Properties

Label 240.2.bk.b.11.17
Level $240$
Weight $2$
Character 240.11
Analytic conductor $1.916$
Analytic rank $0$
Dimension $60$
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] = [240,2,Mod(11,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bk (of order \(4\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(30\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.17
Character \(\chi\) \(=\) 240.11
Dual form 240.2.bk.b.131.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.371549 - 1.36453i) q^{2} +(-0.516584 - 1.65322i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.44781 + 0.0906432i) q^{6} -1.29120 q^{7} +(-2.02413 + 1.97558i) q^{8} +(-2.46628 + 1.70806i) q^{9} +O(q^{10})\) \(q+(0.371549 - 1.36453i) q^{2} +(-0.516584 - 1.65322i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.44781 + 0.0906432i) q^{6} -1.29120 q^{7} +(-2.02413 + 1.97558i) q^{8} +(-2.46628 + 1.70806i) q^{9} +(0.702146 + 1.22760i) q^{10} +(-4.09936 - 4.09936i) q^{11} +(-0.785797 + 3.37380i) q^{12} +(4.40407 - 4.40407i) q^{13} +(-0.479744 + 1.76189i) q^{14} +(1.53428 + 0.803724i) q^{15} +(1.94368 + 3.49601i) q^{16} +2.75677i q^{17} +(1.41435 + 3.99995i) q^{18} +(1.31048 + 1.31048i) q^{19} +(1.93598 - 0.501989i) q^{20} +(0.667013 + 2.13464i) q^{21} +(-7.11683 + 4.07060i) q^{22} -2.76043i q^{23} +(4.31170 + 2.32578i) q^{24} -1.00000i q^{25} +(-4.37317 - 7.64582i) q^{26} +(4.09784 + 3.19496i) q^{27} +(2.22590 + 1.30925i) q^{28} +(-4.08036 - 4.08036i) q^{29} +(1.66677 - 1.79496i) q^{30} -10.0767i q^{31} +(5.49260 - 1.35327i) q^{32} +(-4.65948 + 8.89481i) q^{33} +(3.76170 + 1.02428i) q^{34} +(0.913016 - 0.913016i) q^{35} +(5.98357 - 0.443755i) q^{36} +(3.31466 + 3.31466i) q^{37} +(2.27511 - 1.30129i) q^{38} +(-9.55596 - 5.00582i) q^{39} +(0.0343297 - 2.82822i) q^{40} -0.387829 q^{41} +(3.16061 - 0.117038i) q^{42} +(3.66350 - 3.66350i) q^{43} +(2.91022 + 11.2236i) q^{44} +(0.536147 - 2.95170i) q^{45} +(-3.76670 - 1.02564i) q^{46} -0.00218401 q^{47} +(4.77561 - 5.01932i) q^{48} -5.33280 q^{49} +(-1.36453 - 0.371549i) q^{50} +(4.55755 - 1.42410i) q^{51} +(-12.0578 + 3.12653i) q^{52} +(1.76845 - 1.76845i) q^{53} +(5.88217 - 4.40455i) q^{54} +5.79737 q^{55} +(2.61355 - 2.55087i) q^{56} +(1.48954 - 2.84349i) q^{57} +(-7.08384 + 4.05173i) q^{58} +(-0.279145 - 0.279145i) q^{59} +(-1.82999 - 2.94128i) q^{60} +(5.12461 - 5.12461i) q^{61} +(-13.7500 - 3.74399i) q^{62} +(3.18446 - 2.20544i) q^{63} +(0.194184 - 7.99764i) q^{64} +6.22829i q^{65} +(10.4060 + 9.66288i) q^{66} +(0.763263 + 0.763263i) q^{67} +(2.79532 - 4.75240i) q^{68} +(-4.56361 + 1.42600i) q^{69} +(-0.906611 - 1.58507i) q^{70} +9.45616i q^{71} +(1.61767 - 8.32965i) q^{72} +14.2158i q^{73} +(5.75453 - 3.29141i) q^{74} +(-1.65322 + 0.516584i) q^{75} +(-0.930338 - 3.58795i) q^{76} +(5.29309 + 5.29309i) q^{77} +(-10.3811 + 11.1795i) q^{78} +8.54188i q^{79} +(-3.84644 - 1.09767i) q^{80} +(3.16509 - 8.42509i) q^{81} +(-0.144098 + 0.529206i) q^{82} +(8.60385 - 8.60385i) q^{83} +(1.01462 - 4.35625i) q^{84} +(-1.94933 - 1.94933i) q^{85} +(-3.63780 - 6.36015i) q^{86} +(-4.63789 + 8.85358i) q^{87} +(16.3962 + 0.199022i) q^{88} +4.67026 q^{89} +(-3.82849 - 1.82829i) q^{90} +(-5.68653 + 5.68653i) q^{91} +(-2.79903 + 4.75872i) q^{92} +(-16.6590 + 5.20547i) q^{93} +(-0.000811466 + 0.00298015i) q^{94} -1.85330 q^{95} +(-5.07465 - 8.38140i) q^{96} -6.69158 q^{97} +(-1.98140 + 7.27679i) q^{98} +(17.1121 + 3.10824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.371549 1.36453i 0.262725 0.964871i
\(3\) −0.516584 1.65322i −0.298250 0.954488i
\(4\) −1.72390 1.01398i −0.861951 0.506991i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −2.44781 + 0.0906432i −0.999315 + 0.0370049i
\(7\) −1.29120 −0.488028 −0.244014 0.969772i \(-0.578464\pi\)
−0.244014 + 0.969772i \(0.578464\pi\)
\(8\) −2.02413 + 1.97558i −0.715637 + 0.698472i
\(9\) −2.46628 + 1.70806i −0.822094 + 0.569352i
\(10\) 0.702146 + 1.22760i 0.222038 + 0.388200i
\(11\) −4.09936 4.09936i −1.23600 1.23600i −0.961621 0.274383i \(-0.911526\pi\)
−0.274383 0.961621i \(-0.588474\pi\)
\(12\) −0.785797 + 3.37380i −0.226840 + 0.973932i
\(13\) 4.40407 4.40407i 1.22147 1.22147i 0.254358 0.967110i \(-0.418136\pi\)
0.967110 0.254358i \(-0.0818641\pi\)
\(14\) −0.479744 + 1.76189i −0.128217 + 0.470884i
\(15\) 1.53428 + 0.803724i 0.396150 + 0.207521i
\(16\) 1.94368 + 3.49601i 0.485920 + 0.874003i
\(17\) 2.75677i 0.668615i 0.942464 + 0.334307i \(0.108502\pi\)
−0.942464 + 0.334307i \(0.891498\pi\)
\(18\) 1.41435 + 3.99995i 0.333366 + 0.942797i
\(19\) 1.31048 + 1.31048i 0.300646 + 0.300646i 0.841266 0.540621i \(-0.181811\pi\)
−0.540621 + 0.841266i \(0.681811\pi\)
\(20\) 1.93598 0.501989i 0.432898 0.112248i
\(21\) 0.667013 + 2.13464i 0.145554 + 0.465816i
\(22\) −7.11683 + 4.07060i −1.51731 + 0.867855i
\(23\) 2.76043i 0.575590i −0.957692 0.287795i \(-0.907078\pi\)
0.957692 0.287795i \(-0.0929222\pi\)
\(24\) 4.31170 + 2.32578i 0.880122 + 0.474748i
\(25\) 1.00000i 0.200000i
\(26\) −4.37317 7.64582i −0.857649 1.49947i
\(27\) 4.09784 + 3.19496i 0.788629 + 0.614869i
\(28\) 2.22590 + 1.30925i 0.420656 + 0.247426i
\(29\) −4.08036 4.08036i −0.757703 0.757703i 0.218201 0.975904i \(-0.429981\pi\)
−0.975904 + 0.218201i \(0.929981\pi\)
\(30\) 1.66677 1.79496i 0.304309 0.327713i
\(31\) 10.0767i 1.80983i −0.425592 0.904915i \(-0.639934\pi\)
0.425592 0.904915i \(-0.360066\pi\)
\(32\) 5.49260 1.35327i 0.970964 0.239227i
\(33\) −4.65948 + 8.89481i −0.811112 + 1.54839i
\(34\) 3.76170 + 1.02428i 0.645127 + 0.175662i
\(35\) 0.913016 0.913016i 0.154328 0.154328i
\(36\) 5.98357 0.443755i 0.997261 0.0739591i
\(37\) 3.31466 + 3.31466i 0.544927 + 0.544927i 0.924969 0.380042i \(-0.124090\pi\)
−0.380042 + 0.924969i \(0.624090\pi\)
\(38\) 2.27511 1.30129i 0.369071 0.211097i
\(39\) −9.55596 5.00582i −1.53018 0.801573i
\(40\) 0.0343297 2.82822i 0.00542800 0.447181i
\(41\) −0.387829 −0.0605687 −0.0302844 0.999541i \(-0.509641\pi\)
−0.0302844 + 0.999541i \(0.509641\pi\)
\(42\) 3.16061 0.117038i 0.487693 0.0180594i
\(43\) 3.66350 3.66350i 0.558679 0.558679i −0.370252 0.928931i \(-0.620729\pi\)
0.928931 + 0.370252i \(0.120729\pi\)
\(44\) 2.91022 + 11.2236i 0.438732 + 1.69202i
\(45\) 0.536147 2.95170i 0.0799240 0.440014i
\(46\) −3.76670 1.02564i −0.555370 0.151222i
\(47\) −0.00218401 −0.000318570 −0.000159285 1.00000i \(-0.500051\pi\)
−0.000159285 1.00000i \(0.500051\pi\)
\(48\) 4.77561 5.01932i 0.689300 0.724476i
\(49\) −5.33280 −0.761829
\(50\) −1.36453 0.371549i −0.192974 0.0525450i
\(51\) 4.55755 1.42410i 0.638185 0.199414i
\(52\) −12.0578 + 3.12653i −1.67212 + 0.433572i
\(53\) 1.76845 1.76845i 0.242916 0.242916i −0.575140 0.818055i \(-0.695052\pi\)
0.818055 + 0.575140i \(0.195052\pi\)
\(54\) 5.88217 4.40455i 0.800462 0.599383i
\(55\) 5.79737 0.781717
\(56\) 2.61355 2.55087i 0.349251 0.340874i
\(57\) 1.48954 2.84349i 0.197295 0.376630i
\(58\) −7.08384 + 4.05173i −0.930153 + 0.532018i
\(59\) −0.279145 0.279145i −0.0363416 0.0363416i 0.688702 0.725044i \(-0.258181\pi\)
−0.725044 + 0.688702i \(0.758181\pi\)
\(60\) −1.82999 2.94128i −0.236251 0.379717i
\(61\) 5.12461 5.12461i 0.656140 0.656140i −0.298325 0.954464i \(-0.596428\pi\)
0.954464 + 0.298325i \(0.0964279\pi\)
\(62\) −13.7500 3.74399i −1.74625 0.475488i
\(63\) 3.18446 2.20544i 0.401205 0.277859i
\(64\) 0.194184 7.99764i 0.0242730 0.999705i
\(65\) 6.22829i 0.772524i
\(66\) 10.4060 + 9.66288i 1.28090 + 1.18942i
\(67\) 0.763263 + 0.763263i 0.0932475 + 0.0932475i 0.752192 0.658944i \(-0.228997\pi\)
−0.658944 + 0.752192i \(0.728997\pi\)
\(68\) 2.79532 4.75240i 0.338982 0.576313i
\(69\) −4.56361 + 1.42600i −0.549394 + 0.171670i
\(70\) −0.906611 1.58507i −0.108361 0.189452i
\(71\) 9.45616i 1.12224i 0.827735 + 0.561120i \(0.189629\pi\)
−0.827735 + 0.561120i \(0.810371\pi\)
\(72\) 1.61767 8.32965i 0.190644 0.981659i
\(73\) 14.2158i 1.66383i 0.554904 + 0.831914i \(0.312755\pi\)
−0.554904 + 0.831914i \(0.687245\pi\)
\(74\) 5.75453 3.29141i 0.668951 0.382619i
\(75\) −1.65322 + 0.516584i −0.190898 + 0.0596500i
\(76\) −0.930338 3.58795i −0.106717 0.411566i
\(77\) 5.29309 + 5.29309i 0.603204 + 0.603204i
\(78\) −10.3811 + 11.1795i −1.17543 + 1.26583i
\(79\) 8.54188i 0.961037i 0.876985 + 0.480519i \(0.159552\pi\)
−0.876985 + 0.480519i \(0.840448\pi\)
\(80\) −3.84644 1.09767i −0.430045 0.122723i
\(81\) 3.16509 8.42509i 0.351677 0.936121i
\(82\) −0.144098 + 0.529206i −0.0159129 + 0.0584410i
\(83\) 8.60385 8.60385i 0.944395 0.944395i −0.0541387 0.998533i \(-0.517241\pi\)
0.998533 + 0.0541387i \(0.0172413\pi\)
\(84\) 1.01462 4.35625i 0.110704 0.475306i
\(85\) −1.94933 1.94933i −0.211435 0.211435i
\(86\) −3.63780 6.36015i −0.392274 0.685832i
\(87\) −4.63789 + 8.85358i −0.497234 + 0.949203i
\(88\) 16.3962 + 0.199022i 1.74784 + 0.0212158i
\(89\) 4.67026 0.495047 0.247523 0.968882i \(-0.420383\pi\)
0.247523 + 0.968882i \(0.420383\pi\)
\(90\) −3.82849 1.82829i −0.403558 0.192719i
\(91\) −5.68653 + 5.68653i −0.596110 + 0.596110i
\(92\) −2.79903 + 4.75872i −0.291819 + 0.496131i
\(93\) −16.6590 + 5.20547i −1.72746 + 0.539782i
\(94\) −0.000811466 0.00298015i −8.36963e−5 0.000307379i
\(95\) −1.85330 −0.190145
\(96\) −5.07465 8.38140i −0.517929 0.855423i
\(97\) −6.69158 −0.679427 −0.339714 0.940529i \(-0.610330\pi\)
−0.339714 + 0.940529i \(0.610330\pi\)
\(98\) −1.98140 + 7.27679i −0.200151 + 0.735067i
\(99\) 17.1121 + 3.10824i 1.71983 + 0.312390i
\(100\) −1.01398 + 1.72390i −0.101398 + 0.172390i
\(101\) 6.31315 6.31315i 0.628182 0.628182i −0.319429 0.947610i \(-0.603491\pi\)
0.947610 + 0.319429i \(0.103491\pi\)
\(102\) −0.249882 6.74805i −0.0247420 0.668157i
\(103\) −2.23091 −0.219818 −0.109909 0.993942i \(-0.535056\pi\)
−0.109909 + 0.993942i \(0.535056\pi\)
\(104\) −0.213815 + 17.6150i −0.0209663 + 1.72729i
\(105\) −1.98107 1.03777i −0.193332 0.101276i
\(106\) −1.75605 3.07018i −0.170562 0.298202i
\(107\) 1.88115 + 1.88115i 0.181857 + 0.181857i 0.792165 0.610307i \(-0.208954\pi\)
−0.610307 + 0.792165i \(0.708954\pi\)
\(108\) −3.82464 9.66293i −0.368026 0.929815i
\(109\) 7.31517 7.31517i 0.700666 0.700666i −0.263887 0.964554i \(-0.585005\pi\)
0.964554 + 0.263887i \(0.0850047\pi\)
\(110\) 2.15401 7.91070i 0.205377 0.754256i
\(111\) 3.76757 7.19218i 0.357602 0.682651i
\(112\) −2.50968 4.51405i −0.237142 0.426538i
\(113\) 3.64060i 0.342478i −0.985229 0.171239i \(-0.945223\pi\)
0.985229 0.171239i \(-0.0547771\pi\)
\(114\) −3.32660 3.08903i −0.311565 0.289314i
\(115\) 1.95192 + 1.95192i 0.182018 + 0.182018i
\(116\) 2.89673 + 11.1715i 0.268954 + 1.03725i
\(117\) −3.33928 + 18.3841i −0.308716 + 1.69961i
\(118\) −0.484618 + 0.277186i −0.0446127 + 0.0255171i
\(119\) 3.55954i 0.326303i
\(120\) −4.69341 + 1.40426i −0.428447 + 0.128191i
\(121\) 22.6095i 2.05541i
\(122\) −5.08866 8.89675i −0.460706 0.805474i
\(123\) 0.200346 + 0.641167i 0.0180646 + 0.0578121i
\(124\) −10.2176 + 17.3713i −0.917568 + 1.55999i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −1.82621 5.16474i −0.162692 0.460111i
\(127\) 10.0049i 0.887794i −0.896078 0.443897i \(-0.853596\pi\)
0.896078 0.443897i \(-0.146404\pi\)
\(128\) −10.8409 3.23649i −0.958209 0.286068i
\(129\) −7.94909 4.16408i −0.699878 0.366626i
\(130\) 8.49871 + 2.31412i 0.745386 + 0.202961i
\(131\) −12.2224 + 12.2224i −1.06787 + 1.06787i −0.0703493 + 0.997522i \(0.522411\pi\)
−0.997522 + 0.0703493i \(0.977589\pi\)
\(132\) 17.0517 10.6092i 1.48416 0.923408i
\(133\) −1.69210 1.69210i −0.146723 0.146723i
\(134\) 1.32509 0.757908i 0.114470 0.0654733i
\(135\) −5.15678 + 0.638433i −0.443825 + 0.0549476i
\(136\) −5.44621 5.58005i −0.467009 0.478486i
\(137\) 17.6432 1.50736 0.753682 0.657239i \(-0.228276\pi\)
0.753682 + 0.657239i \(0.228276\pi\)
\(138\) 0.250214 + 6.75702i 0.0212997 + 0.575196i
\(139\) −15.1869 + 15.1869i −1.28814 + 1.28814i −0.352222 + 0.935916i \(0.614574\pi\)
−0.935916 + 0.352222i \(0.885426\pi\)
\(140\) −2.49973 + 0.648168i −0.211266 + 0.0547802i
\(141\) 0.00112822 + 0.00361065i 9.50135e−5 + 0.000304071i
\(142\) 12.9032 + 3.51343i 1.08282 + 0.294840i
\(143\) −36.1077 −3.01948
\(144\) −10.7650 5.30224i −0.897087 0.441854i
\(145\) 5.77050 0.479214
\(146\) 19.3979 + 5.28185i 1.60538 + 0.437129i
\(147\) 2.75484 + 8.81630i 0.227215 + 0.727156i
\(148\) −2.35315 9.07517i −0.193427 0.745974i
\(149\) −2.32635 + 2.32635i −0.190582 + 0.190582i −0.795948 0.605365i \(-0.793027\pi\)
0.605365 + 0.795948i \(0.293027\pi\)
\(150\) 0.0906432 + 2.44781i 0.00740098 + 0.199863i
\(151\) 3.65301 0.297277 0.148639 0.988892i \(-0.452511\pi\)
0.148639 + 0.988892i \(0.452511\pi\)
\(152\) −5.24155 0.0636233i −0.425146 0.00516053i
\(153\) −4.70872 6.79897i −0.380677 0.549664i
\(154\) 9.18924 5.25596i 0.740490 0.423537i
\(155\) 7.12531 + 7.12531i 0.572319 + 0.572319i
\(156\) 11.3977 + 18.3191i 0.912549 + 1.46670i
\(157\) 5.57374 5.57374i 0.444833 0.444833i −0.448800 0.893632i \(-0.648148\pi\)
0.893632 + 0.448800i \(0.148148\pi\)
\(158\) 11.6557 + 3.17373i 0.927277 + 0.252488i
\(159\) −3.83720 2.01009i −0.304310 0.159411i
\(160\) −2.92695 + 4.84076i −0.231395 + 0.382696i
\(161\) 3.56427i 0.280904i
\(162\) −10.3203 7.44921i −0.810842 0.585265i
\(163\) 1.78354 + 1.78354i 0.139698 + 0.139698i 0.773497 0.633800i \(-0.218506\pi\)
−0.633800 + 0.773497i \(0.718506\pi\)
\(164\) 0.668579 + 0.393252i 0.0522073 + 0.0307078i
\(165\) −2.99483 9.58434i −0.233147 0.746140i
\(166\) −8.54348 14.9370i −0.663103 1.15933i
\(167\) 1.33852i 0.103578i −0.998658 0.0517890i \(-0.983508\pi\)
0.998658 0.0517890i \(-0.0164923\pi\)
\(168\) −5.56727 3.00304i −0.429524 0.231690i
\(169\) 25.7916i 1.98397i
\(170\) −3.38420 + 1.93565i −0.259556 + 0.148458i
\(171\) −5.47040 0.993643i −0.418332 0.0759858i
\(172\) −10.0303 + 2.60079i −0.764800 + 0.198309i
\(173\) −0.228324 0.228324i −0.0173592 0.0173592i 0.698374 0.715733i \(-0.253907\pi\)
−0.715733 + 0.698374i \(0.753907\pi\)
\(174\) 10.3578 + 9.61809i 0.785223 + 0.729145i
\(175\) 1.29120i 0.0976055i
\(176\) 6.36358 22.2993i 0.479673 1.68087i
\(177\) −0.317286 + 0.605690i −0.0238487 + 0.0455264i
\(178\) 1.73523 6.37273i 0.130061 0.477656i
\(179\) −1.48748 + 1.48748i −0.111180 + 0.111180i −0.760508 0.649328i \(-0.775050\pi\)
0.649328 + 0.760508i \(0.275050\pi\)
\(180\) −3.91724 + 4.54480i −0.291974 + 0.338750i
\(181\) −8.95808 8.95808i −0.665849 0.665849i 0.290903 0.956752i \(-0.406044\pi\)
−0.956752 + 0.290903i \(0.906044\pi\)
\(182\) 5.64663 + 9.87228i 0.418556 + 0.731782i
\(183\) −11.1194 5.82483i −0.821971 0.430584i
\(184\) 5.45345 + 5.58747i 0.402034 + 0.411914i
\(185\) −4.68764 −0.344642
\(186\) 0.913385 + 24.6659i 0.0669726 + 1.80859i
\(187\) 11.3010 11.3010i 0.826410 0.826410i
\(188\) 0.00376501 + 0.00221454i 0.000274592 + 0.000161512i
\(189\) −5.29113 4.12533i −0.384873 0.300073i
\(190\) −0.688593 + 2.52889i −0.0499558 + 0.183465i
\(191\) 5.20483 0.376608 0.188304 0.982111i \(-0.439701\pi\)
0.188304 + 0.982111i \(0.439701\pi\)
\(192\) −13.3222 + 3.81043i −0.961446 + 0.274994i
\(193\) 14.0219 1.00932 0.504660 0.863318i \(-0.331618\pi\)
0.504660 + 0.863318i \(0.331618\pi\)
\(194\) −2.48625 + 9.13089i −0.178503 + 0.655560i
\(195\) 10.2967 3.21743i 0.737365 0.230405i
\(196\) 9.19323 + 5.40737i 0.656659 + 0.386241i
\(197\) 3.22869 3.22869i 0.230034 0.230034i −0.582673 0.812707i \(-0.697993\pi\)
0.812707 + 0.582673i \(0.197993\pi\)
\(198\) 10.5993 22.1952i 0.753259 1.57734i
\(199\) 8.52513 0.604330 0.302165 0.953256i \(-0.402291\pi\)
0.302165 + 0.953256i \(0.402291\pi\)
\(200\) 1.97558 + 2.02413i 0.139694 + 0.143127i
\(201\) 0.867554 1.65613i 0.0611925 0.116815i
\(202\) −6.26886 10.9601i −0.441075 0.771153i
\(203\) 5.26856 + 5.26856i 0.369780 + 0.369780i
\(204\) −9.30079 2.16626i −0.651185 0.151669i
\(205\) 0.274237 0.274237i 0.0191535 0.0191535i
\(206\) −0.828894 + 3.04416i −0.0577518 + 0.212096i
\(207\) 4.71497 + 6.80801i 0.327713 + 0.473189i
\(208\) 23.9568 + 6.83658i 1.66110 + 0.474032i
\(209\) 10.7443i 0.743198i
\(210\) −2.15213 + 2.31765i −0.148511 + 0.159933i
\(211\) −7.83228 7.83228i −0.539197 0.539197i 0.384096 0.923293i \(-0.374513\pi\)
−0.923293 + 0.384096i \(0.874513\pi\)
\(212\) −4.84182 + 1.25546i −0.332538 + 0.0862254i
\(213\) 15.6331 4.88490i 1.07116 0.334708i
\(214\) 3.26583 1.86795i 0.223247 0.127690i
\(215\) 5.18098i 0.353340i
\(216\) −14.6064 + 1.62860i −0.993841 + 0.110812i
\(217\) 13.0110i 0.883247i
\(218\) −7.26385 12.6997i −0.491970 0.860135i
\(219\) 23.5018 7.34363i 1.58810 0.496237i
\(220\) −9.99410 5.87843i −0.673802 0.396324i
\(221\) 12.1410 + 12.1410i 0.816692 + 0.816692i
\(222\) −8.41413 7.81322i −0.564719 0.524389i
\(223\) 2.86107i 0.191592i −0.995401 0.0957958i \(-0.969460\pi\)
0.995401 0.0957958i \(-0.0305396\pi\)
\(224\) −7.09204 + 1.74735i −0.473857 + 0.116750i
\(225\) 1.70806 + 2.46628i 0.113870 + 0.164419i
\(226\) −4.96771 1.35266i −0.330447 0.0899776i
\(227\) −8.16483 + 8.16483i −0.541919 + 0.541919i −0.924091 0.382172i \(-0.875176\pi\)
0.382172 + 0.924091i \(0.375176\pi\)
\(228\) −5.45108 + 3.39153i −0.361007 + 0.224610i
\(229\) −10.6262 10.6262i −0.702197 0.702197i 0.262685 0.964882i \(-0.415392\pi\)
−0.964882 + 0.262685i \(0.915392\pi\)
\(230\) 3.38870 1.93823i 0.223444 0.127803i
\(231\) 6.01633 11.4850i 0.395845 0.755656i
\(232\) 16.3202 + 0.198099i 1.07148 + 0.0130059i
\(233\) 13.2569 0.868486 0.434243 0.900796i \(-0.357016\pi\)
0.434243 + 0.900796i \(0.357016\pi\)
\(234\) 23.8449 + 11.3871i 1.55879 + 0.744400i
\(235\) 0.00154433 0.00154433i 0.000100741 0.000100741i
\(236\) 0.198170 + 0.764266i 0.0128998 + 0.0497495i
\(237\) 14.1216 4.41260i 0.917298 0.286629i
\(238\) −4.85711 1.32254i −0.314840 0.0857278i
\(239\) 18.5733 1.20141 0.600704 0.799471i \(-0.294887\pi\)
0.600704 + 0.799471i \(0.294887\pi\)
\(240\) 0.172326 + 6.92606i 0.0111236 + 0.447075i
\(241\) −25.2869 −1.62887 −0.814437 0.580253i \(-0.802954\pi\)
−0.814437 + 0.580253i \(0.802954\pi\)
\(242\) 30.8514 + 8.40054i 1.98320 + 0.540007i
\(243\) −15.5636 0.880327i −0.998404 0.0564730i
\(244\) −14.0306 + 3.63807i −0.898217 + 0.232903i
\(245\) 3.77086 3.77086i 0.240911 0.240911i
\(246\) 0.949332 0.0351540i 0.0605272 0.00224134i
\(247\) 11.5429 0.734458
\(248\) 19.9073 + 20.3965i 1.26412 + 1.29518i
\(249\) −18.6687 9.77945i −1.18308 0.619748i
\(250\) 1.22760 0.702146i 0.0776400 0.0444076i
\(251\) −13.1481 13.1481i −0.829899 0.829899i 0.157604 0.987502i \(-0.449623\pi\)
−0.987502 + 0.157604i \(0.949623\pi\)
\(252\) −7.72598 + 0.572976i −0.486691 + 0.0360941i
\(253\) −11.3160 + 11.3160i −0.711431 + 0.711431i
\(254\) −13.6521 3.71732i −0.856606 0.233246i
\(255\) −2.21568 + 4.22967i −0.138751 + 0.264872i
\(256\) −8.44422 + 13.5903i −0.527764 + 0.849391i
\(257\) 27.4878i 1.71464i −0.514784 0.857320i \(-0.672128\pi\)
0.514784 0.857320i \(-0.327872\pi\)
\(258\) −8.63550 + 9.29964i −0.537623 + 0.578970i
\(259\) −4.27989 4.27989i −0.265940 0.265940i
\(260\) 6.31538 10.7370i 0.391663 0.665878i
\(261\) 17.0328 + 3.09383i 1.05430 + 0.191503i
\(262\) 12.1366 + 21.2190i 0.749802 + 1.31091i
\(263\) 12.3115i 0.759157i 0.925160 + 0.379579i \(0.123931\pi\)
−0.925160 + 0.379579i \(0.876069\pi\)
\(264\) −8.14100 27.2094i −0.501044 1.67462i
\(265\) 2.50097i 0.153633i
\(266\) −2.93762 + 1.68022i −0.180117 + 0.103021i
\(267\) −2.41258 7.72098i −0.147648 0.472516i
\(268\) −0.541856 2.08973i −0.0330991 0.127650i
\(269\) −5.00088 5.00088i −0.304909 0.304909i 0.538022 0.842931i \(-0.319172\pi\)
−0.842931 + 0.538022i \(0.819172\pi\)
\(270\) −1.04483 + 7.27381i −0.0635866 + 0.442670i
\(271\) 2.62351i 0.159367i 0.996820 + 0.0796835i \(0.0253910\pi\)
−0.996820 + 0.0796835i \(0.974609\pi\)
\(272\) −9.63770 + 5.35827i −0.584372 + 0.324893i
\(273\) 12.3387 + 6.46352i 0.746770 + 0.391190i
\(274\) 6.55533 24.0748i 0.396022 1.45441i
\(275\) −4.09936 + 4.09936i −0.247201 + 0.247201i
\(276\) 9.31315 + 2.16914i 0.560586 + 0.130567i
\(277\) −3.14259 3.14259i −0.188820 0.188820i 0.606366 0.795186i \(-0.292627\pi\)
−0.795186 + 0.606366i \(0.792627\pi\)
\(278\) 15.0804 + 26.3658i 0.904461 + 1.58131i
\(279\) 17.2116 + 24.8520i 1.03043 + 1.48785i
\(280\) −0.0443265 + 3.65180i −0.00264901 + 0.218237i
\(281\) 2.04783 0.122163 0.0610816 0.998133i \(-0.480545\pi\)
0.0610816 + 0.998133i \(0.480545\pi\)
\(282\) 0.00534604 0.000197965i 0.000318352 1.17887e-5i
\(283\) 7.60983 7.60983i 0.452357 0.452357i −0.443779 0.896136i \(-0.646362\pi\)
0.896136 + 0.443779i \(0.146362\pi\)
\(284\) 9.58838 16.3015i 0.568966 0.967316i
\(285\) 0.957387 + 3.06392i 0.0567107 + 0.181491i
\(286\) −13.4158 + 49.2702i −0.793292 + 2.91341i
\(287\) 0.500765 0.0295592
\(288\) −11.2348 + 12.7192i −0.662019 + 0.749487i
\(289\) 9.40022 0.552954
\(290\) 2.14402 7.87403i 0.125901 0.462379i
\(291\) 3.45677 + 11.0627i 0.202639 + 0.648505i
\(292\) 14.4145 24.5066i 0.843546 1.43414i
\(293\) 22.8324 22.8324i 1.33388 1.33388i 0.432018 0.901865i \(-0.357802\pi\)
0.901865 0.432018i \(-0.142198\pi\)
\(294\) 13.0537 0.483382i 0.761307 0.0281914i
\(295\) 0.394770 0.0229844
\(296\) −13.2577 0.160925i −0.770587 0.00935360i
\(297\) −3.70123 29.8958i −0.214767 1.73473i
\(298\) 2.31003 + 4.03874i 0.133817 + 0.233958i
\(299\) −12.1571 12.1571i −0.703065 0.703065i
\(300\) 3.37380 + 0.785797i 0.194786 + 0.0453680i
\(301\) −4.73032 + 4.73032i −0.272651 + 0.272651i
\(302\) 1.35727 4.98465i 0.0781022 0.286834i
\(303\) −13.6983 7.17576i −0.786947 0.412237i
\(304\) −2.03431 + 7.12863i −0.116676 + 0.408855i
\(305\) 7.24730i 0.414979i
\(306\) −11.0269 + 3.89905i −0.630368 + 0.222894i
\(307\) −5.25264 5.25264i −0.299784 0.299784i 0.541145 0.840929i \(-0.317991\pi\)
−0.840929 + 0.541145i \(0.817991\pi\)
\(308\) −3.75767 14.4919i −0.214113 0.825751i
\(309\) 1.15245 + 3.68819i 0.0655608 + 0.209814i
\(310\) 12.3701 7.07532i 0.702576 0.401851i
\(311\) 14.6871i 0.832831i 0.909175 + 0.416415i \(0.136714\pi\)
−0.909175 + 0.416415i \(0.863286\pi\)
\(312\) 29.2319 8.74613i 1.65493 0.495152i
\(313\) 4.35735i 0.246292i 0.992389 + 0.123146i \(0.0392983\pi\)
−0.992389 + 0.123146i \(0.960702\pi\)
\(314\) −5.53463 9.67647i −0.312337 0.546075i
\(315\) −0.692273 + 3.81124i −0.0390051 + 0.214739i
\(316\) 8.66132 14.7254i 0.487237 0.828367i
\(317\) −11.8740 11.8740i −0.666911 0.666911i 0.290089 0.957000i \(-0.406315\pi\)
−0.957000 + 0.290089i \(0.906315\pi\)
\(318\) −4.16854 + 4.48914i −0.233760 + 0.251738i
\(319\) 33.4537i 1.87305i
\(320\) 5.51788 + 5.79250i 0.308459 + 0.323810i
\(321\) 2.13818 4.08172i 0.119342 0.227820i
\(322\) 4.86357 + 1.32430i 0.271036 + 0.0738005i
\(323\) −3.61270 + 3.61270i −0.201016 + 0.201016i
\(324\) −13.9992 + 11.3147i −0.777734 + 0.628594i
\(325\) −4.40407 4.40407i −0.244294 0.244294i
\(326\) 3.09637 1.77103i 0.171492 0.0980882i
\(327\) −15.8725 8.31469i −0.877751 0.459804i
\(328\) 0.785015 0.766186i 0.0433452 0.0423056i
\(329\) 0.00281999 0.000155471
\(330\) −14.1909 + 0.525492i −0.781182 + 0.0289274i
\(331\) −17.4316 + 17.4316i −0.958128 + 0.958128i −0.999158 0.0410301i \(-0.986936\pi\)
0.0410301 + 0.999158i \(0.486936\pi\)
\(332\) −23.5563 + 6.10804i −1.29282 + 0.335222i
\(333\) −13.8365 2.51326i −0.758237 0.137726i
\(334\) −1.82646 0.497327i −0.0999394 0.0272125i
\(335\) −1.07942 −0.0589749
\(336\) −6.16627 + 6.48094i −0.336397 + 0.353564i
\(337\) −18.4419 −1.00460 −0.502298 0.864694i \(-0.667512\pi\)
−0.502298 + 0.864694i \(0.667512\pi\)
\(338\) −35.1935 9.58284i −1.91427 0.521238i
\(339\) −6.01871 + 1.88067i −0.326892 + 0.102144i
\(340\) 1.38387 + 5.33704i 0.0750508 + 0.289442i
\(341\) −41.3080 + 41.3080i −2.23696 + 2.23696i
\(342\) −3.38838 + 7.09536i −0.183223 + 0.383673i
\(343\) 15.9241 0.859821
\(344\) −0.177861 + 14.6529i −0.00958964 + 0.790033i
\(345\) 2.21863 4.23529i 0.119447 0.228020i
\(346\) −0.396390 + 0.226722i −0.0213100 + 0.0121887i
\(347\) −4.81148 4.81148i −0.258294 0.258294i 0.566066 0.824360i \(-0.308465\pi\)
−0.824360 + 0.566066i \(0.808465\pi\)
\(348\) 16.9726 10.5600i 0.909829 0.566074i
\(349\) 11.3752 11.3752i 0.608899 0.608899i −0.333759 0.942658i \(-0.608317\pi\)
0.942658 + 0.333759i \(0.108317\pi\)
\(350\) 1.76189 + 0.479744i 0.0941767 + 0.0256434i
\(351\) 32.1179 3.97635i 1.71433 0.212242i
\(352\) −28.0637 16.9686i −1.49580 0.904429i
\(353\) 28.4101i 1.51212i 0.654504 + 0.756059i \(0.272878\pi\)
−0.654504 + 0.756059i \(0.727122\pi\)
\(354\) 0.708597 + 0.657991i 0.0376615 + 0.0349719i
\(355\) −6.68652 6.68652i −0.354883 0.354883i
\(356\) −8.05108 4.73557i −0.426706 0.250984i
\(357\) −5.88471 + 1.83880i −0.311452 + 0.0973197i
\(358\) 1.47705 + 2.58239i 0.0780643 + 0.136484i
\(359\) 26.5436i 1.40092i −0.713692 0.700460i \(-0.752978\pi\)
0.713692 0.700460i \(-0.247022\pi\)
\(360\) 4.74609 + 7.03382i 0.250141 + 0.370715i
\(361\) 15.5653i 0.819225i
\(362\) −15.5520 + 8.89523i −0.817393 + 0.467523i
\(363\) 37.3785 11.6797i 1.96186 0.613026i
\(364\) 15.5691 4.03698i 0.816040 0.211595i
\(365\) −10.0521 10.0521i −0.526149 0.526149i
\(366\) −12.0796 + 13.0086i −0.631410 + 0.679971i
\(367\) 4.45350i 0.232471i 0.993222 + 0.116235i \(0.0370827\pi\)
−0.993222 + 0.116235i \(0.962917\pi\)
\(368\) 9.65051 5.36540i 0.503068 0.279691i
\(369\) 0.956496 0.662434i 0.0497932 0.0344849i
\(370\) −1.74169 + 6.39645i −0.0905462 + 0.332535i
\(371\) −2.28343 + 2.28343i −0.118550 + 0.118550i
\(372\) 33.9968 + 7.91825i 1.76265 + 0.410542i
\(373\) 5.51867 + 5.51867i 0.285746 + 0.285746i 0.835395 0.549650i \(-0.185239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(374\) −11.2217 19.6194i −0.580260 1.01450i
\(375\) 0.803724 1.53428i 0.0415041 0.0792301i
\(376\) 0.00442071 0.00431467i 0.000227981 0.000222512i
\(377\) −35.9403 −1.85102
\(378\) −7.59506 + 5.68716i −0.390648 + 0.292516i
\(379\) −11.0044 + 11.0044i −0.565256 + 0.565256i −0.930796 0.365540i \(-0.880884\pi\)
0.365540 + 0.930796i \(0.380884\pi\)
\(380\) 3.19491 + 1.87922i 0.163896 + 0.0964018i
\(381\) −16.5404 + 5.16839i −0.847388 + 0.264784i
\(382\) 1.93385 7.10216i 0.0989444 0.363378i
\(383\) 1.74498 0.0891642 0.0445821 0.999006i \(-0.485804\pi\)
0.0445821 + 0.999006i \(0.485804\pi\)
\(384\) 0.249606 + 19.5943i 0.0127377 + 0.999919i
\(385\) −7.48556 −0.381500
\(386\) 5.20983 19.1334i 0.265173 0.973863i
\(387\) −2.77776 + 15.2927i −0.141202 + 0.777372i
\(388\) 11.5356 + 6.78515i 0.585633 + 0.344464i
\(389\) −0.0192068 + 0.0192068i −0.000973822 + 0.000973822i −0.707594 0.706620i \(-0.750219\pi\)
0.706620 + 0.707594i \(0.250219\pi\)
\(390\) −0.564552 15.2457i −0.0285872 0.771995i
\(391\) 7.60988 0.384848
\(392\) 10.7943 10.5354i 0.545193 0.532116i
\(393\) 26.5201 + 13.8924i 1.33776 + 0.700778i
\(394\) −3.20603 5.60527i −0.161518 0.282389i
\(395\) −6.04002 6.04002i −0.303907 0.303907i
\(396\) −26.3479 22.7097i −1.32403 1.14120i
\(397\) −22.2917 + 22.2917i −1.11879 + 1.11879i −0.126872 + 0.991919i \(0.540494\pi\)
−0.991919 + 0.126872i \(0.959506\pi\)
\(398\) 3.16750 11.6328i 0.158773 0.583101i
\(399\) −1.92330 + 3.67152i −0.0962854 + 0.183806i
\(400\) 3.49601 1.94368i 0.174801 0.0971840i
\(401\) 31.9602i 1.59602i −0.602647 0.798008i \(-0.705887\pi\)
0.602647 0.798008i \(-0.294113\pi\)
\(402\) −1.93751 1.79914i −0.0966342 0.0897330i
\(403\) −44.3785 44.3785i −2.21065 2.21065i
\(404\) −17.2847 + 4.48183i −0.859945 + 0.222979i
\(405\) 3.71938 + 8.19550i 0.184818 + 0.407238i
\(406\) 9.14665 5.23159i 0.453940 0.259640i
\(407\) 27.1760i 1.34706i
\(408\) −6.41164 + 11.8864i −0.317423 + 0.588463i
\(409\) 15.9890i 0.790605i 0.918551 + 0.395303i \(0.129360\pi\)
−0.918551 + 0.395303i \(0.870640\pi\)
\(410\) −0.272313 0.476097i −0.0134486 0.0235128i
\(411\) −9.11422 29.1682i −0.449571 1.43876i
\(412\) 3.84588 + 2.26211i 0.189473 + 0.111446i
\(413\) 0.360432 + 0.360432i 0.0177357 + 0.0177357i
\(414\) 11.0416 3.90423i 0.542665 0.191882i
\(415\) 12.1677i 0.597288i
\(416\) 18.2299 30.1497i 0.893792 1.47821i
\(417\) 32.9527 + 17.2620i 1.61370 + 0.845325i
\(418\) −14.6609 3.99203i −0.717090 0.195257i
\(419\) 0.759220 0.759220i 0.0370903 0.0370903i −0.688318 0.725409i \(-0.741651\pi\)
0.725409 + 0.688318i \(0.241651\pi\)
\(420\) 2.36289 + 3.79778i 0.115297 + 0.185313i
\(421\) 12.4294 + 12.4294i 0.605771 + 0.605771i 0.941838 0.336067i \(-0.109097\pi\)
−0.336067 + 0.941838i \(0.609097\pi\)
\(422\) −13.5975 + 7.77733i −0.661915 + 0.378595i
\(423\) 0.00538638 0.00373040i 0.000261895 0.000181378i
\(424\) −0.0858576 + 7.07329i −0.00416961 + 0.343509i
\(425\) 2.75677 0.133723
\(426\) −0.857136 23.1469i −0.0415284 1.12147i
\(427\) −6.61690 + 6.61690i −0.320214 + 0.320214i
\(428\) −1.33546 5.15036i −0.0645521 0.248952i
\(429\) 18.6527 + 59.6940i 0.900559 + 2.88205i
\(430\) 7.06962 + 1.92499i 0.340927 + 0.0928312i
\(431\) 24.6661 1.18812 0.594062 0.804419i \(-0.297523\pi\)
0.594062 + 0.804419i \(0.297523\pi\)
\(432\) −3.20473 + 20.5361i −0.154188 + 0.988042i
\(433\) 17.7512 0.853070 0.426535 0.904471i \(-0.359734\pi\)
0.426535 + 0.904471i \(0.359734\pi\)
\(434\) 17.7540 + 4.83424i 0.852219 + 0.232051i
\(435\) −2.98095 9.53991i −0.142925 0.457404i
\(436\) −20.0281 + 5.19318i −0.959172 + 0.248708i
\(437\) 3.61750 3.61750i 0.173049 0.173049i
\(438\) −1.28856 34.7975i −0.0615698 1.66269i
\(439\) −15.5759 −0.743397 −0.371698 0.928354i \(-0.621224\pi\)
−0.371698 + 0.928354i \(0.621224\pi\)
\(440\) −11.7346 + 11.4532i −0.559426 + 0.546008i
\(441\) 13.1522 9.10872i 0.626295 0.433749i
\(442\) 21.0778 12.0558i 1.00257 0.573437i
\(443\) 19.5993 + 19.5993i 0.931192 + 0.931192i 0.997781 0.0665888i \(-0.0212116\pi\)
−0.0665888 + 0.997781i \(0.521212\pi\)
\(444\) −13.7877 + 8.57836i −0.654334 + 0.407111i
\(445\) −3.30237 + 3.30237i −0.156548 + 0.156548i
\(446\) −3.90403 1.06303i −0.184861 0.0503359i
\(447\) 5.04774 + 2.64422i 0.238750 + 0.125067i
\(448\) −0.250730 + 10.3266i −0.0118459 + 0.487884i
\(449\) 35.6088i 1.68048i 0.542211 + 0.840242i \(0.317587\pi\)
−0.542211 + 0.840242i \(0.682413\pi\)
\(450\) 3.99995 1.41435i 0.188559 0.0666733i
\(451\) 1.58985 + 1.58985i 0.0748631 + 0.0748631i
\(452\) −3.69150 + 6.27603i −0.173634 + 0.295200i
\(453\) −1.88709 6.03923i −0.0886630 0.283748i
\(454\) 8.10755 + 14.1748i 0.380506 + 0.665257i
\(455\) 8.04197i 0.377013i
\(456\) 2.60252 + 8.69831i 0.121874 + 0.407335i
\(457\) 19.8497i 0.928530i 0.885696 + 0.464265i \(0.153681\pi\)
−0.885696 + 0.464265i \(0.846319\pi\)
\(458\) −18.4479 + 10.5516i −0.862014 + 0.493044i
\(459\) −8.80775 + 11.2968i −0.411111 + 0.527289i
\(460\) −1.38571 5.34414i −0.0646090 0.249172i
\(461\) 29.9766 + 29.9766i 1.39615 + 1.39615i 0.810733 + 0.585417i \(0.199069\pi\)
0.585417 + 0.810733i \(0.300931\pi\)
\(462\) −13.4363 12.4767i −0.625112 0.580469i
\(463\) 32.1223i 1.49285i 0.665469 + 0.746426i \(0.268232\pi\)
−0.665469 + 0.746426i \(0.731768\pi\)
\(464\) 6.33408 22.1959i 0.294052 1.03042i
\(465\) 8.09889 15.4605i 0.375577 0.716965i
\(466\) 4.92558 18.0894i 0.228173 0.837977i
\(467\) 28.7271 28.7271i 1.32933 1.32933i 0.423376 0.905954i \(-0.360845\pi\)
0.905954 0.423376i \(-0.139155\pi\)
\(468\) 24.3977 28.3063i 1.12778 1.30846i
\(469\) −0.985526 0.985526i −0.0455073 0.0455073i
\(470\) −0.00153349 0.00268108i −7.07347e−5 0.000123669i
\(471\) −12.0939 6.33532i −0.557259 0.291916i
\(472\) 1.11650 + 0.0135523i 0.0513909 + 0.000623797i
\(473\) −30.0360 −1.38106
\(474\) −0.774263 20.9089i −0.0355631 0.960379i
\(475\) 1.31048 1.31048i 0.0601291 0.0601291i
\(476\) −3.60931 + 6.13630i −0.165433 + 0.281257i
\(477\) −1.34089 + 7.38212i −0.0613950 + 0.338004i
\(478\) 6.90090 25.3439i 0.315640 1.15920i
\(479\) 12.8567 0.587436 0.293718 0.955892i \(-0.405107\pi\)
0.293718 + 0.955892i \(0.405107\pi\)
\(480\) 9.51487 + 2.33823i 0.434292 + 0.106725i
\(481\) 29.1960 1.33122
\(482\) −9.39533 + 34.5048i −0.427946 + 1.57165i
\(483\) 5.89253 1.84125i 0.268119 0.0837796i
\(484\) 22.9256 38.9766i 1.04207 1.77166i
\(485\) 4.73166 4.73166i 0.214854 0.214854i
\(486\) −6.98387 + 20.9099i −0.316795 + 0.948494i
\(487\) 19.9584 0.904402 0.452201 0.891916i \(-0.350639\pi\)
0.452201 + 0.891916i \(0.350639\pi\)
\(488\) −0.248798 + 20.4969i −0.0112625 + 0.927853i
\(489\) 2.02724 3.86994i 0.0916749 0.175005i
\(490\) −3.74441 6.54653i −0.169155 0.295742i
\(491\) 14.8307 + 14.8307i 0.669300 + 0.669300i 0.957554 0.288254i \(-0.0930748\pi\)
−0.288254 + 0.957554i \(0.593075\pi\)
\(492\) 0.304755 1.30846i 0.0137394 0.0589898i
\(493\) 11.2486 11.2486i 0.506612 0.506612i
\(494\) 4.28876 15.7507i 0.192960 0.708657i
\(495\) −14.2979 + 9.90223i −0.642645 + 0.445072i
\(496\) 35.2283 19.5859i 1.58180 0.879432i
\(497\) 12.2098i 0.547684i
\(498\) −20.2807 + 21.8405i −0.908801 + 0.978695i
\(499\) 18.6393 + 18.6393i 0.834410 + 0.834410i 0.988117 0.153706i \(-0.0491209\pi\)
−0.153706 + 0.988117i \(0.549121\pi\)
\(500\) −0.501989 1.93598i −0.0224496 0.0865795i
\(501\) −2.21287 + 0.691460i −0.0988639 + 0.0308921i
\(502\) −22.8261 + 13.0558i −1.01878 + 0.582710i
\(503\) 13.4262i 0.598646i −0.954152 0.299323i \(-0.903239\pi\)
0.954152 0.299323i \(-0.0967608\pi\)
\(504\) −2.08874 + 10.7552i −0.0930397 + 0.479077i
\(505\) 8.92814i 0.397297i
\(506\) 11.2366 + 19.6455i 0.499529 + 0.873350i
\(507\) −42.6392 + 13.3235i −1.89367 + 0.591718i
\(508\) −10.1448 + 17.2475i −0.450104 + 0.765235i
\(509\) −11.9058 11.9058i −0.527714 0.527714i 0.392176 0.919890i \(-0.371722\pi\)
−0.919890 + 0.392176i \(0.871722\pi\)
\(510\) 4.94829 + 4.59490i 0.219114 + 0.203466i
\(511\) 18.3554i 0.811994i
\(512\) 15.4069 + 16.5719i 0.680896 + 0.732380i
\(513\) 1.18321 + 9.55708i 0.0522400 + 0.421955i
\(514\) −37.5080 10.2131i −1.65441 0.450479i
\(515\) 1.57749 1.57749i 0.0695127 0.0695127i
\(516\) 9.48116 + 15.2387i 0.417385 + 0.670846i
\(517\) 0.00895303 + 0.00895303i 0.000393754 + 0.000393754i
\(518\) −7.43025 + 4.24987i −0.326466 + 0.186728i
\(519\) −0.259522 + 0.495419i −0.0113917 + 0.0217465i
\(520\) −12.3045 12.6069i −0.539587 0.552847i
\(521\) −19.2979 −0.845457 −0.422729 0.906256i \(-0.638928\pi\)
−0.422729 + 0.906256i \(0.638928\pi\)
\(522\) 10.5502 22.0923i 0.461768 0.966953i
\(523\) −12.5948 + 12.5948i −0.550734 + 0.550734i −0.926653 0.375919i \(-0.877327\pi\)
0.375919 + 0.926653i \(0.377327\pi\)
\(524\) 33.4634 8.67689i 1.46185 0.379052i
\(525\) 2.13464 0.667013i 0.0931633 0.0291108i
\(526\) 16.7994 + 4.57431i 0.732488 + 0.199449i
\(527\) 27.7792 1.21008
\(528\) −40.1529 + 0.999038i −1.74743 + 0.0434775i
\(529\) 15.3800 0.668696
\(530\) 3.41266 + 0.929234i 0.148236 + 0.0403633i
\(531\) 1.16524 + 0.211655i 0.0505673 + 0.00918504i
\(532\) 1.20125 + 4.63276i 0.0520809 + 0.200856i
\(533\) −1.70802 + 1.70802i −0.0739827 + 0.0739827i
\(534\) −11.4319 + 0.423327i −0.494708 + 0.0183192i
\(535\) −2.66034 −0.115017
\(536\) −3.05283 0.0370561i −0.131862 0.00160058i
\(537\) 3.22755 + 1.69073i 0.139279 + 0.0729603i
\(538\) −8.68195 + 4.96580i −0.374305 + 0.214091i
\(539\) 21.8611 + 21.8611i 0.941623 + 0.941623i
\(540\) 9.53715 + 4.12829i 0.410414 + 0.177653i
\(541\) 2.34334 2.34334i 0.100748 0.100748i −0.654936 0.755684i \(-0.727305\pi\)
0.755684 + 0.654936i \(0.227305\pi\)
\(542\) 3.57987 + 0.974764i 0.153769 + 0.0418697i
\(543\) −10.1821 + 19.4373i −0.436955 + 0.834134i
\(544\) 3.73066 + 15.1418i 0.159951 + 0.649201i
\(545\) 10.3452i 0.443140i
\(546\) 13.4041 14.4350i 0.573643 0.617761i
\(547\) −24.2081 24.2081i −1.03506 1.03506i −0.999362 0.0357024i \(-0.988633\pi\)
−0.0357024 0.999362i \(-0.511367\pi\)
\(548\) −30.4152 17.8899i −1.29927 0.764220i
\(549\) −3.88562 + 21.3919i −0.165834 + 0.912983i
\(550\) 4.07060 + 7.11683i 0.173571 + 0.303462i
\(551\) 10.6945i 0.455600i
\(552\) 6.42016 11.9022i 0.273260 0.506590i
\(553\) 11.0293i 0.469013i
\(554\) −5.45579 + 3.12054i −0.231794 + 0.132579i
\(555\) 2.42156 + 7.74971i 0.102790 + 0.328957i
\(556\) 41.5801 10.7815i 1.76339 0.457238i
\(557\) 27.4760 + 27.4760i 1.16420 + 1.16420i 0.983548 + 0.180649i \(0.0578199\pi\)
0.180649 + 0.983548i \(0.442180\pi\)
\(558\) 40.3063 14.2520i 1.70630 0.603337i
\(559\) 32.2686i 1.36482i
\(560\) 4.96653 + 1.41731i 0.209874 + 0.0598921i
\(561\) −24.5209 12.8451i −1.03528 0.542322i
\(562\) 0.760869 2.79433i 0.0320953 0.117872i
\(563\) 15.9779 15.9779i 0.673389 0.673389i −0.285107 0.958496i \(-0.592029\pi\)
0.958496 + 0.285107i \(0.0920292\pi\)
\(564\) 0.00171619 0.00736840i 7.22644e−5 0.000310266i
\(565\) 2.57429 + 2.57429i 0.108301 + 0.108301i
\(566\) −7.55644 13.2113i −0.317621 0.555312i
\(567\) −4.08677 + 10.8785i −0.171628 + 0.456853i
\(568\) −18.6814 19.1405i −0.783853 0.803116i
\(569\) −4.90717 −0.205719 −0.102860 0.994696i \(-0.532799\pi\)
−0.102860 + 0.994696i \(0.532799\pi\)
\(570\) 4.53654 0.167989i 0.190015 0.00703630i
\(571\) 18.1855 18.1855i 0.761040 0.761040i −0.215470 0.976510i \(-0.569128\pi\)
0.976510 + 0.215470i \(0.0691285\pi\)
\(572\) 62.2461 + 36.6126i 2.60264 + 1.53085i
\(573\) −2.68873 8.60473i −0.112323 0.359468i
\(574\) 0.186059 0.683310i 0.00776594 0.0285208i
\(575\) −2.76043 −0.115118
\(576\) 13.1815 + 20.0561i 0.549229 + 0.835672i
\(577\) −3.08085 −0.128257 −0.0641287 0.997942i \(-0.520427\pi\)
−0.0641287 + 0.997942i \(0.520427\pi\)
\(578\) 3.49265 12.8269i 0.145275 0.533529i
\(579\) −7.24350 23.1813i −0.301029 0.963383i
\(580\) −9.94777 5.85118i −0.413059 0.242957i
\(581\) −11.1093 + 11.1093i −0.460891 + 0.460891i
\(582\) 16.3797 0.606546i 0.678962 0.0251422i
\(583\) −14.4991 −0.600489
\(584\) −28.0843 28.7745i −1.16214 1.19070i
\(585\) −10.6383 15.3607i −0.439838 0.635087i
\(586\) −22.6722 39.6389i −0.936581 1.63747i
\(587\) −19.9102 19.9102i −0.821782 0.821782i 0.164582 0.986363i \(-0.447373\pi\)
−0.986363 + 0.164582i \(0.947373\pi\)
\(588\) 4.19050 17.9918i 0.172813 0.741970i
\(589\) 13.2054 13.2054i 0.544117 0.544117i
\(590\) 0.146677 0.538677i 0.00603858 0.0221770i
\(591\) −7.00562 3.66985i −0.288173 0.150957i
\(592\) −5.14547 + 18.0308i −0.211477 + 0.741059i
\(593\) 13.0729i 0.536838i 0.963302 + 0.268419i \(0.0865012\pi\)
−0.963302 + 0.268419i \(0.913499\pi\)
\(594\) −42.1690 6.05729i −1.73021 0.248534i
\(595\) 2.51697 + 2.51697i 0.103186 + 0.103186i
\(596\) 6.36929 1.65153i 0.260896 0.0676491i
\(597\) −4.40395 14.0939i −0.180242 0.576826i
\(598\) −21.1058 + 12.0718i −0.863079 + 0.493654i
\(599\) 20.7034i 0.845917i 0.906149 + 0.422959i \(0.139008\pi\)
−0.906149 + 0.422959i \(0.860992\pi\)
\(600\) 2.32578 4.31170i 0.0949495 0.176024i
\(601\) 31.6818i 1.29233i −0.763199 0.646163i \(-0.776373\pi\)
0.763199 0.646163i \(-0.223627\pi\)
\(602\) 4.69713 + 8.21222i 0.191441 + 0.334705i
\(603\) −3.18612 0.578726i −0.129749 0.0235676i
\(604\) −6.29743 3.70408i −0.256239 0.150717i
\(605\) −15.9873 15.9873i −0.649977 0.649977i
\(606\) −14.8812 + 16.0256i −0.604506 + 0.650997i
\(607\) 31.9791i 1.29799i −0.760791 0.648997i \(-0.775189\pi\)
0.760791 0.648997i \(-0.224811\pi\)
\(608\) 8.97140 + 5.42452i 0.363838 + 0.219993i
\(609\) 5.98844 11.4317i 0.242664 0.463238i
\(610\) 9.88918 + 2.69273i 0.400401 + 0.109025i
\(611\) −0.00961851 + 0.00961851i −0.000389123 + 0.000389123i
\(612\) 1.22333 + 16.4953i 0.0494502 + 0.666784i
\(613\) −19.4142 19.4142i −0.784133 0.784133i 0.196392 0.980525i \(-0.437077\pi\)
−0.980525 + 0.196392i \(0.937077\pi\)
\(614\) −9.11902 + 5.21579i −0.368014 + 0.210492i
\(615\) −0.595040 0.311707i −0.0239943 0.0125693i
\(616\) −21.1708 0.256977i −0.852996 0.0103539i
\(617\) 21.0941 0.849216 0.424608 0.905377i \(-0.360412\pi\)
0.424608 + 0.905377i \(0.360412\pi\)
\(618\) 5.46086 0.202217i 0.219668 0.00813436i
\(619\) 23.5547 23.5547i 0.946744 0.946744i −0.0519076 0.998652i \(-0.516530\pi\)
0.998652 + 0.0519076i \(0.0165301\pi\)
\(620\) −5.05840 19.5083i −0.203150 0.783471i
\(621\) 8.81946 11.3118i 0.353913 0.453927i
\(622\) 20.0411 + 5.45699i 0.803574 + 0.218805i
\(623\) −6.03024 −0.241597
\(624\) −1.07330 43.1375i −0.0429662 1.72688i
\(625\) −1.00000 −0.0400000
\(626\) 5.94574 + 1.61897i 0.237640 + 0.0647070i
\(627\) −17.7627 + 5.55033i −0.709373 + 0.221659i
\(628\) −15.2603 + 3.95691i −0.608950 + 0.157898i
\(629\) −9.13776 + 9.13776i −0.364347 + 0.364347i
\(630\) 4.94335 + 2.36069i 0.196948 + 0.0940522i
\(631\) −0.795228 −0.0316575 −0.0158288 0.999875i \(-0.505039\pi\)
−0.0158288 + 0.999875i \(0.505039\pi\)
\(632\) −16.8752 17.2899i −0.671258 0.687754i
\(633\) −8.90246 + 16.9945i −0.353841 + 0.675472i
\(634\) −20.6143 + 11.7907i −0.818697 + 0.468269i
\(635\) 7.07455 + 7.07455i 0.280745 + 0.280745i
\(636\) 4.57676 + 7.35605i 0.181480 + 0.291686i
\(637\) −23.4860 + 23.4860i −0.930550 + 0.930550i
\(638\) 45.6487 + 12.4297i 1.80725 + 0.492096i
\(639\) −16.1516 23.3216i −0.638949 0.922587i
\(640\) 9.95422 5.37713i 0.393475 0.212550i
\(641\) 11.6040i 0.458331i −0.973387 0.229165i \(-0.926400\pi\)
0.973387 0.229165i \(-0.0735997\pi\)
\(642\) −4.77521 4.43418i −0.188462 0.175003i
\(643\) 18.3792 + 18.3792i 0.724805 + 0.724805i 0.969580 0.244775i \(-0.0787141\pi\)
−0.244775 + 0.969580i \(0.578714\pi\)
\(644\) 3.61411 6.14446i 0.142416 0.242125i
\(645\) 8.56530 2.67641i 0.337258 0.105384i
\(646\) 3.58735 + 6.27195i 0.141143 + 0.246766i
\(647\) 12.5667i 0.494049i 0.969009 + 0.247024i \(0.0794528\pi\)
−0.969009 + 0.247024i \(0.920547\pi\)
\(648\) 10.2379 + 23.3063i 0.402182 + 0.915560i
\(649\) 2.28863i 0.0898366i
\(650\) −7.64582 + 4.37317i −0.299894 + 0.171530i
\(651\) 21.5101 6.72130i 0.843049 0.263428i
\(652\) −1.26617 4.88313i −0.0495871 0.191238i
\(653\) 0.988002 + 0.988002i 0.0386635 + 0.0386635i 0.726174 0.687511i \(-0.241297\pi\)
−0.687511 + 0.726174i \(0.741297\pi\)
\(654\) −17.2431 + 18.5692i −0.674258 + 0.726114i
\(655\) 17.2850i 0.675381i
\(656\) −0.753815 1.35586i −0.0294315 0.0529373i
\(657\) −24.2813 35.0601i −0.947304 1.36782i
\(658\) 0.00104776 0.00384797i 4.08461e−5 0.000150009i
\(659\) −21.1873 + 21.1873i −0.825341 + 0.825341i −0.986868 0.161527i \(-0.948358\pi\)
0.161527 + 0.986868i \(0.448358\pi\)
\(660\) −4.55556 + 19.5592i −0.177325 + 0.761339i
\(661\) 26.2853 + 26.2853i 1.02238 + 1.02238i 0.999744 + 0.0226362i \(0.00720595\pi\)
0.0226362 + 0.999744i \(0.492794\pi\)
\(662\) 17.3093 + 30.2627i 0.672745 + 1.17619i
\(663\) 13.7999 26.3436i 0.535944 1.02310i
\(664\) −0.417713 + 34.4128i −0.0162104 + 1.33548i
\(665\) 2.39299 0.0927960
\(666\) −8.57038 + 17.9466i −0.332096 + 0.695417i
\(667\) −11.2636 + 11.2636i −0.436126 + 0.436126i
\(668\) −1.35724 + 2.30748i −0.0525131 + 0.0892792i
\(669\) −4.72999 + 1.47798i −0.182872 + 0.0571422i
\(670\) −0.401057 + 1.47290i −0.0154942 + 0.0569031i
\(671\) −42.0153 −1.62198
\(672\) 6.55239 + 10.8221i 0.252764 + 0.417470i
\(673\) 27.0401 1.04232 0.521159 0.853459i \(-0.325500\pi\)
0.521159 + 0.853459i \(0.325500\pi\)
\(674\) −6.85209 + 25.1647i −0.263933 + 0.969306i
\(675\) 3.19496 4.09784i 0.122974 0.157726i
\(676\) −26.1522 + 44.4622i −1.00585 + 1.71008i
\(677\) −24.4176 + 24.4176i −0.938445 + 0.938445i −0.998212 0.0597673i \(-0.980964\pi\)
0.0597673 + 0.998212i \(0.480964\pi\)
\(678\) 0.329995 + 8.91149i 0.0126734 + 0.342244i
\(679\) 8.64017 0.331579
\(680\) 7.79675 + 0.0946390i 0.298992 + 0.00362924i
\(681\) 17.7161 + 9.28045i 0.678882 + 0.355628i
\(682\) 41.0182 + 71.7142i 1.57067 + 2.74608i
\(683\) −11.1883 11.1883i −0.428110 0.428110i 0.459874 0.887984i \(-0.347895\pi\)
−0.887984 + 0.459874i \(0.847895\pi\)
\(684\) 8.42290 + 7.25983i 0.322058 + 0.277587i
\(685\) −12.4757 + 12.4757i −0.476670 + 0.476670i
\(686\) 5.91659 21.7290i 0.225897 0.829616i
\(687\) −12.0781 + 23.0567i −0.460808 + 0.879668i
\(688\) 19.9283 + 5.68698i 0.759761 + 0.216814i
\(689\) 15.5768i 0.593428i
\(690\) −4.95486 4.60101i −0.188628 0.175157i
\(691\) 18.8638 + 18.8638i 0.717613 + 0.717613i 0.968116 0.250503i \(-0.0805960\pi\)
−0.250503 + 0.968116i \(0.580596\pi\)
\(692\) 0.162092 + 0.625126i 0.00616181 + 0.0237637i
\(693\) −22.0952 4.01336i −0.839325 0.152455i
\(694\) −8.35313 + 4.77772i −0.317080 + 0.181360i
\(695\) 21.4776i 0.814690i
\(696\) −8.10327 27.0833i −0.307154 1.02659i
\(697\) 1.06916i 0.0404971i
\(698\) −11.2954 19.7482i −0.427536 0.747482i
\(699\) −6.84828 21.9165i −0.259026 0.828959i
\(700\) 1.30925 2.22590i 0.0494852 0.0841312i
\(701\) −9.26133 9.26133i −0.349796 0.349796i 0.510238 0.860033i \(-0.329557\pi\)
−0.860033 + 0.510238i \(0.829557\pi\)
\(702\) 6.50753 45.3034i 0.245611 1.70987i
\(703\) 8.68763i 0.327660i
\(704\) −33.5812 + 31.9892i −1.26564 + 1.20564i
\(705\) −0.00335089 0.00175534i −0.000126202 6.61099e-5i
\(706\) 38.7665 + 10.5558i 1.45900 + 0.397271i
\(707\) −8.15154 + 8.15154i −0.306570 + 0.306570i
\(708\) 1.16113 0.722427i 0.0436379 0.0271505i
\(709\) −21.8388 21.8388i −0.820174 0.820174i 0.165959 0.986133i \(-0.446928\pi\)
−0.986133 + 0.165959i \(0.946928\pi\)
\(710\) −11.6083 + 6.63960i −0.435653 + 0.249180i
\(711\) −14.5900 21.0667i −0.547168 0.790063i
\(712\) −9.45321 + 9.22647i −0.354274 + 0.345777i
\(713\) −27.8161 −1.04172
\(714\) 0.322648 + 8.71309i 0.0120748 + 0.326079i
\(715\) 25.5320 25.5320i 0.954842 0.954842i
\(716\) 4.07255 1.05599i 0.152198 0.0394643i
\(717\) −9.59468 30.7058i −0.358320 1.14673i
\(718\) −36.2197 9.86227i −1.35171 0.368057i
\(719\) 45.7622 1.70664 0.853322 0.521385i \(-0.174584\pi\)
0.853322 + 0.521385i \(0.174584\pi\)
\(720\) 11.3613 3.86279i 0.423410 0.143958i
\(721\) 2.88055 0.107277
\(722\) −21.2393 5.78326i −0.790446 0.215231i
\(723\) 13.0628 + 41.8049i 0.485811 + 1.55474i
\(724\) 6.35952 + 24.5262i 0.236350 + 0.911509i
\(725\) −4.08036 + 4.08036i −0.151541 + 0.151541i
\(726\) −2.04940 55.3438i −0.0760602 2.05400i
\(727\) 18.7642 0.695926 0.347963 0.937508i \(-0.386873\pi\)
0.347963 + 0.937508i \(0.386873\pi\)
\(728\) 0.276078 22.7444i 0.0102321 0.842965i
\(729\) 6.58452 + 26.1848i 0.243871 + 0.969808i
\(730\) −17.4512 + 9.98153i −0.645898 + 0.369433i
\(731\) 10.0994 + 10.0994i 0.373541 + 0.373541i
\(732\) 13.2625 + 21.3163i 0.490197 + 0.787874i
\(733\) −21.7504 + 21.7504i −0.803370 + 0.803370i −0.983621 0.180251i \(-0.942309\pi\)
0.180251 + 0.983621i \(0.442309\pi\)
\(734\) 6.07695 + 1.65469i 0.224304 + 0.0610759i
\(735\) −8.18204 4.28610i −0.301799 0.158095i
\(736\) −3.73562 15.1620i −0.137697 0.558877i
\(737\) 6.25778i 0.230508i
\(738\) −0.548527 1.55130i −0.0201916 0.0571040i
\(739\) −3.50532 3.50532i −0.128945 0.128945i 0.639689 0.768634i \(-0.279063\pi\)
−0.768634 + 0.639689i \(0.779063\pi\)
\(740\) 8.08104 + 4.75319i 0.297065 + 0.174731i
\(741\) −5.96288 19.0830i −0.219052 0.701031i
\(742\) 2.26741 + 3.96422i 0.0832391 + 0.145531i
\(743\) 47.3640i 1.73762i 0.495148 + 0.868809i \(0.335114\pi\)
−0.495148 + 0.868809i \(0.664886\pi\)
\(744\) 23.4362 43.4477i 0.859212 1.59287i
\(745\) 3.28996i 0.120535i
\(746\) 9.58087 5.47995i 0.350780 0.200635i
\(747\) −6.52366 + 35.9154i −0.238688 + 1.31407i
\(748\) −30.9408 + 8.02280i −1.13131 + 0.293343i
\(749\) −2.42894 2.42894i −0.0887514 0.0887514i
\(750\) −1.79496 1.66677i −0.0655426 0.0608618i
\(751\) 39.3076i 1.43436i 0.696890 + 0.717178i \(0.254567\pi\)
−0.696890 + 0.717178i \(0.745433\pi\)
\(752\) −0.00424501 0.00763532i −0.000154799 0.000278431i
\(753\) −14.9446 + 28.5288i −0.544611 + 1.03965i
\(754\) −13.3536 + 49.0418i −0.486309 + 1.78600i
\(755\) −2.58307 + 2.58307i −0.0940074 + 0.0940074i
\(756\) 4.93838 + 12.4768i 0.179607 + 0.453776i
\(757\) 10.8046 + 10.8046i 0.392702 + 0.392702i 0.875649 0.482948i \(-0.160434\pi\)
−0.482948 + 0.875649i \(0.660434\pi\)
\(758\) 10.9272 + 19.1045i 0.396892 + 0.693906i
\(759\) 24.5535 + 12.8622i 0.891237 + 0.466868i
\(760\) 3.75132 3.66135i 0.136075 0.132811i
\(761\) −5.48314 −0.198764 −0.0993818 0.995049i \(-0.531687\pi\)
−0.0993818 + 0.995049i \(0.531687\pi\)
\(762\) 0.906878 + 24.4902i 0.0328527 + 0.887186i
\(763\) −9.44535 + 9.44535i −0.341944 + 0.341944i
\(764\) −8.97262 5.27761i −0.324618 0.190937i
\(765\) 8.13716 + 1.47803i 0.294200 + 0.0534384i
\(766\) 0.648345 2.38108i 0.0234256 0.0860319i
\(767\) −2.45874 −0.0887801
\(768\) 26.8299 + 6.93966i 0.968139 + 0.250413i
\(769\) −8.83223 −0.318498 −0.159249 0.987238i \(-0.550907\pi\)
−0.159249 + 0.987238i \(0.550907\pi\)
\(770\) −2.78125 + 10.2143i −0.100229 + 0.368098i
\(771\) −45.4434 + 14.1997i −1.63660 + 0.511391i
\(772\) −24.1724 14.2180i −0.869984 0.511716i
\(773\) 6.38774 6.38774i 0.229751 0.229751i −0.582838 0.812589i \(-0.698058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(774\) 19.8353 + 9.47234i 0.712966 + 0.340476i
\(775\) −10.0767 −0.361966
\(776\) 13.5446 13.2197i 0.486223 0.474561i
\(777\) −4.86469 + 9.28654i −0.174520 + 0.333153i
\(778\) 0.0190720 + 0.0333446i 0.000683765 + 0.00119546i
\(779\) −0.508243 0.508243i −0.0182097 0.0182097i
\(780\) −21.0130 4.89417i −0.752386 0.175239i
\(781\) 38.7642 38.7642i 1.38709 1.38709i
\(782\) 2.82744 10.3839i 0.101109 0.371329i
\(783\) −3.68408 29.7572i −0.131658 1.06344i
\(784\) −10.3653 18.6436i −0.370188 0.665841i
\(785\) 7.88246i 0.281337i
\(786\) 28.8101 31.0259i 1.02762 1.10666i
\(787\) 28.0915 + 28.0915i 1.00135 + 1.00135i 0.999999 + 0.00135518i \(0.000431367\pi\)
0.00135518 + 0.999999i \(0.499569\pi\)
\(788\) −8.83977 + 2.29211i −0.314904 + 0.0816530i
\(789\) 20.3536 6.35990i 0.724606 0.226419i
\(790\) −10.4860 + 5.99765i −0.373074 + 0.213387i
\(791\) 4.70074i 0.167139i
\(792\) −40.7777 + 27.5148i −1.44897 + 0.977697i
\(793\) 45.1383i 1.60291i
\(794\) 22.1354 + 38.7003i 0.785554 + 1.37342i
\(795\) 4.13466 1.29196i 0.146641 0.0458212i
\(796\) −14.6965 8.64433i −0.520903 0.306390i
\(797\) −33.0086 33.0086i −1.16922 1.16922i −0.982392 0.186832i \(-0.940178\pi\)
−0.186832 0.982392i \(-0.559822\pi\)
\(798\) 4.29531 + 3.98856i 0.152052 + 0.141193i
\(799\) 0.00602080i 0.000213001i
\(800\) −1.35327 5.49260i −0.0478455 0.194193i
\(801\) −11.5182 + 7.97707i −0.406975 + 0.281856i
\(802\) −43.6108 11.8748i −1.53995 0.419313i
\(803\) 58.2755 58.2755i 2.05650 2.05650i
\(804\) −3.17487 + 1.97533i −0.111969 + 0.0696644i
\(805\) −2.52032 2.52032i −0.0888296 0.0888296i
\(806\) −77.0447 + 44.0671i −2.71378 + 1.55220i
\(807\) −5.68419 + 10.8509i −0.200093 + 0.381971i
\(808\) −0.306500 + 25.2507i −0.0107826 + 0.888318i
\(809\) 47.8351 1.68179 0.840897 0.541195i \(-0.182028\pi\)
0.840897 + 0.541195i \(0.182028\pi\)
\(810\) 12.5650 2.03019i 0.441488 0.0713337i
\(811\) 7.63096 7.63096i 0.267959 0.267959i −0.560318 0.828277i \(-0.689321\pi\)
0.828277 + 0.560318i \(0.189321\pi\)
\(812\) −3.74025 14.4247i −0.131257 0.506208i
\(813\) 4.33725 1.35527i 0.152114 0.0475312i
\(814\) −37.0826 10.0972i −1.29974 0.353907i
\(815\) −2.52231 −0.0883526
\(816\) 13.8371 + 13.1653i 0.484395 + 0.460876i
\(817\) 9.60192 0.335929
\(818\) 21.8175 + 5.94070i 0.762832 + 0.207712i
\(819\) 4.31167 23.7375i 0.150662 0.829455i
\(820\) −0.750828 + 0.194686i −0.0262201 + 0.00679873i
\(821\) 7.10751 7.10751i 0.248054 0.248054i −0.572118 0.820171i \(-0.693878\pi\)
0.820171 + 0.572118i \(0.193878\pi\)
\(822\) −43.1874 + 1.59924i −1.50633 + 0.0557799i
\(823\) −0.240830 −0.00839482 −0.00419741 0.999991i \(-0.501336\pi\)
−0.00419741 + 0.999991i \(0.501336\pi\)
\(824\) 4.51565 4.40734i 0.157310 0.153537i
\(825\) 8.89481 + 4.65948i 0.309678 + 0.162222i
\(826\) 0.625739 0.357903i 0.0217723 0.0124530i
\(827\) −18.9041 18.9041i −0.657359 0.657359i 0.297395 0.954754i \(-0.403882\pi\)
−0.954754 + 0.297395i \(0.903882\pi\)
\(828\) −1.22496 16.5172i −0.0425702 0.574014i
\(829\) 12.3933 12.3933i 0.430437 0.430437i −0.458340 0.888777i \(-0.651556\pi\)
0.888777 + 0.458340i \(0.151556\pi\)
\(830\) 16.6032 + 4.52089i 0.576305 + 0.156922i
\(831\) −3.57198 + 6.81880i −0.123911 + 0.236542i
\(832\) −34.3669 36.0773i −1.19146 1.25076i
\(833\) 14.7013i 0.509370i
\(834\) 35.7982 38.5513i 1.23959 1.33492i
\(835\) 0.946479 + 0.946479i 0.0327542 + 0.0327542i
\(836\) −10.8945 + 18.5221i −0.376795 + 0.640600i
\(837\) 32.1946 41.2927i 1.11281 1.42728i
\(838\) −0.753894 1.31807i −0.0260428 0.0455319i
\(839\) 8.32262i 0.287329i 0.989626 + 0.143664i \(0.0458886\pi\)
−0.989626 + 0.143664i \(0.954111\pi\)
\(840\) 6.06012 1.81318i 0.209094 0.0625606i
\(841\) 4.29862i 0.148228i
\(842\) 21.5784 12.3422i 0.743641 0.425339i
\(843\) −1.05788 3.38551i −0.0364352 0.116603i
\(844\) 5.56029 + 21.4439i 0.191393 + 0.738129i
\(845\) 18.2374 + 18.2374i 0.627386 + 0.627386i
\(846\) −0.00308896 0.00873592i −0.000106201 0.000300347i
\(847\) 29.1934i 1.00310i
\(848\) 9.61984 + 2.74523i 0.330347 + 0.0942716i
\(849\) −16.5118 8.64961i −0.566685 0.296854i
\(850\) 1.02428 3.76170i 0.0351324 0.129025i
\(851\) 9.14991 9.14991i 0.313655 0.313655i
\(852\) −31.9032 7.43062i −1.09299 0.254569i
\(853\) −22.3562 22.3562i −0.765462 0.765462i 0.211842 0.977304i \(-0.432054\pi\)
−0.977304 + 0.211842i \(0.932054\pi\)
\(854\) 6.57048 + 11.4875i 0.224837 + 0.393094i
\(855\) 4.57077 3.16555i 0.156317 0.108259i
\(856\) −7.52403 0.0913288i −0.257166 0.00312155i
\(857\) −11.4518 −0.391185 −0.195593 0.980685i \(-0.562663\pi\)
−0.195593 + 0.980685i \(0.562663\pi\)
\(858\) 88.3848 3.27292i 3.01741 0.111735i
\(859\) −16.6861 + 16.6861i −0.569323 + 0.569323i −0.931939 0.362615i \(-0.881884\pi\)
0.362615 + 0.931939i \(0.381884\pi\)
\(860\) 5.25342 8.93150i 0.179140 0.304562i
\(861\) −0.258687 0.827875i −0.00881603 0.0282139i
\(862\) 9.16467 33.6577i 0.312150 1.14639i
\(863\) −30.8952 −1.05168 −0.525842 0.850582i \(-0.676250\pi\)
−0.525842 + 0.850582i \(0.676250\pi\)
\(864\) 26.8314 + 12.0031i 0.912824 + 0.408354i
\(865\) 0.322899 0.0109789
\(866\) 6.59546 24.2222i 0.224123 0.823103i
\(867\) −4.85601 15.5406i −0.164919 0.527788i
\(868\) 13.1930 22.4298i 0.447799 0.761316i
\(869\) 35.0163 35.0163i 1.18785 1.18785i
\(870\) −14.1251 + 0.523056i −0.478885 + 0.0177333i
\(871\) 6.72292 0.227798
\(872\) −0.355148 + 29.2585i −0.0120268 + 0.990819i
\(873\) 16.5033 11.4296i 0.558553 0.386833i
\(874\) −3.59212 6.28028i −0.121505 0.212434i
\(875\) −0.913016 0.913016i −0.0308656 0.0308656i
\(876\) −47.9611 11.1707i −1.62046 0.377423i
\(877\) 38.6385 38.6385i 1.30473 1.30473i 0.379563 0.925166i \(-0.376074\pi\)
0.925166 0.379563i \(-0.123926\pi\)
\(878\) −5.78721 + 21.2538i −0.195309 + 0.717282i
\(879\) −49.5419 25.9522i −1.67101 0.875345i
\(880\) 11.2682 + 20.2677i 0.379852 + 0.683223i
\(881\) 18.6527i 0.628425i −0.949353 0.314212i \(-0.898260\pi\)
0.949353 0.314212i \(-0.101740\pi\)
\(882\) −7.54247 21.3309i −0.253968 0.718250i
\(883\) 31.4827 + 31.4827i 1.05948 + 1.05948i 0.998116 + 0.0613603i \(0.0195439\pi\)
0.0613603 + 0.998116i \(0.480456\pi\)
\(884\) −8.61913 33.2406i −0.289893 1.11800i
\(885\) −0.203932 0.652643i −0.00685510 0.0219383i
\(886\) 34.0260 19.4618i 1.14313 0.653832i
\(887\) 31.5055i 1.05785i 0.848669 + 0.528925i \(0.177405\pi\)
−0.848669 + 0.528925i \(0.822595\pi\)
\(888\) 6.58266 + 22.0010i 0.220900 + 0.738306i
\(889\) 12.9184i 0.433268i
\(890\) 3.27921 + 5.73319i 0.109919 + 0.192177i
\(891\) −47.5123 + 21.5626i −1.59172 + 0.722376i
\(892\) −2.90108 + 4.93221i −0.0971353 + 0.165143i
\(893\) −0.00286210 0.00286210i −9.57767e−5 9.57767e-5i
\(894\) 5.48361 5.90535i 0.183399 0.197504i
\(895\) 2.10362i 0.0703162i
\(896\) 13.9978 + 4.17895i 0.467633 + 0.139609i
\(897\) −13.8182 + 26.3786i −0.461378 + 0.880756i
\(898\) 48.5894 + 13.2304i 1.62145 + 0.441505i
\(899\) −41.1166 + 41.1166i −1.37131 + 1.37131i
\(900\) −0.443755 5.98357i −0.0147918 0.199452i
\(901\) 4.87522 + 4.87522i 0.162417 + 0.162417i
\(902\) 2.76011 1.57870i 0.0919017 0.0525648i
\(903\) 10.2639 + 5.37665i 0.341560 + 0.178924i
\(904\) 7.19228 + 7.36903i 0.239212 + 0.245090i
\(905\) 12.6686 0.421120
\(906\) −8.94187 + 0.331120i −0.297074 + 0.0110007i
\(907\) 26.6887 26.6887i 0.886183 0.886183i −0.107971 0.994154i \(-0.534436\pi\)
0.994154 + 0.107971i \(0.0344355\pi\)
\(908\) 22.3544 5.79638i 0.741856 0.192360i
\(909\) −4.78679 + 26.3532i −0.158768 + 0.874081i
\(910\) −10.9735 2.98799i −0.363769 0.0990508i
\(911\) 39.3861 1.30492 0.652460 0.757823i \(-0.273737\pi\)
0.652460 + 0.757823i \(0.273737\pi\)
\(912\) 12.8361 0.319372i 0.425045 0.0105755i
\(913\) −70.5405 −2.33455
\(914\) 27.0856 + 7.37514i 0.895911 + 0.243948i
\(915\) 11.9814 3.74384i 0.396092 0.123767i
\(916\) 7.54373 + 29.0932i 0.249252 + 0.961267i
\(917\) 15.7815 15.7815i 0.521151 0.521151i
\(918\) 12.1423 + 16.2158i 0.400757 + 0.535201i
\(919\) −46.3916 −1.53032 −0.765158 0.643842i \(-0.777339\pi\)
−0.765158 + 0.643842i \(0.777339\pi\)
\(920\) −7.80711 0.0947648i −0.257393 0.00312430i
\(921\) −5.97035 + 11.3972i −0.196730 + 0.375551i
\(922\) 52.0418 29.7663i 1.71391 0.980300i
\(923\) 41.6455 + 41.6455i 1.37078 + 1.37078i
\(924\) −22.0171 + 13.6985i −0.724310 + 0.450649i
\(925\) 3.31466 3.31466i 0.108985 0.108985i
\(926\) 43.8320 + 11.9350i 1.44041 + 0.392209i
\(927\) 5.50206 3.81052i 0.180711 0.125154i
\(928\) −27.9336 16.8899i −0.916965 0.554439i
\(929\) 52.7805i 1.73167i 0.500329 + 0.865836i \(0.333213\pi\)
−0.500329 + 0.865836i \(0.666787\pi\)
\(930\) −18.0873 16.7956i −0.593105 0.550748i
\(931\) −6.98855 6.98855i −0.229040 0.229040i
\(932\) −22.8535 13.4422i −0.748593 0.440315i
\(933\) 24.2811 7.58714i 0.794927 0.248392i
\(934\) −28.5255 49.8726i −0.933383 1.63188i
\(935\) 15.9820i 0.522668i
\(936\) −29.5600 43.8087i −0.966199 1.43193i
\(937\) 29.1746i 0.953093i 0.879149 + 0.476547i \(0.158112\pi\)
−0.879149 + 0.476547i \(0.841888\pi\)
\(938\) −1.71095 + 0.978611i −0.0558646 + 0.0319528i
\(939\) 7.20366 2.25094i 0.235082 0.0734565i
\(940\) −0.00422819 + 0.00109635i −0.000137908 + 3.57589e-5i
\(941\) −35.4103 35.4103i −1.15434 1.15434i −0.985673 0.168668i \(-0.946053\pi\)
−0.168668 0.985673i \(-0.553947\pi\)
\(942\) −13.1382 + 14.1487i −0.428067 + 0.460989i
\(943\) 1.07058i 0.0348628i
\(944\) 0.433326 1.51846i 0.0141036 0.0494217i
\(945\) 6.65844 0.824345i 0.216599 0.0268159i
\(946\) −11.1599 + 40.9852i −0.362839 + 1.33254i
\(947\) −16.4926 + 16.4926i −0.535937 + 0.535937i −0.922333 0.386396i \(-0.873720\pi\)
0.386396 + 0.922333i \(0.373720\pi\)
\(948\) −28.8186 6.71219i −0.935985 0.218002i
\(949\) 62.6071 + 62.6071i 2.03231 + 2.03231i
\(950\) −1.30129 2.27511i −0.0422194 0.0738142i
\(951\) −13.4964 + 25.7643i −0.437652 + 0.835465i
\(952\) 7.03215 + 7.20496i 0.227913 + 0.233514i
\(953\) −19.2911 −0.624902 −0.312451 0.949934i \(-0.601150\pi\)
−0.312451 + 0.949934i \(0.601150\pi\)
\(954\) 9.57494 + 4.57251i 0.310000 + 0.148040i
\(955\) −3.68037 + 3.68037i −0.119094 + 0.119094i
\(956\) −32.0186 18.8330i −1.03556 0.609104i
\(957\) 55.3064 17.2816i 1.78780 0.558636i
\(958\) 4.77688 17.5433i 0.154334 0.566799i
\(959\) −22.7810 −0.735635
\(960\) 6.72583 12.1146i 0.217075 0.390997i
\(961\) −70.5400 −2.27548
\(962\) 10.8477 39.8389i 0.349745 1.28446i
\(963\) −7.85254 1.42633i −0.253045 0.0459630i
\(964\) 43.5922 + 25.6405i 1.40401 + 0.825824i
\(965\) −9.91499 + 9.91499i −0.319175 + 0.319175i
\(966\) −0.323077 8.72467i −0.0103948 0.280711i
\(967\) −10.5225 −0.338381 −0.169190 0.985583i \(-0.554115\pi\)
−0.169190 + 0.985583i \(0.554115\pi\)
\(968\) −44.6668 45.7645i −1.43565 1.47093i
\(969\) 7.83886 + 4.10633i 0.251820 + 0.131914i
\(970\) −4.69847 8.21456i −0.150859 0.263754i
\(971\) −18.2860 18.2860i −0.586825 0.586825i 0.349945 0.936770i \(-0.386200\pi\)
−0.936770 + 0.349945i \(0.886200\pi\)
\(972\) 25.9375 + 17.2988i 0.831944 + 0.554859i
\(973\) 19.6094 19.6094i 0.628647 0.628647i
\(974\) 7.41553 27.2339i 0.237609 0.872631i
\(975\) −5.00582 + 9.55596i −0.160315 + 0.306036i
\(976\) 27.8763 + 7.95512i 0.892299 + 0.254637i
\(977\) 22.4622i 0.718629i 0.933216 + 0.359315i \(0.116990\pi\)
−0.933216 + 0.359315i \(0.883010\pi\)
\(978\) −4.52744 4.20411i −0.144772 0.134433i
\(979\) −19.1451 19.1451i −0.611880 0.611880i
\(980\) −10.3242 + 2.67701i −0.329794 + 0.0855139i
\(981\) −5.54655 + 30.5360i −0.177088 + 0.974939i
\(982\) 25.7473 14.7266i 0.821629 0.469946i
\(983\) 23.7731i 0.758245i −0.925346 0.379123i \(-0.876226\pi\)
0.925346 0.379123i \(-0.123774\pi\)
\(984\) −1.67220 0.902004i −0.0533079 0.0287548i
\(985\) 4.56605i 0.145487i
\(986\) −11.1697 19.5285i −0.355715 0.621914i
\(987\) −0.00145676 0.00466207i −4.63692e−5 0.000148395i
\(988\) −19.8988 11.7043i −0.633067 0.372364i
\(989\) −10.1129 10.1129i −0.321570 0.321570i
\(990\) 8.19953 + 23.1892i 0.260598 + 0.737001i
\(991\) 6.71379i 0.213271i −0.994298 0.106635i \(-0.965992\pi\)
0.994298 0.106635i \(-0.0340077\pi\)
\(992\) −13.6365 55.3473i −0.432961 1.75728i
\(993\) 37.8232 + 19.8134i 1.20028 + 0.628760i
\(994\) −16.6607 4.53654i −0.528444 0.143890i
\(995\) −6.02818 + 6.02818i −0.191106 + 0.191106i
\(996\) 22.2668 + 35.7885i 0.705550 + 1.13400i
\(997\) −23.6160 23.6160i −0.747925 0.747925i 0.226164 0.974089i \(-0.427381\pi\)
−0.974089 + 0.226164i \(0.927381\pi\)
\(998\) 32.3594 18.5085i 1.02432 0.585878i
\(999\) 2.99275 + 24.1732i 0.0946863 + 0.764805i
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 240.2.bk.b.11.17 yes 60
3.2 odd 2 inner 240.2.bk.b.11.14 60
4.3 odd 2 960.2.bk.b.911.20 60
12.11 even 2 960.2.bk.b.911.28 60
16.3 odd 4 inner 240.2.bk.b.131.14 yes 60
16.13 even 4 960.2.bk.b.431.28 60
48.29 odd 4 960.2.bk.b.431.20 60
48.35 even 4 inner 240.2.bk.b.131.17 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bk.b.11.14 60 3.2 odd 2 inner
240.2.bk.b.11.17 yes 60 1.1 even 1 trivial
240.2.bk.b.131.14 yes 60 16.3 odd 4 inner
240.2.bk.b.131.17 yes 60 48.35 even 4 inner
960.2.bk.b.431.20 60 48.29 odd 4
960.2.bk.b.431.28 60 16.13 even 4
960.2.bk.b.911.20 60 4.3 odd 2
960.2.bk.b.911.28 60 12.11 even 2