Properties

Label 315.2.bs.d.178.1
Level $315$
Weight $2$
Character 315.178
Analytic conductor $2.515$
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] = [315,2,Mod(52,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bs (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: \(2.51528766367\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 178.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.178
Dual form 315.2.bs.d.292.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-2.23205 - 0.133975i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-2.23205 - 0.133975i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +(3.23205 - 2.86603i) q^{10} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 2.59808i) q^{12} +(-5.09808 - 1.36603i) q^{13} +(-4.59808 - 2.23205i) q^{14} +(-3.23205 - 2.13397i) q^{15} +4.46410 q^{16} +(-7.46410 + 2.00000i) q^{17} +(-5.59808 - 1.50000i) q^{18} +(1.36603 + 2.36603i) q^{19} +(-0.232051 + 3.86603i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(-3.73205 - 1.00000i) q^{22} +(3.36603 - 0.901924i) q^{23} +(-0.232051 - 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(8.83013 - 5.09808i) q^{26} +5.19615i q^{27} +(4.33013 - 1.50000i) q^{28} +(-3.40192 - 1.96410i) q^{29} +(7.33013 - 1.50000i) q^{30} -1.46410i q^{31} +(-5.36603 + 5.36603i) q^{32} +3.46410i q^{33} +(7.46410 - 12.9282i) q^{34} +(-1.59808 - 5.69615i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-0.633975 - 0.169873i) q^{37} +(-5.09808 - 1.36603i) q^{38} +(-6.46410 - 6.46410i) q^{39} +(0.767949 + 0.866025i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(-4.96410 - 7.33013i) q^{42} +(3.23205 - 0.866025i) q^{43} +(3.00000 - 1.73205i) q^{44} +(-3.00000 - 6.00000i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(5.36603 + 5.36603i) q^{47} +(6.69615 + 3.86603i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-7.59808 + 5.96410i) q^{50} +(-12.9282 - 3.46410i) q^{51} +(-2.36603 + 8.83013i) q^{52} +(3.73205 - 1.00000i) q^{53} +(-7.09808 - 7.09808i) q^{54} +(-2.00000 - 4.00000i) q^{55} +(0.598076 - 1.23205i) q^{56} +4.73205i q^{57} +(7.33013 - 1.96410i) q^{58} +15.1244 q^{59} +(-3.69615 + 5.59808i) q^{60} -2.92820i q^{61} +(2.00000 + 2.00000i) q^{62} +(-5.19615 + 6.00000i) q^{63} -5.73205i q^{64} +(11.1962 + 3.73205i) q^{65} +(-4.73205 - 4.73205i) q^{66} +(-4.46410 + 4.46410i) q^{67} +(3.46410 + 12.9282i) q^{68} +(5.83013 + 1.56218i) q^{69} +(9.96410 + 5.59808i) q^{70} +4.73205 q^{71} +(0.401924 - 1.50000i) q^{72} +(0.928203 + 3.46410i) q^{73} +(1.09808 - 0.633975i) q^{74} +(6.92820 + 5.19615i) q^{75} +(4.09808 - 2.36603i) q^{76} +(-3.46410 + 4.00000i) q^{77} +17.6603 q^{78} +4.53590i q^{79} +(-9.96410 - 0.598076i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 - 5.59808i) q^{82} +(3.03590 + 11.3301i) q^{83} +(7.79423 + 1.50000i) q^{84} +(16.9282 - 3.46410i) q^{85} +(-3.23205 + 5.59808i) q^{86} +(-3.40192 - 5.89230i) q^{87} +(0.267949 - 1.00000i) q^{88} +(7.46410 + 12.9282i) q^{89} +(12.2942 + 4.09808i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(-1.56218 - 5.83013i) q^{92} +(1.26795 - 2.19615i) q^{93} -14.6603 q^{94} +(-2.73205 - 5.46410i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(-14.5622 + 3.90192i) q^{97} +(1.59808 - 13.4282i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} - 10 q^{13} - 8 q^{14} - 6 q^{15} + 4 q^{16} - 16 q^{17} - 12 q^{18} + 2 q^{19} + 6 q^{20} - 8 q^{22} + 10 q^{23} + 6 q^{24} + 6 q^{25} + 18 q^{26} - 24 q^{29} + 12 q^{30} - 18 q^{32} + 16 q^{34} + 4 q^{35} + 18 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} + 10 q^{40} - 6 q^{42} + 6 q^{43} + 12 q^{44} - 12 q^{45} - 10 q^{46} + 18 q^{47} + 6 q^{48} - 22 q^{49} - 20 q^{50} - 24 q^{51} - 6 q^{52} + 8 q^{53} - 18 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{58} + 12 q^{59} + 6 q^{60} + 8 q^{62} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 6 q^{69} + 26 q^{70} + 12 q^{71} + 12 q^{72} - 24 q^{73} - 6 q^{74} + 6 q^{76} + 36 q^{78} - 26 q^{80} - 18 q^{81} + 6 q^{82} + 26 q^{83} + 40 q^{85} - 6 q^{86} - 24 q^{87} + 8 q^{88} + 16 q^{89} + 18 q^{90} - 4 q^{91} + 18 q^{92} + 12 q^{93} - 24 q^{94} - 4 q^{95} - 30 q^{96} - 34 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 1.36603i −0.965926 + 0.965926i −0.999438 0.0335125i \(-0.989331\pi\)
0.0335125 + 0.999438i \(0.489331\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 1.73205i 0.866025i
\(5\) −2.23205 0.133975i −0.998203 0.0599153i
\(6\) −3.23205 + 0.866025i −1.31948 + 0.353553i
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) −0.366025 0.366025i −0.129410 0.129410i
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 3.23205 2.86603i 1.02206 0.906317i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) −5.09808 1.36603i −1.41395 0.378867i −0.530618 0.847611i \(-0.678040\pi\)
−0.883334 + 0.468744i \(0.844707\pi\)
\(14\) −4.59808 2.23205i −1.22889 0.596541i
\(15\) −3.23205 2.13397i −0.834512 0.550990i
\(16\) 4.46410 1.11603
\(17\) −7.46410 + 2.00000i −1.81031 + 0.485071i −0.995509 0.0946685i \(-0.969821\pi\)
−0.814802 + 0.579740i \(0.803154\pi\)
\(18\) −5.59808 1.50000i −1.31948 0.353553i
\(19\) 1.36603 + 2.36603i 0.313388 + 0.542803i 0.979093 0.203411i \(-0.0652027\pi\)
−0.665706 + 0.746214i \(0.731869\pi\)
\(20\) −0.232051 + 3.86603i −0.0518881 + 0.864470i
\(21\) −0.866025 + 4.50000i −0.188982 + 0.981981i
\(22\) −3.73205 1.00000i −0.795676 0.213201i
\(23\) 3.36603 0.901924i 0.701865 0.188064i 0.109799 0.993954i \(-0.464979\pi\)
0.592066 + 0.805890i \(0.298313\pi\)
\(24\) −0.232051 0.866025i −0.0473672 0.176777i
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) 8.83013 5.09808i 1.73173 0.999815i
\(27\) 5.19615i 1.00000i
\(28\) 4.33013 1.50000i 0.818317 0.283473i
\(29\) −3.40192 1.96410i −0.631721 0.364725i 0.149697 0.988732i \(-0.452170\pi\)
−0.781418 + 0.624007i \(0.785503\pi\)
\(30\) 7.33013 1.50000i 1.33829 0.273861i
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) −5.36603 + 5.36603i −0.948588 + 0.948588i
\(33\) 3.46410i 0.603023i
\(34\) 7.46410 12.9282i 1.28008 2.21717i
\(35\) −1.59808 5.69615i −0.270124 0.962825i
\(36\) 4.50000 2.59808i 0.750000 0.433013i
\(37\) −0.633975 0.169873i −0.104225 0.0279269i 0.206330 0.978483i \(-0.433848\pi\)
−0.310554 + 0.950556i \(0.600515\pi\)
\(38\) −5.09808 1.36603i −0.827017 0.221599i
\(39\) −6.46410 6.46410i −1.03508 1.03508i
\(40\) 0.767949 + 0.866025i 0.121423 + 0.136931i
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) −4.96410 7.33013i −0.765978 1.13106i
\(43\) 3.23205 0.866025i 0.492883 0.132068i −0.00381197 0.999993i \(-0.501213\pi\)
0.496695 + 0.867925i \(0.334547\pi\)
\(44\) 3.00000 1.73205i 0.452267 0.261116i
\(45\) −3.00000 6.00000i −0.447214 0.894427i
\(46\) −3.36603 + 5.83013i −0.496293 + 0.859605i
\(47\) 5.36603 + 5.36603i 0.782715 + 0.782715i 0.980288 0.197573i \(-0.0633059\pi\)
−0.197573 + 0.980288i \(0.563306\pi\)
\(48\) 6.69615 + 3.86603i 0.966506 + 0.558013i
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) −7.59808 + 5.96410i −1.07453 + 0.843451i
\(51\) −12.9282 3.46410i −1.81031 0.485071i
\(52\) −2.36603 + 8.83013i −0.328109 + 1.22452i
\(53\) 3.73205 1.00000i 0.512637 0.137361i 0.00677809 0.999977i \(-0.497842\pi\)
0.505859 + 0.862616i \(0.331176\pi\)
\(54\) −7.09808 7.09808i −0.965926 0.965926i
\(55\) −2.00000 4.00000i −0.269680 0.539360i
\(56\) 0.598076 1.23205i 0.0799213 0.164640i
\(57\) 4.73205i 0.626775i
\(58\) 7.33013 1.96410i 0.962493 0.257899i
\(59\) 15.1244 1.96902 0.984512 0.175319i \(-0.0560957\pi\)
0.984512 + 0.175319i \(0.0560957\pi\)
\(60\) −3.69615 + 5.59808i −0.477171 + 0.722709i
\(61\) 2.92820i 0.374918i −0.982272 0.187459i \(-0.939975\pi\)
0.982272 0.187459i \(-0.0600252\pi\)
\(62\) 2.00000 + 2.00000i 0.254000 + 0.254000i
\(63\) −5.19615 + 6.00000i −0.654654 + 0.755929i
\(64\) 5.73205i 0.716506i
\(65\) 11.1962 + 3.73205i 1.38871 + 0.462904i
\(66\) −4.73205 4.73205i −0.582475 0.582475i
\(67\) −4.46410 + 4.46410i −0.545377 + 0.545377i −0.925100 0.379723i \(-0.876019\pi\)
0.379723 + 0.925100i \(0.376019\pi\)
\(68\) 3.46410 + 12.9282i 0.420084 + 1.56777i
\(69\) 5.83013 + 1.56218i 0.701865 + 0.188064i
\(70\) 9.96410 + 5.59808i 1.19094 + 0.669098i
\(71\) 4.73205 0.561591 0.280796 0.959768i \(-0.409402\pi\)
0.280796 + 0.959768i \(0.409402\pi\)
\(72\) 0.401924 1.50000i 0.0473672 0.176777i
\(73\) 0.928203 + 3.46410i 0.108638 + 0.405442i 0.998732 0.0503336i \(-0.0160285\pi\)
−0.890094 + 0.455776i \(0.849362\pi\)
\(74\) 1.09808 0.633975i 0.127649 0.0736980i
\(75\) 6.92820 + 5.19615i 0.800000 + 0.600000i
\(76\) 4.09808 2.36603i 0.470082 0.271402i
\(77\) −3.46410 + 4.00000i −0.394771 + 0.455842i
\(78\) 17.6603 1.99963
\(79\) 4.53590i 0.510328i 0.966898 + 0.255164i \(0.0821295\pi\)
−0.966898 + 0.255164i \(0.917870\pi\)
\(80\) −9.96410 0.598076i −1.11402 0.0668670i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 1.50000 5.59808i 0.165647 0.618204i
\(83\) 3.03590 + 11.3301i 0.333233 + 1.24364i 0.905772 + 0.423765i \(0.139292\pi\)
−0.572539 + 0.819878i \(0.694041\pi\)
\(84\) 7.79423 + 1.50000i 0.850420 + 0.163663i
\(85\) 16.9282 3.46410i 1.83612 0.375735i
\(86\) −3.23205 + 5.59808i −0.348521 + 0.603656i
\(87\) −3.40192 5.89230i −0.364725 0.631721i
\(88\) 0.267949 1.00000i 0.0285635 0.106600i
\(89\) 7.46410 + 12.9282i 0.791193 + 1.37039i 0.925229 + 0.379410i \(0.123873\pi\)
−0.134035 + 0.990977i \(0.542794\pi\)
\(90\) 12.2942 + 4.09808i 1.29593 + 0.431975i
\(91\) −1.00000 13.9282i −0.104828 1.46007i
\(92\) −1.56218 5.83013i −0.162868 0.607833i
\(93\) 1.26795 2.19615i 0.131480 0.227730i
\(94\) −14.6603 −1.51209
\(95\) −2.73205 5.46410i −0.280302 0.560605i
\(96\) −12.6962 + 3.40192i −1.29580 + 0.347207i
\(97\) −14.5622 + 3.90192i −1.47857 + 0.396180i −0.905859 0.423580i \(-0.860773\pi\)
−0.572707 + 0.819760i \(0.694107\pi\)
\(98\) 1.59808 13.4282i 0.161430 1.35645i
\(99\) −3.00000 + 5.19615i −0.301511 + 0.522233i
\(100\) 1.03590 8.59808i 0.103590 0.859808i
\(101\) 3.23205 1.86603i 0.321601 0.185676i −0.330505 0.943804i \(-0.607219\pi\)
0.652106 + 0.758128i \(0.273886\pi\)
\(102\) 22.3923 12.9282i 2.21717 1.28008i
\(103\) 2.33013 + 8.69615i 0.229594 + 0.856857i 0.980512 + 0.196461i \(0.0629450\pi\)
−0.750917 + 0.660396i \(0.770388\pi\)
\(104\) 1.36603 + 2.36603i 0.133950 + 0.232008i
\(105\) 2.53590 9.92820i 0.247478 0.968893i
\(106\) −3.73205 + 6.46410i −0.362489 + 0.627849i
\(107\) 11.4282 + 3.06218i 1.10481 + 0.296032i 0.764720 0.644362i \(-0.222877\pi\)
0.340086 + 0.940394i \(0.389544\pi\)
\(108\) 9.00000 0.866025
\(109\) 5.42820 + 3.13397i 0.519928 + 0.300180i 0.736905 0.675996i \(-0.236286\pi\)
−0.216977 + 0.976177i \(0.569620\pi\)
\(110\) 8.19615 + 2.73205i 0.781472 + 0.260491i
\(111\) −0.803848 0.803848i −0.0762978 0.0762978i
\(112\) 3.86603 + 11.1603i 0.365305 + 1.05454i
\(113\) 2.53590 9.46410i 0.238557 0.890308i −0.737956 0.674849i \(-0.764209\pi\)
0.976513 0.215459i \(-0.0691246\pi\)
\(114\) −6.46410 6.46410i −0.605419 0.605419i
\(115\) −7.63397 + 1.56218i −0.711872 + 0.145674i
\(116\) −3.40192 + 5.89230i −0.315861 + 0.547087i
\(117\) −4.09808 15.2942i −0.378867 1.41395i
\(118\) −20.6603 + 20.6603i −1.90193 + 1.90193i
\(119\) −11.4641 16.9282i −1.05091 1.55181i
\(120\) 0.401924 + 1.96410i 0.0366905 + 0.179297i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 4.00000 + 4.00000i 0.362143 + 0.362143i
\(123\) −5.19615 −0.468521
\(124\) −2.53590 −0.227730
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) −1.09808 15.2942i −0.0978244 1.36252i
\(127\) 9.63397 9.63397i 0.854877 0.854877i −0.135852 0.990729i \(-0.543377\pi\)
0.990729 + 0.135852i \(0.0433772\pi\)
\(128\) −2.90192 2.90192i −0.256496 0.256496i
\(129\) 5.59808 + 1.50000i 0.492883 + 0.132068i
\(130\) −20.3923 + 10.1962i −1.78852 + 0.894262i
\(131\) −4.39230 2.53590i −0.383757 0.221562i 0.295694 0.955283i \(-0.404449\pi\)
−0.679452 + 0.733720i \(0.737782\pi\)
\(132\) 6.00000 0.522233
\(133\) −4.73205 + 5.46410i −0.410321 + 0.473798i
\(134\) 12.1962i 1.05359i
\(135\) 0.696152 11.5981i 0.0599153 0.998203i
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) −1.36603 0.366025i −0.116707 0.0312717i 0.199993 0.979797i \(-0.435908\pi\)
−0.316700 + 0.948526i \(0.602575\pi\)
\(138\) −10.0981 + 5.83013i −0.859605 + 0.496293i
\(139\) −6.29423 10.9019i −0.533870 0.924689i −0.999217 0.0395611i \(-0.987404\pi\)
0.465348 0.885128i \(-0.345929\pi\)
\(140\) −9.86603 + 2.76795i −0.833831 + 0.233934i
\(141\) 3.40192 + 12.6962i 0.286494 + 1.06921i
\(142\) −6.46410 + 6.46410i −0.542455 + 0.542455i
\(143\) −2.73205 10.1962i −0.228466 0.852645i
\(144\) 6.69615 + 11.5981i 0.558013 + 0.966506i
\(145\) 7.33013 + 4.83975i 0.608734 + 0.401919i
\(146\) −6.00000 3.46410i −0.496564 0.286691i
\(147\) −12.0000 + 1.73205i −0.989743 + 0.142857i
\(148\) −0.294229 + 1.09808i −0.0241854 + 0.0902613i
\(149\) −13.3923 7.73205i −1.09714 0.633434i −0.161672 0.986845i \(-0.551689\pi\)
−0.935468 + 0.353410i \(0.885022\pi\)
\(150\) −16.5622 + 2.36603i −1.35230 + 0.193185i
\(151\) 8.83013 + 15.2942i 0.718586 + 1.24463i 0.961560 + 0.274594i \(0.0885435\pi\)
−0.242975 + 0.970033i \(0.578123\pi\)
\(152\) 0.366025 1.36603i 0.0296886 0.110799i
\(153\) −16.3923 16.3923i −1.32524 1.32524i
\(154\) −0.732051 10.1962i −0.0589903 0.821629i
\(155\) −0.196152 + 3.26795i −0.0157553 + 0.262488i
\(156\) −11.1962 + 11.1962i −0.896410 + 0.896410i
\(157\) −7.19615 7.19615i −0.574315 0.574315i 0.359016 0.933331i \(-0.383112\pi\)
−0.933331 + 0.359016i \(0.883112\pi\)
\(158\) −6.19615 6.19615i −0.492939 0.492939i
\(159\) 6.46410 + 1.73205i 0.512637 + 0.137361i
\(160\) 12.6962 11.2583i 1.00372 0.890049i
\(161\) 5.16987 + 7.63397i 0.407443 + 0.601641i
\(162\) −4.50000 16.7942i −0.353553 1.31948i
\(163\) −2.49038 + 9.29423i −0.195062 + 0.727980i 0.797189 + 0.603730i \(0.206319\pi\)
−0.992251 + 0.124251i \(0.960347\pi\)
\(164\) 2.59808 + 4.50000i 0.202876 + 0.351391i
\(165\) 0.464102 7.73205i 0.0361303 0.601939i
\(166\) −19.6244 11.3301i −1.52315 0.879388i
\(167\) 0.901924 3.36603i 0.0697930 0.260471i −0.922209 0.386691i \(-0.873618\pi\)
0.992002 + 0.126220i \(0.0402846\pi\)
\(168\) 1.96410 1.33013i 0.151534 0.102622i
\(169\) 12.8660 + 7.42820i 0.989694 + 0.571400i
\(170\) −18.3923 + 27.8564i −1.41063 + 2.13649i
\(171\) −4.09808 + 7.09808i −0.313388 + 0.542803i
\(172\) −1.50000 5.59808i −0.114374 0.426849i
\(173\) 16.0000 16.0000i 1.21646 1.21646i 0.247593 0.968864i \(-0.420360\pi\)
0.968864 0.247593i \(-0.0796397\pi\)
\(174\) 12.6962 + 3.40192i 0.962493 + 0.257899i
\(175\) 2.80385 + 12.9282i 0.211951 + 0.977280i
\(176\) 4.46410 + 7.73205i 0.336494 + 0.582825i
\(177\) 22.6865 + 13.0981i 1.70522 + 0.984512i
\(178\) −27.8564 7.46410i −2.08793 0.559458i
\(179\) −1.09808 0.633975i −0.0820741 0.0473855i 0.458401 0.888745i \(-0.348422\pi\)
−0.540475 + 0.841360i \(0.681756\pi\)
\(180\) −10.3923 + 5.19615i −0.774597 + 0.387298i
\(181\) 20.1244i 1.49583i −0.663794 0.747916i \(-0.731055\pi\)
0.663794 0.747916i \(-0.268945\pi\)
\(182\) 20.3923 + 17.6603i 1.51158 + 1.30907i
\(183\) 2.53590 4.39230i 0.187459 0.324689i
\(184\) −1.56218 0.901924i −0.115165 0.0664907i
\(185\) 1.39230 + 0.464102i 0.102364 + 0.0341214i
\(186\) 1.26795 + 4.73205i 0.0929705 + 0.346971i
\(187\) −10.9282 10.9282i −0.799149 0.799149i
\(188\) 9.29423 9.29423i 0.677851 0.677851i
\(189\) −12.9904 + 4.50000i −0.944911 + 0.327327i
\(190\) 11.1962 + 3.73205i 0.812254 + 0.270751i
\(191\) −9.80385 −0.709382 −0.354691 0.934984i \(-0.615414\pi\)
−0.354691 + 0.934984i \(0.615414\pi\)
\(192\) 4.96410 8.59808i 0.358253 0.620513i
\(193\) 0.196152 + 0.196152i 0.0141194 + 0.0141194i 0.714131 0.700012i \(-0.246822\pi\)
−0.700012 + 0.714131i \(0.746822\pi\)
\(194\) 14.5622 25.2224i 1.04550 1.81087i
\(195\) 13.5622 + 15.2942i 0.971208 + 1.09524i
\(196\) 7.50000 + 9.52628i 0.535714 + 0.680449i
\(197\) 4.00000 4.00000i 0.284988 0.284988i −0.550106 0.835095i \(-0.685413\pi\)
0.835095 + 0.550106i \(0.185413\pi\)
\(198\) −3.00000 11.1962i −0.213201 0.795676i
\(199\) −2.19615 + 3.80385i −0.155681 + 0.269648i −0.933307 0.359080i \(-0.883091\pi\)
0.777626 + 0.628727i \(0.216424\pi\)
\(200\) −1.59808 2.03590i −0.113001 0.143960i
\(201\) −10.5622 + 2.83013i −0.744999 + 0.199622i
\(202\) −1.86603 + 6.96410i −0.131293 + 0.489992i
\(203\) 1.96410 10.2058i 0.137853 0.716305i
\(204\) −6.00000 + 22.3923i −0.420084 + 1.56777i
\(205\) 6.00000 3.00000i 0.419058 0.209529i
\(206\) −15.0622 8.69615i −1.04943 0.605890i
\(207\) 7.39230 + 7.39230i 0.513801 + 0.513801i
\(208\) −22.7583 6.09808i −1.57801 0.422826i
\(209\) −2.73205 + 4.73205i −0.188980 + 0.327323i
\(210\) 10.0981 + 17.0263i 0.696833 + 1.17492i
\(211\) −6.53590 11.3205i −0.449950 0.779336i 0.548432 0.836195i \(-0.315225\pi\)
−0.998382 + 0.0568590i \(0.981891\pi\)
\(212\) −1.73205 6.46410i −0.118958 0.443956i
\(213\) 7.09808 + 4.09808i 0.486352 + 0.280796i
\(214\) −19.7942 + 11.4282i −1.35311 + 0.781216i
\(215\) −7.33013 + 1.50000i −0.499911 + 0.102299i
\(216\) 1.90192 1.90192i 0.129410 0.129410i
\(217\) 3.66025 1.26795i 0.248474 0.0860740i
\(218\) −11.6962 + 3.13397i −0.792163 + 0.212260i
\(219\) −1.60770 + 6.00000i −0.108638 + 0.405442i
\(220\) −6.92820 + 3.46410i −0.467099 + 0.233550i
\(221\) 40.7846 2.74347
\(222\) 2.19615 0.147396
\(223\) −1.96410 7.33013i −0.131526 0.490862i 0.868462 0.495756i \(-0.165109\pi\)
−0.999988 + 0.00489404i \(0.998442\pi\)
\(224\) −18.0622 8.76795i −1.20683 0.585833i
\(225\) 5.89230 + 13.7942i 0.392820 + 0.919615i
\(226\) 9.46410 + 16.3923i 0.629543 + 1.09040i
\(227\) 4.97372 18.5622i 0.330117 1.23202i −0.578949 0.815364i \(-0.696537\pi\)
0.909066 0.416651i \(-0.136796\pi\)
\(228\) 8.19615 0.542803
\(229\) 2.66987 4.62436i 0.176430 0.305586i −0.764225 0.644950i \(-0.776878\pi\)
0.940655 + 0.339364i \(0.110212\pi\)
\(230\) 8.29423 12.5622i 0.546905 0.828325i
\(231\) −8.66025 + 3.00000i −0.569803 + 0.197386i
\(232\) 0.526279 + 1.96410i 0.0345519 + 0.128950i
\(233\) −3.33975 + 12.4641i −0.218794 + 0.816550i 0.766002 + 0.642838i \(0.222243\pi\)
−0.984796 + 0.173713i \(0.944424\pi\)
\(234\) 26.4904 + 15.2942i 1.73173 + 0.999815i
\(235\) −11.2583 12.6962i −0.734412 0.828206i
\(236\) 26.1962i 1.70522i
\(237\) −3.92820 + 6.80385i −0.255164 + 0.441957i
\(238\) 38.7846 + 7.46410i 2.51403 + 0.483826i
\(239\) −1.73205 + 1.00000i −0.112037 + 0.0646846i −0.554971 0.831869i \(-0.687271\pi\)
0.442934 + 0.896554i \(0.353937\pi\)
\(240\) −14.4282 9.52628i −0.931337 0.614919i
\(241\) 19.4545 11.2321i 1.25317 0.723520i 0.281435 0.959580i \(-0.409190\pi\)
0.971738 + 0.236060i \(0.0758563\pi\)
\(242\) 3.50000 + 13.0622i 0.224989 + 0.839669i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −5.07180 −0.324689
\(245\) 12.8564 8.92820i 0.821366 0.570402i
\(246\) 7.09808 7.09808i 0.452557 0.452557i
\(247\) −3.73205 13.9282i −0.237465 0.886230i
\(248\) −0.535898 + 0.535898i −0.0340296 + 0.0340296i
\(249\) −5.25833 + 19.6244i −0.333233 + 1.24364i
\(250\) 17.7583 12.2942i 1.12314 0.777555i
\(251\) 3.66025i 0.231033i 0.993306 + 0.115517i \(0.0368523\pi\)
−0.993306 + 0.115517i \(0.963148\pi\)
\(252\) 10.3923 + 9.00000i 0.654654 + 0.566947i
\(253\) 4.92820 + 4.92820i 0.309833 + 0.309833i
\(254\) 26.3205i 1.65150i
\(255\) 28.3923 + 9.46410i 1.77800 + 0.592665i
\(256\) 19.3923 1.21202
\(257\) −0.267949 + 0.0717968i −0.0167142 + 0.00447856i −0.267166 0.963650i \(-0.586087\pi\)
0.250452 + 0.968129i \(0.419421\pi\)
\(258\) −9.69615 + 5.59808i −0.603656 + 0.348521i
\(259\) −0.124356 1.73205i −0.00772708 0.107624i
\(260\) 6.46410 19.3923i 0.400887 1.20266i
\(261\) 11.7846i 0.729449i
\(262\) 9.46410 2.53590i 0.584694 0.156668i
\(263\) 1.42820 5.33013i 0.0880668 0.328670i −0.907810 0.419381i \(-0.862247\pi\)
0.995877 + 0.0907109i \(0.0289139\pi\)
\(264\) 1.26795 1.26795i 0.0780369 0.0780369i
\(265\) −8.46410 + 1.73205i −0.519946 + 0.106399i
\(266\) −1.00000 13.9282i −0.0613139 0.853993i
\(267\) 25.8564i 1.58239i
\(268\) 7.73205 + 7.73205i 0.472310 + 0.472310i
\(269\) −14.1962 + 24.5885i −0.865555 + 1.49918i 0.000940662 1.00000i \(0.499701\pi\)
−0.866495 + 0.499185i \(0.833633\pi\)
\(270\) 14.8923 + 16.7942i 0.906317 + 1.02206i
\(271\) −28.2224 + 16.2942i −1.71439 + 0.989804i −0.785977 + 0.618256i \(0.787840\pi\)
−0.928414 + 0.371548i \(0.878827\pi\)
\(272\) −33.3205 + 8.92820i −2.02035 + 0.541352i
\(273\) 10.5622 21.7583i 0.639252 1.31687i
\(274\) 2.36603 1.36603i 0.142937 0.0825246i
\(275\) 3.92820 + 9.19615i 0.236880 + 0.554549i
\(276\) 2.70577 10.0981i 0.162868 0.607833i
\(277\) 11.1962 + 3.00000i 0.672712 + 0.180253i 0.578976 0.815345i \(-0.303452\pi\)
0.0937356 + 0.995597i \(0.470119\pi\)
\(278\) 23.4904 + 6.29423i 1.40886 + 0.377503i
\(279\) 3.80385 2.19615i 0.227730 0.131480i
\(280\) −1.50000 + 2.66987i −0.0896421 + 0.159555i
\(281\) −11.1340 + 19.2846i −0.664197 + 1.15042i 0.315305 + 0.948990i \(0.397893\pi\)
−0.979502 + 0.201433i \(0.935440\pi\)
\(282\) −21.9904 12.6962i −1.30951 0.756045i
\(283\) −9.63397 + 9.63397i −0.572680 + 0.572680i −0.932877 0.360196i \(-0.882710\pi\)
0.360196 + 0.932877i \(0.382710\pi\)
\(284\) 8.19615i 0.486352i
\(285\) 0.633975 10.5622i 0.0375534 0.625649i
\(286\) 17.6603 + 10.1962i 1.04427 + 0.602911i
\(287\) −6.00000 5.19615i −0.354169 0.306719i
\(288\) −21.9904 5.89230i −1.29580 0.347207i
\(289\) 36.9904 21.3564i 2.17590 1.25626i
\(290\) −16.6244 + 3.40192i −0.976216 + 0.199768i
\(291\) −25.2224 6.75833i −1.47857 0.396180i
\(292\) 6.00000 1.60770i 0.351123 0.0940832i
\(293\) 6.73205 + 1.80385i 0.393291 + 0.105382i 0.450044 0.893006i \(-0.351408\pi\)
−0.0567535 + 0.998388i \(0.518075\pi\)
\(294\) 14.0263 18.7583i 0.818029 1.09401i
\(295\) −33.7583 2.02628i −1.96549 0.117975i
\(296\) 0.169873 + 0.294229i 0.00987367 + 0.0171017i
\(297\) −9.00000 + 5.19615i −0.522233 + 0.301511i
\(298\) 28.8564 7.73205i 1.67161 0.447906i
\(299\) −18.3923 −1.06365
\(300\) 9.00000 12.0000i 0.519615 0.692820i
\(301\) 4.96410 + 7.33013i 0.286126 + 0.422501i
\(302\) −32.9545 8.83013i −1.89632 0.508117i
\(303\) 6.46410 0.371353
\(304\) 6.09808 + 10.5622i 0.349749 + 0.605782i
\(305\) −0.392305 + 6.53590i −0.0224633 + 0.374244i
\(306\) 44.7846 2.56017
\(307\) 5.36603 + 5.36603i 0.306255 + 0.306255i 0.843455 0.537200i \(-0.180518\pi\)
−0.537200 + 0.843455i \(0.680518\pi\)
\(308\) 6.92820 + 6.00000i 0.394771 + 0.341882i
\(309\) −4.03590 + 15.0622i −0.229594 + 0.856857i
\(310\) −4.19615 4.73205i −0.238325 0.268762i
\(311\) 7.12436i 0.403985i −0.979387 0.201993i \(-0.935258\pi\)
0.979387 0.201993i \(-0.0647417\pi\)
\(312\) 4.73205i 0.267900i
\(313\) −1.60770 + 1.60770i −0.0908723 + 0.0908723i −0.751082 0.660209i \(-0.770468\pi\)
0.660209 + 0.751082i \(0.270468\pi\)
\(314\) 19.6603 1.10949
\(315\) 12.4019 12.6962i 0.698769 0.715347i
\(316\) 7.85641 0.441957
\(317\) 8.46410 8.46410i 0.475391 0.475391i −0.428263 0.903654i \(-0.640874\pi\)
0.903654 + 0.428263i \(0.140874\pi\)
\(318\) −11.1962 + 6.46410i −0.627849 + 0.362489i
\(319\) 7.85641i 0.439874i
\(320\) −0.767949 + 12.7942i −0.0429297 + 0.715219i
\(321\) 14.4904 + 14.4904i 0.808774 + 0.808774i
\(322\) −17.4904 3.36603i −0.974701 0.187581i
\(323\) −14.9282 14.9282i −0.830627 0.830627i
\(324\) 13.5000 + 7.79423i 0.750000 + 0.433013i
\(325\) −24.4904 9.83013i −1.35848 0.545277i
\(326\) −9.29423 16.0981i −0.514760 0.891590i
\(327\) 5.42820 + 9.40192i 0.300180 + 0.519928i
\(328\) 1.50000 + 0.401924i 0.0828236 + 0.0221925i
\(329\) −8.76795 + 18.0622i −0.483393 + 0.995800i
\(330\) 9.92820 + 11.1962i 0.546530 + 0.616328i
\(331\) −6.00000 −0.329790 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(332\) 19.6244 5.25833i 1.07703 0.288588i
\(333\) −0.509619 1.90192i −0.0279269 0.104225i
\(334\) 3.36603 + 5.83013i 0.184181 + 0.319010i
\(335\) 10.5622 9.36603i 0.577073 0.511721i
\(336\) −3.86603 + 20.0885i −0.210909 + 1.09592i
\(337\) −7.36603 1.97372i −0.401253 0.107515i 0.0525482 0.998618i \(-0.483266\pi\)
−0.453801 + 0.891103i \(0.649932\pi\)
\(338\) −27.7224 + 7.42820i −1.50790 + 0.404041i
\(339\) 12.0000 12.0000i 0.651751 0.651751i
\(340\) −6.00000 29.3205i −0.325396 1.59013i
\(341\) 2.53590 1.46410i 0.137327 0.0792855i
\(342\) −4.09808 15.2942i −0.221599 0.827017i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) −1.50000 0.866025i −0.0808746 0.0466930i
\(345\) −12.8038 4.26795i −0.689336 0.229779i
\(346\) 43.7128i 2.35002i
\(347\) 6.63397 6.63397i 0.356130 0.356130i −0.506254 0.862384i \(-0.668970\pi\)
0.862384 + 0.506254i \(0.168970\pi\)
\(348\) −10.2058 + 5.89230i −0.547087 + 0.315861i
\(349\) −5.00000 + 8.66025i −0.267644 + 0.463573i −0.968253 0.249973i \(-0.919578\pi\)
0.700609 + 0.713545i \(0.252912\pi\)
\(350\) −21.4904 13.8301i −1.14871 0.739251i
\(351\) 7.09808 26.4904i 0.378867 1.41395i
\(352\) −14.6603 3.92820i −0.781394 0.209374i
\(353\) −17.0263 4.56218i −0.906217 0.242820i −0.224533 0.974467i \(-0.572086\pi\)
−0.681684 + 0.731646i \(0.738752\pi\)
\(354\) −48.8827 + 13.0981i −2.59809 + 0.696155i
\(355\) −10.5622 0.633975i −0.560582 0.0336479i
\(356\) 22.3923 12.9282i 1.18679 0.685193i
\(357\) −2.53590 35.3205i −0.134214 1.86936i
\(358\) 2.36603 0.633975i 0.125048 0.0335066i
\(359\) −9.46410 + 5.46410i −0.499496 + 0.288384i −0.728505 0.685040i \(-0.759785\pi\)
0.229009 + 0.973424i \(0.426451\pi\)
\(360\) −1.09808 + 3.29423i −0.0578737 + 0.173621i
\(361\) 5.76795 9.99038i 0.303576 0.525810i
\(362\) 27.4904 + 27.4904i 1.44486 + 1.44486i
\(363\) 10.5000 6.06218i 0.551107 0.318182i
\(364\) −24.1244 + 1.73205i −1.26446 + 0.0907841i
\(365\) −1.60770 7.85641i −0.0841506 0.411223i
\(366\) 2.53590 + 9.46410i 0.132554 + 0.494697i
\(367\) −1.42820 + 5.33013i −0.0745516 + 0.278230i −0.993131 0.117006i \(-0.962670\pi\)
0.918580 + 0.395236i \(0.129337\pi\)
\(368\) 15.0263 4.02628i 0.783299 0.209884i
\(369\) −7.79423 4.50000i −0.405751 0.234261i
\(370\) −2.53590 + 1.26795i −0.131835 + 0.0659175i
\(371\) 5.73205 + 8.46410i 0.297593 + 0.439434i
\(372\) −3.80385 2.19615i −0.197220 0.113865i
\(373\) 7.56218 2.02628i 0.391555 0.104917i −0.0576697 0.998336i \(-0.518367\pi\)
0.449224 + 0.893419i \(0.351700\pi\)
\(374\) 29.8564 1.54384
\(375\) −14.7679 12.5263i −0.762614 0.646854i
\(376\) 3.92820i 0.202582i
\(377\) 14.6603 + 14.6603i 0.755041 + 0.755041i
\(378\) 11.5981 23.8923i 0.596541 1.22889i
\(379\) 17.5167i 0.899770i 0.893086 + 0.449885i \(0.148535\pi\)
−0.893086 + 0.449885i \(0.851465\pi\)
\(380\) −9.46410 + 4.73205i −0.485498 + 0.242749i
\(381\) 22.7942 6.10770i 1.16778 0.312907i
\(382\) 13.3923 13.3923i 0.685210 0.685210i
\(383\) 2.83975 + 10.5981i 0.145104 + 0.541536i 0.999751 + 0.0223261i \(0.00710720\pi\)
−0.854647 + 0.519210i \(0.826226\pi\)
\(384\) −1.83975 6.86603i −0.0938841 0.350380i
\(385\) 8.26795 8.46410i 0.421374 0.431371i
\(386\) −0.535898 −0.0272765
\(387\) 7.09808 + 7.09808i 0.360815 + 0.360815i
\(388\) 6.75833 + 25.2224i 0.343102 + 1.28047i
\(389\) 7.83975 4.52628i 0.397491 0.229491i −0.287910 0.957658i \(-0.592960\pi\)
0.685401 + 0.728166i \(0.259627\pi\)
\(390\) −39.4186 2.36603i −1.99604 0.119808i
\(391\) −23.3205 + 13.4641i −1.17937 + 0.680909i
\(392\) 3.59808 + 0.428203i 0.181730 + 0.0216275i
\(393\) −4.39230 7.60770i −0.221562 0.383757i
\(394\) 10.9282i 0.550555i
\(395\) 0.607695 10.1244i 0.0305765 0.509412i
\(396\) 9.00000 + 5.19615i 0.452267 + 0.261116i
\(397\) 7.85641 29.3205i 0.394302 1.47155i −0.428664 0.903464i \(-0.641016\pi\)
0.822966 0.568090i \(-0.192318\pi\)
\(398\) −2.19615 8.19615i −0.110083 0.410836i
\(399\) −11.8301 + 4.09808i −0.592247 + 0.205160i
\(400\) 22.1603 + 2.66987i 1.10801 + 0.133494i
\(401\) 4.69615 8.13397i 0.234515 0.406191i −0.724617 0.689152i \(-0.757983\pi\)
0.959132 + 0.282961i \(0.0913166\pi\)
\(402\) 10.5622 18.2942i 0.526794 0.912433i
\(403\) −2.00000 + 7.46410i −0.0996271 + 0.371813i
\(404\) −3.23205 5.59808i −0.160801 0.278515i
\(405\) 11.0885 16.7942i 0.550990 0.834512i
\(406\) 11.2583 + 16.6244i 0.558742 + 0.825053i
\(407\) −0.339746 1.26795i −0.0168406 0.0628499i
\(408\) 3.46410 + 6.00000i 0.171499 + 0.297044i
\(409\) 22.3205 1.10368 0.551839 0.833951i \(-0.313926\pi\)
0.551839 + 0.833951i \(0.313926\pi\)
\(410\) −4.09808 + 12.2942i −0.202390 + 0.607169i
\(411\) −1.73205 1.73205i −0.0854358 0.0854358i
\(412\) 15.0622 4.03590i 0.742060 0.198834i
\(413\) 13.0981 + 37.8109i 0.644514 + 1.86055i
\(414\) −20.1962 −0.992587
\(415\) −5.25833 25.6962i −0.258121 1.26137i
\(416\) 34.6865 20.0263i 1.70065 0.981869i
\(417\) 21.8038i 1.06774i
\(418\) −2.73205 10.1962i −0.133629 0.498710i
\(419\) 1.16987 + 2.02628i 0.0571520 + 0.0989902i 0.893186 0.449688i \(-0.148465\pi\)
−0.836034 + 0.548678i \(0.815131\pi\)
\(420\) −17.1962 4.39230i −0.839086 0.214323i
\(421\) −2.40192 + 4.16025i −0.117063 + 0.202758i −0.918602 0.395183i \(-0.870681\pi\)
0.801540 + 0.597941i \(0.204014\pi\)
\(422\) 24.3923 + 6.53590i 1.18740 + 0.318163i
\(423\) −5.89230 + 21.9904i −0.286494 + 1.06921i
\(424\) −1.73205 1.00000i −0.0841158 0.0485643i
\(425\) −38.2487 + 5.46410i −1.85534 + 0.265048i
\(426\) −15.2942 + 4.09808i −0.741008 + 0.198552i
\(427\) 7.32051 2.53590i 0.354264 0.122721i
\(428\) 5.30385 19.7942i 0.256371 0.956790i
\(429\) 4.73205 17.6603i 0.228466 0.852645i
\(430\) 7.96410 12.0622i 0.384063 0.581690i
\(431\) −10.2942 + 17.8301i −0.495856 + 0.858847i −0.999989 0.00477901i \(-0.998479\pi\)
0.504133 + 0.863626i \(0.331812\pi\)
\(432\) 23.1962i 1.11603i
\(433\) 0.124356 0.124356i 0.00597615 0.00597615i −0.704112 0.710089i \(-0.748655\pi\)
0.710089 + 0.704112i \(0.248655\pi\)
\(434\) −3.26795 + 6.73205i −0.156867 + 0.323149i
\(435\) 6.80385 + 13.6077i 0.326220 + 0.652439i
\(436\) 5.42820 9.40192i 0.259964 0.450270i
\(437\) 6.73205 + 6.73205i 0.322038 + 0.322038i
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) 35.8564 1.71133 0.855666 0.517528i \(-0.173148\pi\)
0.855666 + 0.517528i \(0.173148\pi\)
\(440\) −0.732051 + 2.19615i −0.0348992 + 0.104697i
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) −55.7128 + 55.7128i −2.64999 + 2.64999i
\(443\) 8.63397 + 8.63397i 0.410213 + 0.410213i 0.881813 0.471600i \(-0.156323\pi\)
−0.471600 + 0.881813i \(0.656323\pi\)
\(444\) −1.39230 + 1.39230i −0.0660759 + 0.0660759i
\(445\) −14.9282 29.8564i −0.707665 1.41533i
\(446\) 12.6962 + 7.33013i 0.601180 + 0.347092i
\(447\) −13.3923 23.1962i −0.633434 1.09714i
\(448\) 14.3301 4.96410i 0.677035 0.234532i
\(449\) 7.33975i 0.346384i 0.984888 + 0.173192i \(0.0554081\pi\)
−0.984888 + 0.173192i \(0.944592\pi\)
\(450\) −26.8923 10.7942i −1.26772 0.508845i
\(451\) −5.19615 3.00000i −0.244677 0.141264i
\(452\) −16.3923 4.39230i −0.771029 0.206597i
\(453\) 30.5885i 1.43717i
\(454\) 18.5622 + 32.1506i 0.871166 + 1.50890i
\(455\) 0.366025 + 31.2224i 0.0171595 + 1.46373i
\(456\) 1.73205 1.73205i 0.0811107 0.0811107i
\(457\) −23.0526 + 23.0526i −1.07835 + 1.07835i −0.0816959 + 0.996657i \(0.526034\pi\)
−0.996657 + 0.0816959i \(0.973966\pi\)
\(458\) 2.66987 + 9.96410i 0.124755 + 0.465592i
\(459\) −10.3923 38.7846i −0.485071 1.81031i
\(460\) 2.70577 + 13.2224i 0.126157 + 0.616499i
\(461\) −20.7679 11.9904i −0.967260 0.558448i −0.0688601 0.997626i \(-0.521936\pi\)
−0.898400 + 0.439179i \(0.855270\pi\)
\(462\) 7.73205 15.9282i 0.359728 0.741047i
\(463\) 3.83975 14.3301i 0.178448 0.665977i −0.817490 0.575942i \(-0.804635\pi\)
0.995939 0.0900353i \(-0.0286980\pi\)
\(464\) −15.1865 8.76795i −0.705017 0.407042i
\(465\) −3.12436 + 4.73205i −0.144889 + 0.219444i
\(466\) −12.4641 21.5885i −0.577388 1.00007i
\(467\) −0.669873 + 2.50000i −0.0309980 + 0.115686i −0.979691 0.200511i \(-0.935740\pi\)
0.948693 + 0.316198i \(0.102406\pi\)
\(468\) −26.4904 + 7.09808i −1.22452 + 0.328109i
\(469\) −15.0263 7.29423i −0.693849 0.336816i
\(470\) 32.7224 + 1.96410i 1.50937 + 0.0905973i
\(471\) −4.56218 17.0263i −0.210214 0.784530i
\(472\) −5.53590 5.53590i −0.254810 0.254810i
\(473\) 4.73205 + 4.73205i 0.217580 + 0.217580i
\(474\) −3.92820 14.6603i −0.180428 0.673368i
\(475\) 5.36603 + 12.5622i 0.246210 + 0.576392i
\(476\) −29.3205 + 19.8564i −1.34390 + 0.910117i
\(477\) 8.19615 + 8.19615i 0.375276 + 0.375276i
\(478\) 1.00000 3.73205i 0.0457389 0.170700i
\(479\) −8.63397 14.9545i −0.394496 0.683288i 0.598540 0.801093i \(-0.295748\pi\)
−0.993037 + 0.117805i \(0.962414\pi\)
\(480\) 28.7942 5.89230i 1.31427 0.268946i
\(481\) 3.00000 + 1.73205i 0.136788 + 0.0789747i
\(482\) −11.2321 + 41.9186i −0.511606 + 1.90934i
\(483\) 1.14359 + 15.9282i 0.0520353 + 0.724758i
\(484\) −10.5000 6.06218i −0.477273 0.275554i
\(485\) 33.0263 6.75833i 1.49965 0.306880i
\(486\) 7.79423 29.0885i 0.353553 1.31948i
\(487\) 7.97372 + 29.7583i 0.361324 + 1.34848i 0.872337 + 0.488906i \(0.162604\pi\)
−0.511013 + 0.859573i \(0.670730\pi\)
\(488\) −1.07180 + 1.07180i −0.0485180 + 0.0485180i
\(489\) −11.7846 + 11.7846i −0.532918 + 0.532918i
\(490\) −5.36603 + 29.7583i −0.242412 + 1.34434i
\(491\) 8.29423 + 14.3660i 0.374313 + 0.648330i 0.990224 0.139486i \(-0.0445451\pi\)
−0.615911 + 0.787816i \(0.711212\pi\)
\(492\) 9.00000i 0.405751i
\(493\) 29.3205 + 7.85641i 1.32053 + 0.353835i
\(494\) 24.1244 + 13.9282i 1.08541 + 0.626659i
\(495\) 7.39230 11.1962i 0.332259 0.503230i
\(496\) 6.53590i 0.293471i
\(497\) 4.09808 + 11.8301i 0.183824 + 0.530654i
\(498\) −19.6244 33.9904i −0.879388 1.52315i
\(499\) 15.2487 + 8.80385i 0.682626 + 0.394114i 0.800844 0.598873i \(-0.204385\pi\)
−0.118218 + 0.992988i \(0.537718\pi\)
\(500\) −3.46410 + 19.0526i −0.154919 + 0.852056i
\(501\) 4.26795 4.26795i 0.190678 0.190678i
\(502\) −5.00000 5.00000i −0.223161 0.223161i
\(503\) −4.36603 + 4.36603i −0.194671 + 0.194671i −0.797711 0.603040i \(-0.793956\pi\)
0.603040 + 0.797711i \(0.293956\pi\)
\(504\) 4.09808 0.294229i 0.182543 0.0131060i
\(505\) −7.46410 + 3.73205i −0.332148 + 0.166074i
\(506\) −13.4641 −0.598552
\(507\) 12.8660 + 22.2846i 0.571400 + 0.989694i
\(508\) −16.6865 16.6865i −0.740345 0.740345i
\(509\) −16.4545 + 28.5000i −0.729332 + 1.26324i 0.227834 + 0.973700i \(0.426836\pi\)
−0.957166 + 0.289540i \(0.906498\pi\)
\(510\) −51.7128 + 25.8564i −2.28988 + 1.14494i
\(511\) −7.85641 + 5.32051i −0.347547 + 0.235365i
\(512\) −20.6865 + 20.6865i −0.914224 + 0.914224i
\(513\) −12.2942 + 7.09808i −0.542803 + 0.313388i
\(514\) 0.267949 0.464102i 0.0118187 0.0204706i
\(515\) −4.03590 19.7224i −0.177843 0.869074i
\(516\) 2.59808 9.69615i 0.114374 0.426849i
\(517\) −3.92820 + 14.6603i −0.172762 + 0.644757i
\(518\) 2.53590 + 2.19615i 0.111421 + 0.0964934i
\(519\) 37.8564 10.1436i 1.66171 0.445254i
\(520\) −2.73205 5.46410i −0.119808 0.239617i
\(521\) −6.35641 3.66987i −0.278479 0.160780i 0.354256 0.935149i \(-0.384734\pi\)
−0.632735 + 0.774369i \(0.718068\pi\)
\(522\) 16.0981 + 16.0981i 0.704594 + 0.704594i
\(523\) 23.2583 + 6.23205i 1.01702 + 0.272509i 0.728558 0.684984i \(-0.240191\pi\)
0.288458 + 0.957493i \(0.406858\pi\)
\(524\) −4.39230 + 7.60770i −0.191879 + 0.332344i
\(525\) −6.99038 + 21.8205i −0.305085 + 0.952325i
\(526\) 5.33013 + 9.23205i 0.232405 + 0.402537i
\(527\) 2.92820 + 10.9282i 0.127555 + 0.476040i
\(528\) 15.4641i 0.672989i
\(529\) −9.40192 + 5.42820i −0.408779 + 0.236009i
\(530\) 9.19615 13.9282i 0.399455 0.605002i
\(531\) 22.6865 + 39.2942i 0.984512 + 1.70522i
\(532\) 9.46410 + 8.19615i 0.410321 + 0.355348i
\(533\) 15.2942 4.09808i 0.662467 0.177507i
\(534\) −35.3205 35.3205i −1.52847 1.52847i
\(535\) −25.0981 8.36603i −1.08508 0.361695i
\(536\) 3.26795 0.141154
\(537\) −1.09808 1.90192i −0.0473855 0.0820741i
\(538\) −14.1962 52.9808i −0.612040 2.28416i
\(539\) −13.0000 5.19615i −0.559950 0.223814i
\(540\) −20.0885 1.20577i −0.864470 0.0518881i
\(541\) 3.46410 + 6.00000i 0.148933 + 0.257960i 0.930834 0.365444i \(-0.119083\pi\)
−0.781900 + 0.623404i \(0.785749\pi\)
\(542\) 16.2942 60.8109i 0.699897 2.61205i
\(543\) 17.4282 30.1865i 0.747916 1.29543i
\(544\) 29.3205 50.7846i 1.25711 2.17737i
\(545\) −11.6962 7.72243i −0.501008 0.330793i
\(546\) 15.2942 + 44.1506i 0.654533 + 1.88947i
\(547\) −10.4019 38.8205i −0.444754 1.65985i −0.716585 0.697500i \(-0.754296\pi\)
0.271831 0.962345i \(-0.412371\pi\)
\(548\) −0.633975 + 2.36603i −0.0270821 + 0.101072i
\(549\) 7.60770 4.39230i 0.324689 0.187459i
\(550\) −17.9282 7.19615i −0.764461 0.306845i
\(551\) 10.7321i 0.457201i
\(552\) −1.56218 2.70577i −0.0664907 0.115165i
\(553\) −11.3397 + 3.92820i −0.482215 + 0.167044i
\(554\) −19.3923 + 11.1962i −0.823900 + 0.475679i
\(555\) 1.68653 + 1.90192i 0.0715894 + 0.0807322i
\(556\) −18.8827 + 10.9019i −0.800804 + 0.462345i
\(557\) −11.0718 41.3205i −0.469127 1.75081i −0.642831 0.766008i \(-0.722240\pi\)
0.173704 0.984798i \(-0.444426\pi\)
\(558\) −2.19615 + 8.19615i −0.0929705 + 0.346971i
\(559\) −17.6603 −0.746949
\(560\) −7.13397 25.4282i −0.301465 1.07454i
\(561\) −6.92820 25.8564i −0.292509 1.09166i
\(562\) −11.1340 41.5526i −0.469658 1.75279i
\(563\) 3.00000 3.00000i 0.126435 0.126435i −0.641058 0.767493i \(-0.721504\pi\)
0.767493 + 0.641058i \(0.221504\pi\)
\(564\) 21.9904 5.89230i 0.925962 0.248111i
\(565\) −6.92820 + 20.7846i −0.291472 + 0.874415i
\(566\) 26.3205i 1.10633i
\(567\) −23.3827 4.50000i −0.981981 0.188982i
\(568\) −1.73205 1.73205i −0.0726752 0.0726752i
\(569\) 10.9282i 0.458134i 0.973411 + 0.229067i \(0.0735675\pi\)
−0.973411 + 0.229067i \(0.926432\pi\)
\(570\) 13.5622 + 15.2942i 0.568057 + 0.640605i
\(571\) 6.19615 0.259301 0.129650 0.991560i \(-0.458614\pi\)
0.129650 + 0.991560i \(0.458614\pi\)
\(572\) −17.6603 + 4.73205i −0.738412 + 0.197857i
\(573\) −14.7058 8.49038i −0.614342 0.354691i
\(574\) 15.2942 1.09808i 0.638369 0.0458328i
\(575\) 17.2487 2.46410i 0.719321 0.102760i
\(576\) 14.8923 8.59808i 0.620513 0.358253i
\(577\) 32.8564 8.80385i 1.36783 0.366509i 0.501144 0.865364i \(-0.332913\pi\)
0.866686 + 0.498855i \(0.166246\pi\)
\(578\) −21.3564 + 79.7032i −0.888309 + 3.31522i
\(579\) 0.124356 + 0.464102i 0.00516804 + 0.0192874i
\(580\) 8.38269 12.6962i 0.348072 0.527179i
\(581\) −25.6962 + 17.4019i −1.06606 + 0.721953i
\(582\) 43.6865 25.2224i 1.81087 1.04550i
\(583\) 5.46410 + 5.46410i 0.226300 + 0.226300i
\(584\) 0.928203 1.60770i 0.0384093 0.0665269i
\(585\) 7.09808 + 34.6865i 0.293469 + 1.43411i
\(586\) −11.6603 + 6.73205i −0.481681 + 0.278098i
\(587\) 26.1603 7.00962i 1.07975 0.289318i 0.325256 0.945626i \(-0.394549\pi\)
0.754493 + 0.656308i \(0.227883\pi\)
\(588\) 3.00000 + 20.7846i 0.123718 + 0.857143i
\(589\) 3.46410 2.00000i 0.142736 0.0824086i
\(590\) 48.8827 43.3468i 2.01247 1.78456i
\(591\) 9.46410 2.53590i 0.389301 0.104313i
\(592\) −2.83013 0.758330i −0.116318 0.0311672i
\(593\) 28.9545 + 7.75833i 1.18902 + 0.318596i 0.798498 0.601998i \(-0.205628\pi\)
0.390520 + 0.920594i \(0.372295\pi\)
\(594\) 5.19615 19.3923i 0.213201 0.795676i
\(595\) 23.3205 + 39.3205i 0.956048 + 1.61198i
\(596\) −13.3923 + 23.1962i −0.548570 + 0.950151i
\(597\) −6.58846 + 3.80385i −0.269648 + 0.155681i
\(598\) 25.1244 25.1244i 1.02741 1.02741i
\(599\) 18.1436i 0.741327i −0.928767 0.370664i \(-0.879130\pi\)
0.928767 0.370664i \(-0.120870\pi\)
\(600\) −0.633975 4.43782i −0.0258819 0.181173i
\(601\) −29.3205 16.9282i −1.19601 0.690516i −0.236346 0.971669i \(-0.575950\pi\)
−0.959663 + 0.281153i \(0.909283\pi\)
\(602\) −16.7942 3.23205i −0.684482 0.131729i
\(603\) −18.2942 4.90192i −0.744999 0.199622i
\(604\) 26.4904 15.2942i 1.07788 0.622313i
\(605\) −8.62436 + 13.0622i −0.350630 + 0.531053i
\(606\) −8.83013 + 8.83013i −0.358699 + 0.358699i
\(607\) 3.69615 0.990381i 0.150022 0.0401983i −0.183026 0.983108i \(-0.558589\pi\)
0.333049 + 0.942910i \(0.391923\pi\)
\(608\) −20.0263 5.36603i −0.812173 0.217621i
\(609\) 11.7846 13.6077i 0.477536 0.551412i
\(610\) −8.39230 9.46410i −0.339794 0.383190i
\(611\) −20.0263 34.6865i −0.810177 1.40327i
\(612\) −28.3923 + 28.3923i −1.14769 + 1.14769i
\(613\) −22.7583 + 6.09808i −0.919200 + 0.246299i −0.687244 0.726427i \(-0.741179\pi\)
−0.231957 + 0.972726i \(0.574513\pi\)
\(614\) −14.6603 −0.591640
\(615\) 11.5981 + 0.696152i 0.467680 + 0.0280716i
\(616\) 2.73205 0.196152i 0.110077 0.00790321i
\(617\) 12.3923 + 3.32051i 0.498895 + 0.133679i 0.499487 0.866321i \(-0.333522\pi\)
−0.000591902 1.00000i \(0.500188\pi\)
\(618\) −15.0622 26.0885i −0.605890 1.04943i
\(619\) −20.3923 35.3205i −0.819636 1.41965i −0.905951 0.423383i \(-0.860842\pi\)
0.0863148 0.996268i \(-0.472491\pi\)
\(620\) 5.66025 + 0.339746i 0.227321 + 0.0136445i
\(621\) 4.68653 + 17.4904i 0.188064 + 0.701865i
\(622\) 9.73205 + 9.73205i 0.390220 + 0.390220i
\(623\) −25.8564 + 29.8564i −1.03592 + 1.19617i
\(624\) −28.8564 28.8564i −1.15518 1.15518i
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 4.39230i 0.175552i
\(627\) −8.19615 + 4.73205i −0.327323 + 0.188980i
\(628\) −12.4641 + 12.4641i −0.497372 + 0.497372i
\(629\) 5.07180 0.202226
\(630\) 0.401924 + 34.2846i 0.0160130 + 1.36593i
\(631\) 15.8564 0.631234 0.315617 0.948887i \(-0.397789\pi\)
0.315617 + 0.948887i \(0.397789\pi\)
\(632\) 1.66025 1.66025i 0.0660414 0.0660414i
\(633\) 22.6410i 0.899900i
\(634\) 23.1244i 0.918385i
\(635\) −22.7942 + 20.2128i −0.904561 + 0.802121i
\(636\) 3.00000 11.1962i 0.118958 0.443956i
\(637\) 33.9545 14.5622i 1.34533 0.576974i
\(638\) 10.7321 + 10.7321i 0.424886 + 0.424886i
\(639\) 7.09808 + 12.2942i 0.280796 + 0.486352i
\(640\) 6.08846 + 6.86603i 0.240667 + 0.271403i
\(641\) −19.1962 33.2487i −0.758202 1.31325i −0.943766 0.330613i \(-0.892745\pi\)
0.185564 0.982632i \(-0.440589\pi\)
\(642\) −39.5885 −1.56243
\(643\) 36.6506 + 9.82051i 1.44536 + 0.387283i 0.894407 0.447253i \(-0.147598\pi\)
0.550953 + 0.834536i \(0.314264\pi\)
\(644\) 13.2224 8.95448i 0.521037 0.352856i
\(645\) −12.2942 4.09808i −0.484085 0.161362i
\(646\) 40.7846 1.60465
\(647\) −27.6244 + 7.40192i −1.08603 + 0.291000i −0.757062 0.653343i \(-0.773366\pi\)
−0.328963 + 0.944343i \(0.606699\pi\)
\(648\) 4.50000 1.20577i 0.176777 0.0473672i
\(649\) 15.1244 + 26.1962i 0.593683 + 1.02829i
\(650\) 46.8827 20.0263i 1.83889 0.785495i
\(651\) 6.58846 + 1.26795i 0.258222 + 0.0496948i
\(652\) 16.0981 + 4.31347i 0.630449 + 0.168928i
\(653\) −15.3923 + 4.12436i −0.602347 + 0.161399i −0.547090 0.837074i \(-0.684265\pi\)
−0.0552572 + 0.998472i \(0.517598\pi\)
\(654\) −20.2583 5.42820i −0.792163 0.212260i
\(655\) 9.46410 + 6.24871i 0.369793 + 0.244157i
\(656\) −11.5981 + 6.69615i −0.452829 + 0.261441i
\(657\) −7.60770 + 7.60770i −0.296804 + 0.296804i
\(658\) −12.6962 36.6506i −0.494948 1.42879i
\(659\) 34.3468 + 19.8301i 1.33796 + 0.772472i 0.986505 0.163732i \(-0.0523533\pi\)
0.351456 + 0.936204i \(0.385687\pi\)
\(660\) −13.3923 0.803848i −0.521295 0.0312897i
\(661\) 23.3923i 0.909855i 0.890528 + 0.454928i \(0.150335\pi\)
−0.890528 + 0.454928i \(0.849665\pi\)
\(662\) 8.19615 8.19615i 0.318553 0.318553i
\(663\) 61.1769 + 35.3205i 2.37591 + 1.37173i
\(664\) 3.03590 5.25833i 0.117816 0.204063i
\(665\) 11.2942 11.5622i 0.437971 0.448362i
\(666\) 3.29423 + 1.90192i 0.127649 + 0.0736980i
\(667\) −13.2224 3.54294i −0.511975 0.137183i
\(668\) −5.83013 1.56218i −0.225574 0.0604425i
\(669\) 3.40192 12.6962i 0.131526 0.490862i
\(670\) −1.63397 + 27.2224i −0.0631259 + 1.05169i
\(671\) 5.07180 2.92820i 0.195795 0.113042i
\(672\) −19.5000 28.7942i −0.752229 1.11076i
\(673\) −13.5622 + 3.63397i −0.522784 + 0.140079i −0.510554 0.859846i \(-0.670560\pi\)
−0.0122297 + 0.999925i \(0.503893\pi\)
\(674\) 12.7583 7.36603i 0.491433 0.283729i
\(675\) −3.10770 + 25.7942i −0.119615 + 0.992820i
\(676\) 12.8660 22.2846i 0.494847 0.857100i
\(677\) 34.5167 + 34.5167i 1.32658 + 1.32658i 0.908331 + 0.418252i \(0.137357\pi\)
0.418252 + 0.908331i \(0.362643\pi\)
\(678\) 32.7846i 1.25909i
\(679\) −22.3660 33.0263i −0.858329 1.26743i
\(680\) −7.46410 4.92820i −0.286235 0.188988i
\(681\) 23.5359 23.5359i 0.901898 0.901898i
\(682\) −1.46410 + 5.46410i −0.0560633 + 0.209231i
\(683\) 11.5000 3.08142i 0.440035 0.117907i −0.0319978 0.999488i \(-0.510187\pi\)
0.472033 + 0.881581i \(0.343520\pi\)
\(684\) 12.2942 + 7.09808i 0.470082 + 0.271402i
\(685\) 3.00000 + 1.00000i 0.114624 + 0.0382080i
\(686\) 34.9545 7.63397i 1.33457 0.291467i
\(687\) 8.00962 4.62436i 0.305586 0.176430i
\(688\) 14.4282 3.86603i 0.550070 0.147391i
\(689\) −20.3923 −0.776885
\(690\) 23.3205 11.6603i 0.887797 0.443898i
\(691\) 12.5359i 0.476888i −0.971156 0.238444i \(-0.923363\pi\)
0.971156 0.238444i \(-0.0766374\pi\)
\(692\) −27.7128 27.7128i −1.05348 1.05348i
\(693\) −15.5885 3.00000i −0.592157 0.113961i
\(694\) 18.1244i 0.687991i
\(695\) 12.5885 + 25.1769i 0.477507 + 0.955015i
\(696\) −0.911543 + 3.40192i −0.0345519 + 0.128950i
\(697\) 16.3923 16.3923i 0.620903 0.620903i
\(698\) −5.00000 18.6603i −0.189253 0.706301i
\(699\) −15.8038 + 15.8038i −0.597756 + 0.597756i
\(700\) 22.3923 4.85641i 0.846350 0.183555i
\(701\) −27.0526 −1.02176 −0.510881 0.859652i \(-0.670681\pi\)
−0.510881 + 0.859652i \(0.670681\pi\)
\(702\) 26.4904 + 45.8827i 0.999815 + 1.73173i
\(703\) −0.464102 1.73205i −0.0175039 0.0653255i
\(704\) 9.92820 5.73205i 0.374183 0.216035i
\(705\) −5.89230 28.7942i −0.221917 1.08445i
\(706\) 29.4904 17.0263i 1.10989 0.640792i
\(707\) 7.46410 + 6.46410i 0.280716 + 0.243108i
\(708\) 22.6865 39.2942i 0.852612 1.47677i
\(709\) 28.6410i 1.07564i 0.843061 + 0.537818i \(0.180751\pi\)
−0.843061 + 0.537818i \(0.819249\pi\)
\(710\) 15.2942 13.5622i 0.573982 0.508979i
\(711\) −11.7846 + 6.80385i −0.441957 + 0.255164i
\(712\) 2.00000 7.46410i 0.0749532 0.279729i
\(713\) −1.32051 4.92820i −0.0494534 0.184563i
\(714\) 51.7128 + 44.7846i 1.93530 + 1.67602i
\(715\) 4.73205 + 23.1244i 0.176969 + 0.864802i
\(716\) −1.09808 + 1.90192i −0.0410370 + 0.0710782i
\(717\) −3.46410 −0.129369
\(718\) 5.46410 20.3923i 0.203918 0.761034i
\(719\) −4.53590 7.85641i −0.169160 0.292995i 0.768964 0.639292i \(-0.220772\pi\)
−0.938125 + 0.346297i \(0.887439\pi\)
\(720\) −13.3923 26.7846i −0.499102 0.998203i
\(721\) −19.7224 + 13.3564i −0.734502 + 0.497419i
\(722\) 5.76795 + 21.5263i 0.214661 + 0.801125i
\(723\) 38.9090 1.44704
\(724\) −34.8564 −1.29543
\(725\) −15.7128 11.7846i −0.583559 0.437669i
\(726\) −6.06218 + 22.6244i −0.224989 + 0.839669i
\(727\) 15.7583 4.22243i 0.584444 0.156601i 0.0455314 0.998963i \(-0.485502\pi\)
0.538913 + 0.842362i \(0.318835\pi\)
\(728\) −4.73205 + 5.46410i −0.175381 + 0.202513i
\(729\) −27.0000 −1.00000
\(730\) 12.9282 + 8.53590i 0.478494 + 0.315928i
\(731\) −22.3923 + 12.9282i −0.828209 + 0.478167i
\(732\) −7.60770 4.39230i −0.281189 0.162344i
\(733\) −11.0981 41.4186i −0.409917 1.52983i −0.794804 0.606867i \(-0.792426\pi\)
0.384887 0.922964i \(-0.374240\pi\)
\(734\) −5.33013 9.23205i −0.196739 0.340761i
\(735\) 27.0167 2.25833i 0.996525 0.0832998i
\(736\) −13.2224 + 22.9019i −0.487385 + 0.844176i
\(737\) −12.1962 3.26795i −0.449251 0.120376i
\(738\) 16.7942 4.50000i 0.618204 0.165647i
\(739\) 35.3205 + 20.3923i 1.29929 + 0.750143i 0.980281 0.197610i \(-0.0633179\pi\)
0.319005 + 0.947753i \(0.396651\pi\)
\(740\) 0.803848 2.41154i 0.0295500 0.0886501i
\(741\) 6.46410 24.1244i 0.237465 0.886230i
\(742\) −19.3923 3.73205i −0.711914 0.137008i
\(743\) 4.91858 18.3564i 0.180445 0.673431i −0.815114 0.579300i \(-0.803326\pi\)
0.995560 0.0941313i \(-0.0300073\pi\)
\(744\) −1.26795 + 0.339746i −0.0464853 + 0.0124557i
\(745\) 28.8564 + 19.0526i 1.05722 + 0.698032i
\(746\) −7.56218 + 13.0981i −0.276871 + 0.479555i
\(747\) −24.8827 + 24.8827i −0.910410 + 0.910410i
\(748\) −18.9282 + 18.9282i −0.692084 + 0.692084i
\(749\) 2.24167 + 31.2224i 0.0819088 + 1.14084i
\(750\) 37.2846 3.06218i 1.36144 0.111815i
\(751\) −24.5622 + 42.5429i −0.896287 + 1.55241i −0.0640824 + 0.997945i \(0.520412\pi\)
−0.832204 + 0.554469i \(0.812921\pi\)
\(752\) 23.9545 + 23.9545i 0.873530 + 0.873530i
\(753\) −3.16987 + 5.49038i −0.115517 + 0.200081i
\(754\) −40.0526 −1.45863
\(755\) −17.6603 35.3205i −0.642722 1.28544i
\(756\) 7.79423 + 22.5000i 0.283473 + 0.818317i
\(757\) 6.39230 6.39230i 0.232332 0.232332i −0.581333 0.813666i \(-0.697469\pi\)
0.813666 + 0.581333i \(0.197469\pi\)
\(758\) −23.9282 23.9282i −0.869111 0.869111i
\(759\) 3.12436 + 11.6603i 0.113407 + 0.423240i
\(760\) −1.00000 + 3.00000i −0.0362738 + 0.108821i
\(761\) −1.03590 0.598076i −0.0375513 0.0216802i 0.481107 0.876662i \(-0.340235\pi\)
−0.518658 + 0.854982i \(0.673568\pi\)
\(762\) −22.7942 + 39.4808i −0.825748 + 1.43024i
\(763\) −3.13397 + 16.2846i −0.113457 + 0.589542i
\(764\) 16.9808i 0.614342i
\(765\) 34.3923 + 38.7846i 1.24346 + 1.40226i
\(766\) −18.3564 10.5981i −0.663244 0.382924i
\(767\) −77.1051 20.6603i −2.78410 0.745999i
\(768\) 29.0885 + 16.7942i 1.04964 + 0.606010i
\(769\) 7.40192 + 12.8205i 0.266920 + 0.462319i 0.968065 0.250700i \(-0.0806607\pi\)
−0.701145 + 0.713019i \(0.747327\pi\)
\(770\) 0.267949 + 22.8564i 0.00965622 + 0.823688i
\(771\) −0.464102 0.124356i −0.0167142 0.00447856i
\(772\) 0.339746 0.339746i 0.0122277 0.0122277i
\(773\) −11.9019 44.4186i −0.428082 1.59763i −0.757098 0.653301i \(-0.773384\pi\)
0.329016 0.944324i \(-0.393283\pi\)
\(774\) −19.3923 −0.697042
\(775\) 0.875644 7.26795i 0.0314541 0.261072i
\(776\) 6.75833 + 3.90192i 0.242610 + 0.140071i
\(777\) 1.31347 2.70577i 0.0471203 0.0970690i
\(778\) −4.52628 + 16.8923i −0.162275 + 0.605618i
\(779\) −7.09808 4.09808i −0.254315 0.146829i
\(780\) 26.4904 23.4904i 0.948508 0.841091i
\(781\) 4.73205 + 8.19615i 0.169326 + 0.293281i
\(782\) 13.4641 50.2487i 0.481475 1.79689i
\(783\) 10.2058 17.6769i 0.364725 0.631721i
\(784\) −24.5526 + 19.3301i −0.876877 + 0.690362i
\(785\) 15.0981 + 17.0263i 0.538873 + 0.607694i
\(786\) 16.3923 + 4.39230i 0.584694 + 0.156668i
\(787\) 37.8301 + 37.8301i 1.34850 + 1.34850i 0.887294 + 0.461205i \(0.152583\pi\)
0.461205 + 0.887294i \(0.347417\pi\)
\(788\) −6.92820 6.92820i −0.246807 0.246807i
\(789\) 6.75833 6.75833i 0.240603 0.240603i
\(790\) 13.0000 + 14.6603i 0.462519 + 0.521588i
\(791\) 25.8564 1.85641i 0.919348 0.0660062i
\(792\) 3.00000 0.803848i 0.106600 0.0285635i
\(793\) −4.00000 + 14.9282i −0.142044 + 0.530116i
\(794\) 29.3205 + 50.7846i 1.04055 + 1.80228i
\(795\) −14.1962 4.73205i −0.503486 0.167829i
\(796\) 6.58846 + 3.80385i 0.233522 + 0.134824i
\(797\) 11.8827 44.3468i 0.420906 1.57084i −0.351797 0.936076i \(-0.614429\pi\)
0.772703 0.634767i \(-0.218904\pi\)
\(798\) 10.5622 21.7583i 0.373897 0.770237i
\(799\) −50.7846 29.3205i −1.79663 1.03729i
\(800\) −29.8468 + 23.4282i −1.05524 + 0.828312i
\(801\) −22.3923 + 38.7846i −0.791193 + 1.37039i
\(802\) 4.69615 + 17.5263i 0.165827 + 0.618874i
\(803\) −5.07180 + 5.07180i −0.178980 + 0.178980i
\(804\) 4.90192 + 18.2942i 0.172878 + 0.645188i
\(805\) −10.5167 17.7321i −0.370664 0.624973i
\(806\) −7.46410 12.9282i −0.262912 0.455377i
\(807\) −42.5885 + 24.5885i −1.49918 + 0.865555i
\(808\) −1.86603 0.500000i −0.0656465 0.0175899i
\(809\) 8.38269 + 4.83975i 0.294720 + 0.170156i 0.640068 0.768318i \(-0.278906\pi\)
−0.345349 + 0.938474i \(0.612239\pi\)
\(810\) 7.79423 + 38.0885i 0.273861 + 1.33829i
\(811\) 24.5885i 0.863418i −0.902013 0.431709i \(-0.857911\pi\)
0.902013 0.431709i \(-0.142089\pi\)
\(812\) −17.6769 3.40192i −0.620338 0.119384i
\(813\) −56.4449 −1.97961
\(814\) 2.19615 + 1.26795i 0.0769751 + 0.0444416i
\(815\) 6.80385 20.4115i 0.238328 0.714985i
\(816\) −57.7128 15.4641i −2.02035 0.541352i
\(817\) 6.46410 + 6.46410i 0.226150 + 0.226150i
\(818\) −30.4904 + 30.4904i −1.06607 + 1.06607i
\(819\) 34.6865 23.4904i 1.21205 0.820820i
\(820\) −5.19615 10.3923i −0.181458 0.362915i
\(821\) 10.4115 0.363365 0.181683 0.983357i \(-0.441846\pi\)
0.181683 + 0.983357i \(0.441846\pi\)
\(822\) 4.73205 0.165049
\(823\) 19.5622 + 19.5622i 0.681895 + 0.681895i 0.960427 0.278532i \(-0.0898479\pi\)
−0.278532 + 0.960427i \(0.589848\pi\)
\(824\) 2.33013 4.03590i 0.0811738 0.140597i
\(825\) −2.07180 + 17.1962i −0.0721307 + 0.598693i
\(826\) −69.5429 33.7583i −2.41971 1.17460i
\(827\) 22.8301 22.8301i 0.793881 0.793881i −0.188241 0.982123i \(-0.560279\pi\)
0.982123 + 0.188241i \(0.0602788\pi\)
\(828\) 12.8038 12.8038i 0.444964 0.444964i
\(829\) 4.83975 8.38269i 0.168091 0.291143i −0.769657 0.638457i \(-0.779573\pi\)
0.937749 + 0.347314i \(0.112906\pi\)
\(830\) 42.2846 + 27.9186i 1.46772 + 0.969068i
\(831\) 14.1962 + 14.1962i 0.492459 + 0.492459i
\(832\) −7.83013 + 29.2224i −0.271461 + 1.01311i
\(833\) 32.3923 43.3205i 1.12233 1.50097i
\(834\) 29.7846 + 29.7846i 1.03136 + 1.03136i
\(835\) −2.46410 + 7.39230i −0.0852738 + 0.255821i
\(836\) 8.19615 + 4.73205i 0.283470 + 0.163661i
\(837\) 7.60770 0.262960
\(838\) −4.36603 1.16987i −0.150822 0.0404126i
\(839\) 27.6147 47.8301i 0.953367 1.65128i 0.215304 0.976547i \(-0.430926\pi\)
0.738063 0.674732i \(-0.235741\pi\)
\(840\) −4.56218 + 2.70577i −0.157410 + 0.0933580i
\(841\) −6.78461 11.7513i −0.233952 0.405217i
\(842\) −2.40192 8.96410i −0.0827758 0.308923i
\(843\) −33.4019 + 19.2846i −1.15042 + 0.664197i
\(844\) −19.6077 + 11.3205i −0.674925 + 0.389668i
\(845\) −27.7224 18.3038i −0.953681 0.629671i
\(846\) −21.9904 38.0885i −0.756045 1.30951i
\(847\) 18.1865 + 3.50000i 0.624897 + 0.120261i
\(848\) 16.6603 4.46410i 0.572115 0.153298i
\(849\) −22.7942 + 6.10770i −0.782296 + 0.209616i
\(850\) 44.7846 59.7128i 1.53610 2.04813i
\(851\) −2.28719 −0.0784038
\(852\) 7.09808 12.2942i 0.243176 0.421193i
\(853\) −0.124356 0.464102i −0.00425786 0.0158905i 0.963764 0.266756i \(-0.0859516\pi\)
−0.968022 + 0.250865i \(0.919285\pi\)
\(854\) −6.53590 + 13.4641i −0.223654 + 0.460732i
\(855\) 10.0981 15.2942i 0.345347 0.523052i
\(856\) −3.06218 5.30385i −0.104663 0.181282i
\(857\) −1.80385 + 6.73205i −0.0616183 + 0.229962i −0.989867 0.141998i \(-0.954647\pi\)
0.928249 + 0.371960i \(0.121314\pi\)
\(858\) 17.6603 + 30.5885i 0.602911 + 1.04427i
\(859\) 5.16987 8.95448i 0.176394 0.305523i −0.764249 0.644921i \(-0.776890\pi\)
0.940643 + 0.339398i \(0.110223\pi\)
\(860\) 2.59808 + 12.6962i 0.0885937 + 0.432935i
\(861\) −4.50000 12.9904i −0.153360 0.442711i
\(862\) −10.2942 38.4186i −0.350623 1.30854i
\(863\) 10.0788 37.6147i 0.343088 1.28042i −0.551743 0.834014i \(-0.686037\pi\)
0.894830 0.446406i \(-0.147296\pi\)
\(864\) −27.8827 27.8827i −0.948588 0.948588i
\(865\) −37.8564 + 33.5692i −1.28716 + 1.14139i
\(866\) 0.339746i 0.0115450i
\(867\) 73.9808 2.51252
\(868\) −2.19615 6.33975i −0.0745423 0.215185i
\(869\) −7.85641 + 4.53590i −0.266510 + 0.153870i
\(870\) −27.8827 9.29423i −0.945312 0.315104i
\(871\) 28.8564 16.6603i 0.977762 0.564511i
\(872\) −0.839746 3.13397i −0.0284374 0.106130i
\(873\) −31.9808 31.9808i −1.08238 1.08238i
\(874\) −18.3923 −0.622129
\(875\) −4.52628 29.2321i −0.153016 0.988224i
\(876\) 10.3923 + 2.78461i 0.351123 + 0.0940832i
\(877\) −3.36603 12.5622i −0.113663 0.424195i 0.885521 0.464600i \(-0.153802\pi\)
−0.999183 + 0.0404052i \(0.987135\pi\)
\(878\) −48.9808 + 48.9808i −1.65302 + 1.65302i
\(879\) 8.53590 + 8.53590i 0.287909 + 0.287909i
\(880\) −8.92820 17.8564i −0.300970 0.601939i
\(881\) 51.0333i 1.71936i 0.510836 + 0.859678i \(0.329336\pi\)
−0.510836 + 0.859678i \(0.670664\pi\)
\(882\) 37.2846 15.9904i 1.25544 0.538424i
\(883\) 19.4378 + 19.4378i 0.654135 + 0.654135i 0.953986 0.299851i \(-0.0969370\pi\)
−0.299851 + 0.953986i \(0.596937\pi\)
\(884\) 70.6410i 2.37591i
\(885\) −48.8827 32.2750i −1.64317 1.08491i
\(886\) −23.5885 −0.792470
\(887\) −8.86603 + 2.37564i −0.297692 + 0.0797663i −0.404574 0.914505i \(-0.632580\pi\)
0.106882 + 0.994272i \(0.465913\pi\)
\(888\) 0.588457i 0.0197473i
\(889\) 32.4282 + 15.7417i 1.08761 + 0.527959i
\(890\) 61.1769 + 20.3923i 2.05065 + 0.683552i
\(891\) −18.0000 −0.603023
\(892\) −12.6962 + 3.40192i −0.425099 + 0.113905i
\(893\) −5.36603 + 20.0263i −0.179567 + 0.670154i
\(894\) 49.9808 + 13.3923i 1.67161 + 0.447906i
\(895\) 2.36603 + 1.56218i 0.0790875 + 0.0522178i
\(896\) 4.74167 9.76795i 0.158408 0.326324i
\(897\) −27.5885 15.9282i −0.921152 0.531827i
\(898\) −10.0263 10.0263i −0.334581 0.334581i
\(899\) −2.87564 + 4.98076i −0.0959081 + 0.166118i
\(900\) 23.8923 10.2058i 0.796410 0.340192i
\(901\) −25.8564 + 14.9282i −0.861402 + 0.497331i
\(902\) 11.1962 3.00000i 0.372791 0.0998891i
\(903\) 1.09808 + 15.2942i 0.0365417 + 0.508960i
\(904\) −4.39230 + 2.53590i −0.146086 + 0.0843427i
\(905\) −2.69615 + 44.9186i −0.0896231 + 1.49314i
\(906\) −41.7846 41.7846i −1.38820 1.38820i
\(907\) −12.7942 3.42820i −0.424825 0.113832i 0.0400707 0.999197i \(-0.487242\pi\)
−0.464896 + 0.885365i \(0.653908\pi\)
\(908\) −32.1506 8.61474i −1.06696 0.285890i
\(909\) 9.69615 + 5.59808i 0.321601 + 0.185676i
\(910\) −43.1506 42.1506i −1.43043 1.39728i
\(911\) −0.633975 + 1.09808i −0.0210045 + 0.0363809i −0.876337 0.481699i \(-0.840020\pi\)
0.855332 + 0.518080i \(0.173353\pi\)
\(912\) 21.1244i 0.699497i
\(913\) −16.5885 + 16.5885i −0.548998 + 0.548998i
\(914\) 62.9808i 2.08322i
\(915\) −6.24871 + 9.46410i −0.206576 + 0.312874i
\(916\) −8.00962 4.62436i −0.264645 0.152793i
\(917\) 2.53590 13.1769i 0.0837427 0.435140i
\(918\) 67.1769 + 38.7846i 2.21717 + 1.28008i
\(919\) −16.0981 + 9.29423i −0.531027 + 0.306588i −0.741434 0.671025i \(-0.765854\pi\)
0.210408 + 0.977614i \(0.432521\pi\)
\(920\) 3.36603 + 2.22243i 0.110975 + 0.0732714i
\(921\) 3.40192 + 12.6962i 0.112097 + 0.418352i
\(922\) 44.7487 11.9904i 1.47372 0.394882i
\(923\) −24.1244 6.46410i −0.794063 0.212768i
\(924\) 5.19615 + 15.0000i 0.170941 + 0.493464i
\(925\) −3.04552 1.22243i −0.100136 0.0401933i
\(926\) 14.3301 + 24.8205i 0.470917 + 0.815653i
\(927\) −19.0981 + 19.0981i −0.627263 + 0.627263i
\(928\) 28.7942 7.71539i 0.945217 0.253270i
\(929\) −31.7846 −1.04282 −0.521410 0.853307i \(-0.674594\pi\)
−0.521410 + 0.853307i \(0.674594\pi\)
\(930\) −2.19615 10.7321i −0.0720147 0.351918i
\(931\) −17.7583 7.09808i −0.582006 0.232630i
\(932\) 21.5885 + 5.78461i 0.707153 + 0.189481i
\(933\) 6.16987 10.6865i 0.201993 0.349861i
\(934\) −2.50000 4.33013i −0.0818025 0.141686i
\(935\) 22.9282 + 25.8564i 0.749832 + 0.845595i
\(936\) −4.09808 + 7.09808i −0.133950 + 0.232008i
\(937\) −5.53590 5.53590i −0.180850 0.180850i 0.610876 0.791726i \(-0.290817\pi\)
−0.791726 + 0.610876i \(0.790817\pi\)
\(938\) 30.4904 10.5622i 0.995546 0.344867i
\(939\) −3.80385 + 1.01924i −0.124134 + 0.0332616i
\(940\) −21.9904 + 19.5000i −0.717247 + 0.636020i
\(941\) 7.05256i 0.229907i −0.993371 0.114953i \(-0.963328\pi\)
0.993371 0.114953i \(-0.0366719\pi\)
\(942\) 29.4904 + 17.0263i 0.960849 + 0.554746i
\(943\) −7.39230 + 7.39230i −0.240727 + 0.240727i
\(944\) 67.5167 2.19748
\(945\) 29.5981 8.30385i 0.962825 0.270124i
\(946\) −12.9282 −0.420332
\(947\) 5.00000 5.00000i 0.162478 0.162478i −0.621185 0.783664i \(-0.713349\pi\)
0.783664 + 0.621185i \(0.213349\pi\)
\(948\) 11.7846 + 6.80385i 0.382746 + 0.220979i
\(949\) 18.9282i 0.614435i
\(950\) −24.4904 9.83013i −0.794573 0.318931i
\(951\) 20.0263 5.36603i 0.649397 0.174005i
\(952\) −2.00000 + 10.3923i −0.0648204 + 0.336817i
\(953\) 22.0526 + 22.0526i 0.714352 + 0.714352i 0.967443 0.253090i \(-0.0814470\pi\)
−0.253090 + 0.967443i \(0.581447\pi\)
\(954\) −22.3923 −0.724978
\(955\) 21.8827 + 1.31347i 0.708107 + 0.0425028i
\(956\) 1.73205 + 3.00000i 0.0560185 + 0.0970269i
\(957\) 6.80385 11.7846i 0.219937 0.380942i
\(958\) 32.2224 + 8.63397i 1.04106 + 0.278951i
\(959\) −0.267949 3.73205i −0.00865253 0.120514i
\(960\) −12.2321 + 18.5263i −0.394788 + 0.597933i
\(961\) 28.8564 0.930852
\(962\) −6.46410 + 1.73205i −0.208411 + 0.0558436i
\(963\) 9.18653 + 34.2846i 0.296032 + 1.10481i
\(964\) −19.4545 33.6962i −0.626587 1.08528i
\(965\) −0.411543 0.464102i −0.0132480 0.0149400i
\(966\) −23.3205 20.1962i −0.750325 0.649801i
\(967\) −51.0788 13.6865i −1.64258 0.440129i −0.685061 0.728485i \(-0.740225\pi\)
−0.957523 + 0.288356i \(0.906891\pi\)
\(968\) −3.50000 + 0.937822i −0.112494 + 0.0301427i
\(969\) −9.46410 35.3205i −0.304031 1.13466i
\(970\) −35.8827 + 54.3468i −1.15212 + 1.74497i
\(971\) −13.2224 + 7.63397i −0.424328 + 0.244986i −0.696927 0.717142i \(-0.745450\pi\)
0.272599 + 0.962128i \(0.412117\pi\)
\(972\) 13.5000 + 23.3827i 0.433013 + 0.750000i
\(973\) 21.8038 25.1769i 0.698999 0.807135i
\(974\) −51.5429 29.7583i −1.65154 0.953518i
\(975\) −28.2224 35.9545i −0.903841 1.15146i
\(976\) 13.0718i 0.418418i
\(977\) −28.1962 + 28.1962i −0.902075 + 0.902075i −0.995615 0.0935406i \(-0.970182\pi\)
0.0935406 + 0.995615i \(0.470182\pi\)
\(978\) 32.1962i 1.02952i
\(979\) −14.9282 + 25.8564i −0.477107 + 0.826374i
\(980\) −15.4641 22.2679i −0.493983 0.711324i
\(981\) 18.8038i 0.600361i
\(982\) −30.9545 8.29423i −0.987797 0.264679i
\(983\) 28.6506 + 7.67691i 0.913813 + 0.244856i 0.684939 0.728600i \(-0.259829\pi\)
0.228874 + 0.973456i \(0.426496\pi\)
\(984\) 1.90192 + 1.90192i 0.0606311 + 0.0606311i
\(985\) −9.46410 + 8.39230i −0.301551 + 0.267401i
\(986\) −50.7846 + 29.3205i −1.61731 + 0.933755i
\(987\) −28.7942 + 19.5000i −0.916530 + 0.620692i
\(988\) −24.1244 + 6.46410i −0.767498 + 0.205650i
\(989\) 10.0981 5.83013i 0.321100 0.185387i
\(990\) 5.19615 + 25.3923i 0.165145 + 0.807020i
\(991\) 4.00000 6.92820i 0.127064 0.220082i −0.795474 0.605988i \(-0.792778\pi\)
0.922538 + 0.385906i \(0.126111\pi\)
\(992\) 7.85641 + 7.85641i 0.249441 + 0.249441i
\(993\) −9.00000 5.19615i −0.285606 0.164895i
\(994\) −21.7583 10.5622i −0.690132 0.335012i
\(995\) 5.41154 8.19615i 0.171557 0.259835i
\(996\) 33.9904 + 9.10770i 1.07703 + 0.288588i
\(997\) −12.8827 + 48.0788i −0.407999 + 1.52267i 0.390458 + 0.920621i \(0.372317\pi\)
−0.798457 + 0.602052i \(0.794350\pi\)
\(998\) −32.8564 + 8.80385i −1.04005 + 0.278681i
\(999\) 0.882686 3.29423i 0.0279269 0.104225i
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 315.2.bs.d.178.1 yes 4
3.2 odd 2 945.2.bv.c.73.1 4
5.2 odd 4 315.2.bs.a.52.1 4
7.5 odd 6 315.2.cg.d.313.1 yes 4
9.4 even 3 315.2.cg.b.283.1 yes 4
9.5 odd 6 945.2.cj.c.388.1 4
15.2 even 4 945.2.bv.b.262.1 4
21.5 even 6 945.2.cj.b.208.1 4
35.12 even 12 315.2.cg.b.187.1 yes 4
45.22 odd 12 315.2.cg.d.157.1 yes 4
45.32 even 12 945.2.cj.b.577.1 4
63.5 even 6 945.2.bv.b.523.1 4
63.40 odd 6 315.2.bs.a.103.1 yes 4
105.47 odd 12 945.2.cj.c.397.1 4
315.257 odd 12 945.2.bv.c.712.1 4
315.292 even 12 inner 315.2.bs.d.292.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bs.a.52.1 4 5.2 odd 4
315.2.bs.a.103.1 yes 4 63.40 odd 6
315.2.bs.d.178.1 yes 4 1.1 even 1 trivial
315.2.bs.d.292.1 yes 4 315.292 even 12 inner
315.2.cg.b.187.1 yes 4 35.12 even 12
315.2.cg.b.283.1 yes 4 9.4 even 3
315.2.cg.d.157.1 yes 4 45.22 odd 12
315.2.cg.d.313.1 yes 4 7.5 odd 6
945.2.bv.b.262.1 4 15.2 even 4
945.2.bv.b.523.1 4 63.5 even 6
945.2.bv.c.73.1 4 3.2 odd 2
945.2.bv.c.712.1 4 315.257 odd 12
945.2.cj.b.208.1 4 21.5 even 6
945.2.cj.b.577.1 4 45.32 even 12
945.2.cj.c.388.1 4 9.5 odd 6
945.2.cj.c.397.1 4 105.47 odd 12