Properties

Label 930.2.o.e.491.8
Level $930$
Weight $2$
Character 930.491
Analytic conductor $7.426$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(161,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.8
Character \(\chi\) \(=\) 930.491
Dual form 930.2.o.e.161.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.32888 + 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.11089 - 1.32888i) q^{6} +(-0.581871 + 1.00783i) q^{7} +1.00000i q^{8} +(0.531863 + 2.95248i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.32888 + 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.11089 - 1.32888i) q^{6} +(-0.581871 + 1.00783i) q^{7} +1.00000i q^{8} +(0.531863 + 2.95248i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.0889568 - 0.154078i) q^{11} +(-1.32888 - 1.11089i) q^{12} +(-4.88952 + 2.82297i) q^{13} +(1.00783 + 0.581871i) q^{14} +(-1.70629 - 0.297614i) q^{15} +1.00000 q^{16} +(1.93896 - 3.35837i) q^{17} +(2.95248 - 0.531863i) q^{18} +(-2.57689 + 4.46331i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.89282 + 0.692897i) q^{21} +(-0.154078 + 0.0889568i) q^{22} -5.70722 q^{23} +(-1.11089 + 1.32888i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.82297 + 4.88952i) q^{26} +(-2.57308 + 4.51434i) q^{27} +(0.581871 - 1.00783i) q^{28} -5.56575 q^{29} +(-0.297614 + 1.70629i) q^{30} +(5.12730 + 2.17043i) q^{31} -1.00000i q^{32} +(0.0529495 - 0.303572i) q^{33} +(-3.35837 - 1.93896i) q^{34} -1.16374i q^{35} +(-0.531863 - 2.95248i) q^{36} +(0.782503 + 0.451779i) q^{37} +(4.46331 + 2.57689i) q^{38} +(-9.63360 - 1.68031i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.48692 + 1.43582i) q^{41} +(0.692897 + 1.89282i) q^{42} +(0.735867 + 0.424853i) q^{43} +(0.0889568 + 0.154078i) q^{44} +(-1.93685 - 2.29099i) q^{45} +5.70722i q^{46} -4.11079i q^{47} +(1.32888 + 1.11089i) q^{48} +(2.82285 + 4.88932i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(6.30741 - 2.30892i) q^{51} +(4.88952 - 2.82297i) q^{52} +(6.25104 + 10.8271i) q^{53} +(4.51434 + 2.57308i) q^{54} +(0.154078 + 0.0889568i) q^{55} +(-1.00783 - 0.581871i) q^{56} +(-8.38261 + 3.06858i) q^{57} +5.56575i q^{58} +(4.27376 + 2.46746i) q^{59} +(1.70629 + 0.297614i) q^{60} +0.00227491i q^{61} +(2.17043 - 5.12730i) q^{62} +(-3.28507 - 1.18193i) q^{63} -1.00000 q^{64} +(2.82297 - 4.88952i) q^{65} +(-0.303572 - 0.0529495i) q^{66} +(-3.20296 - 5.54769i) q^{67} +(-1.93896 + 3.35837i) q^{68} +(-7.58423 - 6.34007i) q^{69} -1.16374 q^{70} +(-10.9712 + 6.33424i) q^{71} +(-2.95248 + 0.531863i) q^{72} +(9.32062 - 5.38127i) q^{73} +(0.451779 - 0.782503i) q^{74} +(1.62650 - 0.595404i) q^{75} +(2.57689 - 4.46331i) q^{76} +0.207046 q^{77} +(-1.68031 + 9.63360i) q^{78} +(-2.52627 - 1.45854i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-8.43424 + 3.14063i) q^{81} +(1.43582 + 2.48692i) q^{82} +(7.95846 + 13.7845i) q^{83} +(1.89282 - 0.692897i) q^{84} +3.87791i q^{85} +(0.424853 - 0.735867i) q^{86} +(-7.39624 - 6.18292i) q^{87} +(0.154078 - 0.0889568i) q^{88} +5.20790 q^{89} +(-2.29099 + 1.93685i) q^{90} -6.57041i q^{91} +5.70722 q^{92} +(4.40248 + 8.58010i) q^{93} -4.11079 q^{94} -5.15378i q^{95} +(1.11089 - 1.32888i) q^{96} -13.7078 q^{97} +(4.88932 - 2.82285i) q^{98} +(0.407598 - 0.344591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.32888 + 1.11089i 0.767231 + 0.641370i
\(4\) −1.00000 −0.500000
\(5\) −0.866025 + 0.500000i −0.387298 + 0.223607i
\(6\) 1.11089 1.32888i 0.453517 0.542514i
\(7\) −0.581871 + 1.00783i −0.219927 + 0.380924i −0.954785 0.297296i \(-0.903915\pi\)
0.734859 + 0.678220i \(0.237248\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.531863 + 2.95248i 0.177288 + 0.984159i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −0.0889568 0.154078i −0.0268215 0.0464562i 0.852303 0.523048i \(-0.175205\pi\)
−0.879125 + 0.476592i \(0.841872\pi\)
\(12\) −1.32888 1.11089i −0.383616 0.320685i
\(13\) −4.88952 + 2.82297i −1.35611 + 0.782950i −0.989097 0.147266i \(-0.952953\pi\)
−0.367012 + 0.930216i \(0.619619\pi\)
\(14\) 1.00783 + 0.581871i 0.269354 + 0.155512i
\(15\) −1.70629 0.297614i −0.440562 0.0768436i
\(16\) 1.00000 0.250000
\(17\) 1.93896 3.35837i 0.470266 0.814524i −0.529156 0.848525i \(-0.677491\pi\)
0.999422 + 0.0340003i \(0.0108247\pi\)
\(18\) 2.95248 0.531863i 0.695906 0.125361i
\(19\) −2.57689 + 4.46331i −0.591179 + 1.02395i 0.402895 + 0.915246i \(0.368004\pi\)
−0.994074 + 0.108706i \(0.965329\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) −1.89282 + 0.692897i −0.413048 + 0.151202i
\(22\) −0.154078 + 0.0889568i −0.0328495 + 0.0189656i
\(23\) −5.70722 −1.19004 −0.595019 0.803712i \(-0.702855\pi\)
−0.595019 + 0.803712i \(0.702855\pi\)
\(24\) −1.11089 + 1.32888i −0.226759 + 0.271257i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 2.82297 + 4.88952i 0.553629 + 0.958914i
\(27\) −2.57308 + 4.51434i −0.495190 + 0.868785i
\(28\) 0.581871 1.00783i 0.109963 0.190462i
\(29\) −5.56575 −1.03353 −0.516767 0.856126i \(-0.672865\pi\)
−0.516767 + 0.856126i \(0.672865\pi\)
\(30\) −0.297614 + 1.70629i −0.0543366 + 0.311525i
\(31\) 5.12730 + 2.17043i 0.920891 + 0.389821i
\(32\) 1.00000i 0.176777i
\(33\) 0.0529495 0.303572i 0.00921733 0.0528451i
\(34\) −3.35837 1.93896i −0.575956 0.332528i
\(35\) 1.16374i 0.196708i
\(36\) −0.531863 2.95248i −0.0886439 0.492080i
\(37\) 0.782503 + 0.451779i 0.128643 + 0.0742719i 0.562940 0.826497i \(-0.309670\pi\)
−0.434298 + 0.900769i \(0.643003\pi\)
\(38\) 4.46331 + 2.57689i 0.724044 + 0.418027i
\(39\) −9.63360 1.68031i −1.54261 0.269065i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −2.48692 + 1.43582i −0.388391 + 0.224238i −0.681463 0.731853i \(-0.738656\pi\)
0.293072 + 0.956091i \(0.405323\pi\)
\(42\) 0.692897 + 1.89282i 0.106916 + 0.292069i
\(43\) 0.735867 + 0.424853i 0.112219 + 0.0647895i 0.555059 0.831811i \(-0.312696\pi\)
−0.442840 + 0.896601i \(0.646029\pi\)
\(44\) 0.0889568 + 0.154078i 0.0134107 + 0.0232281i
\(45\) −1.93685 2.29099i −0.288728 0.341520i
\(46\) 5.70722i 0.841484i
\(47\) 4.11079i 0.599620i −0.953999 0.299810i \(-0.903077\pi\)
0.953999 0.299810i \(-0.0969233\pi\)
\(48\) 1.32888 + 1.11089i 0.191808 + 0.160343i
\(49\) 2.82285 + 4.88932i 0.403265 + 0.698475i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 6.30741 2.30892i 0.883214 0.323314i
\(52\) 4.88952 2.82297i 0.678055 0.391475i
\(53\) 6.25104 + 10.8271i 0.858646 + 1.48722i 0.873221 + 0.487325i \(0.162027\pi\)
−0.0145750 + 0.999894i \(0.504640\pi\)
\(54\) 4.51434 + 2.57308i 0.614324 + 0.350152i
\(55\) 0.154078 + 0.0889568i 0.0207758 + 0.0119949i
\(56\) −1.00783 0.581871i −0.134677 0.0777558i
\(57\) −8.38261 + 3.06858i −1.11030 + 0.406443i
\(58\) 5.56575i 0.730819i
\(59\) 4.27376 + 2.46746i 0.556396 + 0.321235i 0.751698 0.659508i \(-0.229235\pi\)
−0.195302 + 0.980743i \(0.562569\pi\)
\(60\) 1.70629 + 0.297614i 0.220281 + 0.0384218i
\(61\) 0.00227491i 0.000291272i 1.00000 0.000145636i \(4.63574e-5\pi\)
−1.00000 0.000145636i \(0.999954\pi\)
\(62\) 2.17043 5.12730i 0.275645 0.651168i
\(63\) −3.28507 1.18193i −0.413880 0.148910i
\(64\) −1.00000 −0.125000
\(65\) 2.82297 4.88952i 0.350146 0.606471i
\(66\) −0.303572 0.0529495i −0.0373671 0.00651764i
\(67\) −3.20296 5.54769i −0.391304 0.677758i 0.601318 0.799010i \(-0.294642\pi\)
−0.992622 + 0.121252i \(0.961309\pi\)
\(68\) −1.93896 + 3.35837i −0.235133 + 0.407262i
\(69\) −7.58423 6.34007i −0.913034 0.763255i
\(70\) −1.16374 −0.139094
\(71\) −10.9712 + 6.33424i −1.30204 + 0.751736i −0.980754 0.195245i \(-0.937450\pi\)
−0.321290 + 0.946981i \(0.604116\pi\)
\(72\) −2.95248 + 0.531863i −0.347953 + 0.0626807i
\(73\) 9.32062 5.38127i 1.09090 0.629829i 0.157082 0.987586i \(-0.449791\pi\)
0.933815 + 0.357756i \(0.116458\pi\)
\(74\) 0.451779 0.782503i 0.0525182 0.0909642i
\(75\) 1.62650 0.595404i 0.187812 0.0687513i
\(76\) 2.57689 4.46331i 0.295590 0.511976i
\(77\) 0.207046 0.0235950
\(78\) −1.68031 + 9.63360i −0.190257 + 1.09079i
\(79\) −2.52627 1.45854i −0.284228 0.164099i 0.351108 0.936335i \(-0.385805\pi\)
−0.635336 + 0.772236i \(0.719138\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −8.43424 + 3.14063i −0.937138 + 0.348959i
\(82\) 1.43582 + 2.48692i 0.158560 + 0.274634i
\(83\) 7.95846 + 13.7845i 0.873555 + 1.51304i 0.858294 + 0.513158i \(0.171524\pi\)
0.0152607 + 0.999884i \(0.495142\pi\)
\(84\) 1.89282 0.692897i 0.206524 0.0756012i
\(85\) 3.87791i 0.420618i
\(86\) 0.424853 0.735867i 0.0458131 0.0793506i
\(87\) −7.39624 6.18292i −0.792960 0.662878i
\(88\) 0.154078 0.0889568i 0.0164247 0.00948282i
\(89\) 5.20790 0.552036 0.276018 0.961152i \(-0.410985\pi\)
0.276018 + 0.961152i \(0.410985\pi\)
\(90\) −2.29099 + 1.93685i −0.241491 + 0.204161i
\(91\) 6.57041i 0.688766i
\(92\) 5.70722 0.595019
\(93\) 4.40248 + 8.58010i 0.456516 + 0.889715i
\(94\) −4.11079 −0.423995
\(95\) 5.15378i 0.528767i
\(96\) 1.11089 1.32888i 0.113379 0.135629i
\(97\) −13.7078 −1.39181 −0.695907 0.718132i \(-0.744997\pi\)
−0.695907 + 0.718132i \(0.744997\pi\)
\(98\) 4.88932 2.82285i 0.493896 0.285151i
\(99\) 0.407598 0.344591i 0.0409651 0.0346327i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 2.34879i 0.233713i −0.993149 0.116856i \(-0.962718\pi\)
0.993149 0.116856i \(-0.0372817\pi\)
\(102\) −2.30892 6.30741i −0.228617 0.624527i
\(103\) −8.49332 14.7109i −0.836872 1.44950i −0.892497 0.451053i \(-0.851048\pi\)
0.0556251 0.998452i \(-0.482285\pi\)
\(104\) −2.82297 4.88952i −0.276815 0.479457i
\(105\) 1.29279 1.54648i 0.126163 0.150921i
\(106\) 10.8271 6.25104i 1.05162 0.607154i
\(107\) 4.00394 + 2.31167i 0.387075 + 0.223478i 0.680892 0.732384i \(-0.261592\pi\)
−0.293817 + 0.955862i \(0.594926\pi\)
\(108\) 2.57308 4.51434i 0.247595 0.434392i
\(109\) 18.3302 1.75571 0.877856 0.478925i \(-0.158973\pi\)
0.877856 + 0.478925i \(0.158973\pi\)
\(110\) 0.0889568 0.154078i 0.00848170 0.0146907i
\(111\) 0.537981 + 1.46963i 0.0510629 + 0.139491i
\(112\) −0.581871 + 1.00783i −0.0549817 + 0.0952310i
\(113\) −0.376805 + 0.217548i −0.0354468 + 0.0204652i −0.517619 0.855611i \(-0.673181\pi\)
0.482172 + 0.876077i \(0.339848\pi\)
\(114\) 3.06858 + 8.38261i 0.287399 + 0.785104i
\(115\) 4.94260 2.85361i 0.460900 0.266101i
\(116\) 5.56575 0.516767
\(117\) −10.9353 12.9348i −1.01097 1.19582i
\(118\) 2.46746 4.27376i 0.227148 0.393431i
\(119\) 2.25644 + 3.90828i 0.206848 + 0.358271i
\(120\) 0.297614 1.70629i 0.0271683 0.155762i
\(121\) 5.48417 9.49887i 0.498561 0.863533i
\(122\) 0.00227491 0.000205960
\(123\) −4.89986 0.854642i −0.441806 0.0770604i
\(124\) −5.12730 2.17043i −0.460445 0.194911i
\(125\) 1.00000i 0.0894427i
\(126\) −1.18193 + 3.28507i −0.105295 + 0.292657i
\(127\) 10.9132 + 6.30073i 0.968388 + 0.559099i 0.898745 0.438473i \(-0.144480\pi\)
0.0696438 + 0.997572i \(0.477814\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.505918 + 1.38204i 0.0445436 + 0.121682i
\(130\) −4.88952 2.82297i −0.428839 0.247591i
\(131\) 18.3335 + 10.5849i 1.60181 + 0.924803i 0.991126 + 0.132925i \(0.0424369\pi\)
0.610679 + 0.791878i \(0.290896\pi\)
\(132\) −0.0529495 + 0.303572i −0.00460867 + 0.0264226i
\(133\) −2.99884 5.19414i −0.260032 0.450389i
\(134\) −5.54769 + 3.20296i −0.479247 + 0.276693i
\(135\) −0.0288151 5.19607i −0.00248001 0.447207i
\(136\) 3.35837 + 1.93896i 0.287978 + 0.166264i
\(137\) −6.42120 11.1218i −0.548600 0.950203i −0.998371 0.0570592i \(-0.981828\pi\)
0.449771 0.893144i \(-0.351506\pi\)
\(138\) −6.34007 + 7.58423i −0.539703 + 0.645613i
\(139\) 0.913499i 0.0774820i −0.999249 0.0387410i \(-0.987665\pi\)
0.999249 0.0387410i \(-0.0123347\pi\)
\(140\) 1.16374i 0.0983542i
\(141\) 4.56662 5.46276i 0.384579 0.460047i
\(142\) 6.33424 + 10.9712i 0.531557 + 0.920685i
\(143\) 0.869912 + 0.502244i 0.0727457 + 0.0419998i
\(144\) 0.531863 + 2.95248i 0.0443220 + 0.246040i
\(145\) 4.82008 2.78288i 0.400286 0.231105i
\(146\) −5.38127 9.32062i −0.445357 0.771380i
\(147\) −1.68024 + 9.63321i −0.138584 + 0.794534i
\(148\) −0.782503 0.451779i −0.0643214 0.0371360i
\(149\) −3.97105 2.29269i −0.325321 0.187824i 0.328441 0.944525i \(-0.393477\pi\)
−0.653762 + 0.756700i \(0.726810\pi\)
\(150\) −0.595404 1.62650i −0.0486145 0.132803i
\(151\) 18.0258i 1.46692i 0.679734 + 0.733458i \(0.262095\pi\)
−0.679734 + 0.733458i \(0.737905\pi\)
\(152\) −4.46331 2.57689i −0.362022 0.209013i
\(153\) 10.9468 + 3.93853i 0.884994 + 0.318411i
\(154\) 0.207046i 0.0166842i
\(155\) −5.52559 + 0.684001i −0.443826 + 0.0549403i
\(156\) 9.63360 + 1.68031i 0.771305 + 0.134532i
\(157\) −9.03549 −0.721111 −0.360555 0.932738i \(-0.617413\pi\)
−0.360555 + 0.932738i \(0.617413\pi\)
\(158\) −1.45854 + 2.52627i −0.116036 + 0.200980i
\(159\) −3.72079 + 21.3322i −0.295078 + 1.69175i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 3.32087 5.75191i 0.261721 0.453314i
\(162\) 3.14063 + 8.43424i 0.246751 + 0.662657i
\(163\) 17.0876 1.33840 0.669201 0.743082i \(-0.266637\pi\)
0.669201 + 0.743082i \(0.266637\pi\)
\(164\) 2.48692 1.43582i 0.194196 0.112119i
\(165\) 0.105930 + 0.289376i 0.00824667 + 0.0225279i
\(166\) 13.7845 7.95846i 1.06988 0.617697i
\(167\) 4.44098 7.69200i 0.343653 0.595225i −0.641455 0.767161i \(-0.721669\pi\)
0.985108 + 0.171936i \(0.0550021\pi\)
\(168\) −0.692897 1.89282i −0.0534581 0.146035i
\(169\) 9.43828 16.3476i 0.726022 1.25751i
\(170\) 3.87791 0.297422
\(171\) −14.5484 5.23434i −1.11254 0.400280i
\(172\) −0.735867 0.424853i −0.0561093 0.0323947i
\(173\) 2.18205 1.25981i 0.165898 0.0957813i −0.414752 0.909934i \(-0.636132\pi\)
0.580650 + 0.814153i \(0.302798\pi\)
\(174\) −6.18292 + 7.39624i −0.468726 + 0.560707i
\(175\) 0.581871 + 1.00783i 0.0439853 + 0.0761848i
\(176\) −0.0889568 0.154078i −0.00670537 0.0116140i
\(177\) 2.93827 + 8.02662i 0.220854 + 0.603318i
\(178\) 5.20790i 0.390348i
\(179\) −7.26572 + 12.5846i −0.543065 + 0.940616i 0.455661 + 0.890153i \(0.349403\pi\)
−0.998726 + 0.0504628i \(0.983930\pi\)
\(180\) 1.93685 + 2.29099i 0.144364 + 0.170760i
\(181\) −3.27223 + 1.88922i −0.243223 + 0.140425i −0.616657 0.787232i \(-0.711513\pi\)
0.373434 + 0.927657i \(0.378180\pi\)
\(182\) −6.57041 −0.487031
\(183\) −0.00252716 + 0.00302309i −0.000186813 + 0.000223473i
\(184\) 5.70722i 0.420742i
\(185\) −0.903557 −0.0664308
\(186\) 8.58010 4.40248i 0.629124 0.322806i
\(187\) −0.689933 −0.0504529
\(188\) 4.11079i 0.299810i
\(189\) −3.05249 5.21999i −0.222036 0.379699i
\(190\) −5.15378 −0.373895
\(191\) −5.58732 + 3.22584i −0.404284 + 0.233414i −0.688331 0.725397i \(-0.741656\pi\)
0.284047 + 0.958810i \(0.408323\pi\)
\(192\) −1.32888 1.11089i −0.0959039 0.0801713i
\(193\) −1.05136 + 1.82101i −0.0756786 + 0.131079i −0.901381 0.433027i \(-0.857446\pi\)
0.825703 + 0.564106i \(0.190779\pi\)
\(194\) 13.7078i 0.984161i
\(195\) 9.18310 3.36161i 0.657615 0.240730i
\(196\) −2.82285 4.88932i −0.201632 0.349237i
\(197\) −9.43359 16.3395i −0.672115 1.16414i −0.977303 0.211846i \(-0.932053\pi\)
0.305188 0.952292i \(-0.401281\pi\)
\(198\) −0.344591 0.407598i −0.0244890 0.0289667i
\(199\) 16.6694 9.62408i 1.18166 0.682233i 0.225263 0.974298i \(-0.427676\pi\)
0.956398 + 0.292065i \(0.0943425\pi\)
\(200\) 0.866025 + 0.500000i 0.0612372 + 0.0353553i
\(201\) 1.90649 10.9304i 0.134473 0.770967i
\(202\) −2.34879 −0.165260
\(203\) 3.23855 5.60933i 0.227302 0.393698i
\(204\) −6.30741 + 2.30892i −0.441607 + 0.161657i
\(205\) 1.43582 2.48692i 0.100282 0.173694i
\(206\) −14.7109 + 8.49332i −1.02495 + 0.591758i
\(207\) −3.03546 16.8504i −0.210979 1.17119i
\(208\) −4.88952 + 2.82297i −0.339027 + 0.195738i
\(209\) 0.916927 0.0634252
\(210\) −1.54648 1.29279i −0.106717 0.0892107i
\(211\) 5.53532 9.58746i 0.381067 0.660028i −0.610148 0.792288i \(-0.708890\pi\)
0.991215 + 0.132260i \(0.0422233\pi\)
\(212\) −6.25104 10.8271i −0.429323 0.743609i
\(213\) −21.6161 3.77031i −1.48111 0.258338i
\(214\) 2.31167 4.00394i 0.158023 0.273703i
\(215\) −0.849706 −0.0579495
\(216\) −4.51434 2.57308i −0.307162 0.175076i
\(217\) −5.17086 + 3.90454i −0.351021 + 0.265057i
\(218\) 18.3302i 1.24148i
\(219\) 18.3640 + 3.20308i 1.24092 + 0.216444i
\(220\) −0.154078 0.0889568i −0.0103879 0.00599746i
\(221\) 21.8944i 1.47278i
\(222\) 1.46963 0.537981i 0.0986353 0.0361069i
\(223\) −3.79542 2.19128i −0.254160 0.146739i 0.367508 0.930020i \(-0.380211\pi\)
−0.621668 + 0.783281i \(0.713545\pi\)
\(224\) 1.00783 + 0.581871i 0.0673385 + 0.0388779i
\(225\) 2.82285 + 1.01563i 0.188190 + 0.0677088i
\(226\) 0.217548 + 0.376805i 0.0144711 + 0.0250647i
\(227\) 14.2337 8.21783i 0.944724 0.545436i 0.0532857 0.998579i \(-0.483031\pi\)
0.891438 + 0.453143i \(0.149697\pi\)
\(228\) 8.38261 3.06858i 0.555152 0.203222i
\(229\) 0.621599 + 0.358880i 0.0410764 + 0.0237155i 0.520398 0.853924i \(-0.325784\pi\)
−0.479321 + 0.877640i \(0.659117\pi\)
\(230\) −2.85361 4.94260i −0.188162 0.325905i
\(231\) 0.275139 + 0.230004i 0.0181028 + 0.0151332i
\(232\) 5.56575i 0.365410i
\(233\) 15.7057i 1.02891i −0.857517 0.514456i \(-0.827994\pi\)
0.857517 0.514456i \(-0.172006\pi\)
\(234\) −12.9348 + 10.9353i −0.845572 + 0.714863i
\(235\) 2.05539 + 3.56005i 0.134079 + 0.232232i
\(236\) −4.27376 2.46746i −0.278198 0.160618i
\(237\) −1.73685 4.74464i −0.112820 0.308197i
\(238\) 3.90828 2.25644i 0.253336 0.146264i
\(239\) 2.90971 + 5.03976i 0.188213 + 0.325995i 0.944655 0.328067i \(-0.106397\pi\)
−0.756441 + 0.654062i \(0.773064\pi\)
\(240\) −1.70629 0.297614i −0.110141 0.0192109i
\(241\) 5.77410 + 3.33368i 0.371942 + 0.214741i 0.674307 0.738451i \(-0.264443\pi\)
−0.302364 + 0.953192i \(0.597776\pi\)
\(242\) −9.49887 5.48417i −0.610610 0.352536i
\(243\) −14.6970 5.19595i −0.942814 0.333321i
\(244\) 0.00227491i 0.000145636i
\(245\) −4.88932 2.82285i −0.312367 0.180345i
\(246\) −0.854642 + 4.89986i −0.0544900 + 0.312404i
\(247\) 29.0979i 1.85146i
\(248\) −2.17043 + 5.12730i −0.137823 + 0.325584i
\(249\) −4.73710 + 27.1589i −0.300201 + 1.72113i
\(250\) 1.00000 0.0632456
\(251\) −4.15063 + 7.18911i −0.261986 + 0.453773i −0.966770 0.255650i \(-0.917711\pi\)
0.704784 + 0.709422i \(0.251044\pi\)
\(252\) 3.28507 + 1.18193i 0.206940 + 0.0744548i
\(253\) 0.507696 + 0.879355i 0.0319186 + 0.0552846i
\(254\) 6.30073 10.9132i 0.395343 0.684754i
\(255\) −4.30792 + 5.15329i −0.269772 + 0.322712i
\(256\) 1.00000 0.0625000
\(257\) −20.8110 + 12.0152i −1.29815 + 0.749490i −0.980085 0.198577i \(-0.936368\pi\)
−0.318070 + 0.948067i \(0.603035\pi\)
\(258\) 1.38204 0.505918i 0.0860423 0.0314971i
\(259\) −0.910632 + 0.525754i −0.0565839 + 0.0326688i
\(260\) −2.82297 + 4.88952i −0.175073 + 0.303235i
\(261\) −2.96022 16.4328i −0.183233 1.01716i
\(262\) 10.5849 18.3335i 0.653934 1.13265i
\(263\) −13.3178 −0.821209 −0.410605 0.911813i \(-0.634682\pi\)
−0.410605 + 0.911813i \(0.634682\pi\)
\(264\) 0.303572 + 0.0529495i 0.0186836 + 0.00325882i
\(265\) −10.8271 6.25104i −0.665104 0.383998i
\(266\) −5.19414 + 2.99884i −0.318473 + 0.183870i
\(267\) 6.92069 + 5.78538i 0.423539 + 0.354060i
\(268\) 3.20296 + 5.54769i 0.195652 + 0.338879i
\(269\) −0.769900 1.33351i −0.0469416 0.0813052i 0.841600 0.540101i \(-0.181614\pi\)
−0.888542 + 0.458796i \(0.848281\pi\)
\(270\) −5.19607 + 0.0288151i −0.316223 + 0.00175363i
\(271\) 8.84626i 0.537372i 0.963228 + 0.268686i \(0.0865894\pi\)
−0.963228 + 0.268686i \(0.913411\pi\)
\(272\) 1.93896 3.35837i 0.117566 0.203631i
\(273\) 7.29898 8.73131i 0.441754 0.528443i
\(274\) −11.1218 + 6.42120i −0.671895 + 0.387919i
\(275\) −0.177914 −0.0107286
\(276\) 7.58423 + 6.34007i 0.456517 + 0.381628i
\(277\) 14.9715i 0.899552i 0.893141 + 0.449776i \(0.148496\pi\)
−0.893141 + 0.449776i \(0.851504\pi\)
\(278\) −0.913499 −0.0547880
\(279\) −3.68113 + 16.2926i −0.220383 + 0.975413i
\(280\) 1.16374 0.0695469
\(281\) 7.32299i 0.436853i 0.975853 + 0.218426i \(0.0700924\pi\)
−0.975853 + 0.218426i \(0.929908\pi\)
\(282\) −5.46276 4.56662i −0.325303 0.271938i
\(283\) −14.6211 −0.869133 −0.434567 0.900640i \(-0.643098\pi\)
−0.434567 + 0.900640i \(0.643098\pi\)
\(284\) 10.9712 6.33424i 0.651022 0.375868i
\(285\) 5.72526 6.84878i 0.339135 0.405686i
\(286\) 0.502244 0.869912i 0.0296983 0.0514390i
\(287\) 3.34186i 0.197263i
\(288\) 2.95248 0.531863i 0.173976 0.0313404i
\(289\) 0.980903 + 1.69897i 0.0577002 + 0.0999397i
\(290\) −2.78288 4.82008i −0.163416 0.283045i
\(291\) −18.2160 15.2278i −1.06784 0.892668i
\(292\) −9.32062 + 5.38127i −0.545448 + 0.314915i
\(293\) −29.5457 17.0582i −1.72608 0.996551i −0.904531 0.426408i \(-0.859779\pi\)
−0.821545 0.570143i \(-0.806888\pi\)
\(294\) 9.63321 + 1.68024i 0.561820 + 0.0979936i
\(295\) −4.93491 −0.287322
\(296\) −0.451779 + 0.782503i −0.0262591 + 0.0454821i
\(297\) 0.924452 0.00512660i 0.0536421 0.000297475i
\(298\) −2.29269 + 3.97105i −0.132812 + 0.230037i
\(299\) 27.9056 16.1113i 1.61382 0.931740i
\(300\) −1.62650 + 0.595404i −0.0939059 + 0.0343757i
\(301\) −0.856359 + 0.494419i −0.0493597 + 0.0284979i
\(302\) 18.0258 1.03727
\(303\) 2.60923 3.12126i 0.149897 0.179312i
\(304\) −2.57689 + 4.46331i −0.147795 + 0.255988i
\(305\) −0.00113745 0.00197013i −6.51304e−5 0.000112809i
\(306\) 3.93853 10.9468i 0.225151 0.625785i
\(307\) 8.94582 15.4946i 0.510565 0.884324i −0.489360 0.872082i \(-0.662770\pi\)
0.999925 0.0122426i \(-0.00389705\pi\)
\(308\) −0.207046 −0.0117975
\(309\) 5.05546 28.9841i 0.287595 1.64885i
\(310\) 0.684001 + 5.52559i 0.0388486 + 0.313832i
\(311\) 14.8875i 0.844194i 0.906551 + 0.422097i \(0.138706\pi\)
−0.906551 + 0.422097i \(0.861294\pi\)
\(312\) 1.68031 9.63360i 0.0951287 0.545395i
\(313\) −6.65729 3.84359i −0.376293 0.217253i 0.299911 0.953967i \(-0.403043\pi\)
−0.676204 + 0.736714i \(0.736376\pi\)
\(314\) 9.03549i 0.509902i
\(315\) 3.43592 0.618952i 0.193592 0.0348740i
\(316\) 2.52627 + 1.45854i 0.142114 + 0.0820495i
\(317\) −4.78141 2.76055i −0.268551 0.155048i 0.359678 0.933076i \(-0.382886\pi\)
−0.628229 + 0.778029i \(0.716220\pi\)
\(318\) 21.3322 + 3.72079i 1.19625 + 0.208652i
\(319\) 0.495111 + 0.857558i 0.0277209 + 0.0480140i
\(320\) 0.866025 0.500000i 0.0484123 0.0279508i
\(321\) 2.75276 + 7.51986i 0.153644 + 0.419718i
\(322\) −5.75191 3.32087i −0.320542 0.185065i
\(323\) 9.99295 + 17.3083i 0.556023 + 0.963060i
\(324\) 8.43424 3.14063i 0.468569 0.174479i
\(325\) 5.64593i 0.313180i
\(326\) 17.0876i 0.946392i
\(327\) 24.3587 + 20.3627i 1.34704 + 1.12606i
\(328\) −1.43582 2.48692i −0.0792800 0.137317i
\(329\) 4.14298 + 2.39195i 0.228410 + 0.131872i
\(330\) 0.289376 0.105930i 0.0159296 0.00583128i
\(331\) −7.77002 + 4.48602i −0.427079 + 0.246574i −0.698101 0.715999i \(-0.745972\pi\)
0.271022 + 0.962573i \(0.412638\pi\)
\(332\) −7.95846 13.7845i −0.436777 0.756521i
\(333\) −0.917681 + 2.55061i −0.0502886 + 0.139772i
\(334\) −7.69200 4.44098i −0.420888 0.243000i
\(335\) 5.54769 + 3.20296i 0.303102 + 0.174996i
\(336\) −1.89282 + 0.692897i −0.103262 + 0.0378006i
\(337\) 2.44574i 0.133228i 0.997779 + 0.0666141i \(0.0212196\pi\)
−0.997779 + 0.0666141i \(0.978780\pi\)
\(338\) −16.3476 9.43828i −0.889191 0.513375i
\(339\) −0.742401 0.129491i −0.0403217 0.00703297i
\(340\) 3.87791i 0.210309i
\(341\) −0.121693 0.983077i −0.00659005 0.0532366i
\(342\) −5.23434 + 14.5484i −0.283041 + 0.786685i
\(343\) −14.7163 −0.794608
\(344\) −0.424853 + 0.735867i −0.0229065 + 0.0396753i
\(345\) 9.73818 + 1.69855i 0.524286 + 0.0914468i
\(346\) −1.25981 2.18205i −0.0677276 0.117308i
\(347\) 8.43977 14.6181i 0.453071 0.784741i −0.545504 0.838108i \(-0.683662\pi\)
0.998575 + 0.0533666i \(0.0169952\pi\)
\(348\) 7.39624 + 6.18292i 0.396480 + 0.331439i
\(349\) 32.6846 1.74957 0.874783 0.484515i \(-0.161004\pi\)
0.874783 + 0.484515i \(0.161004\pi\)
\(350\) 1.00783 0.581871i 0.0538708 0.0311023i
\(351\) −0.162688 29.3367i −0.00868365 1.56588i
\(352\) −0.154078 + 0.0889568i −0.00821237 + 0.00474141i
\(353\) −5.87229 + 10.1711i −0.312551 + 0.541353i −0.978914 0.204274i \(-0.934517\pi\)
0.666363 + 0.745627i \(0.267850\pi\)
\(354\) 8.02662 2.93827i 0.426610 0.156167i
\(355\) 6.33424 10.9712i 0.336186 0.582292i
\(356\) −5.20790 −0.276018
\(357\) −1.34310 + 7.70030i −0.0710843 + 0.407543i
\(358\) 12.5846 + 7.26572i 0.665116 + 0.384005i
\(359\) 9.22320 5.32502i 0.486782 0.281044i −0.236457 0.971642i \(-0.575986\pi\)
0.723238 + 0.690598i \(0.242653\pi\)
\(360\) 2.29099 1.93685i 0.120746 0.102081i
\(361\) −3.78073 6.54841i −0.198986 0.344653i
\(362\) 1.88922 + 3.27223i 0.0992953 + 0.171984i
\(363\) 17.8400 6.53060i 0.936357 0.342767i
\(364\) 6.57041i 0.344383i
\(365\) −5.38127 + 9.32062i −0.281668 + 0.487864i
\(366\) 0.00302309 + 0.00252716i 0.000158019 + 0.000132097i
\(367\) 25.0136 14.4416i 1.30570 0.753847i 0.324326 0.945946i \(-0.394863\pi\)
0.981376 + 0.192099i \(0.0615294\pi\)
\(368\) −5.70722 −0.297510
\(369\) −5.56193 6.57891i −0.289543 0.342484i
\(370\) 0.903557i 0.0469737i
\(371\) −14.5492 −0.755356
\(372\) −4.40248 8.58010i −0.228258 0.444858i
\(373\) −15.4070 −0.797744 −0.398872 0.917007i \(-0.630598\pi\)
−0.398872 + 0.917007i \(0.630598\pi\)
\(374\) 0.689933i 0.0356756i
\(375\) −1.11089 + 1.32888i −0.0573659 + 0.0686233i
\(376\) 4.11079 0.211998
\(377\) 27.2139 15.7119i 1.40159 0.809206i
\(378\) −5.21999 + 3.05249i −0.268487 + 0.157003i
\(379\) −4.66494 + 8.07991i −0.239622 + 0.415037i −0.960606 0.277915i \(-0.910357\pi\)
0.720984 + 0.692952i \(0.243690\pi\)
\(380\) 5.15378i 0.264383i
\(381\) 7.50296 + 20.4962i 0.384388 + 1.05005i
\(382\) 3.22584 + 5.58732i 0.165048 + 0.285872i
\(383\) 11.7909 + 20.4225i 0.602488 + 1.04354i 0.992443 + 0.122706i \(0.0391574\pi\)
−0.389955 + 0.920834i \(0.627509\pi\)
\(384\) −1.11089 + 1.32888i −0.0566897 + 0.0678143i
\(385\) −0.179307 + 0.103523i −0.00913831 + 0.00527601i
\(386\) 1.82101 + 1.05136i 0.0926870 + 0.0535129i
\(387\) −0.862988 + 2.39859i −0.0438681 + 0.121927i
\(388\) 13.7078 0.695907
\(389\) −17.1562 + 29.7153i −0.869852 + 1.50663i −0.00770372 + 0.999970i \(0.502452\pi\)
−0.862148 + 0.506657i \(0.830881\pi\)
\(390\) −3.36161 9.18310i −0.170222 0.465004i
\(391\) −11.0660 + 19.1670i −0.559634 + 0.969315i
\(392\) −4.88932 + 2.82285i −0.246948 + 0.142576i
\(393\) 12.6045 + 34.4325i 0.635814 + 1.73689i
\(394\) −16.3395 + 9.43359i −0.823170 + 0.475257i
\(395\) 2.91709 0.146775
\(396\) −0.407598 + 0.344591i −0.0204826 + 0.0173164i
\(397\) −13.0551 + 22.6122i −0.655218 + 1.13487i 0.326621 + 0.945155i \(0.394090\pi\)
−0.981839 + 0.189716i \(0.939243\pi\)
\(398\) −9.62408 16.6694i −0.482411 0.835561i
\(399\) 1.78499 10.2338i 0.0893613 0.512329i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −1.81201 −0.0904873 −0.0452436 0.998976i \(-0.514406\pi\)
−0.0452436 + 0.998976i \(0.514406\pi\)
\(402\) −10.9304 1.90649i −0.545156 0.0950871i
\(403\) −31.1971 + 3.86182i −1.55404 + 0.192371i
\(404\) 2.34879i 0.116856i
\(405\) 5.73395 6.93699i 0.284922 0.344702i
\(406\) −5.60933 3.23855i −0.278387 0.160727i
\(407\) 0.160755i 0.00796833i
\(408\) 2.30892 + 6.30741i 0.114309 + 0.312263i
\(409\) −21.5022 12.4143i −1.06322 0.613849i −0.136897 0.990585i \(-0.543713\pi\)
−0.926320 + 0.376737i \(0.877046\pi\)
\(410\) −2.48692 1.43582i −0.122820 0.0709102i
\(411\) 3.82208 21.9129i 0.188529 1.08088i
\(412\) 8.49332 + 14.7109i 0.418436 + 0.724752i
\(413\) −4.97356 + 2.87148i −0.244733 + 0.141296i
\(414\) −16.8504 + 3.03546i −0.828154 + 0.149185i
\(415\) −13.7845 7.95846i −0.676653 0.390666i
\(416\) 2.82297 + 4.88952i 0.138407 + 0.239729i
\(417\) 1.01479 1.21393i 0.0496946 0.0594466i
\(418\) 0.916927i 0.0448484i
\(419\) 16.9548i 0.828295i 0.910210 + 0.414148i \(0.135920\pi\)
−0.910210 + 0.414148i \(0.864080\pi\)
\(420\) −1.29279 + 1.54648i −0.0630815 + 0.0754604i
\(421\) 14.5265 + 25.1607i 0.707980 + 1.22626i 0.965605 + 0.260013i \(0.0837267\pi\)
−0.257625 + 0.966245i \(0.582940\pi\)
\(422\) −9.58746 5.53532i −0.466710 0.269455i
\(423\) 12.1370 2.18638i 0.590121 0.106305i
\(424\) −10.8271 + 6.25104i −0.525811 + 0.303577i
\(425\) −1.93896 3.35837i −0.0940532 0.162905i
\(426\) −3.77031 + 21.6161i −0.182672 + 1.04730i
\(427\) −0.00229272 0.00132370i −0.000110953 6.40585e-5i
\(428\) −4.00394 2.31167i −0.193538 0.111739i
\(429\) 0.598076 + 1.63380i 0.0288754 + 0.0788805i
\(430\) 0.849706i 0.0409765i
\(431\) 18.8864 + 10.9041i 0.909726 + 0.525231i 0.880343 0.474337i \(-0.157312\pi\)
0.0293833 + 0.999568i \(0.490646\pi\)
\(432\) −2.57308 + 4.51434i −0.123797 + 0.217196i
\(433\) 22.8178i 1.09655i 0.836297 + 0.548277i \(0.184716\pi\)
−0.836297 + 0.548277i \(0.815284\pi\)
\(434\) 3.90454 + 5.17086i 0.187424 + 0.248209i
\(435\) 9.49679 + 1.65645i 0.455336 + 0.0794205i
\(436\) −18.3302 −0.877856
\(437\) 14.7069 25.4731i 0.703526 1.21854i
\(438\) 3.20308 18.3640i 0.153049 0.877466i
\(439\) 11.9238 + 20.6527i 0.569094 + 0.985699i 0.996656 + 0.0817131i \(0.0260391\pi\)
−0.427562 + 0.903986i \(0.640628\pi\)
\(440\) −0.0889568 + 0.154078i −0.00424085 + 0.00734536i
\(441\) −12.9342 + 10.9349i −0.615916 + 0.520708i
\(442\) 21.8944 1.04141
\(443\) 18.1698 10.4904i 0.863275 0.498412i −0.00183237 0.999998i \(-0.500583\pi\)
0.865108 + 0.501586i \(0.167250\pi\)
\(444\) −0.537981 1.46963i −0.0255315 0.0697457i
\(445\) −4.51017 + 2.60395i −0.213803 + 0.123439i
\(446\) −2.19128 + 3.79542i −0.103760 + 0.179718i
\(447\) −2.73015 7.45810i −0.129132 0.352756i
\(448\) 0.581871 1.00783i 0.0274908 0.0476155i
\(449\) 30.8958 1.45806 0.729032 0.684479i \(-0.239970\pi\)
0.729032 + 0.684479i \(0.239970\pi\)
\(450\) 1.01563 2.82285i 0.0478773 0.133071i
\(451\) 0.442456 + 0.255452i 0.0208345 + 0.0120288i
\(452\) 0.376805 0.217548i 0.0177234 0.0102326i
\(453\) −20.0246 + 23.9542i −0.940837 + 1.12546i
\(454\) −8.21783 14.2337i −0.385682 0.668020i
\(455\) 3.28521 + 5.69014i 0.154013 + 0.266758i
\(456\) −3.06858 8.38261i −0.143699 0.392552i
\(457\) 10.1581i 0.475177i 0.971366 + 0.237589i \(0.0763570\pi\)
−0.971366 + 0.237589i \(0.923643\pi\)
\(458\) 0.358880 0.621599i 0.0167694 0.0290454i
\(459\) 10.1717 + 17.3945i 0.474775 + 0.811904i
\(460\) −4.94260 + 2.85361i −0.230450 + 0.133050i
\(461\) −19.8197 −0.923095 −0.461547 0.887116i \(-0.652706\pi\)
−0.461547 + 0.887116i \(0.652706\pi\)
\(462\) 0.230004 0.275139i 0.0107008 0.0128006i
\(463\) 10.9325i 0.508074i 0.967194 + 0.254037i \(0.0817586\pi\)
−0.967194 + 0.254037i \(0.918241\pi\)
\(464\) −5.56575 −0.258384
\(465\) −8.10271 5.22934i −0.375754 0.242505i
\(466\) −15.7057 −0.727551
\(467\) 11.3377i 0.524644i 0.964980 + 0.262322i \(0.0844883\pi\)
−0.964980 + 0.262322i \(0.915512\pi\)
\(468\) 10.9353 + 12.9348i 0.505485 + 0.597910i
\(469\) 7.45483 0.344232
\(470\) 3.56005 2.05539i 0.164213 0.0948083i
\(471\) −12.0071 10.0374i −0.553259 0.462499i
\(472\) −2.46746 + 4.27376i −0.113574 + 0.196716i
\(473\) 0.151174i 0.00695100i
\(474\) −4.74464 + 1.73685i −0.217928 + 0.0797760i
\(475\) 2.57689 + 4.46331i 0.118236 + 0.204790i
\(476\) −2.25644 3.90828i −0.103424 0.179136i
\(477\) −28.6421 + 24.2146i −1.31143 + 1.10871i
\(478\) 5.03976 2.90971i 0.230513 0.133087i
\(479\) 35.3823 + 20.4280i 1.61666 + 0.933377i 0.987777 + 0.155875i \(0.0498198\pi\)
0.628880 + 0.777502i \(0.283514\pi\)
\(480\) −0.297614 + 1.70629i −0.0135842 + 0.0778811i
\(481\) −5.10142 −0.232605
\(482\) 3.33368 5.77410i 0.151845 0.263003i
\(483\) 10.8028 3.95452i 0.491543 0.179937i
\(484\) −5.48417 + 9.49887i −0.249281 + 0.431767i
\(485\) 11.8713 6.85389i 0.539047 0.311219i
\(486\) −5.19595 + 14.6970i −0.235693 + 0.666670i
\(487\) −31.5249 + 18.2009i −1.42853 + 0.824761i −0.997005 0.0773402i \(-0.975357\pi\)
−0.431524 + 0.902102i \(0.642024\pi\)
\(488\) −0.00227491 −0.000102980
\(489\) 22.7074 + 18.9823i 1.02686 + 0.858411i
\(490\) −2.82285 + 4.88932i −0.127523 + 0.220877i
\(491\) 16.2180 + 28.0904i 0.731908 + 1.26770i 0.956067 + 0.293149i \(0.0947032\pi\)
−0.224159 + 0.974553i \(0.571963\pi\)
\(492\) 4.89986 + 0.854642i 0.220903 + 0.0385302i
\(493\) −10.7917 + 18.6919i −0.486036 + 0.841839i
\(494\) −29.0979 −1.30918
\(495\) −0.180695 + 0.502224i −0.00812162 + 0.0225733i
\(496\) 5.12730 + 2.17043i 0.230223 + 0.0974553i
\(497\) 14.7428i 0.661307i
\(498\) 27.1589 + 4.73710i 1.21702 + 0.212274i
\(499\) 36.8738 + 21.2891i 1.65070 + 0.953030i 0.976786 + 0.214218i \(0.0687203\pi\)
0.673911 + 0.738812i \(0.264613\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 14.4465 5.28835i 0.645421 0.236266i
\(502\) 7.18911 + 4.15063i 0.320866 + 0.185252i
\(503\) 32.1602 + 18.5677i 1.43395 + 0.827893i 0.997419 0.0717951i \(-0.0228728\pi\)
0.436533 + 0.899688i \(0.356206\pi\)
\(504\) 1.18193 3.28507i 0.0526475 0.146329i
\(505\) 1.17439 + 2.03411i 0.0522598 + 0.0905166i
\(506\) 0.879355 0.507696i 0.0390921 0.0225698i
\(507\) 30.7027 11.2392i 1.36355 0.499150i
\(508\) −10.9132 6.30073i −0.484194 0.279550i
\(509\) −7.91070 13.7017i −0.350636 0.607319i 0.635725 0.771915i \(-0.280701\pi\)
−0.986361 + 0.164597i \(0.947368\pi\)
\(510\) 5.15329 + 4.30792i 0.228192 + 0.190758i
\(511\) 12.5248i 0.554065i
\(512\) 1.00000i 0.0441942i
\(513\) −13.5183 23.1174i −0.596848 1.02066i
\(514\) 12.0152 + 20.8110i 0.529970 + 0.917934i
\(515\) 14.7109 + 8.49332i 0.648238 + 0.374261i
\(516\) −0.505918 1.38204i −0.0222718 0.0608411i
\(517\) −0.633381 + 0.365682i −0.0278560 + 0.0160827i
\(518\) 0.525754 + 0.910632i 0.0231003 + 0.0400109i
\(519\) 4.29919 + 0.749872i 0.188713 + 0.0329157i
\(520\) 4.88952 + 2.82297i 0.214420 + 0.123795i
\(521\) −23.6227 13.6385i −1.03493 0.597515i −0.116535 0.993187i \(-0.537179\pi\)
−0.918392 + 0.395671i \(0.870512\pi\)
\(522\) −16.4328 + 2.96022i −0.719242 + 0.129565i
\(523\) 18.7630i 0.820447i −0.911985 0.410224i \(-0.865451\pi\)
0.911985 0.410224i \(-0.134549\pi\)
\(524\) −18.3335 10.5849i −0.800903 0.462401i
\(525\) −0.346346 + 1.98568i −0.0151158 + 0.0866623i
\(526\) 13.3178i 0.580683i
\(527\) 17.2307 13.0110i 0.750582 0.566768i
\(528\) 0.0529495 0.303572i 0.00230433 0.0132113i
\(529\) 9.57238 0.416191
\(530\) −6.25104 + 10.8271i −0.271528 + 0.470300i
\(531\) −5.01205 + 13.9305i −0.217505 + 0.604533i
\(532\) 2.99884 + 5.19414i 0.130016 + 0.225194i
\(533\) 8.10656 14.0410i 0.351134 0.608182i
\(534\) 5.78538 6.92069i 0.250358 0.299488i
\(535\) −4.62335 −0.199885
\(536\) 5.54769 3.20296i 0.239624 0.138347i
\(537\) −23.6353 + 8.65207i −1.01994 + 0.373364i
\(538\) −1.33351 + 0.769900i −0.0574915 + 0.0331927i
\(539\) 0.502224 0.869877i 0.0216323 0.0374682i
\(540\) 0.0288151 + 5.19607i 0.00124000 + 0.223603i
\(541\) 9.14009 15.8311i 0.392963 0.680632i −0.599876 0.800093i \(-0.704783\pi\)
0.992839 + 0.119461i \(0.0381167\pi\)
\(542\) 8.84626 0.379979
\(543\) −6.44712 1.12452i −0.276672 0.0482576i
\(544\) −3.35837 1.93896i −0.143989 0.0831320i
\(545\) −15.8744 + 9.16508i −0.679984 + 0.392589i
\(546\) −8.73131 7.29898i −0.373666 0.312368i
\(547\) 4.88556 + 8.46204i 0.208891 + 0.361811i 0.951366 0.308064i \(-0.0996811\pi\)
−0.742474 + 0.669875i \(0.766348\pi\)
\(548\) 6.42120 + 11.1218i 0.274300 + 0.475102i
\(549\) −0.00671661 + 0.00120994i −0.000286658 + 5.16390e-5i
\(550\) 0.177914i 0.00758626i
\(551\) 14.3423 24.8417i 0.611004 1.05829i
\(552\) 6.34007 7.58423i 0.269851 0.322806i
\(553\) 2.93993 1.69737i 0.125019 0.0721795i
\(554\) 14.9715 0.636080
\(555\) −1.20072 1.00375i −0.0509678 0.0426068i
\(556\) 0.913499i 0.0387410i
\(557\) −23.4375 −0.993081 −0.496540 0.868014i \(-0.665397\pi\)
−0.496540 + 0.868014i \(0.665397\pi\)
\(558\) 16.2926 + 3.68113i 0.689721 + 0.155835i
\(559\) −4.79738 −0.202908
\(560\) 1.16374i 0.0491771i
\(561\) −0.916841 0.766437i −0.0387090 0.0323590i
\(562\) 7.32299 0.308902
\(563\) 3.55872 2.05463i 0.149982 0.0865923i −0.423131 0.906069i \(-0.639069\pi\)
0.573113 + 0.819476i \(0.305736\pi\)
\(564\) −4.56662 + 5.46276i −0.192289 + 0.230024i
\(565\) 0.217548 0.376805i 0.00915232 0.0158523i
\(566\) 14.6211i 0.614570i
\(567\) 1.74242 10.3277i 0.0731748 0.433724i
\(568\) −6.33424 10.9712i −0.265779 0.460342i
\(569\) −20.3967 35.3280i −0.855072 1.48103i −0.876578 0.481260i \(-0.840179\pi\)
0.0215060 0.999769i \(-0.493154\pi\)
\(570\) −6.84878 5.72526i −0.286864 0.239805i
\(571\) −22.6637 + 13.0849i −0.948445 + 0.547585i −0.892598 0.450854i \(-0.851119\pi\)
−0.0558476 + 0.998439i \(0.517786\pi\)
\(572\) −0.869912 0.502244i −0.0363729 0.0209999i
\(573\) −11.0084 1.92011i −0.459884 0.0802137i
\(574\) −3.34186 −0.139486
\(575\) −2.85361 + 4.94260i −0.119004 + 0.206121i
\(576\) −0.531863 2.95248i −0.0221610 0.123020i
\(577\) −10.2691 + 17.7866i −0.427509 + 0.740467i −0.996651 0.0817721i \(-0.973942\pi\)
0.569142 + 0.822239i \(0.307275\pi\)
\(578\) 1.69897 0.980903i 0.0706680 0.0408002i
\(579\) −3.42007 + 1.25197i −0.142133 + 0.0520301i
\(580\) −4.82008 + 2.78288i −0.200143 + 0.115553i
\(581\) −18.5232 −0.768472
\(582\) −15.2278 + 18.2160i −0.631212 + 0.755079i
\(583\) 1.11214 1.92629i 0.0460603 0.0797788i
\(584\) 5.38127 + 9.32062i 0.222678 + 0.385690i
\(585\) 15.9376 + 5.73419i 0.658940 + 0.237079i
\(586\) −17.0582 + 29.5457i −0.704668 + 1.22052i
\(587\) 37.7684 1.55887 0.779433 0.626485i \(-0.215507\pi\)
0.779433 + 0.626485i \(0.215507\pi\)
\(588\) 1.68024 9.63321i 0.0692919 0.397267i
\(589\) −22.8998 + 17.2917i −0.943570 + 0.712494i
\(590\) 4.93491i 0.203167i
\(591\) 5.61513 32.1929i 0.230976 1.32424i
\(592\) 0.782503 + 0.451779i 0.0321607 + 0.0185680i
\(593\) 37.0997i 1.52350i −0.647870 0.761751i \(-0.724340\pi\)
0.647870 0.761751i \(-0.275660\pi\)
\(594\) −0.00512660 0.924452i −0.000210347 0.0379307i
\(595\) −3.90828 2.25644i −0.160224 0.0925052i
\(596\) 3.97105 + 2.29269i 0.162661 + 0.0939121i
\(597\) 32.8429 + 5.72852i 1.34417 + 0.234453i
\(598\) −16.1113 27.9056i −0.658840 1.14114i
\(599\) −17.6250 + 10.1758i −0.720139 + 0.415773i −0.814804 0.579737i \(-0.803155\pi\)
0.0946646 + 0.995509i \(0.469822\pi\)
\(600\) 0.595404 + 1.62650i 0.0243073 + 0.0664015i
\(601\) −35.9489 20.7551i −1.46639 0.846619i −0.467093 0.884208i \(-0.654699\pi\)
−0.999293 + 0.0375894i \(0.988032\pi\)
\(602\) 0.494419 + 0.856359i 0.0201510 + 0.0349026i
\(603\) 14.6759 12.4073i 0.597648 0.505263i
\(604\) 18.0258i 0.733458i
\(605\) 10.9683i 0.445927i
\(606\) −3.12126 2.60923i −0.126793 0.105993i
\(607\) −9.76384 16.9115i −0.396302 0.686415i 0.596964 0.802268i \(-0.296373\pi\)
−0.993266 + 0.115852i \(0.963040\pi\)
\(608\) 4.46331 + 2.57689i 0.181011 + 0.104507i
\(609\) 10.5350 3.85649i 0.426899 0.156273i
\(610\) −0.00197013 + 0.00113745i −7.97681e−5 + 4.60541e-5i
\(611\) 11.6046 + 20.0998i 0.469473 + 0.813150i
\(612\) −10.9468 3.93853i −0.442497 0.159206i
\(613\) −3.94704 2.27883i −0.159420 0.0920409i 0.418168 0.908370i \(-0.362672\pi\)
−0.577587 + 0.816329i \(0.696006\pi\)
\(614\) −15.4946 8.94582i −0.625312 0.361024i
\(615\) 4.67072 1.70979i 0.188342 0.0689453i
\(616\) 0.207046i 0.00834210i
\(617\) 17.5553 + 10.1355i 0.706749 + 0.408042i 0.809856 0.586628i \(-0.199545\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(618\) −28.9841 5.05546i −1.16591 0.203361i
\(619\) 13.7227i 0.551561i −0.961221 0.275781i \(-0.911064\pi\)
0.961221 0.275781i \(-0.0889363\pi\)
\(620\) 5.52559 0.684001i 0.221913 0.0274701i
\(621\) 14.6851 25.7643i 0.589295 1.03389i
\(622\) 14.8875 0.596935
\(623\) −3.03032 + 5.24868i −0.121407 + 0.210284i
\(624\) −9.63360 1.68031i −0.385653 0.0672662i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −3.84359 + 6.65729i −0.153621 + 0.266079i
\(627\) 1.21849 + 1.01860i 0.0486618 + 0.0406790i
\(628\) 9.03549 0.360555
\(629\) 3.03448 1.75196i 0.120993 0.0698551i
\(630\) −0.618952 3.43592i −0.0246596 0.136890i
\(631\) 9.02379 5.20989i 0.359231 0.207402i −0.309512 0.950895i \(-0.600166\pi\)
0.668743 + 0.743493i \(0.266832\pi\)
\(632\) 1.45854 2.52627i 0.0580178 0.100490i
\(633\) 18.0064 6.59151i 0.715689 0.261989i
\(634\) −2.76055 + 4.78141i −0.109635 + 0.189894i
\(635\) −12.6015 −0.500074
\(636\) 3.72079 21.3322i 0.147539 0.845875i
\(637\) −27.6048 15.9376i −1.09374 0.631472i
\(638\) 0.857558 0.495111i 0.0339510 0.0196016i
\(639\) −24.5369 29.0233i −0.970664 1.14815i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 10.4121 + 18.0343i 0.411254 + 0.712313i 0.995027 0.0996039i \(-0.0317576\pi\)
−0.583773 + 0.811917i \(0.698424\pi\)
\(642\) 7.51986 2.75276i 0.296785 0.108643i
\(643\) 45.6261i 1.79932i 0.436595 + 0.899658i \(0.356184\pi\)
−0.436595 + 0.899658i \(0.643816\pi\)
\(644\) −3.32087 + 5.75191i −0.130861 + 0.226657i
\(645\) −1.12916 0.943927i −0.0444606 0.0371671i
\(646\) 17.3083 9.99295i 0.680986 0.393167i
\(647\) −29.3824 −1.15514 −0.577570 0.816341i \(-0.695999\pi\)
−0.577570 + 0.816341i \(0.695999\pi\)
\(648\) −3.14063 8.43424i −0.123376 0.331328i
\(649\) 0.877988i 0.0344640i
\(650\) 5.64593 0.221452
\(651\) −11.2090 0.555557i −0.439314 0.0217740i
\(652\) −17.0876 −0.669201
\(653\) 36.5284i 1.42947i 0.699397 + 0.714734i \(0.253452\pi\)
−0.699397 + 0.714734i \(0.746548\pi\)
\(654\) 20.3627 24.3587i 0.796246 0.952499i
\(655\) −21.1697 −0.827169
\(656\) −2.48692 + 1.43582i −0.0970978 + 0.0560595i
\(657\) 20.8454 + 24.6568i 0.813255 + 0.961955i
\(658\) 2.39195 4.14298i 0.0932479 0.161510i
\(659\) 18.6641i 0.727050i −0.931584 0.363525i \(-0.881573\pi\)
0.931584 0.363525i \(-0.118427\pi\)
\(660\) −0.105930 0.289376i −0.00412334 0.0112639i
\(661\) −16.6494 28.8377i −0.647588 1.12166i −0.983697 0.179833i \(-0.942444\pi\)
0.336109 0.941823i \(-0.390889\pi\)
\(662\) 4.48602 + 7.77002i 0.174354 + 0.301990i
\(663\) −24.3222 + 29.0951i −0.944597 + 1.12996i
\(664\) −13.7845 + 7.95846i −0.534941 + 0.308848i
\(665\) 5.19414 + 2.99884i 0.201420 + 0.116290i
\(666\) 2.55061 + 0.917681i 0.0988340 + 0.0355594i
\(667\) 31.7650 1.22995
\(668\) −4.44098 + 7.69200i −0.171827 + 0.297613i
\(669\) −2.60940 7.12824i −0.100885 0.275594i
\(670\) 3.20296 5.54769i 0.123741 0.214326i
\(671\) 0.000350512 0 0.000202368i 1.35314e−5 0 7.81234e-6i
\(672\) 0.692897 + 1.89282i 0.0267291 + 0.0730173i
\(673\) 28.5063 16.4581i 1.09884 0.634414i 0.162922 0.986639i \(-0.447908\pi\)
0.935915 + 0.352225i \(0.114575\pi\)
\(674\) 2.44574 0.0942066
\(675\) 2.62299 + 4.48552i 0.100959 + 0.172648i
\(676\) −9.43828 + 16.3476i −0.363011 + 0.628753i
\(677\) 3.71782 + 6.43945i 0.142887 + 0.247488i 0.928583 0.371125i \(-0.121028\pi\)
−0.785695 + 0.618614i \(0.787695\pi\)
\(678\) −0.129491 + 0.742401i −0.00497306 + 0.0285117i
\(679\) 7.97616 13.8151i 0.306097 0.530175i
\(680\) −3.87791 −0.148711
\(681\) 28.0440 + 4.89148i 1.07465 + 0.187442i
\(682\) −0.983077 + 0.121693i −0.0376440 + 0.00465987i
\(683\) 27.8306i 1.06491i 0.846459 + 0.532453i \(0.178730\pi\)
−0.846459 + 0.532453i \(0.821270\pi\)
\(684\) 14.5484 + 5.23434i 0.556270 + 0.200140i
\(685\) 11.1218 + 6.42120i 0.424944 + 0.245341i
\(686\) 14.7163i 0.561872i
\(687\) 0.427357 + 1.16744i 0.0163047 + 0.0445405i
\(688\) 0.735867 + 0.424853i 0.0280547 + 0.0161974i
\(689\) −61.1292 35.2929i −2.32884 1.34455i
\(690\) 1.69855 9.73818i 0.0646626 0.370726i
\(691\) −17.9160 31.0315i −0.681558 1.18049i −0.974505 0.224365i \(-0.927969\pi\)
0.292947 0.956129i \(-0.405364\pi\)
\(692\) −2.18205 + 1.25981i −0.0829490 + 0.0478906i
\(693\) 0.110120 + 0.611297i 0.00418311 + 0.0232213i
\(694\) −14.6181 8.43977i −0.554896 0.320369i
\(695\) 0.456749 + 0.791113i 0.0173255 + 0.0300086i
\(696\) 6.18292 7.39624i 0.234363 0.280354i
\(697\) 11.1360i 0.421806i
\(698\) 32.6846i 1.23713i
\(699\) 17.4472 20.8710i 0.659914 0.789414i
\(700\) −0.581871 1.00783i −0.0219927 0.0380924i
\(701\) 6.49145 + 3.74784i 0.245179 + 0.141554i 0.617555 0.786528i \(-0.288123\pi\)
−0.372376 + 0.928082i \(0.621457\pi\)
\(702\) −29.3367 + 0.162688i −1.10724 + 0.00614027i
\(703\) −4.03285 + 2.32837i −0.152102 + 0.0878160i
\(704\) 0.0889568 + 0.154078i 0.00335268 + 0.00580702i
\(705\) −1.22343 + 7.01420i −0.0460769 + 0.264170i
\(706\) 10.1711 + 5.87229i 0.382795 + 0.221007i
\(707\) 2.36718 + 1.36669i 0.0890269 + 0.0513997i
\(708\) −2.93827 8.02662i −0.110427 0.301659i
\(709\) 1.59160i 0.0597738i 0.999553 + 0.0298869i \(0.00951471\pi\)
−0.999553 + 0.0298869i \(0.990485\pi\)
\(710\) −10.9712 6.33424i −0.411743 0.237720i
\(711\) 2.96269 8.23451i 0.111109 0.308818i
\(712\) 5.20790i 0.195174i
\(713\) −29.2626 12.3871i −1.09589 0.463902i
\(714\) 7.70030 + 1.34310i 0.288176 + 0.0502642i
\(715\) −1.00449 −0.0375657
\(716\) 7.26572 12.5846i 0.271533 0.470308i
\(717\) −1.73194 + 9.92961i −0.0646804 + 0.370828i
\(718\) −5.32502 9.22320i −0.198728 0.344207i
\(719\) 1.12193 1.94324i 0.0418410 0.0724707i −0.844347 0.535797i \(-0.820011\pi\)
0.886188 + 0.463327i \(0.153344\pi\)
\(720\) −1.93685 2.29099i −0.0721820 0.0853801i
\(721\) 19.7681 0.736202
\(722\) −6.54841 + 3.78073i −0.243707 + 0.140704i
\(723\) 3.96977 + 10.8444i 0.147637 + 0.403309i
\(724\) 3.27223 1.88922i 0.121611 0.0702124i
\(725\) −2.78288 + 4.82008i −0.103353 + 0.179013i
\(726\) −6.53060 17.8400i −0.242373 0.662104i
\(727\) 16.3097 28.2493i 0.604894 1.04771i −0.387174 0.922007i \(-0.626549\pi\)
0.992068 0.125701i \(-0.0401180\pi\)
\(728\) 6.57041 0.243516
\(729\) −13.7585 23.2315i −0.509574 0.860427i
\(730\) 9.32062 + 5.38127i 0.344972 + 0.199170i
\(731\) 2.85363 1.64754i 0.105545 0.0609365i
\(732\) 0.00252716 0.00302309i 9.34066e−5 0.000111736i
\(733\) −4.82676 8.36019i −0.178280 0.308791i 0.763011 0.646385i \(-0.223720\pi\)
−0.941292 + 0.337594i \(0.890387\pi\)
\(734\) −14.4416 25.0136i −0.533050 0.923270i
\(735\) −3.36147 9.18272i −0.123990 0.338710i
\(736\) 5.70722i 0.210371i
\(737\) −0.569850 + 0.987008i −0.0209907 + 0.0363569i
\(738\) −6.57891 + 5.56193i −0.242173 + 0.204738i
\(739\) 20.5340 11.8553i 0.755355 0.436105i −0.0722704 0.997385i \(-0.523024\pi\)
0.827626 + 0.561281i \(0.189691\pi\)
\(740\) 0.903557 0.0332154
\(741\) 32.3245 38.6677i 1.18747 1.42049i
\(742\) 14.5492i 0.534118i
\(743\) −33.9392 −1.24511 −0.622555 0.782576i \(-0.713905\pi\)
−0.622555 + 0.782576i \(0.713905\pi\)
\(744\) −8.58010 + 4.40248i −0.314562 + 0.161403i
\(745\) 4.58537 0.167995
\(746\) 15.4070i 0.564090i
\(747\) −36.4655 + 30.8286i −1.33420 + 1.12796i
\(748\) 0.689933 0.0252264
\(749\) −4.65955 + 2.69019i −0.170256 + 0.0982975i
\(750\) 1.32888 + 1.11089i 0.0485240 + 0.0405638i
\(751\) −3.61672 + 6.26434i −0.131976 + 0.228589i −0.924438 0.381332i \(-0.875466\pi\)
0.792462 + 0.609921i \(0.208799\pi\)
\(752\) 4.11079i 0.149905i
\(753\) −13.5020 + 4.94261i −0.492040 + 0.180119i
\(754\) −15.7119 27.2139i −0.572195 0.991071i
\(755\) −9.01289 15.6108i −0.328013 0.568134i
\(756\) 3.05249 + 5.21999i 0.111018 + 0.189849i
\(757\) −0.672009 + 0.387984i −0.0244246 + 0.0141015i −0.512163 0.858889i \(-0.671155\pi\)
0.487738 + 0.872990i \(0.337822\pi\)
\(758\) 8.07991 + 4.66494i 0.293475 + 0.169438i
\(759\) −0.302195 + 1.73255i −0.0109690 + 0.0628877i
\(760\) 5.15378 0.186947
\(761\) −3.20580 + 5.55261i −0.116210 + 0.201282i −0.918263 0.395971i \(-0.870408\pi\)
0.802053 + 0.597253i \(0.203741\pi\)
\(762\) 20.4962 7.50296i 0.742500 0.271803i
\(763\) −10.6658 + 18.4737i −0.386128 + 0.668793i
\(764\) 5.58732 3.22584i 0.202142 0.116707i
\(765\) −11.4494 + 2.06252i −0.413955 + 0.0745705i
\(766\) 20.4225 11.7909i 0.737895 0.426024i
\(767\) −27.8622 −1.00605
\(768\) 1.32888 + 1.11089i 0.0479520 + 0.0400857i
\(769\) 9.17949 15.8993i 0.331021 0.573345i −0.651691 0.758484i \(-0.725940\pi\)
0.982712 + 0.185139i \(0.0592736\pi\)
\(770\) 0.103523 + 0.179307i 0.00373070 + 0.00646176i
\(771\) −41.0030 7.15180i −1.47669 0.257566i
\(772\) 1.05136 1.82101i 0.0378393 0.0655396i
\(773\) 11.5363 0.414930 0.207465 0.978242i \(-0.433479\pi\)
0.207465 + 0.978242i \(0.433479\pi\)
\(774\) 2.39859 + 0.862988i 0.0862157 + 0.0310195i
\(775\) 4.44330 3.35516i 0.159608 0.120521i
\(776\) 13.7078i 0.492081i
\(777\) −1.79418 0.312943i −0.0643657 0.0112268i
\(778\) 29.7153 + 17.1562i 1.06535 + 0.615078i
\(779\) 14.7998i 0.530259i
\(780\) −9.18310 + 3.36161i −0.328808 + 0.120365i
\(781\) 1.95193 + 1.12695i 0.0698455 + 0.0403253i
\(782\) 19.1670 + 11.0660i 0.685409 + 0.395721i
\(783\) 14.3211 25.1257i 0.511796 0.897919i
\(784\) 2.82285 + 4.88932i 0.100816 + 0.174619i
\(785\) 7.82497 4.51775i 0.279285 0.161245i
\(786\) 34.4325 12.6045i 1.22817 0.449588i
\(787\) −15.4169 8.90097i −0.549554 0.317285i 0.199388 0.979921i \(-0.436105\pi\)
−0.748942 + 0.662635i \(0.769438\pi\)
\(788\) 9.43359 + 16.3395i 0.336058 + 0.582069i
\(789\) −17.6978 14.7945i −0.630058 0.526699i
\(790\) 2.91709i 0.103785i
\(791\) 0.506340i 0.0180034i
\(792\) 0.344591 + 0.407598i 0.0122445 + 0.0144834i
\(793\) −0.00642199 0.0111232i −0.000228051 0.000394997i
\(794\) 22.6122 + 13.0551i 0.802475 + 0.463309i
\(795\) −7.44378 20.3346i −0.264004 0.721194i
\(796\) −16.6694 + 9.62408i −0.590831 + 0.341116i
\(797\) 18.5843 + 32.1890i 0.658291 + 1.14019i 0.981058 + 0.193715i \(0.0620537\pi\)
−0.322767 + 0.946479i \(0.604613\pi\)
\(798\) −10.2338 1.78499i −0.362272 0.0631880i
\(799\) −13.8055 7.97063i −0.488405 0.281981i
\(800\) −0.866025 0.500000i −0.0306186 0.0176777i
\(801\) 2.76989 + 15.3762i 0.0978693 + 0.543291i
\(802\) 1.81201i 0.0639842i
\(803\) −1.65827 0.957400i −0.0585189 0.0337859i
\(804\) −1.90649 + 10.9304i −0.0672367 + 0.385484i
\(805\) 6.64174i 0.234090i
\(806\) 3.86182 + 31.1971i 0.136027 + 1.09887i
\(807\) 0.458266 2.62734i 0.0161317 0.0924869i
\(808\) 2.34879 0.0826300
\(809\) 6.71526 11.6312i 0.236096 0.408930i −0.723495 0.690330i \(-0.757465\pi\)
0.959591 + 0.281400i \(0.0907987\pi\)
\(810\) −6.93699 5.73395i −0.243741 0.201471i
\(811\) −4.22401 7.31619i −0.148325 0.256906i 0.782284 0.622922i \(-0.214055\pi\)
−0.930608 + 0.366016i \(0.880721\pi\)
\(812\) −3.23855 + 5.60933i −0.113651 + 0.196849i
\(813\) −9.82719 + 11.7556i −0.344654 + 0.412289i
\(814\) −0.160755 −0.00563446
\(815\) −14.7983 + 8.54378i −0.518360 + 0.299276i
\(816\) 6.30741 2.30892i 0.220804 0.0808285i
\(817\) −3.79250 + 2.18960i −0.132683 + 0.0766044i
\(818\) −12.4143 + 21.5022i −0.434056 + 0.751808i
\(819\) 19.3990 3.49456i 0.677856 0.122110i
\(820\) −1.43582 + 2.48692i −0.0501411 + 0.0868469i
\(821\) −21.5718 −0.752861 −0.376431 0.926445i \(-0.622849\pi\)
−0.376431 + 0.926445i \(0.622849\pi\)
\(822\) −21.9129 3.82208i −0.764299 0.133310i
\(823\) −23.2067 13.3984i −0.808934 0.467038i 0.0376515 0.999291i \(-0.488012\pi\)
−0.846586 + 0.532253i \(0.821346\pi\)
\(824\) 14.7109 8.49332i 0.512477 0.295879i
\(825\) −0.236426 0.197642i −0.00823131 0.00688100i
\(826\) 2.87148 + 4.97356i 0.0999117 + 0.173052i
\(827\) 8.45553 + 14.6454i 0.294028 + 0.509271i 0.974758 0.223263i \(-0.0716709\pi\)
−0.680731 + 0.732534i \(0.738338\pi\)
\(828\) 3.03546 + 16.8504i 0.105490 + 0.585593i
\(829\) 6.47384i 0.224846i −0.993660 0.112423i \(-0.964139\pi\)
0.993660 0.112423i \(-0.0358611\pi\)
\(830\) −7.95846 + 13.7845i −0.276242 + 0.478466i
\(831\) −16.6317 + 19.8954i −0.576946 + 0.690165i
\(832\) 4.88952 2.82297i 0.169514 0.0978688i
\(833\) 21.8935 0.758566
\(834\) −1.21393 1.01479i −0.0420351 0.0351394i
\(835\) 8.88196i 0.307373i
\(836\) −0.916927 −0.0317126
\(837\) −22.9910 + 17.5617i −0.794686 + 0.607020i
\(838\) 16.9548 0.585693
\(839\) 43.6645i 1.50747i −0.657180 0.753734i \(-0.728251\pi\)
0.657180 0.753734i \(-0.271749\pi\)
\(840\) 1.54648 + 1.29279i 0.0533586 + 0.0446053i
\(841\) 1.97760 0.0681931
\(842\) 25.1607 14.5265i 0.867095 0.500618i
\(843\) −8.13501 + 9.73140i −0.280184 + 0.335167i
\(844\) −5.53532 + 9.58746i −0.190534 + 0.330014i
\(845\) 18.8766i 0.649374i
\(846\) −2.18638 12.1370i −0.0751692 0.417279i
\(847\) 6.38216 + 11.0542i 0.219294 + 0.379828i
\(848\) 6.25104 + 10.8271i 0.214661 + 0.371805i
\(849\) −19.4297 16.2424i −0.666826 0.557436i
\(850\) −3.35837 + 1.93896i −0.115191 + 0.0665056i
\(851\) −4.46592 2.57840i −0.153090 0.0883864i
\(852\) 21.6161 + 3.77031i 0.740555 + 0.129169i
\(853\) 34.3980 1.17776 0.588882 0.808219i \(-0.299568\pi\)
0.588882 + 0.808219i \(0.299568\pi\)
\(854\) −0.00132370 + 0.00229272i −4.52962e−5 + 7.84553e-5i
\(855\) 15.2164 2.74111i 0.520391 0.0937439i
\(856\) −2.31167 + 4.00394i −0.0790114 + 0.136852i
\(857\) 14.9622 8.63842i 0.511098 0.295083i −0.222187 0.975004i \(-0.571319\pi\)
0.733285 + 0.679921i \(0.237986\pi\)
\(858\) 1.63380 0.598076i 0.0557769 0.0204180i
\(859\) 4.18085 2.41382i 0.142649 0.0823583i −0.426977 0.904262i \(-0.640421\pi\)
0.569626 + 0.821904i \(0.307088\pi\)
\(860\) 0.849706 0.0289747
\(861\) 3.71242 4.44094i 0.126519 0.151347i
\(862\) 10.9041 18.8864i 0.371394 0.643274i
\(863\) −8.63393 14.9544i −0.293902 0.509054i 0.680827 0.732445i \(-0.261621\pi\)
−0.974729 + 0.223391i \(0.928287\pi\)
\(864\) 4.51434 + 2.57308i 0.153581 + 0.0875380i
\(865\) −1.25981 + 2.18205i −0.0428347 + 0.0741919i
\(866\) 22.8178 0.775380
\(867\) −0.583861 + 3.34741i −0.0198290 + 0.113684i
\(868\) 5.17086 3.90454i 0.175510 0.132529i
\(869\) 0.518990i 0.0176055i
\(870\) 1.65645 9.49679i 0.0561588 0.321971i
\(871\) 31.3219 + 18.0837i 1.06130 + 0.612742i
\(872\) 18.3302i 0.620738i
\(873\) −7.29067 40.4719i −0.246752 1.36977i
\(874\) −25.4731 14.7069i −0.861640 0.497468i
\(875\) −1.00783 0.581871i −0.0340709 0.0196708i
\(876\) −18.3640 3.20308i −0.620462 0.108222i
\(877\) −21.8659 37.8729i −0.738359 1.27888i −0.953234 0.302234i \(-0.902268\pi\)
0.214874 0.976642i \(-0.431066\pi\)
\(878\) 20.6527 11.9238i 0.696994 0.402410i
\(879\) −20.3130 55.4902i −0.685142 1.87164i
\(880\) 0.154078 + 0.0889568i 0.00519396 + 0.00299873i
\(881\) −18.1740 31.4783i −0.612298 1.06053i −0.990852 0.134951i \(-0.956912\pi\)
0.378555 0.925579i \(-0.376421\pi\)
\(882\) 10.9349 + 12.9342i 0.368196 + 0.435519i
\(883\) 51.2633i 1.72515i 0.505931 + 0.862574i \(0.331149\pi\)
−0.505931 + 0.862574i \(0.668851\pi\)
\(884\) 21.8944i 0.736389i
\(885\) −6.55792 5.48213i −0.220442 0.184280i
\(886\) −10.4904 18.1698i −0.352431 0.610428i
\(887\) 15.9684 + 9.21935i 0.536166 + 0.309556i 0.743524 0.668710i \(-0.233153\pi\)
−0.207358 + 0.978265i \(0.566486\pi\)
\(888\) −1.46963 + 0.537981i −0.0493177 + 0.0180535i
\(889\) −12.7001 + 7.33242i −0.425949 + 0.245922i
\(890\) 2.60395 + 4.51017i 0.0872846 + 0.151181i
\(891\) 1.23418 + 1.02015i 0.0413467 + 0.0341762i
\(892\) 3.79542 + 2.19128i 0.127080 + 0.0733696i
\(893\) 18.3477 + 10.5930i 0.613982 + 0.354483i
\(894\) −7.45810 + 2.73015i −0.249436 + 0.0913099i
\(895\) 14.5314i 0.485732i
\(896\) −1.00783 0.581871i −0.0336693 0.0194390i
\(897\) 54.9811 + 9.58989i 1.83577 + 0.320197i
\(898\) 30.8958i 1.03101i
\(899\) −28.5373 12.0801i −0.951772 0.402894i
\(900\) −2.82285 1.01563i −0.0940951 0.0338544i
\(901\) 48.4819 1.61517
\(902\) 0.255452 0.442456i 0.00850563 0.0147322i
\(903\) −1.68725 0.294292i −0.0561480 0.00979343i
\(904\) −0.217548 0.376805i −0.00723555 0.0125323i
\(905\) 1.88922 3.27223i 0.0627998 0.108773i
\(906\) 23.9542 + 20.0246i 0.795823 + 0.665272i
\(907\) −4.08947 −0.135789 −0.0678943 0.997693i \(-0.521628\pi\)
−0.0678943 + 0.997693i \(0.521628\pi\)
\(908\) −14.2337 + 8.21783i −0.472362 + 0.272718i
\(909\) 6.93474 1.24923i 0.230011 0.0414345i
\(910\) 5.69014 3.28521i 0.188626 0.108904i
\(911\) −27.6813 + 47.9455i −0.917124 + 1.58851i −0.113363 + 0.993554i \(0.536162\pi\)
−0.803761 + 0.594952i \(0.797171\pi\)
\(912\) −8.38261 + 3.06858i −0.277576 + 0.101611i
\(913\) 1.41592 2.45244i 0.0468601 0.0811640i
\(914\) 10.1581 0.336001
\(915\) 0.000677044 0.00388165i 2.23824e−5 0.000128323i
\(916\) −0.621599 0.358880i −0.0205382 0.0118577i
\(917\) −21.3355 + 12.3180i −0.704559 + 0.406778i
\(918\) 17.3945 10.1717i 0.574103 0.335717i
\(919\) 9.34101 + 16.1791i 0.308132 + 0.533700i 0.977954 0.208822i \(-0.0669630\pi\)
−0.669822 + 0.742522i \(0.733630\pi\)
\(920\) 2.85361 + 4.94260i 0.0940808 + 0.162953i
\(921\) 29.1007 10.6528i 0.958901 0.351020i
\(922\) 19.8197i 0.652727i
\(923\) 35.7627 61.9428i 1.17714 2.03887i
\(924\) −0.275139 0.230004i −0.00905142 0.00756658i
\(925\) 0.782503 0.451779i 0.0257286 0.0148544i
\(926\) 10.9325 0.359263
\(927\) 38.9162 32.9005i 1.27818 1.08059i
\(928\) 5.56575i 0.182705i
\(929\) −11.9745 −0.392870 −0.196435 0.980517i \(-0.562937\pi\)
−0.196435 + 0.980517i \(0.562937\pi\)
\(930\) −5.22934 + 8.10271i −0.171477 + 0.265698i
\(931\) −29.0967 −0.953606
\(932\) 15.7057i 0.514456i
\(933\) −16.5383 + 19.7838i −0.541441 + 0.647692i
\(934\) 11.3377 0.370980
\(935\) 0.597499 0.344966i 0.0195403 0.0112816i
\(936\) 12.9348 10.9353i 0.422786 0.357432i
\(937\) 4.88152 8.45503i 0.159472 0.276214i −0.775206 0.631708i \(-0.782354\pi\)
0.934678 + 0.355494i \(0.115687\pi\)
\(938\) 7.45483i 0.243409i
\(939\) −4.57698 12.5032i −0.149364 0.408026i
\(940\) −2.05539 3.56005i −0.0670396 0.116116i
\(941\) −3.76669 6.52409i −0.122790 0.212679i 0.798077 0.602556i \(-0.205851\pi\)
−0.920867 + 0.389877i \(0.872518\pi\)
\(942\) −10.0374 + 12.0071i −0.327036 + 0.391213i
\(943\) 14.1934 8.19456i 0.462200 0.266852i
\(944\) 4.27376 + 2.46746i 0.139099 + 0.0803089i
\(945\) 5.25353 + 2.99440i 0.170897 + 0.0974080i
\(946\) −0.151174 −0.00491510
\(947\) −17.9100 + 31.0211i −0.581997 + 1.00805i 0.413245 + 0.910620i \(0.364395\pi\)
−0.995242 + 0.0974291i \(0.968938\pi\)
\(948\) 1.73685 + 4.74464i 0.0564101 + 0.154099i
\(949\) −30.3823 + 52.6236i −0.986250 + 1.70824i
\(950\) 4.46331 2.57689i 0.144809 0.0836054i
\(951\) −3.28728 8.98005i −0.106597 0.291198i
\(952\) −3.90828 + 2.25644i −0.126668 + 0.0731318i
\(953\) −8.04230 −0.260516 −0.130258 0.991480i \(-0.541581\pi\)
−0.130258 + 0.991480i \(0.541581\pi\)
\(954\) 24.2146 + 28.6421i 0.783976 + 0.927322i
\(955\) 3.22584 5.58732i 0.104386 0.180801i
\(956\) −2.90971 5.03976i −0.0941067 0.162998i
\(957\) −0.294704 + 1.68961i −0.00952643 + 0.0546172i
\(958\) 20.4280 35.3823i 0.659997 1.14315i
\(959\) 14.9452 0.482607
\(960\) 1.70629 + 0.297614i 0.0550703 + 0.00960545i
\(961\) 21.5784 + 22.2569i 0.696079 + 0.717965i
\(962\) 5.10142i 0.164476i
\(963\) −4.69562 + 13.0510i −0.151314 + 0.420563i
\(964\) −5.77410 3.33368i −0.185971 0.107370i
\(965\) 2.10272i 0.0676890i
\(966\) −3.95452 10.8028i −0.127234 0.347573i
\(967\) 0.283683 + 0.163784i 0.00912262 + 0.00526695i 0.504554 0.863380i \(-0.331657\pi\)
−0.495432 + 0.868647i \(0.664990\pi\)
\(968\) 9.49887 + 5.48417i 0.305305 + 0.176268i
\(969\) −5.94808 + 34.1017i −0.191080 + 1.09551i
\(970\) −6.85389 11.8713i −0.220065 0.381164i
\(971\) 9.78490 5.64932i 0.314013 0.181295i −0.334708 0.942322i \(-0.608638\pi\)
0.648721 + 0.761027i \(0.275304\pi\)
\(972\) 14.6970 + 5.19595i 0.471407 + 0.166660i
\(973\) 0.920652 + 0.531539i 0.0295147 + 0.0170403i
\(974\) 18.2009 + 31.5249i 0.583194 + 1.01012i
\(975\) −6.27199 + 7.50279i −0.200864 + 0.240282i
\(976\) 0.00227491i 7.28180e-5i
\(977\) 34.7208i 1.11082i 0.831578 + 0.555409i \(0.187438\pi\)
−0.831578 + 0.555409i \(0.812562\pi\)
\(978\) 18.9823 22.7074i 0.606988 0.726102i
\(979\) −0.463278 0.802421i −0.0148064 0.0256455i
\(980\) 4.88932 + 2.82285i 0.156184 + 0.0901727i
\(981\) 9.74915 + 54.1194i 0.311266 + 1.72790i
\(982\) 28.0904 16.2180i 0.896400 0.517537i
\(983\) −19.9164 34.4963i −0.635235 1.10026i −0.986465 0.163971i \(-0.947570\pi\)
0.351230 0.936289i \(-0.385764\pi\)
\(984\) 0.854642 4.89986i 0.0272450 0.156202i
\(985\) 16.3395 + 9.43359i 0.520618 + 0.300579i
\(986\) 18.6919 + 10.7917i 0.595270 + 0.343679i
\(987\) 2.84835 + 7.78100i 0.0906640 + 0.247672i
\(988\) 29.0979i 0.925728i
\(989\) −4.19976 2.42473i −0.133544 0.0771019i
\(990\) 0.502224 + 0.180695i 0.0159617 + 0.00574285i
\(991\) 5.61866i 0.178483i 0.996010 + 0.0892413i \(0.0284442\pi\)
−0.996010 + 0.0892413i \(0.971556\pi\)
\(992\) 2.17043 5.12730i 0.0689113 0.162792i
\(993\) −15.3089 2.67021i −0.485814 0.0847364i
\(994\) −14.7428 −0.467615
\(995\) −9.62408 + 16.6694i −0.305104 + 0.528455i
\(996\) 4.73710 27.1589i 0.150101 0.860563i
\(997\) −4.87015 8.43535i −0.154239 0.267150i 0.778542 0.627592i \(-0.215959\pi\)
−0.932782 + 0.360442i \(0.882626\pi\)
\(998\) 21.2891 36.8738i 0.673894 1.16722i
\(999\) −4.05293 + 2.37002i −0.128229 + 0.0749842i
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 930.2.o.e.491.8 yes 40
3.2 odd 2 inner 930.2.o.e.491.19 yes 40
31.6 odd 6 inner 930.2.o.e.161.9 40
93.68 even 6 inner 930.2.o.e.161.18 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.o.e.161.9 40 31.6 odd 6 inner
930.2.o.e.161.18 yes 40 93.68 even 6 inner
930.2.o.e.491.8 yes 40 1.1 even 1 trivial
930.2.o.e.491.19 yes 40 3.2 odd 2 inner