Properties

Label 462.2.j.d.379.1
Level $462$
Weight $2$
Character 462.379
Analytic conductor $3.689$
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] = [462,2,Mod(169,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.j (of order \(5\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 379.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 462.379
Dual form 462.2.j.d.295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +0.618034 q^{10} +(0.309017 + 3.30220i) q^{11} -1.00000 q^{12} +(0.618034 + 1.90211i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.118034 - 0.363271i) q^{17} +(0.809017 - 0.587785i) q^{18} +(3.92705 + 2.85317i) q^{19} +(-0.190983 - 0.587785i) q^{20} -1.00000 q^{21} +(3.04508 - 1.31433i) q^{22} -4.85410 q^{23} +(0.309017 + 0.951057i) q^{24} +(3.73607 + 2.71441i) q^{25} +(1.61803 - 1.17557i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(2.00000 - 1.45309i) q^{29} +(0.500000 + 0.363271i) q^{30} +(1.42705 + 4.39201i) q^{31} -1.00000 q^{32} +(-1.69098 + 2.85317i) q^{33} -0.381966 q^{34} +(-0.190983 - 0.587785i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-3.11803 + 2.26538i) q^{37} +(1.50000 - 4.61653i) q^{38} +(-0.618034 + 1.90211i) q^{39} +(-0.500000 + 0.363271i) q^{40} +(-2.11803 - 1.53884i) q^{41} +(0.309017 + 0.951057i) q^{42} +10.0000 q^{43} +(-2.19098 - 2.48990i) q^{44} -0.618034 q^{45} +(1.50000 + 4.61653i) q^{46} +(-5.23607 - 3.80423i) q^{47} +(0.809017 - 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(1.42705 - 4.39201i) q^{50} +(0.309017 - 0.224514i) q^{51} +(-1.61803 - 1.17557i) q^{52} +(0.145898 + 0.449028i) q^{53} +1.00000 q^{54} +(-2.00000 - 0.449028i) q^{55} -1.00000 q^{56} +(1.50000 + 4.61653i) q^{57} +(-2.00000 - 1.45309i) q^{58} +(4.23607 - 3.07768i) q^{59} +(0.190983 - 0.587785i) q^{60} +(3.76393 - 11.5842i) q^{61} +(3.73607 - 2.71441i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} -1.23607 q^{65} +(3.23607 + 0.726543i) q^{66} -12.1803 q^{67} +(0.118034 + 0.363271i) q^{68} +(-3.92705 - 2.85317i) q^{69} +(-0.500000 + 0.363271i) q^{70} +(2.00000 - 6.15537i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(8.23607 - 5.98385i) q^{73} +(3.11803 + 2.26538i) q^{74} +(1.42705 + 4.39201i) q^{75} -4.85410 q^{76} +(-2.19098 - 2.48990i) q^{77} +2.00000 q^{78} +(4.47214 + 13.7638i) q^{79} +(0.500000 + 0.363271i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.809017 + 2.48990i) q^{82} +(0.854102 - 2.62866i) q^{83} +(0.809017 - 0.587785i) q^{84} +(0.190983 + 0.138757i) q^{85} +(-3.09017 - 9.51057i) q^{86} +2.47214 q^{87} +(-1.69098 + 2.85317i) q^{88} -15.7984 q^{89} +(0.190983 + 0.587785i) q^{90} +(-1.61803 - 1.17557i) q^{91} +(3.92705 - 2.85317i) q^{92} +(-1.42705 + 4.39201i) q^{93} +(-2.00000 + 6.15537i) q^{94} +(-2.42705 + 1.76336i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-3.14590 - 9.68208i) q^{97} -1.00000 q^{98} +(-3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9} - 2 q^{10} - q^{11} - 4 q^{12} - 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} + q^{18} + 9 q^{19} - 3 q^{20} - 4 q^{21} + q^{22} - 6 q^{23} - q^{24} + 6 q^{25} + 2 q^{26} + q^{27} - q^{28} + 8 q^{29} + 2 q^{30} - q^{31} - 4 q^{32} - 9 q^{33} - 6 q^{34} - 3 q^{35} - q^{36} - 8 q^{37} + 6 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} - q^{42} + 40 q^{43} - 11 q^{44} + 2 q^{45} + 6 q^{46} - 12 q^{47} + q^{48} - q^{49} - q^{50} - q^{51} - 2 q^{52} + 14 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} + 6 q^{57} - 8 q^{58} + 8 q^{59} + 3 q^{60} + 24 q^{61} + 6 q^{62} - q^{63} - q^{64} + 4 q^{65} + 4 q^{66} - 4 q^{67} - 4 q^{68} - 9 q^{69} - 2 q^{70} + 8 q^{71} + q^{72} + 24 q^{73} + 8 q^{74} - q^{75} - 6 q^{76} - 11 q^{77} + 8 q^{78} + 2 q^{80} - q^{81} - q^{82} - 10 q^{83} + q^{84} + 3 q^{85} + 10 q^{86} - 8 q^{87} - 9 q^{88} - 14 q^{89} + 3 q^{90} - 2 q^{91} + 9 q^{92} + q^{93} - 8 q^{94} - 3 q^{95} - q^{96} - 26 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −0.190983 + 0.587785i −0.0854102 + 0.262866i −0.984636 0.174619i \(-0.944131\pi\)
0.899226 + 0.437485i \(0.144131\pi\)
\(6\) 0.309017 0.951057i 0.126156 0.388267i
\(7\) −0.809017 + 0.587785i −0.305780 + 0.222162i
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0.618034 0.195440
\(11\) 0.309017 + 3.30220i 0.0931721 + 0.995650i
\(12\) −1.00000 −0.288675
\(13\) 0.618034 + 1.90211i 0.171412 + 0.527551i 0.999451 0.0331183i \(-0.0105438\pi\)
−0.828040 + 0.560670i \(0.810544\pi\)
\(14\) 0.809017 + 0.587785i 0.216219 + 0.157092i
\(15\) −0.500000 + 0.363271i −0.129099 + 0.0937962i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.118034 0.363271i 0.0286274 0.0881062i −0.935722 0.352738i \(-0.885251\pi\)
0.964349 + 0.264632i \(0.0852506\pi\)
\(18\) 0.809017 0.587785i 0.190687 0.138542i
\(19\) 3.92705 + 2.85317i 0.900927 + 0.654562i 0.938704 0.344724i \(-0.112028\pi\)
−0.0377767 + 0.999286i \(0.512028\pi\)
\(20\) −0.190983 0.587785i −0.0427051 0.131433i
\(21\) −1.00000 −0.218218
\(22\) 3.04508 1.31433i 0.649214 0.280216i
\(23\) −4.85410 −1.01215 −0.506075 0.862489i \(-0.668904\pi\)
−0.506075 + 0.862489i \(0.668904\pi\)
\(24\) 0.309017 + 0.951057i 0.0630778 + 0.194134i
\(25\) 3.73607 + 2.71441i 0.747214 + 0.542882i
\(26\) 1.61803 1.17557i 0.317323 0.230548i
\(27\) −0.309017 + 0.951057i −0.0594703 + 0.183031i
\(28\) 0.309017 0.951057i 0.0583987 0.179733i
\(29\) 2.00000 1.45309i 0.371391 0.269831i −0.386397 0.922333i \(-0.626280\pi\)
0.757787 + 0.652502i \(0.226280\pi\)
\(30\) 0.500000 + 0.363271i 0.0912871 + 0.0663240i
\(31\) 1.42705 + 4.39201i 0.256306 + 0.788829i 0.993570 + 0.113223i \(0.0361176\pi\)
−0.737264 + 0.675605i \(0.763882\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.69098 + 2.85317i −0.294362 + 0.496673i
\(34\) −0.381966 −0.0655066
\(35\) −0.190983 0.587785i −0.0322820 0.0993538i
\(36\) −0.809017 0.587785i −0.134836 0.0979642i
\(37\) −3.11803 + 2.26538i −0.512602 + 0.372427i −0.813810 0.581132i \(-0.802610\pi\)
0.301208 + 0.953558i \(0.402610\pi\)
\(38\) 1.50000 4.61653i 0.243332 0.748899i
\(39\) −0.618034 + 1.90211i −0.0989646 + 0.304582i
\(40\) −0.500000 + 0.363271i −0.0790569 + 0.0574382i
\(41\) −2.11803 1.53884i −0.330781 0.240327i 0.409981 0.912094i \(-0.365535\pi\)
−0.740762 + 0.671767i \(0.765535\pi\)
\(42\) 0.309017 + 0.951057i 0.0476824 + 0.146751i
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) −2.19098 2.48990i −0.330303 0.375366i
\(45\) −0.618034 −0.0921311
\(46\) 1.50000 + 4.61653i 0.221163 + 0.680670i
\(47\) −5.23607 3.80423i −0.763759 0.554903i 0.136302 0.990667i \(-0.456478\pi\)
−0.900061 + 0.435764i \(0.856478\pi\)
\(48\) 0.809017 0.587785i 0.116772 0.0848395i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) 1.42705 4.39201i 0.201815 0.621124i
\(51\) 0.309017 0.224514i 0.0432710 0.0314382i
\(52\) −1.61803 1.17557i −0.224381 0.163022i
\(53\) 0.145898 + 0.449028i 0.0200406 + 0.0616787i 0.960577 0.278015i \(-0.0896765\pi\)
−0.940536 + 0.339694i \(0.889677\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.00000 0.449028i −0.269680 0.0605469i
\(56\) −1.00000 −0.133631
\(57\) 1.50000 + 4.61653i 0.198680 + 0.611474i
\(58\) −2.00000 1.45309i −0.262613 0.190799i
\(59\) 4.23607 3.07768i 0.551489 0.400680i −0.276845 0.960915i \(-0.589289\pi\)
0.828334 + 0.560234i \(0.189289\pi\)
\(60\) 0.190983 0.587785i 0.0246558 0.0758827i
\(61\) 3.76393 11.5842i 0.481922 1.48320i −0.354467 0.935068i \(-0.615338\pi\)
0.836390 0.548135i \(-0.184662\pi\)
\(62\) 3.73607 2.71441i 0.474481 0.344731i
\(63\) −0.809017 0.587785i −0.101927 0.0740540i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −1.23607 −0.153315
\(66\) 3.23607 + 0.726543i 0.398332 + 0.0894312i
\(67\) −12.1803 −1.48807 −0.744033 0.668143i \(-0.767089\pi\)
−0.744033 + 0.668143i \(0.767089\pi\)
\(68\) 0.118034 + 0.363271i 0.0143137 + 0.0440531i
\(69\) −3.92705 2.85317i −0.472761 0.343481i
\(70\) −0.500000 + 0.363271i −0.0597614 + 0.0434192i
\(71\) 2.00000 6.15537i 0.237356 0.730508i −0.759444 0.650573i \(-0.774529\pi\)
0.996800 0.0799347i \(-0.0254712\pi\)
\(72\) −0.309017 + 0.951057i −0.0364180 + 0.112083i
\(73\) 8.23607 5.98385i 0.963959 0.700357i 0.00989205 0.999951i \(-0.496851\pi\)
0.954067 + 0.299594i \(0.0968512\pi\)
\(74\) 3.11803 + 2.26538i 0.362464 + 0.263346i
\(75\) 1.42705 + 4.39201i 0.164782 + 0.507146i
\(76\) −4.85410 −0.556804
\(77\) −2.19098 2.48990i −0.249686 0.283750i
\(78\) 2.00000 0.226455
\(79\) 4.47214 + 13.7638i 0.503155 + 1.54855i 0.803851 + 0.594831i \(0.202781\pi\)
−0.300696 + 0.953720i \(0.597219\pi\)
\(80\) 0.500000 + 0.363271i 0.0559017 + 0.0406150i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −0.809017 + 2.48990i −0.0893410 + 0.274963i
\(83\) 0.854102 2.62866i 0.0937499 0.288532i −0.893176 0.449707i \(-0.851528\pi\)
0.986926 + 0.161175i \(0.0515283\pi\)
\(84\) 0.809017 0.587785i 0.0882710 0.0641326i
\(85\) 0.190983 + 0.138757i 0.0207150 + 0.0150503i
\(86\) −3.09017 9.51057i −0.333222 1.02555i
\(87\) 2.47214 0.265041
\(88\) −1.69098 + 2.85317i −0.180259 + 0.304149i
\(89\) −15.7984 −1.67462 −0.837312 0.546725i \(-0.815874\pi\)
−0.837312 + 0.546725i \(0.815874\pi\)
\(90\) 0.190983 + 0.587785i 0.0201314 + 0.0619580i
\(91\) −1.61803 1.17557i −0.169616 0.123233i
\(92\) 3.92705 2.85317i 0.409423 0.297463i
\(93\) −1.42705 + 4.39201i −0.147978 + 0.455430i
\(94\) −2.00000 + 6.15537i −0.206284 + 0.634878i
\(95\) −2.42705 + 1.76336i −0.249010 + 0.180916i
\(96\) −0.809017 0.587785i −0.0825700 0.0599906i
\(97\) −3.14590 9.68208i −0.319418 0.983066i −0.973898 0.226987i \(-0.927113\pi\)
0.654480 0.756079i \(-0.272887\pi\)
\(98\) −1.00000 −0.101015
\(99\) −3.04508 + 1.31433i −0.306043 + 0.132095i
\(100\) −4.61803 −0.461803
\(101\) −3.51722 10.8249i −0.349977 1.07712i −0.958865 0.283861i \(-0.908384\pi\)
0.608889 0.793256i \(-0.291616\pi\)
\(102\) −0.309017 0.224514i −0.0305972 0.0222302i
\(103\) −6.92705 + 5.03280i −0.682543 + 0.495896i −0.874200 0.485566i \(-0.838614\pi\)
0.191658 + 0.981462i \(0.438614\pi\)
\(104\) −0.618034 + 1.90211i −0.0606032 + 0.186518i
\(105\) 0.190983 0.587785i 0.0186380 0.0573620i
\(106\) 0.381966 0.277515i 0.0370998 0.0269546i
\(107\) −0.927051 0.673542i −0.0896214 0.0651138i 0.542072 0.840332i \(-0.317640\pi\)
−0.631694 + 0.775218i \(0.717640\pi\)
\(108\) −0.309017 0.951057i −0.0297352 0.0915155i
\(109\) 4.14590 0.397105 0.198553 0.980090i \(-0.436376\pi\)
0.198553 + 0.980090i \(0.436376\pi\)
\(110\) 0.190983 + 2.04087i 0.0182095 + 0.194589i
\(111\) −3.85410 −0.365815
\(112\) 0.309017 + 0.951057i 0.0291994 + 0.0898664i
\(113\) 9.32624 + 6.77591i 0.877339 + 0.637424i 0.932546 0.361051i \(-0.117582\pi\)
−0.0552074 + 0.998475i \(0.517582\pi\)
\(114\) 3.92705 2.85317i 0.367802 0.267224i
\(115\) 0.927051 2.85317i 0.0864479 0.266059i
\(116\) −0.763932 + 2.35114i −0.0709293 + 0.218298i
\(117\) −1.61803 + 1.17557i −0.149587 + 0.108682i
\(118\) −4.23607 3.07768i −0.389962 0.283324i
\(119\) 0.118034 + 0.363271i 0.0108202 + 0.0333010i
\(120\) −0.618034 −0.0564185
\(121\) −10.8090 + 2.04087i −0.982638 + 0.185534i
\(122\) −12.1803 −1.10276
\(123\) −0.809017 2.48990i −0.0729466 0.224507i
\(124\) −3.73607 2.71441i −0.335509 0.243761i
\(125\) −4.80902 + 3.49396i −0.430132 + 0.312509i
\(126\) −0.309017 + 0.951057i −0.0275294 + 0.0847268i
\(127\) 1.52786 4.70228i 0.135576 0.417260i −0.860103 0.510120i \(-0.829601\pi\)
0.995679 + 0.0928601i \(0.0296009\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) 8.09017 + 5.87785i 0.712300 + 0.517516i
\(130\) 0.381966 + 1.17557i 0.0335006 + 0.103104i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −0.309017 3.30220i −0.0268965 0.287419i
\(133\) −4.85410 −0.420904
\(134\) 3.76393 + 11.5842i 0.325154 + 1.00072i
\(135\) −0.500000 0.363271i −0.0430331 0.0312654i
\(136\) 0.309017 0.224514i 0.0264980 0.0192519i
\(137\) 1.61803 4.97980i 0.138238 0.425453i −0.857842 0.513914i \(-0.828195\pi\)
0.996080 + 0.0884614i \(0.0281950\pi\)
\(138\) −1.50000 + 4.61653i −0.127688 + 0.392985i
\(139\) 1.30902 0.951057i 0.111029 0.0806676i −0.530885 0.847444i \(-0.678140\pi\)
0.641914 + 0.766776i \(0.278140\pi\)
\(140\) 0.500000 + 0.363271i 0.0422577 + 0.0307020i
\(141\) −2.00000 6.15537i −0.168430 0.518375i
\(142\) −6.47214 −0.543130
\(143\) −6.09017 + 2.62866i −0.509286 + 0.219819i
\(144\) 1.00000 0.0833333
\(145\) 0.472136 + 1.45309i 0.0392088 + 0.120672i
\(146\) −8.23607 5.98385i −0.681622 0.495227i
\(147\) 0.809017 0.587785i 0.0667266 0.0484797i
\(148\) 1.19098 3.66547i 0.0978982 0.301300i
\(149\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(150\) 3.73607 2.71441i 0.305049 0.221631i
\(151\) −5.85410 4.25325i −0.476400 0.346125i 0.323530 0.946218i \(-0.395130\pi\)
−0.799930 + 0.600093i \(0.795130\pi\)
\(152\) 1.50000 + 4.61653i 0.121666 + 0.374450i
\(153\) 0.381966 0.0308801
\(154\) −1.69098 + 2.85317i −0.136263 + 0.229915i
\(155\) −2.85410 −0.229247
\(156\) −0.618034 1.90211i −0.0494823 0.152291i
\(157\) −3.00000 2.17963i −0.239426 0.173953i 0.461601 0.887087i \(-0.347275\pi\)
−0.701028 + 0.713134i \(0.747275\pi\)
\(158\) 11.7082 8.50651i 0.931455 0.676741i
\(159\) −0.145898 + 0.449028i −0.0115705 + 0.0356102i
\(160\) 0.190983 0.587785i 0.0150985 0.0464685i
\(161\) 3.92705 2.85317i 0.309495 0.224861i
\(162\) 0.809017 + 0.587785i 0.0635624 + 0.0461808i
\(163\) 3.09017 + 9.51057i 0.242041 + 0.744925i 0.996109 + 0.0881289i \(0.0280887\pi\)
−0.754068 + 0.656796i \(0.771911\pi\)
\(164\) 2.61803 0.204434
\(165\) −1.35410 1.53884i −0.105417 0.119799i
\(166\) −2.76393 −0.214523
\(167\) 3.94427 + 12.1392i 0.305217 + 0.939361i 0.979596 + 0.200976i \(0.0644113\pi\)
−0.674379 + 0.738385i \(0.735589\pi\)
\(168\) −0.809017 0.587785i −0.0624170 0.0453486i
\(169\) 7.28115 5.29007i 0.560089 0.406928i
\(170\) 0.0729490 0.224514i 0.00559493 0.0172194i
\(171\) −1.50000 + 4.61653i −0.114708 + 0.353035i
\(172\) −8.09017 + 5.87785i −0.616870 + 0.448182i
\(173\) −15.1631 11.0167i −1.15283 0.837580i −0.163976 0.986464i \(-0.552432\pi\)
−0.988855 + 0.148884i \(0.952432\pi\)
\(174\) −0.763932 2.35114i −0.0579135 0.178240i
\(175\) −4.61803 −0.349091
\(176\) 3.23607 + 0.726543i 0.243928 + 0.0547652i
\(177\) 5.23607 0.393567
\(178\) 4.88197 + 15.0251i 0.365919 + 1.12618i
\(179\) 12.9721 + 9.42481i 0.969583 + 0.704443i 0.955356 0.295456i \(-0.0954714\pi\)
0.0142265 + 0.999899i \(0.495471\pi\)
\(180\) 0.500000 0.363271i 0.0372678 0.0270766i
\(181\) 5.47214 16.8415i 0.406741 1.25182i −0.512692 0.858572i \(-0.671352\pi\)
0.919433 0.393247i \(-0.128648\pi\)
\(182\) −0.618034 + 1.90211i −0.0458117 + 0.140994i
\(183\) 9.85410 7.15942i 0.728436 0.529240i
\(184\) −3.92705 2.85317i −0.289506 0.210338i
\(185\) −0.736068 2.26538i −0.0541168 0.166554i
\(186\) 4.61803 0.338611
\(187\) 1.23607 + 0.277515i 0.0903902 + 0.0202939i
\(188\) 6.47214 0.472029
\(189\) −0.309017 0.951057i −0.0224777 0.0691792i
\(190\) 2.42705 + 1.76336i 0.176077 + 0.127927i
\(191\) 11.8262 8.59226i 0.855717 0.621714i −0.0709997 0.997476i \(-0.522619\pi\)
0.926716 + 0.375762i \(0.122619\pi\)
\(192\) −0.309017 + 0.951057i −0.0223014 + 0.0686366i
\(193\) 5.60739 17.2578i 0.403629 1.24224i −0.518406 0.855135i \(-0.673474\pi\)
0.922035 0.387107i \(-0.126526\pi\)
\(194\) −8.23607 + 5.98385i −0.591315 + 0.429616i
\(195\) −1.00000 0.726543i −0.0716115 0.0520288i
\(196\) 0.309017 + 0.951057i 0.0220726 + 0.0679326i
\(197\) 20.1803 1.43779 0.718895 0.695119i \(-0.244648\pi\)
0.718895 + 0.695119i \(0.244648\pi\)
\(198\) 2.19098 + 2.48990i 0.155706 + 0.176949i
\(199\) 4.38197 0.310629 0.155315 0.987865i \(-0.450361\pi\)
0.155315 + 0.987865i \(0.450361\pi\)
\(200\) 1.42705 + 4.39201i 0.100908 + 0.310562i
\(201\) −9.85410 7.15942i −0.695055 0.504987i
\(202\) −9.20820 + 6.69015i −0.647887 + 0.470717i
\(203\) −0.763932 + 2.35114i −0.0536175 + 0.165018i
\(204\) −0.118034 + 0.363271i −0.00826403 + 0.0254341i
\(205\) 1.30902 0.951057i 0.0914257 0.0664247i
\(206\) 6.92705 + 5.03280i 0.482631 + 0.350652i
\(207\) −1.50000 4.61653i −0.104257 0.320871i
\(208\) 2.00000 0.138675
\(209\) −8.20820 + 13.8496i −0.567773 + 0.957995i
\(210\) −0.618034 −0.0426484
\(211\) 6.38197 + 19.6417i 0.439353 + 1.35219i 0.888560 + 0.458761i \(0.151707\pi\)
−0.449207 + 0.893428i \(0.648293\pi\)
\(212\) −0.381966 0.277515i −0.0262335 0.0190598i
\(213\) 5.23607 3.80423i 0.358769 0.260661i
\(214\) −0.354102 + 1.08981i −0.0242059 + 0.0744981i
\(215\) −1.90983 + 5.87785i −0.130249 + 0.400866i
\(216\) −0.809017 + 0.587785i −0.0550466 + 0.0399937i
\(217\) −3.73607 2.71441i −0.253621 0.184266i
\(218\) −1.28115 3.94298i −0.0867706 0.267053i
\(219\) 10.1803 0.687924
\(220\) 1.88197 0.812299i 0.126882 0.0547652i
\(221\) 0.763932 0.0513876
\(222\) 1.19098 + 3.66547i 0.0799335 + 0.246010i
\(223\) 3.69098 + 2.68166i 0.247167 + 0.179577i 0.704470 0.709734i \(-0.251185\pi\)
−0.457304 + 0.889311i \(0.651185\pi\)
\(224\) 0.809017 0.587785i 0.0540547 0.0392731i
\(225\) −1.42705 + 4.39201i −0.0951367 + 0.292801i
\(226\) 3.56231 10.9637i 0.236961 0.729291i
\(227\) 5.85410 4.25325i 0.388550 0.282298i −0.376311 0.926493i \(-0.622808\pi\)
0.764861 + 0.644195i \(0.222808\pi\)
\(228\) −3.92705 2.85317i −0.260075 0.188956i
\(229\) −1.23607 3.80423i −0.0816817 0.251390i 0.901873 0.432001i \(-0.142192\pi\)
−0.983555 + 0.180611i \(0.942192\pi\)
\(230\) −3.00000 −0.197814
\(231\) −0.309017 3.30220i −0.0203318 0.217269i
\(232\) 2.47214 0.162304
\(233\) 0.236068 + 0.726543i 0.0154653 + 0.0475974i 0.958491 0.285122i \(-0.0920340\pi\)
−0.943026 + 0.332719i \(0.892034\pi\)
\(234\) 1.61803 + 1.17557i 0.105774 + 0.0768494i
\(235\) 3.23607 2.35114i 0.211098 0.153372i
\(236\) −1.61803 + 4.97980i −0.105325 + 0.324157i
\(237\) −4.47214 + 13.7638i −0.290496 + 0.894056i
\(238\) 0.309017 0.224514i 0.0200306 0.0145531i
\(239\) 20.8713 + 15.1639i 1.35005 + 0.980871i 0.999009 + 0.0445127i \(0.0141735\pi\)
0.351045 + 0.936359i \(0.385826\pi\)
\(240\) 0.190983 + 0.587785i 0.0123279 + 0.0379414i
\(241\) 29.1246 1.87608 0.938041 0.346525i \(-0.112639\pi\)
0.938041 + 0.346525i \(0.112639\pi\)
\(242\) 5.28115 + 9.64932i 0.339485 + 0.620282i
\(243\) −1.00000 −0.0641500
\(244\) 3.76393 + 11.5842i 0.240961 + 0.741602i
\(245\) 0.500000 + 0.363271i 0.0319438 + 0.0232085i
\(246\) −2.11803 + 1.53884i −0.135041 + 0.0981130i
\(247\) −3.00000 + 9.23305i −0.190885 + 0.587485i
\(248\) −1.42705 + 4.39201i −0.0906178 + 0.278893i
\(249\) 2.23607 1.62460i 0.141705 0.102955i
\(250\) 4.80902 + 3.49396i 0.304149 + 0.220977i
\(251\) 7.56231 + 23.2744i 0.477329 + 1.46907i 0.842791 + 0.538240i \(0.180911\pi\)
−0.365463 + 0.930826i \(0.619089\pi\)
\(252\) 1.00000 0.0629941
\(253\) −1.50000 16.0292i −0.0943042 1.00775i
\(254\) −4.94427 −0.310231
\(255\) 0.0729490 + 0.224514i 0.00456824 + 0.0140596i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 11.2533 8.17599i 0.701961 0.510004i −0.178609 0.983920i \(-0.557160\pi\)
0.880570 + 0.473916i \(0.157160\pi\)
\(258\) 3.09017 9.51057i 0.192386 0.592102i
\(259\) 1.19098 3.66547i 0.0740041 0.227761i
\(260\) 1.00000 0.726543i 0.0620174 0.0450583i
\(261\) 2.00000 + 1.45309i 0.123797 + 0.0899437i
\(262\) 0 0
\(263\) 17.0344 1.05039 0.525194 0.850982i \(-0.323993\pi\)
0.525194 + 0.850982i \(0.323993\pi\)
\(264\) −3.04508 + 1.31433i −0.187412 + 0.0808913i
\(265\) −0.291796 −0.0179249
\(266\) 1.50000 + 4.61653i 0.0919709 + 0.283057i
\(267\) −12.7812 9.28605i −0.782194 0.568297i
\(268\) 9.85410 7.15942i 0.601935 0.437331i
\(269\) 2.43769 7.50245i 0.148629 0.457433i −0.848831 0.528664i \(-0.822693\pi\)
0.997460 + 0.0712319i \(0.0226930\pi\)
\(270\) −0.190983 + 0.587785i −0.0116229 + 0.0357715i
\(271\) 7.50000 5.44907i 0.455593 0.331007i −0.336207 0.941788i \(-0.609144\pi\)
0.791800 + 0.610781i \(0.209144\pi\)
\(272\) −0.309017 0.224514i −0.0187369 0.0136132i
\(273\) −0.618034 1.90211i −0.0374051 0.115121i
\(274\) −5.23607 −0.316322
\(275\) −7.80902 + 13.1760i −0.470901 + 0.794545i
\(276\) 4.85410 0.292183
\(277\) −5.11803 15.7517i −0.307513 0.946427i −0.978728 0.205164i \(-0.934227\pi\)
0.671215 0.741263i \(-0.265773\pi\)
\(278\) −1.30902 0.951057i −0.0785096 0.0570406i
\(279\) −3.73607 + 2.71441i −0.223673 + 0.162508i
\(280\) 0.190983 0.587785i 0.0114134 0.0351269i
\(281\) −7.14590 + 21.9928i −0.426289 + 1.31198i 0.475467 + 0.879734i \(0.342279\pi\)
−0.901755 + 0.432247i \(0.857721\pi\)
\(282\) −5.23607 + 3.80423i −0.311803 + 0.226538i
\(283\) −10.1180 7.35118i −0.601455 0.436982i 0.244940 0.969538i \(-0.421232\pi\)
−0.846395 + 0.532556i \(0.821232\pi\)
\(284\) 2.00000 + 6.15537i 0.118678 + 0.365254i
\(285\) −3.00000 −0.177705
\(286\) 4.38197 + 4.97980i 0.259111 + 0.294462i
\(287\) 2.61803 0.154538
\(288\) −0.309017 0.951057i −0.0182090 0.0560415i
\(289\) 13.6353 + 9.90659i 0.802074 + 0.582741i
\(290\) 1.23607 0.898056i 0.0725844 0.0527357i
\(291\) 3.14590 9.68208i 0.184416 0.567573i
\(292\) −3.14590 + 9.68208i −0.184100 + 0.566601i
\(293\) −15.4443 + 11.2209i −0.902264 + 0.655533i −0.939047 0.343790i \(-0.888289\pi\)
0.0367825 + 0.999323i \(0.488289\pi\)
\(294\) −0.809017 0.587785i −0.0471828 0.0342803i
\(295\) 1.00000 + 3.07768i 0.0582223 + 0.179190i
\(296\) −3.85410 −0.224015
\(297\) −3.23607 0.726543i −0.187776 0.0421583i
\(298\) 0 0
\(299\) −3.00000 9.23305i −0.173494 0.533961i
\(300\) −3.73607 2.71441i −0.215702 0.156717i
\(301\) −8.09017 + 5.87785i −0.466310 + 0.338794i
\(302\) −2.23607 + 6.88191i −0.128671 + 0.396009i
\(303\) 3.51722 10.8249i 0.202059 0.621874i
\(304\) 3.92705 2.85317i 0.225232 0.163640i
\(305\) 6.09017 + 4.42477i 0.348722 + 0.253361i
\(306\) −0.118034 0.363271i −0.00674755 0.0207668i
\(307\) 0.437694 0.0249805 0.0124903 0.999922i \(-0.496024\pi\)
0.0124903 + 0.999922i \(0.496024\pi\)
\(308\) 3.23607 + 0.726543i 0.184392 + 0.0413986i
\(309\) −8.56231 −0.487093
\(310\) 0.881966 + 2.71441i 0.0500923 + 0.154168i
\(311\) −26.2705 19.0866i −1.48966 1.08230i −0.974279 0.225345i \(-0.927649\pi\)
−0.515385 0.856959i \(-0.672351\pi\)
\(312\) −1.61803 + 1.17557i −0.0916031 + 0.0665536i
\(313\) 5.47214 16.8415i 0.309303 0.951938i −0.668733 0.743503i \(-0.733163\pi\)
0.978036 0.208435i \(-0.0668370\pi\)
\(314\) −1.14590 + 3.52671i −0.0646668 + 0.199024i
\(315\) 0.500000 0.363271i 0.0281718 0.0204680i
\(316\) −11.7082 8.50651i −0.658638 0.478528i
\(317\) −4.14590 12.7598i −0.232857 0.716660i −0.997398 0.0720853i \(-0.977035\pi\)
0.764542 0.644574i \(-0.222965\pi\)
\(318\) 0.472136 0.0264761
\(319\) 5.41641 + 6.15537i 0.303261 + 0.344634i
\(320\) −0.618034 −0.0345492
\(321\) −0.354102 1.08981i −0.0197640 0.0608275i
\(322\) −3.92705 2.85317i −0.218846 0.159001i
\(323\) 1.50000 1.08981i 0.0834622 0.0606389i
\(324\) 0.309017 0.951057i 0.0171676 0.0528365i
\(325\) −2.85410 + 8.78402i −0.158317 + 0.487250i
\(326\) 8.09017 5.87785i 0.448073 0.325544i
\(327\) 3.35410 + 2.43690i 0.185482 + 0.134761i
\(328\) −0.809017 2.48990i −0.0446705 0.137482i
\(329\) 6.47214 0.356820
\(330\) −1.04508 + 1.76336i −0.0575300 + 0.0970695i
\(331\) 2.76393 0.151919 0.0759597 0.997111i \(-0.475798\pi\)
0.0759597 + 0.997111i \(0.475798\pi\)
\(332\) 0.854102 + 2.62866i 0.0468749 + 0.144266i
\(333\) −3.11803 2.26538i −0.170867 0.124142i
\(334\) 10.3262 7.50245i 0.565027 0.410516i
\(335\) 2.32624 7.15942i 0.127096 0.391161i
\(336\) −0.309017 + 0.951057i −0.0168583 + 0.0518844i
\(337\) −12.6803 + 9.21281i −0.690742 + 0.501854i −0.876904 0.480666i \(-0.840395\pi\)
0.186162 + 0.982519i \(0.440395\pi\)
\(338\) −7.28115 5.29007i −0.396043 0.287742i
\(339\) 3.56231 + 10.9637i 0.193478 + 0.595464i
\(340\) −0.236068 −0.0128026
\(341\) −14.0623 + 6.06961i −0.761517 + 0.328688i
\(342\) 4.85410 0.262480
\(343\) 0.309017 + 0.951057i 0.0166853 + 0.0513522i
\(344\) 8.09017 + 5.87785i 0.436193 + 0.316913i
\(345\) 2.42705 1.76336i 0.130668 0.0949359i
\(346\) −5.79180 + 17.8253i −0.311369 + 0.958295i
\(347\) 0.843459 2.59590i 0.0452792 0.139355i −0.925861 0.377864i \(-0.876659\pi\)
0.971140 + 0.238509i \(0.0766586\pi\)
\(348\) −2.00000 + 1.45309i −0.107211 + 0.0778935i
\(349\) −17.1803 12.4822i −0.919643 0.668159i 0.0237925 0.999717i \(-0.492426\pi\)
−0.943435 + 0.331558i \(0.892426\pi\)
\(350\) 1.42705 + 4.39201i 0.0762791 + 0.234763i
\(351\) −2.00000 −0.106752
\(352\) −0.309017 3.30220i −0.0164707 0.176008i
\(353\) −11.8885 −0.632763 −0.316382 0.948632i \(-0.602468\pi\)
−0.316382 + 0.948632i \(0.602468\pi\)
\(354\) −1.61803 4.97980i −0.0859975 0.264673i
\(355\) 3.23607 + 2.35114i 0.171753 + 0.124786i
\(356\) 12.7812 9.28605i 0.677400 0.492160i
\(357\) −0.118034 + 0.363271i −0.00624702 + 0.0192264i
\(358\) 4.95492 15.2497i 0.261875 0.805970i
\(359\) −28.0623 + 20.3885i −1.48107 + 1.07606i −0.503863 + 0.863784i \(0.668088\pi\)
−0.977209 + 0.212278i \(0.931912\pi\)
\(360\) −0.500000 0.363271i −0.0263523 0.0191461i
\(361\) 1.40983 + 4.33901i 0.0742016 + 0.228369i
\(362\) −17.7082 −0.930723
\(363\) −9.94427 4.70228i −0.521939 0.246806i
\(364\) 2.00000 0.104828
\(365\) 1.94427 + 5.98385i 0.101768 + 0.313209i
\(366\) −9.85410 7.15942i −0.515082 0.374229i
\(367\) −14.4443 + 10.4944i −0.753985 + 0.547802i −0.897059 0.441910i \(-0.854301\pi\)
0.143075 + 0.989712i \(0.454301\pi\)
\(368\) −1.50000 + 4.61653i −0.0781929 + 0.240653i
\(369\) 0.809017 2.48990i 0.0421157 0.129619i
\(370\) −1.92705 + 1.40008i −0.100183 + 0.0727869i
\(371\) −0.381966 0.277515i −0.0198307 0.0144078i
\(372\) −1.42705 4.39201i −0.0739891 0.227715i
\(373\) −3.27051 −0.169341 −0.0846703 0.996409i \(-0.526984\pi\)
−0.0846703 + 0.996409i \(0.526984\pi\)
\(374\) −0.118034 1.26133i −0.00610339 0.0652217i
\(375\) −5.94427 −0.306961
\(376\) −2.00000 6.15537i −0.103142 0.317439i
\(377\) 4.00000 + 2.90617i 0.206010 + 0.149675i
\(378\) −0.809017 + 0.587785i −0.0416113 + 0.0302324i
\(379\) 2.90983 8.95554i 0.149468 0.460015i −0.848091 0.529851i \(-0.822248\pi\)
0.997558 + 0.0698364i \(0.0222477\pi\)
\(380\) 0.927051 2.85317i 0.0475567 0.146365i
\(381\) 4.00000 2.90617i 0.204926 0.148888i
\(382\) −11.8262 8.59226i −0.605083 0.439619i
\(383\) 7.38197 + 22.7194i 0.377201 + 1.16090i 0.941982 + 0.335664i \(0.108961\pi\)
−0.564781 + 0.825241i \(0.691039\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.88197 0.812299i 0.0959139 0.0413986i
\(386\) −18.1459 −0.923602
\(387\) 3.09017 + 9.51057i 0.157082 + 0.483449i
\(388\) 8.23607 + 5.98385i 0.418123 + 0.303784i
\(389\) −1.14590 + 0.832544i −0.0580993 + 0.0422116i −0.616456 0.787389i \(-0.711432\pi\)
0.558357 + 0.829601i \(0.311432\pi\)
\(390\) −0.381966 + 1.17557i −0.0193416 + 0.0595273i
\(391\) −0.572949 + 1.76336i −0.0289753 + 0.0891767i
\(392\) 0.809017 0.587785i 0.0408615 0.0296876i
\(393\) 0 0
\(394\) −6.23607 19.1926i −0.314169 0.966911i
\(395\) −8.94427 −0.450035
\(396\) 1.69098 2.85317i 0.0849751 0.143377i
\(397\) −25.4164 −1.27561 −0.637806 0.770197i \(-0.720158\pi\)
−0.637806 + 0.770197i \(0.720158\pi\)
\(398\) −1.35410 4.16750i −0.0678750 0.208898i
\(399\) −3.92705 2.85317i −0.196598 0.142837i
\(400\) 3.73607 2.71441i 0.186803 0.135721i
\(401\) 4.81966 14.8334i 0.240682 0.740744i −0.755634 0.654994i \(-0.772671\pi\)
0.996317 0.0857504i \(-0.0273287\pi\)
\(402\) −3.76393 + 11.5842i −0.187728 + 0.577767i
\(403\) −7.47214 + 5.42882i −0.372214 + 0.270429i
\(404\) 9.20820 + 6.69015i 0.458125 + 0.332847i
\(405\) −0.190983 0.587785i −0.00949002 0.0292073i
\(406\) 2.47214 0.122690
\(407\) −8.44427 9.59632i −0.418567 0.475672i
\(408\) 0.381966 0.0189101
\(409\) 3.32624 + 10.2371i 0.164472 + 0.506192i 0.998997 0.0447775i \(-0.0142579\pi\)
−0.834525 + 0.550970i \(0.814258\pi\)
\(410\) −1.30902 0.951057i −0.0646477 0.0469693i
\(411\) 4.23607 3.07768i 0.208950 0.151811i
\(412\) 2.64590 8.14324i 0.130354 0.401188i
\(413\) −1.61803 + 4.97980i −0.0796182 + 0.245040i
\(414\) −3.92705 + 2.85317i −0.193004 + 0.140226i
\(415\) 1.38197 + 1.00406i 0.0678380 + 0.0492872i
\(416\) −0.618034 1.90211i −0.0303016 0.0932588i
\(417\) 1.61803 0.0792355
\(418\) 15.7082 + 3.52671i 0.768313 + 0.172497i
\(419\) 36.9443 1.80485 0.902423 0.430851i \(-0.141787\pi\)
0.902423 + 0.430851i \(0.141787\pi\)
\(420\) 0.190983 + 0.587785i 0.00931902 + 0.0286810i
\(421\) 6.92705 + 5.03280i 0.337604 + 0.245284i 0.743650 0.668569i \(-0.233093\pi\)
−0.406046 + 0.913852i \(0.633093\pi\)
\(422\) 16.7082 12.1392i 0.813343 0.590928i
\(423\) 2.00000 6.15537i 0.0972433 0.299284i
\(424\) −0.145898 + 0.449028i −0.00708543 + 0.0218067i
\(425\) 1.42705 1.03681i 0.0692221 0.0502928i
\(426\) −5.23607 3.80423i −0.253688 0.184315i
\(427\) 3.76393 + 11.5842i 0.182149 + 0.560598i
\(428\) 1.14590 0.0553891
\(429\) −6.47214 1.45309i −0.312478 0.0701556i
\(430\) 6.18034 0.298042
\(431\) −11.8435 36.4504i −0.570479 1.75575i −0.651081 0.759008i \(-0.725684\pi\)
0.0806014 0.996746i \(-0.474316\pi\)
\(432\) 0.809017 + 0.587785i 0.0389238 + 0.0282798i
\(433\) −18.5623 + 13.4863i −0.892047 + 0.648110i −0.936411 0.350905i \(-0.885874\pi\)
0.0443636 + 0.999015i \(0.485874\pi\)
\(434\) −1.42705 + 4.39201i −0.0685006 + 0.210823i
\(435\) −0.472136 + 1.45309i −0.0226372 + 0.0696701i
\(436\) −3.35410 + 2.43690i −0.160632 + 0.116706i
\(437\) −19.0623 13.8496i −0.911874 0.662515i
\(438\) −3.14590 9.68208i −0.150317 0.462628i
\(439\) 24.6180 1.17495 0.587477 0.809241i \(-0.300121\pi\)
0.587477 + 0.809241i \(0.300121\pi\)
\(440\) −1.35410 1.53884i −0.0645543 0.0733614i
\(441\) 1.00000 0.0476190
\(442\) −0.236068 0.726543i −0.0112286 0.0345581i
\(443\) −0.927051 0.673542i −0.0440455 0.0320009i 0.565545 0.824718i \(-0.308666\pi\)
−0.609590 + 0.792717i \(0.708666\pi\)
\(444\) 3.11803 2.26538i 0.147975 0.107510i
\(445\) 3.01722 9.28605i 0.143030 0.440201i
\(446\) 1.40983 4.33901i 0.0667574 0.205458i
\(447\) 0 0
\(448\) −0.809017 0.587785i −0.0382225 0.0277702i
\(449\) 7.27051 + 22.3763i 0.343117 + 1.05600i 0.962584 + 0.270982i \(0.0873484\pi\)
−0.619468 + 0.785022i \(0.712652\pi\)
\(450\) 4.61803 0.217696
\(451\) 4.42705 7.46969i 0.208462 0.351734i
\(452\) −11.5279 −0.542225
\(453\) −2.23607 6.88191i −0.105060 0.323340i
\(454\) −5.85410 4.25325i −0.274747 0.199615i
\(455\) 1.00000 0.726543i 0.0468807 0.0340608i
\(456\) −1.50000 + 4.61653i −0.0702439 + 0.216189i
\(457\) 5.67376 17.4620i 0.265407 0.816840i −0.726192 0.687492i \(-0.758712\pi\)
0.991599 0.129348i \(-0.0412884\pi\)
\(458\) −3.23607 + 2.35114i −0.151212 + 0.109862i
\(459\) 0.309017 + 0.224514i 0.0144237 + 0.0104794i
\(460\) 0.927051 + 2.85317i 0.0432240 + 0.133030i
\(461\) 21.0557 0.980663 0.490332 0.871536i \(-0.336876\pi\)
0.490332 + 0.871536i \(0.336876\pi\)
\(462\) −3.04508 + 1.31433i −0.141670 + 0.0611481i
\(463\) −38.5410 −1.79115 −0.895577 0.444907i \(-0.853237\pi\)
−0.895577 + 0.444907i \(0.853237\pi\)
\(464\) −0.763932 2.35114i −0.0354647 0.109149i
\(465\) −2.30902 1.67760i −0.107078 0.0777968i
\(466\) 0.618034 0.449028i 0.0286299 0.0208008i
\(467\) 8.61803 26.5236i 0.398795 1.22736i −0.527171 0.849759i \(-0.676747\pi\)
0.925966 0.377606i \(-0.123253\pi\)
\(468\) 0.618034 1.90211i 0.0285686 0.0879252i
\(469\) 9.85410 7.15942i 0.455020 0.330591i
\(470\) −3.23607 2.35114i −0.149269 0.108450i
\(471\) −1.14590 3.52671i −0.0528002 0.162502i
\(472\) 5.23607 0.241010
\(473\) 3.09017 + 33.0220i 0.142086 + 1.51835i
\(474\) 14.4721 0.664727
\(475\) 6.92705 + 21.3193i 0.317835 + 0.978195i
\(476\) −0.309017 0.224514i −0.0141638 0.0102906i
\(477\) −0.381966 + 0.277515i −0.0174890 + 0.0127065i
\(478\) 7.97214 24.5357i 0.364637 1.12224i
\(479\) −5.70820 + 17.5680i −0.260814 + 0.802704i 0.731814 + 0.681505i \(0.238674\pi\)
−0.992628 + 0.121200i \(0.961326\pi\)
\(480\) 0.500000 0.363271i 0.0228218 0.0165810i
\(481\) −6.23607 4.53077i −0.284340 0.206585i
\(482\) −9.00000 27.6992i −0.409939 1.26166i
\(483\) 4.85410 0.220869
\(484\) 7.54508 8.00448i 0.342958 0.363840i
\(485\) 6.29180 0.285696
\(486\) 0.309017 + 0.951057i 0.0140173 + 0.0431408i
\(487\) 1.90983 + 1.38757i 0.0865427 + 0.0628769i 0.630215 0.776420i \(-0.282967\pi\)
−0.543673 + 0.839297i \(0.682967\pi\)
\(488\) 9.85410 7.15942i 0.446074 0.324092i
\(489\) −3.09017 + 9.51057i −0.139742 + 0.430083i
\(490\) 0.190983 0.587785i 0.00862773 0.0265534i
\(491\) −5.07295 + 3.68571i −0.228939 + 0.166334i −0.696341 0.717711i \(-0.745190\pi\)
0.467402 + 0.884045i \(0.345190\pi\)
\(492\) 2.11803 + 1.53884i 0.0954883 + 0.0693763i
\(493\) −0.291796 0.898056i −0.0131418 0.0404464i
\(494\) 9.70820 0.436793
\(495\) −0.190983 2.04087i −0.00858405 0.0917303i
\(496\) 4.61803 0.207356
\(497\) 2.00000 + 6.15537i 0.0897123 + 0.276106i
\(498\) −2.23607 1.62460i −0.100201 0.0728000i
\(499\) −22.2705 + 16.1805i −0.996965 + 0.724337i −0.961435 0.275031i \(-0.911312\pi\)
−0.0355296 + 0.999369i \(0.511312\pi\)
\(500\) 1.83688 5.65334i 0.0821478 0.252825i
\(501\) −3.94427 + 12.1392i −0.176217 + 0.542340i
\(502\) 19.7984 14.3844i 0.883645 0.642005i
\(503\) −16.3262 11.8617i −0.727951 0.528887i 0.160964 0.986960i \(-0.448540\pi\)
−0.888915 + 0.458073i \(0.848540\pi\)
\(504\) −0.309017 0.951057i −0.0137647 0.0423634i
\(505\) 7.03444 0.313029
\(506\) −14.7812 + 6.37988i −0.657102 + 0.283620i
\(507\) 9.00000 0.399704
\(508\) 1.52786 + 4.70228i 0.0677880 + 0.208630i
\(509\) 11.7361 + 8.52675i 0.520192 + 0.377942i 0.816676 0.577096i \(-0.195814\pi\)
−0.296484 + 0.955038i \(0.595814\pi\)
\(510\) 0.190983 0.138757i 0.00845687 0.00614428i
\(511\) −3.14590 + 9.68208i −0.139166 + 0.428310i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) −3.92705 + 2.85317i −0.173384 + 0.125971i
\(514\) −11.2533 8.17599i −0.496361 0.360628i
\(515\) −1.63525 5.03280i −0.0720579 0.221772i
\(516\) −10.0000 −0.440225
\(517\) 10.9443 18.4661i 0.481329 0.812138i
\(518\) −3.85410 −0.169340
\(519\) −5.79180 17.8253i −0.254232 0.782445i
\(520\) −1.00000 0.726543i −0.0438529 0.0318610i
\(521\) −16.0623 + 11.6699i −0.703702 + 0.511270i −0.881136 0.472863i \(-0.843221\pi\)
0.177434 + 0.984133i \(0.443221\pi\)
\(522\) 0.763932 2.35114i 0.0334364 0.102907i
\(523\) 4.91641 15.1311i 0.214980 0.661639i −0.784176 0.620539i \(-0.786914\pi\)
0.999155 0.0410998i \(-0.0130862\pi\)
\(524\) 0 0
\(525\) −3.73607 2.71441i −0.163055 0.118467i
\(526\) −5.26393 16.2007i −0.229518 0.706385i
\(527\) 1.76393 0.0768381
\(528\) 2.19098 + 2.48990i 0.0953503 + 0.108359i
\(529\) 0.562306 0.0244481
\(530\) 0.0901699 + 0.277515i 0.00391673 + 0.0120545i
\(531\) 4.23607 + 3.07768i 0.183830 + 0.133560i
\(532\) 3.92705 2.85317i 0.170259 0.123701i
\(533\) 1.61803 4.97980i 0.0700848 0.215699i
\(534\) −4.88197 + 15.0251i −0.211263 + 0.650202i
\(535\) 0.572949 0.416272i 0.0247707 0.0179970i
\(536\) −9.85410 7.15942i −0.425632 0.309240i
\(537\) 4.95492 + 15.2497i 0.213820 + 0.658071i
\(538\) −7.88854 −0.340099
\(539\) 3.23607 + 0.726543i 0.139387 + 0.0312944i
\(540\) 0.618034 0.0265959
\(541\) 2.13525 + 6.57164i 0.0918018 + 0.282537i 0.986407 0.164321i \(-0.0525431\pi\)
−0.894605 + 0.446857i \(0.852543\pi\)
\(542\) −7.50000 5.44907i −0.322153 0.234058i
\(543\) 14.3262 10.4086i 0.614798 0.446677i
\(544\) −0.118034 + 0.363271i −0.00506067 + 0.0155751i
\(545\) −0.791796 + 2.43690i −0.0339168 + 0.104385i
\(546\) −1.61803 + 1.17557i −0.0692455 + 0.0503098i
\(547\) −11.5623 8.40051i −0.494369 0.359180i 0.312493 0.949920i \(-0.398836\pi\)
−0.806862 + 0.590740i \(0.798836\pi\)
\(548\) 1.61803 + 4.97980i 0.0691190 + 0.212726i
\(549\) 12.1803 0.519844
\(550\) 14.9443 + 3.35520i 0.637226 + 0.143066i
\(551\) 12.0000 0.511217
\(552\) −1.50000 4.61653i −0.0638442 0.196492i
\(553\) −11.7082 8.50651i −0.497883 0.361734i
\(554\) −13.3992 + 9.73508i −0.569277 + 0.413604i
\(555\) 0.736068 2.26538i 0.0312443 0.0961602i
\(556\) −0.500000 + 1.53884i −0.0212047 + 0.0652614i
\(557\) −9.61803 + 6.98791i −0.407529 + 0.296087i −0.772601 0.634892i \(-0.781045\pi\)
0.365072 + 0.930979i \(0.381045\pi\)
\(558\) 3.73607 + 2.71441i 0.158160 + 0.114910i
\(559\) 6.18034 + 19.0211i 0.261401 + 0.804508i
\(560\) −0.618034 −0.0261167
\(561\) 0.836881 + 0.951057i 0.0353331 + 0.0401536i
\(562\) 23.1246 0.975453
\(563\) −11.9787 36.8667i −0.504843 1.55375i −0.801035 0.598617i \(-0.795717\pi\)
0.296192 0.955128i \(-0.404283\pi\)
\(564\) 5.23607 + 3.80423i 0.220478 + 0.160187i
\(565\) −5.76393 + 4.18774i −0.242490 + 0.176180i
\(566\) −3.86475 + 11.8945i −0.162447 + 0.499962i
\(567\) 0.309017 0.951057i 0.0129775 0.0399406i
\(568\) 5.23607 3.80423i 0.219701 0.159622i
\(569\) 26.2705 + 19.0866i 1.10132 + 0.800154i 0.981274 0.192615i \(-0.0616969\pi\)
0.120043 + 0.992769i \(0.461697\pi\)
\(570\) 0.927051 + 2.85317i 0.0388299 + 0.119506i
\(571\) −43.1246 −1.80471 −0.902354 0.430995i \(-0.858163\pi\)
−0.902354 + 0.430995i \(0.858163\pi\)
\(572\) 3.38197 5.70634i 0.141407 0.238594i
\(573\) 14.6180 0.610677
\(574\) −0.809017 2.48990i −0.0337677 0.103926i
\(575\) −18.1353 13.1760i −0.756292 0.549479i
\(576\) −0.809017 + 0.587785i −0.0337090 + 0.0244911i
\(577\) −8.43769 + 25.9686i −0.351266 + 1.08108i 0.606877 + 0.794795i \(0.292422\pi\)
−0.958143 + 0.286289i \(0.907578\pi\)
\(578\) 5.20820 16.0292i 0.216633 0.666727i
\(579\) 14.6803 10.6659i 0.610094 0.443259i
\(580\) −1.23607 0.898056i −0.0513249 0.0372897i
\(581\) 0.854102 + 2.62866i 0.0354341 + 0.109055i
\(582\) −10.1803 −0.421989
\(583\) −1.43769 + 0.620541i −0.0595432 + 0.0257002i
\(584\) 10.1803 0.421265
\(585\) −0.381966 1.17557i −0.0157924 0.0486039i
\(586\) 15.4443 + 11.2209i 0.637997 + 0.463532i
\(587\) −15.7984 + 11.4782i −0.652069 + 0.473756i −0.863975 0.503534i \(-0.832033\pi\)
0.211907 + 0.977290i \(0.432033\pi\)
\(588\) −0.309017 + 0.951057i −0.0127436 + 0.0392209i
\(589\) −6.92705 + 21.3193i −0.285424 + 0.878445i
\(590\) 2.61803 1.90211i 0.107783 0.0783088i
\(591\) 16.3262 + 11.8617i 0.671572 + 0.487925i
\(592\) 1.19098 + 3.66547i 0.0489491 + 0.150650i
\(593\) −8.50658 −0.349323 −0.174662 0.984629i \(-0.555883\pi\)
−0.174662 + 0.984629i \(0.555883\pi\)
\(594\) 0.309017 + 3.30220i 0.0126791 + 0.135491i
\(595\) −0.236068 −0.00967784
\(596\) 0 0
\(597\) 3.54508 + 2.57565i 0.145091 + 0.105415i
\(598\) −7.85410 + 5.70634i −0.321178 + 0.233350i
\(599\) 1.26393 3.88998i 0.0516429 0.158940i −0.921909 0.387406i \(-0.873371\pi\)
0.973552 + 0.228466i \(0.0733710\pi\)
\(600\) −1.42705 + 4.39201i −0.0582591 + 0.179303i
\(601\) 26.5623 19.2986i 1.08350 0.787208i 0.105209 0.994450i \(-0.466449\pi\)
0.978290 + 0.207242i \(0.0664487\pi\)
\(602\) 8.09017 + 5.87785i 0.329731 + 0.239563i
\(603\) −3.76393 11.5842i −0.153279 0.471745i
\(604\) 7.23607 0.294431
\(605\) 0.864745 6.74315i 0.0351569 0.274148i
\(606\) −11.3820 −0.462361
\(607\) 7.40983 + 22.8051i 0.300756 + 0.925631i 0.981227 + 0.192856i \(0.0617751\pi\)
−0.680471 + 0.732775i \(0.738225\pi\)
\(608\) −3.92705 2.85317i −0.159263 0.115711i
\(609\) −2.00000 + 1.45309i −0.0810441 + 0.0588820i
\(610\) 2.32624 7.15942i 0.0941866 0.289877i
\(611\) 4.00000 12.3107i 0.161823 0.498039i
\(612\) −0.309017 + 0.224514i −0.0124913 + 0.00907544i
\(613\) −14.7812 10.7391i −0.597005 0.433750i 0.247809 0.968809i \(-0.420289\pi\)
−0.844815 + 0.535059i \(0.820289\pi\)
\(614\) −0.135255 0.416272i −0.00545844 0.0167994i
\(615\) 1.61803 0.0652454
\(616\) −0.309017 3.30220i −0.0124506 0.133049i
\(617\) 44.7214 1.80041 0.900207 0.435462i \(-0.143415\pi\)
0.900207 + 0.435462i \(0.143415\pi\)
\(618\) 2.64590 + 8.14324i 0.106434 + 0.327569i
\(619\) −6.59017 4.78804i −0.264881 0.192448i 0.447415 0.894326i \(-0.352345\pi\)
−0.712296 + 0.701879i \(0.752345\pi\)
\(620\) 2.30902 1.67760i 0.0927324 0.0673740i
\(621\) 1.50000 4.61653i 0.0601929 0.185255i
\(622\) −10.0344 + 30.8828i −0.402344 + 1.23829i
\(623\) 12.7812 9.28605i 0.512066 0.372038i
\(624\) 1.61803 + 1.17557i 0.0647732 + 0.0470605i
\(625\) 6.00000 + 18.4661i 0.240000 + 0.738644i
\(626\) −17.7082 −0.707762
\(627\) −14.7812 + 6.37988i −0.590302 + 0.254788i
\(628\) 3.70820 0.147973
\(629\) 0.454915 + 1.40008i 0.0181387 + 0.0558250i
\(630\) −0.500000 0.363271i −0.0199205 0.0144731i
\(631\) −39.2705 + 28.5317i −1.56333 + 1.13583i −0.630126 + 0.776493i \(0.716997\pi\)
−0.933208 + 0.359336i \(0.883003\pi\)
\(632\) −4.47214 + 13.7638i −0.177892 + 0.547495i
\(633\) −6.38197 + 19.6417i −0.253660 + 0.780686i
\(634\) −10.8541 + 7.88597i −0.431071 + 0.313192i
\(635\) 2.47214 + 1.79611i 0.0981037 + 0.0712765i
\(636\) −0.145898 0.449028i −0.00578523 0.0178051i
\(637\) 2.00000 0.0792429
\(638\) 4.18034 7.05342i 0.165501 0.279248i
\(639\) 6.47214 0.256034
\(640\) 0.190983 + 0.587785i 0.00754927 + 0.0232343i
\(641\) 28.4164 + 20.6457i 1.12238 + 0.815457i 0.984568 0.175001i \(-0.0559929\pi\)
0.137812 + 0.990458i \(0.455993\pi\)
\(642\) −0.927051 + 0.673542i −0.0365878 + 0.0265826i
\(643\) 10.8607 33.4257i 0.428303 1.31818i −0.471492 0.881870i \(-0.656284\pi\)
0.899795 0.436312i \(-0.143716\pi\)
\(644\) −1.50000 + 4.61653i −0.0591083 + 0.181917i
\(645\) −5.00000 + 3.63271i −0.196875 + 0.143038i
\(646\) −1.50000 1.08981i −0.0590167 0.0428782i
\(647\) −11.0557 34.0260i −0.434646 1.33770i −0.893449 0.449164i \(-0.851722\pi\)
0.458804 0.888538i \(-0.348278\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 11.4721 + 13.0373i 0.450321 + 0.511758i
\(650\) 9.23607 0.362268
\(651\) −1.42705 4.39201i −0.0559305 0.172136i
\(652\) −8.09017 5.87785i −0.316836 0.230194i
\(653\) −17.1803 + 12.4822i −0.672319 + 0.488468i −0.870801 0.491636i \(-0.836399\pi\)
0.198482 + 0.980105i \(0.436399\pi\)
\(654\) 1.28115 3.94298i 0.0500970 0.154183i
\(655\) 0 0
\(656\) −2.11803 + 1.53884i −0.0826953 + 0.0600817i
\(657\) 8.23607 + 5.98385i 0.321320 + 0.233452i
\(658\) −2.00000 6.15537i −0.0779681 0.239961i
\(659\) −23.0902 −0.899465 −0.449733 0.893163i \(-0.648481\pi\)
−0.449733 + 0.893163i \(0.648481\pi\)
\(660\) 2.00000 + 0.449028i 0.0778499 + 0.0174784i
\(661\) 0.360680 0.0140288 0.00701441 0.999975i \(-0.497767\pi\)
0.00701441 + 0.999975i \(0.497767\pi\)
\(662\) −0.854102 2.62866i −0.0331956 0.102166i
\(663\) 0.618034 + 0.449028i 0.0240025 + 0.0174388i
\(664\) 2.23607 1.62460i 0.0867763 0.0630466i
\(665\) 0.927051 2.85317i 0.0359495 0.110641i
\(666\) −1.19098 + 3.66547i −0.0461497 + 0.142034i
\(667\) −9.70820 + 7.05342i −0.375903 + 0.273110i
\(668\) −10.3262 7.50245i −0.399534 0.290279i
\(669\) 1.40983 + 4.33901i 0.0545072 + 0.167756i
\(670\) −7.52786 −0.290827
\(671\) 39.4164 + 8.84953i 1.52165 + 0.341633i
\(672\) 1.00000 0.0385758
\(673\) 0.798374 + 2.45714i 0.0307751 + 0.0947159i 0.965264 0.261276i \(-0.0841432\pi\)
−0.934489 + 0.355992i \(0.884143\pi\)
\(674\) 12.6803 + 9.21281i 0.488428 + 0.354864i
\(675\) −3.73607 + 2.71441i −0.143801 + 0.104478i
\(676\) −2.78115 + 8.55951i −0.106967 + 0.329212i
\(677\) 4.90983 15.1109i 0.188700 0.580759i −0.811292 0.584641i \(-0.801236\pi\)
0.999992 + 0.00388147i \(0.00123551\pi\)
\(678\) 9.32624 6.77591i 0.358172 0.260227i
\(679\) 8.23607 + 5.98385i 0.316071 + 0.229639i
\(680\) 0.0729490 + 0.224514i 0.00279747 + 0.00860972i
\(681\) 7.23607 0.277287
\(682\) 10.1180 + 11.4984i 0.387440 + 0.440298i
\(683\) −19.3820 −0.741630 −0.370815 0.928707i \(-0.620922\pi\)
−0.370815 + 0.928707i \(0.620922\pi\)
\(684\) −1.50000 4.61653i −0.0573539 0.176517i
\(685\) 2.61803 + 1.90211i 0.100030 + 0.0726760i
\(686\) 0.809017 0.587785i 0.0308884 0.0224417i
\(687\) 1.23607 3.80423i 0.0471589 0.145140i
\(688\) 3.09017 9.51057i 0.117812 0.362587i
\(689\) −0.763932 + 0.555029i −0.0291035 + 0.0211449i
\(690\) −2.42705 1.76336i −0.0923963 0.0671298i
\(691\) 5.08359 + 15.6457i 0.193389 + 0.595190i 0.999992 + 0.00409598i \(0.00130379\pi\)
−0.806603 + 0.591094i \(0.798696\pi\)
\(692\) 18.7426 0.712488
\(693\) 1.69098 2.85317i 0.0642351 0.108383i
\(694\) −2.72949 −0.103610
\(695\) 0.309017 + 0.951057i 0.0117217 + 0.0360756i
\(696\) 2.00000 + 1.45309i 0.0758098 + 0.0550790i
\(697\) −0.809017 + 0.587785i −0.0306437 + 0.0222640i
\(698\) −6.56231 + 20.1967i −0.248387 + 0.764456i
\(699\) −0.236068 + 0.726543i −0.00892891 + 0.0274804i
\(700\) 3.73607 2.71441i 0.141210 0.102595i
\(701\) −8.00000 5.81234i −0.302156 0.219529i 0.426368 0.904550i \(-0.359793\pi\)
−0.728523 + 0.685021i \(0.759793\pi\)
\(702\) 0.618034 + 1.90211i 0.0233262 + 0.0717906i
\(703\) −18.7082 −0.705593
\(704\) −3.04508 + 1.31433i −0.114766 + 0.0495356i
\(705\) 4.00000 0.150649
\(706\) 3.67376 + 11.3067i 0.138264 + 0.425532i
\(707\) 9.20820 + 6.69015i 0.346310 + 0.251609i
\(708\) −4.23607 + 3.07768i −0.159201 + 0.115666i
\(709\) −12.1353 + 37.3485i −0.455749 + 1.40265i 0.414504 + 0.910047i \(0.363955\pi\)
−0.870254 + 0.492604i \(0.836045\pi\)
\(710\) 1.23607 3.80423i 0.0463888 0.142770i
\(711\) −11.7082 + 8.50651i −0.439092 + 0.319019i
\(712\) −12.7812 9.28605i −0.478994 0.348009i
\(713\) −6.92705 21.3193i −0.259420 0.798413i
\(714\) 0.381966 0.0142947
\(715\) −0.381966 4.08174i −0.0142847 0.152648i
\(716\) −16.0344 −0.599235
\(717\) 7.97214 + 24.5357i 0.297725 + 0.916303i
\(718\) 28.0623 + 20.3885i 1.04728 + 0.760891i
\(719\) 37.4164 27.1846i 1.39540 1.01381i 0.400148 0.916451i \(-0.368959\pi\)
0.995249 0.0973643i \(-0.0310412\pi\)
\(720\) −0.190983 + 0.587785i −0.00711752 + 0.0219055i
\(721\) 2.64590 8.14324i 0.0985384 0.303270i
\(722\) 3.69098 2.68166i 0.137364 0.0998009i
\(723\) 23.5623 + 17.1190i 0.876292 + 0.636663i
\(724\) 5.47214 + 16.8415i 0.203370 + 0.625910i
\(725\) 11.4164 0.423995
\(726\) −1.39919 + 10.9106i −0.0519287 + 0.404932i
\(727\) 25.6869 0.952675 0.476338 0.879263i \(-0.341964\pi\)
0.476338 + 0.879263i \(0.341964\pi\)
\(728\) −0.618034 1.90211i −0.0229059 0.0704970i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 5.09017 3.69822i 0.188396 0.136877i
\(731\) 1.18034 3.63271i 0.0436564 0.134361i
\(732\) −3.76393 + 11.5842i −0.139119 + 0.428164i
\(733\) −26.1246 + 18.9806i −0.964935 + 0.701066i −0.954292 0.298877i \(-0.903388\pi\)
−0.0106430 + 0.999943i \(0.503388\pi\)
\(734\) 14.4443 + 10.4944i 0.533148 + 0.387355i
\(735\) 0.190983 + 0.587785i 0.00704451 + 0.0216808i
\(736\) 4.85410 0.178925
\(737\) −3.76393 40.2219i −0.138646 1.48159i
\(738\) −2.61803 −0.0963712
\(739\) −10.2361 31.5034i −0.376540 1.15887i −0.942434 0.334393i \(-0.891469\pi\)
0.565894 0.824478i \(-0.308531\pi\)
\(740\) 1.92705 + 1.40008i 0.0708398 + 0.0514681i
\(741\) −7.85410 + 5.70634i −0.288528 + 0.209628i
\(742\) −0.145898 + 0.449028i −0.00535609 + 0.0164843i
\(743\) 1.28115 3.94298i 0.0470009 0.144654i −0.924802 0.380449i \(-0.875769\pi\)
0.971803 + 0.235795i \(0.0757694\pi\)
\(744\) −3.73607 + 2.71441i −0.136971 + 0.0995152i
\(745\) 0 0
\(746\) 1.01064 + 3.11044i 0.0370023 + 0.113881i
\(747\) 2.76393 0.101127
\(748\) −1.16312 + 0.502029i −0.0425278 + 0.0183560i
\(749\) 1.14590 0.0418702
\(750\) 1.83688 + 5.65334i 0.0670734 + 0.206431i
\(751\) 31.6525 + 22.9969i 1.15502 + 0.839168i 0.989140 0.146979i \(-0.0469550\pi\)
0.165876 + 0.986147i \(0.446955\pi\)
\(752\) −5.23607 + 3.80423i −0.190940 + 0.138726i
\(753\) −7.56231 + 23.2744i −0.275586 + 0.848166i
\(754\) 1.52786 4.70228i 0.0556415 0.171247i
\(755\) 3.61803 2.62866i 0.131674 0.0956666i
\(756\) 0.809017 + 0.587785i 0.0294237 + 0.0213775i
\(757\) −6.40983 19.7274i −0.232969 0.717006i −0.997384 0.0722811i \(-0.976972\pi\)
0.764415 0.644724i \(-0.223028\pi\)
\(758\) −9.41641 −0.342019
\(759\) 8.20820 13.8496i 0.297939 0.502708i
\(760\) −3.00000 −0.108821
\(761\) −14.3262 44.0916i −0.519326 1.59832i −0.775271 0.631629i \(-0.782387\pi\)
0.255945 0.966691i \(-0.417613\pi\)
\(762\) −4.00000 2.90617i −0.144905 0.105279i
\(763\) −3.35410 + 2.43690i −0.121427 + 0.0882216i
\(764\) −4.51722 + 13.9026i −0.163427 + 0.502978i
\(765\) −0.0729490 + 0.224514i −0.00263748 + 0.00811732i
\(766\) 19.3262 14.0413i 0.698285 0.507334i
\(767\) 8.47214 + 6.15537i 0.305911 + 0.222257i
\(768\) −0.309017 0.951057i −0.0111507 0.0343183i
\(769\) −1.34752 −0.0485930 −0.0242965 0.999705i \(-0.507735\pi\)
−0.0242965 + 0.999705i \(0.507735\pi\)
\(770\) −1.35410 1.53884i −0.0487984 0.0554560i
\(771\) 13.9098 0.500950
\(772\) 5.60739 + 17.2578i 0.201814 + 0.621121i
\(773\) −18.5623 13.4863i −0.667640 0.485069i 0.201595 0.979469i \(-0.435388\pi\)
−0.869234 + 0.494400i \(0.835388\pi\)
\(774\) 8.09017 5.87785i 0.290795 0.211275i
\(775\) −6.59017 + 20.2825i −0.236726 + 0.728567i
\(776\) 3.14590 9.68208i 0.112931 0.347566i
\(777\) 3.11803 2.26538i 0.111859 0.0812702i
\(778\) 1.14590 + 0.832544i 0.0410824 + 0.0298481i
\(779\) −3.92705 12.0862i −0.140701 0.433034i
\(780\) 1.23607 0.0442583
\(781\) 20.9443 + 4.70228i 0.749445 + 0.168261i
\(782\) 1.85410 0.0663026
\(783\) 0.763932 + 2.35114i 0.0273007 + 0.0840229i
\(784\) −0.809017 0.587785i −0.0288935 0.0209923i
\(785\) 1.85410 1.34708i 0.0661757 0.0480795i
\(786\) 0 0
\(787\) 7.10081 21.8541i 0.253117 0.779013i −0.741078 0.671419i \(-0.765685\pi\)
0.994195 0.107594i \(-0.0343147\pi\)
\(788\) −16.3262 + 11.8617i −0.581598 + 0.422556i
\(789\) 13.7812 + 10.0126i 0.490622 + 0.356458i
\(790\) 2.76393 + 8.50651i 0.0983363 + 0.302648i
\(791\) −11.5279 −0.409884
\(792\) −3.23607 0.726543i −0.114989 0.0258166i
\(793\) 24.3607 0.865073
\(794\) 7.85410 + 24.1724i 0.278732 + 0.857848i
\(795\) −0.236068 0.171513i −0.00837247 0.00608295i
\(796\) −3.54508 + 2.57565i −0.125652 + 0.0912917i
\(797\) −1.92047 + 5.91061i −0.0680267 + 0.209365i −0.979291 0.202457i \(-0.935107\pi\)
0.911264 + 0.411822i \(0.135107\pi\)
\(798\) −1.50000 + 4.61653i −0.0530994 + 0.163423i
\(799\) −2.00000 + 1.45309i −0.0707549 + 0.0514065i
\(800\) −3.73607 2.71441i −0.132090 0.0959690i
\(801\) −4.88197 15.0251i −0.172496 0.530887i
\(802\) −15.5967 −0.550740
\(803\) 22.3050 + 25.3480i 0.787125 + 0.894512i
\(804\) 12.1803 0.429567
\(805\) 0.927051 + 2.85317i 0.0326743 + 0.100561i
\(806\) 7.47214 + 5.42882i 0.263195 + 0.191222i
\(807\) 6.38197 4.63677i 0.224656 0.163222i
\(808\) 3.51722 10.8249i 0.123735 0.380818i
\(809\) −13.0902 + 40.2874i −0.460226 + 1.41643i 0.404663 + 0.914466i \(0.367389\pi\)
−0.864889 + 0.501964i \(0.832611\pi\)
\(810\) −0.500000 + 0.363271i −0.0175682 + 0.0127641i
\(811\) 10.4721 + 7.60845i 0.367726 + 0.267169i 0.756268 0.654263i \(-0.227021\pi\)
−0.388541 + 0.921431i \(0.627021\pi\)
\(812\) −0.763932 2.35114i −0.0268088 0.0825089i
\(813\) 9.27051 0.325131
\(814\) −6.51722 + 10.9964i −0.228428 + 0.385424i
\(815\) −6.18034 −0.216488
\(816\) −0.118034 0.363271i −0.00413202 0.0127170i
\(817\) 39.2705 + 28.5317i 1.37390 + 0.998198i
\(818\) 8.70820 6.32688i 0.304475 0.221214i
\(819\) 0.618034 1.90211i 0.0215959 0.0664652i
\(820\) −0.500000 + 1.53884i −0.0174608 + 0.0537387i
\(821\) 5.23607 3.80423i 0.182740 0.132768i −0.492655 0.870225i \(-0.663973\pi\)
0.675395 + 0.737457i \(0.263973\pi\)
\(822\) −4.23607 3.07768i −0.147750 0.107347i
\(823\) 15.2918 + 47.0633i 0.533039 + 1.64052i 0.747850 + 0.663868i \(0.231086\pi\)
−0.214811 + 0.976656i \(0.568914\pi\)
\(824\) −8.56231 −0.298282
\(825\) −14.0623 + 6.06961i −0.489587 + 0.211317i
\(826\) 5.23607 0.182186
\(827\) −6.06231 18.6579i −0.210807 0.648797i −0.999425 0.0339136i \(-0.989203\pi\)
0.788618 0.614884i \(-0.210797\pi\)
\(828\) 3.92705 + 2.85317i 0.136474 + 0.0991545i
\(829\) −3.14590 + 2.28563i −0.109262 + 0.0793832i −0.641074 0.767479i \(-0.721511\pi\)
0.531813 + 0.846862i \(0.321511\pi\)
\(830\) 0.527864 1.62460i 0.0183224 0.0563906i
\(831\) 5.11803 15.7517i 0.177543 0.546420i
\(832\) −1.61803 + 1.17557i −0.0560952 + 0.0407556i
\(833\) −0.309017 0.224514i −0.0107068 0.00777895i
\(834\) −0.500000 1.53884i −0.0173136 0.0532857i
\(835\) −7.88854 −0.272994
\(836\) −1.50000 16.0292i −0.0518786 0.554382i
\(837\) −4.61803 −0.159623
\(838\) −11.4164 35.1361i −0.394373 1.21376i
\(839\) −35.2705 25.6255i −1.21767 0.884691i −0.221768 0.975099i \(-0.571183\pi\)
−0.995905 + 0.0904080i \(0.971183\pi\)
\(840\) 0.500000 0.363271i 0.0172516 0.0125340i
\(841\) −7.07295 + 21.7683i −0.243895 + 0.750631i
\(842\) 2.64590 8.14324i 0.0911837 0.280634i
\(843\) −18.7082 + 13.5923i −0.644345 + 0.468144i
\(844\) −16.7082 12.1392i −0.575120 0.417849i
\(845\) 1.71885 + 5.29007i 0.0591301 + 0.181984i
\(846\) −6.47214 −0.222517
\(847\) 7.54508 8.00448i 0.259252 0.275037i
\(848\) 0.472136 0.0162132
\(849\) −3.86475 11.8945i −0.132638 0.408217i
\(850\) −1.42705 1.03681i −0.0489474 0.0355624i
\(851\) 15.1353 10.9964i 0.518830 0.376952i
\(852\) −2.00000 + 6.15537i −0.0685189 + 0.210879i
\(853\) 13.5836 41.8060i 0.465093 1.43141i −0.393772 0.919208i \(-0.628830\pi\)
0.858865 0.512202i \(-0.171170\pi\)
\(854\) 9.85410 7.15942i 0.337200 0.244990i
\(855\) −2.42705 1.76336i −0.0830034 0.0603055i
\(856\) −0.354102 1.08981i −0.0121030 0.0372491i
\(857\) 28.2492 0.964975 0.482488 0.875903i \(-0.339733\pi\)
0.482488 + 0.875903i \(0.339733\pi\)
\(858\) 0.618034 + 6.60440i 0.0210993 + 0.225470i
\(859\) −43.4164 −1.48135 −0.740674 0.671864i \(-0.765494\pi\)
−0.740674 + 0.671864i \(0.765494\pi\)
\(860\) −1.90983 5.87785i −0.0651247 0.200433i
\(861\) 2.11803 + 1.53884i 0.0721824 + 0.0524436i
\(862\) −31.0066 + 22.5276i −1.05609 + 0.767293i
\(863\) 13.5729 41.7732i 0.462029 1.42198i −0.400653 0.916230i \(-0.631217\pi\)
0.862681 0.505748i \(-0.168783\pi\)
\(864\) 0.309017 0.951057i 0.0105130 0.0323556i
\(865\) 9.37132 6.80866i 0.318635 0.231502i
\(866\) 18.5623 + 13.4863i 0.630773 + 0.458283i
\(867\) 5.20820 + 16.0292i 0.176880 + 0.544380i
\(868\) 4.61803 0.156746
\(869\) −44.0689 + 19.0211i −1.49493 + 0.645248i
\(870\) 1.52786 0.0517994
\(871\) −7.52786 23.1684i −0.255072 0.785031i
\(872\) 3.35410 + 2.43690i 0.113584 + 0.0825238i
\(873\) 8.23607 5.98385i 0.278749 0.202523i
\(874\) −7.28115 + 22.4091i −0.246289 + 0.757999i
\(875\) 1.83688 5.65334i 0.0620979 0.191118i
\(876\) −8.23607 + 5.98385i −0.278271 + 0.202176i
\(877\) −9.32624 6.77591i −0.314925 0.228806i 0.419082 0.907948i \(-0.362352\pi\)
−0.734007 + 0.679142i \(0.762352\pi\)
\(878\) −7.60739 23.4131i −0.256737 0.790155i
\(879\) −19.0902 −0.643895
\(880\) −1.04508 + 1.76336i −0.0352298 + 0.0594427i
\(881\) 34.8541 1.17426 0.587132 0.809491i \(-0.300257\pi\)
0.587132 + 0.809491i \(0.300257\pi\)
\(882\) −0.309017 0.951057i −0.0104051 0.0320237i
\(883\) −44.3607 32.2299i −1.49286 1.08462i −0.973121 0.230296i \(-0.926031\pi\)
−0.519735 0.854328i \(-0.673969\pi\)
\(884\) −0.618034 + 0.449028i −0.0207867 + 0.0151024i
\(885\) −1.00000 + 3.07768i −0.0336146 + 0.103455i
\(886\) −0.354102 + 1.08981i −0.0118963 + 0.0366130i
\(887\) 1.00000 0.726543i 0.0335767 0.0243949i −0.570870 0.821040i \(-0.693394\pi\)
0.604447 + 0.796645i \(0.293394\pi\)
\(888\) −3.11803 2.26538i −0.104634 0.0760213i
\(889\) 1.52786 + 4.70228i 0.0512429 + 0.157709i
\(890\) −9.76393 −0.327288
\(891\) −2.19098 2.48990i −0.0734007 0.0834147i
\(892\) −4.56231 −0.152757
\(893\) −9.70820 29.8788i −0.324873 0.999855i
\(894\) 0 0
\(895\) −8.01722 + 5.82485i −0.267986 + 0.194703i
\(896\) −0.309017 + 0.951057i −0.0103235 + 0.0317726i
\(897\) 3.00000 9.23305i 0.100167 0.308283i
\(898\) 19.0344 13.8293i 0.635188 0.461491i
\(899\) 9.23607 + 6.71040i 0.308040 + 0.223804i
\(900\) −1.42705 4.39201i −0.0475684 0.146400i
\(901\) 0.180340 0.00600799
\(902\) −8.47214 1.90211i −0.282091 0.0633334i
\(903\) −10.0000 −0.332779
\(904\) 3.56231 + 10.9637i 0.118481 + 0.364646i
\(905\) 8.85410 + 6.43288i 0.294320 + 0.213836i
\(906\) −5.85410 + 4.25325i −0.194490 + 0.141305i
\(907\) 9.61803 29.6013i 0.319362 0.982894i −0.654560 0.756010i \(-0.727146\pi\)
0.973922 0.226884i \(-0.0728538\pi\)
\(908\) −2.23607 + 6.88191i −0.0742065 + 0.228384i
\(909\) 9.20820 6.69015i 0.305417 0.221898i
\(910\) −1.00000 0.726543i −0.0331497 0.0240847i
\(911\) −15.2361 46.8918i −0.504793 1.55359i −0.801118 0.598507i \(-0.795761\pi\)
0.296324 0.955087i \(-0.404239\pi\)
\(912\) 4.85410 0.160735
\(913\) 8.94427 + 2.00811i 0.296012 + 0.0664589i
\(914\) −18.3607 −0.607317
\(915\) 2.32624 + 7.15942i 0.0769031 + 0.236683i
\(916\) 3.23607 + 2.35114i 0.106923 + 0.0776839i
\(917\) 0 0
\(918\) 0.118034 0.363271i 0.00389570 0.0119897i
\(919\) 17.9443 55.2268i 0.591927 1.82176i 0.0224626 0.999748i \(-0.492849\pi\)
0.569464 0.822016i \(-0.307151\pi\)
\(920\) 2.42705 1.76336i 0.0800175 0.0581361i
\(921\) 0.354102 + 0.257270i 0.0116681 + 0.00847734i
\(922\) −6.50658 20.0252i −0.214283 0.659494i
\(923\) 12.9443 0.426066
\(924\) 2.19098 + 2.48990i 0.0720780 + 0.0819116i
\(925\) −17.7984 −0.585207
\(926\) 11.9098 + 36.6547i 0.391381 + 1.20455i
\(927\) −6.92705 5.03280i −0.227514 0.165299i
\(928\) −2.00000 + 1.45309i −0.0656532 + 0.0476999i
\(929\) −3.35410 + 10.3229i −0.110045 + 0.338682i −0.990881 0.134738i \(-0.956981\pi\)
0.880837 + 0.473420i \(0.156981\pi\)
\(930\) −0.881966 + 2.71441i −0.0289208 + 0.0890091i
\(931\) 3.92705 2.85317i 0.128704 0.0935089i
\(932\) −0.618034 0.449028i −0.0202444 0.0147084i
\(933\) −10.0344 30.8828i −0.328513 1.01106i
\(934\) −27.8885 −0.912541
\(935\) −0.399187 + 0.673542i −0.0130548 + 0.0220272i
\(936\) −2.00000 −0.0653720
\(937\) 1.43769 + 4.42477i 0.0469674 + 0.144551i 0.971790 0.235848i \(-0.0757867\pi\)
−0.924823 + 0.380399i \(0.875787\pi\)
\(938\) −9.85410 7.15942i −0.321748 0.233763i
\(939\) 14.3262 10.4086i 0.467519 0.339673i
\(940\) −1.23607 + 3.80423i −0.0403161 + 0.124080i
\(941\) −6.15248 + 18.9354i −0.200565 + 0.617276i 0.799301 + 0.600930i \(0.205203\pi\)
−0.999866 + 0.0163452i \(0.994797\pi\)
\(942\) −3.00000 + 2.17963i −0.0977453 + 0.0710161i
\(943\) 10.2812 + 7.46969i 0.334800 + 0.243247i
\(944\) −1.61803 4.97980i −0.0526625 0.162079i
\(945\) 0.618034 0.0201046
\(946\) 30.4508 13.1433i 0.990043 0.427325i
\(947\) 33.9230 1.10235 0.551174 0.834390i \(-0.314180\pi\)
0.551174 + 0.834390i \(0.314180\pi\)
\(948\) −4.47214 13.7638i −0.145248 0.447028i
\(949\) 16.4721 + 11.9677i 0.534708 + 0.388488i
\(950\) 18.1353 13.1760i 0.588385 0.427487i
\(951\) 4.14590 12.7598i 0.134440 0.413764i
\(952\) −0.118034 + 0.363271i −0.00382550 + 0.0117737i
\(953\) 9.70820 7.05342i 0.314480 0.228483i −0.419337 0.907831i \(-0.637737\pi\)
0.733816 + 0.679348i \(0.237737\pi\)
\(954\) 0.381966 + 0.277515i 0.0123666 + 0.00898487i
\(955\) 2.79180 + 8.59226i 0.0903404 + 0.278039i
\(956\) −25.7984 −0.834379
\(957\) 0.763932 + 8.16348i 0.0246944 + 0.263888i
\(958\) 18.4721 0.596808
\(959\) 1.61803 + 4.97980i 0.0522490 + 0.160806i
\(960\) −0.500000 0.363271i −0.0161374 0.0117245i
\(961\) 7.82624 5.68609i 0.252459 0.183422i
\(962\) −2.38197 + 7.33094i −0.0767977 + 0.236359i
\(963\) 0.354102 1.08981i 0.0114108 0.0351188i
\(964\) −23.5623 + 17.1190i −0.758891 + 0.551366i
\(965\) 9.07295 + 6.59188i 0.292069 + 0.212200i
\(966\) −1.50000 4.61653i −0.0482617 0.148534i
\(967\) −30.0000 −0.964735 −0.482367 0.875969i \(-0.660223\pi\)
−0.482367 + 0.875969i \(0.660223\pi\)
\(968\) −9.94427 4.70228i −0.319621 0.151137i
\(969\) 1.85410 0.0595623
\(970\) −1.94427 5.98385i −0.0624268 0.192130i
\(971\) −14.0344 10.1966i −0.450387 0.327225i 0.339362 0.940656i \(-0.389789\pi\)
−0.789748 + 0.613431i \(0.789789\pi\)
\(972\) 0.809017 0.587785i 0.0259492 0.0188532i
\(973\) −0.500000 + 1.53884i −0.0160293 + 0.0493330i
\(974\) 0.729490 2.24514i 0.0233744 0.0719389i
\(975\) −7.47214 + 5.42882i −0.239300 + 0.173862i
\(976\) −9.85410 7.15942i −0.315422 0.229168i
\(977\) −3.70820 11.4127i −0.118636 0.365124i 0.874052 0.485832i \(-0.161483\pi\)
−0.992688 + 0.120708i \(0.961483\pi\)
\(978\) 10.0000 0.319765
\(979\) −4.88197 52.1694i −0.156028 1.66734i
\(980\) −0.618034 −0.0197424
\(981\) 1.28115 + 3.94298i 0.0409041 + 0.125890i
\(982\) 5.07295 + 3.68571i 0.161884 + 0.117616i
\(983\) −40.7426 + 29.6013i −1.29949 + 0.944134i −0.999950 0.00995062i \(-0.996833\pi\)
−0.299538 + 0.954084i \(0.596833\pi\)
\(984\) 0.809017 2.48990i 0.0257905 0.0793751i
\(985\) −3.85410 + 11.8617i −0.122802 + 0.377945i
\(986\) −0.763932 + 0.555029i −0.0243286 + 0.0176757i
\(987\) 5.23607 + 3.80423i 0.166666 + 0.121090i
\(988\) −3.00000 9.23305i −0.0954427 0.293742i
\(989\) −48.5410 −1.54351
\(990\) −1.88197 + 0.812299i −0.0598128 + 0.0258166i
\(991\) −1.59675 −0.0507224 −0.0253612 0.999678i \(-0.508074\pi\)
−0.0253612 + 0.999678i \(0.508074\pi\)
\(992\) −1.42705 4.39201i −0.0453089 0.139446i
\(993\) 2.23607 + 1.62460i 0.0709595 + 0.0515551i
\(994\) 5.23607 3.80423i 0.166078 0.120663i
\(995\) −0.836881 + 2.57565i −0.0265309 + 0.0816538i
\(996\) −0.854102 + 2.62866i −0.0270633 + 0.0832921i
\(997\) 46.9787 34.1320i 1.48783 1.08097i 0.512904 0.858446i \(-0.328570\pi\)
0.974927 0.222526i \(-0.0714304\pi\)
\(998\) 22.2705 + 16.1805i 0.704961 + 0.512184i
\(999\) −1.19098 3.66547i −0.0376810 0.115970i
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 462.2.j.d.379.1 yes 4
11.3 even 5 5082.2.a.bf.1.1 2
11.8 odd 10 5082.2.a.bp.1.1 2
11.9 even 5 inner 462.2.j.d.295.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.j.d.295.1 4 11.9 even 5 inner
462.2.j.d.379.1 yes 4 1.1 even 1 trivial
5082.2.a.bf.1.1 2 11.3 even 5
5082.2.a.bp.1.1 2 11.8 odd 10