Properties

Label 756.2.bt.a.103.15
Level $756$
Weight $2$
Character 756.103
Analytic conductor $6.037$
Analytic rank $0$
Dimension $840$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(103,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 14, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bt (of order \(18\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(140\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 103.15
Character \(\chi\) \(=\) 756.103
Dual form 756.2.bt.a.367.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33467 + 0.467620i) q^{2} +(-0.284726 + 1.70849i) q^{3} +(1.56266 - 1.24823i) q^{4} +(1.73945 + 0.306711i) q^{5} +(-0.418909 - 2.41340i) q^{6} +(-0.667920 - 2.56006i) q^{7} +(-1.50193 + 2.39671i) q^{8} +(-2.83786 - 0.972903i) q^{9} +O(q^{10})\) \(q+(-1.33467 + 0.467620i) q^{2} +(-0.284726 + 1.70849i) q^{3} +(1.56266 - 1.24823i) q^{4} +(1.73945 + 0.306711i) q^{5} +(-0.418909 - 2.41340i) q^{6} +(-0.667920 - 2.56006i) q^{7} +(-1.50193 + 2.39671i) q^{8} +(-2.83786 - 0.972903i) q^{9} +(-2.46500 + 0.404043i) q^{10} +(1.66827 - 0.294162i) q^{11} +(1.68766 + 3.02520i) q^{12} +(2.43071 - 2.89681i) q^{13} +(2.08858 + 3.10448i) q^{14} +(-1.01928 + 2.88449i) q^{15} +(0.883831 - 3.90113i) q^{16} -0.108207i q^{17} +(4.24254 - 0.0285419i) q^{18} -2.50349 q^{19} +(3.10101 - 1.69195i) q^{20} +(4.56400 - 0.412219i) q^{21} +(-2.08903 + 1.17273i) q^{22} +(4.18758 - 4.99056i) q^{23} +(-3.66710 - 3.24844i) q^{24} +(-1.76686 - 0.643085i) q^{25} +(-1.88958 + 5.00292i) q^{26} +(2.47021 - 4.57144i) q^{27} +(-4.23928 - 3.16678i) q^{28} +(4.01785 - 3.37138i) q^{29} +(0.0115482 - 4.32647i) q^{30} +(4.44483 - 1.61779i) q^{31} +(0.644630 + 5.62000i) q^{32} +(0.0275704 + 2.93398i) q^{33} +(0.0505997 + 0.144420i) q^{34} +(-0.376614 - 4.65794i) q^{35} +(-5.64903 + 2.02199i) q^{36} +(-3.63400 - 6.29427i) q^{37} +(3.34131 - 1.17068i) q^{38} +(4.25707 + 4.97763i) q^{39} +(-3.34763 + 3.70828i) q^{40} +(-2.53806 + 3.02474i) q^{41} +(-5.89865 + 2.68439i) q^{42} +(-0.336096 + 0.923417i) q^{43} +(2.23977 - 2.54207i) q^{44} +(-4.63791 - 2.56272i) q^{45} +(-3.25533 + 8.61892i) q^{46} +(2.22328 + 0.809206i) q^{47} +(6.41339 + 2.62077i) q^{48} +(-6.10776 + 3.41983i) q^{49} +(2.65889 + 0.0320833i) q^{50} +(0.184870 + 0.0308093i) q^{51} +(0.182491 - 7.56082i) q^{52} +(-1.11508 - 1.93137i) q^{53} +(-1.15920 + 7.25646i) q^{54} +2.99209 q^{55} +(7.13887 + 2.24422i) q^{56} +(0.712808 - 4.27717i) q^{57} +(-3.78596 + 6.37849i) q^{58} +(0.834934 + 0.700593i) q^{59} +(2.00773 + 5.77979i) q^{60} +(0.0390959 - 0.107415i) q^{61} +(-5.17585 + 4.23769i) q^{62} +(-0.595219 + 7.91490i) q^{63} +(-3.48839 - 7.19938i) q^{64} +(5.11657 - 4.29331i) q^{65} +(-1.40879 - 3.90299i) q^{66} +(4.63395 + 0.817090i) q^{67} +(-0.135067 - 0.169091i) q^{68} +(7.33400 + 8.57536i) q^{69} +(2.68080 + 6.04067i) q^{70} +(12.7272 + 7.34807i) q^{71} +(6.59404 - 5.34028i) q^{72} +(12.5023 + 7.21823i) q^{73} +(7.79349 + 6.70141i) q^{74} +(1.60178 - 2.83556i) q^{75} +(-3.91210 + 3.12493i) q^{76} +(-1.86734 - 4.07440i) q^{77} +(-8.00941 - 4.65278i) q^{78} +(-7.21920 + 1.27294i) q^{79} +(2.73390 - 6.51473i) q^{80} +(7.10692 + 5.52193i) q^{81} +(1.97303 - 5.22387i) q^{82} +(6.51932 - 5.47036i) q^{83} +(6.61744 - 6.34109i) q^{84} +(0.0331883 - 0.188220i) q^{85} +(0.0167677 - 1.38962i) q^{86} +(4.61597 + 7.82437i) q^{87} +(-1.80062 + 4.44017i) q^{88} +14.5721i q^{89} +(7.38843 + 1.25159i) q^{90} +(-9.03950 - 4.28791i) q^{91} +(0.314392 - 13.0256i) q^{92} +(1.49841 + 8.05456i) q^{93} +(-3.34573 - 0.0403710i) q^{94} +(-4.35468 - 0.767847i) q^{95} +(-9.78525 - 0.498820i) q^{96} +(4.44084 - 12.2011i) q^{97} +(6.55264 - 7.42044i) q^{98} +(-5.02052 - 0.788277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33467 + 0.467620i −0.943751 + 0.330657i
\(3\) −0.284726 + 1.70849i −0.164387 + 0.986396i
\(4\) 1.56266 1.24823i 0.781331 0.624116i
\(5\) 1.73945 + 0.306711i 0.777904 + 0.137165i 0.548483 0.836162i \(-0.315206\pi\)
0.229421 + 0.973327i \(0.426317\pi\)
\(6\) −0.418909 2.41340i −0.171019 0.985268i
\(7\) −0.667920 2.56006i −0.252450 0.967610i
\(8\) −1.50193 + 2.39671i −0.531014 + 0.847363i
\(9\) −2.83786 0.972903i −0.945954 0.324301i
\(10\) −2.46500 + 0.404043i −0.779502 + 0.127770i
\(11\) 1.66827 0.294162i 0.503003 0.0886931i 0.0836116 0.996498i \(-0.473354\pi\)
0.419392 + 0.907805i \(0.362243\pi\)
\(12\) 1.68766 + 3.02520i 0.487185 + 0.873299i
\(13\) 2.43071 2.89681i 0.674157 0.803430i −0.315186 0.949030i \(-0.602067\pi\)
0.989343 + 0.145600i \(0.0465114\pi\)
\(14\) 2.08858 + 3.10448i 0.558197 + 0.829708i
\(15\) −1.01928 + 2.88449i −0.263177 + 0.744773i
\(16\) 0.883831 3.90113i 0.220958 0.975283i
\(17\) 0.108207i 0.0262440i −0.999914 0.0131220i \(-0.995823\pi\)
0.999914 0.0131220i \(-0.00417698\pi\)
\(18\) 4.24254 0.0285419i 0.999977 0.00672739i
\(19\) −2.50349 −0.574339 −0.287169 0.957880i \(-0.592714\pi\)
−0.287169 + 0.957880i \(0.592714\pi\)
\(20\) 3.10101 1.69195i 0.693408 0.378331i
\(21\) 4.56400 0.412219i 0.995946 0.0899536i
\(22\) −2.08903 + 1.17273i −0.445383 + 0.250026i
\(23\) 4.18758 4.99056i 0.873170 1.04060i −0.125652 0.992074i \(-0.540102\pi\)
0.998822 0.0485289i \(-0.0154533\pi\)
\(24\) −3.66710 3.24844i −0.748544 0.663085i
\(25\) −1.76686 0.643085i −0.353372 0.128617i
\(26\) −1.88958 + 5.00292i −0.370577 + 0.981153i
\(27\) 2.47021 4.57144i 0.475391 0.879774i
\(28\) −4.23928 3.16678i −0.801148 0.598466i
\(29\) 4.01785 3.37138i 0.746096 0.626049i −0.188371 0.982098i \(-0.560321\pi\)
0.934467 + 0.356049i \(0.115876\pi\)
\(30\) 0.0115482 4.32647i 0.00210841 0.789902i
\(31\) 4.44483 1.61779i 0.798315 0.290563i 0.0895270 0.995984i \(-0.471464\pi\)
0.708788 + 0.705421i \(0.249242\pi\)
\(32\) 0.644630 + 5.62000i 0.113956 + 0.993486i
\(33\) 0.0275704 + 2.93398i 0.00479939 + 0.510740i
\(34\) 0.0505997 + 0.144420i 0.00867777 + 0.0247678i
\(35\) −0.376614 4.65794i −0.0636593 0.787335i
\(36\) −5.64903 + 2.02199i −0.941505 + 0.336999i
\(37\) −3.63400 6.29427i −0.597425 1.03477i −0.993200 0.116423i \(-0.962857\pi\)
0.395774 0.918348i \(-0.370476\pi\)
\(38\) 3.34131 1.17068i 0.542033 0.189909i
\(39\) 4.25707 + 4.97763i 0.681677 + 0.797059i
\(40\) −3.34763 + 3.70828i −0.529307 + 0.586331i
\(41\) −2.53806 + 3.02474i −0.396378 + 0.472385i −0.926912 0.375278i \(-0.877547\pi\)
0.530534 + 0.847664i \(0.321992\pi\)
\(42\) −5.89865 + 2.68439i −0.910181 + 0.414211i
\(43\) −0.336096 + 0.923417i −0.0512542 + 0.140820i −0.962678 0.270649i \(-0.912762\pi\)
0.911424 + 0.411469i \(0.134984\pi\)
\(44\) 2.23977 2.54207i 0.337658 0.383231i
\(45\) −4.63791 2.56272i −0.691378 0.382027i
\(46\) −3.25533 + 8.61892i −0.479972 + 1.27079i
\(47\) 2.22328 + 0.809206i 0.324298 + 0.118035i 0.499039 0.866580i \(-0.333687\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(48\) 6.41339 + 2.62077i 0.925693 + 0.378275i
\(49\) −6.10776 + 3.41983i −0.872538 + 0.488547i
\(50\) 2.65889 + 0.0320833i 0.376024 + 0.00453727i
\(51\) 0.184870 + 0.0308093i 0.0258870 + 0.00431417i
\(52\) 0.182491 7.56082i 0.0253069 1.04850i
\(53\) −1.11508 1.93137i −0.153168 0.265294i 0.779223 0.626747i \(-0.215614\pi\)
−0.932390 + 0.361453i \(0.882281\pi\)
\(54\) −1.15920 + 7.25646i −0.157747 + 0.987480i
\(55\) 2.99209 0.403454
\(56\) 7.13887 + 2.24422i 0.953972 + 0.299897i
\(57\) 0.712808 4.27717i 0.0944137 0.566526i
\(58\) −3.78596 + 6.37849i −0.497121 + 0.837537i
\(59\) 0.834934 + 0.700593i 0.108699 + 0.0912094i 0.695517 0.718509i \(-0.255175\pi\)
−0.586818 + 0.809719i \(0.699620\pi\)
\(60\) 2.00773 + 5.77979i 0.259197 + 0.746167i
\(61\) 0.0390959 0.107415i 0.00500572 0.0137531i −0.937165 0.348888i \(-0.886560\pi\)
0.942170 + 0.335134i \(0.108782\pi\)
\(62\) −5.17585 + 4.23769i −0.657334 + 0.538188i
\(63\) −0.595219 + 7.91490i −0.0749905 + 0.997184i
\(64\) −3.48839 7.19938i −0.436049 0.899923i
\(65\) 5.11657 4.29331i 0.634633 0.532520i
\(66\) −1.40879 3.90299i −0.173409 0.480425i
\(67\) 4.63395 + 0.817090i 0.566127 + 0.0998234i 0.449384 0.893339i \(-0.351644\pi\)
0.116743 + 0.993162i \(0.462755\pi\)
\(68\) −0.135067 0.169091i −0.0163793 0.0205053i
\(69\) 7.33400 + 8.57536i 0.882909 + 1.03235i
\(70\) 2.68080 + 6.04067i 0.320417 + 0.721999i
\(71\) 12.7272 + 7.34807i 1.51045 + 0.872056i 0.999926 + 0.0121899i \(0.00388025\pi\)
0.510520 + 0.859866i \(0.329453\pi\)
\(72\) 6.59404 5.34028i 0.777115 0.629358i
\(73\) 12.5023 + 7.21823i 1.46329 + 0.844830i 0.999162 0.0409380i \(-0.0130346\pi\)
0.464128 + 0.885768i \(0.346368\pi\)
\(74\) 7.79349 + 6.70141i 0.905975 + 0.779023i
\(75\) 1.60178 2.83556i 0.184957 0.327422i
\(76\) −3.91210 + 3.12493i −0.448749 + 0.358454i
\(77\) −1.86734 4.07440i −0.212804 0.464320i
\(78\) −8.00941 4.65278i −0.906887 0.526824i
\(79\) −7.21920 + 1.27294i −0.812223 + 0.143217i −0.564307 0.825565i \(-0.690857\pi\)
−0.247916 + 0.968782i \(0.579746\pi\)
\(80\) 2.73390 6.51473i 0.305659 0.728369i
\(81\) 7.10692 + 5.52193i 0.789658 + 0.613547i
\(82\) 1.97303 5.22387i 0.217885 0.576880i
\(83\) 6.51932 5.47036i 0.715589 0.600450i −0.210572 0.977578i \(-0.567533\pi\)
0.926161 + 0.377128i \(0.123088\pi\)
\(84\) 6.61744 6.34109i 0.722022 0.691870i
\(85\) 0.0331883 0.188220i 0.00359977 0.0204153i
\(86\) 0.0167677 1.38962i 0.00180811 0.149846i
\(87\) 4.61597 + 7.82437i 0.494884 + 0.838861i
\(88\) −1.80062 + 4.44017i −0.191946 + 0.473324i
\(89\) 14.5721i 1.54463i 0.635237 + 0.772317i \(0.280902\pi\)
−0.635237 + 0.772317i \(0.719098\pi\)
\(90\) 7.38843 + 1.25159i 0.778809 + 0.131929i
\(91\) −9.03950 4.28791i −0.947598 0.449496i
\(92\) 0.314392 13.0256i 0.0327776 1.35802i
\(93\) 1.49841 + 8.05456i 0.155378 + 0.835219i
\(94\) −3.34573 0.0403710i −0.345086 0.00416395i
\(95\) −4.35468 0.767847i −0.446780 0.0787794i
\(96\) −9.78525 0.498820i −0.998703 0.0509106i
\(97\) 4.44084 12.2011i 0.450899 1.23884i −0.481193 0.876615i \(-0.659796\pi\)
0.932092 0.362221i \(-0.117981\pi\)
\(98\) 6.55264 7.42044i 0.661917 0.749577i
\(99\) −5.02052 0.788277i −0.504581 0.0792249i
\(100\) −3.56373 + 1.20053i −0.356373 + 0.120053i
\(101\) 8.34217 + 9.94181i 0.830077 + 0.989247i 0.999993 + 0.00378834i \(0.00120587\pi\)
−0.169916 + 0.985459i \(0.554350\pi\)
\(102\) −0.261147 + 0.0453288i −0.0258574 + 0.00448822i
\(103\) 2.18841 12.4111i 0.215631 1.22290i −0.664178 0.747574i \(-0.731218\pi\)
0.879809 0.475328i \(-0.157670\pi\)
\(104\) 3.29203 + 10.1765i 0.322810 + 0.997888i
\(105\) 8.06526 + 0.682797i 0.787089 + 0.0666342i
\(106\) 2.39140 + 2.05630i 0.232274 + 0.199726i
\(107\) 4.87433 + 2.81419i 0.471219 + 0.272058i 0.716750 0.697330i \(-0.245629\pi\)
−0.245531 + 0.969389i \(0.578962\pi\)
\(108\) −1.84612 10.2270i −0.177643 0.984095i
\(109\) −0.888204 1.53841i −0.0850745 0.147353i 0.820348 0.571864i \(-0.193779\pi\)
−0.905423 + 0.424511i \(0.860446\pi\)
\(110\) −3.99344 + 1.39916i −0.380760 + 0.133405i
\(111\) 11.7884 4.41650i 1.11890 0.419195i
\(112\) −10.5774 + 0.342991i −0.999475 + 0.0324096i
\(113\) −10.0812 + 3.66926i −0.948360 + 0.345175i −0.769462 0.638693i \(-0.779476\pi\)
−0.178898 + 0.983868i \(0.557253\pi\)
\(114\) 1.04873 + 6.04192i 0.0982228 + 0.565878i
\(115\) 8.81472 7.39643i 0.821977 0.689721i
\(116\) 2.07028 10.2835i 0.192221 0.954803i
\(117\) −9.71633 + 5.85589i −0.898275 + 0.541378i
\(118\) −1.44197 0.544625i −0.132744 0.0501368i
\(119\) −0.277015 + 0.0722735i −0.0253940 + 0.00662530i
\(120\) −5.38239 6.77523i −0.491343 0.618491i
\(121\) −7.64001 + 2.78074i −0.694547 + 0.252794i
\(122\) −0.00195048 + 0.161645i −0.000176588 + 0.0146347i
\(123\) −4.44508 5.19747i −0.400800 0.468640i
\(124\) 4.92640 8.07624i 0.442404 0.725267i
\(125\) −10.5243 6.07623i −0.941325 0.543474i
\(126\) −2.90675 10.8421i −0.258954 0.965890i
\(127\) −13.6677 + 7.89105i −1.21281 + 0.700218i −0.963371 0.268172i \(-0.913580\pi\)
−0.249442 + 0.968390i \(0.580247\pi\)
\(128\) 8.02241 + 7.97752i 0.709088 + 0.705120i
\(129\) −1.48195 0.837138i −0.130479 0.0737059i
\(130\) −4.82127 + 8.12275i −0.422853 + 0.712412i
\(131\) −14.5624 12.2193i −1.27232 1.06761i −0.994254 0.107046i \(-0.965861\pi\)
−0.278070 0.960561i \(-0.589695\pi\)
\(132\) 3.70537 + 4.55041i 0.322511 + 0.396062i
\(133\) 1.67213 + 6.40906i 0.144992 + 0.555736i
\(134\) −6.56686 + 1.07639i −0.567290 + 0.0929855i
\(135\) 5.69890 7.19414i 0.490483 0.619173i
\(136\) 0.259340 + 0.162519i 0.0222382 + 0.0139359i
\(137\) −2.62661 0.956007i −0.224406 0.0816772i 0.227370 0.973808i \(-0.426987\pi\)
−0.451776 + 0.892131i \(0.649210\pi\)
\(138\) −13.7984 8.01572i −1.17460 0.682343i
\(139\) −2.76113 + 15.6591i −0.234196 + 1.32819i 0.610105 + 0.792321i \(0.291127\pi\)
−0.844301 + 0.535870i \(0.819984\pi\)
\(140\) −6.40271 6.80868i −0.541128 0.575439i
\(141\) −2.01554 + 3.56804i −0.169739 + 0.300483i
\(142\) −20.4227 3.85571i −1.71384 0.323564i
\(143\) 3.20296 5.54769i 0.267845 0.463921i
\(144\) −6.30361 + 10.2110i −0.525301 + 0.850916i
\(145\) 8.02288 4.63201i 0.666264 0.384667i
\(146\) −20.0618 3.78758i −1.66033 0.313462i
\(147\) −4.10369 11.4088i −0.338467 0.940978i
\(148\) −13.5354 5.29974i −1.11260 0.435636i
\(149\) −16.6498 + 6.06002i −1.36400 + 0.496456i −0.917289 0.398221i \(-0.869628\pi\)
−0.446713 + 0.894677i \(0.647405\pi\)
\(150\) −0.811869 + 4.53355i −0.0662889 + 0.370162i
\(151\) 17.8573 3.14872i 1.45321 0.256240i 0.609390 0.792871i \(-0.291414\pi\)
0.843817 + 0.536631i \(0.180303\pi\)
\(152\) 3.76007 6.00012i 0.304982 0.486674i
\(153\) −0.105275 + 0.307076i −0.00851095 + 0.0248256i
\(154\) 4.39755 + 4.56475i 0.354364 + 0.367838i
\(155\) 8.22774 1.45077i 0.660868 0.116529i
\(156\) 12.8656 + 2.46455i 1.03007 + 0.197322i
\(157\) 1.35528 1.61516i 0.108163 0.128903i −0.709247 0.704960i \(-0.750965\pi\)
0.817410 + 0.576057i \(0.195409\pi\)
\(158\) 9.03996 5.07479i 0.719181 0.403729i
\(159\) 3.61722 1.35519i 0.286864 0.107473i
\(160\) −0.602419 + 9.97341i −0.0476254 + 0.788467i
\(161\) −15.5731 7.38713i −1.22733 0.582187i
\(162\) −12.0675 4.04658i −0.948114 0.317930i
\(163\) −19.6034 11.3180i −1.53546 0.886497i −0.999096 0.0425094i \(-0.986465\pi\)
−0.536362 0.843988i \(-0.680202\pi\)
\(164\) −0.190551 + 7.89474i −0.0148795 + 0.616476i
\(165\) −0.851928 + 5.11196i −0.0663225 + 0.397965i
\(166\) −6.14306 + 10.3497i −0.476794 + 0.803290i
\(167\) −5.75542 + 2.09480i −0.445368 + 0.162101i −0.554962 0.831876i \(-0.687267\pi\)
0.109594 + 0.993976i \(0.465045\pi\)
\(168\) −5.86685 + 11.5577i −0.452638 + 0.891695i
\(169\) −0.225714 1.28009i −0.0173626 0.0984684i
\(170\) 0.0437202 + 0.266730i 0.00335319 + 0.0204573i
\(171\) 7.10455 + 2.43565i 0.543298 + 0.186259i
\(172\) 0.627434 + 1.86252i 0.0478414 + 0.142016i
\(173\) 0.405981 + 0.483829i 0.0308662 + 0.0367849i 0.781257 0.624210i \(-0.214579\pi\)
−0.750391 + 0.660995i \(0.770135\pi\)
\(174\) −9.81961 8.28440i −0.744423 0.628038i
\(175\) −0.466211 + 4.95279i −0.0352422 + 0.374396i
\(176\) 0.326908 6.76815i 0.0246416 0.510168i
\(177\) −1.43468 + 1.22700i −0.107837 + 0.0922268i
\(178\) −6.81418 19.4488i −0.510745 1.45775i
\(179\) 6.86567i 0.513164i 0.966522 + 0.256582i \(0.0825964\pi\)
−0.966522 + 0.256582i \(0.917404\pi\)
\(180\) −10.4464 + 1.78453i −0.778625 + 0.133011i
\(181\) 22.5668 13.0289i 1.67737 0.968433i 0.714049 0.700095i \(-0.246859\pi\)
0.963325 0.268337i \(-0.0864741\pi\)
\(182\) 14.0698 + 1.49588i 1.04293 + 0.110882i
\(183\) 0.172386 + 0.0973788i 0.0127431 + 0.00719845i
\(184\) 5.67144 + 17.5319i 0.418104 + 1.29247i
\(185\) −4.39062 12.0631i −0.322805 0.886899i
\(186\) −5.76635 10.0495i −0.422809 0.736862i
\(187\) −0.0318303 0.180519i −0.00232766 0.0132008i
\(188\) 4.48431 1.51065i 0.327052 0.110175i
\(189\) −13.3530 3.27050i −0.971291 0.237894i
\(190\) 6.17110 1.01152i 0.447698 0.0733831i
\(191\) 2.65942 0.468927i 0.192429 0.0339304i −0.0766030 0.997062i \(-0.524407\pi\)
0.269032 + 0.963131i \(0.413296\pi\)
\(192\) 13.2933 3.91002i 0.959361 0.282182i
\(193\) 17.2785 6.28886i 1.24373 0.452682i 0.365454 0.930830i \(-0.380914\pi\)
0.878279 + 0.478148i \(0.158692\pi\)
\(194\) −0.221552 + 18.3610i −0.0159065 + 1.31825i
\(195\) 5.87825 + 9.96402i 0.420950 + 0.713538i
\(196\) −5.27564 + 12.9679i −0.376831 + 0.926282i
\(197\) 4.41272 + 7.64305i 0.314393 + 0.544545i 0.979308 0.202374i \(-0.0648656\pi\)
−0.664915 + 0.746919i \(0.731532\pi\)
\(198\) 7.06933 1.29561i 0.502395 0.0920750i
\(199\) 12.3523 0.875630 0.437815 0.899065i \(-0.355752\pi\)
0.437815 + 0.899065i \(0.355752\pi\)
\(200\) 4.19500 3.26878i 0.296631 0.231137i
\(201\) −2.71539 + 7.68440i −0.191529 + 0.542016i
\(202\) −15.7830 9.36802i −1.11049 0.659132i
\(203\) −11.3145 8.03411i −0.794123 0.563884i
\(204\) 0.327347 0.182616i 0.0229189 0.0127857i
\(205\) −5.34254 + 4.48292i −0.373139 + 0.313101i
\(206\) 2.88288 + 17.5880i 0.200860 + 1.22541i
\(207\) −16.7391 + 10.0884i −1.16345 + 0.701193i
\(208\) −9.15249 12.0428i −0.634611 0.835019i
\(209\) −4.17650 + 0.736429i −0.288894 + 0.0509399i
\(210\) −11.0837 + 2.86017i −0.764849 + 0.197371i
\(211\) 1.09745 + 3.01522i 0.0755516 + 0.207576i 0.971719 0.236139i \(-0.0758822\pi\)
−0.896168 + 0.443716i \(0.853660\pi\)
\(212\) −4.15329 1.62621i −0.285249 0.111688i
\(213\) −16.1779 + 19.6521i −1.10849 + 1.34654i
\(214\) −7.82157 1.47667i −0.534671 0.100943i
\(215\) −0.867844 + 1.50315i −0.0591865 + 0.102514i
\(216\) 7.24631 + 12.7864i 0.493049 + 0.870001i
\(217\) −7.11041 10.2985i −0.482686 0.699105i
\(218\) 1.90485 + 1.63793i 0.129013 + 0.110934i
\(219\) −15.8920 + 19.3049i −1.07388 + 1.30450i
\(220\) 4.67563 3.73483i 0.315231 0.251802i
\(221\) −0.313454 0.263019i −0.0210852 0.0176926i
\(222\) −13.6683 + 11.4070i −0.917355 + 0.765589i
\(223\) −3.18396 18.0571i −0.213214 1.20919i −0.883980 0.467526i \(-0.845146\pi\)
0.670766 0.741669i \(-0.265966\pi\)
\(224\) 13.9570 5.40400i 0.932539 0.361070i
\(225\) 4.38845 + 3.54397i 0.292563 + 0.236265i
\(226\) 11.7392 9.61141i 0.780881 0.639341i
\(227\) −2.72857 15.4745i −0.181102 1.02708i −0.930863 0.365370i \(-0.880943\pi\)
0.749761 0.661709i \(-0.230169\pi\)
\(228\) −4.22503 7.57353i −0.279809 0.501569i
\(229\) −3.08694 8.48128i −0.203990 0.560459i 0.794940 0.606687i \(-0.207502\pi\)
−0.998931 + 0.0462284i \(0.985280\pi\)
\(230\) −8.30598 + 13.9937i −0.547680 + 0.922717i
\(231\) 7.49274 2.03025i 0.492986 0.133580i
\(232\) 2.04565 + 14.6932i 0.134304 + 0.964655i
\(233\) −12.9597 22.4469i −0.849021 1.47055i −0.882083 0.471094i \(-0.843859\pi\)
0.0330616 0.999453i \(-0.489474\pi\)
\(234\) 10.2297 12.3592i 0.668737 0.807947i
\(235\) 3.61908 + 2.08947i 0.236082 + 0.136302i
\(236\) 2.17922 + 0.0525986i 0.141855 + 0.00342387i
\(237\) −0.119307 12.6964i −0.00774980 0.824717i
\(238\) 0.335926 0.225999i 0.0217749 0.0146493i
\(239\) −19.0690 3.36239i −1.23347 0.217495i −0.481357 0.876525i \(-0.659856\pi\)
−0.752117 + 0.659030i \(0.770967\pi\)
\(240\) 10.3519 + 6.52575i 0.668214 + 0.421235i
\(241\) 6.89422 18.9417i 0.444096 1.22014i −0.492679 0.870211i \(-0.663982\pi\)
0.936775 0.349932i \(-0.113795\pi\)
\(242\) 8.89653 7.28398i 0.571891 0.468232i
\(243\) −11.4577 + 10.5699i −0.735010 + 0.678056i
\(244\) −0.0729853 0.216654i −0.00467241 0.0138699i
\(245\) −11.6730 + 4.07528i −0.745762 + 0.260360i
\(246\) 8.36314 + 4.85827i 0.533214 + 0.309752i
\(247\) −6.08524 + 7.25211i −0.387195 + 0.461441i
\(248\) −2.79848 + 13.0828i −0.177704 + 0.830756i
\(249\) 7.48982 + 12.6957i 0.474648 + 0.804560i
\(250\) 16.8878 + 3.18834i 1.06808 + 0.201648i
\(251\) 9.22500 + 15.9782i 0.582277 + 1.00853i 0.995209 + 0.0977715i \(0.0311714\pi\)
−0.412932 + 0.910762i \(0.635495\pi\)
\(252\) 8.94952 + 13.1113i 0.563767 + 0.825934i
\(253\) 5.51799 9.55744i 0.346913 0.600871i
\(254\) 14.5518 16.9232i 0.913061 1.06186i
\(255\) 0.312122 + 0.110293i 0.0195458 + 0.00690681i
\(256\) −14.4377 6.89588i −0.902355 0.430993i
\(257\) −2.03940 5.60321i −0.127214 0.349519i 0.859692 0.510813i \(-0.170655\pi\)
−0.986906 + 0.161294i \(0.948433\pi\)
\(258\) 2.36937 + 0.424308i 0.147511 + 0.0264163i
\(259\) −13.6864 + 13.5073i −0.850435 + 0.839303i
\(260\) 2.63642 13.0957i 0.163504 0.812159i
\(261\) −14.6821 + 5.65853i −0.908801 + 0.350254i
\(262\) 25.1499 + 9.49902i 1.55377 + 0.586851i
\(263\) 13.3248 + 15.8799i 0.821645 + 0.979198i 0.999989 0.00477025i \(-0.00151842\pi\)
−0.178344 + 0.983968i \(0.557074\pi\)
\(264\) −7.07330 4.34056i −0.435331 0.267143i
\(265\) −1.34724 3.70152i −0.0827606 0.227383i
\(266\) −5.22874 7.77203i −0.320594 0.476534i
\(267\) −24.8962 4.14905i −1.52362 0.253917i
\(268\) 8.26122 4.50741i 0.504634 0.275334i
\(269\) −5.62385 + 3.24693i −0.342892 + 0.197969i −0.661550 0.749901i \(-0.730101\pi\)
0.318658 + 0.947870i \(0.396768\pi\)
\(270\) −4.24201 + 12.2667i −0.258160 + 0.746527i
\(271\) −4.86705 + 8.42998i −0.295652 + 0.512085i −0.975136 0.221605i \(-0.928870\pi\)
0.679484 + 0.733690i \(0.262204\pi\)
\(272\) −0.422129 0.0956365i −0.0255953 0.00579882i
\(273\) 9.89963 14.2230i 0.599153 0.860815i
\(274\) 3.95269 + 0.0476949i 0.238791 + 0.00288135i
\(275\) −3.13678 0.553099i −0.189155 0.0333531i
\(276\) 22.1646 + 4.24587i 1.33415 + 0.255571i
\(277\) −1.87944 + 1.57703i −0.112924 + 0.0947548i −0.697501 0.716583i \(-0.745705\pi\)
0.584577 + 0.811338i \(0.301260\pi\)
\(278\) −3.63735 22.1909i −0.218153 1.33092i
\(279\) −14.1878 + 0.266666i −0.849399 + 0.0159649i
\(280\) 11.7293 + 6.09328i 0.700963 + 0.364143i
\(281\) 0.937973 + 0.341394i 0.0559548 + 0.0203659i 0.369846 0.929093i \(-0.379410\pi\)
−0.313891 + 0.949459i \(0.601633\pi\)
\(282\) 1.02159 5.70464i 0.0608348 0.339707i
\(283\) 0.741227 4.20371i 0.0440614 0.249885i −0.954819 0.297187i \(-0.903951\pi\)
0.998881 + 0.0473027i \(0.0150625\pi\)
\(284\) 29.0605 4.40399i 1.72442 0.261329i
\(285\) 2.55175 7.22129i 0.151153 0.427752i
\(286\) −1.68067 + 8.90207i −0.0993800 + 0.526391i
\(287\) 9.43873 + 4.47729i 0.557151 + 0.264286i
\(288\) 3.63835 16.5760i 0.214392 0.976748i
\(289\) 16.9883 0.999311
\(290\) −8.54183 + 9.93384i −0.501594 + 0.583335i
\(291\) 19.5810 + 11.0611i 1.14786 + 0.648413i
\(292\) 28.5470 4.32617i 1.67059 0.253170i
\(293\) −11.3597 2.00303i −0.663643 0.117018i −0.168327 0.985731i \(-0.553836\pi\)
−0.495316 + 0.868713i \(0.664948\pi\)
\(294\) 10.8120 + 13.3079i 0.630570 + 0.776133i
\(295\) 1.23744 + 1.47473i 0.0720467 + 0.0858619i
\(296\) 20.5435 + 0.743950i 1.19407 + 0.0432412i
\(297\) 2.77624 8.35305i 0.161094 0.484693i
\(298\) 19.3881 15.8739i 1.12312 0.919548i
\(299\) −4.27790 24.2612i −0.247398 1.40306i
\(300\) −1.03640 6.43041i −0.0598367 0.371260i
\(301\) 2.58848 + 0.243656i 0.149198 + 0.0140441i
\(302\) −22.3611 + 12.5529i −1.28674 + 0.722340i
\(303\) −19.3607 + 11.4218i −1.11224 + 0.656165i
\(304\) −2.21266 + 9.76643i −0.126905 + 0.560143i
\(305\) 0.100951 0.174852i 0.00578042 0.0100120i
\(306\) −0.00308843 0.459072i −0.000176554 0.0262434i
\(307\) −15.7016 + 27.1960i −0.896139 + 1.55216i −0.0637508 + 0.997966i \(0.520306\pi\)
−0.832388 + 0.554193i \(0.813027\pi\)
\(308\) −8.00382 4.03603i −0.456060 0.229974i
\(309\) 20.5811 + 7.27264i 1.17082 + 0.413726i
\(310\) −10.3029 + 5.78375i −0.585163 + 0.328495i
\(311\) 1.15581 6.55494i 0.0655401 0.371696i −0.934343 0.356376i \(-0.884012\pi\)
0.999883 0.0153202i \(-0.00487675\pi\)
\(312\) −18.3238 + 2.72687i −1.03738 + 0.154379i
\(313\) 4.72936 + 5.63623i 0.267319 + 0.318578i 0.882960 0.469449i \(-0.155547\pi\)
−0.615641 + 0.788027i \(0.711103\pi\)
\(314\) −1.05356 + 2.78945i −0.0594559 + 0.157418i
\(315\) −3.46294 + 13.5850i −0.195115 + 0.765427i
\(316\) −9.69225 + 11.0004i −0.545232 + 0.618822i
\(317\) −15.2102 5.53604i −0.854287 0.310935i −0.122500 0.992468i \(-0.539091\pi\)
−0.731787 + 0.681533i \(0.761313\pi\)
\(318\) −4.19406 + 3.50020i −0.235191 + 0.196282i
\(319\) 5.71114 6.80628i 0.319763 0.381078i
\(320\) −3.85974 13.5929i −0.215766 0.759864i
\(321\) −6.19587 + 7.52645i −0.345819 + 0.420086i
\(322\) 24.2392 + 2.57706i 1.35080 + 0.143614i
\(323\) 0.270894i 0.0150730i
\(324\) 17.9984 0.242181i 0.999909 0.0134545i
\(325\) −6.15762 + 3.55510i −0.341563 + 0.197202i
\(326\) 31.4565 + 5.93884i 1.74222 + 0.328922i
\(327\) 2.88126 1.07946i 0.159334 0.0596942i
\(328\) −3.43742 10.6259i −0.189800 0.586720i
\(329\) 0.586641 6.23219i 0.0323426 0.343592i
\(330\) −1.25342 7.22113i −0.0689982 0.397510i
\(331\) 3.66580 10.0717i 0.201491 0.553591i −0.797256 0.603641i \(-0.793716\pi\)
0.998747 + 0.0500501i \(0.0159381\pi\)
\(332\) 3.35922 16.6860i 0.184361 0.915761i
\(333\) 4.18907 + 21.3978i 0.229560 + 1.17259i
\(334\) 6.70199 5.48721i 0.366717 0.300247i
\(335\) 7.80989 + 2.84257i 0.426700 + 0.155306i
\(336\) 2.42568 18.1691i 0.132332 0.991205i
\(337\) 17.7746 + 14.9147i 0.968245 + 0.812454i 0.982275 0.187447i \(-0.0600214\pi\)
−0.0140295 + 0.999902i \(0.504466\pi\)
\(338\) 0.899848 + 1.60294i 0.0489453 + 0.0871885i
\(339\) −3.39850 18.2684i −0.184581 0.992201i
\(340\) −0.183080 0.335551i −0.00992892 0.0181978i
\(341\) 6.93930 4.00641i 0.375784 0.216959i
\(342\) −10.6211 + 0.0714543i −0.574326 + 0.00386380i
\(343\) 12.8344 + 13.3520i 0.692995 + 0.720943i
\(344\) −1.70836 2.19244i −0.0921088 0.118208i
\(345\) 10.1269 + 17.1658i 0.545216 + 0.924176i
\(346\) −0.768097 0.455905i −0.0412932 0.0245096i
\(347\) 0.0265919 + 0.0730606i 0.00142753 + 0.00392210i 0.940404 0.340058i \(-0.110447\pi\)
−0.938977 + 0.343980i \(0.888225\pi\)
\(348\) 16.9798 + 6.46505i 0.910215 + 0.346563i
\(349\) −5.65540 6.73984i −0.302726 0.360775i 0.593140 0.805100i \(-0.297888\pi\)
−0.895866 + 0.444324i \(0.853444\pi\)
\(350\) −1.69379 6.82833i −0.0905369 0.364990i
\(351\) −7.23823 18.2676i −0.386348 0.975050i
\(352\) 2.72861 + 9.18608i 0.145435 + 0.489620i
\(353\) −1.61338 + 4.43273i −0.0858716 + 0.235930i −0.975195 0.221349i \(-0.928954\pi\)
0.889323 + 0.457280i \(0.151176\pi\)
\(354\) 1.34105 2.30852i 0.0712761 0.122696i
\(355\) 19.8846 + 16.6852i 1.05537 + 0.885557i
\(356\) 18.1893 + 22.7712i 0.964032 + 1.20687i
\(357\) −0.0446049 0.493856i −0.00236074 0.0261376i
\(358\) −3.21053 9.16337i −0.169682 0.484299i
\(359\) 13.5198i 0.713547i 0.934191 + 0.356774i \(0.116123\pi\)
−0.934191 + 0.356774i \(0.883877\pi\)
\(360\) 13.1079 7.26667i 0.690847 0.382987i
\(361\) −12.7326 −0.670135
\(362\) −24.0265 + 27.9419i −1.26280 + 1.46860i
\(363\) −2.57554 13.8446i −0.135181 0.726654i
\(364\) −19.4780 + 4.58284i −1.02093 + 0.240206i
\(365\) 19.5332 + 16.3903i 1.02242 + 0.857910i
\(366\) −0.275614 0.0493570i −0.0144066 0.00257993i
\(367\) 0.273468 + 1.55092i 0.0142749 + 0.0809571i 0.991113 0.133023i \(-0.0424684\pi\)
−0.976838 + 0.213980i \(0.931357\pi\)
\(368\) −15.7677 20.7471i −0.821950 1.08152i
\(369\) 10.1454 6.11452i 0.528151 0.318309i
\(370\) 11.5010 + 14.0471i 0.597907 + 0.730274i
\(371\) −4.19964 + 4.14466i −0.218034 + 0.215180i
\(372\) 12.3955 + 10.7162i 0.642675 + 0.555609i
\(373\) −6.13887 + 34.8152i −0.317859 + 1.80267i 0.237865 + 0.971298i \(0.423552\pi\)
−0.555724 + 0.831367i \(0.687559\pi\)
\(374\) 0.126897 + 0.226047i 0.00656168 + 0.0116886i
\(375\) 13.3777 16.2506i 0.690822 0.839179i
\(376\) −5.27864 + 4.11316i −0.272225 + 0.212120i
\(377\) 19.8338i 1.02149i
\(378\) 19.3512 1.87912i 0.995318 0.0966516i
\(379\) 14.2445i 0.731693i 0.930675 + 0.365847i \(0.119220\pi\)
−0.930675 + 0.365847i \(0.880780\pi\)
\(380\) −7.76334 + 4.23576i −0.398251 + 0.217290i
\(381\) −9.59021 25.5979i −0.491322 1.31142i
\(382\) −3.33016 + 1.86946i −0.170386 + 0.0956499i
\(383\) 1.34335 7.61852i 0.0686420 0.389288i −0.931060 0.364867i \(-0.881115\pi\)
0.999702 0.0244214i \(-0.00777435\pi\)
\(384\) −15.9137 + 11.4348i −0.812092 + 0.583529i
\(385\) −1.99848 7.65993i −0.101852 0.390386i
\(386\) −20.1202 + 16.4733i −1.02409 + 0.838468i
\(387\) 1.85219 2.29354i 0.0941521 0.116587i
\(388\) −8.29029 24.6094i −0.420876 1.24935i
\(389\) 4.33246 + 24.5706i 0.219664 + 1.24578i 0.872627 + 0.488388i \(0.162415\pi\)
−0.652962 + 0.757390i \(0.726474\pi\)
\(390\) −12.5049 10.5498i −0.633209 0.534212i
\(391\) −0.540012 0.453124i −0.0273096 0.0229155i
\(392\) 0.977141 19.7749i 0.0493531 0.998781i
\(393\) 25.0229 21.4005i 1.26224 1.07951i
\(394\) −9.46355 8.13744i −0.476767 0.409958i
\(395\) −12.9478 −0.651476
\(396\) −8.82933 + 5.03496i −0.443691 + 0.253017i
\(397\) 22.2313i 1.11576i −0.829922 0.557879i \(-0.811615\pi\)
0.829922 0.557879i \(-0.188385\pi\)
\(398\) −16.4862 + 5.77618i −0.826377 + 0.289534i
\(399\) −11.4259 + 1.03198i −0.572010 + 0.0516638i
\(400\) −4.07037 + 6.32439i −0.203518 + 0.316219i
\(401\) 10.0272 + 8.41378i 0.500732 + 0.420164i 0.857854 0.513894i \(-0.171797\pi\)
−0.357122 + 0.934058i \(0.616242\pi\)
\(402\) 0.0307650 11.5259i 0.00153442 0.574858i
\(403\) 6.11768 16.8082i 0.304743 0.837275i
\(404\) 25.4457 + 5.12273i 1.26597 + 0.254865i
\(405\) 10.6685 + 11.7849i 0.530120 + 0.585595i
\(406\) 18.8580 + 5.43195i 0.935907 + 0.269583i
\(407\) −7.91403 9.43157i −0.392284 0.467506i
\(408\) −0.351503 + 0.396805i −0.0174020 + 0.0196448i
\(409\) 1.74458 + 4.79319i 0.0862638 + 0.237008i 0.975322 0.220786i \(-0.0708621\pi\)
−0.889059 + 0.457793i \(0.848640\pi\)
\(410\) 5.03420 8.48148i 0.248621 0.418871i
\(411\) 2.38119 4.21533i 0.117456 0.207927i
\(412\) −12.0722 22.1260i −0.594754 1.09007i
\(413\) 1.23589 2.60542i 0.0608140 0.128204i
\(414\) 17.6235 21.2922i 0.866150 1.04645i
\(415\) 13.0178 7.51585i 0.639020 0.368938i
\(416\) 17.8470 + 11.7932i 0.875020 + 0.578211i
\(417\) −25.9673 9.17592i −1.27162 0.449347i
\(418\) 5.22986 2.93590i 0.255801 0.143600i
\(419\) 1.98970 + 1.66955i 0.0972030 + 0.0815630i 0.690094 0.723720i \(-0.257569\pi\)
−0.592891 + 0.805283i \(0.702014\pi\)
\(420\) 13.4556 9.00034i 0.656565 0.439172i
\(421\) 4.62605 + 1.68374i 0.225460 + 0.0820607i 0.452280 0.891876i \(-0.350611\pi\)
−0.226820 + 0.973937i \(0.572833\pi\)
\(422\) −2.87471 3.51112i −0.139939 0.170919i
\(423\) −5.52207 4.45945i −0.268492 0.216826i
\(424\) 6.30370 + 0.228278i 0.306135 + 0.0110862i
\(425\) −0.0695862 + 0.191187i −0.00337543 + 0.00927391i
\(426\) 12.4023 33.7941i 0.600894 1.63733i
\(427\) −0.301102 0.0283429i −0.0145713 0.00137161i
\(428\) 11.1297 1.68666i 0.537974 0.0815277i
\(429\) 8.56619 + 7.05179i 0.413580 + 0.340464i
\(430\) 0.455378 2.41202i 0.0219603 0.116318i
\(431\) −32.3745 + 18.6914i −1.55942 + 0.900334i −0.562111 + 0.827062i \(0.690011\pi\)
−0.997312 + 0.0732720i \(0.976656\pi\)
\(432\) −15.6506 13.6770i −0.752988 0.658034i
\(433\) 19.7924i 0.951160i −0.879672 0.475580i \(-0.842238\pi\)
0.879672 0.475580i \(-0.157762\pi\)
\(434\) 14.3058 + 10.4200i 0.686700 + 0.500177i
\(435\) 5.62941 + 15.0258i 0.269910 + 0.720434i
\(436\) −3.30826 1.29534i −0.158437 0.0620354i
\(437\) −10.4835 + 12.4938i −0.501495 + 0.597659i
\(438\) 12.1832 33.1970i 0.582134 1.58621i
\(439\) −10.1146 3.68141i −0.482743 0.175704i 0.0891733 0.996016i \(-0.471577\pi\)
−0.571916 + 0.820312i \(0.693800\pi\)
\(440\) −4.49393 + 7.17117i −0.214240 + 0.341872i
\(441\) 20.6602 3.76273i 0.983817 0.179178i
\(442\) 0.541350 + 0.204465i 0.0257494 + 0.00972542i
\(443\) 6.98363 + 8.32276i 0.331802 + 0.395426i 0.905991 0.423296i \(-0.139127\pi\)
−0.574189 + 0.818723i \(0.694683\pi\)
\(444\) 12.9084 21.6161i 0.612607 1.02586i
\(445\) −4.46941 + 25.3473i −0.211870 + 1.20158i
\(446\) 12.6934 + 22.6113i 0.601050 + 1.07068i
\(447\) −5.61285 30.1714i −0.265479 1.42706i
\(448\) −16.1008 + 13.7391i −0.760694 + 0.649111i
\(449\) 17.2078 29.8049i 0.812089 1.40658i −0.0993112 0.995056i \(-0.531664\pi\)
0.911400 0.411522i \(-0.135003\pi\)
\(450\) −7.51435 2.67789i −0.354230 0.126237i
\(451\) −3.34442 + 5.79270i −0.157482 + 0.272767i
\(452\) −11.1734 + 18.3175i −0.525554 + 0.861583i
\(453\) 0.295115 + 31.4055i 0.0138657 + 1.47556i
\(454\) 10.8779 + 19.3773i 0.510526 + 0.909424i
\(455\) −14.4086 10.2311i −0.675485 0.479642i
\(456\) 9.18054 + 8.13242i 0.429918 + 0.380835i
\(457\) −3.70174 20.9936i −0.173160 0.982039i −0.940246 0.340495i \(-0.889405\pi\)
0.767086 0.641544i \(-0.221706\pi\)
\(458\) 8.08604 + 9.87616i 0.377836 + 0.461483i
\(459\) −0.494661 0.267293i −0.0230888 0.0124762i
\(460\) 4.54197 22.5610i 0.211771 1.05191i
\(461\) 21.4736 + 25.5913i 1.00013 + 1.19190i 0.981379 + 0.192080i \(0.0615233\pi\)
0.0187472 + 0.999824i \(0.494032\pi\)
\(462\) −9.05091 + 6.21345i −0.421087 + 0.289076i
\(463\) 9.18813 + 1.62011i 0.427008 + 0.0752931i 0.383022 0.923739i \(-0.374883\pi\)
0.0439860 + 0.999032i \(0.485994\pi\)
\(464\) −9.60109 18.6539i −0.445720 0.865986i
\(465\) 0.135974 + 14.4701i 0.00630565 + 0.671033i
\(466\) 27.7936 + 23.8989i 1.28751 + 1.10710i
\(467\) 12.9199 0.597862 0.298931 0.954275i \(-0.403370\pi\)
0.298931 + 0.954275i \(0.403370\pi\)
\(468\) −7.87383 + 21.2790i −0.363968 + 0.983623i
\(469\) −1.00331 12.4089i −0.0463287 0.572990i
\(470\) −5.80733 1.09640i −0.267872 0.0505730i
\(471\) 2.37359 + 2.77535i 0.109369 + 0.127881i
\(472\) −2.93313 + 0.948847i −0.135008 + 0.0436742i
\(473\) −0.289067 + 1.63938i −0.0132913 + 0.0753787i
\(474\) 6.09630 + 16.8896i 0.280013 + 0.775765i
\(475\) 4.42331 + 1.60995i 0.202956 + 0.0738698i
\(476\) −0.342668 + 0.458719i −0.0157061 + 0.0210253i
\(477\) 1.28540 + 6.56583i 0.0588545 + 0.300629i
\(478\) 27.0231 4.42941i 1.23601 0.202596i
\(479\) −32.9557 + 27.6531i −1.50579 + 1.26350i −0.634296 + 0.773091i \(0.718710\pi\)
−0.871490 + 0.490413i \(0.836846\pi\)
\(480\) −16.8679 3.86892i −0.769912 0.176591i
\(481\) −27.0665 4.77255i −1.23412 0.217609i
\(482\) −0.343950 + 28.5047i −0.0156665 + 1.29835i
\(483\) 17.0549 24.5031i 0.776024 1.11493i
\(484\) −8.46776 + 13.8819i −0.384898 + 0.630994i
\(485\) 11.4668 19.8611i 0.520682 0.901847i
\(486\) 10.3495 19.4651i 0.469462 0.882953i
\(487\) −7.33423 + 4.23442i −0.332346 + 0.191880i −0.656882 0.753993i \(-0.728125\pi\)
0.324536 + 0.945873i \(0.394792\pi\)
\(488\) 0.198723 + 0.255032i 0.00899576 + 0.0115447i
\(489\) 24.9183 30.2697i 1.12685 1.36884i
\(490\) 13.6739 10.8977i 0.617724 0.492307i
\(491\) 10.2148 + 28.0648i 0.460985 + 1.26655i 0.924745 + 0.380586i \(0.124278\pi\)
−0.463760 + 0.885961i \(0.653500\pi\)
\(492\) −13.4338 2.57339i −0.605643 0.116018i
\(493\) −0.364806 0.434759i −0.0164300 0.0195806i
\(494\) 4.73053 12.5247i 0.212837 0.563514i
\(495\) −8.49115 2.91102i −0.381649 0.130840i
\(496\) −2.38272 18.7697i −0.106987 0.842785i
\(497\) 10.3107 37.4904i 0.462498 1.68167i
\(498\) −15.9332 13.4422i −0.713983 0.602358i
\(499\) 5.16294 + 14.1851i 0.231125 + 0.635010i 0.999990 0.00440031i \(-0.00140067\pi\)
−0.768865 + 0.639411i \(0.779178\pi\)
\(500\) −24.0305 + 3.64172i −1.07468 + 0.162863i
\(501\) −1.94022 10.4295i −0.0866829 0.465956i
\(502\) −19.7840 17.0117i −0.883003 0.759270i
\(503\) −14.6175 + 25.3182i −0.651760 + 1.12888i 0.330935 + 0.943654i \(0.392636\pi\)
−0.982695 + 0.185229i \(0.940697\pi\)
\(504\) −18.0757 13.3142i −0.805156 0.593063i
\(505\) 11.4615 + 19.8519i 0.510029 + 0.883397i
\(506\) −2.89542 + 15.3363i −0.128717 + 0.681782i
\(507\) 2.25128 0.0211551i 0.0999830 0.000939533i
\(508\) −11.5081 + 29.3915i −0.510591 + 1.30404i
\(509\) 18.7808 22.3821i 0.832443 0.992067i −0.167537 0.985866i \(-0.553581\pi\)
0.999981 0.00620171i \(-0.00197408\pi\)
\(510\) −0.468153 0.00124960i −0.0207302 5.53332e-5i
\(511\) 10.1285 36.8279i 0.448059 1.62917i
\(512\) 22.4941 + 2.45234i 0.994110 + 0.108379i
\(513\) −6.18412 + 11.4445i −0.273036 + 0.505289i
\(514\) 5.34209 + 6.52474i 0.235629 + 0.287794i
\(515\) 7.61325 20.9172i 0.335480 0.921723i
\(516\) −3.36073 + 0.541656i −0.147948 + 0.0238451i
\(517\) 3.94707 + 0.695975i 0.173592 + 0.0306089i
\(518\) 11.9505 24.4278i 0.525077 1.07330i
\(519\) −0.942210 + 0.555855i −0.0413584 + 0.0243993i
\(520\) 2.60506 + 18.7112i 0.114239 + 0.820540i
\(521\) −22.7469 13.1329i −0.996560 0.575364i −0.0893315 0.996002i \(-0.528473\pi\)
−0.907229 + 0.420638i \(0.861806\pi\)
\(522\) 16.9497 14.4179i 0.741868 0.631054i
\(523\) 13.6222 + 23.5943i 0.595656 + 1.03171i 0.993454 + 0.114234i \(0.0364412\pi\)
−0.397798 + 0.917473i \(0.630225\pi\)
\(524\) −38.0087 0.917392i −1.66042 0.0400765i
\(525\) −8.32905 2.20671i −0.363509 0.0963085i
\(526\) −25.2100 14.9634i −1.09921 0.652436i
\(527\) −0.175055 0.480961i −0.00762554 0.0209510i
\(528\) 11.4702 + 2.48559i 0.499177 + 0.108171i
\(529\) −3.37597 19.1461i −0.146781 0.832439i
\(530\) 3.52903 + 4.31030i 0.153291 + 0.187227i
\(531\) −1.68782 2.80049i −0.0732451 0.121531i
\(532\) 10.6130 + 7.92799i 0.460131 + 0.343722i
\(533\) 2.59281 + 14.7045i 0.112307 + 0.636924i
\(534\) 35.1682 6.10436i 1.52188 0.264162i
\(535\) 7.61548 + 6.39015i 0.329246 + 0.276270i
\(536\) −8.91820 + 9.87899i −0.385208 + 0.426707i
\(537\) −11.7299 1.95484i −0.506183 0.0843574i
\(538\) 5.98763 6.96340i 0.258145 0.300213i
\(539\) −9.18344 + 7.50187i −0.395559 + 0.323129i
\(540\) −0.0744918 18.3556i −0.00320562 0.789898i
\(541\) −14.4411 + 25.0128i −0.620873 + 1.07538i 0.368450 + 0.929647i \(0.379888\pi\)
−0.989323 + 0.145736i \(0.953445\pi\)
\(542\) 2.55386 13.5271i 0.109698 0.581040i
\(543\) 15.8344 + 42.2647i 0.679520 + 1.81375i
\(544\) 0.608123 0.0697534i 0.0260731 0.00299065i
\(545\) −1.07313 2.94841i −0.0459680 0.126296i
\(546\) −6.56174 + 23.6122i −0.280816 + 1.01051i
\(547\) −30.3782 + 5.35649i −1.29888 + 0.229027i −0.779977 0.625808i \(-0.784769\pi\)
−0.518900 + 0.854835i \(0.673658\pi\)
\(548\) −5.29782 + 1.78470i −0.226312 + 0.0762387i
\(549\) −0.215453 + 0.266793i −0.00919532 + 0.0113864i
\(550\) 4.44519 0.728619i 0.189544 0.0310684i
\(551\) −10.0586 + 8.44019i −0.428512 + 0.359564i
\(552\) −31.5678 + 4.69780i −1.34361 + 0.199952i
\(553\) 8.08064 + 17.6313i 0.343624 + 0.749760i
\(554\) 1.77096 2.98367i 0.0752411 0.126764i
\(555\) 21.8598 4.06663i 0.927898 0.172619i
\(556\) 15.2315 + 27.9165i 0.645961 + 1.18392i
\(557\) −19.3125 −0.818299 −0.409149 0.912467i \(-0.634175\pi\)
−0.409149 + 0.912467i \(0.634175\pi\)
\(558\) 18.8112 6.99039i 0.796342 0.295927i
\(559\) 1.85801 + 3.21816i 0.0785854 + 0.136114i
\(560\) −18.5041 2.64761i −0.781941 0.111882i
\(561\) 0.317477 0.00298330i 0.0134039 0.000125955i
\(562\) −1.41152 0.0170320i −0.0595415 0.000718453i
\(563\) 33.8191 12.3092i 1.42531 0.518769i 0.489724 0.871877i \(-0.337097\pi\)
0.935583 + 0.353108i \(0.114875\pi\)
\(564\) 1.30413 + 8.09151i 0.0549136 + 0.340714i
\(565\) −18.6611 + 3.29046i −0.785079 + 0.138431i
\(566\) 0.976448 + 5.95716i 0.0410432 + 0.250398i
\(567\) 9.38958 21.8823i 0.394325 0.918971i
\(568\) −36.7266 + 19.4671i −1.54102 + 0.816822i
\(569\) 2.17002 + 12.3068i 0.0909721 + 0.515928i 0.995907 + 0.0903793i \(0.0288079\pi\)
−0.904935 + 0.425549i \(0.860081\pi\)
\(570\) −0.0289109 + 10.8313i −0.00121094 + 0.453671i
\(571\) −5.62898 15.4655i −0.235565 0.647211i −0.999997 0.00250574i \(-0.999202\pi\)
0.764431 0.644705i \(-0.223020\pi\)
\(572\) −1.91966 12.6672i −0.0802650 0.529642i
\(573\) 0.0439504 + 4.67710i 0.00183605 + 0.195389i
\(574\) −14.6912 1.56194i −0.613199 0.0651941i
\(575\) −10.6082 + 6.12466i −0.442393 + 0.255416i
\(576\) 2.89528 + 23.8247i 0.120637 + 0.992697i
\(577\) 34.3948i 1.43187i 0.698165 + 0.715937i \(0.254000\pi\)
−0.698165 + 0.715937i \(0.746000\pi\)
\(578\) −22.6737 + 7.94407i −0.943101 + 0.330430i
\(579\) 5.82480 + 31.3107i 0.242070 + 1.30123i
\(580\) 6.75523 17.2527i 0.280495 0.716379i
\(581\) −18.3588 13.0361i −0.761652 0.540827i
\(582\) −31.3065 5.60639i −1.29770 0.232392i
\(583\) −2.42839 2.89404i −0.100574 0.119859i
\(584\) −36.0777 + 19.1231i −1.49290 + 0.791321i
\(585\) −18.6971 + 7.20590i −0.773030 + 0.297927i
\(586\) 16.0981 2.63867i 0.665006 0.109002i
\(587\) 2.97760 + 16.8868i 0.122899 + 0.696994i 0.982534 + 0.186085i \(0.0595800\pi\)
−0.859635 + 0.510909i \(0.829309\pi\)
\(588\) −20.6535 12.7057i −0.851735 0.523973i
\(589\) −11.1276 + 4.05010i −0.458503 + 0.166882i
\(590\) −2.34118 1.38961i −0.0963850 0.0572095i
\(591\) −14.3145 + 5.36290i −0.588819 + 0.220600i
\(592\) −27.7666 + 8.61364i −1.14120 + 0.354018i
\(593\) 35.4415 + 20.4622i 1.45541 + 0.840281i 0.998780 0.0493770i \(-0.0157236\pi\)
0.456628 + 0.889658i \(0.349057\pi\)
\(594\) 0.200710 + 12.4468i 0.00823523 + 0.510697i
\(595\) −0.504020 + 0.0407522i −0.0206628 + 0.00167068i
\(596\) −18.4537 + 30.2526i −0.755892 + 1.23919i
\(597\) −3.51702 + 21.1037i −0.143942 + 0.863718i
\(598\) 17.0546 + 30.3801i 0.697414 + 1.24234i
\(599\) −28.7469 + 34.2592i −1.17456 + 1.39979i −0.275883 + 0.961191i \(0.588970\pi\)
−0.898682 + 0.438600i \(0.855474\pi\)
\(600\) 4.39024 + 8.09781i 0.179231 + 0.330592i
\(601\) 19.7867 3.48893i 0.807116 0.142316i 0.245159 0.969483i \(-0.421160\pi\)
0.561957 + 0.827167i \(0.310049\pi\)
\(602\) −3.56870 + 0.885228i −0.145449 + 0.0360792i
\(603\) −12.3556 6.82717i −0.503157 0.278024i
\(604\) 23.9746 27.2105i 0.975513 1.10718i
\(605\) −14.1423 + 2.49366i −0.574965 + 0.101382i
\(606\) 20.4990 24.2977i 0.832714 0.987028i
\(607\) 35.7658 13.0177i 1.45169 0.528372i 0.508627 0.860987i \(-0.330153\pi\)
0.943063 + 0.332615i \(0.107931\pi\)
\(608\) −1.61382 14.0696i −0.0654491 0.570598i
\(609\) 16.9477 17.0432i 0.686756 0.690625i
\(610\) −0.0529712 + 0.280575i −0.00214474 + 0.0113601i
\(611\) 7.74825 4.47345i 0.313461 0.180977i
\(612\) 0.218793 + 0.611264i 0.00884420 + 0.0247089i
\(613\) −15.2007 + 26.3284i −0.613950 + 1.06339i 0.376618 + 0.926369i \(0.377087\pi\)
−0.990568 + 0.137024i \(0.956246\pi\)
\(614\) 8.23901 43.6400i 0.332500 1.76117i
\(615\) −6.13786 10.4041i −0.247502 0.419533i
\(616\) 12.5698 + 1.64400i 0.506450 + 0.0662386i
\(617\) −7.33489 + 41.5982i −0.295292 + 1.67468i 0.370723 + 0.928744i \(0.379110\pi\)
−0.666014 + 0.745939i \(0.732001\pi\)
\(618\) −30.8697 0.0823977i −1.24176 0.00331452i
\(619\) −15.1013 5.49641i −0.606971 0.220919i 0.0202064 0.999796i \(-0.493568\pi\)
−0.627177 + 0.778876i \(0.715790\pi\)
\(620\) 11.0463 12.5372i 0.443629 0.503506i
\(621\) −12.4699 31.4710i −0.500399 1.26289i
\(622\) 1.52260 + 9.28913i 0.0610506 + 0.372460i
\(623\) 37.3053 9.73297i 1.49460 0.389943i
\(624\) 23.1809 12.2080i 0.927981 0.488712i
\(625\) −9.24107 7.75418i −0.369643 0.310167i
\(626\) −8.94772 5.31093i −0.357623 0.212268i
\(627\) −0.0690221 7.34518i −0.00275648 0.293338i
\(628\) 0.101750 4.21564i 0.00406028 0.168222i
\(629\) −0.681083 + 0.393223i −0.0271565 + 0.0156788i
\(630\) −1.73075 19.7508i −0.0689546 0.786889i
\(631\) 35.3737 + 20.4230i 1.40820 + 0.813027i 0.995215 0.0977095i \(-0.0311516\pi\)
0.412989 + 0.910736i \(0.364485\pi\)
\(632\) 7.79189 19.2142i 0.309945 0.764298i
\(633\) −5.46394 + 1.01647i −0.217172 + 0.0404010i
\(634\) 22.8892 + 0.276191i 0.909047 + 0.0109690i
\(635\) −26.1945 + 9.53402i −1.03950 + 0.378346i
\(636\) 3.96091 6.63283i 0.157060 0.263009i
\(637\) −4.93963 + 26.0056i −0.195715 + 1.03038i
\(638\) −4.43971 + 11.7547i −0.175770 + 0.465375i
\(639\) −28.9692 33.2352i −1.14600 1.31476i
\(640\) 11.5078 + 16.3370i 0.454884 + 0.645778i
\(641\) 3.68277 3.09021i 0.145461 0.122056i −0.567154 0.823612i \(-0.691955\pi\)
0.712614 + 0.701556i \(0.247511\pi\)
\(642\) 4.74989 12.9426i 0.187463 0.510804i
\(643\) −19.5211 + 7.10510i −0.769837 + 0.280198i −0.696928 0.717141i \(-0.745450\pi\)
−0.0729089 + 0.997339i \(0.523228\pi\)
\(644\) −33.5563 + 7.89522i −1.32230 + 0.311115i
\(645\) −2.32102 1.91069i −0.0913899 0.0752332i
\(646\) −0.126676 0.361553i −0.00498398 0.0142251i
\(647\) −15.5846 26.9933i −0.612694 1.06122i −0.990784 0.135448i \(-0.956753\pi\)
0.378091 0.925769i \(-0.376581\pi\)
\(648\) −23.9086 + 8.73963i −0.939217 + 0.343325i
\(649\) 1.59899 + 0.923175i 0.0627657 + 0.0362378i
\(650\) 6.55593 7.62430i 0.257145 0.299050i
\(651\) 19.6193 9.21581i 0.768941 0.361196i
\(652\) −44.7611 + 6.78335i −1.75298 + 0.265656i
\(653\) 0.263709 1.49557i 0.0103197 0.0585261i −0.979213 0.202835i \(-0.934985\pi\)
0.989533 + 0.144308i \(0.0460957\pi\)
\(654\) −3.34074 + 2.78805i −0.130633 + 0.109021i
\(655\) −21.5827 25.7213i −0.843307 1.00501i
\(656\) 9.55671 + 12.5747i 0.373127 + 0.490958i
\(657\) −28.4573 32.6479i −1.11023 1.27372i
\(658\) 2.13133 + 8.59222i 0.0830879 + 0.334960i
\(659\) 12.9947 35.7026i 0.506201 1.39077i −0.378927 0.925427i \(-0.623707\pi\)
0.885128 0.465348i \(-0.154071\pi\)
\(660\) 5.04964 + 9.05167i 0.196557 + 0.352336i
\(661\) 22.2316 + 3.92003i 0.864708 + 0.152471i 0.588373 0.808590i \(-0.299769\pi\)
0.276336 + 0.961061i \(0.410880\pi\)
\(662\) −0.182886 + 15.1566i −0.00710805 + 0.589077i
\(663\) 0.538614 0.460644i 0.0209180 0.0178899i
\(664\) 3.31926 + 23.8410i 0.128812 + 0.925211i
\(665\) 0.942847 + 11.6611i 0.0365620 + 0.452197i
\(666\) −15.5970 26.6000i −0.604373 1.03073i
\(667\) 34.1692i 1.32304i
\(668\) −6.37898 + 10.4576i −0.246810 + 0.404616i
\(669\) 31.7569 0.298418i 1.22779 0.0115375i
\(670\) −11.7528 0.141815i −0.454052 0.00547878i
\(671\) 0.0336253 0.190698i 0.00129809 0.00736183i
\(672\) 5.25876 + 25.3840i 0.202861 + 0.979208i
\(673\) −0.668181 + 0.560670i −0.0257565 + 0.0216123i −0.655575 0.755130i \(-0.727574\pi\)
0.629819 + 0.776742i \(0.283129\pi\)
\(674\) −30.6976 11.5943i −1.18243 0.446597i
\(675\) −7.30434 + 6.48856i −0.281144 + 0.249745i
\(676\) −1.95056 1.71860i −0.0750217 0.0661001i
\(677\) 31.7133 5.59191i 1.21884 0.214914i 0.473014 0.881055i \(-0.343166\pi\)
0.745826 + 0.666141i \(0.232055\pi\)
\(678\) 13.0785 + 22.7929i 0.502277 + 0.875357i
\(679\) −34.2017 3.21943i −1.31254 0.123550i
\(680\) 0.401261 + 0.362236i 0.0153877 + 0.0138911i
\(681\) 27.2149 0.255736i 1.04288 0.00979984i
\(682\) −7.38817 + 8.59217i −0.282908 + 0.329011i
\(683\) −32.1921 18.5861i −1.23180 0.711179i −0.264394 0.964415i \(-0.585172\pi\)
−0.967405 + 0.253236i \(0.918505\pi\)
\(684\) 14.1423 5.06203i 0.540743 0.193552i
\(685\) −4.27563 2.46853i −0.163363 0.0943178i
\(686\) −23.3734 11.8189i −0.892399 0.451246i
\(687\) 15.3691 2.85915i 0.586368 0.109083i
\(688\) 3.30532 + 2.12730i 0.126014 + 0.0811026i
\(689\) −8.30524 1.46444i −0.316405 0.0557907i
\(690\) −21.5431 18.1750i −0.820133 0.691912i
\(691\) −6.66864 + 5.59565i −0.253687 + 0.212869i −0.760758 0.649036i \(-0.775173\pi\)
0.507071 + 0.861904i \(0.330728\pi\)
\(692\) 1.23834 + 0.249303i 0.0470747 + 0.00947709i
\(693\) 1.33527 + 13.3793i 0.0507229 + 0.508238i
\(694\) −0.0696559 0.0850766i −0.00264410 0.00322946i
\(695\) −9.60567 + 26.3914i −0.364364 + 1.00108i
\(696\) −25.6856 0.688562i −0.973610 0.0260999i
\(697\) 0.327298 + 0.274635i 0.0123973 + 0.0104026i
\(698\) 10.6997 + 6.35085i 0.404991 + 0.240383i
\(699\) 42.0403 15.7503i 1.59011 0.595732i
\(700\) 5.45371 + 8.32149i 0.206131 + 0.314523i
\(701\) −22.7327 −0.858601 −0.429301 0.903162i \(-0.641240\pi\)
−0.429301 + 0.903162i \(0.641240\pi\)
\(702\) 18.2029 + 20.9963i 0.687024 + 0.792455i
\(703\) 9.09766 + 15.7576i 0.343125 + 0.594309i
\(704\) −7.93737 10.9844i −0.299151 0.413990i
\(705\) −4.60029 + 5.58822i −0.173257 + 0.210464i
\(706\) 0.0804911 6.67066i 0.00302932 0.251053i
\(707\) 19.8797 27.9967i 0.747652 1.05293i
\(708\) −0.710346 + 3.70820i −0.0266964 + 0.139363i
\(709\) −41.8617 15.2364i −1.57215 0.572215i −0.598670 0.800996i \(-0.704304\pi\)
−0.973478 + 0.228781i \(0.926526\pi\)
\(710\) −34.3416 12.9707i −1.28882 0.486781i
\(711\) 21.7255 + 3.41115i 0.814771 + 0.127928i
\(712\) −34.9249 21.8863i −1.30887 0.820222i
\(713\) 10.5394 28.9568i 0.394704 1.08444i
\(714\) 0.290469 + 0.638274i 0.0108705 + 0.0238868i
\(715\) 7.27291 8.66752i 0.271991 0.324147i
\(716\) 8.56995 + 10.7287i 0.320274 + 0.400951i
\(717\) 11.1741 31.6219i 0.417303 1.18094i
\(718\) −6.32212 18.0444i −0.235940 0.673411i
\(719\) 5.85481 + 10.1408i 0.218347 + 0.378189i 0.954303 0.298841i \(-0.0966001\pi\)
−0.735955 + 0.677030i \(0.763267\pi\)
\(720\) −14.0966 + 15.8281i −0.525350 + 0.589878i
\(721\) −33.2348 + 2.68717i −1.23773 + 0.100075i
\(722\) 16.9937 5.95400i 0.632440 0.221585i
\(723\) 30.3987 + 17.1719i 1.13054 + 0.638630i
\(724\) 19.0011 48.5284i 0.706171 1.80354i
\(725\) −9.26707 + 3.37294i −0.344170 + 0.125268i
\(726\) 9.91151 + 17.2736i 0.367851 + 0.641082i
\(727\) 36.8774 30.9438i 1.36771 1.14764i 0.394191 0.919028i \(-0.371025\pi\)
0.973517 0.228615i \(-0.0734197\pi\)
\(728\) 23.8536 15.2249i 0.884073 0.564271i
\(729\) −14.7962 22.5848i −0.548006 0.836474i
\(730\) −33.7348 12.7415i −1.24858 0.471583i
\(731\) 0.0999200 + 0.0363679i 0.00369568 + 0.00134512i
\(732\) 0.390932 0.0630074i 0.0144493 0.00232882i
\(733\) 21.2415 25.3146i 0.784572 0.935016i −0.214559 0.976711i \(-0.568831\pi\)
0.999130 + 0.0416950i \(0.0132758\pi\)
\(734\) −1.09023 1.94207i −0.0402410 0.0716833i
\(735\) −3.63895 21.1036i −0.134225 0.778417i
\(736\) 30.7464 + 20.3171i 1.13333 + 0.748899i
\(737\) 7.97105 0.293617
\(738\) −10.6815 + 12.9050i −0.393192 + 0.475041i
\(739\) 21.5361i 0.792217i −0.918204 0.396109i \(-0.870360\pi\)
0.918204 0.396109i \(-0.129640\pi\)
\(740\) −21.9186 13.3701i −0.805745 0.491494i
\(741\) −10.6575 12.4614i −0.391514 0.457782i
\(742\) 3.66698 7.49557i 0.134619 0.275171i
\(743\) −1.08218 + 1.28969i −0.0397014 + 0.0473143i −0.785530 0.618824i \(-0.787609\pi\)
0.745828 + 0.666138i \(0.232054\pi\)
\(744\) −21.5549 8.50618i −0.790242 0.311852i
\(745\) −30.8201 + 5.43441i −1.12916 + 0.199101i
\(746\) −8.08698 49.3374i −0.296085 1.80637i
\(747\) −23.8231 + 9.18146i −0.871640 + 0.335932i
\(748\) −0.275069 0.242358i −0.0100575 0.00886149i
\(749\) 3.94883 14.3582i 0.144287 0.524637i
\(750\) −10.2556 + 27.9449i −0.374483 + 1.02040i
\(751\) 17.0832 + 3.01223i 0.623375 + 0.109918i 0.476409 0.879224i \(-0.341938\pi\)
0.146966 + 0.989142i \(0.453049\pi\)
\(752\) 5.12182 7.95809i 0.186774 0.290202i
\(753\) −29.9251 + 11.2114i −1.09053 + 0.408566i
\(754\) 9.27467 + 26.4715i 0.337764 + 0.964034i
\(755\) 32.0276 1.16560
\(756\) −24.9487 + 11.5570i −0.907374 + 0.420324i
\(757\) −26.6625 −0.969065 −0.484532 0.874773i \(-0.661010\pi\)
−0.484532 + 0.874773i \(0.661010\pi\)
\(758\) −6.66103 19.0117i −0.241940 0.690536i
\(759\) 14.7577 + 12.1487i 0.535669 + 0.440969i
\(760\) 8.38074 9.28362i 0.304001 0.336752i
\(761\) 23.0433 + 4.06316i 0.835321 + 0.147290i 0.574919 0.818211i \(-0.305034\pi\)
0.260402 + 0.965500i \(0.416145\pi\)
\(762\) 24.7698 + 29.6800i 0.897316 + 1.07519i
\(763\) −3.34518 + 3.30139i −0.121104 + 0.119518i
\(764\) 3.57045 4.05235i 0.129174 0.146609i
\(765\) −0.277303 + 0.501853i −0.0100259 + 0.0181445i
\(766\) 1.76965 + 10.7964i 0.0639400 + 0.390088i
\(767\) 4.05896 0.715705i 0.146561 0.0258426i
\(768\) 15.8923 22.7032i 0.573465 0.819230i
\(769\) −10.6358 + 12.6753i −0.383538 + 0.457083i −0.922928 0.384974i \(-0.874211\pi\)
0.539390 + 0.842056i \(0.318655\pi\)
\(770\) 6.24924 + 9.28891i 0.225207 + 0.334749i
\(771\) 10.1537 1.88891i 0.365676 0.0680275i
\(772\) 19.1505 31.3949i 0.689242 1.12993i
\(773\) 32.3264i 1.16270i 0.813653 + 0.581351i \(0.197476\pi\)
−0.813653 + 0.581351i \(0.802524\pi\)
\(774\) −1.39955 + 3.92723i −0.0503057 + 0.141161i
\(775\) −8.89378 −0.319474
\(776\) 22.5726 + 28.9687i 0.810310 + 1.03991i
\(777\) −19.1802 27.2290i −0.688085 0.976835i
\(778\) −17.2721 30.7676i −0.619234 1.10307i
\(779\) 6.35400 7.57240i 0.227656 0.271309i
\(780\) 21.6231 + 8.23298i 0.774233 + 0.294788i
\(781\) 23.3940 + 8.51473i 0.837104 + 0.304681i
\(782\) 0.932626 + 0.352249i 0.0333506 + 0.0125964i
\(783\) −5.48714 26.6954i −0.196094 0.954015i
\(784\) 7.94297 + 26.8498i 0.283677 + 0.958920i
\(785\) 2.85282 2.39380i 0.101821 0.0854383i
\(786\) −23.3898 + 40.2638i −0.834287 + 1.43616i
\(787\) 34.7816 12.6595i 1.23983 0.451261i 0.362877 0.931837i \(-0.381794\pi\)
0.876953 + 0.480575i \(0.159572\pi\)
\(788\) 16.4359 + 6.43542i 0.585505 + 0.229252i
\(789\) −30.9246 + 18.2439i −1.10094 + 0.649500i
\(790\) 17.2810 6.05467i 0.614831 0.215415i
\(791\) 16.1270 + 23.3577i 0.573408 + 0.830503i
\(792\) 9.42976 10.8488i 0.335072 0.385494i
\(793\) −0.216130 0.374348i −0.00767500 0.0132935i
\(794\) 10.3958 + 29.6714i 0.368934 + 1.05300i
\(795\) 6.70761 1.24783i 0.237894 0.0442560i
\(796\) 19.3025 15.4185i 0.684157 0.546495i
\(797\) −4.90016 + 5.83978i −0.173573 + 0.206856i −0.845816 0.533474i \(-0.820886\pi\)
0.672244 + 0.740330i \(0.265331\pi\)
\(798\) 14.7672 6.72033i 0.522752 0.237897i
\(799\) 0.0875616 0.240574i 0.00309771 0.00851088i
\(800\) 2.47517 10.3443i 0.0875105 0.365727i
\(801\) 14.1772 41.3535i 0.500926 1.46115i
\(802\) −17.3174 6.54069i −0.611497 0.230960i
\(803\) 22.9807 + 8.36428i 0.810970 + 0.295169i
\(804\) 5.34867 + 15.3976i 0.188633 + 0.543030i
\(805\) −24.8228 17.6259i −0.874889 0.621233i
\(806\) −0.305209 + 25.2940i −0.0107505 + 0.890945i
\(807\) −3.94609 10.5328i −0.138909 0.370771i
\(808\) −36.3570 + 5.06178i −1.27903 + 0.178073i
\(809\) 6.44146 + 11.1569i 0.226470 + 0.392257i 0.956759 0.290880i \(-0.0939482\pi\)
−0.730290 + 0.683138i \(0.760615\pi\)
\(810\) −19.7497 10.7401i −0.693933 0.377367i
\(811\) −40.8971 −1.43609 −0.718045 0.695996i \(-0.754963\pi\)
−0.718045 + 0.695996i \(0.754963\pi\)
\(812\) −27.7092 + 1.56854i −0.972403 + 0.0550451i
\(813\) −13.0167 10.7155i −0.456517 0.375810i
\(814\) 14.9730 + 8.88724i 0.524803 + 0.311497i
\(815\) −30.6277 25.6997i −1.07284 0.900222i
\(816\) 0.283585 0.693973i 0.00992746 0.0242939i
\(817\) 0.841412 2.31176i 0.0294373 0.0808783i
\(818\) −4.56982 5.58150i −0.159780 0.195153i
\(819\) 21.4811 + 20.9631i 0.750612 + 0.732509i
\(820\) −2.75286 + 13.6740i −0.0961340 + 0.477518i
\(821\) −20.5429 + 17.2375i −0.716952 + 0.601595i −0.926540 0.376195i \(-0.877232\pi\)
0.209588 + 0.977790i \(0.432788\pi\)
\(822\) −1.20692 + 6.73955i −0.0420962 + 0.235069i
\(823\) 27.2105 + 4.79794i 0.948498 + 0.167246i 0.626436 0.779473i \(-0.284513\pi\)
0.322062 + 0.946719i \(0.395624\pi\)
\(824\) 26.4589 + 23.8856i 0.921739 + 0.832095i
\(825\) 1.83809 5.20167i 0.0639940 0.181099i
\(826\) −0.431150 + 4.05528i −0.0150016 + 0.141101i
\(827\) −28.5706 16.4953i −0.993499 0.573597i −0.0871804 0.996193i \(-0.527786\pi\)
−0.906318 + 0.422596i \(0.861119\pi\)
\(828\) −13.5649 + 36.6591i −0.471412 + 1.27399i
\(829\) 30.7401 + 17.7478i 1.06765 + 0.616407i 0.927538 0.373729i \(-0.121921\pi\)
0.140110 + 0.990136i \(0.455254\pi\)
\(830\) −13.8599 + 16.1185i −0.481084 + 0.559483i
\(831\) −2.15922 3.66002i −0.0749025 0.126965i
\(832\) −29.3345 7.39441i −1.01699 0.256355i
\(833\) 0.370048 + 0.660902i 0.0128214 + 0.0228989i
\(834\) 38.9485 + 0.103962i 1.34868 + 0.00359990i
\(835\) −10.6537 + 1.87854i −0.368688 + 0.0650097i
\(836\) −5.60722 + 6.36403i −0.193930 + 0.220105i
\(837\) 3.58403 24.3155i 0.123882 0.840468i
\(838\) −3.43630 1.29787i −0.118705 0.0448343i
\(839\) 28.2468 23.7019i 0.975188 0.818280i −0.00816840 0.999967i \(-0.502600\pi\)
0.983356 + 0.181687i \(0.0581557\pi\)
\(840\) −13.7499 + 18.3045i −0.474418 + 0.631567i
\(841\) −0.258854 + 1.46803i −0.00892599 + 0.0506218i
\(842\) −6.96158 0.0840015i −0.239912 0.00289488i
\(843\) −0.850333 + 1.50531i −0.0292870 + 0.0518457i
\(844\) 5.47864 + 3.34190i 0.188583 + 0.115033i
\(845\) 2.29587i 0.0789805i
\(846\) 9.45544 + 3.36964i 0.325085 + 0.115851i
\(847\) 12.2218 + 17.7015i 0.419945 + 0.608232i
\(848\) −8.52008 + 2.64306i −0.292581 + 0.0907631i
\(849\) 6.97094 + 2.46328i 0.239242 + 0.0845397i
\(850\) 0.00347163 0.287710i 0.000119076 0.00986837i
\(851\) −46.6295 8.22204i −1.59844 0.281848i
\(852\) −0.750119 + 50.9034i −0.0256987 + 1.74392i
\(853\) 3.69353 10.1479i 0.126464 0.347457i −0.860262 0.509853i \(-0.829700\pi\)
0.986726 + 0.162396i \(0.0519221\pi\)
\(854\) 0.415124 0.102973i 0.0142052 0.00352366i
\(855\) 11.6109 + 6.41572i 0.397086 + 0.219413i
\(856\) −14.0657 + 7.45559i −0.480756 + 0.254827i
\(857\) 6.91144 + 8.23673i 0.236090 + 0.281361i 0.871061 0.491175i \(-0.163432\pi\)
−0.634971 + 0.772536i \(0.718988\pi\)
\(858\) −14.7306 5.40605i −0.502893 0.184560i
\(859\) 3.17292 17.9945i 0.108259 0.613966i −0.881610 0.471979i \(-0.843540\pi\)
0.989869 0.141987i \(-0.0453490\pi\)
\(860\) 0.520133 + 3.43219i 0.0177364 + 0.117037i
\(861\) −10.3368 + 14.8512i −0.352279 + 0.506126i
\(862\) 34.4686 40.0857i 1.17401 1.36533i
\(863\) 22.3042 + 12.8773i 0.759242 + 0.438349i 0.829024 0.559214i \(-0.188897\pi\)
−0.0697814 + 0.997562i \(0.522230\pi\)
\(864\) 27.2839 + 10.9357i 0.928217 + 0.372039i
\(865\) 0.557786 + 0.966114i 0.0189653 + 0.0328489i
\(866\) 9.25531 + 26.4162i 0.314508 + 0.897658i
\(867\) −4.83701 + 29.0243i −0.164274 + 0.985717i
\(868\) −23.9660 7.21757i −0.813461 0.244980i
\(869\) −11.6691 + 4.24722i −0.395849 + 0.144077i
\(870\) −14.5398 17.4220i −0.492944 0.590663i
\(871\) 13.6307 11.4375i 0.461860 0.387546i
\(872\) 5.02115 + 0.181833i 0.170038 + 0.00615763i
\(873\) −24.4730 + 30.3046i −0.828286 + 1.02565i
\(874\) 8.14966 21.5773i 0.275666 0.729864i
\(875\) −8.52606 + 31.0013i −0.288233 + 1.04804i
\(876\) −0.736864 + 50.0040i −0.0248963 + 1.68948i
\(877\) −41.4914 + 15.1016i −1.40106 + 0.509946i −0.928494 0.371347i \(-0.878896\pi\)
−0.472570 + 0.881293i \(0.656674\pi\)
\(878\) 15.2211 + 0.183664i 0.513687 + 0.00619837i
\(879\) 6.65656 18.8376i 0.224520 0.635378i
\(880\) 2.64450 11.6726i 0.0891462 0.393482i
\(881\) 35.5886 + 20.5471i 1.19901 + 0.692249i 0.960334 0.278851i \(-0.0899535\pi\)
0.238675 + 0.971099i \(0.423287\pi\)
\(882\) −25.8149 + 14.6831i −0.869231 + 0.494405i
\(883\) −2.38817 + 1.37881i −0.0803684 + 0.0464007i −0.539646 0.841892i \(-0.681442\pi\)
0.459277 + 0.888293i \(0.348108\pi\)
\(884\) −0.818133 0.0197468i −0.0275168 0.000664156i
\(885\) −2.87189 + 1.69426i −0.0965374 + 0.0569520i
\(886\) −13.2127 7.84242i −0.443889 0.263471i
\(887\) 20.5913 + 17.2782i 0.691389 + 0.580144i 0.919309 0.393536i \(-0.128748\pi\)
−0.227921 + 0.973680i \(0.573193\pi\)
\(888\) −7.12031 + 34.8865i −0.238942 + 1.17072i
\(889\) 29.3305 + 29.7195i 0.983712 + 0.996759i
\(890\) −5.88774 35.9201i −0.197357 1.20405i
\(891\) 13.4806 + 7.12150i 0.451618 + 0.238579i
\(892\) −27.5150 24.2429i −0.921269 0.811712i
\(893\) −5.56594 2.02584i −0.186257 0.0677920i
\(894\) 21.6000 + 37.6440i 0.722413 + 1.25900i
\(895\) −2.10578 + 11.9425i −0.0703884 + 0.399192i
\(896\) 15.0646 25.8662i 0.503272 0.864128i
\(897\) 42.6680 0.400948i 1.42464 0.0133873i
\(898\) −9.02936 + 47.8263i −0.301314 + 1.59598i
\(899\) 12.4045 21.4852i 0.413713 0.716572i
\(900\) 11.2814 + 0.0602251i 0.376046 + 0.00200750i
\(901\) −0.208988 + 0.120659i −0.00696239 + 0.00401974i
\(902\) 1.75489 9.29523i 0.0584316 0.309497i
\(903\) −1.15329 + 4.35302i −0.0383792 + 0.144859i
\(904\) 6.34717 29.6727i 0.211104 0.986898i
\(905\) 43.2498 15.7416i 1.43767 0.523270i
\(906\) −15.0797 41.7778i −0.500990 1.38798i
\(907\) −6.41946 + 1.13192i −0.213155 + 0.0375849i −0.279206 0.960231i \(-0.590071\pi\)
0.0660510 + 0.997816i \(0.478960\pi\)
\(908\) −23.5796 20.7755i −0.782517 0.689460i
\(909\) −14.0015 36.3296i −0.464401 1.20498i
\(910\) 24.0149 + 6.91737i 0.796086 + 0.229309i
\(911\) 54.5049 9.61069i 1.80583 0.318416i 0.833586 0.552389i \(-0.186284\pi\)
0.972243 + 0.233973i \(0.0751727\pi\)
\(912\) −16.0558 6.56106i −0.531662 0.217258i
\(913\) 9.26684 11.0438i 0.306688 0.365496i
\(914\) 14.7576 + 26.2884i 0.488138 + 0.869544i
\(915\) 0.269989 + 0.222258i 0.00892555 + 0.00734762i
\(916\) −15.4105 9.40018i −0.509176 0.310591i
\(917\) −21.5556 + 45.4421i −0.711828 + 1.50063i
\(918\) 0.785199 + 0.125433i 0.0259154 + 0.00413992i
\(919\) −0.178788 0.103223i −0.00589767 0.00340502i 0.497048 0.867723i \(-0.334417\pi\)
−0.502946 + 0.864318i \(0.667751\pi\)
\(920\) 4.48794 + 32.2352i 0.147963 + 1.06276i
\(921\) −41.9934 34.5695i −1.38373 1.13910i
\(922\) −40.6271 24.1143i −1.33798 0.794162i
\(923\) 52.2222 19.0073i 1.71891 0.625633i
\(924\) 9.17440 12.5253i 0.301816 0.412051i
\(925\) 2.37302 + 13.4581i 0.0780245 + 0.442499i
\(926\) −13.0207 + 2.13424i −0.427886 + 0.0701355i
\(927\) −18.2852 + 33.0919i −0.600565 + 1.08688i
\(928\) 21.5372 + 20.4071i 0.706993 + 0.669894i
\(929\) 6.34698 + 7.56404i 0.208238 + 0.248168i 0.860047 0.510215i \(-0.170434\pi\)
−0.651809 + 0.758383i \(0.725990\pi\)
\(930\) −6.94797 19.2491i −0.227833 0.631203i
\(931\) 15.2907 8.56148i 0.501132 0.280591i
\(932\) −48.2707 18.9002i −1.58116 0.619097i
\(933\) 10.8699 + 3.84105i 0.355866 + 0.125750i
\(934\) −17.2438 + 6.04161i −0.564233 + 0.197687i
\(935\) 0.323765i 0.0105882i
\(936\) 0.558426 32.0823i 0.0182527 1.04864i
\(937\) −33.9757 + 19.6159i −1.10994 + 0.640823i −0.938813 0.344427i \(-0.888073\pi\)
−0.171125 + 0.985249i \(0.554740\pi\)
\(938\) 7.14174 + 16.0926i 0.233186 + 0.525441i
\(939\) −10.9760 + 6.47526i −0.358188 + 0.211312i
\(940\) 8.26355 1.25230i 0.269527 0.0408457i
\(941\) −7.42072 20.3883i −0.241909 0.664638i −0.999923 0.0124006i \(-0.996053\pi\)
0.758015 0.652238i \(-0.226170\pi\)
\(942\) −4.46576 2.59422i −0.145502 0.0845244i
\(943\) 4.46683 + 25.3327i 0.145460 + 0.824945i
\(944\) 3.47105 2.63798i 0.112973 0.0858590i
\(945\) −22.2238 9.78440i −0.722940 0.318286i
\(946\) −0.380799 2.32320i −0.0123808 0.0755336i
\(947\) 48.4327 8.54000i 1.57385 0.277513i 0.682521 0.730866i \(-0.260884\pi\)
0.891331 + 0.453353i \(0.149772\pi\)
\(948\) −16.0344 19.6912i −0.520774 0.639540i
\(949\) 51.2994 18.6715i 1.66525 0.606101i
\(950\) −6.65649 0.0803201i −0.215965 0.00260593i
\(951\) 13.7890 24.4101i 0.447139 0.791552i
\(952\) 0.242840 0.772474i 0.00787050 0.0250360i
\(953\) 14.5854 + 25.2626i 0.472467 + 0.818337i 0.999504 0.0315054i \(-0.0100301\pi\)
−0.527036 + 0.849843i \(0.676697\pi\)
\(954\) −4.78589 8.16211i −0.154949 0.264258i
\(955\) 4.76974 0.154345
\(956\) −33.9955 + 18.5483i −1.09949 + 0.599896i
\(957\) 10.0023 + 11.6953i 0.323329 + 0.378057i
\(958\) 31.0537 52.3184i 1.00330 1.69033i
\(959\) −0.693066 + 7.36280i −0.0223803 + 0.237757i
\(960\) 24.3222 2.72407i 0.784996 0.0879190i
\(961\) −6.60810 + 5.54485i −0.213164 + 0.178866i
\(962\) 38.3564 6.28707i 1.23666 0.202703i
\(963\) −11.0947 12.7285i −0.357523 0.410171i
\(964\) −12.8703 38.2051i −0.414525 1.23050i
\(965\) 31.9839 5.63962i 1.02960 0.181546i
\(966\) −11.3044 + 40.6786i −0.363714 + 1.30881i
\(967\) −18.3256 50.3491i −0.589311 1.61912i −0.771768 0.635905i \(-0.780627\pi\)
0.182457 0.983214i \(-0.441595\pi\)
\(968\) 4.81018 22.4873i 0.154605 0.722771i
\(969\) −0.462819 0.0771307i −0.0148679 0.00247779i
\(970\) −6.01691 + 31.8701i −0.193191 + 1.02329i
\(971\) −5.90796 + 10.2329i −0.189596 + 0.328389i −0.945115 0.326737i \(-0.894051\pi\)
0.755520 + 0.655126i \(0.227384\pi\)
\(972\) −4.71085 + 30.8190i −0.151100 + 0.988518i
\(973\) 41.9325 3.39042i 1.34429 0.108692i
\(974\) 7.80865 9.08117i 0.250205 0.290979i
\(975\) −4.32062 11.5325i −0.138370 0.369334i
\(976\) −0.384487 0.247455i −0.0123071 0.00792085i
\(977\) 36.3363 + 30.4898i 1.16250 + 0.975456i 0.999937 0.0112420i \(-0.00357852\pi\)
0.162566 + 0.986698i \(0.448023\pi\)
\(978\) −19.1029 + 52.0522i −0.610845 + 1.66445i
\(979\) 4.28654 + 24.3102i 0.136998 + 0.776956i
\(980\) −13.1541 + 20.9389i −0.420193 + 0.668870i
\(981\) 1.02387 + 5.22994i 0.0326897 + 0.166979i
\(982\) −26.7570 32.6805i −0.853849 1.04288i
\(983\) −6.65868 37.7632i −0.212379 1.20446i −0.885397 0.464835i \(-0.846114\pi\)
0.673019 0.739626i \(-0.264997\pi\)
\(984\) 19.1330 2.84730i 0.609938 0.0907687i
\(985\) 5.33148 + 14.6481i 0.169875 + 0.466728i
\(986\) 0.690196 + 0.409667i 0.0219803 + 0.0130465i
\(987\) 10.4806 + 2.77674i 0.333601 + 0.0883846i
\(988\) −0.456863 + 18.9284i −0.0145348 + 0.602193i
\(989\) 3.20094 + 5.54419i 0.101784 + 0.176295i
\(990\) 12.6941 0.0854001i 0.403445 0.00271419i
\(991\) −28.5568 16.4873i −0.907138 0.523736i −0.0276287 0.999618i \(-0.508796\pi\)
−0.879509 + 0.475882i \(0.842129\pi\)
\(992\) 11.9572 + 23.9371i 0.379643 + 0.760003i
\(993\) 16.1636 + 9.13066i 0.512938 + 0.289753i
\(994\) 3.76992 + 54.8586i 0.119575 + 1.74001i
\(995\) 21.4861 + 3.78858i 0.681156 + 0.120106i
\(996\) 27.5513 + 10.4901i 0.872997 + 0.332392i
\(997\) −9.39820 + 25.8213i −0.297644 + 0.817770i 0.697249 + 0.716829i \(0.254407\pi\)
−0.994892 + 0.100940i \(0.967815\pi\)
\(998\) −13.5240 16.5180i −0.428095 0.522868i
\(999\) −37.7506 + 1.06447i −1.19438 + 0.0336783i
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 756.2.bt.a.103.15 840
4.3 odd 2 inner 756.2.bt.a.103.140 yes 840
7.3 odd 6 756.2.cd.a.535.80 yes 840
27.16 even 9 756.2.cd.a.691.50 yes 840
28.3 even 6 756.2.cd.a.535.50 yes 840
108.43 odd 18 756.2.cd.a.691.80 yes 840
189.178 odd 18 inner 756.2.bt.a.367.140 yes 840
756.367 even 18 inner 756.2.bt.a.367.15 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bt.a.103.15 840 1.1 even 1 trivial
756.2.bt.a.103.140 yes 840 4.3 odd 2 inner
756.2.bt.a.367.15 yes 840 756.367 even 18 inner
756.2.bt.a.367.140 yes 840 189.178 odd 18 inner
756.2.cd.a.535.50 yes 840 28.3 even 6
756.2.cd.a.535.80 yes 840 7.3 odd 6
756.2.cd.a.691.50 yes 840 27.16 even 9
756.2.cd.a.691.80 yes 840 108.43 odd 18