Properties

Label 315.2.bs.b.292.1
Level $315$
Weight $2$
Character 315.292
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 292.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.292
Dual form 315.2.bs.b.178.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 4.23205i) q^{10} +(2.73205 - 4.73205i) q^{11} +(2.59808 + 1.50000i) q^{12} +(3.73205 - 1.00000i) q^{13} +(0.366025 - 5.09808i) q^{14} +(3.46410 - 1.73205i) q^{15} +4.46410 q^{16} +(-2.73205 - 0.732051i) q^{17} +(-1.50000 + 5.59808i) q^{18} +(-1.63397 + 2.83013i) q^{19} +(-2.13397 + 3.23205i) q^{20} +(4.50000 - 0.866025i) q^{21} +(-10.1962 + 2.73205i) q^{22} +(-4.59808 - 1.23205i) q^{23} +(0.232051 + 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-6.46410 - 3.73205i) q^{26} -5.19615 q^{27} +(-3.46410 + 3.00000i) q^{28} +(6.00000 - 3.46410i) q^{29} +(-7.09808 - 2.36603i) q^{30} +0.196152i q^{31} +(-5.36603 - 5.36603i) q^{32} +(-4.73205 - 8.19615i) q^{33} +(2.73205 + 4.73205i) q^{34} +(0.767949 + 5.86603i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-4.09808 + 1.09808i) q^{37} +(6.09808 - 1.63397i) q^{38} +(1.73205 - 6.46410i) q^{39} +(-1.13397 + 0.232051i) q^{40} +(-2.19615 - 1.26795i) q^{41} +(-7.33013 - 4.96410i) q^{42} +(1.50000 + 0.401924i) q^{43} +(8.19615 + 4.73205i) q^{44} +(0.401924 - 6.69615i) q^{45} +(4.59808 + 7.96410i) q^{46} +(-9.29423 + 9.29423i) q^{47} +(3.86603 - 6.69615i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(3.59808 - 8.96410i) q^{50} +(-3.46410 + 3.46410i) q^{51} +(1.73205 + 6.46410i) q^{52} +(6.09808 + 1.63397i) q^{53} +(7.09808 + 7.09808i) q^{54} +(10.9282 - 5.46410i) q^{55} +(-1.36603 - 0.0980762i) q^{56} +(2.83013 + 4.90192i) q^{57} +(-12.9282 - 3.46410i) q^{58} +3.46410 q^{59} +(3.00000 + 6.00000i) q^{60} -11.3923i q^{61} +(0.267949 - 0.267949i) q^{62} +(2.59808 - 7.50000i) q^{63} +5.73205i q^{64} +(8.19615 + 2.73205i) q^{65} +(-4.73205 + 17.6603i) q^{66} +(0.901924 + 0.901924i) q^{67} +(1.26795 - 4.73205i) q^{68} +(-5.83013 + 5.83013i) q^{69} +(6.96410 - 9.06218i) q^{70} -6.00000 q^{71} +(1.50000 + 0.401924i) q^{72} +(-2.36603 + 8.83013i) q^{73} +(7.09808 + 4.09808i) q^{74} +(8.59808 + 1.03590i) q^{75} +(-4.90192 - 2.83013i) q^{76} +(14.1962 - 2.73205i) q^{77} +(-11.1962 + 6.46410i) q^{78} -4.53590i q^{79} +(8.33013 + 5.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.26795 + 4.73205i) q^{82} +(-0.366025 + 1.36603i) q^{83} +(1.50000 + 7.79423i) q^{84} +(-4.19615 - 4.73205i) q^{85} +(-1.50000 - 2.59808i) q^{86} -12.0000i q^{87} +(0.732051 + 2.73205i) q^{88} +(-4.59808 + 7.96410i) q^{89} +(-9.69615 + 8.59808i) q^{90} +(8.46410 + 5.73205i) q^{91} +(2.13397 - 7.96410i) q^{92} +(0.294229 + 0.169873i) q^{93} +25.3923 q^{94} +(-6.53590 + 3.26795i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(7.83013 + 2.09808i) q^{97} +(10.8301 - 8.09808i) q^{98} -16.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 4 q^{11} + 8 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 12 q^{20} + 18 q^{21} - 20 q^{22} - 8 q^{23} - 6 q^{24} - 6 q^{25} - 12 q^{26} + 24 q^{29} - 18 q^{30} - 18 q^{32} - 12 q^{33} + 4 q^{34} + 10 q^{35} + 18 q^{36} - 6 q^{37} + 14 q^{38} - 8 q^{40} + 12 q^{41} - 12 q^{42} + 6 q^{43} + 12 q^{44} + 12 q^{45} + 8 q^{46} - 6 q^{47} + 12 q^{48} - 4 q^{49} + 4 q^{50} + 14 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{56} - 6 q^{57} - 24 q^{58} + 12 q^{60} + 8 q^{62} + 12 q^{65} - 12 q^{66} + 14 q^{67} + 12 q^{68} - 6 q^{69} + 14 q^{70} - 24 q^{71} + 6 q^{72} - 6 q^{73} + 18 q^{74} + 24 q^{75} - 30 q^{76} + 36 q^{77} - 24 q^{78} + 16 q^{80} - 18 q^{81} + 12 q^{82} + 2 q^{83} + 6 q^{84} + 4 q^{85} - 6 q^{86} - 4 q^{88} - 8 q^{89} - 18 q^{90} + 20 q^{91} + 12 q^{92} - 30 q^{93} + 60 q^{94} - 40 q^{95} - 30 q^{96} + 14 q^{97} + 26 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 1.36603i −0.965926 0.965926i 0.0335125 0.999438i \(-0.489331\pi\)
−0.999438 + 0.0335125i \(0.989331\pi\)
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) 1.73205i 0.866025i
\(5\) 1.86603 + 1.23205i 0.834512 + 0.550990i
\(6\) −3.23205 + 0.866025i −1.31948 + 0.353553i
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) −0.366025 + 0.366025i −0.129410 + 0.129410i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −0.866025 4.23205i −0.273861 1.33829i
\(11\) 2.73205 4.73205i 0.823744 1.42677i −0.0791309 0.996864i \(-0.525215\pi\)
0.902875 0.429903i \(-0.141452\pi\)
\(12\) 2.59808 + 1.50000i 0.750000 + 0.433013i
\(13\) 3.73205 1.00000i 1.03508 0.277350i 0.299010 0.954250i \(-0.403344\pi\)
0.736075 + 0.676900i \(0.236677\pi\)
\(14\) 0.366025 5.09808i 0.0978244 1.36252i
\(15\) 3.46410 1.73205i 0.894427 0.447214i
\(16\) 4.46410 1.11603
\(17\) −2.73205 0.732051i −0.662620 0.177548i −0.0881917 0.996104i \(-0.528109\pi\)
−0.574428 + 0.818555i \(0.694775\pi\)
\(18\) −1.50000 + 5.59808i −0.353553 + 1.31948i
\(19\) −1.63397 + 2.83013i −0.374859 + 0.649276i −0.990306 0.138903i \(-0.955642\pi\)
0.615447 + 0.788179i \(0.288976\pi\)
\(20\) −2.13397 + 3.23205i −0.477171 + 0.722709i
\(21\) 4.50000 0.866025i 0.981981 0.188982i
\(22\) −10.1962 + 2.73205i −2.17383 + 0.582475i
\(23\) −4.59808 1.23205i −0.958765 0.256900i −0.254688 0.967023i \(-0.581973\pi\)
−0.704078 + 0.710123i \(0.748639\pi\)
\(24\) 0.232051 + 0.866025i 0.0473672 + 0.176777i
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) −6.46410 3.73205i −1.26771 0.731915i
\(27\) −5.19615 −1.00000
\(28\) −3.46410 + 3.00000i −0.654654 + 0.566947i
\(29\) 6.00000 3.46410i 1.11417 0.643268i 0.174265 0.984699i \(-0.444245\pi\)
0.939907 + 0.341431i \(0.110912\pi\)
\(30\) −7.09808 2.36603i −1.29593 0.431975i
\(31\) 0.196152i 0.0352300i 0.999845 + 0.0176150i \(0.00560732\pi\)
−0.999845 + 0.0176150i \(0.994393\pi\)
\(32\) −5.36603 5.36603i −0.948588 0.948588i
\(33\) −4.73205 8.19615i −0.823744 1.42677i
\(34\) 2.73205 + 4.73205i 0.468543 + 0.811540i
\(35\) 0.767949 + 5.86603i 0.129807 + 0.991539i
\(36\) 4.50000 2.59808i 0.750000 0.433013i
\(37\) −4.09808 + 1.09808i −0.673720 + 0.180523i −0.579430 0.815022i \(-0.696725\pi\)
−0.0942898 + 0.995545i \(0.530058\pi\)
\(38\) 6.09808 1.63397i 0.989239 0.265066i
\(39\) 1.73205 6.46410i 0.277350 1.03508i
\(40\) −1.13397 + 0.232051i −0.179297 + 0.0366905i
\(41\) −2.19615 1.26795i −0.342981 0.198020i 0.318608 0.947886i \(-0.396785\pi\)
−0.661590 + 0.749866i \(0.730118\pi\)
\(42\) −7.33013 4.96410i −1.13106 0.765978i
\(43\) 1.50000 + 0.401924i 0.228748 + 0.0612928i 0.371372 0.928484i \(-0.378887\pi\)
−0.142624 + 0.989777i \(0.545554\pi\)
\(44\) 8.19615 + 4.73205i 1.23562 + 0.713384i
\(45\) 0.401924 6.69615i 0.0599153 0.998203i
\(46\) 4.59808 + 7.96410i 0.677949 + 1.17424i
\(47\) −9.29423 + 9.29423i −1.35570 + 1.35570i −0.476561 + 0.879141i \(0.658117\pi\)
−0.879141 + 0.476561i \(0.841883\pi\)
\(48\) 3.86603 6.69615i 0.558013 0.966506i
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 3.59808 8.96410i 0.508845 1.26772i
\(51\) −3.46410 + 3.46410i −0.485071 + 0.485071i
\(52\) 1.73205 + 6.46410i 0.240192 + 0.896410i
\(53\) 6.09808 + 1.63397i 0.837635 + 0.224444i 0.652042 0.758183i \(-0.273913\pi\)
0.185593 + 0.982627i \(0.440579\pi\)
\(54\) 7.09808 + 7.09808i 0.965926 + 0.965926i
\(55\) 10.9282 5.46410i 1.47356 0.736779i
\(56\) −1.36603 0.0980762i −0.182543 0.0131060i
\(57\) 2.83013 + 4.90192i 0.374859 + 0.649276i
\(58\) −12.9282 3.46410i −1.69756 0.454859i
\(59\) 3.46410 0.450988 0.225494 0.974245i \(-0.427600\pi\)
0.225494 + 0.974245i \(0.427600\pi\)
\(60\) 3.00000 + 6.00000i 0.387298 + 0.774597i
\(61\) 11.3923i 1.45864i −0.684175 0.729318i \(-0.739838\pi\)
0.684175 0.729318i \(-0.260162\pi\)
\(62\) 0.267949 0.267949i 0.0340296 0.0340296i
\(63\) 2.59808 7.50000i 0.327327 0.944911i
\(64\) 5.73205i 0.716506i
\(65\) 8.19615 + 2.73205i 1.01661 + 0.338869i
\(66\) −4.73205 + 17.6603i −0.582475 + 2.17383i
\(67\) 0.901924 + 0.901924i 0.110188 + 0.110188i 0.760051 0.649863i \(-0.225174\pi\)
−0.649863 + 0.760051i \(0.725174\pi\)
\(68\) 1.26795 4.73205i 0.153761 0.573845i
\(69\) −5.83013 + 5.83013i −0.701865 + 0.701865i
\(70\) 6.96410 9.06218i 0.832369 1.08314i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.50000 + 0.401924i 0.176777 + 0.0473672i
\(73\) −2.36603 + 8.83013i −0.276922 + 1.03349i 0.677620 + 0.735412i \(0.263012\pi\)
−0.954542 + 0.298076i \(0.903655\pi\)
\(74\) 7.09808 + 4.09808i 0.825135 + 0.476392i
\(75\) 8.59808 + 1.03590i 0.992820 + 0.119615i
\(76\) −4.90192 2.83013i −0.562289 0.324638i
\(77\) 14.1962 2.73205i 1.61780 0.311346i
\(78\) −11.1962 + 6.46410i −1.26771 + 0.731915i
\(79\) 4.53590i 0.510328i −0.966898 0.255164i \(-0.917870\pi\)
0.966898 0.255164i \(-0.0821295\pi\)
\(80\) 8.33013 + 5.50000i 0.931337 + 0.614919i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 1.26795 + 4.73205i 0.140022 + 0.522568i
\(83\) −0.366025 + 1.36603i −0.0401765 + 0.149941i −0.983100 0.183068i \(-0.941397\pi\)
0.942924 + 0.333009i \(0.108064\pi\)
\(84\) 1.50000 + 7.79423i 0.163663 + 0.850420i
\(85\) −4.19615 4.73205i −0.455137 0.513263i
\(86\) −1.50000 2.59808i −0.161749 0.280158i
\(87\) 12.0000i 1.28654i
\(88\) 0.732051 + 2.73205i 0.0780369 + 0.291238i
\(89\) −4.59808 + 7.96410i −0.487395 + 0.844193i −0.999895 0.0144942i \(-0.995386\pi\)
0.512500 + 0.858687i \(0.328720\pi\)
\(90\) −9.69615 + 8.59808i −1.02206 + 0.906317i
\(91\) 8.46410 + 5.73205i 0.887279 + 0.600882i
\(92\) 2.13397 7.96410i 0.222482 0.830315i
\(93\) 0.294229 + 0.169873i 0.0305101 + 0.0176150i
\(94\) 25.3923 2.61902
\(95\) −6.53590 + 3.26795i −0.670569 + 0.335285i
\(96\) −12.6962 + 3.40192i −1.29580 + 0.347207i
\(97\) 7.83013 + 2.09808i 0.795029 + 0.213027i 0.633400 0.773824i \(-0.281659\pi\)
0.161629 + 0.986852i \(0.448325\pi\)
\(98\) 10.8301 8.09808i 1.09401 0.818029i
\(99\) −16.3923 −1.64749
\(100\) −7.96410 + 3.40192i −0.796410 + 0.340192i
\(101\) 15.2321 + 8.79423i 1.51565 + 0.875058i 0.999831 + 0.0183580i \(0.00584386\pi\)
0.515814 + 0.856700i \(0.327489\pi\)
\(102\) 9.46410 0.937086
\(103\) 1.06218 3.96410i 0.104659 0.390595i −0.893647 0.448771i \(-0.851862\pi\)
0.998306 + 0.0581764i \(0.0185286\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 9.46410 + 3.92820i 0.923602 + 0.383353i
\(106\) −6.09808 10.5622i −0.592298 1.02589i
\(107\) 2.36603 0.633975i 0.228732 0.0612886i −0.142632 0.989776i \(-0.545557\pi\)
0.371365 + 0.928487i \(0.378890\pi\)
\(108\) 9.00000i 0.866025i
\(109\) 1.73205 1.00000i 0.165900 0.0957826i −0.414751 0.909935i \(-0.636131\pi\)
0.580651 + 0.814152i \(0.302798\pi\)
\(110\) −22.3923 7.46410i −2.13502 0.711674i
\(111\) −1.90192 + 7.09808i −0.180523 + 0.673720i
\(112\) 7.73205 + 8.92820i 0.730610 + 0.843636i
\(113\) 1.90192 + 7.09808i 0.178918 + 0.667731i 0.995851 + 0.0909984i \(0.0290058\pi\)
−0.816933 + 0.576732i \(0.804328\pi\)
\(114\) 2.83013 10.5622i 0.265066 0.989239i
\(115\) −7.06218 7.96410i −0.658551 0.742656i
\(116\) 6.00000 + 10.3923i 0.557086 + 0.964901i
\(117\) −8.19615 8.19615i −0.757735 0.757735i
\(118\) −4.73205 4.73205i −0.435621 0.435621i
\(119\) −3.26795 6.73205i −0.299572 0.617126i
\(120\) −0.633975 + 1.90192i −0.0578737 + 0.173621i
\(121\) −9.42820 16.3301i −0.857109 1.48456i
\(122\) −15.5622 + 15.5622i −1.40893 + 1.40893i
\(123\) −3.80385 + 2.19615i −0.342981 + 0.198020i
\(124\) −0.339746 −0.0305101
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −13.7942 + 6.69615i −1.22889 + 0.596541i
\(127\) −15.7583 15.7583i −1.39833 1.39833i −0.804857 0.593468i \(-0.797758\pi\)
−0.593468 0.804857i \(-0.702242\pi\)
\(128\) −2.90192 + 2.90192i −0.256496 + 0.256496i
\(129\) 1.90192 1.90192i 0.167455 0.167455i
\(130\) −7.46410 14.9282i −0.654645 1.30929i
\(131\) −4.39230 + 2.53590i −0.383757 + 0.221562i −0.679452 0.733720i \(-0.737782\pi\)
0.295694 + 0.955283i \(0.404449\pi\)
\(132\) 14.1962 8.19615i 1.23562 0.713384i
\(133\) −8.49038 + 1.63397i −0.736209 + 0.141684i
\(134\) 2.46410i 0.212866i
\(135\) −9.69615 6.40192i −0.834512 0.550990i
\(136\) 1.26795 0.732051i 0.108726 0.0627728i
\(137\) −2.00000 + 0.535898i −0.170872 + 0.0457849i −0.343240 0.939248i \(-0.611525\pi\)
0.172369 + 0.985032i \(0.444858\pi\)
\(138\) 15.9282 1.35590
\(139\) 3.46410 6.00000i 0.293821 0.508913i −0.680889 0.732387i \(-0.738406\pi\)
0.974710 + 0.223474i \(0.0717396\pi\)
\(140\) −10.1603 + 1.33013i −0.858698 + 0.112416i
\(141\) 5.89230 + 21.9904i 0.496222 + 1.85192i
\(142\) 8.19615 + 8.19615i 0.687806 + 0.687806i
\(143\) 5.46410 20.3923i 0.456931 1.70529i
\(144\) −6.69615 11.5981i −0.558013 0.966506i
\(145\) 15.4641 + 0.928203i 1.28422 + 0.0770831i
\(146\) 15.2942 8.83013i 1.26576 0.730787i
\(147\) 9.52628 + 7.50000i 0.785714 + 0.618590i
\(148\) −1.90192 7.09808i −0.156337 0.583458i
\(149\) −2.89230 + 1.66987i −0.236947 + 0.136801i −0.613773 0.789483i \(-0.710349\pi\)
0.376826 + 0.926284i \(0.377016\pi\)
\(150\) −10.3301 13.1603i −0.843451 1.07453i
\(151\) −2.36603 + 4.09808i −0.192544 + 0.333497i −0.946093 0.323896i \(-0.895007\pi\)
0.753548 + 0.657392i \(0.228341\pi\)
\(152\) −0.437822 1.63397i −0.0355121 0.132533i
\(153\) 2.19615 + 8.19615i 0.177548 + 0.662620i
\(154\) −23.1244 15.6603i −1.86341 1.26194i
\(155\) −0.241670 + 0.366025i −0.0194114 + 0.0293999i
\(156\) 11.1962 + 3.00000i 0.896410 + 0.240192i
\(157\) 1.00000 1.00000i 0.0798087 0.0798087i −0.666076 0.745884i \(-0.732027\pi\)
0.745884 + 0.666076i \(0.232027\pi\)
\(158\) −6.19615 + 6.19615i −0.492939 + 0.492939i
\(159\) 7.73205 7.73205i 0.613192 0.613192i
\(160\) −3.40192 16.6244i −0.268946 1.31427i
\(161\) −5.50000 11.3301i −0.433461 0.892939i
\(162\) 16.7942 4.50000i 1.31948 0.353553i
\(163\) 2.36603 + 8.83013i 0.185321 + 0.691629i 0.994562 + 0.104151i \(0.0332125\pi\)
−0.809240 + 0.587478i \(0.800121\pi\)
\(164\) 2.19615 3.80385i 0.171491 0.297031i
\(165\) 1.26795 21.1244i 0.0987097 1.64453i
\(166\) 2.36603 1.36603i 0.183639 0.106024i
\(167\) 3.62436 + 13.5263i 0.280461 + 1.04669i 0.952093 + 0.305810i \(0.0989271\pi\)
−0.671632 + 0.740885i \(0.734406\pi\)
\(168\) −1.33013 + 1.96410i −0.102622 + 0.151534i
\(169\) 1.66987 0.964102i 0.128452 0.0741617i
\(170\) −0.732051 + 12.1962i −0.0561457 + 0.935402i
\(171\) 9.80385 0.749719
\(172\) −0.696152 + 2.59808i −0.0530811 + 0.198101i
\(173\) 10.0000 + 10.0000i 0.760286 + 0.760286i 0.976374 0.216088i \(-0.0693298\pi\)
−0.216088 + 0.976374i \(0.569330\pi\)
\(174\) −16.3923 + 16.3923i −1.24270 + 1.24270i
\(175\) −5.79423 + 11.8923i −0.438003 + 0.898974i
\(176\) 12.1962 21.1244i 0.919320 1.59231i
\(177\) 3.00000 5.19615i 0.225494 0.390567i
\(178\) 17.1603 4.59808i 1.28622 0.344640i
\(179\) −10.9019 + 6.29423i −0.814848 + 0.470453i −0.848637 0.528976i \(-0.822576\pi\)
0.0337886 + 0.999429i \(0.489243\pi\)
\(180\) 11.5981 + 0.696152i 0.864470 + 0.0518881i
\(181\) 11.4641i 0.852120i 0.904695 + 0.426060i \(0.140099\pi\)
−0.904695 + 0.426060i \(0.859901\pi\)
\(182\) −3.73205 19.3923i −0.276638 1.43745i
\(183\) −17.0885 9.86603i −1.26322 0.729318i
\(184\) 2.13397 1.23205i 0.157319 0.0908280i
\(185\) −9.00000 3.00000i −0.661693 0.220564i
\(186\) −0.169873 0.633975i −0.0124557 0.0464853i
\(187\) −10.9282 + 10.9282i −0.799149 + 0.799149i
\(188\) −16.0981 16.0981i −1.17407 1.17407i
\(189\) −9.00000 10.3923i −0.654654 0.755929i
\(190\) 13.3923 + 4.46410i 0.971580 + 0.323860i
\(191\) −17.6603 −1.27785 −0.638926 0.769269i \(-0.720621\pi\)
−0.638926 + 0.769269i \(0.720621\pi\)
\(192\) 8.59808 + 4.96410i 0.620513 + 0.358253i
\(193\) −14.4641 + 14.4641i −1.04115 + 1.04115i −0.0420326 + 0.999116i \(0.513383\pi\)
−0.999116 + 0.0420326i \(0.986617\pi\)
\(194\) −7.83013 13.5622i −0.562170 0.973708i
\(195\) 11.1962 9.92820i 0.801773 0.710973i
\(196\) −12.0000 1.73205i −0.857143 0.123718i
\(197\) −17.4641 17.4641i −1.24427 1.24427i −0.958214 0.286051i \(-0.907657\pi\)
−0.286051 0.958214i \(-0.592343\pi\)
\(198\) 22.3923 + 22.3923i 1.59135 + 1.59135i
\(199\) 3.92820 + 6.80385i 0.278463 + 0.482312i 0.971003 0.239068i \(-0.0768417\pi\)
−0.692540 + 0.721379i \(0.743508\pi\)
\(200\) −2.40192 0.964102i −0.169842 0.0681723i
\(201\) 2.13397 0.571797i 0.150519 0.0403314i
\(202\) −8.79423 32.8205i −0.618760 2.30924i
\(203\) 17.3205 + 6.00000i 1.21566 + 0.421117i
\(204\) −6.00000 6.00000i −0.420084 0.420084i
\(205\) −2.53590 5.07180i −0.177115 0.354230i
\(206\) −6.86603 + 3.96410i −0.478379 + 0.276192i
\(207\) 3.69615 + 13.7942i 0.256900 + 0.958765i
\(208\) 16.6603 4.46410i 1.15518 0.309530i
\(209\) 8.92820 + 15.4641i 0.617577 + 1.06967i
\(210\) −7.56218 18.2942i −0.521840 1.26242i
\(211\) −4.46410 + 7.73205i −0.307321 + 0.532296i −0.977775 0.209655i \(-0.932766\pi\)
0.670454 + 0.741951i \(0.266099\pi\)
\(212\) −2.83013 + 10.5622i −0.194374 + 0.725413i
\(213\) −5.19615 + 9.00000i −0.356034 + 0.616670i
\(214\) −4.09808 2.36603i −0.280139 0.161738i
\(215\) 2.30385 + 2.59808i 0.157121 + 0.177187i
\(216\) 1.90192 1.90192i 0.129410 0.129410i
\(217\) −0.392305 + 0.339746i −0.0266314 + 0.0230635i
\(218\) −3.73205 1.00000i −0.252766 0.0677285i
\(219\) 11.1962 + 11.1962i 0.756566 + 0.756566i
\(220\) 9.46410 + 18.9282i 0.638070 + 1.27614i
\(221\) −10.9282 −0.735111
\(222\) 12.2942 7.09808i 0.825135 0.476392i
\(223\) 1.33013 4.96410i 0.0890719 0.332421i −0.906982 0.421169i \(-0.861620\pi\)
0.996054 + 0.0887481i \(0.0282866\pi\)
\(224\) 1.43782 20.0263i 0.0960685 1.33806i
\(225\) 9.00000 12.0000i 0.600000 0.800000i
\(226\) 7.09808 12.2942i 0.472157 0.817800i
\(227\) −3.90192 14.5622i −0.258980 0.966526i −0.965833 0.259165i \(-0.916553\pi\)
0.706853 0.707360i \(-0.250114\pi\)
\(228\) −8.49038 + 4.90192i −0.562289 + 0.324638i
\(229\) 2.33013 + 4.03590i 0.153979 + 0.266700i 0.932687 0.360687i \(-0.117458\pi\)
−0.778708 + 0.627387i \(0.784124\pi\)
\(230\) −1.23205 + 20.5263i −0.0812390 + 1.35346i
\(231\) 8.19615 23.6603i 0.539267 1.55673i
\(232\) −0.928203 + 3.46410i −0.0609395 + 0.227429i
\(233\) 3.16987 + 11.8301i 0.207665 + 0.775017i 0.988621 + 0.150430i \(0.0480660\pi\)
−0.780955 + 0.624587i \(0.785267\pi\)
\(234\) 22.3923i 1.46383i
\(235\) −28.7942 + 5.89230i −1.87833 + 0.384372i
\(236\) 6.00000i 0.390567i
\(237\) −6.80385 3.92820i −0.441957 0.255164i
\(238\) −4.73205 + 13.6603i −0.306733 + 0.885463i
\(239\) 19.0526 + 11.0000i 1.23241 + 0.711531i 0.967531 0.252752i \(-0.0813355\pi\)
0.264876 + 0.964282i \(0.414669\pi\)
\(240\) 15.4641 7.73205i 0.998203 0.499102i
\(241\) 8.25833 + 4.76795i 0.531966 + 0.307131i 0.741817 0.670603i \(-0.233964\pi\)
−0.209851 + 0.977733i \(0.567298\pi\)
\(242\) −9.42820 + 35.1865i −0.606068 + 2.26188i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 19.7321 1.26322
\(245\) −10.4019 + 11.6962i −0.664555 + 0.747240i
\(246\) 8.19615 + 2.19615i 0.522568 + 0.140022i
\(247\) −3.26795 + 12.1962i −0.207935 + 0.776023i
\(248\) −0.0717968 0.0717968i −0.00455910 0.00455910i
\(249\) 1.73205 + 1.73205i 0.109764 + 0.109764i
\(250\) 17.7583 12.2942i 1.12314 0.777555i
\(251\) 5.85641i 0.369653i −0.982771 0.184827i \(-0.940828\pi\)
0.982771 0.184827i \(-0.0591723\pi\)
\(252\) 12.9904 + 4.50000i 0.818317 + 0.283473i
\(253\) −18.3923 + 18.3923i −1.15631 + 1.15631i
\(254\) 43.0526i 2.70136i
\(255\) −10.7321 + 2.19615i −0.672067 + 0.137528i
\(256\) 19.3923 1.21202
\(257\) 12.0263 + 3.22243i 0.750179 + 0.201010i 0.613597 0.789619i \(-0.289722\pi\)
0.136581 + 0.990629i \(0.456388\pi\)
\(258\) −5.19615 −0.323498
\(259\) −9.29423 6.29423i −0.577515 0.391104i
\(260\) −4.73205 + 14.1962i −0.293469 + 0.880408i
\(261\) −18.0000 10.3923i −1.11417 0.643268i
\(262\) 9.46410 + 2.53590i 0.584694 + 0.156668i
\(263\) −7.35641 27.4545i −0.453615 1.69292i −0.692127 0.721776i \(-0.743326\pi\)
0.238511 0.971140i \(-0.423341\pi\)
\(264\) 4.73205 + 1.26795i 0.291238 + 0.0780369i
\(265\) 9.36603 + 10.5622i 0.575350 + 0.648829i
\(266\) 13.8301 + 9.36603i 0.847979 + 0.574268i
\(267\) 7.96410 + 13.7942i 0.487395 + 0.844193i
\(268\) −1.56218 + 1.56218i −0.0954252 + 0.0954252i
\(269\) −4.96410 8.59808i −0.302667 0.524234i 0.674072 0.738665i \(-0.264544\pi\)
−0.976739 + 0.214431i \(0.931210\pi\)
\(270\) 4.50000 + 21.9904i 0.273861 + 1.33829i
\(271\) −9.92820 5.73205i −0.603095 0.348197i 0.167163 0.985929i \(-0.446539\pi\)
−0.770258 + 0.637732i \(0.779873\pi\)
\(272\) −12.1962 3.26795i −0.739500 0.198149i
\(273\) 15.9282 7.73205i 0.964019 0.467965i
\(274\) 3.46410 + 2.00000i 0.209274 + 0.120824i
\(275\) 27.1244 + 3.26795i 1.63566 + 0.197065i
\(276\) −10.0981 10.0981i −0.607833 0.607833i
\(277\) 19.3923 5.19615i 1.16517 0.312207i 0.376141 0.926562i \(-0.377251\pi\)
0.789029 + 0.614356i \(0.210584\pi\)
\(278\) −12.9282 + 3.46410i −0.775382 + 0.207763i
\(279\) 0.509619 0.294229i 0.0305101 0.0176150i
\(280\) −2.42820 1.86603i −0.145113 0.111516i
\(281\) 6.86603 + 11.8923i 0.409593 + 0.709435i 0.994844 0.101417i \(-0.0323375\pi\)
−0.585251 + 0.810852i \(0.699004\pi\)
\(282\) 21.9904 38.0885i 1.30951 2.26813i
\(283\) −15.7583 15.7583i −0.936736 0.936736i 0.0613790 0.998115i \(-0.480450\pi\)
−0.998115 + 0.0613790i \(0.980450\pi\)
\(284\) 10.3923i 0.616670i
\(285\) −0.758330 + 12.6340i −0.0449196 + 0.748372i
\(286\) −35.3205 + 20.3923i −2.08855 + 1.20582i
\(287\) −1.26795 6.58846i −0.0748447 0.388904i
\(288\) −5.89230 + 21.9904i −0.347207 + 1.29580i
\(289\) −7.79423 4.50000i −0.458484 0.264706i
\(290\) −19.8564 22.3923i −1.16601 1.31492i
\(291\) 9.92820 9.92820i 0.582002 0.582002i
\(292\) −15.2942 4.09808i −0.895027 0.239822i
\(293\) 20.2942 5.43782i 1.18560 0.317681i 0.388455 0.921468i \(-0.373009\pi\)
0.797146 + 0.603787i \(0.206342\pi\)
\(294\) −2.76795 23.2583i −0.161430 1.35645i
\(295\) 6.46410 + 4.26795i 0.376355 + 0.248490i
\(296\) 1.09808 1.90192i 0.0638244 0.110547i
\(297\) −14.1962 + 24.5885i −0.823744 + 1.42677i
\(298\) 6.23205 + 1.66987i 0.361013 + 0.0967331i
\(299\) −18.3923 −1.06365
\(300\) −1.79423 + 14.8923i −0.103590 + 0.859808i
\(301\) 1.79423 + 3.69615i 0.103418 + 0.213043i
\(302\) 8.83013 2.36603i 0.508117 0.136149i
\(303\) 26.3827 15.2321i 1.51565 0.875058i
\(304\) −7.29423 + 12.6340i −0.418353 + 0.724608i
\(305\) 14.0359 21.2583i 0.803693 1.21725i
\(306\) 8.19615 14.1962i 0.468543 0.811540i
\(307\) 17.5359 17.5359i 1.00083 1.00083i 0.000826926 1.00000i \(-0.499737\pi\)
1.00000 0.000826926i \(-0.000263219\pi\)
\(308\) 4.73205 + 24.5885i 0.269634 + 1.40106i
\(309\) −5.02628 5.02628i −0.285935 0.285935i
\(310\) 0.830127 0.169873i 0.0471480 0.00964814i
\(311\) 16.0000i 0.907277i 0.891186 + 0.453638i \(0.149874\pi\)
−0.891186 + 0.453638i \(0.850126\pi\)
\(312\) 1.73205 + 3.00000i 0.0980581 + 0.169842i
\(313\) −5.19615 5.19615i −0.293704 0.293704i 0.544838 0.838542i \(-0.316591\pi\)
−0.838542 + 0.544838i \(0.816591\pi\)
\(314\) −2.73205 −0.154179
\(315\) 14.0885 10.7942i 0.793795 0.608186i
\(316\) 7.85641 0.441957
\(317\) 8.46410 + 8.46410i 0.475391 + 0.475391i 0.903654 0.428263i \(-0.140874\pi\)
−0.428263 + 0.903654i \(0.640874\pi\)
\(318\) −21.1244 −1.18460
\(319\) 37.8564i 2.11955i
\(320\) −7.06218 + 10.6962i −0.394788 + 0.597933i
\(321\) 1.09808 4.09808i 0.0612886 0.228732i
\(322\) −7.96410 + 22.9904i −0.443822 + 1.28120i
\(323\) 6.53590 6.53590i 0.363667 0.363667i
\(324\) −13.5000 7.79423i −0.750000 0.433013i
\(325\) 11.9282 + 15.1962i 0.661658 + 0.842931i
\(326\) 8.83013 15.2942i 0.489056 0.847069i
\(327\) 3.46410i 0.191565i
\(328\) 1.26795 0.339746i 0.0700108 0.0187593i
\(329\) −34.6865 2.49038i −1.91233 0.137299i
\(330\) −30.5885 + 27.1244i −1.68384 + 1.49315i
\(331\) 18.3397 1.00804 0.504022 0.863691i \(-0.331853\pi\)
0.504022 + 0.863691i \(0.331853\pi\)
\(332\) −2.36603 0.633975i −0.129853 0.0347939i
\(333\) 9.00000 + 9.00000i 0.493197 + 0.493197i
\(334\) 13.5263 23.4282i 0.740125 1.28193i
\(335\) 0.571797 + 2.79423i 0.0312406 + 0.152665i
\(336\) 20.0885 3.86603i 1.09592 0.210909i
\(337\) 4.46410 1.19615i 0.243175 0.0651586i −0.135173 0.990822i \(-0.543159\pi\)
0.378348 + 0.925663i \(0.376492\pi\)
\(338\) −3.59808 0.964102i −0.195710 0.0524402i
\(339\) 12.2942 + 3.29423i 0.667731 + 0.178918i
\(340\) 8.19615 7.26795i 0.444499 0.394160i
\(341\) 0.928203 + 0.535898i 0.0502650 + 0.0290205i
\(342\) −13.3923 13.3923i −0.724173 0.724173i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) −0.696152 + 0.401924i −0.0375340 + 0.0216703i
\(345\) −18.0622 + 3.69615i −0.972435 + 0.198994i
\(346\) 27.3205i 1.46876i
\(347\) −14.8301 14.8301i −0.796123 0.796123i 0.186359 0.982482i \(-0.440331\pi\)
−0.982482 + 0.186359i \(0.940331\pi\)
\(348\) 20.7846 1.11417
\(349\) −17.0622 29.5526i −0.913317 1.58191i −0.809346 0.587332i \(-0.800178\pi\)
−0.103971 0.994580i \(-0.533155\pi\)
\(350\) 24.1603 8.33013i 1.29142 0.445264i
\(351\) −19.3923 + 5.19615i −1.03508 + 0.277350i
\(352\) −40.0526 + 10.7321i −2.13481 + 0.572020i
\(353\) −10.7321 + 2.87564i −0.571209 + 0.153055i −0.532851 0.846209i \(-0.678879\pi\)
−0.0383582 + 0.999264i \(0.512213\pi\)
\(354\) −11.1962 + 3.00000i −0.595069 + 0.159448i
\(355\) −11.1962 7.39230i −0.594230 0.392343i
\(356\) −13.7942 7.96410i −0.731093 0.422097i
\(357\) −12.9282 0.928203i −0.684233 0.0491257i
\(358\) 23.4904 + 6.29423i 1.24151 + 0.332660i
\(359\) −17.9545 10.3660i −0.947601 0.547098i −0.0552664 0.998472i \(-0.517601\pi\)
−0.892335 + 0.451374i \(0.850934\pi\)
\(360\) 2.30385 + 2.59808i 0.121423 + 0.136931i
\(361\) 4.16025 + 7.20577i 0.218961 + 0.379251i
\(362\) 15.6603 15.6603i 0.823085 0.823085i
\(363\) −32.6603 −1.71422
\(364\) −9.92820 + 14.6603i −0.520379 + 0.768406i
\(365\) −15.2942 + 13.5622i −0.800537 + 0.709877i
\(366\) 9.86603 + 36.8205i 0.515705 + 1.92464i
\(367\) −1.76795 6.59808i −0.0922862 0.344417i 0.904308 0.426881i \(-0.140388\pi\)
−0.996594 + 0.0824642i \(0.973721\pi\)
\(368\) −20.5263 5.50000i −1.07001 0.286707i
\(369\) 7.60770i 0.396041i
\(370\) 8.19615 + 16.3923i 0.426098 + 0.852195i
\(371\) 7.29423 + 15.0263i 0.378697 + 0.780126i
\(372\) −0.294229 + 0.509619i −0.0152550 + 0.0264225i
\(373\) −4.09808 1.09808i −0.212190 0.0568562i 0.151158 0.988510i \(-0.451700\pi\)
−0.363348 + 0.931653i \(0.618366\pi\)
\(374\) 29.8564 1.54384
\(375\) 14.7679 + 12.5263i 0.762614 + 0.646854i
\(376\) 6.80385i 0.350882i
\(377\) 18.9282 18.9282i 0.974852 0.974852i
\(378\) −1.90192 + 26.4904i −0.0978244 + 1.36252i
\(379\) 12.5359i 0.643926i −0.946752 0.321963i \(-0.895657\pi\)
0.946752 0.321963i \(-0.104343\pi\)
\(380\) −5.66025 11.3205i −0.290365 0.580730i
\(381\) −37.2846 + 9.99038i −1.91015 + 0.511823i
\(382\) 24.1244 + 24.1244i 1.23431 + 1.23431i
\(383\) 4.23205 15.7942i 0.216248 0.807047i −0.769476 0.638676i \(-0.779482\pi\)
0.985724 0.168372i \(-0.0538508\pi\)
\(384\) 1.83975 + 6.86603i 0.0938841 + 0.350380i
\(385\) 29.8564 + 12.3923i 1.52162 + 0.631570i
\(386\) 39.5167 2.01135
\(387\) −1.20577 4.50000i −0.0612928 0.228748i
\(388\) −3.63397 + 13.5622i −0.184487 + 0.688515i
\(389\) 1.03590 + 0.598076i 0.0525221 + 0.0303237i 0.526031 0.850465i \(-0.323680\pi\)
−0.473509 + 0.880789i \(0.657013\pi\)
\(390\) −28.8564 1.73205i −1.46120 0.0877058i
\(391\) 11.6603 + 6.73205i 0.589684 + 0.340454i
\(392\) −2.16987 2.90192i −0.109595 0.146569i
\(393\) 8.78461i 0.443125i
\(394\) 47.7128i 2.40374i
\(395\) 5.58846 8.46410i 0.281186 0.425875i
\(396\) 28.3923i 1.42677i
\(397\) 8.78461 + 32.7846i 0.440887 + 1.64541i 0.726573 + 0.687089i \(0.241112\pi\)
−0.285686 + 0.958323i \(0.592221\pi\)
\(398\) 3.92820 14.6603i 0.196903 0.734852i
\(399\) −4.90192 + 14.1506i −0.245403 + 0.708418i
\(400\) 8.76795 + 20.5263i 0.438397 + 1.02631i
\(401\) −11.6962 20.2583i −0.584078 1.01165i −0.994990 0.0999776i \(-0.968123\pi\)
0.410912 0.911675i \(-0.365210\pi\)
\(402\) −3.69615 2.13397i −0.184347 0.106433i
\(403\) 0.196152 + 0.732051i 0.00977105 + 0.0364660i
\(404\) −15.2321 + 26.3827i −0.757823 + 1.31259i
\(405\) −18.0000 + 9.00000i −0.894427 + 0.447214i
\(406\) −15.4641 31.8564i −0.767470 1.58101i
\(407\) −6.00000 + 22.3923i −0.297409 + 1.10995i
\(408\) 2.53590i 0.125546i
\(409\) −5.39230 −0.266632 −0.133316 0.991074i \(-0.542563\pi\)
−0.133316 + 0.991074i \(0.542563\pi\)
\(410\) −3.46410 + 10.3923i −0.171080 + 0.513239i
\(411\) −0.928203 + 3.46410i −0.0457849 + 0.170872i
\(412\) 6.86603 + 1.83975i 0.338265 + 0.0906378i
\(413\) 6.00000 + 6.92820i 0.295241 + 0.340915i
\(414\) 13.7942 23.8923i 0.677949 1.17424i
\(415\) −2.36603 + 2.09808i −0.116144 + 0.102991i
\(416\) −25.3923 14.6603i −1.24496 0.718778i
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 8.92820 33.3205i 0.436693 1.62976i
\(419\) 4.00000 6.92820i 0.195413 0.338465i −0.751623 0.659593i \(-0.770729\pi\)
0.947036 + 0.321128i \(0.104062\pi\)
\(420\) −6.80385 + 16.3923i −0.331994 + 0.799863i
\(421\) −11.5263 19.9641i −0.561756 0.972991i −0.997343 0.0728441i \(-0.976792\pi\)
0.435587 0.900147i \(-0.356541\pi\)
\(422\) 16.6603 4.46410i 0.811008 0.217309i
\(423\) 38.0885 + 10.2058i 1.85192 + 0.496222i
\(424\) −2.83013 + 1.63397i −0.137443 + 0.0793528i
\(425\) −2.00000 14.0000i −0.0970143 0.679100i
\(426\) 19.3923 5.19615i 0.939560 0.251754i
\(427\) 22.7846 19.7321i 1.10262 0.954901i
\(428\) 1.09808 + 4.09808i 0.0530775 + 0.198088i
\(429\) −25.8564 25.8564i −1.24836 1.24836i
\(430\) 0.401924 6.69615i 0.0193825 0.322917i
\(431\) 12.0981 + 20.9545i 0.582744 + 1.00934i 0.995153 + 0.0983430i \(0.0313542\pi\)
−0.412409 + 0.910999i \(0.635312\pi\)
\(432\) −23.1962 −1.11603
\(433\) −9.80385 9.80385i −0.471143 0.471143i 0.431141 0.902284i \(-0.358111\pi\)
−0.902284 + 0.431141i \(0.858111\pi\)
\(434\) 1.00000 + 0.0717968i 0.0480015 + 0.00344636i
\(435\) 14.7846 22.3923i 0.708868 1.07363i
\(436\) 1.73205 + 3.00000i 0.0829502 + 0.143674i
\(437\) 11.0000 11.0000i 0.526201 0.526201i
\(438\) 30.5885i 1.46157i
\(439\) 5.85641 0.279511 0.139756 0.990186i \(-0.455368\pi\)
0.139756 + 0.990186i \(0.455368\pi\)
\(440\) −2.00000 + 6.00000i −0.0953463 + 0.286039i
\(441\) 19.5000 7.79423i 0.928571 0.371154i
\(442\) 14.9282 + 14.9282i 0.710062 + 0.710062i
\(443\) −0.660254 + 0.660254i −0.0313696 + 0.0313696i −0.722618 0.691248i \(-0.757061\pi\)
0.691248 + 0.722618i \(0.257061\pi\)
\(444\) −12.2942 3.29423i −0.583458 0.156337i
\(445\) −18.3923 + 9.19615i −0.871879 + 0.435939i
\(446\) −8.59808 + 4.96410i −0.407131 + 0.235057i
\(447\) 5.78461i 0.273603i
\(448\) −11.4641 + 9.92820i −0.541628 + 0.469064i
\(449\) 1.58846i 0.0749639i −0.999297 0.0374820i \(-0.988066\pi\)
0.999297 0.0374820i \(-0.0119337\pi\)
\(450\) −28.6865 + 4.09808i −1.35230 + 0.193185i
\(451\) −12.0000 + 6.92820i −0.565058 + 0.326236i
\(452\) −12.2942 + 3.29423i −0.578272 + 0.154947i
\(453\) 4.09808 + 7.09808i 0.192544 + 0.333497i
\(454\) −14.5622 + 25.2224i −0.683437 + 1.18375i
\(455\) 8.73205 + 21.1244i 0.409365 + 0.990325i
\(456\) −2.83013 0.758330i −0.132533 0.0355121i
\(457\) −7.33975 7.33975i −0.343339 0.343339i 0.514282 0.857621i \(-0.328058\pi\)
−0.857621 + 0.514282i \(0.828058\pi\)
\(458\) 2.33013 8.69615i 0.108880 0.406345i
\(459\) 14.1962 + 3.80385i 0.662620 + 0.177548i
\(460\) 13.7942 12.2321i 0.643159 0.570322i
\(461\) 1.03590 0.598076i 0.0482466 0.0278552i −0.475683 0.879617i \(-0.657799\pi\)
0.523929 + 0.851762i \(0.324466\pi\)
\(462\) −43.5167 + 21.1244i −2.02458 + 0.982794i
\(463\) −9.42820 35.1865i −0.438166 1.63526i −0.733375 0.679824i \(-0.762056\pi\)
0.295209 0.955433i \(-0.404611\pi\)
\(464\) 26.7846 15.4641i 1.24344 0.717903i
\(465\) 0.339746 + 0.679492i 0.0157553 + 0.0315107i
\(466\) 11.8301 20.4904i 0.548020 0.949199i
\(467\) 3.47372 + 12.9641i 0.160745 + 0.599907i 0.998545 + 0.0539300i \(0.0171748\pi\)
−0.837800 + 0.545977i \(0.816159\pi\)
\(468\) 14.1962 14.1962i 0.656217 0.656217i
\(469\) −0.241670 + 3.36603i −0.0111593 + 0.155429i
\(470\) 47.3827 + 31.2846i 2.18560 + 1.44305i
\(471\) −0.633975 2.36603i −0.0292120 0.109021i
\(472\) −1.26795 + 1.26795i −0.0583621 + 0.0583621i
\(473\) 6.00000 6.00000i 0.275880 0.275880i
\(474\) 3.92820 + 14.6603i 0.180428 + 0.673368i
\(475\) −16.2224 1.95448i −0.744336 0.0896778i
\(476\) 11.6603 5.66025i 0.534447 0.259437i
\(477\) −4.90192 18.2942i −0.224444 0.837635i
\(478\) −11.0000 41.0526i −0.503128 1.87770i
\(479\) −2.63397 + 4.56218i −0.120349 + 0.208451i −0.919905 0.392140i \(-0.871735\pi\)
0.799556 + 0.600591i \(0.205068\pi\)
\(480\) −27.8827 9.29423i −1.27266 0.424222i
\(481\) −14.1962 + 8.19615i −0.647289 + 0.373712i
\(482\) −4.76795 17.7942i −0.217174 0.810505i
\(483\) −21.7583 1.56218i −0.990038 0.0710816i
\(484\) 28.2846 16.3301i 1.28566 0.742279i
\(485\) 12.0263 + 13.5622i 0.546085 + 0.615827i
\(486\) 7.79423 29.0885i 0.353553 1.31948i
\(487\) 8.68653 32.4186i 0.393624 1.46903i −0.430486 0.902597i \(-0.641658\pi\)
0.824110 0.566429i \(-0.191675\pi\)
\(488\) 4.16987 + 4.16987i 0.188761 + 0.188761i
\(489\) 15.2942 + 4.09808i 0.691629 + 0.185321i
\(490\) 30.1865 1.76795i 1.36369 0.0798678i
\(491\) 8.46410 14.6603i 0.381980 0.661608i −0.609366 0.792889i \(-0.708576\pi\)
0.991345 + 0.131281i \(0.0419091\pi\)
\(492\) −3.80385 6.58846i −0.171491 0.297031i
\(493\) −18.9282 + 5.07180i −0.852483 + 0.228422i
\(494\) 21.1244 12.1962i 0.950430 0.548731i
\(495\) −30.5885 20.1962i −1.37485 0.907750i
\(496\) 0.875644i 0.0393176i
\(497\) −10.3923 12.0000i −0.466159 0.538274i
\(498\) 4.73205i 0.212048i
\(499\) −6.12436 + 3.53590i −0.274164 + 0.158289i −0.630778 0.775963i \(-0.717264\pi\)
0.356615 + 0.934252i \(0.383931\pi\)
\(500\) −19.0526 3.46410i −0.852056 0.154919i
\(501\) 23.4282 + 6.27757i 1.04669 + 0.280461i
\(502\) −8.00000 + 8.00000i −0.357057 + 0.357057i
\(503\) −10.0718 10.0718i −0.449079 0.449079i 0.445969 0.895048i \(-0.352859\pi\)
−0.895048 + 0.445969i \(0.852859\pi\)
\(504\) 1.79423 + 3.69615i 0.0799213 + 0.164640i
\(505\) 17.5885 + 35.1769i 0.782676 + 1.56535i
\(506\) 50.2487 2.23383
\(507\) 3.33975i 0.148323i
\(508\) 27.2942 27.2942i 1.21099 1.21099i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 17.6603 + 11.6603i 0.782009 + 0.516325i
\(511\) −21.7583 + 10.5622i −0.962532 + 0.467243i
\(512\) −20.6865 20.6865i −0.914224 0.914224i
\(513\) 8.49038 14.7058i 0.374859 0.649276i
\(514\) −12.0263 20.8301i −0.530456 0.918778i
\(515\) 6.86603 6.08846i 0.302553 0.268289i
\(516\) 3.29423 + 3.29423i 0.145020 + 0.145020i
\(517\) 18.5885 + 69.3731i 0.817519 + 3.05102i
\(518\) 4.09808 + 21.2942i 0.180059 + 0.935615i
\(519\) 23.6603 6.33975i 1.03857 0.278284i
\(520\) −4.00000 + 2.00000i −0.175412 + 0.0877058i
\(521\) 37.6244 21.7224i 1.64835 0.951677i 0.670626 0.741796i \(-0.266026\pi\)
0.977727 0.209881i \(-0.0673078\pi\)
\(522\) 10.3923 + 38.7846i 0.454859 + 1.69756i
\(523\) −4.96410 + 1.33013i −0.217065 + 0.0581624i −0.365713 0.930728i \(-0.619175\pi\)
0.148648 + 0.988890i \(0.452508\pi\)
\(524\) −4.39230 7.60770i −0.191879 0.332344i
\(525\) 12.8205 + 18.9904i 0.559533 + 0.828808i
\(526\) −27.4545 + 47.5526i −1.19707 + 2.07339i
\(527\) 0.143594 0.535898i 0.00625503 0.0233441i
\(528\) −21.1244 36.5885i −0.919320 1.59231i
\(529\) −0.294229 0.169873i −0.0127925 0.00738578i
\(530\) 1.63397 27.2224i 0.0709753 1.18247i
\(531\) −5.19615 9.00000i −0.225494 0.390567i
\(532\) −2.83013 14.7058i −0.122702 0.637576i
\(533\) −9.46410 2.53590i −0.409936 0.109842i
\(534\) 7.96410 29.7224i 0.344640 1.28622i
\(535\) 5.19615 + 1.73205i 0.224649 + 0.0748831i
\(536\) −0.660254 −0.0285186
\(537\) 21.8038i 0.940905i
\(538\) −4.96410 + 18.5263i −0.214018 + 0.798725i
\(539\) 30.0526 + 23.6603i 1.29446 + 1.01912i
\(540\) 11.0885 16.7942i 0.477171 0.722709i
\(541\) 4.96410 8.59808i 0.213423 0.369660i −0.739360 0.673310i \(-0.764872\pi\)
0.952784 + 0.303650i \(0.0982053\pi\)
\(542\) 5.73205 + 21.3923i 0.246213 + 0.918878i
\(543\) 17.1962 + 9.92820i 0.737958 + 0.426060i
\(544\) 10.7321 + 18.5885i 0.460133 + 0.796974i
\(545\) 4.46410 + 0.267949i 0.191221 + 0.0114777i
\(546\) −32.3205 11.1962i −1.38319 0.479151i
\(547\) 3.31347 12.3660i 0.141674 0.528733i −0.858207 0.513303i \(-0.828422\pi\)
0.999881 0.0154299i \(-0.00491169\pi\)
\(548\) −0.928203 3.46410i −0.0396509 0.147979i
\(549\) −29.5981 + 17.0885i −1.26322 + 0.729318i
\(550\) −32.5885 41.5167i −1.38958 1.77028i
\(551\) 22.6410i 0.964540i
\(552\) 4.26795i 0.181656i
\(553\) 9.07180 7.85641i 0.385772 0.334088i
\(554\) −33.5885 19.3923i −1.42704 0.823900i
\(555\) −12.2942 + 10.9019i −0.521861 + 0.462761i
\(556\) 10.3923 + 6.00000i 0.440732 + 0.254457i
\(557\) 4.09808 15.2942i 0.173641 0.648037i −0.823138 0.567841i \(-0.807779\pi\)
0.996779 0.0801960i \(-0.0255546\pi\)
\(558\) −1.09808 0.294229i −0.0464853 0.0124557i
\(559\) 6.00000 0.253773
\(560\) 3.42820 + 26.1865i 0.144868 + 1.10658i
\(561\) 6.92820 + 25.8564i 0.292509 + 1.09166i
\(562\) 6.86603 25.6244i 0.289626 1.08090i
\(563\) −15.1699 15.1699i −0.639334 0.639334i 0.311057 0.950391i \(-0.399317\pi\)
−0.950391 + 0.311057i \(0.899317\pi\)
\(564\) −38.0885 + 10.2058i −1.60381 + 0.429740i
\(565\) −5.19615 + 15.5885i −0.218604 + 0.655811i
\(566\) 43.0526i 1.80963i
\(567\) −23.3827 + 4.50000i −0.981981 + 0.188982i
\(568\) 2.19615 2.19615i 0.0921485 0.0921485i
\(569\) 18.7846i 0.787492i −0.919219 0.393746i \(-0.871179\pi\)
0.919219 0.393746i \(-0.128821\pi\)
\(570\) 18.2942 16.2224i 0.766261 0.679483i
\(571\) −20.2487 −0.847382 −0.423691 0.905807i \(-0.639266\pi\)
−0.423691 + 0.905807i \(0.639266\pi\)
\(572\) 35.3205 + 9.46410i 1.47682 + 0.395714i
\(573\) −15.2942 + 26.4904i −0.638926 + 1.10665i
\(574\) −7.26795 + 10.7321i −0.303358 + 0.447947i
\(575\) −3.36603 23.5622i −0.140373 0.982611i
\(576\) 14.8923 8.59808i 0.620513 0.358253i
\(577\) 4.92820 + 1.32051i 0.205164 + 0.0549735i 0.359937 0.932977i \(-0.382798\pi\)
−0.154773 + 0.987950i \(0.549465\pi\)
\(578\) 4.50000 + 16.7942i 0.187175 + 0.698548i
\(579\) 9.16987 + 34.2224i 0.381087 + 1.42224i
\(580\) −1.60770 + 26.7846i −0.0667559 + 1.11217i
\(581\) −3.36603 + 1.63397i −0.139646 + 0.0677887i
\(582\) −27.1244 −1.12434
\(583\) 24.3923 24.3923i 1.01023 1.01023i
\(584\) −2.36603 4.09808i −0.0979068 0.169580i
\(585\) −5.19615 25.3923i −0.214834 1.04984i
\(586\) −35.1506 20.2942i −1.45206 0.838347i
\(587\) −32.1865 8.62436i −1.32848 0.355965i −0.476332 0.879265i \(-0.658034\pi\)
−0.852148 + 0.523300i \(0.824701\pi\)
\(588\) −12.9904 + 16.5000i −0.535714 + 0.680449i
\(589\) −0.555136 0.320508i −0.0228740 0.0132063i
\(590\) −3.00000 14.6603i −0.123508 0.603553i
\(591\) −41.3205 + 11.0718i −1.69970 + 0.455433i
\(592\) −18.2942 + 4.90192i −0.751888 + 0.201468i
\(593\) −2.73205 + 0.732051i −0.112192 + 0.0300617i −0.314478 0.949265i \(-0.601830\pi\)
0.202286 + 0.979326i \(0.435163\pi\)
\(594\) 52.9808 14.1962i 2.17383 0.582475i
\(595\) 2.19615 16.5885i 0.0900335 0.680060i
\(596\) −2.89230 5.00962i −0.118473 0.205202i
\(597\) 13.6077 0.556926
\(598\) 25.1244 + 25.1244i 1.02741 + 1.02741i
\(599\) 30.9808i 1.26584i 0.774217 + 0.632920i \(0.218144\pi\)
−0.774217 + 0.632920i \(0.781856\pi\)
\(600\) −3.52628 + 2.76795i −0.143960 + 0.113001i
\(601\) 20.6603 11.9282i 0.842749 0.486562i −0.0154485 0.999881i \(-0.504918\pi\)
0.858198 + 0.513319i \(0.171584\pi\)
\(602\) 2.59808 7.50000i 0.105890 0.305677i
\(603\) 0.990381 3.69615i 0.0403314 0.150519i
\(604\) −7.09808 4.09808i −0.288817 0.166748i
\(605\) 2.52628 42.0885i 0.102708 1.71114i
\(606\) −56.8468 15.2321i −2.30924 0.618760i
\(607\) −4.09808 1.09808i −0.166336 0.0445695i 0.174690 0.984623i \(-0.444108\pi\)
−0.341026 + 0.940054i \(0.610774\pi\)
\(608\) 23.9545 6.41858i 0.971483 0.260308i
\(609\) 24.0000 20.7846i 0.972529 0.842235i
\(610\) −48.2128 + 9.86603i −1.95208 + 0.399464i
\(611\) −25.3923 + 43.9808i −1.02726 + 1.77927i
\(612\) −14.1962 + 3.80385i −0.573845 + 0.153761i
\(613\) 41.4186 + 11.0981i 1.67288 + 0.448247i 0.965885 0.258971i \(-0.0833833\pi\)
0.706996 + 0.707218i \(0.250050\pi\)
\(614\) −47.9090 −1.93345
\(615\) −9.80385 0.588457i −0.395329 0.0237289i
\(616\) −4.19615 + 6.19615i −0.169068 + 0.249650i
\(617\) −2.09808 + 0.562178i −0.0844654 + 0.0226324i −0.300804 0.953686i \(-0.597255\pi\)
0.216339 + 0.976318i \(0.430588\pi\)
\(618\) 13.7321i 0.552384i
\(619\) −12.4904 + 21.6340i −0.502031 + 0.869543i 0.497966 + 0.867196i \(0.334080\pi\)
−0.999997 + 0.00234656i \(0.999253\pi\)
\(620\) −0.633975 0.418584i −0.0254610 0.0168107i
\(621\) 23.8923 + 6.40192i 0.958765 + 0.256900i
\(622\) 21.8564 21.8564i 0.876362 0.876362i
\(623\) −23.8923 + 4.59808i −0.957225 + 0.184218i
\(624\) 7.73205 28.8564i 0.309530 1.15518i
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 14.1962i 0.567392i
\(627\) 30.9282 1.23515
\(628\) 1.73205 + 1.73205i 0.0691164 + 0.0691164i
\(629\) 12.0000 0.478471
\(630\) −33.9904 4.50000i −1.35421 0.179284i
\(631\) 37.3205 1.48571 0.742853 0.669455i \(-0.233472\pi\)
0.742853 + 0.669455i \(0.233472\pi\)
\(632\) 1.66025 + 1.66025i 0.0660414 + 0.0660414i
\(633\) 7.73205 + 13.3923i 0.307321 + 0.532296i
\(634\) 23.1244i 0.918385i
\(635\) −9.99038 48.8205i −0.396456 1.93738i
\(636\) 13.3923 + 13.3923i 0.531039 + 0.531039i
\(637\) 3.19615 + 26.8564i 0.126636 + 1.06409i
\(638\) −51.7128 + 51.7128i −2.04733 + 2.04733i
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) −8.99038 + 1.83975i −0.355376 + 0.0727223i
\(641\) 15.7224 27.2321i 0.620999 1.07560i −0.368301 0.929706i \(-0.620061\pi\)
0.989300 0.145895i \(-0.0466061\pi\)
\(642\) −7.09808 + 4.09808i −0.280139 + 0.161738i
\(643\) 0.696152 0.186533i 0.0274536 0.00735616i −0.245066 0.969506i \(-0.578810\pi\)
0.272520 + 0.962150i \(0.412143\pi\)
\(644\) 19.6244 9.52628i 0.773308 0.375388i
\(645\) 5.89230 1.20577i 0.232009 0.0474772i
\(646\) −17.8564 −0.702551
\(647\) 18.8301 + 5.04552i 0.740289 + 0.198360i 0.609206 0.793012i \(-0.291488\pi\)
0.131082 + 0.991371i \(0.458155\pi\)
\(648\) −1.20577 4.50000i −0.0473672 0.176777i
\(649\) 9.46410 16.3923i 0.371498 0.643454i
\(650\) 4.46410 37.0526i 0.175096 1.45332i
\(651\) 0.169873 + 0.882686i 0.00665785 + 0.0345952i
\(652\) −15.2942 + 4.09808i −0.598968 + 0.160493i
\(653\) −24.2224 6.49038i −0.947897 0.253988i −0.248427 0.968651i \(-0.579914\pi\)
−0.699470 + 0.714662i \(0.746580\pi\)
\(654\) −4.73205 + 4.73205i −0.185038 + 0.185038i
\(655\) −11.3205 0.679492i −0.442329 0.0265499i
\(656\) −9.80385 5.66025i −0.382776 0.220996i
\(657\) 26.4904 7.09808i 1.03349 0.276922i
\(658\) 43.9808 + 50.7846i 1.71455 + 1.97979i
\(659\) −22.5167 + 13.0000i −0.877125 + 0.506408i −0.869709 0.493564i \(-0.835694\pi\)
−0.00741531 + 0.999973i \(0.502360\pi\)
\(660\) 36.5885 + 2.19615i 1.42420 + 0.0854851i
\(661\) 11.0000i 0.427850i 0.976850 + 0.213925i \(0.0686249\pi\)
−0.976850 + 0.213925i \(0.931375\pi\)
\(662\) −25.0526 25.0526i −0.973695 0.973695i
\(663\) −9.46410 + 16.3923i −0.367555 + 0.636624i
\(664\) −0.366025 0.633975i −0.0142045 0.0246030i
\(665\) −17.8564 7.41154i −0.692442 0.287407i
\(666\) 24.5885i 0.952783i
\(667\) −31.8564 + 8.53590i −1.23348 + 0.330511i
\(668\) −23.4282 + 6.27757i −0.906464 + 0.242886i
\(669\) −6.29423 6.29423i −0.243349 0.243349i
\(670\) 3.03590 4.59808i 0.117287 0.177639i
\(671\) −53.9090 31.1244i −2.08113 1.20154i
\(672\) −28.7942 19.5000i −1.11076 0.752229i
\(673\) 25.8564 + 6.92820i 0.996691 + 0.267063i 0.720059 0.693913i \(-0.244115\pi\)
0.276633 + 0.960976i \(0.410782\pi\)
\(674\) −7.73205 4.46410i −0.297827 0.171951i
\(675\) −10.2058 23.8923i −0.392820 0.919615i
\(676\) 1.66987 + 2.89230i 0.0642259 + 0.111242i
\(677\) 35.9090 35.9090i 1.38009 1.38009i 0.535660 0.844434i \(-0.320063\pi\)
0.844434 0.535660i \(-0.179937\pi\)
\(678\) −12.2942 21.2942i −0.472157 0.817800i
\(679\) 9.36603 + 19.2942i 0.359435 + 0.740445i
\(680\) 3.26795 + 0.196152i 0.125320 + 0.00752210i
\(681\) −25.2224 6.75833i −0.966526 0.258980i
\(682\) −0.535898 2.00000i −0.0205206 0.0765840i
\(683\) 14.9641 + 4.00962i 0.572585 + 0.153424i 0.533482 0.845811i \(-0.320883\pi\)
0.0391034 + 0.999235i \(0.487550\pi\)
\(684\) 16.9808i 0.649276i
\(685\) −4.39230 1.46410i −0.167821 0.0559404i
\(686\) 34.9545 + 7.63397i 1.33457 + 0.291467i
\(687\) 8.07180 0.307958
\(688\) 6.69615 + 1.79423i 0.255288 + 0.0684043i
\(689\) 24.3923 0.929273
\(690\) 29.7224 + 19.6244i 1.13151 + 0.747086i
\(691\) 10.5885i 0.402804i 0.979509 + 0.201402i \(0.0645497\pi\)
−0.979509 + 0.201402i \(0.935450\pi\)
\(692\) −17.3205 + 17.3205i −0.658427 + 0.658427i
\(693\) −28.3923 32.7846i −1.07853 1.24538i
\(694\) 40.5167i 1.53799i
\(695\) 13.8564 6.92820i 0.525603 0.262802i
\(696\) 4.39230 + 4.39230i 0.166490 + 0.166490i
\(697\) 5.07180 + 5.07180i 0.192108 + 0.192108i
\(698\) −17.0622 + 63.6769i −0.645813 + 2.41021i
\(699\) 20.4904 + 5.49038i 0.775017 + 0.207665i
\(700\) −20.5981 10.0359i −0.778534 0.379321i
\(701\) −47.4641 −1.79269 −0.896347 0.443353i \(-0.853789\pi\)
−0.896347 + 0.443353i \(0.853789\pi\)
\(702\) 33.5885 + 19.3923i 1.26771 + 0.731915i
\(703\) 3.58846 13.3923i 0.135341 0.505100i
\(704\) 27.1244 + 15.6603i 1.02229 + 0.590218i
\(705\) −16.0981 + 48.2942i −0.606289 + 1.81887i
\(706\) 18.5885 + 10.7321i 0.699586 + 0.403906i
\(707\) 8.79423 + 45.6962i 0.330741 + 1.71858i
\(708\) 9.00000 + 5.19615i 0.338241 + 0.195283i
\(709\) 6.71281i 0.252105i 0.992024 + 0.126052i \(0.0402308\pi\)
−0.992024 + 0.126052i \(0.959769\pi\)
\(710\) 5.19615 + 25.3923i 0.195008 + 0.952956i
\(711\) −11.7846 + 6.80385i −0.441957 + 0.255164i
\(712\) −1.23205 4.59808i −0.0461731 0.172320i
\(713\) 0.241670 0.901924i 0.00905060 0.0337773i
\(714\) 16.3923 + 18.9282i 0.613467 + 0.708370i
\(715\) 35.3205 31.3205i 1.32091 1.17132i
\(716\) −10.9019 18.8827i −0.407424 0.705679i
\(717\) 33.0000 19.0526i 1.23241 0.711531i
\(718\) 10.3660 + 38.6865i 0.386857 + 1.44377i
\(719\) −15.5622 + 26.9545i −0.580371 + 1.00523i 0.415064 + 0.909792i \(0.363759\pi\)
−0.995435 + 0.0954403i \(0.969574\pi\)
\(720\) 1.79423 29.8923i 0.0668670 1.11402i
\(721\) 9.76795 4.74167i 0.363777 0.176589i
\(722\) 4.16025 15.5263i 0.154829 0.577828i
\(723\) 14.3038 8.25833i 0.531966 0.307131i
\(724\) −19.8564 −0.737958
\(725\) 27.7128 + 20.7846i 1.02923 + 0.771921i
\(726\) 44.6147 + 44.6147i 1.65581 + 1.65581i
\(727\) 5.13397 + 1.37564i 0.190409 + 0.0510198i 0.352763 0.935713i \(-0.385242\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(728\) −5.19615 + 1.00000i −0.192582 + 0.0370625i
\(729\) 27.0000 1.00000
\(730\) 39.4186 + 2.36603i 1.45895 + 0.0875705i
\(731\) −3.80385 2.19615i −0.140690 0.0812276i
\(732\) 17.0885 29.5981i 0.631608 1.09398i
\(733\) −5.73205 + 21.3923i −0.211718 + 0.790143i 0.775578 + 0.631252i \(0.217459\pi\)
−0.987296 + 0.158891i \(0.949208\pi\)
\(734\) −6.59808 + 11.4282i −0.243539 + 0.421823i
\(735\) 8.53590 + 25.7321i 0.314851 + 0.949141i
\(736\) 18.0622 + 31.2846i 0.665781 + 1.15317i
\(737\) 6.73205 1.80385i 0.247978 0.0664456i
\(738\) 10.3923 10.3923i 0.382546 0.382546i
\(739\) 21.1244 12.1962i 0.777072 0.448643i −0.0583196 0.998298i \(-0.518574\pi\)
0.835392 + 0.549655i \(0.185241\pi\)
\(740\) 5.19615 15.5885i 0.191014 0.573043i
\(741\) 15.4641 + 15.4641i 0.568088 + 0.568088i
\(742\) 10.5622 30.4904i 0.387750 1.11934i
\(743\) −2.36603 8.83013i −0.0868011 0.323946i 0.908848 0.417127i \(-0.136963\pi\)
−0.995649 + 0.0931813i \(0.970296\pi\)
\(744\) −0.169873 + 0.0455173i −0.00622785 + 0.00166875i
\(745\) −7.45448 0.447441i −0.273111 0.0163930i
\(746\) 4.09808 + 7.09808i 0.150041 + 0.259879i
\(747\) 4.09808 1.09808i 0.149941 0.0401765i
\(748\) −18.9282 18.9282i −0.692084 0.692084i
\(749\) 5.36603 + 3.63397i 0.196070 + 0.132783i
\(750\) −3.06218 37.2846i −0.111815 1.36144i
\(751\) 23.5622 + 40.8109i 0.859796 + 1.48921i 0.872123 + 0.489286i \(0.162743\pi\)
−0.0123270 + 0.999924i \(0.503924\pi\)
\(752\) −41.4904 + 41.4904i −1.51300 + 1.51300i
\(753\) −8.78461 5.07180i −0.320129 0.184827i
\(754\) −51.7128 −1.88327
\(755\) −9.46410 + 4.73205i −0.344434 + 0.172217i
\(756\) 18.0000 15.5885i 0.654654 0.566947i
\(757\) −8.26795 8.26795i −0.300504 0.300504i 0.540707 0.841211i \(-0.318157\pi\)
−0.841211 + 0.540707i \(0.818157\pi\)
\(758\) −17.1244 + 17.1244i −0.621985 + 0.621985i
\(759\) 11.6603 + 43.5167i 0.423240 + 1.57955i
\(760\) 1.19615 3.58846i 0.0433890 0.130167i
\(761\) 16.9641 9.79423i 0.614948 0.355041i −0.159951 0.987125i \(-0.551134\pi\)
0.774900 + 0.632084i \(0.217800\pi\)
\(762\) 64.5788 + 37.2846i 2.33944 + 1.35068i
\(763\) 5.00000 + 1.73205i 0.181012 + 0.0627044i
\(764\) 30.5885i 1.10665i
\(765\) −6.00000 + 18.0000i −0.216930 + 0.650791i
\(766\) −27.3564 + 15.7942i −0.988427 + 0.570669i
\(767\) 12.9282 3.46410i 0.466810 0.125081i
\(768\) 16.7942 29.0885i 0.606010 1.04964i
\(769\) 7.99038 13.8397i 0.288141 0.499074i −0.685225 0.728331i \(-0.740296\pi\)
0.973366 + 0.229257i \(0.0736296\pi\)
\(770\) −23.8564 57.7128i −0.859725 2.07983i
\(771\) 15.2487 15.2487i 0.549169 0.549169i
\(772\) −25.0526 25.0526i −0.901661 0.901661i
\(773\) −1.88269 + 7.02628i −0.0677155 + 0.252718i −0.991483 0.130236i \(-0.958426\pi\)
0.923768 + 0.382954i \(0.125093\pi\)
\(774\) −4.50000 + 7.79423i −0.161749 + 0.280158i
\(775\) −0.901924 + 0.385263i −0.0323981 + 0.0138391i
\(776\) −3.63397 + 2.09808i −0.130452 + 0.0753165i
\(777\) −17.4904 + 8.49038i −0.627464 + 0.304591i
\(778\) −0.598076 2.23205i −0.0214421 0.0800229i
\(779\) 7.17691 4.14359i 0.257140 0.148460i
\(780\) 17.1962 + 19.3923i 0.615721 + 0.694356i
\(781\) −16.3923 + 28.3923i −0.586563 + 1.01596i
\(782\) −6.73205 25.1244i −0.240738 0.898445i
\(783\) −31.1769 + 18.0000i −1.11417 + 0.643268i
\(784\) −4.46410 + 30.9282i −0.159432 + 1.10458i
\(785\) 3.09808 0.633975i 0.110575 0.0226275i
\(786\) 12.0000 12.0000i 0.428026 0.428026i
\(787\) 11.2942 11.2942i 0.402596 0.402596i −0.476551 0.879147i \(-0.658113\pi\)
0.879147 + 0.476551i \(0.158113\pi\)
\(788\) 30.2487 30.2487i 1.07757 1.07757i
\(789\) −47.5526 12.7417i −1.69292 0.453615i
\(790\) −19.1962 + 3.92820i −0.682968 + 0.139759i
\(791\) −10.9019 + 16.0981i −0.387628 + 0.572382i
\(792\) 6.00000 6.00000i 0.213201 0.213201i
\(793\) −11.3923 42.5167i −0.404553 1.50981i
\(794\) 32.7846 56.7846i 1.16348 2.01521i
\(795\) 23.9545 4.90192i 0.849578 0.173853i
\(796\) −11.7846 + 6.80385i −0.417694 + 0.241156i
\(797\) −10.0788 37.6147i −0.357011 1.33238i −0.877935 0.478780i \(-0.841079\pi\)
0.520924 0.853603i \(-0.325587\pi\)
\(798\) 26.0263 12.6340i 0.921320 0.447238i
\(799\) 32.1962 18.5885i 1.13902 0.657612i
\(800\) 14.1340 35.2128i 0.499711 1.24496i
\(801\) 27.5885 0.974790
\(802\) −11.6962 + 43.6506i −0.413005 + 1.54136i
\(803\) 35.3205 + 35.3205i 1.24643 + 1.24643i
\(804\) 0.990381 + 3.69615i 0.0349280 + 0.130353i
\(805\) 3.69615 27.9186i 0.130272 0.984001i
\(806\) 0.732051 1.26795i 0.0257854 0.0446616i
\(807\) −17.1962 −0.605333
\(808\) −8.79423 + 2.35641i −0.309380 + 0.0828981i
\(809\) −36.4019 + 21.0167i −1.27982 + 0.738906i −0.976816 0.214082i \(-0.931324\pi\)
−0.303008 + 0.952988i \(0.597991\pi\)
\(810\) 36.8827 + 12.2942i 1.29593 + 0.431975i
\(811\) 1.85641i 0.0651872i 0.999469 + 0.0325936i \(0.0103767\pi\)
−0.999469 + 0.0325936i \(0.989623\pi\)
\(812\) −10.3923 + 30.0000i −0.364698 + 1.05279i
\(813\) −17.1962 + 9.92820i −0.603095 + 0.348197i
\(814\) 38.7846 22.3923i 1.35940 0.784850i
\(815\) −6.46410 + 19.3923i −0.226428 + 0.679283i
\(816\) −15.4641 + 15.4641i −0.541352 + 0.541352i
\(817\) −3.58846 + 3.58846i −0.125544 + 0.125544i
\(818\) 7.36603 + 7.36603i 0.257547 + 0.257547i
\(819\) 2.19615 30.5885i 0.0767398 1.06885i
\(820\) 8.78461 4.39230i 0.306772 0.153386i
\(821\) −24.6603 −0.860649 −0.430324 0.902674i \(-0.641601\pi\)
−0.430324 + 0.902674i \(0.641601\pi\)
\(822\) 6.00000 3.46410i 0.209274 0.120824i
\(823\) −14.0718 + 14.0718i −0.490512 + 0.490512i −0.908468 0.417956i \(-0.862747\pi\)
0.417956 + 0.908468i \(0.362747\pi\)
\(824\) 1.06218 + 1.83975i 0.0370027 + 0.0640906i
\(825\) 28.3923 37.8564i 0.988493 1.31799i
\(826\) 1.26795 17.6603i 0.0441176 0.614479i
\(827\) 21.3923 + 21.3923i 0.743883 + 0.743883i 0.973323 0.229440i \(-0.0736893\pi\)
−0.229440 + 0.973323i \(0.573689\pi\)
\(828\) −23.8923 + 6.40192i −0.830315 + 0.222482i
\(829\) −22.1603 38.3827i −0.769657 1.33309i −0.937749 0.347314i \(-0.887094\pi\)
0.168091 0.985771i \(-0.446240\pi\)
\(830\) 6.09808 + 0.366025i 0.211667 + 0.0127049i
\(831\) 9.00000 33.5885i 0.312207 1.16517i
\(832\) 5.73205 + 21.3923i 0.198723 + 0.741645i
\(833\) 7.80385 18.1962i 0.270387 0.630459i
\(834\) −6.00000 + 22.3923i −0.207763 + 0.775382i
\(835\) −9.90192 + 29.7058i −0.342670 + 1.02801i
\(836\) −26.7846 + 15.4641i −0.926365 + 0.534837i
\(837\) 1.01924i 0.0352300i
\(838\) −14.9282 + 4.00000i −0.515686 + 0.138178i
\(839\) 0.0262794 + 0.0455173i 0.000907267 + 0.00157143i 0.866479 0.499214i \(-0.166378\pi\)
−0.865571 + 0.500786i \(0.833045\pi\)
\(840\) −4.90192 + 2.02628i −0.169132 + 0.0699133i
\(841\) 9.50000 16.4545i 0.327586 0.567396i
\(842\) −11.5263 + 43.0167i −0.397222 + 1.48245i
\(843\) 23.7846 0.819185
\(844\) −13.3923 7.73205i −0.460982 0.266148i
\(845\) 4.30385 + 0.258330i 0.148057 + 0.00888683i
\(846\) −38.0885 65.9711i −1.30951 2.26813i
\(847\) 16.3301 47.1410i 0.561110 1.61978i
\(848\) 27.2224 + 7.29423i 0.934822 + 0.250485i
\(849\) −37.2846 + 9.99038i −1.27960 + 0.342869i
\(850\) −16.3923 + 21.8564i −0.562251 + 0.749669i
\(851\) 20.1962 0.692315
\(852\) −15.5885 9.00000i −0.534052 0.308335i
\(853\) 10.8564 40.5167i 0.371716 1.38726i −0.486368 0.873754i \(-0.661678\pi\)
0.858084 0.513510i \(-0.171655\pi\)
\(854\) −58.0788 4.16987i −1.98742 0.142690i
\(855\) 18.2942 + 12.0788i 0.625649 + 0.413088i
\(856\) −0.633975 + 1.09808i −0.0216688 + 0.0375315i
\(857\) 7.70577 + 28.7583i 0.263224 + 0.982366i 0.963328 + 0.268325i \(0.0864702\pi\)
−0.700104 + 0.714041i \(0.746863\pi\)
\(858\) 70.6410i 2.41164i
\(859\) −21.4904 37.2224i −0.733242 1.27001i −0.955490 0.295023i \(-0.904673\pi\)
0.222248 0.974990i \(-0.428661\pi\)
\(860\) −4.50000 + 3.99038i −0.153449 + 0.136071i
\(861\) −10.9808 3.80385i −0.374223 0.129635i
\(862\) 12.0981 45.1506i 0.412062 1.53784i
\(863\) −6.54552 24.4282i −0.222812 0.831546i −0.983269 0.182158i \(-0.941692\pi\)
0.760457 0.649388i \(-0.224975\pi\)
\(864\) 27.8827 + 27.8827i 0.948588 + 0.948588i
\(865\) 6.33975 + 30.9808i 0.215558 + 1.05338i
\(866\) 26.7846i 0.910178i
\(867\) −13.5000 + 7.79423i −0.458484 + 0.264706i
\(868\) −0.588457 0.679492i −0.0199735 0.0230635i
\(869\) −21.4641 12.3923i −0.728120 0.420380i
\(870\) −50.7846 + 10.3923i −1.72176 + 0.352332i
\(871\) 4.26795 + 2.46410i 0.144614 + 0.0834929i
\(872\) −0.267949 + 1.00000i −0.00907390 + 0.0338643i
\(873\) −6.29423 23.4904i −0.213027 0.795029i
\(874\) −30.0526 −1.01654
\(875\) −25.4641 + 15.0526i −0.860844 + 0.508869i
\(876\) −19.3923 + 19.3923i −0.655205 + 0.655205i
\(877\) 3.09808 11.5622i 0.104615 0.390427i −0.893687 0.448692i \(-0.851890\pi\)
0.998301 + 0.0582648i \(0.0185568\pi\)
\(878\) −8.00000 8.00000i −0.269987 0.269987i
\(879\) 9.41858 35.1506i 0.317681 1.18560i
\(880\) 48.7846 24.3923i 1.64453 0.822264i
\(881\) 17.7846i 0.599179i 0.954068 + 0.299589i \(0.0968497\pi\)
−0.954068 + 0.299589i \(0.903150\pi\)
\(882\) −37.2846 15.9904i −1.25544 0.538424i
\(883\) −24.5429 + 24.5429i −0.825936 + 0.825936i −0.986952 0.161016i \(-0.948523\pi\)
0.161016 + 0.986952i \(0.448523\pi\)
\(884\) 18.9282i 0.636624i
\(885\) 12.0000 6.00000i 0.403376 0.201688i
\(886\) 1.80385 0.0606014
\(887\) 17.7942 + 4.76795i 0.597472 + 0.160092i 0.544866 0.838523i \(-0.316581\pi\)
0.0526060 + 0.998615i \(0.483247\pi\)
\(888\) −1.90192 3.29423i −0.0638244 0.110547i
\(889\) 4.22243 58.8109i 0.141616 1.97245i
\(890\) 37.6865 + 12.5622i 1.26326 + 0.421085i
\(891\) 24.5885 + 42.5885i 0.823744 + 1.42677i
\(892\) 8.59808 + 2.30385i 0.287885 + 0.0771385i
\(893\) −11.1173 41.4904i −0.372027 1.38842i
\(894\) 7.90192 7.90192i 0.264280 0.264280i
\(895\) −28.0981 1.68653i −0.939215 0.0563746i
\(896\) −10.8301 0.777568i −0.361809 0.0259767i
\(897\) −15.9282 + 27.5885i −0.531827 + 0.921152i
\(898\) −2.16987 + 2.16987i −0.0724096 + 0.0724096i
\(899\) 0.679492 + 1.17691i 0.0226623 + 0.0392523i
\(900\) 20.7846 + 15.5885i 0.692820 + 0.519615i
\(901\) −15.4641 8.92820i −0.515184 0.297442i
\(902\) 25.8564 + 6.92820i 0.860924 + 0.230684i
\(903\) 7.09808 + 0.509619i 0.236209 + 0.0169591i
\(904\) −3.29423 1.90192i −0.109564 0.0632570i
\(905\) −14.1244 + 21.3923i −0.469509 + 0.711104i
\(906\) 4.09808 15.2942i 0.136149 0.508117i
\(907\) −20.2942 + 5.43782i −0.673859 + 0.180560i −0.579492 0.814978i \(-0.696749\pi\)
−0.0943664 + 0.995538i \(0.530083\pi\)
\(908\) 25.2224 6.75833i 0.837036 0.224283i
\(909\) 52.7654i 1.75012i
\(910\) 16.9282 40.7846i 0.561164 1.35200i
\(911\) −7.43782 12.8827i −0.246426 0.426822i 0.716106 0.697992i \(-0.245923\pi\)
−0.962532 + 0.271170i \(0.912590\pi\)
\(912\) 12.6340 + 21.8827i 0.418353 + 0.724608i
\(913\) 5.46410 + 5.46410i 0.180835 + 0.180835i
\(914\) 20.0526i 0.663280i
\(915\) −19.7321 39.4641i −0.652321 1.30464i
\(916\) −6.99038 + 4.03590i −0.230969 + 0.133350i
\(917\) −12.6795 4.39230i −0.418714 0.145047i
\(918\) −14.1962 24.5885i −0.468543 0.811540i
\(919\) 45.3731 + 26.1962i 1.49672 + 0.864131i 0.999993 0.00377579i \(-0.00120188\pi\)
0.496727 + 0.867907i \(0.334535\pi\)
\(920\) 5.50000 + 0.330127i 0.181330 + 0.0108840i
\(921\) −11.1173 41.4904i −0.366328 1.36715i
\(922\) −2.23205 0.598076i −0.0735087 0.0196966i
\(923\) −22.3923 + 6.00000i −0.737052 + 0.197492i
\(924\) 40.9808 + 14.1962i 1.34817 + 0.467019i
\(925\) −13.0981 16.6865i −0.430662 0.548650i
\(926\) −35.1865 + 60.9449i −1.15630 + 2.00277i
\(927\) −11.8923 + 3.18653i −0.390595 + 0.104659i
\(928\) −50.7846 13.6077i −1.66709 0.446694i
\(929\) 36.3205 1.19164 0.595819 0.803119i \(-0.296828\pi\)
0.595819 + 0.803119i \(0.296828\pi\)
\(930\) 0.464102 1.39230i 0.0152185 0.0456555i
\(931\) −17.9737 14.1506i −0.589065 0.463768i
\(932\) −20.4904 + 5.49038i −0.671185 + 0.179843i
\(933\) 24.0000 + 13.8564i 0.785725 + 0.453638i
\(934\) 12.9641 22.4545i 0.424198 0.734733i
\(935\) −33.8564 + 6.92820i −1.10722 + 0.226576i
\(936\) 6.00000 0.196116
\(937\) 9.46410 9.46410i 0.309179 0.309179i −0.535412 0.844591i \(-0.679844\pi\)
0.844591 + 0.535412i \(0.179844\pi\)
\(938\) 4.92820 4.26795i 0.160912 0.139353i
\(939\) −12.2942 + 3.29423i −0.401207 + 0.107503i
\(940\) −10.2058 49.8731i −0.332876 1.62668i
\(941\) 37.9808i 1.23814i 0.785337 + 0.619069i \(0.212490\pi\)
−0.785337 + 0.619069i \(0.787510\pi\)
\(942\) −2.36603 + 4.09808i −0.0770893 + 0.133523i
\(943\) 8.53590 + 8.53590i 0.277967 + 0.277967i
\(944\) 15.4641 0.503314
\(945\) −3.99038 30.4808i −0.129807 0.991539i
\(946\) −16.3923 −0.532960
\(947\) 18.2224 + 18.2224i 0.592149 + 0.592149i 0.938212 0.346062i \(-0.112481\pi\)
−0.346062 + 0.938212i \(0.612481\pi\)
\(948\) 6.80385 11.7846i 0.220979 0.382746i
\(949\) 35.3205i 1.14655i
\(950\) 19.4904 + 24.8301i 0.632351 + 0.805596i
\(951\) 20.0263 5.36603i 0.649397 0.174005i
\(952\) 3.66025 + 1.26795i 0.118630 + 0.0410945i
\(953\) 21.0000 21.0000i 0.680257 0.680257i −0.279801 0.960058i \(-0.590269\pi\)
0.960058 + 0.279801i \(0.0902686\pi\)
\(954\) −18.2942 + 31.6865i −0.592298 + 1.02589i
\(955\) −32.9545 21.7583i −1.06638 0.704083i
\(956\) −19.0526 + 33.0000i −0.616204 + 1.06730i
\(957\) −56.7846 32.7846i −1.83559 1.05978i
\(958\) 9.83013 2.63397i 0.317597 0.0850999i
\(959\) −4.53590 3.07180i −0.146472 0.0991935i
\(960\) 9.92820 + 19.8564i 0.320431 + 0.640863i
\(961\) 30.9615 0.998759
\(962\) 30.5885 + 8.19615i 0.986211 + 0.264255i
\(963\) −5.19615 5.19615i −0.167444 0.167444i
\(964\) −8.25833 + 14.3038i −0.265983 + 0.460696i
\(965\) −44.8109 + 9.16987i −1.44251 + 0.295189i
\(966\) 27.5885 + 31.8564i 0.887644 + 1.02496i
\(967\) −1.66987 + 0.447441i −0.0536995 + 0.0143887i −0.285569 0.958358i \(-0.592183\pi\)
0.231869 + 0.972747i \(0.425516\pi\)
\(968\) 9.42820 + 2.52628i 0.303034 + 0.0811977i
\(969\) −4.14359 15.4641i −0.133111 0.496779i
\(970\) 2.09808 34.9545i 0.0673652 1.12232i
\(971\) −2.53590 1.46410i −0.0813809 0.0469853i 0.458757 0.888562i \(-0.348295\pi\)
−0.540138 + 0.841576i \(0.681628\pi\)
\(972\) −23.3827 + 13.5000i −0.750000 + 0.433013i
\(973\) 18.0000 3.46410i 0.577054 0.111054i
\(974\) −56.1506 + 32.4186i −1.79918 + 1.03876i
\(975\) 33.1244 4.73205i 1.06083 0.151547i
\(976\) 50.8564i 1.62787i
\(977\) −33.1769 33.1769i −1.06142 1.06142i −0.997986 0.0634377i \(-0.979794\pi\)
−0.0634377 0.997986i \(-0.520206\pi\)
\(978\) −15.2942 26.4904i −0.489056 0.847069i
\(979\) 25.1244 + 43.5167i 0.802978 + 1.39080i
\(980\) −20.2583 18.0167i −0.647129 0.575521i
\(981\) −5.19615 3.00000i −0.165900 0.0957826i
\(982\) −31.5885 + 8.46410i −1.00803 + 0.270100i
\(983\) −3.56218 + 0.954483i −0.113616 + 0.0304433i −0.315179 0.949032i \(-0.602065\pi\)
0.201563 + 0.979476i \(0.435398\pi\)
\(984\) 0.588457 2.19615i 0.0187593 0.0700108i
\(985\) −11.0718 54.1051i −0.352777 1.72393i
\(986\) 32.7846 + 18.9282i 1.04407 + 0.602797i
\(987\) −33.7750 + 49.8731i −1.07507 + 1.58748i
\(988\) −21.1244 5.66025i −0.672055 0.180077i
\(989\) −6.40192 3.69615i −0.203569 0.117531i
\(990\) 14.1962 + 69.3731i 0.451183 + 2.20482i
\(991\) 8.73205 + 15.1244i 0.277383 + 0.480441i 0.970734 0.240159i \(-0.0771997\pi\)
−0.693351 + 0.720600i \(0.743866\pi\)
\(992\) 1.05256 1.05256i 0.0334188 0.0334188i
\(993\) 15.8827 27.5096i 0.504022 0.872991i
\(994\) −2.19615 + 30.5885i −0.0696577 + 0.970207i
\(995\) −1.05256 + 17.5359i −0.0333684 + 0.555925i
\(996\) −3.00000 + 3.00000i −0.0950586 + 0.0950586i
\(997\) −11.7058 43.6865i −0.370725 1.38357i −0.859491 0.511151i \(-0.829219\pi\)
0.488765 0.872415i \(-0.337447\pi\)
\(998\) 13.1962 + 3.53590i 0.417717 + 0.111927i
\(999\) 21.2942 5.70577i 0.673720 0.180523i
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.b.292.1 yes 4
3.2 odd 2 945.2.bv.a.712.1 4
5.3 odd 4 315.2.bs.c.103.1 yes 4
7.3 odd 6 315.2.cg.c.157.1 yes 4
9.2 odd 6 945.2.cj.d.397.1 4
9.7 even 3 315.2.cg.a.187.1 yes 4
15.8 even 4 945.2.bv.d.523.1 4
21.17 even 6 945.2.cj.a.577.1 4
35.3 even 12 315.2.cg.a.283.1 yes 4
45.38 even 12 945.2.cj.a.208.1 4
45.43 odd 12 315.2.cg.c.313.1 yes 4
63.38 even 6 945.2.bv.d.262.1 4
63.52 odd 6 315.2.bs.c.52.1 yes 4
105.38 odd 12 945.2.cj.d.388.1 4
315.38 odd 12 945.2.bv.a.73.1 4
315.178 even 12 inner 315.2.bs.b.178.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bs.b.178.1 4 315.178 even 12 inner
315.2.bs.b.292.1 yes 4 1.1 even 1 trivial
315.2.bs.c.52.1 yes 4 63.52 odd 6
315.2.bs.c.103.1 yes 4 5.3 odd 4
315.2.cg.a.187.1 yes 4 9.7 even 3
315.2.cg.a.283.1 yes 4 35.3 even 12
315.2.cg.c.157.1 yes 4 7.3 odd 6
315.2.cg.c.313.1 yes 4 45.43 odd 12
945.2.bv.a.73.1 4 315.38 odd 12
945.2.bv.a.712.1 4 3.2 odd 2
945.2.bv.d.262.1 4 63.38 even 6
945.2.bv.d.523.1 4 15.8 even 4
945.2.cj.a.208.1 4 45.38 even 12
945.2.cj.a.577.1 4 21.17 even 6
945.2.cj.d.388.1 4 105.38 odd 12
945.2.cj.d.397.1 4 9.2 odd 6