Properties

Label 429.2.x.a.248.1
Level $429$
Weight $2$
Character 429.248
Analytic conductor $3.426$
Analytic rank $0$
Dimension $192$
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] = [429,2,Mod(248,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 9, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.248");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.x (of order \(10\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 248.1
Character \(\chi\) \(=\) 429.248
Dual form 429.2.x.a.365.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.867138 - 2.66878i) q^{2} +(-1.64023 + 0.556462i) q^{3} +(-4.75241 + 3.45283i) q^{4} +(1.12653 + 0.366031i) q^{5} +(2.90738 + 3.89488i) q^{6} +(-1.16567 - 1.60441i) q^{7} +(8.79543 + 6.39025i) q^{8} +(2.38070 - 1.82545i) q^{9} +O(q^{10})\) \(q+(-0.867138 - 2.66878i) q^{2} +(-1.64023 + 0.556462i) q^{3} +(-4.75241 + 3.45283i) q^{4} +(1.12653 + 0.366031i) q^{5} +(2.90738 + 3.89488i) q^{6} +(-1.16567 - 1.60441i) q^{7} +(8.79543 + 6.39025i) q^{8} +(2.38070 - 1.82545i) q^{9} -3.32385i q^{10} +(3.07156 + 1.25120i) q^{11} +(5.87367 - 8.30796i) q^{12} +(0.951057 - 0.309017i) q^{13} +(-3.27101 + 4.50217i) q^{14} +(-2.05144 + 0.0264947i) q^{15} +(5.79679 - 17.8407i) q^{16} +(0.208239 - 0.640895i) q^{17} +(-6.93611 - 4.77064i) q^{18} +(-2.70134 + 3.71808i) q^{19} +(-6.61756 + 2.15018i) q^{20} +(2.80476 + 1.98295i) q^{21} +(0.675693 - 9.28228i) q^{22} -3.03278i q^{23} +(-17.9824 - 5.58716i) q^{24} +(-2.91000 - 2.11424i) q^{25} +(-1.64940 - 2.27020i) q^{26} +(-2.88910 + 4.31892i) q^{27} +(11.0795 + 3.59995i) q^{28} +(3.53233 - 2.56639i) q^{29} +(1.84959 + 5.45187i) q^{30} +(-1.02308 - 3.14870i) q^{31} -30.8960 q^{32} +(-5.73431 - 0.343041i) q^{33} -1.89098 q^{34} +(-0.725898 - 2.23408i) q^{35} +(-5.01111 + 16.8954i) q^{36} +(9.07179 - 6.59104i) q^{37} +(12.2652 + 3.98519i) q^{38} +(-1.38799 + 1.03608i) q^{39} +(7.56926 + 10.4182i) q^{40} +(-1.37398 - 0.998255i) q^{41} +(2.85993 - 9.20478i) q^{42} -0.610070i q^{43} +(-18.9175 + 4.65939i) q^{44} +(3.35009 - 1.18501i) q^{45} +(-8.09380 + 2.62984i) q^{46} +(7.17109 - 9.87015i) q^{47} +(0.419593 + 32.4885i) q^{48} +(0.947779 - 2.91696i) q^{49} +(-3.11906 + 9.59948i) q^{50} +(0.0150731 + 1.16709i) q^{51} +(-3.45283 + 4.75241i) q^{52} +(6.81298 - 2.21367i) q^{53} +(14.0315 + 3.96527i) q^{54} +(3.00222 + 2.53379i) q^{55} -21.5604i q^{56} +(2.36185 - 7.60169i) q^{57} +(-9.91213 - 7.20159i) q^{58} +(4.01022 + 5.51959i) q^{59} +(9.65782 - 7.20920i) q^{60} +(4.63218 + 1.50508i) q^{61} +(-7.51604 + 5.46072i) q^{62} +(-5.70389 - 1.69175i) q^{63} +(15.1975 + 46.7731i) q^{64} +1.18450 q^{65} +(4.05694 + 15.6011i) q^{66} -8.07121 q^{67} +(1.22326 + 3.76481i) q^{68} +(1.68762 + 4.97445i) q^{69} +(-5.33282 + 3.87452i) q^{70} +(2.24884 + 0.730693i) q^{71} +(32.6044 - 0.842320i) q^{72} +(-1.81099 - 2.49262i) q^{73} +(-25.4565 - 18.4952i) q^{74} +(5.94956 + 1.84853i) q^{75} -26.9971i q^{76} +(-1.57301 - 6.38653i) q^{77} +(3.96866 + 2.80582i) q^{78} +(-5.52280 + 1.79447i) q^{79} +(13.0605 - 17.9762i) q^{80} +(2.33548 - 8.69169i) q^{81} +(-1.47269 + 4.53247i) q^{82} +(1.50773 - 4.64031i) q^{83} +(-20.1762 + 0.260578i) q^{84} +(0.469175 - 0.645763i) q^{85} +(-1.62814 + 0.529015i) q^{86} +(-4.36573 + 6.17507i) q^{87} +(19.0203 + 30.6329i) q^{88} +6.98846i q^{89} +(-6.06752 - 7.91309i) q^{90} +(-1.60441 - 1.16567i) q^{91} +(10.4717 + 14.4130i) q^{92} +(3.43021 + 4.59529i) q^{93} +(-32.5596 - 10.5792i) q^{94} +(-4.40407 + 3.19974i) q^{95} +(50.6765 - 17.1924i) q^{96} +(-2.07371 - 6.38223i) q^{97} -8.60658 q^{98} +(9.59647 - 2.62826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.867138 2.66878i −0.613159 1.88711i −0.425793 0.904820i \(-0.640005\pi\)
−0.187366 0.982290i \(-0.559995\pi\)
\(3\) −1.64023 + 0.556462i −0.946987 + 0.321273i
\(4\) −4.75241 + 3.45283i −2.37620 + 1.72641i
\(5\) 1.12653 + 0.366031i 0.503798 + 0.163694i 0.549880 0.835244i \(-0.314673\pi\)
−0.0460817 + 0.998938i \(0.514673\pi\)
\(6\) 2.90738 + 3.89488i 1.18693 + 1.59008i
\(7\) −1.16567 1.60441i −0.440583 0.606410i 0.529759 0.848148i \(-0.322282\pi\)
−0.970341 + 0.241738i \(0.922282\pi\)
\(8\) 8.79543 + 6.39025i 3.10965 + 2.25930i
\(9\) 2.38070 1.82545i 0.793567 0.608483i
\(10\) 3.32385i 1.05109i
\(11\) 3.07156 + 1.25120i 0.926112 + 0.377250i
\(12\) 5.87367 8.30796i 1.69558 2.39830i
\(13\) 0.951057 0.309017i 0.263776 0.0857059i
\(14\) −3.27101 + 4.50217i −0.874215 + 1.20325i
\(15\) −2.05144 + 0.0264947i −0.529681 + 0.00684090i
\(16\) 5.79679 17.8407i 1.44920 4.46017i
\(17\) 0.208239 0.640895i 0.0505055 0.155440i −0.922623 0.385703i \(-0.873959\pi\)
0.973128 + 0.230264i \(0.0739588\pi\)
\(18\) −6.93611 4.77064i −1.63486 1.12445i
\(19\) −2.70134 + 3.71808i −0.619730 + 0.852986i −0.997333 0.0729820i \(-0.976748\pi\)
0.377603 + 0.925968i \(0.376748\pi\)
\(20\) −6.61756 + 2.15018i −1.47973 + 0.480794i
\(21\) 2.80476 + 1.98295i 0.612049 + 0.432715i
\(22\) 0.675693 9.28228i 0.144058 1.97899i
\(23\) 3.03278i 0.632377i −0.948696 0.316189i \(-0.897597\pi\)
0.948696 0.316189i \(-0.102403\pi\)
\(24\) −17.9824 5.58716i −3.67065 1.14047i
\(25\) −2.91000 2.11424i −0.582000 0.422848i
\(26\) −1.64940 2.27020i −0.323473 0.445222i
\(27\) −2.88910 + 4.31892i −0.556008 + 0.831177i
\(28\) 11.0795 + 3.59995i 2.09383 + 0.680326i
\(29\) 3.53233 2.56639i 0.655937 0.476566i −0.209351 0.977840i \(-0.567135\pi\)
0.865288 + 0.501274i \(0.167135\pi\)
\(30\) 1.84959 + 5.45187i 0.337688 + 0.995371i
\(31\) −1.02308 3.14870i −0.183750 0.565523i 0.816175 0.577805i \(-0.196091\pi\)
−0.999925 + 0.0122815i \(0.996091\pi\)
\(32\) −30.8960 −5.46169
\(33\) −5.73431 0.343041i −0.998215 0.0597157i
\(34\) −1.89098 −0.324300
\(35\) −0.725898 2.23408i −0.122699 0.377629i
\(36\) −5.01111 + 16.8954i −0.835185 + 2.81591i
\(37\) 9.07179 6.59104i 1.49139 1.08356i 0.517737 0.855540i \(-0.326775\pi\)
0.973656 0.228020i \(-0.0732253\pi\)
\(38\) 12.2652 + 3.98519i 1.98967 + 0.646483i
\(39\) −1.38799 + 1.03608i −0.222257 + 0.165906i
\(40\) 7.56926 + 10.4182i 1.19681 + 1.64726i
\(41\) −1.37398 0.998255i −0.214580 0.155901i 0.475304 0.879822i \(-0.342338\pi\)
−0.689883 + 0.723921i \(0.742338\pi\)
\(42\) 2.85993 9.20478i 0.441297 1.42033i
\(43\) 0.610070i 0.0930348i −0.998917 0.0465174i \(-0.985188\pi\)
0.998917 0.0465174i \(-0.0148123\pi\)
\(44\) −18.9175 + 4.65939i −2.85192 + 0.702429i
\(45\) 3.35009 1.18501i 0.499403 0.176650i
\(46\) −8.09380 + 2.62984i −1.19337 + 0.387748i
\(47\) 7.17109 9.87015i 1.04601 1.43971i 0.153793 0.988103i \(-0.450851\pi\)
0.892217 0.451607i \(-0.149149\pi\)
\(48\) 0.419593 + 32.4885i 0.0605631 + 4.68931i
\(49\) 0.947779 2.91696i 0.135397 0.416709i
\(50\) −3.11906 + 9.59948i −0.441102 + 1.35757i
\(51\) 0.0150731 + 1.16709i 0.00211066 + 0.163425i
\(52\) −3.45283 + 4.75241i −0.478821 + 0.659041i
\(53\) 6.81298 2.21367i 0.935835 0.304071i 0.198888 0.980022i \(-0.436267\pi\)
0.736946 + 0.675951i \(0.236267\pi\)
\(54\) 14.0315 + 3.96527i 1.90944 + 0.539605i
\(55\) 3.00222 + 2.53379i 0.404820 + 0.341657i
\(56\) 21.5604i 2.88113i
\(57\) 2.36185 7.60169i 0.312835 1.00687i
\(58\) −9.91213 7.20159i −1.30153 0.945615i
\(59\) 4.01022 + 5.51959i 0.522086 + 0.718590i 0.985899 0.167343i \(-0.0535189\pi\)
−0.463812 + 0.885933i \(0.653519\pi\)
\(60\) 9.65782 7.20920i 1.24682 0.930703i
\(61\) 4.63218 + 1.50508i 0.593089 + 0.192706i 0.590156 0.807289i \(-0.299066\pi\)
0.00293339 + 0.999996i \(0.499066\pi\)
\(62\) −7.51604 + 5.46072i −0.954538 + 0.693512i
\(63\) −5.70389 1.69175i −0.718622 0.213140i
\(64\) 15.1975 + 46.7731i 1.89969 + 5.84663i
\(65\) 1.18450 0.146919
\(66\) 4.05694 + 15.6011i 0.499375 + 1.92036i
\(67\) −8.07121 −0.986055 −0.493028 0.870014i \(-0.664110\pi\)
−0.493028 + 0.870014i \(0.664110\pi\)
\(68\) 1.22326 + 3.76481i 0.148342 + 0.456550i
\(69\) 1.68762 + 4.97445i 0.203166 + 0.598853i
\(70\) −5.33282 + 3.87452i −0.637394 + 0.463094i
\(71\) 2.24884 + 0.730693i 0.266889 + 0.0867174i 0.439404 0.898289i \(-0.355190\pi\)
−0.172516 + 0.985007i \(0.555190\pi\)
\(72\) 32.6044 0.842320i 3.84246 0.0992684i
\(73\) −1.81099 2.49262i −0.211960 0.291739i 0.689778 0.724021i \(-0.257708\pi\)
−0.901738 + 0.432283i \(0.857708\pi\)
\(74\) −25.4565 18.4952i −2.95926 2.15003i
\(75\) 5.94956 + 1.84853i 0.686996 + 0.213450i
\(76\) 26.9971i 3.09678i
\(77\) −1.57301 6.38653i −0.179261 0.727813i
\(78\) 3.96866 + 2.80582i 0.449363 + 0.317696i
\(79\) −5.52280 + 1.79447i −0.621363 + 0.201893i −0.602746 0.797933i \(-0.705927\pi\)
−0.0186178 + 0.999827i \(0.505927\pi\)
\(80\) 13.0605 17.9762i 1.46021 2.00980i
\(81\) 2.33548 8.69169i 0.259497 0.965744i
\(82\) −1.47269 + 4.53247i −0.162631 + 0.500528i
\(83\) 1.50773 4.64031i 0.165495 0.509340i −0.833578 0.552402i \(-0.813711\pi\)
0.999072 + 0.0430622i \(0.0137114\pi\)
\(84\) −20.1762 + 0.260578i −2.20140 + 0.0284314i
\(85\) 0.469175 0.645763i 0.0508891 0.0700429i
\(86\) −1.62814 + 0.529015i −0.175567 + 0.0570452i
\(87\) −4.36573 + 6.17507i −0.468056 + 0.662037i
\(88\) 19.0203 + 30.6329i 2.02757 + 3.26548i
\(89\) 6.98846i 0.740775i 0.928877 + 0.370387i \(0.120775\pi\)
−0.928877 + 0.370387i \(0.879225\pi\)
\(90\) −6.06752 7.91309i −0.639572 0.834113i
\(91\) −1.60441 1.16567i −0.168188 0.122196i
\(92\) 10.4717 + 14.4130i 1.09175 + 1.50266i
\(93\) 3.43021 + 4.59529i 0.355696 + 0.476509i
\(94\) −32.5596 10.5792i −3.35826 1.09117i
\(95\) −4.40407 + 3.19974i −0.451848 + 0.328287i
\(96\) 50.6765 17.1924i 5.17214 1.75469i
\(97\) −2.07371 6.38223i −0.210554 0.648017i −0.999439 0.0334776i \(-0.989342\pi\)
0.788886 0.614540i \(-0.210658\pi\)
\(98\) −8.60658 −0.869396
\(99\) 9.59647 2.62826i 0.964482 0.264150i
\(100\) 21.1296 2.11296
\(101\) 2.57327 + 7.91972i 0.256050 + 0.788041i 0.993621 + 0.112772i \(0.0359728\pi\)
−0.737571 + 0.675270i \(0.764027\pi\)
\(102\) 3.10164 1.05226i 0.307108 0.104189i
\(103\) 4.31896 3.13791i 0.425560 0.309187i −0.354311 0.935128i \(-0.615285\pi\)
0.779871 + 0.625940i \(0.215285\pi\)
\(104\) 10.3396 + 3.35956i 1.01389 + 0.329432i
\(105\) 2.43382 + 3.26047i 0.237517 + 0.318190i
\(106\) −11.8156 16.2628i −1.14763 1.57958i
\(107\) 0.213411 + 0.155052i 0.0206313 + 0.0149895i 0.598053 0.801456i \(-0.295941\pi\)
−0.577422 + 0.816446i \(0.695941\pi\)
\(108\) −1.18229 30.5009i −0.113766 2.93495i
\(109\) 16.4347i 1.57416i −0.616850 0.787081i \(-0.711591\pi\)
0.616850 0.787081i \(-0.288409\pi\)
\(110\) 4.15879 10.2094i 0.396525 0.973430i
\(111\) −11.2121 + 15.8589i −1.06421 + 1.50526i
\(112\) −35.3810 + 11.4960i −3.34319 + 1.08627i
\(113\) 3.41143 4.69543i 0.320920 0.441709i −0.617828 0.786313i \(-0.711987\pi\)
0.938748 + 0.344605i \(0.111987\pi\)
\(114\) −22.3353 + 0.288463i −2.09189 + 0.0270170i
\(115\) 1.11009 3.41650i 0.103516 0.318591i
\(116\) −7.92578 + 24.3930i −0.735890 + 2.26484i
\(117\) 1.70009 2.47178i 0.157173 0.228516i
\(118\) 11.2532 15.4886i 1.03594 1.42584i
\(119\) −1.27100 + 0.412972i −0.116512 + 0.0378571i
\(120\) −18.2126 12.8762i −1.66258 1.17543i
\(121\) 7.86902 + 7.68626i 0.715365 + 0.698751i
\(122\) 13.6674i 1.23738i
\(123\) 2.80913 + 0.872800i 0.253291 + 0.0786977i
\(124\) 15.7340 + 11.4314i 1.41295 + 1.02657i
\(125\) −5.98548 8.23830i −0.535357 0.736856i
\(126\) 0.431163 + 16.6894i 0.0384111 + 1.48681i
\(127\) 10.4290 + 3.38858i 0.925422 + 0.300688i 0.732689 0.680563i \(-0.238265\pi\)
0.192733 + 0.981251i \(0.438265\pi\)
\(128\) 61.6578 44.7970i 5.44983 3.95954i
\(129\) 0.339481 + 1.00065i 0.0298896 + 0.0881027i
\(130\) −1.02713 3.16117i −0.0900849 0.277253i
\(131\) −15.0205 −1.31235 −0.656175 0.754609i \(-0.727827\pi\)
−0.656175 + 0.754609i \(0.727827\pi\)
\(132\) 28.4363 18.1693i 2.47506 1.58144i
\(133\) 9.11420 0.790302
\(134\) 6.99886 + 21.5403i 0.604609 + 1.86080i
\(135\) −4.83551 + 3.80788i −0.416175 + 0.327730i
\(136\) 5.92704 4.30624i 0.508239 0.369257i
\(137\) 4.40232 + 1.43040i 0.376115 + 0.122207i 0.490973 0.871175i \(-0.336641\pi\)
−0.114858 + 0.993382i \(0.536641\pi\)
\(138\) 11.8123 8.81742i 1.00553 0.750589i
\(139\) 0.201376 + 0.277171i 0.0170805 + 0.0235093i 0.817472 0.575969i \(-0.195375\pi\)
−0.800391 + 0.599478i \(0.795375\pi\)
\(140\) 11.1637 + 8.11088i 0.943502 + 0.685495i
\(141\) −6.26986 + 20.1797i −0.528018 + 1.69944i
\(142\) 6.63527i 0.556820i
\(143\) 3.30787 + 0.240793i 0.276618 + 0.0201361i
\(144\) −18.7668 53.0551i −1.56390 4.42126i
\(145\) 4.91864 1.59816i 0.408471 0.132720i
\(146\) −5.08186 + 6.99457i −0.420577 + 0.578875i
\(147\) 0.0686037 + 5.31189i 0.00565834 + 0.438117i
\(148\) −20.3551 + 62.6467i −1.67318 + 5.14952i
\(149\) −3.15665 + 9.71517i −0.258603 + 0.795898i 0.734496 + 0.678614i \(0.237419\pi\)
−0.993098 + 0.117284i \(0.962581\pi\)
\(150\) −0.225769 17.4810i −0.0184340 1.42732i
\(151\) −11.1303 + 15.3195i −0.905768 + 1.24668i 0.0628238 + 0.998025i \(0.479989\pi\)
−0.968591 + 0.248658i \(0.920011\pi\)
\(152\) −47.5189 + 15.4398i −3.85429 + 1.25234i
\(153\) −0.674165 1.90591i −0.0545030 0.154084i
\(154\) −15.6802 + 9.73601i −1.26355 + 0.784550i
\(155\) 3.92157i 0.314988i
\(156\) 3.01889 9.71641i 0.241705 0.777935i
\(157\) 4.93237 + 3.58358i 0.393646 + 0.286001i 0.766948 0.641709i \(-0.221774\pi\)
−0.373302 + 0.927710i \(0.621774\pi\)
\(158\) 9.57806 + 13.1831i 0.761990 + 1.04879i
\(159\) −9.94302 + 7.42209i −0.788533 + 0.588610i
\(160\) −34.8051 11.3089i −2.75159 0.894045i
\(161\) −4.86582 + 3.53522i −0.383480 + 0.278615i
\(162\) −25.2214 + 1.30404i −1.98158 + 0.102455i
\(163\) −1.12710 3.46884i −0.0882809 0.271701i 0.897164 0.441699i \(-0.145624\pi\)
−0.985444 + 0.169998i \(0.945624\pi\)
\(164\) 9.97652 0.779035
\(165\) −6.33429 2.48538i −0.493124 0.193486i
\(166\) −13.6914 −1.06266
\(167\) 6.12638 + 18.8551i 0.474074 + 1.45905i 0.847203 + 0.531269i \(0.178285\pi\)
−0.373129 + 0.927779i \(0.621715\pi\)
\(168\) 11.9975 + 35.3640i 0.925631 + 2.72839i
\(169\) 0.809017 0.587785i 0.0622321 0.0452143i
\(170\) −2.13024 0.692156i −0.163382 0.0530860i
\(171\) 0.356073 + 13.7828i 0.0272296 + 1.05400i
\(172\) 2.10647 + 2.89930i 0.160617 + 0.221070i
\(173\) 13.0717 + 9.49713i 0.993821 + 0.722053i 0.960755 0.277400i \(-0.0894726\pi\)
0.0330666 + 0.999453i \(0.489473\pi\)
\(174\) 20.2656 + 6.29653i 1.53633 + 0.477339i
\(175\) 7.13334i 0.539230i
\(176\) 40.1274 47.5459i 3.02472 3.58391i
\(177\) −9.64912 6.82186i −0.725272 0.512763i
\(178\) 18.6506 6.05996i 1.39792 0.454213i
\(179\) 2.43105 3.34605i 0.181705 0.250096i −0.708442 0.705769i \(-0.750602\pi\)
0.890147 + 0.455674i \(0.150602\pi\)
\(180\) −11.8294 + 17.1989i −0.881711 + 1.28193i
\(181\) −3.66674 + 11.2851i −0.272546 + 0.838811i 0.717312 + 0.696752i \(0.245372\pi\)
−0.989858 + 0.142059i \(0.954628\pi\)
\(182\) −1.71967 + 5.29261i −0.127471 + 0.392315i
\(183\) −8.43535 + 0.108944i −0.623559 + 0.00805335i
\(184\) 19.3802 26.6746i 1.42873 1.96647i
\(185\) 12.6321 4.10443i 0.928733 0.301764i
\(186\) 9.28934 13.1392i 0.681127 0.963414i
\(187\) 1.44151 1.70800i 0.105413 0.124901i
\(188\) 71.6675i 5.22689i
\(189\) 10.2971 0.399142i 0.749002 0.0290333i
\(190\) 12.3583 + 8.97885i 0.896568 + 0.651394i
\(191\) −1.72251 2.37083i −0.124636 0.171547i 0.742139 0.670246i \(-0.233811\pi\)
−0.866775 + 0.498699i \(0.833811\pi\)
\(192\) −50.9548 68.2617i −3.67734 4.92636i
\(193\) 10.1218 + 3.28878i 0.728584 + 0.236731i 0.649741 0.760156i \(-0.274877\pi\)
0.0788433 + 0.996887i \(0.474877\pi\)
\(194\) −15.2346 + 11.0686i −1.09378 + 0.794676i
\(195\) −1.94285 + 0.659129i −0.139131 + 0.0472012i
\(196\) 5.56754 + 17.1351i 0.397681 + 1.22394i
\(197\) −5.59541 −0.398657 −0.199328 0.979933i \(-0.563876\pi\)
−0.199328 + 0.979933i \(0.563876\pi\)
\(198\) −15.3357 23.3318i −1.08986 1.65812i
\(199\) −11.3871 −0.807209 −0.403605 0.914934i \(-0.632243\pi\)
−0.403605 + 0.914934i \(0.632243\pi\)
\(200\) −12.0842 37.1913i −0.854481 2.62982i
\(201\) 13.2386 4.49132i 0.933781 0.316793i
\(202\) 18.9046 13.7350i 1.33012 0.966390i
\(203\) −8.23508 2.67574i −0.577989 0.187800i
\(204\) −4.10140 5.49445i −0.287155 0.384689i
\(205\) −1.18243 1.62748i −0.0825848 0.113668i
\(206\) −12.1195 8.80535i −0.844407 0.613498i
\(207\) −5.53617 7.22013i −0.384791 0.501834i
\(208\) 18.7588i 1.30069i
\(209\) −12.9494 + 8.04041i −0.895728 + 0.556167i
\(210\) 6.59102 9.32261i 0.454824 0.643321i
\(211\) 16.1720 5.25461i 1.11333 0.361742i 0.306111 0.951996i \(-0.400972\pi\)
0.807218 + 0.590254i \(0.200972\pi\)
\(212\) −24.7346 + 34.0443i −1.69878 + 2.33817i
\(213\) −4.09522 + 0.0528903i −0.280600 + 0.00362398i
\(214\) 0.228743 0.703999i 0.0156366 0.0481244i
\(215\) 0.223305 0.687261i 0.0152292 0.0468708i
\(216\) −53.0099 + 19.5247i −3.60687 + 1.32849i
\(217\) −3.85924 + 5.31179i −0.261982 + 0.360588i
\(218\) −43.8606 + 14.2512i −2.97062 + 0.965212i
\(219\) 4.35748 + 3.08071i 0.294451 + 0.208175i
\(220\) −23.0166 1.67546i −1.55178 0.112960i
\(221\) 0.673877i 0.0453299i
\(222\) 52.0464 + 16.1709i 3.49313 + 1.08532i
\(223\) −19.9792 14.5157i −1.33791 0.972046i −0.999518 0.0310394i \(-0.990118\pi\)
−0.338388 0.941007i \(-0.609882\pi\)
\(224\) 36.0146 + 49.5698i 2.40632 + 3.31202i
\(225\) −10.7873 + 0.278685i −0.719152 + 0.0185790i
\(226\) −15.4892 5.03276i −1.03033 0.334774i
\(227\) 9.57947 6.95989i 0.635812 0.461944i −0.222597 0.974911i \(-0.571453\pi\)
0.858409 + 0.512966i \(0.171453\pi\)
\(228\) 15.0228 + 44.2814i 0.994912 + 2.93261i
\(229\) −3.31259 10.1951i −0.218902 0.673712i −0.998853 0.0478717i \(-0.984756\pi\)
0.779951 0.625840i \(-0.215244\pi\)
\(230\) −10.0805 −0.664688
\(231\) 6.13395 + 9.60006i 0.403584 + 0.631638i
\(232\) 47.4682 3.11644
\(233\) −7.84150 24.1337i −0.513714 1.58105i −0.785610 0.618722i \(-0.787651\pi\)
0.271897 0.962326i \(-0.412349\pi\)
\(234\) −8.07085 2.39378i −0.527608 0.156486i
\(235\) 11.6912 8.49416i 0.762650 0.554098i
\(236\) −38.1164 12.3848i −2.48117 0.806180i
\(237\) 8.06010 6.01656i 0.523560 0.390818i
\(238\) 2.20426 + 3.03390i 0.142881 + 0.196659i
\(239\) 12.9068 + 9.37736i 0.834874 + 0.606571i 0.920934 0.389719i \(-0.127428\pi\)
−0.0860603 + 0.996290i \(0.527428\pi\)
\(240\) −11.4191 + 36.7528i −0.737101 + 2.37238i
\(241\) 18.4314i 1.18727i 0.804735 + 0.593634i \(0.202307\pi\)
−0.804735 + 0.593634i \(0.797693\pi\)
\(242\) 13.6894 27.6657i 0.879987 1.77842i
\(243\) 1.00588 + 15.5560i 0.0645272 + 0.997916i
\(244\) −27.2108 + 8.84132i −1.74199 + 0.566008i
\(245\) 2.13540 2.93912i 0.136425 0.187774i
\(246\) −0.106599 8.25379i −0.00679649 0.526242i
\(247\) −1.42018 + 4.37086i −0.0903639 + 0.278111i
\(248\) 11.1226 34.2319i 0.706287 2.17373i
\(249\) 0.109135 + 8.45016i 0.00691614 + 0.535507i
\(250\) −16.7960 + 23.1177i −1.06227 + 1.46209i
\(251\) 7.20681 2.34163i 0.454890 0.147803i −0.0726054 0.997361i \(-0.523131\pi\)
0.527495 + 0.849558i \(0.323131\pi\)
\(252\) 32.9485 11.6547i 2.07556 0.734175i
\(253\) 3.79460 9.31536i 0.238564 0.585652i
\(254\) 30.7710i 1.93074i
\(255\) −0.410211 + 1.32028i −0.0256884 + 0.0826790i
\(256\) −93.4441 67.8911i −5.84026 4.24320i
\(257\) −2.24172 3.08546i −0.139835 0.192466i 0.733356 0.679845i \(-0.237953\pi\)
−0.873190 + 0.487379i \(0.837953\pi\)
\(258\) 2.37615 1.77370i 0.147933 0.110426i
\(259\) −21.1495 6.87188i −1.31416 0.426998i
\(260\) −5.62923 + 4.08988i −0.349110 + 0.253643i
\(261\) 3.72461 12.5579i 0.230548 0.777314i
\(262\) 13.0249 + 40.0864i 0.804679 + 2.47655i
\(263\) −7.38026 −0.455086 −0.227543 0.973768i \(-0.573069\pi\)
−0.227543 + 0.973768i \(0.573069\pi\)
\(264\) −48.2436 39.6609i −2.96919 2.44096i
\(265\) 8.48528 0.521246
\(266\) −7.90327 24.3238i −0.484581 1.49139i
\(267\) −3.88881 11.4627i −0.237991 0.701504i
\(268\) 38.3577 27.8685i 2.34307 1.70234i
\(269\) −0.285834 0.0928730i −0.0174276 0.00566257i 0.300290 0.953848i \(-0.402916\pi\)
−0.317718 + 0.948185i \(0.602916\pi\)
\(270\) 14.3554 + 9.60294i 0.873645 + 0.584416i
\(271\) −5.79405 7.97482i −0.351963 0.484436i 0.595924 0.803041i \(-0.296786\pi\)
−0.947888 + 0.318605i \(0.896786\pi\)
\(272\) −10.2269 7.43027i −0.620096 0.450526i
\(273\) 3.28025 + 1.01918i 0.198530 + 0.0616834i
\(274\) 12.9892i 0.784704i
\(275\) −6.29293 10.1350i −0.379478 0.611164i
\(276\) −25.1962 17.8135i −1.51663 1.07225i
\(277\) 10.7258 3.48503i 0.644451 0.209395i 0.0314853 0.999504i \(-0.489976\pi\)
0.612966 + 0.790109i \(0.289976\pi\)
\(278\) 0.565086 0.777774i 0.0338916 0.0466478i
\(279\) −8.18343 5.62855i −0.489929 0.336972i
\(280\) 7.89178 24.2884i 0.471624 1.45151i
\(281\) 4.12427 12.6932i 0.246033 0.757213i −0.749431 0.662082i \(-0.769673\pi\)
0.995465 0.0951309i \(-0.0303270\pi\)
\(282\) 59.2921 0.765765i 3.53079 0.0456006i
\(283\) −6.78591 + 9.34001i −0.403381 + 0.555206i −0.961588 0.274495i \(-0.911489\pi\)
0.558208 + 0.829701i \(0.311489\pi\)
\(284\) −13.2104 + 4.29231i −0.783892 + 0.254702i
\(285\) 5.44314 7.69900i 0.322424 0.456049i
\(286\) −2.22576 9.03678i −0.131612 0.534356i
\(287\) 3.36807i 0.198811i
\(288\) −73.5541 + 56.3990i −4.33421 + 3.32334i
\(289\) 13.3859 + 9.72543i 0.787406 + 0.572084i
\(290\) −8.53028 11.7409i −0.500916 0.689451i
\(291\) 6.95283 + 9.31438i 0.407582 + 0.546018i
\(292\) 17.2131 + 5.59289i 1.00732 + 0.327299i
\(293\) −24.2776 + 17.6387i −1.41832 + 1.03047i −0.426268 + 0.904597i \(0.640172\pi\)
−0.992047 + 0.125869i \(0.959828\pi\)
\(294\) 14.1168 4.78923i 0.823306 0.279314i
\(295\) 2.49728 + 7.68584i 0.145397 + 0.447487i
\(296\) 121.909 7.08580
\(297\) −14.2779 + 9.65101i −0.828487 + 0.560009i
\(298\) 28.6649 1.66051
\(299\) −0.937179 2.88434i −0.0541985 0.166806i
\(300\) −34.6574 + 11.7578i −2.00095 + 0.678838i
\(301\) −0.978803 + 0.711142i −0.0564173 + 0.0409895i
\(302\) 50.5358 + 16.4201i 2.90801 + 0.944869i
\(303\) −8.62777 11.5582i −0.495653 0.664003i
\(304\) 50.6740 + 69.7467i 2.90635 + 4.00025i
\(305\) 4.66736 + 3.39104i 0.267252 + 0.194170i
\(306\) −4.50185 + 3.45188i −0.257354 + 0.197331i
\(307\) 26.8996i 1.53524i −0.640904 0.767621i \(-0.721440\pi\)
0.640904 0.767621i \(-0.278560\pi\)
\(308\) 29.5272 + 24.9201i 1.68247 + 1.41996i
\(309\) −5.33796 + 7.55023i −0.303666 + 0.429517i
\(310\) −10.4658 + 3.40055i −0.594418 + 0.193138i
\(311\) 13.7189 18.8825i 0.777928 1.07073i −0.217580 0.976043i \(-0.569816\pi\)
0.995507 0.0946832i \(-0.0301838\pi\)
\(312\) −18.8289 + 0.243177i −1.06597 + 0.0137672i
\(313\) −8.55847 + 26.3403i −0.483753 + 1.48884i 0.350025 + 0.936740i \(0.386173\pi\)
−0.833779 + 0.552099i \(0.813827\pi\)
\(314\) 5.28672 16.2709i 0.298347 0.918218i
\(315\) −5.80635 3.99360i −0.327151 0.225014i
\(316\) 20.0506 27.5973i 1.12794 1.55247i
\(317\) 17.2115 5.59237i 0.966696 0.314099i 0.217215 0.976124i \(-0.430303\pi\)
0.749482 + 0.662025i \(0.230303\pi\)
\(318\) 28.4299 + 20.0997i 1.59427 + 1.12714i
\(319\) 14.0608 3.46319i 0.787255 0.193901i
\(320\) 58.2539i 3.25649i
\(321\) −0.436324 0.135566i −0.0243532 0.00756657i
\(322\) 13.6541 + 9.92025i 0.760911 + 0.552834i
\(323\) 1.82037 + 2.50553i 0.101288 + 0.139411i
\(324\) 18.9118 + 49.3705i 1.05065 + 2.74280i
\(325\) −3.42091 1.11152i −0.189758 0.0616561i
\(326\) −8.28022 + 6.01593i −0.458599 + 0.333192i
\(327\) 9.14529 + 26.9567i 0.505736 + 1.49071i
\(328\) −5.70564 17.5602i −0.315041 0.969598i
\(329\) −24.1949 −1.33391
\(330\) −1.14022 + 19.0600i −0.0627668 + 1.04922i
\(331\) −20.1870 −1.10958 −0.554789 0.831991i \(-0.687201\pi\)
−0.554789 + 0.831991i \(0.687201\pi\)
\(332\) 8.85684 + 27.2586i 0.486082 + 1.49601i
\(333\) 9.56561 32.2514i 0.524192 1.76736i
\(334\) 45.0075 32.6999i 2.46270 1.78926i
\(335\) −9.09244 2.95431i −0.496773 0.161411i
\(336\) 51.6358 38.5442i 2.81696 2.10276i
\(337\) −9.54900 13.1431i −0.520167 0.715948i 0.465425 0.885087i \(-0.345901\pi\)
−0.985592 + 0.169139i \(0.945901\pi\)
\(338\) −2.27020 1.64940i −0.123482 0.0897153i
\(339\) −2.98270 + 9.59990i −0.161998 + 0.521395i
\(340\) 4.68891i 0.254292i
\(341\) 0.797202 10.9515i 0.0431709 0.593057i
\(342\) 36.4744 12.9019i 1.97231 0.697653i
\(343\) −18.9875 + 6.16941i −1.02523 + 0.333117i
\(344\) 3.89850 5.36583i 0.210193 0.289306i
\(345\) 0.0803524 + 6.22157i 0.00432603 + 0.334958i
\(346\) 14.0108 43.1207i 0.753224 2.31818i
\(347\) −9.39368 + 28.9108i −0.504279 + 1.55201i 0.297700 + 0.954659i \(0.403780\pi\)
−0.801979 + 0.597352i \(0.796220\pi\)
\(348\) −0.573698 44.4206i −0.0307534 2.38119i
\(349\) −9.41728 + 12.9618i −0.504095 + 0.693828i −0.982910 0.184088i \(-0.941067\pi\)
0.478814 + 0.877916i \(0.341067\pi\)
\(350\) 19.0373 6.18560i 1.01759 0.330634i
\(351\) −1.41308 + 5.00032i −0.0754246 + 0.266897i
\(352\) −94.8989 38.6569i −5.05813 2.06042i
\(353\) 30.9347i 1.64649i 0.567686 + 0.823245i \(0.307839\pi\)
−0.567686 + 0.823245i \(0.692161\pi\)
\(354\) −9.83892 + 31.6669i −0.522932 + 1.68307i
\(355\) 2.26593 + 1.64629i 0.120263 + 0.0873761i
\(356\) −24.1299 33.2120i −1.27888 1.76023i
\(357\) 1.85492 1.38463i 0.0981729 0.0732824i
\(358\) −11.0379 3.58644i −0.583372 0.189549i
\(359\) 0.0796687 0.0578827i 0.00420476 0.00305493i −0.585681 0.810542i \(-0.699173\pi\)
0.589886 + 0.807487i \(0.299173\pi\)
\(360\) 37.0380 + 10.9853i 1.95208 + 0.578977i
\(361\) −0.655534 2.01752i −0.0345018 0.106186i
\(362\) 33.2969 1.75004
\(363\) −17.1841 8.22842i −0.901931 0.431880i
\(364\) 11.6497 0.610609
\(365\) −1.12776 3.47088i −0.0590295 0.181674i
\(366\) 7.60536 + 22.4176i 0.397539 + 1.17179i
\(367\) −6.24492 + 4.53720i −0.325982 + 0.236840i −0.738724 0.674008i \(-0.764571\pi\)
0.412742 + 0.910848i \(0.364571\pi\)
\(368\) −54.1068 17.5804i −2.82051 0.916440i
\(369\) −5.09330 + 0.131583i −0.265147 + 0.00684995i
\(370\) −21.9076 30.1533i −1.13892 1.56759i
\(371\) −11.4933 8.35040i −0.596704 0.433531i
\(372\) −32.1685 9.99478i −1.66786 0.518205i
\(373\) 0.280713i 0.0145348i 0.999974 + 0.00726739i \(0.00231330\pi\)
−0.999974 + 0.00726739i \(0.997687\pi\)
\(374\) −5.80826 2.36598i −0.300338 0.122342i
\(375\) 14.4019 + 10.1820i 0.743708 + 0.525797i
\(376\) 126.146 40.9872i 6.50546 2.11375i
\(377\) 2.56639 3.53233i 0.132176 0.181924i
\(378\) −9.99420 27.1345i −0.514046 1.39565i
\(379\) 3.75236 11.5486i 0.192746 0.593211i −0.807250 0.590210i \(-0.799045\pi\)
0.999995 0.00300084i \(-0.000955199\pi\)
\(380\) 9.88177 30.4130i 0.506924 1.56015i
\(381\) −18.9915 + 0.245278i −0.972965 + 0.0125660i
\(382\) −4.83356 + 6.65283i −0.247307 + 0.340388i
\(383\) 18.9733 6.16480i 0.969491 0.315007i 0.218880 0.975752i \(-0.429760\pi\)
0.750610 + 0.660745i \(0.229760\pi\)
\(384\) −76.2051 + 107.788i −3.88883 + 5.50051i
\(385\) 0.565635 7.77037i 0.0288274 0.396015i
\(386\) 29.8647i 1.52007i
\(387\) −1.11365 1.45240i −0.0566101 0.0738294i
\(388\) 31.8919 + 23.1708i 1.61906 + 1.17632i
\(389\) 12.4219 + 17.0973i 0.629818 + 0.866870i 0.998021 0.0628756i \(-0.0200271\pi\)
−0.368204 + 0.929745i \(0.620027\pi\)
\(390\) 3.44379 + 4.61348i 0.174383 + 0.233613i
\(391\) −1.94369 0.631543i −0.0982966 0.0319385i
\(392\) 26.9763 19.5994i 1.36251 0.989919i
\(393\) 24.6371 8.35834i 1.24278 0.421623i
\(394\) 4.85200 + 14.9329i 0.244440 + 0.752309i
\(395\) −6.87841 −0.346090
\(396\) −36.5314 + 45.6255i −1.83577 + 2.29277i
\(397\) −34.2780 −1.72036 −0.860181 0.509989i \(-0.829650\pi\)
−0.860181 + 0.509989i \(0.829650\pi\)
\(398\) 9.87418 + 30.3896i 0.494948 + 1.52329i
\(399\) −14.9494 + 5.07170i −0.748405 + 0.253903i
\(400\) −54.5882 + 39.6606i −2.72941 + 1.98303i
\(401\) −25.6507 8.33442i −1.28094 0.416201i −0.412026 0.911172i \(-0.635179\pi\)
−0.868909 + 0.494971i \(0.835179\pi\)
\(402\) −23.4661 31.4364i −1.17038 1.56790i
\(403\) −1.94600 2.67845i −0.0969374 0.133423i
\(404\) −39.5747 28.7527i −1.96891 1.43050i
\(405\) 5.81240 8.93657i 0.288821 0.444062i
\(406\) 24.2978i 1.20588i
\(407\) 36.1113 8.89422i 1.78997 0.440870i
\(408\) −7.32544 + 10.3614i −0.362663 + 0.512965i
\(409\) 5.80659 1.88667i 0.287117 0.0932900i −0.161918 0.986804i \(-0.551768\pi\)
0.449035 + 0.893514i \(0.351768\pi\)
\(410\) −3.31805 + 4.56690i −0.163867 + 0.225543i
\(411\) −8.01677 + 0.103538i −0.395438 + 0.00510714i
\(412\) −9.69082 + 29.8253i −0.477432 + 1.46939i
\(413\) 4.18109 12.8681i 0.205738 0.633197i
\(414\) −14.4683 + 21.0357i −0.711078 + 1.03385i
\(415\) 3.39699 4.67556i 0.166752 0.229514i
\(416\) −29.3838 + 9.54738i −1.44066 + 0.468099i
\(417\) −0.484538 0.342565i −0.0237279 0.0167755i
\(418\) 32.6870 + 27.5869i 1.59877 + 1.34932i
\(419\) 18.1444i 0.886414i −0.896419 0.443207i \(-0.853841\pi\)
0.896419 0.443207i \(-0.146159\pi\)
\(420\) −22.8244 7.09155i −1.11372 0.346032i
\(421\) −11.0106 7.99966i −0.536623 0.389880i 0.286206 0.958168i \(-0.407606\pi\)
−0.822829 + 0.568289i \(0.807606\pi\)
\(422\) −28.0468 38.6031i −1.36530 1.87917i
\(423\) −0.945244 36.5883i −0.0459593 1.77899i
\(424\) 74.0690 + 24.0665i 3.59711 + 1.16877i
\(425\) −1.96098 + 1.42474i −0.0951216 + 0.0691099i
\(426\) 3.69227 + 10.8834i 0.178891 + 0.527301i
\(427\) −2.98482 9.18635i −0.144446 0.444558i
\(428\) −1.54959 −0.0749021
\(429\) −5.55966 + 1.44575i −0.268423 + 0.0698014i
\(430\) −2.02778 −0.0977883
\(431\) −0.982984 3.02531i −0.0473487 0.145724i 0.924587 0.380971i \(-0.124410\pi\)
−0.971936 + 0.235247i \(0.924410\pi\)
\(432\) 60.3050 + 76.5795i 2.90143 + 3.68443i
\(433\) −10.4846 + 7.61748i −0.503856 + 0.366073i −0.810488 0.585755i \(-0.800798\pi\)
0.306632 + 0.951828i \(0.400798\pi\)
\(434\) 17.5225 + 5.69340i 0.841105 + 0.273292i
\(435\) −7.17838 + 5.35839i −0.344177 + 0.256915i
\(436\) 56.7463 + 78.1046i 2.71765 + 3.74053i
\(437\) 11.2761 + 8.19256i 0.539409 + 0.391903i
\(438\) 4.44319 14.3006i 0.212304 0.683307i
\(439\) 2.56094i 0.122227i 0.998131 + 0.0611134i \(0.0194651\pi\)
−0.998131 + 0.0611134i \(0.980535\pi\)
\(440\) 10.2143 + 41.4708i 0.486946 + 1.97704i
\(441\) −3.06839 8.67454i −0.146114 0.413073i
\(442\) −1.79843 + 0.584344i −0.0855424 + 0.0277944i
\(443\) −19.7401 + 27.1699i −0.937880 + 1.29088i 0.0188256 + 0.999823i \(0.494007\pi\)
−0.956705 + 0.291058i \(0.905993\pi\)
\(444\) −1.47338 114.082i −0.0699235 5.41408i
\(445\) −2.55799 + 7.87269i −0.121260 + 0.373201i
\(446\) −21.4145 + 65.9072i −1.01401 + 3.12080i
\(447\) −0.228490 17.6917i −0.0108072 0.836787i
\(448\) 57.3279 78.9051i 2.70849 3.72791i
\(449\) 11.0597 3.59352i 0.521940 0.169589i −0.0361856 0.999345i \(-0.511521\pi\)
0.558126 + 0.829756i \(0.311521\pi\)
\(450\) 10.0978 + 28.5472i 0.476015 + 1.34573i
\(451\) −2.97126 4.78532i −0.139911 0.225332i
\(452\) 34.0937i 1.60363i
\(453\) 9.73147 31.3210i 0.457224 1.47159i
\(454\) −26.8811 19.5303i −1.26159 0.916602i
\(455\) −1.38074 1.90042i −0.0647301 0.0890933i
\(456\) 69.3502 51.7673i 3.24762 2.42423i
\(457\) −16.1920 5.26110i −0.757430 0.246104i −0.0952550 0.995453i \(-0.530367\pi\)
−0.662175 + 0.749349i \(0.730367\pi\)
\(458\) −24.3360 + 17.6811i −1.13715 + 0.826186i
\(459\) 2.16635 + 2.75098i 0.101117 + 0.128405i
\(460\) 6.52100 + 20.0696i 0.304043 + 0.935749i
\(461\) −8.65253 −0.402988 −0.201494 0.979490i \(-0.564580\pi\)
−0.201494 + 0.979490i \(0.564580\pi\)
\(462\) 20.3014 24.6947i 0.944509 1.14890i
\(463\) −31.9795 −1.48621 −0.743107 0.669173i \(-0.766649\pi\)
−0.743107 + 0.669173i \(0.766649\pi\)
\(464\) −25.3100 77.8960i −1.17499 3.61623i
\(465\) 2.18221 + 6.43228i 0.101197 + 0.298290i
\(466\) −57.6077 + 41.8544i −2.66862 + 1.93887i
\(467\) 36.2650 + 11.7832i 1.67814 + 0.545262i 0.984550 0.175104i \(-0.0560261\pi\)
0.693594 + 0.720366i \(0.256026\pi\)
\(468\) 0.455128 + 17.6170i 0.0210383 + 0.814347i
\(469\) 9.40839 + 12.9495i 0.434439 + 0.597954i
\(470\) −32.8069 23.8356i −1.51327 1.09945i
\(471\) −10.0843 3.13321i −0.464662 0.144371i
\(472\) 74.1735i 3.41411i
\(473\) 0.763318 1.87387i 0.0350974 0.0861606i
\(474\) −23.0461 16.2934i −1.05854 0.748382i
\(475\) 15.7218 5.10833i 0.721366 0.234386i
\(476\) 4.61438 6.35115i 0.211500 0.291104i
\(477\) 12.1787 17.7068i 0.557625 0.810740i
\(478\) 13.8341 42.5769i 0.632756 1.94742i
\(479\) −6.85510 + 21.0978i −0.313217 + 0.963984i 0.663265 + 0.748385i \(0.269170\pi\)
−0.976482 + 0.215599i \(0.930830\pi\)
\(480\) 63.3813 0.818579i 2.89295 0.0373628i
\(481\) 6.59104 9.07179i 0.300526 0.413638i
\(482\) 49.1892 15.9825i 2.24051 0.727985i
\(483\) 6.01384 8.50621i 0.273639 0.387046i
\(484\) −63.9361 9.35790i −2.90619 0.425359i
\(485\) 7.94880i 0.360936i
\(486\) 40.6432 16.1736i 1.84361 0.733652i
\(487\) 16.5962 + 12.0578i 0.752045 + 0.546392i 0.896460 0.443125i \(-0.146130\pi\)
−0.144415 + 0.989517i \(0.546130\pi\)
\(488\) 31.1241 + 42.8386i 1.40892 + 1.93921i
\(489\) 3.77897 + 5.06251i 0.170891 + 0.228935i
\(490\) −9.69554 3.15027i −0.438000 0.142315i
\(491\) −14.6492 + 10.6433i −0.661109 + 0.480324i −0.867037 0.498243i \(-0.833979\pi\)
0.205928 + 0.978567i \(0.433979\pi\)
\(492\) −16.3638 + 5.55155i −0.737736 + 0.250283i
\(493\) −0.909214 2.79827i −0.0409490 0.126028i
\(494\) 12.8964 0.580234
\(495\) 11.7727 + 0.551800i 0.529144 + 0.0248016i
\(496\) −62.1056 −2.78862
\(497\) −1.44908 4.45982i −0.0650002 0.200050i
\(498\) 22.4570 7.61871i 1.00632 0.341403i
\(499\) 16.3053 11.8465i 0.729927 0.530323i −0.159614 0.987180i \(-0.551025\pi\)
0.889540 + 0.456857i \(0.151025\pi\)
\(500\) 56.8909 + 18.4850i 2.54424 + 0.826673i
\(501\) −20.5408 27.5175i −0.917695 1.22939i
\(502\) −12.4986 17.2028i −0.557840 0.767800i
\(503\) 28.8657 + 20.9721i 1.28706 + 0.935102i 0.999742 0.0227345i \(-0.00723724\pi\)
0.287315 + 0.957836i \(0.407237\pi\)
\(504\) −39.3574 51.3289i −1.75312 2.28637i
\(505\) 9.86367i 0.438928i
\(506\) −28.1511 2.04922i −1.25147 0.0910991i
\(507\) −0.999893 + 1.41429i −0.0444068 + 0.0628108i
\(508\) −61.2630 + 19.9055i −2.71810 + 0.883166i
\(509\) 10.9111 15.0179i 0.483627 0.665655i −0.495570 0.868568i \(-0.665041\pi\)
0.979197 + 0.202913i \(0.0650408\pi\)
\(510\) 3.87924 0.0501008i 0.171775 0.00221850i
\(511\) −1.88816 + 5.81114i −0.0835271 + 0.257070i
\(512\) −53.0549 + 163.286i −2.34472 + 7.21630i
\(513\) −8.25363 22.4088i −0.364407 0.989372i
\(514\) −6.29053 + 8.65817i −0.277463 + 0.381896i
\(515\) 6.01400 1.95407i 0.265008 0.0861065i
\(516\) −5.06844 3.58335i −0.223126 0.157748i
\(517\) 34.3760 21.3444i 1.51185 0.938725i
\(518\) 62.4021i 2.74179i
\(519\) −26.7253 8.30358i −1.17311 0.364487i
\(520\) 10.4182 + 7.56926i 0.456868 + 0.331934i
\(521\) 18.5921 + 25.5898i 0.814533 + 1.12111i 0.990608 + 0.136732i \(0.0436598\pi\)
−0.176075 + 0.984377i \(0.556340\pi\)
\(522\) −36.7440 + 0.949265i −1.60824 + 0.0415482i
\(523\) 21.7263 + 7.05930i 0.950025 + 0.308682i 0.742726 0.669596i \(-0.233533\pi\)
0.207299 + 0.978278i \(0.433533\pi\)
\(524\) 71.3837 51.8633i 3.11841 2.26566i
\(525\) −3.96943 11.7003i −0.173240 0.510644i
\(526\) 6.39971 + 19.6963i 0.279041 + 0.858799i
\(527\) −2.23103 −0.0971852
\(528\) −39.3607 + 100.316i −1.71295 + 4.36567i
\(529\) 13.8023 0.600099
\(530\) −7.35791 22.6453i −0.319607 0.983650i
\(531\) 19.6229 + 5.82005i 0.851560 + 0.252569i
\(532\) −43.3144 + 31.4698i −1.87792 + 1.36439i
\(533\) −1.61521 0.524814i −0.0699625 0.0227322i
\(534\) −27.2192 + 20.3181i −1.17789 + 0.879249i
\(535\) 0.183660 + 0.252786i 0.00794030 + 0.0109289i
\(536\) −70.9898 51.5771i −3.06629 2.22779i
\(537\) −2.12553 + 6.84107i −0.0917232 + 0.295214i
\(538\) 0.843360i 0.0363598i
\(539\) 6.56086 7.77378i 0.282596 0.334840i
\(540\) 9.83237 34.7928i 0.423118 1.49724i
\(541\) −20.1942 + 6.56150i −0.868217 + 0.282101i −0.709056 0.705152i \(-0.750879\pi\)
−0.159161 + 0.987253i \(0.550879\pi\)
\(542\) −16.2588 + 22.3783i −0.698374 + 0.961230i
\(543\) −0.265412 20.5505i −0.0113899 0.881905i
\(544\) −6.43376 + 19.8011i −0.275845 + 0.848964i
\(545\) 6.01562 18.5142i 0.257681 0.793060i
\(546\) −0.124476 9.63803i −0.00532710 0.412470i
\(547\) −8.46578 + 11.6521i −0.361970 + 0.498210i −0.950696 0.310123i \(-0.899630\pi\)
0.588726 + 0.808333i \(0.299630\pi\)
\(548\) −25.8605 + 8.40260i −1.10471 + 0.358941i
\(549\) 13.7753 4.87264i 0.587915 0.207959i
\(550\) −21.5912 + 25.5829i −0.920653 + 1.09086i
\(551\) 20.0662i 0.854847i
\(552\) −16.9446 + 54.5367i −0.721210 + 2.32124i
\(553\) 9.31683 + 6.76908i 0.396192 + 0.287850i
\(554\) −18.6015 25.6028i −0.790303 1.08776i
\(555\) −18.4356 + 13.7615i −0.782549 + 0.584143i
\(556\) −1.91405 0.621911i −0.0811736 0.0263749i
\(557\) −9.04767 + 6.57352i −0.383362 + 0.278529i −0.762730 0.646717i \(-0.776141\pi\)
0.379368 + 0.925246i \(0.376141\pi\)
\(558\) −7.92517 + 26.7205i −0.335499 + 1.13117i
\(559\) −0.188522 0.580211i −0.00797363 0.0245403i
\(560\) −44.0655 −1.86211
\(561\) −1.41396 + 3.60366i −0.0596975 + 0.152146i
\(562\) −37.4516 −1.57980
\(563\) −8.46418 26.0501i −0.356722 1.09788i −0.955004 0.296593i \(-0.904150\pi\)
0.598282 0.801286i \(-0.295850\pi\)
\(564\) −39.8802 117.551i −1.67926 4.94980i
\(565\) 5.56174 4.04084i 0.233984 0.169999i
\(566\) 30.8107 + 10.0110i 1.29507 + 0.420794i
\(567\) −16.6674 + 6.38461i −0.699967 + 0.268128i
\(568\) 15.1102 + 20.7974i 0.634011 + 0.872641i
\(569\) −4.48946 3.26178i −0.188208 0.136741i 0.489691 0.871896i \(-0.337109\pi\)
−0.677899 + 0.735155i \(0.737109\pi\)
\(570\) −25.2669 7.85044i −1.05831 0.328819i
\(571\) 20.8993i 0.874609i 0.899314 + 0.437304i \(0.144067\pi\)
−0.899314 + 0.437304i \(0.855933\pi\)
\(572\) −16.5518 + 10.2772i −0.692065 + 0.429710i
\(573\) 4.14458 + 2.93019i 0.173142 + 0.122411i
\(574\) 8.98862 2.92058i 0.375178 0.121903i
\(575\) −6.41201 + 8.82538i −0.267399 + 0.368044i
\(576\) 121.562 + 83.6104i 5.06510 + 3.48377i
\(577\) −7.38341 + 22.7238i −0.307375 + 0.946004i 0.671405 + 0.741091i \(0.265691\pi\)
−0.978780 + 0.204913i \(0.934309\pi\)
\(578\) 14.3476 44.1573i 0.596780 1.83670i
\(579\) −18.4322 + 0.238054i −0.766015 + 0.00989319i
\(580\) −17.8572 + 24.5783i −0.741481 + 1.02056i
\(581\) −9.20247 + 2.99006i −0.381783 + 0.124049i
\(582\) 18.8289 26.6324i 0.780484 1.10395i
\(583\) 23.6962 + 1.72494i 0.981398 + 0.0714397i
\(584\) 33.4963i 1.38609i
\(585\) 2.81994 2.16224i 0.116590 0.0893978i
\(586\) 68.1259 + 49.4964i 2.81426 + 2.04468i
\(587\) −3.04360 4.18916i −0.125623 0.172905i 0.741573 0.670872i \(-0.234080\pi\)
−0.867196 + 0.497967i \(0.834080\pi\)
\(588\) −18.6671 25.0074i −0.769817 1.03129i
\(589\) 14.4708 + 4.70185i 0.596259 + 0.193736i
\(590\) 18.3463 13.3294i 0.755305 0.548761i
\(591\) 9.17776 3.11363i 0.377523 0.128078i
\(592\) −65.0015 200.054i −2.67154 8.22217i
\(593\) −11.9894 −0.492346 −0.246173 0.969226i \(-0.579173\pi\)
−0.246173 + 0.969226i \(0.579173\pi\)
\(594\) 38.1373 + 29.7357i 1.56479 + 1.22007i
\(595\) −1.58297 −0.0648956
\(596\) −18.5431 57.0698i −0.759556 2.33767i
\(597\) 18.6774 6.33648i 0.764416 0.259335i
\(598\) −6.88500 + 5.00224i −0.281549 + 0.204557i
\(599\) 22.1615 + 7.20071i 0.905495 + 0.294213i 0.724503 0.689271i \(-0.242069\pi\)
0.180992 + 0.983485i \(0.442069\pi\)
\(600\) 40.5163 + 54.2778i 1.65407 + 2.21588i
\(601\) 8.10991 + 11.1623i 0.330810 + 0.455321i 0.941729 0.336372i \(-0.109200\pi\)
−0.610919 + 0.791693i \(0.709200\pi\)
\(602\) 2.74664 + 1.99555i 0.111945 + 0.0813325i
\(603\) −19.2151 + 14.7336i −0.782501 + 0.599998i
\(604\) 111.235i 4.52610i
\(605\) 6.05125 + 11.5391i 0.246018 + 0.469130i
\(606\) −23.3648 + 33.0482i −0.949132 + 1.34249i
\(607\) −27.6876 + 8.99624i −1.12380 + 0.365146i −0.811219 0.584743i \(-0.801195\pi\)
−0.312586 + 0.949889i \(0.601195\pi\)
\(608\) 83.4606 114.874i 3.38477 4.65874i
\(609\) 14.9964 0.193680i 0.607683 0.00784831i
\(610\) 5.00268 15.3967i 0.202552 0.623392i
\(611\) 3.77006 11.6031i 0.152520 0.469410i
\(612\) 9.78468 + 6.72989i 0.395522 + 0.272040i
\(613\) 22.1916 30.5442i 0.896312 1.23367i −0.0753173 0.997160i \(-0.523997\pi\)
0.971629 0.236508i \(-0.0760030\pi\)
\(614\) −71.7891 + 23.3257i −2.89717 + 0.941348i
\(615\) 2.84509 + 2.01146i 0.114725 + 0.0811100i
\(616\) 26.9763 66.2242i 1.08691 2.66825i
\(617\) 37.9594i 1.52819i −0.645106 0.764093i \(-0.723187\pi\)
0.645106 0.764093i \(-0.276813\pi\)
\(618\) 24.7786 + 7.69874i 0.996742 + 0.309689i
\(619\) 24.5489 + 17.8358i 0.986702 + 0.716881i 0.959196 0.282741i \(-0.0912436\pi\)
0.0275056 + 0.999622i \(0.491244\pi\)
\(620\) 13.5405 + 18.6369i 0.543800 + 0.748477i
\(621\) 13.0983 + 8.76200i 0.525617 + 0.351607i
\(622\) −62.2893 20.2390i −2.49757 0.811510i
\(623\) 11.2124 8.14625i 0.449213 0.326373i
\(624\) 10.4386 + 30.7688i 0.417877 + 1.23174i
\(625\) 1.83028 + 5.63301i 0.0732111 + 0.225321i
\(626\) 77.7177 3.10622
\(627\) 16.7658 20.3939i 0.669561 0.814456i
\(628\) −35.8141 −1.42914
\(629\) −2.33506 7.18658i −0.0931050 0.286548i
\(630\) −5.62311 + 18.9589i −0.224030 + 0.755339i
\(631\) 1.72523 1.25345i 0.0686802 0.0498991i −0.552915 0.833237i \(-0.686485\pi\)
0.621596 + 0.783338i \(0.286485\pi\)
\(632\) −60.0425 19.5090i −2.38836 0.776026i
\(633\) −23.6018 + 17.6179i −0.938089 + 0.700248i
\(634\) −29.8496 41.0844i −1.18548 1.63167i
\(635\) 10.5082 + 7.63465i 0.417005 + 0.302972i
\(636\) 21.6261 69.6043i 0.857531 2.75999i
\(637\) 3.06708i 0.121522i
\(638\) −21.4352 34.5222i −0.848626 1.36675i
\(639\) 6.68767 2.36558i 0.264560 0.0935811i
\(640\) 85.8563 27.8964i 3.39377 1.10270i
\(641\) −6.38486 + 8.78800i −0.252187 + 0.347105i −0.916276 0.400548i \(-0.868820\pi\)
0.664089 + 0.747654i \(0.268820\pi\)
\(642\) 0.0165573 + 1.28201i 0.000653464 + 0.0505968i
\(643\) 4.45196 13.7017i 0.175568 0.540344i −0.824091 0.566458i \(-0.808313\pi\)
0.999659 + 0.0261143i \(0.00831339\pi\)
\(644\) 10.9178 33.6016i 0.430223 1.32409i
\(645\) 0.0161636 + 1.25153i 0.000636442 + 0.0492788i
\(646\) 5.10818 7.03080i 0.200979 0.276623i
\(647\) −3.42898 + 1.11414i −0.134807 + 0.0438015i −0.375643 0.926764i \(-0.622578\pi\)
0.240836 + 0.970566i \(0.422578\pi\)
\(648\) 76.0836 61.5229i 2.98885 2.41685i
\(649\) 5.41155 + 21.9714i 0.212422 + 0.862451i
\(650\) 10.0935i 0.395899i
\(651\) 3.37423 10.8601i 0.132246 0.425639i
\(652\) 17.3337 + 12.5937i 0.678841 + 0.493207i
\(653\) 3.97286 + 5.46817i 0.155470 + 0.213986i 0.879646 0.475629i \(-0.157780\pi\)
−0.724176 + 0.689615i \(0.757780\pi\)
\(654\) 64.0112 47.7820i 2.50304 1.86842i
\(655\) −16.9210 5.49797i −0.661159 0.214824i
\(656\) −25.7742 + 18.7261i −1.00632 + 0.731131i
\(657\) −8.86157 2.62830i −0.345723 0.102540i
\(658\) 20.9803 + 64.5708i 0.817899 + 2.51723i
\(659\) −11.8385 −0.461161 −0.230581 0.973053i \(-0.574063\pi\)
−0.230581 + 0.973053i \(0.574063\pi\)
\(660\) 38.6847 10.0597i 1.50580 0.391573i
\(661\) 32.9842 1.28294 0.641468 0.767150i \(-0.278326\pi\)
0.641468 + 0.767150i \(0.278326\pi\)
\(662\) 17.5049 + 53.8746i 0.680348 + 2.09390i
\(663\) 0.374986 + 1.10531i 0.0145633 + 0.0429268i
\(664\) 42.9138 31.1787i 1.66538 1.20997i
\(665\) 10.2674 + 3.33608i 0.398152 + 0.129368i
\(666\) −94.3665 + 2.43792i −3.65663 + 0.0944674i
\(667\) −7.78328 10.7128i −0.301370 0.414800i
\(668\) −94.2184 68.4536i −3.64542 2.64855i
\(669\) 40.8479 + 12.6915i 1.57927 + 0.490681i
\(670\) 26.8275i 1.03644i
\(671\) 12.3449 + 10.4187i 0.476568 + 0.402210i
\(672\) −86.6558 61.2651i −3.34282 2.36335i
\(673\) −23.1108 + 7.50915i −0.890856 + 0.289457i −0.718458 0.695571i \(-0.755152\pi\)
−0.172398 + 0.985027i \(0.555152\pi\)
\(674\) −26.7956 + 36.8810i −1.03213 + 1.42060i
\(675\) 17.5385 6.45981i 0.675058 0.248638i
\(676\) −1.81526 + 5.58679i −0.0698177 + 0.214877i
\(677\) 0.255394 0.786023i 0.00981560 0.0302093i −0.946029 0.324083i \(-0.894944\pi\)
0.955844 + 0.293873i \(0.0949444\pi\)
\(678\) 28.2064 0.364290i 1.08326 0.0139905i
\(679\) −7.82245 + 10.7667i −0.300198 + 0.413187i
\(680\) 8.25318 2.68162i 0.316495 0.102836i
\(681\) −11.8396 + 16.7464i −0.453695 + 0.641724i
\(682\) −29.9184 + 7.36892i −1.14564 + 0.282170i
\(683\) 37.7249i 1.44350i −0.692153 0.721751i \(-0.743337\pi\)
0.692153 0.721751i \(-0.256663\pi\)
\(684\) −49.2818 64.2720i −1.88434 2.45750i
\(685\) 4.43576 + 3.22277i 0.169482 + 0.123136i
\(686\) 32.9296 + 45.3236i 1.25726 + 1.73046i
\(687\) 11.1066 + 14.8790i 0.423743 + 0.567669i
\(688\) −10.8841 3.53645i −0.414952 0.134826i
\(689\) 5.79547 4.21065i 0.220790 0.160413i
\(690\) 16.5343 5.60940i 0.629450 0.213546i
\(691\) 3.77218 + 11.6096i 0.143500 + 0.441649i 0.996815 0.0797473i \(-0.0254113\pi\)
−0.853315 + 0.521396i \(0.825411\pi\)
\(692\) −94.9139 −3.60809
\(693\) −15.4031 12.3330i −0.585117 0.468491i
\(694\) 85.3020 3.23802
\(695\) 0.125403 + 0.385950i 0.00475680 + 0.0146399i
\(696\) −77.8587 + 26.4142i −2.95123 + 1.00123i
\(697\) −0.925893 + 0.672701i −0.0350707 + 0.0254804i
\(698\) 42.7582 + 13.8930i 1.61842 + 0.525857i
\(699\) 26.2913 + 35.2212i 0.994428 + 1.33219i
\(700\) −24.6302 33.9006i −0.930934 1.28132i
\(701\) −19.0711 13.8560i −0.720306 0.523333i 0.166176 0.986096i \(-0.446858\pi\)
−0.886482 + 0.462763i \(0.846858\pi\)
\(702\) 14.5701 0.564775i 0.549912 0.0213160i
\(703\) 51.5343i 1.94365i
\(704\) −11.8422 + 162.682i −0.446320 + 6.13129i
\(705\) −14.4496 + 20.4381i −0.544203 + 0.769742i
\(706\) 82.5579 26.8247i 3.10711 1.00956i
\(707\) 9.70688 13.3604i 0.365065 0.502469i
\(708\) 69.4113 0.896456i 2.60864 0.0336909i
\(709\) −5.08169 + 15.6398i −0.190847 + 0.587366i −1.00000 0.000231497i \(-0.999926\pi\)
0.809153 + 0.587598i \(0.199926\pi\)
\(710\) 2.42871 7.47482i 0.0911480 0.280525i
\(711\) −9.87243 + 14.3537i −0.370245 + 0.538305i
\(712\) −44.6580 + 61.4665i −1.67363 + 2.30355i
\(713\) −9.54930 + 3.10276i −0.357624 + 0.116199i
\(714\) −5.30374 3.74971i −0.198488 0.140329i
\(715\) 3.63827 + 1.48204i 0.136064 + 0.0554253i
\(716\) 24.2958i 0.907976i
\(717\) −26.3883 8.19887i −0.985489 0.306192i
\(718\) −0.223560 0.162426i −0.00834318 0.00606168i
\(719\) −6.33030 8.71291i −0.236080 0.324937i 0.674495 0.738279i \(-0.264361\pi\)
−0.910576 + 0.413342i \(0.864361\pi\)
\(720\) −1.72155 66.6373i −0.0641582 2.48342i
\(721\) −10.0690 3.27161i −0.374989 0.121841i
\(722\) −4.81589 + 3.49895i −0.179229 + 0.130217i
\(723\) −10.2563 30.2317i −0.381438 1.12433i
\(724\) −21.5395 66.2918i −0.800510 2.46372i
\(725\) −15.7050 −0.583270
\(726\) −7.05883 + 52.9957i −0.261978 + 1.96685i
\(727\) 8.23598 0.305456 0.152728 0.988268i \(-0.451194\pi\)
0.152728 + 0.988268i \(0.451194\pi\)
\(728\) −6.66254 20.5052i −0.246930 0.759973i
\(729\) −10.3062 24.9556i −0.381710 0.924282i
\(730\) −8.28508 + 6.01946i −0.306644 + 0.222790i
\(731\) −0.390991 0.127041i −0.0144613 0.00469877i
\(732\) 39.7121 29.6436i 1.46780 1.09566i
\(733\) −27.9417 38.4584i −1.03205 1.42049i −0.903397 0.428805i \(-0.858935\pi\)
−0.128653 0.991690i \(-0.541065\pi\)
\(734\) 17.5240 + 12.7319i 0.646822 + 0.469944i
\(735\) −1.86703 + 6.00910i −0.0688665 + 0.221649i
\(736\) 93.7005i 3.45385i
\(737\) −24.7912 10.0987i −0.913197 0.371989i
\(738\) 4.76776 + 13.4788i 0.175504 + 0.496161i
\(739\) 41.3057 13.4210i 1.51945 0.493700i 0.573833 0.818972i \(-0.305456\pi\)
0.945621 + 0.325272i \(0.105456\pi\)
\(740\) −45.8612 + 63.1225i −1.68589 + 2.32043i
\(741\) −0.102798 7.95949i −0.00377637 0.292399i
\(742\) −12.3190 + 37.9141i −0.452246 + 1.39187i
\(743\) 3.67537 11.3116i 0.134836 0.414984i −0.860728 0.509065i \(-0.829991\pi\)
0.995565 + 0.0940812i \(0.0299913\pi\)
\(744\) 0.805097 + 62.3375i 0.0295163 + 2.28540i
\(745\) −7.11210 + 9.78897i −0.260567 + 0.358640i
\(746\) 0.749162 0.243417i 0.0274288 0.00891214i
\(747\) −4.88119 13.7995i −0.178594 0.504896i
\(748\) −0.953191 + 13.0944i −0.0348521 + 0.478778i
\(749\) 0.523140i 0.0191151i
\(750\) 14.6851 47.2645i 0.536225 1.72586i
\(751\) −18.3577 13.3377i −0.669884 0.486699i 0.200103 0.979775i \(-0.435872\pi\)
−0.869986 + 0.493076i \(0.835872\pi\)
\(752\) −134.521 185.152i −4.90548 6.75181i
\(753\) −10.5178 + 7.85112i −0.383289 + 0.286111i
\(754\) −11.6524 3.78610i −0.424356 0.137882i
\(755\) −18.1459 + 13.1838i −0.660398 + 0.479808i
\(756\) −47.5577 + 37.4509i −1.72966 + 1.36208i
\(757\) 3.21522 + 9.89543i 0.116859 + 0.359655i 0.992330 0.123615i \(-0.0394488\pi\)
−0.875471 + 0.483270i \(0.839449\pi\)
\(758\) −34.0744 −1.23764
\(759\) −1.04036 + 17.3909i −0.0377629 + 0.631249i
\(760\) −59.1828 −2.14679
\(761\) −3.61939 11.1393i −0.131203 0.403800i 0.863777 0.503874i \(-0.168092\pi\)
−0.994980 + 0.100073i \(0.968092\pi\)
\(762\) 17.1229 + 50.4715i 0.620296 + 1.82839i
\(763\) −26.3680 + 19.1575i −0.954587 + 0.693548i
\(764\) 16.3721 + 5.31963i 0.592323 + 0.192457i
\(765\) −0.0618434 2.39382i −0.00223595 0.0865489i
\(766\) −32.9050 45.2898i −1.18890 1.63639i
\(767\) 5.51959 + 4.01022i 0.199301 + 0.144801i
\(768\) 191.049 + 59.3589i 6.89387 + 2.14193i
\(769\) 24.5484i 0.885238i 0.896710 + 0.442619i \(0.145951\pi\)
−0.896710 + 0.442619i \(0.854049\pi\)
\(770\) −21.2279 + 5.22843i −0.765000 + 0.188420i
\(771\) 5.39387 + 3.81343i 0.194256 + 0.137337i
\(772\) −59.4586 + 19.3193i −2.13996 + 0.695316i
\(773\) −19.2528 + 26.4993i −0.692476 + 0.953112i 0.307522 + 0.951541i \(0.400500\pi\)
−0.999999 + 0.00157104i \(0.999500\pi\)
\(774\) −2.91043 + 4.23152i −0.104613 + 0.152099i
\(775\) −3.67996 + 11.3257i −0.132188 + 0.406833i
\(776\) 22.5449 69.3860i 0.809314 2.49081i
\(777\) 38.5139 0.497412i 1.38168 0.0178446i
\(778\) 34.8574 47.9772i 1.24970 1.72006i
\(779\) 7.42318 2.41194i 0.265963 0.0864166i
\(780\) 6.95737 9.84079i 0.249114 0.352357i
\(781\) 5.99323 + 5.05812i 0.214454 + 0.180994i
\(782\) 5.73491i 0.205080i
\(783\) 0.878765 + 22.6704i 0.0314045 + 0.810174i
\(784\) −46.5466 33.8181i −1.66238 1.20779i
\(785\) 4.24475 + 5.84240i 0.151502 + 0.208524i
\(786\) −43.6703 58.5031i −1.55767 2.08674i
\(787\) 11.1947 + 3.63738i 0.399048 + 0.129659i 0.501664 0.865062i \(-0.332721\pi\)
−0.102616 + 0.994721i \(0.532721\pi\)
\(788\) 26.5917 19.3200i 0.947290 0.688247i
\(789\) 12.1053 4.10683i 0.430961 0.146207i
\(790\) 5.96453 + 18.3569i 0.212209 + 0.653111i
\(791\) −11.5100 −0.409248
\(792\) 101.200 + 38.2072i 3.59600 + 1.35763i
\(793\) 4.87056 0.172959
\(794\) 29.7237 + 91.4803i 1.05486 + 3.24651i
\(795\) −13.9178 + 4.72173i −0.493613 + 0.167463i
\(796\) 54.1161 39.3176i 1.91809 1.39358i
\(797\) 15.2582 + 4.95768i 0.540472 + 0.175610i 0.566516 0.824051i \(-0.308291\pi\)
−0.0260440 + 0.999661i \(0.508291\pi\)
\(798\) 26.4984 + 35.4987i 0.938034 + 1.25664i
\(799\) −4.83243 6.65127i −0.170959 0.235305i
\(800\) 89.9073 + 65.3215i 3.17870 + 2.30946i
\(801\) 12.7571 + 16.6374i 0.450749 + 0.587855i
\(802\) 75.6831i 2.67246i
\(803\) −2.44382 9.92213i −0.0862407 0.350144i
\(804\) −47.4077 + 67.0553i −1.67194 + 2.36486i
\(805\) −6.77547 + 2.20148i −0.238804 + 0.0775921i
\(806\) −5.46072 + 7.51604i −0.192346 + 0.264741i
\(807\) 0.520513 0.00672249i 0.0183229 0.000236643i
\(808\) −27.9760 + 86.1012i −0.984191 + 3.02903i
\(809\) −2.97589 + 9.15885i −0.104627 + 0.322008i −0.989643 0.143553i \(-0.954147\pi\)
0.885016 + 0.465561i \(0.154147\pi\)
\(810\) −28.8899 7.76277i −1.01509 0.272756i
\(811\) 2.08249 2.86630i 0.0731261 0.100649i −0.770887 0.636972i \(-0.780187\pi\)
0.844013 + 0.536322i \(0.180187\pi\)
\(812\) 48.3753 15.7181i 1.69764 0.551597i
\(813\) 13.9412 + 9.85637i 0.488941 + 0.345678i
\(814\) −55.0502 88.6604i −1.92951 3.10755i
\(815\) 4.32030i 0.151333i
\(816\) 20.9091 + 6.49647i 0.731965 + 0.227422i
\(817\) 2.26829 + 1.64801i 0.0793574 + 0.0576565i
\(818\) −10.0702 13.8605i −0.352097 0.484620i
\(819\) −5.94750 + 0.153651i −0.207822 + 0.00536900i
\(820\) 11.2388 + 3.65171i 0.392477 + 0.127523i
\(821\) −41.3062 + 30.0107i −1.44160 + 1.04738i −0.453891 + 0.891057i \(0.649964\pi\)
−0.987706 + 0.156324i \(0.950036\pi\)
\(822\) 7.22797 + 21.3052i 0.252104 + 0.743104i
\(823\) 6.57892 + 20.2478i 0.229327 + 0.705795i 0.997823 + 0.0659416i \(0.0210051\pi\)
−0.768497 + 0.639854i \(0.778995\pi\)
\(824\) 58.0392 2.02189
\(825\) 15.9616 + 13.1220i 0.555711 + 0.456848i
\(826\) −37.9676 −1.32106
\(827\) 7.63837 + 23.5085i 0.265612 + 0.817470i 0.991552 + 0.129712i \(0.0414052\pi\)
−0.725940 + 0.687758i \(0.758595\pi\)
\(828\) 51.2400 + 15.1976i 1.78071 + 0.528152i
\(829\) −3.05240 + 2.21770i −0.106014 + 0.0770239i −0.639529 0.768767i \(-0.720871\pi\)
0.533515 + 0.845791i \(0.320871\pi\)
\(830\) −15.4237 5.01146i −0.535364 0.173950i
\(831\) −15.6535 + 11.6847i −0.543014 + 0.405339i
\(832\) 28.9073 + 39.7875i 1.00218 + 1.37938i
\(833\) −1.67210 1.21485i −0.0579349 0.0420922i
\(834\) −0.494069 + 1.59018i −0.0171082 + 0.0550633i
\(835\) 23.4832i 0.812669i
\(836\) 33.7787 82.9233i 1.16826 2.86796i
\(837\) 16.5548 + 4.67834i 0.572216 + 0.161707i
\(838\) −48.4235 + 15.7337i −1.67276 + 0.543513i
\(839\) 5.29489 7.28780i 0.182800 0.251603i −0.707776 0.706437i \(-0.750301\pi\)
0.890576 + 0.454834i \(0.150301\pi\)
\(840\) 0.571236 + 44.2300i 0.0197095 + 1.52608i
\(841\) −3.07049 + 9.44999i −0.105879 + 0.325862i
\(842\) −11.8016 + 36.3216i −0.406710 + 1.25173i
\(843\) 0.298530 + 23.1148i 0.0102819 + 0.796114i
\(844\) −58.7129 + 80.8113i −2.02098 + 2.78164i
\(845\) 1.12653 0.366031i 0.0387537 0.0125918i
\(846\) −96.8265 + 34.2498i −3.32896 + 1.17753i
\(847\) 3.15922 21.5848i 0.108552 0.741662i
\(848\) 134.380i 4.61464i
\(849\) 5.93310 19.0959i 0.203623 0.655368i
\(850\) 5.50275 + 3.99798i 0.188743 + 0.137130i
\(851\) −19.9891 27.5127i −0.685219 0.943123i
\(852\) 19.2795 14.3914i 0.660506 0.493043i
\(853\) −14.9217 4.84835i −0.510909 0.166004i 0.0422066 0.999109i \(-0.486561\pi\)
−0.553116 + 0.833104i \(0.686561\pi\)
\(854\) −21.9281 + 15.9317i −0.750363 + 0.545170i
\(855\) −4.64380 + 15.6570i −0.158815 + 0.535459i
\(856\) 0.886220 + 2.72751i 0.0302904 + 0.0932242i
\(857\) −10.7828 −0.368333 −0.184167 0.982895i \(-0.558959\pi\)
−0.184167 + 0.982895i \(0.558959\pi\)
\(858\) 8.67937 + 13.5838i 0.296309 + 0.463744i
\(859\) 29.1060 0.993084 0.496542 0.868013i \(-0.334603\pi\)
0.496542 + 0.868013i \(0.334603\pi\)
\(860\) 1.31176 + 4.03718i 0.0447306 + 0.137667i
\(861\) −1.87420 5.52440i −0.0638725 0.188271i
\(862\) −7.22150 + 5.24673i −0.245965 + 0.178704i
\(863\) −2.14526 0.697036i −0.0730254 0.0237274i 0.272276 0.962219i \(-0.412223\pi\)
−0.345302 + 0.938492i \(0.612223\pi\)
\(864\) 89.2616 133.437i 3.03674 4.53963i
\(865\) 11.2494 + 15.4834i 0.382490 + 0.526452i
\(866\) 29.4209 + 21.3756i 0.999764 + 0.726371i
\(867\) −27.3678 8.50319i −0.929458 0.288783i
\(868\) 38.5691i 1.30912i
\(869\) −19.2089 1.39829i −0.651616 0.0474336i
\(870\) 20.5250 + 14.5110i 0.695863 + 0.491970i
\(871\) −7.67618 + 2.49414i −0.260097 + 0.0845108i
\(872\) 105.022 144.551i 3.55650 4.89510i
\(873\) −16.5873 11.4087i −0.561396 0.386127i
\(874\) 12.0862 37.1975i 0.408822 1.25822i
\(875\) −6.24051 + 19.2063i −0.210968 + 0.649292i
\(876\) −31.3457 + 0.404834i −1.05907 + 0.0136781i
\(877\) 22.2075 30.5660i 0.749893 1.03214i −0.248095 0.968736i \(-0.579804\pi\)
0.997988 0.0634035i \(-0.0201955\pi\)
\(878\) 6.83457 2.22069i 0.230656 0.0749445i
\(879\) 30.0056 42.4411i 1.01206 1.43150i
\(880\) 62.6079 38.8739i 2.11051 1.31044i
\(881\) 24.8997i 0.838892i 0.907780 + 0.419446i \(0.137776\pi\)
−0.907780 + 0.419446i \(0.862224\pi\)
\(882\) −20.4897 + 15.7109i −0.689924 + 0.529012i
\(883\) −2.98942 2.17194i −0.100602 0.0730915i 0.536347 0.843998i \(-0.319804\pi\)
−0.636949 + 0.770906i \(0.719804\pi\)
\(884\) 2.32678 + 3.20254i 0.0782581 + 0.107713i
\(885\) −8.37298 11.2169i −0.281455 0.377052i
\(886\) 89.6278 + 29.1218i 3.01110 + 0.978367i
\(887\) −3.46081 + 2.51443i −0.116203 + 0.0844262i −0.644369 0.764715i \(-0.722880\pi\)
0.528166 + 0.849141i \(0.322880\pi\)
\(888\) −199.958 + 67.8375i −6.71016 + 2.27648i
\(889\) −6.72010 20.6823i −0.225385 0.693663i
\(890\) 23.2286 0.778624
\(891\) 18.0486 23.7750i 0.604650 0.796491i
\(892\) 145.070 4.85729
\(893\) 17.3264 + 53.3253i 0.579807 + 1.78446i
\(894\) −47.0170 + 15.9509i −1.57248 + 0.533478i
\(895\) 3.96340 2.87958i 0.132482 0.0962537i
\(896\) −143.746 46.7058i −4.80221 1.56033i
\(897\) 3.14221 + 4.20947i 0.104915 + 0.140550i
\(898\) −19.1806 26.3998i −0.640065 0.880974i
\(899\) −11.6946 8.49664i −0.390038 0.283379i
\(900\) 50.3033 38.5710i 1.67678 1.28570i
\(901\) 4.82738i 0.160823i
\(902\) −10.1945 + 12.0792i −0.339439 + 0.402192i
\(903\) 1.20974 1.71110i 0.0402576 0.0569419i
\(904\) 60.0099 19.4984i 1.99590 0.648508i
\(905\) −8.26135 + 11.3708i −0.274617 + 0.377977i
\(906\) −92.0274 + 1.18855i −3.05740 + 0.0394868i
\(907\) 9.75992 30.0379i 0.324073 0.997393i −0.647785 0.761824i \(-0.724304\pi\)
0.971857 0.235570i \(-0.0756957\pi\)
\(908\) −21.4943 + 66.1525i −0.713312 + 2.19535i
\(909\) 20.5832 + 14.1571i 0.682703 + 0.469562i
\(910\) −3.87452 + 5.33282i −0.128439 + 0.176781i
\(911\) −26.1415 + 8.49390i −0.866108 + 0.281416i −0.708177 0.706035i \(-0.750482\pi\)
−0.157931 + 0.987450i \(0.550482\pi\)
\(912\) −121.928 86.2025i −4.03745 2.85445i
\(913\) 10.4370 12.3665i 0.345415 0.409273i
\(914\) 47.7750i 1.58026i
\(915\) −9.54253 2.96487i −0.315466 0.0980156i
\(916\) 50.9448 + 37.0135i 1.68326 + 1.22296i
\(917\) 17.5090 + 24.0991i 0.578198 + 0.795822i
\(918\) 5.46323 8.16699i 0.180313 0.269551i
\(919\) −4.36796 1.41924i −0.144086 0.0468163i 0.236086 0.971732i \(-0.424135\pi\)
−0.380172 + 0.924916i \(0.624135\pi\)
\(920\) 31.5960 22.9559i 1.04169 0.756832i
\(921\) 14.9686 + 44.1215i 0.493232 + 1.45385i
\(922\) 7.50294 + 23.0917i 0.247096 + 0.760483i
\(923\) 2.36457 0.0778309
\(924\) −62.2984 24.4439i −2.04947 0.804147i
\(925\) −40.3339 −1.32617
\(926\) 27.7307 + 85.3462i 0.911286 + 2.80465i
\(927\) 4.55406 15.3545i 0.149575 0.504307i
\(928\) −109.135 + 79.2910i −3.58252 + 2.60286i
\(929\) −6.64473 2.15900i −0.218007 0.0708346i 0.197977 0.980207i \(-0.436563\pi\)
−0.415984 + 0.909372i \(0.636563\pi\)
\(930\) 15.2740 11.4015i 0.500856 0.373870i
\(931\) 8.28522 + 11.4036i 0.271537 + 0.373739i
\(932\) 120.595 + 87.6177i 3.95023 + 2.87001i
\(933\) −11.9948 + 38.6056i −0.392692 + 1.26389i
\(934\) 107.001i 3.50118i
\(935\) 2.24908 1.39647i 0.0735527 0.0456696i
\(936\) 30.7483 10.8764i 1.00504 0.355506i
\(937\) 23.5075 7.63806i 0.767958 0.249525i 0.101267 0.994859i \(-0.467710\pi\)
0.666690 + 0.745335i \(0.267710\pi\)
\(938\) 26.4011 36.3379i 0.862025 1.18648i
\(939\) −0.619494 47.9665i −0.0202164 1.56533i
\(940\) −26.2325 + 80.7354i −0.855611 + 2.63330i
\(941\) 2.62001 8.06357i 0.0854099 0.262865i −0.899226 0.437484i \(-0.855870\pi\)
0.984636 + 0.174620i \(0.0558696\pi\)
\(942\) 0.382673 + 29.6298i 0.0124682 + 0.965391i
\(943\) −3.02748 + 4.16697i −0.0985884 + 0.135695i
\(944\) 121.720 39.5492i 3.96164 1.28722i
\(945\) 11.7460 + 3.31940i 0.382098 + 0.107980i
\(946\) −5.66284 0.412220i −0.184115 0.0134024i
\(947\) 48.9000i 1.58904i −0.607239 0.794519i \(-0.707723\pi\)
0.607239 0.794519i \(-0.292277\pi\)
\(948\) −17.5308 + 56.4233i −0.569373 + 1.83254i
\(949\) −2.49262 1.81099i −0.0809137 0.0587873i
\(950\) −27.2660 37.5284i −0.884625 1.21758i
\(951\) −25.1189 + 18.7503i −0.814537 + 0.608021i
\(952\) −13.8180 4.48973i −0.447843 0.145513i
\(953\) 13.4117 9.74418i 0.434448 0.315645i −0.348977 0.937131i \(-0.613471\pi\)
0.783425 + 0.621486i \(0.213471\pi\)
\(954\) −57.8162 17.1480i −1.87187 0.555188i
\(955\) −1.07266 3.30130i −0.0347103 0.106827i
\(956\) −93.7170 −3.03102
\(957\) −21.1358 + 13.5047i −0.683225 + 0.436546i
\(958\) 62.2497 2.01120
\(959\) −2.83671 8.73050i −0.0916022 0.281923i
\(960\) −32.4160 95.5497i −1.04622 3.08385i
\(961\) 16.2119 11.7786i 0.522964 0.379956i
\(962\) −29.9259 9.72352i −0.964851 0.313499i
\(963\) 0.791109 0.0204380i 0.0254931 0.000658604i
\(964\) −63.6403 87.5934i −2.04972 2.82119i
\(965\) 10.1987 + 7.40980i 0.328308 + 0.238530i
\(966\) −27.9160 8.67353i −0.898183 0.279066i
\(967\) 16.0234i 0.515278i 0.966241 + 0.257639i \(0.0829445\pi\)
−0.966241 + 0.257639i \(0.917056\pi\)
\(968\) 20.0942 + 117.889i 0.645853 + 3.78910i
\(969\) −4.38005 3.09667i −0.140708 0.0994794i
\(970\) −21.2136 + 6.89271i −0.681127 + 0.221311i
\(971\) 0.793933 1.09275i 0.0254785 0.0350682i −0.796088 0.605181i \(-0.793101\pi\)
0.821566 + 0.570113i \(0.193101\pi\)
\(972\) −58.4924 70.4552i −1.87615 2.25985i
\(973\) 0.209957 0.646181i 0.00673091 0.0207156i
\(974\) 17.7885 54.7473i 0.569980 1.75422i
\(975\) 6.22959 0.0804561i 0.199507 0.00257666i
\(976\) 53.7035 73.9166i 1.71901 2.36601i
\(977\) −45.2435 + 14.7005i −1.44747 + 0.470311i −0.924217 0.381867i \(-0.875281\pi\)
−0.523252 + 0.852178i \(0.675281\pi\)
\(978\) 10.2338 14.4751i 0.327242 0.462864i
\(979\) −8.74393 + 21.4655i −0.279457 + 0.686040i
\(980\) 21.3411i 0.681715i
\(981\) −30.0008 39.1262i −0.957850 1.24920i
\(982\) 41.1074 + 29.8663i 1.31179 + 0.953070i
\(983\) 5.05417 + 6.95646i 0.161203 + 0.221877i 0.881976 0.471294i \(-0.156213\pi\)
−0.720773 + 0.693171i \(0.756213\pi\)
\(984\) 19.1301 + 25.6277i 0.609846 + 0.816982i
\(985\) −6.30339 2.04809i −0.200843 0.0652577i
\(986\) −6.67956 + 4.85298i −0.212720 + 0.154550i
\(987\) 39.6852 13.4635i 1.26319 0.428549i
\(988\) −8.34256 25.6758i −0.265412 0.816855i
\(989\) −1.85021 −0.0588331
\(990\) −8.73594 31.8972i −0.277646 1.01376i
\(991\) 27.8914 0.886000 0.443000 0.896522i \(-0.353914\pi\)
0.443000 + 0.896522i \(0.353914\pi\)
\(992\) 31.6089 + 97.2822i 1.00358 + 3.08871i
\(993\) 33.1113 11.2333i 1.05076 0.356478i
\(994\) −10.6457 + 7.73455i −0.337661 + 0.245325i
\(995\) −12.8279 4.16802i −0.406671 0.132135i
\(996\) −29.6956 39.7818i −0.940941 1.26053i
\(997\) −31.8390 43.8227i −1.00835 1.38788i −0.920057 0.391784i \(-0.871858\pi\)
−0.0882949 0.996094i \(-0.528142\pi\)
\(998\) −45.7547 33.2427i −1.44834 1.05228i
\(999\) 2.25686 + 58.2225i 0.0714039 + 1.84208i
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 429.2.x.a.248.1 192
3.2 odd 2 inner 429.2.x.a.248.48 yes 192
11.2 odd 10 inner 429.2.x.a.365.48 yes 192
33.2 even 10 inner 429.2.x.a.365.1 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.x.a.248.1 192 1.1 even 1 trivial
429.2.x.a.248.48 yes 192 3.2 odd 2 inner
429.2.x.a.365.1 yes 192 33.2 even 10 inner
429.2.x.a.365.48 yes 192 11.2 odd 10 inner