Properties

Label 462.2.ba.b.73.3
Level $462$
Weight $2$
Character 462.73
Analytic conductor $3.689$
Analytic rank $0$
Dimension $64$
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] = [462,2,Mod(19,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 25, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.ba (of order \(30\), degree \(8\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 73.3
Character \(\chi\) \(=\) 462.73
Dual form 462.2.ba.b.19.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.0572849 - 0.128664i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.64421 - 0.0903816i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})\) \(q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.0572849 - 0.128664i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.64421 - 0.0903816i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(-0.0704201 + 0.121971i) q^{10} +(2.71894 - 1.89931i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(0.467724 + 0.339821i) q^{13} +(2.62027 + 0.366281i) q^{14} +(0.0435220 + 0.133947i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.392700 - 3.73629i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(2.44435 - 0.519562i) q^{19} +(0.0827838 - 0.113942i) q^{20} +(2.02551 - 1.70215i) q^{21} +(-2.90258 + 1.60470i) q^{22} +(-3.21150 - 5.56248i) q^{23} +(0.913545 - 0.406737i) q^{24} +(3.33238 + 3.70098i) q^{25} +(-0.429640 - 0.386850i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-2.56763 - 0.638168i) q^{28} +(7.90362 - 2.56804i) q^{29} +(-0.0292823 - 0.137762i) q^{30} +(2.99583 + 6.72873i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.749682 + 3.23079i) q^{33} +3.75688i q^{34} +(-0.163102 + 0.335036i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.302521 - 0.335984i) q^{37} +(-2.48526 + 0.261212i) q^{38} +(-0.574971 + 0.0604319i) q^{39} +(-0.0942405 + 0.104665i) q^{40} +(2.85327 - 8.78148i) q^{41} +(-2.19233 + 1.48111i) q^{42} -10.6377i q^{43} +(3.05441 - 1.29250i) q^{44} +(-0.121971 - 0.0704201i) q^{45} +(2.61247 + 5.86770i) q^{46} +(-1.31427 - 6.18315i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(6.98366 + 0.477976i) q^{49} +(-2.92727 - 4.02904i) q^{50} +(2.79190 + 2.51384i) q^{51} +(0.386850 + 0.429640i) q^{52} +(11.0637 - 4.92589i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.0886181 - 0.458631i) q^{55} +(2.48686 + 0.903063i) q^{56} +(-1.46885 + 2.02170i) q^{57} +(-8.12875 + 1.72782i) q^{58} +(-2.16420 + 10.1818i) q^{59} +(0.0147218 + 0.140069i) q^{60} +(-7.69110 - 3.42430i) q^{61} +(-2.27607 - 7.00502i) q^{62} +(-0.366281 + 2.62027i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.0705162 - 0.0407125i) q^{65} +(1.08328 - 3.13472i) q^{66} +(3.60283 - 6.24028i) q^{67} +(0.392700 - 3.73629i) q^{68} +(6.10863 + 1.98482i) q^{69} +(0.197229 - 0.316152i) q^{70} +(-8.17275 + 5.93785i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(9.37421 + 1.99255i) q^{73} +(-0.335984 + 0.302521i) q^{74} +(-4.95288 - 0.520569i) q^{75} +2.49895 q^{76} +(-7.36110 + 4.77642i) q^{77} +0.578138 q^{78} +(-12.1905 - 1.28128i) q^{79} +(0.104665 - 0.0942405i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.75556 + 8.43512i) q^{82} +(-5.87852 + 4.27100i) q^{83} +(2.33514 - 1.24383i) q^{84} +(-0.503222 - 0.163507i) q^{85} +(-1.11194 + 10.5794i) q^{86} +(-4.15518 + 7.19698i) q^{87} +(-3.17278 + 0.966149i) q^{88} +(9.87647 - 5.70218i) q^{89} +(0.113942 + 0.0827838i) q^{90} +(-1.20604 - 0.940831i) q^{91} +(-1.98482 - 6.10863i) q^{92} +(-6.72873 - 2.99583i) q^{93} +(0.660754 + 6.28666i) q^{94} +(0.0731752 - 0.344262i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-10.5808 + 14.5632i) q^{97} +(-6.89544 - 1.20535i) q^{98} +(-1.60470 - 2.90258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.994522 0.104528i −0.703233 0.0739128i
\(3\) −0.743145 + 0.669131i −0.429055 + 0.386323i
\(4\) 0.978148 + 0.207912i 0.489074 + 0.103956i
\(5\) 0.0572849 0.128664i 0.0256186 0.0575402i −0.900283 0.435305i \(-0.856641\pi\)
0.925902 + 0.377765i \(0.123307\pi\)
\(6\) 0.809017 0.587785i 0.330280 0.239962i
\(7\) −2.64421 0.0903816i −0.999416 0.0341610i
\(8\) −0.951057 0.309017i −0.336249 0.109254i
\(9\) 0.104528 0.994522i 0.0348428 0.331507i
\(10\) −0.0704201 + 0.121971i −0.0222688 + 0.0385707i
\(11\) 2.71894 1.89931i 0.819791 0.572662i
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 0.467724 + 0.339821i 0.129723 + 0.0942494i 0.650755 0.759288i \(-0.274453\pi\)
−0.521032 + 0.853537i \(0.674453\pi\)
\(14\) 2.62027 + 0.366281i 0.700298 + 0.0978928i
\(15\) 0.0435220 + 0.133947i 0.0112373 + 0.0345850i
\(16\) 0.913545 + 0.406737i 0.228386 + 0.101684i
\(17\) −0.392700 3.73629i −0.0952438 0.906185i −0.932936 0.360042i \(-0.882762\pi\)
0.837692 0.546143i \(-0.183904\pi\)
\(18\) −0.207912 + 0.978148i −0.0490053 + 0.230552i
\(19\) 2.44435 0.519562i 0.560771 0.119196i 0.0811989 0.996698i \(-0.474125\pi\)
0.479572 + 0.877502i \(0.340792\pi\)
\(20\) 0.0827838 0.113942i 0.0185110 0.0254782i
\(21\) 2.02551 1.70215i 0.442002 0.371440i
\(22\) −2.90258 + 1.60470i −0.618832 + 0.342122i
\(23\) −3.21150 5.56248i −0.669644 1.15986i −0.978004 0.208587i \(-0.933113\pi\)
0.308360 0.951270i \(-0.400220\pi\)
\(24\) 0.913545 0.406737i 0.186477 0.0830248i
\(25\) 3.33238 + 3.70098i 0.666476 + 0.740197i
\(26\) −0.429640 0.386850i −0.0842594 0.0758675i
\(27\) 0.587785 + 0.809017i 0.113119 + 0.155695i
\(28\) −2.56763 0.638168i −0.485237 0.120602i
\(29\) 7.90362 2.56804i 1.46766 0.476873i 0.537263 0.843415i \(-0.319458\pi\)
0.930402 + 0.366541i \(0.119458\pi\)
\(30\) −0.0292823 0.137762i −0.00534620 0.0251519i
\(31\) 2.99583 + 6.72873i 0.538066 + 1.20852i 0.954188 + 0.299207i \(0.0967223\pi\)
−0.416122 + 0.909309i \(0.636611\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −0.749682 + 3.23079i −0.130503 + 0.562408i
\(34\) 3.75688i 0.644299i
\(35\) −0.163102 + 0.335036i −0.0275693 + 0.0566315i
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) 0.302521 0.335984i 0.0497342 0.0552355i −0.717764 0.696286i \(-0.754834\pi\)
0.767499 + 0.641051i \(0.221501\pi\)
\(38\) −2.48526 + 0.261212i −0.403163 + 0.0423741i
\(39\) −0.574971 + 0.0604319i −0.0920691 + 0.00967685i
\(40\) −0.0942405 + 0.104665i −0.0149007 + 0.0165489i
\(41\) 2.85327 8.78148i 0.445607 1.37144i −0.436211 0.899845i \(-0.643680\pi\)
0.881817 0.471591i \(-0.156320\pi\)
\(42\) −2.19233 + 1.48111i −0.338284 + 0.228540i
\(43\) 10.6377i 1.62223i −0.584885 0.811116i \(-0.698860\pi\)
0.584885 0.811116i \(-0.301140\pi\)
\(44\) 3.05441 1.29250i 0.460470 0.194852i
\(45\) −0.121971 0.0704201i −0.0181824 0.0104976i
\(46\) 2.61247 + 5.86770i 0.385188 + 0.865145i
\(47\) −1.31427 6.18315i −0.191706 0.901905i −0.963847 0.266455i \(-0.914148\pi\)
0.772142 0.635451i \(-0.219186\pi\)
\(48\) −0.951057 + 0.309017i −0.137273 + 0.0446028i
\(49\) 6.98366 + 0.477976i 0.997666 + 0.0682822i
\(50\) −2.92727 4.02904i −0.413978 0.569792i
\(51\) 2.79190 + 2.51384i 0.390945 + 0.352008i
\(52\) 0.386850 + 0.429640i 0.0536464 + 0.0595804i
\(53\) 11.0637 4.92589i 1.51972 0.676622i 0.534071 0.845439i \(-0.320661\pi\)
0.985647 + 0.168817i \(0.0539947\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −0.0886181 0.458631i −0.0119493 0.0618418i
\(56\) 2.48686 + 0.903063i 0.332321 + 0.120677i
\(57\) −1.46885 + 2.02170i −0.194554 + 0.267780i
\(58\) −8.12875 + 1.72782i −1.06736 + 0.226874i
\(59\) −2.16420 + 10.1818i −0.281755 + 1.32555i 0.578498 + 0.815684i \(0.303639\pi\)
−0.860253 + 0.509868i \(0.829694\pi\)
\(60\) 0.0147218 + 0.140069i 0.00190058 + 0.0180828i
\(61\) −7.69110 3.42430i −0.984745 0.438437i −0.149768 0.988721i \(-0.547853\pi\)
−0.834977 + 0.550285i \(0.814519\pi\)
\(62\) −2.27607 7.00502i −0.289061 0.889639i
\(63\) −0.366281 + 2.62027i −0.0461471 + 0.330124i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) 0.0705162 0.0407125i 0.00874646 0.00504977i
\(66\) 1.08328 3.13472i 0.133343 0.385858i
\(67\) 3.60283 6.24028i 0.440155 0.762371i −0.557545 0.830147i \(-0.688257\pi\)
0.997701 + 0.0677751i \(0.0215900\pi\)
\(68\) 0.392700 3.73629i 0.0476219 0.453092i
\(69\) 6.10863 + 1.98482i 0.735393 + 0.238944i
\(70\) 0.197229 0.316152i 0.0235734 0.0377874i
\(71\) −8.17275 + 5.93785i −0.969927 + 0.704693i −0.955435 0.295202i \(-0.904613\pi\)
−0.0144920 + 0.999895i \(0.504613\pi\)
\(72\) −0.406737 + 0.913545i −0.0479344 + 0.107662i
\(73\) 9.37421 + 1.99255i 1.09717 + 0.233210i 0.720719 0.693227i \(-0.243812\pi\)
0.376449 + 0.926437i \(0.377145\pi\)
\(74\) −0.335984 + 0.302521i −0.0390574 + 0.0351674i
\(75\) −4.95288 0.520569i −0.571910 0.0601101i
\(76\) 2.49895 0.286650
\(77\) −7.36110 + 4.77642i −0.838876 + 0.544323i
\(78\) 0.578138 0.0654613
\(79\) −12.1905 1.28128i −1.37154 0.144155i −0.610068 0.792349i \(-0.708858\pi\)
−0.761475 + 0.648194i \(0.775524\pi\)
\(80\) 0.104665 0.0942405i 0.0117019 0.0105364i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −3.75556 + 8.43512i −0.414732 + 0.931503i
\(83\) −5.87852 + 4.27100i −0.645252 + 0.468803i −0.861650 0.507502i \(-0.830569\pi\)
0.216399 + 0.976305i \(0.430569\pi\)
\(84\) 2.33514 1.24383i 0.254785 0.135713i
\(85\) −0.503222 0.163507i −0.0545821 0.0177348i
\(86\) −1.11194 + 10.5794i −0.119904 + 1.14081i
\(87\) −4.15518 + 7.19698i −0.445482 + 0.771597i
\(88\) −3.17278 + 0.966149i −0.338220 + 0.102992i
\(89\) 9.87647 5.70218i 1.04690 0.604430i 0.125123 0.992141i \(-0.460067\pi\)
0.921781 + 0.387711i \(0.126734\pi\)
\(90\) 0.113942 + 0.0827838i 0.0120106 + 0.00872618i
\(91\) −1.20604 0.940831i −0.126428 0.0986259i
\(92\) −1.98482 6.10863i −0.206931 0.636869i
\(93\) −6.72873 2.99583i −0.697737 0.310653i
\(94\) 0.660754 + 6.28666i 0.0681516 + 0.648419i
\(95\) 0.0731752 0.344262i 0.00750761 0.0353205i
\(96\) 0.978148 0.207912i 0.0998318 0.0212199i
\(97\) −10.5808 + 14.5632i −1.07431 + 1.47867i −0.208683 + 0.977983i \(0.566918\pi\)
−0.865631 + 0.500683i \(0.833082\pi\)
\(98\) −6.89544 1.20535i −0.696545 0.121759i
\(99\) −1.60470 2.90258i −0.161278 0.291720i
\(100\) 2.49008 + 4.31295i 0.249008 + 0.431295i
\(101\) −13.3045 + 5.92354i −1.32385 + 0.589414i −0.942248 0.334915i \(-0.891292\pi\)
−0.381597 + 0.924329i \(0.624626\pi\)
\(102\) −2.51384 2.79190i −0.248907 0.276440i
\(103\) −0.127819 0.115089i −0.0125944 0.0113400i 0.662809 0.748788i \(-0.269364\pi\)
−0.675404 + 0.737448i \(0.736031\pi\)
\(104\) −0.339821 0.467724i −0.0333222 0.0458641i
\(105\) −0.102975 0.358117i −0.0100493 0.0349487i
\(106\) −11.5180 + 3.74243i −1.11873 + 0.363497i
\(107\) 1.43794 + 6.76496i 0.139011 + 0.653993i 0.991376 + 0.131047i \(0.0418338\pi\)
−0.852366 + 0.522946i \(0.824833\pi\)
\(108\) 0.406737 + 0.913545i 0.0391383 + 0.0879060i
\(109\) 1.51381 + 0.874001i 0.144997 + 0.0837141i 0.570743 0.821128i \(-0.306655\pi\)
−0.425746 + 0.904843i \(0.639988\pi\)
\(110\) 0.0401926 + 0.465382i 0.00383221 + 0.0443724i
\(111\) 0.452111i 0.0429125i
\(112\) −2.37884 1.15806i −0.224779 0.109427i
\(113\) −1.21600 + 3.74245i −0.114391 + 0.352060i −0.991820 0.127648i \(-0.959257\pi\)
0.877428 + 0.479708i \(0.159257\pi\)
\(114\) 1.67213 1.85708i 0.156609 0.173932i
\(115\) −0.899661 + 0.0945581i −0.0838938 + 0.00881759i
\(116\) 8.26483 0.868669i 0.767370 0.0806539i
\(117\) 0.386850 0.429640i 0.0357643 0.0397203i
\(118\) 3.21663 9.89976i 0.296114 0.911347i
\(119\) 0.700689 + 9.91503i 0.0642320 + 0.908909i
\(120\) 0.140840i 0.0128569i
\(121\) 3.78527 10.3282i 0.344116 0.938927i
\(122\) 7.29103 + 4.20948i 0.660099 + 0.381108i
\(123\) 3.75556 + 8.43512i 0.338627 + 0.760569i
\(124\) 1.53138 + 7.20456i 0.137522 + 0.646989i
\(125\) 1.33681 0.434357i 0.119568 0.0388501i
\(126\) 0.638168 2.56763i 0.0568525 0.228743i
\(127\) −2.23272 3.07308i −0.198122 0.272691i 0.698384 0.715723i \(-0.253903\pi\)
−0.896506 + 0.443032i \(0.853903\pi\)
\(128\) −0.743145 0.669131i −0.0656853 0.0591433i
\(129\) 7.11800 + 7.90535i 0.626705 + 0.696027i
\(130\) −0.0743855 + 0.0331186i −0.00652404 + 0.00290469i
\(131\) −6.18133 10.7064i −0.540066 0.935421i −0.998900 0.0468992i \(-0.985066\pi\)
0.458834 0.888522i \(-0.348267\pi\)
\(132\) −1.40502 + 3.00432i −0.122291 + 0.261492i
\(133\) −6.51031 + 1.15290i −0.564516 + 0.0999695i
\(134\) −4.23538 + 5.82950i −0.365881 + 0.503592i
\(135\) 0.137762 0.0292823i 0.0118567 0.00252022i
\(136\) −0.781098 + 3.67478i −0.0669786 + 0.315110i
\(137\) −0.140655 1.33824i −0.0120170 0.114334i 0.986869 0.161523i \(-0.0516405\pi\)
−0.998886 + 0.0471887i \(0.984974\pi\)
\(138\) −5.86770 2.61247i −0.499492 0.222388i
\(139\) 1.10383 + 3.39724i 0.0936258 + 0.288151i 0.986893 0.161375i \(-0.0515930\pi\)
−0.893267 + 0.449526i \(0.851593\pi\)
\(140\) −0.229196 + 0.293804i −0.0193706 + 0.0248310i
\(141\) 5.11403 + 3.71556i 0.430679 + 0.312907i
\(142\) 8.74865 5.05104i 0.734171 0.423874i
\(143\) 1.91714 + 0.0356028i 0.160319 + 0.00297726i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0.122343 1.16402i 0.0101601 0.0966666i
\(146\) −9.11458 2.96151i −0.754328 0.245096i
\(147\) −5.50970 + 4.31778i −0.454432 + 0.356124i
\(148\) 0.365766 0.265744i 0.0300658 0.0218441i
\(149\) 4.49833 10.1034i 0.368517 0.827704i −0.630169 0.776458i \(-0.717014\pi\)
0.998686 0.0512454i \(-0.0163191\pi\)
\(150\) 4.87134 + 1.03543i 0.397743 + 0.0845429i
\(151\) 8.36293 7.53002i 0.680566 0.612784i −0.254578 0.967052i \(-0.581937\pi\)
0.935144 + 0.354268i \(0.115270\pi\)
\(152\) −2.48526 0.261212i −0.201582 0.0211871i
\(153\) −3.75688 −0.303725
\(154\) 7.82005 3.98081i 0.630158 0.320783i
\(155\) 1.03736 0.0833228
\(156\) −0.574971 0.0604319i −0.0460345 0.00483842i
\(157\) −5.49837 + 4.95075i −0.438818 + 0.395113i −0.858711 0.512460i \(-0.828734\pi\)
0.419893 + 0.907573i \(0.362068\pi\)
\(158\) 11.9898 + 2.54852i 0.953860 + 0.202749i
\(159\) −4.92589 + 11.0637i −0.390648 + 0.877410i
\(160\) −0.113942 + 0.0827838i −0.00900791 + 0.00654463i
\(161\) 7.98912 + 14.9986i 0.629631 + 1.18206i
\(162\) 0.951057 + 0.309017i 0.0747221 + 0.0242787i
\(163\) 0.428396 4.07592i 0.0335546 0.319250i −0.964851 0.262799i \(-0.915355\pi\)
0.998405 0.0564520i \(-0.0179788\pi\)
\(164\) 4.61670 7.99635i 0.360503 0.624410i
\(165\) 0.372740 + 0.281532i 0.0290178 + 0.0219172i
\(166\) 6.29276 3.63313i 0.488413 0.281985i
\(167\) 2.35762 + 1.71291i 0.182438 + 0.132549i 0.675256 0.737583i \(-0.264033\pi\)
−0.492818 + 0.870132i \(0.664033\pi\)
\(168\) −2.45236 + 0.992928i −0.189204 + 0.0766061i
\(169\) −3.91393 12.0459i −0.301072 0.926604i
\(170\) 0.483374 + 0.215212i 0.0370731 + 0.0165060i
\(171\) −0.261212 2.48526i −0.0199754 0.190053i
\(172\) 2.21170 10.4052i 0.168641 0.793392i
\(173\) −19.2638 + 4.09464i −1.46460 + 0.311310i −0.870135 0.492813i \(-0.835969\pi\)
−0.594463 + 0.804123i \(0.702635\pi\)
\(174\) 4.88470 6.72322i 0.370308 0.509686i
\(175\) −8.47700 10.0874i −0.640801 0.762532i
\(176\) 3.25639 0.629210i 0.245460 0.0474285i
\(177\) −5.20461 9.01465i −0.391203 0.677583i
\(178\) −10.4184 + 4.63857i −0.780893 + 0.347676i
\(179\) 0.818225 + 0.908731i 0.0611570 + 0.0679218i 0.772947 0.634471i \(-0.218782\pi\)
−0.711790 + 0.702392i \(0.752115\pi\)
\(180\) −0.104665 0.0942405i −0.00780124 0.00702427i
\(181\) 6.40714 + 8.81867i 0.476239 + 0.655486i 0.977777 0.209649i \(-0.0672322\pi\)
−0.501538 + 0.865136i \(0.667232\pi\)
\(182\) 1.10109 + 1.06174i 0.0816185 + 0.0787016i
\(183\) 8.00691 2.60160i 0.591888 0.192316i
\(184\) 1.33542 + 6.28264i 0.0984482 + 0.463162i
\(185\) −0.0258991 0.0581704i −0.00190414 0.00427677i
\(186\) 6.37872 + 3.68276i 0.467711 + 0.270033i
\(187\) −8.16410 9.41290i −0.597018 0.688340i
\(188\) 6.32129i 0.461027i
\(189\) −1.48111 2.19233i −0.107735 0.159469i
\(190\) −0.108759 + 0.334727i −0.00789024 + 0.0242837i
\(191\) −2.40234 + 2.66807i −0.173828 + 0.193055i −0.823763 0.566934i \(-0.808129\pi\)
0.649935 + 0.759989i \(0.274796\pi\)
\(192\) −0.994522 + 0.104528i −0.0717734 + 0.00754369i
\(193\) 5.24555 0.551329i 0.377583 0.0396855i 0.0861635 0.996281i \(-0.472539\pi\)
0.291419 + 0.956595i \(0.405873\pi\)
\(194\) 12.0451 13.3774i 0.864786 0.960442i
\(195\) −0.0251617 + 0.0774399i −0.00180187 + 0.00554558i
\(196\) 6.73168 + 1.91952i 0.480834 + 0.137108i
\(197\) 3.99937i 0.284943i −0.989799 0.142472i \(-0.954495\pi\)
0.989799 0.142472i \(-0.0455050\pi\)
\(198\) 1.29250 + 3.05441i 0.0918542 + 0.217068i
\(199\) 12.1561 + 7.01835i 0.861726 + 0.497518i 0.864590 0.502478i \(-0.167578\pi\)
−0.00286369 + 0.999996i \(0.500912\pi\)
\(200\) −2.02562 4.54961i −0.143233 0.321706i
\(201\) 1.49814 + 7.04819i 0.105671 + 0.497141i
\(202\) 13.8508 4.50039i 0.974537 0.316646i
\(203\) −21.1309 + 6.07609i −1.48310 + 0.426458i
\(204\) 2.20824 + 3.03938i 0.154607 + 0.212799i
\(205\) −0.966409 0.870159i −0.0674970 0.0607745i
\(206\) 0.115089 + 0.127819i 0.00801860 + 0.00890555i
\(207\) −5.86770 + 2.61247i −0.407833 + 0.181579i
\(208\) 0.289069 + 0.500682i 0.0200433 + 0.0347161i
\(209\) 5.65922 6.05522i 0.391457 0.418848i
\(210\) 0.0649773 + 0.366919i 0.00448386 + 0.0253198i
\(211\) −8.75395 + 12.0488i −0.602647 + 0.829472i −0.995947 0.0899379i \(-0.971333\pi\)
0.393301 + 0.919410i \(0.371333\pi\)
\(212\) 11.8461 2.51797i 0.813593 0.172935i
\(213\) 2.10034 9.88132i 0.143913 0.677057i
\(214\) −0.722928 6.87820i −0.0494184 0.470184i
\(215\) −1.36869 0.609379i −0.0933437 0.0415593i
\(216\) −0.309017 0.951057i −0.0210259 0.0647112i
\(217\) −7.31343 18.0629i −0.496468 1.22619i
\(218\) −1.41416 1.02745i −0.0957792 0.0695877i
\(219\) −8.29967 + 4.79182i −0.560840 + 0.323801i
\(220\) 0.00867320 0.467033i 0.000584747 0.0314874i
\(221\) 1.08600 1.88100i 0.0730520 0.126530i
\(222\) 0.0472585 0.449635i 0.00317178 0.0301775i
\(223\) 10.6478 + 3.45968i 0.713030 + 0.231678i 0.642999 0.765867i \(-0.277690\pi\)
0.0700316 + 0.997545i \(0.477690\pi\)
\(224\) 2.24476 + 1.40038i 0.149984 + 0.0935666i
\(225\) 4.02904 2.92727i 0.268602 0.195151i
\(226\) 1.60053 3.59484i 0.106465 0.239125i
\(227\) 7.93216 + 1.68603i 0.526476 + 0.111906i 0.463479 0.886108i \(-0.346601\pi\)
0.0629968 + 0.998014i \(0.479934\pi\)
\(228\) −1.85708 + 1.67213i −0.122988 + 0.110739i
\(229\) 22.5860 + 2.37389i 1.49253 + 0.156871i 0.815358 0.578957i \(-0.196540\pi\)
0.677168 + 0.735828i \(0.263207\pi\)
\(230\) 0.904616 0.0596486
\(231\) 2.27432 8.47511i 0.149639 0.557621i
\(232\) −8.31036 −0.545602
\(233\) 21.7923 + 2.29047i 1.42766 + 0.150053i 0.786613 0.617446i \(-0.211833\pi\)
0.641050 + 0.767499i \(0.278499\pi\)
\(234\) −0.429640 + 0.386850i −0.0280865 + 0.0252892i
\(235\) −0.870836 0.185102i −0.0568071 0.0120747i
\(236\) −4.23381 + 9.50930i −0.275598 + 0.619003i
\(237\) 9.91668 7.20489i 0.644157 0.468008i
\(238\) 0.339553 9.93396i 0.0220099 0.643923i
\(239\) −3.74416 1.21655i −0.242190 0.0786922i 0.185407 0.982662i \(-0.440640\pi\)
−0.427597 + 0.903970i \(0.640640\pi\)
\(240\) −0.0147218 + 0.140069i −0.000950289 + 0.00904139i
\(241\) 12.5908 21.8079i 0.811043 1.40477i −0.101091 0.994877i \(-0.532233\pi\)
0.912135 0.409891i \(-0.134433\pi\)
\(242\) −4.84413 + 9.87595i −0.311392 + 0.634850i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −6.81108 4.94854i −0.436035 0.316798i
\(245\) 0.461556 0.871164i 0.0294878 0.0556567i
\(246\) −2.85327 8.78148i −0.181918 0.559886i
\(247\) 1.31984 + 0.587629i 0.0839792 + 0.0373899i
\(248\) −0.769906 7.32517i −0.0488891 0.465149i
\(249\) 1.51074 7.10747i 0.0957392 0.450417i
\(250\) −1.37489 + 0.292242i −0.0869558 + 0.0184830i
\(251\) 1.75153 2.41078i 0.110556 0.152167i −0.750153 0.661264i \(-0.770020\pi\)
0.860709 + 0.509097i \(0.170020\pi\)
\(252\) −0.903063 + 2.48686i −0.0568876 + 0.156658i
\(253\) −19.2967 9.02443i −1.21317 0.567361i
\(254\) 1.89927 + 3.28962i 0.119171 + 0.206409i
\(255\) 0.483374 0.215212i 0.0302701 0.0134771i
\(256\) 0.669131 + 0.743145i 0.0418207 + 0.0464466i
\(257\) 2.77868 + 2.50194i 0.173329 + 0.156067i 0.751230 0.660041i \(-0.229461\pi\)
−0.577900 + 0.816107i \(0.696128\pi\)
\(258\) −6.25268 8.60607i −0.389275 0.535791i
\(259\) −0.830296 + 0.861069i −0.0515921 + 0.0535042i
\(260\) 0.0774399 0.0251617i 0.00480262 0.00156046i
\(261\) −1.72782 8.12875i −0.106949 0.503157i
\(262\) 5.02835 + 11.2939i 0.310653 + 0.697737i
\(263\) 6.76394 + 3.90516i 0.417082 + 0.240803i 0.693828 0.720140i \(-0.255923\pi\)
−0.276746 + 0.960943i \(0.589256\pi\)
\(264\) 1.71136 2.84100i 0.105327 0.174851i
\(265\) 1.70568i 0.104779i
\(266\) 6.59516 0.466076i 0.404375 0.0285769i
\(267\) −3.52414 + 10.8462i −0.215674 + 0.663776i
\(268\) 4.82152 5.35484i 0.294521 0.327099i
\(269\) −17.8373 + 1.87477i −1.08756 + 0.114307i −0.631298 0.775540i \(-0.717478\pi\)
−0.456259 + 0.889847i \(0.650811\pi\)
\(270\) −0.140069 + 0.0147218i −0.00852431 + 0.000895941i
\(271\) −0.828282 + 0.919901i −0.0503146 + 0.0558800i −0.767777 0.640718i \(-0.778637\pi\)
0.717462 + 0.696598i \(0.245304\pi\)
\(272\) 1.16094 3.57300i 0.0703922 0.216645i
\(273\) 1.52580 0.107828i 0.0923459 0.00652602i
\(274\) 1.34562i 0.0812916i
\(275\) 16.0898 + 3.73354i 0.970254 + 0.225141i
\(276\) 5.56248 + 3.21150i 0.334822 + 0.193310i
\(277\) 3.33251 + 7.48493i 0.200231 + 0.449726i 0.985554 0.169360i \(-0.0541700\pi\)
−0.785323 + 0.619086i \(0.787503\pi\)
\(278\) −0.742676 3.49402i −0.0445427 0.209557i
\(279\) 7.00502 2.27607i 0.419380 0.136265i
\(280\) 0.258651 0.268237i 0.0154574 0.0160303i
\(281\) −1.82047 2.50566i −0.108600 0.149475i 0.751257 0.660009i \(-0.229448\pi\)
−0.859857 + 0.510534i \(0.829448\pi\)
\(282\) −4.69763 4.22977i −0.279740 0.251879i
\(283\) 0.565458 + 0.628004i 0.0336130 + 0.0373310i 0.759717 0.650254i \(-0.225338\pi\)
−0.726104 + 0.687585i \(0.758671\pi\)
\(284\) −9.22870 + 4.10888i −0.547623 + 0.243817i
\(285\) 0.175977 + 0.304800i 0.0104239 + 0.0180548i
\(286\) −1.90291 0.235803i −0.112522 0.0139433i
\(287\) −8.33833 + 22.9622i −0.492196 + 1.35541i
\(288\) −0.587785 + 0.809017i −0.0346356 + 0.0476718i
\(289\) 2.82283 0.600010i 0.166049 0.0352947i
\(290\) −0.243346 + 1.14486i −0.0142898 + 0.0672282i
\(291\) −1.88162 17.9025i −0.110303 1.04946i
\(292\) 8.75509 + 3.89802i 0.512353 + 0.228114i
\(293\) 6.69874 + 20.6166i 0.391345 + 1.20444i 0.931772 + 0.363044i \(0.118263\pi\)
−0.540427 + 0.841391i \(0.681737\pi\)
\(294\) 5.93085 3.71820i 0.345894 0.216850i
\(295\) 1.18605 + 0.861715i 0.0690544 + 0.0501710i
\(296\) −0.391540 + 0.226056i −0.0227578 + 0.0131392i
\(297\) 3.13472 + 1.08328i 0.181895 + 0.0628585i
\(298\) −5.52978 + 9.57786i −0.320332 + 0.554831i
\(299\) 0.388154 3.69304i 0.0224475 0.213574i
\(300\) −4.73642 1.53896i −0.273457 0.0888516i
\(301\) −0.961452 + 28.1283i −0.0554172 + 1.62129i
\(302\) −9.10422 + 6.61460i −0.523889 + 0.380628i
\(303\) 5.92354 13.3045i 0.340298 0.764323i
\(304\) 2.44435 + 0.519562i 0.140193 + 0.0297989i
\(305\) −0.881167 + 0.793407i −0.0504555 + 0.0454303i
\(306\) 3.73629 + 0.392700i 0.213590 + 0.0224492i
\(307\) −10.4658 −0.597315 −0.298658 0.954360i \(-0.596539\pi\)
−0.298658 + 0.954360i \(0.596539\pi\)
\(308\) −8.19332 + 3.14158i −0.466858 + 0.179008i
\(309\) 0.171997 0.00978457
\(310\) −1.03168 0.108434i −0.0585954 0.00615862i
\(311\) −5.43519 + 4.89387i −0.308201 + 0.277506i −0.808687 0.588239i \(-0.799821\pi\)
0.500486 + 0.865745i \(0.333155\pi\)
\(312\) 0.565504 + 0.120202i 0.0320154 + 0.00680508i
\(313\) −3.60734 + 8.10221i −0.203899 + 0.457964i −0.986332 0.164771i \(-0.947312\pi\)
0.782433 + 0.622734i \(0.213978\pi\)
\(314\) 5.98574 4.34890i 0.337795 0.245422i
\(315\) 0.316152 + 0.197229i 0.0178132 + 0.0111126i
\(316\) −11.6578 3.78783i −0.655800 0.213082i
\(317\) 0.470984 4.48111i 0.0264531 0.251684i −0.973301 0.229530i \(-0.926281\pi\)
0.999755 0.0221539i \(-0.00705237\pi\)
\(318\) 6.05537 10.4882i 0.339569 0.588150i
\(319\) 16.6120 21.9937i 0.930092 1.23141i
\(320\) 0.121971 0.0704201i 0.00681840 0.00393660i
\(321\) −5.59524 4.06518i −0.312296 0.226896i
\(322\) −6.37758 15.7515i −0.355408 0.877799i
\(323\) −2.90113 8.92876i −0.161423 0.496810i
\(324\) −0.913545 0.406737i −0.0507525 0.0225965i
\(325\) 0.300961 + 2.86345i 0.0166943 + 0.158836i
\(326\) −0.852099 + 4.00881i −0.0471934 + 0.222027i
\(327\) −1.70980 + 0.363430i −0.0945524 + 0.0200977i
\(328\) −5.42725 + 7.46997i −0.299670 + 0.412460i
\(329\) 2.91636 + 16.4683i 0.160784 + 0.907928i
\(330\) −0.341270 0.318952i −0.0187863 0.0175577i
\(331\) −15.1800 26.2925i −0.834368 1.44517i −0.894544 0.446979i \(-0.852500\pi\)
0.0601767 0.998188i \(-0.480834\pi\)
\(332\) −6.63805 + 2.95545i −0.364310 + 0.162201i
\(333\) −0.302521 0.335984i −0.0165781 0.0184118i
\(334\) −2.16566 1.94997i −0.118499 0.106697i
\(335\) −0.596511 0.821027i −0.0325909 0.0448575i
\(336\) 2.54272 0.731147i 0.138717 0.0398873i
\(337\) 33.7085 10.9525i 1.83622 0.596623i 0.837475 0.546476i \(-0.184031\pi\)
0.998742 0.0501469i \(-0.0159690\pi\)
\(338\) 2.63336 + 12.3890i 0.143236 + 0.673872i
\(339\) −1.60053 3.59484i −0.0869287 0.195245i
\(340\) −0.458230 0.264559i −0.0248510 0.0143478i
\(341\) 20.9254 + 12.6050i 1.13317 + 0.682601i
\(342\) 2.49895i 0.135128i
\(343\) −18.4230 1.89506i −0.994751 0.102324i
\(344\) −3.28723 + 10.1170i −0.177235 + 0.545475i
\(345\) 0.605306 0.672261i 0.0325886 0.0361933i
\(346\) 19.5863 2.05860i 1.05296 0.110671i
\(347\) −10.3573 + 1.08860i −0.556011 + 0.0584391i −0.378367 0.925656i \(-0.623514\pi\)
−0.177644 + 0.984095i \(0.556848\pi\)
\(348\) −5.56071 + 6.17580i −0.298086 + 0.331057i
\(349\) 0.402461 1.23865i 0.0215432 0.0663032i −0.939707 0.341981i \(-0.888902\pi\)
0.961250 + 0.275678i \(0.0889022\pi\)
\(350\) 7.37615 + 10.9182i 0.394272 + 0.583601i
\(351\) 0.578138i 0.0308587i
\(352\) −3.30432 + 0.285377i −0.176121 + 0.0152107i
\(353\) −12.0120 6.93516i −0.639337 0.369121i 0.145022 0.989428i \(-0.453675\pi\)
−0.784359 + 0.620307i \(0.787008\pi\)
\(354\) 4.23381 + 9.50930i 0.225025 + 0.505413i
\(355\) 0.295812 + 1.39169i 0.0157001 + 0.0738631i
\(356\) 10.8462 3.52414i 0.574847 0.186779i
\(357\) −7.15516 6.89945i −0.378691 0.365158i
\(358\) −0.718755 0.989281i −0.0379874 0.0522851i
\(359\) 20.3653 + 18.3370i 1.07484 + 0.967788i 0.999568 0.0293748i \(-0.00935164\pi\)
0.0752695 + 0.997163i \(0.476018\pi\)
\(360\) 0.0942405 + 0.104665i 0.00496691 + 0.00551631i
\(361\) −11.6525 + 5.18802i −0.613289 + 0.273054i
\(362\) −5.45024 9.44009i −0.286458 0.496160i
\(363\) 4.09791 + 10.2082i 0.215085 + 0.535791i
\(364\) −0.984080 1.17102i −0.0515798 0.0613782i
\(365\) 0.793369 1.09198i 0.0415269 0.0571568i
\(366\) −8.23498 + 1.75040i −0.430450 + 0.0914949i
\(367\) −6.35224 + 29.8849i −0.331584 + 1.55998i 0.424451 + 0.905451i \(0.360467\pi\)
−0.756035 + 0.654531i \(0.772866\pi\)
\(368\) −0.671386 6.38781i −0.0349984 0.332988i
\(369\) −8.43512 3.75556i −0.439115 0.195507i
\(370\) 0.0196768 + 0.0605589i 0.00102295 + 0.00314831i
\(371\) −29.7000 + 12.0251i −1.54195 + 0.624312i
\(372\) −5.95883 4.32934i −0.308951 0.224466i
\(373\) −7.87007 + 4.54379i −0.407497 + 0.235268i −0.689714 0.724082i \(-0.742264\pi\)
0.282217 + 0.959351i \(0.408930\pi\)
\(374\) 7.13546 + 10.2147i 0.368966 + 0.528191i
\(375\) −0.702804 + 1.21729i −0.0362926 + 0.0628607i
\(376\) −0.660754 + 6.28666i −0.0340758 + 0.324210i
\(377\) 4.56938 + 1.48468i 0.235335 + 0.0764650i
\(378\) 1.24383 + 2.33514i 0.0639758 + 0.120107i
\(379\) 29.2277 21.2351i 1.50132 1.09078i 0.531473 0.847075i \(-0.321639\pi\)
0.969851 0.243700i \(-0.0783613\pi\)
\(380\) 0.143152 0.321525i 0.00734355 0.0164939i
\(381\) 3.71552 + 0.789759i 0.190352 + 0.0404606i
\(382\) 2.66807 2.40234i 0.136511 0.122915i
\(383\) 22.4924 + 2.36405i 1.14931 + 0.120797i 0.659967 0.751295i \(-0.270570\pi\)
0.489342 + 0.872092i \(0.337237\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.192873 + 1.22072i 0.00982970 + 0.0622139i
\(386\) −5.27444 −0.268462
\(387\) −10.5794 1.11194i −0.537782 0.0565232i
\(388\) −13.3774 + 12.0451i −0.679135 + 0.611496i
\(389\) −25.1567 5.34722i −1.27549 0.271115i −0.480103 0.877212i \(-0.659401\pi\)
−0.795390 + 0.606097i \(0.792734\pi\)
\(390\) 0.0331186 0.0743855i 0.00167702 0.00376666i
\(391\) −19.5219 + 14.1835i −0.987265 + 0.717290i
\(392\) −6.49415 2.61265i −0.328004 0.131959i
\(393\) 11.7576 + 3.82027i 0.593092 + 0.192707i
\(394\) −0.418048 + 3.97746i −0.0210610 + 0.200382i
\(395\) −0.863187 + 1.49508i −0.0434317 + 0.0752259i
\(396\) −0.966149 3.17278i −0.0485508 0.159438i
\(397\) −13.0644 + 7.54272i −0.655682 + 0.378558i −0.790630 0.612295i \(-0.790247\pi\)
0.134948 + 0.990853i \(0.456913\pi\)
\(398\) −11.3559 8.25057i −0.569222 0.413564i
\(399\) 4.06666 5.21303i 0.203588 0.260978i
\(400\) 1.53896 + 4.73642i 0.0769478 + 0.236821i
\(401\) −13.7906 6.13996i −0.688669 0.306615i 0.0324036 0.999475i \(-0.489684\pi\)
−0.721072 + 0.692860i \(0.756350\pi\)
\(402\) −0.753196 7.16618i −0.0375660 0.357417i
\(403\) −0.885347 + 4.16523i −0.0441023 + 0.207485i
\(404\) −14.2453 + 3.02794i −0.708731 + 0.150645i
\(405\) −0.0827838 + 0.113942i −0.00411356 + 0.00566183i
\(406\) 21.6503 3.83402i 1.07448 0.190279i
\(407\) 0.184401 1.48810i 0.00914042 0.0737625i
\(408\) −1.87844 3.25355i −0.0929965 0.161075i
\(409\) 15.7133 6.99600i 0.776971 0.345930i 0.0203583 0.999793i \(-0.493519\pi\)
0.756613 + 0.653863i \(0.226853\pi\)
\(410\) 0.870159 + 0.966409i 0.0429741 + 0.0477276i
\(411\) 0.999987 + 0.900393i 0.0493257 + 0.0444131i
\(412\) −0.101097 0.139149i −0.00498071 0.00685536i
\(413\) 6.64283 26.7271i 0.326872 1.31515i
\(414\) 6.10863 1.98482i 0.300223 0.0975484i
\(415\) 0.212773 + 1.00102i 0.0104446 + 0.0491380i
\(416\) −0.235150 0.528156i −0.0115292 0.0258950i
\(417\) −3.09351 1.78604i −0.151490 0.0874626i
\(418\) −6.26116 + 5.43050i −0.306243 + 0.265614i
\(419\) 6.87524i 0.335878i 0.985797 + 0.167939i \(0.0537111\pi\)
−0.985797 + 0.167939i \(0.946289\pi\)
\(420\) −0.0262679 0.371701i −0.00128174 0.0181372i
\(421\) −7.27930 + 22.4034i −0.354771 + 1.09187i 0.601370 + 0.798970i \(0.294622\pi\)
−0.956142 + 0.292904i \(0.905378\pi\)
\(422\) 9.96543 11.0677i 0.485110 0.538769i
\(423\) −6.28666 + 0.660754i −0.305668 + 0.0321270i
\(424\) −12.0444 + 1.26592i −0.584928 + 0.0614784i
\(425\) 12.5193 13.9041i 0.607277 0.674449i
\(426\) −3.12171 + 9.60764i −0.151247 + 0.465492i
\(427\) 20.0274 + 9.74969i 0.969192 + 0.471821i
\(428\) 6.91609i 0.334302i
\(429\) −1.44853 + 1.25636i −0.0699358 + 0.0606575i
\(430\) 1.29749 + 0.749107i 0.0625706 + 0.0361252i
\(431\) −0.470720 1.05725i −0.0226738 0.0509261i 0.901854 0.432042i \(-0.142207\pi\)
−0.924527 + 0.381116i \(0.875540\pi\)
\(432\) 0.207912 + 0.978148i 0.0100032 + 0.0470611i
\(433\) −18.1382 + 5.89346i −0.871667 + 0.283222i −0.710493 0.703704i \(-0.751528\pi\)
−0.161174 + 0.986926i \(0.551528\pi\)
\(434\) 5.38527 + 18.7284i 0.258501 + 0.898994i
\(435\) 0.687963 + 0.946899i 0.0329853 + 0.0454003i
\(436\) 1.29902 + 1.16964i 0.0622117 + 0.0560157i
\(437\) −10.7401 11.9281i −0.513767 0.570596i
\(438\) 8.75509 3.89802i 0.418334 0.186254i
\(439\) 1.26190 + 2.18567i 0.0602270 + 0.104316i 0.894567 0.446934i \(-0.147484\pi\)
−0.834340 + 0.551250i \(0.814151\pi\)
\(440\) −0.0574440 + 0.463568i −0.00273853 + 0.0220998i
\(441\) 1.20535 6.89544i 0.0573976 0.328354i
\(442\) −1.27667 + 1.75718i −0.0607248 + 0.0835805i
\(443\) −14.2922 + 3.03789i −0.679041 + 0.144335i −0.534506 0.845165i \(-0.679502\pi\)
−0.144536 + 0.989500i \(0.546169\pi\)
\(444\) −0.0939992 + 0.442232i −0.00446101 + 0.0209874i
\(445\) −0.167893 1.59739i −0.00795889 0.0757237i
\(446\) −10.2278 4.55373i −0.484303 0.215625i
\(447\) 3.41759 + 10.5183i 0.161647 + 0.497497i
\(448\) −2.08608 1.62735i −0.0985582 0.0768849i
\(449\) 30.7514 + 22.3422i 1.45125 + 1.05439i 0.985538 + 0.169456i \(0.0542009\pi\)
0.465710 + 0.884938i \(0.345799\pi\)
\(450\) −4.31295 + 2.49008i −0.203314 + 0.117384i
\(451\) −8.92083 29.2955i −0.420065 1.37947i
\(452\) −1.96752 + 3.40785i −0.0925445 + 0.160292i
\(453\) −1.17630 + 11.1918i −0.0552676 + 0.525836i
\(454\) −7.71247 2.50593i −0.361964 0.117609i
\(455\) −0.190139 + 0.101279i −0.00891386 + 0.00474803i
\(456\) 2.02170 1.46885i 0.0946746 0.0687851i
\(457\) −15.7826 + 35.4484i −0.738280 + 1.65820i 0.0144674 + 0.999895i \(0.495395\pi\)
−0.752748 + 0.658309i \(0.771272\pi\)
\(458\) −22.2142 4.72176i −1.03800 0.220634i
\(459\) 2.79190 2.51384i 0.130315 0.117336i
\(460\) −0.899661 0.0945581i −0.0419469 0.00440880i
\(461\) −30.8429 −1.43650 −0.718248 0.695787i \(-0.755056\pi\)
−0.718248 + 0.695787i \(0.755056\pi\)
\(462\) −3.14775 + 8.19095i −0.146447 + 0.381078i
\(463\) 19.2980 0.896853 0.448426 0.893820i \(-0.351985\pi\)
0.448426 + 0.893820i \(0.351985\pi\)
\(464\) 8.26483 + 0.868669i 0.383685 + 0.0403269i
\(465\) −0.770909 + 0.694130i −0.0357501 + 0.0321895i
\(466\) −21.4335 4.55584i −0.992889 0.211045i
\(467\) 0.726468 1.63167i 0.0336169 0.0755049i −0.895957 0.444142i \(-0.853509\pi\)
0.929574 + 0.368637i \(0.120175\pi\)
\(468\) 0.467724 0.339821i 0.0216205 0.0157082i
\(469\) −10.0906 + 16.1750i −0.465942 + 0.746890i
\(470\) 0.846717 + 0.275115i 0.0390562 + 0.0126901i
\(471\) 0.773384 7.35825i 0.0356356 0.339050i
\(472\) 5.20461 9.01465i 0.239562 0.414933i
\(473\) −20.2042 28.9232i −0.928992 1.32989i
\(474\) −10.6155 + 6.12884i −0.487585 + 0.281507i
\(475\) 10.0684 + 7.31510i 0.461969 + 0.335640i
\(476\) −1.37607 + 9.84404i −0.0630722 + 0.451201i
\(477\) −3.74243 11.5180i −0.171354 0.527373i
\(478\) 3.59649 + 1.60126i 0.164500 + 0.0732399i
\(479\) 0.381529 + 3.63000i 0.0174325 + 0.165859i 0.999775 0.0212349i \(-0.00675979\pi\)
−0.982342 + 0.187094i \(0.940093\pi\)
\(480\) 0.0292823 0.137762i 0.00133655 0.00628797i
\(481\) 0.255671 0.0543445i 0.0116576 0.00247790i
\(482\) −14.8013 + 20.3723i −0.674183 + 0.927933i
\(483\) −15.9731 5.80037i −0.726801 0.263926i
\(484\) 5.84991 9.31550i 0.265905 0.423432i
\(485\) 1.26764 + 2.19561i 0.0575604 + 0.0996976i
\(486\) −0.913545 + 0.406737i −0.0414393 + 0.0184499i
\(487\) 9.06566 + 10.0684i 0.410804 + 0.456245i 0.912668 0.408702i \(-0.134019\pi\)
−0.501863 + 0.864947i \(0.667352\pi\)
\(488\) 6.25651 + 5.63338i 0.283219 + 0.255011i
\(489\) 2.40896 + 3.31565i 0.108937 + 0.149939i
\(490\) −0.550089 + 0.818146i −0.0248505 + 0.0369601i
\(491\) −8.63941 + 2.80711i −0.389891 + 0.126683i −0.497401 0.867521i \(-0.665712\pi\)
0.107510 + 0.994204i \(0.465712\pi\)
\(492\) 1.91973 + 9.03162i 0.0865481 + 0.407177i
\(493\) −12.6987 28.5218i −0.571921 1.28456i
\(494\) −1.25118 0.722370i −0.0562933 0.0325010i
\(495\) −0.465382 + 0.0401926i −0.0209173 + 0.00180652i
\(496\) 7.36552i 0.330721i
\(497\) 22.1471 14.9622i 0.993434 0.671148i
\(498\) −2.24540 + 6.91062i −0.100619 + 0.309672i
\(499\) −3.46666 + 3.85011i −0.155189 + 0.172355i −0.815726 0.578439i \(-0.803662\pi\)
0.660537 + 0.750794i \(0.270329\pi\)
\(500\) 1.39791 0.146926i 0.0625163 0.00657073i
\(501\) −2.89821 + 0.304615i −0.129483 + 0.0136092i
\(502\) −1.99393 + 2.21449i −0.0889937 + 0.0988375i
\(503\) 3.29156 10.1304i 0.146764 0.451692i −0.850470 0.526023i \(-0.823682\pi\)
0.997234 + 0.0743318i \(0.0236824\pi\)
\(504\) 1.15806 2.37884i 0.0515843 0.105962i
\(505\) 2.05114i 0.0912743i
\(506\) 18.2477 + 10.9921i 0.811210 + 0.488656i
\(507\) 10.9689 + 6.33288i 0.487144 + 0.281253i
\(508\) −1.54500 3.47013i −0.0685484 0.153962i
\(509\) −2.96029 13.9271i −0.131213 0.617307i −0.993780 0.111364i \(-0.964478\pi\)
0.862567 0.505943i \(-0.168855\pi\)
\(510\) −0.503222 + 0.163507i −0.0222830 + 0.00724020i
\(511\) −24.6073 6.11597i −1.08856 0.270555i
\(512\) −0.587785 0.809017i −0.0259767 0.0357538i
\(513\) 1.85708 + 1.67213i 0.0819923 + 0.0738262i
\(514\) −2.50194 2.77868i −0.110356 0.122562i
\(515\) −0.0221298 + 0.00985283i −0.000975156 + 0.000434167i
\(516\) 5.31885 + 9.21251i 0.234149 + 0.405558i
\(517\) −15.3171 14.3154i −0.673646 0.629591i
\(518\) 0.915754 0.769563i 0.0402359 0.0338126i
\(519\) 11.5759 15.9329i 0.508127 0.699377i
\(520\) −0.0796457 + 0.0169292i −0.00349270 + 0.000742396i
\(521\) −0.0567578 + 0.267024i −0.00248660 + 0.0116986i −0.979373 0.202059i \(-0.935237\pi\)
0.976887 + 0.213757i \(0.0685702\pi\)
\(522\) 0.868669 + 8.26483i 0.0380206 + 0.361742i
\(523\) 30.7026 + 13.6697i 1.34253 + 0.597733i 0.947152 0.320785i \(-0.103947\pi\)
0.395378 + 0.918518i \(0.370613\pi\)
\(524\) −3.82027 11.7576i −0.166889 0.513633i
\(525\) 13.0494 + 1.82414i 0.569522 + 0.0796121i
\(526\) −6.31869 4.59079i −0.275508 0.200168i
\(527\) 23.9641 13.8357i 1.04389 0.602691i
\(528\) −1.99895 + 2.64655i −0.0869930 + 0.115176i
\(529\) −9.12746 + 15.8092i −0.396846 + 0.687357i
\(530\) −0.178292 + 1.69634i −0.00774451 + 0.0736841i
\(531\) 9.89976 + 3.21663i 0.429613 + 0.139590i
\(532\) −6.60775 0.225860i −0.286482 0.00979225i
\(533\) 4.31867 3.13770i 0.187063 0.135909i
\(534\) 4.63857 10.4184i 0.200731 0.450849i
\(535\) 0.952778 + 0.202519i 0.0411922 + 0.00875567i
\(536\) −5.35484 + 4.82152i −0.231294 + 0.208258i
\(537\) −1.21612 0.127819i −0.0524794 0.00551581i
\(538\) 17.9355 0.773255
\(539\) 19.8960 11.9645i 0.856981 0.515349i
\(540\) 0.140840 0.00606080
\(541\) −34.4696 3.62291i −1.48197 0.155761i −0.671263 0.741219i \(-0.734248\pi\)
−0.810703 + 0.585458i \(0.800915\pi\)
\(542\) 0.919901 0.828282i 0.0395131 0.0355778i
\(543\) −10.6623 2.26634i −0.457562 0.0972578i
\(544\) −1.52806 + 3.43208i −0.0655150 + 0.147149i
\(545\) 0.199171 0.144706i 0.00853155 0.00619853i
\(546\) −1.52872 0.0522531i −0.0654231 0.00223623i
\(547\) −22.6628 7.36359i −0.968992 0.314844i −0.218583 0.975818i \(-0.570143\pi\)
−0.750409 + 0.660974i \(0.770143\pi\)
\(548\) 0.140655 1.33824i 0.00600849 0.0571670i
\(549\) −4.20948 + 7.29103i −0.179656 + 0.311174i
\(550\) −15.6114 5.39493i −0.665674 0.230041i
\(551\) 17.9849 10.3836i 0.766183 0.442356i
\(552\) −5.19632 3.77534i −0.221170 0.160689i
\(553\) 32.1185 + 4.48976i 1.36582 + 0.190924i
\(554\) −2.53186 7.79227i −0.107569 0.331062i
\(555\) 0.0581704 + 0.0258991i 0.00246920 + 0.00109936i
\(556\) 0.373383 + 3.55251i 0.0158350 + 0.150660i
\(557\) 0.625254 2.94159i 0.0264929 0.124639i −0.962914 0.269809i \(-0.913039\pi\)
0.989407 + 0.145170i \(0.0463728\pi\)
\(558\) −7.20456 + 1.53138i −0.304993 + 0.0648284i
\(559\) 3.61491 4.97550i 0.152894 0.210441i
\(560\) −0.285273 + 0.239732i −0.0120550 + 0.0101305i
\(561\) 12.3656 + 1.53230i 0.522075 + 0.0646939i
\(562\) 1.54858 + 2.68222i 0.0653230 + 0.113143i
\(563\) −31.0278 + 13.8145i −1.30767 + 0.582211i −0.937897 0.346913i \(-0.887230\pi\)
−0.369769 + 0.929124i \(0.620563\pi\)
\(564\) 4.22977 + 4.69763i 0.178105 + 0.197806i
\(565\) 0.411860 + 0.370840i 0.0173271 + 0.0156014i
\(566\) −0.496716 0.683671i −0.0208785 0.0287368i
\(567\) 2.56763 + 0.638168i 0.107830 + 0.0268005i
\(568\) 9.60764 3.12171i 0.403128 0.130984i
\(569\) 9.30341 + 43.7691i 0.390019 + 1.83490i 0.534218 + 0.845347i \(0.320606\pi\)
−0.144199 + 0.989549i \(0.546060\pi\)
\(570\) −0.143152 0.321525i −0.00599599 0.0134672i
\(571\) 40.5545 + 23.4141i 1.69715 + 0.979851i 0.948441 + 0.316952i \(0.102660\pi\)
0.748709 + 0.662898i \(0.230674\pi\)
\(572\) 1.86784 + 0.433420i 0.0780983 + 0.0181222i
\(573\) 3.59025i 0.149985i
\(574\) 10.6929 21.9648i 0.446311 0.916792i
\(575\) 9.88471 30.4220i 0.412221 1.26869i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) 31.2083 3.28013i 1.29922 0.136554i 0.570462 0.821324i \(-0.306764\pi\)
0.728759 + 0.684771i \(0.240098\pi\)
\(578\) −2.87008 + 0.301658i −0.119380 + 0.0125473i
\(579\) −3.52929 + 3.91967i −0.146672 + 0.162896i
\(580\) 0.361683 1.11315i 0.0150181 0.0462209i
\(581\) 15.9300 10.7621i 0.660890 0.446487i
\(582\) 18.0011i 0.746168i
\(583\) 20.7258 34.4066i 0.858376 1.42497i
\(584\) −8.29967 4.79182i −0.343443 0.198287i
\(585\) −0.0331186 0.0743855i −0.00136928 0.00307546i
\(586\) −4.50702 21.2039i −0.186183 0.875924i
\(587\) 31.2526 10.1546i 1.28993 0.419124i 0.417864 0.908510i \(-0.362779\pi\)
0.872068 + 0.489386i \(0.162779\pi\)
\(588\) −6.28702 + 3.07789i −0.259272 + 0.126930i
\(589\) 10.8188 + 14.8908i 0.445782 + 0.613566i
\(590\) −1.08948 0.980970i −0.0448531 0.0403859i
\(591\) 2.67610 + 2.97211i 0.110080 + 0.122256i
\(592\) 0.413024 0.183890i 0.0169752 0.00755784i
\(593\) 3.30091 + 5.71734i 0.135552 + 0.234783i 0.925808 0.377994i \(-0.123386\pi\)
−0.790256 + 0.612777i \(0.790053\pi\)
\(594\) −3.00432 1.40502i −0.123269 0.0576486i
\(595\) 1.31585 + 0.477828i 0.0539444 + 0.0195890i
\(596\) 6.50065 8.94737i 0.266277 0.366499i
\(597\) −13.7300 + 2.91840i −0.561930 + 0.119442i
\(598\) −0.772055 + 3.63223i −0.0315717 + 0.148533i
\(599\) −3.17981 30.2539i −0.129924 1.23614i −0.844104 0.536179i \(-0.819867\pi\)
0.714181 0.699961i \(-0.246800\pi\)
\(600\) 4.54961 + 2.02562i 0.185737 + 0.0826954i
\(601\) −0.619773 1.90747i −0.0252811 0.0778072i 0.937620 0.347662i \(-0.113024\pi\)
−0.962901 + 0.269855i \(0.913024\pi\)
\(602\) 3.89639 27.8737i 0.158805 1.13605i
\(603\) −5.82950 4.23538i −0.237395 0.172478i
\(604\) 9.74576 5.62672i 0.396549 0.228948i
\(605\) −1.11203 1.07868i −0.0452104 0.0438545i
\(606\) −7.28178 + 12.6124i −0.295802 + 0.512345i
\(607\) 1.40496 13.3673i 0.0570254 0.542560i −0.928295 0.371845i \(-0.878725\pi\)
0.985320 0.170716i \(-0.0546080\pi\)
\(608\) −2.37665 0.772219i −0.0963857 0.0313176i
\(609\) 11.6376 18.6548i 0.471580 0.755929i
\(610\) 0.959274 0.696953i 0.0388399 0.0282188i
\(611\) 1.48645 3.33862i 0.0601354 0.135066i
\(612\) −3.67478 0.781098i −0.148544 0.0315740i
\(613\) −15.0361 + 13.5385i −0.607300 + 0.546816i −0.914374 0.404870i \(-0.867317\pi\)
0.307074 + 0.951686i \(0.400650\pi\)
\(614\) 10.4085 + 1.09398i 0.420052 + 0.0441492i
\(615\) 1.30043 0.0524385
\(616\) 8.47682 2.26794i 0.341541 0.0913778i
\(617\) −0.994760 −0.0400475 −0.0200238 0.999800i \(-0.506374\pi\)
−0.0200238 + 0.999800i \(0.506374\pi\)
\(618\) −0.171055 0.0179786i −0.00688084 0.000723205i
\(619\) 33.8469 30.4759i 1.36042 1.22493i 0.410726 0.911759i \(-0.365275\pi\)
0.949697 0.313171i \(-0.101391\pi\)
\(620\) 1.01469 + 0.215679i 0.0407510 + 0.00866189i
\(621\) 2.61247 5.86770i 0.104835 0.235463i
\(622\) 5.91697 4.29893i 0.237249 0.172371i
\(623\) −26.6308 + 14.1851i −1.06694 + 0.568314i
\(624\) −0.549842 0.178655i −0.0220113 0.00715190i
\(625\) −2.58215 + 24.5675i −0.103286 + 0.982701i
\(626\) 4.43449 7.68075i 0.177238 0.306985i
\(627\) −0.153890 + 8.28666i −0.00614578 + 0.330937i
\(628\) −6.40754 + 3.69939i −0.255689 + 0.147622i
\(629\) −1.37414 0.998368i −0.0547904 0.0398076i
\(630\) −0.293804 0.229196i −0.0117054 0.00913138i
\(631\) 3.56477 + 10.9712i 0.141911 + 0.436758i 0.996601 0.0823815i \(-0.0262526\pi\)
−0.854690 + 0.519139i \(0.826253\pi\)
\(632\) 11.1980 + 4.98565i 0.445431 + 0.198319i
\(633\) −1.55675 14.8115i −0.0618754 0.588705i
\(634\) −0.936807 + 4.40733i −0.0372054 + 0.175038i
\(635\) −0.523295 + 0.111230i −0.0207663 + 0.00441402i
\(636\) −7.11852 + 9.79780i −0.282268 + 0.388508i
\(637\) 3.10400 + 2.59676i 0.122985 + 0.102887i
\(638\) −18.8199 + 20.1368i −0.745088 + 0.797225i
\(639\) 5.05104 + 8.74865i 0.199816 + 0.346091i
\(640\) −0.128664 + 0.0572849i −0.00508589 + 0.00226438i
\(641\) −5.47191 6.07717i −0.216127 0.240034i 0.625326 0.780364i \(-0.284966\pi\)
−0.841453 + 0.540330i \(0.818299\pi\)
\(642\) 5.13966 + 4.62777i 0.202846 + 0.182643i
\(643\) 12.2757 + 16.8961i 0.484108 + 0.666317i 0.979288 0.202473i \(-0.0648979\pi\)
−0.495180 + 0.868790i \(0.664898\pi\)
\(644\) 4.69616 + 16.3319i 0.185054 + 0.643566i
\(645\) 1.42489 0.462974i 0.0561048 0.0182296i
\(646\) 1.95193 + 9.18310i 0.0767976 + 0.361304i
\(647\) −16.4538 36.9559i −0.646867 1.45289i −0.877369 0.479816i \(-0.840703\pi\)
0.230502 0.973072i \(-0.425963\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 13.4539 + 31.7941i 0.528114 + 1.24803i
\(650\) 2.87922i 0.112932i
\(651\) 17.5214 + 8.52974i 0.686718 + 0.334307i
\(652\) 1.26647 3.89778i 0.0495986 0.152649i
\(653\) −10.6891 + 11.8714i −0.418296 + 0.464564i −0.915058 0.403322i \(-0.867855\pi\)
0.496762 + 0.867887i \(0.334522\pi\)
\(654\) 1.73843 0.182716i 0.0679779 0.00714476i
\(655\) −1.73162 + 0.182001i −0.0676601 + 0.00711136i
\(656\) 6.17834 6.86175i 0.241224 0.267906i
\(657\) 2.96151 9.11458i 0.115539 0.355594i
\(658\) −1.17897 16.6829i −0.0459612 0.650369i
\(659\) 18.4155i 0.717365i 0.933460 + 0.358683i \(0.116774\pi\)
−0.933460 + 0.358683i \(0.883226\pi\)
\(660\) 0.306061 + 0.352877i 0.0119134 + 0.0137357i
\(661\) −33.6682 19.4384i −1.30954 0.756065i −0.327523 0.944843i \(-0.606214\pi\)
−0.982020 + 0.188779i \(0.939547\pi\)
\(662\) 12.3485 + 27.7352i 0.479939 + 1.07796i
\(663\) 0.451583 + 2.12453i 0.0175380 + 0.0825099i
\(664\) 6.91062 2.24540i 0.268184 0.0871382i
\(665\) −0.224605 + 0.903686i −0.00870982 + 0.0350435i
\(666\) 0.265744 + 0.365766i 0.0102974 + 0.0141731i
\(667\) −39.6671 35.7165i −1.53592 1.38295i
\(668\) 1.94997 + 2.16566i 0.0754465 + 0.0837918i
\(669\) −10.2278 + 4.55373i −0.395431 + 0.176057i
\(670\) 0.507423 + 0.878882i 0.0196034 + 0.0339542i
\(671\) −27.4154 + 5.29729i −1.05836 + 0.204500i
\(672\) −2.60522 + 0.461355i −0.100498 + 0.0177972i
\(673\) −20.4461 + 28.1417i −0.788141 + 1.08478i 0.206196 + 0.978511i \(0.433891\pi\)
−0.994337 + 0.106272i \(0.966109\pi\)
\(674\) −34.6687 + 7.36905i −1.33539 + 0.283845i
\(675\) −1.03543 + 4.87134i −0.0398539 + 0.187498i
\(676\) −1.32393 12.5964i −0.0509205 0.484476i
\(677\) 16.7234 + 7.44575i 0.642734 + 0.286164i 0.702106 0.712072i \(-0.252243\pi\)
−0.0593722 + 0.998236i \(0.518910\pi\)
\(678\) 1.21600 + 3.74245i 0.0467000 + 0.143728i
\(679\) 29.2940 37.5517i 1.12420 1.44110i
\(680\) 0.428066 + 0.311008i 0.0164156 + 0.0119266i
\(681\) −7.02292 + 4.05469i −0.269119 + 0.155376i
\(682\) −19.4932 14.7233i −0.746432 0.563784i
\(683\) −1.88391 + 3.26302i −0.0720856 + 0.124856i −0.899815 0.436271i \(-0.856299\pi\)
0.827730 + 0.561127i \(0.189632\pi\)
\(684\) 0.261212 2.48526i 0.00998768 0.0950264i
\(685\) −0.180241 0.0585639i −0.00688666 0.00223761i
\(686\) 18.1240 + 3.81041i 0.691979 + 0.145482i
\(687\) −18.3731 + 13.3489i −0.700978 + 0.509291i
\(688\) 4.32674 9.71801i 0.164955 0.370496i
\(689\) 6.84868 + 1.45573i 0.260914 + 0.0554590i
\(690\) −0.672261 + 0.605306i −0.0255925 + 0.0230436i
\(691\) −40.6394 4.27137i −1.54599 0.162491i −0.707229 0.706984i \(-0.750055\pi\)
−0.838765 + 0.544494i \(0.816722\pi\)
\(692\) −19.6941 −0.748659
\(693\) 3.98081 + 7.82005i 0.151218 + 0.297059i
\(694\) 10.4144 0.395325
\(695\) 0.500336 + 0.0525874i 0.0189788 + 0.00199475i
\(696\) 6.17580 5.56071i 0.234093 0.210778i
\(697\) −33.9307 7.21218i −1.28522 0.273181i
\(698\) −0.529730 + 1.18979i −0.0200506 + 0.0450343i
\(699\) −17.7275 + 12.8798i −0.670515 + 0.487158i
\(700\) −6.19448 11.6294i −0.234129 0.439550i
\(701\) 9.13000 + 2.96652i 0.344835 + 0.112044i 0.476314 0.879275i \(-0.341973\pi\)
−0.131479 + 0.991319i \(0.541973\pi\)
\(702\) 0.0604319 0.574971i 0.00228085 0.0217009i
\(703\) 0.564903 0.978440i 0.0213057 0.0369026i
\(704\) 3.31605 + 0.0615818i 0.124978 + 0.00232095i
\(705\) 0.771015 0.445146i 0.0290381 0.0167652i
\(706\) 11.2213 + 8.15277i 0.422320 + 0.306833i
\(707\) 35.7152 14.4606i 1.34321 0.543846i
\(708\) −3.21663 9.89976i −0.120888 0.372056i
\(709\) 43.3546 + 19.3027i 1.62821 + 0.724928i 0.998646 0.0520173i \(-0.0165651\pi\)
0.629568 + 0.776945i \(0.283232\pi\)
\(710\) −0.148721 1.41498i −0.00558139 0.0531034i
\(711\) −2.54852 + 11.9898i −0.0955768 + 0.449654i
\(712\) −11.1552 + 2.37110i −0.418057 + 0.0888608i
\(713\) 27.8074 38.2735i 1.04139 1.43336i
\(714\) 6.39478 + 7.60957i 0.239319 + 0.284781i
\(715\) 0.114404 0.244627i 0.00427846 0.00914852i
\(716\) 0.611409 + 1.05899i 0.0228494 + 0.0395764i
\(717\) 3.59649 1.60126i 0.134313 0.0598001i
\(718\) −18.3370 20.3653i −0.684330 0.760025i
\(719\) −8.91124 8.02372i −0.332333 0.299234i 0.486022 0.873946i \(-0.338447\pi\)
−0.818356 + 0.574712i \(0.805114\pi\)
\(720\) −0.0827838 0.113942i −0.00308517 0.00424637i
\(721\) 0.327577 + 0.315870i 0.0121996 + 0.0117636i
\(722\) 12.1309 3.94158i 0.451467 0.146691i
\(723\) 5.23554 + 24.6313i 0.194712 + 0.916047i
\(724\) 4.43362 + 9.95808i 0.164774 + 0.370089i
\(725\) 35.8421 + 20.6935i 1.33114 + 0.768536i
\(726\) −3.00842 10.5806i −0.111653 0.392683i
\(727\) 9.15827i 0.339661i −0.985473 0.169831i \(-0.945678\pi\)
0.985473 0.169831i \(-0.0543221\pi\)
\(728\) 0.856284 + 1.26747i 0.0317360 + 0.0469756i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) −0.903166 + 1.00307i −0.0334277 + 0.0371252i
\(731\) −39.7455 + 4.17743i −1.47004 + 0.154508i
\(732\) 8.37284 0.880021i 0.309469 0.0325265i
\(733\) −24.5197 + 27.2318i −0.905654 + 1.00583i 0.0942928 + 0.995545i \(0.469941\pi\)
−0.999947 + 0.0102865i \(0.996726\pi\)
\(734\) 9.44127 29.0572i 0.348484 1.07252i
\(735\) 0.239920 + 0.956243i 0.00884957 + 0.0352715i
\(736\) 6.42300i 0.236755i
\(737\) −2.05633 23.8098i −0.0757459 0.877046i
\(738\) 7.99635 + 4.61670i 0.294350 + 0.169943i
\(739\) 12.7730 + 28.6886i 0.469862 + 1.05533i 0.980677 + 0.195636i \(0.0626772\pi\)
−0.510815 + 0.859691i \(0.670656\pi\)
\(740\) −0.0132389 0.0622840i −0.000486670 0.00228960i
\(741\) −1.37403 + 0.446449i −0.0504762 + 0.0164007i
\(742\) 30.7942 8.85474i 1.13049 0.325068i
\(743\) 24.2171 + 33.3320i 0.888439 + 1.22283i 0.974011 + 0.226500i \(0.0727283\pi\)
−0.0855719 + 0.996332i \(0.527272\pi\)
\(744\) 5.47365 + 4.92849i 0.200674 + 0.180687i
\(745\) −1.04226 1.15754i −0.0381854 0.0424092i
\(746\) 8.30191 3.69625i 0.303955 0.135329i
\(747\) 3.63313 + 6.29276i 0.132929 + 0.230240i
\(748\) −6.02864 10.9046i −0.220429 0.398712i
\(749\) −3.19077 18.0179i −0.116588 0.658360i
\(750\) 0.826196 1.13716i 0.0301684 0.0415232i
\(751\) −16.2592 + 3.45600i −0.593307 + 0.126111i −0.494773 0.869022i \(-0.664749\pi\)
−0.0985343 + 0.995134i \(0.531415\pi\)
\(752\) 1.31427 6.18315i 0.0479265 0.225476i
\(753\) 0.311483 + 2.96356i 0.0113511 + 0.107998i
\(754\) −4.38916 1.95418i −0.159844 0.0711670i
\(755\) −0.489772 1.50736i −0.0178246 0.0548586i
\(756\) −0.992928 2.45236i −0.0361124 0.0891916i
\(757\) 10.5560 + 7.66937i 0.383664 + 0.278748i 0.762854 0.646571i \(-0.223797\pi\)
−0.379190 + 0.925319i \(0.623797\pi\)
\(758\) −31.2872 + 18.0637i −1.13640 + 0.656102i
\(759\) 20.3788 6.20557i 0.739703 0.225248i
\(760\) −0.175977 + 0.304800i −0.00638334 + 0.0110563i
\(761\) 5.63492 53.6127i 0.204266 1.94346i −0.109565 0.993980i \(-0.534946\pi\)
0.313831 0.949479i \(-0.398388\pi\)
\(762\) −3.61262 1.17381i −0.130871 0.0425227i
\(763\) −3.92384 2.44786i −0.142053 0.0886185i
\(764\) −2.90457 + 2.11029i −0.105084 + 0.0763478i
\(765\) −0.215212 + 0.483374i −0.00778101 + 0.0174764i
\(766\) −22.1221 4.70219i −0.799303 0.169897i
\(767\) −4.47222 + 4.02681i −0.161483 + 0.145400i
\(768\) −0.994522 0.104528i −0.0358867 0.00377185i
\(769\) 22.4354 0.809043 0.404521 0.914529i \(-0.367438\pi\)
0.404521 + 0.914529i \(0.367438\pi\)
\(770\) −0.0642156 1.23420i −0.00231417 0.0444774i
\(771\) −3.73909 −0.134660
\(772\) 5.24555 + 0.551329i 0.188791 + 0.0198428i
\(773\) −3.41640 + 3.07614i −0.122880 + 0.110641i −0.728280 0.685280i \(-0.759680\pi\)
0.605400 + 0.795921i \(0.293013\pi\)
\(774\) 10.4052 + 2.21170i 0.374008 + 0.0794979i
\(775\) −14.9197 + 33.5102i −0.535932 + 1.20372i
\(776\) 14.5632 10.5808i 0.522787 0.379827i
\(777\) 0.0408626 1.19548i 0.00146594 0.0428875i
\(778\) 24.4599 + 7.94751i 0.876931 + 0.284932i
\(779\) 2.41187 22.9474i 0.0864142 0.822176i
\(780\) −0.0407125 + 0.0705162i −0.00145774 + 0.00252488i
\(781\) −10.9434 + 31.6672i −0.391586 + 1.13314i
\(782\) 20.8975 12.0652i 0.747295 0.431451i
\(783\) 6.72322 + 4.88470i 0.240268 + 0.174565i
\(784\) 6.18548 + 3.27716i 0.220910 + 0.117042i
\(785\) 0.322010 + 0.991045i 0.0114930 + 0.0353719i
\(786\) −11.2939 5.02835i −0.402839 0.179355i
\(787\) −0.655997 6.24140i −0.0233838 0.222482i −0.999973 0.00736837i \(-0.997655\pi\)
0.976589 0.215113i \(-0.0690121\pi\)
\(788\) 0.831516 3.91197i 0.0296215 0.139358i
\(789\) −7.63965 + 1.62386i −0.271979 + 0.0578109i
\(790\) 1.01474 1.39667i 0.0361027 0.0496912i
\(791\) 3.55359 9.78591i 0.126351 0.347947i
\(792\) 0.629210 + 3.25639i 0.0223580 + 0.115711i
\(793\) −2.43366 4.21522i −0.0864218 0.149687i
\(794\) 13.7812 6.13580i 0.489077 0.217751i
\(795\) 1.14132 + 1.26757i 0.0404785 + 0.0449560i
\(796\) 10.4313 + 9.39239i 0.369728 + 0.332904i
\(797\) −23.8572 32.8366i −0.845066 1.16313i −0.984928 0.172962i \(-0.944666\pi\)
0.139863 0.990171i \(-0.455334\pi\)
\(798\) −4.58929 + 4.75939i −0.162459 + 0.168480i
\(799\) −22.5860 + 7.33862i −0.799034 + 0.259622i
\(800\) −1.03543 4.87134i −0.0366081 0.172228i
\(801\) −4.63857 10.4184i −0.163896 0.368116i
\(802\) 13.0732 + 7.54783i 0.461632 + 0.266523i
\(803\) 29.2724 12.3869i 1.03300 0.437123i
\(804\) 7.20565i 0.254124i
\(805\) 2.38744 0.168719i 0.0841460 0.00594655i
\(806\) 1.31588 4.04987i 0.0463500 0.142651i
\(807\) 12.0012 13.3287i 0.422462 0.469192i
\(808\) 14.4838 1.52231i 0.509538 0.0535546i
\(809\) −47.2566 + 4.96686i −1.66145 + 0.174626i −0.888195 0.459467i \(-0.848040\pi\)
−0.773257 + 0.634093i \(0.781374\pi\)
\(810\) 0.0942405 0.104665i 0.00331127 0.00367754i
\(811\) 7.94381 24.4485i 0.278945 0.858504i −0.709204 0.705004i \(-0.750945\pi\)
0.988149 0.153501i \(-0.0490547\pi\)
\(812\) −21.9324 + 1.54995i −0.769678 + 0.0543926i
\(813\) 1.23785i 0.0434132i
\(814\) −0.338940 + 1.46067i −0.0118798 + 0.0511966i
\(815\) −0.499883 0.288607i −0.0175101 0.0101095i
\(816\) 1.52806 + 3.43208i 0.0534928 + 0.120147i
\(817\) −5.52694 26.0022i −0.193363 0.909702i
\(818\) −16.3585 + 5.31519i −0.571961 + 0.185841i
\(819\) −1.06174 + 1.10109i −0.0371003 + 0.0384753i
\(820\) −0.764375 1.05207i −0.0266931 0.0367399i
\(821\) −2.18928 1.97124i −0.0764065 0.0687967i 0.630043 0.776561i \(-0.283037\pi\)
−0.706449 + 0.707764i \(0.749704\pi\)
\(822\) −0.900393 0.999987i −0.0314048 0.0348786i
\(823\) 13.9846 6.22636i 0.487474 0.217037i −0.148256 0.988949i \(-0.547366\pi\)
0.635730 + 0.771912i \(0.280699\pi\)
\(824\) 0.0859985 + 0.148954i 0.00299590 + 0.00518905i
\(825\) −14.4553 + 7.99164i −0.503269 + 0.278233i
\(826\) −9.40018 + 25.8863i −0.327074 + 0.900699i
\(827\) −9.11098 + 12.5402i −0.316820 + 0.436065i −0.937493 0.348004i \(-0.886859\pi\)
0.620673 + 0.784069i \(0.286859\pi\)
\(828\) −6.28264 + 1.33542i −0.218337 + 0.0464089i
\(829\) 3.73065 17.5513i 0.129571 0.609582i −0.864664 0.502351i \(-0.832468\pi\)
0.994234 0.107231i \(-0.0341983\pi\)
\(830\) −0.106972 1.01777i −0.00371306 0.0353275i
\(831\) −7.48493 3.33251i −0.259649 0.115603i
\(832\) 0.178655 + 0.549842i 0.00619373 + 0.0190623i
\(833\) −0.956630 26.2807i −0.0331452 0.910573i
\(834\) 2.88987 + 2.09961i 0.100068 + 0.0727036i
\(835\) 0.355446 0.205217i 0.0123007 0.00710182i
\(836\) 6.79451 4.74628i 0.234993 0.164153i
\(837\) −3.68276 + 6.37872i −0.127295 + 0.220481i
\(838\) 0.718659 6.83758i 0.0248256 0.236200i
\(839\) 6.48355 + 2.10663i 0.223837 + 0.0727290i 0.418788 0.908084i \(-0.362455\pi\)
−0.194951 + 0.980813i \(0.562455\pi\)
\(840\) −0.0127294 + 0.372411i −0.000439205 + 0.0128494i
\(841\) 32.4108 23.5479i 1.11762 0.811995i
\(842\) 9.58122 21.5198i 0.330191 0.741620i
\(843\) 3.02948 + 0.643937i 0.104341 + 0.0221784i
\(844\) −11.0677 + 9.96543i −0.380967 + 0.343024i
\(845\) −1.77408 0.186463i −0.0610300 0.00641452i
\(846\) 6.32129 0.217330
\(847\) −10.9425 + 26.9678i −0.375989 + 0.926624i
\(848\) 12.1107 0.415885
\(849\) −0.840434 0.0883332i −0.0288436 0.00303159i
\(850\) −13.9041 + 12.5193i −0.476908 + 0.429410i
\(851\) −2.84045 0.603757i −0.0973695 0.0206965i
\(852\) 4.10888 9.22870i 0.140768 0.316170i
\(853\) −36.4229 + 26.4628i −1.24710 + 0.906069i −0.998050 0.0624225i \(-0.980117\pi\)
−0.249047 + 0.968491i \(0.580117\pi\)
\(854\) −18.8985 11.7897i −0.646695 0.403436i
\(855\) −0.334727 0.108759i −0.0114474 0.00371950i
\(856\) 0.722928 6.87820i 0.0247092 0.235092i
\(857\) 0.0822897 0.142530i 0.00281096 0.00486873i −0.864617 0.502432i \(-0.832439\pi\)
0.867427 + 0.497564i \(0.165772\pi\)
\(858\) 1.57192 1.09806i 0.0536646 0.0374872i
\(859\) 47.0440 27.1609i 1.60512 0.926717i 0.614679 0.788777i \(-0.289285\pi\)
0.990441 0.137940i \(-0.0440480\pi\)
\(860\) −1.21208 0.880628i −0.0413316 0.0300292i
\(861\) −9.16809 22.6436i −0.312448 0.771693i
\(862\) 0.357628 + 1.10067i 0.0121809 + 0.0374888i
\(863\) 39.0594 + 17.3904i 1.32960 + 0.591975i 0.943772 0.330597i \(-0.107250\pi\)
0.385826 + 0.922572i \(0.373917\pi\)
\(864\) −0.104528 0.994522i −0.00355613 0.0338343i
\(865\) −0.576690 + 2.71311i −0.0196081 + 0.0922486i
\(866\) 18.6549 3.96522i 0.633919 0.134744i
\(867\) −1.69628 + 2.33473i −0.0576088 + 0.0792917i
\(868\) −3.39812 19.1888i −0.115340 0.651309i
\(869\) −35.5789 + 19.6699i −1.20693 + 0.667254i
\(870\) −0.585216 1.01362i −0.0198407 0.0343651i
\(871\) 3.80571 1.69441i 0.128951 0.0574129i
\(872\) −1.16964 1.29902i −0.0396091 0.0439903i
\(873\) 13.3774 + 12.0451i 0.452757 + 0.407664i
\(874\) 9.43441 + 12.9854i 0.319124 + 0.439236i
\(875\) −3.57407 + 1.02771i −0.120826 + 0.0347428i
\(876\) −9.11458 + 2.96151i −0.307953 + 0.100060i
\(877\) 5.54458 + 26.0852i 0.187227 + 0.880835i 0.967001 + 0.254773i \(0.0820008\pi\)
−0.779774 + 0.626061i \(0.784666\pi\)
\(878\) −1.02652 2.30560i −0.0346433 0.0778102i
\(879\) −18.7733 10.8388i −0.633209 0.365583i
\(880\) 0.105585 0.455024i 0.00355928 0.0153389i
\(881\) 52.5710i 1.77116i 0.464485 + 0.885581i \(0.346239\pi\)
−0.464485 + 0.885581i \(0.653761\pi\)
\(882\) −1.91952 + 6.73168i −0.0646335 + 0.226667i
\(883\) 4.24279 13.0580i 0.142781 0.439435i −0.853938 0.520375i \(-0.825792\pi\)
0.996719 + 0.0809397i \(0.0257921\pi\)
\(884\) 1.45335 1.61411i 0.0488813 0.0542882i
\(885\) −1.45801 + 0.153243i −0.0490103 + 0.00515119i
\(886\) 14.5314 1.52731i 0.488193 0.0513111i
\(887\) −9.45673 + 10.5028i −0.317526 + 0.352648i −0.880687 0.473699i \(-0.842918\pi\)
0.563161 + 0.826347i \(0.309585\pi\)
\(888\) 0.139710 0.429983i 0.00468836 0.0144293i
\(889\) 5.62603 + 8.32765i 0.188691 + 0.279300i
\(890\) 1.60619i 0.0538397i
\(891\) −3.05441 + 1.29250i −0.102327 + 0.0433005i
\(892\) 9.69583 + 5.59789i 0.324640 + 0.187431i
\(893\) −6.42506 14.4309i −0.215006 0.482912i
\(894\) −2.29941 10.8179i −0.0769038 0.361804i
\(895\) 0.163793 0.0532195i 0.00547499 0.00177893i
\(896\) 1.90455 + 1.83649i 0.0636266 + 0.0613527i
\(897\) 2.18267 + 3.00419i 0.0728772 + 0.100307i
\(898\) −28.2475 25.4342i −0.942632 0.848750i
\(899\) 40.9575 + 45.4879i 1.36601 + 1.51711i
\(900\) 4.54961 2.02562i 0.151654 0.0675205i
\(901\) −22.7493 39.4029i −0.757889 1.31270i
\(902\) 5.80974 + 30.0675i 0.193443 + 1.00114i
\(903\) −18.1070 21.5467i −0.602563 0.717030i
\(904\) 2.31296 3.18352i 0.0769279 0.105882i
\(905\) 1.50168 0.319191i 0.0499174 0.0106103i
\(906\) 2.33972 11.0075i 0.0777320 0.365700i
\(907\) 0.167461 + 1.59328i 0.00556045 + 0.0529041i 0.996950 0.0780394i \(-0.0248660\pi\)
−0.991390 + 0.130944i \(0.958199\pi\)
\(908\) 7.40828 + 3.29838i 0.245852 + 0.109461i
\(909\) 4.50039 + 13.8508i 0.149269 + 0.459401i
\(910\) 0.199684 0.0808493i 0.00661946 0.00268013i
\(911\) −32.6022 23.6869i −1.08016 0.784782i −0.102449 0.994738i \(-0.532668\pi\)
−0.977711 + 0.209957i \(0.932668\pi\)
\(912\) −2.16416 + 1.24948i −0.0716624 + 0.0413743i
\(913\) −7.87142 + 22.7777i −0.260506 + 0.753832i
\(914\) 19.4015 33.6044i 0.641746 1.11154i
\(915\) 0.123942 1.17923i 0.00409741 0.0389842i
\(916\) 21.5989 + 7.01791i 0.713648 + 0.231878i
\(917\) 15.3771 + 28.8686i 0.507795 + 0.953324i
\(918\) −3.03938 + 2.20824i −0.100314 + 0.0728826i
\(919\) −20.5161 + 46.0798i −0.676762 + 1.52003i 0.168512 + 0.985700i \(0.446104\pi\)
−0.845274 + 0.534333i \(0.820563\pi\)
\(920\) 0.884848 + 0.188080i 0.0291726 + 0.00620082i
\(921\) 7.77761 7.00299i 0.256281 0.230757i
\(922\) 30.6739 + 3.22396i 1.01019 + 0.106175i
\(923\) −5.84039 −0.192239
\(924\) 3.98669 7.81705i 0.131153 0.257162i
\(925\) 2.25159 0.0740318
\(926\) −19.1922 2.01719i −0.630696 0.0662889i
\(927\) −0.127819 + 0.115089i −0.00419812 + 0.00378000i
\(928\) −8.12875 1.72782i −0.266839 0.0567185i
\(929\) −3.93271 + 8.83302i −0.129028 + 0.289802i −0.966495 0.256687i \(-0.917369\pi\)
0.837467 + 0.546489i \(0.184036\pi\)
\(930\) 0.839242 0.609745i 0.0275198 0.0199943i
\(931\) 17.3188 2.46011i 0.567601 0.0806267i
\(932\) 20.8399 + 6.77129i 0.682634 + 0.221801i
\(933\) 0.764497 7.27371i 0.0250285 0.238130i
\(934\) −0.893045 + 1.54680i −0.0292213 + 0.0506128i
\(935\) −1.67878 + 0.511208i −0.0549020 + 0.0167183i
\(936\) −0.500682 + 0.289069i −0.0163653 + 0.00944852i
\(937\) −0.0416561 0.0302649i −0.00136084 0.000988711i 0.587105 0.809511i \(-0.300268\pi\)
−0.588465 + 0.808522i \(0.700268\pi\)
\(938\) 11.7261 15.0316i 0.382870 0.490799i
\(939\) −2.74066 8.43489i −0.0894381 0.275262i
\(940\) −0.813321 0.362114i −0.0265276 0.0118109i
\(941\) −2.45546 23.3622i −0.0800458 0.761585i −0.958756 0.284230i \(-0.908262\pi\)
0.878710 0.477355i \(-0.158405\pi\)
\(942\) −1.53829 + 7.23710i −0.0501203 + 0.235798i
\(943\) −58.0101 + 12.3304i −1.88907 + 0.401534i
\(944\) −6.11839 + 8.42124i −0.199137 + 0.274088i
\(945\) −0.366919 + 0.0649773i −0.0119359 + 0.00211371i
\(946\) 17.0703 + 30.8767i 0.555002 + 1.00389i
\(947\) 4.01472 + 6.95369i 0.130461 + 0.225965i 0.923854 0.382744i \(-0.125021\pi\)
−0.793393 + 0.608709i \(0.791688\pi\)
\(948\) 11.1980 4.98565i 0.363693 0.161926i
\(949\) 3.70743 + 4.11752i 0.120348 + 0.133660i
\(950\) −9.24858 8.32746i −0.300064 0.270179i
\(951\) 2.64844 + 3.64526i 0.0858815 + 0.118206i
\(952\) 2.39752 9.64628i 0.0777040 0.312638i
\(953\) 8.02892 2.60875i 0.260082 0.0845058i −0.176074 0.984377i \(-0.556340\pi\)
0.436156 + 0.899871i \(0.356340\pi\)
\(954\) 2.51797 + 11.8461i 0.0815222 + 0.383532i
\(955\) 0.205667 + 0.461935i 0.00665522 + 0.0149479i
\(956\) −3.40941 1.96842i −0.110268 0.0636633i
\(957\) 2.37159 + 27.4601i 0.0766626 + 0.887659i
\(958\) 3.65000i 0.117926i
\(959\) 0.250969 + 3.55131i 0.00810420 + 0.114678i
\(960\) −0.0435220 + 0.133947i −0.00140467 + 0.00432312i
\(961\) −15.5578 + 17.2787i −0.501866 + 0.557378i
\(962\) −0.259951 + 0.0273219i −0.00838115 + 0.000880895i
\(963\) 6.87820 0.722928i 0.221647 0.0232960i
\(964\) 16.8497 18.7135i 0.542694 0.602723i
\(965\) 0.229554 0.706495i 0.00738961 0.0227429i
\(966\) 15.2793 + 7.43824i 0.491603 + 0.239321i
\(967\) 19.5969i 0.630194i 0.949059 + 0.315097i \(0.102037\pi\)
−0.949059 + 0.315097i \(0.897963\pi\)
\(968\) −6.79160 + 8.65299i −0.218290 + 0.278118i
\(969\) 8.13047 + 4.69413i 0.261188 + 0.150797i
\(970\) −1.03119 2.31609i −0.0331095 0.0743651i
\(971\) −11.5219 54.2061i −0.369754 1.73955i −0.632381 0.774658i \(-0.717922\pi\)
0.262627 0.964897i \(-0.415411\pi\)
\(972\) 0.951057 0.309017i 0.0305052 0.00991172i
\(973\) −2.61171 9.08278i −0.0837276 0.291181i
\(974\) −7.96356 10.9609i −0.255169 0.351210i
\(975\) −2.13968 1.92658i −0.0685246 0.0616998i
\(976\) −5.63338 6.25651i −0.180320 0.200266i
\(977\) −43.2276 + 19.2462i −1.38297 + 0.615739i −0.957289 0.289133i \(-0.906633\pi\)
−0.425683 + 0.904872i \(0.639966\pi\)
\(978\) −2.04918 3.54929i −0.0655257 0.113494i
\(979\) 16.0233 34.2623i 0.512108 1.09503i
\(980\) 0.632595 0.756164i 0.0202075 0.0241548i
\(981\) 1.02745 1.41416i 0.0328040 0.0451508i
\(982\) 8.88550 1.88867i 0.283548 0.0602700i
\(983\) 10.2419 48.1841i 0.326664 1.53684i −0.441901 0.897064i \(-0.645696\pi\)
0.768565 0.639771i \(-0.220971\pi\)
\(984\) −0.965152 9.18281i −0.0307679 0.292737i
\(985\) −0.514575 0.229103i −0.0163957 0.00729984i
\(986\) 9.64781 + 29.6929i 0.307249 + 0.945615i
\(987\) −13.1867 10.2869i −0.419738 0.327436i
\(988\) 1.16882 + 0.849197i 0.0371851 + 0.0270166i
\(989\) −59.1719 + 34.1629i −1.88156 + 1.08632i
\(990\) 0.467033 + 0.00867320i 0.0148433 + 0.000275652i
\(991\) −12.5992 + 21.8225i −0.400228 + 0.693215i −0.993753 0.111600i \(-0.964402\pi\)
0.593525 + 0.804815i \(0.297736\pi\)
\(992\) 0.769906 7.32517i 0.0244445 0.232574i
\(993\) 28.8741 + 9.38175i 0.916290 + 0.297721i
\(994\) −23.5898 + 12.5653i −0.748222 + 0.398546i
\(995\) 1.59937 1.16201i 0.0507035 0.0368382i
\(996\) 2.95545 6.63805i 0.0936470 0.210335i
\(997\) −40.8607 8.68520i −1.29407 0.275063i −0.491111 0.871097i \(-0.663409\pi\)
−0.802959 + 0.596034i \(0.796742\pi\)
\(998\) 3.85011 3.46666i 0.121873 0.109735i
\(999\) 0.449635 + 0.0472585i 0.0142258 + 0.00149519i
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 462.2.ba.b.73.3 yes 64
7.5 odd 6 462.2.ba.a.271.7 64
11.8 odd 10 462.2.ba.a.283.7 yes 64
77.19 even 30 inner 462.2.ba.b.19.3 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.ba.a.271.7 64 7.5 odd 6
462.2.ba.a.283.7 yes 64 11.8 odd 10
462.2.ba.b.19.3 yes 64 77.19 even 30 inner
462.2.ba.b.73.3 yes 64 1.1 even 1 trivial