Properties

Label 240.2.s.c.181.9
Level $240$
Weight $2$
Character 240.181
Analytic conductor $1.916$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,2,Mod(61,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.s (of order \(4\), degree \(2\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 181.9
Root \(1.19834 - 0.750988i\) of defining polynomial
Character \(\chi\) \(=\) 240.181
Dual form 240.2.s.c.61.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.19834 - 0.750988i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.872033 - 1.79988i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.316325 + 1.37838i) q^{6} -3.79862i q^{7} +(-0.306697 - 2.81175i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.19834 - 0.750988i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.872033 - 1.79988i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.316325 + 1.37838i) q^{6} -3.79862i q^{7} +(-0.306697 - 2.81175i) q^{8} -1.00000i q^{9} +(-1.37838 - 0.316325i) q^{10} +(3.08662 + 3.08662i) q^{11} +(0.656085 + 1.88933i) q^{12} +(1.54638 - 1.54638i) q^{13} +(-2.85272 - 4.55203i) q^{14} +1.00000 q^{15} +(-2.47912 - 3.13910i) q^{16} +4.32428 q^{17} +(-0.750988 - 1.19834i) q^{18} +(-5.37165 + 5.37165i) q^{19} +(-1.88933 + 0.656085i) q^{20} +(2.68603 + 2.68603i) q^{21} +(6.01683 + 1.38080i) q^{22} +3.91059i q^{23} +(2.20507 + 1.77134i) q^{24} +1.00000i q^{25} +(0.691773 - 3.01440i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-6.83704 - 3.31252i) q^{28} +(1.84243 - 1.84243i) q^{29} +(1.19834 - 0.750988i) q^{30} -9.52790 q^{31} +(-5.32825 - 1.89992i) q^{32} -4.36514 q^{33} +(5.18195 - 3.24748i) q^{34} +(-2.68603 + 2.68603i) q^{35} +(-1.79988 - 0.872033i) q^{36} +(4.55033 + 4.55033i) q^{37} +(-2.40301 + 10.4711i) q^{38} +2.18691i q^{39} +(-1.77134 + 2.20507i) q^{40} -0.580195i q^{41} +(5.23595 + 1.20160i) q^{42} +(0.994741 + 0.994741i) q^{43} +(8.24716 - 2.86390i) q^{44} +(-0.707107 + 0.707107i) q^{45} +(2.93681 + 4.68621i) q^{46} +2.22461 q^{47} +(3.97268 + 0.466680i) q^{48} -7.42948 q^{49} +(0.750988 + 1.19834i) q^{50} +(-3.05773 + 3.05773i) q^{51} +(-1.43480 - 4.13178i) q^{52} +(4.80257 + 4.80257i) q^{53} +(1.37838 + 0.316325i) q^{54} -4.36514i q^{55} +(-10.6808 + 1.16502i) q^{56} -7.59666i q^{57} +(0.824214 - 3.59151i) q^{58} +(7.26404 + 7.26404i) q^{59} +(0.872033 - 1.79988i) q^{60} +(0.301222 - 0.301222i) q^{61} +(-11.4176 + 7.15534i) q^{62} -3.79862 q^{63} +(-7.81187 + 1.72471i) q^{64} -2.18691 q^{65} +(-5.23091 + 3.27817i) q^{66} +(6.97711 - 6.97711i) q^{67} +(3.77091 - 7.78318i) q^{68} +(-2.76520 - 2.76520i) q^{69} +(-1.20160 + 5.23595i) q^{70} -0.585051i q^{71} +(-2.81175 + 0.306697i) q^{72} -11.9999i q^{73} +(8.87009 + 2.03559i) q^{74} +(-0.707107 - 0.707107i) q^{75} +(4.98406 + 14.3526i) q^{76} +(11.7249 - 11.7249i) q^{77} +(1.64234 + 2.62066i) q^{78} +12.6436 q^{79} +(-0.466680 + 3.97268i) q^{80} -1.00000 q^{81} +(-0.435720 - 0.695270i) q^{82} +(-11.1632 + 11.1632i) q^{83} +(7.17682 - 2.49222i) q^{84} +(-3.05773 - 3.05773i) q^{85} +(1.93908 + 0.444998i) q^{86} +2.60559i q^{87} +(7.73214 - 9.62545i) q^{88} +12.9706i q^{89} +(-0.316325 + 1.37838i) q^{90} +(-5.87409 - 5.87409i) q^{91} +(7.03858 + 3.41016i) q^{92} +(6.73724 - 6.73724i) q^{93} +(2.66583 - 1.67065i) q^{94} +7.59666 q^{95} +(5.11109 - 2.42420i) q^{96} -6.78553 q^{97} +(-8.90303 + 5.57945i) q^{98} +(3.08662 - 3.08662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19834 0.750988i 0.847354 0.531029i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 0.872033 1.79988i 0.436016 0.899939i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −0.316325 + 1.37838i −0.129139 + 0.562722i
\(7\) 3.79862i 1.43574i −0.696176 0.717871i \(-0.745117\pi\)
0.696176 0.717871i \(-0.254883\pi\)
\(8\) −0.306697 2.81175i −0.108434 0.994104i
\(9\) 1.00000i 0.333333i
\(10\) −1.37838 0.316325i −0.435883 0.100031i
\(11\) 3.08662 + 3.08662i 0.930650 + 0.930650i 0.997746 0.0670964i \(-0.0213735\pi\)
−0.0670964 + 0.997746i \(0.521374\pi\)
\(12\) 0.656085 + 1.88933i 0.189396 + 0.545401i
\(13\) 1.54638 1.54638i 0.428888 0.428888i −0.459361 0.888249i \(-0.651922\pi\)
0.888249 + 0.459361i \(0.151922\pi\)
\(14\) −2.85272 4.55203i −0.762420 1.21658i
\(15\) 1.00000 0.258199
\(16\) −2.47912 3.13910i −0.619780 0.784776i
\(17\) 4.32428 1.04879 0.524396 0.851474i \(-0.324291\pi\)
0.524396 + 0.851474i \(0.324291\pi\)
\(18\) −0.750988 1.19834i −0.177010 0.282451i
\(19\) −5.37165 + 5.37165i −1.23234 + 1.23234i −0.269279 + 0.963062i \(0.586785\pi\)
−0.963062 + 0.269279i \(0.913215\pi\)
\(20\) −1.88933 + 0.656085i −0.422466 + 0.146705i
\(21\) 2.68603 + 2.68603i 0.586139 + 0.586139i
\(22\) 6.01683 + 1.38080i 1.28279 + 0.294387i
\(23\) 3.91059i 0.815414i 0.913113 + 0.407707i \(0.133671\pi\)
−0.913113 + 0.407707i \(0.866329\pi\)
\(24\) 2.20507 + 1.77134i 0.450109 + 0.361573i
\(25\) 1.00000i 0.200000i
\(26\) 0.691773 3.01440i 0.135668 0.591172i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −6.83704 3.31252i −1.29208 0.626007i
\(29\) 1.84243 1.84243i 0.342131 0.342131i −0.515037 0.857168i \(-0.672222\pi\)
0.857168 + 0.515037i \(0.172222\pi\)
\(30\) 1.19834 0.750988i 0.218786 0.137111i
\(31\) −9.52790 −1.71126 −0.855630 0.517587i \(-0.826830\pi\)
−0.855630 + 0.517587i \(0.826830\pi\)
\(32\) −5.32825 1.89992i −0.941911 0.335862i
\(33\) −4.36514 −0.759873
\(34\) 5.18195 3.24748i 0.888698 0.556939i
\(35\) −2.68603 + 2.68603i −0.454021 + 0.454021i
\(36\) −1.79988 0.872033i −0.299980 0.145339i
\(37\) 4.55033 + 4.55033i 0.748070 + 0.748070i 0.974116 0.226047i \(-0.0725802\pi\)
−0.226047 + 0.974116i \(0.572580\pi\)
\(38\) −2.40301 + 10.4711i −0.389820 + 1.69864i
\(39\) 2.18691i 0.350186i
\(40\) −1.77134 + 2.20507i −0.280073 + 0.348653i
\(41\) 0.580195i 0.0906112i −0.998973 0.0453056i \(-0.985574\pi\)
0.998973 0.0453056i \(-0.0144262\pi\)
\(42\) 5.23595 + 1.20160i 0.807924 + 0.185410i
\(43\) 0.994741 + 0.994741i 0.151697 + 0.151697i 0.778875 0.627179i \(-0.215790\pi\)
−0.627179 + 0.778875i \(0.715790\pi\)
\(44\) 8.24716 2.86390i 1.24331 0.431749i
\(45\) −0.707107 + 0.707107i −0.105409 + 0.105409i
\(46\) 2.93681 + 4.68621i 0.433008 + 0.690944i
\(47\) 2.22461 0.324492 0.162246 0.986750i \(-0.448126\pi\)
0.162246 + 0.986750i \(0.448126\pi\)
\(48\) 3.97268 + 0.466680i 0.573407 + 0.0673595i
\(49\) −7.42948 −1.06135
\(50\) 0.750988 + 1.19834i 0.106206 + 0.169471i
\(51\) −3.05773 + 3.05773i −0.428168 + 0.428168i
\(52\) −1.43480 4.13178i −0.198971 0.572975i
\(53\) 4.80257 + 4.80257i 0.659684 + 0.659684i 0.955305 0.295622i \(-0.0955267\pi\)
−0.295622 + 0.955305i \(0.595527\pi\)
\(54\) 1.37838 + 0.316325i 0.187574 + 0.0430463i
\(55\) 4.36514i 0.588595i
\(56\) −10.6808 + 1.16502i −1.42728 + 0.155683i
\(57\) 7.59666i 1.00620i
\(58\) 0.824214 3.59151i 0.108225 0.471588i
\(59\) 7.26404 + 7.26404i 0.945698 + 0.945698i 0.998600 0.0529020i \(-0.0168471\pi\)
−0.0529020 + 0.998600i \(0.516847\pi\)
\(60\) 0.872033 1.79988i 0.112579 0.232363i
\(61\) 0.301222 0.301222i 0.0385676 0.0385676i −0.687560 0.726128i \(-0.741318\pi\)
0.726128 + 0.687560i \(0.241318\pi\)
\(62\) −11.4176 + 7.15534i −1.45004 + 0.908729i
\(63\) −3.79862 −0.478581
\(64\) −7.81187 + 1.72471i −0.976484 + 0.215588i
\(65\) −2.18691 −0.271253
\(66\) −5.23091 + 3.27817i −0.643881 + 0.403514i
\(67\) 6.97711 6.97711i 0.852389 0.852389i −0.138038 0.990427i \(-0.544079\pi\)
0.990427 + 0.138038i \(0.0440795\pi\)
\(68\) 3.77091 7.78318i 0.457290 0.943849i
\(69\) −2.76520 2.76520i −0.332891 0.332891i
\(70\) −1.20160 + 5.23595i −0.143618 + 0.625815i
\(71\) 0.585051i 0.0694327i −0.999397 0.0347164i \(-0.988947\pi\)
0.999397 0.0347164i \(-0.0110528\pi\)
\(72\) −2.81175 + 0.306697i −0.331368 + 0.0361445i
\(73\) 11.9999i 1.40448i −0.711939 0.702241i \(-0.752183\pi\)
0.711939 0.702241i \(-0.247817\pi\)
\(74\) 8.87009 + 2.03559i 1.03113 + 0.236633i
\(75\) −0.707107 0.707107i −0.0816497 0.0816497i
\(76\) 4.98406 + 14.3526i 0.571711 + 1.64635i
\(77\) 11.7249 11.7249i 1.33617 1.33617i
\(78\) 1.64234 + 2.62066i 0.185959 + 0.296731i
\(79\) 12.6436 1.42252 0.711260 0.702929i \(-0.248125\pi\)
0.711260 + 0.702929i \(0.248125\pi\)
\(80\) −0.466680 + 3.97268i −0.0521765 + 0.444159i
\(81\) −1.00000 −0.111111
\(82\) −0.435720 0.695270i −0.0481172 0.0767797i
\(83\) −11.1632 + 11.1632i −1.22532 + 1.22532i −0.259610 + 0.965713i \(0.583594\pi\)
−0.965713 + 0.259610i \(0.916406\pi\)
\(84\) 7.17682 2.49222i 0.783055 0.271923i
\(85\) −3.05773 3.05773i −0.331657 0.331657i
\(86\) 1.93908 + 0.444998i 0.209096 + 0.0479854i
\(87\) 2.60559i 0.279349i
\(88\) 7.73214 9.62545i 0.824249 1.02608i
\(89\) 12.9706i 1.37488i 0.726241 + 0.687440i \(0.241266\pi\)
−0.726241 + 0.687440i \(0.758734\pi\)
\(90\) −0.316325 + 1.37838i −0.0333435 + 0.145294i
\(91\) −5.87409 5.87409i −0.615772 0.615772i
\(92\) 7.03858 + 3.41016i 0.733822 + 0.355534i
\(93\) 6.73724 6.73724i 0.698619 0.698619i
\(94\) 2.66583 1.67065i 0.274960 0.172315i
\(95\) 7.59666 0.779401
\(96\) 5.11109 2.42420i 0.521649 0.247419i
\(97\) −6.78553 −0.688966 −0.344483 0.938793i \(-0.611946\pi\)
−0.344483 + 0.938793i \(0.611946\pi\)
\(98\) −8.90303 + 5.57945i −0.899342 + 0.563610i
\(99\) 3.08662 3.08662i 0.310217 0.310217i
\(100\) 1.79988 + 0.872033i 0.179988 + 0.0872033i
\(101\) −6.19304 6.19304i −0.616231 0.616231i 0.328332 0.944562i \(-0.393514\pi\)
−0.944562 + 0.328332i \(0.893514\pi\)
\(102\) −1.36788 + 5.96051i −0.135440 + 0.590179i
\(103\) 11.3519i 1.11854i −0.828987 0.559269i \(-0.811082\pi\)
0.828987 0.559269i \(-0.188918\pi\)
\(104\) −4.82230 3.87376i −0.472865 0.379853i
\(105\) 3.79862i 0.370707i
\(106\) 9.36178 + 2.14843i 0.909296 + 0.208674i
\(107\) −8.58488 8.58488i −0.829932 0.829932i 0.157575 0.987507i \(-0.449632\pi\)
−0.987507 + 0.157575i \(0.949632\pi\)
\(108\) 1.88933 0.656085i 0.181800 0.0631318i
\(109\) −10.6624 + 10.6624i −1.02127 + 1.02127i −0.0215039 + 0.999769i \(0.506845\pi\)
−0.999769 + 0.0215039i \(0.993155\pi\)
\(110\) −3.27817 5.23091i −0.312561 0.498748i
\(111\) −6.43514 −0.610797
\(112\) −11.9242 + 9.41722i −1.12674 + 0.889843i
\(113\) −3.11152 −0.292707 −0.146354 0.989232i \(-0.546754\pi\)
−0.146354 + 0.989232i \(0.546754\pi\)
\(114\) −5.70500 9.10337i −0.534323 0.852609i
\(115\) 2.76520 2.76520i 0.257856 0.257856i
\(116\) −1.70949 4.92282i −0.158722 0.457072i
\(117\) −1.54638 1.54638i −0.142963 0.142963i
\(118\) 14.1600 + 3.24957i 1.30353 + 0.299147i
\(119\) 16.4263i 1.50579i
\(120\) −0.306697 2.81175i −0.0279974 0.256676i
\(121\) 8.05441i 0.732219i
\(122\) 0.134752 0.587181i 0.0121999 0.0531609i
\(123\) 0.410260 + 0.410260i 0.0369919 + 0.0369919i
\(124\) −8.30864 + 17.1490i −0.746138 + 1.54003i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) −4.55203 + 2.85272i −0.405527 + 0.254140i
\(127\) −7.16390 −0.635693 −0.317846 0.948142i \(-0.602960\pi\)
−0.317846 + 0.948142i \(0.602960\pi\)
\(128\) −8.06604 + 7.93341i −0.712944 + 0.701221i
\(129\) −1.40678 −0.123860
\(130\) −2.62066 + 1.64234i −0.229847 + 0.144043i
\(131\) −6.55090 + 6.55090i −0.572355 + 0.572355i −0.932786 0.360431i \(-0.882630\pi\)
0.360431 + 0.932786i \(0.382630\pi\)
\(132\) −3.80654 + 7.85671i −0.331317 + 0.683839i
\(133\) 20.4048 + 20.4048i 1.76932 + 1.76932i
\(134\) 3.12121 13.6007i 0.269632 1.17492i
\(135\) 1.00000i 0.0860663i
\(136\) −1.32624 12.1588i −0.113724 1.04261i
\(137\) 11.0502i 0.944082i −0.881577 0.472041i \(-0.843518\pi\)
0.881577 0.472041i \(-0.156482\pi\)
\(138\) −5.39029 1.23701i −0.458852 0.105302i
\(139\) −5.17171 5.17171i −0.438659 0.438659i 0.452902 0.891561i \(-0.350389\pi\)
−0.891561 + 0.452902i \(0.850389\pi\)
\(140\) 2.49222 + 7.17682i 0.210631 + 0.606552i
\(141\) −1.57304 + 1.57304i −0.132473 + 0.132473i
\(142\) −0.439366 0.701089i −0.0368708 0.0588341i
\(143\) 9.54615 0.798289
\(144\) −3.13910 + 2.47912i −0.261592 + 0.206593i
\(145\) −2.60559 −0.216383
\(146\) −9.01178 14.3799i −0.745821 1.19009i
\(147\) 5.25343 5.25343i 0.433296 0.433296i
\(148\) 12.1581 4.22200i 0.999388 0.347046i
\(149\) −5.80335 5.80335i −0.475429 0.475429i 0.428237 0.903666i \(-0.359135\pi\)
−0.903666 + 0.428237i \(0.859135\pi\)
\(150\) −1.37838 0.316325i −0.112544 0.0258278i
\(151\) 13.2591i 1.07901i −0.841982 0.539505i \(-0.818611\pi\)
0.841982 0.539505i \(-0.181389\pi\)
\(152\) 16.7512 + 13.4563i 1.35870 + 1.09145i
\(153\) 4.32428i 0.349597i
\(154\) 5.24513 22.8556i 0.422664 1.84176i
\(155\) 6.73724 + 6.73724i 0.541148 + 0.541148i
\(156\) 3.93617 + 1.90706i 0.315146 + 0.152687i
\(157\) 6.83329 6.83329i 0.545356 0.545356i −0.379738 0.925094i \(-0.623986\pi\)
0.925094 + 0.379738i \(0.123986\pi\)
\(158\) 15.1514 9.49522i 1.20538 0.755399i
\(159\) −6.79186 −0.538629
\(160\) 2.42420 + 5.11109i 0.191650 + 0.404067i
\(161\) 14.8548 1.17072
\(162\) −1.19834 + 0.750988i −0.0941504 + 0.0590032i
\(163\) −7.11541 + 7.11541i −0.557322 + 0.557322i −0.928544 0.371222i \(-0.878939\pi\)
0.371222 + 0.928544i \(0.378939\pi\)
\(164\) −1.04428 0.505949i −0.0815445 0.0395080i
\(165\) 3.08662 + 3.08662i 0.240293 + 0.240293i
\(166\) −4.99388 + 21.7608i −0.387600 + 1.68896i
\(167\) 6.14029i 0.475150i −0.971369 0.237575i \(-0.923648\pi\)
0.971369 0.237575i \(-0.0763525\pi\)
\(168\) 6.72864 8.37623i 0.519126 0.646240i
\(169\) 8.21743i 0.632110i
\(170\) −5.96051 1.36788i −0.457150 0.104911i
\(171\) 5.37165 + 5.37165i 0.410780 + 0.410780i
\(172\) 2.65786 0.922965i 0.202660 0.0703754i
\(173\) −7.29269 + 7.29269i −0.554453 + 0.554453i −0.927723 0.373270i \(-0.878237\pi\)
0.373270 + 0.927723i \(0.378237\pi\)
\(174\) 1.95677 + 3.12239i 0.148342 + 0.236707i
\(175\) 3.79862 0.287148
\(176\) 2.03712 17.3413i 0.153554 1.30715i
\(177\) −10.2729 −0.772159
\(178\) 9.74077 + 15.5432i 0.730101 + 1.16501i
\(179\) 6.22897 6.22897i 0.465575 0.465575i −0.434902 0.900478i \(-0.643217\pi\)
0.900478 + 0.434902i \(0.143217\pi\)
\(180\) 0.656085 + 1.88933i 0.0489017 + 0.140822i
\(181\) −1.27302 1.27302i −0.0946227 0.0946227i 0.658211 0.752834i \(-0.271314\pi\)
−0.752834 + 0.658211i \(0.771314\pi\)
\(182\) −11.4505 2.62778i −0.848770 0.194784i
\(183\) 0.425993i 0.0314903i
\(184\) 10.9956 1.19936i 0.810606 0.0884182i
\(185\) 6.43514i 0.473121i
\(186\) 3.01391 13.1331i 0.220990 0.962965i
\(187\) 13.3474 + 13.3474i 0.976058 + 0.976058i
\(188\) 1.93993 4.00402i 0.141484 0.292023i
\(189\) 2.68603 2.68603i 0.195380 0.195380i
\(190\) 9.10337 5.70500i 0.660428 0.413885i
\(191\) 9.63638 0.697264 0.348632 0.937260i \(-0.386646\pi\)
0.348632 + 0.937260i \(0.386646\pi\)
\(192\) 4.30428 6.74338i 0.310634 0.486662i
\(193\) −3.64530 −0.262394 −0.131197 0.991356i \(-0.541882\pi\)
−0.131197 + 0.991356i \(0.541882\pi\)
\(194\) −8.13137 + 5.09586i −0.583798 + 0.365861i
\(195\) 1.54638 1.54638i 0.110738 0.110738i
\(196\) −6.47875 + 13.3721i −0.462768 + 0.955153i
\(197\) −7.55422 7.55422i −0.538216 0.538216i 0.384789 0.923005i \(-0.374274\pi\)
−0.923005 + 0.384789i \(0.874274\pi\)
\(198\) 1.38080 6.01683i 0.0981292 0.427597i
\(199\) 23.7442i 1.68318i 0.540116 + 0.841591i \(0.318380\pi\)
−0.540116 + 0.841591i \(0.681620\pi\)
\(200\) 2.81175 0.306697i 0.198821 0.0216867i
\(201\) 9.86712i 0.695973i
\(202\) −12.0723 2.77046i −0.849402 0.194929i
\(203\) −6.99870 6.99870i −0.491212 0.491212i
\(204\) 2.83710 + 8.16997i 0.198637 + 0.572013i
\(205\) −0.410260 + 0.410260i −0.0286538 + 0.0286538i
\(206\) −8.52516 13.6034i −0.593976 0.947797i
\(207\) 3.91059 0.271805
\(208\) −8.68789 1.02059i −0.602397 0.0707650i
\(209\) −33.1605 −2.29376
\(210\) −2.85272 4.55203i −0.196856 0.314120i
\(211\) 14.5856 14.5856i 1.00412 1.00412i 0.00412399 0.999991i \(-0.498687\pi\)
0.999991 0.00412399i \(-0.00131271\pi\)
\(212\) 12.8320 4.45604i 0.881308 0.306042i
\(213\) 0.413693 + 0.413693i 0.0283458 + 0.0283458i
\(214\) −16.7347 3.84045i −1.14396 0.262528i
\(215\) 1.40678i 0.0959413i
\(216\) 1.77134 2.20507i 0.120524 0.150036i
\(217\) 36.1928i 2.45693i
\(218\) −4.76983 + 20.7845i −0.323054 + 1.40770i
\(219\) 8.48521 + 8.48521i 0.573377 + 0.573377i
\(220\) −7.85671 3.80654i −0.529699 0.256637i
\(221\) 6.68697 6.68697i 0.449814 0.449814i
\(222\) −7.71148 + 4.83272i −0.517561 + 0.324351i
\(223\) −13.6893 −0.916702 −0.458351 0.888771i \(-0.651560\pi\)
−0.458351 + 0.888771i \(0.651560\pi\)
\(224\) −7.21707 + 20.2400i −0.482211 + 1.35234i
\(225\) 1.00000 0.0666667
\(226\) −3.72865 + 2.33671i −0.248026 + 0.155436i
\(227\) −11.9490 + 11.9490i −0.793085 + 0.793085i −0.981994 0.188910i \(-0.939505\pi\)
0.188910 + 0.981994i \(0.439505\pi\)
\(228\) −13.6731 6.62454i −0.905520 0.438721i
\(229\) 9.40821 + 9.40821i 0.621712 + 0.621712i 0.945969 0.324257i \(-0.105114\pi\)
−0.324257 + 0.945969i \(0.605114\pi\)
\(230\) 1.23701 5.39029i 0.0815663 0.355425i
\(231\) 16.5815i 1.09098i
\(232\) −5.74553 4.61539i −0.377213 0.303016i
\(233\) 11.8223i 0.774505i 0.921974 + 0.387253i \(0.126576\pi\)
−0.921974 + 0.387253i \(0.873424\pi\)
\(234\) −3.01440 0.691773i −0.197057 0.0452226i
\(235\) −1.57304 1.57304i −0.102614 0.102614i
\(236\) 19.4089 6.73990i 1.26341 0.438730i
\(237\) −8.94040 + 8.94040i −0.580741 + 0.580741i
\(238\) −12.3359 19.6842i −0.799621 1.27594i
\(239\) 11.2115 0.725213 0.362607 0.931942i \(-0.381887\pi\)
0.362607 + 0.931942i \(0.381887\pi\)
\(240\) −2.47912 3.13910i −0.160026 0.202628i
\(241\) 7.89997 0.508881 0.254441 0.967088i \(-0.418109\pi\)
0.254441 + 0.967088i \(0.418109\pi\)
\(242\) 6.04877 + 9.65191i 0.388830 + 0.620448i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −0.279488 0.804839i −0.0178924 0.0515245i
\(245\) 5.25343 + 5.25343i 0.335630 + 0.335630i
\(246\) 0.799730 + 0.183530i 0.0509890 + 0.0117014i
\(247\) 16.6132i 1.05707i
\(248\) 2.92217 + 26.7901i 0.185558 + 1.70117i
\(249\) 15.7872i 1.00047i
\(250\) 0.316325 1.37838i 0.0200061 0.0871766i
\(251\) −5.34286 5.34286i −0.337238 0.337238i 0.518089 0.855327i \(-0.326644\pi\)
−0.855327 + 0.518089i \(0.826644\pi\)
\(252\) −3.31252 + 6.83704i −0.208669 + 0.430693i
\(253\) −12.0705 + 12.0705i −0.758865 + 0.758865i
\(254\) −8.58477 + 5.38000i −0.538657 + 0.337571i
\(255\) 4.32428 0.270797
\(256\) −3.70795 + 15.5644i −0.231747 + 0.972776i
\(257\) 15.5250 0.968420 0.484210 0.874952i \(-0.339107\pi\)
0.484210 + 0.874952i \(0.339107\pi\)
\(258\) −1.68579 + 1.05647i −0.104953 + 0.0657731i
\(259\) 17.2850 17.2850i 1.07404 1.07404i
\(260\) −1.90706 + 3.93617i −0.118271 + 0.244111i
\(261\) −1.84243 1.84243i −0.114044 0.114044i
\(262\) −2.93055 + 12.7698i −0.181050 + 0.788924i
\(263\) 14.3705i 0.886126i −0.896491 0.443063i \(-0.853892\pi\)
0.896491 0.443063i \(-0.146108\pi\)
\(264\) 1.33877 + 12.2737i 0.0823957 + 0.755392i
\(265\) 6.79186i 0.417221i
\(266\) 39.7757 + 9.12811i 2.43880 + 0.559680i
\(267\) −9.17160 9.17160i −0.561293 0.561293i
\(268\) −6.47367 18.6422i −0.395443 1.13875i
\(269\) −19.0607 + 19.0607i −1.16215 + 1.16215i −0.178145 + 0.984004i \(0.557010\pi\)
−0.984004 + 0.178145i \(0.942990\pi\)
\(270\) −0.750988 1.19834i −0.0457037 0.0729286i
\(271\) −4.66889 −0.283615 −0.141808 0.989894i \(-0.545291\pi\)
−0.141808 + 0.989894i \(0.545291\pi\)
\(272\) −10.7204 13.5744i −0.650020 0.823067i
\(273\) 8.30722 0.502776
\(274\) −8.29857 13.2419i −0.501335 0.799971i
\(275\) −3.08662 + 3.08662i −0.186130 + 0.186130i
\(276\) −7.38837 + 2.56568i −0.444728 + 0.154436i
\(277\) −6.24572 6.24572i −0.375269 0.375269i 0.494123 0.869392i \(-0.335489\pi\)
−0.869392 + 0.494123i \(0.835489\pi\)
\(278\) −10.0814 2.31357i −0.604640 0.138759i
\(279\) 9.52790i 0.570420i
\(280\) 8.37623 + 6.72864i 0.500575 + 0.402113i
\(281\) 29.7389i 1.77407i 0.461699 + 0.887037i \(0.347240\pi\)
−0.461699 + 0.887037i \(0.652760\pi\)
\(282\) −0.703698 + 3.06636i −0.0419046 + 0.182599i
\(283\) −9.49040 9.49040i −0.564146 0.564146i 0.366337 0.930482i \(-0.380612\pi\)
−0.930482 + 0.366337i \(0.880612\pi\)
\(284\) −1.05302 0.510183i −0.0624852 0.0302738i
\(285\) −5.37165 + 5.37165i −0.318189 + 0.318189i
\(286\) 11.4395 7.16905i 0.676433 0.423915i
\(287\) −2.20394 −0.130094
\(288\) −1.89992 + 5.32825i −0.111954 + 0.313970i
\(289\) 1.69940 0.0999648
\(290\) −3.12239 + 1.95677i −0.183353 + 0.114906i
\(291\) 4.79809 4.79809i 0.281269 0.281269i
\(292\) −21.5983 10.4643i −1.26395 0.612377i
\(293\) −1.72797 1.72797i −0.100949 0.100949i 0.654829 0.755777i \(-0.272741\pi\)
−0.755777 + 0.654829i \(0.772741\pi\)
\(294\) 2.35013 10.2407i 0.137062 0.597248i
\(295\) 10.2729i 0.598112i
\(296\) 11.3988 14.1900i 0.662543 0.824775i
\(297\) 4.36514i 0.253291i
\(298\) −11.3126 2.59613i −0.655323 0.150390i
\(299\) 6.04724 + 6.04724i 0.349721 + 0.349721i
\(300\) −1.88933 + 0.656085i −0.109080 + 0.0378791i
\(301\) 3.77864 3.77864i 0.217797 0.217797i
\(302\) −9.95743 15.8889i −0.572986 0.914304i
\(303\) 8.75828 0.503150
\(304\) 30.1791 + 3.54521i 1.73089 + 0.203332i
\(305\) −0.425993 −0.0243923
\(306\) −3.24748 5.18195i −0.185646 0.296233i
\(307\) 17.5875 17.5875i 1.00377 1.00377i 0.00377977 0.999993i \(-0.498797\pi\)
0.999993 0.00377977i \(-0.00120314\pi\)
\(308\) −10.8789 31.3278i −0.619881 1.78507i
\(309\) 8.02701 + 8.02701i 0.456641 + 0.456641i
\(310\) 13.1331 + 3.01391i 0.745909 + 0.171178i
\(311\) 1.71809i 0.0974241i 0.998813 + 0.0487120i \(0.0155117\pi\)
−0.998813 + 0.0487120i \(0.984488\pi\)
\(312\) 6.14904 0.670717i 0.348121 0.0379719i
\(313\) 16.4421i 0.929363i −0.885478 0.464682i \(-0.846169\pi\)
0.885478 0.464682i \(-0.153831\pi\)
\(314\) 3.05687 13.3203i 0.172509 0.751709i
\(315\) 2.68603 + 2.68603i 0.151340 + 0.151340i
\(316\) 11.0257 22.7570i 0.620242 1.28018i
\(317\) −7.96065 + 7.96065i −0.447114 + 0.447114i −0.894394 0.447280i \(-0.852393\pi\)
0.447280 + 0.894394i \(0.352393\pi\)
\(318\) −8.13895 + 5.10061i −0.456410 + 0.286028i
\(319\) 11.3738 0.636809
\(320\) 6.74338 + 4.30428i 0.376967 + 0.240616i
\(321\) 12.1409 0.677637
\(322\) 17.8011 11.1558i 0.992017 0.621688i
\(323\) −23.2285 + 23.2285i −1.29247 + 1.29247i
\(324\) −0.872033 + 1.79988i −0.0484463 + 0.0999932i
\(325\) 1.54638 + 1.54638i 0.0857776 + 0.0857776i
\(326\) −3.18308 + 13.8703i −0.176295 + 0.768203i
\(327\) 15.0789i 0.833866i
\(328\) −1.63136 + 0.177944i −0.0900769 + 0.00982530i
\(329\) 8.45043i 0.465887i
\(330\) 6.01683 + 1.38080i 0.331215 + 0.0760105i
\(331\) 9.02535 + 9.02535i 0.496078 + 0.496078i 0.910215 0.414137i \(-0.135916\pi\)
−0.414137 + 0.910215i \(0.635916\pi\)
\(332\) 10.3577 + 29.8271i 0.568455 + 1.63698i
\(333\) 4.55033 4.55033i 0.249357 0.249357i
\(334\) −4.61128 7.35814i −0.252318 0.402620i
\(335\) −9.86712 −0.539098
\(336\) 1.77274 15.0907i 0.0967109 0.823265i
\(337\) 7.44173 0.405377 0.202688 0.979243i \(-0.435032\pi\)
0.202688 + 0.979243i \(0.435032\pi\)
\(338\) 6.17120 + 9.84727i 0.335669 + 0.535621i
\(339\) 2.20018 2.20018i 0.119497 0.119497i
\(340\) −8.16997 + 2.83710i −0.443079 + 0.153863i
\(341\) −29.4090 29.4090i −1.59258 1.59258i
\(342\) 10.4711 + 2.40301i 0.566213 + 0.129940i
\(343\) 1.63142i 0.0880882i
\(344\) 2.49188 3.10205i 0.134353 0.167251i
\(345\) 3.91059i 0.210539i
\(346\) −3.26239 + 14.2158i −0.175387 + 0.764249i
\(347\) −0.659315 0.659315i −0.0353939 0.0353939i 0.689188 0.724582i \(-0.257967\pi\)
−0.724582 + 0.689188i \(0.757967\pi\)
\(348\) 4.68975 + 2.27216i 0.251397 + 0.121801i
\(349\) 8.04705 8.04705i 0.430749 0.430749i −0.458134 0.888883i \(-0.651482\pi\)
0.888883 + 0.458134i \(0.151482\pi\)
\(350\) 4.55203 2.85272i 0.243316 0.152484i
\(351\) 2.18691 0.116729
\(352\) −10.5820 22.3106i −0.564020 1.18916i
\(353\) 18.3339 0.975815 0.487907 0.872895i \(-0.337760\pi\)
0.487907 + 0.872895i \(0.337760\pi\)
\(354\) −12.3104 + 7.71483i −0.654292 + 0.410039i
\(355\) −0.413693 + 0.413693i −0.0219566 + 0.0219566i
\(356\) 23.3455 + 11.3108i 1.23731 + 0.599470i
\(357\) 11.6151 + 11.6151i 0.614738 + 0.614738i
\(358\) 2.78653 12.1423i 0.147273 0.641741i
\(359\) 11.8783i 0.626912i 0.949603 + 0.313456i \(0.101487\pi\)
−0.949603 + 0.313456i \(0.898513\pi\)
\(360\) 2.20507 + 1.77134i 0.116218 + 0.0933578i
\(361\) 38.7093i 2.03733i
\(362\) −2.48153 0.569485i −0.130426 0.0299315i
\(363\) −5.69533 5.69533i −0.298927 0.298927i
\(364\) −15.6951 + 5.45025i −0.822644 + 0.285671i
\(365\) −8.48521 + 8.48521i −0.444136 + 0.444136i
\(366\) 0.319916 + 0.510484i 0.0167223 + 0.0266834i
\(367\) −24.0792 −1.25692 −0.628462 0.777841i \(-0.716315\pi\)
−0.628462 + 0.777841i \(0.716315\pi\)
\(368\) 12.2757 9.69481i 0.639917 0.505377i
\(369\) −0.580195 −0.0302037
\(370\) −4.83272 7.71148i −0.251241 0.400901i
\(371\) 18.2431 18.2431i 0.947135 0.947135i
\(372\) −6.25111 18.0013i −0.324105 0.933324i
\(373\) 5.50986 + 5.50986i 0.285290 + 0.285290i 0.835214 0.549925i \(-0.185344\pi\)
−0.549925 + 0.835214i \(0.685344\pi\)
\(374\) 26.0184 + 5.97097i 1.34538 + 0.308751i
\(375\) 1.00000i 0.0516398i
\(376\) −0.682279 6.25504i −0.0351859 0.322579i
\(377\) 5.69820i 0.293472i
\(378\) 1.20160 5.23595i 0.0618034 0.269308i
\(379\) −4.41212 4.41212i −0.226635 0.226635i 0.584650 0.811285i \(-0.301232\pi\)
−0.811285 + 0.584650i \(0.801232\pi\)
\(380\) 6.62454 13.6731i 0.339832 0.701413i
\(381\) 5.06564 5.06564i 0.259521 0.259521i
\(382\) 11.5477 7.23681i 0.590829 0.370267i
\(383\) 12.4394 0.635625 0.317812 0.948154i \(-0.397052\pi\)
0.317812 + 0.948154i \(0.397052\pi\)
\(384\) 0.0937806 11.3133i 0.00478572 0.577330i
\(385\) −16.5815 −0.845070
\(386\) −4.36830 + 2.73757i −0.222341 + 0.139339i
\(387\) 0.994741 0.994741i 0.0505655 0.0505655i
\(388\) −5.91720 + 12.2131i −0.300401 + 0.620027i
\(389\) −22.7006 22.7006i −1.15097 1.15097i −0.986359 0.164609i \(-0.947364\pi\)
−0.164609 0.986359i \(-0.552636\pi\)
\(390\) 0.691773 3.01440i 0.0350293 0.152640i
\(391\) 16.9105i 0.855199i
\(392\) 2.27859 + 20.8898i 0.115086 + 1.05510i
\(393\) 9.26437i 0.467326i
\(394\) −14.7257 3.37939i −0.741868 0.170251i
\(395\) −8.94040 8.94040i −0.449840 0.449840i
\(396\) −2.86390 8.24716i −0.143916 0.414436i
\(397\) −23.2641 + 23.2641i −1.16759 + 1.16759i −0.184819 + 0.982773i \(0.559170\pi\)
−0.982773 + 0.184819i \(0.940830\pi\)
\(398\) 17.8316 + 28.4536i 0.893818 + 1.42625i
\(399\) −28.8568 −1.44465
\(400\) 3.13910 2.47912i 0.156955 0.123956i
\(401\) 31.5965 1.57786 0.788928 0.614486i \(-0.210636\pi\)
0.788928 + 0.614486i \(0.210636\pi\)
\(402\) 7.41009 + 11.8242i 0.369582 + 0.589735i
\(403\) −14.7337 + 14.7337i −0.733939 + 0.733939i
\(404\) −16.5473 + 5.74618i −0.823257 + 0.285883i
\(405\) 0.707107 + 0.707107i 0.0351364 + 0.0351364i
\(406\) −13.6428 3.13087i −0.677078 0.155383i
\(407\) 28.0903i 1.39238i
\(408\) 9.53536 + 7.65977i 0.472071 + 0.379215i
\(409\) 14.4988i 0.716917i −0.933546 0.358459i \(-0.883302\pi\)
0.933546 0.358459i \(-0.116698\pi\)
\(410\) −0.183530 + 0.799730i −0.00906390 + 0.0394959i
\(411\) 7.81367 + 7.81367i 0.385420 + 0.385420i
\(412\) −20.4321 9.89924i −1.00661 0.487700i
\(413\) 27.5933 27.5933i 1.35778 1.35778i
\(414\) 4.68621 2.93681i 0.230315 0.144336i
\(415\) 15.7872 0.774963
\(416\) −11.1775 + 5.30150i −0.548022 + 0.259927i
\(417\) 7.31391 0.358164
\(418\) −39.7375 + 24.9031i −1.94362 + 1.21805i
\(419\) 24.0709 24.0709i 1.17594 1.17594i 0.195169 0.980770i \(-0.437475\pi\)
0.980770 0.195169i \(-0.0625254\pi\)
\(420\) −6.83704 3.31252i −0.333613 0.161634i
\(421\) −20.1095 20.1095i −0.980079 0.980079i 0.0197268 0.999805i \(-0.493720\pi\)
−0.999805 + 0.0197268i \(0.993720\pi\)
\(422\) 6.52488 28.4321i 0.317626 1.38406i
\(423\) 2.22461i 0.108164i
\(424\) 12.0307 14.9766i 0.584262 0.727326i
\(425\) 4.32428i 0.209758i
\(426\) 0.806424 + 0.185066i 0.0390714 + 0.00896647i
\(427\) −1.14423 1.14423i −0.0553730 0.0553730i
\(428\) −22.9380 + 7.96544i −1.10875 + 0.385024i
\(429\) −6.75015 + 6.75015i −0.325900 + 0.325900i
\(430\) −1.05647 1.68579i −0.0509476 0.0812962i
\(431\) −29.9026 −1.44036 −0.720180 0.693787i \(-0.755941\pi\)
−0.720180 + 0.693787i \(0.755941\pi\)
\(432\) 0.466680 3.97268i 0.0224532 0.191136i
\(433\) 17.7487 0.852950 0.426475 0.904499i \(-0.359755\pi\)
0.426475 + 0.904499i \(0.359755\pi\)
\(434\) 27.1804 + 43.3713i 1.30470 + 2.08189i
\(435\) 1.84243 1.84243i 0.0883379 0.0883379i
\(436\) 9.89305 + 28.4890i 0.473791 + 1.36437i
\(437\) −21.0063 21.0063i −1.00487 1.00487i
\(438\) 16.5405 + 3.79586i 0.790333 + 0.181373i
\(439\) 15.1376i 0.722478i −0.932473 0.361239i \(-0.882354\pi\)
0.932473 0.361239i \(-0.117646\pi\)
\(440\) −12.2737 + 1.33877i −0.585124 + 0.0638234i
\(441\) 7.42948i 0.353785i
\(442\) 2.99142 13.0351i 0.142287 0.620016i
\(443\) −16.4687 16.4687i −0.782451 0.782451i 0.197793 0.980244i \(-0.436623\pi\)
−0.980244 + 0.197793i \(0.936623\pi\)
\(444\) −5.61165 + 11.5825i −0.266317 + 0.549679i
\(445\) 9.17160 9.17160i 0.434775 0.434775i
\(446\) −16.4044 + 10.2805i −0.776771 + 0.486795i
\(447\) 8.20718 0.388186
\(448\) 6.55150 + 29.6743i 0.309529 + 1.40198i
\(449\) 35.6078 1.68044 0.840218 0.542249i \(-0.182427\pi\)
0.840218 + 0.542249i \(0.182427\pi\)
\(450\) 1.19834 0.750988i 0.0564902 0.0354019i
\(451\) 1.79084 1.79084i 0.0843273 0.0843273i
\(452\) −2.71335 + 5.60035i −0.127625 + 0.263418i
\(453\) 9.37560 + 9.37560i 0.440504 + 0.440504i
\(454\) −5.34540 + 23.2926i −0.250872 + 1.09317i
\(455\) 8.30722i 0.389449i
\(456\) −21.3599 + 2.32987i −1.00027 + 0.109106i
\(457\) 1.98064i 0.0926502i −0.998926 0.0463251i \(-0.985249\pi\)
0.998926 0.0463251i \(-0.0147510\pi\)
\(458\) 18.3397 + 4.20877i 0.856957 + 0.196663i
\(459\) 3.05773 + 3.05773i 0.142723 + 0.142723i
\(460\) −2.56568 7.38837i −0.119625 0.344485i
\(461\) −4.13532 + 4.13532i −0.192601 + 0.192601i −0.796819 0.604218i \(-0.793486\pi\)
0.604218 + 0.796819i \(0.293486\pi\)
\(462\) 12.4525 + 19.8702i 0.579342 + 0.924446i
\(463\) 23.4228 1.08855 0.544274 0.838907i \(-0.316805\pi\)
0.544274 + 0.838907i \(0.316805\pi\)
\(464\) −10.3512 1.21598i −0.480542 0.0564505i
\(465\) −9.52790 −0.441846
\(466\) 8.87842 + 14.1671i 0.411285 + 0.656280i
\(467\) −4.20786 + 4.20786i −0.194717 + 0.194717i −0.797731 0.603014i \(-0.793966\pi\)
0.603014 + 0.797731i \(0.293966\pi\)
\(468\) −4.13178 + 1.43480i −0.190992 + 0.0663236i
\(469\) −26.5033 26.5033i −1.22381 1.22381i
\(470\) −3.06636 0.703698i −0.141441 0.0324592i
\(471\) 9.66373i 0.445281i
\(472\) 18.1968 22.6525i 0.837576 1.04267i
\(473\) 6.14077i 0.282353i
\(474\) −3.99949 + 17.4278i −0.183703 + 0.800484i
\(475\) −5.37165 5.37165i −0.246468 0.246468i
\(476\) −29.5653 14.3242i −1.35512 0.656551i
\(477\) 4.80257 4.80257i 0.219895 0.219895i
\(478\) 13.4352 8.41973i 0.614512 0.385109i
\(479\) 5.52216 0.252314 0.126157 0.992010i \(-0.459736\pi\)
0.126157 + 0.992010i \(0.459736\pi\)
\(480\) −5.32825 1.89992i −0.243200 0.0867192i
\(481\) 14.0731 0.641676
\(482\) 9.46684 5.93278i 0.431203 0.270231i
\(483\) −10.5039 + 10.5039i −0.477946 + 0.477946i
\(484\) 14.4970 + 7.02371i 0.658952 + 0.319259i
\(485\) 4.79809 + 4.79809i 0.217870 + 0.217870i
\(486\) 0.316325 1.37838i 0.0143488 0.0625247i
\(487\) 28.0612i 1.27158i 0.771864 + 0.635788i \(0.219325\pi\)
−0.771864 + 0.635788i \(0.780675\pi\)
\(488\) −0.939345 0.754578i −0.0425222 0.0341581i
\(489\) 10.0627i 0.455051i
\(490\) 10.2407 + 2.35013i 0.462626 + 0.106168i
\(491\) −1.27407 1.27407i −0.0574979 0.0574979i 0.677773 0.735271i \(-0.262945\pi\)
−0.735271 + 0.677773i \(0.762945\pi\)
\(492\) 1.09618 0.380657i 0.0494195 0.0171614i
\(493\) 7.96720 7.96720i 0.358825 0.358825i
\(494\) 12.4763 + 19.9082i 0.561336 + 0.895714i
\(495\) −4.36514 −0.196198
\(496\) 23.6208 + 29.9091i 1.06060 + 1.34296i
\(497\) −2.22238 −0.0996875
\(498\) −11.8560 18.9184i −0.531280 0.847754i
\(499\) −26.3351 + 26.3351i −1.17892 + 1.17892i −0.198901 + 0.980020i \(0.563737\pi\)
−0.980020 + 0.198901i \(0.936263\pi\)
\(500\) −0.656085 1.88933i −0.0293410 0.0844932i
\(501\) 4.34184 + 4.34184i 0.193979 + 0.193979i
\(502\) −10.4150 2.39013i −0.464843 0.106677i
\(503\) 33.2293i 1.48162i −0.671715 0.740810i \(-0.734442\pi\)
0.671715 0.740810i \(-0.265558\pi\)
\(504\) 1.16502 + 10.6808i 0.0518942 + 0.475759i
\(505\) 8.75828i 0.389739i
\(506\) −5.39974 + 23.5293i −0.240048 + 1.04601i
\(507\) −5.81060 5.81060i −0.258058 0.258058i
\(508\) −6.24715 + 12.8941i −0.277172 + 0.572085i
\(509\) −5.03424 + 5.03424i −0.223139 + 0.223139i −0.809819 0.586680i \(-0.800435\pi\)
0.586680 + 0.809819i \(0.300435\pi\)
\(510\) 5.18195 3.24748i 0.229461 0.143801i
\(511\) −45.5830 −2.01647
\(512\) 7.24532 + 21.4361i 0.320201 + 0.947350i
\(513\) −7.59666 −0.335401
\(514\) 18.6042 11.6591i 0.820594 0.514259i
\(515\) −8.02701 + 8.02701i −0.353713 + 0.353713i
\(516\) −1.22675 + 2.53202i −0.0540049 + 0.111466i
\(517\) 6.86651 + 6.86651i 0.301989 + 0.301989i
\(518\) 7.73244 33.6940i 0.339744 1.48043i
\(519\) 10.3134i 0.452709i
\(520\) 0.670717 + 6.14904i 0.0294129 + 0.269653i
\(521\) 29.6023i 1.29690i 0.761257 + 0.648450i \(0.224582\pi\)
−0.761257 + 0.648450i \(0.775418\pi\)
\(522\) −3.59151 0.824214i −0.157196 0.0360749i
\(523\) 6.90122 + 6.90122i 0.301769 + 0.301769i 0.841706 0.539937i \(-0.181552\pi\)
−0.539937 + 0.841706i \(0.681552\pi\)
\(524\) 6.07822 + 17.5034i 0.265528 + 0.764640i
\(525\) −2.68603 + 2.68603i −0.117228 + 0.117228i
\(526\) −10.7921 17.2208i −0.470559 0.750862i
\(527\) −41.2013 −1.79476
\(528\) 10.8217 + 13.7026i 0.470953 + 0.596330i
\(529\) 7.70731 0.335100
\(530\) −5.10061 8.13895i −0.221556 0.353533i
\(531\) 7.26404 7.26404i 0.315233 0.315233i
\(532\) 54.5199 18.9325i 2.36374 0.820829i
\(533\) −0.897200 0.897200i −0.0388621 0.0388621i
\(534\) −17.8784 4.10292i −0.773676 0.177551i
\(535\) 12.1409i 0.524895i
\(536\) −21.7577 17.4780i −0.939791 0.754936i
\(537\) 8.80909i 0.380140i
\(538\) −8.52680 + 37.1555i −0.367617 + 1.60189i
\(539\) −22.9319 22.9319i −0.987749 0.987749i
\(540\) −1.79988 0.872033i −0.0774544 0.0375263i
\(541\) −7.18248 + 7.18248i −0.308799 + 0.308799i −0.844443 0.535645i \(-0.820069\pi\)
0.535645 + 0.844443i \(0.320069\pi\)
\(542\) −5.59492 + 3.50628i −0.240322 + 0.150608i
\(543\) 1.80032 0.0772591
\(544\) −23.0409 8.21579i −0.987869 0.352249i
\(545\) 15.0789 0.645910
\(546\) 9.95487 6.23863i 0.426029 0.266989i
\(547\) −14.9525 + 14.9525i −0.639323 + 0.639323i −0.950388 0.311066i \(-0.899314\pi\)
0.311066 + 0.950388i \(0.399314\pi\)
\(548\) −19.8890 9.63613i −0.849616 0.411635i
\(549\) −0.301222 0.301222i −0.0128559 0.0128559i
\(550\) −1.38080 + 6.01683i −0.0588775 + 0.256558i
\(551\) 19.7938i 0.843245i
\(552\) −6.92698 + 8.62314i −0.294832 + 0.367025i
\(553\) 48.0283i 2.04237i
\(554\) −12.1749 2.79402i −0.517264 0.118707i
\(555\) 4.55033 + 4.55033i 0.193151 + 0.193151i
\(556\) −13.8184 + 4.79855i −0.586029 + 0.203504i
\(557\) 24.8706 24.8706i 1.05380 1.05380i 0.0553344 0.998468i \(-0.482378\pi\)
0.998468 0.0553344i \(-0.0176225\pi\)
\(558\) 7.15534 + 11.4176i 0.302910 + 0.483348i
\(559\) 3.07649 0.130122
\(560\) 15.0907 + 1.77274i 0.637698 + 0.0749119i
\(561\) −18.8761 −0.796948
\(562\) 22.3336 + 35.6373i 0.942085 + 1.50327i
\(563\) 11.1111 11.1111i 0.468277 0.468277i −0.433079 0.901356i \(-0.642573\pi\)
0.901356 + 0.433079i \(0.142573\pi\)
\(564\) 1.45953 + 4.20301i 0.0614574 + 0.176979i
\(565\) 2.20018 + 2.20018i 0.0925621 + 0.0925621i
\(566\) −18.4999 4.24554i −0.777609 0.178453i
\(567\) 3.79862i 0.159527i
\(568\) −1.64502 + 0.179433i −0.0690233 + 0.00752884i
\(569\) 12.9347i 0.542250i 0.962544 + 0.271125i \(0.0873956\pi\)
−0.962544 + 0.271125i \(0.912604\pi\)
\(570\) −2.40301 + 10.4711i −0.100651 + 0.438586i
\(571\) −14.5979 14.5979i −0.610903 0.610903i 0.332278 0.943181i \(-0.392183\pi\)
−0.943181 + 0.332278i \(0.892183\pi\)
\(572\) 8.32456 17.1819i 0.348067 0.718411i
\(573\) −6.81395 + 6.81395i −0.284657 + 0.284657i
\(574\) −2.64106 + 1.65513i −0.110236 + 0.0690838i
\(575\) −3.91059 −0.163083
\(576\) 1.72471 + 7.81187i 0.0718628 + 0.325495i
\(577\) 15.7906 0.657373 0.328687 0.944439i \(-0.393394\pi\)
0.328687 + 0.944439i \(0.393394\pi\)
\(578\) 2.03646 1.27623i 0.0847055 0.0530842i
\(579\) 2.57761 2.57761i 0.107122 0.107122i
\(580\) −2.27216 + 4.68975i −0.0943465 + 0.194731i
\(581\) 42.4048 + 42.4048i 1.75925 + 1.75925i
\(582\) 2.14643 9.35306i 0.0889724 0.387697i
\(583\) 29.6474i 1.22787i
\(584\) −33.7407 + 3.68033i −1.39620 + 0.152293i
\(585\) 2.18691i 0.0904175i
\(586\) −3.36837 0.773006i −0.139146 0.0319326i
\(587\) 13.9365 + 13.9365i 0.575221 + 0.575221i 0.933583 0.358362i \(-0.116665\pi\)
−0.358362 + 0.933583i \(0.616665\pi\)
\(588\) −4.87437 14.0367i −0.201016 0.578864i
\(589\) 51.1805 51.1805i 2.10886 2.10886i
\(590\) −7.71483 12.3104i −0.317615 0.506812i
\(591\) 10.6833 0.439452
\(592\) 3.00315 25.5648i 0.123429 1.05071i
\(593\) −47.4176 −1.94721 −0.973604 0.228242i \(-0.926702\pi\)
−0.973604 + 0.228242i \(0.926702\pi\)
\(594\) 3.27817 + 5.23091i 0.134505 + 0.214627i
\(595\) −11.6151 + 11.6151i −0.476174 + 0.476174i
\(596\) −15.5060 + 5.38461i −0.635152 + 0.220562i
\(597\) −16.7897 16.7897i −0.687156 0.687156i
\(598\) 11.7881 + 2.70524i 0.482050 + 0.110625i
\(599\) 23.5791i 0.963415i −0.876332 0.481707i \(-0.840017\pi\)
0.876332 0.481707i \(-0.159983\pi\)
\(600\) −1.77134 + 2.20507i −0.0723147 + 0.0900218i
\(601\) 3.86582i 0.157690i −0.996887 0.0788450i \(-0.974877\pi\)
0.996887 0.0788450i \(-0.0251232\pi\)
\(602\) 1.69038 7.36580i 0.0688946 0.300208i
\(603\) −6.97711 6.97711i −0.284130 0.284130i
\(604\) −23.8648 11.5624i −0.971043 0.470466i
\(605\) 5.69533 5.69533i 0.231548 0.231548i
\(606\) 10.4954 6.57737i 0.426346 0.267187i
\(607\) 32.4306 1.31632 0.658159 0.752879i \(-0.271335\pi\)
0.658159 + 0.752879i \(0.271335\pi\)
\(608\) 38.8272 18.4158i 1.57465 0.746860i
\(609\) 9.89765 0.401073
\(610\) −0.510484 + 0.319916i −0.0206689 + 0.0129530i
\(611\) 3.44008 3.44008i 0.139171 0.139171i
\(612\) −7.78318 3.77091i −0.314616 0.152430i
\(613\) 21.7952 + 21.7952i 0.880298 + 0.880298i 0.993565 0.113267i \(-0.0361314\pi\)
−0.113267 + 0.993565i \(0.536131\pi\)
\(614\) 7.86779 34.2838i 0.317518 1.38358i
\(615\) 0.580195i 0.0233957i
\(616\) −36.5634 29.3714i −1.47318 1.18341i
\(617\) 1.49837i 0.0603219i 0.999545 + 0.0301610i \(0.00960199\pi\)
−0.999545 + 0.0301610i \(0.990398\pi\)
\(618\) 15.6473 + 3.59089i 0.629426 + 0.144447i
\(619\) 16.7004 + 16.7004i 0.671246 + 0.671246i 0.958003 0.286757i \(-0.0925772\pi\)
−0.286757 + 0.958003i \(0.592577\pi\)
\(620\) 18.0013 6.25111i 0.722950 0.251051i
\(621\) −2.76520 + 2.76520i −0.110964 + 0.110964i
\(622\) 1.29027 + 2.05886i 0.0517350 + 0.0825526i
\(623\) 49.2703 1.97397
\(624\) 6.86493 5.42160i 0.274817 0.217038i
\(625\) −1.00000 −0.0400000
\(626\) −12.3478 19.7032i −0.493519 0.787499i
\(627\) 23.4480 23.4480i 0.936422 0.936422i
\(628\) −6.34023 18.2579i −0.253003 0.728571i
\(629\) 19.6769 + 19.6769i 0.784570 + 0.784570i
\(630\) 5.23595 + 1.20160i 0.208605 + 0.0478727i
\(631\) 28.6304i 1.13976i 0.821729 + 0.569878i \(0.193010\pi\)
−0.821729 + 0.569878i \(0.806990\pi\)
\(632\) −3.87776 35.5507i −0.154249 1.41413i
\(633\) 20.6272i 0.819857i
\(634\) −3.56120 + 15.5179i −0.141433 + 0.616295i
\(635\) 5.06564 + 5.06564i 0.201024 + 0.201024i
\(636\) −5.92272 + 12.2245i −0.234851 + 0.484733i
\(637\) −11.4888 + 11.4888i −0.455202 + 0.455202i
\(638\) 13.6296 8.54157i 0.539603 0.338164i
\(639\) −0.585051 −0.0231442
\(640\) 11.3133 + 0.0937806i 0.447198 + 0.00370700i
\(641\) −47.4097 −1.87257 −0.936286 0.351239i \(-0.885760\pi\)
−0.936286 + 0.351239i \(0.885760\pi\)
\(642\) 14.5489 9.11764i 0.574198 0.359845i
\(643\) 22.0744 22.0744i 0.870528 0.870528i −0.122002 0.992530i \(-0.538931\pi\)
0.992530 + 0.122002i \(0.0389314\pi\)
\(644\) 12.9539 26.7368i 0.510455 1.05358i
\(645\) 0.994741 + 0.994741i 0.0391679 + 0.0391679i
\(646\) −10.3913 + 45.2800i −0.408840 + 1.78152i
\(647\) 28.8171i 1.13292i 0.824090 + 0.566459i \(0.191687\pi\)
−0.824090 + 0.566459i \(0.808313\pi\)
\(648\) 0.306697 + 2.81175i 0.0120482 + 0.110456i
\(649\) 44.8426i 1.76023i
\(650\) 3.01440 + 0.691773i 0.118234 + 0.0271336i
\(651\) −25.5922 25.5922i −1.00304 1.00304i
\(652\) 6.60200 + 19.0117i 0.258554 + 0.744557i
\(653\) −25.1198 + 25.1198i −0.983015 + 0.983015i −0.999858 0.0168430i \(-0.994638\pi\)
0.0168430 + 0.999858i \(0.494638\pi\)
\(654\) −11.3241 18.0696i −0.442807 0.706579i
\(655\) 9.26437 0.361989
\(656\) −1.82129 + 1.43837i −0.0711095 + 0.0561590i
\(657\) −11.9999 −0.468161
\(658\) −6.34617 10.1265i −0.247400 0.394771i
\(659\) 11.3103 11.3103i 0.440585 0.440585i −0.451623 0.892209i \(-0.649155\pi\)
0.892209 + 0.451623i \(0.149155\pi\)
\(660\) 8.24716 2.86390i 0.321020 0.111477i
\(661\) −19.4036 19.4036i −0.754713 0.754713i 0.220642 0.975355i \(-0.429185\pi\)
−0.975355 + 0.220642i \(0.929185\pi\)
\(662\) 17.5934 + 4.03749i 0.683785 + 0.156922i
\(663\) 9.45680i 0.367272i
\(664\) 34.8119 + 27.9645i 1.35097 + 1.08523i
\(665\) 28.8568i 1.11902i
\(666\) 2.03559 8.87009i 0.0788776 0.343709i
\(667\) 7.20500 + 7.20500i 0.278979 + 0.278979i
\(668\) −11.0518 5.35453i −0.427606 0.207173i
\(669\) 9.67978 9.67978i 0.374242 0.374242i
\(670\) −11.8242 + 7.41009i −0.456807 + 0.286277i
\(671\) 1.85952 0.0717858
\(672\) −9.20859 19.4151i −0.355229 0.748953i
\(673\) −6.76645 −0.260827 −0.130414 0.991460i \(-0.541631\pi\)
−0.130414 + 0.991460i \(0.541631\pi\)
\(674\) 8.91772 5.58865i 0.343498 0.215267i
\(675\) −0.707107 + 0.707107i −0.0272166 + 0.0272166i
\(676\) 14.7904 + 7.16587i 0.568860 + 0.275610i
\(677\) −2.12216 2.12216i −0.0815613 0.0815613i 0.665149 0.746710i \(-0.268368\pi\)
−0.746710 + 0.665149i \(0.768368\pi\)
\(678\) 0.984250 4.28886i 0.0377999 0.164713i
\(679\) 25.7756i 0.989177i
\(680\) −7.65977 + 9.53536i −0.293739 + 0.365664i
\(681\) 16.8985i 0.647551i
\(682\) −57.3277 13.1561i −2.19519 0.503774i
\(683\) 16.9525 + 16.9525i 0.648669 + 0.648669i 0.952671 0.304002i \(-0.0983230\pi\)
−0.304002 + 0.952671i \(0.598323\pi\)
\(684\) 14.3526 4.98406i 0.548784 0.190570i
\(685\) −7.81367 + 7.81367i −0.298545 + 0.298545i
\(686\) 1.22517 + 1.95499i 0.0467774 + 0.0746419i
\(687\) −13.3052 −0.507626
\(688\) 0.656515 5.58867i 0.0250294 0.213066i
\(689\) 14.8532 0.565861
\(690\) 2.93681 + 4.68621i 0.111802 + 0.178401i
\(691\) 18.4439 18.4439i 0.701640 0.701640i −0.263122 0.964763i \(-0.584752\pi\)
0.964763 + 0.263122i \(0.0847523\pi\)
\(692\) 6.76649 + 19.4854i 0.257223 + 0.740725i
\(693\) −11.7249 11.7249i −0.445391 0.445391i
\(694\) −1.28522 0.294945i −0.0487863 0.0111960i
\(695\) 7.31391i 0.277432i
\(696\) 7.32628 0.799127i 0.277702 0.0302908i
\(697\) 2.50893i 0.0950323i
\(698\) 3.59985 15.6863i 0.136256 0.593737i
\(699\) −8.35964 8.35964i −0.316190 0.316190i
\(700\) 3.31252 6.83704i 0.125201 0.258416i
\(701\) 6.59102 6.59102i 0.248940 0.248940i −0.571596 0.820535i \(-0.693675\pi\)
0.820535 + 0.571596i \(0.193675\pi\)
\(702\) 2.62066 1.64234i 0.0989103 0.0619862i
\(703\) −48.8856 −1.84375
\(704\) −29.4358 18.7888i −1.10940 0.708128i
\(705\) 2.22461 0.0837836
\(706\) 21.9702 13.7685i 0.826860 0.518186i
\(707\) −23.5250 + 23.5250i −0.884748 + 0.884748i
\(708\) −8.95831 + 18.4900i −0.336674 + 0.694896i
\(709\) −12.7715 12.7715i −0.479642 0.479642i 0.425375 0.905017i \(-0.360142\pi\)
−0.905017 + 0.425375i \(0.860142\pi\)
\(710\) −0.185066 + 0.806424i −0.00694540 + 0.0302645i
\(711\) 12.6436i 0.474173i
\(712\) 36.4701 3.97804i 1.36677 0.149083i
\(713\) 37.2597i 1.39539i
\(714\) 22.6417 + 5.19604i 0.847344 + 0.194457i
\(715\) −6.75015 6.75015i −0.252441 0.252441i
\(716\) −5.77952 16.6432i −0.215991 0.621987i
\(717\) −7.92775 + 7.92775i −0.296067 + 0.296067i
\(718\) 8.92046 + 14.2342i 0.332908 + 0.531216i
\(719\) 17.1105 0.638115 0.319057 0.947735i \(-0.396634\pi\)
0.319057 + 0.947735i \(0.396634\pi\)
\(720\) 3.97268 + 0.466680i 0.148053 + 0.0173922i
\(721\) −43.1215 −1.60593
\(722\) −29.0702 46.3868i −1.08188 1.72634i
\(723\) −5.58612 + 5.58612i −0.207750 + 0.207750i
\(724\) −3.40139 + 1.18116i −0.126412 + 0.0438976i
\(725\) 1.84243 + 1.84243i 0.0684263 + 0.0684263i
\(726\) −11.1021 2.54781i −0.412036 0.0945580i
\(727\) 43.9133i 1.62865i −0.580407 0.814327i \(-0.697107\pi\)
0.580407 0.814327i \(-0.302893\pi\)
\(728\) −14.7149 + 18.3180i −0.545371 + 0.678912i
\(729\) 1.00000i 0.0370370i
\(730\) −3.79586 + 16.5405i −0.140491 + 0.612190i
\(731\) 4.30154 + 4.30154i 0.159098 + 0.159098i
\(732\) 0.766735 + 0.371479i 0.0283393 + 0.0137303i
\(733\) −16.5301 + 16.5301i −0.610553 + 0.610553i −0.943090 0.332537i \(-0.892095\pi\)
0.332537 + 0.943090i \(0.392095\pi\)
\(734\) −28.8550 + 18.0832i −1.06506 + 0.667463i
\(735\) −7.42948 −0.274040
\(736\) 7.42981 20.8366i 0.273866 0.768047i
\(737\) 43.0713 1.58655
\(738\) −0.695270 + 0.435720i −0.0255932 + 0.0160391i
\(739\) −17.2689 + 17.2689i −0.635246 + 0.635246i −0.949379 0.314133i \(-0.898286\pi\)
0.314133 + 0.949379i \(0.398286\pi\)
\(740\) −11.5825 5.61165i −0.425780 0.206288i
\(741\) −11.7473 11.7473i −0.431548 0.431548i
\(742\) 8.16107 35.5618i 0.299602 1.30551i
\(743\) 20.9862i 0.769909i −0.922936 0.384955i \(-0.874217\pi\)
0.922936 0.384955i \(-0.125783\pi\)
\(744\) −21.0097 16.8771i −0.770254 0.618746i
\(745\) 8.20718i 0.300688i
\(746\) 10.7405 + 2.46484i 0.393239 + 0.0902442i
\(747\) 11.1632 + 11.1632i 0.408441 + 0.408441i
\(748\) 35.6630 12.3843i 1.30397 0.452815i
\(749\) −32.6107 + 32.6107i −1.19157 + 1.19157i
\(750\) 0.750988 + 1.19834i 0.0274222 + 0.0437572i
\(751\) −1.64813 −0.0601413 −0.0300706 0.999548i \(-0.509573\pi\)
−0.0300706 + 0.999548i \(0.509573\pi\)
\(752\) −5.51507 6.98327i −0.201114 0.254654i
\(753\) 7.55594 0.275354
\(754\) −4.27928 6.82837i −0.155842 0.248675i
\(755\) −9.37560 + 9.37560i −0.341213 + 0.341213i
\(756\) −2.49222 7.17682i −0.0906410 0.261018i
\(757\) 2.50864 + 2.50864i 0.0911779 + 0.0911779i 0.751225 0.660047i \(-0.229464\pi\)
−0.660047 + 0.751225i \(0.729464\pi\)
\(758\) −8.60066 1.97376i −0.312390 0.0716903i
\(759\) 17.0702i 0.619611i
\(760\) −2.32987 21.3599i −0.0845132 0.774805i
\(761\) 19.9555i 0.723387i 0.932297 + 0.361693i \(0.117801\pi\)
−0.932297 + 0.361693i \(0.882199\pi\)
\(762\) 2.26612 9.87459i 0.0820927 0.357719i
\(763\) 40.5024 + 40.5024i 1.46628 + 1.46628i
\(764\) 8.40324 17.3443i 0.304019 0.627495i
\(765\) −3.05773 + 3.05773i −0.110552 + 0.110552i
\(766\) 14.9066 9.34187i 0.538599 0.337535i
\(767\) 22.4659 0.811197
\(768\) −8.38379 13.6276i −0.302524 0.491744i
\(769\) 28.8082 1.03885 0.519426 0.854516i \(-0.326146\pi\)
0.519426 + 0.854516i \(0.326146\pi\)
\(770\) −19.8702 + 12.4525i −0.716073 + 0.448757i
\(771\) −10.9778 + 10.9778i −0.395356 + 0.395356i
\(772\) −3.17882 + 6.56109i −0.114408 + 0.236139i
\(773\) 33.6461 + 33.6461i 1.21017 + 1.21017i 0.970972 + 0.239195i \(0.0768836\pi\)
0.239195 + 0.970972i \(0.423116\pi\)
\(774\) 0.444998 1.93908i 0.0159951 0.0696986i
\(775\) 9.52790i 0.342252i
\(776\) 2.08110 + 19.0792i 0.0747071 + 0.684904i
\(777\) 24.4446i 0.876946i
\(778\) −44.2510 10.1551i −1.58647 0.364080i
\(779\) 3.11660 + 3.11660i 0.111664 + 0.111664i
\(780\) −1.43480 4.13178i −0.0513740 0.147942i
\(781\) 1.80583 1.80583i 0.0646176 0.0646176i
\(782\) 12.6996 + 20.2645i 0.454136 + 0.724656i
\(783\) 2.60559 0.0931164
\(784\) 18.4185 + 23.3219i 0.657805 + 0.832925i
\(785\) −9.66373 −0.344913
\(786\) −6.95744 11.1019i −0.248163 0.395990i
\(787\) −11.0029 + 11.0029i −0.392211 + 0.392211i −0.875475 0.483264i \(-0.839451\pi\)
0.483264 + 0.875475i \(0.339451\pi\)
\(788\) −20.1842 + 7.00915i −0.719033 + 0.249691i
\(789\) 10.1615 + 10.1615i 0.361759 + 0.361759i
\(790\) −17.4278 3.99949i −0.620052 0.142296i
\(791\) 11.8195i 0.420252i
\(792\) −9.62545 7.73214i −0.342025 0.274750i
\(793\) 0.931607i 0.0330823i
\(794\) −10.4072 + 45.3493i −0.369338 + 1.60939i
\(795\) 4.80257 + 4.80257i 0.170330 + 0.170330i
\(796\) 42.7366 + 20.7057i 1.51476 + 0.733894i
\(797\) 13.3729 13.3729i 0.473692 0.473692i −0.429415 0.903107i \(-0.641280\pi\)
0.903107 + 0.429415i \(0.141280\pi\)
\(798\) −34.5802 + 21.6711i −1.22413 + 0.767149i
\(799\) 9.61983 0.340325
\(800\) 1.89992 5.32825i 0.0671724 0.188382i
\(801\) 12.9706 0.458293
\(802\) 37.8634 23.7286i 1.33700 0.837887i
\(803\) 37.0391 37.0391i 1.30708 1.30708i
\(804\) 17.7596 + 8.60445i 0.626333 + 0.303456i
\(805\) −10.5039 10.5039i −0.370215 0.370215i
\(806\) −6.59114 + 28.7209i −0.232163 + 1.01165i
\(807\) 26.9559i 0.948891i
\(808\) −15.5139 + 19.3127i −0.545777 + 0.679417i
\(809\) 20.9970i 0.738214i −0.929387 0.369107i \(-0.879664\pi\)
0.929387 0.369107i \(-0.120336\pi\)
\(810\) 1.37838 + 0.316325i 0.0484314 + 0.0111145i
\(811\) 26.7257 + 26.7257i 0.938468 + 0.938468i 0.998214 0.0597459i \(-0.0190290\pi\)
−0.0597459 + 0.998214i \(0.519029\pi\)
\(812\) −18.6999 + 6.49370i −0.656237 + 0.227884i
\(813\) 3.30141 3.30141i 0.115785 0.115785i
\(814\) 21.0955 + 33.6617i 0.739396 + 1.17984i
\(815\) 10.0627 0.352481
\(816\) 17.1790 + 2.01806i 0.601385 + 0.0706461i
\(817\) −10.6868 −0.373884
\(818\) −10.8884 17.3744i −0.380704 0.607482i
\(819\) −5.87409 + 5.87409i −0.205257 + 0.205257i
\(820\) 0.380657 + 1.09618i 0.0132931 + 0.0382802i
\(821\) −9.81609 9.81609i −0.342584 0.342584i 0.514754 0.857338i \(-0.327883\pi\)
−0.857338 + 0.514754i \(0.827883\pi\)
\(822\) 15.2314 + 3.49545i 0.531256 + 0.121918i
\(823\) 23.7241i 0.826969i −0.910511 0.413484i \(-0.864312\pi\)
0.910511 0.413484i \(-0.135688\pi\)
\(824\) −31.9187 + 3.48159i −1.11194 + 0.121287i
\(825\) 4.36514i 0.151975i
\(826\) 12.3439 53.7884i 0.429498 1.87154i
\(827\) 13.8903 + 13.8903i 0.483014 + 0.483014i 0.906093 0.423079i \(-0.139051\pi\)
−0.423079 + 0.906093i \(0.639051\pi\)
\(828\) 3.41016 7.03858i 0.118511 0.244607i
\(829\) 34.7927 34.7927i 1.20840 1.20840i 0.236856 0.971545i \(-0.423883\pi\)
0.971545 0.236856i \(-0.0761169\pi\)
\(830\) 18.9184 11.8560i 0.656668 0.411528i
\(831\) 8.83278 0.306406
\(832\) −9.41306 + 14.7472i −0.326339 + 0.511266i
\(833\) −32.1271 −1.11314
\(834\) 8.76454 5.49266i 0.303491 0.190195i
\(835\) −4.34184 + 4.34184i −0.150256 + 0.150256i
\(836\) −28.9170 + 59.6848i −1.00012 + 2.06424i
\(837\) −6.73724 6.73724i −0.232873 0.232873i
\(838\) 10.7681 46.9220i 0.371978 1.62089i
\(839\) 41.9136i 1.44702i −0.690314 0.723510i \(-0.742528\pi\)
0.690314 0.723510i \(-0.257472\pi\)
\(840\) −10.6808 + 1.16502i −0.368521 + 0.0401971i
\(841\) 22.2109i 0.765892i
\(842\) −39.2001 8.99601i −1.35092 0.310023i
\(843\) −21.0286 21.0286i −0.724262 0.724262i
\(844\) −13.5332 38.9715i −0.465832 1.34145i
\(845\) 5.81060 5.81060i 0.199891 0.199891i
\(846\) −1.67065 2.66583i −0.0574383 0.0916533i
\(847\) 30.5956 1.05128
\(848\) 3.16963 26.9819i 0.108845 0.926562i
\(849\) 13.4215 0.460623
\(850\) 3.24748 + 5.18195i 0.111388 + 0.177740i
\(851\) −17.7945 + 17.7945i −0.609987 + 0.609987i
\(852\) 1.10535 0.383843i 0.0378687 0.0131503i
\(853\) −17.8552 17.8552i −0.611349 0.611349i 0.331949 0.943297i \(-0.392294\pi\)
−0.943297 + 0.331949i \(0.892294\pi\)
\(854\) −2.23047 0.511871i −0.0763252 0.0175159i
\(855\) 7.59666i 0.259800i
\(856\) −21.5056 + 26.7715i −0.735046 + 0.915031i
\(857\) 37.8604i 1.29328i 0.762793 + 0.646642i \(0.223827\pi\)
−0.762793 + 0.646642i \(0.776173\pi\)
\(858\) −3.01968 + 13.1582i −0.103090 + 0.449215i
\(859\) −33.0486 33.0486i −1.12760 1.12760i −0.990566 0.137036i \(-0.956242\pi\)
−0.137036 0.990566i \(-0.543758\pi\)
\(860\) −2.53202 1.22675i −0.0863413 0.0418320i
\(861\) 1.55842 1.55842i 0.0531108 0.0531108i
\(862\) −35.8335 + 22.4565i −1.22049 + 0.764873i
\(863\) 7.90340 0.269035 0.134518 0.990911i \(-0.457052\pi\)
0.134518 + 0.990911i \(0.457052\pi\)
\(864\) −2.42420 5.11109i −0.0824729 0.173883i
\(865\) 10.3134 0.350667
\(866\) 21.2690 13.3291i 0.722750 0.452941i
\(867\) −1.20166 + 1.20166i −0.0408104 + 0.0408104i
\(868\) 65.1426 + 31.5613i 2.21108 + 1.07126i
\(869\) 39.0260 + 39.0260i 1.32387 + 1.32387i
\(870\) 0.824214 3.59151i 0.0279435 0.121763i
\(871\) 21.5785i 0.731159i
\(872\) 33.2501 + 26.7099i 1.12599 + 0.904511i
\(873\) 6.78553i 0.229655i
\(874\) −40.9482 9.39718i −1.38509 0.317864i
\(875\) −2.68603 2.68603i −0.0908043 0.0908043i
\(876\) 22.6717 7.87296i 0.766006 0.266003i
\(877\) −23.4020 + 23.4020i −0.790229 + 0.790229i −0.981531 0.191302i \(-0.938729\pi\)
0.191302 + 0.981531i \(0.438729\pi\)
\(878\) −11.3682 18.1400i −0.383657 0.612194i
\(879\) 2.44371 0.0824243
\(880\) −13.7026 + 10.8217i −0.461915 + 0.364799i
\(881\) 4.99400 0.168252 0.0841261 0.996455i \(-0.473190\pi\)
0.0841261 + 0.996455i \(0.473190\pi\)
\(882\) 5.57945 + 8.90303i 0.187870 + 0.299781i
\(883\) −22.8573 + 22.8573i −0.769209 + 0.769209i −0.977967 0.208758i \(-0.933058\pi\)
0.208758 + 0.977967i \(0.433058\pi\)
\(884\) −6.20447 17.8670i −0.208679 0.600932i
\(885\) 7.26404 + 7.26404i 0.244178 + 0.244178i
\(886\) −32.1029 7.36728i −1.07852 0.247509i
\(887\) 20.5245i 0.689146i −0.938760 0.344573i \(-0.888024\pi\)
0.938760 0.344573i \(-0.111976\pi\)
\(888\) 1.97364 + 18.0940i 0.0662309 + 0.607195i
\(889\) 27.2129i 0.912691i
\(890\) 4.10292 17.8784i 0.137530 0.599287i
\(891\) −3.08662 3.08662i −0.103406 0.103406i
\(892\) −11.9375 + 24.6390i −0.399697 + 0.824975i
\(893\) −11.9498 + 11.9498i −0.399885 + 0.399885i
\(894\) 9.83499 6.16350i 0.328931 0.206138i
\(895\) −8.80909 −0.294456
\(896\) 30.1360 + 30.6398i 1.00677 + 1.02360i
\(897\) −8.55210 −0.285546
\(898\) 42.6702 26.7410i 1.42392 0.892360i
\(899\) −17.5545 + 17.5545i −0.585476 + 0.585476i
\(900\) 0.872033 1.79988i 0.0290678 0.0599959i
\(901\) 20.7677 + 20.7677i 0.691871 + 0.691871i
\(902\) 0.801133 3.49093i 0.0266748 0.116235i
\(903\) 5.34380i 0.177831i
\(904\) 0.954292 + 8.74881i 0.0317393 + 0.290981i
\(905\) 1.80032i 0.0598446i
\(906\) 18.2761 + 4.19418i 0.607183 + 0.139342i
\(907\) −12.1526 12.1526i −0.403521 0.403521i 0.475951 0.879472i \(-0.342104\pi\)
−0.879472 + 0.475951i \(0.842104\pi\)
\(908\) 11.0868 + 31.9267i 0.367930 + 1.05953i
\(909\) −6.19304 + 6.19304i −0.205410 + 0.205410i
\(910\) 6.23863 + 9.95487i 0.206809 + 0.330001i
\(911\) 26.1222 0.865468 0.432734 0.901522i \(-0.357549\pi\)
0.432734 + 0.901522i \(0.357549\pi\)
\(912\) −23.8467 + 18.8330i −0.789643 + 0.623624i
\(913\) −68.9132 −2.28070
\(914\) −1.48743 2.37347i −0.0492000 0.0785075i
\(915\) 0.301222 0.301222i 0.00995810 0.00995810i
\(916\) 25.1379 8.72936i 0.830580 0.288426i
\(917\) 24.8843 + 24.8843i 0.821753 + 0.821753i
\(918\) 5.96051 + 1.36788i 0.196726 + 0.0451466i
\(919\) 12.3754i 0.408228i −0.978947 0.204114i \(-0.934569\pi\)
0.978947 0.204114i \(-0.0654313\pi\)
\(920\) −8.62314 6.92698i −0.284296 0.228376i
\(921\) 24.8725i 0.819577i
\(922\) −1.84994 + 8.06109i −0.0609244 + 0.265478i
\(923\) −0.904709 0.904709i −0.0297789 0.0297789i
\(924\) 29.8446 + 14.4596i 0.981816 + 0.475685i
\(925\) −4.55033 + 4.55033i −0.149614 + 0.149614i
\(926\) 28.0684 17.5902i 0.922385 0.578051i
\(927\) −11.3519 −0.372846
\(928\) −13.3174 + 6.31648i −0.437166 + 0.207349i
\(929\) −14.1300 −0.463591 −0.231795 0.972765i \(-0.574460\pi\)
−0.231795 + 0.972765i \(0.574460\pi\)
\(930\) −11.4176 + 7.15534i −0.374399 + 0.234633i
\(931\) 39.9085 39.9085i 1.30795 1.30795i
\(932\) 21.2787 + 10.3094i 0.697007 + 0.337697i
\(933\) −1.21487 1.21487i −0.0397732 0.0397732i
\(934\) −1.88239 + 8.20250i −0.0615937 + 0.268394i
\(935\) 18.8761i 0.617314i
\(936\) −3.87376 + 4.82230i −0.126618 + 0.157622i
\(937\) 39.1538i 1.27910i −0.768750 0.639549i \(-0.779121\pi\)
0.768750 0.639549i \(-0.220879\pi\)
\(938\) −51.6637 11.8563i −1.68688 0.387121i
\(939\) 11.6263 + 11.6263i 0.379411 + 0.379411i
\(940\) −4.20301 + 1.45953i −0.137087 + 0.0476047i
\(941\) −17.1373 + 17.1373i −0.558661 + 0.558661i −0.928926 0.370265i \(-0.879267\pi\)
0.370265 + 0.928926i \(0.379267\pi\)
\(942\) 7.25735 + 11.5804i 0.236457 + 0.377310i
\(943\) 2.26890 0.0738856
\(944\) 4.79416 40.8110i 0.156037 1.32828i
\(945\) −3.79862 −0.123569
\(946\) 4.61165 + 7.35872i 0.149938 + 0.239253i
\(947\) 21.7252 21.7252i 0.705973 0.705973i −0.259713 0.965686i \(-0.583628\pi\)
0.965686 + 0.259713i \(0.0836279\pi\)
\(948\) 8.29530 + 23.8879i 0.269419 + 0.775844i
\(949\) −18.5564 18.5564i −0.602365 0.602365i
\(950\) −10.4711 2.40301i −0.339728 0.0779640i
\(951\) 11.2581i 0.365067i
\(952\) −46.1866 + 5.03788i −1.49692 + 0.163279i
\(953\) 6.05956i 0.196288i 0.995172 + 0.0981442i \(0.0312906\pi\)
−0.995172 + 0.0981442i \(0.968709\pi\)
\(954\) 2.14843 9.36178i 0.0695580 0.303099i
\(955\) −6.81395 6.81395i −0.220494 0.220494i
\(956\) 9.77682 20.1794i 0.316205 0.652648i
\(957\) −8.04247 + 8.04247i −0.259976 + 0.259976i
\(958\) 6.61742 4.14708i 0.213799 0.133986i
\(959\) −41.9754 −1.35546
\(960\) −7.81187 + 1.72471i −0.252127 + 0.0556647i
\(961\) 59.7808 1.92841
\(962\) 16.8643 10.5687i 0.543727 0.340749i
\(963\) −8.58488 + 8.58488i −0.276644 + 0.276644i
\(964\) 6.88903 14.2190i 0.221881 0.457962i
\(965\) 2.57761 + 2.57761i 0.0829763 + 0.0829763i
\(966\) −4.69894 + 20.4756i −0.151186 + 0.658792i
\(967\) 32.6389i 1.04959i −0.851227 0.524797i \(-0.824141\pi\)
0.851227 0.524797i \(-0.175859\pi\)
\(968\) 22.6470 2.47026i 0.727902 0.0793971i
\(969\) 32.8501i 1.05530i
\(970\) 9.35306 + 2.14643i 0.300309 + 0.0689177i
\(971\) −4.73662 4.73662i −0.152005 0.152005i 0.627008 0.779013i \(-0.284279\pi\)
−0.779013 + 0.627008i \(0.784279\pi\)
\(972\) −0.656085 1.88933i −0.0210439 0.0606002i
\(973\) −19.6453 + 19.6453i −0.629801 + 0.629801i
\(974\) 21.0737 + 33.6269i 0.675244 + 1.07747i
\(975\) −2.18691 −0.0700371
\(976\) −1.69233 0.198802i −0.0541703 0.00636351i
\(977\) −31.9605 −1.02251 −0.511254 0.859430i \(-0.670819\pi\)
−0.511254 + 0.859430i \(0.670819\pi\)
\(978\) −7.55698 12.0585i −0.241645 0.385589i
\(979\) −40.0353 + 40.0353i −1.27953 + 1.27953i
\(980\) 14.0367 4.87437i 0.448386 0.155706i
\(981\) 10.6624 + 10.6624i 0.340424 + 0.340424i
\(982\) −2.48358 0.569955i −0.0792541 0.0181880i
\(983\) 36.1044i 1.15155i 0.817607 + 0.575776i \(0.195300\pi\)
−0.817607 + 0.575776i \(0.804700\pi\)
\(984\) 1.02772 1.27937i 0.0327626 0.0407849i
\(985\) 10.6833i 0.340398i
\(986\) 3.56413 15.5307i 0.113505 0.494598i
\(987\) 5.97536 + 5.97536i 0.190198 + 0.190198i
\(988\) 29.9017 + 14.4873i 0.951301 + 0.460901i
\(989\) −3.89002 + 3.89002i −0.123695 + 0.123695i
\(990\) −5.23091 + 3.27817i −0.166249 + 0.104187i
\(991\) 19.3054 0.613255 0.306628 0.951830i \(-0.400799\pi\)
0.306628 + 0.951830i \(0.400799\pi\)
\(992\) 50.7671 + 18.1023i 1.61186 + 0.574747i
\(993\) −12.7638 −0.405046
\(994\) −2.66317 + 1.66898i −0.0844705 + 0.0529369i
\(995\) 16.7897 16.7897i 0.532269 0.532269i
\(996\) −28.4150 13.7669i −0.900364 0.436222i
\(997\) −6.99944 6.99944i −0.221674 0.221674i 0.587529 0.809203i \(-0.300101\pi\)
−0.809203 + 0.587529i \(0.800101\pi\)
\(998\) −11.7810 + 51.3357i −0.372922 + 1.62500i
\(999\) 6.43514i 0.203599i
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 240.2.s.c.181.9 yes 20
3.2 odd 2 720.2.t.d.181.2 20
4.3 odd 2 960.2.s.c.241.10 20
8.3 odd 2 1920.2.s.f.481.5 20
8.5 even 2 1920.2.s.e.481.6 20
12.11 even 2 2880.2.t.d.2161.10 20
16.3 odd 4 960.2.s.c.721.6 20
16.5 even 4 1920.2.s.e.1441.10 20
16.11 odd 4 1920.2.s.f.1441.1 20
16.13 even 4 inner 240.2.s.c.61.9 20
48.29 odd 4 720.2.t.d.541.2 20
48.35 even 4 2880.2.t.d.721.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.s.c.61.9 20 16.13 even 4 inner
240.2.s.c.181.9 yes 20 1.1 even 1 trivial
720.2.t.d.181.2 20 3.2 odd 2
720.2.t.d.541.2 20 48.29 odd 4
960.2.s.c.241.10 20 4.3 odd 2
960.2.s.c.721.6 20 16.3 odd 4
1920.2.s.e.481.6 20 8.5 even 2
1920.2.s.e.1441.10 20 16.5 even 4
1920.2.s.f.481.5 20 8.3 odd 2
1920.2.s.f.1441.1 20 16.11 odd 4
2880.2.t.d.721.6 20 48.35 even 4
2880.2.t.d.2161.10 20 12.11 even 2