Properties

Label 93.2.g.e.68.2
Level $93$
Weight $2$
Character 93.68
Analytic conductor $0.743$
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] = [93,2,Mod(26,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 68.2
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 93.68
Dual form 93.2.g.e.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.52434i q^{2} +(1.68614 + 0.396143i) q^{3} -4.37228 q^{4} +(-2.18614 - 1.26217i) q^{5} +(-1.00000 + 4.25639i) q^{6} +(1.18614 + 2.05446i) q^{7} -5.98844i q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+2.52434i q^{2} +(1.68614 + 0.396143i) q^{3} -4.37228 q^{4} +(-2.18614 - 1.26217i) q^{5} +(-1.00000 + 4.25639i) q^{6} +(1.18614 + 2.05446i) q^{7} -5.98844i q^{8} +(2.68614 + 1.33591i) q^{9} +(3.18614 - 5.51856i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-7.37228 - 1.73205i) q^{12} +(1.50000 + 0.866025i) q^{13} +(-5.18614 + 2.99422i) q^{14} +(-3.18614 - 2.99422i) q^{15} +6.37228 q^{16} +(0.813859 + 1.40965i) q^{17} +(-3.37228 + 6.78073i) q^{18} +(-3.87228 - 6.70699i) q^{19} +(9.55842 + 5.51856i) q^{20} +(1.18614 + 3.93398i) q^{21} +(9.55842 + 5.51856i) q^{22} +(2.37228 - 10.0974i) q^{24} +(0.686141 + 1.18843i) q^{25} +(-2.18614 + 3.78651i) q^{26} +(4.00000 + 3.31662i) q^{27} +(-5.18614 - 8.98266i) q^{28} -6.00000 q^{29} +(7.55842 - 8.04290i) q^{30} +(-2.00000 + 5.19615i) q^{31} +4.10891i q^{32} +(5.18614 - 5.51856i) q^{33} +(-3.55842 + 2.05446i) q^{34} -5.98844i q^{35} +(-11.7446 - 5.84096i) q^{36} +(1.50000 - 0.866025i) q^{37} +(16.9307 - 9.77495i) q^{38} +(2.18614 + 2.05446i) q^{39} +(-7.55842 + 13.0916i) q^{40} +(-2.18614 - 1.26217i) q^{41} +(-9.93070 + 2.99422i) q^{42} +(-7.50000 + 4.33013i) q^{43} +(-9.55842 + 16.5557i) q^{44} +(-4.18614 - 6.31084i) q^{45} +6.63325i q^{47} +(10.7446 + 2.52434i) q^{48} +(0.686141 - 1.18843i) q^{49} +(-3.00000 + 1.73205i) q^{50} +(0.813859 + 2.69927i) q^{51} +(-6.55842 - 3.78651i) q^{52} +(2.18614 - 3.78651i) q^{53} +(-8.37228 + 10.0974i) q^{54} +(-9.55842 + 5.51856i) q^{55} +(12.3030 - 7.10313i) q^{56} +(-3.87228 - 12.8429i) q^{57} -15.1460i q^{58} +(-1.93070 + 1.11469i) q^{59} +(13.9307 + 13.0916i) q^{60} +(-13.1168 - 5.04868i) q^{62} +(0.441578 + 7.10313i) q^{63} +2.37228 q^{64} +(-2.18614 - 3.78651i) q^{65} +(13.9307 + 13.0916i) q^{66} +(5.55842 - 9.62747i) q^{67} +(-3.55842 - 6.16337i) q^{68} +15.1168 q^{70} +(1.93070 + 1.11469i) q^{71} +(8.00000 - 16.0858i) q^{72} +(5.61684 + 3.24289i) q^{73} +(2.18614 + 3.78651i) q^{74} +(0.686141 + 2.27567i) q^{75} +(16.9307 + 29.3248i) q^{76} +10.3723 q^{77} +(-5.18614 + 5.51856i) q^{78} +(-0.558422 + 0.322405i) q^{79} +(-13.9307 - 8.04290i) q^{80} +(5.43070 + 7.17687i) q^{81} +(3.18614 - 5.51856i) q^{82} +(-3.81386 + 6.60580i) q^{83} +(-5.18614 - 17.2005i) q^{84} -4.10891i q^{85} +(-10.9307 - 18.9325i) q^{86} +(-10.1168 - 2.37686i) q^{87} +(-22.6753 - 13.0916i) q^{88} +6.00000 q^{89} +(15.9307 - 10.5672i) q^{90} +4.10891i q^{91} +(-5.43070 + 7.96916i) q^{93} -16.7446 q^{94} +19.5499i q^{95} +(-1.62772 + 6.92820i) q^{96} -5.37228 q^{97} +(3.00000 + 1.73205i) q^{98} +(10.9307 - 7.25061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - 6 q^{4} - 3 q^{5} - 4 q^{6} - q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} - 6 q^{4} - 3 q^{5} - 4 q^{6} - q^{7} + 5 q^{9} + 7 q^{10} + 3 q^{11} - 18 q^{12} + 6 q^{13} - 15 q^{14} - 7 q^{15} + 14 q^{16} + 9 q^{17} - 2 q^{18} - 4 q^{19} + 21 q^{20} - q^{21} + 21 q^{22} - 2 q^{24} - 3 q^{25} - 3 q^{26} + 16 q^{27} - 15 q^{28} - 24 q^{29} + 13 q^{30} - 8 q^{31} + 15 q^{33} + 3 q^{34} - 24 q^{36} + 6 q^{37} + 39 q^{38} + 3 q^{39} - 13 q^{40} - 3 q^{41} - 11 q^{42} - 30 q^{43} - 21 q^{44} - 11 q^{45} + 20 q^{48} - 3 q^{49} - 12 q^{50} + 9 q^{51} - 9 q^{52} + 3 q^{53} - 22 q^{54} - 21 q^{55} + 9 q^{56} - 4 q^{57} + 21 q^{59} + 27 q^{60} - 18 q^{62} + 19 q^{63} - 2 q^{64} - 3 q^{65} + 27 q^{66} + 5 q^{67} + 3 q^{68} + 26 q^{70} - 21 q^{71} + 32 q^{72} - 12 q^{73} + 3 q^{74} - 3 q^{75} + 39 q^{76} + 30 q^{77} - 15 q^{78} + 15 q^{79} - 27 q^{80} - 7 q^{81} + 7 q^{82} - 21 q^{83} - 15 q^{84} - 15 q^{86} - 6 q^{87} - 39 q^{88} + 24 q^{89} + 35 q^{90} + 7 q^{93} - 44 q^{94} - 18 q^{96} - 10 q^{97} + 12 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52434i 1.78498i 0.451071 + 0.892488i \(0.351042\pi\)
−0.451071 + 0.892488i \(0.648958\pi\)
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) −4.37228 −2.18614
\(5\) −2.18614 1.26217i −0.977672 0.564459i −0.0761054 0.997100i \(-0.524249\pi\)
−0.901566 + 0.432641i \(0.857582\pi\)
\(6\) −1.00000 + 4.25639i −0.408248 + 1.73766i
\(7\) 1.18614 + 2.05446i 0.448319 + 0.776511i 0.998277 0.0586811i \(-0.0186895\pi\)
−0.549958 + 0.835192i \(0.685356\pi\)
\(8\) 5.98844i 2.11723i
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 3.18614 5.51856i 1.00755 1.74512i
\(11\) 2.18614 3.78651i 0.659146 1.14167i −0.321691 0.946845i \(-0.604251\pi\)
0.980837 0.194830i \(-0.0624155\pi\)
\(12\) −7.37228 1.73205i −2.12819 0.500000i
\(13\) 1.50000 + 0.866025i 0.416025 + 0.240192i 0.693375 0.720577i \(-0.256123\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −5.18614 + 2.99422i −1.38605 + 0.800239i
\(15\) −3.18614 2.99422i −0.822658 0.773104i
\(16\) 6.37228 1.59307
\(17\) 0.813859 + 1.40965i 0.197390 + 0.341889i 0.947681 0.319218i \(-0.103420\pi\)
−0.750291 + 0.661107i \(0.770087\pi\)
\(18\) −3.37228 + 6.78073i −0.794854 + 1.59823i
\(19\) −3.87228 6.70699i −0.888362 1.53869i −0.841811 0.539773i \(-0.818510\pi\)
−0.0465514 0.998916i \(-0.514823\pi\)
\(20\) 9.55842 + 5.51856i 2.13733 + 1.23399i
\(21\) 1.18614 + 3.93398i 0.258837 + 0.858466i
\(22\) 9.55842 + 5.51856i 2.03786 + 1.17656i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.37228 10.0974i 0.484240 2.06111i
\(25\) 0.686141 + 1.18843i 0.137228 + 0.237686i
\(26\) −2.18614 + 3.78651i −0.428737 + 0.742595i
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) −5.18614 8.98266i −0.980088 1.69756i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 7.55842 8.04290i 1.37997 1.46843i
\(31\) −2.00000 + 5.19615i −0.359211 + 0.933257i
\(32\) 4.10891i 0.726360i
\(33\) 5.18614 5.51856i 0.902791 0.960658i
\(34\) −3.55842 + 2.05446i −0.610264 + 0.352336i
\(35\) 5.98844i 1.01223i
\(36\) −11.7446 5.84096i −1.95743 0.973494i
\(37\) 1.50000 0.866025i 0.246598 0.142374i −0.371607 0.928390i \(-0.621193\pi\)
0.618206 + 0.786016i \(0.287860\pi\)
\(38\) 16.9307 9.77495i 2.74652 1.58571i
\(39\) 2.18614 + 2.05446i 0.350063 + 0.328976i
\(40\) −7.55842 + 13.0916i −1.19509 + 2.06996i
\(41\) −2.18614 1.26217i −0.341418 0.197118i 0.319481 0.947593i \(-0.396491\pi\)
−0.660899 + 0.750475i \(0.729825\pi\)
\(42\) −9.93070 + 2.99422i −1.53234 + 0.462018i
\(43\) −7.50000 + 4.33013i −1.14374 + 0.660338i −0.947354 0.320189i \(-0.896254\pi\)
−0.196385 + 0.980527i \(0.562920\pi\)
\(44\) −9.55842 + 16.5557i −1.44099 + 2.49586i
\(45\) −4.18614 6.31084i −0.624033 0.940765i
\(46\) 0 0
\(47\) 6.63325i 0.967559i 0.875190 + 0.483779i \(0.160736\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 10.7446 + 2.52434i 1.55084 + 0.364357i
\(49\) 0.686141 1.18843i 0.0980201 0.169776i
\(50\) −3.00000 + 1.73205i −0.424264 + 0.244949i
\(51\) 0.813859 + 2.69927i 0.113963 + 0.377973i
\(52\) −6.55842 3.78651i −0.909489 0.525094i
\(53\) 2.18614 3.78651i 0.300290 0.520117i −0.675912 0.736982i \(-0.736250\pi\)
0.976201 + 0.216866i \(0.0695834\pi\)
\(54\) −8.37228 + 10.0974i −1.13932 + 1.37408i
\(55\) −9.55842 + 5.51856i −1.28886 + 0.744122i
\(56\) 12.3030 7.10313i 1.64406 0.949196i
\(57\) −3.87228 12.8429i −0.512896 1.70108i
\(58\) 15.1460i 1.98877i
\(59\) −1.93070 + 1.11469i −0.251356 + 0.145121i −0.620385 0.784297i \(-0.713024\pi\)
0.369029 + 0.929418i \(0.379690\pi\)
\(60\) 13.9307 + 13.0916i 1.79845 + 1.69011i
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −13.1168 5.04868i −1.66584 0.641182i
\(63\) 0.441578 + 7.10313i 0.0556336 + 0.894910i
\(64\) 2.37228 0.296535
\(65\) −2.18614 3.78651i −0.271157 0.469658i
\(66\) 13.9307 + 13.0916i 1.71475 + 1.61146i
\(67\) 5.55842 9.62747i 0.679069 1.17618i −0.296192 0.955128i \(-0.595717\pi\)
0.975262 0.221054i \(-0.0709498\pi\)
\(68\) −3.55842 6.16337i −0.431522 0.747418i
\(69\) 0 0
\(70\) 15.1168 1.80681
\(71\) 1.93070 + 1.11469i 0.229132 + 0.132290i 0.610172 0.792269i \(-0.291100\pi\)
−0.381039 + 0.924559i \(0.624434\pi\)
\(72\) 8.00000 16.0858i 0.942809 1.89573i
\(73\) 5.61684 + 3.24289i 0.657402 + 0.379551i 0.791286 0.611446i \(-0.209412\pi\)
−0.133884 + 0.990997i \(0.542745\pi\)
\(74\) 2.18614 + 3.78651i 0.254134 + 0.440172i
\(75\) 0.686141 + 2.27567i 0.0792287 + 0.262772i
\(76\) 16.9307 + 29.3248i 1.94208 + 3.36379i
\(77\) 10.3723 1.18203
\(78\) −5.18614 + 5.51856i −0.587215 + 0.624854i
\(79\) −0.558422 + 0.322405i −0.0628274 + 0.0362734i −0.531085 0.847319i \(-0.678215\pi\)
0.468257 + 0.883592i \(0.344882\pi\)
\(80\) −13.9307 8.04290i −1.55750 0.899223i
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 3.18614 5.51856i 0.351850 0.609423i
\(83\) −3.81386 + 6.60580i −0.418625 + 0.725081i −0.995801 0.0915392i \(-0.970821\pi\)
0.577176 + 0.816620i \(0.304155\pi\)
\(84\) −5.18614 17.2005i −0.565854 1.87673i
\(85\) 4.10891i 0.445674i
\(86\) −10.9307 18.9325i −1.17869 2.04155i
\(87\) −10.1168 2.37686i −1.08464 0.254826i
\(88\) −22.6753 13.0916i −2.41719 1.39557i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 15.9307 10.5672i 1.67924 1.11388i
\(91\) 4.10891i 0.430731i
\(92\) 0 0
\(93\) −5.43070 + 7.96916i −0.563138 + 0.826363i
\(94\) −16.7446 −1.72707
\(95\) 19.5499i 2.00578i
\(96\) −1.62772 + 6.92820i −0.166128 + 0.707107i
\(97\) −5.37228 −0.545473 −0.272736 0.962089i \(-0.587929\pi\)
−0.272736 + 0.962089i \(0.587929\pi\)
\(98\) 3.00000 + 1.73205i 0.303046 + 0.174964i
\(99\) 10.9307 7.25061i 1.09858 0.728714i
\(100\) −3.00000 5.19615i −0.300000 0.519615i
\(101\) 5.34363i 0.531711i 0.964013 + 0.265855i \(0.0856544\pi\)
−0.964013 + 0.265855i \(0.914346\pi\)
\(102\) −6.81386 + 2.05446i −0.674673 + 0.203421i
\(103\) −6.87228 + 11.9031i −0.677146 + 1.17285i 0.298691 + 0.954350i \(0.403450\pi\)
−0.975837 + 0.218501i \(0.929883\pi\)
\(104\) 5.18614 8.98266i 0.508543 0.880822i
\(105\) 2.37228 10.0974i 0.231511 0.985401i
\(106\) 9.55842 + 5.51856i 0.928396 + 0.536010i
\(107\) 2.18614 1.26217i 0.211342 0.122018i −0.390593 0.920564i \(-0.627730\pi\)
0.601935 + 0.798545i \(0.294397\pi\)
\(108\) −17.4891 14.5012i −1.68289 1.39538i
\(109\) 6.62772 0.634820 0.317410 0.948288i \(-0.397187\pi\)
0.317410 + 0.948288i \(0.397187\pi\)
\(110\) −13.9307 24.1287i −1.32824 2.30058i
\(111\) 2.87228 0.866025i 0.272625 0.0821995i
\(112\) 7.55842 + 13.0916i 0.714204 + 1.23704i
\(113\) 1.93070 + 1.11469i 0.181625 + 0.104861i 0.588056 0.808820i \(-0.299893\pi\)
−0.406431 + 0.913682i \(0.633227\pi\)
\(114\) 32.4198 9.77495i 3.03640 0.915508i
\(115\) 0 0
\(116\) 26.2337 2.43574
\(117\) 2.87228 + 4.33013i 0.265543 + 0.400320i
\(118\) −2.81386 4.87375i −0.259037 0.448665i
\(119\) −1.93070 + 3.34408i −0.176987 + 0.306551i
\(120\) −17.9307 + 19.0800i −1.63684 + 1.74176i
\(121\) −4.05842 7.02939i −0.368947 0.639036i
\(122\) 0 0
\(123\) −3.18614 2.99422i −0.287285 0.269980i
\(124\) 8.74456 22.7190i 0.785285 2.04023i
\(125\) 9.15759i 0.819080i
\(126\) −17.9307 + 1.11469i −1.59739 + 0.0993047i
\(127\) −11.6168 + 6.70699i −1.03083 + 0.595149i −0.917222 0.398377i \(-0.869574\pi\)
−0.113606 + 0.993526i \(0.536240\pi\)
\(128\) 14.2063i 1.25567i
\(129\) −14.3614 + 4.33013i −1.26445 + 0.381246i
\(130\) 9.55842 5.51856i 0.838329 0.484010i
\(131\) −9.81386 + 5.66603i −0.857441 + 0.495044i −0.863154 0.504940i \(-0.831515\pi\)
0.00571360 + 0.999984i \(0.498181\pi\)
\(132\) −22.6753 + 24.1287i −1.97363 + 2.10013i
\(133\) 9.18614 15.9109i 0.796539 1.37965i
\(134\) 24.3030 + 14.0313i 2.09946 + 1.21212i
\(135\) −4.55842 12.2993i −0.392326 1.05855i
\(136\) 8.44158 4.87375i 0.723859 0.417920i
\(137\) 8.18614 14.1788i 0.699389 1.21138i −0.269289 0.963059i \(-0.586789\pi\)
0.968678 0.248318i \(-0.0798779\pi\)
\(138\) 0 0
\(139\) 10.3923i 0.881464i 0.897639 + 0.440732i \(0.145281\pi\)
−0.897639 + 0.440732i \(0.854719\pi\)
\(140\) 26.1831i 2.21288i
\(141\) −2.62772 + 11.1846i −0.221294 + 0.941913i
\(142\) −2.81386 + 4.87375i −0.236134 + 0.408996i
\(143\) 6.55842 3.78651i 0.548443 0.316644i
\(144\) 17.1168 + 8.51278i 1.42640 + 0.709398i
\(145\) 13.1168 + 7.57301i 1.08929 + 0.628905i
\(146\) −8.18614 + 14.1788i −0.677490 + 1.17345i
\(147\) 1.62772 1.73205i 0.134252 0.142857i
\(148\) −6.55842 + 3.78651i −0.539099 + 0.311249i
\(149\) −0.813859 + 0.469882i −0.0666740 + 0.0384942i −0.532966 0.846136i \(-0.678923\pi\)
0.466292 + 0.884631i \(0.345589\pi\)
\(150\) −5.74456 + 1.73205i −0.469042 + 0.141421i
\(151\) 23.1615i 1.88485i −0.334412 0.942427i \(-0.608538\pi\)
0.334412 0.942427i \(-0.391462\pi\)
\(152\) −40.1644 + 23.1889i −3.25776 + 1.88087i
\(153\) 0.302985 + 4.87375i 0.0244949 + 0.394019i
\(154\) 26.1831i 2.10990i
\(155\) 10.9307 8.83518i 0.877975 0.709659i
\(156\) −9.55842 8.98266i −0.765286 0.719188i
\(157\) 6.62772 0.528950 0.264475 0.964393i \(-0.414801\pi\)
0.264475 + 0.964393i \(0.414801\pi\)
\(158\) −0.813859 1.40965i −0.0647472 0.112145i
\(159\) 5.18614 5.51856i 0.411288 0.437650i
\(160\) 5.18614 8.98266i 0.410000 0.710142i
\(161\) 0 0
\(162\) −18.1168 + 13.7089i −1.42339 + 1.07708i
\(163\) 0.627719 0.0491667 0.0245834 0.999698i \(-0.492174\pi\)
0.0245834 + 0.999698i \(0.492174\pi\)
\(164\) 9.55842 + 5.51856i 0.746387 + 0.430927i
\(165\) −18.3030 + 5.51856i −1.42489 + 0.429619i
\(166\) −16.6753 9.62747i −1.29425 0.747237i
\(167\) −8.18614 14.1788i −0.633463 1.09719i −0.986839 0.161708i \(-0.948300\pi\)
0.353376 0.935481i \(-0.385034\pi\)
\(168\) 23.5584 7.10313i 1.81757 0.548018i
\(169\) −5.00000 8.66025i −0.384615 0.666173i
\(170\) 10.3723 0.795518
\(171\) −1.44158 23.1889i −0.110240 1.77330i
\(172\) 32.7921 18.9325i 2.50037 1.44359i
\(173\) −12.3030 7.10313i −0.935379 0.540041i −0.0468700 0.998901i \(-0.514925\pi\)
−0.888509 + 0.458860i \(0.848258\pi\)
\(174\) 6.00000 25.5383i 0.454859 1.93606i
\(175\) −1.62772 + 2.81929i −0.123044 + 0.213118i
\(176\) 13.9307 24.1287i 1.05007 1.81877i
\(177\) −3.69702 + 1.11469i −0.277885 + 0.0837854i
\(178\) 15.1460i 1.13524i
\(179\) 3.81386 + 6.60580i 0.285061 + 0.493741i 0.972624 0.232384i \(-0.0746527\pi\)
−0.687563 + 0.726125i \(0.741319\pi\)
\(180\) 18.3030 + 27.5928i 1.36422 + 2.05664i
\(181\) 5.61684 + 3.24289i 0.417497 + 0.241042i 0.694006 0.719969i \(-0.255844\pi\)
−0.276509 + 0.961011i \(0.589178\pi\)
\(182\) −10.3723 −0.768845
\(183\) 0 0
\(184\) 0 0
\(185\) −4.37228 −0.321457
\(186\) −20.1168 13.7089i −1.47504 1.00519i
\(187\) 7.11684 0.520435
\(188\) 29.0024i 2.11522i
\(189\) −2.06930 + 12.1518i −0.150519 + 0.883914i
\(190\) −49.3505 −3.58026
\(191\) 15.8139 + 9.13014i 1.14425 + 0.660633i 0.947480 0.319816i \(-0.103621\pi\)
0.196771 + 0.980449i \(0.436954\pi\)
\(192\) 4.00000 + 0.939764i 0.288675 + 0.0678216i
\(193\) −0.872281 1.51084i −0.0627882 0.108752i 0.832923 0.553390i \(-0.186666\pi\)
−0.895711 + 0.444637i \(0.853333\pi\)
\(194\) 13.5615i 0.973656i
\(195\) −2.18614 7.25061i −0.156553 0.519227i
\(196\) −3.00000 + 5.19615i −0.214286 + 0.371154i
\(197\) 12.3030 21.3094i 0.876551 1.51823i 0.0214504 0.999770i \(-0.493172\pi\)
0.855101 0.518462i \(-0.173495\pi\)
\(198\) 18.3030 + 27.5928i 1.30074 + 1.96093i
\(199\) −5.44158 3.14170i −0.385743 0.222709i 0.294571 0.955630i \(-0.404823\pi\)
−0.680314 + 0.732921i \(0.738157\pi\)
\(200\) 7.11684 4.10891i 0.503237 0.290544i
\(201\) 13.1861 14.0313i 0.930079 0.989694i
\(202\) −13.4891 −0.949092
\(203\) −7.11684 12.3267i −0.499505 0.865167i
\(204\) −3.55842 11.8020i −0.249139 0.826302i
\(205\) 3.18614 + 5.51856i 0.222530 + 0.385433i
\(206\) −30.0475 17.3480i −2.09351 1.20869i
\(207\) 0 0
\(208\) 9.55842 + 5.51856i 0.662757 + 0.382643i
\(209\) −33.8614 −2.34224
\(210\) 25.4891 + 5.98844i 1.75892 + 0.413242i
\(211\) 12.2446 + 21.2082i 0.842950 + 1.46003i 0.887389 + 0.461021i \(0.152517\pi\)
−0.0444388 + 0.999012i \(0.514150\pi\)
\(212\) −9.55842 + 16.5557i −0.656475 + 1.13705i
\(213\) 2.81386 + 2.64436i 0.192802 + 0.181189i
\(214\) 3.18614 + 5.51856i 0.217800 + 0.377241i
\(215\) 21.8614 1.49094
\(216\) 19.8614 23.9538i 1.35140 1.62985i
\(217\) −13.0475 + 2.05446i −0.885725 + 0.139466i
\(218\) 16.7306i 1.13314i
\(219\) 8.18614 + 7.69304i 0.553168 + 0.519847i
\(220\) 41.7921 24.1287i 2.81762 1.62676i
\(221\) 2.81929i 0.189646i
\(222\) 2.18614 + 7.25061i 0.146724 + 0.486629i
\(223\) −7.50000 + 4.33013i −0.502237 + 0.289967i −0.729637 0.683835i \(-0.760311\pi\)
0.227400 + 0.973801i \(0.426978\pi\)
\(224\) −8.44158 + 4.87375i −0.564027 + 0.325641i
\(225\) 0.255437 + 4.10891i 0.0170292 + 0.273927i
\(226\) −2.81386 + 4.87375i −0.187175 + 0.324197i
\(227\) −12.3030 7.10313i −0.816578 0.471451i 0.0326571 0.999467i \(-0.489603\pi\)
−0.849235 + 0.528015i \(0.822936\pi\)
\(228\) 16.9307 + 56.1528i 1.12126 + 3.71881i
\(229\) −2.61684 + 1.51084i −0.172926 + 0.0998388i −0.583965 0.811779i \(-0.698499\pi\)
0.411039 + 0.911618i \(0.365166\pi\)
\(230\) 0 0
\(231\) 17.4891 + 4.10891i 1.15070 + 0.270347i
\(232\) 35.9306i 2.35896i
\(233\) 10.0974i 0.661499i 0.943719 + 0.330750i \(0.107302\pi\)
−0.943719 + 0.330750i \(0.892698\pi\)
\(234\) −10.9307 + 7.25061i −0.714562 + 0.473987i
\(235\) 8.37228 14.5012i 0.546147 0.945955i
\(236\) 8.44158 4.87375i 0.549500 0.317254i
\(237\) −1.06930 + 0.322405i −0.0694583 + 0.0209425i
\(238\) −8.44158 4.87375i −0.547186 0.315918i
\(239\) −7.93070 + 13.7364i −0.512995 + 0.888533i 0.486892 + 0.873462i \(0.338131\pi\)
−0.999886 + 0.0150704i \(0.995203\pi\)
\(240\) −20.3030 19.0800i −1.31055 1.23161i
\(241\) 23.6168 13.6352i 1.52129 0.878320i 0.521611 0.853184i \(-0.325331\pi\)
0.999684 0.0251362i \(-0.00800195\pi\)
\(242\) 17.7446 10.2448i 1.14066 0.658562i
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 0 0
\(245\) −3.00000 + 1.73205i −0.191663 + 0.110657i
\(246\) 7.55842 8.04290i 0.481907 0.512796i
\(247\) 13.4140i 0.853511i
\(248\) 31.1168 + 11.9769i 1.97592 + 0.760533i
\(249\) −9.04755 + 9.62747i −0.573365 + 0.610116i
\(250\) −23.1168 −1.46204
\(251\) −8.18614 14.1788i −0.516705 0.894959i −0.999812 0.0193975i \(-0.993825\pi\)
0.483107 0.875561i \(-0.339508\pi\)
\(252\) −1.93070 31.0569i −0.121623 1.95640i
\(253\) 0 0
\(254\) −16.9307 29.3248i −1.06233 1.84000i
\(255\) 1.62772 6.92820i 0.101932 0.433861i
\(256\) −31.1168 −1.94480
\(257\) 24.0475 + 13.8839i 1.50004 + 0.866051i 1.00000 5.17161e-5i \(1.64617e-5\pi\)
0.500045 + 0.866000i \(0.333317\pi\)
\(258\) −10.9307 36.2530i −0.680516 2.25702i
\(259\) 3.55842 + 2.05446i 0.221110 + 0.127658i
\(260\) 9.55842 + 16.5557i 0.592788 + 1.02674i
\(261\) −16.1168 8.01544i −0.997608 0.496144i
\(262\) −14.3030 24.7735i −0.883641 1.53051i
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −33.0475 31.0569i −2.03394 1.91142i
\(265\) −9.55842 + 5.51856i −0.587169 + 0.339002i
\(266\) 40.1644 + 23.1889i 2.46264 + 1.42180i
\(267\) 10.1168 + 2.37686i 0.619141 + 0.145462i
\(268\) −24.3030 + 42.0940i −1.48454 + 2.57130i
\(269\) −7.93070 + 13.7364i −0.483544 + 0.837522i −0.999821 0.0188992i \(-0.993984\pi\)
0.516278 + 0.856421i \(0.327317\pi\)
\(270\) 31.0475 11.5070i 1.88949 0.700294i
\(271\) 2.37686i 0.144384i −0.997391 0.0721920i \(-0.977001\pi\)
0.997391 0.0721920i \(-0.0229994\pi\)
\(272\) 5.18614 + 8.98266i 0.314456 + 0.544654i
\(273\) −1.62772 + 6.92820i −0.0985140 + 0.419314i
\(274\) 35.7921 + 20.6646i 2.16228 + 1.24839i
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) 8.01544i 0.481601i −0.970575 0.240801i \(-0.922590\pi\)
0.970575 0.240801i \(-0.0774100\pi\)
\(278\) −26.2337 −1.57339
\(279\) −12.3139 + 11.2858i −0.737211 + 0.675662i
\(280\) −35.8614 −2.14313
\(281\) 14.8511i 0.885941i 0.896536 + 0.442970i \(0.146075\pi\)
−0.896536 + 0.442970i \(0.853925\pi\)
\(282\) −28.2337 6.63325i −1.68129 0.395004i
\(283\) 26.3505 1.56638 0.783188 0.621785i \(-0.213592\pi\)
0.783188 + 0.621785i \(0.213592\pi\)
\(284\) −8.44158 4.87375i −0.500915 0.289204i
\(285\) −7.74456 + 32.9639i −0.458748 + 1.95261i
\(286\) 9.55842 + 16.5557i 0.565201 + 0.978957i
\(287\) 5.98844i 0.353486i
\(288\) −5.48913 + 11.0371i −0.323450 + 0.650368i
\(289\) 7.17527 12.4279i 0.422074 0.731054i
\(290\) −19.1168 + 33.1113i −1.12258 + 1.94437i
\(291\) −9.05842 2.12819i −0.531014 0.124757i
\(292\) −24.5584 14.1788i −1.43717 0.829752i
\(293\) 17.1861 9.92242i 1.00403 0.579674i 0.0945883 0.995516i \(-0.469847\pi\)
0.909437 + 0.415842i \(0.136513\pi\)
\(294\) 4.37228 + 4.10891i 0.254997 + 0.239637i
\(295\) 5.62772 0.327658
\(296\) −5.18614 8.98266i −0.301438 0.522106i
\(297\) 21.3030 7.89542i 1.23612 0.458139i
\(298\) −1.18614 2.05446i −0.0687113 0.119011i
\(299\) 0 0
\(300\) −3.00000 9.94987i −0.173205 0.574456i
\(301\) −17.7921 10.2723i −1.02552 0.592084i
\(302\) 58.4674 3.36442
\(303\) −2.11684 + 9.01011i −0.121610 + 0.517617i
\(304\) −24.6753 42.7388i −1.41522 2.45124i
\(305\) 0 0
\(306\) −12.3030 + 0.764836i −0.703315 + 0.0437227i
\(307\) 2.12772 + 3.68532i 0.121435 + 0.210332i 0.920334 0.391134i \(-0.127917\pi\)
−0.798899 + 0.601466i \(0.794584\pi\)
\(308\) −45.3505 −2.58409
\(309\) −16.3030 + 17.3480i −0.927444 + 0.986891i
\(310\) 22.3030 + 27.5928i 1.26672 + 1.56717i
\(311\) 30.5870i 1.73443i −0.497934 0.867215i \(-0.665908\pi\)
0.497934 0.867215i \(-0.334092\pi\)
\(312\) 12.3030 13.0916i 0.696519 0.741164i
\(313\) −2.61684 + 1.51084i −0.147913 + 0.0853975i −0.572130 0.820163i \(-0.693883\pi\)
0.424217 + 0.905561i \(0.360549\pi\)
\(314\) 16.7306i 0.944162i
\(315\) 8.00000 16.0858i 0.450749 0.906332i
\(316\) 2.44158 1.40965i 0.137349 0.0792988i
\(317\) 7.06930 4.08146i 0.397051 0.229238i −0.288160 0.957582i \(-0.593043\pi\)
0.685211 + 0.728345i \(0.259710\pi\)
\(318\) 13.9307 + 13.0916i 0.781195 + 0.734139i
\(319\) −13.1168 + 22.7190i −0.734402 + 1.27202i
\(320\) −5.18614 2.99422i −0.289914 0.167382i
\(321\) 4.18614 1.26217i 0.233648 0.0704474i
\(322\) 0 0
\(323\) 6.30298 10.9171i 0.350707 0.607443i
\(324\) −23.7446 31.3793i −1.31914 1.74329i
\(325\) 2.37686i 0.131845i
\(326\) 1.58457i 0.0877614i
\(327\) 11.1753 + 2.62553i 0.617994 + 0.145192i
\(328\) −7.55842 + 13.0916i −0.417344 + 0.722861i
\(329\) −13.6277 + 7.86797i −0.751320 + 0.433775i
\(330\) −13.9307 46.2029i −0.766860 2.54339i
\(331\) 1.50000 + 0.866025i 0.0824475 + 0.0476011i 0.540657 0.841243i \(-0.318176\pi\)
−0.458209 + 0.888844i \(0.651509\pi\)
\(332\) 16.6753 28.8824i 0.915174 1.58513i
\(333\) 5.18614 0.322405i 0.284199 0.0176677i
\(334\) 35.7921 20.6646i 1.95846 1.13072i
\(335\) −24.3030 + 14.0313i −1.32781 + 0.766614i
\(336\) 7.55842 + 25.0684i 0.412346 + 1.36760i
\(337\) 9.50744i 0.517903i 0.965890 + 0.258952i \(0.0833771\pi\)
−0.965890 + 0.258952i \(0.916623\pi\)
\(338\) 21.8614 12.6217i 1.18910 0.686529i
\(339\) 2.81386 + 2.64436i 0.152828 + 0.143622i
\(340\) 17.9653i 0.974306i
\(341\) 15.3030 + 18.9325i 0.828703 + 1.02525i
\(342\) 58.5367 3.63903i 3.16530 0.196776i
\(343\) 19.8614 1.07242
\(344\) 25.9307 + 44.9133i 1.39809 + 2.42156i
\(345\) 0 0
\(346\) 17.9307 31.0569i 0.963961 1.66963i
\(347\) −2.18614 3.78651i −0.117358 0.203270i 0.801362 0.598180i \(-0.204109\pi\)
−0.918720 + 0.394910i \(0.870776\pi\)
\(348\) 44.2337 + 10.3923i 2.37117 + 0.557086i
\(349\) 12.1168 0.648600 0.324300 0.945954i \(-0.394871\pi\)
0.324300 + 0.945954i \(0.394871\pi\)
\(350\) −7.11684 4.10891i −0.380411 0.219631i
\(351\) 3.12772 + 8.43904i 0.166945 + 0.450443i
\(352\) 15.5584 + 8.98266i 0.829267 + 0.478777i
\(353\) 6.81386 + 11.8020i 0.362665 + 0.628154i 0.988399 0.151883i \(-0.0485335\pi\)
−0.625733 + 0.780037i \(0.715200\pi\)
\(354\) −2.81386 9.33252i −0.149555 0.496018i
\(355\) −2.81386 4.87375i −0.149344 0.258672i
\(356\) −26.2337 −1.39038
\(357\) −4.58017 + 4.87375i −0.242408 + 0.257946i
\(358\) −16.6753 + 9.62747i −0.881315 + 0.508828i
\(359\) 15.8139 + 9.13014i 0.834624 + 0.481870i 0.855433 0.517913i \(-0.173291\pi\)
−0.0208095 + 0.999783i \(0.506624\pi\)
\(360\) −37.7921 + 25.0684i −1.99182 + 1.32122i
\(361\) −20.4891 + 35.4882i −1.07838 + 1.86780i
\(362\) −8.18614 + 14.1788i −0.430254 + 0.745222i
\(363\) −4.05842 13.4603i −0.213012 0.706481i
\(364\) 17.9653i 0.941639i
\(365\) −8.18614 14.1788i −0.428482 0.742153i
\(366\) 0 0
\(367\) −28.8505 16.6569i −1.50599 0.869481i −0.999976 0.00695334i \(-0.997787\pi\)
−0.506010 0.862528i \(-0.668880\pi\)
\(368\) 0 0
\(369\) −4.18614 6.31084i −0.217922 0.328529i
\(370\) 11.0371i 0.573792i
\(371\) 10.3723 0.538502
\(372\) 23.7446 34.8434i 1.23110 1.80655i
\(373\) 14.8614 0.769494 0.384747 0.923022i \(-0.374289\pi\)
0.384747 + 0.923022i \(0.374289\pi\)
\(374\) 17.9653i 0.928964i
\(375\) −3.62772 + 15.4410i −0.187335 + 0.797369i
\(376\) 39.7228 2.04855
\(377\) −9.00000 5.19615i −0.463524 0.267615i
\(378\) −30.6753 5.22360i −1.57777 0.268673i
\(379\) −12.6168 21.8530i −0.648084 1.12251i −0.983580 0.180472i \(-0.942237\pi\)
0.335496 0.942042i \(-0.391096\pi\)
\(380\) 85.4776i 4.38491i
\(381\) −22.2446 + 6.70699i −1.13962 + 0.343609i
\(382\) −23.0475 + 39.9195i −1.17922 + 2.04246i
\(383\) 2.18614 3.78651i 0.111707 0.193481i −0.804752 0.593611i \(-0.797702\pi\)
0.916458 + 0.400130i \(0.131035\pi\)
\(384\) −5.62772 + 23.9538i −0.287188 + 1.22239i
\(385\) −22.6753 13.0916i −1.15564 0.667208i
\(386\) 3.81386 2.20193i 0.194120 0.112075i
\(387\) −25.9307 + 1.61203i −1.31813 + 0.0819439i
\(388\) 23.4891 1.19248
\(389\) −11.1861 19.3750i −0.567160 0.982350i −0.996845 0.0793710i \(-0.974709\pi\)
0.429685 0.902979i \(-0.358624\pi\)
\(390\) 18.3030 5.51856i 0.926808 0.279443i
\(391\) 0 0
\(392\) −7.11684 4.10891i −0.359455 0.207531i
\(393\) −18.7921 + 5.66603i −0.947937 + 0.285814i
\(394\) 53.7921 + 31.0569i 2.71001 + 1.56462i
\(395\) 1.62772 0.0818994
\(396\) −47.7921 + 31.7017i −2.40164 + 1.59307i
\(397\) −7.81386 13.5340i −0.392166 0.679252i 0.600569 0.799573i \(-0.294941\pi\)
−0.992735 + 0.120321i \(0.961608\pi\)
\(398\) 7.93070 13.7364i 0.397530 0.688543i
\(399\) 21.7921 23.1889i 1.09097 1.16090i
\(400\) 4.37228 + 7.57301i 0.218614 + 0.378651i
\(401\) −14.2337 −0.710796 −0.355398 0.934715i \(-0.615655\pi\)
−0.355398 + 0.934715i \(0.615655\pi\)
\(402\) 35.4198 + 33.2863i 1.76658 + 1.66017i
\(403\) −7.50000 + 6.06218i −0.373602 + 0.301979i
\(404\) 23.3639i 1.16240i
\(405\) −2.81386 22.5441i −0.139822 1.12023i
\(406\) 31.1168 17.9653i 1.54430 0.891604i
\(407\) 7.57301i 0.375380i
\(408\) 16.1644 4.87375i 0.800257 0.241286i
\(409\) −20.6168 + 11.9031i −1.01944 + 0.588572i −0.913941 0.405847i \(-0.866976\pi\)
−0.105496 + 0.994420i \(0.533643\pi\)
\(410\) −13.9307 + 8.04290i −0.687988 + 0.397210i
\(411\) 19.4198 20.6646i 0.957910 1.01931i
\(412\) 30.0475 52.0439i 1.48034 2.56402i
\(413\) −4.58017 2.64436i −0.225376 0.130121i
\(414\) 0 0
\(415\) 16.6753 9.62747i 0.818557 0.472594i
\(416\) −3.55842 + 6.16337i −0.174466 + 0.302184i
\(417\) −4.11684 + 17.5229i −0.201603 + 0.858100i
\(418\) 85.4776i 4.18085i
\(419\) 35.3407i 1.72651i −0.504770 0.863254i \(-0.668423\pi\)
0.504770 0.863254i \(-0.331577\pi\)
\(420\) −10.3723 + 44.1485i −0.506116 + 2.15422i
\(421\) 10.1861 17.6429i 0.496442 0.859863i −0.503549 0.863966i \(-0.667973\pi\)
0.999992 + 0.00410343i \(0.00130616\pi\)
\(422\) −53.5367 + 30.9094i −2.60612 + 1.50465i
\(423\) −8.86141 + 17.8178i −0.430856 + 0.866333i
\(424\) −22.6753 13.0916i −1.10121 0.635783i
\(425\) −1.11684 + 1.93443i −0.0541749 + 0.0938337i
\(426\) −6.67527 + 7.10313i −0.323418 + 0.344148i
\(427\) 0 0
\(428\) −9.55842 + 5.51856i −0.462024 + 0.266750i
\(429\) 12.5584 3.78651i 0.606326 0.182814i
\(430\) 55.1856i 2.66128i
\(431\) −13.9307 + 8.04290i −0.671018 + 0.387413i −0.796462 0.604688i \(-0.793298\pi\)
0.125444 + 0.992101i \(0.459964\pi\)
\(432\) 25.4891 + 21.1345i 1.22635 + 1.01683i
\(433\) 28.8001i 1.38404i 0.721877 + 0.692021i \(0.243280\pi\)
−0.721877 + 0.692021i \(0.756720\pi\)
\(434\) −5.18614 32.9364i −0.248943 1.58100i
\(435\) 19.1168 + 17.9653i 0.916583 + 0.861371i
\(436\) −28.9783 −1.38781
\(437\) 0 0
\(438\) −19.4198 + 20.6646i −0.927915 + 0.987392i
\(439\) −16.9891 + 29.4260i −0.810847 + 1.40443i 0.101425 + 0.994843i \(0.467660\pi\)
−0.912272 + 0.409585i \(0.865674\pi\)
\(440\) 33.0475 + 57.2400i 1.57548 + 2.72881i
\(441\) 3.43070 2.27567i 0.163367 0.108365i
\(442\) −7.11684 −0.338514
\(443\) 19.9307 + 11.5070i 0.946936 + 0.546714i 0.892128 0.451783i \(-0.149212\pi\)
0.0548084 + 0.998497i \(0.482545\pi\)
\(444\) −12.5584 + 3.78651i −0.595996 + 0.179700i
\(445\) −13.1168 7.57301i −0.621798 0.358995i
\(446\) −10.9307 18.9325i −0.517584 0.896481i
\(447\) −1.55842 + 0.469882i −0.0737108 + 0.0222247i
\(448\) 2.81386 + 4.87375i 0.132942 + 0.230263i
\(449\) 38.2337 1.80436 0.902180 0.431361i \(-0.141966\pi\)
0.902180 + 0.431361i \(0.141966\pi\)
\(450\) −10.3723 + 0.644810i −0.488954 + 0.0303966i
\(451\) −9.55842 + 5.51856i −0.450089 + 0.259859i
\(452\) −8.44158 4.87375i −0.397058 0.229242i
\(453\) 9.17527 39.0535i 0.431092 1.83489i
\(454\) 17.9307 31.0569i 0.841530 1.45757i
\(455\) 5.18614 8.98266i 0.243130 0.421114i
\(456\) −76.9090 + 23.1889i −3.60159 + 1.08592i
\(457\) 12.7692i 0.597316i 0.954360 + 0.298658i \(0.0965390\pi\)
−0.954360 + 0.298658i \(0.903461\pi\)
\(458\) −3.81386 6.60580i −0.178210 0.308669i
\(459\) −1.41983 + 8.33785i −0.0662719 + 0.389177i
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) −10.3723 + 44.1485i −0.482562 + 2.05397i
\(463\) 18.4077i 0.855481i −0.903902 0.427740i \(-0.859310\pi\)
0.903902 0.427740i \(-0.140690\pi\)
\(464\) −38.2337 −1.77495
\(465\) 21.9307 10.5672i 1.01701 0.490044i
\(466\) −25.4891 −1.18076
\(467\) 15.7359i 0.728172i 0.931365 + 0.364086i \(0.118619\pi\)
−0.931365 + 0.364086i \(0.881381\pi\)
\(468\) −12.5584 18.9325i −0.580513 0.875157i
\(469\) 26.3723 1.21776
\(470\) 36.6060 + 21.1345i 1.68851 + 0.974860i
\(471\) 11.1753 + 2.62553i 0.514929 + 0.120978i
\(472\) 6.67527 + 11.5619i 0.307254 + 0.532180i
\(473\) 37.8651i 1.74104i
\(474\) −0.813859 2.69927i −0.0373818 0.123981i
\(475\) 5.31386 9.20387i 0.243817 0.422303i
\(476\) 8.44158 14.6212i 0.386919 0.670164i
\(477\) 10.9307 7.25061i 0.500483 0.331983i
\(478\) −34.6753 20.0198i −1.58601 0.915683i
\(479\) −19.9307 + 11.5070i −0.910657 + 0.525768i −0.880643 0.473781i \(-0.842889\pi\)
−0.0300146 + 0.999549i \(0.509555\pi\)
\(480\) 12.3030 13.0916i 0.561552 0.597546i
\(481\) 3.00000 0.136788
\(482\) 34.4198 + 59.6169i 1.56778 + 2.71548i
\(483\) 0 0
\(484\) 17.7446 + 30.7345i 0.806571 + 1.39702i
\(485\) 11.7446 + 6.78073i 0.533293 + 0.307897i
\(486\) −35.9783 + 15.9383i −1.63201 + 0.722977i
\(487\) 23.6168 + 13.6352i 1.07018 + 0.617869i 0.928231 0.372004i \(-0.121329\pi\)
0.141950 + 0.989874i \(0.454663\pi\)
\(488\) 0 0
\(489\) 1.05842 + 0.248667i 0.0478635 + 0.0112451i
\(490\) −4.37228 7.57301i −0.197520 0.342114i
\(491\) −19.9307 + 34.5210i −0.899460 + 1.55791i −0.0712743 + 0.997457i \(0.522707\pi\)
−0.828186 + 0.560454i \(0.810627\pi\)
\(492\) 13.9307 + 13.0916i 0.628045 + 0.590214i
\(493\) −4.88316 8.45787i −0.219926 0.380924i
\(494\) 33.8614 1.52350
\(495\) −33.0475 + 2.05446i −1.48538 + 0.0923409i
\(496\) −12.7446 + 33.1113i −0.572248 + 1.48674i
\(497\) 5.28873i 0.237232i
\(498\) −24.3030 22.8391i −1.08904 1.02344i
\(499\) −0.558422 + 0.322405i −0.0249984 + 0.0144328i −0.512447 0.858719i \(-0.671261\pi\)
0.487449 + 0.873152i \(0.337928\pi\)
\(500\) 40.0395i 1.79062i
\(501\) −8.18614 27.1504i −0.365730 1.21299i
\(502\) 35.7921 20.6646i 1.59748 0.922306i
\(503\) 16.0693 9.27761i 0.716495 0.413668i −0.0969666 0.995288i \(-0.530914\pi\)
0.813461 + 0.581619i \(0.197581\pi\)
\(504\) 42.5367 2.64436i 1.89473 0.117789i
\(505\) 6.74456 11.6819i 0.300129 0.519839i
\(506\) 0 0
\(507\) −5.00000 16.5831i −0.222058 0.736482i
\(508\) 50.7921 29.3248i 2.25354 1.30108i
\(509\) −7.93070 + 13.7364i −0.351522 + 0.608854i −0.986516 0.163663i \(-0.947669\pi\)
0.634994 + 0.772517i \(0.281003\pi\)
\(510\) 17.4891 + 4.10891i 0.774431 + 0.181946i
\(511\) 15.3861i 0.680640i
\(512\) 50.1369i 2.21576i
\(513\) 6.75544 39.6709i 0.298260 1.75151i
\(514\) −35.0475 + 60.7041i −1.54588 + 2.67754i
\(515\) 30.0475 17.3480i 1.32405 0.764442i
\(516\) 62.7921 18.9325i 2.76427 0.833458i
\(517\) 25.1168 + 14.5012i 1.10464 + 0.637763i
\(518\) −5.18614 + 8.98266i −0.227866 + 0.394675i
\(519\) −17.9307 16.8506i −0.787071 0.739660i
\(520\) −22.6753 + 13.0916i −0.994376 + 0.574103i
\(521\) −4.93070 + 2.84674i −0.216018 + 0.124718i −0.604105 0.796905i \(-0.706469\pi\)
0.388087 + 0.921623i \(0.373136\pi\)
\(522\) 20.2337 40.6844i 0.885604 1.78071i
\(523\) 19.8997i 0.870155i 0.900393 + 0.435078i \(0.143279\pi\)
−0.900393 + 0.435078i \(0.856721\pi\)
\(524\) 42.9090 24.7735i 1.87449 1.08224i
\(525\) −3.86141 + 4.10891i −0.168526 + 0.179328i
\(526\) 60.5841i 2.64159i
\(527\) −8.95245 + 1.40965i −0.389975 + 0.0614051i
\(528\) 33.0475 35.1658i 1.43821 1.53040i
\(529\) −23.0000 −1.00000
\(530\) −13.9307 24.1287i −0.605111 1.04808i
\(531\) −6.67527 + 0.414979i −0.289682 + 0.0180086i
\(532\) −40.1644 + 69.5668i −1.74135 + 3.01610i
\(533\) −2.18614 3.78651i −0.0946923 0.164012i
\(534\) −6.00000 + 25.5383i −0.259645 + 1.10515i
\(535\) −6.37228 −0.275498
\(536\) −57.6535 33.2863i −2.49025 1.43775i
\(537\) 3.81386 + 12.6491i 0.164580 + 0.545851i
\(538\) −34.6753 20.0198i −1.49496 0.863114i
\(539\) −3.00000 5.19615i −0.129219 0.223814i
\(540\) 19.9307 + 53.7759i 0.857681 + 2.31415i
\(541\) −4.98913 8.64142i −0.214499 0.371524i 0.738618 0.674124i \(-0.235479\pi\)
−0.953118 + 0.302600i \(0.902145\pi\)
\(542\) 6.00000 0.257722
\(543\) 8.18614 + 7.69304i 0.351301 + 0.330140i
\(544\) −5.79211 + 3.34408i −0.248335 + 0.143376i
\(545\) −14.4891 8.36530i −0.620646 0.358330i
\(546\) −17.4891 4.10891i −0.748465 0.175845i
\(547\) 7.36141 12.7503i 0.314751 0.545165i −0.664634 0.747170i \(-0.731412\pi\)
0.979385 + 0.202005i \(0.0647456\pi\)
\(548\) −35.7921 + 61.9938i −1.52896 + 2.64824i
\(549\) 0 0
\(550\) 15.1460i 0.645829i
\(551\) 23.2337 + 40.2419i 0.989788 + 1.71436i
\(552\) 0 0
\(553\) −1.32473 0.764836i −0.0563334 0.0325241i
\(554\) 20.2337 0.859647
\(555\) −7.37228 1.73205i −0.312936 0.0735215i
\(556\) 45.4381i 1.92700i
\(557\) 14.2337 0.603101 0.301550 0.953450i \(-0.402496\pi\)
0.301550 + 0.953450i \(0.402496\pi\)
\(558\) −28.4891 31.0843i −1.20604 1.31591i
\(559\) −15.0000 −0.634432
\(560\) 38.1600i 1.61256i
\(561\) 12.0000 + 2.81929i 0.506640 + 0.119031i
\(562\) −37.4891 −1.58138
\(563\) −20.1861 11.6545i −0.850744 0.491178i 0.0101576 0.999948i \(-0.496767\pi\)
−0.860902 + 0.508771i \(0.830100\pi\)
\(564\) 11.4891 48.9022i 0.483779 2.05915i
\(565\) −2.81386 4.87375i −0.118380 0.205040i
\(566\) 66.5176i 2.79595i
\(567\) −8.30298 + 19.6699i −0.348693 + 0.826059i
\(568\) 6.67527 11.5619i 0.280088 0.485127i
\(569\) 6.30298 10.9171i 0.264235 0.457668i −0.703128 0.711063i \(-0.748214\pi\)
0.967363 + 0.253395i \(0.0815473\pi\)
\(570\) −83.2119 19.5499i −3.48536 0.818855i
\(571\) 23.6168 + 13.6352i 0.988334 + 0.570615i 0.904776 0.425888i \(-0.140038\pi\)
0.0835582 + 0.996503i \(0.473372\pi\)
\(572\) −28.6753 + 16.5557i −1.19897 + 0.692227i
\(573\) 23.0475 + 21.6593i 0.962825 + 0.904828i
\(574\) 15.1168 0.630965
\(575\) 0 0
\(576\) 6.37228 + 3.16915i 0.265512 + 0.132048i
\(577\) 7.44158 + 12.8892i 0.309797 + 0.536584i 0.978318 0.207109i \(-0.0664056\pi\)
−0.668521 + 0.743693i \(0.733072\pi\)
\(578\) 31.3723 + 18.1128i 1.30491 + 0.753393i
\(579\) −0.872281 2.89303i −0.0362508 0.120230i
\(580\) −57.3505 33.1113i −2.38135 1.37487i
\(581\) −18.0951 −0.750711
\(582\) 5.37228 22.8665i 0.222688 0.947848i
\(583\) −9.55842 16.5557i −0.395869 0.685666i
\(584\) 19.4198 33.6361i 0.803598 1.39187i
\(585\) −0.813859 13.0916i −0.0336489 0.541270i
\(586\) 25.0475 + 43.3836i 1.03470 + 1.79216i
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −7.11684 + 7.57301i −0.293494 + 0.312306i
\(589\) 42.5951 6.70699i 1.75510 0.276357i
\(590\) 14.2063i 0.584863i
\(591\) 29.1861 31.0569i 1.20056 1.27751i
\(592\) 9.55842 5.51856i 0.392849 0.226811i
\(593\) 29.7021i 1.21972i −0.792509 0.609860i \(-0.791225\pi\)
0.792509 0.609860i \(-0.208775\pi\)
\(594\) 19.9307 + 53.7759i 0.817767 + 2.20645i
\(595\) 8.44158 4.87375i 0.346071 0.199804i
\(596\) 3.55842 2.05446i 0.145759 0.0841538i
\(597\) −7.93070 7.45299i −0.324582 0.305030i
\(598\) 0 0
\(599\) 15.8139 + 9.13014i 0.646137 + 0.373047i 0.786975 0.616985i \(-0.211646\pi\)
−0.140838 + 0.990033i \(0.544980\pi\)
\(600\) 13.6277 4.10891i 0.556349 0.167746i
\(601\) −1.32473 + 0.764836i −0.0540370 + 0.0311983i −0.526775 0.850005i \(-0.676599\pi\)
0.472738 + 0.881203i \(0.343266\pi\)
\(602\) 25.9307 44.9133i 1.05686 1.83053i
\(603\) 27.7921 18.4352i 1.13178 0.750739i
\(604\) 101.268i 4.12056i
\(605\) 20.4897i 0.833023i
\(606\) −22.7446 5.34363i −0.923935 0.217070i
\(607\) −5.50000 + 9.52628i −0.223238 + 0.386660i −0.955789 0.294052i \(-0.904996\pi\)
0.732551 + 0.680712i \(0.238329\pi\)
\(608\) 27.5584 15.9109i 1.11764 0.645271i
\(609\) −7.11684 23.6039i −0.288389 0.956478i
\(610\) 0 0
\(611\) −5.74456 + 9.94987i −0.232400 + 0.402529i
\(612\) −1.32473 21.3094i −0.0535492 0.861381i
\(613\) −12.3832 + 7.14942i −0.500151 + 0.288762i −0.728776 0.684752i \(-0.759910\pi\)
0.228625 + 0.973515i \(0.426577\pi\)
\(614\) −9.30298 + 5.37108i −0.375438 + 0.216759i
\(615\) 3.18614 + 10.5672i 0.128478 + 0.426112i
\(616\) 62.1138i 2.50264i
\(617\) 29.5367 17.0530i 1.18910 0.686528i 0.230999 0.972954i \(-0.425801\pi\)
0.958102 + 0.286426i \(0.0924672\pi\)
\(618\) −43.7921 41.1542i −1.76158 1.65547i
\(619\) 18.4077i 0.739870i −0.929058 0.369935i \(-0.879380\pi\)
0.929058 0.369935i \(-0.120620\pi\)
\(620\) −47.7921 + 38.6299i −1.91938 + 1.55141i
\(621\) 0 0
\(622\) 77.2119 3.09592
\(623\) 7.11684 + 12.3267i 0.285130 + 0.493860i
\(624\) 13.9307 + 13.0916i 0.557674 + 0.524082i
\(625\) 14.9891 25.9619i 0.599565 1.03848i
\(626\) −3.81386 6.60580i −0.152432 0.264021i
\(627\) −57.0951 13.4140i −2.28016 0.535703i
\(628\) −28.9783 −1.15636
\(629\) 2.44158 + 1.40965i 0.0973521 + 0.0562063i
\(630\) 40.6060 + 20.1947i 1.61778 + 0.804576i
\(631\) −5.44158 3.14170i −0.216626 0.125069i 0.387761 0.921760i \(-0.373249\pi\)
−0.604387 + 0.796691i \(0.706582\pi\)
\(632\) 1.93070 + 3.34408i 0.0767993 + 0.133020i
\(633\) 12.2446 + 40.6106i 0.486678 + 1.61413i
\(634\) 10.3030 + 17.8453i 0.409184 + 0.708727i
\(635\) 33.8614 1.34375
\(636\) −22.6753 + 24.1287i −0.899133 + 0.956765i
\(637\) 2.05842 1.18843i 0.0815576 0.0470873i
\(638\) −57.3505 33.1113i −2.27053 1.31089i
\(639\) 3.69702 + 5.57346i 0.146252 + 0.220483i
\(640\) 17.9307 31.0569i 0.708773 1.22763i
\(641\) 14.1861 24.5711i 0.560319 0.970501i −0.437149 0.899389i \(-0.644012\pi\)
0.997468 0.0711119i \(-0.0226547\pi\)
\(642\) 3.18614 + 10.5672i 0.125747 + 0.417055i
\(643\) 27.9152i 1.10087i 0.834879 + 0.550434i \(0.185538\pi\)
−0.834879 + 0.550434i \(0.814462\pi\)
\(644\) 0 0
\(645\) 36.8614 + 8.66025i 1.45142 + 0.340997i
\(646\) 27.5584 + 15.9109i 1.08427 + 0.626005i
\(647\) −32.2337 −1.26724 −0.633619 0.773646i \(-0.718431\pi\)
−0.633619 + 0.773646i \(0.718431\pi\)
\(648\) 42.9783 32.5214i 1.68835 1.27756i
\(649\) 9.74749i 0.382623i
\(650\) −6.00000 −0.235339
\(651\) −22.8139 1.70460i −0.894146 0.0668085i
\(652\) −2.74456 −0.107485
\(653\) 8.51278i 0.333131i −0.986030 0.166565i \(-0.946732\pi\)
0.986030 0.166565i \(-0.0532677\pi\)
\(654\) −6.62772 + 28.2101i −0.259164 + 1.10310i
\(655\) 28.6060 1.11773
\(656\) −13.9307 8.04290i −0.543903 0.314022i
\(657\) 10.7554 + 16.2144i 0.419610 + 0.632585i
\(658\) −19.8614 34.4010i −0.774278 1.34109i
\(659\) 0.294954i 0.0114898i −0.999983 0.00574488i \(-0.998171\pi\)
0.999983 0.00574488i \(-0.00182866\pi\)
\(660\) 80.0258 24.1287i 3.11500 0.939208i
\(661\) −16.9891 + 29.4260i −0.660800 + 1.14454i 0.319605 + 0.947551i \(0.396450\pi\)
−0.980406 + 0.196989i \(0.936884\pi\)
\(662\) −2.18614 + 3.78651i −0.0849668 + 0.147167i
\(663\) −1.11684 + 4.75372i −0.0433746 + 0.184619i
\(664\) 39.5584 + 22.8391i 1.53516 + 0.886328i
\(665\) −40.1644 + 23.1889i −1.55751 + 0.899228i
\(666\) 0.813859 + 13.0916i 0.0315364 + 0.507288i
\(667\) 0 0
\(668\) 35.7921 + 61.9938i 1.38484 + 2.39861i
\(669\) −14.3614 + 4.33013i −0.555244 + 0.167412i
\(670\) −35.4198 61.3489i −1.36839 2.37012i
\(671\) 0 0
\(672\) −16.1644 + 4.87375i −0.623555 + 0.188009i
\(673\) −35.7921 20.6646i −1.37968 0.796561i −0.387563 0.921843i \(-0.626683\pi\)
−0.992121 + 0.125282i \(0.960016\pi\)
\(674\) −24.0000 −0.924445
\(675\) −1.19702 + 7.02939i −0.0460731 + 0.270561i
\(676\) 21.8614 + 37.8651i 0.840823 + 1.45635i
\(677\) 16.4198 28.4400i 0.631065 1.09304i −0.356269 0.934383i \(-0.615951\pi\)
0.987334 0.158654i \(-0.0507153\pi\)
\(678\) −6.67527 + 7.10313i −0.256362 + 0.272794i
\(679\) −6.37228 11.0371i −0.244546 0.423566i
\(680\) −24.6060 −0.943596
\(681\) −17.9307 16.8506i −0.687106 0.645717i
\(682\) −47.7921 + 38.6299i −1.83005 + 1.47922i
\(683\) 35.3407i 1.35228i −0.736775 0.676138i \(-0.763652\pi\)
0.736775 0.676138i \(-0.236348\pi\)
\(684\) 6.30298 + 101.388i 0.241001 + 3.87669i
\(685\) −35.7921 + 20.6646i −1.36755 + 0.789553i
\(686\) 50.1369i 1.91424i
\(687\) −5.01087 + 1.51084i −0.191177 + 0.0576420i
\(688\) −47.7921 + 27.5928i −1.82206 + 1.05197i
\(689\) 6.55842 3.78651i 0.249856 0.144254i
\(690\) 0 0
\(691\) 0.0692967 0.120025i 0.00263617 0.00456598i −0.864704 0.502281i \(-0.832494\pi\)
0.867340 + 0.497715i \(0.165828\pi\)
\(692\) 53.7921 + 31.0569i 2.04487 + 1.18061i
\(693\) 27.8614 + 13.8564i 1.05837 + 0.526361i
\(694\) 9.55842 5.51856i 0.362833 0.209482i
\(695\) 13.1168 22.7190i 0.497550 0.861782i
\(696\) −14.2337 + 60.5841i −0.539527 + 2.29643i
\(697\) 4.10891i 0.155636i
\(698\) 30.5870i 1.15774i
\(699\) −4.00000 + 17.0256i −0.151294 + 0.643966i
\(700\) 7.11684 12.3267i 0.268991 0.465907i
\(701\) −15.0475 + 8.68771i −0.568338 + 0.328130i −0.756485 0.654011i \(-0.773085\pi\)
0.188147 + 0.982141i \(0.439752\pi\)
\(702\) −21.3030 + 7.89542i −0.804029 + 0.297993i
\(703\) −11.6168 6.70699i −0.438138 0.252959i
\(704\) 5.18614 8.98266i 0.195460 0.338547i
\(705\) 19.8614 21.1345i 0.748024 0.795970i
\(706\) −29.7921 + 17.2005i −1.12124 + 0.647349i
\(707\) −10.9783 + 6.33830i −0.412880 + 0.238376i
\(708\) 16.1644 4.87375i 0.607495 0.183167i
\(709\) 22.2766i 0.836616i −0.908305 0.418308i \(-0.862623\pi\)
0.908305 0.418308i \(-0.137377\pi\)
\(710\) 12.3030 7.10313i 0.461723 0.266576i
\(711\) −1.93070 + 0.120025i −0.0724070 + 0.00450130i
\(712\) 35.9306i 1.34656i
\(713\) 0 0
\(714\) −12.3030 11.5619i −0.460428 0.432693i
\(715\) −19.1168 −0.714929
\(716\) −16.6753 28.8824i −0.623184 1.07939i
\(717\) −18.8139 + 20.0198i −0.702616 + 0.747652i
\(718\) −23.0475 + 39.9195i −0.860127 + 1.48978i
\(719\) −10.0693 17.4405i −0.375521 0.650422i 0.614884 0.788618i \(-0.289203\pi\)
−0.990405 + 0.138196i \(0.955870\pi\)
\(720\) −26.6753 40.2145i −0.994128 1.49871i
\(721\) −32.6060 −1.21431
\(722\) −89.5842 51.7215i −3.33398 1.92487i
\(723\) 45.2228 13.6352i 1.68185 0.507098i
\(724\) −24.5584 14.1788i −0.912707 0.526951i
\(725\) −4.11684 7.13058i −0.152896 0.264823i
\(726\) 33.9783 10.2448i 1.26105 0.380221i
\(727\) −1.98913 3.44527i −0.0737726 0.127778i 0.826779 0.562526i \(-0.190171\pi\)
−0.900552 + 0.434749i \(0.856837\pi\)
\(728\) 24.6060 0.911958
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 35.7921 20.6646i 1.32473 0.764831i
\(731\) −12.2079 7.04823i −0.451525 0.260688i
\(732\) 0 0
\(733\) −10.9891 + 19.0337i −0.405893 + 0.703027i −0.994425 0.105447i \(-0.966373\pi\)
0.588532 + 0.808474i \(0.299706\pi\)
\(734\) 42.0475 72.8285i 1.55200 2.68815i
\(735\) −5.74456 + 1.73205i −0.211891 + 0.0638877i
\(736\) 0 0
\(737\) −24.3030 42.0940i −0.895212 1.55055i
\(738\) 15.9307 10.5672i 0.586417 0.388985i
\(739\) −38.6168 22.2954i −1.42054 0.820151i −0.424198 0.905569i \(-0.639444\pi\)
−0.996345 + 0.0854181i \(0.972777\pi\)
\(740\) 19.1168 0.702749
\(741\) 5.31386 22.6179i 0.195210 0.830887i
\(742\) 26.1831i 0.961213i
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 47.7228 + 32.5214i 1.74960 + 1.19229i
\(745\) 2.37228 0.0869137
\(746\) 37.5152i 1.37353i
\(747\) −19.0693 + 12.6491i −0.697709 + 0.462808i
\(748\) −31.1168 −1.13774
\(749\) 5.18614 + 2.99422i 0.189497 + 0.109406i
\(750\) −38.9783 9.15759i −1.42328 0.334388i
\(751\) 12.2446 + 21.2082i 0.446810 + 0.773898i 0.998176 0.0603651i \(-0.0192265\pi\)
−0.551366 + 0.834264i \(0.685893\pi\)
\(752\) 42.2689i 1.54139i
\(753\) −8.18614 27.1504i −0.298320 0.989414i
\(754\) 13.1168 22.7190i 0.477687 0.827379i
\(755\) −29.2337 + 50.6342i −1.06392 + 1.84277i
\(756\) 9.04755 53.1311i 0.329056 1.93236i
\(757\) 34.6753 + 20.0198i 1.26029 + 0.727631i 0.973131 0.230251i \(-0.0739546\pi\)
0.287163 + 0.957882i \(0.407288\pi\)
\(758\) 55.1644 31.8492i 2.00366 1.15681i
\(759\) 0 0
\(760\) 117.073 4.24670
\(761\) −1.06930 1.85208i −0.0387620 0.0671377i 0.845994 0.533193i \(-0.179008\pi\)
−0.884756 + 0.466055i \(0.845675\pi\)
\(762\) −16.9307 56.1528i −0.613335 2.03420i
\(763\) 7.86141 + 13.6164i 0.284602 + 0.492945i
\(764\) −69.1426 39.9195i −2.50149 1.44424i
\(765\) 5.48913 11.0371i 0.198460 0.399048i
\(766\) 9.55842 + 5.51856i 0.345360 + 0.199394i
\(767\) −3.86141 −0.139427
\(768\) −52.4674 12.3267i −1.89325 0.444803i
\(769\) −7.81386 13.5340i −0.281775 0.488049i 0.690047 0.723765i \(-0.257590\pi\)
−0.971822 + 0.235716i \(0.924256\pi\)
\(770\) 33.0475 57.2400i 1.19095 2.06279i
\(771\) 35.0475 + 32.9364i 1.26221 + 1.18618i
\(772\) 3.81386 + 6.60580i 0.137264 + 0.237748i
\(773\) 26.2337 0.943560 0.471780 0.881716i \(-0.343612\pi\)
0.471780 + 0.881716i \(0.343612\pi\)
\(774\) −4.06930 65.4579i −0.146268 2.35283i
\(775\) −7.54755 + 1.18843i −0.271116 + 0.0426897i
\(776\) 32.1716i 1.15489i
\(777\) 5.18614 + 4.87375i 0.186052 + 0.174845i
\(778\) 48.9090 28.2376i 1.75347 1.01237i
\(779\) 19.5499i 0.700448i
\(780\) 9.55842 + 31.7017i 0.342246 + 1.13510i
\(781\) 8.44158 4.87375i 0.302063 0.174396i
\(782\) 0 0
\(783\) −24.0000 19.8997i −0.857690 0.711159i
\(784\) 4.37228 7.57301i 0.156153 0.270465i
\(785\) −14.4891 8.36530i −0.517139 0.298570i
\(786\) −14.3030 47.4376i −0.510171 1.69204i
\(787\) −33.7337 + 19.4762i −1.20248 + 0.694250i −0.961105 0.276183i \(-0.910930\pi\)
−0.241371 + 0.970433i \(0.577597\pi\)
\(788\) −53.7921 + 93.1707i −1.91626 + 3.31907i
\(789\) −40.4674 9.50744i −1.44068 0.338474i
\(790\) 4.10891i 0.146189i
\(791\) 5.28873i 0.188045i
\(792\) −43.4198 65.4579i −1.54286 2.32594i
\(793\) 0 0
\(794\) 34.1644 19.7248i 1.21245 0.700008i
\(795\) −18.3030 + 5.51856i −0.649140 + 0.195723i
\(796\) 23.7921 + 13.7364i 0.843289 + 0.486873i
\(797\) −19.9307 + 34.5210i −0.705982 + 1.22280i 0.260354 + 0.965513i \(0.416161\pi\)
−0.966336 + 0.257283i \(0.917173\pi\)
\(798\) 58.5367 + 55.0106i 2.07218 + 1.94736i
\(799\) −9.35053 + 5.39853i −0.330798 + 0.190986i
\(800\) −4.88316 + 2.81929i −0.172646 + 0.0996770i
\(801\) 16.1168 + 8.01544i 0.569461 + 0.283212i
\(802\) 35.9306i 1.26875i
\(803\) 24.5584 14.1788i 0.866648 0.500359i
\(804\) −57.6535 + 61.3489i −2.03328 + 2.16361i
\(805\) 0 0
\(806\) −15.3030 18.9325i −0.539025 0.666870i
\(807\) −18.8139 + 20.0198i −0.662279 + 0.704729i
\(808\) 32.0000 1.12576
\(809\) −3.30298 5.72094i −0.116127 0.201137i 0.802103 0.597186i \(-0.203715\pi\)
−0.918230 + 0.396048i \(0.870381\pi\)
\(810\) 56.9090 7.10313i 1.99958 0.249579i
\(811\) 0.500000 0.866025i 0.0175574 0.0304103i −0.857113 0.515128i \(-0.827744\pi\)
0.874671 + 0.484718i \(0.161078\pi\)
\(812\) 31.1168 + 53.8960i 1.09199 + 1.89138i
\(813\) 0.941578 4.00772i 0.0330226 0.140557i
\(814\) 19.1168 0.670045
\(815\) −1.37228 0.792287i −0.0480689 0.0277526i
\(816\) 5.18614 + 17.2005i 0.181551 + 0.602137i
\(817\) 58.0842 + 33.5349i 2.03211 + 1.17324i
\(818\) −30.0475 52.0439i −1.05059 1.81967i
\(819\) −5.48913 + 11.0371i −0.191806 + 0.385668i
\(820\) −13.9307 24.1287i −0.486481 0.842610i
\(821\) −50.2337 −1.75317 −0.876584 0.481249i \(-0.840183\pi\)
−0.876584 + 0.481249i \(0.840183\pi\)
\(822\) 52.1644 + 49.0222i 1.81944 + 1.70985i
\(823\) 25.6753 14.8236i 0.894984 0.516719i 0.0194142 0.999812i \(-0.493820\pi\)
0.875569 + 0.483093i \(0.160487\pi\)
\(824\) 71.2812 + 41.1542i 2.48320 + 1.43368i
\(825\) 10.1168 + 2.37686i 0.352223 + 0.0827517i
\(826\) 6.67527 11.5619i 0.232262 0.402290i
\(827\) −18.0475 + 31.2593i −0.627575 + 1.08699i 0.360462 + 0.932774i \(0.382619\pi\)
−0.988037 + 0.154217i \(0.950714\pi\)
\(828\) 0 0
\(829\) 52.5687i 1.82579i −0.408200 0.912893i \(-0.633843\pi\)
0.408200 0.912893i \(-0.366157\pi\)
\(830\) 24.3030 + 42.0940i 0.843569 + 1.46110i
\(831\) 3.17527 13.5152i 0.110149 0.468836i
\(832\) 3.55842 + 2.05446i 0.123366 + 0.0712254i
\(833\) 2.23369 0.0773927
\(834\) −44.2337 10.3923i −1.53169 0.359856i
\(835\) 41.3292i 1.43025i
\(836\) 148.052 5.12047
\(837\) −25.2337 + 14.1514i −0.872204 + 0.489143i
\(838\) 89.2119 3.08178
\(839\) 28.4125i 0.980909i −0.871467 0.490455i \(-0.836831\pi\)
0.871467 0.490455i \(-0.163169\pi\)
\(840\) −60.4674 14.2063i −2.08632 0.490163i
\(841\) 7.00000 0.241379
\(842\) 44.5367 + 25.7133i 1.53484 + 0.886137i
\(843\) −5.88316 + 25.0410i −0.202627 + 0.862458i
\(844\) −53.5367 92.7282i −1.84281 3.19184i
\(845\) 25.2434i 0.868399i
\(846\) −44.9783 22.3692i −1.54638 0.769068i
\(847\) 9.62772 16.6757i 0.330812 0.572984i
\(848\) 13.9307 24.1287i 0.478382 0.828582i
\(849\) 44.4307 + 10.4386i 1.52486 + 0.358252i
\(850\) −4.88316 2.81929i −0.167491 0.0967009i
\(851\) 0 0
\(852\) −12.3030 11.5619i −0.421493 0.396104i
\(853\) −4.35053 −0.148959 −0.0744797 0.997223i \(-0.523730\pi\)
−0.0744797 + 0.997223i \(0.523730\pi\)
\(854\) 0 0
\(855\) −26.1168 + 52.5138i −0.893177 + 1.79593i
\(856\) −7.55842 13.0916i −0.258342 0.447461i
\(857\) 48.3981 + 27.9426i 1.65325 + 0.954503i 0.975725 + 0.219000i \(0.0702795\pi\)
0.677522 + 0.735502i \(0.263054\pi\)
\(858\) 9.55842 + 31.7017i 0.326319 + 1.08228i
\(859\) −28.8505 16.6569i −0.984367 0.568325i −0.0807816 0.996732i \(-0.525742\pi\)
−0.903586 + 0.428407i \(0.859075\pi\)
\(860\) −95.5842 −3.25939
\(861\) 2.37228 10.0974i 0.0808471 0.344117i
\(862\) −20.3030 35.1658i −0.691522 1.19775i
\(863\) −18.0475 + 31.2593i −0.614346 + 1.06408i 0.376153 + 0.926557i \(0.377247\pi\)
−0.990499 + 0.137520i \(0.956087\pi\)
\(864\) −13.6277 + 16.4356i −0.463624 + 0.559152i
\(865\) 17.9307 + 31.0569i 0.609662 + 1.05597i
\(866\) −72.7011 −2.47048
\(867\) 17.0217 18.1128i 0.578089 0.615143i
\(868\) 57.0475 8.98266i 1.93632 0.304891i
\(869\) 2.81929i 0.0956379i
\(870\) −45.3505 + 48.2574i −1.53753 + 1.63608i
\(871\) 16.6753 9.62747i 0.565020 0.326214i
\(872\) 39.6897i 1.34406i
\(873\) −14.4307 7.17687i −0.488405 0.242900i
\(874\) 0 0
\(875\) −18.8139 + 10.8622i −0.636025 + 0.367209i
\(876\) −35.7921 33.6361i −1.20930 1.13646i
\(877\) −6.87228 + 11.9031i −0.232060 + 0.401940i −0.958414 0.285380i \(-0.907880\pi\)
0.726354 + 0.687321i \(0.241213\pi\)
\(878\) −74.2812 42.8863i −2.50687 1.44734i
\(879\) 32.9090 9.92242i 1.10999 0.334675i
\(880\) −60.9090 + 35.1658i −2.05324 + 1.18544i
\(881\) 12.3030 21.3094i 0.414498 0.717932i −0.580878 0.813991i \(-0.697290\pi\)
0.995376 + 0.0960592i \(0.0306238\pi\)
\(882\) 5.74456 + 8.66025i 0.193429 + 0.291606i
\(883\) 27.9152i 0.939421i −0.882820 0.469711i \(-0.844358\pi\)
0.882820 0.469711i \(-0.155642\pi\)
\(884\) 12.3267i 0.414593i
\(885\) 9.48913 + 2.22938i 0.318973 + 0.0749399i
\(886\) −29.0475 + 50.3118i −0.975871 + 1.69026i
\(887\) 2.18614 1.26217i 0.0734034 0.0423795i −0.462849 0.886437i \(-0.653173\pi\)
0.536253 + 0.844058i \(0.319839\pi\)
\(888\) −5.18614 17.2005i −0.174035 0.577210i
\(889\) −27.5584 15.9109i −0.924280 0.533633i
\(890\) 19.1168 33.1113i 0.640798 1.10989i
\(891\) 39.0475 4.87375i 1.30814 0.163277i
\(892\) 32.7921 18.9325i 1.09796 0.633908i
\(893\) 44.4891 25.6858i 1.48877 0.859543i
\(894\) −1.18614 3.93398i −0.0396705 0.131572i
\(895\) 19.2549i 0.643622i
\(896\) −29.1861 + 16.8506i −0.975041 + 0.562940i
\(897\) 0 0
\(898\) 96.5147i 3.22074i
\(899\) 12.0000 31.1769i 0.400222 1.03981i
\(900\) −1.11684 17.9653i −0.0372281 0.598844i
\(901\) 7.11684 0.237096
\(902\) −13.9307 24.1287i −0.463842 0.803397i
\(903\) −25.9307 24.3687i −0.862920 0.810941i
\(904\) 6.67527 11.5619i 0.222016 0.384543i
\(905\) −8.18614 14.1788i −0.272117 0.471320i
\(906\) 98.5842 + 23.1615i 3.27524 + 0.769488i
\(907\) 54.9783 1.82552 0.912761 0.408493i \(-0.133946\pi\)
0.912761 + 0.408493i \(0.133946\pi\)
\(908\) 53.7921 + 31.0569i 1.78515 + 1.03066i
\(909\) −7.13859 + 14.3537i −0.236772 + 0.476083i
\(910\) 22.6753 + 13.0916i 0.751678 + 0.433981i
\(911\) 19.9307 + 34.5210i 0.660334 + 1.14373i 0.980528 + 0.196380i \(0.0629185\pi\)
−0.320194 + 0.947352i \(0.603748\pi\)
\(912\) −24.6753 81.8386i −0.817080 2.70995i
\(913\) 16.6753 + 28.8824i 0.551871 + 0.955868i
\(914\) −32.2337 −1.06620
\(915\) 0 0
\(916\) 11.4416 6.60580i 0.378040 0.218262i
\(917\) −23.2812 13.4414i −0.768814 0.443875i
\(918\) −21.0475 3.58413i −0.694673 0.118294i
\(919\) 22.6168 39.1735i 0.746061 1.29222i −0.203637 0.979047i \(-0.565276\pi\)
0.949697 0.313169i \(-0.101391\pi\)
\(920\) 0 0
\(921\) 2.12772 + 7.05684i 0.0701107 + 0.232531i
\(922\) 15.1460i 0.498808i
\(923\) 1.93070 + 3.34408i 0.0635499 + 0.110072i
\(924\) −76.4674 17.9653i −2.51559 0.591016i
\(925\) 2.05842 + 1.18843i 0.0676805 + 0.0390754i
\(926\) 46.4674 1.52701
\(927\) −34.3614 + 22.7928i −1.12858 + 0.748613i
\(928\) 24.6535i 0.809290i
\(929\) 26.2337 0.860699 0.430350 0.902662i \(-0.358390\pi\)
0.430350 + 0.902662i \(0.358390\pi\)
\(930\) 26.6753 + 55.3605i 0.874716 + 1.81534i
\(931\) −10.6277 −0.348309
\(932\) 44.1485i 1.44613i
\(933\) 12.1168 51.5740i 0.396688 1.68846i
\(934\) −39.7228 −1.29977
\(935\) −15.5584 8.98266i −0.508815 0.293764i
\(936\) 25.9307 17.2005i 0.847572 0.562215i
\(937\) 22.6168 + 39.1735i 0.738860 + 1.27974i 0.953009 + 0.302942i \(0.0979689\pi\)
−0.214149 + 0.976801i \(0.568698\pi\)
\(938\) 66.5725i 2.17367i
\(939\) −5.01087 + 1.51084i −0.163524 + 0.0493043i
\(940\) −36.6060 + 63.4034i −1.19396 + 2.06799i
\(941\) −1.93070 + 3.34408i −0.0629391 + 0.109014i −0.895778 0.444502i \(-0.853381\pi\)
0.832839 + 0.553516i \(0.186714\pi\)
\(942\) −6.62772 + 28.2101i −0.215943 + 0.919136i
\(943\) 0 0
\(944\) −12.3030 + 7.10313i −0.400428 + 0.231187i
\(945\) 19.8614 23.9538i 0.646092 0.779216i
\(946\) −95.5842 −3.10771
\(947\) 1.93070 + 3.34408i 0.0627394 + 0.108668i 0.895689 0.444681i \(-0.146683\pi\)
−0.832950 + 0.553349i \(0.813350\pi\)
\(948\) 4.67527 1.40965i 0.151846 0.0457832i
\(949\) 5.61684 + 9.72866i 0.182330 + 0.315806i
\(950\) 23.2337 + 13.4140i 0.753800 + 0.435207i
\(951\) 13.5367 4.08146i 0.438957 0.132350i
\(952\) 20.0258 + 11.5619i 0.649040 + 0.374723i
\(953\) −34.4674 −1.11651 −0.558254 0.829670i \(-0.688528\pi\)
−0.558254 + 0.829670i \(0.688528\pi\)
\(954\) 18.3030 + 27.5928i 0.592581 + 0.893349i
\(955\) −23.0475 39.9195i −0.745801 1.29177i
\(956\) 34.6753 60.0593i 1.12148 1.94246i
\(957\) −31.1168 + 33.1113i −1.00586 + 1.07034i
\(958\) −29.0475 50.3118i −0.938484 1.62550i
\(959\) 38.8397 1.25420
\(960\) −7.55842 7.10313i −0.243947 0.229253i
\(961\) −23.0000 20.7846i −0.741935 0.670471i
\(962\) 7.57301i 0.244164i
\(963\) 7.55842 0.469882i 0.243567 0.0151417i
\(964\) −103.259 + 59.6169i −3.32576 + 1.92013i
\(965\) 4.40387i 0.141765i
\(966\) 0 0
\(967\) −0.558422 + 0.322405i −0.0179576 + 0.0103678i −0.508952 0.860795i \(-0.669967\pi\)
0.490994 + 0.871163i \(0.336634\pi\)
\(968\) −42.0951 + 24.3036i −1.35299 + 0.781148i
\(969\) 14.9525 15.9109i 0.480342 0.511131i
\(970\) −17.1168 + 29.6472i −0.549589 + 0.951916i
\(971\) 13.9307 + 8.04290i 0.447058 + 0.258109i 0.706587 0.707626i \(-0.250234\pi\)
−0.259529 + 0.965735i \(0.583567\pi\)
\(972\) −27.6060 62.3162i −0.885462 1.99879i
\(973\) −21.3505 + 12.3267i −0.684467 + 0.395177i
\(974\) −34.4198 + 59.6169i −1.10288 + 1.91025i
\(975\) −0.941578 + 4.00772i −0.0301546 + 0.128350i
\(976\) 0 0
\(977\) 40.9793i 1.31104i −0.755176 0.655522i \(-0.772449\pi\)
0.755176 0.655522i \(-0.227551\pi\)
\(978\) −0.627719 + 2.67181i −0.0200722 + 0.0854352i
\(979\) 13.1168 22.7190i 0.419216 0.726104i
\(980\) 13.1168 7.57301i 0.419002 0.241911i
\(981\) 17.8030 + 8.85402i 0.568406 + 0.282687i
\(982\) −87.1426 50.3118i −2.78083 1.60551i
\(983\) −13.9307 + 24.1287i −0.444320 + 0.769586i −0.998005 0.0631412i \(-0.979888\pi\)
0.553684 + 0.832727i \(0.313221\pi\)
\(984\) −17.9307 + 19.0800i −0.571610 + 0.608249i
\(985\) −53.7921 + 31.0569i −1.71396 + 0.989555i
\(986\) 21.3505 12.3267i 0.679939 0.392563i
\(987\) −26.0951 + 7.86797i −0.830616 + 0.250440i
\(988\) 58.6497i 1.86589i
\(989\) 0 0
\(990\) −5.18614 83.4232i −0.164826 2.65136i
\(991\) 13.6540i 0.433734i −0.976201 0.216867i \(-0.930416\pi\)
0.976201 0.216867i \(-0.0695839\pi\)
\(992\) −21.3505 8.21782i −0.677880 0.260916i
\(993\) 2.18614 + 2.05446i 0.0693751 + 0.0651962i
\(994\) −13.3505 −0.423453
\(995\) 7.93070 + 13.7364i 0.251420 + 0.435473i
\(996\) 39.5584 42.0940i 1.25346 1.33380i
\(997\) 16.1861 28.0352i 0.512620 0.887884i −0.487273 0.873250i \(-0.662008\pi\)
0.999893 0.0146344i \(-0.00465844\pi\)
\(998\) −0.813859 1.40965i −0.0257623 0.0446216i
\(999\) 8.87228 + 1.51084i 0.280707 + 0.0478007i
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 93.2.g.e.68.2 yes 4
3.2 odd 2 93.2.g.f.68.1 yes 4
31.26 odd 6 93.2.g.f.26.2 yes 4
93.26 even 6 inner 93.2.g.e.26.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.g.e.26.1 4 93.26 even 6 inner
93.2.g.e.68.2 yes 4 1.1 even 1 trivial
93.2.g.f.26.2 yes 4 31.26 odd 6
93.2.g.f.68.1 yes 4 3.2 odd 2