Properties

Label 539.2.q.b.410.1
Level $539$
Weight $2$
Character 539.410
Analytic conductor $4.304$
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] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + 240 x^{7} + 390 x^{6} - 1375 x^{5} - 300 x^{4} + 500 x^{3} + 375 x^{2} + 625 x + 625 \) 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: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 410.1
Root \(-2.41283 + 0.512862i\) of defining polynomial
Character \(\chi\) \(=\) 539.410
Dual form 539.2.q.b.422.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33993 - 0.596574i) q^{2} +(-1.58268 - 0.336408i) q^{3} +(0.101241 + 0.112439i) q^{4} +(0.0487868 - 0.464175i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(-0.348943 - 0.155360i) q^{9} +O(q^{10})\) \(q+(-1.33993 - 0.596574i) q^{2} +(-1.58268 - 0.336408i) q^{3} +(0.101241 + 0.112439i) q^{4} +(0.0487868 - 0.464175i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(-0.348943 - 0.155360i) q^{9} +(-0.342285 + 0.592855i) q^{10} +(-1.01240 - 3.15833i) q^{11} +(-0.122406 - 0.212013i) q^{12} +(-1.28012 + 0.930062i) q^{13} +(-0.233366 + 0.718226i) q^{15} +(0.447352 - 4.25627i) q^{16} +(-4.77540 + 2.12614i) q^{17} +(0.374875 + 0.416341i) q^{18} +(-2.82502 + 3.13750i) q^{19} +(0.0571308 - 0.0415079i) q^{20} +(-0.527635 + 4.83590i) q^{22} +(0.902527 + 1.56322i) q^{23} +(-0.458605 - 4.36334i) q^{24} +(4.67766 + 0.994267i) q^{25} +(2.27012 - 0.482528i) q^{26} +(4.42705 + 3.21644i) q^{27} +(0.840363 - 2.58637i) q^{29} +(0.741168 - 0.823150i) q^{30} +(0.135245 + 1.28677i) q^{31} +(-0.427051 + 0.739674i) q^{32} +(0.539813 + 5.33919i) q^{33} +7.66708 q^{34} +(-0.0178588 - 0.0549637i) q^{36} +(1.89977 - 0.403808i) q^{37} +(5.65706 - 2.51869i) q^{38} +(2.33890 - 1.04134i) q^{39} +(1.23791 - 0.263126i) q^{40} +(0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(0.252625 - 0.433586i) q^{44} +(-0.0891378 + 0.154391i) q^{45} +(-0.276742 - 2.63303i) q^{46} +(4.27929 - 4.75263i) q^{47} +(-2.13986 + 6.58580i) q^{48} +(-5.67457 - 4.12281i) q^{50} +(8.27316 - 1.75851i) q^{51} +(-0.234176 - 0.0497757i) q^{52} +(1.38024 + 13.1321i) q^{53} +(-4.01308 - 6.95085i) q^{54} +(-1.51541 + 0.315846i) q^{55} +(5.52656 - 4.01528i) q^{57} +(-2.66898 + 2.96421i) q^{58} +(5.75712 + 6.39393i) q^{59} +(-0.104383 + 0.0464744i) q^{60} +(-1.59303 + 15.1567i) q^{61} +(0.586436 - 1.80486i) q^{62} +(-5.91123 + 4.29476i) q^{64} +(0.369259 + 0.639575i) q^{65} +(2.46191 - 7.47616i) q^{66} +(2.33791 - 4.04938i) q^{67} +(-0.722528 - 0.321690i) q^{68} +(-0.902527 - 2.77769i) q^{69} +(-7.88234 - 5.72685i) q^{71} +(0.108262 - 1.03004i) q^{72} +(8.91283 + 9.89870i) q^{73} +(-2.78645 - 0.592278i) q^{74} +(-7.06874 - 3.14721i) q^{75} -0.638786 q^{76} -3.75519 q^{78} +(3.27261 + 1.45706i) q^{79} +(-1.95383 - 0.415299i) q^{80} +(-5.15780 - 5.72831i) q^{81} +(0.159620 - 1.51868i) q^{82} +(-13.9627 - 10.1445i) q^{83} +(0.753927 + 2.32035i) q^{85} +(-11.6684 - 5.19508i) q^{86} +(-2.20010 + 3.81068i) q^{87} +(7.29650 - 5.25721i) q^{88} +(-4.45991 - 7.72479i) q^{89} +(0.211544 - 0.153696i) q^{90} +(-0.0843952 + 0.259742i) q^{92} +(0.218831 - 2.08204i) q^{93} +(-8.56923 + 3.81526i) q^{94} +(1.31852 + 1.46437i) q^{95} +(0.924716 - 1.02700i) q^{96} +(-2.18727 + 1.58915i) q^{97} +(-0.137407 + 1.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33993 0.596574i −0.947471 0.421841i −0.125961 0.992035i \(-0.540201\pi\)
−0.821510 + 0.570194i \(0.806868\pi\)
\(3\) −1.58268 0.336408i −0.913758 0.194225i −0.273041 0.962002i \(-0.588030\pi\)
−0.640717 + 0.767777i \(0.721363\pi\)
\(4\) 0.101241 + 0.112439i 0.0506205 + 0.0562197i
\(5\) 0.0487868 0.464175i 0.0218181 0.207585i −0.978182 0.207750i \(-0.933386\pi\)
1.00000 0.000164961i \(5.25089e-5\pi\)
\(6\) 1.91998 + 1.39494i 0.783827 + 0.569484i
\(7\) 0 0
\(8\) 0.837913 + 2.57883i 0.296247 + 0.911755i
\(9\) −0.348943 0.155360i −0.116314 0.0517865i
\(10\) −0.342285 + 0.592855i −0.108240 + 0.187477i
\(11\) −1.01240 3.15833i −0.305250 0.952272i
\(12\) −0.122406 0.212013i −0.0353356 0.0612030i
\(13\) −1.28012 + 0.930062i −0.355042 + 0.257953i −0.750981 0.660324i \(-0.770419\pi\)
0.395939 + 0.918277i \(0.370419\pi\)
\(14\) 0 0
\(15\) −0.233366 + 0.718226i −0.0602548 + 0.185445i
\(16\) 0.447352 4.25627i 0.111838 1.06407i
\(17\) −4.77540 + 2.12614i −1.15820 + 0.515666i −0.893676 0.448712i \(-0.851883\pi\)
−0.264528 + 0.964378i \(0.585216\pi\)
\(18\) 0.374875 + 0.416341i 0.0883589 + 0.0981324i
\(19\) −2.82502 + 3.13750i −0.648103 + 0.719791i −0.974236 0.225533i \(-0.927588\pi\)
0.326133 + 0.945324i \(0.394254\pi\)
\(20\) 0.0571308 0.0415079i 0.0127748 0.00928146i
\(21\) 0 0
\(22\) −0.527635 + 4.83590i −0.112492 + 1.03102i
\(23\) 0.902527 + 1.56322i 0.188190 + 0.325954i 0.944647 0.328089i \(-0.106405\pi\)
−0.756457 + 0.654044i \(0.773071\pi\)
\(24\) −0.458605 4.36334i −0.0936124 0.890662i
\(25\) 4.67766 + 0.994267i 0.935532 + 0.198853i
\(26\) 2.27012 0.482528i 0.445207 0.0946316i
\(27\) 4.42705 + 3.21644i 0.851986 + 0.619004i
\(28\) 0 0
\(29\) 0.840363 2.58637i 0.156051 0.480277i −0.842215 0.539143i \(-0.818748\pi\)
0.998266 + 0.0588657i \(0.0187484\pi\)
\(30\) 0.741168 0.823150i 0.135318 0.150286i
\(31\) 0.135245 + 1.28677i 0.0242908 + 0.231111i 0.999931 + 0.0117351i \(0.00373548\pi\)
−0.975640 + 0.219376i \(0.929598\pi\)
\(32\) −0.427051 + 0.739674i −0.0754927 + 0.130757i
\(33\) 0.539813 + 5.33919i 0.0939694 + 0.929434i
\(34\) 7.66708 1.31489
\(35\) 0 0
\(36\) −0.0178588 0.0549637i −0.00297647 0.00916062i
\(37\) 1.89977 0.403808i 0.312320 0.0663856i −0.0490852 0.998795i \(-0.515631\pi\)
0.361405 + 0.932409i \(0.382297\pi\)
\(38\) 5.65706 2.51869i 0.917696 0.408585i
\(39\) 2.33890 1.04134i 0.374523 0.166749i
\(40\) 1.23791 0.263126i 0.195730 0.0416038i
\(41\) 0.321724 + 0.990166i 0.0502449 + 0.154638i 0.973031 0.230675i \(-0.0740935\pi\)
−0.922786 + 0.385313i \(0.874093\pi\)
\(42\) 0 0
\(43\) 8.70820 1.32799 0.663994 0.747738i \(-0.268860\pi\)
0.663994 + 0.747738i \(0.268860\pi\)
\(44\) 0.252625 0.433586i 0.0380846 0.0653655i
\(45\) −0.0891378 + 0.154391i −0.0132879 + 0.0230153i
\(46\) −0.276742 2.63303i −0.0408034 0.388219i
\(47\) 4.27929 4.75263i 0.624198 0.693243i −0.345258 0.938508i \(-0.612208\pi\)
0.969456 + 0.245265i \(0.0788751\pi\)
\(48\) −2.13986 + 6.58580i −0.308862 + 0.950578i
\(49\) 0 0
\(50\) −5.67457 4.12281i −0.802505 0.583054i
\(51\) 8.27316 1.75851i 1.15847 0.246241i
\(52\) −0.234176 0.0497757i −0.0324744 0.00690265i
\(53\) 1.38024 + 13.1321i 0.189590 + 1.80383i 0.513867 + 0.857870i \(0.328212\pi\)
−0.324277 + 0.945962i \(0.605121\pi\)
\(54\) −4.01308 6.95085i −0.546111 0.945892i
\(55\) −1.51541 + 0.315846i −0.204338 + 0.0425887i
\(56\) 0 0
\(57\) 5.52656 4.01528i 0.732011 0.531837i
\(58\) −2.66898 + 2.96421i −0.350455 + 0.389219i
\(59\) 5.75712 + 6.39393i 0.749514 + 0.832419i 0.990414 0.138131i \(-0.0441094\pi\)
−0.240900 + 0.970550i \(0.577443\pi\)
\(60\) −0.104383 + 0.0464744i −0.0134758 + 0.00599982i
\(61\) −1.59303 + 15.1567i −0.203967 + 1.94061i 0.116146 + 0.993232i \(0.462946\pi\)
−0.320112 + 0.947380i \(0.603721\pi\)
\(62\) 0.586436 1.80486i 0.0744774 0.229218i
\(63\) 0 0
\(64\) −5.91123 + 4.29476i −0.738904 + 0.536845i
\(65\) 0.369259 + 0.639575i 0.0458009 + 0.0793295i
\(66\) 2.46191 7.47616i 0.303040 0.920252i
\(67\) 2.33791 4.04938i 0.285622 0.494711i −0.687138 0.726527i \(-0.741133\pi\)
0.972760 + 0.231816i \(0.0744666\pi\)
\(68\) −0.722528 0.321690i −0.0876194 0.0390107i
\(69\) −0.902527 2.77769i −0.108651 0.334395i
\(70\) 0 0
\(71\) −7.88234 5.72685i −0.935461 0.679652i 0.0118626 0.999930i \(-0.496224\pi\)
−0.947324 + 0.320277i \(0.896224\pi\)
\(72\) 0.108262 1.03004i 0.0127588 0.121392i
\(73\) 8.91283 + 9.89870i 1.04317 + 1.15856i 0.987096 + 0.160129i \(0.0511909\pi\)
0.0560717 + 0.998427i \(0.482142\pi\)
\(74\) −2.78645 0.592278i −0.323918 0.0688509i
\(75\) −7.06874 3.14721i −0.816228 0.363408i
\(76\) −0.638786 −0.0732737
\(77\) 0 0
\(78\) −3.75519 −0.425191
\(79\) 3.27261 + 1.45706i 0.368197 + 0.163932i 0.582491 0.812837i \(-0.302078\pi\)
−0.214293 + 0.976769i \(0.568745\pi\)
\(80\) −1.95383 0.415299i −0.218445 0.0464318i
\(81\) −5.15780 5.72831i −0.573088 0.636479i
\(82\) 0.159620 1.51868i 0.0176271 0.167710i
\(83\) −13.9627 10.1445i −1.53261 1.11351i −0.954766 0.297357i \(-0.903895\pi\)
−0.577842 0.816148i \(-0.696105\pi\)
\(84\) 0 0
\(85\) 0.753927 + 2.32035i 0.0817748 + 0.251677i
\(86\) −11.6684 5.19508i −1.25823 0.560200i
\(87\) −2.20010 + 3.81068i −0.235875 + 0.408548i
\(88\) 7.29650 5.25721i 0.777809 0.560421i
\(89\) −4.45991 7.72479i −0.472750 0.818826i 0.526764 0.850012i \(-0.323405\pi\)
−0.999514 + 0.0311853i \(0.990072\pi\)
\(90\) 0.211544 0.153696i 0.0222987 0.0162009i
\(91\) 0 0
\(92\) −0.0843952 + 0.259742i −0.00879881 + 0.0270799i
\(93\) 0.218831 2.08204i 0.0226918 0.215898i
\(94\) −8.56923 + 3.81526i −0.883848 + 0.393515i
\(95\) 1.31852 + 1.46437i 0.135278 + 0.150241i
\(96\) 0.924716 1.02700i 0.0943784 0.104818i
\(97\) −2.18727 + 1.58915i −0.222084 + 0.161353i −0.693264 0.720684i \(-0.743828\pi\)
0.471180 + 0.882037i \(0.343828\pi\)
\(98\) 0 0
\(99\) −0.137407 + 1.25936i −0.0138099 + 0.126571i
\(100\) 0.361776 + 0.626614i 0.0361776 + 0.0626614i
\(101\) 0.0186877 + 0.177802i 0.00185950 + 0.0176919i 0.995412 0.0956784i \(-0.0305020\pi\)
−0.993553 + 0.113370i \(0.963835\pi\)
\(102\) −12.1345 2.57927i −1.20150 0.255386i
\(103\) 16.5084 3.50897i 1.62662 0.345749i 0.697806 0.716287i \(-0.254160\pi\)
0.928817 + 0.370538i \(0.120827\pi\)
\(104\) −3.47110 2.52190i −0.340370 0.247293i
\(105\) 0 0
\(106\) 5.98484 18.4195i 0.581299 1.78906i
\(107\) −10.3556 + 11.5011i −1.00111 + 1.11185i −0.00739268 + 0.999973i \(0.502353\pi\)
−0.993722 + 0.111878i \(0.964313\pi\)
\(108\) 0.0865439 + 0.823411i 0.00832769 + 0.0792327i
\(109\) −5.51745 + 9.55650i −0.528476 + 0.915347i 0.470973 + 0.882148i \(0.343903\pi\)
−0.999449 + 0.0331994i \(0.989430\pi\)
\(110\) 2.21896 + 0.480843i 0.211570 + 0.0458466i
\(111\) −3.14256 −0.298278
\(112\) 0 0
\(113\) 0.546984 + 1.68344i 0.0514559 + 0.158365i 0.973482 0.228762i \(-0.0734676\pi\)
−0.922027 + 0.387127i \(0.873468\pi\)
\(114\) −9.80060 + 2.08318i −0.917910 + 0.195108i
\(115\) 0.769640 0.342666i 0.0717693 0.0319538i
\(116\) 0.375889 0.167357i 0.0349004 0.0155387i
\(117\) 0.591184 0.125660i 0.0546550 0.0116173i
\(118\) −3.89967 12.0019i −0.358994 1.10487i
\(119\) 0 0
\(120\) −2.04773 −0.186931
\(121\) −8.95009 + 6.39498i −0.813645 + 0.581362i
\(122\) 11.1766 19.3584i 1.01188 1.75263i
\(123\) −0.176086 1.67534i −0.0158771 0.151061i
\(124\) −0.130992 + 0.145481i −0.0117634 + 0.0130646i
\(125\) 1.41086 4.34219i 0.126191 0.388377i
\(126\) 0 0
\(127\) 6.90919 + 5.01982i 0.613092 + 0.445437i 0.850502 0.525972i \(-0.176298\pi\)
−0.237410 + 0.971410i \(0.576298\pi\)
\(128\) 12.1536 2.58333i 1.07424 0.228337i
\(129\) −13.7823 2.92951i −1.21346 0.257929i
\(130\) −0.113226 1.07727i −0.00993057 0.0944831i
\(131\) −4.83354 8.37194i −0.422308 0.731460i 0.573856 0.818956i \(-0.305447\pi\)
−0.996165 + 0.0874963i \(0.972113\pi\)
\(132\) −0.545685 + 0.601241i −0.0474957 + 0.0523313i
\(133\) 0 0
\(134\) −5.54839 + 4.03114i −0.479308 + 0.348237i
\(135\) 1.70897 1.89801i 0.147085 0.163354i
\(136\) −9.48434 10.5334i −0.813275 0.903234i
\(137\) −12.7995 + 5.69871i −1.09354 + 0.486874i −0.872610 0.488417i \(-0.837574\pi\)
−0.220926 + 0.975291i \(0.570908\pi\)
\(138\) −0.447778 + 4.26033i −0.0381174 + 0.362663i
\(139\) −2.95966 + 9.10889i −0.251035 + 0.772606i 0.743550 + 0.668680i \(0.233140\pi\)
−0.994585 + 0.103926i \(0.966860\pi\)
\(140\) 0 0
\(141\) −8.37155 + 6.08229i −0.705012 + 0.512221i
\(142\) 7.14526 + 12.3760i 0.599617 + 1.03857i
\(143\) 4.23344 + 3.10145i 0.354018 + 0.259356i
\(144\) −0.817352 + 1.41570i −0.0681127 + 0.117975i
\(145\) −1.15953 0.516256i −0.0962937 0.0428727i
\(146\) −6.03723 18.5807i −0.499645 1.53775i
\(147\) 0 0
\(148\) 0.237738 + 0.172727i 0.0195419 + 0.0141980i
\(149\) −1.56401 + 14.8805i −0.128128 + 1.21906i 0.721777 + 0.692126i \(0.243326\pi\)
−0.849905 + 0.526935i \(0.823341\pi\)
\(150\) 7.59405 + 8.43405i 0.620052 + 0.688637i
\(151\) 2.80956 + 0.597191i 0.228639 + 0.0485987i 0.320806 0.947145i \(-0.396046\pi\)
−0.0921673 + 0.995744i \(0.529379\pi\)
\(152\) −10.4582 4.65629i −0.848272 0.377675i
\(153\) 1.99666 0.161420
\(154\) 0 0
\(155\) 0.603886 0.0485053
\(156\) 0.353880 + 0.157558i 0.0283331 + 0.0126147i
\(157\) −18.4697 3.92586i −1.47404 0.313317i −0.600327 0.799755i \(-0.704963\pi\)
−0.873715 + 0.486437i \(0.838296\pi\)
\(158\) −3.51581 3.90470i −0.279703 0.310642i
\(159\) 2.23327 21.2482i 0.177110 1.68509i
\(160\) 0.322504 + 0.234313i 0.0254962 + 0.0185240i
\(161\) 0 0
\(162\) 3.49371 + 10.7525i 0.274491 + 0.844798i
\(163\) 10.5927 + 4.71617i 0.829683 + 0.369399i 0.777224 0.629224i \(-0.216627\pi\)
0.0524596 + 0.998623i \(0.483294\pi\)
\(164\) −0.0787620 + 0.136420i −0.00615028 + 0.0106526i
\(165\) 2.50466 + 0.00991418i 0.194987 + 0.000771818i
\(166\) 12.6571 + 21.9227i 0.982380 + 1.70153i
\(167\) 5.11696 3.71769i 0.395963 0.287684i −0.371932 0.928260i \(-0.621305\pi\)
0.767894 + 0.640576i \(0.221305\pi\)
\(168\) 0 0
\(169\) −3.24353 + 9.98255i −0.249502 + 0.767889i
\(170\) 0.374052 3.55887i 0.0286885 0.272953i
\(171\) 1.47321 0.655916i 0.112659 0.0501591i
\(172\) 0.881627 + 0.979146i 0.0672234 + 0.0746591i
\(173\) −0.896008 + 0.995118i −0.0681222 + 0.0756574i −0.776243 0.630434i \(-0.782877\pi\)
0.708120 + 0.706092i \(0.249543\pi\)
\(174\) 5.22132 3.79351i 0.395827 0.287585i
\(175\) 0 0
\(176\) −13.8956 + 2.89616i −1.04742 + 0.218306i
\(177\) −6.96069 12.0563i −0.523197 0.906205i
\(178\) 1.36754 + 13.0113i 0.102502 + 0.975239i
\(179\) −17.4001 3.69850i −1.30054 0.276439i −0.494957 0.868917i \(-0.664816\pi\)
−0.805586 + 0.592478i \(0.798150\pi\)
\(180\) −0.0263841 + 0.00560811i −0.00196655 + 0.000418004i
\(181\) −0.779712 0.566494i −0.0579555 0.0421072i 0.558430 0.829551i \(-0.311404\pi\)
−0.616386 + 0.787444i \(0.711404\pi\)
\(182\) 0 0
\(183\) 7.62007 23.4522i 0.563292 1.73363i
\(184\) −3.27505 + 3.63731i −0.241440 + 0.268146i
\(185\) −0.0947540 0.901524i −0.00696645 0.0662814i
\(186\) −1.53531 + 2.65923i −0.112574 + 0.194984i
\(187\) 11.5497 + 12.9298i 0.844596 + 0.945519i
\(188\) 0.967622 0.0705711
\(189\) 0 0
\(190\) −0.893121 2.74874i −0.0647938 0.199415i
\(191\) 15.7373 3.34506i 1.13871 0.242040i 0.400294 0.916387i \(-0.368908\pi\)
0.738415 + 0.674347i \(0.235575\pi\)
\(192\) 10.8004 4.80863i 0.779449 0.347033i
\(193\) 11.0973 4.94082i 0.798798 0.355648i 0.0335938 0.999436i \(-0.489305\pi\)
0.765204 + 0.643788i \(0.222638\pi\)
\(194\) 3.87883 0.824470i 0.278484 0.0591935i
\(195\) −0.369259 1.13646i −0.0264432 0.0813837i
\(196\) 0 0
\(197\) −2.30179 −0.163996 −0.0819978 0.996633i \(-0.526130\pi\)
−0.0819978 + 0.996633i \(0.526130\pi\)
\(198\) 0.935418 1.60548i 0.0664773 0.114097i
\(199\) 10.1399 17.5627i 0.718795 1.24499i −0.242682 0.970106i \(-0.578027\pi\)
0.961477 0.274884i \(-0.0886395\pi\)
\(200\) 1.35542 + 12.8960i 0.0958430 + 0.911885i
\(201\) −5.06241 + 5.62237i −0.357075 + 0.396571i
\(202\) 0.0810316 0.249390i 0.00570136 0.0175470i
\(203\) 0 0
\(204\) 1.03531 + 0.752196i 0.0724861 + 0.0526642i
\(205\) 0.475306 0.101029i 0.0331968 0.00705620i
\(206\) −24.2134 5.14672i −1.68703 0.358589i
\(207\) −0.0720692 0.685692i −0.00500915 0.0476589i
\(208\) 3.38593 + 5.86460i 0.234772 + 0.406637i
\(209\) 12.7693 + 5.74593i 0.883271 + 0.397454i
\(210\) 0 0
\(211\) −4.34062 + 3.15364i −0.298820 + 0.217106i −0.727085 0.686548i \(-0.759125\pi\)
0.428264 + 0.903654i \(0.359125\pi\)
\(212\) −1.33683 + 1.48470i −0.0918138 + 0.101970i
\(213\) 10.5486 + 11.7154i 0.722780 + 0.802728i
\(214\) 20.7370 9.23270i 1.41755 0.631135i
\(215\) 0.424845 4.04213i 0.0289742 0.275671i
\(216\) −4.58517 + 14.1117i −0.311982 + 0.960181i
\(217\) 0 0
\(218\) 13.0941 9.51344i 0.886847 0.644332i
\(219\) −10.7761 18.6648i −0.728183 1.26125i
\(220\) −0.188935 0.138415i −0.0127380 0.00933195i
\(221\) 4.13564 7.16314i 0.278193 0.481845i
\(222\) 4.21080 + 1.87477i 0.282610 + 0.125826i
\(223\) 7.85614 + 24.1787i 0.526086 + 1.61913i 0.762158 + 0.647391i \(0.224140\pi\)
−0.236072 + 0.971736i \(0.575860\pi\)
\(224\) 0 0
\(225\) −1.47777 1.07366i −0.0985179 0.0715775i
\(226\) 0.271380 2.58201i 0.0180519 0.171753i
\(227\) 14.5267 + 16.1335i 0.964169 + 1.07082i 0.997450 + 0.0713718i \(0.0227377\pi\)
−0.0332810 + 0.999446i \(0.510596\pi\)
\(228\) 1.01099 + 0.214893i 0.0669545 + 0.0142316i
\(229\) −18.7557 8.35058i −1.23941 0.551822i −0.320861 0.947126i \(-0.603972\pi\)
−0.918550 + 0.395305i \(0.870639\pi\)
\(230\) −1.23569 −0.0814787
\(231\) 0 0
\(232\) 7.37396 0.484124
\(233\) 0.634051 + 0.282298i 0.0415381 + 0.0184939i 0.427401 0.904062i \(-0.359429\pi\)
−0.385862 + 0.922556i \(0.626096\pi\)
\(234\) −0.867108 0.184309i −0.0566846 0.0120487i
\(235\) −1.99728 2.21820i −0.130288 0.144700i
\(236\) −0.136074 + 1.29466i −0.00885765 + 0.0842749i
\(237\) −4.68931 3.40699i −0.304604 0.221307i
\(238\) 0 0
\(239\) 0.107093 + 0.329599i 0.00692728 + 0.0213200i 0.954460 0.298338i \(-0.0964321\pi\)
−0.947533 + 0.319658i \(0.896432\pi\)
\(240\) 2.95257 + 1.31457i 0.190587 + 0.0848550i
\(241\) −5.21858 + 9.03885i −0.336158 + 0.582243i −0.983707 0.179781i \(-0.942461\pi\)
0.647548 + 0.762024i \(0.275794\pi\)
\(242\) 15.8075 3.22942i 1.01615 0.207595i
\(243\) −1.97214 3.41584i −0.126513 0.219126i
\(244\) −1.86549 + 1.35536i −0.119426 + 0.0867677i
\(245\) 0 0
\(246\) −0.763523 + 2.34988i −0.0486805 + 0.149823i
\(247\) 0.698293 6.64382i 0.0444313 0.422736i
\(248\) −3.20505 + 1.42698i −0.203521 + 0.0906132i
\(249\) 18.6858 + 20.7527i 1.18416 + 1.31515i
\(250\) −4.48089 + 4.97653i −0.283396 + 0.314743i
\(251\) −5.65909 + 4.11157i −0.357199 + 0.259520i −0.751883 0.659297i \(-0.770854\pi\)
0.394684 + 0.918817i \(0.370854\pi\)
\(252\) 0 0
\(253\) 4.02345 4.43308i 0.252952 0.278706i
\(254\) −6.26311 10.8480i −0.392983 0.680666i
\(255\) −0.412638 3.92599i −0.0258404 0.245855i
\(256\) −3.53209 0.750768i −0.220755 0.0469230i
\(257\) −9.73103 + 2.06839i −0.607005 + 0.129023i −0.501153 0.865359i \(-0.667090\pi\)
−0.105853 + 0.994382i \(0.533757\pi\)
\(258\) 16.7196 + 12.1475i 1.04091 + 0.756268i
\(259\) 0 0
\(260\) −0.0345293 + 0.106270i −0.00214142 + 0.00659061i
\(261\) −0.695056 + 0.771938i −0.0430229 + 0.0477818i
\(262\) 1.48211 + 14.1013i 0.0915651 + 0.871184i
\(263\) −7.09017 + 12.2805i −0.437199 + 0.757250i −0.997472 0.0710574i \(-0.977363\pi\)
0.560274 + 0.828308i \(0.310696\pi\)
\(264\) −13.3166 + 5.86587i −0.819578 + 0.361019i
\(265\) 6.16293 0.378586
\(266\) 0 0
\(267\) 4.45991 + 13.7262i 0.272942 + 0.840029i
\(268\) 0.692003 0.147090i 0.0422708 0.00898494i
\(269\) 16.8120 7.48521i 1.02505 0.456381i 0.175829 0.984421i \(-0.443739\pi\)
0.849220 + 0.528040i \(0.177073\pi\)
\(270\) −3.42220 + 1.52366i −0.208268 + 0.0927270i
\(271\) 0.714626 0.151898i 0.0434104 0.00922717i −0.186155 0.982520i \(-0.559603\pi\)
0.229566 + 0.973293i \(0.426269\pi\)
\(272\) 6.91316 + 21.2765i 0.419172 + 1.29008i
\(273\) 0 0
\(274\) 20.5501 1.24148
\(275\) −1.59544 15.7802i −0.0962085 0.951581i
\(276\) 0.220949 0.382696i 0.0132996 0.0230356i
\(277\) −1.57466 14.9819i −0.0946120 0.900173i −0.934152 0.356875i \(-0.883842\pi\)
0.839540 0.543298i \(-0.182825\pi\)
\(278\) 9.39985 10.4396i 0.563765 0.626125i
\(279\) 0.152719 0.470022i 0.00914308 0.0281395i
\(280\) 0 0
\(281\) 8.65334 + 6.28702i 0.516215 + 0.375052i 0.815176 0.579213i \(-0.196640\pi\)
−0.298961 + 0.954265i \(0.596640\pi\)
\(282\) 14.8458 3.15557i 0.884054 0.187912i
\(283\) 8.90985 + 1.89385i 0.529636 + 0.112578i 0.464965 0.885329i \(-0.346067\pi\)
0.0646708 + 0.997907i \(0.479400\pi\)
\(284\) −0.154091 1.46608i −0.00914361 0.0869957i
\(285\) −1.59417 2.76119i −0.0944306 0.163559i
\(286\) −3.82225 6.68127i −0.226014 0.395072i
\(287\) 0 0
\(288\) 0.263932 0.191758i 0.0155523 0.0112994i
\(289\) 6.90872 7.67291i 0.406395 0.451347i
\(290\) 1.24570 + 1.38349i 0.0731500 + 0.0812413i
\(291\) 3.99635 1.77929i 0.234270 0.104304i
\(292\) −0.210661 + 2.00431i −0.0123280 + 0.117293i
\(293\) −3.67390 + 11.3071i −0.214632 + 0.660569i 0.784548 + 0.620068i \(0.212895\pi\)
−0.999180 + 0.0405002i \(0.987105\pi\)
\(294\) 0 0
\(295\) 3.24878 2.36037i 0.189151 0.137426i
\(296\) 2.63319 + 4.56082i 0.153051 + 0.265092i
\(297\) 5.67663 17.2384i 0.329392 1.00027i
\(298\) 10.9730 19.0058i 0.635648 1.10097i
\(299\) −2.60924 1.16171i −0.150896 0.0671833i
\(300\) −0.361776 1.11343i −0.0208871 0.0642840i
\(301\) 0 0
\(302\) −3.40834 2.47630i −0.196128 0.142495i
\(303\) 0.0302373 0.287689i 0.00173709 0.0165273i
\(304\) 12.0903 + 13.4276i 0.693424 + 0.770125i
\(305\) 6.95762 + 1.47889i 0.398392 + 0.0846809i
\(306\) −2.67538 1.19115i −0.152941 0.0680938i
\(307\) −2.22072 −0.126743 −0.0633716 0.997990i \(-0.520185\pi\)
−0.0633716 + 0.997990i \(0.520185\pi\)
\(308\) 0 0
\(309\) −27.3079 −1.55349
\(310\) −0.809162 0.360262i −0.0459573 0.0204615i
\(311\) −20.9446 4.45192i −1.18766 0.252445i −0.428619 0.903485i \(-0.641000\pi\)
−0.759043 + 0.651040i \(0.774333\pi\)
\(312\) 4.64524 + 5.15907i 0.262985 + 0.292075i
\(313\) −3.29837 + 31.3819i −0.186435 + 1.77381i 0.356753 + 0.934199i \(0.383884\pi\)
−0.543188 + 0.839611i \(0.682783\pi\)
\(314\) 22.4060 + 16.2789i 1.26444 + 0.918671i
\(315\) 0 0
\(316\) 0.167491 + 0.515484i 0.00942211 + 0.0289983i
\(317\) −12.0594 5.36919i −0.677324 0.301564i 0.0390940 0.999236i \(-0.487553\pi\)
−0.716418 + 0.697672i \(0.754219\pi\)
\(318\) −15.6685 + 27.1387i −0.878647 + 1.52186i
\(319\) −9.01939 0.0357015i −0.504989 0.00199890i
\(320\) 1.70513 + 2.95337i 0.0953197 + 0.165099i
\(321\) 20.2586 14.7188i 1.13073 0.821521i
\(322\) 0 0
\(323\) 6.81980 20.9892i 0.379464 1.16787i
\(324\) 0.121908 1.15988i 0.00677268 0.0644377i
\(325\) −6.91270 + 3.07773i −0.383448 + 0.170722i
\(326\) −11.3799 12.6386i −0.630273 0.699989i
\(327\) 11.9472 13.2687i 0.660683 0.733763i
\(328\) −2.28389 + 1.65935i −0.126107 + 0.0916220i
\(329\) 0 0
\(330\) −3.35014 1.50750i −0.184419 0.0829849i
\(331\) −4.73826 8.20692i −0.260439 0.451093i 0.705920 0.708292i \(-0.250534\pi\)
−0.966359 + 0.257199i \(0.917200\pi\)
\(332\) −0.272956 2.59700i −0.0149804 0.142529i
\(333\) −0.725646 0.154241i −0.0397652 0.00845234i
\(334\) −9.07423 + 1.92879i −0.496520 + 0.105539i
\(335\) −1.76556 1.28276i −0.0964631 0.0700845i
\(336\) 0 0
\(337\) −5.93346 + 18.2613i −0.323216 + 0.994758i 0.649023 + 0.760769i \(0.275178\pi\)
−0.972239 + 0.233989i \(0.924822\pi\)
\(338\) 10.3014 11.4409i 0.560323 0.622302i
\(339\) −0.299374 2.84836i −0.0162598 0.154701i
\(340\) −0.184570 + 0.319685i −0.0100097 + 0.0173374i
\(341\) 3.92713 1.72988i 0.212666 0.0936781i
\(342\) −2.36530 −0.127901
\(343\) 0 0
\(344\) 7.29672 + 22.4570i 0.393413 + 1.21080i
\(345\) −1.33337 + 0.283416i −0.0717860 + 0.0152586i
\(346\) 1.79425 0.798850i 0.0964593 0.0429464i
\(347\) 2.78477 1.23986i 0.149494 0.0665591i −0.330626 0.943762i \(-0.607260\pi\)
0.480120 + 0.877203i \(0.340593\pi\)
\(348\) −0.651211 + 0.138419i −0.0349086 + 0.00742004i
\(349\) −5.99373 18.4468i −0.320837 0.987435i −0.973285 0.229601i \(-0.926258\pi\)
0.652448 0.757834i \(-0.273742\pi\)
\(350\) 0 0
\(351\) −8.65865 −0.462165
\(352\) 2.76848 + 0.599922i 0.147561 + 0.0319759i
\(353\) −5.37926 + 9.31716i −0.286309 + 0.495902i −0.972926 0.231117i \(-0.925762\pi\)
0.686617 + 0.727020i \(0.259095\pi\)
\(354\) 2.13436 + 20.3071i 0.113440 + 1.07931i
\(355\) −3.04282 + 3.37939i −0.161496 + 0.179359i
\(356\) 0.417046 1.28353i 0.0221034 0.0680272i
\(357\) 0 0
\(358\) 21.1084 + 15.3361i 1.11561 + 0.810541i
\(359\) −0.593956 + 0.126249i −0.0313478 + 0.00666318i −0.223559 0.974690i \(-0.571768\pi\)
0.192211 + 0.981354i \(0.438434\pi\)
\(360\) −0.472839 0.100505i −0.0249208 0.00529708i
\(361\) 0.122862 + 1.16895i 0.00646643 + 0.0615239i
\(362\) 0.706801 + 1.22422i 0.0371486 + 0.0643433i
\(363\) 16.3164 7.11030i 0.856390 0.373194i
\(364\) 0 0
\(365\) 5.02956 3.65419i 0.263259 0.191269i
\(366\) −24.2013 + 26.8783i −1.26502 + 1.40495i
\(367\) −18.5101 20.5575i −0.966217 1.07309i −0.997290 0.0735758i \(-0.976559\pi\)
0.0310725 0.999517i \(-0.490108\pi\)
\(368\) 7.05724 3.14209i 0.367884 0.163793i
\(369\) 0.0415682 0.395495i 0.00216395 0.0205886i
\(370\) −0.410862 + 1.26450i −0.0213597 + 0.0657384i
\(371\) 0 0
\(372\) 0.256258 0.186183i 0.0132864 0.00965311i
\(373\) 14.7257 + 25.5056i 0.762465 + 1.32063i 0.941576 + 0.336800i \(0.109345\pi\)
−0.179111 + 0.983829i \(0.557322\pi\)
\(374\) −7.76215 24.2152i −0.401371 1.25214i
\(375\) −3.69369 + 6.39765i −0.190741 + 0.330373i
\(376\) 15.8419 + 7.05327i 0.816984 + 0.363745i
\(377\) 1.32972 + 4.09246i 0.0684840 + 0.210772i
\(378\) 0 0
\(379\) −20.5034 14.8966i −1.05319 0.765188i −0.0803745 0.996765i \(-0.525612\pi\)
−0.972817 + 0.231577i \(0.925612\pi\)
\(380\) −0.0311643 + 0.296508i −0.00159869 + 0.0152106i
\(381\) −9.24630 10.2691i −0.473702 0.526100i
\(382\) −23.0824 4.90630i −1.18100 0.251028i
\(383\) 29.1715 + 12.9880i 1.49059 + 0.663655i 0.980510 0.196469i \(-0.0629475\pi\)
0.510084 + 0.860124i \(0.329614\pi\)
\(384\) −20.1043 −1.02594
\(385\) 0 0
\(386\) −17.8171 −0.906865
\(387\) −3.03867 1.35290i −0.154464 0.0687719i
\(388\) −0.400124 0.0850490i −0.0203132 0.00431771i
\(389\) 11.8782 + 13.1921i 0.602249 + 0.668865i 0.964765 0.263112i \(-0.0847489\pi\)
−0.362516 + 0.931977i \(0.618082\pi\)
\(390\) −0.183203 + 1.74306i −0.00927687 + 0.0882635i
\(391\) −7.63356 5.54611i −0.386046 0.280479i
\(392\) 0 0
\(393\) 4.83354 + 14.8761i 0.243820 + 0.750400i
\(394\) 3.08422 + 1.37319i 0.155381 + 0.0691801i
\(395\) 0.835990 1.44798i 0.0420632 0.0728557i
\(396\) −0.155513 + 0.112049i −0.00781484 + 0.00563069i
\(397\) −6.65233 11.5222i −0.333871 0.578282i 0.649396 0.760450i \(-0.275022\pi\)
−0.983267 + 0.182169i \(0.941688\pi\)
\(398\) −24.0641 + 17.4836i −1.20623 + 0.876374i
\(399\) 0 0
\(400\) 6.32443 19.4646i 0.316221 0.973229i
\(401\) 0.364765 3.47051i 0.0182155 0.173309i −0.981632 0.190785i \(-0.938897\pi\)
0.999847 + 0.0174765i \(0.00556322\pi\)
\(402\) 10.1374 4.51346i 0.505608 0.225111i
\(403\) −1.36991 1.52144i −0.0682400 0.0757882i
\(404\) −0.0181000 + 0.0201020i −0.000900506 + 0.00100011i
\(405\) −2.91057 + 2.11465i −0.144627 + 0.105078i
\(406\) 0 0
\(407\) −3.19868 5.59127i −0.158553 0.277149i
\(408\) 11.4671 + 19.8616i 0.567706 + 0.983296i
\(409\) −3.09671 29.4632i −0.153122 1.45686i −0.753659 0.657265i \(-0.771713\pi\)
0.600537 0.799597i \(-0.294953\pi\)
\(410\) −0.697146 0.148183i −0.0344296 0.00731824i
\(411\) 22.1746 4.71335i 1.09379 0.232492i
\(412\) 2.06587 + 1.50095i 0.101778 + 0.0739463i
\(413\) 0 0
\(414\) −0.312499 + 0.961771i −0.0153585 + 0.0472685i
\(415\) −5.39003 + 5.98623i −0.264586 + 0.293853i
\(416\) −0.141266 1.34406i −0.00692613 0.0658978i
\(417\) 7.74848 13.4208i 0.379445 0.657218i
\(418\) −13.6820 15.3169i −0.669211 0.749176i
\(419\) 11.6452 0.568907 0.284454 0.958690i \(-0.408188\pi\)
0.284454 + 0.958690i \(0.408188\pi\)
\(420\) 0 0
\(421\) 6.14475 + 18.9116i 0.299477 + 0.921696i 0.981681 + 0.190533i \(0.0610217\pi\)
−0.682204 + 0.731162i \(0.738978\pi\)
\(422\) 7.69748 1.63615i 0.374708 0.0796466i
\(423\) −2.23160 + 0.993571i −0.108504 + 0.0483091i
\(424\) −32.7089 + 14.5630i −1.58849 + 0.707240i
\(425\) −24.4516 + 5.19736i −1.18608 + 0.252109i
\(426\) −7.14526 21.9908i −0.346189 1.06546i
\(427\) 0 0
\(428\) −2.34159 −0.113185
\(429\) −5.65681 6.33275i −0.273113 0.305748i
\(430\) −2.98069 + 5.16271i −0.143742 + 0.248968i
\(431\) −3.16161 30.0807i −0.152289 1.44894i −0.757482 0.652856i \(-0.773571\pi\)
0.605193 0.796079i \(-0.293096\pi\)
\(432\) 15.6705 17.4038i 0.753946 0.837342i
\(433\) 1.76362 5.42786i 0.0847542 0.260846i −0.899694 0.436521i \(-0.856211\pi\)
0.984448 + 0.175674i \(0.0562106\pi\)
\(434\) 0 0
\(435\) 1.66149 + 1.20714i 0.0796622 + 0.0578780i
\(436\) −1.63312 + 0.347130i −0.0782122 + 0.0166245i
\(437\) −7.45426 1.58445i −0.356586 0.0757946i
\(438\) 3.30429 + 31.4382i 0.157885 + 1.50217i
\(439\) 3.42437 + 5.93119i 0.163436 + 0.283080i 0.936099 0.351737i \(-0.114409\pi\)
−0.772663 + 0.634817i \(0.781075\pi\)
\(440\) −2.08430 3.64333i −0.0993649 0.173689i
\(441\) 0 0
\(442\) −9.81479 + 7.13086i −0.466842 + 0.339181i
\(443\) 0.0673782 0.0748311i 0.00320123 0.00355533i −0.741542 0.670906i \(-0.765905\pi\)
0.744743 + 0.667351i \(0.232572\pi\)
\(444\) −0.318155 0.353347i −0.0150990 0.0167691i
\(445\) −3.80324 + 1.69331i −0.180291 + 0.0802707i
\(446\) 3.89773 37.0845i 0.184563 1.75600i
\(447\) 7.48125 23.0249i 0.353851 1.08904i
\(448\) 0 0
\(449\) 24.9216 18.1066i 1.17612 0.854502i 0.184392 0.982853i \(-0.440968\pi\)
0.991729 + 0.128351i \(0.0409683\pi\)
\(450\) 1.33958 + 2.32023i 0.0631486 + 0.109377i
\(451\) 2.80156 2.01855i 0.131920 0.0950500i
\(452\) −0.133908 + 0.231936i −0.00629852 + 0.0109093i
\(453\) −4.24573 1.89032i −0.199482 0.0888150i
\(454\) −9.83984 30.2839i −0.461807 1.42129i
\(455\) 0 0
\(456\) 14.9855 + 10.8876i 0.701761 + 0.509859i
\(457\) −2.41833 + 23.0088i −0.113124 + 1.07631i 0.779778 + 0.626057i \(0.215332\pi\)
−0.892902 + 0.450251i \(0.851335\pi\)
\(458\) 20.1495 + 22.3783i 0.941525 + 1.04567i
\(459\) −27.9795 5.94724i −1.30597 0.277593i
\(460\) 0.116448 + 0.0518461i 0.00542943 + 0.00241734i
\(461\) 2.77839 0.129403 0.0647013 0.997905i \(-0.479391\pi\)
0.0647013 + 0.997905i \(0.479391\pi\)
\(462\) 0 0
\(463\) −26.0950 −1.21274 −0.606369 0.795184i \(-0.707374\pi\)
−0.606369 + 0.795184i \(0.707374\pi\)
\(464\) −10.6323 4.73382i −0.493594 0.219762i
\(465\) −0.955756 0.203152i −0.0443221 0.00942095i
\(466\) −0.681171 0.756517i −0.0315546 0.0350450i
\(467\) −0.277867 + 2.64373i −0.0128582 + 0.122337i −0.999068 0.0431620i \(-0.986257\pi\)
0.986210 + 0.165499i \(0.0529235\pi\)
\(468\) 0.0739811 + 0.0537504i 0.00341978 + 0.00248461i
\(469\) 0 0
\(470\) 1.35289 + 4.16375i 0.0624040 + 0.192060i
\(471\) 27.9109 + 12.4267i 1.28606 + 0.572593i
\(472\) −11.6649 + 20.2042i −0.536921 + 0.929974i
\(473\) −8.81618 27.5034i −0.405369 1.26461i
\(474\) 4.25082 + 7.36263i 0.195246 + 0.338177i
\(475\) −16.3340 + 11.8673i −0.749454 + 0.544510i
\(476\) 0 0
\(477\) 1.55857 4.79679i 0.0713621 0.219630i
\(478\) 0.0531330 0.505527i 0.00243025 0.0231223i
\(479\) 7.56620 3.36869i 0.345708 0.153919i −0.226535 0.974003i \(-0.572740\pi\)
0.572244 + 0.820084i \(0.306073\pi\)
\(480\) −0.431594 0.479334i −0.0196995 0.0218785i
\(481\) −2.05636 + 2.28382i −0.0937621 + 0.104133i
\(482\) 12.3848 8.99812i 0.564114 0.409853i
\(483\) 0 0
\(484\) −1.62516 0.358909i −0.0738711 0.0163141i
\(485\) 0.630932 + 1.09281i 0.0286492 + 0.0496218i
\(486\) 0.604717 + 5.75350i 0.0274305 + 0.260984i
\(487\) 19.1674 + 4.07415i 0.868556 + 0.184617i 0.620575 0.784147i \(-0.286899\pi\)
0.247981 + 0.968765i \(0.420233\pi\)
\(488\) −40.4213 + 8.59181i −1.82979 + 0.388933i
\(489\) −15.1782 11.0276i −0.686384 0.498687i
\(490\) 0 0
\(491\) −8.86312 + 27.2779i −0.399987 + 1.23103i 0.525022 + 0.851089i \(0.324057\pi\)
−0.925009 + 0.379945i \(0.875943\pi\)
\(492\) 0.170547 0.189412i 0.00768887 0.00853936i
\(493\) 1.48593 + 14.1377i 0.0669229 + 0.636729i
\(494\) −4.89919 + 8.48564i −0.220425 + 0.381787i
\(495\) 0.577862 + 0.125221i 0.0259730 + 0.00562827i
\(496\) 5.53735 0.248634
\(497\) 0 0
\(498\) −12.6571 38.9545i −0.567177 1.74559i
\(499\) −27.3391 + 5.81111i −1.22387 + 0.260141i −0.774134 0.633022i \(-0.781814\pi\)
−0.449734 + 0.893163i \(0.648481\pi\)
\(500\) 0.631070 0.280970i 0.0282223 0.0125654i
\(501\) −9.34916 + 4.16251i −0.417690 + 0.185967i
\(502\) 10.0356 2.13314i 0.447912 0.0952066i
\(503\) 2.50222 + 7.70104i 0.111568 + 0.343373i 0.991216 0.132254i \(-0.0422214\pi\)
−0.879647 + 0.475626i \(0.842221\pi\)
\(504\) 0 0
\(505\) 0.0834428 0.00371316
\(506\) −8.03579 + 3.53972i −0.357235 + 0.157360i
\(507\) 8.49166 14.7080i 0.377128 0.653205i
\(508\) 0.135067 + 1.28508i 0.00599263 + 0.0570161i
\(509\) −10.9069 + 12.1134i −0.483441 + 0.536916i −0.934681 0.355487i \(-0.884315\pi\)
0.451240 + 0.892403i \(0.350982\pi\)
\(510\) −1.78924 + 5.50670i −0.0792287 + 0.243841i
\(511\) 0 0
\(512\) −15.8195 11.4935i −0.699129 0.507947i
\(513\) −22.5981 + 4.80337i −0.997729 + 0.212074i
\(514\) 14.2728 + 3.03378i 0.629547 + 0.133814i
\(515\) −0.823385 7.83399i −0.0362827 0.345207i
\(516\) −1.06594 1.84626i −0.0469252 0.0812769i
\(517\) −19.3427 8.70384i −0.850692 0.382795i
\(518\) 0 0
\(519\) 1.75286 1.27352i 0.0769419 0.0559015i
\(520\) −1.33995 + 1.48816i −0.0587606 + 0.0652603i
\(521\) −5.14297 5.71185i −0.225318 0.250241i 0.619877 0.784699i \(-0.287182\pi\)
−0.845195 + 0.534458i \(0.820516\pi\)
\(522\) 1.39184 0.619688i 0.0609193 0.0271230i
\(523\) 2.73059 25.9798i 0.119400 1.13602i −0.756657 0.653812i \(-0.773169\pi\)
0.876058 0.482207i \(-0.160165\pi\)
\(524\) 0.451984 1.39106i 0.0197450 0.0607689i
\(525\) 0 0
\(526\) 16.8265 12.2252i 0.733672 0.533044i
\(527\) −3.38171 5.85730i −0.147310 0.255148i
\(528\) 22.9665 + 0.0909084i 0.999489 + 0.00395628i
\(529\) 9.87089 17.0969i 0.429169 0.743343i
\(530\) −8.25787 3.67664i −0.358699 0.159703i
\(531\) −1.01555 3.12554i −0.0440712 0.135637i
\(532\) 0 0
\(533\) −1.33276 0.968308i −0.0577283 0.0419421i
\(534\) 2.21273 21.0527i 0.0957543 0.911042i
\(535\) 4.83329 + 5.36792i 0.208961 + 0.232075i
\(536\) 12.4016 + 2.63605i 0.535670 + 0.113860i
\(537\) 26.2945 + 11.7071i 1.13469 + 0.505197i
\(538\) −26.9924 −1.16372
\(539\) 0 0
\(540\) 0.386429 0.0166292
\(541\) −23.6404 10.5254i −1.01638 0.452522i −0.170195 0.985410i \(-0.554440\pi\)
−0.846186 + 0.532888i \(0.821107\pi\)
\(542\) −1.04816 0.222794i −0.0450225 0.00956983i
\(543\) 1.04346 + 1.15888i 0.0447791 + 0.0497322i
\(544\) 0.466685 4.44021i 0.0200089 0.190372i
\(545\) 4.16671 + 3.02729i 0.178482 + 0.129675i
\(546\) 0 0
\(547\) −11.7726 36.2322i −0.503359 1.54918i −0.803513 0.595288i \(-0.797038\pi\)
0.300154 0.953891i \(-0.402962\pi\)
\(548\) −1.93659 0.862227i −0.0827272 0.0368325i
\(549\) 2.91061 5.04132i 0.124222 0.215158i
\(550\) −7.27627 + 22.0961i −0.310261 + 0.942180i
\(551\) 5.74069 + 9.94317i 0.244562 + 0.423593i
\(552\) 6.40696 4.65493i 0.272698 0.198127i
\(553\) 0 0
\(554\) −6.82786 + 21.0140i −0.290088 + 0.892799i
\(555\) −0.153315 + 1.45870i −0.00650787 + 0.0619182i
\(556\) −1.32384 + 0.589410i −0.0561432 + 0.0249966i
\(557\) 23.1132 + 25.6698i 0.979339 + 1.08767i 0.996138 + 0.0878070i \(0.0279859\pi\)
−0.0167988 + 0.999859i \(0.505347\pi\)
\(558\) −0.485036 + 0.538687i −0.0205332 + 0.0228044i
\(559\) −11.1476 + 8.09917i −0.471491 + 0.342558i
\(560\) 0 0
\(561\) −13.9297 24.3490i −0.588113 1.02802i
\(562\) −7.84417 13.5865i −0.330886 0.573112i
\(563\) 2.03642 + 19.3752i 0.0858247 + 0.816568i 0.949763 + 0.312970i \(0.101324\pi\)
−0.863938 + 0.503598i \(0.832009\pi\)
\(564\) −1.53143 0.325516i −0.0644850 0.0137067i
\(565\) 0.808098 0.171767i 0.0339969 0.00722627i
\(566\) −10.8087 7.85300i −0.454325 0.330086i
\(567\) 0 0
\(568\) 8.16387 25.1258i 0.342549 1.05426i
\(569\) 11.4614 12.7292i 0.480486 0.533634i −0.453351 0.891332i \(-0.649772\pi\)
0.933837 + 0.357698i \(0.116438\pi\)
\(570\) 0.488821 + 4.65083i 0.0204745 + 0.194802i
\(571\) 1.92790 3.33923i 0.0806802 0.139742i −0.822862 0.568241i \(-0.807624\pi\)
0.903542 + 0.428499i \(0.140957\pi\)
\(572\) 0.0798719 + 0.789999i 0.00333961 + 0.0330315i
\(573\) −26.0323 −1.08751
\(574\) 0 0
\(575\) 2.66745 + 8.20958i 0.111240 + 0.342363i
\(576\) 2.72992 0.580262i 0.113747 0.0241776i
\(577\) 8.93616 3.97864i 0.372017 0.165633i −0.212208 0.977225i \(-0.568065\pi\)
0.584225 + 0.811592i \(0.301399\pi\)
\(578\) −13.8346 + 6.15957i −0.575444 + 0.256204i
\(579\) −19.2255 + 4.08650i −0.798984 + 0.169829i
\(580\) −0.0593443 0.182643i −0.00246414 0.00758384i
\(581\) 0 0
\(582\) −6.41628 −0.265964
\(583\) 40.0781 17.6542i 1.65987 0.731161i
\(584\) −18.0589 + 31.2789i −0.747283 + 1.29433i
\(585\) −0.0294863 0.280543i −0.00121911 0.0115990i
\(586\) 11.6683 12.9589i 0.482012 0.535329i
\(587\) 1.88467 5.80041i 0.0777886 0.239409i −0.904599 0.426264i \(-0.859830\pi\)
0.982387 + 0.186855i \(0.0598295\pi\)
\(588\) 0 0
\(589\) −4.41932 3.21082i −0.182095 0.132300i
\(590\) −5.76126 + 1.22459i −0.237187 + 0.0504157i
\(591\) 3.64298 + 0.774340i 0.149852 + 0.0318521i
\(592\) −0.868850 8.26656i −0.0357095 0.339753i
\(593\) 6.61648 + 11.4601i 0.271706 + 0.470609i 0.969299 0.245886i \(-0.0790787\pi\)
−0.697593 + 0.716495i \(0.745745\pi\)
\(594\) −17.8903 + 19.7117i −0.734046 + 0.808780i
\(595\) 0 0
\(596\) −1.83150 + 1.33066i −0.0750212 + 0.0545061i
\(597\) −21.9564 + 24.3850i −0.898614 + 0.998012i
\(598\) 2.80314 + 3.11320i 0.114629 + 0.127308i
\(599\) −5.41289 + 2.40997i −0.221165 + 0.0984689i −0.514328 0.857593i \(-0.671959\pi\)
0.293163 + 0.956062i \(0.405292\pi\)
\(600\) 2.19312 20.8662i 0.0895339 0.851858i
\(601\) −3.93712 + 12.1172i −0.160599 + 0.494272i −0.998685 0.0512657i \(-0.983674\pi\)
0.838086 + 0.545538i \(0.183674\pi\)
\(602\) 0 0
\(603\) −1.44491 + 1.04979i −0.0588413 + 0.0427507i
\(604\) 0.217295 + 0.376366i 0.00884161 + 0.0153141i
\(605\) 2.53175 + 4.46640i 0.102930 + 0.181585i
\(606\) −0.212144 + 0.367443i −0.00861774 + 0.0149264i
\(607\) −7.63853 3.40089i −0.310038 0.138038i 0.245819 0.969316i \(-0.420943\pi\)
−0.555857 + 0.831278i \(0.687610\pi\)
\(608\) −1.11430 3.42946i −0.0451908 0.139083i
\(609\) 0 0
\(610\) −8.44044 6.13234i −0.341743 0.248291i
\(611\) −1.05776 + 10.0639i −0.0427925 + 0.407144i
\(612\) 0.202144 + 0.224503i 0.00817118 + 0.00907501i
\(613\) 6.53690 + 1.38946i 0.264023 + 0.0561198i 0.338021 0.941139i \(-0.390243\pi\)
−0.0739981 + 0.997258i \(0.523576\pi\)
\(614\) 2.97560 + 1.32482i 0.120086 + 0.0534655i
\(615\) −0.786243 −0.0317044
\(616\) 0 0
\(617\) 11.8669 0.477741 0.238871 0.971051i \(-0.423223\pi\)
0.238871 + 0.971051i \(0.423223\pi\)
\(618\) 36.5906 + 16.2912i 1.47189 + 0.655328i
\(619\) 20.1700 + 4.28727i 0.810702 + 0.172320i 0.594570 0.804044i \(-0.297322\pi\)
0.216132 + 0.976364i \(0.430656\pi\)
\(620\) 0.0611379 + 0.0679006i 0.00245536 + 0.00272695i
\(621\) −1.03248 + 9.82339i −0.0414320 + 0.394199i
\(622\) 25.4084 + 18.4603i 1.01878 + 0.740189i
\(623\) 0 0
\(624\) −3.38593 10.4208i −0.135546 0.417167i
\(625\) 19.8969 + 8.85867i 0.795876 + 0.354347i
\(626\) 23.1412 40.0817i 0.924908 1.60199i
\(627\) −18.2767 13.3896i −0.729900 0.534731i
\(628\) −1.42847 2.47418i −0.0570021 0.0987305i
\(629\) −8.21358 + 5.96752i −0.327497 + 0.237941i
\(630\) 0 0
\(631\) −4.78342 + 14.7219i −0.190425 + 0.586068i −1.00000 0.000949112i \(-0.999698\pi\)
0.809575 + 0.587017i \(0.199698\pi\)
\(632\) −1.01535 + 9.66040i −0.0403884 + 0.384270i
\(633\) 7.93070 3.53097i 0.315217 0.140344i
\(634\) 12.9556 + 14.3886i 0.514532 + 0.571446i
\(635\) 2.66715 2.96217i 0.105843 0.117550i
\(636\) 2.61523 1.90008i 0.103701 0.0753430i
\(637\) 0 0
\(638\) 12.0640 + 5.42857i 0.477619 + 0.214919i
\(639\) 1.86077 + 3.22294i 0.0736108 + 0.127498i
\(640\) −0.606183 5.76744i −0.0239615 0.227978i
\(641\) 23.0632 + 4.90224i 0.910943 + 0.193627i 0.639467 0.768819i \(-0.279155\pi\)
0.271476 + 0.962445i \(0.412488\pi\)
\(642\) −35.9259 + 7.63628i −1.41788 + 0.301380i
\(643\) 23.2031 + 16.8581i 0.915042 + 0.664817i 0.942285 0.334812i \(-0.108673\pi\)
−0.0272428 + 0.999629i \(0.508673\pi\)
\(644\) 0 0
\(645\) −2.03220 + 6.25446i −0.0800177 + 0.246269i
\(646\) −21.6596 + 24.0555i −0.852187 + 0.946449i
\(647\) 0.567342 + 5.39789i 0.0223045 + 0.212213i 0.999998 + 0.00217472i \(0.000692234\pi\)
−0.977693 + 0.210038i \(0.932641\pi\)
\(648\) 10.4506 18.1009i 0.410537 0.711071i
\(649\) 14.3656 24.6561i 0.563901 0.967837i
\(650\) 11.0986 0.435323
\(651\) 0 0
\(652\) 0.542130 + 1.66851i 0.0212315 + 0.0653437i
\(653\) 12.0724 2.56606i 0.472429 0.100418i 0.0344564 0.999406i \(-0.489030\pi\)
0.437973 + 0.898988i \(0.355697\pi\)
\(654\) −23.9242 + 10.6517i −0.935509 + 0.416516i
\(655\) −4.12186 + 1.83517i −0.161054 + 0.0717060i
\(656\) 4.35833 0.926392i 0.170164 0.0361695i
\(657\) −1.57221 4.83878i −0.0613379 0.188779i
\(658\) 0 0
\(659\) 16.2115 0.631512 0.315756 0.948840i \(-0.397742\pi\)
0.315756 + 0.948840i \(0.397742\pi\)
\(660\) 0.252459 + 0.282626i 0.00982695 + 0.0110012i
\(661\) 21.8525 37.8497i 0.849964 1.47218i −0.0312751 0.999511i \(-0.509957\pi\)
0.881239 0.472670i \(-0.156710\pi\)
\(662\) 1.45290 + 13.8234i 0.0564684 + 0.537261i
\(663\) −8.95512 + 9.94567i −0.347788 + 0.386258i
\(664\) 14.4614 44.5078i 0.561213 1.72724i
\(665\) 0 0
\(666\) 0.880296 + 0.639573i 0.0341108 + 0.0247829i
\(667\) 4.80152 1.02059i 0.185916 0.0395176i
\(668\) 0.936061 + 0.198966i 0.0362173 + 0.00769822i
\(669\) −4.29981 40.9100i −0.166240 1.58167i
\(670\) 1.60047 + 2.77209i 0.0618314 + 0.107095i
\(671\) 49.4825 10.3133i 1.91025 0.398140i
\(672\) 0 0
\(673\) 4.74166 3.44502i 0.182778 0.132796i −0.492634 0.870237i \(-0.663966\pi\)
0.675412 + 0.737441i \(0.263966\pi\)
\(674\) 18.8446 20.9291i 0.725868 0.806158i
\(675\) 17.5102 + 19.4471i 0.673969 + 0.748519i
\(676\) −1.45081 + 0.645942i −0.0558004 + 0.0248439i
\(677\) −2.14575 + 20.4155i −0.0824679 + 0.784630i 0.872638 + 0.488367i \(0.162407\pi\)
−0.955106 + 0.296263i \(0.904260\pi\)
\(678\) −1.29811 + 3.99519i −0.0498538 + 0.153434i
\(679\) 0 0
\(680\) −5.35206 + 3.88850i −0.205242 + 0.149117i
\(681\) −17.5636 30.4210i −0.673037 1.16573i
\(682\) −6.29406 0.0249138i −0.241012 0.000953999i
\(683\) −19.3528 + 33.5200i −0.740513 + 1.28261i 0.211749 + 0.977324i \(0.432084\pi\)
−0.952262 + 0.305282i \(0.901249\pi\)
\(684\) 0.222900 + 0.0992415i 0.00852279 + 0.00379459i
\(685\) 2.02075 + 6.21923i 0.0772090 + 0.237625i
\(686\) 0 0
\(687\) 26.8750 + 19.5258i 1.02535 + 0.744957i
\(688\) 3.89563 37.0644i 0.148520 1.41307i
\(689\) −13.9805 15.5270i −0.532616 0.591530i
\(690\) 1.95569 + 0.415695i 0.0744519 + 0.0158252i
\(691\) 21.1303 + 9.40783i 0.803835 + 0.357891i 0.767175 0.641437i \(-0.221662\pi\)
0.0366598 + 0.999328i \(0.488328\pi\)
\(692\) −0.202603 −0.00770182
\(693\) 0 0
\(694\) −4.47105 −0.169719
\(695\) 4.08373 + 1.81819i 0.154905 + 0.0689680i
\(696\) −11.6706 2.48066i −0.442373 0.0940292i
\(697\) −3.64160 4.04440i −0.137935 0.153193i
\(698\) −2.97372 + 28.2931i −0.112557 + 1.07091i
\(699\) −0.908531 0.660086i −0.0343638 0.0249668i
\(700\) 0 0
\(701\) 10.9734 + 33.7727i 0.414460 + 1.27558i 0.912733 + 0.408557i \(0.133968\pi\)
−0.498273 + 0.867020i \(0.666032\pi\)
\(702\) 11.6020 + 5.16552i 0.437887 + 0.194960i
\(703\) −4.09992 + 7.10127i −0.154632 + 0.267830i
\(704\) 19.5488 + 14.3216i 0.736773 + 0.539766i
\(705\) 2.41483 + 4.18260i 0.0909476 + 0.157526i
\(706\) 12.7662 9.27518i 0.480462 0.349076i
\(707\) 0 0
\(708\) 0.650893 2.00324i 0.0244621 0.0752865i
\(709\) −4.57881 + 43.5645i −0.171961 + 1.63610i 0.479589 + 0.877493i \(0.340786\pi\)
−0.651550 + 0.758606i \(0.725881\pi\)
\(710\) 6.09320 2.71287i 0.228674 0.101812i
\(711\) −0.915587 1.01686i −0.0343372 0.0381353i
\(712\) 16.1839 17.9741i 0.606518 0.673606i
\(713\) −1.88945 + 1.37277i −0.0707604 + 0.0514105i
\(714\) 0 0
\(715\) 1.64615 1.81375i 0.0615625 0.0678303i
\(716\) −1.34574 2.33090i −0.0502928 0.0871096i
\(717\) −0.0586140 0.557675i −0.00218898 0.0208268i
\(718\) 0.871175 + 0.185174i 0.0325119 + 0.00691063i
\(719\) 15.5139 3.29758i 0.578570 0.122979i 0.0906741 0.995881i \(-0.471098\pi\)
0.487896 + 0.872902i \(0.337765\pi\)
\(720\) 0.617255 + 0.448462i 0.0230037 + 0.0167132i
\(721\) 0 0
\(722\) 0.532741 1.63961i 0.0198266 0.0610199i
\(723\) 11.3001 12.5500i 0.420254 0.466739i
\(724\) −0.0152425 0.145023i −0.000566483 0.00538973i
\(725\) 6.50247 11.2626i 0.241496 0.418283i
\(726\) −26.1046 0.206663i −0.968833 0.00766999i
\(727\) −13.7719 −0.510770 −0.255385 0.966839i \(-0.582202\pi\)
−0.255385 + 0.966839i \(0.582202\pi\)
\(728\) 0 0
\(729\) 9.11803 + 28.0624i 0.337705 + 1.03935i
\(730\) −8.91923 + 1.89584i −0.330115 + 0.0701682i
\(731\) −41.5851 + 18.5149i −1.53808 + 0.684798i
\(732\) 3.40841 1.51752i 0.125979 0.0560893i
\(733\) −19.1401 + 4.06836i −0.706956 + 0.150268i −0.547339 0.836911i \(-0.684359\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(734\) 12.5380 + 38.5881i 0.462788 + 1.42431i
\(735\) 0 0
\(736\) −1.54170 −0.0568278
\(737\) −15.1562 3.28430i −0.558286 0.120979i
\(738\) −0.291640 + 0.505135i −0.0107354 + 0.0185943i
\(739\) 1.16593 + 11.0931i 0.0428894 + 0.408066i 0.994812 + 0.101728i \(0.0324371\pi\)
−0.951923 + 0.306338i \(0.900896\pi\)
\(740\) 0.0917739 0.101925i 0.00337368 0.00374685i
\(741\) −3.34021 + 10.2801i −0.122706 + 0.377649i
\(742\) 0 0
\(743\) −16.7102 12.1407i −0.613038 0.445398i 0.237445 0.971401i \(-0.423690\pi\)
−0.850483 + 0.526003i \(0.823690\pi\)
\(744\) 5.55260 1.18024i 0.203568 0.0432697i
\(745\) 6.83087 + 1.45195i 0.250264 + 0.0531952i
\(746\) −4.51533 42.9605i −0.165318 1.57290i
\(747\) 3.29615 + 5.70911i 0.120600 + 0.208885i
\(748\) −0.284517 + 2.60766i −0.0104030 + 0.0953455i
\(749\) 0 0
\(750\) 8.76593 6.36882i 0.320087 0.232557i
\(751\) 17.7983 19.7670i 0.649468 0.721307i −0.325030 0.945704i \(-0.605374\pi\)
0.974498 + 0.224397i \(0.0720412\pi\)
\(752\) −18.3141 20.3399i −0.667847 0.741720i
\(753\) 10.3397 4.60352i 0.376799 0.167762i
\(754\) 0.659725 6.27686i 0.0240258 0.228590i
\(755\) 0.414271 1.27499i 0.0150769 0.0464018i
\(756\) 0 0
\(757\) −17.0702 + 12.4022i −0.620427 + 0.450767i −0.853071 0.521796i \(-0.825262\pi\)
0.232644 + 0.972562i \(0.425262\pi\)
\(758\) 18.5862 + 32.1922i 0.675080 + 1.16927i
\(759\) −7.85915 + 5.66261i −0.285269 + 0.205540i
\(760\) −2.67155 + 4.62727i −0.0969075 + 0.167849i
\(761\) 7.30602 + 3.25285i 0.264843 + 0.117916i 0.534862 0.844939i \(-0.320363\pi\)
−0.270019 + 0.962855i \(0.587030\pi\)
\(762\) 6.26311 + 19.2759i 0.226889 + 0.698292i
\(763\) 0 0
\(764\) 1.96937 + 1.43083i 0.0712494 + 0.0517657i
\(765\) 0.0974106 0.926800i 0.00352189 0.0335085i
\(766\) −31.3394 34.8059i −1.13234 1.25759i
\(767\) −13.3166 2.83052i −0.480833 0.102204i
\(768\) 5.33758 + 2.37645i 0.192603 + 0.0857526i
\(769\) 52.0476 1.87689 0.938443 0.345435i \(-0.112269\pi\)
0.938443 + 0.345435i \(0.112269\pi\)
\(770\) 0 0
\(771\) 16.0969 0.579716
\(772\) 1.67904 + 0.747556i 0.0604299 + 0.0269051i
\(773\) −1.54644 0.328707i −0.0556218 0.0118228i 0.180017 0.983664i \(-0.442385\pi\)
−0.235639 + 0.971841i \(0.575718\pi\)
\(774\) 3.26449 + 3.62558i 0.117340 + 0.130319i
\(775\) −0.646765 + 6.15355i −0.0232325 + 0.221042i
\(776\) −5.93089 4.30904i −0.212906 0.154686i
\(777\) 0 0
\(778\) −8.04587 24.7626i −0.288458 0.887784i
\(779\) −4.01552 1.78782i −0.143871 0.0640554i
\(780\) 0.0903990 0.156576i 0.00323680 0.00560631i
\(781\) −10.1072 + 30.6929i −0.361665 + 1.09828i
\(782\) 6.91975 + 11.9854i 0.247450 + 0.428595i
\(783\) 12.0392 8.74702i 0.430247 0.312593i
\(784\) 0 0
\(785\) −2.72336 + 8.38164i −0.0972009 + 0.299154i
\(786\) 2.39811 22.8165i 0.0855376 0.813836i
\(787\) −21.3685 + 9.51386i −0.761704 + 0.339132i −0.750557 0.660805i \(-0.770215\pi\)
−0.0111467 + 0.999938i \(0.503548\pi\)
\(788\) −0.233035 0.258812i −0.00830153 0.00921978i
\(789\) 15.3527 17.0509i 0.546571 0.607029i
\(790\) −1.98399 + 1.44145i −0.0705872 + 0.0512846i
\(791\) 0 0
\(792\) −3.36282 + 0.700889i −0.119493 + 0.0249050i
\(793\) −12.0574 20.8840i −0.428170 0.741612i
\(794\) 2.03981 + 19.4075i 0.0723901 + 0.688746i
\(795\) −9.75392 2.07326i −0.345936 0.0735309i
\(796\) 3.00131 0.637949i 0.106379 0.0226115i
\(797\) −37.3376 27.1274i −1.32257 0.960900i −0.999896 0.0143887i \(-0.995420\pi\)
−0.322669 0.946512i \(-0.604580\pi\)
\(798\) 0 0
\(799\) −10.3305 + 31.7941i −0.365468 + 1.12479i
\(800\) −2.73303 + 3.03534i −0.0966273 + 0.107315i
\(801\) 0.356136 + 3.38840i 0.0125834 + 0.119723i
\(802\) −2.55917 + 4.43261i −0.0903675 + 0.156521i
\(803\) 22.2400 38.1711i 0.784833 1.34703i
\(804\) −1.14470 −0.0403704
\(805\) 0 0
\(806\) 0.927927 + 2.85587i 0.0326848 + 0.100594i
\(807\) −29.1261 + 6.19095i −1.02529 + 0.217932i
\(808\) −0.442862 + 0.197175i −0.0155798 + 0.00693658i
\(809\) 30.8323 13.7274i 1.08400 0.482630i 0.214586 0.976705i \(-0.431160\pi\)
0.869419 + 0.494075i \(0.164493\pi\)
\(810\) 5.16150 1.09711i 0.181357 0.0385485i
\(811\) 9.50690 + 29.2592i 0.333833 + 1.02743i 0.967294 + 0.253657i \(0.0816334\pi\)
−0.633462 + 0.773774i \(0.718367\pi\)
\(812\) 0 0
\(813\) −1.18212 −0.0414588
\(814\) 0.950391 + 9.40014i 0.0333112 + 0.329475i
\(815\) 2.70591 4.68677i 0.0947839 0.164171i
\(816\) −3.78370 35.9995i −0.132456 1.26023i
\(817\) −24.6008 + 27.3220i −0.860673 + 0.955875i
\(818\) −13.4276 + 41.3259i −0.469485 + 1.44493i
\(819\) 0 0
\(820\) 0.0594801 + 0.0432148i 0.00207714 + 0.00150913i
\(821\) −11.8144 + 2.51123i −0.412326 + 0.0876426i −0.409404 0.912353i \(-0.634263\pi\)
−0.00292180 + 0.999996i \(0.500930\pi\)
\(822\) −32.5241 6.91322i −1.13441 0.241126i
\(823\) 2.59426 + 24.6827i 0.0904301 + 0.860385i 0.941880 + 0.335949i \(0.109057\pi\)
−0.851450 + 0.524436i \(0.824276\pi\)
\(824\) 22.8817 + 39.6322i 0.797121 + 1.38065i
\(825\) −2.78352 + 25.5116i −0.0969098 + 0.888201i
\(826\) 0 0
\(827\) −4.18529 + 3.04079i −0.145537 + 0.105739i −0.658171 0.752868i \(-0.728670\pi\)
0.512634 + 0.858607i \(0.328670\pi\)
\(828\) 0.0698025 0.0775235i 0.00242580 0.00269413i
\(829\) −21.1134 23.4488i −0.733299 0.814412i 0.254999 0.966941i \(-0.417925\pi\)
−0.988299 + 0.152530i \(0.951258\pi\)
\(830\) 10.7935 4.80556i 0.374647 0.166803i
\(831\) −2.54785 + 24.2412i −0.0883840 + 0.840917i
\(832\) 3.57270 10.9956i 0.123861 0.381205i
\(833\) 0 0
\(834\) −18.3889 + 13.3603i −0.636755 + 0.462629i
\(835\) −1.47602 2.55654i −0.0510798 0.0884727i
\(836\) 0.646707 + 2.01750i 0.0223668 + 0.0697766i
\(837\) −3.54009 + 6.13162i −0.122363 + 0.211940i
\(838\) −15.6038 6.94724i −0.539023 0.239989i
\(839\) 1.80355 + 5.55077i 0.0622656 + 0.191634i 0.977350 0.211628i \(-0.0678765\pi\)
−0.915085 + 0.403262i \(0.867876\pi\)
\(840\) 0 0
\(841\) 17.4784 + 12.6988i 0.602703 + 0.437889i
\(842\) 3.04865 29.0060i 0.105063 0.999611i
\(843\) −11.5804 12.8614i −0.398851 0.442969i
\(844\) −0.794042 0.168779i −0.0273320 0.00580960i
\(845\) 4.47541 + 1.99258i 0.153959 + 0.0685469i
\(846\) 3.58291 0.123183
\(847\) 0 0
\(848\) 56.5112 1.94060
\(849\) −13.4643 5.99470i −0.462094 0.205737i
\(850\) 35.8640 + 7.62313i 1.23013 + 0.261471i
\(851\) 2.34583 + 2.60531i 0.0804140 + 0.0893088i
\(852\) −0.249324 + 2.37216i −0.00854171 + 0.0812690i
\(853\) −16.4604 11.9592i −0.563593 0.409475i 0.269179 0.963090i \(-0.413248\pi\)
−0.832772 + 0.553616i \(0.813248\pi\)
\(854\) 0 0
\(855\) −0.232586 0.715828i −0.00795429 0.0244808i
\(856\) −38.3364 17.0685i −1.31031 0.583389i
\(857\) −7.55436 + 13.0845i −0.258052 + 0.446959i −0.965720 0.259586i \(-0.916414\pi\)
0.707668 + 0.706545i \(0.249747\pi\)
\(858\) 3.80175 + 11.8601i 0.129790 + 0.404898i
\(859\) −16.9821 29.4138i −0.579420 1.00359i −0.995546 0.0942781i \(-0.969946\pi\)
0.416126 0.909307i \(-0.363388\pi\)
\(860\) 0.497507 0.361460i 0.0169648 0.0123257i
\(861\) 0 0
\(862\) −13.7090 + 42.1920i −0.466931 + 1.43707i
\(863\) 0.290311 2.76212i 0.00988230 0.0940238i −0.988469 0.151424i \(-0.951614\pi\)
0.998351 + 0.0573997i \(0.0182809\pi\)
\(864\) −4.26969 + 1.90099i −0.145258 + 0.0646730i
\(865\) 0.418196 + 0.464453i 0.0142191 + 0.0157919i
\(866\) −5.60124 + 6.22081i −0.190338 + 0.211392i
\(867\) −13.5155 + 9.81958i −0.459010 + 0.333490i
\(868\) 0 0
\(869\) 1.28869 11.8111i 0.0437156 0.400664i
\(870\) −1.50612 2.60868i −0.0510623 0.0884425i
\(871\) 0.773368 + 7.35811i 0.0262046 + 0.249320i
\(872\) −29.2678 6.22105i −0.991131 0.210671i
\(873\) 1.01012 0.214708i 0.0341875 0.00726678i
\(874\) 9.04292 + 6.57006i 0.305881 + 0.222236i
\(875\) 0 0
\(876\) 1.00767 3.10130i 0.0340461 0.104783i
\(877\) 33.2413 36.9182i 1.12248 1.24664i 0.156595 0.987663i \(-0.449948\pi\)
0.965884 0.258976i \(-0.0833849\pi\)
\(878\) −1.05002 9.99024i −0.0354364 0.337154i
\(879\) 9.61840 16.6596i 0.324421 0.561913i
\(880\) 0.666404 + 6.59128i 0.0224645 + 0.222192i
\(881\) 27.3064 0.919975 0.459988 0.887925i \(-0.347854\pi\)
0.459988 + 0.887925i \(0.347854\pi\)
\(882\) 0 0
\(883\) −5.50388 16.9392i −0.185220 0.570049i 0.814732 0.579838i \(-0.196884\pi\)
−0.999952 + 0.00978852i \(0.996884\pi\)
\(884\) 1.22412 0.260194i 0.0411715 0.00875126i
\(885\) −5.93581 + 2.64279i −0.199530 + 0.0888365i
\(886\) −0.134924 + 0.0600721i −0.00453286 + 0.00201816i
\(887\) −16.1129 + 3.42490i −0.541018 + 0.114997i −0.470312 0.882500i \(-0.655859\pi\)
−0.0707063 + 0.997497i \(0.522525\pi\)
\(888\) −2.63319 8.10413i −0.0883641 0.271957i
\(889\) 0 0
\(890\) 6.10625 0.204682
\(891\) −12.8701 + 22.0894i −0.431166 + 0.740021i
\(892\) −1.92328 + 3.33122i −0.0643961 + 0.111537i
\(893\) 2.82231 + 26.8525i 0.0944451 + 0.898585i
\(894\) −23.7604 + 26.3886i −0.794666 + 0.882566i
\(895\) −2.56565 + 7.89625i −0.0857601 + 0.263942i
\(896\) 0 0
\(897\) 3.73877 + 2.71638i 0.124834 + 0.0906971i
\(898\) −44.1950 + 9.39393i −1.47480 + 0.313479i
\(899\) 3.44172 + 0.731561i 0.114788 + 0.0243989i
\(900\) −0.0288887 0.274858i −0.000962958 0.00916194i
\(901\) −34.5119 59.7764i −1.14976 1.99144i
\(902\) −4.95809 + 1.03338i −0.165086 + 0.0344078i
\(903\) 0 0
\(904\) −3.88299 + 2.82116i −0.129146 + 0.0938304i
\(905\) −0.300992 + 0.334285i −0.0100053 + 0.0111120i
\(906\) 4.56125 + 5.06578i 0.151537 + 0.168299i
\(907\) 26.0248 11.5870i 0.864139 0.384739i 0.0737001 0.997280i \(-0.476519\pi\)
0.790439 + 0.612541i \(0.209853\pi\)
\(908\) −0.343348 + 3.26674i −0.0113944 + 0.108411i
\(909\) 0.0211022 0.0649460i 0.000699917 0.00215412i
\(910\) 0 0
\(911\) 9.08955 6.60394i 0.301150 0.218798i −0.426940 0.904280i \(-0.640408\pi\)
0.728090 + 0.685482i \(0.240408\pi\)
\(912\) −14.6178 25.3188i −0.484044 0.838389i
\(913\) −17.9039 + 54.3692i −0.592531 + 1.79936i
\(914\) 16.9668 29.3874i 0.561213 0.972049i
\(915\) −10.5142 4.68120i −0.347587 0.154756i
\(916\) −0.959910 2.95430i −0.0317163 0.0976128i
\(917\) 0 0
\(918\) 33.9426 + 24.6607i 1.12027 + 0.813925i
\(919\) −0.0815799 + 0.776181i −0.00269107 + 0.0256039i −0.995785 0.0917179i \(-0.970764\pi\)
0.993094 + 0.117322i \(0.0374309\pi\)
\(920\) 1.52857 + 1.69765i 0.0503954 + 0.0559698i
\(921\) 3.51468 + 0.747069i 0.115813 + 0.0246167i
\(922\) −3.72284 1.65752i −0.122605 0.0545874i
\(923\) 15.4167 0.507446
\(924\) 0 0
\(925\) 9.28795 0.305386
\(926\) 34.9654 + 15.5676i 1.14903 + 0.511583i
\(927\) −6.30566 1.34031i −0.207105 0.0440215i
\(928\) 1.55419 + 1.72611i 0.0510189 + 0.0566622i
\(929\) 2.78007 26.4506i 0.0912112 0.867817i −0.849267 0.527963i \(-0.822956\pi\)
0.940478 0.339853i \(-0.110377\pi\)
\(930\) 1.15945 + 0.842387i 0.0380198 + 0.0276230i
\(931\) 0 0
\(932\) 0.0324505 + 0.0998725i 0.00106295 + 0.00327143i
\(933\) 31.6509 + 14.0919i 1.03620 + 0.461348i
\(934\) 1.94950 3.37663i 0.0637896 0.110487i
\(935\) 6.56515 4.73027i 0.214703 0.154696i
\(936\) 0.819416 + 1.41927i 0.0267835 + 0.0463903i
\(937\) 33.9542 24.6691i 1.10923 0.805906i 0.126691 0.991942i \(-0.459564\pi\)
0.982543 + 0.186036i \(0.0595642\pi\)
\(938\) 0 0
\(939\) 15.7774 48.5578i 0.514875 1.58462i
\(940\) 0.0472072 0.449146i 0.00153973 0.0146495i
\(941\) 44.7938 19.9435i 1.46024 0.650140i 0.485651 0.874153i \(-0.338582\pi\)
0.974586 + 0.224013i \(0.0719158\pi\)
\(942\) −29.9850 33.3018i −0.976965 1.08503i
\(943\) −1.25748 + 1.39658i −0.0409493 + 0.0454788i
\(944\) 29.7897 21.6435i 0.969574 0.704437i
\(945\) 0 0
\(946\) −4.59475 + 42.1120i −0.149388 + 1.36918i
\(947\) 13.6476 + 23.6384i 0.443489 + 0.768145i 0.997946 0.0640672i \(-0.0204072\pi\)
−0.554457 + 0.832213i \(0.687074\pi\)
\(948\) −0.0916709 0.872190i −0.00297733 0.0283274i
\(949\) −20.6159 4.38205i −0.669221 0.142247i
\(950\) 28.9661 6.15692i 0.939783 0.199757i
\(951\) 17.2799 + 12.5546i 0.560339 + 0.407110i
\(952\) 0 0
\(953\) 6.10023 18.7746i 0.197606 0.608169i −0.802330 0.596880i \(-0.796407\pi\)
0.999936 0.0112883i \(-0.00359326\pi\)
\(954\) −4.95001 + 5.49754i −0.160262 + 0.177990i
\(955\) −0.784923 7.46804i −0.0253995 0.241660i
\(956\) −0.0262177 + 0.0454104i −0.000847941 + 0.00146868i
\(957\) 14.2628 + 3.09070i 0.461050 + 0.0999082i
\(958\) −12.1478 −0.392478
\(959\) 0 0
\(960\) −1.70513 5.24785i −0.0550329 0.169374i
\(961\) 28.6851 6.09720i 0.925325 0.196684i
\(962\) 4.11784 1.83338i 0.132765 0.0591106i
\(963\) 5.40032 2.40438i 0.174023 0.0774800i
\(964\) −1.54466 + 0.328327i −0.0497500 + 0.0105747i
\(965\) −1.75200 5.39211i −0.0563990 0.173578i
\(966\) 0 0
\(967\) −12.6734 −0.407551 −0.203775 0.979018i \(-0.565321\pi\)
−0.203775 + 0.979018i \(0.565321\pi\)
\(968\) −23.9910 17.7223i −0.771100 0.569618i
\(969\) −17.8545 + 30.9249i −0.573568 + 0.993449i
\(970\) −0.193463 1.84068i −0.00621172 0.0591006i
\(971\) −11.1769 + 12.4132i −0.358684 + 0.398359i −0.895297 0.445470i \(-0.853037\pi\)
0.536613 + 0.843828i \(0.319703\pi\)
\(972\) 0.184414 0.567569i 0.00591509 0.0182048i
\(973\) 0 0
\(974\) −23.2523 16.8938i −0.745052 0.541312i
\(975\) 11.9759 2.54556i 0.383537 0.0815233i
\(976\) 63.7982 + 13.5607i 2.04213 + 0.434068i
\(977\) −2.85835 27.1954i −0.0914468 0.870058i −0.940052 0.341031i \(-0.889224\pi\)
0.848605 0.529027i \(-0.177443\pi\)
\(978\) 13.7589 + 23.8312i 0.439962 + 0.762036i
\(979\) −19.8822 + 21.9064i −0.635439 + 0.700133i
\(980\) 0 0
\(981\) 3.40997 2.47749i 0.108872 0.0791001i
\(982\) 28.1492 31.2628i 0.898277 0.997637i
\(983\) 36.8065 + 40.8778i 1.17395 + 1.30380i 0.943752 + 0.330654i \(0.107269\pi\)
0.230194 + 0.973145i \(0.426064\pi\)
\(984\) 4.17288 1.85789i 0.133027 0.0592272i
\(985\) −0.112297 + 1.06843i −0.00357807 + 0.0340431i
\(986\) 6.44313 19.8299i 0.205191 0.631513i
\(987\) 0 0
\(988\) 0.817723 0.594110i 0.0260152 0.0189012i
\(989\) 7.85939 + 13.6129i 0.249914 + 0.432864i
\(990\) −0.699588 0.512524i −0.0222344 0.0162891i
\(991\) −26.6164 + 46.1009i −0.845497 + 1.46444i 0.0396921 + 0.999212i \(0.487362\pi\)
−0.885189 + 0.465232i \(0.845971\pi\)
\(992\) −1.00955 0.449480i −0.0320532 0.0142710i
\(993\) 4.73826 + 14.5829i 0.150364 + 0.462774i
\(994\) 0 0
\(995\) −7.65750 5.56350i −0.242759 0.176375i
\(996\) −0.441652 + 4.20204i −0.0139943 + 0.133147i
\(997\) −21.9171 24.3414i −0.694121 0.770900i 0.288307 0.957538i \(-0.406908\pi\)
−0.982429 + 0.186638i \(0.940241\pi\)
\(998\) 40.0992 + 8.52334i 1.26932 + 0.269802i
\(999\) 9.70918 + 4.32281i 0.307185 + 0.136768i
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 539.2.q.b.410.1 16
7.2 even 3 inner 539.2.q.b.520.2 16
7.3 odd 6 77.2.f.a.36.2 yes 8
7.4 even 3 539.2.f.d.344.2 8
7.5 odd 6 539.2.q.c.520.2 16
7.6 odd 2 539.2.q.c.410.1 16
11.4 even 5 inner 539.2.q.b.312.2 16
21.17 even 6 693.2.m.g.190.1 8
77.3 odd 30 847.2.f.p.148.1 8
77.4 even 15 539.2.f.d.246.2 8
77.10 even 6 847.2.f.q.729.1 8
77.17 even 30 847.2.f.s.372.2 8
77.24 even 30 847.2.a.k.1.4 4
77.26 odd 30 539.2.q.c.422.1 16
77.31 odd 30 847.2.a.l.1.1 4
77.37 even 15 inner 539.2.q.b.422.1 16
77.38 odd 30 847.2.f.p.372.1 8
77.46 odd 30 5929.2.a.bb.1.4 4
77.48 odd 10 539.2.q.c.312.2 16
77.52 even 30 847.2.f.s.148.2 8
77.53 even 15 5929.2.a.bi.1.1 4
77.59 odd 30 77.2.f.a.15.2 8
77.73 even 30 847.2.f.q.323.1 8
231.59 even 30 693.2.m.g.631.1 8
231.101 odd 30 7623.2.a.co.1.1 4
231.185 even 30 7623.2.a.ch.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.15.2 8 77.59 odd 30
77.2.f.a.36.2 yes 8 7.3 odd 6
539.2.f.d.246.2 8 77.4 even 15
539.2.f.d.344.2 8 7.4 even 3
539.2.q.b.312.2 16 11.4 even 5 inner
539.2.q.b.410.1 16 1.1 even 1 trivial
539.2.q.b.422.1 16 77.37 even 15 inner
539.2.q.b.520.2 16 7.2 even 3 inner
539.2.q.c.312.2 16 77.48 odd 10
539.2.q.c.410.1 16 7.6 odd 2
539.2.q.c.422.1 16 77.26 odd 30
539.2.q.c.520.2 16 7.5 odd 6
693.2.m.g.190.1 8 21.17 even 6
693.2.m.g.631.1 8 231.59 even 30
847.2.a.k.1.4 4 77.24 even 30
847.2.a.l.1.1 4 77.31 odd 30
847.2.f.p.148.1 8 77.3 odd 30
847.2.f.p.372.1 8 77.38 odd 30
847.2.f.q.323.1 8 77.73 even 30
847.2.f.q.729.1 8 77.10 even 6
847.2.f.s.148.2 8 77.52 even 30
847.2.f.s.372.2 8 77.17 even 30
5929.2.a.bb.1.4 4 77.46 odd 30
5929.2.a.bi.1.1 4 77.53 even 15
7623.2.a.ch.1.4 4 231.185 even 30
7623.2.a.co.1.1 4 231.101 odd 30