Properties

Label 847.2.f.a.372.1
Level $847$
Weight $2$
Character 847.372
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 372.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 847.372
Dual form 847.2.f.a.148.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.690983 + 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-2.23607 - 6.88191i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} +O(q^{10})\) \(q+(-0.690983 + 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-2.23607 - 6.88191i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} +4.47214 q^{10} +9.70820 q^{12} +(-0.381966 + 1.17557i) q^{13} +(1.80902 - 1.31433i) q^{14} +(5.23607 + 3.80423i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(0.381966 + 1.17557i) q^{17} +(13.5172 + 9.82084i) q^{18} +(2.00000 - 1.45309i) q^{19} +(-1.85410 + 5.70634i) q^{20} +3.23607 q^{21} -6.47214 q^{23} +(-2.23607 + 6.88191i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-2.23607 - 1.62460i) q^{26} +(4.47214 + 13.7638i) q^{27} +(0.927051 + 2.85317i) q^{28} +(0.381966 + 0.277515i) q^{29} +(-11.7082 + 8.50651i) q^{30} +(-2.23607 + 6.88191i) q^{31} +6.70820 q^{32} -2.76393 q^{34} +(-0.618034 + 1.90211i) q^{35} +(-18.1353 + 13.1760i) q^{36} +(-0.381966 - 0.277515i) q^{37} +(1.70820 + 5.25731i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(-3.61803 - 2.62866i) q^{40} +(5.47214 - 3.97574i) q^{41} +(-2.23607 + 6.88191i) q^{42} +8.00000 q^{43} -14.9443 q^{45} +(4.47214 - 13.7638i) q^{46} +(-5.85410 + 4.25325i) q^{47} +(2.61803 + 1.90211i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.690983 + 2.12663i) q^{50} +(-3.23607 - 2.35114i) q^{51} +(3.00000 - 2.17963i) q^{52} +(2.61803 - 8.05748i) q^{53} -32.3607 q^{54} -2.23607 q^{56} +(-2.47214 + 7.60845i) q^{57} +(-0.854102 + 0.620541i) q^{58} +(-2.61803 - 1.90211i) q^{59} +(-6.00000 - 18.4661i) q^{60} +(-0.854102 - 2.62866i) q^{61} +(-13.0902 - 9.51057i) q^{62} +(-6.04508 + 4.39201i) q^{63} +(-4.01722 + 12.3637i) q^{64} +2.47214 q^{65} +5.52786 q^{67} +(1.14590 - 3.52671i) q^{68} +(16.9443 - 12.3107i) q^{69} +(-3.61803 - 2.62866i) q^{70} +(-0.472136 - 1.45309i) q^{71} +(-5.16312 - 15.8904i) q^{72} +(4.23607 + 3.07768i) q^{73} +(0.854102 - 0.620541i) q^{74} +(-1.00000 + 3.07768i) q^{75} -7.41641 q^{76} +8.94427 q^{78} +(2.76393 - 8.50651i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(4.67376 + 14.3844i) q^{82} +(4.76393 + 14.6619i) q^{83} +(-7.85410 - 5.70634i) q^{84} +(2.00000 - 1.45309i) q^{85} +(-5.52786 + 17.0130i) q^{86} -1.52786 q^{87} +2.00000 q^{89} +(10.3262 - 31.7809i) q^{90} +(1.00000 - 0.726543i) q^{91} +(15.7082 + 11.4127i) q^{92} +(-7.23607 - 22.2703i) q^{93} +(-5.00000 - 15.3884i) q^{94} +(-4.00000 - 2.90617i) q^{95} +(-17.5623 + 12.7598i) q^{96} +(-2.90983 + 8.95554i) q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 12 q^{12} - 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} + 6 q^{17} + 25 q^{18} + 8 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + q^{25} - 3 q^{28} + 6 q^{29} - 20 q^{30} - 20 q^{34} + 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} + 4 q^{39} - 10 q^{40} + 4 q^{41} + 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} + 5 q^{50} - 4 q^{51} + 12 q^{52} + 6 q^{53} - 40 q^{54} + 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} + 10 q^{61} - 30 q^{62} - 13 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} + 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} - 5 q^{72} + 8 q^{73} - 10 q^{74} - 4 q^{75} + 24 q^{76} + 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} + 28 q^{83} - 18 q^{84} + 8 q^{85} - 40 q^{86} - 24 q^{87} + 8 q^{89} + 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} - 20 q^{94} - 16 q^{95} - 30 q^{96} - 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.690983 + 2.12663i −0.488599 + 1.50375i 0.338101 + 0.941110i \(0.390215\pi\)
−0.826700 + 0.562643i \(0.809785\pi\)
\(3\) −2.61803 + 1.90211i −1.51152 + 1.09819i −0.546027 + 0.837768i \(0.683860\pi\)
−0.965496 + 0.260418i \(0.916140\pi\)
\(4\) −2.42705 1.76336i −1.21353 0.881678i
\(5\) −0.618034 1.90211i −0.276393 0.850651i −0.988847 0.148932i \(-0.952416\pi\)
0.712454 0.701719i \(-0.247584\pi\)
\(6\) −2.23607 6.88191i −0.912871 2.80953i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) 1.80902 1.31433i 0.639584 0.464685i
\(9\) 2.30902 7.10642i 0.769672 2.36881i
\(10\) 4.47214 1.41421
\(11\) 0 0
\(12\) 9.70820 2.80252
\(13\) −0.381966 + 1.17557i −0.105938 + 0.326045i −0.989950 0.141421i \(-0.954833\pi\)
0.884011 + 0.467466i \(0.154833\pi\)
\(14\) 1.80902 1.31433i 0.483480 0.351269i
\(15\) 5.23607 + 3.80423i 1.35195 + 0.982247i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) 0.381966 + 1.17557i 0.0926404 + 0.285118i 0.986632 0.162967i \(-0.0521064\pi\)
−0.893991 + 0.448085i \(0.852106\pi\)
\(18\) 13.5172 + 9.82084i 3.18604 + 2.31479i
\(19\) 2.00000 1.45309i 0.458831 0.333361i −0.334241 0.942488i \(-0.608480\pi\)
0.793073 + 0.609127i \(0.208480\pi\)
\(20\) −1.85410 + 5.70634i −0.414590 + 1.27598i
\(21\) 3.23607 0.706168
\(22\) 0 0
\(23\) −6.47214 −1.34953 −0.674767 0.738031i \(-0.735756\pi\)
−0.674767 + 0.738031i \(0.735756\pi\)
\(24\) −2.23607 + 6.88191i −0.456435 + 1.40476i
\(25\) 0.809017 0.587785i 0.161803 0.117557i
\(26\) −2.23607 1.62460i −0.438529 0.318610i
\(27\) 4.47214 + 13.7638i 0.860663 + 2.64885i
\(28\) 0.927051 + 2.85317i 0.175196 + 0.539198i
\(29\) 0.381966 + 0.277515i 0.0709293 + 0.0515332i 0.622685 0.782473i \(-0.286042\pi\)
−0.551756 + 0.834006i \(0.686042\pi\)
\(30\) −11.7082 + 8.50651i −2.13762 + 1.55307i
\(31\) −2.23607 + 6.88191i −0.401610 + 1.23603i 0.522083 + 0.852894i \(0.325155\pi\)
−0.923693 + 0.383133i \(0.874845\pi\)
\(32\) 6.70820 1.18585
\(33\) 0 0
\(34\) −2.76393 −0.474010
\(35\) −0.618034 + 1.90211i −0.104467 + 0.321516i
\(36\) −18.1353 + 13.1760i −3.02254 + 2.19601i
\(37\) −0.381966 0.277515i −0.0627948 0.0456231i 0.555945 0.831219i \(-0.312356\pi\)
−0.618740 + 0.785596i \(0.712356\pi\)
\(38\) 1.70820 + 5.25731i 0.277107 + 0.852848i
\(39\) −1.23607 3.80423i −0.197929 0.609164i
\(40\) −3.61803 2.62866i −0.572061 0.415627i
\(41\) 5.47214 3.97574i 0.854604 0.620906i −0.0718076 0.997419i \(-0.522877\pi\)
0.926412 + 0.376512i \(0.122877\pi\)
\(42\) −2.23607 + 6.88191i −0.345033 + 1.06190i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −14.9443 −2.22776
\(46\) 4.47214 13.7638i 0.659380 2.02936i
\(47\) −5.85410 + 4.25325i −0.853909 + 0.620401i −0.926221 0.376981i \(-0.876962\pi\)
0.0723124 + 0.997382i \(0.476962\pi\)
\(48\) 2.61803 + 1.90211i 0.377881 + 0.274546i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) 0.690983 + 2.12663i 0.0977198 + 0.300750i
\(51\) −3.23607 2.35114i −0.453140 0.329226i
\(52\) 3.00000 2.17963i 0.416025 0.302260i
\(53\) 2.61803 8.05748i 0.359615 1.10678i −0.593671 0.804708i \(-0.702322\pi\)
0.953285 0.302072i \(-0.0976782\pi\)
\(54\) −32.3607 −4.40373
\(55\) 0 0
\(56\) −2.23607 −0.298807
\(57\) −2.47214 + 7.60845i −0.327442 + 1.00776i
\(58\) −0.854102 + 0.620541i −0.112149 + 0.0814811i
\(59\) −2.61803 1.90211i −0.340839 0.247634i 0.404177 0.914681i \(-0.367558\pi\)
−0.745016 + 0.667047i \(0.767558\pi\)
\(60\) −6.00000 18.4661i −0.774597 2.38396i
\(61\) −0.854102 2.62866i −0.109357 0.336565i 0.881372 0.472423i \(-0.156621\pi\)
−0.990728 + 0.135859i \(0.956621\pi\)
\(62\) −13.0902 9.51057i −1.66245 1.20784i
\(63\) −6.04508 + 4.39201i −0.761609 + 0.553341i
\(64\) −4.01722 + 12.3637i −0.502153 + 1.54547i
\(65\) 2.47214 0.306631
\(66\) 0 0
\(67\) 5.52786 0.675336 0.337668 0.941265i \(-0.390362\pi\)
0.337668 + 0.941265i \(0.390362\pi\)
\(68\) 1.14590 3.52671i 0.138961 0.427677i
\(69\) 16.9443 12.3107i 2.03985 1.48204i
\(70\) −3.61803 2.62866i −0.432438 0.314184i
\(71\) −0.472136 1.45309i −0.0560322 0.172449i 0.919124 0.393969i \(-0.128898\pi\)
−0.975156 + 0.221520i \(0.928898\pi\)
\(72\) −5.16312 15.8904i −0.608479 1.87271i
\(73\) 4.23607 + 3.07768i 0.495794 + 0.360216i 0.807408 0.589993i \(-0.200870\pi\)
−0.311614 + 0.950209i \(0.600870\pi\)
\(74\) 0.854102 0.620541i 0.0992873 0.0721365i
\(75\) −1.00000 + 3.07768i −0.115470 + 0.355380i
\(76\) −7.41641 −0.850720
\(77\) 0 0
\(78\) 8.94427 1.01274
\(79\) 2.76393 8.50651i 0.310967 0.957057i −0.666416 0.745580i \(-0.732173\pi\)
0.977383 0.211477i \(-0.0678274\pi\)
\(80\) −1.61803 + 1.17557i −0.180902 + 0.131433i
\(81\) −19.7533 14.3516i −2.19481 1.59462i
\(82\) 4.67376 + 14.3844i 0.516131 + 1.58849i
\(83\) 4.76393 + 14.6619i 0.522909 + 1.60935i 0.768413 + 0.639954i \(0.221047\pi\)
−0.245504 + 0.969396i \(0.578953\pi\)
\(84\) −7.85410 5.70634i −0.856953 0.622613i
\(85\) 2.00000 1.45309i 0.216930 0.157609i
\(86\) −5.52786 + 17.0130i −0.596085 + 1.83456i
\(87\) −1.52786 −0.163804
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 10.3262 31.7809i 1.08848 3.35000i
\(91\) 1.00000 0.726543i 0.104828 0.0761624i
\(92\) 15.7082 + 11.4127i 1.63769 + 1.18985i
\(93\) −7.23607 22.2703i −0.750345 2.30933i
\(94\) −5.00000 15.3884i −0.515711 1.58719i
\(95\) −4.00000 2.90617i −0.410391 0.298167i
\(96\) −17.5623 + 12.7598i −1.79245 + 1.30229i
\(97\) −2.90983 + 8.95554i −0.295448 + 0.909297i 0.687622 + 0.726069i \(0.258655\pi\)
−0.983070 + 0.183228i \(0.941345\pi\)
\(98\) −2.23607 −0.225877
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −2.85410 + 8.78402i −0.283994 + 0.874043i 0.702705 + 0.711482i \(0.251976\pi\)
−0.986698 + 0.162561i \(0.948024\pi\)
\(102\) 7.23607 5.25731i 0.716477 0.520551i
\(103\) 4.61803 + 3.35520i 0.455028 + 0.330597i 0.791578 0.611068i \(-0.209260\pi\)
−0.336549 + 0.941666i \(0.609260\pi\)
\(104\) 0.854102 + 2.62866i 0.0837516 + 0.257761i
\(105\) −2.00000 6.15537i −0.195180 0.600702i
\(106\) 15.3262 + 11.1352i 1.48862 + 1.08154i
\(107\) 3.23607 2.35114i 0.312842 0.227293i −0.420273 0.907398i \(-0.638066\pi\)
0.733115 + 0.680104i \(0.238066\pi\)
\(108\) 13.4164 41.2915i 1.29099 3.97327i
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) 0 0
\(111\) 1.52786 0.145018
\(112\) −0.309017 + 0.951057i −0.0291994 + 0.0898664i
\(113\) −1.61803 + 1.17557i −0.152212 + 0.110588i −0.661285 0.750135i \(-0.729988\pi\)
0.509073 + 0.860724i \(0.329988\pi\)
\(114\) −14.4721 10.5146i −1.35544 0.984785i
\(115\) 4.00000 + 12.3107i 0.373002 + 1.14798i
\(116\) −0.437694 1.34708i −0.0406389 0.125074i
\(117\) 7.47214 + 5.42882i 0.690799 + 0.501895i
\(118\) 5.85410 4.25325i 0.538914 0.391544i
\(119\) 0.381966 1.17557i 0.0350148 0.107764i
\(120\) 14.4721 1.32112
\(121\) 0 0
\(122\) 6.18034 0.559542
\(123\) −6.76393 + 20.8172i −0.609883 + 1.87703i
\(124\) 17.5623 12.7598i 1.57714 1.14586i
\(125\) −9.70820 7.05342i −0.868328 0.630877i
\(126\) −5.16312 15.8904i −0.459967 1.41563i
\(127\) 6.47214 + 19.9192i 0.574309 + 1.76754i 0.638520 + 0.769606i \(0.279547\pi\)
−0.0642104 + 0.997936i \(0.520453\pi\)
\(128\) −12.6631 9.20029i −1.11927 0.813199i
\(129\) −20.9443 + 15.2169i −1.84404 + 1.33977i
\(130\) −1.70820 + 5.25731i −0.149819 + 0.461097i
\(131\) −13.8885 −1.21345 −0.606724 0.794913i \(-0.707517\pi\)
−0.606724 + 0.794913i \(0.707517\pi\)
\(132\) 0 0
\(133\) −2.47214 −0.214361
\(134\) −3.81966 + 11.7557i −0.329968 + 1.01554i
\(135\) 23.4164 17.0130i 2.01536 1.46425i
\(136\) 2.23607 + 1.62460i 0.191741 + 0.139308i
\(137\) 2.32624 + 7.15942i 0.198744 + 0.611671i 0.999912 + 0.0132321i \(0.00421203\pi\)
−0.801169 + 0.598439i \(0.795788\pi\)
\(138\) 14.4721 + 44.5407i 1.23195 + 3.79155i
\(139\) 8.47214 + 6.15537i 0.718597 + 0.522091i 0.885936 0.463808i \(-0.153517\pi\)
−0.167339 + 0.985899i \(0.553517\pi\)
\(140\) 4.85410 3.52671i 0.410246 0.298062i
\(141\) 7.23607 22.2703i 0.609387 1.87550i
\(142\) 3.41641 0.286699
\(143\) 0 0
\(144\) −7.47214 −0.622678
\(145\) 0.291796 0.898056i 0.0242323 0.0745795i
\(146\) −9.47214 + 6.88191i −0.783920 + 0.569551i
\(147\) −2.61803 1.90211i −0.215932 0.156884i
\(148\) 0.437694 + 1.34708i 0.0359782 + 0.110730i
\(149\) 4.32624 + 13.3148i 0.354419 + 1.09079i 0.956345 + 0.292239i \(0.0944001\pi\)
−0.601926 + 0.798552i \(0.705600\pi\)
\(150\) −5.85410 4.25325i −0.477985 0.347277i
\(151\) 7.23607 5.25731i 0.588863 0.427834i −0.253046 0.967454i \(-0.581432\pi\)
0.841908 + 0.539620i \(0.181432\pi\)
\(152\) 1.70820 5.25731i 0.138554 0.426424i
\(153\) 9.23607 0.746692
\(154\) 0 0
\(155\) 14.4721 1.16243
\(156\) −3.70820 + 11.4127i −0.296894 + 0.913746i
\(157\) 5.61803 4.08174i 0.448368 0.325758i −0.340583 0.940214i \(-0.610624\pi\)
0.788951 + 0.614456i \(0.210624\pi\)
\(158\) 16.1803 + 11.7557i 1.28724 + 0.935234i
\(159\) 8.47214 + 26.0746i 0.671884 + 2.06785i
\(160\) −4.14590 12.7598i −0.327762 1.00875i
\(161\) 5.23607 + 3.80423i 0.412660 + 0.299815i
\(162\) 44.1697 32.0912i 3.47030 2.52132i
\(163\) 7.23607 22.2703i 0.566773 1.74435i −0.0958527 0.995396i \(-0.530558\pi\)
0.662625 0.748951i \(-0.269442\pi\)
\(164\) −20.2918 −1.58452
\(165\) 0 0
\(166\) −34.4721 −2.67556
\(167\) −4.00000 + 12.3107i −0.309529 + 0.952633i 0.668419 + 0.743785i \(0.266971\pi\)
−0.977948 + 0.208848i \(0.933029\pi\)
\(168\) 5.85410 4.25325i 0.451654 0.328146i
\(169\) 9.28115 + 6.74315i 0.713935 + 0.518704i
\(170\) 1.70820 + 5.25731i 0.131013 + 0.403217i
\(171\) −5.70820 17.5680i −0.436517 1.34346i
\(172\) −19.4164 14.1068i −1.48049 1.07564i
\(173\) 13.9443 10.1311i 1.06016 0.770254i 0.0860448 0.996291i \(-0.472577\pi\)
0.974119 + 0.226038i \(0.0725772\pi\)
\(174\) 1.05573 3.24920i 0.0800345 0.246321i
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 10.4721 0.787134
\(178\) −1.38197 + 4.25325i −0.103583 + 0.318795i
\(179\) −7.23607 + 5.25731i −0.540849 + 0.392950i −0.824400 0.566007i \(-0.808487\pi\)
0.283551 + 0.958957i \(0.408487\pi\)
\(180\) 36.2705 + 26.3521i 2.70344 + 1.96417i
\(181\) 0.437694 + 1.34708i 0.0325335 + 0.100128i 0.966005 0.258525i \(-0.0832363\pi\)
−0.933471 + 0.358653i \(0.883236\pi\)
\(182\) 0.854102 + 2.62866i 0.0633102 + 0.194849i
\(183\) 7.23607 + 5.25731i 0.534906 + 0.388632i
\(184\) −11.7082 + 8.50651i −0.863140 + 0.627108i
\(185\) −0.291796 + 0.898056i −0.0214533 + 0.0660264i
\(186\) 52.3607 3.83927
\(187\) 0 0
\(188\) 21.7082 1.58323
\(189\) 4.47214 13.7638i 0.325300 1.00117i
\(190\) 8.94427 6.49839i 0.648886 0.471443i
\(191\) 16.9443 + 12.3107i 1.22604 + 0.890773i 0.996587 0.0825453i \(-0.0263049\pi\)
0.229457 + 0.973319i \(0.426305\pi\)
\(192\) −13.0000 40.0099i −0.938194 2.88746i
\(193\) −7.38197 22.7194i −0.531366 1.63537i −0.751374 0.659877i \(-0.770608\pi\)
0.220008 0.975498i \(-0.429392\pi\)
\(194\) −17.0344 12.3762i −1.22300 0.888563i
\(195\) −6.47214 + 4.70228i −0.463479 + 0.336737i
\(196\) 0.927051 2.85317i 0.0662179 0.203798i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 20.1803 1.43055 0.715273 0.698845i \(-0.246302\pi\)
0.715273 + 0.698845i \(0.246302\pi\)
\(200\) 0.690983 2.12663i 0.0488599 0.150375i
\(201\) −14.4721 + 10.5146i −1.02079 + 0.741644i
\(202\) −16.7082 12.1392i −1.17559 0.854113i
\(203\) −0.145898 0.449028i −0.0102400 0.0315156i
\(204\) 3.70820 + 11.4127i 0.259626 + 0.799047i
\(205\) −10.9443 7.95148i −0.764381 0.555355i
\(206\) −10.3262 + 7.50245i −0.719463 + 0.522721i
\(207\) −14.9443 + 45.9937i −1.03870 + 3.19679i
\(208\) 1.23607 0.0857059
\(209\) 0 0
\(210\) 14.4721 0.998672
\(211\) 6.76393 20.8172i 0.465648 1.43312i −0.392517 0.919745i \(-0.628396\pi\)
0.858165 0.513373i \(-0.171604\pi\)
\(212\) −20.5623 + 14.9394i −1.41222 + 1.02604i
\(213\) 4.00000 + 2.90617i 0.274075 + 0.199127i
\(214\) 2.76393 + 8.50651i 0.188939 + 0.581493i
\(215\) −4.94427 15.2169i −0.337197 1.03778i
\(216\) 26.1803 + 19.0211i 1.78135 + 1.29422i
\(217\) 5.85410 4.25325i 0.397402 0.288730i
\(218\) −3.09017 + 9.51057i −0.209293 + 0.644137i
\(219\) −16.9443 −1.14499
\(220\) 0 0
\(221\) −1.52786 −0.102775
\(222\) −1.05573 + 3.24920i −0.0708558 + 0.218072i
\(223\) −9.85410 + 7.15942i −0.659879 + 0.479431i −0.866622 0.498965i \(-0.833714\pi\)
0.206743 + 0.978395i \(0.433714\pi\)
\(224\) −5.42705 3.94298i −0.362610 0.263452i
\(225\) −2.30902 7.10642i −0.153934 0.473762i
\(226\) −1.38197 4.25325i −0.0919270 0.282922i
\(227\) 24.1803 + 17.5680i 1.60491 + 1.16603i 0.877177 + 0.480166i \(0.159424\pi\)
0.727728 + 0.685866i \(0.240576\pi\)
\(228\) 19.4164 14.1068i 1.28588 0.934249i
\(229\) 1.38197 4.25325i 0.0913229 0.281063i −0.894955 0.446156i \(-0.852793\pi\)
0.986278 + 0.165093i \(0.0527925\pi\)
\(230\) −28.9443 −1.90853
\(231\) 0 0
\(232\) 1.05573 0.0693119
\(233\) −5.38197 + 16.5640i −0.352584 + 1.08514i 0.604813 + 0.796368i \(0.293248\pi\)
−0.957397 + 0.288775i \(0.906752\pi\)
\(234\) −16.7082 + 12.1392i −1.09225 + 0.793566i
\(235\) 11.7082 + 8.50651i 0.763759 + 0.554903i
\(236\) 3.00000 + 9.23305i 0.195283 + 0.601020i
\(237\) 8.94427 + 27.5276i 0.580993 + 1.78811i
\(238\) 2.23607 + 1.62460i 0.144943 + 0.105307i
\(239\) −20.9443 + 15.2169i −1.35477 + 0.984300i −0.356014 + 0.934481i \(0.615864\pi\)
−0.998758 + 0.0498191i \(0.984136\pi\)
\(240\) 2.00000 6.15537i 0.129099 0.397327i
\(241\) 27.1246 1.74725 0.873625 0.486600i \(-0.161763\pi\)
0.873625 + 0.486600i \(0.161763\pi\)
\(242\) 0 0
\(243\) 35.5967 2.28353
\(244\) −2.56231 + 7.88597i −0.164035 + 0.504847i
\(245\) 1.61803 1.17557i 0.103372 0.0751044i
\(246\) −39.5967 28.7687i −2.52460 1.83423i
\(247\) 0.944272 + 2.90617i 0.0600826 + 0.184915i
\(248\) 5.00000 + 15.3884i 0.317500 + 0.977166i
\(249\) −40.3607 29.3238i −2.55775 1.85832i
\(250\) 21.7082 15.7719i 1.37295 0.997505i
\(251\) 5.47214 16.8415i 0.345398 1.06303i −0.615972 0.787768i \(-0.711237\pi\)
0.961370 0.275258i \(-0.0887634\pi\)
\(252\) 22.4164 1.41210
\(253\) 0 0
\(254\) −46.8328 −2.93855
\(255\) −2.47214 + 7.60845i −0.154811 + 0.476460i
\(256\) 7.28115 5.29007i 0.455072 0.330629i
\(257\) 4.85410 + 3.52671i 0.302791 + 0.219990i 0.728797 0.684730i \(-0.240080\pi\)
−0.426006 + 0.904720i \(0.640080\pi\)
\(258\) −17.8885 55.0553i −1.11369 3.42759i
\(259\) 0.145898 + 0.449028i 0.00906566 + 0.0279012i
\(260\) −6.00000 4.35926i −0.372104 0.270350i
\(261\) 2.85410 2.07363i 0.176664 0.128354i
\(262\) 9.59675 29.5358i 0.592889 1.82472i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −16.9443 −1.04088
\(266\) 1.70820 5.25731i 0.104737 0.322346i
\(267\) −5.23607 + 3.80423i −0.320442 + 0.232815i
\(268\) −13.4164 9.74759i −0.819538 0.595429i
\(269\) −4.14590 12.7598i −0.252780 0.777976i −0.994259 0.107000i \(-0.965875\pi\)
0.741479 0.670976i \(-0.234125\pi\)
\(270\) 20.0000 + 61.5537i 1.21716 + 3.74604i
\(271\) 1.23607 + 0.898056i 0.0750858 + 0.0545530i 0.624695 0.780869i \(-0.285223\pi\)
−0.549609 + 0.835422i \(0.685223\pi\)
\(272\) 1.00000 0.726543i 0.0606339 0.0440531i
\(273\) −1.23607 + 3.80423i −0.0748102 + 0.230242i
\(274\) −16.8328 −1.01691
\(275\) 0 0
\(276\) −62.8328 −3.78209
\(277\) 4.90983 15.1109i 0.295003 0.907926i −0.688217 0.725505i \(-0.741606\pi\)
0.983220 0.182422i \(-0.0583936\pi\)
\(278\) −18.9443 + 13.7638i −1.13620 + 0.825499i
\(279\) 43.7426 + 31.7809i 2.61880 + 1.90267i
\(280\) 1.38197 + 4.25325i 0.0825883 + 0.254181i
\(281\) −3.85410 11.8617i −0.229916 0.707610i −0.997755 0.0669669i \(-0.978668\pi\)
0.767839 0.640643i \(-0.221332\pi\)
\(282\) 42.3607 + 30.7768i 2.52254 + 1.83273i
\(283\) 4.76393 3.46120i 0.283186 0.205747i −0.437120 0.899403i \(-0.644001\pi\)
0.720306 + 0.693656i \(0.244001\pi\)
\(284\) −1.41641 + 4.35926i −0.0840483 + 0.258674i
\(285\) 16.0000 0.947758
\(286\) 0 0
\(287\) −6.76393 −0.399262
\(288\) 15.4894 47.6713i 0.912719 2.80906i
\(289\) 12.5172 9.09429i 0.736307 0.534958i
\(290\) 1.70820 + 1.24108i 0.100309 + 0.0728789i
\(291\) −9.41641 28.9807i −0.552000 1.69888i
\(292\) −4.85410 14.9394i −0.284065 0.874262i
\(293\) −12.2361 8.89002i −0.714839 0.519361i 0.169892 0.985463i \(-0.445658\pi\)
−0.884731 + 0.466102i \(0.845658\pi\)
\(294\) 5.85410 4.25325i 0.341418 0.248055i
\(295\) −2.00000 + 6.15537i −0.116445 + 0.358379i
\(296\) −1.05573 −0.0613629
\(297\) 0 0
\(298\) −31.3050 −1.81345
\(299\) 2.47214 7.60845i 0.142967 0.440008i
\(300\) 7.85410 5.70634i 0.453457 0.329456i
\(301\) −6.47214 4.70228i −0.373048 0.271035i
\(302\) 6.18034 + 19.0211i 0.355639 + 1.09454i
\(303\) −9.23607 28.4257i −0.530598 1.63301i
\(304\) −2.00000 1.45309i −0.114708 0.0833401i
\(305\) −4.47214 + 3.24920i −0.256074 + 0.186048i
\(306\) −6.38197 + 19.6417i −0.364833 + 1.12284i
\(307\) 8.94427 0.510477 0.255238 0.966878i \(-0.417846\pi\)
0.255238 + 0.966878i \(0.417846\pi\)
\(308\) 0 0
\(309\) −18.4721 −1.05084
\(310\) −10.0000 + 30.7768i −0.567962 + 1.74801i
\(311\) 17.5623 12.7598i 0.995867 0.723540i 0.0346689 0.999399i \(-0.488962\pi\)
0.961198 + 0.275859i \(0.0889623\pi\)
\(312\) −7.23607 5.25731i −0.409662 0.297637i
\(313\) −0.909830 2.80017i −0.0514266 0.158275i 0.922045 0.387083i \(-0.126517\pi\)
−0.973472 + 0.228808i \(0.926517\pi\)
\(314\) 4.79837 + 14.7679i 0.270788 + 0.833399i
\(315\) 12.0902 + 8.78402i 0.681204 + 0.494924i
\(316\) −21.7082 + 15.7719i −1.22118 + 0.887241i
\(317\) 4.32624 13.3148i 0.242986 0.747833i −0.752975 0.658049i \(-0.771382\pi\)
0.995961 0.0897846i \(-0.0286179\pi\)
\(318\) −61.3050 −3.43781
\(319\) 0 0
\(320\) 26.0000 1.45344
\(321\) −4.00000 + 12.3107i −0.223258 + 0.687118i
\(322\) −11.7082 + 8.50651i −0.652473 + 0.474049i
\(323\) 2.47214 + 1.79611i 0.137553 + 0.0999383i
\(324\) 22.6353 + 69.6642i 1.25751 + 3.87023i
\(325\) 0.381966 + 1.17557i 0.0211877 + 0.0652089i
\(326\) 42.3607 + 30.7768i 2.34614 + 1.70457i
\(327\) −11.7082 + 8.50651i −0.647465 + 0.470411i
\(328\) 4.67376 14.3844i 0.258065 0.794243i
\(329\) 7.23607 0.398937
\(330\) 0 0
\(331\) 21.8885 1.20310 0.601552 0.798834i \(-0.294549\pi\)
0.601552 + 0.798834i \(0.294549\pi\)
\(332\) 14.2918 43.9856i 0.784364 2.41402i
\(333\) −2.85410 + 2.07363i −0.156404 + 0.113634i
\(334\) −23.4164 17.0130i −1.28129 0.930911i
\(335\) −3.41641 10.5146i −0.186658 0.574475i
\(336\) −1.00000 3.07768i −0.0545545 0.167901i
\(337\) 16.5623 + 12.0332i 0.902206 + 0.655491i 0.939032 0.343830i \(-0.111725\pi\)
−0.0368254 + 0.999322i \(0.511725\pi\)
\(338\) −20.7533 + 15.0781i −1.12883 + 0.820143i
\(339\) 2.00000 6.15537i 0.108625 0.334314i
\(340\) −7.41641 −0.402211
\(341\) 0 0
\(342\) 41.3050 2.23352
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) 14.4721 10.5146i 0.780285 0.566910i
\(345\) −33.8885 24.6215i −1.82450 1.32558i
\(346\) 11.9098 + 36.6547i 0.640276 + 1.97057i
\(347\) 0.944272 + 2.90617i 0.0506912 + 0.156011i 0.973198 0.229970i \(-0.0738628\pi\)
−0.922507 + 0.385982i \(0.873863\pi\)
\(348\) 3.70820 + 2.69417i 0.198781 + 0.144423i
\(349\) 2.23607 1.62460i 0.119694 0.0869628i −0.526328 0.850282i \(-0.676432\pi\)
0.646022 + 0.763319i \(0.276432\pi\)
\(350\) 0.690983 2.12663i 0.0369346 0.113673i
\(351\) −17.8885 −0.954820
\(352\) 0 0
\(353\) −15.8885 −0.845662 −0.422831 0.906209i \(-0.638964\pi\)
−0.422831 + 0.906209i \(0.638964\pi\)
\(354\) −7.23607 + 22.2703i −0.384593 + 1.18365i
\(355\) −2.47214 + 1.79611i −0.131207 + 0.0953277i
\(356\) −4.85410 3.52671i −0.257267 0.186915i
\(357\) 1.23607 + 3.80423i 0.0654197 + 0.201341i
\(358\) −6.18034 19.0211i −0.326641 1.00530i
\(359\) 5.70820 + 4.14725i 0.301267 + 0.218884i 0.728140 0.685428i \(-0.240385\pi\)
−0.426873 + 0.904312i \(0.640385\pi\)
\(360\) −27.0344 + 19.6417i −1.42484 + 1.03521i
\(361\) −3.98278 + 12.2577i −0.209620 + 0.645144i
\(362\) −3.16718 −0.166464
\(363\) 0 0
\(364\) −3.70820 −0.194363
\(365\) 3.23607 9.95959i 0.169384 0.521309i
\(366\) −16.1803 + 11.7557i −0.845760 + 0.614481i
\(367\) −13.8541 10.0656i −0.723178 0.525420i 0.164220 0.986424i \(-0.447489\pi\)
−0.887398 + 0.461004i \(0.847489\pi\)
\(368\) 2.00000 + 6.15537i 0.104257 + 0.320871i
\(369\) −15.6180 48.0674i −0.813042 2.50229i
\(370\) −1.70820 1.24108i −0.0888053 0.0645208i
\(371\) −6.85410 + 4.97980i −0.355847 + 0.258538i
\(372\) −21.7082 + 66.8110i −1.12552 + 3.46399i
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) 38.8328 2.00532
\(376\) −5.00000 + 15.3884i −0.257855 + 0.793597i
\(377\) −0.472136 + 0.343027i −0.0243162 + 0.0176668i
\(378\) 26.1803 + 19.0211i 1.34657 + 0.978341i
\(379\) −7.81966 24.0664i −0.401669 1.23621i −0.923645 0.383250i \(-0.874805\pi\)
0.521976 0.852960i \(-0.325195\pi\)
\(380\) 4.58359 + 14.1068i 0.235133 + 0.723666i
\(381\) −54.8328 39.8384i −2.80917 2.04098i
\(382\) −37.8885 + 27.5276i −1.93855 + 1.40844i
\(383\) 8.23607 25.3480i 0.420843 1.29522i −0.486075 0.873917i \(-0.661572\pi\)
0.906919 0.421306i \(-0.138428\pi\)
\(384\) 50.6525 2.58485
\(385\) 0 0
\(386\) 53.4164 2.71882
\(387\) 18.4721 56.8514i 0.938991 2.88992i
\(388\) 22.8541 16.6045i 1.16024 0.842965i
\(389\) 16.0902 + 11.6902i 0.815804 + 0.592716i 0.915508 0.402301i \(-0.131789\pi\)
−0.0997035 + 0.995017i \(0.531789\pi\)
\(390\) −5.52786 17.0130i −0.279914 0.861488i
\(391\) −2.47214 7.60845i −0.125021 0.384776i
\(392\) 1.80902 + 1.31433i 0.0913692 + 0.0663836i
\(393\) 36.3607 26.4176i 1.83415 1.33259i
\(394\) 1.38197 4.25325i 0.0696224 0.214276i
\(395\) −17.8885 −0.900070
\(396\) 0 0
\(397\) −0.111456 −0.00559383 −0.00279691 0.999996i \(-0.500890\pi\)
−0.00279691 + 0.999996i \(0.500890\pi\)
\(398\) −13.9443 + 42.9161i −0.698963 + 2.15119i
\(399\) 6.47214 4.70228i 0.324012 0.235409i
\(400\) −0.809017 0.587785i −0.0404508 0.0293893i
\(401\) 1.56231 + 4.80828i 0.0780178 + 0.240114i 0.982457 0.186488i \(-0.0597105\pi\)
−0.904439 + 0.426602i \(0.859710\pi\)
\(402\) −12.3607 38.0423i −0.616495 1.89738i
\(403\) −7.23607 5.25731i −0.360454 0.261885i
\(404\) 22.4164 16.2865i 1.11526 0.810282i
\(405\) −15.0902 + 46.4428i −0.749837 + 2.30776i
\(406\) 1.05573 0.0523949
\(407\) 0 0
\(408\) −8.94427 −0.442807
\(409\) −9.61803 + 29.6013i −0.475581 + 1.46369i 0.369591 + 0.929194i \(0.379498\pi\)
−0.845172 + 0.534494i \(0.820502\pi\)
\(410\) 24.4721 17.7800i 1.20859 0.878094i
\(411\) −19.7082 14.3188i −0.972134 0.706297i
\(412\) −5.29180 16.2865i −0.260708 0.802377i
\(413\) 1.00000 + 3.07768i 0.0492068 + 0.151443i
\(414\) −87.4853 63.5618i −4.29967 3.12389i
\(415\) 24.9443 18.1231i 1.22447 0.889627i
\(416\) −2.56231 + 7.88597i −0.125627 + 0.386641i
\(417\) −33.8885 −1.65953
\(418\) 0 0
\(419\) −6.65248 −0.324995 −0.162497 0.986709i \(-0.551955\pi\)
−0.162497 + 0.986709i \(0.551955\pi\)
\(420\) −6.00000 + 18.4661i −0.292770 + 0.901053i
\(421\) 18.0902 13.1433i 0.881661 0.640564i −0.0520294 0.998646i \(-0.516569\pi\)
0.933690 + 0.358081i \(0.116569\pi\)
\(422\) 39.5967 + 28.7687i 1.92754 + 1.40044i
\(423\) 16.7082 + 51.4226i 0.812381 + 2.50025i
\(424\) −5.85410 18.0171i −0.284300 0.874986i
\(425\) 1.00000 + 0.726543i 0.0485071 + 0.0352425i
\(426\) −8.94427 + 6.49839i −0.433351 + 0.314848i
\(427\) −0.854102 + 2.62866i −0.0413329 + 0.127210i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 35.7771 1.72532
\(431\) 3.70820 11.4127i 0.178618 0.549729i −0.821162 0.570695i \(-0.806674\pi\)
0.999780 + 0.0209654i \(0.00667397\pi\)
\(432\) 11.7082 8.50651i 0.563311 0.409270i
\(433\) −0.381966 0.277515i −0.0183561 0.0133365i 0.578569 0.815633i \(-0.303611\pi\)
−0.596925 + 0.802297i \(0.703611\pi\)
\(434\) 5.00000 + 15.3884i 0.240008 + 0.738668i
\(435\) 0.944272 + 2.90617i 0.0452744 + 0.139340i
\(436\) −10.8541 7.88597i −0.519817 0.377669i
\(437\) −12.9443 + 9.40456i −0.619208 + 0.449881i
\(438\) 11.7082 36.0341i 0.559440 1.72178i
\(439\) 1.52786 0.0729210 0.0364605 0.999335i \(-0.488392\pi\)
0.0364605 + 0.999335i \(0.488392\pi\)
\(440\) 0 0
\(441\) 7.47214 0.355816
\(442\) 1.05573 3.24920i 0.0502159 0.154549i
\(443\) 5.70820 4.14725i 0.271205 0.197042i −0.443867 0.896093i \(-0.646394\pi\)
0.715072 + 0.699051i \(0.246394\pi\)
\(444\) −3.70820 2.69417i −0.175984 0.127860i
\(445\) −1.23607 3.80423i −0.0585952 0.180338i
\(446\) −8.41641 25.9030i −0.398528 1.22654i
\(447\) −36.6525 26.6296i −1.73360 1.25954i
\(448\) 10.5172 7.64121i 0.496892 0.361013i
\(449\) −6.03444 + 18.5721i −0.284783 + 0.876472i 0.701681 + 0.712492i \(0.252433\pi\)
−0.986464 + 0.163980i \(0.947567\pi\)
\(450\) 16.7082 0.787632
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −8.94427 + 27.5276i −0.420239 + 1.29336i
\(454\) −54.0689 + 39.2833i −2.53758 + 1.84366i
\(455\) −2.00000 1.45309i −0.0937614 0.0681217i
\(456\) 5.52786 + 17.0130i 0.258866 + 0.796707i
\(457\) 7.67376 + 23.6174i 0.358963 + 1.10478i 0.953676 + 0.300837i \(0.0972661\pi\)
−0.594712 + 0.803939i \(0.702734\pi\)
\(458\) 8.09017 + 5.87785i 0.378029 + 0.274654i
\(459\) −14.4721 + 10.5146i −0.675501 + 0.490781i
\(460\) 12.0000 36.9322i 0.559503 1.72197i
\(461\) 10.1803 0.474146 0.237073 0.971492i \(-0.423812\pi\)
0.237073 + 0.971492i \(0.423812\pi\)
\(462\) 0 0
\(463\) −14.4721 −0.672577 −0.336289 0.941759i \(-0.609172\pi\)
−0.336289 + 0.941759i \(0.609172\pi\)
\(464\) 0.145898 0.449028i 0.00677315 0.0208456i
\(465\) −37.8885 + 27.5276i −1.75704 + 1.27656i
\(466\) −31.5066 22.8909i −1.45951 1.06040i
\(467\) −10.5279 32.4014i −0.487171 1.49936i −0.828811 0.559529i \(-0.810982\pi\)
0.341640 0.939831i \(-0.389018\pi\)
\(468\) −8.56231 26.3521i −0.395793 1.21812i
\(469\) −4.47214 3.24920i −0.206504 0.150034i
\(470\) −26.1803 + 19.0211i −1.20761 + 0.877379i
\(471\) −6.94427 + 21.3723i −0.319975 + 0.984782i
\(472\) −7.23607 −0.333067
\(473\) 0 0
\(474\) −64.7214 −2.97275
\(475\) 0.763932 2.35114i 0.0350516 0.107878i
\(476\) −3.00000 + 2.17963i −0.137505 + 0.0999031i
\(477\) −51.2148 37.2097i −2.34496 1.70372i
\(478\) −17.8885 55.0553i −0.818203 2.51817i
\(479\) 6.94427 + 21.3723i 0.317292 + 0.976524i 0.974801 + 0.223077i \(0.0716102\pi\)
−0.657509 + 0.753447i \(0.728390\pi\)
\(480\) 35.1246 + 25.5195i 1.60321 + 1.16480i
\(481\) 0.472136 0.343027i 0.0215275 0.0156407i
\(482\) −18.7426 + 57.6839i −0.853704 + 2.62743i
\(483\) −20.9443 −0.952997
\(484\) 0 0
\(485\) 18.8328 0.855154
\(486\) −24.5967 + 75.7010i −1.11573 + 3.43387i
\(487\) −6.76393 + 4.91428i −0.306503 + 0.222687i −0.730395 0.683025i \(-0.760664\pi\)
0.423892 + 0.905713i \(0.360664\pi\)
\(488\) −5.00000 3.63271i −0.226339 0.164445i
\(489\) 23.4164 + 72.0683i 1.05893 + 3.25904i
\(490\) 1.38197 + 4.25325i 0.0624309 + 0.192142i
\(491\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(492\) 53.1246 38.5973i 2.39504 1.74010i
\(493\) −0.180340 + 0.555029i −0.00812210 + 0.0249973i
\(494\) −6.83282 −0.307423
\(495\) 0 0
\(496\) 7.23607 0.324909
\(497\) −0.472136 + 1.45309i −0.0211782 + 0.0651798i
\(498\) 90.2492 65.5699i 4.04416 2.93826i
\(499\) −8.47214 6.15537i −0.379265 0.275552i 0.381777 0.924254i \(-0.375312\pi\)
−0.761042 + 0.648702i \(0.775312\pi\)
\(500\) 11.1246 + 34.2380i 0.497508 + 1.53117i
\(501\) −12.9443 39.8384i −0.578307 1.77985i
\(502\) 32.0344 + 23.2744i 1.42977 + 1.03879i
\(503\) 2.76393 2.00811i 0.123238 0.0895374i −0.524459 0.851436i \(-0.675732\pi\)
0.647697 + 0.761898i \(0.275732\pi\)
\(504\) −5.16312 + 15.8904i −0.229984 + 0.707817i
\(505\) 18.4721 0.821999
\(506\) 0 0
\(507\) −37.1246 −1.64876
\(508\) 19.4164 59.7576i 0.861464 2.65131i
\(509\) −25.5066 + 18.5316i −1.13056 + 0.821399i −0.985776 0.168064i \(-0.946248\pi\)
−0.144783 + 0.989463i \(0.546248\pi\)
\(510\) −14.4721 10.5146i −0.640837 0.465595i
\(511\) −1.61803 4.97980i −0.0715776 0.220293i
\(512\) −3.45492 10.6331i −0.152687 0.469923i
\(513\) 28.9443 + 21.0292i 1.27792 + 0.928464i
\(514\) −10.8541 + 7.88597i −0.478754 + 0.347835i
\(515\) 3.52786 10.8576i 0.155456 0.478445i
\(516\) 77.6656 3.41904
\(517\) 0 0
\(518\) −1.05573 −0.0463860
\(519\) −17.2361 + 53.0472i −0.756579 + 2.32851i
\(520\) 4.47214 3.24920i 0.196116 0.142487i
\(521\) 11.6180 + 8.44100i 0.508995 + 0.369807i 0.812442 0.583042i \(-0.198138\pi\)
−0.303447 + 0.952848i \(0.598138\pi\)
\(522\) 2.43769 + 7.50245i 0.106695 + 0.328373i
\(523\) 13.5967 + 41.8465i 0.594544 + 1.82982i 0.556982 + 0.830525i \(0.311959\pi\)
0.0375627 + 0.999294i \(0.488041\pi\)
\(524\) 33.7082 + 24.4904i 1.47255 + 1.06987i
\(525\) 2.61803 1.90211i 0.114260 0.0830150i
\(526\) 0 0
\(527\) −8.94427 −0.389619
\(528\) 0 0
\(529\) 18.8885 0.821241
\(530\) 11.7082 36.0341i 0.508572 1.56522i
\(531\) −19.5623 + 14.2128i −0.848932 + 0.616785i
\(532\) 6.00000 + 4.35926i 0.260133 + 0.188998i
\(533\) 2.58359 + 7.95148i 0.111908 + 0.344417i
\(534\) −4.47214 13.7638i −0.193528 0.595619i
\(535\) −6.47214 4.70228i −0.279815 0.203297i
\(536\) 10.0000 7.26543i 0.431934 0.313819i
\(537\) 8.94427 27.5276i 0.385974 1.18791i
\(538\) 30.0000 1.29339
\(539\) 0 0
\(540\) −86.8328 −3.73669
\(541\) −10.1459 + 31.2259i −0.436206 + 1.34250i 0.455639 + 0.890165i \(0.349411\pi\)
−0.891845 + 0.452340i \(0.850589\pi\)
\(542\) −2.76393 + 2.00811i −0.118721 + 0.0862559i
\(543\) −3.70820 2.69417i −0.159134 0.115618i
\(544\) 2.56231 + 7.88597i 0.109858 + 0.338108i
\(545\) −2.76393 8.50651i −0.118394 0.364379i
\(546\) −7.23607 5.25731i −0.309675 0.224992i
\(547\) −22.6525 + 16.4580i −0.968550 + 0.703693i −0.955121 0.296217i \(-0.904275\pi\)
−0.0134293 + 0.999910i \(0.504275\pi\)
\(548\) 6.97871 21.4783i 0.298116 0.917506i
\(549\) −20.6525 −0.881426
\(550\) 0 0
\(551\) 1.16718 0.0497237
\(552\) 14.4721 44.5407i 0.615975 1.89578i
\(553\) −7.23607 + 5.25731i −0.307709 + 0.223564i
\(554\) 28.7426 + 20.8828i 1.22116 + 0.887223i
\(555\) −0.944272 2.90617i −0.0400821 0.123360i
\(556\) −9.70820 29.8788i −0.411720 1.26714i
\(557\) 17.0344 + 12.3762i 0.721772 + 0.524398i 0.886950 0.461865i \(-0.152820\pi\)
−0.165178 + 0.986264i \(0.552820\pi\)
\(558\) −97.8115 + 71.0642i −4.14069 + 3.00839i
\(559\) −3.05573 + 9.40456i −0.129244 + 0.397771i
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) 27.8885 1.17641
\(563\) 12.1803 37.4872i 0.513340 1.57990i −0.272942 0.962031i \(-0.587997\pi\)
0.786282 0.617868i \(-0.212003\pi\)
\(564\) −56.8328 + 41.2915i −2.39309 + 1.73868i
\(565\) 3.23607 + 2.35114i 0.136142 + 0.0989132i
\(566\) 4.06888 + 12.5227i 0.171028 + 0.526370i
\(567\) 7.54508 + 23.2214i 0.316864 + 0.975206i
\(568\) −2.76393 2.00811i −0.115972 0.0842586i
\(569\) −13.3262 + 9.68208i −0.558665 + 0.405894i −0.830970 0.556317i \(-0.812214\pi\)
0.272305 + 0.962211i \(0.412214\pi\)
\(570\) −11.0557 + 34.0260i −0.463073 + 1.42519i
\(571\) −32.9443 −1.37867 −0.689337 0.724440i \(-0.742098\pi\)
−0.689337 + 0.724440i \(0.742098\pi\)
\(572\) 0 0
\(573\) −67.7771 −2.83143
\(574\) 4.67376 14.3844i 0.195079 0.600392i
\(575\) −5.23607 + 3.80423i −0.218359 + 0.158647i
\(576\) 78.5861 + 57.0961i 3.27442 + 2.37901i
\(577\) −8.79837 27.0786i −0.366281 1.12730i −0.949175 0.314749i \(-0.898080\pi\)
0.582894 0.812548i \(-0.301920\pi\)
\(578\) 10.6910 + 32.9035i 0.444686 + 1.36860i
\(579\) 62.5410 + 45.4387i 2.59912 + 1.88837i
\(580\) −2.29180 + 1.66509i −0.0951617 + 0.0691390i
\(581\) 4.76393 14.6619i 0.197641 0.608277i
\(582\) 68.1378 2.82440
\(583\) 0 0
\(584\) 11.7082 0.484489
\(585\) 5.70820 17.5680i 0.236005 0.726349i
\(586\) 27.3607 19.8787i 1.13026 0.821181i
\(587\) 10.6180 + 7.71445i 0.438253 + 0.318410i 0.784940 0.619571i \(-0.212693\pi\)
−0.346687 + 0.937981i \(0.612693\pi\)
\(588\) 3.00000 + 9.23305i 0.123718 + 0.380765i
\(589\) 5.52786 + 17.0130i 0.227772 + 0.701009i
\(590\) −11.7082 8.50651i −0.482019 0.350207i
\(591\) 5.23607 3.80423i 0.215383 0.156485i
\(592\) −0.145898 + 0.449028i −0.00599637 + 0.0184549i
\(593\) −32.2918 −1.32607 −0.663033 0.748591i \(-0.730731\pi\)
−0.663033 + 0.748591i \(0.730731\pi\)
\(594\) 0 0
\(595\) −2.47214 −0.101348
\(596\) 12.9787 39.9444i 0.531629 1.63619i
\(597\) −52.8328 + 38.3853i −2.16230 + 1.57101i
\(598\) 14.4721 + 10.5146i 0.591810 + 0.429975i
\(599\) 1.05573 + 3.24920i 0.0431359 + 0.132759i 0.970305 0.241884i \(-0.0777654\pi\)
−0.927169 + 0.374643i \(0.877765\pi\)
\(600\) 2.23607 + 6.88191i 0.0912871 + 0.280953i
\(601\) −2.52786 1.83660i −0.103114 0.0749165i 0.535034 0.844831i \(-0.320299\pi\)
−0.638147 + 0.769914i \(0.720299\pi\)
\(602\) 14.4721 10.5146i 0.589840 0.428544i
\(603\) 12.7639 39.2833i 0.519787 1.59974i
\(604\) −26.8328 −1.09181
\(605\) 0 0
\(606\) 66.8328 2.71490
\(607\) −1.52786 + 4.70228i −0.0620141 + 0.190860i −0.977264 0.212028i \(-0.931993\pi\)
0.915250 + 0.402887i \(0.131993\pi\)
\(608\) 13.4164 9.74759i 0.544107 0.395317i
\(609\) 1.23607 + 0.898056i 0.0500880 + 0.0363911i
\(610\) −3.81966 11.7557i −0.154654 0.475975i
\(611\) −2.76393 8.50651i −0.111817 0.344136i
\(612\) −22.4164 16.2865i −0.906130 0.658342i
\(613\) 38.2705 27.8052i 1.54573 1.12304i 0.599121 0.800658i \(-0.295517\pi\)
0.946610 0.322381i \(-0.104483\pi\)
\(614\) −6.18034 + 19.0211i −0.249418 + 0.767630i
\(615\) 43.7771 1.76526
\(616\) 0 0
\(617\) 33.4164 1.34529 0.672647 0.739964i \(-0.265157\pi\)
0.672647 + 0.739964i \(0.265157\pi\)
\(618\) 12.7639 39.2833i 0.513441 1.58021i
\(619\) 23.5623 17.1190i 0.947049 0.688071i −0.00305805 0.999995i \(-0.500973\pi\)
0.950107 + 0.311924i \(0.100973\pi\)
\(620\) −35.1246 25.5195i −1.41064 1.02489i
\(621\) −28.9443 89.0813i −1.16149 3.57471i
\(622\) 15.0000 + 46.1653i 0.601445 + 1.85106i
\(623\) −1.61803 1.17557i −0.0648252 0.0470982i
\(624\) −3.23607 + 2.35114i −0.129546 + 0.0941210i
\(625\) −5.87132 + 18.0701i −0.234853 + 0.722803i
\(626\) 6.58359 0.263133
\(627\) 0 0
\(628\) −20.8328 −0.831320
\(629\) 0.180340 0.555029i 0.00719062 0.0221305i
\(630\) −27.0344 + 19.6417i −1.07708 + 0.782543i
\(631\) 19.4164 + 14.1068i 0.772955 + 0.561585i 0.902856 0.429942i \(-0.141466\pi\)
−0.129901 + 0.991527i \(0.541466\pi\)
\(632\) −6.18034 19.0211i −0.245841 0.756620i
\(633\) 21.8885 + 67.3660i 0.869992 + 2.67756i
\(634\) 25.3262 + 18.4006i 1.00583 + 0.730781i
\(635\) 33.8885 24.6215i 1.34483 0.977073i
\(636\) 25.4164 78.2237i 1.00783 3.10177i
\(637\) −1.23607 −0.0489748
\(638\) 0 0
\(639\) −11.4164 −0.451626
\(640\) −9.67376 + 29.7728i −0.382389 + 1.17687i
\(641\) 19.7984 14.3844i 0.781989 0.568148i −0.123586 0.992334i \(-0.539440\pi\)
0.905575 + 0.424186i \(0.139440\pi\)
\(642\) −23.4164 17.0130i −0.924172 0.671450i
\(643\) −9.00000 27.6992i −0.354925 1.09235i −0.956053 0.293195i \(-0.905282\pi\)
0.601127 0.799153i \(-0.294718\pi\)
\(644\) −6.00000 18.4661i −0.236433 0.727666i
\(645\) 41.8885 + 30.4338i 1.64936 + 1.19833i
\(646\) −5.52786 + 4.01623i −0.217491 + 0.158016i
\(647\) −6.81966 + 20.9888i −0.268109 + 0.825153i 0.722852 + 0.691002i \(0.242831\pi\)
−0.990961 + 0.134151i \(0.957169\pi\)
\(648\) −54.5967 −2.14476
\(649\) 0 0
\(650\) −2.76393 −0.108410
\(651\) −7.23607 + 22.2703i −0.283604 + 0.872843i
\(652\) −56.8328 + 41.2915i −2.22574 + 1.61710i
\(653\) −34.7426 25.2420i −1.35958 0.987796i −0.998471 0.0552743i \(-0.982397\pi\)
−0.361114 0.932522i \(-0.617603\pi\)
\(654\) −10.0000 30.7768i −0.391031 1.20347i
\(655\) 8.58359 + 26.4176i 0.335389 + 1.03222i
\(656\) −5.47214 3.97574i −0.213651 0.155227i
\(657\) 31.6525 22.9969i 1.23488 0.897193i
\(658\) −5.00000 + 15.3884i −0.194920 + 0.599903i
\(659\) 17.8885 0.696839 0.348419 0.937339i \(-0.386719\pi\)
0.348419 + 0.937339i \(0.386719\pi\)
\(660\) 0 0
\(661\) 12.8328 0.499139 0.249569 0.968357i \(-0.419711\pi\)
0.249569 + 0.968357i \(0.419711\pi\)
\(662\) −15.1246 + 46.5488i −0.587835 + 1.80917i
\(663\) 4.00000 2.90617i 0.155347 0.112866i
\(664\) 27.8885 + 20.2622i 1.08229 + 0.786326i
\(665\) 1.52786 + 4.70228i 0.0592480 + 0.182347i
\(666\) −2.43769 7.50245i −0.0944587 0.290714i
\(667\) −2.47214 1.79611i −0.0957215 0.0695457i
\(668\) 31.4164 22.8254i 1.21554 0.883140i
\(669\) 12.1803 37.4872i 0.470919 1.44934i
\(670\) 24.7214 0.955069
\(671\) 0 0
\(672\) 21.7082 0.837412
\(673\) 1.67376 5.15131i 0.0645188 0.198568i −0.913601 0.406613i \(-0.866710\pi\)
0.978119 + 0.208044i \(0.0667098\pi\)
\(674\) −37.0344 + 26.9071i −1.42651 + 1.03642i
\(675\) 11.7082 + 8.50651i 0.450649 + 0.327416i
\(676\) −10.6353 32.7319i −0.409048 1.25892i
\(677\) 1.14590 + 3.52671i 0.0440404 + 0.135543i 0.970659 0.240460i \(-0.0772983\pi\)
−0.926619 + 0.376003i \(0.877298\pi\)
\(678\) 11.7082 + 8.50651i 0.449651 + 0.326690i
\(679\) 7.61803 5.53483i 0.292353 0.212407i
\(680\) 1.70820 5.25731i 0.0655066 0.201609i
\(681\) −96.7214 −3.70637
\(682\) 0 0
\(683\) 29.8885 1.14365 0.571827 0.820374i \(-0.306235\pi\)
0.571827 + 0.820374i \(0.306235\pi\)
\(684\) −17.1246 + 52.7041i −0.654776 + 2.01519i
\(685\) 12.1803 8.84953i 0.465387 0.338123i
\(686\) 1.80902 + 1.31433i 0.0690686 + 0.0501813i
\(687\) 4.47214 + 13.7638i 0.170623 + 0.525122i
\(688\) −2.47214 7.60845i −0.0942493 0.290070i
\(689\) 8.47214 + 6.15537i 0.322763 + 0.234501i
\(690\) 75.7771 55.0553i 2.88478 2.09592i
\(691\) −15.0000 + 46.1653i −0.570627 + 1.75621i 0.0799823 + 0.996796i \(0.474514\pi\)
−0.650609 + 0.759413i \(0.725486\pi\)
\(692\) −51.7082 −1.96565
\(693\) 0 0
\(694\) −6.83282 −0.259370
\(695\) 6.47214 19.9192i 0.245502 0.755578i
\(696\) −2.76393 + 2.00811i −0.104767 + 0.0761174i
\(697\) 6.76393 + 4.91428i 0.256202 + 0.186142i
\(698\) 1.90983 + 5.87785i 0.0722881 + 0.222480i
\(699\) −17.4164 53.6022i −0.658749 2.02742i
\(700\) 2.42705 + 1.76336i 0.0917339 + 0.0666486i
\(701\) 19.7984 14.3844i 0.747774 0.543290i −0.147362 0.989083i \(-0.547078\pi\)
0.895136 + 0.445793i \(0.147078\pi\)
\(702\) 12.3607 38.0423i 0.466524 1.43581i
\(703\) −1.16718 −0.0440212
\(704\) 0 0
\(705\) −46.8328 −1.76383
\(706\) 10.9787 33.7890i 0.413189 1.27167i
\(707\) 7.47214 5.42882i 0.281019 0.204172i
\(708\) −25.4164 18.4661i −0.955207 0.693999i
\(709\) 0.909830 + 2.80017i 0.0341694 + 0.105163i 0.966687 0.255963i \(-0.0823926\pi\)
−0.932517 + 0.361126i \(0.882393\pi\)
\(710\) −2.11146 6.49839i −0.0792415 0.243880i
\(711\) −54.0689 39.2833i −2.02774 1.47324i
\(712\) 3.61803 2.62866i 0.135592 0.0985130i
\(713\) 14.4721 44.5407i 0.541986 1.66806i
\(714\) −8.94427 −0.334731
\(715\) 0 0
\(716\) 26.8328 1.00279
\(717\) 25.8885 79.6767i 0.966825 2.97558i
\(718\) −12.7639 + 9.27354i −0.476346 + 0.346085i
\(719\) −27.0902 19.6822i −1.01029 0.734021i −0.0460224 0.998940i \(-0.514655\pi\)
−0.964270 + 0.264920i \(0.914655\pi\)
\(720\) 4.61803 + 14.2128i 0.172104 + 0.529682i
\(721\) −1.76393 5.42882i −0.0656923 0.202180i
\(722\) −23.3156 16.9398i −0.867717 0.630433i
\(723\) −71.0132 + 51.5941i −2.64101 + 1.91880i
\(724\) 1.31308 4.04125i 0.0488003 0.150192i
\(725\) 0.472136 0.0175347
\(726\) 0 0
\(727\) −51.0132 −1.89197 −0.945987 0.324206i \(-0.894903\pi\)
−0.945987 + 0.324206i \(0.894903\pi\)
\(728\) 0.854102 2.62866i 0.0316551 0.0974245i
\(729\) −33.9336 + 24.6542i −1.25680 + 0.913119i
\(730\) 18.9443 + 13.7638i 0.701159 + 0.509422i
\(731\) 3.05573 + 9.40456i 0.113020 + 0.347840i
\(732\) −8.29180 25.5195i −0.306474 0.943229i
\(733\) −10.7082 7.77997i −0.395517 0.287360i 0.372196 0.928154i \(-0.378605\pi\)
−0.767712 + 0.640795i \(0.778605\pi\)
\(734\) 30.9787 22.5074i 1.14345 0.830762i
\(735\) −2.00000 + 6.15537i −0.0737711 + 0.227044i
\(736\) −43.4164 −1.60035
\(737\) 0 0
\(738\) 113.013 4.16007
\(739\) 2.18034 6.71040i 0.0802051 0.246846i −0.902911 0.429827i \(-0.858575\pi\)
0.983116 + 0.182981i \(0.0585746\pi\)
\(740\) 2.29180 1.66509i 0.0842481 0.0612098i
\(741\) −8.00000 5.81234i −0.293887 0.213522i
\(742\) −5.85410 18.0171i −0.214911 0.661428i
\(743\) −10.4721 32.2299i −0.384185 1.18240i −0.937069 0.349143i \(-0.886473\pi\)
0.552884 0.833258i \(-0.313527\pi\)
\(744\) −42.3607 30.7768i −1.55302 1.12833i
\(745\) 22.6525 16.4580i 0.829923 0.602974i
\(746\) −4.14590 + 12.7598i −0.151792 + 0.467168i
\(747\) 115.193 4.21471
\(748\) 0 0
\(749\) −4.00000 −0.146157
\(750\) −26.8328 + 82.5829i −0.979796 + 3.01550i
\(751\) −31.1246 + 22.6134i −1.13575 + 0.825173i −0.986522 0.163629i \(-0.947680\pi\)
−0.149231 + 0.988802i \(0.547680\pi\)
\(752\) 5.85410 + 4.25325i 0.213477 + 0.155100i
\(753\) 17.7082 + 54.5002i 0.645323 + 1.98610i
\(754\) −0.403252 1.24108i −0.0146856 0.0451976i
\(755\) −14.4721 10.5146i −0.526695 0.382666i
\(756\) −35.1246 + 25.5195i −1.27747 + 0.928136i
\(757\) −6.14590 + 18.9151i −0.223376 + 0.687482i 0.775076 + 0.631868i \(0.217712\pi\)
−0.998452 + 0.0556139i \(0.982288\pi\)
\(758\) 56.5836 2.05521
\(759\) 0 0
\(760\) −11.0557 −0.401033
\(761\) 5.43769 16.7355i 0.197116 0.606661i −0.802829 0.596209i \(-0.796673\pi\)
0.999945 0.0104523i \(-0.00332712\pi\)
\(762\) 122.610 89.0813i 4.44169 3.22708i
\(763\) −3.61803 2.62866i −0.130982 0.0951637i
\(764\) −19.4164 59.7576i −0.702461 2.16195i
\(765\) −5.70820 17.5680i −0.206381 0.635174i
\(766\) 48.2148 + 35.0301i 1.74207 + 1.26569i
\(767\) 3.23607 2.35114i 0.116848 0.0848948i
\(768\) −9.00000 + 27.6992i −0.324760 + 0.999507i
\(769\) 31.7082 1.14343 0.571714 0.820453i \(-0.306279\pi\)
0.571714 + 0.820453i \(0.306279\pi\)
\(770\) 0 0
\(771\) −19.4164 −0.699265
\(772\) −22.1459 + 68.1581i −0.797048 + 2.45306i
\(773\) −5.14590 + 3.73871i −0.185085 + 0.134472i −0.676470 0.736471i \(-0.736491\pi\)
0.491385 + 0.870943i \(0.336491\pi\)
\(774\) 108.138 + 78.5667i 3.88693 + 2.82402i
\(775\) 2.23607 + 6.88191i 0.0803219 + 0.247205i
\(776\) 6.50658 + 20.0252i 0.233573 + 0.718862i
\(777\) −1.23607 0.898056i −0.0443437 0.0322176i
\(778\) −35.9787 + 26.1401i −1.28990 + 0.937167i
\(779\) 5.16718 15.9030i 0.185134 0.569783i
\(780\) 24.0000 0.859338
\(781\) 0 0
\(782\) 17.8885 0.639693
\(783\) −2.11146 + 6.49839i −0.0754573 + 0.232234i
\(784\) 0.809017 0.587785i 0.0288935 0.0209923i
\(785\) −11.2361 8.16348i −0.401032 0.291367i
\(786\) 31.0557 + 95.5797i 1.10772 + 3.40922i
\(787\) −5.12461 15.7719i −0.182673 0.562209i 0.817228 0.576315i \(-0.195510\pi\)
−0.999901 + 0.0141060i \(0.995510\pi\)
\(788\) 4.85410 + 3.52671i 0.172920 + 0.125634i
\(789\) 0 0
\(790\) 12.3607 38.0423i 0.439773 1.35348i
\(791\) 2.00000 0.0711118
\(792\) 0 0
\(793\) 3.41641 0.121320
\(794\) 0.0770143 0.237026i 0.00273314 0.00841173i
\(795\) 44.3607 32.2299i 1.57331 1.14308i
\(796\) −48.9787 35.5851i −1.73600 1.26128i
\(797\) 0.909830 + 2.80017i 0.0322278 + 0.0991871i 0.965877 0.259003i \(-0.0833940\pi\)
−0.933649 + 0.358190i \(0.883394\pi\)
\(798\) 5.52786 + 17.0130i 0.195684 + 0.602254i
\(799\) −7.23607 5.25731i −0.255994 0.185990i
\(800\) 5.42705 3.94298i 0.191875 0.139406i
\(801\) 4.61803 14.2128i 0.163170 0.502186i
\(802\) −11.3050 −0.399192
\(803\) 0 0
\(804\) 53.6656 1.89264
\(805\) 4.00000 12.3107i 0.140981 0.433896i
\(806\) 16.1803 11.7557i 0.569928 0.414077i
\(807\) 35.1246 + 25.5195i 1.23644 + 0.898330i
\(808\) 6.38197 + 19.6417i 0.224517 + 0.690992i
\(809\) 12.0344 + 37.0382i 0.423108 + 1.30219i 0.904794 + 0.425850i \(0.140025\pi\)
−0.481685 + 0.876344i \(0.659975\pi\)
\(810\) −88.3394 64.1823i −3.10393 2.25514i
\(811\) −15.2361 + 11.0697i −0.535011 + 0.388708i −0.822229 0.569157i \(-0.807270\pi\)
0.287218 + 0.957865i \(0.407270\pi\)
\(812\) −0.437694 + 1.34708i −0.0153601 + 0.0472734i
\(813\) −4.94427 −0.173403
\(814\) 0 0
\(815\) −46.8328 −1.64048
\(816\) −1.23607 + 3.80423i −0.0432710 + 0.133175i
\(817\) 16.0000 11.6247i 0.559769 0.406696i
\(818\) −56.3050 40.9079i −1.96866 1.43031i
\(819\) −2.85410 8.78402i −0.0997304 0.306939i
\(820\) 12.5410 + 38.5973i 0.437951 + 1.34788i
\(821\) 7.14590 + 5.19180i 0.249394 + 0.181195i 0.705458 0.708752i \(-0.250741\pi\)
−0.456064 + 0.889947i \(0.650741\pi\)
\(822\) 44.0689 32.0179i 1.53708 1.11675i
\(823\) −15.4164 + 47.4468i −0.537382 + 1.65389i 0.201063 + 0.979578i \(0.435561\pi\)
−0.738445 + 0.674314i \(0.764439\pi\)
\(824\) 12.7639 0.444653
\(825\) 0 0
\(826\) −7.23607 −0.251775
\(827\) 1.52786 4.70228i 0.0531290 0.163514i −0.920971 0.389630i \(-0.872603\pi\)
0.974100 + 0.226116i \(0.0726028\pi\)
\(828\) 117.374 85.2771i 4.07902 2.96358i
\(829\) 13.6180 + 9.89408i 0.472974 + 0.343636i 0.798599 0.601863i \(-0.205575\pi\)
−0.325625 + 0.945499i \(0.605575\pi\)
\(830\) 21.3050 + 65.5699i 0.739506 + 2.27596i
\(831\) 15.8885 + 48.8999i 0.551167 + 1.69632i
\(832\) −13.0000 9.44505i −0.450694 0.327448i
\(833\) −1.00000 + 0.726543i −0.0346479 + 0.0251732i
\(834\) 23.4164 72.0683i 0.810844 2.49552i
\(835\) 25.8885 0.895910
\(836\) 0 0
\(837\) −104.721 −3.61970
\(838\) 4.59675 14.1473i 0.158792 0.488712i
\(839\) 11.3820 8.26948i 0.392949 0.285494i −0.373714 0.927544i \(-0.621916\pi\)
0.766663 + 0.642050i \(0.221916\pi\)
\(840\) −11.7082 8.50651i −0.403971 0.293502i
\(841\) −8.89261 27.3686i −0.306642 0.943746i
\(842\) 15.4508 + 47.5528i 0.532471 + 1.63878i
\(843\) 32.6525 + 23.7234i 1.12461 + 0.817078i
\(844\) −53.1246 + 38.5973i −1.82862 + 1.32857i
\(845\) 7.09017 21.8213i 0.243909 0.750676i
\(846\) −120.902 −4.15669
\(847\) 0 0
\(848\) −8.47214 −0.290934
\(849\) −5.88854 + 18.1231i −0.202094 + 0.621982i
\(850\) −2.23607 + 1.62460i −0.0766965 + 0.0557233i
\(851\) 2.47214 + 1.79611i 0.0847437 + 0.0615699i
\(852\) −4.58359 14.1068i −0.157031 0.483293i
\(853\) 0.201626 + 0.620541i 0.00690355 + 0.0212469i 0.954449 0.298374i \(-0.0964443\pi\)
−0.947545 + 0.319621i \(0.896444\pi\)
\(854\) −5.00000 3.63271i −0.171096 0.124309i
\(855\) −29.8885 + 21.7153i −1.02217 + 0.742648i
\(856\) 2.76393 8.50651i 0.0944693 0.290746i
\(857\) 10.7639 0.367689 0.183844 0.982955i \(-0.441146\pi\)
0.183844 + 0.982955i \(0.441146\pi\)
\(858\) 0 0
\(859\) 40.5410 1.38324 0.691621 0.722261i \(-0.256897\pi\)
0.691621 + 0.722261i \(0.256897\pi\)
\(860\) −14.8328 + 45.6507i −0.505795 + 1.55668i
\(861\) 17.7082 12.8658i 0.603494 0.438464i
\(862\) 21.7082 + 15.7719i 0.739384 + 0.537194i
\(863\) −6.47214 19.9192i −0.220314 0.678057i −0.998734 0.0503125i \(-0.983978\pi\)
0.778419 0.627744i \(-0.216022\pi\)
\(864\) 30.0000 + 92.3305i 1.02062 + 3.14115i
\(865\) −27.8885 20.2622i −0.948239 0.688936i
\(866\) 0.854102 0.620541i 0.0290236 0.0210869i
\(867\) −15.4721 + 47.6183i −0.525461 + 1.61720i
\(868\) −21.7082 −0.736824
\(869\) 0 0
\(870\) −6.83282 −0.231654
\(871\) −2.11146 + 6.49839i −0.0715440 + 0.220190i
\(872\) 8.09017 5.87785i 0.273968 0.199049i
\(873\) 56.9230 + 41.3570i 1.92655 + 1.39972i
\(874\) −11.0557 34.0260i −0.373966 1.15095i
\(875\) 3.70820 + 11.4127i 0.125360 + 0.385819i
\(876\) 41.1246 + 29.8788i 1.38947 + 1.00951i
\(877\) −33.5066 + 24.3440i −1.13144 + 0.822037i −0.985903 0.167316i \(-0.946490\pi\)
−0.145533 + 0.989353i \(0.546490\pi\)
\(878\) −1.05573 + 3.24920i −0.0356291 + 0.109655i
\(879\) 48.9443 1.65085
\(880\) 0 0
\(881\) 29.4164 0.991064 0.495532 0.868590i \(-0.334973\pi\)
0.495532 + 0.868590i \(0.334973\pi\)
\(882\) −5.16312 + 15.8904i −0.173851 + 0.535059i
\(883\) −7.23607 + 5.25731i −0.243513 + 0.176923i −0.702847 0.711341i \(-0.748088\pi\)
0.459334 + 0.888264i \(0.348088\pi\)
\(884\) 3.70820 + 2.69417i 0.124720 + 0.0906147i
\(885\) −6.47214 19.9192i −0.217558 0.669576i
\(886\) 4.87539 + 15.0049i 0.163792 + 0.504100i
\(887\) −32.6525 23.7234i −1.09636 0.796554i −0.115900 0.993261i \(-0.536975\pi\)
−0.980462 + 0.196707i \(0.936975\pi\)
\(888\) 2.76393 2.00811i 0.0927515 0.0673879i
\(889\) 6.47214 19.9192i 0.217068 0.668068i
\(890\) 8.94427 0.299813
\(891\) 0 0
\(892\) 36.5410 1.22348
\(893\) −5.52786 + 17.0130i −0.184983 + 0.569319i
\(894\) 81.9574 59.5456i 2.74107 1.99150i
\(895\) 14.4721 + 10.5146i 0.483750 + 0.351465i
\(896\) 4.83688 + 14.8864i 0.161589 + 0.497319i
\(897\) 8.00000 + 24.6215i 0.267112 + 0.822087i
\(898\) −35.3262 25.6660i −1.17885 0.856486i
\(899\) −2.76393 + 2.00811i −0.0921823 + 0.0669744i
\(900\) −6.92705 + 21.3193i −0.230902 + 0.710642i
\(901\) 10.4721 0.348877
\(902\) 0 0
\(903\) 25.8885 0.861517
\(904\) −1.38197 + 4.25325i −0.0459635 + 0.141461i
\(905\) 2.29180 1.66509i 0.0761819 0.0553494i
\(906\) −52.3607 38.0423i −1.73957 1.26387i
\(907\) 4.18034 + 12.8658i 0.138806 + 0.427201i 0.996163 0.0875221i \(-0.0278948\pi\)
−0.857357 + 0.514723i \(0.827895\pi\)
\(908\) −27.7082 85.2771i −0.919529 2.83002i
\(909\) 55.8328 + 40.5649i 1.85186 + 1.34545i
\(910\) 4.47214 3.24920i 0.148250 0.107710i
\(911\) 10.3607 31.8869i 0.343265 1.05646i −0.619242 0.785200i \(-0.712560\pi\)
0.962506 0.271259i \(-0.0874401\pi\)
\(912\) 8.00000 0.264906
\(913\) 0 0
\(914\) −55.5279 −1.83670
\(915\) 5.52786 17.0130i 0.182746 0.562433i
\(916\) −10.8541 + 7.88597i −0.358630 + 0.260560i
\(917\) 11.2361 + 8.16348i 0.371048 + 0.269582i
\(918\) −12.3607 38.0423i −0.407963 1.25558i
\(919\) 1.88854 + 5.81234i 0.0622973 + 0.191731i 0.977361 0.211577i \(-0.0678600\pi\)
−0.915064 + 0.403309i \(0.867860\pi\)
\(920\) 23.4164 + 17.0130i 0.772016 + 0.560903i
\(921\) −23.4164 + 17.0130i −0.771597 + 0.560598i
\(922\) −7.03444 + 21.6498i −0.231667 + 0.712998i
\(923\) 1.88854 0.0621622
\(924\) 0 0
\(925\) −0.472136 −0.0155237
\(926\) 10.0000 30.7768i 0.328620 1.01139i
\(927\) 34.5066 25.0705i 1.13334 0.823423i
\(928\) 2.56231 + 1.86162i 0.0841118 + 0.0611108i
\(929\) 8.72949 + 26.8666i 0.286405 + 0.881465i 0.985974 + 0.166899i \(0.0533755\pi\)
−0.699569 + 0.714565i \(0.746624\pi\)
\(930\) −32.3607 99.5959i −1.06115 3.26588i
\(931\) 2.00000 + 1.45309i 0.0655474 + 0.0476229i
\(932\) 42.2705 30.7113i 1.38462 1.00598i
\(933\) −21.7082 + 66.8110i −0.710695 + 2.18729i
\(934\) 76.1803 2.49270
\(935\) 0 0
\(936\) 20.6525 0.675047
\(937\) 6.38197 19.6417i 0.208490 0.641665i −0.791062 0.611736i \(-0.790472\pi\)
0.999552 0.0299298i \(-0.00952837\pi\)
\(938\) 10.0000 7.26543i 0.326512 0.237225i
\(939\) 7.70820 + 5.60034i 0.251548 + 0.182760i
\(940\) −13.4164 41.2915i −0.437595 1.34678i
\(941\) −12.8541 39.5609i −0.419032 1.28965i −0.908595 0.417679i \(-0.862844\pi\)
0.489563 0.871968i \(-0.337156\pi\)
\(942\) −40.6525 29.5358i −1.32453 0.962327i
\(943\) −35.4164 + 25.7315i −1.15332 + 0.837934i
\(944\) −1.00000 + 3.07768i −0.0325472 + 0.100170i
\(945\) −28.9443 −0.941557
\(946\) 0 0
\(947\) −58.8328 −1.91181 −0.955905 0.293677i \(-0.905121\pi\)
−0.955905 + 0.293677i \(0.905121\pi\)
\(948\) 26.8328 82.5829i 0.871489 2.68217i
\(949\) −5.23607 + 3.80423i −0.169970 + 0.123490i
\(950\) 4.47214 + 3.24920i 0.145095 + 0.105418i
\(951\) 14.0000 + 43.0876i 0.453981 + 1.39721i
\(952\) −0.854102 2.62866i −0.0276816 0.0851952i
\(953\) −4.09017 2.97168i −0.132494 0.0962622i 0.519565 0.854431i \(-0.326094\pi\)
−0.652058 + 0.758169i \(0.726094\pi\)
\(954\) 114.520 83.2035i 3.70771 2.69381i
\(955\) 12.9443 39.8384i 0.418867 1.28914i
\(956\) 77.6656 2.51189
\(957\) 0 0
\(958\) −50.2492 −1.62348
\(959\) 2.32624 7.15942i 0.0751181 0.231190i
\(960\) −68.0689 + 49.4549i −2.19691 + 1.59615i
\(961\) −17.2812 12.5555i −0.557457 0.405016i
\(962\) 0.403252 + 1.24108i 0.0130014 + 0.0400141i
\(963\) −9.23607 28.4257i −0.297628 0.916005i
\(964\) −65.8328 47.8303i −2.12033 1.54051i
\(965\) −38.6525 + 28.0827i −1.24427 + 0.904013i
\(966\) 14.4721 44.5407i 0.465633 1.43307i
\(967\) 21.8885 0.703888 0.351944 0.936021i \(-0.385521\pi\)
0.351944 + 0.936021i \(0.385521\pi\)
\(968\) 0 0
\(969\) −9.88854 −0.317666
\(970\) −13.0132 + 40.0504i −0.417827 + 1.28594i
\(971\) 23.5623 17.1190i 0.756150 0.549375i −0.141577 0.989927i \(-0.545217\pi\)
0.897727 + 0.440552i \(0.145217\pi\)
\(972\) −86.3951 62.7697i −2.77112 2.01334i
\(973\) −3.23607 9.95959i −0.103744 0.319290i
\(974\) −5.77709 17.7800i −0.185110 0.569709i
\(975\) −3.23607 2.35114i −0.103637 0.0752968i
\(976\) −2.23607 + 1.62460i −0.0715748 + 0.0520021i
\(977\) 1.56231 4.80828i 0.0499826 0.153831i −0.922950 0.384920i \(-0.874229\pi\)
0.972933 + 0.231089i \(0.0742290\pi\)
\(978\) −169.443 −5.41818
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) 10.3262 31.7809i 0.329691 1.01469i
\(982\) 0 0
\(983\) −35.7426 25.9686i −1.14001 0.828268i −0.152892 0.988243i \(-0.548859\pi\)
−0.987121 + 0.159975i \(0.948859\pi\)
\(984\) 15.1246 + 46.5488i 0.482155 + 1.48392i
\(985\) 1.23607 + 3.80423i 0.0393844 + 0.121213i
\(986\) −1.05573 0.767031i −0.0336212 0.0244273i
\(987\) −18.9443 + 13.7638i −0.603003 + 0.438107i
\(988\) 2.83282 8.71851i 0.0901239 0.277373i
\(989\) −51.7771 −1.64642
\(990\) 0 0
\(991\) −26.2492 −0.833834 −0.416917 0.908945i \(-0.636889\pi\)
−0.416917 + 0.908945i \(0.636889\pi\)
\(992\) −15.0000 + 46.1653i −0.476250 + 1.46575i
\(993\) −57.3050 + 41.6345i −1.81852 + 1.32123i
\(994\) −2.76393 2.00811i −0.0876666 0.0636935i
\(995\) −12.4721 38.3853i −0.395393 1.21690i
\(996\) 46.2492 + 142.340i 1.46546 + 4.51023i
\(997\) −26.4164 19.1926i −0.836616 0.607837i 0.0848073 0.996397i \(-0.472973\pi\)
−0.921423 + 0.388560i \(0.872973\pi\)
\(998\) 18.9443 13.7638i 0.599670 0.435686i
\(999\) 2.11146 6.49839i 0.0668035 0.205600i
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 847.2.f.a.372.1 4
11.2 odd 10 847.2.f.b.729.1 4
11.3 even 5 847.2.f.n.323.1 4
11.4 even 5 77.2.a.d.1.1 2
11.5 even 5 inner 847.2.f.a.148.1 4
11.6 odd 10 847.2.f.m.148.1 4
11.7 odd 10 847.2.a.f.1.2 2
11.8 odd 10 847.2.f.b.323.1 4
11.9 even 5 847.2.f.n.729.1 4
11.10 odd 2 847.2.f.m.372.1 4
33.26 odd 10 693.2.a.h.1.2 2
33.29 even 10 7623.2.a.bl.1.1 2
44.15 odd 10 1232.2.a.m.1.1 2
55.4 even 10 1925.2.a.r.1.2 2
55.37 odd 20 1925.2.b.h.1849.1 4
55.48 odd 20 1925.2.b.h.1849.4 4
77.4 even 15 539.2.e.i.177.2 4
77.26 odd 30 539.2.e.j.67.2 4
77.37 even 15 539.2.e.i.67.2 4
77.48 odd 10 539.2.a.f.1.1 2
77.59 odd 30 539.2.e.j.177.2 4
77.62 even 10 5929.2.a.m.1.2 2
88.37 even 10 4928.2.a.bm.1.1 2
88.59 odd 10 4928.2.a.bv.1.2 2
231.125 even 10 4851.2.a.y.1.2 2
308.279 even 10 8624.2.a.ce.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.d.1.1 2 11.4 even 5
539.2.a.f.1.1 2 77.48 odd 10
539.2.e.i.67.2 4 77.37 even 15
539.2.e.i.177.2 4 77.4 even 15
539.2.e.j.67.2 4 77.26 odd 30
539.2.e.j.177.2 4 77.59 odd 30
693.2.a.h.1.2 2 33.26 odd 10
847.2.a.f.1.2 2 11.7 odd 10
847.2.f.a.148.1 4 11.5 even 5 inner
847.2.f.a.372.1 4 1.1 even 1 trivial
847.2.f.b.323.1 4 11.8 odd 10
847.2.f.b.729.1 4 11.2 odd 10
847.2.f.m.148.1 4 11.6 odd 10
847.2.f.m.372.1 4 11.10 odd 2
847.2.f.n.323.1 4 11.3 even 5
847.2.f.n.729.1 4 11.9 even 5
1232.2.a.m.1.1 2 44.15 odd 10
1925.2.a.r.1.2 2 55.4 even 10
1925.2.b.h.1849.1 4 55.37 odd 20
1925.2.b.h.1849.4 4 55.48 odd 20
4851.2.a.y.1.2 2 231.125 even 10
4928.2.a.bm.1.1 2 88.37 even 10
4928.2.a.bv.1.2 2 88.59 odd 10
5929.2.a.m.1.2 2 77.62 even 10
7623.2.a.bl.1.1 2 33.29 even 10
8624.2.a.ce.1.2 2 308.279 even 10