Properties

Label 605.2.g.n.81.2
Level $605$
Weight $2$
Character 605.81
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) 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 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.2
Root \(-0.762262 + 2.34600i\) of defining polynomial
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.n.366.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.04238 + 1.48388i) q^{2} +(-0.762262 + 2.34600i) q^{3} +(1.35140 + 4.15918i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-5.03801 + 3.66033i) q^{6} +(-0.646930 - 1.99105i) q^{7} +(-1.85140 + 5.69802i) q^{8} +(-2.49563 - 1.81318i) q^{9} +O(q^{10})\) \(q+(2.04238 + 1.48388i) q^{2} +(-0.762262 + 2.34600i) q^{3} +(1.35140 + 4.15918i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-5.03801 + 3.66033i) q^{6} +(-0.646930 - 1.99105i) q^{7} +(-1.85140 + 5.69802i) q^{8} +(-2.49563 - 1.81318i) q^{9} -2.52452 q^{10} -10.7876 q^{12} +(1.04238 + 0.757336i) q^{13} +(1.63319 - 5.02644i) q^{14} +(-0.762262 - 2.34600i) q^{15} +(-5.16042 + 3.74926i) q^{16} +(-2.41998 + 1.75822i) q^{17} +(-2.40649 - 7.40641i) q^{18} +(-0.664789 + 2.04601i) q^{19} +(-3.53801 - 2.57052i) q^{20} +5.16413 q^{21} +8.77882 q^{23} +(-11.9563 - 8.68677i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.00515 + 3.09354i) q^{26} +(0.169161 - 0.122903i) q^{27} +(7.40686 - 5.38140i) q^{28} +(0.189313 + 0.582646i) q^{29} +(1.92435 - 5.92254i) q^{30} +(2.94887 + 2.14248i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(1.69369 + 1.23053i) q^{35} +(4.16875 - 12.8301i) q^{36} +(-0.578100 - 1.77921i) q^{37} +(-4.39378 + 3.19227i) q^{38} +(-2.57128 + 1.86814i) q^{39} +(-1.85140 - 5.69802i) q^{40} +(1.57810 - 4.85689i) q^{41} +(10.5471 + 7.66294i) q^{42} -5.17287 q^{43} +3.08477 q^{45} +(17.9297 + 13.0267i) q^{46} +(-2.25789 + 6.94907i) q^{47} +(-4.86218 - 14.9643i) q^{48} +(2.11737 - 1.53836i) q^{49} +(2.04238 - 1.48388i) q^{50} +(-2.28012 - 7.01749i) q^{51} +(-1.74122 + 5.35892i) q^{52} +(2.38030 + 1.72939i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(-4.29320 - 3.11919i) q^{57} +(-0.477925 + 1.47090i) q^{58} +(-2.00682 - 6.17636i) q^{59} +(8.72732 - 6.34077i) q^{60} +(-0.406490 + 0.295332i) q^{61} +(2.84355 + 8.75154i) q^{62} +(-1.99563 + 6.14191i) q^{63} +(1.90523 + 1.38423i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(-10.5831 - 7.68907i) q^{68} +(-6.69176 + 20.5951i) q^{69} +(1.63319 + 5.02644i) q^{70} +(9.14526 - 6.64442i) q^{71} +(14.9519 - 10.8632i) q^{72} +(3.43539 + 10.5730i) q^{73} +(1.45943 - 4.49166i) q^{74} +(1.99563 + 1.44991i) q^{75} -9.40812 q^{76} -8.02363 q^{78} +(4.33558 + 3.14998i) q^{79} +(1.97110 - 6.06643i) q^{80} +(-2.70035 - 8.31082i) q^{81} +(10.4301 - 7.57793i) q^{82} +(8.77408 - 6.37474i) q^{83} +(6.97880 + 21.4785i) q^{84} +(0.924349 - 2.84485i) q^{85} +(-10.5650 - 7.67591i) q^{86} -1.51119 q^{87} -4.32336 q^{89} +(6.30027 + 4.57742i) q^{90} +(0.833541 - 2.56538i) q^{91} +(11.8637 + 36.5127i) q^{92} +(-7.27408 + 5.28493i) q^{93} +(-14.9230 + 10.8422i) q^{94} +(-0.664789 - 2.04601i) q^{95} +(3.14089 - 9.66666i) q^{96} +(0.284493 + 0.206696i) q^{97} +6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.04238 + 1.48388i 1.44418 + 1.04926i 0.987148 + 0.159812i \(0.0510887\pi\)
0.457035 + 0.889449i \(0.348911\pi\)
\(3\) −0.762262 + 2.34600i −0.440092 + 1.35446i 0.447685 + 0.894191i \(0.352249\pi\)
−0.887777 + 0.460273i \(0.847751\pi\)
\(4\) 1.35140 + 4.15918i 0.675700 + 2.07959i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) −5.03801 + 3.66033i −2.05676 + 1.49432i
\(7\) −0.646930 1.99105i −0.244517 0.752545i −0.995716 0.0924689i \(-0.970524\pi\)
0.751199 0.660076i \(-0.229476\pi\)
\(8\) −1.85140 + 5.69802i −0.654569 + 2.01456i
\(9\) −2.49563 1.81318i −0.831876 0.604393i
\(10\) −2.52452 −0.798325
\(11\) 0 0
\(12\) −10.7876 −3.11410
\(13\) 1.04238 + 0.757336i 0.289105 + 0.210047i 0.722879 0.690975i \(-0.242818\pi\)
−0.433774 + 0.901022i \(0.642818\pi\)
\(14\) 1.63319 5.02644i 0.436489 1.34337i
\(15\) −0.762262 2.34600i −0.196815 0.605735i
\(16\) −5.16042 + 3.74926i −1.29010 + 0.937316i
\(17\) −2.41998 + 1.75822i −0.586931 + 0.426430i −0.841216 0.540699i \(-0.818160\pi\)
0.254285 + 0.967129i \(0.418160\pi\)
\(18\) −2.40649 7.40641i −0.567215 1.74571i
\(19\) −0.664789 + 2.04601i −0.152513 + 0.469387i −0.997900 0.0647668i \(-0.979370\pi\)
0.845387 + 0.534154i \(0.179370\pi\)
\(20\) −3.53801 2.57052i −0.791123 0.574785i
\(21\) 5.16413 1.12690
\(22\) 0 0
\(23\) 8.77882 1.83051 0.915255 0.402874i \(-0.131989\pi\)
0.915255 + 0.402874i \(0.131989\pi\)
\(24\) −11.9563 8.68677i −2.44057 1.77318i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 1.00515 + 3.09354i 0.197126 + 0.606693i
\(27\) 0.169161 0.122903i 0.0325550 0.0236526i
\(28\) 7.40686 5.38140i 1.39977 1.01699i
\(29\) 0.189313 + 0.582646i 0.0351545 + 0.108195i 0.967094 0.254419i \(-0.0818844\pi\)
−0.931939 + 0.362614i \(0.881884\pi\)
\(30\) 1.92435 5.92254i 0.351336 1.08130i
\(31\) 2.94887 + 2.14248i 0.529633 + 0.384801i 0.820221 0.572047i \(-0.193851\pi\)
−0.290587 + 0.956848i \(0.593851\pi\)
\(32\) −4.12048 −0.728405
\(33\) 0 0
\(34\) −7.55150 −1.29507
\(35\) 1.69369 + 1.23053i 0.286285 + 0.207998i
\(36\) 4.16875 12.8301i 0.694792 2.13835i
\(37\) −0.578100 1.77921i −0.0950391 0.292500i 0.892225 0.451592i \(-0.149144\pi\)
−0.987264 + 0.159091i \(0.949144\pi\)
\(38\) −4.39378 + 3.19227i −0.712766 + 0.517855i
\(39\) −2.57128 + 1.86814i −0.411734 + 0.299142i
\(40\) −1.85140 5.69802i −0.292732 0.900937i
\(41\) 1.57810 4.85689i 0.246458 0.758519i −0.748935 0.662643i \(-0.769435\pi\)
0.995393 0.0958763i \(-0.0305653\pi\)
\(42\) 10.5471 + 7.66294i 1.62746 + 1.18242i
\(43\) −5.17287 −0.788856 −0.394428 0.918927i \(-0.629057\pi\)
−0.394428 + 0.918927i \(0.629057\pi\)
\(44\) 0 0
\(45\) 3.08477 0.459850
\(46\) 17.9297 + 13.0267i 2.64359 + 1.92068i
\(47\) −2.25789 + 6.94907i −0.329347 + 1.01363i 0.640093 + 0.768298i \(0.278896\pi\)
−0.969440 + 0.245329i \(0.921104\pi\)
\(48\) −4.86218 14.9643i −0.701796 2.15991i
\(49\) 2.11737 1.53836i 0.302482 0.219766i
\(50\) 2.04238 1.48388i 0.288837 0.209852i
\(51\) −2.28012 7.01749i −0.319281 0.982645i
\(52\) −1.74122 + 5.35892i −0.241464 + 0.743149i
\(53\) 2.38030 + 1.72939i 0.326959 + 0.237549i 0.739139 0.673553i \(-0.235233\pi\)
−0.412180 + 0.911102i \(0.635233\pi\)
\(54\) 0.527864 0.0718332
\(55\) 0 0
\(56\) 12.5428 1.67610
\(57\) −4.29320 3.11919i −0.568648 0.413147i
\(58\) −0.477925 + 1.47090i −0.0627547 + 0.193139i
\(59\) −2.00682 6.17636i −0.261266 0.804094i −0.992530 0.121999i \(-0.961069\pi\)
0.731264 0.682094i \(-0.238931\pi\)
\(60\) 8.72732 6.34077i 1.12669 0.818590i
\(61\) −0.406490 + 0.295332i −0.0520457 + 0.0378134i −0.613504 0.789692i \(-0.710241\pi\)
0.561458 + 0.827505i \(0.310241\pi\)
\(62\) 2.84355 + 8.75154i 0.361131 + 1.11145i
\(63\) −1.99563 + 6.14191i −0.251425 + 0.773808i
\(64\) 1.90523 + 1.38423i 0.238154 + 0.173029i
\(65\) −1.28846 −0.159813
\(66\) 0 0
\(67\) −7.80964 −0.954099 −0.477050 0.878876i \(-0.658294\pi\)
−0.477050 + 0.878876i \(0.658294\pi\)
\(68\) −10.5831 7.68907i −1.28339 0.932437i
\(69\) −6.69176 + 20.5951i −0.805594 + 2.47936i
\(70\) 1.63319 + 5.02644i 0.195204 + 0.600775i
\(71\) 9.14526 6.64442i 1.08534 0.788548i 0.106736 0.994287i \(-0.465960\pi\)
0.978607 + 0.205740i \(0.0659600\pi\)
\(72\) 14.9519 10.8632i 1.76210 1.28024i
\(73\) 3.43539 + 10.5730i 0.402082 + 1.23748i 0.923308 + 0.384061i \(0.125475\pi\)
−0.521226 + 0.853419i \(0.674525\pi\)
\(74\) 1.45943 4.49166i 0.169655 0.522145i
\(75\) 1.99563 + 1.44991i 0.230435 + 0.167421i
\(76\) −9.40812 −1.07919
\(77\) 0 0
\(78\) −8.02363 −0.908498
\(79\) 4.33558 + 3.14998i 0.487791 + 0.354401i 0.804334 0.594177i \(-0.202522\pi\)
−0.316543 + 0.948578i \(0.602522\pi\)
\(80\) 1.97110 6.06643i 0.220376 0.678248i
\(81\) −2.70035 8.31082i −0.300039 0.923425i
\(82\) 10.4301 7.57793i 1.15181 0.836842i
\(83\) 8.77408 6.37474i 0.963080 0.699719i 0.00921619 0.999958i \(-0.497066\pi\)
0.953864 + 0.300239i \(0.0970664\pi\)
\(84\) 6.97880 + 21.4785i 0.761450 + 2.34350i
\(85\) 0.924349 2.84485i 0.100260 0.308568i
\(86\) −10.5650 7.67591i −1.13925 0.827715i
\(87\) −1.51119 −0.162017
\(88\) 0 0
\(89\) −4.32336 −0.458275 −0.229137 0.973394i \(-0.573591\pi\)
−0.229137 + 0.973394i \(0.573591\pi\)
\(90\) 6.30027 + 4.57742i 0.664107 + 0.482502i
\(91\) 0.833541 2.56538i 0.0873788 0.268924i
\(92\) 11.8637 + 36.5127i 1.23688 + 3.80671i
\(93\) −7.27408 + 5.28493i −0.754287 + 0.548021i
\(94\) −14.9230 + 10.8422i −1.53920 + 1.11829i
\(95\) −0.664789 2.04601i −0.0682059 0.209916i
\(96\) 3.14089 9.66666i 0.320566 0.986599i
\(97\) 0.284493 + 0.206696i 0.0288859 + 0.0209868i 0.602135 0.798395i \(-0.294317\pi\)
−0.573249 + 0.819381i \(0.694317\pi\)
\(98\) 6.60723 0.667431
\(99\) 0 0
\(100\) 4.37322 0.437322
\(101\) −12.7011 9.22791i −1.26381 0.918211i −0.264872 0.964284i \(-0.585330\pi\)
−0.998938 + 0.0460722i \(0.985330\pi\)
\(102\) 5.75622 17.7158i 0.569951 1.75413i
\(103\) 2.06420 + 6.35297i 0.203392 + 0.625977i 0.999776 + 0.0211846i \(0.00674378\pi\)
−0.796383 + 0.604792i \(0.793256\pi\)
\(104\) −6.24518 + 4.53739i −0.612391 + 0.444928i
\(105\) −4.17787 + 3.03540i −0.407718 + 0.296225i
\(106\) 2.29528 + 7.06414i 0.222937 + 0.686130i
\(107\) −4.82313 + 14.8441i −0.466269 + 1.43503i 0.391110 + 0.920344i \(0.372091\pi\)
−0.857379 + 0.514685i \(0.827909\pi\)
\(108\) 0.739779 + 0.537481i 0.0711852 + 0.0517191i
\(109\) −11.5070 −1.10217 −0.551087 0.834448i \(-0.685787\pi\)
−0.551087 + 0.834448i \(0.685787\pi\)
\(110\) 0 0
\(111\) 4.61469 0.438007
\(112\) 10.8034 + 7.84912i 1.02082 + 0.741672i
\(113\) 2.79606 8.60538i 0.263031 0.809526i −0.729110 0.684397i \(-0.760066\pi\)
0.992140 0.125129i \(-0.0399345\pi\)
\(114\) −4.13986 12.7412i −0.387733 1.19332i
\(115\) −7.10222 + 5.16006i −0.662285 + 0.481178i
\(116\) −2.16749 + 1.57477i −0.201246 + 0.146214i
\(117\) −1.22821 3.78006i −0.113548 0.349466i
\(118\) 5.06627 15.5924i 0.466388 1.43539i
\(119\) 5.06625 + 3.68084i 0.464422 + 0.337422i
\(120\) 14.7788 1.34912
\(121\) 0 0
\(122\) −1.26845 −0.114840
\(123\) 10.1914 + 7.40445i 0.918923 + 0.667637i
\(124\) −4.92586 + 15.1602i −0.442356 + 1.36143i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) −13.1897 + 9.58287i −1.17503 + 0.853710i
\(127\) 15.2371 11.0704i 1.35207 0.982339i 0.353169 0.935560i \(-0.385104\pi\)
0.998905 0.0467796i \(-0.0148959\pi\)
\(128\) 4.38378 + 13.4919i 0.387475 + 1.19252i
\(129\) 3.94308 12.1356i 0.347169 1.06848i
\(130\) −2.63152 1.91191i −0.230800 0.167686i
\(131\) 20.0997 1.75612 0.878058 0.478555i \(-0.158839\pi\)
0.878058 + 0.478555i \(0.158839\pi\)
\(132\) 0 0
\(133\) 4.50377 0.390527
\(134\) −15.9503 11.5886i −1.37789 1.00110i
\(135\) −0.0646137 + 0.198861i −0.00556107 + 0.0171152i
\(136\) −5.53801 17.0442i −0.474881 1.46153i
\(137\) 14.5390 10.5632i 1.24215 0.902478i 0.244414 0.969671i \(-0.421404\pi\)
0.997740 + 0.0671930i \(0.0214043\pi\)
\(138\) −44.2278 + 32.1334i −3.76492 + 2.73537i
\(139\) −5.21098 16.0377i −0.441989 1.36030i −0.885752 0.464159i \(-0.846357\pi\)
0.443762 0.896145i \(-0.353643\pi\)
\(140\) −2.82917 + 8.70729i −0.239108 + 0.735900i
\(141\) −14.5814 10.5940i −1.22798 0.892178i
\(142\) 28.5376 2.39482
\(143\) 0 0
\(144\) 19.6766 1.63971
\(145\) −0.495628 0.360095i −0.0411597 0.0299042i
\(146\) −8.67272 + 26.6919i −0.717759 + 2.20904i
\(147\) 1.99500 + 6.13999i 0.164545 + 0.506418i
\(148\) 6.61881 4.80885i 0.544063 0.395285i
\(149\) 1.88797 1.37169i 0.154669 0.112373i −0.507759 0.861499i \(-0.669526\pi\)
0.662428 + 0.749126i \(0.269526\pi\)
\(150\) 1.92435 + 5.92254i 0.157122 + 0.483573i
\(151\) 1.21718 3.74609i 0.0990525 0.304852i −0.889236 0.457448i \(-0.848763\pi\)
0.988289 + 0.152596i \(0.0487634\pi\)
\(152\) −10.4274 7.57597i −0.845776 0.614492i
\(153\) 9.22732 0.745985
\(154\) 0 0
\(155\) −3.64501 −0.292774
\(156\) −11.2448 8.16981i −0.900302 0.654108i
\(157\) −1.50834 + 4.64218i −0.120378 + 0.370486i −0.993031 0.117856i \(-0.962398\pi\)
0.872652 + 0.488342i \(0.162398\pi\)
\(158\) 4.18073 + 12.8669i 0.332601 + 1.02364i
\(159\) −5.87155 + 4.26593i −0.465644 + 0.338310i
\(160\) 3.33354 2.42196i 0.263540 0.191473i
\(161\) −5.67928 17.4790i −0.447590 1.37754i
\(162\) 6.81710 20.9809i 0.535602 1.64841i
\(163\) 5.69202 + 4.13549i 0.445833 + 0.323917i 0.787948 0.615741i \(-0.211143\pi\)
−0.342115 + 0.939658i \(0.611143\pi\)
\(164\) 22.3333 1.74394
\(165\) 0 0
\(166\) 27.3794 2.12505
\(167\) 8.67223 + 6.30075i 0.671078 + 0.487566i 0.870386 0.492370i \(-0.163869\pi\)
−0.199308 + 0.979937i \(0.563869\pi\)
\(168\) −9.56086 + 29.4253i −0.737637 + 2.27021i
\(169\) −3.50422 10.7849i −0.269555 0.829605i
\(170\) 6.10929 4.43866i 0.468561 0.340430i
\(171\) 5.36885 3.90070i 0.410566 0.298294i
\(172\) −6.99062 21.5149i −0.533030 1.64050i
\(173\) −2.59940 + 8.00012i −0.197628 + 0.608238i 0.802307 + 0.596911i \(0.203605\pi\)
−0.999936 + 0.0113267i \(0.996395\pi\)
\(174\) −3.08644 2.24243i −0.233982 0.169998i
\(175\) −2.09351 −0.158254
\(176\) 0 0
\(177\) 16.0195 1.20410
\(178\) −8.82995 6.41533i −0.661833 0.480850i
\(179\) 6.50062 20.0069i 0.485879 1.49538i −0.344824 0.938667i \(-0.612061\pi\)
0.830703 0.556716i \(-0.187939\pi\)
\(180\) 4.16875 + 12.8301i 0.310720 + 0.956299i
\(181\) 1.41020 1.02457i 0.104819 0.0761557i −0.534141 0.845395i \(-0.679365\pi\)
0.638960 + 0.769240i \(0.279365\pi\)
\(182\) 5.50911 4.00261i 0.408363 0.296693i
\(183\) −0.382998 1.17875i −0.0283120 0.0871355i
\(184\) −16.2531 + 50.0219i −1.19820 + 3.68767i
\(185\) 1.51349 + 1.09961i 0.111274 + 0.0808451i
\(186\) −22.6986 −1.66435
\(187\) 0 0
\(188\) −31.9538 −2.33047
\(189\) −0.354140 0.257298i −0.0257599 0.0187157i
\(190\) 1.67828 5.16520i 0.121755 0.374723i
\(191\) 0.00771200 + 0.0237351i 0.000558021 + 0.00171741i 0.951335 0.308158i \(-0.0997126\pi\)
−0.950777 + 0.309876i \(0.899713\pi\)
\(192\) −4.69969 + 3.41452i −0.339171 + 0.246422i
\(193\) 1.17894 0.856548i 0.0848618 0.0616557i −0.544545 0.838731i \(-0.683298\pi\)
0.629407 + 0.777076i \(0.283298\pi\)
\(194\) 0.274331 + 0.844306i 0.0196959 + 0.0606176i
\(195\) 0.982141 3.02272i 0.0703326 0.216461i
\(196\) 9.25974 + 6.72759i 0.661410 + 0.480542i
\(197\) −22.7027 −1.61750 −0.808751 0.588151i \(-0.799856\pi\)
−0.808751 + 0.588151i \(0.799856\pi\)
\(198\) 0 0
\(199\) −6.62834 −0.469870 −0.234935 0.972011i \(-0.575488\pi\)
−0.234935 + 0.972011i \(0.575488\pi\)
\(200\) 4.84703 + 3.52157i 0.342737 + 0.249013i
\(201\) 5.95299 18.3214i 0.419892 1.29229i
\(202\) −12.2475 37.6939i −0.861729 2.65213i
\(203\) 1.03760 0.753862i 0.0728254 0.0529107i
\(204\) 26.1057 18.9669i 1.82776 1.32795i
\(205\) 1.57810 + 4.85689i 0.110219 + 0.339220i
\(206\) −5.21114 + 16.0382i −0.363077 + 1.11744i
\(207\) −21.9087 15.9176i −1.52276 1.10635i
\(208\) −8.21858 −0.569856
\(209\) 0 0
\(210\) −13.0370 −0.899636
\(211\) 4.57709 + 3.32545i 0.315100 + 0.228934i 0.734082 0.679061i \(-0.237613\pi\)
−0.418982 + 0.907995i \(0.637613\pi\)
\(212\) −3.97610 + 12.2372i −0.273080 + 0.840453i
\(213\) 8.61673 + 26.5196i 0.590409 + 1.81709i
\(214\) −31.8774 + 23.1603i −2.17910 + 1.58321i
\(215\) 4.18494 3.04054i 0.285411 0.207363i
\(216\) 0.387117 + 1.19143i 0.0263400 + 0.0810662i
\(217\) 2.35807 7.25738i 0.160076 0.492663i
\(218\) −23.5018 17.0750i −1.59174 1.15647i
\(219\) −27.4230 −1.85308
\(220\) 0 0
\(221\) −3.85410 −0.259255
\(222\) 9.42497 + 6.84764i 0.632563 + 0.459584i
\(223\) 2.43642 7.49852i 0.163155 0.502138i −0.835741 0.549124i \(-0.814961\pi\)
0.998896 + 0.0469856i \(0.0149615\pi\)
\(224\) 2.66566 + 8.20407i 0.178107 + 0.548158i
\(225\) −2.49563 + 1.81318i −0.166375 + 0.120879i
\(226\) 18.4800 13.4265i 1.22927 0.893116i
\(227\) 3.46451 + 10.6627i 0.229948 + 0.707706i 0.997752 + 0.0670213i \(0.0213495\pi\)
−0.767804 + 0.640685i \(0.778650\pi\)
\(228\) 7.17145 22.0715i 0.474941 1.46172i
\(229\) −21.8360 15.8647i −1.44296 1.04837i −0.987413 0.158160i \(-0.949444\pi\)
−0.455547 0.890212i \(-0.650556\pi\)
\(230\) −22.1623 −1.46134
\(231\) 0 0
\(232\) −3.67042 −0.240975
\(233\) −8.77845 6.37792i −0.575095 0.417831i 0.261857 0.965107i \(-0.415665\pi\)
−0.836953 + 0.547275i \(0.815665\pi\)
\(234\) 3.10066 9.54284i 0.202696 0.623835i
\(235\) −2.25789 6.94907i −0.147289 0.453307i
\(236\) 22.9766 16.6935i 1.49565 1.08665i
\(237\) −10.6947 + 7.77017i −0.694697 + 0.504727i
\(238\) 4.88529 + 15.0354i 0.316666 + 0.974599i
\(239\) 3.54327 10.9051i 0.229195 0.705391i −0.768643 0.639678i \(-0.779068\pi\)
0.997839 0.0657129i \(-0.0209322\pi\)
\(240\) 12.7294 + 9.24842i 0.821677 + 0.596983i
\(241\) −12.7542 −0.821572 −0.410786 0.911732i \(-0.634746\pi\)
−0.410786 + 0.911732i \(0.634746\pi\)
\(242\) 0 0
\(243\) 22.1829 1.42303
\(244\) −1.77767 1.29155i −0.113804 0.0826833i
\(245\) −0.808764 + 2.48912i −0.0516701 + 0.159024i
\(246\) 9.82734 + 30.2455i 0.626568 + 1.92838i
\(247\) −2.24248 + 1.62926i −0.142686 + 0.103667i
\(248\) −17.6675 + 12.8362i −1.12188 + 0.815097i
\(249\) 8.26700 + 25.4432i 0.523900 + 1.61240i
\(250\) −0.780121 + 2.40097i −0.0493392 + 0.151850i
\(251\) 9.87130 + 7.17192i 0.623071 + 0.452687i 0.853993 0.520285i \(-0.174174\pi\)
−0.230922 + 0.972972i \(0.574174\pi\)
\(252\) −28.2422 −1.77909
\(253\) 0 0
\(254\) 47.5471 2.98337
\(255\) 5.96943 + 4.33705i 0.373820 + 0.271596i
\(256\) −9.61149 + 29.5811i −0.600718 + 1.84882i
\(257\) −1.82198 5.60747i −0.113652 0.349784i 0.878012 0.478639i \(-0.158870\pi\)
−0.991663 + 0.128855i \(0.958870\pi\)
\(258\) 26.0610 18.9344i 1.62249 1.17881i
\(259\) −3.16850 + 2.30205i −0.196881 + 0.143042i
\(260\) −1.74122 5.35892i −0.107986 0.332346i
\(261\) 0.583986 1.79733i 0.0361478 0.111252i
\(262\) 41.0512 + 29.8254i 2.53615 + 1.84262i
\(263\) 21.7305 1.33996 0.669980 0.742379i \(-0.266302\pi\)
0.669980 + 0.742379i \(0.266302\pi\)
\(264\) 0 0
\(265\) −2.94221 −0.180738
\(266\) 9.19843 + 6.68305i 0.563992 + 0.409764i
\(267\) 3.29553 10.1426i 0.201683 0.620717i
\(268\) −10.5539 32.4817i −0.644685 1.98414i
\(269\) 3.66042 2.65945i 0.223180 0.162149i −0.470577 0.882359i \(-0.655954\pi\)
0.693757 + 0.720209i \(0.255954\pi\)
\(270\) −0.427051 + 0.310271i −0.0259895 + 0.0188825i
\(271\) 6.72447 + 20.6958i 0.408482 + 1.25718i 0.917952 + 0.396691i \(0.129841\pi\)
−0.509470 + 0.860488i \(0.670159\pi\)
\(272\) 5.89608 18.1463i 0.357502 1.10028i
\(273\) 5.38300 + 3.91098i 0.325794 + 0.236703i
\(274\) 45.3688 2.74083
\(275\) 0 0
\(276\) −94.7021 −5.70040
\(277\) −10.5452 7.66154i −0.633600 0.460337i 0.224046 0.974579i \(-0.428074\pi\)
−0.857645 + 0.514241i \(0.828074\pi\)
\(278\) 13.1552 40.4877i 0.788999 2.42829i
\(279\) −3.47459 10.6937i −0.208018 0.640214i
\(280\) −10.1473 + 7.37245i −0.606417 + 0.440588i
\(281\) 7.59310 5.51671i 0.452966 0.329099i −0.337799 0.941218i \(-0.609683\pi\)
0.790766 + 0.612119i \(0.209683\pi\)
\(282\) −14.0606 43.2741i −0.837297 2.57694i
\(283\) −4.30760 + 13.2574i −0.256060 + 0.788072i 0.737559 + 0.675283i \(0.235979\pi\)
−0.993619 + 0.112789i \(0.964021\pi\)
\(284\) 39.9943 + 29.0575i 2.37322 + 1.72425i
\(285\) 5.30669 0.314341
\(286\) 0 0
\(287\) −10.6912 −0.631083
\(288\) 10.2832 + 7.47118i 0.605943 + 0.440243i
\(289\) −2.48832 + 7.65828i −0.146372 + 0.450487i
\(290\) −0.477925 1.47090i −0.0280647 0.0863744i
\(291\) −0.701768 + 0.509864i −0.0411383 + 0.0298888i
\(292\) −39.3326 + 28.5768i −2.30176 + 1.67233i
\(293\) −9.41576 28.9787i −0.550075 1.69296i −0.708608 0.705602i \(-0.750677\pi\)
0.158534 0.987354i \(-0.449323\pi\)
\(294\) −5.03644 + 15.5006i −0.293731 + 0.904011i
\(295\) 5.25393 + 3.81720i 0.305895 + 0.222246i
\(296\) 11.2083 0.651468
\(297\) 0 0
\(298\) 5.89138 0.341278
\(299\) 9.15089 + 6.64851i 0.529210 + 0.384493i
\(300\) −3.33354 + 10.2596i −0.192462 + 0.592337i
\(301\) 3.34649 + 10.2994i 0.192888 + 0.593649i
\(302\) 8.04468 5.84480i 0.462919 0.336330i
\(303\) 31.3303 22.7628i 1.79988 1.30769i
\(304\) −4.24044 13.0507i −0.243206 0.748511i
\(305\) 0.155265 0.477858i 0.00889047 0.0273621i
\(306\) 18.8457 + 13.6922i 1.07734 + 0.782732i
\(307\) −5.08609 −0.290278 −0.145139 0.989411i \(-0.546363\pi\)
−0.145139 + 0.989411i \(0.546363\pi\)
\(308\) 0 0
\(309\) −16.4775 −0.937375
\(310\) −7.44450 5.40875i −0.422819 0.307196i
\(311\) 4.25249 13.0878i 0.241136 0.742141i −0.755112 0.655596i \(-0.772417\pi\)
0.996248 0.0865451i \(-0.0275827\pi\)
\(312\) −5.88426 18.1099i −0.333131 1.02527i
\(313\) −12.9060 + 9.37676i −0.729491 + 0.530006i −0.889402 0.457125i \(-0.848879\pi\)
0.159912 + 0.987131i \(0.448879\pi\)
\(314\) −9.96903 + 7.24292i −0.562585 + 0.408742i
\(315\) −1.99563 6.14191i −0.112441 0.346057i
\(316\) −7.24225 + 22.2894i −0.407408 + 1.25387i
\(317\) −8.66246 6.29364i −0.486532 0.353486i 0.317317 0.948320i \(-0.397218\pi\)
−0.803849 + 0.594833i \(0.797218\pi\)
\(318\) −18.3221 −1.02745
\(319\) 0 0
\(320\) −2.35499 −0.131648
\(321\) −31.1477 22.6301i −1.73849 1.26309i
\(322\) 14.3375 44.1263i 0.798997 2.45906i
\(323\) −1.98855 6.12014i −0.110646 0.340534i
\(324\) 30.9170 22.4625i 1.71761 1.24792i
\(325\) 1.04238 0.757336i 0.0578210 0.0420094i
\(326\) 5.48871 + 16.8925i 0.303992 + 0.935590i
\(327\) 8.77138 26.9955i 0.485058 1.49286i
\(328\) 24.7530 + 17.9841i 1.36676 + 0.993006i
\(329\) 15.2966 0.843330
\(330\) 0 0
\(331\) −8.84618 −0.486230 −0.243115 0.969997i \(-0.578169\pi\)
−0.243115 + 0.969997i \(0.578169\pi\)
\(332\) 38.3710 + 27.8782i 2.10588 + 1.53001i
\(333\) −1.78330 + 5.48845i −0.0977245 + 0.300765i
\(334\) 8.36248 + 25.7371i 0.457575 + 1.40827i
\(335\) 6.31813 4.59039i 0.345196 0.250800i
\(336\) −26.6491 + 19.3617i −1.45382 + 1.05627i
\(337\) 3.58143 + 11.0225i 0.195093 + 0.600434i 0.999976 + 0.00699978i \(0.00222812\pi\)
−0.804883 + 0.593434i \(0.797772\pi\)
\(338\) 8.84648 27.2267i 0.481185 1.48093i
\(339\) 18.0569 + 13.1191i 0.980716 + 0.712532i
\(340\) 13.0814 0.709440
\(341\) 0 0
\(342\) 16.7534 0.905920
\(343\) −16.2885 11.8343i −0.879498 0.638993i
\(344\) 9.57705 29.4751i 0.516360 1.58919i
\(345\) −6.69176 20.5951i −0.360272 1.10880i
\(346\) −17.1802 + 12.4821i −0.923611 + 0.671043i
\(347\) −3.95529 + 2.87368i −0.212331 + 0.154267i −0.688868 0.724887i \(-0.741892\pi\)
0.476537 + 0.879155i \(0.341892\pi\)
\(348\) −2.04223 6.28533i −0.109475 0.336929i
\(349\) −0.294654 + 0.906853i −0.0157725 + 0.0485427i −0.958633 0.284645i \(-0.908124\pi\)
0.942861 + 0.333188i \(0.108124\pi\)
\(350\) −4.27575 3.10651i −0.228548 0.166050i
\(351\) 0.269409 0.0143800
\(352\) 0 0
\(353\) −15.5166 −0.825865 −0.412933 0.910762i \(-0.635495\pi\)
−0.412933 + 0.910762i \(0.635495\pi\)
\(354\) 32.7179 + 23.7709i 1.73894 + 1.26341i
\(355\) −3.49318 + 10.7509i −0.185399 + 0.570598i
\(356\) −5.84258 17.9816i −0.309656 0.953024i
\(357\) −12.4971 + 9.07965i −0.661415 + 0.480546i
\(358\) 42.9645 31.2155i 2.27074 1.64979i
\(359\) −6.25915 19.2637i −0.330345 1.01670i −0.968970 0.247180i \(-0.920496\pi\)
0.638624 0.769519i \(-0.279504\pi\)
\(360\) −5.71114 + 17.5771i −0.301003 + 0.926393i
\(361\) 11.6271 + 8.44759i 0.611953 + 0.444610i
\(362\) 4.40051 0.231286
\(363\) 0 0
\(364\) 11.7963 0.618295
\(365\) −8.99396 6.53449i −0.470765 0.342031i
\(366\) 0.966888 2.97578i 0.0505400 0.155546i
\(367\) 11.0180 + 33.9099i 0.575135 + 1.77008i 0.635719 + 0.771920i \(0.280704\pi\)
−0.0605844 + 0.998163i \(0.519296\pi\)
\(368\) −45.3024 + 32.9141i −2.36155 + 1.71577i
\(369\) −12.7448 + 9.25962i −0.663466 + 0.482037i
\(370\) 1.45943 + 4.49166i 0.0758721 + 0.233510i
\(371\) 1.90340 5.85807i 0.0988198 0.304136i
\(372\) −31.8112 23.1122i −1.64933 1.19831i
\(373\) −12.1358 −0.628370 −0.314185 0.949362i \(-0.601731\pi\)
−0.314185 + 0.949362i \(0.601731\pi\)
\(374\) 0 0
\(375\) −2.46673 −0.127381
\(376\) −35.4157 25.7310i −1.82643 1.32698i
\(377\) −0.243922 + 0.750713i −0.0125626 + 0.0386637i
\(378\) −0.341491 1.05100i −0.0175644 0.0540577i
\(379\) −5.77971 + 4.19921i −0.296884 + 0.215699i −0.726248 0.687433i \(-0.758738\pi\)
0.429364 + 0.903131i \(0.358738\pi\)
\(380\) 7.61133 5.52996i 0.390453 0.283681i
\(381\) 14.3565 + 44.1848i 0.735506 + 2.26366i
\(382\) −0.0194691 + 0.0599198i −0.000996127 + 0.00306576i
\(383\) −12.9143 9.38279i −0.659890 0.479438i 0.206736 0.978397i \(-0.433716\pi\)
−0.866626 + 0.498959i \(0.833716\pi\)
\(384\) −34.9936 −1.78576
\(385\) 0 0
\(386\) 3.67885 0.187249
\(387\) 12.9096 + 9.37935i 0.656230 + 0.476779i
\(388\) −0.475223 + 1.46259i −0.0241258 + 0.0742516i
\(389\) −7.75336 23.8624i −0.393111 1.20987i −0.930423 0.366488i \(-0.880560\pi\)
0.537312 0.843384i \(-0.319440\pi\)
\(390\) 6.49126 4.71617i 0.328698 0.238813i
\(391\) −21.2445 + 15.4351i −1.07438 + 0.780585i
\(392\) 4.84551 + 14.9130i 0.244735 + 0.753218i
\(393\) −15.3212 + 47.1538i −0.772853 + 2.37860i
\(394\) −46.3677 33.6881i −2.33597 1.69718i
\(395\) −5.35907 −0.269644
\(396\) 0 0
\(397\) 3.57490 0.179419 0.0897094 0.995968i \(-0.471406\pi\)
0.0897094 + 0.995968i \(0.471406\pi\)
\(398\) −13.5376 9.83564i −0.678579 0.493016i
\(399\) −3.43305 + 10.5659i −0.171868 + 0.528954i
\(400\) 1.97110 + 6.06643i 0.0985552 + 0.303322i
\(401\) −23.3675 + 16.9775i −1.16692 + 0.847815i −0.990637 0.136524i \(-0.956407\pi\)
−0.176281 + 0.984340i \(0.556407\pi\)
\(402\) 39.3451 28.5859i 1.96235 1.42573i
\(403\) 1.45128 + 4.46657i 0.0722933 + 0.222496i
\(404\) 21.2162 65.2969i 1.05555 3.24864i
\(405\) 7.06961 + 5.13637i 0.351292 + 0.255228i
\(406\) 3.23782 0.160690
\(407\) 0 0
\(408\) 44.2072 2.18858
\(409\) 7.78197 + 5.65393i 0.384794 + 0.279569i 0.763319 0.646022i \(-0.223569\pi\)
−0.378525 + 0.925591i \(0.623569\pi\)
\(410\) −3.98395 + 12.2613i −0.196753 + 0.605545i
\(411\) 13.6988 + 42.1606i 0.675712 + 2.07963i
\(412\) −23.6336 + 17.1708i −1.16434 + 0.845945i
\(413\) −10.9991 + 7.99135i −0.541233 + 0.393229i
\(414\) −21.1261 65.0196i −1.03829 3.19554i
\(415\) −3.35140 + 10.3145i −0.164514 + 0.506321i
\(416\) −4.29512 3.12059i −0.210586 0.152999i
\(417\) 41.5967 2.03700
\(418\) 0 0
\(419\) −30.6537 −1.49753 −0.748765 0.662836i \(-0.769353\pi\)
−0.748765 + 0.662836i \(0.769353\pi\)
\(420\) −18.2707 13.2745i −0.891521 0.647728i
\(421\) −2.14755 + 6.60949i −0.104665 + 0.322127i −0.989652 0.143490i \(-0.954168\pi\)
0.884986 + 0.465617i \(0.154168\pi\)
\(422\) 4.41361 + 13.5837i 0.214851 + 0.661244i
\(423\) 18.2348 13.2483i 0.886605 0.644156i
\(424\) −14.2610 + 10.3612i −0.692574 + 0.503184i
\(425\) 0.924349 + 2.84485i 0.0448375 + 0.137996i
\(426\) −21.7532 + 66.9493i −1.05394 + 3.24371i
\(427\) 0.850991 + 0.618281i 0.0411823 + 0.0299207i
\(428\) −68.2571 −3.29933
\(429\) 0 0
\(430\) 13.0590 0.629763
\(431\) −2.61636 1.90090i −0.126026 0.0915631i 0.522987 0.852341i \(-0.324818\pi\)
−0.649013 + 0.760778i \(0.724818\pi\)
\(432\) −0.412147 + 1.26846i −0.0198294 + 0.0610287i
\(433\) −9.39161 28.9044i −0.451332 1.38906i −0.875388 0.483421i \(-0.839394\pi\)
0.424056 0.905636i \(-0.360606\pi\)
\(434\) 15.5851 11.3233i 0.748110 0.543534i
\(435\) 1.22258 0.888257i 0.0586183 0.0425887i
\(436\) −15.5506 47.8598i −0.744739 2.29207i
\(437\) −5.83606 + 17.9616i −0.279177 + 0.859218i
\(438\) −56.0083 40.6924i −2.67618 1.94436i
\(439\) −36.5311 −1.74353 −0.871767 0.489921i \(-0.837026\pi\)
−0.871767 + 0.489921i \(0.837026\pi\)
\(440\) 0 0
\(441\) −8.07350 −0.384452
\(442\) −7.87155 5.71902i −0.374412 0.272026i
\(443\) −0.667949 + 2.05574i −0.0317352 + 0.0976710i −0.965669 0.259774i \(-0.916352\pi\)
0.933934 + 0.357445i \(0.116352\pi\)
\(444\) 6.23630 + 19.1933i 0.295962 + 0.910876i
\(445\) 3.49767 2.54120i 0.165805 0.120465i
\(446\) 16.1030 11.6995i 0.762499 0.553988i
\(447\) 1.77886 + 5.47477i 0.0841372 + 0.258948i
\(448\) 1.52352 4.68890i 0.0719793 0.221530i
\(449\) 9.32124 + 6.77228i 0.439897 + 0.319604i 0.785594 0.618742i \(-0.212358\pi\)
−0.345697 + 0.938346i \(0.612358\pi\)
\(450\) −7.78757 −0.367109
\(451\) 0 0
\(452\) 39.5699 1.86121
\(453\) 7.86051 + 5.71100i 0.369319 + 0.268326i
\(454\) −8.74624 + 26.9182i −0.410482 + 1.26333i
\(455\) 0.833541 + 2.56538i 0.0390770 + 0.120267i
\(456\) 25.7217 18.6879i 1.20453 0.875140i
\(457\) −12.8888 + 9.36427i −0.602913 + 0.438042i −0.846912 0.531734i \(-0.821541\pi\)
0.243999 + 0.969776i \(0.421541\pi\)
\(458\) −21.0560 64.8038i −0.983883 3.02808i
\(459\) −0.193276 + 0.594843i −0.00902136 + 0.0277649i
\(460\) −31.0596 22.5661i −1.44816 1.05215i
\(461\) −1.52527 −0.0710387 −0.0355193 0.999369i \(-0.511309\pi\)
−0.0355193 + 0.999369i \(0.511309\pi\)
\(462\) 0 0
\(463\) 14.2073 0.660268 0.330134 0.943934i \(-0.392906\pi\)
0.330134 + 0.943934i \(0.392906\pi\)
\(464\) −3.16143 2.29691i −0.146765 0.106631i
\(465\) 2.77845 8.55119i 0.128848 0.396552i
\(466\) −8.46491 26.0523i −0.392129 1.20685i
\(467\) 4.90020 3.56020i 0.226754 0.164746i −0.468608 0.883406i \(-0.655244\pi\)
0.695362 + 0.718660i \(0.255244\pi\)
\(468\) 14.0621 10.2167i 0.650022 0.472269i
\(469\) 5.05229 + 15.5494i 0.233293 + 0.718002i
\(470\) 5.70010 17.5431i 0.262926 0.809203i
\(471\) −9.74081 7.07711i −0.448833 0.326096i
\(472\) 38.9085 1.79091
\(473\) 0 0
\(474\) −33.3727 −1.53286
\(475\) 1.74044 + 1.26450i 0.0798569 + 0.0580194i
\(476\) −8.46277 + 26.0457i −0.387890 + 1.19380i
\(477\) −2.80464 8.63181i −0.128416 0.395223i
\(478\) 23.4185 17.0146i 1.07114 0.778227i
\(479\) −14.2455 + 10.3500i −0.650894 + 0.472902i −0.863576 0.504219i \(-0.831780\pi\)
0.212681 + 0.977122i \(0.431780\pi\)
\(480\) 3.14089 + 9.66666i 0.143361 + 0.441221i
\(481\) 0.744857 2.29243i 0.0339626 0.104526i
\(482\) −26.0490 18.9257i −1.18650 0.862043i
\(483\) 45.3350 2.06281
\(484\) 0 0
\(485\) −0.351653 −0.0159677
\(486\) 45.3059 + 32.9167i 2.05512 + 1.49313i
\(487\) 2.09619 6.45140i 0.0949874 0.292341i −0.892263 0.451516i \(-0.850883\pi\)
0.987250 + 0.159175i \(0.0508834\pi\)
\(488\) −0.930235 2.86297i −0.0421097 0.129600i
\(489\) −14.0407 + 10.2011i −0.634941 + 0.461312i
\(490\) −5.34536 + 3.88363i −0.241479 + 0.175445i
\(491\) −0.160261 0.493232i −0.00723247 0.0222592i 0.947375 0.320125i \(-0.103725\pi\)
−0.954608 + 0.297866i \(0.903725\pi\)
\(492\) −17.0239 + 52.3941i −0.767495 + 2.36211i
\(493\) −1.48255 1.07714i −0.0667707 0.0485117i
\(494\) −6.99762 −0.314838
\(495\) 0 0
\(496\) −23.2501 −1.04396
\(497\) −19.1457 13.9102i −0.858802 0.623956i
\(498\) −20.8703 + 64.2320i −0.935218 + 2.87831i
\(499\) 6.75534 + 20.7908i 0.302411 + 0.930725i 0.980631 + 0.195866i \(0.0627516\pi\)
−0.678220 + 0.734859i \(0.737248\pi\)
\(500\) −3.53801 + 2.57052i −0.158225 + 0.114957i
\(501\) −21.3921 + 15.5423i −0.955727 + 0.694377i
\(502\) 9.51872 + 29.2956i 0.424841 + 1.30753i
\(503\) −0.932202 + 2.86902i −0.0415649 + 0.127923i −0.969686 0.244356i \(-0.921424\pi\)
0.928121 + 0.372279i \(0.121424\pi\)
\(504\) −31.3020 22.7423i −1.39430 1.01302i
\(505\) 15.6995 0.698617
\(506\) 0 0
\(507\) 27.9724 1.24230
\(508\) 66.6352 + 48.4133i 2.95646 + 2.14799i
\(509\) −7.94418 + 24.4497i −0.352119 + 1.08371i 0.605542 + 0.795814i \(0.292957\pi\)
−0.957661 + 0.287898i \(0.907043\pi\)
\(510\) 5.75622 + 17.7158i 0.254890 + 0.784470i
\(511\) 18.8289 13.6800i 0.832943 0.605169i
\(512\) −40.5713 + 29.4768i −1.79302 + 1.30270i
\(513\) 0.139004 + 0.427809i 0.00613716 + 0.0188882i
\(514\) 4.59962 14.1562i 0.202881 0.624403i
\(515\) −5.40416 3.92635i −0.238136 0.173016i
\(516\) 55.8027 2.45658
\(517\) 0 0
\(518\) −9.88725 −0.434421
\(519\) −16.7869 12.1964i −0.736862 0.535361i
\(520\) 2.38545 7.34165i 0.104609 0.321953i
\(521\) 3.44017 + 10.5877i 0.150716 + 0.463858i 0.997702 0.0677588i \(-0.0215848\pi\)
−0.846985 + 0.531616i \(0.821585\pi\)
\(522\) 3.85974 2.80426i 0.168936 0.122739i
\(523\) −5.28968 + 3.84318i −0.231302 + 0.168050i −0.697399 0.716683i \(-0.745660\pi\)
0.466098 + 0.884733i \(0.345660\pi\)
\(524\) 27.1627 + 83.5981i 1.18661 + 3.65200i
\(525\) 1.59580 4.91138i 0.0696466 0.214350i
\(526\) 44.3820 + 32.2454i 1.93515 + 1.40597i
\(527\) −10.9032 −0.474949
\(528\) 0 0
\(529\) 54.0677 2.35077
\(530\) −6.00911 4.36588i −0.261019 0.189642i
\(531\) −6.19057 + 19.0526i −0.268648 + 0.826814i
\(532\) 6.08640 + 18.7320i 0.263879 + 0.812135i
\(533\) 5.32328 3.86759i 0.230577 0.167524i
\(534\) 21.7811 15.8249i 0.942561 0.684811i
\(535\) −4.82313 14.8441i −0.208522 0.641765i
\(536\) 14.4588 44.4995i 0.624524 1.92209i
\(537\) 41.9809 + 30.5009i 1.81161 + 1.31621i
\(538\) 11.4223 0.492449
\(539\) 0 0
\(540\) −0.914417 −0.0393502
\(541\) 33.7684 + 24.5342i 1.45182 + 1.05481i 0.985403 + 0.170239i \(0.0544538\pi\)
0.466413 + 0.884567i \(0.345546\pi\)
\(542\) −16.9761 + 52.2470i −0.729185 + 2.24420i
\(543\) 1.32870 + 4.08932i 0.0570201 + 0.175490i
\(544\) 9.97147 7.24470i 0.427523 0.310614i
\(545\) 9.30939 6.76367i 0.398770 0.289724i
\(546\) 5.19073 + 15.9754i 0.222143 + 0.683685i
\(547\) 1.37703 4.23806i 0.0588775 0.181206i −0.917292 0.398215i \(-0.869630\pi\)
0.976170 + 0.217008i \(0.0696299\pi\)
\(548\) 63.5825 + 46.1954i 2.71611 + 1.97337i
\(549\) 1.54994 0.0661498
\(550\) 0 0
\(551\) −1.31795 −0.0561466
\(552\) −104.962 76.2596i −4.46750 3.24583i
\(553\) 3.46695 10.6702i 0.147430 0.453742i
\(554\) −10.1686 31.2956i −0.432020 1.32962i
\(555\) −3.73337 + 2.71245i −0.158473 + 0.115137i
\(556\) 59.6618 43.3468i 2.53022 1.83831i
\(557\) −5.98608 18.4233i −0.253638 0.780619i −0.994095 0.108514i \(-0.965391\pi\)
0.740456 0.672104i \(-0.234609\pi\)
\(558\) 8.77167 26.9964i 0.371335 1.14285i
\(559\) −5.39211 3.91760i −0.228062 0.165697i
\(560\) −13.3537 −0.564298
\(561\) 0 0
\(562\) 23.6941 0.999477
\(563\) 16.7816 + 12.1925i 0.707259 + 0.513853i 0.882288 0.470710i \(-0.156002\pi\)
−0.175030 + 0.984563i \(0.556002\pi\)
\(564\) 24.3571 74.9636i 1.02562 3.15654i
\(565\) 2.79606 + 8.60538i 0.117631 + 0.362031i
\(566\) −28.4702 + 20.6848i −1.19669 + 0.869447i
\(567\) −14.8003 + 10.7530i −0.621554 + 0.451585i
\(568\) 20.9285 + 64.4114i 0.878141 + 2.70264i
\(569\) 13.0945 40.3007i 0.548950 1.68949i −0.162458 0.986716i \(-0.551942\pi\)
0.711408 0.702779i \(-0.248058\pi\)
\(570\) 10.8383 + 7.87447i 0.453966 + 0.329825i
\(571\) 5.03980 0.210909 0.105455 0.994424i \(-0.466370\pi\)
0.105455 + 0.994424i \(0.466370\pi\)
\(572\) 0 0
\(573\) −0.0615611 −0.00257175
\(574\) −21.8356 15.8645i −0.911399 0.662170i
\(575\) 2.71281 8.34916i 0.113132 0.348184i
\(576\) −2.24488 6.90905i −0.0935369 0.287877i
\(577\) −28.1877 + 20.4796i −1.17347 + 0.852576i −0.991420 0.130713i \(-0.958273\pi\)
−0.182050 + 0.983289i \(0.558273\pi\)
\(578\) −16.4461 + 11.9488i −0.684066 + 0.497003i
\(579\) 1.11080 + 3.41870i 0.0461634 + 0.142076i
\(580\) 0.827908 2.54804i 0.0343770 0.105802i
\(581\) −18.3686 13.3456i −0.762059 0.553668i
\(582\) −2.18985 −0.0907724
\(583\) 0 0
\(584\) −66.6057 −2.75616
\(585\) 3.21551 + 2.33620i 0.132945 + 0.0965901i
\(586\) 23.7703 73.1575i 0.981943 3.02211i
\(587\) −4.25772 13.1039i −0.175735 0.540857i 0.823931 0.566690i \(-0.191776\pi\)
−0.999666 + 0.0258331i \(0.991776\pi\)
\(588\) −22.8413 + 16.5952i −0.941959 + 0.684373i
\(589\) −6.34392 + 4.60913i −0.261397 + 0.189916i
\(590\) 5.06627 + 15.5924i 0.208575 + 0.641928i
\(591\) 17.3054 53.2606i 0.711850 2.19085i
\(592\) 9.65397 + 7.01402i 0.396776 + 0.288274i
\(593\) 25.1595 1.03318 0.516588 0.856234i \(-0.327202\pi\)
0.516588 + 0.856234i \(0.327202\pi\)
\(594\) 0 0
\(595\) −6.26222 −0.256726
\(596\) 8.25651 + 5.99871i 0.338200 + 0.245717i
\(597\) 5.05253 15.5501i 0.206786 0.636423i
\(598\) 8.82405 + 27.1576i 0.360842 + 1.11056i
\(599\) 13.3539 9.70216i 0.545624 0.396419i −0.280545 0.959841i \(-0.590515\pi\)
0.826170 + 0.563421i \(0.190515\pi\)
\(600\) −11.9563 + 8.68677i −0.488115 + 0.354636i
\(601\) −12.2509 37.7045i −0.499726 1.53800i −0.809460 0.587175i \(-0.800240\pi\)
0.309734 0.950823i \(-0.399760\pi\)
\(602\) −8.44829 + 26.0011i −0.344326 + 1.05973i
\(603\) 19.4900 + 14.1603i 0.793692 + 0.576651i
\(604\) 17.2255 0.700897
\(605\) 0 0
\(606\) 97.7656 3.97146
\(607\) 11.4795 + 8.34036i 0.465939 + 0.338525i 0.795857 0.605485i \(-0.207021\pi\)
−0.329917 + 0.944010i \(0.607021\pi\)
\(608\) 2.73925 8.43055i 0.111091 0.341904i
\(609\) 0.977637 + 3.00886i 0.0396158 + 0.121925i
\(610\) 1.02619 0.745574i 0.0415494 0.0301874i
\(611\) −7.61636 + 5.53361i −0.308125 + 0.223866i
\(612\) 12.4698 + 38.3781i 0.504062 + 1.55134i
\(613\) −9.31820 + 28.6785i −0.376359 + 1.15831i 0.566199 + 0.824269i \(0.308414\pi\)
−0.942557 + 0.334044i \(0.891586\pi\)
\(614\) −10.3877 7.54714i −0.419215 0.304578i
\(615\) −12.5972 −0.507968
\(616\) 0 0
\(617\) −31.3844 −1.26349 −0.631744 0.775177i \(-0.717661\pi\)
−0.631744 + 0.775177i \(0.717661\pi\)
\(618\) −33.6534 24.4507i −1.35374 0.983550i
\(619\) 10.8876 33.5087i 0.437611 1.34683i −0.452775 0.891625i \(-0.649566\pi\)
0.890387 0.455205i \(-0.150434\pi\)
\(620\) −4.92586 15.1602i −0.197827 0.608850i
\(621\) 1.48503 1.07894i 0.0595924 0.0432964i
\(622\) 28.1059 20.4201i 1.12694 0.818773i
\(623\) 2.79691 + 8.60800i 0.112056 + 0.344872i
\(624\) 6.26471 19.2808i 0.250789 0.771850i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) −40.2730 −1.60963
\(627\) 0 0
\(628\) −21.3460 −0.851799
\(629\) 4.52723 + 3.28922i 0.180512 + 0.131150i
\(630\) 5.03801 15.5054i 0.200719 0.617750i
\(631\) 1.77213 + 5.45404i 0.0705472 + 0.217122i 0.980114 0.198436i \(-0.0635863\pi\)
−0.909567 + 0.415558i \(0.863586\pi\)
\(632\) −25.9756 + 18.8724i −1.03325 + 0.750702i
\(633\) −11.2905 + 8.20300i −0.448755 + 0.326040i
\(634\) −8.35306 25.7081i −0.331742 1.02100i
\(635\) −5.82005 + 17.9123i −0.230962 + 0.710827i
\(636\) −25.6776 18.6559i −1.01818 0.739753i
\(637\) 3.37217 0.133610
\(638\) 0 0
\(639\) −34.8707 −1.37946
\(640\) −11.4769 8.33844i −0.453663 0.329606i
\(641\) −2.20167 + 6.77605i −0.0869608 + 0.267638i −0.985075 0.172124i \(-0.944937\pi\)
0.898115 + 0.439762i \(0.144937\pi\)
\(642\) −30.0352 92.4388i −1.18539 3.64827i
\(643\) 17.1427 12.4549i 0.676042 0.491173i −0.196000 0.980604i \(-0.562795\pi\)
0.872042 + 0.489431i \(0.162795\pi\)
\(644\) 65.0235 47.2423i 2.56229 1.86161i
\(645\) 3.94308 + 12.1356i 0.155259 + 0.477837i
\(646\) 5.02015 15.4504i 0.197515 0.607889i
\(647\) 4.57074 + 3.32083i 0.179694 + 0.130555i 0.673996 0.738735i \(-0.264576\pi\)
−0.494302 + 0.869290i \(0.664576\pi\)
\(648\) 52.3547 2.05669
\(649\) 0 0
\(650\) 3.25274 0.127583
\(651\) 15.2284 + 11.0640i 0.596846 + 0.433634i
\(652\) −9.50807 + 29.2628i −0.372365 + 1.14602i
\(653\) −4.85563 14.9441i −0.190016 0.584808i 0.809983 0.586453i \(-0.199476\pi\)
−0.999999 + 0.00164558i \(0.999476\pi\)
\(654\) 57.9726 42.1195i 2.26691 1.64700i
\(655\) −16.2610 + 11.8143i −0.635368 + 0.461622i
\(656\) 10.0661 + 30.9803i 0.393016 + 1.20958i
\(657\) 10.5974 32.6153i 0.413442 1.27245i
\(658\) 31.2416 + 22.6983i 1.21792 + 0.884872i
\(659\) 41.7884 1.62784 0.813922 0.580975i \(-0.197329\pi\)
0.813922 + 0.580975i \(0.197329\pi\)
\(660\) 0 0
\(661\) 15.8742 0.617435 0.308717 0.951154i \(-0.400100\pi\)
0.308717 + 0.951154i \(0.400100\pi\)
\(662\) −18.0673 13.1266i −0.702205 0.510182i
\(663\) 2.93784 9.04173i 0.114096 0.351152i
\(664\) 20.0791 + 61.7971i 0.779220 + 2.39819i
\(665\) −3.64363 + 2.64725i −0.141294 + 0.102656i
\(666\) −11.7864 + 8.56330i −0.456713 + 0.331821i
\(667\) 1.66195 + 5.11494i 0.0643508 + 0.198051i
\(668\) −14.4863 + 44.5842i −0.560491 + 1.72502i
\(669\) 15.7344 + 11.4317i 0.608325 + 0.441974i
\(670\) 19.7156 0.761681
\(671\) 0 0
\(672\) −21.2787 −0.820844
\(673\) 26.0864 + 18.9529i 1.00556 + 0.730580i 0.963273 0.268525i \(-0.0865363\pi\)
0.0422850 + 0.999106i \(0.486536\pi\)
\(674\) −9.04140 + 27.8266i −0.348262 + 1.07184i
\(675\) −0.0646137 0.198861i −0.00248698 0.00765415i
\(676\) 40.1206 29.1493i 1.54310 1.12113i
\(677\) 14.2084 10.3230i 0.546073 0.396745i −0.280263 0.959923i \(-0.590422\pi\)
0.826336 + 0.563178i \(0.190422\pi\)
\(678\) 17.4120 + 53.5885i 0.668702 + 2.05805i
\(679\) 0.227495 0.700157i 0.00873044 0.0268695i
\(680\) 14.4987 + 10.5339i 0.556000 + 0.403957i
\(681\) −27.6555 −1.05976
\(682\) 0 0
\(683\) −5.93856 −0.227233 −0.113616 0.993525i \(-0.536243\pi\)
−0.113616 + 0.993525i \(0.536243\pi\)
\(684\) 23.4792 + 17.0586i 0.897749 + 0.652253i
\(685\) −5.55342 + 17.0917i −0.212185 + 0.653039i
\(686\) −15.7067 48.3404i −0.599686 1.84565i
\(687\) 53.8634 39.1341i 2.05502 1.49306i
\(688\) 26.6942 19.3945i 1.01771 0.739407i
\(689\) 1.17145 + 3.60537i 0.0446289 + 0.137353i
\(690\) 16.8935 51.9929i 0.643125 1.97934i
\(691\) −17.7463 12.8934i −0.675100 0.490489i 0.196629 0.980478i \(-0.437001\pi\)
−0.871728 + 0.489989i \(0.837001\pi\)
\(692\) −36.7868 −1.39842
\(693\) 0 0
\(694\) −12.3424 −0.468511
\(695\) 13.6425 + 9.91187i 0.517490 + 0.375979i
\(696\) 2.79782 8.61082i 0.106051 0.326392i
\(697\) 4.72050 + 14.5282i 0.178802 + 0.550295i
\(698\) −1.94746 + 1.41491i −0.0737123 + 0.0535551i
\(699\) 21.6541 15.7326i 0.819033 0.595062i
\(700\) −2.82917 8.70729i −0.106933 0.329105i
\(701\) −10.0186 + 30.8341i −0.378397 + 1.16459i 0.562761 + 0.826620i \(0.309739\pi\)
−0.941158 + 0.337967i \(0.890261\pi\)
\(702\) 0.550236 + 0.399770i 0.0207673 + 0.0150884i
\(703\) 4.02460 0.151791
\(704\) 0 0
\(705\) 18.0236 0.678809
\(706\) −31.6908 23.0247i −1.19270 0.866547i
\(707\) −10.1565 + 31.2584i −0.381973 + 1.17559i
\(708\) 21.6487 + 66.6279i 0.813609 + 2.50403i
\(709\) 13.0256 9.46362i 0.489185 0.355414i −0.315686 0.948864i \(-0.602235\pi\)
0.804871 + 0.593450i \(0.202235\pi\)
\(710\) −23.0874 + 16.7740i −0.866456 + 0.629517i
\(711\) −5.10851 15.7224i −0.191584 0.589635i
\(712\) 8.00426 24.6346i 0.299972 0.923220i
\(713\) 25.8876 + 18.8085i 0.969499 + 0.704383i
\(714\) −38.9969 −1.45942
\(715\) 0 0
\(716\) 91.9971 3.43809
\(717\) 22.8824 + 16.6250i 0.854559 + 0.620874i
\(718\) 15.8014 48.6316i 0.589702 1.81492i
\(719\) −2.41409 7.42981i −0.0900304 0.277085i 0.895896 0.444263i \(-0.146534\pi\)
−0.985927 + 0.167178i \(0.946534\pi\)
\(720\) −15.9187 + 11.5656i −0.593254 + 0.431024i
\(721\) 11.3137 8.21985i 0.421343 0.306123i
\(722\) 11.2118 + 34.5064i 0.417261 + 1.28420i
\(723\) 9.72206 29.9214i 0.361567 1.11279i
\(724\) 6.16712 + 4.48068i 0.229199 + 0.166523i
\(725\) 0.612630 0.0227525
\(726\) 0 0
\(727\) −49.1218 −1.82183 −0.910914 0.412597i \(-0.864622\pi\)
−0.910914 + 0.412597i \(0.864622\pi\)
\(728\) 13.0744 + 9.49907i 0.484568 + 0.352059i
\(729\) −8.80810 + 27.1086i −0.326226 + 1.00402i
\(730\) −8.67272 26.6919i −0.320992 0.987911i
\(731\) 12.5182 9.09503i 0.463003 0.336392i
\(732\) 4.38504 3.18592i 0.162076 0.117755i
\(733\) 0.206407 + 0.635255i 0.00762382 + 0.0234637i 0.954796 0.297262i \(-0.0960734\pi\)
−0.947172 + 0.320725i \(0.896073\pi\)
\(734\) −27.8152 + 85.6064i −1.02668 + 3.15979i
\(735\) −5.22299 3.79472i −0.192653 0.139971i
\(736\) −36.1730 −1.33335
\(737\) 0 0
\(738\) −39.7699 −1.46395
\(739\) 30.8186 + 22.3911i 1.13368 + 0.823668i 0.986227 0.165400i \(-0.0528916\pi\)
0.147456 + 0.989069i \(0.452892\pi\)
\(740\) −2.52816 + 7.78088i −0.0929371 + 0.286031i
\(741\) −2.11288 6.50278i −0.0776187 0.238886i
\(742\) 12.5801 9.14001i 0.461832 0.335540i
\(743\) −25.3511 + 18.4186i −0.930041 + 0.675714i −0.946003 0.324159i \(-0.894919\pi\)
0.0159622 + 0.999873i \(0.494919\pi\)
\(744\) −16.6464 51.2324i −0.610287 1.87827i
\(745\) −0.721140 + 2.21944i −0.0264205 + 0.0813140i
\(746\) −24.7860 18.0081i −0.907480 0.659323i
\(747\) −33.4554 −1.22407
\(748\) 0 0
\(749\) 32.6754 1.19393
\(750\) −5.03801 3.66033i −0.183962 0.133656i
\(751\) −11.4915 + 35.3673i −0.419332 + 1.29057i 0.488986 + 0.872292i \(0.337367\pi\)
−0.908318 + 0.418280i \(0.862633\pi\)
\(752\) −14.4022 44.3255i −0.525196 1.61639i
\(753\) −24.3498 + 17.6912i −0.887358 + 0.644703i
\(754\) −1.61215 + 1.17129i −0.0587110 + 0.0426560i
\(755\) 1.21718 + 3.74609i 0.0442976 + 0.136334i
\(756\) 0.591564 1.82065i 0.0215150 0.0662162i
\(757\) −5.40478 3.92680i −0.196440 0.142722i 0.485217 0.874394i \(-0.338741\pi\)
−0.681657 + 0.731672i \(0.738741\pi\)
\(758\) −18.0355 −0.655079
\(759\) 0 0
\(760\) 12.8890 0.467533
\(761\) −18.5213 13.4565i −0.671398 0.487799i 0.199095 0.979980i \(-0.436200\pi\)
−0.870493 + 0.492181i \(0.836200\pi\)
\(762\) −36.2434 + 111.546i −1.31296 + 4.04087i
\(763\) 7.44425 + 22.9110i 0.269500 + 0.829435i
\(764\) −0.0882966 + 0.0641512i −0.00319446 + 0.00232091i
\(765\) −7.46506 + 5.42368i −0.269900 + 0.196094i
\(766\) −12.4530 38.3265i −0.449947 1.38479i
\(767\) 2.58570 7.95797i 0.0933643 0.287346i
\(768\) −62.0709 45.0971i −2.23979 1.62730i
\(769\) 13.1946 0.475808 0.237904 0.971289i \(-0.423540\pi\)
0.237904 + 0.971289i \(0.423540\pi\)
\(770\) 0 0
\(771\) 14.5440 0.523788
\(772\) 5.15575 + 3.74587i 0.185560 + 0.134817i
\(773\) −3.83827 + 11.8130i −0.138053 + 0.424883i −0.996052 0.0887673i \(-0.971707\pi\)
0.857999 + 0.513651i \(0.171707\pi\)
\(774\) 12.4485 + 38.3124i 0.447451 + 1.37711i
\(775\) 2.94887 2.14248i 0.105927 0.0769602i
\(776\) −1.70447 + 1.23837i −0.0611869 + 0.0444549i
\(777\) −2.98538 9.18807i −0.107100 0.329620i
\(778\) 19.5735 60.2412i 0.701746 2.15975i
\(779\) 8.88815 + 6.45762i 0.318451 + 0.231368i
\(780\) 13.8993 0.497675
\(781\) 0 0
\(782\) −66.2932 −2.37064
\(783\) 0.103633 + 0.0752938i 0.00370354 + 0.00269078i
\(784\) −5.15881 + 15.8772i −0.184243 + 0.567042i
\(785\) −1.50834 4.64218i −0.0538348 0.165686i
\(786\) −101.262 + 73.5714i −3.61191 + 2.62420i
\(787\) 17.3818 12.6286i 0.619595 0.450162i −0.233185 0.972432i \(-0.574915\pi\)
0.852780 + 0.522270i \(0.174915\pi\)
\(788\) −30.6805 94.4247i −1.09295 3.36374i
\(789\) −16.5643 + 50.9798i −0.589706 + 1.81493i
\(790\) −10.9453 7.95221i −0.389416 0.282927i
\(791\) −18.9426 −0.673520
\(792\) 0 0
\(793\) −0.647384 −0.0229893
\(794\) 7.30130 + 5.30471i 0.259114 + 0.188257i
\(795\) 2.24273 6.90242i 0.0795416 0.244804i
\(796\) −8.95753 27.5685i −0.317491 0.977138i
\(797\) −1.72264 + 1.25157i −0.0610191 + 0.0443330i −0.617877 0.786275i \(-0.712007\pi\)
0.556858 + 0.830608i \(0.312007\pi\)
\(798\) −22.6901 + 16.4853i −0.803219 + 0.583573i
\(799\) −6.75393 20.7864i −0.238937 0.735372i
\(800\) −1.27330 + 3.91881i −0.0450179 + 0.138551i
\(801\) 10.7895 + 7.83902i 0.381228 + 0.276978i
\(802\) −72.9179 −2.57482
\(803\) 0 0
\(804\) 84.2470 2.97116
\(805\) 14.8686 + 10.8026i 0.524048 + 0.380743i
\(806\) −3.66378 + 11.2760i −0.129051 + 0.397179i
\(807\) 3.44887 + 10.6145i 0.121406 + 0.373649i
\(808\) 76.0957 55.2868i 2.67704 1.94498i
\(809\) −4.33820 + 3.15189i −0.152523 + 0.110815i −0.661430 0.750007i \(-0.730050\pi\)
0.508906 + 0.860822i \(0.330050\pi\)
\(810\) 6.81710 + 20.9809i 0.239528 + 0.737193i
\(811\) −6.05047 + 18.6214i −0.212461 + 0.653887i 0.786863 + 0.617127i \(0.211704\pi\)
−0.999324 + 0.0367600i \(0.988296\pi\)
\(812\) 4.53766 + 3.29681i 0.159241 + 0.115695i
\(813\) −53.6781 −1.88257
\(814\) 0 0
\(815\) −7.03572 −0.246450
\(816\) 38.0768 + 27.6644i 1.33295 + 0.968448i
\(817\) 3.43887 10.5837i 0.120311 0.370278i
\(818\) 7.50402 + 23.0950i 0.262372 + 0.807497i
\(819\) −6.73170 + 4.89086i −0.235224 + 0.170901i
\(820\) −18.0681 + 13.1272i −0.630964 + 0.458422i
\(821\) 5.14095 + 15.8222i 0.179420 + 0.552199i 0.999808 0.0196092i \(-0.00624219\pi\)
−0.820387 + 0.571808i \(0.806242\pi\)
\(822\) −34.5829 + 106.435i −1.20622 + 3.71236i
\(823\) 14.7993 + 10.7523i 0.515870 + 0.374801i 0.815046 0.579397i \(-0.196712\pi\)
−0.299176 + 0.954198i \(0.596712\pi\)
\(824\) −40.0210 −1.39420
\(825\) 0 0
\(826\) −34.3227 −1.19424
\(827\) −30.7575 22.3466i −1.06954 0.777069i −0.0937136 0.995599i \(-0.529874\pi\)
−0.975830 + 0.218530i \(0.929874\pi\)
\(828\) 36.5967 112.633i 1.27182 3.91427i
\(829\) 15.9762 + 49.1698i 0.554877 + 1.70774i 0.696267 + 0.717783i \(0.254843\pi\)
−0.141389 + 0.989954i \(0.545157\pi\)
\(830\) −22.1504 + 16.0932i −0.768851 + 0.558603i
\(831\) 26.0122 18.8990i 0.902353 0.655598i
\(832\) 0.937652 + 2.88580i 0.0325072 + 0.100047i
\(833\) −2.41922 + 7.44560i −0.0838210 + 0.257975i
\(834\) 84.9564 + 61.7244i 2.94180 + 2.13734i
\(835\) −10.7195 −0.370963
\(836\) 0 0
\(837\) 0.762151 0.0263438
\(838\) −62.6065 45.4863i −2.16271 1.57130i
\(839\) 11.9288 36.7132i 0.411829 1.26748i −0.503227 0.864154i \(-0.667854\pi\)
0.915056 0.403326i \(-0.132146\pi\)
\(840\) −9.56086 29.4253i −0.329881 1.01527i
\(841\) 23.1579 16.8252i 0.798547 0.580178i
\(842\) −14.1938 + 10.3124i −0.489151 + 0.355389i
\(843\) 7.15428 + 22.0186i 0.246406 + 0.758361i
\(844\) −7.64568 + 23.5310i −0.263175 + 0.809969i
\(845\) 9.17416 + 6.66541i 0.315601 + 0.229297i
\(846\) 56.9013 1.95631
\(847\) 0 0
\(848\) −18.7672 −0.644470
\(849\) −27.8184 20.2113i −0.954726 0.693649i
\(850\) −2.33354 + 7.18190i −0.0800398 + 0.246337i
\(851\) −5.07504 15.6194i −0.173970 0.535425i
\(852\) −98.6551 + 71.6771i −3.37987 + 2.45562i
\(853\) 27.4303 19.9293i 0.939197 0.682366i −0.00903033 0.999959i \(-0.502874\pi\)
0.948227 + 0.317593i \(0.102874\pi\)
\(854\) 0.820596 + 2.52553i 0.0280802 + 0.0864220i
\(855\) −2.05072 + 6.31146i −0.0701331 + 0.215847i
\(856\) −75.6523 54.9646i −2.58574 1.87865i
\(857\) 56.7117 1.93723 0.968617 0.248558i \(-0.0799568\pi\)
0.968617 + 0.248558i \(0.0799568\pi\)
\(858\) 0 0
\(859\) −25.7505 −0.878597 −0.439298 0.898341i \(-0.644773\pi\)
−0.439298 + 0.898341i \(0.644773\pi\)
\(860\) 18.3017 + 13.2969i 0.624082 + 0.453422i
\(861\) 8.14951 25.0816i 0.277735 0.854779i
\(862\) −2.52291 7.76473i −0.0859308 0.264468i
\(863\) −28.9345 + 21.0222i −0.984942 + 0.715603i −0.958808 0.284056i \(-0.908320\pi\)
−0.0261347 + 0.999658i \(0.508320\pi\)
\(864\) −0.697025 + 0.506418i −0.0237133 + 0.0172287i
\(865\) −2.59940 8.00012i −0.0883821 0.272012i
\(866\) 23.7093 72.9698i 0.805676 2.47962i
\(867\) −16.0696 11.6752i −0.545751 0.396511i
\(868\) 33.3714 1.13270
\(869\) 0 0
\(870\) 3.81504 0.129342
\(871\) −8.14064 5.91452i −0.275835 0.200406i
\(872\) 21.3041 65.5674i 0.721449 2.22039i
\(873\) −0.335211 1.03167i −0.0113452 0.0349169i
\(874\) −38.5722 + 28.0244i −1.30473 + 0.947938i
\(875\) 1.69369 1.23053i 0.0572570 0.0415996i
\(876\) −37.0595 114.057i −1.25212 3.85364i
\(877\) −5.34913 + 16.4629i −0.180627 + 0.555913i −0.999846 0.0175682i \(-0.994408\pi\)
0.819218 + 0.573482i \(0.194408\pi\)
\(878\) −74.6105 54.2077i −2.51798 1.82942i
\(879\) 75.1614 2.53513
\(880\) 0 0
\(881\) −4.15822 −0.140094 −0.0700470 0.997544i \(-0.522315\pi\)
−0.0700470 + 0.997544i \(0.522315\pi\)
\(882\) −16.4892 11.9801i −0.555219 0.403391i
\(883\) −12.7533 + 39.2505i −0.429182 + 1.32088i 0.469751 + 0.882799i \(0.344344\pi\)
−0.898933 + 0.438086i \(0.855656\pi\)
\(884\) −5.20843 16.0299i −0.175179 0.539144i
\(885\) −12.9600 + 9.41601i −0.435647 + 0.316516i
\(886\) −4.41467 + 3.20744i −0.148314 + 0.107756i
\(887\) −9.41854 28.9873i −0.316243 0.973297i −0.975240 0.221151i \(-0.929019\pi\)
0.658996 0.752146i \(-0.270981\pi\)
\(888\) −8.54364 + 26.2946i −0.286706 + 0.882390i
\(889\) −31.8990 23.1760i −1.06986 0.777298i
\(890\) 10.9144 0.365852
\(891\) 0 0
\(892\) 34.4803 1.15449
\(893\) −12.7168 9.23933i −0.425553 0.309182i
\(894\) −4.49077 + 13.8212i −0.150194 + 0.462249i
\(895\) 6.50062 + 20.0069i 0.217292 + 0.668756i
\(896\) 24.0270 17.4566i 0.802684 0.583184i
\(897\) −22.5728 + 16.4001i −0.753684 + 0.547583i
\(898\) 8.98831 + 27.6632i 0.299944 + 0.923132i
\(899\) −0.690047 + 2.12375i −0.0230144 + 0.0708309i
\(900\) −10.9139 7.92944i −0.363798 0.264315i
\(901\) −8.80090 −0.293200
\(902\) 0 0
\(903\) −26.7134 −0.888965
\(904\) 43.8570 + 31.8640i 1.45866 + 1.05978i
\(905\) −0.538649 + 1.65779i −0.0179053 + 0.0551068i
\(906\) 7.57976 + 23.3281i 0.251821 + 0.775024i
\(907\) −9.13337 + 6.63578i −0.303269 + 0.220338i −0.729003 0.684511i \(-0.760016\pi\)
0.425734 + 0.904848i \(0.360016\pi\)
\(908\) −39.6660 + 28.8191i −1.31636 + 0.956394i
\(909\) 14.9654 + 46.0589i 0.496372 + 1.52768i
\(910\) −2.10429 + 6.47635i −0.0697567 + 0.214689i
\(911\) −40.9417 29.7459i −1.35646 0.985525i −0.998661 0.0517251i \(-0.983528\pi\)
−0.357797 0.933799i \(-0.616472\pi\)
\(912\) 33.8494 1.12086
\(913\) 0 0
\(914\) −40.2193 −1.33034
\(915\) 1.00270 + 0.728506i 0.0331483 + 0.0240837i
\(916\) 36.4753 112.259i 1.20518 3.70915i
\(917\) −13.0031 40.0193i −0.429399 1.32156i
\(918\) −1.27742 + 0.928099i −0.0421611 + 0.0306318i
\(919\) −22.0198 + 15.9983i −0.726366 + 0.527736i −0.888412 0.459048i \(-0.848191\pi\)
0.162046 + 0.986783i \(0.448191\pi\)
\(920\) −16.2531 50.0219i −0.535849 1.64917i
\(921\) 3.87693 11.9320i 0.127749 0.393172i
\(922\) −3.11518 2.26331i −0.102593 0.0745381i
\(923\) 14.5649 0.479410
\(924\) 0 0
\(925\) −1.87077 −0.0615106
\(926\) 29.0167 + 21.0819i 0.953547 + 0.692793i
\(927\) 6.36759 19.5974i 0.209139 0.643664i
\(928\) −0.780061 2.40078i −0.0256068 0.0788095i
\(929\) 18.7776 13.6427i 0.616073 0.447603i −0.235475 0.971880i \(-0.575664\pi\)
0.851548 + 0.524277i \(0.175664\pi\)
\(930\) 18.3636 13.3419i 0.602166 0.437499i
\(931\) 1.73990 + 5.35485i 0.0570228 + 0.175498i
\(932\) 14.6637 45.1303i 0.480326 1.47829i
\(933\) 27.4625 + 19.9527i 0.899082 + 0.653221i
\(934\) 15.2910 0.500336
\(935\) 0 0
\(936\) 23.8128 0.778344
\(937\) −34.1500 24.8114i −1.11563 0.810554i −0.132090 0.991238i \(-0.542169\pi\)
−0.983541 + 0.180684i \(0.942169\pi\)
\(938\) −12.7546 + 39.2547i −0.416453 + 1.28171i
\(939\) −12.1601 37.4251i −0.396831 1.22132i
\(940\) 25.8511 18.7819i 0.843171 0.612600i
\(941\) −23.6336 + 17.1708i −0.770435 + 0.559754i −0.902093 0.431542i \(-0.857970\pi\)
0.131658 + 0.991295i \(0.457970\pi\)
\(942\) −9.39289 28.9083i −0.306037 0.941885i
\(943\) 13.8539 42.6378i 0.451144 1.38848i
\(944\) 33.5128 + 24.3485i 1.09075 + 0.792476i
\(945\) 0.437741 0.0142397
\(946\) 0 0
\(947\) 9.63809 0.313196 0.156598 0.987662i \(-0.449947\pi\)
0.156598 + 0.987662i \(0.449947\pi\)
\(948\) −46.7704 33.9807i −1.51903 1.10364i
\(949\) −4.42634 + 13.6229i −0.143685 + 0.442218i
\(950\) 1.67828 + 5.16520i 0.0544505 + 0.167581i
\(951\) 21.3680 15.5247i 0.692904 0.503424i
\(952\) −30.3532 + 22.0529i −0.983752 + 0.714738i
\(953\) −1.61353 4.96593i −0.0522673 0.160862i 0.921516 0.388341i \(-0.126952\pi\)
−0.973783 + 0.227479i \(0.926952\pi\)
\(954\) 7.08039 21.7912i 0.229236 0.705517i
\(955\) −0.0201903 0.0146691i −0.000653342 0.000474681i
\(956\) 50.1446 1.62179
\(957\) 0 0
\(958\) −44.4529 −1.43621
\(959\) −30.4376 22.1142i −0.982882 0.714106i
\(960\) 1.79512 5.52482i 0.0579373 0.178313i
\(961\) −5.47390 16.8469i −0.176577 0.543450i
\(962\) 4.92298 3.57675i 0.158723 0.115319i
\(963\) 38.9517 28.3001i 1.25520 0.911956i
\(964\) −17.2361 53.0471i −0.555136 1.70853i
\(965\) −0.450314 + 1.38592i −0.0144961 + 0.0446145i
\(966\) 92.5913 + 67.2715i 2.97908 + 2.16443i
\(967\) −38.4583 −1.23674 −0.618368 0.785889i \(-0.712206\pi\)
−0.618368 + 0.785889i \(0.712206\pi\)
\(968\) 0 0
\(969\) 15.8737 0.509935
\(970\) −0.718209 0.521810i −0.0230603 0.0167543i
\(971\) 13.4928 41.5267i 0.433006 1.33265i −0.462111 0.886822i \(-0.652908\pi\)
0.895116 0.445832i \(-0.147092\pi\)
\(972\) 29.9779 + 92.2625i 0.961542 + 2.95932i
\(973\) −28.5608 + 20.7506i −0.915616 + 0.665234i
\(974\) 13.8543 10.0658i 0.443921 0.322527i
\(975\) 0.982141 + 3.02272i 0.0314537 + 0.0968045i
\(976\) 0.990380 3.04808i 0.0317013 0.0975665i
\(977\) 9.50330 + 6.90455i 0.304038 + 0.220896i 0.729334 0.684158i \(-0.239830\pi\)
−0.425296 + 0.905054i \(0.639830\pi\)
\(978\) −43.8137 −1.40101
\(979\) 0 0
\(980\) −11.4457 −0.365618
\(981\) 28.7173 + 20.8643i 0.916872 + 0.666147i
\(982\) 0.404582 1.24518i 0.0129107 0.0397351i
\(983\) 2.88989 + 8.89417i 0.0921733 + 0.283680i 0.986507 0.163721i \(-0.0523497\pi\)
−0.894333 + 0.447401i \(0.852350\pi\)
\(984\) −61.0590 + 44.3620i −1.94649 + 1.41421i
\(985\) 18.3669 13.3443i 0.585218 0.425186i
\(986\) −1.42960 4.39985i −0.0455276 0.140120i
\(987\) −11.6600 + 35.8859i −0.371143 + 1.14226i
\(988\) −9.80687 7.12510i −0.311998 0.226680i
\(989\) −45.4117 −1.44401
\(990\) 0 0
\(991\) −32.3450 −1.02747 −0.513737 0.857948i \(-0.671739\pi\)
−0.513737 + 0.857948i \(0.671739\pi\)
\(992\) −12.1508 8.82806i −0.385788 0.280291i
\(993\) 6.74310 20.7531i 0.213986 0.658581i
\(994\) −18.4619 56.8197i −0.585574 1.80221i
\(995\) 5.36244 3.89604i 0.170001 0.123513i
\(996\) −94.6510 + 68.7679i −2.99913 + 2.17900i
\(997\) 8.99777 + 27.6923i 0.284962 + 0.877023i 0.986410 + 0.164302i \(0.0525373\pi\)
−0.701448 + 0.712721i \(0.747463\pi\)
\(998\) −17.0540 + 52.4869i −0.539836 + 1.66144i
\(999\) −0.316462 0.229923i −0.0100124 0.00727444i
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 605.2.g.n.81.2 8
11.2 odd 10 605.2.g.j.511.2 8
11.3 even 5 inner 605.2.g.n.366.2 8
11.4 even 5 605.2.g.g.251.1 8
11.5 even 5 605.2.a.i.1.1 4
11.6 odd 10 605.2.a.l.1.4 4
11.7 odd 10 605.2.g.j.251.2 8
11.8 odd 10 55.2.g.a.36.1 yes 8
11.9 even 5 605.2.g.g.511.1 8
11.10 odd 2 55.2.g.a.26.1 8
33.5 odd 10 5445.2.a.bu.1.4 4
33.8 even 10 495.2.n.f.91.2 8
33.17 even 10 5445.2.a.bg.1.1 4
33.32 even 2 495.2.n.f.136.2 8
44.19 even 10 880.2.bo.e.641.2 8
44.27 odd 10 9680.2.a.cv.1.4 4
44.39 even 10 9680.2.a.cs.1.4 4
44.43 even 2 880.2.bo.e.81.2 8
55.8 even 20 275.2.z.b.124.4 16
55.19 odd 10 275.2.h.b.201.2 8
55.32 even 4 275.2.z.b.224.4 16
55.39 odd 10 3025.2.a.v.1.1 4
55.43 even 4 275.2.z.b.224.1 16
55.49 even 10 3025.2.a.be.1.4 4
55.52 even 20 275.2.z.b.124.1 16
55.54 odd 2 275.2.h.b.26.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.a.26.1 8 11.10 odd 2
55.2.g.a.36.1 yes 8 11.8 odd 10
275.2.h.b.26.2 8 55.54 odd 2
275.2.h.b.201.2 8 55.19 odd 10
275.2.z.b.124.1 16 55.52 even 20
275.2.z.b.124.4 16 55.8 even 20
275.2.z.b.224.1 16 55.43 even 4
275.2.z.b.224.4 16 55.32 even 4
495.2.n.f.91.2 8 33.8 even 10
495.2.n.f.136.2 8 33.32 even 2
605.2.a.i.1.1 4 11.5 even 5
605.2.a.l.1.4 4 11.6 odd 10
605.2.g.g.251.1 8 11.4 even 5
605.2.g.g.511.1 8 11.9 even 5
605.2.g.j.251.2 8 11.7 odd 10
605.2.g.j.511.2 8 11.2 odd 10
605.2.g.n.81.2 8 1.1 even 1 trivial
605.2.g.n.366.2 8 11.3 even 5 inner
880.2.bo.e.81.2 8 44.43 even 2
880.2.bo.e.641.2 8 44.19 even 10
3025.2.a.v.1.1 4 55.39 odd 10
3025.2.a.be.1.4 4 55.49 even 10
5445.2.a.bg.1.1 4 33.17 even 10
5445.2.a.bu.1.4 4 33.5 odd 10
9680.2.a.cs.1.4 4 44.39 even 10
9680.2.a.cv.1.4 4 44.27 odd 10