Properties

Label 154.2.f.c.113.1
Level $154$
Weight $2$
Character 154.113
Analytic conductor $1.230$
Analytic rank $0$
Dimension $4$
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] = [154,2,Mod(15,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([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("154.15");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.f (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: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 113.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 154.113
Dual form 154.2.f.c.15.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} -2.00000 q^{10} +(2.54508 - 2.12663i) q^{11} -1.61803 q^{12} +(-2.61803 + 1.90211i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.00000 + 3.07768i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.73607 + 3.44095i) q^{17} +(0.118034 - 0.363271i) q^{18} +(-0.0450850 - 0.138757i) q^{19} +(-1.61803 + 1.17557i) q^{20} +1.61803 q^{21} +(0.809017 - 3.21644i) q^{22} +8.47214 q^{23} +(-1.30902 + 0.951057i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-1.00000 + 3.07768i) q^{26} +(-4.42705 - 3.21644i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.47214 + 7.60845i) q^{29} +(1.00000 + 3.07768i) q^{30} +(3.61803 - 2.62866i) q^{31} -1.00000 q^{32} +(-4.54508 - 2.85317i) q^{33} +5.85410 q^{34} +(1.61803 - 1.17557i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-2.38197 + 7.33094i) q^{37} +(-0.118034 - 0.0857567i) q^{38} +(4.23607 + 3.07768i) q^{39} +(-0.618034 + 1.90211i) q^{40} +(0.263932 + 0.812299i) q^{41} +(1.30902 - 0.951057i) q^{42} -4.85410 q^{43} +(-1.23607 - 3.07768i) q^{44} -0.763932 q^{45} +(6.85410 - 4.97980i) q^{46} +(0.527864 + 1.62460i) q^{47} +(-0.500000 + 1.53884i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(2.92705 - 9.00854i) q^{51} +(1.00000 + 3.07768i) q^{52} +(-4.00000 + 2.90617i) q^{53} -5.47214 q^{54} +(-6.61803 + 0.449028i) q^{55} +1.00000 q^{56} +(-0.190983 + 0.138757i) q^{57} +(2.47214 + 7.60845i) q^{58} +(1.28115 - 3.94298i) q^{59} +(2.61803 + 1.90211i) q^{60} +(-5.23607 - 3.80423i) q^{61} +(1.38197 - 4.25325i) q^{62} +(0.118034 + 0.363271i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.47214 q^{65} +(-5.35410 + 0.363271i) q^{66} +1.09017 q^{67} +(4.73607 - 3.44095i) q^{68} +(-4.23607 - 13.0373i) q^{69} +(0.618034 - 1.90211i) q^{70} +(-8.47214 - 6.15537i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(-0.736068 + 2.26538i) q^{73} +(2.38197 + 7.33094i) q^{74} +(-1.30902 + 0.951057i) q^{75} -0.145898 q^{76} +(1.23607 + 3.07768i) q^{77} +5.23607 q^{78} +(1.00000 - 0.726543i) q^{79} +(0.618034 + 1.90211i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(0.690983 + 0.502029i) q^{82} +(10.5451 + 7.66145i) q^{83} +(0.500000 - 1.53884i) q^{84} +(-3.61803 - 11.1352i) q^{85} +(-3.92705 + 2.85317i) q^{86} +12.9443 q^{87} +(-2.80902 - 1.76336i) q^{88} -15.3262 q^{89} +(-0.618034 + 0.449028i) q^{90} +(-1.00000 - 3.07768i) q^{91} +(2.61803 - 8.05748i) q^{92} +(-5.85410 - 4.25325i) q^{93} +(1.38197 + 1.00406i) q^{94} +(-0.0901699 + 0.277515i) q^{95} +(0.500000 + 1.53884i) q^{96} +(2.54508 - 1.84911i) q^{97} -1.00000 q^{98} +(0.309017 - 1.22857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} - 6 q^{13} - q^{14} - 4 q^{15} - q^{16} + 10 q^{17} - 4 q^{18} + 11 q^{19} - 2 q^{20} + 2 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + q^{25} - 4 q^{26} - 11 q^{27} + q^{28} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 4 q^{32} - 7 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} - 14 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 10 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 12 q^{45} + 14 q^{46} + 20 q^{47} - 2 q^{48} - q^{49} - q^{50} + 5 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 22 q^{55} + 4 q^{56} - 3 q^{57} - 8 q^{58} - 15 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} - 4 q^{63} - q^{64} + 8 q^{65} - 8 q^{66} - 18 q^{67} + 10 q^{68} - 8 q^{69} - 2 q^{70} - 16 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} - 3 q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 4 q^{79} - 2 q^{80} - 14 q^{81} + 5 q^{82} + 31 q^{83} + 2 q^{84} - 10 q^{85} - 9 q^{86} + 16 q^{87} - 9 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 6 q^{92} - 10 q^{93} + 10 q^{94} + 22 q^{95} + 2 q^{96} - q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) −0.500000 1.53884i −0.288675 0.888451i −0.985273 0.170989i \(-0.945304\pi\)
0.696598 0.717462i \(-0.254696\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −1.61803 1.17557i −0.723607 0.525731i 0.163928 0.986472i \(-0.447584\pi\)
−0.887535 + 0.460741i \(0.847584\pi\)
\(6\) −1.30902 0.951057i −0.534404 0.388267i
\(7\) −0.309017 + 0.951057i −0.116797 + 0.359466i
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0.309017 0.224514i 0.103006 0.0748380i
\(10\) −2.00000 −0.632456
\(11\) 2.54508 2.12663i 0.767372 0.641202i
\(12\) −1.61803 −0.467086
\(13\) −2.61803 + 1.90211i −0.726112 + 0.527551i −0.888331 0.459204i \(-0.848135\pi\)
0.162219 + 0.986755i \(0.448135\pi\)
\(14\) 0.309017 + 0.951057i 0.0825883 + 0.254181i
\(15\) −1.00000 + 3.07768i −0.258199 + 0.794654i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 4.73607 + 3.44095i 1.14867 + 0.834554i 0.988303 0.152504i \(-0.0487337\pi\)
0.160362 + 0.987058i \(0.448734\pi\)
\(18\) 0.118034 0.363271i 0.0278209 0.0856239i
\(19\) −0.0450850 0.138757i −0.0103432 0.0318331i 0.945752 0.324890i \(-0.105327\pi\)
−0.956095 + 0.293057i \(0.905327\pi\)
\(20\) −1.61803 + 1.17557i −0.361803 + 0.262866i
\(21\) 1.61803 0.353084
\(22\) 0.809017 3.21644i 0.172483 0.685747i
\(23\) 8.47214 1.76656 0.883281 0.468844i \(-0.155329\pi\)
0.883281 + 0.468844i \(0.155329\pi\)
\(24\) −1.30902 + 0.951057i −0.267202 + 0.194134i
\(25\) −0.309017 0.951057i −0.0618034 0.190211i
\(26\) −1.00000 + 3.07768i −0.196116 + 0.603583i
\(27\) −4.42705 3.21644i −0.851986 0.619004i
\(28\) 0.809017 + 0.587785i 0.152890 + 0.111081i
\(29\) −2.47214 + 7.60845i −0.459064 + 1.41285i 0.407233 + 0.913324i \(0.366494\pi\)
−0.866297 + 0.499530i \(0.833506\pi\)
\(30\) 1.00000 + 3.07768i 0.182574 + 0.561906i
\(31\) 3.61803 2.62866i 0.649818 0.472120i −0.213391 0.976967i \(-0.568451\pi\)
0.863209 + 0.504846i \(0.168451\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.54508 2.85317i −0.791198 0.496673i
\(34\) 5.85410 1.00397
\(35\) 1.61803 1.17557i 0.273498 0.198708i
\(36\) −0.118034 0.363271i −0.0196723 0.0605452i
\(37\) −2.38197 + 7.33094i −0.391593 + 1.20520i 0.539991 + 0.841671i \(0.318428\pi\)
−0.931583 + 0.363528i \(0.881572\pi\)
\(38\) −0.118034 0.0857567i −0.0191476 0.0139116i
\(39\) 4.23607 + 3.07768i 0.678314 + 0.492824i
\(40\) −0.618034 + 1.90211i −0.0977198 + 0.300750i
\(41\) 0.263932 + 0.812299i 0.0412193 + 0.126860i 0.969549 0.244899i \(-0.0787548\pi\)
−0.928329 + 0.371759i \(0.878755\pi\)
\(42\) 1.30902 0.951057i 0.201986 0.146751i
\(43\) −4.85410 −0.740244 −0.370122 0.928983i \(-0.620684\pi\)
−0.370122 + 0.928983i \(0.620684\pi\)
\(44\) −1.23607 3.07768i −0.186344 0.463978i
\(45\) −0.763932 −0.113880
\(46\) 6.85410 4.97980i 1.01058 0.734231i
\(47\) 0.527864 + 1.62460i 0.0769969 + 0.236972i 0.982145 0.188123i \(-0.0602405\pi\)
−0.905149 + 0.425096i \(0.860241\pi\)
\(48\) −0.500000 + 1.53884i −0.0721688 + 0.222113i
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) −0.809017 0.587785i −0.114412 0.0831254i
\(51\) 2.92705 9.00854i 0.409869 1.26145i
\(52\) 1.00000 + 3.07768i 0.138675 + 0.426798i
\(53\) −4.00000 + 2.90617i −0.549442 + 0.399193i −0.827580 0.561348i \(-0.810283\pi\)
0.278138 + 0.960541i \(0.410283\pi\)
\(54\) −5.47214 −0.744663
\(55\) −6.61803 + 0.449028i −0.892376 + 0.0605469i
\(56\) 1.00000 0.133631
\(57\) −0.190983 + 0.138757i −0.0252963 + 0.0183789i
\(58\) 2.47214 + 7.60845i 0.324607 + 0.999039i
\(59\) 1.28115 3.94298i 0.166792 0.513333i −0.832372 0.554217i \(-0.813018\pi\)
0.999164 + 0.0408847i \(0.0130176\pi\)
\(60\) 2.61803 + 1.90211i 0.337987 + 0.245562i
\(61\) −5.23607 3.80423i −0.670410 0.487081i 0.199753 0.979846i \(-0.435986\pi\)
−0.870162 + 0.492765i \(0.835986\pi\)
\(62\) 1.38197 4.25325i 0.175510 0.540164i
\(63\) 0.118034 + 0.363271i 0.0148709 + 0.0457679i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 6.47214 0.802770
\(66\) −5.35410 + 0.363271i −0.659044 + 0.0447156i
\(67\) 1.09017 0.133185 0.0665927 0.997780i \(-0.478787\pi\)
0.0665927 + 0.997780i \(0.478787\pi\)
\(68\) 4.73607 3.44095i 0.574333 0.417277i
\(69\) −4.23607 13.0373i −0.509963 1.56950i
\(70\) 0.618034 1.90211i 0.0738692 0.227346i
\(71\) −8.47214 6.15537i −1.00546 0.730508i −0.0422061 0.999109i \(-0.513439\pi\)
−0.963251 + 0.268601i \(0.913439\pi\)
\(72\) −0.309017 0.224514i −0.0364180 0.0264592i
\(73\) −0.736068 + 2.26538i −0.0861502 + 0.265143i −0.984846 0.173428i \(-0.944515\pi\)
0.898696 + 0.438572i \(0.144515\pi\)
\(74\) 2.38197 + 7.33094i 0.276898 + 0.852204i
\(75\) −1.30902 + 0.951057i −0.151152 + 0.109819i
\(76\) −0.145898 −0.0167357
\(77\) 1.23607 + 3.07768i 0.140863 + 0.350735i
\(78\) 5.23607 0.592868
\(79\) 1.00000 0.726543i 0.112509 0.0817424i −0.530108 0.847930i \(-0.677849\pi\)
0.642617 + 0.766188i \(0.277849\pi\)
\(80\) 0.618034 + 1.90211i 0.0690983 + 0.212663i
\(81\) −2.38197 + 7.33094i −0.264663 + 0.814549i
\(82\) 0.690983 + 0.502029i 0.0763063 + 0.0554398i
\(83\) 10.5451 + 7.66145i 1.15747 + 0.840954i 0.989456 0.144830i \(-0.0462637\pi\)
0.168017 + 0.985784i \(0.446264\pi\)
\(84\) 0.500000 1.53884i 0.0545545 0.167901i
\(85\) −3.61803 11.1352i −0.392431 1.20778i
\(86\) −3.92705 + 2.85317i −0.423465 + 0.307665i
\(87\) 12.9443 1.38777
\(88\) −2.80902 1.76336i −0.299442 0.187974i
\(89\) −15.3262 −1.62458 −0.812289 0.583255i \(-0.801779\pi\)
−0.812289 + 0.583255i \(0.801779\pi\)
\(90\) −0.618034 + 0.449028i −0.0651465 + 0.0473317i
\(91\) −1.00000 3.07768i −0.104828 0.322629i
\(92\) 2.61803 8.05748i 0.272949 0.840050i
\(93\) −5.85410 4.25325i −0.607042 0.441042i
\(94\) 1.38197 + 1.00406i 0.142539 + 0.103561i
\(95\) −0.0901699 + 0.277515i −0.00925124 + 0.0284724i
\(96\) 0.500000 + 1.53884i 0.0510310 + 0.157057i
\(97\) 2.54508 1.84911i 0.258414 0.187749i −0.451033 0.892507i \(-0.648944\pi\)
0.709448 + 0.704758i \(0.248944\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.309017 1.22857i 0.0310574 0.123476i
\(100\) −1.00000 −0.100000
\(101\) 15.0902 10.9637i 1.50153 1.09092i 0.531760 0.846895i \(-0.321531\pi\)
0.969768 0.244029i \(-0.0784692\pi\)
\(102\) −2.92705 9.00854i −0.289821 0.891978i
\(103\) −3.00000 + 9.23305i −0.295599 + 0.909760i 0.687421 + 0.726259i \(0.258743\pi\)
−0.983020 + 0.183500i \(0.941257\pi\)
\(104\) 2.61803 + 1.90211i 0.256719 + 0.186518i
\(105\) −2.61803 1.90211i −0.255494 0.185627i
\(106\) −1.52786 + 4.70228i −0.148399 + 0.456726i
\(107\) −2.26393 6.96767i −0.218863 0.673590i −0.998857 0.0478030i \(-0.984778\pi\)
0.779994 0.625787i \(-0.215222\pi\)
\(108\) −4.42705 + 3.21644i −0.425993 + 0.309502i
\(109\) −10.1803 −0.975100 −0.487550 0.873095i \(-0.662109\pi\)
−0.487550 + 0.873095i \(0.662109\pi\)
\(110\) −5.09017 + 4.25325i −0.485329 + 0.405532i
\(111\) 12.4721 1.18380
\(112\) 0.809017 0.587785i 0.0764449 0.0555405i
\(113\) 1.42705 + 4.39201i 0.134246 + 0.413166i 0.995472 0.0950561i \(-0.0303030\pi\)
−0.861226 + 0.508222i \(0.830303\pi\)
\(114\) −0.0729490 + 0.224514i −0.00683230 + 0.0210277i
\(115\) −13.7082 9.95959i −1.27830 0.928737i
\(116\) 6.47214 + 4.70228i 0.600923 + 0.436596i
\(117\) −0.381966 + 1.17557i −0.0353128 + 0.108682i
\(118\) −1.28115 3.94298i −0.117940 0.362981i
\(119\) −4.73607 + 3.44095i −0.434155 + 0.315432i
\(120\) 3.23607 0.295411
\(121\) 1.95492 10.8249i 0.177720 0.984081i
\(122\) −6.47214 −0.585960
\(123\) 1.11803 0.812299i 0.100810 0.0732426i
\(124\) −1.38197 4.25325i −0.124104 0.381953i
\(125\) −3.70820 + 11.4127i −0.331672 + 1.02078i
\(126\) 0.309017 + 0.224514i 0.0275294 + 0.0200013i
\(127\) 7.09017 + 5.15131i 0.629151 + 0.457105i 0.856106 0.516800i \(-0.172877\pi\)
−0.226955 + 0.973905i \(0.572877\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 2.42705 + 7.46969i 0.213690 + 0.657670i
\(130\) 5.23607 3.80423i 0.459234 0.333653i
\(131\) 15.5623 1.35968 0.679842 0.733358i \(-0.262048\pi\)
0.679842 + 0.733358i \(0.262048\pi\)
\(132\) −4.11803 + 3.44095i −0.358429 + 0.299497i
\(133\) 0.145898 0.0126510
\(134\) 0.881966 0.640786i 0.0761903 0.0553555i
\(135\) 3.38197 + 10.4086i 0.291073 + 0.895831i
\(136\) 1.80902 5.56758i 0.155122 0.477416i
\(137\) 15.6353 + 11.3597i 1.33581 + 0.970523i 0.999587 + 0.0287404i \(0.00914961\pi\)
0.336223 + 0.941782i \(0.390850\pi\)
\(138\) −11.0902 8.05748i −0.944058 0.685898i
\(139\) −4.47214 + 13.7638i −0.379322 + 1.16743i 0.561195 + 0.827684i \(0.310342\pi\)
−0.940516 + 0.339748i \(0.889658\pi\)
\(140\) −0.618034 1.90211i −0.0522334 0.160758i
\(141\) 2.23607 1.62460i 0.188311 0.136816i
\(142\) −10.4721 −0.878802
\(143\) −2.61803 + 10.4086i −0.218931 + 0.870413i
\(144\) −0.381966 −0.0318305
\(145\) 12.9443 9.40456i 1.07496 0.781007i
\(146\) 0.736068 + 2.26538i 0.0609174 + 0.187485i
\(147\) −0.500000 + 1.53884i −0.0412393 + 0.126922i
\(148\) 6.23607 + 4.53077i 0.512602 + 0.372427i
\(149\) 8.70820 + 6.32688i 0.713404 + 0.518318i 0.884270 0.466976i \(-0.154657\pi\)
−0.170866 + 0.985294i \(0.554657\pi\)
\(150\) −0.500000 + 1.53884i −0.0408248 + 0.125646i
\(151\) −0.708204 2.17963i −0.0576328 0.177376i 0.918096 0.396358i \(-0.129726\pi\)
−0.975729 + 0.218983i \(0.929726\pi\)
\(152\) −0.118034 + 0.0857567i −0.00957382 + 0.00695579i
\(153\) 2.23607 0.180775
\(154\) 2.80902 + 1.76336i 0.226357 + 0.142095i
\(155\) −8.94427 −0.718421
\(156\) 4.23607 3.07768i 0.339157 0.246412i
\(157\) −0.854102 2.62866i −0.0681648 0.209790i 0.911172 0.412026i \(-0.135179\pi\)
−0.979337 + 0.202237i \(0.935179\pi\)
\(158\) 0.381966 1.17557i 0.0303876 0.0935234i
\(159\) 6.47214 + 4.70228i 0.513274 + 0.372915i
\(160\) 1.61803 + 1.17557i 0.127917 + 0.0929370i
\(161\) −2.61803 + 8.05748i −0.206330 + 0.635018i
\(162\) 2.38197 + 7.33094i 0.187145 + 0.575973i
\(163\) −18.8262 + 13.6781i −1.47458 + 1.07135i −0.495333 + 0.868703i \(0.664954\pi\)
−0.979252 + 0.202645i \(0.935046\pi\)
\(164\) 0.854102 0.0666942
\(165\) 4.00000 + 9.95959i 0.311400 + 0.775353i
\(166\) 13.0344 1.01167
\(167\) −13.3262 + 9.68208i −1.03122 + 0.749222i −0.968552 0.248813i \(-0.919960\pi\)
−0.0626637 + 0.998035i \(0.519960\pi\)
\(168\) −0.500000 1.53884i −0.0385758 0.118724i
\(169\) −0.781153 + 2.40414i −0.0600887 + 0.184934i
\(170\) −9.47214 6.88191i −0.726480 0.527818i
\(171\) −0.0450850 0.0327561i −0.00344773 0.00250493i
\(172\) −1.50000 + 4.61653i −0.114374 + 0.352007i
\(173\) 0.708204 + 2.17963i 0.0538437 + 0.165714i 0.974362 0.224985i \(-0.0722333\pi\)
−0.920518 + 0.390699i \(0.872233\pi\)
\(174\) 10.4721 7.60845i 0.793891 0.576795i
\(175\) 1.00000 0.0755929
\(176\) −3.30902 + 0.224514i −0.249427 + 0.0169234i
\(177\) −6.70820 −0.504219
\(178\) −12.3992 + 9.00854i −0.929358 + 0.675218i
\(179\) −7.57295 23.3071i −0.566029 1.74206i −0.664875 0.746955i \(-0.731515\pi\)
0.0988461 0.995103i \(-0.468485\pi\)
\(180\) −0.236068 + 0.726543i −0.0175955 + 0.0541533i
\(181\) 15.1803 + 11.0292i 1.12835 + 0.819791i 0.985453 0.169947i \(-0.0543597\pi\)
0.142893 + 0.989738i \(0.454360\pi\)
\(182\) −2.61803 1.90211i −0.194062 0.140994i
\(183\) −3.23607 + 9.95959i −0.239217 + 0.736234i
\(184\) −2.61803 8.05748i −0.193004 0.594005i
\(185\) 12.4721 9.06154i 0.916970 0.666217i
\(186\) −7.23607 −0.530574
\(187\) 19.3713 1.31433i 1.41657 0.0961132i
\(188\) 1.70820 0.124584
\(189\) 4.42705 3.21644i 0.322021 0.233962i
\(190\) 0.0901699 + 0.277515i 0.00654162 + 0.0201330i
\(191\) 3.85410 11.8617i 0.278873 0.858283i −0.709296 0.704911i \(-0.750987\pi\)
0.988169 0.153372i \(-0.0490132\pi\)
\(192\) 1.30902 + 0.951057i 0.0944702 + 0.0686366i
\(193\) −14.0902 10.2371i −1.01423 0.736883i −0.0491400 0.998792i \(-0.515648\pi\)
−0.965093 + 0.261909i \(0.915648\pi\)
\(194\) 0.972136 2.99193i 0.0697953 0.214808i
\(195\) −3.23607 9.95959i −0.231740 0.713221i
\(196\) −0.809017 + 0.587785i −0.0577869 + 0.0419847i
\(197\) −3.52786 −0.251350 −0.125675 0.992071i \(-0.540110\pi\)
−0.125675 + 0.992071i \(0.540110\pi\)
\(198\) −0.472136 1.17557i −0.0335532 0.0835442i
\(199\) −20.1803 −1.43055 −0.715273 0.698845i \(-0.753698\pi\)
−0.715273 + 0.698845i \(0.753698\pi\)
\(200\) −0.809017 + 0.587785i −0.0572061 + 0.0415627i
\(201\) −0.545085 1.67760i −0.0384473 0.118329i
\(202\) 5.76393 17.7396i 0.405549 1.24815i
\(203\) −6.47214 4.70228i −0.454255 0.330035i
\(204\) −7.66312 5.56758i −0.536526 0.389809i
\(205\) 0.527864 1.62460i 0.0368676 0.113467i
\(206\) 3.00000 + 9.23305i 0.209020 + 0.643297i
\(207\) 2.61803 1.90211i 0.181966 0.132206i
\(208\) 3.23607 0.224381
\(209\) −0.409830 0.257270i −0.0283485 0.0177957i
\(210\) −3.23607 −0.223310
\(211\) 12.8713 9.35156i 0.886098 0.643788i −0.0487594 0.998811i \(-0.515527\pi\)
0.934858 + 0.355022i \(0.115527\pi\)
\(212\) 1.52786 + 4.70228i 0.104934 + 0.322954i
\(213\) −5.23607 + 16.1150i −0.358769 + 1.10418i
\(214\) −5.92705 4.30625i −0.405165 0.294370i
\(215\) 7.85410 + 5.70634i 0.535645 + 0.389169i
\(216\) −1.69098 + 5.20431i −0.115057 + 0.354108i
\(217\) 1.38197 + 4.25325i 0.0938140 + 0.288730i
\(218\) −8.23607 + 5.98385i −0.557817 + 0.405278i
\(219\) 3.85410 0.260436
\(220\) −1.61803 + 6.43288i −0.109088 + 0.433705i
\(221\) −18.9443 −1.27433
\(222\) 10.0902 7.33094i 0.677208 0.492020i
\(223\) −5.38197 16.5640i −0.360403 1.10921i −0.952810 0.303568i \(-0.901822\pi\)
0.592407 0.805639i \(-0.298178\pi\)
\(224\) 0.309017 0.951057i 0.0206471 0.0635451i
\(225\) −0.309017 0.224514i −0.0206011 0.0149676i
\(226\) 3.73607 + 2.71441i 0.248520 + 0.180560i
\(227\) 8.42705 25.9358i 0.559323 1.72142i −0.124922 0.992167i \(-0.539868\pi\)
0.684245 0.729253i \(-0.260132\pi\)
\(228\) 0.0729490 + 0.224514i 0.00483117 + 0.0148688i
\(229\) 18.4164 13.3803i 1.21699 0.884195i 0.221144 0.975241i \(-0.429021\pi\)
0.995847 + 0.0910459i \(0.0290210\pi\)
\(230\) −16.9443 −1.11727
\(231\) 4.11803 3.44095i 0.270947 0.226398i
\(232\) 8.00000 0.525226
\(233\) −6.39919 + 4.64928i −0.419225 + 0.304585i −0.777326 0.629098i \(-0.783424\pi\)
0.358101 + 0.933683i \(0.383424\pi\)
\(234\) 0.381966 + 1.17557i 0.0249699 + 0.0768494i
\(235\) 1.05573 3.24920i 0.0688681 0.211954i
\(236\) −3.35410 2.43690i −0.218333 0.158629i
\(237\) −1.61803 1.17557i −0.105103 0.0763615i
\(238\) −1.80902 + 5.56758i −0.117261 + 0.360893i
\(239\) 0.0901699 + 0.277515i 0.00583261 + 0.0179509i 0.953930 0.300028i \(-0.0969960\pi\)
−0.948098 + 0.317979i \(0.896996\pi\)
\(240\) 2.61803 1.90211i 0.168993 0.122781i
\(241\) −6.79837 −0.437922 −0.218961 0.975734i \(-0.570267\pi\)
−0.218961 + 0.975734i \(0.570267\pi\)
\(242\) −4.78115 9.90659i −0.307344 0.636820i
\(243\) −3.94427 −0.253025
\(244\) −5.23607 + 3.80423i −0.335205 + 0.243541i
\(245\) 0.618034 + 1.90211i 0.0394847 + 0.121522i
\(246\) 0.427051 1.31433i 0.0272278 0.0837985i
\(247\) 0.381966 + 0.277515i 0.0243039 + 0.0176578i
\(248\) −3.61803 2.62866i −0.229745 0.166920i
\(249\) 6.51722 20.0579i 0.413012 1.27112i
\(250\) 3.70820 + 11.4127i 0.234527 + 0.721801i
\(251\) 4.00000 2.90617i 0.252478 0.183436i −0.454346 0.890825i \(-0.650127\pi\)
0.706824 + 0.707389i \(0.250127\pi\)
\(252\) 0.381966 0.0240616
\(253\) 21.5623 18.0171i 1.35561 1.13272i
\(254\) 8.76393 0.549898
\(255\) −15.3262 + 11.1352i −0.959766 + 0.697311i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 7.91641 24.3642i 0.493812 1.51980i −0.324988 0.945718i \(-0.605360\pi\)
0.818800 0.574079i \(-0.194640\pi\)
\(258\) 6.35410 + 4.61653i 0.395589 + 0.287412i
\(259\) −6.23607 4.53077i −0.387490 0.281528i
\(260\) 2.00000 6.15537i 0.124035 0.381740i
\(261\) 0.944272 + 2.90617i 0.0584490 + 0.179887i
\(262\) 12.5902 9.14729i 0.777823 0.565122i
\(263\) −12.9443 −0.798178 −0.399089 0.916912i \(-0.630674\pi\)
−0.399089 + 0.916912i \(0.630674\pi\)
\(264\) −1.30902 + 5.20431i −0.0805644 + 0.320303i
\(265\) 9.88854 0.607448
\(266\) 0.118034 0.0857567i 0.00723713 0.00525808i
\(267\) 7.66312 + 23.5847i 0.468975 + 1.44336i
\(268\) 0.336881 1.03681i 0.0205783 0.0633334i
\(269\) 2.09017 + 1.51860i 0.127440 + 0.0925905i 0.649679 0.760208i \(-0.274903\pi\)
−0.522239 + 0.852799i \(0.674903\pi\)
\(270\) 8.85410 + 6.43288i 0.538843 + 0.391493i
\(271\) −5.76393 + 17.7396i −0.350134 + 1.07760i 0.608644 + 0.793444i \(0.291714\pi\)
−0.958778 + 0.284158i \(0.908286\pi\)
\(272\) −1.80902 5.56758i −0.109688 0.337584i
\(273\) −4.23607 + 3.07768i −0.256378 + 0.186270i
\(274\) 19.3262 1.16754
\(275\) −2.80902 1.76336i −0.169390 0.106334i
\(276\) −13.7082 −0.825137
\(277\) −18.7984 + 13.6578i −1.12948 + 0.820619i −0.985620 0.168979i \(-0.945953\pi\)
−0.143865 + 0.989597i \(0.545953\pi\)
\(278\) 4.47214 + 13.7638i 0.268221 + 0.825499i
\(279\) 0.527864 1.62460i 0.0316024 0.0972622i
\(280\) −1.61803 1.17557i −0.0966960 0.0702538i
\(281\) −7.92705 5.75934i −0.472888 0.343573i 0.325678 0.945481i \(-0.394408\pi\)
−0.798566 + 0.601907i \(0.794408\pi\)
\(282\) 0.854102 2.62866i 0.0508610 0.156534i
\(283\) 3.41641 + 10.5146i 0.203084 + 0.625029i 0.999787 + 0.0206574i \(0.00657592\pi\)
−0.796702 + 0.604372i \(0.793424\pi\)
\(284\) −8.47214 + 6.15537i −0.502729 + 0.365254i
\(285\) 0.472136 0.0279669
\(286\) 4.00000 + 9.95959i 0.236525 + 0.588923i
\(287\) −0.854102 −0.0504160
\(288\) −0.309017 + 0.224514i −0.0182090 + 0.0132296i
\(289\) 5.33688 + 16.4252i 0.313934 + 0.966190i
\(290\) 4.94427 15.2169i 0.290338 0.893567i
\(291\) −4.11803 2.99193i −0.241403 0.175390i
\(292\) 1.92705 + 1.40008i 0.112772 + 0.0819337i
\(293\) 8.09017 24.8990i 0.472633 1.45461i −0.376491 0.926420i \(-0.622869\pi\)
0.849124 0.528194i \(-0.177131\pi\)
\(294\) 0.500000 + 1.53884i 0.0291606 + 0.0897471i
\(295\) −6.70820 + 4.87380i −0.390567 + 0.283763i
\(296\) 7.70820 0.448030
\(297\) −18.1074 + 1.22857i −1.05070 + 0.0712889i
\(298\) 10.7639 0.623538
\(299\) −22.1803 + 16.1150i −1.28272 + 0.931952i
\(300\) 0.500000 + 1.53884i 0.0288675 + 0.0888451i
\(301\) 1.50000 4.61653i 0.0864586 0.266092i
\(302\) −1.85410 1.34708i −0.106692 0.0775160i
\(303\) −24.4164 17.7396i −1.40269 1.01911i
\(304\) −0.0450850 + 0.138757i −0.00258580 + 0.00795828i
\(305\) 4.00000 + 12.3107i 0.229039 + 0.704911i
\(306\) 1.80902 1.31433i 0.103415 0.0751351i
\(307\) −17.6180 −1.00551 −0.502757 0.864428i \(-0.667681\pi\)
−0.502757 + 0.864428i \(0.667681\pi\)
\(308\) 3.30902 0.224514i 0.188549 0.0127929i
\(309\) 15.7082 0.893609
\(310\) −7.23607 + 5.25731i −0.410981 + 0.298595i
\(311\) −1.32624 4.08174i −0.0752041 0.231454i 0.906387 0.422448i \(-0.138829\pi\)
−0.981591 + 0.190994i \(0.938829\pi\)
\(312\) 1.61803 4.97980i 0.0916031 0.281925i
\(313\) 8.73607 + 6.34712i 0.493792 + 0.358761i 0.806641 0.591042i \(-0.201283\pi\)
−0.312849 + 0.949803i \(0.601283\pi\)
\(314\) −2.23607 1.62460i −0.126189 0.0916814i
\(315\) 0.236068 0.726543i 0.0133009 0.0409360i
\(316\) −0.381966 1.17557i −0.0214873 0.0661310i
\(317\) −9.70820 + 7.05342i −0.545267 + 0.396160i −0.826037 0.563615i \(-0.809410\pi\)
0.280770 + 0.959775i \(0.409410\pi\)
\(318\) 8.00000 0.448618
\(319\) 9.88854 + 24.6215i 0.553652 + 1.37854i
\(320\) 2.00000 0.111803
\(321\) −9.59017 + 6.96767i −0.535271 + 0.388897i
\(322\) 2.61803 + 8.05748i 0.145897 + 0.449026i
\(323\) 0.263932 0.812299i 0.0146856 0.0451975i
\(324\) 6.23607 + 4.53077i 0.346448 + 0.251709i
\(325\) 2.61803 + 1.90211i 0.145222 + 0.105510i
\(326\) −7.19098 + 22.1316i −0.398272 + 1.22575i
\(327\) 5.09017 + 15.6659i 0.281487 + 0.866328i
\(328\) 0.690983 0.502029i 0.0381532 0.0277199i
\(329\) −1.70820 −0.0941763
\(330\) 9.09017 + 5.70634i 0.500397 + 0.314124i
\(331\) −4.27051 −0.234728 −0.117364 0.993089i \(-0.537444\pi\)
−0.117364 + 0.993089i \(0.537444\pi\)
\(332\) 10.5451 7.66145i 0.578737 0.420477i
\(333\) 0.909830 + 2.80017i 0.0498584 + 0.153448i
\(334\) −5.09017 + 15.6659i −0.278522 + 0.857202i
\(335\) −1.76393 1.28157i −0.0963739 0.0700197i
\(336\) −1.30902 0.951057i −0.0714127 0.0518844i
\(337\) 0.371323 1.14281i 0.0202272 0.0622531i −0.940433 0.339978i \(-0.889580\pi\)
0.960661 + 0.277725i \(0.0895804\pi\)
\(338\) 0.781153 + 2.40414i 0.0424891 + 0.130768i
\(339\) 6.04508 4.39201i 0.328324 0.238541i
\(340\) −11.7082 −0.634967
\(341\) 3.61803 14.3844i 0.195928 0.778957i
\(342\) −0.0557281 −0.00301343
\(343\) 0.809017 0.587785i 0.0436828 0.0317374i
\(344\) 1.50000 + 4.61653i 0.0808746 + 0.248906i
\(345\) −8.47214 + 26.0746i −0.456124 + 1.40381i
\(346\) 1.85410 + 1.34708i 0.0996771 + 0.0724197i
\(347\) −9.82624 7.13918i −0.527500 0.383251i 0.291922 0.956442i \(-0.405705\pi\)
−0.819422 + 0.573191i \(0.805705\pi\)
\(348\) 4.00000 12.3107i 0.214423 0.659925i
\(349\) −1.41641 4.35926i −0.0758186 0.233346i 0.905964 0.423356i \(-0.139148\pi\)
−0.981782 + 0.190010i \(0.939148\pi\)
\(350\) 0.809017 0.587785i 0.0432438 0.0314184i
\(351\) 17.7082 0.945194
\(352\) −2.54508 + 2.12663i −0.135653 + 0.113350i
\(353\) 1.27051 0.0676224 0.0338112 0.999428i \(-0.489236\pi\)
0.0338112 + 0.999428i \(0.489236\pi\)
\(354\) −5.42705 + 3.94298i −0.288445 + 0.209567i
\(355\) 6.47214 + 19.9192i 0.343505 + 1.05720i
\(356\) −4.73607 + 14.5761i −0.251011 + 0.772533i
\(357\) 7.66312 + 5.56758i 0.405575 + 0.294668i
\(358\) −19.8262 14.4046i −1.04785 0.761307i
\(359\) 5.32624 16.3925i 0.281108 0.865162i −0.706430 0.707783i \(-0.749696\pi\)
0.987538 0.157379i \(-0.0503044\pi\)
\(360\) 0.236068 + 0.726543i 0.0124419 + 0.0382922i
\(361\) 15.3541 11.1554i 0.808111 0.587127i
\(362\) 18.7639 0.986210
\(363\) −17.6353 + 2.40414i −0.925611 + 0.126185i
\(364\) −3.23607 −0.169616
\(365\) 3.85410 2.80017i 0.201733 0.146568i
\(366\) 3.23607 + 9.95959i 0.169152 + 0.520596i
\(367\) −3.70820 + 11.4127i −0.193567 + 0.595737i 0.806424 + 0.591338i \(0.201400\pi\)
−0.999990 + 0.00439874i \(0.998600\pi\)
\(368\) −6.85410 4.97980i −0.357295 0.259590i
\(369\) 0.263932 + 0.191758i 0.0137398 + 0.00998251i
\(370\) 4.76393 14.6619i 0.247665 0.762235i
\(371\) −1.52786 4.70228i −0.0793227 0.244130i
\(372\) −5.85410 + 4.25325i −0.303521 + 0.220521i
\(373\) 30.4721 1.57779 0.788894 0.614530i \(-0.210654\pi\)
0.788894 + 0.614530i \(0.210654\pi\)
\(374\) 14.8992 12.4495i 0.770419 0.643748i
\(375\) 19.4164 1.00266
\(376\) 1.38197 1.00406i 0.0712695 0.0517803i
\(377\) −8.00000 24.6215i −0.412021 1.26807i
\(378\) 1.69098 5.20431i 0.0869748 0.267681i
\(379\) 10.3992 + 7.55545i 0.534170 + 0.388097i 0.821915 0.569610i \(-0.192906\pi\)
−0.287745 + 0.957707i \(0.592906\pi\)
\(380\) 0.236068 + 0.171513i 0.0121100 + 0.00879845i
\(381\) 4.38197 13.4863i 0.224495 0.690924i
\(382\) −3.85410 11.8617i −0.197193 0.606898i
\(383\) −2.70820 + 1.96763i −0.138383 + 0.100541i −0.654823 0.755782i \(-0.727257\pi\)
0.516440 + 0.856323i \(0.327257\pi\)
\(384\) 1.61803 0.0825700
\(385\) 1.61803 6.43288i 0.0824626 0.327850i
\(386\) −17.4164 −0.886472
\(387\) −1.50000 + 1.08981i −0.0762493 + 0.0553983i
\(388\) −0.972136 2.99193i −0.0493527 0.151892i
\(389\) 2.00000 6.15537i 0.101404 0.312089i −0.887466 0.460874i \(-0.847536\pi\)
0.988870 + 0.148784i \(0.0475360\pi\)
\(390\) −8.47214 6.15537i −0.429003 0.311689i
\(391\) 40.1246 + 29.1522i 2.02919 + 1.47429i
\(392\) −0.309017 + 0.951057i −0.0156077 + 0.0480356i
\(393\) −7.78115 23.9479i −0.392507 1.20801i
\(394\) −2.85410 + 2.07363i −0.143788 + 0.104468i
\(395\) −2.47214 −0.124387
\(396\) −1.07295 0.673542i −0.0539177 0.0338468i
\(397\) −31.5967 −1.58580 −0.792898 0.609355i \(-0.791429\pi\)
−0.792898 + 0.609355i \(0.791429\pi\)
\(398\) −16.3262 + 11.8617i −0.818360 + 0.594574i
\(399\) −0.0729490 0.224514i −0.00365202 0.0112398i
\(400\) −0.309017 + 0.951057i −0.0154508 + 0.0475528i
\(401\) −3.78115 2.74717i −0.188822 0.137187i 0.489358 0.872083i \(-0.337231\pi\)
−0.678180 + 0.734896i \(0.737231\pi\)
\(402\) −1.42705 1.03681i −0.0711748 0.0517115i
\(403\) −4.47214 + 13.7638i −0.222773 + 0.685625i
\(404\) −5.76393 17.7396i −0.286766 0.882576i
\(405\) 12.4721 9.06154i 0.619745 0.450271i
\(406\) −8.00000 −0.397033
\(407\) 9.52786 + 23.7234i 0.472279 + 1.17593i
\(408\) −9.47214 −0.468941
\(409\) −14.8541 + 10.7921i −0.734488 + 0.533637i −0.890980 0.454042i \(-0.849981\pi\)
0.156492 + 0.987679i \(0.449981\pi\)
\(410\) −0.527864 1.62460i −0.0260693 0.0802332i
\(411\) 9.66312 29.7400i 0.476647 1.46697i
\(412\) 7.85410 + 5.70634i 0.386944 + 0.281131i
\(413\) 3.35410 + 2.43690i 0.165045 + 0.119912i
\(414\) 1.00000 3.07768i 0.0491473 0.151260i
\(415\) −8.05573 24.7930i −0.395440 1.21704i
\(416\) 2.61803 1.90211i 0.128360 0.0932588i
\(417\) 23.4164 1.14671
\(418\) −0.482779 + 0.0327561i −0.0236135 + 0.00160216i
\(419\) 11.5066 0.562133 0.281067 0.959688i \(-0.409312\pi\)
0.281067 + 0.959688i \(0.409312\pi\)
\(420\) −2.61803 + 1.90211i −0.127747 + 0.0928136i
\(421\) −1.38197 4.25325i −0.0673529 0.207291i 0.911716 0.410822i \(-0.134758\pi\)
−0.979068 + 0.203531i \(0.934758\pi\)
\(422\) 4.91641 15.1311i 0.239327 0.736573i
\(423\) 0.527864 + 0.383516i 0.0256656 + 0.0186472i
\(424\) 4.00000 + 2.90617i 0.194257 + 0.141136i
\(425\) 1.80902 5.56758i 0.0877502 0.270067i
\(426\) 5.23607 + 16.1150i 0.253688 + 0.780772i
\(427\) 5.23607 3.80423i 0.253391 0.184099i
\(428\) −7.32624 −0.354127
\(429\) 17.3262 1.17557i 0.836519 0.0567571i
\(430\) 9.70820 0.468171
\(431\) −19.9443 + 14.4904i −0.960682 + 0.697976i −0.953309 0.301997i \(-0.902347\pi\)
−0.00737279 + 0.999973i \(0.502347\pi\)
\(432\) 1.69098 + 5.20431i 0.0813575 + 0.250393i
\(433\) 2.01064 6.18812i 0.0966253 0.297382i −0.891049 0.453908i \(-0.850029\pi\)
0.987674 + 0.156526i \(0.0500294\pi\)
\(434\) 3.61803 + 2.62866i 0.173671 + 0.126180i
\(435\) −20.9443 15.2169i −1.00420 0.729595i
\(436\) −3.14590 + 9.68208i −0.150661 + 0.463687i
\(437\) −0.381966 1.17557i −0.0182719 0.0562352i
\(438\) 3.11803 2.26538i 0.148985 0.108244i
\(439\) −16.9443 −0.808706 −0.404353 0.914603i \(-0.632503\pi\)
−0.404353 + 0.914603i \(0.632503\pi\)
\(440\) 2.47214 + 6.15537i 0.117854 + 0.293446i
\(441\) −0.381966 −0.0181889
\(442\) −15.3262 + 11.1352i −0.728995 + 0.529646i
\(443\) 9.91641 + 30.5196i 0.471143 + 1.45003i 0.851090 + 0.525020i \(0.175942\pi\)
−0.379947 + 0.925008i \(0.624058\pi\)
\(444\) 3.85410 11.8617i 0.182908 0.562932i
\(445\) 24.7984 + 18.0171i 1.17556 + 0.854091i
\(446\) −14.0902 10.2371i −0.667189 0.484741i
\(447\) 5.38197 16.5640i 0.254558 0.783450i
\(448\) −0.309017 0.951057i −0.0145997 0.0449332i
\(449\) −15.9721 + 11.6044i −0.753772 + 0.547647i −0.896994 0.442043i \(-0.854254\pi\)
0.143222 + 0.989691i \(0.454254\pi\)
\(450\) −0.381966 −0.0180061
\(451\) 2.39919 + 1.50609i 0.112973 + 0.0709188i
\(452\) 4.61803 0.217214
\(453\) −3.00000 + 2.17963i −0.140952 + 0.102408i
\(454\) −8.42705 25.9358i −0.395501 1.21723i
\(455\) −2.00000 + 6.15537i −0.0937614 + 0.288568i
\(456\) 0.190983 + 0.138757i 0.00894360 + 0.00649790i
\(457\) −30.7254 22.3233i −1.43727 1.04424i −0.988603 0.150544i \(-0.951897\pi\)
−0.448672 0.893697i \(-0.648103\pi\)
\(458\) 7.03444 21.6498i 0.328698 1.01163i
\(459\) −9.89919 30.4666i −0.462054 1.42206i
\(460\) −13.7082 + 9.95959i −0.639148 + 0.464368i
\(461\) −41.0132 −1.91017 −0.955087 0.296327i \(-0.904238\pi\)
−0.955087 + 0.296327i \(0.904238\pi\)
\(462\) 1.30902 5.20431i 0.0609010 0.242126i
\(463\) 24.7639 1.15088 0.575439 0.817845i \(-0.304831\pi\)
0.575439 + 0.817845i \(0.304831\pi\)
\(464\) 6.47214 4.70228i 0.300461 0.218298i
\(465\) 4.47214 + 13.7638i 0.207390 + 0.638282i
\(466\) −2.44427 + 7.52270i −0.113229 + 0.348482i
\(467\) −17.7082 12.8658i −0.819438 0.595357i 0.0971135 0.995273i \(-0.469039\pi\)
−0.916551 + 0.399917i \(0.869039\pi\)
\(468\) 1.00000 + 0.726543i 0.0462250 + 0.0335844i
\(469\) −0.336881 + 1.03681i −0.0155557 + 0.0478756i
\(470\) −1.05573 3.24920i −0.0486971 0.149874i
\(471\) −3.61803 + 2.62866i −0.166710 + 0.121122i
\(472\) −4.14590 −0.190830
\(473\) −12.3541 + 10.3229i −0.568042 + 0.474646i
\(474\) −2.00000 −0.0918630
\(475\) −0.118034 + 0.0857567i −0.00541577 + 0.00393479i
\(476\) 1.80902 + 5.56758i 0.0829162 + 0.255190i
\(477\) −0.583592 + 1.79611i −0.0267208 + 0.0822383i
\(478\) 0.236068 + 0.171513i 0.0107975 + 0.00784484i
\(479\) 7.00000 + 5.08580i 0.319838 + 0.232376i 0.736106 0.676866i \(-0.236662\pi\)
−0.416268 + 0.909242i \(0.636662\pi\)
\(480\) 1.00000 3.07768i 0.0456435 0.140476i
\(481\) −7.70820 23.7234i −0.351464 1.08169i
\(482\) −5.50000 + 3.99598i −0.250518 + 0.182012i
\(483\) 13.7082 0.623745
\(484\) −9.69098 5.20431i −0.440499 0.236560i
\(485\) −6.29180 −0.285696
\(486\) −3.19098 + 2.31838i −0.144746 + 0.105164i
\(487\) −5.96556 18.3601i −0.270325 0.831976i −0.990419 0.138098i \(-0.955901\pi\)
0.720093 0.693877i \(-0.244099\pi\)
\(488\) −2.00000 + 6.15537i −0.0905357 + 0.278640i
\(489\) 30.4615 + 22.1316i 1.37752 + 1.00082i
\(490\) 1.61803 + 1.17557i 0.0730953 + 0.0531069i
\(491\) −5.50000 + 16.9273i −0.248212 + 0.763917i 0.746880 + 0.664959i \(0.231551\pi\)
−0.995092 + 0.0989578i \(0.968449\pi\)
\(492\) −0.427051 1.31433i −0.0192529 0.0592545i
\(493\) −37.8885 + 27.5276i −1.70641 + 1.23978i
\(494\) 0.472136 0.0212424
\(495\) −1.94427 + 1.62460i −0.0873885 + 0.0730203i
\(496\) −4.47214 −0.200805
\(497\) 8.47214 6.15537i 0.380027 0.276106i
\(498\) −6.51722 20.0579i −0.292044 0.898818i
\(499\) 8.73607 26.8869i 0.391080 1.20362i −0.540892 0.841092i \(-0.681913\pi\)
0.931972 0.362529i \(-0.118087\pi\)
\(500\) 9.70820 + 7.05342i 0.434164 + 0.315439i
\(501\) 21.5623 + 15.6659i 0.963333 + 0.699902i
\(502\) 1.52786 4.70228i 0.0681919 0.209873i
\(503\) 6.67376 + 20.5397i 0.297568 + 0.915821i 0.982347 + 0.187070i \(0.0598990\pi\)
−0.684778 + 0.728751i \(0.740101\pi\)
\(504\) 0.309017 0.224514i 0.0137647 0.0100006i
\(505\) −37.3050 −1.66005
\(506\) 6.85410 27.2501i 0.304702 1.21142i
\(507\) 4.09017 0.181651
\(508\) 7.09017 5.15131i 0.314575 0.228552i
\(509\) 6.09017 + 18.7436i 0.269942 + 0.830796i 0.990513 + 0.137415i \(0.0438795\pi\)
−0.720571 + 0.693381i \(0.756120\pi\)
\(510\) −5.85410 + 18.0171i −0.259224 + 0.797809i
\(511\) −1.92705 1.40008i −0.0852477 0.0619361i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) −0.246711 + 0.759299i −0.0108926 + 0.0335239i
\(514\) −7.91641 24.3642i −0.349178 1.07466i
\(515\) 15.7082 11.4127i 0.692186 0.502903i
\(516\) 7.85410 0.345758
\(517\) 4.79837 + 3.01217i 0.211032 + 0.132475i
\(518\) −7.70820 −0.338679
\(519\) 3.00000 2.17963i 0.131685 0.0956750i
\(520\) −2.00000 6.15537i −0.0877058 0.269931i
\(521\) −1.04508 + 3.21644i −0.0457860 + 0.140915i −0.971336 0.237710i \(-0.923603\pi\)
0.925550 + 0.378625i \(0.123603\pi\)
\(522\) 2.47214 + 1.79611i 0.108202 + 0.0786137i
\(523\) −7.88197 5.72658i −0.344654 0.250406i 0.401969 0.915653i \(-0.368326\pi\)
−0.746623 + 0.665247i \(0.768326\pi\)
\(524\) 4.80902 14.8006i 0.210083 0.646569i
\(525\) −0.500000 1.53884i −0.0218218 0.0671606i
\(526\) −10.4721 + 7.60845i −0.456607 + 0.331744i
\(527\) 26.1803 1.14043
\(528\) 2.00000 + 4.97980i 0.0870388 + 0.216718i
\(529\) 48.7771 2.12074
\(530\) 8.00000 5.81234i 0.347498 0.252472i
\(531\) −0.489357 1.50609i −0.0212363 0.0653585i
\(532\) 0.0450850 0.138757i 0.00195468 0.00601589i
\(533\) −2.23607 1.62460i −0.0968549 0.0703692i
\(534\) 20.0623 + 14.5761i 0.868181 + 0.630770i
\(535\) −4.52786 + 13.9353i −0.195757 + 0.602477i
\(536\) −0.336881 1.03681i −0.0145510 0.0447835i
\(537\) −32.0795 + 23.3071i −1.38433 + 1.00578i
\(538\) 2.58359 0.111387
\(539\) −3.30902 + 0.224514i −0.142529 + 0.00967050i
\(540\) 10.9443 0.470966
\(541\) 23.6525 17.1845i 1.01690 0.738821i 0.0512544 0.998686i \(-0.483678\pi\)
0.965645 + 0.259865i \(0.0836781\pi\)
\(542\) 5.76393 + 17.7396i 0.247582 + 0.761979i
\(543\) 9.38197 28.8747i 0.402619 1.23913i
\(544\) −4.73607 3.44095i −0.203057 0.147530i
\(545\) 16.4721 + 11.9677i 0.705589 + 0.512640i
\(546\) −1.61803 + 4.97980i −0.0692455 + 0.213116i
\(547\) 2.71885 + 8.36775i 0.116250 + 0.357779i 0.992206 0.124612i \(-0.0397685\pi\)
−0.875956 + 0.482391i \(0.839769\pi\)
\(548\) 15.6353 11.3597i 0.667905 0.485261i
\(549\) −2.47214 −0.105508
\(550\) −3.30902 + 0.224514i −0.141097 + 0.00957331i
\(551\) 1.16718 0.0497237
\(552\) −11.0902 + 8.05748i −0.472029 + 0.342949i
\(553\) 0.381966 + 1.17557i 0.0162428 + 0.0499903i
\(554\) −7.18034 + 22.0988i −0.305063 + 0.938889i
\(555\) −20.1803 14.6619i −0.856608 0.622362i
\(556\) 11.7082 + 8.50651i 0.496538 + 0.360756i
\(557\) 5.52786 17.0130i 0.234223 0.720865i −0.763000 0.646398i \(-0.776275\pi\)
0.997224 0.0744666i \(-0.0237254\pi\)
\(558\) −0.527864 1.62460i −0.0223463 0.0687747i
\(559\) 12.7082 9.23305i 0.537500 0.390516i
\(560\) −2.00000 −0.0845154
\(561\) −11.7082 29.1522i −0.494321 1.23081i
\(562\) −9.79837 −0.413319
\(563\) 18.5451 13.4738i 0.781582 0.567853i −0.123871 0.992298i \(-0.539531\pi\)
0.905453 + 0.424446i \(0.139531\pi\)
\(564\) −0.854102 2.62866i −0.0359642 0.110686i
\(565\) 2.85410 8.78402i 0.120073 0.369547i
\(566\) 8.94427 + 6.49839i 0.375956 + 0.273148i
\(567\) −6.23607 4.53077i −0.261890 0.190274i
\(568\) −3.23607 + 9.95959i −0.135782 + 0.417895i
\(569\) 13.0451 + 40.1486i 0.546878 + 1.68312i 0.716481 + 0.697606i \(0.245751\pi\)
−0.169603 + 0.985512i \(0.554249\pi\)
\(570\) 0.381966 0.277515i 0.0159988 0.0116238i
\(571\) 18.8328 0.788129 0.394064 0.919083i \(-0.371069\pi\)
0.394064 + 0.919083i \(0.371069\pi\)
\(572\) 9.09017 + 5.70634i 0.380079 + 0.238594i
\(573\) −20.1803 −0.843046
\(574\) −0.690983 + 0.502029i −0.0288411 + 0.0209543i
\(575\) −2.61803 8.05748i −0.109180 0.336020i
\(576\) −0.118034 + 0.363271i −0.00491808 + 0.0151363i
\(577\) 33.9164 + 24.6417i 1.41196 + 1.02585i 0.993034 + 0.117827i \(0.0375928\pi\)
0.418924 + 0.908021i \(0.362407\pi\)
\(578\) 13.9721 + 10.1514i 0.581164 + 0.422241i
\(579\) −8.70820 + 26.8011i −0.361901 + 1.11382i
\(580\) −4.94427 15.2169i −0.205300 0.631848i
\(581\) −10.5451 + 7.66145i −0.437484 + 0.317851i
\(582\) −5.09017 −0.210994
\(583\) −4.00000 + 15.9030i −0.165663 + 0.658633i
\(584\) 2.38197 0.0985665
\(585\) 2.00000 1.45309i 0.0826898 0.0600777i
\(586\) −8.09017 24.8990i −0.334202 1.02857i
\(587\) 5.66312 17.4293i 0.233742 0.719384i −0.763544 0.645756i \(-0.776542\pi\)
0.997286 0.0736277i \(-0.0234577\pi\)
\(588\) 1.30902 + 0.951057i 0.0539830 + 0.0392209i
\(589\) −0.527864 0.383516i −0.0217503 0.0158025i
\(590\) −2.56231 + 7.88597i −0.105488 + 0.324660i
\(591\) 1.76393 + 5.42882i 0.0725585 + 0.223312i
\(592\) 6.23607 4.53077i 0.256301 0.186213i
\(593\) −11.0902 −0.455419 −0.227709 0.973729i \(-0.573124\pi\)
−0.227709 + 0.973729i \(0.573124\pi\)
\(594\) −13.9271 + 11.6372i −0.571434 + 0.477480i
\(595\) 11.7082 0.479990
\(596\) 8.70820 6.32688i 0.356702 0.259159i
\(597\) 10.0902 + 31.0543i 0.412963 + 1.27097i
\(598\) −8.47214 + 26.0746i −0.346451 + 1.06627i
\(599\) −2.00000 1.45309i −0.0817178 0.0593714i 0.546176 0.837670i \(-0.316083\pi\)
−0.627894 + 0.778299i \(0.716083\pi\)
\(600\) 1.30902 + 0.951057i 0.0534404 + 0.0388267i
\(601\) −9.79180 + 30.1360i −0.399416 + 1.22928i 0.526053 + 0.850452i \(0.323671\pi\)
−0.925469 + 0.378823i \(0.876329\pi\)
\(602\) −1.50000 4.61653i −0.0611354 0.188156i
\(603\) 0.336881 0.244758i 0.0137189 0.00996733i
\(604\) −2.29180 −0.0932519
\(605\) −15.8885 + 15.2169i −0.645961 + 0.618655i
\(606\) −30.1803 −1.22599
\(607\) −12.0902 + 8.78402i −0.490725 + 0.356532i −0.805463 0.592646i \(-0.798083\pi\)
0.314738 + 0.949179i \(0.398083\pi\)
\(608\) 0.0450850 + 0.138757i 0.00182844 + 0.00562735i
\(609\) −4.00000 + 12.3107i −0.162088 + 0.498856i
\(610\) 10.4721 + 7.60845i 0.424004 + 0.308057i
\(611\) −4.47214 3.24920i −0.180923 0.131448i
\(612\) 0.690983 2.12663i 0.0279313 0.0859638i
\(613\) −4.38197 13.4863i −0.176986 0.544707i 0.822733 0.568429i \(-0.192448\pi\)
−0.999719 + 0.0237218i \(0.992448\pi\)
\(614\) −14.2533 + 10.3556i −0.575216 + 0.417919i
\(615\) −2.76393 −0.111452
\(616\) 2.54508 2.12663i 0.102544 0.0856842i
\(617\) −39.1591 −1.57648 −0.788242 0.615365i \(-0.789009\pi\)
−0.788242 + 0.615365i \(0.789009\pi\)
\(618\) 12.7082 9.23305i 0.511199 0.371408i
\(619\) −4.33688 13.3475i −0.174314 0.536483i 0.825287 0.564713i \(-0.191013\pi\)
−0.999601 + 0.0282296i \(0.991013\pi\)
\(620\) −2.76393 + 8.50651i −0.111002 + 0.341630i
\(621\) −37.5066 27.2501i −1.50509 1.09351i
\(622\) −3.47214 2.52265i −0.139220 0.101149i
\(623\) 4.73607 14.5761i 0.189747 0.583980i
\(624\) −1.61803 4.97980i −0.0647732 0.199351i
\(625\) 15.3713 11.1679i 0.614853 0.446717i
\(626\) 10.7984 0.431590
\(627\) −0.190983 + 0.759299i −0.00762713 + 0.0303235i
\(628\) −2.76393 −0.110293
\(629\) −36.5066 + 26.5236i −1.45561 + 1.05756i
\(630\) −0.236068 0.726543i −0.00940517 0.0289461i
\(631\) 10.8885 33.5115i 0.433466 1.33407i −0.461184 0.887304i \(-0.652575\pi\)
0.894650 0.446767i \(-0.147425\pi\)
\(632\) −1.00000 0.726543i −0.0397779 0.0289003i
\(633\) −20.8262 15.1311i −0.827769 0.601409i
\(634\) −3.70820 + 11.4127i −0.147272 + 0.453255i
\(635\) −5.41641 16.6700i −0.214944 0.661528i
\(636\) 6.47214 4.70228i 0.256637 0.186458i
\(637\) 3.23607 0.128218
\(638\) 22.4721 + 14.1068i 0.889680 + 0.558495i
\(639\) −4.00000 −0.158238
\(640\) 1.61803 1.17557i 0.0639584 0.0464685i
\(641\) 7.26393 + 22.3561i 0.286908 + 0.883012i 0.985820 + 0.167805i \(0.0536678\pi\)
−0.698912 + 0.715207i \(0.746332\pi\)
\(642\) −3.66312 + 11.2739i −0.144572 + 0.444946i
\(643\) 11.6353 + 8.45351i 0.458850 + 0.333374i 0.793080 0.609118i \(-0.208476\pi\)
−0.334230 + 0.942491i \(0.608476\pi\)
\(644\) 6.85410 + 4.97980i 0.270089 + 0.196231i
\(645\) 4.85410 14.9394i 0.191130 0.588238i
\(646\) −0.263932 0.812299i −0.0103843 0.0319595i
\(647\) 30.2705 21.9928i 1.19006 0.864627i 0.196786 0.980446i \(-0.436949\pi\)
0.993270 + 0.115820i \(0.0369495\pi\)
\(648\) 7.70820 0.302807
\(649\) −5.12461 12.7598i −0.201159 0.500864i
\(650\) 3.23607 0.126929
\(651\) 5.85410 4.25325i 0.229440 0.166698i
\(652\) 7.19098 + 22.1316i 0.281621 + 0.866739i
\(653\) −1.96556 + 6.04937i −0.0769182 + 0.236730i −0.982121 0.188249i \(-0.939719\pi\)
0.905203 + 0.424979i \(0.139719\pi\)
\(654\) 13.3262 + 9.68208i 0.521097 + 0.378599i
\(655\) −25.1803 18.2946i −0.983877 0.714829i
\(656\) 0.263932 0.812299i 0.0103048 0.0317150i
\(657\) 0.281153 + 0.865300i 0.0109688 + 0.0337586i
\(658\) −1.38197 + 1.00406i −0.0538746 + 0.0391422i
\(659\) 16.5066 0.643005 0.321502 0.946909i \(-0.395812\pi\)
0.321502 + 0.946909i \(0.395812\pi\)
\(660\) 10.7082 0.726543i 0.416816 0.0282806i
\(661\) 16.4721 0.640692 0.320346 0.947301i \(-0.396201\pi\)
0.320346 + 0.947301i \(0.396201\pi\)
\(662\) −3.45492 + 2.51014i −0.134279 + 0.0975595i
\(663\) 9.47214 + 29.1522i 0.367867 + 1.13218i
\(664\) 4.02786 12.3965i 0.156311 0.481077i
\(665\) −0.236068 0.171513i −0.00915432 0.00665101i
\(666\) 2.38197 + 1.73060i 0.0922993 + 0.0670594i
\(667\) −20.9443 + 64.4598i −0.810965 + 2.49590i
\(668\) 5.09017 + 15.6659i 0.196945 + 0.606133i
\(669\) −22.7984 + 16.5640i −0.881436 + 0.640401i
\(670\) −2.18034 −0.0842339
\(671\) −21.4164 + 1.45309i −0.826771 + 0.0560957i
\(672\) −1.61803 −0.0624170
\(673\) 37.6246 27.3359i 1.45032 1.05372i 0.464566 0.885538i \(-0.346210\pi\)
0.985756 0.168182i \(-0.0537898\pi\)
\(674\) −0.371323 1.14281i −0.0143028 0.0440196i
\(675\) −1.69098 + 5.20431i −0.0650860 + 0.200314i
\(676\) 2.04508 + 1.48584i 0.0786571 + 0.0571477i
\(677\) 29.0344 + 21.0948i 1.11588 + 0.810737i 0.983580 0.180472i \(-0.0577625\pi\)
0.132304 + 0.991209i \(0.457762\pi\)
\(678\) 2.30902 7.10642i 0.0886773 0.272921i
\(679\) 0.972136 + 2.99193i 0.0373072 + 0.114820i
\(680\) −9.47214 + 6.88191i −0.363240 + 0.263909i
\(681\) −44.1246 −1.69086
\(682\) −5.52786 13.7638i −0.211673 0.527044i
\(683\) 24.3607 0.932136 0.466068 0.884749i \(-0.345670\pi\)
0.466068 + 0.884749i \(0.345670\pi\)
\(684\) −0.0450850 + 0.0327561i −0.00172387 + 0.00125246i
\(685\) −11.9443 36.7607i −0.456367 1.40455i
\(686\) 0.309017 0.951057i 0.0117983 0.0363115i
\(687\) −29.7984 21.6498i −1.13688 0.825991i
\(688\) 3.92705 + 2.85317i 0.149717 + 0.108776i
\(689\) 4.94427 15.2169i 0.188362 0.579718i
\(690\) 8.47214 + 26.0746i 0.322529 + 0.992641i
\(691\) −1.88197 + 1.36733i −0.0715934 + 0.0520156i −0.623006 0.782217i \(-0.714089\pi\)
0.551413 + 0.834232i \(0.314089\pi\)
\(692\) 2.29180 0.0871210
\(693\) 1.07295 + 0.673542i 0.0407580 + 0.0255857i
\(694\) −12.1459 −0.461052
\(695\) 23.4164 17.0130i 0.888235 0.645340i
\(696\) −4.00000 12.3107i −0.151620 0.466637i
\(697\) −1.54508 + 4.75528i −0.0585243 + 0.180119i
\(698\) −3.70820 2.69417i −0.140358 0.101976i
\(699\) 10.3541 + 7.52270i 0.391628 + 0.284534i
\(700\) 0.309017 0.951057i 0.0116797 0.0359466i
\(701\) 15.1803 + 46.7203i 0.573354 + 1.76460i 0.641718 + 0.766940i \(0.278222\pi\)
−0.0683649 + 0.997660i \(0.521778\pi\)
\(702\) 14.3262 10.4086i 0.540709 0.392848i
\(703\) 1.12461 0.0424155
\(704\) −0.809017 + 3.21644i −0.0304910 + 0.121224i
\(705\) −5.52786 −0.208191
\(706\) 1.02786 0.746787i 0.0386842 0.0281057i
\(707\) 5.76393 + 17.7396i 0.216775 + 0.667165i
\(708\) −2.07295 + 6.37988i −0.0779062 + 0.239771i
\(709\) −7.56231 5.49434i −0.284008 0.206344i 0.436656 0.899629i \(-0.356163\pi\)
−0.720664 + 0.693285i \(0.756163\pi\)
\(710\) 16.9443 + 12.3107i 0.635907 + 0.462014i
\(711\) 0.145898 0.449028i 0.00547160 0.0168399i
\(712\) 4.73607 + 14.5761i 0.177492 + 0.546263i
\(713\) 30.6525 22.2703i 1.14794 0.834030i
\(714\) 9.47214 0.354486
\(715\) 16.4721 13.7638i 0.616023 0.514738i
\(716\) −24.5066 −0.915854
\(717\) 0.381966 0.277515i 0.0142648 0.0103640i
\(718\) −5.32624 16.3925i −0.198773 0.611762i
\(719\) 1.85410 5.70634i 0.0691463 0.212811i −0.910512 0.413482i \(-0.864312\pi\)
0.979659 + 0.200672i \(0.0643124\pi\)
\(720\) 0.618034 + 0.449028i 0.0230328 + 0.0167343i
\(721\) −7.85410 5.70634i −0.292502 0.212515i
\(722\) 5.86475 18.0498i 0.218263 0.671745i
\(723\) 3.39919 + 10.4616i 0.126417 + 0.389072i
\(724\) 15.1803 11.0292i 0.564173 0.409896i
\(725\) 8.00000 0.297113
\(726\) −12.8541 + 12.3107i −0.477060 + 0.456894i
\(727\) −29.5279 −1.09513 −0.547564 0.836764i \(-0.684445\pi\)
−0.547564 + 0.836764i \(0.684445\pi\)
\(728\) −2.61803 + 1.90211i −0.0970308 + 0.0704970i
\(729\) 9.11803 + 28.0624i 0.337705 + 1.03935i
\(730\) 1.47214 4.53077i 0.0544862 0.167691i
\(731\) −22.9894 16.7027i −0.850292 0.617773i
\(732\) 8.47214 + 6.15537i 0.313139 + 0.227509i
\(733\) 7.00000 21.5438i 0.258551 0.795738i −0.734558 0.678546i \(-0.762611\pi\)
0.993109 0.117192i \(-0.0373894\pi\)
\(734\) 3.70820 + 11.4127i 0.136872 + 0.421250i
\(735\) 2.61803 1.90211i 0.0965676 0.0701605i
\(736\) −8.47214 −0.312287
\(737\) 2.77458 2.31838i 0.102203 0.0853988i
\(738\) 0.326238 0.0120090
\(739\) −0.354102 + 0.257270i −0.0130259 + 0.00946383i −0.594279 0.804259i \(-0.702563\pi\)
0.581253 + 0.813723i \(0.302563\pi\)
\(740\) −4.76393 14.6619i −0.175126 0.538981i
\(741\) 0.236068 0.726543i 0.00867217 0.0266902i
\(742\) −4.00000 2.90617i −0.146845 0.106689i
\(743\) 2.38197 + 1.73060i 0.0873859 + 0.0634895i 0.630620 0.776091i \(-0.282801\pi\)
−0.543234 + 0.839581i \(0.682801\pi\)
\(744\) −2.23607 + 6.88191i −0.0819782 + 0.252303i
\(745\) −6.65248 20.4742i −0.243728 0.750117i
\(746\) 24.6525 17.9111i 0.902591 0.655771i
\(747\) 4.97871 0.182162
\(748\) 4.73607 18.8294i 0.173168 0.688470i
\(749\) 7.32624 0.267695
\(750\) 15.7082 11.4127i 0.573583 0.416732i
\(751\) −15.2016 46.7858i −0.554715 1.70724i −0.696694 0.717368i \(-0.745347\pi\)
0.141979 0.989870i \(-0.454653\pi\)
\(752\) 0.527864 1.62460i 0.0192492 0.0592430i
\(753\) −6.47214 4.70228i −0.235858 0.171361i
\(754\) −20.9443 15.2169i −0.762745 0.554167i
\(755\) −1.41641 + 4.35926i −0.0515484 + 0.158650i
\(756\) −1.69098 5.20431i −0.0615005 0.189279i
\(757\) −11.3820 + 8.26948i −0.413685 + 0.300559i −0.775092 0.631849i \(-0.782296\pi\)
0.361407 + 0.932408i \(0.382296\pi\)
\(758\) 12.8541 0.466882
\(759\) −38.5066 24.1724i −1.39770 0.877404i
\(760\) 0.291796 0.0105846
\(761\) 11.6803 8.48626i 0.423412 0.307627i −0.355597 0.934639i \(-0.615723\pi\)
0.779009 + 0.627012i \(0.215723\pi\)
\(762\) −4.38197 13.4863i −0.158742 0.488557i
\(763\) 3.14590 9.68208i 0.113889 0.350515i
\(764\) −10.0902 7.33094i −0.365050 0.265224i
\(765\) −3.61803 2.62866i −0.130810 0.0950392i
\(766\) −1.03444 + 3.18368i −0.0373759 + 0.115031i
\(767\) 4.14590 + 12.7598i 0.149700 + 0.460728i
\(768\) 1.30902 0.951057i 0.0472351 0.0343183i
\(769\) −22.5836 −0.814385 −0.407193 0.913342i \(-0.633492\pi\)
−0.407193 + 0.913342i \(0.633492\pi\)
\(770\) −2.47214 6.15537i −0.0890896 0.221824i
\(771\) −41.4508 −1.49282
\(772\) −14.0902 + 10.2371i −0.507116 + 0.368442i
\(773\) −9.52786 29.3238i −0.342693 1.05470i −0.962807 0.270190i \(-0.912913\pi\)
0.620114 0.784512i \(-0.287087\pi\)
\(774\) −0.572949 + 1.76336i −0.0205942 + 0.0633825i
\(775\) −3.61803 2.62866i −0.129964 0.0944241i
\(776\) −2.54508 1.84911i −0.0913632 0.0663793i
\(777\) −3.85410 + 11.8617i −0.138265 + 0.425536i
\(778\) −2.00000 6.15537i −0.0717035 0.220681i
\(779\) 0.100813 0.0732450i 0.00361200 0.00262427i
\(780\) −10.4721 −0.374963
\(781\) −34.6525 + 2.35114i −1.23996 + 0.0841304i
\(782\) 49.5967 1.77358
\(783\) 35.4164 25.7315i 1.26568 0.919570i
\(784\) 0.309017 + 0.951057i 0.0110363 + 0.0339663i
\(785\) −1.70820 + 5.25731i −0.0609684 + 0.187641i
\(786\) −20.3713 14.8006i −0.726621 0.527921i
\(787\) −3.35410 2.43690i −0.119561 0.0868660i 0.526398 0.850238i \(-0.323542\pi\)
−0.645959 + 0.763372i \(0.723542\pi\)
\(788\) −1.09017 + 3.35520i −0.0388357 + 0.119524i
\(789\) 6.47214 + 19.9192i 0.230414 + 0.709142i
\(790\) −2.00000 + 1.45309i −0.0711568 + 0.0516984i
\(791\) −4.61803 −0.164198
\(792\) −1.26393 + 0.0857567i −0.0449119 + 0.00304723i
\(793\) 20.9443 0.743753
\(794\) −25.5623 + 18.5721i −0.907172 + 0.659099i
\(795\) −4.94427 15.2169i −0.175355 0.539688i
\(796\) −6.23607 + 19.1926i −0.221032 + 0.680265i
\(797\) −34.6525 25.1765i −1.22745 0.891797i −0.230757 0.973011i \(-0.574120\pi\)
−0.996697 + 0.0812141i \(0.974120\pi\)
\(798\) −0.190983 0.138757i −0.00676073 0.00491195i
\(799\) −3.09017 + 9.51057i −0.109322 + 0.336460i
\(800\) 0.309017 + 0.951057i 0.0109254 + 0.0336249i
\(801\) −4.73607 + 3.44095i −0.167341 + 0.121580i
\(802\) −4.67376 −0.165036
\(803\) 2.94427 + 7.33094i 0.103901 + 0.258703i
\(804\) −1.76393 −0.0622091
\(805\) 13.7082 9.95959i 0.483151 0.351030i
\(806\) 4.47214 + 13.7638i 0.157524 + 0.484810i
\(807\) 1.29180 3.97574i 0.0454734 0.139953i
\(808\) −15.0902 10.9637i −0.530870 0.385700i
\(809\) −0.444272 0.322782i −0.0156198 0.0113484i 0.579948 0.814654i \(-0.303073\pi\)
−0.595568 + 0.803305i \(0.703073\pi\)
\(810\) 4.76393 14.6619i 0.167388 0.515166i
\(811\) 9.61146 + 29.5810i 0.337504 + 1.03873i 0.965475 + 0.260494i \(0.0838854\pi\)
−0.627972 + 0.778236i \(0.716115\pi\)
\(812\) −6.47214 + 4.70228i −0.227127 + 0.165018i
\(813\) 30.1803 1.05847
\(814\) 21.6525 + 13.5923i 0.758919 + 0.476410i
\(815\) 46.5410 1.63026
\(816\) −7.66312 + 5.56758i −0.268263 + 0.194904i
\(817\) 0.218847 + 0.673542i 0.00765649 + 0.0235643i
\(818\) −5.67376 + 17.4620i −0.198378 + 0.610546i
\(819\) −1.00000 0.726543i −0.0349428 0.0253875i
\(820\) −1.38197 1.00406i −0.0482603 0.0350632i
\(821\) 5.00000 15.3884i 0.174501 0.537059i −0.825109 0.564973i \(-0.808886\pi\)
0.999610 + 0.0279139i \(0.00888643\pi\)
\(822\) −9.66312 29.7400i −0.337040 1.03730i
\(823\) −7.00000 + 5.08580i −0.244005 + 0.177280i −0.703066 0.711125i \(-0.748186\pi\)
0.459061 + 0.888405i \(0.348186\pi\)
\(824\) 9.70820 0.338201
\(825\) −1.30902 + 5.20431i −0.0455741 + 0.181191i
\(826\) 4.14590 0.144254
\(827\) −5.59017 + 4.06150i −0.194389 + 0.141232i −0.680723 0.732541i \(-0.738334\pi\)
0.486333 + 0.873773i \(0.338334\pi\)
\(828\) −1.00000 3.07768i −0.0347524 0.106957i
\(829\) 1.20163 3.69822i 0.0417342 0.128445i −0.928019 0.372534i \(-0.878489\pi\)
0.969753 + 0.244089i \(0.0784890\pi\)
\(830\) −21.0902 15.3229i −0.732050 0.531866i
\(831\) 30.4164 + 22.0988i 1.05513 + 0.766599i
\(832\) 1.00000 3.07768i 0.0346688 0.106699i
\(833\) −1.80902 5.56758i −0.0626787 0.192905i
\(834\) 18.9443 13.7638i 0.655986 0.476602i
\(835\) 32.9443 1.14008
\(836\) −0.371323 + 0.310271i −0.0128425 + 0.0107309i
\(837\) −24.4721 −0.845881
\(838\) 9.30902 6.76340i 0.321575 0.233638i
\(839\) −15.0000 46.1653i −0.517858 1.59380i −0.778022 0.628237i \(-0.783777\pi\)
0.260164 0.965564i \(-0.416223\pi\)
\(840\) −1.00000 + 3.07768i −0.0345033 + 0.106190i
\(841\) −28.3156 20.5725i −0.976400 0.709396i
\(842\) −3.61803 2.62866i −0.124686 0.0905895i
\(843\) −4.89919 + 15.0781i −0.168737 + 0.519319i
\(844\) −4.91641 15.1311i −0.169230 0.520836i
\(845\) 4.09017 2.97168i 0.140706 0.102229i
\(846\) 0.652476 0.0224326
\(847\) 9.69098 + 5.20431i 0.332986 + 0.178822i
\(848\) 4.94427 0.169787
\(849\) 14.4721 10.5146i 0.496682 0.360861i
\(850\) −1.80902 5.56758i −0.0620488 0.190966i
\(851\) −20.1803 + 62.1087i −0.691773 + 2.12906i
\(852\) 13.7082 + 9.95959i 0.469635 + 0.341210i
\(853\) −22.7082 16.4985i −0.777514 0.564897i 0.126718 0.991939i \(-0.459556\pi\)
−0.904232 + 0.427042i \(0.859556\pi\)
\(854\) 2.00000 6.15537i 0.0684386 0.210632i
\(855\) 0.0344419 + 0.106001i 0.00117789 + 0.00362516i
\(856\) −5.92705 + 4.30625i −0.202582 + 0.147185i
\(857\) −16.0902 −0.549630 −0.274815 0.961497i \(-0.588617\pi\)
−0.274815 + 0.961497i \(0.588617\pi\)
\(858\) 13.3262 11.1352i 0.454950 0.380148i
\(859\) 25.3820 0.866022 0.433011 0.901389i \(-0.357451\pi\)
0.433011 + 0.901389i \(0.357451\pi\)
\(860\) 7.85410 5.70634i 0.267823 0.194585i
\(861\) 0.427051 + 1.31433i 0.0145539 + 0.0447922i
\(862\) −7.61803 + 23.4459i −0.259471 + 0.798570i
\(863\) 32.5623 + 23.6579i 1.10843 + 0.805324i 0.982416 0.186704i \(-0.0597804\pi\)
0.126018 + 0.992028i \(0.459780\pi\)
\(864\) 4.42705 + 3.21644i 0.150611 + 0.109426i
\(865\) 1.41641 4.35926i 0.0481593 0.148219i
\(866\) −2.01064 6.18812i −0.0683244 0.210281i
\(867\) 22.6074 16.4252i 0.767787 0.557830i
\(868\) 4.47214 0.151794
\(869\) 1.00000 3.97574i 0.0339227 0.134868i
\(870\) −25.8885 −0.877704
\(871\) −2.85410 + 2.07363i −0.0967076 + 0.0702622i
\(872\) 3.14590 + 9.68208i 0.106534 + 0.327877i
\(873\) 0.371323 1.14281i 0.0125674 0.0386784i
\(874\) −1.00000 0.726543i −0.0338255 0.0245757i
\(875\) −9.70820 7.05342i −0.328197 0.238449i
\(876\) 1.19098 3.66547i 0.0402396 0.123845i
\(877\) 11.2918 + 34.7526i 0.381297 + 1.17351i 0.939131 + 0.343559i \(0.111632\pi\)
−0.557834 + 0.829952i \(0.688368\pi\)
\(878\) −13.7082 + 9.95959i −0.462629 + 0.336120i
\(879\) −42.3607 −1.42879
\(880\) 5.61803 + 3.52671i 0.189384 + 0.118885i
\(881\) 42.9230 1.44611 0.723056 0.690789i \(-0.242737\pi\)
0.723056 + 0.690789i \(0.242737\pi\)
\(882\) −0.309017 + 0.224514i −0.0104051 + 0.00755978i
\(883\) 7.97214 + 24.5357i 0.268284 + 0.825692i 0.990919 + 0.134463i \(0.0429308\pi\)
−0.722635 + 0.691230i \(0.757069\pi\)
\(884\) −5.85410 + 18.0171i −0.196895 + 0.605980i
\(885\) 10.8541 + 7.88597i 0.364857 + 0.265084i
\(886\) 25.9615 + 18.8621i 0.872193 + 0.633686i
\(887\) −3.85410 + 11.8617i −0.129408 + 0.398277i −0.994678 0.103028i \(-0.967147\pi\)
0.865270 + 0.501306i \(0.167147\pi\)
\(888\) −3.85410 11.8617i −0.129335 0.398053i
\(889\) −7.09017 + 5.15131i −0.237797 + 0.172769i
\(890\) 30.6525 1.02747
\(891\) 9.52786 + 23.7234i 0.319195 + 0.794764i
\(892\) −17.4164 −0.583144
\(893\) 0.201626 0.146490i 0.00674716 0.00490210i
\(894\) −5.38197 16.5640i −0.180000 0.553983i
\(895\) −15.1459 + 46.6143i −0.506272 + 1.55814i
\(896\) −0.809017 0.587785i −0.0270274 0.0196365i
\(897\) 35.8885 + 26.0746i 1.19828 + 0.870604i
\(898\) −6.10081 + 18.7764i −0.203587 + 0.626576i
\(899\) 11.0557 + 34.0260i 0.368729 + 1.13483i
\(900\) −0.309017 + 0.224514i −0.0103006 + 0.00748380i
\(901\) −28.9443 −0.964274
\(902\) 2.82624 0.191758i 0.0941034 0.00638484i
\(903\) −7.85410 −0.261368
\(904\) 3.73607 2.71441i 0.124260 0.0902800i
\(905\) −11.5967 35.6911i −0.385489 1.18641i
\(906\) −1.14590 + 3.52671i −0.0380699 + 0.117167i
\(907\) 2.40983 + 1.75084i 0.0800171 + 0.0581358i 0.627075 0.778959i \(-0.284252\pi\)
−0.547058 + 0.837095i \(0.684252\pi\)
\(908\) −22.0623 16.0292i −0.732163 0.531948i
\(909\) 2.20163 6.77591i 0.0730233 0.224743i
\(910\) 2.00000 + 6.15537i 0.0662994 + 0.204048i
\(911\) 20.7984 15.1109i 0.689081 0.500647i −0.187277 0.982307i \(-0.559966\pi\)
0.876358 + 0.481661i \(0.159966\pi\)
\(912\) 0.236068 0.00781699
\(913\) 43.1312 2.92641i 1.42743 0.0968502i
\(914\) −37.9787 −1.25622
\(915\) 16.9443 12.3107i 0.560160 0.406980i
\(916\) −7.03444 21.6498i −0.232425 0.715329i
\(917\) −4.80902 + 14.8006i −0.158808 + 0.488760i
\(918\) −25.9164 18.8294i −0.855369 0.621462i
\(919\) −22.7082 16.4985i −0.749075 0.544235i 0.146465 0.989216i \(-0.453210\pi\)
−0.895540 + 0.444981i \(0.853210\pi\)
\(920\) −5.23607 + 16.1150i −0.172628 + 0.531295i
\(921\) 8.80902 + 27.1114i 0.290267 + 0.893350i
\(922\) −33.1803 + 24.1069i −1.09274 + 0.793919i
\(923\) 33.8885 1.11546
\(924\) −2.00000 4.97980i −0.0657952 0.163823i
\(925\) 7.70820 0.253444
\(926\) 20.0344 14.5559i 0.658373 0.478336i
\(927\) 1.14590 + 3.52671i 0.0376362 + 0.115832i
\(928\) 2.47214 7.60845i 0.0811518 0.249760i
\(929\) 32.6246 + 23.7032i 1.07038 + 0.777676i 0.975980 0.217859i \(-0.0699072\pi\)
0.0943985 + 0.995534i \(0.469907\pi\)
\(930\) 11.7082 + 8.50651i 0.383927 + 0.278939i
\(931\) −0.0450850 + 0.138757i −0.00147760 + 0.00454759i
\(932\) 2.44427 + 7.52270i 0.0800648 + 0.246414i
\(933\) −5.61803 + 4.08174i −0.183926 + 0.133630i
\(934\) −21.8885 −0.716215
\(935\) −32.8885 20.6457i −1.07557 0.675188i
\(936\) 1.23607 0.0404021
\(937\) 21.1525 15.3682i 0.691021 0.502056i −0.185974 0.982555i \(-0.559544\pi\)
0.876996 + 0.480498i \(0.159544\pi\)
\(938\) 0.336881 + 1.03681i 0.0109996 + 0.0338532i
\(939\) 5.39919 16.6170i 0.176196 0.542275i
\(940\) −2.76393 2.00811i −0.0901495 0.0654975i
\(941\) 17.0344 + 12.3762i 0.555307 + 0.403454i 0.829738 0.558153i \(-0.188490\pi\)
−0.274431 + 0.961607i \(0.588490\pi\)
\(942\) −1.38197 + 4.25325i −0.0450269 + 0.138579i
\(943\) 2.23607 + 6.88191i 0.0728164 + 0.224106i
\(944\) −3.35410 + 2.43690i −0.109167 + 0.0793143i
\(945\) −10.9443 −0.356017
\(946\) −3.92705 + 15.6129i −0.127679 + 0.507620i
\(947\) −27.2705 −0.886172 −0.443086 0.896479i \(-0.646116\pi\)
−0.443086 + 0.896479i \(0.646116\pi\)
\(948\) −1.61803 + 1.17557i −0.0525513 + 0.0381808i
\(949\) −2.38197 7.33094i −0.0773219 0.237972i
\(950\) −0.0450850 + 0.138757i −0.00146275 + 0.00450188i
\(951\) 15.7082 + 11.4127i 0.509373 + 0.370081i
\(952\) 4.73607 + 3.44095i 0.153497 + 0.111522i
\(953\) −12.4443 + 38.2995i −0.403110 + 1.24064i 0.519354 + 0.854559i \(0.326173\pi\)
−0.922464 + 0.386084i \(0.873827\pi\)
\(954\) 0.583592 + 1.79611i 0.0188945 + 0.0581513i
\(955\) −20.1803 + 14.6619i −0.653020 + 0.474447i
\(956\) 0.291796 0.00943736
\(957\) 32.9443 27.5276i 1.06494 0.889842i
\(958\) 8.65248 0.279549
\(959\) −15.6353 + 11.3597i −0.504889 + 0.366823i
\(960\) −1.00000 3.07768i −0.0322749 0.0993318i
\(961\) −3.39919 + 10.4616i −0.109651 + 0.337472i
\(962\) −20.1803 14.6619i −0.650640 0.472718i
\(963\) −2.26393 1.64484i −0.0729542 0.0530043i
\(964\) −2.10081 + 6.46564i −0.0676626 + 0.208244i
\(965\) 10.7639 + 33.1280i 0.346503 + 1.06643i
\(966\) 11.0902 8.05748i 0.356820 0.259245i
\(967\) 0.472136 0.0151829 0.00759143 0.999971i \(-0.497584\pi\)
0.00759143 + 0.999971i \(0.497584\pi\)
\(968\) −10.8992 + 1.48584i −0.350313 + 0.0477567i
\(969\) −1.38197 −0.0443951
\(970\) −5.09017 + 3.69822i −0.163436 + 0.118743i
\(971\) 7.88854 + 24.2784i 0.253155 + 0.779132i 0.994187 + 0.107663i \(0.0343366\pi\)
−0.741032 + 0.671470i \(0.765663\pi\)
\(972\) −1.21885 + 3.75123i −0.0390945 + 0.120321i
\(973\) −11.7082 8.50651i −0.375348 0.272706i
\(974\) −15.6180 11.3472i −0.500434 0.363587i
\(975\) 1.61803 4.97980i 0.0518186 0.159481i
\(976\) 2.00000 + 6.15537i 0.0640184 + 0.197028i
\(977\) 22.2705 16.1805i 0.712497 0.517659i −0.171481 0.985187i \(-0.554855\pi\)
0.883978 + 0.467528i \(0.154855\pi\)
\(978\) 37.6525 1.20399
\(979\) −39.0066 + 32.5932i −1.24666 + 1.04168i
\(980\) 2.00000 0.0638877
\(981\) −3.14590 + 2.28563i −0.100441 + 0.0729745i
\(982\) 5.50000 + 16.9273i 0.175512 + 0.540171i
\(983\) −0.708204 + 2.17963i −0.0225882 + 0.0695193i −0.961715 0.274051i \(-0.911636\pi\)
0.939127 + 0.343570i \(0.111636\pi\)
\(984\) −1.11803 0.812299i −0.0356416 0.0258952i
\(985\) 5.70820 + 4.14725i 0.181879 + 0.132142i
\(986\) −14.4721 + 44.5407i −0.460887 + 1.41846i
\(987\) 0.854102 + 2.62866i 0.0271864 + 0.0836710i
\(988\) 0.381966 0.277515i 0.0121520 0.00882891i
\(989\) −41.1246 −1.30769
\(990\) −0.618034 + 2.45714i −0.0196424 + 0.0780931i
\(991\) 33.2361 1.05578 0.527889 0.849313i \(-0.322984\pi\)
0.527889 + 0.849313i \(0.322984\pi\)
\(992\) −3.61803 + 2.62866i −0.114873 + 0.0834599i
\(993\) 2.13525 + 6.57164i 0.0677603 + 0.208545i
\(994\) 3.23607 9.95959i 0.102642 0.315899i
\(995\) 32.6525 + 23.7234i 1.03515 + 0.752083i
\(996\) −17.0623 12.3965i −0.540640 0.392798i
\(997\) −4.85410 + 14.9394i −0.153731 + 0.473135i −0.998030 0.0627369i \(-0.980017\pi\)
0.844299 + 0.535872i \(0.180017\pi\)
\(998\) −8.73607 26.8869i −0.276535 0.851088i
\(999\) 34.1246 24.7930i 1.07965 0.784415i
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 154.2.f.c.113.1 yes 4
11.2 odd 10 1694.2.a.r.1.1 2
11.4 even 5 inner 154.2.f.c.15.1 4
11.9 even 5 1694.2.a.m.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.f.c.15.1 4 11.4 even 5 inner
154.2.f.c.113.1 yes 4 1.1 even 1 trivial
1694.2.a.m.1.1 2 11.9 even 5
1694.2.a.r.1.1 2 11.2 odd 10