Properties

Label 55.2.g.b.16.2
Level $55$
Weight $2$
Character 55.16
Analytic conductor $0.439$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,2,Mod(16,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.g (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.2
Root \(-0.386111 - 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 55.16
Dual form 55.2.g.b.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.147481 + 0.453901i) q^{2} +(-0.261370 - 0.189896i) q^{3} +(1.43376 - 1.04169i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.0476470 - 0.146642i) q^{6} +(-2.17239 + 1.57833i) q^{7} +(1.45650 + 1.05821i) q^{8} +(-0.894797 - 2.75390i) q^{9} +O(q^{10})\) \(q+(0.147481 + 0.453901i) q^{2} +(-0.261370 - 0.189896i) q^{3} +(1.43376 - 1.04169i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.0476470 - 0.146642i) q^{6} +(-2.17239 + 1.57833i) q^{7} +(1.45650 + 1.05821i) q^{8} +(-0.894797 - 2.75390i) q^{9} -0.477260 q^{10} +(-2.79042 + 1.79264i) q^{11} -0.572554 q^{12} +(-1.44244 - 4.43939i) q^{13} +(-1.03679 - 0.753275i) q^{14} +(0.261370 - 0.189896i) q^{15} +(0.829779 - 2.55380i) q^{16} +(-1.42961 + 4.39990i) q^{17} +(1.11803 - 0.812299i) q^{18} +(3.51149 + 2.55125i) q^{19} +(0.547647 + 1.68548i) q^{20} +0.867517 q^{21} +(-1.22522 - 1.00220i) q^{22} +2.77222 q^{23} +(-0.179735 - 0.553168i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(1.80231 - 1.30945i) q^{26} +(-0.588587 + 1.81148i) q^{27} +(-1.47055 + 4.52590i) q^{28} +(2.43790 - 1.77124i) q^{29} +(0.124741 + 0.0906300i) q^{30} +(0.737407 + 2.26951i) q^{31} +4.88221 q^{32} +(1.06975 + 0.0613500i) q^{33} -2.20796 q^{34} +(-0.829779 - 2.55380i) q^{35} +(-4.15163 - 3.01633i) q^{36} +(8.61029 - 6.25574i) q^{37} +(-0.640135 + 1.97013i) q^{38} +(-0.466012 + 1.43424i) q^{39} +(-1.45650 + 1.05821i) q^{40} +(1.78826 + 1.29924i) q^{41} +(0.127943 + 0.393767i) q^{42} -7.06719 q^{43} +(-2.13343 + 5.47695i) q^{44} +2.89563 q^{45} +(0.408851 + 1.25832i) q^{46} +(-3.52905 - 2.56401i) q^{47} +(-0.701836 + 0.509914i) q^{48} +(0.0650188 - 0.200107i) q^{49} +(0.147481 - 0.453901i) q^{50} +(1.20918 - 0.878523i) q^{51} +(-6.69257 - 4.86243i) q^{52} +(-1.95733 - 6.02403i) q^{53} -0.909040 q^{54} +(-0.842610 - 3.20780i) q^{55} -4.83428 q^{56} +(-0.433326 - 1.33364i) q^{57} +(1.16351 + 0.845342i) q^{58} +(-9.50375 + 6.90488i) q^{59} +(0.176929 - 0.544531i) q^{60} +(-1.23070 + 3.78770i) q^{61} +(-0.921378 + 0.669420i) q^{62} +(6.29042 + 4.57026i) q^{63} +(-0.939522 - 2.89155i) q^{64} +4.66785 q^{65} +(0.129921 + 0.494608i) q^{66} +7.31984 q^{67} +(2.53359 + 7.79760i) q^{68} +(-0.724576 - 0.526435i) q^{69} +(1.03679 - 0.753275i) q^{70} +(0.369495 - 1.13719i) q^{71} +(1.61093 - 4.95794i) q^{72} +(-0.826577 + 0.600544i) q^{73} +(4.10935 + 2.98562i) q^{74} +(0.0998345 + 0.307259i) q^{75} +7.69223 q^{76} +(3.23251 - 8.29852i) q^{77} -0.719730 q^{78} +(1.08222 + 3.33073i) q^{79} +(2.17239 + 1.57833i) q^{80} +(-6.53000 + 4.74432i) q^{81} +(-0.325994 + 1.00331i) q^{82} +(3.43498 - 10.5718i) q^{83} +(1.24381 - 0.903681i) q^{84} +(-3.74278 - 2.71929i) q^{85} +(-1.04228 - 3.20780i) q^{86} -0.973547 q^{87} +(-5.96123 - 0.341876i) q^{88} +2.76978 q^{89} +(0.427051 + 1.31433i) q^{90} +(10.1404 + 7.36742i) q^{91} +(3.97470 - 2.88779i) q^{92} +(0.238235 - 0.733212i) q^{93} +(0.643336 - 1.97998i) q^{94} +(-3.51149 + 2.55125i) q^{95} +(-1.27606 - 0.927114i) q^{96} +(5.72738 + 17.6271i) q^{97} +0.100418 q^{98} +(7.43361 + 6.08051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} - 7 q^{6} - q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} - 7 q^{6} - q^{7} + 4 q^{8} - 5 q^{9} + 2 q^{10} + 3 q^{11} + 16 q^{12} - 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} - 13 q^{17} + 15 q^{19} - 3 q^{20} - 20 q^{21} - 7 q^{22} + 10 q^{23} + 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 9 q^{29} - 8 q^{30} - 10 q^{31} + 16 q^{32} + 5 q^{33} + 4 q^{34} - 4 q^{35} - 15 q^{36} + 24 q^{37} + 21 q^{39} - 4 q^{40} + 8 q^{41} + 9 q^{42} - 38 q^{43} - 12 q^{44} + 3 q^{46} + 5 q^{48} + q^{49} - 2 q^{50} + q^{51} - 28 q^{52} + 13 q^{53} + 16 q^{54} + 7 q^{55} + 22 q^{56} - 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} + 6 q^{61} - 30 q^{62} + 25 q^{63} - 26 q^{64} + 2 q^{65} + 13 q^{66} - 38 q^{67} + 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} - 30 q^{72} + 13 q^{73} + 20 q^{74} + 5 q^{75} + 34 q^{77} - 16 q^{78} + 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} + 27 q^{83} + 28 q^{84} - 12 q^{85} - 3 q^{86} + 38 q^{87} - 36 q^{88} - 16 q^{89} - 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} + 17 q^{94} - 15 q^{95} - 17 q^{96} + 24 q^{97} + 16 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.147481 + 0.453901i 0.104285 + 0.320957i 0.989562 0.144108i \(-0.0460312\pi\)
−0.885277 + 0.465064i \(0.846031\pi\)
\(3\) −0.261370 0.189896i −0.150902 0.109637i 0.509772 0.860309i \(-0.329730\pi\)
−0.660674 + 0.750673i \(0.729730\pi\)
\(4\) 1.43376 1.04169i 0.716879 0.520843i
\(5\) −0.309017 + 0.951057i −0.138197 + 0.425325i
\(6\) 0.0476470 0.146642i 0.0194518 0.0598665i
\(7\) −2.17239 + 1.57833i −0.821086 + 0.596554i −0.917023 0.398834i \(-0.869415\pi\)
0.0959376 + 0.995387i \(0.469415\pi\)
\(8\) 1.45650 + 1.05821i 0.514950 + 0.374133i
\(9\) −0.894797 2.75390i −0.298266 0.917968i
\(10\) −0.477260 −0.150923
\(11\) −2.79042 + 1.79264i −0.841344 + 0.540500i
\(12\) −0.572554 −0.165282
\(13\) −1.44244 4.43939i −0.400062 1.23126i −0.924949 0.380092i \(-0.875892\pi\)
0.524886 0.851172i \(-0.324108\pi\)
\(14\) −1.03679 0.753275i −0.277095 0.201321i
\(15\) 0.261370 0.189896i 0.0674854 0.0490310i
\(16\) 0.829779 2.55380i 0.207445 0.638449i
\(17\) −1.42961 + 4.39990i −0.346732 + 1.06713i 0.613918 + 0.789370i \(0.289593\pi\)
−0.960650 + 0.277762i \(0.910407\pi\)
\(18\) 1.11803 0.812299i 0.263523 0.191461i
\(19\) 3.51149 + 2.55125i 0.805592 + 0.585297i 0.912549 0.408967i \(-0.134111\pi\)
−0.106958 + 0.994264i \(0.534111\pi\)
\(20\) 0.547647 + 1.68548i 0.122458 + 0.376886i
\(21\) 0.867517 0.189308
\(22\) −1.22522 1.00220i −0.261217 0.213669i
\(23\) 2.77222 0.578048 0.289024 0.957322i \(-0.406669\pi\)
0.289024 + 0.957322i \(0.406669\pi\)
\(24\) −0.179735 0.553168i −0.0366883 0.112915i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 1.80231 1.30945i 0.353462 0.256805i
\(27\) −0.588587 + 1.81148i −0.113274 + 0.348620i
\(28\) −1.47055 + 4.52590i −0.277908 + 0.855314i
\(29\) 2.43790 1.77124i 0.452707 0.328911i −0.337956 0.941162i \(-0.609736\pi\)
0.790664 + 0.612251i \(0.209736\pi\)
\(30\) 0.124741 + 0.0906300i 0.0227746 + 0.0165467i
\(31\) 0.737407 + 2.26951i 0.132442 + 0.407615i 0.995183 0.0980305i \(-0.0312543\pi\)
−0.862741 + 0.505646i \(0.831254\pi\)
\(32\) 4.88221 0.863061
\(33\) 1.06975 + 0.0613500i 0.186219 + 0.0106797i
\(34\) −2.20796 −0.378662
\(35\) −0.829779 2.55380i −0.140258 0.431670i
\(36\) −4.15163 3.01633i −0.691938 0.502722i
\(37\) 8.61029 6.25574i 1.41552 1.02844i 0.423033 0.906114i \(-0.360965\pi\)
0.992490 0.122324i \(-0.0390346\pi\)
\(38\) −0.640135 + 1.97013i −0.103844 + 0.319598i
\(39\) −0.466012 + 1.43424i −0.0746217 + 0.229662i
\(40\) −1.45650 + 1.05821i −0.230293 + 0.167317i
\(41\) 1.78826 + 1.29924i 0.279279 + 0.202908i 0.718603 0.695421i \(-0.244782\pi\)
−0.439324 + 0.898329i \(0.644782\pi\)
\(42\) 0.127943 + 0.393767i 0.0197420 + 0.0607596i
\(43\) −7.06719 −1.07774 −0.538868 0.842390i \(-0.681148\pi\)
−0.538868 + 0.842390i \(0.681148\pi\)
\(44\) −2.13343 + 5.47695i −0.321626 + 0.825682i
\(45\) 2.89563 0.431654
\(46\) 0.408851 + 1.25832i 0.0602819 + 0.185528i
\(47\) −3.52905 2.56401i −0.514765 0.373999i 0.299863 0.953982i \(-0.403059\pi\)
−0.814628 + 0.579983i \(0.803059\pi\)
\(48\) −0.701836 + 0.509914i −0.101301 + 0.0735997i
\(49\) 0.0650188 0.200107i 0.00928840 0.0285868i
\(50\) 0.147481 0.453901i 0.0208570 0.0641913i
\(51\) 1.20918 0.878523i 0.169319 0.123018i
\(52\) −6.69257 4.86243i −0.928092 0.674298i
\(53\) −1.95733 6.02403i −0.268859 0.827464i −0.990779 0.135487i \(-0.956740\pi\)
0.721920 0.691977i \(-0.243260\pi\)
\(54\) −0.909040 −0.123705
\(55\) −0.842610 3.20780i −0.113617 0.432540i
\(56\) −4.83428 −0.646008
\(57\) −0.433326 1.33364i −0.0573954 0.176645i
\(58\) 1.16351 + 0.845342i 0.152777 + 0.110999i
\(59\) −9.50375 + 6.90488i −1.23728 + 0.898939i −0.997414 0.0718667i \(-0.977104\pi\)
−0.239869 + 0.970805i \(0.577104\pi\)
\(60\) 0.176929 0.544531i 0.0228414 0.0702987i
\(61\) −1.23070 + 3.78770i −0.157575 + 0.484966i −0.998413 0.0563214i \(-0.982063\pi\)
0.840838 + 0.541287i \(0.182063\pi\)
\(62\) −0.921378 + 0.669420i −0.117015 + 0.0850164i
\(63\) 6.29042 + 4.57026i 0.792519 + 0.575799i
\(64\) −0.939522 2.89155i −0.117440 0.361444i
\(65\) 4.66785 0.578975
\(66\) 0.129921 + 0.494608i 0.0159922 + 0.0608820i
\(67\) 7.31984 0.894260 0.447130 0.894469i \(-0.352446\pi\)
0.447130 + 0.894469i \(0.352446\pi\)
\(68\) 2.53359 + 7.79760i 0.307243 + 0.945598i
\(69\) −0.724576 0.526435i −0.0872287 0.0633754i
\(70\) 1.03679 0.753275i 0.123921 0.0900336i
\(71\) 0.369495 1.13719i 0.0438510 0.134960i −0.926734 0.375718i \(-0.877396\pi\)
0.970585 + 0.240758i \(0.0773961\pi\)
\(72\) 1.61093 4.95794i 0.189850 0.584299i
\(73\) −0.826577 + 0.600544i −0.0967436 + 0.0702883i −0.635105 0.772425i \(-0.719043\pi\)
0.538362 + 0.842714i \(0.319043\pi\)
\(74\) 4.10935 + 2.98562i 0.477702 + 0.347071i
\(75\) 0.0998345 + 0.307259i 0.0115279 + 0.0354792i
\(76\) 7.69223 0.882360
\(77\) 3.23251 8.29852i 0.368378 0.945704i
\(78\) −0.719730 −0.0814934
\(79\) 1.08222 + 3.33073i 0.121759 + 0.374736i 0.993297 0.115593i \(-0.0368767\pi\)
−0.871538 + 0.490329i \(0.836877\pi\)
\(80\) 2.17239 + 1.57833i 0.242880 + 0.176463i
\(81\) −6.53000 + 4.74432i −0.725555 + 0.527147i
\(82\) −0.325994 + 1.00331i −0.0360000 + 0.110797i
\(83\) 3.43498 10.5718i 0.377038 1.16040i −0.565055 0.825053i \(-0.691145\pi\)
0.942093 0.335351i \(-0.108855\pi\)
\(84\) 1.24381 0.903681i 0.135711 0.0985996i
\(85\) −3.74278 2.71929i −0.405961 0.294948i
\(86\) −1.04228 3.20780i −0.112392 0.345906i
\(87\) −0.973547 −0.104375
\(88\) −5.96123 0.341876i −0.635469 0.0364442i
\(89\) 2.76978 0.293596 0.146798 0.989167i \(-0.453103\pi\)
0.146798 + 0.989167i \(0.453103\pi\)
\(90\) 0.427051 + 1.31433i 0.0450151 + 0.138542i
\(91\) 10.1404 + 7.36742i 1.06300 + 0.772315i
\(92\) 3.97470 2.88779i 0.414391 0.301073i
\(93\) 0.238235 0.733212i 0.0247038 0.0760305i
\(94\) 0.643336 1.97998i 0.0663550 0.204220i
\(95\) −3.51149 + 2.55125i −0.360271 + 0.261753i
\(96\) −1.27606 0.927114i −0.130238 0.0946232i
\(97\) 5.72738 + 17.6271i 0.581528 + 1.78976i 0.612789 + 0.790247i \(0.290048\pi\)
−0.0312615 + 0.999511i \(0.509952\pi\)
\(98\) 0.100418 0.0101438
\(99\) 7.43361 + 6.08051i 0.747106 + 0.611114i
\(100\) −1.77222 −0.177222
\(101\) −2.19852 6.76634i −0.218761 0.673276i −0.998865 0.0476270i \(-0.984834\pi\)
0.780104 0.625649i \(-0.215166\pi\)
\(102\) 0.577094 + 0.419284i 0.0571409 + 0.0415153i
\(103\) −6.09056 + 4.42505i −0.600121 + 0.436014i −0.845922 0.533307i \(-0.820949\pi\)
0.245801 + 0.969320i \(0.420949\pi\)
\(104\) 2.59688 7.99237i 0.254645 0.783716i
\(105\) −0.268077 + 0.825058i −0.0261617 + 0.0805174i
\(106\) 2.44565 1.77687i 0.237542 0.172584i
\(107\) −14.5859 10.5973i −1.41008 1.02448i −0.993312 0.115465i \(-0.963164\pi\)
−0.416764 0.909015i \(-0.636836\pi\)
\(108\) 1.04311 + 3.21035i 0.100373 + 0.308916i
\(109\) −16.3653 −1.56751 −0.783756 0.621068i \(-0.786699\pi\)
−0.783756 + 0.621068i \(0.786699\pi\)
\(110\) 1.33176 0.855553i 0.126978 0.0815738i
\(111\) −3.43842 −0.326360
\(112\) 2.22814 + 6.85750i 0.210539 + 0.647973i
\(113\) 1.66154 + 1.20718i 0.156304 + 0.113562i 0.663188 0.748453i \(-0.269203\pi\)
−0.506884 + 0.862014i \(0.669203\pi\)
\(114\) 0.541433 0.393374i 0.0507099 0.0368429i
\(115\) −0.856664 + 2.63654i −0.0798843 + 0.245859i
\(116\) 1.65029 5.07906i 0.153225 0.471579i
\(117\) −10.9349 + 7.94470i −1.01094 + 0.734488i
\(118\) −4.53576 3.29542i −0.417551 0.303368i
\(119\) −3.83883 11.8147i −0.351905 1.08305i
\(120\) 0.581635 0.0530958
\(121\) 4.57291 10.0044i 0.415720 0.909493i
\(122\) −1.90075 −0.172086
\(123\) −0.220675 0.679167i −0.0198976 0.0612384i
\(124\) 3.42138 + 2.48578i 0.307249 + 0.223229i
\(125\) 0.809017 0.587785i 0.0723607 0.0525731i
\(126\) −1.14673 + 3.52926i −0.102158 + 0.314411i
\(127\) −0.0235677 + 0.0725340i −0.00209130 + 0.00643635i −0.952097 0.305797i \(-0.901077\pi\)
0.950005 + 0.312233i \(0.101077\pi\)
\(128\) 9.07350 6.59228i 0.801992 0.582681i
\(129\) 1.84715 + 1.34203i 0.162633 + 0.118159i
\(130\) 0.688421 + 2.11874i 0.0603785 + 0.185826i
\(131\) −11.4831 −1.00328 −0.501642 0.865075i \(-0.667270\pi\)
−0.501642 + 0.865075i \(0.667270\pi\)
\(132\) 1.59767 1.02638i 0.139059 0.0893350i
\(133\) −11.6550 −1.01062
\(134\) 1.07954 + 3.32248i 0.0932580 + 0.287019i
\(135\) −1.54094 1.11956i −0.132623 0.0963562i
\(136\) −6.73823 + 4.89561i −0.577799 + 0.419795i
\(137\) −5.66406 + 17.4322i −0.483914 + 1.48933i 0.349635 + 0.936886i \(0.386306\pi\)
−0.833548 + 0.552447i \(0.813694\pi\)
\(138\) 0.132088 0.406525i 0.0112441 0.0346057i
\(139\) 18.7590 13.6292i 1.59111 1.15601i 0.688785 0.724966i \(-0.258145\pi\)
0.902330 0.431046i \(-0.141855\pi\)
\(140\) −3.84996 2.79716i −0.325381 0.236403i
\(141\) 0.435493 + 1.34031i 0.0366751 + 0.112874i
\(142\) 0.570666 0.0478892
\(143\) 11.9832 + 9.80199i 1.00209 + 0.819683i
\(144\) −7.77539 −0.647949
\(145\) 0.931196 + 2.86593i 0.0773317 + 0.238002i
\(146\) −0.394492 0.286615i −0.0326484 0.0237205i
\(147\) −0.0549936 + 0.0399552i −0.00453580 + 0.00329545i
\(148\) 5.82856 17.9385i 0.479104 1.47453i
\(149\) 4.53161 13.9469i 0.371244 1.14257i −0.574733 0.818341i \(-0.694894\pi\)
0.945978 0.324232i \(-0.105106\pi\)
\(150\) −0.124741 + 0.0906300i −0.0101851 + 0.00739991i
\(151\) 6.08301 + 4.41957i 0.495028 + 0.359659i 0.807115 0.590394i \(-0.201028\pi\)
−0.312086 + 0.950054i \(0.601028\pi\)
\(152\) 2.41473 + 7.43178i 0.195861 + 0.602797i
\(153\) 13.3961 1.08301
\(154\) 4.24344 + 0.243361i 0.341946 + 0.0196106i
\(155\) −2.38630 −0.191672
\(156\) 0.825877 + 2.54179i 0.0661231 + 0.203506i
\(157\) 10.8262 + 7.86568i 0.864023 + 0.627750i 0.928977 0.370139i \(-0.120690\pi\)
−0.0649531 + 0.997888i \(0.520690\pi\)
\(158\) −1.35221 + 0.982441i −0.107576 + 0.0781588i
\(159\) −0.632355 + 1.94619i −0.0501491 + 0.154343i
\(160\) −1.50869 + 4.64326i −0.119272 + 0.367082i
\(161\) −6.02234 + 4.37549i −0.474627 + 0.344837i
\(162\) −3.11651 2.26427i −0.244856 0.177898i
\(163\) −0.238558 0.734206i −0.0186853 0.0575075i 0.941279 0.337629i \(-0.109625\pi\)
−0.959964 + 0.280122i \(0.909625\pi\)
\(164\) 3.91733 0.305892
\(165\) −0.388918 + 0.998432i −0.0302772 + 0.0777279i
\(166\) 5.30514 0.411759
\(167\) −2.62118 8.06716i −0.202833 0.624256i −0.999795 0.0202268i \(-0.993561\pi\)
0.796962 0.604029i \(-0.206439\pi\)
\(168\) 1.26354 + 0.918013i 0.0974840 + 0.0708263i
\(169\) −7.11029 + 5.16593i −0.546946 + 0.397379i
\(170\) 0.682297 2.09989i 0.0523298 0.161055i
\(171\) 3.88382 11.9532i 0.297003 0.914081i
\(172\) −10.1326 + 7.36179i −0.772606 + 0.561331i
\(173\) −4.10876 2.98519i −0.312384 0.226960i 0.420535 0.907276i \(-0.361842\pi\)
−0.732919 + 0.680316i \(0.761842\pi\)
\(174\) −0.143580 0.441894i −0.0108848 0.0334999i
\(175\) 2.68522 0.202984
\(176\) 2.26259 + 8.61366i 0.170549 + 0.649279i
\(177\) 3.79521 0.285265
\(178\) 0.408491 + 1.25721i 0.0306177 + 0.0942315i
\(179\) 9.15568 + 6.65199i 0.684328 + 0.497193i 0.874791 0.484501i \(-0.160999\pi\)
−0.190463 + 0.981694i \(0.560999\pi\)
\(180\) 4.15163 3.01633i 0.309444 0.224824i
\(181\) 2.28674 7.03787i 0.169972 0.523121i −0.829396 0.558661i \(-0.811315\pi\)
0.999368 + 0.0355402i \(0.0113152\pi\)
\(182\) −1.84856 + 5.68929i −0.137025 + 0.421718i
\(183\) 1.04094 0.756287i 0.0769485 0.0559063i
\(184\) 4.03774 + 2.93359i 0.297666 + 0.216267i
\(185\) 3.28884 + 10.1220i 0.241800 + 0.744185i
\(186\) 0.367941 0.0269787
\(187\) −3.89819 14.8403i −0.285064 1.08523i
\(188\) −7.73070 −0.563819
\(189\) −1.58048 4.86423i −0.114963 0.353821i
\(190\) −1.67589 1.21761i −0.121582 0.0883346i
\(191\) 4.17135 3.03067i 0.301829 0.219291i −0.426554 0.904462i \(-0.640272\pi\)
0.728382 + 0.685171i \(0.240272\pi\)
\(192\) −0.303532 + 0.934176i −0.0219056 + 0.0674184i
\(193\) −1.24605 + 3.83494i −0.0896925 + 0.276045i −0.985834 0.167723i \(-0.946359\pi\)
0.896142 + 0.443768i \(0.146359\pi\)
\(194\) −7.15627 + 5.19933i −0.513790 + 0.373290i
\(195\) −1.22004 0.886408i −0.0873686 0.0634770i
\(196\) −0.115228 0.354635i −0.00823056 0.0253311i
\(197\) 11.4176 0.813469 0.406734 0.913547i \(-0.366667\pi\)
0.406734 + 0.913547i \(0.366667\pi\)
\(198\) −1.66363 + 4.27089i −0.118229 + 0.303519i
\(199\) −7.16644 −0.508015 −0.254008 0.967202i \(-0.581749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(200\) −0.556333 1.71222i −0.0393387 0.121072i
\(201\) −1.91319 1.39001i −0.134946 0.0980438i
\(202\) 2.74701 1.99582i 0.193279 0.140425i
\(203\) −2.50047 + 7.69565i −0.175498 + 0.540128i
\(204\) 0.818531 2.51918i 0.0573086 0.176378i
\(205\) −1.78826 + 1.29924i −0.124897 + 0.0907431i
\(206\) −2.90678 2.11190i −0.202525 0.147143i
\(207\) −2.48058 7.63443i −0.172412 0.530630i
\(208\) −12.5342 −0.869090
\(209\) −14.3720 0.824235i −0.994132 0.0570135i
\(210\) −0.414031 −0.0285709
\(211\) 1.07649 + 3.31309i 0.0741086 + 0.228083i 0.981249 0.192746i \(-0.0617393\pi\)
−0.907140 + 0.420829i \(0.861739\pi\)
\(212\) −9.08148 6.59808i −0.623719 0.453158i
\(213\) −0.312523 + 0.227061i −0.0214137 + 0.0155580i
\(214\) 2.65897 8.18348i 0.181764 0.559411i
\(215\) 2.18388 6.72129i 0.148939 0.458388i
\(216\) −2.77420 + 2.01558i −0.188760 + 0.137143i
\(217\) −5.18397 3.76638i −0.351911 0.255678i
\(218\) −2.41358 7.42824i −0.163468 0.503104i
\(219\) 0.330084 0.0223050
\(220\) −4.54963 3.72148i −0.306736 0.250902i
\(221\) 21.5950 1.45264
\(222\) −0.507102 1.56070i −0.0340345 0.104747i
\(223\) −8.53103 6.19816i −0.571280 0.415059i 0.264290 0.964443i \(-0.414862\pi\)
−0.835570 + 0.549384i \(0.814862\pi\)
\(224\) −10.6061 + 7.70575i −0.708647 + 0.514862i
\(225\) −0.894797 + 2.75390i −0.0596532 + 0.183594i
\(226\) −0.302893 + 0.932209i −0.0201481 + 0.0620096i
\(227\) −0.174762 + 0.126972i −0.0115994 + 0.00842743i −0.593570 0.804782i \(-0.702282\pi\)
0.581970 + 0.813210i \(0.302282\pi\)
\(228\) −2.01052 1.46073i −0.133150 0.0967390i
\(229\) −0.0233956 0.0720042i −0.00154602 0.00475817i 0.950281 0.311395i \(-0.100796\pi\)
−0.951827 + 0.306637i \(0.900796\pi\)
\(230\) −1.32307 −0.0872407
\(231\) −2.42074 + 1.55514i −0.159273 + 0.102321i
\(232\) 5.42514 0.356178
\(233\) 4.67235 + 14.3800i 0.306096 + 0.942067i 0.979266 + 0.202579i \(0.0649323\pi\)
−0.673170 + 0.739488i \(0.735068\pi\)
\(234\) −5.21881 3.79169i −0.341164 0.247870i
\(235\) 3.52905 2.56401i 0.230210 0.167257i
\(236\) −6.43336 + 19.7999i −0.418776 + 1.28886i
\(237\) 0.349634 1.07606i 0.0227111 0.0698977i
\(238\) 4.79655 3.48489i 0.310914 0.225892i
\(239\) 18.7406 + 13.6158i 1.21223 + 0.880734i 0.995431 0.0954825i \(-0.0304394\pi\)
0.216796 + 0.976217i \(0.430439\pi\)
\(240\) −0.268077 0.825058i −0.0173043 0.0532572i
\(241\) −21.3349 −1.37430 −0.687151 0.726515i \(-0.741139\pi\)
−0.687151 + 0.726515i \(0.741139\pi\)
\(242\) 5.21544 + 0.600185i 0.335261 + 0.0385814i
\(243\) 8.32179 0.533843
\(244\) 2.18107 + 6.71266i 0.139629 + 0.429734i
\(245\) 0.170221 + 0.123673i 0.0108750 + 0.00790119i
\(246\) 0.275729 0.200329i 0.0175798 0.0127725i
\(247\) 6.26085 19.2689i 0.398368 1.22605i
\(248\) −1.32758 + 4.08586i −0.0843012 + 0.259453i
\(249\) −2.90535 + 2.11086i −0.184119 + 0.133770i
\(250\) 0.386111 + 0.280526i 0.0244198 + 0.0177420i
\(251\) −1.92266 5.91734i −0.121357 0.373499i 0.871863 0.489751i \(-0.162912\pi\)
−0.993220 + 0.116251i \(0.962912\pi\)
\(252\) 13.7797 0.868041
\(253\) −7.73567 + 4.96959i −0.486338 + 0.312435i
\(254\) −0.0363991 −0.00228388
\(255\) 0.461867 + 1.42148i 0.0289232 + 0.0890165i
\(256\) −0.588982 0.427920i −0.0368113 0.0267450i
\(257\) 11.5611 8.39964i 0.721163 0.523955i −0.165593 0.986194i \(-0.552954\pi\)
0.886755 + 0.462239i \(0.152954\pi\)
\(258\) −0.336730 + 1.03635i −0.0209639 + 0.0645203i
\(259\) −8.83126 + 27.1798i −0.548748 + 1.68887i
\(260\) 6.69257 4.86243i 0.415055 0.301555i
\(261\) −7.05926 5.12885i −0.436957 0.317468i
\(262\) −1.69355 5.21220i −0.104628 0.322011i
\(263\) 4.13132 0.254748 0.127374 0.991855i \(-0.459345\pi\)
0.127374 + 0.991855i \(0.459345\pi\)
\(264\) 1.49316 + 1.22137i 0.0918979 + 0.0751703i
\(265\) 6.33404 0.389097
\(266\) −1.71890 5.29024i −0.105393 0.324365i
\(267\) −0.723937 0.525971i −0.0443042 0.0321889i
\(268\) 10.4949 7.62497i 0.641077 0.465769i
\(269\) −0.520367 + 1.60152i −0.0317273 + 0.0976466i −0.965666 0.259786i \(-0.916348\pi\)
0.933939 + 0.357433i \(0.116348\pi\)
\(270\) 0.280909 0.864548i 0.0170956 0.0526147i
\(271\) 14.9110 10.8335i 0.905778 0.658086i −0.0341657 0.999416i \(-0.510877\pi\)
0.939943 + 0.341330i \(0.110877\pi\)
\(272\) 10.0502 + 7.30188i 0.609381 + 0.442741i
\(273\) −1.25134 3.85124i −0.0757348 0.233088i
\(274\) −8.74784 −0.528476
\(275\) 3.31118 + 0.189896i 0.199672 + 0.0114512i
\(276\) −1.58725 −0.0955411
\(277\) −1.05914 3.25969i −0.0636375 0.195856i 0.914183 0.405303i \(-0.132834\pi\)
−0.977820 + 0.209446i \(0.932834\pi\)
\(278\) 8.95290 + 6.50466i 0.536959 + 0.390124i
\(279\) 5.59017 4.06150i 0.334675 0.243155i
\(280\) 1.49388 4.59768i 0.0892762 0.274764i
\(281\) −7.05230 + 21.7048i −0.420705 + 1.29480i 0.486342 + 0.873769i \(0.338331\pi\)
−0.907047 + 0.421029i \(0.861669\pi\)
\(282\) −0.544141 + 0.395341i −0.0324031 + 0.0235422i
\(283\) 23.5416 + 17.1040i 1.39941 + 1.01673i 0.994758 + 0.102255i \(0.0326057\pi\)
0.404647 + 0.914473i \(0.367394\pi\)
\(284\) −0.654828 2.01535i −0.0388569 0.119589i
\(285\) 1.40227 0.0830634
\(286\) −2.68183 + 6.88482i −0.158580 + 0.407108i
\(287\) −5.93542 −0.350357
\(288\) −4.36859 13.4451i −0.257422 0.792262i
\(289\) −3.56201 2.58795i −0.209530 0.152232i
\(290\) −1.16351 + 0.845342i −0.0683239 + 0.0496402i
\(291\) 1.85035 5.69480i 0.108470 0.333835i
\(292\) −0.559534 + 1.72207i −0.0327443 + 0.100776i
\(293\) −17.1621 + 12.4690i −1.00262 + 0.728448i −0.962649 0.270753i \(-0.912727\pi\)
−0.0399740 + 0.999201i \(0.512727\pi\)
\(294\) −0.0262463 0.0190690i −0.00153071 0.00111213i
\(295\) −3.63011 11.1723i −0.211353 0.650478i
\(296\) 19.1608 1.11370
\(297\) −1.60492 6.10992i −0.0931271 0.354534i
\(298\) 6.99883 0.405432
\(299\) −3.99878 12.3070i −0.231255 0.711731i
\(300\) 0.463206 + 0.336539i 0.0267432 + 0.0194301i
\(301\) 15.3527 11.1544i 0.884913 0.642927i
\(302\) −1.10892 + 3.41289i −0.0638109 + 0.196390i
\(303\) −0.710278 + 2.18601i −0.0408044 + 0.125583i
\(304\) 9.42913 6.85066i 0.540798 0.392912i
\(305\) −3.22201 2.34093i −0.184492 0.134041i
\(306\) 1.97568 + 6.08051i 0.112942 + 0.347599i
\(307\) −6.87520 −0.392388 −0.196194 0.980565i \(-0.562858\pi\)
−0.196194 + 0.980565i \(0.562858\pi\)
\(308\) −4.00982 15.2653i −0.228481 0.869823i
\(309\) 2.43219 0.138363
\(310\) −0.351935 1.08314i −0.0199886 0.0615185i
\(311\) −20.3530 14.7873i −1.15411 0.838511i −0.165089 0.986279i \(-0.552791\pi\)
−0.989022 + 0.147768i \(0.952791\pi\)
\(312\) −2.19647 + 1.59583i −0.124350 + 0.0903459i
\(313\) −3.57821 + 11.0126i −0.202252 + 0.622469i 0.797563 + 0.603236i \(0.206122\pi\)
−0.999815 + 0.0192328i \(0.993878\pi\)
\(314\) −1.97358 + 6.07406i −0.111376 + 0.342779i
\(315\) −6.29042 + 4.57026i −0.354425 + 0.257505i
\(316\) 5.02121 + 3.64812i 0.282465 + 0.205223i
\(317\) 6.40940 + 19.7261i 0.359988 + 1.10793i 0.953061 + 0.302780i \(0.0979146\pi\)
−0.593073 + 0.805149i \(0.702085\pi\)
\(318\) −0.976639 −0.0547672
\(319\) −3.62759 + 9.31278i −0.203106 + 0.521416i
\(320\) 3.04036 0.169961
\(321\) 1.79994 + 5.53963i 0.100463 + 0.309192i
\(322\) −2.87422 2.08825i −0.160174 0.116373i
\(323\) −16.2453 + 11.8029i −0.903913 + 0.656731i
\(324\) −4.42034 + 13.6044i −0.245575 + 0.755801i
\(325\) −1.44244 + 4.43939i −0.0800124 + 0.246253i
\(326\) 0.298074 0.216564i 0.0165088 0.0119943i
\(327\) 4.27740 + 3.10771i 0.236541 + 0.171857i
\(328\) 1.22972 + 3.78469i 0.0679000 + 0.208975i
\(329\) 11.7133 0.645777
\(330\) −0.510548 0.0292799i −0.0281047 0.00161181i
\(331\) −32.1415 −1.76665 −0.883327 0.468757i \(-0.844702\pi\)
−0.883327 + 0.468757i \(0.844702\pi\)
\(332\) −6.08755 18.7356i −0.334098 1.02825i
\(333\) −24.9322 18.1143i −1.36627 0.992657i
\(334\) 3.27512 2.37951i 0.179207 0.130201i
\(335\) −2.26195 + 6.96158i −0.123584 + 0.380352i
\(336\) 0.719847 2.21546i 0.0392709 0.120863i
\(337\) 14.5594 10.5780i 0.793100 0.576221i −0.115782 0.993275i \(-0.536937\pi\)
0.908882 + 0.417054i \(0.136937\pi\)
\(338\) −3.39346 2.46549i −0.184580 0.134105i
\(339\) −0.205037 0.631039i −0.0111361 0.0342734i
\(340\) −8.19888 −0.444647
\(341\) −6.12608 5.01098i −0.331746 0.271360i
\(342\) 5.99834 0.324353
\(343\) −5.63386 17.3392i −0.304200 0.936231i
\(344\) −10.2933 7.47855i −0.554980 0.403217i
\(345\) 0.724576 0.526435i 0.0390099 0.0283423i
\(346\) 0.749016 2.30523i 0.0402673 0.123930i
\(347\) −2.48753 + 7.65583i −0.133538 + 0.410986i −0.995360 0.0962243i \(-0.969323\pi\)
0.861822 + 0.507211i \(0.169323\pi\)
\(348\) −1.39583 + 1.01413i −0.0748244 + 0.0543631i
\(349\) −15.5569 11.3027i −0.832741 0.605022i 0.0875926 0.996156i \(-0.472083\pi\)
−0.920333 + 0.391135i \(0.872083\pi\)
\(350\) 0.396020 + 1.21882i 0.0211682 + 0.0651489i
\(351\) 8.89088 0.474560
\(352\) −13.6234 + 8.75202i −0.726131 + 0.466484i
\(353\) 14.8497 0.790371 0.395186 0.918601i \(-0.370680\pi\)
0.395186 + 0.918601i \(0.370680\pi\)
\(354\) 0.559723 + 1.72265i 0.0297489 + 0.0915578i
\(355\) 0.967351 + 0.702822i 0.0513417 + 0.0373019i
\(356\) 3.97119 2.88524i 0.210473 0.152917i
\(357\) −1.24021 + 3.81698i −0.0656391 + 0.202016i
\(358\) −1.66905 + 5.13682i −0.0882123 + 0.271489i
\(359\) −8.27079 + 6.00908i −0.436516 + 0.317147i −0.784249 0.620446i \(-0.786952\pi\)
0.347733 + 0.937594i \(0.386952\pi\)
\(360\) 4.21747 + 3.06417i 0.222280 + 0.161496i
\(361\) −0.0496143 0.152697i −0.00261128 0.00803670i
\(362\) 3.53175 0.185625
\(363\) −3.09503 + 1.74648i −0.162447 + 0.0916662i
\(364\) 22.2134 1.16430
\(365\) −0.315724 0.971700i −0.0165258 0.0508611i
\(366\) 0.496799 + 0.360945i 0.0259681 + 0.0188669i
\(367\) −11.4422 + 8.31327i −0.597280 + 0.433949i −0.844912 0.534905i \(-0.820347\pi\)
0.247632 + 0.968854i \(0.420347\pi\)
\(368\) 2.30033 7.07969i 0.119913 0.369054i
\(369\) 1.97786 6.08724i 0.102964 0.316889i
\(370\) −4.10935 + 2.98562i −0.213635 + 0.155215i
\(371\) 13.7600 + 9.99722i 0.714383 + 0.519030i
\(372\) −0.422205 1.29941i −0.0218903 0.0673715i
\(373\) 12.4600 0.645154 0.322577 0.946543i \(-0.395451\pi\)
0.322577 + 0.946543i \(0.395451\pi\)
\(374\) 6.16114 3.95807i 0.318585 0.204667i
\(375\) −0.323071 −0.0166833
\(376\) −2.42681 7.46894i −0.125153 0.385181i
\(377\) −11.3798 8.26788i −0.586088 0.425818i
\(378\) 1.97479 1.43477i 0.101572 0.0737965i
\(379\) 5.04840 15.5374i 0.259319 0.798102i −0.733629 0.679550i \(-0.762175\pi\)
0.992948 0.118552i \(-0.0378251\pi\)
\(380\) −2.37703 + 7.31575i −0.121939 + 0.375290i
\(381\) 0.0199338 0.0144828i 0.00102124 0.000741975i
\(382\) 1.99082 + 1.44642i 0.101859 + 0.0740051i
\(383\) −0.251122 0.772874i −0.0128317 0.0394920i 0.944436 0.328696i \(-0.106609\pi\)
−0.957267 + 0.289204i \(0.906609\pi\)
\(384\) −3.62339 −0.184905
\(385\) 6.89346 + 5.63868i 0.351323 + 0.287374i
\(386\) −1.92445 −0.0979522
\(387\) 6.32370 + 19.4623i 0.321452 + 0.989327i
\(388\) 26.5736 + 19.3068i 1.34907 + 0.980155i
\(389\) 24.5894 17.8652i 1.24673 0.905802i 0.248702 0.968580i \(-0.419996\pi\)
0.998028 + 0.0627780i \(0.0199960\pi\)
\(390\) 0.222409 0.684504i 0.0112621 0.0346612i
\(391\) −3.96321 + 12.1975i −0.200428 + 0.616854i
\(392\) 0.306455 0.222653i 0.0154783 0.0112457i
\(393\) 3.00134 + 2.18060i 0.151398 + 0.109997i
\(394\) 1.68388 + 5.18245i 0.0848327 + 0.261088i
\(395\) −3.50213 −0.176211
\(396\) 16.9920 + 0.974490i 0.853879 + 0.0489700i
\(397\) −14.8996 −0.747789 −0.373894 0.927471i \(-0.621978\pi\)
−0.373894 + 0.927471i \(0.621978\pi\)
\(398\) −1.05692 3.25285i −0.0529784 0.163051i
\(399\) 3.04628 + 2.21325i 0.152505 + 0.110801i
\(400\) −2.17239 + 1.57833i −0.108619 + 0.0789166i
\(401\) 3.76049 11.5736i 0.187790 0.577957i −0.812196 0.583385i \(-0.801728\pi\)
0.999985 + 0.00542792i \(0.00172777\pi\)
\(402\) 0.348768 1.07340i 0.0173950 0.0535362i
\(403\) 9.01155 6.54727i 0.448897 0.326143i
\(404\) −10.2006 7.41114i −0.507496 0.368718i
\(405\) −2.49424 7.67647i −0.123940 0.381447i
\(406\) −3.86184 −0.191660
\(407\) −12.8121 + 32.8913i −0.635071 + 1.63036i
\(408\) 2.69083 0.133216
\(409\) −0.0809957 0.249279i −0.00400498 0.0123261i 0.949034 0.315174i \(-0.102063\pi\)
−0.953039 + 0.302847i \(0.902063\pi\)
\(410\) −0.853463 0.620077i −0.0421495 0.0306234i
\(411\) 4.79073 3.48067i 0.236309 0.171689i
\(412\) −4.12288 + 12.6889i −0.203120 + 0.625138i
\(413\) 9.74764 30.0002i 0.479650 1.47621i
\(414\) 3.09944 2.25187i 0.152329 0.110674i
\(415\) 8.99290 + 6.53372i 0.441444 + 0.320728i
\(416\) −7.04232 21.6740i −0.345278 1.06266i
\(417\) −7.49116 −0.366844
\(418\) −1.74548 6.64503i −0.0853744 0.325019i
\(419\) −1.26916 −0.0620023 −0.0310012 0.999519i \(-0.509870\pi\)
−0.0310012 + 0.999519i \(0.509870\pi\)
\(420\) 0.475093 + 1.46219i 0.0231822 + 0.0713474i
\(421\) 23.9999 + 17.4369i 1.16968 + 0.849824i 0.990971 0.134078i \(-0.0428071\pi\)
0.178712 + 0.983902i \(0.442807\pi\)
\(422\) −1.34506 + 0.977240i −0.0654763 + 0.0475713i
\(423\) −3.90324 + 12.0129i −0.189782 + 0.584089i
\(424\) 3.52384 10.8452i 0.171133 0.526692i
\(425\) 3.74278 2.71929i 0.181551 0.131905i
\(426\) −0.149155 0.108367i −0.00722658 0.00525041i
\(427\) −3.30470 10.1708i −0.159926 0.492200i
\(428\) −31.9518 −1.54445
\(429\) −1.27070 4.83752i −0.0613497 0.233558i
\(430\) 3.37289 0.162655
\(431\) 9.68919 + 29.8203i 0.466712 + 1.43639i 0.856817 + 0.515621i \(0.172439\pi\)
−0.390105 + 0.920771i \(0.627561\pi\)
\(432\) 4.13776 + 3.00626i 0.199078 + 0.144639i
\(433\) 21.0607 15.3015i 1.01212 0.735345i 0.0474634 0.998873i \(-0.484886\pi\)
0.964652 + 0.263528i \(0.0848863\pi\)
\(434\) 0.945023 2.90848i 0.0453625 0.139612i
\(435\) 0.300843 0.925898i 0.0144243 0.0443934i
\(436\) −23.4639 + 17.0475i −1.12372 + 0.816429i
\(437\) 9.73464 + 7.07263i 0.465671 + 0.338330i
\(438\) 0.0486812 + 0.149825i 0.00232608 + 0.00715893i
\(439\) 14.4191 0.688185 0.344093 0.938936i \(-0.388187\pi\)
0.344093 + 0.938936i \(0.388187\pi\)
\(440\) 2.16726 5.56382i 0.103320 0.265245i
\(441\) −0.609255 −0.0290121
\(442\) 3.18486 + 9.80199i 0.151488 + 0.466233i
\(443\) 0.267467 + 0.194326i 0.0127078 + 0.00923273i 0.594121 0.804376i \(-0.297500\pi\)
−0.581413 + 0.813608i \(0.697500\pi\)
\(444\) −4.92986 + 3.58175i −0.233961 + 0.169982i
\(445\) −0.855908 + 2.63421i −0.0405739 + 0.124874i
\(446\) 1.55518 4.78636i 0.0736400 0.226641i
\(447\) −3.83289 + 2.78476i −0.181289 + 0.131715i
\(448\) 6.60483 + 4.79869i 0.312049 + 0.226717i
\(449\) 2.62920 + 8.09185i 0.124080 + 0.381878i 0.993732 0.111786i \(-0.0356571\pi\)
−0.869653 + 0.493664i \(0.835657\pi\)
\(450\) −1.38197 −0.0651465
\(451\) −7.31906 0.419748i −0.344641 0.0197652i
\(452\) 3.63974 0.171199
\(453\) −0.750657 2.31028i −0.0352689 0.108547i
\(454\) −0.0834069 0.0605986i −0.00391448 0.00284404i
\(455\) −10.1404 + 7.36742i −0.475388 + 0.345390i
\(456\) 0.780130 2.40099i 0.0365329 0.112437i
\(457\) 0.351807 1.08275i 0.0164569 0.0506490i −0.942491 0.334232i \(-0.891523\pi\)
0.958948 + 0.283583i \(0.0915231\pi\)
\(458\) 0.0292324 0.0212386i 0.00136594 0.000992413i
\(459\) −7.12889 5.17944i −0.332748 0.241756i
\(460\) 1.51820 + 4.67254i 0.0707864 + 0.217858i
\(461\) 14.5073 0.675670 0.337835 0.941205i \(-0.390305\pi\)
0.337835 + 0.941205i \(0.390305\pi\)
\(462\) −1.06289 0.869422i −0.0494503 0.0404492i
\(463\) −4.89739 −0.227601 −0.113801 0.993504i \(-0.536302\pi\)
−0.113801 + 0.993504i \(0.536302\pi\)
\(464\) −2.50047 7.69565i −0.116081 0.357261i
\(465\) 0.623707 + 0.453150i 0.0289237 + 0.0210143i
\(466\) −5.83803 + 4.24157i −0.270441 + 0.196487i
\(467\) 10.0193 30.8361i 0.463637 1.42693i −0.397053 0.917796i \(-0.629967\pi\)
0.860689 0.509131i \(-0.170033\pi\)
\(468\) −7.40218 + 22.7816i −0.342166 + 1.05308i
\(469\) −15.9015 + 11.5531i −0.734264 + 0.533474i
\(470\) 1.68428 + 1.22370i 0.0776898 + 0.0564450i
\(471\) −1.33597 4.11171i −0.0615585 0.189457i
\(472\) −21.1490 −0.973461
\(473\) 19.7204 12.6689i 0.906747 0.582516i
\(474\) 0.539990 0.0248026
\(475\) −1.34127 4.12801i −0.0615417 0.189406i
\(476\) −17.8111 12.9406i −0.816373 0.593129i
\(477\) −14.8382 + 10.7806i −0.679394 + 0.493609i
\(478\) −3.41635 + 10.5145i −0.156260 + 0.480920i
\(479\) 5.48054 16.8674i 0.250412 0.770690i −0.744287 0.667860i \(-0.767210\pi\)
0.994699 0.102830i \(-0.0327897\pi\)
\(480\) 1.27606 0.927114i 0.0582441 0.0423168i
\(481\) −40.1915 29.2009i −1.83258 1.33144i
\(482\) −3.14650 9.68394i −0.143319 0.441091i
\(483\) 2.40495 0.109429
\(484\) −3.86502 19.1075i −0.175683 0.868521i
\(485\) −18.5342 −0.841595
\(486\) 1.22731 + 3.77727i 0.0556719 + 0.171341i
\(487\) 14.9347 + 10.8507i 0.676754 + 0.491691i 0.872279 0.489008i \(-0.162641\pi\)
−0.195525 + 0.980699i \(0.562641\pi\)
\(488\) −5.80069 + 4.21445i −0.262585 + 0.190779i
\(489\) −0.0770712 + 0.237201i −0.00348528 + 0.0107266i
\(490\) −0.0310309 + 0.0955032i −0.00140183 + 0.00431440i
\(491\) 9.25018 6.72065i 0.417455 0.303299i −0.359158 0.933277i \(-0.616936\pi\)
0.776613 + 0.629978i \(0.216936\pi\)
\(492\) −1.02387 0.743887i −0.0461597 0.0335370i
\(493\) 4.30802 + 13.2587i 0.194023 + 0.597142i
\(494\) 9.66954 0.435053
\(495\) −8.08002 + 5.19080i −0.363170 + 0.233309i
\(496\) 6.40774 0.287716
\(497\) 0.992176 + 3.05360i 0.0445052 + 0.136973i
\(498\) −1.38661 1.00743i −0.0621353 0.0451439i
\(499\) −8.80335 + 6.39601i −0.394092 + 0.286325i −0.767130 0.641491i \(-0.778316\pi\)
0.373038 + 0.927816i \(0.378316\pi\)
\(500\) 0.547647 1.68548i 0.0244915 0.0753771i
\(501\) −0.846827 + 2.60627i −0.0378335 + 0.116439i
\(502\) 2.40233 1.74540i 0.107221 0.0779009i
\(503\) −36.1830 26.2885i −1.61332 1.17215i −0.851490 0.524371i \(-0.824301\pi\)
−0.761831 0.647776i \(-0.775699\pi\)
\(504\) 4.32571 + 13.3132i 0.192682 + 0.593015i
\(505\) 7.11455 0.316594
\(506\) −3.39657 2.77831i −0.150996 0.123511i
\(507\) 2.83941 0.126103
\(508\) 0.0417673 + 0.128546i 0.00185312 + 0.00570332i
\(509\) 11.1720 + 8.11693i 0.495190 + 0.359777i 0.807177 0.590310i \(-0.200994\pi\)
−0.311987 + 0.950086i \(0.600994\pi\)
\(510\) −0.577094 + 0.419284i −0.0255542 + 0.0185662i
\(511\) 0.847790 2.60923i 0.0375040 0.115425i
\(512\) 7.03891 21.6635i 0.311079 0.957402i
\(513\) −6.68836 + 4.85938i −0.295298 + 0.214547i
\(514\) 5.51766 + 4.00881i 0.243374 + 0.176821i
\(515\) −2.32639 7.15989i −0.102513 0.315502i
\(516\) 4.04635 0.178130
\(517\) 14.4439 + 0.828356i 0.635241 + 0.0364311i
\(518\) −13.6394 −0.599281
\(519\) 0.507030 + 1.56048i 0.0222562 + 0.0684974i
\(520\) 6.79871 + 4.93955i 0.298143 + 0.216614i
\(521\) 2.95269 2.14525i 0.129360 0.0939852i −0.521224 0.853420i \(-0.674524\pi\)
0.650584 + 0.759435i \(0.274524\pi\)
\(522\) 1.28688 3.96061i 0.0563253 0.173351i
\(523\) −1.54109 + 4.74299i −0.0673872 + 0.207396i −0.979080 0.203476i \(-0.934776\pi\)
0.911693 + 0.410873i \(0.134776\pi\)
\(524\) −16.4640 + 11.9618i −0.719233 + 0.522553i
\(525\) −0.701836 0.509914i −0.0306306 0.0222545i
\(526\) 0.609292 + 1.87521i 0.0265664 + 0.0817630i
\(527\) −11.0398 −0.480901
\(528\) 1.04433 2.68101i 0.0454486 0.116676i
\(529\) −15.3148 −0.665860
\(530\) 0.934153 + 2.87503i 0.0405770 + 0.124883i
\(531\) 27.5193 + 19.9939i 1.19424 + 0.867663i
\(532\) −16.7105 + 12.1409i −0.724493 + 0.526375i
\(533\) 3.18839 9.81284i 0.138104 0.425041i
\(534\) 0.131972 0.406167i 0.00571097 0.0175766i
\(535\) 14.5859 10.5973i 0.630605 0.458161i
\(536\) 10.6613 + 7.74591i 0.460499 + 0.334572i
\(537\) −1.12983 3.47726i −0.0487558 0.150055i
\(538\) −0.803678 −0.0346490
\(539\) 0.177290 + 0.674939i 0.00763640 + 0.0290717i
\(540\) −3.37556 −0.145261
\(541\) 0.0765109 + 0.235476i 0.00328946 + 0.0101239i 0.952688 0.303951i \(-0.0983058\pi\)
−0.949398 + 0.314075i \(0.898306\pi\)
\(542\) 7.11642 + 5.17038i 0.305676 + 0.222087i
\(543\) −1.93415 + 1.40524i −0.0830025 + 0.0603048i
\(544\) −6.97967 + 21.4812i −0.299251 + 0.921000i
\(545\) 5.05716 15.5643i 0.216625 0.666703i
\(546\) 1.56353 1.13597i 0.0669131 0.0486152i
\(547\) 20.4779 + 14.8780i 0.875570 + 0.636139i 0.932076 0.362263i \(-0.117996\pi\)
−0.0565056 + 0.998402i \(0.517996\pi\)
\(548\) 10.0380 + 30.8937i 0.428801 + 1.31971i
\(549\) 11.5322 0.492182
\(550\) 0.402144 + 1.53096i 0.0171475 + 0.0652802i
\(551\) 13.0796 0.557208
\(552\) −0.498266 1.53350i −0.0212076 0.0652703i
\(553\) −7.60799 5.52753i −0.323525 0.235054i
\(554\) 1.32338 0.961489i 0.0562249 0.0408498i
\(555\) 1.06253 3.27013i 0.0451018 0.138809i
\(556\) 12.6985 39.0819i 0.538536 1.65744i
\(557\) 31.2824 22.7280i 1.32548 0.963015i 0.325630 0.945497i \(-0.394424\pi\)
0.999847 0.0175177i \(-0.00557635\pi\)
\(558\) 2.66796 + 1.93839i 0.112944 + 0.0820586i
\(559\) 10.1940 + 31.3740i 0.431161 + 1.32698i
\(560\) −7.21041 −0.304695
\(561\) −1.79926 + 4.61907i −0.0759648 + 0.195017i
\(562\) −10.8919 −0.459447
\(563\) 4.30653 + 13.2541i 0.181498 + 0.558595i 0.999870 0.0160940i \(-0.00512309\pi\)
−0.818372 + 0.574689i \(0.805123\pi\)
\(564\) 2.02057 + 1.46803i 0.0850815 + 0.0618153i
\(565\) −1.66154 + 1.20718i −0.0699013 + 0.0507863i
\(566\) −4.29157 + 13.2081i −0.180388 + 0.555178i
\(567\) 6.69757 20.6130i 0.281272 0.865665i
\(568\) 1.74155 1.26531i 0.0730739 0.0530913i
\(569\) −22.5817 16.4065i −0.946672 0.687798i 0.00334520 0.999994i \(-0.498935\pi\)
−0.950017 + 0.312197i \(0.898935\pi\)
\(570\) 0.206809 + 0.636493i 0.00866228 + 0.0266598i
\(571\) −31.4113 −1.31452 −0.657261 0.753663i \(-0.728285\pi\)
−0.657261 + 0.753663i \(0.728285\pi\)
\(572\) 27.3917 + 1.57091i 1.14530 + 0.0656831i
\(573\) −1.66578 −0.0695889
\(574\) −0.875365 2.69410i −0.0365370 0.112449i
\(575\) −2.24278 1.62947i −0.0935302 0.0679537i
\(576\) −7.12237 + 5.17470i −0.296765 + 0.215613i
\(577\) 6.40744 19.7201i 0.266745 0.820958i −0.724541 0.689232i \(-0.757948\pi\)
0.991286 0.131726i \(-0.0420519\pi\)
\(578\) 0.649343 1.99847i 0.0270091 0.0831255i
\(579\) 1.05392 0.765719i 0.0437995 0.0318222i
\(580\) 4.32051 + 3.13903i 0.179399 + 0.130341i
\(581\) 9.22368 + 28.3876i 0.382663 + 1.17771i
\(582\) 2.85777 0.118458
\(583\) 16.2607 + 13.3008i 0.673448 + 0.550864i
\(584\) −1.83941 −0.0761153
\(585\) −4.17678 12.8548i −0.172689 0.531481i
\(586\) −8.19080 5.95097i −0.338359 0.245832i
\(587\) −12.3267 + 8.95591i −0.508779 + 0.369650i −0.812360 0.583156i \(-0.801818\pi\)
0.303581 + 0.952806i \(0.401818\pi\)
\(588\) −0.0372268 + 0.114572i −0.00153521 + 0.00472488i
\(589\) −3.20067 + 9.85066i −0.131881 + 0.405889i
\(590\) 4.53576 3.29542i 0.186734 0.135670i
\(591\) −2.98421 2.16816i −0.122754 0.0891860i
\(592\) −8.83126 27.1798i −0.362962 1.11708i
\(593\) 27.5413 1.13098 0.565492 0.824754i \(-0.308686\pi\)
0.565492 + 0.824754i \(0.308686\pi\)
\(594\) 2.53661 1.62958i 0.104078 0.0668624i
\(595\) 12.4227 0.509281
\(596\) −8.03103 24.7170i −0.328964 1.01245i
\(597\) 1.87309 + 1.36088i 0.0766605 + 0.0556971i
\(598\) 4.99640 3.63010i 0.204318 0.148446i
\(599\) −8.26097 + 25.4247i −0.337534 + 1.03882i 0.627926 + 0.778273i \(0.283904\pi\)
−0.965460 + 0.260551i \(0.916096\pi\)
\(600\) −0.179735 + 0.553168i −0.00733765 + 0.0225830i
\(601\) −1.94714 + 1.41468i −0.0794255 + 0.0577060i −0.626789 0.779189i \(-0.715631\pi\)
0.547364 + 0.836895i \(0.315631\pi\)
\(602\) 7.32722 + 5.32353i 0.298635 + 0.216971i
\(603\) −6.54977 20.1581i −0.266727 0.820902i
\(604\) 13.3254 0.542202
\(605\) 8.10166 + 7.44064i 0.329379 + 0.302505i
\(606\) −1.09699 −0.0445620
\(607\) 3.18067 + 9.78909i 0.129099 + 0.397327i 0.994626 0.103536i \(-0.0330159\pi\)
−0.865526 + 0.500864i \(0.833016\pi\)
\(608\) 17.1438 + 12.4557i 0.695275 + 0.505147i
\(609\) 2.11492 1.53658i 0.0857010 0.0622654i
\(610\) 0.587364 1.80772i 0.0237817 0.0731924i
\(611\) −6.29216 + 19.3653i −0.254553 + 0.783435i
\(612\) 19.2068 13.9545i 0.776388 0.564079i
\(613\) −22.5519 16.3849i −0.910861 0.661779i 0.0303715 0.999539i \(-0.490331\pi\)
−0.941232 + 0.337759i \(0.890331\pi\)
\(614\) −1.01396 3.12066i −0.0409203 0.125940i
\(615\) 0.714118 0.0287960
\(616\) 13.4897 8.66611i 0.543515 0.349168i
\(617\) −28.7216 −1.15629 −0.578143 0.815935i \(-0.696222\pi\)
−0.578143 + 0.815935i \(0.696222\pi\)
\(618\) 0.358703 + 1.10398i 0.0144292 + 0.0444084i
\(619\) −18.3621 13.3408i −0.738035 0.536214i 0.154060 0.988061i \(-0.450765\pi\)
−0.892095 + 0.451848i \(0.850765\pi\)
\(620\) −3.42138 + 2.48578i −0.137406 + 0.0998312i
\(621\) −1.63169 + 5.02183i −0.0654776 + 0.201519i
\(622\) 3.71029 11.4191i 0.148769 0.457864i
\(623\) −6.01703 + 4.37163i −0.241067 + 0.175146i
\(624\) 3.27606 + 2.38020i 0.131147 + 0.0952842i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −5.52635 −0.220877
\(627\) 3.59989 + 2.94462i 0.143766 + 0.117597i
\(628\) 23.7157 0.946360
\(629\) 15.2152 + 46.8277i 0.606671 + 1.86714i
\(630\) −3.00217 2.18120i −0.119609 0.0869012i
\(631\) −23.0864 + 16.7733i −0.919056 + 0.667733i −0.943289 0.331973i \(-0.892286\pi\)
0.0242327 + 0.999706i \(0.492286\pi\)
\(632\) −1.94835 + 5.99641i −0.0775013 + 0.238524i
\(633\) 0.347783 1.07037i 0.0138231 0.0425432i
\(634\) −8.00844 + 5.81847i −0.318056 + 0.231081i
\(635\) −0.0617011 0.0448285i −0.00244853 0.00177896i
\(636\) 1.12067 + 3.44908i 0.0444376 + 0.136765i
\(637\) −0.982140 −0.0389138
\(638\) −4.76209 0.273106i −0.188533 0.0108124i
\(639\) −3.46233 −0.136968
\(640\) 3.46577 + 10.6665i 0.136997 + 0.421632i
\(641\) −1.92040 1.39526i −0.0758514 0.0551093i 0.549213 0.835682i \(-0.314927\pi\)
−0.625065 + 0.780573i \(0.714927\pi\)
\(642\) −2.24899 + 1.63399i −0.0887605 + 0.0644883i
\(643\) 3.51053 10.8043i 0.138442 0.426080i −0.857668 0.514204i \(-0.828087\pi\)
0.996109 + 0.0881244i \(0.0280873\pi\)
\(644\) −4.07670 + 12.5468i −0.160644 + 0.494413i
\(645\) −1.84715 + 1.34203i −0.0727315 + 0.0528425i
\(646\) −7.75323 5.63305i −0.305047 0.221630i
\(647\) −14.9632 46.0520i −0.588264 1.81049i −0.585746 0.810495i \(-0.699198\pi\)
−0.00251822 0.999997i \(-0.500802\pi\)
\(648\) −14.5314 −0.570848
\(649\) 14.1415 36.3043i 0.555104 1.42507i
\(650\) −2.22778 −0.0873806
\(651\) 0.639713 + 1.96883i 0.0250723 + 0.0771647i
\(652\) −1.10685 0.804171i −0.0433475 0.0314938i
\(653\) −24.0722 + 17.4894i −0.942016 + 0.684415i −0.948905 0.315562i \(-0.897807\pi\)
0.00688905 + 0.999976i \(0.497807\pi\)
\(654\) −0.779758 + 2.39985i −0.0304910 + 0.0938415i
\(655\) 3.54847 10.9211i 0.138650 0.426722i
\(656\) 4.80186 3.48875i 0.187481 0.136213i
\(657\) 2.39346 + 1.73895i 0.0933777 + 0.0678429i
\(658\) 1.72750 + 5.31669i 0.0673449 + 0.207266i
\(659\) −28.4931 −1.10993 −0.554966 0.831873i \(-0.687269\pi\)
−0.554966 + 0.831873i \(0.687269\pi\)
\(660\) 0.482440 + 1.83664i 0.0187789 + 0.0714912i
\(661\) −1.02875 −0.0400139 −0.0200070 0.999800i \(-0.506369\pi\)
−0.0200070 + 0.999800i \(0.506369\pi\)
\(662\) −4.74027 14.5890i −0.184236 0.567019i
\(663\) −5.64428 4.10081i −0.219206 0.159262i
\(664\) 16.1902 11.7629i 0.628301 0.456488i
\(665\) 3.60161 11.0846i 0.139664 0.429843i
\(666\) 4.54506 13.9883i 0.176118 0.542034i
\(667\) 6.75841 4.91027i 0.261687 0.190127i
\(668\) −12.1616 8.83591i −0.470546 0.341872i
\(669\) 1.05275 + 3.24002i 0.0407016 + 0.125267i
\(670\) −3.49346 −0.134964
\(671\) −3.35580 12.7755i −0.129549 0.493192i
\(672\) 4.23540 0.163384
\(673\) 4.02863 + 12.3988i 0.155292 + 0.477940i 0.998190 0.0601327i \(-0.0191524\pi\)
−0.842898 + 0.538073i \(0.819152\pi\)
\(674\) 6.94861 + 5.04846i 0.267651 + 0.194459i
\(675\) 1.54094 1.11956i 0.0593108 0.0430918i
\(676\) −4.81316 + 14.8134i −0.185122 + 0.569746i
\(677\) −11.4665 + 35.2903i −0.440694 + 1.35632i 0.446444 + 0.894812i \(0.352690\pi\)
−0.887138 + 0.461505i \(0.847310\pi\)
\(678\) 0.256190 0.186133i 0.00983893 0.00714840i
\(679\) −40.2635 29.2531i −1.54517 1.12263i
\(680\) −2.57378 7.92127i −0.0986998 0.303767i
\(681\) 0.0697890 0.00267432
\(682\) 1.37101 3.51966i 0.0524986 0.134775i
\(683\) −32.8992 −1.25885 −0.629426 0.777061i \(-0.716710\pi\)
−0.629426 + 0.777061i \(0.716710\pi\)
\(684\) −6.88299 21.1837i −0.263178 0.809978i
\(685\) −14.8287 10.7737i −0.566576 0.411641i
\(686\) 7.03941 5.11443i 0.268766 0.195270i
\(687\) −0.00755844 + 0.0232625i −0.000288372 + 0.000887519i
\(688\) −5.86420 + 18.0481i −0.223570 + 0.688079i
\(689\) −23.9197 + 17.3787i −0.911267 + 0.662074i
\(690\) 0.345811 + 0.251246i 0.0131648 + 0.00956479i
\(691\) 11.3409 + 34.9036i 0.431427 + 1.32780i 0.896704 + 0.442631i \(0.145955\pi\)
−0.465277 + 0.885165i \(0.654045\pi\)
\(692\) −9.00061 −0.342152
\(693\) −25.7457 1.47652i −0.978000 0.0560883i
\(694\) −3.84185 −0.145835
\(695\) 7.16529 + 22.0525i 0.271795 + 0.836498i
\(696\) −1.41797 1.03022i −0.0537480 0.0390502i
\(697\) −8.27305 + 6.01072i −0.313364 + 0.227672i
\(698\) 2.83597 8.72823i 0.107343 0.330368i
\(699\) 1.50950 4.64577i 0.0570946 0.175719i
\(700\) 3.84996 2.79716i 0.145515 0.105723i
\(701\) 29.3266 + 21.3070i 1.10765 + 0.804755i 0.982292 0.187356i \(-0.0599919\pi\)
0.125359 + 0.992111i \(0.459992\pi\)
\(702\) 1.31124 + 4.03558i 0.0494895 + 0.152313i
\(703\) 46.1949 1.74227
\(704\) 7.80516 + 6.38443i 0.294168 + 0.240622i
\(705\) −1.40928 −0.0530767
\(706\) 2.19006 + 6.74031i 0.0824240 + 0.253675i
\(707\) 15.4556 + 11.2291i 0.581267 + 0.422315i
\(708\) 5.44141 3.95342i 0.204501 0.148578i
\(709\) −5.74811 + 17.6909i −0.215875 + 0.664394i 0.783216 + 0.621750i \(0.213578\pi\)
−0.999090 + 0.0426440i \(0.986422\pi\)
\(710\) −0.176345 + 0.542735i −0.00661812 + 0.0203685i
\(711\) 8.20413 5.96065i 0.307679 0.223542i
\(712\) 4.03418 + 2.93100i 0.151187 + 0.109844i
\(713\) 2.04426 + 6.29158i 0.0765580 + 0.235621i
\(714\) −1.91544 −0.0716836
\(715\) −13.0253 + 8.36775i −0.487117 + 0.312936i
\(716\) 20.0563 0.749540
\(717\) −2.31263 7.11754i −0.0863667 0.265809i
\(718\) −3.94732 2.86790i −0.147313 0.107029i
\(719\) 30.2799 21.9996i 1.12925 0.820447i 0.143664 0.989627i \(-0.454112\pi\)
0.985585 + 0.169179i \(0.0541117\pi\)
\(720\) 2.40273 7.39484i 0.0895444 0.275589i
\(721\) 6.24687 19.2259i 0.232645 0.716009i
\(722\) 0.0619923 0.0450400i 0.00230711 0.00167622i
\(723\) 5.57630 + 4.05142i 0.207385 + 0.150674i
\(724\) −4.05262 12.4727i −0.150614 0.463544i
\(725\) −3.01341 −0.111915
\(726\) −1.24919 1.14726i −0.0463617 0.0425789i
\(727\) 14.6011 0.541526 0.270763 0.962646i \(-0.412724\pi\)
0.270763 + 0.962646i \(0.412724\pi\)
\(728\) 6.97319 + 21.4613i 0.258443 + 0.795407i
\(729\) 17.4149 + 12.6527i 0.644997 + 0.468618i
\(730\) 0.394492 0.286615i 0.0146008 0.0106081i
\(731\) 10.1033 31.0949i 0.373686 1.15009i
\(732\) 0.704642 2.16867i 0.0260443 0.0801562i
\(733\) −33.8468 + 24.5911i −1.25016 + 0.908293i −0.998231 0.0594528i \(-0.981064\pi\)
−0.251927 + 0.967746i \(0.581064\pi\)
\(734\) −5.46092 3.96759i −0.201566 0.146447i
\(735\) −0.0210057 0.0646489i −0.000774807 0.00238461i
\(736\) 13.5346 0.498891
\(737\) −20.4254 + 13.1218i −0.752381 + 0.483348i
\(738\) 3.05470 0.112445
\(739\) −3.68654 11.3460i −0.135612 0.417370i 0.860073 0.510171i \(-0.170418\pi\)
−0.995685 + 0.0928012i \(0.970418\pi\)
\(740\) 15.2594 + 11.0866i 0.560945 + 0.407550i
\(741\) −5.29549 + 3.84740i −0.194535 + 0.141338i
\(742\) −2.50841 + 7.72008i −0.0920865 + 0.283413i
\(743\) 14.4250 44.3956i 0.529202 1.62872i −0.226652 0.973976i \(-0.572778\pi\)
0.755854 0.654740i \(-0.227222\pi\)
\(744\) 1.12288 0.815820i 0.0411668 0.0299094i
\(745\) 11.8639 + 8.61964i 0.434660 + 0.315799i
\(746\) 1.83762 + 5.65561i 0.0672800 + 0.207067i
\(747\) −32.1873 −1.17767
\(748\) −21.0480 17.2168i −0.769593 0.629508i
\(749\) 48.4124 1.76895
\(750\) −0.0476470 0.146642i −0.00173982 0.00535462i
\(751\) −11.6530 8.46642i −0.425225 0.308944i 0.354512 0.935052i \(-0.384647\pi\)
−0.779737 + 0.626108i \(0.784647\pi\)
\(752\) −9.47628 + 6.88492i −0.345564 + 0.251067i
\(753\) −0.621156 + 1.91172i −0.0226362 + 0.0696670i
\(754\) 2.07450 6.38465i 0.0755488 0.232515i
\(755\) −6.08301 + 4.41957i −0.221383 + 0.160845i
\(756\) −7.33304 5.32776i −0.266700 0.193769i
\(757\) −4.96330 15.2755i −0.180394 0.555196i 0.819444 0.573159i \(-0.194282\pi\)
−0.999839 + 0.0179624i \(0.994282\pi\)
\(758\) 7.79698 0.283199
\(759\) 2.96558 + 0.170076i 0.107644 + 0.00617337i
\(760\) −7.81423 −0.283452
\(761\) −12.0158 36.9809i −0.435573 1.34056i −0.892498 0.451051i \(-0.851049\pi\)
0.456925 0.889505i \(-0.348951\pi\)
\(762\) 0.00951362 + 0.00691205i 0.000344642 + 0.000250397i
\(763\) 35.5518 25.8299i 1.28706 0.935106i
\(764\) 2.82371 8.69049i 0.102158 0.314411i
\(765\) −4.13962 + 12.7405i −0.149668 + 0.460632i
\(766\) 0.313773 0.227969i 0.0113371 0.00823686i
\(767\) 44.3621 + 32.2309i 1.60182 + 1.16379i
\(768\) 0.0726816 + 0.223691i 0.00262267 + 0.00807175i
\(769\) 43.0017 1.55068 0.775341 0.631543i \(-0.217578\pi\)
0.775341 + 0.631543i \(0.217578\pi\)
\(770\) −1.54275 + 3.96055i −0.0555967 + 0.142728i
\(771\) −4.61679 −0.166270
\(772\) 2.20828 + 6.79637i 0.0794776 + 0.244607i
\(773\) 6.35452 + 4.61683i 0.228556 + 0.166056i 0.696170 0.717877i \(-0.254886\pi\)
−0.467613 + 0.883933i \(0.654886\pi\)
\(774\) −7.90135 + 5.74067i −0.284008 + 0.206344i
\(775\) 0.737407 2.26951i 0.0264885 0.0815231i
\(776\) −10.3112 + 31.7346i −0.370150 + 1.13920i
\(777\) 7.46957 5.42696i 0.267969 0.194691i
\(778\) 11.7355 + 8.52635i 0.420739 + 0.305684i
\(779\) 2.96475 + 9.12457i 0.106223 + 0.326922i
\(780\) −2.67259 −0.0956942
\(781\) 1.00752 + 3.83561i 0.0360519 + 0.137249i
\(782\) −6.12096 −0.218885
\(783\) 1.77366 + 5.45875i 0.0633853 + 0.195080i
\(784\) −0.457082 0.332090i −0.0163244 0.0118603i
\(785\) −10.8262 + 7.86568i −0.386403 + 0.280738i
\(786\) −0.547135 + 1.68391i −0.0195157 + 0.0600631i
\(787\) −3.53048 + 10.8657i −0.125848 + 0.387321i −0.994055 0.108882i \(-0.965273\pi\)
0.868206 + 0.496203i \(0.165273\pi\)
\(788\) 16.3700 11.8935i 0.583159 0.423690i
\(789\) −1.07980 0.784522i −0.0384420 0.0279297i
\(790\) −0.516500 1.58962i −0.0183762 0.0565562i
\(791\) −5.51483 −0.196085
\(792\) 4.39260 + 16.7226i 0.156084 + 0.594210i
\(793\) 18.5903 0.660161
\(794\) −2.19741 6.76294i −0.0779832 0.240008i
\(795\) −1.65553 1.20281i −0.0587155 0.0426593i
\(796\) −10.2749 + 7.46518i −0.364186 + 0.264596i
\(797\) −1.32414 + 4.07529i −0.0469035 + 0.144354i −0.971766 0.235949i \(-0.924180\pi\)
0.924862 + 0.380303i \(0.124180\pi\)
\(798\) −0.555328 + 1.70912i −0.0196584 + 0.0605023i
\(799\) 16.3265 11.8619i 0.577592 0.419645i
\(800\) −3.94979 2.86969i −0.139646 0.101459i
\(801\) −2.47839 7.62770i −0.0875696 0.269511i
\(802\) 5.80787 0.205083
\(803\) 1.22994 3.15752i 0.0434038 0.111427i
\(804\) −4.19100 −0.147805
\(805\) −2.30033 7.07969i −0.0810760 0.249526i
\(806\) 4.30085 + 3.12475i 0.151491 + 0.110065i
\(807\) 0.440132 0.319774i 0.0154934 0.0112566i
\(808\) 3.95806 12.1817i 0.139244 0.428549i
\(809\) −6.13350 + 18.8770i −0.215642 + 0.663679i 0.783465 + 0.621436i \(0.213450\pi\)
−0.999107 + 0.0422430i \(0.986550\pi\)
\(810\) 3.11651 2.26427i 0.109503 0.0795585i
\(811\) 2.53899 + 1.84468i 0.0891559 + 0.0647756i 0.631470 0.775400i \(-0.282452\pi\)
−0.542314 + 0.840176i \(0.682452\pi\)
\(812\) 4.43138 + 13.6384i 0.155511 + 0.478614i
\(813\) −5.95452 −0.208834
\(814\) −16.8189 0.964566i −0.589504 0.0338080i
\(815\) 0.771990 0.0270416
\(816\) −1.24021 3.81698i −0.0434162 0.133621i
\(817\) −24.8164 18.0301i −0.868215 0.630795i
\(818\) 0.101203 0.0735281i 0.00353847 0.00257085i
\(819\) 11.2156 34.5180i 0.391904 1.20616i
\(820\) −1.21052 + 3.72560i −0.0422733 + 0.130104i
\(821\) −19.0118 + 13.8129i −0.663516 + 0.482073i −0.867849 0.496829i \(-0.834498\pi\)
0.204332 + 0.978902i \(0.434498\pi\)
\(822\) 2.28642 + 1.66118i 0.0797481 + 0.0579404i
\(823\) −3.91103 12.0369i −0.136330 0.419580i 0.859465 0.511195i \(-0.170797\pi\)
−0.995795 + 0.0916150i \(0.970797\pi\)
\(824\) −13.5535 −0.472159
\(825\) −0.829384 0.678415i −0.0288754 0.0236194i
\(826\) 15.0547 0.523820
\(827\) 9.33959 + 28.7443i 0.324770 + 0.999538i 0.971545 + 0.236857i \(0.0761173\pi\)
−0.646775 + 0.762681i \(0.723883\pi\)
\(828\) −11.5092 8.36195i −0.399974 0.290598i
\(829\) −1.61937 + 1.17654i −0.0562432 + 0.0408630i −0.615552 0.788097i \(-0.711067\pi\)
0.559308 + 0.828960i \(0.311067\pi\)
\(830\) −1.63938 + 5.04549i −0.0569037 + 0.175132i
\(831\) −0.342177 + 1.05311i −0.0118700 + 0.0365321i
\(832\) −11.4815 + 8.34180i −0.398050 + 0.289200i
\(833\) 0.787500 + 0.572152i 0.0272852 + 0.0198239i
\(834\) −1.10481 3.40025i −0.0382564 0.117741i
\(835\) 8.48232 0.293543
\(836\) −21.4646 + 13.7894i −0.742368 + 0.476915i
\(837\) −4.54520 −0.157105
\(838\) −0.187177 0.576072i −0.00646592 0.0199001i
\(839\) −28.6185 20.7925i −0.988019 0.717838i −0.0285326 0.999593i \(-0.509083\pi\)
−0.959486 + 0.281755i \(0.909083\pi\)
\(840\) −1.26354 + 0.918013i −0.0435962 + 0.0316745i
\(841\) −6.15541 + 18.9444i −0.212256 + 0.653255i
\(842\) −4.37511 + 13.4652i −0.150776 + 0.464041i
\(843\) 5.96492 4.33377i 0.205443 0.149263i
\(844\) 4.99463 + 3.62881i 0.171922 + 0.124909i
\(845\) −2.71589 8.35865i −0.0934295 0.287546i
\(846\) −6.02834 −0.207259
\(847\) 5.85616 + 28.9511i 0.201220 + 0.994771i
\(848\) −17.0083 −0.584067
\(849\) −2.90509 8.94095i −0.0997024 0.306853i
\(850\) 1.78628 + 1.29781i 0.0612688 + 0.0445144i
\(851\) 23.8696 17.3423i 0.818241 0.594487i
\(852\) −0.211556 + 0.651102i −0.00724779 + 0.0223064i
\(853\) −5.62515 + 17.3124i −0.192602 + 0.592767i 0.807395 + 0.590012i \(0.200877\pi\)
−0.999996 + 0.00275489i \(0.999123\pi\)
\(854\) 4.12917 3.00001i 0.141297 0.102658i
\(855\) 10.1680 + 7.38746i 0.347737 + 0.252646i
\(856\) −10.0302 30.8699i −0.342827 1.05511i
\(857\) −29.2837 −1.00031 −0.500156 0.865935i \(-0.666724\pi\)
−0.500156 + 0.865935i \(0.666724\pi\)
\(858\) 2.00835 1.29021i 0.0685640 0.0440472i
\(859\) 8.44030 0.287979 0.143990 0.989579i \(-0.454007\pi\)
0.143990 + 0.989579i \(0.454007\pi\)
\(860\) −3.87032 11.9116i −0.131977 0.406183i
\(861\) 1.55134 + 1.12712i 0.0528696 + 0.0384120i
\(862\) −12.1065 + 8.79587i −0.412348 + 0.299589i
\(863\) −5.97907 + 18.4017i −0.203530 + 0.626400i 0.796241 + 0.604980i \(0.206819\pi\)
−0.999771 + 0.0214204i \(0.993181\pi\)
\(864\) −2.87360 + 8.84404i −0.0977620 + 0.300880i
\(865\) 4.10876 2.98519i 0.139702 0.101500i
\(866\) 10.0515 + 7.30281i 0.341562 + 0.248160i
\(867\) 0.439559 + 1.35282i 0.0149282 + 0.0459443i
\(868\) −11.3559 −0.385446
\(869\) −8.99063 7.35411i −0.304986 0.249471i
\(870\) 0.464635 0.0157526
\(871\) −10.5585 32.4956i −0.357760 1.10107i
\(872\) −23.8361 17.3179i −0.807191 0.586458i
\(873\) 43.4184 31.5453i 1.46949 1.06765i
\(874\) −1.77460 + 5.46165i −0.0600266 + 0.184743i
\(875\) −0.829779 + 2.55380i −0.0280516 + 0.0863341i
\(876\) 0.473260 0.343844i 0.0159900 0.0116174i
\(877\) −14.1691 10.2945i −0.478456 0.347619i 0.322271 0.946647i \(-0.395554\pi\)
−0.800728 + 0.599028i \(0.795554\pi\)
\(878\) 2.12655 + 6.54484i 0.0717675 + 0.220878i
\(879\) 6.85349 0.231163
\(880\) −8.89126 0.509914i −0.299724 0.0171892i
\(881\) −20.0575 −0.675754 −0.337877 0.941190i \(-0.609709\pi\)
−0.337877 + 0.941190i \(0.609709\pi\)
\(882\) −0.0898538 0.276542i −0.00302553 0.00931164i
\(883\) −21.7609 15.8102i −0.732313 0.532057i 0.157981 0.987442i \(-0.449501\pi\)
−0.890294 + 0.455386i \(0.849501\pi\)
\(884\) 30.9620 22.4952i 1.04136 0.756595i
\(885\) −1.17278 + 3.60946i −0.0394227 + 0.121331i
\(886\) −0.0487585 + 0.150063i −0.00163807 + 0.00504148i
\(887\) −5.50591 + 4.00028i −0.184870 + 0.134316i −0.676371 0.736561i \(-0.736448\pi\)
0.491501 + 0.870877i \(0.336448\pi\)
\(888\) −5.00805 3.63856i −0.168059 0.122102i
\(889\) −0.0632845 0.194770i −0.00212249 0.00653237i
\(890\) −1.32190 −0.0443103
\(891\) 9.71661 24.9446i 0.325519 0.835674i
\(892\) −18.6880 −0.625720
\(893\) −5.85082 18.0070i −0.195790 0.602581i
\(894\) −1.82928 1.32905i −0.0611804 0.0444502i
\(895\) −9.15568 + 6.65199i −0.306041 + 0.222352i
\(896\) −9.30635 + 28.6420i −0.310903 + 0.956862i
\(897\) −1.29189 + 3.97603i −0.0431349 + 0.132756i
\(898\) −3.28514 + 2.38680i −0.109627 + 0.0796484i
\(899\) 5.81757 + 4.22671i 0.194027 + 0.140969i
\(900\) 1.58578 + 4.88053i 0.0528593 + 0.162684i
\(901\) 29.3033 0.976235
\(902\) −0.888901 3.38403i −0.0295972 0.112676i
\(903\) −6.13090 −0.204024
\(904\) 1.14258 + 3.51650i 0.0380017 + 0.116957i
\(905\) 5.98677 + 4.34965i 0.199007 + 0.144587i
\(906\) 0.937933 0.681448i 0.0311607 0.0226396i
\(907\) −6.59174 + 20.2873i −0.218875 + 0.673629i 0.779981 + 0.625804i \(0.215229\pi\)
−0.998856 + 0.0478248i \(0.984771\pi\)
\(908\) −0.118301 + 0.364094i −0.00392597 + 0.0120829i
\(909\) −16.6666 + 12.1090i −0.552797 + 0.401631i
\(910\) −4.83960 3.51617i −0.160431 0.116560i
\(911\) −8.52542 26.2385i −0.282460 0.869322i −0.987149 0.159805i \(-0.948913\pi\)
0.704689 0.709516i \(-0.251087\pi\)
\(912\) −3.76541 −0.124685
\(913\) 9.36631 + 35.6574i 0.309980 + 1.18009i
\(914\) 0.543347 0.0179723
\(915\) 0.397604 + 1.22370i 0.0131444 + 0.0404542i
\(916\) −0.108549 0.0788658i −0.00358657 0.00260580i
\(917\) 24.9458 18.1242i 0.823782 0.598512i
\(918\) 1.29958 3.99968i 0.0428924 0.132009i
\(919\) −1.85685 + 5.71479i −0.0612518 + 0.188514i −0.977000 0.213239i \(-0.931599\pi\)
0.915748 + 0.401752i \(0.131599\pi\)
\(920\) −4.03774 + 2.93359i −0.133120 + 0.0967176i
\(921\) 1.79697 + 1.30558i 0.0592122 + 0.0430202i
\(922\) 2.13955 + 6.58486i 0.0704624 + 0.216861i
\(923\) −5.58140 −0.183714
\(924\) −1.85078 + 4.75135i −0.0608863 + 0.156308i
\(925\) −10.6429 −0.349937
\(926\) −0.722274 2.22293i −0.0237354 0.0730501i
\(927\) 17.6360 + 12.8133i 0.579242 + 0.420844i
\(928\) 11.9024 8.64757i 0.390714 0.283870i
\(929\) 2.96576 9.12766i 0.0973034 0.299469i −0.890544 0.454898i \(-0.849676\pi\)
0.987847 + 0.155429i \(0.0496759\pi\)
\(930\) −0.113700 + 0.349933i −0.00372837 + 0.0114747i
\(931\) 0.738836 0.536796i 0.0242144 0.0175928i
\(932\) 21.6785 + 15.7504i 0.710103 + 0.515920i
\(933\) 2.51160 + 7.72992i 0.0822261 + 0.253066i
\(934\) 15.4742 0.506332
\(935\) 15.3186 + 0.878523i 0.500972 + 0.0287308i
\(936\) −24.3339 −0.795378
\(937\) −11.9255 36.7029i −0.389589 1.19903i −0.933096 0.359628i \(-0.882904\pi\)
0.543507 0.839405i \(-0.317096\pi\)
\(938\) −7.58916 5.51385i −0.247795 0.180034i
\(939\) 3.02649 2.19887i 0.0987658 0.0717575i
\(940\) 2.38892 7.35233i 0.0779179 0.239807i
\(941\) −9.01854 + 27.7562i −0.293996 + 0.904826i 0.689561 + 0.724228i \(0.257804\pi\)
−0.983557 + 0.180599i \(0.942196\pi\)
\(942\) 1.66928 1.21280i 0.0543880 0.0395152i
\(943\) 4.95744 + 3.60179i 0.161437 + 0.117291i
\(944\) 9.74764 + 30.0002i 0.317259 + 0.976422i
\(945\) 5.11455 0.166376
\(946\) 8.65882 + 7.08270i 0.281523 + 0.230279i
\(947\) 46.7623 1.51957 0.759785 0.650174i \(-0.225304\pi\)
0.759785 + 0.650174i \(0.225304\pi\)
\(948\) −0.619629 1.90702i −0.0201246 0.0619371i
\(949\) 3.85834 + 2.80325i 0.125247 + 0.0909972i
\(950\) 1.67589 1.21761i 0.0543732 0.0395044i
\(951\) 2.07069 6.37293i 0.0671468 0.206657i
\(952\) 6.91116 21.2704i 0.223992 0.689376i
\(953\) 4.97738 3.61628i 0.161233 0.117143i −0.504243 0.863562i \(-0.668228\pi\)
0.665476 + 0.746419i \(0.268228\pi\)
\(954\) −7.08167 5.14514i −0.229278 0.166580i
\(955\) 1.59332 + 4.90372i 0.0515585 + 0.158681i
\(956\) 41.0529 1.32774
\(957\) 2.71661 1.74522i 0.0878155 0.0564148i
\(958\) 8.46440 0.273472
\(959\) −15.2093 46.8093i −0.491132 1.51155i
\(960\) −0.794658 0.577353i −0.0256475 0.0186340i
\(961\) 20.4726 14.8742i 0.660408 0.479814i
\(962\) 7.32680 22.5496i 0.236226 0.727027i
\(963\) −16.1325 + 49.6507i −0.519862 + 1.59997i
\(964\) −30.5891 + 22.2243i −0.985209 + 0.715796i
\(965\) −3.26220 2.37013i −0.105014 0.0762970i
\(966\) 0.354686 + 1.09161i 0.0114118 + 0.0351220i
\(967\) 3.39625 0.109216 0.0546080 0.998508i \(-0.482609\pi\)
0.0546080 + 0.998508i \(0.482609\pi\)
\(968\) 17.2472 9.73233i 0.554346 0.312809i
\(969\) 6.48736 0.208404
\(970\) −2.73345 8.41270i −0.0877658 0.270115i
\(971\) 7.60072 + 5.52224i 0.243919 + 0.177217i 0.703027 0.711163i \(-0.251831\pi\)
−0.459109 + 0.888380i \(0.651831\pi\)
\(972\) 11.9314 8.66870i 0.382701 0.278049i
\(973\) −19.2404 + 59.2158i −0.616818 + 1.89837i
\(974\) −2.72255 + 8.37914i −0.0872360 + 0.268485i
\(975\) 1.22004 0.886408i 0.0390724 0.0283878i
\(976\) 8.65182 + 6.28591i 0.276938 + 0.201207i
\(977\) −5.11585 15.7450i −0.163671 0.503726i 0.835265 0.549847i \(-0.185314\pi\)
−0.998936 + 0.0461210i \(0.985314\pi\)
\(978\) −0.119032 −0.00380623
\(979\) −7.72885 + 4.96520i −0.247015 + 0.158689i
\(980\) 0.372885 0.0119114
\(981\) 14.6436 + 45.0685i 0.467535 + 1.43893i
\(982\) 4.41474 + 3.20750i 0.140880 + 0.102355i
\(983\) −41.1126 + 29.8701i −1.31129 + 0.952707i −0.311291 + 0.950315i \(0.600762\pi\)
−0.999997 + 0.00239240i \(0.999238\pi\)
\(984\) 0.397287 1.22272i 0.0126651 0.0389790i
\(985\) −3.52822 + 10.8588i −0.112419 + 0.345989i
\(986\) −5.38279 + 3.91083i −0.171423 + 0.124546i
\(987\) −3.06151 2.22432i −0.0974490 0.0708009i
\(988\) −11.0956 34.1488i −0.352999 1.08642i
\(989\) −19.5918 −0.622983
\(990\) −3.54776 2.90198i −0.112755 0.0922311i
\(991\) 11.3642 0.360996 0.180498 0.983575i \(-0.442229\pi\)
0.180498 + 0.983575i \(0.442229\pi\)
\(992\) 3.60018 + 11.0802i 0.114306 + 0.351797i
\(993\) 8.40081 + 6.10355i 0.266592 + 0.193690i
\(994\) −1.23971 + 0.900700i −0.0393211 + 0.0285685i
\(995\) 2.21455 6.81569i 0.0702060 0.216072i
\(996\) −1.96671 + 6.05292i −0.0623177 + 0.191794i
\(997\) 23.5945 17.1424i 0.747246 0.542906i −0.147726 0.989028i \(-0.547195\pi\)
0.894972 + 0.446122i \(0.147195\pi\)
\(998\) −4.20149 3.05256i −0.132996 0.0966271i
\(999\) 6.26427 + 19.2794i 0.198193 + 0.609975i
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 55.2.g.b.16.2 8
3.2 odd 2 495.2.n.e.181.1 8
4.3 odd 2 880.2.bo.h.401.1 8
5.2 odd 4 275.2.z.a.49.2 16
5.3 odd 4 275.2.z.a.49.3 16
5.4 even 2 275.2.h.a.126.1 8
11.2 odd 10 605.2.g.k.251.1 8
11.3 even 5 605.2.a.j.1.3 4
11.4 even 5 605.2.g.m.366.1 8
11.5 even 5 605.2.g.m.81.1 8
11.6 odd 10 605.2.g.e.81.2 8
11.7 odd 10 605.2.g.e.366.2 8
11.8 odd 10 605.2.a.k.1.2 4
11.9 even 5 inner 55.2.g.b.31.2 yes 8
11.10 odd 2 605.2.g.k.511.1 8
33.8 even 10 5445.2.a.bi.1.3 4
33.14 odd 10 5445.2.a.bp.1.2 4
33.20 odd 10 495.2.n.e.361.1 8
44.3 odd 10 9680.2.a.cn.1.3 4
44.19 even 10 9680.2.a.cm.1.3 4
44.31 odd 10 880.2.bo.h.801.1 8
55.9 even 10 275.2.h.a.251.1 8
55.14 even 10 3025.2.a.bd.1.2 4
55.19 odd 10 3025.2.a.w.1.3 4
55.42 odd 20 275.2.z.a.174.3 16
55.53 odd 20 275.2.z.a.174.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.16.2 8 1.1 even 1 trivial
55.2.g.b.31.2 yes 8 11.9 even 5 inner
275.2.h.a.126.1 8 5.4 even 2
275.2.h.a.251.1 8 55.9 even 10
275.2.z.a.49.2 16 5.2 odd 4
275.2.z.a.49.3 16 5.3 odd 4
275.2.z.a.174.2 16 55.53 odd 20
275.2.z.a.174.3 16 55.42 odd 20
495.2.n.e.181.1 8 3.2 odd 2
495.2.n.e.361.1 8 33.20 odd 10
605.2.a.j.1.3 4 11.3 even 5
605.2.a.k.1.2 4 11.8 odd 10
605.2.g.e.81.2 8 11.6 odd 10
605.2.g.e.366.2 8 11.7 odd 10
605.2.g.k.251.1 8 11.2 odd 10
605.2.g.k.511.1 8 11.10 odd 2
605.2.g.m.81.1 8 11.5 even 5
605.2.g.m.366.1 8 11.4 even 5
880.2.bo.h.401.1 8 4.3 odd 2
880.2.bo.h.801.1 8 44.31 odd 10
3025.2.a.w.1.3 4 55.19 odd 10
3025.2.a.bd.1.2 4 55.14 even 10
5445.2.a.bi.1.3 4 33.8 even 10
5445.2.a.bp.1.2 4 33.14 odd 10
9680.2.a.cm.1.3 4 44.19 even 10
9680.2.a.cn.1.3 4 44.3 odd 10