Properties

Label 475.2.n.b.39.15
Level $475$
Weight $2$
Character 475.39
Analytic conductor $3.793$
Analytic rank $0$
Dimension $96$
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] = [475,2,Mod(39,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.39");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.n (of order \(10\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 39.15
Character \(\chi\) \(=\) 475.39
Dual form 475.2.n.b.134.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.216810 + 0.298413i) q^{2} +(1.05547 + 0.342943i) q^{3} +(0.575990 - 1.77272i) q^{4} +(0.566211 - 2.16319i) q^{5} +(0.126498 + 0.389319i) q^{6} -0.311701i q^{7} +(1.35549 - 0.440426i) q^{8} +(-1.43064 - 1.03942i) q^{9} +O(q^{10})\) \(q+(0.216810 + 0.298413i) q^{2} +(1.05547 + 0.342943i) q^{3} +(0.575990 - 1.77272i) q^{4} +(0.566211 - 2.16319i) q^{5} +(0.126498 + 0.389319i) q^{6} -0.311701i q^{7} +(1.35549 - 0.440426i) q^{8} +(-1.43064 - 1.03942i) q^{9} +(0.768285 - 0.300037i) q^{10} +(-1.32359 + 0.961642i) q^{11} +(1.21588 - 1.67352i) q^{12} +(0.395753 - 0.544708i) q^{13} +(0.0930157 - 0.0675798i) q^{14} +(1.33947 - 2.08901i) q^{15} +(-2.59061 - 1.88219i) q^{16} +(1.23769 - 0.402151i) q^{17} -0.652280i q^{18} +(0.309017 + 0.951057i) q^{19} +(-3.50859 - 2.24971i) q^{20} +(0.106896 - 0.328991i) q^{21} +(-0.573933 - 0.186482i) q^{22} +(3.08863 + 4.25114i) q^{23} +1.58172 q^{24} +(-4.35881 - 2.44965i) q^{25} +0.248351 q^{26} +(-3.11049 - 4.28122i) q^{27} +(-0.552557 - 0.179537i) q^{28} +(0.707432 - 2.17725i) q^{29} +(0.913797 - 0.0532016i) q^{30} +(2.52866 + 7.78242i) q^{31} -4.03165i q^{32} +(-1.72679 + 0.561069i) q^{33} +(0.388351 + 0.282154i) q^{34} +(-0.674270 - 0.176489i) q^{35} +(-2.66664 + 1.93743i) q^{36} +(1.28888 - 1.77399i) q^{37} +(-0.216810 + 0.298413i) q^{38} +(0.604509 - 0.439202i) q^{39} +(-0.185232 - 3.18157i) q^{40} +(6.31601 + 4.58885i) q^{41} +(0.121351 - 0.0394294i) q^{42} -0.444096i q^{43} +(0.942344 + 2.90024i) q^{44} +(-3.05852 + 2.50623i) q^{45} +(-0.598949 + 1.84338i) q^{46} +(7.16588 + 2.32833i) q^{47} +(-2.08883 - 2.87503i) q^{48} +6.90284 q^{49} +(-0.214025 - 1.83183i) q^{50} +1.44426 q^{51} +(-0.737661 - 1.01530i) q^{52} +(3.11437 + 1.01192i) q^{53} +(0.603187 - 1.85642i) q^{54} +(1.33079 + 3.40766i) q^{55} +(-0.137281 - 0.422509i) q^{56} +1.10979i q^{57} +(0.803098 - 0.260942i) q^{58} +(3.76841 + 2.73791i) q^{59} +(-2.93169 - 3.57775i) q^{60} +(-7.79219 + 5.66136i) q^{61} +(-1.77414 + 2.44189i) q^{62} +(-0.323989 + 0.445933i) q^{63} +(-3.97812 + 2.89028i) q^{64} +(-0.954228 - 1.16451i) q^{65} +(-0.541816 - 0.393652i) q^{66} +(10.2882 - 3.34285i) q^{67} -2.42572i q^{68} +(1.80206 + 5.54617i) q^{69} +(-0.0935217 - 0.239475i) q^{70} +(1.11670 - 3.43684i) q^{71} +(-2.39702 - 0.778838i) q^{72} +(-1.00132 - 1.37819i) q^{73} +0.808824 q^{74} +(-3.76050 - 4.08035i) q^{75} +1.86394 q^{76} +(0.299745 + 0.412563i) q^{77} +(0.262127 + 0.0851702i) q^{78} +(-3.40838 + 10.4899i) q^{79} +(-5.53837 + 4.53827i) q^{80} +(-0.175441 - 0.539951i) q^{81} +2.87969i q^{82} +(-14.5727 + 4.73495i) q^{83} +(-0.521637 - 0.378991i) q^{84} +(-0.169135 - 2.90508i) q^{85} +(0.132524 - 0.0962843i) q^{86} +(1.49335 - 2.05541i) q^{87} +(-1.37058 + 1.88644i) q^{88} +(9.39557 - 6.82628i) q^{89} +(-1.41101 - 0.369328i) q^{90} +(-0.169786 - 0.123357i) q^{91} +(9.31508 - 3.02665i) q^{92} +9.08130i q^{93} +(0.858827 + 2.64320i) q^{94} +(2.23229 - 0.129965i) q^{95} +(1.38263 - 4.25528i) q^{96} +(-12.0883 - 3.92772i) q^{97} +(1.49660 + 2.05990i) q^{98} +2.89313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.216810 + 0.298413i 0.153308 + 0.211010i 0.878762 0.477261i \(-0.158370\pi\)
−0.725454 + 0.688270i \(0.758370\pi\)
\(3\) 1.05547 + 0.342943i 0.609376 + 0.197998i 0.597418 0.801930i \(-0.296193\pi\)
0.0119583 + 0.999928i \(0.496193\pi\)
\(4\) 0.575990 1.77272i 0.287995 0.886358i
\(5\) 0.566211 2.16319i 0.253217 0.967409i
\(6\) 0.126498 + 0.389319i 0.0516424 + 0.158939i
\(7\) 0.311701i 0.117812i −0.998264 0.0589060i \(-0.981239\pi\)
0.998264 0.0589060i \(-0.0187612\pi\)
\(8\) 1.35549 0.440426i 0.479239 0.155714i
\(9\) −1.43064 1.03942i −0.476881 0.346475i
\(10\) 0.768285 0.300037i 0.242953 0.0948799i
\(11\) −1.32359 + 0.961642i −0.399076 + 0.289946i −0.769165 0.639051i \(-0.779327\pi\)
0.370088 + 0.928997i \(0.379327\pi\)
\(12\) 1.21588 1.67352i 0.350995 0.483103i
\(13\) 0.395753 0.544708i 0.109762 0.151075i −0.750602 0.660755i \(-0.770236\pi\)
0.860364 + 0.509680i \(0.170236\pi\)
\(14\) 0.0930157 0.0675798i 0.0248595 0.0180615i
\(15\) 1.33947 2.08901i 0.345850 0.539379i
\(16\) −2.59061 1.88219i −0.647653 0.470547i
\(17\) 1.23769 0.402151i 0.300185 0.0975360i −0.155052 0.987906i \(-0.549555\pi\)
0.455237 + 0.890370i \(0.349555\pi\)
\(18\) 0.652280i 0.153744i
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i
\(20\) −3.50859 2.24971i −0.784545 0.503050i
\(21\) 0.106896 0.328991i 0.0233266 0.0717918i
\(22\) −0.573933 0.186482i −0.122363 0.0397581i
\(23\) 3.08863 + 4.25114i 0.644024 + 0.886424i 0.998822 0.0485195i \(-0.0154503\pi\)
−0.354798 + 0.934943i \(0.615450\pi\)
\(24\) 1.58172 0.322868
\(25\) −4.35881 2.44965i −0.871762 0.489930i
\(26\) 0.248351 0.0487056
\(27\) −3.11049 4.28122i −0.598614 0.823921i
\(28\) −0.552557 0.179537i −0.104424 0.0339293i
\(29\) 0.707432 2.17725i 0.131367 0.404305i −0.863640 0.504108i \(-0.831821\pi\)
0.995007 + 0.0998030i \(0.0318212\pi\)
\(30\) 0.913797 0.0532016i 0.166836 0.00971324i
\(31\) 2.52866 + 7.78242i 0.454161 + 1.39776i 0.872117 + 0.489297i \(0.162747\pi\)
−0.417956 + 0.908467i \(0.637253\pi\)
\(32\) 4.03165i 0.712701i
\(33\) −1.72679 + 0.561069i −0.300596 + 0.0976696i
\(34\) 0.388351 + 0.282154i 0.0666017 + 0.0483890i
\(35\) −0.674270 0.176489i −0.113972 0.0298320i
\(36\) −2.66664 + 1.93743i −0.444440 + 0.322904i
\(37\) 1.28888 1.77399i 0.211891 0.291642i −0.689821 0.723980i \(-0.742311\pi\)
0.901712 + 0.432337i \(0.142311\pi\)
\(38\) −0.216810 + 0.298413i −0.0351712 + 0.0484090i
\(39\) 0.604509 0.439202i 0.0967990 0.0703286i
\(40\) −0.185232 3.18157i −0.0292877 0.503050i
\(41\) 6.31601 + 4.58885i 0.986395 + 0.716658i 0.959129 0.282970i \(-0.0913198\pi\)
0.0272664 + 0.999628i \(0.491320\pi\)
\(42\) 0.121351 0.0394294i 0.0187249 0.00608409i
\(43\) 0.444096i 0.0677239i −0.999427 0.0338620i \(-0.989219\pi\)
0.999427 0.0338620i \(-0.0107807\pi\)
\(44\) 0.942344 + 2.90024i 0.142064 + 0.437227i
\(45\) −3.05852 + 2.50623i −0.455937 + 0.373606i
\(46\) −0.598949 + 1.84338i −0.0883103 + 0.271791i
\(47\) 7.16588 + 2.32833i 1.04525 + 0.339623i 0.780803 0.624777i \(-0.214810\pi\)
0.264448 + 0.964400i \(0.414810\pi\)
\(48\) −2.08883 2.87503i −0.301496 0.414974i
\(49\) 6.90284 0.986120
\(50\) −0.214025 1.83183i −0.0302678 0.259060i
\(51\) 1.44426 0.202238
\(52\) −0.737661 1.01530i −0.102295 0.140797i
\(53\) 3.11437 + 1.01192i 0.427792 + 0.138998i 0.514996 0.857192i \(-0.327793\pi\)
−0.0872042 + 0.996190i \(0.527793\pi\)
\(54\) 0.603187 1.85642i 0.0820834 0.252627i
\(55\) 1.33079 + 3.40766i 0.179443 + 0.459489i
\(56\) −0.137281 0.422509i −0.0183450 0.0564601i
\(57\) 1.10979i 0.146995i
\(58\) 0.803098 0.260942i 0.105452 0.0342634i
\(59\) 3.76841 + 2.73791i 0.490605 + 0.356446i 0.805417 0.592708i \(-0.201941\pi\)
−0.314812 + 0.949154i \(0.601941\pi\)
\(60\) −2.93169 3.57775i −0.378480 0.461885i
\(61\) −7.79219 + 5.66136i −0.997687 + 0.724862i −0.961591 0.274486i \(-0.911492\pi\)
−0.0360963 + 0.999348i \(0.511492\pi\)
\(62\) −1.77414 + 2.44189i −0.225316 + 0.310120i
\(63\) −0.323989 + 0.445933i −0.0408188 + 0.0561823i
\(64\) −3.97812 + 2.89028i −0.497266 + 0.361285i
\(65\) −0.954228 1.16451i −0.118357 0.144440i
\(66\) −0.541816 0.393652i −0.0666930 0.0484553i
\(67\) 10.2882 3.34285i 1.25691 0.408394i 0.396516 0.918028i \(-0.370219\pi\)
0.860391 + 0.509634i \(0.170219\pi\)
\(68\) 2.42572i 0.294161i
\(69\) 1.80206 + 5.54617i 0.216943 + 0.667681i
\(70\) −0.0935217 0.239475i −0.0111780 0.0286228i
\(71\) 1.11670 3.43684i 0.132527 0.407878i −0.862670 0.505768i \(-0.831209\pi\)
0.995197 + 0.0978900i \(0.0312093\pi\)
\(72\) −2.39702 0.778838i −0.282491 0.0917869i
\(73\) −1.00132 1.37819i −0.117195 0.161305i 0.746389 0.665510i \(-0.231786\pi\)
−0.863584 + 0.504204i \(0.831786\pi\)
\(74\) 0.808824 0.0940238
\(75\) −3.76050 4.08035i −0.434226 0.471159i
\(76\) 1.86394 0.213809
\(77\) 0.299745 + 0.412563i 0.0341591 + 0.0470159i
\(78\) 0.262127 + 0.0851702i 0.0296800 + 0.00964363i
\(79\) −3.40838 + 10.4899i −0.383473 + 1.18021i 0.554109 + 0.832444i \(0.313059\pi\)
−0.937582 + 0.347765i \(0.886941\pi\)
\(80\) −5.53837 + 4.53827i −0.619209 + 0.507395i
\(81\) −0.175441 0.539951i −0.0194934 0.0599945i
\(82\) 2.87969i 0.318008i
\(83\) −14.5727 + 4.73495i −1.59956 + 0.519729i −0.966999 0.254781i \(-0.917997\pi\)
−0.632562 + 0.774510i \(0.717997\pi\)
\(84\) −0.521637 0.378991i −0.0569152 0.0413513i
\(85\) −0.169135 2.90508i −0.0183452 0.315100i
\(86\) 0.132524 0.0962843i 0.0142904 0.0103826i
\(87\) 1.49335 2.05541i 0.160103 0.220364i
\(88\) −1.37058 + 1.88644i −0.146104 + 0.201095i
\(89\) 9.39557 6.82628i 0.995928 0.723584i 0.0347168 0.999397i \(-0.488947\pi\)
0.961211 + 0.275813i \(0.0889471\pi\)
\(90\) −1.41101 0.369328i −0.148733 0.0389306i
\(91\) −0.169786 0.123357i −0.0177984 0.0129313i
\(92\) 9.31508 3.02665i 0.971164 0.315550i
\(93\) 9.08130i 0.941687i
\(94\) 0.858827 + 2.64320i 0.0885812 + 0.272625i
\(95\) 2.23229 0.129965i 0.229028 0.0133341i
\(96\) 1.38263 4.25528i 0.141114 0.434303i
\(97\) −12.0883 3.92772i −1.22738 0.398800i −0.377615 0.925963i \(-0.623256\pi\)
−0.849764 + 0.527163i \(0.823256\pi\)
\(98\) 1.49660 + 2.05990i 0.151180 + 0.208081i
\(99\) 2.89313 0.290771
\(100\) −6.85316 + 6.31596i −0.685316 + 0.631596i
\(101\) −3.94038 −0.392083 −0.196041 0.980596i \(-0.562809\pi\)
−0.196041 + 0.980596i \(0.562809\pi\)
\(102\) 0.313131 + 0.430987i 0.0310046 + 0.0426741i
\(103\) −11.4473 3.71947i −1.12794 0.366490i −0.315147 0.949043i \(-0.602054\pi\)
−0.812793 + 0.582553i \(0.802054\pi\)
\(104\) 0.296537 0.912647i 0.0290779 0.0894924i
\(105\) −0.651146 0.417515i −0.0635453 0.0407453i
\(106\) 0.373256 + 1.14876i 0.0362538 + 0.111578i
\(107\) 0.622852i 0.0602134i 0.999547 + 0.0301067i \(0.00958470\pi\)
−0.999547 + 0.0301067i \(0.990415\pi\)
\(108\) −9.38099 + 3.04807i −0.902686 + 0.293301i
\(109\) −14.9586 10.8681i −1.43277 1.04097i −0.989492 0.144590i \(-0.953814\pi\)
−0.443283 0.896382i \(-0.646186\pi\)
\(110\) −0.728364 + 1.13594i −0.0694468 + 0.108308i
\(111\) 1.96875 1.43038i 0.186866 0.135766i
\(112\) −0.586680 + 0.807496i −0.0554361 + 0.0763012i
\(113\) −1.13093 + 1.55659i −0.106389 + 0.146432i −0.858892 0.512157i \(-0.828847\pi\)
0.752503 + 0.658589i \(0.228847\pi\)
\(114\) −0.331175 + 0.240613i −0.0310174 + 0.0225354i
\(115\) 10.9449 4.27427i 1.02061 0.398577i
\(116\) −3.45217 2.50815i −0.320526 0.232876i
\(117\) −1.13236 + 0.367927i −0.104687 + 0.0340149i
\(118\) 1.71815i 0.158168i
\(119\) −0.125351 0.385791i −0.0114909 0.0353654i
\(120\) 0.895589 3.42157i 0.0817557 0.312345i
\(121\) −2.57206 + 7.91599i −0.233824 + 0.719636i
\(122\) −3.37884 1.09785i −0.305906 0.0993950i
\(123\) 5.09265 + 7.00943i 0.459188 + 0.632019i
\(124\) 15.2525 1.36972
\(125\) −7.76707 + 8.04193i −0.694708 + 0.719292i
\(126\) −0.203316 −0.0181129
\(127\) −2.47761 3.41014i −0.219853 0.302601i 0.684817 0.728715i \(-0.259882\pi\)
−0.904669 + 0.426114i \(0.859882\pi\)
\(128\) −9.39364 3.05218i −0.830288 0.269777i
\(129\) 0.152299 0.468730i 0.0134092 0.0412693i
\(130\) 0.140619 0.537231i 0.0123331 0.0471183i
\(131\) 5.57069 + 17.1448i 0.486714 + 1.49795i 0.829483 + 0.558531i \(0.188635\pi\)
−0.342770 + 0.939419i \(0.611365\pi\)
\(132\) 3.38428i 0.294564i
\(133\) 0.296445 0.0963209i 0.0257051 0.00835208i
\(134\) 3.22814 + 2.34538i 0.278869 + 0.202610i
\(135\) −11.0223 + 4.30451i −0.948648 + 0.370473i
\(136\) 1.50057 1.09023i 0.128673 0.0934862i
\(137\) 1.41753 1.95106i 0.121107 0.166690i −0.744159 0.668003i \(-0.767149\pi\)
0.865266 + 0.501313i \(0.167149\pi\)
\(138\) −1.26435 + 1.74022i −0.107628 + 0.148138i
\(139\) −3.38373 + 2.45843i −0.287005 + 0.208521i −0.721967 0.691928i \(-0.756762\pi\)
0.434962 + 0.900449i \(0.356762\pi\)
\(140\) −0.701237 + 1.09363i −0.0592653 + 0.0924288i
\(141\) 6.76488 + 4.91498i 0.569706 + 0.413916i
\(142\) 1.26771 0.411903i 0.106384 0.0345661i
\(143\) 1.10154i 0.0921154i
\(144\) 1.74985 + 5.38548i 0.145821 + 0.448790i
\(145\) −4.30926 2.76310i −0.357864 0.229463i
\(146\) 0.194176 0.597612i 0.0160701 0.0494587i
\(147\) 7.28574 + 2.36728i 0.600918 + 0.195250i
\(148\) −2.40240 3.30662i −0.197476 0.271802i
\(149\) 7.06405 0.578709 0.289355 0.957222i \(-0.406559\pi\)
0.289355 + 0.957222i \(0.406559\pi\)
\(150\) 0.402317 2.00684i 0.0328490 0.163858i
\(151\) −10.7635 −0.875922 −0.437961 0.898994i \(-0.644299\pi\)
−0.437961 + 0.898994i \(0.644299\pi\)
\(152\) 0.837741 + 1.15305i 0.0679497 + 0.0935248i
\(153\) −2.18871 0.711154i −0.176946 0.0574934i
\(154\) −0.0581267 + 0.178895i −0.00468398 + 0.0144158i
\(155\) 18.2666 1.06349i 1.46721 0.0854216i
\(156\) −0.430388 1.32460i −0.0344586 0.106053i
\(157\) 7.14853i 0.570515i −0.958451 0.285257i \(-0.907921\pi\)
0.958451 0.285257i \(-0.0920791\pi\)
\(158\) −3.86930 + 1.25721i −0.307825 + 0.100018i
\(159\) 2.94010 + 2.13611i 0.233165 + 0.169404i
\(160\) −8.72123 2.28276i −0.689474 0.180468i
\(161\) 1.32508 0.962730i 0.104431 0.0758738i
\(162\) 0.123091 0.169420i 0.00967095 0.0133109i
\(163\) −4.54491 + 6.25553i −0.355985 + 0.489971i −0.949025 0.315202i \(-0.897928\pi\)
0.593040 + 0.805173i \(0.297928\pi\)
\(164\) 11.7727 8.55336i 0.919292 0.667905i
\(165\) 0.235971 + 4.05307i 0.0183703 + 0.315531i
\(166\) −4.57247 3.32210i −0.354893 0.257845i
\(167\) 18.3304 5.95592i 1.41845 0.460883i 0.503342 0.864087i \(-0.332104\pi\)
0.915110 + 0.403205i \(0.132104\pi\)
\(168\) 0.493025i 0.0380377i
\(169\) 3.87714 + 11.9326i 0.298241 + 0.917892i
\(170\) 0.830242 0.680321i 0.0636767 0.0521782i
\(171\) 0.546457 1.68182i 0.0417886 0.128612i
\(172\) −0.787255 0.255795i −0.0600276 0.0195042i
\(173\) 1.37427 + 1.89153i 0.104484 + 0.143810i 0.858057 0.513554i \(-0.171671\pi\)
−0.753573 + 0.657364i \(0.771671\pi\)
\(174\) 0.937134 0.0710440
\(175\) −0.763558 + 1.35865i −0.0577196 + 0.102704i
\(176\) 5.23889 0.394896
\(177\) 3.03850 + 4.18213i 0.228387 + 0.314348i
\(178\) 4.07410 + 1.32376i 0.305367 + 0.0992197i
\(179\) 2.13246 6.56303i 0.159387 0.490544i −0.839192 0.543836i \(-0.816971\pi\)
0.998579 + 0.0532920i \(0.0169714\pi\)
\(180\) 2.68115 + 6.86545i 0.199841 + 0.511720i
\(181\) 1.26933 + 3.90658i 0.0943483 + 0.290374i 0.987083 0.160208i \(-0.0512165\pi\)
−0.892735 + 0.450582i \(0.851216\pi\)
\(182\) 0.0774113i 0.00573811i
\(183\) −10.1659 + 3.30312i −0.751488 + 0.244173i
\(184\) 6.05893 + 4.40207i 0.446670 + 0.324525i
\(185\) −3.10771 3.79255i −0.228483 0.278834i
\(186\) −2.70998 + 1.96891i −0.198705 + 0.144368i
\(187\) −1.25147 + 1.72250i −0.0915165 + 0.125962i
\(188\) 8.25495 11.3620i 0.602054 0.828656i
\(189\) −1.33446 + 0.969543i −0.0970677 + 0.0705238i
\(190\) 0.522765 + 0.637966i 0.0379254 + 0.0462829i
\(191\) 3.33911 + 2.42601i 0.241610 + 0.175540i 0.702000 0.712177i \(-0.252291\pi\)
−0.460391 + 0.887716i \(0.652291\pi\)
\(192\) −5.18999 + 1.68633i −0.374555 + 0.121700i
\(193\) 3.39065i 0.244064i −0.992526 0.122032i \(-0.961059\pi\)
0.992526 0.122032i \(-0.0389411\pi\)
\(194\) −1.44877 4.45887i −0.104016 0.320128i
\(195\) −0.607798 1.55635i −0.0435253 0.111453i
\(196\) 3.97597 12.2368i 0.283998 0.874055i
\(197\) −8.00346 2.60048i −0.570223 0.185277i 0.00969302 0.999953i \(-0.496915\pi\)
−0.579916 + 0.814676i \(0.696915\pi\)
\(198\) 0.627259 + 0.863349i 0.0445774 + 0.0613555i
\(199\) −10.5811 −0.750072 −0.375036 0.927010i \(-0.622370\pi\)
−0.375036 + 0.927010i \(0.622370\pi\)
\(200\) −6.98722 1.40075i −0.494071 0.0990477i
\(201\) 12.0053 0.846790
\(202\) −0.854314 1.17586i −0.0601093 0.0827334i
\(203\) −0.678652 0.220507i −0.0476320 0.0154766i
\(204\) 0.831882 2.56027i 0.0582434 0.179255i
\(205\) 13.5028 11.0645i 0.943074 0.772778i
\(206\) −1.37196 4.22245i −0.0955888 0.294192i
\(207\) 9.29226i 0.645857i
\(208\) −2.05048 + 0.666243i −0.142176 + 0.0461956i
\(209\) −1.32359 0.961642i −0.0915544 0.0665181i
\(210\) −0.0165830 0.284832i −0.00114434 0.0196553i
\(211\) −2.94417 + 2.13907i −0.202685 + 0.147259i −0.684498 0.729015i \(-0.739979\pi\)
0.481813 + 0.876274i \(0.339979\pi\)
\(212\) 3.58770 4.93804i 0.246404 0.339146i
\(213\) 2.35728 3.24452i 0.161518 0.222311i
\(214\) −0.185867 + 0.135040i −0.0127056 + 0.00923117i
\(215\) −0.960665 0.251452i −0.0655168 0.0171489i
\(216\) −6.10181 4.43322i −0.415175 0.301642i
\(217\) 2.42579 0.788187i 0.164673 0.0535056i
\(218\) 6.82015i 0.461919i
\(219\) −0.584218 1.79804i −0.0394778 0.121500i
\(220\) 6.80734 0.396326i 0.458951 0.0267203i
\(221\) 0.270767 0.833334i 0.0182137 0.0560561i
\(222\) 0.853689 + 0.277380i 0.0572959 + 0.0186166i
\(223\) −7.67294 10.5609i −0.513818 0.707210i 0.470739 0.882272i \(-0.343987\pi\)
−0.984557 + 0.175062i \(0.943987\pi\)
\(224\) −1.25667 −0.0839647
\(225\) 3.68968 + 8.03522i 0.245979 + 0.535682i
\(226\) −0.709705 −0.0472089
\(227\) −12.8317 17.6614i −0.851673 1.17223i −0.983492 0.180953i \(-0.942082\pi\)
0.131819 0.991274i \(-0.457918\pi\)
\(228\) 1.96734 + 0.639226i 0.130290 + 0.0423338i
\(229\) −2.00674 + 6.17612i −0.132609 + 0.408129i −0.995210 0.0977551i \(-0.968834\pi\)
0.862601 + 0.505884i \(0.168834\pi\)
\(230\) 3.64845 + 2.33938i 0.240572 + 0.154254i
\(231\) 0.174886 + 0.538244i 0.0115066 + 0.0354138i
\(232\) 3.26282i 0.214215i
\(233\) −11.0402 + 3.58718i −0.723268 + 0.235004i −0.647440 0.762117i \(-0.724160\pi\)
−0.0758288 + 0.997121i \(0.524160\pi\)
\(234\) −0.355302 0.258142i −0.0232268 0.0168753i
\(235\) 9.09404 14.1828i 0.593230 0.925187i
\(236\) 7.02410 5.10331i 0.457230 0.332197i
\(237\) −7.19490 + 9.90292i −0.467359 + 0.643264i
\(238\) 0.0879477 0.121050i 0.00570080 0.00784648i
\(239\) 13.8228 10.0428i 0.894120 0.649616i −0.0428290 0.999082i \(-0.513637\pi\)
0.936949 + 0.349466i \(0.113637\pi\)
\(240\) −7.40195 + 2.89067i −0.477794 + 0.186592i
\(241\) −2.84984 2.07053i −0.183574 0.133374i 0.492203 0.870480i \(-0.336192\pi\)
−0.675777 + 0.737106i \(0.736192\pi\)
\(242\) −2.91988 + 0.948727i −0.187697 + 0.0609865i
\(243\) 15.2456i 0.978004i
\(244\) 5.54775 + 17.0742i 0.355158 + 1.09306i
\(245\) 3.90847 14.9322i 0.249703 0.953982i
\(246\) −0.987569 + 3.03942i −0.0629651 + 0.193787i
\(247\) 0.640342 + 0.208060i 0.0407440 + 0.0132385i
\(248\) 6.85517 + 9.43533i 0.435304 + 0.599144i
\(249\) −17.0049 −1.07764
\(250\) −4.08379 0.574226i −0.258282 0.0363172i
\(251\) 21.0563 1.32906 0.664530 0.747261i \(-0.268632\pi\)
0.664530 + 0.747261i \(0.268632\pi\)
\(252\) 0.603898 + 0.831194i 0.0380420 + 0.0523603i
\(253\) −8.17614 2.65659i −0.514030 0.167018i
\(254\) 0.480460 1.47870i 0.0301468 0.0927822i
\(255\) 0.817759 3.12422i 0.0512100 0.195646i
\(256\) 1.91319 + 5.88820i 0.119575 + 0.368013i
\(257\) 7.72037i 0.481583i 0.970577 + 0.240792i \(0.0774070\pi\)
−0.970577 + 0.240792i \(0.922593\pi\)
\(258\) 0.172895 0.0561770i 0.0107640 0.00349743i
\(259\) −0.552955 0.401745i −0.0343589 0.0249632i
\(260\) −2.61397 + 1.02083i −0.162112 + 0.0633091i
\(261\) −3.27517 + 2.37955i −0.202728 + 0.147290i
\(262\) −3.90846 + 5.37953i −0.241465 + 0.332349i
\(263\) 14.6052 20.1023i 0.900595 1.23956i −0.0696833 0.997569i \(-0.522199\pi\)
0.970278 0.241993i \(-0.0778011\pi\)
\(264\) −2.09355 + 1.52105i −0.128849 + 0.0936142i
\(265\) 3.95238 6.16403i 0.242793 0.378654i
\(266\) 0.0930157 + 0.0675798i 0.00570316 + 0.00414359i
\(267\) 12.2578 3.98279i 0.750163 0.243743i
\(268\) 20.1636i 1.23168i
\(269\) −3.50052 10.7735i −0.213430 0.656871i −0.999261 0.0384296i \(-0.987764\pi\)
0.785831 0.618441i \(-0.212236\pi\)
\(270\) −3.67426 2.35594i −0.223609 0.143378i
\(271\) 1.58819 4.88795i 0.0964757 0.296922i −0.891160 0.453690i \(-0.850107\pi\)
0.987635 + 0.156768i \(0.0501075\pi\)
\(272\) −3.96331 1.28776i −0.240311 0.0780818i
\(273\) −0.136900 0.188426i −0.00828554 0.0114041i
\(274\) 0.889555 0.0537400
\(275\) 8.12494 0.949292i 0.489953 0.0572445i
\(276\) 10.8698 0.654283
\(277\) −8.84310 12.1715i −0.531330 0.731313i 0.456002 0.889979i \(-0.349281\pi\)
−0.987332 + 0.158665i \(0.949281\pi\)
\(278\) −1.46725 0.476739i −0.0880000 0.0285929i
\(279\) 4.47162 13.7622i 0.267709 0.823923i
\(280\) −0.991698 + 0.0577370i −0.0592653 + 0.00345045i
\(281\) 2.26046 + 6.95699i 0.134848 + 0.415019i 0.995566 0.0940621i \(-0.0299852\pi\)
−0.860718 + 0.509081i \(0.829985\pi\)
\(282\) 3.08434i 0.183670i
\(283\) 27.2808 8.86407i 1.62167 0.526914i 0.649339 0.760499i \(-0.275046\pi\)
0.972336 + 0.233585i \(0.0750458\pi\)
\(284\) −5.44933 3.95917i −0.323358 0.234933i
\(285\) 2.40068 + 0.628374i 0.142204 + 0.0372216i
\(286\) −0.328714 + 0.238825i −0.0194373 + 0.0141220i
\(287\) 1.43035 1.96871i 0.0844309 0.116209i
\(288\) −4.19059 + 5.76785i −0.246933 + 0.339874i
\(289\) −12.3831 + 8.99687i −0.728419 + 0.529228i
\(290\) −0.109746 1.88500i −0.00644449 0.110691i
\(291\) −11.4118 8.29119i −0.668974 0.486038i
\(292\) −3.01989 + 0.981223i −0.176726 + 0.0574217i
\(293\) 20.8837i 1.22004i 0.792388 + 0.610018i \(0.208838\pi\)
−0.792388 + 0.610018i \(0.791162\pi\)
\(294\) 0.873193 + 2.68741i 0.0509256 + 0.156733i
\(295\) 8.05635 6.60157i 0.469059 0.384358i
\(296\) 0.965755 2.97229i 0.0561334 0.172761i
\(297\) 8.23400 + 2.67539i 0.477785 + 0.155242i
\(298\) 1.53155 + 2.10800i 0.0887206 + 0.122113i
\(299\) 3.53796 0.204606
\(300\) −9.39932 + 4.31606i −0.542670 + 0.249188i
\(301\) −0.138425 −0.00797869
\(302\) −2.33363 3.21197i −0.134286 0.184828i
\(303\) −4.15896 1.35133i −0.238926 0.0776317i
\(304\) 0.989525 3.04545i 0.0567532 0.174668i
\(305\) 7.83458 + 20.0615i 0.448607 + 1.14872i
\(306\) −0.262315 0.807323i −0.0149956 0.0461516i
\(307\) 6.69100i 0.381876i 0.981602 + 0.190938i \(0.0611529\pi\)
−0.981602 + 0.190938i \(0.938847\pi\)
\(308\) 0.904007 0.293730i 0.0515106 0.0167368i
\(309\) −10.8068 7.85157i −0.614775 0.446660i
\(310\) 4.27775 + 5.22043i 0.242960 + 0.296500i
\(311\) −14.1813 + 10.3033i −0.804146 + 0.584246i −0.912127 0.409907i \(-0.865561\pi\)
0.107982 + 0.994153i \(0.465561\pi\)
\(312\) 0.625972 0.861576i 0.0354387 0.0487772i
\(313\) 16.8870 23.2430i 0.954510 1.31377i 0.00501576 0.999987i \(-0.498403\pi\)
0.949495 0.313783i \(-0.101597\pi\)
\(314\) 2.13321 1.54987i 0.120384 0.0874643i
\(315\) 0.781193 + 0.953344i 0.0440153 + 0.0537149i
\(316\) 16.6325 + 12.0842i 0.935649 + 0.679789i
\(317\) 20.6565 6.71172i 1.16019 0.376968i 0.335215 0.942142i \(-0.391191\pi\)
0.824972 + 0.565174i \(0.191191\pi\)
\(318\) 1.34049i 0.0751711i
\(319\) 1.15739 + 3.56207i 0.0648013 + 0.199438i
\(320\) 3.99977 + 10.2420i 0.223594 + 0.572543i
\(321\) −0.213603 + 0.657402i −0.0119221 + 0.0366926i
\(322\) 0.574583 + 0.186693i 0.0320202 + 0.0104040i
\(323\) 0.764937 + 1.05285i 0.0425623 + 0.0585819i
\(324\) −1.05823 −0.0587906
\(325\) −3.05935 + 1.40482i −0.169702 + 0.0779254i
\(326\) −2.85211 −0.157964
\(327\) −12.0612 16.6009i −0.666988 0.918030i
\(328\) 10.5824 + 3.43842i 0.584313 + 0.189855i
\(329\) 0.725745 2.23361i 0.0400116 0.123143i
\(330\) −1.15833 + 0.949162i −0.0637639 + 0.0522497i
\(331\) 5.83213 + 17.9495i 0.320563 + 0.986591i 0.973404 + 0.229096i \(0.0735771\pi\)
−0.652841 + 0.757495i \(0.726423\pi\)
\(332\) 28.5605i 1.56746i
\(333\) −3.68786 + 1.19826i −0.202093 + 0.0656641i
\(334\) 5.75154 + 4.17874i 0.314710 + 0.228650i
\(335\) −1.40592 24.1482i −0.0768134 1.31936i
\(336\) −0.896149 + 0.651090i −0.0488889 + 0.0355199i
\(337\) −19.4366 + 26.7522i −1.05878 + 1.45728i −0.177837 + 0.984060i \(0.556910\pi\)
−0.880942 + 0.473224i \(0.843090\pi\)
\(338\) −2.72024 + 3.74409i −0.147962 + 0.203652i
\(339\) −1.72749 + 1.25509i −0.0938243 + 0.0681673i
\(340\) −5.24729 1.37347i −0.284574 0.0744867i
\(341\) −10.8308 7.86904i −0.586521 0.426132i
\(342\) 0.620355 0.201566i 0.0335450 0.0108994i
\(343\) 4.33353i 0.233989i
\(344\) −0.195591 0.601968i −0.0105456 0.0324560i
\(345\) 13.0178 0.757901i 0.700854 0.0408040i
\(346\) −0.266500 + 0.820202i −0.0143271 + 0.0440943i
\(347\) −21.1370 6.86782i −1.13469 0.368684i −0.319335 0.947642i \(-0.603460\pi\)
−0.815357 + 0.578958i \(0.803460\pi\)
\(348\) −2.78351 3.83118i −0.149212 0.205373i
\(349\) −28.9814 −1.55134 −0.775671 0.631138i \(-0.782588\pi\)
−0.775671 + 0.631138i \(0.782588\pi\)
\(350\) −0.570984 + 0.0667120i −0.0305204 + 0.00356591i
\(351\) −3.56300 −0.190179
\(352\) 3.87700 + 5.33623i 0.206645 + 0.284422i
\(353\) 25.8928 + 8.41307i 1.37813 + 0.447782i 0.902055 0.431621i \(-0.142058\pi\)
0.476078 + 0.879403i \(0.342058\pi\)
\(354\) −0.589227 + 1.81345i −0.0313171 + 0.0963840i
\(355\) −6.80226 4.36161i −0.361026 0.231490i
\(356\) −6.68930 20.5875i −0.354532 1.09114i
\(357\) 0.450179i 0.0238260i
\(358\) 2.42083 0.786576i 0.127945 0.0415718i
\(359\) −7.15276 5.19678i −0.377508 0.274276i 0.382809 0.923827i \(-0.374957\pi\)
−0.760317 + 0.649552i \(0.774957\pi\)
\(360\) −3.04199 + 4.74422i −0.160327 + 0.250043i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) −0.890573 + 1.22577i −0.0468075 + 0.0644250i
\(363\) −5.42947 + 7.47302i −0.284973 + 0.392232i
\(364\) −0.316471 + 0.229930i −0.0165876 + 0.0120516i
\(365\) −3.54826 + 1.38569i −0.185724 + 0.0725304i
\(366\) −3.18977 2.31750i −0.166732 0.121138i
\(367\) 10.7117 3.48045i 0.559148 0.181678i −0.0157900 0.999875i \(-0.505026\pi\)
0.574938 + 0.818197i \(0.305026\pi\)
\(368\) 16.8264i 0.877138i
\(369\) −4.26620 13.1300i −0.222090 0.683522i
\(370\) 0.457965 1.74964i 0.0238085 0.0909595i
\(371\) 0.315417 0.970754i 0.0163756 0.0503990i
\(372\) 16.0986 + 5.23074i 0.834672 + 0.271201i
\(373\) 10.2635 + 14.1265i 0.531422 + 0.731440i 0.987346 0.158579i \(-0.0506911\pi\)
−0.455924 + 0.890019i \(0.650691\pi\)
\(374\) −0.785347 −0.0406094
\(375\) −10.9558 + 5.82435i −0.565757 + 0.300768i
\(376\) 10.7388 0.553809
\(377\) −0.905997 1.24700i −0.0466612 0.0642236i
\(378\) −0.578648 0.188014i −0.0297625 0.00967041i
\(379\) −5.96126 + 18.3469i −0.306209 + 0.942416i 0.673014 + 0.739630i \(0.264999\pi\)
−0.979223 + 0.202786i \(0.935001\pi\)
\(380\) 1.05539 4.03207i 0.0541401 0.206841i
\(381\) −1.44556 4.44898i −0.0740584 0.227928i
\(382\) 1.52242i 0.0778936i
\(383\) 5.86963 1.90716i 0.299924 0.0974512i −0.155189 0.987885i \(-0.549599\pi\)
0.455113 + 0.890434i \(0.349599\pi\)
\(384\) −8.86798 6.44297i −0.452542 0.328791i
\(385\) 1.06217 0.414808i 0.0541333 0.0211406i
\(386\) 1.01181 0.735126i 0.0515000 0.0374169i
\(387\) −0.461603 + 0.635343i −0.0234646 + 0.0322963i
\(388\) −13.9255 + 19.1668i −0.706958 + 0.973045i
\(389\) −2.03727 + 1.48016i −0.103294 + 0.0750473i −0.638233 0.769843i \(-0.720334\pi\)
0.534939 + 0.844890i \(0.320334\pi\)
\(390\) 0.332659 0.518807i 0.0168448 0.0262708i
\(391\) 5.53239 + 4.01951i 0.279785 + 0.203276i
\(392\) 9.35675 3.04019i 0.472587 0.153553i
\(393\) 20.0063i 1.00918i
\(394\) −0.959210 2.95215i −0.0483243 0.148727i
\(395\) 20.7619 + 13.3125i 1.04464 + 0.669825i
\(396\) 1.66642 5.12870i 0.0837406 0.257727i
\(397\) −35.9085 11.6674i −1.80220 0.585569i −0.802261 0.596974i \(-0.796370\pi\)
−0.999935 + 0.0114046i \(0.996370\pi\)
\(398\) −2.29408 3.15753i −0.114992 0.158273i
\(399\) 0.345922 0.0173178
\(400\) 6.68128 + 14.5502i 0.334064 + 0.727509i
\(401\) −38.8483 −1.93999 −0.969995 0.243126i \(-0.921827\pi\)
−0.969995 + 0.243126i \(0.921827\pi\)
\(402\) 2.60287 + 3.58255i 0.129819 + 0.178681i
\(403\) 5.23987 + 1.70254i 0.261017 + 0.0848094i
\(404\) −2.26962 + 6.98518i −0.112918 + 0.347526i
\(405\) −1.26735 + 0.0737858i −0.0629753 + 0.00366645i
\(406\) −0.0813360 0.250327i −0.00403664 0.0124235i
\(407\) 3.58747i 0.177824i
\(408\) 1.95769 0.636092i 0.0969201 0.0314913i
\(409\) 6.56132 + 4.76708i 0.324436 + 0.235717i 0.738066 0.674728i \(-0.235739\pi\)
−0.413630 + 0.910445i \(0.635739\pi\)
\(410\) 6.22932 + 1.63051i 0.307644 + 0.0805252i
\(411\) 2.16526 1.57315i 0.106804 0.0775979i
\(412\) −13.1871 + 18.1505i −0.649682 + 0.894211i
\(413\) 0.853410 1.17462i 0.0419936 0.0577992i
\(414\) 2.77293 2.01465i 0.136282 0.0990148i
\(415\) 1.99140 + 34.2045i 0.0977540 + 1.67903i
\(416\) −2.19607 1.59554i −0.107671 0.0782277i
\(417\) −4.41453 + 1.43437i −0.216180 + 0.0702413i
\(418\) 0.603469i 0.0295166i
\(419\) −2.35098 7.23556i −0.114853 0.353480i 0.877064 0.480374i \(-0.159499\pi\)
−0.991916 + 0.126894i \(0.959499\pi\)
\(420\) −1.11519 + 0.913812i −0.0544156 + 0.0445895i
\(421\) 4.29401 13.2156i 0.209277 0.644089i −0.790233 0.612806i \(-0.790041\pi\)
0.999511 0.0312832i \(-0.00995939\pi\)
\(422\) −1.27665 0.414809i −0.0621463 0.0201926i
\(423\) −7.83169 10.7794i −0.380790 0.524112i
\(424\) 4.66719 0.226659
\(425\) −6.38001 1.27902i −0.309476 0.0620414i
\(426\) 1.47929 0.0716717
\(427\) 1.76465 + 2.42883i 0.0853974 + 0.117539i
\(428\) 1.10414 + 0.358757i 0.0533706 + 0.0173412i
\(429\) −0.377765 + 1.16264i −0.0182387 + 0.0561329i
\(430\) −0.133245 0.341192i −0.00642564 0.0164537i
\(431\) 3.38670 + 10.4232i 0.163132 + 0.502067i 0.998894 0.0470242i \(-0.0149738\pi\)
−0.835762 + 0.549092i \(0.814974\pi\)
\(432\) 16.9455i 0.815291i
\(433\) 34.3618 11.1648i 1.65132 0.536547i 0.672296 0.740283i \(-0.265308\pi\)
0.979026 + 0.203736i \(0.0653083\pi\)
\(434\) 0.761140 + 0.553001i 0.0365359 + 0.0265449i
\(435\) −3.60071 4.39419i −0.172641 0.210685i
\(436\) −27.8820 + 20.2575i −1.33531 + 0.970156i
\(437\) −3.08863 + 4.25114i −0.147749 + 0.203360i
\(438\) 0.409894 0.564170i 0.0195855 0.0269571i
\(439\) 12.6712 9.20616i 0.604763 0.439386i −0.242803 0.970076i \(-0.578067\pi\)
0.847566 + 0.530689i \(0.178067\pi\)
\(440\) 3.30470 + 4.03295i 0.157545 + 0.192263i
\(441\) −9.87551 7.17498i −0.470262 0.341666i
\(442\) 0.307383 0.0998747i 0.0146207 0.00475055i
\(443\) 16.2985i 0.774364i −0.922003 0.387182i \(-0.873449\pi\)
0.922003 0.387182i \(-0.126551\pi\)
\(444\) −1.40168 4.31392i −0.0665207 0.204730i
\(445\) −9.44668 24.1895i −0.447816 1.14669i
\(446\) 1.48794 4.57941i 0.0704561 0.216841i
\(447\) 7.45589 + 2.42257i 0.352652 + 0.114583i
\(448\) 0.900902 + 1.23999i 0.0425636 + 0.0585838i
\(449\) −19.0042 −0.896865 −0.448432 0.893817i \(-0.648018\pi\)
−0.448432 + 0.893817i \(0.648018\pi\)
\(450\) −1.59786 + 2.84316i −0.0753237 + 0.134028i
\(451\) −12.7726 −0.601439
\(452\) 2.10799 + 2.90140i 0.0991516 + 0.136471i
\(453\) −11.3606 3.69127i −0.533766 0.173431i
\(454\) 2.48834 7.65832i 0.116784 0.359423i
\(455\) −0.362979 + 0.297434i −0.0170167 + 0.0139439i
\(456\) 0.488779 + 1.50431i 0.0228892 + 0.0704457i
\(457\) 35.4316i 1.65742i 0.559677 + 0.828711i \(0.310925\pi\)
−0.559677 + 0.828711i \(0.689075\pi\)
\(458\) −2.27812 + 0.740205i −0.106449 + 0.0345875i
\(459\) −5.57153 4.04796i −0.260057 0.188942i
\(460\) −1.27293 21.8640i −0.0593508 1.01942i
\(461\) −11.6050 + 8.43155i −0.540500 + 0.392696i −0.824271 0.566196i \(-0.808415\pi\)
0.283771 + 0.958892i \(0.408415\pi\)
\(462\) −0.122702 + 0.168885i −0.00570861 + 0.00785723i
\(463\) 12.1165 16.6769i 0.563102 0.775043i −0.428615 0.903487i \(-0.640998\pi\)
0.991717 + 0.128444i \(0.0409983\pi\)
\(464\) −5.93068 + 4.30889i −0.275325 + 0.200035i
\(465\) 19.6446 + 5.14193i 0.910997 + 0.238452i
\(466\) −3.46409 2.51681i −0.160471 0.116589i
\(467\) 13.7502 4.46771i 0.636284 0.206741i 0.0269271 0.999637i \(-0.491428\pi\)
0.609357 + 0.792896i \(0.291428\pi\)
\(468\) 2.21928i 0.102586i
\(469\) −1.04197 3.20685i −0.0481137 0.148079i
\(470\) 6.20402 0.361200i 0.286170 0.0166609i
\(471\) 2.45154 7.54506i 0.112961 0.347658i
\(472\) 6.31390 + 2.05151i 0.290621 + 0.0944285i
\(473\) 0.427061 + 0.587799i 0.0196363 + 0.0270270i
\(474\) −4.51509 −0.207385
\(475\) 0.982808 4.90246i 0.0450943 0.224940i
\(476\) −0.756098 −0.0346557
\(477\) −3.40375 4.68485i −0.155847 0.214505i
\(478\) 5.99382 + 1.94751i 0.274151 + 0.0890770i
\(479\) −2.22660 + 6.85276i −0.101736 + 0.313111i −0.988950 0.148246i \(-0.952637\pi\)
0.887215 + 0.461357i \(0.152637\pi\)
\(480\) −8.42214 5.40027i −0.384416 0.246488i
\(481\) −0.456228 1.40412i −0.0208022 0.0640226i
\(482\) 1.29934i 0.0591833i
\(483\) 1.72875 0.561704i 0.0786608 0.0255584i
\(484\) 12.5513 + 9.11907i 0.570514 + 0.414503i
\(485\) −15.3409 + 23.9254i −0.696596 + 1.08640i
\(486\) −4.54948 + 3.30539i −0.206368 + 0.149935i
\(487\) −6.04434 + 8.31933i −0.273895 + 0.376985i −0.923700 0.383117i \(-0.874851\pi\)
0.649805 + 0.760101i \(0.274851\pi\)
\(488\) −8.06884 + 11.1058i −0.365259 + 0.502736i
\(489\) −6.94231 + 5.04388i −0.313942 + 0.228092i
\(490\) 5.30335 2.07111i 0.239581 0.0935630i
\(491\) −11.1681 8.11408i −0.504008 0.366183i 0.306538 0.951858i \(-0.400829\pi\)
−0.810546 + 0.585675i \(0.800829\pi\)
\(492\) 15.3590 4.99045i 0.692439 0.224987i
\(493\) 2.97927i 0.134179i
\(494\) 0.0767447 + 0.236196i 0.00345291 + 0.0106270i
\(495\) 1.63812 6.25841i 0.0736282 0.281294i
\(496\) 8.09721 24.9206i 0.363575 1.11897i
\(497\) −1.07127 0.348075i −0.0480528 0.0156133i
\(498\) −3.68682 5.07447i −0.165210 0.227393i
\(499\) −34.7698 −1.55651 −0.778255 0.627949i \(-0.783895\pi\)
−0.778255 + 0.627949i \(0.783895\pi\)
\(500\) 9.78230 + 18.4009i 0.437478 + 0.822912i
\(501\) 21.3898 0.955624
\(502\) 4.56521 + 6.28347i 0.203755 + 0.280445i
\(503\) 28.5005 + 9.26036i 1.27077 + 0.412899i 0.865321 0.501218i \(-0.167114\pi\)
0.405451 + 0.914117i \(0.367114\pi\)
\(504\) −0.242765 + 0.747153i −0.0108136 + 0.0332808i
\(505\) −2.23109 + 8.52381i −0.0992822 + 0.379305i
\(506\) −0.979906 3.01584i −0.0435622 0.134071i
\(507\) 13.9241i 0.618392i
\(508\) −7.47229 + 2.42790i −0.331529 + 0.107720i
\(509\) −8.23792 5.98520i −0.365139 0.265289i 0.390053 0.920792i \(-0.372457\pi\)
−0.755192 + 0.655503i \(0.772457\pi\)
\(510\) 1.10961 0.433332i 0.0491342 0.0191883i
\(511\) −0.429585 + 0.312111i −0.0190037 + 0.0138070i
\(512\) −12.9535 + 17.8290i −0.572469 + 0.787936i
\(513\) 3.11049 4.28122i 0.137331 0.189020i
\(514\) −2.30386 + 1.67385i −0.101619 + 0.0738304i
\(515\) −14.5275 + 22.6568i −0.640160 + 0.998378i
\(516\) −0.743201 0.539967i −0.0327176 0.0237707i
\(517\) −11.7237 + 3.80925i −0.515607 + 0.167531i
\(518\) 0.252111i 0.0110771i
\(519\) 0.801819 + 2.46775i 0.0351960 + 0.108322i
\(520\) −1.80633 1.15822i −0.0792128 0.0507912i
\(521\) 4.00401 12.3231i 0.175419 0.539884i −0.824233 0.566250i \(-0.808394\pi\)
0.999652 + 0.0263663i \(0.00839362\pi\)
\(522\) −1.42018 0.461444i −0.0621595 0.0201968i
\(523\) −8.57687 11.8050i −0.375040 0.516199i 0.579222 0.815170i \(-0.303357\pi\)
−0.954262 + 0.298971i \(0.903357\pi\)
\(524\) 33.6016 1.46789
\(525\) −1.27185 + 1.17215i −0.0555081 + 0.0511570i
\(526\) 9.16534 0.399628
\(527\) 6.25942 + 8.61536i 0.272665 + 0.375291i
\(528\) 5.52949 + 1.79664i 0.240640 + 0.0781887i
\(529\) −1.42513 + 4.38611i −0.0619623 + 0.190700i
\(530\) 2.69634 0.156982i 0.117122 0.00681886i
\(531\) −2.54541 7.83395i −0.110461 0.339965i
\(532\) 0.580993i 0.0251892i
\(533\) 4.99916 1.62433i 0.216538 0.0703574i
\(534\) 3.84612 + 2.79437i 0.166438 + 0.120924i
\(535\) 1.34735 + 0.352666i 0.0582510 + 0.0152471i
\(536\) 12.4733 9.06241i 0.538766 0.391437i
\(537\) 4.50149 6.19577i 0.194254 0.267367i
\(538\) 2.45600 3.38040i 0.105886 0.145739i
\(539\) −9.13651 + 6.63806i −0.393537 + 0.285921i
\(540\) 1.28194 + 22.0188i 0.0551659 + 0.947536i
\(541\) −18.4539 13.4075i −0.793394 0.576435i 0.115575 0.993299i \(-0.463129\pi\)
−0.908969 + 0.416864i \(0.863129\pi\)
\(542\) 1.80296 0.585818i 0.0774439 0.0251630i
\(543\) 4.55859i 0.195628i
\(544\) −1.62133 4.98995i −0.0695141 0.213942i
\(545\) −31.9795 + 26.2047i −1.36985 + 1.12249i
\(546\) 0.0265477 0.0817053i 0.00113613 0.00349666i
\(547\) 5.23210 + 1.70001i 0.223708 + 0.0726873i 0.418727 0.908112i \(-0.362477\pi\)
−0.195018 + 0.980800i \(0.562477\pi\)
\(548\) −2.64219 3.63666i −0.112869 0.155350i
\(549\) 17.0324 0.726925
\(550\) 2.04485 + 2.21877i 0.0871926 + 0.0946088i
\(551\) 2.28930 0.0975273
\(552\) 4.88536 + 6.72412i 0.207935 + 0.286198i
\(553\) 3.26972 + 1.06240i 0.139043 + 0.0451777i
\(554\) 1.71486 5.27779i 0.0728573 0.224232i
\(555\) −1.97946 5.06869i −0.0840235 0.215154i
\(556\) 2.40909 + 7.41443i 0.102168 + 0.314442i
\(557\) 42.1332i 1.78524i 0.450809 + 0.892620i \(0.351135\pi\)
−0.450809 + 0.892620i \(0.648865\pi\)
\(558\) 5.07632 1.64940i 0.214898 0.0698245i
\(559\) −0.241902 0.175752i −0.0102314 0.00743353i
\(560\) 1.41459 + 1.72632i 0.0597771 + 0.0729502i
\(561\) −1.91161 + 1.38886i −0.0807082 + 0.0586379i
\(562\) −1.58597 + 2.18290i −0.0668999 + 0.0920799i
\(563\) −13.5153 + 18.6022i −0.569603 + 0.783991i −0.992508 0.122183i \(-0.961010\pi\)
0.422905 + 0.906174i \(0.361010\pi\)
\(564\) 12.6094 9.16124i 0.530950 0.385758i
\(565\) 2.72687 + 3.32779i 0.114720 + 0.140001i
\(566\) 8.55990 + 6.21913i 0.359799 + 0.261409i
\(567\) −0.168303 + 0.0546850i −0.00706807 + 0.00229656i
\(568\) 5.15043i 0.216107i
\(569\) −8.32882 25.6335i −0.349162 1.07461i −0.959318 0.282329i \(-0.908893\pi\)
0.610155 0.792282i \(-0.291107\pi\)
\(570\) 0.332977 + 0.852633i 0.0139469 + 0.0357129i
\(571\) 5.08090 15.6374i 0.212629 0.654405i −0.786684 0.617355i \(-0.788204\pi\)
0.999313 0.0370495i \(-0.0117959\pi\)
\(572\) 1.95272 + 0.634476i 0.0816472 + 0.0265288i
\(573\) 2.69235 + 3.70570i 0.112474 + 0.154808i
\(574\) 0.897602 0.0374652
\(575\) −3.04897 26.0960i −0.127151 1.08828i
\(576\) 8.69550 0.362313
\(577\) −22.4481 30.8972i −0.934529 1.28627i −0.958067 0.286545i \(-0.907493\pi\)
0.0235381 0.999723i \(-0.492507\pi\)
\(578\) −5.36957 1.74468i −0.223344 0.0725690i
\(579\) 1.16280 3.57873i 0.0483243 0.148727i
\(580\) −7.38027 + 6.04757i −0.306449 + 0.251112i
\(581\) 1.47589 + 4.54232i 0.0612303 + 0.188447i
\(582\) 5.20305i 0.215673i
\(583\) −5.09525 + 1.65555i −0.211024 + 0.0685657i
\(584\) −1.96427 1.42713i −0.0812821 0.0590549i
\(585\) 0.154741 + 2.65785i 0.00639774 + 0.109888i
\(586\) −6.23195 + 4.52778i −0.257440 + 0.187041i
\(587\) 13.7033 18.8610i 0.565597 0.778478i −0.426427 0.904522i \(-0.640228\pi\)
0.992025 + 0.126044i \(0.0402280\pi\)
\(588\) 8.39303 11.5520i 0.346123 0.476397i
\(589\) −6.62012 + 4.80980i −0.272777 + 0.198184i
\(590\) 3.71669 + 0.972835i 0.153014 + 0.0400510i
\(591\) −7.55559 5.48946i −0.310796 0.225806i
\(592\) −6.67797 + 2.16980i −0.274463 + 0.0891784i
\(593\) 22.3100i 0.916162i 0.888910 + 0.458081i \(0.151463\pi\)
−0.888910 + 0.458081i \(0.848537\pi\)
\(594\) 0.986840 + 3.03718i 0.0404905 + 0.124617i
\(595\) −0.905515 + 0.0527194i −0.0371225 + 0.00216129i
\(596\) 4.06882 12.5225i 0.166665 0.512943i
\(597\) −11.1680 3.62870i −0.457076 0.148513i
\(598\) 0.767065 + 1.05577i 0.0313676 + 0.0431738i
\(599\) 2.68060 0.109526 0.0547632 0.998499i \(-0.482560\pi\)
0.0547632 + 0.998499i \(0.482560\pi\)
\(600\) −6.89443 3.87467i −0.281464 0.158183i
\(601\) 20.5985 0.840232 0.420116 0.907470i \(-0.361989\pi\)
0.420116 + 0.907470i \(0.361989\pi\)
\(602\) −0.0300119 0.0413079i −0.00122319 0.00168358i
\(603\) −18.1934 5.91140i −0.740894 0.240731i
\(604\) −6.19967 + 19.0806i −0.252261 + 0.776380i
\(605\) 15.6675 + 10.0460i 0.636974 + 0.408428i
\(606\) −0.498449 1.53407i −0.0202481 0.0623173i
\(607\) 14.7532i 0.598813i −0.954126 0.299406i \(-0.903211\pi\)
0.954126 0.299406i \(-0.0967886\pi\)
\(608\) 3.83432 1.24585i 0.155502 0.0505258i
\(609\) −0.640675 0.465478i −0.0259615 0.0188621i
\(610\) −4.28801 + 6.68748i −0.173616 + 0.270768i
\(611\) 4.10418 2.98186i 0.166037 0.120633i
\(612\) −2.52135 + 3.47033i −0.101919 + 0.140280i
\(613\) −2.97532 + 4.09518i −0.120172 + 0.165403i −0.864865 0.502005i \(-0.832596\pi\)
0.744693 + 0.667407i \(0.232596\pi\)
\(614\) −1.99668 + 1.45067i −0.0805795 + 0.0585444i
\(615\) 18.0463 7.04756i 0.727695 0.284185i
\(616\) 0.588006 + 0.427211i 0.0236914 + 0.0172128i
\(617\) 1.38084 0.448662i 0.0555906 0.0180625i −0.281090 0.959681i \(-0.590696\pi\)
0.336680 + 0.941619i \(0.390696\pi\)
\(618\) 4.92717i 0.198200i
\(619\) −2.27735 7.00897i −0.0915346 0.281714i 0.894800 0.446466i \(-0.147318\pi\)
−0.986335 + 0.164752i \(0.947318\pi\)
\(620\) 8.63614 32.9941i 0.346836 1.32508i
\(621\) 8.59290 26.4462i 0.344821 1.06125i
\(622\) −6.14927 1.99802i −0.246563 0.0801133i
\(623\) −2.12776 2.92861i −0.0852468 0.117332i
\(624\) −2.39271 −0.0957850
\(625\) 12.9984 + 21.3551i 0.519938 + 0.854204i
\(626\) 10.5973 0.423552
\(627\) −1.06722 1.46890i −0.0426205 0.0586622i
\(628\) −12.6723 4.11748i −0.505680 0.164305i
\(629\) 0.881827 2.71398i 0.0351607 0.108214i
\(630\) −0.115120 + 0.439813i −0.00458649 + 0.0175226i
\(631\) 3.85356 + 11.8600i 0.153408 + 0.472140i 0.997996 0.0632758i \(-0.0201548\pi\)
−0.844588 + 0.535416i \(0.820155\pi\)
\(632\) 15.7202i 0.625315i
\(633\) −3.84106 + 1.24804i −0.152668 + 0.0496050i
\(634\) 6.48140 + 4.70902i 0.257409 + 0.187019i
\(635\) −8.77965 + 3.42870i −0.348410 + 0.136064i
\(636\) 5.48018 3.98158i 0.217303 0.157880i
\(637\) 2.73182 3.76003i 0.108239 0.148978i
\(638\) −0.812036 + 1.11767i −0.0321488 + 0.0442491i
\(639\) −5.16992 + 3.75617i −0.204519 + 0.148592i
\(640\) −11.9212 + 18.5921i −0.471228 + 0.734917i
\(641\) −19.5338 14.1922i −0.771540 0.560557i 0.130888 0.991397i \(-0.458217\pi\)
−0.902428 + 0.430840i \(0.858217\pi\)
\(642\) −0.242488 + 0.0787892i −0.00957025 + 0.00310956i
\(643\) 8.03199i 0.316751i 0.987379 + 0.158375i \(0.0506256\pi\)
−0.987379 + 0.158375i \(0.949374\pi\)
\(644\) −0.943411 2.90352i −0.0371756 0.114415i
\(645\) −0.927719 0.594853i −0.0365289 0.0234223i
\(646\) −0.148337 + 0.456535i −0.00583624 + 0.0179621i
\(647\) 2.24545 + 0.729592i 0.0882779 + 0.0286832i 0.352823 0.935690i \(-0.385222\pi\)
−0.264545 + 0.964373i \(0.585222\pi\)
\(648\) −0.475617 0.654630i −0.0186840 0.0257163i
\(649\) −7.62071 −0.299139
\(650\) −1.08251 0.608373i −0.0424597 0.0238623i
\(651\) 2.83065 0.110942
\(652\) 8.47145 + 11.6600i 0.331768 + 0.456639i
\(653\) 11.2859 + 3.66701i 0.441651 + 0.143501i 0.521397 0.853314i \(-0.325411\pi\)
−0.0797464 + 0.996815i \(0.525411\pi\)
\(654\) 2.33892 7.19846i 0.0914591 0.281482i
\(655\) 40.2418 2.34289i 1.57238 0.0915443i
\(656\) −7.72524 23.7758i −0.301620 0.928291i
\(657\) 3.01250i 0.117529i
\(658\) 0.823887 0.267697i 0.0321185 0.0104359i
\(659\) 30.1386 + 21.8970i 1.17403 + 0.852986i 0.991486 0.130211i \(-0.0415653\pi\)
0.182549 + 0.983197i \(0.441565\pi\)
\(660\) 7.32086 + 1.91622i 0.284964 + 0.0745887i
\(661\) 10.1845 7.39949i 0.396132 0.287807i −0.371831 0.928300i \(-0.621270\pi\)
0.767964 + 0.640493i \(0.221270\pi\)
\(662\) −4.09189 + 5.63200i −0.159036 + 0.218894i
\(663\) 0.571572 0.786702i 0.0221980 0.0305530i
\(664\) −17.6678 + 12.8364i −0.685643 + 0.498149i
\(665\) −0.0405101 0.695807i −0.00157091 0.0269822i
\(666\) −1.15714 0.840710i −0.0448382 0.0325769i
\(667\) 11.4408 3.71734i 0.442989 0.143936i
\(668\) 35.9252i 1.38999i
\(669\) −4.47677 13.7781i −0.173082 0.532692i
\(670\) 6.90132 5.65511i 0.266621 0.218476i
\(671\) 4.86944 14.9866i 0.187982 0.578551i
\(672\) −1.32638 0.430966i −0.0511661 0.0166249i
\(673\) −6.66421 9.17250i −0.256886 0.353574i 0.661022 0.750367i \(-0.270123\pi\)
−0.917908 + 0.396793i \(0.870123\pi\)
\(674\) −12.1972 −0.469820
\(675\) 3.07054 + 26.2806i 0.118185 + 1.01154i
\(676\) 23.3863 0.899473
\(677\) −9.39844 12.9358i −0.361212 0.497165i 0.589274 0.807933i \(-0.299414\pi\)
−0.950486 + 0.310768i \(0.899414\pi\)
\(678\) −0.749072 0.243388i −0.0287680 0.00934727i
\(679\) −1.22428 + 3.76793i −0.0469834 + 0.144600i
\(680\) −1.50873 3.86332i −0.0578572 0.148151i
\(681\) −7.48667 23.0416i −0.286890 0.882957i
\(682\) 4.93814i 0.189091i
\(683\) 46.4112 15.0799i 1.77588 0.577017i 0.777239 0.629205i \(-0.216620\pi\)
0.998637 + 0.0521882i \(0.0166196\pi\)
\(684\) −2.66664 1.93743i −0.101961 0.0740794i
\(685\) −3.41790 4.17109i −0.130591 0.159369i
\(686\) 1.29318 0.939552i 0.0493739 0.0358723i
\(687\) −4.23611 + 5.83051i −0.161618 + 0.222448i
\(688\) −0.835872 + 1.15048i −0.0318673 + 0.0438616i
\(689\) 1.78373 1.29595i 0.0679545 0.0493718i
\(690\) 3.04855 + 3.72036i 0.116056 + 0.141632i
\(691\) −9.02732 6.55874i −0.343416 0.249506i 0.402686 0.915338i \(-0.368077\pi\)
−0.746102 + 0.665832i \(0.768077\pi\)
\(692\) 4.14470 1.34670i 0.157558 0.0511937i
\(693\) 0.901793i 0.0342563i
\(694\) −2.53326 7.79656i −0.0961611 0.295953i
\(695\) 3.40214 + 8.71166i 0.129051 + 0.330452i
\(696\) 1.11896 3.44381i 0.0424141 0.130537i
\(697\) 9.66270 + 3.13960i 0.366001 + 0.118921i
\(698\) −6.28346 8.64844i −0.237832 0.327348i
\(699\) −12.8828 −0.487273
\(700\) 1.96869 + 2.13614i 0.0744095 + 0.0807384i
\(701\) −25.5975 −0.966803 −0.483401 0.875399i \(-0.660599\pi\)
−0.483401 + 0.875399i \(0.660599\pi\)
\(702\) −0.772493 1.06324i −0.0291559 0.0401296i
\(703\) 2.08545 + 0.677604i 0.0786543 + 0.0255563i
\(704\) 2.48598 7.65106i 0.0936939 0.288360i
\(705\) 14.4624 11.8508i 0.544685 0.446328i
\(706\) 3.10323 + 9.55077i 0.116792 + 0.359448i
\(707\) 1.22822i 0.0461920i
\(708\) 9.16388 2.97752i 0.344400 0.111902i
\(709\) −17.6536 12.8261i −0.662993 0.481693i 0.204679 0.978829i \(-0.434385\pi\)
−0.867672 + 0.497136i \(0.834385\pi\)
\(710\) −0.173236 2.97552i −0.00650143 0.111669i
\(711\) 15.7797 11.4646i 0.591784 0.429956i
\(712\) 9.72915 13.3910i 0.364615 0.501850i
\(713\) −25.2740 + 34.7867i −0.946521 + 1.30277i
\(714\) 0.134339 0.0976032i 0.00502752 0.00365271i
\(715\) 2.38284 + 0.623704i 0.0891133 + 0.0233252i
\(716\) −10.4061 7.56048i −0.388894 0.282548i
\(717\) 18.0336 5.85948i 0.673478 0.218826i
\(718\) 3.26119i 0.121707i
\(719\) 4.94412 + 15.2164i 0.184385 + 0.567477i 0.999937 0.0112056i \(-0.00356694\pi\)
−0.815553 + 0.578683i \(0.803567\pi\)
\(720\) 12.6406 0.735942i 0.471088 0.0274269i
\(721\) −1.15936 + 3.56815i −0.0431769 + 0.132885i
\(722\) −0.350806 0.113984i −0.0130556 0.00424203i
\(723\) −2.29784 3.16271i −0.0854578 0.117623i
\(724\) 7.65638 0.284547
\(725\) −8.41706 + 7.75726i −0.312602 + 0.288098i
\(726\) −3.40721 −0.126453
\(727\) −30.5904 42.1041i −1.13454 1.56155i −0.779152 0.626834i \(-0.784350\pi\)
−0.355384 0.934721i \(-0.615650\pi\)
\(728\) −0.284473 0.0924309i −0.0105433 0.00342572i
\(729\) −5.75468 + 17.7111i −0.213136 + 0.655966i
\(730\) −1.18281 0.758414i −0.0437776 0.0280702i
\(731\) −0.178594 0.549655i −0.00660552 0.0203297i
\(732\) 19.9239i 0.736408i
\(733\) 45.6981 14.8482i 1.68790 0.548431i 0.701479 0.712690i \(-0.252523\pi\)
0.986417 + 0.164259i \(0.0525234\pi\)
\(734\) 3.36102 + 2.44192i 0.124057 + 0.0901330i
\(735\) 9.24616 14.4201i 0.341050 0.531893i
\(736\) 17.1391 12.4523i 0.631755 0.458997i
\(737\) −10.4027 + 14.3181i −0.383190 + 0.527415i
\(738\) 2.99321 4.11981i 0.110182 0.151652i
\(739\) −22.9695 + 16.6883i −0.844947 + 0.613890i −0.923748 0.383000i \(-0.874891\pi\)
0.0788012 + 0.996890i \(0.474891\pi\)
\(740\) −8.51312 + 3.32461i −0.312948 + 0.122215i
\(741\) 0.604509 + 0.439202i 0.0222072 + 0.0161345i
\(742\) 0.358071 0.116344i 0.0131452 0.00427114i
\(743\) 19.0875i 0.700253i −0.936702 0.350126i \(-0.886139\pi\)
0.936702 0.350126i \(-0.113861\pi\)
\(744\) 3.99964 + 12.3096i 0.146634 + 0.451293i
\(745\) 3.99974 15.2809i 0.146539 0.559849i
\(746\) −1.99030 + 6.12551i −0.0728700 + 0.224271i
\(747\) 25.7700 + 8.37317i 0.942873 + 0.306358i
\(748\) 2.33267 + 3.21064i 0.0852908 + 0.117393i
\(749\) 0.194144 0.00709385
\(750\) −4.11339 2.00659i −0.150200 0.0732702i
\(751\) 16.0854 0.586965 0.293482 0.955964i \(-0.405186\pi\)
0.293482 + 0.955964i \(0.405186\pi\)
\(752\) −14.1816 19.5193i −0.517151 0.711797i
\(753\) 22.2243 + 7.22110i 0.809898 + 0.263152i
\(754\) 0.175691 0.540722i 0.00639830 0.0196919i
\(755\) −6.09442 + 23.2835i −0.221799 + 0.847375i
\(756\) 0.950087 + 2.92407i 0.0345543 + 0.106347i
\(757\) 7.64700i 0.277935i −0.990297 0.138968i \(-0.955622\pi\)
0.990297 0.138968i \(-0.0443784\pi\)
\(758\) −6.76741 + 2.19886i −0.245803 + 0.0798663i
\(759\) −7.71861 5.60790i −0.280168 0.203554i
\(760\) 2.96861 1.15932i 0.107683 0.0420531i
\(761\) −5.09895 + 3.70461i −0.184837 + 0.134292i −0.676356 0.736575i \(-0.736442\pi\)
0.491519 + 0.870867i \(0.336442\pi\)
\(762\) 1.01422 1.39596i 0.0367414 0.0505702i
\(763\) −3.38759 + 4.66261i −0.122639 + 0.168798i
\(764\) 6.22391 4.52194i 0.225173 0.163598i
\(765\) −2.77763 + 4.33193i −0.100426 + 0.156621i
\(766\) 1.84171 + 1.33808i 0.0665438 + 0.0483469i
\(767\) 2.98272 0.969145i 0.107700 0.0349938i
\(768\) 6.87094i 0.247934i
\(769\) −3.32967 10.2477i −0.120071 0.369541i 0.872900 0.487899i \(-0.162237\pi\)
−0.992971 + 0.118359i \(0.962237\pi\)
\(770\) 0.354073 + 0.227032i 0.0127599 + 0.00818166i
\(771\) −2.64765 + 8.14862i −0.0953526 + 0.293465i
\(772\) −6.01066 1.95298i −0.216328 0.0702893i
\(773\) −29.2089 40.2026i −1.05057 1.44599i −0.888312 0.459240i \(-0.848122\pi\)
−0.162259 0.986748i \(-0.551878\pi\)
\(774\) −0.289675 −0.0104121
\(775\) 8.04224 40.1164i 0.288886 1.44102i
\(776\) −18.1155 −0.650307
\(777\) −0.445852 0.613662i −0.0159948 0.0220150i
\(778\) −0.883401 0.287034i −0.0316714 0.0102907i
\(779\) −2.41250 + 7.42492i −0.0864368 + 0.266025i
\(780\) −3.10905 + 0.181010i −0.111322 + 0.00648121i
\(781\) 1.82696 + 5.62281i 0.0653738 + 0.201200i
\(782\) 2.52241i 0.0902010i
\(783\) −11.5217 + 3.74364i −0.411754 + 0.133787i
\(784\) −17.8826 12.9925i −0.638663 0.464016i
\(785\) −15.4636 4.04758i −0.551921 0.144464i
\(786\) −5.97014 + 4.33756i −0.212948 + 0.154716i
\(787\) 32.0921 44.1709i 1.14396 1.57452i 0.385626 0.922655i \(-0.373986\pi\)
0.758333 0.651868i \(-0.226014\pi\)
\(788\) −9.21983 + 12.6900i −0.328443 + 0.452063i
\(789\) 22.3093 16.2086i 0.794232 0.577043i
\(790\) 0.528751 + 9.08190i 0.0188121 + 0.323119i
\(791\) 0.485192 + 0.352513i 0.0172514 + 0.0125339i
\(792\) 3.92162 1.27421i 0.139349 0.0452771i
\(793\) 6.48496i 0.230288i
\(794\) −4.30362 13.2452i −0.152730 0.470053i
\(795\) 6.28553 5.15051i 0.222925 0.182670i
\(796\) −6.09459 + 18.7572i −0.216017 + 0.664832i
\(797\) −26.7436 8.68952i −0.947307 0.307799i −0.205686 0.978618i \(-0.565943\pi\)
−0.741621 + 0.670819i \(0.765943\pi\)
\(798\) 0.0749992 + 0.103228i 0.00265494 + 0.00365422i
\(799\) 9.80551 0.346894
\(800\) −9.87612 + 17.5732i −0.349174 + 0.621306i
\(801\) −20.5371 −0.725643
\(802\) −8.42268 11.5928i −0.297415 0.409357i
\(803\) 2.65066 + 0.861251i 0.0935396 + 0.0303929i
\(804\) 6.91495 21.2820i 0.243871 0.750559i
\(805\) −1.33229 3.41152i −0.0469572 0.120240i
\(806\) 0.627996 + 1.93277i 0.0221202 + 0.0680790i
\(807\) 12.5716i 0.442540i
\(808\) −5.34116 + 1.73545i −0.187901 + 0.0610529i
\(809\) 21.3936 + 15.5434i 0.752160 + 0.546476i 0.896496 0.443053i \(-0.146105\pi\)
−0.144336 + 0.989529i \(0.546105\pi\)
\(810\) −0.296793 0.362197i −0.0104283 0.0127263i
\(811\) −3.70509 + 2.69191i −0.130103 + 0.0945256i −0.650934 0.759135i \(-0.725622\pi\)
0.520830 + 0.853660i \(0.325622\pi\)
\(812\) −0.781793 + 1.07605i −0.0274356 + 0.0377618i
\(813\) 3.35258 4.61442i 0.117580 0.161835i
\(814\) −1.07055 + 0.777798i −0.0375227 + 0.0272618i
\(815\) 10.9585 + 13.3735i 0.383861 + 0.468452i
\(816\) −3.74153 2.71838i −0.130980 0.0951623i
\(817\) 0.422360 0.137233i 0.0147765 0.00480118i
\(818\) 2.99153i 0.104596i
\(819\) 0.114683 + 0.352959i 0.00400736 + 0.0123334i
\(820\) −11.8367 30.3096i −0.413357 1.05846i
\(821\) −9.90193 + 30.4750i −0.345580 + 1.06358i 0.615693 + 0.787986i \(0.288876\pi\)
−0.961273 + 0.275599i \(0.911124\pi\)
\(822\) 0.938898 + 0.305067i 0.0327478 + 0.0106404i
\(823\) 10.5716 + 14.5505i 0.368502 + 0.507199i 0.952493 0.304561i \(-0.0985098\pi\)
−0.583991 + 0.811760i \(0.698510\pi\)
\(824\) −17.1549 −0.597620
\(825\) 8.90119 + 1.78444i 0.309900 + 0.0621263i
\(826\) 0.535549 0.0186341
\(827\) −3.56552 4.90752i −0.123985 0.170651i 0.742512 0.669833i \(-0.233634\pi\)
−0.866498 + 0.499181i \(0.833634\pi\)
\(828\) −16.4725 5.35225i −0.572460 0.186004i
\(829\) 10.4222 32.0763i 0.361979 1.11406i −0.589873 0.807496i \(-0.700822\pi\)
0.951851 0.306560i \(-0.0991779\pi\)
\(830\) −9.77532 + 8.01014i −0.339306 + 0.278036i
\(831\) −5.15950 15.8793i −0.178981 0.550847i
\(832\) 3.31075i 0.114780i
\(833\) 8.54361 2.77599i 0.296019 0.0961823i
\(834\) −1.38515 1.00637i −0.0479637 0.0348477i
\(835\) −2.50491 43.0246i −0.0866859 1.48893i
\(836\) −2.46709 + 1.79245i −0.0853261 + 0.0619930i
\(837\) 25.4529 35.0329i 0.879780 1.21091i
\(838\) 1.64947 2.27030i 0.0569800 0.0784263i
\(839\) −32.1630 + 23.3678i −1.11039 + 0.806747i −0.982725 0.185071i \(-0.940749\pi\)
−0.127666 + 0.991817i \(0.540749\pi\)
\(840\) −1.06651 0.279156i −0.0367980 0.00963180i
\(841\) 19.2215 + 13.9653i 0.662811 + 0.481561i
\(842\) 4.87469 1.58388i 0.167993 0.0545843i
\(843\) 8.11811i 0.279602i
\(844\) 2.09614 + 6.45126i 0.0721521 + 0.222061i
\(845\) 28.0078 1.63062i 0.963497 0.0560952i
\(846\) 1.51873 4.67416i 0.0522149 0.160701i
\(847\) 2.46742 + 0.801714i 0.0847817 + 0.0275472i
\(848\) −6.16350 8.48334i −0.211656 0.291319i
\(849\) 31.8339 1.09254
\(850\) −1.00157 2.18118i −0.0343537 0.0748138i
\(851\) 11.5224 0.394981
\(852\) −4.39383 6.04759i −0.150530 0.207187i
\(853\) 47.5274 + 15.4426i 1.62731 + 0.528744i 0.973650 0.228047i \(-0.0732340\pi\)
0.653657 + 0.756791i \(0.273234\pi\)
\(854\) −0.342202 + 1.05319i −0.0117099 + 0.0360394i
\(855\) −3.32870 2.13436i −0.113839 0.0729936i
\(856\) 0.274320 + 0.844271i 0.00937608 + 0.0288566i
\(857\) 29.8274i 1.01888i 0.860505 + 0.509442i \(0.170148\pi\)
−0.860505 + 0.509442i \(0.829852\pi\)
\(858\) −0.428851 + 0.139342i −0.0146407 + 0.00475706i
\(859\) 30.1634 + 21.9150i 1.02916 + 0.747729i 0.968140 0.250408i \(-0.0805647\pi\)
0.0610199 + 0.998137i \(0.480565\pi\)
\(860\) −0.999086 + 1.55815i −0.0340685 + 0.0531325i
\(861\) 2.18485 1.58738i 0.0744593 0.0540979i
\(862\) −2.37615 + 3.27049i −0.0809319 + 0.111393i
\(863\) −5.87441 + 8.08543i −0.199967 + 0.275231i −0.897210 0.441604i \(-0.854410\pi\)
0.697243 + 0.716835i \(0.254410\pi\)
\(864\) −17.2604 + 12.5404i −0.587210 + 0.426633i
\(865\) 4.86986 1.90182i 0.165580 0.0646637i
\(866\) 10.7817 + 7.83336i 0.366377 + 0.266188i
\(867\) −16.1554 + 5.24922i −0.548667 + 0.178273i
\(868\) 4.75422i 0.161369i
\(869\) −5.57626 17.1620i −0.189162 0.582180i
\(870\) 0.530616 2.02720i 0.0179896 0.0687286i
\(871\) 2.25073 6.92702i 0.0762629 0.234713i
\(872\) −25.0629 8.14342i −0.848736 0.275771i
\(873\) 13.2115 + 18.1840i 0.447140 + 0.615436i
\(874\) −1.93824 −0.0655620
\(875\) 2.50668 + 2.42100i 0.0847412 + 0.0818449i
\(876\) −3.52391 −0.119062
\(877\) −6.28647 8.65259i −0.212279 0.292177i 0.689578 0.724211i \(-0.257796\pi\)
−0.901857 + 0.432034i \(0.857796\pi\)
\(878\) 5.49448 + 1.78526i 0.185430 + 0.0602497i
\(879\) −7.16190 + 22.0421i −0.241565 + 0.743461i
\(880\) 2.96632 11.3327i 0.0999945 0.382026i
\(881\) 13.9024 + 42.7873i 0.468385 + 1.44154i 0.854675 + 0.519163i \(0.173756\pi\)
−0.386291 + 0.922377i \(0.626244\pi\)
\(882\) 4.50259i 0.151610i
\(883\) −6.03467 + 1.96078i −0.203083 + 0.0659856i −0.408792 0.912628i \(-0.634050\pi\)
0.205709 + 0.978613i \(0.434050\pi\)
\(884\) −1.32131 0.959985i −0.0444403 0.0322878i
\(885\) 10.7672 4.20489i 0.361935 0.141346i
\(886\) 4.86368 3.53367i 0.163398 0.118716i
\(887\) 7.42499 10.2196i 0.249307 0.343141i −0.665962 0.745986i \(-0.731979\pi\)
0.915268 + 0.402845i \(0.131979\pi\)
\(888\) 2.03865 2.80596i 0.0684126 0.0941619i
\(889\) −1.06295 + 0.772275i −0.0356500 + 0.0259013i
\(890\) 5.17034 8.06354i 0.173310 0.270291i
\(891\) 0.751450 + 0.545960i 0.0251745 + 0.0182904i
\(892\) −23.1410 + 7.51897i −0.774818 + 0.251754i
\(893\) 7.53465i 0.252137i
\(894\) 0.893585 + 2.75017i 0.0298859 + 0.0919795i
\(895\) −12.9897 8.32898i −0.434197 0.278407i
\(896\) −0.951368 + 2.92801i −0.0317830 + 0.0978179i
\(897\) 3.73421 + 1.21332i 0.124682 + 0.0405116i
\(898\) −4.12030 5.67111i −0.137496 0.189247i
\(899\) 18.7331 0.624785
\(900\) 16.3694 1.91255i 0.545646 0.0637515i
\(901\) 4.26159 0.141974
\(902\) −2.76923 3.81151i −0.0922052 0.126910i
\(903\) −0.146104 0.0474719i −0.00486202 0.00157977i
\(904\) −0.847405 + 2.60804i −0.0281843 + 0.0867423i
\(905\) 9.16940 0.533846i 0.304801 0.0177456i
\(906\) −1.36156 4.19044i −0.0452347 0.139218i
\(907\) 10.0093i 0.332354i 0.986096 + 0.166177i \(0.0531423\pi\)
−0.986096 + 0.166177i \(0.946858\pi\)
\(908\) −38.6996 + 12.5742i −1.28429 + 0.417291i
\(909\) 5.63729 + 4.09573i 0.186977 + 0.135847i
\(910\) −0.167456 0.0438311i −0.00555110 0.00145299i
\(911\) −27.2326 + 19.7856i −0.902255 + 0.655527i −0.939044 0.343796i \(-0.888287\pi\)
0.0367892 + 0.999323i \(0.488287\pi\)
\(912\) 2.08883 2.87503i 0.0691680 0.0952016i
\(913\) 14.7349 20.2808i 0.487653 0.671197i
\(914\) −10.5733 + 7.68192i −0.349732 + 0.254095i
\(915\) 1.38921 + 23.8612i 0.0459257 + 0.788826i
\(916\) 9.79264 + 7.11477i 0.323558 + 0.235078i
\(917\) 5.34406 1.73639i 0.176477 0.0573407i
\(918\) 2.54025i 0.0838409i
\(919\) 7.42435 + 22.8498i 0.244907 + 0.753746i 0.995652 + 0.0931535i \(0.0296947\pi\)
−0.750745 + 0.660592i \(0.770305\pi\)
\(920\) 12.9532 10.6141i 0.427053 0.349938i
\(921\) −2.29463 + 7.06215i −0.0756107 + 0.232706i
\(922\) −5.03217 1.63505i −0.165726 0.0538475i
\(923\) −1.43014 1.96841i −0.0470735 0.0647911i
\(924\) 1.05489 0.0347032
\(925\) −9.96364 + 4.57519i −0.327602 + 0.150431i
\(926\) 7.60359 0.249870
\(927\) 12.5110 + 17.2199i 0.410914 + 0.565575i
\(928\) −8.77791 2.85212i −0.288149 0.0936253i
\(929\) −15.6936 + 48.2998i −0.514889 + 1.58467i 0.268594 + 0.963253i \(0.413441\pi\)
−0.783484 + 0.621413i \(0.786559\pi\)
\(930\) 2.72472 + 6.97703i 0.0893472 + 0.228786i
\(931\) 2.13310 + 6.56499i 0.0699094 + 0.215159i
\(932\) 21.6373i 0.708755i
\(933\) −18.5013 + 6.01145i −0.605707 + 0.196806i
\(934\) 4.31440 + 3.13460i 0.141172 + 0.102567i
\(935\) 3.01751 + 3.68247i 0.0986830 + 0.120430i
\(936\) −1.37287 + 0.997446i −0.0448735 + 0.0326025i
\(937\) −24.1573 + 33.2497i −0.789184 + 1.08622i 0.205025 + 0.978757i \(0.434272\pi\)
−0.994209 + 0.107462i \(0.965728\pi\)
\(938\) 0.731057 1.00621i 0.0238699 0.0328541i
\(939\) 25.7948 18.7410i 0.841780 0.611589i
\(940\) −19.9041 24.2903i −0.649199 0.792263i
\(941\) −33.2774 24.1775i −1.08481 0.788163i −0.106297 0.994334i \(-0.533899\pi\)
−0.978516 + 0.206172i \(0.933899\pi\)
\(942\) 2.78306 0.904271i 0.0906770 0.0294627i
\(943\) 41.0235i 1.33591i
\(944\) −4.60922 14.1857i −0.150017 0.461706i
\(945\) 1.34172 + 3.43566i 0.0436462 + 0.111762i
\(946\) −0.0828159 + 0.254881i −0.00269258 + 0.00828690i
\(947\) 24.0024 + 7.79884i 0.779972 + 0.253428i 0.671828 0.740707i \(-0.265509\pi\)
0.108144 + 0.994135i \(0.465509\pi\)
\(948\) 13.4109 + 18.4585i 0.435565 + 0.599504i
\(949\) −1.14699 −0.0372328
\(950\) 1.67604 0.769618i 0.0543779 0.0249697i
\(951\) 24.1041 0.781629
\(952\) −0.339825 0.467729i −0.0110138 0.0151592i
\(953\) −22.9199 7.44712i −0.742448 0.241236i −0.0867194 0.996233i \(-0.527638\pi\)
−0.655728 + 0.754997i \(0.727638\pi\)
\(954\) 0.660056 2.03144i 0.0213701 0.0657704i
\(955\) 7.13856 5.84951i 0.230998 0.189286i
\(956\) −9.84129 30.2884i −0.318290 0.979596i
\(957\) 4.15658i 0.134363i
\(958\) −2.52770 + 0.821300i −0.0816663 + 0.0265350i
\(959\) −0.608147 0.441845i −0.0196381 0.0142679i
\(960\) 0.709227 + 12.1818i 0.0228902 + 0.393165i
\(961\) −29.0925 + 21.1369i −0.938466 + 0.681836i
\(962\) 0.320095 0.440572i 0.0103203 0.0142046i
\(963\) 0.647407 0.891079i 0.0208624 0.0287146i
\(964\) −5.31193 + 3.85935i −0.171086 + 0.124301i
\(965\) −7.33463 1.91982i −0.236110 0.0618013i
\(966\) 0.542430 + 0.394098i 0.0174524 + 0.0126799i
\(967\) −37.2339 + 12.0980i −1.19736 + 0.389047i −0.838790 0.544455i \(-0.816737\pi\)
−0.358573 + 0.933502i \(0.616737\pi\)
\(968\) 11.8629i 0.381287i
\(969\) 0.446302 + 1.37358i 0.0143373 + 0.0441257i
\(970\) −10.4657 + 0.609318i −0.336034 + 0.0195640i
\(971\) −9.83422 + 30.2666i −0.315595 + 0.971302i 0.659914 + 0.751341i \(0.270593\pi\)
−0.975509 + 0.219960i \(0.929407\pi\)
\(972\) 27.0260 + 8.78130i 0.866861 + 0.281660i
\(973\) 0.766294 + 1.05471i 0.0245663 + 0.0338126i
\(974\) −3.79307 −0.121538
\(975\) −3.71083 + 0.433561i −0.118842 + 0.0138851i
\(976\) 30.8423 0.987237
\(977\) −4.95338 6.81774i −0.158473 0.218119i 0.722396 0.691480i \(-0.243041\pi\)
−0.880869 + 0.473361i \(0.843041\pi\)
\(978\) −3.01032 0.978112i −0.0962594 0.0312766i
\(979\) −5.87141 + 18.0703i −0.187651 + 0.577530i
\(980\) −24.2193 15.5294i −0.773656 0.496068i
\(981\) 10.1039 + 31.0967i 0.322593 + 0.992840i
\(982\) 5.09191i 0.162489i
\(983\) −55.8069 + 18.1327i −1.77996 + 0.578345i −0.998934 0.0461513i \(-0.985304\pi\)
−0.781028 + 0.624496i \(0.785304\pi\)
\(984\) 9.99018 + 7.25829i 0.318475 + 0.231386i
\(985\) −10.1570 + 15.8406i −0.323629 + 0.504724i
\(986\) 0.889052 0.645934i 0.0283132 0.0205707i
\(987\) 1.53200 2.10862i 0.0487642 0.0671182i
\(988\) 0.737661 1.01530i 0.0234681 0.0323011i
\(989\) 1.88791 1.37165i 0.0600321 0.0436159i
\(990\) 2.22275 0.868046i 0.0706437 0.0275883i
\(991\) 47.5843 + 34.5720i 1.51156 + 1.09822i 0.965478 + 0.260486i \(0.0838829\pi\)
0.546086 + 0.837729i \(0.316117\pi\)
\(992\) 31.3760 10.1947i 0.996189 0.323681i
\(993\) 20.9452i 0.664676i
\(994\) −0.128391 0.395146i −0.00407231 0.0125333i
\(995\) −5.99112 + 22.8889i −0.189931 + 0.725627i
\(996\) −9.79463 + 30.1448i −0.310355 + 0.955174i
\(997\) 15.0633 + 4.89437i 0.477060 + 0.155006i 0.537670 0.843155i \(-0.319305\pi\)
−0.0606099 + 0.998162i \(0.519305\pi\)
\(998\) −7.53843 10.3758i −0.238625 0.328439i
\(999\) −11.6039 −0.367131
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 475.2.n.b.39.15 96
25.9 even 10 inner 475.2.n.b.134.15 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.n.b.39.15 96 1.1 even 1 trivial
475.2.n.b.134.15 yes 96 25.9 even 10 inner