Properties

Label 231.2.j.g.169.2
Level $231$
Weight $2$
Character 231.169
Analytic conductor $1.845$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(64,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.j (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} - 1174 x^{11} + 15808 x^{10} - 3393 x^{9} + 26062 x^{8} - 15494 x^{7} + 11660 x^{6} + \cdots + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 169.2
Root \(0.705143 - 0.512316i\) of defining polynomial
Character \(\chi\) \(=\) 231.169
Dual form 231.2.j.g.190.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.705143 - 0.512316i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.383276 - 1.17960i) q^{4} +(3.28814 - 2.38897i) q^{5} +(-0.705143 + 0.512316i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.872746 + 2.68604i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.705143 - 0.512316i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.383276 - 1.17960i) q^{4} +(3.28814 - 2.38897i) q^{5} +(-0.705143 + 0.512316i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.872746 + 2.68604i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.54252 q^{10} +(-2.96738 + 1.48143i) q^{11} -1.24031 q^{12} +(4.92697 + 3.57965i) q^{13} +(-0.269341 + 0.828945i) q^{14} +(-1.25596 - 3.86544i) q^{15} +(-0.0153474 + 0.0111506i) q^{16} +(-1.37664 + 1.00019i) q^{17} +(0.269341 + 0.828945i) q^{18} +(1.68634 - 5.19003i) q^{19} +(-4.07830 - 2.96306i) q^{20} -1.00000 q^{21} +(2.85139 + 0.475616i) q^{22} -6.39153 q^{23} +(2.28488 + 1.66006i) q^{24} +(3.55958 - 10.9553i) q^{25} +(-1.64030 - 5.04833i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.00343 + 0.729034i) q^{28} +(1.46763 + 4.51690i) q^{29} +(-1.09470 + 3.36913i) q^{30} +(3.52981 + 2.56456i) q^{31} +5.66506 q^{32} +(0.491955 + 3.27994i) q^{33} +1.48314 q^{34} +(-3.28814 - 2.38897i) q^{35} +(-0.383276 + 1.17960i) q^{36} +(0.753854 + 2.32012i) q^{37} +(-3.84805 + 2.79577i) q^{38} +(4.92697 - 3.57965i) q^{39} +(3.54716 + 10.9170i) q^{40} +(-0.992058 + 3.05324i) q^{41} +(0.705143 + 0.512316i) q^{42} +0.127191 q^{43} +(2.88483 + 2.93253i) q^{44} -4.06436 q^{45} +(4.50694 + 3.27449i) q^{46} +(2.61671 - 8.05340i) q^{47} +(0.00586220 + 0.0180420i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.12258 + 5.90140i) q^{50} +(0.525831 + 1.61834i) q^{51} +(2.33417 - 7.18385i) q^{52} +(3.81374 + 2.77084i) q^{53} +0.871604 q^{54} +(-6.21806 + 11.9602i) q^{55} +2.82426 q^{56} +(-4.41490 - 3.20761i) q^{57} +(1.27919 - 3.93695i) q^{58} +(1.43188 + 4.40689i) q^{59} +(-4.07830 + 2.96306i) q^{60} +(-4.29654 + 3.12162i) q^{61} +(-1.17516 - 3.61676i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-3.96398 - 2.88000i) q^{64} +24.7522 q^{65} +(1.33347 - 2.56486i) q^{66} +14.0686 q^{67} +(1.70746 + 1.24054i) q^{68} +(-1.97509 + 6.07871i) q^{69} +(1.09470 + 3.36913i) q^{70} +(-1.79507 + 1.30420i) q^{71} +(2.28488 - 1.66006i) q^{72} +(-1.72244 - 5.30112i) q^{73} +(0.657063 - 2.02223i) q^{74} +(-9.31911 - 6.77073i) q^{75} -6.76849 q^{76} +(2.32590 + 2.36436i) q^{77} -5.30813 q^{78} +(-5.07362 - 3.68620i) q^{79} +(-0.0238261 + 0.0733293i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.26377 - 1.64472i) q^{82} +(0.103329 - 0.0750731i) q^{83} +(0.383276 + 1.17960i) q^{84} +(-2.13717 + 6.57753i) q^{85} +(-0.0896877 - 0.0651619i) q^{86} +4.74935 q^{87} +(-1.38941 - 9.26341i) q^{88} -8.12736 q^{89} +(2.86596 + 2.08224i) q^{90} +(1.88193 - 5.79200i) q^{91} +(2.44972 + 7.53946i) q^{92} +(3.52981 - 2.56456i) q^{93} +(-5.97104 + 4.33821i) q^{94} +(-6.85391 - 21.0942i) q^{95} +(1.75060 - 5.38780i) q^{96} +(2.10118 + 1.52660i) q^{97} +0.871604 q^{98} +(3.27143 + 0.545679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.705143 0.512316i −0.498611 0.362262i 0.309875 0.950777i \(-0.399713\pi\)
−0.808486 + 0.588515i \(0.799713\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) −0.383276 1.17960i −0.191638 0.589800i
\(5\) 3.28814 2.38897i 1.47050 1.06838i 0.490033 0.871704i \(-0.336985\pi\)
0.980468 0.196677i \(-0.0630151\pi\)
\(6\) −0.705143 + 0.512316i −0.287873 + 0.209152i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) −0.872746 + 2.68604i −0.308562 + 0.949657i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) −3.54252 −1.12024
\(11\) −2.96738 + 1.48143i −0.894699 + 0.446669i
\(12\) −1.24031 −0.358045
\(13\) 4.92697 + 3.57965i 1.36649 + 0.992816i 0.998002 + 0.0631857i \(0.0201260\pi\)
0.368493 + 0.929631i \(0.379874\pi\)
\(14\) −0.269341 + 0.828945i −0.0719843 + 0.221545i
\(15\) −1.25596 3.86544i −0.324287 0.998052i
\(16\) −0.0153474 + 0.0111506i −0.00383686 + 0.00278764i
\(17\) −1.37664 + 1.00019i −0.333885 + 0.242582i −0.742077 0.670314i \(-0.766159\pi\)
0.408192 + 0.912896i \(0.366159\pi\)
\(18\) 0.269341 + 0.828945i 0.0634842 + 0.195384i
\(19\) 1.68634 5.19003i 0.386873 1.19067i −0.548239 0.836322i \(-0.684702\pi\)
0.935112 0.354352i \(-0.115298\pi\)
\(20\) −4.07830 2.96306i −0.911935 0.662560i
\(21\) −1.00000 −0.218218
\(22\) 2.85139 + 0.475616i 0.607918 + 0.101402i
\(23\) −6.39153 −1.33273 −0.666363 0.745627i \(-0.732150\pi\)
−0.666363 + 0.745627i \(0.732150\pi\)
\(24\) 2.28488 + 1.66006i 0.466399 + 0.338859i
\(25\) 3.55958 10.9553i 0.711917 2.19106i
\(26\) −1.64030 5.04833i −0.321690 0.990059i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −1.00343 + 0.729034i −0.189630 + 0.137774i
\(29\) 1.46763 + 4.51690i 0.272532 + 0.838767i 0.989862 + 0.142033i \(0.0453640\pi\)
−0.717330 + 0.696733i \(0.754636\pi\)
\(30\) −1.09470 + 3.36913i −0.199864 + 0.615117i
\(31\) 3.52981 + 2.56456i 0.633973 + 0.460608i 0.857774 0.514026i \(-0.171847\pi\)
−0.223801 + 0.974635i \(0.571847\pi\)
\(32\) 5.66506 1.00145
\(33\) 0.491955 + 3.27994i 0.0856384 + 0.570964i
\(34\) 1.48314 0.254357
\(35\) −3.28814 2.38897i −0.555797 0.403810i
\(36\) −0.383276 + 1.17960i −0.0638793 + 0.196600i
\(37\) 0.753854 + 2.32012i 0.123933 + 0.381426i 0.993705 0.112027i \(-0.0357344\pi\)
−0.869772 + 0.493453i \(0.835734\pi\)
\(38\) −3.84805 + 2.79577i −0.624236 + 0.453534i
\(39\) 4.92697 3.57965i 0.788946 0.573203i
\(40\) 3.54716 + 10.9170i 0.560855 + 1.72613i
\(41\) −0.992058 + 3.05324i −0.154933 + 0.476836i −0.998154 0.0607314i \(-0.980657\pi\)
0.843221 + 0.537568i \(0.180657\pi\)
\(42\) 0.705143 + 0.512316i 0.108806 + 0.0790521i
\(43\) 0.127191 0.0193964 0.00969821 0.999953i \(-0.496913\pi\)
0.00969821 + 0.999953i \(0.496913\pi\)
\(44\) 2.88483 + 2.93253i 0.434904 + 0.442095i
\(45\) −4.06436 −0.605880
\(46\) 4.50694 + 3.27449i 0.664512 + 0.482797i
\(47\) 2.61671 8.05340i 0.381686 1.17471i −0.557170 0.830399i \(-0.688113\pi\)
0.938856 0.344310i \(-0.111887\pi\)
\(48\) 0.00586220 + 0.0180420i 0.000846136 + 0.00260414i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) −8.12258 + 5.90140i −1.14871 + 0.834584i
\(51\) 0.525831 + 1.61834i 0.0736311 + 0.226613i
\(52\) 2.33417 7.18385i 0.323692 0.996220i
\(53\) 3.81374 + 2.77084i 0.523857 + 0.380604i 0.818055 0.575140i \(-0.195052\pi\)
−0.294198 + 0.955745i \(0.595052\pi\)
\(54\) 0.871604 0.118610
\(55\) −6.21806 + 11.9602i −0.838443 + 1.61271i
\(56\) 2.82426 0.377408
\(57\) −4.41490 3.20761i −0.584768 0.424859i
\(58\) 1.27919 3.93695i 0.167966 0.516946i
\(59\) 1.43188 + 4.40689i 0.186416 + 0.573728i 0.999970 0.00776089i \(-0.00247039\pi\)
−0.813554 + 0.581489i \(0.802470\pi\)
\(60\) −4.07830 + 2.96306i −0.526506 + 0.382529i
\(61\) −4.29654 + 3.12162i −0.550115 + 0.399682i −0.827828 0.560982i \(-0.810424\pi\)
0.277713 + 0.960664i \(0.410424\pi\)
\(62\) −1.17516 3.61676i −0.149245 0.459329i
\(63\) −0.309017 + 0.951057i −0.0389325 + 0.119822i
\(64\) −3.96398 2.88000i −0.495498 0.360000i
\(65\) 24.7522 3.07014
\(66\) 1.33347 2.56486i 0.164138 0.315712i
\(67\) 14.0686 1.71876 0.859379 0.511340i \(-0.170851\pi\)
0.859379 + 0.511340i \(0.170851\pi\)
\(68\) 1.70746 + 1.24054i 0.207060 + 0.150438i
\(69\) −1.97509 + 6.07871i −0.237773 + 0.731790i
\(70\) 1.09470 + 3.36913i 0.130841 + 0.402689i
\(71\) −1.79507 + 1.30420i −0.213036 + 0.154780i −0.689186 0.724584i \(-0.742032\pi\)
0.476150 + 0.879364i \(0.342032\pi\)
\(72\) 2.28488 1.66006i 0.269275 0.195640i
\(73\) −1.72244 5.30112i −0.201596 0.620449i −0.999836 0.0181095i \(-0.994235\pi\)
0.798240 0.602340i \(-0.205765\pi\)
\(74\) 0.657063 2.02223i 0.0763820 0.235080i
\(75\) −9.31911 6.77073i −1.07608 0.781817i
\(76\) −6.76849 −0.776400
\(77\) 2.32590 + 2.36436i 0.265061 + 0.269444i
\(78\) −5.30813 −0.601027
\(79\) −5.07362 3.68620i −0.570827 0.414730i 0.264579 0.964364i \(-0.414767\pi\)
−0.835406 + 0.549634i \(0.814767\pi\)
\(80\) −0.0238261 + 0.0733293i −0.00266384 + 0.00819846i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 2.26377 1.64472i 0.249991 0.181629i
\(83\) 0.103329 0.0750731i 0.0113419 0.00824034i −0.582100 0.813117i \(-0.697769\pi\)
0.593442 + 0.804877i \(0.297769\pi\)
\(84\) 0.383276 + 1.17960i 0.0418188 + 0.128705i
\(85\) −2.13717 + 6.57753i −0.231809 + 0.713433i
\(86\) −0.0896877 0.0651619i −0.00967127 0.00702659i
\(87\) 4.74935 0.509183
\(88\) −1.38941 9.26341i −0.148112 0.987483i
\(89\) −8.12736 −0.861498 −0.430749 0.902472i \(-0.641751\pi\)
−0.430749 + 0.902472i \(0.641751\pi\)
\(90\) 2.86596 + 2.08224i 0.302098 + 0.219487i
\(91\) 1.88193 5.79200i 0.197280 0.607166i
\(92\) 2.44972 + 7.53946i 0.255401 + 0.786043i
\(93\) 3.52981 2.56456i 0.366025 0.265932i
\(94\) −5.97104 + 4.33821i −0.615866 + 0.447453i
\(95\) −6.85391 21.0942i −0.703196 2.16422i
\(96\) 1.75060 5.38780i 0.178670 0.549890i
\(97\) 2.10118 + 1.52660i 0.213343 + 0.155003i 0.689325 0.724452i \(-0.257907\pi\)
−0.475982 + 0.879455i \(0.657907\pi\)
\(98\) 0.871604 0.0880453
\(99\) 3.27143 + 0.545679i 0.328791 + 0.0548428i
\(100\) −14.2872 −1.42872
\(101\) 4.87492 + 3.54184i 0.485073 + 0.352426i 0.803286 0.595593i \(-0.203083\pi\)
−0.318214 + 0.948019i \(0.603083\pi\)
\(102\) 0.458317 1.41055i 0.0453801 0.139666i
\(103\) 3.98440 + 12.2627i 0.392595 + 1.20828i 0.930819 + 0.365481i \(0.119095\pi\)
−0.538224 + 0.842802i \(0.680905\pi\)
\(104\) −13.9151 + 10.1099i −1.36448 + 0.991355i
\(105\) −3.28814 + 2.38897i −0.320890 + 0.233140i
\(106\) −1.26968 3.90768i −0.123322 0.379547i
\(107\) −1.65250 + 5.08587i −0.159753 + 0.491669i −0.998611 0.0526805i \(-0.983224\pi\)
0.838858 + 0.544350i \(0.183224\pi\)
\(108\) 1.00343 + 0.729034i 0.0965550 + 0.0701513i
\(109\) −1.44173 −0.138093 −0.0690465 0.997613i \(-0.521996\pi\)
−0.0690465 + 0.997613i \(0.521996\pi\)
\(110\) 10.5120 5.24800i 1.00228 0.500377i
\(111\) 2.43952 0.231549
\(112\) 0.0153474 + 0.0111506i 0.00145020 + 0.00105363i
\(113\) 6.03121 18.5621i 0.567368 1.74618i −0.0934402 0.995625i \(-0.529786\pi\)
0.660808 0.750555i \(-0.270214\pi\)
\(114\) 1.46982 + 4.52365i 0.137662 + 0.423679i
\(115\) −21.0163 + 15.2692i −1.95978 + 1.42386i
\(116\) 4.76563 3.46243i 0.442478 0.321479i
\(117\) −1.88193 5.79200i −0.173985 0.535470i
\(118\) 1.24804 3.84106i 0.114891 0.353598i
\(119\) 1.37664 + 1.00019i 0.126197 + 0.0916873i
\(120\) 11.4788 1.04787
\(121\) 6.61071 8.79196i 0.600974 0.799269i
\(122\) 4.62893 0.419083
\(123\) 2.59724 + 1.88701i 0.234185 + 0.170146i
\(124\) 1.67227 5.14670i 0.150174 0.462188i
\(125\) −8.18766 25.1990i −0.732327 2.25387i
\(126\) 0.705143 0.512316i 0.0628191 0.0456408i
\(127\) 0.519157 0.377189i 0.0460677 0.0334701i −0.564513 0.825424i \(-0.690936\pi\)
0.610581 + 0.791954i \(0.290936\pi\)
\(128\) −2.18150 6.71397i −0.192819 0.593436i
\(129\) 0.0393041 0.120966i 0.00346053 0.0106504i
\(130\) −17.4539 12.6810i −1.53081 1.11220i
\(131\) −13.9987 −1.22307 −0.611537 0.791216i \(-0.709448\pi\)
−0.611537 + 0.791216i \(0.709448\pi\)
\(132\) 3.68046 1.83743i 0.320343 0.159928i
\(133\) −5.45712 −0.473192
\(134\) −9.92039 7.20759i −0.856992 0.622641i
\(135\) −1.25596 + 3.86544i −0.108096 + 0.332684i
\(136\) −1.48509 4.57062i −0.127345 0.391928i
\(137\) 2.18449 1.58712i 0.186633 0.135597i −0.490545 0.871416i \(-0.663202\pi\)
0.677179 + 0.735819i \(0.263202\pi\)
\(138\) 4.50694 3.27449i 0.383656 0.278743i
\(139\) −0.637168 1.96100i −0.0540439 0.166330i 0.920391 0.390998i \(-0.127870\pi\)
−0.974435 + 0.224668i \(0.927870\pi\)
\(140\) −1.55777 + 4.79433i −0.131656 + 0.405195i
\(141\) −6.85063 4.97727i −0.576927 0.419162i
\(142\) 1.93395 0.162293
\(143\) −19.9232 3.32322i −1.66606 0.277902i
\(144\) 0.0189705 0.00158087
\(145\) 15.6165 + 11.3461i 1.29688 + 0.942239i
\(146\) −1.50128 + 4.62048i −0.124247 + 0.382394i
\(147\) 0.309017 + 0.951057i 0.0254873 + 0.0784418i
\(148\) 2.44789 1.77849i 0.201215 0.146191i
\(149\) −8.15727 + 5.92661i −0.668270 + 0.485526i −0.869446 0.494029i \(-0.835524\pi\)
0.201176 + 0.979555i \(0.435524\pi\)
\(150\) 3.10255 + 9.54867i 0.253322 + 0.779645i
\(151\) −4.62410 + 14.2315i −0.376304 + 1.15815i 0.566290 + 0.824206i \(0.308378\pi\)
−0.942595 + 0.333939i \(0.891622\pi\)
\(152\) 12.4688 + 9.05915i 1.01136 + 0.734794i
\(153\) 1.70162 0.137568
\(154\) −0.428790 2.85881i −0.0345529 0.230369i
\(155\) 17.7332 1.42436
\(156\) −6.11094 4.43986i −0.489267 0.355473i
\(157\) 6.01162 18.5019i 0.479780 1.47661i −0.359622 0.933098i \(-0.617094\pi\)
0.839401 0.543512i \(-0.182906\pi\)
\(158\) 1.68913 + 5.19860i 0.134380 + 0.413578i
\(159\) 3.81374 2.77084i 0.302449 0.219742i
\(160\) 18.6275 13.5337i 1.47264 1.06993i
\(161\) 1.97509 + 6.07871i 0.155659 + 0.479069i
\(162\) 0.269341 0.828945i 0.0211614 0.0651281i
\(163\) −9.79754 7.11833i −0.767403 0.557551i 0.133769 0.991013i \(-0.457292\pi\)
−0.901172 + 0.433462i \(0.857292\pi\)
\(164\) 3.98184 0.310929
\(165\) 9.45330 + 9.60962i 0.735938 + 0.748108i
\(166\) −0.111323 −0.00864034
\(167\) 10.6531 + 7.73994i 0.824363 + 0.598935i 0.917959 0.396675i \(-0.129836\pi\)
−0.0935958 + 0.995610i \(0.529836\pi\)
\(168\) 0.872746 2.68604i 0.0673338 0.207232i
\(169\) 7.44388 + 22.9099i 0.572606 + 1.76230i
\(170\) 4.87678 3.54319i 0.374032 0.271750i
\(171\) −4.41490 + 3.20761i −0.337616 + 0.245292i
\(172\) −0.0487491 0.150034i −0.00371709 0.0114400i
\(173\) −4.54809 + 13.9976i −0.345785 + 1.06422i 0.615377 + 0.788233i \(0.289004\pi\)
−0.961162 + 0.275984i \(0.910996\pi\)
\(174\) −3.34897 2.43317i −0.253885 0.184458i
\(175\) −11.5191 −0.870759
\(176\) 0.0290229 0.0558242i 0.00218768 0.00420791i
\(177\) 4.63368 0.348288
\(178\) 5.73095 + 4.16378i 0.429553 + 0.312088i
\(179\) −3.61252 + 11.1182i −0.270013 + 0.831014i 0.720483 + 0.693472i \(0.243920\pi\)
−0.990496 + 0.137541i \(0.956080\pi\)
\(180\) 1.55777 + 4.79433i 0.116109 + 0.357348i
\(181\) −15.9378 + 11.5795i −1.18465 + 0.860698i −0.992689 0.120704i \(-0.961485\pi\)
−0.191961 + 0.981403i \(0.561485\pi\)
\(182\) −4.29436 + 3.12004i −0.318319 + 0.231273i
\(183\) 1.64113 + 5.05088i 0.121316 + 0.373372i
\(184\) 5.57818 17.1679i 0.411229 1.26563i
\(185\) 8.02149 + 5.82796i 0.589752 + 0.428480i
\(186\) −3.80289 −0.278841
\(187\) 2.60331 5.00735i 0.190373 0.366174i
\(188\) −10.5027 −0.765989
\(189\) 0.809017 + 0.587785i 0.0588473 + 0.0427551i
\(190\) −5.97390 + 18.3858i −0.433392 + 1.33384i
\(191\) 2.15136 + 6.62120i 0.155667 + 0.479093i 0.998228 0.0595077i \(-0.0189531\pi\)
−0.842561 + 0.538601i \(0.818953\pi\)
\(192\) −3.96398 + 2.88000i −0.286076 + 0.207846i
\(193\) −13.6427 + 9.91199i −0.982022 + 0.713481i −0.958160 0.286234i \(-0.907596\pi\)
−0.0238626 + 0.999715i \(0.507596\pi\)
\(194\) −0.699533 2.15294i −0.0502235 0.154572i
\(195\) 7.64886 23.5408i 0.547747 1.68579i
\(196\) 1.00343 + 0.729034i 0.0716735 + 0.0520738i
\(197\) 6.42145 0.457510 0.228755 0.973484i \(-0.426535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(198\) −2.02726 2.06079i −0.144071 0.146454i
\(199\) −13.2645 −0.940297 −0.470149 0.882587i \(-0.655800\pi\)
−0.470149 + 0.882587i \(0.655800\pi\)
\(200\) 26.3196 + 19.1223i 1.86108 + 1.35215i
\(201\) 4.34745 13.3801i 0.306645 0.943757i
\(202\) −1.62297 4.99500i −0.114192 0.351447i
\(203\) 3.84230 2.79160i 0.269677 0.195932i
\(204\) 1.70746 1.24054i 0.119546 0.0868553i
\(205\) 4.03209 + 12.4095i 0.281613 + 0.866716i
\(206\) 3.47282 10.6882i 0.241963 0.744685i
\(207\) 5.17086 + 3.75685i 0.359399 + 0.261119i
\(208\) −0.115531 −0.00801067
\(209\) 2.68466 + 17.8990i 0.185702 + 1.23810i
\(210\) 3.54252 0.244457
\(211\) −2.35552 1.71139i −0.162161 0.117817i 0.503746 0.863852i \(-0.331955\pi\)
−0.665906 + 0.746035i \(0.731955\pi\)
\(212\) 1.80678 5.56068i 0.124090 0.381909i
\(213\) 0.685658 + 2.11024i 0.0469805 + 0.144591i
\(214\) 3.77082 2.73966i 0.257768 0.187279i
\(215\) 0.418221 0.303855i 0.0285224 0.0207228i
\(216\) −0.872746 2.68604i −0.0593828 0.182762i
\(217\) 1.34827 4.14954i 0.0915264 0.281689i
\(218\) 1.01663 + 0.738623i 0.0688547 + 0.0500259i
\(219\) −5.57393 −0.376651
\(220\) 16.4914 + 2.75080i 1.11185 + 0.185459i
\(221\) −10.3630 −0.697091
\(222\) −1.72021 1.24981i −0.115453 0.0838816i
\(223\) −1.03697 + 3.19146i −0.0694406 + 0.213716i −0.979755 0.200202i \(-0.935840\pi\)
0.910314 + 0.413918i \(0.135840\pi\)
\(224\) −1.75060 5.38780i −0.116967 0.359987i
\(225\) −9.31911 + 6.77073i −0.621274 + 0.451382i
\(226\) −13.7625 + 9.99908i −0.915471 + 0.665129i
\(227\) 1.03147 + 3.17454i 0.0684612 + 0.210702i 0.979434 0.201764i \(-0.0646675\pi\)
−0.910973 + 0.412466i \(0.864668\pi\)
\(228\) −2.09158 + 6.43722i −0.138518 + 0.426315i
\(229\) −5.50248 3.99778i −0.363614 0.264181i 0.390944 0.920414i \(-0.372149\pi\)
−0.754558 + 0.656234i \(0.772149\pi\)
\(230\) 22.6421 1.49298
\(231\) 2.96738 1.48143i 0.195239 0.0974711i
\(232\) −13.4134 −0.880634
\(233\) −5.00420 3.63576i −0.327836 0.238187i 0.411676 0.911330i \(-0.364944\pi\)
−0.739512 + 0.673144i \(0.764944\pi\)
\(234\) −1.64030 + 5.04833i −0.107230 + 0.330020i
\(235\) −10.6353 32.7319i −0.693767 2.13520i
\(236\) 4.64956 3.37811i 0.302661 0.219896i
\(237\) −5.07362 + 3.68620i −0.329567 + 0.239444i
\(238\) −0.458317 1.41055i −0.0297082 0.0914326i
\(239\) 6.32817 19.4761i 0.409335 1.25980i −0.507885 0.861425i \(-0.669573\pi\)
0.917220 0.398380i \(-0.130427\pi\)
\(240\) 0.0623776 + 0.0453200i 0.00402646 + 0.00292539i
\(241\) 1.04113 0.0670653 0.0335326 0.999438i \(-0.489324\pi\)
0.0335326 + 0.999438i \(0.489324\pi\)
\(242\) −9.16576 + 2.81281i −0.589197 + 0.180814i
\(243\) 1.00000 0.0641500
\(244\) 5.32902 + 3.87176i 0.341155 + 0.247864i
\(245\) −1.25596 + 3.86544i −0.0802402 + 0.246954i
\(246\) −0.864682 2.66122i −0.0551301 0.169673i
\(247\) 26.8870 19.5346i 1.71078 1.24295i
\(248\) −9.96913 + 7.24299i −0.633040 + 0.459931i
\(249\) −0.0394683 0.121471i −0.00250120 0.00769790i
\(250\) −7.13640 + 21.9636i −0.451346 + 1.38910i
\(251\) −5.36621 3.89878i −0.338712 0.246089i 0.405406 0.914137i \(-0.367130\pi\)
−0.744118 + 0.668048i \(0.767130\pi\)
\(252\) 1.24031 0.0781319
\(253\) 18.9661 9.46863i 1.19239 0.595287i
\(254\) −0.559320 −0.0350948
\(255\) 5.59518 + 4.06514i 0.350384 + 0.254569i
\(256\) −4.92962 + 15.1718i −0.308101 + 0.948238i
\(257\) 0.890729 + 2.74138i 0.0555622 + 0.171003i 0.974986 0.222264i \(-0.0713448\pi\)
−0.919424 + 0.393267i \(0.871345\pi\)
\(258\) −0.0896877 + 0.0651619i −0.00558371 + 0.00405680i
\(259\) 1.97362 1.43392i 0.122635 0.0890992i
\(260\) −9.48693 29.1978i −0.588354 1.81077i
\(261\) 1.46763 4.51690i 0.0908439 0.279589i
\(262\) 9.87109 + 7.17177i 0.609838 + 0.443073i
\(263\) −21.1018 −1.30119 −0.650595 0.759425i \(-0.725480\pi\)
−0.650595 + 0.759425i \(0.725480\pi\)
\(264\) −9.23938 1.54114i −0.568644 0.0948507i
\(265\) 19.1596 1.17696
\(266\) 3.84805 + 2.79577i 0.235939 + 0.171420i
\(267\) −2.51149 + 7.72958i −0.153701 + 0.473042i
\(268\) −5.39216 16.5954i −0.329379 1.01372i
\(269\) 13.8597 10.0696i 0.845040 0.613957i −0.0787342 0.996896i \(-0.525088\pi\)
0.923774 + 0.382938i \(0.125088\pi\)
\(270\) 2.86596 2.08224i 0.174417 0.126721i
\(271\) 5.05547 + 15.5591i 0.307098 + 0.945151i 0.978886 + 0.204407i \(0.0655266\pi\)
−0.671788 + 0.740744i \(0.734473\pi\)
\(272\) 0.00997527 0.0307007i 0.000604839 0.00186150i
\(273\) −4.92697 3.57965i −0.298194 0.216650i
\(274\) −2.35348 −0.142179
\(275\) 5.66686 + 37.7818i 0.341725 + 2.27833i
\(276\) 7.92745 0.477177
\(277\) 2.00516 + 1.45684i 0.120479 + 0.0875329i 0.646393 0.763005i \(-0.276277\pi\)
−0.525914 + 0.850538i \(0.676277\pi\)
\(278\) −0.555358 + 1.70922i −0.0333082 + 0.102512i
\(279\) −1.34827 4.14954i −0.0807187 0.248427i
\(280\) 9.28658 6.74709i 0.554979 0.403216i
\(281\) −19.5740 + 14.2214i −1.16769 + 0.848375i −0.990730 0.135843i \(-0.956626\pi\)
−0.176958 + 0.984218i \(0.556626\pi\)
\(282\) 2.28073 + 7.01938i 0.135816 + 0.417998i
\(283\) −9.01893 + 27.7574i −0.536119 + 1.65001i 0.205098 + 0.978741i \(0.434249\pi\)
−0.741218 + 0.671265i \(0.765751\pi\)
\(284\) 2.22644 + 1.61760i 0.132115 + 0.0959872i
\(285\) −22.1797 −1.31381
\(286\) 12.3462 + 12.5503i 0.730044 + 0.742116i
\(287\) 3.21037 0.189502
\(288\) −4.58313 3.32984i −0.270064 0.196213i
\(289\) −4.35852 + 13.4142i −0.256384 + 0.789068i
\(290\) −5.19910 16.0012i −0.305302 0.939622i
\(291\) 2.10118 1.52660i 0.123174 0.0894908i
\(292\) −5.59304 + 4.06358i −0.327308 + 0.237803i
\(293\) −8.40272 25.8609i −0.490892 1.51081i −0.823262 0.567662i \(-0.807848\pi\)
0.332369 0.943149i \(-0.392152\pi\)
\(294\) 0.269341 0.828945i 0.0157083 0.0483451i
\(295\) 15.2362 + 11.0697i 0.887085 + 0.644505i
\(296\) −6.88986 −0.400465
\(297\) 1.52990 2.94269i 0.0887737 0.170752i
\(298\) 8.78834 0.509095
\(299\) −31.4909 22.8794i −1.82116 1.32315i
\(300\) −4.41497 + 13.5879i −0.254899 + 0.784497i
\(301\) −0.0393041 0.120966i −0.00226545 0.00697234i
\(302\) 10.5517 7.66625i 0.607182 0.441143i
\(303\) 4.87492 3.54184i 0.280057 0.203473i
\(304\) 0.0319907 + 0.0984573i 0.00183479 + 0.00564691i
\(305\) −6.67015 + 20.5286i −0.381932 + 1.17547i
\(306\) −1.19989 0.871770i −0.0685931 0.0498358i
\(307\) −9.95364 −0.568084 −0.284042 0.958812i \(-0.591676\pi\)
−0.284042 + 0.958812i \(0.591676\pi\)
\(308\) 1.89754 3.64983i 0.108122 0.207969i
\(309\) 12.8938 0.733502
\(310\) −12.5044 9.08500i −0.710204 0.515993i
\(311\) 5.01864 15.4458i 0.284581 0.875850i −0.701943 0.712233i \(-0.747684\pi\)
0.986524 0.163617i \(-0.0523161\pi\)
\(312\) 5.31508 + 16.3581i 0.300907 + 0.926097i
\(313\) −13.4417 + 9.76594i −0.759768 + 0.552004i −0.898839 0.438279i \(-0.855588\pi\)
0.139071 + 0.990282i \(0.455588\pi\)
\(314\) −13.7179 + 9.96661i −0.774144 + 0.562448i
\(315\) 1.25596 + 3.86544i 0.0707652 + 0.217793i
\(316\) −2.40365 + 7.39768i −0.135216 + 0.416152i
\(317\) −6.55305 4.76107i −0.368056 0.267408i 0.388348 0.921513i \(-0.373046\pi\)
−0.756404 + 0.654104i \(0.773046\pi\)
\(318\) −4.10878 −0.230409
\(319\) −11.0465 11.2292i −0.618485 0.628713i
\(320\) −19.9144 −1.11325
\(321\) 4.32630 + 3.14324i 0.241470 + 0.175438i
\(322\) 1.72150 5.29823i 0.0959354 0.295259i
\(323\) 2.86952 + 8.83148i 0.159664 + 0.491397i
\(324\) 1.00343 0.729034i 0.0557460 0.0405019i
\(325\) 56.7540 41.2342i 3.14815 2.28726i
\(326\) 3.26183 + 10.0389i 0.180656 + 0.556002i
\(327\) −0.445520 + 1.37117i −0.0246373 + 0.0758258i
\(328\) −7.33530 5.32941i −0.405024 0.294267i
\(329\) −8.46784 −0.466847
\(330\) −1.74276 11.6192i −0.0959358 0.639618i
\(331\) −6.64605 −0.365300 −0.182650 0.983178i \(-0.558468\pi\)
−0.182650 + 0.983178i \(0.558468\pi\)
\(332\) −0.128160 0.0931136i −0.00703369 0.00511027i
\(333\) 0.753854 2.32012i 0.0413110 0.127142i
\(334\) −3.54667 10.9155i −0.194065 0.597271i
\(335\) 46.2596 33.6096i 2.52743 1.83629i
\(336\) 0.0153474 0.0111506i 0.000837272 0.000608313i
\(337\) −6.47454 19.9266i −0.352691 1.08547i −0.957336 0.288976i \(-0.906685\pi\)
0.604646 0.796494i \(-0.293315\pi\)
\(338\) 6.48811 19.9684i 0.352907 1.08614i
\(339\) −15.7899 11.4720i −0.857590 0.623075i
\(340\) 8.57798 0.465207
\(341\) −14.2735 2.38084i −0.772955 0.128930i
\(342\) 4.75645 0.257199
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) −0.111005 + 0.341639i −0.00598500 + 0.0184199i
\(345\) 8.02749 + 24.7061i 0.432186 + 1.33013i
\(346\) 10.3782 7.54023i 0.557938 0.405365i
\(347\) 14.3901 10.4550i 0.772500 0.561254i −0.130219 0.991485i \(-0.541568\pi\)
0.902719 + 0.430231i \(0.141568\pi\)
\(348\) −1.82031 5.60233i −0.0975788 0.300317i
\(349\) 3.62603 11.1598i 0.194097 0.597368i −0.805889 0.592066i \(-0.798312\pi\)
0.999986 0.00530193i \(-0.00168767\pi\)
\(350\) 8.12258 + 5.90140i 0.434170 + 0.315443i
\(351\) −6.09006 −0.325064
\(352\) −16.8104 + 8.39241i −0.895998 + 0.447317i
\(353\) 15.2682 0.812642 0.406321 0.913730i \(-0.366811\pi\)
0.406321 + 0.913730i \(0.366811\pi\)
\(354\) −3.26740 2.37391i −0.173661 0.126172i
\(355\) −2.78676 + 8.57677i −0.147906 + 0.455208i
\(356\) 3.11502 + 9.58704i 0.165096 + 0.508112i
\(357\) 1.37664 1.00019i 0.0728597 0.0529357i
\(358\) 8.24338 5.98917i 0.435676 0.316537i
\(359\) 2.08338 + 6.41200i 0.109957 + 0.338412i 0.990862 0.134881i \(-0.0430651\pi\)
−0.880905 + 0.473293i \(0.843065\pi\)
\(360\) 3.54716 10.9170i 0.186952 0.575378i
\(361\) −8.72130 6.33640i −0.459016 0.333495i
\(362\) 17.1708 0.902478
\(363\) −6.31882 9.00402i −0.331652 0.472589i
\(364\) −7.55354 −0.395913
\(365\) −18.3279 13.3160i −0.959324 0.696989i
\(366\) 1.43042 4.40237i 0.0747691 0.230116i
\(367\) −6.48141 19.9477i −0.338327 1.04126i −0.965060 0.262029i \(-0.915608\pi\)
0.626733 0.779234i \(-0.284392\pi\)
\(368\) 0.0980937 0.0712692i 0.00511349 0.00371516i
\(369\) 2.59724 1.88701i 0.135207 0.0982337i
\(370\) −2.67054 8.21908i −0.138835 0.427290i
\(371\) 1.45672 4.48332i 0.0756290 0.232762i
\(372\) −4.37805 3.18084i −0.226991 0.164919i
\(373\) 29.1253 1.50805 0.754027 0.656844i \(-0.228109\pi\)
0.754027 + 0.656844i \(0.228109\pi\)
\(374\) −4.40105 + 2.19718i −0.227573 + 0.113613i
\(375\) −26.4958 −1.36824
\(376\) 19.3480 + 14.0571i 0.997796 + 0.724942i
\(377\) −8.93795 + 27.5082i −0.460328 + 1.41674i
\(378\) −0.269341 0.828945i −0.0138534 0.0426363i
\(379\) −25.8362 + 18.7711i −1.32712 + 0.964207i −0.327303 + 0.944919i \(0.606140\pi\)
−0.999814 + 0.0192874i \(0.993860\pi\)
\(380\) −22.2558 + 16.1698i −1.14170 + 0.829491i
\(381\) −0.198300 0.610305i −0.0101592 0.0312669i
\(382\) 1.87513 5.77107i 0.0959402 0.295273i
\(383\) −2.90411 2.10996i −0.148393 0.107814i 0.511111 0.859514i \(-0.329234\pi\)
−0.659505 + 0.751700i \(0.729234\pi\)
\(384\) −7.05948 −0.360253
\(385\) 13.2963 + 2.21784i 0.677641 + 0.113031i
\(386\) 14.6981 0.748115
\(387\) −0.102900 0.0747609i −0.00523068 0.00380031i
\(388\) 0.995445 3.06367i 0.0505361 0.155534i
\(389\) 3.23572 + 9.95853i 0.164058 + 0.504917i 0.998966 0.0454722i \(-0.0144792\pi\)
−0.834908 + 0.550389i \(0.814479\pi\)
\(390\) −17.4539 + 12.6810i −0.883811 + 0.642126i
\(391\) 8.79886 6.39275i 0.444977 0.323295i
\(392\) −0.872746 2.68604i −0.0440803 0.135665i
\(393\) −4.32584 + 13.3136i −0.218210 + 0.671581i
\(394\) −4.52804 3.28981i −0.228119 0.165738i
\(395\) −25.4890 −1.28249
\(396\) −0.610175 4.06812i −0.0306624 0.204431i
\(397\) 17.7269 0.889686 0.444843 0.895609i \(-0.353259\pi\)
0.444843 + 0.895609i \(0.353259\pi\)
\(398\) 9.35338 + 6.79563i 0.468843 + 0.340634i
\(399\) −1.68634 + 5.19003i −0.0844227 + 0.259826i
\(400\) 0.0675270 + 0.207827i 0.00337635 + 0.0103913i
\(401\) −6.53714 + 4.74951i −0.326449 + 0.237179i −0.738922 0.673791i \(-0.764665\pi\)
0.412473 + 0.910970i \(0.364665\pi\)
\(402\) −9.92039 + 7.20759i −0.494784 + 0.359482i
\(403\) 8.21104 + 25.2710i 0.409021 + 1.25884i
\(404\) 2.30952 7.10796i 0.114903 0.353634i
\(405\) 3.28814 + 2.38897i 0.163389 + 0.118709i
\(406\) −4.13955 −0.205442
\(407\) −5.67408 5.76791i −0.281254 0.285905i
\(408\) −4.80584 −0.237924
\(409\) −32.1090 23.3286i −1.58769 1.15352i −0.907148 0.420811i \(-0.861746\pi\)
−0.680539 0.732712i \(-0.738254\pi\)
\(410\) 3.51438 10.8162i 0.173563 0.534172i
\(411\) −0.834399 2.56802i −0.0411579 0.126671i
\(412\) 12.9380 9.40001i 0.637409 0.463105i
\(413\) 3.74872 2.72361i 0.184463 0.134020i
\(414\) −1.72150 5.29823i −0.0846070 0.260394i
\(415\) 0.160413 0.493702i 0.00787438 0.0242349i
\(416\) 27.9116 + 20.2789i 1.36848 + 0.994257i
\(417\) −2.06192 −0.100973
\(418\) 7.27688 13.9967i 0.355924 0.684603i
\(419\) 16.1715 0.790028 0.395014 0.918675i \(-0.370740\pi\)
0.395014 + 0.918675i \(0.370740\pi\)
\(420\) 4.07830 + 2.96306i 0.199001 + 0.144582i
\(421\) 7.66622 23.5942i 0.373629 1.14991i −0.570770 0.821110i \(-0.693355\pi\)
0.944399 0.328802i \(-0.106645\pi\)
\(422\) 0.784207 + 2.41354i 0.0381746 + 0.117489i
\(423\) −6.85063 + 4.97727i −0.333089 + 0.242003i
\(424\) −10.7710 + 7.82559i −0.523086 + 0.380044i
\(425\) 6.05708 + 18.6418i 0.293811 + 0.904259i
\(426\) 0.597622 1.83929i 0.0289549 0.0891140i
\(427\) 4.29654 + 3.12162i 0.207924 + 0.151066i
\(428\) 6.63265 0.320601
\(429\) −9.31718 + 17.9212i −0.449838 + 0.865242i
\(430\) −0.450576 −0.0217287
\(431\) −17.7030 12.8620i −0.852724 0.619540i 0.0731719 0.997319i \(-0.476688\pi\)
−0.925896 + 0.377779i \(0.876688\pi\)
\(432\) 0.00586220 0.0180420i 0.000282045 0.000868046i
\(433\) 12.1579 + 37.4183i 0.584273 + 1.79821i 0.602170 + 0.798368i \(0.294303\pi\)
−0.0178973 + 0.999840i \(0.505697\pi\)
\(434\) −3.07660 + 2.23528i −0.147682 + 0.107297i
\(435\) 15.6165 11.3461i 0.748755 0.544002i
\(436\) 0.552581 + 1.70067i 0.0264638 + 0.0814473i
\(437\) −10.7783 + 33.1722i −0.515596 + 1.58684i
\(438\) 3.93041 + 2.85561i 0.187802 + 0.136446i
\(439\) 9.59194 0.457799 0.228899 0.973450i \(-0.426487\pi\)
0.228899 + 0.973450i \(0.426487\pi\)
\(440\) −26.6986 27.1401i −1.27281 1.29385i
\(441\) 1.00000 0.0476190
\(442\) 7.30740 + 5.30914i 0.347577 + 0.252530i
\(443\) −0.194414 + 0.598344i −0.00923687 + 0.0284282i −0.955569 0.294768i \(-0.904758\pi\)
0.946332 + 0.323197i \(0.104758\pi\)
\(444\) −0.935010 2.87766i −0.0443736 0.136568i
\(445\) −26.7239 + 19.4160i −1.26683 + 0.920409i
\(446\) 2.36625 1.71918i 0.112045 0.0814055i
\(447\) 3.11580 + 9.58945i 0.147372 + 0.453565i
\(448\) −1.51411 + 4.65994i −0.0715348 + 0.220162i
\(449\) 14.0254 + 10.1901i 0.661900 + 0.480899i 0.867304 0.497779i \(-0.165851\pi\)
−0.205404 + 0.978677i \(0.565851\pi\)
\(450\) 10.0401 0.473293
\(451\) −1.57936 10.5298i −0.0743690 0.495829i
\(452\) −24.2075 −1.13863
\(453\) 12.1061 + 8.79557i 0.568792 + 0.413252i
\(454\) 0.899035 2.76695i 0.0421938 0.129859i
\(455\) −7.64886 23.5408i −0.358584 1.10361i
\(456\) 12.4688 9.05915i 0.583907 0.424233i
\(457\) 23.5549 17.1136i 1.10185 0.800541i 0.120489 0.992715i \(-0.461554\pi\)
0.981361 + 0.192174i \(0.0615539\pi\)
\(458\) 1.83190 + 5.63801i 0.0855991 + 0.263447i
\(459\) 0.525831 1.61834i 0.0245437 0.0755377i
\(460\) 26.0666 + 18.9385i 1.21536 + 0.883011i
\(461\) 15.1850 0.707236 0.353618 0.935390i \(-0.384951\pi\)
0.353618 + 0.935390i \(0.384951\pi\)
\(462\) −2.85139 0.475616i −0.132659 0.0221277i
\(463\) 17.8886 0.831355 0.415677 0.909512i \(-0.363545\pi\)
0.415677 + 0.909512i \(0.363545\pi\)
\(464\) −0.0728903 0.0529579i −0.00338385 0.00245851i
\(465\) 5.47985 16.8653i 0.254122 0.782108i
\(466\) 1.66601 + 5.12747i 0.0771766 + 0.237525i
\(467\) 24.5214 17.8158i 1.13472 0.824419i 0.148341 0.988936i \(-0.452607\pi\)
0.986374 + 0.164517i \(0.0526067\pi\)
\(468\) −6.11094 + 4.43986i −0.282479 + 0.205233i
\(469\) −4.34745 13.3801i −0.200746 0.617834i
\(470\) −9.26973 + 28.5293i −0.427581 + 1.31596i
\(471\) −15.7386 11.4348i −0.725198 0.526887i
\(472\) −13.0867 −0.602366
\(473\) −0.377424 + 0.188425i −0.0173540 + 0.00866377i
\(474\) 5.46613 0.251068
\(475\) −50.8555 36.9487i −2.33341 1.69532i
\(476\) 0.652191 2.00724i 0.0298931 0.0920016i
\(477\) −1.45672 4.48332i −0.0666985 0.205277i
\(478\) −14.4402 + 10.4914i −0.660479 + 0.479866i
\(479\) 6.42966 4.67142i 0.293779 0.213443i −0.431126 0.902292i \(-0.641884\pi\)
0.724905 + 0.688849i \(0.241884\pi\)
\(480\) −7.11508 21.8980i −0.324758 0.999501i
\(481\) −4.59102 + 14.1297i −0.209333 + 0.644259i
\(482\) −0.734147 0.533389i −0.0334395 0.0242952i
\(483\) 6.39153 0.290825
\(484\) −12.9047 4.42826i −0.586578 0.201285i
\(485\) 10.5560 0.479323
\(486\) −0.705143 0.512316i −0.0319859 0.0232391i
\(487\) −3.14304 + 9.67329i −0.142425 + 0.438338i −0.996671 0.0815305i \(-0.974019\pi\)
0.854246 + 0.519869i \(0.174019\pi\)
\(488\) −4.63499 14.2650i −0.209816 0.645747i
\(489\) −9.79754 + 7.11833i −0.443060 + 0.321902i
\(490\) 2.86596 2.08224i 0.129471 0.0940660i
\(491\) 0.332923 + 1.02463i 0.0150246 + 0.0462409i 0.958288 0.285805i \(-0.0922610\pi\)
−0.943263 + 0.332046i \(0.892261\pi\)
\(492\) 1.23046 3.78695i 0.0554732 0.170729i
\(493\) −6.53816 4.75025i −0.294464 0.213940i
\(494\) −28.9671 −1.30329
\(495\) 12.0605 6.02108i 0.542080 0.270628i
\(496\) −0.0827699 −0.00371648
\(497\) 1.79507 + 1.30420i 0.0805201 + 0.0585013i
\(498\) −0.0344007 + 0.105874i −0.00154153 + 0.00474435i
\(499\) 10.6969 + 32.9217i 0.478859 + 1.47378i 0.840682 + 0.541530i \(0.182155\pi\)
−0.361823 + 0.932247i \(0.617845\pi\)
\(500\) −26.5867 + 19.3163i −1.18899 + 0.863853i
\(501\) 10.6531 7.73994i 0.475946 0.345795i
\(502\) 1.78654 + 5.49840i 0.0797371 + 0.245405i
\(503\) 0.852636 2.62414i 0.0380172 0.117005i −0.930247 0.366934i \(-0.880407\pi\)
0.968264 + 0.249929i \(0.0804074\pi\)
\(504\) −2.28488 1.66006i −0.101777 0.0739450i
\(505\) 24.4908 1.08982
\(506\) −18.2247 3.03991i −0.810189 0.135141i
\(507\) 24.0889 1.06983
\(508\) −0.643913 0.467830i −0.0285690 0.0207566i
\(509\) 4.50899 13.8773i 0.199858 0.615099i −0.800028 0.599963i \(-0.795182\pi\)
0.999885 0.0151357i \(-0.00481803\pi\)
\(510\) −1.86277 5.73300i −0.0824846 0.253862i
\(511\) −4.50940 + 3.27627i −0.199484 + 0.144934i
\(512\) −0.173635 + 0.126153i −0.00767364 + 0.00557523i
\(513\) 1.68634 + 5.19003i 0.0744538 + 0.229145i
\(514\) 0.776364 2.38940i 0.0342439 0.105392i
\(515\) 42.3966 + 30.8029i 1.86822 + 1.35734i
\(516\) −0.157755 −0.00694480
\(517\) 4.16580 + 27.7740i 0.183212 + 1.22150i
\(518\) −2.12630 −0.0934242
\(519\) 11.9071 + 8.65098i 0.522662 + 0.379736i
\(520\) −21.6024 + 66.4854i −0.947329 + 2.91558i
\(521\) −4.24334 13.0597i −0.185904 0.572154i 0.814059 0.580783i \(-0.197253\pi\)
−0.999963 + 0.00862850i \(0.997253\pi\)
\(522\) −3.34897 + 2.43317i −0.146580 + 0.106497i
\(523\) −6.10491 + 4.43548i −0.266949 + 0.193950i −0.713205 0.700956i \(-0.752757\pi\)
0.446256 + 0.894905i \(0.352757\pi\)
\(524\) 5.36537 + 16.5129i 0.234387 + 0.721369i
\(525\) −3.55958 + 10.9553i −0.155353 + 0.478127i
\(526\) 14.8798 + 10.8108i 0.648788 + 0.471372i
\(527\) −7.42434 −0.323409
\(528\) −0.0441234 0.0448530i −0.00192022 0.00195198i
\(529\) 17.8517 0.776160
\(530\) −13.5102 9.81576i −0.586847 0.426369i
\(531\) 1.43188 4.40689i 0.0621385 0.191243i
\(532\) 2.09158 + 6.43722i 0.0906815 + 0.279089i
\(533\) −15.8174 + 11.4920i −0.685126 + 0.497774i
\(534\) 5.73095 4.16378i 0.248002 0.180184i
\(535\) 6.71635 + 20.6708i 0.290373 + 0.893677i
\(536\) −12.2783 + 37.7888i −0.530344 + 1.63223i
\(537\) 9.45771 + 6.87143i 0.408130 + 0.296524i
\(538\) −14.9319 −0.643760
\(539\) 1.52990 2.94269i 0.0658974 0.126751i
\(540\) 5.04106 0.216932
\(541\) 1.63162 + 1.18544i 0.0701486 + 0.0509659i 0.622307 0.782773i \(-0.286196\pi\)
−0.552158 + 0.833739i \(0.686196\pi\)
\(542\) 4.40637 13.5614i 0.189270 0.582513i
\(543\) 6.08771 + 18.7360i 0.261249 + 0.804041i
\(544\) −7.79877 + 5.66614i −0.334370 + 0.242934i
\(545\) −4.74062 + 3.44426i −0.203066 + 0.147536i
\(546\) 1.64030 + 5.04833i 0.0701984 + 0.216049i
\(547\) 12.7165 39.1373i 0.543718 1.67339i −0.180301 0.983612i \(-0.557707\pi\)
0.724019 0.689780i \(-0.242293\pi\)
\(548\) −2.70943 1.96852i −0.115741 0.0840908i
\(549\) 5.31081 0.226660
\(550\) 15.3603 29.5448i 0.654964 1.25979i
\(551\) 25.9177 1.10413
\(552\) −14.6039 10.6103i −0.621582 0.451606i
\(553\) −1.93795 + 5.96440i −0.0824100 + 0.253632i
\(554\) −0.667566 2.05456i −0.0283622 0.0872897i
\(555\) 8.02149 5.82796i 0.340493 0.247383i
\(556\) −2.06899 + 1.50321i −0.0877446 + 0.0637502i
\(557\) −5.70473 17.5574i −0.241717 0.743930i −0.996159 0.0875624i \(-0.972092\pi\)
0.754442 0.656367i \(-0.227908\pi\)
\(558\) −1.17516 + 3.61676i −0.0497483 + 0.153110i
\(559\) 0.626665 + 0.455299i 0.0265051 + 0.0192571i
\(560\) 0.0771030 0.00325819
\(561\) −3.95781 4.02325i −0.167099 0.169862i
\(562\) 21.0883 0.889557
\(563\) 23.0694 + 16.7609i 0.972260 + 0.706388i 0.955966 0.293479i \(-0.0948131\pi\)
0.0162945 + 0.999867i \(0.494813\pi\)
\(564\) −3.24552 + 9.98868i −0.136661 + 0.420599i
\(565\) −24.5130 75.4433i −1.03127 3.17392i
\(566\) 20.5802 14.9524i 0.865050 0.628496i
\(567\) 0.809017 0.587785i 0.0339755 0.0246847i
\(568\) −1.93648 5.95987i −0.0812528 0.250070i
\(569\) 5.48146 16.8702i 0.229795 0.707235i −0.767975 0.640480i \(-0.778735\pi\)
0.997769 0.0667550i \(-0.0212646\pi\)
\(570\) 15.6399 + 11.3630i 0.655082 + 0.475945i
\(571\) −20.8488 −0.872496 −0.436248 0.899827i \(-0.643693\pi\)
−0.436248 + 0.899827i \(0.643693\pi\)
\(572\) 3.71600 + 24.7751i 0.155374 + 1.03590i
\(573\) 6.96194 0.290839
\(574\) −2.26377 1.64472i −0.0944878 0.0686494i
\(575\) −22.7512 + 70.0210i −0.948791 + 2.92008i
\(576\) 1.51411 + 4.65994i 0.0630878 + 0.194164i
\(577\) −17.2311 + 12.5191i −0.717339 + 0.521178i −0.885533 0.464576i \(-0.846207\pi\)
0.168194 + 0.985754i \(0.446207\pi\)
\(578\) 9.94567 7.22595i 0.413685 0.300560i
\(579\) 5.21104 + 16.0379i 0.216564 + 0.666514i
\(580\) 7.39840 22.7699i 0.307202 0.945470i
\(581\) −0.103329 0.0750731i −0.00428682 0.00311456i
\(582\) −2.26374 −0.0938349
\(583\) −15.4216 2.57235i −0.638699 0.106536i
\(584\) 15.7422 0.651419
\(585\) −20.0250 14.5490i −0.827931 0.601527i
\(586\) −7.32385 + 22.5405i −0.302545 + 0.931139i
\(587\) 9.01940 + 27.7589i 0.372271 + 1.14573i 0.945302 + 0.326197i \(0.105767\pi\)
−0.573031 + 0.819534i \(0.694233\pi\)
\(588\) 1.00343 0.729034i 0.0413807 0.0300648i
\(589\) 19.2626 13.9951i 0.793702 0.576658i
\(590\) −5.07248 15.6115i −0.208831 0.642714i
\(591\) 1.98434 6.10717i 0.0816248 0.251215i
\(592\) −0.0374404 0.0272021i −0.00153879 0.00111800i
\(593\) −37.3094 −1.53212 −0.766058 0.642772i \(-0.777784\pi\)
−0.766058 + 0.642772i \(0.777784\pi\)
\(594\) −2.58638 + 1.29122i −0.106121 + 0.0529795i
\(595\) 6.91602 0.283529
\(596\) 10.1175 + 7.35080i 0.414430 + 0.301101i
\(597\) −4.09896 + 12.6153i −0.167759 + 0.516310i
\(598\) 10.4840 + 32.2666i 0.428724 + 1.31948i
\(599\) 4.00761 2.91170i 0.163747 0.118969i −0.502894 0.864348i \(-0.667731\pi\)
0.666641 + 0.745379i \(0.267731\pi\)
\(600\) 26.3196 19.1223i 1.07450 0.780666i
\(601\) 9.10277 + 28.0155i 0.371310 + 1.14277i 0.945935 + 0.324357i \(0.105148\pi\)
−0.574625 + 0.818417i \(0.694852\pi\)
\(602\) −0.0342576 + 0.105434i −0.00139624 + 0.00429718i
\(603\) −11.3818 8.26933i −0.463501 0.336753i
\(604\) 18.5598 0.755189
\(605\) 0.733195 44.7020i 0.0298086 1.81739i
\(606\) −5.25205 −0.213350
\(607\) 21.3116 + 15.4838i 0.865011 + 0.628467i 0.929243 0.369468i \(-0.120460\pi\)
−0.0642329 + 0.997935i \(0.520460\pi\)
\(608\) 9.55323 29.4018i 0.387435 1.19240i
\(609\) −1.46763 4.51690i −0.0594713 0.183034i
\(610\) 15.2206 11.0584i 0.616262 0.447741i
\(611\) 41.7208 30.3119i 1.68784 1.22629i
\(612\) −0.652191 2.00724i −0.0263633 0.0811378i
\(613\) 14.8974 45.8494i 0.601699 1.85184i 0.0836366 0.996496i \(-0.473347\pi\)
0.518062 0.855343i \(-0.326653\pi\)
\(614\) 7.01873 + 5.09941i 0.283253 + 0.205795i
\(615\) 13.0481 0.526150
\(616\) −8.38067 + 4.18396i −0.337667 + 0.168577i
\(617\) −29.2376 −1.17706 −0.588532 0.808474i \(-0.700294\pi\)
−0.588532 + 0.808474i \(0.700294\pi\)
\(618\) −9.09196 6.60570i −0.365732 0.265720i
\(619\) 1.89856 5.84318i 0.0763097 0.234857i −0.905624 0.424081i \(-0.860597\pi\)
0.981934 + 0.189224i \(0.0605972\pi\)
\(620\) −6.79670 20.9181i −0.272962 0.840090i
\(621\) 5.17086 3.75685i 0.207499 0.150757i
\(622\) −11.4520 + 8.32035i −0.459183 + 0.333616i
\(623\) 2.51149 + 7.72958i 0.100621 + 0.309679i
\(624\) −0.0357012 + 0.109877i −0.00142919 + 0.00439860i
\(625\) −40.5264 29.4442i −1.62106 1.17777i
\(626\) 14.4815 0.578799
\(627\) 17.8526 + 2.97783i 0.712963 + 0.118923i
\(628\) −24.1289 −0.962849
\(629\) −3.35835 2.43999i −0.133906 0.0972886i
\(630\) 1.09470 3.36913i 0.0436138 0.134230i
\(631\) 12.5351 + 38.5792i 0.499016 + 1.53581i 0.810603 + 0.585596i \(0.199139\pi\)
−0.311587 + 0.950217i \(0.600861\pi\)
\(632\) 14.3292 10.4108i 0.569987 0.414120i
\(633\) −2.35552 + 1.71139i −0.0936235 + 0.0680215i
\(634\) 2.18166 + 6.71447i 0.0866449 + 0.266666i
\(635\) 0.805964 2.48050i 0.0319837 0.0984357i
\(636\) −4.73020 3.43669i −0.187565 0.136274i
\(637\) −6.09006 −0.241297
\(638\) 2.03647 + 13.5775i 0.0806248 + 0.537537i
\(639\) 2.21883 0.0877757
\(640\) −23.2126 16.8649i −0.917557 0.666644i
\(641\) 7.27011 22.3751i 0.287152 0.883763i −0.698593 0.715519i \(-0.746190\pi\)
0.985745 0.168244i \(-0.0538097\pi\)
\(642\) −1.44032 4.43286i −0.0568451 0.174951i
\(643\) 17.0009 12.3519i 0.670452 0.487112i −0.199725 0.979852i \(-0.564005\pi\)
0.870176 + 0.492740i \(0.164005\pi\)
\(644\) 6.41345 4.65964i 0.252725 0.183616i
\(645\) −0.159746 0.491648i −0.00629000 0.0193586i
\(646\) 2.50109 7.69755i 0.0984040 0.302856i
\(647\) −0.366260 0.266103i −0.0143992 0.0104616i 0.580562 0.814216i \(-0.302833\pi\)
−0.594962 + 0.803754i \(0.702833\pi\)
\(648\) −2.82426 −0.110948
\(649\) −10.7775 10.9557i −0.423052 0.430048i
\(650\) −61.1446 −2.39829
\(651\) −3.52981 2.56456i −0.138344 0.100513i
\(652\) −4.64163 + 14.2855i −0.181780 + 0.559462i
\(653\) −6.81098 20.9620i −0.266534 0.820308i −0.991336 0.131350i \(-0.958069\pi\)
0.724802 0.688957i \(-0.241931\pi\)
\(654\) 1.01663 0.738623i 0.0397533 0.0288824i
\(655\) −46.0297 + 33.4426i −1.79853 + 1.30671i
\(656\) −0.0188198 0.0579215i −0.000734791 0.00226145i
\(657\) −1.72244 + 5.30112i −0.0671987 + 0.206816i
\(658\) 5.97104 + 4.33821i 0.232775 + 0.169121i
\(659\) 18.3859 0.716215 0.358107 0.933680i \(-0.383422\pi\)
0.358107 + 0.933680i \(0.383422\pi\)
\(660\) 7.71230 14.8343i 0.300201 0.577422i
\(661\) −45.9605 −1.78766 −0.893829 0.448408i \(-0.851991\pi\)
−0.893829 + 0.448408i \(0.851991\pi\)
\(662\) 4.68641 + 3.40488i 0.182143 + 0.132334i
\(663\) −3.20234 + 9.85580i −0.124369 + 0.382768i
\(664\) 0.111469 + 0.343066i 0.00432583 + 0.0133135i
\(665\) −17.9438 + 13.0369i −0.695829 + 0.505550i
\(666\) −1.72021 + 1.24981i −0.0666569 + 0.0484290i
\(667\) −9.38040 28.8699i −0.363210 1.11785i
\(668\) 5.04697 15.5330i 0.195273 0.600988i
\(669\) 2.71482 + 1.97243i 0.104961 + 0.0762586i
\(670\) −49.8384 −1.92542
\(671\) 8.12500 15.6281i 0.313662 0.603315i
\(672\) −5.66506 −0.218535
\(673\) −24.0603 17.4808i −0.927457 0.673837i 0.0179118 0.999840i \(-0.494298\pi\)
−0.945369 + 0.326003i \(0.894298\pi\)
\(674\) −5.64324 + 17.3681i −0.217369 + 0.668994i
\(675\) 3.55958 + 10.9553i 0.137008 + 0.421669i
\(676\) 24.1715 17.5616i 0.929672 0.675446i
\(677\) −22.4767 + 16.3303i −0.863851 + 0.627624i −0.928930 0.370256i \(-0.879270\pi\)
0.0650791 + 0.997880i \(0.479270\pi\)
\(678\) 5.25683 + 16.1788i 0.201887 + 0.621345i
\(679\) 0.802581 2.47009i 0.0308002 0.0947933i
\(680\) −15.8023 11.4810i −0.605989 0.440277i
\(681\) 3.33791 0.127909
\(682\) 8.84513 + 8.99139i 0.338697 + 0.344298i
\(683\) 40.8297 1.56231 0.781153 0.624339i \(-0.214632\pi\)
0.781153 + 0.624339i \(0.214632\pi\)
\(684\) 5.47583 + 3.97842i 0.209373 + 0.152119i
\(685\) 3.39130 10.4374i 0.129575 0.398791i
\(686\) −0.269341 0.828945i −0.0102835 0.0316493i
\(687\) −5.50248 + 3.99778i −0.209933 + 0.152525i
\(688\) −0.00195205 + 0.00141825i −7.44213e−5 + 5.40703e-5i
\(689\) 8.87151 + 27.3037i 0.337977 + 1.04019i
\(690\) 6.99680 21.5339i 0.266364 0.819783i
\(691\) −30.5934 22.2274i −1.16383 0.845571i −0.173572 0.984821i \(-0.555531\pi\)
−0.990257 + 0.139250i \(0.955531\pi\)
\(692\) 18.2547 0.693941
\(693\) −0.491955 3.27994i −0.0186878 0.124594i
\(694\) −15.5033 −0.588498
\(695\) −6.77988 4.92587i −0.257175 0.186849i
\(696\) −4.14497 + 12.7569i −0.157115 + 0.483549i
\(697\) −1.68811 5.19547i −0.0639418 0.196792i
\(698\) −8.27419 + 6.01155i −0.313183 + 0.227541i
\(699\) −5.00420 + 3.63576i −0.189276 + 0.137517i
\(700\) 4.41497 + 13.5879i 0.166870 + 0.513574i
\(701\) 8.47498 26.0833i 0.320096 0.985153i −0.653510 0.756918i \(-0.726704\pi\)
0.973606 0.228235i \(-0.0732956\pi\)
\(702\) 4.29436 + 3.12004i 0.162080 + 0.117758i
\(703\) 13.3128 0.502100
\(704\) 16.0292 + 2.67369i 0.604123 + 0.100769i
\(705\) −34.4164 −1.29620
\(706\) −10.7662 7.82213i −0.405192 0.294390i
\(707\) 1.86205 5.73081i 0.0700297 0.215529i
\(708\) −1.77598 5.46589i −0.0667452 0.205421i
\(709\) 25.7623 18.7174i 0.967522 0.702946i 0.0126366 0.999920i \(-0.495978\pi\)
0.954885 + 0.296974i \(0.0959775\pi\)
\(710\) 6.35908 4.62014i 0.238652 0.173391i
\(711\) 1.93795 + 5.96440i 0.0726788 + 0.223682i
\(712\) 7.09312 21.8304i 0.265826 0.818128i
\(713\) −22.5609 16.3915i −0.844913 0.613865i
\(714\) −1.48314 −0.0555053
\(715\) −73.4494 + 36.6688i −2.74685 + 1.37134i
\(716\) 14.4996 0.541877
\(717\) −16.5674 12.0369i −0.618720 0.449526i
\(718\) 1.81589 5.58873i 0.0677683 0.208569i
\(719\) −4.71151 14.5005i −0.175710 0.540778i 0.823956 0.566654i \(-0.191763\pi\)
−0.999665 + 0.0258760i \(0.991763\pi\)
\(720\) 0.0623776 0.0453200i 0.00232468 0.00168898i
\(721\) 10.4313 7.57878i 0.388482 0.282249i
\(722\) 2.90352 + 8.93613i 0.108058 + 0.332568i
\(723\) 0.321728 0.990176i 0.0119652 0.0368250i
\(724\) 19.7678 + 14.3621i 0.734664 + 0.533765i
\(725\) 54.7080 2.03180
\(726\) −0.157234 + 9.58636i −0.00583550 + 0.355783i
\(727\) −33.7158 −1.25045 −0.625225 0.780445i \(-0.714993\pi\)
−0.625225 + 0.780445i \(0.714993\pi\)
\(728\) 13.9151 + 10.1099i 0.515726 + 0.374697i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 6.10177 + 18.7793i 0.225837 + 0.695054i
\(731\) −0.175096 + 0.127215i −0.00647617 + 0.00470521i
\(732\) 5.32902 3.87176i 0.196966 0.143104i
\(733\) −1.39567 4.29543i −0.0515503 0.158655i 0.921967 0.387268i \(-0.126581\pi\)
−0.973518 + 0.228612i \(0.926581\pi\)
\(734\) −5.64923 + 17.3865i −0.208517 + 0.641749i
\(735\) 3.28814 + 2.38897i 0.121285 + 0.0881186i
\(736\) −36.2084 −1.33466
\(737\) −41.7470 + 20.8417i −1.53777 + 0.767715i
\(738\) −2.79817 −0.103002
\(739\) −8.12253 5.90136i −0.298792 0.217085i 0.428280 0.903646i \(-0.359120\pi\)
−0.727072 + 0.686561i \(0.759120\pi\)
\(740\) 3.80022 11.6959i 0.139699 0.429949i
\(741\) −10.2699 31.6076i −0.377275 1.16113i
\(742\) −3.32407 + 2.41508i −0.122030 + 0.0886603i
\(743\) 12.7037 9.22981i 0.466055 0.338609i −0.329847 0.944035i \(-0.606997\pi\)
0.795902 + 0.605426i \(0.206997\pi\)
\(744\) 3.80787 + 11.7194i 0.139603 + 0.429654i
\(745\) −12.6638 + 38.9750i −0.463964 + 1.42793i
\(746\) −20.5375 14.9214i −0.751932 0.546311i
\(747\) −0.127722 −0.00467310
\(748\) −6.90446 1.15167i −0.252452 0.0421094i
\(749\) 5.34760 0.195397
\(750\) 18.6833 + 13.5742i 0.682219 + 0.495661i
\(751\) 5.95724 18.3345i 0.217383 0.669036i −0.781593 0.623789i \(-0.785593\pi\)
0.998976 0.0452468i \(-0.0144074\pi\)
\(752\) 0.0496402 + 0.152777i 0.00181019 + 0.00557120i
\(753\) −5.36621 + 3.89878i −0.195556 + 0.142080i
\(754\) 20.3954 14.8181i 0.742758 0.539645i
\(755\) 18.7940 + 57.8421i 0.683985 + 2.10509i
\(756\) 0.383276 1.17960i 0.0139396 0.0429017i
\(757\) −30.3730 22.0673i −1.10393 0.802049i −0.122229 0.992502i \(-0.539004\pi\)
−0.981696 + 0.190453i \(0.939004\pi\)
\(758\) 27.8350 1.01101
\(759\) −3.14435 20.9638i −0.114133 0.760938i
\(760\) 62.6414 2.27224
\(761\) 31.3469 + 22.7749i 1.13633 + 0.825588i 0.986603 0.163140i \(-0.0521621\pi\)
0.149722 + 0.988728i \(0.452162\pi\)
\(762\) −0.172839 + 0.531945i −0.00626131 + 0.0192703i
\(763\) 0.445520 + 1.37117i 0.0161289 + 0.0496397i
\(764\) 6.98581 5.07549i 0.252738 0.183625i
\(765\) 5.59518 4.06514i 0.202294 0.146975i
\(766\) 0.966847 + 2.97565i 0.0349336 + 0.107515i
\(767\) −8.72027 + 26.8382i −0.314871 + 0.969072i
\(768\) 12.9059 + 9.37669i 0.465702 + 0.338352i
\(769\) −24.0014 −0.865513 −0.432756 0.901511i \(-0.642459\pi\)
−0.432756 + 0.901511i \(0.642459\pi\)
\(770\) −8.23954 8.37579i −0.296932 0.301842i
\(771\) 2.88246 0.103809
\(772\) 16.9211 + 12.2939i 0.609004 + 0.442467i
\(773\) −12.1355 + 37.3493i −0.436485 + 1.34336i 0.455072 + 0.890455i \(0.349613\pi\)
−0.891557 + 0.452908i \(0.850387\pi\)
\(774\) 0.0342576 + 0.105434i 0.00123137 + 0.00378975i
\(775\) 40.6601 29.5413i 1.46055 1.06116i
\(776\) −5.93430 + 4.31152i −0.213029 + 0.154775i
\(777\) −0.753854 2.32012i −0.0270444 0.0832340i
\(778\) 2.82027 8.67989i 0.101112 0.311189i
\(779\) 14.1735 + 10.2976i 0.507817 + 0.368950i
\(780\) −30.7004 −1.09925
\(781\) 3.39459 6.52934i 0.121468 0.233638i
\(782\) −9.47956 −0.338988
\(783\) −3.84230 2.79160i −0.137313 0.0997635i
\(784\) 0.00586220 0.0180420i 0.000209364 0.000644357i
\(785\) −24.4334 75.1983i −0.872066 2.68394i
\(786\) 9.87109 7.17177i 0.352090 0.255809i
\(787\) −20.5681 + 14.9436i −0.733172 + 0.532681i −0.890565 0.454855i \(-0.849691\pi\)
0.157393 + 0.987536i \(0.449691\pi\)
\(788\) −2.46119 7.57475i −0.0876761 0.269839i
\(789\) −6.52080 + 20.0690i −0.232147 + 0.714474i
\(790\) 17.9734 + 13.0584i 0.639465 + 0.464598i
\(791\) −19.5174 −0.693959
\(792\) −4.32084 + 8.31093i −0.153534 + 0.295316i
\(793\) −32.3432 −1.14854
\(794\) −12.5000 9.08176i −0.443607 0.322300i
\(795\) 5.92063 18.2218i 0.209983 0.646262i
\(796\) 5.08397 + 15.6468i 0.180197 + 0.554588i
\(797\) 29.7416 21.6085i 1.05350 0.765413i 0.0806252 0.996744i \(-0.474308\pi\)
0.972875 + 0.231332i \(0.0743083\pi\)
\(798\) 3.84805 2.79577i 0.136219 0.0989692i
\(799\) 4.45265 + 13.7039i 0.157524 + 0.484808i
\(800\) 20.1653 62.0623i 0.712950 2.19424i
\(801\) 6.57517 + 4.77714i 0.232322 + 0.168792i
\(802\) 7.04287 0.248692
\(803\) 12.9644 + 13.1788i 0.457503 + 0.465069i
\(804\) −17.4494 −0.615393
\(805\) 21.0163 + 15.2692i 0.740726 + 0.538169i
\(806\) 7.15678 22.0263i 0.252087 0.775844i
\(807\) −5.29393 16.2930i −0.186355 0.573542i
\(808\) −13.7681 + 10.0031i −0.484359 + 0.351907i
\(809\) 32.7478 23.7926i 1.15135 0.836505i 0.162690 0.986677i \(-0.447983\pi\)
0.988660 + 0.150172i \(0.0479828\pi\)
\(810\) −1.09470 3.36913i −0.0384638 0.118379i
\(811\) −2.95118 + 9.08279i −0.103630 + 0.318940i −0.989406 0.145172i \(-0.953626\pi\)
0.885777 + 0.464112i \(0.153626\pi\)
\(812\) −4.76563 3.46243i −0.167241 0.121508i
\(813\) 16.3599 0.573765
\(814\) 1.04604 + 6.97412i 0.0366638 + 0.244443i
\(815\) −49.2212 −1.72414
\(816\) −0.0261156 0.0189741i −0.000914228 0.000664226i
\(817\) 0.214487 0.660124i 0.00750395 0.0230948i
\(818\) 10.6898 + 32.8999i 0.373761 + 1.15032i
\(819\) −4.92697 + 3.57965i −0.172162 + 0.125083i
\(820\) 13.0928 9.51251i 0.457222 0.332191i
\(821\) −11.2046 34.4843i −0.391044 1.20351i −0.932000 0.362458i \(-0.881938\pi\)
0.540956 0.841051i \(-0.318062\pi\)
\(822\) −0.727266 + 2.23829i −0.0253663 + 0.0780695i
\(823\) 33.7670 + 24.5332i 1.17704 + 0.855173i 0.991835 0.127526i \(-0.0407037\pi\)
0.185209 + 0.982699i \(0.440704\pi\)
\(824\) −36.4155 −1.26859
\(825\) 37.6838 + 6.28571i 1.31198 + 0.218840i
\(826\) −4.03873 −0.140525
\(827\) −22.8676 16.6143i −0.795183 0.577735i 0.114314 0.993445i \(-0.463533\pi\)
−0.909497 + 0.415710i \(0.863533\pi\)
\(828\) 2.44972 7.53946i 0.0851336 0.262014i
\(829\) −0.621234 1.91196i −0.0215764 0.0664052i 0.939689 0.342031i \(-0.111115\pi\)
−0.961265 + 0.275626i \(0.911115\pi\)
\(830\) −0.366046 + 0.265948i −0.0127056 + 0.00923118i
\(831\) 2.00516 1.45684i 0.0695584 0.0505371i
\(832\) −9.22101 28.3794i −0.319681 0.983877i
\(833\) 0.525831 1.61834i 0.0182190 0.0560722i
\(834\) 1.45395 + 1.05635i 0.0503461 + 0.0365785i
\(835\) 53.5195 1.85212
\(836\) 20.0847 10.0271i 0.694644 0.346794i
\(837\) −4.36309 −0.150810
\(838\) −11.4032 8.28491i −0.393917 0.286197i
\(839\) −7.48127 + 23.0250i −0.258282 + 0.794911i 0.734883 + 0.678194i \(0.237237\pi\)
−0.993165 + 0.116717i \(0.962763\pi\)
\(840\) −3.54716 10.9170i −0.122389 0.376673i
\(841\) 5.21307 3.78752i 0.179761 0.130604i
\(842\) −17.4935 + 12.7098i −0.602865 + 0.438007i
\(843\) 7.47661 + 23.0106i 0.257508 + 0.792529i
\(844\) −1.11594 + 3.43451i −0.0384122 + 0.118221i
\(845\) 79.2076 + 57.5477i 2.72483 + 1.97970i
\(846\) 7.38061 0.253751
\(847\) −10.4045 3.57030i −0.357502 0.122677i
\(848\) −0.0894276 −0.00307096
\(849\) 23.6119 + 17.1550i 0.810357 + 0.588759i
\(850\) 5.27938 16.2482i 0.181081 0.557310i
\(851\) −4.81828 14.8291i −0.165169 0.508337i
\(852\) 2.22644 1.61760i 0.0762766 0.0554182i
\(853\) −16.2959 + 11.8397i −0.557963 + 0.405384i −0.830713 0.556701i \(-0.812067\pi\)
0.272750 + 0.962085i \(0.412067\pi\)
\(854\) −1.43042 4.40237i −0.0489479 0.150646i
\(855\) −6.85391 + 21.0942i −0.234399 + 0.721405i
\(856\) −12.2186 8.87734i −0.417623 0.303421i
\(857\) −26.6092 −0.908953 −0.454477 0.890759i \(-0.650174\pi\)
−0.454477 + 0.890759i \(0.650174\pi\)
\(858\) 15.7512 7.86364i 0.537738 0.268460i
\(859\) 14.4645 0.493522 0.246761 0.969076i \(-0.420634\pi\)
0.246761 + 0.969076i \(0.420634\pi\)
\(860\) −0.518722 0.376874i −0.0176883 0.0128513i
\(861\) 0.992058 3.05324i 0.0338093 0.104054i
\(862\) 5.89374 + 18.1391i 0.200742 + 0.617819i
\(863\) −22.9456 + 16.6710i −0.781078 + 0.567487i −0.905302 0.424768i \(-0.860356\pi\)
0.124224 + 0.992254i \(0.460356\pi\)
\(864\) −4.58313 + 3.32984i −0.155921 + 0.113283i
\(865\) 18.4851 + 56.8913i 0.628512 + 1.93436i
\(866\) 10.5969 32.6139i 0.360098 1.10827i
\(867\) 11.4108 + 8.29040i 0.387530 + 0.281557i
\(868\) −5.41156 −0.183680
\(869\) 20.5162 + 3.42214i 0.695965 + 0.116088i
\(870\) −16.8246 −0.570409
\(871\) 69.3157 + 50.3608i 2.34867 + 1.70641i
\(872\) 1.25827 3.87255i 0.0426103 0.131141i
\(873\) −0.802581 2.47009i −0.0271632 0.0835999i
\(874\) 24.5949 17.8692i 0.831935 0.604436i
\(875\) −21.4356 + 15.5739i −0.724655 + 0.526493i
\(876\) 2.13635 + 6.57501i 0.0721806 + 0.222149i
\(877\) 3.13396 9.64535i 0.105826 0.325700i −0.884097 0.467303i \(-0.845226\pi\)
0.989924 + 0.141603i \(0.0452256\pi\)
\(878\) −6.76369 4.91411i −0.228263 0.165843i
\(879\) −27.1918 −0.917156
\(880\) −0.0379312 0.252893i −0.00127866 0.00852501i
\(881\) −3.71883 −0.125291 −0.0626453 0.998036i \(-0.519954\pi\)
−0.0626453 + 0.998036i \(0.519954\pi\)
\(882\) −0.705143 0.512316i −0.0237434 0.0172506i
\(883\) 5.35542 16.4823i 0.180224 0.554673i −0.819609 0.572923i \(-0.805809\pi\)
0.999833 + 0.0182500i \(0.00580947\pi\)
\(884\) 3.97189 + 12.2242i 0.133589 + 0.411145i
\(885\) 15.2362 11.0697i 0.512158 0.372105i
\(886\) 0.443631 0.322316i 0.0149041 0.0108284i
\(887\) −1.67084 5.14232i −0.0561014 0.172662i 0.919079 0.394072i \(-0.128934\pi\)
−0.975181 + 0.221410i \(0.928934\pi\)
\(888\) −2.12908 + 6.55265i −0.0714474 + 0.219892i
\(889\) −0.519157 0.377189i −0.0174120 0.0126505i
\(890\) 28.7913 0.965087
\(891\) −2.32590 2.36436i −0.0779205 0.0792090i
\(892\) 4.16210 0.139357
\(893\) −37.3847 27.1616i −1.25103 0.908927i
\(894\) 2.71575 8.35821i 0.0908281 0.279540i
\(895\) 14.6826 + 45.1884i 0.490786 + 1.51048i
\(896\) −5.71124 + 4.14946i −0.190799 + 0.138624i
\(897\) −31.4909 + 22.8794i −1.05145 + 0.763923i
\(898\) −4.66939 14.3709i −0.155819 0.479563i
\(899\) −6.40339 + 19.7076i −0.213565 + 0.657286i
\(900\) 11.5586 + 8.39778i 0.385285 + 0.279926i
\(901\) −8.02152 −0.267236
\(902\) −4.28092 + 8.23414i −0.142539 + 0.274167i
\(903\) −0.127191 −0.00423264
\(904\) 44.5949 + 32.4001i 1.48320 + 1.07761i
\(905\) −24.7427 + 76.1501i −0.822474 + 2.53132i
\(906\) −4.03039 12.4043i −0.133901 0.412104i
\(907\) 8.65808 6.29046i 0.287487 0.208871i −0.434690 0.900580i \(-0.643142\pi\)
0.722176 + 0.691709i \(0.243142\pi\)
\(908\) 3.34936 2.43345i 0.111152 0.0807569i
\(909\) −1.86205 5.73081i −0.0617604 0.190079i
\(910\) −6.66678 + 20.5182i −0.221002 + 0.680173i
\(911\) 22.3053 + 16.2057i 0.739007 + 0.536920i 0.892400 0.451245i \(-0.149020\pi\)
−0.153393 + 0.988165i \(0.549020\pi\)
\(912\) 0.103524 0.00342803
\(913\) −0.195402 + 0.375846i −0.00646685 + 0.0124387i
\(914\) −25.3771 −0.839400
\(915\) 17.4627 + 12.6874i 0.577299 + 0.419432i
\(916\) −2.60682 + 8.02298i −0.0861319 + 0.265087i
\(917\) 4.32584 + 13.3136i 0.142852 + 0.439653i
\(918\) −1.19989 + 0.871770i −0.0396022 + 0.0287727i
\(919\) −29.4499 + 21.3966i −0.971464 + 0.705810i −0.955785 0.294067i \(-0.904991\pi\)
−0.0156789 + 0.999877i \(0.504991\pi\)
\(920\) −22.6718 69.7765i −0.747466 2.30046i
\(921\) −3.07584 + 9.46647i −0.101352 + 0.311931i
\(922\) −10.7076 7.77952i −0.352636 0.256205i
\(923\) −13.5128 −0.444781
\(924\) −2.88483 2.93253i −0.0949038 0.0964731i
\(925\) 28.1010 0.923956
\(926\) −12.6140 9.16463i −0.414523 0.301168i
\(927\) 3.98440 12.2627i 0.130865 0.402761i
\(928\) 8.31421 + 25.5885i 0.272927 + 0.839984i
\(929\) −21.2287 + 15.4235i −0.696491 + 0.506030i −0.878787 0.477214i \(-0.841647\pi\)
0.182297 + 0.983244i \(0.441647\pi\)
\(930\) −12.5044 + 9.08500i −0.410036 + 0.297909i
\(931\) 1.68634 + 5.19003i 0.0552676 + 0.170096i
\(932\) −2.37076 + 7.29646i −0.0776569 + 0.239003i
\(933\) −13.1390 9.54602i −0.430150 0.312523i
\(934\) −26.4184 −0.864437
\(935\) −3.40237 22.6841i −0.111270 0.741850i
\(936\) 17.2000 0.562198
\(937\) −19.3192 14.0362i −0.631131 0.458544i 0.225661 0.974206i \(-0.427546\pi\)
−0.856792 + 0.515662i \(0.827546\pi\)
\(938\) −3.78925 + 11.6621i −0.123724 + 0.380782i
\(939\) 5.13426 + 15.8016i 0.167550 + 0.515667i
\(940\) −34.5344 + 25.0907i −1.12639 + 0.818369i
\(941\) −14.3837 + 10.4504i −0.468896 + 0.340673i −0.797011 0.603965i \(-0.793587\pi\)
0.328115 + 0.944638i \(0.393587\pi\)
\(942\) 5.23976 + 16.1263i 0.170720 + 0.525424i
\(943\) 6.34077 19.5149i 0.206484 0.635492i
\(944\) −0.0711151 0.0516681i −0.00231460 0.00168165i
\(945\) 4.06436 0.132214
\(946\) 0.362671 + 0.0604940i 0.0117914 + 0.00196683i
\(947\) 31.7071 1.03034 0.515171 0.857088i \(-0.327729\pi\)
0.515171 + 0.857088i \(0.327729\pi\)
\(948\) 6.29284 + 4.57202i 0.204382 + 0.148492i
\(949\) 10.4898 32.2842i 0.340512 1.04799i
\(950\) 16.9310 + 52.1082i 0.549313 + 1.69061i
\(951\) −6.55305 + 4.76107i −0.212497 + 0.154388i
\(952\) −3.88801 + 2.82480i −0.126011 + 0.0915523i
\(953\) −1.01423 3.12149i −0.0328543 0.101115i 0.933285 0.359138i \(-0.116929\pi\)
−0.966139 + 0.258023i \(0.916929\pi\)
\(954\) −1.26968 + 3.90768i −0.0411075 + 0.126516i
\(955\) 22.8918 + 16.6319i 0.740762 + 0.538195i
\(956\) −25.3995 −0.821478
\(957\) −14.0931 + 7.03584i −0.455566 + 0.227436i
\(958\) −6.92707 −0.223804
\(959\) −2.18449 1.58712i −0.0705407 0.0512508i
\(960\) −6.15388 + 18.9397i −0.198616 + 0.611276i
\(961\) −3.69691 11.3779i −0.119255 0.367030i
\(962\) 10.4762 7.61141i 0.337766 0.245402i
\(963\) 4.32630 3.14324i 0.139413 0.101289i
\(964\) −0.399041 1.22812i −0.0128522 0.0395551i
\(965\) −21.1796 + 65.1840i −0.681795 + 2.09835i
\(966\) −4.50694 3.27449i −0.145008 0.105355i
\(967\) −3.83683 −0.123384 −0.0616921 0.998095i \(-0.519650\pi\)
−0.0616921 + 0.998095i \(0.519650\pi\)
\(968\) 17.8460 + 25.4297i 0.573593 + 0.817343i
\(969\) 9.28597 0.298308
\(970\) −7.44348 5.40800i −0.238996 0.173641i
\(971\) 13.6977 42.1573i 0.439581 1.35289i −0.448738 0.893663i \(-0.648126\pi\)
0.888319 0.459228i \(-0.151874\pi\)
\(972\) −0.383276 1.17960i −0.0122936 0.0378357i
\(973\) −1.66813 + 1.21197i −0.0534777 + 0.0388538i
\(974\) 7.17207 5.21082i 0.229808 0.166965i
\(975\) −21.6781 66.7183i −0.694255 2.13670i
\(976\) 0.0311330 0.0958176i 0.000996544 0.00306705i
\(977\) −7.84564 5.70019i −0.251004 0.182365i 0.455168 0.890406i \(-0.349579\pi\)
−0.706172 + 0.708041i \(0.749579\pi\)
\(978\) 10.5555 0.337528
\(979\) 24.1170 12.0401i 0.770782 0.384804i
\(980\) 5.04106 0.161031
\(981\) 1.16639 + 0.847429i 0.0372399 + 0.0270563i
\(982\) 0.290177 0.893073i 0.00925992 0.0284991i
\(983\) 8.86112 + 27.2717i 0.282626 + 0.869833i 0.987100 + 0.160104i \(0.0511829\pi\)
−0.704474 + 0.709730i \(0.748817\pi\)
\(984\) −7.33530 + 5.32941i −0.233841 + 0.169895i
\(985\) 21.1146 15.3407i 0.672768 0.488795i
\(986\) 2.17670 + 6.69921i 0.0693204 + 0.213346i
\(987\) −2.61671 + 8.05340i −0.0832907 + 0.256342i
\(988\) −33.3481 24.2288i −1.06095 0.770822i
\(989\) −0.812944 −0.0258501
\(990\) −11.5891 1.93308i −0.368325 0.0614372i
\(991\) −14.0455 −0.446170 −0.223085 0.974799i \(-0.571613\pi\)
−0.223085 + 0.974799i \(0.571613\pi\)
\(992\) 19.9966 + 14.5284i 0.634893 + 0.461277i
\(993\) −2.05374 + 6.32077i −0.0651736 + 0.200584i
\(994\) −0.597622 1.83929i −0.0189554 0.0583388i
\(995\) −43.6156 + 31.6886i −1.38271 + 1.00460i
\(996\) −0.128160 + 0.0931136i −0.00406090 + 0.00295042i
\(997\) −11.1896 34.4379i −0.354377 1.09066i −0.956370 0.292159i \(-0.905626\pi\)
0.601993 0.798501i \(-0.294374\pi\)
\(998\) 9.32347 28.6947i 0.295129 0.908314i
\(999\) −1.97362 1.43392i −0.0624424 0.0453671i
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 231.2.j.g.169.2 20
3.2 odd 2 693.2.m.j.631.4 20
11.3 even 5 inner 231.2.j.g.190.2 yes 20
11.5 even 5 2541.2.a.bq.1.7 10
11.6 odd 10 2541.2.a.br.1.4 10
33.5 odd 10 7623.2.a.cx.1.4 10
33.14 odd 10 693.2.m.j.190.4 20
33.17 even 10 7623.2.a.cy.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.169.2 20 1.1 even 1 trivial
231.2.j.g.190.2 yes 20 11.3 even 5 inner
693.2.m.j.190.4 20 33.14 odd 10
693.2.m.j.631.4 20 3.2 odd 2
2541.2.a.bq.1.7 10 11.5 even 5
2541.2.a.br.1.4 10 11.6 odd 10
7623.2.a.cx.1.4 10 33.5 odd 10
7623.2.a.cy.1.7 10 33.17 even 10