Properties

Label 252.2.ba.a.239.6
Level $252$
Weight $2$
Character 252.239
Analytic conductor $2.012$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(155,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 239.6
Character \(\chi\) \(=\) 252.239
Dual form 252.2.ba.a.155.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24454 - 0.671660i) q^{2} +(-0.586217 + 1.62983i) q^{3} +(1.09775 + 1.67181i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(1.82426 - 1.63465i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(-0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +O(q^{10})\) \(q+(-1.24454 - 0.671660i) q^{2} +(-0.586217 + 1.62983i) q^{3} +(1.09775 + 1.67181i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(1.82426 - 1.63465i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(-0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +(1.85728 + 3.01367i) q^{10} +(0.351433 + 0.608700i) q^{11} +(-3.36829 + 0.809097i) q^{12} +(1.55324 - 2.69030i) q^{13} +(1.41363 - 0.0405943i) q^{14} +(3.31068 - 2.79946i) q^{15} +(-1.58991 + 3.67045i) q^{16} -7.91554i q^{17} +(1.59479 + 3.93150i) q^{18} -2.37413i q^{19} +(-0.287291 - 4.99809i) q^{20} +(-0.307237 - 1.70458i) q^{21} +(-0.0285324 - 0.993594i) q^{22} +(0.346619 - 0.600362i) q^{23} +(4.73540 + 1.25539i) q^{24} +(0.632931 + 1.09627i) q^{25} +(-3.74003 + 2.30492i) q^{26} +(4.47014 - 2.64912i) q^{27} +(-1.78658 - 0.898958i) q^{28} +(-8.70126 + 5.02368i) q^{29} +(-6.00055 + 1.26039i) q^{30} +(-7.34846 - 4.24264i) q^{31} +(4.44399 - 3.50014i) q^{32} +(-1.19809 + 0.215946i) q^{33} +(-5.31655 + 9.85118i) q^{34} +2.50317 q^{35} +(0.655856 - 5.96405i) q^{36} +2.85107 q^{37} +(-1.59460 + 2.95469i) q^{38} +(3.47419 + 4.10862i) q^{39} +(-2.99947 + 6.41327i) q^{40} +(5.82034 + 3.36037i) q^{41} +(-0.762533 + 2.32778i) q^{42} +(-3.17043 + 1.83045i) q^{43} +(-0.631847 + 1.25573i) q^{44} +(2.62187 + 7.03694i) q^{45} +(-0.834620 + 0.514363i) q^{46} +(-3.67787 - 6.37026i) q^{47} +(-5.05018 - 4.74296i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-0.0513868 - 1.78946i) q^{50} +(12.9010 + 4.64022i) q^{51} +(6.20273 - 0.356534i) q^{52} -0.889576i q^{53} +(-7.34256 + 0.294523i) q^{54} -1.75939i q^{55} +(1.61967 + 2.31876i) q^{56} +(3.86942 + 1.39175i) q^{57} +(14.2032 - 0.407865i) q^{58} +(-3.63052 + 6.28824i) q^{59} +(8.31446 + 2.46173i) q^{60} +(-2.39732 - 4.15228i) q^{61} +(6.29583 + 10.2158i) q^{62} +(2.95829 + 0.498512i) q^{63} +(-7.88161 + 1.37120i) q^{64} +(-6.73427 + 3.88803i) q^{65} +(1.63612 + 0.535959i) q^{66} +(7.40811 + 4.27707i) q^{67} +(13.2333 - 8.68925i) q^{68} +(0.775295 + 0.916874i) q^{69} +(-3.11529 - 1.68128i) q^{70} -6.34514 q^{71} +(-4.82205 + 6.98197i) q^{72} +8.20222 q^{73} +(-3.54826 - 1.91495i) q^{74} +(-2.15777 + 0.388920i) q^{75} +(3.96909 - 2.60619i) q^{76} +(-0.608700 - 0.351433i) q^{77} +(-1.56416 - 7.44681i) q^{78} +(-2.27268 + 1.31214i) q^{79} +(8.04049 - 5.96693i) q^{80} +(1.69715 + 8.83853i) q^{81} +(-4.98660 - 8.09139i) q^{82} +(6.50432 + 11.2658i) q^{83} +(2.51247 - 2.38484i) q^{84} +(-9.90697 + 17.1594i) q^{85} +(5.17515 - 0.148611i) q^{86} +(-3.08692 - 17.1266i) q^{87} +(1.62978 - 1.13841i) q^{88} -1.71842i q^{89} +(1.46341 - 10.5187i) q^{90} +3.10649i q^{91} +(1.38419 - 0.0795635i) q^{92} +(11.2226 - 9.48965i) q^{93} +(0.298601 + 10.3983i) q^{94} +(-2.97142 + 5.14665i) q^{95} +(3.09949 + 9.29479i) q^{96} +(-6.81083 - 11.7967i) q^{97} +(-1.20394 + 0.741971i) q^{98} +(0.350387 - 2.07928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24454 0.671660i −0.880021 0.474935i
\(3\) −0.586217 + 1.62983i −0.338453 + 0.940983i
\(4\) 1.09775 + 1.67181i 0.548873 + 0.835906i
\(5\) −2.16781 1.25159i −0.969474 0.559726i −0.0703980 0.997519i \(-0.522427\pi\)
−0.899076 + 0.437793i \(0.855760\pi\)
\(6\) 1.82426 1.63465i 0.744751 0.667342i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) −0.243298 2.81794i −0.0860189 0.996294i
\(9\) −2.31270 1.91087i −0.770900 0.636957i
\(10\) 1.85728 + 3.01367i 0.587324 + 0.953008i
\(11\) 0.351433 + 0.608700i 0.105961 + 0.183530i 0.914130 0.405420i \(-0.132875\pi\)
−0.808169 + 0.588950i \(0.799541\pi\)
\(12\) −3.36829 + 0.809097i −0.972341 + 0.233566i
\(13\) 1.55324 2.69030i 0.430792 0.746154i −0.566150 0.824302i \(-0.691568\pi\)
0.996942 + 0.0781487i \(0.0249009\pi\)
\(14\) 1.41363 0.0405943i 0.377809 0.0108493i
\(15\) 3.31068 2.79946i 0.854814 0.722818i
\(16\) −1.58991 + 3.67045i −0.397476 + 0.917612i
\(17\) 7.91554i 1.91980i −0.280343 0.959900i \(-0.590448\pi\)
0.280343 0.959900i \(-0.409552\pi\)
\(18\) 1.59479 + 3.93150i 0.375895 + 0.926662i
\(19\) 2.37413i 0.544662i −0.962204 0.272331i \(-0.912205\pi\)
0.962204 0.272331i \(-0.0877945\pi\)
\(20\) −0.287291 4.99809i −0.0642401 1.11761i
\(21\) −0.307237 1.70458i −0.0670445 0.371971i
\(22\) −0.0285324 0.993594i −0.00608312 0.211835i
\(23\) 0.346619 0.600362i 0.0722751 0.125184i −0.827623 0.561284i \(-0.810307\pi\)
0.899898 + 0.436100i \(0.143641\pi\)
\(24\) 4.73540 + 1.25539i 0.966609 + 0.256256i
\(25\) 0.632931 + 1.09627i 0.126586 + 0.219254i
\(26\) −3.74003 + 2.30492i −0.733481 + 0.452033i
\(27\) 4.47014 2.64912i 0.860279 0.509824i
\(28\) −1.78658 0.898958i −0.337632 0.169887i
\(29\) −8.70126 + 5.02368i −1.61578 + 0.932873i −0.627789 + 0.778383i \(0.716040\pi\)
−0.987994 + 0.154490i \(0.950627\pi\)
\(30\) −6.00055 + 1.26039i −1.09555 + 0.230114i
\(31\) −7.34846 4.24264i −1.31982 0.762000i −0.336123 0.941818i \(-0.609116\pi\)
−0.983700 + 0.179818i \(0.942449\pi\)
\(32\) 4.44399 3.50014i 0.785594 0.618743i
\(33\) −1.19809 + 0.215946i −0.208561 + 0.0375914i
\(34\) −5.31655 + 9.85118i −0.911780 + 1.68946i
\(35\) 2.50317 0.423113
\(36\) 0.655856 5.96405i 0.109309 0.994008i
\(37\) 2.85107 0.468712 0.234356 0.972151i \(-0.424702\pi\)
0.234356 + 0.972151i \(0.424702\pi\)
\(38\) −1.59460 + 2.95469i −0.258679 + 0.479314i
\(39\) 3.47419 + 4.10862i 0.556316 + 0.657906i
\(40\) −2.99947 + 6.41327i −0.474258 + 1.01403i
\(41\) 5.82034 + 3.36037i 0.908984 + 0.524802i 0.880104 0.474781i \(-0.157473\pi\)
0.0288798 + 0.999583i \(0.490806\pi\)
\(42\) −0.762533 + 2.32778i −0.117661 + 0.359184i
\(43\) −3.17043 + 1.83045i −0.483485 + 0.279140i −0.721868 0.692031i \(-0.756716\pi\)
0.238383 + 0.971171i \(0.423383\pi\)
\(44\) −0.631847 + 1.25573i −0.0952545 + 0.189308i
\(45\) 2.62187 + 7.03694i 0.390846 + 1.04901i
\(46\) −0.834620 + 0.514363i −0.123058 + 0.0758387i
\(47\) −3.67787 6.37026i −0.536473 0.929198i −0.999091 0.0426400i \(-0.986423\pi\)
0.462618 0.886558i \(-0.346910\pi\)
\(48\) −5.05018 4.74296i −0.728931 0.684587i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −0.0513868 1.78946i −0.00726719 0.253068i
\(51\) 12.9010 + 4.64022i 1.80650 + 0.649761i
\(52\) 6.20273 0.356534i 0.860164 0.0494423i
\(53\) 0.889576i 0.122193i −0.998132 0.0610964i \(-0.980540\pi\)
0.998132 0.0610964i \(-0.0194597\pi\)
\(54\) −7.34256 + 0.294523i −0.999196 + 0.0400795i
\(55\) 1.75939i 0.237237i
\(56\) 1.61967 + 2.31876i 0.216438 + 0.309858i
\(57\) 3.86942 + 1.39175i 0.512518 + 0.184342i
\(58\) 14.2032 0.407865i 1.86498 0.0535553i
\(59\) −3.63052 + 6.28824i −0.472653 + 0.818660i −0.999510 0.0312945i \(-0.990037\pi\)
0.526857 + 0.849954i \(0.323370\pi\)
\(60\) 8.31446 + 2.46173i 1.07339 + 0.317808i
\(61\) −2.39732 4.15228i −0.306946 0.531645i 0.670747 0.741686i \(-0.265974\pi\)
−0.977693 + 0.210041i \(0.932640\pi\)
\(62\) 6.29583 + 10.2158i 0.799571 + 1.29741i
\(63\) 2.95829 + 0.498512i 0.372710 + 0.0628066i
\(64\) −7.88161 + 1.37120i −0.985201 + 0.171400i
\(65\) −6.73427 + 3.88803i −0.835283 + 0.482251i
\(66\) 1.63612 + 0.535959i 0.201392 + 0.0659719i
\(67\) 7.40811 + 4.27707i 0.905044 + 0.522528i 0.878833 0.477129i \(-0.158323\pi\)
0.0262109 + 0.999656i \(0.491656\pi\)
\(68\) 13.2333 8.68925i 1.60477 1.05373i
\(69\) 0.775295 + 0.916874i 0.0933345 + 0.110379i
\(70\) −3.11529 1.68128i −0.372348 0.200951i
\(71\) −6.34514 −0.753030 −0.376515 0.926411i \(-0.622878\pi\)
−0.376515 + 0.926411i \(0.622878\pi\)
\(72\) −4.82205 + 6.98197i −0.568284 + 0.822833i
\(73\) 8.20222 0.959998 0.479999 0.877269i \(-0.340637\pi\)
0.479999 + 0.877269i \(0.340637\pi\)
\(74\) −3.54826 1.91495i −0.412477 0.222608i
\(75\) −2.15777 + 0.388920i −0.249158 + 0.0449086i
\(76\) 3.96909 2.60619i 0.455286 0.298950i
\(77\) −0.608700 0.351433i −0.0693678 0.0400495i
\(78\) −1.56416 7.44681i −0.177107 0.843185i
\(79\) −2.27268 + 1.31214i −0.255697 + 0.147627i −0.622370 0.782723i \(-0.713830\pi\)
0.366673 + 0.930350i \(0.380497\pi\)
\(80\) 8.04049 5.96693i 0.898954 0.667123i
\(81\) 1.69715 + 8.83853i 0.188573 + 0.982059i
\(82\) −4.98660 8.09139i −0.550678 0.893545i
\(83\) 6.50432 + 11.2658i 0.713942 + 1.23658i 0.963366 + 0.268189i \(0.0864252\pi\)
−0.249425 + 0.968394i \(0.580241\pi\)
\(84\) 2.51247 2.38484i 0.274133 0.260208i
\(85\) −9.90697 + 17.1594i −1.07456 + 1.86120i
\(86\) 5.17515 0.148611i 0.558051 0.0160252i
\(87\) −3.08692 17.1266i −0.330952 1.83616i
\(88\) 1.62978 1.13841i 0.173735 0.121355i
\(89\) 1.71842i 0.182152i −0.995844 0.0910760i \(-0.970969\pi\)
0.995844 0.0910760i \(-0.0290306\pi\)
\(90\) 1.46341 10.5187i 0.154257 1.10877i
\(91\) 3.10649i 0.325648i
\(92\) 1.38419 0.0795635i 0.144312 0.00829507i
\(93\) 11.2226 9.48965i 1.16373 0.984031i
\(94\) 0.298601 + 10.3983i 0.0307984 + 1.07250i
\(95\) −2.97142 + 5.14665i −0.304861 + 0.528035i
\(96\) 3.09949 + 9.29479i 0.316340 + 0.948646i
\(97\) −6.81083 11.7967i −0.691535 1.19777i −0.971335 0.237716i \(-0.923601\pi\)
0.279800 0.960058i \(-0.409732\pi\)
\(98\) −1.20394 + 0.741971i −0.121617 + 0.0749504i
\(99\) 0.350387 2.07928i 0.0352153 0.208976i
\(100\) −1.13796 + 2.26157i −0.113796 + 0.226157i
\(101\) 2.23784 1.29202i 0.222673 0.128560i −0.384514 0.923119i \(-0.625631\pi\)
0.607187 + 0.794559i \(0.292298\pi\)
\(102\) −12.9391 14.4400i −1.28116 1.42977i
\(103\) −11.6579 6.73069i −1.14869 0.663195i −0.200120 0.979771i \(-0.564133\pi\)
−0.948567 + 0.316576i \(0.897467\pi\)
\(104\) −7.95900 3.72241i −0.780444 0.365012i
\(105\) −1.46740 + 4.07975i −0.143204 + 0.398142i
\(106\) −0.597493 + 1.10711i −0.0580336 + 0.107532i
\(107\) −17.0371 −1.64703 −0.823517 0.567291i \(-0.807991\pi\)
−0.823517 + 0.567291i \(0.807991\pi\)
\(108\) 9.33592 + 4.56516i 0.898349 + 0.439283i
\(109\) −2.43459 −0.233191 −0.116596 0.993179i \(-0.537198\pi\)
−0.116596 + 0.993179i \(0.537198\pi\)
\(110\) −1.18171 + 2.18963i −0.112672 + 0.208773i
\(111\) −1.67134 + 4.64675i −0.158637 + 0.441050i
\(112\) −0.458326 3.97366i −0.0433078 0.375475i
\(113\) −4.13789 2.38901i −0.389260 0.224739i 0.292580 0.956241i \(-0.405486\pi\)
−0.681839 + 0.731502i \(0.738820\pi\)
\(114\) −3.88086 4.33103i −0.363476 0.405638i
\(115\) −1.50281 + 0.867647i −0.140138 + 0.0809085i
\(116\) −17.9504 9.03215i −1.66665 0.838614i
\(117\) −8.73299 + 3.25380i −0.807365 + 0.300814i
\(118\) 8.74188 5.38748i 0.804755 0.495958i
\(119\) 3.95777 + 6.85506i 0.362808 + 0.628402i
\(120\) −8.69421 8.64820i −0.793669 0.789469i
\(121\) 5.25299 9.09844i 0.477544 0.827131i
\(122\) 0.194635 + 6.77786i 0.0176214 + 0.613638i
\(123\) −8.88882 + 7.51626i −0.801478 + 0.677718i
\(124\) −0.973861 16.9426i −0.0874553 1.52149i
\(125\) 9.34718i 0.836037i
\(126\) −3.34687 2.60738i −0.298163 0.232284i
\(127\) 4.91393i 0.436041i −0.975944 0.218020i \(-0.930040\pi\)
0.975944 0.218020i \(-0.0699599\pi\)
\(128\) 10.7299 + 3.58725i 0.948402 + 0.317071i
\(129\) −1.12476 6.24030i −0.0990296 0.549427i
\(130\) 10.9925 0.315664i 0.964105 0.0276855i
\(131\) 2.61968 4.53741i 0.228882 0.396435i −0.728595 0.684945i \(-0.759826\pi\)
0.957477 + 0.288509i \(0.0931596\pi\)
\(132\) −1.67623 1.76593i −0.145897 0.153705i
\(133\) 1.18706 + 2.05605i 0.102931 + 0.178282i
\(134\) −6.34693 10.2987i −0.548291 0.889672i
\(135\) −13.0060 + 0.148038i −1.11938 + 0.0127411i
\(136\) −22.3055 + 1.92584i −1.91268 + 0.165139i
\(137\) 9.03659 5.21728i 0.772048 0.445742i −0.0615566 0.998104i \(-0.519606\pi\)
0.833605 + 0.552361i \(0.186273\pi\)
\(138\) −0.349056 1.66182i −0.0297137 0.141463i
\(139\) −10.2848 5.93796i −0.872349 0.503651i −0.00422072 0.999991i \(-0.501344\pi\)
−0.868128 + 0.496340i \(0.834677\pi\)
\(140\) 2.74785 + 4.18483i 0.232235 + 0.353683i
\(141\) 12.5385 2.25995i 1.05593 0.190322i
\(142\) 7.89677 + 4.26178i 0.662682 + 0.357640i
\(143\) 2.18344 0.182589
\(144\) 10.6907 5.45054i 0.890894 0.454212i
\(145\) 25.1502 2.08861
\(146\) −10.2080 5.50910i −0.844818 0.455937i
\(147\) 1.11837 + 1.32259i 0.0922413 + 0.109086i
\(148\) 3.12975 + 4.76644i 0.257264 + 0.391799i
\(149\) 15.3300 + 8.85079i 1.25588 + 0.725085i 0.972272 0.233854i \(-0.0751337\pi\)
0.283612 + 0.958939i \(0.408467\pi\)
\(150\) 2.94665 + 0.965262i 0.240593 + 0.0788133i
\(151\) 18.1796 10.4960i 1.47944 0.854152i 0.479706 0.877429i \(-0.340743\pi\)
0.999729 + 0.0232767i \(0.00740988\pi\)
\(152\) −6.69015 + 0.577621i −0.542643 + 0.0468512i
\(153\) −15.1256 + 18.3063i −1.22283 + 1.47997i
\(154\) 0.521507 + 0.846211i 0.0420242 + 0.0681896i
\(155\) 10.6200 + 18.3945i 0.853022 + 1.47748i
\(156\) −3.05506 + 10.3184i −0.244600 + 0.826134i
\(157\) −0.841990 + 1.45837i −0.0671981 + 0.116391i −0.897667 0.440675i \(-0.854739\pi\)
0.830469 + 0.557065i \(0.188073\pi\)
\(158\) 3.70975 0.106530i 0.295132 0.00847510i
\(159\) 1.44986 + 0.521485i 0.114981 + 0.0413564i
\(160\) −14.0144 + 2.02560i −1.10794 + 0.160137i
\(161\) 0.693239i 0.0546349i
\(162\) 3.82431 12.1398i 0.300467 0.953792i
\(163\) 14.9299i 1.16940i −0.811249 0.584700i \(-0.801212\pi\)
0.811249 0.584700i \(-0.198788\pi\)
\(164\) 0.771345 + 13.4193i 0.0602319 + 1.04787i
\(165\) 2.86752 + 1.03139i 0.223236 + 0.0802934i
\(166\) −0.528076 18.3894i −0.0409867 1.42729i
\(167\) −1.17066 + 2.02764i −0.0905885 + 0.156904i −0.907759 0.419492i \(-0.862208\pi\)
0.817170 + 0.576396i \(0.195541\pi\)
\(168\) −4.72867 + 1.28050i −0.364825 + 0.0987926i
\(169\) 1.67487 + 2.90097i 0.128836 + 0.223151i
\(170\) 23.8549 14.7014i 1.82958 1.12754i
\(171\) −4.53665 + 5.49064i −0.346926 + 0.419880i
\(172\) −6.54048 3.29099i −0.498707 0.250935i
\(173\) 0.875908 0.505706i 0.0665940 0.0384481i −0.466333 0.884609i \(-0.654425\pi\)
0.532927 + 0.846161i \(0.321092\pi\)
\(174\) −7.66143 + 23.3880i −0.580812 + 1.77304i
\(175\) −1.09627 0.632931i −0.0828702 0.0478451i
\(176\) −2.79295 + 0.322142i −0.210526 + 0.0242824i
\(177\) −8.12050 9.60341i −0.610374 0.721836i
\(178\) −1.15419 + 2.13864i −0.0865104 + 0.160298i
\(179\) 11.8651 0.886837 0.443419 0.896315i \(-0.353765\pi\)
0.443419 + 0.896315i \(0.353765\pi\)
\(180\) −8.88628 + 12.1081i −0.662344 + 0.902481i
\(181\) −11.7216 −0.871262 −0.435631 0.900125i \(-0.643475\pi\)
−0.435631 + 0.900125i \(0.643475\pi\)
\(182\) 2.08650 3.86614i 0.154662 0.286577i
\(183\) 8.17287 1.47309i 0.604156 0.108894i
\(184\) −1.77612 0.830687i −0.130937 0.0612390i
\(185\) −6.18057 3.56835i −0.454404 0.262350i
\(186\) −20.3407 + 4.27247i −1.49145 + 0.313273i
\(187\) 4.81819 2.78178i 0.352341 0.203424i
\(188\) 6.61250 13.1416i 0.482266 0.958452i
\(189\) −2.54669 + 4.52928i −0.185245 + 0.329457i
\(190\) 7.15484 4.40942i 0.519067 0.319893i
\(191\) −3.38132 5.85662i −0.244664 0.423770i 0.717373 0.696689i \(-0.245344\pi\)
−0.962037 + 0.272919i \(0.912011\pi\)
\(192\) 2.38551 13.6495i 0.172159 0.985069i
\(193\) −1.38307 + 2.39554i −0.0995553 + 0.172435i −0.911501 0.411299i \(-0.865075\pi\)
0.811945 + 0.583733i \(0.198409\pi\)
\(194\) 0.552962 + 19.2560i 0.0397003 + 1.38250i
\(195\) −2.38909 13.2550i −0.171086 0.949207i
\(196\) 1.99670 0.114771i 0.142622 0.00819791i
\(197\) 17.2636i 1.22998i −0.788536 0.614989i \(-0.789161\pi\)
0.788536 0.614989i \(-0.210839\pi\)
\(198\) −1.83264 + 2.35240i −0.130240 + 0.167178i
\(199\) 14.4922i 1.02732i 0.857993 + 0.513662i \(0.171711\pi\)
−0.857993 + 0.513662i \(0.828289\pi\)
\(200\) 2.93523 2.05029i 0.207552 0.144977i
\(201\) −11.3137 + 9.56667i −0.798004 + 0.674781i
\(202\) −3.65287 + 0.104897i −0.257015 + 0.00738052i
\(203\) 5.02368 8.70126i 0.352593 0.610709i
\(204\) 6.40444 + 26.6618i 0.448400 + 1.86670i
\(205\) −8.41159 14.5693i −0.587491 1.01756i
\(206\) 9.98796 + 16.2067i 0.695894 + 1.12918i
\(207\) −1.94884 + 0.726113i −0.135454 + 0.0504683i
\(208\) 7.40509 + 9.97842i 0.513450 + 0.691879i
\(209\) 1.44513 0.834347i 0.0999618 0.0577130i
\(210\) 4.56644 4.09180i 0.315114 0.282361i
\(211\) 22.1795 + 12.8053i 1.52690 + 0.881555i 0.999490 + 0.0319420i \(0.0101692\pi\)
0.527407 + 0.849612i \(0.323164\pi\)
\(212\) 1.48720 0.976529i 0.102142 0.0670683i
\(213\) 3.71963 10.3415i 0.254865 0.708589i
\(214\) 21.2033 + 11.4431i 1.44942 + 0.782235i
\(215\) 9.16384 0.624968
\(216\) −8.55266 11.9521i −0.581935 0.813235i
\(217\) 8.48527 0.576018
\(218\) 3.02994 + 1.63522i 0.205213 + 0.110751i
\(219\) −4.80828 + 13.3682i −0.324914 + 0.903342i
\(220\) 2.94138 1.93137i 0.198307 0.130213i
\(221\) −21.2951 12.2948i −1.43247 0.827035i
\(222\) 5.20109 4.66049i 0.349074 0.312791i
\(223\) 13.2137 7.62891i 0.884853 0.510870i 0.0125973 0.999921i \(-0.495990\pi\)
0.872255 + 0.489051i \(0.162657\pi\)
\(224\) −2.09854 + 5.25320i −0.140215 + 0.350994i
\(225\) 0.631048 3.74479i 0.0420699 0.249653i
\(226\) 3.54515 + 5.75247i 0.235820 + 0.382648i
\(227\) −3.88279 6.72519i −0.257710 0.446367i 0.707918 0.706295i \(-0.249635\pi\)
−0.965628 + 0.259928i \(0.916301\pi\)
\(228\) 1.92090 + 7.99674i 0.127215 + 0.529597i
\(229\) −5.70048 + 9.87351i −0.376698 + 0.652460i −0.990580 0.136938i \(-0.956274\pi\)
0.613882 + 0.789398i \(0.289607\pi\)
\(230\) 2.45307 0.0704431i 0.161750 0.00464488i
\(231\) 0.929607 0.786062i 0.0611637 0.0517191i
\(232\) 16.2734 + 23.2974i 1.06840 + 1.52955i
\(233\) 19.4113i 1.27167i 0.771824 + 0.635837i \(0.219345\pi\)
−0.771824 + 0.635837i \(0.780655\pi\)
\(234\) 13.0540 + 1.81612i 0.853365 + 0.118724i
\(235\) 18.4127i 1.20111i
\(236\) −14.4981 + 0.833354i −0.943749 + 0.0542467i
\(237\) −0.806272 4.47329i −0.0523730 0.290571i
\(238\) −0.321326 11.1896i −0.0208284 0.725317i
\(239\) 3.57434 6.19093i 0.231205 0.400458i −0.726958 0.686682i \(-0.759067\pi\)
0.958163 + 0.286224i \(0.0924000\pi\)
\(240\) 5.01162 + 16.6026i 0.323499 + 1.07169i
\(241\) −1.19735 2.07386i −0.0771279 0.133589i 0.824882 0.565305i \(-0.191242\pi\)
−0.902010 + 0.431716i \(0.857908\pi\)
\(242\) −12.6486 + 7.79513i −0.813083 + 0.501090i
\(243\) −15.4002 2.41522i −0.987924 0.154937i
\(244\) 4.31018 8.56602i 0.275931 0.548383i
\(245\) −2.16781 + 1.25159i −0.138496 + 0.0799609i
\(246\) 16.1108 3.38400i 1.02719 0.215756i
\(247\) −6.38710 3.68759i −0.406401 0.234636i
\(248\) −10.1676 + 21.7398i −0.645646 + 1.38048i
\(249\) −22.1743 + 3.99673i −1.40524 + 0.253283i
\(250\) 6.27813 11.6329i 0.397064 0.735730i
\(251\) 3.05973 0.193129 0.0965644 0.995327i \(-0.469215\pi\)
0.0965644 + 0.995327i \(0.469215\pi\)
\(252\) 2.41404 + 5.49294i 0.152070 + 0.346023i
\(253\) 0.487254 0.0306334
\(254\) −3.30049 + 6.11557i −0.207091 + 0.383725i
\(255\) −22.1593 26.2058i −1.38767 1.64107i
\(256\) −10.9444 11.6713i −0.684025 0.729459i
\(257\) 17.1928 + 9.92624i 1.07245 + 0.619182i 0.928851 0.370453i \(-0.120798\pi\)
0.143603 + 0.989635i \(0.454131\pi\)
\(258\) −2.79155 + 8.52174i −0.173794 + 0.530540i
\(259\) −2.46909 + 1.42553i −0.153422 + 0.0885783i
\(260\) −13.8926 6.99035i −0.861581 0.433523i
\(261\) 29.7230 + 5.00873i 1.83981 + 0.310032i
\(262\) −6.30788 + 3.88745i −0.389702 + 0.240167i
\(263\) −9.51239 16.4759i −0.586559 1.01595i −0.994679 0.103022i \(-0.967149\pi\)
0.408120 0.912928i \(-0.366184\pi\)
\(264\) 0.900019 + 3.32362i 0.0553923 + 0.204555i
\(265\) −1.11338 + 1.92843i −0.0683944 + 0.118463i
\(266\) −0.0963760 3.35614i −0.00590919 0.205778i
\(267\) 2.80073 + 1.00737i 0.171402 + 0.0616498i
\(268\) 0.981765 + 17.0801i 0.0599708 + 1.04333i
\(269\) 27.0790i 1.65103i −0.564378 0.825517i \(-0.690884\pi\)
0.564378 0.825517i \(-0.309116\pi\)
\(270\) 16.2859 + 8.55138i 0.991128 + 0.520420i
\(271\) 29.1249i 1.76921i 0.466337 + 0.884607i \(0.345573\pi\)
−0.466337 + 0.884607i \(0.654427\pi\)
\(272\) 29.0536 + 12.5850i 1.76163 + 0.763075i
\(273\) −5.06305 1.82107i −0.306430 0.110216i
\(274\) −14.7506 + 0.423583i −0.891117 + 0.0255896i
\(275\) −0.444866 + 0.770531i −0.0268264 + 0.0464648i
\(276\) −0.681762 + 2.30264i −0.0410373 + 0.138603i
\(277\) 8.22279 + 14.2423i 0.494060 + 0.855737i 0.999977 0.00684565i \(-0.00217905\pi\)
−0.505917 + 0.862582i \(0.668846\pi\)
\(278\) 8.81158 + 14.2979i 0.528484 + 0.857532i
\(279\) 8.88766 + 23.8539i 0.532090 + 1.42810i
\(280\) −0.609017 7.05379i −0.0363957 0.421545i
\(281\) 5.47490 3.16093i 0.326605 0.188566i −0.327728 0.944772i \(-0.606283\pi\)
0.654333 + 0.756207i \(0.272950\pi\)
\(282\) −17.1225 5.60899i −1.01963 0.334011i
\(283\) −7.14839 4.12712i −0.424927 0.245332i 0.272256 0.962225i \(-0.412230\pi\)
−0.697183 + 0.716893i \(0.745564\pi\)
\(284\) −6.96536 10.6079i −0.413318 0.629462i
\(285\) −6.64628 7.85997i −0.393691 0.465584i
\(286\) −2.71738 1.46653i −0.160682 0.0867178i
\(287\) −6.72075 −0.396713
\(288\) −16.9659 0.397124i −0.999726 0.0234007i
\(289\) −45.6557 −2.68563
\(290\) −31.3004 16.8924i −1.83802 0.991956i
\(291\) 23.2193 4.18508i 1.36114 0.245333i
\(292\) 9.00396 + 13.7126i 0.526917 + 0.802467i
\(293\) 6.70404 + 3.87058i 0.391654 + 0.226122i 0.682877 0.730534i \(-0.260729\pi\)
−0.291222 + 0.956655i \(0.594062\pi\)
\(294\) −0.503516 2.39718i −0.0293656 0.139806i
\(295\) 15.7405 9.08781i 0.916450 0.529113i
\(296\) −0.693659 8.03414i −0.0403181 0.466975i
\(297\) 3.18348 + 1.78998i 0.184724 + 0.103865i
\(298\) −13.1341 21.3117i −0.760836 1.23455i
\(299\) −1.07677 1.86502i −0.0622711 0.107857i
\(300\) −3.01888 3.18045i −0.174295 0.183623i
\(301\) 1.83045 3.17043i 0.105505 0.182740i
\(302\) −29.6749 + 0.852155i −1.70760 + 0.0490360i
\(303\) 0.793909 + 4.40470i 0.0456089 + 0.253043i
\(304\) 8.71411 + 3.77464i 0.499788 + 0.216490i
\(305\) 12.0018i 0.687222i
\(306\) 31.1199 12.6236i 1.77901 0.721643i
\(307\) 14.7032i 0.839154i 0.907720 + 0.419577i \(0.137822\pi\)
−0.907720 + 0.419577i \(0.862178\pi\)
\(308\) −0.0806685 1.40342i −0.00459651 0.0799671i
\(309\) 17.8040 15.0548i 1.01283 0.856436i
\(310\) −0.862226 30.0256i −0.0489712 1.70534i
\(311\) 6.26710 10.8549i 0.355375 0.615527i −0.631807 0.775125i \(-0.717687\pi\)
0.987182 + 0.159599i \(0.0510200\pi\)
\(312\) 10.7326 10.7897i 0.607614 0.610846i
\(313\) −11.6110 20.1108i −0.656292 1.13673i −0.981568 0.191112i \(-0.938790\pi\)
0.325276 0.945619i \(-0.394543\pi\)
\(314\) 2.02742 1.24946i 0.114414 0.0705113i
\(315\) −5.78908 4.78323i −0.326178 0.269505i
\(316\) −4.68847 2.35911i −0.263747 0.132710i
\(317\) 5.93134 3.42446i 0.333137 0.192337i −0.324096 0.946024i \(-0.605060\pi\)
0.657233 + 0.753687i \(0.271727\pi\)
\(318\) −1.45414 1.62282i −0.0815443 0.0910032i
\(319\) −6.11582 3.53097i −0.342420 0.197697i
\(320\) 18.8020 + 6.89201i 1.05106 + 0.385275i
\(321\) 9.98741 27.7675i 0.557443 1.54983i
\(322\) 0.465620 0.862761i 0.0259480 0.0480798i
\(323\) −18.7925 −1.04564
\(324\) −12.9133 + 12.5398i −0.717406 + 0.696655i
\(325\) 3.93239 0.218129
\(326\) −10.0278 + 18.5808i −0.555389 + 1.02910i
\(327\) 1.42720 3.96797i 0.0789242 0.219429i
\(328\) 8.05326 17.2190i 0.444667 0.950758i
\(329\) 6.37026 + 3.67787i 0.351204 + 0.202768i
\(330\) −2.87599 3.20959i −0.158318 0.176682i
\(331\) 6.98234 4.03126i 0.383784 0.221578i −0.295679 0.955287i \(-0.595546\pi\)
0.679463 + 0.733709i \(0.262213\pi\)
\(332\) −11.6942 + 23.2410i −0.641803 + 1.27552i
\(333\) −6.59366 5.44801i −0.361330 0.298549i
\(334\) 2.81882 1.73719i 0.154239 0.0950550i
\(335\) −10.7062 18.5438i −0.584944 1.01315i
\(336\) 6.74507 + 1.58243i 0.367974 + 0.0863286i
\(337\) −8.08375 + 14.0015i −0.440350 + 0.762708i −0.997715 0.0675590i \(-0.978479\pi\)
0.557365 + 0.830267i \(0.311812\pi\)
\(338\) −0.135981 4.73530i −0.00739637 0.257567i
\(339\) 6.31939 5.34358i 0.343222 0.290223i
\(340\) −39.5626 + 2.27406i −2.14558 + 0.123328i
\(341\) 5.96401i 0.322969i
\(342\) 9.33387 3.78622i 0.504718 0.204736i
\(343\) 1.00000i 0.0539949i
\(344\) 5.92945 + 8.48873i 0.319695 + 0.457682i
\(345\) −0.533146 2.95795i −0.0287036 0.159251i
\(346\) −1.42976 + 0.0410575i −0.0768645 + 0.00220727i
\(347\) 3.82900 6.63203i 0.205552 0.356026i −0.744757 0.667336i \(-0.767434\pi\)
0.950308 + 0.311310i \(0.100768\pi\)
\(348\) 25.2437 23.9614i 1.35321 1.28446i
\(349\) 4.40927 + 7.63708i 0.236023 + 0.408803i 0.959569 0.281472i \(-0.0908227\pi\)
−0.723547 + 0.690275i \(0.757489\pi\)
\(350\) 0.939234 + 1.52403i 0.0502042 + 0.0814627i
\(351\) −0.183718 16.1407i −0.00980613 0.861528i
\(352\) 3.69230 + 1.47499i 0.196800 + 0.0786174i
\(353\) −2.81435 + 1.62487i −0.149793 + 0.0864830i −0.573023 0.819539i \(-0.694229\pi\)
0.423230 + 0.906022i \(0.360896\pi\)
\(354\) 3.65605 + 17.4060i 0.194317 + 0.925119i
\(355\) 13.7551 + 7.94149i 0.730043 + 0.421490i
\(356\) 2.87287 1.88639i 0.152262 0.0999783i
\(357\) −13.4927 + 2.43194i −0.714109 + 0.128712i
\(358\) −14.7665 7.96929i −0.780435 0.421190i
\(359\) 28.4033 1.49907 0.749533 0.661967i \(-0.230278\pi\)
0.749533 + 0.661967i \(0.230278\pi\)
\(360\) 19.1918 9.10037i 1.01150 0.479632i
\(361\) 13.3635 0.703343
\(362\) 14.5880 + 7.87295i 0.766729 + 0.413793i
\(363\) 11.7495 + 13.8951i 0.616691 + 0.729306i
\(364\) −5.19346 + 3.41013i −0.272211 + 0.178740i
\(365\) −17.7809 10.2658i −0.930692 0.537336i
\(366\) −11.1609 3.65607i −0.583387 0.191106i
\(367\) −4.00164 + 2.31035i −0.208884 + 0.120599i −0.600793 0.799405i \(-0.705148\pi\)
0.391909 + 0.920004i \(0.371815\pi\)
\(368\) 1.65251 + 2.22677i 0.0861429 + 0.116078i
\(369\) −7.03945 18.8934i −0.366459 0.983553i
\(370\) 5.29523 + 8.59218i 0.275286 + 0.446686i
\(371\) 0.444788 + 0.770396i 0.0230923 + 0.0399970i
\(372\) 28.1844 + 8.34480i 1.46130 + 0.432658i
\(373\) −13.7859 + 23.8779i −0.713808 + 1.23635i 0.249609 + 0.968347i \(0.419698\pi\)
−0.963417 + 0.268005i \(0.913636\pi\)
\(374\) −7.86483 + 0.225849i −0.406681 + 0.0116784i
\(375\) −15.2343 5.47948i −0.786697 0.282959i
\(376\) −17.0562 + 11.9139i −0.879607 + 0.614413i
\(377\) 31.2120i 1.60750i
\(378\) 6.21159 3.92635i 0.319490 0.201949i
\(379\) 20.5766i 1.05695i 0.848949 + 0.528475i \(0.177236\pi\)
−0.848949 + 0.528475i \(0.822764\pi\)
\(380\) −11.8661 + 0.682064i −0.608718 + 0.0349892i
\(381\) 8.00888 + 2.88063i 0.410307 + 0.147579i
\(382\) 0.274525 + 9.55988i 0.0140459 + 0.489126i
\(383\) 0.0457558 0.0792514i 0.00233801 0.00404955i −0.864854 0.502023i \(-0.832589\pi\)
0.867192 + 0.497974i \(0.165922\pi\)
\(384\) −12.1367 + 15.3851i −0.619348 + 0.785117i
\(385\) 0.879697 + 1.52368i 0.0448335 + 0.0776539i
\(386\) 3.33027 2.05239i 0.169506 0.104464i
\(387\) 10.8300 + 1.82500i 0.550519 + 0.0927699i
\(388\) 12.2453 24.3362i 0.621661 1.23548i
\(389\) −1.65481 + 0.955404i −0.0839021 + 0.0484409i −0.541364 0.840788i \(-0.682092\pi\)
0.457462 + 0.889229i \(0.348759\pi\)
\(390\) −5.92950 + 18.1009i −0.300252 + 0.916577i
\(391\) −4.75219 2.74368i −0.240329 0.138754i
\(392\) −2.56206 1.19827i −0.129404 0.0605217i
\(393\) 5.85951 + 6.92954i 0.295573 + 0.349549i
\(394\) −11.5952 + 21.4851i −0.584160 + 1.08241i
\(395\) 6.56900 0.330522
\(396\) 3.86081 1.69674i 0.194013 0.0852646i
\(397\) 30.4353 1.52750 0.763751 0.645511i \(-0.223355\pi\)
0.763751 + 0.645511i \(0.223355\pi\)
\(398\) 9.73382 18.0361i 0.487912 0.904066i
\(399\) −4.04690 + 0.729419i −0.202598 + 0.0365166i
\(400\) −5.03010 + 0.580178i −0.251505 + 0.0290089i
\(401\) 18.9221 + 10.9247i 0.944922 + 0.545551i 0.891500 0.453021i \(-0.149654\pi\)
0.0534223 + 0.998572i \(0.482987\pi\)
\(402\) 20.5058 4.30715i 1.02274 0.214821i
\(403\) −22.8279 + 13.1797i −1.13714 + 0.656527i
\(404\) 4.61658 + 2.32294i 0.229684 + 0.115570i
\(405\) 7.38307 21.2844i 0.366868 1.05763i
\(406\) −12.0964 + 7.45484i −0.600336 + 0.369978i
\(407\) 1.00196 + 1.73544i 0.0496653 + 0.0860228i
\(408\) 9.93710 37.4832i 0.491960 1.85570i
\(409\) 2.23786 3.87609i 0.110655 0.191660i −0.805379 0.592760i \(-0.798038\pi\)
0.916035 + 0.401099i \(0.131372\pi\)
\(410\) 0.682925 + 23.7818i 0.0337273 + 1.17450i
\(411\) 3.20588 + 17.7866i 0.158134 + 0.877347i
\(412\) −1.54497 26.8784i −0.0761154 1.32420i
\(413\) 7.26104i 0.357292i
\(414\) 2.91311 + 0.405283i 0.143171 + 0.0199186i
\(415\) 32.5628i 1.59845i
\(416\) −2.51381 17.3922i −0.123249 0.852723i
\(417\) 15.7070 13.2816i 0.769176 0.650404i
\(418\) −2.35892 + 0.0677394i −0.115378 + 0.00331324i
\(419\) 11.4022 19.7492i 0.557033 0.964809i −0.440709 0.897650i \(-0.645273\pi\)
0.997742 0.0671595i \(-0.0213936\pi\)
\(420\) −8.43140 + 2.02531i −0.411410 + 0.0988249i
\(421\) −14.0510 24.3370i −0.684803 1.18611i −0.973499 0.228693i \(-0.926555\pi\)
0.288696 0.957421i \(-0.406778\pi\)
\(422\) −19.0024 30.8337i −0.925020 1.50096i
\(423\) −3.66693 + 21.7604i −0.178292 + 1.05803i
\(424\) −2.50678 + 0.216432i −0.121740 + 0.0105109i
\(425\) 8.67756 5.00999i 0.420924 0.243020i
\(426\) −11.5752 + 10.3721i −0.560820 + 0.502528i
\(427\) 4.15228 + 2.39732i 0.200943 + 0.116015i
\(428\) −18.7024 28.4827i −0.904013 1.37677i
\(429\) −1.27997 + 3.55865i −0.0617976 + 0.171813i
\(430\) −11.4047 6.15498i −0.549985 0.296819i
\(431\) 0.610755 0.0294190 0.0147095 0.999892i \(-0.495318\pi\)
0.0147095 + 0.999892i \(0.495318\pi\)
\(432\) 2.61638 + 20.6193i 0.125881 + 0.992045i
\(433\) 10.5169 0.505410 0.252705 0.967543i \(-0.418680\pi\)
0.252705 + 0.967543i \(0.418680\pi\)
\(434\) −10.5602 5.69922i −0.506908 0.273571i
\(435\) −14.7435 + 40.9906i −0.706897 + 1.96535i
\(436\) −2.67256 4.07017i −0.127993 0.194926i
\(437\) −1.42534 0.822918i −0.0681830 0.0393655i
\(438\) 14.9630 13.4077i 0.714960 0.640647i
\(439\) −32.6334 + 18.8409i −1.55751 + 0.899227i −0.560012 + 0.828485i \(0.689203\pi\)
−0.997495 + 0.0707423i \(0.977463\pi\)
\(440\) −4.95787 + 0.428057i −0.236357 + 0.0204068i
\(441\) −2.81121 + 1.04742i −0.133867 + 0.0498772i
\(442\) 18.2447 + 29.6044i 0.867812 + 1.40814i
\(443\) −20.7455 35.9322i −0.985647 1.70719i −0.639025 0.769186i \(-0.720662\pi\)
−0.346622 0.938005i \(-0.612671\pi\)
\(444\) −9.60321 + 2.30679i −0.455748 + 0.109475i
\(445\) −2.15075 + 3.72520i −0.101955 + 0.176592i
\(446\) −21.5689 + 0.619381i −1.02132 + 0.0293285i
\(447\) −23.4120 + 19.7969i −1.10735 + 0.936359i
\(448\) 6.14008 5.12830i 0.290091 0.242289i
\(449\) 31.9656i 1.50855i 0.656559 + 0.754275i \(0.272011\pi\)
−0.656559 + 0.754275i \(0.727989\pi\)
\(450\) −3.30059 + 4.23668i −0.155591 + 0.199719i
\(451\) 4.72379i 0.222434i
\(452\) −0.548377 9.54030i −0.0257935 0.448738i
\(453\) 6.44951 + 35.7826i 0.303025 + 1.68121i
\(454\) 0.315238 + 10.9777i 0.0147949 + 0.515208i
\(455\) 3.88803 6.73427i 0.182274 0.315707i
\(456\) 2.98046 11.2424i 0.139573 0.526475i
\(457\) −14.8515 25.7236i −0.694724 1.20330i −0.970274 0.242011i \(-0.922193\pi\)
0.275549 0.961287i \(-0.411140\pi\)
\(458\) 13.7261 8.45918i 0.641378 0.395271i
\(459\) −20.9692 35.3835i −0.978761 1.65156i
\(460\) −3.10025 1.55996i −0.144550 0.0727333i
\(461\) −8.96753 + 5.17741i −0.417659 + 0.241136i −0.694075 0.719902i \(-0.744187\pi\)
0.276416 + 0.961038i \(0.410853\pi\)
\(462\) −1.68490 + 0.353904i −0.0783885 + 0.0164651i
\(463\) −13.7219 7.92236i −0.637712 0.368183i 0.146021 0.989282i \(-0.453353\pi\)
−0.783733 + 0.621098i \(0.786687\pi\)
\(464\) −4.60497 39.9247i −0.213780 1.85346i
\(465\) −36.2055 + 6.52573i −1.67899 + 0.302624i
\(466\) 13.0378 24.1580i 0.603963 1.11910i
\(467\) 27.9844 1.29496 0.647481 0.762081i \(-0.275822\pi\)
0.647481 + 0.762081i \(0.275822\pi\)
\(468\) −15.0263 11.0281i −0.694593 0.509772i
\(469\) −8.55414 −0.394994
\(470\) 12.3671 22.9153i 0.570450 1.05700i
\(471\) −1.88331 2.22722i −0.0867782 0.102625i
\(472\) 18.6032 + 8.70068i 0.856282 + 0.400481i
\(473\) −2.22839 1.28656i −0.102461 0.0591560i
\(474\) −2.00109 + 6.10871i −0.0919132 + 0.280583i
\(475\) 2.60268 1.50266i 0.119419 0.0689467i
\(476\) −7.11573 + 14.1418i −0.326149 + 0.648186i
\(477\) −1.69986 + 2.05732i −0.0778314 + 0.0941983i
\(478\) −8.60659 + 5.30411i −0.393656 + 0.242604i
\(479\) −11.5844 20.0648i −0.529306 0.916785i −0.999416 0.0341768i \(-0.989119\pi\)
0.470110 0.882608i \(-0.344214\pi\)
\(480\) 4.91413 24.0286i 0.224298 1.09675i
\(481\) 4.42840 7.67021i 0.201918 0.349731i
\(482\) 0.0972109 + 3.38521i 0.00442783 + 0.154192i
\(483\) −1.12986 0.406388i −0.0514105 0.0184913i
\(484\) 20.9773 1.20578i 0.953515 0.0548081i
\(485\) 34.0973i 1.54828i
\(486\) 17.5439 + 13.3495i 0.795809 + 0.605547i
\(487\) 13.8456i 0.627406i 0.949521 + 0.313703i \(0.101570\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(488\) −11.1176 + 7.76576i −0.503272 + 0.351539i
\(489\) 24.3332 + 8.75216i 1.10039 + 0.395787i
\(490\) 3.53856 0.101614i 0.159856 0.00459047i
\(491\) −1.97999 + 3.42944i −0.0893557 + 0.154769i −0.907239 0.420616i \(-0.861814\pi\)
0.817883 + 0.575384i \(0.195147\pi\)
\(492\) −22.3234 6.60948i −1.00642 0.297979i
\(493\) 39.7651 + 68.8752i 1.79093 + 3.10198i
\(494\) 5.47218 + 8.87931i 0.246205 + 0.399499i
\(495\) −3.36197 + 4.06895i −0.151109 + 0.182886i
\(496\) 27.2557 20.2268i 1.22382 0.908209i
\(497\) 5.49505 3.17257i 0.246487 0.142309i
\(498\) 30.2812 + 9.91951i 1.35693 + 0.444504i
\(499\) 18.6834 + 10.7868i 0.836382 + 0.482886i 0.856033 0.516921i \(-0.172922\pi\)
−0.0196506 + 0.999807i \(0.506255\pi\)
\(500\) −15.6267 + 10.2608i −0.698848 + 0.458879i
\(501\) −2.61846 3.09662i −0.116984 0.138347i
\(502\) −3.80795 2.05510i −0.169957 0.0917236i
\(503\) −24.7621 −1.10409 −0.552044 0.833815i \(-0.686152\pi\)
−0.552044 + 0.833815i \(0.686152\pi\)
\(504\) 0.685032 8.45758i 0.0305138 0.376731i
\(505\) −6.46827 −0.287834
\(506\) −0.606406 0.327269i −0.0269580 0.0145489i
\(507\) −5.70992 + 1.02916i −0.253587 + 0.0457068i
\(508\) 8.21516 5.39425i 0.364489 0.239331i
\(509\) −22.5133 12.9980i −0.997882 0.576128i −0.0902614 0.995918i \(-0.528770\pi\)
−0.907621 + 0.419790i \(0.862104\pi\)
\(510\) 9.97663 + 47.4976i 0.441773 + 2.10323i
\(511\) −7.10333 + 4.10111i −0.314233 + 0.181422i
\(512\) 5.78155 + 21.8763i 0.255511 + 0.966806i
\(513\) −6.28936 10.6127i −0.277682 0.468561i
\(514\) −14.7300 23.9013i −0.649711 1.05424i
\(515\) 16.8481 + 29.1817i 0.742415 + 1.28590i
\(516\) 9.19790 8.73065i 0.404915 0.384345i
\(517\) 2.58505 4.47744i 0.113690 0.196918i
\(518\) 4.03035 0.115737i 0.177084 0.00508519i
\(519\) 0.310743 + 1.72404i 0.0136401 + 0.0756767i
\(520\) 12.5947 + 18.0308i 0.552314 + 0.790705i
\(521\) 16.4772i 0.721880i −0.932589 0.360940i \(-0.882456\pi\)
0.932589 0.360940i \(-0.117544\pi\)
\(522\) −33.6272 26.1973i −1.47182 1.14662i
\(523\) 35.6352i 1.55822i −0.626888 0.779110i \(-0.715671\pi\)
0.626888 0.779110i \(-0.284329\pi\)
\(524\) 10.4614 0.601324i 0.457010 0.0262690i
\(525\) 1.67422 1.41570i 0.0730691 0.0617862i
\(526\) 0.772297 + 26.8940i 0.0336738 + 1.17263i
\(527\) −33.5827 + 58.1670i −1.46289 + 2.53380i
\(528\) 1.11224 4.74088i 0.0484039 0.206320i
\(529\) 11.2597 + 19.5024i 0.489553 + 0.847930i
\(530\) 2.68089 1.65219i 0.116451 0.0717667i
\(531\) 20.4123 7.60537i 0.885819 0.330045i
\(532\) −2.13424 + 4.24157i −0.0925310 + 0.183895i
\(533\) 18.0808 10.4390i 0.783166 0.452161i
\(534\) −2.80901 3.13484i −0.121558 0.135658i
\(535\) 36.9331 + 21.3233i 1.59676 + 0.921888i
\(536\) 10.2502 21.9162i 0.442740 0.946637i
\(537\) −6.95551 + 19.3381i −0.300152 + 0.834499i
\(538\) −18.1878 + 33.7008i −0.784134 + 1.45294i
\(539\) 0.702866 0.0302746
\(540\) −14.5248 21.5811i −0.625048 0.928702i
\(541\) 16.0235 0.688903 0.344452 0.938804i \(-0.388065\pi\)
0.344452 + 0.938804i \(0.388065\pi\)
\(542\) 19.5621 36.2471i 0.840262 1.55695i
\(543\) 6.87142 19.1043i 0.294881 0.819843i
\(544\) −27.7055 35.1766i −1.18786 1.50818i
\(545\) 5.27773 + 3.04710i 0.226073 + 0.130523i
\(546\) 5.07801 + 5.66704i 0.217319 + 0.242527i
\(547\) 9.75181 5.63021i 0.416957 0.240730i −0.276817 0.960923i \(-0.589280\pi\)
0.693775 + 0.720192i \(0.255946\pi\)
\(548\) 18.6422 + 9.38023i 0.796355 + 0.400703i
\(549\) −2.39019 + 14.1840i −0.102011 + 0.605356i
\(550\) 1.07119 0.660156i 0.0456756 0.0281491i
\(551\) 11.9268 + 20.6579i 0.508100 + 0.880056i
\(552\) 2.39507 2.40781i 0.101941 0.102483i
\(553\) 1.31214 2.27268i 0.0557977 0.0966444i
\(554\) −0.667597 23.2480i −0.0283635 0.987712i
\(555\) 9.43896 7.98145i 0.400662 0.338794i
\(556\) −1.36301 23.7127i −0.0578044 1.00564i
\(557\) 25.2666i 1.07058i −0.844669 0.535289i \(-0.820203\pi\)
0.844669 0.535289i \(-0.179797\pi\)
\(558\) 4.96068 35.6565i 0.210002 1.50946i
\(559\) 11.3725i 0.481006i
\(560\) −3.97980 + 9.18776i −0.168177 + 0.388254i
\(561\) 1.70933 + 9.48356i 0.0721680 + 0.400396i
\(562\) −8.93679 + 0.256632i −0.376976 + 0.0108254i
\(563\) −6.29010 + 10.8948i −0.265096 + 0.459160i −0.967589 0.252531i \(-0.918737\pi\)
0.702493 + 0.711691i \(0.252070\pi\)
\(564\) 17.5423 + 18.4811i 0.738663 + 0.778195i
\(565\) 5.98010 + 10.3578i 0.251585 + 0.435758i
\(566\) 6.12441 + 9.93764i 0.257428 + 0.417710i
\(567\) −5.88905 6.80582i −0.247317 0.285817i
\(568\) 1.54376 + 17.8803i 0.0647748 + 0.750239i
\(569\) −9.64118 + 5.56634i −0.404179 + 0.233353i −0.688286 0.725440i \(-0.741636\pi\)
0.284107 + 0.958793i \(0.408303\pi\)
\(570\) 2.99231 + 14.2461i 0.125334 + 0.596702i
\(571\) −38.6886 22.3369i −1.61907 0.934769i −0.987162 0.159724i \(-0.948939\pi\)
−0.631906 0.775045i \(-0.717727\pi\)
\(572\) 2.39687 + 3.65031i 0.100218 + 0.152627i
\(573\) 11.5275 2.07773i 0.481568 0.0867985i
\(574\) 8.36422 + 4.51405i 0.349116 + 0.188413i
\(575\) 0.877545 0.0365962
\(576\) 20.8480 + 11.8896i 0.868666 + 0.495398i
\(577\) 0.773772 0.0322125 0.0161063 0.999870i \(-0.494873\pi\)
0.0161063 + 0.999870i \(0.494873\pi\)
\(578\) 56.8203 + 30.6651i 2.36341 + 1.27550i
\(579\) −3.09355 3.65847i −0.128564 0.152041i
\(580\) 27.6086 + 42.0464i 1.14638 + 1.74588i
\(581\) −11.2658 6.50432i −0.467385 0.269845i
\(582\) −31.7082 10.3870i −1.31435 0.430553i
\(583\) 0.541485 0.312627i 0.0224260 0.0129477i
\(584\) −1.99559 23.1134i −0.0825779 0.956439i
\(585\) 23.0039 + 3.87646i 0.951093 + 0.160272i
\(586\) −5.74372 9.31992i −0.237271 0.385002i
\(587\) 3.95356 + 6.84776i 0.163181 + 0.282637i 0.936008 0.351979i \(-0.114491\pi\)
−0.772827 + 0.634617i \(0.781158\pi\)
\(588\) −0.983445 + 3.32157i −0.0405566 + 0.136979i
\(589\) −10.0726 + 17.4462i −0.415032 + 0.718857i
\(590\) −25.6936 + 0.737826i −1.05779 + 0.0303758i
\(591\) 28.1367 + 10.1202i 1.15739 + 0.416289i
\(592\) −4.53292 + 10.4647i −0.186302 + 0.430096i
\(593\) 13.0459i 0.535732i −0.963456 0.267866i \(-0.913682\pi\)
0.963456 0.267866i \(-0.0863184\pi\)
\(594\) −2.75970 4.36592i −0.113232 0.179136i
\(595\) 19.8139i 0.812292i
\(596\) 2.03162 + 35.3448i 0.0832185 + 1.44778i
\(597\) −23.6198 8.49557i −0.966695 0.347700i
\(598\) 0.0874213 + 3.04430i 0.00357492 + 0.124491i
\(599\) 5.35898 9.28202i 0.218962 0.379253i −0.735529 0.677493i \(-0.763066\pi\)
0.954491 + 0.298240i \(0.0963996\pi\)
\(600\) 1.62093 + 5.98585i 0.0661744 + 0.244371i
\(601\) −2.22698 3.85725i −0.0908406 0.157341i 0.817024 0.576603i \(-0.195622\pi\)
−0.907865 + 0.419262i \(0.862289\pi\)
\(602\) −4.40750 + 2.71628i −0.179636 + 0.110707i
\(603\) −8.95979 24.0475i −0.364871 0.979290i
\(604\) 37.5039 + 18.8709i 1.52601 + 0.767847i
\(605\) −22.7750 + 13.1491i −0.925934 + 0.534588i
\(606\) 1.97041 6.01505i 0.0800424 0.244345i
\(607\) 29.7000 + 17.1473i 1.20549 + 0.695988i 0.961770 0.273858i \(-0.0882999\pi\)
0.243717 + 0.969846i \(0.421633\pi\)
\(608\) −8.30976 10.5506i −0.337005 0.427883i
\(609\) 11.2366 + 13.2886i 0.455331 + 0.538480i
\(610\) 8.06113 14.9367i 0.326386 0.604769i
\(611\) −22.8505 −0.924433
\(612\) −47.2086 5.19145i −1.90830 0.209852i
\(613\) −27.5606 −1.11316 −0.556581 0.830794i \(-0.687887\pi\)
−0.556581 + 0.830794i \(0.687887\pi\)
\(614\) 9.87553 18.2986i 0.398544 0.738473i
\(615\) 28.6765 5.16870i 1.15635 0.208422i
\(616\) −0.842223 + 1.80079i −0.0339341 + 0.0725557i
\(617\) 21.8157 + 12.5953i 0.878268 + 0.507068i 0.870087 0.492899i \(-0.164063\pi\)
0.00818075 + 0.999967i \(0.497396\pi\)
\(618\) −32.2694 + 6.77802i −1.29806 + 0.272652i
\(619\) 2.44808 1.41340i 0.0983968 0.0568094i −0.449994 0.893032i \(-0.648574\pi\)
0.548391 + 0.836222i \(0.315241\pi\)
\(620\) −19.0939 + 37.9472i −0.766831 + 1.52399i
\(621\) −0.0409982 3.60194i −0.00164520 0.144541i
\(622\) −15.0905 + 9.30001i −0.605072 + 0.372897i
\(623\) 0.859209 + 1.48819i 0.0344235 + 0.0596232i
\(624\) −20.6041 + 6.21952i −0.824825 + 0.248980i
\(625\) 14.8635 25.7443i 0.594538 1.02977i
\(626\) 0.942680 + 32.8273i 0.0376771 + 1.31204i
\(627\) 0.512684 + 2.84443i 0.0204746 + 0.113595i
\(628\) −3.36241 + 0.193271i −0.134175 + 0.00771237i
\(629\) 22.5677i 0.899834i
\(630\) 3.99202 + 9.84120i 0.159046 + 0.392083i
\(631\) 35.3279i 1.40638i −0.711002 0.703190i \(-0.751758\pi\)
0.711002 0.703190i \(-0.248242\pi\)
\(632\) 4.25046 + 6.08506i 0.169074 + 0.242051i
\(633\) −33.8725 + 28.6421i −1.34631 + 1.13842i
\(634\) −9.68185 + 0.278027i −0.384515 + 0.0110419i
\(635\) −6.15020 + 10.6525i −0.244063 + 0.422730i
\(636\) 0.719754 + 2.99635i 0.0285401 + 0.118813i
\(637\) −1.55324 2.69030i −0.0615417 0.106593i
\(638\) 5.23976 + 8.50218i 0.207444 + 0.336605i
\(639\) 14.6744 + 12.1247i 0.580510 + 0.479647i
\(640\) −18.7707 21.2059i −0.741978 0.838237i
\(641\) 17.8094 10.2823i 0.703431 0.406126i −0.105193 0.994452i \(-0.533546\pi\)
0.808624 + 0.588326i \(0.200213\pi\)
\(642\) −31.0800 + 27.8496i −1.22663 + 1.09914i
\(643\) −16.6218 9.59659i −0.655499 0.378453i 0.135061 0.990837i \(-0.456877\pi\)
−0.790560 + 0.612385i \(0.790210\pi\)
\(644\) −1.15896 + 0.761000i −0.0456696 + 0.0299876i
\(645\) −5.37200 + 14.9355i −0.211522 + 0.588085i
\(646\) 23.3879 + 12.6222i 0.920186 + 0.496612i
\(647\) 30.9160 1.21544 0.607718 0.794153i \(-0.292085\pi\)
0.607718 + 0.794153i \(0.292085\pi\)
\(648\) 24.4936 6.93288i 0.962198 0.272349i
\(649\) −5.10354 −0.200331
\(650\) −4.89400 2.64122i −0.191958 0.103597i
\(651\) −4.97421 + 13.8296i −0.194955 + 0.542023i
\(652\) 24.9600 16.3893i 0.977508 0.641853i
\(653\) −14.2740 8.24109i −0.558584 0.322499i 0.193993 0.981003i \(-0.437856\pi\)
−0.752577 + 0.658504i \(0.771190\pi\)
\(654\) −4.44133 + 3.97970i −0.173670 + 0.155618i
\(655\) −11.3579 + 6.55749i −0.443790 + 0.256222i
\(656\) −21.5879 + 16.0206i −0.842864 + 0.625498i
\(657\) −18.9693 15.6734i −0.740062 0.611477i
\(658\) −5.45775 8.85589i −0.212765 0.345239i
\(659\) −13.7838 23.8743i −0.536942 0.930010i −0.999067 0.0431955i \(-0.986246\pi\)
0.462125 0.886815i \(-0.347087\pi\)
\(660\) 1.42352 + 5.92615i 0.0554105 + 0.230675i
\(661\) 5.86138 10.1522i 0.227981 0.394875i −0.729229 0.684270i \(-0.760121\pi\)
0.957210 + 0.289395i \(0.0934542\pi\)
\(662\) −11.3974 + 0.327292i −0.442973 + 0.0127206i
\(663\) 32.5219 27.5001i 1.26305 1.06801i
\(664\) 30.1639 21.0698i 1.17059 0.817665i
\(665\) 5.94284i 0.230454i
\(666\) 4.54684 + 11.2089i 0.176186 + 0.434338i
\(667\) 6.96521i 0.269694i
\(668\) −4.67493 + 0.268715i −0.180878 + 0.0103969i
\(669\) 4.68777 + 26.0082i 0.181239 + 1.00554i
\(670\) 0.869225 + 30.2693i 0.0335811 + 1.16941i
\(671\) 1.68500 2.91850i 0.0650486 0.112667i
\(672\) −7.33163 6.49978i −0.282824 0.250735i
\(673\) −3.04565 5.27522i −0.117401 0.203345i 0.801336 0.598215i \(-0.204123\pi\)
−0.918737 + 0.394870i \(0.870790\pi\)
\(674\) 19.4647 11.9958i 0.749754 0.462062i
\(675\) 5.73345 + 3.22376i 0.220680 + 0.124083i
\(676\) −3.01128 + 5.98460i −0.115818 + 0.230177i
\(677\) 25.8756 14.9393i 0.994481 0.574164i 0.0878702 0.996132i \(-0.471994\pi\)
0.906611 + 0.421968i \(0.138661\pi\)
\(678\) −11.4538 + 2.40581i −0.439880 + 0.0923945i
\(679\) 11.7967 + 6.81083i 0.452716 + 0.261376i
\(680\) 50.7645 + 23.7424i 1.94673 + 0.910481i
\(681\) 13.2371 2.38587i 0.507246 0.0914268i
\(682\) −4.00579 + 7.42244i −0.153390 + 0.284220i
\(683\) −5.57818 −0.213443 −0.106722 0.994289i \(-0.534035\pi\)
−0.106722 + 0.994289i \(0.534035\pi\)
\(684\) −14.1594 1.55708i −0.541398 0.0595366i
\(685\) −26.1195 −0.997974
\(686\) 0.671660 1.24454i 0.0256441 0.0475167i
\(687\) −12.7504 15.0788i −0.486460 0.575294i
\(688\) −1.67788 14.5471i −0.0639687 0.554604i
\(689\) −2.39322 1.38173i −0.0911745 0.0526396i
\(690\) −1.32322 + 4.03938i −0.0503741 + 0.153776i
\(691\) −6.59535 + 3.80783i −0.250899 + 0.144857i −0.620176 0.784463i \(-0.712939\pi\)
0.369277 + 0.929319i \(0.379605\pi\)
\(692\) 1.80697 + 0.909216i 0.0686907 + 0.0345632i
\(693\) 0.736197 + 1.97591i 0.0279658 + 0.0750585i
\(694\) −9.21981 + 5.68202i −0.349979 + 0.215687i
\(695\) 14.8637 + 25.7447i 0.563813 + 0.976553i
\(696\) −47.5106 + 12.8656i −1.80089 + 0.487670i
\(697\) 26.5992 46.0711i 1.00751 1.74507i
\(698\) −0.357982 12.4662i −0.0135498 0.471851i
\(699\) −31.6371 11.3792i −1.19662 0.430401i
\(700\) −0.145284 2.52755i −0.00549122 0.0955326i
\(701\) 13.6591i 0.515896i 0.966159 + 0.257948i \(0.0830463\pi\)
−0.966159 + 0.257948i \(0.916954\pi\)
\(702\) −10.6124 + 20.2111i −0.400540 + 0.762820i
\(703\) 6.76879i 0.255290i
\(704\) −3.60451 4.31565i −0.135850 0.162652i
\(705\) −30.0096 10.7938i −1.13023 0.406519i
\(706\) 4.59393 0.131921i 0.172895 0.00496490i
\(707\) −1.29202 + 2.23784i −0.0485913 + 0.0841625i
\(708\) 7.14083 24.1181i 0.268369 0.906412i
\(709\) −11.1244 19.2680i −0.417784 0.723624i 0.577932 0.816085i \(-0.303860\pi\)
−0.995716 + 0.0924613i \(0.970527\pi\)
\(710\) −11.7847 19.1222i −0.442272 0.717643i
\(711\) 7.76336 + 1.30823i 0.291149 + 0.0490625i
\(712\) −4.84241 + 0.418088i −0.181477 + 0.0156685i
\(713\) −5.09424 + 2.94116i −0.190781 + 0.110147i
\(714\) 18.4256 + 6.03586i 0.689561 + 0.225886i
\(715\) −4.73329 2.73277i −0.177015 0.102200i
\(716\) 13.0248 + 19.8362i 0.486761 + 0.741312i
\(717\) 7.99484 + 9.45479i 0.298573 + 0.353096i
\(718\) −35.3489 19.0773i −1.31921 0.711959i
\(719\) 17.7827 0.663184 0.331592 0.943423i \(-0.392414\pi\)
0.331592 + 0.943423i \(0.392414\pi\)
\(720\) −29.9973 1.56461i −1.11793 0.0583097i
\(721\) 13.4614 0.501328
\(722\) −16.6314 8.97574i −0.618957 0.334043i
\(723\) 4.08195 0.735737i 0.151810 0.0273624i
\(724\) −12.8674 19.5964i −0.478212 0.728293i
\(725\) −11.0146 6.35929i −0.409072 0.236178i
\(726\) −5.28992 25.1847i −0.196328 0.934693i
\(727\) 45.2123 26.1034i 1.67683 0.968120i 0.713173 0.700988i \(-0.247258\pi\)
0.963660 0.267131i \(-0.0860758\pi\)
\(728\) 8.75390 0.755802i 0.324441 0.0280119i
\(729\) 12.9643 23.6839i 0.480158 0.877182i
\(730\) 15.2338 + 24.7188i 0.563829 + 0.914885i
\(731\) 14.4890 + 25.0956i 0.535894 + 0.928195i
\(732\) 11.4345 + 12.0464i 0.422630 + 0.445248i
\(733\) −5.30936 + 9.19609i −0.196106 + 0.339665i −0.947262 0.320459i \(-0.896163\pi\)
0.751157 + 0.660124i \(0.229496\pi\)
\(734\) 6.53196 0.187574i 0.241099 0.00692348i
\(735\) −0.769066 4.26686i −0.0283674 0.157386i
\(736\) −0.560977 3.88122i −0.0206779 0.143064i
\(737\) 6.01242i 0.221470i
\(738\) −3.92910 + 28.2417i −0.144632 + 1.03959i
\(739\) 25.7536i 0.947362i −0.880696 0.473681i \(-0.842925\pi\)
0.880696 0.473681i \(-0.157075\pi\)
\(740\) −0.819084 14.2499i −0.0301101 0.523836i
\(741\) 9.75438 8.24816i 0.358336 0.303004i
\(742\) −0.0361117 1.25753i −0.00132570 0.0461655i
\(743\) −1.97016 + 3.41241i −0.0722780 + 0.125189i −0.899899 0.436098i \(-0.856360\pi\)
0.827621 + 0.561287i \(0.189694\pi\)
\(744\) −29.4717 29.3158i −1.08049 1.07477i
\(745\) −22.1550 38.3737i −0.811698 1.40590i
\(746\) 33.1949 20.4575i 1.21535 0.749003i
\(747\) 6.48496 38.4833i 0.237272 1.40803i
\(748\) 9.93976 + 5.00141i 0.363434 + 0.182870i
\(749\) 14.7545 8.51853i 0.539119 0.311260i
\(750\) 15.2793 + 17.0517i 0.557923 + 0.622640i
\(751\) −10.3540 5.97786i −0.377821 0.218135i 0.299049 0.954238i \(-0.403331\pi\)
−0.676870 + 0.736103i \(0.736664\pi\)
\(752\) 29.2292 3.37133i 1.06588 0.122940i
\(753\) −1.79367 + 4.98685i −0.0653649 + 0.181731i
\(754\) 20.9638 38.8444i 0.763457 1.41463i
\(755\) −52.5466 −1.91237
\(756\) −10.3677 + 0.714413i −0.377070 + 0.0259829i
\(757\) 1.73758 0.0631534 0.0315767 0.999501i \(-0.489947\pi\)
0.0315767 + 0.999501i \(0.489947\pi\)
\(758\) 13.8205 25.6084i 0.501983 0.930138i
\(759\) −0.285637 + 0.794142i −0.0103680 + 0.0288255i
\(760\) 15.2259 + 7.12113i 0.552302 + 0.258310i
\(761\) −25.7786 14.8833i −0.934473 0.539518i −0.0462496 0.998930i \(-0.514727\pi\)
−0.888223 + 0.459412i \(0.848060\pi\)
\(762\) −8.03254 8.96429i −0.290988 0.324742i
\(763\) 2.10842 1.21729i 0.0763298 0.0440690i
\(764\) 6.07933 12.0820i 0.219942 0.437112i
\(765\) 55.7012 20.7535i 2.01388 0.750346i
\(766\) −0.110175 + 0.0678989i −0.00398077 + 0.00245329i
\(767\) 11.2782 + 19.5343i 0.407231 + 0.705344i
\(768\) 25.4381 10.9956i 0.917918 0.396769i
\(769\) 11.5167 19.9475i 0.415303 0.719327i −0.580157 0.814505i \(-0.697009\pi\)
0.995460 + 0.0951782i \(0.0303421\pi\)
\(770\) −0.0714214 2.48713i −0.00257385 0.0896301i
\(771\) −26.2568 + 22.2024i −0.945615 + 0.799598i
\(772\) −5.52315 + 0.317471i −0.198783 + 0.0114260i
\(773\) 1.33102i 0.0478734i −0.999713 0.0239367i \(-0.992380\pi\)
0.999713 0.0239367i \(-0.00762002\pi\)
\(774\) −12.2525 9.54534i −0.440408 0.343100i
\(775\) 10.7412i 0.385835i
\(776\) −31.5854 + 22.0627i −1.13385 + 0.792003i
\(777\) −0.875952 4.85988i −0.0314246 0.174347i
\(778\) 2.70118 0.0775679i 0.0968419 0.00278094i
\(779\) 7.97795 13.8182i 0.285840 0.495089i
\(780\) 19.5372 18.5447i 0.699543 0.664006i
\(781\) −2.22989 3.86229i −0.0797919 0.138204i
\(782\) 4.07146 + 6.60646i 0.145595 + 0.236247i
\(783\) −25.5875 + 45.5073i −0.914423 + 1.62630i
\(784\) 2.38375 + 3.21212i 0.0851339 + 0.114719i
\(785\) 3.65055 2.10764i 0.130294 0.0752250i
\(786\) −2.63810 12.5597i −0.0940977 0.447988i
\(787\) −1.23901 0.715343i −0.0441659 0.0254992i 0.477754 0.878493i \(-0.341451\pi\)
−0.521920 + 0.852994i \(0.674784\pi\)
\(788\) 28.8614 18.9510i 1.02815 0.675102i
\(789\) 32.4293 5.84511i 1.15451 0.208091i
\(790\) −8.17536 4.41213i −0.290866 0.156977i
\(791\) 4.77802 0.169887
\(792\) −5.94455 0.481486i −0.211230 0.0171089i
\(793\) −14.8945 −0.528919
\(794\) −37.8778 20.4421i −1.34423 0.725465i
\(795\) −2.49034 2.94510i −0.0883231 0.104452i
\(796\) −24.2282 + 15.9087i −0.858746 + 0.563871i
\(797\) −29.9747 17.3059i −1.06176 0.613007i −0.135841 0.990731i \(-0.543373\pi\)
−0.925918 + 0.377724i \(0.876707\pi\)
\(798\) 5.52643 + 1.81035i 0.195634 + 0.0640856i
\(799\) −50.4240 + 29.1123i −1.78387 + 1.02992i
\(800\) 6.64983 + 2.65646i 0.235107 + 0.0939202i
\(801\) −3.28367 + 3.97418i −0.116023 + 0.140421i
\(802\) −16.2116 26.3053i −0.572450 0.928873i
\(803\) 2.88253 + 4.99269i 0.101722 + 0.176188i
\(804\) −28.4132 8.41253i −1.00206 0.296687i
\(805\) 0.867647 1.50281i 0.0305805 0.0529671i
\(806\) 37.2624 1.07004i 1.31251 0.0376906i
\(807\) 44.1341 + 15.8741i 1.55359 + 0.558796i
\(808\) −4.18529 5.99175i −0.147238 0.210789i
\(809\) 21.7895i 0.766078i 0.923732 + 0.383039i \(0.125122\pi\)
−0.923732 + 0.383039i \(0.874878\pi\)
\(810\) −23.4844 + 21.5303i −0.825157 + 0.756498i
\(811\) 14.6383i 0.514020i −0.966409 0.257010i \(-0.917263\pi\)
0.966409 0.257010i \(-0.0827374\pi\)
\(812\) 20.0616 1.15314i 0.704024 0.0404673i
\(813\) −47.4687 17.0735i −1.66480 0.598795i
\(814\) −0.0813476 2.83280i −0.00285123 0.0992896i
\(815\) −18.6860 + 32.3652i −0.654544 + 1.13370i
\(816\) −37.5431 + 39.9749i −1.31427 + 1.39940i
\(817\) 4.34571 + 7.52699i 0.152037 + 0.263336i
\(818\) −5.38851 + 3.32086i −0.188405 + 0.116111i
\(819\) 5.93609 7.18437i 0.207424 0.251042i
\(820\) 15.1233 30.0560i 0.528129 1.04960i
\(821\) −15.6555 + 9.03872i −0.546382 + 0.315454i −0.747661 0.664080i \(-0.768823\pi\)
0.201280 + 0.979534i \(0.435490\pi\)
\(822\) 7.95669 24.2893i 0.277521 0.847187i
\(823\) 10.4800 + 6.05062i 0.365309 + 0.210911i 0.671407 0.741089i \(-0.265690\pi\)
−0.306098 + 0.952000i \(0.599024\pi\)
\(824\) −16.1304 + 34.4889i −0.561928 + 1.20148i
\(825\) −0.995047 1.17676i −0.0346431 0.0409694i
\(826\) −4.87695 + 9.03663i −0.169691 + 0.314425i
\(827\) −50.7180 −1.76364 −0.881819 0.471588i \(-0.843681\pi\)
−0.881819 + 0.471588i \(0.843681\pi\)
\(828\) −3.35326 2.46100i −0.116534 0.0855258i
\(829\) −14.5505 −0.505359 −0.252679 0.967550i \(-0.581312\pi\)
−0.252679 + 0.967550i \(0.581312\pi\)
\(830\) −21.8711 + 40.5257i −0.759159 + 1.40667i
\(831\) −28.0329 + 5.05269i −0.972450 + 0.175276i
\(832\) −8.55312 + 23.3337i −0.296526 + 0.808950i
\(833\) −6.85506 3.95777i −0.237514 0.137129i
\(834\) −28.4687 + 5.97971i −0.985790 + 0.207060i
\(835\) 5.07554 2.93036i 0.175646 0.101409i
\(836\) 2.98126 + 1.50008i 0.103109 + 0.0518815i
\(837\) −44.0879 + 0.501820i −1.52390 + 0.0173454i
\(838\) −27.4552 + 16.9202i −0.948423 + 0.584498i
\(839\) 7.34607 + 12.7238i 0.253615 + 0.439273i 0.964518 0.264016i \(-0.0850472\pi\)
−0.710904 + 0.703289i \(0.751714\pi\)
\(840\) 11.8535 + 3.14246i 0.408985 + 0.108425i
\(841\) 35.9746 62.3099i 1.24050 2.14862i
\(842\) 1.14078 + 39.7258i 0.0393138 + 1.36904i
\(843\) 1.94231 + 10.7762i 0.0668967 + 0.371150i
\(844\) 2.93935 + 51.1369i 0.101177 + 1.76020i
\(845\) 8.38499i 0.288452i
\(846\) 19.1792 24.6187i 0.659395 0.846409i
\(847\) 10.5060i 0.360990i
\(848\) 3.26515 + 1.41434i 0.112126 + 0.0485687i
\(849\) 10.9170 9.23127i 0.374671 0.316816i
\(850\) −14.1646 + 0.406754i −0.485840 + 0.0139516i
\(851\) 0.988234 1.71167i 0.0338762 0.0586754i
\(852\) 21.3723 5.13384i 0.732202 0.175882i
\(853\) 0.885883 + 1.53439i 0.0303321 + 0.0525367i 0.880793 0.473502i \(-0.157010\pi\)
−0.850461 + 0.526038i \(0.823677\pi\)
\(854\) −3.55749 5.77248i −0.121735 0.197530i
\(855\) 16.7066 6.22466i 0.571353 0.212879i
\(856\) 4.14508 + 48.0095i 0.141676 + 1.64093i
\(857\) 0.277829 0.160404i 0.00949045 0.00547931i −0.495247 0.868752i \(-0.664923\pi\)
0.504738 + 0.863273i \(0.331589\pi\)
\(858\) 3.98317 3.56916i 0.135983 0.121849i
\(859\) −27.9931 16.1618i −0.955112 0.551434i −0.0604467 0.998171i \(-0.519253\pi\)
−0.894665 + 0.446737i \(0.852586\pi\)
\(860\) 10.0596 + 15.3202i 0.343028 + 0.522415i
\(861\) 3.93982 10.9537i 0.134269 0.373300i
\(862\) −0.760107 0.410219i −0.0258893 0.0139721i
\(863\) 18.8459 0.641522 0.320761 0.947160i \(-0.396061\pi\)
0.320761 + 0.947160i \(0.396061\pi\)
\(864\) 10.5930 27.4188i 0.360380 0.932806i
\(865\) −2.53174 −0.0860816
\(866\) −13.0887 7.06378i −0.444772 0.240037i
\(867\) 26.7642 74.4111i 0.908959 2.52713i
\(868\) 9.31468 + 14.1858i 0.316161 + 0.481497i
\(869\) −1.59739 0.922256i −0.0541879 0.0312854i
\(870\) 45.8806 41.1118i 1.55550 1.39382i
\(871\) 23.0132 13.2867i 0.779772 0.450201i
\(872\) 0.592331 + 6.86054i 0.0200589 + 0.232327i
\(873\) −6.79056 + 40.2968i −0.229826 + 1.36384i
\(874\) 1.22116 + 1.98149i 0.0413064 + 0.0670250i
\(875\) −4.67359 8.09490i −0.157996 0.273657i
\(876\) −27.6274 + 6.63639i −0.933445 + 0.224223i
\(877\) −20.0001 + 34.6412i −0.675355 + 1.16975i 0.301010 + 0.953621i \(0.402676\pi\)
−0.976365 + 0.216129i \(0.930657\pi\)
\(878\) 53.2681 1.52967i 1.79771 0.0516237i
\(879\) −10.2384 + 8.65746i −0.345333 + 0.292009i
\(880\) 6.45777 + 2.79727i 0.217691 + 0.0942960i
\(881\) 4.11680i 0.138699i 0.997592 + 0.0693493i \(0.0220923\pi\)
−0.997592 + 0.0693493i \(0.977908\pi\)
\(882\) 4.20217 + 0.584622i 0.141494 + 0.0196853i
\(883\) 58.6257i 1.97291i −0.164027 0.986456i \(-0.552449\pi\)
0.164027 0.986456i \(-0.447551\pi\)
\(884\) −2.82215 49.0980i −0.0949193 1.65134i
\(885\) 5.58422 + 30.9819i 0.187711 + 1.04144i
\(886\) 1.68430 + 58.6529i 0.0565850 + 1.97048i
\(887\) −14.3027 + 24.7730i −0.480238 + 0.831797i −0.999743 0.0226703i \(-0.992783\pi\)
0.519505 + 0.854468i \(0.326117\pi\)
\(888\) 13.5009 + 3.57920i 0.453061 + 0.120110i
\(889\) 2.45696 + 4.25559i 0.0824040 + 0.142728i
\(890\) 5.17875 3.19158i 0.173592 0.106982i
\(891\) −4.78358 + 4.13921i −0.160256 + 0.138669i
\(892\) 27.2594 + 13.7161i 0.912711 + 0.459250i
\(893\) −15.1238 + 8.73173i −0.506099 + 0.292196i
\(894\) 42.4339 8.91302i 1.41920 0.298096i
\(895\) −25.7212 14.8502i −0.859766 0.496386i
\(896\) −11.0860 + 2.25832i −0.370358 + 0.0754452i
\(897\) 3.67088 0.661645i 0.122567 0.0220917i
\(898\) 21.4700 39.7824i 0.716463 1.32756i
\(899\) 85.2545 2.84340
\(900\) 6.95331 3.05584i 0.231777 0.101861i
\(901\) −7.04147 −0.234586
\(902\) 3.17278 5.87893i 0.105642 0.195747i
\(903\) 4.09422 + 4.84187i 0.136247 + 0.161128i
\(904\) −5.72536 + 12.2416i −0.190423 + 0.407149i
\(905\) 25.4103 + 14.6706i 0.844666 + 0.487668i
\(906\) 16.0071 48.8647i 0.531800 1.62342i
\(907\) 9.05264 5.22654i 0.300588 0.173545i −0.342119 0.939657i \(-0.611145\pi\)
0.642707 + 0.766112i \(0.277811\pi\)
\(908\) 6.98093 13.8739i 0.231670 0.460420i
\(909\) −7.64432 1.28817i −0.253546 0.0427259i
\(910\) −9.36194 + 5.76961i −0.310345 + 0.191261i
\(911\) 7.21831 + 12.5025i 0.239153 + 0.414226i 0.960472 0.278378i \(-0.0897968\pi\)
−0.721318 + 0.692604i \(0.756463\pi\)
\(912\) −11.2604 + 11.9898i −0.372868 + 0.397021i
\(913\) −4.57167 + 7.91836i −0.151300 + 0.262059i
\(914\) 1.20577 + 41.9891i 0.0398834 + 1.38888i
\(915\) −19.5609 7.03567i −0.646664 0.232592i
\(916\) −22.7643 + 1.30850i −0.752155 + 0.0432339i
\(917\) 5.23935i 0.173019i
\(918\) 2.33131 + 58.1203i 0.0769445 + 1.91826i
\(919\) 12.1505i 0.400810i −0.979713 0.200405i \(-0.935774\pi\)
0.979713 0.200405i \(-0.0642257\pi\)
\(920\) 2.81061 + 4.02373i 0.0926631 + 0.132659i
\(921\) −23.9637 8.61925i −0.789630 0.284014i
\(922\) 14.6379 0.420346i 0.482073 0.0138434i
\(923\) −9.85555 + 17.0703i −0.324399 + 0.561876i
\(924\) 2.33462 + 0.691231i 0.0768034 + 0.0227398i
\(925\) 1.80453 + 3.12554i 0.0593325 + 0.102767i
\(926\) 11.7563 + 19.0761i 0.386337 + 0.626881i
\(927\) 14.0997 + 37.8428i 0.463096 + 1.24292i
\(928\) −21.0848 + 52.7808i −0.692142 + 1.73261i
\(929\) −38.7325 + 22.3622i −1.27077 + 0.733680i −0.975133 0.221620i \(-0.928866\pi\)
−0.295638 + 0.955300i \(0.595532\pi\)
\(930\) 49.4422 + 16.1963i 1.62127 + 0.531096i
\(931\) −2.05605 1.18706i −0.0673844 0.0389044i
\(932\) −32.4520 + 21.3086i −1.06300 + 0.697988i
\(933\) 14.0178 + 16.5777i 0.458923 + 0.542728i
\(934\) −34.8276 18.7960i −1.13959 0.615023i
\(935\) −13.9266 −0.455447
\(936\) 11.2937 + 23.8174i 0.369148 + 0.778497i
\(937\) −28.8712 −0.943180 −0.471590 0.881818i \(-0.656320\pi\)
−0.471590 + 0.881818i \(0.656320\pi\)
\(938\) 10.6460 + 5.74547i 0.347603 + 0.187596i
\(939\) 39.5838 7.13465i 1.29177 0.232830i
\(940\) −30.7825 + 20.2124i −1.00401 + 0.659257i
\(941\) 31.0674 + 17.9368i 1.01277 + 0.584723i 0.912001 0.410187i \(-0.134537\pi\)
0.100768 + 0.994910i \(0.467870\pi\)
\(942\) 0.847910 + 4.03680i 0.0276264 + 0.131526i
\(943\) 4.03488 2.32954i 0.131394 0.0758603i
\(944\) −17.3085 23.3233i −0.563344 0.759110i
\(945\) 11.1895 6.63121i 0.363995 0.215713i
\(946\) 1.90918 + 3.09789i 0.0620728 + 0.100721i
\(947\) 8.81974 + 15.2762i 0.286603 + 0.496411i 0.972997 0.230819i \(-0.0741406\pi\)
−0.686394 + 0.727230i \(0.740807\pi\)
\(948\) 6.59341 6.25847i 0.214144 0.203266i
\(949\) 12.7400 22.0664i 0.413559 0.716306i
\(950\) −4.24841 + 0.121999i −0.137837 + 0.00395816i
\(951\) 2.10424 + 11.6746i 0.0682347 + 0.378574i
\(952\) 18.3542 12.8206i 0.594864 0.415518i
\(953\) 9.66882i 0.313204i −0.987662 0.156602i \(-0.949946\pi\)
0.987662 0.156602i \(-0.0500540\pi\)
\(954\) 3.49737 1.41868i 0.113231 0.0459316i
\(955\) 16.9280i 0.547779i
\(956\) 14.2738 0.820458i 0.461647 0.0265355i
\(957\) 9.34009 7.89784i 0.301922 0.255301i
\(958\) 0.940523 + 32.7522i 0.0303869 + 1.05818i
\(959\) −5.21728 + 9.03659i −0.168475 + 0.291807i
\(960\) −22.2549 + 26.6039i −0.718273 + 0.858637i
\(961\) 20.4999 + 35.5069i 0.661288 + 1.14538i
\(962\) −10.6631 + 6.57148i −0.343791 + 0.211873i
\(963\) 39.4016 + 32.5556i 1.26970 + 1.04909i
\(964\) 2.15273 4.27831i 0.0693347 0.137795i
\(965\) 5.99645 3.46205i 0.193033 0.111447i
\(966\) 1.13320 + 1.26465i 0.0364601 + 0.0406894i
\(967\) 2.67131 + 1.54228i 0.0859036 + 0.0495964i 0.542336 0.840161i \(-0.317540\pi\)
−0.456433 + 0.889758i \(0.650873\pi\)
\(968\) −26.9169 12.5890i −0.865143 0.404626i
\(969\) 11.0165 30.6286i 0.353900 0.983932i
\(970\) 22.9018 42.4354i 0.735333 1.36252i
\(971\) −24.5223 −0.786958 −0.393479 0.919334i \(-0.628729\pi\)
−0.393479 + 0.919334i \(0.628729\pi\)
\(972\) −12.8677 28.3976i −0.412733 0.910852i
\(973\) 11.8759 0.380724
\(974\) 9.29956 17.2314i 0.297977 0.552130i
\(975\) −2.30523 + 6.40912i −0.0738265 + 0.205256i
\(976\) 19.0523 2.19751i 0.609848 0.0703406i
\(977\) 9.43845 + 5.44929i 0.301963 + 0.174338i 0.643324 0.765594i \(-0.277555\pi\)
−0.341362 + 0.939932i \(0.610888\pi\)
\(978\) −24.4051 27.2360i −0.780390 0.870913i
\(979\) 1.04600 0.603909i 0.0334304 0.0193010i
\(980\) −4.47212 2.25024i −0.142857 0.0718814i
\(981\) 5.63047 + 4.65218i 0.179767 + 0.148533i
\(982\) 4.76759 2.93819i 0.152140 0.0937615i
\(983\) −14.8209 25.6706i −0.472715 0.818766i 0.526798 0.849991i \(-0.323393\pi\)
−0.999512 + 0.0312247i \(0.990059\pi\)
\(984\) 23.3430 + 23.2195i 0.744148 + 0.740211i
\(985\) −21.6068 + 37.4241i −0.688450 + 1.19243i
\(986\) −3.22847 112.426i −0.102815 3.58038i
\(987\) −9.72866 + 8.22642i −0.309667 + 0.261850i
\(988\) −0.846455 14.7261i −0.0269293 0.468499i
\(989\) 2.53787i 0.0806996i
\(990\) 6.91705 2.80586i 0.219838 0.0891760i
\(991\) 20.5496i 0.652779i 0.945235 + 0.326390i \(0.105832\pi\)
−0.945235 + 0.326390i \(0.894168\pi\)
\(992\) −47.5063 + 6.86638i −1.50833 + 0.218008i
\(993\) 2.47710 + 13.7432i 0.0786084 + 0.436128i
\(994\) −8.96969 + 0.257577i −0.284501 + 0.00816983i
\(995\) 18.1382 31.4163i 0.575020 0.995963i
\(996\) −31.0235 32.6839i −0.983019 1.03563i
\(997\) 6.42074 + 11.1210i 0.203347 + 0.352207i 0.949605 0.313450i \(-0.101485\pi\)
−0.746258 + 0.665657i \(0.768151\pi\)
\(998\) −16.0071 25.9735i −0.506695 0.822177i
\(999\) 12.7447 7.55283i 0.403223 0.238961i
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 252.2.ba.a.239.6 yes 72
3.2 odd 2 756.2.ba.a.71.31 72
4.3 odd 2 inner 252.2.ba.a.239.17 yes 72
9.2 odd 6 inner 252.2.ba.a.155.17 yes 72
9.7 even 3 756.2.ba.a.575.20 72
12.11 even 2 756.2.ba.a.71.20 72
36.7 odd 6 756.2.ba.a.575.31 72
36.11 even 6 inner 252.2.ba.a.155.6 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.ba.a.155.6 72 36.11 even 6 inner
252.2.ba.a.155.17 yes 72 9.2 odd 6 inner
252.2.ba.a.239.6 yes 72 1.1 even 1 trivial
252.2.ba.a.239.17 yes 72 4.3 odd 2 inner
756.2.ba.a.71.20 72 12.11 even 2
756.2.ba.a.71.31 72 3.2 odd 2
756.2.ba.a.575.20 72 9.7 even 3
756.2.ba.a.575.31 72 36.7 odd 6