Properties

Label 69.2.e.b.49.1
Level $69$
Weight $2$
Character 69.49
Analytic conductor $0.551$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 49.1
Root \(0.142315 + 0.989821i\) of defining polynomial
Character \(\chi\) \(=\) 69.49
Dual form 69.2.e.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.357685 + 2.48775i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-4.14200 + 1.21620i) q^{4} +(2.65565 - 3.06479i) q^{5} +(-2.41153 - 0.708089i) q^{6} +(-1.15843 + 0.744479i) q^{7} +(-2.41899 - 5.29684i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(0.357685 + 2.48775i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-4.14200 + 1.21620i) q^{4} +(2.65565 - 3.06479i) q^{5} +(-2.41153 - 0.708089i) q^{6} +(-1.15843 + 0.744479i) q^{7} +(-2.41899 - 5.29684i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(8.57432 + 5.51038i) q^{10} +(-0.00388573 + 0.0270259i) q^{11} +(0.614354 - 4.27292i) q^{12} +(-0.527646 - 0.339098i) q^{13} +(-2.26643 - 2.61561i) q^{14} +(1.68463 + 3.68882i) q^{15} +(5.04885 - 3.24470i) q^{16} +(4.13515 + 1.21419i) q^{17} +(1.64589 - 1.89945i) q^{18} +(-4.79898 + 1.40911i) q^{19} +(-7.27232 + 15.9241i) q^{20} +(-0.195972 - 1.36301i) q^{21} -0.0686236 q^{22} +(1.11722 - 4.66388i) q^{23} +5.82306 q^{24} +(-1.62885 - 11.3289i) q^{25} +(0.654861 - 1.43394i) q^{26} +(0.959493 - 0.281733i) q^{27} +(3.89279 - 4.49252i) q^{28} +(-3.54487 - 1.04087i) q^{29} +(-8.57432 + 5.51038i) q^{30} +(-0.200359 - 0.438726i) q^{31} +(2.25133 + 2.59818i) q^{32} +(-0.0229694 - 0.0147615i) q^{33} +(-1.54152 + 10.7215i) q^{34} +(-0.794723 + 5.52742i) q^{35} +(3.63158 + 2.33387i) q^{36} +(1.44203 + 1.66419i) q^{37} +(-5.22204 - 11.4347i) q^{38} +(0.527646 - 0.339098i) q^{39} +(-22.6577 - 6.65289i) q^{40} +(-6.56243 + 7.57345i) q^{41} +(3.32075 - 0.975060i) q^{42} +(-1.36272 + 2.98394i) q^{43} +(-0.0167742 - 0.116667i) q^{44} -4.05529 q^{45} +(12.0022 + 1.11118i) q^{46} +8.98345 q^{47} +(0.854114 + 5.94049i) q^{48} +(-2.12019 + 4.64257i) q^{49} +(27.6009 - 8.10436i) q^{50} +(-2.82227 + 3.25707i) q^{51} +(2.59792 + 0.762819i) q^{52} +(1.54567 - 0.993342i) q^{53} +(1.04408 + 2.28621i) q^{54} +(0.0725093 + 0.0836802i) q^{55} +(6.74562 + 4.33514i) q^{56} +(0.711799 - 4.95067i) q^{57} +(1.32148 - 9.19107i) q^{58} +(-3.51609 - 2.25965i) q^{59} +(-11.4641 - 13.2303i) q^{60} +(1.92053 + 4.20538i) q^{61} +(1.01978 - 0.655371i) q^{62} +(1.32125 + 0.387954i) q^{63} +(2.20204 - 2.54129i) q^{64} +(-2.44051 + 0.716597i) q^{65} +(0.0285073 - 0.0624222i) q^{66} +(-0.630353 - 4.38420i) q^{67} -18.6045 q^{68} +(3.77831 + 2.95371i) q^{69} -14.0351 q^{70} +(1.02832 + 7.15212i) q^{71} +(-2.41899 + 5.29684i) q^{72} +(-5.72936 + 1.68229i) q^{73} +(-3.62430 + 4.18266i) q^{74} +(10.9818 + 3.22454i) q^{75} +(18.1636 - 11.6731i) q^{76} +(-0.0156188 - 0.0342005i) q^{77} +(1.03232 + 1.19136i) q^{78} +(1.26938 + 0.815780i) q^{79} +(3.46368 - 24.0904i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-21.1882 - 13.6168i) q^{82} +(5.61081 + 6.47522i) q^{83} +(2.46941 + 5.40726i) q^{84} +(14.7027 - 9.44888i) q^{85} +(-7.91074 - 2.32280i) q^{86} +(2.41940 - 2.79213i) q^{87} +(0.152551 - 0.0447931i) q^{88} +(5.53741 - 12.1252i) q^{89} +(-1.45052 - 10.0886i) q^{90} +0.863693 q^{91} +(1.04468 + 20.6766i) q^{92} +0.482312 q^{93} +(3.21325 + 22.3486i) q^{94} +(-8.42581 + 18.4500i) q^{95} +(-3.29862 + 0.968563i) q^{96} +(-1.41765 + 1.63606i) q^{97} +(-12.3079 - 3.61394i) q^{98} +(0.0229694 - 0.0147615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{8}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.357685 + 2.48775i 0.252922 + 1.75911i 0.580477 + 0.814276i \(0.302866\pi\)
−0.327556 + 0.944832i \(0.606225\pi\)
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) −4.14200 + 1.21620i −2.07100 + 0.608100i
\(5\) 2.65565 3.06479i 1.18764 1.37061i 0.275213 0.961383i \(-0.411252\pi\)
0.912431 0.409230i \(-0.134203\pi\)
\(6\) −2.41153 0.708089i −0.984503 0.289076i
\(7\) −1.15843 + 0.744479i −0.437846 + 0.281387i −0.740936 0.671575i \(-0.765618\pi\)
0.303090 + 0.952962i \(0.401982\pi\)
\(8\) −2.41899 5.29684i −0.855241 1.87272i
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 8.57432 + 5.51038i 2.71144 + 1.74254i
\(11\) −0.00388573 + 0.0270259i −0.00117159 + 0.00814861i −0.990399 0.138239i \(-0.955856\pi\)
0.989227 + 0.146388i \(0.0467648\pi\)
\(12\) 0.614354 4.27292i 0.177349 1.23349i
\(13\) −0.527646 0.339098i −0.146343 0.0940488i 0.465420 0.885090i \(-0.345903\pi\)
−0.611763 + 0.791041i \(0.709539\pi\)
\(14\) −2.26643 2.61561i −0.605730 0.699050i
\(15\) 1.68463 + 3.68882i 0.434969 + 0.952450i
\(16\) 5.04885 3.24470i 1.26221 0.811175i
\(17\) 4.13515 + 1.21419i 1.00292 + 0.294484i 0.741654 0.670783i \(-0.234042\pi\)
0.261267 + 0.965267i \(0.415860\pi\)
\(18\) 1.64589 1.89945i 0.387939 0.447705i
\(19\) −4.79898 + 1.40911i −1.10096 + 0.323272i −0.781234 0.624238i \(-0.785410\pi\)
−0.319728 + 0.947509i \(0.603591\pi\)
\(20\) −7.27232 + 15.9241i −1.62614 + 3.56075i
\(21\) −0.195972 1.36301i −0.0427646 0.297434i
\(22\) −0.0686236 −0.0146306
\(23\) 1.11722 4.66388i 0.232957 0.972487i
\(24\) 5.82306 1.18863
\(25\) −1.62885 11.3289i −0.325770 2.26578i
\(26\) 0.654861 1.43394i 0.128429 0.281220i
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 3.89279 4.49252i 0.735668 0.849006i
\(29\) −3.54487 1.04087i −0.658266 0.193284i −0.0644943 0.997918i \(-0.520543\pi\)
−0.593771 + 0.804634i \(0.702362\pi\)
\(30\) −8.57432 + 5.51038i −1.56545 + 1.00605i
\(31\) −0.200359 0.438726i −0.0359856 0.0787975i 0.890786 0.454424i \(-0.150155\pi\)
−0.926771 + 0.375626i \(0.877428\pi\)
\(32\) 2.25133 + 2.59818i 0.397983 + 0.459297i
\(33\) −0.0229694 0.0147615i −0.00399846 0.00256965i
\(34\) −1.54152 + 10.7215i −0.264369 + 1.83873i
\(35\) −0.794723 + 5.52742i −0.134333 + 0.934305i
\(36\) 3.63158 + 2.33387i 0.605263 + 0.388979i
\(37\) 1.44203 + 1.66419i 0.237067 + 0.273590i 0.861800 0.507249i \(-0.169337\pi\)
−0.624732 + 0.780839i \(0.714792\pi\)
\(38\) −5.22204 11.4347i −0.847127 1.85495i
\(39\) 0.527646 0.339098i 0.0844910 0.0542991i
\(40\) −22.6577 6.65289i −3.58249 1.05191i
\(41\) −6.56243 + 7.57345i −1.02488 + 1.18277i −0.0418888 + 0.999122i \(0.513338\pi\)
−0.982991 + 0.183652i \(0.941208\pi\)
\(42\) 3.32075 0.975060i 0.512403 0.150455i
\(43\) −1.36272 + 2.98394i −0.207813 + 0.455047i −0.984624 0.174687i \(-0.944109\pi\)
0.776811 + 0.629734i \(0.216836\pi\)
\(44\) −0.0167742 0.116667i −0.00252880 0.0175882i
\(45\) −4.05529 −0.604527
\(46\) 12.0022 + 1.11118i 1.76963 + 0.163834i
\(47\) 8.98345 1.31037 0.655186 0.755468i \(-0.272590\pi\)
0.655186 + 0.755468i \(0.272590\pi\)
\(48\) 0.854114 + 5.94049i 0.123281 + 0.857437i
\(49\) −2.12019 + 4.64257i −0.302884 + 0.663224i
\(50\) 27.6009 8.10436i 3.90336 1.14613i
\(51\) −2.82227 + 3.25707i −0.395196 + 0.456081i
\(52\) 2.59792 + 0.762819i 0.360267 + 0.105784i
\(53\) 1.54567 0.993342i 0.212314 0.136446i −0.430162 0.902752i \(-0.641544\pi\)
0.642476 + 0.766306i \(0.277907\pi\)
\(54\) 1.04408 + 2.28621i 0.142081 + 0.311114i
\(55\) 0.0725093 + 0.0836802i 0.00977716 + 0.0112834i
\(56\) 6.74562 + 4.33514i 0.901421 + 0.579308i
\(57\) 0.711799 4.95067i 0.0942801 0.655733i
\(58\) 1.32148 9.19107i 0.173518 1.20685i
\(59\) −3.51609 2.25965i −0.457756 0.294182i 0.291369 0.956611i \(-0.405889\pi\)
−0.749125 + 0.662429i \(0.769526\pi\)
\(60\) −11.4641 13.2303i −1.48001 1.70802i
\(61\) 1.92053 + 4.20538i 0.245899 + 0.538444i 0.991828 0.127582i \(-0.0407215\pi\)
−0.745929 + 0.666025i \(0.767994\pi\)
\(62\) 1.01978 0.655371i 0.129512 0.0832322i
\(63\) 1.32125 + 0.387954i 0.166462 + 0.0488776i
\(64\) 2.20204 2.54129i 0.275255 0.317661i
\(65\) −2.44051 + 0.716597i −0.302708 + 0.0888830i
\(66\) 0.0285073 0.0624222i 0.00350900 0.00768365i
\(67\) −0.630353 4.38420i −0.0770099 0.535616i −0.991409 0.130801i \(-0.958245\pi\)
0.914399 0.404815i \(-0.132664\pi\)
\(68\) −18.6045 −2.25612
\(69\) 3.77831 + 2.95371i 0.454855 + 0.355585i
\(70\) −14.0351 −1.67752
\(71\) 1.02832 + 7.15212i 0.122039 + 0.848801i 0.955240 + 0.295831i \(0.0955965\pi\)
−0.833201 + 0.552970i \(0.813494\pi\)
\(72\) −2.41899 + 5.29684i −0.285080 + 0.624239i
\(73\) −5.72936 + 1.68229i −0.670571 + 0.196898i −0.599257 0.800556i \(-0.704537\pi\)
−0.0713140 + 0.997454i \(0.522719\pi\)
\(74\) −3.62430 + 4.18266i −0.421316 + 0.486224i
\(75\) 10.9818 + 3.22454i 1.26807 + 0.372338i
\(76\) 18.1636 11.6731i 2.08351 1.33899i
\(77\) −0.0156188 0.0342005i −0.00177993 0.00389751i
\(78\) 1.03232 + 1.19136i 0.116888 + 0.134895i
\(79\) 1.26938 + 0.815780i 0.142816 + 0.0917824i 0.610098 0.792326i \(-0.291130\pi\)
−0.467281 + 0.884109i \(0.654767\pi\)
\(80\) 3.46368 24.0904i 0.387252 2.69339i
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) −21.1882 13.6168i −2.33984 1.50373i
\(83\) 5.61081 + 6.47522i 0.615866 + 0.710748i 0.974917 0.222570i \(-0.0714447\pi\)
−0.359050 + 0.933318i \(0.616899\pi\)
\(84\) 2.46941 + 5.40726i 0.269435 + 0.589981i
\(85\) 14.7027 9.44888i 1.59474 1.02487i
\(86\) −7.91074 2.32280i −0.853037 0.250474i
\(87\) 2.41940 2.79213i 0.259387 0.299348i
\(88\) 0.152551 0.0447931i 0.0162620 0.00477496i
\(89\) 5.53741 12.1252i 0.586965 1.28527i −0.350295 0.936640i \(-0.613919\pi\)
0.937259 0.348634i \(-0.113354\pi\)
\(90\) −1.45052 10.0886i −0.152898 1.06343i
\(91\) 0.863693 0.0905397
\(92\) 1.04468 + 20.6766i 0.108916 + 2.15568i
\(93\) 0.482312 0.0500134
\(94\) 3.21325 + 22.3486i 0.331421 + 2.30509i
\(95\) −8.42581 + 18.4500i −0.864470 + 1.89293i
\(96\) −3.29862 + 0.968563i −0.336664 + 0.0988536i
\(97\) −1.41765 + 1.63606i −0.143941 + 0.166117i −0.823142 0.567835i \(-0.807781\pi\)
0.679201 + 0.733952i \(0.262326\pi\)
\(98\) −12.3079 3.61394i −1.24329 0.365063i
\(99\) 0.0229694 0.0147615i 0.00230851 0.00148359i
\(100\) 20.5249 + 44.9433i 2.05249 + 4.49433i
\(101\) −8.74204 10.0889i −0.869866 1.00388i −0.999923 0.0123724i \(-0.996062\pi\)
0.130058 0.991506i \(-0.458484\pi\)
\(102\) −9.11228 5.85610i −0.902250 0.579841i
\(103\) −1.34518 + 9.35596i −0.132545 + 0.921870i 0.809676 + 0.586877i \(0.199643\pi\)
−0.942221 + 0.334993i \(0.891266\pi\)
\(104\) −0.519777 + 3.61513i −0.0509684 + 0.354493i
\(105\) −4.69778 3.01908i −0.458456 0.294632i
\(106\) 3.02406 + 3.48995i 0.293722 + 0.338974i
\(107\) −5.72839 12.5434i −0.553785 1.21262i −0.954992 0.296632i \(-0.904137\pi\)
0.401207 0.915987i \(-0.368591\pi\)
\(108\) −3.63158 + 2.33387i −0.349449 + 0.224577i
\(109\) 7.83275 + 2.29990i 0.750242 + 0.220291i 0.634430 0.772980i \(-0.281235\pi\)
0.115812 + 0.993271i \(0.463053\pi\)
\(110\) −0.182240 + 0.210317i −0.0173759 + 0.0200529i
\(111\) −2.11284 + 0.620384i −0.200541 + 0.0588843i
\(112\) −3.43314 + 7.51753i −0.324401 + 0.710340i
\(113\) 2.08128 + 14.4756i 0.195790 + 1.36175i 0.816335 + 0.577578i \(0.196002\pi\)
−0.620545 + 0.784171i \(0.713089\pi\)
\(114\) 12.5707 1.17735
\(115\) −11.3268 15.8097i −1.05623 1.47426i
\(116\) 15.9488 1.48080
\(117\) 0.0892619 + 0.620830i 0.00825227 + 0.0573958i
\(118\) 4.36381 9.55541i 0.401721 0.879647i
\(119\) −5.69422 + 1.67197i −0.521989 + 0.153270i
\(120\) 15.4640 17.8464i 1.41167 1.62915i
\(121\) 10.5537 + 3.09885i 0.959428 + 0.281713i
\(122\) −9.77501 + 6.28201i −0.884987 + 0.568747i
\(123\) −4.16292 9.11553i −0.375358 0.821919i
\(124\) 1.36347 + 1.57353i 0.122443 + 0.141307i
\(125\) −21.9887 14.1313i −1.96673 1.26394i
\(126\) −0.492543 + 3.42571i −0.0438792 + 0.305187i
\(127\) −0.258432 + 1.79743i −0.0229321 + 0.159496i −0.998070 0.0621040i \(-0.980219\pi\)
0.975138 + 0.221600i \(0.0711281\pi\)
\(128\) 12.8940 + 8.28647i 1.13968 + 0.732428i
\(129\) −2.14820 2.47915i −0.189138 0.218277i
\(130\) −2.65565 5.81507i −0.232916 0.510015i
\(131\) 4.99336 3.20904i 0.436272 0.280375i −0.304013 0.952668i \(-0.598327\pi\)
0.740285 + 0.672293i \(0.234690\pi\)
\(132\) 0.113092 + 0.0332069i 0.00984342 + 0.00289029i
\(133\) 4.51024 5.20510i 0.391088 0.451339i
\(134\) 10.6814 3.13633i 0.922728 0.270938i
\(135\) 1.68463 3.68882i 0.144990 0.317483i
\(136\) −3.57150 24.8403i −0.306254 2.13004i
\(137\) 8.05383 0.688085 0.344043 0.938954i \(-0.388204\pi\)
0.344043 + 0.938954i \(0.388204\pi\)
\(138\) −5.99666 + 10.4560i −0.510470 + 0.890074i
\(139\) −7.68012 −0.651419 −0.325709 0.945470i \(-0.605603\pi\)
−0.325709 + 0.945470i \(0.605603\pi\)
\(140\) −3.43071 23.8611i −0.289948 2.01663i
\(141\) −3.73186 + 8.17164i −0.314279 + 0.688176i
\(142\) −17.4249 + 5.11642i −1.46227 + 0.429360i
\(143\) 0.0112147 0.0129425i 0.000937821 0.00108230i
\(144\) −5.75848 1.69084i −0.479873 0.140903i
\(145\) −12.6040 + 8.10008i −1.04670 + 0.672675i
\(146\) −6.23444 13.6515i −0.515966 1.12981i
\(147\) −3.34227 3.85719i −0.275666 0.318135i
\(148\) −7.99685 5.13926i −0.657337 0.422445i
\(149\) 0.411897 2.86481i 0.0337439 0.234694i −0.965969 0.258658i \(-0.916720\pi\)
0.999713 + 0.0239640i \(0.00762872\pi\)
\(150\) −4.09385 + 28.4733i −0.334261 + 2.32484i
\(151\) 1.73780 + 1.11682i 0.141420 + 0.0908852i 0.609438 0.792834i \(-0.291395\pi\)
−0.468018 + 0.883719i \(0.655032\pi\)
\(152\) 19.0725 + 22.0108i 1.54698 + 1.78531i
\(153\) −1.79032 3.92026i −0.144739 0.316934i
\(154\) 0.0794958 0.0510888i 0.00640595 0.00411685i
\(155\) −1.87669 0.551045i −0.150739 0.0442610i
\(156\) −1.77310 + 2.04627i −0.141962 + 0.163832i
\(157\) 18.5997 5.46138i 1.48442 0.435865i 0.563665 0.826003i \(-0.309391\pi\)
0.920756 + 0.390138i \(0.127573\pi\)
\(158\) −1.57542 + 3.44970i −0.125334 + 0.274443i
\(159\) 0.261481 + 1.81864i 0.0207368 + 0.144228i
\(160\) 13.9416 1.10218
\(161\) 2.17794 + 6.23454i 0.171645 + 0.491351i
\(162\) −2.51334 −0.197466
\(163\) −3.33835 23.2187i −0.261480 1.81863i −0.521753 0.853097i \(-0.674722\pi\)
0.260273 0.965535i \(-0.416188\pi\)
\(164\) 17.9708 39.3505i 1.40328 3.07276i
\(165\) −0.106240 + 0.0311948i −0.00827075 + 0.00242851i
\(166\) −14.1019 + 16.2744i −1.09452 + 1.26314i
\(167\) 19.9215 + 5.84948i 1.54157 + 0.452647i 0.938569 0.345092i \(-0.112152\pi\)
0.603004 + 0.797738i \(0.293970\pi\)
\(168\) −6.74562 + 4.33514i −0.520436 + 0.334464i
\(169\) −5.23697 11.4674i −0.402844 0.882105i
\(170\) 28.7654 + 33.1971i 2.20621 + 2.54610i
\(171\) 4.20760 + 2.70406i 0.321763 + 0.206785i
\(172\) 2.01532 14.0168i 0.153666 1.06877i
\(173\) 0.510183 3.54840i 0.0387885 0.269780i −0.961193 0.275877i \(-0.911032\pi\)
0.999981 + 0.00609715i \(0.00194080\pi\)
\(174\) 7.81153 + 5.02016i 0.592190 + 0.380578i
\(175\) 10.3210 + 11.9111i 0.780197 + 0.900396i
\(176\) 0.0680724 + 0.149058i 0.00513115 + 0.0112356i
\(177\) 3.51609 2.25965i 0.264285 0.169846i
\(178\) 32.1453 + 9.43871i 2.40939 + 0.707461i
\(179\) 13.5335 15.6184i 1.01154 1.16738i 0.0257010 0.999670i \(-0.491818\pi\)
0.985837 0.167707i \(-0.0536363\pi\)
\(180\) 16.7970 4.93205i 1.25198 0.367613i
\(181\) −10.7612 + 23.5637i −0.799873 + 1.75148i −0.153943 + 0.988080i \(0.549197\pi\)
−0.645929 + 0.763397i \(0.723530\pi\)
\(182\) 0.308930 + 2.14866i 0.0228994 + 0.159269i
\(183\) −4.62316 −0.341754
\(184\) −27.4064 + 5.36412i −2.02043 + 0.395448i
\(185\) 8.92989 0.656539
\(186\) 0.172516 + 1.19987i 0.0126495 + 0.0879790i
\(187\) −0.0488826 + 0.107038i −0.00357465 + 0.00782739i
\(188\) −37.2095 + 10.9257i −2.71378 + 0.796837i
\(189\) −0.901763 + 1.04069i −0.0655936 + 0.0756991i
\(190\) −48.9128 14.3621i −3.54850 1.04193i
\(191\) −6.97368 + 4.48171i −0.504598 + 0.324285i −0.768053 0.640386i \(-0.778774\pi\)
0.263455 + 0.964672i \(0.415138\pi\)
\(192\) 1.39688 + 3.05874i 0.100811 + 0.220745i
\(193\) 11.1106 + 12.8223i 0.799756 + 0.922967i 0.998368 0.0571110i \(-0.0181889\pi\)
−0.198612 + 0.980078i \(0.563643\pi\)
\(194\) −4.57719 2.94158i −0.328623 0.211193i
\(195\) 0.361983 2.51765i 0.0259222 0.180293i
\(196\) 3.13553 21.8081i 0.223966 1.55772i
\(197\) −11.4221 7.34055i −0.813792 0.522992i 0.0662977 0.997800i \(-0.478881\pi\)
−0.880090 + 0.474808i \(0.842518\pi\)
\(198\) 0.0449389 + 0.0518623i 0.00319367 + 0.00368569i
\(199\) −5.33322 11.6781i −0.378062 0.827840i −0.999031 0.0440054i \(-0.985988\pi\)
0.620969 0.783835i \(-0.286739\pi\)
\(200\) −56.0672 + 36.0322i −3.96455 + 2.54786i
\(201\) 4.24987 + 1.24787i 0.299763 + 0.0880183i
\(202\) 21.9717 25.3567i 1.54592 1.78409i
\(203\) 4.88139 1.43331i 0.342607 0.100598i
\(204\) 7.72858 16.9232i 0.541109 1.18486i
\(205\) 5.78347 + 40.2249i 0.403935 + 2.80943i
\(206\) −23.7565 −1.65519
\(207\) −4.25635 + 2.20985i −0.295837 + 0.153595i
\(208\) −3.76428 −0.261006
\(209\) −0.0194348 0.135172i −0.00134433 0.00935005i
\(210\) 5.83040 12.7668i 0.402336 0.880993i
\(211\) 1.29335 0.379761i 0.0890377 0.0261438i −0.236910 0.971532i \(-0.576135\pi\)
0.325948 + 0.945388i \(0.394317\pi\)
\(212\) −5.19406 + 5.99427i −0.356730 + 0.411688i
\(213\) −6.93298 2.03571i −0.475040 0.139484i
\(214\) 29.1560 18.7374i 1.99306 1.28086i
\(215\) 5.52623 + 12.1008i 0.376886 + 0.825265i
\(216\) −3.81329 4.40077i −0.259462 0.299435i
\(217\) 0.558725 + 0.359071i 0.0379287 + 0.0243753i
\(218\) −2.91994 + 20.3086i −0.197763 + 1.37547i
\(219\) 0.849796 5.91046i 0.0574239 0.399392i
\(220\) −0.402106 0.258418i −0.0271100 0.0174225i
\(221\) −1.77017 2.04288i −0.119074 0.137419i
\(222\) −2.29909 5.03431i −0.154305 0.337881i
\(223\) −19.6245 + 12.6119i −1.31415 + 0.844555i −0.994677 0.103039i \(-0.967143\pi\)
−0.319476 + 0.947594i \(0.603507\pi\)
\(224\) −4.54231 1.33374i −0.303496 0.0891143i
\(225\) −7.49514 + 8.64986i −0.499676 + 0.576657i
\(226\) −35.2673 + 10.3554i −2.34594 + 0.688831i
\(227\) 2.54103 5.56408i 0.168654 0.369301i −0.806366 0.591416i \(-0.798569\pi\)
0.975020 + 0.222116i \(0.0712962\pi\)
\(228\) 3.07274 + 21.3714i 0.203497 + 1.41535i
\(229\) 13.7597 0.909269 0.454635 0.890678i \(-0.349770\pi\)
0.454635 + 0.890678i \(0.349770\pi\)
\(230\) 35.2792 33.8333i 2.32624 2.23090i
\(231\) 0.0375981 0.00247378
\(232\) 3.06168 + 21.2944i 0.201009 + 1.39805i
\(233\) 5.88397 12.8841i 0.385472 0.844065i −0.613067 0.790031i \(-0.710065\pi\)
0.998539 0.0540345i \(-0.0172081\pi\)
\(234\) −1.51255 + 0.444124i −0.0988782 + 0.0290333i
\(235\) 23.8569 27.5324i 1.55625 1.79601i
\(236\) 17.3118 + 5.08321i 1.12690 + 0.330889i
\(237\) −1.26938 + 0.815780i −0.0824550 + 0.0529906i
\(238\) −6.19620 13.5678i −0.401640 0.879469i
\(239\) −13.3179 15.3697i −0.861465 0.994183i −0.999993 0.00382482i \(-0.998783\pi\)
0.138528 0.990359i \(-0.455763\pi\)
\(240\) 20.4746 + 13.1582i 1.32163 + 0.849359i
\(241\) −1.11118 + 7.72840i −0.0715772 + 0.497830i 0.922224 + 0.386657i \(0.126370\pi\)
−0.993801 + 0.111174i \(0.964539\pi\)
\(242\) −3.93427 + 27.3634i −0.252904 + 1.75899i
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) −13.0694 15.0829i −0.836684 0.965585i
\(245\) 8.59799 + 18.8270i 0.549305 + 1.20281i
\(246\) 21.1882 13.6168i 1.35091 0.868177i
\(247\) 3.00999 + 0.883813i 0.191521 + 0.0562357i
\(248\) −1.83920 + 2.12254i −0.116789 + 0.134782i
\(249\) −8.22088 + 2.41387i −0.520977 + 0.152973i
\(250\) 27.2901 59.7570i 1.72598 3.77936i
\(251\) −2.12432 14.7750i −0.134086 0.932587i −0.940151 0.340759i \(-0.889316\pi\)
0.806065 0.591827i \(-0.201593\pi\)
\(252\) −5.94445 −0.374465
\(253\) 0.121704 + 0.0483165i 0.00765148 + 0.00303763i
\(254\) −4.56401 −0.286372
\(255\) 2.48726 + 17.2993i 0.155758 + 1.08332i
\(256\) −13.2090 + 28.9236i −0.825560 + 1.80772i
\(257\) −13.0843 + 3.84190i −0.816177 + 0.239651i −0.663069 0.748558i \(-0.730746\pi\)
−0.153108 + 0.988209i \(0.548928\pi\)
\(258\) 5.39914 6.23094i 0.336136 0.387921i
\(259\) −2.90944 0.854288i −0.180784 0.0530829i
\(260\) 9.23705 5.93629i 0.572858 0.368153i
\(261\) 1.53476 + 3.36066i 0.0949993 + 0.208019i
\(262\) 9.76935 + 11.2744i 0.603553 + 0.696537i
\(263\) 5.98538 + 3.84657i 0.369075 + 0.237190i 0.712010 0.702169i \(-0.247785\pi\)
−0.342936 + 0.939359i \(0.611421\pi\)
\(264\) −0.0226269 + 0.157373i −0.00139259 + 0.00968565i
\(265\) 1.06038 7.37512i 0.0651388 0.453050i
\(266\) 14.5623 + 9.35859i 0.892869 + 0.573812i
\(267\) 8.72918 + 10.0740i 0.534217 + 0.616520i
\(268\) 7.94299 + 17.3927i 0.485196 + 1.06243i
\(269\) −11.9712 + 7.69340i −0.729894 + 0.469075i −0.852066 0.523434i \(-0.824651\pi\)
0.122172 + 0.992509i \(0.461014\pi\)
\(270\) 9.77946 + 2.87151i 0.595159 + 0.174754i
\(271\) −5.31964 + 6.13920i −0.323145 + 0.372930i −0.893958 0.448151i \(-0.852083\pi\)
0.570813 + 0.821080i \(0.306628\pi\)
\(272\) 24.8174 7.28705i 1.50478 0.441843i
\(273\) −0.358791 + 0.785643i −0.0217150 + 0.0475493i
\(274\) 2.88074 + 20.0360i 0.174032 + 1.21042i
\(275\) 0.312503 0.0188446
\(276\) −19.2421 7.63908i −1.15824 0.459819i
\(277\) −3.71245 −0.223060 −0.111530 0.993761i \(-0.535575\pi\)
−0.111530 + 0.993761i \(0.535575\pi\)
\(278\) −2.74706 19.1062i −0.164758 1.14592i
\(279\) −0.200359 + 0.438726i −0.0119952 + 0.0262658i
\(280\) 31.2003 9.16123i 1.86457 0.547488i
\(281\) −8.20261 + 9.46632i −0.489327 + 0.564713i −0.945686 0.325083i \(-0.894608\pi\)
0.456359 + 0.889796i \(0.349153\pi\)
\(282\) −21.6639 6.36108i −1.29006 0.378797i
\(283\) −20.5721 + 13.2209i −1.22289 + 0.785901i −0.982768 0.184842i \(-0.940823\pi\)
−0.240118 + 0.970744i \(0.577186\pi\)
\(284\) −12.9577 28.3735i −0.768899 1.68365i
\(285\) −13.2825 15.3288i −0.786785 0.907998i
\(286\) 0.0362090 + 0.0232701i 0.00214108 + 0.00137599i
\(287\) 1.96386 13.6589i 0.115923 0.806261i
\(288\) 0.489262 3.40289i 0.0288300 0.200517i
\(289\) 1.32388 + 0.850806i 0.0778753 + 0.0500474i
\(290\) −24.6593 28.4583i −1.44804 1.67113i
\(291\) −0.899298 1.96919i −0.0527178 0.115436i
\(292\) 21.6850 13.9361i 1.26902 0.815550i
\(293\) 16.3811 + 4.80992i 0.956993 + 0.280999i 0.722696 0.691166i \(-0.242903\pi\)
0.234297 + 0.972165i \(0.424721\pi\)
\(294\) 8.40025 9.69441i 0.489913 0.565389i
\(295\) −16.2629 + 4.77521i −0.946860 + 0.278023i
\(296\) 5.32669 11.6638i 0.309607 0.677946i
\(297\) 0.00388573 + 0.0270259i 0.000225473 + 0.00156820i
\(298\) 7.27427 0.421387
\(299\) −2.17101 + 2.08203i −0.125553 + 0.120407i
\(300\) −49.4082 −2.85258
\(301\) −0.642863 4.47121i −0.0370540 0.257716i
\(302\) −2.15678 + 4.72269i −0.124109 + 0.271760i
\(303\) 12.8087 3.76098i 0.735842 0.216063i
\(304\) −19.6572 + 22.6856i −1.12742 + 1.30111i
\(305\) 17.9888 + 5.28200i 1.03004 + 0.302447i
\(306\) 9.11228 5.85610i 0.520914 0.334771i
\(307\) 9.16309 + 20.0644i 0.522965 + 1.14513i 0.968305 + 0.249772i \(0.0803556\pi\)
−0.445340 + 0.895362i \(0.646917\pi\)
\(308\) 0.106288 + 0.122663i 0.00605631 + 0.00698936i
\(309\) −7.95167 5.11023i −0.452355 0.290711i
\(310\) 0.699602 4.86584i 0.0397347 0.276361i
\(311\) 0.775655 5.39480i 0.0439833 0.305911i −0.955940 0.293561i \(-0.905160\pi\)
0.999924 0.0123500i \(-0.00393124\pi\)
\(312\) −3.07252 1.97459i −0.173947 0.111789i
\(313\) −20.0600 23.1505i −1.13386 1.30854i −0.945198 0.326498i \(-0.894131\pi\)
−0.188659 0.982043i \(-0.560414\pi\)
\(314\) 20.2394 + 44.3182i 1.14218 + 2.50102i
\(315\) 4.69778 3.01908i 0.264690 0.170106i
\(316\) −6.24992 1.83514i −0.351585 0.103235i
\(317\) −0.468539 + 0.540723i −0.0263158 + 0.0303700i −0.768755 0.639544i \(-0.779123\pi\)
0.742439 + 0.669914i \(0.233669\pi\)
\(318\) −4.43080 + 1.30100i −0.248467 + 0.0729566i
\(319\) 0.0419048 0.0917586i 0.00234622 0.00513750i
\(320\) −1.94066 13.4976i −0.108486 0.754536i
\(321\) 13.7896 0.769659
\(322\) −14.7310 + 7.64817i −0.820926 + 0.426216i
\(323\) −21.5554 −1.19938
\(324\) −0.614354 4.27292i −0.0341308 0.237385i
\(325\) −2.98215 + 6.52999i −0.165420 + 0.362219i
\(326\) 56.5685 16.6100i 3.13304 0.919943i
\(327\) −5.34591 + 6.16951i −0.295630 + 0.341175i
\(328\) 55.9898 + 16.4401i 3.09152 + 0.907752i
\(329\) −10.4067 + 6.68799i −0.573741 + 0.368721i
\(330\) −0.115605 0.253140i −0.00636386 0.0139349i
\(331\) −18.3506 21.1777i −1.00864 1.16403i −0.986414 0.164281i \(-0.947470\pi\)
−0.0222271 0.999753i \(-0.507076\pi\)
\(332\) −31.1151 19.9965i −1.70767 1.09745i
\(333\) 0.313382 2.17962i 0.0171732 0.119442i
\(334\) −7.42645 + 51.6521i −0.406357 + 2.82628i
\(335\) −15.1106 9.71102i −0.825582 0.530570i
\(336\) −5.41201 6.24579i −0.295249 0.340736i
\(337\) −7.81892 17.1210i −0.425924 0.932643i −0.993971 0.109647i \(-0.965028\pi\)
0.568047 0.822996i \(-0.307699\pi\)
\(338\) 26.6548 17.1300i 1.44983 0.931750i
\(339\) −14.0321 4.12018i −0.762116 0.223778i
\(340\) −49.4070 + 57.0187i −2.67947 + 3.09228i
\(341\) 0.0126355 0.00371012i 0.000684251 0.000200914i
\(342\) −5.22204 + 11.4347i −0.282376 + 0.618317i
\(343\) −2.37200 16.4976i −0.128076 0.890789i
\(344\) 19.1019 1.02990
\(345\) 19.0864 3.73568i 1.02757 0.201122i
\(346\) 9.01004 0.484383
\(347\) −2.03201 14.1329i −0.109084 0.758696i −0.968786 0.247900i \(-0.920260\pi\)
0.859702 0.510796i \(-0.170649\pi\)
\(348\) −6.62535 + 14.5075i −0.355156 + 0.777683i
\(349\) 4.50865 1.32386i 0.241343 0.0708646i −0.158824 0.987307i \(-0.550770\pi\)
0.400167 + 0.916442i \(0.368952\pi\)
\(350\) −25.9402 + 29.9366i −1.38656 + 1.60018i
\(351\) −0.601808 0.176707i −0.0321221 0.00943191i
\(352\) −0.0789661 + 0.0507484i −0.00420891 + 0.00270490i
\(353\) 7.42472 + 16.2579i 0.395178 + 0.865320i 0.997737 + 0.0672447i \(0.0214208\pi\)
−0.602558 + 0.798075i \(0.705852\pi\)
\(354\) 6.87912 + 7.93892i 0.365621 + 0.421949i
\(355\) 24.6506 + 15.8420i 1.30832 + 0.840805i
\(356\) −8.18923 + 56.9574i −0.434028 + 3.01873i
\(357\) 0.844584 5.87421i 0.0447001 0.310896i
\(358\) 43.6956 + 28.0814i 2.30938 + 1.48415i
\(359\) 22.9288 + 26.4612i 1.21013 + 1.39657i 0.894127 + 0.447814i \(0.147797\pi\)
0.316008 + 0.948757i \(0.397657\pi\)
\(360\) 9.80970 + 21.4802i 0.517016 + 1.13211i
\(361\) 5.06084 3.25240i 0.266360 0.171179i
\(362\) −62.4699 18.3428i −3.28334 0.964076i
\(363\) −7.20298 + 8.31268i −0.378058 + 0.436303i
\(364\) −3.57742 + 1.05042i −0.187508 + 0.0550572i
\(365\) −10.0593 + 22.0269i −0.526529 + 1.15294i
\(366\) −1.65364 11.5013i −0.0864370 0.601183i
\(367\) 14.8756 0.776498 0.388249 0.921554i \(-0.373080\pi\)
0.388249 + 0.921554i \(0.373080\pi\)
\(368\) −9.49221 27.1723i −0.494816 1.41645i
\(369\) 10.0211 0.521678
\(370\) 3.19409 + 22.2154i 0.166053 + 1.15492i
\(371\) −1.05103 + 2.30144i −0.0545668 + 0.119485i
\(372\) −1.99773 + 0.586588i −0.103578 + 0.0304132i
\(373\) 11.4264 13.1868i 0.591636 0.682785i −0.378429 0.925630i \(-0.623535\pi\)
0.970065 + 0.242846i \(0.0780809\pi\)
\(374\) −0.283769 0.0833220i −0.0146733 0.00430848i
\(375\) 21.9887 14.1313i 1.13549 0.729735i
\(376\) −21.7308 47.5839i −1.12068 2.45395i
\(377\) 1.51748 + 1.75127i 0.0781543 + 0.0901948i
\(378\) −2.91153 1.87113i −0.149753 0.0962403i
\(379\) 1.67590 11.6561i 0.0860852 0.598736i −0.900422 0.435018i \(-0.856742\pi\)
0.986507 0.163718i \(-0.0523487\pi\)
\(380\) 12.4609 86.6672i 0.639229 4.44593i
\(381\) −1.52765 0.981759i −0.0782637 0.0502970i
\(382\) −13.6438 15.7458i −0.698077 0.805624i
\(383\) 1.19882 + 2.62505i 0.0612568 + 0.134134i 0.937785 0.347217i \(-0.112873\pi\)
−0.876528 + 0.481351i \(0.840146\pi\)
\(384\) −12.8940 + 8.28647i −0.657994 + 0.422867i
\(385\) −0.146295 0.0429562i −0.00745590 0.00218925i
\(386\) −27.9246 + 32.2267i −1.42132 + 1.64030i
\(387\) 3.14751 0.924191i 0.159997 0.0469793i
\(388\) 3.88215 8.50072i 0.197086 0.431559i
\(389\) 0.649215 + 4.51539i 0.0329165 + 0.228939i 0.999638 0.0268904i \(-0.00856050\pi\)
−0.966722 + 0.255830i \(0.917651\pi\)
\(390\) 6.39277 0.323710
\(391\) 10.2827 17.9293i 0.520019 0.906725i
\(392\) 29.7197 1.50107
\(393\) 0.844727 + 5.87521i 0.0426108 + 0.296365i
\(394\) 14.1760 31.0410i 0.714175 1.56382i
\(395\) 5.87122 1.72395i 0.295413 0.0867411i
\(396\) −0.0771863 + 0.0890777i −0.00387876 + 0.00447632i
\(397\) −4.25519 1.24944i −0.213562 0.0627074i 0.173202 0.984886i \(-0.444589\pi\)
−0.386763 + 0.922179i \(0.626407\pi\)
\(398\) 27.1447 17.4448i 1.36064 0.874431i
\(399\) 2.86110 + 6.26494i 0.143234 + 0.313639i
\(400\) −44.9827 51.9128i −2.24914 2.59564i
\(401\) 4.63189 + 2.97674i 0.231306 + 0.148651i 0.651160 0.758940i \(-0.274283\pi\)
−0.419855 + 0.907591i \(0.637919\pi\)
\(402\) −1.58429 + 11.0190i −0.0790172 + 0.549577i
\(403\) −0.0430521 + 0.299434i −0.00214458 + 0.0149159i
\(404\) 48.4796 + 31.1560i 2.41195 + 1.55007i
\(405\) 2.65565 + 3.06479i 0.131960 + 0.152290i
\(406\) 5.31172 + 11.6310i 0.263616 + 0.577239i
\(407\) −0.0505794 + 0.0325054i −0.00250713 + 0.00161123i
\(408\) 24.0792 + 7.07029i 1.19210 + 0.350032i
\(409\) −20.4190 + 23.5648i −1.00966 + 1.16521i −0.0234433 + 0.999725i \(0.507463\pi\)
−0.986213 + 0.165480i \(0.947083\pi\)
\(410\) −98.0011 + 28.7757i −4.83993 + 1.42113i
\(411\) −3.34568 + 7.32602i −0.165030 + 0.361366i
\(412\) −5.80697 40.3884i −0.286089 1.98979i
\(413\) 5.75541 0.283205
\(414\) −7.02001 9.79833i −0.345015 0.481562i
\(415\) 34.7455 1.70559
\(416\) −0.306872 2.13434i −0.0150456 0.104645i
\(417\) 3.19044 6.98608i 0.156236 0.342110i
\(418\) 0.329324 0.0966981i 0.0161077 0.00472966i
\(419\) −25.3369 + 29.2403i −1.23779 + 1.42848i −0.371880 + 0.928281i \(0.621287\pi\)
−0.865908 + 0.500203i \(0.833259\pi\)
\(420\) 23.1300 + 6.79158i 1.12863 + 0.331395i
\(421\) 5.63619 3.62216i 0.274691 0.176533i −0.396041 0.918233i \(-0.629616\pi\)
0.670732 + 0.741699i \(0.265980\pi\)
\(422\) 1.40736 + 3.08170i 0.0685094 + 0.150015i
\(423\) −5.88291 6.78924i −0.286037 0.330104i
\(424\) −9.00053 5.78429i −0.437104 0.280910i
\(425\) 7.01989 48.8244i 0.340515 2.36833i
\(426\) 2.58452 17.9757i 0.125220 0.870925i
\(427\) −5.35562 3.44185i −0.259177 0.166563i
\(428\) 38.9823 + 44.9880i 1.88428 + 2.17458i
\(429\) 0.00711412 + 0.0155777i 0.000343473 + 0.000752101i
\(430\) −28.1271 + 18.0762i −1.35641 + 0.871711i
\(431\) −4.72227 1.38658i −0.227464 0.0667894i 0.166015 0.986123i \(-0.446910\pi\)
−0.393478 + 0.919334i \(0.628728\pi\)
\(432\) 3.93020 4.53569i 0.189092 0.218224i
\(433\) 24.8366 7.29268i 1.19357 0.350464i 0.376179 0.926547i \(-0.377238\pi\)
0.817391 + 0.576083i \(0.195420\pi\)
\(434\) −0.693432 + 1.51841i −0.0332858 + 0.0728858i
\(435\) −2.13221 14.8299i −0.102232 0.711038i
\(436\) −35.2404 −1.68771
\(437\) 1.21038 + 23.9562i 0.0579005 + 1.14598i
\(438\) 15.0077 0.717098
\(439\) −0.315656 2.19544i −0.0150655 0.104783i 0.980901 0.194507i \(-0.0623106\pi\)
−0.995967 + 0.0897241i \(0.971401\pi\)
\(440\) 0.267842 0.586492i 0.0127689 0.0279599i
\(441\) 4.89705 1.43790i 0.233193 0.0684716i
\(442\) 4.44903 5.13445i 0.211619 0.244221i
\(443\) −7.47429 2.19465i −0.355114 0.104271i 0.0993095 0.995057i \(-0.468337\pi\)
−0.454424 + 0.890786i \(0.650155\pi\)
\(444\) 7.99685 5.13926i 0.379514 0.243899i
\(445\) −22.4558 49.1714i −1.06451 2.33095i
\(446\) −38.3947 44.3098i −1.81804 2.09813i
\(447\) 2.43481 + 1.56476i 0.115163 + 0.0740106i
\(448\) −0.658976 + 4.58328i −0.0311337 + 0.216540i
\(449\) 1.01858 7.08436i 0.0480697 0.334332i −0.951569 0.307437i \(-0.900529\pi\)
0.999638 0.0268953i \(-0.00856207\pi\)
\(450\) −24.1996 15.5522i −1.14078 0.733135i
\(451\) −0.179179 0.206784i −0.00843722 0.00973707i
\(452\) −26.2259 57.4266i −1.23356 2.70112i
\(453\) −1.73780 + 1.11682i −0.0816490 + 0.0524726i
\(454\) 14.7510 + 4.33127i 0.692297 + 0.203277i
\(455\) 2.29367 2.64703i 0.107529 0.124095i
\(456\) −27.9448 + 8.20532i −1.30863 + 0.384249i
\(457\) −1.85262 + 4.05667i −0.0866618 + 0.189763i −0.948001 0.318268i \(-0.896899\pi\)
0.861339 + 0.508030i \(0.169626\pi\)
\(458\) 4.92165 + 34.2309i 0.229974 + 1.59950i
\(459\) 4.30972 0.201161
\(460\) 66.1436 + 51.7081i 3.08396 + 2.41090i
\(461\) −24.0540 −1.12031 −0.560153 0.828389i \(-0.689258\pi\)
−0.560153 + 0.828389i \(0.689258\pi\)
\(462\) 0.0134483 + 0.0935349i 0.000625671 + 0.00435164i
\(463\) −1.36569 + 2.99043i −0.0634688 + 0.138977i −0.938708 0.344712i \(-0.887976\pi\)
0.875240 + 0.483690i \(0.160704\pi\)
\(464\) −21.2748 + 6.24685i −0.987659 + 0.290003i
\(465\) 1.28085 1.47818i 0.0593981 0.0685490i
\(466\) 34.1571 + 10.0294i 1.58230 + 0.464604i
\(467\) 11.5767 7.43992i 0.535708 0.344278i −0.244650 0.969611i \(-0.578673\pi\)
0.780358 + 0.625333i \(0.215037\pi\)
\(468\) −1.12478 2.46292i −0.0519928 0.113848i
\(469\) 3.99417 + 4.60951i 0.184434 + 0.212848i
\(470\) 77.0270 + 49.5023i 3.55299 + 2.28337i
\(471\) −2.75877 + 19.1877i −0.127117 + 0.884121i
\(472\) −3.46365 + 24.0902i −0.159428 + 1.10884i
\(473\) −0.0753485 0.0484235i −0.00346453 0.00222652i
\(474\) −2.48350 2.86611i −0.114071 0.131645i
\(475\) 23.7805 + 52.0720i 1.09112 + 2.38923i
\(476\) 21.5520 13.8506i 0.987835 0.634843i
\(477\) −1.76292 0.517639i −0.0807184 0.0237011i
\(478\) 33.4724 38.6292i 1.53099 1.76686i
\(479\) 22.1960 6.51733i 1.01416 0.297784i 0.267906 0.963445i \(-0.413668\pi\)
0.746255 + 0.665661i \(0.231850\pi\)
\(480\) −5.79156 + 12.6817i −0.264347 + 0.578840i
\(481\) −0.196558 1.36709i −0.00896226 0.0623339i
\(482\) −19.6238 −0.893841
\(483\) −6.57588 0.608801i −0.299213 0.0277014i
\(484\) −47.4823 −2.15829
\(485\) 1.24938 + 8.68962i 0.0567313 + 0.394575i
\(486\) 1.04408 2.28621i 0.0473603 0.103705i
\(487\) −11.1600 + 3.27689i −0.505710 + 0.148490i −0.524629 0.851331i \(-0.675796\pi\)
0.0189187 + 0.999821i \(0.493978\pi\)
\(488\) 17.6295 20.3455i 0.798049 0.920998i
\(489\) 22.5073 + 6.60874i 1.01782 + 0.298858i
\(490\) −43.7615 + 28.1238i −1.97694 + 1.27050i
\(491\) −12.6159 27.6249i −0.569346 1.24669i −0.947145 0.320806i \(-0.896046\pi\)
0.377799 0.925888i \(-0.376681\pi\)
\(492\) 28.3291 + 32.6936i 1.27718 + 1.47394i
\(493\) −13.3947 8.60828i −0.603269 0.387697i
\(494\) −1.12208 + 7.80425i −0.0504848 + 0.351130i
\(495\) 0.0157578 0.109598i 0.000708260 0.00492606i
\(496\) −2.43512 1.56496i −0.109340 0.0702686i
\(497\) −6.51584 7.51968i −0.292276 0.337304i
\(498\) −8.94560 19.5881i −0.400862 0.877765i
\(499\) −29.3390 + 18.8551i −1.31340 + 0.844068i −0.994603 0.103756i \(-0.966914\pi\)
−0.318793 + 0.947824i \(0.603277\pi\)
\(500\) 108.264 + 31.7890i 4.84169 + 1.42165i
\(501\) −13.5966 + 15.6913i −0.607450 + 0.701035i
\(502\) 35.9966 10.5696i 1.60661 0.471743i
\(503\) 4.66816 10.2218i 0.208143 0.455770i −0.776553 0.630052i \(-0.783033\pi\)
0.984696 + 0.174283i \(0.0557607\pi\)
\(504\) −1.14116 7.93691i −0.0508311 0.353538i
\(505\) −54.1360 −2.40902
\(506\) −0.0766679 + 0.320053i −0.00340830 + 0.0142281i
\(507\) 12.6066 0.559879
\(508\) −1.11562 7.75927i −0.0494974 0.344262i
\(509\) 1.81739 3.97954i 0.0805546 0.176390i −0.865069 0.501653i \(-0.832726\pi\)
0.945624 + 0.325263i \(0.105453\pi\)
\(510\) −42.1467 + 12.3754i −1.86629 + 0.547992i
\(511\) 5.38465 6.21421i 0.238203 0.274901i
\(512\) −47.2669 13.8788i −2.08892 0.613363i
\(513\) −4.20760 + 2.70406i −0.185770 + 0.119387i
\(514\) −14.2378 31.1764i −0.628001 1.37513i
\(515\) 25.1017 + 28.9689i 1.10611 + 1.27652i
\(516\) 11.9130 + 7.65600i 0.524439 + 0.337037i
\(517\) −0.0349073 + 0.242786i −0.00153522 + 0.0106777i
\(518\) 1.08460 7.54354i 0.0476544 0.331444i
\(519\) 3.01580 + 1.93814i 0.132379 + 0.0850748i
\(520\) 9.69925 + 11.1935i 0.425340 + 0.490869i
\(521\) −1.29520 2.83608i −0.0567436 0.124251i 0.879136 0.476571i \(-0.158120\pi\)
−0.935880 + 0.352319i \(0.885393\pi\)
\(522\) −7.81153 + 5.02016i −0.341901 + 0.219727i
\(523\) −12.4643 3.65986i −0.545027 0.160034i −0.00238288 0.999997i \(-0.500758\pi\)
−0.542644 + 0.839963i \(0.682577\pi\)
\(524\) −16.7797 + 19.3648i −0.733023 + 0.845954i
\(525\) −15.1222 + 4.44029i −0.659989 + 0.193790i
\(526\) −7.42845 + 16.2660i −0.323896 + 0.709233i
\(527\) −0.295820 2.05747i −0.0128861 0.0896249i
\(528\) −0.163866 −0.00713135
\(529\) −20.5036 10.4212i −0.891462 0.453096i
\(530\) 18.7268 0.813439
\(531\) 0.594817 + 4.13704i 0.0258128 + 0.179532i
\(532\) −12.3510 + 27.0449i −0.535483 + 1.17254i
\(533\) 6.03079 1.77080i 0.261222 0.0767018i
\(534\) −21.9394 + 25.3194i −0.949410 + 1.09568i
\(535\) −53.6555 15.7547i −2.31973 0.681135i
\(536\) −21.6976 + 13.9442i −0.937194 + 0.602298i
\(537\) 8.58503 + 18.7986i 0.370471 + 0.811219i
\(538\) −23.4212 27.0295i −1.00976 1.16532i
\(539\) −0.117231 0.0753398i −0.00504949 0.00324511i
\(540\) −2.49138 + 17.3280i −0.107212 + 0.745677i
\(541\) 4.61797 32.1187i 0.198542 1.38089i −0.609976 0.792420i \(-0.708821\pi\)
0.808518 0.588471i \(-0.200270\pi\)
\(542\) −17.1756 11.0381i −0.737754 0.474126i
\(543\) −16.9639 19.5774i −0.727993 0.840148i
\(544\) 6.15492 + 13.4774i 0.263890 + 0.577839i
\(545\) 27.8498 17.8980i 1.19295 0.766665i
\(546\) −2.08282 0.611572i −0.0891365 0.0261728i
\(547\) 5.89308 6.80097i 0.251970 0.290789i −0.615647 0.788022i \(-0.711105\pi\)
0.867617 + 0.497233i \(0.165651\pi\)
\(548\) −33.3590 + 9.79507i −1.42502 + 0.418425i
\(549\) 1.92053 4.20538i 0.0819663 0.179481i
\(550\) 0.111778 + 0.777430i 0.00476621 + 0.0331497i
\(551\) 18.4785 0.787209
\(552\) 6.50566 27.1581i 0.276899 1.15592i
\(553\) −2.07782 −0.0883579
\(554\) −1.32789 9.23567i −0.0564166 0.392386i
\(555\) −3.70961 + 8.12291i −0.157464 + 0.344798i
\(556\) 31.8110 9.34056i 1.34909 0.396128i
\(557\) 20.6639 23.8474i 0.875556 1.01045i −0.124279 0.992247i \(-0.539662\pi\)
0.999834 0.0181980i \(-0.00579291\pi\)
\(558\) −1.16311 0.341519i −0.0492383 0.0144577i
\(559\) 1.73088 1.11237i 0.0732086 0.0470483i
\(560\) 13.9224 + 30.4858i 0.588328 + 1.28826i
\(561\) −0.0770586 0.0889303i −0.00325342 0.00375464i
\(562\) −26.4838 17.0201i −1.11715 0.717951i
\(563\) −5.12498 + 35.6450i −0.215992 + 1.50226i 0.536636 + 0.843814i \(0.319695\pi\)
−0.752628 + 0.658446i \(0.771214\pi\)
\(564\) 5.51902 38.3856i 0.232393 1.61633i
\(565\) 49.8917 + 32.0635i 2.09896 + 1.34892i
\(566\) −40.2487 46.4495i −1.69178 1.95242i
\(567\) −0.572039 1.25259i −0.0240234 0.0526039i
\(568\) 35.3962 22.7477i 1.48519 0.954474i
\(569\) −31.2963 9.18942i −1.31201 0.385241i −0.450406 0.892824i \(-0.648721\pi\)
−0.861603 + 0.507583i \(0.830539\pi\)
\(570\) 33.3833 38.5264i 1.39827 1.61369i
\(571\) 32.7363 9.61224i 1.36997 0.402260i 0.487704 0.873009i \(-0.337835\pi\)
0.882267 + 0.470749i \(0.156016\pi\)
\(572\) −0.0307107 + 0.0672470i −0.00128408 + 0.00281174i
\(573\) −1.17974 8.20526i −0.0492842 0.342779i
\(574\) 34.6825 1.44762
\(575\) −54.6565 5.06014i −2.27933 0.211022i
\(576\) −3.36261 −0.140109
\(577\) 5.54883 + 38.5929i 0.231001 + 1.60664i 0.693791 + 0.720177i \(0.255939\pi\)
−0.462790 + 0.886468i \(0.653152\pi\)
\(578\) −1.64306 + 3.59781i −0.0683425 + 0.149649i
\(579\) −16.2790 + 4.77996i −0.676534 + 0.198648i
\(580\) 42.3543 48.8795i 1.75867 2.02961i
\(581\) −11.3204 3.32397i −0.469650 0.137902i
\(582\) 4.57719 2.94158i 0.189731 0.121933i
\(583\) 0.0208399 + 0.0456330i 0.000863099 + 0.00188992i
\(584\) 22.7701 + 26.2781i 0.942233 + 1.08739i
\(585\) 2.13976 + 1.37514i 0.0884682 + 0.0568551i
\(586\) −6.10663 + 42.4726i −0.252263 + 1.75453i
\(587\) −4.67494 + 32.5149i −0.192955 + 1.34203i 0.631177 + 0.775638i \(0.282572\pi\)
−0.824133 + 0.566396i \(0.808337\pi\)
\(588\) 18.5348 + 11.9116i 0.764362 + 0.491226i
\(589\) 1.57973 + 1.82311i 0.0650918 + 0.0751200i
\(590\) −17.6965 38.7500i −0.728555 1.59531i
\(591\) 11.4221 7.34055i 0.469843 0.301950i
\(592\) 12.6804 + 3.72329i 0.521159 + 0.153026i
\(593\) 0.143737 0.165882i 0.00590259 0.00681195i −0.752791 0.658260i \(-0.771293\pi\)
0.758693 + 0.651448i \(0.225838\pi\)
\(594\) −0.0658439 + 0.0193335i −0.00270161 + 0.000793263i
\(595\) −9.99763 + 21.8918i −0.409863 + 0.897475i
\(596\) 1.77810 + 12.3670i 0.0728340 + 0.506572i
\(597\) 12.8383 0.525436
\(598\) −5.95613 4.65623i −0.243564 0.190407i
\(599\) −3.53619 −0.144485 −0.0722425 0.997387i \(-0.523016\pi\)
−0.0722425 + 0.997387i \(0.523016\pi\)
\(600\) −9.48489 65.9689i −0.387219 2.69317i
\(601\) 15.0669 32.9918i 0.614590 1.34577i −0.304799 0.952417i \(-0.598589\pi\)
0.919389 0.393348i \(-0.128683\pi\)
\(602\) 10.8933 3.19857i 0.443979 0.130364i
\(603\) −2.90057 + 3.34743i −0.118120 + 0.136318i
\(604\) −8.55624 2.51234i −0.348148 0.102226i
\(605\) 37.5243 24.1154i 1.52558 0.980430i
\(606\) 13.9379 + 30.5197i 0.566188 + 1.23978i
\(607\) 29.3523 + 33.8743i 1.19137 + 1.37492i 0.909626 + 0.415428i \(0.136368\pi\)
0.281746 + 0.959489i \(0.409086\pi\)
\(608\) −14.4652 9.29624i −0.586643 0.377012i
\(609\) −0.724023 + 5.03569i −0.0293389 + 0.204056i
\(610\) −6.70598 + 46.6411i −0.271517 + 1.88844i
\(611\) −4.74009 3.04627i −0.191763 0.123239i
\(612\) 12.1833 + 14.0603i 0.492482 + 0.568355i
\(613\) 0.674111 + 1.47610i 0.0272271 + 0.0596190i 0.922757 0.385382i \(-0.125930\pi\)
−0.895530 + 0.445001i \(0.853203\pi\)
\(614\) −46.6377 + 29.9722i −1.88214 + 1.20958i
\(615\) −38.9924 11.4492i −1.57233 0.461676i
\(616\) −0.143373 + 0.165461i −0.00577665 + 0.00666661i
\(617\) 18.6179 5.46671i 0.749529 0.220082i 0.115411 0.993318i \(-0.463182\pi\)
0.634118 + 0.773236i \(0.281363\pi\)
\(618\) 9.86880 21.6097i 0.396981 0.869268i
\(619\) 1.55013 + 10.7814i 0.0623051 + 0.433341i 0.996968 + 0.0778073i \(0.0247919\pi\)
−0.934663 + 0.355534i \(0.884299\pi\)
\(620\) 8.44342 0.339096
\(621\) −0.242000 4.78972i −0.00971114 0.192205i
\(622\) 13.6984 0.549255
\(623\) 2.61227 + 18.1688i 0.104658 + 0.727916i
\(624\) 1.56374 3.42411i 0.0625996 0.137074i
\(625\) −46.7946 + 13.7401i −1.87178 + 0.549606i
\(626\) 50.4175 58.1849i 2.01509 2.32554i
\(627\) 0.131030 + 0.0384740i 0.00523285 + 0.00153650i
\(628\) −70.3980 + 45.2421i −2.80919 + 1.80535i
\(629\) 3.94235 + 8.63254i 0.157192 + 0.344202i
\(630\) 9.19106 + 10.6070i 0.366180 + 0.422595i
\(631\) 36.6812 + 23.5736i 1.46026 + 0.938449i 0.998681 + 0.0513479i \(0.0163517\pi\)
0.461575 + 0.887101i \(0.347285\pi\)
\(632\) 1.25045 8.69706i 0.0497401 0.345950i
\(633\) −0.191833 + 1.33423i −0.00762468 + 0.0530308i
\(634\) −1.51278 0.972203i −0.0600800 0.0386111i
\(635\) 4.82244 + 5.56540i 0.191373 + 0.220856i
\(636\) −3.29489 7.21480i −0.130651 0.286085i
\(637\) 2.69299 1.73068i 0.106700 0.0685721i
\(638\) 0.243262 + 0.0714281i 0.00963082 + 0.00282786i
\(639\) 4.73181 5.46080i 0.187187 0.216026i
\(640\) 59.6382 17.5114i 2.35741 0.692198i
\(641\) −2.92279 + 6.40002i −0.115443 + 0.252786i −0.958530 0.284993i \(-0.908009\pi\)
0.843086 + 0.537778i \(0.180736\pi\)
\(642\) 4.93232 + 34.3051i 0.194663 + 1.35391i
\(643\) −9.53363 −0.375970 −0.187985 0.982172i \(-0.560196\pi\)
−0.187985 + 0.982172i \(0.560196\pi\)
\(644\) −16.6035 23.1747i −0.654268 0.913209i
\(645\) −13.3029 −0.523802
\(646\) −7.71006 53.6246i −0.303348 2.10983i
\(647\) −7.37566 + 16.1504i −0.289967 + 0.634939i −0.997417 0.0718238i \(-0.977118\pi\)
0.707450 + 0.706763i \(0.249845\pi\)
\(648\) 5.58718 1.64055i 0.219485 0.0644467i
\(649\) 0.0747317 0.0862450i 0.00293347 0.00338541i
\(650\) −17.3117 5.08317i −0.679020 0.199378i
\(651\) −0.558725 + 0.359071i −0.0218982 + 0.0140731i
\(652\) 42.0661 + 92.1119i 1.64744 + 3.60738i
\(653\) 16.0888 + 18.5675i 0.629604 + 0.726602i 0.977501 0.210931i \(-0.0676495\pi\)
−0.347897 + 0.937533i \(0.613104\pi\)
\(654\) −17.2604 11.0926i −0.674934 0.433754i
\(655\) 3.42562 23.8257i 0.133850 0.930946i
\(656\) −8.55918 + 59.5304i −0.334180 + 2.32427i
\(657\) 5.02333 + 3.22830i 0.195979 + 0.125948i
\(658\) −20.3604 23.4972i −0.793731 0.916015i
\(659\) −0.693556 1.51868i −0.0270171 0.0591592i 0.895642 0.444775i \(-0.146716\pi\)
−0.922659 + 0.385616i \(0.873989\pi\)
\(660\) 0.402106 0.258418i 0.0156519 0.0100589i
\(661\) −12.6102 3.70269i −0.490480 0.144018i 0.0271347 0.999632i \(-0.491362\pi\)
−0.517615 + 0.855614i \(0.673180\pi\)
\(662\) 46.1213 53.2268i 1.79255 2.06872i
\(663\) 2.59362 0.761557i 0.100728 0.0295764i
\(664\) 20.7257 45.3830i 0.804315 1.76120i
\(665\) −3.97487 27.6459i −0.154139 1.07206i
\(666\) 5.53445 0.214456
\(667\) −8.81489 + 15.3700i −0.341314 + 0.595128i
\(668\) −89.6290 −3.46785
\(669\) −3.31988 23.0902i −0.128354 0.892720i
\(670\) 18.7538 41.0651i 0.724522 1.58648i
\(671\) −0.121117 + 0.0355631i −0.00467566 + 0.00137290i
\(672\) 3.10016 3.57777i 0.119591 0.138015i
\(673\) 22.3895 + 6.57416i 0.863053 + 0.253415i 0.683158 0.730271i \(-0.260606\pi\)
0.179895 + 0.983686i \(0.442424\pi\)
\(674\) 39.7963 25.5755i 1.53289 0.985131i
\(675\) −4.75459 10.4111i −0.183004 0.400723i
\(676\) 35.6382 + 41.1286i 1.37070 + 1.58187i
\(677\) −20.2228 12.9964i −0.777224 0.499491i 0.0908875 0.995861i \(-0.471030\pi\)
−0.868111 + 0.496370i \(0.834666\pi\)
\(678\) 5.23095 36.3820i 0.200893 1.39724i
\(679\) 0.424244 2.95068i 0.0162810 0.113237i
\(680\) −85.6149 55.0214i −3.28318 2.10997i
\(681\) 4.00568 + 4.62280i 0.153498 + 0.177146i
\(682\) 0.0137494 + 0.0301070i 0.000526491 + 0.00115286i
\(683\) −5.04023 + 3.23916i −0.192859 + 0.123943i −0.633507 0.773737i \(-0.718385\pi\)
0.440648 + 0.897680i \(0.354749\pi\)
\(684\) −20.7166 6.08293i −0.792117 0.232587i
\(685\) 21.3882 24.6833i 0.817200 0.943099i
\(686\) 40.1936 11.8019i 1.53460 0.450599i
\(687\) −5.71600 + 12.5163i −0.218079 + 0.477527i
\(688\) 2.80182 + 19.4871i 0.106819 + 0.742939i
\(689\) −1.15241 −0.0439032
\(690\) 16.1204 + 46.1460i 0.613691 + 1.75675i
\(691\) 27.1419 1.03253 0.516264 0.856430i \(-0.327322\pi\)
0.516264 + 0.856430i \(0.327322\pi\)
\(692\) 2.20239 + 15.3180i 0.0837223 + 0.582302i
\(693\) −0.0156188 + 0.0342005i −0.000593310 + 0.00129917i
\(694\) 34.4325 10.1103i 1.30704 0.383781i
\(695\) −20.3957 + 23.5379i −0.773654 + 0.892844i
\(696\) −20.6420 6.06103i −0.782432 0.229743i
\(697\) −36.3322 + 23.3493i −1.37618 + 0.884418i
\(698\) 4.90612 + 10.7429i 0.185699 + 0.406625i
\(699\) 9.27550 + 10.7045i 0.350831 + 0.404881i
\(700\) −57.2360 36.7834i −2.16332 1.39028i
\(701\) 7.12129 49.5297i 0.268967 1.87071i −0.189334 0.981913i \(-0.560633\pi\)
0.458301 0.888797i \(-0.348458\pi\)
\(702\) 0.224345 1.56036i 0.00846737 0.0588918i
\(703\) −9.26527 5.95443i −0.349446 0.224576i
\(704\) 0.0601240 + 0.0693868i 0.00226601 + 0.00261511i
\(705\) 15.1338 + 33.1384i 0.569972 + 1.24806i
\(706\) −37.7899 + 24.2861i −1.42224 + 0.914019i
\(707\) 17.6380 + 5.17898i 0.663345 + 0.194776i
\(708\) −11.8154 + 13.6358i −0.444052 + 0.512463i
\(709\) −29.6798 + 8.71476i −1.11465 + 0.327290i −0.786656 0.617391i \(-0.788190\pi\)
−0.327990 + 0.944681i \(0.606371\pi\)
\(710\) −30.5938 + 66.9911i −1.14816 + 2.51413i
\(711\) −0.214741 1.49355i −0.00805341 0.0560127i
\(712\) −77.6204 −2.90895
\(713\) −2.27001 + 0.444298i −0.0850127 + 0.0166391i
\(714\) 14.9157 0.558206
\(715\) −0.00988351 0.0687413i −0.000369622 0.00257078i
\(716\) −37.0604 + 81.1510i −1.38501 + 3.03275i
\(717\) 19.5132 5.72960i 0.728735 0.213976i
\(718\) −57.6278 + 66.5060i −2.15065 + 2.48198i
\(719\) 18.1350 + 5.32490i 0.676320 + 0.198585i 0.601815 0.798635i \(-0.294444\pi\)
0.0745044 + 0.997221i \(0.476263\pi\)
\(720\) −20.4746 + 13.1582i −0.763042 + 0.490378i
\(721\) −5.40701 11.8397i −0.201368 0.440933i
\(722\) 9.90136 + 11.4268i 0.368491 + 0.425261i
\(723\) −6.56840 4.22126i −0.244282 0.156990i
\(724\) 15.9146 110.689i 0.591462 4.11371i
\(725\) −6.01782 + 41.8549i −0.223496 + 1.55445i
\(726\) −23.2563 14.9459i −0.863123 0.554695i
\(727\) −1.32855 1.53323i −0.0492731 0.0568642i 0.730578 0.682829i \(-0.239251\pi\)
−0.779851 + 0.625965i \(0.784705\pi\)
\(728\) −2.08926 4.57485i −0.0774332 0.169555i
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) −58.3955 17.1465i −2.16131 0.634619i
\(731\) −9.25812 + 10.6844i −0.342424 + 0.395178i
\(732\) 19.1491 5.62270i 0.707773 0.207821i
\(733\) 16.5986 36.3460i 0.613085 1.34247i −0.307359 0.951594i \(-0.599445\pi\)
0.920444 0.390875i \(-0.127828\pi\)
\(734\) 5.32077 + 37.0068i 0.196393 + 1.36594i
\(735\) −20.6974 −0.763433
\(736\) 14.6328 7.59722i 0.539374 0.280037i
\(737\) 0.120936 0.00445474
\(738\) 3.58440 + 24.9301i 0.131944 + 0.917689i
\(739\) 0.869793 1.90458i 0.0319958 0.0700611i −0.892959 0.450137i \(-0.851375\pi\)
0.924955 + 0.380076i \(0.124102\pi\)
\(740\) −36.9876 + 10.8605i −1.35969 + 0.399241i
\(741\) −2.05434 + 2.37084i −0.0754681 + 0.0870948i
\(742\) −6.10135 1.79152i −0.223988 0.0657687i
\(743\) 42.2305 27.1399i 1.54929 0.995666i 0.563801 0.825911i \(-0.309338\pi\)
0.985486 0.169756i \(-0.0542979\pi\)
\(744\) −1.16671 2.55473i −0.0427735 0.0936609i
\(745\) −7.68617 8.87031i −0.281599 0.324983i
\(746\) 36.8925 + 23.7094i 1.35073 + 0.868061i
\(747\) 1.21935 8.48074i 0.0446135 0.310294i
\(748\) 0.0722920 0.502802i 0.00264326 0.0183843i
\(749\) 15.9743 + 10.2660i 0.583687 + 0.375113i
\(750\) 43.0201 + 49.6479i 1.57087 + 1.81288i
\(751\) 6.50791 + 14.2503i 0.237477 + 0.520002i 0.990421 0.138083i \(-0.0440941\pi\)
−0.752944 + 0.658085i \(0.771367\pi\)
\(752\) 45.3561 29.1486i 1.65397 1.06294i
\(753\) 14.3222 + 4.20539i 0.521932 + 0.153253i
\(754\) −3.81394 + 4.40152i −0.138896 + 0.160294i
\(755\) 8.03779 2.36011i 0.292525 0.0858932i
\(756\) 2.46941 5.40726i 0.0898117 0.196660i
\(757\) 4.29183 + 29.8503i 0.155989 + 1.08493i 0.905931 + 0.423425i \(0.139172\pi\)
−0.749942 + 0.661503i \(0.769919\pi\)
\(758\) 29.5971 1.07501
\(759\) −0.0945080 + 0.0906347i −0.00343042 + 0.00328983i
\(760\) 118.108 4.28424
\(761\) 3.59171 + 24.9809i 0.130199 + 0.905555i 0.945292 + 0.326225i \(0.105777\pi\)
−0.815093 + 0.579330i \(0.803314\pi\)
\(762\) 1.89596 4.15157i 0.0686833 0.150396i
\(763\) −10.7859 + 3.16704i −0.390477 + 0.114654i
\(764\) 23.4343 27.0447i 0.847824 0.978441i
\(765\) −16.7692 4.92389i −0.606293 0.178024i
\(766\) −6.10168 + 3.92131i −0.220463 + 0.141683i
\(767\) 1.08901 + 2.38460i 0.0393218 + 0.0861028i
\(768\) −20.8226 24.0306i −0.751372 0.867129i
\(769\) 21.5111 + 13.8243i 0.775708 + 0.498517i 0.867607 0.497251i \(-0.165657\pi\)
−0.0918985 + 0.995768i \(0.529294\pi\)
\(770\) 0.0545368 0.379312i 0.00196537 0.0136694i
\(771\) 1.94070 13.4979i 0.0698928 0.486115i
\(772\) −61.6144 39.5972i −2.21755 1.42513i
\(773\) 17.3482 + 20.0209i 0.623971 + 0.720101i 0.976456 0.215716i \(-0.0692086\pi\)
−0.352485 + 0.935818i \(0.614663\pi\)
\(774\) 3.42498 + 7.49965i 0.123108 + 0.269570i
\(775\) −4.64393 + 2.98447i −0.166815 + 0.107205i
\(776\) 12.0952 + 3.55148i 0.434194 + 0.127491i
\(777\) 1.98571 2.29163i 0.0712370 0.0822119i
\(778\) −11.0010 + 3.23017i −0.394404 + 0.115807i
\(779\) 20.8212 45.5921i 0.745997 1.63350i
\(780\) 1.56263 + 10.8683i 0.0559512 + 0.389149i
\(781\) −0.197288 −0.00705952
\(782\) 48.2817 + 19.1678i 1.72655 + 0.685440i
\(783\) −3.69452 −0.132031
\(784\) 4.35922 + 30.3190i 0.155686 + 1.08282i
\(785\) 32.6565 71.5078i 1.16556 2.55222i
\(786\) −14.3139 + 4.20295i −0.510561 + 0.149914i
\(787\) 11.2996 13.0404i 0.402786 0.464839i −0.517731 0.855544i \(-0.673223\pi\)
0.920516 + 0.390704i \(0.127768\pi\)
\(788\) 56.2380 + 16.5130i 2.00340 + 0.588250i
\(789\) −5.98538 + 3.84657i −0.213085 + 0.136942i
\(790\) 6.38880 + 13.9895i 0.227303 + 0.497725i
\(791\) −13.1878 15.2195i −0.468904 0.541144i
\(792\) −0.133752 0.0859573i −0.00475268 0.00305436i
\(793\) 0.412673 2.87020i 0.0146544 0.101924i
\(794\) 1.58627 11.0328i 0.0562947 0.391538i
\(795\) 6.26815 + 4.02829i 0.222308 + 0.142869i
\(796\) 36.2931 + 41.8845i 1.28638 + 1.48456i
\(797\) −13.3136 29.1526i −0.471590 1.03264i −0.984691 0.174310i \(-0.944231\pi\)
0.513101 0.858328i \(-0.328497\pi\)
\(798\) −14.5623 + 9.35859i −0.515498 + 0.331291i
\(799\) 37.1479 + 10.9076i 1.31420 + 0.385883i
\(800\) 25.7674 29.7372i 0.911016 1.05137i
\(801\) −12.7899 + 3.75545i −0.451908 + 0.132692i
\(802\) −5.74863 + 12.5877i −0.202991 + 0.444489i
\(803\) −0.0232027 0.161378i −0.000818804 0.00569491i
\(804\) −19.1206 −0.674332
\(805\) 24.8914 + 9.88186i 0.877305 + 0.348290i
\(806\) −0.760317 −0.0267810
\(807\) −2.02516 14.0853i −0.0712890 0.495826i
\(808\) −32.2922 + 70.7100i −1.13604 + 2.48757i
\(809\) −12.0192 + 3.52914i −0.422571 + 0.124078i −0.486102 0.873902i \(-0.661582\pi\)
0.0635315 + 0.997980i \(0.479764\pi\)
\(810\) −6.67455 + 7.70284i −0.234520 + 0.270650i
\(811\) −7.39961 2.17272i −0.259836 0.0762946i 0.149220 0.988804i \(-0.452324\pi\)
−0.409056 + 0.912509i \(0.634142\pi\)
\(812\) −18.4755 + 11.8735i −0.648364 + 0.416678i
\(813\) −3.37455 7.38923i −0.118351 0.259152i
\(814\) −0.0989570 0.114202i −0.00346844 0.00400279i
\(815\) −80.0260 51.4296i −2.80319 1.80150i
\(816\) −3.68099 + 25.6019i −0.128861 + 0.896245i
\(817\) 2.33498 16.2401i 0.0816905 0.568170i
\(818\) −65.9271 42.3688i −2.30509 1.48139i
\(819\) −0.565599 0.652736i −0.0197636 0.0228084i
\(820\) −72.8767 159.578i −2.54496 5.57270i
\(821\) −27.6782 + 17.7877i −0.965977 + 0.620796i −0.925646 0.378390i \(-0.876478\pi\)
−0.0403314 + 0.999186i \(0.512841\pi\)
\(822\) −19.4220 5.70283i −0.677422 0.198909i
\(823\) −18.7991 + 21.6953i −0.655295 + 0.756251i −0.982001 0.188875i \(-0.939516\pi\)
0.326706 + 0.945126i \(0.394061\pi\)
\(824\) 52.8110 15.5067i 1.83976 0.540202i
\(825\) −0.129818 + 0.284262i −0.00451969 + 0.00989675i
\(826\) 2.05863 + 14.3181i 0.0716288 + 0.498189i
\(827\) −10.6363 −0.369861 −0.184931 0.982752i \(-0.559206\pi\)
−0.184931 + 0.982752i \(0.559206\pi\)
\(828\) 14.9422 14.3298i 0.519277 0.497995i
\(829\) −22.6856 −0.787903 −0.393952 0.919131i \(-0.628892\pi\)
−0.393952 + 0.919131i \(0.628892\pi\)
\(830\) 12.4280 + 86.4383i 0.431381 + 3.00032i
\(831\) 1.54221 3.37697i 0.0534986 0.117146i
\(832\) −2.02364 + 0.594195i −0.0701572 + 0.0206000i
\(833\) −14.4043 + 16.6234i −0.499078 + 0.575966i
\(834\) 18.5208 + 5.43820i 0.641324 + 0.188310i
\(835\) 70.8320 45.5210i 2.45124 1.57532i
\(836\) 0.244895 + 0.536246i 0.00846989 + 0.0185465i
\(837\) −0.315847 0.364507i −0.0109173 0.0125992i
\(838\) −81.8054 52.5731i −2.82592 1.81611i
\(839\) −1.65201 + 11.4900i −0.0570337 + 0.396678i 0.941230 + 0.337767i \(0.109672\pi\)
−0.998263 + 0.0589104i \(0.981237\pi\)
\(840\) −4.62772 + 32.1865i −0.159672 + 1.11054i
\(841\) −12.9137 8.29911i −0.445299 0.286176i
\(842\) 11.0270 + 12.7259i 0.380016 + 0.438562i
\(843\) −5.20338 11.3938i −0.179214 0.392424i
\(844\) −4.89518 + 3.14594i −0.168499 + 0.108288i
\(845\) −49.0526 14.4031i −1.68746 0.495483i
\(846\) 14.7857 17.0637i 0.508344 0.586660i
\(847\) −14.5328 + 4.26721i −0.499352 + 0.146623i
\(848\) 4.58077 10.0305i 0.157304 0.344448i
\(849\) −3.48019 24.2052i −0.119440 0.830721i
\(850\) 123.974 4.25228
\(851\) 9.37263 4.86617i 0.321290 0.166810i
\(852\) 31.1922 1.06863
\(853\) 2.17228 + 15.1086i 0.0743776 + 0.517307i 0.992618 + 0.121284i \(0.0387011\pi\)
−0.918240 + 0.396024i \(0.870390\pi\)
\(854\) 6.64685 14.5546i 0.227450 0.498047i
\(855\) 19.4613 5.71435i 0.665562 0.195427i
\(856\) −52.5836 + 60.6848i −1.79727 + 2.07416i
\(857\) −26.1726 7.68498i −0.894040 0.262514i −0.197731 0.980256i \(-0.563357\pi\)
−0.696309 + 0.717742i \(0.745176\pi\)
\(858\) −0.0362090 + 0.0232701i −0.00123615 + 0.000794428i
\(859\) 5.19844 + 11.3830i 0.177368 + 0.388383i 0.977346 0.211647i \(-0.0678827\pi\)
−0.799978 + 0.600030i \(0.795155\pi\)
\(860\) −37.6066 43.4003i −1.28237 1.47994i
\(861\) 11.6088 + 7.46051i 0.395626 + 0.254253i
\(862\) 1.76039 12.2438i 0.0599593 0.417026i
\(863\) 2.92036 20.3116i 0.0994102 0.691413i −0.877783 0.479059i \(-0.840978\pi\)
0.977193 0.212354i \(-0.0681130\pi\)
\(864\) 2.89213 + 1.85866i 0.0983923 + 0.0632329i
\(865\) −9.52022 10.9869i −0.323697 0.373567i
\(866\) 27.0261 + 59.1789i 0.918384 + 2.01098i
\(867\) −1.32388 + 0.850806i −0.0449613 + 0.0288949i
\(868\) −2.75094 0.807749i −0.0933730 0.0274168i
\(869\) −0.0269796 + 0.0311362i −0.000915221 + 0.00105622i
\(870\) 36.1304 10.6089i 1.22494 0.359674i
\(871\) −1.15407 + 2.52706i −0.0391042 + 0.0856262i
\(872\) −6.76510 47.0523i −0.229095 1.59339i
\(873\) 2.16482 0.0732680
\(874\) −59.1642 + 11.5799i −2.00126 + 0.391696i
\(875\) 35.9928 1.21678
\(876\) 3.66845 + 25.5147i 0.123946 + 0.862061i
\(877\) −19.8073 + 43.3720i −0.668846 + 1.46457i 0.205197 + 0.978721i \(0.434217\pi\)
−0.874043 + 0.485849i \(0.838511\pi\)
\(878\) 5.34880 1.57055i 0.180513 0.0530035i
\(879\) −11.1802 + 12.9026i −0.377099 + 0.435195i
\(880\) 0.637606 + 0.187218i 0.0214937 + 0.00631112i
\(881\) −44.2013 + 28.4064i −1.48918 + 0.957038i −0.492970 + 0.870046i \(0.664089\pi\)
−0.996209 + 0.0869915i \(0.972275\pi\)
\(882\) 5.32875 + 11.6683i 0.179428 + 0.392893i
\(883\) 10.7972 + 12.4607i 0.363356 + 0.419336i 0.907761 0.419487i \(-0.137790\pi\)
−0.544405 + 0.838822i \(0.683245\pi\)
\(884\) 9.81658 + 6.30874i 0.330167 + 0.212186i
\(885\) 2.41216 16.7769i 0.0810837 0.563950i
\(886\) 2.78631 19.3792i 0.0936078 0.651057i
\(887\) −22.1023 14.2043i −0.742121 0.476933i 0.114147 0.993464i \(-0.463587\pi\)
−0.856268 + 0.516531i \(0.827223\pi\)
\(888\) 8.39700 + 9.69065i 0.281785 + 0.325197i
\(889\) −1.03878 2.27460i −0.0348394 0.0762877i
\(890\) 114.294 73.4525i 3.83115 2.46213i
\(891\) −0.0261978 0.00769236i −0.000877659 0.000257704i
\(892\) 65.9461 76.1058i 2.20804 2.54821i
\(893\) −43.1114 + 12.6587i −1.44267 + 0.423606i
\(894\) −3.02184 + 6.61691i −0.101066 + 0.221303i
\(895\) −11.9270 82.9543i −0.398676 2.77286i
\(896\) −21.1059 −0.705099
\(897\) −0.992014 2.83973i −0.0331224 0.0948158i
\(898\) 17.9885 0.600284
\(899\) 0.253592 + 1.76377i 0.00845778 + 0.0588252i
\(900\) 20.5249 44.9433i 0.684164 1.49811i
\(901\) 7.59768 2.23088i 0.253115 0.0743214i
\(902\) 0.450338 0.519718i 0.0149946 0.0173047i
\(903\) 4.33421 + 1.27264i 0.144234 + 0.0423508i
\(904\) 71.6403 46.0404i 2.38272 1.53128i
\(905\) 43.6398 + 95.5577i 1.45063 + 3.17645i
\(906\) −3.39995 3.92375i −0.112956 0.130358i
\(907\) 32.9483 + 21.1746i 1.09403 + 0.703091i 0.957757 0.287580i \(-0.0928508\pi\)
0.136274 + 0.990671i \(0.456487\pi\)
\(908\) −3.75791 + 26.1368i −0.124711 + 0.867381i
\(909\) −1.89983 + 13.2136i −0.0630133 + 0.438267i
\(910\) 7.40559 + 4.75928i 0.245493 + 0.157769i
\(911\) −17.4784 20.1712i −0.579086 0.668301i 0.388322 0.921524i \(-0.373055\pi\)
−0.967408 + 0.253223i \(0.918509\pi\)
\(912\) −12.4697 27.3048i −0.412912 0.904152i
\(913\) −0.196801 + 0.126476i −0.00651315 + 0.00418575i
\(914\) −10.7546 3.15785i −0.355732 0.104452i
\(915\) −12.2775 + 14.1690i −0.405882 + 0.468413i
\(916\) −56.9928 + 16.7346i −1.88310 + 0.552927i
\(917\) −3.39541 + 7.43490i −0.112126 + 0.245522i
\(918\) 1.54152 + 10.7215i 0.0508779 + 0.353863i
\(919\) 25.3453 0.836064 0.418032 0.908432i \(-0.362720\pi\)
0.418032 + 0.908432i \(0.362720\pi\)
\(920\) −56.3420 + 98.2400i −1.85754 + 3.23888i
\(921\) −22.0577 −0.726825
\(922\) −8.60376 59.8404i −0.283350 1.97074i
\(923\) 1.88268 4.12249i 0.0619691 0.135694i
\(924\) −0.155731 + 0.0457269i −0.00512319 + 0.00150430i
\(925\) 16.5046 19.0473i 0.542666 0.626270i
\(926\) −7.92795 2.32786i −0.260529 0.0764981i
\(927\) 7.95167 5.11023i 0.261167 0.167842i
\(928\) −5.27633 11.5535i −0.173204 0.379264i
\(929\) 5.35859 + 6.18415i 0.175810 + 0.202895i 0.836815 0.547486i \(-0.184415\pi\)
−0.661005 + 0.750382i \(0.729870\pi\)
\(930\) 4.13550 + 2.65772i 0.135608 + 0.0871501i
\(931\) 3.63287 25.2672i 0.119063 0.828099i
\(932\) −8.70175 + 60.5220i −0.285035 + 1.98246i
\(933\) 4.58506 + 2.94664i 0.150108 + 0.0964687i
\(934\) 22.6495 + 26.1389i 0.741115 + 0.855292i
\(935\) 0.198233 + 0.434070i 0.00648292 + 0.0141956i
\(936\) 3.07252 1.97459i 0.100428 0.0645414i
\(937\) −26.8166 7.87408i −0.876061 0.257235i −0.187370 0.982289i \(-0.559996\pi\)
−0.688691 + 0.725055i \(0.741815\pi\)
\(938\) −10.0387 + 11.5853i −0.327775 + 0.378272i
\(939\) 29.3916 8.63016i 0.959159 0.281634i
\(940\) −65.3305 + 143.054i −2.13085 + 4.66590i
\(941\) 4.68100 + 32.5571i 0.152596 + 1.06133i 0.911846 + 0.410532i \(0.134657\pi\)
−0.759250 + 0.650799i \(0.774434\pi\)
\(942\) −48.7210 −1.58742
\(943\) 27.9900 + 39.0677i 0.911480 + 1.27222i
\(944\) −25.0841 −0.816418
\(945\) 0.794723 + 5.52742i 0.0258523 + 0.179807i
\(946\) 0.0935148 0.204769i 0.00304043 0.00665761i
\(947\) −19.2462 + 5.65120i −0.625418 + 0.183639i −0.579059 0.815286i \(-0.696580\pi\)
−0.0463589 + 0.998925i \(0.514762\pi\)
\(948\) 4.26561 4.92278i 0.138541 0.159884i
\(949\) 3.59354 + 1.05516i 0.116651 + 0.0342519i
\(950\) −121.036 + 77.7854i −3.92694 + 2.52369i
\(951\) −0.297221 0.650823i −0.00963805 0.0211044i
\(952\) 22.6304 + 26.1169i 0.733456 + 0.846454i
\(953\) 24.5517 + 15.7784i 0.795308 + 0.511113i 0.874082 0.485779i \(-0.161464\pi\)
−0.0787738 + 0.996893i \(0.525100\pi\)
\(954\) 0.657190 4.57086i 0.0212773 0.147987i
\(955\) −4.78418 + 33.2747i −0.154812 + 1.07674i
\(956\) 73.8555 + 47.4640i 2.38866 + 1.53510i
\(957\) 0.0660587 + 0.0762358i 0.00213538 + 0.00246435i
\(958\) 24.1527 + 52.8870i 0.780338 + 1.70870i
\(959\) −9.32981 + 5.99591i −0.301275 + 0.193618i
\(960\) 13.0840 + 3.84181i 0.422284 + 0.123994i
\(961\) 20.1483 23.2524i 0.649947 0.750078i
\(962\) 3.33068 0.977975i 0.107385 0.0315312i
\(963\) −5.72839 + 12.5434i −0.184595 + 0.404206i
\(964\) −4.79680 33.3625i −0.154494 1.07453i
\(965\) 68.8033 2.21486
\(966\) −0.837549 16.5769i −0.0269477 0.533355i
\(967\) −48.3376 −1.55443 −0.777216 0.629233i \(-0.783369\pi\)
−0.777216 + 0.629233i \(0.783369\pi\)
\(968\) −9.11517 63.3974i −0.292973 2.03767i
\(969\) 8.95445 19.6075i 0.287658 0.629884i
\(970\) −21.1708 + 6.21629i −0.679752 + 0.199593i
\(971\) 23.1379 26.7026i 0.742532 0.856927i −0.251291 0.967912i \(-0.580855\pi\)
0.993822 + 0.110985i \(0.0354004\pi\)
\(972\) 4.14200 + 1.21620i 0.132855 + 0.0390097i
\(973\) 8.89689 5.71768i 0.285221 0.183301i
\(974\) −12.1439 26.5914i −0.389115 0.852042i
\(975\) −4.70106 5.42531i −0.150554 0.173749i
\(976\) 23.3417 + 15.0008i 0.747149 + 0.480163i
\(977\) 1.79485 12.4835i 0.0574224 0.399382i −0.940758 0.339079i \(-0.889884\pi\)
0.998180 0.0603022i \(-0.0192064\pi\)
\(978\) −8.39040 + 58.3565i −0.268295 + 1.86604i
\(979\) 0.306178 + 0.196769i 0.00978550 + 0.00628876i
\(980\) −58.5103 67.5244i −1.86904 2.15699i
\(981\) −3.39121 7.42572i −0.108273 0.237085i
\(982\) 64.2114 41.2662i 2.04907 1.31686i
\(983\) −11.0543 3.24584i −0.352577 0.103526i 0.100648 0.994922i \(-0.467908\pi\)
−0.453225 + 0.891396i \(0.649727\pi\)
\(984\) −38.2134 + 44.1007i −1.21820 + 1.40588i
\(985\) −52.8304 + 15.5124i −1.68332 + 0.494266i
\(986\) 16.6242 36.4019i 0.529422 1.15927i
\(987\) −1.76050 12.2446i −0.0560375 0.389749i
\(988\) −13.5423 −0.430837
\(989\) 12.3943 + 9.68930i 0.394116 + 0.308102i
\(990\) 0.278289 0.00884460
\(991\) −3.57914 24.8934i −0.113695 0.790766i −0.964272 0.264915i \(-0.914656\pi\)
0.850577 0.525851i \(-0.176253\pi\)
\(992\) 0.688812 1.50829i 0.0218698 0.0478882i
\(993\) 26.8871 7.89475i 0.853235 0.250532i
\(994\) 16.3765 18.8995i 0.519431 0.599456i
\(995\) −49.9541 14.6679i −1.58365 0.465002i
\(996\) 31.1151 19.9965i 0.985921 0.633613i
\(997\) −5.65570 12.3843i −0.179118 0.392214i 0.798682 0.601753i \(-0.205531\pi\)
−0.977800 + 0.209539i \(0.932804\pi\)
\(998\) −57.4009 66.2442i −1.81699 2.09692i
\(999\) 1.85247 + 1.19051i 0.0586095 + 0.0376660i
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 69.2.e.b.49.1 yes 10
3.2 odd 2 207.2.i.a.118.1 10
23.8 even 11 inner 69.2.e.b.31.1 10
23.10 odd 22 1587.2.a.r.1.1 5
23.13 even 11 1587.2.a.q.1.1 5
69.8 odd 22 207.2.i.a.100.1 10
69.56 even 22 4761.2.a.bm.1.5 5
69.59 odd 22 4761.2.a.bp.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.b.31.1 10 23.8 even 11 inner
69.2.e.b.49.1 yes 10 1.1 even 1 trivial
207.2.i.a.100.1 10 69.8 odd 22
207.2.i.a.118.1 10 3.2 odd 2
1587.2.a.q.1.1 5 23.13 even 11
1587.2.a.r.1.1 5 23.10 odd 22
4761.2.a.bm.1.5 5 69.56 even 22
4761.2.a.bp.1.5 5 69.59 odd 22