Properties

Label 175.2.x.a.47.14
Level $175$
Weight $2$
Character 175.47
Analytic conductor $1.397$
Analytic rank $0$
Dimension $288$
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] = [175,2,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.x (of order \(60\), degree \(16\), 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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 47.14
Character \(\chi\) \(=\) 175.47
Dual form 175.2.x.a.108.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0712442 - 1.35942i) q^{2} +(-0.508971 + 0.412156i) q^{3} +(0.146098 + 0.0153555i) q^{4} +(2.05291 + 0.886307i) q^{5} +(0.524032 + 0.721269i) q^{6} +(1.38618 + 2.25355i) q^{7} +(0.457187 - 2.88657i) q^{8} +(-0.534557 + 2.51489i) q^{9} +O(q^{10})\) \(q+(0.0712442 - 1.35942i) q^{2} +(-0.508971 + 0.412156i) q^{3} +(0.146098 + 0.0153555i) q^{4} +(2.05291 + 0.886307i) q^{5} +(0.524032 + 0.721269i) q^{6} +(1.38618 + 2.25355i) q^{7} +(0.457187 - 2.88657i) q^{8} +(-0.534557 + 2.51489i) q^{9} +(1.35112 - 2.72763i) q^{10} +(-3.52517 + 0.749298i) q^{11} +(-0.0806882 + 0.0523996i) q^{12} +(3.11121 - 6.10609i) q^{13} +(3.16228 - 1.72385i) q^{14} +(-1.41017 + 0.395017i) q^{15} +(-3.60410 - 0.766075i) q^{16} +(-0.931067 + 0.357403i) q^{17} +(3.38071 + 0.905858i) q^{18} +(-0.467578 - 4.44871i) q^{19} +(0.286316 + 0.161011i) q^{20} +(-1.63434 - 0.575668i) q^{21} +(0.767463 + 4.84557i) q^{22} +(-3.95372 - 0.207206i) q^{23} +(0.957022 + 1.65761i) q^{24} +(3.42892 + 3.63903i) q^{25} +(-8.07908 - 4.66446i) q^{26} +(-1.65644 - 3.25095i) q^{27} +(0.167914 + 0.350524i) q^{28} +(-4.04983 + 5.57411i) q^{29} +(0.436528 + 1.94516i) q^{30} +(-2.51836 + 5.65634i) q^{31} +(0.214634 - 0.801024i) q^{32} +(1.48538 - 1.83429i) q^{33} +(0.419528 + 1.29117i) q^{34} +(0.848377 + 5.85493i) q^{35} +(-0.116715 + 0.359211i) q^{36} +(-1.65200 - 2.54385i) q^{37} +(-6.08098 + 0.318691i) q^{38} +(0.933150 + 4.39013i) q^{39} +(3.49695 - 5.52066i) q^{40} +(5.72350 - 1.85968i) q^{41} +(-0.899011 + 2.18074i) q^{42} +(3.08766 - 3.08766i) q^{43} +(-0.526525 + 0.0553400i) q^{44} +(-3.32637 + 4.68908i) q^{45} +(-0.563360 + 5.36001i) q^{46} +(-1.75279 + 4.56618i) q^{47} +(2.15012 - 1.09554i) q^{48} +(-3.15699 + 6.24767i) q^{49} +(5.19126 - 4.40208i) q^{50} +(0.326580 - 0.565653i) q^{51} +(0.548302 - 0.844311i) q^{52} +(-5.55763 - 6.86310i) q^{53} +(-4.53742 + 2.02019i) q^{54} +(-7.90099 - 1.58614i) q^{55} +(7.13877 - 2.97101i) q^{56} +(2.07155 + 2.07155i) q^{57} +(7.28903 + 5.90254i) q^{58} +(1.85136 - 2.05614i) q^{59} +(-0.212088 + 0.0360572i) q^{60} +(2.72091 - 2.44992i) q^{61} +(7.50992 + 3.82650i) q^{62} +(-6.40843 + 2.28145i) q^{63} +(-8.08219 - 2.62606i) q^{64} +(11.7989 - 9.77780i) q^{65} +(-2.38775 - 2.14994i) q^{66} +(5.05490 + 13.1685i) q^{67} +(-0.141515 + 0.0379187i) q^{68} +(2.09773 - 1.52409i) q^{69} +(8.01976 - 0.736170i) q^{70} +(-7.11767 - 5.17129i) q^{71} +(7.01501 + 2.69281i) q^{72} +(-4.33954 - 2.81813i) q^{73} +(-3.57586 + 2.06452i) q^{74} +(-3.24507 - 0.438908i) q^{75} -0.657126i q^{76} +(-6.57512 - 6.90549i) q^{77} +(6.03451 - 0.955772i) q^{78} +(-0.406571 - 0.913173i) q^{79} +(-6.71993 - 4.76702i) q^{80} +(-4.86340 - 2.16533i) q^{81} +(-2.12032 - 7.91313i) q^{82} +(-13.6728 - 2.16555i) q^{83} +(-0.229934 - 0.109200i) q^{84} +(-2.22817 - 0.0914934i) q^{85} +(-3.97744 - 4.41740i) q^{86} +(-0.236161 - 4.50622i) q^{87} +(0.551236 + 10.5182i) q^{88} +(1.15288 + 1.28040i) q^{89} +(6.13744 + 4.85600i) q^{90} +(18.0731 - 1.45289i) q^{91} +(-0.574448 - 0.0909836i) q^{92} +(-1.04952 - 3.91687i) q^{93} +(6.08249 + 2.70810i) q^{94} +(2.98303 - 9.54724i) q^{95} +(0.220905 + 0.496160i) q^{96} +(13.1356 - 2.08048i) q^{97} +(8.26829 + 4.73679i) q^{98} -9.26597i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0712442 1.35942i 0.0503772 0.961255i −0.850173 0.526503i \(-0.823503\pi\)
0.900550 0.434752i \(-0.143164\pi\)
\(3\) −0.508971 + 0.412156i −0.293854 + 0.237959i −0.764898 0.644151i \(-0.777211\pi\)
0.471044 + 0.882110i \(0.343877\pi\)
\(4\) 0.146098 + 0.0153555i 0.0730488 + 0.00767773i
\(5\) 2.05291 + 0.886307i 0.918091 + 0.396369i
\(6\) 0.524032 + 0.721269i 0.213935 + 0.294457i
\(7\) 1.38618 + 2.25355i 0.523928 + 0.851763i
\(8\) 0.457187 2.88657i 0.161640 1.02055i
\(9\) −0.534557 + 2.51489i −0.178186 + 0.838297i
\(10\) 1.35112 2.72763i 0.427262 0.862552i
\(11\) −3.52517 + 0.749298i −1.06288 + 0.225922i −0.705988 0.708224i \(-0.749497\pi\)
−0.356891 + 0.934146i \(0.616163\pi\)
\(12\) −0.0806882 + 0.0523996i −0.0232927 + 0.0151264i
\(13\) 3.11121 6.10609i 0.862894 1.69352i 0.154164 0.988045i \(-0.450732\pi\)
0.708730 0.705480i \(-0.249268\pi\)
\(14\) 3.16228 1.72385i 0.845155 0.460719i
\(15\) −1.41017 + 0.395017i −0.364105 + 0.101993i
\(16\) −3.60410 0.766075i −0.901024 0.191519i
\(17\) −0.931067 + 0.357403i −0.225817 + 0.0866830i −0.468646 0.883386i \(-0.655258\pi\)
0.242829 + 0.970069i \(0.421925\pi\)
\(18\) 3.38071 + 0.905858i 0.796841 + 0.213513i
\(19\) −0.467578 4.44871i −0.107270 1.02060i −0.907254 0.420583i \(-0.861825\pi\)
0.799984 0.600021i \(-0.204841\pi\)
\(20\) 0.286316 + 0.161011i 0.0640222 + 0.0360031i
\(21\) −1.63434 0.575668i −0.356643 0.125621i
\(22\) 0.767463 + 4.84557i 0.163624 + 1.03308i
\(23\) −3.95372 0.207206i −0.824409 0.0432054i −0.364535 0.931190i \(-0.618772\pi\)
−0.459874 + 0.887984i \(0.652105\pi\)
\(24\) 0.957022 + 1.65761i 0.195351 + 0.338358i
\(25\) 3.42892 + 3.63903i 0.685784 + 0.727805i
\(26\) −8.07908 4.66446i −1.58444 0.914776i
\(27\) −1.65644 3.25095i −0.318782 0.625646i
\(28\) 0.167914 + 0.350524i 0.0317327 + 0.0662428i
\(29\) −4.04983 + 5.57411i −0.752034 + 1.03509i 0.245801 + 0.969320i \(0.420949\pi\)
−0.997835 + 0.0657661i \(0.979051\pi\)
\(30\) 0.436528 + 1.94516i 0.0796987 + 0.355135i
\(31\) −2.51836 + 5.65634i −0.452312 + 1.01591i 0.533152 + 0.846020i \(0.321008\pi\)
−0.985463 + 0.169889i \(0.945659\pi\)
\(32\) 0.214634 0.801024i 0.0379422 0.141602i
\(33\) 1.48538 1.83429i 0.258572 0.319310i
\(34\) 0.419528 + 1.29117i 0.0719484 + 0.221434i
\(35\) 0.848377 + 5.85493i 0.143402 + 0.989665i
\(36\) −0.116715 + 0.359211i −0.0194525 + 0.0598685i
\(37\) −1.65200 2.54385i −0.271587 0.418207i 0.676391 0.736542i \(-0.263543\pi\)
−0.947978 + 0.318336i \(0.896876\pi\)
\(38\) −6.08098 + 0.318691i −0.986465 + 0.0516984i
\(39\) 0.933150 + 4.39013i 0.149424 + 0.702983i
\(40\) 3.49695 5.52066i 0.552916 0.872894i
\(41\) 5.72350 1.85968i 0.893861 0.290433i 0.174160 0.984717i \(-0.444279\pi\)
0.719701 + 0.694285i \(0.244279\pi\)
\(42\) −0.899011 + 2.18074i −0.138720 + 0.336496i
\(43\) 3.08766 3.08766i 0.470863 0.470863i −0.431331 0.902194i \(-0.641956\pi\)
0.902194 + 0.431331i \(0.141956\pi\)
\(44\) −0.526525 + 0.0553400i −0.0793766 + 0.00834282i
\(45\) −3.32637 + 4.68908i −0.495865 + 0.699006i
\(46\) −0.563360 + 5.36001i −0.0830628 + 0.790290i
\(47\) −1.75279 + 4.56618i −0.255671 + 0.666046i −0.999998 0.00176869i \(-0.999437\pi\)
0.744327 + 0.667815i \(0.232770\pi\)
\(48\) 2.15012 1.09554i 0.310344 0.158128i
\(49\) −3.15699 + 6.24767i −0.450999 + 0.892525i
\(50\) 5.19126 4.40208i 0.734154 0.622548i
\(51\) 0.326580 0.565653i 0.0457303 0.0792072i
\(52\) 0.548302 0.844311i 0.0760358 0.117085i
\(53\) −5.55763 6.86310i −0.763399 0.942719i 0.236181 0.971709i \(-0.424104\pi\)
−0.999580 + 0.0289903i \(0.990771\pi\)
\(54\) −4.53742 + 2.02019i −0.617464 + 0.274913i
\(55\) −7.90099 1.58614i −1.06537 0.213875i
\(56\) 7.13877 2.97101i 0.953958 0.397018i
\(57\) 2.07155 + 2.07155i 0.274383 + 0.274383i
\(58\) 7.28903 + 5.90254i 0.957097 + 0.775042i
\(59\) 1.85136 2.05614i 0.241027 0.267687i −0.610479 0.792032i \(-0.709023\pi\)
0.851506 + 0.524345i \(0.175690\pi\)
\(60\) −0.212088 + 0.0360572i −0.0273805 + 0.00465497i
\(61\) 2.72091 2.44992i 0.348377 0.313680i −0.476301 0.879282i \(-0.658023\pi\)
0.824678 + 0.565602i \(0.191356\pi\)
\(62\) 7.50992 + 3.82650i 0.953761 + 0.485965i
\(63\) −6.40843 + 2.28145i −0.807387 + 0.287436i
\(64\) −8.08219 2.62606i −1.01027 0.328258i
\(65\) 11.7989 9.77780i 1.46348 1.21279i
\(66\) −2.38775 2.14994i −0.293912 0.264639i
\(67\) 5.05490 + 13.1685i 0.617554 + 1.60878i 0.782619 + 0.622501i \(0.213883\pi\)
−0.165065 + 0.986283i \(0.552783\pi\)
\(68\) −0.141515 + 0.0379187i −0.0171612 + 0.00459832i
\(69\) 2.09773 1.52409i 0.252537 0.183479i
\(70\) 8.01976 0.736170i 0.958544 0.0879891i
\(71\) −7.11767 5.17129i −0.844711 0.613719i 0.0789713 0.996877i \(-0.474836\pi\)
−0.923683 + 0.383158i \(0.874836\pi\)
\(72\) 7.01501 + 2.69281i 0.826726 + 0.317351i
\(73\) −4.33954 2.81813i −0.507905 0.329837i 0.265118 0.964216i \(-0.414589\pi\)
−0.773022 + 0.634379i \(0.781256\pi\)
\(74\) −3.57586 + 2.06452i −0.415685 + 0.239996i
\(75\) −3.24507 0.438908i −0.374708 0.0506807i
\(76\) 0.657126i 0.0753775i
\(77\) −6.57512 6.90549i −0.749304 0.786954i
\(78\) 6.03451 0.955772i 0.683273 0.108220i
\(79\) −0.406571 0.913173i −0.0457428 0.102740i 0.889229 0.457463i \(-0.151242\pi\)
−0.934971 + 0.354723i \(0.884575\pi\)
\(80\) −6.71993 4.76702i −0.751311 0.532970i
\(81\) −4.86340 2.16533i −0.540378 0.240592i
\(82\) −2.12032 7.91313i −0.234150 0.873859i
\(83\) −13.6728 2.16555i −1.50078 0.237700i −0.648674 0.761067i \(-0.724676\pi\)
−0.852108 + 0.523366i \(0.824676\pi\)
\(84\) −0.229934 0.109200i −0.0250878 0.0119147i
\(85\) −2.22817 0.0914934i −0.241679 0.00992386i
\(86\) −3.97744 4.41740i −0.428899 0.476340i
\(87\) −0.236161 4.50622i −0.0253191 0.483118i
\(88\) 0.551236 + 10.5182i 0.0587620 + 1.12124i
\(89\) 1.15288 + 1.28040i 0.122205 + 0.135722i 0.801142 0.598474i \(-0.204226\pi\)
−0.678938 + 0.734196i \(0.737559\pi\)
\(90\) 6.13744 + 4.85600i 0.646943 + 0.511867i
\(91\) 18.0731 1.45289i 1.89458 0.152304i
\(92\) −0.574448 0.0909836i −0.0598903 0.00948569i
\(93\) −1.04952 3.91687i −0.108830 0.406161i
\(94\) 6.08249 + 2.70810i 0.627360 + 0.279319i
\(95\) 2.98303 9.54724i 0.306052 0.979527i
\(96\) 0.220905 + 0.496160i 0.0225460 + 0.0506391i
\(97\) 13.1356 2.08048i 1.33372 0.211240i 0.551464 0.834198i \(-0.314069\pi\)
0.782255 + 0.622958i \(0.214069\pi\)
\(98\) 8.26829 + 4.73679i 0.835224 + 0.478488i
\(99\) 9.26597i 0.931265i
\(100\) 0.445078 + 0.584306i 0.0445078 + 0.0584306i
\(101\) 7.91198 4.56798i 0.787271 0.454531i −0.0517297 0.998661i \(-0.516473\pi\)
0.839001 + 0.544130i \(0.183140\pi\)
\(102\) −0.745693 0.484259i −0.0738346 0.0479487i
\(103\) 5.86959 + 2.25312i 0.578347 + 0.222007i 0.629917 0.776663i \(-0.283089\pi\)
−0.0515693 + 0.998669i \(0.516422\pi\)
\(104\) −16.2032 11.7723i −1.58886 1.15437i
\(105\) −2.84495 2.63033i −0.277638 0.256694i
\(106\) −9.72578 + 7.06619i −0.944651 + 0.686329i
\(107\) −6.62424 + 1.77496i −0.640389 + 0.171592i −0.564380 0.825515i \(-0.690885\pi\)
−0.0760096 + 0.997107i \(0.524218\pi\)
\(108\) −0.192082 0.500391i −0.0184831 0.0481502i
\(109\) 9.51892 + 8.57087i 0.911747 + 0.820940i 0.984314 0.176423i \(-0.0564527\pi\)
−0.0725677 + 0.997363i \(0.523119\pi\)
\(110\) −2.71913 + 10.6278i −0.259259 + 1.01332i
\(111\) 1.88928 + 0.613866i 0.179323 + 0.0582655i
\(112\) −3.26955 9.18394i −0.308944 0.867801i
\(113\) 8.69911 + 4.43242i 0.818343 + 0.416967i 0.812461 0.583016i \(-0.198128\pi\)
0.00588239 + 0.999983i \(0.498128\pi\)
\(114\) 2.96369 2.66852i 0.277575 0.249930i
\(115\) −7.93301 3.92959i −0.739757 0.366436i
\(116\) −0.677263 + 0.752177i −0.0628823 + 0.0698379i
\(117\) 13.6930 + 11.0884i 1.26592 + 1.02512i
\(118\) −2.66326 2.66326i −0.245173 0.245173i
\(119\) −2.09606 1.60278i −0.192145 0.146927i
\(120\) 0.495532 + 4.25115i 0.0452356 + 0.388075i
\(121\) 1.81639 0.808709i 0.165126 0.0735190i
\(122\) −3.13662 3.87341i −0.283976 0.350682i
\(123\) −2.14662 + 3.30550i −0.193554 + 0.298047i
\(124\) −0.454783 + 0.787707i −0.0408407 + 0.0707381i
\(125\) 3.81398 + 10.5097i 0.341133 + 0.940015i
\(126\) 2.64488 + 8.87429i 0.235625 + 0.790584i
\(127\) −4.29960 + 2.19076i −0.381528 + 0.194398i −0.634227 0.773147i \(-0.718682\pi\)
0.252699 + 0.967545i \(0.418682\pi\)
\(128\) −3.55136 + 9.25160i −0.313898 + 0.817733i
\(129\) −0.298930 + 2.84413i −0.0263193 + 0.250411i
\(130\) −12.4515 16.7363i −1.09207 1.46787i
\(131\) 12.0485 1.26635i 1.05268 0.110641i 0.437651 0.899145i \(-0.355810\pi\)
0.615030 + 0.788504i \(0.289144\pi\)
\(132\) 0.245177 0.245177i 0.0213399 0.0213399i
\(133\) 9.37725 7.22044i 0.813111 0.626092i
\(134\) 18.2616 5.93355i 1.57756 0.512581i
\(135\) −0.519192 8.14204i −0.0446850 0.700755i
\(136\) 0.605996 + 2.85098i 0.0519637 + 0.244470i
\(137\) 5.85847 0.307030i 0.500523 0.0262313i 0.199596 0.979878i \(-0.436037\pi\)
0.300928 + 0.953647i \(0.402704\pi\)
\(138\) −1.92243 2.96028i −0.163648 0.251996i
\(139\) −2.24141 + 6.89834i −0.190114 + 0.585110i −0.999999 0.00147871i \(-0.999529\pi\)
0.809885 + 0.586588i \(0.199529\pi\)
\(140\) 0.0340405 + 0.868419i 0.00287694 + 0.0733948i
\(141\) −0.989861 3.04648i −0.0833614 0.256560i
\(142\) −7.53704 + 9.30747i −0.632494 + 0.781066i
\(143\) −6.39226 + 23.8562i −0.534548 + 1.99496i
\(144\) 3.85319 8.65440i 0.321099 0.721200i
\(145\) −13.2543 + 7.85378i −1.10071 + 0.652221i
\(146\) −4.14019 + 5.69848i −0.342644 + 0.471610i
\(147\) −0.968202 4.48106i −0.0798559 0.369591i
\(148\) −0.202291 0.397018i −0.0166282 0.0326347i
\(149\) 9.32624 + 5.38451i 0.764035 + 0.441116i 0.830743 0.556657i \(-0.187916\pi\)
−0.0667075 + 0.997773i \(0.521249\pi\)
\(150\) −0.827852 + 4.38014i −0.0675939 + 0.357637i
\(151\) −0.720397 1.24776i −0.0586251 0.101542i 0.835223 0.549911i \(-0.185338\pi\)
−0.893848 + 0.448369i \(0.852005\pi\)
\(152\) −13.0553 0.684198i −1.05892 0.0554957i
\(153\) −0.401122 2.53258i −0.0324288 0.204747i
\(154\) −9.85590 + 8.44637i −0.794211 + 0.680628i
\(155\) −10.1832 + 9.37994i −0.817938 + 0.753415i
\(156\) 0.0689185 + 0.655716i 0.00551790 + 0.0524993i
\(157\) −14.6975 3.93818i −1.17299 0.314301i −0.380846 0.924639i \(-0.624367\pi\)
−0.792141 + 0.610338i \(0.791034\pi\)
\(158\) −1.27035 + 0.487642i −0.101064 + 0.0387947i
\(159\) 5.65734 + 1.20250i 0.448656 + 0.0953648i
\(160\) 1.15058 1.45420i 0.0909611 0.114965i
\(161\) −5.01364 9.19715i −0.395130 0.724837i
\(162\) −3.29008 + 6.45714i −0.258493 + 0.507321i
\(163\) 12.7778 8.29798i 1.00083 0.649948i 0.0633532 0.997991i \(-0.479821\pi\)
0.937478 + 0.348044i \(0.113154\pi\)
\(164\) 0.864745 0.183807i 0.0675253 0.0143529i
\(165\) 4.67511 2.44914i 0.363957 0.190666i
\(166\) −3.91800 + 18.4327i −0.304096 + 1.43066i
\(167\) 0.913290 5.76628i 0.0706725 0.446208i −0.926824 0.375495i \(-0.877473\pi\)
0.997497 0.0707130i \(-0.0225274\pi\)
\(168\) −2.40890 + 4.45445i −0.185851 + 0.343668i
\(169\) −19.9635 27.4774i −1.53566 2.11365i
\(170\) −0.283122 + 3.02250i −0.0217145 + 0.231815i
\(171\) 11.4380 + 1.20218i 0.874684 + 0.0919330i
\(172\) 0.498512 0.403687i 0.0380111 0.0307808i
\(173\) −0.0427033 + 0.814828i −0.00324667 + 0.0619502i −0.999772 0.0213357i \(-0.993208\pi\)
0.996526 + 0.0832859i \(0.0265415\pi\)
\(174\) −6.14267 −0.465675
\(175\) −3.44763 + 12.7716i −0.260616 + 0.965443i
\(176\) 13.2791 1.00095
\(177\) −0.0948354 + 1.80957i −0.00712827 + 0.136015i
\(178\) 1.82274 1.47602i 0.136620 0.110633i
\(179\) 1.96641 + 0.206678i 0.146976 + 0.0154478i 0.177731 0.984079i \(-0.443124\pi\)
−0.0307546 + 0.999527i \(0.509791\pi\)
\(180\) −0.557977 + 0.633985i −0.0415891 + 0.0472544i
\(181\) 4.55620 + 6.27107i 0.338660 + 0.466125i 0.944049 0.329804i \(-0.106983\pi\)
−0.605390 + 0.795929i \(0.706983\pi\)
\(182\) −0.687487 24.6724i −0.0509599 1.82884i
\(183\) −0.375115 + 2.36838i −0.0277293 + 0.175076i
\(184\) −2.40570 + 11.3180i −0.177351 + 0.834370i
\(185\) −1.13677 6.68649i −0.0835773 0.491601i
\(186\) −5.39945 + 1.14769i −0.395907 + 0.0841525i
\(187\) 3.01437 1.95755i 0.220432 0.143151i
\(188\) −0.326195 + 0.640193i −0.0237902 + 0.0466909i
\(189\) 5.03005 8.23929i 0.365882 0.599320i
\(190\) −12.7662 4.73537i −0.926157 0.343540i
\(191\) −1.25696 0.267176i −0.0909508 0.0193322i 0.162211 0.986756i \(-0.448137\pi\)
−0.253162 + 0.967424i \(0.581471\pi\)
\(192\) 5.19595 1.99454i 0.374985 0.143943i
\(193\) −14.0029 3.75206i −1.00795 0.270080i −0.283178 0.959067i \(-0.591389\pi\)
−0.724773 + 0.688988i \(0.758055\pi\)
\(194\) −1.89241 18.0050i −0.135867 1.29269i
\(195\) −1.97532 + 9.83961i −0.141456 + 0.704629i
\(196\) −0.557165 + 0.864292i −0.0397975 + 0.0617352i
\(197\) 2.25387 + 14.2303i 0.160581 + 1.01387i 0.927961 + 0.372677i \(0.121560\pi\)
−0.767380 + 0.641193i \(0.778440\pi\)
\(198\) −12.5963 0.660146i −0.895183 0.0469145i
\(199\) −1.05487 1.82709i −0.0747779 0.129519i 0.826212 0.563360i \(-0.190491\pi\)
−0.900990 + 0.433841i \(0.857158\pi\)
\(200\) 12.0719 8.23408i 0.853616 0.582237i
\(201\) −8.00026 4.61895i −0.564295 0.325796i
\(202\) −5.64612 11.0811i −0.397260 0.779667i
\(203\) −18.1754 1.39976i −1.27566 0.0982438i
\(204\) 0.0563984 0.0776257i 0.00394868 0.00543489i
\(205\) 13.3981 + 1.25502i 0.935764 + 0.0876544i
\(206\) 3.48111 7.81871i 0.242541 0.544755i
\(207\) 2.63459 9.83243i 0.183117 0.683401i
\(208\) −15.8908 + 19.6235i −1.10183 + 1.36065i
\(209\) 4.98171 + 15.3321i 0.344592 + 1.06054i
\(210\) −3.77840 + 3.68008i −0.260735 + 0.253950i
\(211\) −2.58367 + 7.95173i −0.177867 + 0.547420i −0.999753 0.0222332i \(-0.992922\pi\)
0.821885 + 0.569653i \(0.192922\pi\)
\(212\) −0.706569 1.08802i −0.0485274 0.0747256i
\(213\) 5.75406 0.301558i 0.394262 0.0206624i
\(214\) 1.94098 + 9.13158i 0.132682 + 0.624222i
\(215\) 9.07531 3.60208i 0.618931 0.245660i
\(216\) −10.1414 + 3.29513i −0.690034 + 0.224206i
\(217\) −16.2378 + 2.16546i −1.10229 + 0.147001i
\(218\) 12.3296 12.3296i 0.835064 0.835064i
\(219\) 3.37021 0.354223i 0.227738 0.0239362i
\(220\) −1.12996 0.353055i −0.0761818 0.0238029i
\(221\) −0.714408 + 6.79713i −0.0480562 + 0.457225i
\(222\) 0.969101 2.52460i 0.0650418 0.169440i
\(223\) 9.17376 4.67427i 0.614321 0.313012i −0.119001 0.992894i \(-0.537969\pi\)
0.733321 + 0.679882i \(0.237969\pi\)
\(224\) 2.10267 0.626678i 0.140491 0.0418717i
\(225\) −10.9847 + 6.67809i −0.732314 + 0.445206i
\(226\) 6.64527 11.5100i 0.442037 0.765631i
\(227\) 2.84858 4.38643i 0.189067 0.291138i −0.731407 0.681941i \(-0.761136\pi\)
0.920474 + 0.390803i \(0.127803\pi\)
\(228\) 0.270839 + 0.334458i 0.0179367 + 0.0221500i
\(229\) 22.0154 9.80188i 1.45482 0.647727i 0.481346 0.876531i \(-0.340148\pi\)
0.973472 + 0.228804i \(0.0734816\pi\)
\(230\) −5.90715 + 10.5043i −0.389506 + 0.692635i
\(231\) 6.19269 + 0.804717i 0.407449 + 0.0529465i
\(232\) 14.2385 + 14.2385i 0.934804 + 0.934804i
\(233\) 7.93033 + 6.42185i 0.519533 + 0.420709i 0.852890 0.522091i \(-0.174848\pi\)
−0.333357 + 0.942801i \(0.608181\pi\)
\(234\) 16.0493 17.8246i 1.04918 1.16523i
\(235\) −7.64538 + 7.82047i −0.498730 + 0.510151i
\(236\) 0.302052 0.271969i 0.0196619 0.0177037i
\(237\) 0.583303 + 0.297208i 0.0378896 + 0.0193057i
\(238\) −2.32818 + 2.73523i −0.150914 + 0.177299i
\(239\) 27.2863 + 8.86585i 1.76500 + 0.573484i 0.997699 0.0678002i \(-0.0215981\pi\)
0.767303 + 0.641284i \(0.221598\pi\)
\(240\) 5.38501 0.343385i 0.347601 0.0221654i
\(241\) 6.01914 + 5.41966i 0.387727 + 0.349111i 0.839825 0.542857i \(-0.182658\pi\)
−0.452098 + 0.891968i \(0.649324\pi\)
\(242\) −0.969968 2.52685i −0.0623519 0.162432i
\(243\) 13.9407 3.73540i 0.894296 0.239626i
\(244\) 0.435138 0.316147i 0.0278569 0.0202392i
\(245\) −12.0184 + 10.0279i −0.767827 + 0.640657i
\(246\) 4.34063 + 3.15365i 0.276748 + 0.201069i
\(247\) −28.6190 10.9858i −1.82098 0.699009i
\(248\) 15.1760 + 9.85543i 0.963679 + 0.625820i
\(249\) 7.85159 4.53312i 0.497574 0.287275i
\(250\) 14.5588 4.43604i 0.920779 0.280560i
\(251\) 14.7687i 0.932189i 0.884735 + 0.466095i \(0.154339\pi\)
−0.884735 + 0.466095i \(0.845661\pi\)
\(252\) −0.971289 + 0.234910i −0.0611854 + 0.0147979i
\(253\) 14.0928 2.23208i 0.886008 0.140330i
\(254\) 2.67184 + 6.00104i 0.167646 + 0.376539i
\(255\) 1.17178 0.871787i 0.0733799 0.0545934i
\(256\) −3.20304 1.42609i −0.200190 0.0891304i
\(257\) −1.95215 7.28553i −0.121772 0.454459i 0.877932 0.478785i \(-0.158923\pi\)
−0.999704 + 0.0243262i \(0.992256\pi\)
\(258\) 3.84506 + 0.608998i 0.239383 + 0.0379146i
\(259\) 3.44273 7.24911i 0.213921 0.450438i
\(260\) 1.87394 1.24733i 0.116217 0.0773564i
\(261\) −11.8534 13.1646i −0.733708 0.814866i
\(262\) −0.863113 16.4692i −0.0533233 1.01747i
\(263\) −0.938971 17.9166i −0.0578994 1.10479i −0.860889 0.508794i \(-0.830092\pi\)
0.802989 0.595994i \(-0.203242\pi\)
\(264\) −4.61571 5.12627i −0.284077 0.315500i
\(265\) −5.32652 19.0151i −0.327205 1.16809i
\(266\) −9.14754 13.2620i −0.560871 0.813148i
\(267\) −1.11451 0.176520i −0.0682066 0.0108029i
\(268\) 0.536300 + 2.00150i 0.0327598 + 0.122261i
\(269\) 14.9039 + 6.63566i 0.908708 + 0.404583i 0.807218 0.590253i \(-0.200972\pi\)
0.101490 + 0.994837i \(0.467639\pi\)
\(270\) −11.1054 + 0.125728i −0.675855 + 0.00765154i
\(271\) 1.54742 + 3.47556i 0.0939989 + 0.211125i 0.954425 0.298450i \(-0.0964695\pi\)
−0.860427 + 0.509575i \(0.829803\pi\)
\(272\) 3.62945 0.574849i 0.220068 0.0348553i
\(273\) −8.59986 + 8.18842i −0.520487 + 0.495586i
\(274\) 7.98600i 0.482452i
\(275\) −14.8142 10.2589i −0.893333 0.618636i
\(276\) 0.329877 0.190454i 0.0198562 0.0114640i
\(277\) −5.63237 3.65771i −0.338417 0.219770i 0.364230 0.931309i \(-0.381332\pi\)
−0.702647 + 0.711539i \(0.747999\pi\)
\(278\) 9.21805 + 3.53848i 0.552862 + 0.212224i
\(279\) −12.8789 9.35705i −0.771038 0.560192i
\(280\) 17.2885 + 0.227906i 1.03319 + 0.0136200i
\(281\) −2.64391 + 1.92091i −0.157723 + 0.114592i −0.663847 0.747868i \(-0.731078\pi\)
0.506125 + 0.862460i \(0.331078\pi\)
\(282\) −4.21197 + 1.12859i −0.250819 + 0.0672067i
\(283\) −1.78630 4.65348i −0.106185 0.276621i 0.870186 0.492724i \(-0.163999\pi\)
−0.976371 + 0.216103i \(0.930665\pi\)
\(284\) −0.960466 0.864807i −0.0569932 0.0513169i
\(285\) 2.41668 + 6.08874i 0.143152 + 0.360666i
\(286\) 31.9752 + 10.3894i 1.89074 + 0.614337i
\(287\) 12.1247 + 10.3203i 0.715698 + 0.609191i
\(288\) 1.89975 + 0.967973i 0.111944 + 0.0570383i
\(289\) −11.8943 + 10.7097i −0.699666 + 0.629982i
\(290\) 9.73229 + 18.5777i 0.571500 + 1.09092i
\(291\) −5.82816 + 6.47283i −0.341653 + 0.379444i
\(292\) −0.590722 0.478358i −0.0345694 0.0279938i
\(293\) −10.3729 10.3729i −0.605994 0.605994i 0.335903 0.941897i \(-0.390959\pi\)
−0.941897 + 0.335903i \(0.890959\pi\)
\(294\) −6.16062 + 0.996944i −0.359294 + 0.0581429i
\(295\) 5.62306 2.58021i 0.327387 0.150226i
\(296\) −8.09827 + 3.60558i −0.470702 + 0.209570i
\(297\) 8.27517 + 10.2190i 0.480174 + 0.592966i
\(298\) 7.98424 12.2947i 0.462515 0.712210i
\(299\) −13.5661 + 23.4971i −0.784547 + 1.35887i
\(300\) −0.467357 0.113953i −0.0269829 0.00657908i
\(301\) 11.2383 + 2.67814i 0.647762 + 0.154365i
\(302\) −1.74756 + 0.890426i −0.100561 + 0.0512383i
\(303\) −2.14424 + 5.58594i −0.123184 + 0.320904i
\(304\) −1.72285 + 16.3918i −0.0988120 + 0.940134i
\(305\) 7.75719 2.61791i 0.444175 0.149901i
\(306\) −3.47142 + 0.364861i −0.198448 + 0.0208577i
\(307\) 3.13382 3.13382i 0.178857 0.178857i −0.612001 0.790857i \(-0.709635\pi\)
0.790857 + 0.612001i \(0.209635\pi\)
\(308\) −0.854571 1.10984i −0.0486937 0.0632390i
\(309\) −3.91609 + 1.27241i −0.222778 + 0.0723851i
\(310\) 12.0258 + 14.5116i 0.683018 + 0.824202i
\(311\) 1.08865 + 5.12170i 0.0617318 + 0.290425i 0.998175 0.0603952i \(-0.0192361\pi\)
−0.936443 + 0.350820i \(0.885903\pi\)
\(312\) 13.0990 0.686490i 0.741586 0.0388649i
\(313\) −4.36337 6.71899i −0.246632 0.379780i 0.693575 0.720385i \(-0.256035\pi\)
−0.940207 + 0.340605i \(0.889368\pi\)
\(314\) −6.40075 + 19.6995i −0.361215 + 1.11171i
\(315\) −15.1780 0.996219i −0.855185 0.0561306i
\(316\) −0.0453768 0.139655i −0.00255264 0.00785623i
\(317\) 3.99830 4.93748i 0.224567 0.277317i −0.652393 0.757881i \(-0.726235\pi\)
0.876960 + 0.480564i \(0.159568\pi\)
\(318\) 2.03776 7.60503i 0.114272 0.426469i
\(319\) 10.0997 22.6842i 0.565473 1.27007i
\(320\) −14.2645 12.5544i −0.797413 0.701812i
\(321\) 2.63998 3.63363i 0.147350 0.202809i
\(322\) −12.8600 + 6.16040i −0.716659 + 0.343305i
\(323\) 2.02533 + 3.97493i 0.112692 + 0.221171i
\(324\) −0.677282 0.391029i −0.0376268 0.0217238i
\(325\) 32.8883 9.61551i 1.82432 0.533373i
\(326\) −10.3701 17.9615i −0.574346 0.994797i
\(327\) −8.37739 0.439040i −0.463271 0.0242790i
\(328\) −2.75137 17.3715i −0.151919 0.959179i
\(329\) −12.7198 + 2.37956i −0.701267 + 0.131189i
\(330\) −2.99634 6.52992i −0.164943 0.359460i
\(331\) −2.19682 20.9013i −0.120748 1.14884i −0.872233 0.489090i \(-0.837329\pi\)
0.751485 0.659750i \(-0.229338\pi\)
\(332\) −1.96430 0.526334i −0.107805 0.0288863i
\(333\) 7.28060 2.79476i 0.398974 0.153152i
\(334\) −7.77373 1.65236i −0.425360 0.0904130i
\(335\) −1.29403 + 31.5139i −0.0707004 + 1.72179i
\(336\) 5.44933 + 3.32679i 0.297285 + 0.181491i
\(337\) 4.24522 8.33171i 0.231252 0.453857i −0.745998 0.665948i \(-0.768027\pi\)
0.977250 + 0.212091i \(0.0680273\pi\)
\(338\) −38.7756 + 25.1812i −2.10912 + 1.36968i
\(339\) −6.25444 + 1.32942i −0.339695 + 0.0722043i
\(340\) −0.324125 0.0475816i −0.0175782 0.00258047i
\(341\) 4.63938 21.8266i 0.251237 1.18198i
\(342\) 2.44916 15.4634i 0.132435 0.836163i
\(343\) −18.4556 + 1.54598i −0.996510 + 0.0834748i
\(344\) −7.50109 10.3244i −0.404432 0.556652i
\(345\) 5.65728 1.26959i 0.304578 0.0683527i
\(346\) 1.10465 + 0.116103i 0.0593864 + 0.00624176i
\(347\) −14.1674 + 11.4726i −0.760548 + 0.615880i −0.929107 0.369812i \(-0.879422\pi\)
0.168558 + 0.985692i \(0.446089\pi\)
\(348\) 0.0346926 0.661974i 0.00185972 0.0354856i
\(349\) −20.7570 −1.11110 −0.555548 0.831484i \(-0.687491\pi\)
−0.555548 + 0.831484i \(0.687491\pi\)
\(350\) 17.1163 + 5.59668i 0.914907 + 0.299155i
\(351\) −25.0041 −1.33462
\(352\) −0.156415 + 2.98457i −0.00833693 + 0.159078i
\(353\) −14.5749 + 11.8025i −0.775742 + 0.628183i −0.933206 0.359341i \(-0.883001\pi\)
0.157464 + 0.987525i \(0.449668\pi\)
\(354\) 2.45321 + 0.257842i 0.130386 + 0.0137042i
\(355\) −10.0286 16.9247i −0.532263 0.898267i
\(356\) 0.148771 + 0.204766i 0.00788486 + 0.0108526i
\(357\) 1.72743 0.0481340i 0.0914252 0.00254752i
\(358\) 0.421057 2.65845i 0.0222535 0.140503i
\(359\) 0.468555 2.20438i 0.0247294 0.116343i −0.964052 0.265715i \(-0.914392\pi\)
0.988781 + 0.149372i \(0.0477253\pi\)
\(360\) 12.0146 + 11.7456i 0.633223 + 0.619045i
\(361\) −0.987600 + 0.209921i −0.0519790 + 0.0110485i
\(362\) 8.84962 5.74701i 0.465126 0.302056i
\(363\) −0.591175 + 1.16025i −0.0310287 + 0.0608972i
\(364\) 2.66274 + 0.0652570i 0.139566 + 0.00342040i
\(365\) −6.41098 9.63155i −0.335566 0.504138i
\(366\) 3.19290 + 0.678672i 0.166895 + 0.0354747i
\(367\) 9.09954 3.49299i 0.474992 0.182332i −0.109082 0.994033i \(-0.534791\pi\)
0.584074 + 0.811700i \(0.301458\pi\)
\(368\) 14.0909 + 3.77564i 0.734538 + 0.196819i
\(369\) 1.61735 + 15.3881i 0.0841960 + 0.801072i
\(370\) −9.17074 + 1.06898i −0.476764 + 0.0555736i
\(371\) 7.76245 22.0379i 0.403007 1.14415i
\(372\) −0.0931873 0.588361i −0.00483153 0.0305051i
\(373\) 2.38962 + 0.125235i 0.123730 + 0.00648441i 0.114100 0.993469i \(-0.463601\pi\)
0.00962952 + 0.999954i \(0.496935\pi\)
\(374\) −2.44638 4.23726i −0.126499 0.219103i
\(375\) −6.27284 3.77717i −0.323928 0.195052i
\(376\) 12.3792 + 7.14715i 0.638410 + 0.368586i
\(377\) 21.4362 + 42.0708i 1.10402 + 2.16676i
\(378\) −10.8423 7.42495i −0.557667 0.381898i
\(379\) −15.4544 + 21.2711i −0.793838 + 1.09262i 0.199781 + 0.979841i \(0.435977\pi\)
−0.993620 + 0.112784i \(0.964023\pi\)
\(380\) 0.582415 1.34902i 0.0298773 0.0692034i
\(381\) 1.28544 2.88714i 0.0658550 0.147913i
\(382\) −0.452756 + 1.68971i −0.0231650 + 0.0864530i
\(383\) 0.428854 0.529590i 0.0219134 0.0270608i −0.766071 0.642755i \(-0.777791\pi\)
0.787985 + 0.615695i \(0.211124\pi\)
\(384\) −2.00557 6.17251i −0.102346 0.314989i
\(385\) −7.37777 20.0040i −0.376006 1.01950i
\(386\) −6.09826 + 18.7685i −0.310393 + 0.955291i
\(387\) 6.11460 + 9.41565i 0.310822 + 0.478624i
\(388\) 1.95103 0.102249i 0.0990484 0.00519091i
\(389\) −5.53936 26.0606i −0.280857 1.32133i −0.861745 0.507342i \(-0.830628\pi\)
0.580888 0.813984i \(-0.302705\pi\)
\(390\) 13.2354 + 3.38631i 0.670202 + 0.171472i
\(391\) 3.75524 1.22015i 0.189911 0.0617057i
\(392\) 16.5910 + 11.9692i 0.837971 + 0.604537i
\(393\) −5.61040 + 5.61040i −0.283007 + 0.283007i
\(394\) 19.5056 2.05012i 0.982677 0.103284i
\(395\) −0.0253032 2.23501i −0.00127314 0.112456i
\(396\) 0.142283 1.35374i 0.00715000 0.0680277i
\(397\) −12.0631 + 31.4255i −0.605430 + 1.57720i 0.196968 + 0.980410i \(0.436891\pi\)
−0.802398 + 0.596789i \(0.796443\pi\)
\(398\) −2.55894 + 1.30384i −0.128268 + 0.0653558i
\(399\) −1.79680 + 7.53989i −0.0899523 + 0.377467i
\(400\) −9.57039 15.7422i −0.478519 0.787111i
\(401\) −15.1960 + 26.3202i −0.758852 + 1.31437i 0.184585 + 0.982817i \(0.440906\pi\)
−0.943436 + 0.331553i \(0.892427\pi\)
\(402\) −6.84907 + 10.5466i −0.341601 + 0.526019i
\(403\) 26.7030 + 32.9754i 1.33017 + 1.64262i
\(404\) 1.22606 0.545879i 0.0609990 0.0271585i
\(405\) −8.06501 8.75570i −0.400753 0.435074i
\(406\) −3.19775 + 24.6082i −0.158702 + 1.22128i
\(407\) 7.72968 + 7.72968i 0.383146 + 0.383146i
\(408\) −1.48349 1.20130i −0.0734435 0.0594734i
\(409\) −13.1521 + 14.6068i −0.650328 + 0.722262i −0.974663 0.223680i \(-0.928193\pi\)
0.324335 + 0.945942i \(0.394859\pi\)
\(410\) 2.66064 18.1242i 0.131399 0.895092i
\(411\) −2.85525 + 2.57088i −0.140839 + 0.126812i
\(412\) 0.822934 + 0.419306i 0.0405431 + 0.0206577i
\(413\) 7.19995 + 1.32194i 0.354286 + 0.0650486i
\(414\) −13.1787 4.28202i −0.647697 0.210450i
\(415\) −26.1497 16.5640i −1.28364 0.813094i
\(416\) −4.22335 3.80272i −0.207067 0.186444i
\(417\) −1.70238 4.43486i −0.0833661 0.217176i
\(418\) 21.1977 5.67991i 1.03681 0.277813i
\(419\) 18.2082 13.2290i 0.889527 0.646280i −0.0462273 0.998931i \(-0.514720\pi\)
0.935755 + 0.352651i \(0.114720\pi\)
\(420\) −0.375250 0.427970i −0.0183103 0.0208828i
\(421\) −6.80767 4.94606i −0.331786 0.241056i 0.409402 0.912354i \(-0.365737\pi\)
−0.741188 + 0.671298i \(0.765737\pi\)
\(422\) 10.6257 + 4.07881i 0.517250 + 0.198553i
\(423\) −10.5465 6.84897i −0.512788 0.333008i
\(424\) −22.3516 + 12.9047i −1.08549 + 0.626709i
\(425\) −4.49315 2.16267i −0.217950 0.104905i
\(426\) 7.84367i 0.380027i
\(427\) 9.29271 + 2.73568i 0.449706 + 0.132389i
\(428\) −0.995040 + 0.157599i −0.0480971 + 0.00761783i
\(429\) −6.57903 14.7767i −0.317639 0.713428i
\(430\) −4.25018 12.5938i −0.204962 0.607326i
\(431\) −8.08965 3.60175i −0.389665 0.173490i 0.202546 0.979273i \(-0.435078\pi\)
−0.592211 + 0.805783i \(0.701745\pi\)
\(432\) 3.47951 + 12.9857i 0.167408 + 0.624775i
\(433\) −6.72335 1.06487i −0.323104 0.0511746i −0.00722408 0.999974i \(-0.502300\pi\)
−0.315879 + 0.948799i \(0.602300\pi\)
\(434\) 1.78692 + 22.2282i 0.0857749 + 1.06699i
\(435\) 3.50908 9.46020i 0.168248 0.453582i
\(436\) 1.25908 + 1.39835i 0.0602990 + 0.0669688i
\(437\) 0.926877 + 17.6859i 0.0443385 + 0.846030i
\(438\) −0.241430 4.60677i −0.0115360 0.220120i
\(439\) 6.03256 + 6.69983i 0.287918 + 0.319766i 0.869701 0.493578i \(-0.164311\pi\)
−0.581783 + 0.813344i \(0.697645\pi\)
\(440\) −8.19073 + 22.0816i −0.390478 + 1.05270i
\(441\) −14.0246 11.2792i −0.667839 0.537106i
\(442\) 9.18926 + 1.45544i 0.437089 + 0.0692280i
\(443\) 3.01374 + 11.2474i 0.143187 + 0.534382i 0.999829 + 0.0184709i \(0.00587980\pi\)
−0.856642 + 0.515911i \(0.827454\pi\)
\(444\) 0.266594 + 0.118695i 0.0126520 + 0.00563302i
\(445\) 1.23193 + 3.65035i 0.0583991 + 0.173043i
\(446\) −5.70071 12.8040i −0.269937 0.606287i
\(447\) −6.96604 + 1.10331i −0.329482 + 0.0521849i
\(448\) −5.28543 21.8538i −0.249713 1.03250i
\(449\) 6.67674i 0.315095i −0.987511 0.157547i \(-0.949641\pi\)
0.987511 0.157547i \(-0.0503587\pi\)
\(450\) 8.29573 + 15.4086i 0.391065 + 0.726369i
\(451\) −18.7829 + 10.8443i −0.884451 + 0.510638i
\(452\) 1.20286 + 0.781144i 0.0565776 + 0.0367419i
\(453\) 0.880936 + 0.338159i 0.0413900 + 0.0158881i
\(454\) −5.76006 4.18493i −0.270333 0.196408i
\(455\) 38.3902 + 13.0357i 1.79976 + 0.611121i
\(456\) 6.92675 5.03258i 0.324375 0.235672i
\(457\) −5.50864 + 1.47604i −0.257684 + 0.0690461i −0.385348 0.922771i \(-0.625919\pi\)
0.127664 + 0.991817i \(0.459252\pi\)
\(458\) −11.7564 30.6265i −0.549341 1.43108i
\(459\) 2.70416 + 2.43483i 0.126219 + 0.113648i
\(460\) −1.09865 0.695919i −0.0512249 0.0324474i
\(461\) −6.41686 2.08497i −0.298863 0.0971065i 0.155747 0.987797i \(-0.450221\pi\)
−0.454610 + 0.890690i \(0.650221\pi\)
\(462\) 1.53514 8.36113i 0.0714212 0.388995i
\(463\) 37.8440 + 19.2825i 1.75876 + 0.896133i 0.952481 + 0.304599i \(0.0985226\pi\)
0.806280 + 0.591534i \(0.201477\pi\)
\(464\) 18.8662 16.9872i 0.875840 0.788610i
\(465\) 1.31697 8.97120i 0.0610731 0.416030i
\(466\) 9.29498 10.3231i 0.430582 0.478209i
\(467\) 2.78580 + 2.25590i 0.128912 + 0.104390i 0.691608 0.722273i \(-0.256903\pi\)
−0.562696 + 0.826664i \(0.690236\pi\)
\(468\) 1.83025 + 1.83025i 0.0846034 + 0.0846034i
\(469\) −22.6688 + 29.6454i −1.04675 + 1.36890i
\(470\) 10.0866 + 10.9504i 0.465261 + 0.505106i
\(471\) 9.10374 4.05325i 0.419478 0.186764i
\(472\) −5.08878 6.28411i −0.234230 0.289250i
\(473\) −8.57095 + 13.1981i −0.394093 + 0.606849i
\(474\) 0.445587 0.771779i 0.0204665 0.0354490i
\(475\) 14.5857 16.9558i 0.669238 0.777985i
\(476\) −0.281617 0.266348i −0.0129079 0.0122081i
\(477\) 20.2308 10.3081i 0.926305 0.471976i
\(478\) 13.9964 36.4619i 0.640180 1.66773i
\(479\) 2.27170 21.6138i 0.103797 0.987560i −0.811383 0.584515i \(-0.801285\pi\)
0.915180 0.403046i \(-0.132048\pi\)
\(480\) 0.0137481 + 1.21436i 0.000627514 + 0.0554279i
\(481\) −20.6727 + 2.17279i −0.942594 + 0.0990706i
\(482\) 7.79642 7.79642i 0.355117 0.355117i
\(483\) 6.34246 + 2.61468i 0.288592 + 0.118972i
\(484\) 0.277788 0.0902589i 0.0126267 0.00410268i
\(485\) 28.8102 + 7.37115i 1.30821 + 0.334707i
\(486\) −4.08478 19.2174i −0.185289 0.871718i
\(487\) −12.0853 + 0.633363i −0.547637 + 0.0287004i −0.324148 0.946006i \(-0.605078\pi\)
−0.223488 + 0.974707i \(0.571744\pi\)
\(488\) −5.82789 8.97417i −0.263816 0.406241i
\(489\) −3.08344 + 9.48987i −0.139438 + 0.429147i
\(490\) 12.7758 + 17.0525i 0.577154 + 0.770352i
\(491\) 9.93766 + 30.5850i 0.448480 + 1.38028i 0.878622 + 0.477518i \(0.158464\pi\)
−0.430142 + 0.902761i \(0.641536\pi\)
\(492\) −0.364373 + 0.449963i −0.0164272 + 0.0202859i
\(493\) 1.77846 6.63729i 0.0800977 0.298929i
\(494\) −16.9732 + 38.1225i −0.763662 + 1.71521i
\(495\) 8.21250 19.0222i 0.369124 0.854986i
\(496\) 13.4096 18.4567i 0.602109 0.828732i
\(497\) 1.78737 23.2084i 0.0801746 1.04104i
\(498\) −5.60303 10.9966i −0.251078 0.492768i
\(499\) 34.5237 + 19.9323i 1.54549 + 0.892292i 0.998477 + 0.0551705i \(0.0175702\pi\)
0.547018 + 0.837121i \(0.315763\pi\)
\(500\) 0.395832 + 1.59401i 0.0177021 + 0.0712861i
\(501\) 1.91177 + 3.31129i 0.0854117 + 0.147937i
\(502\) 20.0768 + 1.05218i 0.896071 + 0.0469611i
\(503\) 1.52863 + 9.65138i 0.0681582 + 0.430334i 0.998046 + 0.0624896i \(0.0199040\pi\)
−0.929887 + 0.367844i \(0.880096\pi\)
\(504\) 3.65570 + 19.5414i 0.162838 + 0.870443i
\(505\) 20.2913 2.36523i 0.902949 0.105252i
\(506\) −2.03031 19.3171i −0.0902581 0.858749i
\(507\) 21.4858 + 5.75712i 0.954220 + 0.255682i
\(508\) −0.661802 + 0.254042i −0.0293627 + 0.0112713i
\(509\) −20.7863 4.41826i −0.921336 0.195836i −0.277258 0.960796i \(-0.589426\pi\)
−0.644078 + 0.764960i \(0.722759\pi\)
\(510\) −1.10164 1.65505i −0.0487815 0.0732871i
\(511\) 0.335404 13.6858i 0.0148374 0.605425i
\(512\) −11.1648 + 21.9121i −0.493417 + 0.968386i
\(513\) −13.6880 + 8.88911i −0.604341 + 0.392464i
\(514\) −10.0432 + 2.13474i −0.442985 + 0.0941594i
\(515\) 10.0528 + 9.82773i 0.442979 + 0.433061i
\(516\) −0.0873458 + 0.410930i −0.00384518 + 0.0180902i
\(517\) 2.75747 17.4100i 0.121273 0.765689i
\(518\) −9.60931 5.19658i −0.422209 0.228324i
\(519\) −0.314102 0.432324i −0.0137875 0.0189769i
\(520\) −22.8299 38.5286i −1.00116 1.68959i
\(521\) −25.8230 2.71411i −1.13133 0.118907i −0.479690 0.877438i \(-0.659251\pi\)
−0.651638 + 0.758530i \(0.725918\pi\)
\(522\) −18.7406 + 15.1759i −0.820256 + 0.664230i
\(523\) 2.26533 43.2251i 0.0990560 1.89010i −0.273181 0.961963i \(-0.588076\pi\)
0.372237 0.928138i \(-0.378591\pi\)
\(524\) 1.77970 0.0777466
\(525\) −3.50916 7.92134i −0.153152 0.345715i
\(526\) −24.4231 −1.06490
\(527\) 0.323173 6.16650i 0.0140776 0.268617i
\(528\) −6.75867 + 5.47306i −0.294133 + 0.238184i
\(529\) −7.28500 0.765684i −0.316739 0.0332906i
\(530\) −26.2290 + 5.88626i −1.13932 + 0.255683i
\(531\) 4.18132 + 5.75510i 0.181454 + 0.249750i
\(532\) 1.48087 0.910897i 0.0642037 0.0394924i
\(533\) 6.45164 40.7341i 0.279452 1.76439i
\(534\) −0.319367 + 1.50250i −0.0138204 + 0.0650197i
\(535\) −15.1722 2.22727i −0.655950 0.0962934i
\(536\) 40.3227 8.57085i 1.74167 0.370204i
\(537\) −1.08603 + 0.705275i −0.0468656 + 0.0304348i
\(538\) 10.0825 19.7879i 0.434686 0.853119i
\(539\) 6.44757 24.3896i 0.277716 1.05054i
\(540\) 0.0491721 1.19750i 0.00211603 0.0515324i
\(541\) 3.28498 + 0.698243i 0.141232 + 0.0300198i 0.277985 0.960585i \(-0.410333\pi\)
−0.136753 + 0.990605i \(0.543667\pi\)
\(542\) 4.83498 1.85598i 0.207680 0.0797210i
\(543\) −4.90363 1.31392i −0.210435 0.0563859i
\(544\) 0.0864500 + 0.822517i 0.00370651 + 0.0352651i
\(545\) 11.9451 + 26.0320i 0.511672 + 1.11509i
\(546\) 10.5188 + 12.2742i 0.450164 + 0.525287i
\(547\) −6.75980 42.6797i −0.289028 1.82485i −0.522678 0.852530i \(-0.675067\pi\)
0.233650 0.972321i \(-0.424933\pi\)
\(548\) 0.860623 + 0.0451034i 0.0367640 + 0.00192672i
\(549\) 4.70680 + 8.15242i 0.200882 + 0.347937i
\(550\) −15.0016 + 19.4079i −0.639670 + 0.827555i
\(551\) 26.6912 + 15.4102i 1.13708 + 0.656496i
\(552\) −3.44033 6.75203i −0.146430 0.287386i
\(553\) 1.49430 2.18205i 0.0635441 0.0927903i
\(554\) −5.37363 + 7.39617i −0.228304 + 0.314233i
\(555\) 3.33447 + 2.93470i 0.141540 + 0.124571i
\(556\) −0.433391 + 0.973413i −0.0183799 + 0.0412819i
\(557\) −3.82777 + 14.2854i −0.162188 + 0.605293i 0.836194 + 0.548433i \(0.184776\pi\)
−0.998382 + 0.0568601i \(0.981891\pi\)
\(558\) −13.6377 + 16.8412i −0.577330 + 0.712943i
\(559\) −9.24717 28.4599i −0.391114 1.20372i
\(560\) 1.42768 21.7517i 0.0603307 0.919176i
\(561\) −0.727407 + 2.23873i −0.0307112 + 0.0945192i
\(562\) 2.42297 + 3.73104i 0.102207 + 0.157384i
\(563\) 8.84078 0.463325i 0.372594 0.0195268i 0.134880 0.990862i \(-0.456935\pi\)
0.237714 + 0.971335i \(0.423602\pi\)
\(564\) −0.0978362 0.460283i −0.00411965 0.0193814i
\(565\) 13.9300 + 16.8095i 0.586041 + 0.707179i
\(566\) −6.45330 + 2.09680i −0.271252 + 0.0881353i
\(567\) −1.86189 13.9615i −0.0781922 0.586327i
\(568\) −18.1814 + 18.1814i −0.762873 + 0.762873i
\(569\) −16.4720 + 1.73128i −0.690542 + 0.0725789i −0.443298 0.896374i \(-0.646192\pi\)
−0.247244 + 0.968953i \(0.579525\pi\)
\(570\) 8.44933 2.85150i 0.353904 0.119436i
\(571\) 1.21684 11.5775i 0.0509233 0.484502i −0.939105 0.343631i \(-0.888343\pi\)
0.990028 0.140871i \(-0.0449903\pi\)
\(572\) −1.30022 + 3.38718i −0.0543648 + 0.141625i
\(573\) 0.749877 0.382081i 0.0313265 0.0159617i
\(574\) 14.8935 15.7473i 0.621643 0.657279i
\(575\) −12.8030 15.0982i −0.533921 0.629639i
\(576\) 10.9247 18.9221i 0.455194 0.788419i
\(577\) −20.5125 + 31.5864i −0.853946 + 1.31496i 0.0936880 + 0.995602i \(0.470134\pi\)
−0.947634 + 0.319359i \(0.896532\pi\)
\(578\) 13.7116 + 16.9324i 0.570326 + 0.704294i
\(579\) 8.67350 3.86169i 0.360458 0.160486i
\(580\) −2.05702 + 0.943892i −0.0854132 + 0.0391930i
\(581\) −14.0728 33.8141i −0.583837 1.40285i
\(582\) 8.38407 + 8.38407i 0.347531 + 0.347531i
\(583\) 24.7341 + 20.0293i 1.02438 + 0.829528i
\(584\) −10.1187 + 11.2380i −0.418715 + 0.465030i
\(585\) 18.2829 + 34.8998i 0.755905 + 1.44293i
\(586\) −14.8402 + 13.3622i −0.613043 + 0.551986i
\(587\) −28.8080 14.6784i −1.18903 0.605843i −0.256367 0.966580i \(-0.582526\pi\)
−0.932668 + 0.360736i \(0.882526\pi\)
\(588\) −0.0726432 0.669539i −0.00299575 0.0276113i
\(589\) 26.3410 + 8.55870i 1.08536 + 0.352655i
\(590\) −3.10698 7.82792i −0.127912 0.322271i
\(591\) −7.01228 6.31389i −0.288447 0.259719i
\(592\) 4.00518 + 10.4338i 0.164612 + 0.428828i
\(593\) −0.721886 + 0.193429i −0.0296443 + 0.00794316i −0.273611 0.961841i \(-0.588218\pi\)
0.243966 + 0.969784i \(0.421551\pi\)
\(594\) 14.4815 10.5214i 0.594181 0.431698i
\(595\) −2.88247 5.14812i −0.118170 0.211052i
\(596\) 1.27986 + 0.929872i 0.0524251 + 0.0380890i
\(597\) 1.28995 + 0.495164i 0.0527940 + 0.0202657i
\(598\) 30.9760 + 20.1160i 1.26670 + 0.822606i
\(599\) 30.0127 17.3279i 1.22629 0.707997i 0.260036 0.965599i \(-0.416266\pi\)
0.966251 + 0.257602i \(0.0829323\pi\)
\(600\) −2.75054 + 9.16644i −0.112290 + 0.374218i
\(601\) 20.7380i 0.845922i 0.906148 + 0.422961i \(0.139009\pi\)
−0.906148 + 0.422961i \(0.860991\pi\)
\(602\) 4.44137 15.0867i 0.181017 0.614888i
\(603\) −35.8194 + 5.67323i −1.45868 + 0.231032i
\(604\) −0.0860883 0.193357i −0.00350288 0.00786760i
\(605\) 4.44566 0.0503305i 0.180742 0.00204623i
\(606\) 7.44088 + 3.31289i 0.302265 + 0.134577i
\(607\) −4.20723 15.7016i −0.170766 0.637308i −0.997234 0.0743240i \(-0.976320\pi\)
0.826468 0.562984i \(-0.190347\pi\)
\(608\) −3.66388 0.580302i −0.148590 0.0235343i
\(609\) 9.82765 6.77865i 0.398236 0.274685i
\(610\) −3.00619 10.7318i −0.121717 0.434517i
\(611\) 22.4282 + 24.9091i 0.907349 + 1.00771i
\(612\) −0.0197139 0.376164i −0.000796887 0.0152055i
\(613\) 0.193868 + 3.69923i 0.00783026 + 0.149410i 0.999746 + 0.0225158i \(0.00716762\pi\)
−0.991916 + 0.126894i \(0.959499\pi\)
\(614\) −4.03691 4.48345i −0.162917 0.180937i
\(615\) −7.33651 + 4.88335i −0.295837 + 0.196916i
\(616\) −22.9392 + 15.8224i −0.924247 + 0.637503i
\(617\) 0.473002 + 0.0749161i 0.0190423 + 0.00301601i 0.165948 0.986134i \(-0.446931\pi\)
−0.146906 + 0.989150i \(0.546931\pi\)
\(618\) 1.45075 + 5.41426i 0.0583576 + 0.217793i
\(619\) −24.2549 10.7990i −0.974887 0.434048i −0.143444 0.989658i \(-0.545818\pi\)
−0.831443 + 0.555611i \(0.812484\pi\)
\(620\) −1.63178 + 1.21402i −0.0655339 + 0.0487561i
\(621\) 5.87550 + 13.1966i 0.235776 + 0.529561i
\(622\) 7.04010 1.11504i 0.282282 0.0447091i
\(623\) −1.28735 + 4.37294i −0.0515765 + 0.175198i
\(624\) 16.5373i 0.662022i
\(625\) −1.48504 + 24.9559i −0.0594016 + 0.998234i
\(626\) −9.44480 + 5.45296i −0.377490 + 0.217944i
\(627\) −8.85478 5.75036i −0.353626 0.229647i
\(628\) −2.08679 0.801045i −0.0832721 0.0319652i
\(629\) 2.44730 + 1.77807i 0.0975803 + 0.0708962i
\(630\) −2.43563 + 20.5623i −0.0970377 + 0.819223i
\(631\) −13.2040 + 9.59330i −0.525645 + 0.381903i −0.818726 0.574184i \(-0.805319\pi\)
0.293081 + 0.956088i \(0.405319\pi\)
\(632\) −2.82181 + 0.756102i −0.112246 + 0.0300761i
\(633\) −1.96234 5.11208i −0.0779961 0.203187i
\(634\) −6.42726 5.78713i −0.255259 0.229836i
\(635\) −10.7684 + 0.686667i −0.427331 + 0.0272496i
\(636\) 0.808058 + 0.262554i 0.0320416 + 0.0104109i
\(637\) 28.3268 + 38.7147i 1.12235 + 1.53393i
\(638\) −30.1179 15.3458i −1.19238 0.607547i
\(639\) 16.8100 15.1358i 0.664994 0.598763i
\(640\) −15.4904 + 15.8451i −0.612311 + 0.626334i
\(641\) −26.4913 + 29.4215i −1.04634 + 1.16208i −0.0598609 + 0.998207i \(0.519066\pi\)
−0.986481 + 0.163874i \(0.947601\pi\)
\(642\) −4.75154 3.84772i −0.187528 0.151857i
\(643\) −1.27966 1.27966i −0.0504649 0.0504649i 0.681424 0.731889i \(-0.261361\pi\)
−0.731889 + 0.681424i \(0.761361\pi\)
\(644\) −0.591254 1.42067i −0.0232987 0.0559821i
\(645\) −3.13445 + 5.57380i −0.123419 + 0.219468i
\(646\) 5.54790 2.47008i 0.218279 0.0971841i
\(647\) −7.91208 9.77061i −0.311056 0.384122i 0.597511 0.801860i \(-0.296156\pi\)
−0.908567 + 0.417738i \(0.862823\pi\)
\(648\) −8.47384 + 13.0486i −0.332884 + 0.512596i
\(649\) −4.98570 + 8.63548i −0.195706 + 0.338972i
\(650\) −10.7284 45.3941i −0.420803 1.78050i
\(651\) 7.37204 7.79466i 0.288933 0.305497i
\(652\) 1.99422 1.01611i 0.0780996 0.0397938i
\(653\) 12.7671 33.2594i 0.499615 1.30154i −0.419572 0.907722i \(-0.637820\pi\)
0.919187 0.393821i \(-0.128847\pi\)
\(654\) −1.19368 + 11.3571i −0.0466766 + 0.444098i
\(655\) 25.8569 + 8.07896i 1.01031 + 0.315671i
\(656\) −22.0527 + 2.31783i −0.861013 + 0.0904962i
\(657\) 9.40702 9.40702i 0.367003 0.367003i
\(658\) 2.32860 + 17.4611i 0.0907784 + 0.680705i
\(659\) 40.6379 13.2041i 1.58303 0.514357i 0.620193 0.784449i \(-0.287054\pi\)
0.962834 + 0.270092i \(0.0870542\pi\)
\(660\) 0.720630 0.286025i 0.0280505 0.0111335i
\(661\) −8.91071 41.9216i −0.346586 1.63056i −0.713748 0.700403i \(-0.753004\pi\)
0.367161 0.930157i \(-0.380330\pi\)
\(662\) −28.5702 + 1.49730i −1.11041 + 0.0581942i
\(663\) −2.43787 3.75399i −0.0946790 0.145793i
\(664\) −12.5020 + 38.4773i −0.485173 + 1.49321i
\(665\) 25.6502 6.51182i 0.994673 0.252518i
\(666\) −3.28055 10.0965i −0.127119 0.391232i
\(667\) 17.1669 21.1994i 0.664705 0.820842i
\(668\) 0.221973 0.828416i 0.00858841 0.0320524i
\(669\) −2.74265 + 6.16009i −0.106037 + 0.238163i
\(670\) 42.7485 + 4.00431i 1.65152 + 0.154700i
\(671\) −7.75597 + 10.6752i −0.299416 + 0.412110i
\(672\) −0.811908 + 1.18559i −0.0313200 + 0.0457351i
\(673\) 1.16847 + 2.29326i 0.0450413 + 0.0883986i 0.912430 0.409232i \(-0.134203\pi\)
−0.867389 + 0.497631i \(0.834203\pi\)
\(674\) −11.0238 6.36462i −0.424623 0.245156i
\(675\) 6.15049 17.1751i 0.236733 0.661069i
\(676\) −2.49469 4.32093i −0.0959497 0.166190i
\(677\) −20.2362 1.06054i −0.777741 0.0407597i −0.340666 0.940184i \(-0.610652\pi\)
−0.437076 + 0.899425i \(0.643986\pi\)
\(678\) 1.36165 + 8.59712i 0.0522939 + 0.330170i
\(679\) 22.8968 + 26.7179i 0.878700 + 1.02534i
\(680\) −1.28279 + 6.38993i −0.0491928 + 0.245043i
\(681\) 0.358051 + 3.40663i 0.0137205 + 0.130542i
\(682\) −29.3410 7.86188i −1.12352 0.301047i
\(683\) 6.07130 2.33055i 0.232312 0.0891762i −0.239427 0.970914i \(-0.576960\pi\)
0.471739 + 0.881738i \(0.343626\pi\)
\(684\) 1.65260 + 0.351271i 0.0631887 + 0.0134312i
\(685\) 12.2991 + 4.56210i 0.469923 + 0.174309i
\(686\) 0.786774 + 25.1991i 0.0300392 + 0.962105i
\(687\) −7.16528 + 14.0627i −0.273373 + 0.536524i
\(688\) −13.4936 + 8.76284i −0.514438 + 0.334080i
\(689\) −59.1976 + 12.5828i −2.25525 + 0.479368i
\(690\) −1.32286 7.78107i −0.0503606 0.296220i
\(691\) 4.25124 20.0005i 0.161725 0.760855i −0.820275 0.571970i \(-0.806179\pi\)
0.981999 0.188885i \(-0.0604873\pi\)
\(692\) −0.0187509 + 0.118389i −0.000712803 + 0.00450046i
\(693\) 20.8813 12.8443i 0.793216 0.487916i
\(694\) 14.5867 + 20.0769i 0.553703 + 0.762107i
\(695\) −10.7155 + 12.1751i −0.406461 + 0.461829i
\(696\) −13.1155 1.37849i −0.497141 0.0522516i
\(697\) −4.66431 + 3.77708i −0.176673 + 0.143067i
\(698\) −1.47881 + 28.2175i −0.0559739 + 1.06805i
\(699\) −6.68311 −0.252779
\(700\) −0.699804 + 1.81296i −0.0264501 + 0.0685234i
\(701\) 40.8116 1.54143 0.770717 0.637178i \(-0.219898\pi\)
0.770717 + 0.637178i \(0.219898\pi\)
\(702\) −1.78140 + 33.9911i −0.0672346 + 1.28291i
\(703\) −10.5444 + 8.53871i −0.397691 + 0.322044i
\(704\) 30.4588 + 3.20135i 1.14796 + 0.120655i
\(705\) 0.668017 7.13149i 0.0251590 0.268587i
\(706\) 15.0062 + 20.6542i 0.564765 + 0.777332i
\(707\) 21.2616 + 11.4980i 0.799626 + 0.432427i
\(708\) −0.0416420 + 0.262917i −0.00156500 + 0.00988103i
\(709\) −6.86073 + 32.2772i −0.257660 + 1.21220i 0.638906 + 0.769285i \(0.279387\pi\)
−0.896566 + 0.442910i \(0.853946\pi\)
\(710\) −23.7222 + 12.4273i −0.890278 + 0.466389i
\(711\) 2.51387 0.534339i 0.0942773 0.0200393i
\(712\) 4.22304 2.74247i 0.158265 0.102778i
\(713\) 11.1289 21.8418i 0.416782 0.817981i
\(714\) 0.0576348 2.35173i 0.00215693 0.0880112i
\(715\) −34.2667 + 43.3093i −1.28150 + 1.61968i
\(716\) 0.284114 + 0.0603902i 0.0106178 + 0.00225689i
\(717\) −17.5420 + 6.73376i −0.655119 + 0.251477i
\(718\) −2.96329 0.794012i −0.110589 0.0296323i
\(719\) 1.46687 + 13.9564i 0.0547051 + 0.520484i 0.987221 + 0.159356i \(0.0509417\pi\)
−0.932516 + 0.361128i \(0.882392\pi\)
\(720\) 15.5807 14.3516i 0.580660 0.534854i
\(721\) 3.05879 + 16.3507i 0.113915 + 0.608930i
\(722\) 0.215010 + 1.35752i 0.00800184 + 0.0505216i
\(723\) −5.29732 0.277621i −0.197009 0.0103248i
\(724\) 0.569354 + 0.986150i 0.0211599 + 0.0366500i
\(725\) −34.1709 + 4.37573i −1.26907 + 0.162511i
\(726\) 1.53514 + 0.886316i 0.0569746 + 0.0328943i
\(727\) −6.09289 11.9580i −0.225973 0.443496i 0.749985 0.661454i \(-0.230060\pi\)
−0.975958 + 0.217958i \(0.930060\pi\)
\(728\) 4.06892 52.8334i 0.150804 1.95814i
\(729\) 3.83166 5.27383i 0.141914 0.195327i
\(730\) −13.5501 + 8.02901i −0.501510 + 0.297167i
\(731\) −1.77128 + 3.97835i −0.0655130 + 0.147145i
\(732\) −0.0911709 + 0.340255i −0.00336977 + 0.0125762i
\(733\) −19.3207 + 23.8591i −0.713628 + 0.881257i −0.996972 0.0777611i \(-0.975223\pi\)
0.283344 + 0.959018i \(0.408556\pi\)
\(734\) −4.10015 12.6190i −0.151339 0.465774i
\(735\) 1.98396 10.0574i 0.0731794 0.370971i
\(736\) −1.01458 + 3.12255i −0.0373979 + 0.115099i
\(737\) −27.6865 42.6335i −1.01985 1.57042i
\(738\) 21.0341 1.10235i 0.774276 0.0405781i
\(739\) −5.15551 24.2548i −0.189648 0.892225i −0.965316 0.261084i \(-0.915920\pi\)
0.775668 0.631141i \(-0.217413\pi\)
\(740\) −0.0634057 0.994335i −0.00233084 0.0365525i
\(741\) 19.0941 6.20405i 0.701439 0.227911i
\(742\) −29.4057 12.1225i −1.07952 0.445031i
\(743\) −0.916200 + 0.916200i −0.0336121 + 0.0336121i −0.723713 0.690101i \(-0.757566\pi\)
0.690101 + 0.723713i \(0.257566\pi\)
\(744\) −11.7861 + 1.23877i −0.432101 + 0.0454156i
\(745\) 14.3736 + 19.3198i 0.526610 + 0.707824i
\(746\) 0.340493 3.23958i 0.0124663 0.118609i
\(747\) 12.7550 33.2279i 0.466681 1.21575i
\(748\) 0.470451 0.239707i 0.0172014 0.00876455i
\(749\) −13.1824 12.4676i −0.481673 0.455558i
\(750\) −5.58166 + 8.25832i −0.203813 + 0.301551i
\(751\) −8.30560 + 14.3857i −0.303076 + 0.524942i −0.976831 0.214012i \(-0.931347\pi\)
0.673755 + 0.738954i \(0.264680\pi\)
\(752\) 9.81528 15.1142i 0.357926 0.551158i
\(753\) −6.08700 7.51681i −0.221822 0.273928i
\(754\) 58.7191 26.1434i 2.13842 0.952088i
\(755\) −0.373011 3.20005i −0.0135753 0.116462i
\(756\) 0.861396 1.12650i 0.0313287 0.0409704i
\(757\) −21.3401 21.3401i −0.775621 0.775621i 0.203462 0.979083i \(-0.434781\pi\)
−0.979083 + 0.203462i \(0.934781\pi\)
\(758\) 27.8154 + 22.5244i 1.01030 + 0.818124i
\(759\) −6.25287 + 6.94451i −0.226965 + 0.252070i
\(760\) −26.1949 12.9756i −0.950190 0.470674i
\(761\) −12.3286 + 11.1007i −0.446910 + 0.402400i −0.861620 0.507554i \(-0.830550\pi\)
0.414710 + 0.909954i \(0.363883\pi\)
\(762\) −3.83326 1.95314i −0.138864 0.0707549i
\(763\) −6.11994 + 33.3322i −0.221557 + 1.20671i
\(764\) −0.179537 0.0583350i −0.00649541 0.00211049i
\(765\) 1.42118 5.55470i 0.0513828 0.200830i
\(766\) −0.689382 0.620722i −0.0249084 0.0224276i
\(767\) −6.79503 17.7017i −0.245354 0.639170i
\(768\) 2.21803 0.594318i 0.0800361 0.0214456i
\(769\) 19.4798 14.1529i 0.702460 0.510367i −0.178273 0.983981i \(-0.557051\pi\)
0.880732 + 0.473614i \(0.157051\pi\)
\(770\) −27.7194 + 8.60432i −0.998938 + 0.310078i
\(771\) 3.99637 + 2.90353i 0.143926 + 0.104568i
\(772\) −1.98817 0.763188i −0.0715559 0.0274678i
\(773\) −6.27790 4.07691i −0.225800 0.146636i 0.426781 0.904355i \(-0.359647\pi\)
−0.652582 + 0.757718i \(0.726314\pi\)
\(774\) 13.2355 7.64149i 0.475738 0.274668i
\(775\) −29.2188 + 10.2307i −1.04957 + 0.367499i
\(776\) 38.8680i 1.39528i
\(777\) 1.23552 + 5.10853i 0.0443239 + 0.183267i
\(778\) −35.8220 + 5.67364i −1.28428 + 0.203410i
\(779\) −10.9494 24.5927i −0.392301 0.881123i
\(780\) −0.439682 + 1.40721i −0.0157431 + 0.0503863i
\(781\) 28.9658 + 12.8964i 1.03648 + 0.461470i
\(782\) −1.39116 5.19187i −0.0497477 0.185661i
\(783\) 24.8295 + 3.93260i 0.887333 + 0.140540i
\(784\) 16.1643 20.0987i 0.577296 0.717812i
\(785\) −26.6822 21.1112i −0.952330 0.753492i
\(786\) 7.22718 + 8.02659i 0.257785 + 0.286299i
\(787\) −0.485380 9.26160i −0.0173019 0.330140i −0.993543 0.113454i \(-0.963808\pi\)
0.976241 0.216686i \(-0.0695248\pi\)
\(788\) 0.110771 + 2.11363i 0.00394604 + 0.0752949i
\(789\) 7.86237 + 8.73204i 0.279908 + 0.310869i
\(790\) −3.04012 0.124834i −0.108163 0.00444139i
\(791\) 2.06988 + 25.7480i 0.0735964 + 0.915494i
\(792\) −26.7468 4.23628i −0.950407 0.150530i
\(793\) −6.49411 24.2364i −0.230613 0.860658i
\(794\) 41.8610 + 18.6377i 1.48559 + 0.661428i
\(795\) 10.5482 + 7.48278i 0.374108 + 0.265387i
\(796\) −0.126058 0.283132i −0.00446802 0.0100353i
\(797\) 38.0317 6.02362i 1.34715 0.213368i 0.559162 0.829058i \(-0.311123\pi\)
0.787988 + 0.615691i \(0.211123\pi\)
\(798\) 10.1219 + 2.97977i 0.358310 + 0.105483i
\(799\) 4.87788i 0.172567i
\(800\) 3.65091 1.96559i 0.129079 0.0694940i
\(801\) −3.83634 + 2.21491i −0.135551 + 0.0782601i
\(802\) 34.6976 + 22.5329i 1.22522 + 0.795664i
\(803\) 17.4092 + 6.68278i 0.614359 + 0.235830i
\(804\) −1.09789 0.797666i −0.0387197 0.0281315i
\(805\) −2.14107 23.3246i −0.0754628 0.822084i
\(806\) 46.7299 33.9512i 1.64599 1.19588i
\(807\) −10.3206 + 2.76539i −0.363302 + 0.0973465i
\(808\) −9.56853 24.9269i −0.336620 0.876924i
\(809\) −41.7849 37.6233i −1.46908 1.32277i −0.836072 0.548620i \(-0.815153\pi\)
−0.633008 0.774145i \(-0.718180\pi\)
\(810\) −12.4773 + 10.3399i −0.438406 + 0.363308i
\(811\) −37.3508 12.1360i −1.31156 0.426153i −0.431974 0.901886i \(-0.642183\pi\)
−0.879590 + 0.475733i \(0.842183\pi\)
\(812\) −2.63388 0.483592i −0.0924311 0.0169708i
\(813\) −2.22006 1.13118i −0.0778610 0.0396722i
\(814\) 11.0586 9.95719i 0.387603 0.348999i
\(815\) 33.5862 5.71001i 1.17647 0.200013i
\(816\) −1.61036 + 1.78848i −0.0563738 + 0.0626095i
\(817\) −15.1798 12.2924i −0.531075 0.430056i
\(818\) 18.9198 + 18.9198i 0.661516 + 0.661516i
\(819\) −6.00723 + 46.2285i −0.209910 + 1.61536i
\(820\) 1.93816 + 0.389090i 0.0676834 + 0.0135876i
\(821\) −9.40564 + 4.18766i −0.328259 + 0.146150i −0.564248 0.825605i \(-0.690834\pi\)
0.235989 + 0.971756i \(0.424167\pi\)
\(822\) 3.29148 + 4.06464i 0.114804 + 0.141771i
\(823\) −2.77331 + 4.27053i −0.0966716 + 0.148861i −0.883697 0.468059i \(-0.844953\pi\)
0.787025 + 0.616921i \(0.211620\pi\)
\(824\) 9.18728 15.9128i 0.320054 0.554350i
\(825\) 11.7683 0.884298i 0.409720 0.0307873i
\(826\) 2.31003 9.69358i 0.0803763 0.337283i
\(827\) 47.9120 24.4124i 1.66606 0.848902i 0.671945 0.740601i \(-0.265459\pi\)
0.994118 0.108300i \(-0.0345408\pi\)
\(828\) 0.535889 1.39604i 0.0186234 0.0485157i
\(829\) 3.19208 30.3706i 0.110866 1.05482i −0.787725 0.616027i \(-0.788741\pi\)
0.898590 0.438789i \(-0.144592\pi\)
\(830\) −24.3804 + 34.3683i −0.846256 + 1.19294i
\(831\) 4.37426 0.459753i 0.151741 0.0159487i
\(832\) −41.1804 + 41.1804i −1.42767 + 1.42767i
\(833\) 0.706433 6.94532i 0.0244764 0.240641i
\(834\) −6.15013 + 1.99830i −0.212961 + 0.0691954i
\(835\) 6.98561 11.0282i 0.241747 0.381648i
\(836\) 0.492383 + 2.31648i 0.0170294 + 0.0801172i
\(837\) 22.5600 1.18232i 0.779788 0.0408669i
\(838\) −16.6866 25.6950i −0.576427 0.887620i
\(839\) 5.20568 16.0214i 0.179720 0.553121i −0.820097 0.572224i \(-0.806081\pi\)
0.999818 + 0.0191024i \(0.00608084\pi\)
\(840\) −8.89328 + 7.00958i −0.306847 + 0.241853i
\(841\) −5.70811 17.5678i −0.196831 0.605785i
\(842\) −7.20878 + 8.90211i −0.248431 + 0.306787i
\(843\) 0.553957 2.06739i 0.0190793 0.0712048i
\(844\) −0.499571 + 1.12205i −0.0171959 + 0.0386227i
\(845\) −16.6300 74.1026i −0.572088 2.54921i
\(846\) −10.0620 + 13.8492i −0.345939 + 0.476144i
\(847\) 4.34032 + 2.97231i 0.149135 + 0.102130i
\(848\) 14.7726 + 28.9928i 0.507293 + 0.995618i
\(849\) 2.82714 + 1.63225i 0.0970272 + 0.0560187i
\(850\) −3.26009 + 5.95400i −0.111820 + 0.204221i
\(851\) 6.00444 + 10.4000i 0.205830 + 0.356507i
\(852\) 0.845285 + 0.0442995i 0.0289590 + 0.00151768i
\(853\) 6.94371 + 43.8409i 0.237748 + 1.50108i 0.760915 + 0.648852i \(0.224751\pi\)
−0.523167 + 0.852230i \(0.675249\pi\)
\(854\) 4.38099 12.4378i 0.149914 0.425613i
\(855\) 22.4157 + 12.6055i 0.766600 + 0.431100i
\(856\) 2.09502 + 19.9328i 0.0716063 + 0.681289i
\(857\) 26.3229 + 7.05321i 0.899174 + 0.240933i 0.678661 0.734451i \(-0.262560\pi\)
0.220512 + 0.975384i \(0.429227\pi\)
\(858\) −20.5565 + 7.89091i −0.701788 + 0.269391i
\(859\) −51.7675 11.0035i −1.76628 0.375435i −0.793758 0.608234i \(-0.791878\pi\)
−0.972525 + 0.232799i \(0.925212\pi\)
\(860\) 1.38119 0.386900i 0.0470983 0.0131932i
\(861\) −10.4247 0.255483i −0.355273 0.00870684i
\(862\) −5.47262 + 10.7406i −0.186398 + 0.365827i
\(863\) −19.0573 + 12.3760i −0.648719 + 0.421283i −0.826616 0.562766i \(-0.809737\pi\)
0.177897 + 0.984049i \(0.443071\pi\)
\(864\) −2.95962 + 0.629086i −0.100688 + 0.0214019i
\(865\) −0.809854 + 1.63492i −0.0275359 + 0.0555891i
\(866\) −1.92661 + 9.06399i −0.0654689 + 0.308007i
\(867\) 1.63979 10.3532i 0.0556902 0.351614i
\(868\) −2.40555 + 0.0670296i −0.0816497 + 0.00227513i
\(869\) 2.11747 + 2.91445i 0.0718303 + 0.0988659i
\(870\) −12.6104 5.44430i −0.427532 0.184579i
\(871\) 96.1347 + 10.1042i 3.25740 + 0.342366i
\(872\) 29.0923 23.5585i 0.985190 0.797791i
\(873\) −1.78956 + 34.1468i −0.0605673 + 1.15569i
\(874\) 24.1085 0.815484
\(875\) −18.3973 + 23.1634i −0.621941 + 0.783064i
\(876\) 0.497819 0.0168197
\(877\) 1.01832 19.4307i 0.0343861 0.656127i −0.926012 0.377495i \(-0.876786\pi\)
0.960398 0.278632i \(-0.0898810\pi\)
\(878\) 9.53767 7.72345i 0.321881 0.260654i
\(879\) 9.55480 + 1.00425i 0.322275 + 0.0338725i
\(880\) 27.2608 + 11.7694i 0.918962 + 0.396745i
\(881\) −22.4359 30.8804i −0.755886 1.04039i −0.997545 0.0700265i \(-0.977692\pi\)
0.241659 0.970361i \(-0.422308\pi\)
\(882\) −16.3324 + 18.2618i −0.549940 + 0.614906i
\(883\) −7.81845 + 49.3637i −0.263112 + 1.66122i 0.402873 + 0.915256i \(0.368012\pi\)
−0.665984 + 0.745966i \(0.731988\pi\)
\(884\) −0.208746 + 0.982074i −0.00702090 + 0.0330307i
\(885\) −1.79852 + 3.63083i −0.0604567 + 0.122049i
\(886\) 15.5047 3.29563i 0.520891 0.110719i
\(887\) 26.5223 17.2238i 0.890532 0.578318i −0.0162737 0.999868i \(-0.505180\pi\)
0.906805 + 0.421550i \(0.138514\pi\)
\(888\) 2.63572 5.17289i 0.0884489 0.173591i
\(889\) −10.8970 6.65259i −0.365474 0.223121i
\(890\) 5.05013 1.41464i 0.169281 0.0474190i
\(891\) 18.7668 + 3.98901i 0.628712 + 0.133637i
\(892\) 1.41204 0.542031i 0.0472786 0.0181486i
\(893\) 21.1332 + 5.66263i 0.707196 + 0.189493i
\(894\) 1.00358 + 9.54838i 0.0335646 + 0.319346i
\(895\) 3.85369 + 2.16713i 0.128815 + 0.0724393i
\(896\) −25.7718 + 4.82125i −0.860975 + 0.161067i
\(897\) −2.77976 17.5507i −0.0928134 0.586001i
\(898\) −9.07649 0.475678i −0.302886 0.0158736i
\(899\) −21.3301 36.9449i −0.711399 1.23218i
\(900\) −1.70738 + 0.806977i −0.0569128 + 0.0268992i
\(901\) 7.62741 + 4.40369i 0.254106 + 0.146708i
\(902\) 13.4038 + 26.3064i 0.446297 + 0.875907i
\(903\) −6.82376 + 3.26883i −0.227080 + 0.108780i
\(904\) 16.7716 23.0841i 0.557814 0.767765i
\(905\) 3.79539 + 16.9122i 0.126163 + 0.562179i
\(906\) 0.522462 1.17347i 0.0173576 0.0389859i
\(907\) 0.872580 3.25651i 0.0289735 0.108131i −0.949925 0.312479i \(-0.898841\pi\)
0.978898 + 0.204348i \(0.0655074\pi\)
\(908\) 0.483526 0.597105i 0.0160464 0.0198156i
\(909\) 7.25858 + 22.3396i 0.240752 + 0.740958i
\(910\) 20.4560 51.2597i 0.678110 1.69924i
\(911\) 0.771586 2.37470i 0.0255638 0.0786772i −0.937461 0.348091i \(-0.886830\pi\)
0.963024 + 0.269414i \(0.0868300\pi\)
\(912\) −5.87910 9.05303i −0.194677 0.299776i
\(913\) 49.8215 2.61103i 1.64885 0.0864126i
\(914\) 1.61409 + 7.59372i 0.0533895 + 0.251178i
\(915\) −2.86919 + 4.52962i −0.0948526 + 0.149745i
\(916\) 3.36691 1.09397i 0.111246 0.0361459i
\(917\) 19.5552 + 25.3965i 0.645769 + 0.838667i
\(918\) 3.50262 3.50262i 0.115604 0.115604i
\(919\) −27.0905 + 2.84732i −0.893632 + 0.0939245i −0.540201 0.841536i \(-0.681652\pi\)
−0.353431 + 0.935461i \(0.614985\pi\)
\(920\) −14.9699 + 21.1026i −0.493543 + 0.695732i
\(921\) −0.303399 + 2.88665i −0.00999734 + 0.0951183i
\(922\) −3.29151 + 8.57467i −0.108400 + 0.282392i
\(923\) −53.7209 + 27.3722i −1.76824 + 0.900966i
\(924\) 0.892379 + 0.212659i 0.0293571 + 0.00699596i
\(925\) 3.59259 14.7343i 0.118124 0.484462i
\(926\) 28.9092 50.0721i 0.950014 1.64547i
\(927\) −8.80399 + 13.5569i −0.289161 + 0.445269i
\(928\) 3.59576 + 4.44040i 0.118037 + 0.145763i
\(929\) 37.8502 16.8520i 1.24183 0.552896i 0.322565 0.946547i \(-0.395455\pi\)
0.919260 + 0.393651i \(0.128788\pi\)
\(930\) −12.1018 2.42946i −0.396834 0.0796653i
\(931\) 29.2702 + 11.1233i 0.959293 + 0.364550i
\(932\) 1.05999 + 1.05999i 0.0347211 + 0.0347211i
\(933\) −2.66503 2.15810i −0.0872493 0.0706531i
\(934\) 3.26518 3.62635i 0.106840 0.118658i
\(935\) 7.92324 1.34703i 0.259118 0.0440527i
\(936\) 38.2677 34.4564i 1.25082 1.12624i
\(937\) −33.1975 16.9150i −1.08452 0.552588i −0.182023 0.983294i \(-0.558265\pi\)
−0.902492 + 0.430706i \(0.858265\pi\)
\(938\) 38.6855 + 32.9285i 1.26313 + 1.07515i
\(939\) 4.99010 + 1.62138i 0.162846 + 0.0529118i
\(940\) −1.23706 + 1.02515i −0.0403484 + 0.0334368i
\(941\) 24.7151 + 22.2536i 0.805691 + 0.725447i 0.965133 0.261760i \(-0.0843029\pi\)
−0.159442 + 0.987207i \(0.550970\pi\)
\(942\) −4.86147 12.6646i −0.158395 0.412634i
\(943\) −23.0145 + 6.16671i −0.749455 + 0.200816i
\(944\) −8.24764 + 5.99226i −0.268438 + 0.195032i
\(945\) 17.6288 12.4564i 0.573465 0.405206i
\(946\) 17.3311 + 12.5918i 0.563484 + 0.409395i
\(947\) 15.3985 + 5.91093i 0.500384 + 0.192079i 0.595451 0.803392i \(-0.296973\pi\)
−0.0950675 + 0.995471i \(0.530307\pi\)
\(948\) 0.0806553 + 0.0523782i 0.00261956 + 0.00170116i
\(949\) −30.7090 + 17.7298i −0.996855 + 0.575535i
\(950\) −22.0109 21.0361i −0.714128 0.682501i
\(951\) 4.16096i 0.134928i
\(952\) −5.58482 + 5.31763i −0.181005 + 0.172345i
\(953\) 23.6472 3.74535i 0.766009 0.121324i 0.238810 0.971066i \(-0.423243\pi\)
0.527198 + 0.849742i \(0.323243\pi\)
\(954\) −12.5717 28.2366i −0.407025 0.914192i
\(955\) −2.34364 1.66255i −0.0758384 0.0537987i
\(956\) 3.85032 + 1.71427i 0.124528 + 0.0554435i
\(957\) 4.20902 + 15.7083i 0.136058 + 0.507776i
\(958\) −29.2204 4.62806i −0.944068 0.149526i
\(959\) 8.81283 + 12.7768i 0.284581 + 0.412584i
\(960\) 12.4346 + 0.510592i 0.401325 + 0.0164793i
\(961\) −4.90897 5.45196i −0.158354 0.175870i
\(962\) 1.48092 + 28.2577i 0.0477469 + 0.911064i
\(963\) −0.922799 17.6081i −0.0297368 0.567412i
\(964\) 0.796161 + 0.884226i 0.0256426 + 0.0284790i
\(965\) −25.4213 20.1135i −0.818340 0.647478i
\(966\) 4.00631 8.43578i 0.128901 0.271417i
\(967\) −19.7981 3.13572i −0.636665 0.100838i −0.170246 0.985402i \(-0.554456\pi\)
−0.466419 + 0.884564i \(0.654456\pi\)
\(968\) −1.50396 5.61286i −0.0483392 0.180404i
\(969\) −2.66913 1.18837i −0.0857448 0.0381760i
\(970\) 12.0731 38.6401i 0.387642 1.24066i
\(971\) −8.58616 19.2848i −0.275543 0.618880i 0.721770 0.692133i \(-0.243329\pi\)
−0.997313 + 0.0732528i \(0.976662\pi\)
\(972\) 2.09406 0.331666i 0.0671670 0.0106382i
\(973\) −18.6528 + 4.51124i −0.597980 + 0.144624i
\(974\) 16.4741i 0.527864i
\(975\) −12.7761 + 18.4491i −0.409163 + 0.590846i
\(976\) −11.6833 + 6.74533i −0.373972 + 0.215913i
\(977\) −32.7964 21.2982i −1.04925 0.681390i −0.0997026 0.995017i \(-0.531789\pi\)
−0.949546 + 0.313627i \(0.898456\pi\)
\(978\) 12.6810 + 4.86779i 0.405495 + 0.155655i
\(979\) −5.02349 3.64978i −0.160551 0.116647i
\(980\) −1.90984 + 1.28050i −0.0610076 + 0.0409041i
\(981\) −26.6432 + 19.3574i −0.850652 + 0.618035i
\(982\) 42.2858 11.3304i 1.34939 0.361569i
\(983\) −12.8109 33.3735i −0.408604 1.06445i −0.971315 0.237796i \(-0.923575\pi\)
0.562712 0.826653i \(-0.309758\pi\)
\(984\) 8.56013 + 7.70758i 0.272887 + 0.245709i
\(985\) −7.98547 + 31.2113i −0.254438 + 0.994475i
\(986\) −8.89616 2.89054i −0.283311 0.0920535i
\(987\) 5.49327 6.45368i 0.174853 0.205423i
\(988\) −4.01247 2.04446i −0.127654 0.0650428i
\(989\) −12.8475 + 11.5680i −0.408528 + 0.367840i
\(990\) −25.2741 12.5195i −0.803264 0.397894i
\(991\) 38.4732 42.7288i 1.22214 1.35732i 0.308281 0.951295i \(-0.400246\pi\)
0.913860 0.406029i \(-0.133087\pi\)
\(992\) 3.99034 + 3.23131i 0.126693 + 0.102594i
\(993\) 9.73272 + 9.73272i 0.308859 + 0.308859i
\(994\) −31.4226 4.08325i −0.996664 0.129513i
\(995\) −0.546197 4.68580i −0.0173156 0.148550i
\(996\) 1.21671 0.541712i 0.0385528 0.0171648i
\(997\) 33.1714 + 40.9632i 1.05055 + 1.29732i 0.953289 + 0.302060i \(0.0976742\pi\)
0.0972591 + 0.995259i \(0.468992\pi\)
\(998\) 29.5560 45.5122i 0.935577 1.44066i
\(999\) −5.53350 + 9.58430i −0.175072 + 0.303234i
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 175.2.x.a.47.14 yes 288
5.2 odd 4 875.2.bb.a.243.14 288
5.3 odd 4 875.2.bb.b.243.5 288
5.4 even 2 875.2.bb.c.257.5 288
7.3 odd 6 inner 175.2.x.a.122.14 yes 288
25.6 even 5 875.2.bb.b.607.14 288
25.8 odd 20 inner 175.2.x.a.33.14 288
25.17 odd 20 875.2.bb.c.768.5 288
25.19 even 10 875.2.bb.a.607.5 288
35.3 even 12 875.2.bb.b.493.14 288
35.17 even 12 875.2.bb.a.493.5 288
35.24 odd 6 875.2.bb.c.507.5 288
175.17 even 60 875.2.bb.c.143.5 288
175.31 odd 30 875.2.bb.b.857.5 288
175.94 odd 30 875.2.bb.a.857.14 288
175.108 even 60 inner 175.2.x.a.108.14 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.33.14 288 25.8 odd 20 inner
175.2.x.a.47.14 yes 288 1.1 even 1 trivial
175.2.x.a.108.14 yes 288 175.108 even 60 inner
175.2.x.a.122.14 yes 288 7.3 odd 6 inner
875.2.bb.a.243.14 288 5.2 odd 4
875.2.bb.a.493.5 288 35.17 even 12
875.2.bb.a.607.5 288 25.19 even 10
875.2.bb.a.857.14 288 175.94 odd 30
875.2.bb.b.243.5 288 5.3 odd 4
875.2.bb.b.493.14 288 35.3 even 12
875.2.bb.b.607.14 288 25.6 even 5
875.2.bb.b.857.5 288 175.31 odd 30
875.2.bb.c.143.5 288 175.17 even 60
875.2.bb.c.257.5 288 5.4 even 2
875.2.bb.c.507.5 288 35.24 odd 6
875.2.bb.c.768.5 288 25.17 odd 20