Properties

Label 63.2.h.b.25.2
Level $63$
Weight $2$
Character 63.25
Analytic conductor $0.503$
Analytic rank $0$
Dimension $10$
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] = [63,2,Mod(25,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.h (of order \(3\), 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: \(0.503057532734\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.2
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 63.25
Dual form 63.2.h.b.58.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.84124 q^{2} +(1.39291 + 1.02946i) q^{3} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 - 1.89549i) q^{6} +(1.90267 + 1.83844i) q^{7} +1.12285 q^{8} +(0.880416 + 2.86790i) q^{9} +O(q^{10})\) \(q-1.84124 q^{2} +(1.39291 + 1.02946i) q^{3} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 - 1.89549i) q^{6} +(1.90267 + 1.83844i) q^{7} +1.12285 q^{8} +(0.880416 + 2.86790i) q^{9} +(1.22880 - 2.12835i) q^{10} +(-0.756508 - 1.31031i) q^{11} +(1.93638 + 1.43112i) q^{12} +(-2.58800 - 4.48254i) q^{13} +(-3.50326 - 3.38501i) q^{14} +(-2.11958 + 0.923072i) q^{15} -4.84777 q^{16} +(0.774463 - 1.34141i) q^{17} +(-1.62106 - 5.28050i) q^{18} +(-1.25211 - 2.16872i) q^{19} +(-0.927765 + 1.60694i) q^{20} +(0.757642 + 4.51951i) q^{21} +(1.39291 + 2.41260i) q^{22} +(3.68039 - 6.37463i) q^{23} +(1.56403 + 1.15593i) q^{24} +(1.60922 + 2.78725i) q^{25} +(4.76513 + 8.25344i) q^{26} +(-1.72605 + 4.90110i) q^{27} +(2.64502 + 2.55574i) q^{28} +(-0.0309713 + 0.0536439i) q^{29} +(3.90267 - 1.69960i) q^{30} -3.84777 q^{31} +6.68021 q^{32} +(0.295165 - 2.60395i) q^{33} +(-1.42597 + 2.46986i) q^{34} +(-3.39490 + 0.972416i) q^{35} +(1.22392 + 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +(2.30543 + 3.99313i) q^{38} +(1.00975 - 8.90804i) q^{39} +(-0.749363 + 1.29794i) q^{40} +(4.51188 + 7.81481i) q^{41} +(-1.39500 - 8.32151i) q^{42} +(5.09988 - 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(-3.90267 - 0.896273i) q^{45} +(-6.77649 + 11.7372i) q^{46} -9.51851 q^{47} +(-6.75252 - 4.99060i) q^{48} +(0.240269 + 6.99588i) q^{49} +(-2.96296 - 5.13199i) q^{50} +(2.45969 - 1.07119i) q^{51} +(-3.59775 - 6.23148i) q^{52} +(0.755374 - 1.30835i) q^{53} +(3.17808 - 9.02410i) q^{54} +2.01950 q^{55} +(2.13641 + 2.06429i) q^{56} +(0.488532 - 4.30983i) q^{57} +(0.0570257 - 0.0987714i) q^{58} -8.44331 q^{59} +(-2.94658 + 1.28322i) q^{60} +3.23917 q^{61} +7.08467 q^{62} +(-3.59733 + 7.07525i) q^{63} -2.60434 q^{64} +6.90868 q^{65} +(-0.543469 + 4.79449i) q^{66} +6.93339 q^{67} +(1.07663 - 1.86478i) q^{68} +(11.6889 - 5.09048i) q^{69} +(6.25084 - 1.79045i) q^{70} -12.3304 q^{71} +(0.988574 + 3.22022i) q^{72} +(-1.37936 + 2.38912i) q^{73} +(0.518508 + 0.898083i) q^{74} +(-0.627864 + 5.53902i) q^{75} +(-1.74064 - 3.01488i) q^{76} +(0.969547 - 3.88388i) q^{77} +(-1.85920 + 16.4018i) q^{78} -5.91938 q^{79} +(3.23529 - 5.60368i) q^{80} +(-7.44974 + 5.04989i) q^{81} +(-8.30746 - 14.3889i) q^{82} +(2.80111 - 4.85167i) q^{83} +(1.05325 + 6.28288i) q^{84} +(1.03372 + 1.79045i) q^{85} +(-9.39010 + 16.2641i) q^{86} +(-0.0983648 + 0.0428375i) q^{87} +(-0.849444 - 1.47128i) q^{88} +(0.703287 + 1.21813i) q^{89} +(7.18575 + 1.65025i) q^{90} +(3.31680 - 13.2867i) q^{91} +(5.11636 - 8.86180i) q^{92} +(-5.35961 - 3.96113i) q^{93} +17.5259 q^{94} +3.34251 q^{95} +(9.30496 + 6.87703i) q^{96} +(-6.09713 + 10.5605i) q^{97} +(-0.442393 - 12.8811i) q^{98} +(3.09180 - 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9} - 7 q^{10} + 4 q^{11} - 20 q^{12} - 8 q^{13} - 20 q^{14} - 19 q^{15} - 4 q^{16} + 12 q^{17} + 4 q^{18} + q^{19} + 5 q^{20} + 13 q^{21} - q^{22} + 3 q^{23} + 6 q^{24} - q^{25} + 11 q^{26} - 7 q^{27} - 2 q^{28} + 7 q^{29} + 16 q^{30} + 6 q^{31} + 4 q^{32} + 14 q^{33} + 3 q^{34} + 5 q^{35} + 34 q^{36} + 20 q^{38} + 2 q^{39} - 3 q^{40} + 5 q^{41} - 4 q^{42} - 7 q^{43} - 10 q^{44} - 16 q^{45} + 3 q^{46} - 54 q^{47} - 5 q^{48} - 8 q^{49} + 19 q^{50} - 9 q^{51} - 10 q^{52} - 21 q^{53} + q^{54} + 4 q^{55} + 18 q^{56} - 4 q^{57} - 10 q^{58} - 60 q^{59} + 10 q^{60} + 28 q^{61} - 12 q^{62} - 59 q^{63} - 50 q^{64} + 22 q^{65} + 19 q^{66} + 4 q^{67} + 27 q^{68} + 15 q^{69} + 40 q^{70} - 6 q^{71} - 36 q^{72} + 15 q^{73} - 36 q^{74} - 14 q^{75} + 5 q^{76} + 11 q^{77} - 20 q^{78} + 8 q^{79} + 20 q^{80} + 23 q^{81} - 5 q^{82} + 9 q^{83} + 35 q^{84} - 6 q^{85} - 8 q^{86} + 2 q^{87} - 18 q^{88} + 28 q^{89} + 28 q^{90} - 4 q^{91} + 27 q^{92} - 6 q^{93} + 6 q^{94} + 28 q^{95} + 59 q^{96} - 12 q^{97} + 59 q^{98} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84124 −1.30195 −0.650977 0.759098i \(-0.725641\pi\)
−0.650977 + 0.759098i \(0.725641\pi\)
\(3\) 1.39291 + 1.02946i 0.804199 + 0.594360i
\(4\) 1.39017 0.695084
\(5\) −0.667377 + 1.15593i −0.298460 + 0.516948i −0.975784 0.218737i \(-0.929806\pi\)
0.677324 + 0.735685i \(0.263140\pi\)
\(6\) −2.56469 1.89549i −1.04703 0.773830i
\(7\) 1.90267 + 1.83844i 0.719140 + 0.694865i
\(8\) 1.12285 0.396987
\(9\) 0.880416 + 2.86790i 0.293472 + 0.955968i
\(10\) 1.22880 2.12835i 0.388581 0.673042i
\(11\) −0.756508 1.31031i −0.228096 0.395073i 0.729148 0.684356i \(-0.239917\pi\)
−0.957244 + 0.289283i \(0.906583\pi\)
\(12\) 1.93638 + 1.43112i 0.558986 + 0.413130i
\(13\) −2.58800 4.48254i −0.717781 1.24323i −0.961877 0.273482i \(-0.911824\pi\)
0.244096 0.969751i \(-0.421509\pi\)
\(14\) −3.50326 3.38501i −0.936287 0.904683i
\(15\) −2.11958 + 0.923072i −0.547274 + 0.238336i
\(16\) −4.84777 −1.21194
\(17\) 0.774463 1.34141i 0.187835 0.325340i −0.756693 0.653770i \(-0.773186\pi\)
0.944528 + 0.328430i \(0.106520\pi\)
\(18\) −1.62106 5.28050i −0.382087 1.24463i
\(19\) −1.25211 2.16872i −0.287254 0.497538i 0.685900 0.727696i \(-0.259409\pi\)
−0.973153 + 0.230158i \(0.926076\pi\)
\(20\) −0.927765 + 1.60694i −0.207455 + 0.359322i
\(21\) 0.757642 + 4.51951i 0.165331 + 0.986238i
\(22\) 1.39291 + 2.41260i 0.296970 + 0.514367i
\(23\) 3.68039 6.37463i 0.767415 1.32920i −0.171545 0.985176i \(-0.554876\pi\)
0.938960 0.344025i \(-0.111791\pi\)
\(24\) 1.56403 + 1.15593i 0.319257 + 0.235953i
\(25\) 1.60922 + 2.78725i 0.321843 + 0.557449i
\(26\) 4.76513 + 8.25344i 0.934518 + 1.61863i
\(27\) −1.72605 + 4.90110i −0.332179 + 0.943216i
\(28\) 2.64502 + 2.55574i 0.499862 + 0.482990i
\(29\) −0.0309713 + 0.0536439i −0.00575123 + 0.00996143i −0.868887 0.495011i \(-0.835164\pi\)
0.863135 + 0.504972i \(0.168497\pi\)
\(30\) 3.90267 1.69960i 0.712526 0.310303i
\(31\) −3.84777 −0.691080 −0.345540 0.938404i \(-0.612304\pi\)
−0.345540 + 0.938404i \(0.612304\pi\)
\(32\) 6.68021 1.18091
\(33\) 0.295165 2.60395i 0.0513816 0.453289i
\(34\) −1.42597 + 2.46986i −0.244552 + 0.423577i
\(35\) −3.39490 + 0.972416i −0.573844 + 0.164368i
\(36\) 1.22392 + 3.98687i 0.203987 + 0.664478i
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) 2.30543 + 3.99313i 0.373991 + 0.647771i
\(39\) 1.00975 8.90804i 0.161690 1.42643i
\(40\) −0.749363 + 1.29794i −0.118485 + 0.205222i
\(41\) 4.51188 + 7.81481i 0.704638 + 1.22047i 0.966822 + 0.255450i \(0.0822237\pi\)
−0.262185 + 0.965018i \(0.584443\pi\)
\(42\) −1.39500 8.32151i −0.215253 1.28404i
\(43\) 5.09988 8.83325i 0.777724 1.34706i −0.155526 0.987832i \(-0.549707\pi\)
0.933251 0.359226i \(-0.116959\pi\)
\(44\) −1.05167 1.82155i −0.158546 0.274609i
\(45\) −3.90267 0.896273i −0.581775 0.133608i
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) −9.51851 −1.38842 −0.694209 0.719774i \(-0.744245\pi\)
−0.694209 + 0.719774i \(0.744245\pi\)
\(48\) −6.75252 4.99060i −0.974643 0.720330i
\(49\) 0.240269 + 6.99588i 0.0343242 + 0.999411i
\(50\) −2.96296 5.13199i −0.419025 0.725773i
\(51\) 2.45969 1.07119i 0.344426 0.149996i
\(52\) −3.59775 6.23148i −0.498918 0.864151i
\(53\) 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i \(-0.800246\pi\)
0.913230 + 0.407444i \(0.133580\pi\)
\(54\) 3.17808 9.02410i 0.432482 1.22802i
\(55\) 2.01950 0.272310
\(56\) 2.13641 + 2.06429i 0.285489 + 0.275853i
\(57\) 0.488532 4.30983i 0.0647077 0.570851i
\(58\) 0.0570257 0.0987714i 0.00748784 0.0129693i
\(59\) −8.44331 −1.09923 −0.549613 0.835419i \(-0.685225\pi\)
−0.549613 + 0.835419i \(0.685225\pi\)
\(60\) −2.94658 + 1.28322i −0.380401 + 0.165664i
\(61\) 3.23917 0.414733 0.207367 0.978263i \(-0.433511\pi\)
0.207367 + 0.978263i \(0.433511\pi\)
\(62\) 7.08467 0.899754
\(63\) −3.59733 + 7.07525i −0.453222 + 0.891398i
\(64\) −2.60434 −0.325543
\(65\) 6.90868 0.856916
\(66\) −0.543469 + 4.79449i −0.0668964 + 0.590161i
\(67\) 6.93339 0.847049 0.423524 0.905885i \(-0.360793\pi\)
0.423524 + 0.905885i \(0.360793\pi\)
\(68\) 1.07663 1.86478i 0.130561 0.226138i
\(69\) 11.6889 5.09048i 1.40718 0.612822i
\(70\) 6.25084 1.79045i 0.747118 0.214000i
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) 0.988574 + 3.22022i 0.116505 + 0.379507i
\(73\) −1.37936 + 2.38912i −0.161442 + 0.279625i −0.935386 0.353629i \(-0.884948\pi\)
0.773944 + 0.633254i \(0.218281\pi\)
\(74\) 0.518508 + 0.898083i 0.0602754 + 0.104400i
\(75\) −0.627864 + 5.53902i −0.0724995 + 0.639591i
\(76\) −1.74064 3.01488i −0.199665 0.345830i
\(77\) 0.969547 3.88388i 0.110490 0.442609i
\(78\) −1.85920 + 16.4018i −0.210512 + 1.85714i
\(79\) −5.91938 −0.665982 −0.332991 0.942930i \(-0.608058\pi\)
−0.332991 + 0.942930i \(0.608058\pi\)
\(80\) 3.23529 5.60368i 0.361716 0.626511i
\(81\) −7.44974 + 5.04989i −0.827749 + 0.561099i
\(82\) −8.30746 14.3889i −0.917406 1.58899i
\(83\) 2.80111 4.85167i 0.307462 0.532540i −0.670344 0.742050i \(-0.733854\pi\)
0.977806 + 0.209510i \(0.0671870\pi\)
\(84\) 1.05325 + 6.28288i 0.114919 + 0.685518i
\(85\) 1.03372 + 1.79045i 0.112122 + 0.194202i
\(86\) −9.39010 + 16.2641i −1.01256 + 1.75381i
\(87\) −0.0983648 + 0.0428375i −0.0105458 + 0.00459267i
\(88\) −0.849444 1.47128i −0.0905511 0.156839i
\(89\) 0.703287 + 1.21813i 0.0745483 + 0.129121i 0.900890 0.434048i \(-0.142915\pi\)
−0.826341 + 0.563169i \(0.809582\pi\)
\(90\) 7.18575 + 1.65025i 0.757444 + 0.173952i
\(91\) 3.31680 13.2867i 0.347695 1.39282i
\(92\) 5.11636 8.86180i 0.533418 0.923906i
\(93\) −5.35961 3.96113i −0.555766 0.410750i
\(94\) 17.5259 1.80765
\(95\) 3.34251 0.342935
\(96\) 9.30496 + 6.87703i 0.949683 + 0.701884i
\(97\) −6.09713 + 10.5605i −0.619070 + 1.07226i 0.370586 + 0.928798i \(0.379157\pi\)
−0.989656 + 0.143462i \(0.954176\pi\)
\(98\) −0.442393 12.8811i −0.0446885 1.30119i
\(99\) 3.09180 3.32321i 0.310738 0.333995i
\(100\) 2.23708 + 3.87474i 0.223708 + 0.387474i
\(101\) −0.559336 0.968798i −0.0556560 0.0963990i 0.836855 0.547425i \(-0.184392\pi\)
−0.892511 + 0.451025i \(0.851058\pi\)
\(102\) −4.52888 + 1.97231i −0.448426 + 0.195288i
\(103\) −0.965224 + 1.67182i −0.0951063 + 0.164729i −0.909653 0.415369i \(-0.863652\pi\)
0.814547 + 0.580098i \(0.196986\pi\)
\(104\) −2.90593 5.03322i −0.284950 0.493548i
\(105\) −5.72987 2.14043i −0.559178 0.208885i
\(106\) −1.39082 + 2.40898i −0.135089 + 0.233981i
\(107\) 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i \(-0.0765454\pi\)
−0.691868 + 0.722024i \(0.743212\pi\)
\(108\) −2.39951 + 6.81334i −0.230892 + 0.655614i
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) −3.71839 −0.354535
\(111\) 0.109874 0.969312i 0.0104288 0.0920030i
\(112\) −9.22368 8.91234i −0.871556 0.842137i
\(113\) 7.25105 + 12.5592i 0.682121 + 1.18147i 0.974332 + 0.225115i \(0.0722758\pi\)
−0.292211 + 0.956354i \(0.594391\pi\)
\(114\) −0.899505 + 7.93544i −0.0842464 + 0.743222i
\(115\) 4.91242 + 8.50856i 0.458085 + 0.793427i
\(116\) −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
\(117\) 10.5770 11.3686i 0.977843 1.05103i
\(118\) 15.5462 1.43114
\(119\) 3.93965 1.12845i 0.361147 0.103445i
\(120\) −2.37997 + 1.03647i −0.217261 + 0.0946164i
\(121\) 4.35539 7.54376i 0.395945 0.685796i
\(122\) −5.96409 −0.539963
\(123\) −1.76039 + 15.5302i −0.158729 + 1.40031i
\(124\) −5.34904 −0.480358
\(125\) −10.9696 −0.981149
\(126\) 6.62356 13.0272i 0.590074 1.16056i
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) −8.56521 −0.757065
\(129\) 16.1972 7.05382i 1.42608 0.621054i
\(130\) −12.7205 −1.11566
\(131\) 1.00673 1.74371i 0.0879585 0.152349i −0.818690 0.574236i \(-0.805299\pi\)
0.906648 + 0.421888i \(0.138632\pi\)
\(132\) 0.410328 3.61992i 0.0357145 0.315074i
\(133\) 1.60471 6.42827i 0.139146 0.557402i
\(134\) −12.7660 −1.10282
\(135\) −4.51340 5.26608i −0.388451 0.453232i
\(136\) 0.869605 1.50620i 0.0745680 0.129156i
\(137\) −1.10870 1.92032i −0.0947225 0.164064i 0.814770 0.579784i \(-0.196863\pi\)
−0.909493 + 0.415720i \(0.863530\pi\)
\(138\) −21.5221 + 9.37280i −1.83208 + 0.797865i
\(139\) 0.377669 + 0.654143i 0.0320335 + 0.0554836i 0.881598 0.472002i \(-0.156468\pi\)
−0.849564 + 0.527485i \(0.823135\pi\)
\(140\) −4.71948 + 1.35182i −0.398869 + 0.114250i
\(141\) −13.2585 9.79894i −1.11656 0.825220i
\(142\) 22.7032 1.90521
\(143\) −3.91568 + 6.78216i −0.327446 + 0.567153i
\(144\) −4.26805 13.9029i −0.355671 1.15858i
\(145\) −0.0413391 0.0716014i −0.00343303 0.00594618i
\(146\) 2.53973 4.39894i 0.210189 0.364059i
\(147\) −6.86731 + 9.99200i −0.566407 + 0.824126i
\(148\) −0.391482 0.678068i −0.0321797 0.0557368i
\(149\) −3.29249 + 5.70277i −0.269732 + 0.467189i −0.968792 0.247873i \(-0.920268\pi\)
0.699061 + 0.715062i \(0.253602\pi\)
\(150\) 1.15605 10.1987i 0.0943909 0.832718i
\(151\) −6.33356 10.9700i −0.515417 0.892729i −0.999840 0.0178950i \(-0.994304\pi\)
0.484422 0.874834i \(-0.339030\pi\)
\(152\) −1.40593 2.43514i −0.114036 0.197516i
\(153\) 4.52888 + 1.04009i 0.366138 + 0.0840861i
\(154\) −1.78517 + 7.15115i −0.143853 + 0.576256i
\(155\) 2.56791 4.44775i 0.206260 0.357252i
\(156\) 1.40372 12.3837i 0.112388 0.991487i
\(157\) −17.3074 −1.38128 −0.690642 0.723197i \(-0.742672\pi\)
−0.690642 + 0.723197i \(0.742672\pi\)
\(158\) 10.8990 0.867078
\(159\) 2.39906 1.04478i 0.190258 0.0828567i
\(160\) −4.45822 + 7.72186i −0.352453 + 0.610467i
\(161\) 18.7219 5.36260i 1.47549 0.422632i
\(162\) 13.7168 9.29807i 1.07769 0.730525i
\(163\) 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i \(-0.00783167\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(164\) 6.27227 + 10.8639i 0.489782 + 0.848327i
\(165\) 2.81299 + 2.07900i 0.218991 + 0.161850i
\(166\) −5.15752 + 8.93309i −0.400301 + 0.693342i
\(167\) 1.76248 + 3.05270i 0.136385 + 0.236225i 0.926126 0.377215i \(-0.123118\pi\)
−0.789741 + 0.613440i \(0.789785\pi\)
\(168\) 0.850718 + 5.07473i 0.0656343 + 0.391524i
\(169\) −6.89546 + 11.9433i −0.530420 + 0.918714i
\(170\) −1.90332 3.29665i −0.145978 0.252842i
\(171\) 5.11729 5.50030i 0.391329 0.420618i
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) 10.1409 0.770999 0.385500 0.922708i \(-0.374029\pi\)
0.385500 + 0.922708i \(0.374029\pi\)
\(174\) 0.181113 0.0788742i 0.0137302 0.00597944i
\(175\) −2.06239 + 8.26164i −0.155902 + 0.624522i
\(176\) 3.66738 + 6.35208i 0.276439 + 0.478806i
\(177\) −11.7608 8.69207i −0.883996 0.653336i
\(178\) −1.29492 2.24287i −0.0970584 0.168110i
\(179\) 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i \(-0.813083\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(180\) −5.42536 1.24597i −0.404382 0.0928690i
\(181\) −16.9941 −1.26316 −0.631581 0.775310i \(-0.717594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(182\) −6.10702 + 24.4639i −0.452683 + 1.81339i
\(183\) 4.51188 + 3.33460i 0.333528 + 0.246501i
\(184\) 4.13252 7.15774i 0.304654 0.527676i
\(185\) 0.751755 0.0552701
\(186\) 9.86833 + 7.29340i 0.723581 + 0.534778i
\(187\) −2.34355 −0.171377
\(188\) −13.2323 −0.965066
\(189\) −12.2945 + 6.15189i −0.894292 + 0.447484i
\(190\) −6.15437 −0.446485
\(191\) 22.6939 1.64208 0.821038 0.570873i \(-0.193395\pi\)
0.821038 + 0.570873i \(0.193395\pi\)
\(192\) −3.62762 2.68107i −0.261801 0.193490i
\(193\) 6.18698 0.445348 0.222674 0.974893i \(-0.428521\pi\)
0.222674 + 0.974893i \(0.428521\pi\)
\(194\) 11.2263 19.4445i 0.806001 1.39603i
\(195\) 9.62319 + 7.11222i 0.689131 + 0.509317i
\(196\) 0.334014 + 9.72544i 0.0238582 + 0.694674i
\(197\) 9.77010 0.696091 0.348045 0.937478i \(-0.386846\pi\)
0.348045 + 0.937478i \(0.386846\pi\)
\(198\) −5.69275 + 6.11883i −0.404566 + 0.434846i
\(199\) −4.33973 + 7.51664i −0.307636 + 0.532840i −0.977845 0.209332i \(-0.932871\pi\)
0.670209 + 0.742172i \(0.266204\pi\)
\(200\) 1.80691 + 3.12965i 0.127768 + 0.221300i
\(201\) 9.65762 + 7.13767i 0.681196 + 0.503452i
\(202\) 1.02987 + 1.78379i 0.0724615 + 0.125507i
\(203\) −0.157549 + 0.0451275i −0.0110578 + 0.00316733i
\(204\) 3.41938 1.48913i 0.239405 0.104260i
\(205\) −12.0445 −0.841224
\(206\) 1.77721 3.07822i 0.123824 0.214470i
\(207\) 21.5221 + 4.94269i 1.49589 + 0.343541i
\(208\) 12.5460 + 21.7303i 0.869909 + 1.50673i
\(209\) −1.89446 + 3.28130i −0.131043 + 0.226973i
\(210\) 10.5501 + 3.94105i 0.728024 + 0.271959i
\(211\) −2.84219 4.92283i −0.195665 0.338901i 0.751453 0.659786i \(-0.229353\pi\)
−0.947118 + 0.320885i \(0.896020\pi\)
\(212\) 1.05010 1.81882i 0.0721209 0.124917i
\(213\) −17.1751 12.6936i −1.17682 0.869754i
\(214\) −5.32062 9.21558i −0.363710 0.629964i
\(215\) 6.80708 + 11.7902i 0.464239 + 0.804086i
\(216\) −1.93810 + 5.50319i −0.131871 + 0.374445i
\(217\) −7.32102 7.07390i −0.496983 0.480207i
\(218\) 7.58786 13.1426i 0.513915 0.890126i
\(219\) −4.38083 + 1.90784i −0.296029 + 0.128920i
\(220\) 2.80745 0.189278
\(221\) −8.01723 −0.539298
\(222\) −0.202305 + 1.78474i −0.0135778 + 0.119784i
\(223\) 5.86133 10.1521i 0.392503 0.679836i −0.600276 0.799793i \(-0.704942\pi\)
0.992779 + 0.119957i \(0.0382758\pi\)
\(224\) 12.7102 + 12.2812i 0.849236 + 0.820571i
\(225\) −6.57677 + 7.06901i −0.438451 + 0.471267i
\(226\) −13.3509 23.1245i −0.888091 1.53822i
\(227\) −5.59154 9.68482i −0.371123 0.642804i 0.618615 0.785694i \(-0.287694\pi\)
−0.989739 + 0.142890i \(0.954361\pi\)
\(228\) 0.679141 5.99139i 0.0449772 0.396790i
\(229\) 4.82824 8.36275i 0.319059 0.552626i −0.661233 0.750181i \(-0.729967\pi\)
0.980292 + 0.197554i \(0.0632999\pi\)
\(230\) −9.04494 15.6663i −0.596406 1.03301i
\(231\) 5.34880 4.41179i 0.351925 0.290275i
\(232\) −0.0347761 + 0.0602340i −0.00228317 + 0.00395456i
\(233\) −9.64492 16.7055i −0.631860 1.09441i −0.987171 0.159666i \(-0.948958\pi\)
0.355311 0.934748i \(-0.384375\pi\)
\(234\) −19.4748 + 20.9324i −1.27311 + 1.36839i
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) −11.7376 −0.764054
\(237\) −8.24519 6.09378i −0.535582 0.395833i
\(238\) −7.25384 + 2.07775i −0.470197 + 0.134680i
\(239\) −0.194641 0.337128i −0.0125903 0.0218070i 0.859662 0.510864i \(-0.170674\pi\)
−0.872252 + 0.489057i \(0.837341\pi\)
\(240\) 10.2753 4.47484i 0.663265 0.288850i
\(241\) −5.31807 9.21117i −0.342567 0.593344i 0.642342 0.766419i \(-0.277963\pi\)
−0.984909 + 0.173075i \(0.944630\pi\)
\(242\) −8.01932 + 13.8899i −0.515502 + 0.892875i
\(243\) −15.5755 0.635158i −0.999170 0.0407454i
\(244\) 4.50299 0.288274
\(245\) −8.24709 4.39115i −0.526888 0.280540i
\(246\) 3.24130 28.5948i 0.206658 1.82314i
\(247\) −6.48091 + 11.2253i −0.412370 + 0.714247i
\(248\) −4.32046 −0.274350
\(249\) 8.89631 3.87431i 0.563781 0.245525i
\(250\) 20.1976 1.27741
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) −5.00090 + 9.83578i −0.315027 + 0.619596i
\(253\) −11.1370 −0.700176
\(254\) −15.6506 −0.982007
\(255\) −0.403323 + 3.55812i −0.0252570 + 0.222818i
\(256\) 20.9793 1.31121
\(257\) 2.34787 4.06663i 0.146456 0.253669i −0.783459 0.621443i \(-0.786547\pi\)
0.929915 + 0.367774i \(0.119880\pi\)
\(258\) −29.8229 + 12.9878i −1.85669 + 0.808584i
\(259\) 0.360911 1.44576i 0.0224259 0.0898354i
\(260\) 9.60421 0.595628
\(261\) −0.181113 0.0415939i −0.0112106 0.00257459i
\(262\) −1.85363 + 3.21059i −0.114518 + 0.198351i
\(263\) −9.77491 16.9306i −0.602747 1.04399i −0.992403 0.123028i \(-0.960740\pi\)
0.389656 0.920960i \(-0.372594\pi\)
\(264\) 0.331425 2.92384i 0.0203978 0.179950i
\(265\) 1.00824 + 1.74632i 0.0619355 + 0.107276i
\(266\) −2.95466 + 11.8360i −0.181162 + 0.725711i
\(267\) −0.274400 + 2.42076i −0.0167930 + 0.148148i
\(268\) 9.63858 0.588770
\(269\) 7.88365 13.6549i 0.480675 0.832553i −0.519079 0.854726i \(-0.673725\pi\)
0.999754 + 0.0221730i \(0.00705846\pi\)
\(270\) 8.31025 + 9.69611i 0.505746 + 0.590087i
\(271\) 7.39882 + 12.8151i 0.449446 + 0.778464i 0.998350 0.0574218i \(-0.0182880\pi\)
−0.548904 + 0.835886i \(0.684955\pi\)
\(272\) −3.75442 + 6.50285i −0.227645 + 0.394293i
\(273\) 18.2981 15.0926i 1.10745 0.913448i
\(274\) 2.04138 + 3.53578i 0.123324 + 0.213604i
\(275\) 2.43477 4.21715i 0.146822 0.254304i
\(276\) 16.2495 7.07662i 0.978107 0.425962i
\(277\) 3.72561 + 6.45295i 0.223850 + 0.387720i 0.955974 0.293452i \(-0.0948040\pi\)
−0.732124 + 0.681172i \(0.761471\pi\)
\(278\) −0.695380 1.20443i −0.0417061 0.0722371i
\(279\) −3.38764 11.0350i −0.202812 0.660650i
\(280\) −3.81196 + 1.09188i −0.227808 + 0.0652521i
\(281\) −12.9938 + 22.5060i −0.775146 + 1.34259i 0.159566 + 0.987187i \(0.448991\pi\)
−0.934712 + 0.355406i \(0.884343\pi\)
\(282\) 24.4120 + 18.0422i 1.45371 + 1.07440i
\(283\) 18.7554 1.11489 0.557445 0.830214i \(-0.311782\pi\)
0.557445 + 0.830214i \(0.311782\pi\)
\(284\) −17.1413 −1.01715
\(285\) 4.65583 + 3.44099i 0.275788 + 0.203827i
\(286\) 7.20971 12.4876i 0.426319 0.738406i
\(287\) −5.78246 + 23.1638i −0.341328 + 1.36732i
\(288\) 5.88136 + 19.1582i 0.346563 + 1.12891i
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) 0.0761152 + 0.131835i 0.00446964 + 0.00774165i
\(291\) −19.3645 + 8.43316i −1.13516 + 0.494360i
\(292\) −1.91754 + 3.32127i −0.112215 + 0.194363i
\(293\) −1.23089 2.13196i −0.0719093 0.124551i 0.827829 0.560981i \(-0.189576\pi\)
−0.899738 + 0.436430i \(0.856243\pi\)
\(294\) 12.6444 18.3977i 0.737435 1.07297i
\(295\) 5.63487 9.75988i 0.328075 0.568242i
\(296\) −0.316203 0.547680i −0.0183790 0.0318333i
\(297\) 7.72773 1.44605i 0.448408 0.0839083i
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) −38.0994 −2.20334
\(300\) −0.872835 + 7.70016i −0.0503932 + 0.444569i
\(301\) 25.9428 7.43089i 1.49532 0.428309i
\(302\) 11.6616 + 20.1985i 0.671050 + 1.16229i
\(303\) 0.218235 1.92527i 0.0125372 0.110604i
\(304\) 6.06994 + 10.5134i 0.348135 + 0.602987i
\(305\) −2.16175 + 3.74425i −0.123781 + 0.214395i
\(306\) −8.33876 1.91505i −0.476695 0.109476i
\(307\) −4.66277 −0.266118 −0.133059 0.991108i \(-0.542480\pi\)
−0.133059 + 0.991108i \(0.542480\pi\)
\(308\) 1.34783 5.39924i 0.0767999 0.307650i
\(309\) −3.06555 + 1.33503i −0.174393 + 0.0759475i
\(310\) −4.72814 + 8.18938i −0.268541 + 0.465126i
\(311\) 27.4821 1.55837 0.779183 0.626797i \(-0.215634\pi\)
0.779183 + 0.626797i \(0.215634\pi\)
\(312\) 1.13380 10.0024i 0.0641887 0.566273i
\(313\) 5.49332 0.310501 0.155250 0.987875i \(-0.450382\pi\)
0.155250 + 0.987875i \(0.450382\pi\)
\(314\) 31.8671 1.79837
\(315\) −5.77772 8.88013i −0.325538 0.500338i
\(316\) −8.22893 −0.462914
\(317\) 9.87758 0.554780 0.277390 0.960757i \(-0.410531\pi\)
0.277390 + 0.960757i \(0.410531\pi\)
\(318\) −4.41725 + 1.92370i −0.247707 + 0.107876i
\(319\) 0.0937203 0.00524733
\(320\) 1.73808 3.01044i 0.0971614 0.168288i
\(321\) −1.12746 + 9.94649i −0.0629288 + 0.555159i
\(322\) −34.4716 + 9.87383i −1.92103 + 0.550247i
\(323\) −3.87885 −0.215825
\(324\) −10.3564 + 7.02020i −0.575354 + 0.390011i
\(325\) 8.32930 14.4268i 0.462026 0.800253i
\(326\) −11.2493 19.4844i −0.623041 1.07914i
\(327\) −13.0885 + 5.69998i −0.723793 + 0.315209i
\(328\) 5.06616 + 8.77485i 0.279732 + 0.484510i
\(329\) −18.1105 17.4992i −0.998466 0.964763i
\(330\) −5.17940 3.82794i −0.285116 0.210721i
\(331\) −20.6942 −1.13746 −0.568729 0.822525i \(-0.692565\pi\)
−0.568729 + 0.822525i \(0.692565\pi\)
\(332\) 3.89401 6.74463i 0.213712 0.370160i
\(333\) 1.15092 1.23706i 0.0630698 0.0677903i
\(334\) −3.24514 5.62076i −0.177566 0.307554i
\(335\) −4.62718 + 8.01452i −0.252810 + 0.437880i
\(336\) −3.67288 21.9095i −0.200372 1.19526i
\(337\) 0.748747 + 1.29687i 0.0407869 + 0.0706449i 0.885698 0.464261i \(-0.153680\pi\)
−0.844911 + 0.534906i \(0.820347\pi\)
\(338\) 12.6962 21.9905i 0.690582 1.19612i
\(339\) −2.82912 + 24.9585i −0.153657 + 1.35556i
\(340\) 1.43704 + 2.48903i 0.0779344 + 0.134986i
\(341\) 2.91087 + 5.04177i 0.157632 + 0.273027i
\(342\) −9.42217 + 10.1274i −0.509493 + 0.547626i
\(343\) −12.4044 + 13.7525i −0.669772 + 0.742567i
\(344\) 5.72639 9.91840i 0.308746 0.534764i
\(345\) −1.91666 + 16.9088i −0.103190 + 0.910341i
\(346\) −18.6719 −1.00381
\(347\) −29.5388 −1.58572 −0.792862 0.609401i \(-0.791410\pi\)
−0.792862 + 0.609401i \(0.791410\pi\)
\(348\) −0.136744 + 0.0595513i −0.00733022 + 0.00319229i
\(349\) 18.0006 31.1780i 0.963551 1.66892i 0.250094 0.968222i \(-0.419539\pi\)
0.713458 0.700698i \(-0.247128\pi\)
\(350\) 3.79735 15.2117i 0.202977 0.813098i
\(351\) 26.4364 4.94691i 1.41107 0.264046i
\(352\) −5.05363 8.75315i −0.269360 0.466545i
\(353\) 14.7465 + 25.5417i 0.784877 + 1.35945i 0.929073 + 0.369897i \(0.120607\pi\)
−0.144196 + 0.989549i \(0.546060\pi\)
\(354\) 21.6545 + 16.0042i 1.15092 + 0.850613i
\(355\) 8.22900 14.2530i 0.436750 0.756473i
\(356\) 0.977687 + 1.69340i 0.0518173 + 0.0897502i
\(357\) 6.64928 + 2.48389i 0.351917 + 0.131461i
\(358\) −1.56612 + 2.71260i −0.0827720 + 0.143365i
\(359\) 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i \(-0.121062\pi\)
−0.785761 + 0.618531i \(0.787728\pi\)
\(360\) −4.38210 1.00638i −0.230957 0.0530408i
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) 31.2902 1.64458
\(363\) 13.8327 6.02409i 0.726028 0.316183i
\(364\) 4.61090 18.4707i 0.241677 0.968126i
\(365\) −1.84110 3.18888i −0.0963676 0.166914i
\(366\) −8.30746 6.13980i −0.434238 0.320933i
\(367\) 11.5422 + 19.9916i 0.602496 + 1.04355i 0.992442 + 0.122715i \(0.0391602\pi\)
−0.389946 + 0.920838i \(0.627506\pi\)
\(368\) −17.8417 + 30.9027i −0.930063 + 1.61092i
\(369\) −18.4398 + 19.8199i −0.959937 + 1.03178i
\(370\) −1.38416 −0.0719591
\(371\) 3.84254 1.10063i 0.199495 0.0571421i
\(372\) −7.45075 5.50664i −0.386304 0.285506i
\(373\) −10.7515 + 18.6222i −0.556692 + 0.964219i 0.441078 + 0.897469i \(0.354596\pi\)
−0.997770 + 0.0667498i \(0.978737\pi\)
\(374\) 4.31504 0.223125
\(375\) −15.2797 11.2928i −0.789039 0.583156i
\(376\) −10.6878 −0.551184
\(377\) 0.320615 0.0165125
\(378\) 22.6371 11.3271i 1.16433 0.582604i
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) 4.64665 0.238368
\(381\) 11.8398 + 8.75047i 0.606572 + 0.448300i
\(382\) −41.7850 −2.13791
\(383\) 17.4604 30.2424i 0.892187 1.54531i 0.0549390 0.998490i \(-0.482504\pi\)
0.837248 0.546823i \(-0.184163\pi\)
\(384\) −11.9306 8.81756i −0.608831 0.449969i
\(385\) 3.84244 + 3.71274i 0.195829 + 0.189219i
\(386\) −11.3917 −0.579823
\(387\) 29.8229 + 6.84903i 1.51598 + 0.348156i
\(388\) −8.47603 + 14.6809i −0.430305 + 0.745311i
\(389\) 14.4411 + 25.0127i 0.732192 + 1.26819i 0.955944 + 0.293548i \(0.0948361\pi\)
−0.223752 + 0.974646i \(0.571831\pi\)
\(390\) −17.7186 13.0953i −0.897216 0.663107i
\(391\) −5.70066 9.87383i −0.288295 0.499341i
\(392\) 0.269786 + 7.85531i 0.0136262 + 0.396753i
\(393\) 3.19737 1.39244i 0.161286 0.0702395i
\(394\) −17.9891 −0.906278
\(395\) 3.95046 6.84239i 0.198769 0.344278i
\(396\) 4.29812 4.61982i 0.215989 0.232155i
\(397\) 5.59226 + 9.68607i 0.280667 + 0.486130i 0.971549 0.236838i \(-0.0761109\pi\)
−0.690882 + 0.722968i \(0.742778\pi\)
\(398\) 7.99049 13.8399i 0.400527 0.693734i
\(399\) 8.85289 7.30203i 0.443199 0.365559i
\(400\) −7.80111 13.5119i −0.390056 0.675596i
\(401\) 0.541061 0.937146i 0.0270193 0.0467988i −0.852200 0.523217i \(-0.824732\pi\)
0.879219 + 0.476418i \(0.158065\pi\)
\(402\) −17.7820 13.1422i −0.886885 0.655471i
\(403\) 9.95802 + 17.2478i 0.496044 + 0.859174i
\(404\) −0.777570 1.34679i −0.0386856 0.0670054i
\(405\) −0.865544 11.9816i −0.0430092 0.595368i
\(406\) 0.290086 0.0830905i 0.0143967 0.00412371i
\(407\) −0.426078 + 0.737988i −0.0211199 + 0.0365807i
\(408\) 2.76186 1.20278i 0.136732 0.0595465i
\(409\) −21.7349 −1.07472 −0.537360 0.843353i \(-0.680578\pi\)
−0.537360 + 0.843353i \(0.680578\pi\)
\(410\) 22.1768 1.09524
\(411\) 0.432578 3.81621i 0.0213375 0.188240i
\(412\) −1.34182 + 2.32410i −0.0661069 + 0.114500i
\(413\) −16.0648 15.5225i −0.790497 0.763814i
\(414\) −39.6273 9.10068i −1.94758 0.447274i
\(415\) 3.73879 + 6.47578i 0.183530 + 0.317884i
\(416\) −17.2884 29.9443i −0.847632 1.46814i
\(417\) −0.147354 + 1.29996i −0.00721597 + 0.0636593i
\(418\) 3.48816 6.04167i 0.170611 0.295508i
\(419\) 12.5906 + 21.8075i 0.615090 + 1.06537i 0.990369 + 0.138455i \(0.0442135\pi\)
−0.375279 + 0.926912i \(0.622453\pi\)
\(420\) −7.96548 2.97556i −0.388676 0.145193i
\(421\) −14.8304 + 25.6869i −0.722788 + 1.25191i 0.237090 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280418i \(0.909527\pi\)
\(422\) 5.23316 + 9.06411i 0.254746 + 0.441234i
\(423\) −8.38024 27.2982i −0.407461 1.32728i
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) 4.98512 0.241814
\(426\) 31.6236 + 23.3721i 1.53217 + 1.13238i
\(427\) 6.16305 + 5.95502i 0.298251 + 0.288184i
\(428\) 4.01715 + 6.95791i 0.194176 + 0.336323i
\(429\) −12.4362 + 5.41591i −0.600424 + 0.261483i
\(430\) −12.5335 21.7086i −0.604418 1.04688i
\(431\) 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i \(-0.795756\pi\)
0.918887 + 0.394520i \(0.129089\pi\)
\(432\) 8.36752 23.7594i 0.402582 1.14312i
\(433\) 9.71430 0.466839 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(434\) 13.4798 + 13.0247i 0.647049 + 0.625208i
\(435\) 0.0161292 0.142292i 0.000773334 0.00682236i
\(436\) −5.72896 + 9.92285i −0.274367 + 0.475218i
\(437\) −18.4330 −0.881771
\(438\) 8.06616 3.51279i 0.385416 0.167847i
\(439\) −14.8235 −0.707488 −0.353744 0.935342i \(-0.615092\pi\)
−0.353744 + 0.935342i \(0.615092\pi\)
\(440\) 2.26760 0.108103
\(441\) −19.8520 + 6.84835i −0.945331 + 0.326112i
\(442\) 14.7617 0.702141
\(443\) −21.9020 −1.04059 −0.520297 0.853986i \(-0.674179\pi\)
−0.520297 + 0.853986i \(0.674179\pi\)
\(444\) 0.152744 1.34751i 0.00724889 0.0639498i
\(445\) −1.87743 −0.0889987
\(446\) −10.7921 + 18.6925i −0.511021 + 0.885115i
\(447\) −10.4569 + 4.55396i −0.494596 + 0.215395i
\(448\) −4.95519 4.78793i −0.234111 0.226208i
\(449\) 21.4952 1.01442 0.507212 0.861822i \(-0.330676\pi\)
0.507212 + 0.861822i \(0.330676\pi\)
\(450\) 12.1094 13.0158i 0.570843 0.613568i
\(451\) 6.82655 11.8239i 0.321450 0.556767i
\(452\) 10.0802 + 17.4594i 0.474131 + 0.821220i
\(453\) 2.47115 21.8005i 0.116105 1.02428i
\(454\) 10.2954 + 17.8321i 0.483185 + 0.836902i
\(455\) 13.1449 + 12.7012i 0.616242 + 0.595441i
\(456\) 0.548548 4.83929i 0.0256881 0.226621i
\(457\) 40.6255 1.90038 0.950190 0.311670i \(-0.100888\pi\)
0.950190 + 0.311670i \(0.100888\pi\)
\(458\) −8.88995 + 15.3978i −0.415400 + 0.719494i
\(459\) 5.23761 + 6.11107i 0.244471 + 0.285240i
\(460\) 6.82908 + 11.8283i 0.318408 + 0.551498i
\(461\) 1.41541 2.45155i 0.0659220 0.114180i −0.831181 0.556003i \(-0.812334\pi\)
0.897103 + 0.441822i \(0.145668\pi\)
\(462\) −9.84843 + 8.12317i −0.458190 + 0.377924i
\(463\) −13.9324 24.1317i −0.647494 1.12149i −0.983719 0.179711i \(-0.942484\pi\)
0.336225 0.941782i \(-0.390850\pi\)
\(464\) 0.150142 0.260053i 0.00697016 0.0120727i
\(465\) 8.15567 3.55177i 0.378210 0.164709i
\(466\) 17.7586 + 30.7588i 0.822653 + 1.42488i
\(467\) −13.3219 23.0742i −0.616464 1.06775i −0.990126 0.140182i \(-0.955231\pi\)
0.373661 0.927565i \(-0.378102\pi\)
\(468\) 14.7038 15.8043i 0.679682 0.730554i
\(469\) 13.1919 + 12.7466i 0.609146 + 0.588585i
\(470\) −11.6964 + 20.2587i −0.539513 + 0.934463i
\(471\) −24.1078 17.8173i −1.11083 0.820980i
\(472\) −9.48056 −0.436378
\(473\) −15.4324 −0.709582
\(474\) 15.1814 + 11.2201i 0.697304 + 0.515357i
\(475\) 4.02983 6.97987i 0.184901 0.320258i
\(476\) 5.47677 1.56873i 0.251027 0.0719027i
\(477\) 4.41725 + 1.01445i 0.202252 + 0.0464485i
\(478\) 0.358381 + 0.620734i 0.0163920 + 0.0283917i
\(479\) 15.7895 + 27.3483i 0.721443 + 1.24958i 0.960422 + 0.278551i \(0.0898540\pi\)
−0.238979 + 0.971025i \(0.576813\pi\)
\(480\) −14.1593 + 6.16632i −0.646280 + 0.281453i
\(481\) −1.45760 + 2.52464i −0.0664609 + 0.115114i
\(482\) 9.79185 + 16.9600i 0.446007 + 0.772506i
\(483\) 31.5986 + 11.8039i 1.43779 + 0.537095i
\(484\) 6.05472 10.4871i 0.275215 0.476686i
\(485\) −8.13817 14.0957i −0.369535 0.640054i
\(486\) 28.6783 + 1.16948i 1.30087 + 0.0530486i
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) 3.63710 0.164644
\(489\) −2.38378 + 21.0297i −0.107798 + 0.950996i
\(490\) 15.1849 + 8.08516i 0.685983 + 0.365250i
\(491\) −9.06981 15.7094i −0.409315 0.708954i 0.585498 0.810674i \(-0.300899\pi\)
−0.994813 + 0.101720i \(0.967566\pi\)
\(492\) −2.44723 + 21.5895i −0.110330 + 0.973331i
\(493\) 0.0479723 + 0.0830905i 0.00216057 + 0.00374221i
\(494\) 11.9329 20.6684i 0.536887 0.929916i
\(495\) 1.77800 + 5.79174i 0.0799153 + 0.260319i
\(496\) 18.6531 0.837549
\(497\) −23.4606 22.6687i −1.05235 1.01683i
\(498\) −16.3803 + 7.13355i −0.734017 + 0.319662i
\(499\) 10.6546 18.4543i 0.476964 0.826126i −0.522687 0.852524i \(-0.675070\pi\)
0.999652 + 0.0263983i \(0.00840381\pi\)
\(500\) −15.2496 −0.681981
\(501\) −0.687661 + 6.06655i −0.0307224 + 0.271033i
\(502\) 6.01401 0.268418
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) −4.03926 + 7.94444i −0.179923 + 0.353873i
\(505\) 1.49315 0.0664443
\(506\) 20.5059 0.911597
\(507\) −21.8999 + 9.53735i −0.972610 + 0.423568i
\(508\) 11.8165 0.524271
\(509\) −18.3868 + 31.8468i −0.814979 + 1.41159i 0.0943635 + 0.995538i \(0.469918\pi\)
−0.909343 + 0.416048i \(0.863415\pi\)
\(510\) 0.742614 6.55135i 0.0328835 0.290099i
\(511\) −7.01670 + 2.00982i −0.310401 + 0.0889093i
\(512\) −21.4975 −0.950065
\(513\) 12.7903 2.39338i 0.564705 0.105670i
\(514\) −4.32299 + 7.48764i −0.190679 + 0.330265i
\(515\) −1.28834 2.23146i −0.0567709 0.0983300i
\(516\) 22.5168 9.80599i 0.991247 0.431685i
\(517\) 7.20083 + 12.4722i 0.316692 + 0.548527i
\(518\) −0.664525 + 2.66200i −0.0291975 + 0.116961i
\(519\) 14.1254 + 10.4397i 0.620037 + 0.458251i
\(520\) 7.75740 0.340184
\(521\) −9.57535 + 16.5850i −0.419504 + 0.726602i −0.995890 0.0905758i \(-0.971129\pi\)
0.576386 + 0.817178i \(0.304463\pi\)
\(522\) 0.333473 + 0.0765843i 0.0145957 + 0.00335200i
\(523\) −20.9715 36.3236i −0.917018 1.58832i −0.803920 0.594737i \(-0.797256\pi\)
−0.113097 0.993584i \(-0.536077\pi\)
\(524\) 1.39952 2.42405i 0.0611385 0.105895i
\(525\) −11.3778 + 9.38461i −0.496567 + 0.409578i
\(526\) 17.9980 + 31.1734i 0.784749 + 1.35922i
\(527\) −2.97996 + 5.16144i −0.129809 + 0.224836i
\(528\) −1.43089 + 12.6233i −0.0622715 + 0.549360i
\(529\) −15.5906 27.0037i −0.677851 1.17407i
\(530\) −1.85641 3.21539i −0.0806372 0.139668i
\(531\) −7.43362 24.2146i −0.322592 1.05082i
\(532\) 2.23082 8.93637i 0.0967183 0.387441i
\(533\) 23.3535 40.4494i 1.01155 1.75206i
\(534\) 0.505236 4.45719i 0.0218637 0.192882i
\(535\) −7.71405 −0.333507
\(536\) 7.78515 0.336267
\(537\) 2.70143 1.17646i 0.116575 0.0507682i
\(538\) −14.5157 + 25.1419i −0.625816 + 1.08395i
\(539\) 8.98500 5.60726i 0.387011 0.241522i
\(540\) −6.27438 7.32073i −0.270006 0.315034i
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) −13.6230 23.5957i −0.585158 1.01352i
\(543\) −23.6713 17.4948i −1.01583 0.750773i
\(544\) 5.17358 8.96090i 0.221815 0.384196i
\(545\) −5.50059 9.52731i −0.235620 0.408105i
\(546\) −33.6912 + 27.7892i −1.44185 + 1.18927i
\(547\) 1.38738 2.40301i 0.0593201 0.102745i −0.834840 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147773\pi\)
\(548\) −1.54128 2.66957i −0.0658401 0.114038i
\(549\) 2.85181 + 9.28962i 0.121712 + 0.396471i
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) 0.155118 0.00660825
\(552\) 13.1249 5.71584i 0.558632 0.243282i
\(553\) −11.2626 10.8824i −0.478935 0.462768i
\(554\) −6.85975 11.8814i −0.291443 0.504794i
\(555\) 1.04713 + 0.773903i 0.0444482 + 0.0328504i
\(556\) 0.525024 + 0.909368i 0.0222660 + 0.0385658i
\(557\) 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i \(-0.604646\pi\)
0.981078 0.193614i \(-0.0620211\pi\)
\(558\) 6.23745 + 20.3181i 0.264052 + 0.860136i
\(559\) −52.7939 −2.23294
\(560\) 16.4577 4.71405i 0.695465 0.199205i
\(561\) −3.26436 2.41260i −0.137822 0.101860i
\(562\) 23.9248 41.4389i 1.00920 1.74799i
\(563\) 0.288041 0.0121395 0.00606973 0.999982i \(-0.498068\pi\)
0.00606973 + 0.999982i \(0.498068\pi\)
\(564\) −18.4315 13.6222i −0.776105 0.573597i
\(565\) −19.3567 −0.814344
\(566\) −34.5331 −1.45154
\(567\) −23.4583 4.08765i −0.985155 0.171665i
\(568\) −13.8451 −0.580929
\(569\) −16.0801 −0.674112 −0.337056 0.941485i \(-0.609431\pi\)
−0.337056 + 0.941485i \(0.609431\pi\)
\(570\) −8.57251 6.33569i −0.359063 0.265373i
\(571\) −15.2858 −0.639690 −0.319845 0.947470i \(-0.603631\pi\)
−0.319845 + 0.947470i \(0.603631\pi\)
\(572\) −5.44345 + 9.42834i −0.227602 + 0.394218i
\(573\) 31.6107 + 23.3626i 1.32056 + 0.975985i
\(574\) 10.6469 42.6501i 0.444393 1.78018i
\(575\) 23.6902 0.987950
\(576\) −2.29290 7.46900i −0.0955376 0.311208i
\(577\) 12.0812 20.9253i 0.502949 0.871133i −0.497045 0.867725i \(-0.665582\pi\)
0.999994 0.00340833i \(-0.00108491\pi\)
\(578\) −13.4418 23.2819i −0.559106 0.968400i
\(579\) 8.61793 + 6.36926i 0.358149 + 0.264697i
\(580\) −0.0574683 0.0995380i −0.00238624 0.00413309i
\(581\) 14.2491 4.08142i 0.591152 0.169326i
\(582\) 35.6546 15.5275i 1.47793 0.643634i
\(583\) −2.28579 −0.0946676
\(584\) −1.54881 + 2.68262i −0.0640902 + 0.111007i
\(585\) 6.08251 + 19.8134i 0.251481 + 0.819184i
\(586\) 2.26636 + 3.92546i 0.0936226 + 0.162159i
\(587\) 18.0145 31.2020i 0.743537 1.28784i −0.207339 0.978269i \(-0.566480\pi\)
0.950875 0.309574i \(-0.100186\pi\)
\(588\) −9.54672 + 13.8905i −0.393700 + 0.572836i
\(589\) 4.81783 + 8.34472i 0.198515 + 0.343838i
\(590\) −10.3752 + 17.9703i −0.427138 + 0.739825i
\(591\) 13.6089 + 10.0579i 0.559795 + 0.413729i
\(592\) 1.36517 + 2.36455i 0.0561082 + 0.0971823i
\(593\) 12.4668 + 21.5932i 0.511951 + 0.886726i 0.999904 + 0.0138558i \(0.00441057\pi\)
−0.487953 + 0.872870i \(0.662256\pi\)
\(594\) −14.2286 + 2.66253i −0.583807 + 0.109245i
\(595\) −1.32482 + 5.30706i −0.0543124 + 0.217568i
\(596\) −4.57712 + 7.92780i −0.187486 + 0.324735i
\(597\) −13.7830 + 6.00244i −0.564099 + 0.245663i
\(598\) 70.1501 2.86865
\(599\) 39.5283 1.61508 0.807542 0.589810i \(-0.200797\pi\)
0.807542 + 0.589810i \(0.200797\pi\)
\(600\) −0.704996 + 6.21948i −0.0287813 + 0.253909i
\(601\) 1.86447 3.22936i 0.0760534 0.131728i −0.825490 0.564416i \(-0.809101\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(602\) −47.7669 + 13.6821i −1.94683 + 0.557639i
\(603\) 6.10427 + 19.8843i 0.248585 + 0.809751i
\(604\) −8.80470 15.2502i −0.358258 0.620521i
\(605\) 5.81337 + 10.0691i 0.236347 + 0.409365i
\(606\) −0.401822 + 3.54488i −0.0163229 + 0.144001i
\(607\) −11.8264 + 20.4839i −0.480018 + 0.831415i −0.999737 0.0229218i \(-0.992703\pi\)
0.519719 + 0.854337i \(0.326036\pi\)
\(608\) −8.36436 14.4875i −0.339219 0.587545i
\(609\) −0.265910 0.0993324i −0.0107752 0.00402515i
\(610\) 3.98029 6.89407i 0.161157 0.279133i
\(611\) 24.6339 + 42.6671i 0.996580 + 1.72613i
\(612\) 6.29590 + 1.44590i 0.254497 + 0.0584469i
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) 8.58528 0.346474
\(615\) −16.7769 12.3994i −0.676512 0.499990i
\(616\) 1.08865 4.36101i 0.0438631 0.175710i
\(617\) −17.5615 30.4174i −0.706999 1.22456i −0.965965 0.258672i \(-0.916715\pi\)
0.258966 0.965886i \(-0.416618\pi\)
\(618\) 5.64441 2.45812i 0.227051 0.0988801i
\(619\) 10.5816 + 18.3279i 0.425311 + 0.736660i 0.996449 0.0841934i \(-0.0268314\pi\)
−0.571138 + 0.820854i \(0.693498\pi\)
\(620\) 3.56983 6.18312i 0.143368 0.248320i
\(621\) 24.8901 + 29.0409i 0.998805 + 1.16537i
\(622\) −50.6011 −2.02892
\(623\) −0.901339 + 3.61064i −0.0361114 + 0.144657i
\(624\) −4.89504 + 43.1841i −0.195959 + 1.72875i
\(625\) −0.725240 + 1.25615i −0.0290096 + 0.0502461i
\(626\) −10.1145 −0.404257
\(627\) −6.01680 + 2.62030i −0.240288 + 0.104645i
\(628\) −24.0602 −0.960107
\(629\) −0.872381 −0.0347841
\(630\) 10.6382 + 16.3505i 0.423835 + 0.651418i
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) −6.64657 −0.264386
\(633\) 1.10893 9.78300i 0.0440761 0.388839i
\(634\) −18.1870 −0.722298
\(635\) −5.67273 + 9.82546i −0.225115 + 0.389911i
\(636\) 3.33510 1.45242i 0.132245 0.0575924i
\(637\) 30.7375 19.1823i 1.21786 0.760031i
\(638\) −0.172562 −0.00683178
\(639\) −10.8558 35.3623i −0.429451 1.39891i
\(640\) 5.71622 9.90078i 0.225953 0.391363i
\(641\) 4.93735 + 8.55174i 0.195013 + 0.337773i 0.946905 0.321514i \(-0.104192\pi\)
−0.751891 + 0.659287i \(0.770858\pi\)
\(642\) 2.07593 18.3139i 0.0819304 0.722791i
\(643\) 21.9748 + 38.0615i 0.866602 + 1.50100i 0.865448 + 0.501000i \(0.167034\pi\)
0.00115462 + 0.999999i \(0.499632\pi\)
\(644\) 26.0266 7.45491i 1.02559 0.293764i
\(645\) −2.65590 + 23.4304i −0.104576 + 0.922570i
\(646\) 7.14190 0.280994
\(647\) 22.1936 38.4404i 0.872521 1.51125i 0.0131398 0.999914i \(-0.495817\pi\)
0.859381 0.511336i \(-0.170849\pi\)
\(648\) −8.36493 + 5.67027i −0.328605 + 0.222749i
\(649\) 6.38743 + 11.0634i 0.250729 + 0.434275i
\(650\) −15.3362 + 26.5631i −0.601537 + 1.04189i
\(651\) −2.91523 17.3900i −0.114257 0.681569i
\(652\) 8.49341 + 14.7110i 0.332628 + 0.576128i
\(653\) −20.9956 + 36.3655i −0.821622 + 1.42309i 0.0828523 + 0.996562i \(0.473597\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(654\) 24.0990 10.4950i 0.942345 0.410388i
\(655\) 1.34374 + 2.32742i 0.0525042 + 0.0909399i
\(656\) −21.8726 37.8844i −0.853980 1.47914i
\(657\) −8.06616 1.85245i −0.314691 0.0722708i
\(658\) 33.3459 + 32.2203i 1.29996 + 1.25608i
\(659\) −19.6365 + 34.0114i −0.764928 + 1.32489i 0.175356 + 0.984505i \(0.443892\pi\)
−0.940284 + 0.340390i \(0.889441\pi\)
\(660\) 3.91053 + 2.89016i 0.152217 + 0.112499i
\(661\) −0.186739 −0.00726330 −0.00363165 0.999993i \(-0.501156\pi\)
−0.00363165 + 0.999993i \(0.501156\pi\)
\(662\) 38.1030 1.48092
\(663\) −11.1673 8.25344i −0.433703 0.320537i
\(664\) 3.14522 5.44769i 0.122058 0.211411i
\(665\) 6.35969 + 6.14502i 0.246618 + 0.238293i
\(666\) −2.11911 + 2.27772i −0.0821139 + 0.0882598i
\(667\) 0.227973 + 0.394862i 0.00882717 + 0.0152891i
\(668\) 2.45014 + 4.24376i 0.0947987 + 0.164196i
\(669\) 18.6155 8.10700i 0.719718 0.313435i
\(670\) 8.51976 14.7567i 0.329147 0.570099i
\(671\) −2.45046 4.24432i −0.0945989 0.163850i
\(672\) 5.06121 + 30.1913i 0.195241 + 1.16465i
\(673\) −5.43382 + 9.41166i −0.209458 + 0.362793i −0.951544 0.307512i \(-0.900503\pi\)
0.742086 + 0.670305i \(0.233837\pi\)
\(674\) −1.37862 2.38785i −0.0531026 0.0919764i
\(675\) −16.4381 + 3.07599i −0.632705 + 0.118395i
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) 28.3901 1.09112 0.545560 0.838072i \(-0.316317\pi\)
0.545560 + 0.838072i \(0.316317\pi\)
\(678\) 5.20910 45.9547i 0.200054 1.76488i
\(679\) −31.0157 + 8.88396i −1.19027 + 0.340935i
\(680\) 1.16071 + 2.01041i 0.0445111 + 0.0770956i
\(681\) 2.18163 19.2464i 0.0836004 0.737524i
\(682\) −5.35961 9.28312i −0.205230 0.355469i
\(683\) 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i \(-0.760593\pi\)
0.956779 + 0.290816i \(0.0939267\pi\)
\(684\) 7.11389 7.64634i 0.272007 0.292365i
\(685\) 2.95968 0.113083
\(686\) 22.8394 25.3217i 0.872012 0.966788i
\(687\) 15.3345 6.67810i 0.585046 0.254786i
\(688\) −24.7230 + 42.8216i −0.942557 + 1.63256i
\(689\) −7.81962 −0.297904
\(690\) 3.52904 31.1332i 0.134348 1.18522i
\(691\) 11.9083 0.453014 0.226507 0.974010i \(-0.427269\pi\)
0.226507 + 0.974010i \(0.427269\pi\)
\(692\) 14.0976 0.535909
\(693\) 11.9922 0.638859i 0.455546 0.0242683i
\(694\) 54.3880 2.06454
\(695\) −1.00819 −0.0382429
\(696\) −0.110449 + 0.0481001i −0.00418655 + 0.00182323i
\(697\) 13.9771 0.529422
\(698\) −33.1435 + 57.4062i −1.25450 + 2.17286i
\(699\) 3.76313 33.1984i 0.142335 1.25568i
\(700\) −2.86706 + 11.4851i −0.108365 + 0.434095i
\(701\) −31.3902 −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(702\) −48.6758 + 9.10844i −1.83715 + 0.343776i
\(703\) −0.705208 + 1.22146i −0.0265974 + 0.0460681i
\(704\) 1.97020 + 3.41249i 0.0742549 + 0.128613i
\(705\) 20.1753 8.78627i 0.759845 0.330910i
\(706\) −27.1518 47.0284i −1.02187 1.76994i
\(707\) 0.716849 2.87160i 0.0269599 0.107998i
\(708\) −16.3495 12.0834i −0.614451 0.454123i
\(709\) 0.625218 0.0234806 0.0117403 0.999931i \(-0.496263\pi\)
0.0117403 + 0.999931i \(0.496263\pi\)
\(710\) −15.1516 + 26.2433i −0.568628 + 0.984893i
\(711\) −5.21152 16.9762i −0.195447 0.636658i
\(712\) 0.789685 + 1.36777i 0.0295947 + 0.0512595i
\(713\) −14.1613 + 24.5281i −0.530345 + 0.918584i
\(714\) −12.2429 4.57343i −0.458180 0.171156i
\(715\) −5.22647 9.05251i −0.195459 0.338545i
\(716\) 1.18245 2.04806i 0.0441901 0.0765395i
\(717\) 0.0759426 0.669966i 0.00283613 0.0250203i
\(718\) −4.98119 8.62768i −0.185897 0.321982i
\(719\) 12.1969 + 21.1257i 0.454869 + 0.787857i 0.998681 0.0513506i \(-0.0163526\pi\)
−0.543811 + 0.839208i \(0.683019\pi\)
\(720\) 18.9192 + 4.34492i 0.705078 + 0.161926i
\(721\) −4.91003 + 1.40640i −0.182859 + 0.0523771i
\(722\) −11.7185 + 20.2970i −0.436116 + 0.755376i
\(723\) 2.07494 18.3051i 0.0771678 0.680775i
\(724\) −23.6246 −0.878003
\(725\) −0.199358 −0.00740399
\(726\) −25.4693 + 11.0918i −0.945255 + 0.411655i
\(727\) −18.9253 + 32.7796i −0.701900 + 1.21573i 0.265899 + 0.964001i \(0.414331\pi\)
−0.967799 + 0.251726i \(0.919002\pi\)
\(728\) 3.72426 14.9189i 0.138030 0.552932i
\(729\) −21.0415 16.9191i −0.779314 0.626634i
\(730\) 3.38991 + 5.87150i 0.125466 + 0.217314i
\(731\) −7.89934 13.6821i −0.292168 0.506049i
\(732\) 6.27227 + 4.63565i 0.231830 + 0.171339i
\(733\) −1.20077 + 2.07980i −0.0443516 + 0.0768193i −0.887349 0.461098i \(-0.847456\pi\)
0.842997 + 0.537918i \(0.180789\pi\)
\(734\) −21.2519 36.8093i −0.784421 1.35866i
\(735\) −6.96697 14.6066i −0.256980 0.538771i
\(736\) 24.5858 42.5839i 0.906245 1.56966i
\(737\) −5.24517 9.08490i −0.193208 0.334646i
\(738\) 33.9521 36.4932i 1.24979 1.34333i
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) 1.04507 0.0384174
\(741\) −20.5833 + 8.96397i −0.756148 + 0.329300i
\(742\) −7.07504 + 2.02653i −0.259733 + 0.0743963i
\(743\) −2.54785 4.41300i −0.0934715 0.161897i 0.815498 0.578760i \(-0.196463\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(744\) −6.01803 4.44775i −0.220632 0.163063i
\(745\) −4.39467 7.61179i −0.161008 0.278874i
\(746\) 19.7961 34.2879i 0.724787 1.25537i
\(747\) 16.3803 + 3.76183i 0.599322 + 0.137638i
\(748\) −3.25793 −0.119122
\(749\) −3.70345 + 14.8355i −0.135321 + 0.542079i
\(750\) 28.1336 + 20.7927i 1.02729 + 0.759242i
\(751\) 0.487506 0.844384i 0.0177893 0.0308120i −0.856994 0.515327i \(-0.827671\pi\)
0.874783 + 0.484515i \(0.161004\pi\)
\(752\) 46.1435 1.68268
\(753\) −4.54965 3.36251i −0.165798 0.122537i
\(754\) −0.590329 −0.0214985
\(755\) 16.9075 0.615326
\(756\) −17.0914 + 8.55216i −0.621608 + 0.311039i
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) −10.5350 −0.382648
\(759\) −15.5129 11.4651i −0.563081 0.416157i
\(760\) 3.75314 0.136141
\(761\) 27.0875 46.9169i 0.981920 1.70073i 0.327023 0.945016i \(-0.393955\pi\)
0.654897 0.755718i \(-0.272712\pi\)
\(762\) −21.8000 16.1117i −0.789729 0.583666i
\(763\) −20.9636 + 6.00468i −0.758932 + 0.217384i
\(764\) 31.5484 1.14138
\(765\) −4.22474 + 4.54094i −0.152746 + 0.164178i
\(766\) −32.1489 + 55.6835i −1.16159 + 2.01193i
\(767\) 21.8513 + 37.8475i 0.789004 + 1.36659i
\(768\) 29.2223 + 21.5974i 1.05447 + 0.779328i
\(769\) −10.4326 18.0698i −0.376208 0.651612i 0.614299 0.789074i \(-0.289439\pi\)
−0.990507 + 0.137462i \(0.956106\pi\)
\(770\) −7.07485 6.83604i −0.254960 0.246354i
\(771\) 7.45681 3.24742i 0.268551 0.116953i
\(772\) 8.60094 0.309554
\(773\) −27.4972 + 47.6266i −0.989007 + 1.71301i −0.366447 + 0.930439i \(0.619426\pi\)
−0.622561 + 0.782572i \(0.713908\pi\)
\(774\) −54.9112 12.6107i −1.97374 0.453283i
\(775\) −6.19189 10.7247i −0.222419 0.385242i
\(776\) −6.84616 + 11.8579i −0.245763 + 0.425674i
\(777\) 1.99108 1.64228i 0.0714295 0.0589164i
\(778\) −26.5895 46.0544i −0.953281 1.65113i
\(779\) 11.2987 19.5700i 0.404819 0.701168i
\(780\) 13.3778 + 9.88718i 0.479003 + 0.354018i
\(781\) 9.32802 + 16.1566i 0.333783 + 0.578129i
\(782\) 10.4963 + 18.1801i 0.375346 + 0.650119i
\(783\) −0.209456 0.244386i −0.00748534 0.00873364i
\(784\) −1.16477 33.9144i −0.0415989 1.21123i
\(785\) 11.5506 20.0062i 0.412258 0.714051i
\(786\) −5.88713 + 2.56383i −0.209987 + 0.0914486i
\(787\) 9.18949 0.327570 0.163785 0.986496i \(-0.447630\pi\)
0.163785 + 0.986496i \(0.447630\pi\)
\(788\) 13.5821 0.483841
\(789\) 3.81385 33.6458i 0.135777 1.19782i
\(790\) −7.27374 + 12.5985i −0.258788 + 0.448234i
\(791\) −9.29301 + 37.2266i −0.330421 + 1.32362i
\(792\) 3.47163 3.73146i 0.123359 0.132592i
\(793\) −8.38296 14.5197i −0.297688 0.515610i
\(794\) −10.2967 17.8344i −0.365416 0.632919i
\(795\) −0.393381 + 3.47041i −0.0139518 + 0.123083i
\(796\) −6.03296 + 10.4494i −0.213832 + 0.370369i
\(797\) 3.53774 + 6.12754i 0.125313 + 0.217049i 0.921855 0.387534i \(-0.126673\pi\)
−0.796542 + 0.604583i \(0.793340\pi\)
\(798\) −16.3003 + 13.4448i −0.577024 + 0.475941i
\(799\) −7.37174 + 12.7682i −0.260793 + 0.451707i
\(800\) 10.7499 + 18.6194i 0.380067 + 0.658295i
\(801\) −2.87429 + 3.08942i −0.101558 + 0.109159i
\(802\) −0.996224 + 1.72551i −0.0351779 + 0.0609299i
\(803\) 4.17398 0.147297
\(804\) 13.4257 + 9.92255i 0.473488 + 0.349941i
\(805\) −6.29579 + 25.2201i −0.221898 + 0.888892i
\(806\) −18.3351 31.7573i −0.645827 1.11860i
\(807\) 25.0384 10.9042i 0.881394 0.383844i
\(808\) −0.628050 1.08781i −0.0220947 0.0382692i
\(809\) −2.97060 + 5.14522i −0.104441 + 0.180896i −0.913510 0.406817i \(-0.866639\pi\)
0.809069 + 0.587714i \(0.199972\pi\)
\(810\) 1.59367 + 22.0609i 0.0559960 + 0.775142i
\(811\) 44.4139 1.55958 0.779791 0.626039i \(-0.215325\pi\)
0.779791 + 0.626039i \(0.215325\pi\)
\(812\) −0.219020 + 0.0627347i −0.00768609 + 0.00220156i
\(813\) −2.88678 + 25.4672i −0.101244 + 0.893173i
\(814\) 0.784512 1.35881i 0.0274971 0.0476264i
\(815\) −16.3097 −0.571304
\(816\) −11.9240 + 5.19287i −0.417424 + 0.181787i
\(817\) −25.5424 −0.893616
\(818\) 40.0191 1.39924
\(819\) 41.0250 2.18552i 1.43353 0.0763684i
\(820\) −16.7439 −0.584721
\(821\) 6.35522 0.221799 0.110899 0.993832i \(-0.464627\pi\)
0.110899 + 0.993832i \(0.464627\pi\)
\(822\) −0.796480 + 7.02655i −0.0277804 + 0.245079i
\(823\) −9.46433 −0.329906 −0.164953 0.986301i \(-0.552747\pi\)
−0.164953 + 0.986301i \(0.552747\pi\)
\(824\) −1.08380 + 1.87720i −0.0377560 + 0.0653953i
\(825\) 7.73282 3.36762i 0.269222 0.117245i
\(826\) 29.5792 + 28.5807i 1.02919 + 0.994450i
\(827\) −4.86261 −0.169090 −0.0845448 0.996420i \(-0.526944\pi\)
−0.0845448 + 0.996420i \(0.526944\pi\)
\(828\) 29.9193 + 6.87116i 1.03977 + 0.238789i
\(829\) 20.3926 35.3211i 0.708266 1.22675i −0.257234 0.966349i \(-0.582811\pi\)
0.965500 0.260403i \(-0.0838555\pi\)
\(830\) −6.88402 11.9235i −0.238948 0.413870i
\(831\) −1.45361 + 12.8238i −0.0504252 + 0.444852i
\(832\) 6.74003 + 11.6741i 0.233668 + 0.404725i
\(833\) 9.57041 + 5.09575i 0.331595 + 0.176557i
\(834\) 0.271315 2.39354i 0.00939486 0.0828815i
\(835\) −4.70494 −0.162821
\(836\) −2.63362 + 4.56156i −0.0910856 + 0.157765i
\(837\) 6.64146 18.8583i 0.229562 0.651838i
\(838\) −23.1823 40.1529i −0.800818 1.38706i
\(839\) 9.60171 16.6307i 0.331488 0.574154i −0.651316 0.758807i \(-0.725783\pi\)
0.982804 + 0.184653i \(0.0591161\pi\)
\(840\) −6.43378 2.40338i −0.221987 0.0829246i
\(841\) 14.4981 + 25.1114i 0.499934 + 0.865911i
\(842\) 27.3063 47.2959i 0.941036 1.62992i
\(843\) −41.2683 + 17.9722i −1.42136 + 0.618996i
\(844\) −3.95113 6.84355i −0.136003 0.235565i
\(845\) −9.20374 15.9413i −0.316618 0.548399i
\(846\) 15.4300 + 50.2625i 0.530496 + 1.72806i
\(847\) 22.1556 6.34612i 0.761276 0.218055i
\(848\) −3.66188 + 6.34256i −0.125749 + 0.217804i
\(849\) 26.1246 + 19.3079i 0.896594 + 0.662647i
\(850\) −9.17880 −0.314830
\(851\) −4.14571 −0.142113
\(852\) −23.8763 17.6463i −0.817989 0.604552i
\(853\) −6.95055 + 12.0387i −0.237982 + 0.412198i −0.960135 0.279536i \(-0.909819\pi\)
0.722153 + 0.691734i \(0.243153\pi\)
\(854\) −11.3477 10.9646i −0.388309 0.375202i
\(855\) 2.94280 + 9.58601i 0.100642 + 0.327835i
\(856\) 3.24469 + 5.61996i 0.110901 + 0.192086i
\(857\) −28.4919 49.3494i −0.973265 1.68574i −0.685547 0.728029i \(-0.740437\pi\)
−0.287718 0.957715i \(-0.592897\pi\)
\(858\) 22.8980 9.97200i 0.781725 0.340439i
\(859\) 10.0501 17.4073i 0.342905 0.593929i −0.642066 0.766650i \(-0.721922\pi\)
0.984971 + 0.172721i \(0.0552557\pi\)
\(860\) 9.46298 + 16.3904i 0.322685 + 0.558907i
\(861\) −31.9007 + 26.3123i −1.08717 + 0.896722i
\(862\) −4.50214 + 7.79794i −0.153344 + 0.265599i
\(863\) −3.08893 5.35018i −0.105148 0.182122i 0.808650 0.588289i \(-0.200198\pi\)
−0.913799 + 0.406167i \(0.866865\pi\)
\(864\) −11.5304 + 32.7404i −0.392273 + 1.11385i
\(865\) −6.76781 + 11.7222i −0.230112 + 0.398566i
\(866\) −17.8864 −0.607803
\(867\) −2.84838 + 25.1285i −0.0967361 + 0.853407i
\(868\) −10.1774 9.83390i −0.345445 0.333784i
\(869\) 4.47806 + 7.75623i 0.151908 + 0.263112i
\(870\) −0.0296977 + 0.261993i −0.00100685 + 0.00888240i
\(871\) −17.9436 31.0792i −0.607996 1.05308i
\(872\) −4.62732 + 8.01476i −0.156701 + 0.271414i
\(873\) −35.6546 8.18832i −1.20673 0.277133i
\(874\) 33.9396 1.14802
\(875\) −20.8714 20.1669i −0.705583 0.681767i
\(876\) −6.09009 + 2.65221i −0.205765 + 0.0896099i
\(877\) 18.6287 32.2658i 0.629046 1.08954i −0.358697 0.933454i \(-0.616779\pi\)
0.987743 0.156086i \(-0.0498877\pi\)
\(878\) 27.2937 0.921117
\(879\) 0.480253 4.23679i 0.0161985 0.142904i
\(880\) −9.79009 −0.330024
\(881\) −11.7848 −0.397041 −0.198520 0.980097i \(-0.563614\pi\)
−0.198520 + 0.980097i \(0.563614\pi\)
\(882\) 36.5522 12.6095i 1.23078 0.424582i
\(883\) −29.2308 −0.983693 −0.491847 0.870682i \(-0.663678\pi\)
−0.491847 + 0.870682i \(0.663678\pi\)
\(884\) −11.1453 −0.374857
\(885\) 17.8963 7.79378i 0.601578 0.261985i
\(886\) 40.3268 1.35480
\(887\) −14.2581 + 24.6957i −0.478739 + 0.829201i −0.999703 0.0243782i \(-0.992239\pi\)
0.520964 + 0.853579i \(0.325573\pi\)
\(888\) 0.123372 1.08839i 0.00414010 0.0365240i
\(889\) 16.1727 + 15.6268i 0.542416 + 0.524107i
\(890\) 3.45680 0.115872
\(891\) 12.2527 + 5.94118i 0.410481 + 0.199037i
\(892\) 8.14822 14.1131i 0.272823 0.472543i
\(893\) 11.9182 + 20.6430i 0.398828 + 0.690790i
\(894\) 19.2537 8.38494i 0.643942 0.280434i
\(895\) 1.13531 + 1.96642i 0.0379493 + 0.0657301i
\(896\) −16.2967 15.7466i −0.544435 0.526058i
\(897\) −53.0691 39.2219i −1.77193 1.30958i
\(898\) −39.5779 −1.32073
\(899\) 0.119171 0.206410i 0.00397456 0.00688414i
\(900\) −9.14281 + 9.82711i −0.304760 + 0.327570i
\(901\) −1.17002 2.02653i −0.0389790 0.0675135i
\(902\) −12.5693 + 21.7707i −0.418513 + 0.724885i
\(903\) 43.7858 + 16.3565i 1.45710 + 0.544311i
\(904\) 8.14183 + 14.1021i 0.270793 + 0.469028i
\(905\) 11.3415 19.6440i 0.377003 0.652989i
\(906\) −4.54997 + 40.1399i −0.151163 + 1.33356i
\(907\) 3.94577 + 6.83428i 0.131017 + 0.226929i 0.924069 0.382226i \(-0.124842\pi\)
−0.793052 + 0.609154i \(0.791509\pi\)
\(908\) −7.77317 13.4635i −0.257962 0.446803i
\(909\) 2.28597 2.45707i 0.0758209 0.0814957i
\(910\) −24.2029 23.3860i −0.802319 0.775237i
\(911\) −14.2206 + 24.6308i −0.471150 + 0.816055i −0.999455 0.0329991i \(-0.989494\pi\)
0.528306 + 0.849054i \(0.322827\pi\)
\(912\) −2.36829 + 20.8931i −0.0784219 + 0.691839i
\(913\) −8.47625 −0.280523
\(914\) −74.8013 −2.47421
\(915\) −6.86569 + 2.98999i −0.226973 + 0.0988459i
\(916\) 6.71206 11.6256i 0.221773 0.384121i
\(917\) 5.12118 1.46688i 0.169116 0.0484406i
\(918\) −9.64370 11.2519i −0.318290 0.371369i
\(919\) 3.99271 + 6.91558i 0.131707 + 0.228124i 0.924335 0.381582i \(-0.124621\pi\)
−0.792627 + 0.609706i \(0.791287\pi\)
\(920\) 5.51590 + 9.55382i 0.181854 + 0.314980i
\(921\) −6.49483 4.80014i −0.214012 0.158170i
\(922\) −2.60610 + 4.51390i −0.0858274 + 0.148657i
\(923\) 31.9110 + 55.2714i 1.05036 + 1.81928i
\(924\) 7.43573 6.13313i 0.244617 0.201765i
\(925\) 0.906337 1.56982i 0.0298002 0.0516154i
\(926\) 25.6529 + 44.4322i 0.843008 + 1.46013i
\(927\) −5.64441 1.29628i −0.185387 0.0425753i
\(928\) −0.206895 + 0.358353i −0.00679167 + 0.0117635i
\(929\) 18.8006 0.616829 0.308414 0.951252i \(-0.400202\pi\)
0.308414 + 0.951252i \(0.400202\pi\)
\(930\) −15.0166 + 6.53966i −0.492412 + 0.214444i
\(931\) 14.8712 9.28068i 0.487385 0.304162i
\(932\) −13.4081 23.2234i −0.439196 0.760709i
\(933\) 38.2801 + 28.2917i 1.25324 + 0.926230i
\(934\) 24.5288 + 42.4852i 0.802608 + 1.39016i
\(935\) 1.56403 2.70898i 0.0511493 0.0885932i
\(936\) 11.8764 12.7652i 0.388191 0.417245i
\(937\) 48.5788 1.58700 0.793500 0.608570i \(-0.208256\pi\)
0.793500 + 0.608570i \(0.208256\pi\)
\(938\) −24.2895 23.4696i −0.793081 0.766310i
\(939\) 7.65172 + 5.65516i 0.249704 + 0.184549i
\(940\) 8.83094 15.2956i 0.288034 0.498889i
\(941\) 20.4851 0.667795 0.333898 0.942609i \(-0.391636\pi\)
0.333898 + 0.942609i \(0.391636\pi\)
\(942\) 44.3882 + 32.8060i 1.44624 + 1.06888i
\(943\) 66.4220 2.16300
\(944\) 40.9312 1.33220
\(945\) 1.09389 18.3172i 0.0355842 0.595858i
\(946\) 28.4148 0.923843
\(947\) −14.8505 −0.482576 −0.241288 0.970454i \(-0.577570\pi\)
−0.241288 + 0.970454i \(0.577570\pi\)
\(948\) −11.4622 8.47137i −0.372275 0.275137i
\(949\) 14.2791 0.463519
\(950\) −7.41989 + 12.8516i −0.240733 + 0.416962i
\(951\) 13.7586 + 10.1686i 0.446154 + 0.329739i
\(952\) 4.42363 1.26708i 0.143371 0.0410662i
\(953\) 46.4678 1.50524 0.752620 0.658456i \(-0.228790\pi\)
0.752620 + 0.658456i \(0.228790\pi\)
\(954\) −8.13322 1.86785i −0.263323 0.0604738i
\(955\) −15.1454 + 26.2326i −0.490094 + 0.848868i
\(956\) −0.270584 0.468665i −0.00875130 0.0151577i
\(957\) 0.130544 + 0.0964815i 0.00421990 + 0.00311880i
\(958\) −29.0724 50.3548i −0.939285 1.62689i
\(959\) 1.42092 5.69201i 0.0458838 0.183804i
\(960\) 5.52012 2.40399i 0.178161 0.0775886i
\(961\) −16.1947 −0.522409
\(962\) 2.68380 4.64847i 0.0865291 0.149873i
\(963\) −11.8100 + 12.6939i −0.380572 + 0.409056i
\(964\) −7.39301 12.8051i −0.238113 0.412423i
\(965\) −4.12905 + 7.15172i −0.132919 + 0.230222i
\(966\) −58.1807 21.7338i −1.87193 0.699273i
\(967\) 0.863670 + 1.49592i 0.0277738 + 0.0481056i 0.879578 0.475754i \(-0.157825\pi\)
−0.851804 + 0.523860i \(0.824492\pi\)
\(968\) 4.89045 8.47050i 0.157185 0.272252i
\(969\) −5.40290 3.99313i −0.173566 0.128278i
\(970\) 14.9843 + 25.9536i 0.481118 + 0.833320i
\(971\) −3.78085 6.54863i −0.121333 0.210156i 0.798960 0.601384i \(-0.205384\pi\)
−0.920294 + 0.391228i \(0.872050\pi\)
\(972\) −21.6526 0.882976i −0.694506 0.0283215i
\(973\) −0.484024 + 1.93894i −0.0155171 + 0.0621595i
\(974\) 0.281870 0.488213i 0.00903169 0.0156434i
\(975\) 26.4538 11.5205i 0.847199 0.368953i
\(976\) −15.7027 −0.502633
\(977\) −56.6202 −1.81144 −0.905721 0.423875i \(-0.860670\pi\)
−0.905721 + 0.423875i \(0.860670\pi\)
\(978\) 4.38911 38.7208i 0.140348 1.23815i
\(979\) 1.06408 1.84305i 0.0340083 0.0589041i
\(980\) −11.4648 6.10443i −0.366231 0.194999i
\(981\) −24.0990 5.53449i −0.769422 0.176703i
\(982\) 16.6997 + 28.9247i 0.532909 + 0.923025i
\(983\) −16.1486 27.9702i −0.515061 0.892112i −0.999847 0.0174790i \(-0.994436\pi\)
0.484786 0.874633i \(-0.338897\pi\)
\(984\) −1.97665 + 17.4380i −0.0630133 + 0.555904i
\(985\) −6.52033 + 11.2936i −0.207755 + 0.359842i
\(986\) −0.0883286 0.152990i −0.00281296 0.00487218i
\(987\) −7.21163 43.0190i −0.229549 1.36931i
\(988\) −9.00955 + 15.6050i −0.286632 + 0.496461i
\(989\) −37.5391 65.0197i −1.19367 2.06750i
\(990\) −3.27373 10.6640i −0.104046 0.338924i
\(991\) −7.15502 + 12.3929i −0.227287 + 0.393672i −0.957003 0.290078i \(-0.906319\pi\)
0.729716 + 0.683750i \(0.239652\pi\)
\(992\) −25.7039 −0.816100
\(993\) −28.8253 21.3039i −0.914742 0.676059i
\(994\) 43.1965 + 41.7384i 1.37011 + 1.32386i
\(995\) −5.79247 10.0329i −0.183634 0.318063i
\(996\) 12.3674 5.38595i 0.391875 0.170660i
\(997\) −28.1262 48.7160i −0.890765 1.54285i −0.838960 0.544194i \(-0.816836\pi\)
−0.0518058 0.998657i \(-0.516498\pi\)
\(998\) −19.6176 + 33.9787i −0.620985 + 1.07558i
\(999\) 2.87663 0.538288i 0.0910125 0.0170307i
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 63.2.h.b.25.2 yes 10
3.2 odd 2 189.2.h.b.46.4 10
4.3 odd 2 1008.2.q.i.529.2 10
7.2 even 3 63.2.g.b.16.4 yes 10
7.3 odd 6 441.2.f.f.295.4 10
7.4 even 3 441.2.f.e.295.4 10
7.5 odd 6 441.2.g.f.79.4 10
7.6 odd 2 441.2.h.f.214.2 10
9.2 odd 6 567.2.e.e.487.2 10
9.4 even 3 63.2.g.b.4.4 10
9.5 odd 6 189.2.g.b.172.2 10
9.7 even 3 567.2.e.f.487.4 10
12.11 even 2 3024.2.q.i.2881.4 10
21.2 odd 6 189.2.g.b.100.2 10
21.5 even 6 1323.2.g.f.667.2 10
21.11 odd 6 1323.2.f.e.883.2 10
21.17 even 6 1323.2.f.f.883.2 10
21.20 even 2 1323.2.h.f.802.4 10
28.23 odd 6 1008.2.t.i.961.5 10
36.23 even 6 3024.2.t.i.1873.2 10
36.31 odd 6 1008.2.t.i.193.5 10
63.2 odd 6 567.2.e.e.163.2 10
63.4 even 3 441.2.f.e.148.4 10
63.5 even 6 1323.2.h.f.226.4 10
63.11 odd 6 3969.2.a.bc.1.4 5
63.13 odd 6 441.2.g.f.67.4 10
63.16 even 3 567.2.e.f.163.4 10
63.23 odd 6 189.2.h.b.37.4 10
63.25 even 3 3969.2.a.z.1.2 5
63.31 odd 6 441.2.f.f.148.4 10
63.32 odd 6 1323.2.f.e.442.2 10
63.38 even 6 3969.2.a.bb.1.4 5
63.40 odd 6 441.2.h.f.373.2 10
63.41 even 6 1323.2.g.f.361.2 10
63.52 odd 6 3969.2.a.ba.1.2 5
63.58 even 3 inner 63.2.h.b.58.2 yes 10
63.59 even 6 1323.2.f.f.442.2 10
84.23 even 6 3024.2.t.i.289.2 10
252.23 even 6 3024.2.q.i.2305.4 10
252.247 odd 6 1008.2.q.i.625.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 9.4 even 3
63.2.g.b.16.4 yes 10 7.2 even 3
63.2.h.b.25.2 yes 10 1.1 even 1 trivial
63.2.h.b.58.2 yes 10 63.58 even 3 inner
189.2.g.b.100.2 10 21.2 odd 6
189.2.g.b.172.2 10 9.5 odd 6
189.2.h.b.37.4 10 63.23 odd 6
189.2.h.b.46.4 10 3.2 odd 2
441.2.f.e.148.4 10 63.4 even 3
441.2.f.e.295.4 10 7.4 even 3
441.2.f.f.148.4 10 63.31 odd 6
441.2.f.f.295.4 10 7.3 odd 6
441.2.g.f.67.4 10 63.13 odd 6
441.2.g.f.79.4 10 7.5 odd 6
441.2.h.f.214.2 10 7.6 odd 2
441.2.h.f.373.2 10 63.40 odd 6
567.2.e.e.163.2 10 63.2 odd 6
567.2.e.e.487.2 10 9.2 odd 6
567.2.e.f.163.4 10 63.16 even 3
567.2.e.f.487.4 10 9.7 even 3
1008.2.q.i.529.2 10 4.3 odd 2
1008.2.q.i.625.2 10 252.247 odd 6
1008.2.t.i.193.5 10 36.31 odd 6
1008.2.t.i.961.5 10 28.23 odd 6
1323.2.f.e.442.2 10 63.32 odd 6
1323.2.f.e.883.2 10 21.11 odd 6
1323.2.f.f.442.2 10 63.59 even 6
1323.2.f.f.883.2 10 21.17 even 6
1323.2.g.f.361.2 10 63.41 even 6
1323.2.g.f.667.2 10 21.5 even 6
1323.2.h.f.226.4 10 63.5 even 6
1323.2.h.f.802.4 10 21.20 even 2
3024.2.q.i.2305.4 10 252.23 even 6
3024.2.q.i.2881.4 10 12.11 even 2
3024.2.t.i.289.2 10 84.23 even 6
3024.2.t.i.1873.2 10 36.23 even 6
3969.2.a.z.1.2 5 63.25 even 3
3969.2.a.ba.1.2 5 63.52 odd 6
3969.2.a.bb.1.4 5 63.38 even 6
3969.2.a.bc.1.4 5 63.11 odd 6