Properties

Label 240.2.bl.a.229.17
Level $240$
Weight $2$
Character 240.229
Analytic conductor $1.916$
Analytic rank $0$
Dimension $48$
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(109,240)]
 
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([0, 3, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bl (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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 229.17
Character \(\chi\) \(=\) 240.229
Dual form 240.2.bl.a.109.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.750333 - 1.19875i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.874002 - 1.79892i) q^{4} +(1.95942 + 1.07735i) q^{5} +(1.37821 - 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 - 0.302081i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.750333 - 1.19875i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.874002 - 1.79892i) q^{4} +(1.95942 + 1.07735i) q^{5} +(1.37821 - 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 - 0.302081i) q^{8} +1.00000i q^{9} +(2.76169 - 1.54047i) q^{10} +(1.38208 + 1.38208i) q^{11} +(0.654018 - 1.89004i) q^{12} +(-2.12237 - 2.12237i) q^{13} +(0.916431 - 1.46411i) q^{14} +(0.623711 + 2.14732i) q^{15} +(-2.47224 + 3.14452i) q^{16} -6.00218i q^{17} +(1.19875 + 0.750333i) q^{18} +(-3.06223 + 3.06223i) q^{19} +(0.225545 - 4.46644i) q^{20} +(0.863636 + 0.863636i) q^{21} +(2.69379 - 0.619748i) q^{22} -2.90813 q^{23} +(-1.77496 - 2.20216i) q^{24} +(2.67861 + 4.22197i) q^{25} +(-4.13668 + 0.951709i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.06748 - 2.19714i) q^{28} +(3.18392 - 3.18392i) q^{29} +(3.04209 + 0.863531i) q^{30} -3.88079 q^{31} +(1.91449 + 5.32304i) q^{32} +1.95456i q^{33} +(-7.19511 - 4.50363i) q^{34} +(2.39316 + 1.31584i) q^{35} +(1.79892 - 0.874002i) q^{36} +(-2.44376 + 2.44376i) q^{37} +(1.37316 + 5.96855i) q^{38} -3.00149i q^{39} +(-5.18492 - 3.62169i) q^{40} +2.38396i q^{41} +(1.68330 - 0.387269i) q^{42} +(-9.00811 + 9.00811i) q^{43} +(1.27831 - 3.69420i) q^{44} +(-1.07735 + 1.95942i) q^{45} +(-2.18206 + 3.48612i) q^{46} -0.586179i q^{47} +(-3.97165 + 0.475374i) q^{48} -5.50826 q^{49} +(7.07094 - 0.0431074i) q^{50} +(4.24418 - 4.24418i) q^{51} +(-1.96303 + 5.67295i) q^{52} +(2.36822 - 2.36822i) q^{53} +(0.317079 + 1.37821i) q^{54} +(1.21908 + 4.19706i) q^{55} +(-3.43479 - 0.368951i) q^{56} -4.33065 q^{57} +(-1.42772 - 6.20572i) q^{58} +(8.43447 + 8.43447i) q^{59} +(3.31774 - 2.99877i) q^{60} +(9.98062 - 9.98062i) q^{61} +(-2.91189 + 4.65210i) q^{62} +1.22137i q^{63} +(7.81749 + 1.69905i) q^{64} +(-1.87206 - 6.44516i) q^{65} +(2.34302 + 1.46657i) q^{66} +(3.82203 + 3.82203i) q^{67} +(-10.7974 + 5.24591i) q^{68} +(-2.05636 - 2.05636i) q^{69} +(3.37304 - 1.88148i) q^{70} -11.5314i q^{71} +(0.302081 - 2.81225i) q^{72} -1.31108 q^{73} +(1.09583 + 4.76310i) q^{74} +(-1.09132 + 4.87945i) q^{75} +(8.18512 + 2.83232i) q^{76} +(1.68803 + 1.68803i) q^{77} +(-3.59804 - 2.25212i) q^{78} -12.5967 q^{79} +(-8.23191 + 3.49794i) q^{80} -1.00000 q^{81} +(2.85777 + 1.78876i) q^{82} +(2.91633 + 2.91633i) q^{83} +(0.798795 - 2.30843i) q^{84} +(6.46647 - 11.7608i) q^{85} +(4.03939 + 17.5575i) q^{86} +4.50274 q^{87} +(-3.46926 - 4.30426i) q^{88} +9.58659i q^{89} +(1.54047 + 2.76169i) q^{90} +(-2.59220 - 2.59220i) q^{91} +(2.54171 + 5.23150i) q^{92} +(-2.74413 - 2.74413i) q^{93} +(-0.702682 - 0.439829i) q^{94} +(-9.29930 + 2.70108i) q^{95} +(-2.41021 + 5.11770i) q^{96} +9.45309i q^{97} +(-4.13303 + 6.60303i) q^{98} +(-1.38208 + 1.38208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.750333 1.19875i 0.530565 0.847644i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −0.874002 1.79892i −0.437001 0.899461i
\(5\) 1.95942 + 1.07735i 0.876277 + 0.481808i
\(6\) 1.37821 0.317079i 0.562652 0.129447i
\(7\) 1.22137 0.461633 0.230817 0.972997i \(-0.425860\pi\)
0.230817 + 0.972997i \(0.425860\pi\)
\(8\) −2.81225 0.302081i −0.994280 0.106802i
\(9\) 1.00000i 0.333333i
\(10\) 2.76169 1.54047i 0.873324 0.487141i
\(11\) 1.38208 + 1.38208i 0.416713 + 0.416713i 0.884069 0.467356i \(-0.154793\pi\)
−0.467356 + 0.884069i \(0.654793\pi\)
\(12\) 0.654018 1.89004i 0.188799 0.545608i
\(13\) −2.12237 2.12237i −0.588641 0.588641i 0.348622 0.937263i \(-0.386650\pi\)
−0.937263 + 0.348622i \(0.886650\pi\)
\(14\) 0.916431 1.46411i 0.244926 0.391300i
\(15\) 0.623711 + 2.14732i 0.161042 + 0.554436i
\(16\) −2.47224 + 3.14452i −0.618061 + 0.786130i
\(17\) 6.00218i 1.45574i −0.685714 0.727871i \(-0.740510\pi\)
0.685714 0.727871i \(-0.259490\pi\)
\(18\) 1.19875 + 0.750333i 0.282548 + 0.176855i
\(19\) −3.06223 + 3.06223i −0.702525 + 0.702525i −0.964952 0.262427i \(-0.915477\pi\)
0.262427 + 0.964952i \(0.415477\pi\)
\(20\) 0.225545 4.46644i 0.0504333 0.998727i
\(21\) 0.863636 + 0.863636i 0.188461 + 0.188461i
\(22\) 2.69379 0.619748i 0.574318 0.132131i
\(23\) −2.90813 −0.606387 −0.303193 0.952929i \(-0.598053\pi\)
−0.303193 + 0.952929i \(0.598053\pi\)
\(24\) −1.77496 2.20216i −0.362312 0.449515i
\(25\) 2.67861 + 4.22197i 0.535723 + 0.844394i
\(26\) −4.13668 + 0.951709i −0.811270 + 0.186645i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −1.06748 2.19714i −0.201734 0.415221i
\(29\) 3.18392 3.18392i 0.591239 0.591239i −0.346727 0.937966i \(-0.612707\pi\)
0.937966 + 0.346727i \(0.112707\pi\)
\(30\) 3.04209 + 0.863531i 0.555407 + 0.157659i
\(31\) −3.88079 −0.697011 −0.348505 0.937307i \(-0.613311\pi\)
−0.348505 + 0.937307i \(0.613311\pi\)
\(32\) 1.91449 + 5.32304i 0.338437 + 0.940989i
\(33\) 1.95456i 0.340245i
\(34\) −7.19511 4.50363i −1.23395 0.772366i
\(35\) 2.39316 + 1.31584i 0.404518 + 0.222418i
\(36\) 1.79892 0.874002i 0.299820 0.145667i
\(37\) −2.44376 + 2.44376i −0.401752 + 0.401752i −0.878850 0.477098i \(-0.841689\pi\)
0.477098 + 0.878850i \(0.341689\pi\)
\(38\) 1.37316 + 5.96855i 0.222756 + 0.968226i
\(39\) 3.00149i 0.480623i
\(40\) −5.18492 3.62169i −0.819807 0.572640i
\(41\) 2.38396i 0.372312i 0.982520 + 0.186156i \(0.0596029\pi\)
−0.982520 + 0.186156i \(0.940397\pi\)
\(42\) 1.68330 0.387269i 0.259739 0.0597569i
\(43\) −9.00811 + 9.00811i −1.37372 + 1.37372i −0.518871 + 0.854852i \(0.673648\pi\)
−0.854852 + 0.518871i \(0.826352\pi\)
\(44\) 1.27831 3.69420i 0.192713 0.556921i
\(45\) −1.07735 + 1.95942i −0.160603 + 0.292092i
\(46\) −2.18206 + 3.48612i −0.321728 + 0.514000i
\(47\) 0.586179i 0.0855030i −0.999086 0.0427515i \(-0.986388\pi\)
0.999086 0.0427515i \(-0.0136124\pi\)
\(48\) −3.97165 + 0.475374i −0.573259 + 0.0686143i
\(49\) −5.50826 −0.786895
\(50\) 7.07094 0.0431074i 0.999981 0.00609631i
\(51\) 4.24418 4.24418i 0.594304 0.594304i
\(52\) −1.96303 + 5.67295i −0.272223 + 0.786696i
\(53\) 2.36822 2.36822i 0.325300 0.325300i −0.525496 0.850796i \(-0.676120\pi\)
0.850796 + 0.525496i \(0.176120\pi\)
\(54\) 0.317079 + 1.37821i 0.0431489 + 0.187551i
\(55\) 1.21908 + 4.19706i 0.164381 + 0.565931i
\(56\) −3.43479 0.368951i −0.458993 0.0493032i
\(57\) −4.33065 −0.573609
\(58\) −1.42772 6.20572i −0.187469 0.814851i
\(59\) 8.43447 + 8.43447i 1.09807 + 1.09807i 0.994636 + 0.103438i \(0.0329844\pi\)
0.103438 + 0.994636i \(0.467016\pi\)
\(60\) 3.31774 2.99877i 0.428318 0.387139i
\(61\) 9.98062 9.98062i 1.27789 1.27789i 0.336040 0.941848i \(-0.390912\pi\)
0.941848 0.336040i \(-0.109088\pi\)
\(62\) −2.91189 + 4.65210i −0.369810 + 0.590817i
\(63\) 1.22137i 0.153878i
\(64\) 7.81749 + 1.69905i 0.977187 + 0.212382i
\(65\) −1.87206 6.44516i −0.232201 0.799424i
\(66\) 2.34302 + 1.46657i 0.288406 + 0.180522i
\(67\) 3.82203 + 3.82203i 0.466936 + 0.466936i 0.900920 0.433985i \(-0.142893\pi\)
−0.433985 + 0.900920i \(0.642893\pi\)
\(68\) −10.7974 + 5.24591i −1.30938 + 0.636160i
\(69\) −2.05636 2.05636i −0.247556 0.247556i
\(70\) 3.37304 1.88148i 0.403155 0.224880i
\(71\) 11.5314i 1.36852i −0.729238 0.684260i \(-0.760125\pi\)
0.729238 0.684260i \(-0.239875\pi\)
\(72\) 0.302081 2.81225i 0.0356006 0.331427i
\(73\) −1.31108 −0.153450 −0.0767250 0.997052i \(-0.524446\pi\)
−0.0767250 + 0.997052i \(0.524446\pi\)
\(74\) 1.09583 + 4.76310i 0.127387 + 0.553699i
\(75\) −1.09132 + 4.87945i −0.126014 + 0.563430i
\(76\) 8.18512 + 2.83232i 0.938897 + 0.324890i
\(77\) 1.68803 + 1.68803i 0.192368 + 0.192368i
\(78\) −3.59804 2.25212i −0.407397 0.255002i
\(79\) −12.5967 −1.41724 −0.708619 0.705592i \(-0.750681\pi\)
−0.708619 + 0.705592i \(0.750681\pi\)
\(80\) −8.23191 + 3.49794i −0.920356 + 0.391082i
\(81\) −1.00000 −0.111111
\(82\) 2.85777 + 1.78876i 0.315588 + 0.197536i
\(83\) 2.91633 + 2.91633i 0.320108 + 0.320108i 0.848809 0.528700i \(-0.177320\pi\)
−0.528700 + 0.848809i \(0.677320\pi\)
\(84\) 0.798795 2.30843i 0.0871557 0.251871i
\(85\) 6.46647 11.7608i 0.701387 1.27563i
\(86\) 4.03939 + 17.5575i 0.435578 + 1.89328i
\(87\) 4.50274 0.482744
\(88\) −3.46926 4.30426i −0.369824 0.458835i
\(89\) 9.58659i 1.01618i 0.861305 + 0.508088i \(0.169648\pi\)
−0.861305 + 0.508088i \(0.830352\pi\)
\(90\) 1.54047 + 2.76169i 0.162380 + 0.291108i
\(91\) −2.59220 2.59220i −0.271736 0.271736i
\(92\) 2.54171 + 5.23150i 0.264991 + 0.545421i
\(93\) −2.74413 2.74413i −0.284553 0.284553i
\(94\) −0.702682 0.439829i −0.0724761 0.0453649i
\(95\) −9.29930 + 2.70108i −0.954088 + 0.277125i
\(96\) −2.41021 + 5.11770i −0.245991 + 0.522324i
\(97\) 9.45309i 0.959816i 0.877319 + 0.479908i \(0.159330\pi\)
−0.877319 + 0.479908i \(0.840670\pi\)
\(98\) −4.13303 + 6.60303i −0.417499 + 0.667007i
\(99\) −1.38208 + 1.38208i −0.138904 + 0.138904i
\(100\) 5.25388 8.50863i 0.525388 0.850863i
\(101\) −11.6519 11.6519i −1.15940 1.15940i −0.984604 0.174798i \(-0.944073\pi\)
−0.174798 0.984604i \(-0.555927\pi\)
\(102\) −1.90316 8.27226i −0.188441 0.819075i
\(103\) 2.15006 0.211852 0.105926 0.994374i \(-0.466219\pi\)
0.105926 + 0.994374i \(0.466219\pi\)
\(104\) 5.32752 + 6.60978i 0.522406 + 0.648142i
\(105\) 0.761780 + 2.62266i 0.0743421 + 0.255946i
\(106\) −1.06195 4.61585i −0.103146 0.448331i
\(107\) 13.4992 13.4992i 1.30501 1.30501i 0.380048 0.924967i \(-0.375908\pi\)
0.924967 0.380048i \(-0.124092\pi\)
\(108\) 1.89004 + 0.654018i 0.181869 + 0.0629329i
\(109\) 10.7618 10.7618i 1.03079 1.03079i 0.0312781 0.999511i \(-0.490042\pi\)
0.999511 0.0312781i \(-0.00995775\pi\)
\(110\) 5.94594 + 1.68782i 0.566923 + 0.160927i
\(111\) −3.45601 −0.328029
\(112\) −3.01951 + 3.84061i −0.285317 + 0.362904i
\(113\) 12.6206i 1.18725i −0.804742 0.593624i \(-0.797696\pi\)
0.804742 0.593624i \(-0.202304\pi\)
\(114\) −3.24943 + 5.19137i −0.304337 + 0.486216i
\(115\) −5.69823 3.13308i −0.531363 0.292162i
\(116\) −8.51037 2.94487i −0.790168 0.273424i
\(117\) 2.12237 2.12237i 0.196214 0.196214i
\(118\) 16.4395 3.78216i 1.51338 0.348176i
\(119\) 7.33086i 0.672018i
\(120\) −1.10537 6.22721i −0.100906 0.568464i
\(121\) 7.17971i 0.652701i
\(122\) −4.47548 19.4531i −0.405191 1.76120i
\(123\) −1.68571 + 1.68571i −0.151996 + 0.151996i
\(124\) 3.39182 + 6.98124i 0.304594 + 0.626934i
\(125\) 0.699962 + 11.1584i 0.0626065 + 0.998038i
\(126\) 1.46411 + 0.916431i 0.130433 + 0.0816422i
\(127\) 9.66786i 0.857883i −0.903332 0.428942i \(-0.858887\pi\)
0.903332 0.428942i \(-0.141113\pi\)
\(128\) 7.90246 8.09636i 0.698486 0.715624i
\(129\) −12.7394 −1.12164
\(130\) −9.13081 2.59188i −0.800825 0.227323i
\(131\) 10.5362 10.5362i 0.920553 0.920553i −0.0765154 0.997068i \(-0.524379\pi\)
0.997068 + 0.0765154i \(0.0243794\pi\)
\(132\) 3.51610 1.70829i 0.306037 0.148687i
\(133\) −3.74011 + 3.74011i −0.324309 + 0.324309i
\(134\) 7.44946 1.71386i 0.643535 0.148055i
\(135\) −2.14732 + 0.623711i −0.184812 + 0.0536805i
\(136\) −1.81314 + 16.8796i −0.155476 + 1.44742i
\(137\) −12.9189 −1.10374 −0.551869 0.833931i \(-0.686085\pi\)
−0.551869 + 0.833931i \(0.686085\pi\)
\(138\) −4.00801 + 0.922106i −0.341184 + 0.0784948i
\(139\) 11.5153 + 11.5153i 0.976718 + 0.976718i 0.999735 0.0230167i \(-0.00732710\pi\)
−0.0230167 + 0.999735i \(0.507327\pi\)
\(140\) 0.275473 5.45516i 0.0232817 0.461046i
\(141\) 0.414491 0.414491i 0.0349064 0.0349064i
\(142\) −13.8232 8.65235i −1.16002 0.726089i
\(143\) 5.86659i 0.490589i
\(144\) −3.14452 2.47224i −0.262043 0.206020i
\(145\) 9.66882 2.80841i 0.802952 0.233226i
\(146\) −0.983744 + 1.57165i −0.0814153 + 0.130071i
\(147\) −3.89493 3.89493i −0.321249 0.321249i
\(148\) 6.53200 + 2.26029i 0.536927 + 0.185795i
\(149\) 11.8344 + 11.8344i 0.969513 + 0.969513i 0.999549 0.0300356i \(-0.00956208\pi\)
−0.0300356 + 0.999549i \(0.509562\pi\)
\(150\) 5.03039 + 4.96943i 0.410730 + 0.405752i
\(151\) 0.240930i 0.0196066i −0.999952 0.00980330i \(-0.996879\pi\)
0.999952 0.00980330i \(-0.00312054\pi\)
\(152\) 9.53681 7.68672i 0.773537 0.623476i
\(153\) 6.00218 0.485247
\(154\) 3.29010 0.756940i 0.265124 0.0609959i
\(155\) −7.60408 4.18099i −0.610775 0.335825i
\(156\) −5.39945 + 2.62331i −0.432302 + 0.210033i
\(157\) 7.19573 + 7.19573i 0.574282 + 0.574282i 0.933322 0.359040i \(-0.116896\pi\)
−0.359040 + 0.933322i \(0.616896\pi\)
\(158\) −9.45170 + 15.1003i −0.751937 + 1.20131i
\(159\) 3.34917 0.265606
\(160\) −1.98352 + 12.4926i −0.156811 + 0.987629i
\(161\) −3.55189 −0.279928
\(162\) −0.750333 + 1.19875i −0.0589517 + 0.0941827i
\(163\) −11.7446 11.7446i −0.919910 0.919910i 0.0771120 0.997022i \(-0.475430\pi\)
−0.997022 + 0.0771120i \(0.975430\pi\)
\(164\) 4.28855 2.08358i 0.334880 0.162700i
\(165\) −2.10575 + 3.82979i −0.163932 + 0.298149i
\(166\) 5.68416 1.30773i 0.441176 0.101500i
\(167\) 0.213418 0.0165148 0.00825739 0.999966i \(-0.497372\pi\)
0.00825739 + 0.999966i \(0.497372\pi\)
\(168\) −2.16787 2.68965i −0.167255 0.207511i
\(169\) 3.99105i 0.307004i
\(170\) −9.24620 16.5762i −0.709151 1.27133i
\(171\) −3.06223 3.06223i −0.234175 0.234175i
\(172\) 24.0780 + 8.33178i 1.83593 + 0.635293i
\(173\) 6.36918 + 6.36918i 0.484240 + 0.484240i 0.906483 0.422243i \(-0.138757\pi\)
−0.422243 + 0.906483i \(0.638757\pi\)
\(174\) 3.37855 5.39766i 0.256127 0.409195i
\(175\) 3.27157 + 5.15657i 0.247307 + 0.389800i
\(176\) −7.76282 + 0.929145i −0.585145 + 0.0700369i
\(177\) 11.9281i 0.896574i
\(178\) 11.4919 + 7.19313i 0.861356 + 0.539148i
\(179\) −6.53473 + 6.53473i −0.488428 + 0.488428i −0.907810 0.419382i \(-0.862247\pi\)
0.419382 + 0.907810i \(0.362247\pi\)
\(180\) 4.46644 + 0.225545i 0.332909 + 0.0168111i
\(181\) 5.23014 + 5.23014i 0.388753 + 0.388753i 0.874242 0.485490i \(-0.161359\pi\)
−0.485490 + 0.874242i \(0.661359\pi\)
\(182\) −5.05241 + 1.16239i −0.374509 + 0.0861617i
\(183\) 14.1147 1.04339
\(184\) 8.17838 + 0.878490i 0.602918 + 0.0647632i
\(185\) −7.42115 + 2.15555i −0.545614 + 0.158479i
\(186\) −5.34854 + 1.23052i −0.392174 + 0.0902258i
\(187\) 8.29549 8.29549i 0.606626 0.606626i
\(188\) −1.05449 + 0.512321i −0.0769066 + 0.0373649i
\(189\) −0.863636 + 0.863636i −0.0628203 + 0.0628203i
\(190\) −3.73965 + 13.1742i −0.271303 + 0.955760i
\(191\) 13.1318 0.950181 0.475090 0.879937i \(-0.342415\pi\)
0.475090 + 0.879937i \(0.342415\pi\)
\(192\) 4.32639 + 6.72922i 0.312230 + 0.485639i
\(193\) 20.0131i 1.44057i 0.693676 + 0.720287i \(0.255990\pi\)
−0.693676 + 0.720287i \(0.744010\pi\)
\(194\) 11.3319 + 7.09296i 0.813582 + 0.509245i
\(195\) 3.23367 5.88117i 0.231568 0.421159i
\(196\) 4.81423 + 9.90894i 0.343874 + 0.707781i
\(197\) −19.2424 + 19.2424i −1.37096 + 1.37096i −0.511941 + 0.859021i \(0.671073\pi\)
−0.859021 + 0.511941i \(0.828927\pi\)
\(198\) 0.619748 + 2.69379i 0.0440436 + 0.191439i
\(199\) 5.18227i 0.367361i −0.982986 0.183681i \(-0.941199\pi\)
0.982986 0.183681i \(-0.0588012\pi\)
\(200\) −6.25756 12.6824i −0.442476 0.896780i
\(201\) 5.40517i 0.381251i
\(202\) −22.7104 + 5.22489i −1.59790 + 0.367622i
\(203\) 3.88873 3.88873i 0.272935 0.272935i
\(204\) −11.3444 3.92553i −0.794265 0.274842i
\(205\) −2.56837 + 4.67116i −0.179383 + 0.326248i
\(206\) 1.61326 2.57738i 0.112401 0.179575i
\(207\) 2.90813i 0.202129i
\(208\) 11.9209 1.42683i 0.826564 0.0989328i
\(209\) −8.46451 −0.585502
\(210\) 3.71551 + 1.05469i 0.256394 + 0.0727804i
\(211\) −5.53295 + 5.53295i −0.380904 + 0.380904i −0.871428 0.490524i \(-0.836805\pi\)
0.490524 + 0.871428i \(0.336805\pi\)
\(212\) −6.33007 2.19041i −0.434751 0.150438i
\(213\) 8.15390 8.15390i 0.558696 0.558696i
\(214\) −6.05326 26.3110i −0.413792 1.79858i
\(215\) −27.3555 + 7.94570i −1.86563 + 0.541892i
\(216\) 2.20216 1.77496i 0.149838 0.120771i
\(217\) −4.73987 −0.321763
\(218\) −4.82575 20.9755i −0.326841 1.42064i
\(219\) −0.927072 0.927072i −0.0626457 0.0626457i
\(220\) 6.48471 5.86127i 0.437199 0.395166i
\(221\) −12.7389 + 12.7389i −0.856909 + 0.856909i
\(222\) −2.59315 + 4.14289i −0.174041 + 0.278052i
\(223\) 0.639576i 0.0428292i 0.999771 + 0.0214146i \(0.00681700\pi\)
−0.999771 + 0.0214146i \(0.993183\pi\)
\(224\) 2.33829 + 6.50138i 0.156234 + 0.434392i
\(225\) −4.22197 + 2.67861i −0.281465 + 0.178574i
\(226\) −15.1290 9.46967i −1.00636 0.629913i
\(227\) 0.272194 + 0.272194i 0.0180662 + 0.0180662i 0.716082 0.698016i \(-0.245934\pi\)
−0.698016 + 0.716082i \(0.745934\pi\)
\(228\) 3.78500 + 7.79051i 0.250668 + 0.515939i
\(229\) 4.80055 + 4.80055i 0.317229 + 0.317229i 0.847702 0.530473i \(-0.177986\pi\)
−0.530473 + 0.847702i \(0.677986\pi\)
\(230\) −8.03135 + 4.47990i −0.529572 + 0.295396i
\(231\) 2.38723i 0.157068i
\(232\) −9.91577 + 7.99217i −0.651002 + 0.524712i
\(233\) 21.8025 1.42833 0.714166 0.699977i \(-0.246806\pi\)
0.714166 + 0.699977i \(0.246806\pi\)
\(234\) −0.951709 4.13668i −0.0622152 0.270423i
\(235\) 0.631522 1.14857i 0.0411960 0.0749243i
\(236\) 7.80121 22.5447i 0.507816 1.46753i
\(237\) −8.90720 8.90720i −0.578585 0.578585i
\(238\) −8.78786 5.50058i −0.569632 0.356550i
\(239\) 2.01781 0.130521 0.0652606 0.997868i \(-0.479212\pi\)
0.0652606 + 0.997868i \(0.479212\pi\)
\(240\) −8.29426 3.34742i −0.535392 0.216075i
\(241\) 15.4653 0.996209 0.498105 0.867117i \(-0.334030\pi\)
0.498105 + 0.867117i \(0.334030\pi\)
\(242\) −8.60667 5.38717i −0.553258 0.346300i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −26.6774 9.23128i −1.70785 0.590972i
\(245\) −10.7930 5.93435i −0.689538 0.379132i
\(246\) 0.755902 + 3.28559i 0.0481946 + 0.209482i
\(247\) 12.9984 0.827069
\(248\) 10.9138 + 1.17231i 0.693024 + 0.0744420i
\(249\) 4.12431i 0.261367i
\(250\) 13.9013 + 7.53344i 0.879198 + 0.476457i
\(251\) 3.43023 + 3.43023i 0.216514 + 0.216514i 0.807028 0.590514i \(-0.201075\pi\)
−0.590514 + 0.807028i \(0.701075\pi\)
\(252\) 2.19714 1.06748i 0.138407 0.0672447i
\(253\) −4.01927 4.01927i −0.252689 0.252689i
\(254\) −11.5893 7.25411i −0.727180 0.455163i
\(255\) 12.8886 3.74362i 0.807115 0.234435i
\(256\) −3.77604 15.5480i −0.236002 0.971752i
\(257\) 19.3076i 1.20437i 0.798355 + 0.602187i \(0.205704\pi\)
−0.798355 + 0.602187i \(0.794296\pi\)
\(258\) −9.55878 + 15.2713i −0.595104 + 0.950752i
\(259\) −2.98473 + 2.98473i −0.185462 + 0.185462i
\(260\) −9.95816 + 9.00078i −0.617579 + 0.558205i
\(261\) 3.18392 + 3.18392i 0.197080 + 0.197080i
\(262\) −4.72462 20.5359i −0.291888 1.26871i
\(263\) −9.26068 −0.571038 −0.285519 0.958373i \(-0.592166\pi\)
−0.285519 + 0.958373i \(0.592166\pi\)
\(264\) 0.590434 5.49670i 0.0363387 0.338299i
\(265\) 7.19173 2.08891i 0.441785 0.128321i
\(266\) 1.67713 + 7.28978i 0.102831 + 0.446965i
\(267\) −6.77874 + 6.77874i −0.414852 + 0.414852i
\(268\) 3.53508 10.2160i 0.215939 0.624042i
\(269\) 5.68909 5.68909i 0.346870 0.346870i −0.512073 0.858942i \(-0.671122\pi\)
0.858942 + 0.512073i \(0.171122\pi\)
\(270\) −0.863531 + 3.04209i −0.0525528 + 0.185136i
\(271\) 1.56587 0.0951199 0.0475599 0.998868i \(-0.484855\pi\)
0.0475599 + 0.998868i \(0.484855\pi\)
\(272\) 18.8740 + 14.8388i 1.14440 + 0.899736i
\(273\) 3.66592i 0.221872i
\(274\) −9.69350 + 15.4866i −0.585606 + 0.935578i
\(275\) −2.13304 + 9.53716i −0.128627 + 0.575113i
\(276\) −1.90197 + 5.49649i −0.114485 + 0.330850i
\(277\) −11.2915 + 11.2915i −0.678441 + 0.678441i −0.959647 0.281206i \(-0.909266\pi\)
0.281206 + 0.959647i \(0.409266\pi\)
\(278\) 22.4443 5.16367i 1.34612 0.309697i
\(279\) 3.88079i 0.232337i
\(280\) −6.33268 4.42341i −0.378450 0.264349i
\(281\) 15.8017i 0.942653i −0.881959 0.471326i \(-0.843775\pi\)
0.881959 0.471326i \(-0.156225\pi\)
\(282\) −0.185865 0.807877i −0.0110681 0.0481084i
\(283\) −2.32452 + 2.32452i −0.138178 + 0.138178i −0.772813 0.634634i \(-0.781151\pi\)
0.634634 + 0.772813i \(0.281151\pi\)
\(284\) −20.7440 + 10.0784i −1.23093 + 0.598044i
\(285\) −8.48555 4.66565i −0.502640 0.276369i
\(286\) −7.03257 4.40189i −0.415845 0.260289i
\(287\) 2.91169i 0.171871i
\(288\) −5.32304 + 1.91449i −0.313663 + 0.112812i
\(289\) −19.0261 −1.11918
\(290\) 3.88826 13.6977i 0.228326 0.804359i
\(291\) −6.68434 + 6.68434i −0.391843 + 0.391843i
\(292\) 1.14588 + 2.35853i 0.0670578 + 0.138022i
\(293\) −7.44154 + 7.44154i −0.434739 + 0.434739i −0.890237 0.455498i \(-0.849461\pi\)
0.455498 + 0.890237i \(0.349461\pi\)
\(294\) −7.59154 + 1.74655i −0.442748 + 0.101861i
\(295\) 7.43971 + 25.6135i 0.433157 + 1.49128i
\(296\) 7.61069 6.13426i 0.442362 0.356547i
\(297\) −1.95456 −0.113415
\(298\) 23.0663 5.30675i 1.33619 0.307412i
\(299\) 6.17214 + 6.17214i 0.356944 + 0.356944i
\(300\) 9.73156 2.30145i 0.561852 0.132875i
\(301\) −11.0022 + 11.0022i −0.634156 + 0.634156i
\(302\) −0.288815 0.180778i −0.0166194 0.0104026i
\(303\) 16.4782i 0.946648i
\(304\) −2.05868 17.1998i −0.118073 0.986479i
\(305\) 30.3088 8.80351i 1.73548 0.504088i
\(306\) 4.50363 7.19511i 0.257455 0.411317i
\(307\) −3.28621 3.28621i −0.187554 0.187554i 0.607084 0.794638i \(-0.292339\pi\)
−0.794638 + 0.607084i \(0.792339\pi\)
\(308\) 1.56129 4.51197i 0.0889628 0.257093i
\(309\) 1.52032 + 1.52032i 0.0864881 + 0.0864881i
\(310\) −10.7176 + 5.97826i −0.608716 + 0.339542i
\(311\) 29.0235i 1.64577i 0.568206 + 0.822886i \(0.307638\pi\)
−0.568206 + 0.822886i \(0.692362\pi\)
\(312\) −0.906693 + 8.44094i −0.0513314 + 0.477874i
\(313\) −5.50831 −0.311348 −0.155674 0.987808i \(-0.549755\pi\)
−0.155674 + 0.987808i \(0.549755\pi\)
\(314\) 14.0251 3.22669i 0.791480 0.182092i
\(315\) −1.31584 + 2.39316i −0.0741394 + 0.134839i
\(316\) 11.0095 + 22.6605i 0.619334 + 1.27475i
\(317\) 10.6401 + 10.6401i 0.597609 + 0.597609i 0.939676 0.342067i \(-0.111127\pi\)
−0.342067 + 0.939676i \(0.611127\pi\)
\(318\) 2.51299 4.01481i 0.140921 0.225139i
\(319\) 8.80086 0.492754
\(320\) 13.4872 + 11.7514i 0.753959 + 0.656921i
\(321\) 19.0907 1.06554
\(322\) −2.66510 + 4.25783i −0.148520 + 0.237279i
\(323\) 18.3801 + 18.3801i 1.02269 + 1.02269i
\(324\) 0.874002 + 1.79892i 0.0485556 + 0.0999401i
\(325\) 3.27558 14.6456i 0.181696 0.812393i
\(326\) −22.8913 + 5.26649i −1.26783 + 0.291684i
\(327\) 15.2194 0.841636
\(328\) 0.720148 6.70428i 0.0397635 0.370182i
\(329\) 0.715939i 0.0394710i
\(330\) 3.01094 + 5.39788i 0.165747 + 0.297144i
\(331\) −8.08181 8.08181i −0.444217 0.444217i 0.449210 0.893426i \(-0.351706\pi\)
−0.893426 + 0.449210i \(0.851706\pi\)
\(332\) 2.69737 7.79512i 0.148037 0.427813i
\(333\) −2.44376 2.44376i −0.133917 0.133917i
\(334\) 0.160135 0.255835i 0.00876217 0.0139987i
\(335\) 3.37126 + 11.6066i 0.184192 + 0.634138i
\(336\) −4.85084 + 0.580605i −0.264635 + 0.0316746i
\(337\) 24.4098i 1.32969i −0.746983 0.664843i \(-0.768498\pi\)
0.746983 0.664843i \(-0.231502\pi\)
\(338\) −4.78427 2.99461i −0.260230 0.162886i
\(339\) 8.92413 8.92413i 0.484692 0.484692i
\(340\) −26.8084 1.35376i −1.45389 0.0734179i
\(341\) −5.36357 5.36357i −0.290453 0.290453i
\(342\) −5.96855 + 1.37316i −0.322742 + 0.0742519i
\(343\) −15.2772 −0.824890
\(344\) 28.0542 22.6119i 1.51258 1.21915i
\(345\) −1.81383 6.24468i −0.0976534 0.336202i
\(346\) 12.4141 2.85605i 0.667384 0.153542i
\(347\) −1.40907 + 1.40907i −0.0756427 + 0.0756427i −0.743916 0.668273i \(-0.767034\pi\)
0.668273 + 0.743916i \(0.267034\pi\)
\(348\) −3.93540 8.10008i −0.210960 0.434210i
\(349\) −6.11269 + 6.11269i −0.327205 + 0.327205i −0.851523 0.524318i \(-0.824320\pi\)
0.524318 + 0.851523i \(0.324320\pi\)
\(350\) 8.63620 0.0526499i 0.461624 0.00281426i
\(351\) 3.00149 0.160208
\(352\) −4.71089 + 10.0028i −0.251091 + 0.533154i
\(353\) 10.7150i 0.570304i −0.958482 0.285152i \(-0.907956\pi\)
0.958482 0.285152i \(-0.0920441\pi\)
\(354\) 14.2989 + 8.95007i 0.759975 + 0.475691i
\(355\) 12.4234 22.5947i 0.659363 1.19920i
\(356\) 17.2455 8.37870i 0.914011 0.444070i
\(357\) 5.18370 5.18370i 0.274350 0.274350i
\(358\) 2.93028 + 12.7367i 0.154870 + 0.673157i
\(359\) 31.7234i 1.67430i −0.546975 0.837149i \(-0.684221\pi\)
0.546975 0.837149i \(-0.315779\pi\)
\(360\) 3.62169 5.18492i 0.190880 0.273269i
\(361\) 0.245451i 0.0129185i
\(362\) 10.1940 2.34528i 0.535783 0.123265i
\(363\) 5.07682 5.07682i 0.266464 0.266464i
\(364\) −2.39758 + 6.92875i −0.125667 + 0.363165i
\(365\) −2.56895 1.41250i −0.134465 0.0739334i
\(366\) 10.5907 16.9200i 0.553587 0.884424i
\(367\) 31.8025i 1.66008i −0.557707 0.830038i \(-0.688319\pi\)
0.557707 0.830038i \(-0.311681\pi\)
\(368\) 7.18960 9.14467i 0.374784 0.476699i
\(369\) −2.38396 −0.124104
\(370\) −2.98437 + 10.5135i −0.155150 + 0.546570i
\(371\) 2.89246 2.89246i 0.150169 0.150169i
\(372\) −2.53811 + 7.33486i −0.131595 + 0.380295i
\(373\) 17.3861 17.3861i 0.900220 0.900220i −0.0952347 0.995455i \(-0.530360\pi\)
0.995455 + 0.0952347i \(0.0303602\pi\)
\(374\) −3.71984 16.1686i −0.192348 0.836058i
\(375\) −7.39524 + 8.38513i −0.381888 + 0.433006i
\(376\) −0.177073 + 1.64848i −0.00913187 + 0.0850139i
\(377\) −13.5149 −0.696054
\(378\) 0.387269 + 1.68330i 0.0199190 + 0.0865795i
\(379\) −16.4215 16.4215i −0.843513 0.843513i 0.145801 0.989314i \(-0.453424\pi\)
−0.989314 + 0.145801i \(0.953424\pi\)
\(380\) 12.9866 + 14.3680i 0.666200 + 0.737061i
\(381\) 6.83621 6.83621i 0.350229 0.350229i
\(382\) 9.85319 15.7417i 0.504133 0.805415i
\(383\) 9.00561i 0.460165i 0.973171 + 0.230083i \(0.0738997\pi\)
−0.973171 + 0.230083i \(0.926100\pi\)
\(384\) 11.3129 0.137109i 0.577308 0.00699679i
\(385\) 1.48894 + 5.12615i 0.0758835 + 0.261253i
\(386\) 23.9907 + 15.0165i 1.22109 + 0.764318i
\(387\) −9.00811 9.00811i −0.457908 0.457908i
\(388\) 17.0054 8.26201i 0.863317 0.419440i
\(389\) 1.84497 + 1.84497i 0.0935438 + 0.0935438i 0.752330 0.658786i \(-0.228930\pi\)
−0.658786 + 0.752330i \(0.728930\pi\)
\(390\) −4.62372 8.28919i −0.234131 0.419740i
\(391\) 17.4551i 0.882742i
\(392\) 15.4906 + 1.66394i 0.782394 + 0.0840418i
\(393\) 14.9005 0.751628
\(394\) 8.62860 + 37.5050i 0.434703 + 1.88947i
\(395\) −24.6821 13.5711i −1.24189 0.682836i
\(396\) 3.69420 + 1.27831i 0.185640 + 0.0642377i
\(397\) −24.0894 24.0894i −1.20901 1.20901i −0.971348 0.237663i \(-0.923619\pi\)
−0.237663 0.971348i \(-0.576381\pi\)
\(398\) −6.21224 3.88843i −0.311392 0.194909i
\(399\) −5.28931 −0.264797
\(400\) −19.8983 2.01477i −0.994913 0.100738i
\(401\) −10.4494 −0.521817 −0.260909 0.965364i \(-0.584022\pi\)
−0.260909 + 0.965364i \(0.584022\pi\)
\(402\) 6.47945 + 4.05568i 0.323165 + 0.202279i
\(403\) 8.23650 + 8.23650i 0.410289 + 0.410289i
\(404\) −10.7770 + 31.1445i −0.536178 + 1.54950i
\(405\) −1.95942 1.07735i −0.0973641 0.0535342i
\(406\) −1.74377 7.57945i −0.0865420 0.376162i
\(407\) −6.75496 −0.334831
\(408\) −13.2178 + 10.6536i −0.654378 + 0.527432i
\(409\) 6.67465i 0.330040i 0.986290 + 0.165020i \(0.0527689\pi\)
−0.986290 + 0.165020i \(0.947231\pi\)
\(410\) 3.67242 + 6.58376i 0.181368 + 0.325149i
\(411\) −9.13506 9.13506i −0.450599 0.450599i
\(412\) −1.87916 3.86779i −0.0925793 0.190552i
\(413\) 10.3016 + 10.3016i 0.506907 + 0.506907i
\(414\) −3.48612 2.18206i −0.171333 0.107243i
\(415\) 2.57238 + 8.85621i 0.126273 + 0.434734i
\(416\) 7.23421 15.3607i 0.354687 0.753123i
\(417\) 16.2851i 0.797487i
\(418\) −6.35120 + 10.1468i −0.310647 + 0.496297i
\(419\) −15.8121 + 15.8121i −0.772472 + 0.772472i −0.978538 0.206066i \(-0.933934\pi\)
0.206066 + 0.978538i \(0.433934\pi\)
\(420\) 4.05217 3.66260i 0.197726 0.178716i
\(421\) −1.69730 1.69730i −0.0827211 0.0827211i 0.664536 0.747257i \(-0.268629\pi\)
−0.747257 + 0.664536i \(0.768629\pi\)
\(422\) 2.48107 + 10.7842i 0.120776 + 0.524965i
\(423\) 0.586179 0.0285010
\(424\) −7.37541 + 5.94463i −0.358182 + 0.288697i
\(425\) 25.3410 16.0775i 1.22922 0.779874i
\(426\) −3.65635 15.8926i −0.177151 0.770000i
\(427\) 12.1900 12.1900i 0.589915 0.589915i
\(428\) −36.0823 12.4857i −1.74410 0.603517i
\(429\) 4.14830 4.14830i 0.200282 0.200282i
\(430\) −11.0009 + 38.7544i −0.530509 + 1.86890i
\(431\) 7.28686 0.350996 0.175498 0.984480i \(-0.443847\pi\)
0.175498 + 0.984480i \(0.443847\pi\)
\(432\) −0.475374 3.97165i −0.0228714 0.191086i
\(433\) 2.13785i 0.102738i 0.998680 + 0.0513692i \(0.0163585\pi\)
−0.998680 + 0.0513692i \(0.983641\pi\)
\(434\) −3.55648 + 5.68192i −0.170716 + 0.272741i
\(435\) 8.82274 + 4.85105i 0.423018 + 0.232590i
\(436\) −28.7653 9.95376i −1.37761 0.476699i
\(437\) 8.90537 8.90537i 0.426002 0.426002i
\(438\) −1.80694 + 0.415715i −0.0863389 + 0.0198636i
\(439\) 33.2103i 1.58504i −0.609846 0.792520i \(-0.708769\pi\)
0.609846 0.792520i \(-0.291231\pi\)
\(440\) −2.16050 12.1714i −0.102998 0.580251i
\(441\) 5.50826i 0.262298i
\(442\) 5.71233 + 24.8291i 0.271708 + 1.18100i
\(443\) 12.4343 12.4343i 0.590771 0.590771i −0.347068 0.937840i \(-0.612823\pi\)
0.937840 + 0.347068i \(0.112823\pi\)
\(444\) 3.02055 + 6.21708i 0.143349 + 0.295050i
\(445\) −10.3282 + 18.7841i −0.489602 + 0.890452i
\(446\) 0.766691 + 0.479895i 0.0363039 + 0.0227237i
\(447\) 16.7364i 0.791604i
\(448\) 9.54802 + 2.07517i 0.451102 + 0.0980424i
\(449\) 10.8408 0.511607 0.255803 0.966729i \(-0.417660\pi\)
0.255803 + 0.966729i \(0.417660\pi\)
\(450\) 0.0431074 + 7.07094i 0.00203210 + 0.333327i
\(451\) −3.29482 + 3.29482i −0.155147 + 0.155147i
\(452\) −22.7035 + 11.0304i −1.06788 + 0.518829i
\(453\) 0.170363 0.170363i 0.00800436 0.00800436i
\(454\) 0.530529 0.122057i 0.0248990 0.00572840i
\(455\) −2.28648 7.87190i −0.107192 0.369041i
\(456\) 12.1789 + 1.30821i 0.570328 + 0.0612624i
\(457\) 32.6178 1.52580 0.762899 0.646518i \(-0.223776\pi\)
0.762899 + 0.646518i \(0.223776\pi\)
\(458\) 9.35667 2.15265i 0.437209 0.100587i
\(459\) 4.24418 + 4.24418i 0.198101 + 0.198101i
\(460\) −0.655913 + 12.9890i −0.0305821 + 0.605615i
\(461\) −18.9449 + 18.9449i −0.882353 + 0.882353i −0.993773 0.111421i \(-0.964460\pi\)
0.111421 + 0.993773i \(0.464460\pi\)
\(462\) 2.86169 + 1.79122i 0.133138 + 0.0833349i
\(463\) 37.7663i 1.75515i 0.479441 + 0.877574i \(0.340840\pi\)
−0.479441 + 0.877574i \(0.659160\pi\)
\(464\) 2.14048 + 17.8833i 0.0993694 + 0.830212i
\(465\) −2.42049 8.33330i −0.112248 0.386448i
\(466\) 16.3592 26.1358i 0.757823 1.21072i
\(467\) 3.10601 + 3.10601i 0.143729 + 0.143729i 0.775310 0.631581i \(-0.217594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(468\) −5.67295 1.96303i −0.262232 0.0907410i
\(469\) 4.66810 + 4.66810i 0.215553 + 0.215553i
\(470\) −0.902993 1.61884i −0.0416520 0.0746717i
\(471\) 10.1763i 0.468899i
\(472\) −21.1719 26.2677i −0.974517 1.20907i
\(473\) −24.8999 −1.14490
\(474\) −17.3609 + 3.99414i −0.797411 + 0.183457i
\(475\) −21.1312 4.72611i −0.969566 0.216849i
\(476\) −13.1876 + 6.40718i −0.604454 + 0.293673i
\(477\) 2.36822 + 2.36822i 0.108433 + 0.108433i
\(478\) 1.51403 2.41885i 0.0692500 0.110635i
\(479\) −8.23987 −0.376489 −0.188245 0.982122i \(-0.560280\pi\)
−0.188245 + 0.982122i \(0.560280\pi\)
\(480\) −10.2362 + 7.43106i −0.467215 + 0.339180i
\(481\) 10.3732 0.472976
\(482\) 11.6041 18.5391i 0.528554 0.844431i
\(483\) −2.51157 2.51157i −0.114280 0.114280i
\(484\) −12.9157 + 6.27508i −0.587079 + 0.285231i
\(485\) −10.1843 + 18.5225i −0.462446 + 0.841064i
\(486\) −1.37821 + 0.317079i −0.0625168 + 0.0143830i
\(487\) −15.7527 −0.713822 −0.356911 0.934138i \(-0.616170\pi\)
−0.356911 + 0.934138i \(0.616170\pi\)
\(488\) −31.0830 + 25.0530i −1.40706 + 1.13410i
\(489\) 16.6094i 0.751104i
\(490\) −15.2121 + 8.48534i −0.687214 + 0.383329i
\(491\) −9.14298 9.14298i −0.412617 0.412617i 0.470032 0.882649i \(-0.344242\pi\)
−0.882649 + 0.470032i \(0.844242\pi\)
\(492\) 4.50578 + 1.55915i 0.203136 + 0.0702919i
\(493\) −19.1104 19.1104i −0.860691 0.860691i
\(494\) 9.75314 15.5818i 0.438814 0.701060i
\(495\) −4.19706 + 1.21908i −0.188644 + 0.0547935i
\(496\) 9.59426 12.2032i 0.430795 0.547941i
\(497\) 14.0840i 0.631754i
\(498\) 4.94401 + 3.09460i 0.221546 + 0.138672i
\(499\) −5.93929 + 5.93929i −0.265879 + 0.265879i −0.827437 0.561558i \(-0.810202\pi\)
0.561558 + 0.827437i \(0.310202\pi\)
\(500\) 19.4613 11.0116i 0.870338 0.492456i
\(501\) 0.150909 + 0.150909i 0.00674213 + 0.00674213i
\(502\) 6.68580 1.53817i 0.298402 0.0686521i
\(503\) −3.53406 −0.157576 −0.0787879 0.996891i \(-0.525105\pi\)
−0.0787879 + 0.996891i \(0.525105\pi\)
\(504\) 0.368951 3.43479i 0.0164344 0.152998i
\(505\) −10.2776 35.3840i −0.457349 1.57457i
\(506\) −7.83388 + 1.80231i −0.348259 + 0.0801224i
\(507\) 2.82210 2.82210i 0.125334 0.125334i
\(508\) −17.3917 + 8.44972i −0.771633 + 0.374896i
\(509\) 8.43955 8.43955i 0.374076 0.374076i −0.494883 0.868960i \(-0.664789\pi\)
0.868960 + 0.494883i \(0.164789\pi\)
\(510\) 5.18307 18.2592i 0.229510 0.808529i
\(511\) −1.60131 −0.0708376
\(512\) −21.4715 7.13968i −0.948915 0.315532i
\(513\) 4.33065i 0.191203i
\(514\) 23.1450 + 14.4871i 1.02088 + 0.638999i
\(515\) 4.21286 + 2.31638i 0.185641 + 0.102072i
\(516\) 11.1342 + 22.9172i 0.490158 + 1.00887i
\(517\) 0.810146 0.810146i 0.0356302 0.0356302i
\(518\) 1.33840 + 5.81749i 0.0588061 + 0.255606i
\(519\) 9.00739i 0.395380i
\(520\) 3.31775 + 18.6909i 0.145493 + 0.819651i
\(521\) 9.64810i 0.422691i 0.977411 + 0.211345i \(0.0677845\pi\)
−0.977411 + 0.211345i \(0.932216\pi\)
\(522\) 6.20572 1.42772i 0.271617 0.0624897i
\(523\) −25.7409 + 25.7409i −1.12557 + 1.12557i −0.134683 + 0.990889i \(0.543002\pi\)
−0.990889 + 0.134683i \(0.956998\pi\)
\(524\) −28.1625 9.74516i −1.23028 0.425719i
\(525\) −1.33290 + 5.95959i −0.0581724 + 0.260098i
\(526\) −6.94859 + 11.1012i −0.302973 + 0.484037i
\(527\) 23.2932i 1.01467i
\(528\) −6.14615 4.83214i −0.267477 0.210292i
\(529\) −14.5428 −0.632295
\(530\) 2.89211 10.1885i 0.125625 0.442559i
\(531\) −8.43447 + 8.43447i −0.366025 + 0.366025i
\(532\) 9.99703 + 3.45930i 0.433426 + 0.149980i
\(533\) 5.05965 5.05965i 0.219158 0.219158i
\(534\) 3.03970 + 13.2123i 0.131541 + 0.571753i
\(535\) 40.9939 11.9071i 1.77232 0.514788i
\(536\) −9.59395 11.9031i −0.414395 0.514134i
\(537\) −9.24150 −0.398800
\(538\) −2.55108 11.0885i −0.109985 0.478059i
\(539\) −7.61287 7.61287i −0.327909 0.327909i
\(540\) 2.99877 + 3.31774i 0.129046 + 0.142773i
\(541\) −19.2087 + 19.2087i −0.825846 + 0.825846i −0.986939 0.161093i \(-0.948498\pi\)
0.161093 + 0.986939i \(0.448498\pi\)
\(542\) 1.17492 1.87709i 0.0504673 0.0806278i
\(543\) 7.39653i 0.317415i
\(544\) 31.9498 11.4911i 1.36984 0.492677i
\(545\) 32.6810 9.49252i 1.39990 0.406615i
\(546\) −4.39452 2.75066i −0.188068 0.117717i
\(547\) 27.9722 + 27.9722i 1.19600 + 1.19600i 0.975353 + 0.220652i \(0.0708185\pi\)
0.220652 + 0.975353i \(0.429181\pi\)
\(548\) 11.2912 + 23.2402i 0.482335 + 0.992770i
\(549\) 9.98062 + 9.98062i 0.425963 + 0.425963i
\(550\) 9.83218 + 9.71303i 0.419246 + 0.414165i
\(551\) 19.4998i 0.830719i
\(552\) 5.16180 + 6.40418i 0.219701 + 0.272580i
\(553\) −15.3852 −0.654244
\(554\) 5.06331 + 22.0081i 0.215119 + 0.935034i
\(555\) −6.77175 3.72334i −0.287445 0.158047i
\(556\) 10.6508 30.7796i 0.451693 1.30535i
\(557\) −15.4266 15.4266i −0.653647 0.653647i 0.300222 0.953869i \(-0.402939\pi\)
−0.953869 + 0.300222i \(0.902939\pi\)
\(558\) −4.65210 2.91189i −0.196939 0.123270i
\(559\) 38.2372 1.61726
\(560\) −10.0542 + 4.27227i −0.424867 + 0.180536i
\(561\) 11.7316 0.495308
\(562\) −18.9423 11.8566i −0.799034 0.500139i
\(563\) −18.2389 18.2389i −0.768676 0.768676i 0.209197 0.977874i \(-0.432915\pi\)
−0.977874 + 0.209197i \(0.932915\pi\)
\(564\) −1.10790 0.383371i −0.0466511 0.0161428i
\(565\) 13.5969 24.7290i 0.572025 1.04036i
\(566\) 1.04235 + 4.53067i 0.0438133 + 0.190438i
\(567\) −1.22137 −0.0512926
\(568\) −3.48340 + 32.4291i −0.146160 + 1.36069i
\(569\) 34.0254i 1.42642i −0.700950 0.713210i \(-0.747240\pi\)
0.700950 0.713210i \(-0.252760\pi\)
\(570\) −11.9599 + 6.67126i −0.500946 + 0.279428i
\(571\) −17.9297 17.9297i −0.750335 0.750335i 0.224207 0.974542i \(-0.428021\pi\)
−0.974542 + 0.224207i \(0.928021\pi\)
\(572\) −10.5535 + 5.12741i −0.441265 + 0.214388i
\(573\) 9.28556 + 9.28556i 0.387910 + 0.387910i
\(574\) 3.49038 + 2.18473i 0.145686 + 0.0911890i
\(575\) −7.78976 12.2780i −0.324855 0.512029i
\(576\) −1.69905 + 7.81749i −0.0707939 + 0.325729i
\(577\) 0.122769i 0.00511093i −0.999997 0.00255547i \(-0.999187\pi\)
0.999997 0.00255547i \(-0.000813431\pi\)
\(578\) −14.2759 + 22.8076i −0.593800 + 0.948669i
\(579\) −14.1514 + 14.1514i −0.588112 + 0.588112i
\(580\) −13.5027 14.9389i −0.560668 0.620304i
\(581\) 3.56190 + 3.56190i 0.147773 + 0.147773i
\(582\) 2.99737 + 13.0283i 0.124245 + 0.540042i
\(583\) 6.54614 0.271113
\(584\) 3.68708 + 0.396052i 0.152572 + 0.0163887i
\(585\) 6.44516 1.87206i 0.266475 0.0774003i
\(586\) 3.33691 + 14.5042i 0.137847 + 0.599162i
\(587\) −6.93139 + 6.93139i −0.286089 + 0.286089i −0.835531 0.549443i \(-0.814840\pi\)
0.549443 + 0.835531i \(0.314840\pi\)
\(588\) −3.60250 + 10.4109i −0.148565 + 0.429336i
\(589\) 11.8839 11.8839i 0.489667 0.489667i
\(590\) 36.2865 + 10.3003i 1.49389 + 0.424057i
\(591\) −27.2128 −1.11939
\(592\) −1.64289 13.7261i −0.0675225 0.564137i
\(593\) 21.4611i 0.881303i −0.897678 0.440652i \(-0.854747\pi\)
0.897678 0.440652i \(-0.145253\pi\)
\(594\) −1.46657 + 2.34302i −0.0601740 + 0.0961355i
\(595\) 7.89793 14.3642i 0.323784 0.588874i
\(596\) 10.9459 31.6325i 0.448361 1.29572i
\(597\) 3.66442 3.66442i 0.149975 0.149975i
\(598\) 12.0300 2.76769i 0.491944 0.113179i
\(599\) 4.94482i 0.202040i −0.994884 0.101020i \(-0.967789\pi\)
0.994884 0.101020i \(-0.0322106\pi\)
\(600\) 4.54304 13.3926i 0.185469 0.546749i
\(601\) 20.1862i 0.823414i 0.911316 + 0.411707i \(0.135067\pi\)
−0.911316 + 0.411707i \(0.864933\pi\)
\(602\) 4.93357 + 21.4442i 0.201077 + 0.874000i
\(603\) −3.82203 + 3.82203i −0.155645 + 0.155645i
\(604\) −0.433414 + 0.210573i −0.0176354 + 0.00856810i
\(605\) 7.73509 14.0680i 0.314476 0.571947i
\(606\) −19.7532 12.3641i −0.802421 0.502259i
\(607\) 23.8529i 0.968161i 0.875024 + 0.484080i \(0.160846\pi\)
−0.875024 + 0.484080i \(0.839154\pi\)
\(608\) −22.1630 10.4378i −0.898828 0.423307i
\(609\) 5.49949 0.222851
\(610\) 12.1885 42.9383i 0.493498 1.73852i
\(611\) −1.24409 + 1.24409i −0.0503305 + 0.0503305i
\(612\) −5.24591 10.7974i −0.212053 0.436461i
\(613\) −24.1159 + 24.1159i −0.974031 + 0.974031i −0.999671 0.0256404i \(-0.991838\pi\)
0.0256404 + 0.999671i \(0.491838\pi\)
\(614\) −6.40509 + 1.47359i −0.258488 + 0.0594693i
\(615\) −5.11912 + 1.48690i −0.206423 + 0.0599576i
\(616\) −4.23723 5.25707i −0.170723 0.211813i
\(617\) 8.63876 0.347783 0.173892 0.984765i \(-0.444366\pi\)
0.173892 + 0.984765i \(0.444366\pi\)
\(618\) 2.96323 0.681738i 0.119199 0.0274235i
\(619\) 32.3601 + 32.3601i 1.30066 + 1.30066i 0.927945 + 0.372716i \(0.121573\pi\)
0.372716 + 0.927945i \(0.378427\pi\)
\(620\) −0.875292 + 17.3333i −0.0351526 + 0.696124i
\(621\) 2.05636 2.05636i 0.0825188 0.0825188i
\(622\) 34.7919 + 21.7773i 1.39503 + 0.873190i
\(623\) 11.7087i 0.469101i
\(624\) 9.43826 + 7.42041i 0.377833 + 0.297054i
\(625\) −10.6500 + 22.6181i −0.426002 + 0.904722i
\(626\) −4.13306 + 6.60308i −0.165190 + 0.263912i
\(627\) −5.98531 5.98531i −0.239030 0.239030i
\(628\) 6.65548 19.2336i 0.265582 0.767506i
\(629\) 14.6679 + 14.6679i 0.584848 + 0.584848i
\(630\) 1.88148 + 3.37304i 0.0749601 + 0.134385i
\(631\) 11.3652i 0.452443i 0.974076 + 0.226222i \(0.0726373\pi\)
−0.974076 + 0.226222i \(0.927363\pi\)
\(632\) 35.4250 + 3.80522i 1.40913 + 0.151363i
\(633\) −7.82477 −0.311007
\(634\) 20.7385 4.77121i 0.823630 0.189489i
\(635\) 10.4157 18.9433i 0.413335 0.751744i
\(636\) −2.92718 6.02489i −0.116070 0.238902i
\(637\) 11.6906 + 11.6906i 0.463199 + 0.463199i
\(638\) 6.60357 10.5500i 0.261438 0.417680i
\(639\) 11.5314 0.456173
\(640\) 24.2069 7.35038i 0.956860 0.290549i
\(641\) −13.9081 −0.549336 −0.274668 0.961539i \(-0.588568\pi\)
−0.274668 + 0.961539i \(0.588568\pi\)
\(642\) 14.3244 22.8850i 0.565339 0.903199i
\(643\) −18.4850 18.4850i −0.728977 0.728977i 0.241439 0.970416i \(-0.422381\pi\)
−0.970416 + 0.241439i \(0.922381\pi\)
\(644\) 3.10436 + 6.38957i 0.122329 + 0.251784i
\(645\) −24.9618 13.7248i −0.982868 0.540415i
\(646\) 35.8243 8.24193i 1.40949 0.324275i
\(647\) −1.15900 −0.0455649 −0.0227825 0.999740i \(-0.507253\pi\)
−0.0227825 + 0.999740i \(0.507253\pi\)
\(648\) 2.81225 + 0.302081i 0.110476 + 0.0118669i
\(649\) 23.3142i 0.915163i
\(650\) −15.0987 14.9157i −0.592219 0.585041i
\(651\) −3.35159 3.35159i −0.131359 0.131359i
\(652\) −10.8629 + 31.3925i −0.425422 + 1.22943i
\(653\) −11.8412 11.8412i −0.463383 0.463383i 0.436380 0.899763i \(-0.356260\pi\)
−0.899763 + 0.436380i \(0.856260\pi\)
\(654\) 11.4196 18.2443i 0.446543 0.713407i
\(655\) 31.9960 9.29358i 1.25019 0.363130i
\(656\) −7.49641 5.89372i −0.292686 0.230111i
\(657\) 1.31108i 0.0511500i
\(658\) −0.858232 0.537192i −0.0334573 0.0209419i
\(659\) −1.22941 + 1.22941i −0.0478909 + 0.0478909i −0.730647 0.682756i \(-0.760781\pi\)
0.682756 + 0.730647i \(0.260781\pi\)
\(660\) 8.72992 + 0.440840i 0.339812 + 0.0171597i
\(661\) 13.2100 + 13.2100i 0.513810 + 0.513810i 0.915692 0.401882i \(-0.131644\pi\)
−0.401882 + 0.915692i \(0.631644\pi\)
\(662\) −15.7521 + 3.62402i −0.612223 + 0.140852i
\(663\) −18.0155 −0.699663
\(664\) −7.32047 9.08240i −0.284089 0.352466i
\(665\) −11.3578 + 3.29900i −0.440438 + 0.127930i
\(666\) −4.76310 + 1.09583i −0.184566 + 0.0424624i
\(667\) −9.25924 + 9.25924i −0.358519 + 0.358519i
\(668\) −0.186528 0.383922i −0.00721697 0.0148544i
\(669\) −0.452248 + 0.452248i −0.0174849 + 0.0174849i
\(670\) 16.4430 + 4.66753i 0.635249 + 0.180323i
\(671\) 27.5880 1.06502
\(672\) −2.94374 + 6.25059i −0.113557 + 0.241122i
\(673\) 4.69175i 0.180854i 0.995903 + 0.0904268i \(0.0288231\pi\)
−0.995903 + 0.0904268i \(0.971177\pi\)
\(674\) −29.2612 18.3155i −1.12710 0.705486i
\(675\) −4.87945 1.09132i −0.187810 0.0420048i
\(676\) −7.17959 + 3.48818i −0.276138 + 0.134161i
\(677\) 36.1893 36.1893i 1.39087 1.39087i 0.567483 0.823385i \(-0.307917\pi\)
0.823385 0.567483i \(-0.192083\pi\)
\(678\) −4.00173 17.3939i −0.153686 0.668007i
\(679\) 11.5457i 0.443083i
\(680\) −21.7380 + 31.1208i −0.833615 + 1.19343i
\(681\) 0.384941i 0.0147510i
\(682\) −10.4540 + 2.40511i −0.400306 + 0.0920966i
\(683\) 18.7839 18.7839i 0.718744 0.718744i −0.249604 0.968348i \(-0.580300\pi\)
0.968348 + 0.249604i \(0.0803004\pi\)
\(684\) −2.83232 + 8.18512i −0.108297 + 0.312966i
\(685\) −25.3135 13.9183i −0.967181 0.531790i
\(686\) −11.4630 + 18.3135i −0.437658 + 0.699213i
\(687\) 6.78901i 0.259017i
\(688\) −6.05597 50.5964i −0.230882 1.92897i
\(689\) −10.0525 −0.382969
\(690\) −8.84679 2.51126i −0.336792 0.0956020i
\(691\) 12.0077 12.0077i 0.456795 0.456795i −0.440807 0.897602i \(-0.645308\pi\)
0.897602 + 0.440807i \(0.145308\pi\)
\(692\) 5.89099 17.0243i 0.223942 0.647168i
\(693\) −1.68803 + 1.68803i −0.0641228 + 0.0641228i
\(694\) 0.631850 + 2.74639i 0.0239847 + 0.104251i
\(695\) 10.1572 + 34.9694i 0.385286 + 1.32647i
\(696\) −12.6628 1.36019i −0.479983 0.0515579i
\(697\) 14.3089 0.541990
\(698\) 2.74104 + 11.9141i 0.103750 + 0.450957i
\(699\) 15.4167 + 15.4167i 0.583114 + 0.583114i
\(700\) 6.41691 10.3922i 0.242536 0.392786i
\(701\) −18.6671 + 18.6671i −0.705046 + 0.705046i −0.965489 0.260443i \(-0.916131\pi\)
0.260443 + 0.965489i \(0.416131\pi\)
\(702\) 2.25212 3.59804i 0.0850007 0.135799i
\(703\) 14.9668i 0.564482i
\(704\) 8.45618 + 13.1526i 0.318704 + 0.495709i
\(705\) 1.25871 0.365606i 0.0474059 0.0137695i
\(706\) −12.8447 8.03985i −0.483415 0.302584i
\(707\) −14.2312 14.2312i −0.535219 0.535219i
\(708\) 21.4578 10.4252i 0.806433 0.391803i
\(709\) −0.320563 0.320563i −0.0120390 0.0120390i 0.701062 0.713101i \(-0.252710\pi\)
−0.713101 + 0.701062i \(0.752710\pi\)
\(710\) −17.7638 31.8460i −0.666662 1.19516i
\(711\) 12.5967i 0.472413i
\(712\) 2.89593 26.9599i 0.108529 1.01036i
\(713\) 11.2858 0.422658
\(714\) −2.32446 10.1035i −0.0869907 0.378112i
\(715\) 6.32039 11.4951i 0.236369 0.429892i
\(716\) 17.4668 + 6.04410i 0.652766 + 0.225879i
\(717\) 1.42681 + 1.42681i 0.0532850 + 0.0532850i
\(718\) −38.0284 23.8031i −1.41921 0.888324i
\(719\) −48.8907 −1.82332 −0.911658 0.410951i \(-0.865197\pi\)
−0.911658 + 0.410951i \(0.865197\pi\)
\(720\) −3.49794 8.23191i −0.130361 0.306785i
\(721\) 2.62601 0.0977977
\(722\) 0.294234 + 0.184170i 0.0109503 + 0.00685409i
\(723\) 10.9356 + 10.9356i 0.406701 + 0.406701i
\(724\) 4.83746 13.9798i 0.179783 0.519554i
\(725\) 21.9709 + 4.91391i 0.815978 + 0.182498i
\(726\) −2.27653 9.89514i −0.0844900 0.367243i
\(727\) −24.5201 −0.909401 −0.454700 0.890644i \(-0.650254\pi\)
−0.454700 + 0.890644i \(0.650254\pi\)
\(728\) 6.50685 + 8.07296i 0.241160 + 0.299204i
\(729\) 1.00000i 0.0370370i
\(730\) −3.62079 + 2.01968i −0.134012 + 0.0747517i
\(731\) 54.0683 + 54.0683i 1.99979 + 1.99979i
\(732\) −12.3363 25.3913i −0.455963 0.938489i
\(733\) 27.3958 + 27.3958i 1.01189 + 1.01189i 0.999928 + 0.0119594i \(0.00380688\pi\)
0.0119594 + 0.999928i \(0.496193\pi\)
\(734\) −38.1232 23.8624i −1.40715 0.880779i
\(735\) −3.43557 11.8280i −0.126723 0.436283i
\(736\) −5.56758 15.4801i −0.205224 0.570603i
\(737\) 10.5647i 0.389156i
\(738\) −1.78876 + 2.85777i −0.0658452 + 0.105196i
\(739\) 19.1011 19.1011i 0.702644 0.702644i −0.262333 0.964977i \(-0.584492\pi\)
0.964977 + 0.262333i \(0.0844919\pi\)
\(740\) 10.3638 + 11.4661i 0.380979 + 0.421503i
\(741\) 9.19127 + 9.19127i 0.337650 + 0.337650i
\(742\) −1.29703 5.63765i −0.0476154 0.206964i
\(743\) −0.305994 −0.0112258 −0.00561291 0.999984i \(-0.501787\pi\)
−0.00561291 + 0.999984i \(0.501787\pi\)
\(744\) 6.88824 + 8.54614i 0.252535 + 0.313317i
\(745\) 10.4387 + 35.9384i 0.382443 + 1.31668i
\(746\) −7.79624 33.8870i −0.285441 1.24069i
\(747\) −2.91633 + 2.91633i −0.106703 + 0.106703i
\(748\) −22.1732 7.67267i −0.810733 0.280541i
\(749\) 16.4874 16.4874i 0.602438 0.602438i
\(750\) 4.50279 + 15.1567i 0.164419 + 0.553444i
\(751\) −7.13631 −0.260408 −0.130204 0.991487i \(-0.541563\pi\)
−0.130204 + 0.991487i \(0.541563\pi\)
\(752\) 1.84325 + 1.44918i 0.0672165 + 0.0528460i
\(753\) 4.85108i 0.176783i
\(754\) −10.1407 + 16.2010i −0.369302 + 0.590006i
\(755\) 0.259567 0.472082i 0.00944660 0.0171808i
\(756\) 2.30843 + 0.798795i 0.0839569 + 0.0290519i
\(757\) −25.8469 + 25.8469i −0.939422 + 0.939422i −0.998267 0.0588455i \(-0.981258\pi\)
0.0588455 + 0.998267i \(0.481258\pi\)
\(758\) −32.0068 + 7.36366i −1.16254 + 0.267460i
\(759\) 5.68410i 0.206320i
\(760\) 26.9679 4.78696i 0.978228 0.173641i
\(761\) 11.9718i 0.433979i 0.976174 + 0.216989i \(0.0696237\pi\)
−0.976174 + 0.216989i \(0.930376\pi\)
\(762\) −3.06547 13.3243i −0.111050 0.482690i
\(763\) 13.1440 13.1440i 0.475846 0.475846i
\(764\) −11.4772 23.6230i −0.415230 0.854651i
\(765\) 11.7608 + 6.46647i 0.425211 + 0.233796i
\(766\) 10.7955 + 6.75721i 0.390056 + 0.244148i
\(767\) 35.8022i 1.29274i
\(768\) 8.32406 13.6642i 0.300369 0.493064i
\(769\) −27.2266 −0.981816 −0.490908 0.871211i \(-0.663335\pi\)
−0.490908 + 0.871211i \(0.663335\pi\)
\(770\) 7.26217 + 2.06145i 0.261710 + 0.0742894i
\(771\) −13.6525 + 13.6525i −0.491684 + 0.491684i
\(772\) 36.0020 17.4915i 1.29574 0.629532i
\(773\) −8.83729 + 8.83729i −0.317855 + 0.317855i −0.847943 0.530088i \(-0.822159\pi\)
0.530088 + 0.847943i \(0.322159\pi\)
\(774\) −17.5575 + 4.03939i −0.631093 + 0.145193i
\(775\) −10.3951 16.3846i −0.373405 0.588552i
\(776\) 2.85560 26.5844i 0.102510 0.954326i
\(777\) −4.22105 −0.151429
\(778\) 3.59600 0.827316i 0.128923 0.0296607i
\(779\) −7.30024 7.30024i −0.261558 0.261558i
\(780\) −13.4060 0.676971i −0.480012 0.0242394i
\(781\) 15.9373 15.9373i 0.570280 0.570280i
\(782\) 20.9243 + 13.0971i 0.748251 + 0.468352i
\(783\) 4.50274i 0.160915i
\(784\) 13.6178 17.3209i 0.486349 0.618602i
\(785\) 6.34707 + 21.8518i 0.226537 + 0.779923i
\(786\) 11.1803 17.8619i 0.398788 0.637113i
\(787\) 21.7150 + 21.7150i 0.774058 + 0.774058i 0.978813 0.204755i \(-0.0656399\pi\)
−0.204755 + 0.978813i \(0.565640\pi\)
\(788\) 51.4334 + 17.7977i 1.83224 + 0.634015i
\(789\) −6.54829 6.54829i −0.233125 0.233125i
\(790\) −34.7882 + 19.4049i −1.23771 + 0.690394i
\(791\) 15.4144i 0.548073i
\(792\) 4.30426 3.46926i 0.152945 0.123275i
\(793\) −42.3652 −1.50443
\(794\) −46.9522 + 10.8021i −1.66627 + 0.383352i
\(795\) 6.56241 + 3.60824i 0.232745 + 0.127971i
\(796\) −9.32250 + 4.52931i −0.330427 + 0.160537i
\(797\) 28.4134 + 28.4134i 1.00645 + 1.00645i 0.999979 + 0.00647582i \(0.00206133\pi\)
0.00647582 + 0.999979i \(0.497939\pi\)
\(798\) −3.96874 + 6.34056i −0.140492 + 0.224453i
\(799\) −3.51835 −0.124470
\(800\) −17.3455 + 22.3413i −0.613257 + 0.789884i
\(801\) −9.58659 −0.338726
\(802\) −7.84051 + 12.5262i −0.276858 + 0.442315i
\(803\) −1.81201 1.81201i −0.0639446 0.0639446i
\(804\) 9.72348 4.72413i 0.342921 0.166607i
\(805\) −6.95963 3.82664i −0.245295 0.134871i
\(806\) 16.0536 3.69338i 0.565464 0.130094i
\(807\) 8.04558 0.283218
\(808\) 29.2481 + 36.2877i 1.02894 + 1.27660i
\(809\) 26.4356i 0.929426i 0.885461 + 0.464713i \(0.153842\pi\)
−0.885461 + 0.464713i \(0.846158\pi\)
\(810\) −2.76169 + 1.54047i −0.0970359 + 0.0541267i
\(811\) 15.0962 + 15.0962i 0.530100 + 0.530100i 0.920602 0.390502i \(-0.127699\pi\)
−0.390502 + 0.920602i \(0.627699\pi\)
\(812\) −10.3943 3.59677i −0.364768 0.126222i
\(813\) 1.10724 + 1.10724i 0.0388325 + 0.0388325i
\(814\) −5.06847 + 8.09751i −0.177650 + 0.283817i
\(815\) −10.3595 35.6657i −0.362877 1.24932i
\(816\) 2.85328 + 23.8386i 0.0998846 + 0.834516i
\(817\) 55.1699i 1.93015i
\(818\) 8.00123 + 5.00821i 0.279757 + 0.175108i
\(819\) 2.59220 2.59220i 0.0905787 0.0905787i
\(820\) 10.6478 + 0.537689i 0.371838 + 0.0187769i
\(821\) −29.4997 29.4997i −1.02955 1.02955i −0.999550 0.0299962i \(-0.990450\pi\)
−0.0299962 0.999550i \(-0.509550\pi\)
\(822\) −17.8050 + 4.09632i −0.621020 + 0.142875i
\(823\) 21.2908 0.742152 0.371076 0.928602i \(-0.378989\pi\)
0.371076 + 0.928602i \(0.378989\pi\)
\(824\) −6.04650 0.649492i −0.210640 0.0226261i
\(825\) −8.25208 + 5.23551i −0.287301 + 0.182277i
\(826\) 20.0786 4.61940i 0.698624 0.160729i
\(827\) −14.4619 + 14.4619i −0.502888 + 0.502888i −0.912334 0.409446i \(-0.865722\pi\)
0.409446 + 0.912334i \(0.365722\pi\)
\(828\) −5.23150 + 2.54171i −0.181807 + 0.0883305i
\(829\) 5.64651 5.64651i 0.196111 0.196111i −0.602219 0.798331i \(-0.705717\pi\)
0.798331 + 0.602219i \(0.205717\pi\)
\(830\) 12.5465 + 3.56147i 0.435496 + 0.123620i
\(831\) −15.9686 −0.553945
\(832\) −12.9856 20.1977i −0.450196 0.700229i
\(833\) 33.0616i 1.14552i
\(834\) 19.5218 + 12.2193i 0.675985 + 0.423119i
\(835\) 0.418175 + 0.229927i 0.0144715 + 0.00795695i
\(836\) 7.39799 + 15.2270i 0.255865 + 0.526636i
\(837\) 2.74413 2.74413i 0.0948512 0.0948512i
\(838\) 7.09042 + 30.8191i 0.244934 + 1.06463i
\(839\) 21.4686i 0.741178i 0.928797 + 0.370589i \(0.120844\pi\)
−0.928797 + 0.370589i \(0.879156\pi\)
\(840\) −1.35006 7.60571i −0.0465814 0.262422i
\(841\) 8.72534i 0.300874i
\(842\) −3.30817 + 0.761096i −0.114007 + 0.0262291i
\(843\) 11.1735 11.1735i 0.384836 0.384836i
\(844\) 14.7891 + 5.11754i 0.509063 + 0.176153i
\(845\) 4.29977 7.82012i 0.147917 0.269020i
\(846\) 0.439829 0.702682i 0.0151216 0.0241587i
\(847\) 8.76905i 0.301308i
\(848\) 1.59210 + 13.3017i 0.0546731 + 0.456783i
\(849\) −3.28736 −0.112822
\(850\) −0.258738 42.4410i −0.00887465 1.45571i
\(851\) 7.10678 7.10678i 0.243617 0.243617i
\(852\) −21.7948 7.54171i −0.746676 0.258375i
\(853\) 5.10917 5.10917i 0.174935 0.174935i −0.614209 0.789143i \(-0.710525\pi\)
0.789143 + 0.614209i \(0.210525\pi\)
\(854\) −5.46620 23.7593i −0.187050 0.813027i
\(855\) −2.70108 9.29930i −0.0923748 0.318029i
\(856\) −42.0409 + 33.8852i −1.43693 + 1.15817i
\(857\) 7.14205 0.243968 0.121984 0.992532i \(-0.461074\pi\)
0.121984 + 0.992532i \(0.461074\pi\)
\(858\) −1.86017 8.08538i −0.0635051 0.276030i
\(859\) 12.9070 + 12.9070i 0.440381 + 0.440381i 0.892140 0.451759i \(-0.149203\pi\)
−0.451759 + 0.892140i \(0.649203\pi\)
\(860\) 38.2025 + 42.2660i 1.30269 + 1.44126i
\(861\) −2.05887 + 2.05887i −0.0701662 + 0.0701662i
\(862\) 5.46757 8.73512i 0.186226 0.297519i
\(863\) 34.4382i 1.17229i −0.810206 0.586145i \(-0.800645\pi\)
0.810206 0.586145i \(-0.199355\pi\)
\(864\) −5.11770 2.41021i −0.174108 0.0819969i
\(865\) 5.61801 + 19.3417i 0.191018 + 0.657639i
\(866\) 2.56274 + 1.60410i 0.0870856 + 0.0545094i
\(867\) −13.4535 13.4535i −0.456905 0.456905i
\(868\) 4.14265 + 8.52665i 0.140611 + 0.289413i
\(869\) −17.4096 17.4096i −0.590581 0.590581i
\(870\) 12.4352 6.93635i 0.421592 0.235164i
\(871\) 16.2236i 0.549715i
\(872\) −33.5156 + 27.0138i −1.13498 + 0.914803i
\(873\) −9.45309 −0.319939
\(874\) −3.99332 17.3573i −0.135076 0.587119i
\(875\) 0.854909 + 13.6285i 0.0289012 + 0.460727i
\(876\) −0.857468 + 2.47799i −0.0289712 + 0.0837236i
\(877\) 20.5999 + 20.5999i 0.695609 + 0.695609i 0.963460 0.267851i \(-0.0863136\pi\)
−0.267851 + 0.963460i \(0.586314\pi\)
\(878\) −39.8108 24.9187i −1.34355 0.840967i
\(879\) −10.5239 −0.354963
\(880\) −16.2116 6.54273i −0.546493 0.220555i
\(881\) 22.0289 0.742171 0.371086 0.928599i \(-0.378986\pi\)
0.371086 + 0.928599i \(0.378986\pi\)
\(882\) −6.60303 4.13303i −0.222336 0.139166i
\(883\) −15.2149 15.2149i −0.512022 0.512022i 0.403123 0.915146i \(-0.367925\pi\)
−0.915146 + 0.403123i \(0.867925\pi\)
\(884\) 34.0500 + 11.7824i 1.14523 + 0.396286i
\(885\) −12.8508 + 23.3722i −0.431976 + 0.785647i
\(886\) −5.57575 24.2355i −0.187321 0.814207i
\(887\) 41.6823 1.39956 0.699778 0.714361i \(-0.253282\pi\)
0.699778 + 0.714361i \(0.253282\pi\)
\(888\) 9.71915 + 1.04399i 0.326153 + 0.0350341i
\(889\) 11.8080i 0.396027i
\(890\) 14.7679 + 26.4752i 0.495021 + 0.887451i
\(891\) −1.38208 1.38208i −0.0463014 0.0463014i
\(892\) 1.15055 0.558990i 0.0385232 0.0187164i
\(893\) 1.79502 + 1.79502i 0.0600679 + 0.0600679i
\(894\) 20.0627 + 12.5579i 0.670999 + 0.419998i
\(895\) −19.8445 + 5.76403i −0.663327 + 0.192670i
\(896\) 9.65180 9.88862i 0.322444 0.330356i
\(897\) 8.72872i 0.291444i
\(898\) 8.13417 12.9953i 0.271441 0.433660i
\(899\) −12.3561 + 12.3561i −0.412100 + 0.412100i
\(900\) 8.50863 + 5.25388i 0.283621 + 0.175129i
\(901\) −14.2145 14.2145i −0.473552 0.473552i
\(902\) 1.47745 + 6.42188i 0.0491938 + 0.213825i
\(903\) −15.5595 −0.517786
\(904\) −3.81245 + 35.4924i −0.126800 + 1.18046i
\(905\) 4.61330 + 15.8827i 0.153351 + 0.527959i
\(906\) −0.0763937 0.332052i −0.00253801 0.0110317i
\(907\) −27.7322 + 27.7322i −0.920834 + 0.920834i −0.997088 0.0762544i \(-0.975704\pi\)
0.0762544 + 0.997088i \(0.475704\pi\)
\(908\) 0.251758 0.727555i 0.00835489 0.0241448i
\(909\) 11.6519 11.6519i 0.386468 0.386468i
\(910\) −11.1521 3.16564i −0.369687 0.104940i
\(911\) 32.3043 1.07029 0.535145 0.844760i \(-0.320257\pi\)
0.535145 + 0.844760i \(0.320257\pi\)
\(912\) 10.7064 13.6178i 0.354525 0.450931i
\(913\) 8.06119i 0.266787i
\(914\) 24.4742 39.1006i 0.809535 1.29333i
\(915\) 27.6566 + 15.2066i 0.914299 + 0.502714i
\(916\) 4.44013 12.8315i 0.146706 0.423965i
\(917\) 12.8686 12.8686i 0.424958 0.424958i
\(918\) 8.27226 1.90316i 0.273025 0.0628137i
\(919\) 54.5387i 1.79907i −0.436853 0.899533i \(-0.643907\pi\)
0.436853 0.899533i \(-0.356093\pi\)
\(920\) 15.0784 + 10.5323i 0.497120 + 0.347241i
\(921\) 4.64740i 0.153137i
\(922\) 8.49522 + 36.9252i 0.279775 + 1.21607i
\(923\) −24.4739 + 24.4739i −0.805567 + 0.805567i
\(924\) 4.29444 2.08644i 0.141277 0.0686389i
\(925\) −16.8634 3.77159i −0.554465 0.124009i
\(926\) 45.2723 + 28.3373i 1.48774 + 0.931221i
\(927\) 2.15006i 0.0706172i
\(928\) 23.0437 + 10.8525i 0.756446 + 0.356252i
\(929\) −41.8714 −1.37375 −0.686877 0.726773i \(-0.741019\pi\)
−0.686877 + 0.726773i \(0.741019\pi\)
\(930\) −11.8057 3.35119i −0.387125 0.109890i
\(931\) 16.8676 16.8676i 0.552813 0.552813i
\(932\) −19.0555 39.2211i −0.624182 1.28473i
\(933\) −20.5227 + 20.5227i −0.671884 + 0.671884i
\(934\) 6.05387 1.39279i 0.198089 0.0455734i
\(935\) 25.1915 7.31713i 0.823850 0.239296i
\(936\) −6.60978 + 5.32752i −0.216047 + 0.174135i
\(937\) 12.5314 0.409384 0.204692 0.978826i \(-0.434381\pi\)
0.204692 + 0.978826i \(0.434381\pi\)
\(938\) 9.09851 2.09326i 0.297077 0.0683472i
\(939\) −3.89496 3.89496i −0.127107 0.127107i
\(940\) −2.61814 0.132210i −0.0853941 0.00431220i
\(941\) 40.1881 40.1881i 1.31009 1.31009i 0.388751 0.921343i \(-0.372907\pi\)
0.921343 0.388751i \(-0.127093\pi\)
\(942\) 12.1988 + 7.63561i 0.397459 + 0.248782i
\(943\) 6.93285i 0.225765i
\(944\) −47.3744 + 5.67032i −1.54191 + 0.184553i
\(945\) −2.62266 + 0.761780i −0.0853153 + 0.0247807i
\(946\) −18.6832 + 29.8487i −0.607443 + 0.970465i
\(947\) −26.2243 26.2243i −0.852174 0.852174i 0.138227 0.990401i \(-0.455860\pi\)
−0.990401 + 0.138227i \(0.955860\pi\)
\(948\) −8.23845 + 23.8083i −0.267572 + 0.773257i
\(949\) 2.78260 + 2.78260i 0.0903270 + 0.0903270i
\(950\) −21.5209 + 21.7849i −0.698229 + 0.706794i
\(951\) 15.0474i 0.487945i
\(952\) −2.21451 + 20.6162i −0.0717727 + 0.668175i
\(953\) 2.51475 0.0814607 0.0407304 0.999170i \(-0.487032\pi\)
0.0407304 + 0.999170i \(0.487032\pi\)
\(954\) 4.61585 1.06195i 0.149444 0.0343819i
\(955\) 25.7306 + 14.1476i 0.832622 + 0.457804i
\(956\) −1.76357 3.62988i −0.0570378 0.117399i
\(957\) 6.22315 + 6.22315i 0.201166 + 0.201166i
\(958\) −6.18264 + 9.87754i −0.199752 + 0.319129i
\(959\) −15.7787 −0.509522
\(960\) 1.22744 + 17.8464i 0.0396156 + 0.575990i
\(961\) −15.9395 −0.514176
\(962\) 7.78333 12.4348i 0.250945 0.400915i
\(963\) 13.4992 + 13.4992i 0.435005 + 0.435005i
\(964\) −13.5167 27.8209i −0.435344 0.896051i
\(965\) −21.5612 + 39.2139i −0.694079 + 1.26234i
\(966\) −4.89525 + 1.12623i −0.157502 + 0.0362358i
\(967\) −51.5088 −1.65641 −0.828205 0.560425i \(-0.810638\pi\)
−0.828205 + 0.560425i \(0.810638\pi\)
\(968\) −2.16885 + 20.1911i −0.0697096 + 0.648967i
\(969\) 25.9933i 0.835026i
\(970\) 14.5622 + 26.1065i 0.467565 + 0.838230i
\(971\) −26.0586 26.0586i −0.836259 0.836259i 0.152105 0.988364i \(-0.451395\pi\)
−0.988364 + 0.152105i \(0.951395\pi\)
\(972\) −0.654018 + 1.89004i −0.0209776 + 0.0606231i
\(973\) 14.0644 + 14.0644i 0.450885 + 0.450885i
\(974\) −11.8198 + 18.8835i −0.378729 + 0.605067i
\(975\) 12.6722 8.03984i 0.405835 0.257481i
\(976\) 6.70977 + 56.0588i 0.214774 + 1.79440i
\(977\) 17.6258i 0.563899i 0.959429 + 0.281950i \(0.0909811\pi\)
−0.959429 + 0.281950i \(0.909019\pi\)
\(978\) −19.9105 12.4626i −0.636669 0.398510i
\(979\) −13.2494 + 13.2494i −0.423454 + 0.423454i
\(980\) −1.24236 + 24.6024i −0.0396857 + 0.785894i
\(981\) 10.7618 + 10.7618i 0.343596 + 0.343596i
\(982\) −17.8204 + 4.09987i −0.568672 + 0.130832i
\(983\) −1.64257 −0.0523899 −0.0261949 0.999657i \(-0.508339\pi\)
−0.0261949 + 0.999657i \(0.508339\pi\)
\(984\) 5.24987 4.23142i 0.167360 0.134893i
\(985\) −58.4346 + 16.9729i −1.86188 + 0.540803i
\(986\) −37.2478 + 8.56944i −1.18621 + 0.272907i
\(987\) 0.506245 0.506245i 0.0161140 0.0161140i
\(988\) −11.3606 23.3831i −0.361430 0.743917i
\(989\) 26.1967 26.1967i 0.833008 0.833008i
\(990\) −1.68782 + 5.94594i −0.0536425 + 0.188974i
\(991\) −62.3434 −1.98040 −0.990202 0.139642i \(-0.955405\pi\)
−0.990202 + 0.139642i \(0.955405\pi\)
\(992\) −7.42974 20.6576i −0.235894 0.655879i
\(993\) 11.4294i 0.362701i
\(994\) −16.8832 10.5677i −0.535503 0.335187i
\(995\) 5.58314 10.1542i 0.176997 0.321910i
\(996\) 7.41931 3.60465i 0.235090 0.114218i
\(997\) −30.0563 + 30.0563i −0.951891 + 0.951891i −0.998895 0.0470037i \(-0.985033\pi\)
0.0470037 + 0.998895i \(0.485033\pi\)
\(998\) 2.66328 + 11.5762i 0.0843047 + 0.366437i
\(999\) 3.45601i 0.109343i
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.bl.a.229.17 yes 48
3.2 odd 2 720.2.bm.h.469.8 48
4.3 odd 2 960.2.bl.a.49.11 48
5.4 even 2 inner 240.2.bl.a.229.8 yes 48
8.3 odd 2 1920.2.bl.b.1249.17 48
8.5 even 2 1920.2.bl.a.1249.8 48
15.14 odd 2 720.2.bm.h.469.17 48
16.3 odd 4 960.2.bl.a.529.20 48
16.5 even 4 1920.2.bl.a.289.17 48
16.11 odd 4 1920.2.bl.b.289.8 48
16.13 even 4 inner 240.2.bl.a.109.8 48
20.19 odd 2 960.2.bl.a.49.20 48
40.19 odd 2 1920.2.bl.b.1249.8 48
40.29 even 2 1920.2.bl.a.1249.17 48
48.29 odd 4 720.2.bm.h.109.17 48
80.19 odd 4 960.2.bl.a.529.11 48
80.29 even 4 inner 240.2.bl.a.109.17 yes 48
80.59 odd 4 1920.2.bl.b.289.17 48
80.69 even 4 1920.2.bl.a.289.8 48
240.29 odd 4 720.2.bm.h.109.8 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bl.a.109.8 48 16.13 even 4 inner
240.2.bl.a.109.17 yes 48 80.29 even 4 inner
240.2.bl.a.229.8 yes 48 5.4 even 2 inner
240.2.bl.a.229.17 yes 48 1.1 even 1 trivial
720.2.bm.h.109.8 48 240.29 odd 4
720.2.bm.h.109.17 48 48.29 odd 4
720.2.bm.h.469.8 48 3.2 odd 2
720.2.bm.h.469.17 48 15.14 odd 2
960.2.bl.a.49.11 48 4.3 odd 2
960.2.bl.a.49.20 48 20.19 odd 2
960.2.bl.a.529.11 48 80.19 odd 4
960.2.bl.a.529.20 48 16.3 odd 4
1920.2.bl.a.289.8 48 80.69 even 4
1920.2.bl.a.289.17 48 16.5 even 4
1920.2.bl.a.1249.8 48 8.5 even 2
1920.2.bl.a.1249.17 48 40.29 even 2
1920.2.bl.b.289.8 48 16.11 odd 4
1920.2.bl.b.289.17 48 80.59 odd 4
1920.2.bl.b.1249.8 48 40.19 odd 2
1920.2.bl.b.1249.17 48 8.3 odd 2