Properties

Label 177.2.e.b.169.5
Level $177$
Weight $2$
Character 177.169
Analytic conductor $1.413$
Analytic rank $0$
Dimension $140$
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] = [177,2,Mod(4,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
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("177.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\), degree \(28\), 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: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(5\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 169.5
Character \(\chi\) \(=\) 177.169
Dual form 177.2.e.b.22.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.302557 - 1.84551i) q^{2} +(-0.267528 + 0.963550i) q^{3} +(-1.41907 - 0.478141i) q^{4} +(1.62093 + 2.39070i) q^{5} +(1.69730 + 0.785256i) q^{6} +(1.15886 - 0.255085i) q^{7} +(0.440222 - 0.830346i) q^{8} +(-0.856857 - 0.515554i) q^{9} +O(q^{10})\) \(q+(0.302557 - 1.84551i) q^{2} +(-0.267528 + 0.963550i) q^{3} +(-1.41907 - 0.478141i) q^{4} +(1.62093 + 2.39070i) q^{5} +(1.69730 + 0.785256i) q^{6} +(1.15886 - 0.255085i) q^{7} +(0.440222 - 0.830346i) q^{8} +(-0.856857 - 0.515554i) q^{9} +(4.90248 - 2.26813i) q^{10} +(3.14625 - 2.39171i) q^{11} +(0.840355 - 1.23943i) q^{12} +(-3.86478 + 2.32536i) q^{13} +(-0.120141 - 2.21587i) q^{14} +(-2.73720 + 0.922270i) q^{15} +(-3.78346 - 2.87611i) q^{16} +(0.853899 + 0.187957i) q^{17} +(-1.21071 + 1.42536i) q^{18} +(-3.75273 + 0.408134i) q^{19} +(-1.15713 - 4.16761i) q^{20} +(-0.0642415 + 1.18486i) q^{21} +(-3.46202 - 6.53007i) q^{22} +(2.31962 + 2.73087i) q^{23} +(0.682308 + 0.646317i) q^{24} +(-1.23732 + 3.10543i) q^{25} +(3.12217 + 7.83606i) q^{26} +(0.725995 - 0.687699i) q^{27} +(-1.76648 - 0.192116i) q^{28} +(-0.671290 - 4.09469i) q^{29} +(0.873904 + 5.33058i) q^{30} +(-5.65169 - 0.614658i) q^{31} +(-5.08799 + 4.81960i) q^{32} +(1.46283 + 3.67142i) q^{33} +(0.605231 - 1.51901i) q^{34} +(2.48827 + 2.35701i) q^{35} +(0.969435 + 1.14131i) q^{36} +(-2.58442 - 4.87473i) q^{37} +(-0.382196 + 7.04920i) q^{38} +(-1.20666 - 4.34601i) q^{39} +(2.69868 - 0.293499i) q^{40} +(-4.30020 + 5.06259i) q^{41} +(2.16725 + 0.477047i) q^{42} +(7.31003 + 5.55694i) q^{43} +(-5.60833 + 1.88967i) q^{44} +(-0.156375 - 2.88416i) q^{45} +(5.74167 - 3.45465i) q^{46} +(5.31007 - 7.83177i) q^{47} +(3.78346 - 2.87611i) q^{48} +(-5.07513 + 2.34801i) q^{49} +(5.35675 + 3.22305i) q^{50} +(-0.409549 + 0.772491i) q^{51} +(6.59626 - 1.45195i) q^{52} +(-9.18831 - 4.25096i) q^{53} +(-1.04950 - 1.54790i) q^{54} +(10.8177 + 3.64491i) q^{55} +(0.298348 - 1.07455i) q^{56} +(0.610704 - 3.72513i) q^{57} -7.75991 q^{58} +(-3.84234 + 6.65105i) q^{59} +4.32526 q^{60} +(-1.88706 + 11.5105i) q^{61} +(-2.84432 + 10.2443i) q^{62} +(-1.12449 - 0.378885i) q^{63} +(2.02112 + 2.98093i) q^{64} +(-11.8238 - 5.47027i) q^{65} +(7.21824 - 1.58885i) q^{66} +(-0.875003 + 1.65043i) q^{67} +(-1.12187 - 0.675010i) q^{68} +(-3.25189 + 1.50448i) q^{69} +(5.10274 - 3.87900i) q^{70} +(2.55264 - 3.76487i) q^{71} +(-0.805296 + 0.484530i) q^{72} +(-0.451075 - 8.31958i) q^{73} +(-9.77832 + 3.29470i) q^{74} +(-2.66122 - 2.02300i) q^{75} +(5.52054 + 1.21516i) q^{76} +(3.03598 - 3.57423i) q^{77} +(-8.38571 + 0.912001i) q^{78} +(-3.71762 - 13.3896i) q^{79} +(0.743176 - 13.7071i) q^{80} +(0.468408 + 0.883512i) q^{81} +(8.04202 + 9.46780i) q^{82} +(11.1642 + 10.5753i) q^{83} +(0.657696 - 1.65069i) q^{84} +(0.934763 + 2.34608i) q^{85} +(12.4671 - 11.8095i) q^{86} +(4.12503 + 0.448624i) q^{87} +(-0.600905 - 3.66536i) q^{88} +(-0.307465 - 1.87545i) q^{89} +(-5.37007 - 0.584031i) q^{90} +(-3.88559 + 3.68062i) q^{91} +(-1.98597 - 4.98441i) q^{92} +(2.10424 - 5.28125i) q^{93} +(-12.8470 - 12.1694i) q^{94} +(-7.05864 - 8.31008i) q^{95} +(-3.28275 - 6.19192i) q^{96} +(0.436458 - 8.04999i) q^{97} +(2.79776 + 10.0766i) q^{98} +(-3.92894 + 0.427298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{16}{29}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.302557 1.84551i 0.213940 1.30498i −0.633359 0.773858i \(-0.718324\pi\)
0.847299 0.531117i \(-0.178227\pi\)
\(3\) −0.267528 + 0.963550i −0.154458 + 0.556306i
\(4\) −1.41907 0.478141i −0.709536 0.239071i
\(5\) 1.62093 + 2.39070i 0.724903 + 1.06915i 0.994352 + 0.106137i \(0.0338482\pi\)
−0.269449 + 0.963015i \(0.586841\pi\)
\(6\) 1.69730 + 0.785256i 0.692921 + 0.320579i
\(7\) 1.15886 0.255085i 0.438009 0.0964130i 0.00950872 0.999955i \(-0.496973\pi\)
0.428500 + 0.903542i \(0.359042\pi\)
\(8\) 0.440222 0.830346i 0.155642 0.293572i
\(9\) −0.856857 0.515554i −0.285619 0.171851i
\(10\) 4.90248 2.26813i 1.55030 0.717246i
\(11\) 3.14625 2.39171i 0.948629 0.721129i −0.0117196 0.999931i \(-0.503731\pi\)
0.960348 + 0.278802i \(0.0899374\pi\)
\(12\) 0.840355 1.23943i 0.242590 0.357793i
\(13\) −3.86478 + 2.32536i −1.07190 + 0.644940i −0.938204 0.346083i \(-0.887512\pi\)
−0.133694 + 0.991023i \(0.542684\pi\)
\(14\) −0.120141 2.21587i −0.0321091 0.592217i
\(15\) −2.73720 + 0.922270i −0.706742 + 0.238129i
\(16\) −3.78346 2.87611i −0.945865 0.719028i
\(17\) 0.853899 + 0.187957i 0.207101 + 0.0455864i 0.317309 0.948322i \(-0.397221\pi\)
−0.110208 + 0.993909i \(0.535152\pi\)
\(18\) −1.21071 + 1.42536i −0.285367 + 0.335960i
\(19\) −3.75273 + 0.408134i −0.860935 + 0.0936323i −0.527925 0.849291i \(-0.677030\pi\)
−0.333010 + 0.942923i \(0.608064\pi\)
\(20\) −1.15713 4.16761i −0.258742 0.931905i
\(21\) −0.0642415 + 1.18486i −0.0140186 + 0.258559i
\(22\) −3.46202 6.53007i −0.738106 1.39222i
\(23\) 2.31962 + 2.73087i 0.483674 + 0.569425i 0.948823 0.315807i \(-0.102275\pi\)
−0.465149 + 0.885232i \(0.653999\pi\)
\(24\) 0.682308 + 0.646317i 0.139276 + 0.131929i
\(25\) −1.23732 + 3.10543i −0.247463 + 0.621085i
\(26\) 3.12217 + 7.83606i 0.612308 + 1.53678i
\(27\) 0.725995 0.687699i 0.139718 0.132348i
\(28\) −1.76648 0.192116i −0.333833 0.0363065i
\(29\) −0.671290 4.09469i −0.124655 0.760365i −0.972980 0.230888i \(-0.925837\pi\)
0.848325 0.529476i \(-0.177612\pi\)
\(30\) 0.873904 + 5.33058i 0.159552 + 0.973226i
\(31\) −5.65169 0.614658i −1.01507 0.110396i −0.414570 0.910018i \(-0.636068\pi\)
−0.600504 + 0.799622i \(0.705033\pi\)
\(32\) −5.08799 + 4.81960i −0.899439 + 0.851994i
\(33\) 1.46283 + 3.67142i 0.254645 + 0.639112i
\(34\) 0.605231 1.51901i 0.103796 0.260509i
\(35\) 2.48827 + 2.35701i 0.420594 + 0.398408i
\(36\) 0.969435 + 1.14131i 0.161573 + 0.190218i
\(37\) −2.58442 4.87473i −0.424876 0.801401i 0.574984 0.818165i \(-0.305008\pi\)
−0.999859 + 0.0167639i \(0.994664\pi\)
\(38\) −0.382196 + 7.04920i −0.0620004 + 1.14353i
\(39\) −1.20666 4.34601i −0.193221 0.695919i
\(40\) 2.69868 0.293499i 0.426698 0.0464062i
\(41\) −4.30020 + 5.06259i −0.671579 + 0.790644i −0.987412 0.158171i \(-0.949440\pi\)
0.315833 + 0.948815i \(0.397716\pi\)
\(42\) 2.16725 + 0.477047i 0.334413 + 0.0736099i
\(43\) 7.31003 + 5.55694i 1.11477 + 0.847426i 0.989476 0.144694i \(-0.0462199\pi\)
0.125293 + 0.992120i \(0.460013\pi\)
\(44\) −5.60833 + 1.88967i −0.845488 + 0.284878i
\(45\) −0.156375 2.88416i −0.0233110 0.429946i
\(46\) 5.74167 3.45465i 0.846563 0.509360i
\(47\) 5.31007 7.83177i 0.774554 1.14238i −0.211731 0.977328i \(-0.567910\pi\)
0.986285 0.165053i \(-0.0527796\pi\)
\(48\) 3.78346 2.87611i 0.546095 0.415131i
\(49\) −5.07513 + 2.34801i −0.725019 + 0.335430i
\(50\) 5.35675 + 3.22305i 0.757559 + 0.455808i
\(51\) −0.409549 + 0.772491i −0.0573483 + 0.108170i
\(52\) 6.59626 1.45195i 0.914737 0.201349i
\(53\) −9.18831 4.25096i −1.26211 0.583915i −0.329281 0.944232i \(-0.606806\pi\)
−0.932830 + 0.360317i \(0.882668\pi\)
\(54\) −1.04950 1.54790i −0.142819 0.210643i
\(55\) 10.8177 + 3.64491i 1.45866 + 0.491480i
\(56\) 0.298348 1.07455i 0.0398684 0.143593i
\(57\) 0.610704 3.72513i 0.0808897 0.493406i
\(58\) −7.75991 −1.01893
\(59\) −3.84234 + 6.65105i −0.500230 + 0.865893i
\(60\) 4.32526 0.558389
\(61\) −1.88706 + 11.5105i −0.241613 + 1.47377i 0.535566 + 0.844494i \(0.320098\pi\)
−0.777179 + 0.629280i \(0.783350\pi\)
\(62\) −2.84432 + 10.2443i −0.361229 + 1.30103i
\(63\) −1.12449 0.378885i −0.141672 0.0477350i
\(64\) 2.02112 + 2.98093i 0.252640 + 0.372616i
\(65\) −11.8238 5.47027i −1.46656 0.678503i
\(66\) 7.21824 1.58885i 0.888503 0.195574i
\(67\) −0.875003 + 1.65043i −0.106899 + 0.201632i −0.931191 0.364533i \(-0.881229\pi\)
0.824292 + 0.566165i \(0.191574\pi\)
\(68\) −1.12187 0.675010i −0.136047 0.0818570i
\(69\) −3.25189 + 1.50448i −0.391482 + 0.181119i
\(70\) 5.10274 3.87900i 0.609894 0.463629i
\(71\) 2.55264 3.76487i 0.302943 0.446808i −0.645498 0.763762i \(-0.723350\pi\)
0.948441 + 0.316955i \(0.102660\pi\)
\(72\) −0.805296 + 0.484530i −0.0949050 + 0.0571024i
\(73\) −0.451075 8.31958i −0.0527943 0.973733i −0.898194 0.439599i \(-0.855121\pi\)
0.845400 0.534134i \(-0.179362\pi\)
\(74\) −9.77832 + 3.29470i −1.13671 + 0.383001i
\(75\) −2.66122 2.02300i −0.307291 0.233596i
\(76\) 5.52054 + 1.21516i 0.633250 + 0.139389i
\(77\) 3.03598 3.57423i 0.345982 0.407321i
\(78\) −8.38571 + 0.912001i −0.949494 + 0.103264i
\(79\) −3.71762 13.3896i −0.418264 1.50645i −0.810031 0.586387i \(-0.800550\pi\)
0.391766 0.920065i \(-0.371864\pi\)
\(80\) 0.743176 13.7071i 0.0830896 1.53250i
\(81\) 0.468408 + 0.883512i 0.0520454 + 0.0981680i
\(82\) 8.04202 + 9.46780i 0.888093 + 1.04554i
\(83\) 11.1642 + 10.5753i 1.22543 + 1.16079i 0.981594 + 0.190978i \(0.0611658\pi\)
0.243840 + 0.969815i \(0.421593\pi\)
\(84\) 0.657696 1.65069i 0.0717605 0.180105i
\(85\) 0.934763 + 2.34608i 0.101389 + 0.254468i
\(86\) 12.4671 11.8095i 1.34436 1.27345i
\(87\) 4.12503 + 0.448624i 0.442249 + 0.0480975i
\(88\) −0.600905 3.66536i −0.0640567 0.390729i
\(89\) −0.307465 1.87545i −0.0325912 0.198798i 0.965512 0.260358i \(-0.0838406\pi\)
−0.998103 + 0.0615604i \(0.980392\pi\)
\(90\) −5.37007 0.584031i −0.566055 0.0615622i
\(91\) −3.88559 + 3.68062i −0.407320 + 0.385834i
\(92\) −1.98597 4.98441i −0.207052 0.519660i
\(93\) 2.10424 5.28125i 0.218200 0.547640i
\(94\) −12.8470 12.1694i −1.32507 1.25517i
\(95\) −7.05864 8.31008i −0.724202 0.852596i
\(96\) −3.28275 6.19192i −0.335044 0.631960i
\(97\) 0.436458 8.04999i 0.0443156 0.817353i −0.888914 0.458073i \(-0.848540\pi\)
0.933230 0.359279i \(-0.116977\pi\)
\(98\) 2.79776 + 10.0766i 0.282617 + 1.01789i
\(99\) −3.92894 + 0.427298i −0.394873 + 0.0429451i
\(100\) 3.24067 3.81522i 0.324067 0.381522i
\(101\) −12.7461 2.80564i −1.26829 0.279171i −0.470656 0.882317i \(-0.655983\pi\)
−0.797631 + 0.603145i \(0.793914\pi\)
\(102\) 1.30173 + 0.989550i 0.128890 + 0.0979800i
\(103\) 5.37770 1.81196i 0.529881 0.178538i −0.0416285 0.999133i \(-0.513255\pi\)
0.571509 + 0.820595i \(0.306358\pi\)
\(104\) 0.229495 + 4.23278i 0.0225038 + 0.415059i
\(105\) −2.93678 + 1.76700i −0.286600 + 0.172442i
\(106\) −10.6252 + 15.6710i −1.03201 + 1.52210i
\(107\) 10.2068 7.75903i 0.986731 0.750093i 0.0184172 0.999830i \(-0.494137\pi\)
0.968314 + 0.249737i \(0.0803442\pi\)
\(108\) −1.35906 + 0.628767i −0.130775 + 0.0605032i
\(109\) 15.9202 + 9.57886i 1.52488 + 0.917489i 0.997704 + 0.0677313i \(0.0215761\pi\)
0.527174 + 0.849757i \(0.323252\pi\)
\(110\) 9.99970 18.8614i 0.953434 1.79837i
\(111\) 5.38845 1.18609i 0.511449 0.112579i
\(112\) −5.11816 2.36791i −0.483621 0.223747i
\(113\) 0.800441 + 1.18056i 0.0752991 + 0.111058i 0.863474 0.504394i \(-0.168284\pi\)
−0.788175 + 0.615452i \(0.788974\pi\)
\(114\) −6.69000 2.25412i −0.626576 0.211118i
\(115\) −2.76873 + 9.97205i −0.258185 + 0.929899i
\(116\) −1.00523 + 6.13163i −0.0933333 + 0.569308i
\(117\) 4.51042 0.416988
\(118\) 11.1121 + 9.10341i 1.02295 + 0.838036i
\(119\) 1.03750 0.0951071
\(120\) −0.439172 + 2.67883i −0.0400907 + 0.244542i
\(121\) 1.23576 4.45079i 0.112341 0.404617i
\(122\) 20.6719 + 6.96518i 1.87155 + 0.630598i
\(123\) −3.72763 5.49785i −0.336109 0.495724i
\(124\) 7.72627 + 3.57455i 0.693839 + 0.321004i
\(125\) 4.67461 1.02896i 0.418110 0.0920330i
\(126\) −1.03946 + 1.96063i −0.0926023 + 0.174666i
\(127\) 2.81601 + 1.69434i 0.249881 + 0.150348i 0.634984 0.772525i \(-0.281007\pi\)
−0.385103 + 0.922873i \(0.625834\pi\)
\(128\) −6.60828 + 3.05732i −0.584095 + 0.270231i
\(129\) −7.31003 + 5.55694i −0.643612 + 0.489261i
\(130\) −13.6728 + 20.1659i −1.19918 + 1.76867i
\(131\) 13.2655 7.98156i 1.15901 0.697352i 0.199740 0.979849i \(-0.435990\pi\)
0.959268 + 0.282496i \(0.0911625\pi\)
\(132\) −0.320401 5.90945i −0.0278873 0.514351i
\(133\) −4.24479 + 1.43024i −0.368070 + 0.124017i
\(134\) 2.78115 + 2.11418i 0.240255 + 0.182637i
\(135\) 2.82087 + 0.620920i 0.242782 + 0.0534403i
\(136\) 0.531975 0.626289i 0.0456165 0.0537039i
\(137\) 11.8886 1.29296i 1.01571 0.110465i 0.414908 0.909863i \(-0.363814\pi\)
0.600802 + 0.799398i \(0.294848\pi\)
\(138\) 1.79267 + 6.45660i 0.152602 + 0.549622i
\(139\) −0.490886 + 9.05387i −0.0416364 + 0.767939i 0.900939 + 0.433946i \(0.142879\pi\)
−0.942575 + 0.333993i \(0.891604\pi\)
\(140\) −2.40405 4.53451i −0.203179 0.383236i
\(141\) 6.12571 + 7.21174i 0.515878 + 0.607338i
\(142\) −6.17580 5.85003i −0.518261 0.490923i
\(143\) −6.59796 + 16.5596i −0.551749 + 1.38478i
\(144\) 1.75909 + 4.41499i 0.146591 + 0.367916i
\(145\) 8.70104 8.24206i 0.722582 0.684466i
\(146\) −15.4904 1.68468i −1.28199 0.139425i
\(147\) −0.904680 5.51830i −0.0746168 0.455142i
\(148\) 1.33667 + 8.15332i 0.109873 + 0.670199i
\(149\) −3.05282 0.332014i −0.250097 0.0271997i −0.0177882 0.999842i \(-0.505662\pi\)
−0.232309 + 0.972642i \(0.574628\pi\)
\(150\) −4.53865 + 4.29924i −0.370579 + 0.351031i
\(151\) 7.92992 + 19.9026i 0.645328 + 1.61965i 0.777835 + 0.628468i \(0.216318\pi\)
−0.132507 + 0.991182i \(0.542303\pi\)
\(152\) −1.31314 + 3.29573i −0.106510 + 0.267319i
\(153\) −0.634767 0.601284i −0.0513179 0.0486109i
\(154\) −5.67773 6.68434i −0.457524 0.538639i
\(155\) −7.69154 14.5078i −0.617800 1.16529i
\(156\) −0.365663 + 6.74426i −0.0292765 + 0.539973i
\(157\) 1.59809 + 5.75580i 0.127542 + 0.459363i 0.999546 0.0301351i \(-0.00959377\pi\)
−0.872004 + 0.489498i \(0.837180\pi\)
\(158\) −25.8355 + 2.80979i −2.05537 + 0.223535i
\(159\) 6.55415 7.71614i 0.519778 0.611930i
\(160\) −19.7695 4.35160i −1.56292 0.344024i
\(161\) 3.38472 + 2.57300i 0.266753 + 0.202781i
\(162\) 1.77225 0.597142i 0.139241 0.0469159i
\(163\) 0.00987540 + 0.182141i 0.000773501 + 0.0142664i 0.998895 0.0470043i \(-0.0149675\pi\)
−0.998121 + 0.0612707i \(0.980485\pi\)
\(164\) 8.52293 5.12808i 0.665529 0.400436i
\(165\) −6.40610 + 9.44829i −0.498714 + 0.735548i
\(166\) 22.8947 17.4041i 1.77698 1.35082i
\(167\) −13.4410 + 6.21845i −1.04009 + 0.481198i −0.864167 0.503205i \(-0.832154\pi\)
−0.175926 + 0.984403i \(0.556292\pi\)
\(168\) 0.955567 + 0.574946i 0.0737236 + 0.0443580i
\(169\) 3.43993 6.48839i 0.264610 0.499107i
\(170\) 4.61254 1.01530i 0.353766 0.0778697i
\(171\) 3.42597 + 1.58502i 0.261990 + 0.121210i
\(172\) −7.71646 11.3809i −0.588375 0.867788i
\(173\) 11.2785 + 3.80016i 0.857485 + 0.288920i 0.713496 0.700659i \(-0.247110\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(174\) 2.07599 7.47706i 0.157381 0.566834i
\(175\) −0.641730 + 3.91438i −0.0485103 + 0.295899i
\(176\) −18.7825 −1.41579
\(177\) −5.38068 5.48163i −0.404437 0.412024i
\(178\) −3.55420 −0.266399
\(179\) 0.849504 5.18175i 0.0634949 0.387302i −0.935892 0.352287i \(-0.885404\pi\)
0.999387 0.0350145i \(-0.0111477\pi\)
\(180\) −1.15713 + 4.16761i −0.0862474 + 0.310635i
\(181\) −16.2009 5.45871i −1.20420 0.405743i −0.355531 0.934665i \(-0.615700\pi\)
−0.848670 + 0.528922i \(0.822596\pi\)
\(182\) 5.61703 + 8.28450i 0.416362 + 0.614088i
\(183\) −10.5861 4.89767i −0.782550 0.362046i
\(184\) 3.28871 0.723900i 0.242447 0.0533666i
\(185\) 7.46483 14.0802i 0.548825 1.03519i
\(186\) −9.10996 5.48128i −0.667975 0.401907i
\(187\) 3.13612 1.45092i 0.229336 0.106102i
\(188\) −11.2801 + 8.57489i −0.822684 + 0.625388i
\(189\) 0.665907 0.982139i 0.0484376 0.0714401i
\(190\) −17.4720 + 10.5126i −1.26755 + 0.762661i
\(191\) −1.13544 20.9420i −0.0821578 1.51531i −0.691484 0.722392i \(-0.743043\pi\)
0.609326 0.792920i \(-0.291440\pi\)
\(192\) −3.41298 + 1.14997i −0.246310 + 0.0829916i
\(193\) 7.85441 + 5.97077i 0.565373 + 0.429785i 0.848422 0.529320i \(-0.177553\pi\)
−0.283049 + 0.959105i \(0.591346\pi\)
\(194\) −14.7243 3.24107i −1.05714 0.232695i
\(195\) 8.43407 9.92936i 0.603976 0.711056i
\(196\) 8.32467 0.905362i 0.594619 0.0646687i
\(197\) 3.85177 + 13.8728i 0.274427 + 0.988397i 0.964375 + 0.264538i \(0.0852196\pi\)
−0.689948 + 0.723859i \(0.742367\pi\)
\(198\) −0.400143 + 7.38020i −0.0284369 + 0.524488i
\(199\) 1.07304 + 2.02396i 0.0760654 + 0.143475i 0.918628 0.395125i \(-0.129299\pi\)
−0.842562 + 0.538599i \(0.818954\pi\)
\(200\) 2.03389 + 2.39448i 0.143818 + 0.169315i
\(201\) −1.35618 1.28465i −0.0956579 0.0906120i
\(202\) −9.03426 + 22.6743i −0.635649 + 1.59536i
\(203\) −1.82243 4.57394i −0.127909 0.321028i
\(204\) 0.950539 0.900398i 0.0665510 0.0630405i
\(205\) −19.0734 2.07436i −1.33215 0.144880i
\(206\) −1.71694 10.4728i −0.119625 0.729678i
\(207\) −0.579673 3.53585i −0.0402901 0.245759i
\(208\) 21.3102 + 2.31763i 1.47760 + 0.160699i
\(209\) −10.8309 + 10.2595i −0.749187 + 0.709668i
\(210\) 2.37248 + 5.95449i 0.163717 + 0.410899i
\(211\) −6.90875 + 17.3396i −0.475618 + 1.19371i 0.474063 + 0.880491i \(0.342787\pi\)
−0.949681 + 0.313220i \(0.898592\pi\)
\(212\) 11.0063 + 10.4257i 0.755917 + 0.716043i
\(213\) 2.94473 + 3.46681i 0.201770 + 0.237542i
\(214\) −11.2312 21.1844i −0.767752 1.44813i
\(215\) −1.43589 + 26.4835i −0.0979271 + 1.80616i
\(216\) −0.251430 0.905568i −0.0171076 0.0616161i
\(217\) −6.70632 + 0.729356i −0.455255 + 0.0495119i
\(218\) 22.4947 26.4828i 1.52353 1.79364i
\(219\) 8.13701 + 1.79109i 0.549848 + 0.121031i
\(220\) −13.6083 10.3448i −0.917474 0.697446i
\(221\) −3.73720 + 1.25921i −0.251392 + 0.0847037i
\(222\) −0.558630 10.3033i −0.0374928 0.691514i
\(223\) 12.1848 7.33135i 0.815954 0.490943i −0.0453876 0.998969i \(-0.514452\pi\)
0.861342 + 0.508026i \(0.169625\pi\)
\(224\) −4.66688 + 6.88313i −0.311819 + 0.459898i
\(225\) 2.66122 2.02300i 0.177414 0.134867i
\(226\) 2.42092 1.12004i 0.161037 0.0745038i
\(227\) 3.62467 + 2.18089i 0.240578 + 0.144751i 0.630737 0.775996i \(-0.282753\pi\)
−0.390159 + 0.920747i \(0.627580\pi\)
\(228\) −2.64777 + 4.99423i −0.175353 + 0.330751i
\(229\) 14.3527 3.15926i 0.948450 0.208770i 0.286299 0.958140i \(-0.407575\pi\)
0.662151 + 0.749370i \(0.269644\pi\)
\(230\) 17.5659 + 8.12683i 1.15826 + 0.535868i
\(231\) 2.63174 + 3.88152i 0.173156 + 0.255385i
\(232\) −3.69553 1.24517i −0.242623 0.0817493i
\(233\) −7.16169 + 25.7941i −0.469178 + 1.68983i 0.228608 + 0.973519i \(0.426583\pi\)
−0.697786 + 0.716307i \(0.745831\pi\)
\(234\) 1.36466 8.32403i 0.0892104 0.544159i
\(235\) 27.3306 1.78286
\(236\) 8.63270 7.60114i 0.561941 0.494792i
\(237\) 13.8962 0.902652
\(238\) 0.313901 1.91471i 0.0203472 0.124112i
\(239\) −0.476138 + 1.71489i −0.0307988 + 0.110927i −0.977352 0.211621i \(-0.932126\pi\)
0.946553 + 0.322548i \(0.104540\pi\)
\(240\) 13.0086 + 4.38312i 0.839704 + 0.282929i
\(241\) −8.01002 11.8139i −0.515971 0.761000i 0.477058 0.878872i \(-0.341703\pi\)
−0.993029 + 0.117872i \(0.962393\pi\)
\(242\) −7.84011 3.62722i −0.503981 0.233167i
\(243\) −0.976621 + 0.214970i −0.0626502 + 0.0137904i
\(244\) 8.18154 15.4320i 0.523769 0.987934i
\(245\) −13.8398 8.32714i −0.884194 0.532002i
\(246\) −11.2742 + 5.21599i −0.718815 + 0.332559i
\(247\) 13.5544 10.3038i 0.862447 0.655616i
\(248\) −2.99838 + 4.42227i −0.190397 + 0.280815i
\(249\) −13.1766 + 7.92810i −0.835034 + 0.502423i
\(250\) −0.484625 8.93838i −0.0306504 0.565313i
\(251\) 10.4444 3.51914i 0.659246 0.222126i 0.0302597 0.999542i \(-0.490367\pi\)
0.628987 + 0.777416i \(0.283470\pi\)
\(252\) 1.41457 + 1.07533i 0.0891097 + 0.0677394i
\(253\) 13.8295 + 3.04411i 0.869456 + 0.191382i
\(254\) 3.97893 4.68436i 0.249660 0.293923i
\(255\) −2.51064 + 0.273049i −0.157222 + 0.0170990i
\(256\) 5.56995 + 20.0611i 0.348122 + 1.25382i
\(257\) −0.699976 + 12.9103i −0.0436633 + 0.805322i 0.891915 + 0.452203i \(0.149362\pi\)
−0.935578 + 0.353119i \(0.885121\pi\)
\(258\) 8.04371 + 15.1720i 0.500780 + 0.944571i
\(259\) −4.23846 4.98990i −0.263365 0.310057i
\(260\) 14.1633 + 13.4161i 0.878368 + 0.832034i
\(261\) −1.53583 + 3.85465i −0.0950657 + 0.238597i
\(262\) −10.7165 26.8965i −0.662069 1.66167i
\(263\) 17.2907 16.3786i 1.06619 1.00995i 0.0662646 0.997802i \(-0.478892\pi\)
0.999926 0.0121475i \(-0.00386677\pi\)
\(264\) 3.69252 + 0.401585i 0.227259 + 0.0247159i
\(265\) −4.73086 28.8570i −0.290614 1.77267i
\(266\) 1.35523 + 8.26654i 0.0830945 + 0.506854i
\(267\) 1.88935 + 0.205479i 0.115626 + 0.0125751i
\(268\) 2.03083 1.92371i 0.124053 0.117509i
\(269\) −2.85747 7.17171i −0.174223 0.437267i 0.815771 0.578375i \(-0.196313\pi\)
−0.989994 + 0.141108i \(0.954934\pi\)
\(270\) 1.99939 5.01809i 0.121679 0.305391i
\(271\) −22.3118 21.1349i −1.35535 1.28385i −0.924373 0.381489i \(-0.875411\pi\)
−0.430974 0.902364i \(-0.641830\pi\)
\(272\) −2.69011 3.16704i −0.163112 0.192030i
\(273\) −2.50696 4.72863i −0.151728 0.286190i
\(274\) 1.21079 22.3317i 0.0731466 1.34911i
\(275\) 3.53439 + 12.7297i 0.213132 + 0.767632i
\(276\) 5.33403 0.580110i 0.321071 0.0349185i
\(277\) −9.15014 + 10.7724i −0.549779 + 0.647250i −0.964931 0.262502i \(-0.915452\pi\)
0.415153 + 0.909752i \(0.363728\pi\)
\(278\) 16.5605 + 3.64524i 0.993233 + 0.218627i
\(279\) 4.52580 + 3.44043i 0.270953 + 0.205973i
\(280\) 3.05253 1.02852i 0.182423 0.0614656i
\(281\) 1.37726 + 25.4021i 0.0821607 + 1.51537i 0.691454 + 0.722420i \(0.256970\pi\)
−0.609294 + 0.792945i \(0.708547\pi\)
\(282\) 15.1627 9.12312i 0.902928 0.543274i
\(283\) 6.48088 9.55858i 0.385248 0.568199i −0.584780 0.811192i \(-0.698819\pi\)
0.970028 + 0.242994i \(0.0781294\pi\)
\(284\) −5.42253 + 4.12210i −0.321768 + 0.244602i
\(285\) 9.89556 4.57817i 0.586162 0.271188i
\(286\) 28.5647 + 17.1868i 1.68907 + 1.01628i
\(287\) −3.69195 + 6.96376i −0.217929 + 0.411058i
\(288\) 6.84445 1.50658i 0.403313 0.0887759i
\(289\) −14.7350 6.81712i −0.866763 0.401007i
\(290\) −12.5783 18.5516i −0.738622 1.08939i
\(291\) 7.63980 + 2.57415i 0.447853 + 0.150899i
\(292\) −3.33783 + 12.0218i −0.195332 + 0.703521i
\(293\) 1.76218 10.7488i 0.102947 0.627952i −0.884072 0.467351i \(-0.845209\pi\)
0.987019 0.160601i \(-0.0513432\pi\)
\(294\) −10.4578 −0.609913
\(295\) −22.1288 + 1.59503i −1.28839 + 0.0928664i
\(296\) −5.18543 −0.301397
\(297\) 0.639380 3.90005i 0.0371006 0.226304i
\(298\) −1.53639 + 5.53357i −0.0890006 + 0.320551i
\(299\) −15.3151 5.16025i −0.885694 0.298425i
\(300\) 2.80918 + 4.14323i 0.162188 + 0.239209i
\(301\) 9.88881 + 4.57505i 0.569982 + 0.263702i
\(302\) 39.1298 8.61311i 2.25166 0.495629i
\(303\) 6.11332 11.5309i 0.351201 0.662436i
\(304\) 15.3721 + 9.24911i 0.881652 + 0.530473i
\(305\) −30.5770 + 14.1464i −1.75083 + 0.810022i
\(306\) −1.30173 + 0.989550i −0.0744150 + 0.0565688i
\(307\) 0.881102 1.29953i 0.0502872 0.0741680i −0.801714 0.597708i \(-0.796078\pi\)
0.852001 + 0.523539i \(0.175389\pi\)
\(308\) −6.01726 + 3.62046i −0.342865 + 0.206295i
\(309\) 0.307225 + 5.66644i 0.0174774 + 0.322352i
\(310\) −29.1015 + 9.80542i −1.65285 + 0.556910i
\(311\) −20.3931 15.5024i −1.15639 0.879062i −0.162202 0.986758i \(-0.551860\pi\)
−0.994184 + 0.107695i \(0.965653\pi\)
\(312\) −4.13990 0.911260i −0.234375 0.0515899i
\(313\) 11.3386 13.3489i 0.640897 0.754522i −0.341794 0.939775i \(-0.611034\pi\)
0.982691 + 0.185252i \(0.0593103\pi\)
\(314\) 11.1059 1.20784i 0.626744 0.0681625i
\(315\) −0.916923 3.30246i −0.0516628 0.186072i
\(316\) −1.12657 + 20.7784i −0.0633747 + 1.16888i
\(317\) 9.00923 + 16.9932i 0.506009 + 0.954433i 0.996548 + 0.0830145i \(0.0264548\pi\)
−0.490540 + 0.871419i \(0.663200\pi\)
\(318\) −12.2572 14.4303i −0.687352 0.809213i
\(319\) −11.9054 11.2774i −0.666573 0.631411i
\(320\) −3.85039 + 9.66375i −0.215243 + 0.540220i
\(321\) 4.74559 + 11.9105i 0.264873 + 0.664782i
\(322\) 5.77257 5.46807i 0.321693 0.304724i
\(323\) −3.28116 0.356848i −0.182569 0.0198556i
\(324\) −0.242262 1.47773i −0.0134590 0.0820963i
\(325\) −2.43929 14.8790i −0.135307 0.825339i
\(326\) 0.339131 + 0.0368828i 0.0187828 + 0.00204275i
\(327\) −13.4888 + 12.7773i −0.745933 + 0.706585i
\(328\) 2.31066 + 5.79932i 0.127585 + 0.320214i
\(329\) 4.15588 10.4305i 0.229121 0.575050i
\(330\) 15.4987 + 14.6812i 0.853177 + 0.808173i
\(331\) −1.58762 1.86909i −0.0872634 0.102734i 0.716797 0.697281i \(-0.245607\pi\)
−0.804061 + 0.594547i \(0.797331\pi\)
\(332\) −10.7864 20.3452i −0.591979 1.11659i
\(333\) −0.298709 + 5.50936i −0.0163691 + 0.301911i
\(334\) 7.40958 + 26.6869i 0.405434 + 1.46024i
\(335\) −5.36400 + 0.583370i −0.293067 + 0.0318729i
\(336\) 3.65085 4.29812i 0.199170 0.234482i
\(337\) −4.18445 0.921067i −0.227942 0.0501737i 0.0995308 0.995034i \(-0.468266\pi\)
−0.327472 + 0.944861i \(0.606197\pi\)
\(338\) −10.9336 8.31154i −0.594711 0.452088i
\(339\) −1.35167 + 0.455431i −0.0734127 + 0.0247356i
\(340\) −0.204740 3.77621i −0.0111036 0.204794i
\(341\) −19.2517 + 11.5834i −1.04254 + 0.627274i
\(342\) 3.96173 5.84311i 0.214226 0.315959i
\(343\) −11.8950 + 9.04232i −0.642268 + 0.488240i
\(344\) 7.83222 3.62357i 0.422285 0.195370i
\(345\) −8.86786 5.33561i −0.477430 0.287260i
\(346\) 10.4256 19.6648i 0.560484 1.05719i
\(347\) 4.50870 0.992440i 0.242040 0.0532770i −0.0922938 0.995732i \(-0.529420\pi\)
0.334333 + 0.942455i \(0.391489\pi\)
\(348\) −5.63921 2.60898i −0.302293 0.139856i
\(349\) −1.37485 2.02775i −0.0735941 0.108543i 0.789111 0.614251i \(-0.210542\pi\)
−0.862705 + 0.505708i \(0.831231\pi\)
\(350\) 7.02988 + 2.36864i 0.375763 + 0.126609i
\(351\) −1.20666 + 4.34601i −0.0644070 + 0.231973i
\(352\) −4.48097 + 27.3327i −0.238836 + 1.45684i
\(353\) 6.40798 0.341063 0.170531 0.985352i \(-0.445452\pi\)
0.170531 + 0.985352i \(0.445452\pi\)
\(354\) −11.7444 + 8.27162i −0.624207 + 0.439632i
\(355\) 13.1383 0.697310
\(356\) −0.460417 + 2.80842i −0.0244020 + 0.148846i
\(357\) −0.277560 + 0.999680i −0.0146900 + 0.0529087i
\(358\) −9.30596 3.13554i −0.491835 0.165719i
\(359\) −13.8222 20.3862i −0.729508 1.07594i −0.993765 0.111491i \(-0.964437\pi\)
0.264258 0.964452i \(-0.414873\pi\)
\(360\) −2.46369 1.13983i −0.129848 0.0600741i
\(361\) −4.63939 + 1.02121i −0.244178 + 0.0537477i
\(362\) −14.9758 + 28.2474i −0.787111 + 1.48465i
\(363\) 3.95796 + 2.38143i 0.207739 + 0.124992i
\(364\) 7.27379 3.36521i 0.381250 0.176385i
\(365\) 19.1584 14.5639i 1.00280 0.762307i
\(366\) −12.2416 + 18.0550i −0.639880 + 0.943752i
\(367\) −27.2409 + 16.3903i −1.42196 + 0.855566i −0.998726 0.0504541i \(-0.983933\pi\)
−0.423235 + 0.906020i \(0.639106\pi\)
\(368\) −0.921909 17.0036i −0.0480578 0.886374i
\(369\) 6.29470 2.12093i 0.327689 0.110411i
\(370\) −23.7266 18.0365i −1.23349 0.937673i
\(371\) −11.7323 2.58248i −0.609113 0.134076i
\(372\) −5.51125 + 6.48835i −0.285745 + 0.336405i
\(373\) 11.5338 1.25438i 0.597199 0.0649493i 0.195473 0.980709i \(-0.437376\pi\)
0.401726 + 0.915760i \(0.368410\pi\)
\(374\) −1.72884 6.22673i −0.0893964 0.321977i
\(375\) −0.259137 + 4.77950i −0.0133818 + 0.246812i
\(376\) −4.16547 7.85692i −0.214818 0.405190i
\(377\) 12.1160 + 14.2641i 0.624007 + 0.734638i
\(378\) −1.61108 1.52609i −0.0828648 0.0784938i
\(379\) −4.78732 + 12.0153i −0.245908 + 0.617183i −0.999178 0.0405283i \(-0.987096\pi\)
0.753270 + 0.657711i \(0.228475\pi\)
\(380\) 6.04334 + 15.1676i 0.310017 + 0.778083i
\(381\) −2.38594 + 2.26009i −0.122236 + 0.115788i
\(382\) −38.9923 4.24067i −1.99502 0.216972i
\(383\) 0.913356 + 5.57122i 0.0466703 + 0.284676i 0.999842 0.0177521i \(-0.00565098\pi\)
−0.953172 + 0.302428i \(0.902203\pi\)
\(384\) −1.17797 7.18533i −0.0601133 0.366675i
\(385\) 13.4660 + 1.46452i 0.686291 + 0.0746386i
\(386\) 13.3955 12.6889i 0.681815 0.645849i
\(387\) −3.39875 8.53022i −0.172768 0.433615i
\(388\) −4.46840 + 11.2148i −0.226849 + 0.569347i
\(389\) 8.02265 + 7.59946i 0.406764 + 0.385308i 0.863545 0.504272i \(-0.168239\pi\)
−0.456781 + 0.889579i \(0.650998\pi\)
\(390\) −15.7730 18.5694i −0.798696 0.940297i
\(391\) 1.46743 + 2.76787i 0.0742113 + 0.139977i
\(392\) −0.284525 + 5.24776i −0.0143707 + 0.265052i
\(393\) 4.14175 + 14.9172i 0.208924 + 0.752475i
\(394\) 26.7678 2.91118i 1.34854 0.146663i
\(395\) 25.9846 30.5914i 1.30742 1.53922i
\(396\) 5.77976 + 1.27222i 0.290444 + 0.0639316i
\(397\) −26.8202 20.3882i −1.34607 1.02325i −0.996258 0.0864304i \(-0.972454\pi\)
−0.349807 0.936822i \(-0.613753\pi\)
\(398\) 4.05990 1.36794i 0.203504 0.0685686i
\(399\) −0.242502 4.47269i −0.0121403 0.223915i
\(400\) 13.6129 8.19060i 0.680644 0.409530i
\(401\) 21.5174 31.7358i 1.07453 1.58481i 0.298174 0.954512i \(-0.403623\pi\)
0.776354 0.630298i \(-0.217067\pi\)
\(402\) −2.78115 + 2.11418i −0.138711 + 0.105446i
\(403\) 23.2719 10.7667i 1.15925 0.536328i
\(404\) 16.7462 + 10.0759i 0.833155 + 0.501292i
\(405\) −1.35295 + 2.55193i −0.0672286 + 0.126807i
\(406\) −8.99266 + 1.97943i −0.446298 + 0.0982377i
\(407\) −19.7902 9.15591i −0.980963 0.453842i
\(408\) 0.461143 + 0.680134i 0.0228300 + 0.0336717i
\(409\) 19.2455 + 6.48456i 0.951628 + 0.320641i 0.751949 0.659221i \(-0.229114\pi\)
0.199678 + 0.979862i \(0.436010\pi\)
\(410\) −9.59906 + 34.5727i −0.474064 + 1.70742i
\(411\) −1.93470 + 11.8011i −0.0954317 + 0.582108i
\(412\) −8.49773 −0.418653
\(413\) −2.75616 + 8.68777i −0.135622 + 0.427497i
\(414\) −6.70085 −0.329329
\(415\) −7.18592 + 43.8322i −0.352743 + 2.15164i
\(416\) 8.45667 30.4582i 0.414622 1.49333i
\(417\) −8.59253 2.89516i −0.420778 0.141777i
\(418\) 15.6572 + 23.0926i 0.765818 + 1.12950i
\(419\) 6.55876 + 3.03441i 0.320417 + 0.148241i 0.573504 0.819203i \(-0.305584\pi\)
−0.253087 + 0.967444i \(0.581446\pi\)
\(420\) 5.01238 1.10331i 0.244579 0.0538360i
\(421\) −17.8034 + 33.5808i −0.867684 + 1.63663i −0.100739 + 0.994913i \(0.532121\pi\)
−0.766945 + 0.641713i \(0.778224\pi\)
\(422\) 29.9103 + 17.9964i 1.45601 + 0.876051i
\(423\) −8.58767 + 3.97308i −0.417547 + 0.193178i
\(424\) −7.57467 + 5.75811i −0.367858 + 0.279639i
\(425\) −1.64023 + 2.41916i −0.0795629 + 0.117346i
\(426\) 7.28899 4.38564i 0.353153 0.212485i
\(427\) 0.749325 + 13.8205i 0.0362624 + 0.668820i
\(428\) −18.1941 + 6.13032i −0.879447 + 0.296320i
\(429\) −14.1909 10.7876i −0.685142 0.520832i
\(430\) 48.4412 + 10.6627i 2.33604 + 0.514202i
\(431\) −15.3179 + 18.0336i −0.737836 + 0.868648i −0.995220 0.0976615i \(-0.968864\pi\)
0.257384 + 0.966309i \(0.417140\pi\)
\(432\) −4.72467 + 0.513839i −0.227316 + 0.0247221i
\(433\) −5.78217 20.8255i −0.277873 1.00081i −0.962359 0.271783i \(-0.912387\pi\)
0.684485 0.729027i \(-0.260027\pi\)
\(434\) −0.683004 + 12.5973i −0.0327853 + 0.604689i
\(435\) 5.61386 + 10.5889i 0.269164 + 0.507698i
\(436\) −18.0119 21.2052i −0.862612 1.01555i
\(437\) −9.81946 9.30149i −0.469729 0.444951i
\(438\) 5.76739 14.4750i 0.275576 0.691645i
\(439\) 2.93715 + 7.37168i 0.140182 + 0.351831i 0.982260 0.187526i \(-0.0600467\pi\)
−0.842077 + 0.539357i \(0.818667\pi\)
\(440\) 7.78873 7.37788i 0.371313 0.351727i
\(441\) 5.55919 + 0.604598i 0.264723 + 0.0287904i
\(442\) 1.19317 + 7.27804i 0.0567535 + 0.346181i
\(443\) 3.38241 + 20.6318i 0.160703 + 0.980245i 0.936860 + 0.349705i \(0.113718\pi\)
−0.776157 + 0.630540i \(0.782834\pi\)
\(444\) −8.21373 0.893297i −0.389806 0.0423940i
\(445\) 3.98526 3.77504i 0.188919 0.178954i
\(446\) −9.84351 24.7053i −0.466104 1.16983i
\(447\) 1.13663 2.85272i 0.0537607 0.134929i
\(448\) 3.10259 + 2.93892i 0.146583 + 0.138851i
\(449\) 16.6475 + 19.5990i 0.785644 + 0.924932i 0.998641 0.0521212i \(-0.0165982\pi\)
−0.212997 + 0.977053i \(0.568322\pi\)
\(450\) −2.92831 5.52338i −0.138042 0.260375i
\(451\) −1.42123 + 26.2130i −0.0669230 + 1.23432i
\(452\) −0.571408 2.05803i −0.0268768 0.0968014i
\(453\) −21.2986 + 2.31637i −1.00070 + 0.108832i
\(454\) 5.12153 6.02954i 0.240365 0.282980i
\(455\) −15.0975 3.32322i −0.707783 0.155795i
\(456\) −2.82430 2.14698i −0.132260 0.100542i
\(457\) −29.5864 + 9.96883i −1.38400 + 0.466322i −0.910147 0.414284i \(-0.864032\pi\)
−0.473848 + 0.880607i \(0.657135\pi\)
\(458\) −1.48796 27.4439i −0.0695280 1.28237i
\(459\) 0.749185 0.450770i 0.0349690 0.0210401i
\(460\) 8.69708 12.8272i 0.405503 0.598073i
\(461\) −25.9676 + 19.7400i −1.20943 + 0.919386i −0.998312 0.0580747i \(-0.981504\pi\)
−0.211119 + 0.977460i \(0.567711\pi\)
\(462\) 7.95965 3.68253i 0.370316 0.171327i
\(463\) 9.88101 + 5.94521i 0.459210 + 0.276297i 0.726305 0.687373i \(-0.241236\pi\)
−0.267095 + 0.963670i \(0.586064\pi\)
\(464\) −9.23698 + 17.4228i −0.428816 + 0.808833i
\(465\) 16.0367 3.52994i 0.743684 0.163697i
\(466\) 45.4365 + 21.0211i 2.10480 + 0.973786i
\(467\) −5.53352 8.16133i −0.256061 0.377661i 0.677831 0.735218i \(-0.262920\pi\)
−0.933891 + 0.357557i \(0.883610\pi\)
\(468\) −6.40061 2.15662i −0.295868 0.0996896i
\(469\) −0.593008 + 2.13582i −0.0273826 + 0.0986231i
\(470\) 8.26907 50.4391i 0.381424 2.32658i
\(471\) −5.97354 −0.275246
\(472\) 3.83119 + 6.11841i 0.176345 + 0.281623i
\(473\) 36.2898 1.66861
\(474\) 4.20437 25.6455i 0.193113 1.17794i
\(475\) 3.37588 12.1588i 0.154896 0.557885i
\(476\) −1.47228 0.496070i −0.0674820 0.0227373i
\(477\) 5.68147 + 8.37954i 0.260136 + 0.383673i
\(478\) 3.02080 + 1.39757i 0.138168 + 0.0639235i
\(479\) 25.1716 5.54068i 1.15012 0.253160i 0.401308 0.915943i \(-0.368556\pi\)
0.748811 + 0.662783i \(0.230625\pi\)
\(480\) 9.48188 17.8847i 0.432787 0.816322i
\(481\) 21.3237 + 12.8301i 0.972279 + 0.585001i
\(482\) −24.2262 + 11.2082i −1.10347 + 0.510521i
\(483\) −3.38472 + 2.57300i −0.154010 + 0.117075i
\(484\) −3.88174 + 5.72513i −0.176443 + 0.260233i
\(485\) 19.9525 12.0050i 0.905998 0.545121i
\(486\) 0.101248 + 1.86741i 0.00459270 + 0.0847073i
\(487\) −27.7445 + 9.34820i −1.25722 + 0.423608i −0.867552 0.497347i \(-0.834308\pi\)
−0.389671 + 0.920954i \(0.627411\pi\)
\(488\) 8.72701 + 6.63410i 0.395053 + 0.300312i
\(489\) −0.178144 0.0392124i −0.00805594 0.00177325i
\(490\) −19.5552 + 23.0221i −0.883413 + 1.04003i
\(491\) −5.10061 + 0.554725i −0.230187 + 0.0250344i −0.222486 0.974936i \(-0.571417\pi\)
−0.00770174 + 0.999970i \(0.502452\pi\)
\(492\) 2.66103 + 9.58418i 0.119969 + 0.432088i
\(493\) 0.196413 3.62263i 0.00884600 0.163155i
\(494\) −14.9148 28.1324i −0.671050 1.26573i
\(495\) −7.39009 8.70028i −0.332160 0.391049i
\(496\) 19.6151 + 18.5804i 0.880745 + 0.834286i
\(497\) 1.99780 5.01411i 0.0896137 0.224913i
\(498\) 10.6447 + 26.7163i 0.477003 + 1.19719i
\(499\) 24.8248 23.5153i 1.11131 1.05269i 0.113060 0.993588i \(-0.463935\pi\)
0.998252 0.0591025i \(-0.0188239\pi\)
\(500\) −7.12561 0.774956i −0.318667 0.0346571i
\(501\) −2.39595 14.6146i −0.107043 0.652934i
\(502\) −3.33458 20.3401i −0.148830 0.907822i
\(503\) −4.65227 0.505965i −0.207435 0.0225599i 0.00381172 0.999993i \(-0.498787\pi\)
−0.211246 + 0.977433i \(0.567752\pi\)
\(504\) −0.809630 + 0.766922i −0.0360638 + 0.0341614i
\(505\) −13.9532 35.0199i −0.620909 1.55836i
\(506\) 9.80217 24.6016i 0.435760 1.09367i
\(507\) 5.33161 + 5.05037i 0.236785 + 0.224295i
\(508\) −3.18599 3.75084i −0.141356 0.166417i
\(509\) −17.4886 32.9870i −0.775169 1.46212i −0.883712 0.468031i \(-0.844963\pi\)
0.108543 0.994092i \(-0.465381\pi\)
\(510\) −0.255696 + 4.71603i −0.0113224 + 0.208829i
\(511\) −2.64493 9.52618i −0.117005 0.421414i
\(512\) 24.2312 2.63530i 1.07088 0.116465i
\(513\) −2.44379 + 2.87705i −0.107896 + 0.127025i
\(514\) 23.6143 + 5.19791i 1.04158 + 0.229270i
\(515\) 13.0487 + 9.91939i 0.574996 + 0.437101i
\(516\) 13.0305 4.39048i 0.573634 0.193280i
\(517\) −2.02456 37.3409i −0.0890402 1.64225i
\(518\) −10.4913 + 6.31240i −0.460961 + 0.277351i
\(519\) −6.67895 + 9.85071i −0.293173 + 0.432398i
\(520\) −9.74730 + 7.40971i −0.427448 + 0.324937i
\(521\) 10.5812 4.89536i 0.463569 0.214470i −0.174181 0.984714i \(-0.555728\pi\)
0.637749 + 0.770244i \(0.279866\pi\)
\(522\) 6.64913 + 4.00065i 0.291025 + 0.175104i
\(523\) −7.69401 + 14.5124i −0.336435 + 0.634584i −0.992790 0.119868i \(-0.961753\pi\)
0.656354 + 0.754453i \(0.272098\pi\)
\(524\) −22.6410 + 4.98366i −0.989076 + 0.217712i
\(525\) −3.60002 1.66555i −0.157118 0.0726904i
\(526\) −24.9956 36.8657i −1.08986 1.60742i
\(527\) −4.71044 1.58713i −0.205190 0.0691366i
\(528\) 5.02486 18.0979i 0.218679 0.787610i
\(529\) 1.64399 10.0279i 0.0714776 0.435994i
\(530\) −54.6873 −2.37546
\(531\) 6.72131 3.71807i 0.291680 0.161350i
\(532\) 6.70752 0.290808
\(533\) 4.84699 29.5653i 0.209947 1.28062i
\(534\) 0.950849 3.42465i 0.0411473 0.148199i
\(535\) 35.0940 + 11.8246i 1.51725 + 0.511220i
\(536\) 0.985234 + 1.45311i 0.0425556 + 0.0627649i
\(537\) 4.76560 + 2.20480i 0.205651 + 0.0951443i
\(538\) −14.1000 + 3.10365i −0.607895 + 0.133808i
\(539\) −10.3519 + 19.5257i −0.445886 + 0.841031i
\(540\) −3.70613 2.22991i −0.159487 0.0959599i
\(541\) 35.4118 16.3832i 1.52247 0.704370i 0.532603 0.846365i \(-0.321214\pi\)
0.989867 + 0.141995i \(0.0453517\pi\)
\(542\) −45.7553 + 34.7823i −1.96536 + 1.49403i
\(543\) 9.59393 14.1500i 0.411715 0.607234i
\(544\) −5.25051 + 3.15913i −0.225114 + 0.135447i
\(545\) 2.90540 + 53.5870i 0.124454 + 2.29542i
\(546\) −9.48524 + 3.19595i −0.405931 + 0.136774i
\(547\) 2.47782 + 1.88359i 0.105944 + 0.0805364i 0.656805 0.754061i \(-0.271908\pi\)
−0.550861 + 0.834597i \(0.685701\pi\)
\(548\) −17.4890 3.84962i −0.747092 0.164447i
\(549\) 7.55124 8.89001i 0.322279 0.379416i
\(550\) 24.5623 2.67131i 1.04734 0.113905i
\(551\) 4.19035 + 15.0923i 0.178515 + 0.642953i
\(552\) −0.182310 + 3.36250i −0.00775961 + 0.143118i
\(553\) −7.72370 14.5684i −0.328445 0.619513i
\(554\) 17.1121 + 20.1460i 0.727025 + 0.855920i
\(555\) 11.5699 + 10.9596i 0.491115 + 0.465208i
\(556\) 5.02563 12.6134i 0.213134 0.534927i
\(557\) −2.56271 6.43191i −0.108585 0.272529i 0.864636 0.502399i \(-0.167549\pi\)
−0.973221 + 0.229870i \(0.926170\pi\)
\(558\) 7.71866 7.31150i 0.326757 0.309521i
\(559\) −41.1736 4.47790i −1.74146 0.189395i
\(560\) −2.63523 16.0742i −0.111359 0.679258i
\(561\) 0.559036 + 3.40997i 0.0236025 + 0.143969i
\(562\) 47.2967 + 5.14383i 1.99509 + 0.216979i
\(563\) 19.9925 18.9379i 0.842584 0.798138i −0.138775 0.990324i \(-0.544316\pi\)
0.981358 + 0.192186i \(0.0615577\pi\)
\(564\) −5.24460 13.1629i −0.220837 0.554260i
\(565\) −1.52490 + 3.82722i −0.0641532 + 0.161012i
\(566\) −15.6797 14.8526i −0.659065 0.624300i
\(567\) 0.768191 + 0.904385i 0.0322610 + 0.0379806i
\(568\) −2.00242 3.77696i −0.0840195 0.158478i
\(569\) 1.00837 18.5984i 0.0422733 0.779684i −0.898152 0.439685i \(-0.855090\pi\)
0.940426 0.340000i \(-0.110427\pi\)
\(570\) −5.45512 19.6475i −0.228490 0.822945i
\(571\) 12.2363 1.33078i 0.512074 0.0556914i 0.151565 0.988447i \(-0.451569\pi\)
0.360509 + 0.932756i \(0.382603\pi\)
\(572\) 17.2808 20.3446i 0.722547 0.850648i
\(573\) 20.4825 + 4.50853i 0.855667 + 0.188347i
\(574\) 11.7347 + 8.92048i 0.489796 + 0.372334i
\(575\) −11.3506 + 3.82446i −0.473353 + 0.159491i
\(576\) −0.194981 3.59622i −0.00812423 0.149843i
\(577\) 20.4141 12.2828i 0.849851 0.511338i −0.0227675 0.999741i \(-0.507248\pi\)
0.872619 + 0.488402i \(0.162420\pi\)
\(578\) −17.0392 + 25.1310i −0.708739 + 1.04531i
\(579\) −7.85441 + 5.97077i −0.326418 + 0.248137i
\(580\) −16.2883 + 7.53576i −0.676334 + 0.312905i
\(581\) 15.6354 + 9.40752i 0.648667 + 0.390290i
\(582\) 7.06210 13.3205i 0.292733 0.552154i
\(583\) −39.0758 + 8.60123i −1.61835 + 0.356226i
\(584\) −7.10671 3.28791i −0.294078 0.136055i
\(585\) 7.31108 + 10.7830i 0.302276 + 0.445824i
\(586\) −19.3039 6.50424i −0.797437 0.268688i
\(587\) 3.65289 13.1565i 0.150771 0.543028i −0.849119 0.528201i \(-0.822867\pi\)
0.999890 0.0148263i \(-0.00471953\pi\)
\(588\) −1.35472 + 8.26344i −0.0558678 + 0.340779i
\(589\) 21.4601 0.884249
\(590\) −3.75156 + 41.3216i −0.154449 + 1.70118i
\(591\) −14.3976 −0.592239
\(592\) −4.24222 + 25.8764i −0.174354 + 1.06351i
\(593\) −6.78804 + 24.4483i −0.278751 + 1.00397i 0.683083 + 0.730340i \(0.260639\pi\)
−0.961835 + 0.273631i \(0.911775\pi\)
\(594\) −7.00414 2.35997i −0.287383 0.0968307i
\(595\) 1.68171 + 2.48034i 0.0689434 + 0.101684i
\(596\) 4.17343 + 1.93083i 0.170950 + 0.0790900i
\(597\) −2.23725 + 0.492457i −0.0915647 + 0.0201549i
\(598\) −14.1570 + 26.7029i −0.578923 + 1.09196i
\(599\) −5.90112 3.55058i −0.241113 0.145073i 0.389869 0.920870i \(-0.372520\pi\)
−0.630982 + 0.775797i \(0.717348\pi\)
\(600\) −2.85132 + 1.31916i −0.116405 + 0.0538545i
\(601\) 34.5482 26.2629i 1.40925 1.07129i 0.422984 0.906137i \(-0.360983\pi\)
0.986269 0.165149i \(-0.0528104\pi\)
\(602\) 11.4352 16.8657i 0.466066 0.687395i
\(603\) 1.60064 0.963072i 0.0651831 0.0392193i
\(604\) −1.73688 32.0349i −0.0706726 1.30348i
\(605\) 12.6436 4.26011i 0.514034 0.173198i
\(606\) −19.4309 14.7710i −0.789326 0.600030i
\(607\) −37.6243 8.28173i −1.52712 0.336145i −0.629531 0.776975i \(-0.716753\pi\)
−0.897591 + 0.440830i \(0.854684\pi\)
\(608\) 17.1268 20.1633i 0.694584 0.817728i
\(609\) 4.89477 0.532339i 0.198346 0.0215715i
\(610\) 16.8561 + 60.7103i 0.682485 + 2.45809i
\(611\) −2.31057 + 42.6159i −0.0934756 + 1.72406i
\(612\) 0.613283 + 1.15677i 0.0247905 + 0.0467598i
\(613\) −7.44202 8.76142i −0.300580 0.353870i 0.591050 0.806635i \(-0.298714\pi\)
−0.891630 + 0.452765i \(0.850438\pi\)
\(614\) −2.13171 2.01927i −0.0860290 0.0814910i
\(615\) 7.10144 17.8233i 0.286358 0.718704i
\(616\) −1.63134 4.09436i −0.0657287 0.164967i
\(617\) −16.2580 + 15.4004i −0.654523 + 0.619998i −0.941128 0.338052i \(-0.890232\pi\)
0.286604 + 0.958049i \(0.407474\pi\)
\(618\) 10.5504 + 1.14743i 0.424401 + 0.0461564i
\(619\) −4.39859 26.8302i −0.176794 1.07840i −0.914891 0.403702i \(-0.867723\pi\)
0.738096 0.674695i \(-0.235725\pi\)
\(620\) 3.97809 + 24.2653i 0.159764 + 0.974516i
\(621\) 3.56205 + 0.387396i 0.142940 + 0.0155457i
\(622\) −34.7800 + 32.9454i −1.39455 + 1.32099i
\(623\) −0.834709 2.09496i −0.0334419 0.0839329i
\(624\) −7.93425 + 19.9135i −0.317624 + 0.797176i
\(625\) 22.1716 + 21.0021i 0.886865 + 0.840083i
\(626\) −21.2049 24.9644i −0.847520 0.997777i
\(627\) −6.98802 13.1808i −0.279075 0.526391i
\(628\) 0.484280 8.93202i 0.0193249 0.356426i
\(629\) −1.29059 4.64829i −0.0514593 0.185339i
\(630\) −6.37215 + 0.693013i −0.253873 + 0.0276103i
\(631\) −13.2758 + 15.6295i −0.528501 + 0.622200i −0.960029 0.279900i \(-0.909699\pi\)
0.431528 + 0.902100i \(0.357975\pi\)
\(632\) −12.7546 2.80750i −0.507351 0.111676i
\(633\) −14.8593 11.2958i −0.590605 0.448967i
\(634\) 34.0870 11.4852i 1.35377 0.456137i
\(635\) 0.513917 + 9.47864i 0.0203942 + 0.376148i
\(636\) −12.9902 + 7.81596i −0.515096 + 0.309923i
\(637\) 14.1543 20.8761i 0.560815 0.827140i
\(638\) −24.4146 + 18.5595i −0.966582 + 0.734777i
\(639\) −4.12824 + 1.90993i −0.163311 + 0.0755556i
\(640\) −18.0207 10.8427i −0.712330 0.428595i
\(641\) 4.19457 7.91179i 0.165675 0.312497i −0.786748 0.617274i \(-0.788237\pi\)
0.952424 + 0.304777i \(0.0985819\pi\)
\(642\) 23.4169 5.15445i 0.924191 0.203430i
\(643\) 7.46527 + 3.45380i 0.294401 + 0.136205i 0.561530 0.827456i \(-0.310213\pi\)
−0.267129 + 0.963661i \(0.586075\pi\)
\(644\) −3.57291 5.26965i −0.140792 0.207653i
\(645\) −25.1340 8.46864i −0.989651 0.333452i
\(646\) −1.65131 + 5.94747i −0.0649698 + 0.234000i
\(647\) 2.86088 17.4506i 0.112473 0.686053i −0.869053 0.494720i \(-0.835271\pi\)
0.981525 0.191333i \(-0.0612810\pi\)
\(648\) 0.939825 0.0369198
\(649\) 3.81846 + 30.1156i 0.149888 + 1.18214i
\(650\) −28.1974 −1.10599
\(651\) 1.09136 6.65700i 0.0427737 0.260908i
\(652\) 0.0730752 0.263193i 0.00286185 0.0103074i
\(653\) 3.63705 + 1.22547i 0.142329 + 0.0479562i 0.389564 0.920999i \(-0.372626\pi\)
−0.247236 + 0.968955i \(0.579522\pi\)
\(654\) 19.4995 + 28.7596i 0.762492 + 1.12459i
\(655\) 40.5839 + 18.7761i 1.58574 + 0.733643i
\(656\) 30.8302 6.78624i 1.20372 0.264958i
\(657\) −3.90268 + 7.36124i −0.152258 + 0.287190i
\(658\) −17.9922 10.8255i −0.701408 0.422023i
\(659\) 15.5712 7.20400i 0.606567 0.280628i −0.0924674 0.995716i \(-0.529475\pi\)
0.699035 + 0.715088i \(0.253613\pi\)
\(660\) 13.6083 10.3448i 0.529704 0.402670i
\(661\) −21.6587 + 31.9442i −0.842425 + 1.24248i 0.125713 + 0.992067i \(0.459878\pi\)
−0.968138 + 0.250417i \(0.919432\pi\)
\(662\) −3.92977 + 2.36447i −0.152735 + 0.0918976i
\(663\) −0.213504 3.93786i −0.00829183 0.152934i
\(664\) 13.6959 4.61470i 0.531505 0.179085i
\(665\) −10.2998 7.82968i −0.399408 0.303622i
\(666\) 10.0772 + 2.21816i 0.390484 + 0.0859521i
\(667\) 9.62491 11.3313i 0.372678 0.438751i
\(668\) 22.0470 2.39776i 0.853024 0.0927719i
\(669\) 3.80434 + 13.7020i 0.147084 + 0.529750i
\(670\) −0.546296 + 10.0758i −0.0211053 + 0.389263i
\(671\) 21.5928 + 40.7283i 0.833580 + 1.57230i
\(672\) −5.38372 6.33820i −0.207681 0.244501i
\(673\) −21.5786 20.4404i −0.831795 0.787918i 0.147775 0.989021i \(-0.452789\pi\)
−0.979570 + 0.201103i \(0.935547\pi\)
\(674\) −2.96588 + 7.44379i −0.114241 + 0.286724i
\(675\) 1.23732 + 3.10543i 0.0476243 + 0.119528i
\(676\) −7.98387 + 7.56273i −0.307072 + 0.290874i
\(677\) 25.7297 + 2.79828i 0.988874 + 0.107547i 0.588235 0.808690i \(-0.299823\pi\)
0.400638 + 0.916236i \(0.368788\pi\)
\(678\) 0.431547 + 2.63232i 0.0165735 + 0.101094i
\(679\) −1.54764 9.44016i −0.0593928 0.362280i
\(680\) 2.35956 + 0.256618i 0.0904851 + 0.00984084i
\(681\) −3.07110 + 2.90910i −0.117685 + 0.111477i
\(682\) 15.5525 + 39.0339i 0.595537 + 1.49468i
\(683\) 12.9974 32.6211i 0.497333 1.24821i −0.439440 0.898272i \(-0.644823\pi\)
0.936772 0.349939i \(-0.113798\pi\)
\(684\) −4.10383 3.88736i −0.156914 0.148637i
\(685\) 22.3617 + 26.3262i 0.854395 + 1.00587i
\(686\) 13.0888 + 24.6881i 0.499734 + 0.942598i
\(687\) −0.795639 + 14.6747i −0.0303555 + 0.559875i
\(688\) −11.6748 42.0489i −0.445098 1.60310i
\(689\) 45.3958 4.93710i 1.72944 0.188088i
\(690\) −12.5300 + 14.7514i −0.477008 + 0.561577i
\(691\) −17.1678 3.77892i −0.653094 0.143757i −0.123949 0.992289i \(-0.539556\pi\)
−0.529145 + 0.848532i \(0.677487\pi\)
\(692\) −14.1879 10.7854i −0.539345 0.409999i
\(693\) −4.44410 + 1.49739i −0.168818 + 0.0568813i
\(694\) −0.467424 8.62113i −0.0177432 0.327254i
\(695\) −22.4407 + 13.5021i −0.851225 + 0.512165i
\(696\) 2.18844 3.22771i 0.0829526 0.122346i
\(697\) −4.62349 + 3.51469i −0.175127 + 0.133128i
\(698\) −4.15822 + 1.92380i −0.157391 + 0.0728167i
\(699\) −22.9379 13.8013i −0.867592 0.522013i
\(700\) 2.78229 5.24796i 0.105161 0.198354i
\(701\) 14.5880 3.21106i 0.550980 0.121280i 0.0692499 0.997599i \(-0.477939\pi\)
0.481731 + 0.876319i \(0.340008\pi\)
\(702\) 7.65554 + 3.54183i 0.288940 + 0.133678i
\(703\) 11.6882 + 17.2388i 0.440828 + 0.650172i
\(704\) 13.4885 + 4.54479i 0.508365 + 0.171288i
\(705\) −7.31172 + 26.3344i −0.275375 + 0.991813i
\(706\) 1.93878 11.8260i 0.0729669 0.445078i
\(707\) −15.4867 −0.582437
\(708\) 5.01459 + 10.3516i 0.188460 + 0.389035i
\(709\) 2.80753 0.105439 0.0527195 0.998609i \(-0.483211\pi\)
0.0527195 + 0.998609i \(0.483211\pi\)
\(710\) 3.97509 24.2469i 0.149182 0.909972i
\(711\) −3.71762 + 13.3896i −0.139421 + 0.502151i
\(712\) −1.69263 0.570313i −0.0634340 0.0213734i
\(713\) −11.4312 16.8598i −0.428103 0.631404i
\(714\) 1.76094 + 0.814700i 0.0659017 + 0.0304894i
\(715\) −50.2839 + 11.0683i −1.88051 + 0.413931i
\(716\) −3.68312 + 6.94709i −0.137644 + 0.259625i
\(717\) −1.52501 0.917566i −0.0569524 0.0342671i
\(718\) −41.8050 + 19.3411i −1.56015 + 0.721802i
\(719\) 18.4061 13.9919i 0.686431 0.521811i −0.202829 0.979214i \(-0.565013\pi\)
0.889260 + 0.457403i \(0.151220\pi\)
\(720\) −7.70353 + 11.3619i −0.287094 + 0.423432i
\(721\) 5.76981 3.47158i 0.214879 0.129288i
\(722\) 0.480973 + 8.87102i 0.0179000 + 0.330145i
\(723\) 13.5262 4.55750i 0.503045 0.169495i
\(724\) 20.3802 + 15.4926i 0.757423 + 0.575778i
\(725\) 13.5464 + 2.98178i 0.503099 + 0.110740i
\(726\) 5.59246 6.58395i 0.207556 0.244353i
\(727\) −12.7587 + 1.38759i −0.473194 + 0.0514630i −0.341610 0.939842i \(-0.610972\pi\)
−0.131585 + 0.991305i \(0.542007\pi\)
\(728\) 1.34567 + 4.84667i 0.0498739 + 0.179630i
\(729\) 0.0541389 0.998533i 0.00200514 0.0369827i
\(730\) −21.0813 39.7635i −0.780253 1.47171i
\(731\) 5.19756 + 6.11904i 0.192239 + 0.226321i
\(732\) 12.6807 + 12.0118i 0.468693 + 0.443970i
\(733\) 3.42572 8.59791i 0.126532 0.317571i −0.852040 0.523477i \(-0.824635\pi\)
0.978572 + 0.205906i \(0.0660140\pi\)
\(734\) 22.0066 + 55.2324i 0.812278 + 2.03866i
\(735\) 11.7262 11.1076i 0.432526 0.409710i
\(736\) −24.9639 2.71499i −0.920182 0.100076i
\(737\) 1.19438 + 7.28542i 0.0439957 + 0.268362i
\(738\) −2.00970 12.2586i −0.0739782 0.451247i
\(739\) 0.746198 + 0.0811539i 0.0274493 + 0.00298530i 0.121833 0.992551i \(-0.461123\pi\)
−0.0943840 + 0.995536i \(0.530088\pi\)
\(740\) −17.3255 + 16.4115i −0.636896 + 0.603300i
\(741\) 6.30204 + 15.8169i 0.231511 + 0.581049i
\(742\) −8.31570 + 20.8708i −0.305279 + 0.766193i
\(743\) −17.9691 17.0212i −0.659222 0.624448i 0.283126 0.959083i \(-0.408629\pi\)
−0.942348 + 0.334634i \(0.891387\pi\)
\(744\) −3.45893 4.07217i −0.126811 0.149293i
\(745\) −4.15467 7.83654i −0.152215 0.287109i
\(746\) 1.17466 21.6654i 0.0430074 0.793225i
\(747\) −4.11401 14.8173i −0.150524 0.542137i
\(748\) −5.14413 + 0.559457i −0.188088 + 0.0204558i
\(749\) 9.84909 11.5952i 0.359878 0.423681i
\(750\) 8.74223 + 1.92431i 0.319221 + 0.0702659i
\(751\) −18.8673 14.3426i −0.688478 0.523368i 0.201432 0.979502i \(-0.435440\pi\)
−0.889911 + 0.456135i \(0.849233\pi\)
\(752\) −42.6155 + 14.3588i −1.55403 + 0.523613i
\(753\) 0.596684 + 11.0052i 0.0217444 + 0.401052i
\(754\) 29.9904 18.0446i 1.09218 0.657146i
\(755\) −34.7272 + 51.2188i −1.26385 + 1.86404i
\(756\) −1.41457 + 1.07533i −0.0514475 + 0.0391094i
\(757\) 4.90510 2.26934i 0.178279 0.0824806i −0.328719 0.944428i \(-0.606617\pi\)
0.506998 + 0.861947i \(0.330755\pi\)
\(758\) 20.7259 + 12.4704i 0.752799 + 0.452944i
\(759\) −6.63295 + 12.5111i −0.240761 + 0.454123i
\(760\) −10.0076 + 2.20284i −0.363014 + 0.0799055i
\(761\) −3.70010 1.71185i −0.134128 0.0620544i 0.351677 0.936121i \(-0.385612\pi\)
−0.485805 + 0.874067i \(0.661474\pi\)
\(762\) 3.44914 + 5.08710i 0.124949 + 0.184286i
\(763\) 20.8927 + 7.03958i 0.756368 + 0.254850i
\(764\) −8.40197 + 30.2612i −0.303973 + 1.09481i
\(765\) 0.408571 2.49218i 0.0147719 0.0901048i
\(766\) 10.5581 0.381480
\(767\) −0.616293 34.6397i −0.0222531 1.25077i
\(768\) −20.8200 −0.751278
\(769\) −6.18583 + 37.7319i −0.223067 + 1.36065i 0.603300 + 0.797515i \(0.293852\pi\)
−0.826366 + 0.563133i \(0.809596\pi\)
\(770\) 6.77701 24.4086i 0.244226 0.879624i
\(771\) −12.2525 4.12833i −0.441261 0.148678i
\(772\) −8.29111 12.2285i −0.298404 0.440112i
\(773\) 1.52185 + 0.704084i 0.0547372 + 0.0253241i 0.447067 0.894501i \(-0.352469\pi\)
−0.392330 + 0.919825i \(0.628331\pi\)
\(774\) −16.7709 + 3.69156i −0.602819 + 0.132691i
\(775\) 8.90170 16.7904i 0.319758 0.603128i
\(776\) −6.49214 3.90619i −0.233054 0.140224i
\(777\) 5.94192 2.74903i 0.213165 0.0986207i
\(778\) 16.4522 12.5066i 0.589840 0.448385i
\(779\) 14.0713 20.7536i 0.504156 0.743574i
\(780\) −16.7162 + 10.0578i −0.598536 + 0.360127i
\(781\) −0.973242 17.9504i −0.0348254 0.642316i
\(782\) 5.55213 1.87073i 0.198544 0.0668972i
\(783\) −3.30327 2.51108i −0.118049 0.0897387i
\(784\) 25.9547 + 5.71306i 0.926953 + 0.204038i
\(785\) −11.1700 + 13.1503i −0.398674 + 0.469355i
\(786\) 28.7831 3.13035i 1.02666 0.111656i
\(787\) −9.96886 35.9046i −0.355352 1.27986i −0.898035 0.439923i \(-0.855006\pi\)
0.542684 0.839937i \(-0.317408\pi\)
\(788\) 1.16723 21.5282i 0.0415807 0.766911i
\(789\) 11.1559 + 21.0422i 0.397160 + 0.749123i
\(790\) −48.5950 57.2105i −1.72893 2.03546i
\(791\) 1.22874 + 1.16393i 0.0436891 + 0.0413845i
\(792\) −1.37480 + 3.45049i −0.0488514 + 0.122608i
\(793\) −19.4731 48.8738i −0.691511 1.73556i
\(794\) −45.7412 + 43.3284i −1.62330 + 1.53767i
\(795\) 29.0708 + 3.16164i 1.03103 + 0.112132i
\(796\) −0.554977 3.38521i −0.0196706 0.119986i
\(797\) −3.59183 21.9092i −0.127229 0.776063i −0.970950 0.239281i \(-0.923088\pi\)
0.843721 0.536782i \(-0.180360\pi\)
\(798\) −8.32779 0.905701i −0.294800 0.0320615i
\(799\) 6.00631 5.68948i 0.212488 0.201279i
\(800\) −8.67147 21.7638i −0.306583 0.769465i
\(801\) −0.703444 + 1.76551i −0.0248550 + 0.0623813i
\(802\) −52.0586 49.3125i −1.83825 1.74129i
\(803\) −21.3172 25.0966i −0.752269 0.885640i
\(804\) 1.31028 + 2.47145i 0.0462101 + 0.0871615i
\(805\) −0.664853 + 12.2625i −0.0234330 + 0.432196i
\(806\) −12.8291 46.2061i −0.451884 1.62754i
\(807\) 7.67475 0.834680i 0.270164 0.0293821i
\(808\) −7.94077 + 9.34860i −0.279355 + 0.328883i
\(809\) −21.9054 4.82174i −0.770153 0.169523i −0.187522 0.982260i \(-0.560046\pi\)
−0.582631 + 0.812737i \(0.697977\pi\)
\(810\) 4.30029 + 3.26899i 0.151097 + 0.114861i
\(811\) 7.44156 2.50735i 0.261308 0.0880450i −0.185598 0.982626i \(-0.559422\pi\)
0.446906 + 0.894581i \(0.352526\pi\)
\(812\) 0.399163 + 7.36214i 0.0140079 + 0.258360i
\(813\) 26.3336 15.8444i 0.923559 0.555687i
\(814\) −22.8850 + 33.7529i −0.802119 + 1.18304i
\(815\) −0.419436 + 0.318847i −0.0146922 + 0.0111687i
\(816\) 3.77128 1.74478i 0.132021 0.0610795i
\(817\) −29.7005 17.8702i −1.03909 0.625200i
\(818\) 17.7902 33.5558i 0.622019 1.17325i
\(819\) 5.22695 1.15054i 0.182644 0.0402031i
\(820\) 26.0748 + 12.0635i 0.910571 + 0.421275i
\(821\) −1.85474 2.73554i −0.0647308 0.0954709i 0.793946 0.607988i \(-0.208023\pi\)
−0.858677 + 0.512518i \(0.828713\pi\)
\(822\) 21.1938 + 7.14103i 0.739219 + 0.249072i
\(823\) 8.19430 29.5132i 0.285635 1.02877i −0.671945 0.740601i \(-0.734541\pi\)
0.957581 0.288165i \(-0.0930452\pi\)
\(824\) 0.862829 5.26302i 0.0300581 0.183346i
\(825\) −13.2113 −0.459958
\(826\) 15.1995 + 7.71507i 0.528858 + 0.268442i
\(827\) 4.53150 0.157576 0.0787879 0.996891i \(-0.474895\pi\)
0.0787879 + 0.996891i \(0.474895\pi\)
\(828\) −0.868038 + 5.29480i −0.0301664 + 0.184007i
\(829\) −14.3774 + 51.7828i −0.499348 + 1.79849i 0.0964280 + 0.995340i \(0.469258\pi\)
−0.595776 + 0.803150i \(0.703156\pi\)
\(830\) 78.7187 + 26.5234i 2.73237 + 0.920642i
\(831\) −7.93181 11.6985i −0.275151 0.405818i
\(832\) −14.7429 6.82080i −0.511119 0.236469i
\(833\) −4.77498 + 1.05105i −0.165443 + 0.0364168i
\(834\) −7.94278 + 14.9817i −0.275036 + 0.518773i
\(835\) −36.6533 22.0536i −1.26844 0.763195i
\(836\) 20.2753 9.38036i 0.701236 0.324426i
\(837\) −4.52580 + 3.44043i −0.156435 + 0.118918i
\(838\) 7.58444 11.1862i 0.262000 0.386421i
\(839\) 22.3234 13.4315i 0.770688 0.463708i −0.0751335 0.997173i \(-0.523938\pi\)
0.845822 + 0.533466i \(0.179111\pi\)
\(840\) 0.174389 + 3.21642i 0.00601700 + 0.110977i
\(841\) 11.1661 3.76230i 0.385038 0.129734i
\(842\) 56.5872 + 43.0165i 1.95012 + 1.48245i
\(843\) −24.8447 5.46873i −0.855697 0.188353i
\(844\) 18.0948 21.3029i 0.622849 0.733275i
\(845\) 21.0877 2.29342i 0.725437 0.0788961i
\(846\) 4.73412 + 17.0507i 0.162762 + 0.586217i
\(847\) 0.296742 5.47308i 0.0101962 0.188057i
\(848\) 22.5373 + 42.5099i 0.773935 + 1.45980i
\(849\) 7.47635 + 8.80184i 0.256588 + 0.302078i
\(850\) 3.96833 + 3.75900i 0.136113 + 0.128933i
\(851\) 7.31738 18.3652i 0.250836 0.629552i
\(852\) −2.52117 6.32766i −0.0863738 0.216782i
\(853\) −25.2700 + 23.9370i −0.865229 + 0.819588i −0.984882 0.173228i \(-0.944580\pi\)
0.119653 + 0.992816i \(0.461822\pi\)
\(854\) 25.7326 + 2.79859i 0.880552 + 0.0957658i
\(855\) 1.76396 + 10.7597i 0.0603260 + 0.367973i
\(856\) −1.94941 11.8909i −0.0666296 0.406422i
\(857\) 24.0640 + 2.61712i 0.822012 + 0.0893991i 0.509452 0.860499i \(-0.329848\pi\)
0.312560 + 0.949898i \(0.398814\pi\)
\(858\) −24.2023 + 22.9256i −0.826251 + 0.782667i
\(859\) 6.31870 + 15.8588i 0.215591 + 0.541094i 0.996504 0.0835469i \(-0.0266248\pi\)
−0.780912 + 0.624641i \(0.785246\pi\)
\(860\) 14.7005 36.8954i 0.501282 1.25812i
\(861\) −5.72223 5.42038i −0.195013 0.184726i
\(862\) 28.6467 + 33.7255i 0.975711 + 1.14870i
\(863\) −6.52130 12.3005i −0.221988 0.418713i 0.747355 0.664425i \(-0.231323\pi\)
−0.969343 + 0.245711i \(0.920979\pi\)
\(864\) −0.379422 + 6.99802i −0.0129082 + 0.238078i
\(865\) 9.19660 + 33.1232i 0.312694 + 1.12622i
\(866\) −40.1832 + 4.37018i −1.36548 + 0.148505i
\(867\) 10.5107 12.3741i 0.356961 0.420247i
\(868\) 9.86549 + 2.17156i 0.334857 + 0.0737075i
\(869\) −43.7207 33.2356i −1.48312 1.12744i
\(870\) 21.2404 7.15673i 0.720118 0.242636i
\(871\) −0.456154 8.41326i −0.0154562 0.285072i
\(872\) 14.9622 9.00245i 0.506684 0.304861i
\(873\) −4.52419 + 6.67267i −0.153120 + 0.225836i
\(874\) −20.1370 + 15.3077i −0.681143 + 0.517792i
\(875\) 5.15476 2.38485i 0.174263 0.0806225i
\(876\) −10.6906 6.43233i −0.361202 0.217328i
\(877\) 13.0110 24.5414i 0.439350 0.828703i −0.560649 0.828053i \(-0.689448\pi\)
1.00000 0.000649567i \(-0.000206764\pi\)
\(878\) 14.4932 3.19019i 0.489122 0.107664i
\(879\) 9.88557 + 4.57355i 0.333432 + 0.154262i
\(880\) −30.4452 44.9033i −1.02631 1.51369i
\(881\) −18.1915 6.12944i −0.612888 0.206506i −0.00429793 0.999991i \(-0.501368\pi\)
−0.608590 + 0.793485i \(0.708265\pi\)
\(882\) 2.79776 10.0766i 0.0942056 0.339298i
\(883\) −6.12345 + 37.3514i −0.206070 + 1.25697i 0.657774 + 0.753215i \(0.271498\pi\)
−0.863845 + 0.503759i \(0.831950\pi\)
\(884\) 5.90545 0.198622
\(885\) 4.38319 21.7489i 0.147339 0.731082i
\(886\) 39.0996 1.31358
\(887\) 0.380446 2.32062i 0.0127741 0.0779187i −0.979670 0.200615i \(-0.935706\pi\)
0.992444 + 0.122697i \(0.0391542\pi\)
\(888\) 1.38725 4.99643i 0.0465531 0.167669i
\(889\) 3.69557 + 1.24518i 0.123945 + 0.0417621i
\(890\) −5.76112 8.49701i −0.193113 0.284821i
\(891\) 3.58684 + 1.65945i 0.120164 + 0.0555936i
\(892\) −20.7965 + 4.57766i −0.696319 + 0.153271i
\(893\) −16.7309 + 31.5577i −0.559877 + 1.05604i
\(894\) −4.92084 2.96077i −0.164578 0.0990231i
\(895\) 13.7650 6.36835i 0.460112 0.212871i
\(896\) −6.87821 + 5.22868i −0.229785 + 0.174678i
\(897\) 9.06938 13.3763i 0.302818 0.446623i
\(898\) 41.2069 24.7934i 1.37509 0.827366i
\(899\) 1.27709 + 23.5545i 0.0425933 + 0.785587i
\(900\) −4.74374 + 1.59835i −0.158125 + 0.0532784i
\(901\) −7.04689 5.35690i −0.234766 0.178464i
\(902\) 47.9465 + 10.5538i 1.59644 + 0.351404i
\(903\) −7.05383 + 8.30441i −0.234737 + 0.276353i
\(904\) 1.33265 0.144934i 0.0443232 0.00482043i
\(905\) −13.2104 47.5795i −0.439128 1.58160i
\(906\) −2.16916 + 40.0077i −0.0720654 + 1.32917i
\(907\) 19.5695 + 36.9119i 0.649793 + 1.22564i 0.961328 + 0.275405i \(0.0888121\pi\)
−0.311535 + 0.950235i \(0.600843\pi\)
\(908\) −4.10090 4.82795i −0.136093 0.160221i
\(909\) 9.47516 + 8.97535i 0.314271 + 0.297693i
\(910\) −10.7009 + 26.8572i −0.354731 + 0.890308i
\(911\) 2.93208 + 7.35897i 0.0971442 + 0.243814i 0.969515 0.245031i \(-0.0787980\pi\)
−0.872371 + 0.488844i \(0.837419\pi\)
\(912\) −13.0245 + 12.3374i −0.431283 + 0.408533i
\(913\) 60.4186 + 6.57092i 1.99956 + 0.217466i
\(914\) 9.44604 + 57.6183i 0.312447 + 1.90584i
\(915\) −5.45057 33.2470i −0.180190 1.09911i
\(916\) −21.8780 2.37938i −0.722871 0.0786169i
\(917\) 13.3369 12.6334i 0.440422 0.417190i
\(918\) −0.605231 1.51901i −0.0199756 0.0501350i
\(919\) 8.39388 21.0670i 0.276888 0.694938i −0.723103 0.690740i \(-0.757285\pi\)
0.999991 0.00419707i \(-0.00133597\pi\)
\(920\) 7.06140 + 6.68892i 0.232808 + 0.220527i
\(921\) 1.01644 + 1.19665i 0.0334929 + 0.0394309i
\(922\) 28.5739 + 53.8960i 0.941030 + 1.77497i
\(923\) −1.11073 + 20.4862i −0.0365602 + 0.674312i
\(924\) −1.87871 6.76650i −0.0618050 0.222602i
\(925\) 18.3359 1.99415i 0.602880 0.0655671i
\(926\) 13.9615 16.4368i 0.458804 0.540146i
\(927\) −5.54209 1.21991i −0.182026 0.0400670i
\(928\) 23.1503 + 17.5984i 0.759946 + 0.577696i
\(929\) −48.0436 + 16.1878i −1.57626 + 0.531103i −0.965431 0.260660i \(-0.916060\pi\)
−0.610828 + 0.791763i \(0.709163\pi\)
\(930\) −1.66255 30.6639i −0.0545172 1.00551i
\(931\) 18.0873 10.8828i 0.592788 0.356668i
\(932\) 22.4962 33.1794i 0.736886 1.08683i
\(933\) 20.3931 15.5024i 0.667640 0.507527i
\(934\) −16.7360 + 7.74292i −0.547620 + 0.253356i
\(935\) 8.55215 + 5.14566i 0.279685 + 0.168281i
\(936\) 1.98558 3.74521i 0.0649008 0.122416i
\(937\) −5.42599 + 1.19435i −0.177259 + 0.0390177i −0.302713 0.953082i \(-0.597892\pi\)
0.125454 + 0.992099i \(0.459961\pi\)
\(938\) 3.76227 + 1.74061i 0.122842 + 0.0568330i
\(939\) 9.82889 + 14.4965i 0.320754 + 0.473077i
\(940\) −38.7842 13.0679i −1.26500 0.426228i
\(941\) −3.55331 + 12.7979i −0.115835 + 0.417199i −0.998616 0.0525843i \(-0.983254\pi\)
0.882782 + 0.469783i \(0.155668\pi\)
\(942\) −1.80733 + 11.0242i −0.0588861 + 0.359189i
\(943\) −23.8001 −0.775038
\(944\) 33.6665 14.1130i 1.09575 0.459338i
\(945\) 3.42739 0.111493
\(946\) 10.9797 66.9733i 0.356981 2.17749i
\(947\) −5.15880 + 18.5803i −0.167638 + 0.603779i 0.831217 + 0.555948i \(0.187645\pi\)
−0.998855 + 0.0478311i \(0.984769\pi\)
\(948\) −19.7197 6.64433i −0.640465 0.215798i
\(949\) 21.0893 + 31.1045i 0.684589 + 1.00969i
\(950\) −21.4179 9.90896i −0.694887 0.321489i
\(951\) −18.7840 + 4.13468i −0.609114 + 0.134076i
\(952\) 0.456729 0.861481i 0.0148027 0.0279208i
\(953\) −18.6656 11.2307i −0.604639 0.363799i 0.180079 0.983652i \(-0.442365\pi\)
−0.784718 + 0.619853i \(0.787192\pi\)
\(954\) 17.1835 7.94994i 0.556337 0.257389i
\(955\) 48.2255 36.6601i 1.56054 1.18629i
\(956\) 1.49564 2.20590i 0.0483724 0.0713439i
\(957\) 14.0513 8.45440i 0.454215 0.273292i
\(958\) −2.60958 48.1309i −0.0843117 1.55504i
\(959\) 13.4474 4.53096i 0.434240 0.146312i
\(960\) −8.28142 6.29537i −0.267282 0.203182i
\(961\) 1.28856 + 0.283634i 0.0415665 + 0.00914947i
\(962\) 30.1297 35.4714i 0.971421 1.14364i
\(963\) −12.7460 + 1.38621i −0.410734 + 0.0446700i
\(964\) 5.71809 + 20.5947i 0.184167 + 0.663311i
\(965\) −1.54282 + 28.4557i −0.0496653 + 0.916022i
\(966\) 3.72443 + 7.02503i 0.119832 + 0.226027i
\(967\) −7.95439 9.36464i −0.255796 0.301146i 0.619242 0.785200i \(-0.287440\pi\)
−0.875038 + 0.484054i \(0.839164\pi\)
\(968\) −3.15169 2.98544i −0.101299 0.0959557i
\(969\) 1.22165 3.06610i 0.0392449 0.0984973i
\(970\) −16.1187 40.4549i −0.517540 1.29893i
\(971\) −25.2258 + 23.8951i −0.809534 + 0.766831i −0.975664 0.219273i \(-0.929632\pi\)
0.166130 + 0.986104i \(0.446873\pi\)
\(972\) 1.48868 + 0.161904i 0.0477495 + 0.00519307i
\(973\) 1.74063 + 10.6174i 0.0558022 + 0.340378i
\(974\) 8.85796 + 54.0312i 0.283827 + 1.73127i
\(975\) 14.9892 + 1.63018i 0.480040 + 0.0522075i
\(976\) 40.2452 38.1223i 1.28822 1.22026i
\(977\) −3.47589 8.72382i −0.111204 0.279100i 0.862834 0.505488i \(-0.168688\pi\)
−0.974037 + 0.226388i \(0.927308\pi\)
\(978\) −0.126266 + 0.316903i −0.00403753 + 0.0101334i
\(979\) −5.45291 5.16527i −0.174276 0.165083i
\(980\) 15.6582 + 18.4342i 0.500182 + 0.588859i
\(981\) −8.70291 16.4154i −0.277863 0.524104i
\(982\) −0.519471 + 9.58109i −0.0165770 + 0.305745i
\(983\) 7.52091 + 27.0879i 0.239880 + 0.863969i 0.981228 + 0.192849i \(0.0617727\pi\)
−0.741349 + 0.671120i \(0.765814\pi\)
\(984\) −6.20610 + 0.674954i −0.197843 + 0.0215168i
\(985\) −26.9222 + 31.6953i −0.857814 + 1.00990i
\(986\) −6.62618 1.45853i −0.211020 0.0464491i
\(987\) 8.93846 + 6.79484i 0.284514 + 0.216282i
\(988\) −24.1614 + 8.14092i −0.768676 + 0.258997i
\(989\) 1.78122 + 32.8527i 0.0566396 + 1.04466i
\(990\) −18.2924 + 11.0062i −0.581371 + 0.349799i
\(991\) −7.32453 + 10.8029i −0.232671 + 0.343164i −0.926045 0.377414i \(-0.876813\pi\)
0.693373 + 0.720579i \(0.256124\pi\)
\(992\) 31.7182 24.1115i 1.00705 0.765542i
\(993\) 2.22569 1.02972i 0.0706302 0.0326770i
\(994\) −8.64915 5.20402i −0.274334 0.165062i
\(995\) −3.09935 + 5.84600i −0.0982561 + 0.185331i
\(996\) 22.4893 4.95027i 0.712601 0.156855i
\(997\) 24.3829 + 11.2807i 0.772215 + 0.357265i 0.766104 0.642717i \(-0.222193\pi\)
0.00611111 + 0.999981i \(0.498055\pi\)
\(998\) −35.8869 52.9293i −1.13598 1.67545i
\(999\) −5.22863 1.76173i −0.165426 0.0557387i
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 177.2.e.b.169.5 yes 140
3.2 odd 2 531.2.i.b.523.1 140
59.22 even 29 inner 177.2.e.b.22.5 140
177.140 odd 58 531.2.i.b.199.1 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.e.b.22.5 140 59.22 even 29 inner
177.2.e.b.169.5 yes 140 1.1 even 1 trivial
531.2.i.b.199.1 140 177.140 odd 58
531.2.i.b.523.1 140 3.2 odd 2