Properties

Label 315.2.cg.d.157.1
Level $315$
Weight $2$
Character 315.157
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(157,315)]
 
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([4, 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("315.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.cg (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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 157.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.157
Dual form 315.2.cg.d.313.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.86603 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.86603 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.866025 + 4.23205i) q^{10} -2.00000 q^{11} +3.00000 q^{12} +(5.09808 - 1.36603i) q^{13} +(-0.366025 - 5.09808i) q^{14} +(-3.23205 + 2.13397i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-2.00000 - 7.46410i) q^{17} +(4.09808 + 4.09808i) q^{18} +(-1.36603 - 2.36603i) q^{19} +(0.232051 + 3.86603i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-3.73205 + 1.00000i) q^{22} +(-2.46410 + 2.46410i) q^{23} +(-0.866025 + 0.232051i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(8.83013 - 5.09808i) q^{26} +5.19615i q^{27} +(-1.50000 - 4.33013i) q^{28} +(-3.40192 + 1.96410i) q^{29} +(-4.96410 + 5.59808i) q^{30} +(-1.26795 + 0.732051i) q^{31} +(-1.96410 + 7.33013i) q^{32} +(-3.00000 - 1.73205i) q^{33} +(-7.46410 - 12.9282i) q^{34} +(4.69615 + 3.59808i) q^{35} +(4.50000 + 2.59808i) q^{36} +(0.169873 - 0.633975i) q^{37} +(-3.73205 - 3.73205i) q^{38} +(8.83013 + 2.36603i) q^{39} +(-0.366025 - 1.09808i) q^{40} +(2.59808 + 1.50000i) q^{41} +(3.86603 - 7.96410i) q^{42} +(3.23205 + 0.866025i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(-6.69615 + 0.401924i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(-1.96410 - 7.33013i) q^{47} +(-6.69615 + 3.86603i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-7.59808 - 5.96410i) q^{50} +(3.46410 - 12.9282i) q^{51} +(6.46410 - 6.46410i) q^{52} +(-1.00000 - 3.73205i) q^{53} +(2.59808 + 9.69615i) q^{54} +(2.00000 - 4.00000i) q^{55} +(0.767949 + 1.13397i) q^{56} -4.73205i q^{57} +(-5.36603 + 5.36603i) q^{58} +(7.56218 + 13.0981i) q^{59} +(-3.00000 + 6.00000i) q^{60} +(2.53590 + 1.46410i) q^{61} +(-2.00000 + 2.00000i) q^{62} +(7.50000 - 2.59808i) q^{63} +5.73205i q^{64} +(-2.36603 + 11.5622i) q^{65} +(-6.46410 - 1.73205i) q^{66} +(-1.63397 + 6.09808i) q^{67} +(-9.46410 - 9.46410i) q^{68} +(-5.83013 + 1.56218i) q^{69} +(10.5622 + 4.36603i) q^{70} +4.73205 q^{71} +(-1.50000 - 0.401924i) q^{72} +(3.46410 - 0.928203i) q^{73} -1.26795i q^{74} +(-1.03590 - 8.59808i) q^{75} +(-4.09808 - 2.36603i) q^{76} +(-1.00000 + 5.19615i) q^{77} +17.6603 q^{78} +(3.92820 + 2.26795i) q^{79} +(-5.50000 - 8.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.59808 + 1.50000i) q^{82} +(-3.03590 + 11.3301i) q^{83} +(1.50000 - 7.79423i) q^{84} +(16.9282 + 3.46410i) q^{85} +6.46410 q^{86} -6.80385 q^{87} +(0.732051 - 0.732051i) 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} -2.53590 q^{93} +(-7.33013 - 12.6962i) q^{94} +(6.09808 - 0.366025i) q^{95} +(-9.29423 + 9.29423i) q^{96} +(14.5622 + 3.90192i) q^{97} +(-13.4282 - 1.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 2 q^{19} - 6 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{25} + 18 q^{26} - 6 q^{28} - 24 q^{29} - 6 q^{30} - 12 q^{31} + 6 q^{32} - 12 q^{33} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 8 q^{38} + 18 q^{39} + 2 q^{40} + 12 q^{42} + 6 q^{43} - 12 q^{44} - 6 q^{45} - 10 q^{46} + 6 q^{47} - 6 q^{48} - 26 q^{49} - 20 q^{50} + 12 q^{52} - 4 q^{53} + 8 q^{55} + 10 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{60} + 24 q^{61} - 8 q^{62} + 30 q^{63} - 6 q^{65} - 12 q^{66} - 10 q^{67} - 24 q^{68} - 6 q^{69} + 18 q^{70} + 12 q^{71} - 6 q^{72} - 18 q^{75} - 6 q^{76} - 4 q^{77} + 36 q^{78} - 12 q^{79} - 22 q^{80} - 18 q^{81} + 12 q^{82} - 26 q^{83} + 6 q^{84} + 40 q^{85} + 12 q^{86} - 48 q^{87} - 4 q^{88} - 16 q^{89} - 18 q^{90} - 4 q^{91} + 18 q^{92} - 24 q^{93} - 12 q^{94} + 14 q^{95} - 6 q^{96} + 34 q^{97} - 26 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86603 0.500000i 1.31948 0.353553i 0.470696 0.882295i \(-0.344003\pi\)
0.848783 + 0.528742i \(0.177336\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 1.50000 0.866025i 0.750000 0.433013i
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 3.23205 + 0.866025i 1.31948 + 0.353553i
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) −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
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 3.00000 0.866025
\(13\) 5.09808 1.36603i 1.41395 0.378867i 0.530618 0.847611i \(-0.321960\pi\)
0.883334 + 0.468744i \(0.155293\pi\)
\(14\) −0.366025 5.09808i −0.0978244 1.36252i
\(15\) −3.23205 + 2.13397i −0.834512 + 0.550990i
\(16\) −2.23205 + 3.86603i −0.558013 + 0.966506i
\(17\) −2.00000 7.46410i −0.485071 1.81031i −0.579740 0.814802i \(-0.696846\pi\)
0.0946685 0.995509i \(-0.469821\pi\)
\(18\) 4.09808 + 4.09808i 0.965926 + 0.965926i
\(19\) −1.36603 2.36603i −0.313388 0.542803i 0.665706 0.746214i \(-0.268131\pi\)
−0.979093 + 0.203411i \(0.934797\pi\)
\(20\) 0.232051 + 3.86603i 0.0518881 + 0.864470i
\(21\) 3.00000 3.46410i 0.654654 0.755929i
\(22\) −3.73205 + 1.00000i −0.795676 + 0.213201i
\(23\) −2.46410 + 2.46410i −0.513801 + 0.513801i −0.915689 0.401888i \(-0.868354\pi\)
0.401888 + 0.915689i \(0.368354\pi\)
\(24\) −0.866025 + 0.232051i −0.176777 + 0.0473672i
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 8.83013 5.09808i 1.73173 0.999815i
\(27\) 5.19615i 1.00000i
\(28\) −1.50000 4.33013i −0.283473 0.818317i
\(29\) −3.40192 + 1.96410i −0.631721 + 0.364725i −0.781418 0.624007i \(-0.785503\pi\)
0.149697 + 0.988732i \(0.452170\pi\)
\(30\) −4.96410 + 5.59808i −0.906317 + 1.02206i
\(31\) −1.26795 + 0.732051i −0.227730 + 0.131480i −0.609525 0.792767i \(-0.708640\pi\)
0.381794 + 0.924247i \(0.375306\pi\)
\(32\) −1.96410 + 7.33013i −0.347207 + 1.29580i
\(33\) −3.00000 1.73205i −0.522233 0.301511i
\(34\) −7.46410 12.9282i −1.28008 2.21717i
\(35\) 4.69615 + 3.59808i 0.793795 + 0.608186i
\(36\) 4.50000 + 2.59808i 0.750000 + 0.433013i
\(37\) 0.169873 0.633975i 0.0279269 0.104225i −0.950556 0.310554i \(-0.899485\pi\)
0.978483 + 0.206330i \(0.0661519\pi\)
\(38\) −3.73205 3.73205i −0.605419 0.605419i
\(39\) 8.83013 + 2.36603i 1.41395 + 0.378867i
\(40\) −0.366025 1.09808i −0.0578737 0.173621i
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 3.86603 7.96410i 0.596541 1.22889i
\(43\) 3.23205 + 0.866025i 0.492883 + 0.132068i 0.496695 0.867925i \(-0.334547\pi\)
−0.00381197 + 0.999993i \(0.501213\pi\)
\(44\) −3.00000 + 1.73205i −0.452267 + 0.261116i
\(45\) −6.69615 + 0.401924i −0.998203 + 0.0599153i
\(46\) −3.36603 + 5.83013i −0.496293 + 0.859605i
\(47\) −1.96410 7.33013i −0.286494 1.06921i −0.947741 0.319041i \(-0.896639\pi\)
0.661247 0.750168i \(-0.270027\pi\)
\(48\) −6.69615 + 3.86603i −0.966506 + 0.558013i
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −7.59808 5.96410i −1.07453 0.843451i
\(51\) 3.46410 12.9282i 0.485071 1.81031i
\(52\) 6.46410 6.46410i 0.896410 0.896410i
\(53\) −1.00000 3.73205i −0.137361 0.512637i −0.999977 0.00677809i \(-0.997842\pi\)
0.862616 0.505859i \(-0.168824\pi\)
\(54\) 2.59808 + 9.69615i 0.353553 + 1.31948i
\(55\) 2.00000 4.00000i 0.269680 0.539360i
\(56\) 0.767949 + 1.13397i 0.102622 + 0.151534i
\(57\) 4.73205i 0.626775i
\(58\) −5.36603 + 5.36603i −0.704594 + 0.704594i
\(59\) 7.56218 + 13.0981i 0.984512 + 1.70522i 0.644086 + 0.764953i \(0.277238\pi\)
0.340425 + 0.940272i \(0.389429\pi\)
\(60\) −3.00000 + 6.00000i −0.387298 + 0.774597i
\(61\) 2.53590 + 1.46410i 0.324689 + 0.187459i 0.653480 0.756943i \(-0.273308\pi\)
−0.328792 + 0.944402i \(0.606641\pi\)
\(62\) −2.00000 + 2.00000i −0.254000 + 0.254000i
\(63\) 7.50000 2.59808i 0.944911 0.327327i
\(64\) 5.73205i 0.716506i
\(65\) −2.36603 + 11.5622i −0.293469 + 1.43411i
\(66\) −6.46410 1.73205i −0.795676 0.213201i
\(67\) −1.63397 + 6.09808i −0.199622 + 0.744999i 0.791400 + 0.611299i \(0.209353\pi\)
−0.991022 + 0.133700i \(0.957314\pi\)
\(68\) −9.46410 9.46410i −1.14769 1.14769i
\(69\) −5.83013 + 1.56218i −0.701865 + 0.188064i
\(70\) 10.5622 + 4.36603i 1.26242 + 0.521840i
\(71\) 4.73205 0.561591 0.280796 0.959768i \(-0.409402\pi\)
0.280796 + 0.959768i \(0.409402\pi\)
\(72\) −1.50000 0.401924i −0.176777 0.0473672i
\(73\) 3.46410 0.928203i 0.405442 0.108638i −0.0503336 0.998732i \(-0.516028\pi\)
0.455776 + 0.890094i \(0.349362\pi\)
\(74\) 1.26795i 0.147396i
\(75\) −1.03590 8.59808i −0.119615 0.992820i
\(76\) −4.09808 2.36603i −0.470082 0.271402i
\(77\) −1.00000 + 5.19615i −0.113961 + 0.592157i
\(78\) 17.6603 1.99963
\(79\) 3.92820 + 2.26795i 0.441957 + 0.255164i 0.704428 0.709776i \(-0.251204\pi\)
−0.262470 + 0.964940i \(0.584537\pi\)
\(80\) −5.50000 8.33013i −0.614919 0.931337i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 5.59808 + 1.50000i 0.618204 + 0.165647i
\(83\) −3.03590 + 11.3301i −0.333233 + 1.24364i 0.572539 + 0.819878i \(0.305959\pi\)
−0.905772 + 0.423765i \(0.860708\pi\)
\(84\) 1.50000 7.79423i 0.163663 0.850420i
\(85\) 16.9282 + 3.46410i 1.83612 + 0.375735i
\(86\) 6.46410 0.697042
\(87\) −6.80385 −0.729449
\(88\) 0.732051 0.732051i 0.0780369 0.0780369i
\(89\) −7.46410 12.9282i −0.791193 1.37039i −0.925229 0.379410i \(-0.876127\pi\)
0.134035 0.990977i \(-0.457206\pi\)
\(90\) −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
\(93\) −2.53590 −0.262960
\(94\) −7.33013 12.6962i −0.756045 1.30951i
\(95\) 6.09808 0.366025i 0.625649 0.0375534i
\(96\) −9.29423 + 9.29423i −0.948588 + 0.948588i
\(97\) 14.5622 + 3.90192i 1.47857 + 0.396180i 0.905859 0.423580i \(-0.139227\pi\)
0.572707 + 0.819760i \(0.305893\pi\)
\(98\) −13.4282 1.59808i −1.35645 0.161430i
\(99\) −3.00000 5.19615i −0.301511 0.522233i
\(100\) −7.96410 3.40192i −0.796410 0.340192i
\(101\) 3.73205i 0.371353i 0.982611 + 0.185676i \(0.0594476\pi\)
−0.982611 + 0.185676i \(0.940552\pi\)
\(102\) 25.8564i 2.56017i
\(103\) −6.36603 6.36603i −0.627263 0.627263i 0.320115 0.947379i \(-0.396278\pi\)
−0.947379 + 0.320115i \(0.896278\pi\)
\(104\) −1.36603 + 2.36603i −0.133950 + 0.232008i
\(105\) 3.92820 + 9.46410i 0.383353 + 0.923602i
\(106\) −3.73205 6.46410i −0.362489 0.627849i
\(107\) −3.06218 + 11.4282i −0.296032 + 1.10481i 0.644362 + 0.764720i \(0.277123\pi\)
−0.940394 + 0.340086i \(0.889544\pi\)
\(108\) 4.50000 + 7.79423i 0.433013 + 0.750000i
\(109\) −5.42820 3.13397i −0.519928 0.300180i 0.216977 0.976177i \(-0.430380\pi\)
−0.736905 + 0.675996i \(0.763714\pi\)
\(110\) 1.73205 8.46410i 0.165145 0.807020i
\(111\) 0.803848 0.803848i 0.0762978 0.0762978i
\(112\) 8.92820 + 7.73205i 0.843636 + 0.730610i
\(113\) 2.53590 + 9.46410i 0.238557 + 0.890308i 0.976513 + 0.215459i \(0.0691246\pi\)
−0.737956 + 0.674849i \(0.764209\pi\)
\(114\) −2.36603 8.83013i −0.221599 0.827017i
\(115\) −2.46410 7.39230i −0.229779 0.689336i
\(116\) −3.40192 + 5.89230i −0.315861 + 0.547087i
\(117\) 11.1962 + 11.1962i 1.03508 + 1.03508i
\(118\) 20.6603 + 20.6603i 1.90193 + 1.90193i
\(119\) −20.3923 + 1.46410i −1.86936 + 0.134214i
\(120\) 0.401924 1.96410i 0.0366905 0.179297i
\(121\) −7.00000 −0.636364
\(122\) 5.46410 + 1.46410i 0.494697 + 0.132554i
\(123\) 2.59808 + 4.50000i 0.234261 + 0.405751i
\(124\) −1.26795 + 2.19615i −0.113865 + 0.197220i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 12.6962 8.59808i 1.13106 0.765978i
\(127\) 9.63397 + 9.63397i 0.854877 + 0.854877i 0.990729 0.135852i \(-0.0433772\pi\)
−0.135852 + 0.990729i \(0.543377\pi\)
\(128\) −1.06218 3.96410i −0.0938841 0.350380i
\(129\) 4.09808 + 4.09808i 0.360815 + 0.360815i
\(130\) 1.36603 + 22.7583i 0.119808 + 1.99604i
\(131\) 5.07180i 0.443125i 0.975146 + 0.221562i \(0.0711157\pi\)
−0.975146 + 0.221562i \(0.928884\pi\)
\(132\) −6.00000 −0.522233
\(133\) −6.83013 + 2.36603i −0.592247 + 0.205160i
\(134\) 12.1962i 1.05359i
\(135\) −10.3923 5.19615i −0.894427 0.447214i
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) 1.00000 + 1.00000i 0.0854358 + 0.0854358i 0.748533 0.663097i \(-0.230758\pi\)
−0.663097 + 0.748533i \(0.730758\pi\)
\(138\) −10.0981 + 5.83013i −0.859605 + 0.496293i
\(139\) 6.29423 10.9019i 0.533870 0.924689i −0.465348 0.885128i \(-0.654071\pi\)
0.999217 0.0395611i \(-0.0125960\pi\)
\(140\) 10.1603 + 1.33013i 0.858698 + 0.112416i
\(141\) 3.40192 12.6962i 0.286494 1.06921i
\(142\) 8.83013 2.36603i 0.741008 0.198552i
\(143\) −10.1962 + 2.73205i −0.852645 + 0.228466i
\(144\) −13.3923 −1.11603
\(145\) −0.526279 8.76795i −0.0437051 0.728139i
\(146\) 6.00000 3.46410i 0.496564 0.286691i
\(147\) −7.50000 9.52628i −0.618590 0.785714i
\(148\) −0.294229 1.09808i −0.0241854 0.0902613i
\(149\) 15.4641i 1.26687i −0.773796 0.633434i \(-0.781645\pi\)
0.773796 0.633434i \(-0.218355\pi\)
\(150\) −6.23205 15.5263i −0.508845 1.26772i
\(151\) −17.6603 −1.43717 −0.718586 0.695439i \(-0.755210\pi\)
−0.718586 + 0.695439i \(0.755210\pi\)
\(152\) 1.36603 + 0.366025i 0.110799 + 0.0296886i
\(153\) 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
\(156\) 15.2942 4.09808i 1.22452 0.328109i
\(157\) −9.83013 2.63397i −0.784530 0.210214i −0.155749 0.987797i \(-0.549779\pi\)
−0.628781 + 0.777583i \(0.716446\pi\)
\(158\) 8.46410 + 2.26795i 0.673368 + 0.180428i
\(159\) 1.73205 6.46410i 0.137361 0.512637i
\(160\) −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
\(163\) 9.29423 + 2.49038i 0.727980 + 0.195062i 0.603730 0.797189i \(-0.293681\pi\)
0.124251 + 0.992251i \(0.460347\pi\)
\(164\) 5.19615 0.405751
\(165\) 6.46410 4.26795i 0.503230 0.332259i
\(166\) 22.6603i 1.75878i
\(167\) −0.901924 3.36603i −0.0697930 0.260471i 0.922209 0.386691i \(-0.126382\pi\)
−0.992002 + 0.126220i \(0.959715\pi\)
\(168\) 0.169873 + 2.36603i 0.0131060 + 0.182543i
\(169\) 12.8660 7.42820i 0.989694 0.571400i
\(170\) 33.3205 2.00000i 2.55557 0.153393i
\(171\) 4.09808 7.09808i 0.313388 0.542803i
\(172\) 5.59808 1.50000i 0.426849 0.114374i
\(173\) 21.8564 5.85641i 1.66171 0.445254i 0.698854 0.715264i \(-0.253694\pi\)
0.962858 + 0.270010i \(0.0870269\pi\)
\(174\) −12.6962 + 3.40192i −0.962493 + 0.257899i
\(175\) −11.8923 + 5.79423i −0.898974 + 0.438003i
\(176\) 4.46410 7.73205i 0.336494 0.582825i
\(177\) 26.1962i 1.96902i
\(178\) −20.3923 20.3923i −1.52847 1.52847i
\(179\) 1.09808 + 0.633975i 0.0820741 + 0.0473855i 0.540475 0.841360i \(-0.318244\pi\)
−0.458401 + 0.888745i \(0.651578\pi\)
\(180\) −9.69615 + 6.40192i −0.722709 + 0.477171i
\(181\) 20.1244i 1.49583i −0.663794 0.747916i \(-0.731055\pi\)
0.663794 0.747916i \(-0.268945\pi\)
\(182\) −8.83013 25.4904i −0.654533 1.88947i
\(183\) 2.53590 + 4.39230i 0.187459 + 0.324689i
\(184\) 1.80385i 0.132981i
\(185\) 1.09808 + 0.973721i 0.0807322 + 0.0715894i
\(186\) −4.73205 + 1.26795i −0.346971 + 0.0929705i
\(187\) 4.00000 + 14.9282i 0.292509 + 1.09166i
\(188\) −9.29423 9.29423i −0.677851 0.677851i
\(189\) 13.5000 + 2.59808i 0.981981 + 0.188982i
\(190\) 11.1962 3.73205i 0.812254 0.270751i
\(191\) 4.90192 8.49038i 0.354691 0.614342i −0.632374 0.774663i \(-0.717919\pi\)
0.987065 + 0.160321i \(0.0512528\pi\)
\(192\) −4.96410 + 8.59808i −0.358253 + 0.620513i
\(193\) −0.267949 0.0717968i −0.0192874 0.00516804i 0.249162 0.968462i \(-0.419845\pi\)
−0.268450 + 0.963294i \(0.586511\pi\)
\(194\) 29.1244 2.09101
\(195\) −13.5622 + 15.2942i −0.971208 + 1.09524i
\(196\) −12.0000 + 1.73205i −0.857143 + 0.123718i
\(197\) 4.00000 + 4.00000i 0.284988 + 0.284988i 0.835095 0.550106i \(-0.185413\pi\)
−0.550106 + 0.835095i \(0.685413\pi\)
\(198\) −8.19615 8.19615i −0.582475 0.582475i
\(199\) 2.19615 3.80385i 0.155681 0.269648i −0.777626 0.628727i \(-0.783576\pi\)
0.933307 + 0.359080i \(0.116909\pi\)
\(200\) 2.56218 + 0.366025i 0.181173 + 0.0258819i
\(201\) −7.73205 + 7.73205i −0.545377 + 0.545377i
\(202\) 1.86603 + 6.96410i 0.131293 + 0.489992i
\(203\) 3.40192 + 9.82051i 0.238768 + 0.689265i
\(204\) −6.00000 22.3923i −0.420084 1.56777i
\(205\) −5.59808 + 3.69615i −0.390987 + 0.258150i
\(206\) −15.0622 8.69615i −1.04943 0.605890i
\(207\) −10.0981 2.70577i −0.701865 0.188064i
\(208\) −6.09808 + 22.7583i −0.422826 + 1.57801i
\(209\) 2.73205 + 4.73205i 0.188980 + 0.327323i
\(210\) 12.0622 + 15.6962i 0.832369 + 1.08314i
\(211\) −6.53590 + 11.3205i −0.449950 + 0.779336i −0.998382 0.0568590i \(-0.981891\pi\)
0.548432 + 0.836195i \(0.315225\pi\)
\(212\) −4.73205 4.73205i −0.324999 0.324999i
\(213\) 7.09808 + 4.09808i 0.486352 + 0.280796i
\(214\) 22.8564i 1.56243i
\(215\) −4.96410 + 5.59808i −0.338549 + 0.381786i
\(216\) −1.90192 1.90192i −0.129410 0.129410i
\(217\) 1.26795 + 3.66025i 0.0860740 + 0.248474i
\(218\) −11.6962 3.13397i −0.792163 0.212260i
\(219\) 6.00000 + 1.60770i 0.405442 + 0.108638i
\(220\) −0.464102 7.73205i −0.0312897 0.521295i
\(221\) −20.3923 35.3205i −1.37173 2.37591i
\(222\) 1.09808 1.90192i 0.0736980 0.127649i
\(223\) 1.96410 7.33013i 0.131526 0.490862i −0.868462 0.495756i \(-0.834891\pi\)
0.999988 + 0.00489404i \(0.00155783\pi\)
\(224\) 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
\(227\) −13.5885 + 13.5885i −0.901898 + 0.901898i −0.995600 0.0937026i \(-0.970130\pi\)
0.0937026 + 0.995600i \(0.470130\pi\)
\(228\) −4.09808 7.09808i −0.271402 0.470082i
\(229\) 5.33975 0.352860 0.176430 0.984313i \(-0.443545\pi\)
0.176430 + 0.984313i \(0.443545\pi\)
\(230\) −8.29423 12.5622i −0.546905 0.828325i
\(231\) −6.00000 + 6.92820i −0.394771 + 0.455842i
\(232\) 0.526279 1.96410i 0.0345519 0.128950i
\(233\) 12.4641 + 3.33975i 0.816550 + 0.218794i 0.642838 0.766002i \(-0.277757\pi\)
0.173713 + 0.984796i \(0.444424\pi\)
\(234\) 26.4904 + 15.2942i 1.73173 + 0.999815i
\(235\) 16.6244 + 3.40192i 1.08445 + 0.221917i
\(236\) 22.6865 + 13.0981i 1.47677 + 0.852612i
\(237\) 3.92820 + 6.80385i 0.255164 + 0.441957i
\(238\) −37.3205 + 12.9282i −2.41913 + 0.838011i
\(239\) −1.73205 1.00000i −0.112037 0.0646846i 0.442934 0.896554i \(-0.353937\pi\)
−0.554971 + 0.831869i \(0.687271\pi\)
\(240\) −1.03590 17.2583i −0.0668670 1.11402i
\(241\) 22.4641i 1.44704i 0.690303 + 0.723520i \(0.257477\pi\)
−0.690303 + 0.723520i \(0.742523\pi\)
\(242\) −13.0622 + 3.50000i −0.839669 + 0.224989i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 5.07180 0.324689
\(245\) 11.6962 10.4019i 0.747240 0.664555i
\(246\) 7.09808 + 7.09808i 0.452557 + 0.452557i
\(247\) −10.1962 10.1962i −0.648766 0.648766i
\(248\) 0.196152 0.732051i 0.0124557 0.0464853i
\(249\) −14.3660 + 14.3660i −0.910410 + 0.910410i
\(250\) 19.5263 9.23205i 1.23495 0.583886i
\(251\) 3.66025i 0.231033i 0.993306 + 0.115517i \(0.0368523\pi\)
−0.993306 + 0.115517i \(0.963148\pi\)
\(252\) 9.00000 10.3923i 0.566947 0.654654i
\(253\) 4.92820 4.92820i 0.309833 0.309833i
\(254\) 22.7942 + 13.1603i 1.43024 + 0.825748i
\(255\) 22.3923 + 19.8564i 1.40226 + 1.24346i
\(256\) −9.69615 16.7942i −0.606010 1.04964i
\(257\) −0.196152 + 0.196152i −0.0122357 + 0.0122357i −0.713198 0.700962i \(-0.752754\pi\)
0.700962 + 0.713198i \(0.252754\pi\)
\(258\) 9.69615 + 5.59808i 0.603656 + 0.348521i
\(259\) −1.56218 0.758330i −0.0970690 0.0471203i
\(260\) 6.46410 + 19.3923i 0.400887 + 1.20266i
\(261\) −10.2058 5.89230i −0.631721 0.364725i
\(262\) 2.53590 + 9.46410i 0.156668 + 0.584694i
\(263\) 3.90192 3.90192i 0.240603 0.240603i −0.576497 0.817100i \(-0.695581\pi\)
0.817100 + 0.576497i \(0.195581\pi\)
\(264\) 1.73205 0.464102i 0.106600 0.0285635i
\(265\) 8.46410 + 1.73205i 0.519946 + 0.106399i
\(266\) −11.5622 + 7.83013i −0.708923 + 0.480096i
\(267\) 25.8564i 1.58239i
\(268\) 2.83013 + 10.5622i 0.172878 + 0.645188i
\(269\) 14.1962 24.5885i 0.865555 1.49918i −0.000940662 1.00000i \(-0.500299\pi\)
0.866495 0.499185i \(-0.166367\pi\)
\(270\) −21.9904 4.50000i −1.33829 0.273861i
\(271\) −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
\(275\) 6.00000 + 8.00000i 0.361814 + 0.482418i
\(276\) −7.39230 + 7.39230i −0.444964 + 0.444964i
\(277\) −8.19615 8.19615i −0.492459 0.492459i 0.416621 0.909080i \(-0.363214\pi\)
−0.909080 + 0.416621i \(0.863214\pi\)
\(278\) 6.29423 23.4904i 0.377503 1.40886i
\(279\) −3.80385 2.19615i −0.227730 0.131480i
\(280\) −3.03590 + 0.401924i −0.181430 + 0.0240195i
\(281\) −11.1340 19.2846i −0.664197 1.15042i −0.979502 0.201433i \(-0.935440\pi\)
0.315305 0.948990i \(-0.397893\pi\)
\(282\) 25.3923i 1.51209i
\(283\) 3.52628 13.1603i 0.209616 0.782296i −0.778377 0.627797i \(-0.783957\pi\)
0.987993 0.154499i \(-0.0493764\pi\)
\(284\) 7.09808 4.09808i 0.421193 0.243176i
\(285\) 9.46410 + 4.73205i 0.560605 + 0.280302i
\(286\) −17.6603 + 10.1962i −1.04427 + 0.602911i
\(287\) 5.19615 6.00000i 0.306719 0.354169i
\(288\) −21.9904 + 5.89230i −1.29580 + 0.347207i
\(289\) −36.9904 + 21.3564i −2.17590 + 1.25626i
\(290\) −5.36603 16.0981i −0.315104 0.945312i
\(291\) 18.4641 + 18.4641i 1.08238 + 1.08238i
\(292\) 4.39230 4.39230i 0.257040 0.257040i
\(293\) −6.73205 + 1.80385i −0.393291 + 0.105382i −0.450044 0.893006i \(-0.648592\pi\)
0.0567535 + 0.998388i \(0.481925\pi\)
\(294\) −18.7583 14.0263i −1.09401 0.818029i
\(295\) −33.7583 + 2.02628i −1.96549 + 0.117975i
\(296\) 0.169873 + 0.294229i 0.00987367 + 0.0171017i
\(297\) 10.3923i 0.603023i
\(298\) −7.73205 28.8564i −0.447906 1.67161i
\(299\) −9.19615 + 15.9282i −0.531827 + 0.921152i
\(300\) −9.00000 12.0000i −0.519615 0.692820i
\(301\) 3.86603 7.96410i 0.222834 0.459043i
\(302\) −32.9545 + 8.83013i −1.89632 + 0.508117i
\(303\) −3.23205 + 5.59808i −0.185676 + 0.321601i
\(304\) 12.1962 0.699497
\(305\) −5.46410 + 3.60770i −0.312874 + 0.206576i
\(306\) 22.3923 38.7846i 1.28008 2.21717i
\(307\) −5.36603 + 5.36603i −0.306255 + 0.306255i −0.843455 0.537200i \(-0.819482\pi\)
0.537200 + 0.843455i \(0.319482\pi\)
\(308\) 3.00000 + 8.66025i 0.170941 + 0.493464i
\(309\) −4.03590 15.0622i −0.229594 0.856857i
\(310\) −2.00000 6.00000i −0.113592 0.340777i
\(311\) −6.16987 + 3.56218i −0.349861 + 0.201993i −0.664624 0.747178i \(-0.731408\pi\)
0.314763 + 0.949170i \(0.398075\pi\)
\(312\) −4.09808 + 2.36603i −0.232008 + 0.133950i
\(313\) −2.19615 + 0.588457i −0.124134 + 0.0332616i −0.320351 0.947299i \(-0.603801\pi\)
0.196217 + 0.980560i \(0.437134\pi\)
\(314\) −19.6603 −1.10949
\(315\) −2.30385 + 17.5981i −0.129807 + 0.991539i
\(316\) 7.85641 0.441957
\(317\) −11.5622 + 3.09808i −0.649397 + 0.174005i −0.568456 0.822714i \(-0.692459\pi\)
−0.0809406 + 0.996719i \(0.525792\pi\)
\(318\) 12.9282i 0.724978i
\(319\) 6.80385 3.92820i 0.380942 0.219937i
\(320\) −11.4641 5.73205i −0.640863 0.320431i
\(321\) −14.4904 + 14.4904i −0.808774 + 0.808774i
\(322\) 13.4641 + 11.6603i 0.750325 + 0.649801i
\(323\) −14.9282 + 14.9282i −0.830627 + 0.830627i
\(324\) 15.5885i 0.866025i
\(325\) −20.7583 16.2942i −1.15146 0.903841i
\(326\) 18.5885 1.02952
\(327\) −5.42820 9.40192i −0.300180 0.519928i
\(328\) −1.50000 + 0.401924i −0.0828236 + 0.0221925i
\(329\) −20.0263 + 1.43782i −1.10408 + 0.0792697i
\(330\) 9.92820 11.1962i 0.546530 0.616328i
\(331\) 3.00000 5.19615i 0.164895 0.285606i −0.771723 0.635959i \(-0.780605\pi\)
0.936618 + 0.350352i \(0.113938\pi\)
\(332\) 5.25833 + 19.6244i 0.288588 + 1.07703i
\(333\) 1.90192 0.509619i 0.104225 0.0279269i
\(334\) −3.36603 5.83013i −0.184181 0.319010i
\(335\) −10.5622 9.36603i −0.577073 0.511721i
\(336\) 6.69615 + 19.3301i 0.365305 + 1.05454i
\(337\) −7.36603 + 1.97372i −0.401253 + 0.107515i −0.453801 0.891103i \(-0.649932\pi\)
0.0525482 + 0.998618i \(0.483266\pi\)
\(338\) 20.2942 20.2942i 1.10386 1.10386i
\(339\) −4.39230 + 16.3923i −0.238557 + 0.890308i
\(340\) 28.3923 9.46410i 1.53979 0.513263i
\(341\) 2.53590 1.46410i 0.137327 0.0792855i
\(342\) 4.09808 15.2942i 0.221599 0.827017i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −1.50000 + 0.866025i −0.0808746 + 0.0466930i
\(345\) 2.70577 13.2224i 0.145674 0.711872i
\(346\) 37.8564 21.8564i 2.03517 1.17501i
\(347\) 2.42820 9.06218i 0.130353 0.486483i −0.869621 0.493720i \(-0.835637\pi\)
0.999974 + 0.00723662i \(0.00230351\pi\)
\(348\) −10.2058 + 5.89230i −0.547087 + 0.315861i
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) −19.2942 + 16.7583i −1.03132 + 0.895770i
\(351\) 7.09808 + 26.4904i 0.378867 + 1.41395i
\(352\) 3.92820 14.6603i 0.209374 0.781394i
\(353\) −12.4641 12.4641i −0.663397 0.663397i 0.292782 0.956179i \(-0.405419\pi\)
−0.956179 + 0.292782i \(0.905419\pi\)
\(354\) 13.0981 + 48.8827i 0.696155 + 2.59809i
\(355\) −4.73205 + 9.46410i −0.251151 + 0.502302i
\(356\) −22.3923 12.9282i −1.18679 0.685193i
\(357\) −31.8564 15.4641i −1.68602 0.818447i
\(358\) 2.36603 + 0.633975i 0.125048 + 0.0335066i
\(359\) 9.46410 5.46410i 0.499496 0.288384i −0.229009 0.973424i \(-0.573549\pi\)
0.728505 + 0.685040i \(0.240215\pi\)
\(360\) 2.30385 2.59808i 0.121423 0.136931i
\(361\) 5.76795 9.99038i 0.303576 0.525810i
\(362\) −10.0622 37.5526i −0.528856 1.97372i
\(363\) −10.5000 6.06218i −0.551107 0.318182i
\(364\) −13.5622 20.0263i −0.710851 1.04966i
\(365\) −1.60770 + 7.85641i −0.0841506 + 0.411223i
\(366\) 6.92820 + 6.92820i 0.362143 + 0.362143i
\(367\) 3.90192 3.90192i 0.203679 0.203679i −0.597895 0.801574i \(-0.703996\pi\)
0.801574 + 0.597895i \(0.203996\pi\)
\(368\) −4.02628 15.0263i −0.209884 0.783299i
\(369\) 9.00000i 0.468521i
\(370\) 2.53590 + 1.26795i 0.131835 + 0.0659175i
\(371\) −10.1962 + 0.732051i −0.529358 + 0.0380062i
\(372\) −3.80385 + 2.19615i −0.197220 + 0.113865i
\(373\) −5.53590 + 5.53590i −0.286638 + 0.286638i −0.835749 0.549111i \(-0.814966\pi\)
0.549111 + 0.835749i \(0.314966\pi\)
\(374\) 14.9282 + 25.8564i 0.771919 + 1.33700i
\(375\) 18.2321 + 6.52628i 0.941499 + 0.337016i
\(376\) 3.40192 + 1.96410i 0.175441 + 0.101291i
\(377\) −14.6603 + 14.6603i −0.755041 + 0.755041i
\(378\) 26.4904 1.90192i 1.36252 0.0978244i
\(379\) 17.5167i 0.899770i −0.893086 0.449885i \(-0.851465\pi\)
0.893086 0.449885i \(-0.148535\pi\)
\(380\) 8.83013 5.83013i 0.452976 0.299079i
\(381\) 6.10770 + 22.7942i 0.312907 + 1.16778i
\(382\) 4.90192 18.2942i 0.250804 0.936014i
\(383\) −7.75833 7.75833i −0.396432 0.396432i 0.480540 0.876973i \(-0.340441\pi\)
−0.876973 + 0.480540i \(0.840441\pi\)
\(384\) 1.83975 6.86603i 0.0938841 0.350380i
\(385\) −9.39230 7.19615i −0.478676 0.366750i
\(386\) −0.535898 −0.0272765
\(387\) 2.59808 + 9.69615i 0.132068 + 0.492883i
\(388\) 25.2224 6.75833i 1.28047 0.343102i
\(389\) 9.05256i 0.458983i −0.973311 0.229491i \(-0.926294\pi\)
0.973311 0.229491i \(-0.0737063\pi\)
\(390\) −17.6603 + 35.3205i −0.894262 + 1.78852i
\(391\) 23.3205 + 13.4641i 1.17937 + 0.680909i
\(392\) 3.33013 1.42820i 0.168197 0.0721352i
\(393\) −4.39230 + 7.60770i −0.221562 + 0.383757i
\(394\) 9.46410 + 5.46410i 0.476795 + 0.275277i
\(395\) −8.46410 + 5.58846i −0.425875 + 0.281186i
\(396\) −9.00000 5.19615i −0.452267 0.261116i
\(397\) 29.3205 + 7.85641i 1.47155 + 0.394302i 0.903464 0.428664i \(-0.141016\pi\)
0.568090 + 0.822966i \(0.307682\pi\)
\(398\) 2.19615 8.19615i 0.110083 0.410836i
\(399\) −12.2942 2.36603i −0.615481 0.118449i
\(400\) 22.1603 2.66987i 1.10801 0.133494i
\(401\) −9.39230 −0.469029 −0.234515 0.972113i \(-0.575350\pi\)
−0.234515 + 0.972113i \(0.575350\pi\)
\(402\) −10.5622 + 18.2942i −0.526794 + 0.912433i
\(403\) −5.46410 + 5.46410i −0.272186 + 0.272186i
\(404\) 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
\(409\) 11.1603 + 19.3301i 0.551839 + 0.955813i 0.998142 + 0.0609313i \(0.0194071\pi\)
−0.446303 + 0.894882i \(0.647260\pi\)
\(410\) −8.59808 + 9.69615i −0.424629 + 0.478859i
\(411\) 0.633975 + 2.36603i 0.0312717 + 0.116707i
\(412\) −15.0622 4.03590i −0.742060 0.198834i
\(413\) 37.8109 13.0981i 1.86055 0.644514i
\(414\) −20.1962 −0.992587
\(415\) −19.6244 17.4019i −0.963322 0.854227i
\(416\) 40.0526i 1.96374i
\(417\) 18.8827 10.9019i 0.924689 0.533870i
\(418\) 7.46410 + 7.46410i 0.365081 + 0.365081i
\(419\) −1.16987 + 2.02628i −0.0571520 + 0.0989902i −0.893186 0.449688i \(-0.851535\pi\)
0.836034 + 0.548678i \(0.184869\pi\)
\(420\) 14.0885 + 10.7942i 0.687446 + 0.526704i
\(421\) −2.40192 4.16025i −0.117063 0.202758i 0.801540 0.597941i \(-0.204014\pi\)
−0.918602 + 0.395183i \(0.870681\pi\)
\(422\) −6.53590 + 24.3923i −0.318163 + 1.18740i
\(423\) 16.0981 16.0981i 0.782715 0.782715i
\(424\) 1.73205 + 1.00000i 0.0841158 + 0.0485643i
\(425\) −23.8564 + 30.3923i −1.15721 + 1.47424i
\(426\) 15.2942 + 4.09808i 0.741008 + 0.198552i
\(427\) 5.07180 5.85641i 0.245441 0.283411i
\(428\) 5.30385 + 19.7942i 0.256371 + 0.956790i
\(429\) −17.6603 4.73205i −0.852645 0.228466i
\(430\) −6.46410 + 12.9282i −0.311727 + 0.623453i
\(431\) −10.2942 + 17.8301i −0.495856 + 0.858847i −0.999989 0.00477901i \(-0.998479\pi\)
0.504133 + 0.863626i \(0.331812\pi\)
\(432\) −20.0885 11.5981i −0.966506 0.558013i
\(433\) −0.124356 0.124356i −0.00597615 0.00597615i 0.704112 0.710089i \(-0.251345\pi\)
−0.710089 + 0.704112i \(0.751345\pi\)
\(434\) 4.19615 + 6.19615i 0.201422 + 0.297425i
\(435\) 6.80385 13.6077i 0.326220 0.652439i
\(436\) −10.8564 −0.519928
\(437\) 9.19615 + 2.46410i 0.439912 + 0.117874i
\(438\) 12.0000 0.573382
\(439\) 17.9282 31.0526i 0.855666 1.48206i −0.0203589 0.999793i \(-0.506481\pi\)
0.876025 0.482265i \(-0.160186\pi\)
\(440\) 0.732051 + 2.19615i 0.0348992 + 0.104697i
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) −55.7128 55.7128i −2.64999 2.64999i
\(443\) 3.16025 + 11.7942i 0.150148 + 0.560361i 0.999472 + 0.0324887i \(0.0103433\pi\)
−0.849324 + 0.527872i \(0.822990\pi\)
\(444\) 0.509619 1.90192i 0.0241854 0.0902613i
\(445\) 33.3205 2.00000i 1.57954 0.0948091i
\(446\) 14.6603i 0.694183i
\(447\) 13.3923 23.1962i 0.633434 1.09714i
\(448\) 14.8923 + 2.86603i 0.703595 + 0.135407i
\(449\) 7.33975i 0.346384i −0.984888 0.173192i \(-0.944592\pi\)
0.984888 0.173192i \(-0.0554081\pi\)
\(450\) 4.09808 28.6865i 0.193185 1.35230i
\(451\) −5.19615 3.00000i −0.244677 0.141264i
\(452\) 12.0000 + 12.0000i 0.564433 + 0.564433i
\(453\) −26.4904 15.2942i −1.24463 0.718586i
\(454\) −18.5622 + 32.1506i −0.871166 + 1.50890i
\(455\) 28.8564 + 11.9282i 1.35281 + 0.559203i
\(456\) 1.73205 + 1.73205i 0.0811107 + 0.0811107i
\(457\) 31.4904 8.43782i 1.47306 0.394705i 0.569079 0.822283i \(-0.307300\pi\)
0.903979 + 0.427578i \(0.140633\pi\)
\(458\) 9.96410 2.66987i 0.465592 0.124755i
\(459\) 38.7846 10.3923i 1.81031 0.485071i
\(460\) −10.0981 8.95448i −0.470825 0.417505i
\(461\) 20.7679 11.9904i 0.967260 0.558448i 0.0688601 0.997626i \(-0.478064\pi\)
0.898400 + 0.439179i \(0.144730\pi\)
\(462\) −7.73205 + 15.9282i −0.359728 + 0.741047i
\(463\) 3.83975 + 14.3301i 0.178448 + 0.665977i 0.995939 + 0.0900353i \(0.0286980\pi\)
−0.817490 + 0.575942i \(0.804635\pi\)
\(464\) 17.5359i 0.814084i
\(465\) 2.53590 5.07180i 0.117599 0.235199i
\(466\) 24.9282 1.15478
\(467\) −2.50000 0.669873i −0.115686 0.0309980i 0.200511 0.979691i \(-0.435740\pi\)
−0.316198 + 0.948693i \(0.602406\pi\)
\(468\) 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
\(471\) −12.4641 12.4641i −0.574315 0.574315i
\(472\) −7.56218 2.02628i −0.348077 0.0932671i
\(473\) −6.46410 1.73205i −0.297220 0.0796398i
\(474\) 10.7321 + 10.7321i 0.492939 + 0.492939i
\(475\) −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
\(478\) −3.73205 1.00000i −0.170700 0.0457389i
\(479\) −17.2679 −0.788993 −0.394496 0.918897i \(-0.629081\pi\)
−0.394496 + 0.918897i \(0.629081\pi\)
\(480\) −9.29423 27.8827i −0.424222 1.27266i
\(481\) 3.46410i 0.157949i
\(482\) 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
\(485\) −22.3660 + 25.2224i −1.01559 + 1.14529i
\(486\) −21.2942 + 21.2942i −0.965926 + 0.965926i
\(487\) −29.7583 + 7.97372i −1.34848 + 0.361324i −0.859573 0.511013i \(-0.829270\pi\)
−0.488906 + 0.872337i \(0.662604\pi\)
\(488\) −1.46410 + 0.392305i −0.0662768 + 0.0177588i
\(489\) 11.7846 + 11.7846i 0.532918 + 0.532918i
\(490\) 16.6244 25.2583i 0.751012 1.14106i
\(491\) 8.29423 14.3660i 0.374313 0.648330i −0.615911 0.787816i \(-0.711212\pi\)
0.990224 + 0.139486i \(0.0445451\pi\)
\(492\) 7.79423 + 4.50000i 0.351391 + 0.202876i
\(493\) 21.4641 + 21.4641i 0.966695 + 0.966695i
\(494\) −24.1244 13.9282i −1.08541 0.626659i
\(495\) 13.3923 0.803848i 0.601939 0.0361303i
\(496\) 6.53590i 0.293471i
\(497\) 2.36603 12.2942i 0.106131 0.551472i
\(498\) −19.6244 + 33.9904i −0.879388 + 1.52315i
\(499\) 17.6077i 0.788229i 0.919061 + 0.394114i \(0.128949\pi\)
−0.919061 + 0.394114i \(0.871051\pi\)
\(500\) 14.7679 12.5263i 0.660443 0.560192i
\(501\) 1.56218 5.83013i 0.0697930 0.260471i
\(502\) 1.83013 + 6.83013i 0.0816826 + 0.304843i
\(503\) 4.36603 + 4.36603i 0.194671 + 0.194671i 0.797711 0.603040i \(-0.206044\pi\)
−0.603040 + 0.797711i \(0.706044\pi\)
\(504\) −1.79423 + 3.69615i −0.0799213 + 0.164640i
\(505\) −7.46410 3.73205i −0.332148 0.166074i
\(506\) 6.73205 11.6603i 0.299276 0.518362i
\(507\) 25.7321 1.14280
\(508\) 22.7942 + 6.10770i 1.01133 + 0.270985i
\(509\) −32.9090 −1.45866 −0.729332 0.684160i \(-0.760169\pi\)
−0.729332 + 0.684160i \(0.760169\pi\)
\(510\) 51.7128 + 25.8564i 2.28988 + 1.14494i
\(511\) −0.679492 9.46410i −0.0300590 0.418667i
\(512\) −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
\(515\) 19.0981 6.36603i 0.841562 0.280521i
\(516\) 9.69615 + 2.59808i 0.426849 + 0.114374i
\(517\) 3.92820 + 14.6603i 0.172762 + 0.644757i
\(518\) −3.29423 0.633975i −0.144740 0.0278552i
\(519\) 37.8564 + 10.1436i 1.66171 + 0.445254i
\(520\) −3.36603 5.09808i −0.147610 0.223565i
\(521\) −6.35641 3.66987i −0.278479 0.160780i 0.354256 0.935149i \(-0.384734\pi\)
−0.632735 + 0.774369i \(0.718068\pi\)
\(522\) −21.9904 5.89230i −0.962493 0.257899i
\(523\) 6.23205 23.2583i 0.272509 1.01702i −0.684984 0.728558i \(-0.740191\pi\)
0.957493 0.288458i \(-0.0931425\pi\)
\(524\) 4.39230 + 7.60770i 0.191879 + 0.332344i
\(525\) −22.8564 1.60770i −0.997535 0.0701656i
\(526\) 5.33013 9.23205i 0.232405 0.402537i
\(527\) 8.00000 + 8.00000i 0.348485 + 0.348485i
\(528\) 13.3923 7.73205i 0.582825 0.336494i
\(529\) 10.8564i 0.472018i
\(530\) 16.6603 1.00000i 0.723675 0.0434372i
\(531\) −22.6865 + 39.2942i −0.984512 + 1.70522i
\(532\) −8.19615 + 9.46410i −0.355348 + 0.410321i
\(533\) 15.2942 + 4.09808i 0.662467 + 0.177507i
\(534\) −12.9282 48.2487i −0.559458 2.08793i
\(535\) −19.7942 17.5526i −0.855779 0.758863i
\(536\) −1.63397 2.83013i −0.0705770 0.122243i
\(537\) 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 \(0.785749\pi\)
\(542\) −44.5167 + 44.5167i −1.91215 + 1.91215i
\(543\) 17.4282 30.1865i 0.747916 1.29543i
\(544\) 58.6410 2.51421
\(545\) 11.6962 7.72243i 0.501008 0.330793i
\(546\) 8.83013 45.8827i 0.377895 1.96360i
\(547\) −10.4019 + 38.8205i −0.444754 + 1.65985i 0.271831 + 0.962345i \(0.412371\pi\)
−0.716585 + 0.697500i \(0.754296\pi\)
\(548\) 2.36603 + 0.633975i 0.101072 + 0.0270821i
\(549\) 8.78461i 0.374918i
\(550\) 15.1962 + 11.9282i 0.647966 + 0.508620i
\(551\) 9.29423 + 5.36603i 0.395947 + 0.228600i
\(552\) 1.56218 2.70577i 0.0664907 0.115165i
\(553\) 7.85641 9.07180i 0.334088 0.385772i
\(554\) −19.3923 11.1962i −0.823900 0.475679i
\(555\) 0.803848 + 2.41154i 0.0341214 + 0.102364i
\(556\) 21.8038i 0.924689i
\(557\) 41.3205 11.0718i 1.75081 0.469127i 0.766008 0.642831i \(-0.222240\pi\)
0.984798 + 0.173704i \(0.0555735\pi\)
\(558\) −8.19615 2.19615i −0.346971 0.0929705i
\(559\) 17.6603 0.746949
\(560\) −24.3923 + 10.1244i −1.03076 + 0.427832i
\(561\) −6.92820 + 25.8564i −0.292509 + 1.09166i
\(562\) −30.4186 30.4186i −1.28313 1.28313i
\(563\) −1.09808 + 4.09808i −0.0462784 + 0.172713i −0.985197 0.171426i \(-0.945163\pi\)
0.938919 + 0.344139i \(0.111829\pi\)
\(564\) −5.89230 21.9904i −0.248111 0.925962i
\(565\) −21.4641 4.39230i −0.903002 0.184786i
\(566\) 26.3205i 1.10633i
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −1.73205 + 1.73205i −0.0726752 + 0.0726752i
\(569\) 9.46410 + 5.46410i 0.396756 + 0.229067i 0.685083 0.728465i \(-0.259766\pi\)
−0.288327 + 0.957532i \(0.593099\pi\)
\(570\) 20.0263 + 4.09808i 0.838809 + 0.171650i
\(571\) −3.09808 5.36603i −0.129650 0.224561i 0.793891 0.608060i \(-0.208052\pi\)
−0.923541 + 0.383499i \(0.874719\pi\)
\(572\) −12.9282 + 12.9282i −0.540555 + 0.540555i
\(573\) 14.7058 8.49038i 0.614342 0.354691i
\(574\) 6.69615 13.7942i 0.279492 0.575760i
\(575\) 17.2487 + 2.46410i 0.719321 + 0.102760i
\(576\) −14.8923 + 8.59808i −0.620513 + 0.358253i
\(577\) 8.80385 + 32.8564i 0.366509 + 1.36783i 0.865364 + 0.501144i \(0.167087\pi\)
−0.498855 + 0.866686i \(0.666246\pi\)
\(578\) −58.3468 + 58.3468i −2.42691 + 2.42691i
\(579\) −0.339746 0.339746i −0.0141194 0.0141194i
\(580\) −8.38269 12.6962i −0.348072 0.527179i
\(581\) 27.9186 + 13.5526i 1.15826 + 0.562255i
\(582\) 43.6865 + 25.2224i 1.81087 + 1.04550i
\(583\) 2.00000 + 7.46410i 0.0828315 + 0.309132i
\(584\) −0.928203 + 1.60770i −0.0384093 + 0.0665269i
\(585\) −33.5885 + 11.1962i −1.38871 + 0.462904i
\(586\) −11.6603 + 6.73205i −0.481681 + 0.278098i
\(587\) −26.1603 7.00962i −1.07975 0.289318i −0.325256 0.945626i \(-0.605451\pi\)
−0.754493 + 0.656308i \(0.772117\pi\)
\(588\) −19.5000 7.79423i −0.804166 0.321429i
\(589\) 3.46410 + 2.00000i 0.142736 + 0.0824086i
\(590\) −61.9808 + 20.6603i −2.55171 + 0.850569i
\(591\) 2.53590 + 9.46410i 0.104313 + 0.389301i
\(592\) 2.07180 + 2.07180i 0.0851503 + 0.0851503i
\(593\) 7.75833 28.9545i 0.318596 1.18902i −0.601998 0.798498i \(-0.705628\pi\)
0.920594 0.390520i \(-0.127705\pi\)
\(594\) −5.19615 19.3923i −0.213201 0.795676i
\(595\) 17.4641 42.2487i 0.715958 1.73203i
\(596\) −13.3923 23.1962i −0.548570 0.950151i
\(597\) 6.58846 3.80385i 0.269648 0.155681i
\(598\) −9.19615 + 34.3205i −0.376059 + 1.40347i
\(599\) 15.7128 9.07180i 0.642008 0.370664i −0.143380 0.989668i \(-0.545797\pi\)
0.785388 + 0.619004i \(0.212464\pi\)
\(600\) 3.52628 + 2.76795i 0.143960 + 0.113001i
\(601\) 29.3205 16.9282i 1.19601 0.690516i 0.236346 0.971669i \(-0.424050\pi\)
0.959663 + 0.281153i \(0.0907169\pi\)
\(602\) 3.23205 16.7942i 0.131729 0.684482i
\(603\) −18.2942 + 4.90192i −0.744999 + 0.199622i
\(604\) −26.4904 + 15.2942i −1.07788 + 0.622313i
\(605\) 7.00000 14.0000i 0.284590 0.569181i
\(606\) −3.23205 + 12.0622i −0.131293 + 0.489992i
\(607\) 2.70577 2.70577i 0.109824 0.109824i −0.650059 0.759883i \(-0.725256\pi\)
0.759883 + 0.650059i \(0.225256\pi\)
\(608\) 20.0263 5.36603i 0.812173 0.217621i
\(609\) −3.40192 + 17.6769i −0.137853 + 0.716305i
\(610\) −8.39230 + 9.46410i −0.339794 + 0.383190i
\(611\) −20.0263 34.6865i −0.810177 1.40327i
\(612\) 10.3923 38.7846i 0.420084 1.56777i
\(613\) 6.09808 + 22.7583i 0.246299 + 0.919200i 0.972726 + 0.231957i \(0.0745128\pi\)
−0.726427 + 0.687244i \(0.758821\pi\)
\(614\) −7.33013 + 12.6962i −0.295820 + 0.512375i
\(615\) −11.5981 + 0.696152i −0.467680 + 0.0280716i
\(616\) −1.53590 2.26795i −0.0618831 0.0913783i
\(617\) 12.3923 3.32051i 0.498895 0.133679i −0.000591902 1.00000i \(-0.500188\pi\)
0.499487 + 0.866321i \(0.333522\pi\)
\(618\) −15.0622 26.0885i −0.605890 1.04943i
\(619\) −40.7846 −1.63927 −0.819636 0.572885i \(-0.805824\pi\)
−0.819636 + 0.572885i \(0.805824\pi\)
\(620\) −3.12436 4.73205i −0.125477 0.190044i
\(621\) −12.8038 12.8038i −0.513801 0.513801i
\(622\) −9.73205 + 9.73205i −0.390220 + 0.390220i
\(623\) −37.3205 + 12.9282i −1.49521 + 0.517958i
\(624\) −28.8564 + 28.8564i −1.15518 + 1.15518i
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −3.80385 + 2.19615i −0.152032 + 0.0877759i
\(627\) 9.46410i 0.377960i
\(628\) −17.0263 + 4.56218i −0.679423 + 0.182051i
\(629\) −5.07180 −0.202226
\(630\) 4.50000 + 33.9904i 0.179284 + 1.35421i
\(631\) 15.8564 0.631234 0.315617 0.948887i \(-0.397789\pi\)
0.315617 + 0.948887i \(0.397789\pi\)
\(632\) −2.26795 + 0.607695i −0.0902142 + 0.0241728i
\(633\) −19.6077 + 11.3205i −0.779336 + 0.449950i
\(634\) −20.0263 + 11.5622i −0.795345 + 0.459193i
\(635\) −28.9019 + 9.63397i −1.14694 + 0.382313i
\(636\) −3.00000 11.1962i −0.118958 0.443956i
\(637\) −36.6865 4.36603i −1.45357 0.172988i
\(638\) 10.7321 10.7321i 0.424886 0.424886i
\(639\) 7.09808 + 12.2942i 0.280796 + 0.486352i
\(640\) 8.99038 + 1.83975i 0.355376 + 0.0727223i
\(641\) 38.3923 1.51640 0.758202 0.652019i \(-0.226078\pi\)
0.758202 + 0.652019i \(0.226078\pi\)
\(642\) −19.7942 + 34.2846i −0.781216 + 1.35311i
\(643\) −36.6506 + 9.82051i −1.44536 + 0.387283i −0.894407 0.447253i \(-0.852402\pi\)
−0.550953 + 0.834536i \(0.685736\pi\)
\(644\) 14.3660 + 6.97372i 0.566101 + 0.274803i
\(645\) −12.2942 + 4.09808i −0.484085 + 0.161362i
\(646\) −20.3923 + 35.3205i −0.802325 + 1.38967i
\(647\) −7.40192 27.6244i −0.291000 1.08603i −0.944343 0.328963i \(-0.893301\pi\)
0.653343 0.757062i \(-0.273366\pi\)
\(648\) −1.20577 4.50000i −0.0473672 0.176777i
\(649\) −15.1244 26.1962i −0.593683 1.02829i
\(650\) −46.8827 20.0263i −1.83889 0.785495i
\(651\) −1.26795 + 6.58846i −0.0496948 + 0.258222i
\(652\) 16.0981 4.31347i 0.630449 0.168928i
\(653\) 11.2679 11.2679i 0.440949 0.440949i −0.451382 0.892331i \(-0.649069\pi\)
0.892331 + 0.451382i \(0.149069\pi\)
\(654\) −14.8301 14.8301i −0.579904 0.579904i
\(655\) −10.1436 5.07180i −0.396343 0.198171i
\(656\) −11.5981 + 6.69615i −0.452829 + 0.261441i
\(657\) 7.60770 + 7.60770i 0.296804 + 0.296804i
\(658\) −36.6506 + 12.6962i −1.42879 + 0.494948i
\(659\) 34.3468 19.8301i 1.33796 0.772472i 0.351456 0.936204i \(-0.385687\pi\)
0.986505 + 0.163732i \(0.0523533\pi\)
\(660\) 6.00000 12.0000i 0.233550 0.467099i
\(661\) 20.2583 11.6962i 0.787958 0.454928i −0.0512854 0.998684i \(-0.516332\pi\)
0.839243 + 0.543756i \(0.182998\pi\)
\(662\) 3.00000 11.1962i 0.116598 0.435151i
\(663\) 70.6410i 2.74347i
\(664\) −3.03590 5.25833i −0.117816 0.204063i
\(665\) 2.09808 16.0263i 0.0813599 0.621472i
\(666\) 3.29423 1.90192i 0.127649 0.0736980i
\(667\) 3.54294 13.2224i 0.137183 0.511975i
\(668\) −4.26795 4.26795i −0.165132 0.165132i
\(669\) 9.29423 9.29423i 0.359336 0.359336i
\(670\) −24.3923 12.1962i −0.942357 0.471178i
\(671\) −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 −0.0122297 0.999925i \(-0.503893\pi\)
−0.510554 + 0.859846i \(0.670560\pi\)
\(674\) −12.7583 + 7.36603i −0.491433 + 0.283729i
\(675\) 20.7846 15.5885i 0.800000 0.600000i
\(676\) 12.8660 22.2846i 0.494847 0.857100i
\(677\) −12.6340 47.1506i −0.485563 1.81215i −0.577512 0.816382i \(-0.695976\pi\)
0.0919487 0.995764i \(-0.470690\pi\)
\(678\) 32.7846i 1.25909i
\(679\) 17.4186 35.8827i 0.668464 1.37705i
\(680\) −7.46410 + 4.92820i −0.286235 + 0.188988i
\(681\) −32.1506 + 8.61474i −1.23202 + 0.330117i
\(682\) 4.00000 4.00000i 0.153168 0.153168i
\(683\) −3.08142 11.5000i −0.117907 0.440035i 0.881581 0.472033i \(-0.156480\pi\)
−0.999488 + 0.0319978i \(0.989813\pi\)
\(684\) 14.1962i 0.542803i
\(685\) −3.00000 + 1.00000i −0.114624 + 0.0382080i
\(686\) −10.8660 + 34.0885i −0.414867 + 1.30150i
\(687\) 8.00962 + 4.62436i 0.305586 + 0.176430i
\(688\) −10.5622 + 10.5622i −0.402679 + 0.402679i
\(689\) −10.1962 17.6603i −0.388442 0.672802i
\(690\) −1.56218 26.0263i −0.0594711 0.990804i
\(691\) 10.8564 + 6.26795i 0.412997 + 0.238444i 0.692077 0.721824i \(-0.256696\pi\)
−0.279080 + 0.960268i \(0.590029\pi\)
\(692\) 27.7128 27.7128i 1.05348 1.05348i
\(693\) −15.0000 + 5.19615i −0.569803 + 0.197386i
\(694\) 18.1244i 0.687991i
\(695\) 15.5096 + 23.4904i 0.588313 + 0.891041i
\(696\) 2.49038 2.49038i 0.0943977 0.0943977i
\(697\) 6.00000 22.3923i 0.227266 0.848169i
\(698\) 13.6603 + 13.6603i 0.517048 + 0.517048i
\(699\) 15.8038 + 15.8038i 0.597756 + 0.597756i
\(700\) −12.8205 + 18.9904i −0.484570 + 0.717769i
\(701\) −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
\(703\) −1.73205 + 0.464102i −0.0653255 + 0.0175039i
\(704\) 11.4641i 0.432070i
\(705\) 21.9904 + 19.5000i 0.828206 + 0.734412i
\(706\) −29.4904 17.0263i −1.10989 0.640792i
\(707\) 9.69615 + 1.86603i 0.364661 + 0.0701791i
\(708\) 22.6865 + 39.2942i 0.852612 + 1.47677i
\(709\) 24.8038 + 14.3205i 0.931528 + 0.537818i 0.887295 0.461203i \(-0.152582\pi\)
0.0442335 + 0.999021i \(0.485915\pi\)
\(710\) −4.09808 + 20.0263i −0.153798 + 0.751573i
\(711\) 13.6077i 0.510328i
\(712\) 7.46410 + 2.00000i 0.279729 + 0.0749532i
\(713\) 1.32051 4.92820i 0.0494534 0.184563i
\(714\) −67.1769 12.9282i −2.51403 0.483826i
\(715\) 4.73205 23.1244i 0.176969 0.864802i
\(716\) 2.19615 0.0820741
\(717\) −1.73205 3.00000i −0.0646846 0.112037i
\(718\) 14.9282 14.9282i 0.557116 0.557116i
\(719\) 4.53590 + 7.85641i 0.169160 + 0.292995i 0.938125 0.346297i \(-0.112561\pi\)
−0.768964 + 0.639292i \(0.779228\pi\)
\(720\) 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
\(723\) −19.4545 + 33.6962i −0.723520 + 1.25317i
\(724\) −17.4282 30.1865i −0.647714 1.12187i
\(725\) 18.0622 + 7.71539i 0.670812 + 0.286542i
\(726\) −22.6244 6.06218i −0.839669 0.224989i
\(727\) −15.7583 4.22243i −0.584444 0.156601i −0.0455314 0.998963i \(-0.514498\pi\)
−0.538913 + 0.842362i \(0.681165\pi\)
\(728\) 5.46410 + 4.73205i 0.202513 + 0.175381i
\(729\) −27.0000 −1.00000
\(730\) 0.928203 + 15.4641i 0.0343543 + 0.572352i
\(731\) 25.8564i 0.956334i
\(732\) 7.60770 + 4.39230i 0.281189 + 0.162344i
\(733\) 30.3205 + 30.3205i 1.11991 + 1.11991i 0.991754 + 0.128160i \(0.0409071\pi\)
0.128160 + 0.991754i \(0.459093\pi\)
\(734\) 5.33013 9.23205i 0.196739 0.340761i
\(735\) 26.5526 5.47372i 0.979406 0.201901i
\(736\) −13.2224 22.9019i −0.487385 0.844176i
\(737\) 3.26795 12.1962i 0.120376 0.449251i
\(738\) 4.50000 + 16.7942i 0.165647 + 0.618204i
\(739\) −35.3205 20.3923i −1.29929 0.750143i −0.319005 0.947753i \(-0.603349\pi\)
−0.980281 + 0.197610i \(0.936682\pi\)
\(740\) 2.49038 + 0.509619i 0.0915482 + 0.0187340i
\(741\) −6.46410 24.1244i −0.237465 0.886230i
\(742\) −18.6603 + 6.46410i −0.685039 + 0.237305i
\(743\) 4.91858 + 18.3564i 0.180445 + 0.673431i 0.995560 + 0.0941313i \(0.0300073\pi\)
−0.815114 + 0.579300i \(0.803326\pi\)
\(744\) 0.928203 0.928203i 0.0340296 0.0340296i
\(745\) 30.9282 + 15.4641i 1.13312 + 0.566561i
\(746\) −7.56218 + 13.0981i −0.276871 + 0.479555i
\(747\) −33.9904 + 9.10770i −1.24364 + 0.333233i
\(748\) 18.9282 + 18.9282i 0.692084 + 0.692084i
\(749\) 28.1603 + 13.6699i 1.02895 + 0.499486i
\(750\) 37.2846 + 3.06218i 1.36144 + 0.111815i
\(751\) 49.1244 1.79257 0.896287 0.443475i \(-0.146255\pi\)
0.896287 + 0.443475i \(0.146255\pi\)
\(752\) 32.7224 + 8.76795i 1.19326 + 0.319734i
\(753\) −3.16987 + 5.49038i −0.115517 + 0.200081i
\(754\) −20.0263 + 34.6865i −0.729314 + 1.26321i
\(755\) 17.6603 35.3205i 0.642722 1.28544i
\(756\) 22.5000 7.79423i 0.818317 0.283473i
\(757\) 6.39230 + 6.39230i 0.232332 + 0.232332i 0.813666 0.581333i \(-0.197469\pi\)
−0.581333 + 0.813666i \(0.697469\pi\)
\(758\) −8.75833 32.6865i −0.318117 1.18723i
\(759\) 11.6603 3.12436i 0.423240 0.113407i
\(760\) −2.09808 + 2.36603i −0.0761052 + 0.0858248i
\(761\) 1.19615i 0.0433605i 0.999765 + 0.0216802i \(0.00690158\pi\)
−0.999765 + 0.0216802i \(0.993098\pi\)
\(762\) 22.7942 + 39.4808i 0.825748 + 1.43024i
\(763\) −10.8564 + 12.5359i −0.393028 + 0.453830i
\(764\) 16.9808i 0.614342i
\(765\) 16.3923 + 49.1769i 0.592665 + 1.77800i
\(766\) −18.3564 10.5981i −0.663244 0.382924i
\(767\) 56.4449 + 56.4449i 2.03811 + 2.03811i
\(768\) 33.5885i 1.21202i
\(769\) −7.40192 + 12.8205i −0.266920 + 0.462319i −0.968065 0.250700i \(-0.919339\pi\)
0.701145 + 0.713019i \(0.252673\pi\)
\(770\) −21.1244 8.73205i −0.761269 0.314681i
\(771\) −0.464102 + 0.124356i −0.0167142 + 0.00447856i
\(772\) −0.464102 + 0.124356i −0.0167034 + 0.00447566i
\(773\) −44.4186 + 11.9019i −1.59763 + 0.428082i −0.944324 0.329016i \(-0.893283\pi\)
−0.653301 + 0.757098i \(0.726616\pi\)
\(774\) 9.69615 + 16.7942i 0.348521 + 0.603656i
\(775\) 6.73205 + 2.87564i 0.241822 + 0.103296i
\(776\) −6.75833 + 3.90192i −0.242610 + 0.140071i
\(777\) −1.68653 2.49038i −0.0605041 0.0893419i
\(778\) −4.52628 16.8923i −0.162275 0.605618i
\(779\) 8.19615i 0.293658i
\(780\) −7.09808 + 34.6865i −0.254152 + 1.24198i
\(781\) −9.46410 −0.338652
\(782\) 50.2487 + 13.4641i 1.79689 + 0.481475i
\(783\) −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
\(786\) −4.39230 + 16.3923i −0.156668 + 0.584694i
\(787\) 51.6769 + 13.8468i 1.84208 + 0.493585i 0.999021 0.0442321i \(-0.0140841\pi\)
0.843062 + 0.537817i \(0.180751\pi\)
\(788\) 9.46410 + 2.53590i 0.337145 + 0.0903376i
\(789\) 9.23205 2.47372i 0.328670 0.0880668i
\(790\) −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
\(793\) 14.9282 + 4.00000i 0.530116 + 0.142044i
\(794\) 58.6410 2.08109
\(795\) 11.1962 + 9.92820i 0.397087 + 0.352117i
\(796\) 7.60770i 0.269648i
\(797\) −11.8827 44.3468i −0.420906 1.57084i −0.772703 0.634767i \(-0.781096\pi\)
0.351797 0.936076i \(-0.385571\pi\)
\(798\) −24.1244 + 1.73205i −0.853993 + 0.0613139i
\(799\) −50.7846 + 29.3205i −1.79663 + 1.03729i
\(800\) 35.2128 14.1340i 1.24496 0.499711i
\(801\) 22.3923 38.7846i 0.791193 1.37039i
\(802\) −17.5263 + 4.69615i −0.618874 + 0.165827i
\(803\) −6.92820 + 1.85641i −0.244491 + 0.0655112i
\(804\) −4.90192 + 18.2942i −0.172878 + 0.645188i
\(805\) −20.4378 + 2.70577i −0.720339 + 0.0953659i
\(806\) −7.46410 + 12.9282i −0.262912 + 0.455377i
\(807\) 42.5885 24.5885i 1.49918 0.865555i
\(808\) −1.36603 1.36603i −0.0480566 0.0480566i
\(809\) −8.38269 4.83975i −0.294720 0.170156i 0.345349 0.938474i \(-0.387761\pi\)
−0.640068 + 0.768318i \(0.721094\pi\)
\(810\) −29.0885 25.7942i −1.02206 0.906317i
\(811\) 24.5885i 0.863418i −0.902013 0.431709i \(-0.857911\pi\)
0.902013 0.431709i \(-0.142089\pi\)
\(812\) 13.6077 + 11.7846i 0.477536 + 0.413559i
\(813\) −56.4449 −1.97961
\(814\) 2.53590i 0.0888832i
\(815\) −14.2750 + 16.0981i −0.500031 + 0.563891i
\(816\) 42.2487 + 42.2487i 1.47900 + 1.47900i
\(817\) −2.36603 8.83013i −0.0827768 0.308927i
\(818\) 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
\(821\) −5.20577 + 9.01666i −0.181683 + 0.314684i −0.942454 0.334337i \(-0.891488\pi\)
0.760771 + 0.649020i \(0.224821\pi\)
\(822\) 2.36603 + 4.09808i 0.0825246 + 0.142937i
\(823\) −26.7224 7.16025i −0.931485 0.249591i −0.238997 0.971020i \(-0.576819\pi\)
−0.692488 + 0.721429i \(0.743485\pi\)
\(824\) 4.66025 0.162348
\(825\) 2.07180 + 17.1962i 0.0721307 + 0.598693i
\(826\) 64.0070 43.3468i 2.22709 1.50823i
\(827\) 22.8301 + 22.8301i 0.793881 + 0.793881i 0.982123 0.188241i \(-0.0602788\pi\)
−0.188241 + 0.982123i \(0.560279\pi\)
\(828\) −17.4904 + 4.68653i −0.607833 + 0.162868i
\(829\) −4.83975 + 8.38269i −0.168091 + 0.291143i −0.937749 0.347314i \(-0.887094\pi\)
0.769657 + 0.638457i \(0.220427\pi\)
\(830\) −45.3205 22.6603i −1.57310 0.786549i
\(831\) −5.19615 19.3923i −0.180253 0.672712i
\(832\) 7.83013 + 29.2224i 0.271461 + 1.01311i
\(833\) −6.39230 + 53.7128i −0.221480 + 1.86104i
\(834\) 29.7846 29.7846i 1.03136 1.03136i
\(835\) 7.63397 + 1.56218i 0.264185 + 0.0540614i
\(836\) 8.19615 + 4.73205i 0.283470 + 0.163661i
\(837\) −3.80385 6.58846i −0.131480 0.227730i
\(838\) −1.16987 + 4.36603i −0.0404126 + 0.150822i
\(839\) −27.6147 47.8301i −0.953367 1.65128i −0.738063 0.674732i \(-0.764259\pi\)
−0.215304 0.976547i \(-0.569074\pi\)
\(840\) −4.90192 2.02628i −0.169132 0.0699133i
\(841\) −6.78461 + 11.7513i −0.233952 + 0.405217i
\(842\) −6.56218 6.56218i −0.226148 0.226148i
\(843\) 38.5692i 1.32839i
\(844\) 22.6410i 0.779336i
\(845\) 1.99038 + 33.1603i 0.0684712 + 1.14075i
\(846\) 21.9904 38.0885i 0.756045 1.30951i
\(847\) −3.50000 + 18.1865i −0.120261 + 0.624897i
\(848\) 16.6603 + 4.46410i 0.572115 + 0.153298i
\(849\) 16.6865 16.6865i 0.572680 0.572680i
\(850\) −29.3205 + 68.6410i −1.00569 + 2.35437i
\(851\) 1.14359 + 1.98076i 0.0392019 + 0.0678997i
\(852\) 14.1962 0.486352
\(853\) 0.124356 0.464102i 0.00425786 0.0158905i −0.963764 0.266756i \(-0.914048\pi\)
0.968022 + 0.250865i \(0.0807150\pi\)
\(854\) 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
\(857\) 4.92820 4.92820i 0.168344 0.168344i −0.617907 0.786251i \(-0.712019\pi\)
0.786251 + 0.617907i \(0.212019\pi\)
\(858\) −35.3205 −1.20582
\(859\) 10.3397 0.352788 0.176394 0.984320i \(-0.443557\pi\)
0.176394 + 0.984320i \(0.443557\pi\)
\(860\) −2.59808 + 12.6962i −0.0885937 + 0.432935i
\(861\) 12.9904 4.50000i 0.442711 0.153360i
\(862\) −10.2942 + 38.4186i −0.350623 + 1.30854i
\(863\) −37.6147 10.0788i −1.28042 0.343088i −0.446406 0.894830i \(-0.647296\pi\)
−0.834014 + 0.551743i \(0.813963\pi\)
\(864\) −38.0885 10.2058i −1.29580 0.347207i
\(865\) −10.1436 + 49.5692i −0.344893 + 1.68540i
\(866\) −0.294229 0.169873i −0.00999830 0.00577252i
\(867\) −73.9808 −2.51252
\(868\) 5.07180 + 4.39230i 0.172148 + 0.149085i
\(869\) −7.85641 4.53590i −0.266510 0.153870i
\(870\) 5.89230 28.7942i 0.199768 0.976216i
\(871\) 33.3205i 1.12902i
\(872\) 3.13397 0.839746i 0.106130 0.0284374i
\(873\) 11.7058 + 43.6865i 0.396180 + 1.47857i
\(874\) 18.3923 0.622129
\(875\) 0.303848 29.5788i 0.0102719 0.999947i
\(876\) 10.3923 2.78461i 0.351123 0.0940832i
\(877\) −9.19615 9.19615i −0.310532 0.310532i 0.534584 0.845116i \(-0.320468\pi\)
−0.845116 + 0.534584i \(0.820468\pi\)
\(878\) 17.9282 66.9090i 0.605048 2.25807i
\(879\) −11.6603 3.12436i −0.393291 0.105382i
\(880\) 11.0000 + 16.6603i 0.370810 + 0.561617i
\(881\) 51.0333i 1.71936i 0.510836 + 0.859678i \(0.329336\pi\)
−0.510836 + 0.859678i \(0.670664\pi\)
\(882\) −15.9904 37.2846i −0.538424 1.25544i
\(883\) 19.4378 19.4378i 0.654135 0.654135i −0.299851 0.953986i \(-0.596937\pi\)
0.953986 + 0.299851i \(0.0969370\pi\)
\(884\) −61.1769 35.3205i −2.05760 1.18796i
\(885\) −52.3923 26.1962i −1.76115 0.880574i
\(886\) 11.7942 + 20.4282i 0.396235 + 0.686299i
\(887\) −6.49038 + 6.49038i −0.217926 + 0.217926i −0.807624 0.589698i \(-0.799247\pi\)
0.589698 + 0.807624i \(0.299247\pi\)
\(888\) 0.588457i 0.0197473i
\(889\) 29.8468 20.2128i 1.00103 0.677916i
\(890\) 61.1769 20.3923i 2.05065 0.683552i
\(891\) 9.00000 15.5885i 0.301511 0.522233i
\(892\) −3.40192 12.6962i −0.113905 0.425099i
\(893\) −14.6603 + 14.6603i −0.490587 + 0.490587i
\(894\) 13.3923 49.9808i 0.447906 1.67161i
\(895\) −2.36603 + 1.56218i −0.0790875 + 0.0522178i
\(896\) −10.8301 + 0.777568i −0.361809 + 0.0259767i
\(897\) −27.5885 + 15.9282i −0.921152 + 0.531827i
\(898\) −3.66987 13.6962i −0.122465 0.457047i
\(899\) 2.87564 4.98076i 0.0959081 0.166118i
\(900\) −3.10770 25.7942i −0.103590 0.859808i
\(901\) −25.8564 + 14.9282i −0.861402 + 0.497331i
\(902\) −11.1962 3.00000i −0.372791 0.0998891i
\(903\) 12.6962 8.59808i 0.422501 0.286126i
\(904\) −4.39230 2.53590i −0.146086 0.0843427i
\(905\) 40.2487 + 20.1244i 1.33791 + 0.668956i
\(906\) −57.0788 15.2942i −1.89632 0.508117i
\(907\) 9.36603 + 9.36603i 0.310994 + 0.310994i 0.845294 0.534301i \(-0.179425\pi\)
−0.534301 + 0.845294i \(0.679425\pi\)
\(908\) −8.61474 + 32.1506i −0.285890 + 1.06696i
\(909\) −9.69615 + 5.59808i −0.321601 + 0.185676i
\(910\) 59.8109 + 7.83013i 1.98271 + 0.259566i
\(911\) −0.633975 1.09808i −0.0210045 0.0363809i 0.855332 0.518080i \(-0.173353\pi\)
−0.876337 + 0.481699i \(0.840020\pi\)
\(912\) 18.2942 + 10.5622i 0.605782 + 0.349749i
\(913\) 6.07180 22.6603i 0.200947 0.749945i
\(914\) 54.5429 31.4904i 1.80412 1.04161i
\(915\) −11.3205 + 0.679492i −0.374244 + 0.0224633i
\(916\) 8.00962 4.62436i 0.264645 0.152793i
\(917\) 13.1769 + 2.53590i 0.435140 + 0.0837427i
\(918\) 67.1769 38.7846i 2.21717 1.28008i
\(919\) 16.0981 9.29423i 0.531027 0.306588i −0.210408 0.977614i \(-0.567479\pi\)
0.741434 + 0.671025i \(0.234146\pi\)
\(920\) 3.60770 + 1.80385i 0.118942 + 0.0594711i
\(921\) −12.6962 + 3.40192i −0.418352 + 0.112097i
\(922\) 32.7583 32.7583i 1.07884 1.07884i
\(923\) 24.1244 6.46410i 0.794063 0.212768i
\(924\) −3.00000 + 15.5885i −0.0986928 + 0.512823i
\(925\) −3.04552 + 1.22243i −0.100136 + 0.0401933i
\(926\) 14.3301 + 24.8205i 0.470917 + 0.815653i
\(927\) 6.99038 26.0885i 0.229594 0.856857i
\(928\) −7.71539 28.7942i −0.253270 0.945217i
\(929\) −15.8923 + 27.5263i −0.521410 + 0.903108i 0.478280 + 0.878207i \(0.341260\pi\)
−0.999690 + 0.0249007i \(0.992073\pi\)
\(930\) 2.19615 10.7321i 0.0720147 0.351918i
\(931\) 2.73205 + 18.9282i 0.0895393 + 0.620347i
\(932\) 21.5885 5.78461i 0.707153 0.189481i
\(933\) −12.3397 −0.403985
\(934\) −5.00000 −0.163605
\(935\) −33.8564 6.92820i −1.10722 0.226576i
\(936\) −8.19615 −0.267900
\(937\) 5.53590 5.53590i 0.180850 0.180850i −0.610876 0.791726i \(-0.709183\pi\)
0.791726 + 0.610876i \(0.209183\pi\)
\(938\) 31.6865 + 6.09808i 1.03460 + 0.199109i
\(939\) −3.80385 1.01924i −0.124134 0.0332616i
\(940\) 27.8827 9.29423i 0.909433 0.303144i
\(941\) −6.10770 + 3.52628i −0.199105 + 0.114953i −0.596238 0.802808i \(-0.703339\pi\)
0.397133 + 0.917761i \(0.370005\pi\)
\(942\) −29.4904 17.0263i −0.960849 0.554746i
\(943\) −10.0981 + 2.70577i −0.328839 + 0.0881120i
\(944\) −67.5167 −2.19748
\(945\) −18.6962 + 24.4019i −0.608186 + 0.793795i
\(946\) −12.9282 −0.420332
\(947\) −6.83013 + 1.83013i −0.221949 + 0.0594711i −0.368080 0.929794i \(-0.619985\pi\)
0.146131 + 0.989265i \(0.453318\pi\)
\(948\) 11.7846 + 6.80385i 0.382746 + 0.220979i
\(949\) 16.3923 9.46410i 0.532117 0.307218i
\(950\) −3.73205 + 26.1244i −0.121084 + 0.847586i
\(951\) −20.0263 5.36603i −0.649397 0.174005i
\(952\) 6.92820 8.00000i 0.224544 0.259281i
\(953\) 22.0526 22.0526i 0.714352 0.714352i −0.253090 0.967443i \(-0.581447\pi\)
0.967443 + 0.253090i \(0.0814470\pi\)
\(954\) 11.1962 19.3923i 0.362489 0.627849i
\(955\) 12.0788 + 18.2942i 0.390862 + 0.591987i
\(956\) −3.46410 −0.112037
\(957\) 13.6077 0.439874
\(958\) −32.2224 + 8.63397i −1.04106 + 0.278951i
\(959\) 3.09808 2.09808i 0.100042 0.0677504i
\(960\) −12.2321 18.5263i −0.394788 0.597933i
\(961\) −14.4282 + 24.9904i −0.465426 + 0.806141i
\(962\) −1.73205 6.46410i −0.0558436 0.208411i
\(963\) −34.2846 + 9.18653i −1.10481 + 0.296032i
\(964\) 19.4545 + 33.6962i 0.626587 + 1.08528i
\(965\) 0.411543 0.464102i 0.0132480 0.0149400i
\(966\) 10.0981 + 29.1506i 0.324900 + 0.937906i
\(967\) −51.0788 + 13.6865i −1.64258 + 0.440129i −0.957523 0.288356i \(-0.906891\pi\)
−0.685061 + 0.728485i \(0.740225\pi\)
\(968\) 2.56218 2.56218i 0.0823515 0.0823515i
\(969\) −35.3205 + 9.46410i −1.13466 + 0.304031i
\(970\) −29.1244 + 58.2487i −0.935127 + 1.87025i
\(971\) −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
\(973\) −25.1769 21.8038i −0.807135 0.698999i
\(974\) −51.5429 + 29.7583i −1.65154 + 0.953518i
\(975\) −17.0263 42.4186i −0.545277 1.35848i
\(976\) −11.3205 + 6.53590i −0.362361 + 0.209209i
\(977\) −10.3205 + 38.5167i −0.330182 + 1.23226i 0.578816 + 0.815458i \(0.303515\pi\)
−0.908999 + 0.416799i \(0.863152\pi\)
\(978\) 27.8827 + 16.0981i 0.891590 + 0.514760i
\(979\) 14.9282 + 25.8564i 0.477107 + 0.826374i
\(980\) 8.53590 25.7321i 0.272669 0.821980i
\(981\) 18.8038i 0.600361i
\(982\) 8.29423 30.9545i 0.264679 0.987797i
\(983\) 20.9737 + 20.9737i 0.668958 + 0.668958i 0.957475 0.288517i \(-0.0931622\pi\)
−0.288517 + 0.957475i \(0.593162\pi\)
\(984\) −2.59808 0.696152i −0.0828236 0.0221925i
\(985\) −12.0000 + 4.00000i −0.382352 + 0.127451i
\(986\) 50.7846 + 29.3205i 1.61731 + 0.933755i
\(987\) −31.2846 15.1865i −0.995800 0.483393i
\(988\) −24.1244 6.46410i −0.767498 0.205650i
\(989\) −10.0981 + 5.83013i −0.321100 + 0.185387i
\(990\) 24.5885 8.19615i 0.781472 0.260491i
\(991\) 4.00000 6.92820i 0.127064 0.220082i −0.795474 0.605988i \(-0.792778\pi\)
0.922538 + 0.385906i \(0.126111\pi\)
\(992\) −2.87564 10.7321i −0.0913018 0.340743i
\(993\) 9.00000 5.19615i 0.285606 0.164895i
\(994\) −1.73205 24.1244i −0.0549373 0.765178i
\(995\) 5.41154 + 8.19615i 0.171557 + 0.259835i
\(996\) −9.10770 + 33.9904i −0.288588 + 1.07703i
\(997\) 35.1962 35.1962i 1.11467 1.11467i 0.122163 0.992510i \(-0.461017\pi\)
0.992510 0.122163i \(-0.0389832\pi\)
\(998\) 8.80385 + 32.8564i 0.278681 + 1.04005i
\(999\) 3.29423 + 0.882686i 0.104225 + 0.0279269i
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.cg.d.157.1 yes 4
3.2 odd 2 945.2.cj.b.577.1 4
5.3 odd 4 315.2.cg.b.283.1 yes 4
7.5 odd 6 315.2.bs.d.292.1 yes 4
9.2 odd 6 945.2.bv.b.262.1 4
9.7 even 3 315.2.bs.a.52.1 4
15.8 even 4 945.2.cj.c.388.1 4
21.5 even 6 945.2.bv.c.712.1 4
35.33 even 12 315.2.bs.a.103.1 yes 4
45.38 even 12 945.2.bv.c.73.1 4
45.43 odd 12 315.2.bs.d.178.1 yes 4
63.47 even 6 945.2.cj.c.397.1 4
63.61 odd 6 315.2.cg.b.187.1 yes 4
105.68 odd 12 945.2.bv.b.523.1 4
315.173 odd 12 945.2.cj.b.208.1 4
315.313 even 12 inner 315.2.cg.d.313.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bs.a.52.1 4 9.7 even 3
315.2.bs.a.103.1 yes 4 35.33 even 12
315.2.bs.d.178.1 yes 4 45.43 odd 12
315.2.bs.d.292.1 yes 4 7.5 odd 6
315.2.cg.b.187.1 yes 4 63.61 odd 6
315.2.cg.b.283.1 yes 4 5.3 odd 4
315.2.cg.d.157.1 yes 4 1.1 even 1 trivial
315.2.cg.d.313.1 yes 4 315.313 even 12 inner
945.2.bv.b.262.1 4 9.2 odd 6
945.2.bv.b.523.1 4 105.68 odd 12
945.2.bv.c.73.1 4 45.38 even 12
945.2.bv.c.712.1 4 21.5 even 6
945.2.cj.b.208.1 4 315.173 odd 12
945.2.cj.b.577.1 4 3.2 odd 2
945.2.cj.c.388.1 4 15.8 even 4
945.2.cj.c.397.1 4 63.47 even 6