Properties

Label 504.2.bf.b.115.12
Level $504$
Weight $2$
Character 504.115
Analytic conductor $4.024$
Analytic rank $0$
Dimension $180$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(115,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.bf (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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(180\)
Relative dimension: \(90\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 115.12
Character \(\chi\) \(=\) 504.115
Dual form 504.2.bf.b.355.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32350 + 0.498350i) q^{2} +(0.336489 + 1.69905i) q^{3} +(1.50330 - 1.31913i) q^{4} +(-0.402355 + 0.696900i) q^{5} +(-1.29206 - 2.08100i) q^{6} +(-0.321531 + 2.62614i) q^{7} +(-1.33222 + 2.49503i) q^{8} +(-2.77355 + 1.14342i) q^{9} +O(q^{10})\) \(q+(-1.32350 + 0.498350i) q^{2} +(0.336489 + 1.69905i) q^{3} +(1.50330 - 1.31913i) q^{4} +(-0.402355 + 0.696900i) q^{5} +(-1.29206 - 2.08100i) q^{6} +(-0.321531 + 2.62614i) q^{7} +(-1.33222 + 2.49503i) q^{8} +(-2.77355 + 1.14342i) q^{9} +(0.185217 - 1.12286i) q^{10} +(-2.08797 - 3.61648i) q^{11} +(2.74711 + 2.11030i) q^{12} +(2.23425 + 3.86983i) q^{13} +(-0.883190 - 3.63593i) q^{14} +(-1.31946 - 0.449123i) q^{15} +(0.519794 - 3.96608i) q^{16} +(-4.52578 - 2.61296i) q^{17} +(3.10096 - 2.89552i) q^{18} +(-2.90923 + 1.67964i) q^{19} +(0.314442 + 1.57840i) q^{20} +(-4.57014 + 0.337369i) q^{21} +(4.56570 + 3.74586i) q^{22} +(1.98398 + 1.14545i) q^{23} +(-4.68747 - 1.42396i) q^{24} +(2.17622 + 3.76932i) q^{25} +(-4.88555 - 4.00828i) q^{26} +(-2.87600 - 4.32766i) q^{27} +(2.98086 + 4.37201i) q^{28} +(4.46249 + 2.57642i) q^{29} +(1.97012 - 0.0631367i) q^{30} -9.27464 q^{31} +(1.28855 + 5.50814i) q^{32} +(5.44200 - 4.76448i) q^{33} +(7.29203 + 1.20283i) q^{34} +(-1.70079 - 1.28072i) q^{35} +(-2.66114 + 5.37758i) q^{36} +(4.27641 - 2.46899i) q^{37} +(3.01331 - 3.67282i) q^{38} +(-5.82324 + 5.09826i) q^{39} +(-1.20276 - 1.93231i) q^{40} +(-4.82128 + 2.78357i) q^{41} +(5.88045 - 2.72403i) q^{42} +(4.64279 - 8.04155i) q^{43} +(-7.90945 - 2.68233i) q^{44} +(0.319101 - 2.39295i) q^{45} +(-3.19663 - 0.527288i) q^{46} -8.89595 q^{47} +(6.91348 - 0.451386i) q^{48} +(-6.79324 - 1.68877i) q^{49} +(-4.75867 - 3.90418i) q^{50} +(2.91668 - 8.56876i) q^{51} +(8.46354 + 2.87024i) q^{52} +(-2.97069 - 1.71513i) q^{53} +(5.96307 + 4.29439i) q^{54} +3.36043 q^{55} +(-6.12396 - 4.30083i) q^{56} +(-3.83272 - 4.37775i) q^{57} +(-7.19005 - 1.18601i) q^{58} +4.09696i q^{59} +(-2.57598 + 1.06537i) q^{60} +2.15794 q^{61} +(12.2750 - 4.62201i) q^{62} +(-2.11101 - 7.65138i) q^{63} +(-4.45037 - 6.64787i) q^{64} -3.59585 q^{65} +(-4.82810 + 9.01780i) q^{66} -6.25372 q^{67} +(-10.2504 + 2.04204i) q^{68} +(-1.27860 + 3.75632i) q^{69} +(2.88923 + 0.847439i) q^{70} +10.6689i q^{71} +(0.842104 - 8.44339i) q^{72} +(5.31556 + 3.06894i) q^{73} +(-4.42940 + 5.39885i) q^{74} +(-5.67200 + 4.96585i) q^{75} +(-2.15776 + 6.36265i) q^{76} +(10.1687 - 4.32051i) q^{77} +(5.16634 - 9.64955i) q^{78} -2.38293i q^{79} +(2.55482 + 1.95802i) q^{80} +(6.38517 - 6.34268i) q^{81} +(4.99377 - 6.08673i) q^{82} +(7.13350 + 4.11853i) q^{83} +(-6.42524 + 6.53577i) q^{84} +(3.64194 - 2.10268i) q^{85} +(-2.13722 + 12.9567i) q^{86} +(-2.87589 + 8.44893i) q^{87} +(11.8049 - 0.391617i) q^{88} +(4.22836 - 2.44124i) q^{89} +(0.770195 + 3.32609i) q^{90} +(-10.8811 + 4.62318i) q^{91} +(4.49351 - 0.895177i) q^{92} +(-3.12081 - 15.7581i) q^{93} +(11.7738 - 4.43329i) q^{94} -2.70325i q^{95} +(-8.92503 + 4.04274i) q^{96} +(7.23900 + 4.17944i) q^{97} +(9.83243 - 1.15032i) q^{98} +(9.92627 + 7.64305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32350 + 0.498350i −0.935855 + 0.352386i
\(3\) 0.336489 + 1.69905i 0.194272 + 0.980948i
\(4\) 1.50330 1.31913i 0.751648 0.659565i
\(5\) −0.402355 + 0.696900i −0.179939 + 0.311663i −0.941859 0.336007i \(-0.890923\pi\)
0.761921 + 0.647670i \(0.224257\pi\)
\(6\) −1.29206 2.08100i −0.527483 0.849566i
\(7\) −0.321531 + 2.62614i −0.121527 + 0.992588i
\(8\) −1.33222 + 2.49503i −0.471011 + 0.882127i
\(9\) −2.77355 + 1.14342i −0.924517 + 0.381141i
\(10\) 0.185217 1.12286i 0.0585707 0.355079i
\(11\) −2.08797 3.61648i −0.629548 1.09041i −0.987642 0.156724i \(-0.949907\pi\)
0.358094 0.933685i \(-0.383427\pi\)
\(12\) 2.74711 + 2.11030i 0.793023 + 0.609192i
\(13\) 2.23425 + 3.86983i 0.619669 + 1.07330i 0.989546 + 0.144217i \(0.0460665\pi\)
−0.369877 + 0.929081i \(0.620600\pi\)
\(14\) −0.883190 3.63593i −0.236043 0.971743i
\(15\) −1.31946 0.449123i −0.340682 0.115963i
\(16\) 0.519794 3.96608i 0.129948 0.991521i
\(17\) −4.52578 2.61296i −1.09766 0.633736i −0.162056 0.986782i \(-0.551813\pi\)
−0.935606 + 0.353046i \(0.885146\pi\)
\(18\) 3.10096 2.89552i 0.730904 0.682480i
\(19\) −2.90923 + 1.67964i −0.667423 + 0.385337i −0.795099 0.606479i \(-0.792581\pi\)
0.127677 + 0.991816i \(0.459248\pi\)
\(20\) 0.314442 + 1.57840i 0.0703114 + 0.352942i
\(21\) −4.57014 + 0.337369i −0.997286 + 0.0736199i
\(22\) 4.56570 + 3.74586i 0.973411 + 0.798620i
\(23\) 1.98398 + 1.14545i 0.413689 + 0.238843i 0.692374 0.721539i \(-0.256565\pi\)
−0.278685 + 0.960383i \(0.589898\pi\)
\(24\) −4.68747 1.42396i −0.956825 0.290665i
\(25\) 2.17622 + 3.76932i 0.435244 + 0.753865i
\(26\) −4.88555 4.00828i −0.958136 0.786088i
\(27\) −2.87600 4.32766i −0.553487 0.832858i
\(28\) 2.98086 + 4.37201i 0.563330 + 0.826232i
\(29\) 4.46249 + 2.57642i 0.828663 + 0.478429i 0.853395 0.521265i \(-0.174540\pi\)
−0.0247314 + 0.999694i \(0.507873\pi\)
\(30\) 1.97012 0.0631367i 0.359693 0.0115271i
\(31\) −9.27464 −1.66577 −0.832887 0.553443i \(-0.813314\pi\)
−0.832887 + 0.553443i \(0.813314\pi\)
\(32\) 1.28855 + 5.50814i 0.227786 + 0.973711i
\(33\) 5.44200 4.76448i 0.947331 0.829390i
\(34\) 7.29203 + 1.20283i 1.25057 + 0.206283i
\(35\) −1.70079 1.28072i −0.287485 0.216481i
\(36\) −2.66114 + 5.37758i −0.443524 + 0.896263i
\(37\) 4.27641 2.46899i 0.703038 0.405899i −0.105440 0.994426i \(-0.533625\pi\)
0.808478 + 0.588527i \(0.200292\pi\)
\(38\) 3.01331 3.67282i 0.488823 0.595810i
\(39\) −5.82324 + 5.09826i −0.932465 + 0.816375i
\(40\) −1.20276 1.93231i −0.190173 0.305526i
\(41\) −4.82128 + 2.78357i −0.752958 + 0.434720i −0.826762 0.562552i \(-0.809819\pi\)
0.0738038 + 0.997273i \(0.476486\pi\)
\(42\) 5.88045 2.72403i 0.907372 0.420328i
\(43\) 4.64279 8.04155i 0.708019 1.22632i −0.257572 0.966259i \(-0.582923\pi\)
0.965591 0.260065i \(-0.0837441\pi\)
\(44\) −7.90945 2.68233i −1.19239 0.404376i
\(45\) 0.319101 2.39295i 0.0475688 0.356720i
\(46\) −3.19663 0.527288i −0.471318 0.0777444i
\(47\) −8.89595 −1.29761 −0.648803 0.760956i \(-0.724730\pi\)
−0.648803 + 0.760956i \(0.724730\pi\)
\(48\) 6.91348 0.451386i 0.997875 0.0651520i
\(49\) −6.79324 1.68877i −0.970462 0.241253i
\(50\) −4.75867 3.90418i −0.672977 0.552134i
\(51\) 2.91668 8.56876i 0.408417 1.19987i
\(52\) 8.46354 + 2.87024i 1.17368 + 0.398030i
\(53\) −2.97069 1.71513i −0.408056 0.235591i 0.281898 0.959444i \(-0.409036\pi\)
−0.689954 + 0.723853i \(0.742369\pi\)
\(54\) 5.96307 + 4.29439i 0.811471 + 0.584392i
\(55\) 3.36043 0.453120
\(56\) −6.12396 4.30083i −0.818348 0.574723i
\(57\) −3.83272 4.37775i −0.507657 0.579847i
\(58\) −7.19005 1.18601i −0.944100 0.155730i
\(59\) 4.09696i 0.533379i 0.963783 + 0.266689i \(0.0859298\pi\)
−0.963783 + 0.266689i \(0.914070\pi\)
\(60\) −2.57598 + 1.06537i −0.332558 + 0.137539i
\(61\) 2.15794 0.276296 0.138148 0.990412i \(-0.455885\pi\)
0.138148 + 0.990412i \(0.455885\pi\)
\(62\) 12.2750 4.62201i 1.55892 0.586996i
\(63\) −2.11101 7.65138i −0.265962 0.963984i
\(64\) −4.45037 6.64787i −0.556297 0.830984i
\(65\) −3.59585 −0.446010
\(66\) −4.82810 + 9.01780i −0.594298 + 1.11001i
\(67\) −6.25372 −0.764013 −0.382006 0.924160i \(-0.624767\pi\)
−0.382006 + 0.924160i \(0.624767\pi\)
\(68\) −10.2504 + 2.04204i −1.24305 + 0.247634i
\(69\) −1.27860 + 3.75632i −0.153925 + 0.452208i
\(70\) 2.88923 + 0.847439i 0.345329 + 0.101288i
\(71\) 10.6689i 1.26617i 0.774082 + 0.633085i \(0.218212\pi\)
−0.774082 + 0.633085i \(0.781788\pi\)
\(72\) 0.842104 8.44339i 0.0992429 0.995063i
\(73\) 5.31556 + 3.06894i 0.622139 + 0.359192i 0.777702 0.628634i \(-0.216386\pi\)
−0.155562 + 0.987826i \(0.549719\pi\)
\(74\) −4.42940 + 5.39885i −0.514908 + 0.627603i
\(75\) −5.67200 + 4.96585i −0.654946 + 0.573406i
\(76\) −2.15776 + 6.36265i −0.247512 + 0.729846i
\(77\) 10.1687 4.32051i 1.15883 0.492367i
\(78\) 5.16634 9.64955i 0.584973 1.09260i
\(79\) 2.38293i 0.268101i −0.990974 0.134051i \(-0.957202\pi\)
0.990974 0.134051i \(-0.0427985\pi\)
\(80\) 2.55482 + 1.95802i 0.285638 + 0.218913i
\(81\) 6.38517 6.34268i 0.709463 0.704743i
\(82\) 4.99377 6.08673i 0.551470 0.672167i
\(83\) 7.13350 + 4.11853i 0.783003 + 0.452067i 0.837494 0.546447i \(-0.184020\pi\)
−0.0544902 + 0.998514i \(0.517353\pi\)
\(84\) −6.42524 + 6.53577i −0.701051 + 0.713111i
\(85\) 3.64194 2.10268i 0.395024 0.228067i
\(86\) −2.13722 + 12.9567i −0.230463 + 1.39716i
\(87\) −2.87589 + 8.44893i −0.308328 + 0.905821i
\(88\) 11.8049 0.391617i 1.25840 0.0417465i
\(89\) 4.22836 2.44124i 0.448205 0.258771i −0.258867 0.965913i \(-0.583349\pi\)
0.707072 + 0.707142i \(0.250016\pi\)
\(90\) 0.770195 + 3.32609i 0.0811857 + 0.350600i
\(91\) −10.8811 + 4.62318i −1.14065 + 0.484641i
\(92\) 4.49351 0.895177i 0.468481 0.0933286i
\(93\) −3.12081 15.7581i −0.323613 1.63404i
\(94\) 11.7738 4.43329i 1.21437 0.457259i
\(95\) 2.70325i 0.277348i
\(96\) −8.92503 + 4.04274i −0.910908 + 0.412611i
\(97\) 7.23900 + 4.17944i 0.735009 + 0.424358i 0.820252 0.572003i \(-0.193833\pi\)
−0.0852428 + 0.996360i \(0.527167\pi\)
\(98\) 9.83243 1.15032i 0.993226 0.116200i
\(99\) 9.92627 + 7.64305i 0.997628 + 0.768155i
\(100\) 8.24373 + 2.79569i 0.824373 + 0.279569i
\(101\) 2.92570 + 5.06747i 0.291118 + 0.504232i 0.974074 0.226228i \(-0.0726393\pi\)
−0.682956 + 0.730459i \(0.739306\pi\)
\(102\) 0.410020 + 12.7943i 0.0405980 + 1.26682i
\(103\) −9.29575 + 16.1007i −0.915938 + 1.58645i −0.110416 + 0.993886i \(0.535218\pi\)
−0.805522 + 0.592565i \(0.798115\pi\)
\(104\) −12.6319 + 0.419052i −1.23866 + 0.0410914i
\(105\) 1.60371 3.32067i 0.156506 0.324064i
\(106\) 4.78644 + 0.789527i 0.464900 + 0.0766857i
\(107\) 0.356666 + 0.617764i 0.0344802 + 0.0597215i 0.882751 0.469842i \(-0.155689\pi\)
−0.848270 + 0.529563i \(0.822356\pi\)
\(108\) −10.0322 2.71192i −0.965351 0.260955i
\(109\) −3.75958 2.17059i −0.360102 0.207905i 0.309023 0.951054i \(-0.399998\pi\)
−0.669126 + 0.743149i \(0.733331\pi\)
\(110\) −4.44752 + 1.67467i −0.424055 + 0.159673i
\(111\) 5.63390 + 6.43506i 0.534746 + 0.610789i
\(112\) 10.2484 + 2.64027i 0.968379 + 0.249482i
\(113\) 7.27450 + 12.5998i 0.684328 + 1.18529i 0.973648 + 0.228058i \(0.0732375\pi\)
−0.289320 + 0.957232i \(0.593429\pi\)
\(114\) 7.25425 + 3.88390i 0.679423 + 0.363761i
\(115\) −1.59653 + 0.921758i −0.148877 + 0.0859544i
\(116\) 10.1071 2.01348i 0.938418 0.186947i
\(117\) −10.6217 8.17848i −0.981972 0.756101i
\(118\) −2.04172 5.42232i −0.187955 0.499165i
\(119\) 8.31718 11.0452i 0.762435 1.01251i
\(120\) 2.87838 2.69375i 0.262759 0.245905i
\(121\) −3.21928 + 5.57595i −0.292661 + 0.506905i
\(122\) −2.85603 + 1.07541i −0.258573 + 0.0973630i
\(123\) −6.35173 7.25497i −0.572717 0.654158i
\(124\) −13.9425 + 12.2345i −1.25208 + 1.09869i
\(125\) −7.52601 −0.673146
\(126\) 6.60698 + 9.07457i 0.588596 + 0.808427i
\(127\) 19.8925i 1.76517i 0.470152 + 0.882586i \(0.344199\pi\)
−0.470152 + 0.882586i \(0.655801\pi\)
\(128\) 9.20303 + 6.58060i 0.813440 + 0.581648i
\(129\) 15.2252 + 5.18245i 1.34051 + 0.456289i
\(130\) 4.75909 1.79199i 0.417400 0.157168i
\(131\) 9.34844 + 5.39733i 0.816777 + 0.471567i 0.849304 0.527904i \(-0.177022\pi\)
−0.0325266 + 0.999471i \(0.510355\pi\)
\(132\) 1.89597 14.3411i 0.165023 1.24823i
\(133\) −3.47557 8.18010i −0.301370 0.709305i
\(134\) 8.27678 3.11654i 0.715005 0.269228i
\(135\) 4.17312 0.263031i 0.359165 0.0226381i
\(136\) 12.5488 7.81092i 1.07605 0.669781i
\(137\) 1.89603 + 3.28401i 0.161988 + 0.280572i 0.935582 0.353110i \(-0.114876\pi\)
−0.773593 + 0.633682i \(0.781543\pi\)
\(138\) −0.179742 5.60867i −0.0153006 0.477442i
\(139\) 2.21663 1.27977i 0.188012 0.108549i −0.403039 0.915183i \(-0.632046\pi\)
0.591052 + 0.806634i \(0.298713\pi\)
\(140\) −4.24622 + 0.318264i −0.358871 + 0.0268982i
\(141\) −2.99339 15.1147i −0.252089 1.27288i
\(142\) −5.31686 14.1203i −0.446181 1.18495i
\(143\) 9.33011 16.1602i 0.780223 1.35139i
\(144\) 3.09324 + 11.5945i 0.257770 + 0.966206i
\(145\) −3.59101 + 2.07327i −0.298217 + 0.172176i
\(146\) −8.56454 1.41273i −0.708807 0.116918i
\(147\) 0.583465 12.1103i 0.0481234 0.998841i
\(148\) 3.17180 9.35276i 0.260720 0.768792i
\(149\) 9.48733 + 5.47751i 0.777232 + 0.448735i 0.835449 0.549569i \(-0.185208\pi\)
−0.0582162 + 0.998304i \(0.518541\pi\)
\(150\) 5.03216 9.39893i 0.410874 0.767419i
\(151\) 15.2898 8.82754i 1.24426 0.718375i 0.274303 0.961643i \(-0.411553\pi\)
0.969959 + 0.243268i \(0.0782195\pi\)
\(152\) −0.315031 9.49627i −0.0255524 0.770250i
\(153\) 15.5402 + 2.07230i 1.25635 + 0.167535i
\(154\) −11.3052 + 10.7858i −0.910997 + 0.869142i
\(155\) 3.73170 6.46349i 0.299737 0.519160i
\(156\) −2.02879 + 15.3458i −0.162433 + 1.22865i
\(157\) 24.8578 1.98387 0.991936 0.126742i \(-0.0404521\pi\)
0.991936 + 0.126742i \(0.0404521\pi\)
\(158\) 1.18753 + 3.15381i 0.0944752 + 0.250904i
\(159\) 1.91449 5.62447i 0.151829 0.446050i
\(160\) −4.35708 1.31824i −0.344457 0.104216i
\(161\) −3.64603 + 4.84192i −0.287348 + 0.381597i
\(162\) −5.28988 + 11.5766i −0.415612 + 0.909542i
\(163\) −2.85675 4.94803i −0.223758 0.387560i 0.732188 0.681102i \(-0.238499\pi\)
−0.955946 + 0.293543i \(0.905166\pi\)
\(164\) −3.57592 + 10.5444i −0.279233 + 0.823381i
\(165\) 1.13075 + 5.70954i 0.0880285 + 0.444487i
\(166\) −11.4936 1.89589i −0.892080 0.147149i
\(167\) −2.90682 5.03476i −0.224937 0.389602i 0.731364 0.681988i \(-0.238884\pi\)
−0.956300 + 0.292386i \(0.905551\pi\)
\(168\) 5.24669 11.8521i 0.404791 0.914409i
\(169\) −3.48373 + 6.03400i −0.267979 + 0.464154i
\(170\) −3.77223 + 4.59785i −0.289317 + 0.352639i
\(171\) 6.14835 7.98506i 0.470176 0.610632i
\(172\) −3.62836 18.2133i −0.276660 1.38875i
\(173\) 3.93205 0.298948 0.149474 0.988766i \(-0.452242\pi\)
0.149474 + 0.988766i \(0.452242\pi\)
\(174\) −0.404286 12.6153i −0.0306488 0.956367i
\(175\) −10.5985 + 4.50311i −0.801171 + 0.340403i
\(176\) −15.4286 + 6.40126i −1.16297 + 0.482513i
\(177\) −6.96094 + 1.37858i −0.523217 + 0.103620i
\(178\) −4.37963 + 5.33818i −0.328267 + 0.400114i
\(179\) −11.9149 + 20.6372i −0.890559 + 1.54249i −0.0513535 + 0.998681i \(0.516354\pi\)
−0.839206 + 0.543814i \(0.816980\pi\)
\(180\) −2.67691 4.01824i −0.199525 0.299502i
\(181\) 3.27658 0.243547 0.121773 0.992558i \(-0.461142\pi\)
0.121773 + 0.992558i \(0.461142\pi\)
\(182\) 12.0972 11.5414i 0.896701 0.855503i
\(183\) 0.726123 + 3.66645i 0.0536766 + 0.271032i
\(184\) −5.50105 + 3.42411i −0.405543 + 0.252428i
\(185\) 3.97364i 0.292148i
\(186\) 11.9834 + 19.3005i 0.878667 + 1.41518i
\(187\) 21.8232i 1.59587i
\(188\) −13.3732 + 11.7349i −0.975343 + 0.855856i
\(189\) 12.2898 6.16131i 0.893949 0.448170i
\(190\) 1.34717 + 3.57775i 0.0977336 + 0.259557i
\(191\) 13.4704i 0.974682i −0.873212 0.487341i \(-0.837967\pi\)
0.873212 0.487341i \(-0.162033\pi\)
\(192\) 9.79757 9.79835i 0.707079 0.707135i
\(193\) −13.5951 −0.978597 −0.489299 0.872116i \(-0.662747\pi\)
−0.489299 + 0.872116i \(0.662747\pi\)
\(194\) −11.6636 1.92393i −0.837399 0.138130i
\(195\) −1.20996 6.10953i −0.0866471 0.437512i
\(196\) −12.4399 + 6.42243i −0.888568 + 0.458745i
\(197\) 24.0837i 1.71589i 0.513739 + 0.857947i \(0.328260\pi\)
−0.513739 + 0.857947i \(0.671740\pi\)
\(198\) −16.9463 5.16881i −1.20432 0.367331i
\(199\) −6.10021 + 10.5659i −0.432432 + 0.748995i −0.997082 0.0763358i \(-0.975678\pi\)
0.564650 + 0.825331i \(0.309011\pi\)
\(200\) −12.3038 + 0.408168i −0.870010 + 0.0288618i
\(201\) −2.10430 10.6254i −0.148426 0.749457i
\(202\) −6.39754 5.24876i −0.450129 0.369302i
\(203\) −8.20087 + 10.8907i −0.575588 + 0.764379i
\(204\) −6.91868 16.7289i −0.484404 1.17125i
\(205\) 4.47993i 0.312892i
\(206\) 4.27913 25.9418i 0.298141 1.80745i
\(207\) −6.81242 0.908440i −0.473496 0.0631410i
\(208\) 16.5094 6.84970i 1.14472 0.474941i
\(209\) 12.1488 + 7.01411i 0.840349 + 0.485176i
\(210\) −0.467649 + 5.19411i −0.0322708 + 0.358428i
\(211\) −5.90798 10.2329i −0.406722 0.704463i 0.587798 0.809008i \(-0.299995\pi\)
−0.994520 + 0.104544i \(0.966662\pi\)
\(212\) −6.72830 + 1.34038i −0.462102 + 0.0920577i
\(213\) −18.1271 + 3.58998i −1.24205 + 0.245981i
\(214\) −0.779909 0.639865i −0.0533135 0.0437403i
\(215\) 3.73610 + 6.47112i 0.254800 + 0.441326i
\(216\) 14.6291 1.41033i 0.995385 0.0959607i
\(217\) 2.98209 24.3565i 0.202437 1.65343i
\(218\) 6.05751 + 0.999192i 0.410266 + 0.0676738i
\(219\) −3.42566 + 10.0641i −0.231485 + 0.680067i
\(220\) 5.05172 4.43284i 0.340587 0.298862i
\(221\) 23.3520i 1.57083i
\(222\) −10.6634 5.70913i −0.715678 0.383172i
\(223\) −11.9638 + 20.7220i −0.801158 + 1.38765i 0.117696 + 0.993050i \(0.462449\pi\)
−0.918854 + 0.394597i \(0.870884\pi\)
\(224\) −14.8795 + 1.61287i −0.994176 + 0.107765i
\(225\) −10.3458 7.96607i −0.689719 0.531071i
\(226\) −15.9069 13.0506i −1.05811 0.868111i
\(227\) 0.0501958 0.0289805i 0.00333161 0.00192351i −0.498333 0.866986i \(-0.666054\pi\)
0.501665 + 0.865062i \(0.332721\pi\)
\(228\) −11.5365 1.52519i −0.764025 0.101008i
\(229\) −6.03979 + 10.4612i −0.399120 + 0.691297i −0.993618 0.112801i \(-0.964018\pi\)
0.594497 + 0.804098i \(0.297351\pi\)
\(230\) 1.65365 2.01558i 0.109038 0.132903i
\(231\) 10.7624 + 15.8234i 0.708115 + 1.04110i
\(232\) −12.3733 + 7.70170i −0.812345 + 0.505641i
\(233\) −12.5886 21.8040i −0.824703 1.42843i −0.902146 0.431431i \(-0.858009\pi\)
0.0774422 0.996997i \(-0.475325\pi\)
\(234\) 18.1335 + 5.53091i 1.18542 + 0.361567i
\(235\) 3.57933 6.19958i 0.233490 0.404416i
\(236\) 5.40442 + 6.15894i 0.351798 + 0.400913i
\(237\) 4.04873 0.801831i 0.262993 0.0520845i
\(238\) −5.50341 + 18.7631i −0.356733 + 1.21623i
\(239\) 19.8493 11.4600i 1.28394 0.741286i 0.306377 0.951910i \(-0.400883\pi\)
0.977567 + 0.210625i \(0.0675498\pi\)
\(240\) −2.46710 + 4.99962i −0.159251 + 0.322724i
\(241\) −6.91008 + 3.98954i −0.445118 + 0.256989i −0.705766 0.708445i \(-0.749397\pi\)
0.260648 + 0.965434i \(0.416064\pi\)
\(242\) 1.48193 8.98409i 0.0952623 0.577519i
\(243\) 12.9251 + 8.71448i 0.829144 + 0.559034i
\(244\) 3.24402 2.84661i 0.207677 0.182235i
\(245\) 3.91020 4.05472i 0.249813 0.259046i
\(246\) 12.0220 + 6.43655i 0.766496 + 0.410380i
\(247\) −12.9999 7.50548i −0.827162 0.477562i
\(248\) 12.3559 23.1405i 0.784598 1.46943i
\(249\) −4.59725 + 13.5060i −0.291339 + 0.855909i
\(250\) 9.96066 3.75058i 0.629967 0.237208i
\(251\) 22.3012i 1.40764i −0.710378 0.703820i \(-0.751476\pi\)
0.710378 0.703820i \(-0.248524\pi\)
\(252\) −13.2666 8.71759i −0.835719 0.549157i
\(253\) 9.56671i 0.601454i
\(254\) −9.91340 26.3276i −0.622022 1.65194i
\(255\) 4.79802 + 5.48032i 0.300464 + 0.343191i
\(256\) −15.4596 4.12309i −0.966227 0.257693i
\(257\) 18.5562 + 10.7134i 1.15750 + 0.668285i 0.950705 0.310098i \(-0.100362\pi\)
0.206800 + 0.978383i \(0.433695\pi\)
\(258\) −22.7333 + 0.728536i −1.41531 + 0.0453567i
\(259\) 5.10891 + 12.0243i 0.317452 + 0.747155i
\(260\) −5.40562 + 4.74339i −0.335242 + 0.294172i
\(261\) −15.3229 2.04332i −0.948462 0.126478i
\(262\) −15.0624 2.48456i −0.930558 0.153497i
\(263\) −6.14609 + 3.54844i −0.378984 + 0.218806i −0.677376 0.735637i \(-0.736883\pi\)
0.298392 + 0.954443i \(0.403550\pi\)
\(264\) 4.63758 + 19.9253i 0.285424 + 1.22632i
\(265\) 2.39054 1.38018i 0.146850 0.0847839i
\(266\) 8.67647 + 9.09430i 0.531988 + 0.557607i
\(267\) 5.57060 + 6.36275i 0.340915 + 0.389394i
\(268\) −9.40118 + 8.24946i −0.574269 + 0.503916i
\(269\) −4.13772 + 7.16675i −0.252282 + 0.436964i −0.964154 0.265345i \(-0.914514\pi\)
0.711872 + 0.702309i \(0.247848\pi\)
\(270\) −5.39203 + 2.42779i −0.328149 + 0.147751i
\(271\) −7.59718 13.1587i −0.461496 0.799334i 0.537540 0.843238i \(-0.319354\pi\)
−0.999036 + 0.0439042i \(0.986020\pi\)
\(272\) −12.7157 + 16.5914i −0.771002 + 1.00600i
\(273\) −11.5164 16.9319i −0.697004 1.02477i
\(274\) −4.14597 3.40150i −0.250467 0.205492i
\(275\) 9.08779 15.7405i 0.548014 0.949188i
\(276\) 3.03297 + 7.33349i 0.182563 + 0.441424i
\(277\) 18.1365 10.4711i 1.08972 0.629150i 0.156218 0.987723i \(-0.450070\pi\)
0.933502 + 0.358573i \(0.116737\pi\)
\(278\) −2.29593 + 2.79844i −0.137701 + 0.167839i
\(279\) 25.7237 10.6048i 1.54004 0.634895i
\(280\) 5.46125 2.53732i 0.326372 0.151634i
\(281\) −6.02628 + 10.4378i −0.359497 + 0.622668i −0.987877 0.155239i \(-0.950385\pi\)
0.628379 + 0.777907i \(0.283719\pi\)
\(282\) 11.4941 + 18.5125i 0.684465 + 1.10240i
\(283\) 13.3574i 0.794018i −0.917815 0.397009i \(-0.870048\pi\)
0.917815 0.397009i \(-0.129952\pi\)
\(284\) 14.0737 + 16.0386i 0.835122 + 0.951714i
\(285\) 4.59297 0.909614i 0.272064 0.0538809i
\(286\) −4.29494 + 26.0377i −0.253965 + 1.53964i
\(287\) −5.75985 13.5564i −0.339993 0.800208i
\(288\) −9.87200 13.8038i −0.581713 0.813394i
\(289\) 5.15511 + 8.92891i 0.303242 + 0.525230i
\(290\) 3.71948 4.53355i 0.218416 0.266219i
\(291\) −4.66524 + 13.7058i −0.273481 + 0.803446i
\(292\) 12.0392 2.39839i 0.704540 0.140355i
\(293\) −5.24051 9.07683i −0.306154 0.530274i 0.671364 0.741128i \(-0.265709\pi\)
−0.977518 + 0.210854i \(0.932375\pi\)
\(294\) 5.26295 + 16.3187i 0.306942 + 0.951728i
\(295\) −2.85517 1.64843i −0.166234 0.0959754i
\(296\) 0.463079 + 13.9590i 0.0269159 + 0.811352i
\(297\) −9.64585 + 19.4370i −0.559709 + 1.12785i
\(298\) −15.2862 2.52147i −0.885505 0.146065i
\(299\) 10.2369i 0.592016i
\(300\) −1.97610 + 14.9472i −0.114090 + 0.862979i
\(301\) 19.6254 + 14.7782i 1.13119 + 0.851803i
\(302\) −15.8368 + 19.3029i −0.911303 + 1.11076i
\(303\) −7.62542 + 6.67607i −0.438069 + 0.383530i
\(304\) 5.14941 + 12.4113i 0.295339 + 0.711837i
\(305\) −0.868259 + 1.50387i −0.0497164 + 0.0861113i
\(306\) −21.6001 + 5.00177i −1.23480 + 0.285932i
\(307\) 20.4335i 1.16620i −0.812400 0.583101i \(-0.801839\pi\)
0.812400 0.583101i \(-0.198161\pi\)
\(308\) 9.58730 19.9089i 0.546287 1.13441i
\(309\) −30.4839 10.3763i −1.73417 0.590284i
\(310\) −1.71782 + 10.4141i −0.0975655 + 0.591482i
\(311\) −6.40907 −0.363425 −0.181712 0.983352i \(-0.558164\pi\)
−0.181712 + 0.983352i \(0.558164\pi\)
\(312\) −4.96247 21.3212i −0.280945 1.20707i
\(313\) 18.1502i 1.02591i −0.858415 0.512956i \(-0.828551\pi\)
0.858415 0.512956i \(-0.171449\pi\)
\(314\) −32.8993 + 12.3879i −1.85662 + 0.699089i
\(315\) 6.18162 + 1.60741i 0.348295 + 0.0905674i
\(316\) −3.14340 3.58225i −0.176830 0.201518i
\(317\) 6.32534i 0.355267i 0.984097 + 0.177633i \(0.0568441\pi\)
−0.984097 + 0.177633i \(0.943156\pi\)
\(318\) 0.269134 + 8.39807i 0.0150923 + 0.470940i
\(319\) 21.5180i 1.20478i
\(320\) 6.42353 0.426660i 0.359086 0.0238510i
\(321\) −0.929598 + 0.813865i −0.0518851 + 0.0454255i
\(322\) 2.41255 8.22527i 0.134446 0.458377i
\(323\) 17.5554 0.976806
\(324\) 1.23197 17.9578i 0.0684427 0.997655i
\(325\) −9.72443 + 16.8432i −0.539415 + 0.934293i
\(326\) 6.24675 + 5.12505i 0.345975 + 0.283850i
\(327\) 2.42289 7.11810i 0.133986 0.393632i
\(328\) −0.522081 15.7376i −0.0288271 0.868963i
\(329\) 2.86032 23.3620i 0.157695 1.28799i
\(330\) −4.34189 6.99306i −0.239013 0.384955i
\(331\) 0.843469 0.0463612 0.0231806 0.999731i \(-0.492621\pi\)
0.0231806 + 0.999731i \(0.492621\pi\)
\(332\) 16.1566 3.21865i 0.886710 0.176646i
\(333\) −9.03775 + 11.7376i −0.495266 + 0.643217i
\(334\) 6.35625 + 5.21489i 0.347798 + 0.285346i
\(335\) 2.51621 4.35821i 0.137475 0.238115i
\(336\) −1.03750 + 18.3009i −0.0566001 + 0.998397i
\(337\) −2.14033 3.70716i −0.116591 0.201942i 0.801823 0.597561i \(-0.203863\pi\)
−0.918415 + 0.395619i \(0.870530\pi\)
\(338\) 1.60367 9.72210i 0.0872282 0.528813i
\(339\) −18.9599 + 16.5994i −1.02976 + 0.901558i
\(340\) 2.70121 7.96513i 0.146494 0.431970i
\(341\) 19.3652 + 33.5415i 1.04869 + 1.81638i
\(342\) −4.15798 + 13.6322i −0.224838 + 0.737147i
\(343\) 6.61919 17.2970i 0.357403 0.933950i
\(344\) 13.8787 + 22.2970i 0.748289 + 1.20218i
\(345\) −2.10333 2.40243i −0.113239 0.129342i
\(346\) −5.20406 + 1.95954i −0.279772 + 0.105345i
\(347\) 18.3155 0.983226 0.491613 0.870814i \(-0.336407\pi\)
0.491613 + 0.870814i \(0.336407\pi\)
\(348\) 6.82193 + 16.4949i 0.365694 + 0.884220i
\(349\) −5.20017 + 9.00696i −0.278359 + 0.482131i −0.970977 0.239173i \(-0.923124\pi\)
0.692618 + 0.721304i \(0.256457\pi\)
\(350\) 11.7830 11.2416i 0.629827 0.600890i
\(351\) 10.3216 20.7987i 0.550926 1.11015i
\(352\) 17.2296 16.1609i 0.918342 0.861378i
\(353\) 18.0803 10.4387i 0.962317 0.555594i 0.0654316 0.997857i \(-0.479158\pi\)
0.896885 + 0.442263i \(0.145824\pi\)
\(354\) 8.52578 5.29353i 0.453140 0.281348i
\(355\) −7.43518 4.29270i −0.394618 0.227833i
\(356\) 3.13615 9.24767i 0.166216 0.490125i
\(357\) 21.5650 + 10.4147i 1.14134 + 0.551206i
\(358\) 5.48479 33.2510i 0.289880 1.75737i
\(359\) 11.6548 6.72889i 0.615116 0.355137i −0.159849 0.987141i \(-0.551101\pi\)
0.774965 + 0.632004i \(0.217767\pi\)
\(360\) 5.54537 + 3.98410i 0.292267 + 0.209981i
\(361\) −3.85759 + 6.68155i −0.203031 + 0.351661i
\(362\) −4.33655 + 1.63288i −0.227924 + 0.0858225i
\(363\) −10.5571 3.59347i −0.554103 0.188608i
\(364\) −10.2589 + 21.3036i −0.537715 + 1.11661i
\(365\) −4.27749 + 2.46961i −0.223894 + 0.129265i
\(366\) −2.78820 4.49068i −0.145742 0.234732i
\(367\) 7.69086 + 13.3210i 0.401459 + 0.695348i 0.993902 0.110264i \(-0.0351698\pi\)
−0.592443 + 0.805612i \(0.701836\pi\)
\(368\) 5.57422 7.27324i 0.290576 0.379144i
\(369\) 10.1893 13.2331i 0.530433 0.688890i
\(370\) −1.98026 5.25910i −0.102949 0.273408i
\(371\) 5.45934 7.24998i 0.283435 0.376400i
\(372\) −25.4785 19.5723i −1.32100 1.01478i
\(373\) −14.0368 8.10418i −0.726800 0.419618i 0.0904501 0.995901i \(-0.471169\pi\)
−0.817250 + 0.576283i \(0.804503\pi\)
\(374\) −10.8756 28.8829i −0.562362 1.49350i
\(375\) −2.53242 12.7871i −0.130773 0.660321i
\(376\) 11.8514 22.1957i 0.611187 1.14465i
\(377\) 23.0254i 1.18587i
\(378\) −13.1950 + 14.2791i −0.678677 + 0.734437i
\(379\) 26.9713 1.38542 0.692711 0.721216i \(-0.256416\pi\)
0.692711 + 0.721216i \(0.256416\pi\)
\(380\) −3.56594 4.06379i −0.182929 0.208468i
\(381\) −33.7983 + 6.69359i −1.73154 + 0.342923i
\(382\) 6.71296 + 17.8280i 0.343465 + 0.912161i
\(383\) −2.35048 + 4.07115i −0.120104 + 0.208026i −0.919808 0.392368i \(-0.871656\pi\)
0.799705 + 0.600394i \(0.204989\pi\)
\(384\) −8.08406 + 17.8507i −0.412538 + 0.910940i
\(385\) −1.08048 + 8.82496i −0.0550665 + 0.449762i
\(386\) 17.9931 6.77512i 0.915825 0.344844i
\(387\) −3.68212 + 27.6123i −0.187173 + 1.40361i
\(388\) 16.3956 3.26625i 0.832359 0.165819i
\(389\) −15.3405 + 8.85682i −0.777793 + 0.449059i −0.835647 0.549266i \(-0.814907\pi\)
0.0578548 + 0.998325i \(0.481574\pi\)
\(390\) 4.64606 + 7.48296i 0.235262 + 0.378915i
\(391\) −5.98604 10.3681i −0.302727 0.524339i
\(392\) 13.2636 14.6995i 0.669915 0.742438i
\(393\) −6.02469 + 17.6996i −0.303905 + 0.892828i
\(394\) −12.0021 31.8747i −0.604657 1.60583i
\(395\) 1.66067 + 0.958786i 0.0835572 + 0.0482418i
\(396\) 25.0043 1.60428i 1.25651 0.0806181i
\(397\) −3.92980 6.80661i −0.197231 0.341614i 0.750399 0.660986i \(-0.229862\pi\)
−0.947630 + 0.319371i \(0.896528\pi\)
\(398\) 2.80812 17.0239i 0.140758 0.853333i
\(399\) 12.7289 8.65769i 0.637243 0.433427i
\(400\) 16.0806 6.67180i 0.804032 0.333590i
\(401\) 3.55714 6.16115i 0.177635 0.307673i −0.763435 0.645885i \(-0.776489\pi\)
0.941070 + 0.338212i \(0.109822\pi\)
\(402\) 8.08020 + 13.0140i 0.403004 + 0.649079i
\(403\) −20.7218 35.8913i −1.03223 1.78787i
\(404\) 11.0828 + 3.75852i 0.551392 + 0.186993i
\(405\) 1.85111 + 7.00183i 0.0919824 + 0.347924i
\(406\) 5.42645 18.5008i 0.269310 0.918177i
\(407\) −17.8581 10.3104i −0.885192 0.511066i
\(408\) 17.4937 + 18.6927i 0.866066 + 0.925426i
\(409\) 19.6823i 0.973229i 0.873617 + 0.486615i \(0.161768\pi\)
−0.873617 + 0.486615i \(0.838232\pi\)
\(410\) 2.23257 + 5.92918i 0.110259 + 0.292822i
\(411\) −4.94171 + 4.32648i −0.243757 + 0.213409i
\(412\) 7.26467 + 36.4664i 0.357905 + 1.79657i
\(413\) −10.7592 1.31730i −0.529425 0.0648201i
\(414\) 9.46894 2.19265i 0.465373 0.107763i
\(415\) −5.74040 + 3.31422i −0.281785 + 0.162689i
\(416\) −18.4366 + 17.2930i −0.903931 + 0.847861i
\(417\) 2.92027 + 3.33554i 0.143006 + 0.163342i
\(418\) −19.5744 3.22881i −0.957414 0.157926i
\(419\) −3.99352 + 2.30566i −0.195096 + 0.112639i −0.594366 0.804195i \(-0.702597\pi\)
0.399270 + 0.916833i \(0.369264\pi\)
\(420\) −1.96955 7.10745i −0.0961042 0.346808i
\(421\) 0.244794 + 0.141332i 0.0119305 + 0.00688808i 0.505953 0.862561i \(-0.331141\pi\)
−0.494023 + 0.869449i \(0.664474\pi\)
\(422\) 12.9188 + 10.5990i 0.628876 + 0.515952i
\(423\) 24.6734 10.1718i 1.19966 0.494571i
\(424\) 8.23692 5.12704i 0.400020 0.248991i
\(425\) 22.7455i 1.10332i
\(426\) 22.2021 13.7850i 1.07570 0.667883i
\(427\) −0.693846 + 5.66706i −0.0335776 + 0.274248i
\(428\) 1.35109 + 0.458193i 0.0653072 + 0.0221476i
\(429\) 30.5965 + 10.4146i 1.47721 + 0.502822i
\(430\) −8.16960 6.70263i −0.393973 0.323229i
\(431\) −13.1372 7.58478i −0.632798 0.365346i 0.149037 0.988832i \(-0.452383\pi\)
−0.781835 + 0.623486i \(0.785716\pi\)
\(432\) −18.6588 + 9.15698i −0.897721 + 0.440565i
\(433\) 6.22569i 0.299187i −0.988748 0.149594i \(-0.952203\pi\)
0.988748 0.149594i \(-0.0477966\pi\)
\(434\) 8.19127 + 33.7219i 0.393194 + 1.61870i
\(435\) −4.73093 5.40368i −0.226831 0.259087i
\(436\) −8.51505 + 1.69633i −0.407797 + 0.0812394i
\(437\) −7.69581 −0.368141
\(438\) −0.481571 15.0270i −0.0230104 0.718016i
\(439\) −5.66768 −0.270504 −0.135252 0.990811i \(-0.543184\pi\)
−0.135252 + 0.990811i \(0.543184\pi\)
\(440\) −4.47683 + 8.38438i −0.213425 + 0.399710i
\(441\) 20.7724 3.08365i 0.989160 0.146840i
\(442\) 11.6375 + 30.9063i 0.553537 + 1.47006i
\(443\) 25.8639 1.22883 0.614416 0.788983i \(-0.289392\pi\)
0.614416 + 0.788983i \(0.289392\pi\)
\(444\) 16.9581 + 2.24194i 0.804795 + 0.106398i
\(445\) 3.92899i 0.186252i
\(446\) 5.50733 33.3877i 0.260780 1.58095i
\(447\) −6.11420 + 17.9626i −0.289192 + 0.849601i
\(448\) 18.8892 9.54981i 0.892430 0.451186i
\(449\) −38.4945 −1.81667 −0.908333 0.418247i \(-0.862645\pi\)
−0.908333 + 0.418247i \(0.862645\pi\)
\(450\) 17.6625 + 5.38726i 0.832619 + 0.253958i
\(451\) 20.1334 + 11.6240i 0.948046 + 0.547355i
\(452\) 27.5565 + 9.34522i 1.29615 + 0.439562i
\(453\) 20.1433 + 23.0077i 0.946414 + 1.08100i
\(454\) −0.0519916 + 0.0633707i −0.00244009 + 0.00297414i
\(455\) 1.15618 9.44320i 0.0542024 0.442704i
\(456\) 16.0287 3.73064i 0.750610 0.174703i
\(457\) 20.7490 0.970596 0.485298 0.874349i \(-0.338711\pi\)
0.485298 + 0.874349i \(0.338711\pi\)
\(458\) 2.78030 16.8553i 0.129915 0.787598i
\(459\) 1.70816 + 27.1009i 0.0797303 + 1.26496i
\(460\) −1.18414 + 3.49171i −0.0552108 + 0.162802i
\(461\) −10.4981 + 18.1832i −0.488944 + 0.846876i −0.999919 0.0127197i \(-0.995951\pi\)
0.510975 + 0.859595i \(0.329284\pi\)
\(462\) −22.1296 15.5788i −1.02956 0.724791i
\(463\) 0.536750 0.309893i 0.0249449 0.0144019i −0.487476 0.873137i \(-0.662082\pi\)
0.512421 + 0.858735i \(0.328749\pi\)
\(464\) 12.5379 16.3594i 0.582056 0.759466i
\(465\) 12.2375 + 4.16546i 0.567500 + 0.193168i
\(466\) 27.5269 + 22.5841i 1.27516 + 1.04619i
\(467\) 0.243873 0.140800i 0.0112851 0.00651546i −0.494347 0.869265i \(-0.664593\pi\)
0.505632 + 0.862749i \(0.331259\pi\)
\(468\) −26.7560 + 1.71667i −1.23679 + 0.0793530i
\(469\) 2.01077 16.4231i 0.0928485 0.758350i
\(470\) −1.64768 + 9.98889i −0.0760017 + 0.460753i
\(471\) 8.36438 + 42.2347i 0.385410 + 1.94607i
\(472\) −10.2220 5.45805i −0.470508 0.251227i
\(473\) −38.7761 −1.78293
\(474\) −4.95889 + 3.07890i −0.227770 + 0.141419i
\(475\) −12.6622 7.31055i −0.580984 0.335431i
\(476\) −2.06685 27.5756i −0.0947341 1.26393i
\(477\) 10.2005 + 1.36024i 0.467048 + 0.0622811i
\(478\) −20.5594 + 25.0592i −0.940366 + 1.14618i
\(479\) −12.9607 22.4486i −0.592190 1.02570i −0.993937 0.109953i \(-0.964930\pi\)
0.401746 0.915751i \(-0.368403\pi\)
\(480\) 0.773649 7.84647i 0.0353121 0.358141i
\(481\) 19.1091 + 11.0327i 0.871301 + 0.503046i
\(482\) 7.15730 8.72379i 0.326006 0.397358i
\(483\) −9.45352 4.56555i −0.430150 0.207740i
\(484\) 2.51588 + 12.6289i 0.114358 + 0.574043i
\(485\) −5.82530 + 3.36324i −0.264513 + 0.152717i
\(486\) −21.4492 5.09239i −0.972955 0.230996i
\(487\) 6.30644 + 3.64102i 0.285772 + 0.164991i 0.636034 0.771661i \(-0.280574\pi\)
−0.350262 + 0.936652i \(0.613907\pi\)
\(488\) −2.87486 + 5.38414i −0.130139 + 0.243728i
\(489\) 7.44569 6.51872i 0.336706 0.294787i
\(490\) −3.15447 + 7.31506i −0.142505 + 0.330461i
\(491\) −6.22066 10.7745i −0.280735 0.486246i 0.690831 0.723016i \(-0.257245\pi\)
−0.971566 + 0.236770i \(0.923911\pi\)
\(492\) −19.1188 2.52760i −0.861941 0.113953i
\(493\) −13.4642 23.3206i −0.606395 1.05031i
\(494\) 20.9457 + 3.45501i 0.942390 + 0.155448i
\(495\) −9.32032 + 3.84239i −0.418917 + 0.172703i
\(496\) −4.82090 + 36.7840i −0.216465 + 1.65165i
\(497\) −28.0182 3.43040i −1.25679 0.153874i
\(498\) −0.646270 20.1662i −0.0289601 0.903671i
\(499\) −0.666841 + 1.15500i −0.0298519 + 0.0517050i −0.880565 0.473925i \(-0.842837\pi\)
0.850713 + 0.525630i \(0.176170\pi\)
\(500\) −11.3138 + 9.92778i −0.505969 + 0.443984i
\(501\) 7.57621 6.63298i 0.338480 0.296340i
\(502\) 11.1138 + 29.5156i 0.496033 + 1.31735i
\(503\) 8.50358 0.379156 0.189578 0.981866i \(-0.439288\pi\)
0.189578 + 0.981866i \(0.439288\pi\)
\(504\) 21.9028 + 4.92630i 0.975627 + 0.219435i
\(505\) −4.70869 −0.209534
\(506\) 4.76757 + 12.6615i 0.211944 + 0.562873i
\(507\) −11.4243 3.88866i −0.507371 0.172702i
\(508\) 26.2407 + 29.9043i 1.16424 + 1.32679i
\(509\) −6.64663 + 11.5123i −0.294607 + 0.510274i −0.974893 0.222672i \(-0.928522\pi\)
0.680287 + 0.732946i \(0.261855\pi\)
\(510\) −9.08129 4.86210i −0.402126 0.215297i
\(511\) −9.76859 + 12.9727i −0.432137 + 0.573877i
\(512\) 22.5155 2.24740i 0.995055 0.0993220i
\(513\) 15.6359 + 7.75948i 0.690340 + 0.342589i
\(514\) −29.8981 4.93173i −1.31875 0.217529i
\(515\) −7.48039 12.9564i −0.329625 0.570928i
\(516\) 29.7244 12.2933i 1.30854 0.541184i
\(517\) 18.5745 + 32.1720i 0.816906 + 1.41492i
\(518\) −12.7539 13.3681i −0.560376 0.587362i
\(519\) 1.32309 + 6.68075i 0.0580772 + 0.293253i
\(520\) 4.79046 8.97175i 0.210076 0.393437i
\(521\) 6.47838 + 3.74030i 0.283823 + 0.163865i 0.635153 0.772386i \(-0.280937\pi\)
−0.351330 + 0.936252i \(0.614270\pi\)
\(522\) 21.2981 4.93182i 0.932192 0.215860i
\(523\) −17.3175 + 9.99829i −0.757243 + 0.437195i −0.828305 0.560277i \(-0.810695\pi\)
0.0710619 + 0.997472i \(0.477361\pi\)
\(524\) 21.1732 4.21803i 0.924957 0.184266i
\(525\) −11.2173 16.4922i −0.489563 0.719777i
\(526\) 6.36597 7.75926i 0.277569 0.338320i
\(527\) 41.9750 + 24.2343i 1.82846 + 1.05566i
\(528\) −16.0676 24.0600i −0.699253 1.04708i
\(529\) −8.87587 15.3735i −0.385908 0.668412i
\(530\) −2.47607 + 3.01799i −0.107554 + 0.131093i
\(531\) −4.68456 11.3631i −0.203292 0.493118i
\(532\) −16.0154 7.71238i −0.694357 0.334374i
\(533\) −21.5439 12.4384i −0.933169 0.538766i
\(534\) −10.5435 5.64498i −0.456264 0.244282i
\(535\) −0.574026 −0.0248173
\(536\) 8.33133 15.6032i 0.359859 0.673957i
\(537\) −39.0728 13.2998i −1.68612 0.573929i
\(538\) 1.90472 11.5472i 0.0821185 0.497836i
\(539\) 8.07669 + 28.0937i 0.347888 + 1.21008i
\(540\) 5.92645 5.90029i 0.255034 0.253908i
\(541\) −23.1061 + 13.3403i −0.993408 + 0.573544i −0.906291 0.422654i \(-0.861099\pi\)
−0.0871169 + 0.996198i \(0.527765\pi\)
\(542\) 16.6125 + 13.6295i 0.713567 + 0.585436i
\(543\) 1.10253 + 5.56709i 0.0473143 + 0.238907i
\(544\) 8.56086 28.2956i 0.367044 1.21316i
\(545\) 3.02537 1.74670i 0.129593 0.0748204i
\(546\) 23.6799 + 16.6702i 1.01341 + 0.713417i
\(547\) −10.4812 + 18.1539i −0.448142 + 0.776205i −0.998265 0.0588790i \(-0.981247\pi\)
0.550123 + 0.835083i \(0.314581\pi\)
\(548\) 7.18232 + 2.43574i 0.306814 + 0.104050i
\(549\) −5.98516 + 2.46744i −0.255441 + 0.105308i
\(550\) −4.18339 + 25.3614i −0.178381 + 1.08142i
\(551\) −17.3099 −0.737425
\(552\) −7.66877 8.19439i −0.326405 0.348776i
\(553\) 6.25792 + 0.766188i 0.266114 + 0.0325816i
\(554\) −18.7854 + 22.8969i −0.798115 + 0.972795i
\(555\) −6.75142 + 1.33708i −0.286582 + 0.0567561i
\(556\) 1.64407 4.84790i 0.0697239 0.205597i
\(557\) 15.0606 + 8.69525i 0.638139 + 0.368430i 0.783897 0.620891i \(-0.213229\pi\)
−0.145758 + 0.989320i \(0.546562\pi\)
\(558\) −28.7603 + 26.8549i −1.21752 + 1.13686i
\(559\) 41.4926 1.75495
\(560\) −5.96349 + 6.07975i −0.252003 + 0.256916i
\(561\) −37.0787 + 7.34325i −1.56546 + 0.310032i
\(562\) 2.77408 16.8176i 0.117018 0.709409i
\(563\) 31.9460i 1.34636i 0.739477 + 0.673182i \(0.235073\pi\)
−0.739477 + 0.673182i \(0.764927\pi\)
\(564\) −24.4381 18.7731i −1.02903 0.790492i
\(565\) −11.7077 −0.492548
\(566\) 6.65668 + 17.6786i 0.279801 + 0.743085i
\(567\) 14.6038 + 18.8077i 0.613300 + 0.789850i
\(568\) −26.6194 14.2134i −1.11692 0.596381i
\(569\) −4.90634 −0.205684 −0.102842 0.994698i \(-0.532794\pi\)
−0.102842 + 0.994698i \(0.532794\pi\)
\(570\) −5.62548 + 3.49278i −0.235625 + 0.146296i
\(571\) 6.78557 0.283967 0.141984 0.989869i \(-0.454652\pi\)
0.141984 + 0.989869i \(0.454652\pi\)
\(572\) −7.29152 36.6012i −0.304874 1.53037i
\(573\) 22.8869 4.53263i 0.956112 0.189353i
\(574\) 14.3790 + 15.0714i 0.600167 + 0.629069i
\(575\) 9.97103i 0.415821i
\(576\) 19.9447 + 13.3495i 0.831028 + 0.556231i
\(577\) −1.74178 1.00562i −0.0725112 0.0418644i 0.463306 0.886198i \(-0.346663\pi\)
−0.535817 + 0.844334i \(0.679996\pi\)
\(578\) −11.2725 9.24835i −0.468874 0.384681i
\(579\) −4.57460 23.0988i −0.190114 0.959953i
\(580\) −2.66344 + 7.85375i −0.110593 + 0.326109i
\(581\) −13.1095 + 17.4093i −0.543873 + 0.722261i
\(582\) −0.655828 20.4645i −0.0271849 0.848280i
\(583\) 14.3246i 0.593263i
\(584\) −14.7386 + 9.17399i −0.609888 + 0.379623i
\(585\) 9.97326 4.11157i 0.412344 0.169993i
\(586\) 11.4592 + 9.40156i 0.473377 + 0.388375i
\(587\) −23.1528 13.3673i −0.955618 0.551726i −0.0607963 0.998150i \(-0.519364\pi\)
−0.894822 + 0.446424i \(0.852697\pi\)
\(588\) −15.0979 18.9750i −0.622629 0.782517i
\(589\) 26.9820 15.5781i 1.11178 0.641884i
\(590\) 4.60031 + 0.758825i 0.189392 + 0.0312403i
\(591\) −40.9195 + 8.10390i −1.68320 + 0.333350i
\(592\) −7.56936 18.2440i −0.311099 0.749822i
\(593\) 11.4452 6.60786i 0.469996 0.271352i −0.246242 0.969208i \(-0.579196\pi\)
0.716238 + 0.697856i \(0.245862\pi\)
\(594\) 3.07983 30.5319i 0.126367 1.25274i
\(595\) 4.35092 + 10.2403i 0.178370 + 0.419812i
\(596\) 21.4878 4.28070i 0.880175 0.175344i
\(597\) −20.0046 6.80927i −0.818734 0.278685i
\(598\) −5.10156 13.5485i −0.208618 0.554041i
\(599\) 4.85144i 0.198225i −0.995076 0.0991123i \(-0.968400\pi\)
0.995076 0.0991123i \(-0.0316003\pi\)
\(600\) −4.83359 20.7674i −0.197330 0.847827i
\(601\) 15.7458 + 9.09083i 0.642284 + 0.370823i 0.785494 0.618869i \(-0.212409\pi\)
−0.143210 + 0.989692i \(0.545742\pi\)
\(602\) −33.3390 9.77863i −1.35879 0.398547i
\(603\) 17.3450 7.15064i 0.706343 0.291197i
\(604\) 11.3403 33.4396i 0.461432 1.36064i
\(605\) −2.59058 4.48702i −0.105322 0.182423i
\(606\) 6.76522 12.6359i 0.274818 0.513298i
\(607\) 17.5622 30.4187i 0.712830 1.23466i −0.250961 0.967997i \(-0.580747\pi\)
0.963791 0.266660i \(-0.0859201\pi\)
\(608\) −13.0004 13.8601i −0.527236 0.562103i
\(609\) −21.2634 10.2691i −0.861637 0.416125i
\(610\) 0.399687 2.42306i 0.0161829 0.0981070i
\(611\) −19.8758 34.4258i −0.804087 1.39272i
\(612\) 26.0951 17.3843i 1.05483 0.702717i
\(613\) −21.3502 12.3266i −0.862328 0.497866i 0.00246295 0.999997i \(-0.499216\pi\)
−0.864791 + 0.502131i \(0.832549\pi\)
\(614\) 10.1830 + 27.0437i 0.410954 + 1.09140i
\(615\) 7.61164 1.50745i 0.306931 0.0607861i
\(616\) −2.76720 + 31.1272i −0.111493 + 1.25415i
\(617\) −3.16618 5.48398i −0.127465 0.220777i 0.795228 0.606310i \(-0.207351\pi\)
−0.922694 + 0.385533i \(0.874018\pi\)
\(618\) 45.5163 1.45867i 1.83094 0.0586763i
\(619\) 6.30854 3.64224i 0.253561 0.146394i −0.367832 0.929892i \(-0.619900\pi\)
0.621394 + 0.783498i \(0.286567\pi\)
\(620\) −2.91634 14.6391i −0.117123 0.587922i
\(621\) −0.748814 11.8803i −0.0300489 0.476741i
\(622\) 8.48239 3.19396i 0.340113 0.128066i
\(623\) 5.05150 + 11.8892i 0.202384 + 0.476331i
\(624\) 17.1932 + 25.7455i 0.688280 + 1.03065i
\(625\) −7.85298 + 13.6018i −0.314119 + 0.544070i
\(626\) 9.04516 + 24.0218i 0.361517 + 0.960104i
\(627\) −7.82940 + 23.0016i −0.312676 + 0.918595i
\(628\) 37.3687 32.7907i 1.49117 1.30849i
\(629\) −25.8055 −1.02893
\(630\) −8.98242 + 0.953200i −0.357868 + 0.0379764i
\(631\) 24.0110i 0.955862i −0.878397 0.477931i \(-0.841387\pi\)
0.878397 0.477931i \(-0.158613\pi\)
\(632\) 5.94550 + 3.17460i 0.236499 + 0.126279i
\(633\) 15.3983 13.4812i 0.612027 0.535831i
\(634\) −3.15223 8.37158i −0.125191 0.332478i
\(635\) −13.8631 8.00384i −0.550138 0.317623i
\(636\) −4.54137 10.9807i −0.180077 0.435413i
\(637\) −8.64251 30.0618i −0.342429 1.19109i
\(638\) 10.7235 + 28.4790i 0.424547 + 1.12750i
\(639\) −12.1991 29.5909i −0.482590 1.17060i
\(640\) −8.28890 + 3.76585i −0.327648 + 0.148858i
\(641\) −15.6097 27.0369i −0.616548 1.06789i −0.990111 0.140287i \(-0.955197\pi\)
0.373563 0.927605i \(-0.378136\pi\)
\(642\) 0.824733 1.54041i 0.0325496 0.0607953i
\(643\) 38.4887 22.2215i 1.51785 0.876329i 0.518066 0.855340i \(-0.326652\pi\)
0.999780 0.0209884i \(-0.00668129\pi\)
\(644\) 0.906055 + 12.0884i 0.0357036 + 0.476351i
\(645\) −9.73760 + 8.52528i −0.383418 + 0.335683i
\(646\) −23.2345 + 8.74871i −0.914149 + 0.344213i
\(647\) −5.36870 + 9.29886i −0.211065 + 0.365576i −0.952048 0.305948i \(-0.901027\pi\)
0.740983 + 0.671524i \(0.234360\pi\)
\(648\) 7.31875 + 24.3811i 0.287508 + 0.957778i
\(649\) 14.8166 8.55435i 0.581601 0.335787i
\(650\) 4.47646 27.1381i 0.175581 1.06445i
\(651\) 42.3864 3.12897i 1.66125 0.122634i
\(652\) −10.8216 3.66993i −0.423808 0.143726i
\(653\) 35.9305 + 20.7445i 1.40607 + 0.811794i 0.995006 0.0998130i \(-0.0318244\pi\)
0.411063 + 0.911607i \(0.365158\pi\)
\(654\) 0.340605 + 10.6282i 0.0133187 + 0.415597i
\(655\) −7.52279 + 4.34328i −0.293940 + 0.169706i
\(656\) 8.53379 + 20.5685i 0.333189 + 0.803065i
\(657\) −18.2521 2.43393i −0.712081 0.0949565i
\(658\) 7.85681 + 32.3450i 0.306290 + 1.26094i
\(659\) 20.8734 36.1538i 0.813113 1.40835i −0.0975613 0.995230i \(-0.531104\pi\)
0.910675 0.413124i \(-0.135562\pi\)
\(660\) 9.23147 + 7.09153i 0.359335 + 0.276037i
\(661\) −19.9630 −0.776469 −0.388235 0.921561i \(-0.626915\pi\)
−0.388235 + 0.921561i \(0.626915\pi\)
\(662\) −1.11633 + 0.420342i −0.0433874 + 0.0163371i
\(663\) 39.6762 7.85768i 1.54090 0.305167i
\(664\) −19.7793 + 12.3115i −0.767584 + 0.477780i
\(665\) 7.09912 + 0.869180i 0.275292 + 0.0337054i
\(666\) 6.11201 20.0387i 0.236836 0.776483i
\(667\) 5.90233 + 10.2231i 0.228539 + 0.395842i
\(668\) −11.0113 3.73426i −0.426041 0.144483i
\(669\) −39.2334 13.3545i −1.51685 0.516314i
\(670\) −1.15829 + 7.02204i −0.0447487 + 0.271285i
\(671\) −4.50573 7.80415i −0.173942 0.301276i
\(672\) −7.74713 24.7383i −0.298852 0.954299i
\(673\) 20.9561 36.2970i 0.807798 1.39915i −0.106587 0.994303i \(-0.533992\pi\)
0.914386 0.404844i \(-0.132674\pi\)
\(674\) 4.68019 + 3.83979i 0.180274 + 0.147903i
\(675\) 10.0535 20.2585i 0.386960 0.779751i
\(676\) 2.72255 + 13.6664i 0.104713 + 0.525630i
\(677\) −2.86286 −0.110028 −0.0550142 0.998486i \(-0.517520\pi\)
−0.0550142 + 0.998486i \(0.517520\pi\)
\(678\) 16.8211 31.4180i 0.646011 1.20660i
\(679\) −13.3034 + 17.6668i −0.510536 + 0.677990i
\(680\) 0.394374 + 11.8880i 0.0151236 + 0.455883i
\(681\) 0.0661297 + 0.0755336i 0.00253410 + 0.00289445i
\(682\) −42.3452 34.7415i −1.62148 1.33032i
\(683\) −15.0873 + 26.1319i −0.577298 + 0.999909i 0.418490 + 0.908221i \(0.362559\pi\)
−0.995788 + 0.0916875i \(0.970774\pi\)
\(684\) −1.29054 20.1144i −0.0493451 0.769092i
\(685\) −3.05150 −0.116592
\(686\) −0.140538 + 26.1912i −0.00536576 + 0.999986i
\(687\) −19.8065 6.74183i −0.755664 0.257217i
\(688\) −29.4802 22.5936i −1.12392 0.861374i
\(689\) 15.3281i 0.583954i
\(690\) 3.98100 + 2.13142i 0.151554 + 0.0811416i
\(691\) 31.0315i 1.18049i 0.807222 + 0.590247i \(0.200970\pi\)
−0.807222 + 0.590247i \(0.799030\pi\)
\(692\) 5.91103 5.18688i 0.224704 0.197176i
\(693\) −23.2633 + 23.6103i −0.883701 + 0.896881i
\(694\) −24.2405 + 9.12751i −0.920156 + 0.346475i
\(695\) 2.05969i 0.0781286i
\(696\) −17.2490 18.4313i −0.653823 0.698636i
\(697\) 29.0934 1.10199
\(698\) 2.39380 14.5122i 0.0906067 0.549295i
\(699\) 32.8102 28.7254i 1.24100 1.08649i
\(700\) −9.99250 + 20.7503i −0.377681 + 0.784288i
\(701\) 39.4997i 1.49188i −0.666012 0.745941i \(-0.732000\pi\)
0.666012 0.745941i \(-0.268000\pi\)
\(702\) −3.29558 + 32.6708i −0.124384 + 1.23308i
\(703\) −8.29404 + 14.3657i −0.312816 + 0.541812i
\(704\) −14.7496 + 29.9753i −0.555897 + 1.12974i
\(705\) 11.7378 + 3.99538i 0.442071 + 0.150475i
\(706\) −18.7271 + 22.8259i −0.704805 + 0.859063i
\(707\) −14.2486 + 6.05396i −0.535874 + 0.227683i
\(708\) −8.64583 + 11.2548i −0.324930 + 0.422981i
\(709\) 29.9484i 1.12473i 0.826888 + 0.562367i \(0.190109\pi\)
−0.826888 + 0.562367i \(0.809891\pi\)
\(710\) 11.9797 + 1.97607i 0.449591 + 0.0741605i
\(711\) 2.72470 + 6.60919i 0.102184 + 0.247864i
\(712\) 0.457875 + 13.8022i 0.0171596 + 0.517258i
\(713\) −18.4007 10.6237i −0.689113 0.397859i
\(714\) −33.7314 3.03699i −1.26237 0.113656i
\(715\) 7.50803 + 13.0043i 0.280785 + 0.486333i
\(716\) 9.31153 + 46.7410i 0.347988 + 1.74679i
\(717\) 26.1502 + 29.8688i 0.976597 + 1.11547i
\(718\) −12.0717 + 14.7138i −0.450514 + 0.549116i
\(719\) 14.1334 + 24.4797i 0.527086 + 0.912939i 0.999502 + 0.0315633i \(0.0100486\pi\)
−0.472416 + 0.881376i \(0.656618\pi\)
\(720\) −9.32477 2.50942i −0.347513 0.0935206i
\(721\) −39.2939 29.5888i −1.46338 1.10195i
\(722\) 1.77577 10.7655i 0.0660874 0.400649i
\(723\) −9.10360 10.3982i −0.338566 0.386711i
\(724\) 4.92567 4.32224i 0.183061 0.160635i
\(725\) 22.4274i 0.832934i
\(726\) 15.7631 0.505162i 0.585023 0.0187483i
\(727\) 5.30381 9.18647i 0.196707 0.340707i −0.750751 0.660585i \(-0.770308\pi\)
0.947459 + 0.319877i \(0.103642\pi\)
\(728\) 2.96105 33.3078i 0.109744 1.23447i
\(729\) −10.4572 + 24.8927i −0.387304 + 0.921952i
\(730\) 4.43052 5.40021i 0.163981 0.199871i
\(731\) −42.0245 + 24.2628i −1.55433 + 0.897393i
\(732\) 5.92811 + 4.55391i 0.219109 + 0.168317i
\(733\) 23.2029 40.1886i 0.857019 1.48440i −0.0177408 0.999843i \(-0.505647\pi\)
0.874760 0.484557i \(-0.161019\pi\)
\(734\) −16.8173 13.7975i −0.620739 0.509276i
\(735\) 8.20491 + 5.27926i 0.302643 + 0.194728i
\(736\) −3.75286 + 12.4040i −0.138332 + 0.457219i
\(737\) 13.0576 + 22.6164i 0.480983 + 0.833087i
\(738\) −6.89076 + 22.5919i −0.253652 + 0.831618i
\(739\) −5.83019 + 10.0982i −0.214467 + 0.371468i −0.953108 0.302632i \(-0.902135\pi\)
0.738641 + 0.674100i \(0.235468\pi\)
\(740\) 5.24175 + 5.97355i 0.192690 + 0.219592i
\(741\) 8.37789 24.6130i 0.307769 0.904180i
\(742\) −3.61240 + 12.3160i −0.132615 + 0.452135i
\(743\) −36.6987 + 21.1880i −1.34635 + 0.777313i −0.987730 0.156172i \(-0.950084\pi\)
−0.358616 + 0.933485i \(0.616751\pi\)
\(744\) 43.4746 + 13.2067i 1.59385 + 0.484182i
\(745\) −7.63455 + 4.40781i −0.279708 + 0.161490i
\(746\) 22.6165 + 3.73061i 0.828047 + 0.136587i
\(747\) −24.4943 3.26634i −0.896201 0.119509i
\(748\) 28.7876 + 32.8067i 1.05258 + 1.19953i
\(749\) −1.73701 + 0.738025i −0.0634691 + 0.0269669i
\(750\) 9.72408 + 15.6616i 0.355073 + 0.571882i
\(751\) −17.3263 10.0033i −0.632244 0.365026i 0.149377 0.988780i \(-0.452273\pi\)
−0.781621 + 0.623754i \(0.785607\pi\)
\(752\) −4.62405 + 35.2821i −0.168622 + 1.28660i
\(753\) 37.8909 7.50411i 1.38082 0.273465i
\(754\) −11.4747 30.4741i −0.417885 1.10980i
\(755\) 14.2072i 0.517054i
\(756\) 10.3476 25.4741i 0.376337 0.926483i
\(757\) 37.2793i 1.35494i 0.735551 + 0.677470i \(0.236923\pi\)
−0.735551 + 0.677470i \(0.763077\pi\)
\(758\) −35.6964 + 13.4411i −1.29655 + 0.488204i
\(759\) 16.2543 3.21909i 0.589995 0.116846i
\(760\) 6.74470 + 3.60133i 0.244656 + 0.130634i
\(761\) 36.5541 + 21.1045i 1.32508 + 0.765038i 0.984535 0.175189i \(-0.0560537\pi\)
0.340549 + 0.940227i \(0.389387\pi\)
\(762\) 41.3963 25.7023i 1.49963 0.931097i
\(763\) 6.90911 9.17527i 0.250126 0.332167i
\(764\) −17.7692 20.2500i −0.642866 0.732618i
\(765\) −7.69686 + 9.99615i −0.278280 + 0.361412i
\(766\) 1.08200 6.55952i 0.0390942 0.237005i
\(767\) −15.8545 + 9.15362i −0.572474 + 0.330518i
\(768\) 1.80335 27.6541i 0.0650727 0.997881i
\(769\) −14.8881 + 8.59566i −0.536880 + 0.309968i −0.743813 0.668387i \(-0.766985\pi\)
0.206934 + 0.978355i \(0.433652\pi\)
\(770\) −2.96790 12.2183i −0.106956 0.440316i
\(771\) −11.9587 + 35.1329i −0.430683 + 1.26528i
\(772\) −20.4375 + 17.9337i −0.735560 + 0.645448i
\(773\) 6.20965 10.7554i 0.223345 0.386846i −0.732476 0.680792i \(-0.761636\pi\)
0.955822 + 0.293947i \(0.0949689\pi\)
\(774\) −8.88731 38.3798i −0.319448 1.37953i
\(775\) −20.1837 34.9591i −0.725019 1.25577i
\(776\) −20.0718 + 12.4936i −0.720535 + 0.448494i
\(777\) −18.7108 + 12.7263i −0.671248 + 0.456555i
\(778\) 15.8893 19.3669i 0.569659 0.694337i
\(779\) 9.35081 16.1961i 0.335027 0.580285i
\(780\) −9.87819 7.58832i −0.353696 0.271706i
\(781\) 38.5840 22.2765i 1.38064 0.797115i
\(782\) 13.0895 + 10.7391i 0.468079 + 0.384028i
\(783\) −1.68428 26.7219i −0.0601911 0.954963i
\(784\) −10.2289 + 26.0647i −0.365318 + 0.930883i
\(785\) −10.0017 + 17.3234i −0.356975 + 0.618299i
\(786\) −0.846936 26.4278i −0.0302092 0.942649i
\(787\) 41.3224i 1.47298i 0.676447 + 0.736492i \(0.263519\pi\)
−0.676447 + 0.736492i \(0.736481\pi\)
\(788\) 31.7695 + 36.2049i 1.13174 + 1.28975i
\(789\) −8.09708 9.24850i −0.288264 0.329255i
\(790\) −2.67570 0.441359i −0.0951971 0.0157029i
\(791\) −35.4278 + 15.0526i −1.25967 + 0.535210i
\(792\) −32.2936 + 14.5841i −1.14750 + 0.518225i
\(793\) 4.82138 + 8.35087i 0.171212 + 0.296548i
\(794\) 8.59316 + 7.05013i 0.304960 + 0.250200i
\(795\) 3.14939 + 3.59724i 0.111697 + 0.127581i
\(796\) 4.76734 + 23.9306i 0.168974 + 0.848197i
\(797\) −16.2710 28.1822i −0.576348 0.998265i −0.995894 0.0905304i \(-0.971144\pi\)
0.419545 0.907734i \(-0.362190\pi\)
\(798\) −12.5321 + 17.8019i −0.443633 + 0.630180i
\(799\) 40.2611 + 23.2447i 1.42433 + 0.822340i
\(800\) −17.9578 + 16.8439i −0.634904 + 0.595522i
\(801\) −8.93619 + 11.6057i −0.315745 + 0.410068i
\(802\) −1.63746 + 9.92696i −0.0578208 + 0.350533i
\(803\) 25.6315i 0.904515i
\(804\) −17.1797 13.1972i −0.605880 0.465431i
\(805\) −1.90733 4.48909i −0.0672246 0.158220i
\(806\) 45.3117 + 37.1753i 1.59604 + 1.30945i
\(807\) −13.5690 4.61868i −0.477650 0.162585i
\(808\) −16.5412 + 0.548740i −0.581917 + 0.0193046i
\(809\) 6.96555 12.0647i 0.244896 0.424172i −0.717207 0.696861i \(-0.754580\pi\)
0.962102 + 0.272689i \(0.0879129\pi\)
\(810\) −5.93930 8.34441i −0.208686 0.293193i
\(811\) 19.4191i 0.681896i −0.940082 0.340948i \(-0.889252\pi\)
0.940082 0.340948i \(-0.110748\pi\)
\(812\) 2.03795 + 27.1900i 0.0715181 + 0.954182i
\(813\) 19.8009 17.3357i 0.694449 0.607991i
\(814\) 28.7733 + 4.74619i 1.00850 + 0.166354i
\(815\) 4.59771 0.161051
\(816\) −32.4683 16.0218i −1.13662 0.560874i
\(817\) 31.1929i 1.09130i
\(818\) −9.80869 26.0496i −0.342953 0.910801i
\(819\) 24.8930 25.2643i 0.869833 0.882807i
\(820\) −5.90961 6.73466i −0.206373 0.235185i
\(821\) 34.9473i 1.21967i −0.792528 0.609835i \(-0.791236\pi\)
0.792528 0.609835i \(-0.208764\pi\)
\(822\) 4.38425 8.18879i 0.152918 0.285617i
\(823\) 0.685412i 0.0238920i 0.999929 + 0.0119460i \(0.00380262\pi\)
−0.999929 + 0.0119460i \(0.996197\pi\)
\(824\) −27.7878 44.6429i −0.968035 1.55521i
\(825\) 29.8019 + 10.1441i 1.03757 + 0.353173i
\(826\) 14.8962 3.61839i 0.518307 0.125900i
\(827\) 26.3012 0.914582 0.457291 0.889317i \(-0.348820\pi\)
0.457291 + 0.889317i \(0.348820\pi\)
\(828\) −11.4394 + 7.62081i −0.397547 + 0.264841i
\(829\) 11.6766 20.2245i 0.405546 0.702425i −0.588839 0.808250i \(-0.700415\pi\)
0.994385 + 0.105825i \(0.0337482\pi\)
\(830\) 5.94577 7.24709i 0.206381 0.251550i
\(831\) 23.8937 + 27.2915i 0.828865 + 0.946732i
\(832\) 15.7829 32.0752i 0.547173 1.11201i
\(833\) 26.3320 + 25.3935i 0.912349 + 0.879831i
\(834\) −5.52724 2.95927i −0.191393 0.102471i
\(835\) 4.67830 0.161899
\(836\) 27.5157 5.48156i 0.951652 0.189584i
\(837\) 26.6739 + 40.1374i 0.921985 + 1.38735i
\(838\) 4.13639 5.04171i 0.142889 0.174163i
\(839\) −14.5017 + 25.1176i −0.500654 + 0.867157i 0.499346 + 0.866403i \(0.333574\pi\)
−1.00000 0.000754864i \(0.999760\pi\)
\(840\) 6.14869 + 8.42517i 0.212150 + 0.290696i
\(841\) −1.22413 2.12025i −0.0422113 0.0731122i
\(842\) −0.394417 0.0650594i −0.0135925 0.00224210i
\(843\) −19.7622 6.72674i −0.680645 0.231681i
\(844\) −22.3800 7.58971i −0.770351 0.261249i
\(845\) −2.80339 4.85562i −0.0964397 0.167038i
\(846\) −27.5860 + 25.7584i −0.948427 + 0.885591i
\(847\) −13.6081 10.2471i −0.467581 0.352095i
\(848\) −8.34649 + 10.8905i −0.286620 + 0.373981i
\(849\) 22.6950 4.49463i 0.778890 0.154255i
\(850\) 11.3352 + 30.1036i 0.388795 + 1.03255i
\(851\) 11.3124 0.387785
\(852\) −22.5147 + 29.3088i −0.771341 + 1.00410i
\(853\) −0.261399 + 0.452756i −0.00895013 + 0.0155021i −0.870466 0.492229i \(-0.836182\pi\)
0.861516 + 0.507731i \(0.169516\pi\)
\(854\) −1.90587 7.84612i −0.0652177 0.268489i
\(855\) 3.09096 + 7.49761i 0.105709 + 0.256413i
\(856\) −2.01650 + 0.0668957i −0.0689225 + 0.00228645i
\(857\) 33.8028 19.5161i 1.15468 0.666657i 0.204659 0.978833i \(-0.434391\pi\)
0.950024 + 0.312177i \(0.101058\pi\)
\(858\) −45.6846 + 1.46406i −1.55964 + 0.0499822i
\(859\) −10.5834 6.11034i −0.361102 0.208482i 0.308462 0.951237i \(-0.400186\pi\)
−0.669564 + 0.742754i \(0.733519\pi\)
\(860\) 14.1527 + 4.79960i 0.482603 + 0.163665i
\(861\) 21.0949 14.3479i 0.718911 0.488973i
\(862\) 21.1670 + 3.49151i 0.720950 + 0.118921i
\(863\) 27.3951 15.8166i 0.932539 0.538402i 0.0449255 0.998990i \(-0.485695\pi\)
0.887614 + 0.460589i \(0.152362\pi\)
\(864\) 20.1315 21.4178i 0.684887 0.728650i
\(865\) −1.58208 + 2.74024i −0.0537923 + 0.0931711i
\(866\) 3.10257 + 8.23968i 0.105430 + 0.279996i
\(867\) −13.4360 + 11.7633i −0.456312 + 0.399502i
\(868\) −27.6464 40.5488i −0.938381 1.37632i
\(869\) −8.61783 + 4.97551i −0.292340 + 0.168783i
\(870\) 8.95430 + 4.79410i 0.303579 + 0.162535i
\(871\) −13.9724 24.2008i −0.473435 0.820014i
\(872\) 10.4243 6.48856i 0.353011 0.219730i
\(873\) −24.8566 3.31464i −0.841268 0.112184i
\(874\) 10.1854 3.83520i 0.344526 0.129728i
\(875\) 2.41985 19.7644i 0.0818057 0.668157i
\(876\) 8.12604 + 19.6482i 0.274553 + 0.663850i
\(877\) 20.1898 + 11.6566i 0.681760 + 0.393615i 0.800518 0.599309i \(-0.204558\pi\)
−0.118758 + 0.992923i \(0.537891\pi\)
\(878\) 7.50116 2.82449i 0.253152 0.0953218i
\(879\) 13.6586 11.9581i 0.460694 0.403338i
\(880\) 1.74673 13.3277i 0.0588822 0.449278i
\(881\) 0.502608i 0.0169333i −0.999964 0.00846665i \(-0.997305\pi\)
0.999964 0.00846665i \(-0.00269505\pi\)
\(882\) −25.9555 + 14.4331i −0.873966 + 0.485988i
\(883\) −32.7335 −1.10157 −0.550786 0.834647i \(-0.685672\pi\)
−0.550786 + 0.834647i \(0.685672\pi\)
\(884\) −30.8043 35.1049i −1.03606 1.18071i
\(885\) 1.84004 5.40576i 0.0618522 0.181713i
\(886\) −34.2308 + 12.8893i −1.15001 + 0.433023i
\(887\) −1.08547 + 1.88008i −0.0364464 + 0.0631270i −0.883673 0.468104i \(-0.844937\pi\)
0.847227 + 0.531231i \(0.178270\pi\)
\(888\) −23.5613 + 5.48385i −0.790665 + 0.184026i
\(889\) −52.2404 6.39605i −1.75209 0.214517i
\(890\) −1.95801 5.20001i −0.0656327 0.174305i
\(891\) −36.2702 9.84845i −1.21510 0.329936i
\(892\) 9.34980 + 46.9331i 0.313054 + 1.57144i
\(893\) 25.8803 14.9420i 0.866052 0.500016i
\(894\) −0.859519 26.8205i −0.0287466 0.897010i
\(895\) −9.58802 16.6069i −0.320492 0.555109i
\(896\) −20.2406 + 22.0526i −0.676193 + 0.736725i
\(897\) −17.3930 + 3.44460i −0.580736 + 0.115012i
\(898\) 50.9474 19.1837i 1.70014 0.640169i
\(899\) −41.3880 23.8954i −1.38037 0.796955i
\(900\) −26.0611 + 1.67208i −0.868702 + 0.0557361i
\(901\) 8.96312 + 15.5246i 0.298605 + 0.517199i
\(902\) −32.4394 5.35091i −1.08011 0.178166i
\(903\) −18.5052 + 38.3173i −0.615816 + 1.27512i
\(904\) −41.1282 + 1.36439i −1.36790 + 0.0453790i
\(905\) −1.31835 + 2.28345i −0.0438235 + 0.0759045i
\(906\) −38.1255 20.4123i −1.26663 0.678152i
\(907\) −4.51111 7.81347i −0.149789 0.259442i 0.781360 0.624080i \(-0.214526\pi\)
−0.931149 + 0.364638i \(0.881193\pi\)
\(908\) 0.0372300 0.109781i 0.00123552 0.00364321i
\(909\) −13.9089 10.7096i −0.461327 0.355214i
\(910\) 3.17582 + 13.0742i 0.105277 + 0.433407i
\(911\) 21.6895 + 12.5224i 0.718604 + 0.414886i 0.814239 0.580530i \(-0.197155\pi\)
−0.0956345 + 0.995417i \(0.530488\pi\)
\(912\) −19.3547 + 12.9254i −0.640899 + 0.428002i
\(913\) 34.3975i 1.13839i
\(914\) −27.4612 + 10.3402i −0.908337 + 0.342025i
\(915\) −2.84731 0.969182i −0.0941292 0.0320402i
\(916\) 4.72012 + 23.6936i 0.155957 + 0.782858i
\(917\) −17.1800 + 22.8149i −0.567332 + 0.753415i
\(918\) −15.7665 35.0167i −0.520371 1.15572i
\(919\) 31.6326 18.2631i 1.04346 0.602444i 0.122652 0.992450i \(-0.460860\pi\)
0.920813 + 0.390006i \(0.127527\pi\)
\(920\) −0.172883 5.21138i −0.00569979 0.171814i
\(921\) 34.7176 6.87564i 1.14398 0.226560i
\(922\) 4.83259 29.2971i 0.159153 0.964850i
\(923\) −41.2870 + 23.8371i −1.35898 + 0.784607i
\(924\) 37.0522 + 9.59020i 1.21893 + 0.315495i
\(925\) 18.6128 + 10.7461i 0.611986 + 0.353330i
\(926\) −0.555953 + 0.677632i −0.0182698 + 0.0222684i
\(927\) 7.37231 55.2851i 0.242138 1.81580i
\(928\) −8.44114 + 27.8999i −0.277094 + 0.915858i
\(929\) 9.19393i 0.301643i −0.988561 0.150822i \(-0.951808\pi\)
0.988561 0.150822i \(-0.0481919\pi\)
\(930\) −18.2721 + 0.585570i −0.599167 + 0.0192016i
\(931\) 22.5996 6.49719i 0.740672 0.212937i
\(932\) −47.6866 16.1719i −1.56203 0.529729i
\(933\) −2.15658 10.8893i −0.0706032 0.356501i
\(934\) −0.252598 + 0.307883i −0.00826527 + 0.0100742i
\(935\) −15.2086 8.78066i −0.497373 0.287158i
\(936\) 34.5560 15.6058i 1.12950 0.510093i
\(937\) 57.2969i 1.87181i 0.352255 + 0.935904i \(0.385415\pi\)
−0.352255 + 0.935904i \(0.614585\pi\)
\(938\) 5.52322 + 22.7381i 0.180340 + 0.742424i
\(939\) 30.8382 6.10735i 1.00637 0.199306i
\(940\) −2.79726 14.0414i −0.0912366 0.457980i
\(941\) 30.6212 0.998223 0.499112 0.866538i \(-0.333660\pi\)
0.499112 + 0.866538i \(0.333660\pi\)
\(942\) −32.1179 51.7292i −1.04646 1.68543i
\(943\) −12.7538 −0.415321
\(944\) 16.2489 + 2.12957i 0.528856 + 0.0693117i
\(945\) −0.651032 + 11.0438i −0.0211781 + 0.359254i
\(946\) 51.3201 19.3241i 1.66856 0.628279i
\(947\) −21.4185 −0.696009 −0.348004 0.937493i \(-0.613141\pi\)
−0.348004 + 0.937493i \(0.613141\pi\)
\(948\) 5.02872 6.54619i 0.163325 0.212610i
\(949\) 27.4271i 0.890322i
\(950\) 20.4017 + 3.36528i 0.661918 + 0.109184i
\(951\) −10.7471 + 2.12841i −0.348498 + 0.0690183i
\(952\) 16.4778 + 35.4663i 0.534048 + 1.14947i
\(953\) 9.56899 0.309970 0.154985 0.987917i \(-0.450467\pi\)
0.154985 + 0.987917i \(0.450467\pi\)
\(954\) −14.1782 + 3.28313i −0.459036 + 0.106295i
\(955\) 9.38750 + 5.41987i 0.303772 + 0.175383i
\(956\) 14.7221 43.4116i 0.476148 1.40403i
\(957\) 36.5602 7.24056i 1.18182 0.234054i
\(958\) 28.3408 + 23.2517i 0.915648 + 0.751230i
\(959\) −9.23391 + 3.92332i −0.298179 + 0.126691i
\(960\) 2.88636 + 10.7703i 0.0931569 + 0.347611i
\(961\) 55.0189 1.77480
\(962\) −30.7890 5.07868i −0.992678 0.163743i
\(963\) −1.69560 1.30558i −0.0546399 0.0420717i
\(964\) −5.12518 + 15.1128i −0.165071 + 0.486749i
\(965\) 5.47006 9.47442i 0.176088 0.304992i
\(966\) 14.7870 + 1.33134i 0.475763 + 0.0428350i
\(967\) 7.00100 4.04203i 0.225137 0.129983i −0.383190 0.923670i \(-0.625174\pi\)
0.608327 + 0.793687i \(0.291841\pi\)
\(968\) −9.62339 15.4606i −0.309307 0.496922i
\(969\) 5.90718 + 29.8275i 0.189766 + 0.958196i
\(970\) 6.03370 7.35427i 0.193731 0.236131i
\(971\) 8.36682 4.83059i 0.268504 0.155021i −0.359704 0.933067i \(-0.617122\pi\)
0.628208 + 0.778046i \(0.283789\pi\)
\(972\) 30.9258 3.94942i 0.991944 0.126678i
\(973\) 2.64815 + 6.23268i 0.0848957 + 0.199810i
\(974\) −10.1611 1.67608i −0.325581 0.0537050i
\(975\) −31.8896 10.8548i −1.02129 0.347631i
\(976\) 1.12168 8.55858i 0.0359042 0.273953i
\(977\) −59.5605 −1.90551 −0.952755 0.303741i \(-0.901764\pi\)
−0.952755 + 0.303741i \(0.901764\pi\)
\(978\) −6.60576 + 12.3381i −0.211229 + 0.394528i
\(979\) −17.6574 10.1945i −0.564333 0.325818i
\(980\) 0.529486 11.2535i 0.0169138 0.359480i
\(981\) 12.9093 + 1.72146i 0.412162 + 0.0549621i
\(982\) 13.6025 + 11.1600i 0.434073 + 0.356129i
\(983\) 12.3019 + 21.3075i 0.392369 + 0.679603i 0.992762 0.120102i \(-0.0383223\pi\)
−0.600393 + 0.799705i \(0.704989\pi\)
\(984\) 26.5633 6.18256i 0.846807 0.197093i
\(985\) −16.7839 9.69020i −0.534780 0.308756i
\(986\) 29.4416 + 24.1549i 0.937612 + 0.769249i
\(987\) 40.6557 3.00121i 1.29409 0.0955297i
\(988\) −29.4434 + 5.86557i −0.936718 + 0.186609i
\(989\) 18.4224 10.6362i 0.585799 0.338211i
\(990\) 10.4206 9.73018i 0.331188 0.309245i
\(991\) 39.0527 + 22.5471i 1.24055 + 0.716232i 0.969206 0.246250i \(-0.0791985\pi\)
0.271344 + 0.962482i \(0.412532\pi\)
\(992\) −11.9508 51.0860i −0.379440 1.62198i
\(993\) 0.283818 + 1.43310i 0.00900668 + 0.0454780i
\(994\) 38.7915 9.42271i 1.23039 0.298870i
\(995\) −4.90890 8.50247i −0.155623 0.269546i
\(996\) 10.9052 + 26.3679i 0.345544 + 0.835499i
\(997\) −26.9649 46.7046i −0.853988 1.47915i −0.877581 0.479428i \(-0.840844\pi\)
0.0235932 0.999722i \(-0.492489\pi\)
\(998\) 0.306968 1.86096i 0.00971690 0.0589078i
\(999\) −22.9839 11.4060i −0.727179 0.360871i
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 504.2.bf.b.115.12 yes 180
7.5 odd 6 504.2.cz.b.187.71 yes 180
8.3 odd 2 inner 504.2.bf.b.115.11 180
9.4 even 3 504.2.cz.b.283.49 yes 180
56.19 even 6 504.2.cz.b.187.49 yes 180
63.40 odd 6 inner 504.2.bf.b.355.12 yes 180
72.67 odd 6 504.2.cz.b.283.71 yes 180
504.355 even 6 inner 504.2.bf.b.355.11 yes 180
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bf.b.115.11 180 8.3 odd 2 inner
504.2.bf.b.115.12 yes 180 1.1 even 1 trivial
504.2.bf.b.355.11 yes 180 504.355 even 6 inner
504.2.bf.b.355.12 yes 180 63.40 odd 6 inner
504.2.cz.b.187.49 yes 180 56.19 even 6
504.2.cz.b.187.71 yes 180 7.5 odd 6
504.2.cz.b.283.49 yes 180 9.4 even 3
504.2.cz.b.283.71 yes 180 72.67 odd 6