Properties

Label 91.2.r.a.25.4
Level $91$
Weight $2$
Character 91.25
Analytic conductor $0.727$
Analytic rank $0$
Dimension $16$
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] = [91,2,Mod(25,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.r (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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.4
Root \(0.287846 + 0.166188i\) of defining polynomial
Character \(\chi\) \(=\) 91.25
Dual form 91.2.r.a.51.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +O(q^{10})\) \(q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +(0.240245 - 0.416116i) q^{10} +(5.15732 + 2.97758i) q^{11} +(-1.37920 - 2.38885i) q^{12} +(1.88953 + 3.07078i) q^{13} +(0.879201 + 0.0178849i) q^{14} -2.11037i q^{15} +(-1.67468 - 2.90063i) q^{16} +(2.16436 - 3.74877i) q^{17} +(-0.250102 - 0.144396i) q^{18} +(-1.69527 + 0.978767i) q^{19} -2.73154i q^{20} +(3.38349 - 1.86276i) q^{21} -1.97935 q^{22} +(-0.270081 - 0.467795i) q^{23} +(1.63441 + 0.943626i) q^{24} +(-1.45509 + 2.52029i) q^{25} +(-1.05422 - 0.569894i) q^{26} -5.64793 q^{27} +(4.37939 - 2.41104i) q^{28} +7.15857 q^{29} +(0.350718 + 0.607461i) q^{30} +(-5.28968 - 3.05400i) q^{31} +(3.20327 + 1.84941i) q^{32} +(-7.52885 + 4.34678i) q^{33} +1.43876i q^{34} +(3.82396 + 0.0777879i) q^{35} -1.64176 q^{36} +(6.95316 - 4.01441i) q^{37} +(0.325318 - 0.563467i) q^{38} +(-5.26145 + 0.147426i) q^{39} +(0.934437 + 1.61849i) q^{40} +7.55362i q^{41} +(-0.664356 + 1.09848i) q^{42} -4.24839 q^{43} +(-9.74489 + 5.62622i) q^{44} +(-1.08778 - 0.628032i) q^{45} +(0.155483 + 0.0897684i) q^{46} +(5.42204 - 3.13042i) q^{47} +4.88953 q^{48} +(3.25057 + 6.19950i) q^{49} -0.967272i q^{50} +(3.15961 + 5.47260i) q^{51} +(-6.81011 + 0.190820i) q^{52} +(1.38953 - 2.40673i) q^{53} +(1.62573 - 0.938616i) q^{54} -8.60891 q^{55} +(-1.77008 + 2.92674i) q^{56} -2.85768i q^{57} +(-2.06056 + 1.18967i) q^{58} +(0.737119 + 0.425576i) q^{59} +(3.45337 + 1.99380i) q^{60} +(-3.38953 - 5.87083i) q^{61} +2.03015 q^{62} +(0.0467536 - 2.29835i) q^{63} +5.46933 q^{64} +(-4.58518 - 2.47868i) q^{65} +(1.44476 - 2.50240i) q^{66} +(-0.854859 - 0.493553i) q^{67} +(4.08961 + 7.08341i) q^{68} +0.788550 q^{69} +(-1.11364 + 0.613105i) q^{70} -3.76223i q^{71} +(0.972777 - 0.561633i) q^{72} +(7.91131 + 4.56760i) q^{73} +(-1.33429 + 2.31106i) q^{74} +(-2.12419 - 3.67921i) q^{75} -3.69881i q^{76} +(-7.59879 - 13.8024i) q^{77} +(1.48999 - 0.916825i) q^{78} +(0.0655625 + 0.113558i) q^{79} +(4.19322 + 2.42096i) q^{80} +(2.81922 - 4.88303i) q^{81} +(-1.25532 - 2.17428i) q^{82} -2.66812i q^{83} +(-0.148428 + 7.29653i) q^{84} +6.25768i q^{85} +(1.22288 - 0.706030i) q^{86} +(-5.22517 + 9.05026i) q^{87} +(3.84936 - 6.66729i) q^{88} +(8.41550 - 4.85869i) q^{89} +0.417485 q^{90} +(-0.0731980 - 9.53911i) q^{91} +1.02065 q^{92} +(7.72207 - 4.45834i) q^{93} +(-1.04047 + 1.80215i) q^{94} +(1.41493 - 2.45072i) q^{95} +(-4.67625 + 2.69983i) q^{96} -6.58319i q^{97} +(-1.96594 - 1.24429i) q^{98} +5.17429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{3} + 6 q^{4} - 12 q^{9} - 6 q^{10} + 18 q^{12} - 12 q^{13} - 26 q^{14} + 2 q^{16} + 8 q^{17} - 36 q^{22} - 12 q^{23} - 6 q^{26} + 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} + 34 q^{38} + 18 q^{39} - 4 q^{40} + 16 q^{42} + 16 q^{43} + 36 q^{48} + 40 q^{49} + 16 q^{51} - 42 q^{52} - 20 q^{53} + 24 q^{55} - 36 q^{56} - 12 q^{61} + 44 q^{62} + 88 q^{64} - 30 q^{65} + 2 q^{66} - 2 q^{68} - 56 q^{69} + 42 q^{74} + 8 q^{75} - 76 q^{77} + 20 q^{78} + 20 q^{79} - 24 q^{81} - 16 q^{82} - 68 q^{87} + 4 q^{88} - 216 q^{90} + 56 q^{91} + 12 q^{92} - 26 q^{94} - 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.287846 + 0.166188i −0.203538 + 0.117512i −0.598304 0.801269i \(-0.704159\pi\)
0.394767 + 0.918781i \(0.370825\pi\)
\(3\) −0.729919 + 1.26426i −0.421419 + 0.729919i −0.996079 0.0884737i \(-0.971801\pi\)
0.574660 + 0.818392i \(0.305134\pi\)
\(4\) −0.944763 + 1.63638i −0.472382 + 0.818189i
\(5\) −1.25195 + 0.722811i −0.559887 + 0.323251i −0.753100 0.657906i \(-0.771442\pi\)
0.193213 + 0.981157i \(0.438109\pi\)
\(6\) 0.485214i 0.198088i
\(7\) −2.26391 1.36920i −0.855677 0.517510i
\(8\) 1.29278i 0.457068i
\(9\) 0.434437 + 0.752468i 0.144812 + 0.250823i
\(10\) 0.240245 0.416116i 0.0759720 0.131587i
\(11\) 5.15732 + 2.97758i 1.55499 + 0.897774i 0.997723 + 0.0674405i \(0.0214833\pi\)
0.557267 + 0.830333i \(0.311850\pi\)
\(12\) −1.37920 2.38885i −0.398141 0.689600i
\(13\) 1.88953 + 3.07078i 0.524060 + 0.851681i
\(14\) 0.879201 + 0.0178849i 0.234976 + 0.00477994i
\(15\) 2.11037i 0.544896i
\(16\) −1.67468 2.90063i −0.418670 0.725159i
\(17\) 2.16436 3.74877i 0.524933 0.909211i −0.474645 0.880177i \(-0.657424\pi\)
0.999578 0.0290341i \(-0.00924314\pi\)
\(18\) −0.250102 0.144396i −0.0589496 0.0340345i
\(19\) −1.69527 + 0.978767i −0.388923 + 0.224545i −0.681693 0.731638i \(-0.738756\pi\)
0.292771 + 0.956183i \(0.405423\pi\)
\(20\) 2.73154i 0.610791i
\(21\) 3.38349 1.86276i 0.738339 0.406486i
\(22\) −1.97935 −0.421998
\(23\) −0.270081 0.467795i −0.0563158 0.0975419i 0.836493 0.547977i \(-0.184602\pi\)
−0.892809 + 0.450436i \(0.851269\pi\)
\(24\) 1.63441 + 0.943626i 0.333622 + 0.192617i
\(25\) −1.45509 + 2.52029i −0.291018 + 0.504058i
\(26\) −1.05422 0.569894i −0.206749 0.111765i
\(27\) −5.64793 −1.08694
\(28\) 4.37939 2.41104i 0.827627 0.455644i
\(29\) 7.15857 1.32931 0.664656 0.747149i \(-0.268578\pi\)
0.664656 + 0.747149i \(0.268578\pi\)
\(30\) 0.350718 + 0.607461i 0.0640320 + 0.110907i
\(31\) −5.28968 3.05400i −0.950055 0.548514i −0.0569568 0.998377i \(-0.518140\pi\)
−0.893098 + 0.449862i \(0.851473\pi\)
\(32\) 3.20327 + 1.84941i 0.566263 + 0.326932i
\(33\) −7.52885 + 4.34678i −1.31060 + 0.756678i
\(34\) 1.43876i 0.246745i
\(35\) 3.82396 + 0.0777879i 0.646368 + 0.0131486i
\(36\) −1.64176 −0.273627
\(37\) 6.95316 4.01441i 1.14309 0.659964i 0.195897 0.980624i \(-0.437238\pi\)
0.947194 + 0.320660i \(0.103905\pi\)
\(38\) 0.325318 0.563467i 0.0527736 0.0914065i
\(39\) −5.26145 + 0.147426i −0.842507 + 0.0236071i
\(40\) 0.934437 + 1.61849i 0.147748 + 0.255906i
\(41\) 7.55362i 1.17968i 0.807521 + 0.589839i \(0.200809\pi\)
−0.807521 + 0.589839i \(0.799191\pi\)
\(42\) −0.664356 + 1.09848i −0.102512 + 0.169499i
\(43\) −4.24839 −0.647873 −0.323936 0.946079i \(-0.605006\pi\)
−0.323936 + 0.946079i \(0.605006\pi\)
\(44\) −9.74489 + 5.62622i −1.46910 + 0.848184i
\(45\) −1.08778 0.628032i −0.162157 0.0936215i
\(46\) 0.155483 + 0.0897684i 0.0229248 + 0.0132356i
\(47\) 5.42204 3.13042i 0.790886 0.456618i −0.0493882 0.998780i \(-0.515727\pi\)
0.840274 + 0.542161i \(0.182394\pi\)
\(48\) 4.88953 0.705742
\(49\) 3.25057 + 6.19950i 0.464367 + 0.885643i
\(50\) 0.967272i 0.136793i
\(51\) 3.15961 + 5.47260i 0.442434 + 0.766317i
\(52\) −6.81011 + 0.190820i −0.944393 + 0.0264619i
\(53\) 1.38953 2.40673i 0.190866 0.330590i −0.754671 0.656103i \(-0.772204\pi\)
0.945538 + 0.325513i \(0.105537\pi\)
\(54\) 1.62573 0.938616i 0.221234 0.127729i
\(55\) −8.60891 −1.16082
\(56\) −1.77008 + 2.92674i −0.236537 + 0.391103i
\(57\) 2.85768i 0.378509i
\(58\) −2.06056 + 1.18967i −0.270565 + 0.156211i
\(59\) 0.737119 + 0.425576i 0.0959647 + 0.0554053i 0.547214 0.836993i \(-0.315688\pi\)
−0.451250 + 0.892398i \(0.649022\pi\)
\(60\) 3.45337 + 1.99380i 0.445828 + 0.257399i
\(61\) −3.38953 5.87083i −0.433984 0.751683i 0.563228 0.826302i \(-0.309559\pi\)
−0.997212 + 0.0746187i \(0.976226\pi\)
\(62\) 2.03015 0.257829
\(63\) 0.0467536 2.29835i 0.00589039 0.289565i
\(64\) 5.46933 0.683667
\(65\) −4.58518 2.47868i −0.568721 0.307442i
\(66\) 1.44476 2.50240i 0.177838 0.308025i
\(67\) −0.854859 0.493553i −0.104438 0.0602971i 0.446871 0.894598i \(-0.352538\pi\)
−0.551309 + 0.834301i \(0.685871\pi\)
\(68\) 4.08961 + 7.08341i 0.495938 + 0.858990i
\(69\) 0.788550 0.0949302
\(70\) −1.11364 + 0.613105i −0.133105 + 0.0732801i
\(71\) 3.76223i 0.446494i −0.974762 0.223247i \(-0.928334\pi\)
0.974762 0.223247i \(-0.0716657\pi\)
\(72\) 0.972777 0.561633i 0.114643 0.0661891i
\(73\) 7.91131 + 4.56760i 0.925949 + 0.534597i 0.885528 0.464586i \(-0.153797\pi\)
0.0404208 + 0.999183i \(0.487130\pi\)
\(74\) −1.33429 + 2.31106i −0.155108 + 0.268655i
\(75\) −2.12419 3.67921i −0.245281 0.424839i
\(76\) 3.69881i 0.424283i
\(77\) −7.59879 13.8024i −0.865963 1.57293i
\(78\) 1.48999 0.916825i 0.168708 0.103810i
\(79\) 0.0655625 + 0.113558i 0.00737636 + 0.0127762i 0.869690 0.493598i \(-0.164319\pi\)
−0.862314 + 0.506375i \(0.830985\pi\)
\(80\) 4.19322 + 2.42096i 0.468816 + 0.270671i
\(81\) 2.81922 4.88303i 0.313246 0.542558i
\(82\) −1.25532 2.17428i −0.138627 0.240109i
\(83\) 2.66812i 0.292865i −0.989221 0.146432i \(-0.953221\pi\)
0.989221 0.146432i \(-0.0467791\pi\)
\(84\) −0.148428 + 7.29653i −0.0161948 + 0.796117i
\(85\) 6.25768i 0.678741i
\(86\) 1.22288 0.706030i 0.131866 0.0761331i
\(87\) −5.22517 + 9.05026i −0.560197 + 0.970290i
\(88\) 3.84936 6.66729i 0.410344 0.710736i
\(89\) 8.41550 4.85869i 0.892042 0.515021i 0.0174319 0.999848i \(-0.494451\pi\)
0.874610 + 0.484828i \(0.161118\pi\)
\(90\) 0.417485 0.0440068
\(91\) −0.0731980 9.53911i −0.00767324 0.999971i
\(92\) 1.02065 0.106410
\(93\) 7.72207 4.45834i 0.800742 0.462308i
\(94\) −1.04047 + 1.80215i −0.107317 + 0.185878i
\(95\) 1.41493 2.45072i 0.145168 0.251439i
\(96\) −4.67625 + 2.69983i −0.477267 + 0.275550i
\(97\) 6.58319i 0.668422i −0.942498 0.334211i \(-0.891530\pi\)
0.942498 0.334211i \(-0.108470\pi\)
\(98\) −1.96594 1.24429i −0.198590 0.125693i
\(99\) 5.17429i 0.520036i
\(100\) −2.74943 4.76215i −0.274943 0.476215i
\(101\) −0.0354144 + 0.0613396i −0.00352387 + 0.00610352i −0.867782 0.496945i \(-0.834455\pi\)
0.864258 + 0.503049i \(0.167788\pi\)
\(102\) −1.81896 1.05018i −0.180104 0.103983i
\(103\) 3.16910 + 5.48905i 0.312261 + 0.540852i 0.978852 0.204572i \(-0.0655803\pi\)
−0.666590 + 0.745424i \(0.732247\pi\)
\(104\) 3.96985 2.44275i 0.389276 0.239531i
\(105\) −2.88953 + 4.77769i −0.281989 + 0.466255i
\(106\) 0.923689i 0.0897166i
\(107\) −3.87476 6.71129i −0.374588 0.648805i 0.615678 0.787998i \(-0.288882\pi\)
−0.990265 + 0.139193i \(0.955549\pi\)
\(108\) 5.33596 9.24215i 0.513453 0.889326i
\(109\) −0.0290658 0.0167811i −0.00278400 0.00160734i 0.498607 0.866828i \(-0.333845\pi\)
−0.501391 + 0.865221i \(0.667178\pi\)
\(110\) 2.47804 1.43069i 0.236271 0.136411i
\(111\) 11.7208i 1.11249i
\(112\) −0.180227 + 8.85975i −0.0170298 + 0.837168i
\(113\) −9.19987 −0.865451 −0.432725 0.901526i \(-0.642448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(114\) 0.474911 + 0.822571i 0.0444795 + 0.0770408i
\(115\) 0.676254 + 0.390435i 0.0630610 + 0.0364083i
\(116\) −6.76315 + 11.7141i −0.627943 + 1.08763i
\(117\) −1.48978 + 2.75587i −0.137730 + 0.254780i
\(118\) −0.282902 −0.0260432
\(119\) −10.0327 + 5.52344i −0.919699 + 0.506333i
\(120\) −2.72825 −0.249054
\(121\) 12.2320 + 21.1864i 1.11200 + 1.92603i
\(122\) 1.95132 + 1.12660i 0.176664 + 0.101997i
\(123\) −9.54971 5.51353i −0.861068 0.497138i
\(124\) 9.99499 5.77061i 0.897577 0.518216i
\(125\) 11.4351i 1.02279i
\(126\) 0.368500 + 0.669340i 0.0328286 + 0.0596296i
\(127\) −14.3952 −1.27737 −0.638683 0.769470i \(-0.720520\pi\)
−0.638683 + 0.769470i \(0.720520\pi\)
\(128\) −7.98085 + 4.60775i −0.705414 + 0.407271i
\(129\) 3.10098 5.37105i 0.273026 0.472895i
\(130\) 1.73175 0.0485237i 0.151884 0.00425581i
\(131\) 4.73414 + 8.19978i 0.413624 + 0.716418i 0.995283 0.0970151i \(-0.0309295\pi\)
−0.581659 + 0.813433i \(0.697596\pi\)
\(132\) 16.4267i 1.42976i
\(133\) 5.17808 + 0.105334i 0.448996 + 0.00913357i
\(134\) 0.328090 0.0283426
\(135\) 7.07090 4.08238i 0.608566 0.351356i
\(136\) −4.84635 2.79804i −0.415571 0.239930i
\(137\) −14.3814 8.30313i −1.22869 0.709384i −0.261934 0.965086i \(-0.584360\pi\)
−0.966756 + 0.255702i \(0.917693\pi\)
\(138\) −0.226980 + 0.131047i −0.0193219 + 0.0111555i
\(139\) 18.4778 1.56726 0.783632 0.621225i \(-0.213365\pi\)
0.783632 + 0.621225i \(0.213365\pi\)
\(140\) −3.74003 + 6.18396i −0.316090 + 0.522640i
\(141\) 9.13980i 0.769710i
\(142\) 0.625236 + 1.08294i 0.0524687 + 0.0908784i
\(143\) 0.601400 + 21.4632i 0.0502916 + 1.79484i
\(144\) 1.45509 2.52029i 0.121257 0.210024i
\(145\) −8.96213 + 5.17429i −0.744264 + 0.429701i
\(146\) −3.03631 −0.251287
\(147\) −10.2104 0.415577i −0.842140 0.0342762i
\(148\) 15.1707i 1.24702i
\(149\) 2.66805 1.54040i 0.218575 0.126195i −0.386715 0.922199i \(-0.626390\pi\)
0.605290 + 0.796005i \(0.293057\pi\)
\(150\) 1.22288 + 0.706030i 0.0998477 + 0.0576471i
\(151\) −2.20737 1.27442i −0.179633 0.103711i 0.407487 0.913211i \(-0.366405\pi\)
−0.587120 + 0.809500i \(0.699738\pi\)
\(152\) 1.26533 + 2.19162i 0.102632 + 0.177764i
\(153\) 3.76111 0.304068
\(154\) 4.48106 + 2.71013i 0.361095 + 0.218388i
\(155\) 8.82985 0.709231
\(156\) 4.72958 8.74901i 0.378670 0.700481i
\(157\) 4.70452 8.14847i 0.375461 0.650318i −0.614935 0.788578i \(-0.710818\pi\)
0.990396 + 0.138260i \(0.0441509\pi\)
\(158\) −0.0377438 0.0217914i −0.00300273 0.00173363i
\(159\) 2.02848 + 3.51344i 0.160869 + 0.278634i
\(160\) −5.34708 −0.422724
\(161\) −0.0290658 + 1.42884i −0.00229070 + 0.112608i
\(162\) 1.87408i 0.147241i
\(163\) 0.602023 0.347578i 0.0471541 0.0272244i −0.476238 0.879317i \(-0.658000\pi\)
0.523392 + 0.852092i \(0.324666\pi\)
\(164\) −12.3606 7.13638i −0.965199 0.557258i
\(165\) 6.28380 10.8839i 0.489193 0.847308i
\(166\) 0.443409 + 0.768007i 0.0344152 + 0.0596089i
\(167\) 13.9840i 1.08211i 0.840986 + 0.541056i \(0.181975\pi\)
−0.840986 + 0.541056i \(0.818025\pi\)
\(168\) −2.40814 4.37412i −0.185792 0.337471i
\(169\) −5.85938 + 11.6046i −0.450721 + 0.892665i
\(170\) −1.03995 1.80125i −0.0797605 0.138149i
\(171\) −1.47298 0.850426i −0.112642 0.0650337i
\(172\) 4.01372 6.95197i 0.306043 0.530083i
\(173\) −2.71824 4.70813i −0.206664 0.357952i 0.743998 0.668182i \(-0.232927\pi\)
−0.950662 + 0.310230i \(0.899594\pi\)
\(174\) 3.47344i 0.263321i
\(175\) 6.74497 3.71339i 0.509872 0.280706i
\(176\) 19.9460i 1.50349i
\(177\) −1.07607 + 0.621272i −0.0808827 + 0.0466976i
\(178\) −1.61491 + 2.79711i −0.121043 + 0.209652i
\(179\) 2.67912 4.64037i 0.200247 0.346838i −0.748361 0.663292i \(-0.769159\pi\)
0.948608 + 0.316454i \(0.102492\pi\)
\(180\) 2.05540 1.18668i 0.153200 0.0884502i
\(181\) −7.54016 −0.560456 −0.280228 0.959933i \(-0.590410\pi\)
−0.280228 + 0.959933i \(0.590410\pi\)
\(182\) 1.60635 + 2.73363i 0.119071 + 0.202630i
\(183\) 9.89632 0.731557
\(184\) −0.604757 + 0.349157i −0.0445833 + 0.0257402i
\(185\) −5.80331 + 10.0516i −0.426668 + 0.739011i
\(186\) −1.48184 + 2.56663i −0.108654 + 0.188194i
\(187\) 22.3245 12.8891i 1.63253 0.942543i
\(188\) 11.8300i 0.862793i
\(189\) 12.7864 + 7.73316i 0.930074 + 0.562504i
\(190\) 0.940574i 0.0682364i
\(191\) −6.77316 11.7315i −0.490089 0.848859i 0.509846 0.860266i \(-0.329702\pi\)
−0.999935 + 0.0114067i \(0.996369\pi\)
\(192\) −3.99217 + 6.91464i −0.288110 + 0.499021i
\(193\) −16.0702 9.27812i −1.15676 0.667853i −0.206232 0.978503i \(-0.566120\pi\)
−0.950524 + 0.310650i \(0.899453\pi\)
\(194\) 1.09405 + 1.89494i 0.0785479 + 0.136049i
\(195\) 6.48049 3.98760i 0.464077 0.285558i
\(196\) −13.2157 0.537898i −0.943982 0.0384213i
\(197\) 2.66812i 0.190096i 0.995473 + 0.0950480i \(0.0303004\pi\)
−0.995473 + 0.0950480i \(0.969700\pi\)
\(198\) −0.859903 1.48940i −0.0611106 0.105847i
\(199\) 10.0999 17.4936i 0.715965 1.24009i −0.246621 0.969112i \(-0.579320\pi\)
0.962586 0.270976i \(-0.0873465\pi\)
\(200\) 3.25819 + 1.88111i 0.230389 + 0.133015i
\(201\) 1.24795 0.720507i 0.0880239 0.0508206i
\(202\) 0.0235418i 0.00165639i
\(203\) −16.2063 9.80152i −1.13746 0.687932i
\(204\) −11.9403 −0.835990
\(205\) −5.45984 9.45672i −0.381332 0.660486i
\(206\) −1.82443 1.05333i −0.127114 0.0733891i
\(207\) 0.234667 0.406455i 0.0163105 0.0282506i
\(208\) 5.74285 10.6234i 0.398195 0.736601i
\(209\) −11.6574 −0.806361
\(210\) 0.0377438 1.85544i 0.00260457 0.128038i
\(211\) 13.1268 0.903683 0.451842 0.892098i \(-0.350767\pi\)
0.451842 + 0.892098i \(0.350767\pi\)
\(212\) 2.62555 + 4.54758i 0.180323 + 0.312329i
\(213\) 4.75642 + 2.74612i 0.325905 + 0.188161i
\(214\) 2.23067 + 1.28788i 0.152485 + 0.0880374i
\(215\) 5.31875 3.07078i 0.362736 0.209425i
\(216\) 7.30155i 0.496807i
\(217\) 7.79382 + 14.1566i 0.529079 + 0.961014i
\(218\) 0.0111553 0.000755530
\(219\) −11.5492 + 6.66795i −0.780424 + 0.450578i
\(220\) 8.13338 14.0874i 0.548352 0.949774i
\(221\) 15.6013 0.437148i 1.04946 0.0294058i
\(222\) −1.94785 3.37377i −0.130731 0.226433i
\(223\) 2.22334i 0.148886i 0.997225 + 0.0744428i \(0.0237178\pi\)
−0.997225 + 0.0744428i \(0.976282\pi\)
\(224\) −4.71969 8.57281i −0.315348 0.572795i
\(225\) −2.52858 −0.168572
\(226\) 2.64814 1.52890i 0.176152 0.101701i
\(227\) 23.4732 + 13.5523i 1.55797 + 0.899495i 0.997451 + 0.0713539i \(0.0227320\pi\)
0.560520 + 0.828141i \(0.310601\pi\)
\(228\) 4.67625 + 2.69983i 0.309692 + 0.178801i
\(229\) −16.4447 + 9.49437i −1.08670 + 0.627406i −0.932696 0.360665i \(-0.882550\pi\)
−0.154003 + 0.988070i \(0.549217\pi\)
\(230\) −0.259542 −0.0171137
\(231\) 22.9962 + 0.467795i 1.51304 + 0.0307786i
\(232\) 9.25447i 0.607586i
\(233\) 10.8700 + 18.8274i 0.712118 + 1.23343i 0.964060 + 0.265683i \(0.0855974\pi\)
−0.251942 + 0.967742i \(0.581069\pi\)
\(234\) −0.0291646 1.04085i −0.00190655 0.0680424i
\(235\) −4.52540 + 7.83822i −0.295205 + 0.511309i
\(236\) −1.39281 + 0.804137i −0.0906639 + 0.0523449i
\(237\) −0.191421 −0.0124342
\(238\) 1.96995 3.25722i 0.127693 0.211134i
\(239\) 19.9695i 1.29172i −0.763455 0.645861i \(-0.776499\pi\)
0.763455 0.645861i \(-0.223501\pi\)
\(240\) −6.12142 + 3.53420i −0.395136 + 0.228132i
\(241\) −2.79768 1.61524i −0.180214 0.104047i 0.407179 0.913348i \(-0.366513\pi\)
−0.587393 + 0.809302i \(0.699846\pi\)
\(242\) −7.04183 4.06560i −0.452666 0.261347i
\(243\) −4.35630 7.54533i −0.279456 0.484033i
\(244\) 12.8092 0.820025
\(245\) −8.55060 5.41188i −0.546278 0.345753i
\(246\) 3.66512 0.233680
\(247\) −6.20884 3.35641i −0.395059 0.213563i
\(248\) −3.94816 + 6.83841i −0.250708 + 0.434239i
\(249\) 3.37319 + 1.94751i 0.213767 + 0.123419i
\(250\) 1.90038 + 3.29155i 0.120190 + 0.208176i
\(251\) −12.4916 −0.788466 −0.394233 0.919011i \(-0.628990\pi\)
−0.394233 + 0.919011i \(0.628990\pi\)
\(252\) 3.71680 + 2.24790i 0.234136 + 0.141605i
\(253\) 3.21675i 0.202236i
\(254\) 4.14359 2.39230i 0.259992 0.150106i
\(255\) −7.91131 4.56760i −0.495425 0.286034i
\(256\) −3.93783 + 6.82052i −0.246114 + 0.426283i
\(257\) 2.91379 + 5.04682i 0.181757 + 0.314812i 0.942479 0.334266i \(-0.108488\pi\)
−0.760722 + 0.649078i \(0.775155\pi\)
\(258\) 2.06138i 0.128336i
\(259\) −21.2378 0.432025i −1.31966 0.0268447i
\(260\) 8.38796 5.16132i 0.520199 0.320091i
\(261\) 3.10995 + 5.38659i 0.192501 + 0.333422i
\(262\) −2.72540 1.57351i −0.168376 0.0972119i
\(263\) −8.75736 + 15.1682i −0.540002 + 0.935311i 0.458901 + 0.888487i \(0.348243\pi\)
−0.998903 + 0.0468234i \(0.985090\pi\)
\(264\) 5.61945 + 9.73316i 0.345853 + 0.599035i
\(265\) 4.01746i 0.246791i
\(266\) −1.50799 + 0.830213i −0.0924609 + 0.0509036i
\(267\) 14.1858i 0.868157i
\(268\) 1.61528 0.932581i 0.0986688 0.0569665i
\(269\) −11.1644 + 19.3372i −0.680703 + 1.17901i 0.294064 + 0.955786i \(0.404992\pi\)
−0.974767 + 0.223226i \(0.928341\pi\)
\(270\) −1.35688 + 2.35019i −0.0825773 + 0.143028i
\(271\) −22.8366 + 13.1847i −1.38723 + 0.800916i −0.993002 0.118098i \(-0.962320\pi\)
−0.394225 + 0.919014i \(0.628987\pi\)
\(272\) −14.4984 −0.879097
\(273\) 12.1133 + 6.87023i 0.733131 + 0.415805i
\(274\) 5.51951 0.333446
\(275\) −15.0087 + 8.66529i −0.905060 + 0.522536i
\(276\) −0.744993 + 1.29037i −0.0448433 + 0.0776709i
\(277\) −4.68809 + 8.12001i −0.281680 + 0.487884i −0.971799 0.235812i \(-0.924225\pi\)
0.690119 + 0.723696i \(0.257558\pi\)
\(278\) −5.31875 + 3.07078i −0.318997 + 0.184173i
\(279\) 5.30709i 0.317727i
\(280\) 0.100563 4.94356i 0.00600978 0.295434i
\(281\) 17.7754i 1.06039i −0.847876 0.530195i \(-0.822119\pi\)
0.847876 0.530195i \(-0.177881\pi\)
\(282\) −1.51892 2.63085i −0.0904505 0.156665i
\(283\) −4.80331 + 8.31958i −0.285527 + 0.494548i −0.972737 0.231911i \(-0.925502\pi\)
0.687210 + 0.726459i \(0.258835\pi\)
\(284\) 6.15643 + 3.55442i 0.365317 + 0.210916i
\(285\) 2.06556 + 3.57766i 0.122353 + 0.211922i
\(286\) −3.74003 6.07814i −0.221153 0.359408i
\(287\) 10.3424 17.1007i 0.610494 1.00942i
\(288\) 3.21380i 0.189375i
\(289\) −0.868875 1.50494i −0.0511103 0.0885256i
\(290\) 1.71981 2.97879i 0.100990 0.174921i
\(291\) 8.32284 + 4.80519i 0.487894 + 0.281685i
\(292\) −14.9486 + 8.63060i −0.874803 + 0.505067i
\(293\) 11.6338i 0.679654i −0.940488 0.339827i \(-0.889631\pi\)
0.940488 0.339827i \(-0.110369\pi\)
\(294\) 3.00808 1.57722i 0.175435 0.0919855i
\(295\) −1.23044 −0.0716392
\(296\) −5.18976 8.98892i −0.301648 0.522470i
\(297\) −29.1282 16.8172i −1.69019 0.975830i
\(298\) −0.511991 + 0.886795i −0.0296588 + 0.0513706i
\(299\) 0.926168 1.71327i 0.0535617 0.0990810i
\(300\) 8.02744 0.463464
\(301\) 9.61796 + 5.81690i 0.554370 + 0.335281i
\(302\) 0.847174 0.0487494
\(303\) −0.0516993 0.0895459i −0.00297005 0.00514427i
\(304\) 5.67809 + 3.27825i 0.325661 + 0.188020i
\(305\) 8.48700 + 4.89997i 0.485964 + 0.280572i
\(306\) −1.08262 + 0.625050i −0.0618892 + 0.0357317i
\(307\) 13.8280i 0.789204i 0.918852 + 0.394602i \(0.129118\pi\)
−0.918852 + 0.394602i \(0.870882\pi\)
\(308\) 29.7650 + 0.605485i 1.69602 + 0.0345007i
\(309\) −9.25275 −0.526371
\(310\) −2.54163 + 1.46741i −0.144355 + 0.0833435i
\(311\) 15.3572 26.5994i 0.870827 1.50832i 0.00968369 0.999953i \(-0.496918\pi\)
0.861143 0.508363i \(-0.169749\pi\)
\(312\) 0.190590 + 6.80192i 0.0107900 + 0.385083i
\(313\) −5.54334 9.60135i −0.313328 0.542701i 0.665752 0.746173i \(-0.268111\pi\)
−0.979081 + 0.203472i \(0.934777\pi\)
\(314\) 3.12733i 0.176486i
\(315\) 1.60274 + 2.91120i 0.0903042 + 0.164028i
\(316\) −0.247764 −0.0139378
\(317\) 20.6836 11.9417i 1.16171 0.670712i 0.209994 0.977703i \(-0.432656\pi\)
0.951712 + 0.306991i \(0.0993222\pi\)
\(318\) −1.16778 0.674218i −0.0654858 0.0378083i
\(319\) 36.9190 + 21.3152i 2.06707 + 1.19342i
\(320\) −6.84731 + 3.95329i −0.382776 + 0.220996i
\(321\) 11.3130 0.631433
\(322\) −0.229089 0.416116i −0.0127666 0.0231892i
\(323\) 8.47360i 0.471484i
\(324\) 5.32698 + 9.22661i 0.295944 + 0.512589i
\(325\) −10.4887 + 0.293893i −0.581807 + 0.0163023i
\(326\) −0.115526 + 0.200098i −0.00639842 + 0.0110824i
\(327\) 0.0424313 0.0244977i 0.00234646 0.00135473i
\(328\) 9.76519 0.539192
\(329\) −16.5612 0.336891i −0.913048 0.0185734i
\(330\) 4.17716i 0.229945i
\(331\) 15.8690 9.16200i 0.872241 0.503589i 0.00414903 0.999991i \(-0.498679\pi\)
0.868092 + 0.496403i \(0.165346\pi\)
\(332\) 4.36606 + 2.52075i 0.239619 + 0.138344i
\(333\) 6.04142 + 3.48802i 0.331068 + 0.191142i
\(334\) −2.32396 4.02522i −0.127162 0.220250i
\(335\) 1.42698 0.0779643
\(336\) −11.0694 6.69475i −0.603888 0.365229i
\(337\) 7.21762 0.393169 0.196584 0.980487i \(-0.437015\pi\)
0.196584 + 0.980487i \(0.437015\pi\)
\(338\) −0.241953 4.31410i −0.0131605 0.234656i
\(339\) 6.71516 11.6310i 0.364717 0.631709i
\(340\) −10.2399 5.91203i −0.555338 0.320625i
\(341\) −18.1870 31.5009i −0.984884 1.70587i
\(342\) 0.565321 0.0305691
\(343\) 1.12937 18.4858i 0.0609804 0.998139i
\(344\) 5.49224i 0.296122i
\(345\) −0.987221 + 0.569972i −0.0531502 + 0.0306863i
\(346\) 1.56487 + 0.903476i 0.0841277 + 0.0485712i
\(347\) 10.5391 18.2543i 0.565770 0.979942i −0.431208 0.902253i \(-0.641912\pi\)
0.996978 0.0776892i \(-0.0247542\pi\)
\(348\) −9.87310 17.1007i −0.529254 0.916694i
\(349\) 30.7629i 1.64670i −0.567534 0.823350i \(-0.692102\pi\)
0.567534 0.823350i \(-0.307898\pi\)
\(350\) −1.32439 + 2.18982i −0.0707917 + 0.117051i
\(351\) −10.6719 17.3435i −0.569624 0.925730i
\(352\) 11.0135 + 19.0760i 0.587022 + 1.01675i
\(353\) 5.30157 + 3.06086i 0.282174 + 0.162913i 0.634407 0.772999i \(-0.281244\pi\)
−0.352233 + 0.935912i \(0.614578\pi\)
\(354\) 0.206495 0.357660i 0.0109751 0.0190094i
\(355\) 2.71938 + 4.71010i 0.144330 + 0.249986i
\(356\) 18.3613i 0.973145i
\(357\) 0.340033 16.7156i 0.0179964 0.884684i
\(358\) 1.78095i 0.0941259i
\(359\) −16.8257 + 9.71433i −0.888028 + 0.512703i −0.873297 0.487189i \(-0.838022\pi\)
−0.0147308 + 0.999891i \(0.504689\pi\)
\(360\) −0.811909 + 1.40627i −0.0427914 + 0.0741168i
\(361\) −7.58403 + 13.1359i −0.399160 + 0.691365i
\(362\) 2.17040 1.25308i 0.114074 0.0658605i
\(363\) −35.7133 −1.87446
\(364\) 15.6787 + 8.89242i 0.821790 + 0.466090i
\(365\) −13.2060 −0.691235
\(366\) −2.84861 + 1.64465i −0.148899 + 0.0859670i
\(367\) 2.70234 4.68058i 0.141061 0.244324i −0.786836 0.617163i \(-0.788282\pi\)
0.927896 + 0.372838i \(0.121615\pi\)
\(368\) −0.904601 + 1.56681i −0.0471556 + 0.0816758i
\(369\) −5.68385 + 3.28158i −0.295890 + 0.170832i
\(370\) 3.85776i 0.200555i
\(371\) −6.44106 + 3.54608i −0.334403 + 0.184103i
\(372\) 16.8483i 0.873544i
\(373\) −8.12533 14.0735i −0.420714 0.728698i 0.575296 0.817946i \(-0.304887\pi\)
−0.996009 + 0.0892478i \(0.971554\pi\)
\(374\) −4.28401 + 7.42013i −0.221521 + 0.383686i
\(375\) 14.4569 + 8.34671i 0.746553 + 0.431022i
\(376\) −4.04695 7.00952i −0.208706 0.361489i
\(377\) 13.5263 + 21.9824i 0.696640 + 1.13215i
\(378\) −4.96566 0.101013i −0.255406 0.00519553i
\(379\) 25.1730i 1.29305i −0.762893 0.646525i \(-0.776222\pi\)
0.762893 0.646525i \(-0.223778\pi\)
\(380\) 2.67354 + 4.63071i 0.137150 + 0.237550i
\(381\) 10.5073 18.1992i 0.538306 0.932373i
\(382\) 3.89925 + 2.25123i 0.199503 + 0.115183i
\(383\) −3.30335 + 1.90719i −0.168793 + 0.0974529i −0.582017 0.813177i \(-0.697736\pi\)
0.413223 + 0.910630i \(0.364403\pi\)
\(384\) 13.4531i 0.686527i
\(385\) 19.4898 + 11.7873i 0.993291 + 0.600738i
\(386\) 6.16764 0.313924
\(387\) −1.84566 3.19677i −0.0938201 0.162501i
\(388\) 10.7726 + 6.21956i 0.546895 + 0.315750i
\(389\) −1.43548 + 2.48632i −0.0727817 + 0.126062i −0.900119 0.435643i \(-0.856521\pi\)
0.827338 + 0.561705i \(0.189854\pi\)
\(390\) −1.20269 + 2.22479i −0.0609005 + 0.112657i
\(391\) −2.33821 −0.118248
\(392\) 8.01461 4.20228i 0.404799 0.212247i
\(393\) −13.8222 −0.697236
\(394\) −0.443409 0.768007i −0.0223386 0.0386917i
\(395\) −0.164161 0.0947786i −0.00825986 0.00476883i
\(396\) −8.46709 4.88848i −0.425487 0.245655i
\(397\) −16.5570 + 9.55919i −0.830972 + 0.479762i −0.854185 0.519968i \(-0.825944\pi\)
0.0232131 + 0.999731i \(0.492610\pi\)
\(398\) 6.71394i 0.336539i
\(399\) −3.91274 + 6.46953i −0.195882 + 0.323882i
\(400\) 9.74725 0.487362
\(401\) 2.59655 1.49912i 0.129666 0.0748625i −0.433764 0.901026i \(-0.642815\pi\)
0.563430 + 0.826164i \(0.309482\pi\)
\(402\) −0.239479 + 0.414789i −0.0119441 + 0.0206878i
\(403\) −0.616835 22.0141i −0.0307267 1.09660i
\(404\) −0.0669165 0.115903i −0.00332922 0.00576638i
\(405\) 8.15104i 0.405028i
\(406\) 6.29382 + 0.128030i 0.312357 + 0.00635403i
\(407\) 47.8129 2.37000
\(408\) 7.07489 4.08469i 0.350259 0.202222i
\(409\) −29.5146 17.0403i −1.45940 0.842587i −0.460422 0.887700i \(-0.652302\pi\)
−0.998982 + 0.0451127i \(0.985635\pi\)
\(410\) 3.14318 + 1.81472i 0.155231 + 0.0896224i
\(411\) 20.9946 12.1212i 1.03559 0.597896i
\(412\) −11.9762 −0.590026
\(413\) −1.08607 1.97273i −0.0534421 0.0970717i
\(414\) 0.155995i 0.00766674i
\(415\) 1.92855 + 3.34034i 0.0946687 + 0.163971i
\(416\) 0.373536 + 13.3310i 0.0183141 + 0.653607i
\(417\) −13.4873 + 23.3606i −0.660475 + 1.14398i
\(418\) 3.35554 1.93732i 0.164125 0.0947574i
\(419\) 34.7759 1.69891 0.849457 0.527657i \(-0.176929\pi\)
0.849457 + 0.527657i \(0.176929\pi\)
\(420\) −5.08819 9.24215i −0.248278 0.450971i
\(421\) 24.1400i 1.17651i 0.808674 + 0.588257i \(0.200186\pi\)
−0.808674 + 0.588257i \(0.799814\pi\)
\(422\) −3.77848 + 2.18151i −0.183933 + 0.106194i
\(423\) 4.71108 + 2.71994i 0.229060 + 0.132248i
\(424\) −3.11138 1.79636i −0.151102 0.0872388i
\(425\) 6.29866 + 10.9096i 0.305530 + 0.529193i
\(426\) −1.82549 −0.0884451
\(427\) −0.364776 + 17.9320i −0.0176528 + 0.867789i
\(428\) 14.6429 0.707793
\(429\) −27.5740 14.9061i −1.33128 0.719672i
\(430\) −1.02065 + 1.76782i −0.0492202 + 0.0852519i
\(431\) −4.12641 2.38238i −0.198762 0.114755i 0.397316 0.917682i \(-0.369942\pi\)
−0.596078 + 0.802927i \(0.703275\pi\)
\(432\) 9.45848 + 16.3826i 0.455071 + 0.788207i
\(433\) −22.0231 −1.05836 −0.529181 0.848509i \(-0.677501\pi\)
−0.529181 + 0.848509i \(0.677501\pi\)
\(434\) −4.59607 2.77968i −0.220618 0.133429i
\(435\) 15.1072i 0.724337i
\(436\) 0.0549206 0.0317084i 0.00263022 0.00151856i
\(437\) 0.915724 + 0.528693i 0.0438050 + 0.0252908i
\(438\) 2.21626 3.83868i 0.105897 0.183419i
\(439\) 1.71620 + 2.97254i 0.0819097 + 0.141872i 0.904070 0.427384i \(-0.140565\pi\)
−0.822161 + 0.569256i \(0.807231\pi\)
\(440\) 11.1294i 0.530576i
\(441\) −3.25275 + 5.13924i −0.154893 + 0.244726i
\(442\) −4.41811 + 2.71857i −0.210148 + 0.129309i
\(443\) 4.35297 + 7.53957i 0.206816 + 0.358216i 0.950710 0.310082i \(-0.100357\pi\)
−0.743894 + 0.668298i \(0.767023\pi\)
\(444\) −19.1796 11.0733i −0.910223 0.525518i
\(445\) −7.02383 + 12.1656i −0.332962 + 0.576706i
\(446\) −0.369491 0.639977i −0.0174959 0.0303038i
\(447\) 4.49747i 0.212723i
\(448\) −12.3821 7.48862i −0.584998 0.353804i
\(449\) 17.6120i 0.831159i −0.909557 0.415580i \(-0.863579\pi\)
0.909557 0.415580i \(-0.136421\pi\)
\(450\) 0.727841 0.420219i 0.0343107 0.0198093i
\(451\) −22.4915 + 38.9564i −1.05908 + 1.83439i
\(452\) 8.69170 15.0545i 0.408823 0.708102i
\(453\) 3.22240 1.86045i 0.151401 0.0874116i
\(454\) −9.00887 −0.422807
\(455\) 6.98661 + 11.8895i 0.327537 + 0.557390i
\(456\) −3.69436 −0.173004
\(457\) −7.85717 + 4.53634i −0.367543 + 0.212201i −0.672384 0.740202i \(-0.734730\pi\)
0.304842 + 0.952403i \(0.401396\pi\)
\(458\) 3.15570 5.46583i 0.147456 0.255401i
\(459\) −12.2241 + 21.1728i −0.570573 + 0.988262i
\(460\) −1.27780 + 0.737738i −0.0595777 + 0.0343972i
\(461\) 6.58319i 0.306610i 0.988179 + 0.153305i \(0.0489917\pi\)
−0.988179 + 0.153305i \(0.951008\pi\)
\(462\) −6.69711 + 3.68704i −0.311578 + 0.171537i
\(463\) 3.47344i 0.161424i −0.996737 0.0807121i \(-0.974281\pi\)
0.996737 0.0807121i \(-0.0257194\pi\)
\(464\) −11.9883 20.7644i −0.556544 0.963962i
\(465\) −6.44507 + 11.1632i −0.298883 + 0.517681i
\(466\) −6.25777 3.61293i −0.289886 0.167366i
\(467\) 14.8927 + 25.7949i 0.689152 + 1.19365i 0.972112 + 0.234515i \(0.0753502\pi\)
−0.282960 + 0.959132i \(0.591316\pi\)
\(468\) −3.10215 5.04149i −0.143397 0.233043i
\(469\) 1.25955 + 2.28783i 0.0581606 + 0.105642i
\(470\) 3.00826i 0.138761i
\(471\) 6.86783 + 11.8954i 0.316453 + 0.548113i
\(472\) 0.550177 0.952935i 0.0253240 0.0438624i
\(473\) −21.9103 12.6499i −1.00744 0.581643i
\(474\) 0.0550998 0.0318119i 0.00253082 0.00146117i
\(475\) 5.69677i 0.261386i
\(476\) 0.440118 21.6357i 0.0201728 0.991671i
\(477\) 2.41465 0.110559
\(478\) 3.31869 + 5.74814i 0.151793 + 0.262914i
\(479\) 30.4715 + 17.5927i 1.39228 + 0.803833i 0.993567 0.113243i \(-0.0361240\pi\)
0.398712 + 0.917076i \(0.369457\pi\)
\(480\) 3.90294 6.76008i 0.178144 0.308554i
\(481\) 25.4655 + 13.7663i 1.16113 + 0.627688i
\(482\) 1.07373 0.0489072
\(483\) −1.78520 1.07968i −0.0812296 0.0491273i
\(484\) −46.2252 −2.10115
\(485\) 4.75840 + 8.24179i 0.216068 + 0.374241i
\(486\) 2.50788 + 1.44793i 0.113760 + 0.0656792i
\(487\) 1.56018 + 0.900769i 0.0706984 + 0.0408178i 0.534933 0.844895i \(-0.320337\pi\)
−0.464234 + 0.885713i \(0.653670\pi\)
\(488\) −7.58971 + 4.38192i −0.343570 + 0.198360i
\(489\) 1.01482i 0.0458916i
\(490\) 3.36064 + 0.136782i 0.151818 + 0.00617920i
\(491\) 8.19322 0.369755 0.184877 0.982762i \(-0.440811\pi\)
0.184877 + 0.982762i \(0.440811\pi\)
\(492\) 18.0444 10.4180i 0.813506 0.469678i
\(493\) 15.4937 26.8358i 0.697800 1.20863i
\(494\) 2.34498 0.0657065i 0.105506 0.00295627i
\(495\) −3.74003 6.47792i −0.168102 0.291161i
\(496\) 20.4579i 0.918587i
\(497\) −5.15125 + 8.51734i −0.231065 + 0.382055i
\(498\) −1.29461 −0.0580129
\(499\) −31.6242 + 18.2582i −1.41569 + 0.817350i −0.995917 0.0902781i \(-0.971224\pi\)
−0.419775 + 0.907628i \(0.637891\pi\)
\(500\) 18.7122 + 10.8035i 0.836834 + 0.483147i
\(501\) −17.6793 10.2072i −0.789854 0.456022i
\(502\) 3.59566 2.07596i 0.160482 0.0926545i
\(503\) −3.02972 −0.135089 −0.0675443 0.997716i \(-0.521516\pi\)
−0.0675443 + 0.997716i \(0.521516\pi\)
\(504\) −2.97127 0.0604422i −0.132351 0.00269231i
\(505\) 0.102392i 0.00455637i
\(506\) 0.534585 + 0.925928i 0.0237652 + 0.0411625i
\(507\) −10.3944 15.8782i −0.461630 0.705176i
\(508\) 13.6000 23.5559i 0.603404 1.04513i
\(509\) 25.4133 14.6724i 1.12642 0.650341i 0.183391 0.983040i \(-0.441293\pi\)
0.943033 + 0.332699i \(0.107959\pi\)
\(510\) 3.03631 0.134450
\(511\) −11.6565 21.1728i −0.515654 0.936630i
\(512\) 21.0487i 0.930229i
\(513\) 9.57479 5.52800i 0.422737 0.244067i
\(514\) −1.67744 0.968471i −0.0739887 0.0427174i
\(515\) −7.93509 4.58133i −0.349662 0.201877i
\(516\) 5.85938 + 10.1487i 0.257945 + 0.446773i
\(517\) 37.2843 1.63976
\(518\) 6.18502 3.40511i 0.271754 0.149612i
\(519\) 7.93637 0.348368
\(520\) −3.20439 + 5.92764i −0.140522 + 0.259944i
\(521\) 14.8419 25.7069i 0.650236 1.12624i −0.332830 0.942987i \(-0.608003\pi\)
0.983066 0.183254i \(-0.0586632\pi\)
\(522\) −1.79037 1.03367i −0.0783624 0.0452425i
\(523\) −10.2864 17.8165i −0.449791 0.779062i 0.548581 0.836098i \(-0.315168\pi\)
−0.998372 + 0.0570361i \(0.981835\pi\)
\(524\) −17.8906 −0.781553
\(525\) −0.228603 + 11.2379i −0.00997704 + 0.490460i
\(526\) 5.82146i 0.253828i
\(527\) −22.8975 + 13.2199i −0.997431 + 0.575867i
\(528\) 25.2168 + 14.5590i 1.09742 + 0.633597i
\(529\) 11.3541 19.6659i 0.493657 0.855039i
\(530\) −0.667652 1.15641i −0.0290010 0.0502311i
\(531\) 0.739544i 0.0320935i
\(532\) −5.06442 + 8.37377i −0.219571 + 0.363049i
\(533\) −23.1955 + 14.2728i −1.00471 + 0.618222i
\(534\) −2.35751 4.08332i −0.102019 0.176703i
\(535\) 9.70198 + 5.60144i 0.419453 + 0.242171i
\(536\) −0.638057 + 1.10515i −0.0275599 + 0.0477351i
\(537\) 3.91108 + 6.77419i 0.168775 + 0.292328i
\(538\) 7.42151i 0.319964i
\(539\) −1.69527 + 41.6516i −0.0730206 + 1.79406i
\(540\) 15.4275i 0.663896i
\(541\) 29.5027 17.0334i 1.26842 0.732324i 0.293732 0.955888i \(-0.405103\pi\)
0.974689 + 0.223564i \(0.0717692\pi\)
\(542\) 4.38228 7.59034i 0.188235 0.326033i
\(543\) 5.50371 9.53270i 0.236187 0.409087i
\(544\) 13.8660 8.00555i 0.594500 0.343235i
\(545\) 0.0485183 0.00207830
\(546\) −4.62851 + 0.0355167i −0.198082 + 0.00151997i
\(547\) −0.850931 −0.0363832 −0.0181916 0.999835i \(-0.505791\pi\)
−0.0181916 + 0.999835i \(0.505791\pi\)
\(548\) 27.1741 15.6890i 1.16082 0.670200i
\(549\) 2.94507 5.10102i 0.125693 0.217706i
\(550\) 2.88013 4.98853i 0.122809 0.212712i
\(551\) −12.1357 + 7.00657i −0.516999 + 0.298490i
\(552\) 1.01942i 0.0433895i
\(553\) 0.00705575 0.346853i 0.000300041 0.0147497i
\(554\) 3.11641i 0.132404i
\(555\) −8.47189 14.6737i −0.359612 0.622866i
\(556\) −17.4571 + 30.2366i −0.740347 + 1.28232i
\(557\) 15.3530 + 8.86404i 0.650526 + 0.375581i 0.788658 0.614833i \(-0.210776\pi\)
−0.138132 + 0.990414i \(0.544110\pi\)
\(558\) 0.881972 + 1.52762i 0.0373369 + 0.0646694i
\(559\) −8.02744 13.0459i −0.339525 0.551781i
\(560\) −6.17829 11.2222i −0.261080 0.474224i
\(561\) 37.6319i 1.58882i
\(562\) 2.95405 + 5.11656i 0.124609 + 0.215829i
\(563\) −12.0903 + 20.9410i −0.509545 + 0.882558i 0.490394 + 0.871501i \(0.336853\pi\)
−0.999939 + 0.0110571i \(0.996480\pi\)
\(564\) −14.9562 8.63495i −0.629768 0.363597i
\(565\) 11.5177 6.64976i 0.484555 0.279758i
\(566\) 3.19301i 0.134212i
\(567\) −13.0683 + 7.19465i −0.548817 + 0.302147i
\(568\) −4.86375 −0.204078
\(569\) −21.3874 37.0441i −0.896608 1.55297i −0.831802 0.555073i \(-0.812690\pi\)
−0.0648066 0.997898i \(-0.520643\pi\)
\(570\) −1.18913 0.686542i −0.0498070 0.0287561i
\(571\) 3.68140 6.37637i 0.154062 0.266843i −0.778655 0.627452i \(-0.784098\pi\)
0.932717 + 0.360609i \(0.117431\pi\)
\(572\) −35.6901 19.2935i −1.49228 0.806703i
\(573\) 19.7754 0.826131
\(574\) −0.135096 + 6.64115i −0.00563878 + 0.277196i
\(575\) 1.57197 0.0655557
\(576\) 2.37608 + 4.11550i 0.0990035 + 0.171479i
\(577\) −7.09615 4.09696i −0.295417 0.170559i 0.344965 0.938615i \(-0.387891\pi\)
−0.640382 + 0.768057i \(0.721224\pi\)
\(578\) 0.500204 + 0.288793i 0.0208057 + 0.0120122i
\(579\) 23.4598 13.5445i 0.974957 0.562892i
\(580\) 19.5539i 0.811932i
\(581\) −3.65320 + 6.04039i −0.151560 + 0.250598i
\(582\) −3.19426 −0.132406
\(583\) 14.3325 8.27485i 0.593590 0.342709i
\(584\) 5.90491 10.2276i 0.244347 0.423221i
\(585\) −0.126848 4.52703i −0.00524450 0.187170i
\(586\) 1.93339 + 3.34874i 0.0798678 + 0.138335i
\(587\) 39.1141i 1.61441i −0.590271 0.807205i \(-0.700979\pi\)
0.590271 0.807205i \(-0.299021\pi\)
\(588\) 10.3265 16.3155i 0.425856 0.672838i
\(589\) 11.9566 0.492664
\(590\) 0.354178 0.204485i 0.0145813 0.00841849i
\(591\) −3.37319 1.94751i −0.138755 0.0801100i
\(592\) −23.2886 13.4457i −0.957158 0.552615i
\(593\) −1.05082 + 0.606691i −0.0431520 + 0.0249138i −0.521421 0.853300i \(-0.674598\pi\)
0.478269 + 0.878213i \(0.341264\pi\)
\(594\) 11.1792 0.458689
\(595\) 8.56803 14.1668i 0.351255 0.580783i
\(596\) 5.82125i 0.238448i
\(597\) 14.7443 + 25.5378i 0.603442 + 1.04519i
\(598\) 0.0181311 + 0.647075i 0.000741435 + 0.0264609i
\(599\) −16.3319 + 28.2877i −0.667303 + 1.15580i 0.311352 + 0.950295i \(0.399218\pi\)
−0.978655 + 0.205508i \(0.934115\pi\)
\(600\) −4.75642 + 2.74612i −0.194180 + 0.112110i
\(601\) 2.50114 0.102024 0.0510118 0.998698i \(-0.483755\pi\)
0.0510118 + 0.998698i \(0.483755\pi\)
\(602\) −3.73519 0.0759819i −0.152235 0.00309679i
\(603\) 0.857671i 0.0349271i
\(604\) 4.17088 2.40806i 0.169711 0.0979825i
\(605\) −30.6275 17.6828i −1.24518 0.718907i
\(606\) 0.0297628 + 0.0171836i 0.00120903 + 0.000698035i
\(607\) −6.32282 10.9515i −0.256635 0.444506i 0.708703 0.705507i \(-0.249281\pi\)
−0.965338 + 0.261001i \(0.915947\pi\)
\(608\) −7.24055 −0.293643
\(609\) 24.2209 13.3347i 0.981482 0.540347i
\(610\) −3.25726 −0.131883
\(611\) 19.8579 + 10.7349i 0.803365 + 0.434287i
\(612\) −3.55336 + 6.15460i −0.143636 + 0.248785i
\(613\) 17.3448 + 10.0140i 0.700548 + 0.404462i 0.807552 0.589797i \(-0.200792\pi\)
−0.107003 + 0.994259i \(0.534126\pi\)
\(614\) −2.29804 3.98032i −0.0927413 0.160633i
\(615\) 15.9409 0.642801
\(616\) −17.8435 + 9.82359i −0.718934 + 0.395804i
\(617\) 45.2926i 1.82341i 0.410846 + 0.911705i \(0.365233\pi\)
−0.410846 + 0.911705i \(0.634767\pi\)
\(618\) 2.66336 1.53769i 0.107136 0.0618551i
\(619\) 3.83922 + 2.21658i 0.154311 + 0.0890917i 0.575167 0.818036i \(-0.304937\pi\)
−0.420856 + 0.907127i \(0.638270\pi\)
\(620\) −8.34212 + 14.4490i −0.335028 + 0.580285i
\(621\) 1.52540 + 2.64207i 0.0612122 + 0.106023i
\(622\) 10.2087i 0.409332i
\(623\) −25.7045 0.522886i −1.02983 0.0209490i
\(624\) 9.23889 + 15.0147i 0.369852 + 0.601067i
\(625\) 0.989985 + 1.71471i 0.0395994 + 0.0685882i
\(626\) 3.19125 + 1.84247i 0.127548 + 0.0736400i
\(627\) 8.50897 14.7380i 0.339816 0.588578i
\(628\) 8.88931 + 15.3967i 0.354722 + 0.614397i
\(629\) 34.7544i 1.38575i
\(630\) −0.945148 0.571621i −0.0376556 0.0227739i
\(631\) 19.7358i 0.785672i 0.919609 + 0.392836i \(0.128506\pi\)
−0.919609 + 0.392836i \(0.871494\pi\)
\(632\) 0.146805 0.0847581i 0.00583961 0.00337150i
\(633\) −9.58147 + 16.5956i −0.380829 + 0.659615i
\(634\) −3.96912 + 6.87472i −0.157634 + 0.273030i
\(635\) 18.0220 10.4050i 0.715180 0.412909i
\(636\) −7.66574 −0.303967
\(637\) −12.8953 + 21.6959i −0.510929 + 0.859623i
\(638\) −14.1693 −0.560968
\(639\) 2.83096 1.63445i 0.111991 0.0646580i
\(640\) 6.66106 11.5373i 0.263302 0.456052i
\(641\) 19.8213 34.3314i 0.782893 1.35601i −0.147357 0.989083i \(-0.547077\pi\)
0.930250 0.366926i \(-0.119590\pi\)
\(642\) −3.25641 + 1.88009i −0.128520 + 0.0742012i
\(643\) 20.8300i 0.821453i 0.911759 + 0.410727i \(0.134725\pi\)
−0.911759 + 0.410727i \(0.865275\pi\)
\(644\) −2.31066 1.39748i −0.0910529 0.0550684i
\(645\) 8.96568i 0.353023i
\(646\) −1.40821 2.43909i −0.0554052 0.0959646i
\(647\) −7.87206 + 13.6348i −0.309482 + 0.536039i −0.978249 0.207433i \(-0.933489\pi\)
0.668767 + 0.743472i \(0.266822\pi\)
\(648\) −6.31269 3.64463i −0.247986 0.143175i
\(649\) 2.53437 + 4.38966i 0.0994828 + 0.172309i
\(650\) 2.97028 1.82769i 0.116504 0.0716877i
\(651\) −23.5864 0.479800i −0.924426 0.0188049i
\(652\) 1.31352i 0.0514413i
\(653\) 13.5132 + 23.4055i 0.528812 + 0.915930i 0.999436 + 0.0335954i \(0.0106958\pi\)
−0.470623 + 0.882334i \(0.655971\pi\)
\(654\) −0.00814244 + 0.0141031i −0.000318395 + 0.000551476i
\(655\) −11.8538 6.84378i −0.463165 0.267409i
\(656\) 21.9103 12.6499i 0.855453 0.493896i
\(657\) 7.93734i 0.309665i
\(658\) 4.82305 2.65529i 0.188022 0.103514i
\(659\) −6.79491 −0.264692 −0.132346 0.991204i \(-0.542251\pi\)
−0.132346 + 0.991204i \(0.542251\pi\)
\(660\) 11.8734 + 20.5653i 0.462172 + 0.800505i
\(661\) 6.23994 + 3.60263i 0.242705 + 0.140126i 0.616420 0.787418i \(-0.288583\pi\)
−0.373714 + 0.927544i \(0.621916\pi\)
\(662\) −3.04522 + 5.27448i −0.118356 + 0.204998i
\(663\) −10.8350 + 20.0431i −0.420796 + 0.778409i
\(664\) −3.44930 −0.133859
\(665\) −6.55880 + 3.61090i −0.254339 + 0.140025i
\(666\) −2.31866 −0.0898463
\(667\) −1.93339 3.34874i −0.0748613 0.129664i
\(668\) −22.8831 13.2115i −0.885372 0.511170i
\(669\) −2.81087 1.62285i −0.108674 0.0627432i
\(670\) −0.410750 + 0.237147i −0.0158687 + 0.00916178i
\(671\) 40.3703i 1.55848i
\(672\) 14.2832 + 0.290552i 0.550987 + 0.0112083i
\(673\) −8.32130 −0.320763 −0.160381 0.987055i \(-0.551272\pi\)
−0.160381 + 0.987055i \(0.551272\pi\)
\(674\) −2.07756 + 1.19948i −0.0800246 + 0.0462022i
\(675\) 8.21824 14.2344i 0.316320 0.547883i
\(676\) −13.4539 20.5518i −0.517456 0.790454i
\(677\) 14.9978 + 25.9770i 0.576413 + 0.998376i 0.995887 + 0.0906086i \(0.0288812\pi\)
−0.419474 + 0.907767i \(0.637785\pi\)
\(678\) 4.46391i 0.171435i
\(679\) −9.01372 + 14.9037i −0.345915 + 0.571953i
\(680\) 8.08982 0.310231
\(681\) −34.2671 + 19.7841i −1.31312 + 0.758128i
\(682\) 10.4701 + 6.04493i 0.400922 + 0.231472i
\(683\) −31.2496 18.0420i −1.19573 0.690356i −0.236132 0.971721i \(-0.575880\pi\)
−0.959601 + 0.281365i \(0.909213\pi\)
\(684\) 2.78324 1.60690i 0.106420 0.0614415i
\(685\) 24.0064 0.917236
\(686\) 2.74703 + 5.50874i 0.104882 + 0.210325i
\(687\) 27.7205i 1.05760i
\(688\) 7.11470 + 12.3230i 0.271245 + 0.469811i
\(689\) 10.0161 0.280651i 0.381583 0.0106920i
\(690\) 0.189445 0.328128i 0.00721204 0.0124916i
\(691\) −22.3155 + 12.8838i −0.848920 + 0.490124i −0.860286 0.509811i \(-0.829715\pi\)
0.0113665 + 0.999935i \(0.496382\pi\)
\(692\) 10.2724 0.390497
\(693\) 7.08465 11.7141i 0.269123 0.444983i
\(694\) 7.00589i 0.265940i
\(695\) −23.1332 + 13.3559i −0.877491 + 0.506620i
\(696\) 11.7000 + 6.75501i 0.443488 + 0.256048i
\(697\) 28.3168 + 16.3487i 1.07258 + 0.619252i
\(698\) 5.11242 + 8.85496i 0.193508 + 0.335165i
\(699\) −31.7369 −1.20040
\(700\) −0.295890 + 14.5456i −0.0111836 + 0.549772i
\(701\) −41.7872 −1.57828 −0.789141 0.614213i \(-0.789474\pi\)
−0.789141 + 0.614213i \(0.789474\pi\)
\(702\) 5.95415 + 3.21872i 0.224725 + 0.121483i
\(703\) −7.85834 + 13.6110i −0.296383 + 0.513350i
\(704\) 28.2071 + 16.2854i 1.06310 + 0.613778i
\(705\) −6.60635 11.4425i −0.248809 0.430951i
\(706\) −2.03471 −0.0765774
\(707\) 0.164161 0.0903778i 0.00617393 0.00339901i
\(708\) 2.34782i 0.0882364i
\(709\) −0.297781 + 0.171924i −0.0111834 + 0.00645673i −0.505581 0.862779i \(-0.668722\pi\)
0.494398 + 0.869236i \(0.335389\pi\)
\(710\) −1.56552 0.903855i −0.0587530 0.0339211i
\(711\) −0.0569657 + 0.0986674i −0.00213638 + 0.00370032i
\(712\) −6.28124 10.8794i −0.235399 0.407724i
\(713\) 3.29931i 0.123560i
\(714\) 2.68005 + 4.86802i 0.100298 + 0.182181i
\(715\) −16.2668 26.4361i −0.608342 0.988652i
\(716\) 5.06227 + 8.76810i 0.189186 + 0.327679i
\(717\) 25.2466 + 14.5761i 0.942852 + 0.544356i
\(718\) 3.22881 5.59246i 0.120498 0.208709i
\(719\) 4.39005 + 7.60379i 0.163721 + 0.283574i 0.936200 0.351467i \(-0.114317\pi\)
−0.772479 + 0.635040i \(0.780984\pi\)
\(720\) 4.20702i 0.156786i
\(721\) 0.341055 16.7659i 0.0127015 0.624393i
\(722\) 5.04149i 0.187625i
\(723\) 4.08416 2.35799i 0.151891 0.0876946i
\(724\) 7.12367 12.3386i 0.264749 0.458559i
\(725\) −10.4164 + 18.0416i −0.386854 + 0.670050i
\(726\) 10.2799 5.93512i 0.381524 0.220273i
\(727\) 17.3658 0.644064 0.322032 0.946729i \(-0.395634\pi\)
0.322032 + 0.946729i \(0.395634\pi\)
\(728\) −12.3320 + 0.0946291i −0.457054 + 0.00350719i
\(729\) 29.6343 1.09757
\(730\) 3.80130 2.19468i 0.140692 0.0812288i
\(731\) −9.19502 + 15.9262i −0.340090 + 0.589053i
\(732\) −9.34968 + 16.1941i −0.345574 + 0.598552i
\(733\) −7.84528 + 4.52947i −0.289772 + 0.167300i −0.637839 0.770170i \(-0.720172\pi\)
0.348067 + 0.937470i \(0.386838\pi\)
\(734\) 1.79638i 0.0663056i
\(735\) 13.0833 6.85991i 0.482583 0.253032i
\(736\) 1.99796i 0.0736458i
\(737\) −2.93919 5.09082i −0.108266 0.187523i
\(738\) 1.09071 1.88917i 0.0401498 0.0695414i
\(739\) −6.13010 3.53921i −0.225499 0.130192i 0.382995 0.923751i \(-0.374893\pi\)
−0.608494 + 0.793558i \(0.708226\pi\)
\(740\) −10.9655 18.9928i −0.403100 0.698190i
\(741\) 8.77531 5.39966i 0.322369 0.198362i
\(742\) 1.26472 2.09115i 0.0464292 0.0767685i
\(743\) 14.6779i 0.538479i −0.963073 0.269240i \(-0.913228\pi\)
0.963073 0.269240i \(-0.0867724\pi\)
\(744\) −5.76367 9.98297i −0.211306 0.365993i
\(745\) −2.22684 + 3.85699i −0.0815849 + 0.141309i
\(746\) 4.67768 + 2.70066i 0.171262 + 0.0988782i
\(747\) 2.00768 1.15913i 0.0734571 0.0424105i
\(748\) 48.7085i 1.78096i
\(749\) −0.416997 + 20.4991i −0.0152367 + 0.749020i
\(750\) −5.54848 −0.202602
\(751\) −15.8556 27.4628i −0.578580 1.00213i −0.995643 0.0932523i \(-0.970274\pi\)
0.417062 0.908878i \(-0.363060\pi\)
\(752\) −18.1604 10.4849i −0.662241 0.382345i
\(753\) 9.11788 15.7926i 0.332274 0.575516i
\(754\) −7.54669 4.07962i −0.274834 0.148571i
\(755\) 3.68467 0.134099
\(756\) −24.7345 + 13.6174i −0.899585 + 0.495259i
\(757\) 15.5317 0.564510 0.282255 0.959339i \(-0.408918\pi\)
0.282255 + 0.959339i \(0.408918\pi\)
\(758\) 4.18344 + 7.24593i 0.151949 + 0.263184i
\(759\) 4.06680 + 2.34797i 0.147616 + 0.0852259i
\(760\) −3.16825 1.82919i −0.114925 0.0663518i
\(761\) −0.216826 + 0.125185i −0.00785993 + 0.00453794i −0.503925 0.863748i \(-0.668111\pi\)
0.496065 + 0.868285i \(0.334778\pi\)
\(762\) 6.98474i 0.253030i
\(763\) 0.0428255 + 0.0777879i 0.00155039 + 0.00281611i
\(764\) 25.5961 0.926036
\(765\) −4.70870 + 2.71857i −0.170243 + 0.0982901i
\(766\) 0.633903 1.09795i 0.0229039 0.0396706i
\(767\) 0.0859562 + 3.06767i 0.00310370 + 0.110767i
\(768\) −5.74859 9.95686i −0.207435 0.359287i
\(769\) 24.0146i 0.865988i −0.901397 0.432994i \(-0.857457\pi\)
0.901397 0.432994i \(-0.142543\pi\)
\(770\) −7.56896 0.153969i −0.272766 0.00554867i
\(771\) −8.50731 −0.306383
\(772\) 30.3650 17.5312i 1.09286 0.630963i
\(773\) −26.4192 15.2531i −0.950231 0.548616i −0.0570784 0.998370i \(-0.518179\pi\)
−0.893153 + 0.449753i \(0.851512\pi\)
\(774\) 1.06253 + 0.613451i 0.0381918 + 0.0220501i
\(775\) 15.3939 8.88768i 0.552966 0.319255i
\(776\) −8.51064 −0.305514
\(777\) 16.0481 26.5347i 0.575722 0.951928i
\(778\) 0.954237i 0.0342110i
\(779\) −7.39323 12.8055i −0.264890 0.458803i
\(780\) 0.402701 + 14.3719i 0.0144190 + 0.514596i
\(781\) 11.2023 19.4030i 0.400851 0.694294i
\(782\) 0.673043 0.388582i 0.0240680 0.0138956i
\(783\) −40.4311 −1.44489
\(784\) 12.5388 19.8109i 0.447815 0.707532i
\(785\) 13.6019i 0.485473i
\(786\) 3.97865 2.29707i 0.141914 0.0819339i
\(787\) 17.1899 + 9.92461i 0.612755 + 0.353774i 0.774043 0.633133i \(-0.218231\pi\)
−0.161288 + 0.986907i \(0.551565\pi\)
\(788\) −4.36606 2.52075i −0.155534 0.0897978i
\(789\) −12.7843 22.1431i −0.455134 0.788315i
\(790\) 0.0630042 0.00224159
\(791\) 20.8277 + 12.5965i 0.740547 + 0.447879i
\(792\) 6.68923 0.237691
\(793\) 11.6234 21.5016i 0.412760 0.763544i
\(794\) 3.17724 5.50314i 0.112756 0.195299i
\(795\) −5.07910 2.93242i −0.180137 0.104002i
\(796\) 19.0841 + 33.0546i 0.676418 + 1.17159i
\(797\) −52.2894 −1.85219 −0.926093 0.377296i \(-0.876854\pi\)
−0.926093 + 0.377296i \(0.876854\pi\)
\(798\) 0.0511093 2.51248i 0.00180925 0.0889407i
\(799\) 27.1014i 0.958777i
\(800\) −9.32207 + 5.38210i −0.329585 + 0.190286i
\(801\) 7.31202 + 4.22160i 0.258358 + 0.149163i
\(802\) −0.498271 + 0.863031i −0.0175946 + 0.0304747i
\(803\) 27.2008 + 47.1131i 0.959894 + 1.66259i
\(804\) 2.72283i 0.0960269i
\(805\) −0.996393 1.80984i −0.0351182 0.0637884i
\(806\) 3.83602 + 6.23414i 0.135118 + 0.219588i
\(807\) −16.2981 28.2292i −0.573722 0.993715i
\(808\) 0.0792988 + 0.0457832i 0.00278972 + 0.00161065i
\(809\) 1.18230 2.04780i 0.0415674 0.0719969i −0.844493 0.535566i \(-0.820098\pi\)
0.886061 + 0.463569i \(0.153432\pi\)
\(810\) −1.35460 2.34624i −0.0475959 0.0824385i
\(811\) 23.6646i 0.830978i 0.909598 + 0.415489i \(0.136390\pi\)
−0.909598 + 0.415489i \(0.863610\pi\)
\(812\) 31.3502 17.2596i 1.10017 0.605693i
\(813\) 38.4952i 1.35008i
\(814\) −13.7627 + 7.94591i −0.482383 + 0.278504i
\(815\) −0.502467 + 0.870298i −0.0176006 + 0.0304852i
\(816\) 10.5827 18.3297i 0.370468 0.641669i
\(817\) 7.20218 4.15818i 0.251972 0.145476i
\(818\) 11.3275 0.396058
\(819\) 7.14607 4.19923i 0.249704 0.146733i
\(820\) 20.6330 0.720536
\(821\) −3.09823 + 1.78877i −0.108129 + 0.0624284i −0.553089 0.833122i \(-0.686551\pi\)
0.444960 + 0.895550i \(0.353218\pi\)
\(822\) −4.02879 + 6.97808i −0.140520 + 0.243388i
\(823\) −14.9711 + 25.9307i −0.521859 + 0.903887i 0.477817 + 0.878459i \(0.341428\pi\)
−0.999677 + 0.0254278i \(0.991905\pi\)
\(824\) 7.09615 4.09696i 0.247206 0.142725i
\(825\) 25.2998i 0.880827i
\(826\) 0.640464 + 0.387350i 0.0222846 + 0.0134776i
\(827\) 9.32620i 0.324304i 0.986766 + 0.162152i \(0.0518435\pi\)
−0.986766 + 0.162152i \(0.948157\pi\)
\(828\) 0.443409 + 0.768007i 0.0154095 + 0.0266901i
\(829\) 19.1134 33.1054i 0.663836 1.14980i −0.315763 0.948838i \(-0.602261\pi\)
0.979599 0.200960i \(-0.0644062\pi\)
\(830\) −1.11025 0.641002i −0.0385373 0.0222495i
\(831\) −6.84385 11.8539i −0.237411 0.411207i
\(832\) 10.3345 + 16.7951i 0.358283 + 0.582266i
\(833\) 30.2759 + 1.23227i 1.04900 + 0.0426956i
\(834\) 8.96568i 0.310456i
\(835\) −10.1078 17.5072i −0.349794 0.605860i
\(836\) 11.0135 19.0760i 0.380910 0.659756i
\(837\) 29.8757 + 17.2488i 1.03266 + 0.596205i
\(838\) −10.0101 + 5.77933i −0.345793 + 0.199644i
\(839\) 23.4981i 0.811244i 0.914041 + 0.405622i \(0.132945\pi\)
−0.914041 + 0.405622i \(0.867055\pi\)
\(840\) 6.17652 + 3.73553i 0.213110 + 0.128888i
\(841\) 22.2451 0.767071
\(842\) −4.01178 6.94860i −0.138255 0.239465i
\(843\) 22.4726 + 12.9746i 0.773998 + 0.446868i
\(844\) −12.4017 + 21.4803i −0.426883 + 0.739384i
\(845\) −1.05234 18.7636i −0.0362016 0.645487i
\(846\) −1.80808 −0.0621632
\(847\) 1.31639 64.7121i 0.0452316 2.22353i
\(848\) −9.30806 −0.319640
\(849\) −7.01205 12.1452i −0.240653 0.416823i
\(850\) −3.62608 2.09352i −0.124374 0.0718072i
\(851\) −3.75584 2.16843i −0.128748 0.0743329i
\(852\) −8.98738 + 5.18887i −0.307903 + 0.177768i
\(853\) 40.9295i 1.40140i 0.713456 + 0.700700i \(0.247129\pi\)
−0.713456 + 0.700700i \(0.752871\pi\)
\(854\) −2.87508 5.22226i −0.0983830 0.178702i
\(855\) 2.45879 0.0840888
\(856\) −8.67624 + 5.00923i −0.296548 + 0.171212i
\(857\) −5.83099 + 10.0996i −0.199183 + 0.344995i −0.948264 0.317484i \(-0.897162\pi\)
0.749081 + 0.662479i \(0.230495\pi\)
\(858\) 10.4142 0.291808i 0.355537 0.00996215i
\(859\) −14.1388 24.4891i −0.482410 0.835559i 0.517386 0.855752i \(-0.326905\pi\)
−0.999796 + 0.0201934i \(0.993572\pi\)
\(860\) 11.6046i 0.395715i
\(861\) 14.0705 + 25.5576i 0.479523 + 0.871001i
\(862\) 1.58369 0.0539407
\(863\) −9.91101 + 5.72212i −0.337375 + 0.194783i −0.659110 0.752046i \(-0.729067\pi\)
0.321736 + 0.946829i \(0.395734\pi\)
\(864\) −18.0918 10.4453i −0.615496 0.355357i
\(865\) 6.80617 + 3.92954i 0.231417 + 0.133609i
\(866\) 6.33924 3.65996i 0.215416 0.124371i
\(867\) 2.53683 0.0861553
\(868\) −30.5289 0.621025i −1.03622 0.0210790i
\(869\) 0.780871i 0.0264892i
\(870\) 2.51064 + 4.34855i 0.0851186 + 0.147430i
\(871\) −0.0996859 3.55766i −0.00337773 0.120547i
\(872\) −0.0216944 + 0.0375757i −0.000734664 + 0.00127248i
\(873\) 4.95364 2.85998i 0.167655 0.0967958i
\(874\) −0.351449 −0.0118879
\(875\) −15.6570 + 25.8881i −0.529303 + 0.875177i
\(876\) 25.1985i 0.851380i
\(877\) −48.7993 + 28.1743i −1.64783 + 0.951378i −0.669904 + 0.742447i \(0.733665\pi\)
−0.977930 + 0.208930i \(0.933002\pi\)
\(878\) −0.988000 0.570422i −0.0333434 0.0192508i
\(879\) 14.7081 + 8.49173i 0.496092 + 0.286419i
\(880\) 14.4172 + 24.9713i 0.486003 + 0.841782i
\(881\) 1.16418 0.0392221 0.0196111 0.999808i \(-0.493757\pi\)
0.0196111 + 0.999808i \(0.493757\pi\)
\(882\) 0.0822115 2.01988i 0.00276821 0.0680128i
\(883\) 12.1881 0.410162 0.205081 0.978745i \(-0.434254\pi\)
0.205081 + 0.978745i \(0.434254\pi\)
\(884\) −14.0242 + 25.9426i −0.471684 + 0.872543i
\(885\) 0.898123 1.55560i 0.0301901 0.0522908i
\(886\) −2.50597 1.44682i −0.0841896 0.0486069i
\(887\) −15.3320 26.5559i −0.514799 0.891659i −0.999853 0.0171740i \(-0.994533\pi\)
0.485053 0.874485i \(-0.338800\pi\)
\(888\) 15.1524 0.508481
\(889\) 32.5894 + 19.7099i 1.09301 + 0.661049i
\(890\) 4.66910i 0.156509i
\(891\) 29.0792 16.7889i 0.974190 0.562449i
\(892\) −3.63822 2.10053i −0.121817 0.0703308i
\(893\) −6.12790 + 10.6138i −0.205062 + 0.355178i
\(894\) −0.747424 1.29458i −0.0249976 0.0432971i
\(895\) 7.74598i 0.258920i
\(896\) 24.3769 + 0.495879i 0.814374 + 0.0165662i
\(897\) 1.48999 + 2.42146i 0.0497492 + 0.0808503i
\(898\) 2.92689 + 5.06952i 0.0976716 + 0.169172i
\(899\) −37.8665 21.8622i −1.26292 0.729147i
\(900\) 2.38891 4.13771i 0.0796303 0.137924i
\(901\) −6.01486 10.4180i −0.200384 0.347075i
\(902\) 14.9512i 0.497822i
\(903\) −14.3744 + 7.91370i −0.478350 + 0.263352i
\(904\) 11.8934i 0.395570i
\(905\) 9.43987 5.45011i 0.313792 0.181168i
\(906\) −0.618368 + 1.07105i −0.0205439 + 0.0355831i
\(907\) −5.82396 + 10.0874i −0.193382 + 0.334947i −0.946369 0.323088i \(-0.895279\pi\)
0.752987 + 0.658035i \(0.228612\pi\)
\(908\) −44.3532 + 25.6074i −1.47191 + 0.849810i
\(909\) −0.0615414 −0.00204120
\(910\) −3.98696 2.26126i −0.132166 0.0749601i
\(911\) −26.5833 −0.880743 −0.440371 0.897816i \(-0.645153\pi\)
−0.440371 + 0.897816i \(0.645153\pi\)
\(912\) −8.28909 + 4.78571i −0.274479 + 0.158471i
\(913\) 7.94455 13.7604i 0.262926 0.455402i
\(914\) 1.50777 2.61153i 0.0498725 0.0863817i
\(915\) −12.3896 + 7.15316i −0.409589 + 0.236476i
\(916\) 35.8797i 1.18550i
\(917\) 0.509482 25.0455i 0.0168246 0.827077i
\(918\) 8.12600i 0.268198i
\(919\) 22.8540 + 39.5842i 0.753883 + 1.30576i 0.945928 + 0.324377i \(0.105155\pi\)
−0.192045 + 0.981386i \(0.561512\pi\)
\(920\) 0.504748 0.874250i 0.0166411 0.0288232i
\(921\) −17.4821 10.0933i −0.576055 0.332585i
\(922\) −1.09405 1.89494i −0.0360305 0.0624066i
\(923\) 11.5530 7.10883i 0.380271 0.233990i
\(924\) −22.4915 + 37.1886i −0.739916 + 1.22342i
\(925\) 23.3653i 0.768246i
\(926\) 0.577242 + 0.999813i 0.0189694 + 0.0328559i
\(927\) −2.75356 + 4.76930i −0.0904386 + 0.156644i
\(928\) 22.9308 + 13.2391i 0.752740 + 0.434595i
\(929\) −9.58268 + 5.53257i −0.314398 + 0.181518i −0.648893 0.760880i \(-0.724768\pi\)
0.334495 + 0.942398i \(0.391434\pi\)
\(930\) 4.28437i 0.140490i
\(931\) −11.5785 7.32830i −0.379469 0.240175i
\(932\) −41.0784 −1.34557
\(933\) 22.4190 + 38.8309i 0.733965 + 1.27127i
\(934\) −8.57360 4.94997i −0.280537 0.161968i
\(935\) −18.6327 + 32.2729i −0.609356 + 1.05544i
\(936\) 3.56274 + 1.92596i 0.116452 + 0.0629521i
\(937\) −57.6584 −1.88362 −0.941808 0.336150i \(-0.890875\pi\)
−0.941808 + 0.336150i \(0.890875\pi\)
\(938\) −0.742765 0.449221i −0.0242521 0.0146676i
\(939\) 16.1848 0.528170
\(940\) −8.55086 14.8105i −0.278898 0.483066i
\(941\) 14.7003 + 8.48723i 0.479216 + 0.276676i 0.720090 0.693881i \(-0.244101\pi\)
−0.240874 + 0.970557i \(0.577434\pi\)
\(942\) −3.95375 2.28270i −0.128820 0.0743743i
\(943\) 3.53354 2.04009i 0.115068 0.0664345i
\(944\) 2.85082i 0.0927862i
\(945\) −21.5975 0.439340i −0.702566 0.0142917i
\(946\) 8.40904 0.273401
\(947\) 14.4593 8.34808i 0.469864 0.271276i −0.246319 0.969189i \(-0.579221\pi\)
0.716183 + 0.697913i \(0.245888\pi\)
\(948\) 0.180848 0.313238i 0.00587366 0.0101735i
\(949\) 0.922546 + 32.9245i 0.0299471 + 1.06877i
\(950\) 0.946733 + 1.63979i 0.0307161 + 0.0532018i
\(951\) 34.8658i 1.13060i
\(952\) 7.14062 + 12.9702i 0.231429 + 0.420365i
\(953\) 18.2473 0.591089 0.295545 0.955329i \(-0.404499\pi\)
0.295545 + 0.955329i \(0.404499\pi\)
\(954\) −0.695046 + 0.401285i −0.0225029 + 0.0129921i
\(955\) 16.9593 + 9.79143i 0.548789 + 0.316843i
\(956\) 32.6777 + 18.8665i 1.05687 + 0.610186i
\(957\) −53.8957 + 31.1167i −1.74220 + 1.00586i
\(958\) −11.6948 −0.377841
\(959\) 21.1896 + 38.4886i 0.684248 + 1.24286i
\(960\) 11.5423i 0.372527i
\(961\) 3.15382 + 5.46257i 0.101736 + 0.176212i
\(962\) −9.61793 + 0.269495i −0.310094 + 0.00868886i
\(963\) 3.36669 5.83127i 0.108490 0.187910i
\(964\) 5.28629 3.05204i 0.170260 0.0982996i
\(965\) 26.8253 0.863537
\(966\) 0.693293 + 0.0141031i 0.0223063 + 0.000453760i
\(967\) 29.5845i 0.951374i −0.879615 0.475687i \(-0.842199\pi\)
0.879615 0.475687i \(-0.157801\pi\)
\(968\) 27.3894 15.8133i 0.880328 0.508258i
\(969\) −10.7128 6.18504i −0.344145 0.198692i
\(970\) −2.73937 1.58158i −0.0879558 0.0507813i
\(971\) −7.56504 13.1030i −0.242774 0.420497i 0.718730 0.695290i \(-0.244724\pi\)
−0.961503 + 0.274793i \(0.911391\pi\)
\(972\) 16.4627 0.528040
\(973\) −41.8320 25.2998i −1.34107 0.811075i
\(974\) −0.598787 −0.0191864
\(975\) 7.28433 13.4749i 0.233285 0.431542i
\(976\) −11.3528 + 19.6636i −0.363393 + 0.629415i
\(977\) −28.1143 16.2318i −0.899457 0.519301i −0.0224327 0.999748i \(-0.507141\pi\)
−0.877024 + 0.480447i \(0.840474\pi\)
\(978\) −0.168650 0.292110i −0.00539283 0.00934065i
\(979\) 57.8686 1.84949
\(980\) 16.9342 8.87906i 0.540943 0.283631i
\(981\) 0.0291614i 0.000931052i
\(982\) −2.35838 + 1.36161i −0.0752590 + 0.0434508i
\(983\) −38.3602 22.1473i −1.22350 0.706388i −0.257838 0.966188i \(-0.583010\pi\)
−0.965662 + 0.259800i \(0.916343\pi\)
\(984\) −7.12779 + 12.3457i −0.227226 + 0.393567i
\(985\) −1.92855 3.34034i −0.0614487 0.106432i
\(986\) 10.2994i 0.328001i
\(987\) 12.5142 20.6917i 0.398333 0.658624i
\(988\) 11.3582 6.98900i 0.361354 0.222350i
\(989\) 1.14741 + 1.98737i 0.0364855 + 0.0631948i
\(990\) 2.15310 + 1.24309i 0.0684301 + 0.0395081i
\(991\) 4.26058 7.37955i 0.135342 0.234419i −0.790386 0.612609i \(-0.790120\pi\)
0.925728 + 0.378190i \(0.123453\pi\)
\(992\) −11.2962 19.5655i −0.358654 0.621206i
\(993\) 26.7500i 0.848887i
\(994\) 0.0672870 3.30775i 0.00213422 0.104916i
\(995\) 29.2014i 0.925746i
\(996\) −6.37374 + 3.67988i −0.201960 + 0.116601i
\(997\) 3.38953 5.87083i 0.107347 0.185931i −0.807347 0.590076i \(-0.799098\pi\)
0.914695 + 0.404145i \(0.132431\pi\)
\(998\) 6.06858 10.5111i 0.192098 0.332723i
\(999\) −39.2709 + 22.6731i −1.24248 + 0.717344i
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 91.2.r.a.25.4 16
3.2 odd 2 819.2.dl.e.298.5 16
7.2 even 3 inner 91.2.r.a.51.5 yes 16
7.3 odd 6 637.2.c.e.246.4 8
7.4 even 3 637.2.c.f.246.4 8
7.5 odd 6 637.2.r.f.324.5 16
7.6 odd 2 637.2.r.f.116.4 16
13.5 odd 4 1183.2.e.i.508.5 16
13.8 odd 4 1183.2.e.i.508.4 16
13.12 even 2 inner 91.2.r.a.25.5 yes 16
21.2 odd 6 819.2.dl.e.415.4 16
39.38 odd 2 819.2.dl.e.298.4 16
91.12 odd 6 637.2.r.f.324.4 16
91.18 odd 12 8281.2.a.ck.1.4 8
91.25 even 6 637.2.c.f.246.5 8
91.31 even 12 8281.2.a.cj.1.4 8
91.38 odd 6 637.2.c.e.246.5 8
91.44 odd 12 1183.2.e.i.170.5 16
91.51 even 6 inner 91.2.r.a.51.4 yes 16
91.60 odd 12 8281.2.a.ck.1.5 8
91.73 even 12 8281.2.a.cj.1.5 8
91.86 odd 12 1183.2.e.i.170.4 16
91.90 odd 2 637.2.r.f.116.5 16
273.233 odd 6 819.2.dl.e.415.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.r.a.25.4 16 1.1 even 1 trivial
91.2.r.a.25.5 yes 16 13.12 even 2 inner
91.2.r.a.51.4 yes 16 91.51 even 6 inner
91.2.r.a.51.5 yes 16 7.2 even 3 inner
637.2.c.e.246.4 8 7.3 odd 6
637.2.c.e.246.5 8 91.38 odd 6
637.2.c.f.246.4 8 7.4 even 3
637.2.c.f.246.5 8 91.25 even 6
637.2.r.f.116.4 16 7.6 odd 2
637.2.r.f.116.5 16 91.90 odd 2
637.2.r.f.324.4 16 91.12 odd 6
637.2.r.f.324.5 16 7.5 odd 6
819.2.dl.e.298.4 16 39.38 odd 2
819.2.dl.e.298.5 16 3.2 odd 2
819.2.dl.e.415.4 16 21.2 odd 6
819.2.dl.e.415.5 16 273.233 odd 6
1183.2.e.i.170.4 16 91.86 odd 12
1183.2.e.i.170.5 16 91.44 odd 12
1183.2.e.i.508.4 16 13.8 odd 4
1183.2.e.i.508.5 16 13.5 odd 4
8281.2.a.cj.1.4 8 91.31 even 12
8281.2.a.cj.1.5 8 91.73 even 12
8281.2.a.ck.1.4 8 91.18 odd 12
8281.2.a.ck.1.5 8 91.60 odd 12