Properties

Label 546.2.bb.a.269.13
Level $546$
Weight $2$
Character 546.269
Analytic conductor $4.360$
Analytic rank $0$
Dimension $76$
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] = [546,2,Mod(269,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bb (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.13
Character \(\chi\) \(=\) 546.269
Dual form 546.2.bb.a.341.32

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.03468 - 1.38904i) q^{3} -1.00000 q^{4} +(0.587127 + 1.01693i) q^{5} +(-1.38904 - 1.03468i) q^{6} +(-0.859975 - 2.50209i) q^{7} +1.00000i q^{8} +(-0.858887 - 2.87442i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.03468 - 1.38904i) q^{3} -1.00000 q^{4} +(0.587127 + 1.01693i) q^{5} +(-1.38904 - 1.03468i) q^{6} +(-0.859975 - 2.50209i) q^{7} +1.00000i q^{8} +(-0.858887 - 2.87442i) q^{9} +(1.01693 - 0.587127i) q^{10} +(-0.795863 + 0.459492i) q^{11} +(-1.03468 + 1.38904i) q^{12} +(0.207654 - 3.59957i) q^{13} +(-2.50209 + 0.859975i) q^{14} +(2.02005 + 0.236653i) q^{15} +1.00000 q^{16} -2.17235 q^{17} +(-2.87442 + 0.858887i) q^{18} +(-0.0258726 - 0.0149376i) q^{19} +(-0.587127 - 1.01693i) q^{20} +(-4.36531 - 1.39431i) q^{21} +(0.459492 + 0.795863i) q^{22} -2.87353i q^{23} +(1.38904 + 1.03468i) q^{24} +(1.81056 - 3.13599i) q^{25} +(-3.59957 - 0.207654i) q^{26} +(-4.88137 - 1.78107i) q^{27} +(0.859975 + 2.50209i) q^{28} +(-0.0565664 - 0.0326586i) q^{29} +(0.236653 - 2.02005i) q^{30} +(3.64262 + 2.10307i) q^{31} -1.00000i q^{32} +(-0.185207 + 1.58091i) q^{33} +2.17235i q^{34} +(2.03954 - 2.34358i) q^{35} +(0.858887 + 2.87442i) q^{36} -2.94317 q^{37} +(-0.0149376 + 0.0258726i) q^{38} +(-4.78510 - 4.01283i) q^{39} +(-1.01693 + 0.587127i) q^{40} +(4.01799 - 6.95937i) q^{41} +(-1.39431 + 4.36531i) q^{42} +(2.74795 + 4.75959i) q^{43} +(0.795863 - 0.459492i) q^{44} +(2.41882 - 2.56108i) q^{45} -2.87353 q^{46} +(6.53683 + 11.3221i) q^{47} +(1.03468 - 1.38904i) q^{48} +(-5.52089 + 4.30346i) q^{49} +(-3.13599 - 1.81056i) q^{50} +(-2.24768 + 3.01749i) q^{51} +(-0.207654 + 3.59957i) q^{52} +(-1.75697 - 1.01439i) q^{53} +(-1.78107 + 4.88137i) q^{54} +(-0.934545 - 0.539560i) q^{55} +(2.50209 - 0.859975i) q^{56} +(-0.0475187 + 0.0204827i) q^{57} +(-0.0326586 + 0.0565664i) q^{58} -3.61157 q^{59} +(-2.02005 - 0.236653i) q^{60} +(0.657869 + 0.379821i) q^{61} +(2.10307 - 3.64262i) q^{62} +(-6.45344 + 4.62094i) q^{63} -1.00000 q^{64} +(3.78244 - 1.90223i) q^{65} +(1.58091 + 0.185207i) q^{66} +(6.54101 + 11.3294i) q^{67} +2.17235 q^{68} +(-3.99146 - 2.97318i) q^{69} +(-2.34358 - 2.03954i) q^{70} +(8.16075 - 4.71161i) q^{71} +(2.87442 - 0.858887i) q^{72} +(-2.34499 - 1.35388i) q^{73} +2.94317i q^{74} +(-2.48268 - 5.75969i) q^{75} +(0.0258726 + 0.0149376i) q^{76} +(1.83411 + 1.59617i) q^{77} +(-4.01283 + 4.78510i) q^{78} +(3.71017 + 6.42620i) q^{79} +(0.587127 + 1.01693i) q^{80} +(-7.52463 + 4.93761i) q^{81} +(-6.95937 - 4.01799i) q^{82} +11.8735 q^{83} +(4.36531 + 1.39431i) q^{84} +(-1.27545 - 2.20914i) q^{85} +(4.75959 - 2.74795i) q^{86} +(-0.103892 + 0.0447821i) q^{87} +(-0.459492 - 0.795863i) q^{88} -10.0347 q^{89} +(-2.56108 - 2.41882i) q^{90} +(-9.18501 + 2.57597i) q^{91} +2.87353i q^{92} +(6.69019 - 2.88376i) q^{93} +(11.3221 - 6.53683i) q^{94} -0.0350810i q^{95} +(-1.38904 - 1.03468i) q^{96} +(8.74505 - 5.04896i) q^{97} +(4.30346 + 5.52089i) q^{98} +(2.00433 + 1.89300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.03468 1.38904i 0.597371 0.801965i
\(4\) −1.00000 −0.500000
\(5\) 0.587127 + 1.01693i 0.262571 + 0.454786i 0.966924 0.255063i \(-0.0820963\pi\)
−0.704353 + 0.709850i \(0.748763\pi\)
\(6\) −1.38904 1.03468i −0.567075 0.422405i
\(7\) −0.859975 2.50209i −0.325040 0.945700i
\(8\) 1.00000i 0.353553i
\(9\) −0.858887 2.87442i −0.286296 0.958141i
\(10\) 1.01693 0.587127i 0.321583 0.185666i
\(11\) −0.795863 + 0.459492i −0.239962 + 0.138542i −0.615159 0.788403i \(-0.710908\pi\)
0.375197 + 0.926945i \(0.377575\pi\)
\(12\) −1.03468 + 1.38904i −0.298686 + 0.400982i
\(13\) 0.207654 3.59957i 0.0575928 0.998340i
\(14\) −2.50209 + 0.859975i −0.668711 + 0.229838i
\(15\) 2.02005 + 0.236653i 0.521575 + 0.0611034i
\(16\) 1.00000 0.250000
\(17\) −2.17235 −0.526873 −0.263436 0.964677i \(-0.584856\pi\)
−0.263436 + 0.964677i \(0.584856\pi\)
\(18\) −2.87442 + 0.858887i −0.677508 + 0.202442i
\(19\) −0.0258726 0.0149376i −0.00593559 0.00342691i 0.497029 0.867734i \(-0.334424\pi\)
−0.502965 + 0.864307i \(0.667757\pi\)
\(20\) −0.587127 1.01693i −0.131286 0.227393i
\(21\) −4.36531 1.39431i −0.952588 0.304263i
\(22\) 0.459492 + 0.795863i 0.0979640 + 0.169679i
\(23\) 2.87353i 0.599173i −0.954069 0.299586i \(-0.903151\pi\)
0.954069 0.299586i \(-0.0968487\pi\)
\(24\) 1.38904 + 1.03468i 0.283537 + 0.211203i
\(25\) 1.81056 3.13599i 0.362113 0.627198i
\(26\) −3.59957 0.207654i −0.705933 0.0407243i
\(27\) −4.88137 1.78107i −0.939421 0.342767i
\(28\) 0.859975 + 2.50209i 0.162520 + 0.472850i
\(29\) −0.0565664 0.0326586i −0.0105041 0.00606455i 0.494739 0.869042i \(-0.335264\pi\)
−0.505243 + 0.862977i \(0.668597\pi\)
\(30\) 0.236653 2.02005i 0.0432066 0.368809i
\(31\) 3.64262 + 2.10307i 0.654234 + 0.377722i 0.790076 0.613008i \(-0.210041\pi\)
−0.135843 + 0.990730i \(0.543374\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.185207 + 1.58091i −0.0322404 + 0.275202i
\(34\) 2.17235i 0.372555i
\(35\) 2.03954 2.34358i 0.344746 0.396137i
\(36\) 0.858887 + 2.87442i 0.143148 + 0.479071i
\(37\) −2.94317 −0.483853 −0.241927 0.970295i \(-0.577779\pi\)
−0.241927 + 0.970295i \(0.577779\pi\)
\(38\) −0.0149376 + 0.0258726i −0.00242319 + 0.00419709i
\(39\) −4.78510 4.01283i −0.766230 0.642567i
\(40\) −1.01693 + 0.587127i −0.160791 + 0.0928329i
\(41\) 4.01799 6.95937i 0.627505 1.08687i −0.360546 0.932742i \(-0.617410\pi\)
0.988051 0.154129i \(-0.0492571\pi\)
\(42\) −1.39431 + 4.36531i −0.215147 + 0.673581i
\(43\) 2.74795 + 4.75959i 0.419059 + 0.725831i 0.995845 0.0910640i \(-0.0290268\pi\)
−0.576786 + 0.816895i \(0.695693\pi\)
\(44\) 0.795863 0.459492i 0.119981 0.0692710i
\(45\) 2.41882 2.56108i 0.360577 0.381784i
\(46\) −2.87353 −0.423679
\(47\) 6.53683 + 11.3221i 0.953495 + 1.65150i 0.737774 + 0.675047i \(0.235877\pi\)
0.215721 + 0.976455i \(0.430790\pi\)
\(48\) 1.03468 1.38904i 0.149343 0.200491i
\(49\) −5.52089 + 4.30346i −0.788698 + 0.614781i
\(50\) −3.13599 1.81056i −0.443496 0.256052i
\(51\) −2.24768 + 3.01749i −0.314739 + 0.422534i
\(52\) −0.207654 + 3.59957i −0.0287964 + 0.499170i
\(53\) −1.75697 1.01439i −0.241339 0.139337i 0.374453 0.927246i \(-0.377830\pi\)
−0.615792 + 0.787909i \(0.711164\pi\)
\(54\) −1.78107 + 4.88137i −0.242373 + 0.664271i
\(55\) −0.934545 0.539560i −0.126014 0.0727542i
\(56\) 2.50209 0.859975i 0.334356 0.114919i
\(57\) −0.0475187 + 0.0204827i −0.00629401 + 0.00271299i
\(58\) −0.0326586 + 0.0565664i −0.00428829 + 0.00742753i
\(59\) −3.61157 −0.470187 −0.235093 0.971973i \(-0.575540\pi\)
−0.235093 + 0.971973i \(0.575540\pi\)
\(60\) −2.02005 0.236653i −0.260788 0.0305517i
\(61\) 0.657869 + 0.379821i 0.0842314 + 0.0486310i 0.541524 0.840685i \(-0.317847\pi\)
−0.457293 + 0.889316i \(0.651181\pi\)
\(62\) 2.10307 3.64262i 0.267090 0.462613i
\(63\) −6.45344 + 4.62094i −0.813057 + 0.582184i
\(64\) −1.00000 −0.125000
\(65\) 3.78244 1.90223i 0.469154 0.235943i
\(66\) 1.58091 + 0.185207i 0.194597 + 0.0227974i
\(67\) 6.54101 + 11.3294i 0.799112 + 1.38410i 0.920195 + 0.391460i \(0.128030\pi\)
−0.121083 + 0.992642i \(0.538637\pi\)
\(68\) 2.17235 0.263436
\(69\) −3.99146 2.97318i −0.480516 0.357928i
\(70\) −2.34358 2.03954i −0.280111 0.243772i
\(71\) 8.16075 4.71161i 0.968503 0.559166i 0.0697237 0.997566i \(-0.477788\pi\)
0.898780 + 0.438401i \(0.144455\pi\)
\(72\) 2.87442 0.858887i 0.338754 0.101221i
\(73\) −2.34499 1.35388i −0.274460 0.158460i 0.356453 0.934313i \(-0.383986\pi\)
−0.630913 + 0.775854i \(0.717319\pi\)
\(74\) 2.94317i 0.342136i
\(75\) −2.48268 5.75969i −0.286675 0.665072i
\(76\) 0.0258726 + 0.0149376i 0.00296779 + 0.00171346i
\(77\) 1.83411 + 1.59617i 0.209016 + 0.181900i
\(78\) −4.01283 + 4.78510i −0.454363 + 0.541806i
\(79\) 3.71017 + 6.42620i 0.417427 + 0.723004i 0.995680 0.0928534i \(-0.0295988\pi\)
−0.578253 + 0.815857i \(0.696265\pi\)
\(80\) 0.587127 + 1.01693i 0.0656428 + 0.113697i
\(81\) −7.52463 + 4.93761i −0.836070 + 0.548623i
\(82\) −6.95937 4.01799i −0.768533 0.443713i
\(83\) 11.8735 1.30329 0.651645 0.758524i \(-0.274079\pi\)
0.651645 + 0.758524i \(0.274079\pi\)
\(84\) 4.36531 + 1.39431i 0.476294 + 0.152132i
\(85\) −1.27545 2.20914i −0.138342 0.239615i
\(86\) 4.75959 2.74795i 0.513240 0.296319i
\(87\) −0.103892 + 0.0447821i −0.0111384 + 0.00480114i
\(88\) −0.459492 0.795863i −0.0489820 0.0848393i
\(89\) −10.0347 −1.06368 −0.531840 0.846845i \(-0.678499\pi\)
−0.531840 + 0.846845i \(0.678499\pi\)
\(90\) −2.56108 2.41882i −0.269962 0.254966i
\(91\) −9.18501 + 2.57597i −0.962851 + 0.270035i
\(92\) 2.87353i 0.299586i
\(93\) 6.69019 2.88376i 0.693740 0.299032i
\(94\) 11.3221 6.53683i 1.16779 0.674223i
\(95\) 0.0350810i 0.00359923i
\(96\) −1.38904 1.03468i −0.141769 0.105601i
\(97\) 8.74505 5.04896i 0.887925 0.512644i 0.0146618 0.999893i \(-0.495333\pi\)
0.873263 + 0.487249i \(0.161999\pi\)
\(98\) 4.30346 + 5.52089i 0.434716 + 0.557694i
\(99\) 2.00433 + 1.89300i 0.201443 + 0.190253i
\(100\) −1.81056 + 3.13599i −0.181056 + 0.313599i
\(101\) −4.42478 7.66394i −0.440282 0.762590i 0.557429 0.830225i \(-0.311788\pi\)
−0.997710 + 0.0676348i \(0.978455\pi\)
\(102\) 3.01749 + 2.24768i 0.298776 + 0.222554i
\(103\) 8.65368 4.99621i 0.852673 0.492291i −0.00887895 0.999961i \(-0.502826\pi\)
0.861552 + 0.507670i \(0.169493\pi\)
\(104\) 3.59957 + 0.207654i 0.352967 + 0.0203621i
\(105\) −1.14507 5.25786i −0.111747 0.513115i
\(106\) −1.01439 + 1.75697i −0.0985261 + 0.170652i
\(107\) 4.08949i 0.395346i −0.980268 0.197673i \(-0.936662\pi\)
0.980268 0.197673i \(-0.0633384\pi\)
\(108\) 4.88137 + 1.78107i 0.469710 + 0.171383i
\(109\) 3.22047 5.57802i 0.308465 0.534277i −0.669562 0.742756i \(-0.733518\pi\)
0.978027 + 0.208479i \(0.0668514\pi\)
\(110\) −0.539560 + 0.934545i −0.0514450 + 0.0891054i
\(111\) −3.04523 + 4.08819i −0.289040 + 0.388033i
\(112\) −0.859975 2.50209i −0.0812600 0.236425i
\(113\) 18.3720 10.6071i 1.72829 0.997828i 0.831207 0.555963i \(-0.187650\pi\)
0.897081 0.441865i \(-0.145683\pi\)
\(114\) 0.0204827 + 0.0475187i 0.00191838 + 0.00445054i
\(115\) 2.92219 1.68713i 0.272496 0.157325i
\(116\) 0.0565664 + 0.0326586i 0.00525206 + 0.00303228i
\(117\) −10.5250 + 2.49474i −0.973040 + 0.230638i
\(118\) 3.61157i 0.332472i
\(119\) 1.86817 + 5.43542i 0.171255 + 0.498264i
\(120\) −0.236653 + 2.02005i −0.0216033 + 0.184405i
\(121\) −5.07773 + 8.79489i −0.461612 + 0.799536i
\(122\) 0.379821 0.657869i 0.0343873 0.0595606i
\(123\) −5.50954 12.7819i −0.496779 1.15250i
\(124\) −3.64262 2.10307i −0.327117 0.188861i
\(125\) 10.1234 0.905464
\(126\) 4.62094 + 6.45344i 0.411666 + 0.574918i
\(127\) 0.00158663 0.00274813i 0.000140791 0.000243857i −0.865955 0.500122i \(-0.833289\pi\)
0.866096 + 0.499878i \(0.166622\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 9.45453 + 1.10761i 0.832425 + 0.0975200i
\(130\) −1.90223 3.78244i −0.166837 0.331742i
\(131\) −3.60456 6.24329i −0.314932 0.545478i 0.664491 0.747296i \(-0.268648\pi\)
−0.979423 + 0.201818i \(0.935315\pi\)
\(132\) 0.185207 1.58091i 0.0161202 0.137601i
\(133\) −0.0151253 + 0.0775815i −0.00131153 + 0.00672717i
\(134\) 11.3294 6.54101i 0.978708 0.565057i
\(135\) −1.05476 6.00974i −0.0907790 0.517236i
\(136\) 2.17235i 0.186278i
\(137\) 20.5804i 1.75830i 0.476542 + 0.879151i \(0.341890\pi\)
−0.476542 + 0.879151i \(0.658110\pi\)
\(138\) −2.97318 + 3.99146i −0.253094 + 0.339776i
\(139\) 5.48328 3.16577i 0.465085 0.268517i −0.249095 0.968479i \(-0.580133\pi\)
0.714180 + 0.699962i \(0.246800\pi\)
\(140\) −2.03954 + 2.34358i −0.172373 + 0.198069i
\(141\) 22.4905 + 2.63480i 1.89404 + 0.221890i
\(142\) −4.71161 8.16075i −0.395390 0.684835i
\(143\) 1.48871 + 2.96018i 0.124492 + 0.247543i
\(144\) −0.858887 2.87442i −0.0715739 0.239535i
\(145\) 0.0766990i 0.00636950i
\(146\) −1.35388 + 2.34499i −0.112048 + 0.194073i
\(147\) 0.265367 + 12.1215i 0.0218871 + 0.999760i
\(148\) 2.94317 0.241927
\(149\) 6.33047 + 3.65490i 0.518612 + 0.299421i 0.736367 0.676583i \(-0.236540\pi\)
−0.217754 + 0.976004i \(0.569873\pi\)
\(150\) −5.75969 + 2.48268i −0.470277 + 0.202710i
\(151\) −4.87258 + 8.43956i −0.396525 + 0.686802i −0.993295 0.115611i \(-0.963117\pi\)
0.596769 + 0.802413i \(0.296451\pi\)
\(152\) 0.0149376 0.0258726i 0.00121160 0.00209855i
\(153\) 1.86581 + 6.24426i 0.150841 + 0.504819i
\(154\) 1.59617 1.83411i 0.128623 0.147797i
\(155\) 4.93907i 0.396716i
\(156\) 4.78510 + 4.01283i 0.383115 + 0.321283i
\(157\) −7.68731 4.43827i −0.613514 0.354213i 0.160825 0.986983i \(-0.448584\pi\)
−0.774340 + 0.632770i \(0.781918\pi\)
\(158\) 6.42620 3.71017i 0.511241 0.295165i
\(159\) −3.22693 + 1.39095i −0.255912 + 0.110309i
\(160\) 1.01693 0.587127i 0.0803956 0.0464164i
\(161\) −7.18983 + 2.47116i −0.566638 + 0.194755i
\(162\) 4.93761 + 7.52463i 0.387935 + 0.591190i
\(163\) −1.55883 + 2.69997i −0.122097 + 0.211478i −0.920594 0.390520i \(-0.872295\pi\)
0.798497 + 0.601998i \(0.205629\pi\)
\(164\) −4.01799 + 6.95937i −0.313752 + 0.543435i
\(165\) −1.71642 + 0.739854i −0.133623 + 0.0575976i
\(166\) 11.8735i 0.921566i
\(167\) 3.69401 6.39822i 0.285851 0.495109i −0.686964 0.726691i \(-0.741057\pi\)
0.972815 + 0.231583i \(0.0743903\pi\)
\(168\) 1.39431 4.36531i 0.107573 0.336791i
\(169\) −12.9138 1.49493i −0.993366 0.114994i
\(170\) −2.20914 + 1.27545i −0.169433 + 0.0978222i
\(171\) −0.0207152 + 0.0871986i −0.00158413 + 0.00666824i
\(172\) −2.74795 4.75959i −0.209529 0.362916i
\(173\) 4.98811 8.63966i 0.379239 0.656861i −0.611713 0.791080i \(-0.709519\pi\)
0.990952 + 0.134219i \(0.0428525\pi\)
\(174\) 0.0447821 + 0.103892i 0.00339492 + 0.00787605i
\(175\) −9.40356 1.83332i −0.710842 0.138586i
\(176\) −0.795863 + 0.459492i −0.0599905 + 0.0346355i
\(177\) −3.73681 + 5.01664i −0.280876 + 0.377073i
\(178\) 10.0347i 0.752135i
\(179\) −13.9845 + 8.07398i −1.04525 + 0.603477i −0.921317 0.388813i \(-0.872885\pi\)
−0.123937 + 0.992290i \(0.539552\pi\)
\(180\) −2.41882 + 2.56108i −0.180288 + 0.190892i
\(181\) 11.7575i 0.873927i −0.899479 0.436964i \(-0.856054\pi\)
0.899479 0.436964i \(-0.143946\pi\)
\(182\) 2.57597 + 9.18501i 0.190943 + 0.680838i
\(183\) 1.20827 0.520817i 0.0893178 0.0384999i
\(184\) 2.87353 0.211840
\(185\) −1.72801 2.99300i −0.127046 0.220050i
\(186\) −2.88376 6.69019i −0.211448 0.490548i
\(187\) 1.72890 0.998178i 0.126429 0.0729940i
\(188\) −6.53683 11.3221i −0.476748 0.825751i
\(189\) −0.258532 + 13.7453i −0.0188055 + 0.999823i
\(190\) −0.0350810 −0.00254504
\(191\) −0.971600 0.560953i −0.0703025 0.0405892i 0.464437 0.885606i \(-0.346257\pi\)
−0.534739 + 0.845017i \(0.679590\pi\)
\(192\) −1.03468 + 1.38904i −0.0746714 + 0.100246i
\(193\) 8.37481 + 14.5056i 0.602832 + 1.04414i 0.992390 + 0.123133i \(0.0392943\pi\)
−0.389558 + 0.921002i \(0.627372\pi\)
\(194\) −5.04896 8.74505i −0.362494 0.627858i
\(195\) 1.27132 7.22217i 0.0910410 0.517190i
\(196\) 5.52089 4.30346i 0.394349 0.307390i
\(197\) 18.6511 + 10.7682i 1.32883 + 0.767202i 0.985119 0.171873i \(-0.0549817\pi\)
0.343714 + 0.939075i \(0.388315\pi\)
\(198\) 1.89300 2.00433i 0.134529 0.142442i
\(199\) 13.0222i 0.923122i 0.887108 + 0.461561i \(0.152710\pi\)
−0.887108 + 0.461561i \(0.847290\pi\)
\(200\) 3.13599 + 1.81056i 0.221748 + 0.128026i
\(201\) 22.5048 + 2.63648i 1.58737 + 0.185963i
\(202\) −7.66394 + 4.42478i −0.539233 + 0.311326i
\(203\) −0.0330691 + 0.169620i −0.00232099 + 0.0119050i
\(204\) 2.24768 3.01749i 0.157369 0.211267i
\(205\) 9.43628 0.659059
\(206\) −4.99621 8.65368i −0.348102 0.602931i
\(207\) −8.25975 + 2.46804i −0.574092 + 0.171541i
\(208\) 0.207654 3.59957i 0.0143982 0.249585i
\(209\) 0.0274548 0.00189909
\(210\) −5.25786 + 1.14507i −0.362827 + 0.0790172i
\(211\) −10.6556 + 18.4561i −0.733562 + 1.27057i 0.221789 + 0.975095i \(0.428810\pi\)
−0.955351 + 0.295472i \(0.904523\pi\)
\(212\) 1.75697 + 1.01439i 0.120669 + 0.0696684i
\(213\) 1.89911 16.2106i 0.130125 1.11074i
\(214\) −4.08949 −0.279552
\(215\) −3.22679 + 5.58897i −0.220065 + 0.381164i
\(216\) 1.78107 4.88137i 0.121186 0.332135i
\(217\) 2.12950 10.9227i 0.144560 0.741484i
\(218\) −5.57802 3.22047i −0.377791 0.218118i
\(219\) −4.30690 + 1.85646i −0.291034 + 0.125448i
\(220\) 0.934545 + 0.539560i 0.0630070 + 0.0363771i
\(221\) −0.451097 + 7.81953i −0.0303441 + 0.525998i
\(222\) 4.08819 + 3.04523i 0.274381 + 0.204382i
\(223\) 20.1451 + 11.6308i 1.34902 + 0.778856i 0.988110 0.153746i \(-0.0491337\pi\)
0.360907 + 0.932602i \(0.382467\pi\)
\(224\) −2.50209 + 0.859975i −0.167178 + 0.0574595i
\(225\) −10.5692 2.51087i −0.704616 0.167391i
\(226\) −10.6071 18.3720i −0.705571 1.22208i
\(227\) −23.3571 −1.55027 −0.775133 0.631798i \(-0.782317\pi\)
−0.775133 + 0.631798i \(0.782317\pi\)
\(228\) 0.0475187 0.0204827i 0.00314701 0.00135650i
\(229\) 3.19792 1.84632i 0.211325 0.122008i −0.390602 0.920560i \(-0.627733\pi\)
0.601927 + 0.798551i \(0.294400\pi\)
\(230\) −1.68713 2.92219i −0.111246 0.192683i
\(231\) 4.11486 0.896143i 0.270738 0.0589619i
\(232\) 0.0326586 0.0565664i 0.00214414 0.00371377i
\(233\) −7.98666 + 4.61110i −0.523223 + 0.302083i −0.738252 0.674524i \(-0.764349\pi\)
0.215029 + 0.976608i \(0.431015\pi\)
\(234\) 2.49474 + 10.5250i 0.163086 + 0.688043i
\(235\) −7.67590 + 13.2950i −0.500721 + 0.867273i
\(236\) 3.61157 0.235093
\(237\) 12.7651 + 1.49545i 0.829182 + 0.0971402i
\(238\) 5.43542 1.86817i 0.352326 0.121095i
\(239\) 13.3075i 0.860788i −0.902641 0.430394i \(-0.858375\pi\)
0.902641 0.430394i \(-0.141625\pi\)
\(240\) 2.02005 + 0.236653i 0.130394 + 0.0152759i
\(241\) 25.7424i 1.65821i −0.559090 0.829107i \(-0.688850\pi\)
0.559090 0.829107i \(-0.311150\pi\)
\(242\) 8.79489 + 5.07773i 0.565357 + 0.326409i
\(243\) −0.926997 + 15.5609i −0.0594669 + 0.998230i
\(244\) −0.657869 0.379821i −0.0421157 0.0243155i
\(245\) −7.61780 3.08769i −0.486683 0.197266i
\(246\) −12.7819 + 5.50954i −0.814942 + 0.351276i
\(247\) −0.0591413 + 0.0900284i −0.00376307 + 0.00572837i
\(248\) −2.10307 + 3.64262i −0.133545 + 0.231307i
\(249\) 12.2853 16.4929i 0.778548 1.04519i
\(250\) 10.1234i 0.640259i
\(251\) −15.4915 26.8320i −0.977813 1.69362i −0.670320 0.742072i \(-0.733843\pi\)
−0.307493 0.951550i \(-0.599490\pi\)
\(252\) 6.45344 4.62094i 0.406529 0.291092i
\(253\) 1.32036 + 2.28694i 0.0830106 + 0.143779i
\(254\) −0.00274813 0.00158663i −0.000172433 9.95541e-5i
\(255\) −4.38826 0.514093i −0.274804 0.0321937i
\(256\) 1.00000 0.0625000
\(257\) −31.2860 −1.95157 −0.975784 0.218735i \(-0.929807\pi\)
−0.975784 + 0.218735i \(0.929807\pi\)
\(258\) 1.10761 9.45453i 0.0689571 0.588613i
\(259\) 2.53105 + 7.36406i 0.157272 + 0.457580i
\(260\) −3.78244 + 1.90223i −0.234577 + 0.117971i
\(261\) −0.0452906 + 0.190646i −0.00280342 + 0.0118007i
\(262\) −6.24329 + 3.60456i −0.385711 + 0.222691i
\(263\) 2.83858 1.63886i 0.175035 0.101056i −0.409923 0.912120i \(-0.634444\pi\)
0.584958 + 0.811064i \(0.301111\pi\)
\(264\) −1.58091 0.185207i −0.0972986 0.0113987i
\(265\) 2.38230i 0.146343i
\(266\) 0.0775815 + 0.0151253i 0.00475683 + 0.000927391i
\(267\) −10.3827 + 13.9387i −0.635411 + 0.853034i
\(268\) −6.54101 11.3294i −0.399556 0.692051i
\(269\) −7.84705 −0.478443 −0.239222 0.970965i \(-0.576892\pi\)
−0.239222 + 0.970965i \(0.576892\pi\)
\(270\) −6.00974 + 1.05476i −0.365741 + 0.0641904i
\(271\) 11.1613i 0.678000i −0.940786 0.339000i \(-0.889911\pi\)
0.940786 0.339000i \(-0.110089\pi\)
\(272\) −2.17235 −0.131718
\(273\) −5.92538 + 15.4237i −0.358621 + 0.933483i
\(274\) 20.5804 1.24331
\(275\) 3.32776i 0.200671i
\(276\) 3.99146 + 2.97318i 0.240258 + 0.178964i
\(277\) 19.0907 1.14705 0.573524 0.819189i \(-0.305576\pi\)
0.573524 + 0.819189i \(0.305576\pi\)
\(278\) −3.16577 5.48328i −0.189870 0.328865i
\(279\) 2.91651 12.2767i 0.174607 0.734989i
\(280\) 2.34358 + 2.03954i 0.140056 + 0.121886i
\(281\) 12.3375i 0.735995i 0.929827 + 0.367997i \(0.119956\pi\)
−0.929827 + 0.367997i \(0.880044\pi\)
\(282\) 2.63480 22.4905i 0.156900 1.33929i
\(283\) −9.33979 + 5.39233i −0.555193 + 0.320541i −0.751214 0.660059i \(-0.770531\pi\)
0.196021 + 0.980600i \(0.437198\pi\)
\(284\) −8.16075 + 4.71161i −0.484252 + 0.279583i
\(285\) −0.0487290 0.0362975i −0.00288646 0.00215008i
\(286\) 2.96018 1.48871i 0.175039 0.0880291i
\(287\) −20.8683 4.06849i −1.23182 0.240155i
\(288\) −2.87442 + 0.858887i −0.169377 + 0.0506104i
\(289\) −12.2809 −0.722405
\(290\) −0.0766990 −0.00450392
\(291\) 2.03508 17.3713i 0.119298 1.01832i
\(292\) 2.34499 + 1.35388i 0.137230 + 0.0792298i
\(293\) −8.93398 15.4741i −0.521929 0.904007i −0.999675 0.0255089i \(-0.991879\pi\)
0.477746 0.878498i \(-0.341454\pi\)
\(294\) 12.1215 0.265367i 0.706937 0.0154765i
\(295\) −2.12045 3.67273i −0.123457 0.213835i
\(296\) 2.94317i 0.171068i
\(297\) 4.70329 0.825464i 0.272913 0.0478983i
\(298\) 3.65490 6.33047i 0.211723 0.366714i
\(299\) −10.3435 0.596700i −0.598178 0.0345080i
\(300\) 2.48268 + 5.75969i 0.143338 + 0.332536i
\(301\) 9.54575 10.9687i 0.550208 0.632228i
\(302\) 8.43956 + 4.87258i 0.485642 + 0.280386i
\(303\) −15.2238 1.78349i −0.874582 0.102459i
\(304\) −0.0258726 0.0149376i −0.00148390 0.000856728i
\(305\) 0.892011i 0.0510764i
\(306\) 6.24426 1.86581i 0.356961 0.106661i
\(307\) 15.9984i 0.913075i 0.889704 + 0.456537i \(0.150911\pi\)
−0.889704 + 0.456537i \(0.849089\pi\)
\(308\) −1.83411 1.59617i −0.104508 0.0909501i
\(309\) 2.01382 17.1898i 0.114562 0.977894i
\(310\) 4.93907 0.280520
\(311\) −7.50229 + 12.9943i −0.425416 + 0.736842i −0.996459 0.0840780i \(-0.973205\pi\)
0.571043 + 0.820920i \(0.306539\pi\)
\(312\) 4.01283 4.78510i 0.227182 0.270903i
\(313\) −7.96283 + 4.59734i −0.450086 + 0.259857i −0.707866 0.706346i \(-0.750342\pi\)
0.257781 + 0.966203i \(0.417009\pi\)
\(314\) −4.43827 + 7.68731i −0.250466 + 0.433820i
\(315\) −8.48818 3.84964i −0.478255 0.216903i
\(316\) −3.71017 6.42620i −0.208713 0.361502i
\(317\) −26.2887 + 15.1778i −1.47652 + 0.852470i −0.999649 0.0265020i \(-0.991563\pi\)
−0.476873 + 0.878972i \(0.658230\pi\)
\(318\) 1.39095 + 3.22693i 0.0780004 + 0.180957i
\(319\) 0.0600255 0.00336078
\(320\) −0.587127 1.01693i −0.0328214 0.0568483i
\(321\) −5.68048 4.23130i −0.317054 0.236168i
\(322\) 2.47116 + 7.18983i 0.137713 + 0.400673i
\(323\) 0.0562044 + 0.0324496i 0.00312730 + 0.00180555i
\(324\) 7.52463 4.93761i 0.418035 0.274312i
\(325\) −10.9122 7.16845i −0.605302 0.397634i
\(326\) 2.69997 + 1.55883i 0.149538 + 0.0863357i
\(327\) −4.41597 10.2448i −0.244203 0.566540i
\(328\) 6.95937 + 4.01799i 0.384267 + 0.221857i
\(329\) 22.7075 26.0925i 1.25190 1.43853i
\(330\) 0.739854 + 1.71642i 0.0407276 + 0.0944861i
\(331\) −15.1261 + 26.1992i −0.831405 + 1.44004i 0.0655183 + 0.997851i \(0.479130\pi\)
−0.896924 + 0.442185i \(0.854203\pi\)
\(332\) −11.8735 −0.651645
\(333\) 2.52785 + 8.45990i 0.138525 + 0.463600i
\(334\) −6.39822 3.69401i −0.350095 0.202127i
\(335\) −7.68081 + 13.3035i −0.419647 + 0.726850i
\(336\) −4.36531 1.39431i −0.238147 0.0760658i
\(337\) −15.1212 −0.823705 −0.411852 0.911251i \(-0.635118\pi\)
−0.411852 + 0.911251i \(0.635118\pi\)
\(338\) −1.49493 + 12.9138i −0.0813133 + 0.702416i
\(339\) 4.27538 36.4943i 0.232207 1.98210i
\(340\) 1.27545 + 2.20914i 0.0691708 + 0.119807i
\(341\) −3.86537 −0.209322
\(342\) 0.0871986 + 0.0207152i 0.00471516 + 0.00112015i
\(343\) 15.5155 + 10.1129i 0.837757 + 0.546044i
\(344\) −4.75959 + 2.74795i −0.256620 + 0.148160i
\(345\) 0.680029 5.80468i 0.0366115 0.312514i
\(346\) −8.63966 4.98811i −0.464471 0.268162i
\(347\) 3.24211i 0.174046i 0.996206 + 0.0870229i \(0.0277353\pi\)
−0.996206 + 0.0870229i \(0.972265\pi\)
\(348\) 0.103892 0.0447821i 0.00556921 0.00240057i
\(349\) −8.93794 5.16032i −0.478437 0.276226i 0.241328 0.970444i \(-0.422417\pi\)
−0.719765 + 0.694218i \(0.755750\pi\)
\(350\) −1.83332 + 9.40356i −0.0979950 + 0.502641i
\(351\) −7.42471 + 17.2010i −0.396302 + 0.918120i
\(352\) 0.459492 + 0.795863i 0.0244910 + 0.0424197i
\(353\) 11.4304 + 19.7980i 0.608377 + 1.05374i 0.991508 + 0.130046i \(0.0415123\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(354\) 5.01664 + 3.73681i 0.266631 + 0.198609i
\(355\) 9.58279 + 5.53263i 0.508602 + 0.293641i
\(356\) 10.0347 0.531840
\(357\) 9.48298 + 3.02893i 0.501893 + 0.160308i
\(358\) 8.07398 + 13.9845i 0.426723 + 0.739106i
\(359\) 0.0612770 0.0353783i 0.00323408 0.00186719i −0.498382 0.866957i \(-0.666072\pi\)
0.501616 + 0.865090i \(0.332739\pi\)
\(360\) 2.56108 + 2.41882i 0.134981 + 0.127483i
\(361\) −9.49955 16.4537i −0.499977 0.865985i
\(362\) −11.7575 −0.617960
\(363\) 6.96268 + 16.1531i 0.365446 + 0.847816i
\(364\) 9.18501 2.57597i 0.481425 0.135017i
\(365\) 3.17960i 0.166428i
\(366\) −0.520817 1.20827i −0.0272235 0.0631572i
\(367\) 14.2236 8.21199i 0.742465 0.428662i −0.0804999 0.996755i \(-0.525652\pi\)
0.822965 + 0.568092i \(0.192318\pi\)
\(368\) 2.87353i 0.149793i
\(369\) −23.4552 5.57210i −1.22103 0.290072i
\(370\) −2.99300 + 1.72801i −0.155599 + 0.0898350i
\(371\) −1.02714 + 5.26844i −0.0533263 + 0.273524i
\(372\) −6.69019 + 2.88376i −0.346870 + 0.149516i
\(373\) −0.140266 + 0.242947i −0.00726269 + 0.0125793i −0.869634 0.493697i \(-0.835645\pi\)
0.862371 + 0.506276i \(0.168978\pi\)
\(374\) −0.998178 1.72890i −0.0516146 0.0893991i
\(375\) 10.4744 14.0618i 0.540898 0.726150i
\(376\) −11.3221 + 6.53683i −0.583894 + 0.337112i
\(377\) −0.129303 + 0.196833i −0.00665945 + 0.0101374i
\(378\) 13.7453 + 0.258532i 0.706982 + 0.0132975i
\(379\) −15.8106 + 27.3847i −0.812133 + 1.40666i 0.0992346 + 0.995064i \(0.468361\pi\)
−0.911368 + 0.411592i \(0.864973\pi\)
\(380\) 0.0350810i 0.00179962i
\(381\) −0.00217562 0.00504732i −0.000111460 0.000258582i
\(382\) −0.560953 + 0.971600i −0.0287009 + 0.0497114i
\(383\) 13.1914 22.8482i 0.674050 1.16749i −0.302696 0.953087i \(-0.597887\pi\)
0.976746 0.214402i \(-0.0687801\pi\)
\(384\) 1.38904 + 1.03468i 0.0708844 + 0.0528006i
\(385\) −0.546341 + 2.80232i −0.0278441 + 0.142820i
\(386\) 14.5056 8.37481i 0.738315 0.426266i
\(387\) 11.3209 11.9867i 0.575474 0.609320i
\(388\) −8.74505 + 5.04896i −0.443963 + 0.256322i
\(389\) 20.3683 + 11.7596i 1.03271 + 0.596237i 0.917760 0.397135i \(-0.129995\pi\)
0.114952 + 0.993371i \(0.463329\pi\)
\(390\) −7.22217 1.27132i −0.365709 0.0643757i
\(391\) 6.24232i 0.315688i
\(392\) −4.30346 5.52089i −0.217358 0.278847i
\(393\) −12.4018 1.45289i −0.625586 0.0732885i
\(394\) 10.7682 18.6511i 0.542494 0.939627i
\(395\) −4.35668 + 7.54599i −0.219208 + 0.379680i
\(396\) −2.00433 1.89300i −0.100721 0.0951267i
\(397\) 9.64915 + 5.57094i 0.484277 + 0.279598i 0.722197 0.691687i \(-0.243132\pi\)
−0.237920 + 0.971285i \(0.576466\pi\)
\(398\) 13.0222 0.652746
\(399\) 0.0921143 + 0.101281i 0.00461148 + 0.00507042i
\(400\) 1.81056 3.13599i 0.0905282 0.156799i
\(401\) 1.12561i 0.0562102i −0.999605 0.0281051i \(-0.991053\pi\)
0.999605 0.0281051i \(-0.00894732\pi\)
\(402\) 2.63648 22.5048i 0.131496 1.12244i
\(403\) 8.32654 12.6751i 0.414774 0.631394i
\(404\) 4.42478 + 7.66394i 0.220141 + 0.381295i
\(405\) −9.43913 4.75304i −0.469034 0.236180i
\(406\) 0.169620 + 0.0330691i 0.00841808 + 0.00164119i
\(407\) 2.34236 1.35236i 0.116106 0.0670340i
\(408\) −3.01749 2.24768i −0.149388 0.111277i
\(409\) 9.06948i 0.448457i −0.974537 0.224228i \(-0.928014\pi\)
0.974537 0.224228i \(-0.0719862\pi\)
\(410\) 9.43628i 0.466025i
\(411\) 28.5871 + 21.2941i 1.41010 + 1.05036i
\(412\) −8.65368 + 4.99621i −0.426336 + 0.246145i
\(413\) 3.10586 + 9.03648i 0.152830 + 0.444656i
\(414\) 2.46804 + 8.25975i 0.121297 + 0.405944i
\(415\) 6.97127 + 12.0746i 0.342206 + 0.592719i
\(416\) −3.59957 0.207654i −0.176483 0.0101811i
\(417\) 1.27602 10.8921i 0.0624872 0.533387i
\(418\) 0.0274548i 0.00134286i
\(419\) −14.1783 + 24.5576i −0.692657 + 1.19972i 0.278307 + 0.960492i \(0.410227\pi\)
−0.970964 + 0.239225i \(0.923107\pi\)
\(420\) 1.14507 + 5.25786i 0.0558736 + 0.256557i
\(421\) 19.4027 0.945627 0.472814 0.881162i \(-0.343238\pi\)
0.472814 + 0.881162i \(0.343238\pi\)
\(422\) 18.4561 + 10.6556i 0.898427 + 0.518707i
\(423\) 26.9302 28.5141i 1.30939 1.38640i
\(424\) 1.01439 1.75697i 0.0492630 0.0853261i
\(425\) −3.93318 + 6.81247i −0.190787 + 0.330454i
\(426\) −16.2106 1.89911i −0.785408 0.0920120i
\(427\) 0.384594 1.97268i 0.0186118 0.0954647i
\(428\) 4.08949i 0.197673i
\(429\) 5.65215 + 0.994948i 0.272888 + 0.0480365i
\(430\) 5.58897 + 3.22679i 0.269524 + 0.155610i
\(431\) 15.3493 8.86192i 0.739350 0.426864i −0.0824831 0.996592i \(-0.526285\pi\)
0.821833 + 0.569729i \(0.192952\pi\)
\(432\) −4.88137 1.78107i −0.234855 0.0856917i
\(433\) −0.325897 + 0.188157i −0.0156616 + 0.00904223i −0.507810 0.861469i \(-0.669545\pi\)
0.492149 + 0.870511i \(0.336212\pi\)
\(434\) −10.9227 2.12950i −0.524308 0.102219i
\(435\) −0.106538 0.0793587i −0.00510812 0.00380496i
\(436\) −3.22047 + 5.57802i −0.154233 + 0.267139i
\(437\) −0.0429236 + 0.0743458i −0.00205331 + 0.00355644i
\(438\) 1.85646 + 4.30690i 0.0887053 + 0.205792i
\(439\) 28.0432i 1.33843i −0.743070 0.669214i \(-0.766631\pi\)
0.743070 0.669214i \(-0.233369\pi\)
\(440\) 0.539560 0.934545i 0.0257225 0.0445527i
\(441\) 17.1118 + 12.1732i 0.814848 + 0.579675i
\(442\) 7.81953 + 0.451097i 0.371937 + 0.0214565i
\(443\) 13.9270 8.04074i 0.661691 0.382027i −0.131230 0.991352i \(-0.541893\pi\)
0.792921 + 0.609325i \(0.208559\pi\)
\(444\) 3.04523 4.08819i 0.144520 0.194017i
\(445\) −5.89166 10.2047i −0.279291 0.483747i
\(446\) 11.6308 20.1451i 0.550734 0.953900i
\(447\) 11.6268 5.01166i 0.549929 0.237043i
\(448\) 0.859975 + 2.50209i 0.0406300 + 0.118213i
\(449\) 30.1974 17.4345i 1.42510 0.822783i 0.428374 0.903602i \(-0.359087\pi\)
0.996729 + 0.0808182i \(0.0257533\pi\)
\(450\) −2.51087 + 10.5692i −0.118363 + 0.498238i
\(451\) 7.38494i 0.347743i
\(452\) −18.3720 + 10.6071i −0.864144 + 0.498914i
\(453\) 6.68137 + 15.5005i 0.313918 + 0.728275i
\(454\) 23.3571i 1.09620i
\(455\) −8.01235 7.82812i −0.375625 0.366988i
\(456\) −0.0204827 0.0475187i −0.000959188 0.00222527i
\(457\) 2.79700 0.130838 0.0654191 0.997858i \(-0.479162\pi\)
0.0654191 + 0.997858i \(0.479162\pi\)
\(458\) −1.84632 3.19792i −0.0862730 0.149429i
\(459\) 10.6041 + 3.86911i 0.494955 + 0.180594i
\(460\) −2.92219 + 1.68713i −0.136248 + 0.0786627i
\(461\) 11.5533 + 20.0109i 0.538091 + 0.932001i 0.999007 + 0.0445574i \(0.0141878\pi\)
−0.460916 + 0.887444i \(0.652479\pi\)
\(462\) −0.896143 4.11486i −0.0416923 0.191441i
\(463\) 7.03737 0.327054 0.163527 0.986539i \(-0.447713\pi\)
0.163527 + 0.986539i \(0.447713\pi\)
\(464\) −0.0565664 0.0326586i −0.00262603 0.00151614i
\(465\) 6.86058 + 5.11034i 0.318152 + 0.236986i
\(466\) 4.61110 + 7.98666i 0.213605 + 0.369975i
\(467\) 14.7390 + 25.5287i 0.682039 + 1.18133i 0.974358 + 0.225005i \(0.0722398\pi\)
−0.292319 + 0.956321i \(0.594427\pi\)
\(468\) 10.5250 2.49474i 0.486520 0.115319i
\(469\) 22.7220 26.1092i 1.04920 1.20561i
\(470\) 13.2950 + 7.67590i 0.613255 + 0.354063i
\(471\) −14.1188 + 6.08584i −0.650562 + 0.280421i
\(472\) 3.61157i 0.166236i
\(473\) −4.37399 2.52532i −0.201116 0.116114i
\(474\) 1.49545 12.7651i 0.0686885 0.586320i
\(475\) −0.0936881 + 0.0540908i −0.00429870 + 0.00248186i
\(476\) −1.86817 5.43542i −0.0856273 0.249132i
\(477\) −1.40674 + 5.92153i −0.0644102 + 0.271128i
\(478\) −13.3075 −0.608669
\(479\) −7.42009 12.8520i −0.339033 0.587222i 0.645218 0.763998i \(-0.276766\pi\)
−0.984251 + 0.176776i \(0.943433\pi\)
\(480\) 0.236653 2.02005i 0.0108017 0.0922023i
\(481\) −0.611159 + 10.5941i −0.0278665 + 0.483050i
\(482\) −25.7424 −1.17253
\(483\) −4.00659 + 12.5438i −0.182306 + 0.570765i
\(484\) 5.07773 8.79489i 0.230806 0.399768i
\(485\) 10.2689 + 5.92875i 0.466287 + 0.269211i
\(486\) 15.5609 + 0.926997i 0.705855 + 0.0420495i
\(487\) −26.0894 −1.18222 −0.591111 0.806590i \(-0.701310\pi\)
−0.591111 + 0.806590i \(0.701310\pi\)
\(488\) −0.379821 + 0.657869i −0.0171937 + 0.0297803i
\(489\) 2.13750 + 4.95889i 0.0966610 + 0.224249i
\(490\) −3.08769 + 7.61780i −0.139488 + 0.344137i
\(491\) −19.2964 11.1408i −0.870834 0.502776i −0.00320842 0.999995i \(-0.501021\pi\)
−0.867625 + 0.497219i \(0.834355\pi\)
\(492\) 5.50954 + 12.7819i 0.248389 + 0.576251i
\(493\) 0.122882 + 0.0709460i 0.00553433 + 0.00319525i
\(494\) 0.0900284 + 0.0591413i 0.00405057 + 0.00266089i
\(495\) −0.748255 + 3.14970i −0.0336316 + 0.141568i
\(496\) 3.64262 + 2.10307i 0.163558 + 0.0944305i
\(497\) −18.8069 16.3671i −0.843605 0.734163i
\(498\) −16.4929 12.2853i −0.739063 0.550517i
\(499\) −11.3535 19.6649i −0.508254 0.880321i −0.999954 0.00955703i \(-0.996958\pi\)
0.491701 0.870764i \(-0.336375\pi\)
\(500\) −10.1234 −0.452732
\(501\) −5.06530 11.7512i −0.226301 0.525006i
\(502\) −26.8320 + 15.4915i −1.19757 + 0.691418i
\(503\) 13.8434 + 23.9774i 0.617246 + 1.06910i 0.989986 + 0.141165i \(0.0450849\pi\)
−0.372740 + 0.927936i \(0.621582\pi\)
\(504\) −4.62094 6.45344i −0.205833 0.287459i
\(505\) 5.19581 8.99940i 0.231210 0.400468i
\(506\) 2.28694 1.32036i 0.101667 0.0586974i
\(507\) −15.4381 + 16.3910i −0.685630 + 0.727951i
\(508\) −0.00158663 + 0.00274813i −7.03954e−5 + 0.000121928i
\(509\) 19.1126 0.847151 0.423575 0.905861i \(-0.360775\pi\)
0.423575 + 0.905861i \(0.360775\pi\)
\(510\) −0.514093 + 4.38826i −0.0227644 + 0.194316i
\(511\) −1.37090 + 7.03167i −0.0606448 + 0.311063i
\(512\) 1.00000i 0.0441942i
\(513\) 0.0996891 + 0.118997i 0.00440138 + 0.00525383i
\(514\) 31.2860i 1.37997i
\(515\) 10.1616 + 5.86681i 0.447774 + 0.258523i
\(516\) −9.45453 1.10761i −0.416212 0.0487600i
\(517\) −10.4049 6.00725i −0.457605 0.264198i
\(518\) 7.36406 2.53105i 0.323558 0.111208i
\(519\) −6.83978 15.8680i −0.300233 0.696526i
\(520\) 1.90223 + 3.78244i 0.0834184 + 0.165871i
\(521\) 7.05557 12.2206i 0.309110 0.535394i −0.669058 0.743210i \(-0.733302\pi\)
0.978168 + 0.207816i \(0.0666355\pi\)
\(522\) 0.190646 + 0.0452906i 0.00834434 + 0.00198231i
\(523\) 1.35929i 0.0594377i 0.999558 + 0.0297188i \(0.00946119\pi\)
−0.999558 + 0.0297188i \(0.990539\pi\)
\(524\) 3.60456 + 6.24329i 0.157466 + 0.272739i
\(525\) −12.2762 + 11.1651i −0.535778 + 0.487284i
\(526\) −1.63886 2.83858i −0.0714576 0.123768i
\(527\) −7.91305 4.56860i −0.344698 0.199012i
\(528\) −0.185207 + 1.58091i −0.00806010 + 0.0688005i
\(529\) 14.7428 0.640992
\(530\) −2.38230 −0.103480
\(531\) 3.10193 + 10.3812i 0.134612 + 0.450506i
\(532\) 0.0151253 0.0775815i 0.000655765 0.00336358i
\(533\) −24.2164 15.9082i −1.04893 0.689059i
\(534\) 13.9387 + 10.3827i 0.603186 + 0.449304i
\(535\) 4.15874 2.40105i 0.179798 0.103806i
\(536\) −11.3294 + 6.54101i −0.489354 + 0.282529i
\(537\) −3.25437 + 27.7791i −0.140436 + 1.19876i
\(538\) 7.84705i 0.338310i
\(539\) 2.41646 5.96177i 0.104084 0.256792i
\(540\) 1.05476 + 6.00974i 0.0453895 + 0.258618i
\(541\) 16.1920 + 28.0454i 0.696150 + 1.20577i 0.969792 + 0.243935i \(0.0784383\pi\)
−0.273642 + 0.961832i \(0.588228\pi\)
\(542\) −11.1613 −0.479418
\(543\) −16.3317 12.1652i −0.700859 0.522059i
\(544\) 2.17235i 0.0931388i
\(545\) 7.56329 0.323976
\(546\) 15.4237 + 5.92538i 0.660072 + 0.253583i
\(547\) −20.9799 −0.897036 −0.448518 0.893774i \(-0.648048\pi\)
−0.448518 + 0.893774i \(0.648048\pi\)
\(548\) 20.5804i 0.879151i
\(549\) 0.526731 2.21722i 0.0224803 0.0946285i
\(550\) 3.32776 0.141896
\(551\) 0.000975680 0.00168993i 4.15654e−5 7.19934e-5i
\(552\) 2.97318 3.99146i 0.126547 0.169888i
\(553\) 12.8883 14.8095i 0.548065 0.629765i
\(554\) 19.0907i 0.811086i
\(555\) −5.94535 0.696508i −0.252366 0.0295651i
\(556\) −5.48328 + 3.16577i −0.232543 + 0.134259i
\(557\) −1.77057 + 1.02224i −0.0750216 + 0.0433137i −0.537042 0.843556i \(-0.680458\pi\)
0.462020 + 0.886870i \(0.347125\pi\)
\(558\) −12.2767 2.91651i −0.519716 0.123466i
\(559\) 17.7031 8.90309i 0.748761 0.376561i
\(560\) 2.03954 2.34358i 0.0861864 0.0990343i
\(561\) 0.402335 3.43430i 0.0169866 0.144996i
\(562\) 12.3375 0.520427
\(563\) 34.6535 1.46047 0.730235 0.683196i \(-0.239411\pi\)
0.730235 + 0.683196i \(0.239411\pi\)
\(564\) −22.4905 2.63480i −0.947019 0.110945i
\(565\) 21.5733 + 12.4554i 0.907597 + 0.524001i
\(566\) 5.39233 + 9.33979i 0.226656 + 0.392580i
\(567\) 18.8253 + 14.5811i 0.790589 + 0.612347i
\(568\) 4.71161 + 8.16075i 0.197695 + 0.342418i
\(569\) 10.1933i 0.427323i −0.976908 0.213662i \(-0.931461\pi\)
0.976908 0.213662i \(-0.0685390\pi\)
\(570\) −0.0362975 + 0.0487290i −0.00152033 + 0.00204103i
\(571\) 4.05162 7.01761i 0.169555 0.293678i −0.768709 0.639599i \(-0.779100\pi\)
0.938263 + 0.345922i \(0.112434\pi\)
\(572\) −1.48871 2.96018i −0.0622460 0.123771i
\(573\) −1.78448 + 0.769189i −0.0745478 + 0.0321333i
\(574\) −4.06849 + 20.8683i −0.169815 + 0.871027i
\(575\) −9.01136 5.20271i −0.375800 0.216968i
\(576\) 0.858887 + 2.87442i 0.0357870 + 0.119768i
\(577\) 14.1521 + 8.17074i 0.589161 + 0.340153i 0.764766 0.644308i \(-0.222855\pi\)
−0.175604 + 0.984461i \(0.556188\pi\)
\(578\) 12.2809i 0.510818i
\(579\) 28.8141 + 3.37562i 1.19747 + 0.140286i
\(580\) 0.0766990i 0.00318475i
\(581\) −10.2109 29.7086i −0.423621 1.23252i
\(582\) −17.3713 2.03508i −0.720063 0.0843567i
\(583\) 1.86441 0.0772161
\(584\) 1.35388 2.34499i 0.0560239 0.0970363i
\(585\) −8.71651 9.23853i −0.360383 0.381966i
\(586\) −15.4741 + 8.93398i −0.639229 + 0.369059i
\(587\) −11.5145 + 19.9438i −0.475256 + 0.823167i −0.999598 0.0283405i \(-0.990978\pi\)
0.524343 + 0.851507i \(0.324311\pi\)
\(588\) −0.265367 12.1215i −0.0109436 0.499880i
\(589\) −0.0628294 0.108824i −0.00258884 0.00448400i
\(590\) −3.67273 + 2.12045i −0.151204 + 0.0872976i
\(591\) 34.2553 14.7655i 1.40908 0.607373i
\(592\) −2.94317 −0.120963
\(593\) −3.13509 5.43014i −0.128743 0.222989i 0.794447 0.607334i \(-0.207761\pi\)
−0.923190 + 0.384344i \(0.874428\pi\)
\(594\) −0.825464 4.70329i −0.0338692 0.192978i
\(595\) −4.43060 + 5.09108i −0.181637 + 0.208714i
\(596\) −6.33047 3.65490i −0.259306 0.149710i
\(597\) 18.0885 + 13.4738i 0.740311 + 0.551446i
\(598\) −0.596700 + 10.3435i −0.0244009 + 0.422976i
\(599\) −4.15122 2.39671i −0.169614 0.0979269i 0.412790 0.910826i \(-0.364554\pi\)
−0.582404 + 0.812900i \(0.697888\pi\)
\(600\) 5.75969 2.48268i 0.235138 0.101355i
\(601\) −42.1719 24.3480i −1.72023 0.993174i −0.918434 0.395574i \(-0.870546\pi\)
−0.801794 0.597601i \(-0.796121\pi\)
\(602\) −10.9687 9.54575i −0.447053 0.389056i
\(603\) 26.9474 28.5323i 1.09738 1.16192i
\(604\) 4.87258 8.43956i 0.198263 0.343401i
\(605\) −11.9251 −0.484824
\(606\) −1.78349 + 15.2238i −0.0724493 + 0.618423i
\(607\) −30.5881 17.6601i −1.24153 0.716800i −0.272128 0.962261i \(-0.587727\pi\)
−0.969406 + 0.245461i \(0.921061\pi\)
\(608\) −0.0149376 + 0.0258726i −0.000605798 + 0.00104927i
\(609\) 0.201393 + 0.221436i 0.00816087 + 0.00897304i
\(610\) 0.892011 0.0361165
\(611\) 42.1122 21.1787i 1.70368 0.856798i
\(612\) −1.86581 6.24426i −0.0754207 0.252409i
\(613\) −20.8629 36.1356i −0.842645 1.45950i −0.887650 0.460518i \(-0.847664\pi\)
0.0450051 0.998987i \(-0.485670\pi\)
\(614\) 15.9984 0.645641
\(615\) 9.76350 13.1074i 0.393702 0.528542i
\(616\) −1.59617 + 1.83411i −0.0643115 + 0.0738985i
\(617\) −25.8310 + 14.9135i −1.03992 + 0.600395i −0.919809 0.392366i \(-0.871657\pi\)
−0.120106 + 0.992761i \(0.538323\pi\)
\(618\) −17.1898 2.01382i −0.691476 0.0810076i
\(619\) 11.2355 + 6.48683i 0.451594 + 0.260728i 0.708503 0.705708i \(-0.249371\pi\)
−0.256909 + 0.966436i \(0.582704\pi\)
\(620\) 4.93907i 0.198358i
\(621\) −5.11796 + 14.0268i −0.205376 + 0.562875i
\(622\) 12.9943 + 7.50229i 0.521026 + 0.300814i
\(623\) 8.62962 + 25.1078i 0.345738 + 1.00592i
\(624\) −4.78510 4.01283i −0.191557 0.160642i
\(625\) −3.10911 5.38514i −0.124364 0.215405i
\(626\) 4.59734 + 7.96283i 0.183747 + 0.318259i
\(627\) 0.0284068 0.0381359i 0.00113446 0.00152300i
\(628\) 7.68731 + 4.43827i 0.306757 + 0.177106i
\(629\) 6.39359 0.254929
\(630\) −3.84964 + 8.48818i −0.153373 + 0.338177i
\(631\) −14.7342 25.5203i −0.586557 1.01595i −0.994679 0.103020i \(-0.967150\pi\)
0.408122 0.912927i \(-0.366184\pi\)
\(632\) −6.42620 + 3.71017i −0.255620 + 0.147583i
\(633\) 14.6112 + 33.8972i 0.580741 + 1.34729i
\(634\) 15.1778 + 26.2887i 0.602787 + 1.04406i
\(635\) 0.00372621 0.000147870
\(636\) 3.22693 1.39095i 0.127956 0.0551546i
\(637\) 14.3442 + 20.7664i 0.568337 + 0.822796i
\(638\) 0.0600255i 0.00237643i
\(639\) −20.5523 19.4107i −0.813038 0.767876i
\(640\) −1.01693 + 0.587127i −0.0401978 + 0.0232082i
\(641\) 28.4150i 1.12233i 0.827705 + 0.561163i \(0.189646\pi\)
−0.827705 + 0.561163i \(0.810354\pi\)
\(642\) −4.23130 + 5.68048i −0.166996 + 0.224191i
\(643\) 27.7370 16.0140i 1.09384 0.631530i 0.159245 0.987239i \(-0.449094\pi\)
0.934597 + 0.355709i \(0.115761\pi\)
\(644\) 7.18983 2.47116i 0.283319 0.0973775i
\(645\) 4.42464 + 10.2649i 0.174220 + 0.404181i
\(646\) 0.0324496 0.0562044i 0.00127671 0.00221133i
\(647\) 7.52581 + 13.0351i 0.295870 + 0.512462i 0.975187 0.221383i \(-0.0710570\pi\)
−0.679317 + 0.733845i \(0.737724\pi\)
\(648\) −4.93761 7.52463i −0.193968 0.295595i
\(649\) 2.87432 1.65949i 0.112827 0.0651406i
\(650\) −7.16845 + 10.9122i −0.281170 + 0.428013i
\(651\) −12.9688 14.2595i −0.508288 0.558873i
\(652\) 1.55883 2.69997i 0.0610485 0.105739i
\(653\) 13.6394i 0.533749i 0.963731 + 0.266875i \(0.0859909\pi\)
−0.963731 + 0.266875i \(0.914009\pi\)
\(654\) −10.2448 + 4.41597i −0.400604 + 0.172678i
\(655\) 4.23267 7.33120i 0.165384 0.286454i
\(656\) 4.01799 6.95937i 0.156876 0.271718i
\(657\) −1.87754 + 7.90332i −0.0732500 + 0.308338i
\(658\) −26.0925 22.7075i −1.01719 0.885229i
\(659\) 7.63539 4.40829i 0.297432 0.171723i −0.343856 0.939022i \(-0.611733\pi\)
0.641289 + 0.767300i \(0.278400\pi\)
\(660\) 1.71642 0.739854i 0.0668117 0.0287988i
\(661\) −24.7707 + 14.3013i −0.963467 + 0.556258i −0.897238 0.441547i \(-0.854430\pi\)
−0.0662286 + 0.997804i \(0.521097\pi\)
\(662\) 26.1992 + 15.1261i 1.01826 + 0.587892i
\(663\) 10.3949 + 8.71728i 0.403706 + 0.338551i
\(664\) 11.8735i 0.460783i
\(665\) −0.0877757 + 0.0301687i −0.00340379 + 0.00116989i
\(666\) 8.45990 2.52785i 0.327815 0.0979521i
\(667\) −0.0938456 + 0.162545i −0.00363371 + 0.00629378i
\(668\) −3.69401 + 6.39822i −0.142926 + 0.247554i
\(669\) 36.9994 15.9484i 1.43048 0.616599i
\(670\) 13.3035 + 7.68081i 0.513961 + 0.296735i
\(671\) −0.698098 −0.0269498
\(672\) −1.39431 + 4.36531i −0.0537867 + 0.168395i
\(673\) 9.49994 16.4544i 0.366196 0.634270i −0.622771 0.782404i \(-0.713993\pi\)
0.988967 + 0.148134i \(0.0473267\pi\)
\(674\) 15.1212i 0.582447i
\(675\) −14.4235 + 12.0832i −0.555159 + 0.465082i
\(676\) 12.9138 + 1.49493i 0.496683 + 0.0574972i
\(677\) 24.1275 + 41.7901i 0.927297 + 1.60612i 0.787825 + 0.615899i \(0.211207\pi\)
0.139471 + 0.990226i \(0.455460\pi\)
\(678\) −36.4943 4.27538i −1.40156 0.164195i
\(679\) −20.1535 17.5389i −0.773418 0.673081i
\(680\) 2.20914 1.27545i 0.0847165 0.0489111i
\(681\) −24.1671 + 32.4441i −0.926084 + 1.24326i
\(682\) 3.86537i 0.148013i
\(683\) 7.06486i 0.270329i −0.990823 0.135165i \(-0.956844\pi\)
0.990823 0.135165i \(-0.0431564\pi\)
\(684\) 0.0207152 0.0871986i 0.000792067 0.00333412i
\(685\) −20.9289 + 12.0833i −0.799652 + 0.461679i
\(686\) 10.1129 15.5155i 0.386111 0.592383i
\(687\) 0.744195 6.35241i 0.0283928 0.242359i
\(688\) 2.74795 + 4.75959i 0.104765 + 0.181458i
\(689\) −4.01620 + 6.11369i −0.153005 + 0.232913i
\(690\) −5.80468 0.680029i −0.220980 0.0258882i
\(691\) 27.5162i 1.04677i 0.852097 + 0.523384i \(0.175331\pi\)
−0.852097 + 0.523384i \(0.824669\pi\)
\(692\) −4.98811 + 8.63966i −0.189619 + 0.328430i
\(693\) 3.01277 6.64294i 0.114446 0.252344i
\(694\) 3.24211 0.123069
\(695\) 6.43876 + 3.71742i 0.244236 + 0.141010i
\(696\) −0.0447821 0.103892i −0.00169746 0.00393802i
\(697\) −8.72849 + 15.1182i −0.330615 + 0.572643i
\(698\) −5.16032 + 8.93794i −0.195321 + 0.338306i
\(699\) −1.85859 + 15.8648i −0.0702984 + 0.600063i
\(700\) 9.40356 + 1.83332i 0.355421 + 0.0692930i
\(701\) 1.43708i 0.0542779i −0.999632 0.0271389i \(-0.991360\pi\)
0.999632 0.0271389i \(-0.00863965\pi\)
\(702\) 17.2010 + 7.42471i 0.649209 + 0.280228i
\(703\) 0.0761474 + 0.0439637i 0.00287195 + 0.00165812i
\(704\) 0.795863 0.459492i 0.0299952 0.0173178i
\(705\) 10.5253 + 24.4182i 0.396407 + 0.919644i
\(706\) 19.7980 11.4304i 0.745106 0.430187i
\(707\) −15.3706 + 17.6620i −0.578073 + 0.664247i
\(708\) 3.73681 5.01664i 0.140438 0.188537i
\(709\) −9.50734 + 16.4672i −0.357056 + 0.618438i −0.987468 0.157822i \(-0.949553\pi\)
0.630412 + 0.776261i \(0.282886\pi\)
\(710\) 5.53263 9.58279i 0.207636 0.359636i
\(711\) 15.2850 16.1840i 0.573233 0.606946i
\(712\) 10.0347i 0.376068i
\(713\) 6.04323 10.4672i 0.226321 0.391999i
\(714\) 3.02893 9.48298i 0.113355 0.354892i
\(715\) −2.13624 + 3.25192i −0.0798910 + 0.121615i
\(716\) 13.9845 8.07398i 0.522627 0.301739i
\(717\) −18.4847 13.7689i −0.690322 0.514210i
\(718\) −0.0353783 0.0612770i −0.00132031 0.00228684i
\(719\) 19.1696 33.2027i 0.714904 1.23825i −0.248092 0.968736i \(-0.579804\pi\)
0.962996 0.269514i \(-0.0868630\pi\)
\(720\) 2.41882 2.56108i 0.0901442 0.0954459i
\(721\) −19.9429 17.3557i −0.742712 0.646359i
\(722\) −16.4537 + 9.49955i −0.612344 + 0.353537i
\(723\) −35.7573 26.6351i −1.32983 0.990569i
\(724\) 11.7575i 0.436964i
\(725\) −0.204834 + 0.118261i −0.00760735 + 0.00439211i
\(726\) 16.1531 6.96268i 0.599497 0.258409i
\(727\) 36.3302i 1.34741i −0.738998 0.673707i \(-0.764701\pi\)
0.738998 0.673707i \(-0.235299\pi\)
\(728\) −2.57597 9.18501i −0.0954717 0.340419i
\(729\) 20.6556 + 17.3881i 0.765022 + 0.644004i
\(730\) −3.17960 −0.117682
\(731\) −5.96952 10.3395i −0.220791 0.382421i
\(732\) −1.20827 + 0.520817i −0.0446589 + 0.0192499i
\(733\) −16.1295 + 9.31236i −0.595756 + 0.343960i −0.767370 0.641204i \(-0.778435\pi\)
0.171614 + 0.985164i \(0.445102\pi\)
\(734\) −8.21199 14.2236i −0.303110 0.525002i
\(735\) −12.1709 + 7.38669i −0.448931 + 0.272462i
\(736\) −2.87353 −0.105920
\(737\) −10.4115 6.01108i −0.383513 0.221421i
\(738\) −5.57210 + 23.4552i −0.205112 + 0.863397i
\(739\) 16.5130 + 28.6014i 0.607442 + 1.05212i 0.991661 + 0.128878i \(0.0411374\pi\)
−0.384219 + 0.923242i \(0.625529\pi\)
\(740\) 1.72801 + 2.99300i 0.0635229 + 0.110025i
\(741\) 0.0638612 + 0.175300i 0.00234600 + 0.00643981i
\(742\) 5.26844 + 1.02714i 0.193411 + 0.0377074i
\(743\) 2.44292 + 1.41042i 0.0896221 + 0.0517434i 0.544141 0.838994i \(-0.316856\pi\)
−0.454519 + 0.890737i \(0.650189\pi\)
\(744\) 2.88376 + 6.69019i 0.105724 + 0.245274i
\(745\) 8.58355i 0.314477i
\(746\) 0.242947 + 0.140266i 0.00889494 + 0.00513549i
\(747\) −10.1980 34.1296i −0.373126 1.24874i
\(748\) −1.72890 + 0.998178i −0.0632147 + 0.0364970i
\(749\) −10.2323 + 3.51686i −0.373879 + 0.128503i
\(750\) −14.0618 10.4744i −0.513466 0.382472i
\(751\) 43.4465 1.58539 0.792693 0.609621i \(-0.208678\pi\)
0.792693 + 0.609621i \(0.208678\pi\)
\(752\) 6.53683 + 11.3221i 0.238374 + 0.412876i
\(753\) −53.2995 6.24413i −1.94234 0.227549i
\(754\) 0.196833 + 0.129303i 0.00716823 + 0.00470894i
\(755\) −11.4433 −0.416464
\(756\) 0.258532 13.7453i 0.00940273 0.499912i
\(757\) 4.02158 6.96557i 0.146167 0.253168i −0.783641 0.621214i \(-0.786640\pi\)
0.929808 + 0.368046i \(0.119973\pi\)
\(758\) 27.3847 + 15.8106i 0.994656 + 0.574265i
\(759\) 4.54281 + 0.532198i 0.164893 + 0.0193176i
\(760\) 0.0350810 0.00127252
\(761\) 17.3333 30.0222i 0.628332 1.08830i −0.359554 0.933124i \(-0.617071\pi\)
0.987886 0.155179i \(-0.0495955\pi\)
\(762\) −0.00504732 + 0.00217562i −0.000182845 + 7.88143e-5i
\(763\) −16.7262 3.26094i −0.605530 0.118054i
\(764\) 0.971600 + 0.560953i 0.0351512 + 0.0202946i
\(765\) −5.25453 + 5.56357i −0.189978 + 0.201151i
\(766\) −22.8482 13.1914i −0.825539 0.476625i
\(767\) −0.749957 + 13.0001i −0.0270794 + 0.469406i
\(768\) 1.03468 1.38904i 0.0373357 0.0501228i
\(769\) −37.8048 21.8266i −1.36328 0.787089i −0.373219 0.927743i \(-0.621746\pi\)
−0.990059 + 0.140655i \(0.955079\pi\)
\(770\) 2.80232 + 0.546341i 0.100989 + 0.0196888i
\(771\) −32.3709 + 43.4577i −1.16581 + 1.56509i
\(772\) −8.37481 14.5056i −0.301416 0.522068i
\(773\) −30.7181 −1.10485 −0.552426 0.833562i \(-0.686298\pi\)
−0.552426 + 0.833562i \(0.686298\pi\)
\(774\) −11.9867 11.3209i −0.430854 0.406922i
\(775\) 13.1904 7.61548i 0.473813 0.273556i
\(776\) 5.04896 + 8.74505i 0.181247 + 0.313929i
\(777\) 12.8478 + 4.10368i 0.460913 + 0.147219i
\(778\) 11.7596 20.3683i 0.421603 0.730238i
\(779\) −0.207912 + 0.120038i −0.00744922 + 0.00430081i
\(780\) −1.27132 + 7.22217i −0.0455205 + 0.258595i
\(781\) −4.32990 + 7.49960i −0.154936 + 0.268357i
\(782\) 6.24232 0.223225
\(783\) 0.217954 + 0.260167i 0.00778905 + 0.00929763i
\(784\) −5.52089 + 4.30346i −0.197175 + 0.153695i
\(785\) 10.4233i 0.372024i
\(786\) −1.45289 + 12.4018i −0.0518228 + 0.442356i
\(787\) 49.2113i 1.75419i −0.480315 0.877096i \(-0.659478\pi\)
0.480315 0.877096i \(-0.340522\pi\)
\(788\) −18.6511 10.7682i −0.664416 0.383601i
\(789\) 0.660573 5.63861i 0.0235170 0.200740i
\(790\) 7.54599 + 4.35668i 0.268474 + 0.155004i
\(791\) −42.3392 36.8465i −1.50541 1.31011i
\(792\) −1.89300 + 2.00433i −0.0672647 + 0.0712208i
\(793\) 1.50380 2.28917i 0.0534014 0.0812908i
\(794\) 5.57094 9.64915i 0.197705 0.342436i
\(795\) −3.30912 2.46491i −0.117362 0.0874213i
\(796\) 13.0222i 0.461561i
\(797\) −5.88110 10.1864i −0.208319 0.360819i 0.742866 0.669440i \(-0.233466\pi\)
−0.951185 + 0.308621i \(0.900133\pi\)
\(798\) 0.101281 0.0921143i 0.00358533 0.00326081i
\(799\) −14.2003 24.5957i −0.502371 0.870132i
\(800\) −3.13599 1.81056i −0.110874 0.0640131i
\(801\) 8.61870 + 28.8441i 0.304527 + 1.01916i
\(802\) −1.12561 −0.0397466
\(803\) 2.48839 0.0878133
\(804\) −22.5048 2.63648i −0.793684 0.0929815i
\(805\) −6.73435 5.86069i −0.237355 0.206562i
\(806\) −12.6751 8.32654i −0.446463 0.293290i
\(807\) −8.11916 + 10.8999i −0.285808 + 0.383695i
\(808\) 7.66394 4.42478i 0.269616 0.155663i
\(809\) 42.6424 24.6196i 1.49923 0.865579i 0.499227 0.866471i \(-0.333617\pi\)
1.00000 0.000892258i \(0.000284015\pi\)
\(810\) −4.75304 + 9.43913i −0.167005 + 0.331657i
\(811\) 24.8223i 0.871628i 0.900037 + 0.435814i \(0.143539\pi\)
−0.900037 + 0.435814i \(0.856461\pi\)
\(812\) 0.0330691 0.169620i 0.00116050 0.00595248i
\(813\) −15.5035 11.5483i −0.543732 0.405018i
\(814\) −1.35236 2.34236i −0.0474002 0.0820996i
\(815\) −3.66093 −0.128237
\(816\) −2.24768 + 3.01749i −0.0786846 + 0.105633i
\(817\) 0.164191i 0.00574431i
\(818\) −9.06948 −0.317107
\(819\) 15.2933 + 24.1891i 0.534392 + 0.845237i
\(820\) −9.43628 −0.329529
\(821\) 35.0049i 1.22168i −0.791754 0.610840i \(-0.790832\pi\)
0.791754 0.610840i \(-0.209168\pi\)
\(822\) 21.2941 28.5871i 0.742716 0.997089i
\(823\) −5.33806 −0.186073 −0.0930365 0.995663i \(-0.529657\pi\)
−0.0930365 + 0.995663i \(0.529657\pi\)
\(824\) 4.99621 + 8.65368i 0.174051 + 0.301465i
\(825\) 4.62240 + 3.44316i 0.160931 + 0.119875i
\(826\) 9.03648 3.10586i 0.314419 0.108067i
\(827\) 19.8191i 0.689178i −0.938754 0.344589i \(-0.888018\pi\)
0.938754 0.344589i \(-0.111982\pi\)
\(828\) 8.25975 2.46804i 0.287046 0.0857703i
\(829\) −7.97067 + 4.60187i −0.276833 + 0.159830i −0.631989 0.774978i \(-0.717761\pi\)
0.355156 + 0.934807i \(0.384428\pi\)
\(830\) 12.0746 6.97127i 0.419116 0.241976i
\(831\) 19.7527 26.5178i 0.685214 0.919893i
\(832\) −0.207654 + 3.59957i −0.00719910 + 0.124793i
\(833\) 11.9933 9.34864i 0.415544 0.323911i
\(834\) −10.8921 1.27602i −0.377161 0.0441851i
\(835\) 8.67541 0.300225
\(836\) −0.0274548 −0.000949543
\(837\) −14.0353 16.7536i −0.485130 0.579090i
\(838\) 24.5576 + 14.1783i 0.848328 + 0.489782i
\(839\) 16.4881 + 28.5582i 0.569231 + 0.985937i 0.996642 + 0.0818800i \(0.0260924\pi\)
−0.427411 + 0.904057i \(0.640574\pi\)
\(840\) 5.25786 1.14507i 0.181413 0.0395086i
\(841\) −14.4979 25.1110i −0.499926 0.865898i
\(842\) 19.4027i 0.668660i
\(843\) 17.1374 + 12.7654i 0.590242 + 0.439662i
\(844\) 10.6556 18.4561i 0.366781 0.635284i
\(845\) −6.06177 14.0101i −0.208531 0.481964i
\(846\) −28.5141 26.9302i −0.980334 0.925879i
\(847\) 26.3723 + 5.14155i 0.906164 + 0.176666i
\(848\) −1.75697 1.01439i −0.0603346 0.0348342i
\(849\) −2.17348 + 18.5527i −0.0745936 + 0.636727i
\(850\) 6.81247 + 3.93318i 0.233666 + 0.134907i
\(851\) 8.45728i 0.289912i
\(852\) −1.89911 + 16.2106i −0.0650623 + 0.555368i
\(853\) 8.39823i 0.287550i 0.989610 + 0.143775i \(0.0459241\pi\)
−0.989610 + 0.143775i \(0.954076\pi\)
\(854\) −1.97268 0.384594i −0.0675038 0.0131605i
\(855\) −0.100838 + 0.0301306i −0.00344857 + 0.00103044i
\(856\) 4.08949 0.139776
\(857\) −20.9307 + 36.2531i −0.714980 + 1.23838i 0.247988 + 0.968763i \(0.420231\pi\)
−0.962967 + 0.269618i \(0.913103\pi\)
\(858\) 0.994948 5.65215i 0.0339670 0.192961i
\(859\) −22.3299 + 12.8922i −0.761887 + 0.439875i −0.829973 0.557804i \(-0.811644\pi\)
0.0680860 + 0.997679i \(0.478311\pi\)
\(860\) 3.22679 5.58897i 0.110033 0.190582i
\(861\) −27.2433 + 24.7774i −0.928449 + 0.844413i
\(862\) −8.86192 15.3493i −0.301838 0.522799i
\(863\) −23.6109 + 13.6317i −0.803724 + 0.464030i −0.844772 0.535127i \(-0.820264\pi\)
0.0410479 + 0.999157i \(0.486930\pi\)
\(864\) −1.78107 + 4.88137i −0.0605932 + 0.166068i
\(865\) 11.7146 0.398309
\(866\) 0.188157 + 0.325897i 0.00639382 + 0.0110744i
\(867\) −12.7067 + 17.0587i −0.431544 + 0.579344i
\(868\) −2.12950 + 10.9227i −0.0722799 + 0.370742i
\(869\) −5.90557 3.40958i −0.200333 0.115662i
\(870\) −0.0793587 + 0.106538i −0.00269051 + 0.00361199i
\(871\) 42.1391 21.1922i 1.42783 0.718071i
\(872\) 5.57802 + 3.22047i 0.188895 + 0.109059i
\(873\) −22.0238 20.8005i −0.745394 0.703990i
\(874\) 0.0743458 + 0.0429236i 0.00251478 + 0.00145191i
\(875\) −8.70586 25.3296i −0.294312 0.856297i
\(876\) 4.30690 1.85646i 0.145517 0.0627241i
\(877\) −9.69170 + 16.7865i −0.327266 + 0.566841i −0.981968 0.189046i \(-0.939461\pi\)
0.654703 + 0.755887i \(0.272794\pi\)
\(878\) −28.0432 −0.946411
\(879\) −30.7380 3.60101i −1.03677 0.121459i
\(880\) −0.934545 0.539560i −0.0315035 0.0181886i
\(881\) −2.46823 + 4.27510i −0.0831568 + 0.144032i −0.904604 0.426252i \(-0.859834\pi\)
0.821447 + 0.570284i \(0.193167\pi\)
\(882\) 12.1732 17.1118i 0.409892 0.576184i
\(883\) 50.5405 1.70082 0.850411 0.526118i \(-0.176353\pi\)
0.850411 + 0.526118i \(0.176353\pi\)
\(884\) 0.451097 7.81953i 0.0151720 0.262999i
\(885\) −7.29557 0.854688i −0.245238 0.0287300i
\(886\) −8.04074 13.9270i −0.270134 0.467886i
\(887\) 51.6838 1.73537 0.867687 0.497111i \(-0.165606\pi\)
0.867687 + 0.497111i \(0.165606\pi\)
\(888\) −4.08819 3.04523i −0.137191 0.102191i
\(889\) −0.00824051 0.00160657i −0.000276378 5.38827e-5i
\(890\) −10.2047 + 5.89166i −0.342061 + 0.197489i
\(891\) 3.71978 7.38717i 0.124617 0.247479i
\(892\) −20.1451 11.6308i −0.674509 0.389428i
\(893\) 0.390578i 0.0130702i
\(894\) −5.01166 11.6268i −0.167615 0.388859i
\(895\) −16.4214 9.48089i −0.548907 0.316911i
\(896\) 2.50209 0.859975i 0.0835889 0.0287297i
\(897\) −11.5310 + 13.7501i −0.385009 + 0.459104i
\(898\) −17.4345 30.1974i −0.581796 1.00770i
\(899\) −0.137367 0.237926i −0.00458143 0.00793527i
\(900\) 10.5692 + 2.51087i 0.352308 + 0.0836956i
\(901\) 3.81676 + 2.20361i 0.127155 + 0.0734128i
\(902\) 7.38494 0.245892
\(903\) −5.35931 24.6086i −0.178347 0.818922i
\(904\) 10.6071 + 18.3720i 0.352785 + 0.611042i
\(905\) 11.9566 6.90313i 0.397450 0.229468i
\(906\) 15.5005 6.68137i 0.514968 0.221974i
\(907\) −3.09477 5.36029i −0.102760 0.177986i 0.810061 0.586346i \(-0.199434\pi\)
−0.912821 + 0.408360i \(0.866101\pi\)
\(908\) 23.3571 0.775133
\(909\) −18.2290 + 19.3011i −0.604618 + 0.640178i
\(910\) −7.82812 + 8.01235i −0.259500 + 0.265607i
\(911\) 24.1747i 0.800943i 0.916309 + 0.400472i \(0.131154\pi\)
−0.916309 + 0.400472i \(0.868846\pi\)
\(912\) −0.0475187 + 0.0204827i −0.00157350 + 0.000678248i
\(913\) −9.44972 + 5.45580i −0.312740 + 0.180561i
\(914\) 2.79700i 0.0925166i
\(915\) 1.23904 + 0.922944i 0.0409615 + 0.0305116i
\(916\) −3.19792 + 1.84632i −0.105662 + 0.0610042i
\(917\) −12.5214 + 14.3880i −0.413494 + 0.475134i
\(918\) 3.86911 10.6041i 0.127700 0.349986i
\(919\) 24.9444 43.2049i 0.822839 1.42520i −0.0807208 0.996737i \(-0.525722\pi\)
0.903560 0.428462i \(-0.140944\pi\)
\(920\) 1.68713 + 2.92219i 0.0556229 + 0.0963417i
\(921\) 22.2224 + 16.5531i 0.732254 + 0.545444i
\(922\) 20.0109 11.5533i 0.659024 0.380488i
\(923\) −15.2652 30.3536i −0.502459 0.999100i
\(924\) −4.11486 + 0.896143i −0.135369 + 0.0294809i
\(925\) −5.32879 + 9.22974i −0.175210 + 0.303472i
\(926\) 7.03737i 0.231262i
\(927\) −21.7938 20.5832i −0.715801 0.676040i
\(928\) −0.0326586 + 0.0565664i −0.00107207 + 0.00185688i
\(929\) −11.2582 + 19.4998i −0.369369 + 0.639767i −0.989467 0.144758i \(-0.953760\pi\)
0.620098 + 0.784525i \(0.287093\pi\)
\(930\) 5.11034 6.86058i 0.167575 0.224967i
\(931\) 0.207123 0.0288733i 0.00678818 0.000946284i
\(932\) 7.98666 4.61110i 0.261612 0.151042i
\(933\) 10.2873 + 23.8660i 0.336790 + 0.781337i
\(934\) 25.5287 14.7390i 0.835323 0.482274i
\(935\) 2.03016 + 1.17211i 0.0663934 + 0.0383322i
\(936\) −2.49474 10.5250i −0.0815430 0.344021i
\(937\) 50.9552i 1.66463i −0.554300 0.832317i \(-0.687014\pi\)
0.554300 0.832317i \(-0.312986\pi\)
\(938\) −26.1092 22.7220i −0.852494 0.741898i
\(939\) −1.85305 + 15.8175i −0.0604719 + 0.516184i
\(940\) 7.67590 13.2950i 0.250360 0.433637i
\(941\) 7.47373 12.9449i 0.243637 0.421991i −0.718111 0.695929i \(-0.754993\pi\)
0.961747 + 0.273938i \(0.0883263\pi\)
\(942\) 6.08584 + 14.1188i 0.198287 + 0.460017i
\(943\) −19.9980 11.5458i −0.651223 0.375984i
\(944\) −3.61157 −0.117547
\(945\) −14.1298 + 7.80732i −0.459644 + 0.253972i
\(946\) −2.52532 + 4.37399i −0.0821053 + 0.142211i
\(947\) 2.69835i 0.0876847i 0.999038 + 0.0438424i \(0.0139599\pi\)
−0.999038 + 0.0438424i \(0.986040\pi\)
\(948\) −12.7651 1.49545i −0.414591 0.0485701i
\(949\) −5.36033 + 8.15980i −0.174004 + 0.264878i
\(950\) 0.0540908 + 0.0936881i 0.00175494 + 0.00303964i
\(951\) −6.11770 + 52.2203i −0.198380 + 1.69336i
\(952\) −5.43542 + 1.86817i −0.176163 + 0.0605477i
\(953\) −17.2962 + 9.98599i −0.560280 + 0.323478i −0.753258 0.657725i \(-0.771519\pi\)
0.192978 + 0.981203i \(0.438185\pi\)
\(954\) 5.92153 + 1.40674i 0.191716 + 0.0455449i
\(955\) 1.31740i 0.0426302i
\(956\) 13.3075i 0.430394i
\(957\) 0.0621070 0.0833780i 0.00200763 0.00269523i
\(958\) −12.8520 + 7.42009i −0.415229 + 0.239732i
\(959\) 51.4940 17.6986i 1.66283 0.571519i
\(960\) −2.02005 0.236653i −0.0651969 0.00763793i
\(961\) −6.65421 11.5254i −0.214652 0.371788i
\(962\) 10.5941 + 0.611159i 0.341568 + 0.0197046i
\(963\) −11.7549 + 3.51241i −0.378797 + 0.113186i
\(964\) 25.7424i 0.829107i
\(965\) −9.83415 + 17.0332i −0.316572 + 0.548319i
\(966\) 12.5438 + 4.00659i 0.403592 + 0.128910i
\(967\) −27.3039 −0.878035 −0.439017 0.898479i \(-0.644673\pi\)
−0.439017 + 0.898479i \(0.644673\pi\)
\(968\) −8.79489 5.07773i −0.282679 0.163205i
\(969\) 0.103227 0.0444955i 0.00331614 0.00142940i
\(970\) 5.92875 10.2689i 0.190361 0.329715i
\(971\) 7.74032 13.4066i 0.248399 0.430239i −0.714683 0.699449i \(-0.753429\pi\)
0.963082 + 0.269209i \(0.0867623\pi\)
\(972\) 0.926997 15.5609i 0.0297335 0.499115i
\(973\) −12.6365 10.9972i −0.405108 0.352553i
\(974\) 26.0894i 0.835957i
\(975\) −21.2479 + 7.74055i −0.680478 + 0.247896i
\(976\) 0.657869 + 0.379821i 0.0210579 + 0.0121578i
\(977\) 19.4291 11.2174i 0.621591 0.358876i −0.155897 0.987773i \(-0.549827\pi\)
0.777488 + 0.628897i \(0.216493\pi\)
\(978\) 4.95889 2.13750i 0.158568 0.0683496i
\(979\) 7.98628 4.61088i 0.255242 0.147364i
\(980\) 7.61780 + 3.08769i 0.243342 + 0.0986328i
\(981\) −18.7996 4.46611i −0.600225 0.142592i
\(982\) −11.1408 + 19.2964i −0.355516 + 0.615772i
\(983\) 1.46260 2.53330i 0.0466498 0.0807999i −0.841758 0.539856i \(-0.818479\pi\)
0.888407 + 0.459056i \(0.151812\pi\)
\(984\) 12.7819 5.50954i 0.407471 0.175638i
\(985\) 25.2892i 0.805780i
\(986\) 0.0709460 0.122882i 0.00225938 0.00391336i
\(987\) −12.7487 58.5389i −0.405797 1.86332i
\(988\) 0.0591413 0.0900284i 0.00188154 0.00286418i
\(989\) 13.6768 7.89633i 0.434898 0.251089i
\(990\) 3.14970 + 0.748255i 0.100104 + 0.0237811i
\(991\) 8.30241 + 14.3802i 0.263735 + 0.456802i 0.967231 0.253897i \(-0.0817123\pi\)
−0.703497 + 0.710699i \(0.748379\pi\)
\(992\) 2.10307 3.64262i 0.0667725 0.115653i
\(993\) 20.7412 + 48.1185i 0.658201 + 1.52699i
\(994\) −16.3671 + 18.8069i −0.519131 + 0.596519i
\(995\) −13.2427 + 7.64570i −0.419823 + 0.242385i
\(996\) −12.2853 + 16.4929i −0.389274 + 0.522597i
\(997\) 43.6283i 1.38172i 0.722988 + 0.690860i \(0.242768\pi\)
−0.722988 + 0.690860i \(0.757232\pi\)
\(998\) −19.6649 + 11.3535i −0.622481 + 0.359390i
\(999\) 14.3667 + 5.24198i 0.454542 + 0.165849i
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 546.2.bb.a.269.13 yes 76
3.2 odd 2 inner 546.2.bb.a.269.38 yes 76
7.5 odd 6 546.2.u.a.425.7 yes 76
13.3 even 3 546.2.u.a.185.32 yes 76
21.5 even 6 546.2.u.a.425.32 yes 76
39.29 odd 6 546.2.u.a.185.7 76
91.68 odd 6 inner 546.2.bb.a.341.19 yes 76
273.68 even 6 inner 546.2.bb.a.341.32 yes 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.u.a.185.7 76 39.29 odd 6
546.2.u.a.185.32 yes 76 13.3 even 3
546.2.u.a.425.7 yes 76 7.5 odd 6
546.2.u.a.425.32 yes 76 21.5 even 6
546.2.bb.a.269.13 yes 76 1.1 even 1 trivial
546.2.bb.a.269.38 yes 76 3.2 odd 2 inner
546.2.bb.a.341.19 yes 76 91.68 odd 6 inner
546.2.bb.a.341.32 yes 76 273.68 even 6 inner