Properties

Label 304.2.v.a.197.34
Level $304$
Weight $2$
Character 304.197
Analytic conductor $2.427$
Analytic rank $0$
Dimension $152$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [304,2,Mod(45,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.v (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(152\)
Relative dimension: \(38\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 197.34
Character \(\chi\) \(=\) 304.197
Dual form 304.2.v.a.125.34

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.32483 - 0.494789i) q^{2} +(0.514836 + 0.137950i) q^{3} +(1.51037 - 1.31103i) q^{4} +(0.425723 - 1.58882i) q^{5} +(0.750327 - 0.0719746i) q^{6} +0.191074i q^{7} +(1.35230 - 2.48421i) q^{8} +(-2.35205 - 1.35796i) q^{9} +O(q^{10})\) \(q+(1.32483 - 0.494789i) q^{2} +(0.514836 + 0.137950i) q^{3} +(1.51037 - 1.31103i) q^{4} +(0.425723 - 1.58882i) q^{5} +(0.750327 - 0.0719746i) q^{6} +0.191074i q^{7} +(1.35230 - 2.48421i) q^{8} +(-2.35205 - 1.35796i) q^{9} +(-0.222119 - 2.31556i) q^{10} +(-2.27261 - 2.27261i) q^{11} +(0.958447 - 0.466608i) q^{12} +(1.44896 + 5.40759i) q^{13} +(0.0945412 + 0.253141i) q^{14} +(0.438354 - 0.759252i) q^{15} +(0.562419 - 3.96026i) q^{16} +(3.39065 + 5.87278i) q^{17} +(-3.78798 - 0.635298i) q^{18} +(1.41338 + 4.12339i) q^{19} +(-1.43999 - 2.95783i) q^{20} +(-0.0263586 + 0.0983716i) q^{21} +(-4.13530 - 1.88637i) q^{22} +(-0.00874195 - 0.00504717i) q^{23} +(1.03891 - 1.09241i) q^{24} +(1.98702 + 1.14721i) q^{25} +(4.59525 + 6.44723i) q^{26} +(-2.15425 - 2.15425i) q^{27} +(0.250503 + 0.288592i) q^{28} +(-1.55646 - 5.80879i) q^{29} +(0.205077 - 1.22278i) q^{30} -6.57597 q^{31} +(-1.21438 - 5.52497i) q^{32} +(-0.856515 - 1.48353i) q^{33} +(7.39783 + 6.10280i) q^{34} +(0.303582 + 0.0813444i) q^{35} +(-5.33278 + 1.03259i) q^{36} +(0.615729 + 0.615729i) q^{37} +(3.91270 + 4.76348i) q^{38} +2.98390i q^{39} +(-3.37124 - 3.20615i) q^{40} +(5.18775 - 2.99515i) q^{41} +(0.0137525 + 0.143368i) q^{42} +(-1.12939 + 4.21495i) q^{43} +(-6.41193 - 0.453024i) q^{44} +(-3.15887 + 3.15887i) q^{45} +(-0.0140789 - 0.00236123i) q^{46} +(-6.37448 + 11.0409i) q^{47} +(0.835871 - 1.96130i) q^{48} +6.96349 q^{49} +(3.20010 + 0.536702i) q^{50} +(0.935479 + 3.49125i) q^{51} +(9.27795 + 6.26782i) q^{52} +(-3.41532 + 0.915132i) q^{53} +(-3.91992 - 1.78812i) q^{54} +(-4.57827 + 2.64327i) q^{55} +(0.474667 + 0.258390i) q^{56} +(0.158838 + 2.31784i) q^{57} +(-4.93618 - 6.92556i) q^{58} +(2.62929 - 9.81263i) q^{59} +(-0.333323 - 1.72144i) q^{60} +(-2.33667 - 8.72057i) q^{61} +(-8.71206 + 3.25372i) q^{62} +(0.259470 - 0.449415i) q^{63} +(-4.34255 - 6.71880i) q^{64} +9.20853 q^{65} +(-1.86877 - 1.54163i) q^{66} +(0.547979 + 2.04509i) q^{67} +(12.8205 + 4.42482i) q^{68} +(-0.00380441 - 0.00380441i) q^{69} +(0.442443 - 0.0424410i) q^{70} +(-11.9185 + 6.88113i) q^{71} +(-6.55413 + 4.00661i) q^{72} +(-13.0545 + 7.53703i) q^{73} +(1.12039 + 0.511082i) q^{74} +(0.864733 + 0.864733i) q^{75} +(7.54060 + 4.37486i) q^{76} +(0.434237 - 0.434237i) q^{77} +(1.47640 + 3.95317i) q^{78} +(-6.82620 - 11.8233i) q^{79} +(-6.05270 - 2.57956i) q^{80} +(3.26197 + 5.64989i) q^{81} +(5.39094 - 6.53492i) q^{82} +(8.97442 - 8.97442i) q^{83} +(0.0891566 + 0.183134i) q^{84} +(10.7743 - 2.88695i) q^{85} +(0.589255 + 6.14292i) q^{86} -3.20528i q^{87} +(-8.71889 + 2.57237i) q^{88} +(-1.48669 - 0.858343i) q^{89} +(-2.62200 + 5.74795i) q^{90} +(-1.03325 + 0.276858i) q^{91} +(-0.0198205 + 0.00383785i) q^{92} +(-3.38554 - 0.907153i) q^{93} +(-2.98220 + 17.7814i) q^{94} +(7.15303 - 0.490184i) q^{95} +(0.136960 - 3.01197i) q^{96} +(2.48158 + 4.29822i) q^{97} +(9.22547 - 3.44546i) q^{98} +(2.25919 + 8.43141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 152 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 20 q^{8} - 8 q^{11} - 8 q^{12} - 2 q^{13} + 2 q^{14} - 20 q^{15} + 2 q^{16} - 4 q^{17} - 16 q^{18} - 12 q^{19} - 36 q^{20} + 4 q^{21} - 2 q^{22} - 10 q^{24} + 44 q^{26} - 20 q^{27} + 26 q^{28} - 2 q^{29} + 56 q^{30} - 64 q^{31} + 28 q^{32} - 4 q^{33} - 12 q^{34} + 32 q^{35} - 2 q^{36} - 8 q^{37} + 18 q^{38} - 12 q^{40} - 10 q^{42} - 2 q^{43} - 52 q^{44} - 16 q^{45} + 24 q^{46} - 4 q^{47} - 42 q^{48} - 120 q^{49} - 60 q^{50} + 2 q^{51} - 18 q^{52} - 2 q^{53} - 64 q^{54} + 60 q^{56} - 36 q^{58} - 2 q^{59} + 48 q^{60} + 30 q^{61} - 38 q^{62} + 24 q^{63} + 52 q^{64} - 16 q^{65} + 90 q^{66} - 26 q^{67} - 8 q^{68} - 84 q^{69} - 72 q^{70} + 42 q^{72} + 6 q^{74} + 112 q^{75} + 30 q^{76} + 48 q^{77} + 26 q^{78} - 12 q^{79} + 6 q^{80} + 40 q^{81} - 70 q^{82} - 48 q^{83} + 4 q^{84} + 34 q^{85} + 30 q^{86} + 12 q^{88} - 50 q^{90} + 12 q^{91} - 30 q^{92} - 8 q^{93} - 40 q^{94} - 32 q^{95} - 288 q^{96} - 4 q^{97} + 74 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32483 0.494789i 0.936799 0.349869i
\(3\) 0.514836 + 0.137950i 0.297240 + 0.0796453i 0.404357 0.914601i \(-0.367495\pi\)
−0.107117 + 0.994246i \(0.534162\pi\)
\(4\) 1.51037 1.31103i 0.755184 0.655513i
\(5\) 0.425723 1.58882i 0.190389 0.710541i −0.803023 0.595947i \(-0.796777\pi\)
0.993412 0.114594i \(-0.0365567\pi\)
\(6\) 0.750327 0.0719746i 0.306320 0.0293835i
\(7\) 0.191074i 0.0722191i 0.999348 + 0.0361096i \(0.0114965\pi\)
−0.999348 + 0.0361096i \(0.988503\pi\)
\(8\) 1.35230 2.48421i 0.478111 0.878299i
\(9\) −2.35205 1.35796i −0.784017 0.452652i
\(10\) −0.222119 2.31556i −0.0702401 0.732245i
\(11\) −2.27261 2.27261i −0.685218 0.685218i 0.275953 0.961171i \(-0.411007\pi\)
−0.961171 + 0.275953i \(0.911007\pi\)
\(12\) 0.958447 0.466608i 0.276680 0.134698i
\(13\) 1.44896 + 5.40759i 0.401869 + 1.49980i 0.809758 + 0.586764i \(0.199598\pi\)
−0.407889 + 0.913031i \(0.633735\pi\)
\(14\) 0.0945412 + 0.253141i 0.0252672 + 0.0676548i
\(15\) 0.438354 0.759252i 0.113183 0.196038i
\(16\) 0.562419 3.96026i 0.140605 0.990066i
\(17\) 3.39065 + 5.87278i 0.822353 + 1.42436i 0.903925 + 0.427690i \(0.140673\pi\)
−0.0815718 + 0.996667i \(0.525994\pi\)
\(18\) −3.78798 0.635298i −0.892835 0.149741i
\(19\) 1.41338 + 4.12339i 0.324252 + 0.945971i
\(20\) −1.43999 2.95783i −0.321991 0.661392i
\(21\) −0.0263586 + 0.0983716i −0.00575192 + 0.0214664i
\(22\) −4.13530 1.88637i −0.881648 0.402175i
\(23\) −0.00874195 0.00504717i −0.00182282 0.00105241i 0.499088 0.866551i \(-0.333668\pi\)
−0.500911 + 0.865499i \(0.667002\pi\)
\(24\) 1.03891 1.09241i 0.212067 0.222987i
\(25\) 1.98702 + 1.14721i 0.397405 + 0.229442i
\(26\) 4.59525 + 6.44723i 0.901202 + 1.26440i
\(27\) −2.15425 2.15425i −0.414585 0.414585i
\(28\) 0.250503 + 0.288592i 0.0473406 + 0.0545387i
\(29\) −1.55646 5.80879i −0.289027 1.07867i −0.945846 0.324616i \(-0.894765\pi\)
0.656818 0.754049i \(-0.271902\pi\)
\(30\) 0.205077 1.22278i 0.0374417 0.223247i
\(31\) −6.57597 −1.18108 −0.590539 0.807009i \(-0.701085\pi\)
−0.590539 + 0.807009i \(0.701085\pi\)
\(32\) −1.21438 5.52497i −0.214675 0.976686i
\(33\) −0.856515 1.48353i −0.149100 0.258249i
\(34\) 7.39783 + 6.10280i 1.26872 + 1.04662i
\(35\) 0.303582 + 0.0813444i 0.0513147 + 0.0137497i
\(36\) −5.33278 + 1.03259i −0.888796 + 0.172098i
\(37\) 0.615729 + 0.615729i 0.101225 + 0.101225i 0.755906 0.654681i \(-0.227197\pi\)
−0.654681 + 0.755906i \(0.727197\pi\)
\(38\) 3.91270 + 4.76348i 0.634724 + 0.772739i
\(39\) 2.98390i 0.477807i
\(40\) −3.37124 3.20615i −0.533041 0.506936i
\(41\) 5.18775 2.99515i 0.810191 0.467764i −0.0368312 0.999322i \(-0.511726\pi\)
0.847022 + 0.531557i \(0.178393\pi\)
\(42\) 0.0137525 + 0.143368i 0.00212205 + 0.0221221i
\(43\) −1.12939 + 4.21495i −0.172231 + 0.642774i 0.824776 + 0.565459i \(0.191301\pi\)
−0.997007 + 0.0773142i \(0.975366\pi\)
\(44\) −6.41193 0.453024i −0.966635 0.0682960i
\(45\) −3.15887 + 3.15887i −0.470896 + 0.470896i
\(46\) −0.0140789 0.00236123i −0.00207582 0.000348145i
\(47\) −6.37448 + 11.0409i −0.929814 + 1.61049i −0.146184 + 0.989257i \(0.546699\pi\)
−0.783630 + 0.621228i \(0.786634\pi\)
\(48\) 0.835871 1.96130i 0.120648 0.283089i
\(49\) 6.96349 0.994784
\(50\) 3.20010 + 0.536702i 0.452563 + 0.0759012i
\(51\) 0.935479 + 3.49125i 0.130993 + 0.488873i
\(52\) 9.27795 + 6.26782i 1.28662 + 0.869190i
\(53\) −3.41532 + 0.915132i −0.469130 + 0.125703i −0.485637 0.874161i \(-0.661412\pi\)
0.0165066 + 0.999864i \(0.494746\pi\)
\(54\) −3.91992 1.78812i −0.533433 0.243332i
\(55\) −4.57827 + 2.64327i −0.617334 + 0.356418i
\(56\) 0.474667 + 0.258390i 0.0634300 + 0.0345288i
\(57\) 0.158838 + 2.31784i 0.0210386 + 0.307006i
\(58\) −4.93618 6.92556i −0.648152 0.909370i
\(59\) 2.62929 9.81263i 0.342304 1.27750i −0.553426 0.832898i \(-0.686680\pi\)
0.895730 0.444598i \(-0.146653\pi\)
\(60\) −0.333323 1.72144i −0.0430319 0.222237i
\(61\) −2.33667 8.72057i −0.299180 1.11655i −0.937841 0.347066i \(-0.887178\pi\)
0.638661 0.769488i \(-0.279489\pi\)
\(62\) −8.71206 + 3.25372i −1.10643 + 0.413223i
\(63\) 0.259470 0.449415i 0.0326901 0.0566210i
\(64\) −4.34255 6.71880i −0.542819 0.839850i
\(65\) 9.20853 1.14218
\(66\) −1.86877 1.54163i −0.230030 0.189762i
\(67\) 0.547979 + 2.04509i 0.0669463 + 0.249847i 0.991287 0.131722i \(-0.0420506\pi\)
−0.924340 + 0.381569i \(0.875384\pi\)
\(68\) 12.8205 + 4.42482i 1.55471 + 0.536588i
\(69\) −0.00380441 0.00380441i −0.000457997 0.000457997i
\(70\) 0.442443 0.0424410i 0.0528821 0.00507268i
\(71\) −11.9185 + 6.88113i −1.41446 + 0.816640i −0.995805 0.0915037i \(-0.970833\pi\)
−0.418658 + 0.908144i \(0.637499\pi\)
\(72\) −6.55413 + 4.00661i −0.772412 + 0.472183i
\(73\) −13.0545 + 7.53703i −1.52792 + 0.882143i −0.528468 + 0.848954i \(0.677233\pi\)
−0.999449 + 0.0331896i \(0.989433\pi\)
\(74\) 1.12039 + 0.511082i 0.130243 + 0.0594121i
\(75\) 0.864733 + 0.864733i 0.0998508 + 0.0998508i
\(76\) 7.54060 + 4.37486i 0.864966 + 0.501830i
\(77\) 0.434237 0.434237i 0.0494858 0.0494858i
\(78\) 1.47640 + 3.95317i 0.167170 + 0.447609i
\(79\) −6.82620 11.8233i −0.768008 1.33023i −0.938642 0.344894i \(-0.887915\pi\)
0.170634 0.985334i \(-0.445418\pi\)
\(80\) −6.05270 2.57956i −0.676713 0.288403i
\(81\) 3.26197 + 5.64989i 0.362441 + 0.627766i
\(82\) 5.39094 6.53492i 0.595330 0.721661i
\(83\) 8.97442 8.97442i 0.985071 0.985071i −0.0148196 0.999890i \(-0.504717\pi\)
0.999890 + 0.0148196i \(0.00471739\pi\)
\(84\) 0.0891566 + 0.183134i 0.00972778 + 0.0199816i
\(85\) 10.7743 2.88695i 1.16863 0.313134i
\(86\) 0.589255 + 6.14292i 0.0635410 + 0.662408i
\(87\) 3.20528i 0.343643i
\(88\) −8.71889 + 2.57237i −0.929437 + 0.274216i
\(89\) −1.48669 0.858343i −0.157589 0.0909842i 0.419132 0.907926i \(-0.362335\pi\)
−0.576721 + 0.816941i \(0.695668\pi\)
\(90\) −2.62200 + 5.74795i −0.276383 + 0.605887i
\(91\) −1.03325 + 0.276858i −0.108314 + 0.0290226i
\(92\) −0.0198205 + 0.00383785i −0.00206643 + 0.000400124i
\(93\) −3.38554 0.907153i −0.351064 0.0940674i
\(94\) −2.98220 + 17.7814i −0.307590 + 1.83401i
\(95\) 7.15303 0.490184i 0.733885 0.0502918i
\(96\) 0.136960 3.01197i 0.0139784 0.307408i
\(97\) 2.48158 + 4.29822i 0.251966 + 0.436418i 0.964067 0.265659i \(-0.0855896\pi\)
−0.712101 + 0.702077i \(0.752256\pi\)
\(98\) 9.22547 3.44546i 0.931913 0.348044i
\(99\) 2.25919 + 8.43141i 0.227057 + 0.847388i
\(100\) 4.50515 0.872334i 0.450515 0.0872334i
\(101\) 6.61506 1.77250i 0.658223 0.176370i 0.0857793 0.996314i \(-0.472662\pi\)
0.572444 + 0.819944i \(0.305995\pi\)
\(102\) 2.96679 + 4.16247i 0.293756 + 0.412146i
\(103\) 7.75787i 0.764405i −0.924079 0.382203i \(-0.875166\pi\)
0.924079 0.382203i \(-0.124834\pi\)
\(104\) 15.3930 + 3.71319i 1.50941 + 0.364108i
\(105\) 0.145073 + 0.0837580i 0.0141577 + 0.00817395i
\(106\) −4.07193 + 2.90226i −0.395501 + 0.281892i
\(107\) −3.32392 3.32392i −0.321336 0.321336i 0.527944 0.849279i \(-0.322963\pi\)
−0.849279 + 0.527944i \(0.822963\pi\)
\(108\) −6.07798 0.429429i −0.584854 0.0413219i
\(109\) 1.96804 + 0.527335i 0.188504 + 0.0505095i 0.351836 0.936062i \(-0.385557\pi\)
−0.163332 + 0.986571i \(0.552224\pi\)
\(110\) −4.75759 + 5.76716i −0.453618 + 0.549878i
\(111\) 0.232059 + 0.401939i 0.0220261 + 0.0381503i
\(112\) 0.756703 + 0.107464i 0.0715017 + 0.0101543i
\(113\) −2.14429 −0.201718 −0.100859 0.994901i \(-0.532159\pi\)
−0.100859 + 0.994901i \(0.532159\pi\)
\(114\) 1.35728 + 2.99217i 0.127121 + 0.280242i
\(115\) −0.0117407 + 0.0117407i −0.00109482 + 0.00109482i
\(116\) −9.96630 6.73284i −0.925348 0.625129i
\(117\) 3.93525 14.6865i 0.363814 1.35777i
\(118\) −1.37182 14.3010i −0.126286 1.31652i
\(119\) −1.12213 + 0.647864i −0.102866 + 0.0593896i
\(120\) −1.29335 2.11570i −0.118066 0.193136i
\(121\) 0.670472i 0.0609520i
\(122\) −7.41054 10.3971i −0.670919 0.941313i
\(123\) 3.08402 0.826361i 0.278077 0.0745105i
\(124\) −9.93213 + 8.62127i −0.891931 + 0.774213i
\(125\) 8.48411 8.48411i 0.758841 0.758841i
\(126\) 0.121389 0.723783i 0.0108142 0.0644797i
\(127\) −0.113605 + 0.196769i −0.0100808 + 0.0174605i −0.871022 0.491244i \(-0.836542\pi\)
0.860941 + 0.508705i \(0.169876\pi\)
\(128\) −9.07755 6.75264i −0.802349 0.596855i
\(129\) −1.16290 + 2.01421i −0.102388 + 0.177341i
\(130\) 12.1998 4.55628i 1.06999 0.399612i
\(131\) −11.9927 3.21343i −1.04781 0.280759i −0.306461 0.951883i \(-0.599145\pi\)
−0.741345 + 0.671124i \(0.765812\pi\)
\(132\) −3.23860 1.11776i −0.281884 0.0972883i
\(133\) −0.787872 + 0.270060i −0.0683172 + 0.0234172i
\(134\) 1.73787 + 2.43827i 0.150129 + 0.210634i
\(135\) −4.33982 + 2.50560i −0.373512 + 0.215647i
\(136\) 19.1744 0.481293i 1.64419 0.0412705i
\(137\) 16.2088 + 9.35813i 1.38481 + 0.799519i 0.992724 0.120411i \(-0.0384213\pi\)
0.392083 + 0.919930i \(0.371755\pi\)
\(138\) −0.00692259 0.00315783i −0.000589290 0.000268812i
\(139\) 6.38980 1.71214i 0.541976 0.145222i 0.0225630 0.999745i \(-0.492817\pi\)
0.519413 + 0.854523i \(0.326151\pi\)
\(140\) 0.565164 0.275144i 0.0477651 0.0232539i
\(141\) −4.80490 + 4.80490i −0.404646 + 0.404646i
\(142\) −12.3853 + 15.0135i −1.03935 + 1.25990i
\(143\) 8.99643 15.5823i 0.752319 1.30305i
\(144\) −6.70071 + 8.55100i −0.558392 + 0.712583i
\(145\) −9.89173 −0.821464
\(146\) −13.5658 + 16.4446i −1.12272 + 1.36096i
\(147\) 3.58505 + 0.960612i 0.295690 + 0.0792299i
\(148\) 1.73721 + 0.122740i 0.142798 + 0.0100892i
\(149\) 4.20577 15.6961i 0.344550 1.28588i −0.548587 0.836093i \(-0.684834\pi\)
0.893137 0.449784i \(-0.148499\pi\)
\(150\) 1.57349 + 0.717767i 0.128475 + 0.0586054i
\(151\) 12.5151i 1.01846i 0.860629 + 0.509232i \(0.170070\pi\)
−0.860629 + 0.509232i \(0.829930\pi\)
\(152\) 12.1547 + 2.06495i 0.985874 + 0.167490i
\(153\) 18.4174i 1.48896i
\(154\) 0.360436 0.790147i 0.0290447 0.0636718i
\(155\) −2.79954 + 10.4480i −0.224864 + 0.839205i
\(156\) 3.91198 + 4.50679i 0.313209 + 0.360832i
\(157\) −9.55645 2.56064i −0.762688 0.204362i −0.143549 0.989643i \(-0.545852\pi\)
−0.619139 + 0.785282i \(0.712518\pi\)
\(158\) −14.8936 12.2864i −1.18487 0.977454i
\(159\) −1.88457 −0.149456
\(160\) −9.29516 0.422668i −0.734847 0.0334148i
\(161\) 0.000964381 0.00167036i 7.60039e−5 0.000131643i
\(162\) 7.11707 + 5.87118i 0.559170 + 0.461283i
\(163\) 5.70770 5.70770i 0.447061 0.447061i −0.447315 0.894376i \(-0.647620\pi\)
0.894376 + 0.447315i \(0.147620\pi\)
\(164\) 3.90869 11.3251i 0.305218 0.884339i
\(165\) −2.72169 + 0.729276i −0.211884 + 0.0567740i
\(166\) 7.44917 16.3301i 0.578167 1.26746i
\(167\) −3.64518 2.10454i −0.282072 0.162855i 0.352289 0.935891i \(-0.385403\pi\)
−0.634361 + 0.773037i \(0.718737\pi\)
\(168\) 0.208730 + 0.198508i 0.0161039 + 0.0153153i
\(169\) −15.8842 + 9.17075i −1.22186 + 0.705442i
\(170\) 12.8457 9.15572i 0.985217 0.702211i
\(171\) 2.27505 11.6177i 0.173977 0.888430i
\(172\) 3.82011 + 7.84678i 0.291281 + 0.598312i
\(173\) 7.07021 + 1.89446i 0.537538 + 0.144033i 0.517367 0.855764i \(-0.326912\pi\)
0.0201713 + 0.999797i \(0.493579\pi\)
\(174\) −1.58594 4.24647i −0.120230 0.321924i
\(175\) −0.219201 + 0.379668i −0.0165701 + 0.0287002i
\(176\) −10.2783 + 7.72198i −0.774756 + 0.582066i
\(177\) 2.70730 4.68918i 0.203493 0.352461i
\(178\) −2.39432 0.401562i −0.179462 0.0300983i
\(179\) 7.40496 7.40496i 0.553472 0.553472i −0.373969 0.927441i \(-0.622003\pi\)
0.927441 + 0.373969i \(0.122003\pi\)
\(180\) −0.629691 + 8.91241i −0.0469344 + 0.664292i
\(181\) −19.8214 + 5.31114i −1.47332 + 0.394774i −0.904067 0.427391i \(-0.859433\pi\)
−0.569249 + 0.822165i \(0.692766\pi\)
\(182\) −1.23190 + 0.878031i −0.0913142 + 0.0650840i
\(183\) 4.81200i 0.355713i
\(184\) −0.0243600 + 0.0148915i −0.00179584 + 0.00109782i
\(185\) 1.24041 0.716151i 0.0911968 0.0526525i
\(186\) −4.93413 + 0.473303i −0.361788 + 0.0347042i
\(187\) 5.64091 21.0522i 0.412504 1.53949i
\(188\) 4.84714 + 25.0330i 0.353514 + 1.82572i
\(189\) 0.411620 0.411620i 0.0299410 0.0299410i
\(190\) 9.23403 4.18865i 0.669907 0.303877i
\(191\) −4.98447 −0.360663 −0.180332 0.983606i \(-0.557717\pi\)
−0.180332 + 0.983606i \(0.557717\pi\)
\(192\) −1.30884 4.05813i −0.0944576 0.292870i
\(193\) 3.91454 + 6.78018i 0.281774 + 0.488048i 0.971822 0.235716i \(-0.0757437\pi\)
−0.690047 + 0.723764i \(0.742410\pi\)
\(194\) 5.41439 + 4.46656i 0.388730 + 0.320681i
\(195\) 4.74088 + 1.27031i 0.339501 + 0.0909691i
\(196\) 10.5174 9.12932i 0.751245 0.652094i
\(197\) 3.47114 + 3.47114i 0.247309 + 0.247309i 0.819865 0.572557i \(-0.194048\pi\)
−0.572557 + 0.819865i \(0.694048\pi\)
\(198\) 7.16482 + 10.0524i 0.509181 + 0.714392i
\(199\) 12.9077 + 7.45226i 0.915002 + 0.528277i 0.882037 0.471180i \(-0.156172\pi\)
0.0329651 + 0.999457i \(0.489505\pi\)
\(200\) 5.53696 3.38480i 0.391522 0.239341i
\(201\) 1.12848i 0.0795966i
\(202\) 7.88684 5.62133i 0.554916 0.395515i
\(203\) 1.10991 0.297399i 0.0779002 0.0208733i
\(204\) 5.99004 + 4.04664i 0.419387 + 0.283321i
\(205\) −2.55021 9.51750i −0.178114 0.664731i
\(206\) −3.83851 10.2779i −0.267442 0.716094i
\(207\) 0.0137077 + 0.0237424i 0.000952749 + 0.00165021i
\(208\) 22.2304 2.69693i 1.54140 0.186998i
\(209\) 6.15880 12.5829i 0.426013 0.870380i
\(210\) 0.233640 + 0.0391848i 0.0161227 + 0.00270401i
\(211\) 4.80459 + 1.28739i 0.330761 + 0.0886273i 0.420378 0.907349i \(-0.361897\pi\)
−0.0896165 + 0.995976i \(0.528564\pi\)
\(212\) −3.95862 + 5.85976i −0.271879 + 0.402450i
\(213\) −7.08531 + 1.89850i −0.485477 + 0.130083i
\(214\) −6.04828 2.75900i −0.413452 0.188602i
\(215\) 6.21598 + 3.58880i 0.423926 + 0.244754i
\(216\) −8.26479 + 2.43840i −0.562348 + 0.165912i
\(217\) 1.25650i 0.0852964i
\(218\) 2.86825 0.275134i 0.194262 0.0186344i
\(219\) −7.76067 + 2.07946i −0.524417 + 0.140517i
\(220\) −3.44948 + 9.99453i −0.232564 + 0.673831i
\(221\) −26.8447 + 26.8447i −1.80577 + 1.80577i
\(222\) 0.506315 + 0.417681i 0.0339816 + 0.0280329i
\(223\) 2.22112 + 3.84709i 0.148737 + 0.257620i 0.930761 0.365628i \(-0.119146\pi\)
−0.782024 + 0.623248i \(0.785813\pi\)
\(224\) 1.05568 0.232037i 0.0705354 0.0155036i
\(225\) −3.11572 5.39658i −0.207715 0.359772i
\(226\) −2.84083 + 1.06097i −0.188969 + 0.0705749i
\(227\) 14.8243 14.8243i 0.983922 0.983922i −0.0159510 0.999873i \(-0.505078\pi\)
0.999873 + 0.0159510i \(0.00507759\pi\)
\(228\) 3.27866 + 3.29256i 0.217134 + 0.218055i
\(229\) −0.574876 0.574876i −0.0379889 0.0379889i 0.687857 0.725846i \(-0.258552\pi\)
−0.725846 + 0.687857i \(0.758552\pi\)
\(230\) −0.00974528 + 0.0213636i −0.000642585 + 0.00140867i
\(231\) 0.283463 0.163658i 0.0186505 0.0107679i
\(232\) −16.5350 3.98868i −1.08558 0.261870i
\(233\) 6.73689 3.88955i 0.441349 0.254813i −0.262821 0.964845i \(-0.584653\pi\)
0.704170 + 0.710032i \(0.251320\pi\)
\(234\) −2.05320 21.4043i −0.134222 1.39925i
\(235\) 14.8283 + 14.8283i 0.967290 + 0.967290i
\(236\) −8.89343 18.2677i −0.578913 1.18913i
\(237\) −1.88335 7.02874i −0.122336 0.456566i
\(238\) −1.16608 + 1.41353i −0.0755860 + 0.0916257i
\(239\) 21.5037 1.39096 0.695480 0.718545i \(-0.255192\pi\)
0.695480 + 0.718545i \(0.255192\pi\)
\(240\) −2.76030 2.16302i −0.178177 0.139622i
\(241\) −4.40984 + 7.63807i −0.284063 + 0.492011i −0.972382 0.233397i \(-0.925016\pi\)
0.688319 + 0.725409i \(0.258349\pi\)
\(242\) −0.331742 0.888264i −0.0213252 0.0570998i
\(243\) 3.26550 + 12.1870i 0.209482 + 0.781798i
\(244\) −14.9621 10.1078i −0.957852 0.647087i
\(245\) 2.96452 11.0637i 0.189396 0.706835i
\(246\) 3.67694 2.62073i 0.234433 0.167092i
\(247\) −20.2497 + 13.6176i −1.28846 + 0.866467i
\(248\) −8.89270 + 16.3361i −0.564687 + 1.03734i
\(249\) 5.85837 3.38233i 0.371259 0.214347i
\(250\) 7.04218 15.4379i 0.445387 0.976377i
\(251\) −6.75563 + 1.81017i −0.426412 + 0.114257i −0.465641 0.884974i \(-0.654176\pi\)
0.0392296 + 0.999230i \(0.487510\pi\)
\(252\) −0.197300 1.01895i −0.0124287 0.0641881i
\(253\) 0.00839681 + 0.0313373i 0.000527903 + 0.00197016i
\(254\) −0.0531482 + 0.316897i −0.00333481 + 0.0198839i
\(255\) 5.94522 0.372304
\(256\) −15.3674 4.45465i −0.960461 0.278416i
\(257\) −8.53160 + 14.7772i −0.532187 + 0.921774i 0.467107 + 0.884201i \(0.345296\pi\)
−0.999294 + 0.0375737i \(0.988037\pi\)
\(258\) −0.544045 + 3.24388i −0.0338707 + 0.201955i
\(259\) −0.117650 + 0.117650i −0.00731039 + 0.00731039i
\(260\) 13.9083 12.0726i 0.862554 0.748713i
\(261\) −4.22721 + 15.7762i −0.261658 + 0.976521i
\(262\) −17.4783 + 1.67659i −1.07981 + 0.103580i
\(263\) −1.48231 + 0.855813i −0.0914032 + 0.0527717i −0.545005 0.838433i \(-0.683472\pi\)
0.453602 + 0.891205i \(0.350139\pi\)
\(264\) −4.84366 + 0.121580i −0.298106 + 0.00748272i
\(265\) 5.81591i 0.357269i
\(266\) −0.910176 + 0.747615i −0.0558065 + 0.0458392i
\(267\) −0.646995 0.646995i −0.0395954 0.0395954i
\(268\) 3.50881 + 2.37042i 0.214335 + 0.144796i
\(269\) 11.0710 + 2.96646i 0.675009 + 0.180868i 0.580010 0.814609i \(-0.303049\pi\)
0.0949988 + 0.995477i \(0.469715\pi\)
\(270\) −4.50980 + 5.46679i −0.274457 + 0.332698i
\(271\) 6.73129 + 11.6589i 0.408897 + 0.708230i 0.994766 0.102175i \(-0.0325803\pi\)
−0.585870 + 0.810405i \(0.699247\pi\)
\(272\) 25.1647 10.1249i 1.52583 0.613913i
\(273\) −0.570146 −0.0345068
\(274\) 26.1042 + 4.37804i 1.57701 + 0.264487i
\(275\) −1.90857 7.12289i −0.115091 0.429526i
\(276\) −0.0107337 0.000758374i −0.000646095 4.56488e-5i
\(277\) −15.8893 15.8893i −0.954698 0.954698i 0.0443193 0.999017i \(-0.485888\pi\)
−0.999017 + 0.0443193i \(0.985888\pi\)
\(278\) 7.61827 5.42991i 0.456914 0.325664i
\(279\) 15.4670 + 8.92988i 0.925986 + 0.534618i
\(280\) 0.612611 0.644157i 0.0366105 0.0384957i
\(281\) −11.7596 6.78944i −0.701522 0.405024i 0.106392 0.994324i \(-0.466070\pi\)
−0.807914 + 0.589300i \(0.799403\pi\)
\(282\) −3.98828 + 8.74311i −0.237499 + 0.520645i
\(283\) −6.62926 + 24.7407i −0.394069 + 1.47068i 0.429292 + 0.903166i \(0.358763\pi\)
−0.823361 + 0.567519i \(0.807903\pi\)
\(284\) −8.97992 + 26.0185i −0.532860 + 1.54391i
\(285\) 3.75025 + 0.734395i 0.222146 + 0.0435018i
\(286\) 4.20883 25.0952i 0.248873 1.48391i
\(287\) 0.572295 + 0.991244i 0.0337815 + 0.0585113i
\(288\) −4.64638 + 14.6441i −0.273790 + 0.862911i
\(289\) −14.4930 + 25.1026i −0.852530 + 1.47663i
\(290\) −13.1049 + 4.89432i −0.769546 + 0.287404i
\(291\) 0.684666 + 2.55521i 0.0401358 + 0.149789i
\(292\) −9.83588 + 28.4985i −0.575601 + 1.66775i
\(293\) 3.93766 + 3.93766i 0.230041 + 0.230041i 0.812710 0.582669i \(-0.197992\pi\)
−0.582669 + 0.812710i \(0.697992\pi\)
\(294\) 5.22490 0.501194i 0.304722 0.0292303i
\(295\) −14.4711 8.35492i −0.842543 0.486442i
\(296\) 2.36225 0.696944i 0.137303 0.0405091i
\(297\) 9.79153i 0.568162i
\(298\) −2.19434 22.8757i −0.127115 1.32516i
\(299\) 0.0146263 0.0545860i 0.000845859 0.00315679i
\(300\) 2.43975 + 0.172377i 0.140859 + 0.00995216i
\(301\) −0.805366 0.215797i −0.0464205 0.0124383i
\(302\) 6.19233 + 16.5804i 0.356329 + 0.954096i
\(303\) 3.65019 0.209698
\(304\) 17.1246 3.27829i 0.982165 0.188023i
\(305\) −14.8502 −0.850319
\(306\) −9.11274 24.4000i −0.520941 1.39486i
\(307\) −23.7003 6.35047i −1.35265 0.362441i −0.491536 0.870857i \(-0.663564\pi\)
−0.861111 + 0.508417i \(0.830231\pi\)
\(308\) 0.0865611 1.22515i 0.00493227 0.0698095i
\(309\) 1.07020 3.99403i 0.0608813 0.227212i
\(310\) 1.46064 + 15.2271i 0.0829591 + 0.864839i
\(311\) 21.4706i 1.21749i −0.793367 0.608743i \(-0.791674\pi\)
0.793367 0.608743i \(-0.208326\pi\)
\(312\) 7.41263 + 4.03514i 0.419657 + 0.228445i
\(313\) −7.22851 4.17338i −0.408579 0.235893i 0.281600 0.959532i \(-0.409135\pi\)
−0.690179 + 0.723639i \(0.742468\pi\)
\(314\) −13.9277 + 1.33600i −0.785985 + 0.0753950i
\(315\) −0.603577 0.603577i −0.0340077 0.0340077i
\(316\) −25.8108 8.90824i −1.45197 0.501127i
\(317\) 5.21151 + 19.4496i 0.292708 + 1.09240i 0.943021 + 0.332733i \(0.107971\pi\)
−0.650313 + 0.759666i \(0.725362\pi\)
\(318\) −2.49674 + 0.932465i −0.140010 + 0.0522900i
\(319\) −9.66389 + 16.7384i −0.541074 + 0.937168i
\(320\) −12.5237 + 4.03918i −0.700095 + 0.225797i
\(321\) −1.25274 2.16981i −0.0699211 0.121107i
\(322\) 0.000451170 0.00269011i 2.51427e−5 0.000149914i
\(323\) −19.4235 + 22.2814i −1.08075 + 1.23977i
\(324\) 12.3339 + 4.25689i 0.685218 + 0.236494i
\(325\) −3.32452 + 12.4073i −0.184411 + 0.688231i
\(326\) 4.73764 10.3859i 0.262394 0.575219i
\(327\) 0.940472 + 0.542982i 0.0520082 + 0.0300269i
\(328\) −0.425153 16.9378i −0.0234751 0.935233i
\(329\) −2.10963 1.21800i −0.116308 0.0671503i
\(330\) −3.24495 + 2.31283i −0.178629 + 0.127317i
\(331\) 3.64546 + 3.64546i 0.200373 + 0.200373i 0.800160 0.599787i \(-0.204748\pi\)
−0.599787 + 0.800160i \(0.704748\pi\)
\(332\) 1.78897 25.3204i 0.0981824 1.38964i
\(333\) −0.612092 2.28436i −0.0335424 0.125182i
\(334\) −5.87056 0.984576i −0.321223 0.0538736i
\(335\) 3.48256 0.190273
\(336\) 0.374753 + 0.159713i 0.0204444 + 0.00871306i
\(337\) −6.54667 11.3392i −0.356620 0.617684i 0.630774 0.775967i \(-0.282738\pi\)
−0.987394 + 0.158283i \(0.949404\pi\)
\(338\) −16.5063 + 20.0090i −0.897826 + 1.08835i
\(339\) −1.10396 0.295805i −0.0599588 0.0160659i
\(340\) 12.4882 18.4857i 0.677268 1.00253i
\(341\) 14.9446 + 14.9446i 0.809297 + 0.809297i
\(342\) −2.73427 16.5172i −0.147853 0.893150i
\(343\) 2.66806i 0.144062i
\(344\) 8.94352 + 8.50553i 0.482202 + 0.458588i
\(345\) −0.00766414 + 0.00442489i −0.000412624 + 0.000238228i
\(346\) 10.3042 0.988424i 0.553958 0.0531380i
\(347\) −0.286543 + 1.06939i −0.0153824 + 0.0574081i −0.973190 0.230001i \(-0.926127\pi\)
0.957808 + 0.287409i \(0.0927938\pi\)
\(348\) −4.20221 4.84116i −0.225262 0.259513i
\(349\) 0.152567 0.152567i 0.00816671 0.00816671i −0.703012 0.711178i \(-0.748162\pi\)
0.711178 + 0.703012i \(0.248162\pi\)
\(350\) −0.102550 + 0.611455i −0.00548151 + 0.0326837i
\(351\) 8.52787 14.7707i 0.455184 0.788401i
\(352\) −9.79628 + 15.3159i −0.522144 + 0.816342i
\(353\) 19.9451 1.06157 0.530784 0.847507i \(-0.321897\pi\)
0.530784 + 0.847507i \(0.321897\pi\)
\(354\) 1.26657 7.55193i 0.0673172 0.401381i
\(355\) 5.85891 + 21.8657i 0.310959 + 1.16051i
\(356\) −3.37076 + 0.652682i −0.178650 + 0.0345921i
\(357\) −0.667087 + 0.178745i −0.0353060 + 0.00946021i
\(358\) 6.14644 13.4742i 0.324850 0.712135i
\(359\) 9.67331 5.58489i 0.510538 0.294759i −0.222517 0.974929i \(-0.571427\pi\)
0.733055 + 0.680170i \(0.238094\pi\)
\(360\) 3.57553 + 12.1190i 0.188447 + 0.638729i
\(361\) −15.0047 + 11.6558i −0.789722 + 0.613465i
\(362\) −23.6322 + 16.8438i −1.24208 + 0.885291i
\(363\) 0.0924915 0.345183i 0.00485454 0.0181174i
\(364\) −1.19762 + 1.77277i −0.0627722 + 0.0929186i
\(365\) 6.41737 + 23.9500i 0.335901 + 1.25360i
\(366\) −2.38093 6.37510i −0.124453 0.333232i
\(367\) −8.13980 + 14.0986i −0.424894 + 0.735939i −0.996411 0.0846522i \(-0.973022\pi\)
0.571516 + 0.820591i \(0.306355\pi\)
\(368\) −0.0249047 + 0.0317818i −0.00129825 + 0.00165674i
\(369\) −16.2691 −0.846938
\(370\) 1.28899 1.56252i 0.0670116 0.0812317i
\(371\) −0.174858 0.652578i −0.00907816 0.0338802i
\(372\) −6.30271 + 3.06840i −0.326781 + 0.159089i
\(373\) −9.15640 9.15640i −0.474100 0.474100i 0.429138 0.903239i \(-0.358817\pi\)
−0.903239 + 0.429138i \(0.858817\pi\)
\(374\) −2.94312 30.6817i −0.152185 1.58651i
\(375\) 5.53830 3.19754i 0.285997 0.165120i
\(376\) 18.8077 + 30.7662i 0.969933 + 1.58665i
\(377\) 29.1563 16.8334i 1.50163 0.866964i
\(378\) 0.341663 0.748993i 0.0175732 0.0385241i
\(379\) 4.47387 + 4.47387i 0.229807 + 0.229807i 0.812612 0.582805i \(-0.198045\pi\)
−0.582805 + 0.812612i \(0.698045\pi\)
\(380\) 10.1611 10.1182i 0.521251 0.519051i
\(381\) −0.0856321 + 0.0856321i −0.00438707 + 0.00438707i
\(382\) −6.60359 + 2.46626i −0.337869 + 0.126185i
\(383\) −3.41100 5.90803i −0.174294 0.301886i 0.765623 0.643290i \(-0.222431\pi\)
−0.939917 + 0.341404i \(0.889098\pi\)
\(384\) −3.74192 4.72875i −0.190954 0.241313i
\(385\) −0.505059 0.874787i −0.0257402 0.0445833i
\(386\) 8.54087 + 7.04573i 0.434719 + 0.358618i
\(387\) 8.38011 8.38011i 0.425985 0.425985i
\(388\) 9.38317 + 3.23847i 0.476358 + 0.164409i
\(389\) −24.0747 + 6.45081i −1.22064 + 0.327069i −0.810928 0.585147i \(-0.801037\pi\)
−0.409711 + 0.912216i \(0.634370\pi\)
\(390\) 6.90941 0.662780i 0.349872 0.0335612i
\(391\) 0.0684527i 0.00346180i
\(392\) 9.41675 17.2987i 0.475618 0.873718i
\(393\) −5.73097 3.30878i −0.289089 0.166906i
\(394\) 6.31617 + 2.88120i 0.318204 + 0.145153i
\(395\) −21.6912 + 5.81214i −1.09140 + 0.292440i
\(396\) 14.4660 + 9.77267i 0.726944 + 0.491095i
\(397\) −4.80265 1.28687i −0.241038 0.0645860i 0.136277 0.990671i \(-0.456486\pi\)
−0.377316 + 0.926085i \(0.623153\pi\)
\(398\) 20.7878 + 3.48642i 1.04200 + 0.174758i
\(399\) −0.442879 + 0.0303497i −0.0221717 + 0.00151939i
\(400\) 5.66078 7.22392i 0.283039 0.361196i
\(401\) −13.8448 23.9800i −0.691379 1.19750i −0.971386 0.237505i \(-0.923670\pi\)
0.280008 0.959998i \(-0.409663\pi\)
\(402\) 0.558358 + 1.49504i 0.0278484 + 0.0745660i
\(403\) −9.52831 35.5601i −0.474639 1.77138i
\(404\) 7.66738 11.3497i 0.381466 0.564666i
\(405\) 10.3653 2.77739i 0.515058 0.138009i
\(406\) 1.32329 0.943174i 0.0656739 0.0468089i
\(407\) 2.79862i 0.138723i
\(408\) 9.93804 + 2.39731i 0.492006 + 0.118685i
\(409\) 28.9423 + 16.7098i 1.43110 + 0.826247i 0.997205 0.0747149i \(-0.0238047\pi\)
0.433897 + 0.900962i \(0.357138\pi\)
\(410\) −8.08776 11.3473i −0.399426 0.560403i
\(411\) 7.05389 + 7.05389i 0.347943 + 0.347943i
\(412\) −10.1708 11.7172i −0.501078 0.577266i
\(413\) 1.87494 + 0.502388i 0.0922596 + 0.0247209i
\(414\) 0.0299079 + 0.0246723i 0.00146989 + 0.00121258i
\(415\) −10.4381 18.0793i −0.512387 0.887480i
\(416\) 28.1172 14.5723i 1.37856 0.714468i
\(417\) 3.52589 0.172663
\(418\) 1.93349 19.7176i 0.0945700 0.964419i
\(419\) 15.0662 15.0662i 0.736032 0.736032i −0.235776 0.971808i \(-0.575763\pi\)
0.971808 + 0.235776i \(0.0757631\pi\)
\(420\) 0.328923 0.0636894i 0.0160498 0.00310772i
\(421\) −4.14179 + 15.4574i −0.201858 + 0.753346i 0.788526 + 0.615002i \(0.210845\pi\)
−0.990384 + 0.138344i \(0.955822\pi\)
\(422\) 7.00226 0.671687i 0.340865 0.0326972i
\(423\) 29.9862 17.3126i 1.45798 0.841765i
\(424\) −2.34517 + 9.72189i −0.113892 + 0.472137i
\(425\) 15.5591i 0.754728i
\(426\) −8.44749 + 6.02093i −0.409282 + 0.291715i
\(427\) 1.66627 0.446476i 0.0806366 0.0216065i
\(428\) −9.37809 0.662593i −0.453307 0.0320277i
\(429\) 6.78125 6.78125i 0.327402 0.327402i
\(430\) 10.0108 + 1.67896i 0.482765 + 0.0809666i
\(431\) −13.7848 + 23.8759i −0.663988 + 1.15006i 0.315570 + 0.948902i \(0.397804\pi\)
−0.979559 + 0.201159i \(0.935529\pi\)
\(432\) −9.74297 + 7.31980i −0.468759 + 0.352174i
\(433\) 18.2626 31.6318i 0.877647 1.52013i 0.0237306 0.999718i \(-0.492446\pi\)
0.853916 0.520410i \(-0.174221\pi\)
\(434\) −0.621700 1.66465i −0.0298426 0.0799056i
\(435\) −5.09262 1.36456i −0.244172 0.0654257i
\(436\) 3.66381 1.78368i 0.175465 0.0854230i
\(437\) 0.00845574 0.0431800i 0.000404493 0.00206558i
\(438\) −9.25269 + 6.59484i −0.442111 + 0.315114i
\(439\) 16.0073 9.24184i 0.763989 0.441089i −0.0667372 0.997771i \(-0.521259\pi\)
0.830726 + 0.556681i \(0.187926\pi\)
\(440\) 0.375204 + 14.9479i 0.0178871 + 0.712611i
\(441\) −16.3785 9.45612i −0.779928 0.450292i
\(442\) −22.2823 + 48.8471i −1.05986 + 2.32342i
\(443\) 22.0126 5.89826i 1.04585 0.280235i 0.305315 0.952252i \(-0.401238\pi\)
0.740536 + 0.672017i \(0.234572\pi\)
\(444\) 0.877447 + 0.302839i 0.0416418 + 0.0143721i
\(445\) −1.99667 + 1.99667i −0.0946513 + 0.0946513i
\(446\) 4.84611 + 3.99777i 0.229470 + 0.189300i
\(447\) 4.33056 7.50074i 0.204828 0.354773i
\(448\) 1.28379 0.829748i 0.0606532 0.0392019i
\(449\) −4.67297 −0.220531 −0.110266 0.993902i \(-0.535170\pi\)
−0.110266 + 0.993902i \(0.535170\pi\)
\(450\) −6.79798 5.60795i −0.320460 0.264361i
\(451\) −18.5966 4.98293i −0.875678 0.234637i
\(452\) −3.23867 + 2.81123i −0.152334 + 0.132229i
\(453\) −1.72645 + 6.44322i −0.0811159 + 0.302729i
\(454\) 12.3048 26.9746i 0.577493 1.26598i
\(455\) 1.75951i 0.0824871i
\(456\) 5.97280 + 2.73984i 0.279702 + 0.128305i
\(457\) 18.1710i 0.850004i −0.905193 0.425002i \(-0.860273\pi\)
0.905193 0.425002i \(-0.139727\pi\)
\(458\) −1.04606 0.477172i −0.0488790 0.0222968i
\(459\) 5.34712 19.9557i 0.249582 0.931453i
\(460\) −0.00234040 + 0.0331251i −0.000109122 + 0.00154446i
\(461\) 19.1595 + 5.13378i 0.892349 + 0.239104i 0.675727 0.737152i \(-0.263830\pi\)
0.216621 + 0.976256i \(0.430496\pi\)
\(462\) 0.294566 0.357074i 0.0137044 0.0166126i
\(463\) 20.1714 0.937443 0.468721 0.883346i \(-0.344715\pi\)
0.468721 + 0.883346i \(0.344715\pi\)
\(464\) −23.8797 + 2.89702i −1.10859 + 0.134491i
\(465\) −2.88260 + 4.99282i −0.133678 + 0.231536i
\(466\) 7.00076 8.48634i 0.324304 0.393122i
\(467\) −18.8219 + 18.8219i −0.870974 + 0.870974i −0.992579 0.121605i \(-0.961196\pi\)
0.121605 + 0.992579i \(0.461196\pi\)
\(468\) −13.3108 27.3413i −0.615291 1.26385i
\(469\) −0.390763 + 0.104705i −0.0180437 + 0.00483480i
\(470\) 26.9819 + 12.3081i 1.24458 + 0.567731i
\(471\) −4.56676 2.63662i −0.210425 0.121489i
\(472\) −20.8210 19.8013i −0.958364 0.911431i
\(473\) 12.1456 7.01227i 0.558456 0.322425i
\(474\) −5.97287 8.38005i −0.274343 0.384909i
\(475\) −1.92197 + 9.81471i −0.0881860 + 0.450330i
\(476\) −0.845467 + 2.44966i −0.0387519 + 0.112280i
\(477\) 9.27571 + 2.48542i 0.424706 + 0.113800i
\(478\) 28.4889 10.6398i 1.30305 0.486654i
\(479\) −9.74966 + 16.8869i −0.445474 + 0.771583i −0.998085 0.0618562i \(-0.980298\pi\)
0.552612 + 0.833439i \(0.313631\pi\)
\(480\) −4.72717 1.49987i −0.215765 0.0684594i
\(481\) −2.43744 + 4.22177i −0.111138 + 0.192496i
\(482\) −2.06307 + 12.3011i −0.0939704 + 0.560300i
\(483\) 0.000726923 0 0.000726923i 3.30762e−5 0 3.30762e-5i
\(484\) −0.879007 1.01266i −0.0399549 0.0460300i
\(485\) 7.88555 2.11293i 0.358064 0.0959430i
\(486\) 10.3563 + 14.5300i 0.469769 + 0.659096i
\(487\) 24.2969i 1.10100i −0.834836 0.550499i \(-0.814437\pi\)
0.834836 0.550499i \(-0.185563\pi\)
\(488\) −24.8236 5.98809i −1.12371 0.271068i
\(489\) 3.72590 2.15115i 0.168491 0.0972783i
\(490\) −1.54672 16.1244i −0.0698737 0.728426i
\(491\) −8.50995 + 31.7596i −0.384049 + 1.43329i 0.455612 + 0.890178i \(0.349420\pi\)
−0.839661 + 0.543111i \(0.817246\pi\)
\(492\) 3.57462 5.29134i 0.161156 0.238552i
\(493\) 28.8363 28.8363i 1.29872 1.29872i
\(494\) −20.0896 + 28.0604i −0.903874 + 1.26250i
\(495\) 14.3578 0.645333
\(496\) −3.69845 + 26.0426i −0.166065 + 1.16935i
\(497\) −1.31480 2.27731i −0.0589770 0.102151i
\(498\) 6.08782 7.37968i 0.272802 0.330692i
\(499\) 36.5500 + 9.79354i 1.63620 + 0.438419i 0.955704 0.294330i \(-0.0950966\pi\)
0.680498 + 0.732749i \(0.261763\pi\)
\(500\) 1.69123 23.9370i 0.0756340 1.07050i
\(501\) −1.58635 1.58635i −0.0708727 0.0708727i
\(502\) −8.05444 + 5.74078i −0.359487 + 0.256224i
\(503\) −4.74144 2.73747i −0.211410 0.122058i 0.390556 0.920579i \(-0.372283\pi\)
−0.601967 + 0.798521i \(0.705616\pi\)
\(504\) −0.765558 1.25232i −0.0341006 0.0557829i
\(505\) 11.2647i 0.501274i
\(506\) 0.0266297 + 0.0373621i 0.00118384 + 0.00166095i
\(507\) −9.44286 + 2.53021i −0.419372 + 0.112370i
\(508\) 0.0863848 + 0.446133i 0.00383271 + 0.0197940i
\(509\) −7.85157 29.3024i −0.348015 1.29881i −0.889051 0.457809i \(-0.848634\pi\)
0.541036 0.840999i \(-0.318032\pi\)
\(510\) 7.87643 2.94163i 0.348774 0.130258i
\(511\) −1.44013 2.49438i −0.0637076 0.110345i
\(512\) −22.5633 + 1.70193i −0.997167 + 0.0752156i
\(513\) 5.83803 11.9276i 0.257755 0.526615i
\(514\) −3.99137 + 23.7986i −0.176052 + 1.04971i
\(515\) −12.3258 3.30270i −0.543141 0.145534i
\(516\) 0.884268 + 4.56679i 0.0389277 + 0.201042i
\(517\) 39.5785 10.6050i 1.74066 0.466408i
\(518\) −0.0976544 + 0.214078i −0.00429069 + 0.00940604i
\(519\) 3.37866 + 1.95067i 0.148307 + 0.0856249i
\(520\) 12.4527 22.8759i 0.546088 1.00317i
\(521\) 4.84370i 0.212206i −0.994355 0.106103i \(-0.966163\pi\)
0.994355 0.106103i \(-0.0338374\pi\)
\(522\) 2.20553 + 22.9924i 0.0965333 + 1.00635i
\(523\) 9.76122 2.61551i 0.426828 0.114368i −0.0390086 0.999239i \(-0.512420\pi\)
0.465837 + 0.884871i \(0.345753\pi\)
\(524\) −22.3263 + 10.8693i −0.975327 + 0.474826i
\(525\) −0.165228 + 0.165228i −0.00721113 + 0.00721113i
\(526\) −1.54037 + 1.86724i −0.0671633 + 0.0814156i
\(527\) −22.2968 38.6192i −0.971264 1.68228i
\(528\) −6.35688 + 2.55766i −0.276648 + 0.111308i
\(529\) −11.4999 19.9185i −0.499998 0.866022i
\(530\) 2.87765 + 7.70512i 0.124997 + 0.334689i
\(531\) −19.5094 + 19.5094i −0.846634 + 0.846634i
\(532\) −0.835920 + 1.44081i −0.0362417 + 0.0624671i
\(533\) 23.7134 + 23.7134i 1.02714 + 1.02714i
\(534\) −1.17729 0.537034i −0.0509462 0.0232397i
\(535\) −6.69618 + 3.86604i −0.289501 + 0.167143i
\(536\) 5.82145 + 1.40428i 0.251448 + 0.0606559i
\(537\) 4.83385 2.79082i 0.208596 0.120433i
\(538\) 16.1350 1.54773i 0.695627 0.0667275i
\(539\) −15.8253 15.8253i −0.681644 0.681644i
\(540\) −3.26982 + 9.47399i −0.140711 + 0.407696i
\(541\) −7.75257 28.9330i −0.333309 1.24393i −0.905691 0.423939i \(-0.860647\pi\)
0.572382 0.819987i \(-0.306019\pi\)
\(542\) 14.6866 + 12.1156i 0.630841 + 0.520409i
\(543\) −10.9375 −0.469371
\(544\) 28.3294 25.8650i 1.21461 1.10895i
\(545\) 1.67568 2.90236i 0.0717782 0.124323i
\(546\) −0.755348 + 0.282102i −0.0323259 + 0.0120728i
\(547\) −0.601671 2.24547i −0.0257256 0.0960092i 0.951869 0.306504i \(-0.0991592\pi\)
−0.977595 + 0.210495i \(0.932493\pi\)
\(548\) 36.7499 7.11589i 1.56988 0.303976i
\(549\) −6.34619 + 23.6843i −0.270849 + 1.01082i
\(550\) −6.05287 8.49230i −0.258095 0.362113i
\(551\) 21.7520 14.6279i 0.926668 0.623170i
\(552\) −0.0145957 + 0.00430622i −0.000621232 + 0.000183285i
\(553\) 2.25913 1.30431i 0.0960679 0.0554648i
\(554\) −28.9126 13.1889i −1.22838 0.560341i
\(555\) 0.737400 0.197586i 0.0313009 0.00838705i
\(556\) 7.40628 10.9632i 0.314096 0.464942i
\(557\) 4.17480 + 15.5805i 0.176892 + 0.660169i 0.996222 + 0.0868467i \(0.0276790\pi\)
−0.819330 + 0.573322i \(0.805654\pi\)
\(558\) 24.9096 + 4.17770i 1.05451 + 0.176856i
\(559\) −24.4292 −1.03324
\(560\) 0.492885 1.15651i 0.0208282 0.0488716i
\(561\) 5.80829 10.0602i 0.245226 0.424744i
\(562\) −18.9389 3.17633i −0.798890 0.133985i
\(563\) −31.6416 + 31.6416i −1.33353 + 1.33353i −0.431349 + 0.902185i \(0.641962\pi\)
−0.902185 + 0.431349i \(0.858038\pi\)
\(564\) −0.957814 + 13.5565i −0.0403312 + 0.570833i
\(565\) −0.912874 + 3.40689i −0.0384049 + 0.143329i
\(566\) 3.45878 + 36.0575i 0.145384 + 1.51561i
\(567\) −1.07955 + 0.623276i −0.0453367 + 0.0261751i
\(568\) 0.976756 + 38.9133i 0.0409838 + 1.63277i
\(569\) 2.16981i 0.0909634i 0.998965 + 0.0454817i \(0.0144823\pi\)
−0.998965 + 0.0454817i \(0.985518\pi\)
\(570\) 5.33183 0.882635i 0.223326 0.0369695i
\(571\) 4.57662 + 4.57662i 0.191526 + 0.191526i 0.796355 0.604829i \(-0.206759\pi\)
−0.604829 + 0.796355i \(0.706759\pi\)
\(572\) −6.84086 35.3295i −0.286031 1.47720i
\(573\) −2.56618 0.687606i −0.107204 0.0287252i
\(574\) 1.24865 + 1.03007i 0.0521177 + 0.0429942i
\(575\) −0.0115803 0.0200577i −0.000482932 0.000836463i
\(576\) 1.09006 + 21.7000i 0.0454192 + 0.904165i
\(577\) −11.0460 −0.459853 −0.229926 0.973208i \(-0.573849\pi\)
−0.229926 + 0.973208i \(0.573849\pi\)
\(578\) −6.78032 + 40.4278i −0.282024 + 1.68157i
\(579\) 1.08002 + 4.03069i 0.0448841 + 0.167510i
\(580\) −14.9401 + 12.9683i −0.620356 + 0.538480i
\(581\) 1.71478 + 1.71478i 0.0711409 + 0.0711409i
\(582\) 2.17136 + 3.04646i 0.0900056 + 0.126280i
\(583\) 9.84143 + 5.68195i 0.407590 + 0.235322i
\(584\) 1.06986 + 42.6225i 0.0442711 + 1.76373i
\(585\) −21.6589 12.5048i −0.895487 0.517009i
\(586\) 7.16506 + 3.26843i 0.295986 + 0.135018i
\(587\) 2.96822 11.0776i 0.122512 0.457220i −0.877227 0.480076i \(-0.840609\pi\)
0.999739 + 0.0228560i \(0.00727592\pi\)
\(588\) 6.67413 3.24922i 0.275237 0.133996i
\(589\) −9.29434 27.1153i −0.382967 1.11727i
\(590\) −23.3058 3.90871i −0.959484 0.160919i
\(591\) 1.30822 + 2.26591i 0.0538132 + 0.0932071i
\(592\) 2.78474 2.09215i 0.114452 0.0859868i
\(593\) 3.25592 5.63943i 0.133705 0.231583i −0.791397 0.611302i \(-0.790646\pi\)
0.925102 + 0.379719i \(0.123979\pi\)
\(594\) 4.84474 + 12.9722i 0.198782 + 0.532254i
\(595\) 0.551621 + 2.05868i 0.0226143 + 0.0843976i
\(596\) −14.2258 29.2208i −0.582711 1.19693i
\(597\) 5.61730 + 5.61730i 0.229901 + 0.229901i
\(598\) −0.00763119 0.0795543i −0.000312062 0.00325322i
\(599\) −24.6340 14.2225i −1.00652 0.581114i −0.0963479 0.995348i \(-0.530716\pi\)
−0.910170 + 0.414234i \(0.864049\pi\)
\(600\) 3.31756 0.978793i 0.135439 0.0399590i
\(601\) 44.8123i 1.82793i 0.405791 + 0.913966i \(0.366996\pi\)
−0.405791 + 0.913966i \(0.633004\pi\)
\(602\) −1.17375 + 0.112591i −0.0478385 + 0.00458887i
\(603\) 1.48827 5.55428i 0.0606068 0.226188i
\(604\) 16.4076 + 18.9024i 0.667617 + 0.769127i
\(605\) −1.06526 0.285435i −0.0433089 0.0116046i
\(606\) 4.83589 1.80607i 0.196445 0.0733667i
\(607\) 1.87806 0.0762280 0.0381140 0.999273i \(-0.487865\pi\)
0.0381140 + 0.999273i \(0.487865\pi\)
\(608\) 21.0652 12.8163i 0.854307 0.519768i
\(609\) 0.612446 0.0248176
\(610\) −19.6740 + 7.34771i −0.796577 + 0.297500i
\(611\) −68.9412 18.4727i −2.78906 0.747327i
\(612\) −24.1457 27.8171i −0.976034 1.12444i
\(613\) −8.94970 + 33.4008i −0.361475 + 1.34904i 0.510662 + 0.859782i \(0.329400\pi\)
−0.872137 + 0.489262i \(0.837266\pi\)
\(614\) −34.5411 + 3.31333i −1.39396 + 0.133715i
\(615\) 5.25175i 0.211771i
\(616\) −0.491513 1.66595i −0.0198036 0.0671231i
\(617\) −9.89372 5.71214i −0.398306 0.229962i 0.287447 0.957797i \(-0.407194\pi\)
−0.685753 + 0.727834i \(0.740527\pi\)
\(618\) −0.558369 5.82094i −0.0224609 0.234153i
\(619\) 26.4542 + 26.4542i 1.06328 + 1.06328i 0.997857 + 0.0654250i \(0.0208403\pi\)
0.0654250 + 0.997857i \(0.479160\pi\)
\(620\) 9.46930 + 19.4506i 0.380296 + 0.781155i
\(621\) 0.00795947 + 0.0297052i 0.000319403 + 0.00119203i
\(622\) −10.6234 28.4450i −0.425961 1.14054i
\(623\) 0.164007 0.284068i 0.00657080 0.0113810i
\(624\) 11.8170 + 1.67820i 0.473060 + 0.0671819i
\(625\) −4.13179 7.15647i −0.165271 0.286259i
\(626\) −11.6415 1.95245i −0.465288 0.0780355i
\(627\) 4.90658 5.62854i 0.195950 0.224782i
\(628\) −17.7908 + 8.66125i −0.709931 + 0.345622i
\(629\) −1.52832 + 5.70376i −0.0609380 + 0.227424i
\(630\) −1.09828 0.500996i −0.0437566 0.0199601i
\(631\) 30.8113 + 17.7889i 1.22658 + 0.708166i 0.966313 0.257371i \(-0.0828562\pi\)
0.260267 + 0.965537i \(0.416190\pi\)
\(632\) −38.6027 + 0.968959i −1.53553 + 0.0385431i
\(633\) 2.29598 + 1.32558i 0.0912569 + 0.0526872i
\(634\) 16.5278 + 23.1889i 0.656404 + 0.920949i
\(635\) 0.264267 + 0.264267i 0.0104871 + 0.0104871i
\(636\) −2.84639 + 2.47072i −0.112867 + 0.0979705i
\(637\) 10.0898 + 37.6557i 0.399773 + 1.49197i
\(638\) −4.52109 + 26.9571i −0.178992 + 1.06724i
\(639\) 37.3771 1.47862
\(640\) −14.5932 + 11.5478i −0.576848 + 0.456468i
\(641\) 5.08407 + 8.80587i 0.200809 + 0.347811i 0.948789 0.315910i \(-0.102310\pi\)
−0.747980 + 0.663721i \(0.768976\pi\)
\(642\) −2.73327 2.25479i −0.107873 0.0889896i
\(643\) 18.2415 + 4.88779i 0.719374 + 0.192756i 0.599892 0.800081i \(-0.295210\pi\)
0.119482 + 0.992836i \(0.461877\pi\)
\(644\) −0.000733313 0.00378718i −2.88966e−5 0.000149236i
\(645\) 2.70513 + 2.70513i 0.106515 + 0.106515i
\(646\) −14.7083 + 39.1297i −0.578689 + 1.53954i
\(647\) 3.01622i 0.118580i 0.998241 + 0.0592899i \(0.0188836\pi\)
−0.998241 + 0.0592899i \(0.981116\pi\)
\(648\) 18.4467 0.463026i 0.724653 0.0181894i
\(649\) −28.2757 + 16.3250i −1.10992 + 0.640811i
\(650\) 1.73455 + 18.0825i 0.0680346 + 0.709253i
\(651\) 0.173333 0.646888i 0.00679346 0.0253536i
\(652\) 1.13778 16.1037i 0.0445588 0.630668i
\(653\) −10.9451 + 10.9451i −0.428315 + 0.428315i −0.888054 0.459739i \(-0.847943\pi\)
0.459739 + 0.888054i \(0.347943\pi\)
\(654\) 1.51463 + 0.254025i 0.0592267 + 0.00993316i
\(655\) −10.2111 + 17.6862i −0.398982 + 0.691056i
\(656\) −8.94390 22.2294i −0.349200 0.867912i
\(657\) 40.9399 1.59722
\(658\) −3.39756 0.569820i −0.132451 0.0222139i
\(659\) −9.94129 37.1014i −0.387258 1.44526i −0.834577 0.550891i \(-0.814288\pi\)
0.447320 0.894374i \(-0.352379\pi\)
\(660\) −3.15466 + 4.66969i −0.122795 + 0.181767i
\(661\) −4.34511 + 1.16427i −0.169005 + 0.0452848i −0.342329 0.939580i \(-0.611216\pi\)
0.173324 + 0.984865i \(0.444549\pi\)
\(662\) 6.63337 + 3.02590i 0.257813 + 0.117605i
\(663\) −17.5238 + 10.1174i −0.680568 + 0.392926i
\(664\) −10.1582 34.4304i −0.394213 1.33616i
\(665\) 0.0936613 + 1.36676i 0.00363203 + 0.0530005i
\(666\) −1.94120 2.72354i −0.0752198 0.105535i
\(667\) −0.0157114 + 0.0586359i −0.000608349 + 0.00227039i
\(668\) −8.26467 + 1.60029i −0.319770 + 0.0619171i
\(669\) 0.612805 + 2.28702i 0.0236924 + 0.0884213i
\(670\) 4.61381 1.72313i 0.178247 0.0665704i
\(671\) −14.5081 + 25.1288i −0.560080 + 0.970087i
\(672\) 0.575509 + 0.0261695i 0.0222008 + 0.00100951i
\(673\) 14.8313 0.571706 0.285853 0.958274i \(-0.407723\pi\)
0.285853 + 0.958274i \(0.407723\pi\)
\(674\) −14.2838 11.7833i −0.550190 0.453875i
\(675\) −1.80917 6.75191i −0.0696349 0.259881i
\(676\) −11.9679 + 34.6758i −0.460303 + 1.33369i
\(677\) −20.0270 20.0270i −0.769700 0.769700i 0.208354 0.978054i \(-0.433190\pi\)
−0.978054 + 0.208354i \(0.933190\pi\)
\(678\) −1.60892 + 0.154335i −0.0617903 + 0.00592719i
\(679\) −0.821276 + 0.474164i −0.0315177 + 0.0181967i
\(680\) 7.39828 30.6695i 0.283711 1.17612i
\(681\) 9.67707 5.58706i 0.370826 0.214097i
\(682\) 27.1936 + 12.4047i 1.04130 + 0.475000i
\(683\) −33.7175 33.7175i −1.29017 1.29017i −0.934683 0.355483i \(-0.884316\pi\)
−0.355483 0.934683i \(-0.615684\pi\)
\(684\) −11.7950 20.5297i −0.450993 0.784972i
\(685\) 21.7688 21.7688i 0.831743 0.831743i
\(686\) 1.32013 + 3.53473i 0.0504026 + 0.134957i
\(687\) −0.216663 0.375271i −0.00826619 0.0143175i
\(688\) 16.0571 + 6.84326i 0.612172 + 0.260897i
\(689\) −9.89731 17.1427i −0.377058 0.653083i
\(690\) −0.00796432 + 0.00965438i −0.000303197 + 0.000367536i
\(691\) 11.3775 11.3775i 0.432820 0.432820i −0.456766 0.889587i \(-0.650992\pi\)
0.889587 + 0.456766i \(0.150992\pi\)
\(692\) 13.1623 6.40791i 0.500356 0.243592i
\(693\) −1.61102 + 0.431672i −0.0611976 + 0.0163979i
\(694\) 0.149502 + 1.55855i 0.00567503 + 0.0591616i
\(695\) 10.8811i 0.412745i
\(696\) −7.96258 4.33452i −0.301821 0.164299i
\(697\) 35.1797 + 20.3110i 1.33253 + 0.769335i
\(698\) 0.126637 0.277614i 0.00479329 0.0105078i
\(699\) 4.00495 1.07312i 0.151481 0.0405893i
\(700\) 0.166680 + 0.860817i 0.00629992 + 0.0325358i
\(701\) −13.8586 3.71341i −0.523433 0.140254i −0.0125792 0.999921i \(-0.504004\pi\)
−0.510854 + 0.859667i \(0.670671\pi\)
\(702\) 3.98962 23.7882i 0.150579 0.897828i
\(703\) −1.66863 + 3.40915i −0.0629336 + 0.128578i
\(704\) −5.40029 + 25.1382i −0.203531 + 0.947430i
\(705\) 5.58856 + 9.67968i 0.210478 + 0.364558i
\(706\) 26.4239 9.86860i 0.994476 0.371410i
\(707\) 0.338678 + 1.26397i 0.0127373 + 0.0475363i
\(708\) −2.05862 10.6317i −0.0773678 0.399565i
\(709\) 5.25711 1.40864i 0.197435 0.0529026i −0.158746 0.987319i \(-0.550745\pi\)
0.356181 + 0.934417i \(0.384079\pi\)
\(710\) 18.5810 + 26.0695i 0.697333 + 0.978373i
\(711\) 37.0788i 1.39056i
\(712\) −4.14276 + 2.53251i −0.155257 + 0.0949099i
\(713\) 0.0574868 + 0.0331900i 0.00215290 + 0.00124298i
\(714\) −0.795338 + 0.566876i −0.0297648 + 0.0212148i
\(715\) −20.9274 20.9274i −0.782641 0.782641i
\(716\) 1.47611 20.8923i 0.0551648 0.780782i
\(717\) 11.0709 + 2.96643i 0.413450 + 0.110784i
\(718\) 10.0522 12.1853i 0.375144 0.454751i
\(719\) 1.47622 + 2.55689i 0.0550537 + 0.0953557i 0.892239 0.451564i \(-0.149134\pi\)
−0.837185 + 0.546920i \(0.815800\pi\)
\(720\) 10.7333 + 14.2866i 0.400008 + 0.532429i
\(721\) 1.48232 0.0552047
\(722\) −14.1116 + 22.8662i −0.525178 + 0.850992i
\(723\) −3.32401 + 3.32401i −0.123621 + 0.123621i
\(724\) −22.9746 + 34.0082i −0.853845 + 1.26390i
\(725\) 3.57117 13.3278i 0.132630 0.494981i
\(726\) −0.0482570 0.503074i −0.00179098 0.0186708i
\(727\) 37.0159 21.3712i 1.37285 0.792613i 0.381560 0.924344i \(-0.375387\pi\)
0.991285 + 0.131731i \(0.0420536\pi\)
\(728\) −0.709493 + 2.94120i −0.0262956 + 0.109008i
\(729\) 12.8470i 0.475815i
\(730\) 20.3521 + 28.5545i 0.753266 + 1.05685i
\(731\) −28.5828 + 7.65875i −1.05717 + 0.283269i
\(732\) −6.30866 7.26789i −0.233175 0.268629i
\(733\) 5.41912 5.41912i 0.200160 0.200160i −0.599909 0.800068i \(-0.704796\pi\)
0.800068 + 0.599909i \(0.204796\pi\)
\(734\) −3.80807 + 22.7057i −0.140559 + 0.838084i
\(735\) 3.05248 5.28704i 0.112592 0.195016i
\(736\) −0.0172694 + 0.0544282i −0.000636557 + 0.00200625i
\(737\) 3.40234 5.89303i 0.125327 0.217073i
\(738\) −21.5539 + 8.04980i −0.793410 + 0.296317i
\(739\) −25.3837 6.80154i −0.933754 0.250199i −0.240299 0.970699i \(-0.577246\pi\)
−0.693455 + 0.720500i \(0.743912\pi\)
\(740\) 0.934582 2.70786i 0.0343559 0.0995430i
\(741\) −12.3038 + 4.21739i −0.451991 + 0.154930i
\(742\) −0.554546 0.778039i −0.0203580 0.0285627i
\(743\) −16.0435 + 9.26272i −0.588579 + 0.339816i −0.764535 0.644582i \(-0.777032\pi\)
0.175956 + 0.984398i \(0.443698\pi\)
\(744\) −6.83183 + 7.18363i −0.250467 + 0.263365i
\(745\) −23.1478 13.3644i −0.848071 0.489634i
\(746\) −16.6612 7.60022i −0.610010 0.278264i
\(747\) −33.2952 + 8.92141i −1.21821 + 0.326417i
\(748\) −19.0801 39.1919i −0.697638 1.43300i
\(749\) 0.635114 0.635114i 0.0232066 0.0232066i
\(750\) 5.75522 6.97650i 0.210151 0.254746i
\(751\) 15.0608 26.0861i 0.549576 0.951894i −0.448727 0.893669i \(-0.648122\pi\)
0.998303 0.0582254i \(-0.0185442\pi\)
\(752\) 40.1399 + 31.4543i 1.46375 + 1.14702i
\(753\) −3.72775 −0.135847
\(754\) 30.2983 36.7277i 1.10340 1.33754i
\(755\) 19.8842 + 5.32796i 0.723661 + 0.193904i
\(756\) 0.0820527 1.16134i 0.00298423 0.0422376i
\(757\) −7.02913 + 26.2331i −0.255478 + 0.953457i 0.712346 + 0.701828i \(0.247633\pi\)
−0.967824 + 0.251628i \(0.919034\pi\)
\(758\) 8.14075 + 3.71351i 0.295685 + 0.134881i
\(759\) 0.0172919i 0.000627656i
\(760\) 8.45535 18.4325i 0.306708 0.668616i
\(761\) 2.78728i 0.101039i −0.998723 0.0505194i \(-0.983912\pi\)
0.998723 0.0505194i \(-0.0160877\pi\)
\(762\) −0.0710785 + 0.155818i −0.00257490 + 0.00564470i
\(763\) −0.100760 + 0.376041i −0.00364775 + 0.0136136i
\(764\) −7.52838 + 6.53477i −0.272367 + 0.236420i
\(765\) −29.2620 7.84072i −1.05797 0.283482i
\(766\) −7.44224 6.13942i −0.268899 0.221826i
\(767\) 56.8724 2.05354
\(768\) −7.29715 4.41334i −0.263313 0.159253i
\(769\) 18.2546 31.6180i 0.658279 1.14017i −0.322781 0.946474i \(-0.604618\pi\)
0.981061 0.193700i \(-0.0620488\pi\)
\(770\) −1.10195 0.909050i −0.0397117 0.0327599i
\(771\) −6.43088 + 6.43088i −0.231602 + 0.231602i
\(772\) 14.8014 + 5.10849i 0.532713 + 0.183859i
\(773\) 10.4306 2.79488i 0.375163 0.100525i −0.0663101 0.997799i \(-0.521123\pi\)
0.441473 + 0.897274i \(0.354456\pi\)
\(774\) 6.95586 15.2486i 0.250023 0.548101i
\(775\) −13.0666 7.54400i −0.469366 0.270989i
\(776\) 14.0335 0.352252i 0.503773 0.0126451i
\(777\) −0.0767999 + 0.0443405i −0.00275518 + 0.00159071i
\(778\) −28.7032 + 20.4582i −1.02906 + 0.733461i
\(779\) 19.6825 + 17.1579i 0.705197 + 0.614744i
\(780\) 8.82589 4.29678i 0.316017 0.153849i
\(781\) 42.7242 + 11.4479i 1.52879 + 0.409639i
\(782\) −0.0338697 0.0906884i −0.00121118 0.00324301i
\(783\) −9.16057 + 15.8666i −0.327372 + 0.567025i
\(784\) 3.91640 27.5773i 0.139871 0.984902i
\(785\) −8.13680 + 14.0933i −0.290415 + 0.503013i
\(786\) −9.22973 1.54796i −0.329214 0.0552138i
\(787\) 3.12760 3.12760i 0.111487 0.111487i −0.649163 0.760650i \(-0.724881\pi\)
0.760650 + 0.649163i \(0.224881\pi\)
\(788\) 9.79346 + 0.691940i 0.348878 + 0.0246494i
\(789\) −0.881206 + 0.236118i −0.0313718 + 0.00840604i
\(790\) −25.8614 + 18.4327i −0.920108 + 0.655805i
\(791\) 0.409718i 0.0145679i
\(792\) 24.0005 + 5.78953i 0.852819 + 0.205722i
\(793\) 43.7715 25.2715i 1.55437 0.897417i
\(794\) −6.99944 + 0.671416i −0.248401 + 0.0238277i
\(795\) −0.802304 + 2.99424i −0.0284548 + 0.106195i
\(796\) 29.2655 5.66668i 1.03729 0.200850i
\(797\) −10.2214 + 10.2214i −0.362062 + 0.362062i −0.864572 0.502510i \(-0.832410\pi\)
0.502510 + 0.864572i \(0.332410\pi\)
\(798\) −0.571725 + 0.259340i −0.0202388 + 0.00918054i
\(799\) −86.4546 −3.05854
\(800\) 3.92528 12.3714i 0.138780 0.437395i
\(801\) 2.33119 + 4.03773i 0.0823684 + 0.142666i
\(802\) −30.2071 24.9192i −1.06665 0.879927i
\(803\) 46.7966 + 12.5391i 1.65142 + 0.442496i
\(804\) 1.47946 + 1.70442i 0.0521767 + 0.0601101i
\(805\) −0.00224334 0.00224334i −7.90672e−5 7.90672e-5i
\(806\) −30.2182 42.3967i −1.06439 1.49336i
\(807\) 5.29051 + 3.05448i 0.186235 + 0.107523i
\(808\) 4.54232 18.8301i 0.159798 0.662442i
\(809\) 1.90884i 0.0671113i 0.999437 + 0.0335557i \(0.0106831\pi\)
−0.999437 + 0.0335557i \(0.989317\pi\)
\(810\) 12.3581 8.80823i 0.434221 0.309490i
\(811\) 1.43601 0.384778i 0.0504252 0.0135114i −0.233518 0.972352i \(-0.575024\pi\)
0.283943 + 0.958841i \(0.408357\pi\)
\(812\) 1.28647 1.90430i 0.0451462 0.0668278i
\(813\) 1.85716 + 6.93101i 0.0651334 + 0.243081i
\(814\) −1.38473 3.70771i −0.0485347 0.129955i
\(815\) −6.63860 11.4984i −0.232540 0.402771i
\(816\) 14.3524 1.74119i 0.502435 0.0609540i
\(817\) −18.9761 + 1.30040i −0.663891 + 0.0454952i
\(818\) 46.6115 + 7.81741i 1.62973 + 0.273329i
\(819\) 2.80621 + 0.751923i 0.0980571 + 0.0262743i
\(820\) −16.3294 11.0315i −0.570249 0.385238i
\(821\) 37.8372 10.1385i 1.32053 0.353834i 0.471352 0.881945i \(-0.343766\pi\)
0.849176 + 0.528110i \(0.177099\pi\)
\(822\) 12.8354 + 5.85504i 0.447687 + 0.204218i
\(823\) 37.8604 + 21.8587i 1.31973 + 0.761947i 0.983685 0.179898i \(-0.0575768\pi\)
0.336046 + 0.941845i \(0.390910\pi\)
\(824\) −19.2721 10.4910i −0.671377 0.365471i
\(825\) 3.93040i 0.136839i
\(826\) 2.73256 0.262118i 0.0950778 0.00912026i
\(827\) −1.59518 + 0.427429i −0.0554700 + 0.0148631i −0.286447 0.958096i \(-0.592474\pi\)
0.230977 + 0.972959i \(0.425808\pi\)
\(828\) 0.0518305 + 0.0178886i 0.00180123 + 0.000621672i
\(829\) 18.3212 18.3212i 0.636323 0.636323i −0.313324 0.949646i \(-0.601443\pi\)
0.949646 + 0.313324i \(0.101443\pi\)
\(830\) −22.7742 18.7874i −0.790505 0.652122i
\(831\) −5.98847 10.3723i −0.207738 0.359812i
\(832\) 30.0403 33.2180i 1.04146 1.15163i
\(833\) 23.6108 + 40.8950i 0.818064 + 1.41693i
\(834\) 4.67121 1.74457i 0.161751 0.0604095i
\(835\) −4.89557 + 4.89557i −0.169418 + 0.169418i
\(836\) −7.19450 27.0792i −0.248827 0.936554i
\(837\) 14.1663 + 14.1663i 0.489657 + 0.489657i
\(838\) 12.5056 27.4148i 0.431999 0.947028i
\(839\) −12.7500 + 7.36122i −0.440179 + 0.254137i −0.703673 0.710523i \(-0.748458\pi\)
0.263495 + 0.964661i \(0.415125\pi\)
\(840\) 0.404255 0.247125i 0.0139481 0.00852663i
\(841\) −6.20472 + 3.58230i −0.213956 + 0.123528i
\(842\) 2.16096 + 22.5278i 0.0744715 + 0.776358i
\(843\) −5.11768 5.11768i −0.176262 0.176262i
\(844\) 8.94449 4.35452i 0.307882 0.149889i
\(845\) 7.80839 + 29.1413i 0.268617 + 1.00249i
\(846\) 31.1607 37.7731i 1.07133 1.29867i
\(847\) 0.128110 0.00440190
\(848\) 1.70332 + 14.0402i 0.0584924 + 0.482144i
\(849\) −6.82596 + 11.8229i −0.234266 + 0.405761i
\(850\) 7.69849 + 20.6132i 0.264056 + 0.707029i
\(851\) −0.00227498 0.00849035i −7.79854e−5 0.000291046i
\(852\) −8.21243 + 12.1565i −0.281353 + 0.416473i
\(853\) 4.98598 18.6079i 0.170717 0.637123i −0.826525 0.562900i \(-0.809686\pi\)
0.997242 0.0742233i \(-0.0236478\pi\)
\(854\) 1.98662 1.41596i 0.0679808 0.0484532i
\(855\) −17.4899 8.56057i −0.598143 0.292765i
\(856\) −12.7523 + 3.76235i −0.435863 + 0.128595i
\(857\) 0.205233 0.118491i 0.00701062 0.00404759i −0.496491 0.868042i \(-0.665378\pi\)
0.503501 + 0.863995i \(0.332045\pi\)
\(858\) 5.62874 12.3393i 0.192162 0.421257i
\(859\) 31.1030 8.33403i 1.06122 0.284353i 0.314340 0.949311i \(-0.398217\pi\)
0.746881 + 0.664957i \(0.231550\pi\)
\(860\) 14.0934 2.72891i 0.480582 0.0930551i
\(861\) 0.157896 + 0.589276i 0.00538108 + 0.0200825i
\(862\) −6.44897 + 38.4521i −0.219653 + 1.30968i
\(863\) 27.1777 0.925140 0.462570 0.886583i \(-0.346927\pi\)
0.462570 + 0.886583i \(0.346927\pi\)
\(864\) −9.28606 + 14.5182i −0.315918 + 0.493920i
\(865\) 6.01990 10.4268i 0.204683 0.354521i
\(866\) 8.54388 50.9431i 0.290333 1.73112i
\(867\) −10.9244 + 10.9244i −0.371013 + 0.371013i
\(868\) −1.64730 1.89777i −0.0559129 0.0644145i
\(869\) −11.3565 + 42.3831i −0.385244 + 1.43775i
\(870\) −7.42204 + 0.711953i −0.251631 + 0.0241375i
\(871\) −10.2650 + 5.92649i −0.347816 + 0.200812i
\(872\) 3.97140 4.17590i 0.134488 0.141414i
\(873\) 13.4795i 0.456212i
\(874\) −0.0101626 0.0613902i −0.000343754 0.00207655i
\(875\) 1.62109 + 1.62109i 0.0548028 + 0.0548028i
\(876\) −8.99522 + 13.3152i −0.303920 + 0.449879i
\(877\) 36.1844 + 9.69559i 1.22186 + 0.327397i 0.811406 0.584484i \(-0.198703\pi\)
0.410456 + 0.911880i \(0.365370\pi\)
\(878\) 16.6343 20.1642i 0.561380 0.680508i
\(879\) 1.48405 + 2.57045i 0.0500557 + 0.0866990i
\(880\) 7.89312 + 19.6178i 0.266077 + 0.661315i
\(881\) −52.3185 −1.76265 −0.881327 0.472507i \(-0.843349\pi\)
−0.881327 + 0.472507i \(0.843349\pi\)
\(882\) −26.3775 4.42389i −0.888178 0.148960i
\(883\) 2.11503 + 7.89341i 0.0711766 + 0.265635i 0.992339 0.123543i \(-0.0394258\pi\)
−0.921163 + 0.389178i \(0.872759\pi\)
\(884\) −5.35124 + 75.7393i −0.179982 + 2.54739i
\(885\) −6.29770 6.29770i −0.211695 0.211695i
\(886\) 26.2446 18.7058i 0.881706 0.628434i
\(887\) 7.63169 + 4.40616i 0.256247 + 0.147944i 0.622621 0.782523i \(-0.286068\pi\)
−0.366374 + 0.930468i \(0.619401\pi\)
\(888\) 1.31231 0.0329401i 0.0440383 0.00110540i
\(889\) −0.0375975 0.0217069i −0.00126098 0.000728027i
\(890\) −1.65733 + 3.63319i −0.0555537 + 0.121785i
\(891\) 5.42683 20.2532i 0.181806 0.678507i
\(892\) 8.39834 + 2.89857i 0.281197 + 0.0970514i
\(893\) −54.5356 10.6795i −1.82497 0.357374i
\(894\) 2.02598 12.0800i 0.0677589 0.404014i
\(895\) −8.61267 14.9176i −0.287890 0.498640i
\(896\) 1.29025 1.73448i 0.0431043 0.0579449i
\(897\) 0.0150603 0.0260851i 0.000502847 0.000870957i
\(898\) −6.19091 + 2.31214i −0.206593 + 0.0771570i
\(899\) 10.2352 + 38.1984i 0.341364 + 1.27399i
\(900\) −11.7809 4.06603i −0.392698 0.135534i
\(901\) −16.9545 16.9545i −0.564837 0.564837i
\(902\) −27.1029 + 2.59982i −0.902426 + 0.0865646i
\(903\) −0.384862 0.222200i −0.0128074 0.00739436i
\(904\) −2.89974 + 5.32686i −0.0964438 + 0.177169i
\(905\) 33.7537i 1.12201i
\(906\) 0.900769 + 9.39042i 0.0299260 + 0.311976i
\(907\) −12.9190 + 48.2143i −0.428968 + 1.60093i 0.326134 + 0.945323i \(0.394254\pi\)
−0.755102 + 0.655607i \(0.772413\pi\)
\(908\) 2.95508 41.8251i 0.0980679 1.38802i
\(909\) −17.9659 4.81396i −0.595893 0.159669i
\(910\) 0.870586 + 2.33106i 0.0288596 + 0.0772738i
\(911\) 14.1150 0.467651 0.233825 0.972279i \(-0.424876\pi\)
0.233825 + 0.972279i \(0.424876\pi\)
\(912\) 9.26861 + 0.674561i 0.306914 + 0.0223369i
\(913\) −40.7907 −1.34998
\(914\) −8.99081 24.0735i −0.297390 0.796282i
\(915\) −7.64540 2.04858i −0.252749 0.0677239i
\(916\) −1.62195 0.114596i −0.0535908 0.00378637i
\(917\) 0.614003 2.29149i 0.0202762 0.0756716i
\(918\) −2.78983 29.0837i −0.0920781 0.959905i
\(919\) 40.2036i 1.32620i −0.748533 0.663098i \(-0.769241\pi\)
0.748533 0.663098i \(-0.230759\pi\)
\(920\) 0.0132893 + 0.0450432i 0.000438135 + 0.00148503i
\(921\) −11.3257 6.53890i −0.373195 0.215464i
\(922\) 27.9233 2.67852i 0.919606 0.0882125i
\(923\) −54.4797 54.4797i −1.79322 1.79322i
\(924\) 0.213574 0.618811i 0.00702608 0.0203574i
\(925\) 0.517098 + 1.92984i 0.0170021 + 0.0634526i
\(926\) 26.7237 9.98057i 0.878195 0.327982i
\(927\) −10.5348 + 18.2469i −0.346010 + 0.599307i
\(928\) −30.2032 + 15.6535i −0.991470 + 0.513851i
\(929\) 12.2995 + 21.3034i 0.403534 + 0.698942i 0.994150 0.108011i \(-0.0344483\pi\)
−0.590615 + 0.806953i \(0.701115\pi\)
\(930\) −1.34858 + 8.04093i −0.0442216 + 0.263673i
\(931\) 9.84206 + 28.7132i 0.322561 + 0.941037i
\(932\) 5.07588 14.7069i 0.166266 0.481740i
\(933\) 2.96187 11.0538i 0.0969671 0.361886i
\(934\) −15.6230 + 34.2488i −0.511201 + 1.12065i
\(935\) −31.0466 17.9248i −1.01533 0.586203i
\(936\) −31.1627 29.6366i −1.01859 0.968704i
\(937\) −26.4424 15.2665i −0.863835 0.498735i 0.00145953 0.999999i \(-0.499535\pi\)
−0.865295 + 0.501263i \(0.832869\pi\)
\(938\) −0.465889 + 0.332061i −0.0152118 + 0.0108422i
\(939\) −3.14578 3.14578i −0.102659 0.102659i
\(940\) 41.8364 + 2.95588i 1.36455 + 0.0964102i
\(941\) 7.59406 + 28.3414i 0.247559 + 0.923904i 0.972080 + 0.234651i \(0.0753946\pi\)
−0.724520 + 0.689253i \(0.757939\pi\)
\(942\) −7.35477 1.23350i −0.239631 0.0401896i
\(943\) −0.0604681 −0.00196911
\(944\) −37.3818 15.9315i −1.21668 0.518525i
\(945\) −0.478754 0.829226i −0.0155739 0.0269747i
\(946\) 12.6213 15.2996i 0.410354 0.497433i
\(947\) 26.7972 + 7.18028i 0.870791 + 0.233328i 0.666430 0.745568i \(-0.267822\pi\)
0.204361 + 0.978896i \(0.434488\pi\)
\(948\) −12.0594 8.14687i −0.391672 0.264598i
\(949\) −59.6727 59.6727i −1.93706 1.93706i
\(950\) 2.30993 + 13.9538i 0.0749439 + 0.452722i
\(951\) 10.7323i 0.348018i
\(952\) 0.0919624 + 3.66372i 0.00298052 + 0.118742i
\(953\) 9.27416 5.35444i 0.300419 0.173447i −0.342212 0.939623i \(-0.611176\pi\)
0.642631 + 0.766176i \(0.277843\pi\)
\(954\) 13.5185 1.29676i 0.437679 0.0419840i
\(955\) −2.12200 + 7.91941i −0.0686663 + 0.256266i
\(956\) 32.4785 28.1920i 1.05043 0.911793i
\(957\) −7.28437 + 7.28437i −0.235470 + 0.235470i
\(958\) −4.56122 + 27.1964i −0.147366 + 0.878675i
\(959\) −1.78809 + 3.09707i −0.0577405 + 0.100010i
\(960\) −7.00484 + 0.351876i −0.226080 + 0.0113568i
\(961\) 12.2433 0.394947
\(962\) −1.14032 + 6.79917i −0.0367653 + 0.219214i
\(963\) 3.30429 + 12.3318i 0.106479 + 0.397386i
\(964\) 3.35323 + 17.3177i 0.108000 + 0.557766i
\(965\) 12.4390 3.33301i 0.400425 0.107293i
\(966\) 0.000603378 0.00132273i 1.94134e−5 4.25580e-5i
\(967\) 21.6668 12.5093i 0.696757 0.402273i −0.109381 0.994000i \(-0.534887\pi\)
0.806139 + 0.591727i \(0.201554\pi\)
\(968\) −1.66559 0.906682i −0.0535341 0.0291419i
\(969\) −13.0736 + 8.79182i −0.419985 + 0.282434i
\(970\) 9.40158 6.70096i 0.301867 0.215155i
\(971\) −5.33156 + 19.8977i −0.171098 + 0.638546i 0.826085 + 0.563545i \(0.190563\pi\)
−0.997183 + 0.0750014i \(0.976104\pi\)
\(972\) 20.9096 + 14.1257i 0.670676 + 0.453083i
\(973\) 0.327145 + 1.22092i 0.0104878 + 0.0391410i
\(974\) −12.0219 32.1894i −0.385205 1.03141i
\(975\) −3.42316 + 5.92908i −0.109629 + 0.189883i
\(976\) −35.8499 + 4.34921i −1.14753 + 0.139215i
\(977\) −46.0366 −1.47284 −0.736421 0.676523i \(-0.763486\pi\)
−0.736421 + 0.676523i \(0.763486\pi\)
\(978\) 3.87183 4.69345i 0.123808 0.150080i
\(979\) 1.42800 + 5.32936i 0.0456390 + 0.170327i
\(980\) −10.0273 20.5968i −0.320311 0.657942i
\(981\) −3.91283 3.91283i −0.124927 0.124927i
\(982\) 4.44002 + 46.2868i 0.141687 + 1.47707i
\(983\) −30.7039 + 17.7269i −0.979302 + 0.565400i −0.902059 0.431612i \(-0.857945\pi\)
−0.0772427 + 0.997012i \(0.524612\pi\)
\(984\) 2.11768 8.77883i 0.0675092 0.279859i
\(985\) 6.99276 4.03727i 0.222808 0.128638i
\(986\) 23.9354 52.4712i 0.762259 1.67102i
\(987\) −0.918091 0.918091i −0.0292232 0.0292232i
\(988\) −12.7314 + 47.1154i −0.405040 + 1.49894i
\(989\) 0.0311466 0.0311466i 0.000990405 0.000990405i
\(990\) 19.0216 7.10407i 0.604548 0.225782i
\(991\) 23.5637 + 40.8136i 0.748527 + 1.29649i 0.948529 + 0.316691i \(0.102572\pi\)
−0.200002 + 0.979796i \(0.564095\pi\)
\(992\) 7.98575 + 36.3320i 0.253548 + 1.15354i
\(993\) 1.37392 + 2.37971i 0.0436002 + 0.0755177i
\(994\) −2.86868 2.36650i −0.0909891 0.0750609i
\(995\) 17.3354 17.3354i 0.549569 0.549569i
\(996\) 4.41396 12.7890i 0.139862 0.405236i
\(997\) 40.4402 10.8359i 1.28075 0.343177i 0.446612 0.894728i \(-0.352631\pi\)
0.834141 + 0.551551i \(0.185964\pi\)
\(998\) 53.2684 5.10973i 1.68618 0.161746i
\(999\) 2.65286i 0.0839329i
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 304.2.v.a.197.34 yes 152
16.13 even 4 inner 304.2.v.a.45.9 152
19.11 even 3 inner 304.2.v.a.277.9 yes 152
304.125 even 12 inner 304.2.v.a.125.34 yes 152
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.v.a.45.9 152 16.13 even 4 inner
304.2.v.a.125.34 yes 152 304.125 even 12 inner
304.2.v.a.197.34 yes 152 1.1 even 1 trivial
304.2.v.a.277.9 yes 152 19.11 even 3 inner