Properties

Label 63.2.g.b.4.4
Level $63$
Weight $2$
Character 63.4
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(4,63)]
 
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([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.g (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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 63.4
Dual form 63.2.g.b.16.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.920620 - 1.59456i) q^{2} +(-1.58800 - 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} +(-2.56469 + 1.89549i) q^{6} +(-2.54347 + 0.728536i) q^{7} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +O(q^{10})\) \(q+(0.920620 - 1.59456i) q^{2} +(-1.58800 - 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} +(-2.56469 + 1.89549i) q^{6} +(-2.54347 + 0.728536i) q^{7} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(1.22880 - 2.12835i) q^{10} +1.51302 q^{11} +(0.271199 + 2.39252i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-1.17987 + 4.72642i) q^{14} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(-1.25211 - 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(4.54285 + 0.602068i) q^{21} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(-1.78308 - 0.776526i) q^{24} -3.21843 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} +(-3.42323 + 2.53001i) q^{30} +(1.92388 + 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(-2.40267 - 1.04635i) 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} -4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} +1.49873 q^{40} +(4.51188 - 7.81481i) q^{41} +(5.14228 - 6.68958i) q^{42} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(2.72753 + 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(4.75925 - 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(5.93847 - 3.70602i) q^{49} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} +7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(-9.40414 - 1.75975i) q^{54} +2.01950 q^{55} +(-2.85593 + 0.818036i) q^{56} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(4.22166 + 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(-1.61958 + 2.80520i) q^{61} +7.08467 q^{62} +(-6.79767 - 4.09777i) q^{63} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(-3.88042 + 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} -2.15327 q^{68} +(11.6889 + 5.09048i) q^{69} +(-1.57484 + 6.30861i) q^{70} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(-1.37936 + 2.38912i) q^{73} -1.03702 q^{74} +(5.11086 + 2.22576i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-3.84831 + 1.10229i) q^{77} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(-8.30746 - 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(-2.43282 - 5.88772i) q^{84} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(0.0120840 + 0.106605i) q^{87} +1.69889 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} +(-0.750637 - 6.62212i) q^{93} +(-8.76293 - 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(1.30320 + 11.4968i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(-0.442393 - 12.8811i) q^{98} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20} - 2 q^{21} - q^{22} - 6 q^{23} + 3 q^{24} + 2 q^{25} + 11 q^{26} - 7 q^{27} - 2 q^{28} + 7 q^{29} - 26 q^{30} - 3 q^{31} - 2 q^{32} - q^{33} + 3 q^{34} + 5 q^{35} + 34 q^{36} - 40 q^{38} + 20 q^{39} + 6 q^{40} + 5 q^{41} + 32 q^{42} - 7 q^{43} - 10 q^{44} - q^{45} + 3 q^{46} + 27 q^{47} - 5 q^{48} + 25 q^{49} + 19 q^{50} + 24 q^{51} + 20 q^{52} - 21 q^{53} - 53 q^{54} + 4 q^{55} - 45 q^{56} - 4 q^{57} + 20 q^{58} + 30 q^{59} - 41 q^{60} - 14 q^{61} - 12 q^{62} - 35 q^{63} - 50 q^{64} - 11 q^{65} - 41 q^{66} - 2 q^{67} - 54 q^{68} + 15 q^{69} - 29 q^{70} - 6 q^{71} + 48 q^{72} + 15 q^{73} + 72 q^{74} + 31 q^{75} + 5 q^{76} - 31 q^{77} - 20 q^{78} - 4 q^{79} + 20 q^{80} + 8 q^{81} - 5 q^{82} + 9 q^{83} + 2 q^{84} - 6 q^{85} + 16 q^{86} + 32 q^{87} + 36 q^{88} + 28 q^{89} + 28 q^{90} - 4 q^{91} + 27 q^{92} - 12 q^{93} - 3 q^{94} - 14 q^{95} - q^{96} - 12 q^{97} + 59 q^{98} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920620 1.59456i 0.650977 1.12753i −0.331909 0.943311i \(-0.607693\pi\)
0.982886 0.184214i \(-0.0589739\pi\)
\(3\) −1.58800 0.691567i −0.916831 0.399277i
\(4\) −0.695084 1.20392i −0.347542 0.601960i
\(5\) 1.33475 0.596920 0.298460 0.954422i \(-0.403527\pi\)
0.298460 + 0.954422i \(0.403527\pi\)
\(6\) −2.56469 + 1.89549i −1.04703 + 0.773830i
\(7\) −2.54347 + 0.728536i −0.961341 + 0.275361i
\(8\) 1.12285 0.396987
\(9\) 2.04347 + 2.19641i 0.681156 + 0.732138i
\(10\) 1.22880 2.12835i 0.388581 0.673042i
\(11\) 1.51302 0.456192 0.228096 0.973639i \(-0.426750\pi\)
0.228096 + 0.973639i \(0.426750\pi\)
\(12\) 0.271199 + 2.39252i 0.0782884 + 0.690661i
\(13\) −2.58800 + 4.48254i −0.717781 + 1.24323i 0.244096 + 0.969751i \(0.421509\pi\)
−0.961877 + 0.273482i \(0.911824\pi\)
\(14\) −1.17987 + 4.72642i −0.315335 + 1.26319i
\(15\) −2.11958 0.923072i −0.547274 0.238336i
\(16\) 2.42388 4.19829i 0.605971 1.04957i
\(17\) 0.774463 1.34141i 0.187835 0.325340i −0.756693 0.653770i \(-0.773186\pi\)
0.944528 + 0.328430i \(0.106520\pi\)
\(18\) 5.38358 1.23637i 1.26892 0.291416i
\(19\) −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
\(21\) 4.54285 + 0.602068i 0.991332 + 0.131382i
\(22\) 1.39291 2.41260i 0.296970 0.514367i
\(23\) −7.36079 −1.53483 −0.767415 0.641151i \(-0.778457\pi\)
−0.767415 + 0.641151i \(0.778457\pi\)
\(24\) −1.78308 0.776526i −0.363970 0.158508i
\(25\) −3.21843 −0.643687
\(26\) 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 0.863135 0.504972i \(-0.168497\pi\)
−0.868887 + 0.495011i \(0.835164\pi\)
\(30\) −3.42323 + 2.53001i −0.624993 + 0.461914i
\(31\) 1.92388 + 3.33227i 0.345540 + 0.598493i 0.985452 0.169956i \(-0.0543625\pi\)
−0.639912 + 0.768448i \(0.721029\pi\)
\(32\) −3.34011 5.78523i −0.590453 1.02269i
\(33\) −2.40267 1.04635i −0.418250 0.182147i
\(34\) −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 \(0.848075\pi\)
\(38\) −4.61087 −0.747982
\(39\) 7.20971 5.32849i 1.15448 0.853241i
\(40\) 1.49873 0.236969
\(41\) 4.51188 7.81481i 0.704638 1.22047i −0.262185 0.965018i \(-0.584443\pi\)
0.966822 0.255450i \(-0.0822237\pi\)
\(42\) 5.14228 6.68958i 0.793471 1.03222i
\(43\) 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i \(0.116959\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(44\) −1.05167 1.82155i −0.158546 0.274609i
\(45\) 2.72753 + 2.93167i 0.406596 + 0.437028i
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) 4.75925 8.24327i 0.694209 1.20240i −0.276238 0.961089i \(-0.589088\pi\)
0.970447 0.241315i \(-0.0775788\pi\)
\(48\) −6.75252 + 4.99060i −0.974643 + 0.720330i
\(49\) 5.93847 3.70602i 0.848353 0.529431i
\(50\) −2.96296 + 5.13199i −0.419025 + 0.725773i
\(51\) −2.15752 + 1.59456i −0.302113 + 0.223283i
\(52\) 7.19550 0.997836
\(53\) 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i \(-0.800246\pi\)
0.913230 + 0.407444i \(0.133580\pi\)
\(54\) −9.40414 1.75975i −1.27974 0.239471i
\(55\) 2.01950 0.272310
\(56\) −2.85593 + 0.818036i −0.381640 + 0.109315i
\(57\) 0.488532 + 4.30983i 0.0647077 + 0.570851i
\(58\) −0.114051 −0.0149757
\(59\) 4.22166 + 7.31212i 0.549613 + 0.951957i 0.998301 + 0.0582689i \(0.0185581\pi\)
−0.448688 + 0.893688i \(0.648109\pi\)
\(60\) 0.361984 + 3.19342i 0.0467319 + 0.412269i
\(61\) −1.61958 + 2.80520i −0.207367 + 0.359169i −0.950884 0.309547i \(-0.899823\pi\)
0.743518 + 0.668716i \(0.233156\pi\)
\(62\) 7.08467 0.899754
\(63\) −6.79767 4.09777i −0.856426 0.516271i
\(64\) −2.60434 −0.325543
\(65\) −3.45434 + 5.98309i −0.428458 + 0.742111i
\(66\) −3.88042 + 2.86790i −0.477646 + 0.353014i
\(67\) −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i \(-0.305874\pi\)
−0.996281 + 0.0861595i \(0.972541\pi\)
\(68\) −2.15327 −0.261122
\(69\) 11.6889 + 5.09048i 1.40718 + 0.612822i
\(70\) −1.57484 + 6.30861i −0.188230 + 0.754023i
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) 2.29451 + 2.46624i 0.270410 + 0.290649i
\(73\) −1.37936 + 2.38912i −0.161442 + 0.279625i −0.935386 0.353629i \(-0.884948\pi\)
0.773944 + 0.633254i \(0.218281\pi\)
\(74\) −1.03702 −0.120551
\(75\) 5.11086 + 2.22576i 0.590152 + 0.257009i
\(76\) −1.74064 + 3.01488i −0.199665 + 0.345830i
\(77\) −3.84831 + 1.10229i −0.438556 + 0.125617i
\(78\) −1.85920 16.4018i −0.210512 1.85714i
\(79\) 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i \(-0.725275\pi\)
0.983097 + 0.183086i \(0.0586087\pi\)
\(80\) 3.23529 5.60368i 0.361716 0.626511i
\(81\) −0.648467 + 8.97661i −0.0720519 + 0.997401i
\(82\) −8.30746 14.3889i −0.917406 1.58899i
\(83\) 2.80111 + 4.85167i 0.307462 + 0.532540i 0.977806 0.209510i \(-0.0671870\pi\)
−0.670344 + 0.742050i \(0.733854\pi\)
\(84\) −2.43282 5.88772i −0.265443 0.642403i
\(85\) 1.03372 1.79045i 0.112122 0.194202i
\(86\) 18.7802 2.02512
\(87\) 0.0120840 + 0.106605i 0.00129554 + 0.0114293i
\(88\) 1.69889 0.181102
\(89\) 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
\(93\) −0.750637 6.62212i −0.0778374 0.686682i
\(94\) −8.76293 15.1778i −0.903827 1.56548i
\(95\) −1.67126 2.89470i −0.171467 0.296990i
\(96\) 1.30320 + 11.4968i 0.133007 + 1.17339i
\(97\) −6.09713 10.5605i −0.619070 1.07226i −0.989656 0.143462i \(-0.954176\pi\)
0.370586 0.928798i \(-0.379157\pi\)
\(98\) −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
\(101\) 1.11867 0.111312 0.0556560 0.998450i \(-0.482275\pi\)
0.0556560 + 0.998450i \(0.482275\pi\)
\(102\) 0.556368 + 4.90828i 0.0550886 + 0.485993i
\(103\) 1.93045 0.190213 0.0951063 0.995467i \(-0.469681\pi\)
0.0951063 + 0.995467i \(0.469681\pi\)
\(104\) −2.90593 + 5.03322i −0.284950 + 0.493548i
\(105\) 6.06359 + 0.803612i 0.591746 + 0.0784245i
\(106\) −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 \(0.743212\pi\)
\(108\) −4.70077 + 5.48470i −0.452332 + 0.527766i
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) 1.85920 3.22022i 0.177267 0.307036i
\(111\) 0.109874 + 0.969312i 0.0104288 + 0.0920030i
\(112\) −3.10647 + 12.4441i −0.293534 + 1.17586i
\(113\) 7.25105 12.5592i 0.682121 1.18147i −0.292211 0.956354i \(-0.594391\pi\)
0.974332 0.225115i \(-0.0722758\pi\)
\(114\) 7.32205 + 3.18873i 0.685773 + 0.298652i
\(115\) −9.82483 −0.916170
\(116\) −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
\(117\) −15.1340 + 3.47562i −1.39914 + 0.321322i
\(118\) 15.5462 1.43114
\(119\) −0.992558 + 3.97606i −0.0909877 + 0.364485i
\(120\) −2.37997 1.03647i −0.217261 0.0946164i
\(121\) −8.71078 −0.791889
\(122\) 2.98204 + 5.16505i 0.269982 + 0.467622i
\(123\) −12.5693 + 9.28962i −1.13334 + 0.837617i
\(124\) 2.67452 4.63241i 0.240179 0.416002i
\(125\) −10.9696 −0.981149
\(126\) −12.7922 + 7.06681i −1.13962 + 0.629561i
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) 4.28260 7.41769i 0.378532 0.655637i
\(129\) −1.98981 17.5541i −0.175193 1.54555i
\(130\) 6.36027 + 11.0163i 0.557832 + 0.966194i
\(131\) −2.01346 −0.175917 −0.0879585 0.996124i \(-0.528034\pi\)
−0.0879585 + 0.996124i \(0.528034\pi\)
\(132\) 0.410328 + 3.61992i 0.0357145 + 0.315074i
\(133\) 4.76469 + 4.60386i 0.413151 + 0.399205i
\(134\) −12.7660 −1.10282
\(135\) −2.30386 6.54175i −0.198285 0.563024i
\(136\) 0.869605 1.50620i 0.0745680 0.129156i
\(137\) 2.21740 0.189445 0.0947225 0.995504i \(-0.469804\pi\)
0.0947225 + 0.995504i \(0.469804\pi\)
\(138\) 18.8781 13.9523i 1.60701 1.18770i
\(139\) 0.377669 0.654143i 0.0320335 0.0554836i −0.849564 0.527485i \(-0.823135\pi\)
0.881598 + 0.472002i \(0.156468\pi\)
\(140\) 3.53045 + 3.41128i 0.298378 + 0.288306i
\(141\) −13.2585 + 9.79894i −1.11656 + 0.825220i
\(142\) −11.3516 + 19.6615i −0.952604 + 1.64996i
\(143\) −3.91568 + 6.78216i −0.327446 + 0.567153i
\(144\) 14.1743 3.25523i 1.18119 0.271269i
\(145\) −0.0413391 0.0716014i −0.00343303 0.00594618i
\(146\) 2.53973 + 4.39894i 0.210189 + 0.364059i
\(147\) −11.9932 + 1.77829i −0.989185 + 0.146671i
\(148\) −0.391482 + 0.678068i −0.0321797 + 0.0557368i
\(149\) 6.58499 0.539463 0.269732 0.962936i \(-0.413065\pi\)
0.269732 + 0.962936i \(0.413065\pi\)
\(150\) 8.25428 6.10050i 0.673959 0.498104i
\(151\) 12.6671 1.03083 0.515417 0.856939i \(-0.327637\pi\)
0.515417 + 0.856939i \(0.327637\pi\)
\(152\) −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
\(156\) −11.4264 4.97617i −0.914846 0.398413i
\(157\) 8.65372 + 14.9887i 0.690642 + 1.19623i 0.971628 + 0.236515i \(0.0760052\pi\)
−0.280986 + 0.959712i \(0.590662\pi\)
\(158\) −5.44950 9.43882i −0.433539 0.750912i
\(159\) −2.10434 + 1.55526i −0.166885 + 0.123340i
\(160\) −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 \(0.674498\pi\)
\(164\) −12.5445 −0.979564
\(165\) −3.20697 1.39662i −0.249662 0.108727i
\(166\) 10.3150 0.800602
\(167\) 1.76248 3.05270i 0.136385 0.236225i −0.789741 0.613440i \(-0.789785\pi\)
0.926126 + 0.377215i \(0.123118\pi\)
\(168\) 5.10094 + 0.676031i 0.393546 + 0.0521569i
\(169\) −6.89546 11.9433i −0.530420 0.918714i
\(170\) −1.90332 3.29665i −0.145978 0.252842i
\(171\) 2.20475 7.18186i 0.168602 0.549210i
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) −5.07046 + 8.78229i −0.385500 + 0.667705i −0.991838 0.127502i \(-0.959304\pi\)
0.606339 + 0.795206i \(0.292638\pi\)
\(174\) 0.181113 + 0.0788742i 0.0137302 + 0.00597944i
\(175\) 8.18599 2.34474i 0.618802 0.177246i
\(176\) 3.66738 6.35208i 0.276439 0.478806i
\(177\) −1.64715 14.5312i −0.123808 1.09223i
\(178\) 2.58984 0.194117
\(179\) 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i \(-0.813083\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(180\) 1.63364 5.32148i 0.121764 0.396640i
\(181\) −16.9941 −1.26316 −0.631581 0.775310i \(-0.717594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(182\) −18.1329 17.5208i −1.34410 1.29873i
\(183\) 4.51188 3.33460i 0.333528 0.246501i
\(184\) −8.26505 −0.609308
\(185\) −0.375877 0.651039i −0.0276351 0.0478653i
\(186\) −11.2504 4.89953i −0.824922 0.359251i
\(187\) 1.17178 2.02957i 0.0856887 0.148417i
\(188\) −13.2323 −0.965066
\(189\) 7.96079 + 11.2083i 0.579062 + 0.815283i
\(190\) −6.15437 −0.446485
\(191\) −11.3470 + 19.6535i −0.821038 + 1.42208i 0.0838717 + 0.996477i \(0.473271\pi\)
−0.904910 + 0.425603i \(0.860062\pi\)
\(192\) 4.13568 + 1.80108i 0.298467 + 0.129982i
\(193\) −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i \(-0.238145\pi\)
−0.955619 + 0.294605i \(0.904812\pi\)
\(194\) −22.4526 −1.61200
\(195\) 9.62319 7.11222i 0.689131 0.509317i
\(196\) −8.58948 4.57345i −0.613534 0.326675i
\(197\) 9.77010 0.696091 0.348045 0.937478i \(-0.386846\pi\)
0.348045 + 0.937478i \(0.386846\pi\)
\(198\) 8.14544 1.87065i 0.578871 0.132942i
\(199\) −4.33973 + 7.51664i −0.307636 + 0.532840i −0.977845 0.209332i \(-0.932871\pi\)
0.670209 + 0.742172i \(0.266204\pi\)
\(200\) −3.61381 −0.255535
\(201\) 1.35259 + 11.9326i 0.0954044 + 0.841659i
\(202\) 1.02987 1.78379i 0.0724615 0.125507i
\(203\) 0.117856 + 0.113878i 0.00827188 + 0.00799267i
\(204\) 3.41938 + 1.48913i 0.239405 + 0.104260i
\(205\) 6.02225 10.4308i 0.420612 0.728522i
\(206\) 1.77721 3.07822i 0.123824 0.214470i
\(207\) −15.0415 16.1673i −1.04546 1.12371i
\(208\) 12.5460 + 21.7303i 0.869909 + 1.50673i
\(209\) −1.89446 3.28130i −0.131043 0.226973i
\(210\) 6.86367 8.92894i 0.473638 0.616156i
\(211\) −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(212\) −2.10019 −0.144242
\(213\) 19.5806 + 8.52728i 1.34164 + 0.584280i
\(214\) 10.6412 0.727420
\(215\) 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
\(219\) 3.84265 2.83999i 0.259662 0.191909i
\(220\) −1.40372 2.43132i −0.0946390 0.163920i
\(221\) 4.00862 + 6.94313i 0.269649 + 0.467045i
\(222\) 1.64678 + 0.717167i 0.110525 + 0.0481331i
\(223\) 5.86133 + 10.1521i 0.392503 + 0.679836i 0.992779 0.119957i \(-0.0382758\pi\)
−0.600276 + 0.799793i \(0.704942\pi\)
\(224\) 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
\(227\) 11.1831 0.742247 0.371123 0.928584i \(-0.378973\pi\)
0.371123 + 0.928584i \(0.378973\pi\)
\(228\) 4.84913 3.58385i 0.321141 0.237346i
\(229\) −9.65647 −0.638118 −0.319059 0.947735i \(-0.603367\pi\)
−0.319059 + 0.947735i \(0.603367\pi\)
\(230\) −9.04494 + 15.6663i −0.596406 + 1.03301i
\(231\) 6.87341 + 0.910938i 0.452237 + 0.0599353i
\(232\) −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 \(-0.384375\pi\)
\(234\) −8.39058 + 27.3318i −0.548509 + 1.78674i
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) 5.86881 10.1651i 0.382027 0.661690i
\(237\) −8.24519 + 6.09378i −0.535582 + 0.395833i
\(238\) 5.42630 + 5.24314i 0.351735 + 0.339862i
\(239\) −0.194641 + 0.337128i −0.0125903 + 0.0218070i −0.872252 0.489057i \(-0.837341\pi\)
0.859662 + 0.510864i \(0.170674\pi\)
\(240\) −9.01295 + 6.66121i −0.581784 + 0.429979i
\(241\) 10.6361 0.685134 0.342567 0.939493i \(-0.388704\pi\)
0.342567 + 0.939493i \(0.388704\pi\)
\(242\) −8.01932 + 13.8899i −0.515502 + 0.892875i
\(243\) 7.23769 13.8064i 0.464298 0.885679i
\(244\) 4.50299 0.288274
\(245\) 7.92639 4.94662i 0.506399 0.316028i
\(246\) 3.24130 + 28.5948i 0.206658 + 1.82314i
\(247\) 12.9618 0.824741
\(248\) 2.16023 + 3.74163i 0.137175 + 0.237594i
\(249\) −1.09290 9.64159i −0.0692599 0.611011i
\(250\) −10.0988 + 17.4917i −0.638705 + 1.10627i
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) −0.208441 + 11.0321i −0.0131306 + 0.694960i
\(253\) −11.1370 −0.700176
\(254\) 7.82531 13.5538i 0.491004 0.850443i
\(255\) −2.87976 + 2.12835i −0.180337 + 0.133282i
\(256\) −10.4896 18.1686i −0.655603 1.13554i
\(257\) −4.69573 −0.292912 −0.146456 0.989217i \(-0.546787\pi\)
−0.146456 + 0.989217i \(0.546787\pi\)
\(258\) −29.8229 12.9878i −1.85669 0.808584i
\(259\) 1.07161 + 1.03544i 0.0665867 + 0.0643391i
\(260\) 9.60421 0.595628
\(261\) 0.0545353 0.177646i 0.00337565 0.0109960i
\(262\) −1.85363 + 3.21059i −0.114518 + 0.198351i
\(263\) 19.5498 1.20549 0.602747 0.797932i \(-0.294073\pi\)
0.602747 + 0.797932i \(0.294073\pi\)
\(264\) −2.69783 1.17490i −0.166040 0.0723098i
\(265\) 1.00824 1.74632i 0.0619355 0.107276i
\(266\) 11.7276 3.35918i 0.719066 0.205965i
\(267\) −0.274400 2.42076i −0.0167930 0.148148i
\(268\) −4.81929 + 8.34725i −0.294385 + 0.509890i
\(269\) 7.88365 13.6549i 0.480675 0.832553i −0.519079 0.854726i \(-0.673725\pi\)
0.999754 + 0.0221730i \(0.00705846\pi\)
\(270\) −12.5522 2.34883i −0.763903 0.142945i
\(271\) 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
\(273\) −14.4557 + 18.8054i −0.874898 + 1.13815i
\(274\) 2.04138 3.53578i 0.123324 0.213604i
\(275\) −4.86954 −0.293644
\(276\) −1.99624 17.6108i −0.120159 1.06005i
\(277\) −7.45122 −0.447701 −0.223850 0.974624i \(-0.571863\pi\)
−0.223850 + 0.974624i \(0.571863\pi\)
\(278\) −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 −0.934712 0.355406i \(-0.884343\pi\)
0.159566 0.987187i \(-0.448991\pi\)
\(282\) 3.41901 + 30.1625i 0.203599 + 1.79615i
\(283\) −9.37768 16.2426i −0.557445 0.965524i −0.997709 0.0676550i \(-0.978448\pi\)
0.440263 0.897869i \(-0.354885\pi\)
\(284\) 8.57064 + 14.8448i 0.508574 + 0.880876i
\(285\) 0.652070 + 5.75257i 0.0386253 + 0.340753i
\(286\) 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
\(290\) −0.152230 −0.00893928
\(291\) 2.37890 + 20.9867i 0.139454 + 1.23026i
\(292\) 3.83507 0.224431
\(293\) −1.23089 + 2.13196i −0.0719093 + 0.124551i −0.899738 0.436430i \(-0.856243\pi\)
0.827829 + 0.560981i \(0.189576\pi\)
\(294\) −8.20562 + 20.7611i −0.478562 + 1.21081i
\(295\) 5.63487 + 9.75988i 0.328075 + 0.568242i
\(296\) −0.316203 0.547680i −0.0183790 0.0318333i
\(297\) −2.61155 7.41544i −0.151537 0.430287i
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) 19.0497 32.9950i 1.10167 1.90815i
\(300\) −0.872835 7.70016i −0.0503932 0.444569i
\(301\) −19.4067 18.7517i −1.11858 1.08083i
\(302\) 11.6616 20.1985i 0.671050 1.16229i
\(303\) −1.77645 0.773637i −0.102054 0.0444443i
\(304\) −12.1399 −0.696270
\(305\) −2.16175 + 3.74425i −0.123781 + 0.214395i
\(306\) 2.51090 8.17911i 0.143538 0.467568i
\(307\) −4.66277 −0.266118 −0.133059 0.991108i \(-0.542480\pi\)
−0.133059 + 0.991108i \(0.542480\pi\)
\(308\) 4.00196 + 3.86688i 0.228033 + 0.220336i
\(309\) −3.06555 1.33503i −0.174393 0.0759475i
\(310\) 9.45629 0.537081
\(311\) −13.7410 23.8002i −0.779183 1.34958i −0.932413 0.361393i \(-0.882301\pi\)
0.153231 0.988190i \(-0.451032\pi\)
\(312\) 8.09542 5.98309i 0.458313 0.338726i
\(313\) −2.74666 + 4.75735i −0.155250 + 0.268901i −0.933150 0.359487i \(-0.882952\pi\)
0.777900 + 0.628388i \(0.216285\pi\)
\(314\) 31.8671 1.79837
\(315\) −9.07321 5.46951i −0.511217 0.308172i
\(316\) −8.22893 −0.462914
\(317\) −4.93879 + 8.55424i −0.277390 + 0.480454i −0.970735 0.240152i \(-0.922803\pi\)
0.693345 + 0.720606i \(0.256136\pi\)
\(318\) 0.542654 + 4.78730i 0.0304305 + 0.268459i
\(319\) −0.0468601 0.0811641i −0.00262366 0.00454432i
\(320\) −3.47615 −0.194323
\(321\) −1.12746 9.94649i −0.0629288 0.555159i
\(322\) 8.68480 34.7902i 0.483985 1.93878i
\(323\) −3.87885 −0.215825
\(324\) 11.2579 5.45879i 0.625437 0.303266i
\(325\) 8.32930 14.4268i 0.462026 0.800253i
\(326\) 22.4986 1.24608
\(327\) 11.4806 8.48494i 0.634876 0.469218i
\(328\) 5.06616 8.77485i 0.279732 0.484510i
\(329\) −6.09950 + 24.4338i −0.336276 + 1.34708i
\(330\) −5.17940 + 3.82794i −0.285116 + 0.210721i
\(331\) 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i \(-0.640769\pi\)
0.996692 0.0812710i \(-0.0258979\pi\)
\(332\) 3.89401 6.74463i 0.213712 0.370160i
\(333\) 0.495864 1.61525i 0.0271732 0.0885152i
\(334\) −3.24514 5.62076i −0.177566 0.307554i
\(335\) −4.62718 8.01452i −0.252810 0.437880i
\(336\) 13.5390 17.6129i 0.738613 0.960861i
\(337\) 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i \(-0.820347\pi\)
0.885698 + 0.464261i \(0.153680\pi\)
\(338\) −25.3924 −1.38116
\(339\) −20.2002 + 14.9294i −1.09712 + 0.810852i
\(340\) −2.87408 −0.155869
\(341\) 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
\(345\) 15.6018 + 6.79453i 0.839973 + 0.365805i
\(346\) 9.33593 + 16.1703i 0.501903 + 0.869321i
\(347\) 14.7694 + 25.5813i 0.792862 + 1.37328i 0.924188 + 0.381938i \(0.124743\pi\)
−0.131326 + 0.991339i \(0.541923\pi\)
\(348\) 0.119945 0.0886477i 0.00642971 0.00475202i
\(349\) 18.0006 + 31.1780i 0.963551 + 1.66892i 0.713458 + 0.700698i \(0.247128\pi\)
0.250094 + 0.968222i \(0.419539\pi\)
\(350\) 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
\(353\) −29.4930 −1.56975 −0.784877 0.619652i \(-0.787274\pi\)
−0.784877 + 0.619652i \(0.787274\pi\)
\(354\) −24.6873 10.7512i −1.31211 0.571421i
\(355\) −16.4580 −0.873500
\(356\) 0.977687 1.69340i 0.0518173 0.0897502i
\(357\) 4.32589 5.62755i 0.228950 0.297841i
\(358\) −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 \(0.787728\pi\)
\(360\) 3.06260 + 3.29182i 0.161413 + 0.173494i
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) −15.6451 + 27.0981i −0.822289 + 1.42425i
\(363\) 13.8327 + 6.02409i 0.726028 + 0.316183i
\(364\) −18.3015 + 5.24218i −0.959261 + 0.274765i
\(365\) −1.84110 + 3.18888i −0.0963676 + 0.166914i
\(366\) −1.16350 10.2644i −0.0608169 0.536527i
\(367\) −23.0843 −1.20499 −0.602496 0.798122i \(-0.705827\pi\)
−0.602496 + 0.798122i \(0.705827\pi\)
\(368\) −17.8417 + 30.9027i −0.930063 + 1.61092i
\(369\) 26.3844 6.05936i 1.37352 0.315438i
\(370\) −1.38416 −0.0719591
\(371\) −0.968093 + 3.87805i −0.0502609 + 0.201339i
\(372\) −7.45075 + 5.50664i −0.386304 + 0.285506i
\(373\) 21.5030 1.11338 0.556692 0.830719i \(-0.312070\pi\)
0.556692 + 0.830719i \(0.312070\pi\)
\(374\) −2.15752 3.73694i −0.111563 0.193232i
\(375\) 17.4197 + 7.58620i 0.899548 + 0.391750i
\(376\) 5.34392 9.25595i 0.275592 0.477339i
\(377\) 0.320615 0.0165125
\(378\) 25.2012 2.37539i 1.29621 0.122177i
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) −2.32333 + 4.02412i −0.119184 + 0.206433i
\(381\) −13.4980 5.87835i −0.691526 0.301157i
\(382\) 20.8925 + 36.1869i 1.06895 + 1.85148i
\(383\) −34.9209 −1.78437 −0.892187 0.451666i \(-0.850830\pi\)
−0.892187 + 0.451666i \(0.850830\pi\)
\(384\) −11.9306 + 8.81756i −0.608831 + 0.449969i
\(385\) −5.13654 + 1.47128i −0.261783 + 0.0749834i
\(386\) −11.3917 −0.579823
\(387\) −8.98003 + 29.2519i −0.456480 + 1.48696i
\(388\) −8.47603 + 14.6809i −0.430305 + 0.745311i
\(389\) −28.8822 −1.46438 −0.732192 0.681098i \(-0.761503\pi\)
−0.732192 + 0.681098i \(0.761503\pi\)
\(390\) −2.48157 21.8924i −0.125659 1.10857i
\(391\) −5.70066 + 9.87383i −0.288295 + 0.499341i
\(392\) 6.66801 4.16130i 0.336785 0.210177i
\(393\) 3.19737 + 1.39244i 0.161286 + 0.0702395i
\(394\) 8.99455 15.5790i 0.453139 0.784860i
\(395\) 3.95046 6.84239i 0.198769 0.344278i
\(396\) 1.85182 6.03219i 0.0930574 0.303129i
\(397\) 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
\(399\) −4.38243 10.6060i −0.219396 0.530965i
\(400\) −7.80111 + 13.5119i −0.390056 + 0.675596i
\(401\) −1.08212 −0.0540386 −0.0270193 0.999635i \(-0.508602\pi\)
−0.0270193 + 0.999635i \(0.508602\pi\)
\(402\) 20.2724 + 8.82858i 1.01110 + 0.440330i
\(403\) −19.9160 −0.992088
\(404\) −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
\(408\) −2.42257 + 1.79045i −0.119935 + 0.0886405i
\(409\) 10.8674 + 18.8229i 0.537360 + 0.930735i 0.999045 + 0.0436908i \(0.0139116\pi\)
−0.461685 + 0.887044i \(0.652755\pi\)
\(410\) −11.0884 19.2057i −0.547618 0.948501i
\(411\) −3.52122 1.53348i −0.173689 0.0756410i
\(412\) −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
\(416\) 34.5767 1.69526
\(417\) −1.05212 + 0.777593i −0.0515226 + 0.0380789i
\(418\) −6.97632 −0.341223
\(419\) 12.5906 21.8075i 0.615090 1.06537i −0.375279 0.926912i \(-0.622453\pi\)
0.990369 0.138455i \(-0.0442135\pi\)
\(420\) −3.24722 7.85865i −0.158448 0.383463i
\(421\) −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i \(-0.909527\pi\)
0.237090 0.971488i \(-0.423806\pi\)
\(422\) 5.23316 + 9.06411i 0.254746 + 0.441234i
\(423\) 27.8310 6.39158i 1.35319 0.310769i
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) −2.49256 + 4.31724i −0.120907 + 0.209417i
\(426\) 31.6236 23.3721i 1.53217 1.13238i
\(427\) 2.07567 8.31487i 0.100449 0.402385i
\(428\) 4.01715 6.95791i 0.194176 0.336323i
\(429\) 10.9084 8.06209i 0.526663 0.389241i
\(430\) 25.0669 1.20884
\(431\) 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i \(-0.795756\pi\)
0.918887 + 0.394520i \(0.129089\pi\)
\(432\) −24.7600 4.63321i −1.19127 0.222915i
\(433\) 9.71430 0.466839 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(434\) −18.0196 + 5.16144i −0.864970 + 0.247757i
\(435\) 0.0161292 + 0.142292i 0.000773334 + 0.00682236i
\(436\) 11.4579 0.548735
\(437\) 9.21651 + 15.9635i 0.440885 + 0.763636i
\(438\) −0.990919 8.74189i −0.0473479 0.417704i
\(439\) 7.41176 12.8375i 0.353744 0.612703i −0.633158 0.774022i \(-0.718242\pi\)
0.986902 + 0.161320i \(0.0515751\pi\)
\(440\) 2.26760 0.108103
\(441\) 20.2750 + 5.47021i 0.965478 + 0.260486i
\(442\) 14.7617 0.702141
\(443\) 10.9510 18.9676i 0.520297 0.901180i −0.479425 0.877583i \(-0.659155\pi\)
0.999722 0.0235972i \(-0.00751192\pi\)
\(444\) 1.09060 0.806033i 0.0517577 0.0382526i
\(445\) 0.938715 + 1.62590i 0.0444994 + 0.0770751i
\(446\) 21.5842 1.02204
\(447\) −10.4569 4.55396i −0.494596 0.215395i
\(448\) 6.62406 1.89736i 0.312957 0.0896416i
\(449\) 21.4952 1.01442 0.507212 0.861822i \(-0.330676\pi\)
0.507212 + 0.861822i \(0.330676\pi\)
\(450\) −17.3267 + 3.97919i −0.816787 + 0.187581i
\(451\) 6.82655 11.8239i 0.321450 0.556767i
\(452\) −20.1603 −0.948263
\(453\) −20.1153 8.76016i −0.945101 0.411588i
\(454\) 10.2954 17.8321i 0.483185 0.836902i
\(455\) 4.42711 17.7344i 0.207546 0.831402i
\(456\) 0.548548 + 4.83929i 0.0256881 + 0.226621i
\(457\) −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i \(0.565778\pi\)
−0.745009 + 0.667054i \(0.767555\pi\)
\(458\) −8.88995 + 15.3978i −0.415400 + 0.719494i
\(459\) −7.91114 1.48037i −0.369261 0.0690978i
\(460\) 6.82908 + 11.8283i 0.318408 + 0.551498i
\(461\) 1.41541 + 2.45155i 0.0659220 + 0.114180i 0.897103 0.441822i \(-0.145668\pi\)
−0.831181 + 0.556003i \(0.812334\pi\)
\(462\) 7.78035 10.1214i 0.361975 0.470892i
\(463\) −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i \(0.390850\pi\)
−0.983719 + 0.179711i \(0.942484\pi\)
\(464\) −0.300284 −0.0139403
\(465\) −1.00192 8.83890i −0.0464627 0.409894i
\(466\) −35.5173 −1.64531
\(467\) −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
\(471\) −3.37640 29.7866i −0.155576 1.37249i
\(472\) 4.74028 + 8.21041i 0.218189 + 0.377915i
\(473\) 7.71620 + 13.3648i 0.354791 + 0.614516i
\(474\) 2.12622 + 18.7575i 0.0976604 + 0.861561i
\(475\) 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
\(479\) −31.5791 −1.44289 −0.721443 0.692474i \(-0.756521\pi\)
−0.721443 + 0.692474i \(0.756521\pi\)
\(480\) 1.73945 + 15.3455i 0.0793947 + 0.700421i
\(481\) 2.91520 0.132922
\(482\) 9.79185 16.9600i 0.446007 0.772506i
\(483\) −33.4390 4.43169i −1.52153 0.201649i
\(484\) 6.05472 + 10.4871i 0.275215 + 0.476686i
\(485\) −8.13817 14.0957i −0.369535 0.640054i
\(486\) −15.3519 24.2514i −0.696378 1.10006i
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) −1.81855 + 3.14982i −0.0823218 + 0.142586i
\(489\) −2.38378 21.0297i −0.107798 0.950996i
\(490\) −0.590486 17.1931i −0.0266754 0.776704i
\(491\) −9.06981 + 15.7094i −0.409315 + 0.708954i −0.994813 0.101720i \(-0.967566\pi\)
0.585498 + 0.810674i \(0.300899\pi\)
\(492\) 19.9207 + 8.67539i 0.898094 + 0.391117i
\(493\) −0.0959447 −0.00432113
\(494\) 11.9329 20.6684i 0.536887 0.929916i
\(495\) 4.12679 + 4.43567i 0.185486 + 0.199368i
\(496\) 18.6531 0.837549
\(497\) 31.3619 8.98311i 1.40677 0.402948i
\(498\) −16.3803 7.13355i −0.734017 0.319662i
\(499\) −21.3091 −0.953928 −0.476964 0.878923i \(-0.658263\pi\)
−0.476964 + 0.878923i \(0.658263\pi\)
\(500\) 7.62478 + 13.2065i 0.340990 + 0.590613i
\(501\) −4.90996 + 3.62881i −0.219361 + 0.162123i
\(502\) −3.00701 + 5.20829i −0.134209 + 0.232457i
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) −7.63275 4.60118i −0.339990 0.204953i
\(505\) 1.49315 0.0664443
\(506\) −10.2529 + 17.7586i −0.455799 + 0.789466i
\(507\) 2.69038 + 23.7346i 0.119484 + 1.05409i
\(508\) −5.90824 10.2334i −0.262136 0.454032i
\(509\) 36.7735 1.62996 0.814979 0.579490i \(-0.196748\pi\)
0.814979 + 0.579490i \(0.196748\pi\)
\(510\) 0.742614 + 6.55135i 0.0328835 + 0.290099i
\(511\) 1.76780 7.08155i 0.0782027 0.313270i
\(512\) −21.4975 −0.950065
\(513\) −8.46788 + 9.88003i −0.373866 + 0.436214i
\(514\) −4.32299 + 7.48764i −0.190679 + 0.330265i
\(515\) 2.57667 0.113542
\(516\) −19.7506 + 14.5971i −0.869473 + 0.642603i
\(517\) 7.20083 12.4722i 0.316692 0.548527i
\(518\) 2.63762 0.755504i 0.115890 0.0331949i
\(519\) 14.1254 10.4397i 0.620037 0.458251i
\(520\) −3.87870 + 6.71810i −0.170092 + 0.294608i
\(521\) −9.57535 + 16.5850i −0.419504 + 0.726602i −0.995890 0.0905758i \(-0.971129\pi\)
0.576386 + 0.817178i \(0.304463\pi\)
\(522\) −0.233061 0.250504i −0.0102008 0.0109643i
\(523\) −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
\(525\) −14.6209 1.93771i −0.638107 0.0845688i
\(526\) 17.9980 31.1734i 0.784749 1.35922i
\(527\) 5.95991 0.259618
\(528\) −10.2167 + 7.55085i −0.444624 + 0.328609i
\(529\) 31.1812 1.35570
\(530\) −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
\(534\) −4.11266 1.79105i −0.177972 0.0775063i
\(535\) 3.85702 + 6.68056i 0.166754 + 0.288826i
\(536\) −3.89258 6.74214i −0.168134 0.291216i
\(537\) −2.36956 + 1.75128i −0.102254 + 0.0755732i
\(538\) −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 \(0.853090\pi\)
\(542\) 27.2460 1.17032
\(543\) 26.9866 + 11.7526i 1.15811 + 0.504351i
\(544\) −10.3472 −0.443631
\(545\) −5.50059 + 9.52731i −0.235620 + 0.408105i
\(546\) 16.6781 + 40.3631i 0.713758 + 1.72738i
\(547\) 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i \(-0.147773\pi\)
−0.834840 + 0.550492i \(0.814440\pi\)
\(548\) −1.54128 2.66957i −0.0658401 0.114038i
\(549\) −9.47096 + 2.17507i −0.404211 + 0.0928296i
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) −0.0775590 + 0.134336i −0.00330413 + 0.00572291i
\(552\) 13.1249 + 5.71584i 0.558632 + 0.243282i
\(553\) −3.79316 + 15.1949i −0.161302 + 0.646154i
\(554\) −6.85975 + 11.8814i −0.291443 + 0.504794i
\(555\) 0.146655 + 1.29379i 0.00622516 + 0.0549184i
\(556\) −1.05005 −0.0445319
\(557\) 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i \(-0.604646\pi\)
0.981078 0.193614i \(-0.0620211\pi\)
\(558\) 14.4773 + 15.5609i 0.612873 + 0.658744i
\(559\) −52.7939 −2.23294
\(560\) −4.14637 + 16.6098i −0.175216 + 0.701893i
\(561\) −3.26436 + 2.41260i −0.137822 + 0.101860i
\(562\) −47.8495 −2.01841
\(563\) −0.144020 0.249451i −0.00606973 0.0105131i 0.862975 0.505247i \(-0.168599\pi\)
−0.869044 + 0.494734i \(0.835265\pi\)
\(564\) 21.0129 + 9.15104i 0.884802 + 0.385328i
\(565\) 9.67836 16.7634i 0.407172 0.705242i
\(566\) −34.5331 −1.45154
\(567\) −4.89042 23.3042i −0.205378 0.978683i
\(568\) −13.8451 −0.580929
\(569\) 8.04004 13.9258i 0.337056 0.583798i −0.646821 0.762641i \(-0.723902\pi\)
0.983878 + 0.178843i \(0.0572354\pi\)
\(570\) 9.77313 + 4.25616i 0.409351 + 0.178271i
\(571\) 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i \(-0.0630358\pi\)
−0.660610 + 0.750729i \(0.729702\pi\)
\(572\) 10.8869 0.455204
\(573\) 31.6107 23.3626i 1.32056 0.975985i
\(574\) 31.6126 + 30.5456i 1.31949 + 1.27495i
\(575\) 23.6902 0.987950
\(576\) −5.32189 5.72021i −0.221745 0.238342i
\(577\) 12.0812 20.9253i 0.502949 0.871133i −0.497045 0.867725i \(-0.665582\pi\)
0.999994 0.00340833i \(-0.00108491\pi\)
\(578\) 26.8836 1.11821
\(579\) 1.20698 + 10.6480i 0.0501603 + 0.442515i
\(580\) −0.0574683 + 0.0995380i −0.00238624 + 0.00413309i
\(581\) −10.6592 10.2994i −0.442216 0.427289i
\(582\) 35.6546 + 15.5275i 1.47793 + 0.643634i
\(583\) 1.14289 1.97955i 0.0473338 0.0819845i
\(584\) −1.54881 + 2.68262i −0.0640902 + 0.111007i
\(585\) −20.2002 + 4.63910i −0.835174 + 0.191803i
\(586\) 2.26636 + 3.92546i 0.0936226 + 0.162159i
\(587\) 18.0145 + 31.2020i 0.743537 + 1.28784i 0.950875 + 0.309574i \(0.100186\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(588\) 10.4772 + 13.2028i 0.432073 + 0.544476i
\(589\) 4.81783 8.34472i 0.198515 0.343838i
\(590\) 20.7503 0.854276
\(591\) −15.5149 6.75668i −0.638197 0.277933i
\(592\) −2.73034 −0.112216
\(593\) 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
\(597\) 12.0897 8.93518i 0.494800 0.365693i
\(598\) −35.0751 60.7518i −1.43433 2.48433i
\(599\) −19.7642 34.2325i −0.807542 1.39870i −0.914561 0.404447i \(-0.867464\pi\)
0.107019 0.994257i \(-0.465869\pi\)
\(600\) 5.73873 + 2.49920i 0.234283 + 0.102029i
\(601\) 1.86447 + 3.22936i 0.0760534 + 0.131728i 0.901544 0.432688i \(-0.142435\pi\)
−0.825490 + 0.564416i \(0.809101\pi\)
\(602\) −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
\(605\) −11.6267 −0.472694
\(606\) −2.86904 + 2.12043i −0.116547 + 0.0861365i
\(607\) 23.6528 0.960036 0.480018 0.877259i \(-0.340630\pi\)
0.480018 + 0.877259i \(0.340630\pi\)
\(608\) −8.36436 + 14.4875i −0.339219 + 0.587545i
\(609\) −0.108401 0.262343i −0.00439263 0.0106307i
\(610\) 3.98029 + 6.89407i 0.161157 + 0.279133i
\(611\) 24.6339 + 42.6671i 0.996580 + 1.72613i
\(612\) −4.40013 4.72947i −0.177865 0.191177i
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) −4.29264 + 7.43507i −0.173237 + 0.300055i
\(615\) −16.7769 + 12.3994i −0.676512 + 0.499990i
\(616\) −4.32107 + 1.23770i −0.174101 + 0.0498684i
\(617\) −17.5615 + 30.4174i −0.706999 + 1.22456i 0.258966 + 0.965886i \(0.416618\pi\)
−0.965965 + 0.258672i \(0.916715\pi\)
\(618\) −4.95100 + 3.65914i −0.199158 + 0.147192i
\(619\) −21.1632 −0.850622 −0.425311 0.905047i \(-0.639835\pi\)
−0.425311 + 0.905047i \(0.639835\pi\)
\(620\) 3.56983 6.18312i 0.143368 0.248320i
\(621\) 12.7051 + 36.0759i 0.509839 + 1.44768i
\(622\) −50.6011 −2.02892
\(623\) −2.67624 2.58590i −0.107221 0.103602i
\(624\) −4.89504 43.1841i −0.195959 1.72875i
\(625\) 1.45048 0.0580192
\(626\) 5.05726 + 8.75943i 0.202129 + 0.350097i
\(627\) 0.739157 + 6.52085i 0.0295191 + 0.260418i
\(628\) 12.0301 20.8368i 0.480054 0.831477i
\(629\) −0.872381 −0.0347841
\(630\) −17.0745 + 9.43244i −0.680263 + 0.375798i
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) 3.32329 5.75610i 0.132193 0.228965i
\(633\) 7.91786 5.85186i 0.314707 0.232591i
\(634\) 9.09350 + 15.7504i 0.361149 + 0.625529i
\(635\) 11.3455 0.450231
\(636\) 3.33510 + 1.45242i 0.132245 + 0.0575924i
\(637\) 1.24363 + 36.2106i 0.0492745 + 1.43472i
\(638\) −0.172562 −0.00683178
\(639\) −25.1967 27.0826i −0.996767 1.07137i
\(640\) 5.71622 9.90078i 0.225953 0.391363i
\(641\) −9.87469 −0.390027 −0.195013 0.980801i \(-0.562475\pi\)
−0.195013 + 0.980801i \(0.562475\pi\)
\(642\) −16.8982 7.35913i −0.666921 0.290442i
\(643\) 21.9748 38.0615i 0.866602 1.50100i 0.00115462 0.999999i \(-0.499632\pi\)
0.865448 0.501000i \(-0.167034\pi\)
\(644\) −19.4694 18.8123i −0.767204 0.741307i
\(645\) −2.65590 23.4304i −0.104576 0.922570i
\(646\) −3.57095 + 6.18507i −0.140497 + 0.243348i
\(647\) 22.1936 38.4404i 0.872521 1.51125i 0.0131398 0.999914i \(-0.495817\pi\)
0.859381 0.511336i \(-0.170849\pi\)
\(648\) −0.728131 + 10.0794i −0.0286037 + 0.395955i
\(649\) 6.38743 + 11.0634i 0.250729 + 0.434275i
\(650\) −15.3362 26.5631i −0.601537 1.04189i
\(651\) 6.73368 + 16.2963i 0.263914 + 0.638703i
\(652\) 8.49341 14.7110i 0.332628 0.576128i
\(653\) 41.9912 1.64324 0.821622 0.570033i \(-0.193070\pi\)
0.821622 + 0.570033i \(0.193070\pi\)
\(654\) −2.96053 26.1179i −0.115766 1.02129i
\(655\) −2.68748 −0.105008
\(656\) −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 −0.940284 0.340390i \(-0.889441\pi\)
0.175356 0.984505i \(-0.443892\pi\)
\(660\) 0.547687 + 4.83170i 0.0213187 + 0.188074i
\(661\) 0.0933694 + 0.161721i 0.00363165 + 0.00629020i 0.867836 0.496852i \(-0.165511\pi\)
−0.864204 + 0.503142i \(0.832177\pi\)
\(662\) −19.0515 32.9982i −0.740459 1.28251i
\(663\) −1.56403 13.7979i −0.0607419 0.535866i
\(664\) 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
\(668\) −4.90028 −0.189597
\(669\) −2.28690 20.1750i −0.0884166 0.780012i
\(670\) −17.0395 −0.658294
\(671\) −2.45046 + 4.24432i −0.0945989 + 0.163850i
\(672\) −11.6905 28.2924i −0.450971 1.09140i
\(673\) −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(674\) −1.37862 2.38785i −0.0531026 0.0919764i
\(675\) 5.55519 + 15.7738i 0.213819 + 0.607136i
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) −14.1950 + 24.5865i −0.545560 + 0.944937i 0.453012 + 0.891505i \(0.350350\pi\)
−0.998571 + 0.0534326i \(0.982984\pi\)
\(678\) 5.20910 + 45.9547i 0.200054 + 1.76488i
\(679\) 23.2016 + 22.4184i 0.890396 + 0.860341i
\(680\) 1.16071 2.01041i 0.0445111 0.0770956i
\(681\) −17.7587 7.73385i −0.680514 0.296362i
\(682\) 10.7192 0.410460
\(683\) 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i \(-0.760593\pi\)
0.956779 + 0.290816i \(0.0939267\pi\)
\(684\) −10.1789 + 2.33764i −0.389199 + 0.0893821i
\(685\) 2.95968 0.113083
\(686\) 10.5095 + 32.4404i 0.401256 + 1.23858i
\(687\) 15.3345 + 6.67810i 0.585046 + 0.254786i
\(688\) 49.4461 1.88511
\(689\) 3.90981 + 6.77199i 0.148952 + 0.257992i
\(690\) 25.1976 18.6228i 0.959258 0.708960i
\(691\) −5.95416 + 10.3129i −0.226507 + 0.392321i −0.956770 0.290844i \(-0.906064\pi\)
0.730264 + 0.683165i \(0.239397\pi\)
\(692\) 14.0976 0.535909
\(693\) −10.2850 6.19999i −0.390694 0.235518i
\(694\) 54.3880 2.06454
\(695\) 0.504096 0.873119i 0.0191214 0.0331193i
\(696\) 0.0135685 + 0.119702i 0.000514313 + 0.00453727i
\(697\) −6.98857 12.1046i −0.264711 0.458493i
\(698\) 66.2870 2.50900
\(699\) 3.76313 + 33.1984i 0.142335 + 1.25568i
\(700\) −8.51283 8.22548i −0.321755 0.310894i
\(701\) −31.3902 −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(702\) 32.2260 37.6002i 1.21629 1.41913i
\(703\) −0.705208 + 1.22146i −0.0265974 + 0.0460681i
\(704\) −3.94041 −0.148510
\(705\) −17.6968 + 13.0792i −0.666499 + 0.492590i
\(706\) −27.1518 + 47.0284i −1.02187 + 1.76994i
\(707\) −2.84531 + 0.814992i −0.107009 + 0.0306509i
\(708\) −16.3495 + 12.0834i −0.614451 + 0.454123i
\(709\) −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i \(-0.837070\pi\)
0.860096 + 0.510133i \(0.170404\pi\)
\(710\) −15.1516 + 26.2433i −0.568628 + 0.984893i
\(711\) 17.3076 3.97480i 0.649085 0.149067i
\(712\) 0.789685 + 1.36777i 0.0295947 + 0.0512595i
\(713\) −14.1613 24.5281i −0.530345 0.918584i
\(714\) −4.99097 12.0787i −0.186782 0.452035i
\(715\) −5.22647 + 9.05251i −0.195459 + 0.338545i
\(716\) −2.36489 −0.0883802
\(717\) 0.542236 0.400751i 0.0202502 0.0149663i
\(718\) 9.96239 0.371793
\(719\) 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
\(723\) −16.8902 7.35561i −0.628152 0.273558i
\(724\) 11.8123 + 20.4595i 0.439002 + 0.760373i
\(725\) 0.0996792 + 0.172649i 0.00370199 + 0.00641204i
\(726\) 22.3404 16.5112i 0.829132 0.612787i
\(727\) −18.9253 32.7796i −0.701900 1.21573i −0.967799 0.251726i \(-0.919002\pi\)
0.265899 0.964001i \(-0.414331\pi\)
\(728\) 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
\(731\) 15.7987 0.584335
\(732\) −7.15073 3.11412i −0.264299 0.115101i
\(733\) 2.40155 0.0887033 0.0443516 0.999016i \(-0.485878\pi\)
0.0443516 + 0.999016i \(0.485878\pi\)
\(734\) −21.2519 + 36.8093i −0.784421 + 1.35866i
\(735\) −16.0080 + 2.37358i −0.590464 + 0.0875508i
\(736\) 24.5858 + 42.5839i 0.906245 + 1.56966i
\(737\) −5.24517 9.08490i −0.193208 0.334646i
\(738\) 14.6280 47.6500i 0.538465 1.75402i
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) −0.522533 + 0.905053i −0.0192087 + 0.0332704i
\(741\) −20.5833 8.96397i −0.756148 0.329300i
\(742\) 5.29255 + 5.11390i 0.194296 + 0.187737i
\(743\) −2.54785 + 4.41300i −0.0934715 + 0.161897i −0.908970 0.416862i \(-0.863130\pi\)
0.815498 + 0.578760i \(0.196463\pi\)
\(744\) −0.842852 7.43565i −0.0309004 0.272604i
\(745\) 8.78934 0.322016
\(746\) 19.7961 34.2879i 0.724787 1.25537i
\(747\) −4.93228 + 16.0666i −0.180463 + 0.587847i
\(748\) −3.25793 −0.119122
\(749\) −10.9962 10.6251i −0.401793 0.388231i
\(750\) 28.1336 20.7927i 1.02729 0.759242i
\(751\) −0.975011 −0.0355787 −0.0177893 0.999842i \(-0.505663\pi\)
−0.0177893 + 0.999842i \(0.505663\pi\)
\(752\) −23.0718 39.9615i −0.841341 1.45724i
\(753\) 5.18685 + 2.25885i 0.189019 + 0.0823172i
\(754\) 0.295165 0.511240i 0.0107493 0.0186183i
\(755\) 16.9075 0.615326
\(756\) 7.96047 17.3749i 0.289520 0.631917i
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) 5.26750 9.12357i 0.191324 0.331383i
\(759\) 17.6855 + 7.70198i 0.641943 + 0.279564i
\(760\) −1.87657 3.25031i −0.0680703 0.117901i
\(761\) −54.1749 −1.96384 −0.981920 0.189298i \(-0.939379\pi\)
−0.981920 + 0.189298i \(0.939379\pi\)
\(762\) −21.8000 + 16.1117i −0.789729 + 0.583666i
\(763\) 5.28158 21.1573i 0.191206 0.765946i
\(764\) 31.5484 1.14138
\(765\) 6.04494 1.38826i 0.218555 0.0501927i
\(766\) −32.1489 + 55.6835i −1.16159 + 2.01193i
\(767\) −43.7025 −1.57801
\(768\) 4.09272 + 36.1060i 0.147683 + 1.30286i
\(769\) −10.4326 + 18.0698i −0.376208 + 0.651612i −0.990507 0.137462i \(-0.956106\pi\)
0.614299 + 0.789074i \(0.289439\pi\)
\(770\) −2.38276 + 9.54503i −0.0858687 + 0.343979i
\(771\) 7.45681 + 3.24742i 0.268551 + 0.116953i
\(772\) −4.30047 + 7.44863i −0.154777 + 0.268082i
\(773\) −27.4972 + 47.6266i −0.989007 + 1.71301i −0.366447 + 0.930439i \(0.619426\pi\)
−0.622561 + 0.782572i \(0.713908\pi\)
\(774\) 38.3768 + 41.2491i 1.37942 + 1.48267i
\(775\) −6.19189 10.7247i −0.222419 0.385242i
\(776\) −6.84616 11.8579i −0.245763 0.425674i
\(777\) −0.985640 2.38537i −0.0353596 0.0855746i
\(778\) −26.5895 + 46.0544i −0.953281 + 1.65113i
\(779\) −22.5975 −0.809639
\(780\) −15.2515 6.64196i −0.546090 0.237820i
\(781\) −18.6560 −0.667566
\(782\) 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
\(786\) 5.16390 3.81649i 0.184190 0.136130i
\(787\) −4.59475 7.95833i −0.163785 0.283684i 0.772438 0.635090i \(-0.219037\pi\)
−0.936223 + 0.351406i \(0.885704\pi\)
\(788\) −6.79103 11.7624i −0.241921 0.419019i
\(789\) −31.0451 13.5200i −1.10523 0.481325i
\(790\) −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
\(794\) 20.5934 0.730832
\(795\) −2.80878 + 2.07588i −0.0996170 + 0.0736241i
\(796\) 12.0659 0.427665
\(797\) 3.53774 6.12754i 0.125313 0.217049i −0.796542 0.604583i \(-0.793340\pi\)
0.921855 + 0.387534i \(0.126673\pi\)
\(798\) −20.9465 2.77605i −0.741498 0.0982713i
\(799\) −7.37174 12.7682i −0.260793 0.451707i
\(800\) 10.7499 + 18.6194i 0.380067 + 0.658295i
\(801\) −1.23837 + 4.03392i −0.0437556 + 0.142532i
\(802\) −0.996224 + 1.72551i −0.0351779 + 0.0609299i
\(803\) −2.08699 + 3.61477i −0.0736483 + 0.127563i
\(804\) 13.4257 9.92255i 0.473488 0.349941i
\(805\) 24.9892 7.15774i 0.880752 0.252277i
\(806\) −18.3351 + 31.7573i −0.645827 + 1.11860i
\(807\) −21.9625 + 16.2318i −0.773116 + 0.571388i
\(808\) 1.25610 0.0441894
\(809\) −2.97060 + 5.14522i −0.104441 + 0.180896i −0.913510 0.406817i \(-0.866639\pi\)
0.809069 + 0.587714i \(0.199972\pi\)
\(810\) 18.3085 + 12.4106i 0.643295 + 0.436065i
\(811\) 44.4139 1.55958 0.779791 0.626039i \(-0.215325\pi\)
0.779791 + 0.626039i \(0.215325\pi\)
\(812\) 0.0551801 0.221044i 0.00193644 0.00775713i
\(813\) −2.88678 25.4672i −0.101244 0.893173i
\(814\) −1.56902 −0.0549942
\(815\) 8.15485 + 14.1246i 0.285652 + 0.494764i
\(816\) 1.46485 + 12.9229i 0.0512801 + 0.452393i
\(817\) 12.7712 22.1204i 0.446808 0.773894i
\(818\) 40.0191 1.39924
\(819\) 35.9608 19.8658i 1.25657 0.694168i
\(820\) −16.7439 −0.584721
\(821\) −3.17761 + 5.50378i −0.110899 + 0.192083i −0.916133 0.400874i \(-0.868706\pi\)
0.805234 + 0.592958i \(0.202040\pi\)
\(822\) −5.68693 + 4.20305i −0.198355 + 0.146598i
\(823\) 4.73216 + 8.19635i 0.164953 + 0.285707i 0.936639 0.350297i \(-0.113919\pi\)
−0.771686 + 0.636004i \(0.780586\pi\)
\(824\) 2.16760 0.0755120
\(825\) 7.73282 + 3.36762i 0.269222 + 0.117245i
\(826\) −39.5412 + 11.3259i −1.37581 + 0.394080i
\(827\) −4.86261 −0.169090 −0.0845448 0.996420i \(-0.526944\pi\)
−0.0845448 + 0.996420i \(0.526944\pi\)
\(828\) −9.00905 + 29.3465i −0.313086 + 1.01986i
\(829\) 20.3926 35.3211i 0.708266 1.22675i −0.257234 0.966349i \(-0.582811\pi\)
0.965500 0.260403i \(-0.0838555\pi\)
\(830\) 13.7680 0.477896
\(831\) 11.8325 + 5.15302i 0.410466 + 0.178756i
\(832\) 6.74003 11.6741i 0.233668 0.404725i
\(833\) −0.372159 10.8361i −0.0128946 0.375449i
\(834\) 0.271315 + 2.39354i 0.00939486 + 0.0828815i
\(835\) 2.35247 4.07460i 0.0814107 0.141007i
\(836\) −2.63362 + 4.56156i −0.0910856 + 0.157765i
\(837\) 13.0110 15.1808i 0.449727 0.524726i
\(838\) −23.1823 40.1529i −0.800818 1.38706i
\(839\) 9.60171 + 16.6307i 0.331488 + 0.574154i 0.982804 0.184653i \(-0.0591161\pi\)
−0.651316 + 0.758807i \(0.725783\pi\)
\(840\) 6.80849 + 0.902334i 0.234915 + 0.0311335i
\(841\) 14.4981 25.1114i 0.499934 0.865911i
\(842\) −54.6126 −1.88207
\(843\) 5.06976 + 44.7255i 0.174612 + 1.54043i
\(844\) 7.90225 0.272007
\(845\) −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
\(849\) 3.65886 + 32.2785i 0.125572 + 1.10780i
\(850\) 4.58940 + 7.94907i 0.157415 + 0.272651i
\(851\) 2.07286 + 3.59029i 0.0710566 + 0.123074i
\(852\) −3.34398 29.5006i −0.114563 1.01068i
\(853\) −6.95055 12.0387i −0.237982 0.412198i 0.722153 0.691734i \(-0.243153\pi\)
−0.960135 + 0.279536i \(0.909819\pi\)
\(854\) −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
\(857\) 56.9838 1.94653 0.973265 0.229686i \(-0.0737700\pi\)
0.973265 + 0.229686i \(0.0737700\pi\)
\(858\) −2.81299 24.8163i −0.0960340 0.847213i
\(859\) −20.1002 −0.685810 −0.342905 0.939370i \(-0.611411\pi\)
−0.342905 + 0.939370i \(0.611411\pi\)
\(860\) 9.46298 16.3904i 0.322685 0.558907i
\(861\) 25.2019 32.7851i 0.858877 1.11731i
\(862\) −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 \(0.866865\pi\)
\(864\) −22.5888 + 26.3558i −0.768486 + 0.896643i
\(865\) −6.76781 + 11.7222i −0.230112 + 0.398566i
\(866\) 8.94318 15.4900i 0.303902 0.526373i
\(867\) −2.84838 25.1285i −0.0967361 0.853407i
\(868\) −3.42769 + 13.7309i −0.116343 + 0.466056i
\(869\) 4.47806 7.75623i 0.151908 0.263112i
\(870\) 0.241742 + 0.105278i 0.00819581 + 0.00356925i
\(871\) 35.8872 1.21599
\(872\) −4.62732 + 8.01476i −0.156701 + 0.271414i
\(873\) 10.7360 34.9720i 0.363359 1.18362i
\(874\) 33.9396 1.14802
\(875\) 27.9008 7.99173i 0.943219 0.270170i
\(876\) −6.09009 2.65221i −0.205765 0.0896099i
\(877\) −37.2574 −1.25809 −0.629046 0.777368i \(-0.716554\pi\)
−0.629046 + 0.777368i \(0.716554\pi\)
\(878\) −13.6468 23.6370i −0.460558 0.797710i
\(879\) 3.42905 2.53431i 0.115659 0.0854801i
\(880\) 4.89504 8.47846i 0.165012 0.285809i
\(881\) −11.7848 −0.397041 −0.198520 0.980097i \(-0.563614\pi\)
−0.198520 + 0.980097i \(0.563614\pi\)
\(882\) 27.3882 27.2938i 0.922208 0.919030i
\(883\) −29.2308 −0.983693 −0.491847 0.870682i \(-0.663678\pi\)
−0.491847 + 0.870682i \(0.663678\pi\)
\(884\) 5.57265 9.65211i 0.187428 0.324636i
\(885\) −2.19854 19.3956i −0.0739032 0.651974i
\(886\) −20.1634 34.9240i −0.677402 1.17329i
\(887\) 28.5161 0.957479 0.478739 0.877957i \(-0.341094\pi\)
0.478739 + 0.877957i \(0.341094\pi\)
\(888\) 0.123372 + 1.08839i 0.00414010 + 0.0365240i
\(889\) −21.6196 + 6.19258i −0.725098 + 0.207693i
\(890\) 3.45680 0.115872
\(891\) −0.981141 + 13.5818i −0.0328695 + 0.455006i
\(892\) 8.14822 14.1131i 0.272823 0.472543i
\(893\) −23.8364 −0.797656
\(894\) −16.8884 + 12.4818i −0.564834 + 0.417453i
\(895\) 1.13531 1.96642i 0.0379493 0.0657301i
\(896\) −5.48862 + 21.9867i −0.183362 + 0.734524i
\(897\) −53.0691 + 39.2219i −1.77193 + 1.30958i
\(898\) 19.7890 34.2755i 0.660366 1.14379i
\(899\) 0.119171 0.206410i 0.00397456 0.00688414i
\(900\) −3.93912 + 12.8315i −0.131304 + 0.427715i
\(901\) −1.17002 2.02653i −0.0389790 0.0675135i
\(902\) −12.5693 21.7707i −0.418513 0.724885i
\(903\) 17.8498 + 43.1986i 0.594004 + 1.43756i
\(904\) 8.14183 14.1021i 0.270793 0.469028i
\(905\) −22.6829 −0.754006
\(906\) −32.4872 + 24.0104i −1.07931 + 0.797690i
\(907\) −7.89155 −0.262035 −0.131017 0.991380i \(-0.541824\pi\)
−0.131017 + 0.991380i \(0.541824\pi\)
\(908\) −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 0.528306 0.849054i \(-0.322827\pi\)
−0.999455 + 0.0329991i \(0.989494\pi\)
\(912\) 19.2781 + 8.39554i 0.638361 + 0.278004i
\(913\) 4.23813 + 7.34065i 0.140262 + 0.242940i
\(914\) 37.4007 + 64.7798i 1.23710 + 2.14273i
\(915\) 6.02225 4.45087i 0.199089 0.147141i
\(916\) 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 \(0.791287\pi\)
\(920\) −11.0318 −0.363708
\(921\) 7.40446 + 3.22462i 0.243985 + 0.106255i
\(922\) 5.21221 0.171655
\(923\) 31.9110 55.2714i 1.05036 1.81928i
\(924\) −3.68090 8.90821i −0.121093 0.293059i
\(925\) 0.906337 + 1.56982i 0.0298002 + 0.0516154i
\(926\) 25.6529 + 44.4322i 0.843008 + 1.46013i
\(927\) 3.94481 + 4.24006i 0.129565 + 0.139262i
\(928\) −0.206895 + 0.358353i −0.00679167 + 0.0117635i
\(929\) −9.40031 + 16.2818i −0.308414 + 0.534189i −0.978016 0.208531i \(-0.933132\pi\)
0.669601 + 0.742721i \(0.266465\pi\)
\(930\) −15.0166 6.53966i −0.492412 0.214444i
\(931\) −15.4729 8.23853i −0.507104 0.270007i
\(932\) −13.4081 + 23.2234i −0.439196 + 0.760709i
\(933\) 5.36130 + 47.2974i 0.175521 + 1.54845i
\(934\) −49.0577 −1.60522
\(935\) 1.56403 2.70898i 0.0511493 0.0885932i
\(936\) −16.9932 + 3.90260i −0.555440 + 0.127561i
\(937\) 48.5788 1.58700 0.793500 0.608570i \(-0.208256\pi\)
0.793500 + 0.608570i \(0.208256\pi\)
\(938\) 32.4700 9.30052i 1.06018 0.303673i
\(939\) 7.65172 5.65516i 0.249704 0.184549i
\(940\) −17.6619 −0.576067
\(941\) −10.2425 17.7406i −0.333898 0.578328i 0.649375 0.760468i \(-0.275031\pi\)
−0.983272 + 0.182141i \(0.941697\pi\)
\(942\) −50.6049 22.0383i −1.64880 0.718046i
\(943\) −33.2110 + 57.5231i −1.08150 + 1.87321i
\(944\) 40.9312 1.33220
\(945\) 10.6257 + 14.9603i 0.345654 + 0.486659i
\(946\) 28.4148 0.923843
\(947\) 7.42524 12.8609i 0.241288 0.417923i −0.719793 0.694188i \(-0.755764\pi\)
0.961081 + 0.276265i \(0.0890969\pi\)
\(948\) 13.0675 + 5.69086i 0.424413 + 0.184831i
\(949\) −7.13954 12.3661i −0.231759 0.401419i
\(950\) 14.8398 0.481466
\(951\) 13.7586 10.1686i 0.446154 0.329739i
\(952\) −1.11449 + 4.46451i −0.0361209 + 0.144696i
\(953\) 46.4678 1.50524 0.752620 0.658456i \(-0.228790\pi\)
0.752620 + 0.658456i \(0.228790\pi\)
\(954\) 2.44901 7.97750i 0.0792896 0.258281i
\(955\) −15.1454 + 26.2326i −0.490094 + 0.848868i
\(956\) 0.541167 0.0175026
\(957\) 0.0182833 + 0.161295i 0.000591015 + 0.00521394i
\(958\) −29.0724 + 50.3548i −0.939285 + 1.62689i
\(959\) −5.63988 + 1.61545i −0.182121 + 0.0521657i
\(960\) 5.52012 + 2.40399i 0.178161 + 0.0775886i
\(961\) 8.09733 14.0250i 0.261204 0.452419i
\(962\) 2.68380 4.64847i 0.0865291 0.149873i
\(963\) −5.08826 + 16.5747i −0.163967 + 0.534112i
\(964\) −7.39301 12.8051i −0.238113 0.412423i
\(965\) −4.12905 7.15172i −0.132919 0.230222i
\(966\) −37.8512 + 49.2406i −1.21784 + 1.58429i
\(967\) 0.863670 1.49592i 0.0277738 0.0481056i −0.851804 0.523860i \(-0.824492\pi\)
0.879578 + 0.475754i \(0.157825\pi\)
\(968\) −9.78089 −0.314370
\(969\) 6.15960 + 2.68249i 0.197875 + 0.0861739i
\(970\) −29.9687 −0.962235
\(971\) −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
\(975\) −23.2040 + 17.1494i −0.743122 + 0.549220i
\(976\) 7.85137 + 13.5990i 0.251316 + 0.435293i
\(977\) 28.3101 + 49.0345i 0.905721 + 1.56875i 0.819947 + 0.572440i \(0.194003\pi\)
0.0857737 + 0.996315i \(0.472664\pi\)
\(978\) −35.7277 15.5593i −1.14245 0.497531i
\(979\) 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
\(983\) 32.2972 1.03012 0.515061 0.857154i \(-0.327769\pi\)
0.515061 + 0.857154i \(0.327769\pi\)
\(984\) −14.1134 + 10.4308i −0.449920 + 0.332523i
\(985\) 13.0407 0.415510
\(986\) −0.0883286 + 0.152990i −0.00281296 + 0.00487218i
\(987\) 26.5836 34.5826i 0.846165 1.10078i
\(988\) −9.00955 15.6050i −0.286632 0.496461i
\(989\) −37.5391 65.0197i −1.19367 2.06750i
\(990\) 10.8721 2.49686i 0.345540 0.0793554i
\(991\) −7.15502 + 12.3929i −0.227287 + 0.393672i −0.957003 0.290078i \(-0.906319\pi\)
0.729716 + 0.683750i \(0.239652\pi\)
\(992\) 12.8520 22.2602i 0.408050 0.706764i
\(993\) −28.8253 + 21.3039i −0.914742 + 0.676059i
\(994\) 14.5483 58.2785i 0.461444 1.84848i
\(995\) −5.79247 + 10.0329i −0.183634 + 0.318063i
\(996\) −10.8480 + 8.01748i −0.343734 + 0.254044i
\(997\) 56.2524 1.78153 0.890765 0.454463i \(-0.150169\pi\)
0.890765 + 0.454463i \(0.150169\pi\)
\(998\) −19.6176 + 33.9787i −0.620985 + 1.07558i
\(999\) −1.90449 + 2.22209i −0.0602553 + 0.0703038i
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.g.b.4.4 10
3.2 odd 2 189.2.g.b.172.2 10
4.3 odd 2 1008.2.t.i.193.5 10
7.2 even 3 63.2.h.b.58.2 yes 10
7.3 odd 6 441.2.f.f.148.4 10
7.4 even 3 441.2.f.e.148.4 10
7.5 odd 6 441.2.h.f.373.2 10
7.6 odd 2 441.2.g.f.67.4 10
9.2 odd 6 189.2.h.b.46.4 10
9.4 even 3 567.2.e.f.487.4 10
9.5 odd 6 567.2.e.e.487.2 10
9.7 even 3 63.2.h.b.25.2 yes 10
12.11 even 2 3024.2.t.i.1873.2 10
21.2 odd 6 189.2.h.b.37.4 10
21.5 even 6 1323.2.h.f.226.4 10
21.11 odd 6 1323.2.f.e.442.2 10
21.17 even 6 1323.2.f.f.442.2 10
21.20 even 2 1323.2.g.f.361.2 10
28.23 odd 6 1008.2.q.i.625.2 10
36.7 odd 6 1008.2.q.i.529.2 10
36.11 even 6 3024.2.q.i.2881.4 10
63.2 odd 6 189.2.g.b.100.2 10
63.4 even 3 3969.2.a.z.1.2 5
63.11 odd 6 1323.2.f.e.883.2 10
63.16 even 3 inner 63.2.g.b.16.4 yes 10
63.20 even 6 1323.2.h.f.802.4 10
63.23 odd 6 567.2.e.e.163.2 10
63.25 even 3 441.2.f.e.295.4 10
63.31 odd 6 3969.2.a.ba.1.2 5
63.32 odd 6 3969.2.a.bc.1.4 5
63.34 odd 6 441.2.h.f.214.2 10
63.38 even 6 1323.2.f.f.883.2 10
63.47 even 6 1323.2.g.f.667.2 10
63.52 odd 6 441.2.f.f.295.4 10
63.58 even 3 567.2.e.f.163.4 10
63.59 even 6 3969.2.a.bb.1.4 5
63.61 odd 6 441.2.g.f.79.4 10
84.23 even 6 3024.2.q.i.2305.4 10
252.79 odd 6 1008.2.t.i.961.5 10
252.191 even 6 3024.2.t.i.289.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 1.1 even 1 trivial
63.2.g.b.16.4 yes 10 63.16 even 3 inner
63.2.h.b.25.2 yes 10 9.7 even 3
63.2.h.b.58.2 yes 10 7.2 even 3
189.2.g.b.100.2 10 63.2 odd 6
189.2.g.b.172.2 10 3.2 odd 2
189.2.h.b.37.4 10 21.2 odd 6
189.2.h.b.46.4 10 9.2 odd 6
441.2.f.e.148.4 10 7.4 even 3
441.2.f.e.295.4 10 63.25 even 3
441.2.f.f.148.4 10 7.3 odd 6
441.2.f.f.295.4 10 63.52 odd 6
441.2.g.f.67.4 10 7.6 odd 2
441.2.g.f.79.4 10 63.61 odd 6
441.2.h.f.214.2 10 63.34 odd 6
441.2.h.f.373.2 10 7.5 odd 6
567.2.e.e.163.2 10 63.23 odd 6
567.2.e.e.487.2 10 9.5 odd 6
567.2.e.f.163.4 10 63.58 even 3
567.2.e.f.487.4 10 9.4 even 3
1008.2.q.i.529.2 10 36.7 odd 6
1008.2.q.i.625.2 10 28.23 odd 6
1008.2.t.i.193.5 10 4.3 odd 2
1008.2.t.i.961.5 10 252.79 odd 6
1323.2.f.e.442.2 10 21.11 odd 6
1323.2.f.e.883.2 10 63.11 odd 6
1323.2.f.f.442.2 10 21.17 even 6
1323.2.f.f.883.2 10 63.38 even 6
1323.2.g.f.361.2 10 21.20 even 2
1323.2.g.f.667.2 10 63.47 even 6
1323.2.h.f.226.4 10 21.5 even 6
1323.2.h.f.802.4 10 63.20 even 6
3024.2.q.i.2305.4 10 84.23 even 6
3024.2.q.i.2881.4 10 36.11 even 6
3024.2.t.i.289.2 10 252.191 even 6
3024.2.t.i.1873.2 10 12.11 even 2
3969.2.a.z.1.2 5 63.4 even 3
3969.2.a.ba.1.2 5 63.31 odd 6
3969.2.a.bb.1.4 5 63.59 even 6
3969.2.a.bc.1.4 5 63.32 odd 6