Properties

Label 144.2.x.d.61.1
Level $144$
Weight $2$
Character 144.61
Analytic conductor $1.150$
Analytic rank $0$
Dimension $4$
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] = [144,2,Mod(13,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), 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: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 61.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 144.61
Dual form 144.2.x.d.85.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 + 0.133975i) q^{5} +(0.633975 - 2.36603i) q^{6} +(-2.13397 - 1.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 + 0.133975i) q^{5} +(0.633975 - 2.36603i) q^{6} +(-2.13397 - 1.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +(0.633975 + 0.366025i) q^{10} +(0.133975 + 0.500000i) q^{11} +(1.73205 - 3.00000i) q^{12} +(-1.23205 + 4.59808i) q^{13} +(-2.46410 - 2.46410i) q^{14} +(0.232051 - 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +4.00000 q^{17} +(-4.09808 - 1.09808i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(0.732051 + 0.732051i) q^{20} +(-2.13397 + 3.69615i) q^{21} +0.732051i q^{22} +(0.401924 - 0.232051i) q^{23} +(3.46410 - 3.46410i) q^{24} +(-4.09808 - 2.36603i) q^{25} +(-3.36603 + 5.83013i) q^{26} +5.19615i q^{27} +(-2.46410 - 4.26795i) q^{28} +(-3.23205 + 0.866025i) q^{29} +(0.633975 - 1.09808i) q^{30} +(0.598076 + 1.03590i) q^{31} +(1.46410 + 5.46410i) q^{32} +(0.866025 - 0.232051i) q^{33} +(5.46410 + 1.46410i) q^{34} +(-0.901924 - 0.901924i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(-7.73205 + 7.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(7.96410 + 2.13397i) q^{39} +(0.732051 + 1.26795i) q^{40} +(9.69615 - 5.59808i) q^{41} +(-4.26795 + 4.26795i) q^{42} +(-2.33013 - 8.69615i) q^{43} +(-0.267949 + 1.00000i) q^{44} +(-1.50000 - 0.401924i) q^{45} +(0.633975 - 0.169873i) q^{46} +(4.59808 - 7.96410i) q^{47} +(6.00000 - 3.46410i) q^{48} +(-0.464102 - 0.803848i) q^{49} +(-4.73205 - 4.73205i) q^{50} -6.92820i q^{51} +(-6.73205 + 6.73205i) q^{52} +(2.26795 - 2.26795i) q^{53} +(-1.90192 + 7.09808i) q^{54} +0.267949i q^{55} +(-1.80385 - 6.73205i) q^{56} +(-5.19615 + 5.19615i) q^{57} -4.73205 q^{58} +(5.59808 + 1.50000i) q^{59} +(1.26795 - 1.26795i) q^{60} +(14.4282 - 3.86603i) q^{61} +(0.437822 + 1.63397i) q^{62} +(6.40192 + 3.69615i) q^{63} +8.00000i q^{64} +(-1.23205 + 2.13397i) q^{65} +1.26795 q^{66} +(-0.330127 + 1.23205i) q^{67} +(6.92820 + 4.00000i) q^{68} +(-0.401924 - 0.696152i) q^{69} +(-0.901924 - 1.56218i) q^{70} +10.9282i q^{71} +(-6.00000 - 6.00000i) q^{72} +0.535898i q^{73} +(-13.3923 + 7.73205i) q^{74} +(-4.09808 + 7.09808i) q^{75} +(-2.19615 - 8.19615i) q^{76} +(0.330127 - 1.23205i) q^{77} +(10.0981 + 5.83013i) q^{78} +(0.866025 - 1.50000i) q^{79} +(0.535898 + 2.00000i) q^{80} +9.00000 q^{81} +(15.2942 - 4.09808i) q^{82} +(-11.7942 + 3.16025i) q^{83} +(-7.39230 + 4.26795i) q^{84} +(2.00000 + 0.535898i) q^{85} -12.7321i q^{86} +(1.50000 + 5.59808i) q^{87} +(-0.732051 + 1.26795i) q^{88} -11.8564i q^{89} +(-1.90192 - 1.09808i) q^{90} +(8.29423 - 8.29423i) q^{91} +0.928203 q^{92} +(1.79423 - 1.03590i) q^{93} +(9.19615 - 9.19615i) q^{94} +(-1.09808 - 1.90192i) q^{95} +(9.46410 - 2.53590i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-0.339746 - 1.26795i) q^{98} +(-0.401924 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9} + 6 q^{10} + 4 q^{11} + 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 16 q^{17} - 6 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{28} - 6 q^{29} + 6 q^{30} - 8 q^{31} - 8 q^{32} + 8 q^{34} - 14 q^{35} - 24 q^{37} - 12 q^{38} + 18 q^{39} - 4 q^{40} + 18 q^{41} - 24 q^{42} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 6 q^{46} + 8 q^{47} + 24 q^{48} + 12 q^{49} - 12 q^{50} - 20 q^{52} + 16 q^{53} - 18 q^{54} - 28 q^{56} - 12 q^{58} + 12 q^{59} + 12 q^{60} + 30 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 12 q^{66} + 16 q^{67} - 12 q^{69} - 14 q^{70} - 24 q^{72} - 12 q^{74} - 6 q^{75} + 12 q^{76} - 16 q^{77} + 30 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 16 q^{83} + 12 q^{84} + 8 q^{85} + 6 q^{87} + 4 q^{88} - 18 q^{90} + 2 q^{91} - 24 q^{92} - 24 q^{93} + 16 q^{94} + 6 q^{95} + 24 q^{96} - 2 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 1.73205i 1.00000i
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 0.500000 + 0.133975i 0.223607 + 0.0599153i 0.368883 0.929476i \(-0.379740\pi\)
−0.145276 + 0.989391i \(0.546407\pi\)
\(6\) 0.633975 2.36603i 0.258819 0.965926i
\(7\) −2.13397 1.23205i −0.806567 0.465671i 0.0391956 0.999232i \(-0.487520\pi\)
−0.845762 + 0.533560i \(0.820854\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) −3.00000 −1.00000
\(10\) 0.633975 + 0.366025i 0.200480 + 0.115747i
\(11\) 0.133975 + 0.500000i 0.0403949 + 0.150756i 0.983178 0.182652i \(-0.0584681\pi\)
−0.942783 + 0.333408i \(0.891801\pi\)
\(12\) 1.73205 3.00000i 0.500000 0.866025i
\(13\) −1.23205 + 4.59808i −0.341709 + 1.27528i 0.554700 + 0.832050i \(0.312833\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) −2.46410 2.46410i −0.658559 0.658559i
\(15\) 0.232051 0.866025i 0.0599153 0.223607i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −4.09808 1.09808i −0.965926 0.258819i
\(19\) −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i \(-0.411786\pi\)
−0.961844 + 0.273597i \(0.911786\pi\)
\(20\) 0.732051 + 0.732051i 0.163692 + 0.163692i
\(21\) −2.13397 + 3.69615i −0.465671 + 0.806567i
\(22\) 0.732051i 0.156074i
\(23\) 0.401924 0.232051i 0.0838069 0.0483859i −0.457511 0.889204i \(-0.651259\pi\)
0.541318 + 0.840818i \(0.317926\pi\)
\(24\) 3.46410 3.46410i 0.707107 0.707107i
\(25\) −4.09808 2.36603i −0.819615 0.473205i
\(26\) −3.36603 + 5.83013i −0.660132 + 1.14338i
\(27\) 5.19615i 1.00000i
\(28\) −2.46410 4.26795i −0.465671 0.806567i
\(29\) −3.23205 + 0.866025i −0.600177 + 0.160817i −0.546100 0.837720i \(-0.683888\pi\)
−0.0540766 + 0.998537i \(0.517222\pi\)
\(30\) 0.633975 1.09808i 0.115747 0.200480i
\(31\) 0.598076 + 1.03590i 0.107418 + 0.186053i 0.914723 0.404081i \(-0.132408\pi\)
−0.807306 + 0.590133i \(0.799075\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) 0.866025 0.232051i 0.150756 0.0403949i
\(34\) 5.46410 + 1.46410i 0.937086 + 0.251091i
\(35\) −0.901924 0.901924i −0.152453 0.152453i
\(36\) −5.19615 3.00000i −0.866025 0.500000i
\(37\) −7.73205 + 7.73205i −1.27114 + 1.27114i −0.325651 + 0.945490i \(0.605584\pi\)
−0.945490 + 0.325651i \(0.894416\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 7.96410 + 2.13397i 1.27528 + 0.341709i
\(40\) 0.732051 + 1.26795i 0.115747 + 0.200480i
\(41\) 9.69615 5.59808i 1.51428 0.874273i 0.514425 0.857536i \(-0.328006\pi\)
0.999860 0.0167371i \(-0.00532782\pi\)
\(42\) −4.26795 + 4.26795i −0.658559 + 0.658559i
\(43\) −2.33013 8.69615i −0.355341 1.32615i −0.880055 0.474872i \(-0.842494\pi\)
0.524714 0.851279i \(-0.324172\pi\)
\(44\) −0.267949 + 1.00000i −0.0403949 + 0.150756i
\(45\) −1.50000 0.401924i −0.223607 0.0599153i
\(46\) 0.633975 0.169873i 0.0934745 0.0250464i
\(47\) 4.59808 7.96410i 0.670698 1.16168i −0.307008 0.951707i \(-0.599328\pi\)
0.977706 0.209977i \(-0.0673388\pi\)
\(48\) 6.00000 3.46410i 0.866025 0.500000i
\(49\) −0.464102 0.803848i −0.0663002 0.114835i
\(50\) −4.73205 4.73205i −0.669213 0.669213i
\(51\) 6.92820i 0.970143i
\(52\) −6.73205 + 6.73205i −0.933567 + 0.933567i
\(53\) 2.26795 2.26795i 0.311527 0.311527i −0.533974 0.845501i \(-0.679302\pi\)
0.845501 + 0.533974i \(0.179302\pi\)
\(54\) −1.90192 + 7.09808i −0.258819 + 0.965926i
\(55\) 0.267949i 0.0361303i
\(56\) −1.80385 6.73205i −0.241049 0.899608i
\(57\) −5.19615 + 5.19615i −0.688247 + 0.688247i
\(58\) −4.73205 −0.621349
\(59\) 5.59808 + 1.50000i 0.728807 + 0.195283i 0.604098 0.796910i \(-0.293533\pi\)
0.124709 + 0.992193i \(0.460200\pi\)
\(60\) 1.26795 1.26795i 0.163692 0.163692i
\(61\) 14.4282 3.86603i 1.84734 0.494994i 0.847957 0.530065i \(-0.177832\pi\)
0.999385 + 0.0350707i \(0.0111656\pi\)
\(62\) 0.437822 + 1.63397i 0.0556035 + 0.207515i
\(63\) 6.40192 + 3.69615i 0.806567 + 0.465671i
\(64\) 8.00000i 1.00000i
\(65\) −1.23205 + 2.13397i −0.152817 + 0.264687i
\(66\) 1.26795 0.156074
\(67\) −0.330127 + 1.23205i −0.0403314 + 0.150519i −0.983155 0.182773i \(-0.941493\pi\)
0.942824 + 0.333292i \(0.108159\pi\)
\(68\) 6.92820 + 4.00000i 0.840168 + 0.485071i
\(69\) −0.401924 0.696152i −0.0483859 0.0838069i
\(70\) −0.901924 1.56218i −0.107801 0.186716i
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) −6.00000 6.00000i −0.707107 0.707107i
\(73\) 0.535898i 0.0627222i 0.999508 + 0.0313611i \(0.00998418\pi\)
−0.999508 + 0.0313611i \(0.990016\pi\)
\(74\) −13.3923 + 7.73205i −1.55682 + 0.898833i
\(75\) −4.09808 + 7.09808i −0.473205 + 0.819615i
\(76\) −2.19615 8.19615i −0.251916 0.940163i
\(77\) 0.330127 1.23205i 0.0376215 0.140405i
\(78\) 10.0981 + 5.83013i 1.14338 + 0.660132i
\(79\) 0.866025 1.50000i 0.0974355 0.168763i −0.813187 0.582003i \(-0.802269\pi\)
0.910622 + 0.413239i \(0.135603\pi\)
\(80\) 0.535898 + 2.00000i 0.0599153 + 0.223607i
\(81\) 9.00000 1.00000
\(82\) 15.2942 4.09808i 1.68897 0.452557i
\(83\) −11.7942 + 3.16025i −1.29458 + 0.346883i −0.839400 0.543514i \(-0.817093\pi\)
−0.455185 + 0.890397i \(0.650427\pi\)
\(84\) −7.39230 + 4.26795i −0.806567 + 0.465671i
\(85\) 2.00000 + 0.535898i 0.216930 + 0.0581263i
\(86\) 12.7321i 1.37293i
\(87\) 1.50000 + 5.59808i 0.160817 + 0.600177i
\(88\) −0.732051 + 1.26795i −0.0780369 + 0.135164i
\(89\) 11.8564i 1.25678i −0.777900 0.628388i \(-0.783715\pi\)
0.777900 0.628388i \(-0.216285\pi\)
\(90\) −1.90192 1.09808i −0.200480 0.115747i
\(91\) 8.29423 8.29423i 0.869471 0.869471i
\(92\) 0.928203 0.0967719
\(93\) 1.79423 1.03590i 0.186053 0.107418i
\(94\) 9.19615 9.19615i 0.948511 0.948511i
\(95\) −1.09808 1.90192i −0.112660 0.195133i
\(96\) 9.46410 2.53590i 0.965926 0.258819i
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) −0.339746 1.26795i −0.0343195 0.128082i
\(99\) −0.401924 1.50000i −0.0403949 0.150756i
\(100\) −4.73205 8.19615i −0.473205 0.819615i
\(101\) 0.500000 + 1.86603i 0.0497519 + 0.185676i 0.986330 0.164783i \(-0.0526922\pi\)
−0.936578 + 0.350459i \(0.886026\pi\)
\(102\) 2.53590 9.46410i 0.251091 0.937086i
\(103\) 1.79423 1.03590i 0.176791 0.102070i −0.408993 0.912537i \(-0.634120\pi\)
0.585784 + 0.810467i \(0.300787\pi\)
\(104\) −11.6603 + 6.73205i −1.14338 + 0.660132i
\(105\) −1.56218 + 1.56218i −0.152453 + 0.152453i
\(106\) 3.92820 2.26795i 0.381541 0.220283i
\(107\) −11.3923 + 11.3923i −1.10134 + 1.10134i −0.107086 + 0.994250i \(0.534152\pi\)
−0.994250 + 0.107086i \(0.965848\pi\)
\(108\) −5.19615 + 9.00000i −0.500000 + 0.866025i
\(109\) 1.73205 + 1.73205i 0.165900 + 0.165900i 0.785175 0.619274i \(-0.212573\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(110\) −0.0980762 + 0.366025i −0.00935120 + 0.0348992i
\(111\) 13.3923 + 13.3923i 1.27114 + 1.27114i
\(112\) 9.85641i 0.931343i
\(113\) −2.76795 4.79423i −0.260387 0.451003i 0.705958 0.708254i \(-0.250517\pi\)
−0.966345 + 0.257251i \(0.917183\pi\)
\(114\) −9.00000 + 5.19615i −0.842927 + 0.486664i
\(115\) 0.232051 0.0621778i 0.0216388 0.00579811i
\(116\) −6.46410 1.73205i −0.600177 0.160817i
\(117\) 3.69615 13.7942i 0.341709 1.27528i
\(118\) 7.09808 + 4.09808i 0.653431 + 0.377258i
\(119\) −8.53590 4.92820i −0.782485 0.451768i
\(120\) 2.19615 1.26795i 0.200480 0.115747i
\(121\) 9.29423 5.36603i 0.844930 0.487820i
\(122\) 21.1244 1.91251
\(123\) −9.69615 16.7942i −0.874273 1.51428i
\(124\) 2.39230i 0.214835i
\(125\) −3.56218 3.56218i −0.318611 0.318611i
\(126\) 7.39230 + 7.39230i 0.658559 + 0.658559i
\(127\) −20.3923 −1.80952 −0.904762 0.425917i \(-0.859952\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) −15.0622 + 4.03590i −1.32615 + 0.355341i
\(130\) −2.46410 + 2.46410i −0.216116 + 0.216116i
\(131\) −3.13397 + 11.6962i −0.273817 + 1.02190i 0.682814 + 0.730593i \(0.260756\pi\)
−0.956630 + 0.291305i \(0.905911\pi\)
\(132\) 1.73205 + 0.464102i 0.150756 + 0.0403949i
\(133\) 2.70577 + 10.0981i 0.234620 + 0.875614i
\(134\) −0.901924 + 1.56218i −0.0779143 + 0.134952i
\(135\) −0.696152 + 2.59808i −0.0599153 + 0.223607i
\(136\) 8.00000 + 8.00000i 0.685994 + 0.685994i
\(137\) 14.4282 + 8.33013i 1.23268 + 0.711691i 0.967589 0.252531i \(-0.0812631\pi\)
0.265096 + 0.964222i \(0.414596\pi\)
\(138\) −0.294229 1.09808i −0.0250464 0.0934745i
\(139\) 4.33013 + 1.16025i 0.367277 + 0.0984115i 0.437737 0.899103i \(-0.355780\pi\)
−0.0704603 + 0.997515i \(0.522447\pi\)
\(140\) −0.660254 2.46410i −0.0558017 0.208255i
\(141\) −13.7942 7.96410i −1.16168 0.670698i
\(142\) −4.00000 + 14.9282i −0.335673 + 1.25275i
\(143\) −2.46410 −0.206059
\(144\) −6.00000 10.3923i −0.500000 0.866025i
\(145\) −1.73205 −0.143839
\(146\) −0.196152 + 0.732051i −0.0162337 + 0.0605850i
\(147\) −1.39230 + 0.803848i −0.114835 + 0.0663002i
\(148\) −21.1244 + 5.66025i −1.73641 + 0.465270i
\(149\) −14.6962 3.93782i −1.20396 0.322599i −0.399568 0.916704i \(-0.630840\pi\)
−0.804388 + 0.594105i \(0.797507\pi\)
\(150\) −8.19615 + 8.19615i −0.669213 + 0.669213i
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) 12.0000i 0.973329i
\(153\) −12.0000 −0.970143
\(154\) 0.901924 1.56218i 0.0726791 0.125884i
\(155\) 0.160254 + 0.598076i 0.0128719 + 0.0480386i
\(156\) 11.6603 + 11.6603i 0.933567 + 0.933567i
\(157\) −0.232051 + 0.866025i −0.0185197 + 0.0691164i −0.974567 0.224095i \(-0.928057\pi\)
0.956048 + 0.293212i \(0.0947240\pi\)
\(158\) 1.73205 1.73205i 0.137795 0.137795i
\(159\) −3.92820 3.92820i −0.311527 0.311527i
\(160\) 2.92820i 0.231495i
\(161\) −1.14359 −0.0901278
\(162\) 12.2942 + 3.29423i 0.965926 + 0.258819i
\(163\) 11.9282 + 11.9282i 0.934289 + 0.934289i 0.997970 0.0636813i \(-0.0202841\pi\)
−0.0636813 + 0.997970i \(0.520284\pi\)
\(164\) 22.3923 1.74855
\(165\) 0.464102 0.0361303
\(166\) −17.2679 −1.34025
\(167\) −8.25833 + 4.76795i −0.639049 + 0.368955i −0.784248 0.620447i \(-0.786951\pi\)
0.145199 + 0.989402i \(0.453618\pi\)
\(168\) −11.6603 + 3.12436i −0.899608 + 0.241049i
\(169\) −8.36603 4.83013i −0.643540 0.371548i
\(170\) 2.53590 + 1.46410i 0.194495 + 0.112291i
\(171\) 9.00000 + 9.00000i 0.688247 + 0.688247i
\(172\) 4.66025 17.3923i 0.355341 1.32615i
\(173\) −8.96410 + 2.40192i −0.681528 + 0.182615i −0.582942 0.812514i \(-0.698099\pi\)
−0.0985859 + 0.995129i \(0.531432\pi\)
\(174\) 8.19615i 0.621349i
\(175\) 5.83013 + 10.0981i 0.440716 + 0.763343i
\(176\) −1.46410 + 1.46410i −0.110361 + 0.110361i
\(177\) 2.59808 9.69615i 0.195283 0.728807i
\(178\) 4.33975 16.1962i 0.325278 1.21395i
\(179\) 7.92820 + 7.92820i 0.592582 + 0.592582i 0.938328 0.345746i \(-0.112374\pi\)
−0.345746 + 0.938328i \(0.612374\pi\)
\(180\) −2.19615 2.19615i −0.163692 0.163692i
\(181\) −4.26795 + 4.26795i −0.317234 + 0.317234i −0.847704 0.530470i \(-0.822016\pi\)
0.530470 + 0.847704i \(0.322016\pi\)
\(182\) 14.3660 8.29423i 1.06488 0.614809i
\(183\) −6.69615 24.9904i −0.494994 1.84734i
\(184\) 1.26795 + 0.339746i 0.0934745 + 0.0250464i
\(185\) −4.90192 + 2.83013i −0.360397 + 0.208075i
\(186\) 2.83013 0.758330i 0.207515 0.0556035i
\(187\) 0.535898 + 2.00000i 0.0391888 + 0.146254i
\(188\) 15.9282 9.19615i 1.16168 0.670698i
\(189\) 6.40192 11.0885i 0.465671 0.806567i
\(190\) −0.803848 3.00000i −0.0583172 0.217643i
\(191\) 6.59808 11.4282i 0.477420 0.826916i −0.522245 0.852795i \(-0.674905\pi\)
0.999665 + 0.0258797i \(0.00823869\pi\)
\(192\) 13.8564 1.00000
\(193\) −1.23205 2.13397i −0.0886850 0.153607i 0.818271 0.574833i \(-0.194933\pi\)
−0.906956 + 0.421226i \(0.861600\pi\)
\(194\) −1.00000 + 1.00000i −0.0717958 + 0.0717958i
\(195\) 3.69615 + 2.13397i 0.264687 + 0.152817i
\(196\) 1.85641i 0.132600i
\(197\) 10.4641 10.4641i 0.745536 0.745536i −0.228101 0.973637i \(-0.573252\pi\)
0.973637 + 0.228101i \(0.0732517\pi\)
\(198\) 2.19615i 0.156074i
\(199\) 5.85641i 0.415150i 0.978219 + 0.207575i \(0.0665570\pi\)
−0.978219 + 0.207575i \(0.933443\pi\)
\(200\) −3.46410 12.9282i −0.244949 0.914162i
\(201\) 2.13397 + 0.571797i 0.150519 + 0.0403314i
\(202\) 2.73205i 0.192226i
\(203\) 7.96410 + 2.13397i 0.558970 + 0.149776i
\(204\) 6.92820 12.0000i 0.485071 0.840168i
\(205\) 5.59808 1.50000i 0.390987 0.104765i
\(206\) 2.83013 0.758330i 0.197184 0.0528354i
\(207\) −1.20577 + 0.696152i −0.0838069 + 0.0483859i
\(208\) −18.3923 + 4.92820i −1.27528 + 0.341709i
\(209\) 1.09808 1.90192i 0.0759555 0.131559i
\(210\) −2.70577 + 1.56218i −0.186716 + 0.107801i
\(211\) −0.526279 + 1.96410i −0.0362306 + 0.135214i −0.981672 0.190577i \(-0.938964\pi\)
0.945442 + 0.325791i \(0.105631\pi\)
\(212\) 6.19615 1.66025i 0.425553 0.114027i
\(213\) 18.9282 1.29694
\(214\) −19.7321 + 11.3923i −1.34886 + 0.778762i
\(215\) 4.66025i 0.317827i
\(216\) −10.3923 + 10.3923i −0.707107 + 0.707107i
\(217\) 2.94744i 0.200085i
\(218\) 1.73205 + 3.00000i 0.117309 + 0.203186i
\(219\) 0.928203 0.0627222
\(220\) −0.267949 + 0.464102i −0.0180651 + 0.0312897i
\(221\) −4.92820 + 18.3923i −0.331507 + 1.23720i
\(222\) 13.3923 + 23.1962i 0.898833 + 1.55682i
\(223\) −7.79423 + 13.5000i −0.521940 + 0.904027i 0.477734 + 0.878504i \(0.341458\pi\)
−0.999674 + 0.0255224i \(0.991875\pi\)
\(224\) 3.60770 13.4641i 0.241049 0.899608i
\(225\) 12.2942 + 7.09808i 0.819615 + 0.473205i
\(226\) −2.02628 7.56218i −0.134786 0.503029i
\(227\) 17.2583 4.62436i 1.14548 0.306929i 0.364325 0.931272i \(-0.381300\pi\)
0.781151 + 0.624343i \(0.214633\pi\)
\(228\) −14.1962 + 3.80385i −0.940163 + 0.251916i
\(229\) 9.42820 + 2.52628i 0.623033 + 0.166941i 0.556506 0.830843i \(-0.312142\pi\)
0.0665269 + 0.997785i \(0.478808\pi\)
\(230\) 0.339746 0.0224022
\(231\) −2.13397 0.571797i −0.140405 0.0376215i
\(232\) −8.19615 4.73205i −0.538104 0.310674i
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) 10.0981 17.4904i 0.660132 1.14338i
\(235\) 3.36603 3.36603i 0.219575 0.219575i
\(236\) 8.19615 + 8.19615i 0.533524 + 0.533524i
\(237\) −2.59808 1.50000i −0.168763 0.0974355i
\(238\) −9.85641 9.85641i −0.638896 0.638896i
\(239\) −5.59808 9.69615i −0.362109 0.627192i 0.626198 0.779664i \(-0.284610\pi\)
−0.988308 + 0.152472i \(0.951277\pi\)
\(240\) 3.46410 0.928203i 0.223607 0.0599153i
\(241\) −6.23205 + 10.7942i −0.401442 + 0.695317i −0.993900 0.110284i \(-0.964824\pi\)
0.592458 + 0.805601i \(0.298157\pi\)
\(242\) 14.6603 3.92820i 0.942397 0.252514i
\(243\) 15.5885i 1.00000i
\(244\) 28.8564 + 7.73205i 1.84734 + 0.494994i
\(245\) −0.124356 0.464102i −0.00794479 0.0296504i
\(246\) −7.09808 26.4904i −0.452557 1.68897i
\(247\) 17.4904 10.0981i 1.11289 0.642525i
\(248\) −0.875644 + 3.26795i −0.0556035 + 0.207515i
\(249\) 5.47372 + 20.4282i 0.346883 + 1.29458i
\(250\) −3.56218 6.16987i −0.225292 0.390217i
\(251\) 7.39230 7.39230i 0.466598 0.466598i −0.434212 0.900811i \(-0.642973\pi\)
0.900811 + 0.434212i \(0.142973\pi\)
\(252\) 7.39230 + 12.8038i 0.465671 + 0.806567i
\(253\) 0.169873 + 0.169873i 0.0106798 + 0.0106798i
\(254\) −27.8564 7.46410i −1.74787 0.468339i
\(255\) 0.928203 3.46410i 0.0581263 0.216930i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −5.16025 8.93782i −0.321888 0.557526i 0.658990 0.752152i \(-0.270984\pi\)
−0.980878 + 0.194626i \(0.937651\pi\)
\(258\) −22.0526 −1.37293
\(259\) 26.0263 6.97372i 1.61719 0.433326i
\(260\) −4.26795 + 2.46410i −0.264687 + 0.152817i
\(261\) 9.69615 2.59808i 0.600177 0.160817i
\(262\) −8.56218 + 14.8301i −0.528973 + 0.916208i
\(263\) 3.40192 + 1.96410i 0.209772 + 0.121112i 0.601205 0.799095i \(-0.294687\pi\)
−0.391434 + 0.920206i \(0.628021\pi\)
\(264\) 2.19615 + 1.26795i 0.135164 + 0.0780369i
\(265\) 1.43782 0.830127i 0.0883247 0.0509943i
\(266\) 14.7846i 0.906503i
\(267\) −20.5359 −1.25678
\(268\) −1.80385 + 1.80385i −0.110188 + 0.110188i
\(269\) 7.73205 + 7.73205i 0.471431 + 0.471431i 0.902378 0.430946i \(-0.141820\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(270\) −1.90192 + 3.29423i −0.115747 + 0.200480i
\(271\) −14.9282 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(272\) 8.00000 + 13.8564i 0.485071 + 0.840168i
\(273\) −14.3660 14.3660i −0.869471 0.869471i
\(274\) 16.6603 + 16.6603i 1.00648 + 1.00648i
\(275\) 0.633975 2.36603i 0.0382301 0.142677i
\(276\) 1.60770i 0.0967719i
\(277\) −3.69615 13.7942i −0.222080 0.828815i −0.983553 0.180618i \(-0.942190\pi\)
0.761473 0.648197i \(-0.224477\pi\)
\(278\) 5.49038 + 3.16987i 0.329291 + 0.190116i
\(279\) −1.79423 3.10770i −0.107418 0.186053i
\(280\) 3.60770i 0.215601i
\(281\) 16.9641 + 9.79423i 1.01199 + 0.584275i 0.911775 0.410691i \(-0.134712\pi\)
0.100219 + 0.994965i \(0.468046\pi\)
\(282\) −15.9282 15.9282i −0.948511 0.948511i
\(283\) −15.5263 4.16025i −0.922942 0.247301i −0.234099 0.972213i \(-0.575214\pi\)
−0.688842 + 0.724911i \(0.741881\pi\)
\(284\) −10.9282 + 18.9282i −0.648470 + 1.12318i
\(285\) −3.29423 + 1.90192i −0.195133 + 0.112660i
\(286\) −3.36603 0.901924i −0.199037 0.0533319i
\(287\) −27.5885 −1.62850
\(288\) −4.39230 16.3923i −0.258819 0.965926i
\(289\) −1.00000 −0.0588235
\(290\) −2.36603 0.633975i −0.138938 0.0372283i
\(291\) 1.50000 + 0.866025i 0.0879316 + 0.0507673i
\(292\) −0.535898 + 0.928203i −0.0313611 + 0.0543190i
\(293\) −14.4282 3.86603i −0.842905 0.225856i −0.188569 0.982060i \(-0.560385\pi\)
−0.654336 + 0.756204i \(0.727052\pi\)
\(294\) −2.19615 + 0.588457i −0.128082 + 0.0343195i
\(295\) 2.59808 + 1.50000i 0.151266 + 0.0873334i
\(296\) −30.9282 −1.79767
\(297\) −2.59808 + 0.696152i −0.150756 + 0.0403949i
\(298\) −18.6340 10.7583i −1.07944 0.623213i
\(299\) 0.571797 + 2.13397i 0.0330679 + 0.123411i
\(300\) −14.1962 + 8.19615i −0.819615 + 0.473205i
\(301\) −5.74167 + 21.4282i −0.330944 + 1.23510i
\(302\) −7.00000 7.00000i −0.402805 0.402805i
\(303\) 3.23205 0.866025i 0.185676 0.0497519i
\(304\) 4.39230 16.3923i 0.251916 0.940163i
\(305\) 7.73205 0.442736
\(306\) −16.3923 4.39230i −0.937086 0.251091i
\(307\) −5.92820 5.92820i −0.338340 0.338340i 0.517402 0.855742i \(-0.326899\pi\)
−0.855742 + 0.517402i \(0.826899\pi\)
\(308\) 1.80385 1.80385i 0.102784 0.102784i
\(309\) −1.79423 3.10770i −0.102070 0.176791i
\(310\) 0.875644i 0.0497333i
\(311\) 27.1865 15.6962i 1.54161 0.890047i 0.542869 0.839817i \(-0.317338\pi\)
0.998738 0.0502299i \(-0.0159954\pi\)
\(312\) 11.6603 + 20.1962i 0.660132 + 1.14338i
\(313\) −7.83975 4.52628i −0.443129 0.255840i 0.261795 0.965123i \(-0.415686\pi\)
−0.704924 + 0.709283i \(0.749019\pi\)
\(314\) −0.633975 + 1.09808i −0.0357773 + 0.0619680i
\(315\) 2.70577 + 2.70577i 0.152453 + 0.152453i
\(316\) 3.00000 1.73205i 0.168763 0.0974355i
\(317\) 2.03590 0.545517i 0.114347 0.0306393i −0.201192 0.979552i \(-0.564481\pi\)
0.315539 + 0.948913i \(0.397815\pi\)
\(318\) −3.92820 6.80385i −0.220283 0.381541i
\(319\) −0.866025 1.50000i −0.0484881 0.0839839i
\(320\) −1.07180 + 4.00000i −0.0599153 + 0.223607i
\(321\) 19.7321 + 19.7321i 1.10134 + 1.10134i
\(322\) −1.56218 0.418584i −0.0870568 0.0233268i
\(323\) −12.0000 12.0000i −0.667698 0.667698i
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 15.9282 15.9282i 0.883538 0.883538i
\(326\) 11.9282 + 20.6603i 0.660642 + 1.14427i
\(327\) 3.00000 3.00000i 0.165900 0.165900i
\(328\) 30.5885 + 8.19615i 1.68897 + 0.452557i
\(329\) −19.6244 + 11.3301i −1.08193 + 0.624650i
\(330\) 0.633975 + 0.169873i 0.0348992 + 0.00935120i
\(331\) 7.06218 + 26.3564i 0.388172 + 1.44868i 0.833105 + 0.553115i \(0.186561\pi\)
−0.444933 + 0.895564i \(0.646772\pi\)
\(332\) −23.5885 6.32051i −1.29458 0.346883i
\(333\) 23.1962 23.1962i 1.27114 1.27114i
\(334\) −13.0263 + 3.49038i −0.712766 + 0.190985i
\(335\) −0.330127 + 0.571797i −0.0180368 + 0.0312406i
\(336\) −17.0718 −0.931343
\(337\) 0.696152 + 1.20577i 0.0379218 + 0.0656826i 0.884363 0.466799i \(-0.154593\pi\)
−0.846442 + 0.532482i \(0.821260\pi\)
\(338\) −9.66025 9.66025i −0.525449 0.525449i
\(339\) −8.30385 + 4.79423i −0.451003 + 0.260387i
\(340\) 2.92820 + 2.92820i 0.158804 + 0.158804i
\(341\) −0.437822 + 0.437822i −0.0237094 + 0.0237094i
\(342\) 9.00000 + 15.5885i 0.486664 + 0.842927i
\(343\) 19.5359i 1.05484i
\(344\) 12.7321 22.0526i 0.686466 1.18899i
\(345\) −0.107695 0.401924i −0.00579811 0.0216388i
\(346\) −13.1244 −0.705570
\(347\) 19.5263 + 5.23205i 1.04823 + 0.280871i 0.741518 0.670933i \(-0.234106\pi\)
0.306707 + 0.951804i \(0.400773\pi\)
\(348\) −3.00000 + 11.1962i −0.160817 + 0.600177i
\(349\) 7.96410 2.13397i 0.426309 0.114229i −0.0392843 0.999228i \(-0.512508\pi\)
0.465593 + 0.884999i \(0.345841\pi\)
\(350\) 4.26795 + 15.9282i 0.228131 + 0.851398i
\(351\) −23.8923 6.40192i −1.27528 0.341709i
\(352\) −2.53590 + 1.46410i −0.135164 + 0.0780369i
\(353\) −15.2321 + 26.3827i −0.810720 + 1.40421i 0.101640 + 0.994821i \(0.467591\pi\)
−0.912361 + 0.409387i \(0.865742\pi\)
\(354\) 7.09808 12.2942i 0.377258 0.653431i
\(355\) −1.46410 + 5.46410i −0.0777064 + 0.290004i
\(356\) 11.8564 20.5359i 0.628388 1.08840i
\(357\) −8.53590 + 14.7846i −0.451768 + 0.782485i
\(358\) 7.92820 + 13.7321i 0.419019 + 0.725761i
\(359\) 15.0718i 0.795459i −0.917503 0.397730i \(-0.869798\pi\)
0.917503 0.397730i \(-0.130202\pi\)
\(360\) −2.19615 3.80385i −0.115747 0.200480i
\(361\) 1.00000i 0.0526316i
\(362\) −7.39230 + 4.26795i −0.388531 + 0.224318i
\(363\) −9.29423 16.0981i −0.487820 0.844930i
\(364\) 22.6603 6.07180i 1.18772 0.318249i
\(365\) −0.0717968 + 0.267949i −0.00375801 + 0.0140251i
\(366\) 36.5885i 1.91251i
\(367\) 15.4545 26.7679i 0.806717 1.39728i −0.108408 0.994106i \(-0.534575\pi\)
0.915125 0.403169i \(-0.132091\pi\)
\(368\) 1.60770 + 0.928203i 0.0838069 + 0.0483859i
\(369\) −29.0885 + 16.7942i −1.51428 + 0.874273i
\(370\) −7.73205 + 2.07180i −0.401970 + 0.107708i
\(371\) −7.63397 + 2.04552i −0.396336 + 0.106198i
\(372\) 4.14359 0.214835
\(373\) −13.4282 3.59808i −0.695286 0.186301i −0.106168 0.994348i \(-0.533858\pi\)
−0.589118 + 0.808047i \(0.700525\pi\)
\(374\) 2.92820i 0.151414i
\(375\) −6.16987 + 6.16987i −0.318611 + 0.318611i
\(376\) 25.1244 6.73205i 1.29569 0.347179i
\(377\) 15.9282i 0.820344i
\(378\) 12.8038 12.8038i 0.658559 0.658559i
\(379\) 15.5885 15.5885i 0.800725 0.800725i −0.182484 0.983209i \(-0.558414\pi\)
0.983209 + 0.182484i \(0.0584137\pi\)
\(380\) 4.39230i 0.225320i
\(381\) 35.3205i 1.80952i
\(382\) 13.1962 13.1962i 0.675174 0.675174i
\(383\) 12.3301 + 21.3564i 0.630040 + 1.09126i 0.987543 + 0.157349i \(0.0502949\pi\)
−0.357503 + 0.933912i \(0.616372\pi\)
\(384\) 18.9282 + 5.07180i 0.965926 + 0.258819i
\(385\) 0.330127 0.571797i 0.0168248 0.0291415i
\(386\) −0.901924 3.36603i −0.0459067 0.171326i
\(387\) 6.99038 + 26.0885i 0.355341 + 1.32615i
\(388\) −1.73205 + 1.00000i −0.0879316 + 0.0507673i
\(389\) −2.03590 7.59808i −0.103224 0.385238i 0.894914 0.446240i \(-0.147237\pi\)
−0.998138 + 0.0610019i \(0.980570\pi\)
\(390\) 4.26795 + 4.26795i 0.216116 + 0.216116i
\(391\) 1.60770 0.928203i 0.0813046 0.0469413i
\(392\) 0.679492 2.53590i 0.0343195 0.128082i
\(393\) 20.2583 + 5.42820i 1.02190 + 0.273817i
\(394\) 18.1244 10.4641i 0.913092 0.527174i
\(395\) 0.633975 0.633975i 0.0318987 0.0318987i
\(396\) 0.803848 3.00000i 0.0403949 0.150756i
\(397\) −21.0526 21.0526i −1.05660 1.05660i −0.998299 0.0582984i \(-0.981433\pi\)
−0.0582984 0.998299i \(-0.518567\pi\)
\(398\) −2.14359 + 8.00000i −0.107449 + 0.401004i
\(399\) 17.4904 4.68653i 0.875614 0.234620i
\(400\) 18.9282i 0.946410i
\(401\) 1.16025 + 2.00962i 0.0579403 + 0.100356i 0.893541 0.448982i \(-0.148213\pi\)
−0.835600 + 0.549338i \(0.814880\pi\)
\(402\) 2.70577 + 1.56218i 0.134952 + 0.0779143i
\(403\) −5.50000 + 1.47372i −0.273975 + 0.0734112i
\(404\) −1.00000 + 3.73205i −0.0497519 + 0.185676i
\(405\) 4.50000 + 1.20577i 0.223607 + 0.0599153i
\(406\) 10.0981 + 5.83013i 0.501159 + 0.289344i
\(407\) −4.90192 2.83013i −0.242979 0.140284i
\(408\) 13.8564 13.8564i 0.685994 0.685994i
\(409\) −4.62436 + 2.66987i −0.228660 + 0.132017i −0.609954 0.792437i \(-0.708812\pi\)
0.381294 + 0.924454i \(0.375479\pi\)
\(410\) 8.19615 0.404779
\(411\) 14.4282 24.9904i 0.711691 1.23268i
\(412\) 4.14359 0.204140
\(413\) −10.0981 10.0981i −0.496894 0.496894i
\(414\) −1.90192 + 0.509619i −0.0934745 + 0.0250464i
\(415\) −6.32051 −0.310262
\(416\) −26.9282 −1.32026
\(417\) 2.00962 7.50000i 0.0984115 0.367277i
\(418\) 2.19615 2.19615i 0.107417 0.107417i
\(419\) −0.526279 + 1.96410i −0.0257104 + 0.0959526i −0.977589 0.210523i \(-0.932483\pi\)
0.951878 + 0.306476i \(0.0991499\pi\)
\(420\) −4.26795 + 1.14359i −0.208255 + 0.0558017i
\(421\) −2.89230 10.7942i −0.140962 0.526079i −0.999902 0.0140017i \(-0.995543\pi\)
0.858940 0.512077i \(-0.171124\pi\)
\(422\) −1.43782 + 2.49038i −0.0699921 + 0.121230i
\(423\) −13.7942 + 23.8923i −0.670698 + 1.16168i
\(424\) 9.07180 0.440565
\(425\) −16.3923 9.46410i −0.795144 0.459076i
\(426\) 25.8564 + 6.92820i 1.25275 + 0.335673i
\(427\) −35.5526 9.52628i −1.72051 0.461009i
\(428\) −31.1244 + 8.33975i −1.50445 + 0.403117i
\(429\) 4.26795i 0.206059i
\(430\) 1.70577 6.36603i 0.0822596 0.306997i
\(431\) 31.3205 1.50866 0.754328 0.656498i \(-0.227963\pi\)
0.754328 + 0.656498i \(0.227963\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) 1.07884 4.02628i 0.0517859 0.193268i
\(435\) 3.00000i 0.143839i
\(436\) 1.26795 + 4.73205i 0.0607238 + 0.226624i
\(437\) −1.90192 0.509619i −0.0909814 0.0243784i
\(438\) 1.26795 + 0.339746i 0.0605850 + 0.0162337i
\(439\) −18.0622 10.4282i −0.862061 0.497711i 0.00264111 0.999997i \(-0.499159\pi\)
−0.864702 + 0.502286i \(0.832493\pi\)
\(440\) −0.535898 + 0.535898i −0.0255480 + 0.0255480i
\(441\) 1.39230 + 2.41154i 0.0663002 + 0.114835i
\(442\) −13.4641 + 23.3205i −0.640422 + 1.10924i
\(443\) −4.33013 16.1603i −0.205731 0.767797i −0.989226 0.146399i \(-0.953232\pi\)
0.783495 0.621398i \(-0.213435\pi\)
\(444\) 9.80385 + 36.5885i 0.465270 + 1.73641i
\(445\) 1.58846 5.92820i 0.0753001 0.281024i
\(446\) −15.5885 + 15.5885i −0.738135 + 0.738135i
\(447\) −6.82051 + 25.4545i −0.322599 + 1.20396i
\(448\) 9.85641 17.0718i 0.465671 0.806567i
\(449\) 0.679492 0.0320672 0.0160336 0.999871i \(-0.494896\pi\)
0.0160336 + 0.999871i \(0.494896\pi\)
\(450\) 14.1962 + 14.1962i 0.669213 + 0.669213i
\(451\) 4.09808 + 4.09808i 0.192971 + 0.192971i
\(452\) 11.0718i 0.520774i
\(453\) −6.06218 + 10.5000i −0.284826 + 0.493333i
\(454\) 25.2679 1.18588
\(455\) 5.25833 3.03590i 0.246514 0.142325i
\(456\) −20.7846 −0.973329
\(457\) −19.0359 10.9904i −0.890462 0.514108i −0.0163683 0.999866i \(-0.505210\pi\)
−0.874094 + 0.485758i \(0.838544\pi\)
\(458\) 11.9545 + 6.90192i 0.558596 + 0.322506i
\(459\) 20.7846i 0.970143i
\(460\) 0.464102 + 0.124356i 0.0216388 + 0.00579811i
\(461\) 2.23205 0.598076i 0.103957 0.0278552i −0.206466 0.978454i \(-0.566196\pi\)
0.310423 + 0.950599i \(0.399529\pi\)
\(462\) −2.70577 1.56218i −0.125884 0.0726791i
\(463\) 3.33013 + 5.76795i 0.154764 + 0.268059i 0.932973 0.359946i \(-0.117205\pi\)
−0.778209 + 0.628005i \(0.783872\pi\)
\(464\) −9.46410 9.46410i −0.439360 0.439360i
\(465\) 1.03590 0.277568i 0.0480386 0.0128719i
\(466\) −8.39230 + 31.3205i −0.388766 + 1.45089i
\(467\) −19.7846 19.7846i −0.915523 0.915523i 0.0811771 0.996700i \(-0.474132\pi\)
−0.996700 + 0.0811771i \(0.974132\pi\)
\(468\) 20.1962 20.1962i 0.933567 0.933567i
\(469\) 2.22243 2.22243i 0.102622 0.102622i
\(470\) 5.83013 3.36603i 0.268924 0.155263i
\(471\) 1.50000 + 0.401924i 0.0691164 + 0.0185197i
\(472\) 8.19615 + 14.1962i 0.377258 + 0.653431i
\(473\) 4.03590 2.33013i 0.185571 0.107139i
\(474\) −3.00000 3.00000i −0.137795 0.137795i
\(475\) 5.19615 + 19.3923i 0.238416 + 0.889780i
\(476\) −9.85641 17.0718i −0.451768 0.782485i
\(477\) −6.80385 + 6.80385i −0.311527 + 0.311527i
\(478\) −4.09808 15.2942i −0.187442 0.699542i
\(479\) 0.669873 1.16025i 0.0306073 0.0530134i −0.850316 0.526272i \(-0.823589\pi\)
0.880923 + 0.473259i \(0.156923\pi\)
\(480\) 5.07180 0.231495
\(481\) −26.0263 45.0788i −1.18670 2.05542i
\(482\) −12.4641 + 12.4641i −0.567724 + 0.567724i
\(483\) 1.98076i 0.0901278i
\(484\) 21.4641 0.975641
\(485\) −0.366025 + 0.366025i −0.0166204 + 0.0166204i
\(486\) 5.70577 21.2942i 0.258819 0.965926i
\(487\) 34.7846i 1.57624i 0.615521 + 0.788121i \(0.288946\pi\)
−0.615521 + 0.788121i \(0.711054\pi\)
\(488\) 36.5885 + 21.1244i 1.65628 + 0.956255i
\(489\) 20.6603 20.6603i 0.934289 0.934289i
\(490\) 0.679492i 0.0306963i
\(491\) −1.86603 0.500000i −0.0842125 0.0225647i 0.216467 0.976290i \(-0.430547\pi\)
−0.300679 + 0.953725i \(0.597213\pi\)
\(492\) 38.7846i 1.74855i
\(493\) −12.9282 + 3.46410i −0.582257 + 0.156015i
\(494\) 27.5885 7.39230i 1.24126 0.332596i
\(495\) 0.803848i 0.0361303i
\(496\) −2.39230 + 4.14359i −0.107418 + 0.186053i
\(497\) 13.4641 23.3205i 0.603947 1.04607i
\(498\) 29.9090i 1.34025i
\(499\) 0.669873 2.50000i 0.0299876 0.111915i −0.949310 0.314342i \(-0.898216\pi\)
0.979297 + 0.202427i \(0.0648828\pi\)
\(500\) −2.60770 9.73205i −0.116620 0.435231i
\(501\) 8.25833 + 14.3038i 0.368955 + 0.639049i
\(502\) 12.8038 7.39230i 0.571464 0.329935i
\(503\) 13.8564i 0.617827i −0.951090 0.308913i \(-0.900035\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(504\) 5.41154 + 20.1962i 0.241049 + 0.899608i
\(505\) 1.00000i 0.0444994i
\(506\) 0.169873 + 0.294229i 0.00755178 + 0.0130801i
\(507\) −8.36603 + 14.4904i −0.371548 + 0.643540i
\(508\) −35.3205 20.3923i −1.56709 0.904762i
\(509\) 5.69615 21.2583i 0.252478 0.942259i −0.716999 0.697074i \(-0.754485\pi\)
0.969476 0.245185i \(-0.0788486\pi\)
\(510\) 2.53590 4.39230i 0.112291 0.194495i
\(511\) 0.660254 1.14359i 0.0292079 0.0505896i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 15.5885 15.5885i 0.688247 0.688247i
\(514\) −3.77757 14.0981i −0.166621 0.621839i
\(515\) 1.03590 0.277568i 0.0456471 0.0122311i
\(516\) −30.1244 8.07180i −1.32615 0.355341i
\(517\) 4.59808 + 1.23205i 0.202223 + 0.0541855i
\(518\) 38.1051 1.67424
\(519\) 4.16025 + 15.5263i 0.182615 + 0.681528i
\(520\) −6.73205 + 1.80385i −0.295220 + 0.0791039i
\(521\) 14.1436i 0.619642i −0.950795 0.309821i \(-0.899731\pi\)
0.950795 0.309821i \(-0.100269\pi\)
\(522\) 14.1962 0.621349
\(523\) −2.12436 + 2.12436i −0.0928916 + 0.0928916i −0.752026 0.659134i \(-0.770923\pi\)
0.659134 + 0.752026i \(0.270923\pi\)
\(524\) −17.1244 + 17.1244i −0.748081 + 0.748081i
\(525\) 17.4904 10.0981i 0.763343 0.440716i
\(526\) 3.92820 + 3.92820i 0.171278 + 0.171278i
\(527\) 2.39230 + 4.14359i 0.104210 + 0.180498i
\(528\) 2.53590 + 2.53590i 0.110361 + 0.110361i
\(529\) −11.3923 + 19.7321i −0.495318 + 0.857915i
\(530\) 2.26795 0.607695i 0.0985134 0.0263966i
\(531\) −16.7942 4.50000i −0.728807 0.195283i
\(532\) −5.41154 + 20.1962i −0.234620 + 0.875614i
\(533\) 13.7942 + 51.4808i 0.597494 + 2.22988i
\(534\) −28.0526 7.51666i −1.21395 0.325278i
\(535\) −7.22243 + 4.16987i −0.312253 + 0.180279i
\(536\) −3.12436 + 1.80385i −0.134952 + 0.0779143i
\(537\) 13.7321 13.7321i 0.592582 0.592582i
\(538\) 7.73205 + 13.3923i 0.333352 + 0.577383i
\(539\) 0.339746 0.339746i 0.0146339 0.0146339i
\(540\) −3.80385 + 3.80385i −0.163692 + 0.163692i
\(541\) −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) −20.3923 5.46410i −0.875924 0.234703i
\(543\) 7.39230 + 7.39230i 0.317234 + 0.317234i
\(544\) 5.85641 + 21.8564i 0.251091 + 0.937086i
\(545\) 0.633975 + 1.09808i 0.0271565 + 0.0470364i
\(546\) −14.3660 24.8827i −0.614809 1.06488i
\(547\) −28.2583 + 7.57180i −1.20824 + 0.323747i −0.806071 0.591819i \(-0.798410\pi\)
−0.402168 + 0.915566i \(0.631743\pi\)
\(548\) 16.6603 + 28.8564i 0.711691 + 1.23268i
\(549\) −43.2846 + 11.5981i −1.84734 + 0.494994i
\(550\) 1.73205 3.00000i 0.0738549 0.127920i
\(551\) 12.2942 + 7.09808i 0.523752 + 0.302388i
\(552\) 0.588457 2.19615i 0.0250464 0.0934745i
\(553\) −3.69615 + 2.13397i −0.157176 + 0.0907458i
\(554\) 20.1962i 0.858052i
\(555\) 4.90192 + 8.49038i 0.208075 + 0.360397i
\(556\) 6.33975 + 6.33975i 0.268865 + 0.268865i
\(557\) 27.9808 + 27.9808i 1.18558 + 1.18558i 0.978276 + 0.207307i \(0.0664699\pi\)
0.207307 + 0.978276i \(0.433530\pi\)
\(558\) −1.31347 4.90192i −0.0556035 0.207515i
\(559\) 42.8564 1.81263
\(560\) 1.32051 4.92820i 0.0558017 0.208255i
\(561\) 3.46410 0.928203i 0.146254 0.0391888i
\(562\) 19.5885 + 19.5885i 0.826289 + 0.826289i
\(563\) 7.86603 29.3564i 0.331513 1.23723i −0.576086 0.817389i \(-0.695421\pi\)
0.907600 0.419836i \(-0.137912\pi\)
\(564\) −15.9282 27.5885i −0.670698 1.16168i
\(565\) −0.741670 2.76795i −0.0312023 0.116448i
\(566\) −19.6865 11.3660i −0.827487 0.477750i
\(567\) −19.2058 11.0885i −0.806567 0.465671i
\(568\) −21.8564 + 21.8564i −0.917074 + 0.917074i
\(569\) −24.4808 14.1340i −1.02629 0.592527i −0.110368 0.993891i \(-0.535203\pi\)
−0.915919 + 0.401364i \(0.868536\pi\)
\(570\) −5.19615 + 1.39230i −0.217643 + 0.0583172i
\(571\) −5.40192 1.44744i −0.226063 0.0605735i 0.144009 0.989576i \(-0.454001\pi\)
−0.370073 + 0.929003i \(0.620667\pi\)
\(572\) −4.26795 2.46410i −0.178452 0.103029i
\(573\) −19.7942 11.4282i −0.826916 0.477420i
\(574\) −37.6865 10.0981i −1.57301 0.421486i
\(575\) −2.19615 −0.0915859
\(576\) 24.0000i 1.00000i
\(577\) 37.1769 1.54770 0.773848 0.633372i \(-0.218330\pi\)
0.773848 + 0.633372i \(0.218330\pi\)
\(578\) −1.36603 0.366025i −0.0568192 0.0152246i
\(579\) −3.69615 + 2.13397i −0.153607 + 0.0886850i
\(580\) −3.00000 1.73205i −0.124568 0.0719195i
\(581\) 29.0622 + 7.78719i 1.20570 + 0.323067i
\(582\) 1.73205 + 1.73205i 0.0717958 + 0.0717958i
\(583\) 1.43782 + 0.830127i 0.0595485 + 0.0343803i
\(584\) −1.07180 + 1.07180i −0.0443513 + 0.0443513i
\(585\) 3.69615 6.40192i 0.152817 0.264687i
\(586\) −18.2942 10.5622i −0.755728 0.436320i
\(587\) 0.794229 + 2.96410i 0.0327813 + 0.122342i 0.980378 0.197129i \(-0.0631617\pi\)
−0.947596 + 0.319470i \(0.896495\pi\)
\(588\) −3.21539 −0.132600
\(589\) 1.31347 4.90192i 0.0541204 0.201980i
\(590\) 3.00000 + 3.00000i 0.123508 + 0.123508i
\(591\) −18.1244 18.1244i −0.745536 0.745536i
\(592\) −42.2487 11.3205i −1.73641 0.465270i
\(593\) 1.46410 0.0601234 0.0300617 0.999548i \(-0.490430\pi\)
0.0300617 + 0.999548i \(0.490430\pi\)
\(594\) −3.80385 −0.156074
\(595\) −3.60770 3.60770i −0.147901 0.147901i
\(596\) −21.5167 21.5167i −0.881357 0.881357i
\(597\) 10.1436 0.415150
\(598\) 3.12436i 0.127764i
\(599\) −30.3109 + 17.5000i −1.23847 + 0.715031i −0.968781 0.247917i \(-0.920254\pi\)
−0.269688 + 0.962948i \(0.586921\pi\)
\(600\) −22.3923 + 6.00000i −0.914162 + 0.244949i
\(601\) 30.2321 + 17.4545i 1.23319 + 0.711983i 0.967694 0.252128i \(-0.0811305\pi\)
0.265497 + 0.964112i \(0.414464\pi\)
\(602\) −15.6865 + 27.1699i −0.639335 + 1.10736i
\(603\) 0.990381 3.69615i 0.0403314 0.150519i
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) 5.36603 1.43782i 0.218160 0.0584558i
\(606\) 4.73205 0.192226
\(607\) −4.59808 7.96410i −0.186630 0.323253i 0.757494 0.652842i \(-0.226423\pi\)
−0.944125 + 0.329589i \(0.893090\pi\)
\(608\) 12.0000 20.7846i 0.486664 0.842927i
\(609\) 3.69615 13.7942i 0.149776 0.558970i
\(610\) 10.5622 + 2.83013i 0.427650 + 0.114588i
\(611\) 30.9545 + 30.9545i 1.25228 + 1.25228i
\(612\) −20.7846 12.0000i −0.840168 0.485071i
\(613\) −7.58846 + 7.58846i −0.306495 + 0.306495i −0.843548 0.537053i \(-0.819537\pi\)
0.537053 + 0.843548i \(0.319537\pi\)
\(614\) −5.92820 10.2679i −0.239243 0.414381i
\(615\) −2.59808 9.69615i −0.104765 0.390987i
\(616\) 3.12436 1.80385i 0.125884 0.0726791i
\(617\) 8.08846 4.66987i 0.325629 0.188002i −0.328270 0.944584i \(-0.606466\pi\)
0.653899 + 0.756582i \(0.273132\pi\)
\(618\) −1.31347 4.90192i −0.0528354 0.197184i
\(619\) 8.86603 + 33.0885i 0.356356 + 1.32994i 0.878770 + 0.477246i \(0.158365\pi\)
−0.522414 + 0.852692i \(0.674969\pi\)
\(620\) −0.320508 + 1.19615i −0.0128719 + 0.0480386i
\(621\) 1.20577 + 2.08846i 0.0483859 + 0.0838069i
\(622\) 42.8827 11.4904i 1.71944 0.460722i
\(623\) −14.6077 + 25.3013i −0.585245 + 1.01367i
\(624\) 8.53590 + 31.8564i 0.341709 + 1.27528i
\(625\) 10.5263 + 18.2321i 0.421051 + 0.729282i
\(626\) −9.05256 9.05256i −0.361813 0.361813i
\(627\) −3.29423 1.90192i −0.131559 0.0759555i
\(628\) −1.26795 + 1.26795i −0.0505967 + 0.0505967i
\(629\) −30.9282 + 30.9282i −1.23319 + 1.23319i
\(630\) 2.70577 + 4.68653i 0.107801 + 0.186716i
\(631\) 32.2487i 1.28380i −0.766788 0.641900i \(-0.778146\pi\)
0.766788 0.641900i \(-0.221854\pi\)
\(632\) 4.73205 1.26795i 0.188231 0.0504363i
\(633\) 3.40192 + 0.911543i 0.135214 + 0.0362306i
\(634\) 2.98076 0.118381
\(635\) −10.1962 2.73205i −0.404622 0.108418i
\(636\) −2.87564 10.7321i −0.114027 0.425553i
\(637\) 4.26795 1.14359i 0.169102 0.0453108i
\(638\) −0.633975 2.36603i −0.0250993 0.0936718i
\(639\) 32.7846i 1.29694i
\(640\) −2.92820 + 5.07180i −0.115747 + 0.200480i
\(641\) 5.76795 9.99038i 0.227820 0.394596i −0.729342 0.684150i \(-0.760173\pi\)
0.957162 + 0.289553i \(0.0935068\pi\)
\(642\) 19.7321 + 34.1769i 0.778762 + 1.34886i
\(643\) −0.277568 + 1.03590i −0.0109462 + 0.0408518i −0.971183 0.238335i \(-0.923398\pi\)
0.960237 + 0.279187i \(0.0900650\pi\)
\(644\) −1.98076 1.14359i −0.0780530 0.0450639i
\(645\) −8.07180 −0.317827
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 46.3923i 1.82387i 0.410335 + 0.911935i \(0.365412\pi\)
−0.410335 + 0.911935i \(0.634588\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 3.00000i 0.117760i
\(650\) 27.5885 15.9282i 1.08211 0.624756i
\(651\) −5.10512 −0.200085
\(652\) 8.73205 + 32.5885i 0.341974 + 1.27626i
\(653\) 5.71539 21.3301i 0.223661 0.834712i −0.759276 0.650768i \(-0.774447\pi\)
0.982937 0.183944i \(-0.0588865\pi\)
\(654\) 5.19615 3.00000i 0.203186 0.117309i
\(655\) −3.13397 + 5.42820i −0.122455 + 0.212097i
\(656\) 38.7846 + 22.3923i 1.51428 + 0.874273i
\(657\) 1.60770i 0.0627222i
\(658\) −30.9545 + 8.29423i −1.20673 + 0.323343i
\(659\) 8.33013 2.23205i 0.324496 0.0869484i −0.0928939 0.995676i \(-0.529612\pi\)
0.417390 + 0.908728i \(0.362945\pi\)
\(660\) 0.803848 + 0.464102i 0.0312897 + 0.0180651i
\(661\) −15.6962 4.20577i −0.610510 0.163586i −0.0596998 0.998216i \(-0.519014\pi\)
−0.550810 + 0.834631i \(0.685681\pi\)
\(662\) 38.5885i 1.49978i
\(663\) 31.8564 + 8.53590i 1.23720 + 0.331507i
\(664\) −29.9090 17.2679i −1.16069 0.670126i
\(665\) 5.41154i 0.209851i
\(666\) 40.1769 23.1962i 1.55682 0.898833i
\(667\) −1.09808 + 1.09808i −0.0425177 + 0.0425177i
\(668\) −19.0718 −0.737910
\(669\) 23.3827 + 13.5000i 0.904027 + 0.521940i
\(670\) −0.660254 + 0.660254i −0.0255078 + 0.0255078i
\(671\) 3.86603 + 6.69615i 0.149246 + 0.258502i
\(672\) −23.3205 6.24871i −0.899608 0.241049i
\(673\) 3.83975 6.65064i 0.148011 0.256363i −0.782481 0.622674i \(-0.786046\pi\)
0.930492 + 0.366311i \(0.119379\pi\)
\(674\) 0.509619 + 1.90192i 0.0196298 + 0.0732594i
\(675\) 12.2942 21.2942i 0.473205 0.819615i
\(676\) −9.66025 16.7321i −0.371548 0.643540i
\(677\) −12.2321 45.6506i −0.470116 1.75450i −0.639345 0.768920i \(-0.720795\pi\)
0.169229 0.985577i \(-0.445872\pi\)
\(678\) −13.0981 + 3.50962i −0.503029 + 0.134786i
\(679\) 2.13397 1.23205i 0.0818944 0.0472818i
\(680\) 2.92820 + 5.07180i 0.112291 + 0.194495i
\(681\) −8.00962 29.8923i −0.306929 1.14548i
\(682\) −0.758330 + 0.437822i −0.0290380 + 0.0167651i
\(683\) −5.39230 + 5.39230i −0.206331 + 0.206331i −0.802706 0.596375i \(-0.796607\pi\)
0.596375 + 0.802706i \(0.296607\pi\)
\(684\) 6.58846 + 24.5885i 0.251916 + 0.940163i
\(685\) 6.09808 + 6.09808i 0.232996 + 0.232996i
\(686\) −7.15064 + 26.6865i −0.273013 + 1.01890i
\(687\) 4.37564 16.3301i 0.166941 0.623033i
\(688\) 25.4641 25.4641i 0.970810 0.970810i
\(689\) 7.63397 + 13.2224i 0.290831 + 0.503735i
\(690\) 0.588457i 0.0224022i
\(691\) −18.5263 + 4.96410i −0.704773 + 0.188843i −0.593367 0.804932i \(-0.702202\pi\)
−0.111405 + 0.993775i \(0.535535\pi\)
\(692\) −17.9282 4.80385i −0.681528 0.182615i
\(693\) −0.990381 + 3.69615i −0.0376215 + 0.140405i
\(694\) 24.7583 + 14.2942i 0.939813 + 0.542601i
\(695\) 2.00962 + 1.16025i 0.0762292 + 0.0440109i
\(696\) −8.19615 + 14.1962i −0.310674 + 0.538104i
\(697\) 38.7846 22.3923i 1.46907 0.848169i
\(698\) 11.6603 0.441347
\(699\) 39.7128 1.50208
\(700\) 23.3205i 0.881432i
\(701\) −21.0526 21.0526i −0.795144 0.795144i 0.187181 0.982325i \(-0.440065\pi\)
−0.982325 + 0.187181i \(0.940065\pi\)
\(702\) −30.2942 17.4904i −1.14338 0.660132i
\(703\) 46.3923 1.74972
\(704\) −4.00000 + 1.07180i −0.150756 + 0.0403949i
\(705\) −5.83013 5.83013i −0.219575 0.219575i
\(706\) −30.4641 + 30.4641i −1.14653 + 1.14653i
\(707\) 1.23205 4.59808i 0.0463360 0.172928i
\(708\) 14.1962 14.1962i 0.533524 0.533524i
\(709\) 10.7487 + 40.1147i 0.403676 + 1.50654i 0.806484 + 0.591256i \(0.201368\pi\)
−0.402808 + 0.915285i \(0.631966\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) −2.59808 + 4.50000i −0.0974355 + 0.168763i
\(712\) 23.7128 23.7128i 0.888675 0.888675i
\(713\) 0.480762 + 0.277568i 0.0180047 + 0.0103950i
\(714\) −17.0718 + 17.0718i −0.638896 + 0.638896i
\(715\) −1.23205 0.330127i −0.0460761 0.0123461i
\(716\) 5.80385 + 21.6603i 0.216900 + 0.809482i
\(717\) −16.7942 + 9.69615i −0.627192 + 0.362109i
\(718\) 5.51666 20.5885i 0.205880 0.768354i
\(719\) 23.3205 0.869708 0.434854 0.900501i \(-0.356800\pi\)
0.434854 + 0.900501i \(0.356800\pi\)
\(720\) −1.60770 6.00000i −0.0599153 0.223607i
\(721\) −5.10512 −0.190125
\(722\) 0.366025 1.36603i 0.0136221 0.0508382i
\(723\) 18.6962 + 10.7942i 0.695317 + 0.401442i
\(724\) −11.6603 + 3.12436i −0.433350 + 0.116116i
\(725\) 15.2942 + 4.09808i 0.568013 + 0.152199i
\(726\) −6.80385 25.3923i −0.252514 0.942397i
\(727\) 9.06218 + 5.23205i 0.336098 + 0.194046i 0.658545 0.752541i \(-0.271172\pi\)
−0.322447 + 0.946587i \(0.604506\pi\)
\(728\) 33.1769 1.22962
\(729\) −27.0000 −1.00000
\(730\) −0.196152 + 0.339746i −0.00725993 + 0.0125746i
\(731\) −9.32051 34.7846i −0.344731 1.28656i
\(732\) 13.3923 49.9808i 0.494994 1.84734i
\(733\) −7.37564 + 27.5263i −0.272426 + 1.01671i 0.685121 + 0.728429i \(0.259749\pi\)
−0.957547 + 0.288277i \(0.906917\pi\)
\(734\) 30.9090 30.9090i 1.14087 1.14087i
\(735\) −0.803848 + 0.215390i −0.0296504 + 0.00794479i
\(736\) 1.85641 + 1.85641i 0.0684280 + 0.0684280i
\(737\) −0.660254 −0.0243208
\(738\) −45.8827 + 12.2942i −1.68897 + 0.452557i
\(739\) −29.7321 29.7321i −1.09371 1.09371i −0.995129 0.0985823i \(-0.968569\pi\)
−0.0985823 0.995129i \(-0.531431\pi\)
\(740\) −11.3205 −0.416150
\(741\) −17.4904 30.2942i −0.642525 1.11289i
\(742\) −11.1769 −0.410317
\(743\) 25.1147 14.5000i 0.921370 0.531953i 0.0372984 0.999304i \(-0.488125\pi\)
0.884072 + 0.467351i \(0.154791\pi\)
\(744\) 5.66025 + 1.51666i 0.207515 + 0.0556035i
\(745\) −6.82051 3.93782i −0.249884 0.144271i
\(746\) −17.0263 9.83013i −0.623376 0.359907i
\(747\) 35.3827 9.48076i 1.29458 0.346883i
\(748\) −1.07180 + 4.00000i −0.0391888 + 0.146254i
\(749\) 38.3468 10.2750i 1.40116 0.375440i
\(750\) −10.6865 + 6.16987i −0.390217 + 0.225292i
\(751\) 4.72243 + 8.17949i 0.172324 + 0.298474i 0.939232 0.343283i \(-0.111539\pi\)
−0.766908 + 0.641757i \(0.778206\pi\)
\(752\) 36.7846 1.34140
\(753\) −12.8038 12.8038i −0.466598 0.466598i
\(754\) 5.83013 21.7583i 0.212321 0.792392i
\(755\) −2.56218 2.56218i −0.0932472 0.0932472i
\(756\) 22.1769 12.8038i 0.806567 0.465671i
\(757\) 8.46410 8.46410i 0.307633 0.307633i −0.536358 0.843991i \(-0.680200\pi\)
0.843991 + 0.536358i \(0.180200\pi\)
\(758\) 27.0000 15.5885i 0.980684 0.566198i
\(759\) 0.294229 0.294229i 0.0106798 0.0106798i
\(760\) 1.60770 6.00000i 0.0583172 0.217643i
\(761\) −25.2846 + 14.5981i −0.916566 + 0.529180i −0.882538 0.470241i \(-0.844167\pi\)
−0.0340283 + 0.999421i \(0.510834\pi\)
\(762\) −12.9282 + 48.2487i −0.468339 + 1.74787i
\(763\) −1.56218 5.83013i −0.0565546 0.211065i
\(764\) 22.8564 13.1962i 0.826916 0.477420i
\(765\) −6.00000 1.60770i −0.216930 0.0581263i
\(766\) 9.02628 + 33.6865i 0.326133 + 1.21714i
\(767\) −13.7942 + 23.8923i −0.498081 + 0.862701i
\(768\) 24.0000 + 13.8564i 0.866025 + 0.500000i
\(769\) −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) 0.660254 0.660254i 0.0237939 0.0237939i
\(771\) −15.4808 + 8.93782i −0.557526 + 0.321888i
\(772\) 4.92820i 0.177370i
\(773\) 7.58846 7.58846i 0.272938 0.272938i −0.557344 0.830282i \(-0.688179\pi\)
0.830282 + 0.557344i \(0.188179\pi\)
\(774\) 38.1962i 1.37293i
\(775\) 5.66025i 0.203322i
\(776\) −2.73205 + 0.732051i −0.0980749 + 0.0262791i
\(777\) −12.0788 45.0788i −0.433326 1.61719i
\(778\) 11.1244i 0.398827i
\(779\) −45.8827 12.2942i −1.64392 0.440486i
\(780\) 4.26795 + 7.39230i 0.152817 + 0.264687i
\(781\) −5.46410 + 1.46410i −0.195521 + 0.0523897i
\(782\) 2.53590 0.679492i 0.0906835 0.0242986i
\(783\) −4.50000 16.7942i −0.160817 0.600177i
\(784\) 1.85641 3.21539i 0.0663002 0.114835i
\(785\) −0.232051 + 0.401924i −0.00828225 + 0.0143453i
\(786\) 25.6865 + 14.8301i 0.916208 + 0.528973i
\(787\) 9.06218 33.8205i 0.323032 1.20557i −0.593244 0.805023i \(-0.702153\pi\)
0.916276 0.400548i \(-0.131180\pi\)
\(788\) 28.5885 7.66025i 1.01842 0.272885i
\(789\) 3.40192 5.89230i 0.121112 0.209772i
\(790\) 1.09808 0.633975i 0.0390678 0.0225558i
\(791\) 13.6410i 0.485019i
\(792\) 2.19615 3.80385i 0.0780369 0.135164i
\(793\) 71.1051i 2.52502i
\(794\) −21.0526 36.4641i −0.747127 1.29406i
\(795\) −1.43782 2.49038i −0.0509943 0.0883247i
\(796\) −5.85641 + 10.1436i −0.207575 + 0.359530i
\(797\) 0.284610 1.06218i 0.0100814 0.0376243i −0.960702 0.277582i \(-0.910467\pi\)
0.970783 + 0.239958i \(0.0771336\pi\)
\(798\) 25.6077 0.906503
\(799\) 18.3923 31.8564i 0.650673 1.12700i
\(800\) 6.92820 25.8564i 0.244949 0.914162i
\(801\) 35.5692i 1.25678i
\(802\) 0.849365 + 3.16987i 0.0299921 + 0.111932i
\(803\) −0.267949 + 0.0717968i −0.00945572 + 0.00253365i
\(804\) 3.12436 + 3.12436i 0.110188 + 0.110188i
\(805\) −0.571797 0.153212i −0.0201532 0.00540003i
\(806\) −8.05256 −0.283639
\(807\) 13.3923 13.3923i 0.471431 0.471431i
\(808\) −2.73205 + 4.73205i −0.0961132 + 0.166473i
\(809\) 32.6410i 1.14760i 0.818997 + 0.573799i \(0.194531\pi\)
−0.818997 + 0.573799i \(0.805469\pi\)
\(810\) 5.70577 + 3.29423i 0.200480 + 0.115747i
\(811\) −11.5359 + 11.5359i −0.405080 + 0.405080i −0.880019 0.474939i \(-0.842470\pi\)
0.474939 + 0.880019i \(0.342470\pi\)
\(812\) 11.6603 + 11.6603i 0.409195 + 0.409195i
\(813\) 25.8564i 0.906824i
\(814\) −5.66025 5.66025i −0.198392 0.198392i
\(815\) 4.36603 + 7.56218i 0.152935 + 0.264892i
\(816\) 24.0000 13.8564i 0.840168 0.485071i
\(817\) −19.0981 + 33.0788i −0.668157 + 1.15728i
\(818\) −7.29423 + 1.95448i −0.255037 + 0.0683369i
\(819\) −24.8827 + 24.8827i −0.869471 + 0.869471i
\(820\) 11.1962 + 3.00000i 0.390987 + 0.104765i
\(821\) 5.01666 + 18.7224i 0.175083 + 0.653417i 0.996538 + 0.0831439i \(0.0264961\pi\)
−0.821455 + 0.570273i \(0.806837\pi\)
\(822\) 28.8564 28.8564i 1.00648 1.00648i
\(823\) 6.65064 3.83975i 0.231827 0.133845i −0.379588 0.925156i \(-0.623934\pi\)
0.611414 + 0.791311i \(0.290601\pi\)
\(824\) 5.66025 + 1.51666i 0.197184 + 0.0528354i
\(825\) −4.09808 1.09808i −0.142677 0.0382301i
\(826\) −10.0981 17.4904i −0.351357 0.608568i
\(827\) −10.6077 + 10.6077i −0.368866 + 0.368866i −0.867063 0.498198i \(-0.833995\pi\)
0.498198 + 0.867063i \(0.333995\pi\)
\(828\) −2.78461 −0.0967719
\(829\) −17.7321 17.7321i −0.615860 0.615860i 0.328607 0.944467i \(-0.393421\pi\)
−0.944467 + 0.328607i \(0.893421\pi\)
\(830\) −8.63397 2.31347i −0.299690 0.0803016i
\(831\) −23.8923 + 6.40192i −0.828815 + 0.222080i
\(832\) −36.7846 9.85641i −1.27528 0.341709i
\(833\) −1.85641 3.21539i −0.0643207 0.111407i
\(834\) 5.49038 9.50962i 0.190116 0.329291i
\(835\) −4.76795 + 1.27757i −0.165002 + 0.0442121i
\(836\) 3.80385 2.19615i 0.131559 0.0759555i
\(837\) −5.38269 + 3.10770i −0.186053 + 0.107418i
\(838\) −1.43782 + 2.49038i −0.0496687 + 0.0860288i
\(839\) −29.2583 16.8923i −1.01011 0.583187i −0.0988859 0.995099i \(-0.531528\pi\)
−0.911224 + 0.411912i \(0.864861\pi\)
\(840\) −6.24871 −0.215601
\(841\) −15.4186 + 8.90192i −0.531675 + 0.306963i
\(842\) 15.8038i 0.544637i
\(843\) 16.9641 29.3827i 0.584275 1.01199i
\(844\) −2.87564 + 2.87564i −0.0989838 + 0.0989838i
\(845\) −3.53590 3.53590i −0.121639 0.121639i
\(846\) −27.5885 + 27.5885i −0.948511 + 0.948511i
\(847\) −26.4449 −0.908656
\(848\) 12.3923 + 3.32051i 0.425553 + 0.114027i
\(849\) −7.20577 + 26.8923i −0.247301 + 0.922942i
\(850\) −18.9282 18.9282i −0.649232 0.649232i
\(851\) −1.31347 + 4.90192i −0.0450251 + 0.168036i
\(852\) 32.7846 + 18.9282i 1.12318 + 0.648470i
\(853\) −2.69615 10.0622i −0.0923145 0.344522i 0.904284 0.426931i \(-0.140405\pi\)
−0.996599 + 0.0824088i \(0.973739\pi\)
\(854\) −45.0788 26.0263i −1.54257 0.890601i
\(855\) 3.29423 + 5.70577i 0.112660 + 0.195133i
\(856\) −45.5692 −1.55752
\(857\) −42.3564 24.4545i −1.44687 0.835349i −0.448574 0.893746i \(-0.648068\pi\)
−0.998293 + 0.0583966i \(0.981401\pi\)
\(858\) −1.56218 + 5.83013i −0.0533319 + 0.199037i
\(859\) 16.7942 + 4.50000i 0.573012 + 0.153538i 0.533677 0.845688i \(-0.320810\pi\)
0.0393342 + 0.999226i \(0.487476\pi\)
\(860\) 4.66025 8.07180i 0.158913 0.275246i
\(861\) 47.7846i 1.62850i
\(862\) 42.7846 + 11.4641i 1.45725 + 0.390469i
\(863\) −33.4641 −1.13913 −0.569566 0.821946i \(-0.692889\pi\)
−0.569566 + 0.821946i \(0.692889\pi\)
\(864\) −28.3923 + 7.60770i −0.965926 + 0.258819i
\(865\) −4.80385 −0.163336
\(866\) 33.3205 + 8.92820i 1.13228 + 0.303393i
\(867\) 1.73205i 0.0588235i
\(868\) 2.94744 5.10512i 0.100043 0.173279i
\(869\) 0.866025 + 0.232051i 0.0293779 + 0.00787178i
\(870\) −1.09808 + 4.09808i −0.0372283 + 0.138938i
\(871\) −5.25833 3.03590i −0.178172 0.102867i
\(872\) 6.92820i 0.234619i
\(873\) 1.50000 2.59808i 0.0507673 0.0879316i
\(874\) −2.41154 1.39230i −0.0815716 0.0470954i
\(875\) 3.21281 + 11.9904i 0.108613 + 0.405349i
\(876\) 1.60770 + 0.928203i 0.0543190 + 0.0313611i
\(877\) −8.94486 + 33.3827i −0.302047 + 1.12725i 0.633411 + 0.773815i \(0.281654\pi\)
−0.935458 + 0.353438i \(0.885013\pi\)
\(878\) −20.8564 20.8564i −0.703870 0.703870i
\(879\) −6.69615 + 24.9904i −0.225856 + 0.842905i
\(880\) −0.928203 + 0.535898i −0.0312897 + 0.0180651i
\(881\) −3.32051 −0.111871 −0.0559354 0.998434i \(-0.517814\pi\)
−0.0559354 + 0.998434i \(0.517814\pi\)
\(882\) 1.01924 + 3.80385i 0.0343195 + 0.128082i
\(883\) −3.00000 3.00000i −0.100958 0.100958i 0.654824 0.755782i \(-0.272743\pi\)
−0.755782 + 0.654824i \(0.772743\pi\)
\(884\) −26.9282 + 26.9282i −0.905693 + 0.905693i
\(885\) 2.59808 4.50000i 0.0873334 0.151266i
\(886\) 23.6603i 0.794882i
\(887\) −21.0622 + 12.1603i −0.707199 + 0.408301i −0.810023 0.586398i \(-0.800545\pi\)
0.102824 + 0.994700i \(0.467212\pi\)
\(888\) 53.5692i 1.79767i
\(889\) 43.5167 + 25.1244i 1.45950 + 0.842644i
\(890\) 4.33975 7.51666i 0.145469 0.251959i
\(891\) 1.20577 + 4.50000i 0.0403949 + 0.150756i
\(892\) −27.0000 + 15.5885i −0.904027 + 0.521940i
\(893\) −37.6865 + 10.0981i −1.26113 + 0.337919i
\(894\) −18.6340 + 32.2750i −0.623213 + 1.07944i
\(895\) 2.90192 + 5.02628i 0.0970006 + 0.168010i
\(896\) 19.7128 19.7128i 0.658559 0.658559i
\(897\) 3.69615 0.990381i 0.123411 0.0330679i
\(898\) 0.928203 + 0.248711i 0.0309745 + 0.00829960i
\(899\) −2.83013 2.83013i −0.0943900 0.0943900i
\(900\) 14.1962 + 24.5885i 0.473205 + 0.819615i
\(901\) 9.07180 9.07180i 0.302225 0.302225i
\(902\) 4.09808 + 7.09808i 0.136451 + 0.236340i
\(903\) 37.1147 + 9.94486i 1.23510 + 0.330944i
\(904\) 4.05256 15.1244i 0.134786 0.503029i
\(905\) −2.70577 + 1.56218i −0.0899429 + 0.0519285i
\(906\) −12.1244 + 12.1244i −0.402805 + 0.402805i
\(907\) −3.06218 11.4282i −0.101678 0.379467i 0.896269 0.443510i \(-0.146267\pi\)
−0.997947 + 0.0640432i \(0.979600\pi\)
\(908\) 34.5167 + 9.24871i 1.14548 + 0.306929i
\(909\) −1.50000 5.59808i −0.0497519 0.185676i
\(910\) 8.29423 2.22243i 0.274951 0.0736729i
\(911\) −5.86603 + 10.1603i −0.194350 + 0.336624i −0.946687 0.322154i \(-0.895593\pi\)
0.752337 + 0.658778i \(0.228926\pi\)
\(912\) −28.3923 7.60770i −0.940163 0.251916i
\(913\) −3.16025 5.47372i −0.104589 0.181154i
\(914\) −21.9808 21.9808i −0.727059 0.727059i
\(915\) 13.3923i 0.442736i
\(916\) 13.8038 + 13.8038i 0.456092 + 0.456092i
\(917\) 21.0981 21.0981i 0.696720 0.696720i
\(918\) −7.60770 + 28.3923i −0.251091 + 0.937086i
\(919\) 43.4641i 1.43375i −0.697203 0.716874i \(-0.745572\pi\)
0.697203 0.716874i \(-0.254428\pi\)
\(920\) 0.588457 + 0.339746i 0.0194009 + 0.0112011i
\(921\) −10.2679 + 10.2679i −0.338340 + 0.338340i
\(922\) 3.26795 0.107624
\(923\) −50.2487 13.4641i −1.65396 0.443176i
\(924\) −3.12436 3.12436i −0.102784 0.102784i
\(925\) 49.9808 13.3923i 1.64336 0.440336i
\(926\) 2.43782 + 9.09808i 0.0801118 + 0.298981i
\(927\) −5.38269 + 3.10770i −0.176791 + 0.102070i
\(928\) −9.46410 16.3923i −0.310674 0.538104i
\(929\) −18.3564 + 31.7942i −0.602254 + 1.04313i 0.390225 + 0.920720i \(0.372397\pi\)
−0.992479 + 0.122415i \(0.960936\pi\)
\(930\) 1.51666 0.0497333
\(931\) −1.01924 + 3.80385i −0.0334042 + 0.124666i
\(932\) −22.9282 + 39.7128i −0.751038 + 1.30084i
\(933\) −27.1865 47.0885i −0.890047 1.54161i
\(934\) −19.7846 34.2679i −0.647372 1.12128i
\(935\) 1.07180i 0.0350515i
\(936\) 34.9808 20.1962i 1.14338 0.660132i
\(937\) 32.9282i 1.07572i 0.843035 + 0.537859i \(0.180767\pi\)
−0.843035 + 0.537859i \(0.819233\pi\)
\(938\) 3.84936 2.22243i 0.125686 0.0725650i
\(939\) −7.83975 + 13.5788i −0.255840 + 0.443129i
\(940\) 9.19615 2.46410i 0.299945 0.0803701i
\(941\) −2.91154 + 10.8660i −0.0949136 + 0.354222i −0.997006 0.0773199i \(-0.975364\pi\)
0.902093 + 0.431542i \(0.142030\pi\)
\(942\) 1.90192 + 1.09808i 0.0619680 + 0.0357773i
\(943\) 2.59808 4.50000i 0.0846050 0.146540i
\(944\) 6.00000 + 22.3923i 0.195283 + 0.728807i
\(945\) 4.68653 4.68653i 0.152453 0.152453i
\(946\) 6.36603 1.70577i 0.206977 0.0554594i
\(947\) −14.9904 + 4.01666i −0.487122 + 0.130524i −0.494017 0.869452i \(-0.664472\pi\)
0.00689497 + 0.999976i \(0.497805\pi\)
\(948\) −3.00000 5.19615i −0.0974355 0.168763i
\(949\) −2.46410 0.660254i −0.0799881 0.0214328i
\(950\) 28.3923i 0.921168i
\(951\) −0.944864 3.52628i −0.0306393 0.114347i
\(952\) −7.21539 26.9282i −0.233852 0.872748i
\(953\) 39.4641i 1.27837i −0.769054 0.639184i \(-0.779272\pi\)
0.769054 0.639184i \(-0.220728\pi\)
\(954\) −11.7846 + 6.80385i −0.381541 + 0.220283i
\(955\) 4.83013 4.83013i 0.156299 0.156299i
\(956\) 22.3923i 0.724219i
\(957\) −2.59808 + 1.50000i −0.0839839 + 0.0484881i
\(958\) 1.33975 1.33975i 0.0432852 0.0432852i
\(959\) −20.5263 35.5526i −0.662828 1.14805i
\(960\) 6.92820 + 1.85641i 0.223607 + 0.0599153i
\(961\) 14.7846 25.6077i 0.476923 0.826055i
\(962\) −19.0526 71.1051i −0.614279 2.29252i
\(963\) 34.1769 34.1769i 1.10134 1.10134i
\(964\) −21.5885 + 12.4641i −0.695317 + 0.401442i
\(965\) −0.330127 1.23205i −0.0106272 0.0396611i
\(966\) −0.725009 + 2.70577i −0.0233268 + 0.0870568i
\(967\) 14.9378 8.62436i 0.480368 0.277341i −0.240202 0.970723i \(-0.577214\pi\)
0.720570 + 0.693382i \(0.243880\pi\)
\(968\) 29.3205 + 7.85641i 0.942397 + 0.252514i
\(969\) −20.7846 + 20.7846i −0.667698 + 0.667698i
\(970\) −0.633975 + 0.366025i −0.0203557 + 0.0117524i
\(971\) 27.9808 27.9808i 0.897945 0.897945i −0.0973088 0.995254i \(-0.531023\pi\)
0.995254 + 0.0973088i \(0.0310235\pi\)
\(972\) 15.5885 27.0000i 0.500000 0.866025i
\(973\) −7.81089 7.81089i −0.250406 0.250406i
\(974\) −12.7321 + 47.5167i −0.407961 + 1.52253i
\(975\) −27.5885 27.5885i −0.883538 0.883538i
\(976\) 42.2487 + 42.2487i 1.35235 + 1.35235i
\(977\) 17.2846 + 29.9378i 0.552984 + 0.957796i 0.998057 + 0.0623018i \(0.0198441\pi\)
−0.445074 + 0.895494i \(0.646823\pi\)
\(978\) 35.7846 20.6603i 1.14427 0.660642i
\(979\) 5.92820 1.58846i 0.189466 0.0507673i
\(980\) 0.248711 0.928203i 0.00794479 0.0296504i
\(981\) −5.19615 5.19615i −0.165900 0.165900i
\(982\) −2.36603 1.36603i −0.0755029 0.0435916i
\(983\) 40.9186 + 23.6244i 1.30510 + 0.753500i 0.981274 0.192617i \(-0.0616974\pi\)
0.323826 + 0.946117i \(0.395031\pi\)
\(984\) 14.1962 52.9808i 0.452557 1.68897i
\(985\) 6.63397 3.83013i 0.211376 0.122038i
\(986\) −18.9282 −0.602797
\(987\) 19.6244 + 33.9904i 0.624650 + 1.08193i
\(988\) 40.3923 1.28505
\(989\) −2.95448 2.95448i −0.0939471 0.0939471i
\(990\) 0.294229 1.09808i 0.00935120 0.0348992i
\(991\) −23.6077 −0.749923 −0.374962 0.927040i \(-0.622344\pi\)
−0.374962 + 0.927040i \(0.622344\pi\)
\(992\) −4.78461 + 4.78461i −0.151912 + 0.151912i
\(993\) 45.6506 12.2321i 1.44868 0.388172i
\(994\) 26.9282 26.9282i 0.854111 0.854111i
\(995\) −0.784610 + 2.92820i −0.0248738 + 0.0928303i
\(996\) −10.9474 + 40.8564i −0.346883 + 1.29458i
\(997\) −2.96410 11.0622i −0.0938740 0.350343i 0.902972 0.429699i \(-0.141380\pi\)
−0.996846 + 0.0793561i \(0.974714\pi\)
\(998\) 1.83013 3.16987i 0.0579317 0.100341i
\(999\) −40.1769 40.1769i −1.27114 1.27114i
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 144.2.x.d.61.1 yes 4
3.2 odd 2 432.2.y.a.397.1 4
4.3 odd 2 576.2.bb.b.529.1 4
9.4 even 3 144.2.x.a.13.1 4
9.5 odd 6 432.2.y.d.253.1 4
12.11 even 2 1728.2.bc.b.721.1 4
16.5 even 4 144.2.x.a.133.1 yes 4
16.11 odd 4 576.2.bb.a.241.1 4
36.23 even 6 1728.2.bc.c.145.1 4
36.31 odd 6 576.2.bb.a.337.1 4
48.5 odd 4 432.2.y.d.181.1 4
48.11 even 4 1728.2.bc.c.1585.1 4
144.5 odd 12 432.2.y.a.37.1 4
144.59 even 12 1728.2.bc.b.1009.1 4
144.85 even 12 inner 144.2.x.d.85.1 yes 4
144.139 odd 12 576.2.bb.b.49.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.a.13.1 4 9.4 even 3
144.2.x.a.133.1 yes 4 16.5 even 4
144.2.x.d.61.1 yes 4 1.1 even 1 trivial
144.2.x.d.85.1 yes 4 144.85 even 12 inner
432.2.y.a.37.1 4 144.5 odd 12
432.2.y.a.397.1 4 3.2 odd 2
432.2.y.d.181.1 4 48.5 odd 4
432.2.y.d.253.1 4 9.5 odd 6
576.2.bb.a.241.1 4 16.11 odd 4
576.2.bb.a.337.1 4 36.31 odd 6
576.2.bb.b.49.1 4 144.139 odd 12
576.2.bb.b.529.1 4 4.3 odd 2
1728.2.bc.b.721.1 4 12.11 even 2
1728.2.bc.b.1009.1 4 144.59 even 12
1728.2.bc.c.145.1 4 36.23 even 6
1728.2.bc.c.1585.1 4 48.11 even 4