Properties

Label 648.2.bd.a.13.7
Level $648$
Weight $2$
Character 648.13
Analytic conductor $5.174$
Analytic rank $0$
Dimension $1908$
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] = [648,2,Mod(13,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([0, 27, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.bd (of order \(54\), degree \(18\), 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: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(1908\)
Relative dimension: \(106\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 13.7
Character \(\chi\) \(=\) 648.13
Dual form 648.2.bd.a.349.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39070 + 0.256830i) q^{2} +(1.07027 + 1.36181i) q^{3} +(1.86808 - 0.714346i) q^{4} +(1.22125 - 0.365619i) q^{5} +(-1.83818 - 1.61898i) q^{6} +(0.532782 + 1.23513i) q^{7} +(-2.41446 + 1.47322i) q^{8} +(-0.709034 + 2.91501i) q^{9} +O(q^{10})\) \(q+(-1.39070 + 0.256830i) q^{2} +(1.07027 + 1.36181i) q^{3} +(1.86808 - 0.714346i) q^{4} +(1.22125 - 0.365619i) q^{5} +(-1.83818 - 1.61898i) q^{6} +(0.532782 + 1.23513i) q^{7} +(-2.41446 + 1.47322i) q^{8} +(-0.709034 + 2.91501i) q^{9} +(-1.60449 + 0.822120i) q^{10} +(-0.619840 - 2.61531i) q^{11} +(2.97215 + 1.77941i) q^{12} +(-2.95766 + 4.49690i) q^{13} +(-1.05816 - 1.58085i) q^{14} +(1.80498 + 1.27180i) q^{15} +(2.97942 - 2.66891i) q^{16} +(0.278388 - 0.101325i) q^{17} +(0.237388 - 4.23599i) q^{18} +(-2.68815 + 7.38562i) q^{19} +(2.02022 - 1.55540i) q^{20} +(-1.11178 + 2.04747i) q^{21} +(1.53370 + 3.47791i) q^{22} +(-0.374244 + 0.867596i) q^{23} +(-4.59037 - 1.71129i) q^{24} +(-2.81966 + 1.85452i) q^{25} +(2.95827 - 7.01344i) q^{26} +(-4.72854 + 2.15429i) q^{27} +(1.87759 + 1.92672i) q^{28} +(6.85265 - 0.399122i) q^{29} +(-2.83681 - 1.30511i) q^{30} +(9.53881 - 1.11493i) q^{31} +(-3.45801 + 4.47685i) q^{32} +(2.89815 - 3.64319i) q^{33} +(-0.361130 + 0.212411i) q^{34} +(1.10225 + 1.31361i) q^{35} +(0.757796 + 5.95195i) q^{36} +(4.68278 - 5.58071i) q^{37} +(1.84155 - 10.9616i) q^{38} +(-9.28941 + 0.785151i) q^{39} +(-2.41003 + 2.68195i) q^{40} +(5.11848 - 2.57060i) q^{41} +(1.02030 - 3.13295i) q^{42} +(-5.54810 + 5.23436i) q^{43} +(-3.02614 - 4.44282i) q^{44} +(0.199873 + 3.81920i) q^{45} +(0.297636 - 1.30268i) q^{46} +(-0.624605 - 0.0730059i) q^{47} +(6.82332 + 1.20093i) q^{48} +(3.56201 - 3.77551i) q^{49} +(3.44499 - 3.30325i) q^{50} +(0.435936 + 0.270665i) q^{51} +(-2.31279 + 10.5133i) q^{52} +(-9.12039 - 5.26566i) q^{53} +(6.02267 - 4.21039i) q^{54} +(-1.71319 - 2.96733i) q^{55} +(-3.10599 - 2.19726i) q^{56} +(-12.9348 + 4.24389i) q^{57} +(-9.42746 + 2.31503i) q^{58} +(-3.32843 + 14.0438i) q^{59} +(4.28034 + 1.08644i) q^{60} +(11.7659 + 8.75938i) q^{61} +(-12.9792 + 4.00038i) q^{62} +(-3.97817 + 0.677317i) q^{63} +(3.65926 - 7.11406i) q^{64} +(-1.96790 + 6.57323i) q^{65} +(-3.09476 + 5.81091i) q^{66} +(-6.61586 - 0.385330i) q^{67} +(0.447669 - 0.388148i) q^{68} +(-1.58204 + 0.418916i) q^{69} +(-1.87027 - 1.54374i) q^{70} +(0.592949 - 3.36278i) q^{71} +(-2.58251 - 8.08274i) q^{72} +(-0.581521 - 3.29797i) q^{73} +(-5.07903 + 8.96376i) q^{74} +(-5.54330 - 1.85499i) q^{75} +(0.254228 + 15.7172i) q^{76} +(2.90000 - 2.15897i) q^{77} +(12.7171 - 3.47771i) q^{78} +(3.06222 + 1.53791i) q^{79} +(2.66282 - 4.34874i) q^{80} +(-7.99454 - 4.13368i) q^{81} +(-6.45805 + 4.88950i) q^{82} +(1.55050 - 3.08731i) q^{83} +(-0.614293 + 4.61903i) q^{84} +(0.302936 - 0.225527i) q^{85} +(6.37138 - 8.70433i) q^{86} +(7.87773 + 8.90482i) q^{87} +(5.34950 + 5.40141i) q^{88} +(-2.53990 - 14.4045i) q^{89} +(-1.25885 - 5.26002i) q^{90} +(-7.13003 - 1.25722i) q^{91} +(-0.0793532 + 1.88808i) q^{92} +(11.7274 + 11.7967i) q^{93} +(0.887386 - 0.0588885i) q^{94} +(-0.582582 + 10.0026i) q^{95} +(-9.79761 + 0.0823007i) q^{96} +(0.244406 - 0.816373i) q^{97} +(-3.98401 + 6.16542i) q^{98} +(8.06313 + 0.0475044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1908 q - 18 q^{2} - 18 q^{4} - 18 q^{6} - 36 q^{7} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1908 q - 18 q^{2} - 18 q^{4} - 18 q^{6} - 36 q^{7} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 18 q^{14} - 36 q^{15} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 18 q^{22} - 36 q^{23} - 18 q^{24} - 36 q^{25} - 9 q^{26} - 9 q^{28} - 18 q^{30} - 36 q^{31} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 18 q^{38} - 36 q^{39} - 18 q^{40} - 36 q^{41} + 27 q^{42} - 90 q^{44} - 18 q^{46} - 36 q^{47} - 117 q^{48} - 36 q^{49} + 99 q^{50} - 18 q^{52} + 108 q^{54} - 18 q^{55} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} + 81 q^{62} - 36 q^{63} - 18 q^{64} - 36 q^{65} + 54 q^{66} - 63 q^{68} - 18 q^{70} - 36 q^{71} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 45 q^{78} - 36 q^{79} - 36 q^{80} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 18 q^{86} - 36 q^{87} - 18 q^{88} - 36 q^{89} - 81 q^{90} - 108 q^{92} - 18 q^{94} - 36 q^{95} - 135 q^{96} - 36 q^{97} - 189 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{4}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39070 + 0.256830i −0.983371 + 0.181606i
\(3\) 1.07027 + 1.36181i 0.617922 + 0.786239i
\(4\) 1.86808 0.714346i 0.934038 0.357173i
\(5\) 1.22125 0.365619i 0.546161 0.163510i −0.00182350 0.999998i \(-0.500580\pi\)
0.547985 + 0.836488i \(0.315395\pi\)
\(6\) −1.83818 1.61898i −0.750433 0.660947i
\(7\) 0.532782 + 1.23513i 0.201373 + 0.466834i 0.988739 0.149651i \(-0.0478151\pi\)
−0.787366 + 0.616486i \(0.788556\pi\)
\(8\) −2.41446 + 1.47322i −0.853641 + 0.520861i
\(9\) −0.709034 + 2.91501i −0.236345 + 0.971669i
\(10\) −1.60449 + 0.822120i −0.507385 + 0.259977i
\(11\) −0.619840 2.61531i −0.186889 0.788545i −0.983032 0.183437i \(-0.941278\pi\)
0.796143 0.605109i \(-0.206870\pi\)
\(12\) 2.97215 + 1.77941i 0.857986 + 0.513672i
\(13\) −2.95766 + 4.49690i −0.820307 + 1.24722i 0.145862 + 0.989305i \(0.453404\pi\)
−0.966169 + 0.257911i \(0.916966\pi\)
\(14\) −1.05816 1.58085i −0.282804 0.422501i
\(15\) 1.80498 + 1.27180i 0.466043 + 0.328377i
\(16\) 2.97942 2.66891i 0.744855 0.667227i
\(17\) 0.278388 0.101325i 0.0675190 0.0245749i −0.308040 0.951373i \(-0.599673\pi\)
0.375559 + 0.926799i \(0.377451\pi\)
\(18\) 0.237388 4.23599i 0.0559530 0.998433i
\(19\) −2.68815 + 7.38562i −0.616703 + 1.69438i 0.0982107 + 0.995166i \(0.468688\pi\)
−0.714914 + 0.699213i \(0.753534\pi\)
\(20\) 2.02022 1.55540i 0.451734 0.347799i
\(21\) −1.11178 + 2.04747i −0.242611 + 0.446794i
\(22\) 1.53370 + 3.47791i 0.326986 + 0.741493i
\(23\) −0.374244 + 0.867596i −0.0780354 + 0.180906i −0.952768 0.303700i \(-0.901778\pi\)
0.874732 + 0.484606i \(0.161037\pi\)
\(24\) −4.59037 1.71129i −0.937005 0.349315i
\(25\) −2.81966 + 1.85452i −0.563931 + 0.370904i
\(26\) 2.95827 7.01344i 0.580164 1.37545i
\(27\) −4.72854 + 2.15429i −0.910007 + 0.414593i
\(28\) 1.87759 + 1.92672i 0.354830 + 0.364116i
\(29\) 6.85265 0.399122i 1.27251 0.0741150i 0.591447 0.806344i \(-0.298557\pi\)
0.681059 + 0.732229i \(0.261520\pi\)
\(30\) −2.83681 1.30511i −0.517929 0.238280i
\(31\) 9.53881 1.11493i 1.71322 0.200247i 0.797849 0.602857i \(-0.205971\pi\)
0.915371 + 0.402611i \(0.131897\pi\)
\(32\) −3.45801 + 4.47685i −0.611296 + 0.791402i
\(33\) 2.89815 3.64319i 0.504503 0.634199i
\(34\) −0.361130 + 0.212411i −0.0619333 + 0.0364281i
\(35\) 1.10225 + 1.31361i 0.186314 + 0.222040i
\(36\) 0.757796 + 5.95195i 0.126299 + 0.991992i
\(37\) 4.68278 5.58071i 0.769844 0.917464i −0.228584 0.973524i \(-0.573409\pi\)
0.998427 + 0.0560604i \(0.0178539\pi\)
\(38\) 1.84155 10.9616i 0.298738 1.77820i
\(39\) −9.28941 + 0.785151i −1.48750 + 0.125725i
\(40\) −2.41003 + 2.68195i −0.381060 + 0.424053i
\(41\) 5.11848 2.57060i 0.799372 0.401460i −0.00172181 0.999999i \(-0.500548\pi\)
0.801094 + 0.598539i \(0.204252\pi\)
\(42\) 1.02030 3.13295i 0.157436 0.483424i
\(43\) −5.54810 + 5.23436i −0.846077 + 0.798233i −0.981280 0.192585i \(-0.938313\pi\)
0.135203 + 0.990818i \(0.456831\pi\)
\(44\) −3.02614 4.44282i −0.456208 0.669780i
\(45\) 0.199873 + 3.81920i 0.0297954 + 0.569333i
\(46\) 0.297636 1.30268i 0.0438840 0.192070i
\(47\) −0.624605 0.0730059i −0.0911080 0.0106490i 0.0704167 0.997518i \(-0.477567\pi\)
−0.161525 + 0.986869i \(0.551641\pi\)
\(48\) 6.82332 + 1.20093i 0.984862 + 0.173340i
\(49\) 3.56201 3.77551i 0.508858 0.539358i
\(50\) 3.44499 3.30325i 0.487195 0.467149i
\(51\) 0.435936 + 0.270665i 0.0610432 + 0.0379007i
\(52\) −2.31279 + 10.5133i −0.320726 + 1.45794i
\(53\) −9.12039 5.26566i −1.25278 0.723294i −0.281121 0.959672i \(-0.590706\pi\)
−0.971661 + 0.236378i \(0.924040\pi\)
\(54\) 6.02267 4.21039i 0.819582 0.572962i
\(55\) −1.71319 2.96733i −0.231006 0.400115i
\(56\) −3.10599 2.19726i −0.415056 0.293622i
\(57\) −12.9348 + 4.24389i −1.71326 + 0.562117i
\(58\) −9.42746 + 2.31503i −1.23789 + 0.303978i
\(59\) −3.32843 + 14.0438i −0.433325 + 1.82834i 0.116664 + 0.993171i \(0.462780\pi\)
−0.549990 + 0.835171i \(0.685368\pi\)
\(60\) 4.28034 + 1.08644i 0.552589 + 0.140259i
\(61\) 11.7659 + 8.75938i 1.50647 + 1.12152i 0.958525 + 0.285008i \(0.0919961\pi\)
0.547942 + 0.836516i \(0.315411\pi\)
\(62\) −12.9792 + 4.00038i −1.64837 + 0.508049i
\(63\) −3.97817 + 0.677317i −0.501202 + 0.0853339i
\(64\) 3.65926 7.11406i 0.457407 0.889257i
\(65\) −1.96790 + 6.57323i −0.244087 + 0.815309i
\(66\) −3.09476 + 5.81091i −0.380939 + 0.715274i
\(67\) −6.61586 0.385330i −0.808256 0.0470755i −0.350960 0.936390i \(-0.614145\pi\)
−0.457295 + 0.889315i \(0.651182\pi\)
\(68\) 0.447669 0.388148i 0.0542878 0.0470699i
\(69\) −1.58204 + 0.418916i −0.190455 + 0.0504315i
\(70\) −1.87027 1.54374i −0.223540 0.184512i
\(71\) 0.592949 3.36278i 0.0703702 0.399089i −0.929195 0.369591i \(-0.879498\pi\)
0.999565 0.0294983i \(-0.00939097\pi\)
\(72\) −2.58251 8.08274i −0.304351 0.952560i
\(73\) −0.581521 3.29797i −0.0680618 0.385998i −0.999742 0.0227180i \(-0.992768\pi\)
0.931680 0.363280i \(-0.118343\pi\)
\(74\) −5.07903 + 8.96376i −0.590425 + 1.04202i
\(75\) −5.54330 1.85499i −0.640085 0.214196i
\(76\) 0.254228 + 15.7172i 0.0291620 + 1.80288i
\(77\) 2.90000 2.15897i 0.330486 0.246037i
\(78\) 12.7171 3.47771i 1.43993 0.393773i
\(79\) 3.06222 + 1.53791i 0.344527 + 0.173028i 0.612645 0.790358i \(-0.290105\pi\)
−0.268118 + 0.963386i \(0.586402\pi\)
\(80\) 2.66282 4.34874i 0.297712 0.486204i
\(81\) −7.99454 4.13368i −0.888283 0.459297i
\(82\) −6.45805 + 4.88950i −0.713172 + 0.539955i
\(83\) 1.55050 3.08731i 0.170190 0.338876i −0.792327 0.610096i \(-0.791131\pi\)
0.962517 + 0.271220i \(0.0874271\pi\)
\(84\) −0.614293 + 4.61903i −0.0670249 + 0.503977i
\(85\) 0.302936 0.225527i 0.0328580 0.0244619i
\(86\) 6.37138 8.70433i 0.687044 0.938612i
\(87\) 7.87773 + 8.90482i 0.844581 + 0.954697i
\(88\) 5.34950 + 5.40141i 0.570258 + 0.575792i
\(89\) −2.53990 14.4045i −0.269229 1.52687i −0.756716 0.653743i \(-0.773198\pi\)
0.487487 0.873130i \(-0.337913\pi\)
\(90\) −1.25885 5.26002i −0.132694 0.554454i
\(91\) −7.13003 1.25722i −0.747430 0.131792i
\(92\) −0.0793532 + 1.88808i −0.00827314 + 0.196846i
\(93\) 11.7274 + 11.7967i 1.21608 + 1.22326i
\(94\) 0.887386 0.0588885i 0.0915269 0.00607388i
\(95\) −0.582582 + 10.0026i −0.0597717 + 1.02624i
\(96\) −9.79761 + 0.0823007i −0.999965 + 0.00839978i
\(97\) 0.244406 0.816373i 0.0248157 0.0828901i −0.944685 0.327980i \(-0.893632\pi\)
0.969500 + 0.245090i \(0.0788174\pi\)
\(98\) −3.98401 + 6.16542i −0.402446 + 0.622802i
\(99\) 8.06313 + 0.0475044i 0.810375 + 0.00477437i
\(100\) −3.94257 + 5.47859i −0.394257 + 0.547859i
\(101\) 4.72810 + 3.51994i 0.470463 + 0.350247i 0.806135 0.591732i \(-0.201556\pi\)
−0.335671 + 0.941979i \(0.608963\pi\)
\(102\) −0.675770 0.264452i −0.0669112 0.0261846i
\(103\) 5.57323 + 1.32088i 0.549146 + 0.130150i 0.495817 0.868427i \(-0.334869\pi\)
0.0533291 + 0.998577i \(0.483017\pi\)
\(104\) 0.516240 15.2149i 0.0506215 1.49194i
\(105\) −0.609174 + 2.90697i −0.0594493 + 0.283691i
\(106\) 14.0361 + 4.98055i 1.36331 + 0.483753i
\(107\) −2.17833 + 1.25766i −0.210587 + 0.121583i −0.601584 0.798809i \(-0.705464\pi\)
0.390997 + 0.920392i \(0.372130\pi\)
\(108\) −7.29436 + 7.40218i −0.701900 + 0.712275i
\(109\) −9.57733 5.52947i −0.917341 0.529627i −0.0345555 0.999403i \(-0.511002\pi\)
−0.882786 + 0.469775i \(0.844335\pi\)
\(110\) 3.14463 + 3.68666i 0.299828 + 0.351509i
\(111\) 12.6117 + 0.404149i 1.19705 + 0.0383601i
\(112\) 4.88382 + 2.25802i 0.461478 + 0.213362i
\(113\) −4.57230 + 4.84636i −0.430126 + 0.455907i −0.905794 0.423718i \(-0.860725\pi\)
0.475668 + 0.879625i \(0.342206\pi\)
\(114\) 16.8985 9.22403i 1.58269 0.863909i
\(115\) −0.139837 + 1.19639i −0.0130399 + 0.111564i
\(116\) 12.5162 5.64076i 1.16210 0.523731i
\(117\) −11.0114 11.8100i −1.01801 1.09184i
\(118\) 1.02198 20.3855i 0.0940807 1.87663i
\(119\) 0.273469 + 0.289860i 0.0250689 + 0.0265715i
\(120\) −6.23168 0.411586i −0.568872 0.0375725i
\(121\) 3.37432 1.69465i 0.306756 0.154059i
\(122\) −18.6125 9.15981i −1.68509 0.829290i
\(123\) 8.97882 + 4.21914i 0.809593 + 0.380427i
\(124\) 17.0228 8.89678i 1.52869 0.798954i
\(125\) −6.86262 + 8.17856i −0.613812 + 0.731512i
\(126\) 5.35847 1.96366i 0.477370 0.174936i
\(127\) 5.02534 4.21676i 0.445927 0.374177i −0.391995 0.919967i \(-0.628215\pi\)
0.837922 + 0.545790i \(0.183770\pi\)
\(128\) −3.26181 + 10.8333i −0.288306 + 0.957538i
\(129\) −13.0662 1.95324i −1.15041 0.171974i
\(130\) 1.04854 9.64679i 0.0919632 0.846079i
\(131\) −1.40762 12.0429i −0.122984 1.05220i −0.903954 0.427629i \(-0.859349\pi\)
0.780970 0.624568i \(-0.214725\pi\)
\(132\) 2.81146 8.87605i 0.244706 0.772561i
\(133\) −10.5544 + 0.614723i −0.915181 + 0.0533032i
\(134\) 9.29962 1.16328i 0.803365 0.100492i
\(135\) −4.98709 + 4.35977i −0.429220 + 0.375230i
\(136\) −0.522884 + 0.654771i −0.0448369 + 0.0561462i
\(137\) 15.3701 10.1091i 1.31316 0.863677i 0.316762 0.948505i \(-0.397404\pi\)
0.996396 + 0.0848278i \(0.0270340\pi\)
\(138\) 2.09255 0.988901i 0.178130 0.0841809i
\(139\) −4.16414 1.79623i −0.353198 0.152355i 0.212086 0.977251i \(-0.431974\pi\)
−0.565284 + 0.824896i \(0.691233\pi\)
\(140\) 2.99745 + 1.66653i 0.253331 + 0.140848i
\(141\) −0.569078 0.928727i −0.0479250 0.0782129i
\(142\) 0.0390516 + 4.82890i 0.00327714 + 0.405232i
\(143\) 13.5941 + 4.94783i 1.13679 + 0.413758i
\(144\) 5.66738 + 10.5774i 0.472281 + 0.881448i
\(145\) 8.22290 2.99289i 0.682874 0.248546i
\(146\) 1.65574 + 4.43712i 0.137030 + 0.367219i
\(147\) 8.95383 + 0.809943i 0.738500 + 0.0668030i
\(148\) 4.76122 13.7703i 0.391370 1.13191i
\(149\) 2.45852 3.73800i 0.201410 0.306229i −0.720633 0.693317i \(-0.756149\pi\)
0.922043 + 0.387088i \(0.126519\pi\)
\(150\) 8.18546 + 1.15604i 0.668340 + 0.0943903i
\(151\) 5.11654 1.21264i 0.416378 0.0986834i −0.0170866 0.999854i \(-0.505439\pi\)
0.433464 + 0.901171i \(0.357291\pi\)
\(152\) −4.39020 21.7925i −0.356092 1.76761i
\(153\) 0.0979766 + 0.883346i 0.00792094 + 0.0714143i
\(154\) −3.47853 + 3.74728i −0.280308 + 0.301964i
\(155\) 11.2417 4.84918i 0.902952 0.389495i
\(156\) −16.7925 + 8.10257i −1.34447 + 0.648725i
\(157\) 5.49389 1.64476i 0.438460 0.131266i −0.0599624 0.998201i \(-0.519098\pi\)
0.498422 + 0.866934i \(0.333913\pi\)
\(158\) −4.65361 1.35229i −0.370221 0.107582i
\(159\) −2.59049 18.0559i −0.205440 1.43193i
\(160\) −2.58629 + 6.73168i −0.204464 + 0.532186i
\(161\) −1.27098 −0.100167
\(162\) 12.1796 + 3.69545i 0.956923 + 0.290342i
\(163\) 7.97111i 0.624346i −0.950025 0.312173i \(-0.898943\pi\)
0.950025 0.312173i \(-0.101057\pi\)
\(164\) 7.72541 8.45844i 0.603253 0.660493i
\(165\) 2.20735 5.50888i 0.171842 0.428866i
\(166\) −1.36337 + 4.69173i −0.105818 + 0.364149i
\(167\) 0.624372 + 2.08555i 0.0483154 + 0.161385i 0.978743 0.205092i \(-0.0657493\pi\)
−0.930427 + 0.366476i \(0.880564\pi\)
\(168\) −0.332010 6.58143i −0.0256151 0.507769i
\(169\) −6.32533 14.6638i −0.486564 1.12798i
\(170\) −0.363370 + 0.391443i −0.0278692 + 0.0300223i
\(171\) −19.6232 13.0726i −1.50062 0.999689i
\(172\) −6.62513 + 13.7415i −0.505161 + 1.04778i
\(173\) −5.66495 23.9023i −0.430698 1.81726i −0.563499 0.826117i \(-0.690545\pi\)
0.132801 0.991143i \(-0.457603\pi\)
\(174\) −13.2426 10.3607i −1.00392 0.785440i
\(175\) −3.79283 2.49458i −0.286711 0.188573i
\(176\) −8.82678 6.13781i −0.665343 0.462655i
\(177\) −22.6872 + 10.4980i −1.70528 + 0.789076i
\(178\) 7.23174 + 19.3800i 0.542042 + 1.45259i
\(179\) 4.25717 + 11.6965i 0.318196 + 0.874235i 0.990933 + 0.134354i \(0.0428960\pi\)
−0.672738 + 0.739881i \(0.734882\pi\)
\(180\) 3.10161 + 6.99178i 0.231180 + 0.521136i
\(181\) 7.70793 21.1774i 0.572926 1.57410i −0.226931 0.973911i \(-0.572869\pi\)
0.799857 0.600191i \(-0.204909\pi\)
\(182\) 10.2386 0.0828002i 0.758936 0.00613756i
\(183\) 0.664128 + 25.3978i 0.0490937 + 1.87746i
\(184\) −0.374559 2.64612i −0.0276128 0.195075i
\(185\) 3.67844 8.52758i 0.270444 0.626960i
\(186\) −19.3391 13.3937i −1.41801 0.982075i
\(187\) −0.437552 0.665265i −0.0319970 0.0486490i
\(188\) −1.21896 + 0.309804i −0.0889019 + 0.0225948i
\(189\) −5.18010 4.69258i −0.376797 0.341335i
\(190\) −1.75876 14.0601i −0.127594 1.02003i
\(191\) 0.796301 + 13.6720i 0.0576183 + 0.989269i 0.895963 + 0.444128i \(0.146487\pi\)
−0.838345 + 0.545140i \(0.816476\pi\)
\(192\) 13.6044 2.63078i 0.981811 0.189860i
\(193\) 10.1980 1.19197i 0.734067 0.0858001i 0.259158 0.965835i \(-0.416555\pi\)
0.474909 + 0.880035i \(0.342481\pi\)
\(194\) −0.130225 + 1.19810i −0.00934964 + 0.0860184i
\(195\) −11.0577 + 4.35525i −0.791855 + 0.311886i
\(196\) 3.95708 9.59745i 0.282649 0.685532i
\(197\) 1.80459 + 2.15062i 0.128572 + 0.153226i 0.826490 0.562952i \(-0.190334\pi\)
−0.697918 + 0.716178i \(0.745890\pi\)
\(198\) −11.2256 + 2.00479i −0.797767 + 0.142474i
\(199\) −8.60276 7.21857i −0.609834 0.511711i 0.284756 0.958600i \(-0.408087\pi\)
−0.894589 + 0.446889i \(0.852532\pi\)
\(200\) 4.07585 8.63163i 0.288206 0.610349i
\(201\) −6.55603 9.42192i −0.462426 0.664571i
\(202\) −7.47938 3.68085i −0.526247 0.258984i
\(203\) 4.14394 + 8.25125i 0.290847 + 0.579124i
\(204\) 1.00771 + 0.194214i 0.0705538 + 0.0135977i
\(205\) 5.31110 5.01076i 0.370943 0.349967i
\(206\) −8.08991 0.405569i −0.563651 0.0282573i
\(207\) −2.26370 1.70608i −0.157338 0.118581i
\(208\) 3.18971 + 21.2919i 0.221166 + 1.47632i
\(209\) 20.9819 + 2.45243i 1.45135 + 0.169638i
\(210\) 0.100579 4.19916i 0.00694064 0.289770i
\(211\) −6.25310 5.89949i −0.430481 0.406138i 0.440267 0.897867i \(-0.354884\pi\)
−0.870748 + 0.491729i \(0.836365\pi\)
\(212\) −20.7991 3.32154i −1.42849 0.228124i
\(213\) 5.21408 2.79161i 0.357263 0.191278i
\(214\) 2.70640 2.30849i 0.185005 0.157805i
\(215\) −4.86185 + 8.42097i −0.331576 + 0.574306i
\(216\) 8.24314 12.1676i 0.560875 0.827901i
\(217\) 6.45918 + 11.1876i 0.438478 + 0.759466i
\(218\) 14.7393 + 5.23007i 0.998271 + 0.354225i
\(219\) 3.86881 4.32164i 0.261430 0.292029i
\(220\) −5.32007 4.31939i −0.358679 0.291213i
\(221\) −0.367728 + 1.55157i −0.0247361 + 0.104370i
\(222\) −17.6429 + 2.67702i −1.18411 + 0.179670i
\(223\) −1.88968 + 2.53828i −0.126542 + 0.169976i −0.860879 0.508809i \(-0.830086\pi\)
0.734337 + 0.678785i \(0.237493\pi\)
\(224\) −7.37184 1.88590i −0.492552 0.126007i
\(225\) −3.40670 9.53424i −0.227113 0.635616i
\(226\) 5.11400 7.91412i 0.340178 0.526440i
\(227\) 26.6276 + 7.97179i 1.76734 + 0.529107i 0.994429 0.105409i \(-0.0336153\pi\)
0.772910 + 0.634516i \(0.218800\pi\)
\(228\) −21.1317 + 17.1679i −1.39948 + 1.13697i
\(229\) 22.4509 + 1.30761i 1.48359 + 0.0864095i 0.780709 0.624894i \(-0.214858\pi\)
0.702885 + 0.711304i \(0.251895\pi\)
\(230\) −0.112797 1.69972i −0.00743759 0.112076i
\(231\) 6.04389 + 1.63855i 0.397659 + 0.107809i
\(232\) −15.9575 + 11.0591i −1.04766 + 0.726066i
\(233\) −4.52178 + 25.6443i −0.296232 + 1.68001i 0.365922 + 0.930645i \(0.380754\pi\)
−0.662154 + 0.749368i \(0.730358\pi\)
\(234\) 18.3467 + 13.5961i 1.19936 + 0.888807i
\(235\) −0.789493 + 0.139209i −0.0515009 + 0.00908099i
\(236\) 3.81434 + 28.6125i 0.248293 + 1.86251i
\(237\) 1.18308 + 5.81614i 0.0768495 + 0.377799i
\(238\) −0.454758 0.332873i −0.0294776 0.0215769i
\(239\) 3.84462 + 5.16423i 0.248688 + 0.334046i 0.908885 0.417046i \(-0.136935\pi\)
−0.660197 + 0.751092i \(0.729527\pi\)
\(240\) 8.77209 1.02809i 0.566236 0.0663632i
\(241\) 14.8792 + 7.47262i 0.958455 + 0.481354i 0.858035 0.513591i \(-0.171685\pi\)
0.100420 + 0.994945i \(0.467981\pi\)
\(242\) −4.25742 + 3.22337i −0.273677 + 0.207206i
\(243\) −2.92707 15.3112i −0.187772 0.982213i
\(244\) 28.2368 + 7.95827i 1.80768 + 0.509476i
\(245\) 2.96972 5.91319i 0.189728 0.377780i
\(246\) −13.5704 3.56151i −0.865219 0.227074i
\(247\) −25.2618 33.9325i −1.60737 2.15907i
\(248\) −21.3886 + 16.7447i −1.35818 + 1.06329i
\(249\) 5.86378 1.19277i 0.371602 0.0755890i
\(250\) 7.44333 13.1364i 0.470757 0.830820i
\(251\) −10.7356 + 1.89297i −0.677622 + 0.119483i −0.501859 0.864949i \(-0.667350\pi\)
−0.175763 + 0.984433i \(0.556239\pi\)
\(252\) −6.94768 + 4.10707i −0.437663 + 0.258721i
\(253\) 2.50100 + 0.440994i 0.157237 + 0.0277251i
\(254\) −5.90574 + 7.15490i −0.370559 + 0.448939i
\(255\) 0.631349 + 0.171164i 0.0395366 + 0.0107187i
\(256\) 1.75387 15.9036i 0.109617 0.993974i
\(257\) 1.30036 22.3263i 0.0811141 1.39268i −0.674798 0.738003i \(-0.735769\pi\)
0.755912 0.654673i \(-0.227194\pi\)
\(258\) 18.6727 0.639417i 1.16251 0.0398083i
\(259\) 9.38779 + 2.81052i 0.583329 + 0.174637i
\(260\) 1.01938 + 13.6851i 0.0632194 + 0.848711i
\(261\) −3.69532 + 20.2585i −0.228734 + 1.25397i
\(262\) 5.05056 + 16.3866i 0.312025 + 1.01237i
\(263\) −6.31097 + 8.47711i −0.389151 + 0.522721i −0.952924 0.303209i \(-0.901942\pi\)
0.563773 + 0.825930i \(0.309349\pi\)
\(264\) −1.63025 + 13.0660i −0.100335 + 0.804154i
\(265\) −13.0635 3.09612i −0.802487 0.190193i
\(266\) 14.5201 3.56558i 0.890282 0.218620i
\(267\) 16.8977 18.8756i 1.03413 1.15517i
\(268\) −12.6342 + 4.00619i −0.771756 + 0.244717i
\(269\) −9.42326 + 5.44052i −0.574546 + 0.331714i −0.758963 0.651134i \(-0.774294\pi\)
0.184417 + 0.982848i \(0.440960\pi\)
\(270\) 5.81581 7.34396i 0.353939 0.446939i
\(271\) 3.27538 5.67313i 0.198965 0.344618i −0.749228 0.662312i \(-0.769575\pi\)
0.948193 + 0.317694i \(0.102909\pi\)
\(272\) 0.559008 1.04488i 0.0338948 0.0633552i
\(273\) −5.91899 11.0553i −0.358234 0.669096i
\(274\) −18.7789 + 18.0062i −1.13447 + 1.08779i
\(275\) 6.59787 + 6.22477i 0.397867 + 0.375368i
\(276\) −2.65612 + 1.91269i −0.159880 + 0.115131i
\(277\) 0.357153 3.05564i 0.0214593 0.183596i −0.978258 0.207394i \(-0.933502\pi\)
0.999717 + 0.0237982i \(0.00757592\pi\)
\(278\) 6.25238 + 1.42854i 0.374993 + 0.0856781i
\(279\) −3.51331 + 28.5962i −0.210337 + 1.71201i
\(280\) −4.59657 1.54781i −0.274697 0.0924991i
\(281\) −10.4535 11.0801i −0.623604 0.660981i 0.336155 0.941807i \(-0.390873\pi\)
−0.959759 + 0.280825i \(0.909392\pi\)
\(282\) 1.02994 + 1.14542i 0.0613320 + 0.0682089i
\(283\) 10.5745 + 21.0555i 0.628586 + 1.25162i 0.952214 + 0.305433i \(0.0988013\pi\)
−0.323627 + 0.946185i \(0.604902\pi\)
\(284\) −1.29452 6.70551i −0.0768155 0.397899i
\(285\) −14.2451 + 9.91209i −0.843805 + 0.587142i
\(286\) −20.1760 3.38957i −1.19303 0.200429i
\(287\) 5.90205 + 4.95240i 0.348387 + 0.292331i
\(288\) −10.5982 13.2544i −0.624505 0.781021i
\(289\) −12.9555 + 10.8710i −0.762090 + 0.639469i
\(290\) −10.6669 + 6.27409i −0.626382 + 0.368427i
\(291\) 1.37332 0.540908i 0.0805056 0.0317086i
\(292\) −3.44222 5.74545i −0.201440 0.336227i
\(293\) −1.00696 8.61512i −0.0588274 0.503301i −0.990244 0.139345i \(-0.955500\pi\)
0.931416 0.363955i \(-0.118574\pi\)
\(294\) −12.6601 + 1.17323i −0.738351 + 0.0684241i
\(295\) 1.06981 + 18.3679i 0.0622868 + 1.06942i
\(296\) −3.08478 + 20.3732i −0.179299 + 1.18417i
\(297\) 8.56506 + 11.0313i 0.496995 + 0.640099i
\(298\) −2.45902 + 5.82984i −0.142447 + 0.337714i
\(299\) −2.79461 4.24899i −0.161616 0.245726i
\(300\) −11.6804 + 0.494573i −0.674368 + 0.0285542i
\(301\) −9.42103 4.06384i −0.543019 0.234236i
\(302\) −6.80411 + 3.00050i −0.391533 + 0.172659i
\(303\) 0.266878 + 10.2061i 0.0153318 + 0.586322i
\(304\) 11.7024 + 29.1793i 0.671180 + 1.67355i
\(305\) 17.5717 + 6.39559i 1.00615 + 0.366210i
\(306\) −0.363126 1.20330i −0.0207585 0.0687883i
\(307\) −7.00312 19.2409i −0.399689 1.09814i −0.962436 0.271508i \(-0.912478\pi\)
0.562747 0.826629i \(-0.309744\pi\)
\(308\) 3.87517 6.10472i 0.220808 0.347849i
\(309\) 4.16609 + 9.00336i 0.237001 + 0.512183i
\(310\) −14.3883 + 9.63094i −0.817202 + 0.547000i
\(311\) 8.41077 + 5.53185i 0.476931 + 0.313683i 0.765116 0.643892i \(-0.222681\pi\)
−0.288185 + 0.957575i \(0.593052\pi\)
\(312\) 21.2722 15.5810i 1.20430 0.882103i
\(313\) −3.43018 + 0.812968i −0.193885 + 0.0459517i −0.326411 0.945228i \(-0.605839\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(314\) −7.21791 + 3.69836i −0.407330 + 0.208711i
\(315\) −4.61071 + 2.28167i −0.259784 + 0.128558i
\(316\) 6.81907 + 0.685439i 0.383603 + 0.0385590i
\(317\) −8.25674 + 3.56161i −0.463745 + 0.200040i −0.615115 0.788437i \(-0.710891\pi\)
0.151370 + 0.988477i \(0.451631\pi\)
\(318\) 8.23990 + 24.4450i 0.462070 + 1.37081i
\(319\) −5.29137 17.6744i −0.296260 0.989577i
\(320\) 1.86784 10.0260i 0.104416 0.560468i
\(321\) −4.04410 1.62043i −0.225720 0.0904435i
\(322\) 1.76755 0.326427i 0.0985018 0.0181911i
\(323\) 2.32845i 0.129558i
\(324\) −17.8873 2.01115i −0.993739 0.111731i
\(325\) 18.1647i 1.00760i
\(326\) 2.04722 + 11.0854i 0.113385 + 0.613964i
\(327\) −2.72028 18.9605i −0.150432 1.04852i
\(328\) −8.57133 + 13.7472i −0.473272 + 0.759064i
\(329\) −0.242607 0.810363i −0.0133753 0.0446767i
\(330\) −1.65491 + 8.22810i −0.0910996 + 0.452942i
\(331\) −4.04572 + 1.74515i −0.222373 + 0.0959223i −0.504352 0.863498i \(-0.668268\pi\)
0.281979 + 0.959421i \(0.409009\pi\)
\(332\) 0.691054 6.87492i 0.0379265 0.377311i
\(333\) 12.9476 + 17.6072i 0.709523 + 0.964871i
\(334\) −1.40394 2.74001i −0.0768204 0.149927i
\(335\) −8.22052 + 1.94830i −0.449135 + 0.106447i
\(336\) 2.15204 + 9.06751i 0.117403 + 0.494673i
\(337\) −9.32661 6.13421i −0.508053 0.334152i 0.269467 0.963010i \(-0.413152\pi\)
−0.777520 + 0.628858i \(0.783523\pi\)
\(338\) 12.5627 + 18.7683i 0.683322 + 1.02086i
\(339\) −11.4934 1.03967i −0.624236 0.0564670i
\(340\) 0.404803 0.637704i 0.0219535 0.0345843i
\(341\) −8.82841 24.2558i −0.478085 1.31353i
\(342\) 30.6473 + 13.1402i 1.65722 + 0.710543i
\(343\) 15.4091 + 5.60846i 0.832014 + 0.302828i
\(344\) 5.68432 20.8117i 0.306478 1.12209i
\(345\) −1.77891 + 1.09003i −0.0957733 + 0.0586851i
\(346\) 14.0171 + 31.7859i 0.753562 + 1.70882i
\(347\) 11.3666 + 4.90308i 0.610192 + 0.263211i 0.678672 0.734441i \(-0.262556\pi\)
−0.0684800 + 0.997652i \(0.521815\pi\)
\(348\) 21.0773 + 11.0075i 1.12986 + 0.590061i
\(349\) 12.7614 + 19.4027i 0.683101 + 1.03860i 0.996046 + 0.0888336i \(0.0283140\pi\)
−0.312945 + 0.949771i \(0.601316\pi\)
\(350\) 5.91536 + 2.49509i 0.316189 + 0.133368i
\(351\) 4.29778 27.6354i 0.229398 1.47507i
\(352\) 13.8517 + 6.26884i 0.738301 + 0.334131i
\(353\) 0.786138 + 13.4975i 0.0418419 + 0.718398i 0.952369 + 0.304948i \(0.0986391\pi\)
−0.910527 + 0.413449i \(0.864324\pi\)
\(354\) 28.8549 20.4263i 1.53362 1.08564i
\(355\) −0.505357 4.32360i −0.0268216 0.229473i
\(356\) −15.0345 25.0943i −0.796828 1.33000i
\(357\) −0.102047 + 0.682642i −0.00540091 + 0.0361292i
\(358\) −8.92444 15.1729i −0.471671 0.801911i
\(359\) 7.88204 6.61382i 0.415998 0.349064i −0.410640 0.911798i \(-0.634695\pi\)
0.826638 + 0.562733i \(0.190250\pi\)
\(360\) −6.10910 8.92686i −0.321978 0.470487i
\(361\) −32.7665 27.4943i −1.72455 1.44707i
\(362\) −5.28041 + 31.4309i −0.277532 + 1.65197i
\(363\) 5.91923 + 2.78144i 0.310679 + 0.145988i
\(364\) −14.2175 + 2.74473i −0.745201 + 0.143863i
\(365\) −1.91598 3.81504i −0.100287 0.199688i
\(366\) −7.44652 35.1501i −0.389236 1.83732i
\(367\) −10.7619 11.4070i −0.561769 0.595440i 0.382768 0.923844i \(-0.374971\pi\)
−0.944537 + 0.328404i \(0.893489\pi\)
\(368\) 1.20050 + 3.58376i 0.0625805 + 0.186816i
\(369\) 3.86414 + 16.7430i 0.201159 + 0.871608i
\(370\) −2.92545 + 12.8040i −0.152087 + 0.665649i
\(371\) 1.64458 14.0703i 0.0853824 0.730493i
\(372\) 30.3347 + 13.6597i 1.57278 + 0.708225i
\(373\) 14.2530 + 13.4470i 0.737990 + 0.696258i 0.960378 0.278700i \(-0.0899036\pi\)
−0.222388 + 0.974958i \(0.571385\pi\)
\(374\) 0.779362 + 0.812806i 0.0402999 + 0.0420292i
\(375\) −18.4825 0.592281i −0.954432 0.0305853i
\(376\) 1.61564 0.743909i 0.0833202 0.0383642i
\(377\) −18.4730 + 31.9962i −0.951407 + 1.64789i
\(378\) 8.40914 + 5.19555i 0.432520 + 0.267230i
\(379\) −1.65563 + 0.955881i −0.0850442 + 0.0491003i −0.541919 0.840431i \(-0.682302\pi\)
0.456875 + 0.889531i \(0.348969\pi\)
\(380\) 6.05698 + 19.1017i 0.310716 + 0.979897i
\(381\) 11.1209 + 2.33046i 0.569741 + 0.119393i
\(382\) −4.61879 18.8090i −0.236318 0.962355i
\(383\) 6.79594 + 1.61067i 0.347257 + 0.0823013i 0.400543 0.916278i \(-0.368822\pi\)
−0.0532865 + 0.998579i \(0.516970\pi\)
\(384\) −18.2439 + 7.15263i −0.931005 + 0.365006i
\(385\) 2.75227 3.69694i 0.140269 0.188414i
\(386\) −13.8762 + 4.27683i −0.706279 + 0.217685i
\(387\) −11.3244 19.8841i −0.575653 1.01077i
\(388\) −0.126604 1.69964i −0.00642733 0.0862860i
\(389\) 3.88036 + 1.16170i 0.196742 + 0.0589007i 0.383658 0.923475i \(-0.374664\pi\)
−0.186916 + 0.982376i \(0.559849\pi\)
\(390\) 14.2593 8.89678i 0.722047 0.450506i
\(391\) −0.0162760 + 0.279449i −0.000823114 + 0.0141323i
\(392\) −3.03819 + 14.3634i −0.153452 + 0.725463i
\(393\) 14.8936 14.8061i 0.751284 0.746871i
\(394\) −3.06198 2.52739i −0.154260 0.127328i
\(395\) 4.30204 + 0.758566i 0.216459 + 0.0381676i
\(396\) 15.0965 5.67113i 0.758627 0.284985i
\(397\) 4.57272 0.806295i 0.229498 0.0404668i −0.0577161 0.998333i \(-0.518382\pi\)
0.287215 + 0.957866i \(0.407271\pi\)
\(398\) 13.8178 + 7.82940i 0.692623 + 0.392452i
\(399\) −12.1332 13.7151i −0.607420 0.686614i
\(400\) −3.45140 + 13.0508i −0.172570 + 0.652539i
\(401\) −1.60090 2.15038i −0.0799451 0.107385i 0.760352 0.649512i \(-0.225027\pi\)
−0.840297 + 0.542127i \(0.817619\pi\)
\(402\) 11.5373 + 11.4193i 0.575427 + 0.569541i
\(403\) −23.1988 + 46.1926i −1.15562 + 2.30102i
\(404\) 11.3469 + 3.19802i 0.564530 + 0.159107i
\(405\) −11.2747 2.12531i −0.560245 0.105607i
\(406\) −7.88213 10.4107i −0.391184 0.516675i
\(407\) −17.4979 8.78776i −0.867337 0.435593i
\(408\) −1.45130 0.0112825i −0.0718500 0.000558566i
\(409\) 18.3248 + 24.6144i 0.906101 + 1.21711i 0.975607 + 0.219524i \(0.0704504\pi\)
−0.0695057 + 0.997582i \(0.522142\pi\)
\(410\) −6.09921 + 8.33250i −0.301219 + 0.411513i
\(411\) 30.2168 + 10.1116i 1.49049 + 0.498771i
\(412\) 11.3548 1.51371i 0.559410 0.0745752i
\(413\) −19.1192 + 3.37123i −0.940793 + 0.165887i
\(414\) 3.58629 + 1.79125i 0.176257 + 0.0880354i
\(415\) 0.764779 4.33728i 0.0375415 0.212909i
\(416\) −9.90431 28.7913i −0.485599 1.41161i
\(417\) −2.01064 7.59321i −0.0984614 0.371841i
\(418\) −29.8093 + 1.97820i −1.45802 + 0.0967568i
\(419\) −12.9433 0.753862i −0.632322 0.0368286i −0.261009 0.965336i \(-0.584055\pi\)
−0.371313 + 0.928508i \(0.621092\pi\)
\(420\) 0.938597 + 5.86560i 0.0457988 + 0.286212i
\(421\) −4.09909 1.22719i −0.199778 0.0598095i 0.185351 0.982672i \(-0.440658\pi\)
−0.385129 + 0.922863i \(0.625843\pi\)
\(422\) 10.2113 + 6.59842i 0.497080 + 0.321206i
\(423\) 0.655679 1.76896i 0.0318802 0.0860100i
\(424\) 29.7783 0.722584i 1.44616 0.0350918i
\(425\) −0.597050 + 0.801977i −0.0289612 + 0.0389016i
\(426\) −6.53423 + 5.22142i −0.316585 + 0.252979i
\(427\) −4.55030 + 19.1992i −0.220204 + 0.929115i
\(428\) −3.17089 + 3.90549i −0.153271 + 0.188779i
\(429\) 7.81135 + 23.8080i 0.377136 + 1.14946i
\(430\) 4.59860 12.9597i 0.221764 0.624972i
\(431\) −14.3542 24.8621i −0.691415 1.19757i −0.971374 0.237555i \(-0.923654\pi\)
0.279959 0.960012i \(-0.409679\pi\)
\(432\) −8.33870 + 19.0385i −0.401196 + 0.915992i
\(433\) −5.97611 + 10.3509i −0.287194 + 0.497434i −0.973139 0.230219i \(-0.926056\pi\)
0.685945 + 0.727653i \(0.259389\pi\)
\(434\) −11.8561 13.8997i −0.569110 0.667206i
\(435\) 12.8765 + 7.99479i 0.617380 + 0.383321i
\(436\) −21.8411 3.48795i −1.04600 0.167042i
\(437\) −5.40171 5.09625i −0.258399 0.243787i
\(438\) −4.27041 + 7.00372i −0.204048 + 0.334651i
\(439\) −34.5997 4.04413i −1.65136 0.193016i −0.761150 0.648576i \(-0.775365\pi\)
−0.890205 + 0.455560i \(0.849439\pi\)
\(440\) 8.50795 + 4.64061i 0.405601 + 0.221232i
\(441\) 8.48005 + 13.0602i 0.403812 + 0.621916i
\(442\) 0.112909 2.25220i 0.00537053 0.107126i
\(443\) 23.7195 22.3782i 1.12695 1.06322i 0.129515 0.991577i \(-0.458658\pi\)
0.997431 0.0716406i \(-0.0228235\pi\)
\(444\) 23.8483 8.25414i 1.13179 0.391724i
\(445\) −8.36842 16.6629i −0.396701 0.789897i
\(446\) 1.97606 4.01530i 0.0935692 0.190130i
\(447\) 7.72171 0.652648i 0.365225 0.0308692i
\(448\) 10.7364 + 0.729408i 0.507245 + 0.0344613i
\(449\) −14.0360 11.7776i −0.662401 0.555821i 0.248404 0.968656i \(-0.420094\pi\)
−0.910805 + 0.412836i \(0.864538\pi\)
\(450\) 7.18637 + 12.3843i 0.338769 + 0.583801i
\(451\) −9.89554 11.7930i −0.465963 0.555313i
\(452\) −5.07943 + 12.3196i −0.238916 + 0.579464i
\(453\) 7.12747 + 5.66988i 0.334878 + 0.266394i
\(454\) −39.0784 4.24756i −1.83404 0.199348i
\(455\) −9.16723 + 1.07150i −0.429767 + 0.0502325i
\(456\) 24.9785 29.3026i 1.16973 1.37222i
\(457\) 0.178962 + 3.07266i 0.00837149 + 0.143733i 0.999904 + 0.0138725i \(0.00441588\pi\)
−0.991532 + 0.129860i \(0.958547\pi\)
\(458\) −31.5582 + 3.94756i −1.47462 + 0.184458i
\(459\) −1.09808 + 1.07885i −0.0512542 + 0.0503562i
\(460\) 0.593407 + 2.33483i 0.0276677 + 0.108862i
\(461\) −12.3833 18.8279i −0.576749 0.876905i 0.422821 0.906213i \(-0.361040\pi\)
−0.999570 + 0.0293084i \(0.990670\pi\)
\(462\) −8.82605 0.726476i −0.410625 0.0337987i
\(463\) 10.7072 24.8220i 0.497603 1.15357i −0.465647 0.884970i \(-0.654178\pi\)
0.963251 0.268604i \(-0.0865623\pi\)
\(464\) 19.3517 19.4782i 0.898380 0.904255i
\(465\) 18.6353 + 10.1190i 0.864191 + 0.469258i
\(466\) −0.297804 36.8248i −0.0137955 1.70587i
\(467\) −13.0145 + 35.7571i −0.602240 + 1.65464i 0.144483 + 0.989507i \(0.453848\pi\)
−0.746724 + 0.665134i \(0.768374\pi\)
\(468\) −29.0066 14.1961i −1.34083 0.656215i
\(469\) −3.04888 8.37672i −0.140784 0.386801i
\(470\) 1.06219 0.396363i 0.0489953 0.0182829i
\(471\) 8.11980 + 5.72127i 0.374141 + 0.263622i
\(472\) −12.6531 38.8117i −0.582408 1.78645i
\(473\) 17.1284 + 11.2655i 0.787565 + 0.517990i
\(474\) −3.13907 7.78463i −0.144182 0.357560i
\(475\) −6.11712 25.8101i −0.280673 1.18425i
\(476\) 0.717922 + 0.346130i 0.0329059 + 0.0158648i
\(477\) 21.8161 22.8525i 0.998891 1.04634i
\(478\) −6.67304 6.19446i −0.305218 0.283328i
\(479\) −4.48003 10.3859i −0.204698 0.474543i 0.784682 0.619899i \(-0.212826\pi\)
−0.989379 + 0.145356i \(0.953567\pi\)
\(480\) −11.9353 + 3.68271i −0.544768 + 0.168092i
\(481\) 11.2459 + 37.5638i 0.512767 + 1.71276i
\(482\) −22.6117 6.57072i −1.02993 0.299288i
\(483\) −1.36030 1.73083i −0.0618957 0.0787556i
\(484\) 5.09292 5.57616i 0.231497 0.253462i
\(485\) 1.08636i 0.0493289i
\(486\) 8.00304 + 20.5415i 0.363025 + 0.931779i
\(487\) 19.0919 0.865136 0.432568 0.901601i \(-0.357607\pi\)
0.432568 + 0.901601i \(0.357607\pi\)
\(488\) −41.3128 3.81548i −1.87014 0.172719i
\(489\) 10.8551 8.53126i 0.490885 0.385797i
\(490\) −2.61129 + 8.98617i −0.117966 + 0.405954i
\(491\) −29.2271 + 8.75003i −1.31900 + 0.394883i −0.867523 0.497398i \(-0.834289\pi\)
−0.451480 + 0.892281i \(0.649104\pi\)
\(492\) 19.7870 + 1.46768i 0.892069 + 0.0661683i
\(493\) 1.86726 0.805455i 0.0840969 0.0362759i
\(494\) 43.8464 + 40.7018i 1.97274 + 1.83126i
\(495\) 9.86450 2.89002i 0.443376 0.129897i
\(496\) 25.4445 28.7800i 1.14249 1.29226i
\(497\) 4.46938 1.05926i 0.200479 0.0475144i
\(498\) −7.84840 + 3.16478i −0.351695 + 0.141817i
\(499\) 18.0661 27.4681i 0.808749 1.22964i −0.161341 0.986899i \(-0.551582\pi\)
0.970090 0.242744i \(-0.0780476\pi\)
\(500\) −6.97758 + 20.1805i −0.312047 + 0.902498i
\(501\) −2.17187 + 3.08238i −0.0970318 + 0.137711i
\(502\) 14.4437 5.38976i 0.644655 0.240557i
\(503\) −11.9114 + 4.33539i −0.531103 + 0.193306i −0.593631 0.804738i \(-0.702306\pi\)
0.0625279 + 0.998043i \(0.480084\pi\)
\(504\) 8.60730 7.49606i 0.383400 0.333901i
\(505\) 7.06116 + 2.57005i 0.314218 + 0.114366i
\(506\) −3.59140 + 0.0290439i −0.159657 + 0.00129116i
\(507\) 13.1994 24.3081i 0.586205 1.07956i
\(508\) 6.37550 11.4671i 0.282867 0.508769i
\(509\) 28.9174 + 12.4738i 1.28174 + 0.552890i 0.924521 0.381130i \(-0.124465\pi\)
0.357221 + 0.934020i \(0.383724\pi\)
\(510\) −0.921975 0.0758882i −0.0408257 0.00336038i
\(511\) 3.76359 2.47535i 0.166491 0.109503i
\(512\) 1.64542 + 22.5675i 0.0727178 + 0.997353i
\(513\) −3.19975 40.7142i −0.141272 1.79758i
\(514\) 3.92566 + 31.3831i 0.173154 + 1.38425i
\(515\) 7.28926 0.424551i 0.321203 0.0187080i
\(516\) −25.8039 + 5.68496i −1.13595 + 0.250266i
\(517\) 0.196222 + 1.67879i 0.00862983 + 0.0738330i
\(518\) −13.7774 1.49751i −0.605344 0.0657969i
\(519\) 26.4873 33.2966i 1.16266 1.46156i
\(520\) −4.93239 18.7700i −0.216300 0.823117i
\(521\) 17.2348 14.4617i 0.755072 0.633581i −0.181767 0.983342i \(-0.558182\pi\)
0.936839 + 0.349761i \(0.113737\pi\)
\(522\) −0.0639357 29.1225i −0.00279839 1.27466i
\(523\) 10.0643 11.9941i 0.440079 0.524466i −0.499723 0.866185i \(-0.666565\pi\)
0.939802 + 0.341719i \(0.111009\pi\)
\(524\) −11.2324 21.4916i −0.490688 0.938866i
\(525\) −0.662221 7.83498i −0.0289017 0.341947i
\(526\) 6.59947 13.4099i 0.287751 0.584701i
\(527\) 2.54252 1.27690i 0.110754 0.0556227i
\(528\) −1.08855 18.5895i −0.0473732 0.809004i
\(529\) 15.1709 + 16.0802i 0.659604 + 0.699139i
\(530\) 18.9626 + 0.950646i 0.823683 + 0.0412934i
\(531\) −38.5777 19.6599i −1.67413 0.853168i
\(532\) −19.2773 + 8.68783i −0.835775 + 0.376665i
\(533\) −3.57899 + 30.6202i −0.155023 + 1.32631i
\(534\) −18.6518 + 30.5901i −0.807143 + 1.32376i
\(535\) −2.20047 + 2.33236i −0.0951347 + 0.100837i
\(536\) 16.5414 8.81623i 0.714480 0.380803i
\(537\) −11.3720 + 18.3158i −0.490738 + 0.790387i
\(538\) 11.7076 9.98630i 0.504751 0.430540i
\(539\) −12.0820 6.97554i −0.520408 0.300458i
\(540\) −6.20188 + 11.7069i −0.266886 + 0.503785i
\(541\) −1.11467 + 0.643555i −0.0479234 + 0.0276686i −0.523770 0.851860i \(-0.675475\pi\)
0.475847 + 0.879528i \(0.342142\pi\)
\(542\) −3.09803 + 8.73082i −0.133072 + 0.375021i
\(543\) 37.0891 12.1688i 1.59164 0.522215i
\(544\) −0.509053 + 1.59668i −0.0218255 + 0.0684572i
\(545\) −13.7180 3.25123i −0.587615 0.139267i
\(546\) 11.0709 + 13.8544i 0.473789 + 0.592913i
\(547\) −26.4574 19.6968i −1.13124 0.842176i −0.142201 0.989838i \(-0.545418\pi\)
−0.989038 + 0.147662i \(0.952825\pi\)
\(548\) 21.4912 29.8641i 0.918057 1.27573i
\(549\) −33.8761 + 28.0870i −1.44580 + 1.19872i
\(550\) −10.7743 6.96224i −0.459420 0.296871i
\(551\) −15.4732 + 51.6840i −0.659179 + 2.20181i
\(552\) 3.20263 3.34215i 0.136313 0.142251i
\(553\) −0.268013 + 4.60161i −0.0113971 + 0.195680i
\(554\) 0.288089 + 4.34120i 0.0122397 + 0.184440i
\(555\) 15.5498 4.11751i 0.660054 0.174779i
\(556\) −9.06206 0.380866i −0.384317 0.0161523i
\(557\) 3.87758 + 0.683722i 0.164298 + 0.0289702i 0.255192 0.966890i \(-0.417861\pi\)
−0.0908937 + 0.995861i \(0.528972\pi\)
\(558\) −2.45842 40.6710i −0.104073 1.72174i
\(559\) −7.12902 40.4307i −0.301526 1.71004i
\(560\) 6.78996 + 0.971991i 0.286928 + 0.0410741i
\(561\) 0.437663 1.30788i 0.0184781 0.0552186i
\(562\) 17.3834 + 12.7242i 0.733273 + 0.536740i
\(563\) 12.1310 9.03118i 0.511260 0.380619i −0.310392 0.950609i \(-0.600460\pi\)
0.821652 + 0.569990i \(0.193053\pi\)
\(564\) −1.72651 1.32841i −0.0726993 0.0559364i
\(565\) −3.81202 + 7.59035i −0.160373 + 0.319329i
\(566\) −20.1135 26.5659i −0.845435 1.11665i
\(567\) 0.846269 12.0766i 0.0355400 0.507171i
\(568\) 3.52246 + 8.99286i 0.147799 + 0.377332i
\(569\) 14.1141 + 7.08836i 0.591694 + 0.297160i 0.719338 0.694660i \(-0.244445\pi\)
−0.127644 + 0.991820i \(0.540742\pi\)
\(570\) 17.2648 17.4433i 0.723145 0.730619i
\(571\) −5.86490 + 4.36626i −0.245438 + 0.182722i −0.712848 0.701319i \(-0.752595\pi\)
0.467409 + 0.884041i \(0.345187\pi\)
\(572\) 28.9292 0.467935i 1.20959 0.0195654i
\(573\) −17.7663 + 15.7171i −0.742198 + 0.656593i
\(574\) −9.47989 5.37147i −0.395683 0.224201i
\(575\) −0.553731 3.14037i −0.0230922 0.130962i
\(576\) 18.1430 + 15.7109i 0.755958 + 0.654620i
\(577\) −4.54911 + 25.7993i −0.189382 + 1.07404i 0.730813 + 0.682578i \(0.239141\pi\)
−0.920195 + 0.391461i \(0.871970\pi\)
\(578\) 15.2252 18.4456i 0.633285 0.767236i
\(579\) 12.5379 + 12.6119i 0.521056 + 0.524135i
\(580\) 13.2230 11.4649i 0.549057 0.476056i
\(581\) 4.63930 + 0.270208i 0.192471 + 0.0112101i
\(582\) −1.77095 + 1.10495i −0.0734084 + 0.0458016i
\(583\) −8.11815 + 27.1165i −0.336219 + 1.12305i
\(584\) 6.26268 + 7.10611i 0.259152 + 0.294053i
\(585\) −17.7657 10.3971i −0.734522 0.429866i
\(586\) 3.61300 + 11.7224i 0.149252 + 0.484248i
\(587\) −3.13106 2.33099i −0.129233 0.0962103i 0.530601 0.847621i \(-0.321966\pi\)
−0.659834 + 0.751411i \(0.729374\pi\)
\(588\) 17.3050 4.88310i 0.713647 0.201376i
\(589\) −17.4073 + 73.4471i −0.717255 + 3.02634i
\(590\) −6.20522 25.2695i −0.255465 1.04033i
\(591\) −0.997333 + 4.75925i −0.0410248 + 0.195769i
\(592\) −0.942457 29.1252i −0.0387347 1.19704i
\(593\) −2.12067 3.67310i −0.0870853 0.150836i 0.819193 0.573519i \(-0.194422\pi\)
−0.906278 + 0.422682i \(0.861089\pi\)
\(594\) −14.7446 13.1414i −0.604977 0.539198i
\(595\) 0.439954 + 0.254007i 0.0180363 + 0.0104133i
\(596\) 1.92248 8.73910i 0.0787478 0.357967i
\(597\) 0.623002 19.4411i 0.0254978 0.795673i
\(598\) 4.97772 + 5.19132i 0.203554 + 0.212289i
\(599\) −16.9222 + 17.9364i −0.691420 + 0.732863i −0.974042 0.226369i \(-0.927315\pi\)
0.282621 + 0.959232i \(0.408796\pi\)
\(600\) 16.1169 3.68768i 0.657969 0.150549i
\(601\) 32.6704 + 3.81862i 1.33265 + 0.155765i 0.752419 0.658685i \(-0.228887\pi\)
0.580234 + 0.814450i \(0.302961\pi\)
\(602\) 14.1455 + 3.23196i 0.576528 + 0.131725i
\(603\) 5.81410 19.0121i 0.236769 0.774231i
\(604\) 8.69184 5.92029i 0.353666 0.240893i
\(605\) 3.50130 3.30331i 0.142348 0.134299i
\(606\) −2.99237 14.1250i −0.121557 0.573788i
\(607\) −38.8809 + 19.5267i −1.57813 + 0.792565i −0.999731 0.0231926i \(-0.992617\pi\)
−0.578395 + 0.815757i \(0.696321\pi\)
\(608\) −23.7686 37.5740i −0.963946 1.52383i
\(609\) −6.80147 + 14.4743i −0.275609 + 0.586529i
\(610\) −26.0795 4.38137i −1.05593 0.177396i
\(611\) 2.17567 2.59286i 0.0880181 0.104896i
\(612\) 0.814043 + 1.58017i 0.0329057 + 0.0638745i
\(613\) −13.7391 16.3736i −0.554916 0.661324i 0.413546 0.910483i \(-0.364290\pi\)
−0.968462 + 0.249160i \(0.919846\pi\)
\(614\) 14.6809 + 24.9597i 0.592471 + 1.00729i
\(615\) 12.5080 + 1.86981i 0.504372 + 0.0753979i
\(616\) −3.82131 + 9.48508i −0.153965 + 0.382165i
\(617\) 5.66221 0.661818i 0.227952 0.0266438i −0.00134996 0.999999i \(-0.500430\pi\)
0.229302 + 0.973355i \(0.426356\pi\)
\(618\) −8.10610 11.4510i −0.326075 0.460625i
\(619\) −10.0771 + 0.586925i −0.405033 + 0.0235905i −0.259453 0.965756i \(-0.583542\pi\)
−0.145581 + 0.989346i \(0.546505\pi\)
\(620\) 17.5363 17.0891i 0.704274 0.686314i
\(621\) −0.0994223 4.90869i −0.00398968 0.196979i
\(622\) −13.1176 5.53299i −0.525967 0.221853i
\(623\) 16.4382 10.8116i 0.658581 0.433156i
\(624\) −25.5815 + 27.1319i −1.02408 + 1.08614i
\(625\) 1.29281 2.99707i 0.0517124 0.119883i
\(626\) 4.56155 2.01157i 0.182316 0.0803984i
\(627\) 19.1166 + 31.1981i 0.763444 + 1.24593i
\(628\) 9.08807 6.99708i 0.362654 0.279214i
\(629\) 0.738163 2.02809i 0.0294325 0.0808651i
\(630\) 5.82610 4.35728i 0.232117 0.173598i
\(631\) −11.7544 + 4.27826i −0.467936 + 0.170315i −0.565217 0.824942i \(-0.691208\pi\)
0.0972812 + 0.995257i \(0.468985\pi\)
\(632\) −9.65930 + 0.798105i −0.384226 + 0.0317469i
\(633\) 1.34145 14.8296i 0.0533178 0.589423i
\(634\) 10.5679 7.07371i 0.419705 0.280933i
\(635\) 4.59549 6.98710i 0.182366 0.277275i
\(636\) −17.7374 31.8793i −0.703334 1.26410i
\(637\) 6.44288 + 27.1847i 0.255276 + 1.07710i
\(638\) 11.8980 + 23.2208i 0.471047 + 0.919319i
\(639\) 9.38212 + 4.11278i 0.371151 + 0.162699i
\(640\) −0.0226354 + 14.4228i −0.000894742 + 0.570111i
\(641\) −1.54824 3.58922i −0.0611517 0.141765i 0.884900 0.465781i \(-0.154226\pi\)
−0.946052 + 0.324015i \(0.894967\pi\)
\(642\) 6.04030 + 1.21488i 0.238391 + 0.0479474i
\(643\) 29.1101 8.71499i 1.14799 0.343686i 0.344374 0.938833i \(-0.388091\pi\)
0.803617 + 0.595147i \(0.202906\pi\)
\(644\) −2.37429 + 0.907921i −0.0935602 + 0.0357771i
\(645\) −16.6712 + 2.39184i −0.656430 + 0.0941785i
\(646\) −0.598015 3.23816i −0.0235286 0.127404i
\(647\) −2.92162 −0.114861 −0.0574304 0.998350i \(-0.518291\pi\)
−0.0574304 + 0.998350i \(0.518291\pi\)
\(648\) 25.3923 1.79710i 0.997505 0.0705966i
\(649\) 38.7919 1.52271
\(650\) 4.66526 + 25.2617i 0.182986 + 0.990844i
\(651\) −8.32230 + 20.7700i −0.326177 + 0.814039i
\(652\) −5.69414 14.8907i −0.223000 0.583163i
\(653\) 0.556806 0.166697i 0.0217895 0.00652335i −0.275890 0.961189i \(-0.588973\pi\)
0.297679 + 0.954666i \(0.403787\pi\)
\(654\) 8.65271 + 25.6697i 0.338348 + 1.00376i
\(655\) −6.12219 14.1928i −0.239214 0.554560i
\(656\) 8.38941 21.3196i 0.327551 0.832391i
\(657\) 10.0259 + 0.643232i 0.391148 + 0.0250949i
\(658\) 0.545518 + 1.06466i 0.0212665 + 0.0415048i
\(659\) −0.827097 3.48980i −0.0322191 0.135943i 0.954558 0.298024i \(-0.0963276\pi\)
−0.986777 + 0.162081i \(0.948179\pi\)
\(660\) 0.188249 11.8678i 0.00732757 0.461954i
\(661\) 4.84223 7.36225i 0.188341 0.286358i −0.728958 0.684559i \(-0.759995\pi\)
0.917298 + 0.398201i \(0.130365\pi\)
\(662\) 5.17816 3.46604i 0.201255 0.134712i
\(663\) −2.50650 + 1.15983i −0.0973445 + 0.0450439i
\(664\) 0.804643 + 9.73842i 0.0312262 + 0.377924i
\(665\) −12.6648 + 4.60962i −0.491121 + 0.178753i
\(666\) −22.5282 21.1610i −0.872952 0.819972i
\(667\) −2.21829 + 6.09470i −0.0858926 + 0.235988i
\(668\) 2.65618 + 3.44995i 0.102771 + 0.133482i
\(669\) −5.47911 + 0.143273i −0.211835 + 0.00553927i
\(670\) 10.9319 4.82077i 0.422335 0.186243i
\(671\) 15.6155 36.2008i 0.602830 1.39752i
\(672\) −5.32164 12.0575i −0.205287 0.465126i
\(673\) −15.1396 + 9.95748i −0.583589 + 0.383833i −0.806701 0.590960i \(-0.798749\pi\)
0.223111 + 0.974793i \(0.428379\pi\)
\(674\) 14.5459 + 6.13547i 0.560289 + 0.236329i
\(675\) 9.33769 14.8435i 0.359408 0.571327i
\(676\) −22.2912 22.8746i −0.857354 0.879791i
\(677\) −6.96343 + 0.405573i −0.267626 + 0.0155875i −0.191433 0.981506i \(-0.561314\pi\)
−0.0761930 + 0.997093i \(0.524277\pi\)
\(678\) 16.2509 1.50599i 0.624111 0.0578373i
\(679\) 1.13854 0.133076i 0.0436931 0.00510699i
\(680\) −0.399176 + 0.990818i −0.0153077 + 0.0379961i
\(681\) 17.6428 + 44.7937i 0.676073 + 1.71650i
\(682\) 18.5073 + 31.4651i 0.708680 + 1.20486i
\(683\) 10.8061 + 12.8782i 0.413483 + 0.492770i 0.932082 0.362248i \(-0.117991\pi\)
−0.518599 + 0.855018i \(0.673546\pi\)
\(684\) −45.9959 10.4029i −1.75870 0.397766i
\(685\) 15.0747 17.9654i 0.575976 0.686421i
\(686\) −22.8698 3.84214i −0.873175 0.146694i
\(687\) 22.2478 + 31.9732i 0.848807 + 1.21985i
\(688\) −2.56009 + 30.4027i −0.0976025 + 1.15909i
\(689\) 50.6542 25.4395i 1.92977 0.969167i
\(690\) 2.19397 1.97278i 0.0835231 0.0751023i
\(691\) −18.9957 + 17.9215i −0.722631 + 0.681767i −0.956904 0.290404i \(-0.906210\pi\)
0.234273 + 0.972171i \(0.424729\pi\)
\(692\) −27.6571 40.6046i −1.05137 1.54356i
\(693\) 4.23722 + 9.98430i 0.160959 + 0.379272i
\(694\) −17.0668 3.89941i −0.647846 0.148020i
\(695\) −5.74220 0.671167i −0.217814 0.0254588i
\(696\) −32.1392 9.89473i −1.21823 0.375059i
\(697\) 1.16446 1.23425i 0.0441070 0.0467507i
\(698\) −22.7304 23.7058i −0.860359 0.897279i
\(699\) −39.7621 + 21.2886i −1.50394 + 0.805208i
\(700\) −8.86729 1.95068i −0.335152 0.0737287i
\(701\) −30.7375 17.7463i −1.16094 0.670268i −0.209409 0.977828i \(-0.567154\pi\)
−0.951529 + 0.307560i \(0.900487\pi\)
\(702\) 1.12070 + 39.5363i 0.0422980 + 1.49220i
\(703\) 28.6291 + 49.5870i 1.07977 + 1.87021i
\(704\) −20.8736 5.16052i −0.786704 0.194494i
\(705\) −1.03455 0.926145i −0.0389634 0.0348807i
\(706\) −4.55984 18.5690i −0.171612 0.698853i
\(707\) −1.82853 + 7.71516i −0.0687689 + 0.290159i
\(708\) −34.8823 + 35.8176i −1.31096 + 1.34611i
\(709\) 8.06933 + 6.00739i 0.303050 + 0.225612i 0.737932 0.674875i \(-0.235803\pi\)
−0.434882 + 0.900487i \(0.643210\pi\)
\(710\) 1.81323 + 5.88303i 0.0680493 + 0.220786i
\(711\) −6.65423 + 7.83598i −0.249553 + 0.293872i
\(712\) 27.3535 + 31.0373i 1.02511 + 1.16317i
\(713\) −2.60254 + 8.69309i −0.0974659 + 0.325559i
\(714\) −0.0334063 0.975557i −0.00125020 0.0365093i
\(715\) 18.4108 + 1.07231i 0.688525 + 0.0401020i
\(716\) 16.3080 + 18.8088i 0.609460 + 0.702918i
\(717\) −2.91788 + 10.7628i −0.108970 + 0.401943i
\(718\) −9.26290 + 11.2222i −0.345689 + 0.418808i
\(719\) −4.62277 + 26.2170i −0.172400 + 0.977729i 0.768702 + 0.639607i \(0.220903\pi\)
−0.941102 + 0.338122i \(0.890208\pi\)
\(720\) 10.7886 + 10.8456i 0.402067 + 0.404190i
\(721\) 1.33786 + 7.58738i 0.0498245 + 0.282569i
\(722\) 52.6296 + 29.8208i 1.95867 + 1.10982i
\(723\) 5.74855 + 28.2604i 0.213791 + 1.05101i
\(724\) −0.728969 45.0671i −0.0270919 1.67491i
\(725\) −18.5820 + 13.8338i −0.690116 + 0.513773i
\(726\) −8.94621 2.34790i −0.332025 0.0871387i
\(727\) 41.0231 + 20.6026i 1.52146 + 0.764107i 0.996222 0.0868470i \(-0.0276791\pi\)
0.525240 + 0.850954i \(0.323975\pi\)
\(728\) 19.0673 7.46858i 0.706683 0.276804i
\(729\) 17.7181 20.3732i 0.656226 0.754564i
\(730\) 3.64437 + 4.81348i 0.134884 + 0.178155i
\(731\) −1.01415 + 2.01934i −0.0375098 + 0.0746882i
\(732\) 19.3835 + 46.9706i 0.716433 + 1.73608i
\(733\) 21.4906 15.9992i 0.793775 0.590943i −0.122049 0.992524i \(-0.538947\pi\)
0.915824 + 0.401581i \(0.131539\pi\)
\(734\) 17.8963 + 13.0997i 0.660563 + 0.483518i
\(735\) 11.2310 2.28455i 0.414263 0.0842668i
\(736\) −2.58995 4.67559i −0.0954669 0.172345i
\(737\) 3.09301 + 17.5413i 0.113933 + 0.646144i
\(738\) −9.67396 22.2921i −0.356104 0.820583i
\(739\) 31.5912 + 5.57038i 1.16210 + 0.204910i 0.721253 0.692672i \(-0.243567\pi\)
0.440848 + 0.897582i \(0.354678\pi\)
\(740\) 0.779960 18.5578i 0.0286719 0.682200i
\(741\) 19.1725 70.7187i 0.704318 2.59791i
\(742\) 1.32656 + 19.9899i 0.0486997 + 0.733852i
\(743\) −0.414853 + 7.12275i −0.0152195 + 0.261308i 0.982112 + 0.188299i \(0.0602974\pi\)
−0.997331 + 0.0730095i \(0.976740\pi\)
\(744\) −45.6946 11.2057i −1.67525 0.410821i
\(745\) 1.63579 5.46392i 0.0599308 0.200183i
\(746\) −23.2751 15.0401i −0.852163 0.550656i
\(747\) 7.90017 + 6.70874i 0.289052 + 0.245460i
\(748\) −1.29261 0.930203i −0.0472625 0.0340116i
\(749\) −2.71395 2.02046i −0.0991655 0.0738260i
\(750\) 25.8557 3.92318i 0.944115 0.143254i
\(751\) −31.1876 7.39159i −1.13805 0.269723i −0.381953 0.924182i \(-0.624749\pi\)
−0.756098 + 0.654458i \(0.772897\pi\)
\(752\) −2.05581 + 1.44950i −0.0749675 + 0.0528577i
\(753\) −14.0678 12.5938i −0.512660 0.458942i
\(754\) 17.4727 49.2414i 0.636320 1.79327i
\(755\) 5.80522 3.35165i 0.211274 0.121979i
\(756\) −13.0289 5.06571i −0.473858 0.184238i
\(757\) −8.50103 4.90807i −0.308975 0.178387i 0.337493 0.941328i \(-0.390421\pi\)
−0.646468 + 0.762941i \(0.723755\pi\)
\(758\) 2.05699 1.75456i 0.0747131 0.0637284i
\(759\) 2.07621 + 3.87787i 0.0753615 + 0.140758i
\(760\) −13.3293 25.0091i −0.483505 0.907174i
\(761\) −1.22821 + 1.30183i −0.0445226 + 0.0471912i −0.749252 0.662285i \(-0.769587\pi\)
0.704730 + 0.709476i \(0.251068\pi\)
\(762\) −16.0643 0.384777i −0.581950 0.0139390i
\(763\) 1.72698 14.7752i 0.0625207 0.534899i
\(764\) 11.2541 + 24.9714i 0.407158 + 0.903435i
\(765\) 0.442622 + 1.04297i 0.0160030 + 0.0377086i
\(766\) −9.86477 0.494547i −0.356429 0.0178687i
\(767\) −53.3090 56.5043i −1.92488 2.04025i
\(768\) 23.5347 14.6327i 0.849236 0.528013i
\(769\) −16.1107 + 8.09109i −0.580966 + 0.291772i −0.714910 0.699217i \(-0.753532\pi\)
0.133944 + 0.990989i \(0.457236\pi\)
\(770\) −2.87809 + 5.84820i −0.103719 + 0.210754i
\(771\) 31.7958 22.1244i 1.14510 0.796790i
\(772\) 18.1991 9.51159i 0.655001 0.342330i
\(773\) −32.3311 + 38.5307i −1.16287 + 1.38585i −0.254822 + 0.966988i \(0.582017\pi\)
−0.908048 + 0.418866i \(0.862428\pi\)
\(774\) 20.8557 + 24.7443i 0.749642 + 0.889415i
\(775\) −24.8285 + 20.8336i −0.891866 + 0.748365i
\(776\) 0.612586 + 2.33116i 0.0219905 + 0.0836839i
\(777\) 6.22011 + 15.7924i 0.223145 + 0.566548i
\(778\) −5.69477 0.618984i −0.204167 0.0221916i
\(779\) 5.22623 + 44.7133i 0.187249 + 1.60202i
\(780\) −17.5454 + 16.0349i −0.628225 + 0.574143i
\(781\) −9.16225 + 0.533640i −0.327851 + 0.0190952i
\(782\) −0.0491358 0.392809i −0.00175709 0.0140468i
\(783\) −31.5432 + 16.6498i −1.12726 + 0.595017i
\(784\) 0.536235 20.7555i 0.0191513 0.741268i
\(785\) 6.10807 4.01734i 0.218006 0.143385i
\(786\) −16.9099 + 24.4160i −0.603155 + 0.870889i
\(787\) 27.0421 + 11.6648i 0.963946 + 0.415806i 0.819102 0.573649i \(-0.194472\pi\)
0.144845 + 0.989454i \(0.453732\pi\)
\(788\) 4.90740 + 2.72843i 0.174819 + 0.0971962i
\(789\) −18.2986 + 0.478492i −0.651449 + 0.0170348i
\(790\) −6.17766 + 0.0499591i −0.219791 + 0.00177747i
\(791\) −8.42191 3.06532i −0.299449 0.108990i
\(792\) −19.5381 + 11.7641i −0.694257 + 0.418017i
\(793\) −74.1895 + 27.0028i −2.63455 + 0.958897i
\(794\) −6.15219 + 2.29573i −0.218333 + 0.0814723i
\(795\) −9.76524 21.1037i −0.346337 0.748471i
\(796\) −21.2272 7.33950i −0.752377 0.260142i
\(797\) −4.63773 + 7.05133i −0.164277 + 0.249771i −0.908240 0.418450i \(-0.862573\pi\)
0.743963 + 0.668221i \(0.232944\pi\)
\(798\) 20.3961 + 15.9574i 0.722012 + 0.564885i
\(799\) −0.181280 + 0.0429641i −0.00641322 + 0.00151996i
\(800\) 1.44802 19.0361i 0.0511953 0.673028i
\(801\) 43.7901 + 2.80944i 1.54725 + 0.0992666i
\(802\) 2.77865 + 2.57937i 0.0981175 + 0.0910807i
\(803\) −8.26475 + 3.56507i −0.291657 + 0.125808i
\(804\) −18.9777 12.9176i −0.669291 0.455569i
\(805\) −1.55219 + 0.464696i −0.0547076 + 0.0163784i
\(806\) 20.3988 70.1981i 0.718519 2.47262i
\(807\) −17.4944 7.00982i −0.615832 0.246757i
\(808\) −16.6015 1.53324i −0.584037 0.0539393i
\(809\) −30.9367 −1.08768 −0.543838 0.839190i \(-0.683029\pi\)
−0.543838 + 0.839190i \(0.683029\pi\)
\(810\) 16.2256 + 0.0599714i 0.570108 + 0.00210718i
\(811\) 39.9018i 1.40114i 0.713582 + 0.700572i \(0.247072\pi\)
−0.713582 + 0.700572i \(0.752928\pi\)
\(812\) 13.6354 + 12.4538i 0.478510 + 0.437042i
\(813\) 11.2313 1.61136i 0.393897 0.0565127i
\(814\) 26.5912 + 7.72713i 0.932021 + 0.270836i
\(815\) −2.91439 9.73475i −0.102087 0.340993i
\(816\) 2.02122 0.357047i 0.0707567 0.0124992i
\(817\) −23.7449 55.0469i −0.830730 1.92585i
\(818\) −31.8059 29.5249i −1.11207 1.03231i
\(819\) 8.72023 19.8927i 0.304709 0.695107i
\(820\) 6.34212 13.1545i 0.221476 0.459373i
\(821\) 6.84751 + 28.8919i 0.238980 + 1.00833i 0.951735 + 0.306922i \(0.0992989\pi\)
−0.712755 + 0.701413i \(0.752553\pi\)
\(822\) −44.6194 6.30164i −1.55628 0.219795i
\(823\) 19.9325 + 13.1098i 0.694804 + 0.456980i 0.847155 0.531347i \(-0.178314\pi\)
−0.152350 + 0.988327i \(0.548684\pi\)
\(824\) −15.4023 + 5.02136i −0.536564 + 0.174927i
\(825\) −1.41541 + 15.6472i −0.0492783 + 0.544766i
\(826\) 25.7231 9.59874i 0.895022 0.333983i
\(827\) −10.3689 28.4884i −0.360563 0.990639i −0.978831 0.204671i \(-0.934387\pi\)
0.618268 0.785968i \(-0.287835\pi\)
\(828\) −5.44749 1.57002i −0.189313 0.0545621i
\(829\) −0.875314 + 2.40490i −0.0304009 + 0.0835258i −0.953965 0.299919i \(-0.903040\pi\)
0.923564 + 0.383445i \(0.125262\pi\)
\(830\) 0.0503683 + 6.22826i 0.00174831 + 0.216186i
\(831\) 4.54344 2.78399i 0.157610 0.0965757i
\(832\) 21.1684 + 37.4963i 0.733881 + 1.29995i
\(833\) 0.609067 1.41198i 0.0211029 0.0489221i
\(834\) 4.74636 + 10.0435i 0.164353 + 0.347777i
\(835\) 1.52503 + 2.31870i 0.0527760 + 0.0802419i
\(836\) 40.9477 10.4070i 1.41621 0.359934i
\(837\) −42.7027 + 25.8213i −1.47602 + 0.892514i
\(838\) 18.1938 2.27584i 0.628496 0.0786176i
\(839\) −3.15876 54.2339i −0.109053 1.87236i −0.401203 0.915989i \(-0.631408\pi\)
0.292151 0.956372i \(-0.405629\pi\)
\(840\) −2.81177 7.91621i −0.0970152 0.273135i
\(841\) 17.9956 2.10339i 0.620539 0.0725306i
\(842\) 6.01577 + 0.653875i 0.207317 + 0.0225340i
\(843\) 3.90081 26.0943i 0.134351 0.898737i
\(844\) −15.8955 6.55383i −0.547147 0.225592i
\(845\) −13.0862 15.5955i −0.450179 0.536502i
\(846\) −0.457526 + 2.62849i −0.0157301 + 0.0903694i
\(847\) 3.89088 + 3.26484i 0.133692 + 0.112181i
\(848\) −41.2270 + 8.65287i −1.41574 + 0.297141i
\(849\) −17.3559 + 36.9355i −0.595654 + 1.26762i
\(850\) 0.624343 1.26865i 0.0214148 0.0435142i
\(851\) 3.08930 + 6.15131i 0.105900 + 0.210864i
\(852\) 7.74612 8.93960i 0.265378 0.306266i
\(853\) 26.9907 25.4644i 0.924143 0.871884i −0.0679115 0.997691i \(-0.521634\pi\)
0.992055 + 0.125807i \(0.0401521\pi\)
\(854\) 1.39714 27.8689i 0.0478093 0.953655i
\(855\) −28.7445 8.79038i −0.983040 0.300625i
\(856\) 3.40670 6.24574i 0.116438 0.213475i
\(857\) −39.1520 4.57622i −1.33741 0.156321i −0.582864 0.812570i \(-0.698068\pi\)
−0.754544 + 0.656249i \(0.772142\pi\)
\(858\) −16.9778 31.1035i −0.579614 1.06186i
\(859\) −4.15899 3.92381i −0.141903 0.133879i 0.612018 0.790844i \(-0.290358\pi\)
−0.753921 + 0.656966i \(0.771840\pi\)
\(860\) −3.06682 + 19.2041i −0.104578 + 0.654853i
\(861\) −0.427419 + 13.3379i −0.0145664 + 0.454553i
\(862\) 26.3476 + 30.8891i 0.897404 + 1.05209i
\(863\) 6.04283 10.4665i 0.205700 0.356283i −0.744655 0.667449i \(-0.767386\pi\)
0.950356 + 0.311166i \(0.100719\pi\)
\(864\) 6.70693 28.6185i 0.228174 0.973620i
\(865\) −15.6575 27.1196i −0.532371 0.922093i
\(866\) 5.65253 15.9299i 0.192081 0.541319i
\(867\) −28.6701 6.00801i −0.973688 0.204043i
\(868\) 20.0581 + 16.2853i 0.680816 + 0.552757i
\(869\) 2.12401 8.96192i 0.0720522 0.304012i
\(870\) −19.9606 7.81126i −0.676727 0.264826i
\(871\) 21.3002 28.6112i 0.721731 0.969453i
\(872\) 31.2702 0.758785i 1.05894 0.0256957i
\(873\) 2.20644 + 1.29128i 0.0746767 + 0.0437032i
\(874\) 8.82102 + 5.70002i 0.298375 + 0.192806i
\(875\) −13.7578 4.11883i −0.465100 0.139242i
\(876\) 4.14008 10.8368i 0.139880 0.366142i
\(877\) −23.0214 1.34084i −0.777377 0.0452771i −0.335132 0.942171i \(-0.608781\pi\)
−0.442245 + 0.896894i \(0.645818\pi\)
\(878\) 49.1564 3.26210i 1.65895 0.110091i
\(879\) 10.6544 10.5918i 0.359364 0.357253i
\(880\) −13.0238 4.26858i −0.439033 0.143894i
\(881\) 5.06538 28.7272i 0.170657 0.967843i −0.772381 0.635159i \(-0.780935\pi\)
0.943038 0.332684i \(-0.107954\pi\)
\(882\) −15.1475 15.9849i −0.510041 0.538240i
\(883\) −30.0818 + 5.30423i −1.01233 + 0.178502i −0.655123 0.755522i \(-0.727383\pi\)
−0.357210 + 0.934024i \(0.616272\pi\)
\(884\) 0.421412 + 3.16113i 0.0141736 + 0.106320i
\(885\) −23.8686 + 21.1156i −0.802334 + 0.709792i
\(886\) −27.2392 + 37.2131i −0.915118 + 1.25020i
\(887\) 20.5241 + 27.5686i 0.689130 + 0.925663i 0.999690 0.0248910i \(-0.00792388\pi\)
−0.310560 + 0.950554i \(0.600516\pi\)
\(888\) −31.0459 + 17.6040i −1.04183 + 0.590751i
\(889\) 7.88565 + 3.96032i 0.264476 + 0.132825i
\(890\) 15.9175 + 21.0238i 0.533555 + 0.704719i
\(891\) −5.85551 + 23.4704i −0.196167 + 0.786288i
\(892\) −1.71685 + 6.09158i −0.0574845 + 0.203961i
\(893\) 2.21822 4.41685i 0.0742300 0.147804i
\(894\) −10.5709 + 2.89081i −0.353545 + 0.0966830i
\(895\) 9.47553 + 12.7279i 0.316732 + 0.425445i
\(896\) −15.1183 + 1.74303i −0.505069 + 0.0582307i
\(897\) 2.79531 8.35329i 0.0933328 0.278908i
\(898\) 22.5447 + 12.7742i 0.752327 + 0.426282i
\(899\) 64.9211 11.4473i 2.16524 0.381790i
\(900\) −13.1747 15.3771i −0.439158 0.512571i
\(901\) −3.07255 0.541774i −0.102362 0.0180491i
\(902\) 16.7905 + 13.8591i 0.559063 + 0.461457i
\(903\) −4.54891 17.1790i −0.151378 0.571682i
\(904\) 3.89991 18.4373i 0.129709 0.613217i
\(905\) 1.67048 28.6811i 0.0555288 0.953392i
\(906\) −11.3683 6.05453i −0.377688 0.201148i
\(907\) −19.0468 5.70225i −0.632440 0.189340i −0.0454918 0.998965i \(-0.514485\pi\)
−0.586948 + 0.809625i \(0.699671\pi\)
\(908\) 55.4371 4.12944i 1.83974 0.137040i
\(909\) −13.6130 + 11.2867i −0.451516 + 0.374356i
\(910\) 12.4737 3.84455i 0.413498 0.127446i
\(911\) 16.0207 21.5195i 0.530790 0.712974i −0.453158 0.891430i \(-0.649703\pi\)
0.983948 + 0.178456i \(0.0571102\pi\)
\(912\) −27.2117 + 47.1662i −0.901071 + 1.56183i
\(913\) −9.03533 2.14141i −0.299026 0.0708704i
\(914\) −1.03803 4.22717i −0.0343351 0.139822i
\(915\) 10.0970 + 30.7743i 0.333796 + 1.01737i
\(916\) 42.8740 13.5950i 1.41660 0.449190i
\(917\) 14.1246 8.15485i 0.466436 0.269297i
\(918\) 1.25002 1.78237i 0.0412569 0.0588270i
\(919\) −16.1923 + 28.0459i −0.534136 + 0.925150i 0.465069 + 0.885274i \(0.346030\pi\)
−0.999205 + 0.0398757i \(0.987304\pi\)
\(920\) −1.42490 3.09464i −0.0469777 0.102027i
\(921\) 18.7071 30.1299i 0.616421 0.992814i
\(922\) 22.0571 + 23.0036i 0.726410 + 0.757582i
\(923\) 13.3684 + 12.6124i 0.440025 + 0.415142i
\(924\) 12.4609 1.25649i 0.409935 0.0413354i
\(925\) −2.85429 + 24.4200i −0.0938484 + 0.802924i
\(926\) −8.51537 + 37.2698i −0.279832 + 1.22476i
\(927\) −7.80198 + 15.3095i −0.256251 + 0.502828i
\(928\) −21.9098 + 32.0584i −0.719223 + 1.05237i
\(929\) −26.7131 28.3142i −0.876427 0.928958i 0.121547 0.992586i \(-0.461215\pi\)
−0.997974 + 0.0636273i \(0.979733\pi\)
\(930\) −28.5149 9.28639i −0.935041 0.304513i
\(931\) 18.3093 + 36.4568i 0.600062 + 1.19482i
\(932\) 9.87187 + 51.1356i 0.323364 + 1.67500i
\(933\) 1.46851 + 17.3744i 0.0480767 + 0.568813i
\(934\) 8.91575 53.0698i 0.291732 1.73650i
\(935\) −0.777595 0.652480i −0.0254301 0.0213384i
\(936\) 43.9854 + 12.2927i 1.43771 + 0.401799i
\(937\) −2.67379 + 2.24358i −0.0873490 + 0.0732945i −0.685417 0.728151i \(-0.740380\pi\)
0.598068 + 0.801446i \(0.295935\pi\)
\(938\) 6.39146 + 10.8664i 0.208689 + 0.354802i
\(939\) −4.77834 3.80115i −0.155935 0.124046i
\(940\) −1.37539 + 0.824024i −0.0448603 + 0.0268767i
\(941\) 1.66085 + 14.2095i 0.0541421 + 0.463215i 0.992928 + 0.118715i \(0.0378775\pi\)
−0.938786 + 0.344500i \(0.888048\pi\)
\(942\) −12.7616 5.87114i −0.415795 0.191292i
\(943\) 0.314677 + 5.40280i 0.0102473 + 0.175939i
\(944\) 27.5647 + 50.7255i 0.897155 + 1.65098i
\(945\) −8.04191 3.83688i −0.261603 0.124814i
\(946\) −26.7138 11.2678i −0.868539 0.366349i
\(947\) −5.55995 8.45349i −0.180674 0.274702i 0.733784 0.679383i \(-0.237753\pi\)
−0.914458 + 0.404682i \(0.867382\pi\)
\(948\) 6.36483 + 10.0199i 0.206720 + 0.325430i
\(949\) 16.5506 + 7.13922i 0.537254 + 0.231749i
\(950\) 15.1359 + 34.3230i 0.491073 + 1.11359i
\(951\) −13.6872 7.43219i −0.443838 0.241005i
\(952\) −1.08731 0.296977i −0.0352399 0.00962510i
\(953\) 14.0194 + 5.10266i 0.454134 + 0.165291i 0.558952 0.829200i \(-0.311204\pi\)
−0.104818 + 0.994491i \(0.533426\pi\)
\(954\) −24.4704 + 37.3839i −0.792258 + 1.21035i
\(955\) 5.97122 + 16.4058i 0.193224 + 0.530879i
\(956\) 10.8711 + 6.90078i 0.351596 + 0.223187i
\(957\) 18.4059 26.1223i 0.594979 0.844413i
\(958\) 8.89777 + 13.2930i 0.287474 + 0.429477i
\(959\) 20.6749 + 13.5981i 0.667628 + 0.439106i
\(960\) 15.6525 8.18687i 0.505183 0.264230i
\(961\) 59.5814 14.1210i 1.92198 0.455518i
\(962\) −25.2871 49.3516i −0.815290 1.59116i
\(963\) −2.12158 7.24158i −0.0683670 0.233357i
\(964\) 33.1336 + 3.33052i 1.06716 + 0.107269i
\(965\) 12.0185 5.18428i 0.386890 0.166888i
\(966\) 2.33629 + 2.05770i 0.0751689 + 0.0662053i
\(967\) 7.45174 + 24.8906i 0.239632 + 0.800426i 0.990203 + 0.139637i \(0.0445934\pi\)
−0.750571 + 0.660790i \(0.770221\pi\)
\(968\) −5.65059 + 9.06277i −0.181617 + 0.291289i
\(969\) −3.17089 + 2.49207i −0.101864 + 0.0800568i
\(970\) 0.279009 + 1.51079i 0.00895845 + 0.0485087i
\(971\) 36.2630i 1.16373i 0.813284 + 0.581867i \(0.197678\pi\)
−0.813284 + 0.581867i \(0.802322\pi\)
\(972\) −16.4055 26.5115i −0.526206 0.850357i
\(973\) 6.10024i 0.195565i
\(974\) −26.5510 + 4.90338i −0.850750 + 0.157114i
\(975\) 24.7369 19.4412i 0.792214 0.622617i
\(976\) 58.4335 5.30420i 1.87041 0.169783i
\(977\) 7.21801 + 24.1098i 0.230925 + 0.771342i 0.992390 + 0.123136i \(0.0392953\pi\)
−0.761465 + 0.648206i \(0.775520\pi\)
\(978\) −12.9051 + 14.6523i −0.412659 + 0.468530i
\(979\) −36.0979 + 15.5711i −1.15369 + 0.497654i
\(980\) 1.32359 13.1677i 0.0422806 0.420627i
\(981\) 22.9091 23.9974i 0.731431 0.766178i
\(982\) 38.3988 19.6751i 1.22536 0.627856i
\(983\) −46.2577 + 10.9633i −1.47539 + 0.349674i −0.888080 0.459688i \(-0.847961\pi\)
−0.587310 + 0.809362i \(0.699813\pi\)
\(984\) −27.8947 + 3.04081i −0.889252 + 0.0969374i
\(985\) 2.99017 + 1.96666i 0.0952746 + 0.0626631i
\(986\) −2.38992 + 1.59971i −0.0761106 + 0.0509452i
\(987\) 0.843902 1.19769i 0.0268617 0.0381230i
\(988\) −71.4305 45.3428i −2.27251 1.44255i
\(989\) −2.46497 6.77244i −0.0783814 0.215351i
\(990\) −12.9763 + 6.55265i −0.412413 + 0.208257i
\(991\) 23.3831 + 8.51076i 0.742790 + 0.270353i 0.685568 0.728008i \(-0.259554\pi\)
0.0572212 + 0.998362i \(0.481776\pi\)
\(992\) −27.9940 + 46.5592i −0.888809 + 1.47826i
\(993\) −6.70659 3.64170i −0.212827 0.115566i
\(994\) −5.94350 + 2.62098i −0.188516 + 0.0831326i
\(995\) −13.1454 5.67037i −0.416737 0.179763i
\(996\) 10.1019 6.41696i 0.320092 0.203329i
\(997\) −1.26413 1.92202i −0.0400355 0.0608710i 0.814916 0.579580i \(-0.196783\pi\)
−0.854951 + 0.518709i \(0.826413\pi\)
\(998\) −18.0698 + 42.8398i −0.571989 + 1.35607i
\(999\) −10.1202 + 36.4766i −0.320189 + 1.15407i
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 648.2.bd.a.13.7 1908
8.5 even 2 inner 648.2.bd.a.13.39 yes 1908
81.25 even 27 inner 648.2.bd.a.349.39 yes 1908
648.349 even 54 inner 648.2.bd.a.349.7 yes 1908
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.2.bd.a.13.7 1908 1.1 even 1 trivial
648.2.bd.a.13.39 yes 1908 8.5 even 2 inner
648.2.bd.a.349.7 yes 1908 648.349 even 54 inner
648.2.bd.a.349.39 yes 1908 81.25 even 27 inner