620 1.73367i −0.547431 0.397732i 0.279406 0.960173i \(-0.409862\pi\)
−0.826837 + 0.562441i \(0.809862\pi\)
\(20\) 6.45390 + 4.53042i 1.44314 + 1.01303i
\(21\) 2.81691 2.04660i 0.614699 0.446605i
\(22\) −4.05015 5.57456i −0.863496 1.18850i
\(23\) −5.22149 + 1.69656i −1.08876 + 0.353758i −0.797765 0.602968i \(-0.793985\pi\)
−0.290990 + 0.956726i \(0.593985\pi\)
\(24\) 3.58831 0.732460
\(25\) −3.94730 + 3.06900i −0.789461 + 0.613801i
\(26\) −4.40956 −0.864786
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) 7.21714 + 9.93354i 1.36391 + 1.87726i
\(29\) 2.06779 1.50234i 0.383980 0.278978i −0.379004 0.925395i \(-0.623733\pi\)
0.762984 + 0.646417i \(0.223733\pi\)
\(30\) −1.54281 + 5.02511i −0.281678 + 0.917455i
\(31\) −0.338237 0.245744i −0.0607492 0.0441369i 0.556996 0.830515i \(-0.311954\pi\)
−0.617745 + 0.786378i \(0.711954\pi\)
\(32\) 3.92613i 0.694048i
\(33\) 1.72286 2.37132i 0.299912 0.412793i
\(34\) −4.92942 + 15.1712i −0.845388 + 2.60184i
\(35\) −7.36454 + 2.52610i −1.24483 + 0.426989i
\(36\) 1.08972 + 3.35381i 0.181620 + 0.558968i
\(37\) 4.98314 + 1.61912i 0.819224 + 0.266182i 0.688500 0.725237i \(-0.258270\pi\)
0.130724 + 0.991419i \(0.458270\pi\)
\(38\) 6.59441 + 2.14265i 1.06975 + 0.347584i
\(39\) −0.579638 1.78394i −0.0928163 0.285659i
\(40\) −7.67033 2.35495i −1.21279 0.372350i
\(41\) 0.518744 1.59653i 0.0810142 0.249336i −0.902343 0.431019i \(-0.858154\pi\)
0.983357 + 0.181683i \(0.0581543\pi\)
\(42\) −4.81121 + 6.62206i −0.742386 + 1.02181i
\(43\) 10.9233i 1.66578i −0.553436 0.832892i \(-0.686684\pi\)
0.553436 0.832892i \(-0.313316\pi\)
\(44\) 8.36221 + 6.07550i 1.26065 + 0.915916i
\(45\) −2.23577 + 0.0363878i −0.333289 + 0.00542438i
\(46\) 10.4416 7.58626i 1.53953 1.11853i
\(47\) 4.40356 + 6.06098i 0.642325 + 0.884084i 0.998737 0.0502446i \(-0.0160001\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(48\) −1.31502 + 0.427277i −0.189807 + 0.0616721i
\(49\) −5.12353 −0.731933
\(50\) 6.59580 9.72910i 0.932788 1.37590i
\(51\) −6.78566 −0.950183
\(52\) 6.29089 2.04403i 0.872390 0.283457i
\(53\) 2.18041 + 3.00107i 0.299502 + 0.412229i 0.932071 0.362275i \(-0.118000\pi\)
−0.632570 + 0.774504i \(0.718000\pi\)
\(54\) −1.90186 + 1.38178i −0.258811 + 0.188037i
\(55\) −5.23903 + 3.93821i −0.706431 + 0.531028i
\(56\) −10.1079 7.34383i −1.35073 0.981361i
\(57\) 2.94950i 0.390671i
\(58\) −3.53175 + 4.86103i −0.463741 + 0.638285i
\(59\) 2.19666 6.76062i 0.285981 0.880158i −0.700122 0.714023i \(-0.746871\pi\)
0.986103 0.166135i \(-0.0531288\pi\)
\(60\) −0.128318 7.88423i −0.0165658 1.01785i
\(61\) −1.98917 6.12204i −0.254687 0.783847i −0.993891 0.110365i \(-0.964798\pi\)
0.739204 0.673482i \(-0.235202\pi\)
\(62\) 0.934741 + 0.303716i 0.118712 + 0.0385719i
\(63\) −3.31147 1.07596i −0.417206 0.135558i
\(64\) 3.70667 + 11.4080i 0.463334 + 1.42600i
\(65\) 0.0682544 + 4.19374i 0.00846591 + 0.520170i
\(66\) −2.12929 + 6.55329i −0.262098 + 0.806654i
\(67\) 5.90225 8.12376i 0.721075 0.992475i −0.278412 0.960462i \(-0.589808\pi\)
0.999487 0.0320131i \(-0.0101918\pi\)
\(68\) 23.9290i 2.90181i
\(69\) 4.44166 + 3.22706i 0.534713 + 0.388492i
\(70\) 14.6304 10.9977i 1.74866 1.31448i
\(71\) −0.589451 + 0.428261i −0.0699550 + 0.0508253i −0.622213 0.782848i \(-0.713766\pi\)
0.552258 + 0.833673i \(0.313766\pi\)
\(72\) −2.10915 2.90300i −0.248566 0.342122i
\(73\) −3.41685 + 1.11020i −0.399912 + 0.129939i −0.502066 0.864829i \(-0.667427\pi\)
0.102154 + 0.994769i \(0.467427\pi\)
\(74\) −12.3174 −1.43187
\(75\) 4.80304 + 1.38952i 0.554608 + 0.160448i
\(76\) −10.4011 −1.19309
\(77\) −9.70628 + 3.15376i −1.10613 + 0.359404i
\(78\) 2.59188 + 3.56741i 0.293472 + 0.403930i
\(79\) 2.48583 1.80606i 0.279677 0.203197i −0.439099 0.898439i \(-0.644702\pi\)
0.718777 + 0.695241i \(0.244702\pi\)
\(80\) 3.09140 0.0503134i 0.345629 0.00562521i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 3.94632i 0.435798i
\(83\) −5.94559 + 8.18340i −0.652613 + 0.898245i −0.999209 0.0397694i \(-0.987338\pi\)
0.346595 + 0.938015i \(0.387338\pi\)
\(84\) 3.79427 11.6776i 0.413989 1.27413i
\(85\) 14.5050 + 4.45333i 1.57328 + 0.483031i
\(86\) 7.93517 + 24.4219i 0.855672 + 2.63349i
\(87\) −2.43084 0.789827i −0.260613 0.0846784i
\(88\) −10.0029 3.25015i −1.06632 0.346467i
\(89\) −0.0888461 0.273440i −0.00941767 0.0289846i 0.946237 0.323473i \(-0.104851\pi\)
−0.955655 + 0.294489i \(0.904851\pi\)
\(90\) 4.97224 1.70552i 0.524120 0.179778i
\(91\) −2.01823 + 6.21148i −0.211568 + 0.651140i
\(92\) −11.3799 + 15.6631i −1.18644 + 1.63299i
\(93\) 0.418084i 0.0433533i
\(94\) −14.2483 10.3520i −1.46960 1.06773i
\(95\) 1.93571 6.30482i 0.198600 0.646861i
\(96\) −3.17630 + 2.30772i −0.324180 + 0.235531i
\(97\) 6.11828 + 8.42109i 0.621217 + 0.855032i 0.997441 0.0714966i \(-0.0227775\pi\)
−0.376224 + 0.926529i \(0.622778\pi\)
\(98\) 11.4551 3.72197i 1.15714 0.375976i
\(99\) −2.93111 −0.294587
\(100\) −4.90001 + 16.9375i −0.490001 + 1.69375i
\(101\) 7.65744 0.761943 0.380972 0.924587i \(-0.375590\pi\)
0.380972 + 0.924587i \(0.375590\pi\)
\(102\) 15.1712 4.92942i 1.50217 0.488085i
\(103\) −1.75514 2.41574i −0.172939 0.238030i 0.713745 0.700405i \(-0.246997\pi\)
−0.886684 + 0.462375i \(0.846997\pi\)
\(104\) −5.44530 + 3.95624i −0.533955 + 0.387941i
\(105\) 6.37243 + 4.47323i 0.621885 + 0.436543i
\(106\) −7.05501 5.12576i −0.685243 0.497858i
\(107\) 7.07213i 0.683689i −0.939757 0.341844i \(-0.888948\pi\)
0.939757 0.341844i \(-0.111052\pi\)
\(108\) 2.07277 2.85292i 0.199452 0.274522i
\(109\) 4.11060 12.6511i 0.393724 1.21176i −0.536227 0.844074i \(-0.680151\pi\)
0.929951 0.367683i \(-0.119849\pi\)
\(110\) 8.85237 12.6108i 0.844041 1.20239i
\(111\) −1.61912 4.98314i −0.153680 0.472979i
\(112\) 4.57876 + 1.48773i 0.432653 + 0.140577i
\(113\) −9.53271 3.09737i −0.896762 0.291376i −0.175862 0.984415i \(-0.556271\pi\)
−0.720900 + 0.693039i \(0.756271\pi\)
\(114\) −2.14265 6.59441i −0.200678 0.617623i
\(115\) −7.37658 9.81312i −0.687870 0.915078i
\(116\) 2.78525 8.57211i 0.258604 0.795900i
\(117\) −1.10254 + 1.51751i −0.101930 + 0.140294i
\(118\) 16.7110i 1.53837i
\(119\) 19.1146 + 13.8875i 1.75223 + 1.27307i
\(120\) 2.60331 + 7.58963i 0.237649 + 0.692835i
\(121\) 1.94861 1.41575i 0.177146 0.128704i
\(122\) 8.89467 + 12.2425i 0.805286 + 1.10838i
\(123\) −1.59653 + 0.518744i −0.143954 + 0.0467736i
\(124\) −1.47433 −0.132399
\(125\) −9.35502 6.12239i −0.836738 0.547603i
\(126\) 8.18532 0.729206
\(127\) −10.0556 + 3.26725i −0.892286 + 0.289921i −0.719049 0.694959i \(-0.755423\pi\)
−0.173237 + 0.984880i \(0.555423\pi\)
\(128\) −11.9591 16.4603i −1.05705 1.45490i
\(129\) −8.83711 + 6.42054i −0.778064 + 0.565297i
\(130\) −3.19913 9.32667i −0.280582 0.818003i
\(131\) 7.30225 + 5.30540i 0.638001 + 0.463535i 0.859163 0.511703i \(-0.170985\pi\)
−0.221162 + 0.975237i \(0.570985\pi\)
\(132\) 10.3363i 0.899656i
\(133\) 6.03645 8.30847i 0.523427 0.720435i
\(134\) −7.29462 + 22.4505i −0.630159 + 1.93943i
\(135\) 1.34359 + 1.78739i 0.115638 + 0.153834i
\(136\) 7.52427 + 23.1573i 0.645200 + 1.98572i
\(137\) −18.7021 6.07669i −1.59783 0.519167i −0.631261 0.775571i \(-0.717462\pi\)
−0.966570 + 0.256404i \(0.917462\pi\)
\(138\) −12.2748 3.98833i −1.04490 0.339509i
\(139\) 3.60067 + 11.0817i 0.305404 + 0.939938i 0.979526 + 0.201318i \(0.0645224\pi\)
−0.674122 + 0.738620i \(0.735478\pi\)
\(140\) −15.7744 + 22.4717i −1.33318 + 1.89921i
\(141\) 2.31509 7.12511i 0.194965 0.600042i
\(142\) 1.00677 1.38570i 0.0844862 0.116285i
\(143\) 5.49801i 0.459767i
\(144\) 1.11863 + 0.812729i 0.0932188 + 0.0677275i
\(145\) 4.67778 + 3.28365i 0.388469 + 0.272692i
\(146\) 6.83280 4.96432i 0.565486 0.410850i
\(147\) 3.01154 + 4.14503i 0.248387 + 0.341876i
\(148\) 17.5726 5.70967i 1.44446 0.469332i
\(149\) 7.33020 0.600513 0.300257 0.953858i \(-0.402928\pi\)
0.300257 + 0.953858i \(0.402928\pi\)
\(150\) −11.7479 + 0.382503i −0.959214 + 0.0312312i
\(151\) −16.7358 −1.36194 −0.680968 0.732313i \(-0.738441\pi\)
−0.680968 + 0.732313i \(0.738441\pi\)
\(152\) 10.0657 3.27055i 0.816437 0.265276i
\(153\) 3.98851 + 5.48972i 0.322452 + 0.443817i
\(154\) 19.4100 14.1022i 1.56410 1.13639i
\(155\) 0.274382 0.893692i 0.0220389 0.0717831i
\(156\) −5.35135 3.88798i −0.428451 0.311288i
\(157\) 7.88635i 0.629399i 0.949191 + 0.314700i \(0.101904\pi\)
−0.949191 + 0.314700i \(0.898096\pi\)
\(158\) −4.24574 + 5.84375i −0.337773 + 0.464904i
\(159\) 1.14631 3.52797i 0.0909081 0.279786i
\(160\) 8.30415 2.84840i 0.656501 0.225186i
\(161\) −5.90724 18.1806i −0.465556 1.43283i
\(162\) 2.23577 + 0.726446i 0.175659 + 0.0570750i
\(163\) 9.45343 + 3.07160i 0.740450 + 0.240587i 0.654867 0.755744i \(-0.272725\pi\)
0.0855829 + 0.996331i \(0.472725\pi\)
\(164\) −1.82930 5.63000i −0.142844 0.439629i
\(165\) 6.26550 + 1.92364i 0.487769 + 0.149755i
\(166\) 7.34818 22.6154i 0.570330 1.75529i
\(167\) 3.27847 4.51243i 0.253696 0.349182i −0.663106 0.748526i \(-0.730762\pi\)
0.916801 + 0.399344i \(0.130762\pi\)
\(168\) 12.4941i 0.963939i
\(169\) −7.67075 5.57313i −0.590058 0.428702i
\(170\) −35.6649 + 0.580456i −2.73537 + 0.0445190i
\(171\) 2.38620 1.73367i 0.182477 0.132577i
\(172\) −22.6414 31.1632i −1.72639 2.37617i
\(173\) 15.7573 5.11985i 1.19800 0.389255i 0.358978 0.933346i \(-0.383125\pi\)
0.839026 + 0.544091i \(0.183125\pi\)
\(174\) 6.00857 0.455508
\(175\) −10.6859 13.7441i −0.807780 1.03895i
\(176\) 4.05284 0.305494
\(177\) −6.76062 + 2.19666i −0.508160 + 0.165111i
\(178\) 0.397279 + 0.546808i 0.0297773 + 0.0409850i
\(179\) −4.33650 + 3.15065i −0.324125 + 0.235491i −0.737934 0.674873i \(-0.764198\pi\)
0.413808 + 0.910364i \(0.364198\pi\)
\(180\) −6.30305 + 4.73804i −0.469802 + 0.353153i
\(181\) 0.265151 + 0.192643i 0.0197085 + 0.0143191i 0.597596 0.801797i \(-0.296123\pi\)
−0.577887 + 0.816117i \(0.696123\pi\)
\(182\) 15.3536i 1.13808i
\(183\) −3.78363 + 5.20772i −0.279694 + 0.384966i
\(184\) 6.08779 18.7363i 0.448798 1.38126i
\(185\) 0.190657 + 11.7145i 0.0140174 + 0.861269i
\(186\) −0.303716 0.934741i −0.0222695 0.0685385i
\(187\) 18.9160 + 6.14619i 1.38328 + 0.449454i
\(188\) 25.1260 + 8.16392i 1.83250 + 0.595415i
\(189\) 1.07596 + 3.31147i 0.0782647 + 0.240874i
\(190\) 0.252305 + 15.5023i 0.0183041 + 1.12466i
\(191\) −1.07226 + 3.30009i −0.0775862 + 0.238786i −0.982326 0.187179i \(-0.940065\pi\)
0.904740 + 0.425965i \(0.140065\pi\)
\(192\) 7.05051 9.70420i 0.508827 0.700340i
\(193\) 24.3134i 1.75012i 0.484018 + 0.875058i \(0.339177\pi\)
−0.484018 + 0.875058i \(0.660823\pi\)
\(194\) −19.7966 14.3830i −1.42131 1.03264i
\(195\) 3.35269 2.52024i 0.240091 0.180478i
\(196\) −14.6170 + 10.6199i −1.04407 + 0.758563i
\(197\) −8.79098 12.0997i −0.626331 0.862071i 0.371463 0.928448i \(-0.378856\pi\)
−0.997795 + 0.0663764i \(0.978856\pi\)
\(198\) 6.55329 2.12929i 0.465722 0.151322i
\(199\) 11.3251 0.802817 0.401408 0.915899i \(-0.368521\pi\)
0.401408 + 0.915899i \(0.368521\pi\)
\(200\) −0.583853 17.9320i −0.0412846 1.26799i
\(201\) −10.0415 −0.708274
\(202\) −17.1203 + 5.56272i −1.20458 + 0.391391i
\(203\) 5.23098 + 7.19983i 0.367143 + 0.505329i
\(204\) −19.3589 + 14.0651i −1.35540 + 0.984753i
\(205\) 3.75317 0.0610839i 0.262133 0.00426628i
\(206\) 5.67900 + 4.12603i 0.395674 + 0.287474i
\(207\) 5.49019i 0.381595i
\(208\) 1.52447 2.09826i 0.105703 0.145488i
\(209\) 2.67155 8.22217i 0.184795 0.568739i
\(210\) −17.4969 5.37190i −1.20740 0.370696i
\(211\) 2.33086 + 7.17366i 0.160463 + 0.493855i 0.998673 0.0514924i \(-0.0163978\pi\)
−0.838210 + 0.545347i \(0.816398\pi\)
\(212\) 12.4410 + 4.04234i 0.854454 + 0.277629i
\(213\) 0.692941 + 0.225150i 0.0474796 + 0.0154270i
\(214\) 5.13752 + 15.8117i 0.351194 + 1.08086i
\(215\) 23.1038 7.92482i 1.57567 0.540468i
\(216\) −1.10885 + 3.41268i −0.0754475 + 0.232204i
\(217\) 0.855651 1.17770i 0.0580854 0.0799477i
\(218\) 31.2711i 2.11795i
\(219\) 2.90655 + 2.11173i 0.196406 + 0.142697i
\(220\) −6.78353 + 22.0947i −0.457345 + 1.48962i
\(221\) 10.2973 7.48144i 0.692672 0.503256i
\(222\) 7.23997 + 9.96497i 0.485915 + 0.668805i
\(223\) −7.41386 + 2.40891i −0.496469 + 0.161313i −0.546540 0.837433i \(-0.684055\pi\)
0.0500709 + 0.998746i \(0.484055\pi\)
\(224\) 13.6703 0.913387
\(225\) −1.69901 4.70248i −0.113268 0.313499i
\(226\) 23.5630 1.56739
\(227\) 12.2039 3.96529i 0.810001 0.263185i 0.125403 0.992106i \(-0.459978\pi\)
0.684598 + 0.728921i \(0.259978\pi\)
\(228\) 6.11363 + 8.41468i 0.404885 + 0.557276i
\(229\) −11.7334 + 8.52483i −0.775366 + 0.563337i −0.903585 0.428409i \(-0.859074\pi\)
0.128218 + 0.991746i \(0.459074\pi\)
\(230\) 23.6211 + 16.5812i 1.55753 + 1.09333i
\(231\) 8.25665 + 5.99881i 0.543248 + 0.394693i
\(232\) 9.17148i 0.602137i
\(233\) −6.69902 + 9.22041i −0.438867 + 0.604049i −0.969960 0.243265i \(-0.921782\pi\)
0.531093 + 0.847314i \(0.321782\pi\)
\(234\) 1.36263 4.19374i 0.0890779 0.274153i
\(235\) −9.62480 + 13.7112i −0.627853 + 0.894420i
\(236\) −7.74630 23.8407i −0.504241 1.55190i
\(237\) −2.92226 0.949501i −0.189821 0.0616767i
\(238\) −52.8244 17.1637i −3.42410 1.11256i
\(239\) −2.13244 6.56298i −0.137936 0.424524i 0.858099 0.513484i \(-0.171646\pi\)
−0.996035 + 0.0889605i \(0.971646\pi\)
\(240\) −1.85778 2.47142i −0.119919 0.159529i
\(241\) −8.79052 + 27.0545i −0.566247 + 1.74273i 0.0979683 + 0.995190i \(0.468766\pi\)
−0.664216 + 0.747541i \(0.731234\pi\)
\(242\) −3.32818 + 4.58085i −0.213943 + 0.294468i
\(243\) 1.00000i 0.0641500i
\(244\) −18.3645 13.3426i −1.17567 0.854172i
\(245\) −3.71712 10.8368i −0.237478 0.692337i
\(246\) 3.19264 2.31959i 0.203555 0.147891i
\(247\) −3.25193 4.47590i −0.206915 0.284795i
\(248\) 1.42679 0.463592i 0.0906011 0.0294381i
\(249\) 10.1152 0.641028
\(250\) 25.3633 + 6.89235i 1.60411 + 0.435910i
\(251\) −12.3258 −0.777999 −0.389000 0.921238i \(-0.627179\pi\)
−0.389000 + 0.921238i \(0.627179\pi\)
\(252\) −11.6776 + 3.79427i −0.735618 + 0.239017i
\(253\) −9.45885 13.0190i −0.594673 0.818496i
\(254\) 20.1084 14.6096i 1.26172 0.916690i
\(255\) −4.92299 14.3524i −0.308289 0.898780i
\(256\) 19.2870 + 14.0128i 1.20544 + 0.875801i
\(257\) 20.8274i 1.29918i 0.760285 + 0.649590i \(0.225059\pi\)
−0.760285 + 0.649590i \(0.774941\pi\)
\(258\) 15.0936 20.7745i 0.939686 1.29337i
\(259\) −5.63760 + 17.3507i −0.350303 + 1.07812i
\(260\) 8.88737 + 11.8229i 0.551171 + 0.733227i
\(261\) 0.789827 + 2.43084i 0.0488891 + 0.150465i
\(262\) −20.1802 6.55696i −1.24674 0.405090i
\(263\) −2.12577 0.690704i −0.131080 0.0425906i 0.242742 0.970091i \(-0.421953\pi\)
−0.373823 + 0.927500i \(0.621953\pi\)
\(264\) 3.25015 + 10.0029i 0.200033 + 0.615638i
\(265\) −4.76569 + 6.78905i −0.292754 + 0.417048i
\(266\) −7.46048 + 22.9610i −0.457431 + 1.40783i
\(267\) −0.168995 + 0.232602i −0.0103423 + 0.0142350i
\(268\) 35.4104i 2.16303i
\(269\) −15.6170 11.3464i −0.952183 0.691802i −0.000861106 1.00000i \(-0.500274\pi\)
−0.951322 + 0.308198i \(0.900274\pi\)
\(270\) −4.30241 3.02015i −0.261836 0.183800i
\(271\) 9.66058 7.01882i 0.586838 0.426363i −0.254345 0.967114i \(-0.581860\pi\)
0.841183 + 0.540751i \(0.181860\pi\)
\(272\) −5.51491 7.59062i −0.334390 0.460249i
\(273\) 6.21148 2.01823i 0.375936 0.122149i
\(274\) 46.2281 2.79274
\(275\) −12.1306 8.22391i −0.731504 0.495920i
\(276\) 19.3606 1.16537
\(277\) −24.8669 + 8.07975i −1.49411 + 0.485465i −0.938293 0.345841i \(-0.887594\pi\)
−0.555815 + 0.831306i \(0.687594\pi\)
\(278\) −16.1005 22.1605i −0.965646 1.32910i
\(279\) 0.338237 0.245744i 0.0202497 0.0147123i
\(280\) 8.19967 26.7072i 0.490024 1.59606i
\(281\) −8.18876 5.94948i −0.488500 0.354916i 0.316107 0.948724i \(-0.397624\pi\)
−0.804607 + 0.593807i \(0.797624\pi\)
\(282\) 17.6119i 1.04877i
\(283\) 18.7290 25.7783i 1.11333 1.53236i 0.296903 0.954907i \(-0.404046\pi\)
0.816423 0.577455i \(-0.195954\pi\)
\(284\) −0.793970 + 2.44359i −0.0471135 + 0.145000i
\(285\) −6.23849 + 2.13986i −0.369536 + 0.126754i
\(286\) −3.99401 12.2923i −0.236171 0.726859i
\(287\) 5.55893 + 1.80621i 0.328134 + 0.106617i
\(288\) 3.73397 + 1.21324i 0.220026 + 0.0714908i
\(289\) −8.97546 27.6236i −0.527968 1.62492i
\(290\) −12.8439 3.94333i −0.754217 0.231560i
\(291\) 3.21657 9.89959i 0.188559 0.580324i
\(292\) −7.44680 + 10.2496i −0.435791 + 0.599815i
\(293\) 16.6235i 0.971153i −0.874194 0.485576i \(-0.838610\pi\)
0.874194 0.485576i \(-0.161390\pi\)
\(294\) −9.74425 7.07961i −0.568296 0.412891i
\(295\) 15.8931 0.258664i 0.925331 0.0150600i
\(296\) −15.2105 + 11.0511i −0.884094 + 0.642332i
\(297\) 1.72286 + 2.37132i 0.0999706 + 0.137598i
\(298\) −16.3886 + 5.32499i −0.949369 + 0.308469i
\(299\) −10.2982 −0.595561
\(300\) 16.5828 5.99140i 0.957411 0.345914i
\(301\) 38.0336 2.19222
\(302\) 37.4173 12.1576i 2.15312 0.699593i
\(303\) −4.50093 6.19500i −0.258572 0.355893i
\(304\) −3.29939 + 2.39715i −0.189233 + 0.137486i
\(305\) 11.5056 8.64883i 0.658809 0.495231i
\(306\) −12.9054 9.37631i −0.737752 0.536008i
\(307\) 14.1643i 0.808402i −0.914670 0.404201i \(-0.867550\pi\)
0.914670 0.404201i \(-0.132450\pi\)
\(308\) −21.1542 + 29.1163i −1.20537 + 1.65905i
\(309\) −0.922731 + 2.83987i −0.0524923 + 0.161555i
\(310\) 0.0357636 + 2.19742i 0.00203123 + 0.124805i
\(311\) 4.65070 + 14.3134i 0.263717 + 0.811637i 0.991986 + 0.126346i \(0.0403250\pi\)
−0.728269 + 0.685291i \(0.759675\pi\)
\(312\) 6.40133 + 2.07992i 0.362404 + 0.117752i
\(313\) 3.39980 + 1.10466i 0.192168 + 0.0624392i 0.403520 0.914971i \(-0.367787\pi\)
−0.211352 + 0.977410i \(0.567787\pi\)
\(314\) −5.72901 17.6321i −0.323307 0.995036i
\(315\) −0.126698 7.78470i −0.00713864 0.438618i
\(316\) 3.34832 10.3051i 0.188358 0.579706i
\(317\) 7.51306 10.3408i 0.421975 0.580799i −0.544113 0.839012i \(-0.683134\pi\)
0.966088 + 0.258213i \(0.0831336\pi\)
\(318\) 8.72047i 0.489020i
\(319\) 6.06093 + 4.40352i 0.339347 + 0.246550i
\(320\) −21.4398 + 16.1165i −1.19852 + 0.900937i
\(321\) −5.72147 + 4.15689i −0.319342 + 0.232015i
\(322\) 26.4145 + 36.3564i 1.47202 + 2.02606i
\(323\) −19.0347 + 6.18476i −1.05912 + 0.344129i
\(324\) −3.52640 −0.195911
\(325\) −8.82067 + 3.18692i −0.489283 + 0.176778i
\(326\) −23.3671 −1.29418
\(327\) −12.6511 + 4.11060i −0.699608 + 0.227317i
\(328\) 3.54062 + 4.87324i 0.195498 + 0.269080i
\(329\) −21.1036 + 15.3327i −1.16348 + 0.845318i
\(330\) −15.4057 + 0.250732i −0.848054 + 0.0138023i
\(331\) −3.80646 2.76555i −0.209222 0.152009i 0.478240 0.878229i \(-0.341275\pi\)
−0.687462 + 0.726221i \(0.741275\pi\)
\(332\) 35.6704i 1.95767i
\(333\) −3.07975 + 4.23892i −0.168769 + 0.232291i
\(334\) −4.05187 + 12.4704i −0.221709 + 0.682349i
\(335\) 21.4646 + 6.59009i 1.17274 + 0.360055i
\(336\) −1.48773 4.57876i −0.0811624 0.249792i
\(337\) −16.5529 5.37837i −0.901694 0.292978i −0.178758 0.983893i \(-0.557208\pi\)
−0.722936 + 0.690915i \(0.757208\pi\)
\(338\) 21.1986 + 6.88785i 1.15305 + 0.374650i
\(339\) 3.09737 + 9.53271i 0.168226 + 0.517746i
\(340\) 50.6122 17.3604i 2.74483 0.941501i
\(341\) 0.378685 1.16547i 0.0205069 0.0631138i
\(342\) −4.07557 + 5.60954i −0.220382 + 0.303329i
\(343\) 6.53364i 0.352783i
\(344\) 31.7103 + 23.0389i 1.70970 + 1.24217i
\(345\) −3.60313 + 11.7358i −0.193986 + 0.631833i
\(346\) −31.5104 + 22.8936i −1.69401 + 1.23077i
\(347\) −8.23525 11.3348i −0.442091 0.608486i 0.528584 0.848881i \(-0.322723\pi\)
−0.970675 + 0.240395i \(0.922723\pi\)
\(348\) −8.57211 + 2.78525i −0.459513 + 0.149305i
\(349\) −35.9459 −1.92414 −0.962069 0.272806i \(-0.912048\pi\)
−0.962069 + 0.272806i \(0.912048\pi\)
\(350\) 33.8756 + 22.9658i 1.81073 + 1.22758i
\(351\) 1.87575 0.100120
\(352\) 10.9447 3.55614i 0.583352 0.189543i
\(353\) 5.17367 + 7.12095i 0.275367 + 0.379010i 0.924192 0.381927i \(-0.124740\pi\)
−0.648826 + 0.760937i \(0.724740\pi\)
\(354\) 13.5195 9.82246i 0.718551 0.522058i
\(355\) −1.33346 0.936046i −0.0707728 0.0496802i
\(356\) −0.820248 0.595945i −0.0434731 0.0315850i
\(357\) 23.6269i 1.25047i
\(358\) 7.40665 10.1944i 0.391454 0.538790i
\(359\) −1.86326 + 5.73451i −0.0983389 + 0.302656i −0.988109 0.153752i \(-0.950864\pi\)
0.889771 + 0.456408i \(0.150864\pi\)
\(360\) 4.60995 6.56720i 0.242966 0.346122i
\(361\) −3.18301 9.79630i −0.167527 0.515595i
\(362\) −0.732762 0.238089i −0.0385131 0.0125137i
\(363\) −2.29073 0.744302i −0.120232 0.0390657i
\(364\) 7.11710 + 21.9042i 0.373037 + 1.14809i
\(365\) −4.82711 6.42153i −0.252662 0.336118i
\(366\) 4.67621 14.3919i 0.244429 0.752276i
\(367\) 16.9084 23.2724i 0.882609 1.21481i −0.0930825 0.995658i \(-0.529672\pi\)
0.975691 0.219149i \(-0.0703280\pi\)
\(368\) 7.59128i 0.395723i
\(369\) 1.35809 + 0.986709i 0.0706993 + 0.0513660i
\(370\) −8.93624 26.0525i −0.464573 1.35440i
\(371\) −10.4494 + 7.59193i −0.542505 + 0.394153i
\(372\) 0.866590 + 1.19276i 0.0449306 + 0.0618417i
\(373\) 31.9555 10.3830i 1.65459 0.537610i 0.674866 0.737940i \(-0.264201\pi\)
0.979729 + 0.200330i \(0.0642013\pi\)
\(374\) −46.7568 −2.41774
\(375\) 0.545625 + 11.1670i 0.0281759 + 0.576662i
\(376\) −26.8828 −1.38637
\(377\) 4.55964 1.48152i 0.234833 0.0763020i
\(378\) −4.81121 6.62206i −0.247462 0.340602i
\(379\) 3.74901 2.72381i 0.192574 0.139913i −0.487321 0.873223i \(-0.662026\pi\)
0.679894 + 0.733310i \(0.262026\pi\)
\(380\) −7.54600 21.9994i −0.387101 1.12855i
\(381\) 8.55377 + 6.21467i 0.438223 + 0.318387i
\(382\) 8.15718i 0.417358i
\(383\) 7.58581 10.4410i 0.387617 0.533509i −0.569965 0.821669i \(-0.693043\pi\)
0.957582 + 0.288160i \(0.0930434\pi\)
\(384\) −6.28728 + 19.3503i −0.320846 + 0.987464i
\(385\) −13.7124 18.2417i −0.698849 0.929683i
\(386\) −17.6624 54.3592i −0.898991 2.76681i
\(387\) 10.3886 + 3.37548i 0.528085 + 0.171585i
\(388\) 34.9099 + 11.3429i 1.77228 + 0.575849i
\(389\) 5.41540 + 16.6669i 0.274571 + 0.845044i 0.989332 + 0.145675i \(0.0465355\pi\)
−0.714761 + 0.699369i \(0.753465\pi\)
\(390\) −5.66503 + 8.07023i −0.286860 + 0.408652i
\(391\) −11.5123 + 35.4312i −0.582202 + 1.79183i
\(392\) 10.8063 14.8736i 0.545802 0.751232i
\(393\) 9.02608i 0.455305i
\(394\) 28.4444 + 20.6661i 1.43301 + 1.04114i
\(395\) 5.62346 + 3.94748i 0.282947 + 0.198619i
\(396\) −8.36221 + 6.07550i −0.420217 + 0.305305i
\(397\) 15.8805 + 21.8577i 0.797021 + 1.09701i 0.993198 + 0.116437i \(0.0371473\pi\)
−0.196177 + 0.980569i \(0.562853\pi\)
\(398\) −25.3204 + 8.22709i −1.26920 + 0.412387i
\(399\) −10.2698 −0.514134
\(400\) 2.34922 + 6.50211i 0.117461 + 0.325106i
\(401\) −15.9792 −0.797965 −0.398983 0.916958i \(-0.630637\pi\)
−0.398983 + 0.916958i \(0.630637\pi\)
\(402\) 22.4505 7.29462i 1.11973 0.363823i
\(403\) −0.460953 0.634447i −0.0229617 0.0316041i
\(404\) 21.8460 15.8721i 1.08688 0.789665i
\(405\) 0.656285 2.13759i 0.0326110 0.106218i
\(406\) −16.9256 12.2971i −0.840002 0.610297i
\(407\) 15.3578i 0.761258i
\(408\) 14.3120 19.6988i 0.708550 0.975235i
\(409\) 9.57834 29.4791i 0.473618 1.45765i −0.374193 0.927351i \(-0.622080\pi\)
0.847812 0.530297i \(-0.177920\pi\)
\(410\) −8.34686 + 2.86305i −0.412222 + 0.141396i
\(411\) 6.07669 + 18.7021i 0.299741 + 0.922508i
\(412\) −10.0145 3.25392i −0.493381 0.160309i
\(413\) 23.5397 + 7.64852i 1.15831 + 0.376359i
\(414\) 3.98833 + 12.2748i 0.196016 + 0.603275i
\(415\) −21.6222 6.63848i −1.06139 0.325870i
\(416\) 2.27573 7.00398i 0.111577 0.343398i
\(417\) 6.84887 9.42666i 0.335391 0.461626i
\(418\) 20.3236i 0.994061i
\(419\) 20.9660 + 15.2327i 1.02425 + 0.744164i 0.967151 0.254204i \(-0.0818135\pi\)
0.0571034 + 0.998368i \(0.481814\pi\)
\(420\) 27.4520 0.446789i 1.33952 0.0218011i
\(421\) −3.17658 + 2.30792i −0.154817 + 0.112481i −0.662497 0.749065i \(-0.730503\pi\)
0.507680 + 0.861546i \(0.330503\pi\)
\(422\) −10.4226 14.3454i −0.507362 0.698324i
\(423\) −7.12511 + 2.31509i −0.346434 + 0.112563i
\(424\) −13.3109 −0.646436
\(425\) 1.10409 + 33.9103i 0.0535564 + 1.64489i
\(426\) −1.71282 −0.0829863
\(427\) 21.3163 6.92607i 1.03157 0.335176i
\(428\) −14.6589 20.1762i −0.708563 0.975254i
\(429\) 4.44799 3.23165i 0.214751 0.156026i
\(430\) −45.8979 + 34.5018i −2.21339 + 1.66382i
\(431\) 28.6903 + 20.8447i 1.38196 + 1.00406i 0.996694 + 0.0812518i \(0.0258918\pi\)
0.385270 + 0.922804i \(0.374108\pi\)
\(432\) 1.38270i 0.0665251i
\(433\) −5.93423 + 8.16776i −0.285181 + 0.392518i −0.927441 0.373969i \(-0.877997\pi\)
0.642261 + 0.766486i \(0.277997\pi\)
\(434\) −1.05750 + 3.25466i −0.0507618 + 0.156229i
\(435\) −0.0930049 5.71449i −0.00445924 0.273989i
\(436\) −14.4956 44.6129i −0.694214 2.13657i
\(437\) 15.4008 + 5.00402i 0.736719 + 0.239375i
\(438\) −8.03243 2.60990i −0.383804 0.124706i
\(439\) −2.19575 6.75783i −0.104798 0.322534i 0.884885 0.465809i \(-0.154237\pi\)
−0.989683 + 0.143275i \(0.954237\pi\)
\(440\) −0.382717 23.5152i −0.0182453 1.12104i
\(441\) 1.58326 4.87277i 0.0753933 0.232037i
\(442\) −17.5876 + 24.2072i −0.836556 + 1.15142i
\(443\) 20.6841i 0.982733i −0.870953 0.491366i \(-0.836498\pi\)
0.870953 0.491366i \(-0.163502\pi\)
\(444\) −14.9481 10.8604i −0.709406 0.515414i
\(445\) 0.513896 0.386299i 0.0243610 0.0183123i
\(446\) 14.8258 10.7715i 0.702020 0.510047i
\(447\) −4.30858 5.93025i −0.203789 0.280491i
\(448\) −39.7213 + 12.9062i −1.87665 + 0.609762i
\(449\) −19.4940 −0.919980 −0.459990 0.887924i \(-0.652147\pi\)
−0.459990 + 0.887924i \(0.652147\pi\)
\(450\) 7.21471 + 9.27944i 0.340105 + 0.437437i
\(451\) 4.92042 0.231694
\(452\) −33.6162 + 10.9225i −1.58117 + 0.513754i
\(453\) 9.83703 + 13.5395i 0.462184 + 0.636142i
\(454\) −24.4046 + 17.7310i −1.14536 + 0.832155i
\(455\) −14.6021 + 0.237654i −0.684559 + 0.0111414i
\(456\) −8.56240 6.22095i −0.400971 0.291323i
\(457\) 4.34194i 0.203107i −0.994830 0.101554i \(-0.967619\pi\)
0.994830 0.101554i \(-0.0323813\pi\)
\(458\) 20.0404 27.5833i 0.936427 1.28888i
\(459\) 2.09688 6.45355i 0.0978742 0.301226i
\(460\) −41.3851 12.7061i −1.92959 0.592424i
\(461\) 3.64322 + 11.2127i 0.169682 + 0.522227i 0.999351 0.0360287i \(-0.0114708\pi\)
−0.829669 + 0.558256i \(0.811471\pi\)
\(462\) −22.8178 7.41395i −1.06158 0.344928i
\(463\) 8.63436 + 2.80547i 0.401273 + 0.130381i 0.502699 0.864462i \(-0.332341\pi\)
−0.101426 + 0.994843i \(0.532341\pi\)
\(464\) −1.09209 3.36112i −0.0506991 0.156036i
\(465\) −0.884290 + 0.303319i −0.0410080 + 0.0140661i
\(466\) 8.27934 25.4812i 0.383533 1.18039i
\(467\) −20.5244 + 28.2494i −0.949755 + 1.30723i 0.00188168 + 0.999998i \(0.499401\pi\)
−0.951636 + 0.307227i \(0.900599\pi\)
\(468\) 6.61463i 0.305762i
\(469\) 28.2860 + 20.5510i 1.30613 + 0.948956i
\(470\) 11.5584 37.6470i 0.533150 1.73653i
\(471\) 6.38019 4.63548i 0.293984 0.213592i
\(472\) 14.9930 + 20.6361i 0.690109 + 0.949854i
\(473\) 30.4502 9.89388i 1.40010 0.454921i
\(474\) 7.22328 0.331776
\(475\) 14.7397 0.479913i 0.676304 0.0220199i
\(476\) 83.3179 3.81887
\(477\) −3.52797 + 1.14631i −0.161535 + 0.0524858i
\(478\) 9.53530 + 13.1242i 0.436135 + 0.600288i
\(479\) −6.99515 + 5.08228i −0.319617 + 0.232215i −0.736012 0.676969i \(-0.763293\pi\)
0.416395 + 0.909184i \(0.363293\pi\)
\(480\) −7.18546 5.04396i −0.327970 0.230224i
\(481\) 7.95113 + 5.77684i 0.362540 + 0.263401i
\(482\) 66.8734i 3.04600i
\(483\) −11.2362 + 15.4654i −0.511267 + 0.703698i
\(484\) 2.62471 8.07802i 0.119305 0.367183i
\(485\) −13.3727 + 19.0503i −0.607221 + 0.865028i
\(486\) −0.726446 2.23577i −0.0329523 0.101417i
\(487\) 2.70539 + 0.879035i 0.122593 + 0.0398329i 0.369671 0.929163i \(-0.379470\pi\)
−0.247078 + 0.968996i \(0.579470\pi\)
\(488\) 21.9678 + 7.13776i 0.994434 + 0.323111i
\(489\) −3.07160 9.45343i −0.138903 0.427499i
\(490\) 16.1830 + 21.5283i 0.731072 + 0.972550i
\(491\) 11.3731 35.0028i 0.513260 1.57965i −0.273165 0.961967i \(-0.588070\pi\)
0.786425 0.617686i \(-0.211930\pi\)
\(492\) −3.47953 + 4.78917i −0.156869 + 0.215912i
\(493\) 17.3437i 0.781121i
\(494\) 10.5221 + 7.64474i 0.473411 + 0.343953i
\(495\) −2.12651 6.19959i −0.0955797 0.278651i
\(496\) −0.467680 + 0.339789i −0.0209994 + 0.0152570i
\(497\) −1.49116 2.05240i −0.0668876 0.0920628i
\(498\) −22.6154 + 7.34818i −1.01342 + 0.329280i
\(499\) −5.85775 −0.262229 −0.131114 0.991367i \(-0.541856\pi\)
−0.131114 + 0.991367i \(0.541856\pi\)
\(500\) −39.3794 + 1.92409i −1.76110 + 0.0860480i
\(501\) −5.57767 −0.249192
\(502\) 27.5577 8.95405i 1.22996 0.399639i
\(503\) −17.8025 24.5030i −0.793773 1.09253i −0.993628 0.112709i \(-0.964047\pi\)
0.199855 0.979825i \(-0.435953\pi\)
\(504\) 10.1079 7.34383i 0.450243 0.327120i
\(505\) 5.55546 + 16.1963i 0.247215 + 0.720724i
\(506\) 30.6054 + 22.2361i 1.36058 + 0.988517i
\(507\) 9.48157i 0.421091i
\(508\) −21.9154 + 30.1640i −0.972340 + 1.33831i
\(509\) −4.67944 + 14.4018i −0.207413 + 0.638350i 0.792193 + 0.610270i \(0.208939\pi\)
−0.999606 + 0.0280797i \(0.991061\pi\)
\(510\) 21.4329 + 28.5123i 0.949064 + 1.26255i
\(511\) −3.86560 11.8971i −0.171004 0.526296i
\(512\) −14.6004 4.74395i −0.645251 0.209655i
\(513\) −2.80514 0.911446i −0.123850 0.0402413i
\(514\) −15.1300 46.5654i −0.667356 2.05391i
\(515\) 3.83619 5.46491i 0.169043 0.240813i
\(516\) −11.9033 + 36.6345i −0.524013 + 1.61275i
\(517\) −12.9073 + 17.7654i −0.567662 + 0.781320i
\(518\) 42.8877i 1.88438i
\(519\) −13.4039 9.73854i −0.588368 0.427474i
\(520\) −12.3184 8.64710i −0.540197 0.379201i
\(521\) −31.6190 + 22.9726i −1.38525 + 1.00645i −0.388887 + 0.921286i \(0.627140\pi\)
−0.996367 + 0.0851601i \(0.972860\pi\)
\(522\) −3.53175 4.86103i −0.154580 0.212762i
\(523\) −36.8987 + 11.9891i −1.61347 + 0.524248i −0.970388 0.241550i \(-0.922344\pi\)
−0.643081 + 0.765798i \(0.722344\pi\)
\(524\) 31.8296 1.39048
\(525\) −4.83815 + 16.7237i −0.211154 + 0.729880i
\(526\) 5.25449 0.229107
\(527\) −2.69813 + 0.876674i −0.117532 + 0.0381885i
\(528\) −2.38220 3.27881i −0.103672 0.142692i
\(529\) 5.77819 4.19810i 0.251226 0.182526i
\(530\) 5.72311 18.6408i 0.248596 0.809704i
\(531\) 5.75093 + 4.17830i 0.249569 + 0.181323i
\(532\) 36.2155i 1.57014i
\(533\) 1.85082 2.54743i 0.0801678 0.110341i
\(534\) 0.208862 0.642811i 0.00903835 0.0278172i
\(535\) 14.9583 5.13082i 0.646702 0.221825i
\(536\) 11.1345 + 34.2685i 0.480938 + 1.48017i
\(537\) 5.09787 + 1.65640i 0.219989 + 0.0714788i
\(538\) 43.1585 + 14.0231i 1.86070 + 0.604577i
\(539\) −4.64070 14.2826i −0.199889 0.615196i
\(540\) 7.53800 + 2.31432i 0.324384 + 0.0995926i
\(541\) 4.39669 13.5316i 0.189029 0.581770i −0.810966 0.585094i \(-0.801058\pi\)
0.999994 + 0.00332312i \(0.00105778\pi\)
\(542\) −16.5001 + 22.7104i −0.708738 + 0.975494i
\(543\) 0.327745i 0.0140649i
\(544\) −21.5533 15.6594i −0.924091 0.671391i
\(545\) 29.7406 0.484037i 1.27395 0.0207339i
\(546\) −12.4213 + 9.02462i −0.531583 + 0.386218i
\(547\) −23.1134 31.8129i −0.988259 1.36022i −0.932259 0.361790i \(-0.882166\pi\)
−0.0559991 0.998431i \(-0.517834\pi\)
\(548\) −65.9512 + 21.4288i −2.81730 + 0.915395i
\(549\) 6.43710 0.274729
\(550\) 33.0955 + 9.57454i 1.41120 + 0.408260i
\(551\) −7.53873 −0.321161
\(552\) −18.7363 + 6.08779i −0.797470 + 0.259114i
\(553\) 6.28849 + 8.65537i 0.267414 + 0.368064i
\(554\) 49.7272 36.1290i 2.11271 1.53497i
\(555\) 9.36518 7.03987i 0.397530 0.298826i
\(556\) 33.2422 + 24.1519i 1.40978 + 1.02427i
\(557\) 35.3849i 1.49931i 0.661830 + 0.749654i \(0.269780\pi\)
−0.661830 + 0.749654i \(0.730220\pi\)
\(558\) −0.577701 + 0.795138i −0.0244561 + 0.0336609i
\(559\) 6.33154 19.4865i 0.267796 0.824190i
\(560\) 0.175185 + 10.7639i 0.00740294 + 0.454858i
\(561\) −6.14619 18.9160i −0.259492 0.798636i
\(562\) 22.6302 + 7.35299i 0.954597 + 0.310167i
\(563\) −14.3025 4.64717i −0.602780 0.195855i −0.00830000 0.999966i \(-0.502642\pi\)
−0.594480 + 0.804111i \(0.702642\pi\)
\(564\) −8.16392 25.1260i −0.343763 1.05799i
\(565\) −0.364726 22.4098i −0.0153441 0.942786i
\(566\) −23.1473 + 71.2401i −0.972954 + 2.99444i
\(567\) 2.04660 2.81691i 0.0859492 0.118299i
\(568\) 2.61445i 0.109700i
\(569\) −2.20383 1.60118i −0.0923895 0.0671249i 0.540632 0.841260i \(-0.318185\pi\)
−0.633021 + 0.774135i \(0.718185\pi\)
\(570\) 12.3934 9.31616i 0.519100 0.390211i
\(571\) −10.2127 + 7.41997i −0.427389 + 0.310516i −0.780604 0.625026i \(-0.785088\pi\)
0.353215 + 0.935542i \(0.385088\pi\)
\(572\) 11.3961 + 15.6854i 0.476495 + 0.655839i
\(573\) 3.30009 1.07226i 0.137863 0.0447944i
\(574\) −13.7406 −0.573522
\(575\) 15.4040 22.7216i 0.642392 0.947557i
\(576\) −11.9951 −0.499794
\(577\) 22.4301 7.28797i 0.933776 0.303402i 0.197670 0.980269i \(-0.436662\pi\)
0.736106 + 0.676866i \(0.236662\pi\)
\(578\) 40.1342 + 55.2399i 1.66936 + 2.29768i
\(579\) 19.6700 14.2911i 0.817455 0.593916i
\(580\) 20.1516 0.327973i 0.836748 0.0136183i
\(581\) −28.4937 20.7019i −1.18212 0.858858i
\(582\) 24.4699i 1.01431i
\(583\) −6.39100 + 8.79646i −0.264688 + 0.364312i
\(584\) 3.98374 12.2607i 0.164849 0.507352i
\(585\) −4.00958 1.23102i −0.165776 0.0508966i
\(586\) 12.0761 + 37.1663i 0.498857 + 1.53532i
\(587\) −21.5673 7.00764i −0.890177 0.289236i −0.172000 0.985097i \(-0.555023\pi\)
−0.718177 + 0.695861i \(0.755023\pi\)
\(588\) 17.1833 + 5.58321i 0.708629 + 0.230248i
\(589\) 0.381061 + 1.17279i 0.0157013 + 0.0483238i
\(590\) −35.3454 + 12.1238i −1.45515 + 0.499128i
\(591\) −4.62169 + 14.2241i −0.190111 + 0.585102i
\(592\) 4.25837 5.86114i 0.175018 0.240891i
\(593\) 8.74287i 0.359027i 0.983756 + 0.179513i \(0.0574523\pi\)
−0.983756 + 0.179513i \(0.942548\pi\)
\(594\) −5.57456 4.05015i −0.228727 0.166180i
\(595\) −15.5060 + 50.5046i −0.635683 + 2.07049i
\(596\) 20.9124 15.1938i 0.856607 0.622362i
\(597\) −6.65674 9.16222i −0.272442 0.374985i
\(598\) 23.0245 7.48110i 0.941540 0.305925i
\(599\) −16.3209 −0.666854 −0.333427 0.942776i \(-0.608205\pi\)
−0.333427 + 0.942776i \(0.608205\pi\)
\(600\) −14.1641 + 11.0125i −0.578249 + 0.449585i
\(601\) 36.2713 1.47954 0.739768 0.672862i \(-0.234935\pi\)
0.739768 + 0.672862i \(0.234935\pi\)
\(602\) −85.0344 + 27.6294i −3.46575 + 1.12609i
\(603\) 5.90225 + 8.12376i 0.240358 + 0.330825i
\(604\) −47.7457 + 34.6893i −1.94275 + 1.41149i
\(605\) 4.40816 + 3.09438i 0.179217 + 0.125804i
\(606\) 14.5634 + 10.5809i 0.591597 + 0.429820i
\(607\) 16.6820i 0.677102i −0.940948 0.338551i \(-0.890063\pi\)
0.940948 0.338551i \(-0.109937\pi\)
\(608\) −6.80662 + 9.36851i −0.276045 + 0.379943i
\(609\) 2.75009 8.46390i 0.111439 0.342975i
\(610\) −19.4410 + 27.6950i −0.787142 + 1.12134i
\(611\) 4.34252 + 13.3649i 0.175679 + 0.540686i
\(612\) 22.7578 + 7.39445i 0.919929 + 0.298903i
\(613\) −23.5831 7.66260i −0.952511 0.309490i −0.208776 0.977964i \(-0.566948\pi\)
−0.743736 + 0.668474i \(0.766948\pi\)
\(614\) 10.2896 + 31.6682i 0.415256 + 1.27803i
\(615\) −2.25548 3.00047i −0.0909495 0.120991i
\(616\) 11.3167 34.8291i 0.455961 1.40330i
\(617\) 16.4386 22.6257i 0.661791 0.910877i −0.337748 0.941237i \(-0.609665\pi\)
0.999539 + 0.0303592i \(0.00966511\pi\)
\(618\) 7.01963i 0.282371i
\(619\) 22.0608 + 16.0281i 0.886697 + 0.644223i 0.935015 0.354609i \(-0.115386\pi\)
−0.0483179 + 0.998832i \(0.515386\pi\)
\(620\) −1.06963 3.11836i −0.0429572 0.125236i
\(621\) −4.44166 + 3.22706i −0.178238 + 0.129497i
\(622\) −20.7958 28.6230i −0.833836 1.14768i
\(623\) 0.952088 0.309352i 0.0381446 0.0123939i
\(624\) −2.59359 −0.103827
\(625\) 6.16242 24.2286i 0.246497 0.969144i
\(626\) −8.40365 −0.335878
\(627\) −8.22217 + 2.67155i −0.328362 + 0.106691i
\(628\) 16.3466 + 22.4991i 0.652299 + 0.897812i
\(629\) 28.7638 20.8982i 1.14689 0.833264i
\(630\) 5.93844 + 17.3128i 0.236593 + 0.689758i
\(631\) −34.1893 24.8400i −1.36105 0.988863i −0.998377 0.0569481i \(-0.981863\pi\)
−0.362676 0.931915i \(-0.618137\pi\)
\(632\) 11.0256i 0.438575i
\(633\) 4.43356 6.10228i 0.176218 0.242544i
\(634\) −9.28542 + 28.5776i −0.368771 + 1.13496i
\(635\) −14.2058 18.8981i −0.563742 0.749949i
\(636\) −4.04234 12.4410i −0.160289 0.493319i
\(637\) −9.14008 2.96979i −0.362143 0.117667i
\(638\) −16.7498 5.44233i −0.663130 0.215464i
\(639\) −0.225150 0.692941i −0.00890681 0.0274123i
\(640\) 26.1389 37.2367i 1.03323 1.47191i
\(641\) 14.1671 43.6017i 0.559565 1.72217i −0.124006 0.992281i \(-0.539574\pi\)
0.683571 0.729884i \(-0.260426\pi\)
\(642\) 9.77215 13.4502i 0.385676 0.530837i
\(643\) 46.6710i 1.84052i 0.391304 + 0.920261i \(0.372024\pi\)
−0.391304 + 0.920261i \(0.627976\pi\)
\(644\) −54.5370 39.6235i −2.14906 1.56138i
\(645\) −19.9914 14.0333i −0.787161 0.552560i
\(646\) 38.0644 27.6554i 1.49763 1.08809i
\(647\) 7.12775 + 9.81050i 0.280221 + 0.385691i 0.925807 0.377997i \(-0.123387\pi\)
−0.645586 + 0.763687i \(0.723387\pi\)
\(648\) 3.41268 1.10885i 0.134063 0.0435597i
\(649\) 20.8359 0.817880
\(650\) 17.4059 13.5330i 0.682715 0.530807i
\(651\) −1.45572 −0.0570542
\(652\) 33.3366 10.8317i 1.30556 0.424202i
\(653\) −1.01109 1.39164i −0.0395670 0.0544593i 0.788775 0.614682i \(-0.210716\pi\)
−0.828342 + 0.560223i \(0.810716\pi\)
\(654\) 25.2989 18.3807i 0.989264 0.718743i
\(655\) −5.92368 + 19.2941i −0.231457 + 0.753881i
\(656\) −1.87783 1.36432i −0.0733168 0.0532678i
\(657\) 3.59269i 0.140164i
\(658\) 36.0445 49.6110i 1.40516 1.93404i
\(659\) −1.69325 + 5.21129i −0.0659596 + 0.203003i −0.978604 0.205751i \(-0.934036\pi\)
0.912645 + 0.408754i \(0.134036\pi\)
\(660\) 21.8622 7.49894i 0.850986 0.291896i
\(661\) 0.246425 + 0.758418i 0.00958482 + 0.0294990i 0.955735 0.294230i \(-0.0950633\pi\)
−0.946150 + 0.323729i \(0.895063\pi\)
\(662\) 10.5194 + 3.41796i 0.408848 + 0.132843i
\(663\) −12.1052 3.93322i −0.470128 0.152754i
\(664\) −11.2163 34.5201i −0.435276 1.33964i
\(665\) 21.9527 + 6.73993i 0.851288 + 0.261363i
\(666\) 3.80628 11.7145i 0.147490 0.453929i
\(667\) −8.24814 + 11.3526i −0.319369 + 0.439574i
\(668\) 19.6691i 0.761020i
\(669\) 6.30661 + 4.58202i 0.243827 + 0.177151i
\(670\) −52.7774 + 0.858967i −2.03897 + 0.0331848i
\(671\) 15.2644 11.0902i 0.589275 0.428133i
\(672\) −8.03522 11.0595i −0.309965 0.426631i
\(673\) −48.8158 + 15.8612i −1.88171 + 0.611405i −0.895716 + 0.444627i \(0.853336\pi\)
−0.985995 + 0.166777i \(0.946664\pi\)
\(674\) 40.9156 1.57601
\(675\) −2.80573 + 4.13858i −0.107993 + 0.159294i
\(676\) −33.4358 −1.28599
\(677\) −14.3542 + 4.66397i −0.551678 + 0.179251i −0.571573 0.820551i \(-0.693667\pi\)
0.0198952 + 0.999802i \(0.493667\pi\)
\(678\) −13.8500 19.0629i −0.531906 0.732106i
\(679\) −29.3213 + 21.3032i −1.12525 + 0.817540i
\(680\) −43.5212 + 32.7152i −1.66896 + 1.25457i
\(681\) −10.3813 7.54242i −0.397811 0.289026i
\(682\) 2.88082i 0.110312i
\(683\) 6.38347 8.78610i 0.244257 0.336191i −0.669233 0.743053i \(-0.733377\pi\)
0.913490 + 0.406862i \(0.133377\pi\)
\(684\) 3.21412 9.89205i 0.122895 0.378232i
\(685\) −0.715551 43.9655i −0.0273398 1.67984i
\(686\) −4.74634 14.6077i −0.181216 0.557726i
\(687\) 13.7935 + 4.48177i 0.526253 + 0.170990i
\(688\) −14.3644 4.66726i −0.547636 0.177938i
\(689\) 2.15018 + 6.61758i 0.0819154 + 0.252110i
\(690\) −0.469640 28.8560i −0.0178789 1.09853i
\(691\) 2.60981 8.03217i 0.0992818 0.305558i −0.889064 0.457783i \(-0.848644\pi\)
0.988346 + 0.152225i \(0.0486438\pi\)
\(692\) 34.3420 47.2677i 1.30549 1.79685i
\(693\) 10.2058i 0.387686i
\(694\) 26.6463 + 19.3597i 1.01148 + 0.734883i
\(695\) −20.8267 + 15.6555i −0.790000 + 0.593848i
\(696\) 7.41988 5.39086i 0.281250 0.204340i
\(697\) −6.69548 9.21553i −0.253609 0.349063i
\(698\) 80.3668 26.1127i 3.04193 0.988382i
\(699\) 11.3970 0.431076
\(700\) −58.9743 17.0613i −2.22902 0.644855i
\(701\) 48.9399 1.84843 0.924216 0.381869i \(-0.124719\pi\)
0.924216 + 0.381869i \(0.124719\pi\)
\(702\) −4.19374 + 1.36263i −0.158283 + 0.0514291i
\(703\) −9.08373 12.5027i −0.342599 0.471548i
\(704\) −28.4440 + 20.6658i −1.07203 + 0.778872i
\(705\) 16.7499 0.272610i 0.630838 0.0102671i
\(706\) −16.7401 12.1624i −0.630023 0.457739i
\(707\) 26.6623i 1.00274i
\(708\) −14.7343 + 20.2801i −0.553750 + 0.762172i
\(709\) −7.65850 + 23.5705i −0.287621 + 0.885207i 0.697980 + 0.716118i \(0.254083\pi\)
−0.985601 + 0.169089i \(0.945917\pi\)
\(710\) 3.66130 + 1.12410i 0.137406 + 0.0421866i
\(711\) 0.949501 + 2.92226i 0.0356091 + 0.109593i
\(712\) 0.981187 + 0.318807i 0.0367716 + 0.0119478i
\(713\) 2.18302 + 0.709306i 0.0817547 + 0.0265637i
\(714\) 17.1637 + 52.8244i 0.642334 + 1.97690i
\(715\) −11.6289 + 3.98880i −0.434895 + 0.149173i
\(716\) −5.84112 + 17.9771i −0.218293 + 0.671836i
\(717\) −4.05614 + 5.58280i −0.151479 + 0.208494i
\(718\) 14.1746i 0.528992i
\(719\) −14.7379 10.7077i −0.549631 0.399331i 0.278018 0.960576i \(-0.410322\pi\)
−0.827650 + 0.561245i \(0.810322\pi\)
\(720\) −0.907443 + 2.95564i −0.0338184 + 0.110150i
\(721\) 8.41134 6.11119i 0.313255 0.227593i
\(722\) 14.2330 + 19.5900i 0.529697 + 0.729065i
\(723\) 27.0545 8.79052i 1.00617 0.326923i
\(724\) 1.15576 0.0429534
\(725\) −3.55152 + 12.2763i −0.131900 + 0.455929i
\(726\) 5.66224 0.210145
\(727\) −15.8540 + 5.15129i −0.587994 + 0.191051i −0.587878 0.808949i \(-0.700037\pi\)
−0.000115145 1.00000i \(0.500037\pi\)
\(728\) −13.7752 18.9599i −0.510542 0.702701i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 15.4572 + 10.8504i 0.572097 + 0.401593i
\(731\) −59.9657 43.5676i −2.21791 1.61141i
\(732\) 22.6998i 0.839008i
\(733\) −11.7935 + 16.2324i −0.435604 + 0.599558i −0.969228 0.246164i \(-0.920830\pi\)
0.533624 + 0.845722i \(0.320830\pi\)
\(734\) −20.8971 + 64.3147i −0.771326 + 2.37390i
\(735\) −6.58228 + 9.37692i −0.242791 + 0.345873i
\(736\) 6.66092 + 20.5002i 0.245525 + 0.755648i
\(737\) 27.9922 + 9.09522i 1.03111 + 0.335027i
\(738\) −3.75317 1.21948i −0.138156 0.0448896i
\(739\) 10.5242 + 32.3903i 0.387140 + 1.19149i 0.934916 + 0.354870i \(0.115475\pi\)
−0.547776 + 0.836625i \(0.684525\pi\)
\(740\) 24.8254 + 33.0254i 0.912600 + 1.21404i
\(741\) −1.70964 + 5.26174i −0.0628053 + 0.193295i
\(742\) 17.8473 24.5647i 0.655196 0.901800i
\(743\) 38.5355i 1.41373i 0.707348 + 0.706865i \(0.249891\pi\)
−0.707348 + 0.706865i \(0.750109\pi\)
\(744\) −1.21370 0.881804i −0.0444963 0.0323285i
\(745\) 5.31805 + 15.5041i 0.194838 + 0.568026i
\(746\) −63.9026 + 46.4280i −2.33964 + 1.69985i
\(747\) −5.94559 8.18340i −0.217538 0.299415i
\(748\) 66.7055 21.6739i 2.43900 0.792478i
\(749\) 24.6244 0.899754
\(750\) −9.33213 24.5705i −0.340761 0.897189i
\(751\) −36.0351 −1.31494 −0.657470 0.753481i \(-0.728373\pi\)
−0.657470 + 0.753481i \(0.728373\pi\)
\(752\) 9.85187 3.20107i 0.359261 0.116731i
\(753\) 7.24494 + 9.97181i 0.264020 + 0.363393i
\(754\) −9.11807 + 6.62466i −0.332060 + 0.241256i
\(755\) −12.1418 35.3978i −0.441884 1.28826i
\(756\) 9.93354 + 7.21714i 0.361279 + 0.262485i
\(757\) 35.0131i 1.27257i 0.771453 + 0.636287i \(0.219530\pi\)
−0.771453 + 0.636287i \(0.780470\pi\)
\(758\) −6.40322 + 8.81328i −0.232576 + 0.320113i
\(759\) −4.97281 + 15.3047i −0.180502 + 0.555527i
\(760\) 14.2202 + 18.9172i 0.515821 + 0.686200i
\(761\) 9.69007 + 29.8230i 0.351265 + 1.08108i 0.958144 + 0.286288i \(0.0924213\pi\)
−0.606879 + 0.794794i \(0.707579\pi\)
\(762\) −23.6389 7.68074i −0.856347 0.278244i
\(763\) 44.0497 + 14.3126i 1.59471 + 0.518152i
\(764\) 3.78123 + 11.6374i 0.136800 + 0.421027i
\(765\) −8.71764 + 12.4189i −0.315187 + 0.449006i
\(766\) −9.37534 + 28.8543i −0.338745 + 1.04255i
\(767\) 7.83742 10.7873i 0.282993 0.389506i
\(768\) 23.8400i 0.860253i
\(769\) 1.94014 + 1.40959i 0.0699633 + 0.0508313i 0.622217 0.782845i \(-0.286232\pi\)
−0.552254 + 0.833676i \(0.686232\pi\)
\(770\) 43.9094 + 30.8230i 1.58239 + 1.11078i
\(771\) 16.8497 12.2421i 0.606829 0.440887i
\(772\) 50.3960 + 69.3641i 1.81379 + 2.49647i
\(773\) −10.3880 + 3.37526i −0.373630 + 0.121400i −0.489812 0.871828i \(-0.662935\pi\)
0.116182 + 0.993228i \(0.462935\pi\)
\(774\) −25.6788 −0.923004
\(775\) 2.08931 0.0680264i 0.0750503 0.00244358i
\(776\) −37.3508 −1.34082
\(777\) 17.3507 5.63760i 0.622454 0.202248i
\(778\) −24.2152 33.3293i −0.868156 1.19491i
\(779\) −4.00568 + 2.91030i −0.143519 + 0.104272i
\(780\) 4.34108 14.1394i 0.155436 0.506271i
\(781\) −1.72774 1.25528i −0.0618236 0.0449174i
\(782\) 87.5792i 3.13183i
\(783\) 1.50234 2.06779i 0.0536893 0.0738970i
\(784\) −2.18917 + 6.73757i −0.0781846 + 0.240627i
\(785\) −16.6804 + 5.72154i −0.595350 + 0.204210i
\(786\) 6.55696 + 20.1802i 0.233879 + 0.719806i
\(787\) 11.0060 + 3.57607i 0.392321 + 0.127473i 0.498533 0.866871i \(-0.333872\pi\)
−0.106212 + 0.994344i \(0.533872\pi\)
\(788\) −50.1599 16.2979i −1.78687 0.580590i
\(789\) 0.690704 + 2.12577i 0.0245897 + 0.0756794i
\(790\) −15.4404 4.74053i −0.549345 0.168660i
\(791\) 10.7847 33.1918i 0.383459 1.18017i
\(792\) 6.18216 8.50901i 0.219673 0.302354i
\(793\) 12.0744i 0.428773i
\(794\) −51.3837 37.3324i −1.82354 1.32488i
\(795\) 8.29366 0.134982i 0.294146 0.00478731i
\(796\) 32.3096 23.4743i 1.14518 0.832026i
\(797\) −12.8680 17.7113i −0.455808 0.627366i 0.517825 0.855487i \(-0.326742\pi\)
−0.973633 + 0.228121i \(0.926742\pi\)
\(798\) 22.9610 7.46048i 0.812810 0.264098i
\(799\) 50.8367 1.79847
\(800\) 12.0493 + 15.4976i 0.426007 + 0.547923i
\(801\) 0.287512 0.0101587
\(802\) 35.7259 11.6081i 1.26153 0.409895i
\(803\) −6.18970 8.51940i −0.218430 0.300643i
\(804\) −28.6476 + 20.8137i −1.01032 + 0.734043i
\(805\) 34.1682 25.6844i 1.20427 0.905257i
\(806\) 1.49148 + 1.08362i 0.0525350 + 0.0381689i
\(807\) 19.3036i 0.679520i
\(808\) −16.1507 + 22.2295i −0.568180 + 0.782033i
\(809\) 6.65926 20.4951i 0.234127 0.720570i −0.763109 0.646270i \(-0.776328\pi\)
0.997236 0.0742994i \(-0.0236721\pi\)
\(810\) 0.0855416 + 5.25592i 0.00300563 + 0.184674i
\(811\) −13.5848 41.8098i −0.477028 1.46814i −0.843203 0.537596i \(-0.819333\pi\)
0.366175 0.930546i \(-0.380667\pi\)
\(812\) 29.8471 + 9.69791i 1.04743 + 0.340330i
\(813\) −11.3567 3.69001i −0.398297 0.129414i
\(814\) −11.1566 34.3365i −0.391039 1.20349i
\(815\) 0.361692 + 22.2234i 0.0126695 + 0.778452i
\(816\) −2.89936 + 8.92331i −0.101498 + 0.312378i
\(817\) −18.9374 + 26.0651i −0.662535 + 0.911901i
\(818\) 72.8667i 2.54772i
\(819\) −5.28380 3.83891i −0.184631 0.134142i
\(820\) 10.5809 7.95371i 0.369500 0.277756i
\(821\) −27.1070 + 19.6944i −0.946042 + 0.687340i −0.949867 0.312653i \(-0.898782\pi\)
0.00382568 + 0.999993i \(0.498782\pi\)
\(822\) −27.1722 37.3993i −0.947739 1.30445i
\(823\) 53.2458 17.3006i 1.85603 0.603061i 0.860409 0.509604i \(-0.170208\pi\)
0.995623 0.0934576i \(-0.0297920\pi\)
\(824\) 10.7148 0.373266
\(825\) 0.476920 + 14.6478i 0.0166042 + 0.509970i
\(826\) −58.1857 −2.02454
\(827\) 38.8126 12.6110i 1.34965 0.438527i 0.457074 0.889429i \(-0.348897\pi\)
0.892574 + 0.450901i \(0.148897\pi\)
\(828\) −11.3799 15.6631i −0.395478 0.544329i
\(829\) 0.0994391 0.0722468i 0.00345366 0.00250923i −0.586057 0.810270i \(-0.699321\pi\)
0.589511 + 0.807761i \(0.299321\pi\)
\(830\) 53.1649 0.865274i 1.84538 0.0300341i
\(831\) 21.1531 + 15.3686i 0.733791 + 0.533131i
\(832\) 22.4997i 0.780036i
\(833\) −20.4353 + 28.1267i −0.708040 + 0.974534i
\(834\) −8.46455 + 26.0512i −0.293103 + 0.902080i
\(835\) 11.9228 + 3.66054i 0.412604 + 0.126678i
\(836\) −9.42094 28.9947i −0.325830 1.00280i
\(837\) −0.397622 0.129195i −0.0137438 0.00446564i
\(838\) −57.9408 18.8261i −2.00153 0.650337i
\(839\) −4.57603 14.0836i −0.157982 0.486219i 0.840469 0.541860i \(-0.182280\pi\)
−0.998451 + 0.0556411i \(0.982280\pi\)
\(840\) −26.4262 + 9.06443i −0.911792 + 0.312753i
\(841\) −6.94275 + 21.3676i −0.239405 + 0.736813i
\(842\) 5.42552 7.46759i 0.186976 0.257350i
\(843\) 10.1219i 0.348616i
\(844\) 21.5191 + 15.6345i 0.740717 + 0.538162i
\(845\) 6.22261 20.2677i 0.214064 0.697231i
\(846\) 14.2483 10.3520i 0.489867 0.355910i
\(847\) 4.92947 + 6.78483i 0.169379 + 0.233130i
\(848\) 4.87812 1.58500i 0.167515 0.0544290i
\(849\) −31.8638 −1.09356
\(850\) −27.1025 75.0137i −0.929609 2.57295i
\(851\) −28.7664 −0.986098
\(852\) 2.44359 0.793970i 0.0837160 0.0272010i
\(853\) 4.27011 + 5.87730i 0.146206 + 0.201235i 0.875839 0.482604i \(-0.160309\pi\)
−0.729633 + 0.683839i \(0.760309\pi\)
\(854\) −42.6269 + 30.9702i −1.45866 + 1.05978i
\(855\) 5.39808 + 3.78927i 0.184610 + 0.129590i
\(856\) 20.5304 + 14.9162i 0.701715 + 0.509826i
\(857\) 26.8175i 0.916068i −0.888935 0.458034i \(-0.848554\pi\)
0.888935 0.458034i \(-0.151446\pi\)
\(858\) −7.59706 + 10.4565i −0.259359 + 0.356978i
\(859\) 6.36691 19.5953i 0.217236 0.668584i −0.781751 0.623591i \(-0.785673\pi\)
0.998987 0.0449937i \(-0.0143268\pi\)
\(860\) 49.4870 70.4977i 1.68749 2.40395i
\(861\) −1.80621 5.55893i −0.0615554 0.189448i
\(862\) −79.2876 25.7621i −2.70055 0.877461i
\(863\) −13.0759 4.24862i −0.445109 0.144625i 0.0778827 0.996963i \(-0.475184\pi\)
−0.522991 + 0.852338i \(0.675184\pi\)
\(864\) −1.21324 3.73397i −0.0412753 0.127032i
\(865\) 22.2609 + 29.6138i 0.756893 + 1.00690i
\(866\) 7.33413 22.5721i 0.249224 0.767033i
\(867\) −17.0723 + 23.4981i −0.579807 + 0.798036i
\(868\) 5.13346i 0.174241i
\(869\) 7.28622 + 5.29375i 0.247168 + 0.179578i
\(870\) 4.35921 + 12.7087i 0.147791 + 0.430866i
\(871\) 15.2381 11.0711i 0.516324 0.375131i
\(872\) 28.0563 + 38.6162i 0.950107 + 1.30771i
\(873\) −9.89959 + 3.21657i −0.335050 + 0.108864i
\(874\) −38.0678 −1.28766
\(875\) 21.3175 32.5731i 0.720662 1.10117i
\(876\) 12.6693 0.428055
\(877\) −20.9641 + 6.81166i −0.707909 + 0.230014i −0.640773 0.767730i \(-0.721386\pi\)
−0.0671357 + 0.997744i \(0.521386\pi\)
\(878\) 9.81840 + 13.5139i 0.331355 + 0.456071i
\(879\) −13.4487 + 9.77103i −0.453612 + 0.329569i
\(880\) 2.94033 + 8.57216i 0.0991184 + 0.288967i
\(881\) 7.31294 + 5.31316i 0.246379 + 0.179005i 0.704121 0.710080i \(-0.251341\pi\)
−0.457741 + 0.889085i \(0.651341\pi\)
\(882\) 12.0446i 0.405561i
\(883\) 0.941165 1.29540i 0.0316727 0.0435937i −0.792887 0.609369i \(-0.791423\pi\)
0.824560 + 0.565775i \(0.191423\pi\)
\(884\) 13.8701 42.6879i 0.466503 1.43575i
\(885\) −9.55098 12.7057i −0.321053 0.427098i
\(886\) 15.0259 + 46.2450i 0.504805 + 1.55363i
\(887\) 16.5724 + 5.38470i 0.556447 + 0.180801i 0.573722 0.819050i \(-0.305499\pi\)
−0.0172750 + 0.999851i \(0.505499\pi\)
\(888\) 17.8811 + 5.80991i 0.600049 + 0.194968i
\(889\) −11.3762 35.0123i −0.381545 1.17427i
\(890\) −0.868329 + 1.23699i −0.0291064 + 0.0414641i
\(891\) 0.905762 2.78765i 0.0303442 0.0933897i
\(892\) −16.1580 + 22.2396i −0.541011 + 0.744638i
\(893\) 22.0970i 0.739448i
\(894\) 13.9410 + 10.1287i 0.466257 + 0.338756i
\(895\) −9.81008 6.88635i −0.327915 0.230185i
\(896\) 57.3129 41.6403i 1.91469 1.39110i
\(897\) 6.05314 + 8.33143i 0.202108 + 0.278178i
\(898\) 43.5842 14.1614i 1.45442 0.472571i
\(899\) −1.06860 −0.0356397
\(900\) −14.5943 9.89414i −0.486476 0.329805i
\(901\) 25.1716 0.838588
\(902\) −11.0009 + 3.57442i −0.366291 + 0.119015i
\(903\) −22.3556 30.7698i −0.743947 1.02396i
\(904\) 29.0976 21.1406i 0.967772 0.703128i
\(905\) −0.215094 + 0.700584i −0.00714996 + 0.0232882i
\(906\) −31.8291 23.1252i −1.05745 0.768283i
\(907\) 20.8690i 0.692942i −0.938061 0.346471i \(-0.887380\pi\)
0.938061 0.346471i \(-0.112620\pi\)
\(908\) 26.5976 36.6085i 0.882673 1.21489i
\(909\) −2.36628 + 7.28266i −0.0784845 + 0.241550i
\(910\) 32.4744 11.1390i 1.07652 0.369254i
\(911\) 15.1958 + 46.7680i 0.503461 + 1.54949i 0.803343 + 0.595517i \(0.203053\pi\)
−0.299882 + 0.953976i \(0.596947\pi\)
\(912\) 3.87866 + 1.26025i 0.128435 + 0.0417312i
\(913\) −28.1977 9.16200i −0.933209 0.303218i
\(914\) 3.15418 + 9.70758i 0.104331 + 0.321098i
\(915\) −13.7599 4.22457i −0.454887 0.139660i
\(916\) −15.8045 + 48.6413i −0.522196 + 1.60715i
\(917\) −18.4728 + 25.4256i −0.610025 + 0.839627i
\(918\) 15.9519i 0.526492i
\(919\) −9.05765 6.58077i −0.298784 0.217079i 0.428285 0.903644i \(-0.359118\pi\)
−0.727069 + 0.686564i \(0.759118\pi\)
\(920\) 44.0458 0.716859i 1.45215 0.0236341i
\(921\) −11.4592 + 8.32559i −0.377593 + 0.274338i
\(922\) −16.2908 22.4224i −0.536510 0.738443i
\(923\) −1.29978 + 0.422325i −0.0427829 + 0.0139010i
\(924\) 35.9897 1.18397
\(925\) −24.6391 + 8.90213i −0.810128 + 0.292700i
\(926\) −21.3425 −0.701357
\(927\) 2.83987 0.922731i 0.0932737 0.0303065i
\(928\) −5.89838 8.11842i −0.193624 0.266500i
\(929\) 39.0181 28.3483i 1.28014 0.930077i 0.280584 0.959830i \(-0.409472\pi\)
0.999557 + 0.0297529i \(0.00947204\pi\)
\(930\) 1.75673 1.32054i 0.0576053 0.0433023i
\(931\) 12.2258 + 8.88253i 0.400683 + 0.291113i
\(932\) 40.1906i 1.31649i
\(933\) 8.84615 12.1757i 0.289610 0.398614i
\(934\) 25.3662 78.0690i 0.830006 2.55450i
\(935\) 0.723736 + 44.4684i 0.0236687 + 1.45427i
\(936\) −2.07992 6.40133i −0.0679842 0.209234i
\(937\) 48.0661 + 15.6176i 1.57025 + 0.510205i 0.959522 0.281635i \(-0.0908768\pi\)
0.610728 + 0.791840i \(0.290877\pi\)
\(938\) −78.1702 25.3990i −2.55235 0.829308i
\(939\) −1.10466 3.39980i −0.0360493 0.110948i
\(940\) 0.961330 + 59.0669i 0.0313551 + 1.92655i
\(941\) −11.7934 + 36.2965i −0.384455 + 1.18323i 0.552420 + 0.833566i \(0.313705\pi\)
−0.936875 + 0.349665i \(0.886295\pi\)
\(942\) −10.8972 + 14.9987i −0.355051 + 0.488686i
\(943\) 9.21634i 0.300125i
\(944\) −7.95180 5.77732i −0.258809 0.188036i
\(945\) −6.22349 + 4.67824i −0.202450 + 0.152183i
\(946\) −60.8924 + 44.2409i −1.97978 + 1.43840i
\(947\) −14.4119 19.8363i −0.468323 0.644592i 0.507885 0.861425i \(-0.330427\pi\)
−0.976209 + 0.216833i \(0.930427\pi\)
\(948\) −10.3051 + 3.34832i −0.334693 + 0.108748i
\(949\) −6.73897 −0.218756
\(950\) −32.6060 + 11.7806i −1.05788 + 0.382212i
\(951\) −12.7820 −0.414484
\(952\) −80.6311 + 26.1986i −2.61327 + 0.849103i
\(953\) 7.64232 + 10.5187i 0.247559 + 0.340736i 0.914655 0.404236i \(-0.132463\pi\)
−0.667096 + 0.744972i \(0.732463\pi\)
\(954\) 7.05501 5.12576i 0.228414 0.165953i
\(955\) −7.75794 + 0.126263i −0.251041 + 0.00408577i
\(956\) −19.6872 14.3036i −0.636729 0.462611i
\(957\) 7.49172i 0.242173i
\(958\) 11.9476 16.4444i 0.386008 0.531295i
\(959\) 21.1583 65.1187i 0.683239 2.10279i
\(960\) 25.6405 + 7.87217i 0.827544 + 0.254073i
\(961\) −9.52551 29.3165i −0.307275 0.945694i
\(962\) −21.9735 7.13962i −0.708453 0.230190i
\(963\) 6.72600 + 2.18541i 0.216742 + 0.0704238i
\(964\) 30.9989 + 95.4048i 0.998408 + 3.07278i
\(965\) −51.4253 + 17.6393i −1.65544 + 0.567830i
\(966\) 13.8869 42.7395i 0.446804 1.37512i
\(967\) −25.4636 + 35.0476i −0.818854 + 1.12706i 0.171043 + 0.985264i \(0.445286\pi\)
−0.989896 + 0.141792i \(0.954714\pi\)
\(968\) 8.64284i 0.277791i
\(969\) 16.1919 + 11.7641i 0.520159 + 0.377918i
\(970\) 16.0592 52.3066i 0.515630 1.67946i
\(971\) 23.8922 17.3587i 0.766738 0.557068i −0.134231 0.990950i \(-0.542857\pi\)
0.900970 + 0.433882i \(0.142857\pi\)
\(972\) 2.07277 + 2.85292i 0.0664840 + 0.0915074i
\(973\) −38.5853 + 12.5371i −1.23699 + 0.401921i
\(974\) −6.68721 −0.214272
\(975\) 7.76293 + 5.26285i 0.248613 + 0.168546i
\(976\) −8.90056 −0.284900
\(977\) 57.6486 18.7312i 1.84434 0.599263i 0.846591 0.532244i \(-0.178651\pi\)
0.997752 0.0670189i \(-0.0213488\pi\)
\(978\) 13.7348 + 18.9044i 0.439191 + 0.604495i
\(979\) 0.681782 0.495343i 0.0217898 0.0158312i
\(980\) −33.0668 23.2118i −1.05628 0.741473i
\(981\) 10.7617 + 7.81882i 0.343594 + 0.249636i
\(982\) 86.5202i 2.76097i
\(983\) 23.6757 32.5868i 0.755138 1.03936i −0.242465 0.970160i \(-0.577956\pi\)
0.997603 0.0691986i \(-0.0220442\pi\)
\(984\) 1.86141 5.72884i 0.0593397 0.182629i
\(985\) 19.2143 27.3722i 0.612220 0.872150i
\(986\) 12.5993 + 38.7766i 0.401243 + 1.23490i
\(987\) 24.8088 + 8.06087i 0.789673 + 0.256580i
\(988\) −18.5550 6.02888i −0.590313 0.191804i
\(989\) 18.5320 + 57.0357i 0.589284 + 1.81363i
\(990\) 9.25807 + 12.3161i 0.294241 + 0.391430i
\(991\) 11.7889 36.2824i 0.374485 1.15255i −0.569340 0.822102i \(-0.692801\pi\)
0.943825 0.330445i \(-0.107199\pi\)
\(992\) −0.964821 + 1.32796i −0.0306331 + 0.0421628i
\(993\) 4.70504i 0.149310i
\(994\) 4.82485 + 3.50546i 0.153035 + 0.111186i
\(995\) 8.21636 + 23.9538i 0.260476 + 0.759386i
\(996\) 28.8580 20.9665i 0.914399 0.664350i
\(997\) −15.6220 21.5018i −0.494753 0.680969i 0.486503 0.873679i \(-0.338272\pi\)
−0.981256 + 0.192710i \(0.938272\pi\)
\(998\) 13.0966 4.25534i 0.414565 0.134700i
\(999\) 5.23959 0.165773
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.i.a.19.1 yes 16
3.2 odd 2 225.2.m.b.19.4 16
5.2 odd 4 375.2.g.e.151.1 16
5.3 odd 4 375.2.g.d.151.4 16
5.4 even 2 375.2.i.c.349.4 16
25.2 odd 20 1875.2.a.m.1.2 8
25.3 odd 20 375.2.g.d.226.4 16
25.4 even 10 inner 75.2.i.a.4.1 16
25.11 even 5 1875.2.b.h.1249.15 16
25.14 even 10 1875.2.b.h.1249.2 16
25.21 even 5 375.2.i.c.274.4 16
25.22 odd 20 375.2.g.e.226.1 16
25.23 odd 20 1875.2.a.p.1.7 8
75.2 even 20 5625.2.a.bd.1.7 8
75.23 even 20 5625.2.a.t.1.2 8
75.29 odd 10 225.2.m.b.154.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.i.a.4.1 16 25.4 even 10 inner
75.2.i.a.19.1 yes 16 1.1 even 1 trivial
225.2.m.b.19.4 16 3.2 odd 2
225.2.m.b.154.4 16 75.29 odd 10
375.2.g.d.151.4 16 5.3 odd 4
375.2.g.d.226.4 16 25.3 odd 20
375.2.g.e.151.1 16 5.2 odd 4
375.2.g.e.226.1 16 25.22 odd 20
375.2.i.c.274.4 16 25.21 even 5
375.2.i.c.349.4 16 5.4 even 2
1875.2.a.m.1.2 8 25.2 odd 20
1875.2.a.p.1.7 8 25.23 odd 20
1875.2.b.h.1249.2 16 25.14 even 10
1875.2.b.h.1249.15 16 25.11 even 5
5625.2.a.t.1.2 8 75.23 even 20
5625.2.a.bd.1.7 8 75.2 even 20