Properties

Label 525.2.n.b.316.3
Level $525$
Weight $2$
Character 525.316
Analytic conductor $4.192$
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] = [525,2,Mod(106,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.n (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: \(4.19214610612\)
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: \( x^{20} - 8 x^{19} + 31 x^{18} - 74 x^{17} + 109 x^{16} - 72 x^{15} - 51 x^{14} + 9 x^{13} + 866 x^{12} - 3240 x^{11} + 6385 x^{10} - 6775 x^{9} + 330 x^{8} + 11325 x^{7} - 18525 x^{6} + \cdots + 3125 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 316.3
Root \(0.670843 - 1.77989i\) of defining polynomial
Character \(\chi\) \(=\) 525.316
Dual form 525.2.n.b.211.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.140253 + 0.101900i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.608747 - 1.87353i) q^{4} +(-0.103443 + 2.23367i) q^{5} +(0.0535718 - 0.164877i) q^{6} -1.00000 q^{7} +(0.212677 - 0.654553i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.140253 + 0.101900i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.608747 - 1.87353i) q^{4} +(-0.103443 + 2.23367i) q^{5} +(0.0535718 - 0.164877i) q^{6} -1.00000 q^{7} +(0.212677 - 0.654553i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.242119 + 0.302738i) q^{10} +(-3.98347 - 2.89416i) q^{11} +(-1.59372 + 1.15790i) q^{12} +(-3.12241 + 2.26857i) q^{13} +(-0.140253 - 0.101900i) q^{14} +(2.15632 - 0.591863i) q^{15} +(-3.09091 + 2.24568i) q^{16} +(1.66834 - 5.13463i) q^{17} -0.173362 q^{18} +(-1.78685 + 5.49935i) q^{19} +(4.24783 - 1.16594i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-0.263779 - 0.811828i) q^{22} +(-0.272132 - 0.197715i) q^{23} -0.688238 q^{24} +(-4.97860 - 0.462118i) q^{25} -0.669093 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.608747 + 1.87353i) q^{28} +(-0.417431 - 1.28472i) q^{29} +(0.362740 + 0.136717i) q^{30} +(-0.343308 + 1.05659i) q^{31} -2.03882 q^{32} +(-1.52155 + 4.68285i) q^{33} +(0.757206 - 0.550143i) q^{34} +(0.103443 - 2.23367i) q^{35} +(1.59372 + 1.15790i) q^{36} +(3.76515 - 2.73554i) q^{37} +(-0.810992 + 0.589220i) q^{38} +(3.12241 + 2.26857i) q^{39} +(1.44006 + 0.542760i) q^{40} +(-8.43156 + 6.12589i) q^{41} +(-0.0535718 + 0.164877i) q^{42} -12.9331 q^{43} +(-2.99737 + 9.22496i) q^{44} +(-1.22923 - 1.86788i) q^{45} +(-0.0180201 - 0.0554602i) q^{46} +(-2.99015 - 9.20273i) q^{47} +(3.09091 + 2.24568i) q^{48} +1.00000 q^{49} +(-0.651173 - 0.572131i) q^{50} -5.39887 q^{51} +(6.15098 + 4.46895i) q^{52} +(1.75047 + 5.38738i) q^{53} +(0.0535718 + 0.164877i) q^{54} +(6.87668 - 8.59839i) q^{55} +(-0.212677 + 0.654553i) q^{56} +5.78236 q^{57} +(0.0723666 - 0.222722i) q^{58} +(7.51633 - 5.46094i) q^{59} +(-2.42152 - 3.67963i) q^{60} +(11.2981 + 8.20855i) q^{61} +(-0.155816 + 0.113207i) q^{62} +(0.809017 - 0.587785i) q^{63} +(5.89587 + 4.28360i) q^{64} +(-4.74424 - 7.20912i) q^{65} +(-0.690582 + 0.501737i) q^{66} +(1.34247 - 4.13171i) q^{67} -10.6355 q^{68} +(-0.103945 + 0.319910i) q^{69} +(0.242119 - 0.302738i) q^{70} +(-2.22269 - 6.84074i) q^{71} +(0.212677 + 0.654553i) q^{72} +(-3.13204 - 2.27556i) q^{73} +0.806824 q^{74} +(1.09897 + 4.87773i) q^{75} +11.3909 q^{76} +(3.98347 + 2.89416i) q^{77} +(0.206761 + 0.636345i) q^{78} +(-2.05233 - 6.31641i) q^{79} +(-4.69638 - 7.13639i) q^{80} +(0.309017 - 0.951057i) q^{81} -1.80678 q^{82} +(3.87703 - 11.9323i) q^{83} +(1.59372 - 1.15790i) q^{84} +(11.2965 + 4.25768i) q^{85} +(-1.81390 - 1.31788i) q^{86} +(-1.09285 + 0.794001i) q^{87} +(-2.74157 + 1.99187i) q^{88} +(-0.344926 - 0.250603i) q^{89} +(0.0179332 - 0.387234i) q^{90} +(3.12241 - 2.26857i) q^{91} +(-0.204766 + 0.630205i) q^{92} +1.11097 q^{93} +(0.518378 - 1.59540i) q^{94} +(-12.0989 - 4.56011i) q^{95} +(0.630029 + 1.93903i) q^{96} +(-0.998049 - 3.07168i) q^{97} +(0.140253 + 0.101900i) q^{98} +4.92384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.140253 + 0.101900i 0.0991737 + 0.0720539i 0.636267 0.771469i \(-0.280478\pi\)
−0.537093 + 0.843523i \(0.680478\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) −0.608747 1.87353i −0.304373 0.936765i
\(5\) −0.103443 + 2.23367i −0.0462613 + 0.998929i
\(6\) 0.0535718 0.164877i 0.0218706 0.0673108i
\(7\) −1.00000 −0.377964
\(8\) 0.212677 0.654553i 0.0751927 0.231419i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −0.242119 + 0.302738i −0.0765647 + 0.0957342i
\(11\) −3.98347 2.89416i −1.20106 0.872622i −0.206673 0.978410i \(-0.566264\pi\)
−0.994389 + 0.105788i \(0.966264\pi\)
\(12\) −1.59372 + 1.15790i −0.460067 + 0.334258i
\(13\) −3.12241 + 2.26857i −0.866001 + 0.629187i −0.929511 0.368794i \(-0.879771\pi\)
0.0635096 + 0.997981i \(0.479771\pi\)
\(14\) −0.140253 0.101900i −0.0374841 0.0272338i
\(15\) 2.15632 0.591863i 0.556758 0.152818i
\(16\) −3.09091 + 2.24568i −0.772728 + 0.561420i
\(17\) 1.66834 5.13463i 0.404632 1.24533i −0.516569 0.856245i \(-0.672791\pi\)
0.921202 0.389085i \(-0.127209\pi\)
\(18\) −0.173362 −0.0408618
\(19\) −1.78685 + 5.49935i −0.409931 + 1.26164i 0.506776 + 0.862078i \(0.330837\pi\)
−0.916707 + 0.399560i \(0.869163\pi\)
\(20\) 4.24783 1.16594i 0.949843 0.260712i
\(21\) 0.309017 + 0.951057i 0.0674330 + 0.207538i
\(22\) −0.263779 0.811828i −0.0562379 0.173082i
\(23\) −0.272132 0.197715i −0.0567434 0.0412265i 0.559052 0.829133i \(-0.311165\pi\)
−0.615795 + 0.787906i \(0.711165\pi\)
\(24\) −0.688238 −0.140486
\(25\) −4.97860 0.462118i −0.995720 0.0924236i
\(26\) −0.669093 −0.131220
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 0.608747 + 1.87353i 0.115042 + 0.354064i
\(29\) −0.417431 1.28472i −0.0775150 0.238567i 0.904789 0.425860i \(-0.140028\pi\)
−0.982304 + 0.187294i \(0.940028\pi\)
\(30\) 0.362740 + 0.136717i 0.0662269 + 0.0249611i
\(31\) −0.343308 + 1.05659i −0.0616599 + 0.189770i −0.977141 0.212590i \(-0.931810\pi\)
0.915481 + 0.402360i \(0.131810\pi\)
\(32\) −2.03882 −0.360415
\(33\) −1.52155 + 4.68285i −0.264868 + 0.815180i
\(34\) 0.757206 0.550143i 0.129860 0.0943487i
\(35\) 0.103443 2.23367i 0.0174851 0.377560i
\(36\) 1.59372 + 1.15790i 0.265620 + 0.192984i
\(37\) 3.76515 2.73554i 0.618987 0.449721i −0.233580 0.972338i \(-0.575044\pi\)
0.852568 + 0.522617i \(0.175044\pi\)
\(38\) −0.810992 + 0.589220i −0.131560 + 0.0955841i
\(39\) 3.12241 + 2.26857i 0.499986 + 0.363261i
\(40\) 1.44006 + 0.542760i 0.227693 + 0.0858180i
\(41\) −8.43156 + 6.12589i −1.31679 + 0.956703i −0.316822 + 0.948485i \(0.602616\pi\)
−0.999966 + 0.00821814i \(0.997384\pi\)
\(42\) −0.0535718 + 0.164877i −0.00826631 + 0.0254411i
\(43\) −12.9331 −1.97228 −0.986138 0.165926i \(-0.946939\pi\)
−0.986138 + 0.165926i \(0.946939\pi\)
\(44\) −2.99737 + 9.22496i −0.451871 + 1.39072i
\(45\) −1.22923 1.86788i −0.183243 0.278448i
\(46\) −0.0180201 0.0554602i −0.00265692 0.00817716i
\(47\) −2.99015 9.20273i −0.436158 1.34236i −0.891895 0.452242i \(-0.850624\pi\)
0.455737 0.890114i \(-0.349376\pi\)
\(48\) 3.09091 + 2.24568i 0.446135 + 0.324136i
\(49\) 1.00000 0.142857
\(50\) −0.651173 0.572131i −0.0920897 0.0809115i
\(51\) −5.39887 −0.755993
\(52\) 6.15098 + 4.46895i 0.852988 + 0.619732i
\(53\) 1.75047 + 5.38738i 0.240445 + 0.740013i 0.996352 + 0.0853349i \(0.0271960\pi\)
−0.755907 + 0.654679i \(0.772804\pi\)
\(54\) 0.0535718 + 0.164877i 0.00729020 + 0.0224369i
\(55\) 6.87668 8.59839i 0.927251 1.15941i
\(56\) −0.212677 + 0.654553i −0.0284202 + 0.0874683i
\(57\) 5.78236 0.765892
\(58\) 0.0723666 0.222722i 0.00950220 0.0292448i
\(59\) 7.51633 5.46094i 0.978543 0.710953i 0.0211607 0.999776i \(-0.493264\pi\)
0.957383 + 0.288823i \(0.0932638\pi\)
\(60\) −2.42152 3.67963i −0.312617 0.475038i
\(61\) 11.2981 + 8.20855i 1.44657 + 1.05100i 0.986617 + 0.163057i \(0.0521353\pi\)
0.459957 + 0.887941i \(0.347865\pi\)
\(62\) −0.155816 + 0.113207i −0.0197887 + 0.0143773i
\(63\) 0.809017 0.587785i 0.101927 0.0740540i
\(64\) 5.89587 + 4.28360i 0.736984 + 0.535450i
\(65\) −4.74424 7.20912i −0.588451 0.894181i
\(66\) −0.690582 + 0.501737i −0.0850048 + 0.0617596i
\(67\) 1.34247 4.13171i 0.164009 0.504769i −0.834953 0.550322i \(-0.814505\pi\)
0.998962 + 0.0455530i \(0.0145050\pi\)
\(68\) −10.6355 −1.28974
\(69\) −0.103945 + 0.319910i −0.0125135 + 0.0385126i
\(70\) 0.242119 0.302738i 0.0289387 0.0361841i
\(71\) −2.22269 6.84074i −0.263785 0.811846i −0.991971 0.126467i \(-0.959636\pi\)
0.728186 0.685380i \(-0.240364\pi\)
\(72\) 0.212677 + 0.654553i 0.0250642 + 0.0771398i
\(73\) −3.13204 2.27556i −0.366577 0.266334i 0.389213 0.921148i \(-0.372747\pi\)
−0.755790 + 0.654814i \(0.772747\pi\)
\(74\) 0.806824 0.0937914
\(75\) 1.09897 + 4.87773i 0.126898 + 0.563232i
\(76\) 11.3909 1.30663
\(77\) 3.98347 + 2.89416i 0.453959 + 0.329820i
\(78\) 0.206761 + 0.636345i 0.0234111 + 0.0720519i
\(79\) −2.05233 6.31641i −0.230905 0.710652i −0.997638 0.0686864i \(-0.978119\pi\)
0.766733 0.641966i \(-0.221881\pi\)
\(80\) −4.69638 7.13639i −0.525071 0.797873i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −1.80678 −0.199525
\(83\) 3.87703 11.9323i 0.425559 1.30974i −0.476898 0.878958i \(-0.658239\pi\)
0.902458 0.430778i \(-0.141761\pi\)
\(84\) 1.59372 1.15790i 0.173889 0.126338i
\(85\) 11.2965 + 4.25768i 1.22528 + 0.461810i
\(86\) −1.81390 1.31788i −0.195598 0.142110i
\(87\) −1.09285 + 0.794001i −0.117166 + 0.0851258i
\(88\) −2.74157 + 1.99187i −0.292253 + 0.212334i
\(89\) −0.344926 0.250603i −0.0365621 0.0265639i 0.569354 0.822092i \(-0.307193\pi\)
−0.605916 + 0.795528i \(0.707193\pi\)
\(90\) 0.0179332 0.387234i 0.00189032 0.0408181i
\(91\) 3.12241 2.26857i 0.327318 0.237810i
\(92\) −0.204766 + 0.630205i −0.0213483 + 0.0657034i
\(93\) 1.11097 0.115202
\(94\) 0.518378 1.59540i 0.0534666 0.164553i
\(95\) −12.0989 4.56011i −1.24132 0.467857i
\(96\) 0.630029 + 1.93903i 0.0643021 + 0.197902i
\(97\) −0.998049 3.07168i −0.101337 0.311882i 0.887517 0.460776i \(-0.152429\pi\)
−0.988853 + 0.148894i \(0.952429\pi\)
\(98\) 0.140253 + 0.101900i 0.0141677 + 0.0102934i
\(99\) 4.92384 0.494865
\(100\) 2.16491 + 9.60887i 0.216491 + 0.960887i
\(101\) 8.33213 0.829078 0.414539 0.910031i \(-0.363943\pi\)
0.414539 + 0.910031i \(0.363943\pi\)
\(102\) −0.757206 0.550143i −0.0749746 0.0544722i
\(103\) −5.05572 15.5599i −0.498155 1.53316i −0.811981 0.583683i \(-0.801611\pi\)
0.313826 0.949480i \(-0.398389\pi\)
\(104\) 0.820830 + 2.52626i 0.0804890 + 0.247720i
\(105\) −2.15632 + 0.591863i −0.210435 + 0.0577599i
\(106\) −0.303464 + 0.933967i −0.0294750 + 0.0907149i
\(107\) 11.7307 1.13405 0.567025 0.823701i \(-0.308094\pi\)
0.567025 + 0.823701i \(0.308094\pi\)
\(108\) 0.608747 1.87353i 0.0585767 0.180280i
\(109\) −6.97950 + 5.07090i −0.668514 + 0.485704i −0.869528 0.493884i \(-0.835577\pi\)
0.201013 + 0.979589i \(0.435577\pi\)
\(110\) 1.84065 0.505218i 0.175499 0.0481706i
\(111\) −3.76515 2.73554i −0.357373 0.259646i
\(112\) 3.09091 2.24568i 0.292064 0.212197i
\(113\) 1.11215 0.808027i 0.104623 0.0760128i −0.534244 0.845330i \(-0.679404\pi\)
0.638867 + 0.769318i \(0.279404\pi\)
\(114\) 0.810992 + 0.589220i 0.0759564 + 0.0551855i
\(115\) 0.469781 0.587401i 0.0438074 0.0547754i
\(116\) −2.15285 + 1.56414i −0.199887 + 0.145227i
\(117\) 1.19266 3.67062i 0.110261 0.339349i
\(118\) 1.61065 0.148273
\(119\) −1.66834 + 5.13463i −0.152937 + 0.470691i
\(120\) 0.0711936 1.53730i 0.00649906 0.140335i
\(121\) 4.09269 + 12.5960i 0.372062 + 1.14509i
\(122\) 0.748142 + 2.30254i 0.0677336 + 0.208463i
\(123\) 8.43156 + 6.12589i 0.760248 + 0.552353i
\(124\) 2.18855 0.196537
\(125\) 1.54722 11.0728i 0.138388 0.990378i
\(126\) 0.173362 0.0154443
\(127\) 5.59588 + 4.06564i 0.496554 + 0.360767i 0.807699 0.589595i \(-0.200713\pi\)
−0.311145 + 0.950362i \(0.600713\pi\)
\(128\) 1.65047 + 5.07964i 0.145883 + 0.448981i
\(129\) 3.99654 + 12.3001i 0.351876 + 1.08296i
\(130\) 0.0692133 1.49454i 0.00607040 0.131079i
\(131\) −1.66853 + 5.13521i −0.145780 + 0.448665i −0.997110 0.0759648i \(-0.975796\pi\)
0.851330 + 0.524630i \(0.175796\pi\)
\(132\) 9.69970 0.844250
\(133\) 1.78685 5.49935i 0.154939 0.476854i
\(134\) 0.609306 0.442686i 0.0526360 0.0382423i
\(135\) −1.39661 + 1.74628i −0.120201 + 0.150296i
\(136\) −3.00607 2.18404i −0.257768 0.187280i
\(137\) −6.56538 + 4.77003i −0.560918 + 0.407531i −0.831795 0.555083i \(-0.812686\pi\)
0.270877 + 0.962614i \(0.412686\pi\)
\(138\) −0.0471773 + 0.0342763i −0.00401600 + 0.00291779i
\(139\) 7.27751 + 5.28742i 0.617270 + 0.448473i 0.851967 0.523596i \(-0.175410\pi\)
−0.234697 + 0.972069i \(0.575410\pi\)
\(140\) −4.24783 + 1.16594i −0.359007 + 0.0985397i
\(141\) −7.82831 + 5.68760i −0.659263 + 0.478982i
\(142\) 0.385330 1.18592i 0.0323362 0.0995205i
\(143\) 19.0036 1.58916
\(144\) 1.18062 3.63358i 0.0983853 0.302799i
\(145\) 2.91283 0.799509i 0.241897 0.0663956i
\(146\) −0.207399 0.638307i −0.0171644 0.0528267i
\(147\) −0.309017 0.951057i −0.0254873 0.0784418i
\(148\) −7.41715 5.38887i −0.609686 0.442963i
\(149\) −2.58958 −0.212146 −0.106073 0.994358i \(-0.533828\pi\)
−0.106073 + 0.994358i \(0.533828\pi\)
\(150\) −0.342905 + 0.796100i −0.0279981 + 0.0650013i
\(151\) −21.1746 −1.72316 −0.861581 0.507621i \(-0.830525\pi\)
−0.861581 + 0.507621i \(0.830525\pi\)
\(152\) 3.21959 + 2.33917i 0.261144 + 0.189732i
\(153\) 1.66834 + 5.13463i 0.134877 + 0.415110i
\(154\) 0.263779 + 0.811828i 0.0212559 + 0.0654190i
\(155\) −2.32457 0.876135i −0.186714 0.0703729i
\(156\) 2.34947 7.23091i 0.188108 0.578936i
\(157\) 7.69863 0.614418 0.307209 0.951642i \(-0.400605\pi\)
0.307209 + 0.951642i \(0.400605\pi\)
\(158\) 0.355795 1.09503i 0.0283056 0.0871156i
\(159\) 4.58278 3.32958i 0.363438 0.264053i
\(160\) 0.210902 4.55405i 0.0166733 0.360030i
\(161\) 0.272132 + 0.197715i 0.0214470 + 0.0155821i
\(162\) 0.140253 0.101900i 0.0110193 0.00800599i
\(163\) −6.87462 + 4.99470i −0.538461 + 0.391215i −0.823513 0.567297i \(-0.807989\pi\)
0.285052 + 0.958512i \(0.407989\pi\)
\(164\) 16.6097 + 12.0677i 1.29700 + 0.942326i
\(165\) −10.3026 3.88306i −0.802054 0.302296i
\(166\) 1.75966 1.27847i 0.136576 0.0992282i
\(167\) 1.15615 3.55826i 0.0894655 0.275347i −0.896306 0.443435i \(-0.853760\pi\)
0.985772 + 0.168089i \(0.0537595\pi\)
\(168\) 0.688238 0.0530987
\(169\) 0.585850 1.80306i 0.0450654 0.138697i
\(170\) 1.15051 + 1.74826i 0.0882402 + 0.134085i
\(171\) −1.78685 5.49935i −0.136644 0.420546i
\(172\) 7.87297 + 24.2305i 0.600308 + 1.84756i
\(173\) −17.7348 12.8851i −1.34836 0.979637i −0.999092 0.0426128i \(-0.986432\pi\)
−0.349263 0.937025i \(-0.613568\pi\)
\(174\) −0.234183 −0.0177534
\(175\) 4.97860 + 0.462118i 0.376347 + 0.0349328i
\(176\) 18.8119 1.41800
\(177\) −7.51633 5.46094i −0.564962 0.410469i
\(178\) −0.0228404 0.0702957i −0.00171196 0.00526888i
\(179\) 1.34174 + 4.12946i 0.100287 + 0.308650i 0.988595 0.150596i \(-0.0481194\pi\)
−0.888309 + 0.459247i \(0.848119\pi\)
\(180\) −2.75124 + 3.44007i −0.205065 + 0.256408i
\(181\) −2.66192 + 8.19255i −0.197859 + 0.608947i 0.802072 + 0.597227i \(0.203731\pi\)
−0.999931 + 0.0117203i \(0.996269\pi\)
\(182\) 0.669093 0.0495965
\(183\) 4.31549 13.2817i 0.319010 0.981813i
\(184\) −0.187291 + 0.136075i −0.0138073 + 0.0100316i
\(185\) 5.72083 + 8.69310i 0.420604 + 0.639129i
\(186\) 0.155816 + 0.113207i 0.0114250 + 0.00830075i
\(187\) −21.5062 + 15.6252i −1.57269 + 1.14263i
\(188\) −15.4213 + 11.2043i −1.12472 + 0.817155i
\(189\) −0.809017 0.587785i −0.0588473 0.0427551i
\(190\) −1.23223 1.87244i −0.0893956 0.135841i
\(191\) −2.61655 + 1.90103i −0.189327 + 0.137554i −0.678411 0.734683i \(-0.737331\pi\)
0.489084 + 0.872237i \(0.337331\pi\)
\(192\) 2.25202 6.93102i 0.162526 0.500203i
\(193\) −19.4993 −1.40359 −0.701795 0.712379i \(-0.747618\pi\)
−0.701795 + 0.712379i \(0.747618\pi\)
\(194\) 0.173024 0.532512i 0.0124224 0.0382322i
\(195\) −5.39023 + 6.73978i −0.386002 + 0.482646i
\(196\) −0.608747 1.87353i −0.0434819 0.133824i
\(197\) −5.18757 15.9657i −0.369599 1.13751i −0.947051 0.321084i \(-0.895953\pi\)
0.577452 0.816425i \(-0.304047\pi\)
\(198\) 0.690582 + 0.501737i 0.0490775 + 0.0356569i
\(199\) 1.51751 0.107573 0.0537867 0.998552i \(-0.482871\pi\)
0.0537867 + 0.998552i \(0.482871\pi\)
\(200\) −1.36131 + 3.16047i −0.0962595 + 0.223479i
\(201\) −4.34434 −0.306426
\(202\) 1.16860 + 0.849041i 0.0822227 + 0.0597383i
\(203\) 0.417431 + 1.28472i 0.0292979 + 0.0901697i
\(204\) 3.28654 + 10.1149i 0.230104 + 0.708188i
\(205\) −12.8110 19.4670i −0.894762 1.35964i
\(206\) 0.876470 2.69750i 0.0610666 0.187944i
\(207\) 0.336373 0.0233796
\(208\) 4.55663 14.0239i 0.315946 0.972381i
\(209\) 23.0339 16.7351i 1.59329 1.15759i
\(210\) −0.362740 0.136717i −0.0250314 0.00943439i
\(211\) 18.3991 + 13.3677i 1.26664 + 0.920270i 0.999064 0.0432655i \(-0.0137761\pi\)
0.267580 + 0.963536i \(0.413776\pi\)
\(212\) 9.02783 6.55910i 0.620034 0.450481i
\(213\) −5.81908 + 4.22781i −0.398717 + 0.289685i
\(214\) 1.64526 + 1.19535i 0.112468 + 0.0817127i
\(215\) 1.33784 28.8883i 0.0912401 1.97016i
\(216\) 0.556796 0.404536i 0.0378852 0.0275252i
\(217\) 0.343308 1.05659i 0.0233053 0.0717262i
\(218\) −1.49562 −0.101296
\(219\) −1.19633 + 3.68193i −0.0808407 + 0.248802i
\(220\) −20.2955 7.64941i −1.36832 0.515723i
\(221\) 6.43899 + 19.8172i 0.433133 + 1.33305i
\(222\) −0.249322 0.767335i −0.0167334 0.0515002i
\(223\) 18.1226 + 13.1669i 1.21358 + 0.881718i 0.995551 0.0942242i \(-0.0300370\pi\)
0.218030 + 0.975942i \(0.430037\pi\)
\(224\) 2.03882 0.136224
\(225\) 4.29940 2.55249i 0.286626 0.170166i
\(226\) 0.238320 0.0158528
\(227\) 7.08145 + 5.14497i 0.470012 + 0.341484i 0.797446 0.603390i \(-0.206184\pi\)
−0.327434 + 0.944874i \(0.606184\pi\)
\(228\) −3.51999 10.8334i −0.233117 0.717461i
\(229\) −3.29835 10.1513i −0.217961 0.670816i −0.998930 0.0462458i \(-0.985274\pi\)
0.780969 0.624570i \(-0.214726\pi\)
\(230\) 0.125744 0.0345141i 0.00829132 0.00227579i
\(231\) 1.52155 4.68285i 0.100111 0.308109i
\(232\) −0.929695 −0.0610375
\(233\) −2.45494 + 7.55554i −0.160829 + 0.494980i −0.998705 0.0508807i \(-0.983797\pi\)
0.837876 + 0.545861i \(0.183797\pi\)
\(234\) 0.541308 0.393283i 0.0353864 0.0257097i
\(235\) 20.8652 5.72706i 1.36110 0.373592i
\(236\) −14.8068 10.7577i −0.963839 0.700270i
\(237\) −5.37306 + 3.90376i −0.349018 + 0.253576i
\(238\) −0.757206 + 0.550143i −0.0490824 + 0.0356604i
\(239\) −23.6624 17.1918i −1.53060 1.11204i −0.955907 0.293670i \(-0.905123\pi\)
−0.574688 0.818372i \(-0.694877\pi\)
\(240\) −5.33585 + 6.67179i −0.344428 + 0.430662i
\(241\) −14.5962 + 10.6048i −0.940227 + 0.683115i −0.948475 0.316851i \(-0.897374\pi\)
0.00824862 + 0.999966i \(0.497374\pi\)
\(242\) −0.709516 + 2.18367i −0.0456094 + 0.140371i
\(243\) −1.00000 −0.0641500
\(244\) 8.50128 26.1643i 0.544239 1.67500i
\(245\) −0.103443 + 2.23367i −0.00660876 + 0.142704i
\(246\) 0.558324 + 1.71835i 0.0355975 + 0.109558i
\(247\) −6.89636 21.2248i −0.438805 1.35050i
\(248\) 0.618582 + 0.449426i 0.0392800 + 0.0285386i
\(249\) −12.5463 −0.795091
\(250\) 1.34531 1.39532i 0.0850850 0.0882481i
\(251\) −28.6358 −1.80747 −0.903737 0.428089i \(-0.859187\pi\)
−0.903737 + 0.428089i \(0.859187\pi\)
\(252\) −1.59372 1.15790i −0.100395 0.0729412i
\(253\) 0.511809 + 1.57519i 0.0321771 + 0.0990311i
\(254\) 0.370550 + 1.14044i 0.0232504 + 0.0715573i
\(255\) 0.558478 12.0593i 0.0349732 0.755184i
\(256\) 4.21792 12.9814i 0.263620 0.811338i
\(257\) 7.06752 0.440860 0.220430 0.975403i \(-0.429254\pi\)
0.220430 + 0.975403i \(0.429254\pi\)
\(258\) −0.692848 + 2.13237i −0.0431349 + 0.132755i
\(259\) −3.76515 + 2.73554i −0.233955 + 0.169978i
\(260\) −10.6185 + 13.2770i −0.658529 + 0.823405i
\(261\) 1.09285 + 0.794001i 0.0676456 + 0.0491474i
\(262\) −0.757292 + 0.550204i −0.0467856 + 0.0339917i
\(263\) −2.62924 + 1.91025i −0.162126 + 0.117791i −0.665890 0.746050i \(-0.731948\pi\)
0.503764 + 0.863841i \(0.331948\pi\)
\(264\) 2.74157 + 1.99187i 0.168732 + 0.122591i
\(265\) −12.2147 + 3.35268i −0.750345 + 0.205954i
\(266\) 0.810992 0.589220i 0.0497251 0.0361274i
\(267\) −0.131750 + 0.405485i −0.00806297 + 0.0248153i
\(268\) −8.55811 −0.522770
\(269\) −8.47667 + 26.0885i −0.516832 + 1.59065i 0.263092 + 0.964771i \(0.415258\pi\)
−0.779924 + 0.625874i \(0.784742\pi\)
\(270\) −0.373823 + 0.102606i −0.0227502 + 0.00624443i
\(271\) 7.01585 + 21.5926i 0.426183 + 1.31166i 0.901857 + 0.432034i \(0.142204\pi\)
−0.475674 + 0.879621i \(0.657796\pi\)
\(272\) 6.37403 + 19.6172i 0.386482 + 1.18947i
\(273\) −3.12241 2.26857i −0.188977 0.137300i
\(274\) −1.40688 −0.0849925
\(275\) 18.4947 + 16.2497i 1.11527 + 0.979894i
\(276\) 0.662637 0.0398861
\(277\) −10.4356 7.58193i −0.627016 0.455554i 0.228349 0.973579i \(-0.426667\pi\)
−0.855365 + 0.518025i \(0.826667\pi\)
\(278\) 0.481905 + 1.48315i 0.0289027 + 0.0889534i
\(279\) −0.343308 1.05659i −0.0205533 0.0632566i
\(280\) −1.44006 0.542760i −0.0860599 0.0324361i
\(281\) −5.61713 + 17.2877i −0.335090 + 1.03130i 0.631588 + 0.775304i \(0.282403\pi\)
−0.966678 + 0.255996i \(0.917597\pi\)
\(282\) −1.67751 −0.0998941
\(283\) −0.296866 + 0.913659i −0.0176468 + 0.0543114i −0.959492 0.281735i \(-0.909090\pi\)
0.941845 + 0.336047i \(0.109090\pi\)
\(284\) −11.4633 + 8.32855i −0.680220 + 0.494209i
\(285\) −0.598147 + 12.9159i −0.0354312 + 0.765072i
\(286\) 2.66531 + 1.93646i 0.157603 + 0.114505i
\(287\) 8.43156 6.12589i 0.497699 0.361600i
\(288\) 1.64944 1.19839i 0.0971941 0.0706156i
\(289\) −9.82777 7.14029i −0.578104 0.420017i
\(290\) 0.490002 + 0.184683i 0.0287739 + 0.0108449i
\(291\) −2.61293 + 1.89840i −0.153172 + 0.111286i
\(292\) −2.35671 + 7.25321i −0.137916 + 0.424462i
\(293\) 25.4569 1.48721 0.743605 0.668619i \(-0.233114\pi\)
0.743605 + 0.668619i \(0.233114\pi\)
\(294\) 0.0535718 0.164877i 0.00312437 0.00961582i
\(295\) 11.4204 + 17.3539i 0.664923 + 1.01039i
\(296\) −0.989796 3.04628i −0.0575307 0.177061i
\(297\) −1.52155 4.68285i −0.0882893 0.271727i
\(298\) −0.363195 0.263877i −0.0210393 0.0152860i
\(299\) 1.29824 0.0750790
\(300\) 8.46958 5.02826i 0.488991 0.290307i
\(301\) 12.9331 0.745450
\(302\) −2.96979 2.15768i −0.170892 0.124160i
\(303\) −2.57477 7.92433i −0.147917 0.455241i
\(304\) −6.82679 21.0107i −0.391543 1.20505i
\(305\) −19.5039 + 24.3872i −1.11679 + 1.39640i
\(306\) −0.289227 + 0.890149i −0.0165340 + 0.0508865i
\(307\) −14.4583 −0.825179 −0.412589 0.910917i \(-0.635376\pi\)
−0.412589 + 0.910917i \(0.635376\pi\)
\(308\) 2.99737 9.22496i 0.170791 0.525641i
\(309\) −13.2361 + 9.61656i −0.752973 + 0.547067i
\(310\) −0.236750 0.359753i −0.0134465 0.0204326i
\(311\) −3.34568 2.43078i −0.189716 0.137837i 0.488873 0.872355i \(-0.337408\pi\)
−0.678589 + 0.734518i \(0.737408\pi\)
\(312\) 2.14896 1.56131i 0.121661 0.0883919i
\(313\) −18.9735 + 13.7850i −1.07244 + 0.779175i −0.976350 0.216197i \(-0.930635\pi\)
−0.0960932 + 0.995372i \(0.530635\pi\)
\(314\) 1.07975 + 0.784488i 0.0609341 + 0.0442712i
\(315\) 1.22923 + 1.86788i 0.0692594 + 0.105243i
\(316\) −10.5846 + 7.69019i −0.595433 + 0.432607i
\(317\) 6.45204 19.8573i 0.362383 1.11530i −0.589221 0.807972i \(-0.700565\pi\)
0.951604 0.307327i \(-0.0994347\pi\)
\(318\) 0.982031 0.0550695
\(319\) −2.05536 + 6.32576i −0.115078 + 0.354174i
\(320\) −10.1781 + 12.7263i −0.568971 + 0.711425i
\(321\) −3.62499 11.1566i −0.202327 0.622699i
\(322\) 0.0180201 + 0.0554602i 0.00100422 + 0.00309068i
\(323\) 25.2561 + 18.3496i 1.40528 + 1.02100i
\(324\) −1.96995 −0.109441
\(325\) 16.5936 9.85136i 0.920446 0.546455i
\(326\) −1.47314 −0.0815898
\(327\) 6.97950 + 5.07090i 0.385967 + 0.280421i
\(328\) 2.21652 + 6.82174i 0.122387 + 0.376667i
\(329\) 2.99015 + 9.20273i 0.164852 + 0.507363i
\(330\) −1.04928 1.59444i −0.0577610 0.0877709i
\(331\) 5.37110 16.5305i 0.295222 0.908601i −0.687924 0.725782i \(-0.741478\pi\)
0.983147 0.182819i \(-0.0585221\pi\)
\(332\) −24.7156 −1.35644
\(333\) −1.43816 + 4.42620i −0.0788107 + 0.242554i
\(334\) 0.524739 0.381245i 0.0287124 0.0208608i
\(335\) 9.09003 + 3.42605i 0.496641 + 0.187185i
\(336\) −3.09091 2.24568i −0.168623 0.122512i
\(337\) 14.5098 10.5420i 0.790402 0.574261i −0.117681 0.993051i \(-0.537546\pi\)
0.908083 + 0.418791i \(0.137546\pi\)
\(338\) 0.265898 0.193186i 0.0144630 0.0105080i
\(339\) −1.11215 0.808027i −0.0604039 0.0438860i
\(340\) 1.10017 23.7562i 0.0596651 1.28836i
\(341\) 4.42551 3.21532i 0.239655 0.174119i
\(342\) 0.309771 0.953378i 0.0167505 0.0515528i
\(343\) −1.00000 −0.0539949
\(344\) −2.75057 + 8.46538i −0.148301 + 0.456423i
\(345\) −0.703822 0.265272i −0.0378925 0.0142818i
\(346\) −1.17437 3.61435i −0.0631347 0.194308i
\(347\) −2.40870 7.41322i −0.129306 0.397962i 0.865355 0.501159i \(-0.167093\pi\)
−0.994661 + 0.103197i \(0.967093\pi\)
\(348\) 2.15285 + 1.56414i 0.115405 + 0.0838466i
\(349\) −13.7889 −0.738102 −0.369051 0.929409i \(-0.620317\pi\)
−0.369051 + 0.929409i \(0.620317\pi\)
\(350\) 0.651173 + 0.572131i 0.0348066 + 0.0305817i
\(351\) −3.85951 −0.206006
\(352\) 8.12157 + 5.90067i 0.432881 + 0.314507i
\(353\) 3.29322 + 10.1355i 0.175281 + 0.539458i 0.999646 0.0265997i \(-0.00846794\pi\)
−0.824366 + 0.566058i \(0.808468\pi\)
\(354\) −0.497719 1.53182i −0.0264535 0.0814155i
\(355\) 15.5099 4.25714i 0.823180 0.225945i
\(356\) −0.259540 + 0.798783i −0.0137556 + 0.0423354i
\(357\) 5.39887 0.285738
\(358\) −0.232607 + 0.715891i −0.0122937 + 0.0378360i
\(359\) −15.7595 + 11.4500i −0.831757 + 0.604307i −0.920056 0.391787i \(-0.871857\pi\)
0.0882990 + 0.996094i \(0.471857\pi\)
\(360\) −1.48406 + 0.407342i −0.0782167 + 0.0214688i
\(361\) −11.6787 8.48508i −0.614669 0.446583i
\(362\) −1.20816 + 0.877779i −0.0634994 + 0.0461350i
\(363\) 10.7148 7.78475i 0.562381 0.408593i
\(364\) −6.15098 4.46895i −0.322399 0.234237i
\(365\) 5.40685 6.76056i 0.283007 0.353864i
\(366\) 1.95866 1.42305i 0.102381 0.0743841i
\(367\) −6.49527 + 19.9904i −0.339050 + 1.04349i 0.625642 + 0.780110i \(0.284837\pi\)
−0.964692 + 0.263379i \(0.915163\pi\)
\(368\) 1.28514 0.0669925
\(369\) 3.22057 9.91190i 0.167656 0.515993i
\(370\) −0.0834606 + 1.80218i −0.00433891 + 0.0936910i
\(371\) −1.75047 5.38738i −0.0908797 0.279699i
\(372\) −0.676298 2.08143i −0.0350644 0.107917i
\(373\) 1.55506 + 1.12981i 0.0805177 + 0.0584995i 0.627316 0.778765i \(-0.284154\pi\)
−0.546798 + 0.837264i \(0.684154\pi\)
\(374\) −4.60851 −0.238300
\(375\) −11.0089 + 1.95018i −0.568499 + 0.100707i
\(376\) −6.65961 −0.343443
\(377\) 4.21786 + 3.06446i 0.217231 + 0.157828i
\(378\) −0.0535718 0.164877i −0.00275544 0.00848036i
\(379\) −8.44155 25.9804i −0.433613 1.33452i −0.894501 0.447066i \(-0.852469\pi\)
0.460888 0.887458i \(-0.347531\pi\)
\(380\) −1.17832 + 25.4436i −0.0604464 + 1.30523i
\(381\) 2.13743 6.57835i 0.109504 0.337019i
\(382\) −0.560692 −0.0286875
\(383\) 7.66337 23.5854i 0.391580 1.20516i −0.540013 0.841657i \(-0.681581\pi\)
0.931593 0.363503i \(-0.118419\pi\)
\(384\) 4.32100 3.13939i 0.220505 0.160206i
\(385\) −6.87668 + 8.59839i −0.350468 + 0.438215i
\(386\) −2.73483 1.98697i −0.139199 0.101134i
\(387\) 10.4631 7.60187i 0.531868 0.386425i
\(388\) −5.14732 + 3.73975i −0.261316 + 0.189857i
\(389\) 24.1679 + 17.5590i 1.22536 + 0.890275i 0.996534 0.0831923i \(-0.0265116\pi\)
0.228825 + 0.973468i \(0.426512\pi\)
\(390\) −1.44278 + 0.396011i −0.0730578 + 0.0200528i
\(391\) −1.46920 + 1.06744i −0.0743008 + 0.0539827i
\(392\) 0.212677 0.654553i 0.0107418 0.0330599i
\(393\) 5.39948 0.272368
\(394\) 0.899327 2.76784i 0.0453074 0.139442i
\(395\) 14.3211 3.93084i 0.720573 0.197782i
\(396\) −2.99737 9.22496i −0.150624 0.463572i
\(397\) 6.70970 + 20.6503i 0.336750 + 1.03641i 0.965854 + 0.259089i \(0.0834222\pi\)
−0.629103 + 0.777322i \(0.716578\pi\)
\(398\) 0.212835 + 0.154634i 0.0106685 + 0.00775109i
\(399\) −5.78236 −0.289480
\(400\) 16.4262 9.75197i 0.821309 0.487598i
\(401\) 6.80853 0.340002 0.170001 0.985444i \(-0.445623\pi\)
0.170001 + 0.985444i \(0.445623\pi\)
\(402\) −0.609306 0.442686i −0.0303894 0.0220792i
\(403\) −1.32500 4.07794i −0.0660030 0.203136i
\(404\) −5.07216 15.6105i −0.252349 0.776651i
\(405\) 2.09238 + 0.788624i 0.103971 + 0.0391870i
\(406\) −0.0723666 + 0.222722i −0.00359150 + 0.0110535i
\(407\) −22.9155 −1.13588
\(408\) −1.14822 + 3.53384i −0.0568452 + 0.174951i
\(409\) 23.0545 16.7501i 1.13997 0.828239i 0.152858 0.988248i \(-0.451152\pi\)
0.987116 + 0.160009i \(0.0511524\pi\)
\(410\) 0.186899 4.03575i 0.00923028 0.199311i
\(411\) 6.56538 + 4.77003i 0.323846 + 0.235288i
\(412\) −26.0743 + 18.9441i −1.28459 + 0.933308i
\(413\) −7.51633 + 5.46094i −0.369855 + 0.268715i
\(414\) 0.0471773 + 0.0342763i 0.00231864 + 0.00168459i
\(415\) 26.2517 + 9.89434i 1.28865 + 0.485694i
\(416\) 6.36603 4.62519i 0.312120 0.226769i
\(417\) 2.77976 8.55522i 0.136125 0.418951i
\(418\) 4.93586 0.241421
\(419\) −3.17721 + 9.77843i −0.155217 + 0.477708i −0.998183 0.0602589i \(-0.980807\pi\)
0.842966 + 0.537967i \(0.180807\pi\)
\(420\) 2.42152 + 3.67963i 0.118158 + 0.179547i
\(421\) −8.46010 26.0375i −0.412320 1.26899i −0.914626 0.404301i \(-0.867515\pi\)
0.502306 0.864690i \(-0.332485\pi\)
\(422\) 1.21836 + 3.74971i 0.0593086 + 0.182533i
\(423\) 7.82831 + 5.68760i 0.380626 + 0.276541i
\(424\) 3.89861 0.189333
\(425\) −10.6788 + 24.7923i −0.517998 + 1.20260i
\(426\) −1.24695 −0.0604151
\(427\) −11.2981 8.20855i −0.546754 0.397240i
\(428\) −7.14103 21.9778i −0.345175 1.06234i
\(429\) −5.87245 18.0735i −0.283524 0.872598i
\(430\) 3.13134 3.91534i 0.151007 0.188814i
\(431\) 8.11053 24.9616i 0.390670 1.20236i −0.541612 0.840629i \(-0.682186\pi\)
0.932282 0.361731i \(-0.117814\pi\)
\(432\) −3.82058 −0.183818
\(433\) −1.32780 + 4.08654i −0.0638099 + 0.196387i −0.977879 0.209172i \(-0.932923\pi\)
0.914069 + 0.405559i \(0.132923\pi\)
\(434\) 0.155816 0.113207i 0.00747942 0.00543412i
\(435\) −1.66049 2.52320i −0.0796144 0.120978i
\(436\) 13.7492 + 9.98940i 0.658469 + 0.478405i
\(437\) 1.57356 1.14326i 0.0752737 0.0546896i
\(438\) −0.542976 + 0.394495i −0.0259444 + 0.0188497i
\(439\) 12.4416 + 9.03935i 0.593805 + 0.431425i 0.843675 0.536855i \(-0.180388\pi\)
−0.249870 + 0.968280i \(0.580388\pi\)
\(440\) −4.16559 6.32983i −0.198587 0.301763i
\(441\) −0.809017 + 0.587785i −0.0385246 + 0.0279898i
\(442\) −1.11628 + 3.43554i −0.0530958 + 0.163412i
\(443\) −19.9081 −0.945863 −0.472931 0.881099i \(-0.656804\pi\)
−0.472931 + 0.881099i \(0.656804\pi\)
\(444\) −2.83310 + 8.71938i −0.134453 + 0.413803i
\(445\) 0.595447 0.744529i 0.0282269 0.0352941i
\(446\) 1.20005 + 3.69338i 0.0568240 + 0.174886i
\(447\) 0.800223 + 2.46283i 0.0378492 + 0.116488i
\(448\) −5.89587 4.28360i −0.278554 0.202381i
\(449\) 11.6474 0.549674 0.274837 0.961491i \(-0.411376\pi\)
0.274837 + 0.961491i \(0.411376\pi\)
\(450\) 0.863100 + 0.0801136i 0.0406869 + 0.00377659i
\(451\) 51.3162 2.41638
\(452\) −2.19088 1.59177i −0.103050 0.0748705i
\(453\) 6.54330 + 20.1382i 0.307431 + 0.946175i
\(454\) 0.468922 + 1.44319i 0.0220076 + 0.0677324i
\(455\) 4.74424 + 7.20912i 0.222414 + 0.337969i
\(456\) 1.22978 3.78486i 0.0575895 0.177242i
\(457\) −6.45368 −0.301890 −0.150945 0.988542i \(-0.548232\pi\)
−0.150945 + 0.988542i \(0.548232\pi\)
\(458\) 0.571809 1.75985i 0.0267189 0.0822322i
\(459\) 4.36778 3.17338i 0.203870 0.148120i
\(460\) −1.38649 0.522571i −0.0646455 0.0243650i
\(461\) −8.68384 6.30918i −0.404447 0.293848i 0.366903 0.930259i \(-0.380418\pi\)
−0.771350 + 0.636411i \(0.780418\pi\)
\(462\) 0.690582 0.501737i 0.0321288 0.0233429i
\(463\) −18.5034 + 13.4435i −0.859927 + 0.624774i −0.927865 0.372916i \(-0.878358\pi\)
0.0679381 + 0.997690i \(0.478358\pi\)
\(464\) 4.17531 + 3.03354i 0.193834 + 0.140829i
\(465\) −0.114922 + 2.48154i −0.00532939 + 0.115079i
\(466\) −1.11422 + 0.809528i −0.0516152 + 0.0375006i
\(467\) −0.262365 + 0.807476i −0.0121408 + 0.0373655i −0.956943 0.290275i \(-0.906253\pi\)
0.944803 + 0.327640i \(0.106253\pi\)
\(468\) −7.60303 −0.351450
\(469\) −1.34247 + 4.13171i −0.0619897 + 0.190785i
\(470\) 3.50999 + 1.32292i 0.161904 + 0.0610218i
\(471\) −2.37901 7.32184i −0.109619 0.337372i
\(472\) −1.97592 6.08125i −0.0909490 0.279912i
\(473\) 51.5186 + 37.4304i 2.36883 + 1.72105i
\(474\) −1.15138 −0.0528846
\(475\) 11.4373 26.5533i 0.524781 1.21835i
\(476\) 10.6355 0.487476
\(477\) −4.58278 3.32958i −0.209831 0.152451i
\(478\) −1.56689 4.82238i −0.0716678 0.220571i
\(479\) −6.69653 20.6098i −0.305972 0.941685i −0.979313 0.202353i \(-0.935141\pi\)
0.673341 0.739332i \(-0.264859\pi\)
\(480\) −4.39634 + 1.20670i −0.200664 + 0.0550781i
\(481\) −5.55060 + 17.0830i −0.253086 + 0.778918i
\(482\) −3.12779 −0.142467
\(483\) 0.103945 0.319910i 0.00472966 0.0145564i
\(484\) 21.1076 15.3355i 0.959434 0.697070i
\(485\) 6.96437 1.91157i 0.316236 0.0868000i
\(486\) −0.140253 0.101900i −0.00636199 0.00462226i
\(487\) −4.93797 + 3.58764i −0.223761 + 0.162572i −0.694018 0.719958i \(-0.744161\pi\)
0.470257 + 0.882529i \(0.344161\pi\)
\(488\) 7.77578 5.64943i 0.351993 0.255738i
\(489\) 6.87462 + 4.99470i 0.310881 + 0.225868i
\(490\) −0.242119 + 0.302738i −0.0109378 + 0.0136763i
\(491\) 26.6920 19.3929i 1.20460 0.875189i 0.209866 0.977730i \(-0.432697\pi\)
0.994729 + 0.102541i \(0.0326972\pi\)
\(492\) 6.34435 19.5259i 0.286025 0.880295i
\(493\) −7.29298 −0.328459
\(494\) 1.19557 3.67958i 0.0537911 0.165552i
\(495\) −0.509339 + 10.9983i −0.0228931 + 0.494335i
\(496\) −1.31163 4.03679i −0.0588941 0.181257i
\(497\) 2.22269 + 6.84074i 0.0997013 + 0.306849i
\(498\) −1.75966 1.27847i −0.0788521 0.0572894i
\(499\) −40.4940 −1.81276 −0.906380 0.422463i \(-0.861166\pi\)
−0.906380 + 0.422463i \(0.861166\pi\)
\(500\) −21.6870 + 3.84174i −0.969873 + 0.171808i
\(501\) −3.74138 −0.167152
\(502\) −4.01624 2.91797i −0.179254 0.130235i
\(503\) 9.68700 + 29.8135i 0.431922 + 1.32932i 0.896208 + 0.443634i \(0.146311\pi\)
−0.464286 + 0.885685i \(0.653689\pi\)
\(504\) −0.212677 0.654553i −0.00947339 0.0291561i
\(505\) −0.861904 + 18.6113i −0.0383542 + 0.828191i
\(506\) −0.0887282 + 0.273077i −0.00394445 + 0.0121398i
\(507\) −1.89585 −0.0841977
\(508\) 4.21063 12.9590i 0.186817 0.574962i
\(509\) −4.50521 + 3.27323i −0.199690 + 0.145083i −0.683137 0.730291i \(-0.739385\pi\)
0.483447 + 0.875374i \(0.339385\pi\)
\(510\) 1.30717 1.63444i 0.0578823 0.0723744i
\(511\) 3.13204 + 2.27556i 0.138553 + 0.100665i
\(512\) 10.5564 7.66965i 0.466530 0.338954i
\(513\) −4.67803 + 3.39879i −0.206540 + 0.150060i
\(514\) 0.991240 + 0.720178i 0.0437217 + 0.0317657i
\(515\) 35.2788 9.68327i 1.55457 0.426696i
\(516\) 20.6117 14.9753i 0.907380 0.659250i
\(517\) −14.7230 + 45.3128i −0.647518 + 1.99285i
\(518\) −0.806824 −0.0354498
\(519\) −6.77411 + 20.8486i −0.297350 + 0.915150i
\(520\) −5.72774 + 1.57214i −0.251178 + 0.0689430i
\(521\) −1.92720 5.93131i −0.0844322 0.259855i 0.899924 0.436047i \(-0.143622\pi\)
−0.984356 + 0.176192i \(0.943622\pi\)
\(522\) 0.0723666 + 0.222722i 0.00316740 + 0.00974826i
\(523\) 25.9536 + 18.8564i 1.13487 + 0.824532i 0.986396 0.164384i \(-0.0525638\pi\)
0.148474 + 0.988916i \(0.452564\pi\)
\(524\) 10.6367 0.464665
\(525\) −1.09897 4.87773i −0.0479631 0.212882i
\(526\) −0.563412 −0.0245659
\(527\) 4.85246 + 3.52552i 0.211376 + 0.153574i
\(528\) −5.81320 17.8912i −0.252987 0.778614i
\(529\) −7.07243 21.7667i −0.307497 0.946378i
\(530\) −2.05479 0.774453i −0.0892542 0.0336401i
\(531\) −2.87098 + 8.83598i −0.124590 + 0.383449i
\(532\) −11.3909 −0.493860
\(533\) 12.4298 38.2551i 0.538396 1.65701i
\(534\) −0.0597971 + 0.0434451i −0.00258767 + 0.00188005i
\(535\) −1.21346 + 26.2026i −0.0524626 + 1.13284i
\(536\) −2.41891 1.75744i −0.104481 0.0759099i
\(537\) 3.51273 2.55215i 0.151585 0.110133i
\(538\) −3.84729 + 2.79522i −0.165868 + 0.120510i
\(539\) −3.98347 2.89416i −0.171580 0.124660i
\(540\) 4.12188 + 1.55355i 0.177378 + 0.0668540i
\(541\) −0.454779 + 0.330416i −0.0195525 + 0.0142057i −0.597519 0.801855i \(-0.703847\pi\)
0.577966 + 0.816061i \(0.303847\pi\)
\(542\) −1.21628 + 3.74333i −0.0522438 + 0.160790i
\(543\) 8.61415 0.369669
\(544\) −3.40145 + 10.4686i −0.145836 + 0.448836i
\(545\) −10.6048 16.1145i −0.454258 0.690268i
\(546\) −0.206761 0.636345i −0.00884856 0.0272331i
\(547\) −1.09768 3.37832i −0.0469335 0.144447i 0.924843 0.380348i \(-0.124196\pi\)
−0.971777 + 0.235901i \(0.924196\pi\)
\(548\) 12.9334 + 9.39669i 0.552489 + 0.401407i
\(549\) −13.9652 −0.596021
\(550\) 0.938089 + 4.16366i 0.0400003 + 0.177539i
\(551\) 7.81101 0.332760
\(552\) 0.187291 + 0.136075i 0.00797164 + 0.00579174i
\(553\) 2.05233 + 6.31641i 0.0872738 + 0.268601i
\(554\) −0.691030 2.12677i −0.0293591 0.0903579i
\(555\) 6.49979 8.12715i 0.275901 0.344978i
\(556\) 5.47598 16.8533i 0.232233 0.714740i
\(557\) 13.2267 0.560432 0.280216 0.959937i \(-0.409594\pi\)
0.280216 + 0.959937i \(0.409594\pi\)
\(558\) 0.0595165 0.183173i 0.00251953 0.00775433i
\(559\) 40.3824 29.3395i 1.70799 1.24093i
\(560\) 4.69638 + 7.13639i 0.198458 + 0.301568i
\(561\) 21.5062 + 15.6252i 0.907994 + 0.659696i
\(562\) −2.54943 + 1.85227i −0.107541 + 0.0781333i
\(563\) −6.75285 + 4.90623i −0.284599 + 0.206773i −0.720921 0.693018i \(-0.756281\pi\)
0.436322 + 0.899791i \(0.356281\pi\)
\(564\) 15.4213 + 11.2043i 0.649356 + 0.471785i
\(565\) 1.68982 + 2.56777i 0.0710914 + 0.108027i
\(566\) −0.134738 + 0.0978927i −0.00566345 + 0.00411474i
\(567\) −0.309017 + 0.951057i −0.0129775 + 0.0399406i
\(568\) −4.95034 −0.207712
\(569\) −6.12609 + 18.8542i −0.256819 + 0.790408i 0.736647 + 0.676278i \(0.236408\pi\)
−0.993466 + 0.114130i \(0.963592\pi\)
\(570\) −1.40002 + 1.75054i −0.0586403 + 0.0733221i
\(571\) −2.82897 8.70667i −0.118389 0.364363i 0.874250 0.485476i \(-0.161354\pi\)
−0.992639 + 0.121113i \(0.961354\pi\)
\(572\) −11.5684 35.6039i −0.483699 1.48867i
\(573\) 2.61655 + 1.90103i 0.109308 + 0.0794167i
\(574\) 1.80678 0.0754133
\(575\) 1.26347 + 1.11010i 0.0526902 + 0.0462944i
\(576\) −7.28770 −0.303654
\(577\) −15.9963 11.6220i −0.665935 0.483830i 0.202727 0.979235i \(-0.435020\pi\)
−0.868662 + 0.495405i \(0.835020\pi\)
\(578\) −0.650779 2.00289i −0.0270688 0.0833093i
\(579\) 6.02562 + 18.5449i 0.250416 + 0.770702i
\(580\) −3.27108 4.97057i −0.135824 0.206392i
\(581\) −3.87703 + 11.9323i −0.160846 + 0.495034i
\(582\) −0.559917 −0.0232093
\(583\) 8.61901 26.5266i 0.356963 1.09862i
\(584\) −2.15559 + 1.56613i −0.0891988 + 0.0648067i
\(585\) 8.07559 + 3.04370i 0.333884 + 0.125842i
\(586\) 3.57040 + 2.59405i 0.147492 + 0.107159i
\(587\) 5.94521 4.31945i 0.245385 0.178283i −0.458294 0.888801i \(-0.651539\pi\)
0.703679 + 0.710518i \(0.251539\pi\)
\(588\) −1.59372 + 1.15790i −0.0657239 + 0.0477512i
\(589\) −5.19714 3.77594i −0.214144 0.155585i
\(590\) −0.166612 + 3.59768i −0.00685929 + 0.148114i
\(591\) −13.5812 + 9.86734i −0.558657 + 0.405888i
\(592\) −5.49460 + 16.9107i −0.225827 + 0.695023i
\(593\) −11.8452 −0.486423 −0.243212 0.969973i \(-0.578201\pi\)
−0.243212 + 0.969973i \(0.578201\pi\)
\(594\) 0.263779 0.811828i 0.0108230 0.0333097i
\(595\) −11.2965 4.25768i −0.463112 0.174548i
\(596\) 1.57640 + 4.85165i 0.0645717 + 0.198731i
\(597\) −0.468936 1.44324i −0.0191923 0.0590678i
\(598\) 0.182081 + 0.132290i 0.00744586 + 0.00540973i
\(599\) 13.4627 0.550072 0.275036 0.961434i \(-0.411310\pi\)
0.275036 + 0.961434i \(0.411310\pi\)
\(600\) 3.42646 + 0.318047i 0.139885 + 0.0129842i
\(601\) −32.3143 −1.31813 −0.659064 0.752087i \(-0.729047\pi\)
−0.659064 + 0.752087i \(0.729047\pi\)
\(602\) 1.81390 + 1.31788i 0.0739291 + 0.0537126i
\(603\) 1.34247 + 4.13171i 0.0546698 + 0.168256i
\(604\) 12.8899 + 39.6712i 0.524484 + 1.61420i
\(605\) −28.5587 + 7.83875i −1.16108 + 0.318691i
\(606\) 0.446367 1.37378i 0.0181324 0.0558059i
\(607\) 24.5815 0.997730 0.498865 0.866680i \(-0.333750\pi\)
0.498865 + 0.866680i \(0.333750\pi\)
\(608\) 3.64306 11.2122i 0.147745 0.454714i
\(609\) 1.09285 0.794001i 0.0442844 0.0321745i
\(610\) −5.22052 + 1.43292i −0.211373 + 0.0580173i
\(611\) 30.2135 + 21.9514i 1.22231 + 0.888058i
\(612\) 8.60428 6.25138i 0.347808 0.252697i
\(613\) 33.8223 24.5733i 1.36607 0.992508i 0.368037 0.929811i \(-0.380030\pi\)
0.998033 0.0626967i \(-0.0199701\pi\)
\(614\) −2.02782 1.47329i −0.0818360 0.0594573i
\(615\) −14.5554 + 18.1997i −0.586931 + 0.733882i
\(616\) 2.74157 1.99187i 0.110461 0.0802547i
\(617\) −3.06236 + 9.42498i −0.123286 + 0.379435i −0.993585 0.113089i \(-0.963926\pi\)
0.870299 + 0.492524i \(0.163926\pi\)
\(618\) −2.83632 −0.114093
\(619\) 5.29367 16.2922i 0.212770 0.654840i −0.786534 0.617547i \(-0.788126\pi\)
0.999304 0.0372931i \(-0.0118735\pi\)
\(620\) −0.226391 + 4.88850i −0.00909207 + 0.196327i
\(621\) −0.103945 0.319910i −0.00417117 0.0128375i
\(622\) −0.221546 0.681847i −0.00888317 0.0273396i
\(623\) 0.344926 + 0.250603i 0.0138192 + 0.0100402i
\(624\) −14.7456 −0.590295
\(625\) 24.5729 + 4.60140i 0.982916 + 0.184056i
\(626\) −4.06577 −0.162501
\(627\) −23.0339 16.7351i −0.919884 0.668335i
\(628\) −4.68652 14.4236i −0.187012 0.575565i
\(629\) −7.76444 23.8965i −0.309589 0.952816i
\(630\) −0.0179332 + 0.387234i −0.000714474 + 0.0154278i
\(631\) 5.11795 15.7514i 0.203742 0.627055i −0.796020 0.605270i \(-0.793065\pi\)
0.999763 0.0217848i \(-0.00693487\pi\)
\(632\) −4.57091 −0.181821
\(633\) 7.02781 21.6294i 0.279331 0.859691i
\(634\) 2.92837 2.12759i 0.116300 0.0844972i
\(635\) −9.66018 + 12.0788i −0.383352 + 0.479333i
\(636\) −9.02783 6.55910i −0.357977 0.260085i
\(637\) −3.12241 + 2.26857i −0.123714 + 0.0898838i
\(638\) −0.932862 + 0.677764i −0.0369324 + 0.0268329i
\(639\) 5.81908 + 4.22781i 0.230199 + 0.167250i
\(640\) −11.5170 + 3.16117i −0.455249 + 0.124956i
\(641\) 24.8810 18.0771i 0.982740 0.714003i 0.0244210 0.999702i \(-0.492226\pi\)
0.958319 + 0.285699i \(0.0922258\pi\)
\(642\) 0.628435 1.93412i 0.0248023 0.0763338i
\(643\) 1.30799 0.0515819 0.0257910 0.999667i \(-0.491790\pi\)
0.0257910 + 0.999667i \(0.491790\pi\)
\(644\) 0.204766 0.630205i 0.00806891 0.0248336i
\(645\) −27.8878 + 7.65461i −1.09808 + 0.301400i
\(646\) 1.67242 + 5.14716i 0.0658003 + 0.202512i
\(647\) 3.89662 + 11.9926i 0.153192 + 0.471477i 0.997973 0.0636352i \(-0.0202694\pi\)
−0.844781 + 0.535112i \(0.820269\pi\)
\(648\) −0.556796 0.404536i −0.0218730 0.0158917i
\(649\) −45.7459 −1.79568
\(650\) 3.33115 + 0.309200i 0.130658 + 0.0121278i
\(651\) −1.11097 −0.0435422
\(652\) 13.5426 + 9.83929i 0.530370 + 0.385336i
\(653\) −5.27402 16.2318i −0.206388 0.635198i −0.999654 0.0263218i \(-0.991621\pi\)
0.793265 0.608876i \(-0.208379\pi\)
\(654\) 0.462171 + 1.42242i 0.0180723 + 0.0556209i
\(655\) −11.2978 4.25816i −0.441441 0.166380i
\(656\) 12.3044 37.8692i 0.480408 1.47854i
\(657\) 3.87141 0.151038
\(658\) −0.518378 + 1.59540i −0.0202085 + 0.0621953i
\(659\) −34.5171 + 25.0782i −1.34460 + 0.976907i −0.345336 + 0.938479i \(0.612235\pi\)
−0.999261 + 0.0384279i \(0.987765\pi\)
\(660\) −1.00337 + 21.6660i −0.0390561 + 0.843347i
\(661\) −12.6955 9.22386i −0.493800 0.358766i 0.312844 0.949805i \(-0.398718\pi\)
−0.806644 + 0.591038i \(0.798718\pi\)
\(662\) 2.43777 1.77114i 0.0947465 0.0688374i
\(663\) 16.8575 12.2477i 0.654691 0.475661i
\(664\) −6.98575 5.07544i −0.271100 0.196965i
\(665\) 12.0989 + 4.56011i 0.469176 + 0.176833i
\(666\) −0.652734 + 0.474239i −0.0252929 + 0.0183764i
\(667\) −0.140413 + 0.432145i −0.00543680 + 0.0167327i
\(668\) −7.37031 −0.285166
\(669\) 6.92223 21.3044i 0.267629 0.823677i
\(670\) 0.925789 + 1.40678i 0.0357663 + 0.0543488i
\(671\) −21.2488 65.3971i −0.820301 2.52463i
\(672\) −0.630029 1.93903i −0.0243039 0.0747997i
\(673\) −5.53938 4.02459i −0.213527 0.155137i 0.475881 0.879510i \(-0.342129\pi\)
−0.689408 + 0.724373i \(0.742129\pi\)
\(674\) 3.10927 0.119765
\(675\) −3.75615 3.30021i −0.144574 0.127025i
\(676\) −3.73472 −0.143643
\(677\) −31.2823 22.7279i −1.20228 0.873506i −0.207771 0.978177i \(-0.566621\pi\)
−0.994507 + 0.104671i \(0.966621\pi\)
\(678\) −0.0736450 0.226656i −0.00282832 0.00870467i
\(679\) 0.998049 + 3.07168i 0.0383016 + 0.117880i
\(680\) 5.18938 6.48865i 0.199004 0.248828i
\(681\) 2.70487 8.32474i 0.103651 0.319005i
\(682\) 0.948329 0.0363134
\(683\) −0.842388 + 2.59260i −0.0322331 + 0.0992032i −0.965879 0.258995i \(-0.916609\pi\)
0.933646 + 0.358198i \(0.116609\pi\)
\(684\) −9.21546 + 6.69542i −0.352362 + 0.256006i
\(685\) −9.97554 15.1583i −0.381146 0.579170i
\(686\) −0.140253 0.101900i −0.00535488 0.00389054i
\(687\) −8.63520 + 6.27384i −0.329453 + 0.239362i
\(688\) 39.9750 29.0435i 1.52403 1.10727i
\(689\) −17.6873 12.8506i −0.673832 0.489568i
\(690\) −0.0716819 0.108924i −0.00272888 0.00414668i
\(691\) 36.6762 26.6468i 1.39523 1.01369i 0.399959 0.916533i \(-0.369024\pi\)
0.995269 0.0971589i \(-0.0309755\pi\)
\(692\) −13.3446 + 41.0705i −0.507286 + 1.56127i
\(693\) −4.92384 −0.187041
\(694\) 0.417577 1.28517i 0.0158510 0.0487844i
\(695\) −12.5632 + 15.7086i −0.476548 + 0.595862i
\(696\) 0.287292 + 0.884193i 0.0108898 + 0.0335152i
\(697\) 17.3874 + 53.5130i 0.658596 + 2.02695i
\(698\) −1.93393 1.40508i −0.0732003 0.0531831i
\(699\) 7.94437 0.300484
\(700\) −2.16491 9.60887i −0.0818261 0.363181i
\(701\) −19.4524 −0.734707 −0.367353 0.930081i \(-0.619736\pi\)
−0.367353 + 0.930081i \(0.619736\pi\)
\(702\) −0.541308 0.393283i −0.0204303 0.0148435i
\(703\) 8.31596 + 25.5939i 0.313642 + 0.965292i
\(704\) −11.0886 34.1272i −0.417918 1.28622i
\(705\) −11.8945 18.0742i −0.447971 0.680715i
\(706\) −0.570919 + 1.75711i −0.0214868 + 0.0661297i
\(707\) −8.33213 −0.313362
\(708\) −5.65568 + 17.4064i −0.212554 + 0.654173i
\(709\) −16.6717 + 12.1127i −0.626119 + 0.454902i −0.855054 0.518539i \(-0.826476\pi\)
0.228934 + 0.973442i \(0.426476\pi\)
\(710\) 2.60911 + 0.983378i 0.0979181 + 0.0369055i
\(711\) 5.37306 + 3.90376i 0.201506 + 0.146402i
\(712\) −0.237391 + 0.172475i −0.00889661 + 0.00646376i
\(713\) 0.302329 0.219655i 0.0113223 0.00822615i
\(714\) 0.757206 + 0.550143i 0.0283377 + 0.0205886i
\(715\) −1.96580 + 42.4479i −0.0735168 + 1.58746i
\(716\) 6.91988 5.02759i 0.258608 0.187890i
\(717\) −9.03824 + 27.8169i −0.337539 + 1.03884i
\(718\) −3.37707 −0.126031
\(719\) 1.84443 5.67657i 0.0687856 0.211700i −0.910755 0.412947i \(-0.864499\pi\)
0.979541 + 0.201247i \(0.0644994\pi\)
\(720\) 7.99412 + 3.01300i 0.297923 + 0.112288i
\(721\) 5.05572 + 15.5599i 0.188285 + 0.579481i
\(722\) −0.773346 2.38011i −0.0287809 0.0885786i
\(723\) 14.5962 + 10.6048i 0.542840 + 0.394396i
\(724\) 16.9694 0.630663
\(725\) 1.48453 + 6.58901i 0.0551340 + 0.244710i
\(726\) 2.29604 0.0852141
\(727\) −30.6769 22.2881i −1.13774 0.826619i −0.150940 0.988543i \(-0.548230\pi\)
−0.986803 + 0.161924i \(0.948230\pi\)
\(728\) −0.820830 2.52626i −0.0304220 0.0936293i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 1.44722 0.397232i 0.0535642 0.0147022i
\(731\) −21.5768 + 66.4066i −0.798047 + 2.45614i
\(732\) −27.5107 −1.01683
\(733\) −0.859674 + 2.64580i −0.0317528 + 0.0977250i −0.965677 0.259746i \(-0.916361\pi\)
0.933924 + 0.357471i \(0.116361\pi\)
\(734\) −2.94799 + 2.14184i −0.108812 + 0.0790568i
\(735\) 2.15632 0.591863i 0.0795369 0.0218312i
\(736\) 0.554827 + 0.403105i 0.0204512 + 0.0148587i
\(737\) −17.3055 + 12.5732i −0.637458 + 0.463140i
\(738\) 1.46171 1.06200i 0.0538064 0.0390926i
\(739\) 21.1638 + 15.3764i 0.778524 + 0.565631i 0.904536 0.426398i \(-0.140218\pi\)
−0.126012 + 0.992029i \(0.540218\pi\)
\(740\) 12.8042 16.0100i 0.470693 0.588541i
\(741\) −18.0549 + 13.1177i −0.663264 + 0.481889i
\(742\) 0.303464 0.933967i 0.0111405 0.0342870i
\(743\) −37.8064 −1.38698 −0.693490 0.720466i \(-0.743928\pi\)
−0.693490 + 0.720466i \(0.743928\pi\)
\(744\) 0.236277 0.727187i 0.00866235 0.0266600i
\(745\) 0.267875 5.78427i 0.00981416 0.211919i
\(746\) 0.102973 + 0.316919i 0.00377012 + 0.0116032i
\(747\) 3.87703 + 11.9323i 0.141853 + 0.436579i
\(748\) 42.3661 + 30.7808i 1.54906 + 1.12546i
\(749\) −11.7307 −0.428631
\(750\) −1.74276 0.848289i −0.0636365 0.0309751i
\(751\) −0.476440 −0.0173855 −0.00869277 0.999962i \(-0.502767\pi\)
−0.00869277 + 0.999962i \(0.502767\pi\)
\(752\) 29.9087 + 21.7299i 1.09066 + 0.792409i
\(753\) 8.84894 + 27.2342i 0.322473 + 0.992470i
\(754\) 0.279300 + 0.859597i 0.0101715 + 0.0313047i
\(755\) 2.19037 47.2971i 0.0797157 1.72132i
\(756\) −0.608747 + 1.87353i −0.0221399 + 0.0681396i
\(757\) 20.1563 0.732592 0.366296 0.930498i \(-0.380626\pi\)
0.366296 + 0.930498i \(0.380626\pi\)
\(758\) 1.46344 4.50401i 0.0531546 0.163593i
\(759\) 1.33993 0.973518i 0.0486365 0.0353365i
\(760\) −5.55799 + 6.94955i −0.201610 + 0.252087i
\(761\) −6.68289 4.85540i −0.242255 0.176008i 0.460033 0.887902i \(-0.347838\pi\)
−0.702287 + 0.711894i \(0.747838\pi\)
\(762\) 0.970112 0.704828i 0.0351435 0.0255332i
\(763\) 6.97950 5.07090i 0.252675 0.183579i
\(764\) 5.15445 + 3.74493i 0.186482 + 0.135487i
\(765\) −11.6417 + 3.19539i −0.420905 + 0.115530i
\(766\) 3.47816 2.52703i 0.125671 0.0913052i
\(767\) −11.0806 + 34.1026i −0.400097 + 1.23137i
\(768\) −13.6495 −0.492533
\(769\) −8.26779 + 25.4457i −0.298144 + 0.917594i 0.684003 + 0.729479i \(0.260238\pi\)
−0.982147 + 0.188114i \(0.939762\pi\)
\(770\) −1.84065 + 0.505218i −0.0663323 + 0.0182068i
\(771\) −2.18399 6.72162i −0.0786543 0.242073i
\(772\) 11.8701 + 36.5325i 0.427216 + 1.31483i
\(773\) −0.619085 0.449791i −0.0222669 0.0161779i 0.576596 0.817029i \(-0.304381\pi\)
−0.598863 + 0.800851i \(0.704381\pi\)
\(774\) 2.24210 0.0805908
\(775\) 2.19746 5.10170i 0.0789352 0.183259i
\(776\) −2.22284 −0.0797952
\(777\) 3.76515 + 2.73554i 0.135074 + 0.0981371i
\(778\) 1.60036 + 4.92539i 0.0573755 + 0.176584i
\(779\) −18.6225 57.3141i −0.667220 2.05349i
\(780\) 15.9085 + 5.99593i 0.569615 + 0.214689i
\(781\) −10.9442 + 33.6827i −0.391613 + 1.20526i
\(782\) −0.314831 −0.0112583
\(783\) 0.417431 1.28472i 0.0149178 0.0459121i
\(784\) −3.09091 + 2.24568i −0.110390 + 0.0802028i
\(785\) −0.796373 + 17.1962i −0.0284238 + 0.613760i
\(786\) 0.757292 + 0.550204i 0.0270117 + 0.0196251i
\(787\) −35.4620 + 25.7646i −1.26408 + 0.918410i −0.998951 0.0458014i \(-0.985416\pi\)
−0.265133 + 0.964212i \(0.585416\pi\)
\(788\) −26.7543 + 19.4381i −0.953082 + 0.692455i
\(789\) 2.62924 + 1.91025i 0.0936034 + 0.0680068i
\(790\) 2.40913 + 0.908004i 0.0857128 + 0.0323053i
\(791\) −1.11215 + 0.808027i −0.0395436 + 0.0287301i
\(792\) 1.04719 3.22291i 0.0372102 0.114521i
\(793\) −53.8990 −1.91401
\(794\) −1.16321 + 3.57998i −0.0412807 + 0.127049i
\(795\) 6.96315 + 10.5809i 0.246957 + 0.375264i
\(796\) −0.923779 2.84310i −0.0327425 0.100771i
\(797\) −1.55052 4.77200i −0.0549221 0.169033i 0.919833 0.392311i \(-0.128324\pi\)
−0.974755 + 0.223278i \(0.928324\pi\)
\(798\) −0.810992 0.589220i −0.0287088 0.0208582i
\(799\) −52.2412 −1.84816
\(800\) 10.1505 + 0.942174i 0.358873 + 0.0333109i
\(801\) 0.426352 0.0150644
\(802\) 0.954915 + 0.693787i 0.0337192 + 0.0244985i
\(803\) 5.89055 + 18.1293i 0.207873 + 0.639767i
\(804\) 2.64460 + 8.13925i 0.0932679 + 0.287049i
\(805\) −0.469781 + 0.587401i −0.0165576 + 0.0207032i
\(806\) 0.229705 0.706959i 0.00809101 0.0249016i
\(807\) 27.4311 0.965620
\(808\) 1.77205 5.45382i 0.0623406 0.191865i
\(809\) 36.6905 26.6572i 1.28997 0.937219i 0.290166 0.956976i \(-0.406289\pi\)
0.999805 + 0.0197574i \(0.00628940\pi\)
\(810\) 0.213102 + 0.323820i 0.00748765 + 0.0113779i
\(811\) 6.25004 + 4.54092i 0.219469 + 0.159453i 0.692087 0.721814i \(-0.256691\pi\)
−0.472619 + 0.881267i \(0.656691\pi\)
\(812\) 2.15285 1.56414i 0.0755503 0.0548905i
\(813\) 18.3677 13.3449i 0.644185 0.468028i
\(814\) −3.21396 2.33508i −0.112649 0.0818445i
\(815\) −10.4454 15.8723i −0.365886 0.555983i
\(816\) 16.6874 12.1241i 0.584177 0.424429i
\(817\) 23.1094 71.1236i 0.808497 2.48830i
\(818\) 4.94029 0.172733
\(819\) −1.19266 + 3.67062i −0.0416748 + 0.128262i
\(820\) −28.6734 + 35.8524i −1.00132 + 1.25202i
\(821\) 9.49461 + 29.2214i 0.331364 + 1.01983i 0.968485 + 0.249070i \(0.0801251\pi\)
−0.637121 + 0.770764i \(0.719875\pi\)
\(822\) 0.434749 + 1.33802i 0.0151636 + 0.0466688i
\(823\) −3.08293 2.23988i −0.107464 0.0780772i 0.532755 0.846269i \(-0.321157\pi\)
−0.640219 + 0.768192i \(0.721157\pi\)
\(824\) −11.2600 −0.392261
\(825\) 9.73922 22.6109i 0.339076 0.787211i
\(826\) −1.61065 −0.0560418
\(827\) −15.0693 10.9485i −0.524011 0.380716i 0.294102 0.955774i \(-0.404979\pi\)
−0.818113 + 0.575058i \(0.804979\pi\)
\(828\) −0.204766 0.630205i −0.00711611 0.0219011i
\(829\) 7.05990 + 21.7281i 0.245201 + 0.754650i 0.995603 + 0.0936689i \(0.0298595\pi\)
−0.750403 + 0.660981i \(0.770140\pi\)
\(830\) 2.67365 + 4.06275i 0.0928038 + 0.141020i
\(831\) −3.98606 + 12.2678i −0.138275 + 0.425566i
\(832\) −28.1270 −0.975128
\(833\) 1.66834 5.13463i 0.0578046 0.177904i
\(834\) 1.26164 0.916637i 0.0436871 0.0317405i
\(835\) 7.82840 + 2.95054i 0.270913 + 0.102108i
\(836\) −45.3755 32.9672i −1.56934 1.14019i
\(837\) −0.898792 + 0.653010i −0.0310668 + 0.0225713i
\(838\) −1.44203 + 1.04770i −0.0498141 + 0.0361921i
\(839\) −26.8997 19.5438i −0.928681 0.674726i 0.0169887 0.999856i \(-0.494592\pi\)
−0.945669 + 0.325130i \(0.894592\pi\)
\(840\) −0.0711936 + 1.53730i −0.00245641 + 0.0530418i
\(841\) 21.9852 15.9732i 0.758112 0.550800i
\(842\) 1.46666 4.51392i 0.0505444 0.155560i
\(843\) 18.1774 0.626063
\(844\) 13.8444 42.6087i 0.476544 1.46665i
\(845\) 3.96685 + 1.49511i 0.136464 + 0.0514334i
\(846\) 0.518378 + 1.59540i 0.0178222 + 0.0548511i
\(847\) −4.09269 12.5960i −0.140626 0.432803i
\(848\) −17.5089 12.7209i −0.601257 0.436839i
\(849\) 0.960678 0.0329704
\(850\) −4.02406 + 2.38902i −0.138024 + 0.0819427i
\(851\) −1.56548 −0.0536638
\(852\) 11.4633 + 8.32855i 0.392725 + 0.285332i
\(853\) 1.92579 + 5.92698i 0.0659379 + 0.202936i 0.978597 0.205785i \(-0.0659749\pi\)
−0.912659 + 0.408721i \(0.865975\pi\)
\(854\) −0.748142 2.30254i −0.0256009 0.0787915i
\(855\) 12.4686 3.42236i 0.426417 0.117042i
\(856\) 2.49485 7.67837i 0.0852723 0.262441i
\(857\) −17.2481 −0.589183 −0.294592 0.955623i \(-0.595184\pi\)
−0.294592 + 0.955623i \(0.595184\pi\)
\(858\) 1.01806 3.13326i 0.0347559 0.106968i
\(859\) −24.1357 + 17.5356i −0.823500 + 0.598308i −0.917713 0.397244i \(-0.869967\pi\)
0.0942126 + 0.995552i \(0.469967\pi\)
\(860\) −54.9375 + 15.0792i −1.87335 + 0.514195i
\(861\) −8.43156 6.12589i −0.287347 0.208770i
\(862\) 3.68111 2.67448i 0.125379 0.0910931i
\(863\) −14.6524 + 10.6456i −0.498774 + 0.362380i −0.808548 0.588430i \(-0.799746\pi\)
0.309775 + 0.950810i \(0.399746\pi\)
\(864\) −1.64944 1.19839i −0.0561150 0.0407700i
\(865\) 30.6157 38.2810i 1.04097 1.30159i
\(866\) −0.602645 + 0.437847i −0.0204787 + 0.0148786i
\(867\) −3.75387 + 11.5532i −0.127488 + 0.392368i
\(868\) −2.18855 −0.0742841
\(869\) −10.1053 + 31.1010i −0.342800 + 1.05503i
\(870\) 0.0242247 0.523089i 0.000821295 0.0177344i
\(871\) 5.18130 + 15.9464i 0.175562 + 0.540323i
\(872\) 1.83479 + 5.64691i 0.0621339 + 0.191229i
\(873\) 2.61293 + 1.89840i 0.0884342 + 0.0642512i
\(874\) 0.337194 0.0114058
\(875\) −1.54722 + 11.0728i −0.0523057 + 0.374328i
\(876\) 7.62647 0.257675
\(877\) −30.3100 22.0215i −1.02350 0.743614i −0.0564997 0.998403i \(-0.517994\pi\)
−0.966997 + 0.254789i \(0.917994\pi\)
\(878\) 0.823862 + 2.53559i 0.0278040 + 0.0855719i
\(879\) −7.86662 24.2110i −0.265335 0.816616i
\(880\) −1.94597 + 42.0197i −0.0655986 + 1.41648i
\(881\) −1.05024 + 3.23231i −0.0353835 + 0.108899i −0.967188 0.254060i \(-0.918234\pi\)
0.931805 + 0.362960i \(0.118234\pi\)
\(882\) −0.173362 −0.00583740
\(883\) −9.30576 + 28.6402i −0.313164 + 0.963819i 0.663340 + 0.748318i \(0.269138\pi\)
−0.976504 + 0.215501i \(0.930862\pi\)
\(884\) 33.2084 24.1273i 1.11692 0.811488i
\(885\) 12.9755 16.2241i 0.436166 0.545369i
\(886\) −2.79217 2.02863i −0.0938047 0.0681531i
\(887\) 29.6912 21.5719i 0.996934 0.724315i 0.0355051 0.999369i \(-0.488696\pi\)
0.961429 + 0.275055i \(0.0886960\pi\)
\(888\) −2.59132 + 1.88270i −0.0869590 + 0.0631794i
\(889\) −5.59588 4.06564i −0.187680 0.136357i
\(890\) 0.159380 0.0437465i 0.00534244 0.00146639i
\(891\) −3.98347 + 2.89416i −0.133451 + 0.0969580i
\(892\) 13.6364 41.9686i 0.456581 1.40521i
\(893\) 55.9520 1.87236
\(894\) −0.138728 + 0.426961i −0.00463976 + 0.0142797i
\(895\) −9.36266 + 2.56985i −0.312959 + 0.0859006i
\(896\) −1.65047 5.07964i −0.0551385 0.169699i
\(897\) −0.401177 1.23470i −0.0133949 0.0412253i
\(898\) 1.63358 + 1.18686i 0.0545132 + 0.0396061i
\(899\) 1.50073 0.0500523
\(900\) −7.39940 6.50123i −0.246647 0.216708i
\(901\) 30.5826 1.01885
\(902\) 7.19724 + 5.22910i 0.239642 + 0.174110i
\(903\) −3.99654 12.3001i −0.132997 0.409321i
\(904\) −0.292367 0.899812i −0.00972397 0.0299273i
\(905\) −18.0241 6.79333i −0.599142 0.225818i
\(906\) −1.13436 + 3.49120i −0.0376865 + 0.115987i
\(907\) 37.5705 1.24751 0.623754 0.781621i \(-0.285607\pi\)
0.623754 + 0.781621i \(0.285607\pi\)
\(908\) 5.32845 16.3993i 0.176831 0.544230i
\(909\) −6.74084 + 4.89751i −0.223579 + 0.162440i
\(910\) −0.0692133 + 1.49454i −0.00229440 + 0.0495434i
\(911\) −26.6532 19.3647i −0.883059 0.641580i 0.0509999 0.998699i \(-0.483759\pi\)
−0.934059 + 0.357119i \(0.883759\pi\)
\(912\) −17.8728 + 12.9853i −0.591826 + 0.429987i
\(913\) −49.9779 + 36.3111i −1.65403 + 1.20172i
\(914\) −0.905146 0.657627i −0.0299396 0.0217524i
\(915\) 29.2206 + 11.0133i 0.966004 + 0.364089i
\(916\) −17.0109 + 12.3591i −0.562055 + 0.408357i
\(917\) 1.66853 5.13521i 0.0550997 0.169579i
\(918\) 0.935958 0.0308912
\(919\) 8.33603 25.6557i 0.274980 0.846303i −0.714244 0.699897i \(-0.753229\pi\)
0.989225 0.146406i \(-0.0467706\pi\)
\(920\) −0.284573 0.432424i −0.00938210 0.0142566i
\(921\) 4.46786 + 13.7507i 0.147221 + 0.453100i
\(922\) −0.575030 1.76976i −0.0189376 0.0582839i
\(923\) 22.4588 + 16.3173i 0.739241 + 0.537090i
\(924\) −9.69970 −0.319097
\(925\) −20.0093 + 11.8792i −0.657903 + 0.390587i
\(926\) −3.96505 −0.130299
\(927\) 13.2361 + 9.61656i 0.434729 + 0.315849i
\(928\) 0.851065 + 2.61931i 0.0279376 + 0.0859831i
\(929\) −4.41083 13.5751i −0.144715 0.445386i 0.852260 0.523119i \(-0.175232\pi\)
−0.996974 + 0.0777333i \(0.975232\pi\)
\(930\) −0.268986 + 0.336332i −0.00882040 + 0.0110288i
\(931\) −1.78685 + 5.49935i −0.0585616 + 0.180234i
\(932\) 15.6500 0.512632
\(933\) −1.27794 + 3.93308i −0.0418378 + 0.128763i
\(934\) −0.119079 + 0.0865158i −0.00389638 + 0.00283088i
\(935\) −32.6769 49.6542i −1.06865 1.62387i
\(936\) −2.14896 1.56131i −0.0702410 0.0510331i
\(937\) 28.3431 20.5925i 0.925929 0.672727i −0.0190640 0.999818i \(-0.506069\pi\)
0.944993 + 0.327092i \(0.106069\pi\)
\(938\) −0.609306 + 0.442686i −0.0198945 + 0.0144542i
\(939\) 18.9735 + 13.7850i 0.619175 + 0.449857i
\(940\) −23.4314 35.6053i −0.764249 1.16132i
\(941\) 2.91523 2.11804i 0.0950338 0.0690461i −0.539254 0.842143i \(-0.681294\pi\)
0.634287 + 0.773097i \(0.281294\pi\)
\(942\) 0.412430 1.26933i 0.0134377 0.0413569i
\(943\) 3.50568 0.114161
\(944\) −10.9688 + 33.7585i −0.357005 + 1.09875i
\(945\) 1.39661 1.74628i 0.0454317 0.0568064i
\(946\) 3.41147 + 10.4994i 0.110917 + 0.341366i
\(947\) −11.1514 34.3206i −0.362373 1.11527i −0.951610 0.307308i \(-0.900572\pi\)
0.589237 0.807960i \(-0.299428\pi\)
\(948\) 10.5846 + 7.69019i 0.343773 + 0.249766i
\(949\) 14.9418 0.485031
\(950\) 4.30989 2.55872i 0.139831 0.0830157i
\(951\) −20.8792 −0.677056
\(952\) 3.00607 + 2.18404i 0.0974272 + 0.0707850i
\(953\) −5.73983 17.6654i −0.185931 0.572238i 0.814032 0.580820i \(-0.197268\pi\)
−0.999963 + 0.00858256i \(0.997268\pi\)
\(954\) −0.303464 0.933967i −0.00982501 0.0302383i
\(955\) −3.97562 6.04116i −0.128648 0.195487i
\(956\) −17.8048 + 54.7977i −0.575850 + 1.77228i
\(957\) 6.65129 0.215006
\(958\) 1.16092 3.57295i 0.0375077 0.115437i
\(959\) 6.56538 4.77003i 0.212007 0.154032i
\(960\) 15.2487 + 5.74725i 0.492149 + 0.185492i
\(961\) 24.0810 + 17.4959i 0.776806 + 0.564383i
\(962\) −2.51924 + 1.83033i −0.0812235 + 0.0590123i
\(963\) −9.49034 + 6.89514i −0.305822 + 0.222193i
\(964\) 28.7538 + 20.8909i 0.926098 + 0.672849i
\(965\) 2.01707 43.5551i 0.0649319 1.40209i
\(966\) 0.0471773 0.0342763i 0.00151790 0.00110282i
\(967\) 6.49368 19.9855i 0.208823 0.642690i −0.790712 0.612188i \(-0.790289\pi\)
0.999535 0.0305019i \(-0.00971056\pi\)
\(968\) 9.11516 0.292972
\(969\) 9.64696 29.6903i 0.309905 0.953789i
\(970\) 1.17156 + 0.441563i 0.0376165 + 0.0141777i
\(971\) −7.17014 22.0674i −0.230101 0.708177i −0.997734 0.0672874i \(-0.978566\pi\)
0.767633 0.640890i \(-0.221434\pi\)
\(972\) 0.608747 + 1.87353i 0.0195256 + 0.0600935i
\(973\) −7.27751 5.28742i −0.233306 0.169507i
\(974\) −1.05814 −0.0339051
\(975\) −14.4969 12.7372i −0.464272 0.407917i
\(976\) −53.3552 −1.70786
\(977\) 0.0522863 + 0.0379882i 0.00167279 + 0.00121535i 0.588621 0.808409i \(-0.299671\pi\)
−0.586949 + 0.809624i \(0.699671\pi\)
\(978\) 0.455226 + 1.40104i 0.0145565 + 0.0448004i
\(979\) 0.648716 + 1.99654i 0.0207331 + 0.0638098i
\(980\) 4.24783 1.16594i 0.135692 0.0372445i
\(981\) 2.66593 8.20489i 0.0851166 0.261962i
\(982\) 5.71976 0.182525
\(983\) 7.09738 21.8435i 0.226371 0.696699i −0.771778 0.635892i \(-0.780633\pi\)
0.998150 0.0608071i \(-0.0193675\pi\)
\(984\) 5.80292 4.21607i 0.184990 0.134403i
\(985\) 36.1988 9.93579i 1.15339 0.316581i
\(986\) −1.02286 0.743152i −0.0325745 0.0236668i
\(987\) 7.82831 5.68760i 0.249178 0.181038i
\(988\) −35.5672 + 25.8411i −1.13154 + 0.822114i
\(989\) 3.51950 + 2.55707i 0.111914 + 0.0813100i
\(990\) −1.19215 + 1.49063i −0.0378891 + 0.0473755i
\(991\) −3.18769 + 2.31600i −0.101260 + 0.0735700i −0.637263 0.770646i \(-0.719934\pi\)
0.536003 + 0.844216i \(0.319934\pi\)
\(992\) 0.699942 2.15420i 0.0222232 0.0683959i
\(993\) −17.3812 −0.551577
\(994\) −0.385330 + 1.18592i −0.0122219 + 0.0376152i
\(995\) −0.156976 + 3.38962i −0.00497649 + 0.107458i
\(996\) 7.63754 + 23.5059i 0.242005 + 0.744814i
\(997\) −6.02515 18.5435i −0.190818 0.587278i 0.809182 0.587559i \(-0.199911\pi\)
−1.00000 0.000280189i \(0.999911\pi\)
\(998\) −5.67940 4.12632i −0.179778 0.130616i
\(999\) 4.65399 0.147246
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 525.2.n.b.316.3 yes 20
25.11 even 5 inner 525.2.n.b.211.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.n.b.211.3 20 25.11 even 5 inner
525.2.n.b.316.3 yes 20 1.1 even 1 trivial