Properties

Label 429.2.n.b.235.5
Level $429$
Weight $2$
Character 429.235
Analytic conductor $3.426$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + 115 x^{11} + 1963 x^{10} + 323 x^{9} + 3007 x^{8} + 1828 x^{7} + 6736 x^{6} + \cdots + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 235.5
Root \(2.01466 - 1.46373i\) of defining polynomial
Character \(\chi\) \(=\) 429.235
Dual form 429.2.n.b.157.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.01466 + 1.46373i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.29829 + 3.99572i) q^{4} +(1.02009 - 0.741137i) q^{5} +(-2.01466 + 1.46373i) q^{6} +(0.590393 + 1.81704i) q^{7} +(-1.69400 + 5.21361i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(2.01466 + 1.46373i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.29829 + 3.99572i) q^{4} +(1.02009 - 0.741137i) q^{5} +(-2.01466 + 1.46373i) q^{6} +(0.590393 + 1.81704i) q^{7} +(-1.69400 + 5.21361i) q^{8} +(-0.809017 - 0.587785i) q^{9} +3.13995 q^{10} +(-1.53494 - 2.94006i) q^{11} -4.20135 q^{12} +(0.809017 + 0.587785i) q^{13} +(-1.47023 + 4.52489i) q^{14} +(0.389639 + 1.19918i) q^{15} +(-4.24623 + 3.08507i) q^{16} +(-1.67827 + 1.21934i) q^{17} +(-0.769530 - 2.36837i) q^{18} +(1.50819 - 4.64172i) q^{19} +(4.28574 + 3.11377i) q^{20} -1.91055 q^{21} +(1.21109 - 8.16995i) q^{22} +0.161641 q^{23} +(-4.43496 - 3.22219i) q^{24} +(-1.05379 + 3.24323i) q^{25} +(0.769530 + 2.36837i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-6.49389 + 4.71809i) q^{28} +(-1.72116 - 5.29718i) q^{29} +(-0.970298 + 2.98627i) q^{30} +(-1.29968 - 0.944270i) q^{31} -2.10659 q^{32} +(3.27049 - 0.551285i) q^{33} -5.16593 q^{34} +(1.94893 + 1.41598i) q^{35} +(1.29829 - 3.99572i) q^{36} +(-0.577942 - 1.77872i) q^{37} +(9.83271 - 7.14388i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(2.13596 + 6.57382i) q^{40} +(-1.17056 + 3.60262i) q^{41} +(-3.84910 - 2.79654i) q^{42} +6.60266 q^{43} +(9.75487 - 9.95023i) q^{44} -1.26090 q^{45} +(0.325650 + 0.236598i) q^{46} +(0.598370 - 1.84159i) q^{47} +(-1.62192 - 4.99174i) q^{48} +(2.71004 - 1.96896i) q^{49} +(-6.87025 + 4.99153i) q^{50} +(-0.641043 - 1.97293i) q^{51} +(-1.29829 + 3.99572i) q^{52} +(2.08681 + 1.51615i) q^{53} +2.49025 q^{54} +(-3.74476 - 1.86152i) q^{55} -10.4735 q^{56} +(3.94848 + 2.86874i) q^{57} +(4.28611 - 13.1913i) q^{58} +(-2.07665 - 6.39128i) q^{59} +(-4.28574 + 3.11377i) q^{60} +(-11.7076 + 8.50611i) q^{61} +(-1.23624 - 3.80476i) q^{62} +(0.590393 - 1.81704i) q^{63} +(4.24842 + 3.08665i) q^{64} +1.26090 q^{65} +(7.39584 + 3.67647i) q^{66} -8.27187 q^{67} +(-7.05101 - 5.12286i) q^{68} +(-0.0499497 + 0.153729i) q^{69} +(1.85380 + 5.70542i) q^{70} +(11.3711 - 8.26161i) q^{71} +(4.43496 - 3.22219i) q^{72} +(3.42658 + 10.5459i) q^{73} +(1.43922 - 4.42947i) q^{74} +(-2.75886 - 2.00443i) q^{75} +20.5051 q^{76} +(4.43600 - 4.52484i) q^{77} -2.49025 q^{78} +(5.58324 + 4.05646i) q^{79} +(-2.04507 + 6.29407i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-7.63156 + 5.54465i) q^{82} +(10.8108 - 7.85451i) q^{83} +(-2.48045 - 7.63402i) q^{84} +(-0.808290 + 2.48766i) q^{85} +(13.3021 + 9.66453i) q^{86} +5.56978 q^{87} +(17.9285 - 3.02209i) q^{88} -6.56886 q^{89} +(-2.54027 - 1.84562i) q^{90} +(-0.590393 + 1.81704i) q^{91} +(0.209856 + 0.645870i) q^{92} +(1.29968 - 0.944270i) q^{93} +(3.90111 - 2.83432i) q^{94} +(-1.90167 - 5.85273i) q^{95} +(0.650971 - 2.00348i) q^{96} +(-7.51024 - 5.45651i) q^{97} +8.34183 q^{98} +(-0.486333 + 3.28077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.01466 + 1.46373i 1.42458 + 1.03502i 0.990995 + 0.133901i \(0.0427504\pi\)
0.433582 + 0.901114i \(0.357250\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 1.29829 + 3.99572i 0.649144 + 1.99786i
\(5\) 1.02009 0.741137i 0.456197 0.331446i −0.335841 0.941919i \(-0.609020\pi\)
0.792038 + 0.610472i \(0.209020\pi\)
\(6\) −2.01466 + 1.46373i −0.822479 + 0.597566i
\(7\) 0.590393 + 1.81704i 0.223147 + 0.686777i 0.998474 + 0.0552171i \(0.0175851\pi\)
−0.775327 + 0.631560i \(0.782415\pi\)
\(8\) −1.69400 + 5.21361i −0.598920 + 1.84329i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 3.13995 0.992939
\(11\) −1.53494 2.94006i −0.462802 0.886462i
\(12\) −4.20135 −1.21282
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i
\(14\) −1.47023 + 4.52489i −0.392934 + 1.20933i
\(15\) 0.389639 + 1.19918i 0.100604 + 0.309628i
\(16\) −4.24623 + 3.08507i −1.06156 + 0.771267i
\(17\) −1.67827 + 1.21934i −0.407041 + 0.295733i −0.772403 0.635133i \(-0.780945\pi\)
0.365362 + 0.930866i \(0.380945\pi\)
\(18\) −0.769530 2.36837i −0.181380 0.558230i
\(19\) 1.50819 4.64172i 0.346001 1.06488i −0.615044 0.788493i \(-0.710862\pi\)
0.961046 0.276390i \(-0.0891382\pi\)
\(20\) 4.28574 + 3.11377i 0.958321 + 0.696261i
\(21\) −1.91055 −0.416916
\(22\) 1.21109 8.16995i 0.258206 1.74184i
\(23\) 0.161641 0.0337044 0.0168522 0.999858i \(-0.494636\pi\)
0.0168522 + 0.999858i \(0.494636\pi\)
\(24\) −4.43496 3.22219i −0.905282 0.657726i
\(25\) −1.05379 + 3.24323i −0.210758 + 0.648647i
\(26\) 0.769530 + 2.36837i 0.150917 + 0.464475i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −6.49389 + 4.71809i −1.22723 + 0.891635i
\(29\) −1.72116 5.29718i −0.319611 0.983662i −0.973815 0.227343i \(-0.926996\pi\)
0.654204 0.756318i \(-0.273004\pi\)
\(30\) −0.970298 + 2.98627i −0.177151 + 0.545216i
\(31\) −1.29968 0.944270i −0.233429 0.169596i 0.464922 0.885352i \(-0.346082\pi\)
−0.698351 + 0.715756i \(0.746082\pi\)
\(32\) −2.10659 −0.372396
\(33\) 3.27049 0.551285i 0.569319 0.0959664i
\(34\) −5.16593 −0.885949
\(35\) 1.94893 + 1.41598i 0.329429 + 0.239344i
\(36\) 1.29829 3.99572i 0.216381 0.665953i
\(37\) −0.577942 1.77872i −0.0950131 0.292420i 0.892244 0.451554i \(-0.149130\pi\)
−0.987257 + 0.159133i \(0.949130\pi\)
\(38\) 9.83271 7.14388i 1.59508 1.15889i
\(39\) −0.809017 + 0.587785i −0.129546 + 0.0941210i
\(40\) 2.13596 + 6.57382i 0.337725 + 1.03941i
\(41\) −1.17056 + 3.60262i −0.182811 + 0.562635i −0.999904 0.0138713i \(-0.995584\pi\)
0.817093 + 0.576507i \(0.195584\pi\)
\(42\) −3.84910 2.79654i −0.593929 0.431515i
\(43\) 6.60266 1.00690 0.503448 0.864025i \(-0.332064\pi\)
0.503448 + 0.864025i \(0.332064\pi\)
\(44\) 9.75487 9.95023i 1.47060 1.50005i
\(45\) −1.26090 −0.187963
\(46\) 0.325650 + 0.236598i 0.0480145 + 0.0348845i
\(47\) 0.598370 1.84159i 0.0872813 0.268624i −0.897884 0.440232i \(-0.854896\pi\)
0.985165 + 0.171608i \(0.0548962\pi\)
\(48\) −1.62192 4.99174i −0.234103 0.720496i
\(49\) 2.71004 1.96896i 0.387149 0.281280i
\(50\) −6.87025 + 4.99153i −0.971601 + 0.705909i
\(51\) −0.641043 1.97293i −0.0897640 0.276265i
\(52\) −1.29829 + 3.99572i −0.180040 + 0.554107i
\(53\) 2.08681 + 1.51615i 0.286645 + 0.208260i 0.721811 0.692091i \(-0.243310\pi\)
−0.435166 + 0.900350i \(0.643310\pi\)
\(54\) 2.49025 0.338880
\(55\) −3.74476 1.86152i −0.504943 0.251007i
\(56\) −10.4735 −1.39958
\(57\) 3.94848 + 2.86874i 0.522989 + 0.379974i
\(58\) 4.28611 13.1913i 0.562794 1.73210i
\(59\) −2.07665 6.39128i −0.270357 0.832074i −0.990411 0.138155i \(-0.955883\pi\)
0.720053 0.693919i \(-0.244117\pi\)
\(60\) −4.28574 + 3.11377i −0.553287 + 0.401986i
\(61\) −11.7076 + 8.50611i −1.49901 + 1.08910i −0.528238 + 0.849097i \(0.677147\pi\)
−0.970773 + 0.239999i \(0.922853\pi\)
\(62\) −1.23624 3.80476i −0.157003 0.483205i
\(63\) 0.590393 1.81704i 0.0743825 0.228926i
\(64\) 4.24842 + 3.08665i 0.531052 + 0.385832i
\(65\) 1.26090 0.156395
\(66\) 7.39584 + 3.67647i 0.910365 + 0.452542i
\(67\) −8.27187 −1.01057 −0.505285 0.862953i \(-0.668612\pi\)
−0.505285 + 0.862953i \(0.668612\pi\)
\(68\) −7.05101 5.12286i −0.855061 0.621238i
\(69\) −0.0499497 + 0.153729i −0.00601323 + 0.0185068i
\(70\) 1.85380 + 5.70542i 0.221572 + 0.681928i
\(71\) 11.3711 8.26161i 1.34950 0.980472i 0.350468 0.936575i \(-0.386022\pi\)
0.999036 0.0438977i \(-0.0139776\pi\)
\(72\) 4.43496 3.22219i 0.522665 0.379738i
\(73\) 3.42658 + 10.5459i 0.401051 + 1.23431i 0.924148 + 0.382035i \(0.124776\pi\)
−0.523097 + 0.852273i \(0.675224\pi\)
\(74\) 1.43922 4.42947i 0.167306 0.514915i
\(75\) −2.75886 2.00443i −0.318566 0.231452i
\(76\) 20.5051 2.35209
\(77\) 4.43600 4.52484i 0.505529 0.515653i
\(78\) −2.49025 −0.281965
\(79\) 5.58324 + 4.05646i 0.628164 + 0.456388i 0.855764 0.517367i \(-0.173088\pi\)
−0.227600 + 0.973755i \(0.573088\pi\)
\(80\) −2.04507 + 6.29407i −0.228646 + 0.703699i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −7.63156 + 5.54465i −0.842765 + 0.612304i
\(83\) 10.8108 7.85451i 1.18664 0.862144i 0.193734 0.981054i \(-0.437940\pi\)
0.992905 + 0.118910i \(0.0379400\pi\)
\(84\) −2.48045 7.63402i −0.270639 0.832940i
\(85\) −0.808290 + 2.48766i −0.0876713 + 0.269825i
\(86\) 13.3021 + 9.66453i 1.43440 + 1.04215i
\(87\) 5.56978 0.597144
\(88\) 17.9285 3.02209i 1.91119 0.322156i
\(89\) −6.56886 −0.696297 −0.348149 0.937439i \(-0.613190\pi\)
−0.348149 + 0.937439i \(0.613190\pi\)
\(90\) −2.54027 1.84562i −0.267768 0.194545i
\(91\) −0.590393 + 1.81704i −0.0618900 + 0.190478i
\(92\) 0.209856 + 0.645870i 0.0218790 + 0.0673366i
\(93\) 1.29968 0.944270i 0.134770 0.0979162i
\(94\) 3.90111 2.83432i 0.402369 0.292338i
\(95\) −1.90167 5.85273i −0.195107 0.600477i
\(96\) 0.650971 2.00348i 0.0664395 0.204480i
\(97\) −7.51024 5.45651i −0.762549 0.554024i 0.137142 0.990551i \(-0.456208\pi\)
−0.899691 + 0.436527i \(0.856208\pi\)
\(98\) 8.34183 0.842652
\(99\) −0.486333 + 3.28077i −0.0488783 + 0.329730i
\(100\) −14.3272 −1.43272
\(101\) −16.0734 11.6780i −1.59936 1.16200i −0.888727 0.458437i \(-0.848409\pi\)
−0.710632 0.703564i \(-0.751591\pi\)
\(102\) 1.59636 4.91309i 0.158063 0.486468i
\(103\) 1.05519 + 3.24755i 0.103971 + 0.319990i 0.989488 0.144618i \(-0.0461952\pi\)
−0.885516 + 0.464608i \(0.846195\pi\)
\(104\) −4.43496 + 3.22219i −0.434883 + 0.315961i
\(105\) −1.94893 + 1.41598i −0.190196 + 0.138185i
\(106\) 1.98495 + 6.10905i 0.192796 + 0.593364i
\(107\) −1.85664 + 5.71416i −0.179488 + 0.552409i −0.999810 0.0194939i \(-0.993794\pi\)
0.820322 + 0.571903i \(0.193794\pi\)
\(108\) 3.39896 + 2.46949i 0.327065 + 0.237627i
\(109\) −6.09330 −0.583633 −0.291816 0.956474i \(-0.594260\pi\)
−0.291816 + 0.956474i \(0.594260\pi\)
\(110\) −4.81963 9.23164i −0.459534 0.880203i
\(111\) 1.87026 0.177517
\(112\) −8.11264 5.89418i −0.766572 0.556947i
\(113\) −3.42824 + 10.5510i −0.322501 + 0.992557i 0.650054 + 0.759888i \(0.274746\pi\)
−0.972556 + 0.232670i \(0.925254\pi\)
\(114\) 3.75576 + 11.5590i 0.351759 + 1.08260i
\(115\) 0.164887 0.119798i 0.0153758 0.0111712i
\(116\) 18.9315 13.7545i 1.75774 1.27708i
\(117\) −0.309017 0.951057i −0.0285686 0.0879252i
\(118\) 5.17139 15.9159i 0.476065 1.46518i
\(119\) −3.20643 2.32961i −0.293933 0.213555i
\(120\) −6.91212 −0.630987
\(121\) −6.28792 + 9.02563i −0.571629 + 0.820512i
\(122\) −36.0375 −3.26269
\(123\) −3.06457 2.22654i −0.276323 0.200761i
\(124\) 2.08568 6.41908i 0.187300 0.576450i
\(125\) 3.27691 + 10.0853i 0.293096 + 0.902057i
\(126\) 3.84910 2.79654i 0.342905 0.249135i
\(127\) 8.67124 6.30002i 0.769448 0.559037i −0.132346 0.991204i \(-0.542251\pi\)
0.901794 + 0.432167i \(0.142251\pi\)
\(128\) 5.34300 + 16.4441i 0.472259 + 1.45346i
\(129\) −2.04033 + 6.27950i −0.179641 + 0.552879i
\(130\) 2.54027 + 1.84562i 0.222797 + 0.161871i
\(131\) −16.5018 −1.44177 −0.720885 0.693054i \(-0.756265\pi\)
−0.720885 + 0.693054i \(0.756265\pi\)
\(132\) 6.44881 + 12.3522i 0.561297 + 1.07512i
\(133\) 9.32462 0.808547
\(134\) −16.6650 12.1078i −1.43963 1.04595i
\(135\) 0.389639 1.19918i 0.0335347 0.103209i
\(136\) −3.51414 10.8154i −0.301335 0.927414i
\(137\) −7.21527 + 5.24220i −0.616442 + 0.447872i −0.851677 0.524067i \(-0.824414\pi\)
0.235235 + 0.971939i \(0.424414\pi\)
\(138\) −0.325650 + 0.236598i −0.0277212 + 0.0201406i
\(139\) 0.943715 + 2.90446i 0.0800449 + 0.246353i 0.983069 0.183238i \(-0.0586579\pi\)
−0.903024 + 0.429591i \(0.858658\pi\)
\(140\) −3.12759 + 9.62572i −0.264329 + 0.813522i
\(141\) 1.56655 + 1.13817i 0.131928 + 0.0958510i
\(142\) 35.0017 2.93728
\(143\) 0.486333 3.28077i 0.0406692 0.274352i
\(144\) 5.24863 0.437386
\(145\) −5.68166 4.12797i −0.471837 0.342809i
\(146\) −8.53304 + 26.2620i −0.706200 + 2.17346i
\(147\) 1.03514 + 3.18585i 0.0853772 + 0.262764i
\(148\) 6.35694 4.61859i 0.522538 0.379646i
\(149\) 2.72614 1.98065i 0.223334 0.162262i −0.470492 0.882404i \(-0.655924\pi\)
0.693826 + 0.720143i \(0.255924\pi\)
\(150\) −2.62420 8.07647i −0.214265 0.659441i
\(151\) −5.66383 + 17.4315i −0.460916 + 1.41855i 0.403132 + 0.915142i \(0.367922\pi\)
−0.864047 + 0.503410i \(0.832078\pi\)
\(152\) 21.6452 + 15.7262i 1.75566 + 1.27556i
\(153\) 2.07446 0.167710
\(154\) 15.5602 2.62288i 1.25387 0.211357i
\(155\) −2.02562 −0.162701
\(156\) −3.39896 2.46949i −0.272135 0.197717i
\(157\) −0.929535 + 2.86081i −0.0741850 + 0.228318i −0.981273 0.192624i \(-0.938300\pi\)
0.907088 + 0.420942i \(0.138300\pi\)
\(158\) 5.31073 + 16.3448i 0.422499 + 1.30032i
\(159\) −2.08681 + 1.51615i −0.165495 + 0.120239i
\(160\) −2.14890 + 1.56127i −0.169886 + 0.123429i
\(161\) 0.0954314 + 0.293708i 0.00752105 + 0.0231474i
\(162\) −0.769530 + 2.36837i −0.0604600 + 0.186077i
\(163\) −14.0565 10.2126i −1.10099 0.799916i −0.119769 0.992802i \(-0.538215\pi\)
−0.981221 + 0.192886i \(0.938215\pi\)
\(164\) −15.9148 −1.24274
\(165\) 2.92760 2.98624i 0.227914 0.232478i
\(166\) 33.2769 2.58279
\(167\) −19.6954 14.3095i −1.52407 1.10730i −0.959422 0.281975i \(-0.909010\pi\)
−0.564652 0.825329i \(-0.690990\pi\)
\(168\) 3.23648 9.96086i 0.249700 0.768497i
\(169\) 0.309017 + 0.951057i 0.0237705 + 0.0731582i
\(170\) −5.26969 + 3.82866i −0.404167 + 0.293645i
\(171\) −3.94848 + 2.86874i −0.301948 + 0.219378i
\(172\) 8.57216 + 26.3824i 0.653621 + 2.01164i
\(173\) 2.47654 7.62202i 0.188288 0.579491i −0.811701 0.584073i \(-0.801458\pi\)
0.999990 + 0.00458136i \(0.00145830\pi\)
\(174\) 11.2212 + 8.15267i 0.850677 + 0.618053i
\(175\) −6.51524 −0.492506
\(176\) 15.5880 + 7.74879i 1.17499 + 0.584087i
\(177\) 6.72019 0.505121
\(178\) −13.2340 9.61505i −0.991929 0.720678i
\(179\) 4.90264 15.0888i 0.366441 1.12779i −0.582634 0.812735i \(-0.697978\pi\)
0.949074 0.315053i \(-0.102022\pi\)
\(180\) −1.63701 5.03819i −0.122015 0.375525i
\(181\) 9.95518 7.23286i 0.739963 0.537614i −0.152737 0.988267i \(-0.548809\pi\)
0.892699 + 0.450652i \(0.148809\pi\)
\(182\) −3.84910 + 2.79654i −0.285314 + 0.207293i
\(183\) −4.47192 13.7632i −0.330574 1.01740i
\(184\) −0.273820 + 0.842730i −0.0201862 + 0.0621269i
\(185\) −1.90783 1.38612i −0.140266 0.101909i
\(186\) 4.00056 0.293335
\(187\) 6.16097 + 3.06262i 0.450535 + 0.223961i
\(188\) 8.13535 0.593332
\(189\) 1.54567 + 1.12299i 0.112431 + 0.0816858i
\(190\) 4.73563 14.5748i 0.343558 1.05736i
\(191\) 0.859957 + 2.64667i 0.0622243 + 0.191507i 0.977336 0.211693i \(-0.0678979\pi\)
−0.915112 + 0.403200i \(0.867898\pi\)
\(192\) −4.24842 + 3.08665i −0.306603 + 0.222760i
\(193\) −14.8153 + 10.7639i −1.06643 + 0.774804i −0.975266 0.221033i \(-0.929057\pi\)
−0.0911594 + 0.995836i \(0.529057\pi\)
\(194\) −7.14367 21.9860i −0.512886 1.57850i
\(195\) −0.389639 + 1.19918i −0.0279026 + 0.0858754i
\(196\) 11.3858 + 8.27229i 0.813274 + 0.590878i
\(197\) 2.73096 0.194573 0.0972864 0.995256i \(-0.468984\pi\)
0.0972864 + 0.995256i \(0.468984\pi\)
\(198\) −5.78197 + 5.89777i −0.410907 + 0.419136i
\(199\) −20.8343 −1.47691 −0.738454 0.674304i \(-0.764444\pi\)
−0.738454 + 0.674304i \(0.764444\pi\)
\(200\) −15.1238 10.9881i −1.06942 0.776976i
\(201\) 2.55615 7.86701i 0.180297 0.554896i
\(202\) −15.2888 47.0542i −1.07572 3.31072i
\(203\) 8.60904 6.25483i 0.604236 0.439003i
\(204\) 7.05101 5.12286i 0.493669 0.358672i
\(205\) 1.47596 + 4.54254i 0.103085 + 0.317265i
\(206\) −2.62769 + 8.08721i −0.183080 + 0.563463i
\(207\) −0.130770 0.0950099i −0.00908914 0.00660365i
\(208\) −5.24863 −0.363927
\(209\) −15.9619 + 2.69059i −1.10411 + 0.186112i
\(210\) −5.99903 −0.413973
\(211\) 10.4669 + 7.60464i 0.720570 + 0.523525i 0.886566 0.462602i \(-0.153084\pi\)
−0.165996 + 0.986126i \(0.553084\pi\)
\(212\) −3.34885 + 10.3067i −0.230000 + 0.707867i
\(213\) 4.34338 + 13.3676i 0.297604 + 0.915930i
\(214\) −12.1045 + 8.79443i −0.827446 + 0.601175i
\(215\) 6.73529 4.89347i 0.459343 0.333732i
\(216\) 1.69400 + 5.21361i 0.115262 + 0.354741i
\(217\) 0.948459 2.91906i 0.0643856 0.198158i
\(218\) −12.2759 8.91897i −0.831429 0.604069i
\(219\) −11.0886 −0.749301
\(220\) 2.57633 17.3798i 0.173696 1.17175i
\(221\) −2.07446 −0.139543
\(222\) 3.76793 + 2.73756i 0.252887 + 0.183733i
\(223\) −1.34274 + 4.13252i −0.0899163 + 0.276734i −0.985895 0.167362i \(-0.946475\pi\)
0.895979 + 0.444096i \(0.146475\pi\)
\(224\) −1.24371 3.82776i −0.0830991 0.255753i
\(225\) 2.75886 2.00443i 0.183924 0.133629i
\(226\) −22.3506 + 16.2387i −1.48674 + 1.08018i
\(227\) 6.84404 + 21.0638i 0.454255 + 1.39805i 0.872008 + 0.489492i \(0.162818\pi\)
−0.417753 + 0.908561i \(0.637182\pi\)
\(228\) −6.33641 + 19.5015i −0.419639 + 1.29152i
\(229\) −16.9314 12.3013i −1.11886 0.812896i −0.134820 0.990870i \(-0.543046\pi\)
−0.984035 + 0.177974i \(0.943046\pi\)
\(230\) 0.507543 0.0334664
\(231\) 2.93258 + 5.61714i 0.192950 + 0.369580i
\(232\) 30.5330 2.00459
\(233\) 11.1219 + 8.08053i 0.728620 + 0.529373i 0.889126 0.457662i \(-0.151313\pi\)
−0.160507 + 0.987035i \(0.551313\pi\)
\(234\) 0.769530 2.36837i 0.0503057 0.154825i
\(235\) −0.754483 2.32206i −0.0492171 0.151475i
\(236\) 22.8417 16.5955i 1.48687 1.08027i
\(237\) −5.58324 + 4.05646i −0.362671 + 0.263496i
\(238\) −3.04992 9.38670i −0.197697 0.608449i
\(239\) 3.56797 10.9811i 0.230793 0.710307i −0.766859 0.641816i \(-0.778181\pi\)
0.997652 0.0684914i \(-0.0218186\pi\)
\(240\) −5.35406 3.88995i −0.345603 0.251095i
\(241\) 19.5720 1.26074 0.630372 0.776293i \(-0.282902\pi\)
0.630372 + 0.776293i \(0.282902\pi\)
\(242\) −25.8791 + 8.97969i −1.66357 + 0.577236i
\(243\) −1.00000 −0.0641500
\(244\) −49.1879 35.7371i −3.14893 2.28783i
\(245\) 1.30521 4.01702i 0.0833868 0.256638i
\(246\) −2.91500 8.97143i −0.185853 0.571998i
\(247\) 3.94848 2.86874i 0.251236 0.182533i
\(248\) 7.12471 5.17640i 0.452419 0.328702i
\(249\) 4.12936 + 12.7089i 0.261687 + 0.805391i
\(250\) −8.16034 + 25.1149i −0.516105 + 1.58841i
\(251\) −15.1285 10.9915i −0.954900 0.693775i −0.00293895 0.999996i \(-0.500935\pi\)
−0.951961 + 0.306221i \(0.900935\pi\)
\(252\) 8.02689 0.505646
\(253\) −0.248108 0.475233i −0.0155984 0.0298776i
\(254\) 26.6911 1.67475
\(255\) −2.11613 1.53746i −0.132517 0.0962794i
\(256\) −10.0599 + 30.9612i −0.628744 + 1.93507i
\(257\) −3.15201 9.70089i −0.196617 0.605125i −0.999954 0.00959999i \(-0.996944\pi\)
0.803337 0.595525i \(-0.203056\pi\)
\(258\) −13.3021 + 9.66453i −0.828152 + 0.601687i
\(259\) 2.89080 2.10029i 0.179626 0.130506i
\(260\) 1.63701 + 5.03819i 0.101523 + 0.312455i
\(261\) −1.72116 + 5.29718i −0.106537 + 0.327887i
\(262\) −33.2455 24.1543i −2.05391 1.49225i
\(263\) 1.76069 0.108569 0.0542843 0.998526i \(-0.482712\pi\)
0.0542843 + 0.998526i \(0.482712\pi\)
\(264\) −2.66603 + 17.9849i −0.164083 + 1.10689i
\(265\) 3.25240 0.199793
\(266\) 18.7859 + 13.6487i 1.15184 + 0.836858i
\(267\) 2.02989 6.24735i 0.124227 0.382332i
\(268\) −10.7393 33.0521i −0.656005 2.01898i
\(269\) 14.5890 10.5995i 0.889506 0.646264i −0.0462433 0.998930i \(-0.514725\pi\)
0.935749 + 0.352666i \(0.114725\pi\)
\(270\) 2.54027 1.84562i 0.154596 0.112321i
\(271\) −0.807860 2.48634i −0.0490740 0.151034i 0.923517 0.383558i \(-0.125302\pi\)
−0.972591 + 0.232524i \(0.925302\pi\)
\(272\) 3.36460 10.3552i 0.204009 0.627875i
\(273\) −1.54567 1.12299i −0.0935481 0.0679667i
\(274\) −22.2095 −1.34172
\(275\) 11.1528 1.87996i 0.672540 0.113366i
\(276\) −0.679108 −0.0408775
\(277\) 25.9247 + 18.8354i 1.55767 + 1.13171i 0.937890 + 0.346932i \(0.112777\pi\)
0.619776 + 0.784779i \(0.287223\pi\)
\(278\) −2.35009 + 7.23283i −0.140949 + 0.433796i
\(279\) 0.496432 + 1.52786i 0.0297206 + 0.0914706i
\(280\) −10.6838 + 7.76227i −0.638482 + 0.463884i
\(281\) 19.3116 14.0307i 1.15203 0.837000i 0.163282 0.986579i \(-0.447792\pi\)
0.988750 + 0.149579i \(0.0477919\pi\)
\(282\) 1.49009 + 4.58603i 0.0887337 + 0.273094i
\(283\) −6.29039 + 19.3598i −0.373925 + 1.15082i 0.570276 + 0.821453i \(0.306836\pi\)
−0.944201 + 0.329369i \(0.893164\pi\)
\(284\) 47.7741 + 34.7099i 2.83487 + 2.05965i
\(285\) 6.15392 0.364527
\(286\) 5.78197 5.89777i 0.341895 0.348742i
\(287\) −7.23721 −0.427199
\(288\) 1.70427 + 1.23822i 0.100425 + 0.0729629i
\(289\) −3.92347 + 12.0752i −0.230792 + 0.710306i
\(290\) −5.40435 16.6329i −0.317354 0.976716i
\(291\) 7.51024 5.45651i 0.440258 0.319866i
\(292\) −37.6899 + 27.3833i −2.20563 + 1.60249i
\(293\) 9.26129 + 28.5033i 0.541050 + 1.66518i 0.730201 + 0.683233i \(0.239427\pi\)
−0.189151 + 0.981948i \(0.560573\pi\)
\(294\) −2.57777 + 7.93355i −0.150338 + 0.462694i
\(295\) −6.85518 4.98058i −0.399124 0.289981i
\(296\) 10.2526 0.595920
\(297\) −2.96992 1.47635i −0.172332 0.0856662i
\(298\) 8.39137 0.486099
\(299\) 0.130770 + 0.0950099i 0.00756262 + 0.00549456i
\(300\) 4.42734 13.6260i 0.255613 0.786695i
\(301\) 3.89816 + 11.9973i 0.224686 + 0.691513i
\(302\) −36.9257 + 26.8281i −2.12483 + 1.54378i
\(303\) 16.0734 11.6780i 0.923390 0.670882i
\(304\) 7.91591 + 24.3627i 0.454008 + 1.39729i
\(305\) −5.63864 + 17.3539i −0.322867 + 0.993683i
\(306\) 4.17932 + 3.03645i 0.238916 + 0.173583i
\(307\) 10.0204 0.571897 0.285948 0.958245i \(-0.407691\pi\)
0.285948 + 0.958245i \(0.407691\pi\)
\(308\) 23.8392 + 11.8505i 1.35836 + 0.675243i
\(309\) −3.41467 −0.194254
\(310\) −4.08092 2.96496i −0.231781 0.168398i
\(311\) −4.28808 + 13.1973i −0.243155 + 0.748353i 0.752780 + 0.658272i \(0.228712\pi\)
−0.995934 + 0.0900805i \(0.971288\pi\)
\(312\) −1.69400 5.21361i −0.0959040 0.295162i
\(313\) −16.1603 + 11.7412i −0.913435 + 0.663649i −0.941881 0.335946i \(-0.890944\pi\)
0.0284464 + 0.999595i \(0.490944\pi\)
\(314\) −6.06016 + 4.40296i −0.341995 + 0.248474i
\(315\) −0.744424 2.29110i −0.0419436 0.129089i
\(316\) −8.95984 + 27.5755i −0.504030 + 1.55125i
\(317\) 12.4786 + 9.06621i 0.700866 + 0.509209i 0.880214 0.474577i \(-0.157399\pi\)
−0.179348 + 0.983786i \(0.557399\pi\)
\(318\) −6.42344 −0.360209
\(319\) −12.9322 + 13.1912i −0.724062 + 0.738563i
\(320\) 6.62139 0.370147
\(321\) −4.86075 3.53154i −0.271301 0.197112i
\(322\) −0.237648 + 0.731405i −0.0132436 + 0.0407596i
\(323\) 3.12867 + 9.62906i 0.174084 + 0.535775i
\(324\) −3.39896 + 2.46949i −0.188831 + 0.137194i
\(325\) −2.75886 + 2.00443i −0.153034 + 0.111186i
\(326\) −13.3704 41.1499i −0.740519 2.27908i
\(327\) 1.88293 5.79508i 0.104127 0.320468i
\(328\) −16.7997 12.2057i −0.927609 0.673948i
\(329\) 3.69953 0.203962
\(330\) 10.2692 1.73101i 0.565299 0.0952888i
\(331\) 28.0595 1.54229 0.771144 0.636660i \(-0.219685\pi\)
0.771144 + 0.636660i \(0.219685\pi\)
\(332\) 45.4199 + 32.9995i 2.49274 + 1.81108i
\(333\) −0.577942 + 1.77872i −0.0316710 + 0.0974734i
\(334\) −18.7341 57.6575i −1.02508 3.15488i
\(335\) −8.43802 + 6.13058i −0.461018 + 0.334950i
\(336\) 8.11264 5.89418i 0.442581 0.321554i
\(337\) −2.27668 7.00690i −0.124019 0.381690i 0.869702 0.493577i \(-0.164311\pi\)
−0.993721 + 0.111886i \(0.964311\pi\)
\(338\) −0.769530 + 2.36837i −0.0418569 + 0.128822i
\(339\) −8.97524 6.52089i −0.487468 0.354166i
\(340\) −10.9894 −0.595983
\(341\) −0.781288 + 5.27052i −0.0423091 + 0.285415i
\(342\) −12.1539 −0.657207
\(343\) 15.9973 + 11.6228i 0.863776 + 0.627570i
\(344\) −11.1849 + 34.4237i −0.603051 + 1.85600i
\(345\) 0.0629814 + 0.193837i 0.00339080 + 0.0104358i
\(346\) 16.1460 11.7307i 0.868013 0.630648i
\(347\) 9.27446 6.73829i 0.497879 0.361730i −0.310327 0.950630i \(-0.600439\pi\)
0.808206 + 0.588900i \(0.200439\pi\)
\(348\) 7.23118 + 22.2553i 0.387632 + 1.19301i
\(349\) −3.00259 + 9.24103i −0.160725 + 0.494661i −0.998696 0.0510540i \(-0.983742\pi\)
0.837971 + 0.545715i \(0.183742\pi\)
\(350\) −13.1260 9.53657i −0.701613 0.509751i
\(351\) 1.00000 0.0533761
\(352\) 3.23348 + 6.19350i 0.172345 + 0.330114i
\(353\) 14.9952 0.798114 0.399057 0.916926i \(-0.369338\pi\)
0.399057 + 0.916926i \(0.369338\pi\)
\(354\) 13.5389 + 9.83656i 0.719583 + 0.522808i
\(355\) 5.47656 16.8551i 0.290666 0.894577i
\(356\) −8.52827 26.2473i −0.451997 1.39110i
\(357\) 3.20643 2.32961i 0.169702 0.123296i
\(358\) 31.9631 23.2225i 1.68930 1.22735i
\(359\) 4.75337 + 14.6294i 0.250873 + 0.772108i 0.994615 + 0.103641i \(0.0330493\pi\)
−0.743742 + 0.668467i \(0.766951\pi\)
\(360\) 2.13596 6.57382i 0.112575 0.346471i
\(361\) −3.89959 2.83322i −0.205242 0.149117i
\(362\) 30.6432 1.61057
\(363\) −6.64081 8.76924i −0.348552 0.460266i
\(364\) −8.02689 −0.420723
\(365\) 11.3114 + 8.21820i 0.592065 + 0.430160i
\(366\) 11.1362 34.2737i 0.582099 1.79152i
\(367\) −6.44465 19.8346i −0.336408 1.03536i −0.966024 0.258451i \(-0.916788\pi\)
0.629617 0.776906i \(-0.283212\pi\)
\(368\) −0.686363 + 0.498672i −0.0357791 + 0.0259951i
\(369\) 3.06457 2.22654i 0.159535 0.115909i
\(370\) −1.81471 5.58510i −0.0943422 0.290356i
\(371\) −1.52288 + 4.68694i −0.0790640 + 0.243334i
\(372\) 5.46039 + 3.96721i 0.283108 + 0.205690i
\(373\) −27.8062 −1.43975 −0.719876 0.694103i \(-0.755801\pi\)
−0.719876 + 0.694103i \(0.755801\pi\)
\(374\) 7.92938 + 15.1881i 0.410018 + 0.785360i
\(375\) −10.6043 −0.547605
\(376\) 8.58771 + 6.23933i 0.442877 + 0.321769i
\(377\) 1.72116 5.29718i 0.0886441 0.272819i
\(378\) 1.47023 + 4.52489i 0.0756202 + 0.232735i
\(379\) 11.5980 8.42642i 0.595748 0.432836i −0.248619 0.968601i \(-0.579977\pi\)
0.844367 + 0.535765i \(0.179977\pi\)
\(380\) 20.9169 15.1970i 1.07302 0.779592i
\(381\) 3.31212 + 10.1936i 0.169685 + 0.522236i
\(382\) −2.14151 + 6.59088i −0.109569 + 0.337219i
\(383\) −0.0800400 0.0581524i −0.00408985 0.00297145i 0.585738 0.810500i \(-0.300805\pi\)
−0.589828 + 0.807529i \(0.700805\pi\)
\(384\) −17.2903 −0.882342
\(385\) 1.17158 7.90341i 0.0597093 0.402795i
\(386\) −45.6031 −2.32114
\(387\) −5.34166 3.88095i −0.271532 0.197280i
\(388\) 12.0522 37.0929i 0.611859 1.88311i
\(389\) 2.90510 + 8.94097i 0.147294 + 0.453325i 0.997299 0.0734500i \(-0.0234009\pi\)
−0.850005 + 0.526775i \(0.823401\pi\)
\(390\) −2.54027 + 1.84562i −0.128632 + 0.0934564i
\(391\) −0.271277 + 0.197094i −0.0137191 + 0.00996748i
\(392\) 5.67456 + 17.4645i 0.286609 + 0.882091i
\(393\) 5.09934 15.6942i 0.257228 0.791666i
\(394\) 5.50194 + 3.99740i 0.277184 + 0.201386i
\(395\) 8.70179 0.437835
\(396\) −13.7405 + 2.31614i −0.690484 + 0.116390i
\(397\) 6.12632 0.307471 0.153736 0.988112i \(-0.450870\pi\)
0.153736 + 0.988112i \(0.450870\pi\)
\(398\) −41.9740 30.4959i −2.10397 1.52862i
\(399\) −2.88146 + 8.86824i −0.144254 + 0.443967i
\(400\) −5.53096 17.0225i −0.276548 0.851127i
\(401\) 24.5645 17.8472i 1.22669 0.891245i 0.230055 0.973178i \(-0.426109\pi\)
0.996638 + 0.0819329i \(0.0261093\pi\)
\(402\) 16.6650 12.1078i 0.831172 0.603882i
\(403\) −0.496432 1.52786i −0.0247290 0.0761082i
\(404\) 25.7941 79.3860i 1.28330 3.94960i
\(405\) 1.02009 + 0.741137i 0.0506885 + 0.0368274i
\(406\) 26.4996 1.31516
\(407\) −4.34245 + 4.42942i −0.215247 + 0.219558i
\(408\) 11.3720 0.562998
\(409\) 14.6140 + 10.6177i 0.722615 + 0.525010i 0.887219 0.461349i \(-0.152635\pi\)
−0.164604 + 0.986360i \(0.552635\pi\)
\(410\) −3.67551 + 11.3121i −0.181520 + 0.558663i
\(411\) −2.75599 8.48206i −0.135943 0.418389i
\(412\) −11.6063 + 8.43251i −0.571804 + 0.415440i
\(413\) 10.3872 7.54673i 0.511120 0.371350i
\(414\) −0.124387 0.382824i −0.00611330 0.0188148i
\(415\) 5.20669 16.0246i 0.255587 0.786615i
\(416\) −1.70427 1.23822i −0.0835585 0.0607088i
\(417\) −3.05393 −0.149551
\(418\) −36.0960 17.9433i −1.76552 0.877638i
\(419\) −26.3754 −1.28852 −0.644262 0.764805i \(-0.722835\pi\)
−0.644262 + 0.764805i \(0.722835\pi\)
\(420\) −8.18813 5.94902i −0.399540 0.290283i
\(421\) −7.27845 + 22.4008i −0.354730 + 1.09175i 0.601436 + 0.798921i \(0.294596\pi\)
−0.956166 + 0.292826i \(0.905404\pi\)
\(422\) 9.95601 + 30.6414i 0.484651 + 1.49160i
\(423\) −1.56655 + 1.13817i −0.0761685 + 0.0553396i
\(424\) −11.4397 + 8.31142i −0.555560 + 0.403638i
\(425\) −2.18605 6.72796i −0.106039 0.326354i
\(426\) −10.8161 + 33.2886i −0.524042 + 1.61284i
\(427\) −22.3681 16.2513i −1.08247 0.786458i
\(428\) −25.2426 −1.22015
\(429\) 2.96992 + 1.47635i 0.143389 + 0.0712786i
\(430\) 20.7320 0.999787
\(431\) 7.67426 + 5.57568i 0.369656 + 0.268571i 0.757068 0.653336i \(-0.226631\pi\)
−0.387412 + 0.921907i \(0.626631\pi\)
\(432\) −1.62192 + 4.99174i −0.0780345 + 0.240165i
\(433\) −7.91492 24.3596i −0.380367 1.17065i −0.939786 0.341764i \(-0.888976\pi\)
0.559419 0.828885i \(-0.311024\pi\)
\(434\) 6.18353 4.49260i 0.296819 0.215652i
\(435\) 5.68166 4.12797i 0.272415 0.197921i
\(436\) −7.91086 24.3471i −0.378862 1.16602i
\(437\) 0.243784 0.750290i 0.0116618 0.0358912i
\(438\) −22.3398 16.2308i −1.06744 0.775538i
\(439\) −4.50447 −0.214987 −0.107493 0.994206i \(-0.534282\pi\)
−0.107493 + 0.994206i \(0.534282\pi\)
\(440\) 16.0489 16.3703i 0.765099 0.780422i
\(441\) −3.34980 −0.159514
\(442\) −4.17932 3.03645i −0.198790 0.144429i
\(443\) 6.95166 21.3950i 0.330284 1.01651i −0.638715 0.769443i \(-0.720534\pi\)
0.968999 0.247065i \(-0.0794662\pi\)
\(444\) 2.42814 + 7.47304i 0.115234 + 0.354655i
\(445\) −6.70080 + 4.86842i −0.317649 + 0.230785i
\(446\) −8.75405 + 6.36019i −0.414516 + 0.301164i
\(447\) 1.04129 + 3.20477i 0.0492514 + 0.151580i
\(448\) −3.10035 + 9.54189i −0.146478 + 0.450812i
\(449\) −2.99271 2.17433i −0.141235 0.102613i 0.514924 0.857236i \(-0.327820\pi\)
−0.656159 + 0.754622i \(0.727820\pi\)
\(450\) 8.49210 0.400321
\(451\) 12.3887 2.08828i 0.583360 0.0983332i
\(452\) −46.6098 −2.19234
\(453\) −14.8281 10.7732i −0.696684 0.506171i
\(454\) −17.0434 + 52.4541i −0.799885 + 2.46179i
\(455\) 0.744424 + 2.29110i 0.0348991 + 0.107409i
\(456\) −21.6452 + 15.7262i −1.01363 + 0.736445i
\(457\) 26.3345 19.1332i 1.23188 0.895012i 0.234848 0.972032i \(-0.424541\pi\)
0.997030 + 0.0770205i \(0.0245407\pi\)
\(458\) −16.1050 49.5659i −0.752535 2.31606i
\(459\) −0.641043 + 1.97293i −0.0299213 + 0.0920884i
\(460\) 0.692749 + 0.503312i 0.0322996 + 0.0234670i
\(461\) 12.2504 0.570558 0.285279 0.958445i \(-0.407914\pi\)
0.285279 + 0.958445i \(0.407914\pi\)
\(462\) −2.31385 + 15.6091i −0.107650 + 0.726201i
\(463\) 25.9828 1.20752 0.603761 0.797166i \(-0.293668\pi\)
0.603761 + 0.797166i \(0.293668\pi\)
\(464\) 23.6506 + 17.1832i 1.09795 + 0.797708i
\(465\) 0.625950 1.92648i 0.0290277 0.0893381i
\(466\) 10.5790 + 32.5590i 0.490065 + 1.50826i
\(467\) 10.3350 7.50884i 0.478248 0.347467i −0.322399 0.946604i \(-0.604489\pi\)
0.800647 + 0.599136i \(0.204489\pi\)
\(468\) 3.39896 2.46949i 0.157117 0.114152i
\(469\) −4.88365 15.0303i −0.225506 0.694036i
\(470\) 1.87885 5.78251i 0.0866650 0.266727i
\(471\) −2.43355 1.76808i −0.112132 0.0814689i
\(472\) 36.8395 1.69567
\(473\) −10.1347 19.4122i −0.465993 0.892575i
\(474\) −17.1859 −0.789374
\(475\) 13.4649 + 9.78280i 0.617810 + 0.448866i
\(476\) 5.14558 15.8365i 0.235847 0.725864i
\(477\) −0.797089 2.45319i −0.0364962 0.112324i
\(478\) 23.2616 16.9005i 1.06396 0.773012i
\(479\) 2.63863 1.91708i 0.120562 0.0875934i −0.525870 0.850565i \(-0.676260\pi\)
0.646432 + 0.762971i \(0.276260\pi\)
\(480\) −0.820808 2.52619i −0.0374646 0.115304i
\(481\) 0.577942 1.77872i 0.0263519 0.0811028i
\(482\) 39.4309 + 28.6482i 1.79603 + 1.30489i
\(483\) −0.308822 −0.0140519
\(484\) −44.2274 13.4069i −2.01034 0.609405i
\(485\) −11.7051 −0.531502
\(486\) −2.01466 1.46373i −0.0913866 0.0663963i
\(487\) 8.63548 26.5773i 0.391311 1.20433i −0.540487 0.841353i \(-0.681760\pi\)
0.931798 0.362978i \(-0.118240\pi\)
\(488\) −24.5147 75.4484i −1.10973 3.41539i
\(489\) 14.0565 10.2126i 0.635657 0.461832i
\(490\) 8.50939 6.18244i 0.384415 0.279294i
\(491\) 3.58734 + 11.0407i 0.161894 + 0.498260i 0.998794 0.0490965i \(-0.0156342\pi\)
−0.836900 + 0.547356i \(0.815634\pi\)
\(492\) 4.91794 15.1359i 0.221718 0.682378i
\(493\) 9.34762 + 6.79144i 0.420996 + 0.305871i
\(494\) 12.1539 0.546829
\(495\) 1.93540 + 3.70711i 0.0869898 + 0.166622i
\(496\) 8.43186 0.378602
\(497\) 21.7251 + 15.7842i 0.974504 + 0.708019i
\(498\) −10.2831 + 31.6482i −0.460798 + 1.41819i
\(499\) 1.63506 + 5.03219i 0.0731953 + 0.225272i 0.980961 0.194206i \(-0.0622131\pi\)
−0.907765 + 0.419478i \(0.862213\pi\)
\(500\) −36.0437 + 26.1873i −1.61192 + 1.17113i
\(501\) 19.6954 14.3095i 0.879924 0.639302i
\(502\) −14.3901 44.2880i −0.642259 1.97667i
\(503\) −9.26606 + 28.5180i −0.413153 + 1.27156i 0.500739 + 0.865598i \(0.333062\pi\)
−0.913892 + 0.405957i \(0.866938\pi\)
\(504\) 8.47321 + 6.15615i 0.377427 + 0.274217i
\(505\) −25.0512 −1.11476
\(506\) 0.195761 1.32059i 0.00870266 0.0587076i
\(507\) −1.00000 −0.0444116
\(508\) 36.4309 + 26.4686i 1.61636 + 1.17435i
\(509\) 4.66586 14.3600i 0.206811 0.636497i −0.792824 0.609451i \(-0.791390\pi\)
0.999634 0.0270463i \(-0.00861016\pi\)
\(510\) −2.01284 6.19490i −0.0891302 0.274315i
\(511\) −17.1394 + 12.4525i −0.758201 + 0.550865i
\(512\) −37.6098 + 27.3252i −1.66214 + 1.20761i
\(513\) −1.50819 4.64172i −0.0665880 0.204937i
\(514\) 7.84929 24.1576i 0.346217 1.06555i
\(515\) 3.48327 + 2.53074i 0.153491 + 0.111518i
\(516\) −27.7401 −1.22119
\(517\) −6.33286 + 1.06749i −0.278519 + 0.0469481i
\(518\) 8.89823 0.390966
\(519\) 6.48368 + 4.71067i 0.284602 + 0.206775i
\(520\) −2.13596 + 6.57382i −0.0936682 + 0.288281i
\(521\) 0.680615 + 2.09472i 0.0298183 + 0.0917712i 0.964858 0.262772i \(-0.0846365\pi\)
−0.935040 + 0.354543i \(0.884637\pi\)
\(522\) −11.2212 + 8.15267i −0.491138 + 0.356833i
\(523\) 30.2212 21.9570i 1.32148 0.960112i 0.321568 0.946887i \(-0.395790\pi\)
0.999913 0.0132251i \(-0.00420981\pi\)
\(524\) −21.4241 65.9366i −0.935917 2.88046i
\(525\) 2.01332 6.19636i 0.0878685 0.270432i
\(526\) 3.54718 + 2.57718i 0.154664 + 0.112370i
\(527\) 3.33260 0.145170
\(528\) −12.1865 + 12.4306i −0.530349 + 0.540970i
\(529\) −22.9739 −0.998864
\(530\) 6.55247 + 4.76065i 0.284621 + 0.206789i
\(531\) −2.07665 + 6.39128i −0.0901191 + 0.277358i
\(532\) 12.1060 + 37.2585i 0.524863 + 1.61536i
\(533\) −3.06457 + 2.22654i −0.132741 + 0.0964423i
\(534\) 13.2340 9.61505i 0.572690 0.416084i
\(535\) 2.34104 + 7.20497i 0.101212 + 0.311498i
\(536\) 14.0126 43.1262i 0.605251 1.86277i
\(537\) 12.8353 + 9.32538i 0.553883 + 0.402420i
\(538\) 44.9066 1.93606
\(539\) −9.94861 4.94546i −0.428517 0.213016i
\(540\) 5.29747 0.227967
\(541\) 36.4346 + 26.4713i 1.56645 + 1.13809i 0.930462 + 0.366388i \(0.119406\pi\)
0.635985 + 0.771702i \(0.280594\pi\)
\(542\) 2.01177 6.19160i 0.0864131 0.265952i
\(543\) 3.80254 + 11.7030i 0.163183 + 0.502225i
\(544\) 3.53543 2.56864i 0.151580 0.110130i
\(545\) −6.21570 + 4.51597i −0.266251 + 0.193443i
\(546\) −1.47023 4.52489i −0.0629198 0.193647i
\(547\) 8.51328 26.2012i 0.364001 1.12028i −0.586602 0.809875i \(-0.699535\pi\)
0.950604 0.310406i \(-0.100465\pi\)
\(548\) −30.3139 22.0243i −1.29494 0.940832i
\(549\) 14.4715 0.617626
\(550\) 25.2208 + 12.5373i 1.07542 + 0.534591i
\(551\) −27.1838 −1.15807
\(552\) −0.716869 0.520836i −0.0305120 0.0221682i
\(553\) −4.07446 + 12.5399i −0.173264 + 0.533251i
\(554\) 24.6594 + 75.8938i 1.04768 + 3.22442i
\(555\) 1.90783 1.38612i 0.0809828 0.0588374i
\(556\) −10.3802 + 7.54164i −0.440218 + 0.319837i
\(557\) −6.81240 20.9664i −0.288651 0.888375i −0.985281 0.170945i \(-0.945318\pi\)
0.696630 0.717431i \(-0.254682\pi\)
\(558\) −1.23624 + 3.80476i −0.0523342 + 0.161068i
\(559\) 5.34166 + 3.88095i 0.225928 + 0.164147i
\(560\) −12.6440 −0.534306
\(561\) −4.81657 + 4.91303i −0.203356 + 0.207428i
\(562\) 59.4433 2.50747
\(563\) 17.0046 + 12.3546i 0.716658 + 0.520683i 0.885315 0.464992i \(-0.153943\pi\)
−0.168657 + 0.985675i \(0.553943\pi\)
\(564\) −2.51396 + 7.73718i −0.105857 + 0.325794i
\(565\) 4.32265 + 13.3038i 0.181855 + 0.559693i
\(566\) −41.0106 + 29.7959i −1.72380 + 1.25242i
\(567\) −1.54567 + 1.12299i −0.0649120 + 0.0471613i
\(568\) 23.8100 + 73.2797i 0.999047 + 3.07475i
\(569\) −9.49743 + 29.2301i −0.398153 + 1.22539i 0.528326 + 0.849042i \(0.322820\pi\)
−0.926479 + 0.376347i \(0.877180\pi\)
\(570\) 12.3980 + 9.00769i 0.519296 + 0.377291i
\(571\) 10.2972 0.430926 0.215463 0.976512i \(-0.430874\pi\)
0.215463 + 0.976512i \(0.430874\pi\)
\(572\) 13.7405 2.31614i 0.574517 0.0968426i
\(573\) −2.78288 −0.116256
\(574\) −14.5805 10.5933i −0.608577 0.442157i
\(575\) −0.170335 + 0.524238i −0.00710347 + 0.0218622i
\(576\) −1.62275 4.99431i −0.0676146 0.208096i
\(577\) 33.7966 24.5547i 1.40697 1.02222i 0.413218 0.910632i \(-0.364405\pi\)
0.993754 0.111592i \(-0.0355951\pi\)
\(578\) −25.5793 + 18.5845i −1.06396 + 0.773011i
\(579\) −5.65893 17.4164i −0.235177 0.723800i
\(580\) 9.11778 28.0616i 0.378595 1.16520i
\(581\) 20.6546 + 15.0064i 0.856896 + 0.622572i
\(582\) 23.1174 0.958248
\(583\) 1.25446 8.46254i 0.0519546 0.350483i
\(584\) −60.7869 −2.51538
\(585\) −1.02009 0.741137i −0.0421754 0.0306422i
\(586\) −23.0629 + 70.9804i −0.952721 + 2.93217i
\(587\) −0.371585 1.14362i −0.0153370 0.0472023i 0.943095 0.332523i \(-0.107900\pi\)
−0.958432 + 0.285321i \(0.907900\pi\)
\(588\) −11.3858 + 8.27229i −0.469544 + 0.341143i
\(589\) −6.34319 + 4.60859i −0.261366 + 0.189894i
\(590\) −6.52059 20.0683i −0.268448 0.826199i
\(591\) −0.843913 + 2.59730i −0.0347139 + 0.106839i
\(592\) 7.94156 + 5.76988i 0.326396 + 0.237141i
\(593\) −27.6102 −1.13381 −0.566907 0.823782i \(-0.691860\pi\)
−0.566907 + 0.823782i \(0.691860\pi\)
\(594\) −3.82238 7.32149i −0.156834 0.300404i
\(595\) −4.99739 −0.204873
\(596\) 11.4534 + 8.32142i 0.469152 + 0.340859i
\(597\) 6.43817 19.8146i 0.263497 0.810959i
\(598\) 0.124387 + 0.382824i 0.00508657 + 0.0156549i
\(599\) −31.4893 + 22.8783i −1.28662 + 0.934782i −0.999731 0.0231829i \(-0.992620\pi\)
−0.286886 + 0.957965i \(0.592620\pi\)
\(600\) 15.1238 10.9881i 0.617427 0.448587i
\(601\) −11.7616 36.1985i −0.479765 1.47657i −0.839422 0.543481i \(-0.817106\pi\)
0.359656 0.933085i \(-0.382894\pi\)
\(602\) −9.70740 + 29.8763i −0.395644 + 1.21767i
\(603\) 6.69208 + 4.86208i 0.272523 + 0.197999i
\(604\) −77.0045 −3.13327
\(605\) 0.274995 + 13.8671i 0.0111801 + 0.563779i
\(606\) 49.4757 2.00981
\(607\) 19.3361 + 14.0485i 0.784830 + 0.570212i 0.906425 0.422368i \(-0.138801\pi\)
−0.121595 + 0.992580i \(0.538801\pi\)
\(608\) −3.17712 + 9.77818i −0.128849 + 0.396558i
\(609\) 3.28836 + 10.1205i 0.133251 + 0.410105i
\(610\) −36.7614 + 26.7087i −1.48843 + 1.08141i
\(611\) 1.56655 1.13817i 0.0633760 0.0460454i
\(612\) 2.69325 + 8.28896i 0.108868 + 0.335061i
\(613\) −0.232089 + 0.714295i −0.00937397 + 0.0288501i −0.955634 0.294556i \(-0.904828\pi\)
0.946260 + 0.323407i \(0.104828\pi\)
\(614\) 20.1877 + 14.6672i 0.814710 + 0.591922i
\(615\) −4.77631 −0.192599
\(616\) 16.0761 + 30.7926i 0.647726 + 1.24067i
\(617\) −0.717569 −0.0288882 −0.0144441 0.999896i \(-0.504598\pi\)
−0.0144441 + 0.999896i \(0.504598\pi\)
\(618\) −6.87939 4.99817i −0.276730 0.201056i
\(619\) −1.18056 + 3.63338i −0.0474505 + 0.146038i −0.971975 0.235086i \(-0.924463\pi\)
0.924524 + 0.381124i \(0.124463\pi\)
\(620\) −2.62983 8.09379i −0.105617 0.325055i
\(621\) 0.130770 0.0950099i 0.00524762 0.00381262i
\(622\) −27.9564 + 20.3115i −1.12095 + 0.814417i
\(623\) −3.87820 11.9359i −0.155377 0.478201i
\(624\) 1.62192 4.99174i 0.0649286 0.199830i
\(625\) −2.97697 2.16290i −0.119079 0.0865160i
\(626\) −49.7434 −1.98814
\(627\) 2.37359 16.0121i 0.0947922 0.639462i
\(628\) −12.6378 −0.504304
\(629\) 3.13881 + 2.28048i 0.125152 + 0.0909286i
\(630\) 1.85380 5.70542i 0.0738573 0.227309i
\(631\) −4.68725 14.4259i −0.186596 0.574285i 0.813376 0.581739i \(-0.197627\pi\)
−0.999972 + 0.00745397i \(0.997627\pi\)
\(632\) −30.6068 + 22.2372i −1.21747 + 0.884547i
\(633\) −10.4669 + 7.60464i −0.416021 + 0.302257i
\(634\) 11.8695 + 36.5306i 0.471398 + 1.45081i
\(635\) 4.17624 12.8531i 0.165729 0.510061i
\(636\) −8.76740 6.36989i −0.347650 0.252583i
\(637\) 3.34980 0.132724
\(638\) −45.3622 + 7.64641i −1.79591 + 0.302724i
\(639\) −14.0555 −0.556026
\(640\) 17.6376 + 12.8145i 0.697188 + 0.506537i
\(641\) −14.6229 + 45.0046i −0.577568 + 1.77757i 0.0496933 + 0.998765i \(0.484176\pi\)
−0.627262 + 0.778808i \(0.715824\pi\)
\(642\) −4.62351 14.2297i −0.182475 0.561601i
\(643\) −1.05779 + 0.768531i −0.0417152 + 0.0303079i −0.608447 0.793594i \(-0.708207\pi\)
0.566732 + 0.823902i \(0.308207\pi\)
\(644\) −1.04968 + 0.762634i −0.0413630 + 0.0300520i
\(645\) 2.57265 + 7.91781i 0.101298 + 0.311763i
\(646\) −7.79117 + 23.9788i −0.306540 + 0.943432i
\(647\) −33.7737 24.5380i −1.32778 0.964689i −0.999800 0.0200041i \(-0.993632\pi\)
−0.327980 0.944685i \(-0.606368\pi\)
\(648\) −5.48191 −0.215350
\(649\) −15.6032 + 15.9157i −0.612480 + 0.624747i
\(650\) −8.49210 −0.333088
\(651\) 2.48310 + 1.80408i 0.0973203 + 0.0707073i
\(652\) 22.5575 69.4248i 0.883419 2.71888i
\(653\) −8.09531 24.9148i −0.316794 0.974991i −0.975010 0.222162i \(-0.928689\pi\)
0.658216 0.752829i \(-0.271311\pi\)
\(654\) 12.2759 8.91897i 0.480026 0.348759i
\(655\) −16.8333 + 12.2301i −0.657731 + 0.477870i
\(656\) −6.14385 18.9088i −0.239877 0.738266i
\(657\) 3.42658 10.5459i 0.133684 0.411436i
\(658\) 7.45327 + 5.41512i 0.290559 + 0.211103i
\(659\) 2.89025 0.112588 0.0562942 0.998414i \(-0.482072\pi\)
0.0562942 + 0.998414i \(0.482072\pi\)
\(660\) 15.7330 + 7.82089i 0.612408 + 0.304428i
\(661\) −37.1700 −1.44575 −0.722874 0.690980i \(-0.757179\pi\)
−0.722874 + 0.690980i \(0.757179\pi\)
\(662\) 56.5302 + 41.0716i 2.19711 + 1.59629i
\(663\) 0.641043 1.97293i 0.0248961 0.0766222i
\(664\) 22.6368 + 69.6688i 0.878477 + 2.70367i
\(665\) 9.51192 6.91081i 0.368856 0.267990i
\(666\) −3.76793 + 2.73756i −0.146004 + 0.106078i
\(667\) −0.278209 0.856239i −0.0107723 0.0331537i
\(668\) 31.6066 97.2751i 1.22290 3.76369i
\(669\) −3.51533 2.55404i −0.135911 0.0987448i
\(670\) −25.9732 −1.00343
\(671\) 42.9790 + 21.3649i 1.65919 + 0.824781i
\(672\) 4.02474 0.155258
\(673\) −38.0215 27.6242i −1.46562 1.06484i −0.981854 0.189638i \(-0.939268\pi\)
−0.483766 0.875197i \(-0.660732\pi\)
\(674\) 5.66950 17.4489i 0.218381 0.672108i
\(675\) 1.05379 + 3.24323i 0.0405604 + 0.124832i
\(676\) −3.39896 + 2.46949i −0.130729 + 0.0949804i
\(677\) −28.1649 + 20.4630i −1.08246 + 0.786456i −0.978111 0.208084i \(-0.933277\pi\)
−0.104353 + 0.994540i \(0.533277\pi\)
\(678\) −8.53717 26.2747i −0.327868 1.00907i
\(679\) 5.48071 16.8679i 0.210330 0.647331i
\(680\) −11.6004 8.42821i −0.444856 0.323207i
\(681\) −22.1478 −0.848705
\(682\) −9.28867 + 9.47469i −0.355681 + 0.362805i
\(683\) −24.2852 −0.929248 −0.464624 0.885508i \(-0.653811\pi\)
−0.464624 + 0.885508i \(0.653811\pi\)
\(684\) −16.5889 12.0526i −0.634294 0.460842i
\(685\) −3.47502 + 10.6950i −0.132774 + 0.408635i
\(686\) 15.2165 + 46.8317i 0.580970 + 1.78804i
\(687\) 16.9314 12.3013i 0.645971 0.469326i
\(688\) −28.0364 + 20.3697i −1.06888 + 0.776586i
\(689\) 0.797089 + 2.45319i 0.0303667 + 0.0934590i
\(690\) −0.156839 + 0.482702i −0.00597077 + 0.0183762i
\(691\) 35.9438 + 26.1147i 1.36737 + 0.993449i 0.997938 + 0.0641895i \(0.0204462\pi\)
0.369428 + 0.929260i \(0.379554\pi\)
\(692\) 33.6707 1.27997
\(693\) −6.24843 + 1.05326i −0.237358 + 0.0400099i
\(694\) 28.5479 1.08366
\(695\) 3.11527 + 2.26338i 0.118169 + 0.0858548i
\(696\) −9.43523 + 29.0387i −0.357642 + 1.10071i
\(697\) −2.42829 7.47350i −0.0919779 0.283079i
\(698\) −19.5756 + 14.2225i −0.740947 + 0.538330i
\(699\) −11.1219 + 8.08053i −0.420669 + 0.305634i
\(700\) −8.45866 26.0331i −0.319707 0.983958i
\(701\) −6.00995 + 18.4967i −0.226993 + 0.698612i 0.771091 + 0.636726i \(0.219712\pi\)
−0.998083 + 0.0618861i \(0.980288\pi\)
\(702\) 2.01466 + 1.46373i 0.0760383 + 0.0552450i
\(703\) −9.12797 −0.344268
\(704\) 2.55390 17.2284i 0.0962536 0.649321i
\(705\) 2.44156 0.0919544
\(706\) 30.2102 + 21.9490i 1.13697 + 0.826060i
\(707\) 11.7298 36.1005i 0.441144 1.35770i
\(708\) 8.72475 + 26.8520i 0.327896 + 1.00916i
\(709\) −3.18721 + 2.31565i −0.119698 + 0.0869659i −0.646024 0.763317i \(-0.723569\pi\)
0.526326 + 0.850283i \(0.323569\pi\)
\(710\) 35.7048 25.9410i 1.33998 0.973549i
\(711\) −2.13261 6.56350i −0.0799791 0.246150i
\(712\) 11.1277 34.2474i 0.417027 1.28348i
\(713\) −0.210080 0.152632i −0.00786757 0.00571612i
\(714\) 9.86976 0.369367
\(715\) −1.93540 3.70711i −0.0723798 0.138638i
\(716\) 66.6555 2.49103
\(717\) 9.34106 + 6.78668i 0.348848 + 0.253453i
\(718\) −11.8371 + 36.4308i −0.441756 + 1.35958i
\(719\) −10.2069 31.4135i −0.380652 1.17153i −0.939586 0.342314i \(-0.888789\pi\)
0.558934 0.829212i \(-0.311211\pi\)
\(720\) 5.35406 3.88995i 0.199534 0.144970i
\(721\) −5.27795 + 3.83466i −0.196561 + 0.142810i
\(722\) −3.70926 11.4159i −0.138044 0.424857i
\(723\) −6.04809 + 18.6141i −0.224931 + 0.692266i
\(724\) 41.8252 + 30.3878i 1.55442 + 1.12935i
\(725\) 18.9937 0.705410
\(726\) −0.543111 27.3874i −0.0201567 1.01644i
\(727\) −19.8138 −0.734853 −0.367427 0.930052i \(-0.619761\pi\)
−0.367427 + 0.930052i \(0.619761\pi\)
\(728\) −8.47321 6.15615i −0.314038 0.228162i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 10.7593 + 33.1137i 0.398219 + 1.22559i
\(731\) −11.0811 + 8.05087i −0.409848 + 0.297772i
\(732\) 49.1879 35.7371i 1.81804 1.32088i
\(733\) 9.82460 + 30.2370i 0.362880 + 1.11683i 0.951298 + 0.308273i \(0.0997509\pi\)
−0.588418 + 0.808557i \(0.700249\pi\)
\(734\) 16.0488 49.3931i 0.592371 1.82313i
\(735\) 3.41708 + 2.48266i 0.126041 + 0.0915742i
\(736\) −0.340510 −0.0125514
\(737\) 12.6968 + 24.3198i 0.467693 + 0.895831i
\(738\) 9.43312 0.347238
\(739\) −3.56988 2.59367i −0.131320 0.0954096i 0.520186 0.854053i \(-0.325863\pi\)
−0.651506 + 0.758643i \(0.725863\pi\)
\(740\) 3.06163 9.42273i 0.112548 0.346386i
\(741\) 1.50819 + 4.64172i 0.0554046 + 0.170518i
\(742\) −9.92850 + 7.21348i −0.364487 + 0.264815i
\(743\) −41.7830 + 30.3572i −1.53287 + 1.11370i −0.578255 + 0.815856i \(0.696266\pi\)
−0.954616 + 0.297840i \(0.903734\pi\)
\(744\) 2.72140 + 8.37559i 0.0997712 + 0.307064i
\(745\) 1.31296 4.04088i 0.0481032 0.148046i
\(746\) −56.0199 40.7009i −2.05104 1.49016i
\(747\) −13.3629 −0.488922
\(748\) −4.23865 + 28.5937i −0.154980 + 1.04549i
\(749\) −11.4790 −0.419434
\(750\) −21.3640 15.5219i −0.780105 0.566779i
\(751\) −14.2945 + 43.9941i −0.521616 + 1.60537i 0.249297 + 0.968427i \(0.419800\pi\)
−0.770913 + 0.636940i \(0.780200\pi\)
\(752\) 3.14062 + 9.66585i 0.114527 + 0.352477i
\(753\) 15.1285 10.9915i 0.551312 0.400551i
\(754\) 11.2212 8.15267i 0.408652 0.296903i
\(755\) 7.14150 + 21.9793i 0.259906 + 0.799908i
\(756\) −2.48045 + 7.63402i −0.0902129 + 0.277647i
\(757\) −7.53673 5.47576i −0.273927 0.199020i 0.442337 0.896849i \(-0.354149\pi\)
−0.716264 + 0.697829i \(0.754149\pi\)
\(758\) 35.6999 1.29668
\(759\) 0.528643 0.0891099i 0.0191885 0.00323449i
\(760\) 33.7352 1.22371
\(761\) 25.3709 + 18.4330i 0.919694 + 0.668196i 0.943448 0.331521i \(-0.107562\pi\)
−0.0237542 + 0.999718i \(0.507562\pi\)
\(762\) −8.24800 + 25.3847i −0.298794 + 0.919592i
\(763\) −3.59744 11.0718i −0.130236 0.400826i
\(764\) −9.45890 + 6.87229i −0.342211 + 0.248631i
\(765\) 2.11613 1.53746i 0.0765088 0.0555869i
\(766\) −0.0761333 0.234314i −0.00275081 0.00846612i
\(767\) 2.07665 6.39128i 0.0749836 0.230776i
\(768\) −26.3372 19.1351i −0.950361 0.690477i
\(769\) 11.2536 0.405816 0.202908 0.979198i \(-0.434961\pi\)
0.202908 + 0.979198i \(0.434961\pi\)
\(770\) 13.9288 14.2078i 0.501959 0.512012i
\(771\) 10.2001 0.367348
\(772\) −62.2441 45.2230i −2.24021 1.62761i
\(773\) −5.73080 + 17.6376i −0.206122 + 0.634380i 0.793543 + 0.608514i \(0.208234\pi\)
−0.999665 + 0.0258655i \(0.991766\pi\)
\(774\) −5.08094 15.6375i −0.182631 0.562080i
\(775\) 4.43208 3.22009i 0.159205 0.115669i
\(776\) 41.1704 29.9121i 1.47793 1.07378i
\(777\) 1.10419 + 3.39834i 0.0396125 + 0.121915i
\(778\) −7.23442 + 22.2653i −0.259367 + 0.798248i
\(779\) 14.9569 + 10.8668i 0.535888 + 0.389345i
\(780\) −5.29747 −0.189680
\(781\) −41.7436 20.7507i −1.49370 0.742520i
\(782\) −0.835023 −0.0298604
\(783\) −4.50605 3.27384i −0.161033 0.116997i
\(784\) −5.43309 + 16.7213i −0.194039 + 0.597190i
\(785\) 1.17205 + 3.60719i 0.0418322 + 0.128746i
\(786\) 33.2455 24.1543i 1.18583 0.861554i
\(787\) 36.7753 26.7188i 1.31090 0.952424i 0.310901 0.950442i \(-0.399369\pi\)
0.999998 0.00198155i \(-0.000630748\pi\)
\(788\) 3.54557 + 10.9122i 0.126306 + 0.388729i
\(789\) −0.544083 + 1.67451i −0.0193699 + 0.0596143i
\(790\) 17.5311 + 12.7371i 0.623729 + 0.453165i
\(791\) −21.1957 −0.753631
\(792\) −16.2808 8.09319i −0.578513 0.287579i
\(793\) −14.4715 −0.513896
\(794\) 12.3424 + 8.96729i 0.438016 + 0.318237i
\(795\) −1.00505 + 3.09322i −0.0356454 + 0.109705i
\(796\) −27.0490 83.2482i −0.958726 2.95065i
\(797\) 9.50516 6.90591i 0.336690 0.244620i −0.406574 0.913618i \(-0.633277\pi\)
0.743264 + 0.668998i \(0.233277\pi\)
\(798\) −18.7859 + 13.6487i −0.665013 + 0.483160i
\(799\) 1.24130 + 3.82031i 0.0439139 + 0.135153i
\(800\) 2.21990 6.83216i 0.0784854 0.241553i
\(801\) 5.31432 + 3.86108i 0.187772 + 0.136424i
\(802\) 75.6125 2.66997
\(803\) 25.7461 26.2617i 0.908560 0.926756i
\(804\) 34.7530 1.22564
\(805\) 0.315026 + 0.228880i 0.0111032 + 0.00806695i
\(806\) 1.23624 3.80476i 0.0435447 0.134017i
\(807\) 5.57249 + 17.1504i 0.196161 + 0.603722i
\(808\) 88.1126 64.0176i 3.09979 2.25213i
\(809\) 15.3353 11.1417i 0.539160 0.391723i −0.284613 0.958643i \(-0.591865\pi\)
0.823773 + 0.566920i \(0.191865\pi\)
\(810\) 0.970298 + 2.98627i 0.0340928 + 0.104927i
\(811\) −4.46416 + 13.7393i −0.156758 + 0.482451i −0.998335 0.0576864i \(-0.981628\pi\)
0.841577 + 0.540137i \(0.181628\pi\)
\(812\) 36.1696 + 26.2787i 1.26930 + 0.922203i
\(813\) 2.61429 0.0916871
\(814\) −15.2320 + 2.56756i −0.533882 + 0.0899930i
\(815\) −21.9078 −0.767397
\(816\) 8.80864 + 6.39985i 0.308364 + 0.224040i
\(817\) 9.95804 30.6477i 0.348388 1.07223i
\(818\) 13.9007 + 42.7819i 0.486026 + 1.49583i
\(819\) 1.54567 1.12299i 0.0540100 0.0392406i
\(820\) −16.2345 + 11.7950i −0.566933 + 0.411901i
\(821\) 3.26399 + 10.0455i 0.113914 + 0.350591i 0.991719 0.128427i \(-0.0409928\pi\)
−0.877805 + 0.479018i \(0.840993\pi\)
\(822\) 6.86310 21.1225i 0.239378 0.736730i
\(823\) −7.97204 5.79203i −0.277888 0.201897i 0.440108 0.897945i \(-0.354940\pi\)
−0.717996 + 0.696048i \(0.754940\pi\)
\(824\) −18.7189 −0.652105
\(825\) −1.65846 + 11.1879i −0.0577403 + 0.389513i
\(826\) 31.9730 1.11248
\(827\) 2.99180 + 2.17367i 0.104035 + 0.0755859i 0.638587 0.769550i \(-0.279519\pi\)
−0.534551 + 0.845136i \(0.679519\pi\)
\(828\) 0.209856 0.645870i 0.00729300 0.0224455i
\(829\) −8.15935 25.1119i −0.283386 0.872172i −0.986878 0.161469i \(-0.948377\pi\)
0.703492 0.710703i \(-0.251623\pi\)
\(830\) 33.9454 24.6627i 1.17826 0.856056i
\(831\) −25.9247 + 18.8354i −0.899319 + 0.653394i
\(832\) 1.62275 + 4.99431i 0.0562587 + 0.173147i
\(833\) −2.14736 + 6.60891i −0.0744018 + 0.228985i
\(834\) −6.15261 4.47013i −0.213047 0.154788i
\(835\) −30.6963 −1.06229
\(836\) −31.4740 60.2861i −1.08855 2.08504i
\(837\) −1.60649 −0.0555284
\(838\) −53.1374 38.6066i −1.83560 1.33364i
\(839\) −13.0433 + 40.1433i −0.450306 + 1.38590i 0.426253 + 0.904604i \(0.359833\pi\)
−0.876559 + 0.481295i \(0.840167\pi\)
\(840\) −4.08087 12.5596i −0.140803 0.433348i
\(841\) −1.63623 + 1.18879i −0.0564219 + 0.0409929i
\(842\) −47.4523 + 34.4761i −1.63531 + 1.18813i
\(843\) 7.37637 + 22.7021i 0.254056 + 0.781903i
\(844\) −16.7970 + 51.6958i −0.578176 + 1.77944i
\(845\) 1.02009 + 0.741137i 0.0350921 + 0.0254959i
\(846\) −4.82204 −0.165785
\(847\) −20.1123 6.09676i −0.691067 0.209487i
\(848\) −13.5385 −0.464914
\(849\) −16.4685 11.9650i −0.565196 0.410639i
\(850\) 5.44380 16.7543i 0.186721 0.574668i
\(851\) −0.0934189 0.287514i −0.00320236 0.00985584i
\(852\) −47.7741 + 34.7099i −1.63671 + 1.18914i
\(853\) −31.2896 + 22.7332i −1.07134 + 0.778371i −0.976152 0.217088i \(-0.930344\pi\)
−0.0951844 + 0.995460i \(0.530344\pi\)
\(854\) −21.2763 65.4817i −0.728060 2.24074i
\(855\) −1.90167 + 5.85273i −0.0650356 + 0.200159i
\(856\) −26.6462 19.3596i −0.910749 0.661698i
\(857\) −22.2215 −0.759072 −0.379536 0.925177i \(-0.623916\pi\)
−0.379536 + 0.925177i \(0.623916\pi\)
\(858\) 3.82238 + 7.32149i 0.130494 + 0.249952i
\(859\) 23.8601 0.814097 0.407049 0.913406i \(-0.366558\pi\)
0.407049 + 0.913406i \(0.366558\pi\)
\(860\) 28.2973 + 20.5592i 0.964930 + 0.701062i
\(861\) 2.23642 6.88299i 0.0762170 0.234572i
\(862\) 7.29969 + 22.4661i 0.248628 + 0.765200i
\(863\) 32.8199 23.8450i 1.11720 0.811694i 0.133418 0.991060i \(-0.457405\pi\)
0.983782 + 0.179366i \(0.0574046\pi\)
\(864\) −1.70427 + 1.23822i −0.0579803 + 0.0421251i
\(865\) −3.12267 9.61058i −0.106174 0.326769i
\(866\) 19.7101 60.6616i 0.669778 2.06136i
\(867\) −10.2718 7.46288i −0.348848 0.253453i
\(868\) 12.8951 0.437688
\(869\) 3.35632 22.6415i 0.113855 0.768061i
\(870\) 17.4888 0.592927
\(871\) −6.69208 4.86208i −0.226752 0.164745i
\(872\) 10.3221 31.7681i 0.349550 1.07580i
\(873\) 2.86866 + 8.82882i 0.0970893 + 0.298810i
\(874\) 1.58936 1.15474i 0.0537610 0.0390597i
\(875\) −16.3908 + 11.9086i −0.554109 + 0.402584i
\(876\) −14.3963 44.3071i −0.486404 1.49700i
\(877\) 5.58578 17.1913i 0.188618 0.580508i −0.811373 0.584528i \(-0.801280\pi\)
0.999992 + 0.00402011i \(0.00127965\pi\)
\(878\) −9.07495 6.59334i −0.306265 0.222514i
\(879\) −29.9701 −1.01087
\(880\) 21.6440 3.64839i 0.729620 0.122987i
\(881\) 20.4421 0.688713 0.344356 0.938839i \(-0.388097\pi\)
0.344356 + 0.938839i \(0.388097\pi\)
\(882\) −6.74868 4.90321i −0.227240 0.165100i
\(883\) 5.71729 17.5960i 0.192402 0.592152i −0.807595 0.589737i \(-0.799231\pi\)
0.999997 0.00241506i \(-0.000768737\pi\)
\(884\) −2.69325 8.28896i −0.0905837 0.278788i
\(885\) 6.85518 4.98058i 0.230434 0.167420i
\(886\) 45.3218 32.9282i 1.52262 1.10625i
\(887\) −6.59708 20.3037i −0.221508 0.681733i −0.998627 0.0523790i \(-0.983320\pi\)
0.777119 0.629354i \(-0.216680\pi\)
\(888\) −3.16823 + 9.75080i −0.106319 + 0.327215i
\(889\) 16.5668 + 12.0365i 0.555634 + 0.403692i
\(890\) −20.6259 −0.691381
\(891\) 2.32184 2.36834i 0.0777847 0.0793425i
\(892\) −18.2556 −0.611244
\(893\) −7.64571 5.55493i −0.255854 0.185889i
\(894\) −2.59308 + 7.98067i −0.0867255 + 0.266914i
\(895\) −6.18172 19.0254i −0.206632 0.635949i
\(896\) −26.7251 + 19.4169i −0.892822 + 0.648673i
\(897\) −0.130770 + 0.0950099i −0.00436628 + 0.00317229i
\(898\) −2.84664 8.76107i −0.0949937 0.292361i
\(899\) −2.76502 + 8.50986i −0.0922186 + 0.283820i
\(900\) 11.5909 + 8.42131i 0.386364 + 0.280710i
\(901\) −5.35093 −0.178265
\(902\) 28.0156 + 13.9265i 0.932817 + 0.463703i
\(903\) −12.6147 −0.419792
\(904\) −49.2014 35.7469i −1.63642 1.18893i
\(905\) 4.79461 14.7563i 0.159378 0.490516i
\(906\) −14.1043 43.4087i −0.468586 1.44216i
\(907\) −32.1360 + 23.3482i −1.06706 + 0.775263i −0.975381 0.220526i \(-0.929223\pi\)
−0.0916766 + 0.995789i \(0.529223\pi\)
\(908\) −75.2795 + 54.6937i −2.49824 + 1.81508i
\(909\) 6.13947 + 18.8954i 0.203633 + 0.626719i
\(910\) −1.85380 + 5.70542i −0.0614530 + 0.189133i
\(911\) −44.7247 32.4944i −1.48180 1.07659i −0.976973 0.213365i \(-0.931558\pi\)
−0.504824 0.863223i \(-0.668442\pi\)
\(912\) −25.6164 −0.848244
\(913\) −39.6866 19.7282i −1.31344 0.652909i
\(914\) 81.0608 2.68125
\(915\) −14.7621 10.7253i −0.488021 0.354568i
\(916\) 27.1710 83.6236i 0.897754 2.76300i
\(917\) −9.74255 29.9845i −0.321727 0.990175i
\(918\) −4.17932 + 3.03645i −0.137938 + 0.100218i
\(919\) 17.0582 12.3935i 0.562697 0.408824i −0.269748 0.962931i \(-0.586940\pi\)
0.832445 + 0.554107i \(0.186940\pi\)
\(920\) 0.345258 + 1.06260i 0.0113828 + 0.0350327i
\(921\) −3.09649 + 9.53000i −0.102033 + 0.314024i
\(922\) 24.6803 + 17.9313i 0.812804 + 0.590536i
\(923\) 14.0555 0.462642
\(924\) −18.6372 + 19.0104i −0.613118 + 0.625397i
\(925\) 6.37785 0.209702
\(926\) 52.3463 + 38.0318i 1.72021 + 1.24980i
\(927\) 1.05519 3.24755i 0.0346571 0.106663i
\(928\) 3.62577 + 11.1590i 0.119022 + 0.366311i
\(929\) 6.60183 4.79651i 0.216599 0.157368i −0.474195 0.880420i \(-0.657261\pi\)
0.690794 + 0.723051i \(0.257261\pi\)
\(930\) 4.08092 2.96496i 0.133819 0.0972249i
\(931\) −5.05211 15.5488i −0.165576 0.509592i
\(932\) −17.8481 + 54.9308i −0.584634 + 1.79932i
\(933\) −11.2263 8.15641i −0.367534 0.267029i
\(934\) 31.8124 1.04093
\(935\) 8.55455 1.44198i 0.279764 0.0471579i
\(936\) 5.48191 0.179182
\(937\) 22.0908 + 16.0499i 0.721676 + 0.524328i 0.886919 0.461925i \(-0.152841\pi\)
−0.165243 + 0.986253i \(0.552841\pi\)
\(938\) 12.1615 37.4293i 0.397087 1.22211i
\(939\) −6.17269 18.9976i −0.201438 0.619963i
\(940\) 8.29877 6.02941i 0.270676 0.196658i
\(941\) −32.9114 + 23.9115i −1.07288 + 0.779493i −0.976428 0.215844i \(-0.930750\pi\)
−0.0964527 + 0.995338i \(0.530750\pi\)
\(942\) −2.31478 7.12415i −0.0754195 0.232117i
\(943\) −0.189210 + 0.582330i −0.00616154 + 0.0189633i
\(944\) 28.5355 + 20.7322i 0.928751 + 0.674777i
\(945\) 2.40901 0.0783650
\(946\) 7.99643 53.9434i 0.259986 1.75385i
\(947\) −42.2692 −1.37356 −0.686782 0.726864i \(-0.740977\pi\)
−0.686782 + 0.726864i \(0.740977\pi\)
\(948\) −23.4572 17.0426i −0.761853 0.553519i
\(949\) −3.42658 + 10.5459i −0.111231 + 0.342335i
\(950\) 12.8077 + 39.4179i 0.415535 + 1.27889i
\(951\) −12.4786 + 9.06621i −0.404645 + 0.293992i
\(952\) 17.5773 12.7707i 0.569685 0.413900i
\(953\) 13.1569 + 40.4928i 0.426194 + 1.31169i 0.901847 + 0.432056i \(0.142212\pi\)
−0.475653 + 0.879633i \(0.657788\pi\)
\(954\) 1.98495 6.10905i 0.0642652 0.197788i
\(955\) 2.83878 + 2.06249i 0.0918607 + 0.0667407i
\(956\) 48.5096 1.56891
\(957\) −8.54928 16.3755i −0.276359 0.529345i
\(958\) 8.12201 0.262410
\(959\) −13.7851 10.0155i −0.445145 0.323417i
\(960\) −2.04612 + 6.29731i −0.0660383 + 0.203245i
\(961\) −8.78201 27.0283i −0.283291 0.871879i
\(962\) 3.76793 2.73756i 0.121483 0.0882625i
\(963\) 4.86075 3.53154i 0.156636 0.113802i
\(964\) 25.4101 + 78.2043i 0.818405 + 2.51879i
\(965\) −7.13532 + 21.9603i −0.229694 + 0.706926i
\(966\) −0.622171 0.452033i −0.0200180 0.0145439i
\(967\) 33.9106 1.09049 0.545246 0.838276i \(-0.316436\pi\)
0.545246 + 0.838276i \(0.316436\pi\)
\(968\) −36.4043 48.0722i −1.17008 1.54510i
\(969\) −10.1246 −0.325249
\(970\) −23.5818 17.1332i −0.757165 0.550113i
\(971\) 5.94329 18.2916i 0.190729 0.587004i −0.809271 0.587436i \(-0.800137\pi\)
1.00000 0.000431941i \(0.000137491\pi\)
\(972\) −1.29829 3.99572i −0.0416426 0.128163i
\(973\) −4.72036 + 3.42954i −0.151328 + 0.109946i
\(974\) 56.2995 40.9040i 1.80395 1.31065i
\(975\) −1.05379 3.24323i −0.0337483 0.103867i
\(976\) 23.4715 72.2378i 0.751304 2.31227i
\(977\) −7.51874 5.46268i −0.240546 0.174767i 0.460981 0.887410i \(-0.347498\pi\)
−0.701526 + 0.712643i \(0.747498\pi\)
\(978\) 43.2676 1.38354
\(979\) 10.0828 + 19.3128i 0.322247 + 0.617241i
\(980\) 17.7454 0.566857
\(981\) 4.92959 + 3.58155i 0.157390 + 0.114350i
\(982\) −8.93338 + 27.4941i −0.285076 + 0.877373i
\(983\) 0.0166207 + 0.0511532i 0.000530118 + 0.00163153i 0.951321 0.308201i \(-0.0997270\pi\)
−0.950791 + 0.309833i \(0.899727\pi\)
\(984\) 16.7997 12.2057i 0.535555 0.389104i
\(985\) 2.78582 2.02401i 0.0887635 0.0644905i
\(986\) 8.89137 + 27.3648i 0.283159 + 0.871474i
\(987\) −1.14322 + 3.51846i −0.0363890 + 0.111994i
\(988\) 16.5889 + 12.0526i 0.527765 + 0.383443i
\(989\) 1.06726 0.0339368
\(990\) −1.52706 + 10.3015i −0.0485332 + 0.327402i
\(991\) 26.5066 0.842011 0.421005 0.907058i \(-0.361677\pi\)
0.421005 + 0.907058i \(0.361677\pi\)
\(992\) 2.73788 + 1.98919i 0.0869278 + 0.0631568i
\(993\) −8.67086 + 26.6862i −0.275161 + 0.846860i
\(994\) 20.6647 + 63.5995i 0.655446 + 2.01725i
\(995\) −21.2528 + 15.4411i −0.673760 + 0.489516i
\(996\) −45.4199 + 32.9995i −1.43919 + 1.04563i
\(997\) 4.89437 + 15.0633i 0.155006 + 0.477060i 0.998162 0.0606100i \(-0.0193046\pi\)
−0.843155 + 0.537670i \(0.819305\pi\)
\(998\) −4.07171 + 12.5314i −0.128888 + 0.396675i
\(999\) −1.51307 1.09931i −0.0478715 0.0347807i
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 429.2.n.b.235.5 yes 20
11.3 even 5 inner 429.2.n.b.157.5 20
11.5 even 5 4719.2.a.bn.1.1 10
11.6 odd 10 4719.2.a.bi.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.b.157.5 20 11.3 even 5 inner
429.2.n.b.235.5 yes 20 1.1 even 1 trivial
4719.2.a.bi.1.10 10 11.6 odd 10
4719.2.a.bn.1.1 10 11.5 even 5