Properties

Label 441.2.z.a.142.41
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
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] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.41
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.41

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.581685 - 1.48211i) q^{2} +(-1.51224 - 0.844464i) q^{3} +(-0.392187 - 0.363896i) q^{4} +(1.51815 - 0.731104i) q^{5} +(-2.13124 + 1.75010i) q^{6} +(2.03794 + 1.68724i) q^{7} +(2.10153 - 1.01204i) q^{8} +(1.57376 + 2.55407i) q^{9} +O(q^{10})\) \(q+(0.581685 - 1.48211i) q^{2} +(-1.51224 - 0.844464i) q^{3} +(-0.392187 - 0.363896i) q^{4} +(1.51815 - 0.731104i) q^{5} +(-2.13124 + 1.75010i) q^{6} +(2.03794 + 1.68724i) q^{7} +(2.10153 - 1.01204i) q^{8} +(1.57376 + 2.55407i) q^{9} +(-0.200489 - 2.67534i) q^{10} +(2.16992 + 2.72099i) q^{11} +(0.285785 + 0.881487i) q^{12} +(2.32596 - 5.92644i) q^{13} +(3.68612 - 2.03901i) q^{14} +(-2.91321 - 0.176418i) q^{15} +(-0.357492 - 4.77040i) q^{16} +(-5.44499 + 5.05221i) q^{17} +(4.70084 - 0.846824i) q^{18} +(1.72418 - 2.98636i) q^{19} +(-0.861446 - 0.265721i) q^{20} +(-1.65705 - 4.27249i) q^{21} +(5.29501 - 1.63329i) q^{22} +(-0.708056 + 3.10220i) q^{23} +(-4.03266 - 0.244209i) q^{24} +(-1.34717 + 1.68930i) q^{25} +(-7.43065 - 6.89464i) q^{26} +(-0.223094 - 5.19136i) q^{27} +(-0.185274 - 1.40331i) q^{28} +(-4.34817 - 1.34123i) q^{29} +(-1.95604 + 4.21508i) q^{30} +(1.08700 - 1.88274i) q^{31} +(-2.82042 - 0.869985i) q^{32} +(-0.983667 - 5.94722i) q^{33} +(4.32066 + 11.0089i) q^{34} +(4.32746 + 1.07154i) q^{35} +(0.312207 - 1.57436i) q^{36} +(-9.21927 - 2.84377i) q^{37} +(-3.42319 - 4.29254i) q^{38} +(-8.52207 + 6.99803i) q^{39} +(2.45053 - 3.07287i) q^{40} +(2.85374 + 1.94565i) q^{41} +(-7.29618 - 0.0293070i) q^{42} +(1.50543 - 1.02639i) q^{43} +(0.139145 - 1.85676i) q^{44} +(4.25651 + 2.72689i) q^{45} +(4.18593 + 2.85392i) q^{46} +(2.61052 - 6.65149i) q^{47} +(-3.48782 + 7.51590i) q^{48} +(1.30643 + 6.87701i) q^{49} +(1.72010 + 2.97930i) q^{50} +(12.5006 - 3.04208i) q^{51} +(-3.06882 + 1.47786i) q^{52} +(0.992574 - 0.306169i) q^{53} +(-7.82393 - 2.68909i) q^{54} +(5.28360 + 2.54445i) q^{55} +(5.99036 + 1.48330i) q^{56} +(-5.12925 + 3.06010i) q^{57} +(-4.51711 + 5.66428i) q^{58} +(-3.12044 + 2.12748i) q^{59} +(1.07832 + 1.12929i) q^{60} +(-2.96963 + 2.75542i) q^{61} +(-2.15813 - 2.70621i) q^{62} +(-1.10209 + 7.86037i) q^{63} +(3.03527 - 3.80611i) q^{64} +(-0.801686 - 10.6978i) q^{65} +(-9.38661 - 2.00150i) q^{66} +(5.86680 - 10.1616i) q^{67} +3.97393 q^{68} +(3.69044 - 4.09335i) q^{69} +(4.10536 - 5.79047i) q^{70} +(-2.78946 + 12.2214i) q^{71} +(5.89213 + 3.77474i) q^{72} +(-0.944618 - 0.142378i) q^{73} +(-9.57749 + 12.0098i) q^{74} +(3.46380 - 1.41700i) q^{75} +(-1.76293 + 0.543790i) q^{76} +(-0.168796 + 9.20640i) q^{77} +(5.41469 + 16.7013i) q^{78} +(5.60914 + 9.71531i) q^{79} +(-4.03039 - 6.98084i) q^{80} +(-4.04654 + 8.03900i) q^{81} +(4.54364 - 3.09780i) q^{82} +(-4.08872 - 10.4179i) q^{83} +(-0.904867 + 2.27861i) q^{84} +(-4.57264 + 11.6509i) q^{85} +(-0.645529 - 2.82825i) q^{86} +(5.44287 + 5.70014i) q^{87} +(7.31390 + 3.52219i) q^{88} +(0.249789 + 0.636452i) q^{89} +(6.51749 - 4.72242i) q^{90} +(14.7395 - 8.15330i) q^{91} +(1.40657 - 0.958981i) q^{92} +(-3.23371 + 1.92923i) q^{93} +(-8.33973 - 7.73814i) q^{94} +(0.434224 - 5.79431i) q^{95} +(3.53049 + 3.69737i) q^{96} +(-3.87860 + 6.71793i) q^{97} +(10.9524 + 2.06397i) q^{98} +(-3.53466 + 9.82431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.581685 1.48211i 0.411313 1.04801i −0.563723 0.825964i \(-0.690631\pi\)
0.975036 0.222046i \(-0.0712734\pi\)
\(3\) −1.51224 0.844464i −0.873094 0.487551i
\(4\) −0.392187 0.363896i −0.196093 0.181948i
\(5\) 1.51815 0.731104i 0.678939 0.326960i −0.0624377 0.998049i \(-0.519887\pi\)
0.741377 + 0.671089i \(0.234173\pi\)
\(6\) −2.13124 + 1.75010i −0.870074 + 0.714475i
\(7\) 2.03794 + 1.68724i 0.770271 + 0.637717i
\(8\) 2.10153 1.01204i 0.743003 0.357811i
\(9\) 1.57376 + 2.55407i 0.524587 + 0.851357i
\(10\) −0.200489 2.67534i −0.0634002 0.846018i
\(11\) 2.16992 + 2.72099i 0.654255 + 0.820409i 0.992704 0.120575i \(-0.0384739\pi\)
−0.338450 + 0.940985i \(0.609902\pi\)
\(12\) 0.285785 + 0.881487i 0.0824990 + 0.254463i
\(13\) 2.32596 5.92644i 0.645104 1.64370i −0.114587 0.993413i \(-0.536554\pi\)
0.759691 0.650285i \(-0.225350\pi\)
\(14\) 3.68612 2.03901i 0.985156 0.544949i
\(15\) −2.91321 0.176418i −0.752188 0.0455508i
\(16\) −0.357492 4.77040i −0.0893731 1.19260i
\(17\) −5.44499 + 5.05221i −1.32060 + 1.22534i −0.364888 + 0.931052i \(0.618893\pi\)
−0.955716 + 0.294290i \(0.904917\pi\)
\(18\) 4.70084 0.846824i 1.10800 0.199598i
\(19\) 1.72418 2.98636i 0.395554 0.685119i −0.597618 0.801781i \(-0.703886\pi\)
0.993172 + 0.116662i \(0.0372194\pi\)
\(20\) −0.861446 0.265721i −0.192625 0.0594170i
\(21\) −1.65705 4.27249i −0.361599 0.932334i
\(22\) 5.29501 1.63329i 1.12890 0.348220i
\(23\) −0.708056 + 3.10220i −0.147640 + 0.646853i 0.845897 + 0.533346i \(0.179066\pi\)
−0.993537 + 0.113507i \(0.963792\pi\)
\(24\) −4.03266 0.244209i −0.823163 0.0498489i
\(25\) −1.34717 + 1.68930i −0.269434 + 0.337860i
\(26\) −7.43065 6.89464i −1.45727 1.35215i
\(27\) −0.223094 5.19136i −0.0429344 0.999078i
\(28\) −0.185274 1.40331i −0.0350135 0.265201i
\(29\) −4.34817 1.34123i −0.807434 0.249060i −0.136560 0.990632i \(-0.543605\pi\)
−0.670874 + 0.741571i \(0.734081\pi\)
\(30\) −1.95604 + 4.21508i −0.357123 + 0.769564i
\(31\) 1.08700 1.88274i 0.195231 0.338150i −0.751745 0.659454i \(-0.770788\pi\)
0.946976 + 0.321304i \(0.104121\pi\)
\(32\) −2.82042 0.869985i −0.498585 0.153793i
\(33\) −0.983667 5.94722i −0.171234 1.03528i
\(34\) 4.32066 + 11.0089i 0.740987 + 1.88800i
\(35\) 4.32746 + 1.07154i 0.731475 + 0.181124i
\(36\) 0.312207 1.57436i 0.0520345 0.262393i
\(37\) −9.21927 2.84377i −1.51564 0.467513i −0.578268 0.815847i \(-0.696271\pi\)
−0.937371 + 0.348334i \(0.886748\pi\)
\(38\) −3.42319 4.29254i −0.555315 0.696342i
\(39\) −8.52207 + 6.99803i −1.36462 + 1.12058i
\(40\) 2.45053 3.07287i 0.387464 0.485864i
\(41\) 2.85374 + 1.94565i 0.445679 + 0.303859i 0.765285 0.643692i \(-0.222598\pi\)
−0.319606 + 0.947551i \(0.603550\pi\)
\(42\) −7.29618 0.0293070i −1.12583 0.00452217i
\(43\) 1.50543 1.02639i 0.229576 0.156522i −0.443069 0.896487i \(-0.646110\pi\)
0.672645 + 0.739965i \(0.265158\pi\)
\(44\) 0.139145 1.85676i 0.0209769 0.279917i
\(45\) 4.25651 + 2.72689i 0.634522 + 0.406500i
\(46\) 4.18593 + 2.85392i 0.617181 + 0.420787i
\(47\) 2.61052 6.65149i 0.380783 0.970219i −0.604086 0.796919i \(-0.706462\pi\)
0.984869 0.173300i \(-0.0554430\pi\)
\(48\) −3.48782 + 7.51590i −0.503423 + 1.08483i
\(49\) 1.30643 + 6.87701i 0.186633 + 0.982430i
\(50\) 1.72010 + 2.97930i 0.243258 + 0.421336i
\(51\) 12.5006 3.04208i 1.75043 0.425976i
\(52\) −3.06882 + 1.47786i −0.425568 + 0.204943i
\(53\) 0.992574 0.306169i 0.136341 0.0420555i −0.225834 0.974166i \(-0.572511\pi\)
0.362174 + 0.932110i \(0.382034\pi\)
\(54\) −7.82393 2.68909i −1.06470 0.365938i
\(55\) 5.28360 + 2.54445i 0.712440 + 0.343093i
\(56\) 5.99036 + 1.48330i 0.800495 + 0.198214i
\(57\) −5.12925 + 3.06010i −0.679386 + 0.405321i
\(58\) −4.51711 + 5.66428i −0.593126 + 0.743757i
\(59\) −3.12044 + 2.12748i −0.406246 + 0.276974i −0.749155 0.662395i \(-0.769540\pi\)
0.342909 + 0.939369i \(0.388588\pi\)
\(60\) 1.07832 + 1.12929i 0.139211 + 0.145791i
\(61\) −2.96963 + 2.75542i −0.380222 + 0.352795i −0.847012 0.531573i \(-0.821601\pi\)
0.466790 + 0.884368i \(0.345410\pi\)
\(62\) −2.15813 2.70621i −0.274083 0.343690i
\(63\) −1.10209 + 7.86037i −0.138850 + 0.990313i
\(64\) 3.03527 3.80611i 0.379408 0.475763i
\(65\) −0.801686 10.6978i −0.0994369 1.32689i
\(66\) −9.38661 2.00150i −1.15541 0.246368i
\(67\) 5.86680 10.1616i 0.716743 1.24144i −0.245540 0.969386i \(-0.578965\pi\)
0.962283 0.272049i \(-0.0877013\pi\)
\(68\) 3.97393 0.481910
\(69\) 3.69044 4.09335i 0.444277 0.492781i
\(70\) 4.10536 5.79047i 0.490685 0.692094i
\(71\) −2.78946 + 12.2214i −0.331048 + 1.45042i 0.486057 + 0.873927i \(0.338435\pi\)
−0.817105 + 0.576489i \(0.804422\pi\)
\(72\) 5.89213 + 3.77474i 0.694395 + 0.444857i
\(73\) −0.944618 0.142378i −0.110559 0.0166641i 0.0935296 0.995617i \(-0.470185\pi\)
−0.204089 + 0.978952i \(0.565423\pi\)
\(74\) −9.57749 + 12.0098i −1.11336 + 1.39611i
\(75\) 3.46380 1.41700i 0.399966 0.163621i
\(76\) −1.76293 + 0.543790i −0.202221 + 0.0623770i
\(77\) −0.168796 + 9.20640i −0.0192361 + 1.04917i
\(78\) 5.41469 + 16.7013i 0.613093 + 1.89105i
\(79\) 5.60914 + 9.71531i 0.631077 + 1.09306i 0.987332 + 0.158669i \(0.0507202\pi\)
−0.356255 + 0.934389i \(0.615946\pi\)
\(80\) −4.03039 6.98084i −0.450611 0.780482i
\(81\) −4.04654 + 8.03900i −0.449616 + 0.893222i
\(82\) 4.54364 3.09780i 0.501761 0.342095i
\(83\) −4.08872 10.4179i −0.448796 1.14351i −0.958986 0.283452i \(-0.908520\pi\)
0.510191 0.860061i \(-0.329575\pi\)
\(84\) −0.904867 + 2.27861i −0.0987291 + 0.248617i
\(85\) −4.57264 + 11.6509i −0.495972 + 1.26372i
\(86\) −0.645529 2.82825i −0.0696092 0.304978i
\(87\) 5.44287 + 5.70014i 0.583536 + 0.611119i
\(88\) 7.31390 + 3.52219i 0.779664 + 0.375467i
\(89\) 0.249789 + 0.636452i 0.0264776 + 0.0674638i 0.943501 0.331369i \(-0.107511\pi\)
−0.917024 + 0.398833i \(0.869415\pi\)
\(90\) 6.51749 4.72242i 0.687004 0.497786i
\(91\) 14.7395 8.15330i 1.54512 0.854698i
\(92\) 1.40657 0.958981i 0.146645 0.0999807i
\(93\) −3.23371 + 1.92923i −0.335321 + 0.200052i
\(94\) −8.33973 7.73814i −0.860178 0.798128i
\(95\) 0.434224 5.79431i 0.0445504 0.594484i
\(96\) 3.53049 + 3.69737i 0.360329 + 0.377361i
\(97\) −3.87860 + 6.71793i −0.393812 + 0.682103i −0.992949 0.118544i \(-0.962177\pi\)
0.599137 + 0.800647i \(0.295511\pi\)
\(98\) 10.9524 + 2.06397i 1.10636 + 0.208493i
\(99\) −3.53466 + 9.82431i −0.355247 + 0.987380i
\(100\) 1.14307 0.172290i 0.114307 0.0172290i
\(101\) −16.2280 + 7.81501i −1.61475 + 0.777623i −0.999939 0.0110513i \(-0.996482\pi\)
−0.614811 + 0.788674i \(0.710768\pi\)
\(102\) 2.76269 20.2967i 0.273547 2.00968i
\(103\) −7.81252 + 3.76231i −0.769791 + 0.370712i −0.777194 0.629261i \(-0.783358\pi\)
0.00740349 + 0.999973i \(0.497643\pi\)
\(104\) −1.10975 14.8085i −0.108820 1.45210i
\(105\) −5.63930 5.27482i −0.550339 0.514769i
\(106\) 0.123590 1.64920i 0.0120041 0.160184i
\(107\) 1.54743 + 3.94279i 0.149596 + 0.381164i 0.985953 0.167020i \(-0.0534146\pi\)
−0.836358 + 0.548184i \(0.815319\pi\)
\(108\) −1.80162 + 2.11717i −0.173361 + 0.203724i
\(109\) 0.115613 0.294577i 0.0110737 0.0282153i −0.925230 0.379407i \(-0.876128\pi\)
0.936304 + 0.351191i \(0.114223\pi\)
\(110\) 6.84453 6.35080i 0.652601 0.605525i
\(111\) 11.5403 + 12.0858i 1.09536 + 1.14713i
\(112\) 7.32027 10.3250i 0.691701 0.975620i
\(113\) 2.97563 + 0.448504i 0.279924 + 0.0421917i 0.287504 0.957780i \(-0.407175\pi\)
−0.00757994 + 0.999971i \(0.502413\pi\)
\(114\) 1.55180 + 9.38213i 0.145339 + 0.878717i
\(115\) 1.19309 + 5.22727i 0.111256 + 0.487446i
\(116\) 1.21722 + 2.10829i 0.113016 + 0.195750i
\(117\) 18.7970 3.38615i 1.73779 0.313050i
\(118\) 1.33804 + 5.86235i 0.123177 + 0.539673i
\(119\) −19.6209 + 1.10912i −1.79864 + 0.101672i
\(120\) −6.30074 + 2.57755i −0.575176 + 0.235297i
\(121\) −0.247515 + 1.08444i −0.0225014 + 0.0985850i
\(122\) 2.35644 + 6.00410i 0.213342 + 0.543586i
\(123\) −2.67252 5.35217i −0.240973 0.482589i
\(124\) −1.11143 + 0.342830i −0.0998092 + 0.0307871i
\(125\) −2.68492 + 11.7634i −0.240147 + 1.05215i
\(126\) 11.0089 + 6.20568i 0.980747 + 0.552846i
\(127\) 0.258596 + 1.13298i 0.0229466 + 0.100536i 0.985104 0.171957i \(-0.0550090\pi\)
−0.962158 + 0.272493i \(0.912152\pi\)
\(128\) −6.82704 11.8248i −0.603431 1.04517i
\(129\) −3.14333 + 0.280864i −0.276755 + 0.0247287i
\(130\) −16.3216 5.03454i −1.43150 0.441558i
\(131\) 6.49040 + 3.12561i 0.567069 + 0.273086i 0.695373 0.718649i \(-0.255239\pi\)
−0.128304 + 0.991735i \(0.540953\pi\)
\(132\) −1.77839 + 2.69037i −0.154789 + 0.234167i
\(133\) 8.55249 3.17694i 0.741595 0.275476i
\(134\) −11.6480 14.6061i −1.00623 1.26177i
\(135\) −4.13412 7.71818i −0.355808 0.664275i
\(136\) −6.32975 + 16.1279i −0.542771 + 1.38296i
\(137\) 14.1560 + 6.81717i 1.20943 + 0.582430i 0.926349 0.376667i \(-0.122930\pi\)
0.283079 + 0.959097i \(0.408644\pi\)
\(138\) −3.92011 7.85068i −0.333702 0.668294i
\(139\) −11.7591 8.01722i −0.997394 0.680012i −0.0495586 0.998771i \(-0.515781\pi\)
−0.947836 + 0.318759i \(0.896734\pi\)
\(140\) −1.30724 1.99499i −0.110482 0.168607i
\(141\) −9.56467 + 7.85418i −0.805491 + 0.661441i
\(142\) 16.4909 + 11.2433i 1.38389 + 0.943517i
\(143\) 21.1729 6.53098i 1.77057 0.546148i
\(144\) 11.6213 8.42054i 0.968445 0.701712i
\(145\) −7.58176 + 1.14277i −0.629631 + 0.0949016i
\(146\) −0.760490 + 1.31721i −0.0629386 + 0.109013i
\(147\) 3.83174 11.5029i 0.316036 0.948747i
\(148\) 2.58084 + 4.47014i 0.212144 + 0.367444i
\(149\) −2.64072 3.31136i −0.216337 0.271277i 0.661807 0.749674i \(-0.269790\pi\)
−0.878144 + 0.478396i \(0.841218\pi\)
\(150\) −0.0852995 5.95798i −0.00696467 0.486467i
\(151\) 0.653255 2.86210i 0.0531611 0.232914i −0.941367 0.337385i \(-0.890458\pi\)
0.994528 + 0.104471i \(0.0333148\pi\)
\(152\) 0.601081 8.02087i 0.0487541 0.650578i
\(153\) −21.4728 5.95590i −1.73597 0.481506i
\(154\) 13.5467 + 5.60540i 1.09162 + 0.451696i
\(155\) 0.273754 3.65300i 0.0219885 0.293416i
\(156\) 5.88880 + 0.356613i 0.471481 + 0.0285519i
\(157\) 13.7721 9.38968i 1.09914 0.749378i 0.128929 0.991654i \(-0.458846\pi\)
0.970207 + 0.242276i \(0.0778938\pi\)
\(158\) 17.6619 2.66210i 1.40511 0.211786i
\(159\) −1.75956 0.375191i −0.139542 0.0297546i
\(160\) −4.91788 + 0.741251i −0.388793 + 0.0586011i
\(161\) −6.67713 + 5.12744i −0.526232 + 0.404099i
\(162\) 9.56086 + 10.6736i 0.751172 + 0.838596i
\(163\) 7.61892 5.19449i 0.596760 0.406864i −0.226925 0.973912i \(-0.572867\pi\)
0.823684 + 0.567048i \(0.191915\pi\)
\(164\) −0.411186 1.80152i −0.0321082 0.140675i
\(165\) −5.84139 8.30963i −0.454752 0.646903i
\(166\) −17.8188 −1.38301
\(167\) −2.95865 + 2.74523i −0.228947 + 0.212432i −0.786302 0.617843i \(-0.788007\pi\)
0.557355 + 0.830275i \(0.311816\pi\)
\(168\) −7.80629 7.30175i −0.602268 0.563342i
\(169\) −20.1829 18.7270i −1.55253 1.44054i
\(170\) 14.6081 + 13.5543i 1.12039 + 1.03957i
\(171\) 10.3408 0.296157i 0.790783 0.0226477i
\(172\) −0.963909 0.145286i −0.0734973 0.0110779i
\(173\) 1.18686 0.366098i 0.0902354 0.0278339i −0.249309 0.968424i \(-0.580203\pi\)
0.339544 + 0.940590i \(0.389727\pi\)
\(174\) 11.6143 4.75124i 0.880475 0.360190i
\(175\) −5.59572 + 1.16970i −0.422996 + 0.0884207i
\(176\) 12.2045 11.3241i 0.919948 0.853587i
\(177\) 6.51544 0.582170i 0.489731 0.0437586i
\(178\) 1.08859 0.0815933
\(179\) −1.61532 + 1.49880i −0.120735 + 0.112026i −0.738230 0.674549i \(-0.764338\pi\)
0.617495 + 0.786575i \(0.288148\pi\)
\(180\) −0.677041 2.61837i −0.0504637 0.195162i
\(181\) −14.9268 + 18.7176i −1.10950 + 1.39127i −0.197888 + 0.980225i \(0.563408\pi\)
−0.911614 + 0.411047i \(0.865163\pi\)
\(182\) −3.51034 26.5882i −0.260204 1.97085i
\(183\) 6.81766 1.65911i 0.503976 0.122645i
\(184\) 1.65156 + 7.23594i 0.121754 + 0.533440i
\(185\) −16.0754 + 2.42297i −1.18188 + 0.178140i
\(186\) 0.978325 + 5.91492i 0.0717343 + 0.433703i
\(187\) −25.5622 3.85288i −1.86929 0.281750i
\(188\) −3.44426 + 1.65867i −0.251198 + 0.120971i
\(189\) 8.30443 10.9561i 0.604058 0.796940i
\(190\) −8.33522 4.01403i −0.604701 0.291209i
\(191\) −0.534398 0.364347i −0.0386677 0.0263632i 0.543832 0.839194i \(-0.316973\pi\)
−0.582500 + 0.812831i \(0.697925\pi\)
\(192\) −7.80418 + 3.19259i −0.563218 + 0.230405i
\(193\) −1.27761 + 17.0486i −0.0919647 + 1.22718i 0.740097 + 0.672500i \(0.234780\pi\)
−0.832062 + 0.554683i \(0.812839\pi\)
\(194\) 7.70059 + 9.65623i 0.552870 + 0.693277i
\(195\) −7.82152 + 16.8546i −0.560111 + 1.20698i
\(196\) 1.99015 3.17248i 0.142154 0.226605i
\(197\) −25.2126 −1.79632 −0.898162 0.439664i \(-0.855098\pi\)
−0.898162 + 0.439664i \(0.855098\pi\)
\(198\) 12.5046 + 10.9534i 0.888666 + 0.778425i
\(199\) −13.9837 9.53395i −0.991281 0.675844i −0.0449320 0.998990i \(-0.514307\pi\)
−0.946349 + 0.323146i \(0.895260\pi\)
\(200\) −1.12148 + 4.91351i −0.0793003 + 0.347437i
\(201\) −17.4531 + 10.4125i −1.23105 + 0.734441i
\(202\) 2.14309 + 28.5976i 0.150788 + 2.01212i
\(203\) −6.59834 10.0698i −0.463113 0.706759i
\(204\) −6.00955 3.35584i −0.420753 0.234956i
\(205\) 5.75489 + 0.867410i 0.401939 + 0.0605825i
\(206\) 1.03173 + 13.7675i 0.0718841 + 0.959226i
\(207\) −9.03754 + 3.07370i −0.628152 + 0.213637i
\(208\) −29.1030 8.97709i −2.01793 0.622449i
\(209\) 11.8672 1.78869i 0.820871 0.123726i
\(210\) −11.0982 + 5.28978i −0.765845 + 0.365029i
\(211\) 21.9579 + 3.30963i 1.51165 + 0.227844i 0.851924 0.523665i \(-0.175436\pi\)
0.659722 + 0.751509i \(0.270674\pi\)
\(212\) −0.500688 0.241119i −0.0343874 0.0165601i
\(213\) 14.5389 16.1262i 0.996188 1.10495i
\(214\) 6.74376 0.460994
\(215\) 1.53508 2.65884i 0.104692 0.181331i
\(216\) −5.72272 10.6840i −0.389382 0.726955i
\(217\) 5.39188 2.00289i 0.366025 0.135965i
\(218\) −0.369345 0.342702i −0.0250152 0.0232107i
\(219\) 1.30826 + 1.01301i 0.0884040 + 0.0684526i
\(220\) −1.14624 2.92058i −0.0772796 0.196905i
\(221\) 17.2768 + 44.0206i 1.16216 + 2.96115i
\(222\) 24.6253 10.0739i 1.65274 0.676115i
\(223\) 12.4985 + 11.5969i 0.836964 + 0.776589i 0.976928 0.213568i \(-0.0685084\pi\)
−0.139965 + 0.990157i \(0.544699\pi\)
\(224\) −4.27999 6.53171i −0.285969 0.436418i
\(225\) −6.43472 0.782213i −0.428981 0.0521476i
\(226\) 2.39561 4.14932i 0.159354 0.276009i
\(227\) −20.2869 −1.34649 −0.673244 0.739420i \(-0.735100\pi\)
−0.673244 + 0.739420i \(0.735100\pi\)
\(228\) 3.12518 + 0.666383i 0.206970 + 0.0441323i
\(229\) 4.06642 + 1.95829i 0.268717 + 0.129407i 0.563390 0.826191i \(-0.309497\pi\)
−0.294674 + 0.955598i \(0.595211\pi\)
\(230\) 8.44139 + 1.27234i 0.556609 + 0.0838953i
\(231\) 8.02973 13.7798i 0.528317 0.906643i
\(232\) −10.4952 + 1.58189i −0.689042 + 0.103856i
\(233\) −15.5288 4.78999i −1.01732 0.313803i −0.259137 0.965840i \(-0.583438\pi\)
−0.758187 + 0.652038i \(0.773914\pi\)
\(234\) 5.91530 29.8289i 0.386696 1.94998i
\(235\) −0.899766 12.0065i −0.0586942 0.783220i
\(236\) 1.99798 + 0.301146i 0.130057 + 0.0196030i
\(237\) −0.278157 19.4286i −0.0180682 1.26202i
\(238\) −9.76934 + 29.7255i −0.633252 + 1.92681i
\(239\) −0.225296 3.00637i −0.0145732 0.194466i −0.999739 0.0228588i \(-0.992723\pi\)
0.985166 0.171607i \(-0.0548959\pi\)
\(240\) 0.199867 + 13.9603i 0.0129013 + 0.901131i
\(241\) 2.83998 12.4428i 0.182939 0.801509i −0.797283 0.603606i \(-0.793730\pi\)
0.980222 0.197902i \(-0.0634129\pi\)
\(242\) 1.46328 + 0.997645i 0.0940629 + 0.0641310i
\(243\) 12.9080 8.73977i 0.828049 0.560656i
\(244\) 2.16733 0.138749
\(245\) 7.01118 + 9.48522i 0.447928 + 0.605988i
\(246\) −9.48707 + 0.847692i −0.604874 + 0.0540469i
\(247\) −13.6881 17.1644i −0.870955 1.09214i
\(248\) 0.378949 5.05672i 0.0240633 0.321102i
\(249\) −2.61439 + 19.2072i −0.165680 + 1.21721i
\(250\) 15.8729 + 10.8220i 1.00389 + 0.684441i
\(251\) 15.0494 + 7.24740i 0.949909 + 0.457452i 0.843654 0.536887i \(-0.180400\pi\)
0.106254 + 0.994339i \(0.466114\pi\)
\(252\) 3.29258 2.68168i 0.207413 0.168930i
\(253\) −9.97747 + 4.80489i −0.627278 + 0.302081i
\(254\) 1.82962 + 0.275771i 0.114801 + 0.0173034i
\(255\) 16.7537 13.7576i 1.04916 0.861532i
\(256\) −11.8692 + 1.78899i −0.741824 + 0.111812i
\(257\) −2.62275 11.4910i −0.163602 0.716789i −0.988464 0.151455i \(-0.951604\pi\)
0.824862 0.565335i \(-0.191253\pi\)
\(258\) −1.41216 + 4.82213i −0.0879170 + 0.300213i
\(259\) −13.9902 21.3506i −0.869311 1.32666i
\(260\) −3.57846 + 4.48725i −0.221927 + 0.278287i
\(261\) −3.41738 13.2163i −0.211531 0.818068i
\(262\) 8.40786 7.80136i 0.519439 0.481969i
\(263\) 2.17505 0.134120 0.0670598 0.997749i \(-0.478638\pi\)
0.0670598 + 0.997749i \(0.478638\pi\)
\(264\) −8.08604 11.5027i −0.497661 0.707944i
\(265\) 1.28304 1.19049i 0.0788165 0.0731310i
\(266\) 0.266287 14.5237i 0.0163271 0.890506i
\(267\) 0.159719 1.17341i 0.00977463 0.0718115i
\(268\) −5.99864 + 1.85034i −0.366425 + 0.113027i
\(269\) −7.66053 1.15464i −0.467071 0.0703996i −0.0887094 0.996058i \(-0.528274\pi\)
−0.378361 + 0.925658i \(0.623512\pi\)
\(270\) −13.8439 + 1.63766i −0.842515 + 0.0996650i
\(271\) 6.01585 + 5.58189i 0.365437 + 0.339076i 0.841423 0.540377i \(-0.181718\pi\)
−0.475986 + 0.879453i \(0.657909\pi\)
\(272\) 26.0476 + 24.1687i 1.57937 + 1.46544i
\(273\) −29.1749 0.117188i −1.76574 0.00709256i
\(274\) 18.3381 17.0153i 1.10785 1.02793i
\(275\) −7.51982 −0.453462
\(276\) −2.93690 + 0.262419i −0.176780 + 0.0157957i
\(277\) −4.41050 19.3237i −0.265001 1.16105i −0.915749 0.401752i \(-0.868402\pi\)
0.650748 0.759294i \(-0.274456\pi\)
\(278\) −18.7225 + 12.7648i −1.12290 + 0.765581i
\(279\) 6.51933 0.186711i 0.390302 0.0111781i
\(280\) 10.1787 2.12770i 0.608296 0.127154i
\(281\) 16.2817 2.45408i 0.971288 0.146398i 0.355815 0.934556i \(-0.384203\pi\)
0.615473 + 0.788158i \(0.288965\pi\)
\(282\) 6.07713 + 18.7446i 0.361888 + 1.11622i
\(283\) 17.4653 2.63247i 1.03820 0.156484i 0.392249 0.919859i \(-0.371697\pi\)
0.645956 + 0.763375i \(0.276459\pi\)
\(284\) 5.54132 3.77801i 0.328817 0.224183i
\(285\) −5.54974 + 8.39573i −0.328738 + 0.497320i
\(286\) 2.63634 35.1795i 0.155890 2.08021i
\(287\) 2.53299 + 8.78007i 0.149518 + 0.518271i
\(288\) −2.21667 8.57270i −0.130619 0.505151i
\(289\) 2.85265 38.0660i 0.167803 2.23918i
\(290\) −2.71649 + 11.9017i −0.159518 + 0.698894i
\(291\) 11.5384 6.88381i 0.676395 0.403536i
\(292\) 0.318656 + 0.399582i 0.0186479 + 0.0233837i
\(293\) −8.35746 14.4755i −0.488248 0.845670i 0.511661 0.859188i \(-0.329030\pi\)
−0.999909 + 0.0135174i \(0.995697\pi\)
\(294\) −14.8198 12.3701i −0.864306 0.721441i
\(295\) −3.18190 + 5.51121i −0.185257 + 0.320875i
\(296\) −22.2526 + 3.35404i −1.29340 + 0.194949i
\(297\) 13.6415 11.8719i 0.791563 0.688875i
\(298\) −6.44387 + 1.98767i −0.373283 + 0.115143i
\(299\) 16.7381 + 11.4118i 0.967987 + 0.659962i
\(300\) −1.87410 0.704738i −0.108201 0.0406880i
\(301\) 4.79975 + 0.448309i 0.276653 + 0.0258401i
\(302\) −3.86195 2.63303i −0.222230 0.151514i
\(303\) 31.1402 + 1.88579i 1.78896 + 0.108336i
\(304\) −14.8625 7.15742i −0.852425 0.410506i
\(305\) −2.49386 + 6.35426i −0.142798 + 0.363844i
\(306\) −21.3177 + 28.3606i −1.21865 + 1.62127i
\(307\) 19.9956 + 25.0736i 1.14121 + 1.43103i 0.885722 + 0.464215i \(0.153664\pi\)
0.255485 + 0.966813i \(0.417765\pi\)
\(308\) 3.41637 3.54920i 0.194666 0.202235i
\(309\) 14.9916 + 0.907857i 0.852841 + 0.0516462i
\(310\) −5.25490 2.53063i −0.298459 0.143730i
\(311\) 15.3701 + 4.74105i 0.871558 + 0.268840i 0.698099 0.716001i \(-0.254029\pi\)
0.173459 + 0.984841i \(0.444506\pi\)
\(312\) −10.8271 + 23.3313i −0.612962 + 1.32087i
\(313\) −1.75155 3.03377i −0.0990033 0.171479i 0.812269 0.583283i \(-0.198232\pi\)
−0.911272 + 0.411804i \(0.864899\pi\)
\(314\) −5.90549 25.8736i −0.333266 1.46013i
\(315\) 4.07361 + 12.7390i 0.229522 + 0.717761i
\(316\) 1.33553 5.85136i 0.0751297 0.329165i
\(317\) 27.0507 8.34404i 1.51932 0.468648i 0.580850 0.814010i \(-0.302720\pi\)
0.938469 + 0.345362i \(0.112244\pi\)
\(318\) −1.57959 + 2.38962i −0.0885787 + 0.134003i
\(319\) −5.78568 14.7417i −0.323936 0.825375i
\(320\) 1.82534 7.99735i 0.102040 0.447065i
\(321\) 0.989449 7.26920i 0.0552256 0.405727i
\(322\) 3.71544 + 12.8788i 0.207053 + 0.717707i
\(323\) 5.69961 + 24.9716i 0.317135 + 1.38946i
\(324\) 4.51236 1.68027i 0.250687 0.0933481i
\(325\) 6.87807 + 11.9132i 0.381526 + 0.660823i
\(326\) −3.26699 14.3136i −0.180942 0.792758i
\(327\) −0.423594 + 0.347841i −0.0234248 + 0.0192357i
\(328\) 7.96630 + 1.20073i 0.439865 + 0.0662990i
\(329\) 16.5427 9.15079i 0.912031 0.504499i
\(330\) −15.7136 + 3.82400i −0.865006 + 0.210504i
\(331\) −5.92715 + 5.49959i −0.325786 + 0.302285i −0.826060 0.563582i \(-0.809423\pi\)
0.500274 + 0.865867i \(0.333232\pi\)
\(332\) −2.18749 + 5.57363i −0.120054 + 0.305893i
\(333\) −7.24576 28.0221i −0.397065 1.53560i
\(334\) 2.34772 + 5.98190i 0.128462 + 0.327315i
\(335\) 1.47752 19.7161i 0.0807254 1.07721i
\(336\) −19.7891 + 9.43220i −1.07958 + 0.514569i
\(337\) −1.63219 21.7801i −0.0889112 1.18644i −0.846021 0.533149i \(-0.821008\pi\)
0.757110 0.653288i \(-0.226611\pi\)
\(338\) −39.4956 + 19.0201i −2.14828 + 1.03455i
\(339\) −4.12113 3.19106i −0.223829 0.173314i
\(340\) 6.03304 2.90536i 0.327188 0.157565i
\(341\) 7.48161 1.12767i 0.405152 0.0610669i
\(342\) 5.57617 15.4985i 0.301525 0.838063i
\(343\) −8.94073 + 16.2192i −0.482754 + 0.875756i
\(344\) 2.12496 3.68054i 0.114570 0.198442i
\(345\) 2.61000 8.91243i 0.140518 0.479829i
\(346\) 0.147782 1.97201i 0.00794480 0.106016i
\(347\) 15.3642 + 14.2559i 0.824794 + 0.765297i 0.974727 0.223399i \(-0.0717153\pi\)
−0.149933 + 0.988696i \(0.547906\pi\)
\(348\) −0.0603620 4.21615i −0.00323574 0.226010i
\(349\) −19.7498 + 13.4652i −1.05718 + 0.720775i −0.961547 0.274641i \(-0.911441\pi\)
−0.0956363 + 0.995416i \(0.530489\pi\)
\(350\) −1.52133 + 8.97386i −0.0813184 + 0.479673i
\(351\) −31.2852 10.7527i −1.66988 0.573938i
\(352\) −3.75286 9.56213i −0.200028 0.509663i
\(353\) 2.51185 + 1.20964i 0.133692 + 0.0643827i 0.499534 0.866294i \(-0.333505\pi\)
−0.365842 + 0.930677i \(0.619219\pi\)
\(354\) 2.92710 9.99524i 0.155573 0.531241i
\(355\) 4.70031 + 20.5934i 0.249466 + 1.09298i
\(356\) 0.133639 0.340505i 0.00708283 0.0180467i
\(357\) 30.6082 + 14.8919i 1.61996 + 0.788161i
\(358\) 1.28178 + 3.26592i 0.0677441 + 0.172609i
\(359\) 4.15470 2.83262i 0.219277 0.149500i −0.448700 0.893682i \(-0.648113\pi\)
0.667977 + 0.744182i \(0.267161\pi\)
\(360\) 11.7049 + 1.42286i 0.616902 + 0.0749915i
\(361\) 3.55442 + 6.15644i 0.187075 + 0.324023i
\(362\) 19.0589 + 33.0110i 1.00171 + 1.73502i
\(363\) 1.29007 1.43091i 0.0677111 0.0751035i
\(364\) −8.74759 2.16603i −0.458498 0.113531i
\(365\) −1.53817 + 0.474462i −0.0805115 + 0.0248345i
\(366\) 1.50674 11.0696i 0.0787585 0.578617i
\(367\) −4.68574 + 5.87573i −0.244594 + 0.306711i −0.888941 0.458023i \(-0.848558\pi\)
0.644347 + 0.764733i \(0.277129\pi\)
\(368\) 15.0519 + 2.26870i 0.784632 + 0.118264i
\(369\) −0.478209 + 10.3506i −0.0248946 + 0.538833i
\(370\) −5.75969 + 25.2349i −0.299432 + 1.31190i
\(371\) 2.53939 + 1.05076i 0.131839 + 0.0545526i
\(372\) 1.97026 + 0.420118i 0.102153 + 0.0217821i
\(373\) 31.4599 1.62893 0.814465 0.580212i \(-0.197030\pi\)
0.814465 + 0.580212i \(0.197030\pi\)
\(374\) −20.5795 + 35.6448i −1.06414 + 1.84315i
\(375\) 13.9940 15.5218i 0.722649 0.801544i
\(376\) −1.24551 16.6202i −0.0642325 0.857123i
\(377\) −18.0624 + 22.6495i −0.930259 + 1.16651i
\(378\) −11.4076 18.6811i −0.586744 0.960851i
\(379\) −14.4073 18.0662i −0.740053 0.927997i 0.259232 0.965815i \(-0.416531\pi\)
−0.999285 + 0.0378180i \(0.987959\pi\)
\(380\) −2.27882 + 2.11444i −0.116901 + 0.108468i
\(381\) 0.565702 1.93172i 0.0289818 0.0989649i
\(382\) −0.850853 + 0.580102i −0.0435334 + 0.0296806i
\(383\) 1.52119 1.90751i 0.0777292 0.0974693i −0.741446 0.671012i \(-0.765860\pi\)
0.819176 + 0.573543i \(0.194431\pi\)
\(384\) 0.338553 + 23.6471i 0.0172767 + 1.20674i
\(385\) 6.47458 + 14.1001i 0.329975 + 0.718610i
\(386\) 24.5247 + 11.8105i 1.24827 + 0.601137i
\(387\) 4.99066 + 2.22969i 0.253689 + 0.113342i
\(388\) 3.96576 1.22328i 0.201331 0.0621024i
\(389\) −9.52120 + 4.58517i −0.482744 + 0.232477i −0.659396 0.751796i \(-0.729188\pi\)
0.176652 + 0.984273i \(0.443473\pi\)
\(390\) 20.4307 + 21.3964i 1.03455 + 1.08345i
\(391\) −11.8176 20.4687i −0.597641 1.03515i
\(392\) 9.70533 + 13.1301i 0.490193 + 0.663168i
\(393\) −7.17560 10.2076i −0.361961 0.514905i
\(394\) −14.6658 + 37.3679i −0.738852 + 1.88257i
\(395\) 15.6184 + 10.6485i 0.785849 + 0.535783i
\(396\) 4.96127 2.56671i 0.249313 0.128982i
\(397\) −2.04281 + 27.2595i −0.102526 + 1.36811i 0.674328 + 0.738432i \(0.264433\pi\)
−0.776854 + 0.629681i \(0.783186\pi\)
\(398\) −22.2645 + 15.1797i −1.11602 + 0.760888i
\(399\) −15.6163 2.41796i −0.781791 0.121050i
\(400\) 8.54024 + 5.82264i 0.427012 + 0.291132i
\(401\) 12.1335 15.2150i 0.605920 0.759799i −0.380368 0.924835i \(-0.624203\pi\)
0.986288 + 0.165036i \(0.0527740\pi\)
\(402\) 5.28025 + 31.9242i 0.263355 + 1.59224i
\(403\) −8.62962 10.8212i −0.429872 0.539043i
\(404\) 9.20827 + 2.84038i 0.458129 + 0.141314i
\(405\) −0.265929 + 15.1629i −0.0132141 + 0.753450i
\(406\) −18.7626 + 3.92203i −0.931174 + 0.194647i
\(407\) −12.2672 31.2563i −0.608062 1.54932i
\(408\) 23.1916 19.0441i 1.14815 0.942824i
\(409\) −0.255921 0.0789412i −0.0126545 0.00390339i 0.288421 0.957504i \(-0.406870\pi\)
−0.301076 + 0.953600i \(0.597346\pi\)
\(410\) 4.63313 8.02481i 0.228814 0.396317i
\(411\) −15.6505 22.2634i −0.771980 1.09817i
\(412\) 4.43306 + 1.36742i 0.218401 + 0.0673678i
\(413\) −9.94885 0.929249i −0.489551 0.0457253i
\(414\) −0.701447 + 15.1825i −0.0344743 + 0.746181i
\(415\) −13.8239 12.8267i −0.678588 0.629638i
\(416\) −11.7161 + 14.6915i −0.574428 + 0.720310i
\(417\) 11.0124 + 22.0541i 0.539279 + 1.08000i
\(418\) 4.25193 18.6289i 0.207969 0.911170i
\(419\) −20.4170 + 6.29780i −0.997434 + 0.307668i −0.750144 0.661274i \(-0.770016\pi\)
−0.247289 + 0.968942i \(0.579540\pi\)
\(420\) 0.292173 + 4.12083i 0.0142566 + 0.201076i
\(421\) −28.5717 8.81320i −1.39250 0.429529i −0.494366 0.869254i \(-0.664600\pi\)
−0.898132 + 0.439725i \(0.855076\pi\)
\(422\) 17.6778 30.6189i 0.860543 1.49050i
\(423\) 21.0967 3.80042i 1.02576 0.184783i
\(424\) 1.77607 1.64795i 0.0862534 0.0800315i
\(425\) −1.19936 16.0044i −0.0581777 0.776328i
\(426\) −15.4437 30.9286i −0.748250 1.49849i
\(427\) −10.7010 + 0.604899i −0.517857 + 0.0292731i
\(428\) 0.827883 2.10941i 0.0400172 0.101962i
\(429\) −37.5338 8.00332i −1.81215 0.386404i
\(430\) −3.04776 3.82177i −0.146976 0.184302i
\(431\) 2.25745 + 30.1235i 0.108737 + 1.45100i 0.738522 + 0.674230i \(0.235524\pi\)
−0.629784 + 0.776770i \(0.716857\pi\)
\(432\) −24.6851 + 2.92012i −1.18766 + 0.140494i
\(433\) 8.86573 4.26951i 0.426060 0.205180i −0.208551 0.978011i \(-0.566875\pi\)
0.634611 + 0.772832i \(0.281160\pi\)
\(434\) 0.167880 9.15641i 0.00805848 0.439522i
\(435\) 12.4305 + 4.67438i 0.595997 + 0.224119i
\(436\) −0.152537 + 0.0734580i −0.00730520 + 0.00351800i
\(437\) 8.04347 + 7.46325i 0.384771 + 0.357016i
\(438\) 2.26238 1.34973i 0.108101 0.0644928i
\(439\) 5.79250 14.7591i 0.276461 0.704411i −0.723441 0.690387i \(-0.757440\pi\)
0.999902 0.0140246i \(-0.00446430\pi\)
\(440\) 13.6787 0.652107
\(441\) −15.5083 + 14.1595i −0.738492 + 0.674262i
\(442\) 75.2930 3.58132
\(443\) −5.77771 + 14.7214i −0.274507 + 0.699434i 0.725431 + 0.688295i \(0.241641\pi\)
−0.999938 + 0.0111382i \(0.996455\pi\)
\(444\) −0.127984 8.93937i −0.00607383 0.424244i
\(445\) 0.844531 + 0.783611i 0.0400346 + 0.0371467i
\(446\) 24.4581 11.7784i 1.15813 0.557725i
\(447\) 1.19709 + 7.23758i 0.0566205 + 0.342326i
\(448\) 12.6075 2.63540i 0.595650 0.124511i
\(449\) 16.6133 8.00055i 0.784031 0.377569i 0.00135521 0.999999i \(-0.499569\pi\)
0.782676 + 0.622430i \(0.213854\pi\)
\(450\) −4.90230 + 9.08195i −0.231097 + 0.428127i
\(451\) 0.898293 + 11.9869i 0.0422990 + 0.564441i
\(452\) −1.00379 1.25872i −0.0472144 0.0592050i
\(453\) −3.40482 + 3.77654i −0.159972 + 0.177437i
\(454\) −11.8006 + 30.0674i −0.553829 + 1.41113i
\(455\) 16.4159 23.1541i 0.769590 1.08548i
\(456\) −7.68231 + 11.6219i −0.359757 + 0.544246i
\(457\) −2.05117 27.3709i −0.0959496 1.28036i −0.812557 0.582882i \(-0.801925\pi\)
0.716607 0.697477i \(-0.245694\pi\)
\(458\) 5.26777 4.88778i 0.246147 0.228391i
\(459\) 27.4426 + 27.1398i 1.28091 + 1.26678i
\(460\) 1.43427 2.48423i 0.0668732 0.115828i
\(461\) 20.9267 + 6.45503i 0.974654 + 0.300641i 0.740871 0.671648i \(-0.234413\pi\)
0.233783 + 0.972289i \(0.424889\pi\)
\(462\) −15.7524 19.9164i −0.732866 0.926596i
\(463\) 2.18055 0.672612i 0.101339 0.0312589i −0.243671 0.969858i \(-0.578352\pi\)
0.345010 + 0.938599i \(0.387876\pi\)
\(464\) −4.84378 + 21.2220i −0.224867 + 0.985206i
\(465\) −3.49881 + 5.29305i −0.162253 + 0.245459i
\(466\) −16.1322 + 20.2291i −0.747307 + 0.937094i
\(467\) 22.3115 + 20.7021i 1.03245 + 0.957978i 0.999140 0.0414670i \(-0.0132031\pi\)
0.0333148 + 0.999445i \(0.489394\pi\)
\(468\) −8.60415 5.51216i −0.397727 0.254800i
\(469\) 29.1013 10.8101i 1.34377 0.499162i
\(470\) −18.3184 5.65047i −0.844964 0.260637i
\(471\) −28.7561 + 2.56942i −1.32501 + 0.118393i
\(472\) −4.40459 + 7.62897i −0.202738 + 0.351152i
\(473\) 6.05945 + 1.86909i 0.278614 + 0.0859410i
\(474\) −28.9571 10.8891i −1.33005 0.500152i
\(475\) 2.72210 + 6.93580i 0.124898 + 0.318236i
\(476\) 8.09865 + 6.70498i 0.371201 + 0.307322i
\(477\) 2.34405 + 2.05327i 0.107327 + 0.0940126i
\(478\) −4.58681 1.41485i −0.209796 0.0647135i
\(479\) −1.15214 1.44473i −0.0526424 0.0660115i 0.754813 0.655940i \(-0.227727\pi\)
−0.807456 + 0.589928i \(0.799156\pi\)
\(480\) 8.06300 + 3.03202i 0.368024 + 0.138392i
\(481\) −38.2970 + 48.0230i −1.74619 + 2.18966i
\(482\) −16.7896 11.4469i −0.764743 0.521393i
\(483\) 14.4274 2.11535i 0.656469 0.0962516i
\(484\) 0.491694 0.335231i 0.0223497 0.0152378i
\(485\) −0.976802 + 13.0345i −0.0443543 + 0.591867i
\(486\) −5.44490 24.2149i −0.246986 1.09841i
\(487\) −17.8213 12.1504i −0.807561 0.550586i 0.0876900 0.996148i \(-0.472052\pi\)
−0.895251 + 0.445562i \(0.853004\pi\)
\(488\) −3.45217 + 8.79598i −0.156272 + 0.398175i
\(489\) −15.9082 + 1.42144i −0.719395 + 0.0642796i
\(490\) 18.1364 4.87392i 0.819320 0.220181i
\(491\) 1.35909 + 2.35402i 0.0613349 + 0.106235i 0.895062 0.445941i \(-0.147131\pi\)
−0.833727 + 0.552176i \(0.813798\pi\)
\(492\) −0.899507 + 3.07157i −0.0405529 + 0.138477i
\(493\) 30.4519 14.6649i 1.37148 0.660472i
\(494\) −33.4017 + 10.3031i −1.50281 + 0.463556i
\(495\) 1.81643 + 17.4990i 0.0816426 + 0.786523i
\(496\) −9.37002 4.51236i −0.420726 0.202611i
\(497\) −26.3053 + 20.2001i −1.17995 + 0.906098i
\(498\) 26.9464 + 15.0473i 1.20750 + 0.674288i
\(499\) −2.58355 + 3.23968i −0.115656 + 0.145028i −0.836289 0.548288i \(-0.815280\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(500\) 5.33365 3.63642i 0.238528 0.162626i
\(501\) 6.79244 1.65298i 0.303464 0.0738496i
\(502\) 19.4954 18.0891i 0.870124 0.807357i
\(503\) −20.2904 25.4434i −0.904705 1.13446i −0.990412 0.138143i \(-0.955887\pi\)
0.0857076 0.996320i \(-0.472685\pi\)
\(504\) 5.63895 + 17.6342i 0.251179 + 0.785488i
\(505\) −18.9231 + 23.7288i −0.842066 + 1.05592i
\(506\) 1.31764 + 17.5826i 0.0585761 + 0.781643i
\(507\) 14.7072 + 45.3635i 0.653170 + 2.01467i
\(508\) 0.310870 0.538442i 0.0137926 0.0238895i
\(509\) 10.0004 0.443261 0.221631 0.975131i \(-0.428862\pi\)
0.221631 + 0.975131i \(0.428862\pi\)
\(510\) −10.6448 32.8334i −0.471361 1.45389i
\(511\) −1.68485 1.88396i −0.0745335 0.0833414i
\(512\) 1.82400 7.99145i 0.0806100 0.353176i
\(513\) −15.8879 8.28459i −0.701470 0.365774i
\(514\) −18.5565 2.79695i −0.818494 0.123368i
\(515\) −9.10997 + 11.4235i −0.401433 + 0.503381i
\(516\) 1.33498 + 1.03369i 0.0587690 + 0.0455058i
\(517\) 23.7632 7.32998i 1.04511 0.322372i
\(518\) −39.7818 + 8.31575i −1.74791 + 0.365373i
\(519\) −2.10398 0.448631i −0.0923545 0.0196927i
\(520\) −12.5114 21.6703i −0.548659 0.950306i
\(521\) −15.6564 27.1176i −0.685918 1.18804i −0.973147 0.230182i \(-0.926068\pi\)
0.287230 0.957862i \(-0.407266\pi\)
\(522\) −21.5758 2.62279i −0.944349 0.114796i
\(523\) −16.3886 + 11.1735i −0.716622 + 0.488584i −0.865904 0.500210i \(-0.833256\pi\)
0.149282 + 0.988795i \(0.452304\pi\)
\(524\) −1.40805 3.58765i −0.0615109 0.156727i
\(525\) 9.44985 + 2.95651i 0.412425 + 0.129033i
\(526\) 1.26520 3.22367i 0.0551652 0.140559i
\(527\) 3.59329 + 15.7432i 0.156526 + 0.685787i
\(528\) −28.0190 + 6.81857i −1.21937 + 0.296740i
\(529\) 11.6000 + 5.58627i 0.504348 + 0.242881i
\(530\) −1.01811 2.59409i −0.0442237 0.112680i
\(531\) −10.3446 4.62167i −0.448916 0.200563i
\(532\) −4.51025 1.86627i −0.195544 0.0809129i
\(533\) 18.1684 12.3870i 0.786962 0.536542i
\(534\) −1.64621 0.919275i −0.0712387 0.0397809i
\(535\) 5.23183 + 4.85442i 0.226192 + 0.209875i
\(536\) 2.04528 27.2923i 0.0883425 1.17885i
\(537\) 3.70845 0.902471i 0.160031 0.0389445i
\(538\) −6.16732 + 10.6821i −0.265892 + 0.460538i
\(539\) −15.8774 + 18.4773i −0.683889 + 0.795875i
\(540\) −1.18727 + 4.53136i −0.0510919 + 0.194999i
\(541\) 6.07600 0.915810i 0.261228 0.0393737i −0.0171225 0.999853i \(-0.505451\pi\)
0.278350 + 0.960480i \(0.410212\pi\)
\(542\) 11.7723 5.66924i 0.505664 0.243515i
\(543\) 38.3794 15.7005i 1.64702 0.673772i
\(544\) 19.7525 9.51230i 0.846882 0.407837i
\(545\) −0.0398482 0.531738i −0.00170691 0.0227772i
\(546\) −17.1443 + 43.1722i −0.733707 + 1.84760i
\(547\) 1.76119 23.5015i 0.0753031 1.00485i −0.823734 0.566977i \(-0.808113\pi\)
0.899037 0.437873i \(-0.144268\pi\)
\(548\) −3.07105 7.82491i −0.131189 0.334264i
\(549\) −11.7110 3.24828i −0.499814 0.138633i
\(550\) −4.37416 + 11.1452i −0.186515 + 0.475232i
\(551\) −11.5024 + 10.6727i −0.490019 + 0.454672i
\(552\) 3.61293 12.3372i 0.153777 0.525105i
\(553\) −4.96096 + 29.2632i −0.210962 + 1.24440i
\(554\) −31.2053 4.70344i −1.32579 0.199830i
\(555\) 26.3560 + 9.91094i 1.11875 + 0.420696i
\(556\) 1.69433 + 7.42334i 0.0718555 + 0.314820i
\(557\) −13.0500 22.6033i −0.552946 0.957731i −0.998060 0.0622571i \(-0.980170\pi\)
0.445114 0.895474i \(-0.353163\pi\)
\(558\) 3.51547 9.77096i 0.148822 0.413638i
\(559\) −2.58125 11.3092i −0.109175 0.478327i
\(560\) 3.56465 21.0268i 0.150634 0.888545i
\(561\) 35.4026 + 27.4128i 1.49470 + 1.15737i
\(562\) 5.83364 25.5588i 0.246077 1.07813i
\(563\) −2.40819 6.13598i −0.101493 0.258601i 0.871103 0.491100i \(-0.163405\pi\)
−0.972597 + 0.232499i \(0.925310\pi\)
\(564\) 6.60924 + 0.400241i 0.278299 + 0.0168532i
\(565\) 4.84536 1.49460i 0.203846 0.0628782i
\(566\) 6.25770 27.4168i 0.263031 1.15241i
\(567\) −21.8104 + 9.55554i −0.915949 + 0.401295i
\(568\) 6.50647 + 28.5067i 0.273006 + 1.19612i
\(569\) −18.3974 31.8652i −0.771257 1.33586i −0.936874 0.349667i \(-0.886295\pi\)
0.165617 0.986190i \(-0.447038\pi\)
\(570\) 9.21519 + 13.1090i 0.385982 + 0.549075i
\(571\) −12.7983 3.94775i −0.535592 0.165208i 0.0151476 0.999885i \(-0.495178\pi\)
−0.550740 + 0.834677i \(0.685654\pi\)
\(572\) −10.6803 5.14337i −0.446567 0.215055i
\(573\) 0.500463 + 1.00226i 0.0209071 + 0.0418700i
\(574\) 14.4864 + 1.35307i 0.604652 + 0.0564761i
\(575\) −4.28667 5.37531i −0.178766 0.224166i
\(576\) 14.4978 + 1.76238i 0.604077 + 0.0734325i
\(577\) −6.60622 + 16.8324i −0.275020 + 0.700740i 0.724909 + 0.688845i \(0.241882\pi\)
−0.999929 + 0.0118957i \(0.996213\pi\)
\(578\) −54.7586 26.3704i −2.27766 1.09686i
\(579\) 16.3290 24.7027i 0.678609 1.02661i
\(580\) 3.38932 + 2.31080i 0.140734 + 0.0959506i
\(581\) 9.24492 28.1298i 0.383544 1.16702i
\(582\) −3.49083 21.1054i −0.144700 0.874849i
\(583\) 2.98688 + 2.03642i 0.123704 + 0.0843400i
\(584\) −2.12924 + 0.656782i −0.0881084 + 0.0271778i
\(585\) 26.0612 18.8833i 1.07750 0.780728i
\(586\) −26.3157 + 3.96646i −1.08709 + 0.163853i
\(587\) −5.24933 + 9.09211i −0.216663 + 0.375271i −0.953786 0.300488i \(-0.902851\pi\)
0.737123 + 0.675759i \(0.236184\pi\)
\(588\) −5.68863 + 3.11695i −0.234595 + 0.128541i
\(589\) −3.74836 6.49236i −0.154449 0.267513i
\(590\) 6.31735 + 7.92170i 0.260081 + 0.326131i
\(591\) 38.1276 + 21.2911i 1.56836 + 0.875800i
\(592\) −10.2701 + 44.9963i −0.422099 + 1.84934i
\(593\) 1.33353 17.7947i 0.0547614 0.730740i −0.900477 0.434903i \(-0.856783\pi\)
0.955239 0.295836i \(-0.0955983\pi\)
\(594\) −9.66031 27.1239i −0.396367 1.11291i
\(595\) −28.9766 + 16.0287i −1.18793 + 0.657114i
\(596\) −0.169335 + 2.25962i −0.00693624 + 0.0925577i
\(597\) 13.0957 + 26.2264i 0.535973 + 1.07338i
\(598\) 26.6498 18.1696i 1.08979 0.743008i
\(599\) −6.62891 + 0.999147i −0.270850 + 0.0408241i −0.283063 0.959101i \(-0.591350\pi\)
0.0122130 + 0.999925i \(0.496112\pi\)
\(600\) 5.84522 6.48337i 0.238630 0.264683i
\(601\) −15.9669 + 2.40662i −0.651302 + 0.0981679i −0.466379 0.884585i \(-0.654442\pi\)
−0.184923 + 0.982753i \(0.559204\pi\)
\(602\) 3.45639 6.85298i 0.140872 0.279307i
\(603\) 35.1863 1.00772i 1.43290 0.0410376i
\(604\) −1.29770 + 0.884759i −0.0528028 + 0.0360004i
\(605\) 0.417069 + 1.82730i 0.0169563 + 0.0742903i
\(606\) 20.9088 45.0563i 0.849360 1.83029i
\(607\) 41.1289 1.66937 0.834685 0.550728i \(-0.185650\pi\)
0.834685 + 0.550728i \(0.185650\pi\)
\(608\) −7.46100 + 6.92279i −0.302583 + 0.280756i
\(609\) 1.47475 + 20.8000i 0.0597599 + 0.842858i
\(610\) 7.96706 + 7.39235i 0.322577 + 0.299308i
\(611\) −33.3477 30.9421i −1.34910 1.25178i
\(612\) 6.25402 + 10.1497i 0.252804 + 0.410277i
\(613\) −13.7679 2.07518i −0.556080 0.0838156i −0.135011 0.990844i \(-0.543107\pi\)
−0.421069 + 0.907028i \(0.638345\pi\)
\(614\) 48.7930 15.0506i 1.96913 0.607395i
\(615\) −7.97030 6.17153i −0.321393 0.248860i
\(616\) 8.96254 + 19.5183i 0.361111 + 0.786416i
\(617\) 17.9500 16.6552i 0.722642 0.670514i −0.230488 0.973075i \(-0.574032\pi\)
0.953130 + 0.302562i \(0.0978418\pi\)
\(618\) 10.0659 21.6911i 0.404911 0.872542i
\(619\) −2.67810 −0.107642 −0.0538210 0.998551i \(-0.517140\pi\)
−0.0538210 + 0.998551i \(0.517140\pi\)
\(620\) −1.43667 + 1.33304i −0.0576982 + 0.0535361i
\(621\) 16.2626 + 2.98369i 0.652595 + 0.119732i
\(622\) 15.9673 20.0224i 0.640231 0.802824i
\(623\) −0.564792 + 1.71851i −0.0226279 + 0.0688506i
\(624\) 36.4300 + 38.1520i 1.45837 + 1.52730i
\(625\) 2.12016 + 9.28904i 0.0848065 + 0.371561i
\(626\) −5.51523 + 0.831286i −0.220433 + 0.0332249i
\(627\) −19.4566 7.31647i −0.777020 0.292192i
\(628\) −8.81811 1.32912i −0.351881 0.0530375i
\(629\) 64.5662 31.0934i 2.57442 1.23978i
\(630\) 21.2501 + 1.37255i 0.846626 + 0.0546838i
\(631\) 18.9390 + 9.12053i 0.753949 + 0.363083i 0.771053 0.636771i \(-0.219730\pi\)
−0.0171042 + 0.999854i \(0.505445\pi\)
\(632\) 21.6201 + 14.7403i 0.860000 + 0.586338i
\(633\) −30.4109 23.5476i −1.20872 0.935935i
\(634\) 3.36822 44.9457i 0.133769 1.78502i
\(635\) 1.22092 + 1.53098i 0.0484505 + 0.0607551i
\(636\) 0.553546 + 0.787443i 0.0219495 + 0.0312241i
\(637\) 43.7949 + 8.25311i 1.73522 + 0.327000i
\(638\) −25.2142 −0.998240
\(639\) −35.6043 + 12.1091i −1.40849 + 0.479030i
\(640\) −19.0097 12.9606i −0.751423 0.512311i
\(641\) 3.45292 15.1282i 0.136382 0.597529i −0.859831 0.510579i \(-0.829431\pi\)
0.996213 0.0869495i \(-0.0277119\pi\)
\(642\) −10.1982 5.69486i −0.402491 0.224758i
\(643\) −0.640178 8.54258i −0.0252462 0.336887i −0.995498 0.0947871i \(-0.969783\pi\)
0.970251 0.242100i \(-0.0778361\pi\)
\(644\) 4.48454 + 0.418868i 0.176716 + 0.0165057i
\(645\) −4.56671 + 2.72449i −0.179814 + 0.107277i
\(646\) 40.3261 + 6.07818i 1.58661 + 0.239143i
\(647\) −2.97921 39.7548i −0.117125 1.56292i −0.678024 0.735040i \(-0.737164\pi\)
0.560899 0.827884i \(-0.310456\pi\)
\(648\) −0.368116 + 20.9895i −0.0144610 + 0.824544i
\(649\) −12.5599 3.87423i −0.493021 0.152077i
\(650\) 21.6575 3.26434i 0.849476 0.128038i
\(651\) −9.84520 1.52439i −0.385864 0.0597457i
\(652\) −4.87829 0.735284i −0.191049 0.0287960i
\(653\) −25.6612 12.3578i −1.00420 0.483597i −0.141839 0.989890i \(-0.545301\pi\)
−0.862362 + 0.506292i \(0.831016\pi\)
\(654\) 0.269140 + 0.830147i 0.0105242 + 0.0324613i
\(655\) 12.1386 0.474293
\(656\) 8.26133 14.3090i 0.322551 0.558674i
\(657\) −1.12296 2.63669i −0.0438109 0.102867i
\(658\) −3.93980 29.8410i −0.153589 1.16332i
\(659\) −26.6446 24.7226i −1.03793 0.963056i −0.0385832 0.999255i \(-0.512284\pi\)
−0.999345 + 0.0361992i \(0.988475\pi\)
\(660\) −0.732924 + 5.38458i −0.0285290 + 0.209595i
\(661\) 0.469156 + 1.19539i 0.0182480 + 0.0464952i 0.939707 0.341979i \(-0.111097\pi\)
−0.921459 + 0.388475i \(0.873002\pi\)
\(662\) 4.70326 + 11.9837i 0.182798 + 0.465761i
\(663\) 11.0470 81.1595i 0.429032 3.15197i
\(664\) −19.1359 17.7556i −0.742618 0.689049i
\(665\) 10.6613 11.0758i 0.413429 0.429503i
\(666\) −45.7465 5.56101i −1.77264 0.215485i
\(667\) 7.23951 12.5392i 0.280315 0.485520i
\(668\) 2.15932 0.0835466
\(669\) −9.10763 28.0920i −0.352121 1.08610i
\(670\) −28.3620 13.6584i −1.09572 0.527670i
\(671\) −13.9413 2.10131i −0.538198 0.0811204i
\(672\) 0.956592 + 13.4918i 0.0369013 + 0.520459i
\(673\) −1.04620 + 0.157689i −0.0403280 + 0.00607847i −0.169175 0.985586i \(-0.554110\pi\)
0.128847 + 0.991664i \(0.458872\pi\)
\(674\) −33.2299 10.2501i −1.27997 0.394818i
\(675\) 9.07031 + 6.61678i 0.349116 + 0.254680i
\(676\) 1.10079 + 14.6890i 0.0423379 + 0.564960i
\(677\) −49.4708 7.45652i −1.90132 0.286577i −0.909646 0.415384i \(-0.863647\pi\)
−0.991670 + 0.128807i \(0.958885\pi\)
\(678\) −7.12669 + 4.25178i −0.273699 + 0.163288i
\(679\) −19.2391 + 7.14664i −0.738331 + 0.274263i
\(680\) 2.18167 + 29.1124i 0.0836633 + 1.11641i
\(681\) 30.6787 + 17.1315i 1.17561 + 0.656482i
\(682\) 2.68061 11.7445i 0.102646 0.449721i
\(683\) 13.6860 + 9.33096i 0.523680 + 0.357039i 0.796125 0.605132i \(-0.206880\pi\)
−0.272445 + 0.962171i \(0.587832\pi\)
\(684\) −4.16330 3.64684i −0.159188 0.139440i
\(685\) 26.4750 1.01156
\(686\) 18.8380 + 22.6856i 0.719237 + 0.866141i
\(687\) −4.49572 6.39535i −0.171522 0.243998i
\(688\) −5.43446 6.81460i −0.207187 0.259804i
\(689\) 0.494194 6.59456i 0.0188273 0.251233i
\(690\) −11.6910 9.05253i −0.445069 0.344624i
\(691\) 31.6435 + 21.5742i 1.20377 + 0.820719i 0.987807 0.155681i \(-0.0497573\pi\)
0.215967 + 0.976401i \(0.430710\pi\)
\(692\) −0.598693 0.288315i −0.0227589 0.0109601i
\(693\) −23.7794 + 14.0576i −0.903306 + 0.534003i
\(694\) 30.0659 14.4790i 1.14129 0.549615i
\(695\) −23.7136 3.57424i −0.899506 0.135579i
\(696\) 17.2071 + 6.47059i 0.652234 + 0.245267i
\(697\) −25.3684 + 3.82367i −0.960897 + 0.144832i
\(698\) 8.46872 + 37.1039i 0.320546 + 1.40440i
\(699\) 19.4383 + 20.3571i 0.735225 + 0.769977i
\(700\) 2.62021 + 1.57752i 0.0990347 + 0.0596246i
\(701\) 6.13638 7.69478i 0.231768 0.290628i −0.652325 0.757940i \(-0.726206\pi\)
0.884092 + 0.467312i \(0.154778\pi\)
\(702\) −34.1348 + 40.1134i −1.28834 + 1.51398i
\(703\) −24.3882 + 22.6289i −0.919818 + 0.853467i
\(704\) 16.9427 0.638550
\(705\) −8.77842 + 18.9166i −0.330614 + 0.712442i
\(706\) 3.25392 3.01920i 0.122463 0.113629i
\(707\) −46.2577 11.4541i −1.73970 0.430774i
\(708\) −2.76712 2.14262i −0.103995 0.0805247i
\(709\) −21.0717 + 6.49975i −0.791363 + 0.244103i −0.663980 0.747750i \(-0.731134\pi\)
−0.127383 + 0.991854i \(0.540658\pi\)
\(710\) 33.2558 + 5.01250i 1.24807 + 0.188116i
\(711\) −15.9861 + 29.6157i −0.599527 + 1.11068i
\(712\) 1.16906 + 1.08473i 0.0438122 + 0.0406518i
\(713\) 5.07097 + 4.70517i 0.189909 + 0.176210i
\(714\) 39.8757 36.7023i 1.49231 1.37355i
\(715\) 27.3689 25.3946i 1.02354 0.949705i
\(716\) 1.17892 0.0440582
\(717\) −2.19806 + 4.73661i −0.0820882 + 0.176892i
\(718\) −1.78153 7.80541i −0.0664863 0.291295i
\(719\) −28.3647 + 19.3387i −1.05783 + 0.721214i −0.961686 0.274154i \(-0.911602\pi\)
−0.0961404 + 0.995368i \(0.530650\pi\)
\(720\) 11.4867 21.2801i 0.428083 0.793062i
\(721\) −22.2694 5.51423i −0.829356 0.205360i
\(722\) 11.1921 1.68693i 0.416526 0.0627811i
\(723\) −14.8022 + 16.4182i −0.550500 + 0.610600i
\(724\) 12.6654 1.90900i 0.470705 0.0709474i
\(725\) 8.12347 5.53849i 0.301698 0.205694i
\(726\) −1.37036 2.74437i −0.0508587 0.101853i
\(727\) 1.43414 19.1373i 0.0531893 0.709762i −0.905325 0.424719i \(-0.860373\pi\)
0.958515 0.285043i \(-0.0920079\pi\)
\(728\) 22.7240 32.0514i 0.842207 1.18790i
\(729\) −26.9005 + 2.31632i −0.996313 + 0.0857896i
\(730\) −0.191525 + 2.55572i −0.00708866 + 0.0945915i
\(731\) −3.01154 + 13.1944i −0.111386 + 0.488014i
\(732\) −3.27754 1.83024i −0.121141 0.0676474i
\(733\) 14.1332 + 17.7225i 0.522023 + 0.654596i 0.971037 0.238929i \(-0.0767963\pi\)
−0.449015 + 0.893524i \(0.648225\pi\)
\(734\) 5.98285 + 10.3626i 0.220831 + 0.382491i
\(735\) −2.59269 20.2646i −0.0956329 0.747473i
\(736\) 4.69588 8.13350i 0.173092 0.299805i
\(737\) 40.3800 6.08631i 1.48742 0.224192i
\(738\) 15.0626 + 6.72957i 0.554462 + 0.247719i
\(739\) 18.0820 5.57756i 0.665158 0.205174i 0.0562520 0.998417i \(-0.482085\pi\)
0.608906 + 0.793243i \(0.291609\pi\)
\(740\) 7.18625 + 4.89950i 0.264172 + 0.180109i
\(741\) 6.20510 + 37.5159i 0.227950 + 1.37818i
\(742\) 3.03446 3.15244i 0.111399 0.115730i
\(743\) 10.9928 + 7.49473i 0.403285 + 0.274955i 0.747929 0.663778i \(-0.231048\pi\)
−0.344644 + 0.938733i \(0.612001\pi\)
\(744\) −4.84328 + 7.32699i −0.177563 + 0.268620i
\(745\) −6.42998 3.09651i −0.235576 0.113447i
\(746\) 18.2997 46.6270i 0.670001 1.70713i
\(747\) 20.1734 26.8382i 0.738105 0.981958i
\(748\) 8.62310 + 10.8130i 0.315292 + 0.395363i
\(749\) −3.49886 + 10.6461i −0.127845 + 0.388999i
\(750\) −14.8649 29.7695i −0.542791 1.08703i
\(751\) 41.1873 + 19.8348i 1.50295 + 0.723781i 0.990827 0.135133i \(-0.0431462\pi\)
0.512120 + 0.858914i \(0.328860\pi\)
\(752\) −32.6635 10.0754i −1.19112 0.367411i
\(753\) −16.6382 23.6685i −0.606329 0.862528i
\(754\) 23.0624 + 39.9453i 0.839883 + 1.45472i
\(755\) −1.10075 4.82270i −0.0400604 0.175516i
\(756\) −7.24377 + 1.27490i −0.263453 + 0.0463675i
\(757\) 2.71835 11.9099i 0.0988001 0.432872i −0.901200 0.433404i \(-0.857312\pi\)
1.00000 0.000532346i \(0.000169451\pi\)
\(758\) −35.1566 + 10.8444i −1.27694 + 0.393885i
\(759\) 19.1459 + 1.15944i 0.694953 + 0.0420848i
\(760\) −4.95156 12.6164i −0.179612 0.457644i
\(761\) −4.32536 + 18.9506i −0.156794 + 0.686960i 0.834021 + 0.551733i \(0.186033\pi\)
−0.990815 + 0.135227i \(0.956824\pi\)
\(762\) −2.53396 1.96208i −0.0917956 0.0710788i
\(763\) 0.732635 0.405264i 0.0265232 0.0146716i
\(764\) 0.0769996 + 0.337357i 0.00278575 + 0.0122052i
\(765\) −36.9534 + 6.65690i −1.33605 + 0.240681i
\(766\) −1.94229 3.36414i −0.0701777 0.121551i
\(767\) 5.35037 + 23.4415i 0.193191 + 0.846423i
\(768\) 19.4598 + 7.31770i 0.702196 + 0.264055i
\(769\) −0.282025 0.0425085i −0.0101701 0.00153290i 0.143955 0.989584i \(-0.454018\pi\)
−0.154125 + 0.988051i \(0.549256\pi\)
\(770\) 24.6641 1.39420i 0.888833 0.0502433i
\(771\) −5.73750 + 19.5920i −0.206631 + 0.705589i
\(772\) 6.70497 6.22131i 0.241317 0.223910i
\(773\) −0.737510 + 1.87914i −0.0265264 + 0.0675881i −0.943523 0.331306i \(-0.892511\pi\)
0.916997 + 0.398894i \(0.130606\pi\)
\(774\) 6.20764 6.09972i 0.223129 0.219250i
\(775\) 1.71614 + 4.37264i 0.0616454 + 0.157070i
\(776\) −1.35215 + 18.0432i −0.0485395 + 0.647714i
\(777\) 3.12687 + 44.1015i 0.112176 + 1.58213i
\(778\) 1.25738 + 16.7786i 0.0450793 + 0.601541i
\(779\) 10.7308 5.16767i 0.384470 0.185151i
\(780\) 9.20082 3.76393i 0.329442 0.134770i
\(781\) −39.3073 + 18.9294i −1.40652 + 0.677347i
\(782\) −37.2109 + 5.60864i −1.33066 + 0.200565i
\(783\) −5.99277 + 22.8721i −0.214164 + 0.817383i
\(784\) 32.3391 8.69070i 1.15497 0.310382i
\(785\) 14.0434 24.3238i 0.501230 0.868155i
\(786\) −19.3027 + 4.69742i −0.688504 + 0.167551i
\(787\) −0.771127 + 10.2900i −0.0274877 + 0.366798i 0.966450 + 0.256854i \(0.0826861\pi\)
−0.993938 + 0.109944i \(0.964933\pi\)
\(788\) 9.88805 + 9.17477i 0.352247 + 0.326838i
\(789\) −3.28921 1.83675i −0.117099 0.0653902i
\(790\) 24.8672 16.9542i 0.884735 0.603202i
\(791\) 5.30743 + 5.93463i 0.188711 + 0.211011i
\(792\) 2.51443 + 24.2233i 0.0893463 + 0.860737i
\(793\) 9.42257 + 24.0083i 0.334605 + 0.852560i
\(794\) 39.2132 + 18.8841i 1.39163 + 0.670171i
\(795\) −2.94559 + 0.716826i −0.104469 + 0.0254232i
\(796\) 2.01487 + 8.82772i 0.0714151 + 0.312890i
\(797\) 17.9208 45.6616i 0.634789 1.61742i −0.143602 0.989635i \(-0.545869\pi\)
0.778391 0.627780i \(-0.216036\pi\)
\(798\) −12.6674 + 21.7385i −0.448422 + 0.769535i
\(799\) 19.3905 + 49.4061i 0.685986 + 1.74786i
\(800\) 5.26925 3.59252i 0.186296 0.127015i
\(801\) −1.23243 + 1.63960i −0.0435459 + 0.0579326i
\(802\) −15.4924 26.8335i −0.547054 0.947525i
\(803\) −1.66233 2.87925i −0.0586625 0.101606i
\(804\) 10.6339 + 2.26747i 0.375030 + 0.0799677i
\(805\) −6.38822 + 12.6659i −0.225155 + 0.446415i
\(806\) −21.0579 + 6.49551i −0.741734 + 0.228795i
\(807\) 10.6095 + 8.21514i 0.373473 + 0.289186i
\(808\) −26.1946 + 32.8469i −0.921522 + 1.15555i
\(809\) 34.3074 + 5.17101i 1.20618 + 0.181803i 0.721204 0.692722i \(-0.243589\pi\)
0.484980 + 0.874525i \(0.338827\pi\)
\(810\) 22.3184 + 9.21416i 0.784187 + 0.323752i
\(811\) 11.3127 49.5643i 0.397244 1.74044i −0.240927 0.970543i \(-0.577452\pi\)
0.638171 0.769895i \(-0.279691\pi\)
\(812\) −1.07657 + 6.35033i −0.0377800 + 0.222853i
\(813\) −4.38373 13.5213i −0.153744 0.474214i
\(814\) −53.4609 −1.87380
\(815\) 7.76898 13.4563i 0.272135 0.471352i
\(816\) −18.9808 58.5452i −0.664461 2.04949i
\(817\) −0.469530 6.26544i −0.0164268 0.219200i
\(818\) −0.265865 + 0.333384i −0.00929575 + 0.0116565i
\(819\) 44.0206 + 24.8143i 1.53820 + 0.867083i
\(820\) −1.94134 2.43437i −0.0677947 0.0850118i
\(821\) −13.9311 + 12.9261i −0.486197 + 0.451125i −0.884781 0.466007i \(-0.845692\pi\)
0.398584 + 0.917132i \(0.369502\pi\)
\(822\) −42.1005 + 10.2454i −1.46842 + 0.357349i
\(823\) 7.78442 5.30733i 0.271348 0.185002i −0.420000 0.907524i \(-0.637970\pi\)
0.691347 + 0.722522i \(0.257017\pi\)
\(824\) −12.6106 + 15.8132i −0.439312 + 0.550879i
\(825\) 11.3718 + 6.35021i 0.395915 + 0.221086i
\(826\) −7.16434 + 14.2048i −0.249279 + 0.494246i
\(827\) 16.2986 + 7.84899i 0.566757 + 0.272936i 0.695242 0.718776i \(-0.255297\pi\)
−0.128485 + 0.991711i \(0.541011\pi\)
\(828\) 4.66291 + 2.08326i 0.162047 + 0.0723983i
\(829\) −26.4041 + 8.14458i −0.917052 + 0.282873i −0.717131 0.696939i \(-0.754545\pi\)
−0.199921 + 0.979812i \(0.564069\pi\)
\(830\) −27.0517 + 13.0274i −0.938978 + 0.452188i
\(831\) −9.64837 + 32.9466i −0.334698 + 1.14290i
\(832\) −15.4967 26.8412i −0.537253 0.930549i
\(833\) −41.8576 30.8448i −1.45028 1.06871i
\(834\) 39.0924 3.49299i 1.35366 0.120953i
\(835\) −2.48464 + 6.33076i −0.0859845 + 0.219085i
\(836\) −5.30505 3.61692i −0.183479 0.125094i
\(837\) −10.0165 5.22298i −0.346220 0.180533i
\(838\) −2.54222 + 33.9235i −0.0878194 + 1.17187i
\(839\) −14.0608 + 9.58647i −0.485432 + 0.330962i −0.781182 0.624304i \(-0.785383\pi\)
0.295750 + 0.955265i \(0.404430\pi\)
\(840\) −17.1895 5.37796i −0.593094 0.185557i
\(841\) −6.85328 4.67249i −0.236320 0.161120i
\(842\) −29.6818 + 37.2198i −1.02290 + 1.28268i
\(843\) −26.6944 10.0382i −0.919402 0.345733i
\(844\) −7.40725 9.28840i −0.254968 0.319720i
\(845\) −44.3322 13.6747i −1.52507 0.470423i
\(846\) 6.63899 33.4782i 0.228253 1.15101i
\(847\) −2.33413 + 1.79240i −0.0802015 + 0.0615876i
\(848\) −1.81539 4.62553i −0.0623406 0.158841i
\(849\) −28.6348 10.7679i −0.982745 0.369553i
\(850\) −24.4179 7.53194i −0.837528 0.258343i
\(851\) 15.3497 26.5864i 0.526181 0.911371i
\(852\) −11.5702 + 1.03383i −0.396389 + 0.0354183i
\(853\) −12.8833 3.97398i −0.441116 0.136066i 0.0662381 0.997804i \(-0.478900\pi\)
−0.507354 + 0.861737i \(0.669377\pi\)
\(854\) −5.32808 + 16.2119i −0.182323 + 0.554760i
\(855\) 15.4824 8.00984i 0.529488 0.273931i
\(856\) 7.24224 + 6.71981i 0.247535 + 0.229678i
\(857\) 10.3383 12.9638i 0.353149 0.442834i −0.573249 0.819381i \(-0.694317\pi\)
0.926398 + 0.376547i \(0.122889\pi\)
\(858\) −33.6946 + 50.9737i −1.15032 + 1.74021i
\(859\) 7.93399 34.7611i 0.270704 1.18603i −0.638480 0.769639i \(-0.720436\pi\)
0.909184 0.416395i \(-0.136707\pi\)
\(860\) −1.56958 + 0.484151i −0.0535223 + 0.0165094i
\(861\) 3.58395 15.4166i 0.122141 0.525397i
\(862\) 45.9595 + 14.1766i 1.56539 + 0.482858i
\(863\) −3.53797 + 6.12794i −0.120434 + 0.208598i −0.919939 0.392062i \(-0.871762\pi\)
0.799505 + 0.600660i \(0.205095\pi\)
\(864\) −3.88719 + 14.8359i −0.132245 + 0.504728i
\(865\) 1.53418 1.42351i 0.0521637 0.0484009i
\(866\) −1.17082 15.6235i −0.0397860 0.530908i
\(867\) −36.4593 + 55.1561i −1.23822 + 1.87320i
\(868\) −2.84347 1.17658i −0.0965135 0.0399357i
\(869\) −14.2639 + 36.3438i −0.483870 + 1.23288i
\(870\) 14.1586 15.7043i 0.480021 0.532427i
\(871\) −46.5761 58.4046i −1.57817 1.97896i
\(872\) −0.0551606 0.736067i −0.00186797 0.0249264i
\(873\) −23.2621 + 0.666215i −0.787302 + 0.0225480i
\(874\) 15.7401 7.58004i 0.532417 0.256399i
\(875\) −25.3195 + 19.4431i −0.855954 + 0.657296i
\(876\) −0.144453 0.873358i −0.00488061 0.0295080i
\(877\) −25.9255 + 12.4850i −0.875441 + 0.421590i −0.816957 0.576698i \(-0.804341\pi\)
−0.0584834 + 0.998288i \(0.518626\pi\)
\(878\) −18.5051 17.1702i −0.624517 0.579467i
\(879\) 0.414446 + 28.9481i 0.0139789 + 0.976396i
\(880\) 10.2492 26.1145i 0.345500 0.880320i
\(881\) 30.4288 1.02517 0.512587 0.858636i \(-0.328687\pi\)
0.512587 + 0.858636i \(0.328687\pi\)
\(882\) 11.9650 + 31.2214i 0.402881 + 1.05128i
\(883\) −8.72980 −0.293781 −0.146891 0.989153i \(-0.546927\pi\)
−0.146891 + 0.989153i \(0.546927\pi\)
\(884\) 9.24319 23.5513i 0.310882 0.792114i
\(885\) 9.46582 5.64729i 0.318190 0.189832i
\(886\) 18.4579 + 17.1264i 0.620104 + 0.575373i
\(887\) −1.06148 + 0.511180i −0.0356409 + 0.0171637i −0.451619 0.892211i \(-0.649153\pi\)
0.415978 + 0.909374i \(0.363439\pi\)
\(888\) 36.4837 + 13.7194i 1.22431 + 0.460392i
\(889\) −1.38461 + 2.74527i −0.0464383 + 0.0920732i
\(890\) 1.65265 0.795873i 0.0553969 0.0266777i
\(891\) −30.6547 + 6.43335i −1.02697 + 0.215525i
\(892\) −0.681676 9.09633i −0.0228242 0.304568i
\(893\) −15.3628 19.2643i −0.514095 0.644655i
\(894\) 11.4232 + 2.43577i 0.382050 + 0.0814644i
\(895\) −1.35653 + 3.45638i −0.0453438 + 0.115534i
\(896\) 6.03813 35.6171i 0.201720 1.18988i
\(897\) −15.6752 31.3921i −0.523379 1.04815i
\(898\) −2.19397 29.2766i −0.0732139 0.976971i
\(899\) −7.25165 + 6.72854i −0.241856 + 0.224410i
\(900\) 2.23897 + 2.64834i 0.0746322 + 0.0882780i
\(901\) −3.85773 + 6.68178i −0.128520 + 0.222602i
\(902\) 18.2884 + 5.64123i 0.608937 + 0.187832i
\(903\) −6.87981 4.73117i −0.228946 0.157443i
\(904\) 6.70727 2.06892i 0.223081 0.0688112i
\(905\) −8.97666 + 39.3293i −0.298394 + 1.30735i
\(906\) 3.61671 + 7.24307i 0.120157 + 0.240635i
\(907\) 13.8167 17.3256i 0.458777 0.575289i −0.497606 0.867403i \(-0.665787\pi\)
0.956383 + 0.292115i \(0.0943589\pi\)
\(908\) 7.95625 + 7.38232i 0.264037 + 0.244991i
\(909\) −45.4992 29.1486i −1.50911 0.966797i
\(910\) −24.7680 37.7985i −0.821051 1.25301i
\(911\) 16.5577 + 5.10737i 0.548581 + 0.169215i 0.556642 0.830753i \(-0.312090\pi\)
−0.00806089 + 0.999968i \(0.502566\pi\)
\(912\) 16.4316 + 23.3746i 0.544105 + 0.774012i
\(913\) 19.4748 33.7314i 0.644522 1.11634i
\(914\) −41.7599 12.8812i −1.38129 0.426073i
\(915\) 9.13726 7.50321i 0.302069 0.248048i
\(916\) −0.882184 2.24777i −0.0291482 0.0742683i
\(917\) 7.95341 + 17.3207i 0.262645 + 0.571979i
\(918\) 56.1871 24.8861i 1.85445 0.821364i
\(919\) −0.549121 0.169381i −0.0181138 0.00558737i 0.285685 0.958324i \(-0.407779\pi\)
−0.303799 + 0.952736i \(0.598255\pi\)
\(920\) 7.79754 + 9.77780i 0.257077 + 0.322365i
\(921\) −9.06439 54.8030i −0.298682 1.80582i
\(922\) 21.7398 27.2609i 0.715963 0.897789i
\(923\) 65.9413 + 44.9580i 2.17049 + 1.47981i
\(924\) −8.16356 + 2.48226i −0.268561 + 0.0816603i
\(925\) 17.2239 11.7431i 0.566319 0.386110i
\(926\) 0.271511 3.62307i 0.00892242 0.119061i
\(927\) −21.9043 14.0327i −0.719430 0.460896i
\(928\) 11.0968 + 7.56567i 0.364270 + 0.248355i
\(929\) −6.61825 + 16.8630i −0.217138 + 0.553258i −0.997390 0.0722073i \(-0.976996\pi\)
0.780252 + 0.625466i \(0.215091\pi\)
\(930\) 5.80967 + 8.26450i 0.190507 + 0.271004i
\(931\) 22.7898 + 7.95570i 0.746905 + 0.260737i
\(932\) 4.34712 + 7.52943i 0.142395 + 0.246635i
\(933\) −19.2397 20.1491i −0.629879 0.659652i
\(934\) 43.6610 21.0260i 1.42863 0.687993i
\(935\) −41.6242 + 12.8394i −1.36126 + 0.419892i
\(936\) 36.0756 26.1395i 1.17917 0.854396i
\(937\) 13.3493 + 6.42871i 0.436104 + 0.210017i 0.639037 0.769176i \(-0.279333\pi\)
−0.202933 + 0.979193i \(0.565047\pi\)
\(938\) 0.906086 49.4193i 0.0295847 1.61360i
\(939\) 0.0868591 + 6.06692i 0.00283454 + 0.197986i
\(940\) −4.01626 + 5.03622i −0.130996 + 0.164264i
\(941\) 20.2393 13.7989i 0.659781 0.449831i −0.186580 0.982440i \(-0.559740\pi\)
0.846362 + 0.532608i \(0.178788\pi\)
\(942\) −12.9188 + 44.1142i −0.420918 + 1.43732i
\(943\) −8.05639 + 7.47524i −0.262352 + 0.243427i
\(944\) 11.2645 + 14.1252i 0.366627 + 0.459736i
\(945\) 4.59733 22.7045i 0.149551 0.738577i
\(946\) 6.29489 7.89354i 0.204665 0.256641i
\(947\) 1.08687 + 14.5032i 0.0353184 + 0.471292i 0.986621 + 0.163032i \(0.0521274\pi\)
−0.951302 + 0.308259i \(0.900254\pi\)
\(948\) −6.96091 + 7.72087i −0.226080 + 0.250762i
\(949\) −3.04094 + 5.26705i −0.0987129 + 0.170976i
\(950\) 11.8630 0.384887
\(951\) −47.9535 10.2251i −1.55500 0.331572i
\(952\) −40.1114 + 22.1880i −1.30002 + 0.719118i
\(953\) −2.30571 + 10.1020i −0.0746891 + 0.327234i −0.998445 0.0557477i \(-0.982246\pi\)
0.923756 + 0.382982i \(0.125103\pi\)
\(954\) 4.40667 2.27979i 0.142671 0.0738108i
\(955\) −1.07767 0.162433i −0.0348727 0.00525622i
\(956\) −1.00565 + 1.26104i −0.0325249 + 0.0407850i
\(957\) −3.69945 + 27.1788i −0.119586 + 0.878566i
\(958\) −2.81143 + 0.867212i −0.0908332 + 0.0280183i
\(959\) 17.3469 + 37.7776i 0.560161 + 1.21990i
\(960\) −9.51384 + 10.5525i −0.307058 + 0.340581i
\(961\) 13.1369 + 22.7537i 0.423770 + 0.733991i
\(962\) 48.8985 + 84.6946i 1.57655 + 2.73066i
\(963\) −7.63486 + 10.1573i −0.246030 + 0.327313i
\(964\) −5.64167 + 3.84643i −0.181706 + 0.123885i
\(965\) 10.5247 + 26.8164i 0.338801 + 0.863252i
\(966\) 5.25702 22.6134i 0.169142 0.727575i
\(967\) −18.4669 + 47.0528i −0.593855 + 1.51312i 0.245424 + 0.969416i \(0.421073\pi\)
−0.839279 + 0.543701i \(0.817022\pi\)
\(968\) 0.577335 + 2.52947i 0.0185562 + 0.0813002i
\(969\) 12.4684 42.5763i 0.400544 1.36775i
\(970\) 18.7504 + 9.02971i 0.602039 + 0.289927i
\(971\) −6.12612 15.6091i −0.196597 0.500920i 0.798248 0.602329i \(-0.205760\pi\)
−0.994845 + 0.101409i \(0.967665\pi\)
\(972\) −8.24271 1.26955i −0.264385 0.0407209i
\(973\) −10.4374 36.1791i −0.334608 1.15985i
\(974\) −28.3746 + 19.3455i −0.909180 + 0.619868i
\(975\) −0.341083 23.8239i −0.0109234 0.762975i
\(976\) 14.2061 + 13.1813i 0.454725 + 0.421923i
\(977\) 0.951845 12.7015i 0.0304522 0.406357i −0.961060 0.276341i \(-0.910878\pi\)
0.991512 0.130016i \(-0.0415028\pi\)
\(978\) −7.14685 + 24.4045i −0.228531 + 0.780371i
\(979\) −1.18976 + 2.06072i −0.0380249 + 0.0658610i
\(980\) 0.701942 6.27131i 0.0224227 0.200330i
\(981\) 0.934317 0.168311i 0.0298304 0.00537374i
\(982\) 4.27947 0.645027i 0.136563 0.0205836i
\(983\) −2.17486 + 1.04736i −0.0693671 + 0.0334054i −0.468246 0.883598i \(-0.655114\pi\)
0.398879 + 0.917004i \(0.369399\pi\)
\(984\) −11.0330 8.54304i −0.351720 0.272342i
\(985\) −38.2766 + 18.4331i −1.21959 + 0.587326i
\(986\) −4.02151 53.6634i −0.128071 1.70899i
\(987\) −32.7442 0.131525i −1.04226 0.00418650i
\(988\) −0.877745 + 11.7127i −0.0279248 + 0.372631i
\(989\) 2.11812 + 5.39689i 0.0673523 + 0.171611i
\(990\) 26.9921 + 7.48677i 0.857864 + 0.237945i
\(991\) 12.9313 32.9485i 0.410777 1.04664i −0.564456 0.825463i \(-0.690914\pi\)
0.975233 0.221180i \(-0.0709907\pi\)
\(992\) −4.70375 + 4.36444i −0.149344 + 0.138571i
\(993\) 13.6075 3.31146i 0.431821 0.105086i
\(994\) 14.6374 + 50.7374i 0.464269 + 1.60929i
\(995\) −28.1998 4.25043i −0.893993 0.134748i
\(996\) 8.01475 6.58144i 0.253957 0.208541i
\(997\) 5.02625 + 22.0214i 0.159183 + 0.697426i 0.990022 + 0.140913i \(0.0450038\pi\)
−0.830839 + 0.556513i \(0.812139\pi\)
\(998\) 3.29874 + 5.71358i 0.104420 + 0.180860i
\(999\) −12.7063 + 48.4950i −0.402009 + 1.53431i
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 441.2.z.a.142.41 yes 648
9.4 even 3 441.2.y.a.436.41 yes 648
49.39 even 21 441.2.y.a.88.41 648
441.382 even 21 inner 441.2.z.a.382.41 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.41 648 49.39 even 21
441.2.y.a.436.41 yes 648 9.4 even 3
441.2.z.a.142.41 yes 648 1.1 even 1 trivial
441.2.z.a.382.41 yes 648 441.382 even 21 inner